LMFDB - Embedded newform 20.10.c.a.9.1

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			9.1
Root			$-23.7825 - 44.2040i$ of defining polynomial
Character	$\chi$	$=$	20.9
Dual form			20.10.c.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-188.155i q^{3} +(1126.30 - 827.388i) q^{5} -1842.93i q^{7} -15719.2 q^{9} +O(q^{10})$	\(q-188.155i q^{3} +(1126.30 - 827.388i) q^{5} -1842.93i q^{7} -15719.2 q^{9} -58687.7 q^{11} -19812.9i q^{13} +(-155677. - 211919. i) q^{15} -441620. i q^{17} -552947. q^{19} -346756. q^{21} +2.52050e6i q^{23} +(583984. - 1.86378e6i) q^{25} -745805. i q^{27} +5.88073e6 q^{29} +3.66966e6 q^{31} +1.10424e7i q^{33} +(-1.52482e6 - 2.07569e6i) q^{35} +5.09462e6i q^{37} -3.72790e6 q^{39} -6.04817e6 q^{41} -3.72873e7i q^{43} +(-1.77046e7 + 1.30059e7i) q^{45} -2.53334e7i q^{47} +3.69572e7 q^{49} -8.30929e7 q^{51} -6.60139e7i q^{53} +(-6.61000e7 + 4.85575e7i) q^{55} +1.04040e8i q^{57} +8.69737e7 q^{59} +1.37693e8 q^{61} +2.89694e7i q^{63} +(-1.63930e7 - 2.23153e7i) q^{65} -8.79763e7i q^{67} +4.74245e8 q^{69} -2.06862e8 q^{71} +3.67573e8i q^{73} +(-3.50678e8 - 1.09879e8i) q^{75} +1.08157e8i q^{77} +3.10242e8 q^{79} -4.49728e8 q^{81} +1.90032e8i q^{83} +(-3.65391e8 - 4.97397e8i) q^{85} -1.10649e9i q^{87} +1.15625e8 q^{89} -3.65138e7 q^{91} -6.90463e8i q^{93} +(-6.22785e8 + 4.57502e8i) q^{95} +1.45941e9i q^{97} +9.22524e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	188.155i		−	1.34113i	−0.741853	−	0.670563i	$-0.766053\pi$
$3$		−	188.155i		−	1.34113i	0.741853	−	0.670563i	$-0.233947\pi$
$4$		0			0
$5$	1126.30	−	827.388i	0.805916	−	0.592031i
$5$	1126.30	−	827.388i	0.805916	−	0.592031i
$6$		0			0
$7$		−	1842.93i		−	0.290113i	−0.989423	−	0.145057i	$-0.953664\pi$
$7$		−	1842.93i		−	0.290113i	0.989423	−	0.145057i	$-0.0463365\pi$
$8$		0			0
$9$	−15719.2			−0.798619
$10$		0			0
$11$	−58687.7			−1.20859			−0.604296	−	0.796760i	$-0.706546\pi$
$11$	−58687.7			−1.20859			−0.604296	+	0.796760i	$0.706546\pi$
$12$		0			0
$13$		−	19812.9i		−	0.192399i	−0.995362	−	0.0961996i	$-0.969331\pi$
$13$		−	19812.9i		−	0.192399i	0.995362	−	0.0961996i	$-0.0306687\pi$
$14$		0			0
$15$	−155677.	−	211919.i	−0.793988	−	1.08083i
$16$		0			0
$17$		−	441620.i		−	1.28241i	−0.767368	−	0.641207i	$-0.778434\pi$
$17$		−	441620.i		−	1.28241i	0.767368	−	0.641207i	$-0.221566\pi$
$18$		0			0
$19$	−552947.			−0.973403			−0.486701	−	0.873568i	$-0.661800\pi$
$19$	−552947.			−0.973403			−0.486701	+	0.873568i	$0.661800\pi$
$20$		0			0
$21$	−346756.			−0.389079
$22$		0			0
$23$			2.52050e6i			1.87807i	0.343821	+	0.939035i	$0.388279\pi$
$23$			2.52050e6i			1.87807i	−0.343821	+	0.939035i	$0.611721\pi$
$24$		0			0
$25$	583984.	−	1.86378e6i	0.299000	−	0.954253i
$26$		0			0
$27$		−	745805.i		−	0.270077i
$28$		0			0
$29$	5.88073e6			1.54398			0.771988	−	0.635637i	$-0.219263\pi$
$29$	5.88073e6			1.54398			0.771988	+	0.635637i	$0.219263\pi$
$30$		0			0
$31$	3.66966e6			0.713671			0.356835	−	0.934167i	$-0.383856\pi$
$31$	3.66966e6			0.713671			0.356835	+	0.934167i	$0.383856\pi$
$32$		0			0
$33$			1.10424e7i			1.62087i
$34$		0			0
$35$	−1.52482e6	−	2.07569e6i	−0.171756	−	0.233807i
$36$		0			0
$37$			5.09462e6i			0.446894i	0.974716	+	0.223447i	$0.0717309\pi$
$37$			5.09462e6i			0.446894i	−0.974716	+	0.223447i	$0.928269\pi$
$38$		0			0
$39$	−3.72790e6			−0.258032
$40$		0			0
$41$	−6.04817e6			−0.334269			−0.167135	−	0.985934i	$-0.553451\pi$
$41$	−6.04817e6			−0.334269			−0.167135	+	0.985934i	$0.553451\pi$
$42$		0			0
$43$		−	3.72873e7i		−	1.66323i	−0.555352	−	0.831615i	$-0.687417\pi$
$43$		−	3.72873e7i		−	1.66323i	0.555352	−	0.831615i	$-0.312583\pi$
$44$		0			0
$45$	−1.77046e7	+	1.30059e7i	−0.643619	+	0.472807i
$46$		0			0
$47$		−	2.53334e7i		−	0.757274i	−0.925545	−	0.378637i	$-0.876393\pi$
$47$		−	2.53334e7i		−	0.757274i	0.925545	−	0.378637i	$-0.123607\pi$
$48$		0			0
$49$	3.69572e7			0.915834
$50$		0			0
$51$	−8.30929e7			−1.71988
$52$		0			0
$53$		−	6.60139e7i		−	1.14920i	−0.818436	−	0.574598i	$-0.805158\pi$
$53$		−	6.60139e7i		−	1.14920i	0.818436	−	0.574598i	$-0.194842\pi$
$54$		0			0
$55$	−6.61000e7	+	4.85575e7i	−0.974023	+	0.715523i
$56$		0			0
$57$			1.04040e8i			1.30546i
$58$		0			0
$59$	8.69737e7			0.934446			0.467223	−	0.884140i	$-0.345255\pi$
$59$	8.69737e7			0.934446			0.467223	+	0.884140i	$0.345255\pi$
$60$		0			0
$61$	1.37693e8			1.27329			0.636644	−	0.771158i	$-0.280322\pi$
$61$	1.37693e8			1.27329			0.636644	+	0.771158i	$0.280322\pi$
$62$		0			0
$63$			2.89694e7i			0.231690i
$64$		0			0
$65$	−1.63930e7	−	2.23153e7i	−0.113906	−	0.155058i
$66$		0			0
$67$		−	8.79763e7i		−	0.533371i	−0.963784	−	0.266685i	$-0.914072\pi$
$67$		−	8.79763e7i		−	0.533371i	0.963784	−	0.266685i	$-0.0859284\pi$
$68$		0			0
$69$	4.74245e8			2.51873
$70$		0			0
$71$	−2.06862e8			−0.966092			−0.483046	−	0.875595i	$-0.660470\pi$
$71$	−2.06862e8			−0.966092			−0.483046	+	0.875595i	$0.660470\pi$
$72$		0			0
$73$			3.67573e8i			1.51492i	0.652879	+	0.757462i	$0.273561\pi$
$73$			3.67573e8i			1.51492i	−0.652879	+	0.757462i	$0.726439\pi$
$74$		0			0
$75$	−3.50678e8	−	1.09879e8i	−1.27977	−	0.400996i
$76$		0			0
$77$			1.08157e8i			0.350629i
$78$		0			0
$79$	3.10242e8			0.896146			0.448073	−	0.893997i	$-0.352110\pi$
$79$	3.10242e8			0.896146			0.448073	+	0.893997i	$0.352110\pi$
$80$		0			0
$81$	−4.49728e8			−1.16083
$82$		0			0
$83$			1.90032e8i			0.439516i	0.975554	+	0.219758i	$0.0705267\pi$
$83$			1.90032e8i			0.439516i	−0.975554	+	0.219758i	$0.929473\pi$
$84$		0			0
$85$	−3.65391e8	−	4.97397e8i	−0.759228	−	1.03352i
$86$		0			0
$87$		−	1.10649e9i		−	2.07067i
$88$		0			0
$89$	1.15625e8			0.195342			0.0976711	−	0.995219i	$-0.468861\pi$
