LMFDB - Embedded newform 20.12.c.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,12,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, 12, names="a")

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

chi := DirichletCharacter("20.9");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
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:	$15.3668636112$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 195547x^{4} + 7296096303x^{2} + 4158054148149 $ x^6 + 195547x^4 + 7296096303x^2 + 4158054148149
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{19}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.2
Root			$-222.078i$ of defining polynomial
Character	$\chi$	$=$	20.9
Dual form			20.12.c.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-444.156i q^{3} +(6461.93 + 2659.24i) q^{5} +56488.4i q^{7} -20127.7 q^{9} +O(q^{10})$	\(q-444.156i q^{3} +(6461.93 + 2659.24i) q^{5} +56488.4i q^{7} -20127.7 q^{9} +383483. q^{11} -1.21532e6i q^{13} +(1.18112e6 - 2.87011e6i) q^{15} +4.49835e6i q^{17} +1.68581e7 q^{19} +2.50897e7 q^{21} -4.22361e7i q^{23} +(3.46850e7 + 3.43677e7i) q^{25} -6.97411e7i q^{27} +2.58702e7 q^{29} +2.62498e7 q^{31} -1.70326e8i q^{33} +(-1.50216e8 + 3.65024e8i) q^{35} +5.75158e8i q^{37} -5.39793e8 q^{39} -9.40368e8 q^{41} -1.37765e9i q^{43} +(-1.30064e8 - 5.35243e7i) q^{45} +1.31801e9i q^{47} -1.21361e9 q^{49} +1.99797e9 q^{51} +2.71171e9i q^{53} +(2.47804e9 + 1.01977e9i) q^{55} -7.48764e9i q^{57} +6.01808e9 q^{59} +4.12243e9 q^{61} -1.13698e9i q^{63} +(3.23184e9 - 7.85334e9i) q^{65} -1.12629e9i q^{67} -1.87594e10 q^{69} +8.09619e9 q^{71} +3.17015e10i q^{73} +(1.52646e10 - 1.54055e10i) q^{75} +2.16623e10i q^{77} -3.33112e10 q^{79} -3.45415e10 q^{81} -3.13536e10i q^{83} +(-1.19622e10 + 2.90680e10i) q^{85} -1.14904e10i q^{87} -1.00403e11 q^{89} +6.86517e10 q^{91} -1.16590e10i q^{93} +(1.08936e11 + 4.48298e10i) q^{95} -4.33591e10i q^{97} -7.71861e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4126 q^{5} - 501494 q^{9}+O(q^{10}) $ 6 * q - 4126 * q^5 - 501494 * q^9	$ 6 q - 4126 q^{5} - 501494 q^{9} + 1298200 q^{11} - 3310648 q^{15} - 244824 q^{19} - 44518024 q^{21} + 34713726 q^{25} - 138940764 q^{29} + 214450176 q^{31} - 308845352 q^{35} + 542728176 q^{39} + 106601836 q^{41} + 3311255374 q^{45} - 4506920718 q^{49} + 571023872 q^{51} - 1741716600 q^{55} - 14817616328 q^{59} + 13263695412 q^{61} + 22042348848 q^{65} - 57831800072 q^{69} + 983424528 q^{71} + 97974745648 q^{75} - 158406142752 q^{79} + 113598783134 q^{81} + 109785881856 q^{85} - 288677471236 q^{89} + 228887753424 q^{91} + 348434078904 q^{95} - 1006608631000 q^{99}+O(q^{100}) $ 6 * q - 4126 * q^5 - 501494 * q^9 + 1298200 * q^11 - 3310648 * q^15 - 244824 * q^19 - 44518024 * q^21 + 34713726 * q^25 - 138940764 * q^29 + 214450176 * q^31 - 308845352 * q^35 + 542728176 * q^39 + 106601836 * q^41 + 3311255374 * q^45 - 4506920718 * q^49 + 571023872 * q^51 - 1741716600 * q^55 - 14817616328 * q^59 + 13263695412 * q^61 + 22042348848 * q^65 - 57831800072 * q^69 + 983424528 * q^71 + 97974745648 * q^75 - 158406142752 * q^79 + 113598783134 * q^81 + 109785881856 * q^85 - 288677471236 * q^89 + 228887753424 * q^91 + 348434078904 * q^95 - 1006608631000 * 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
$3$		−	444.156i		−	1.05528i	−0.849467	−	0.527641i	$-0.823077\pi$
$3$		−	444.156i		−	1.05528i	0.849467	−	0.527641i	$-0.176923\pi$
$4$		0			0
$5$	6461.93	+	2659.24i	0.924756	+	0.380560i
$5$	6461.93	+	2659.24i	0.924756	+	0.380560i
$6$		0			0
$7$			56488.4i			1.27034i	0.772372	+	0.635170i	$0.219070\pi$
$7$			56488.4i			1.27034i	−0.772372	+	0.635170i	$0.780930\pi$
$8$		0			0
$9$	−20127.7			−0.113621
$10$		0			0
$11$	383483.			0.717936			0.358968	−	0.933350i	$-0.383129\pi$
$11$	383483.			0.717936			0.358968	+	0.933350i	$0.383129\pi$
$12$		0			0
$13$		−	1.21532e6i		−	0.907828i	−0.891046	−	0.453914i	$-0.850027\pi$
$13$		−	1.21532e6i		−	0.907828i	0.891046	−	0.453914i	$-0.149973\pi$
$14$		0			0
$15$	1.18112e6	−	2.87011e6i	0.401598	−	0.975879i
$16$		0			0
$17$			4.49835e6i			0.768395i	0.923251	+	0.384197i	$0.125522\pi$
$17$			4.49835e6i			0.768395i	−0.923251	+	0.384197i	$0.874478\pi$
$18$		0			0
$19$	1.68581e7			1.56194			0.780970	−	0.624568i	$-0.214725\pi$
$19$	1.68581e7			1.56194			0.780970	+	0.624568i	$0.214725\pi$
$20$		0			0
$21$	2.50897e7			1.34057
$22$		0			0
$23$		−	4.22361e7i		−	1.36830i	−0.729342	−	0.684149i	$-0.760174\pi$
$23$		−	4.22361e7i		−	1.36830i	0.729342	−	0.684149i	$-0.239826\pi$
$24$		0			0
$25$	3.46850e7	+	3.43677e7i	0.710348	+	0.703850i
$26$		0			0
$27$		−	6.97411e7i		−	0.935380i
$28$		0			0
$29$	2.58702e7			0.234213			0.117106	−	0.993119i	$-0.462638\pi$
$29$	2.58702e7			0.234213			0.117106	+	0.993119i	$0.462638\pi$
$30$		0			0
$31$	2.62498e7			0.164678			0.0823391	−	0.996604i	$-0.473761\pi$
$31$	2.62498e7			0.164678			0.0823391	+	0.996604i	$0.473761\pi$
$32$		0			0
$33$		−	1.70326e8i		−	0.757625i
$34$		0			0
$35$	−1.50216e8	+	3.65024e8i	−0.483440	+	1.17475i
$36$		0			0
$37$			5.75158e8i			1.36357i	0.731553	+	0.681785i	$0.238796\pi$
$37$			5.75158e8i			1.36357i	−0.731553	+	0.681785i	$0.761204\pi$
$38$		0			0
