LMFDB - Embedded newform 20.10.c.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,10,Mod(9,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("20.9");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	20.c (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:	$10.3007167233$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 1095x^{2} - 80251x + 2230844 $ x^4 - x^3 + 1095x^2 - 80251x + 2230844
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.2
Root			$24.2825 + 17.1975i$ of defining polynomial
Character	$\chi$	$=$	20.9
Dual form			20.10.c.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-92.1183i q^{3} +(-796.301 + 1148.49i) q^{5} +2204.86i q^{7} +11197.2 q^{9} +O(q^{10})$	\(q-92.1183i q^{3} +(-796.301 + 1148.49i) q^{5} +2204.86i q^{7} +11197.2 q^{9} +41287.7 q^{11} +167407. i q^{13} +(105797. + 73353.9i) q^{15} +312002. i q^{17} +439115. q^{19} +203108. q^{21} +1.29304e6i q^{23} +(-684934. - 1.82909e6i) q^{25} -2.84463e6i q^{27} -2.74791e6 q^{29} -3.48242e6 q^{31} -3.80335e6i q^{33} +(-2.53226e6 - 1.75573e6i) q^{35} -5.59362e6i q^{37} +1.54212e7 q^{39} -2.77590e6 q^{41} +1.61655e7i q^{43} +(-8.91636e6 + 1.28599e7i) q^{45} +5.28874e7i q^{47} +3.54922e7 q^{49} +2.87411e7 q^{51} -5.94170e7i q^{53} +(-3.28774e7 + 4.74185e7i) q^{55} -4.04506e7i q^{57} +1.32524e8 q^{59} -1.89215e8 q^{61} +2.46883e7i q^{63} +(-1.92265e8 - 1.33306e8i) q^{65} -1.32924e8i q^{67} +1.19113e8 q^{69} -4.51789e7 q^{71} -1.44326e8i q^{73} +(-1.68492e8 + 6.30949e7i) q^{75} +9.10336e7i q^{77} +5.87235e8 q^{79} -4.16480e7 q^{81} +7.24836e8i q^{83} +(-3.58331e8 - 2.48447e8i) q^{85} +2.53132e8i q^{87} +1.07503e9 q^{89} -3.69109e8 q^{91} +3.20795e8i q^{93} +(-3.49668e8 + 5.04320e8i) q^{95} +1.05379e8i q^{97} +4.62307e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 660 q^{5} - 9044 q^{9}+O(q^{10}) $ 4 * q + 660 * q^5 - 9044 * q^9	$ 4 q + 660 q^{5} - 9044 q^{9} - 34800 q^{11} - 99760 q^{15} - 227664 q^{19} - 287296 q^{21} - 201900 q^{25} + 6265656 q^{29} + 374464 q^{31} - 8114160 q^{35} + 23386656 q^{39} - 17648136 q^{41} - 53241860 q^{45} + 144898812 q^{49} - 108703552 q^{51} - 197954800 q^{55} + 438995472 q^{59} - 103044472 q^{61} - 417315840 q^{65} + 1186715008 q^{69} - 504081888 q^{71} - 1038341600 q^{75} + 1794955008 q^{79} - 982752124 q^{81} - 1447443520 q^{85} + 2381318184 q^{89} - 811245024 q^{91} - 1944906960 q^{95} + 2769662000 q^{99}+O(q^{100}) $ 4 * q + 660 * q^5 - 9044 * q^9 - 34800 * q^11 - 99760 * q^15 - 227664 * q^19 - 287296 * q^21 - 201900 * q^25 + 6265656 * q^29 + 374464 * q^31 - 8114160 * q^35 + 23386656 * q^39 - 17648136 * q^41 - 53241860 * q^45 + 144898812 * q^49 - 108703552 * q^51 - 197954800 * q^55 + 438995472 * q^59 - 103044472 * q^61 - 417315840 * q^65 + 1186715008 * q^69 - 504081888 * q^71 - 1038341600 * q^75 + 1794955008 * q^79 - 982752124 * q^81 - 1447443520 * q^85 + 2381318184 * q^89 - 811245024 * q^91 - 1944906960 * q^95 + 2769662000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	92.1183i		−	0.656599i	−0.944574	−	0.328300i	$-0.893524\pi$
$3$		−	92.1183i		−	0.656599i	0.944574	−	0.328300i	$-0.106476\pi$
$4$		0			0
$5$	−796.301	+	1148.49i	−0.569787	+	0.821793i
$5$	−796.301	+	1148.49i	−0.569787	+	0.821793i
$6$		0			0
$7$			2204.86i			0.347088i	0.984826	+	0.173544i	$0.0555220\pi$
$7$			2204.86i			0.347088i	−0.984826	+	0.173544i	$0.944478\pi$
$8$		0			0
$9$	11197.2			0.568878
$10$		0			0
$11$	41287.7			0.850263			0.425131	−	0.905132i	$-0.360228\pi$
$11$	41287.7			0.850263			0.425131	+	0.905132i	$0.360228\pi$
$12$		0			0
$13$			167407.i			1.62565i	0.582506	+	0.812826i	$0.302072\pi$
$13$			167407.i			1.62565i	−0.582506	+	0.812826i	$0.697928\pi$
$14$		0			0
$15$	105797.	+	73353.9i	0.539588	+	0.374122i
$16$		0			0
$17$			312002.i			0.906018i	0.891506	+	0.453009i	$0.149650\pi$
$17$			312002.i			0.906018i	−0.891506	+	0.453009i	$0.850350\pi$
$18$		0			0
$19$	439115.			0.773014			0.386507	−	0.922286i	$-0.373681\pi$
$19$	439115.			0.773014			0.386507	+	0.922286i	$0.373681\pi$
$20$		0			0
$21$	203108.			0.227898
$22$		0			0
$23$			1.29304e6i			0.963469i	0.876317	+	0.481735i	$0.159993\pi$
$23$			1.29304e6i			0.963469i	−0.876317	+	0.481735i	$0.840007\pi$
$24$		0			0
$25$	−684934.	−	1.82909e6i	−0.350686	−	0.936493i
$26$		0			0
$27$		−	2.84463e6i		−	1.03012i
$28$		0			0
$29$	−2.74791e6			−0.721458			−0.360729	−	0.932671i	$-0.617472\pi$
$29$	−2.74791e6			−0.721458			−0.360729	+	0.932671i	$0.617472\pi$
$30$		0			0
$31$	−3.48242e6			−0.677258			−0.338629	−	0.940920i	$-0.609963\pi$
$31$	−3.48242e6			−0.677258			−0.338629	+	0.940920i	$0.609963\pi$
$32$		0			0
$33$		−	3.80335e6i		−	0.558282i
$34$		0			0
$35$	−2.53226e6	−	1.75573e6i	−0.285235	−	0.197766i
$36$		0			0
$37$		−	5.59362e6i		−	0.490665i	−0.969439	−	0.245332i	$-0.921103\pi$
$37$		−	5.59362e6i		−	0.490665i	0.969439	−	0.245332i	$-0.0788971\pi$
$38$		0			0
$39$	1.54212e7			1.06740
$40$		0			0
$41$	−2.77590e6			−0.153418			−0.0767090	−	0.997054i	$-0.524441\pi$
$41$	−2.77590e6			−0.153418			−0.0767090	+	0.997054i	$0.524441\pi$
$42$		0			0
$43$			1.61655e7i			0.721075i	0.932745	+	0.360538i	$0.117407\pi$
$43$			1.61655e7i			0.721075i	−0.932745	+	0.360538i	$0.882593\pi$
$44$		0			0
$45$	−8.91636e6	+	1.28599e7i	−0.324139	+	0.467499i
$46$		0			0
$47$			5.28874e7i			1.58093i	0.612510	+	0.790463i	$0.290160\pi$
$47$			5.28874e7i			1.58093i	−0.612510	+	0.790463i	$0.709840\pi$
$48$		0			0
$49$	3.54922e7			0.879530
$50$		0			0
$51$	2.87411e7			0.594891
$52$		0			0
$53$		−	5.94170e7i		−	1.03435i	−0.855879	−	0.517177i	$-0.826983\pi$
$53$		−	5.94170e7i		−	1.03435i	0.855879	−	0.517177i	$-0.173017\pi$
$54$		0			0
$55$	−3.28774e7	+	4.74185e7i	−0.484469	+	0.698740i
$56$		0			0
$57$		−	4.04506e7i		−	0.507560i
$58$		0			0
$59$	1.32524e8			1.42384			0.711919	−	0.702262i	$-0.247826\pi$
$59$	1.32524e8			1.42384			0.711919	+	0.702262i	$0.247826\pi$
$60$		0			0
$61$	−1.89215e8			−1.74973			−0.874866	−	0.484366i	$-0.839050\pi$
$61$	−1.89215e8			−1.74973			−0.874866	+	0.484366i	$0.839050\pi$
