LMFDB - Embedded newform 315.3.h.d.181.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(181,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.181");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.h (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:	$8.58312832735$
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} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.6
Root			$-1.74681 + 3.02556i$ of defining polynomial
Character	$\chi$	$=$	315.181
Dual form			315.3.h.d.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.112974 q^{2} -3.98724 q^{4} +2.23607i q^{5} +(-6.71303 + 1.98374i) q^{7} -0.902349 q^{8} +O(q^{10})$	\(q+0.112974 q^{2} -3.98724 q^{4} +2.23607i q^{5} +(-6.71303 + 1.98374i) q^{7} -0.902349 q^{8} +0.252617i q^{10} +15.8613 q^{11} -13.3044i q^{13} +(-0.758397 + 0.224110i) q^{14} +15.8470 q^{16} -15.6784i q^{17} -30.8816i q^{19} -8.91573i q^{20} +1.79192 q^{22} -3.63638 q^{23} -5.00000 q^{25} -1.50305i q^{26} +(26.7664 - 7.90963i) q^{28} -14.5640 q^{29} -11.3504i q^{31} +5.39969 q^{32} -1.77125i q^{34} +(-4.43577 - 15.0108i) q^{35} +17.3820 q^{37} -3.48881i q^{38} -2.01771i q^{40} +27.9286i q^{41} -12.1944 q^{43} -63.2429 q^{44} -0.410816 q^{46} -80.5893i q^{47} +(41.1296 - 26.6338i) q^{49} -0.564869 q^{50} +53.0477i q^{52} +55.9152 q^{53} +35.4670i q^{55} +(6.05750 - 1.79002i) q^{56} -1.64536 q^{58} +79.5439i q^{59} -94.5743i q^{61} -1.28230i q^{62} -62.7780 q^{64} +29.7495 q^{65} -103.457 q^{67} +62.5134i q^{68} +(-0.501126 - 1.69583i) q^{70} +113.803 q^{71} +20.3444i q^{73} +1.96371 q^{74} +123.132i q^{76} +(-106.478 + 31.4647i) q^{77} -1.27532 q^{79} +35.4350i q^{80} +3.15520i q^{82} +19.7667i q^{83} +35.0579 q^{85} -1.37765 q^{86} -14.3125 q^{88} -131.258i q^{89} +(26.3924 + 89.3128i) q^{91} +14.4991 q^{92} -9.10448i q^{94} +69.0533 q^{95} -12.4236i q^{97} +(4.64657 - 3.00892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.112974			0.0564869			0.0282435	−	0.999601i	$-0.491009\pi$
$2$	0.112974			0.0564869			0.0282435	+	0.999601i	$0.491009\pi$
$3$		0			0
$3$		0			0
$4$	−3.98724			−0.996809
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		0			0
$7$	−6.71303	+	1.98374i	−0.959004	+	0.283391i
$7$	−6.71303	+	1.98374i	−0.959004	+	0.283391i
$8$	−0.902349			−0.112794
$9$		0			0
$10$			0.252617i			0.0252617i
$11$	15.8613			1.44194			0.720970	−	0.692966i	$-0.243697\pi$
$11$	15.8613			1.44194			0.720970	+	0.692966i	$0.243697\pi$
$12$		0			0
$13$		−	13.3044i		−	1.02341i	−0.859160	−	0.511707i	$-0.829013\pi$
$13$		−	13.3044i		−	1.02341i	0.859160	−	0.511707i	$-0.170987\pi$
$14$	−0.758397	+	0.224110i	−0.0541712	+	0.0160079i
$15$		0			0
$16$	15.8470			0.990438
$17$		−	15.6784i		−	0.922257i	−0.887333	−	0.461129i	$-0.847445\pi$
$17$		−	15.6784i		−	0.922257i	0.887333	−	0.461129i	$-0.152555\pi$
$18$		0			0
$19$		−	30.8816i		−	1.62535i	−0.582719	−	0.812673i	$-0.698011\pi$
$19$		−	30.8816i		−	1.62535i	0.582719	−	0.812673i	$-0.301989\pi$
$20$		−	8.91573i		−	0.445787i
$21$		0			0
$22$	1.79192			0.0814507
$23$	−3.63638			−0.158104			−0.0790518	−	0.996871i	$-0.525189\pi$
$23$	−3.63638			−0.158104			−0.0790518	+	0.996871i	$0.525189\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		−	1.50305i		−	0.0578095i
$27$		0			0
$28$	26.7664	−	7.90963i	0.955944	−	0.282487i
$29$	−14.5640			−0.502208			−0.251104	−	0.967960i	$-0.580794\pi$
$29$	−14.5640			−0.502208			−0.251104	+	0.967960i	$0.580794\pi$
$30$		0			0
$31$		−	11.3504i		−	0.366142i	−0.983100	−	0.183071i	$-0.941396\pi$
$31$		−	11.3504i		−	0.366142i	0.983100	−	0.183071i	$-0.0586038\pi$
$32$	5.39969			0.168740
$33$		0			0
$34$		−	1.77125i		−	0.0520955i
$35$	−4.43577	−	15.0108i	−0.126736	−	0.428880i
$36$		0			0
$37$	17.3820			0.469784			0.234892	−	0.972021i	$-0.424526\pi$
$37$	17.3820			0.469784			0.234892	+	0.972021i	$0.424526\pi$
$38$		−	3.48881i		−	0.0918108i
$39$		0			0
$40$		−	2.01771i		−	0.0504428i
$41$			27.9286i			0.681186i	0.940211	+	0.340593i	$0.110628\pi$
$41$			27.9286i			0.681186i	−0.940211	+	0.340593i	$0.889372\pi$
$42$		0			0
$43$	−12.1944			−0.283591			−0.141796	−	0.989896i	$-0.545288\pi$
$43$	−12.1944			−0.283591			−0.141796	+	0.989896i	$0.545288\pi$
$44$	−63.2429			−1.43734
$45$		0			0
$46$	−0.410816			−0.00893078
$47$		−	80.5893i		−	1.71467i	−0.514762	−	0.857333i	$-0.672120\pi$
$47$		−	80.5893i		−	1.71467i	0.514762	−	0.857333i	$-0.327880\pi$
$48$		0			0
$49$	41.1296	−	26.6338i	0.839379	−	0.543546i
$50$	−0.564869			−0.0112974
$51$		0			0
$52$			53.0477i			1.02015i
$53$	55.9152			1.05500			0.527502	−	0.849554i	$-0.323129\pi$
$53$	55.9152			1.05500			0.527502	+	0.849554i	$0.323129\pi$
$54$		0			0
$55$			35.4670i			0.644855i
$56$	6.05750	−	1.79002i	0.108170	−	0.0319647i
$57$		0			0
$58$	−1.64536			−0.0283682
$59$			79.5439i			1.34820i	0.738640	+	0.674101i	$0.235469\pi$
$59$			79.5439i			1.34820i	−0.738640	+	0.674101i	$0.764531\pi$
$60$		0			0
$61$		−	94.5743i		−	1.55040i	−0.631717	−	0.775199i	$-0.717650\pi$
$61$		−	94.5743i		−	1.55040i	0.631717	−	0.775199i	$-0.282350\pi$
$62$		−	1.28230i		−	0.0206822i
$63$		0			0
$64$	−62.7780			−0.980906
$65$	29.7495			0.457685
$66$		0			0
$67$	−103.457			−1.54414			−0.772068	−	0.635540i	$-0.780778\pi$
$67$	−103.457			−1.54414			−0.772068	+	0.635540i	$0.780778\pi$
$68$			62.5134i			0.919314i
$69$		0			0
$70$	−0.501126	−	1.69583i	−0.00715894	−	0.0242261i
$71$	113.803			1.60286			0.801431	−	0.598087i	$-0.204072\pi$
$71$	113.803			1.60286			0.801431	+	0.598087i	$0.204072\pi$
$72$		0			0
$73$			20.3444i			0.278690i	0.990244	+	0.139345i	$0.0444998\pi$
$73$			20.3444i			0.278690i	−0.990244	+	0.139345i	$0.955500\pi$
$74$	1.96371			0.0265367
$75$		0			0
$76$			123.132i			1.62016i
$77$	−106.478	+	31.4647i	−1.38283	+	0.408633i
$78$		0			0
$79$	−1.27532			−0.0161433			−0.00807165	−	0.999967i	$-0.502569\pi$