$39$	−5.39793e8			−0.958015
$40$		0			0
$41$	−9.40368e8			−1.26761			−0.633807	−	0.773492i	$-0.718509\pi$
$41$	−9.40368e8			−1.26761			−0.633807	+	0.773492i	$0.718509\pi$
$42$		0			0
$43$		−	1.37765e9i		−	1.42910i	−0.699583	−	0.714552i	$-0.746631\pi$
$43$		−	1.37765e9i		−	1.42910i	0.699583	−	0.714552i	$-0.253369\pi$
$44$		0			0
$45$	−1.30064e8	−	5.35243e7i	−0.105072	−	0.0432397i
$46$		0			0
$47$			1.31801e9i			0.838266i	0.907925	+	0.419133i	$0.137666\pi$
$47$			1.31801e9i			0.838266i	−0.907925	+	0.419133i	$0.862334\pi$
$48$		0			0
$49$	−1.21361e9			−0.613763
$50$		0			0
$51$	1.99797e9			0.810874
$52$		0			0
$53$			2.71171e9i			0.890688i	0.895360	+	0.445344i	$0.146919\pi$
$53$			2.71171e9i			0.890688i	−0.895360	+	0.445344i	$0.853081\pi$
$54$		0			0
$55$	2.47804e9	+	1.01977e9i	0.663916	+	0.273218i
$56$		0			0
$57$		−	7.48764e9i		−	1.64829i
$58$		0			0
$59$	6.01808e9			1.09590			0.547951	−	0.836510i	$-0.315408\pi$
$59$	6.01808e9			1.09590			0.547951	+	0.836510i	$0.315408\pi$
$60$		0			0
$61$	4.12243e9			0.624941			0.312471	−	0.949927i	$-0.398843\pi$
$61$	4.12243e9			0.624941			0.312471	+	0.949927i	$0.398843\pi$
$62$		0			0
$63$		−	1.13698e9i		−	0.144338i
$64$		0			0
$65$	3.23184e9	−	7.85334e9i	0.345483	−	0.839520i
$66$		0			0
$67$		−	1.12629e9i		−	0.101916i	−0.998701	−	0.0509578i	$-0.983773\pi$
$67$		−	1.12629e9i		−	0.101916i	0.998701	−	0.0509578i	$-0.0162274\pi$
$68$		0			0
$69$	−1.87594e10			−1.44394
$70$		0			0
$71$	8.09619e9			0.532549			0.266275	−	0.963897i	$-0.414207\pi$
$71$	8.09619e9			0.532549			0.266275	+	0.963897i	$0.414207\pi$
$72$		0			0
$73$			3.17015e10i			1.78980i	0.446268	+	0.894899i	$0.352753\pi$
$73$			3.17015e10i			1.78980i	−0.446268	+	0.894899i	$0.647247\pi$
$74$		0			0
$75$	1.52646e10	−	1.54055e10i	0.742761	−	0.749618i
$76$		0			0
$77$			2.16623e10i			0.912023i
$78$		0			0
$79$	−3.33112e10			−1.21798			−0.608992	−	0.793176i	$-0.708426\pi$
$79$	−3.33112e10			−1.21798			−0.608992	+	0.793176i	$0.708426\pi$
$80$		0			0
$81$	−3.45415e10			−1.10071
$82$		0			0
$83$		−	3.13536e10i		−	0.873690i	−0.899537	−	0.436845i	$-0.856096\pi$
$83$		−	3.13536e10i		−	0.873690i	0.899537	−	0.436845i	$-0.143904\pi$
$84$		0			0
$85$	−1.19622e10	+	2.90680e10i	−0.292420	+	0.710578i
$86$		0			0
$87$		−	1.14904e10i		−	0.247161i
$88$		0			0
$89$	−1.00403e11			−1.90591			−0.952953	−	0.303118i	$-0.901972\pi$
$89$	−1.00403e11			−1.90591			−0.952953	+	0.303118i	$0.901972\pi$
$90$		0			0
$91$	6.86517e10			1.15325
$92$		0			0
$93$		−	1.16590e10i		−	0.173782i
$94$		0			0
$95$	1.08936e11	+	4.48298e10i	1.44441	+	0.594412i
$96$		0			0
$97$		−	4.33591e10i		−	0.512667i	−0.966588	−	0.256334i	$-0.917485\pi$
$97$		−	4.33591e10i		−	0.512667i	0.966588	−	0.256334i	$-0.0825146\pi$
$98$		0			0
$99$	−7.71861e9			−0.0815728
$100$		0			0
$101$	7.36689e10			0.697456			0.348728	−	0.937224i	$-0.386614\pi$
$101$	7.36689e10			0.697456			0.348728	+	0.937224i	$0.386614\pi$
$102$		0			0
$103$		−	8.25065e10i		−	0.701267i	−0.936513	−	0.350634i	$-0.885966\pi$
$103$		−	8.25065e10i		−	0.701267i	0.936513	−	0.350634i	$-0.114034\pi$
$104$		0			0
$105$	1.62128e11	+	6.67195e10i	1.23970	+	0.510166i
$106$		0			0
$107$			1.03794e11i			0.715419i	0.933833	+	0.357709i	$0.116442\pi$
$107$			1.03794e11i			0.715419i	−0.933833	+	0.357709i	$0.883558\pi$
$108$		0			0
$109$	−2.26946e11			−1.41279			−0.706393	−	0.707820i	$-0.749679\pi$
$109$	−2.26946e11			−1.41279			−0.706393	+	0.707820i	$0.749679\pi$
$110$		0			0
$111$	2.55460e11			1.43895
$112$		0			0
$113$		−	2.84595e11i		−	1.45310i	−0.687113	−	0.726551i	$-0.741122\pi$
$113$		−	2.84595e11i		−	1.45310i	0.687113	−	0.726551i	$-0.258878\pi$
$114$		0			0
$115$	1.12316e11	−	2.72927e11i	0.520719	−	1.26534i
$116$		0			0
$117$			2.44616e10i			0.103149i
$118$		0			0
$119$	−2.54105e11			−0.976123
$120$		0			0
$121$	−1.38253e11			−0.484568
$122$		0			0
$123$			4.17670e11i			1.33769i
$124$		0			0
$125$	1.32740e11	+	3.14317e11i	0.389042	+	0.921220i
$126$		0			0
$127$			1.22812e11i			0.329854i	0.986306	+	0.164927i	$0.0527389\pi$
$127$			1.22812e11i			0.329854i	−0.986306	+	0.164927i	$0.947261\pi$
$128$		0			0
$129$	−6.11894e11			−1.50811
$130$		0			0
$131$	−1.57133e11			−0.355857			−0.177928	−	0.984043i	$-0.556940\pi$
$131$	−1.57133e11			−0.355857			−0.177928	+	0.984043i	$0.556940\pi$
$132$		0			0
$133$			9.52288e11i			1.98419i
$134$		0			0
$135$	1.85459e11	−	4.50662e11i	0.355968	−	0.864999i
$136$		0			0
$137$		−	9.32873e11i		−	1.65143i	−0.564090	−	0.825713i	$-0.690773\pi$
$137$		−	9.32873e11i		−	1.65143i	0.564090	−	0.825713i	$-0.309227\pi$
$138$		0			0
$139$	−1.16693e12			−1.90749			−0.953744	−	0.300619i	$-0.902807\pi$
$139$	−1.16693e12			−1.90749			−0.953744	+	0.300619i	$0.902807\pi$
$140$		0			0
$141$	5.85404e11			0.884607
$142$		0			0
$143$		−	4.66055e11i		−	0.651763i
$144$		0			0
$145$	1.67171e11	+	6.87951e10i	0.216590	+	0.0891320i
$146$		0			0
$147$			5.39033e11i			0.647694i
$148$		0			0
$149$	1.13836e12			1.26986			0.634931	−	0.772569i	$-0.281029\pi$
$149$	1.13836e12			1.26986			0.634931	+	0.772569i	$0.281029\pi$
$150$		0			0
$151$	−8.39314e11			−0.870064			−0.435032	−	0.900415i	$-0.643263\pi$