$89$	1.15625e8			0.195342			0.0976711	+	0.995219i	$0.468861\pi$
$90$		0			0
$91$	−3.65138e7			−0.0558176
$92$		0			0
$93$		−	6.90463e8i		−	0.957122i
$94$		0			0
$95$	−6.22785e8	+	4.57502e8i	−0.784481	+	0.576284i
$96$		0			0
$97$			1.45941e9i			1.67380i	0.547354	+	0.836901i	$0.315635\pi$
$97$			1.45941e9i			1.67380i	−0.547354	+	0.836901i	$0.684365\pi$
$98$		0			0
$99$	9.22524e8			0.965205
$100$		0			0
$101$	−6.30529e8			−0.602919			−0.301460	−	0.953479i	$-0.597474\pi$
$101$	−6.30529e8			−0.602919			−0.301460	+	0.953479i	$0.597474\pi$
$102$		0			0
$103$			3.44446e8i			0.301546i	0.988568	+	0.150773i	$0.0481763\pi$
$103$			3.44446e8i			0.301546i	−0.988568	+	0.150773i	$0.951824\pi$
$104$		0			0
$105$	−3.90552e8	+	2.86902e8i	−0.313564	+	0.230346i
$106$		0			0
$107$			3.25760e8i			0.240254i	0.992759	+	0.120127i	$0.0383301\pi$
$107$			3.25760e8i			0.240254i	−0.992759	+	0.120127i	$0.961670\pi$
$108$		0			0
$109$	2.05360e9			1.39347			0.696734	−	0.717329i	$-0.254636\pi$
$109$	2.05360e9			1.39347			0.696734	+	0.717329i	$0.254636\pi$
$110$		0			0
$111$	9.58577e8			0.599341
$112$		0			0
$113$		−	2.55633e9i		−	1.47491i	−0.675399	−	0.737453i	$-0.736028\pi$
$113$		−	2.55633e9i		−	1.47491i	0.675399	−	0.737453i	$-0.263972\pi$
$114$		0			0
$115$	2.08543e9	+	2.83884e9i	1.11187	+	1.51357i
$116$		0			0
$117$			3.11444e8i			0.153654i
$118$		0			0
$119$	−8.13874e8			−0.372046
$120$		0			0
$121$	1.08629e9			0.460695
$122$		0			0
$123$			1.13799e9i			0.448297i
$124$		0			0
$125$	−8.84324e8	−	2.58235e9i	−0.323979	−	0.946064i
$126$		0			0
$127$			1.34207e8i			0.0457783i	0.999738	+	0.0228892i	$0.00728648\pi$
$127$			1.34207e8i			0.0457783i	−0.999738	+	0.0228892i	$0.992714\pi$
$128$		0			0
$129$	−7.01578e9			−2.23060
$130$		0			0
$131$	3.73647e7			0.0110851			0.00554256	−	0.999985i	$-0.498236\pi$
$131$	3.73647e7			0.0110851			0.00554256	+	0.999985i	$0.498236\pi$
$132$		0			0
$133$			1.01904e9i			0.282397i
$134$		0			0
$135$	−6.17070e8	−	8.40001e8i	−0.159894	−	0.217660i
$136$		0			0
$137$		−	2.46078e9i		−	0.596801i	−0.954441	−	0.298401i	$-0.903547\pi$
$137$		−	2.46078e9i		−	0.596801i	0.954441	−	0.298401i	$-0.0964532\pi$
$138$		0			0
$139$	3.59973e8			0.0817906			0.0408953	−	0.999163i	$-0.486979\pi$
$139$	3.59973e8			0.0817906			0.0408953	+	0.999163i	$0.486979\pi$
$140$		0			0
$141$	−4.76660e9			−1.01560
$142$		0			0
$143$			1.16277e9i			0.232532i
$144$		0			0
$145$	6.62348e9	−	4.86565e9i	1.24431	−	0.914081i
$146$		0			0
$147$		−	6.95368e9i		−	1.22825i
$148$		0			0
$149$	−7.97948e9			−1.32628			−0.663142	−	0.748494i	$-0.730777\pi$
$149$	−7.97948e9			−1.32628			−0.663142	+	0.748494i	$0.730777\pi$
$150$		0			0
$151$	8.74081e9			1.36822			0.684109	−	0.729380i	$-0.260191\pi$
$151$	8.74081e9			1.36822			0.684109	+	0.729380i	$0.260191\pi$
$152$		0			0
$153$			6.94192e9i			1.02416i
$154$		0			0
$155$	4.13314e9	−	3.03623e9i	0.575158	−	0.422515i
$156$		0			0
$157$			8.73754e9i			1.14773i	0.818949	+	0.573866i	$0.194557\pi$
$157$			8.73754e9i			1.14773i	−0.818949	+	0.573866i	$0.805443\pi$
$158$		0			0
$159$	−1.24208e10			−1.54122
$160$		0			0
$161$	4.64511e9			0.544853
$162$		0			0
$163$			5.30619e9i			0.588761i	0.955688	+	0.294380i	$0.0951133\pi$
$163$			5.30619e9i			0.588761i	−0.955688	+	0.294380i	$0.904887\pi$
$164$		0			0
$165$	9.13632e9	+	1.24370e10i	0.959607	+	1.30629i
$166$		0			0
$167$			6.84991e9i			0.681492i	0.940155	+	0.340746i	$0.110680\pi$
$167$			6.84991e9i			0.681492i	−0.940155	+	0.340746i	$0.889320\pi$
$168$		0			0
$169$	1.02119e10			0.962983
$170$		0			0
$171$	8.69190e9			0.777378
$172$		0			0
$173$		−	8.17341e9i		−	0.693739i	−0.937913	−	0.346869i	$-0.887245\pi$
$173$		−	8.17341e9i		−	0.693739i	0.937913	−	0.346869i	$-0.112755\pi$
$174$		0			0
$175$	−3.43481e9	−	1.07624e9i	−0.276842	−	0.0867438i
$176$		0			0
$177$		−	1.63645e10i		−	1.25321i
$178$		0			0
$179$	−9.91356e9			−0.721757			−0.360878	−	0.932613i	$-0.617523\pi$
$179$	−9.91356e9			−0.721757			−0.360878	+	0.932613i	$0.617523\pi$
$180$		0			0
$181$	5.69791e9			0.394604			0.197302	−	0.980343i	$-0.436782\pi$
$181$	5.69791e9			0.394604			0.197302	+	0.980343i	$0.436782\pi$
$182$		0			0
$183$		−	2.59076e10i		−	1.70764i
$184$		0			0
$185$	4.21523e9	+	5.73808e9i	0.264575	+	0.360158i
$186$		0			0
$187$			2.59176e10i			1.54992i
$188$		0			0
$189$	−1.37447e9			−0.0783531
$190$		0			0
$191$	−2.82674e10			−1.53686			−0.768432	−	0.639932i	$-0.778963\pi$
$191$	−2.82674e10			−1.53686			−0.768432	+	0.639932i	$0.778963\pi$
$192$		0			0
$193$		−	6.05667e9i		−	0.314214i	−0.987582	−	0.157107i	$-0.949783\pi$
$193$		−	6.05667e9i		−	0.314214i	0.987582	−	0.157107i	$-0.0502168\pi$
$194$		0			0
$195$	−4.19873e9	+	3.08442e9i	−0.207952	+	0.152763i
$196$		0			0
$197$			9.75345e8i			0.0461382i	0.999734	+	0.0230691i	$0.00734377\pi$
$197$			9.75345e8i			0.0461382i	−0.999734	+	0.0230691i	$0.992656\pi$
$198$		0			0
$199$	−2.82478e10			−1.27687			−0.638435	−	0.769676i	$-0.720418\pi$
$199$	−2.82478e10			−1.27687			−0.638435	+	0.769676i	$0.720418\pi$
$200$		0			0
$201$	−1.65532e10			−0.715317
$202$		0			0
$203$		−	1.08378e10i		−	0.447928i
$204$		0			0
$205$	−6.81206e9	+	5.00418e9i	−0.269393	+	0.197898i
$206$		0			0
$207$		−	3.96203e10i		−	1.49986i
$208$		0			0
$209$	3.24512e10			1.17645
$210$		0			0
$211$	2.64129e10			0.917373			0.458686	−	0.888598i	$-0.348320\pi$
$211$	2.64129e10			0.917373			0.458686	+	0.888598i	$0.348320\pi$
$212$		0			0
$213$			3.89221e10i			1.29565i
$214$		0			0
$215$	−3.08510e10	−	4.19967e10i	−0.984683	−	1.34042i
$216$		0			0
$217$		−	6.76292e9i		−	0.207045i
$218$		0			0
$219$	6.91606e10			2.03170
$220$		0			0
$221$	−8.74978e9			−0.246736
$222$		0			0
