LMFDB - Embedded newform 3762.2.g.h.2089.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3762,2,Mod(2089,3762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3762, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3762.2089");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3762.g (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:	$30.0397212404$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14584320320.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} + 11x^{5} - 11x^{4} + 32x^{3} + 44x^{2} - 18x + 46 $ x^8 - x^7 + 4x^6 + 11x^5 - 11x^4 + 32x^3 + 44x^2 - 18x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 418)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2089.4
Root			$0.682410 - 2.29682i$ of defining polynomial
Character	$\chi$	$=$	3762.2089
Dual form			3762.2.g.h.2089.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} -1.36482 q^{5} +0.331974i q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} -1.36482 q^{5} +0.331974i q^{7} +1.00000 q^{8} -1.36482 q^{10} +(-3.31544 - 0.0887375i) q^{11} +5.11734 q^{13} +0.331974i q^{14} +1.00000 q^{16} -2.58582i q^{17} +(-1.77245 - 3.98226i) q^{19} -1.36482 q^{20} +(-3.31544 - 0.0887375i) q^{22} +2.10590 q^{23} -3.13727 q^{25} +5.11734 q^{26} +0.331974i q^{28} -0.741082 q^{29} +5.22421i q^{31} +1.00000 q^{32} -2.58582i q^{34} -0.453085i q^{35} -6.14459i q^{37} +(-1.77245 - 3.98226i) q^{38} -1.36482 q^{40} +2.49361 q^{41} -10.2518i q^{43} +(-3.31544 - 0.0887375i) q^{44} +2.10590 q^{46} +4.21180 q^{47} +6.88979 q^{49} -3.13727 q^{50} +5.11734 q^{52} -7.44290i q^{53} +(4.52497 + 0.121111i) q^{55} +0.331974i q^{56} -0.741082 q^{58} +1.84953i q^{59} -2.61541i q^{61} +5.22421i q^{62} +1.00000 q^{64} -6.98425 q^{65} +2.28344i q^{67} -2.58582i q^{68} -0.453085i q^{70} -12.1385i q^{71} +9.08536i q^{73} -6.14459i q^{74} +(-1.77245 - 3.98226i) q^{76} +(0.0294586 - 1.10064i) q^{77} -5.96397 q^{79} -1.36482 q^{80} +2.49361 q^{82} +13.2221i q^{83} +3.52918i q^{85} -10.2518i q^{86} +(-3.31544 - 0.0887375i) q^{88} -16.4879i q^{89} +1.69883i q^{91} +2.10590 q^{92} +4.21180 q^{94} +(2.41907 + 5.43507i) q^{95} -3.52918i q^{97} +6.88979 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} - 2 q^{5} + 8 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 - 2 * q^5 + 8 * q^8	$ 8 q + 8 q^{2} + 8 q^{4} - 2 q^{5} + 8 q^{8} - 2 q^{10} + 6 q^{11} + 10 q^{13} + 8 q^{16} - 2 q^{20} + 6 q^{22} - 12 q^{23} - 2 q^{25} + 10 q^{26} + 14 q^{29} + 8 q^{32} - 2 q^{40} - 22 q^{41} + 6 q^{44} - 12 q^{46} - 24 q^{47} + 10 q^{49} - 2 q^{50} + 10 q^{52} + 14 q^{58} + 8 q^{64} + 16 q^{65} + 16 q^{77} - 12 q^{79} - 2 q^{80} - 22 q^{82} + 6 q^{88} - 12 q^{92} - 24 q^{94} + 12 q^{95} + 10 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 - 2 * q^5 + 8 * q^8 - 2 * q^10 + 6 * q^11 + 10 * q^13 + 8 * q^16 - 2 * q^20 + 6 * q^22 - 12 * q^23 - 2 * q^25 + 10 * q^26 + 14 * q^29 + 8 * q^32 - 2 * q^40 - 22 * q^41 + 6 * q^44 - 12 * q^46 - 24 * q^47 + 10 * q^49 - 2 * q^50 + 10 * q^52 + 14 * q^58 + 8 * q^64 + 16 * q^65 + 16 * q^77 - 12 * q^79 - 2 * q^80 - 22 * q^82 + 6 * q^88 - 12 * q^92 - 24 * q^94 + 12 * q^95 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3762\mathbb{Z}\right)^\times$.

$n$	$343$	$2377$	$2927$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.36482			−0.610366			−0.305183	−	0.952294i	$-0.598718\pi$
$5$	−1.36482			−0.610366			−0.305183	+	0.952294i	$0.598718\pi$
$6$		0			0
$7$			0.331974i			0.125475i	0.998030	+	0.0627373i	$0.0199830\pi$
$7$			0.331974i			0.125475i	−0.998030	+	0.0627373i	$0.980017\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.36482			−0.431594
$11$	−3.31544	−	0.0887375i	−0.999642	−	0.0267554i
$11$	−3.31544	−	0.0887375i	−0.999642	−	0.0267554i
$12$		0			0
$13$	5.11734			1.41930			0.709648	−	0.704556i	$-0.248854\pi$
$13$	5.11734			1.41930			0.709648	+	0.704556i	$0.248854\pi$
$14$			0.331974i			0.0887239i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.58582i		−	0.627154i	−0.949563	−	0.313577i	$-0.898473\pi$
$17$		−	2.58582i		−	0.627154i	0.949563	−	0.313577i	$-0.101527\pi$
$18$		0			0
$19$	−1.77245	−	3.98226i	−0.406628	−	0.913594i
$19$	−1.77245	−	3.98226i	−0.406628	−	0.913594i
$20$	−1.36482			−0.305183
$21$		0			0
$22$	−3.31544	−	0.0887375i	−0.706854	−	0.0189189i
$23$	2.10590			0.439111			0.219555	−	0.975600i	$-0.429539\pi$
$23$	2.10590			0.439111			0.219555	+	0.975600i	$0.429539\pi$
$24$		0			0
$25$	−3.13727			−0.627454
$26$	5.11734			1.00359
$27$		0			0
$28$			0.331974i			0.0627373i
$29$	−0.741082			−0.137615			−0.0688077	−	0.997630i	$-0.521920\pi$
$29$	−0.741082			−0.137615			−0.0688077	+	0.997630i	$0.521920\pi$
$30$		0			0
$31$			5.22421i			0.938295i	0.883120	+	0.469148i	$0.155439\pi$
$31$			5.22421i			0.938295i	−0.883120	+	0.469148i	$0.844561\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		−	2.58582i		−	0.443465i
$35$		−	0.453085i		−	0.0765854i
$36$		0			0
$37$		−	6.14459i		−	1.01016i	−0.863071	−	0.505082i	$-0.831462\pi$
$37$		−	6.14459i		−	1.01016i	0.863071	−	0.505082i	$-0.168538\pi$
$38$	−1.77245	−	3.98226i	−0.287529	−	0.646009i
$39$		0			0
$40$	−1.36482			−0.215797
$41$	2.49361			0.389436			0.194718	−	0.980859i	$-0.437621\pi$
$41$	2.49361			0.389436			0.194718	+	0.980859i	$0.437621\pi$
$42$		0			0
$43$		−	10.2518i		−	1.56338i	−0.623668	−	0.781690i	$-0.714358\pi$
$43$		−	10.2518i		−	1.56338i	0.623668	−	0.781690i	$-0.285642\pi$
$44$	−3.31544	−	0.0887375i	−0.499821	−	0.0133777i
$45$		0			0
$46$	2.10590			0.310498
$47$	4.21180			0.614355			0.307177	−	0.951652i	$-0.400616\pi$
$47$	4.21180			0.614355			0.307177	+	0.951652i	$0.400616\pi$
$48$		0			0
$49$	6.88979			0.984256
$50$	−3.13727			−0.443677
$51$		0			0
$52$	5.11734			0.709648
$53$		−	7.44290i		−	1.02236i	−0.859473	−	0.511180i	$-0.829208\pi$
$53$		−	7.44290i		−	1.02236i	0.859473	−	0.511180i	$-0.170792\pi$
$54$		0			0
$55$	4.52497	+	0.121111i	0.610147	+	0.0163306i
$56$			0.331974i			0.0443620i
$57$		0			0
$58$	−0.741082			−0.0973088
$59$			1.84953i			0.240788i	0.992726	+	0.120394i	$0.0384158\pi$