$151$	−8.39314e11			−0.870064			−0.435032	+	0.900415i	$0.643263\pi$
$152$		0			0
$153$		−	9.05413e10i		−	0.0873060i
$154$		0			0
$155$	1.69624e11	+	6.98045e10i	0.152287	+	0.0626699i
$156$		0			0
$157$		−	1.28451e11i		−	0.107470i	−0.998555	−	0.0537352i	$-0.982887\pi$
$157$		−	1.28451e11i		−	0.107470i	0.998555	−	0.0537352i	$-0.0171127\pi$
$158$		0			0
$159$	1.20442e12			0.939927
$160$		0			0
$161$	2.38585e12			1.73820
$162$		0			0
$163$		−	7.26064e11i		−	0.494246i	−0.968984	−	0.247123i	$-0.920515\pi$
$163$		−	7.26064e11i		−	0.494246i	0.968984	−	0.247123i	$-0.0794852\pi$
$164$		0			0
$165$	4.52939e11	−	1.10064e12i	0.288322	−	0.700619i
$166$		0			0
$167$			2.06781e12i			1.23189i	0.787791	+	0.615943i	$0.211225\pi$
$167$			2.06781e12i			1.23189i	−0.787791	+	0.615943i	$0.788775\pi$
$168$		0			0
$169$	3.15149e11			0.175848
$170$		0			0
$171$	−3.39315e11			−0.177470
$172$		0			0
$173$		−	2.15563e12i		−	1.05760i	−0.848747	−	0.528799i	$-0.822643\pi$
$173$		−	2.15563e12i		−	1.05760i	0.848747	−	0.528799i	$-0.177357\pi$
$174$		0			0
$175$	−1.94138e12	+	1.95930e12i	−0.894129	+	0.902384i
$176$		0			0
$177$		−	2.67297e12i		−	1.15649i
$178$		0			0
$179$	3.61002e11			0.146831			0.0734156	−	0.997301i	$-0.476610\pi$
$179$	3.61002e11			0.146831			0.0734156	+	0.997301i	$0.476610\pi$
$180$		0			0
$181$	−4.41304e12			−1.68852			−0.844259	−	0.535936i	$-0.819959\pi$
$181$	−4.41304e12			−1.68852			−0.844259	+	0.535936i	$0.819959\pi$
$182$		0			0
$183$		−	1.83100e12i		−	0.659490i
$184$		0			0
$185$	−1.52948e12	+	3.71663e12i	−0.518920	+	1.26097i
$186$		0			0
$187$			1.72504e12i			0.551659i
$188$		0			0
$189$	3.93956e12			1.18825
$190$		0			0
$191$	−1.82936e12			−0.520734			−0.260367	−	0.965510i	$-0.583844\pi$
$191$	−1.82936e12			−0.520734			−0.260367	+	0.965510i	$0.583844\pi$
$192$		0			0
$193$			5.51170e12i			1.48156i	0.671746	+	0.740782i	$0.265545\pi$
$193$			5.51170e12i			1.48156i	−0.671746	+	0.740782i	$0.734455\pi$
$194$		0			0
$195$	−3.48811e12	−	1.43544e12i	−0.885930	−	0.364582i
$196$		0			0
$197$		−	2.26580e11i		−	0.0544073i	−0.999630	−	0.0272037i	$-0.991340\pi$
$197$		−	2.26580e11i		−	0.0544073i	0.999630	−	0.0272037i	$-0.00866026\pi$
$198$		0			0
$199$	4.86063e11			0.110408			0.0552040	−	0.998475i	$-0.482419\pi$
$199$	4.86063e11			0.110408			0.0552040	+	0.998475i	$0.482419\pi$
$200$		0			0
$201$	−5.00250e11			−0.107550
$202$		0			0
$203$			1.46136e12i			0.297530i
$204$		0			0
$205$	−6.07660e12	−	2.50067e12i	−1.17223	−	0.482403i
$206$		0			0
$207$			8.50114e11i			0.155468i
$208$		0			0
$209$	6.46480e12			1.12137
$210$		0			0
$211$	−4.75603e12			−0.782873			−0.391436	−	0.920205i	$-0.628022\pi$
$211$	−4.75603e12			−0.782873			−0.391436	+	0.920205i	$0.628022\pi$
$212$		0			0
$213$		−	3.59597e12i		−	0.561990i
$214$		0			0
$215$	3.66352e12	−	8.90231e12i	0.543859	−	1.32157i
$216$		0			0
$217$			1.48281e12i			0.209197i
$218$		0			0
$219$	1.40804e13			1.88874
$220$		0			0
$221$	5.46696e12			0.697570
$222$		0			0
$223$			5.20030e12i			0.631468i	0.948848	+	0.315734i	$0.102251\pi$
$223$			5.20030e12i			0.631468i	−0.948848	+	0.315734i	$0.897749\pi$
$224$		0			0
$225$	−6.98128e11	−	6.91741e11i	−0.0807107	−	0.0799723i
$226$		0			0
$227$		−	1.38086e13i		−	1.52057i	−0.649589	−	0.760286i	$-0.725059\pi$
$227$		−	1.38086e13i		−	1.52057i	0.649589	−	0.760286i	$-0.274941\pi$
$228$		0			0
$229$	−4.59155e12			−0.481797			−0.240899	−	0.970550i	$-0.577442\pi$
$229$	−4.59155e12			−0.481797			−0.240899	+	0.970550i	$0.577442\pi$
$230$		0			0
$231$	9.62145e12			0.962442
$232$		0			0
$233$			4.94819e12i			0.472051i	0.971747	+	0.236025i	$0.0758448\pi$
$233$			4.94819e12i			0.472051i	−0.971747	+	0.236025i	$0.924155\pi$
$234$		0			0
$235$	−3.50492e12	+	8.51691e12i	−0.319010	+	0.775192i
$236$		0			0
$237$			1.47954e13i			1.28532i
$238$		0			0
$239$	2.08480e13			1.72932			0.864660	−	0.502358i	$-0.167534\pi$
$239$	2.08480e13			1.72932			0.864660	+	0.502358i	$0.167534\pi$
$240$		0			0
$241$	−1.17691e13			−0.932498			−0.466249	−	0.884654i	$-0.654395\pi$
$241$	−1.17691e13			−0.932498			−0.466249	+	0.884654i	$0.654395\pi$
$242$		0			0
$243$			2.98739e12i			0.226182i
$244$		0			0
$245$	−7.84227e12	−	3.22729e12i	−0.567582	−	0.233574i
$246$		0			0
$247$		−	2.04881e13i		−	1.41797i
$248$		0			0
$249$	−1.39259e13			−0.921989
$250$		0			0
$251$	−1.14836e13			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$251$	−1.14836e13			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$252$		0			0
$253$		−	1.61968e13i		−	0.982350i
$254$		0			0
$255$	1.29108e13	+	5.31309e12i	0.749861	+	0.308586i
$256$		0			0
$257$		−	6.30450e11i		−	0.0350767i	−0.999846	−	0.0175383i	$-0.994417\pi$
$257$		−	6.30450e11i		−	0.0350767i	0.999846	−	0.0175383i	$-0.00558291\pi$
$258$		0			0
$259$	−3.24897e13			−1.73220
$260$		0			0
$261$	−5.20706e11			−0.0266115
$262$		0			0
$263$			3.39009e12i			0.166133i	0.996544	+	0.0830663i	$0.0264713\pi$
$263$			3.39009e12i			0.166133i	−0.996544	+	0.0830663i	$0.973529\pi$
$264$		0			0
$265$	−7.21109e12	+	1.75229e13i	−0.338960	+	0.823669i
$266$		0			0
$267$			4.45946e13i			2.01127i
$268$		0			0
$269$	−2.71580e13			−1.17560			−0.587801	−	0.809006i	$-0.700006\pi$
$269$	−2.71580e13			−1.17560			−0.587801	+	0.809006i	$0.700006\pi$