$223$			1.25292e10i			0.339274i	0.985507	+	0.169637i	$0.0542595\pi$
$223$			1.25292e10i			0.339274i	−0.985507	+	0.169637i	$0.945740\pi$
$224$		0			0
$225$	−9.17977e9	+	2.92971e10i	−0.238787	+	0.762085i
$226$		0			0
$227$			6.59658e10i			1.64893i	0.565912	+	0.824466i	$0.308524\pi$
$227$			6.59658e10i			1.64893i	−0.565912	+	0.824466i	$0.691476\pi$
$228$		0			0
$229$	3.65823e10			0.879045			0.439523	−	0.898232i	$-0.355148\pi$
$229$	3.65823e10			0.879045			0.439523	+	0.898232i	$0.355148\pi$
$230$		0			0
$231$	2.03503e10			0.470237
$232$		0			0
$233$			6.54654e10i			1.45516i	0.686024	+	0.727579i	$0.259355\pi$
$233$			6.54654e10i			1.45516i	−0.686024	+	0.727579i	$0.740645\pi$
$234$		0			0
$235$	−2.09605e10	−	2.85330e10i	−0.448329	−	0.610299i
$236$		0			0
$237$		−	5.83735e10i		−	1.20185i
$238$		0			0
$239$	3.29696e10			0.653617			0.326808	−	0.945091i	$-0.394027\pi$
$239$	3.29696e10			0.653617			0.326808	+	0.945091i	$0.394027\pi$
$240$		0			0
$241$	−9.94835e10			−1.89965			−0.949827	−	0.312776i	$-0.898741\pi$
$241$	−9.94835e10			−1.89965			−0.949827	+	0.312776i	$0.898741\pi$
$242$		0			0
$243$			6.99388e10i			1.28674i
$244$		0			0
$245$	4.16250e10	−	3.05779e10i	0.738085	−	0.542202i
$246$		0			0
$247$			1.09555e10i			0.187282i
$248$		0			0
$249$	3.57553e10			0.589446
$250$		0			0
$251$	9.05591e10			1.44013			0.720063	−	0.693909i	$-0.244113\pi$
$251$	9.05591e10			1.44013			0.720063	+	0.693909i	$0.244113\pi$
$252$		0			0
$253$		−	1.47922e11i		−	2.26982i
$254$		0			0
$255$	−9.35876e10	+	6.87500e10i	−1.38608	+	1.01822i
$256$		0			0
$257$			5.83373e9i			0.0834156i	0.999130	+	0.0417078i	$0.0132799\pi$
$257$			5.83373e9i			0.0834156i	−0.999130	+	0.0417078i	$0.986720\pi$
$258$		0			0
$259$	9.38903e9			0.129650
$260$		0			0
$261$	−9.24405e10			−1.23305
$262$		0			0
$263$		−	9.07339e10i		−	1.16941i	−0.811244	−	0.584707i	$-0.801209\pi$
$263$		−	9.07339e10i		−	1.16941i	0.811244	−	0.584707i	$-0.198791\pi$
$264$		0			0
$265$	−5.46191e10	−	7.43515e10i	−0.680359	−	0.926155i
$266$		0			0
$267$		−	2.17554e10i		−	0.261979i
$268$		0			0
$269$	4.21890e9			0.0491263			0.0245631	−	0.999698i	$-0.492181\pi$
$269$	4.21890e9			0.0491263			0.0245631	+	0.999698i	$0.492181\pi$
$270$		0			0
$271$	−5.49788e10			−0.619203			−0.309602	−	0.950866i	$-0.600196\pi$
$271$	−5.49788e10			−0.619203			−0.309602	+	0.950866i	$0.600196\pi$
$272$		0			0
$273$			6.87025e9i			0.0748584i
$274$		0			0
$275$	−3.42726e10	+	1.09381e11i	−0.361369	+	1.15330i
$276$		0			0
$277$			3.45141e10i			0.352239i	0.984369	+	0.176119i	$0.0563545\pi$
$277$			3.45141e10i			0.352239i	−0.984369	+	0.176119i	$0.943645\pi$
$278$		0			0
$279$	−5.76841e10			−0.569951
$280$		0			0
$281$	−5.52698e10			−0.528822			−0.264411	−	0.964410i	$-0.585178\pi$
$281$	−5.52698e10			−0.528822			−0.264411	+	0.964410i	$0.585178\pi$
$282$		0			0
$283$		−	2.91278e10i		−	0.269941i	−0.990850	−	0.134970i	$-0.956906\pi$
$283$		−	2.91278e10i		−	0.269941i	0.990850	−	0.134970i	$-0.0430939\pi$
$284$		0			0
$285$	8.60812e10	+	1.17180e11i	0.772870	+	1.05209i
$286$		0			0
$287$			1.11464e10i			0.0969760i
$288$		0			0
$289$	−7.64401e10			−0.644586
$290$		0			0
$291$	2.74595e11			2.24478
$292$		0			0
$293$		−	1.14477e11i		−	0.907431i	−0.891147	−	0.453715i	$-0.850098\pi$
$293$		−	1.14477e11i		−	0.907431i	0.891147	−	0.453715i	$-0.149902\pi$
$294$		0			0
$295$	9.79586e10	−	7.19610e10i	0.753084	−	0.553220i
$296$		0			0
$297$			4.37695e10i			0.326413i
$298$		0			0
$299$	4.99385e10			0.361339
$300$		0			0
$301$	−6.87178e10			−0.482525
$302$		0			0
$303$			1.18637e11i			0.808591i
$304$		0			0
$305$	1.55084e11	−	1.13925e11i	1.02616	−	0.753826i
$306$		0			0
$307$		−	6.34523e10i		−	0.407685i	−0.979004	−	0.203842i	$-0.934657\pi$
$307$		−	6.34523e10i		−	0.407685i	0.979004	−	0.203842i	$-0.0653430\pi$
$308$		0			0
$309$	6.48092e10			0.404411
$310$		0			0
$311$	6.86415e10			0.416069			0.208034	−	0.978122i	$-0.433293\pi$
$311$	6.86415e10			0.416069			0.208034	+	0.978122i	$0.433293\pi$
$312$		0			0
$313$			2.15640e11i			1.26993i	0.772540	+	0.634966i	$0.218986\pi$
$313$			2.15640e11i			1.26993i	−0.772540	+	0.634966i	$0.781014\pi$
$314$		0			0
$315$	2.39689e10	+	3.26283e10i	0.137168	+	0.186723i
$316$		0			0
$317$			2.99385e11i			1.66519i	0.553884	+	0.832594i	$0.313145\pi$
$317$			2.99385e11i			1.66519i	−0.553884	+	0.832594i	$0.686855\pi$
$318$		0			0
$319$	−3.45127e11			−1.86604
$320$		0			0
$321$	6.12932e10			0.322211
$322$		0			0
$323$			2.44192e11i			1.24831i
$324$		0			0
$325$	−3.69268e10	−	1.15704e10i	−0.183598	−	0.0575273i
$326$		0			0
$327$		−	3.86395e11i		−	1.86882i
$328$		0			0
$329$	−4.66877e10			−0.219695
$330$		0			0
$331$	2.04772e11			0.937658			0.468829	−	0.883289i	$-0.344676\pi$
$331$	2.04772e11			0.937658			0.468829	+	0.883289i	$0.344676\pi$
$332$		0			0
$333$		−	8.00834e10i		−	0.356898i
$334$		0			0
$335$	−7.27905e10	−	9.90878e10i	−0.315772	−	0.429852i
$336$		0			0
$337$		−	1.05174e11i		−	0.444194i	−0.975025	−	0.222097i	$-0.928710\pi$
$337$		−	1.05174e11i		−	0.444194i	0.975025	−	0.222097i	$-0.0712902\pi$
$338$		0			0
$339$	−4.80986e11			−1.97803
$340$		0			0
$341$	−2.15364e11			−0.862537
$342$		0			0
$343$		−	1.42478e11i		−	0.555809i
$344$		0			0
$345$	5.34142e11	−	3.92384e11i	2.02988	−	1.49116i
$346$		0			0
$347$		−	2.10458e11i		−	0.779261i	−0.920971	−	0.389631i	$-0.872603\pi$
$347$		−	2.10458e11i		−	0.779261i	0.920971	−	0.389631i	$-0.127397\pi$
$348$		0			0
$349$	−1.04455e11			−0.376890			−0.188445	−	0.982084i	$-0.560345\pi$
$349$	−1.04455e11			−0.376890			−0.188445	+	0.982084i	$0.560345\pi$
$350$		0			0
$351$	−1.47766e10			−0.0519627
$352$		0			0
$353$			9.02740e10i			0.309440i	0.987958	+	0.154720i	$0.0494476\pi$