$79$	−1.27532			−0.0161433			−0.00807165	+	0.999967i	$0.502569\pi$
$80$			35.4350i			0.442937i
$81$		0			0
$82$			3.15520i			0.0384781i
$83$			19.7667i			0.238153i	0.992885	+	0.119076i	$0.0379934\pi$
$83$			19.7667i			0.238153i	−0.992885	+	0.119076i	$0.962007\pi$
$84$		0			0
$85$	35.0579			0.412446
$86$	−1.37765			−0.0160192
$87$		0			0
$88$	−14.3125			−0.162642
$89$		−	131.258i		−	1.47481i	−0.675450	−	0.737406i	$-0.736051\pi$
$89$		−	131.258i		−	1.47481i	0.675450	−	0.737406i	$-0.263949\pi$
$90$		0			0
$91$	26.3924	+	89.3128i	0.290026	+	0.981459i
$92$	14.4991			0.157599
$93$		0			0
$94$		−	9.10448i		−	0.0968562i
$95$	69.0533			0.726877
$96$		0			0
$97$		−	12.4236i		−	0.128078i	−0.997947	−	0.0640391i	$-0.979602\pi$
$97$		−	12.4236i		−	0.128078i	0.997947	−	0.0640391i	$-0.0203982\pi$
$98$	4.64657	−	3.00892i	0.0474139	−	0.0307033i
$99$		0			0
$100$	19.9362			0.199362
$101$		−	15.0668i		−	0.149176i	−0.997214	−	0.0745882i	$-0.976236\pi$
$101$		−	15.0668i		−	0.149176i	0.997214	−	0.0745882i	$-0.0237642\pi$
$102$		0			0
$103$		−	69.5863i		−	0.675595i	−0.941219	−	0.337798i	$-0.890318\pi$
$103$		−	69.5863i		−	0.675595i	0.941219	−	0.337798i	$-0.109682\pi$
$104$			12.0052i			0.115435i
$105$		0			0
$106$	6.31696			0.0595939
$107$	−104.493			−0.976569			−0.488285	−	0.872684i	$-0.662377\pi$
$107$	−104.493			−0.976569			−0.488285	+	0.872684i	$0.662377\pi$
$108$		0			0
$109$	−19.2137			−0.176273			−0.0881363	−	0.996108i	$-0.528091\pi$
$109$	−19.2137			−0.176273			−0.0881363	+	0.996108i	$0.528091\pi$
$110$			4.00685i			0.0364259i
$111$		0			0
$112$	−106.381	+	31.4363i	−0.949834	+	0.280681i
$113$	−208.552			−1.84559			−0.922795	−	0.385291i	$-0.874101\pi$
$113$	−208.552			−1.84559			−0.922795	+	0.385291i	$0.874101\pi$
$114$		0			0
$115$		−	8.13119i		−	0.0707060i
$116$	58.0703			0.500606
$117$		0			0
$118$			8.98637i			0.0761557i
$119$	31.1018	+	105.249i	0.261359	+	0.884449i
$120$		0			0
$121$	130.582			1.07919
$122$		−	10.6844i		−	0.0875772i
$123$		0			0
$124$			45.2567i			0.364974i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	65.1002			0.512600			0.256300	−	0.966597i	$-0.417496\pi$
$127$	65.1002			0.512600			0.256300	+	0.966597i	$0.417496\pi$
$128$	−28.6910			−0.224149
$129$		0			0
$130$	3.36092			0.0258532
$131$			160.360i			1.22412i	0.790812	+	0.612060i	$0.209659\pi$
$131$			160.360i			1.22412i	−0.790812	+	0.612060i	$0.790341\pi$
$132$		0			0
$133$	61.2610	+	207.309i	0.460609	+	1.55871i
$134$	−11.6879			−0.0872235
$135$		0			0
$136$			14.1474i			0.104025i
$137$	−158.451			−1.15658			−0.578289	−	0.815832i	$-0.696279\pi$
$137$	−158.451			−1.15658			−0.578289	+	0.815832i	$0.696279\pi$
$138$		0			0
$139$			243.471i			1.75159i	0.482684	+	0.875794i	$0.339662\pi$
$139$			243.471i			1.75159i	−0.482684	+	0.875794i	$0.660338\pi$
$140$	17.6865	+	59.8516i	0.126332	+	0.427511i
$141$		0			0
$142$	12.8568			0.0905408
$143$		−	211.025i		−	1.47570i
$144$		0			0
$145$		−	32.5662i		−	0.224594i
$146$			2.29838i			0.0157424i
$147$		0			0
$148$	−69.3062			−0.468285
$149$	134.390			0.901948			0.450974	−	0.892537i	$-0.351077\pi$
$149$	134.390			0.901948			0.450974	+	0.892537i	$0.351077\pi$
$150$		0			0
$151$	1.60056			0.0105997			0.00529987	−	0.999986i	$-0.498313\pi$
$151$	1.60056			0.0105997			0.00529987	+	0.999986i	$0.498313\pi$
$152$			27.8660i			0.183329i
$153$		0			0
$154$	−12.0292	+	3.55469i	−0.0781116	+	0.0230824i
$155$	25.3803			0.163744
$156$		0			0
$157$		−	252.462i		−	1.60804i	−0.594602	−	0.804020i	$-0.702690\pi$
$157$		−	252.462i		−	1.60804i	0.594602	−	0.804020i	$-0.297310\pi$
$158$	−0.144078			−0.000911885
$159$		0			0
$160$			12.0741i			0.0754630i
$161$	24.4111	−	7.21362i	0.151622	−	0.0448051i
$162$		0			0
$163$	−239.023			−1.46640			−0.733199	−	0.680014i	$-0.761974\pi$
$163$	−239.023			−1.46640			−0.733199	+	0.680014i	$0.761974\pi$
$164$		−	111.358i		−	0.679013i
$165$		0			0
$166$			2.23312i			0.0134525i
$167$			170.456i			1.02070i	0.859968	+	0.510348i	$0.170483\pi$
$167$			170.456i			1.02070i	−0.859968	+	0.510348i	$0.829517\pi$
$168$		0			0
$169$	−8.00675			−0.0473772
$170$	3.96063			0.0232978
$171$		0			0
$172$	48.6220			0.282686
$173$		−	269.554i		−	1.55812i	−0.626952	−	0.779058i	$-0.715698\pi$
$173$		−	269.554i		−	1.55812i	0.626952	−	0.779058i	$-0.284302\pi$
$174$		0			0
$175$	33.5652	−	9.91868i	0.191801	−	0.0566782i
$176$	251.355			1.42815
$177$		0			0
$178$		−	14.8287i		−	0.0833076i
$179$	−132.675			−0.741199			−0.370599	−	0.928793i	$-0.620848\pi$
$179$	−132.675			−0.741199			−0.370599	+	0.928793i	$0.620848\pi$
$180$		0			0
$181$		−	231.384i		−	1.27836i	−0.769056	−	0.639182i	$-0.779273\pi$
$181$		−	231.384i		−	1.27836i	0.769056	−	0.639182i	$-0.220727\pi$
$182$	2.98165	+	10.0900i	0.0163827	+	0.0554396i
$183$		0			0
$184$	3.28128			0.0178331
$185$			38.8674i			0.210094i
$186$		0			0
$187$		−	248.680i		−	1.32984i
$188$			321.329i			1.70920i
$189$		0			0
$190$	7.80122			0.0410591
$191$	304.129			1.59230			0.796150	−	0.605099i	$-0.206867\pi$
$191$	304.129			1.59230			0.796150	+	0.605099i	$0.206867\pi$
$192$		0			0
$193$	138.227			0.716202			0.358101	−	0.933683i	$-0.383424\pi$
$193$	138.227			0.716202			0.358101	+	0.933683i	$0.383424\pi$
$194$		−	1.40354i		−	0.00723474i
$195$		0			0
$196$	−163.993	+	106.195i	−0.836701	+	0.541812i
$197$	26.9115			0.136607			0.0683034	−	0.997665i	$-0.478241\pi$
$197$	26.9115			0.136607			0.0683034	+	0.997665i	$0.478241\pi$
$198$		0			0
$199$		−	251.997i		−	1.26632i	−0.774023	−	0.633158i	$-0.781759\pi$
$199$		−	251.997i		−	1.26632i	0.774023	−	0.633158i	$-0.218241\pi$
$200$	4.51174			0.0225587
$201$		0			0
$202$		−	1.70216i		−	0.00842651i
$203$	97.7689	−	28.8912i	0.481620	−	0.142321i
$204$		0			0
$205$	−62.4503			−0.304636
$206$		−	7.86143i		−	0.0381623i
$207$		0			0
$208$		−	210.835i		−	1.01363i
$209$		−	489.823i		−	2.34365i
$210$		0			0