$270$		0			0
$271$	1.05487e13			0.438399			0.219199	−	0.975680i	$-0.429655\pi$
$271$	1.05487e13			0.438399			0.219199	+	0.975680i	$0.429655\pi$
$272$		0			0
$273$		−	3.04921e13i		−	1.21700i
$274$		0			0
$275$	1.33011e13	+	1.31794e13i	0.509985	+	0.505320i
$276$		0			0
$277$			3.60479e13i			1.32813i	0.747674	+	0.664065i	$0.231170\pi$
$277$			3.60479e13i			1.32813i	−0.747674	+	0.664065i	$0.768830\pi$
$278$		0			0
$279$	−5.28347e11			−0.0187109
$280$		0			0
$281$	2.27544e13			0.774783			0.387391	−	0.921915i	$-0.373376\pi$
$281$	2.27544e13			0.774783			0.387391	+	0.921915i	$0.373376\pi$
$282$		0			0
$283$		−	1.80520e13i		−	0.591152i	−0.955319	−	0.295576i	$-0.904488\pi$
$283$		−	1.80520e13i		−	0.591152i	0.955319	−	0.295576i	$-0.0955116\pi$
$284$		0			0
$285$	1.99114e13	−	4.83846e13i	0.627272	−	1.52426i
$286$		0			0
$287$		−	5.31199e13i		−	1.61030i
$288$		0			0
$289$	1.40367e13			0.409569
$290$		0			0
$291$	−1.92582e13			−0.541009
$292$		0			0
$293$			5.39952e13i			1.46077i	0.683033	+	0.730387i	$0.260660\pi$
$293$			5.39952e13i			1.46077i	−0.683033	+	0.730387i	$0.739340\pi$
$294$		0			0
$295$	3.88884e13	+	1.60035e13i	1.01344	+	0.417056i
$296$		0			0
$297$		−	2.67445e13i		−	0.671543i
$298$		0			0
$299$	−5.13305e13			−1.24218
$300$		0			0
$301$	7.78215e13			1.81545
$302$		0			0
$303$		−	3.27205e13i		−	0.736013i
$304$		0			0
$305$	2.66389e13	+	1.09625e13i	0.577918	+	0.237828i
$306$		0			0
$307$		−	4.59159e13i		−	0.960953i	−0.877008	−	0.480476i	$-0.840464\pi$
$307$		−	4.59159e13i		−	0.960953i	0.877008	−	0.480476i	$-0.159536\pi$
$308$		0			0
$309$	−3.66458e13			−0.740035
$310$		0			0
$311$	1.54210e13			0.300560			0.150280	−	0.988643i	$-0.451982\pi$
$311$	1.54210e13			0.300560			0.150280	+	0.988643i	$0.451982\pi$
$312$		0			0
$313$			4.43455e13i			0.834364i	0.908823	+	0.417182i	$0.136982\pi$
$313$			4.43455e13i			0.834364i	−0.908823	+	0.417182i	$0.863018\pi$
$314$		0			0
$315$	3.02350e12	−	7.34708e12i	0.0549291	−	0.133477i
$316$		0			0
$317$		−	5.97559e12i		−	0.104847i	−0.998625	−	0.0524233i	$-0.983305\pi$
$317$		−	5.97559e12i		−	0.104847i	0.998625	−	0.0524233i	$-0.0166945\pi$
$318$		0			0
$319$	9.92076e12			0.168150
$320$		0			0
$321$	4.61006e13			0.754969
$322$		0			0
$323$			7.58338e13i			1.20019i
$324$		0			0
$325$	4.17679e13	−	4.21535e13i	0.638975	−	0.644874i
$326$		0			0
$327$			1.00799e14i			1.49089i
$328$		0			0
$329$	−7.44525e13			−1.06488
$330$		0			0
$331$	−1.30335e14			−1.80305			−0.901527	−	0.432724i	$-0.857553\pi$
$331$	−1.30335e14			−1.80305			−0.901527	+	0.432724i	$0.857553\pi$
$332$		0			0
$333$		−	1.15766e13i		−	0.154930i
$334$		0			0
$335$	2.99509e12	−	7.27803e12i	0.0387850	−	0.0942470i
$336$		0			0
$337$		−	6.95601e13i		−	0.871758i	−0.900005	−	0.435879i	$-0.856438\pi$
$337$		−	6.95601e13i		−	0.871758i	0.900005	−	0.435879i	$-0.143562\pi$
$338$		0			0
$339$	−1.26405e14			−1.53343
$340$		0			0
$341$	1.00663e13			0.118228
$342$		0			0
$343$			4.31411e13i			0.490652i
$344$		0			0
$345$	−1.21222e14	−	4.98859e13i	−1.33529	−	0.549506i
$346$		0			0
$347$			5.49337e13i			0.586175i	0.956086	+	0.293087i	$0.0946827\pi$
$347$			5.49337e13i			0.586175i	−0.956086	+	0.293087i	$0.905317\pi$
$348$		0			0
$349$	6.56394e13			0.678617			0.339309	−	0.940675i	$-0.389807\pi$
$349$	6.56394e13			0.678617			0.339309	+	0.940675i	$0.389807\pi$
$350$		0			0
$351$	−8.47580e13			−0.849164
$352$		0			0
$353$		−	1.71714e14i		−	1.66742i	−0.552200	−	0.833712i	$-0.686212\pi$
$353$		−	1.71714e14i		−	1.66742i	0.552200	−	0.833712i	$-0.313788\pi$
$354$		0			0
$355$	5.23170e13	+	2.15297e13i	0.492478	+	0.202667i
$356$		0			0
$357$			1.12862e14i			1.03009i
$358$		0			0
$359$	1.07878e14			0.954801			0.477401	−	0.878686i	$-0.341579\pi$
$359$	1.07878e14			0.954801			0.477401	+	0.878686i	$0.341579\pi$
$360$		0			0
$361$	1.67706e14			1.43966
$362$		0			0
$363$			6.14058e13i			0.511356i
$364$		0			0
$365$	−8.43020e13	+	2.04853e14i	−0.681126	+	1.65513i
$366$		0			0
$367$		−	9.98300e13i		−	0.782705i	−0.920241	−	0.391352i	$-0.872007\pi$
$367$		−	9.98300e13i		−	0.782705i	0.920241	−	0.391352i	$-0.127993\pi$
$368$		0			0
$369$	1.89274e13			0.144028
$370$		0			0
$371$	−1.53180e14			−1.13148
$372$		0			0
$373$		−	3.68561e13i		−	0.264308i	−0.991229	−	0.132154i	$-0.957811\pi$
$373$		−	3.68561e13i		−	0.264308i	0.991229	−	0.132154i	$-0.0421894\pi$
$374$		0			0
$375$	1.39606e14	−	5.89572e13i	0.972147	−	0.410549i
$376$		0			0
$377$		−	3.14406e13i		−	0.212625i
$378$		0			0
$379$	2.20079e14			1.44565			0.722823	−	0.691033i	$-0.242844\pi$
$379$	2.20079e14			1.44565			0.722823	+	0.691033i	$0.242844\pi$
$380$		0			0
$381$	5.45479e13			0.348089
$382$		0			0
$383$		−	2.75878e14i		−	1.71050i	−0.518215	−	0.855251i	$-0.673403\pi$
$383$		−	2.75878e14i		−	1.71050i	0.518215	−	0.855251i	$-0.326597\pi$
$384$		0			0
$385$	−5.76053e13	+	1.39980e14i	−0.347079	+	0.843399i
$386$		0			0
$387$			2.77290e13i			0.162377i
$388$		0			0
$389$	5.37614e13			0.306019			0.153009	−	0.988225i	$-0.451104\pi$
$389$	5.37614e13			0.306019			0.153009	+	0.988225i	$0.451104\pi$
$390$		0			0
$391$	1.89993e14			1.05139
$392$		0			0
$393$			6.97916e13i			0.375529i
$394$		0			0