$59$			1.84953i			0.240788i	−0.992726	+	0.120394i	$0.961584\pi$
$60$		0			0
$61$		−	2.61541i		−	0.334869i	−0.985883	−	0.167435i	$-0.946452\pi$
$61$		−	2.61541i		−	0.334869i	0.985883	−	0.167435i	$-0.0535483\pi$
$62$			5.22421i			0.663475i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.98425			−0.866290
$66$		0			0
$67$			2.28344i			0.278966i	0.990224	+	0.139483i	$0.0445441\pi$
$67$			2.28344i			0.278966i	−0.990224	+	0.139483i	$0.955456\pi$
$68$		−	2.58582i		−	0.313577i
$69$		0			0
$70$		−	0.453085i		−	0.0541540i
$71$		−	12.1385i		−	1.44057i	−0.693677	−	0.720286i	$-0.744010\pi$
$71$		−	12.1385i		−	1.44057i	0.693677	−	0.720286i	$-0.255990\pi$
$72$		0			0
$73$			9.08536i			1.06336i	0.846945	+	0.531681i	$0.178439\pi$
$73$			9.08536i			1.06336i	−0.846945	+	0.531681i	$0.821561\pi$
$74$		−	6.14459i		−	0.714294i
$75$		0			0
$76$	−1.77245	−	3.98226i	−0.203314	−	0.456797i
$77$	0.0294586	−	1.10064i	0.00335712	−	0.125430i
$78$		0			0
$79$	−5.96397			−0.670999			−0.335499	−	0.942040i	$-0.608905\pi$
$79$	−5.96397			−0.670999			−0.335499	+	0.942040i	$0.608905\pi$
$80$	−1.36482			−0.152591
$81$		0			0
$82$	2.49361			0.275373
$83$			13.2221i			1.45132i	0.688055	+	0.725658i	$0.258465\pi$
$83$			13.2221i			1.45132i	−0.688055	+	0.725658i	$0.741535\pi$
$84$		0			0
$85$			3.52918i			0.382793i
$86$		−	10.2518i		−	1.10548i
$87$		0			0
$88$	−3.31544	−	0.0887375i	−0.353427	−	0.00945945i
$89$		−	16.4879i		−	1.74771i	−0.486186	−	0.873856i	$-0.661612\pi$
$89$		−	16.4879i		−	1.74771i	0.486186	−	0.873856i	$-0.338388\pi$
$90$		0			0
$91$			1.69883i			0.178086i
$92$	2.10590			0.219555
$93$		0			0
$94$	4.21180			0.434414
$95$	2.41907	+	5.43507i	0.248192	+	0.557627i
$96$		0			0
$97$		−	3.52918i		−	0.358334i	−0.983819	−	0.179167i	$-0.942660\pi$
$97$		−	3.52918i		−	0.358334i	0.983819	−	0.179167i	$-0.0573402\pi$
$98$	6.88979			0.695974
$99$		0			0
$100$	−3.13727			−0.313727
$101$		−	16.4879i		−	1.64060i	−0.571930	−	0.820302i	$-0.693805\pi$
$101$		−	16.4879i		−	1.64060i	0.571930	−	0.820302i	$-0.306195\pi$
$102$		0			0
$103$		−	9.20647i		−	0.907141i	−0.891221	−	0.453570i	$-0.850150\pi$
$103$		−	9.20647i		−	0.907141i	0.891221	−	0.453570i	$-0.149850\pi$
$104$	5.11734			0.501797
$105$		0			0
$106$		−	7.44290i		−	0.722918i
$107$	5.77245			0.558044			0.279022	−	0.960285i	$-0.409990\pi$
$107$	5.77245			0.558044			0.279022	+	0.960285i	$0.409990\pi$
$108$		0			0
$109$	11.5291			1.10429			0.552146	−	0.833747i	$-0.313809\pi$
$109$	11.5291			1.10429			0.552146	+	0.833747i	$0.313809\pi$
$110$	4.52497	+	0.121111i	0.431439	+	0.0115475i
$111$		0			0
$112$			0.331974i			0.0313686i
$113$		−	3.17423i		−	0.298606i	−0.988791	−	0.149303i	$-0.952297\pi$
$113$		−	3.17423i		−	0.298606i	0.988791	−	0.149303i	$-0.0477030\pi$
$114$		0			0
$115$	−2.87418			−0.268018
$116$	−0.741082			−0.0688077
$117$		0			0
$118$			1.84953i			0.170263i
$119$	0.858427			0.0786918
$120$		0			0
$121$	10.9843	+	0.588408i	0.998568	+	0.0534916i
$122$		−	2.61541i		−	0.236788i
$123$		0			0
$124$			5.22421i			0.469148i
$125$	11.1059			0.993342
$126$		0			0
$127$	4.50469			0.399727			0.199863	−	0.979824i	$-0.435950\pi$
$127$	4.50469			0.399727			0.199863	+	0.979824i	$0.435950\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−6.98425			−0.612559
$131$		−	11.2637i		−	0.984111i	−0.870564	−	0.492056i	$-0.836246\pi$
$131$		−	11.2637i		−	0.984111i	0.870564	−	0.492056i	$-0.163754\pi$
$132$		0			0
$133$	1.32201	−	0.588408i	0.114633	−	0.0510214i
$134$			2.28344i			0.197259i
$135$		0			0
$136$		−	2.58582i		−	0.221732i
$137$	11.5364			0.985623			0.492811	−	0.870136i	$-0.335969\pi$
$137$	11.5364			0.985623			0.492811	+	0.870136i	$0.335969\pi$
$138$		0			0
$139$			15.3511i			1.30206i	0.759052	+	0.651030i	$0.225663\pi$
$139$			15.3511i			1.30206i	−0.759052	+	0.651030i	$0.774337\pi$
$140$		−	0.453085i		−	0.0382927i
$141$		0			0
$142$		−	12.1385i		−	1.01864i
$143$	−16.9662	−	0.454101i	−1.41879	−	0.0379738i
$144$		0			0
$145$	1.01144			0.0839958
$146$			9.08536i			0.751910i
$147$		0			0
$148$		−	6.14459i		−	0.505082i
$149$		−	9.05577i		−	0.741878i	−0.928657	−	0.370939i	$-0.879036\pi$
$149$		−	9.05577i		−	0.741878i	0.928657	−	0.370939i	$-0.120964\pi$
$150$		0			0
$151$	14.1758			1.15361			0.576804	−	0.816883i	$-0.304300\pi$
$151$	14.1758			1.15361			0.576804	+	0.816883i	$0.304300\pi$
$152$	−1.77245	−	3.98226i	−0.143765	−	0.323004i
$153$		0			0
$154$	0.0294586	−	1.10064i	0.00237384	−	0.0886921i
$155$		−	7.13010i		−	0.572703i
$156$		0			0
$157$	−14.8966			−1.18888			−0.594438	−	0.804142i	$-0.702625\pi$
$157$	−14.8966			−1.18888			−0.594438	+	0.804142i	$0.702625\pi$
$158$	−5.96397			−0.474468
$159$		0			0
$160$	−1.36482			−0.107898
$161$			0.699105i			0.0550972i
$162$		0			0
$163$	3.54108			0.277359			0.138679	−	0.990337i	$-0.455714\pi$
$163$	3.54108			0.277359			0.138679	+	0.990337i	$0.455714\pi$
$164$	2.49361			0.194718
$165$		0			0
$166$			13.2221i			1.02624i
$167$	10.3876			0.803815			0.401907	−	0.915680i	$-0.368347\pi$
$167$	10.3876			0.803815			0.401907	+	0.915680i	$0.368347\pi$
$168$		0			0
$169$	13.1872			1.01440
$170$			3.52918i			0.270676i
$171$		0			0
$172$		−	10.2518i		−	0.781690i
$173$	−11.1804			−0.850033			−0.425016	−	0.905186i	$-0.639732\pi$
$173$	−11.1804			−0.850033			−0.425016	+	0.905186i	$0.639732\pi$
$174$		0			0
$175$		−	1.04149i		−	0.0787295i
$176$	−3.31544	−	0.0887375i	−0.249911	−	0.00668884i
$177$		0			0
$178$		−	16.4879i		−	1.23582i
$179$		−	2.25385i		−	0.168460i	−0.996446	−	0.0842302i	$-0.973157\pi$
$179$		−	2.25385i		−	0.168460i	0.996446	−	0.0842302i	$-0.0268431\pi$
$180$		0			0
$181$		−	24.3153i		−	1.80734i	−0.428227	−	0.903671i	$-0.640861\pi$
$181$		−	24.3153i		−	1.80734i	0.428227	−	0.903671i	$-0.359139\pi$
$182$			1.69883i			0.125925i
$183$		0			0
$184$	2.10590			0.155249
$185$			8.38626i			0.616570i
$186$		0			0
$187$	−0.229459	+	8.57313i	−0.0167797	+	0.626929i
$188$	4.21180			0.307177
$189$		0			0
$190$	2.41907	+	5.43507i	0.175498	+	0.394302i
$191$	−21.4533			−1.55230			−0.776152	−	0.630546i	$-0.782831\pi$
$191$	−21.4533			−1.55230			−0.776152	+	0.630546i	$0.782831\pi$