$211$	235.692			1.11702			0.558511	−	0.829497i	$-0.311373\pi$
$211$	235.692			1.11702			0.558511	+	0.829497i	$0.311373\pi$
$212$	−222.947			−1.05164
$213$		0			0
$214$	−11.8050			−0.0551634
$215$		−	27.2675i		−	0.126826i
$216$		0			0
$217$	22.5162	+	76.1956i	0.103761	+	0.351132i
$218$	−2.17065			−0.00995709
$219$		0			0
$220$		−	141.415i		−	0.642797i
$221$	−208.591			−0.943851
$222$		0			0
$223$		−	142.790i		−	0.640314i	−0.947365	−	0.320157i	$-0.896264\pi$
$223$		−	142.790i		−	0.640314i	0.947365	−	0.320157i	$-0.103736\pi$
$224$	−36.2483	+	10.7116i	−0.161823	+	0.0478195i
$225$		0			0
$226$	−23.5609			−0.104252
$227$		−	30.6210i		−	0.134894i	−0.997723	−	0.0674472i	$-0.978515\pi$
$227$		−	30.6210i		−	0.134894i	0.997723	−	0.0674472i	$-0.0214854\pi$
$228$		0			0
$229$		−	210.682i		−	0.920007i	−0.887917	−	0.460004i	$-0.847848\pi$
$229$		−	210.682i		−	0.920007i	0.887917	−	0.460004i	$-0.152152\pi$
$230$		−	0.918612i		−	0.00399397i
$231$		0			0
$232$	13.1418			0.0566459
$233$	182.891			0.784940			0.392470	−	0.919765i	$-0.371621\pi$
$233$	182.891			0.784940			0.392470	+	0.919765i	$0.371621\pi$
$234$		0			0
$235$	180.203			0.766822
$236$		−	317.160i		−	1.34390i
$237$		0			0
$238$	3.51369	+	11.8904i	0.0147634	+	0.0499598i
$239$	−122.511			−0.512597			−0.256299	−	0.966598i	$-0.582503\pi$
$239$	−122.511			−0.512597			−0.256299	+	0.966598i	$0.582503\pi$
$240$		0			0
$241$			149.941i			0.622160i	0.950384	+	0.311080i	$0.100691\pi$
$241$			149.941i			0.622160i	−0.950384	+	0.311080i	$0.899309\pi$
$242$	14.7524			0.0609601
$243$		0			0
$244$			377.090i			1.54545i
$245$	59.5549	+	91.9685i	0.243081	+	0.375382i
$246$		0			0
$247$	−410.861			−1.66340
$248$			10.2420i			0.0412985i
$249$		0			0
$250$		−	1.26309i		−	0.00505234i
$251$			229.388i			0.913896i	0.889493	+	0.456948i	$0.151058\pi$
$251$			229.388i			0.913896i	−0.889493	+	0.456948i	$0.848942\pi$
$252$		0			0
$253$	−57.6779			−0.227976
$254$	7.35462			0.0289552
$255$		0			0
$256$	247.871			0.968245
$257$			48.6524i			0.189309i	0.995510	+	0.0946545i	$0.0301746\pi$
$257$			48.6524i			0.189309i	−0.995510	+	0.0946545i	$0.969825\pi$
$258$		0			0
$259$	−116.686	+	34.4814i	−0.450525	+	0.133133i
$260$	−118.618			−0.456225
$261$		0			0
$262$			18.1164i			0.0691467i
$263$	37.6942			0.143324			0.0716620	−	0.997429i	$-0.477170\pi$
$263$	37.6942			0.143324			0.0716620	+	0.997429i	$0.477170\pi$
$264$		0			0
$265$			125.030i			0.471812i
$266$	6.92088	+	23.4205i	0.0260184	+	0.0880470i
$267$		0			0
$268$	412.508			1.53921
$269$			291.724i			1.08448i	0.840225	+	0.542238i	$0.182423\pi$
$269$			291.724i			1.08448i	−0.840225	+	0.542238i	$0.817577\pi$
$270$		0			0
$271$		−	102.880i		−	0.379631i	−0.981820	−	0.189815i	$-0.939211\pi$
$271$		−	102.880i		−	0.379631i	0.981820	−	0.189815i	$-0.0607890\pi$
$272$		−	248.455i		−	0.913438i
$273$		0			0
$274$	−17.9008			−0.0653316
$275$	−79.3067			−0.288388
$276$		0			0
$277$	381.417			1.37696			0.688479	−	0.725256i	$-0.258279\pi$
$277$	381.417			1.37696			0.688479	+	0.725256i	$0.258279\pi$
$278$			27.5058i			0.0989418i
$279$		0			0
$280$	4.00261	+	13.5450i	0.0142950	+	0.0483749i
$281$	−17.4853			−0.0622251			−0.0311126	−	0.999516i	$-0.509905\pi$
$281$	−17.4853			−0.0622251			−0.0311126	+	0.999516i	$0.509905\pi$
$282$		0			0
$283$			343.358i			1.21328i	0.794977	+	0.606640i	$0.207483\pi$
$283$			343.358i			1.21328i	−0.794977	+	0.606640i	$0.792517\pi$
$284$	−453.760			−1.59775
$285$		0			0
$286$		−	23.8403i		−	0.0833579i
$287$	−55.4031	−	187.486i	−0.193042	−	0.653260i
$288$		0			0
$289$	43.1887			0.149442
$290$		−	3.67913i		−	0.0126866i
$291$		0			0
$292$		−	81.1179i		−	0.277801i
$293$			244.504i			0.834486i	0.908795	+	0.417243i	$0.137004\pi$
$293$			244.504i			0.834486i	−0.908795	+	0.417243i	$0.862996\pi$
$294$		0			0
$295$	−177.865			−0.602934
$296$	−15.6846			−0.0529887
$297$		0			0
$298$	15.1826			0.0509482
$299$			48.3798i			0.161805i
$300$		0			0
$301$	81.8615	−	24.1905i	0.271965	−	0.0803672i
$302$	0.180822			0.000598747
$303$		0			0
$304$		−	489.381i		−	1.60981i
$305$	211.475			0.693359
$306$		0			0
$307$			347.793i			1.13287i	0.824105	+	0.566437i	$0.191679\pi$
$307$			347.793i			1.13287i	−0.824105	+	0.566437i	$0.808321\pi$
$308$	424.552	−	125.457i	1.37841	−	0.407329i
$309$		0			0
$310$	2.86731			0.00924938
$311$		−	105.360i		−	0.338778i	−0.985549	−	0.169389i	$-0.945821\pi$
$311$		−	105.360i		−	0.338778i	0.985549	−	0.169389i	$-0.0541794\pi$
$312$		0			0
$313$		−	165.880i		−	0.529967i	−0.964253	−	0.264984i	$-0.914633\pi$
$313$		−	165.880i		−	0.529967i	0.964253	−	0.264984i	$-0.0853666\pi$
$314$		−	28.5216i		−	0.0908333i
$315$		0			0
$316$	5.08500			0.0160918
$317$	96.7933			0.305342			0.152671	−	0.988277i	$-0.451213\pi$
$317$	96.7933			0.305342			0.152671	+	0.988277i	$0.451213\pi$
$318$		0			0
$319$	−231.005			−0.724154
$320$		−	140.376i		−	0.438675i
$321$		0			0
$322$	2.75782	−	0.814951i	0.00856466	−	0.00253090i
$323$	−484.173			−1.49899
$324$		0			0
$325$			66.5219i			0.204683i
$326$	−27.0033			−0.0828323
$327$		0			0
$328$		−	25.2014i		−	0.0768334i
$329$	159.868	+	540.999i	0.485921	+	1.64437i
$330$		0			0
$331$	−193.682			−0.585141			−0.292571	−	0.956244i	$-0.594511\pi$
$331$	−193.682			−0.585141			−0.292571	+	0.956244i	$0.594511\pi$
$332$		−	78.8145i		−	0.237393i
$333$		0			0
$334$			19.2571i			0.0576559i
$335$		−	231.337i		−	0.690559i
$336$		0			0
$337$	−238.742			−0.708433			−0.354216	−	0.935163i	$-0.615252\pi$
$337$	−238.742			−0.708433			−0.354216	+	0.935163i	$0.615252\pi$
$338$	−0.904554			−0.00267619
$339$		0			0
$340$	−139.784			−0.411130
$341$		−	180.033i		−	0.527955i
$342$		0			0
$343$	−223.270	+	260.384i	−0.650932	+	0.759136i
$344$	11.0036			0.0319873
$345$		0			0
$346$		−	30.4526i		−	0.0880132i
$347$	533.787			1.53829			0.769145	−	0.639074i	$-0.220682\pi$