$353$			9.02740e10i			0.309440i	−0.987958	+	0.154720i	$0.950552\pi$
$354$		0			0
$355$	−2.32989e11	+	1.71155e11i	−0.778588	+	0.571956i
$356$		0			0
$357$			1.53134e11i			0.498960i
$358$		0			0
$359$	−2.54941e11			−0.810056			−0.405028	−	0.914304i	$-0.632738\pi$
$359$	−2.54941e11			−0.810056			−0.405028	+	0.914304i	$0.632738\pi$
$360$		0			0
$361$	−1.69368e10			−0.0524868
$362$		0			0
$363$		−	2.04391e11i		−	0.617850i
$364$		0			0
$365$	3.04125e11	+	4.13998e11i	0.896881	+	1.22090i
$366$		0			0
$367$			3.05066e11i			0.877801i	0.898536	+	0.438901i	$0.144632\pi$
$367$			3.05066e11i			0.877801i	−0.898536	+	0.438901i	$0.855368\pi$
$368$		0			0
$369$	9.50725e10			0.266954
$370$		0			0
$371$	−1.21659e11			−0.333397
$372$		0			0
$373$		−	1.57715e11i		−	0.421875i	−0.977500	−	0.210938i	$-0.932348\pi$
$373$		−	1.57715e11i		−	0.421875i	0.977500	−	0.210938i	$-0.0676517\pi$
$374$		0			0
$375$	−4.85882e11	+	1.66390e11i	−1.26879	+	0.434496i
$376$		0			0
$377$		−	1.16515e11i		−	0.297060i
$378$		0			0
$379$	4.75272e11			1.18322			0.591610	−	0.806224i	$-0.298493\pi$
$379$	4.75272e11			1.18322			0.591610	+	0.806224i	$0.298493\pi$
$380$		0			0
$381$	2.52518e10			0.0613945
$382$		0			0
$383$		−	2.80869e11i		−	0.666975i	−0.942754	−	0.333488i	$-0.891774\pi$
$383$		−	2.80869e11i		−	0.666975i	0.942754	−	0.333488i	$-0.108226\pi$
$384$		0			0
$385$	8.94880e10	+	1.21818e11i	0.207583	+	0.282577i
$386$		0			0
$387$			5.86126e11i			1.32829i
$388$		0			0
$389$	3.63528e11			0.804942			0.402471	−	0.915433i	$-0.368151\pi$
$389$	3.63528e11			0.804942			0.402471	+	0.915433i	$0.368151\pi$
$390$		0			0
$391$	1.11310e12			2.40846
$392$		0			0
$393$		−	7.03034e9i		−	0.0148665i
$394$		0			0
$395$	3.49426e11	−	2.56691e11i	0.722218	−	0.530546i
$396$		0			0
$397$			1.34475e11i			0.271696i	0.990730	+	0.135848i	$0.0433759\pi$
$397$			1.34475e11i			0.271696i	−0.990730	+	0.135848i	$0.956624\pi$
$398$		0			0
$399$	1.91738e11			0.378730
$400$		0			0
$401$	−4.64233e11			−0.896574			−0.448287	−	0.893890i	$-0.647966\pi$
$401$	−4.64233e11			−0.896574			−0.448287	+	0.893890i	$0.647966\pi$
$402$		0			0
$403$		−	7.27066e10i		−	0.137310i
$404$		0			0
$405$	−5.06529e11	+	3.72100e11i	−0.935528	+	0.687245i
$406$		0			0
$407$		−	2.98991e11i		−	0.540112i
$408$		0			0
$409$	1.95309e11			0.345118			0.172559	−	0.984999i	$-0.444797\pi$
$409$	1.95309e11			0.345118			0.172559	+	0.984999i	$0.444797\pi$
$410$		0			0
$411$	−4.63007e11			−0.800386
$412$		0			0
$413$		−	1.60287e11i		−	0.271095i
$414$		0			0
$415$	1.57230e11	+	2.14033e11i	0.260207	+	0.354212i
$416$		0			0
$417$		−	6.77307e10i		−	0.109692i
$418$		0			0
$419$	3.51860e10			0.0557707			0.0278854	−	0.999611i	$-0.491123\pi$
$419$	3.51860e10			0.0557707			0.0278854	+	0.999611i	$0.491123\pi$
$420$		0			0
$421$	−5.23732e11			−0.812531			−0.406265	−	0.913755i	$-0.633169\pi$
$421$	−5.23732e11			−0.812531			−0.406265	+	0.913755i	$0.633169\pi$
$422$		0			0
$423$			3.98221e11i			0.604773i
$424$		0			0
$425$	−8.23080e11	−	2.57899e11i	−1.22375	−	0.383441i
$426$		0			0
$427$		−	2.53758e11i		−	0.369398i
$428$		0			0
$429$	2.18782e11			0.311855
$430$		0			0
$431$	−6.86873e11			−0.958801			−0.479401	−	0.877596i	$-0.659146\pi$
$431$	−6.86873e11			−0.958801			−0.479401	+	0.877596i	$0.659146\pi$
$432$		0			0
$433$			1.29950e12i			1.77657i	0.459293	+	0.888285i	$0.348103\pi$
$433$			1.29950e12i			1.77657i	−0.459293	+	0.888285i	$0.651897\pi$
$434$		0			0
$435$	−9.15495e11	−	1.24624e12i	−1.22590	−	1.66878i
$436$		0			0
$437$		−	1.39371e12i		−	1.82812i
$438$		0			0
$439$	1.30167e12			1.67266			0.836332	−	0.548223i	$-0.184695\pi$
$439$	1.30167e12			1.67266			0.836332	+	0.548223i	$0.184695\pi$
$440$		0			0
$441$	−5.80938e11			−0.731403
$442$		0			0
$443$		−	3.13418e11i		−	0.386641i	−0.981136	−	0.193320i	$-0.938074\pi$
$443$		−	3.13418e11i		−	0.386641i	0.981136	−	0.193320i	$-0.0619257\pi$
$444$		0			0
$445$	1.30228e11	−	9.56666e10i	0.157429	−	0.115649i
$446$		0			0
$447$			1.50138e12i			1.77871i
$448$		0			0
$449$	4.21433e11			0.489351			0.244675	−	0.969605i	$-0.421319\pi$
$449$	4.21433e11			0.489351			0.244675	+	0.969605i	$0.421319\pi$
$450$		0			0
$451$	3.54953e11			0.403995
$452$		0			0
$453$		−	1.64463e12i		−	1.83495i
$454$		0			0
$455$	−4.11256e10	+	3.02111e10i	−0.0449843	+	0.0330457i
$456$		0			0
$457$		−	1.61183e12i		−	1.72861i	−0.502971	−	0.864303i	$-0.667760\pi$
$457$		−	1.61183e12i		−	1.72861i	0.502971	−	0.864303i	$-0.332240\pi$
$458$		0			0
$459$	−3.29362e11			−0.346351
$460$		0			0
$461$	−2.34519e11			−0.241837			−0.120919	−	0.992662i	$-0.538584\pi$
$461$	−2.34519e11			−0.241837			−0.120919	+	0.992662i	$0.538584\pi$
$462$		0			0
$463$			1.72872e12i			1.74827i	0.485680	+	0.874137i	$0.338572\pi$
$463$			1.72872e12i			1.74827i	−0.485680	+	0.874137i	$0.661428\pi$
$464$		0			0
$465$	−5.71281e11	−	7.77670e11i	−0.566646	−	0.771360i
$466$		0			0
$467$			5.72990e11i			0.557470i	0.960368	+	0.278735i	$0.0899150\pi$
$467$			5.72990e11i			0.557470i	−0.960368	+	0.278735i	$0.910085\pi$
$468$		0			0
$469$	−1.62134e11			−0.154738
$470$		0			0
$471$	1.64401e12			1.53925
$472$		0			0
$473$			2.18830e12i			2.01017i
$474$		0			0
$475$	−3.22912e11	+	1.03057e12i	−0.291047	+	0.928873i
$476$		0			0
$477$			1.03769e12i			0.917769i
$478$		0			0
$479$	7.01933e11			0.609236			0.304618	−	0.952475i	$-0.401471\pi$
$479$	7.01933e11			0.609236			0.304618	+	0.952475i	$0.401471\pi$
$480$		0			0
$481$	1.00939e11			0.0859820
$482$		0			0
$483$		−	8.74000e11i		−	0.730717i
$484$		0			0
$485$	1.20750e12	+	1.64373e12i	0.990942	+	1.34894i
$486$		0			0
$487$			1.04358e12i			0.840712i	0.907359	+	0.420356i	$0.138095\pi$