$395$	−2.15255e14	−	8.85827e13i	−1.12634	−	0.463516i
$396$		0			0
$397$		−	3.67397e14i		−	1.86977i	−0.354954	−	0.934884i	$-0.615504\pi$
$397$		−	3.67397e14i		−	1.86977i	0.354954	−	0.934884i	$-0.384496\pi$
$398$		0			0
$399$	4.22965e14			2.09389
$400$		0			0
$401$	−8.59177e13			−0.413798			−0.206899	−	0.978362i	$-0.566337\pi$
$401$	−8.59177e13			−0.413798			−0.206899	+	0.978362i	$0.566337\pi$
$402$		0			0
$403$		−	3.19020e13i		−	0.149499i
$404$		0			0
$405$	−2.23205e14	−	9.18542e13i	−1.01789	−	0.418887i
$406$		0			0
$407$			2.20563e14i			0.978956i
$408$		0			0
$409$	9.06334e13			0.391570			0.195785	−	0.980647i	$-0.437274\pi$
$409$	9.06334e13			0.391570			0.195785	+	0.980647i	$0.437274\pi$
$410$		0			0
$411$	−4.14341e14			−1.74272
$412$		0			0
$413$			3.39951e14i			1.39217i
$414$		0			0
$415$	8.33767e13	−	2.02604e14i	0.332491	−	0.807950i
$416$		0			0
$417$			5.18297e14i			2.01294i
$418$		0			0
$419$	−1.32289e13			−0.0500433			−0.0250217	−	0.999687i	$-0.507965\pi$
$419$	−1.32289e13			−0.0500433			−0.0250217	+	0.999687i	$0.507965\pi$
$420$		0			0
$421$	−7.57794e13			−0.279254			−0.139627	−	0.990204i	$-0.544590\pi$
$421$	−7.57794e13			−0.279254			−0.139627	+	0.990204i	$0.544590\pi$
$422$		0			0
$423$		−	2.65285e13i		−	0.0952448i
$424$		0			0
$425$	−1.54598e14	+	1.56025e14i	−0.540835	+	0.545828i
$426$		0			0
$427$			2.32869e14i			0.793888i
$428$		0			0
$429$	−2.07001e14			−0.687794
$430$		0			0
$431$	−9.47325e13			−0.306813			−0.153407	−	0.988163i	$-0.549024\pi$
$431$	−9.47325e13			−0.306813			−0.153407	+	0.988163i	$0.549024\pi$
$432$		0			0
$433$			3.00895e13i			0.0950018i	0.998871	+	0.0475009i	$0.0151257\pi$
$433$			3.00895e13i			0.0950018i	−0.998871	+	0.0475009i	$0.984874\pi$
$434$		0			0
$435$	3.05558e13	−	7.42502e13i	0.0940594	−	0.228563i
$436$		0			0
$437$		−	7.12021e14i		−	2.13720i
$438$		0			0
$439$	1.82405e14			0.533926			0.266963	−	0.963707i	$-0.413980\pi$
$439$	1.82405e14			0.533926			0.266963	+	0.963707i	$0.413980\pi$
$440$		0			0
$441$	2.44271e13			0.0697366
$442$		0			0
$443$			3.52003e14i			0.980226i	0.871659	+	0.490113i	$0.163045\pi$
$443$			3.52003e14i			0.980226i	−0.871659	+	0.490113i	$0.836955\pi$
$444$		0			0
$445$	−6.48797e14	−	2.66996e14i	−1.76250	−	0.725311i
$446$		0			0
$447$		−	5.05611e14i		−	1.34006i
$448$		0			0
$449$	−1.66500e14			−0.430586			−0.215293	−	0.976550i	$-0.569071\pi$
$449$	−1.66500e14			−0.430586			−0.215293	+	0.976550i	$0.569071\pi$
$450$		0			0
$451$	−3.60615e14			−0.910065
$452$		0			0
$453$			3.72786e14i			0.918163i
$454$		0			0
$455$	4.43622e14	+	1.82561e14i	1.06648	+	0.438881i
$456$		0			0
$457$			2.43727e14i			0.571958i	0.958236	+	0.285979i	$0.0923188\pi$
$457$			2.43727e14i			0.571958i	−0.958236	+	0.285979i	$0.907681\pi$
$458$		0			0
$459$	3.13720e14			0.718741
$460$		0			0
$461$	5.46758e14			1.22304			0.611520	−	0.791229i	$-0.290559\pi$
$461$	5.46758e14			1.22304			0.611520	+	0.791229i	$0.290559\pi$
$462$		0			0
$463$			1.53457e13i			0.0335190i	0.999860	+	0.0167595i	$0.00533496\pi$
$463$			1.53457e13i			0.0335190i	−0.999860	+	0.0167595i	$0.994665\pi$
$464$		0			0
$465$	3.10041e13	−	7.53396e13i	0.0661345	−	0.160706i
$466$		0			0
$467$			9.34514e13i			0.194690i	0.995251	+	0.0973448i	$0.0310350\pi$
$467$			9.34514e13i			0.194690i	−0.995251	+	0.0973448i	$0.968965\pi$
$468$		0			0
$469$	6.36225e13			0.129467
$470$		0			0
$471$	−5.70522e13			−0.113412
$472$		0			0
$473$		−	5.28306e14i		−	1.02601i
$474$		0			0
$475$	5.84724e14	+	5.79375e14i	1.10952	+	1.09937i
$476$		0			0
$477$		−	5.45803e13i		−	0.101201i
$478$		0			0
$479$	4.07963e14			0.739223			0.369612	−	0.929186i	$-0.379491\pi$
$479$	4.07963e14			0.739223			0.369612	+	0.929186i	$0.379491\pi$
$480$		0			0
$481$	6.99003e14			1.23789
$482$		0			0
$483$		−	1.05969e15i		−	1.83430i
$484$		0			0
$485$	1.15302e14	−	2.80184e14i	0.195101	−	0.474092i
$486$		0			0
$487$			2.61971e14i			0.433356i	0.976243	+	0.216678i	$0.0695221\pi$
$487$			2.61971e14i			0.433356i	−0.976243	+	0.216678i	$0.930478\pi$
$488$		0			0
$489$	−3.22486e14			−0.521569
$490$		0			0
$491$	7.34573e13			0.116168			0.0580841	−	0.998312i	$-0.481501\pi$
$491$	7.34573e13			0.116168			0.0580841	+	0.998312i	$0.481501\pi$
$492$		0			0
$493$			1.16373e14i			0.179968i
$494$		0			0
$495$	−4.98771e13	−	2.05257e13i	−0.0754350	−	0.0310433i
$496$		0			0
$497$			4.57341e14i			0.676519i
$498$		0			0
$499$	−1.21731e15			−1.76136			−0.880680	−	0.473712i	$-0.842914\pi$
$499$	−1.21731e15			−1.76136			−0.880680	+	0.473712i	$0.842914\pi$
$500$		0			0
$501$	9.18431e14			1.29999
$502$		0			0
$503$			3.12458e13i			0.0432681i	0.999766	+	0.0216341i	$0.00688687\pi$
$503$			3.12458e13i			0.0432681i	−0.999766	+	0.0216341i	$0.993113\pi$
$504$		0			0
$505$	4.76043e14	+	1.95904e14i	0.644977	+	0.265424i
$506$		0			0
$507$		−	1.39975e14i		−	0.185570i
$508$		0			0
$509$	−5.74121e14			−0.744828			−0.372414	−	0.928067i	$-0.621470\pi$
$509$	−5.74121e14			−0.744828			−0.372414	+	0.928067i	$0.621470\pi$
$510$		0			0
$511$	−1.79077e15			−2.27365
$512$		0			0
$513$		−	1.17570e15i		−	1.46101i
$514$		0			0
$515$	2.19405e14	−	5.33152e14i	0.266874	−	0.648501i
$516$		0			0
$517$			5.05435e14i			0.601821i