$347$	533.787			1.53829			0.769145	+	0.639074i	$0.220682\pi$
$348$		0			0
$349$			230.498i			0.660454i	0.943902	+	0.330227i	$0.107125\pi$
$349$			230.498i			0.660454i	−0.943902	+	0.330227i	$0.892875\pi$
$350$	3.79198	−	1.12055i	0.0108342	−	0.00320158i
$351$		0			0
$352$	85.6463			0.243313
$353$			12.3883i			0.0350944i	0.999846	+	0.0175472i	$0.00558574\pi$
$353$			12.3883i			0.0350944i	−0.999846	+	0.0175472i	$0.994414\pi$
$354$		0			0
$355$			254.472i			0.716822i
$356$			523.358i			1.47011i
$357$		0			0
$358$	−14.9888			−0.0418680
$359$	442.447			1.23244			0.616222	−	0.787572i	$-0.288662\pi$
$359$	442.447			1.23244			0.616222	+	0.787572i	$0.288662\pi$
$360$		0			0
$361$	−592.673			−1.64175
$362$		−	26.1403i		−	0.0722108i
$363$		0			0
$364$	−105.233	−	356.111i	−0.289101	−	0.978327i
$365$	−45.4915			−0.124634
$366$		0			0
$367$			567.114i			1.54527i	0.634851	+	0.772635i	$0.281062\pi$
$367$			567.114i			1.54527i	−0.634851	+	0.772635i	$0.718938\pi$
$368$	−57.6257			−0.156592
$369$		0			0
$370$			4.39100i			0.0118676i
$371$	−375.361	+	110.921i	−1.01175	+	0.298979i
$372$		0			0
$373$	−106.146			−0.284574			−0.142287	−	0.989825i	$-0.545446\pi$
$373$	−106.146			−0.284574			−0.142287	+	0.989825i	$0.545446\pi$
$374$		−	28.0943i		−	0.0751185i
$375$		0			0
$376$			72.7197i			0.193403i
$377$			193.766i			0.513967i
$378$		0			0
$379$	715.733			1.88848			0.944239	−	0.329262i	$-0.106800\pi$
$379$	715.733			1.88848			0.944239	+	0.329262i	$0.106800\pi$
$380$	−275.332			−0.724558
$381$		0			0
$382$	34.3587			0.0899441
$383$			571.840i			1.49305i	0.665355	+	0.746527i	$0.268280\pi$
$383$			571.840i			1.49305i	−0.665355	+	0.746527i	$0.731720\pi$
$384$		0			0
$385$	−70.3573	−	238.091i	−0.182746	−	0.618419i
$386$	15.6160			0.0404560
$387$		0			0
$388$			49.5358i			0.127670i
$389$	12.6584			0.0325409			0.0162705	−	0.999868i	$-0.494821\pi$
$389$	12.6584			0.0325409			0.0162705	+	0.999868i	$0.494821\pi$
$390$		0			0
$391$			57.0125i			0.145812i
$392$	−37.1132	+	24.0330i	−0.0946766	+	0.0613086i
$393$		0			0
$394$	3.04030			0.00771650
$395$		−	2.85170i		−	0.00721950i
$396$		0			0
$397$		−	29.1232i		−	0.0733582i	−0.999327	−	0.0366791i	$-0.988322\pi$
$397$		−	29.1232i		−	0.0733582i	0.999327	−	0.0366791i	$-0.0116779\pi$
$398$		−	28.4690i		−	0.0715302i
$399$		0			0
$400$	−79.2350			−0.198088
$401$	−144.012			−0.359133			−0.179567	−	0.983746i	$-0.557470\pi$
$401$	−144.012			−0.359133			−0.179567	+	0.983746i	$0.557470\pi$
$402$		0			0
$403$	−151.010			−0.374715
$404$			60.0749i			0.148700i
$405$		0			0
$406$	11.0453	−	3.26395i	0.0272052	−	0.00803929i
$407$	275.702			0.677401
$408$		0			0
$409$			338.914i			0.828641i	0.910131	+	0.414320i	$0.135981\pi$
$409$			338.914i			0.828641i	−0.910131	+	0.414320i	$0.864019\pi$
$410$	−7.05525			−0.0172079
$411$		0			0
$412$			277.457i			0.673440i
$413$	−157.794	−	533.980i	−0.382068	−	1.29293i
$414$		0			0
$415$	−44.1997			−0.106505
$416$		−	71.8396i		−	0.172691i
$417$		0			0
$418$		−	55.3372i		−	0.132386i
$419$			101.585i			0.242446i	0.992625	+	0.121223i	$0.0386816\pi$
$419$			101.585i			0.242446i	−0.992625	+	0.121223i	$0.961318\pi$
$420$		0			0
$421$	−145.700			−0.346081			−0.173041	−	0.984915i	$-0.555359\pi$
$421$	−145.700			−0.346081			−0.173041	+	0.984915i	$0.555359\pi$
$422$	26.6270			0.0630972
$423$		0			0
$424$	−50.4550			−0.118998
$425$			78.3919i			0.184451i
$426$		0			0
$427$	187.610	+	634.880i	0.439369	+	1.48684i
$428$	416.638			0.973453
$429$		0			0
$430$		−	3.08052i		−	0.00716400i
$431$	−497.669			−1.15468			−0.577342	−	0.816502i	$-0.695910\pi$
$431$	−497.669			−1.15468			−0.577342	+	0.816502i	$0.695910\pi$
$432$		0			0
$433$		−	605.000i		−	1.39723i	−0.715499	−	0.698614i	$-0.753801\pi$
$433$		−	605.000i		−	1.39723i	0.715499	−	0.698614i	$-0.246199\pi$
$434$	2.54374	+	8.60811i	0.00586116	+	0.0198344i
$435$		0			0
$436$	76.6096			0.175710
$437$			112.297i			0.256973i
$438$		0			0
$439$			211.605i			0.482015i	0.970523	+	0.241008i	$0.0774779\pi$
$439$			211.605i			0.482015i	−0.970523	+	0.241008i	$0.922522\pi$
$440$		−	32.0036i		−	0.0727355i
$441$		0			0
$442$	−23.5653			−0.0533152
$443$	−794.013			−1.79235			−0.896177	−	0.443697i	$-0.853666\pi$
$443$	−794.013			−1.79235			−0.896177	+	0.443697i	$0.853666\pi$
$444$		0			0
$445$	293.502			0.659556
$446$		−	16.1315i		−	0.0361693i
$447$		0			0
$448$	421.431	−	124.535i	0.940693	−	0.277980i
$449$	486.171			1.08279			0.541393	−	0.840769i	$-0.317897\pi$
$449$	486.171			1.08279			0.541393	+	0.840769i	$0.317897\pi$
$450$		0			0
$451$			442.985i			0.982229i
$452$	831.545			1.83970
$453$		0			0
$454$		−	3.45938i		−	0.00761977i
$455$	−199.709	+	59.0152i	−0.438922	+	0.129704i
$456$		0			0
$457$	114.609			0.250786			0.125393	−	0.992107i	$-0.459981\pi$
$457$	114.609			0.250786			0.125393	+	0.992107i	$0.459981\pi$
$458$		−	23.8015i		−	0.0519684i
$459$		0			0
$460$			32.4210i			0.0704804i
$461$		−	352.184i		−	0.763957i	−0.924171	−	0.381978i	$-0.875243\pi$
$461$		−	352.184i		−	0.763957i	0.924171	−	0.381978i	$-0.124757\pi$
$462$		0			0
$463$	−226.624			−0.489468			−0.244734	−	0.969590i	$-0.578701\pi$
$463$	−226.624			−0.489468			−0.244734	+	0.969590i	$0.578701\pi$
$464$	−230.796			−0.497406
$465$		0			0
$466$	20.6619			0.0443388
$467$		−	405.655i		−	0.868641i	−0.900758	−	0.434320i	$-0.856989\pi$
$467$		−	405.655i		−	0.868641i	0.900758	−	0.434320i	$-0.143011\pi$
$468$		0			0
$469$	694.511	−	205.232i	1.48083	−	0.437594i
$470$	20.3582			0.0433154
$471$		0			0
$472$		−	71.7763i		−	0.152068i
$473$	−193.420			−0.408921
$474$		0			0
$475$			154.408i			0.325069i
$476$	−124.010	−	419.654i	−0.260525	−	0.881627i
$477$		0			0
$478$	−13.8405			−0.0289550
$479$			900.420i			1.87979i	0.341463	+	0.939895i	$0.389078\pi$
$479$			900.420i			1.87979i	−0.341463	+	0.939895i	$0.610922\pi$
$480$		0			0
$481$		−	231.257i		−	0.480784i