$487$			1.04358e12i			0.840712i	−0.907359	+	0.420356i	$0.861905\pi$
$488$		0			0
$489$	9.98386e11			0.789602
$490$		0			0
$491$	−1.91907e12			−1.49013			−0.745065	−	0.666992i	$-0.767581\pi$
$491$	−1.91907e12			−1.49013			−0.745065	+	0.666992i	$0.767581\pi$
$492$		0			0
$493$		−	2.59705e12i		−	1.98002i
$494$		0			0
$495$	1.03904e12	−	7.63285e11i	0.777873	−	0.571431i
$496$		0			0
$497$			3.81232e11i			0.280276i
$498$		0			0
$499$	4.00463e11			0.289141			0.144571	−	0.989494i	$-0.453820\pi$
$499$	4.00463e11			0.289141			0.144571	+	0.989494i	$0.453820\pi$
$500$		0			0
$501$	1.28884e12			0.913966
$502$		0			0
$503$		−	1.53132e12i		−	1.06662i	−0.845919	−	0.533312i	$-0.820947\pi$
$503$		−	1.53132e12i		−	1.06662i	0.845919	−	0.533312i	$-0.179053\pi$
$504$		0			0
$505$	−7.10166e11	+	5.21692e11i	−0.485902	+	0.356947i
$506$		0			0
$507$		−	1.92143e12i		−	1.29148i
$508$		0			0
$509$	−2.82535e11			−0.186570			−0.0932852	−	0.995639i	$-0.529737\pi$
$509$	−2.82535e11			−0.186570			−0.0932852	+	0.995639i	$0.529737\pi$
$510$		0			0
$511$	6.77411e11			0.439500
$512$		0			0
$513$			4.12391e11i			0.262894i
$514$		0			0
$515$	2.84991e11	+	3.87950e11i	0.178525	+	0.243021i
$516$		0			0
$517$			1.48676e12i			0.915235i
$518$		0			0
$519$	−1.53787e12			−0.930391
$520$		0			0
$521$	4.50184e9			0.00267683			0.00133841	−	0.999999i	$-0.499574\pi$
$521$	4.50184e9			0.00267683			0.00133841	+	0.999999i	$0.499574\pi$
$522$		0			0
$523$		−	3.73385e11i		−	0.218222i	−0.994030	−	0.109111i	$-0.965200\pi$
$523$		−	3.73385e11i		−	0.218222i	0.994030	−	0.109111i	$-0.0348005\pi$
$524$		0			0
$525$	−2.02500e11	+	6.46276e11i	−0.116334	+	0.371279i
$526$		0			0
$527$		−	1.62059e12i		−	0.915221i
$528$		0			0
$529$	−4.55178e12			−2.52715
$530$		0			0
$531$	−1.36716e12			−0.746266
$532$		0			0
$533$			1.19832e11i			0.0643132i
$534$		0			0
$535$	2.69529e11	+	3.66903e11i	0.142238	+	0.193624i
$536$		0			0
$537$			1.86528e12i			0.967967i
$538$		0			0
$539$	−2.16893e12			−1.10687
$540$		0			0
$541$	2.33700e12			1.17293			0.586463	−	0.809976i	$-0.300520\pi$
$541$	2.33700e12			1.17293			0.586463	+	0.809976i	$0.300520\pi$
$542$		0			0
$543$		−	1.07209e12i		−	0.529214i
$544$		0			0
$545$	2.31298e12	−	1.69913e12i	1.12302	−	0.824976i
$546$		0			0
$547$		−	1.55115e12i		−	0.740816i	−0.928869	−	0.370408i	$-0.879218\pi$
$547$		−	1.55115e12i		−	0.740816i	0.928869	−	0.370408i	$-0.120782\pi$
$548$		0			0
$549$	−2.16442e12			−1.01687
$550$		0			0
$551$	−3.25174e12			−1.50291
$552$		0			0
$553$		−	5.71755e11i		−	0.259984i
$554$		0			0
$555$	1.07965e12	−	7.93115e11i	0.483018	−	0.354828i
$556$		0			0
$557$		−	2.76579e11i		−	0.121751i	−0.998145	−	0.0608753i	$-0.980611\pi$
$557$		−	2.76579e11i		−	0.121751i	0.998145	−	0.0608753i	$-0.0193892\pi$
$558$		0			0
$559$	−7.38770e11			−0.320004
$560$		0			0
$561$	4.87653e12			2.07863
$562$		0			0
$563$			1.30073e12i			0.545631i	0.962066	+	0.272816i	$0.0879549\pi$
$563$			1.30073e12i			0.545631i	−0.962066	+	0.272816i	$0.912045\pi$
$564$		0			0
$565$	−2.11508e12	−	2.87920e12i	−0.873189	−	1.18865i
$566$		0			0
$567$			8.28818e11i			0.336771i
$568$		0			0
$569$	4.56895e12			1.82731			0.913653	−	0.406496i	$-0.133250\pi$
$569$	4.56895e12			1.82731			0.913653	+	0.406496i	$0.133250\pi$
$570$		0			0
$571$	−7.75928e11			−0.305463			−0.152732	−	0.988268i	$-0.548807\pi$
$571$	−7.75928e11			−0.305463			−0.152732	+	0.988268i	$0.548807\pi$
$572$		0			0
$573$			5.31864e12i			2.06113i
$574$		0			0
$575$	4.69765e12	+	1.47193e12i	1.79215	+	0.561542i
$576$		0			0
$577$		−	3.72103e12i		−	1.39757i	−0.715334	−	0.698783i	$-0.753725\pi$
$577$		−	3.72103e12i		−	1.39757i	0.715334	−	0.698783i	$-0.246275\pi$
$578$		0			0
$579$	−1.13959e12			−0.421401
$580$		0			0
$581$	3.50215e11			0.127509
$582$		0			0
$583$			3.87420e12i			1.38891i
$584$		0			0
$585$	2.57685e11	+	3.50779e11i	0.0909677	+	0.123832i
$586$		0			0
$587$			5.04485e11i			0.175379i	0.996148	+	0.0876894i	$0.0279483\pi$
$587$			5.04485e11i			0.175379i	−0.996148	+	0.0876894i	$0.972052\pi$
$588$		0			0
$589$	−2.02913e12			−0.694689
$590$		0			0
$591$	1.83516e11			0.0618771
$592$		0			0
$593$		−	1.16228e12i		−	0.385981i	−0.981201	−	0.192991i	$-0.938181\pi$
$593$		−	1.16228e12i		−	0.385981i	0.981201	−	0.192991i	$-0.0618187\pi$
$594$		0			0
$595$	−9.16668e11	+	6.73390e11i	−0.299837	+	0.220262i
$596$		0			0
$597$			5.31497e12i			1.71244i
$598$		0			0
$599$	6.20211e10			0.0196843			0.00984213	−	0.999952i	$-0.496867\pi$
$599$	6.20211e10			0.0196843			0.00984213	+	0.999952i	$0.496867\pi$
$600$		0			0
$601$	2.64220e12			0.826096			0.413048	−	0.910709i	$-0.364464\pi$
$601$	2.64220e12			0.826096			0.413048	+	0.910709i	$0.364464\pi$
$602$		0			0
$603$			1.38292e12i			0.425960i
$604$		0			0
$605$	1.22349e12	−	8.98786e11i	0.371281	−	0.272745i
$606$		0			0
$607$		−	3.49167e12i		−	1.04396i	−0.852958	−	0.521980i	$-0.825194\pi$
$607$		−	3.49167e12i		−	1.04396i	0.852958	−	0.521980i	$-0.174806\pi$
$608$		0			0
$609$	−2.03918e12			−0.600728
$610$		0			0
$611$	−5.01929e11			−0.145699
$612$		0			0
$613$		−	3.01588e12i		−	0.862663i	−0.902193	−	0.431332i	$-0.858044\pi$
$613$		−	3.01588e12i		−	0.862663i	0.902193	−	0.431332i	$-0.141956\pi$
$614$		0			0
$615$	9.41561e11	+	1.28172e12i	0.265406	+	0.361290i
$616$		0			0
$617$			4.97051e12i			1.38076i	0.723448	+	0.690379i	$0.242556\pi$
$617$			4.97051e12i			1.38076i	−0.723448	+	0.690379i	$0.757444\pi$
$618$		0			0
$619$	6.20604e11			0.169905			0.0849526	−	0.996385i	$-0.472926\pi$
$619$	6.20604e11			0.169905			0.0849526	+	0.996385i	$0.472926\pi$
$620$		0			0
$621$	1.87980e12			0.507224
$622$		0			0
$623$		−	2.13089e11i		−	0.0566714i
$624$		0			0
$625$	−3.13262e12	−	2.17683e12i	−0.821198	−	0.570643i