$518$		0			0
$519$	−9.57436e14			−1.11606
$520$		0			0
$521$	9.33321e14			1.06518			0.532591	−	0.846373i	$-0.321219\pi$
$521$	9.33321e14			1.06518			0.532591	+	0.846373i	$0.321219\pi$
$522$		0			0
$523$			5.54269e14i			0.619386i	0.950837	+	0.309693i	$0.100226\pi$
$523$			5.54269e14i			0.619386i	−0.950837	+	0.309693i	$0.899774\pi$
$524$		0			0
$525$	8.70234e14	+	8.62274e14i	0.952270	+	0.943559i
$526$		0			0
$527$			1.18081e14i			0.126538i
$528$		0			0
$529$	−8.31078e14			−0.872239
$530$		0			0
$531$	−1.21130e14			−0.124518
$532$		0			0
$533$			1.14285e15i			1.15077i
$534$		0			0
$535$	−2.76013e14	+	6.70708e14i	−0.272260	+	0.661588i
$536$		0			0
$537$		−	1.60341e14i		−	0.154948i
$538$		0			0
$539$	−4.65399e14			−0.440643
$540$		0			0
$541$	−4.05519e14			−0.376206			−0.188103	−	0.982149i	$-0.560234\pi$
$541$	−4.05519e14			−0.376206			−0.188103	+	0.982149i	$0.560234\pi$
$542$		0			0
$543$			1.96008e15i			1.78186i
$544$		0			0
$545$	−1.46651e15	−	6.03504e14i	−1.30648	−	0.537650i
$546$		0			0
$547$		−	1.01695e15i		−	0.887912i	−0.896049	−	0.443956i	$-0.853575\pi$
$547$		−	1.01695e15i		−	0.887912i	0.896049	−	0.443956i	$-0.146425\pi$
$548$		0			0
$549$	−8.29749e13			−0.0710066
$550$		0			0
$551$	4.36123e14			0.365826
$552$		0			0
$553$		−	1.88170e15i		−	1.54725i
$554$		0			0
$555$	1.65076e15	+	6.79330e14i	1.33068	+	0.547607i
$556$		0			0
$557$		−	3.28330e14i		−	0.259482i	−0.991548	−	0.129741i	$-0.958585\pi$
$557$		−	3.28330e14i		−	0.259482i	0.991548	−	0.129741i	$-0.0414146\pi$
$558$		0			0
$559$	−1.67430e15			−1.29738
$560$		0			0
$561$	7.66187e14			0.582156
$562$		0			0
$563$			3.34327e14i			0.249101i	0.992213	+	0.124550i	$0.0397488\pi$
$563$			3.34327e14i			0.249101i	−0.992213	+	0.124550i	$0.960251\pi$
$564$		0			0
$565$	7.56807e14	−	1.83903e15i	0.552992	−	1.34376i
$566$		0			0
$567$		−	1.95119e15i		−	1.39828i
$568$		0			0
$569$	3.78040e13			0.0265718			0.0132859	−	0.999912i	$-0.495771\pi$
$569$	3.78040e13			0.0265718			0.0132859	+	0.999912i	$0.495771\pi$
$570$		0			0
$571$	−2.34056e14			−0.161370			−0.0806848	−	0.996740i	$-0.525711\pi$
$571$	−2.34056e14			−0.161370			−0.0806848	+	0.996740i	$0.525711\pi$
$572$		0			0
$573$			8.12523e14i			0.549522i
$574$		0			0
$575$	1.45156e15	−	1.46496e15i	0.963077	−	0.971968i
$576$		0			0
$577$			1.92177e15i			1.25093i	0.780251	+	0.625467i	$0.215091\pi$
$577$			1.92177e15i			1.25093i	−0.780251	+	0.625467i	$0.784909\pi$
$578$		0			0
$579$	2.44806e15			1.56347
$580$		0			0
$581$	1.77111e15			1.10988
$582$		0			0
$583$			1.03989e15i			0.639457i
$584$		0			0
$585$	−6.50494e13	+	1.58069e14i	−0.0392542	+	0.0953873i
$586$		0			0
$587$			9.26832e14i			0.548898i	0.961602	+	0.274449i	$0.0884954\pi$
$587$			9.26832e14i			0.548898i	−0.961602	+	0.274449i	$0.911505\pi$
$588$		0			0
$589$	4.42522e14			0.257218
$590$		0			0
$591$	−1.00637e14			−0.0574151
$592$		0			0
$593$		−	7.59335e14i		−	0.425239i	−0.977135	−	0.212619i	$-0.931801\pi$
$593$		−	7.59335e14i		−	0.425239i	0.977135	−	0.212619i	$-0.0681994\pi$
$594$		0			0
$595$	−1.64201e15	−	6.75726e14i	−0.902676	−	0.371473i
$596$		0			0
$597$		−	2.15888e14i		−	0.116512i
$598$		0			0
$599$	1.06235e15			0.562885			0.281442	−	0.959578i	$-0.409187\pi$
$599$	1.06235e15			0.562885			0.281442	+	0.959578i	$0.409187\pi$
$600$		0			0
$601$	−5.57074e14			−0.289803			−0.144902	−	0.989446i	$-0.546287\pi$
$601$	−5.57074e14			−0.289803			−0.144902	+	0.989446i	$0.546287\pi$
$602$		0			0
$603$			2.26697e13i			0.0115798i
$604$		0			0
$605$	−8.93380e14	−	3.67648e14i	−0.448107	−	0.184407i
$606$		0			0
$607$			1.52913e15i			0.753192i	0.926378	+	0.376596i	$0.122905\pi$
$607$			1.52913e15i			0.753192i	−0.926378	+	0.376596i	$0.877095\pi$
$608$		0			0
$609$	6.49074e14			0.313978
$610$		0			0
$611$	1.60181e15			0.761001
$612$		0			0
$613$			1.69574e14i			0.0791272i	0.999217	+	0.0395636i	$0.0125968\pi$
$613$			1.69574e14i			0.0791272i	−0.999217	+	0.0395636i	$0.987403\pi$
$614$		0			0
$615$	−1.11069e15	+	2.69896e15i	−0.509071	+	1.23704i
$616$		0			0
$617$		−	1.64642e15i		−	0.741263i	−0.928780	−	0.370632i	$-0.879141\pi$
$617$		−	1.64642e15i		−	0.741263i	0.928780	−	0.370632i	$-0.120859\pi$
$618$		0			0
$619$	2.39050e15			1.05728			0.528640	−	0.848846i	$-0.322702\pi$
$619$	2.39050e15			1.05728			0.528640	+	0.848846i	$0.322702\pi$
$620$		0			0
$621$	−2.94559e15			−1.27988
$622$		0			0
$623$		−	5.67160e15i		−	2.42115i
$624$		0			0
$625$	2.19098e13	+	2.38409e15i	0.00918964	+	0.999958i
$626$		0			0
$627$		−	2.87138e15i		−	1.18337i
$628$		0			0
$629$	−2.58726e15			−1.04776
$630$		0			0
$631$	−3.63917e15			−1.44824			−0.724121	−	0.689673i	$-0.757754\pi$
$631$	−3.63917e15			−1.44824			−0.724121	+	0.689673i	$0.757754\pi$
$632$		0			0
$633$			2.11242e15i			0.826152i
$634$		0			0
$635$	−3.26588e14	+	7.93606e14i	−0.125529	+	0.305035i
$636$		0			0
$637$			1.47493e15i			0.557192i
$638$		0			0
$639$	−1.62957e14			−0.0605089
$640$		0			0
$641$	−2.37308e15			−0.866149			−0.433075	−	0.901358i	$-0.642571\pi$
$641$	−2.37308e15			−0.866149			−0.433075	+	0.901358i	$0.642571\pi$
$642$		0			0
$643$		−	2.78183e14i		−	0.0998091i	−0.998754	−	0.0499046i	$-0.984108\pi$