$62$		0			0
$63$			2.46883e7i			0.197451i
$64$		0			0
$65$	−1.92265e8	−	1.33306e8i	−1.33595	−	0.926275i
$66$		0			0
$67$		−	1.32924e8i		−	0.805876i	−0.915227	−	0.402938i	$-0.867989\pi$
$67$		−	1.32924e8i		−	0.805876i	0.915227	−	0.402938i	$-0.132011\pi$
$68$		0			0
$69$	1.19113e8			0.632613
$70$		0			0
$71$	−4.51789e7			−0.210995			−0.105498	−	0.994420i	$-0.533644\pi$
$71$	−4.51789e7			−0.210995			−0.105498	+	0.994420i	$0.533644\pi$
$72$		0			0
$73$		−	1.44326e8i		−	0.594830i	−0.954748	−	0.297415i	$-0.903875\pi$
$73$		−	1.44326e8i		−	0.594830i	0.954748	−	0.297415i	$-0.0961246\pi$
$74$		0			0
$75$	−1.68492e8	+	6.30949e7i	−0.614901	+	0.230260i
$76$		0			0
$77$			9.10336e7i			0.295116i
$78$		0			0
$79$	5.87235e8			1.69625			0.848126	−	0.529795i	$-0.177731\pi$
$79$	5.87235e8			1.69625			0.848126	+	0.529795i	$0.177731\pi$
$80$		0			0
$81$	−4.16480e7			−0.107501
$82$		0			0
$83$			7.24836e8i			1.67644i	0.545330	+	0.838221i	$0.316404\pi$
$83$			7.24836e8i			1.67644i	−0.545330	+	0.838221i	$0.683596\pi$
$84$		0			0
$85$	−3.58331e8	−	2.48447e8i	−0.744559	−	0.516237i
$86$		0			0
$87$			2.53132e8i			0.473708i
$88$		0			0
$89$	1.07503e9			1.81622			0.908108	−	0.418737i	$-0.137527\pi$
$89$	1.07503e9			1.81622			0.908108	+	0.418737i	$0.137527\pi$
$90$		0			0
$91$	−3.69109e8			−0.564245
$92$		0			0
$93$			3.20795e8i			0.444687i
$94$		0			0
$95$	−3.49668e8	+	5.04320e8i	−0.440453	+	0.635257i
$96$		0			0
$97$			1.05379e8i			0.120860i	0.998172	+	0.0604300i	$0.0192472\pi$
$97$			1.05379e8i			0.120860i	−0.998172	+	0.0604300i	$0.980753\pi$
$98$		0			0
$99$	4.62307e8			0.483695
$100$		0			0
$101$	−1.00614e8			−0.0962081			−0.0481041	−	0.998842i	$-0.515318\pi$
$101$	−1.00614e8			−0.0962081			−0.0481041	+	0.998842i	$0.515318\pi$
$102$		0			0
$103$		−	2.05718e9i		−	1.80097i	−0.434891	−	0.900483i	$-0.643213\pi$
$103$		−	2.05718e9i		−	1.80097i	0.434891	−	0.900483i	$-0.356787\pi$
$104$		0			0
$105$	−1.61735e8	+	2.33268e8i	−0.129853	+	0.187285i
$106$		0			0
$107$		−	1.32892e9i		−	0.980102i	−0.871694	−	0.490051i	$-0.836978\pi$
$107$		−	1.32892e9i		−	0.980102i	0.871694	−	0.490051i	$-0.163022\pi$
$108$		0			0
$109$	−8.61297e8			−0.584431			−0.292216	−	0.956352i	$-0.594392\pi$
$109$	−8.61297e8			−0.584431			−0.292216	+	0.956352i	$0.594392\pi$
$110$		0			0
$111$	−5.15274e8			−0.322170
$112$		0			0
$113$		−	4.84322e8i		−	0.279435i	−0.990191	−	0.139718i	$-0.955380\pi$
$113$		−	4.84322e8i		−	0.279435i	0.990191	−	0.139718i	$-0.0446195\pi$
$114$		0			0
$115$	−1.48505e9	−	1.02965e9i	−0.791772	−	0.548972i
$116$		0			0
$117$			1.87449e9i			0.924797i
$118$		0			0
$119$	−6.87921e8			−0.314469
$120$		0			0
$121$	−6.53277e8			−0.277053
$122$		0			0
$123$			2.55711e8i			0.100734i
$124$		0			0
$125$	2.64610e9	+	6.69865e8i	0.969419	+	0.245410i
$126$		0			0
$127$		−	2.58163e9i		−	0.880597i	−0.897852	−	0.440298i	$-0.854873\pi$
$127$		−	2.58163e9i		−	0.880597i	0.897852	−	0.440298i	$-0.145127\pi$
$128$		0			0
$129$	1.48914e9			0.473458
$130$		0			0
$131$	2.49277e9			0.739538			0.369769	−	0.929124i	$-0.379437\pi$
$131$	2.49277e9			0.739538			0.369769	+	0.929124i	$0.379437\pi$
$132$		0			0
$133$			9.68189e8i			0.268304i
$134$		0			0
$135$	3.26703e9	+	2.26519e9i	0.846548	+	0.586951i
$136$		0			0
$137$			6.01618e9i			1.45908i	0.683940	+	0.729538i	$0.260265\pi$
$137$			6.01618e9i			1.45908i	−0.683940	+	0.729538i	$0.739735\pi$
$138$		0			0
$139$	−7.97541e9			−1.81212			−0.906059	−	0.423152i	$-0.860924\pi$
$139$	−7.97541e9			−1.81212			−0.906059	+	0.423152i	$0.860924\pi$
$140$		0			0
$141$	4.87190e9			1.03803
$142$		0			0
$143$			6.91183e9i			1.38223i
$144$		0			0
$145$	2.18816e9	−	3.15594e9i	0.411077	−	0.592889i
$146$		0			0
$147$		−	3.26948e9i		−	0.577498i
$148$		0			0
$149$	−3.92868e9			−0.652993			−0.326497	−	0.945198i	$-0.605868\pi$
$149$	−3.92868e9			−0.652993			−0.326497	+	0.945198i	$0.605868\pi$
$150$		0			0
$151$	7.85990e8			0.123033			0.0615164	−	0.998106i	$-0.480406\pi$
$151$	7.85990e8			0.123033			0.0615164	+	0.998106i	$0.480406\pi$
$152$		0			0
$153$			3.49355e9i			0.515413i
$154$		0			0
$155$	2.77306e9	−	3.99953e9i	0.385893	−	0.556566i
$156$		0			0
$157$		−	9.51004e9i		−	1.24921i	−0.780943	−	0.624603i	$-0.785261\pi$
$157$		−	9.51004e9i		−	1.24921i	0.780943	−	0.624603i	$-0.214739\pi$
$158$		0			0
$159$	−5.47339e9			−0.679156
$160$		0			0
$161$	−2.85098e9			−0.334409
$162$		0			0
$163$		−	1.58139e10i		−	1.75467i	−0.479876	−	0.877336i	$-0.659318\pi$
$163$		−	1.58139e10i		−	1.75467i	0.479876	−	0.877336i	$-0.340682\pi$
$164$		0			0
$165$	4.36811e9	+	3.02861e9i	0.458792	+	0.318102i
$166$		0			0
$167$			1.16732e10i			1.16136i	0.814132	+	0.580680i	$0.197213\pi$
$167$			1.16732e10i			1.16136i	−0.814132	+	0.580680i	$0.802787\pi$
$168$		0			0
$169$	−1.74205e10			−1.64275
$170$		0			0
$171$	4.91687e9			0.439750
$172$		0			0
$173$		−	9.86567e9i		−	0.837374i	−0.908131	−	0.418687i	$-0.862491\pi$
$173$		−	9.86567e9i		−	0.837374i	0.908131	−	0.418687i	$-0.137509\pi$
$174$		0			0
$175$	4.03289e9	−	1.51018e9i	0.325046	−	0.121719i
$176$		0			0
$177$		−	1.22079e10i		−	0.934891i
$178$		0			0
$179$	−3.89579e9			−0.283633			−0.141817	−	0.989893i	$-0.545294\pi$
$179$	−3.89579e9			−0.283633			−0.141817	+	0.989893i	$0.545294\pi$
$180$		0			0
$181$	−1.02500e10			−0.709855			−0.354928	−	0.934894i	$-0.615494\pi$
$181$	−1.02500e10			−0.709855			−0.354928	+	0.934894i	$0.615494\pi$
$182$		0			0
$183$			1.74302e10i			1.14887i
$184$		0			0
$185$	6.42421e9	+	4.45420e9i	0.403225	+	0.279574i
$186$		0			0
$187$			1.28818e10i			0.770354i
$188$		0			0
$189$	6.27202e9			0.357544
$190$		0			0
$191$	3.05439e10			1.66063			0.830317	−	0.557292i	$-0.188160\pi$
$191$	3.05439e10			1.66063			0.830317	+	0.557292i	$0.188160\pi$
$192$		0			0
$193$		−	1.34781e9i		−	0.0699234i	−0.999389	−	0.0349617i	$-0.988869\pi$
$193$		−	1.34781e9i		−	0.0699234i	0.999389	−	0.0349617i	$-0.0111309\pi$
$194$		0			0
$195$	−1.22799e10	+	1.77111e10i	−0.608192	+	0.877183i
$196$		0			0
$197$			5.92326e9i			0.280196i	0.990138	+	0.140098i	$0.0447418\pi$