$192$		0			0
$193$	−20.6664			−1.48760			−0.743801	−	0.668402i	$-0.766979\pi$
$193$	−20.6664			−1.48760			−0.743801	+	0.668402i	$0.766979\pi$
$194$		−	3.52918i		−	0.253380i
$195$		0			0
$196$	6.88979			0.492128
$197$		−	8.03131i		−	0.572207i	−0.958199	−	0.286103i	$-0.907640\pi$
$197$		−	8.03131i		−	0.572207i	0.958199	−	0.286103i	$-0.0923601\pi$
$198$		0			0
$199$	0.263583			0.0186849			0.00934244	−	0.999956i	$-0.497026\pi$
$199$	0.263583			0.0186849			0.00934244	+	0.999956i	$0.497026\pi$
$200$	−3.13727			−0.221838
$201$		0			0
$202$		−	16.4879i		−	1.16008i
$203$		−	0.246020i		−	0.0172672i
$204$		0			0
$205$	−3.40332			−0.237698
$206$		−	9.20647i		−	0.641445i
$207$		0			0
$208$	5.11734			0.354824
$209$	5.52307	+	13.3602i	0.382038	+	0.924146i
$210$		0			0
$211$	−16.7825			−1.15536			−0.577679	−	0.816264i	$-0.696042\pi$
$211$	−16.7825			−1.15536			−0.577679	+	0.816264i	$0.696042\pi$
$212$		−	7.44290i		−	0.511180i
$213$		0			0
$214$	5.77245			0.394596
$215$			13.9918i			0.954233i
$216$		0			0
$217$	−1.73430			−0.117732
$218$	11.5291			0.780852
$219$		0			0
$220$	4.52497	+	0.121111i	0.305074	+	0.00816528i
$221$		−	13.2325i		−	0.890117i
$222$		0			0
$223$		−	3.91052i		−	0.261868i	−0.991391	−	0.130934i	$-0.958202\pi$
$223$		−	3.91052i		−	0.261868i	0.991391	−	0.130934i	$-0.0417976\pi$
$224$			0.331974i			0.0221810i
$225$		0			0
$226$		−	3.17423i		−	0.211147i
$227$	−18.5791			−1.23314			−0.616569	−	0.787301i	$-0.711478\pi$
$227$	−18.5791			−1.23314			−0.616569	+	0.787301i	$0.711478\pi$
$228$		0			0
$229$	−3.22325			−0.212998			−0.106499	−	0.994313i	$-0.533964\pi$
$229$	−3.22325			−0.212998			−0.106499	+	0.994313i	$0.533964\pi$
$230$	−2.87418			−0.189518
$231$		0			0
$232$	−0.741082			−0.0486544
$233$			8.59012i			0.562758i	0.959597	+	0.281379i	$0.0907918\pi$
$233$			8.59012i			0.562758i	−0.959597	+	0.281379i	$0.909208\pi$
$234$		0			0
$235$	−5.74835			−0.374981
$236$			1.84953i			0.120394i
$237$		0			0
$238$	0.858427			0.0556435
$239$			5.42428i			0.350867i	0.984491	+	0.175434i	$0.0561327\pi$
$239$			5.42428i			0.350867i	−0.984491	+	0.175434i	$0.943867\pi$
$240$		0			0
$241$	−0.436523			−0.0281189			−0.0140594	−	0.999901i	$-0.504475\pi$
$241$	−0.436523			−0.0281189			−0.0140594	+	0.999901i	$0.504475\pi$
$242$	10.9843	+	0.588408i	0.706094	+	0.0378243i
$243$		0			0
$244$		−	2.61541i		−	0.167435i
$245$	−9.40332			−0.600756
$246$		0			0
$247$	−9.07023	−	20.3786i	−0.577125	−	1.29666i
$248$			5.22421i			0.331738i
$249$		0			0
$250$	11.1059			0.702399
$251$	26.0541			1.64452			0.822261	−	0.569111i	$-0.192712\pi$
$251$	26.0541			1.64452			0.822261	+	0.569111i	$0.192712\pi$
$252$		0			0
$253$	−6.98198	−	0.186873i	−0.438954	−	0.0117486i
$254$	4.50469			0.282649
$255$		0			0
$256$	1.00000			0.0625000
$257$			14.9965i			0.935456i	0.883873	+	0.467728i	$0.154927\pi$
$257$			14.9965i			0.935456i	−0.883873	+	0.467728i	$0.845073\pi$
$258$		0			0
$259$	2.03985			0.126750
$260$	−6.98425			−0.433145
$261$		0			0
$262$		−	11.2637i		−	0.695872i
$263$			15.3531i			0.946712i	0.880871	+	0.473356i	$0.156958\pi$
$263$			15.3531i			0.946712i	−0.880871	+	0.473356i	$0.843042\pi$
$264$		0			0
$265$			10.1582i			0.624014i
$266$	1.32201	−	0.588408i	0.0810576	−	0.0360776i
$267$		0			0
$268$			2.28344i			0.139483i
$269$			16.1329i			0.983642i	0.870696	+	0.491821i	$0.163669\pi$
$269$			16.1329i			0.983642i	−0.870696	+	0.491821i	$0.836331\pi$
$270$		0			0
$271$			19.6795i			1.19545i	0.801703	+	0.597723i	$0.203928\pi$
$271$			19.6795i			1.19545i	−0.801703	+	0.597723i	$0.796072\pi$
$272$		−	2.58582i		−	0.156788i
$273$		0			0
$274$	11.5364			0.696940
$275$	10.4014	+	0.278393i	0.627229	+	0.0167878i
$276$		0			0
$277$			24.1642i			1.45189i	0.687754	+	0.725944i	$0.258597\pi$
$277$			24.1642i			1.45189i	−0.687754	+	0.725944i	$0.741403\pi$
$278$			15.3511i			0.920695i
$279$		0			0
$280$		−	0.453085i		−	0.0270770i
$281$	23.1313			1.37990			0.689948	−	0.723859i	$-0.257634\pi$
$281$	23.1313			1.37990			0.689948	+	0.723859i	$0.257634\pi$
$282$		0			0
$283$			5.62638i			0.334453i	0.985918	+	0.167227i	$0.0534812\pi$
$283$			5.62638i			0.334453i	−0.985918	+	0.167227i	$0.946519\pi$
$284$		−	12.1385i		−	0.720286i
$285$		0			0
$286$	−16.9662	−	0.454101i	−1.00323	−	0.0268515i
$287$			0.827814i			0.0488643i
$288$		0			0
$289$	10.3135			0.606678
$290$	1.01144			0.0593940
$291$		0			0
$292$			9.08536i			0.531681i
$293$	−15.9953			−0.934457			−0.467229	−	0.884136i	$-0.654748\pi$
$293$	−15.9953			−0.934457			−0.467229	+	0.884136i	$0.654748\pi$
$294$		0			0
$295$		−	2.52427i		−	0.146969i
$296$		−	6.14459i		−	0.357147i
$297$		0			0
$298$		−	9.05577i		−	0.524587i
$299$	10.7766			0.623228
$300$		0			0
$301$	3.40332			0.196164
$302$	14.1758			0.815724
$303$		0			0
$304$	−1.77245	−	3.98226i	−0.101657	−	0.228399i
$305$			3.56956i			0.204393i
$306$		0			0
$307$	−17.8829			−1.02063			−0.510315	−	0.859988i	$-0.670471\pi$
$307$	−17.8829			−1.02063			−0.510315	+	0.859988i	$0.670471\pi$
$308$	0.0294586	−	1.10064i	0.00167856	−	0.0627148i
$309$		0			0
$310$		−	7.13010i		−	0.404962i
$311$	22.9846			1.30334			0.651669	−	0.758504i	$-0.274069\pi$
$311$	22.9846			1.30334			0.651669	+	0.758504i	$0.274069\pi$
$312$		0			0
$313$	−20.2507			−1.14464			−0.572318	−	0.820032i	$-0.693956\pi$
$313$	−20.2507			−1.14464			−0.572318	+	0.820032i	$0.693956\pi$
$314$	−14.8966			−0.840662
$315$		0			0
$316$	−5.96397			−0.335499
$317$		−	10.1690i		−	0.571148i	−0.958357	−	0.285574i	$-0.907816\pi$
$317$		−	10.1690i		−	0.571148i	0.958357	−	0.285574i	$-0.0921843\pi$
$318$		0			0
$319$	2.45701	+	0.0657618i	0.137566	+	0.00368195i
$320$	−1.36482			−0.0762957
$321$		0			0
$322$			0.699105i			0.0389596i
$323$	−10.2974	+	4.58323i	−0.572964	+	0.255018i
$324$		0			0
$325$	−16.0545			−0.890542
$326$	3.54108			0.196122
$327$		0			0
$328$	2.49361			0.137686
$329$			1.39821i			0.0770859i
$330$		0			0
$331$			19.2264i			1.05678i	0.849002	+	0.528390i	$0.177204\pi$
$331$			19.2264i			1.05678i	−0.849002	+	0.528390i	$0.822796\pi$
$332$			13.2221i			0.725658i
$333$		0			0
$334$	10.3876			0.568383