$643$		−	2.78183e14i		−	0.0998091i	0.998754	−	0.0499046i	$-0.0158917\pi$
$644$		0			0
$645$	−3.95401e15	−	1.62717e15i	−1.39463	−	0.573925i
$646$		0			0
$647$			4.18264e15i			1.45036i	0.688558	+	0.725181i	$0.258244\pi$
$647$			4.18264e15i			1.45036i	−0.688558	+	0.725181i	$0.741756\pi$
$648$		0			0
$649$	2.30783e15			0.786788
$650$		0			0
$651$	6.58598e14			0.220762
$652$		0			0
$653$			4.96295e15i			1.63575i	0.575394	+	0.817876i	$0.304849\pi$
$653$			4.96295e15i			1.63575i	−0.575394	+	0.817876i	$0.695151\pi$
$654$		0			0
$655$	−1.01538e15	−	4.17855e14i	−0.329081	−	0.135425i
$656$		0			0
$657$		−	6.38077e14i		−	0.203359i
$658$		0			0
$659$	3.03322e15			0.950678			0.475339	−	0.879803i	$-0.342325\pi$
$659$	3.03322e15			0.950678			0.475339	+	0.879803i	$0.342325\pi$
$660$		0			0
$661$	1.38120e15			0.425743			0.212871	−	0.977080i	$-0.431718\pi$
$661$	1.38120e15			0.425743			0.212871	+	0.977080i	$0.431718\pi$
$662$		0			0
$663$		−	2.42818e15i		−	0.736134i
$664$		0			0
$665$	−2.53237e15	+	6.15362e15i	−0.755105	+	1.83490i
$666$		0			0
$667$		−	1.09266e15i		−	0.320473i
$668$		0			0
$669$	2.30975e15			0.666378
$670$		0			0
$671$	1.58088e15			0.448668
$672$		0			0
$673$		−	3.93673e15i		−	1.09914i	−0.835448	−	0.549570i	$-0.814792\pi$
$673$		−	3.93673e15i		−	1.09914i	0.835448	−	0.549570i	$-0.185208\pi$
$674$		0			0
$675$	2.39684e15	−	2.41897e15i	0.658367	−	0.664446i
$676$		0			0
$677$			1.02664e15i			0.277448i	0.990331	+	0.138724i	$0.0443001\pi$
$677$			1.02664e15i			0.277448i	−0.990331	+	0.138724i	$0.955700\pi$
$678$		0			0
$679$	2.44929e15			0.651262
$680$		0			0
$681$	−6.13317e15			−1.60463
$682$		0			0
$683$		−	3.59177e15i		−	0.924688i	−0.886701	−	0.462344i	$-0.847009\pi$
$683$		−	3.59177e15i		−	0.924688i	0.886701	−	0.462344i	$-0.152991\pi$
$684$		0			0
$685$	2.48073e15	−	6.02816e15i	0.628467	−	1.52717i
$686$		0			0
$687$			2.03937e15i			0.508432i
$688$		0			0
$689$	3.29560e15			0.808591
$690$		0			0
$691$	4.95364e15			1.19618			0.598089	−	0.801430i	$-0.295927\pi$
$691$	4.95364e15			1.19618			0.598089	+	0.801430i	$0.295927\pi$
$692$		0			0
$693$		−	4.36012e14i		−	0.103625i
$694$		0			0
$695$	−7.54059e15	−	3.10314e15i	−1.76396	−	0.725914i
$696$		0			0
$697$		−	4.23011e15i		−	0.974028i
$698$		0			0
$699$	2.19777e15			0.498147
$700$		0			0
$701$	−6.61391e14			−0.147574			−0.0737869	−	0.997274i	$-0.523508\pi$
$701$	−6.61391e14			−0.147574			−0.0737869	+	0.997274i	$0.523508\pi$
$702$		0			0
$703$			9.69608e15i			2.12981i
$704$		0			0
$705$	3.78284e15	+	1.55673e15i	0.818046	+	0.336646i
$706$		0			0
$707$			4.16144e15i			0.886006i
$708$		0			0
$709$	6.38804e15			1.33910			0.669550	−	0.742767i	$-0.266487\pi$
$709$	6.38804e15			1.33910			0.669550	+	0.742767i	$0.266487\pi$
$710$		0			0
$711$	6.70477e14			0.138389
$712$		0			0
$713$		−	1.10869e15i		−	0.225329i
$714$		0			0
$715$	1.23935e15	−	3.01162e15i	0.248035	−	0.602721i
$716$		0			0
$717$		−	9.25975e15i		−	1.82492i
$718$		0			0
$719$	−5.28492e15			−1.02572			−0.512860	−	0.858472i	$-0.671414\pi$
$719$	−5.28492e15			−1.02572			−0.512860	+	0.858472i	$0.671414\pi$
$720$		0			0
$721$	4.66066e15			0.890848
$722$		0			0
$723$			5.22730e15i			0.984049i
$724$		0			0
$725$	8.97307e14	+	8.89098e14i	0.166373	+	0.164851i
$726$		0			0
$727$		−	1.40273e15i		−	0.256173i	−0.991763	−	0.128087i	$-0.959116\pi$
$727$		−	1.40273e15i		−	0.256173i	0.991763	−	0.128087i	$-0.0408836\pi$
$728$		0			0
$729$	−4.79205e15			−0.862026
$730$		0			0
$731$	6.19718e15			1.09812
$732$		0			0
$733$			1.29894e15i			0.226734i	0.993553	+	0.113367i	$0.0361636\pi$
$733$			1.29894e15i			0.226734i	−0.993553	+	0.113367i	$0.963836\pi$
$734$		0			0
$735$	−1.43342e15	+	3.48319e15i	−0.246486	+	0.598959i
$736$		0			0
$737$		−	4.31914e14i		−	0.0731688i
$738$		0			0
$739$	−3.26209e15			−0.544442			−0.272221	−	0.962235i	$-0.587758\pi$
$739$	−3.26209e15			−0.544442			−0.272221	+	0.962235i	$0.587758\pi$
$740$		0			0
$741$	−9.09990e15			−1.49636
$742$		0			0
$743$			4.26111e15i			0.690373i	0.938534	+	0.345187i	$0.112184\pi$
$743$			4.26111e15i			0.690373i	−0.938534	+	0.345187i	$0.887816\pi$
$744$		0			0
$745$	7.35602e15	+	3.02718e15i	1.17431	+	0.483258i
$746$		0			0
$747$			6.31074e14i			0.0992697i
$748$		0			0
$749$	−5.86314e15			−0.908825
$750$		0			0
$751$	−1.05581e16			−1.61275			−0.806374	−	0.591405i	$-0.798573\pi$
$751$	−1.05581e16			−1.61275			−0.806374	+	0.591405i	$0.798573\pi$
$752$		0			0
$753$			5.10053e15i			0.767790i
$754$		0			0
$755$	−5.42359e15	−	2.23194e15i	−0.804597	−	0.331111i
$756$		0			0
$757$			5.17560e15i			0.756717i	0.925659	+	0.378359i	$0.123511\pi$
$757$			5.17560e15i			0.756717i	−0.925659	+	0.378359i	$0.876489\pi$
$758$		0			0
$759$	−7.19391e15			−1.03666
$760$		0			0
$761$	2.62905e15			0.373407			0.186704	−	0.982416i	$-0.440220\pi$
$761$	2.62905e15			0.373407			0.186704	+	0.982416i	$0.440220\pi$
$762$		0			0
$763$		−	1.28198e16i		−	1.79472i
$764$		0			0
$765$	2.40771e14	−	5.85072e14i	0.0332252	−	0.0807368i
$766$		0			0
$767$		−	7.31391e15i		−	0.994890i
$768$		0			0
$769$	3.83814e15			0.514666			0.257333	−	0.966323i	$-0.417156\pi$
$769$	3.83814e15			0.514666			0.257333	+	0.966323i	$0.417156\pi$
$770$		0			0
$771$	−2.80018e14			−0.0370158