$197$			5.92326e9i			0.280196i	−0.990138	+	0.140098i	$0.955258\pi$
$198$		0			0
$199$	2.69269e10			1.21716			0.608580	−	0.793493i	$-0.291739\pi$
$199$	2.69269e10			1.21716			0.608580	+	0.793493i	$0.291739\pi$
$200$		0			0
$201$	−1.22448e10			−0.529137
$202$		0			0
$203$		−	6.05875e9i		−	0.250410i
$204$		0			0
$205$	2.21045e9	−	3.18809e9i	0.0874156	−	0.126078i
$206$		0			0
$207$			1.44785e10i			0.548096i
$208$		0			0
$209$	1.81300e10			0.657265
$210$		0			0
$211$	−4.86262e9			−0.168888			−0.0844442	−	0.996428i	$-0.526911\pi$
$211$	−4.86262e9			−0.168888			−0.0844442	+	0.996428i	$0.526911\pi$
$212$		0			0
$213$			4.16180e9i			0.138539i
$214$		0			0
$215$	−1.85659e10	−	1.28726e10i	−0.592574	−	0.410859i
$216$		0			0
$217$		−	7.67826e9i		−	0.235068i
$218$		0			0
$219$	−1.32951e10			−0.390565
$220$		0			0
$221$	−5.22312e10			−1.47287
$222$		0			0
$223$			2.13847e10i			0.579072i	0.957167	+	0.289536i	$0.0935009\pi$
$223$			2.13847e10i			0.579072i	−0.957167	+	0.289536i	$0.906499\pi$
$224$		0			0
$225$	−7.66935e9	−	2.04807e10i	−0.199497	−	0.532750i
$226$		0			0
$227$		−	4.41449e10i		−	1.10348i	−0.834016	−	0.551740i	$-0.813964\pi$
$227$		−	4.41449e10i		−	1.10348i	0.834016	−	0.551740i	$-0.186036\pi$
$228$		0			0
$229$	5.15905e10			1.23968			0.619841	−	0.784727i	$-0.287197\pi$
$229$	5.15905e10			1.23968			0.619841	+	0.784727i	$0.287197\pi$
$230$		0			0
$231$	8.38586e9			0.193773
$232$		0			0
$233$		−	1.97876e9i		−	0.0439838i	−0.999758	−	0.0219919i	$-0.992999\pi$
$233$		−	1.97876e9i		−	0.0439838i	0.999758	−	0.0219919i	$-0.00700080\pi$
$234$		0			0
$235$	−6.07406e10	−	4.21143e10i	−1.29919	−	0.900791i
$236$		0			0
$237$		−	5.40951e10i		−	1.11376i
$238$		0			0
$239$	2.99990e10			0.594724			0.297362	−	0.954765i	$-0.403893\pi$
$239$	2.99990e10			0.594724			0.297362	+	0.954765i	$0.403893\pi$
$240$		0			0
$241$	−8.14919e9			−0.155610			−0.0778050	−	0.996969i	$-0.524791\pi$
$241$	−8.14919e9			−0.155610			−0.0778050	+	0.996969i	$0.524791\pi$
$242$		0			0
$243$		−	5.21544e10i		−	0.959539i
$244$		0			0
$245$	−2.82625e10	+	4.07624e10i	−0.501144	+	0.722791i
$246$		0			0
$247$			7.35109e10i			1.25665i
$248$		0			0
$249$	6.67707e10			1.10075
$250$		0			0
$251$	−3.27674e10			−0.521087			−0.260543	−	0.965462i	$-0.583902\pi$
$251$	−3.27674e10			−0.521087			−0.260543	+	0.965462i	$0.583902\pi$
$252$		0			0
$253$			5.33867e10i			0.819202i
$254$		0			0
$255$	−2.28866e10	+	3.30088e10i	−0.338961	+	0.488877i
$256$		0			0
$257$			5.59032e10i			0.799351i	0.916657	+	0.399675i	$0.130877\pi$
$257$			5.59032e10i			0.799351i	−0.916657	+	0.399675i	$0.869123\pi$
$258$		0			0
$259$	1.23332e10			0.170304
$260$		0			0
$261$	−3.07689e10			−0.410421
$262$		0			0
$263$			1.19282e10i			0.153736i	0.997041	+	0.0768680i	$0.0244920\pi$
$263$			1.19282e10i			0.153736i	−0.997041	+	0.0768680i	$0.975508\pi$
$264$		0			0
$265$	6.82398e10	+	4.73138e10i	0.850024	+	0.589361i
$266$		0			0
$267$		−	9.90303e10i		−	1.19253i
$268$		0			0
$269$	6.70842e10			0.781151			0.390575	−	0.920571i	$-0.372276\pi$
$269$	6.70842e10			0.781151			0.390575	+	0.920571i	$0.372276\pi$
$270$		0			0
$271$	1.52109e11			1.71315			0.856573	−	0.516027i	$-0.172589\pi$
$271$	1.52109e11			1.71315			0.856573	+	0.516027i	$0.172589\pi$
$272$		0			0
$273$			3.40017e10i			0.370483i
$274$		0			0
$275$	−2.82793e10	−	7.55188e10i	−0.298175	−	0.796265i
$276$		0			0
$277$			1.85013e11i			1.88818i	0.329694	+	0.944088i	$0.393054\pi$
$277$			1.85013e11i			1.88818i	−0.329694	+	0.944088i	$0.606946\pi$
$278$		0			0
$279$	−3.89935e10			−0.385277
$280$		0			0
$281$	−1.06998e11			−1.02375			−0.511877	−	0.859059i	$-0.671050\pi$
$281$	−1.06998e11			−1.02375			−0.511877	+	0.859059i	$0.671050\pi$
$282$		0			0
$283$		−	6.29396e10i		−	0.583290i	−0.956527	−	0.291645i	$-0.905797\pi$
$283$		−	6.29396e10i		−	0.583290i	0.956527	−	0.291645i	$-0.0942026\pi$
$284$		0			0
$285$	4.64571e10	+	3.22108e10i	0.417109	+	0.289201i
$286$		0			0
$287$		−	6.12047e9i		−	0.0532496i
$288$		0			0
$289$	2.12427e10			0.179131
$290$		0			0
$291$	9.70736e9			0.0793565
$292$		0			0
$293$		−	1.84129e11i		−	1.45954i	−0.683691	−	0.729772i	$-0.739626\pi$
$293$		−	1.84129e11i		−	1.45954i	0.683691	−	0.729772i	$-0.260374\pi$
$294$		0			0
$295$	−1.05529e11	+	1.52203e11i	−0.811284	+	1.17010i
$296$		0			0
$297$		−	1.17448e11i		−	0.875876i
$298$		0			0
$299$	−2.16464e11			−1.56627
$300$		0			0
$301$	−3.56427e10			−0.250277
$302$		0			0
$303$			9.26838e9i			0.0631702i
$304$		0			0
$305$	1.50672e11	−	2.17312e11i	0.996974	−	1.43792i
$306$		0			0
$307$		−	1.53977e11i		−	0.989309i	−0.869090	−	0.494655i	$-0.835295\pi$
$307$		−	1.53977e11i		−	0.989309i	0.869090	−	0.494655i	$-0.164705\pi$
$308$		0			0
$309$	−1.89504e11			−1.18251
$310$		0			0
$311$	1.62695e11			0.986169			0.493084	−	0.869982i	$-0.335869\pi$
$311$	1.62695e11			0.986169			0.493084	+	0.869982i	$0.335869\pi$
$312$		0			0
$313$			1.46080e11i			0.860284i	0.902761	+	0.430142i	$0.141536\pi$
$313$			1.46080e11i			0.860284i	−0.902761	+	0.430142i	$0.858464\pi$
$314$		0			0
$315$	−2.83543e10	−	1.96593e10i	−0.162264	−	0.112505i
$316$		0			0
$317$		−	4.65925e10i		−	0.259149i	−0.991570	−	0.129574i	$-0.958639\pi$
$317$		−	4.65925e10i		−	0.259149i	0.991570	−	0.129574i	$-0.0413611\pi$
$318$		0			0
$319$	−1.13455e11			−0.613429
$320$		0			0
$321$	−1.22418e11			−0.643534
$322$		0			0
$323$			1.37005e11i			0.700365i
$324$		0			0
$325$	3.06202e11	−	1.14663e11i	1.52241	−	0.570094i
$326$		0			0
$327$			7.93412e10i			0.383737i
$328$		0			0
$329$	−1.16609e11			−0.548721
$330$		0			0
$331$	2.54661e11			1.16610			0.583052	−	0.812435i	$-0.301859\pi$
$331$	2.54661e11			1.16610			0.583052	+	0.812435i	$0.301859\pi$
$332$		0			0
$333$		−	6.26329e10i		−	0.279128i
$334$		0			0
$335$	1.52662e11	+	1.05848e11i	0.662263	+	0.459177i
$336$		0			0
$337$			7.54835e10i			0.318799i	0.987214	+	0.159400i	$0.0509558\pi$
$337$			7.54835e10i			0.318799i	−0.987214	+	0.159400i	$0.949044\pi$
$338$		0			0
$339$	−4.46149e10			−0.183477