$482$			16.9394i			0.0351439i
$483$		0			0
$484$	−520.661			−1.07575
$485$	27.7800			0.0572783
$486$		0			0
$487$	55.4219			0.113803			0.0569014	−	0.998380i	$-0.481878\pi$
$487$	55.4219			0.113803			0.0569014	+	0.998380i	$0.481878\pi$
$488$			85.3390i			0.174875i
$489$		0			0
$490$	6.72815	+	10.3900i	0.0137309	+	0.0212042i
$491$	−616.592			−1.25579			−0.627894	−	0.778299i	$-0.716083\pi$
$491$	−616.592			−1.25579			−0.627894	+	0.778299i	$0.716083\pi$
$492$		0			0
$493$			228.340i			0.463165i
$494$	−46.4165			−0.0939605
$495$		0			0
$496$		−	179.870i		−	0.362641i
$497$	−763.965	+	225.756i	−1.53715	+	0.454237i
$498$		0			0
$499$	624.620			1.25174			0.625872	−	0.779926i	$-0.284743\pi$
$499$	624.620			1.25174			0.625872	+	0.779926i	$0.284743\pi$
$500$			44.5787i			0.0891573i
$501$		0			0
$502$			25.9148i			0.0516232i
$503$			226.444i			0.450187i	0.974337	+	0.225093i	$0.0722687\pi$
$503$			226.444i			0.450187i	−0.974337	+	0.225093i	$0.927731\pi$
$504$		0			0
$505$	33.6904			0.0667137
$506$	−6.51609			−0.0128776
$507$		0			0
$508$	−259.570			−0.510965
$509$		−	468.169i		−	0.919781i	−0.887976	−	0.459891i	$-0.847889\pi$
$509$		−	468.169i		−	0.919781i	0.887976	−	0.459891i	$-0.152111\pi$
$510$		0			0
$511$	−40.3579	−	136.573i	−0.0789783	−	0.267265i
$512$	142.767			0.278842
$513$		0			0
$514$			5.49645i			0.0106935i
$515$	155.600			0.302135
$516$		0			0
$517$		−	1278.25i		−	2.47245i
$518$	−13.1825	+	3.89549i	−0.0254488	+	0.00752025i
$519$		0			0
$520$	−26.8444			−0.0516239
$521$		−	458.100i		−	0.879271i	−0.898176	−	0.439635i	$-0.855108\pi$
$521$		−	458.100i		−	0.879271i	0.898176	−	0.439635i	$-0.144892\pi$
$522$		0			0
$523$			256.863i			0.491135i	0.969380	+	0.245567i	$0.0789742\pi$
$523$			256.863i			0.491135i	−0.969380	+	0.245567i	$0.921026\pi$
$524$		−	639.392i		−	1.22021i
$525$		0			0
$526$	4.25846			0.00809593
$527$	−177.956			−0.337677
$528$		0			0
$529$	−515.777			−0.975003
$530$			14.1251i			0.0266512i
$531$		0			0
$532$	−244.262	−	826.590i	−0.459139	−	1.55374i
$533$	371.573			0.697136
$534$		0			0
$535$		−	233.653i		−	0.436735i
$536$	93.3544			0.174169
$537$		0			0
$538$			32.9572i			0.0612587i
$539$	652.370	−	422.447i	1.21033	−	0.783761i
$540$		0			0
$541$	−57.7912			−0.106823			−0.0534115	−	0.998573i	$-0.517009\pi$
$541$	−57.7912			−0.106823			−0.0534115	+	0.998573i	$0.517009\pi$
$542$		−	11.6227i		−	0.0214442i
$543$		0			0
$544$		−	84.6584i		−	0.155622i
$545$		−	42.9632i		−	0.0788315i
$546$		0			0
$547$	658.275			1.20343			0.601714	−	0.798712i	$-0.294485\pi$
$547$	658.275			1.20343			0.601714	+	0.798712i	$0.294485\pi$
$548$	631.783			1.15289
$549$		0			0
$550$	−8.95958			−0.0162901
$551$			449.761i			0.816263i
$552$		0			0
$553$	8.56126	−	2.52990i	0.0154815	−	0.00457486i
$554$	43.0902			0.0777801
$555$		0			0
$556$		−	970.776i		−	1.74600i
$557$	782.705			1.40521			0.702607	−	0.711578i	$-0.252019\pi$
$557$	782.705			1.40521			0.702607	+	0.711578i	$0.252019\pi$
$558$		0			0
$559$			162.239i			0.290231i
$560$	−70.2937	−	237.876i	−0.125524	−	0.424779i
$561$		0			0
$562$	−1.97538			−0.00351491
$563$		−	632.083i		−	1.12271i	−0.827577	−	0.561353i	$-0.810281\pi$
$563$		−	632.083i		−	1.12271i	0.827577	−	0.561353i	$-0.189719\pi$
$564$		0			0
$565$		−	466.336i		−	0.825373i
$566$			38.7905i			0.0685345i
$567$		0			0
$568$	−102.690			−0.180793
$569$	603.746			1.06107			0.530533	−	0.847665i	$-0.321992\pi$
$569$	603.746			1.06107			0.530533	+	0.847665i	$0.321992\pi$
$570$		0			0
$571$	−638.070			−1.11746			−0.558730	−	0.829349i	$-0.688711\pi$
$571$	−638.070			−1.11746			−0.558730	+	0.829349i	$0.688711\pi$
$572$			841.408i			1.47099i
$573$		0			0
$574$	−6.25909	−	21.1810i	−0.0109043	−	0.0369007i
$575$	18.1819			0.0316207
$576$		0			0
$577$		−	449.363i		−	0.778792i	−0.921070	−	0.389396i	$-0.872684\pi$
$577$		−	449.363i		−	0.778792i	0.921070	−	0.389396i	$-0.127316\pi$
$578$	4.87919			0.00844151
$579$		0			0
$580$			129.849i			0.223878i
$581$	−39.2119	−	132.694i	−0.0674904	−	0.228390i
$582$		0			0
$583$	886.890			1.52125
$584$		−	18.3577i		−	0.0314345i
$585$		0			0
$586$			27.6226i			0.0471375i
$587$		−	133.202i		−	0.226920i	−0.993543	−	0.113460i	$-0.963807\pi$
$587$		−	133.202i		−	0.226920i	0.993543	−	0.113460i	$-0.0361935\pi$
$588$		0			0
$589$	−350.519			−0.595108
$590$	−20.0941			−0.0340579
$591$		0			0
$592$	275.453			0.465292
$593$		−	444.341i		−	0.749310i	−0.927164	−	0.374655i	$-0.877761\pi$
$593$		−	444.341i		−	0.749310i	0.927164	−	0.374655i	$-0.122239\pi$
$594$		0			0
$595$	−235.345	+	69.5457i	−0.395537	+	0.116883i
$596$	−535.846			−0.899070
$597$		0			0
$598$			5.46565i			0.00913989i
$599$	230.917			0.385504			0.192752	−	0.981247i	$-0.438259\pi$
$599$	230.917			0.385504			0.192752	+	0.981247i	$0.438259\pi$
$600$		0			0
$601$		−	147.957i		−	0.246185i	−0.992395	−	0.123092i	$-0.960719\pi$
$601$		−	147.957i		−	0.246185i	0.992395	−	0.123092i	$-0.0392812\pi$
$602$	9.24821	−	2.73289i	0.0153625	−	0.00453969i
$603$		0			0
$604$	−6.38182			−0.0105659
$605$			291.990i			0.482629i
$606$		0			0
$607$			1036.13i			1.70697i	0.521119	+	0.853484i	$0.325515\pi$
$607$			1036.13i			1.70697i	−0.521119	+	0.853484i	$0.674485\pi$
$608$		−	166.751i		−	0.274262i
$609$		0			0
$610$	23.8911			0.0391657
$611$	−1072.19			−1.75481
$612$		0			0
$613$	−175.987			−0.287091			−0.143545	−	0.989644i	$-0.545850\pi$
$613$	−175.987			−0.287091			−0.143545	+	0.989644i	$0.545850\pi$
$614$			39.2915i			0.0639926i
$615$		0			0
$616$	96.0800	−	28.3922i	0.155974	−	0.0460912i
$617$	635.690			1.03029			0.515146	−	0.857103i	$-0.327738\pi$
$617$	635.690			1.03029			0.515146	+	0.857103i	$0.327738\pi$
$618$		0			0
$619$		−	581.258i		−	0.939027i	−0.882925	−	0.469514i	$-0.844429\pi$
$619$		−	581.258i		−	0.939027i	0.882925	−	0.469514i	$-0.155571\pi$
$620$	−101.197			−0.163221
$621$		0			0
$622$		−	11.9029i		−	0.0191365i