$626$		0			0
$627$		−	6.10585e12i		−	1.57776i
$628$		0			0
$629$	2.24988e12			0.573103
$630$		0			0
$631$	−3.69271e11			−0.0927285			−0.0463643	−	0.998925i	$-0.514763\pi$
$631$	−3.69271e11			−0.0927285			−0.0463643	+	0.998925i	$0.514763\pi$
$632$		0			0
$633$		−	4.96972e12i		−	1.23031i
$634$		0			0
$635$	1.11042e11	+	1.51158e11i	0.0271022	+	0.0368935i
$636$		0			0
$637$		−	7.32230e11i		−	0.176206i
$638$		0			0
$639$	3.25171e12			0.771539
$640$		0			0
$641$	−7.69788e12			−1.80099			−0.900493	−	0.434871i	$-0.856794\pi$
$641$	−7.69788e12			−1.80099			−0.900493	+	0.434871i	$0.856794\pi$
$642$		0			0
$643$		−	7.32108e12i		−	1.68898i	−0.535568	−	0.844492i	$-0.679902\pi$
$643$		−	7.32108e12i		−	1.68898i	0.535568	−	0.844492i	$-0.320098\pi$
$644$		0			0
$645$	−7.90188e12	+	5.80477e12i	−1.79768	+	1.32058i
$646$		0			0
$647$			3.74864e12i			0.841016i	0.907289	+	0.420508i	$0.138148\pi$
$647$			3.74864e12i			0.841016i	−0.907289	+	0.420508i	$0.861852\pi$
$648$		0			0
$649$	−5.10428e12			−1.12936
$650$		0			0
$651$	−1.27248e12			−0.277674
$652$		0			0
$653$		−	2.66003e12i		−	0.572502i	−0.958155	−	0.286251i	$-0.907591\pi$
$653$		−	2.66003e12i		−	0.572502i	0.958155	−	0.286251i	$-0.0924091\pi$
$654$		0			0
$655$	4.20839e10	−	3.09151e10i	0.00893367	−	0.00656273i
$656$		0			0
$657$		−	5.77796e12i		−	1.20985i
$658$		0			0
$659$	9.46909e12			1.95580			0.977899	−	0.209078i	$-0.0670464\pi$
$659$	9.46909e12			1.95580			0.977899	+	0.209078i	$0.0670464\pi$
$660$		0			0
$661$	−5.79426e12			−1.18057			−0.590285	−	0.807195i	$-0.700985\pi$
$661$	−5.79426e12			−1.18057			−0.590285	+	0.807195i	$0.700985\pi$
$662$		0			0
$663$			1.64631e12i			0.330904i
$664$		0			0
$665$	8.43144e11	+	1.14775e12i	0.167188	+	0.227588i
$666$		0			0
$667$			1.48224e13i			2.89970i
$668$		0			0
$669$	2.35742e12			0.455009
$670$		0			0
$671$	−8.08087e12			−1.53889
$672$		0			0
$673$			2.65650e12i			0.499162i	0.968354	+	0.249581i	$0.0802929\pi$
$673$			2.65650e12i			0.499162i	−0.968354	+	0.249581i	$0.919707\pi$
$674$		0			0
$675$	−1.39001e12	−	4.35538e11i	−0.257722	−	0.0807531i
$676$		0			0
$677$		−	5.35485e12i		−	0.979712i	−0.871803	−	0.489856i	$-0.837049\pi$
$677$		−	5.35485e12i		−	0.979712i	0.871803	−	0.489856i	$-0.162951\pi$
$678$		0			0
$679$	2.68959e12			0.485592
$680$		0			0
$681$	1.24118e13			2.21143
$682$		0			0
$683$			2.74093e12i			0.481953i	0.970531	+	0.240977i	$0.0774677\pi$
$683$			2.74093e12i			0.481953i	−0.970531	+	0.240977i	$0.922532\pi$
$684$		0			0
$685$	−2.03602e12	−	2.77158e12i	−0.353325	−	0.480972i
$686$		0			0
$687$		−	6.88313e12i		−	1.17891i
$688$		0			0
$689$	−1.30793e12			−0.221104
$690$		0			0
$691$	5.36975e12			0.895989			0.447994	−	0.894036i	$-0.352138\pi$
$691$	5.36975e12			0.895989			0.447994	+	0.894036i	$0.352138\pi$
$692$		0			0
$693$		−	1.70015e12i		−	0.280019i
$694$		0			0
$695$	4.05438e11	−	2.97837e11i	0.0659163	−	0.0484225i
$696$		0			0
$697$			2.67099e12i			0.428672i
$698$		0			0
$699$	1.23176e13			1.95155
$700$		0			0
$701$	4.34190e12			0.679124			0.339562	−	0.940584i	$-0.389721\pi$
$701$	4.34190e12			0.679124			0.339562	+	0.940584i	$0.389721\pi$
$702$		0			0
$703$		−	2.81706e12i		−	0.435007i
$704$		0			0
$705$	−5.36863e12	+	3.94383e12i	−0.818488	+	0.601266i
$706$		0			0
$707$			1.16202e12i			0.174915i
$708$		0			0
$709$	7.02227e12			1.04368			0.521842	−	0.853042i	$-0.325245\pi$
$709$	7.02227e12			1.04368			0.521842	+	0.853042i	$0.325245\pi$
$710$		0			0
$711$	−4.87676e12			−0.715679
$712$		0			0
$713$			9.24938e12i			1.34032i
$714$		0			0
$715$	9.62065e11	+	1.30963e12i	0.137666	+	0.187401i
$716$		0			0
$717$		−	6.20339e12i		−	0.876582i
$718$		0			0
$719$	−3.58416e12			−0.500158			−0.250079	−	0.968225i	$-0.580457\pi$
$719$	−3.58416e12			−0.500158			−0.250079	+	0.968225i	$0.580457\pi$
$720$		0			0
$721$	6.34790e11			0.0874826
$722$		0			0
$723$			1.87183e13i			2.54768i
$724$		0			0
$725$	3.43425e12	−	1.09604e13i	0.461648	−	1.47334i
$726$		0			0
$727$			7.05682e12i			0.936923i	0.883484	+	0.468462i	$0.155192\pi$
$727$			7.05682e12i			0.936923i	−0.883484	+	0.468462i	$0.844808\pi$
$728$		0			0
$729$	4.30732e12			0.564850
$730$		0			0
$731$	−1.64668e13			−2.13295
$732$		0			0
$733$			1.16741e13i			1.49367i	0.665011	+	0.746834i	$0.268427\pi$
$733$			1.16741e13i			1.49367i	−0.665011	+	0.746834i	$0.731573\pi$
$734$		0			0
$735$	−5.75339e12	−	7.83193e12i	−0.727161	−	0.989865i
$736$		0			0
$737$			5.16312e12i			0.644628i
$738$		0			0
$739$	4.07617e12			0.502750			0.251375	−	0.967890i	$-0.419117\pi$
$739$	4.07617e12			0.502750			0.251375	+	0.967890i	$0.419117\pi$
$740$		0			0
$741$	2.06133e12			0.251169
$742$		0			0
$743$		−	1.51290e13i		−	1.82122i	−0.413272	−	0.910608i	$-0.635614\pi$
$743$		−	1.51290e13i		−	1.82122i	0.413272	−	0.910608i	$-0.364386\pi$
$744$		0			0
$745$	−8.98730e12	+	6.60212e12i	−1.06887	+	0.785200i
$746$		0			0
$747$		−	2.98715e12i		−	0.351005i
$748$		0			0
$749$	6.00352e11			0.0697008
$750$		0			0
$751$	1.23964e13			1.42206			0.711029	−	0.703163i	$-0.248230\pi$
$751$	1.23964e13			1.42206			0.711029	+	0.703163i	$0.248230\pi$
$752$		0			0
$753$		−	1.70391e13i		−	1.93139i
$754$		0			0
$755$	9.84479e12	−	7.23204e12i	1.10267	−	0.810027i
$756$		0			0
$757$		−	1.65042e13i		−	1.82668i	−0.407201	−	0.913339i	$-0.633495\pi$
$757$		−	1.65042e13i		−	1.82668i	0.407201	−	0.913339i	$-0.366505\pi$
$758$		0			0
$759$	−2.78323e13			−3.04412
$760$		0			0
$761$	−1.47905e13			−1.59864			−0.799322	−	0.600903i	$-0.794808\pi$
$761$	−1.47905e13			−1.59864			−0.799322	+	0.600903i	$0.794808\pi$
$762$		0			0
$763$		−	3.78465e12i		−	0.404264i
$764$		0			0
$765$	5.74366e12	+	7.81869e12i	0.606334	+	0.825387i
$766$		0			0