$340$		0			0
$341$	−1.43781e11			−0.575847
$342$		0			0
$343$			1.67230e11i			0.652363i
$344$		0			0
$345$	−9.48498e10	+	1.36800e11i	−0.360455	+	0.519877i
$346$		0			0
$347$			2.43939e11i			0.903229i	0.892213	+	0.451615i	$0.149152\pi$
$347$			2.43939e11i			0.903229i	−0.892213	+	0.451615i	$0.850848\pi$
$348$		0			0
$349$	−8.74281e10			−0.315455			−0.157727	−	0.987483i	$-0.550417\pi$
$349$	−8.74281e10			−0.315455			−0.157727	+	0.987483i	$0.550417\pi$
$350$		0			0
$351$	4.76211e11			1.67462
$352$		0			0
$353$			1.01592e11i			0.348237i	0.984725	+	0.174118i	$0.0557075\pi$
$353$			1.01592e11i			0.348237i	−0.984725	+	0.174118i	$0.944292\pi$
$354$		0			0
$355$	3.59760e10	−	5.18875e10i	0.120222	−	0.173394i
$356$		0			0
$357$			6.33701e10i			0.206480i
$358$		0			0
$359$	−4.52043e10			−0.143633			−0.0718166	−	0.997418i	$-0.522880\pi$
$359$	−4.52043e10			−0.143633			−0.0718166	+	0.997418i	$0.522880\pi$
$360$		0			0
$361$	−1.29865e11			−0.402449
$362$		0			0
$363$			6.01787e10i			0.181913i
$364$		0			0
$365$	1.65758e11	+	1.14927e11i	0.488827	+	0.338927i
$366$		0			0
$367$		−	7.17132e10i		−	0.206349i	−0.994663	−	0.103174i	$-0.967100\pi$
$367$		−	7.17132e10i		−	0.206349i	0.994663	−	0.103174i	$-0.0329000\pi$
$368$		0			0
$369$	−3.10823e10			−0.0872761
$370$		0			0
$371$	1.31006e11			0.359012
$372$		0			0
$373$		−	4.78190e11i		−	1.27912i	−0.768742	−	0.639559i	$-0.779117\pi$
$373$		−	4.78190e11i		−	1.27912i	0.768742	−	0.639559i	$-0.220883\pi$
$374$		0			0
$375$	6.17069e10	−	2.43755e11i	0.161136	−	0.636520i
$376$		0			0
$377$		−	4.60018e11i		−	1.17284i
$378$		0			0
$379$	−3.67400e11			−0.914666			−0.457333	−	0.889295i	$-0.651195\pi$
$379$	−3.67400e11			−0.914666			−0.457333	+	0.889295i	$0.651195\pi$
$380$		0			0
$381$	−2.37815e11			−0.578199
$382$		0			0
$383$		−	1.30383e11i		−	0.309619i	−0.987944	−	0.154809i	$-0.950524\pi$
$383$		−	1.30383e11i		−	0.309619i	0.987944	−	0.154809i	$-0.0494763\pi$
$384$		0			0
$385$	−1.04551e11	−	7.24902e10i	−0.242525	−	0.168153i
$386$		0			0
$387$			1.81008e11i			0.410204i
$388$		0			0
$389$	2.82567e11			0.625674			0.312837	−	0.949807i	$-0.398721\pi$
$389$	2.82567e11			0.625674			0.312837	+	0.949807i	$0.398721\pi$
$390$		0			0
$391$	−4.03432e11			−0.872921
$392$		0			0
$393$		−	2.29629e11i		−	0.485580i
$394$		0			0
$395$	−4.67616e11	+	6.74434e11i	−0.966502	+	1.39397i
$396$		0			0
$397$		−	9.25580e10i		−	0.187006i	−0.995619	−	0.0935032i	$-0.970193\pi$
$397$		−	9.25580e10i		−	0.187006i	0.995619	−	0.0935032i	$-0.0298065\pi$
$398$		0			0
$399$	8.91879e10			0.176168
$400$		0			0
$401$	−5.66439e11			−1.09397			−0.546983	−	0.837144i	$-0.684224\pi$
$401$	−5.66439e11			−1.09397			−0.546983	+	0.837144i	$0.684224\pi$
$402$		0			0
$403$		−	5.82981e11i		−	1.10099i
$404$		0			0
$405$	3.31644e10	−	4.78323e10i	0.0612525	−	0.0883433i
$406$		0			0
$407$		−	2.30947e11i		−	0.417194i
$408$		0			0
$409$	4.98412e11			0.880712			0.440356	−	0.897823i	$-0.354852\pi$
$409$	4.98412e11			0.880712			0.440356	+	0.897823i	$0.354852\pi$
$410$		0			0
$411$	5.54200e11			0.958029
$412$		0			0
$413$			2.92197e11i			0.494198i
$414$		0			0
$415$	−8.32467e11	−	5.77188e11i	−1.37769	−	0.955215i
$416$		0			0
$417$			7.34681e11i			1.18983i
$418$		0			0
$419$	9.89440e11			1.56829			0.784145	−	0.620577i	$-0.213102\pi$
$419$	9.89440e11			1.56829			0.784145	+	0.620577i	$0.213102\pi$
$420$		0			0
$421$	1.25151e11			0.194162			0.0970809	−	0.995276i	$-0.469049\pi$
$421$	1.25151e11			0.194162			0.0970809	+	0.995276i	$0.469049\pi$
$422$		0			0
$423$			5.92191e11i			0.899354i
$424$		0			0
$425$	5.70679e11	−	2.13701e11i	0.848480	−	0.317728i
$426$		0			0
$427$		−	4.17193e11i		−	0.607312i
$428$		0			0
$429$	6.36706e11			0.907572
$430$		0			0
$431$	−3.56091e11			−0.497066			−0.248533	−	0.968623i	$-0.579948\pi$
$431$	−3.56091e11			−0.497066			−0.248533	+	0.968623i	$0.579948\pi$
$432$		0			0
$433$			1.23857e12i			1.69326i	0.532180	+	0.846631i	$0.321373\pi$
$433$			1.23857e12i			1.69326i	−0.532180	+	0.846631i	$0.678627\pi$
$434$		0			0
$435$	−2.90720e11	−	2.01570e11i	−0.389290	−	0.269913i
$436$		0			0
$437$			5.67795e11i			0.744775i
$438$		0			0
$439$	−3.20478e11			−0.411820			−0.205910	−	0.978571i	$-0.566015\pi$
$439$	−3.20478e11			−0.411820			−0.205910	+	0.978571i	$0.566015\pi$
$440$		0			0
$441$	3.97414e11			0.500345
$442$		0			0
$443$			2.60246e11i			0.321046i	0.987032	+	0.160523i	$0.0513182\pi$
$443$			2.60246e11i			0.321046i	−0.987032	+	0.160523i	$0.948682\pi$
$444$		0			0
$445$	−8.56051e11	+	1.23467e12i	−1.03486	+	1.49255i
$446$		0			0
$447$			3.61904e11i			0.428755i
$448$		0			0
$449$	9.04660e11			1.05045			0.525227	−	0.850962i	$-0.323980\pi$
$449$	9.04660e11			1.05045			0.525227	+	0.850962i	$0.323980\pi$
$450$		0			0
$451$	−1.14610e11			−0.130446
$452$		0			0
$453$		−	7.24041e10i		−	0.0807832i
$454$		0			0
$455$	2.93922e11	−	4.23918e11i	0.321500	−	0.463693i
$456$		0			0
$457$		−	1.37944e12i		−	1.47938i	−0.672949	−	0.739689i	$-0.734973\pi$
$457$		−	1.37944e12i		−	1.47938i	0.672949	−	0.739689i	$-0.265027\pi$
$458$		0			0
$459$	8.87531e11			0.933311
$460$		0			0
$461$	−1.05742e12			−1.09041			−0.545207	−	0.838301i	$-0.683549\pi$
$461$	−1.05742e12			−1.09041			−0.545207	+	0.838301i	$0.683549\pi$
$462$		0			0
$463$		−	1.53298e12i		−	1.55033i	−0.631761	−	0.775164i	$-0.717667\pi$
$463$		−	1.53298e12i		−	1.55033i	0.631761	−	0.775164i	$-0.282333\pi$
$464$		0			0
$465$	−3.68430e11	−	2.55449e11i	−0.365440	−	0.253377i
$466$		0			0
$467$			9.34781e11i			0.909460i	0.890629	+	0.454730i	$0.150264\pi$
$467$			9.34781e11i			0.909460i	−0.890629	+	0.454730i	$0.849736\pi$
$468$		0			0
$469$	2.93080e11			0.279710
$470$		0			0
$471$	−8.76048e11			−0.820227
$472$		0			0
$473$			6.67435e11i			0.613104i
$474$		0			0
$475$	−3.00765e11	−	8.03181e11i	−0.271085	−	0.723922i
$476$		0			0
$477$		−	6.65305e11i		−	0.588421i
$478$		0			0
$479$	−3.27825e10			−0.0284532			−0.0142266	−	0.999899i	$-0.504529\pi$
$479$	−3.27825e10			−0.0284532			−0.0142266	+	0.999899i	$0.504529\pi$
$480$		0			0