$623$	260.382	+	881.141i	0.417948	+	1.41435i
$624$		0			0
$625$	25.0000			0.0400000
$626$		−	18.7401i		−	0.0299362i
$627$		0			0
$628$			1006.63i			1.60291i
$629$		−	272.522i		−	0.433262i
$630$		0			0
$631$	−550.845			−0.872972			−0.436486	−	0.899711i	$-0.643777\pi$
$631$	−550.845			−0.872972			−0.436486	+	0.899711i	$0.643777\pi$
$632$	1.15078			0.00182086
$633$		0			0
$634$	10.9351			0.0172478
$635$			145.569i			0.229242i
$636$		0			0
$637$	−354.346	−	547.204i	−0.556273	−	0.859033i
$638$	−26.0975			−0.0409052
$639$		0			0
$640$		−	64.1551i		−	0.100242i
$641$	64.8667			0.101196			0.0505981	−	0.998719i	$-0.483887\pi$
$641$	64.8667			0.101196			0.0505981	+	0.998719i	$0.483887\pi$
$642$		0			0
$643$		−	812.068i		−	1.26294i	−0.775402	−	0.631468i	$-0.782453\pi$
$643$		−	812.068i		−	1.26294i	0.775402	−	0.631468i	$-0.217547\pi$
$644$	−97.3330	+	28.7624i	−0.151138	+	0.0446621i
$645$		0			0
$646$	−54.6989			−0.0846732
$647$			618.282i			0.955613i	0.878465	+	0.477807i	$0.158568\pi$
$647$			618.282i			0.955613i	−0.878465	+	0.477807i	$0.841432\pi$
$648$		0			0
$649$			1261.67i			1.94402i
$650$			7.51524i			0.0115619i
$651$		0			0
$652$	953.041			1.46172
$653$	694.281			1.06322			0.531609	−	0.846990i	$-0.321588\pi$
$653$	694.281			1.06322			0.531609	+	0.846990i	$0.321588\pi$
$654$		0			0
$655$	−358.575			−0.547443
$656$			442.585i			0.674672i
$657$		0			0
$658$	18.0609	+	61.1187i	0.0274482	+	0.0928855i
$659$	−514.683			−0.781007			−0.390503	−	0.920601i	$-0.627699\pi$
$659$	−514.683			−0.781007			−0.390503	+	0.920601i	$0.627699\pi$
$660$		0			0
$661$			347.998i			0.526472i	0.964731	+	0.263236i	$0.0847899\pi$
$661$			347.998i			0.526472i	−0.964731	+	0.263236i	$0.915210\pi$
$662$	−21.8810			−0.0330528
$663$		0			0
$664$		−	17.8364i		−	0.0268621i
$665$	−463.557	+	136.984i	−0.697079	+	0.205990i
$666$		0			0
$667$	52.9604			0.0794009
$668$		−	679.649i		−	1.01744i
$669$		0			0
$670$		−	26.1350i		−	0.0390075i
$671$		−	1500.07i		−	2.23558i
$672$		0			0
$673$	478.656			0.711227			0.355614	−	0.934633i	$-0.384272\pi$
$673$	478.656			0.711227			0.355614	+	0.934633i	$0.384272\pi$
$674$	−26.9716			−0.0400172
$675$		0			0
$676$	31.9248			0.0472261
$677$			276.403i			0.408277i	0.978942	+	0.204138i	$0.0654393\pi$
$677$			276.403i			0.408277i	−0.978942	+	0.204138i	$0.934561\pi$
$678$		0			0
$679$	24.6451	+	83.3999i	0.0362962	+	0.122828i
$680$	−31.6345			−0.0465213
$681$		0			0
$682$		−	20.3390i		−	0.0298225i
$683$	−311.395			−0.455922			−0.227961	−	0.973670i	$-0.573206\pi$
$683$	−311.395			−0.455922			−0.227961	+	0.973670i	$0.573206\pi$
$684$		0			0
$685$		−	354.308i		−	0.517238i
$686$	−25.2236	+	29.4165i	−0.0367691	+	0.0428812i
$687$		0			0
$688$	−193.245			−0.280879
$689$		−	743.918i		−	1.07971i
$690$		0			0
$691$			569.213i			0.823752i	0.911240	+	0.411876i	$0.135126\pi$
$691$			569.213i			0.823752i	−0.911240	+	0.411876i	$0.864874\pi$
$692$			1074.78i			1.55314i
$693$		0			0
$694$	60.3039			0.0868933
$695$	−544.417			−0.783334
$696$		0			0
$697$	437.875			0.628229
$698$			26.0403i			0.0373070i
$699$		0			0
$700$	−133.832	+	39.5481i	−0.191189	+	0.0564973i
$701$	446.061			0.636321			0.318160	−	0.948037i	$-0.396935\pi$
$701$	446.061			0.636321			0.318160	+	0.948037i	$0.396935\pi$
$702$		0			0
$703$		−	536.785i		−	0.763563i
$704$	−995.743			−1.41441
$705$		0			0
$706$			1.39956i			0.00198238i
$707$	29.8886	+	101.144i	0.0422752	+	0.143061i
$708$		0			0
$709$	−480.480			−0.677686			−0.338843	−	0.940843i	$-0.610036\pi$
$709$	−480.480			−0.677686			−0.338843	+	0.940843i	$0.610036\pi$
$710$			28.7486i			0.0404911i
$711$		0			0
$712$			118.441i			0.166349i
$713$			41.2744i			0.0578883i
$714$		0			0
$715$	471.867			0.659954
$716$	529.005			0.738834
$717$		0			0
$718$	49.9850			0.0696170
$719$			330.338i			0.459441i	0.973257	+	0.229721i	$0.0737813\pi$
$719$			330.338i			0.459441i	−0.973257	+	0.229721i	$0.926219\pi$
$720$		0			0
$721$	138.041	+	467.135i	0.191458	+	0.647899i
$722$	−66.9565			−0.0927375
$723$		0			0
$724$			922.582i			1.27428i
$725$	72.8202			0.100442
$726$		0			0
$727$		−	327.774i		−	0.450858i	−0.974260	−	0.225429i	$-0.927622\pi$
$727$		−	327.774i		−	0.450858i	0.974260	−	0.225429i	$-0.0723783\pi$
$728$	−23.8152	−	80.5913i	−0.0327131	−	0.110702i
$729$		0			0
$730$	−5.13934			−0.00704020
$731$			191.189i			0.261544i
$732$		0			0
$733$		−	124.845i		−	0.170320i	−0.996367	−	0.0851601i	$-0.972860\pi$
$733$		−	124.845i		−	0.170320i	0.996367	−	0.0851601i	$-0.0271402\pi$
$734$			64.0690i			0.0872875i
$735$		0			0
$736$	−19.6353			−0.0266784
$737$	−1640.97			−2.22655
$738$		0			0
$739$	759.049			1.02713			0.513565	−	0.858051i	$-0.328325\pi$
$739$	759.049			1.02713			0.513565	+	0.858051i	$0.328325\pi$
$740$		−	154.973i		−	0.209424i
$741$		0			0
$742$	−42.4059	+	12.5312i	−0.0571508	+	0.0168884i
$743$	−658.165			−0.885820			−0.442910	−	0.896566i	$-0.646054\pi$
$743$	−658.165			−0.885820			−0.442910	+	0.896566i	$0.646054\pi$
$744$		0			0
$745$			300.506i			0.403363i
$746$	−11.9917			−0.0160747
$747$		0			0
$748$			991.546i			1.32560i
$749$	701.464	−	207.286i	0.936534	−	0.276751i
$750$		0			0
$751$	−15.4050			−0.0205127			−0.0102564	−	0.999947i	$-0.503265\pi$
$751$	−15.4050			−0.0205127			−0.0102564	+	0.999947i	$0.503265\pi$
$752$		−	1277.10i		−	1.69827i
$753$		0			0
$754$			21.8904i			0.0290324i
$755$			3.57897i			0.00474035i
$756$		0			0
$757$	−732.280			−0.967345			−0.483673	−	0.875249i	$-0.660697\pi$
$757$	−732.280			−0.967345			−0.483673	+	0.875249i	$0.660697\pi$
$758$	80.8591			0.106674
$759$		0			0
$760$	−62.3102			−0.0819871
$761$			969.037i			1.27337i	0.771123	+	0.636686i	$0.219695\pi$
$761$			969.037i			1.27337i	−0.771123	+	0.636686i	$0.780305\pi$
$762$		0			0
$763$	128.982	−	38.1149i	0.169046	−	0.0499541i
$764$	−1212.64			−1.58722
$765$		0			0
$766$			64.6029i			0.0843380i