$767$		−	1.72320e12i		−	0.179787i
$768$		0			0
$769$	8.11012e11			0.0836293			0.0418147	−	0.999125i	$-0.486686\pi$
$769$	8.11012e11			0.0836293			0.0418147	+	0.999125i	$0.486686\pi$
$770$		0			0
$771$	1.09764e12			0.111871
$772$		0			0
$773$			1.12570e13i			1.13400i	0.823717	+	0.567001i	$0.191896\pi$
$773$			1.12570e13i			1.13400i	−0.823717	+	0.567001i	$0.808104\pi$
$774$		0			0
$775$	2.14302e12	−	6.83942e12i	0.213387	−	0.681022i
$776$		0			0
$777$		−	1.76659e12i		−	0.173877i
$778$		0			0
$779$	3.34432e12			0.325379
$780$		0			0
$781$	1.21403e13			1.16761
$782$		0			0
$783$		−	4.38588e12i		−	0.416993i
$784$		0			0
$785$	7.22933e12	+	9.84110e12i	0.679493	+	0.924975i
$786$		0			0
$787$			6.78959e12i			0.630896i	0.948943	+	0.315448i	$0.102155\pi$
$787$			6.78959e12i			0.630896i	−0.948943	+	0.315448i	$0.897845\pi$
$788$		0			0
$789$	−1.70720e13			−1.56833
$790$		0			0
$791$	−4.71114e12			−0.427890
$792$		0			0
$793$		−	2.72810e12i		−	0.244980i
$794$		0			0
$795$	−1.39896e13	+	1.02768e13i	−1.24209	+	0.912447i
$796$		0			0
$797$			1.12463e13i			0.987295i	0.869662	+	0.493648i	$0.164337\pi$
$797$			1.12463e13i			0.987295i	−0.869662	+	0.493648i	$0.835663\pi$
$798$		0			0
$799$	−1.11877e13			−0.971139
$800$		0			0
$801$	−1.81753e12			−0.156004
$802$		0			0
$803$		−	2.15720e13i		−	1.83092i
$804$		0			0
$805$	5.23179e12	−	3.84331e12i	0.439106	−	0.322570i
$806$		0			0
$807$		−	7.93806e11i		−	0.0658845i
$808$		0			0
$809$	1.00651e13			0.826133			0.413066	−	0.910701i	$-0.364458\pi$
$809$	1.00651e13			0.826133			0.413066	+	0.910701i	$0.364458\pi$
$810$		0			0
$811$	2.29492e13			1.86283			0.931417	−	0.363955i	$-0.118574\pi$
$811$	2.29492e13			1.86283			0.931417	+	0.363955i	$0.118574\pi$
$812$		0			0
$813$			1.03445e13i			0.830430i
$814$		0			0
$815$	4.39028e12	+	5.97637e12i	0.348564	+	0.474491i
$816$		0			0
$817$			2.06179e13i			1.61899i
$818$		0			0
$819$	5.73969e11			0.0445770
$820$		0			0
$821$	−5.85611e12			−0.449847			−0.224924	−	0.974376i	$-0.572213\pi$
$821$	−5.85611e12			−0.449847			−0.224924	+	0.974376i	$0.572213\pi$
$822$		0			0
$823$			5.82056e11i			0.0442248i	0.999755	+	0.0221124i	$0.00703917\pi$
$823$			5.82056e11i			0.0442248i	−0.999755	+	0.0221124i	$0.992961\pi$
$824$		0			0
$825$	2.05805e13	+	6.44856e12i	1.54672	+	0.484641i
$826$		0			0
$827$		−	7.98752e12i		−	0.593796i	−0.954909	−	0.296898i	$-0.904048\pi$
$827$		−	7.98752e12i		−	0.593796i	0.954909	−	0.296898i	$-0.0959521\pi$
$828$		0			0
$829$	−1.66284e12			−0.122280			−0.0611398	−	0.998129i	$-0.519474\pi$
$829$	−1.66284e12			−0.122280			−0.0611398	+	0.998129i	$0.519474\pi$
$830$		0			0
$831$	6.49399e12			0.472397
$832$		0			0
$833$		−	1.63210e13i		−	1.17448i
$834$		0			0
$835$	5.66753e12	+	7.71506e12i	0.403464	+	0.549225i
$836$		0			0
$837$		−	2.73685e12i		−	0.192746i
$838$		0			0
$839$	−5.31687e12			−0.370448			−0.185224	−	0.982696i	$-0.559301\pi$
$839$	−5.31687e12			−0.370448			−0.185224	+	0.982696i	$0.559301\pi$
$840$		0			0
$841$	2.00759e13			1.38386
$842$		0			0
$843$			1.03993e13i			0.709217i
$844$		0			0
$845$	1.15017e13	−	8.44924e12i	0.776083	−	0.570115i
$846$		0			0
$847$		−	2.00196e12i		−	0.133654i
$848$		0			0
$849$	−5.48053e12			−0.362024
$850$		0			0
$851$	−1.28410e13			−0.839298
$852$		0			0
$853$			9.94253e12i			0.643022i	0.946906	+	0.321511i	$0.104191\pi$
$853$			9.94253e12i			0.643022i	−0.946906	+	0.321511i	$0.895809\pi$
$854$		0			0
$855$	9.78970e12	−	7.19157e12i	0.626501	−	0.460232i
$856$		0			0
$857$		−	1.10633e13i		−	0.700599i	−0.936638	−	0.350299i	$-0.886080\pi$
$857$		−	1.10633e13i		−	0.700599i	0.936638	−	0.350299i	$-0.113920\pi$
$858$		0			0
$859$	−1.03065e13			−0.645865			−0.322932	−	0.946422i	$-0.604669\pi$
$859$	−1.03065e13			−0.645865			−0.322932	+	0.946422i	$0.604669\pi$
$860$		0			0
$861$	2.09724e12			0.130057
$862$		0			0
$863$			2.06614e13i			1.26798i	0.773342	+	0.633989i	$0.218584\pi$
$863$			2.06614e13i			1.26798i	−0.773342	+	0.633989i	$0.781416\pi$
$864$		0			0
$865$	−6.76258e12	−	9.20572e12i	−0.410715	−	0.559095i
$866$		0			0
$867$			1.43826e13i			0.864471i
$868$		0			0
$869$	−1.82074e13			−1.08308
$870$		0			0
$871$	−1.74307e12			−0.102620
$872$		0			0
$873$		−	2.29408e13i		−	1.33673i
$874$		0			0
$875$	−4.75910e12	+	1.62975e12i	−0.274466	+	0.0939905i
$876$		0			0
$877$			2.11700e12i			0.120843i	0.998173	+	0.0604216i	$0.0192445\pi$
$877$			2.11700e12i			0.120843i	−0.998173	+	0.0604216i	$0.980755\pi$
$878$		0			0
$879$	−2.15394e13			−1.21698
$880$		0			0
$881$	−2.10661e13			−1.17813			−0.589065	−	0.808086i	$-0.700504\pi$
$881$	−2.10661e13			−1.17813			−0.589065	+	0.808086i	$0.700504\pi$
$882$		0			0
$883$			1.59829e13i			0.884772i	0.896825	+	0.442386i	$0.145868\pi$
$883$			1.59829e13i			0.884772i	−0.896825	+	0.442386i	$0.854132\pi$
$884$		0			0
$885$	−1.35398e13	−	1.84314e13i	−0.741938	−	1.00998i
$886$		0			0
$887$		−	1.21640e13i		−	0.659815i	−0.944013	−	0.329907i	$-0.892983\pi$
$887$		−	1.21640e13i		−	0.659815i	0.944013	−	0.329907i	$-0.107017\pi$
$888$		0			0
$889$	2.47335e11			0.0132809
$890$		0			0
$891$	2.63935e13			1.40297
$892$		0			0
$893$			1.40080e13i			0.737133i
$894$		0			0
$895$	−1.11657e13	+	8.20236e12i	−0.581675	+	0.427302i
$896$		0			0
$897$		−	9.39617e12i		−	0.484602i
$898$		0			0
$899$	2.15803e13			1.10189
$900$		0			0
$901$	−2.91530e13			−1.47374
$902$		0			0
$903$			1.29296e13i			0.647127i
$904$		0			0
$905$	6.41756e12	−	4.71438e12i	0.318018	−	0.233618i
$906$		0			0
$907$		−	3.94282e13i		−	1.93453i	−0.253775	−	0.967263i	$-0.581672\pi$
$907$		−	3.94282e13i		−	1.93453i	0.253775	−	0.967263i	$-0.418328\pi$
$908$		0			0
$909$	9.91143e12			0.481503
$910$		0			0