$481$	9.36409e11			0.797651
$482$		0			0
$483$			2.62628e11i			0.219573i
$484$		0			0
$485$	−1.21027e11	−	8.39136e10i	−0.0993218	−	0.0688644i
$486$		0			0
$487$		−	1.39219e12i		−	1.12155i	−0.827968	−	0.560775i	$-0.810503\pi$
$487$		−	1.39219e12i		−	1.12155i	0.827968	−	0.560775i	$-0.189497\pi$
$488$		0			0
$489$	−1.45675e12			−1.15212
$490$		0			0
$491$	−6.69016e11			−0.519481			−0.259741	−	0.965678i	$-0.583637\pi$
$491$	−6.69016e11			−0.519481			−0.259741	+	0.965678i	$0.583637\pi$
$492$		0			0
$493$		−	8.57352e11i		−	0.653654i
$494$		0			0
$495$	−3.68136e11	+	5.30955e11i	−0.275603	+	0.397497i
$496$		0			0
$497$		−	9.96132e10i		−	0.0732341i
$498$		0			0
$499$	−7.71496e11			−0.557033			−0.278517	−	0.960431i	$-0.589843\pi$
$499$	−7.71496e11			−0.557033			−0.278517	+	0.960431i	$0.589843\pi$
$500$		0			0
$501$	1.07532e12			0.762548
$502$		0			0
$503$		−	1.71646e12i		−	1.19558i	−0.801652	−	0.597790i	$-0.796045\pi$
$503$		−	1.71646e12i		−	1.19558i	0.801652	−	0.597790i	$-0.203955\pi$
$504$		0			0
$505$	8.01190e10	−	1.15554e11i	0.0548181	−	0.0790631i
$506$		0			0
$507$			1.60475e12i			1.07863i
$508$		0			0
$509$	−6.09803e11			−0.402679			−0.201340	−	0.979521i	$-0.564529\pi$
$509$	−6.09803e11			−0.402679			−0.201340	+	0.979521i	$0.564529\pi$
$510$		0			0
$511$	3.18220e11			0.206459
$512$		0			0
$513$		−	1.24912e12i		−	0.796300i
$514$		0			0
$515$	2.36265e12	+	1.63814e12i	1.48002	+	1.02617i
$516$		0			0
$517$			2.18360e12i			1.34420i
$518$		0			0
$519$	−9.08809e11			−0.549819
$520$		0			0
$521$	−6.80962e11			−0.404905			−0.202453	−	0.979292i	$-0.564891\pi$
$521$	−6.80962e11			−0.404905			−0.202453	+	0.979292i	$0.564891\pi$
$522$		0			0
$523$			2.76170e12i			1.61406i	0.590512	+	0.807029i	$0.298926\pi$
$523$			2.76170e12i			1.61406i	−0.590512	+	0.807029i	$0.701074\pi$
$524$		0			0
$525$	−1.39116e11	−	3.71503e11i	−0.0799207	−	0.213425i
$526$		0			0
$527$		−	1.08652e12i		−	0.613608i
$528$		0			0
$529$	1.29192e11			0.0717273
$530$		0			0
$531$	1.48390e12			0.809989
$532$		0			0
$533$		−	4.64704e11i		−	0.249404i
$534$		0			0
$535$	1.52625e12	+	1.05822e12i	0.805441	+	0.558449i
$536$		0			0
$537$			3.58874e11i			0.186233i
$538$		0			0
$539$	1.46539e12			0.747831
$540$		0			0
$541$	2.23576e12			1.12212			0.561058	−	0.827776i	$-0.310394\pi$
$541$	2.23576e12			1.12212			0.561058	+	0.827776i	$0.310394\pi$
$542$		0			0
$543$			9.44211e11i			0.466090i
$544$		0			0
$545$	6.85851e11	−	9.89190e11i	0.333001	−	0.480281i
$546$		0			0
$547$			9.47205e11i			0.452378i	0.974083	+	0.226189i	$0.0726266\pi$
$547$			9.47205e11i			0.452378i	−0.974083	+	0.226189i	$0.927373\pi$
$548$		0			0
$549$	−2.11868e12			−0.995383
$550$		0			0
$551$	−1.20665e12			−0.557697
$552$		0			0
$553$			1.29477e12i			0.588749i
$554$		0			0
$555$	4.10314e11	−	5.91788e11i	0.183568	−	0.264757i
$556$		0			0
$557$		−	3.02116e12i		−	1.32992i	−0.746879	−	0.664960i	$-0.768449\pi$
$557$		−	3.02116e12i		−	1.32992i	0.746879	−	0.664960i	$-0.231551\pi$
$558$		0			0
$559$	−2.70621e12			−1.17222
$560$		0			0
$561$	1.18665e12			0.505814
$562$		0			0
$563$			3.34378e12i			1.40265i	0.712840	+	0.701326i	$0.247408\pi$
$563$			3.34378e12i			1.40265i	−0.712840	+	0.701326i	$0.752592\pi$
$564$		0			0
$565$	5.56239e11	+	3.85666e11i	0.229638	+	0.159219i
$566$		0			0
$567$		−	9.18281e10i		−	0.0373123i
$568$		0			0
$569$	−4.55265e12			−1.82079			−0.910394	−	0.413743i	$-0.864221\pi$
$569$	−4.55265e12			−1.82079			−0.910394	+	0.413743i	$0.864221\pi$
$570$		0			0
$571$	5.67536e11			0.223424			0.111712	−	0.993741i	$-0.464367\pi$
$571$	5.67536e11			0.223424			0.111712	+	0.993741i	$0.464367\pi$
$572$		0			0
$573$		−	2.81365e12i		−	1.09037i
$574$		0			0
$575$	2.36509e12	−	8.85649e11i	0.902282	−	0.337875i
$576$		0			0
$577$			2.11216e12i			0.793298i	0.917970	+	0.396649i	$0.129827\pi$
$577$			2.11216e12i			0.793298i	−0.917970	+	0.396649i	$0.870173\pi$
$578$		0			0
$579$	−1.24158e11			−0.0459116
$580$		0			0
$581$	−1.59816e12			−0.581874
$582$		0			0
$583$		−	2.45319e12i		−	0.879472i
$584$		0			0
$585$	−2.15283e12	−	1.49266e12i	−0.759992	−	0.526937i
$586$		0			0
$587$		−	2.03661e12i		−	0.708004i	−0.935245	−	0.354002i	$-0.884821\pi$
$587$		−	2.03661e12i		−	0.708004i	0.935245	−	0.354002i	$-0.115179\pi$
$588$		0			0
$589$	−1.52919e12			−0.523530
$590$		0			0
$591$	5.45641e11			0.183977
$592$		0			0
$593$		−	2.22548e12i		−	0.739058i	−0.929219	−	0.369529i	$-0.879519\pi$
$593$		−	2.22548e12i		−	0.739058i	0.929219	−	0.369529i	$-0.120481\pi$
$594$		0			0
$595$	5.47792e11	−	7.90070e11i	0.179180	−	0.258428i
$596$		0			0
$597$		−	2.48046e12i		−	0.799186i
$598$		0			0
$599$	1.20679e12			0.383010			0.191505	−	0.981492i	$-0.438663\pi$
$599$	1.20679e12			0.383010			0.191505	+	0.981492i	$0.438663\pi$
$600$		0			0
$601$	3.91261e12			1.22330			0.611648	−	0.791130i	$-0.290507\pi$
$601$	3.91261e12			1.22330			0.611648	+	0.791130i	$0.290507\pi$
$602$		0			0
$603$		−	1.48838e12i		−	0.458445i
$604$		0			0
$605$	5.20205e11	−	7.50282e11i	0.157861	−	0.227680i
$606$		0			0
$607$		−	2.73471e11i		−	0.0817639i	−0.999164	−	0.0408819i	$-0.986983\pi$
$607$		−	2.73471e11i		−	0.0817639i	0.999164	−	0.0408819i	$-0.0130168\pi$
$608$		0			0
$609$	−5.58122e11			−0.164419
$610$		0			0
$611$	−8.85370e12			−2.57004
$612$		0			0
$613$			6.42566e12i			1.83800i	0.394258	+	0.919000i	$0.371002\pi$
$613$			6.42566e12i			1.83800i	−0.394258	+	0.919000i	$0.628998\pi$
$614$		0			0
$615$	−2.93682e11	−	2.03623e11i	−0.0827826	−	0.0573970i
$616$		0			0
$617$			1.35609e12i			0.376707i	0.982101	+	0.188354i	$0.0603151\pi$
$617$			1.35609e12i			0.376707i	−0.982101	+	0.188354i	$0.939685\pi$
$618$		0			0
$619$	3.16878e12			0.867530			0.433765	−	0.901026i	$-0.357185\pi$
$619$	3.16878e12			0.867530			0.433765	+	0.901026i	$0.357185\pi$
$620$		0			0
$621$	3.67823e12			0.992492
$622$		0			0
$623$			2.37030e12i			0.630387i
$624$		0			0
$625$	−2.87643e12	+	2.50561e12i	−0.754039	+	0.656830i
$626$		0			0
$627$		−	1.67011e12i		−	0.431560i
$628$		0			0
$629$	1.74522e12			0.444551