$335$		−	3.11648i		−	0.170271i
$336$		0			0
$337$	1.38474			0.0754317			0.0377159	−	0.999289i	$-0.487992\pi$
$337$	1.38474			0.0754317			0.0377159	+	0.999289i	$0.487992\pi$
$338$	13.1872			0.717290
$339$		0			0
$340$			3.52918i			0.191397i
$341$	0.463583	−	17.3205i	0.0251044	−	0.937959i
$342$		0			0
$343$			4.61106i			0.248974i
$344$		−	10.2518i		−	0.552738i
$345$		0			0
$346$	−11.1804			−0.601064
$347$		−	21.7263i		−	1.16633i	−0.812354	−	0.583164i	$-0.801814\pi$
$347$		−	21.7263i		−	1.16633i	0.812354	−	0.583164i	$-0.198186\pi$
$348$		0			0
$349$		−	8.38626i		−	0.448906i	−0.974485	−	0.224453i	$-0.927940\pi$
$349$		−	8.38626i		−	0.448906i	0.974485	−	0.224453i	$-0.0720595\pi$
$350$		−	1.04149i		−	0.0556701i
$351$		0			0
$352$	−3.31544	−	0.0887375i	−0.176713	−	0.00472973i
$353$	13.1101			0.697779			0.348889	−	0.937164i	$-0.386559\pi$
$353$	13.1101			0.697779			0.348889	+	0.937164i	$0.386559\pi$
$354$		0			0
$355$			16.5668i			0.879276i
$356$		−	16.4879i		−	0.873856i
$357$		0			0
$358$		−	2.25385i		−	0.119119i
$359$			29.8474i			1.57528i	0.616134	+	0.787641i	$0.288698\pi$
$359$			29.8474i			1.57528i	−0.616134	+	0.787641i	$0.711302\pi$
$360$		0			0
$361$	−12.7169	+	14.1167i	−0.669308	+	0.742985i
$362$		−	24.3153i		−	1.27798i
$363$		0			0
$364$			1.69883i			0.0890428i
$365$		−	12.3999i		−	0.649039i
$366$		0			0
$367$	3.49912			0.182653			0.0913264	−	0.995821i	$-0.470889\pi$
$367$	3.49912			0.182653			0.0913264	+	0.995821i	$0.470889\pi$
$368$	2.10590			0.109778
$369$		0			0
$370$			8.38626i			0.435981i
$371$	2.47085			0.128280
$372$		0			0
$373$	14.2004			0.735267			0.367633	−	0.929971i	$-0.380168\pi$
$373$	14.2004			0.735267			0.367633	+	0.929971i	$0.380168\pi$
$374$	−0.229459	+	8.57313i	−0.0118651	+	0.443306i
$375$		0			0
$376$	4.21180			0.217207
$377$	−3.79237			−0.195317
$378$		0			0
$379$		−	19.7199i		−	1.01294i	−0.862257	−	0.506472i	$-0.830950\pi$
$379$		−	19.7199i		−	1.01294i	0.862257	−	0.506472i	$-0.169050\pi$
$380$	2.41907	+	5.43507i	0.124096	+	0.278813i
$381$		0			0
$382$	−21.4533			−1.09764
$383$		−	28.8108i		−	1.47216i	−0.676892	−	0.736082i	$-0.736674\pi$
$383$		−	28.8108i		−	1.47216i	0.676892	−	0.736082i	$-0.263326\pi$
$384$		0			0
$385$	−0.0402057	+	1.50218i	−0.00204907	+	0.0765580i
$386$	−20.6664			−1.05189
$387$		0			0
$388$		−	3.52918i		−	0.179167i
$389$	−9.71255			−0.492446			−0.246223	−	0.969213i	$-0.579190\pi$
$389$	−9.71255			−0.492446			−0.246223	+	0.969213i	$0.579190\pi$
$390$		0			0
$391$		−	5.44548i		−	0.275390i
$392$	6.88979			0.347987
$393$		0			0
$394$		−	8.03131i		−	0.404611i
$395$	8.13974			0.409555
$396$		0			0
$397$	21.8815			1.09820			0.549102	−	0.835756i	$-0.314970\pi$
$397$	21.8815			1.09820			0.549102	+	0.835756i	$0.314970\pi$
$398$	0.263583			0.0132122
$399$		0			0
$400$	−3.13727			−0.156863
$401$		−	20.9308i		−	1.04524i	−0.852567	−	0.522618i	$-0.824956\pi$
$401$		−	20.9308i		−	1.04524i	0.852567	−	0.522618i	$-0.175044\pi$
$402$		0			0
$403$			26.7341i			1.33172i
$404$		−	16.4879i		−	0.820302i
$405$		0			0
$406$		−	0.246020i		−	0.0122098i
$407$	−0.545256	+	20.3720i	−0.0270273	+	1.00980i
$408$		0			0
$409$	25.6935			1.27046			0.635230	−	0.772323i	$-0.280905\pi$
$409$	25.6935			1.27046			0.635230	+	0.772323i	$0.280905\pi$
$410$	−3.40332			−0.168078
$411$		0			0
$412$		−	9.20647i		−	0.453570i
$413$	−0.613996			−0.0302128
$414$		0			0
$415$		−	18.0458i		−	0.885834i
$416$	5.11734			0.250898
$417$		0			0
$418$	5.52307	+	13.3602i	0.270142	+	0.653470i
$419$	−10.6766			−0.521588			−0.260794	−	0.965394i	$-0.583984\pi$
$419$	−10.6766			−0.521588			−0.260794	+	0.965394i	$0.583984\pi$
$420$		0			0
$421$			11.2866i			0.550077i	0.961433	+	0.275039i	$0.0886906\pi$
$421$			11.2866i			0.550077i	−0.961433	+	0.275039i	$0.911309\pi$
$422$	−16.7825			−0.816962
$423$		0			0
$424$		−	7.44290i		−	0.361459i
$425$			8.11241i			0.393510i
$426$		0			0
$427$	0.868250			0.0420175
$428$	5.77245			0.279022
$429$		0			0
$430$			13.9918i			0.674745i
$431$	−33.5141			−1.61432			−0.807159	−	0.590334i	$-0.798996\pi$
$431$	−33.5141			−1.61432			−0.807159	+	0.590334i	$0.798996\pi$
$432$		0			0
$433$			1.36828i			0.0657555i	0.999459	+	0.0328777i	$0.0104672\pi$
$433$			1.36828i			0.0657555i	−0.999459	+	0.0328777i	$0.989533\pi$
$434$	−1.73430			−0.0832492
$435$		0			0
$436$	11.5291			0.552146
$437$	−3.73260	−	8.38626i	−0.178555	−	0.401169i
$438$		0			0
$439$	−37.1544			−1.77328			−0.886641	−	0.462459i	$-0.846967\pi$
$439$	−37.1544			−1.77328			−0.886641	+	0.462459i	$0.846967\pi$
$440$	4.52497	+	0.121111i	0.215720	+	0.00577373i
$441$		0			0
$442$		−	13.2325i		−	0.629408i
$443$	6.38376			0.303302			0.151651	−	0.988434i	$-0.451541\pi$
$443$	6.38376			0.303302			0.151651	+	0.988434i	$0.451541\pi$
$444$		0			0
$445$			22.5030i			1.06674i
$446$		−	3.91052i		−	0.185169i
$447$		0			0
$448$			0.331974i			0.0156843i
$449$			14.6943i			0.693468i	0.937963	+	0.346734i	$0.112709\pi$
$449$			14.6943i			0.693468i	−0.937963	+	0.346734i	$0.887291\pi$
$450$		0			0
$451$	−8.26740	−	0.221277i	−0.389297	−	0.0104195i
$452$		−	3.17423i		−	0.149303i
$453$		0			0
$454$	−18.5791			−0.871960
$455$		−	2.31859i		−	0.108697i
$456$		0			0
$457$			22.5097i			1.05296i	0.850188	+	0.526480i	$0.176488\pi$
$457$			22.5097i			1.05296i	−0.850188	+	0.526480i	$0.823512\pi$
$458$	−3.22325			−0.150612
$459$		0			0
$460$	−2.87418			−0.134009
$461$			18.1532i			0.845479i	0.906251	+	0.422739i	$0.138931\pi$
$461$			18.1532i			0.845479i	−0.906251	+	0.422739i	$0.861069\pi$
$462$		0			0
$463$	2.87799			0.133752			0.0668758	−	0.997761i	$-0.478697\pi$
$463$	2.87799			0.133752			0.0668758	+	0.997761i	$0.478697\pi$
$464$	−0.741082			−0.0344039
$465$		0			0
$466$			8.59012i			0.397930i
$467$	9.14010			0.422953			0.211477	−	0.977383i	$-0.432173\pi$
$467$	9.14010			0.422953			0.211477	+	0.977383i	$0.432173\pi$
$468$		0			0
$469$	−0.758043			−0.0350032
$470$	−5.74835			−0.265152
$471$		0			0
$472$			1.84953i			0.0851314i
$473$	−0.909716	+	33.9891i	−0.0418288	+	1.56282i
$474$		0			0
$475$	5.56065	+	12.4934i	0.255140	+	0.573238i
$476$	0.858427			0.0393459