$911$	1.88838e13			0.908357			0.454179	−	0.890911i	$-0.349933\pi$
$911$	1.88838e13			0.908357			0.454179	+	0.890911i	$0.349933\pi$
$912$		0			0
$913$		−	1.11525e13i		−	0.531195i
$914$		0			0
$915$	−2.14356e13	−	2.91797e13i	−1.01098	−	1.37621i
$916$		0			0
$917$		−	6.88605e10i		−	0.00321594i
$918$		0			0
$919$	9.37917e12			0.433755			0.216878	−	0.976199i	$-0.430413\pi$
$919$	9.37917e12			0.433755			0.216878	+	0.976199i	$0.430413\pi$
$920$		0			0
$921$	−1.19388e13			−0.546756
$922$		0			0
$923$			4.09854e12i			0.185875i
$924$		0			0
$925$	9.49523e12	+	2.97518e12i	0.426450	+	0.133621i
$926$		0			0
$927$		−	5.41442e12i		−	0.240821i
$928$		0			0
$929$	−1.15920e13			−0.510608			−0.255304	−	0.966861i	$-0.582176\pi$
$929$	−1.15920e13			−0.510608			−0.255304	+	0.966861i	$0.582176\pi$
$930$		0			0
$931$	−2.04354e13			−0.891476
$932$		0			0
$933$		−	1.29152e13i		−	0.558000i
$934$		0			0
$935$	2.14439e13	+	2.91911e13i	0.917597	+	1.24910i
$936$		0			0
$937$			2.22572e13i			0.943282i	0.881791	+	0.471641i	$0.156338\pi$
$937$			2.22572e13i			0.943282i	−0.881791	+	0.471641i	$0.843662\pi$
$938$		0			0
$939$	4.05738e13			1.70314
$940$		0			0
$941$	−2.47067e13			−1.02722			−0.513608	−	0.858025i	$-0.671691\pi$
$941$	−2.47067e13			−1.02722			−0.513608	+	0.858025i	$0.671691\pi$
$942$		0			0
$943$		−	1.52444e13i		−	0.627781i
$944$		0			0
$945$	−1.54806e12	+	1.13722e12i	−0.0631459	+	0.0463874i
$946$		0			0
$947$			2.93847e13i			1.18726i	0.804737	+	0.593632i	$0.202306\pi$
$947$			2.93847e13i			1.18726i	−0.804737	+	0.593632i	$0.797694\pi$
$948$		0			0
$949$	7.28270e12			0.291470
$950$		0			0
$951$	5.63307e13			2.23323
$952$		0			0
$953$			2.36915e13i			0.930412i	0.885203	+	0.465206i	$0.154020\pi$
$953$			2.36915e13i			0.930412i	−0.885203	+	0.465206i	$0.845980\pi$
$954$		0			0
$955$	−3.18376e13	+	2.33881e13i	−1.23858	+	0.909870i
$956$		0			0
$957$			6.49372e13i			2.50259i
$958$		0			0
$959$	−4.53504e12			−0.173140
$960$		0			0
$961$	−1.29732e13			−0.490674
$962$		0			0
$963$		−	5.12069e12i		−	0.191871i
$964$		0			0
$965$	−5.01121e12	−	6.82163e12i	−0.186024	−	0.253230i
$966$		0			0
$967$		−	1.90423e13i		−	0.700326i	−0.936689	−	0.350163i	$-0.886126\pi$
$967$		−	1.90423e13i		−	0.700326i	0.936689	−	0.350163i	$-0.113874\pi$
$968$		0			0
$969$	4.59460e13			1.67414
$970$		0			0
$971$	2.00384e13			0.723397			0.361699	−	0.932295i	$-0.382197\pi$
$971$	2.00384e13			0.723397			0.361699	+	0.932295i	$0.382197\pi$
$972$		0			0
$973$		−	6.63405e11i		−	0.0237286i
$974$		0			0
$975$	−2.17703e12	+	6.94796e12i	−0.0771514	+	0.246228i
$976$		0			0
$977$		−	2.32603e13i		−	0.816751i	−0.912814	−	0.408375i	$-0.866095\pi$
$977$		−	2.32603e13i		−	0.816751i	0.912814	−	0.408375i	$-0.133905\pi$
$978$		0			0
$979$	−6.78575e12			−0.236089
$980$		0			0
$981$	−3.22810e13			−1.11285
$982$		0			0
$983$		−	1.59072e13i		−	0.543380i	−0.962385	−	0.271690i	$-0.912418\pi$
$983$		−	1.59072e13i		−	0.543380i	0.962385	−	0.271690i	$-0.0875825\pi$
$984$		0			0
$985$	8.06989e11	+	1.09853e12i	0.0273152	+	0.0371835i
$986$		0			0
$987$			8.78451e12i			0.294639i
$988$		0			0
$989$	9.39826e13			3.12366
$990$		0			0
$991$	3.16366e10			0.00104198			0.000520988	−	1.00000i	$-0.499834\pi$
$991$	3.16366e10			0.00104198			0.000520988		1.00000i	$0.499834\pi$
$992$		0			0
$993$		−	3.85288e13i		−	1.25752i
$994$		0			0
$995$	−3.18156e13	+	2.33719e13i	−1.02905	+	0.755946i
$996$		0			0
$997$		−	6.01640e13i		−	1.92845i	−0.265085	−	0.964225i	$-0.585400\pi$
$997$		−	6.01640e13i		−	1.92845i	0.265085	−	0.964225i	$-0.414600\pi$
$998$		0			0
$999$	3.79959e12			0.120696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.10.c.a.9.1	✓	4
3.2	odd	2		180.10.d.a.109.2		4
4.3	odd	2		80.10.c.b.49.4		4
5.2	odd	4		100.10.a.f.1.1		4
5.3	odd	4		100.10.a.f.1.4		4
5.4	even	2	inner	20.10.c.a.9.4	yes	4
15.14	odd	2		180.10.d.a.109.1		4
20.3	even	4		400.10.a.bb.1.1		4
20.7	even	4		400.10.a.bb.1.4		4
20.19	odd	2		80.10.c.b.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.10.c.a.9.1	✓	4	1.1	even	1	trivial
20.10.c.a.9.4	yes	4	5.4	even	2	inner
80.10.c.b.49.1		4	20.19	odd	2
80.10.c.b.49.4		4	4.3	odd	2
100.10.a.f.1.1		4	5.2	odd	4
100.10.a.f.1.4		4	5.3	odd	4
180.10.d.a.109.1		4	15.14	odd	2
180.10.d.a.109.2		4	3.2	odd	2
400.10.a.bb.1.1		4	20.3	even	4
400.10.a.bb.1.4		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)

\(f(q)\)	\(=\)	\(q-188.155i q^{3} +(1126.30 - 827.388i) q^{5} -1842.93i q^{7} -15719.2 q^{9} +O(q^{10})\)	\(q-188.155i q^{3} +(1126.30 - 827.388i) q^{5} -1842.93i q^{7} -15719.2 q^{9} -58687.7 q^{11} -19812.9i q^{13} +(-155677. - 211919. i) q^{15} -441620. i q^{17} -552947. q^{19} -346756. q^{21} +2.52050e6i q^{23} +(583984. - 1.86378e6i) q^{25} -745805. i q^{27} +5.88073e6 q^{29} +3.66966e6 q^{31} +1.10424e7i q^{33} +(-1.52482e6 - 2.07569e6i) q^{35} +5.09462e6i q^{37} -3.72790e6 q^{39} -6.04817e6 q^{41} -3.72873e7i q^{43} +(-1.77046e7 + 1.30059e7i) q^{45} -2.53334e7i q^{47} +3.69572e7 q^{49} -8.30929e7 q^{51} -6.60139e7i q^{53} +(-6.61000e7 + 4.85575e7i) q^{55} +1.04040e8i q^{57} +8.69737e7 q^{59} +1.37693e8 q^{61} +2.89694e7i q^{63} +(-1.63930e7 - 2.23153e7i) q^{65} -8.79763e7i q^{67} +4.74245e8 q^{69} -2.06862e8 q^{71} +3.67573e8i q^{73} +(-3.50678e8 - 1.09879e8i) q^{75} +1.08157e8i q^{77} +3.10242e8 q^{79} -4.49728e8 q^{81} +1.90032e8i q^{83} +(-3.65391e8 - 4.97397e8i) q^{85} -1.10649e9i q^{87} +1.15625e8 q^{89} -3.65138e7 q^{91} -6.90463e8i q^{93} +(-6.22785e8 + 4.57502e8i) q^{95} +1.45941e9i q^{97} +9.22524e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 660 q^{5} - 9044 q^{9}+O(q^{10}) \) 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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