$630$		0			0
$631$	−4.07859e11			−0.102418			−0.0512092	−	0.998688i	$-0.516308\pi$
$631$	−4.07859e11			−0.102418			−0.0512092	+	0.998688i	$0.516308\pi$
$632$		0			0
$633$			4.47937e11i			0.110892i
$634$		0			0
$635$	2.96497e12	+	2.05575e12i	0.723668	+	0.501752i
$636$		0			0
$637$			5.94163e12i			1.42981i
$638$		0			0
$639$	−5.05878e11			−0.120031
$640$		0			0
$641$	6.94017e11			0.162371			0.0811856	−	0.996699i	$-0.474129\pi$
$641$	6.94017e11			0.162371			0.0811856	+	0.996699i	$0.474129\pi$
$642$		0			0
$643$		−	7.09450e12i		−	1.63671i	−0.574712	−	0.818356i	$-0.694886\pi$
$643$		−	7.09450e12i		−	1.63671i	0.574712	−	0.818356i	$-0.305114\pi$
$644$		0			0
$645$	−1.18580e12	+	1.71026e12i	−0.269770	+	0.389084i
$646$		0			0
$647$			5.00511e12i			1.12291i	0.827507	+	0.561455i	$0.189758\pi$
$647$			5.00511e12i			1.12291i	−0.827507	+	0.561455i	$0.810242\pi$
$648$		0			0
$649$	5.47161e12			1.21064
$650$		0			0
$651$	−7.07309e11			−0.154346
$652$		0			0
$653$		−	4.64412e12i		−	0.999525i	−0.866162	−	0.499763i	$-0.833421\pi$
$653$		−	4.64412e12i		−	0.999525i	0.866162	−	0.499763i	$-0.166579\pi$
$654$		0			0
$655$	−1.98499e12	+	2.86292e12i	−0.421379	+	0.607747i
$656$		0			0
$657$		−	1.61606e12i		−	0.338386i
$658$		0			0
$659$	4.58151e12			0.946289			0.473145	−	0.880985i	$-0.343119\pi$
$659$	4.58151e12			0.946289			0.473145	+	0.880985i	$0.343119\pi$
$660$		0			0
$661$	9.33112e12			1.90120			0.950599	−	0.310423i	$-0.100471\pi$
$661$	9.33112e12			1.90120			0.950599	+	0.310423i	$0.100471\pi$
$662$		0			0
$663$			4.81145e12i			0.967086i
$664$		0			0
$665$	−1.11196e12	−	7.70970e11i	−0.220491	−	0.152876i
$666$		0			0
$667$		−	3.55316e12i		−	0.695102i
$668$		0			0
$669$	1.96993e12			0.380218
$670$		0			0
$671$	−7.81225e12			−1.48773
$672$		0			0
$673$			5.22188e12i			0.981203i	0.871384	+	0.490602i	$0.163223\pi$
$673$			5.22188e12i			0.981203i	−0.871384	+	0.490602i	$0.836777\pi$
$674$		0			0
$675$	−5.20308e12	+	1.94839e12i	−0.964704	+	0.361250i
$676$		0			0
$677$			2.53844e12i			0.464428i	0.972665	+	0.232214i	$0.0745970\pi$
$677$			2.53844e12i			0.464428i	−0.972665	+	0.232214i	$0.925403\pi$
$678$		0			0
$679$	−2.32347e11			−0.0419491
$680$		0			0
$681$	−4.06655e12			−0.724544
$682$		0			0
$683$		−	4.65915e12i		−	0.819245i	−0.912255	−	0.409622i	$-0.865660\pi$
$683$		−	4.65915e12i		−	0.819245i	0.912255	−	0.409622i	$-0.134340\pi$
$684$		0			0
$685$	−6.90952e12	−	4.79069e12i	−1.19906	−	0.831363i
$686$		0			0
$687$		−	4.75243e12i		−	0.813974i
$688$		0			0
$689$	9.94680e12			1.68150
$690$		0			0
$691$	−4.91969e12			−0.820893			−0.410446	−	0.911885i	$-0.634627\pi$
$691$	−4.91969e12			−0.820893			−0.410446	+	0.911885i	$0.634627\pi$
$692$		0			0
$693$			1.01932e12i			0.167885i
$694$		0			0
$695$	6.35083e12	−	9.15968e12i	1.03252	−	1.48918i
$696$		0			0
$697$		−	8.66086e11i		−	0.139000i
$698$		0			0
$699$	−1.82280e11			−0.0288797
$700$		0			0
$701$	−1.14932e13			−1.79767			−0.898835	−	0.438287i	$-0.855585\pi$
$701$	−1.14932e13			−1.79767			−0.898835	+	0.438287i	$0.855585\pi$
$702$		0			0
$703$		−	2.45624e12i		−	0.379291i
$704$		0			0
$705$	−3.87950e12	+	5.59532e12i	−0.591459	+	0.853049i
$706$		0			0
$707$		−	2.21840e11i		−	0.0333927i
$708$		0			0
$709$	−4.33141e12			−0.643756			−0.321878	−	0.946781i	$-0.604314\pi$
$709$	−4.33141e12			−0.643756			−0.321878	+	0.946781i	$0.604314\pi$
$710$		0			0
$711$	6.57540e12			0.964959
$712$		0			0
$713$		−	4.50293e12i		−	0.652517i
$714$		0			0
$715$	−7.93817e12	−	5.50390e12i	−1.13591	−	0.787578i
$716$		0			0
$717$		−	2.76345e12i		−	0.390495i
$718$		0			0
$719$	7.50444e12			1.04722			0.523610	−	0.851958i	$-0.324585\pi$
$719$	7.50444e12			1.04722			0.523610	+	0.851958i	$0.324585\pi$
$720$		0			0
$721$	4.53581e12			0.625095
$722$		0			0
$723$			7.50689e11i			0.102173i
$724$		0			0
$725$	1.88213e12	+	5.02616e12i	0.253005	+	0.675640i
$726$		0			0
$727$		−	1.17398e12i		−	0.155867i	−0.996959	−	0.0779337i	$-0.975168\pi$
$727$		−	1.17398e12i		−	0.155867i	0.996959	−	0.0779337i	$-0.0248322\pi$
$728$		0			0
$729$	−5.62413e12			−0.737533
$730$		0			0
$731$	−5.04366e12			−0.653308
$732$		0			0
$733$			5.01411e12i			0.641543i	0.947157	+	0.320772i	$0.103942\pi$
$733$			5.01411e12i			0.641543i	−0.947157	+	0.320772i	$0.896058\pi$
$734$		0			0
$735$	3.75497e12	+	2.60349e12i	0.474584	+	0.329051i
$736$		0			0
$737$		−	5.48814e12i		−	0.685206i
$738$		0			0
$739$	1.39712e12			0.172319			0.0861597	−	0.996281i	$-0.472540\pi$
$739$	1.39712e12			0.172319			0.0861597	+	0.996281i	$0.472540\pi$
$740$		0			0
$741$	6.77170e12			0.825117
$742$		0			0
$743$			8.14438e12i			0.980411i	0.871607	+	0.490206i	$0.163078\pi$
$743$			8.14438e12i			0.980411i	−0.871607	+	0.490206i	$0.836922\pi$
$744$		0			0
$745$	3.12841e12	−	4.51205e12i	0.372067	−	0.536625i
$746$		0			0
$747$			8.11615e12i			0.953690i
$748$		0			0
$749$	2.93008e12			0.340182
$750$		0			0
$751$	2.56583e12			0.294340			0.147170	−	0.989111i	$-0.452984\pi$
$751$	2.56583e12			0.294340			0.147170	+	0.989111i	$0.452984\pi$
$752$		0			0
$753$			3.01848e12i			0.342145i
$754$		0			0
$755$	−6.25885e11	+	9.02702e11i	−0.0701024	+	0.101107i
$756$		0			0
$757$		−	8.69238e12i		−	0.962072i	−0.876701	−	0.481036i	$-0.840261\pi$
$757$		−	8.69238e12i		−	0.962072i	0.876701	−	0.481036i	$-0.159739\pi$
$758$		0			0
$759$	4.91790e12			0.537887
$760$		0			0
$761$	−1.65082e12			−0.178430			−0.0892150	−	0.996012i	$-0.528436\pi$
$761$	−1.65082e12			−0.178430			−0.0892150	+	0.996012i	$0.528436\pi$
$762$		0			0
$763$		−	1.89904e12i		−	0.202849i
$764$		0			0
$765$	−4.01231e12	−	2.78192e12i	−0.423563	−	0.293676i
$766$		0			0
$767$			2.21854e13i			2.31467i
$768$		0			0
$769$	−7.03400e12			−0.725327			−0.362664	−	0.931920i	$-0.618133\pi$
$769$	−7.03400e12			−0.725327			−0.362664	+	0.931920i	$0.618133\pi$
$770$		0			0
$771$	5.14971e12			0.524853
$772$		0			0
$773$			1.20620e13i			1.21510i	0.794283	+	0.607548i	$0.207847\pi$
$773$			1.20620e13i			1.21510i	−0.794283	+	0.607548i	$0.792153\pi$
$774$		0			0