$477$		0			0
$478$			5.42428i			0.248101i
$479$		−	4.65982i		−	0.212913i	−0.994317	−	0.106456i	$-0.966050\pi$
$479$		−	4.65982i		−	0.212913i	0.994317	−	0.106456i	$-0.0339505\pi$
$480$		0			0
$481$		−	31.4440i		−	1.43372i
$482$	−0.436523			−0.0198831
$483$		0			0
$484$	10.9843	+	0.588408i	0.499284	+	0.0267458i
$485$			4.81669i			0.218715i
$486$		0			0
$487$			0.648308i			0.0293776i	0.999892	+	0.0146888i	$0.00467576\pi$
$487$			0.648308i			0.0293776i	−0.999892	+	0.0146888i	$0.995324\pi$
$488$		−	2.61541i		−	0.118394i
$489$		0			0
$490$	−9.40332			−0.424799
$491$		−	22.1546i		−	0.999825i	−0.866076	−	0.499912i	$-0.833366\pi$
$491$		−	22.1546i		−	0.999825i	0.866076	−	0.499912i	$-0.166634\pi$
$492$		0			0
$493$			1.91631i			0.0863061i
$494$	−9.07023	−	20.3786i	−0.408089	−	0.916877i
$495$		0			0
$496$			5.22421i			0.234574i
$497$	4.02966			0.180755
$498$		0			0
$499$	14.5550			0.651571			0.325786	−	0.945444i	$-0.394371\pi$
$499$	14.5550			0.651571			0.325786	+	0.945444i	$0.394371\pi$
$500$	11.1059			0.496671
$501$		0			0
$502$	26.0541			1.16285
$503$			24.5088i			1.09279i	0.837527	+	0.546396i	$0.184001\pi$
$503$			24.5088i			1.09279i	−0.837527	+	0.546396i	$0.815999\pi$
$504$		0			0
$505$			22.5030i			1.00137i
$506$	−6.98198	−	0.186873i	−0.310387	−	0.00830750i
$507$		0			0
$508$	4.50469			0.199863
$509$			25.8471i			1.14565i	0.819677	+	0.572826i	$0.194153\pi$
$509$			25.8471i			1.14565i	−0.819677	+	0.572826i	$0.805847\pi$
$510$		0			0
$511$	−3.01611			−0.133425
$512$	1.00000			0.0441942
$513$		0			0
$514$			14.9965i			0.661467i
$515$			12.5652i			0.553688i
$516$		0			0
$517$	−13.9640	−	0.373745i	−0.614135	−	0.0164373i
$518$	2.03985			0.0896257
$519$		0			0
$520$	−6.98425			−0.306280
$521$			2.18249i			0.0956165i	0.998857	+	0.0478082i	$0.0152236\pi$
$521$			2.18249i			0.0956165i	−0.998857	+	0.0478082i	$0.984776\pi$
$522$		0			0
$523$	−5.84451			−0.255563			−0.127781	−	0.991802i	$-0.540786\pi$
$523$	−5.84451			−0.255563			−0.127781	+	0.991802i	$0.540786\pi$
$524$		−	11.2637i		−	0.492056i
$525$		0			0
$526$			15.3531i			0.669427i
$527$	13.5089			0.588455
$528$		0			0
$529$	−18.5652			−0.807182
$530$			10.1582i			0.441245i
$531$		0			0
$532$	1.32201	−	0.588408i	0.0573164	−	0.0255107i
$533$	12.7606			0.552725
$534$		0			0
$535$	−7.87835			−0.340611
$536$			2.28344i			0.0986294i
$537$		0			0
$538$			16.1329i			0.695540i
$539$	−22.8427	−	0.611383i	−0.983904	−	0.0263341i
$540$		0			0
$541$		−	29.6720i		−	1.27570i	−0.770161	−	0.637850i	$-0.779824\pi$
$541$		−	29.6720i		−	1.27570i	0.770161	−	0.637850i	$-0.220176\pi$
$542$			19.6795i			0.845307i
$543$		0			0
$544$		−	2.58582i		−	0.110866i
$545$	−15.7352			−0.674022
$546$		0			0
$547$	−16.9102			−0.723028			−0.361514	−	0.932367i	$-0.617740\pi$
$547$	−16.9102			−0.723028			−0.361514	+	0.932367i	$0.617740\pi$
$548$	11.5364			0.492811
$549$		0			0
$550$	10.4014	+	0.278393i	0.443518	+	0.0118707i
$551$	1.31353	+	2.95118i	0.0559582	+	0.125725i
$552$		0			0
$553$		−	1.97989i		−	0.0841933i
$554$			24.1642i			1.02664i
$555$		0			0
$556$			15.3511i			0.651030i
$557$			36.0053i			1.52559i	0.646639	+	0.762797i	$0.276174\pi$
$557$			36.0053i			1.52559i	−0.646639	+	0.762797i	$0.723826\pi$
$558$		0			0
$559$		−	52.4618i		−	2.21890i
$560$		−	0.453085i		−	0.0191463i
$561$		0			0
$562$	23.1313			0.975733
$563$	43.0192			1.81304			0.906521	−	0.422161i	$-0.138728\pi$
$563$	43.0192			1.81304			0.906521	+	0.422161i	$0.138728\pi$
$564$		0			0
$565$			4.33225i			0.182259i
$566$			5.62638i			0.236494i
$567$		0			0
$568$		−	12.1385i		−	0.509319i
$569$	−43.7422			−1.83377			−0.916884	−	0.399153i	$-0.869304\pi$
$569$	−43.7422			−1.83377			−0.916884	+	0.399153i	$0.869304\pi$
$570$		0			0
$571$			31.8799i			1.33413i	0.744998	+	0.667067i	$0.232450\pi$
$571$			31.8799i			1.33413i	−0.744998	+	0.667067i	$0.767550\pi$
$572$	−16.9662	−	0.454101i	−0.709394	−	0.0189869i
$573$		0			0
$574$			0.827814i			0.0345523i
$575$	−6.60678			−0.275522
$576$		0			0
$577$	33.8574			1.40950			0.704752	−	0.709454i	$-0.251058\pi$
$577$	33.8574			1.40950			0.704752	+	0.709454i	$0.251058\pi$
$578$	10.3135			0.428986
$579$		0			0
$580$	1.01144			0.0419979
$581$	−4.38941			−0.182103
$582$		0			0
$583$	−0.660464	+	24.6765i	−0.0273536	+	1.02199i
$584$			9.08536i			0.375955i
$585$		0			0
$586$	−15.9953			−0.660761
$587$	−2.61278			−0.107841			−0.0539206	−	0.998545i	$-0.517172\pi$
$587$	−2.61278			−0.107841			−0.0539206	+	0.998545i	$0.517172\pi$
$588$		0			0
$589$	20.8042	−	9.25964i	0.857221	−	0.381537i
$590$		−	2.52427i		−	0.103923i
$591$		0			0
$592$		−	6.14459i		−	0.252541i
$593$			12.1597i			0.499338i	0.968331	+	0.249669i	$0.0803219\pi$
$593$			12.1597i			0.499338i	−0.968331	+	0.249669i	$0.919678\pi$
$594$		0			0
$595$	−1.17160			−0.0480308
$596$		−	9.05577i		−	0.370939i
$597$		0			0
$598$	10.7766			0.440689
$599$		−	17.5907i		−	0.718736i	−0.933196	−	0.359368i	$-0.882992\pi$
$599$		−	17.5907i		−	0.718736i	0.933196	−	0.359368i	$-0.117008\pi$
$600$		0			0
$601$	−27.3356			−1.11504			−0.557521	−	0.830163i	$-0.688247\pi$
$601$	−27.3356			−1.11504			−0.557521	+	0.830163i	$0.688247\pi$
$602$	3.40332			0.138709
$603$		0			0
$604$	14.1758			0.576804
$605$	−14.9915	−	0.803070i	−0.609492	−	0.0326494i
$606$		0			0
$607$	−29.0905			−1.18075			−0.590374	−	0.807130i	$-0.701020\pi$
$607$	−29.0905			−1.18075			−0.590374	+	0.807130i	$0.701020\pi$
$608$	−1.77245	−	3.98226i	−0.0718823	−	0.161502i
$609$		0			0
$610$			3.56956i			0.144527i
$611$	21.5532			0.871951
$612$		0			0
$613$			36.7152i			1.48291i	0.671001	+	0.741456i	$0.265865\pi$
$613$			36.7152i			1.48291i	−0.671001	+	0.741456i	$0.734135\pi$
$614$	−17.8829			−0.721694
$615$		0			0
$616$	0.0294586	−	1.10064i	0.00118692	−	0.0443461i
$617$	−37.8396			−1.52336			−0.761682	−	0.647951i	$-0.775626\pi$
$617$	−37.8396			−1.52336			−0.761682	+	0.647951i	$0.775626\pi$
$618$		0			0
$619$	−38.5731			−1.55038			−0.775192	−	0.631726i	$-0.782347\pi$
$619$	−38.5731			−1.55038			−0.775192	+	0.631726i	$0.782347\pi$
$620$		−	7.13010i		−	0.286352i
$621$		0			0
$622$	22.9846			0.921599