$767$	1058.28			1.37977
$768$		0			0
$769$		−	1090.28i		−	1.41778i	−0.705317	−	0.708892i	$-0.749195\pi$
$769$		−	1090.28i		−	1.41778i	0.705317	−	0.708892i	$-0.250805\pi$
$770$	−7.94853	−	26.8981i	−0.0103228	−	0.0349326i
$771$		0			0
$772$	−551.144			−0.713917
$773$			1490.66i			1.92841i	0.265155	+	0.964206i	$0.414577\pi$
$773$			1490.66i			1.92841i	−0.265155	+	0.964206i	$0.585423\pi$
$774$		0			0
$775$			56.7520i			0.0732284i
$776$			11.2104i			0.0144464i
$777$		0			0
$778$	1.43007			0.00183814
$779$	862.481			1.10716
$780$		0			0
$781$	1805.07			2.31123
$782$			6.44092i			0.00823647i
$783$		0			0
$784$	651.781	−	422.066i	0.831353	−	0.538349i
$785$	564.523			0.719138
$786$		0			0
$787$			290.045i			0.368545i	0.982875	+	0.184272i	$0.0589928\pi$
$787$			290.045i			0.368545i	−0.982875	+	0.184272i	$0.941007\pi$
$788$	−107.303			−0.136171
$789$		0			0
$790$		−	0.322168i		−	0.000407807i
$791$	1400.01	−	413.712i	1.76993	−	0.523024i
$792$		0			0
$793$	−1258.25			−1.58670
$794$		−	3.29016i		−	0.00414378i
$795$		0			0
$796$			1004.77i			1.26227i
$797$		−	1089.39i		−	1.36686i	−0.730016	−	0.683430i	$-0.760488\pi$
$797$		−	1089.39i		−	1.36686i	0.730016	−	0.683430i	$-0.239512\pi$
$798$		0			0
$799$	−1263.51			−1.58136
$800$	−26.9985			−0.0337481
$801$		0			0
$802$	−16.2696			−0.0202863
$803$			322.689i			0.401855i
$804$		0			0
$805$	16.1302	+	54.5850i	0.0200375	+	0.0678074i
$806$	−17.0602			−0.0211665
$807$		0			0
$808$			13.5955i			0.0168261i
$809$	−1396.14			−1.72576			−0.862880	−	0.505408i	$-0.831342\pi$
$809$	−1396.14			−1.72576			−0.862880	+	0.505408i	$0.831342\pi$
$810$		0			0
$811$		−	1199.88i		−	1.47950i	−0.672881	−	0.739751i	$-0.734943\pi$
$811$		−	1199.88i		−	1.47950i	0.672881	−	0.739751i	$-0.265057\pi$
$812$	−389.828	+	115.196i	−0.480083	+	0.141867i
$813$		0			0
$814$	31.1471			0.0382643
$815$		−	534.472i		−	0.655793i
$816$		0			0
$817$			376.583i			0.460934i
$818$			38.2884i			0.0468073i
$819$		0			0
$820$	249.004			0.303664
$821$	720.125			0.877131			0.438565	−	0.898699i	$-0.355487\pi$
$821$	720.125			0.877131			0.438565	+	0.898699i	$0.355487\pi$
$822$		0			0
$823$	−136.641			−0.166027			−0.0830137	−	0.996548i	$-0.526455\pi$
$823$	−136.641			−0.166027			−0.0830137	+	0.996548i	$0.526455\pi$
$824$			62.7911i			0.0762028i
$825$		0			0
$826$	−17.8266	−	60.3258i	−0.0215818	−	0.0730337i
$827$	732.193			0.885360			0.442680	−	0.896680i	$-0.354028\pi$
$827$	732.193			0.885360			0.442680	+	0.896680i	$0.354028\pi$
$828$		0			0
$829$			478.689i			0.577430i	0.957415	+	0.288715i	$0.0932280\pi$
$829$			478.689i			0.577430i	−0.957415	+	0.288715i	$0.906772\pi$
$830$	−4.99341			−0.00601615
$831$		0			0
$832$			835.223i			1.00387i
$833$	−417.574	−	644.845i	−0.501290	−	0.774123i
$834$		0			0
$835$	−381.151			−0.456469
$836$			1953.04i			2.33617i
$837$		0			0
$838$			11.4764i			0.0136950i
$839$			1156.58i			1.37852i	0.724516	+	0.689258i	$0.242064\pi$
$839$			1156.58i			1.37852i	−0.724516	+	0.689258i	$0.757936\pi$
$840$		0			0
$841$	−628.889			−0.747787
$842$	−16.4603			−0.0195491
$843$		0			0
$844$	−939.759			−1.11346
$845$		−	17.9036i		−	0.0211877i
$846$		0			0
$847$	−876.601	+	259.040i	−1.03495	+	0.305833i
$848$	886.089			1.04492
$849$		0			0
$850$			8.85623i			0.0104191i
$851$	−63.2077			−0.0742746
$852$		0			0
$853$			338.541i			0.396883i	0.980113	+	0.198441i	$0.0635880\pi$
$853$			338.541i			0.396883i	−0.980113	+	0.198441i	$0.936412\pi$
$854$	21.1951	+	71.7248i	0.0248186	+	0.0839869i
$855$		0			0
$856$	94.2890			0.110151
$857$			884.607i			1.03221i	0.856524	+	0.516107i	$0.172619\pi$
$857$			884.607i			1.03221i	−0.856524	+	0.516107i	$0.827381\pi$
$858$		0			0
$859$			87.7088i			0.102106i	0.998696	+	0.0510528i	$0.0162577\pi$
$859$			87.7088i			0.102106i	−0.998696	+	0.0510528i	$0.983742\pi$
$860$			108.722i			0.126421i
$861$		0			0
$862$	−56.2236			−0.0652246
$863$	1419.95			1.64537			0.822683	−	0.568501i	$-0.192476\pi$
$863$	1419.95			1.64537			0.822683	+	0.568501i	$0.192476\pi$
$864$		0			0
$865$	602.741			0.696811
$866$		−	68.3491i		−	0.0789251i
$867$		0			0
$868$	−89.7775	−	303.810i	−0.103430	−	0.350011i
$869$	−20.2283			−0.0232777
$870$		0			0
$871$			1376.43i			1.58029i
$872$	17.3375			0.0198824
$873$		0			0
$874$			12.6866i			0.0145156i
$875$	22.1789	+	75.0540i	0.0253473	+	0.0857760i
$876$		0			0
$877$	−831.389			−0.947992			−0.473996	−	0.880527i	$-0.657189\pi$
$877$	−831.389			−0.947992			−0.473996	+	0.880527i	$0.657189\pi$
$878$			23.9058i			0.0272276i
$879$		0			0
$880$			562.046i			0.638689i
$881$			782.236i			0.887895i	0.896053	+	0.443948i	$0.146422\pi$
$881$			782.236i			0.887895i	−0.896053	+	0.443948i	$0.853578\pi$
$882$		0			0
$883$	10.4243			0.0118056			0.00590278	−	0.999983i	$-0.498121\pi$
$883$	10.4243			0.0118056			0.00590278	+	0.999983i	$0.498121\pi$
$884$	831.702			0.940840
$885$		0			0
$886$	−89.7026			−0.101245
$887$		−	691.076i		−	0.779116i	−0.921002	−	0.389558i	$-0.872628\pi$
$887$		−	691.076i		−	0.779116i	0.921002	−	0.389558i	$-0.127372\pi$
$888$		0			0
$889$	−437.020	+	129.142i	−0.491586	+	0.145266i
$890$	33.1581			0.0372563
$891$		0			0
$892$			569.337i			0.638271i
$893$	−2488.73			−2.78693
$894$		0			0
$895$		−	296.669i		−	0.331474i
$896$	192.604	−	56.9155i	0.214960	−	0.0635217i
$897$		0			0
$898$	54.9246			0.0611633
$899$			165.308i			0.183880i
$900$		0			0
$901$		−	876.660i		−	0.972985i
$902$			50.0458i			0.0554831i
$903$		0			0
$904$	188.186			0.208171
$905$	517.390			0.571701
$906$		0			0
$907$	704.064			0.776256			0.388128	−	0.921606i	$-0.373122\pi$
$907$	704.064			0.776256			0.388128	+	0.921606i	$0.373122\pi$
$908$			122.093i			0.134464i
$909$		0			0
$910$	−22.5619	+	6.66717i	−0.0247933	+	0.00732657i
$911$	−1359.34			−1.49214			−0.746071	−	0.665867i	$-0.768062\pi$
$911$	−1359.34			−1.49214			−0.746071	+	0.665867i	$0.768062\pi$