$775$	2.38523e12	+	6.36966e12i	0.237505	+	0.634247i
$776$		0			0
$777$		−	1.13611e12i		−	0.111822i
$778$		0			0
$779$	−1.21894e12			−0.118594
$780$		0			0
$781$	−1.86533e12			−0.179402
$782$		0			0
$783$			7.81678e12i			0.743191i
$784$		0			0
$785$	1.09222e13	+	7.57285e12i	1.02659	+	0.711780i
$786$		0			0
$787$			2.11707e12i			0.196720i	0.995151	+	0.0983600i	$0.0313597\pi$
$787$			2.11707e12i			0.196720i	−0.995151	+	0.0983600i	$0.968640\pi$
$788$		0			0
$789$	1.09881e12			0.100943
$790$		0			0
$791$	1.06786e12			0.0969888
$792$		0			0
$793$		−	3.16759e13i		−	2.84446i
$794$		0			0
$795$	4.35847e12	−	6.28613e12i	0.386974	−	0.558125i
$796$		0			0
$797$		−	2.82873e12i		−	0.248330i	−0.992262	−	0.124165i	$-0.960375\pi$
$797$		−	2.82873e12i		−	0.248330i	0.992262	−	0.124165i	$-0.0396251\pi$
$798$		0			0
$799$	−1.65010e13			−1.43235
$800$		0			0
$801$	1.20374e13			1.03320
$802$		0			0
$803$		−	5.95890e12i		−	0.505762i
$804$		0			0
$805$	2.27024e12	−	3.27432e12i	0.190542	−	0.274815i
$806$		0			0
$807$		−	6.17968e12i		−	0.512903i
$808$		0			0
$809$	−1.42627e13			−1.17066			−0.585332	−	0.810794i	$-0.699036\pi$
$809$	−1.42627e13			−1.17066			−0.585332	+	0.810794i	$0.699036\pi$
$810$		0			0
$811$	−2.09093e12			−0.169725			−0.0848625	−	0.996393i	$-0.527045\pi$
$811$	−2.09093e12			−0.169725			−0.0848625	+	0.996393i	$0.527045\pi$
$812$		0			0
$813$		−	1.40121e13i		−	1.12485i
$814$		0			0
$815$	1.81622e13	+	1.25927e13i	1.44198	+	0.999789i
$816$		0			0
$817$			7.09851e12i			0.557402i
$818$		0			0
$819$	−4.13299e12			−0.320987
$820$		0			0
$821$	−1.65208e13			−1.26907			−0.634537	−	0.772893i	$-0.718809\pi$
$821$	−1.65208e13			−1.26907			−0.634537	+	0.772893i	$0.718809\pi$
$822$		0			0
$823$		−	2.27738e12i		−	0.173036i	−0.996250	−	0.0865179i	$-0.972426\pi$
$823$		−	2.27738e12i		−	0.173036i	0.996250	−	0.0865179i	$-0.0275740\pi$
$824$		0			0
$825$	−6.95666e12	+	2.60504e12i	−0.522827	+	0.195782i
$826$		0			0
$827$		−	2.44572e13i		−	1.81816i	−0.416619	−	0.909081i	$-0.636785\pi$
$827$		−	2.44572e13i		−	1.81816i	0.416619	−	0.909081i	$-0.363215\pi$
$828$		0			0
$829$	−1.61234e13			−1.18566			−0.592832	−	0.805326i	$-0.701990\pi$
$829$	−1.61234e13			−1.18566			−0.592832	+	0.805326i	$0.701990\pi$
$830$		0			0
$831$	1.70430e13			1.23977
$832$		0			0
$833$			1.10736e13i			0.796870i
$834$		0			0
$835$	−1.34066e13	−	9.29541e12i	−0.954397	−	0.661728i
$836$		0			0
$837$			9.90622e12i			0.697659i
$838$		0			0
$839$	−1.71182e13			−1.19270			−0.596348	−	0.802726i	$-0.703382\pi$
$839$	−1.71182e13			−1.19270			−0.596348	+	0.802726i	$0.703382\pi$
$840$		0			0
$841$	−6.95616e12			−0.479499
$842$		0			0
$843$			9.85643e12i			0.672196i
$844$		0			0
$845$	1.38720e13	−	2.00073e13i	0.936015	−	1.35000i
$846$		0			0
$847$		−	1.44038e12i		−	0.0961619i
$848$		0			0
$849$	−5.79789e12			−0.382988
$850$		0			0
$851$	7.23279e12			0.472740
$852$		0			0
$853$			6.74970e12i			0.436530i	0.975890	+	0.218265i	$0.0700397\pi$
$853$			6.74970e12i			0.436530i	−0.975890	+	0.218265i	$0.929960\pi$
$854$		0			0
$855$	−3.91531e12	+	5.64698e12i	−0.250564	+	0.361384i
$856$		0			0
$857$		−	1.65389e12i		−	0.104735i	−0.998628	−	0.0523675i	$-0.983323\pi$
$857$		−	1.65389e12i		−	0.104735i	0.998628	−	0.0523675i	$-0.0166767\pi$
$858$		0			0
$859$	2.49551e12			0.156383			0.0781916	−	0.996938i	$-0.475085\pi$
$859$	2.49551e12			0.156383			0.0781916	+	0.996938i	$0.475085\pi$
$860$		0			0
$861$	−5.63808e11			−0.0349637
$862$		0			0
$863$		−	1.60703e13i		−	0.986225i	−0.869966	−	0.493112i	$-0.835859\pi$
$863$		−	1.60703e13i		−	0.986225i	0.869966	−	0.493112i	$-0.164141\pi$
$864$		0			0
$865$	1.13306e13	+	7.85605e12i	0.688147	+	0.477124i
$866$		0			0
$867$		−	1.95685e12i		−	0.117617i
$868$		0			0
$869$	2.42456e13			1.44226
$870$		0			0
$871$	2.22524e13			1.31007
$872$		0			0
$873$			1.17995e12i			0.0687545i
$874$		0			0
$875$	−1.47696e12	+	5.83429e12i	−0.0851790	+	0.336474i
$876$		0			0
$877$		−	1.04377e13i		−	0.595811i	−0.954595	−	0.297906i	$-0.903712\pi$
$877$		−	1.04377e13i		−	0.595811i	0.954595	−	0.297906i	$-0.0962881\pi$
$878$		0			0
$879$	−1.69616e13			−0.958335
$880$		0			0
$881$	−1.73238e13			−0.968840			−0.484420	−	0.874836i	$-0.660969\pi$
$881$	−1.73238e13			−0.968840			−0.484420	+	0.874836i	$0.660969\pi$
$882$		0			0
$883$			8.43531e12i			0.466958i	0.972362	+	0.233479i	$0.0750110\pi$
$883$			8.43531e12i			0.466958i	−0.972362	+	0.233479i	$0.924989\pi$
$884$		0			0
$885$	1.40206e13	+	9.72116e12i	0.768286	+	0.532688i
$886$		0			0
$887$			2.11511e13i			1.14730i	0.819100	+	0.573650i	$0.194473\pi$
$887$			2.11511e13i			1.14730i	−0.819100	+	0.573650i	$0.805527\pi$
$888$		0			0
$889$	5.69213e12			0.305645
$890$		0			0
$891$	−1.71955e12			−0.0914039
$892$		0			0
$893$			2.32237e13i			1.22208i
$894$		0			0
$895$	3.10222e12	−	4.47428e12i	0.161610	−	0.233088i
$896$		0			0
$897$			1.99403e13i			1.02841i
$898$		0			0
$899$	9.56937e12			0.488613
$900$		0			0
$901$	1.85382e13			0.937143
$902$		0			0
$903$			3.28334e12i			0.164332i
$904$		0			0
$905$	8.16208e12	−	1.17720e13i	0.404466	−	0.583354i
$906$		0			0
$907$			2.09080e12i			0.102584i	0.998684	+	0.0512920i	$0.0163339\pi$
$907$			2.09080e12i			0.102584i	−0.998684	+	0.0512920i	$0.983666\pi$
$908$		0			0
$909$	−1.12660e12			−0.0547307
$910$		0			0
$911$	−6.14791e12			−0.295729			−0.147865	−	0.989008i	$-0.547240\pi$
$911$	−6.14791e12			−0.295729			−0.147865	+	0.989008i	$0.547240\pi$
$912$		0			0
$913$			2.99268e13i			1.42542i
$914$		0			0
$915$	−2.00184e13	−	1.38797e13i	−0.944134	−	0.654612i
$916$		0			0
$917$			5.49621e12i			0.256685i
$918$		0			0
$919$	−1.34759e13			−0.623215			−0.311608	−	0.950211i	$-0.600867\pi$
$919$	−1.34759e13			−0.623215			−0.311608	+	0.950211i	$0.600867\pi$
$920$		0			0
$921$	−1.41841e13			−0.649579
$922$		0			0
$923$		−	7.56325e12i		−	0.343005i
$924$		0			0
$925$	−1.02312e13	+	3.83126e12i	−0.459504	+	0.172069i
$926$		0			0
$927$		−	2.30347e13i		−	1.02453i
$928$		0			0
$929$	3.08450e13			1.35867			0.679335	−	0.733829i	$-0.262269\pi$