$623$	5.47355			0.219293
$624$		0			0
$625$	0.528789			0.0211516
$626$	−20.2507			−0.809379
$627$		0			0
$628$	−14.8966			−0.594438
$629$	−15.8888			−0.633528
$630$		0			0
$631$	7.98573			0.317907			0.158953	−	0.987286i	$-0.449188\pi$
$631$	7.98573			0.317907			0.158953	+	0.987286i	$0.449188\pi$
$632$	−5.96397			−0.237234
$633$		0			0
$634$		−	10.1690i		−	0.403863i
$635$	−6.14809			−0.243980
$636$		0			0
$637$	35.2574			1.39695
$638$	2.45701	+	0.0657618i	0.0972740	+	0.00260353i
$639$		0			0
$640$	−1.36482			−0.0539492
$641$			19.1625i			0.756872i	0.925627	+	0.378436i	$0.123538\pi$
$641$			19.1625i			0.756872i	−0.925627	+	0.378436i	$0.876462\pi$
$642$		0			0
$643$	32.1803			1.26907			0.634534	−	0.772895i	$-0.281192\pi$
$643$	32.1803			1.26907			0.634534	+	0.772895i	$0.281192\pi$
$644$			0.699105i			0.0275486i
$645$		0			0
$646$	−10.2974	+	4.58323i	−0.405147	+	0.180325i
$647$	−22.8329			−0.897652			−0.448826	−	0.893619i	$-0.648158\pi$
$647$	−22.8329			−0.897652			−0.448826	+	0.893619i	$0.648158\pi$
$648$		0			0
$649$	0.164123	−	6.13199i	0.00644238	−	0.240702i
$650$	−16.0545			−0.629709
$651$		0			0
$652$	3.54108			0.138679
$653$	1.30505			0.0510705			0.0255353	−	0.999674i	$-0.491871\pi$
$653$	1.30505			0.0510705			0.0255353	+	0.999674i	$0.491871\pi$
$654$		0			0
$655$			15.3729i			0.600668i
$656$	2.49361			0.0973590
$657$		0			0
$658$			1.39821i			0.0545079i
$659$	42.5739			1.65844			0.829222	−	0.558920i	$-0.188784\pi$
$659$	42.5739			1.65844			0.829222	+	0.558920i	$0.188784\pi$
$660$		0			0
$661$		−	22.3990i		−	0.871220i	−0.900135	−	0.435610i	$-0.856533\pi$
$661$		−	22.3990i		−	0.871220i	0.900135	−	0.435610i	$-0.143467\pi$
$662$			19.2264i			0.747256i
$663$		0			0
$664$			13.2221i			0.513118i
$665$	−1.80430	+	0.803070i	−0.0699679	+	0.0311417i
$666$		0			0
$667$	−1.56065			−0.0604284
$668$	10.3876			0.401907
$669$		0			0
$670$		−	3.11648i		−	0.120400i
$671$	−0.232085	+	8.67123i	−0.00895955	+	0.334749i
$672$		0			0
$673$	11.3449			0.437314			0.218657	−	0.975802i	$-0.429832\pi$
$673$	11.3449			0.437314			0.218657	+	0.975802i	$0.429832\pi$
$674$	1.38474			0.0533383
$675$		0			0
$676$	13.1872			0.507201
$677$	6.72412			0.258429			0.129214	−	0.991617i	$-0.458754\pi$
$677$	6.72412			0.258429			0.129214	+	0.991617i	$0.458754\pi$
$678$		0			0
$679$	1.17160			0.0449618
$680$			3.52918i			0.135338i
$681$		0			0
$682$	0.463583	−	17.3205i	0.0177515	−	0.663238i
$683$			40.1776i			1.53735i	0.639638	+	0.768676i	$0.279084\pi$
$683$			40.1776i			1.53735i	−0.639638	+	0.768676i	$0.720916\pi$
$684$		0			0
$685$	−15.7451			−0.601590
$686$			4.61106i			0.176051i
$687$		0			0
$688$		−	10.2518i		−	0.390845i
$689$		−	38.0879i		−	1.45103i
$690$		0			0
$691$	15.6846			0.596672			0.298336	−	0.954461i	$-0.403568\pi$
$691$	15.6846			0.596672			0.298336	+	0.954461i	$0.403568\pi$
$692$	−11.1804			−0.425016
$693$		0			0
$694$		−	21.7263i		−	0.824719i
$695$		−	20.9514i		−	0.794733i
$696$		0			0
$697$		−	6.44802i		−	0.244236i
$698$		−	8.38626i		−	0.317424i
$699$		0			0
$700$		−	1.04149i		−	0.0393647i
$701$		−	14.3270i		−	0.541122i	−0.962703	−	0.270561i	$-0.912791\pi$
$701$		−	14.3270i		−	0.541122i	0.962703	−	0.270561i	$-0.0872093\pi$
$702$		0			0
$703$	−24.4694	+	10.8910i	−0.922880	+	0.410761i
$704$	−3.31544	−	0.0887375i	−0.124955	−	0.00334442i
$705$		0			0
$706$	13.1101			0.493404
$707$	5.47355			0.205854
$708$		0			0
$709$	2.48315			0.0932566			0.0466283	−	0.998912i	$-0.485152\pi$
$709$	2.48315			0.0932566			0.0466283	+	0.998912i	$0.485152\pi$
$710$			16.5668i			0.621742i
$711$		0			0
$712$		−	16.4879i		−	0.617909i
$713$			11.0017i			0.412016i
$714$		0			0
$715$	23.1558	+	0.619765i	0.865980	+	0.0231779i
$716$		−	2.25385i		−	0.0842302i
$717$		0			0
$718$			29.8474i			1.11389i
$719$	17.3932			0.648658			0.324329	−	0.945944i	$-0.394862\pi$
$719$	17.3932			0.648658			0.324329	+	0.945944i	$0.394862\pi$
$720$		0			0
$721$	3.05631			0.113823
$722$	−12.7169	+	14.1167i	−0.473272	+	0.525370i
$723$		0			0
$724$		−	24.3153i		−	0.903671i
$725$	2.32497			0.0863473
$726$		0			0
$727$	48.5116			1.79919			0.899597	−	0.436721i	$-0.143860\pi$
$727$	48.5116			1.79919			0.899597	+	0.436721i	$0.143860\pi$
$728$			1.69883i			0.0629627i
$729$		0			0
$730$		−	12.3999i		−	0.458940i
$731$	−26.5092			−0.980479
$732$		0			0
$733$		−	29.7137i		−	1.09750i	−0.835987	−	0.548750i	$-0.815104\pi$
$733$		−	29.7137i		−	1.09750i	0.835987	−	0.548750i	$-0.184896\pi$
$734$	3.49912			0.129155
$735$		0			0
$736$	2.10590			0.0776246
$737$	0.202627	−	7.57059i	0.00746384	−	0.278866i
$738$		0			0
$739$			12.1001i			0.445110i	0.974920	+	0.222555i	$0.0714397\pi$
$739$			12.1001i			0.445110i	−0.974920	+	0.222555i	$0.928560\pi$
$740$			8.38626i			0.308285i
$741$		0			0
$742$	2.47085			0.0907078
$743$	−29.3218			−1.07571			−0.537856	−	0.843037i	$-0.680766\pi$
$743$	−29.3218			−1.07571			−0.537856	+	0.843037i	$0.680766\pi$
$744$		0			0
$745$			12.3595i			0.452817i
$746$	14.2004			0.519912
$747$		0			0
$748$	−0.229459	+	8.57313i	−0.00838987	+	0.313465i
$749$			1.91631i			0.0700203i
$750$		0			0
$751$			30.5782i			1.11581i	0.829903	+	0.557907i	$0.188395\pi$
$751$			30.5782i			1.11581i	−0.829903	+	0.557907i	$0.811605\pi$
$752$	4.21180			0.153589
$753$		0			0
$754$	−3.79237			−0.138110
$755$	−19.3474			−0.704123
$756$		0			0
$757$	39.5549			1.43765			0.718823	−	0.695193i	$-0.244681\pi$
$757$	39.5549			1.43765			0.718823	+	0.695193i	$0.244681\pi$
$758$		−	19.7199i		−	0.716259i
$759$		0			0
$760$	2.41907	+	5.43507i	0.0877490	+	0.197151i
$761$		−	33.3088i		−	1.20744i	−0.797196	−	0.603721i	$-0.793684\pi$
$761$		−	33.3088i		−	1.20744i	0.797196	−	0.603721i	$-0.206316\pi$
$762$		0			0
$763$			3.82738i			0.138561i
$764$	−21.4533			−0.776152
$765$		0			0
$766$		−	28.8108i		−	1.04098i
$767$			9.46467i			0.341750i
$768$		0			0
$769$		−	52.5268i		−	1.89417i	−0.320990	−	0.947083i	$-0.604016\pi$
$769$		−	52.5268i		−	1.89417i	0.320990	−	0.947083i	$-0.395984\pi$
$770$	−0.0402057	+	1.50218i	−0.00144891	+	0.0541347i
$771$		0			0
$772$	−20.6664			−0.743801