$912$		0			0
$913$			313.526i			0.343402i
$914$	12.9479			0.0141662
$915$		0			0
$916$			840.038i			0.917072i
$917$	−318.111	−	1076.50i	−0.346904	−	1.17394i
$918$		0			0
$919$	1475.83			1.60591			0.802953	−	0.596043i	$-0.203261\pi$
$919$	1475.83			1.60591			0.802953	+	0.596043i	$0.203261\pi$
$920$			7.33717i			0.00797519i
$921$		0			0
$922$		−	39.7876i		−	0.0431536i
$923$		−	1514.08i		−	1.64039i
$924$		0			0
$925$	−86.9101			−0.0939569
$926$	−25.6025			−0.0276485
$927$		0			0
$928$	−78.6413			−0.0847428
$929$			795.306i			0.856088i	0.903758	+	0.428044i	$0.140797\pi$
$929$			795.306i			0.856088i	−0.903758	+	0.428044i	$0.859203\pi$
$930$		0			0
$931$	−822.493	−	1270.15i	−0.883452	−	1.36428i
$932$	−729.229			−0.782435
$933$		0			0
$934$		−	45.8284i		−	0.0490668i
$935$	556.065			0.594722
$936$		0			0
$937$			199.954i			0.213398i	0.994291	+	0.106699i	$0.0340281\pi$
$937$			199.954i			0.213398i	−0.994291	+	0.106699i	$0.965972\pi$
$938$	78.4616	−	23.1858i	0.0836477	−	0.0247183i
$939$		0			0
$940$	−718.513			−0.764375
$941$		−	1488.22i		−	1.58153i	−0.612119	−	0.790765i	$-0.709683\pi$
$941$		−	1488.22i		−	1.58153i	0.612119	−	0.790765i	$-0.290317\pi$
$942$		0			0
$943$		−	101.559i		−	0.107698i
$944$			1260.53i			1.33531i
$945$		0			0
$946$	−21.8514			−0.0230987
$947$	−1232.27			−1.30124			−0.650620	−	0.759404i	$-0.725491\pi$
$947$	−1232.27			−1.30124			−0.650620	+	0.759404i	$0.725491\pi$
$948$		0			0
$949$	270.670			0.285216
$950$			17.4441i			0.0183622i
$951$		0			0
$952$	−28.0646	−	94.9717i	−0.0294797	−	0.0997601i
$953$	2.73670			0.00287167			0.00143584	−	0.999999i	$-0.499543\pi$
$953$	2.73670			0.00287167			0.00143584	+	0.999999i	$0.499543\pi$
$954$		0			0
$955$			680.054i			0.712098i
$956$	488.479			0.510961
$957$		0			0
$958$			101.724i			0.106184i
$959$	1063.69	−	314.326i	1.10916	−	0.327764i
$960$		0			0
$961$	832.168			0.865940
$962$		−	26.1260i		−	0.0271580i
$963$		0			0
$964$		−	597.849i		−	0.620175i
$965$			309.085i			0.320295i
$966$		0			0
$967$	831.688			0.860070			0.430035	−	0.902812i	$-0.358501\pi$
$967$	831.688			0.860070			0.430035	+	0.902812i	$0.358501\pi$
$968$	−117.831			−0.121726
$969$		0			0
$970$	3.13841			0.00323548
$971$		−	1800.97i		−	1.85476i	−0.374118	−	0.927381i	$-0.622055\pi$
$971$		−	1800.97i		−	1.85476i	0.374118	−	0.927381i	$-0.377945\pi$
$972$		0			0
$973$	−482.982	−	1634.43i	−0.496384	−	1.67978i
$974$	6.26123			0.00642837
$975$		0			0
$976$		−	1498.72i		−	1.53557i
$977$	681.141			0.697176			0.348588	−	0.937276i	$-0.386661\pi$
$977$	681.141			0.697176			0.348588	+	0.937276i	$0.386661\pi$
$978$		0			0
$979$		−	2081.93i		−	2.12659i
$980$	−237.460	−	366.700i	−0.242306	−	0.374184i
$981$		0			0
$982$	−69.6587			−0.0709356
$983$			1188.81i			1.20937i	0.796465	+	0.604684i	$0.206701\pi$
$983$			1188.81i			1.20937i	−0.796465	+	0.604684i	$0.793299\pi$
$984$		0			0
$985$			60.1761i			0.0610924i
$986$			25.7965i			0.0261628i
$987$		0			0
$988$	1638.20			1.65810
$989$	44.3435			0.0448367
$990$		0			0
$991$	−325.271			−0.328225			−0.164113	−	0.986442i	$-0.552476\pi$
$991$	−325.271			−0.328225			−0.164113	+	0.986442i	$0.552476\pi$
$992$		−	61.2887i		−	0.0617829i
$993$		0			0
$994$	−86.3080	+	25.5045i	−0.0868290	+	0.0256584i
$995$	563.482			0.566313
$996$		0			0
$997$		−	17.2566i		−	0.0173085i	−0.999963	−	0.00865426i	$-0.997245\pi$
$997$		−	17.2566i		−	0.0173085i	0.999963	−	0.00865426i	$-0.00275477\pi$
$998$	70.5657			0.0707071
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.h.d.181.6		12
3.2	odd	2		105.3.h.a.76.7	✓	12
7.6	odd	2	inner	315.3.h.d.181.5		12
12.11	even	2		1680.3.s.c.1441.9		12
15.2	even	4		525.3.e.c.349.5		24
15.8	even	4		525.3.e.c.349.18		24
15.14	odd	2		525.3.h.d.76.6		12
21.20	even	2		105.3.h.a.76.8	yes	12
84.83	odd	2		1680.3.s.c.1441.6		12
105.62	odd	4		525.3.e.c.349.17		24
105.83	odd	4		525.3.e.c.349.6		24
105.104	even	2		525.3.h.d.76.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.7	✓	12	3.2	odd	2
105.3.h.a.76.8	yes	12	21.20	even	2
315.3.h.d.181.5		12	7.6	odd	2	inner
315.3.h.d.181.6		12	1.1	even	1	trivial
525.3.e.c.349.5		24	15.2	even	4
525.3.e.c.349.6		24	105.83	odd	4
525.3.e.c.349.17		24	105.62	odd	4
525.3.e.c.349.18		24	15.8	even	4
525.3.h.d.76.5		12	105.104	even	2
525.3.h.d.76.6		12	15.14	odd	2
1680.3.s.c.1441.6		12	84.83	odd	2
1680.3.s.c.1441.9		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.112974 q^{2} -3.98724 q^{4} +2.23607i q^{5} +(-6.71303 + 1.98374i) q^{7} -0.902349 q^{8} +O(q^{10})\)	\(q+0.112974 q^{2} -3.98724 q^{4} +2.23607i q^{5} +(-6.71303 + 1.98374i) q^{7} -0.902349 q^{8} +0.252617i q^{10} +15.8613 q^{11} -13.3044i q^{13} +(-0.758397 + 0.224110i) q^{14} +15.8470 q^{16} -15.6784i q^{17} -30.8816i q^{19} -8.91573i q^{20} +1.79192 q^{22} -3.63638 q^{23} -5.00000 q^{25} -1.50305i q^{26} +(26.7664 - 7.90963i) q^{28} -14.5640 q^{29} -11.3504i q^{31} +5.39969 q^{32} -1.77125i q^{34} +(-4.43577 - 15.0108i) q^{35} +17.3820 q^{37} -3.48881i q^{38} -2.01771i q^{40} +27.9286i q^{41} -12.1944 q^{43} -63.2429 q^{44} -0.410816 q^{46} -80.5893i q^{47} +(41.1296 - 26.6338i) q^{49} -0.564869 q^{50} +53.0477i q^{52} +55.9152 q^{53} +35.4670i q^{55} +(6.05750 - 1.79002i) q^{56} -1.64536 q^{58} +79.5439i q^{59} -94.5743i q^{61} -1.28230i q^{62} -62.7780 q^{64} +29.7495 q^{65} -103.457 q^{67} +62.5134i q^{68} +(-0.501126 - 1.69583i) q^{70} +113.803 q^{71} +20.3444i q^{73} +1.96371 q^{74} +123.132i q^{76} +(-106.478 + 31.4647i) q^{77} -1.27532 q^{79} +35.4350i q^{80} +3.15520i q^{82} +19.7667i q^{83} +35.0579 q^{85} -1.37765 q^{86} -14.3125 q^{88} -131.258i q^{89} +(26.3924 + 89.3128i) q^{91} +14.4991 q^{92} -9.10448i q^{94} +69.0533 q^{95} -12.4236i q^{97} +(4.64657 - 3.00892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

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