$929$	3.08450e13			1.35867			0.679335	+	0.733829i	$0.262269\pi$
$930$		0			0
$931$	1.55852e13			0.679889
$932$		0			0
$933$		−	1.49871e13i		−	0.647518i
$934$		0			0
$935$	−1.47946e13	−	1.02578e13i	−0.633071	−	0.438937i
$936$		0			0
$937$		−	6.20903e12i		−	0.263145i	−0.991307	−	0.131573i	$-0.957997\pi$
$937$		−	6.20903e12i		−	0.263145i	0.991307	−	0.131573i	$-0.0420026\pi$
$938$		0			0
$939$	1.34567e13			0.564861
$940$		0			0
$941$	−1.70273e13			−0.707932			−0.353966	−	0.935258i	$-0.615167\pi$
$941$	−1.70273e13			−0.707932			−0.353966	+	0.935258i	$0.615167\pi$
$942$		0			0
$943$		−	3.58936e12i		−	0.147814i
$944$		0			0
$945$	−4.99442e12	+	7.20336e12i	−0.203724	+	0.293827i
$946$		0			0
$947$		−	2.09080e13i		−	0.844767i	−0.906417	−	0.422384i	$-0.861194\pi$
$947$		−	2.09080e13i		−	0.844767i	0.906417	−	0.422384i	$-0.138806\pi$
$948$		0			0
$949$	2.41612e13			0.966988
$950$		0			0
$951$	−4.29202e12			−0.170157
$952$		0			0
$953$		−	3.36262e13i		−	1.32057i	−0.751017	−	0.660283i	$-0.770436\pi$
$953$		−	3.36262e13i		−	1.32057i	0.751017	−	0.660283i	$-0.229564\pi$
$954$		0			0
$955$	−2.43221e13	+	3.50793e13i	−0.946207	+	1.36470i
$956$		0			0
$957$			1.04512e13i			0.402777i
$958$		0			0
$959$	−1.32648e13			−0.506429
$960$		0			0
$961$	−1.43123e13			−0.541322
$962$		0			0
$963$		−	1.48802e13i		−	0.557558i
$964$		0			0
$965$	1.54795e12	+	1.07327e12i	0.0574625	+	0.0398414i
$966$		0			0
$967$		−	2.60630e13i		−	0.958529i	−0.877671	−	0.479264i	$-0.840903\pi$
$967$		−	2.60630e13i		−	0.958529i	0.877671	−	0.479264i	$-0.159097\pi$
$968$		0			0
$969$	1.26207e13			0.459859
$970$		0			0
$971$	−3.78861e13			−1.36771			−0.683854	−	0.729619i	$-0.739698\pi$
$971$	−3.78861e13			−1.36771			−0.683854	+	0.729619i	$0.739698\pi$
$972$		0			0
$973$		−	1.75847e13i		−	0.628965i
$974$		0			0
$975$	−1.05625e13	−	2.82068e13i	−0.374323	−	0.999615i
$976$		0			0
$977$			2.00611e13i			0.704415i	0.935922	+	0.352207i	$0.114569\pi$
$977$			2.00611e13i			0.704415i	−0.935922	+	0.352207i	$0.885431\pi$
$978$		0			0
$979$	4.43857e13			1.54426
$980$		0			0
$981$	−9.64412e12			−0.332470
$982$		0			0
$983$		−	1.36885e13i		−	0.467588i	−0.972286	−	0.233794i	$-0.924886\pi$
$983$		−	1.36885e13i		−	0.467588i	0.972286	−	0.233794i	$-0.0751142\pi$
$984$		0			0
$985$	−6.80280e12	−	4.71670e12i	−0.230263	−	0.159652i
$986$		0			0
$987$			1.07419e13i			0.360290i
$988$		0			0
$989$	−2.09027e13			−0.694734
$990$		0			0
$991$	3.18951e13			1.05049			0.525245	−	0.850951i	$-0.323974\pi$
$991$	3.18951e13			1.05049			0.525245	+	0.850951i	$0.323974\pi$
$992$		0			0
$993$		−	2.34590e13i		−	0.765662i
$994$		0			0
$995$	−2.14419e13	+	3.09253e13i	−0.693522	+	1.00025i
$996$		0			0
$997$			1.68723e13i			0.540812i	0.962746	+	0.270406i	$0.0871580\pi$
$997$			1.68723e13i			0.540812i	−0.962746	+	0.270406i	$0.912842\pi$
$998$		0			0
$999$	−1.59118e13			−0.505445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.10.c.a.9.2	✓	4
3.2	odd	2		180.10.d.a.109.3		4
4.3	odd	2		80.10.c.b.49.3		4
5.2	odd	4		100.10.a.f.1.2		4
5.3	odd	4		100.10.a.f.1.3		4
5.4	even	2	inner	20.10.c.a.9.3	yes	4
15.14	odd	2		180.10.d.a.109.4		4
20.3	even	4		400.10.a.bb.1.2		4
20.7	even	4		400.10.a.bb.1.3		4
20.19	odd	2		80.10.c.b.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.10.c.a.9.2	✓	4	1.1	even	1	trivial
20.10.c.a.9.3	yes	4	5.4	even	2	inner
80.10.c.b.49.2		4	20.19	odd	2
80.10.c.b.49.3		4	4.3	odd	2
100.10.a.f.1.2		4	5.2	odd	4
100.10.a.f.1.3		4	5.3	odd	4
180.10.d.a.109.3		4	3.2	odd	2
180.10.d.a.109.4		4	15.14	odd	2
400.10.a.bb.1.2		4	20.3	even	4
400.10.a.bb.1.3		4	20.7	even	4

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-92.1183i q^{3} +(-796.301 + 1148.49i) q^{5} +2204.86i q^{7} +11197.2 q^{9} +O(q^{10})\)	\(q-92.1183i q^{3} +(-796.301 + 1148.49i) q^{5} +2204.86i q^{7} +11197.2 q^{9} +41287.7 q^{11} +167407. i q^{13} +(105797. + 73353.9i) q^{15} +312002. i q^{17} +439115. q^{19} +203108. q^{21} +1.29304e6i q^{23} +(-684934. - 1.82909e6i) q^{25} -2.84463e6i q^{27} -2.74791e6 q^{29} -3.48242e6 q^{31} -3.80335e6i q^{33} +(-2.53226e6 - 1.75573e6i) q^{35} -5.59362e6i q^{37} +1.54212e7 q^{39} -2.77590e6 q^{41} +1.61655e7i q^{43} +(-8.91636e6 + 1.28599e7i) q^{45} +5.28874e7i q^{47} +3.54922e7 q^{49} +2.87411e7 q^{51} -5.94170e7i q^{53} +(-3.28774e7 + 4.74185e7i) q^{55} -4.04506e7i q^{57} +1.32524e8 q^{59} -1.89215e8 q^{61} +2.46883e7i q^{63} +(-1.92265e8 - 1.33306e8i) q^{65} -1.32924e8i q^{67} +1.19113e8 q^{69} -4.51789e7 q^{71} -1.44326e8i q^{73} +(-1.68492e8 + 6.30949e7i) q^{75} +9.10336e7i q^{77} +5.87235e8 q^{79} -4.16480e7 q^{81} +7.24836e8i q^{83} +(-3.58331e8 - 2.48447e8i) q^{85} +2.53132e8i q^{87} +1.07503e9 q^{89} -3.69109e8 q^{91} +3.20795e8i q^{93} +(-3.49668e8 + 5.04320e8i) q^{95} +1.05379e8i q^{97} +4.62307e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 660 q^{5} - 9044 q^{9}+O(q^{10}) \) 4 * q + 660 * q^5 - 9044 * q^9	\( 4 q + 660 q^{5} - 9044 q^{9} - 34800 q^{11} - 99760 q^{15} - 227664 q^{19} - 287296 q^{21} - 201900 q^{25} + 6265656 q^{29} + 374464 q^{31} - 8114160 q^{35} + 23386656 q^{39} - 17648136 q^{41} - 53241860 q^{45} + 144898812 q^{49} - 108703552 q^{51} - 197954800 q^{55} + 438995472 q^{59} - 103044472 q^{61} - 417315840 q^{65} + 1186715008 q^{69} - 504081888 q^{71} - 1038341600 q^{75} + 1794955008 q^{79} - 982752124 q^{81} - 1447443520 q^{85} + 2381318184 q^{89} - 811245024 q^{91} - 1944906960 q^{95} + 2769662000 q^{99}+O(q^{100}) \) 4 * q + 660 * q^5 - 9044 * q^9 - 34800 * q^11 - 99760 * q^15 - 227664 * q^19 - 287296 * q^21 - 201900 * q^25 + 6265656 * q^29 + 374464 * q^31 - 8114160 * q^35 + 23386656 * q^39 - 17648136 * q^41 - 53241860 * q^45 + 144898812 * q^49 - 108703552 * q^51 - 197954800 * q^55 + 438995472 * q^59 - 103044472 * q^61 - 417315840 * q^65 + 1186715008 * q^69 - 504081888 * q^71 - 1038341600 * q^75 + 1794955008 * q^79 - 982752124 * q^81 - 1447443520 * q^85 + 2381318184 * q^89 - 811245024 * q^91 - 1944906960 * q^95 + 2769662000 * q^99

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