$773$			13.6467i			0.490836i	0.969417	+	0.245418i	$0.0789253\pi$
$773$			13.6467i			0.490836i	−0.969417	+	0.245418i	$0.921075\pi$
$774$		0			0
$775$		−	16.3897i		−	0.588737i
$776$		−	3.52918i		−	0.126690i
$777$		0			0
$778$	−9.71255			−0.348212
$779$	−4.41979	−	9.93020i	−0.158355	−	0.355786i
$780$		0			0
$781$	−1.07714	+	40.2444i	−0.0385431	+	1.44006i
$782$		−	5.44548i		−	0.194730i
$783$		0			0
$784$	6.88979			0.246064
$785$	20.3311			0.725649
$786$		0			0
$787$	−20.9801			−0.747859			−0.373929	−	0.927457i	$-0.621990\pi$
$787$	−20.9801			−0.747859			−0.373929	+	0.927457i	$0.621990\pi$
$788$		−	8.03131i		−	0.286103i
$789$		0			0
$790$	8.13974			0.289599
$791$	1.05376			0.0374675
$792$		0			0
$793$		−	13.3840i		−	0.475278i
$794$	21.8815			0.776547
$795$		0			0
$796$	0.263583			0.00934244
$797$			17.5648i			0.622177i	0.950381	+	0.311088i	$0.100693\pi$
$797$			17.5648i			0.622177i	−0.950381	+	0.311088i	$0.899307\pi$
$798$		0			0
$799$		−	10.8910i		−	0.385295i
$800$	−3.13727			−0.110919
$801$		0			0
$802$		−	20.9308i		−	0.739093i
$803$	0.806213	−	30.1219i	0.0284506	−	1.06298i
$804$		0			0
$805$		−	0.954153i		−	0.0336295i
$806$			26.7341i			0.941667i
$807$		0			0
$808$		−	16.4879i		−	0.580041i
$809$			6.97725i			0.245307i	0.992450	+	0.122654i	$0.0391404\pi$
$809$			6.97725i			0.245307i	−0.992450	+	0.122654i	$0.960860\pi$
$810$		0			0
$811$	56.5078			1.98426			0.992128	−	0.125230i	$-0.0399668\pi$
$811$	56.5078			1.98426			0.992128	+	0.125230i	$0.0399668\pi$
$812$		−	0.246020i		−	0.00863362i
$813$		0			0
$814$	−0.545256	+	20.3720i	−0.0191112	+	0.714038i
$815$	−4.83294			−0.169290
$816$		0			0
$817$	−40.8252	+	18.1707i	−1.42829	+	0.635713i
$818$	25.6935			0.898351
$819$		0			0
$820$	−3.40332			−0.118849
$821$			20.3380i			0.709802i	0.934904	+	0.354901i	$0.115485\pi$
$821$			20.3380i			0.709802i	−0.934904	+	0.354901i	$0.884515\pi$
$822$		0			0
$823$	−22.7728			−0.793810			−0.396905	−	0.917860i	$-0.629916\pi$
$823$	−22.7728			−0.793810			−0.396905	+	0.917860i	$0.629916\pi$
$824$		−	9.20647i		−	0.320723i
$825$		0			0
$826$	−0.613996			−0.0213637
$827$	9.52915			0.331361			0.165680	−	0.986179i	$-0.447018\pi$
$827$	9.52915			0.331361			0.165680	+	0.986179i	$0.447018\pi$
$828$		0			0
$829$		−	6.05582i		−	0.210327i	−0.994455	−	0.105164i	$-0.966463\pi$
$829$		−	6.05582i		−	0.210327i	0.994455	−	0.105164i	$-0.0335366\pi$
$830$		−	18.0458i		−	0.626379i
$831$		0			0
$832$	5.11734			0.177412
$833$		−	17.8158i		−	0.617280i
$834$		0			0
$835$	−14.1772			−0.490621
$836$	5.52307	+	13.3602i	0.191019	+	0.462073i
$837$		0			0
$838$	−10.6766			−0.368819
$839$			22.5026i			0.776876i	0.921475	+	0.388438i	$0.126985\pi$
$839$			22.5026i			0.776876i	−0.921475	+	0.388438i	$0.873015\pi$
$840$		0			0
$841$	−28.4508			−0.981062
$842$			11.2866i			0.388963i
$843$		0			0
$844$	−16.7825			−0.577679
$845$	−17.9982			−0.619156
$846$		0			0
$847$	−0.195336	+	3.64649i	−0.00671183	+	0.125295i
$848$		−	7.44290i		−	0.255590i
$849$		0			0
$850$			8.11241i			0.278253i
$851$		−	12.9399i		−	0.443574i
$852$		0			0
$853$		−	54.2908i		−	1.85888i	−0.368973	−	0.929440i	$-0.620290\pi$
$853$		−	54.2908i		−	1.85888i	0.368973	−	0.929440i	$-0.379710\pi$
$854$	0.868250			0.0297109
$855$		0			0
$856$	5.77245			0.197298
$857$	−25.5807			−0.873821			−0.436910	−	0.899505i	$-0.643927\pi$
$857$	−25.5807			−0.873821			−0.436910	+	0.899505i	$0.643927\pi$
$858$		0			0
$859$	−34.2659			−1.16914			−0.584569	−	0.811344i	$-0.698736\pi$
$859$	−34.2659			−1.16914			−0.584569	+	0.811344i	$0.698736\pi$
$860$			13.9918i			0.477117i
$861$		0			0
$862$	−33.5141			−1.14150
$863$			8.18134i			0.278496i	0.990258	+	0.139248i	$0.0444685\pi$
$863$			8.18134i			0.278496i	−0.990258	+	0.139248i	$0.955531\pi$
$864$		0			0
$865$	15.2593			0.518831
$866$			1.36828i			0.0464961i
$867$		0			0
$868$	−1.73430			−0.0588661
$869$	19.7732	+	0.529228i	0.670759	+	0.0179528i
$870$		0			0
$871$			11.6851i			0.395936i
$872$	11.5291			0.390426
$873$		0			0
$874$	−3.73260	−	8.38626i	−0.126257	−	0.283669i
$875$			3.68688i			0.124639i
$876$		0			0
$877$	23.5342			0.794693			0.397346	−	0.917669i	$-0.369931\pi$
$877$	23.5342			0.794693			0.397346	+	0.917669i	$0.369931\pi$
$878$	−37.1544			−1.25390
$879$		0			0
$880$	4.52497	+	0.121111i	0.152537	+	0.00408264i
$881$	−24.2600			−0.817342			−0.408671	−	0.912682i	$-0.634008\pi$
$881$	−24.2600			−0.817342			−0.408671	+	0.912682i	$0.634008\pi$
$882$		0			0
$883$	−41.9782			−1.41268			−0.706340	−	0.707873i	$-0.749655\pi$
$883$	−41.9782			−1.41268			−0.706340	+	0.707873i	$0.749655\pi$
$884$		−	13.2325i		−	0.445058i
$885$		0			0
$886$	6.38376			0.214467
$887$	37.6410			1.26386			0.631930	−	0.775025i	$-0.282263\pi$
$887$	37.6410			1.26386			0.631930	+	0.775025i	$0.282263\pi$
$888$		0			0
$889$			1.49544i			0.0501555i
$890$			22.5030i			0.754301i
$891$		0			0
$892$		−	3.91052i		−	0.130934i
$893$	−7.46520	−	16.7725i	−0.249814	−	0.561271i
$894$		0			0
$895$			3.07609i			0.102822i
$896$			0.331974i			0.0110905i
$897$		0			0
$898$			14.6943i			0.490356i
$899$		−	3.87157i		−	0.129124i
$900$		0			0
$901$	−19.2460			−0.641177
$902$	−8.26740	−	0.221277i	−0.275274	−	0.00736770i
$903$		0			0
$904$		−	3.17423i		−	0.105573i
$905$			33.1860i			1.10314i
$906$		0			0
$907$			57.5321i			1.91032i	0.296086	+	0.955161i	$0.404318\pi$
$907$			57.5321i			1.91032i	−0.296086	+	0.955161i	$0.595682\pi$
$908$	−18.5791			−0.616569
$909$		0			0
$910$		−	2.31859i		−	0.0768606i
$911$			27.6266i			0.915311i	0.889130	+	0.457656i	$0.151311\pi$
$911$			27.6266i			0.915311i	−0.889130	+	0.457656i	$0.848689\pi$
$912$		0			0
$913$	1.17330	−	43.8371i	0.0388305	−	1.45080i
$914$			22.5097i			0.744555i
$915$		0			0
$916$	−3.22325			−0.106499
$917$	3.73925			0.123481
$918$		0			0
$919$			1.18723i			0.0391630i	0.999808	+	0.0195815i	$0.00623339\pi$
$919$			1.18723i			0.0391630i	−0.999808	+	0.0195815i	$0.993767\pi$
$920$	−2.87418			−0.0947588
$921$		0			0
$922$			18.1532i			0.597844i
$923$		−	62.1168i		−	2.04460i
$924$		0			0
$925$			19.2772i			0.633831i
$926$	2.87799			0.0945767
$927$		0			0
$928$	−0.741082			−0.0243272
$929$	21.6626			0.710727			0.355363	−	0.934728i	$-0.384357\pi$
$929$	21.6626			0.710727			0.355363	+	0.934728i	$0.384357\pi$
$930$		0			0
$931$	−12.2118	−	27.4370i	−0.400226	−	0.899211i
$932$			8.59012i			0.281379i
$933$		0			0
$934$	9.14010			0.299073
$935$	0.313171	−	11.7008i	0.0102418	−	0.382656i
$936$		0			0
$937$			4.19836i			0.137154i	0.997646	+	0.0685772i	$0.0218459\pi$
$937$			4.19836i			0.137154i	−0.997646	+	0.0685772i	$0.978154\pi$
$938$	−0.758043			−0.0247510
$939$		0			0
$940$	−5.74835			−0.187491
$941$	51.3865			1.67515			0.837575	−	0.546322i	$-0.183972\pi$
$941$	51.3865			1.67515			0.837575	+	0.546322i	$0.183972\pi$
$942$		0			0
$943$	5.25129			0.171006
$944$			1.84953i			0.0601970i
$945$		0			0
$946$	−0.909716	+	33.9891i	−0.0295774	+	1.10508i
$947$	−24.3658			−0.791783			−0.395891	−	0.918297i	$-0.629564\pi$
$947$	−24.3658			−0.791783			−0.395891	+	0.918297i	$0.629564\pi$
$948$		0			0
$949$			46.4929i			1.50922i
$950$	5.56065	+	12.4934i	0.180411	+	0.405340i
$951$		0			0
$952$	0.858427			0.0278218
$953$	26.6316			0.862682			0.431341	−	0.902189i	$-0.358041\pi$
$953$	26.6316			0.862682			0.431341	+	0.902189i	$0.358041\pi$
$954$		0			0
$955$	29.2798			0.947473
$956$			5.42428i			0.175434i
$957$		0			0
$958$		−	4.65982i		−	0.150552i
$959$			3.82980i			0.123671i
$960$		0			0
$961$	3.70765			0.119602
$962$		−	31.4440i		−	1.01379i
$963$		0			0
$964$	−0.436523			−0.0140594
$965$	28.2059			0.907981
$966$		0			0
$967$			42.6864i			1.37270i	0.727271	+	0.686350i	$0.240788\pi$
$967$			42.6864i			1.37270i	−0.727271	+	0.686350i	$0.759212\pi$
$968$	10.9843	+	0.588408i	0.353047	+	0.0189121i
$969$		0			0
$970$			4.81669i			0.154655i
$971$			35.1642i			1.12847i	0.825613	+	0.564237i	$0.190830\pi$
$971$			35.1642i			1.12847i	−0.825613	+	0.564237i	$0.809170\pi$
$972$		0			0
$973$	−5.09616			−0.163375
$974$			0.648308i			0.0207731i
$975$		0			0
$976$		−	2.61541i		−	0.0837173i
$977$		−	11.7415i		−	0.375644i	−0.982203	−	0.187822i	$-0.939857\pi$
$977$		−	11.7415i		−	0.375644i	0.982203	−	0.187822i	$-0.0601428\pi$
$978$		0			0
$979$	−1.46309	+	54.6645i	−0.0467607	+	1.74709i
$980$	−9.40332			−0.300378
$981$		0			0
$982$		−	22.1546i		−	0.706983i
$983$		−	28.3815i		−	0.905229i	−0.891706	−	0.452615i	$-0.850491\pi$
$983$		−	28.3815i		−	0.905229i	0.891706	−	0.452615i	$-0.149509\pi$
$984$		0			0
$985$			10.9613i			0.349255i
$986$			1.91631i			0.0610276i
$987$		0			0
$988$	−9.07023	−	20.3786i	−0.288562	−	0.648330i
$989$		−	21.5892i		−	0.686497i
$990$		0			0
$991$			45.0141i			1.42992i	0.699166	+	0.714959i	$0.253555\pi$
$991$			45.0141i			1.42992i	−0.699166	+	0.714959i	$0.746445\pi$
$992$			5.22421i			0.165869i
$993$		0			0
$994$	4.02966			0.127813
$995$	−0.359743			−0.0114046
$996$		0			0
$997$			29.4506i			0.932711i	0.884597	+	0.466355i	$0.154433\pi$
$997$			29.4506i			0.932711i	−0.884597	+	0.466355i	$0.845567\pi$
$998$	14.5550			0.460730
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3762.2.g.h.2089.4		8
3.2	odd	2		418.2.b.c.417.2	✓	8
11.10	odd	2		3762.2.g.g.2089.3		8
19.18	odd	2		3762.2.g.g.2089.4		8
33.32	even	2		418.2.b.d.417.2	yes	8
57.56	even	2		418.2.b.d.417.7	yes	8
209.208	even	2	inner	3762.2.g.h.2089.3		8
627.626	odd	2		418.2.b.c.417.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.b.c.417.2	✓	8	3.2	odd	2
418.2.b.c.417.7	yes	8	627.626	odd	2
418.2.b.d.417.2	yes	8	33.32	even	2
418.2.b.d.417.7	yes	8	57.56	even	2
3762.2.g.g.2089.3		8	11.10	odd	2
3762.2.g.g.2089.4		8	19.18	odd	2
3762.2.g.h.2089.3		8	209.208	even	2	inner
3762.2.g.h.2089.4		8	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:	\( N \)	\(=\)	\( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3762.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} -1.36482 q^{5} +0.331974i q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} -1.36482 q^{5} +0.331974i q^{7} +1.00000 q^{8} -1.36482 q^{10} +(-3.31544 - 0.0887375i) q^{11} +5.11734 q^{13} +0.331974i q^{14} +1.00000 q^{16} -2.58582i q^{17} +(-1.77245 - 3.98226i) q^{19} -1.36482 q^{20} +(-3.31544 - 0.0887375i) q^{22} +2.10590 q^{23} -3.13727 q^{25} +5.11734 q^{26} +0.331974i q^{28} -0.741082 q^{29} +5.22421i q^{31} +1.00000 q^{32} -2.58582i q^{34} -0.453085i q^{35} -6.14459i q^{37} +(-1.77245 - 3.98226i) q^{38} -1.36482 q^{40} +2.49361 q^{41} -10.2518i q^{43} +(-3.31544 - 0.0887375i) q^{44} +2.10590 q^{46} +4.21180 q^{47} +6.88979 q^{49} -3.13727 q^{50} +5.11734 q^{52} -7.44290i q^{53} +(4.52497 + 0.121111i) q^{55} +0.331974i q^{56} -0.741082 q^{58} +1.84953i q^{59} -2.61541i q^{61} +5.22421i q^{62} +1.00000 q^{64} -6.98425 q^{65} +2.28344i q^{67} -2.58582i q^{68} -0.453085i q^{70} -12.1385i q^{71} +9.08536i q^{73} -6.14459i q^{74} +(-1.77245 - 3.98226i) q^{76} +(0.0294586 - 1.10064i) q^{77} -5.96397 q^{79} -1.36482 q^{80} +2.49361 q^{82} +13.2221i q^{83} +3.52918i q^{85} -10.2518i q^{86} +(-3.31544 - 0.0887375i) q^{88} -16.4879i q^{89} +1.69883i q^{91} +2.10590 q^{92} +4.21180 q^{94} +(2.41907 + 5.43507i) q^{95} -3.52918i q^{97} +6.88979 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} - 2 q^{5} + 8 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 - 2 * q^5 + 8 * q^8	\( 8 q + 8 q^{2} + 8 q^{4} - 2 q^{5} + 8 q^{8} - 2 q^{10} + 6 q^{11} + 10 q^{13} + 8 q^{16} - 2 q^{20} + 6 q^{22} - 12 q^{23} - 2 q^{25} + 10 q^{26} + 14 q^{29} + 8 q^{32} - 2 q^{40} - 22 q^{41} + 6 q^{44} - 12 q^{46} - 24 q^{47} + 10 q^{49} - 2 q^{50} + 10 q^{52} + 14 q^{58} + 8 q^{64} + 16 q^{65} + 16 q^{77} - 12 q^{79} - 2 q^{80} - 22 q^{82} + 6 q^{88} - 12 q^{92} - 24 q^{94} + 12 q^{95} + 10 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 - 2 * q^5 + 8 * q^8 - 2 * q^10 + 6 * q^11 + 10 * q^13 + 8 * q^16 - 2 * q^20 + 6 * q^22 - 12 * q^23 - 2 * q^25 + 10 * q^26 + 14 * q^29 + 8 * q^32 - 2 * q^40 - 22 * q^41 + 6 * q^44 - 12 * q^46 - 24 * q^47 + 10 * q^49 - 2 * q^50 + 10 * q^52 + 14 * q^58 + 8 * q^64 + 16 * q^65 + 16 * q^77 - 12 * q^79 - 2 * q^80 - 22 * q^82 + 6 * q^88 - 12 * q^92 - 24 * q^94 + 12 * q^95 + 10 * q^98

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