$772$		0			0
$773$		−	8.02378e15i		−	1.04566i	−0.852436	−	0.522832i	$-0.824876\pi$
$773$		−	8.02378e15i		−	1.04566i	0.852436	−	0.522832i	$-0.175124\pi$
$774$		0			0
$775$	9.10473e14	+	9.02144e14i	0.116979	+	0.115909i
$776$		0			0
$777$			1.44305e16i			1.82796i
$778$		0			0
$779$	−1.58528e16			−1.97994
$780$		0			0
$781$	3.10475e15			0.382336
$782$		0			0
$783$		−	1.80421e15i		−	0.219078i
$784$		0			0
$785$	3.41582e14	−	8.30041e14i	0.0408989	−	0.0993839i
$786$		0			0
$787$			4.40335e15i			0.519903i	0.965622	+	0.259951i	$0.0837065\pi$
$787$			4.40335e15i			0.519903i	−0.965622	+	0.259951i	$0.916293\pi$
$788$		0			0
$789$	1.50573e15			0.175317
$790$		0			0
$791$	1.60763e16			1.84593
$792$		0			0
$793$		−	5.01009e15i		−	0.567339i
$794$		0			0
$795$	7.78289e15	+	3.20285e15i	0.869204	+	0.357699i
$796$		0			0
$797$			1.70414e15i			0.187709i	0.995586	+	0.0938544i	$0.0299188\pi$
$797$			1.70414e15i			0.187709i	−0.995586	+	0.0938544i	$0.970081\pi$
$798$		0			0
$799$	−5.92889e15			−0.644119
$800$		0			0
$801$	2.02088e15			0.216551
$802$		0			0
$803$			1.21570e16i			1.28496i
$804$		0			0
$805$	1.54172e16	+	6.34455e15i	1.60741	+	0.661490i
$806$		0			0
$807$			1.20624e16i			1.24059i
$808$		0			0
$809$	−7.20748e15			−0.731251			−0.365625	−	0.930762i	$-0.619145\pi$
$809$	−7.20748e15			−0.731251			−0.365625	+	0.930762i	$0.619145\pi$
$810$		0			0
$811$	−3.41679e15			−0.341982			−0.170991	−	0.985273i	$-0.554697\pi$
$811$	−3.41679e15			−0.341982			−0.170991	+	0.985273i	$0.554697\pi$
$812$		0			0
$813$		−	4.68529e15i		−	0.462635i
$814$		0			0
$815$	1.93078e15	−	4.69178e15i	0.188090	−	0.457057i
$816$		0			0
$817$		−	2.32247e16i		−	2.23217i
$818$		0			0
$819$	−1.38180e15			−0.131034
$820$		0			0
$821$	2.35622e15			0.220459			0.110230	−	0.993906i	$-0.464841\pi$
$821$	2.35622e15			0.220459			0.110230	+	0.993906i	$0.464841\pi$
$822$		0			0
$823$		−	1.41641e16i		−	1.30765i	−0.756648	−	0.653823i	$-0.773164\pi$
$823$		−	1.41641e16i		−	1.30765i	0.756648	−	0.653823i	$-0.226836\pi$
$824$		0			0
$825$	5.85371e15	−	5.90776e15i	0.533255	−	0.538178i
$826$		0			0
$827$		−	5.85548e15i		−	0.526359i	−0.964747	−	0.263179i	$-0.915229\pi$
$827$		−	5.85548e15i		−	0.526359i	0.964747	−	0.263179i	$-0.0847711\pi$
$828$		0			0
$829$	1.14493e16			1.01562			0.507809	−	0.861470i	$-0.330456\pi$
$829$	1.14493e16			1.01562			0.507809	+	0.861470i	$0.330456\pi$
$830$		0			0
$831$	1.60109e16			1.40155
$832$		0			0
$833$		−	5.45925e15i		−	0.471613i
$834$		0			0
$835$	−5.49881e15	+	1.33621e16i	−0.468806	+	1.13919i
$836$		0			0
$837$		−	1.83069e15i		−	0.154037i
$838$		0			0
$839$	3.16050e15			0.262461			0.131231	−	0.991352i	$-0.458107\pi$
$839$	3.16050e15			0.262461			0.131231	+	0.991352i	$0.458107\pi$
$840$		0			0
$841$	−1.15312e16			−0.945144
$842$		0			0
$843$		−	1.01065e16i		−	0.817615i
$844$		0			0
$845$	2.03647e15	+	8.38057e14i	0.162617	+	0.0669209i
$846$		0			0
$847$		−	7.80968e15i		−	0.615566i
$848$		0			0
$849$	−8.01790e15			−0.623833
$850$		0			0
$851$	2.42924e16			1.86577
$852$		0			0
$853$			2.17768e16i			1.65110i	0.564326	+	0.825552i	$0.309136\pi$
$853$			2.17768e16i			1.65110i	−0.564326	+	0.825552i	$0.690864\pi$
$854$		0			0
$855$	−2.19263e15	−	9.02320e14i	−0.164116	−	0.0675378i
$856$		0			0
$857$			9.47411e15i			0.700074i	0.936736	+	0.350037i	$0.113831\pi$
$857$			9.47411e15i			0.700074i	−0.936736	+	0.350037i	$0.886169\pi$
$858$		0			0
$859$	−1.10829e16			−0.808521			−0.404261	−	0.914644i	$-0.632471\pi$
$859$	−1.10829e16			−0.808521			−0.404261	+	0.914644i	$0.632471\pi$
$860$		0			0
$861$	−2.35935e16			−1.69932
$862$		0			0
$863$			2.16707e16i			1.54104i	0.637419	+	0.770518i	$0.280002\pi$
$863$			2.16707e16i			1.54104i	−0.637419	+	0.770518i	$0.719998\pi$
$864$		0			0
$865$	5.73234e15	−	1.39295e16i	0.402479	−	0.978020i
$866$		0			0
$867$		−	6.23449e15i		−	0.432211i
$868$		0			0
$869$	−1.27743e16			−0.874435
$870$		0			0
$871$	−1.36881e15			−0.0925218
$872$		0			0
$873$			8.72718e14i			0.0582499i
$874$		0			0
$875$	−1.77553e16	+	7.49826e15i	−1.17026	+	0.494216i
$876$		0			0
$877$			1.80079e16i			1.17210i	0.810274	+	0.586051i	$0.199318\pi$
$877$			1.80079e16i			1.17210i	−0.810274	+	0.586051i	$0.800682\pi$
$878$		0			0
$879$	2.39823e16			1.54153
$880$		0			0
$881$	−1.09706e16			−0.696407			−0.348204	−	0.937419i	$-0.613208\pi$
$881$	−1.09706e16			−0.696407			−0.348204	+	0.937419i	$0.613208\pi$
$882$		0			0
$883$			2.05525e16i			1.28849i	0.764819	+	0.644246i	$0.222829\pi$
$883$			2.05525e16i			1.28849i	−0.764819	+	0.644246i	$0.777171\pi$
$884$		0			0
$885$	7.10807e15	−	1.72725e16i	0.440112	−	1.06947i
$886$		0			0
$887$		−	2.34060e16i		−	1.43136i	−0.698430	−	0.715679i	$-0.746118\pi$
$887$		−	2.34060e16i		−	1.43136i	0.698430	−	0.715679i	$-0.253882\pi$
$888$		0			0
$889$	−6.93748e15			−0.419027
$890$		0			0
$891$	−1.32461e16			−0.790241
$892$		0			0
$893$			2.22192e16i			1.30932i
$894$		0			0
$895$	2.33277e15	+	9.59992e14i	0.135783	+	0.0558780i
$896$		0			0
$897$			2.27988e16i			1.31085i
$898$		0			0
$899$	6.79086e14			0.0385697
$900$		0			0
$901$	−1.21982e16			−0.684400
$902$		0			0
$903$		−	3.45649e16i		−	1.91581i
$904$		0			0
$905$	−2.85168e16	−	1.17353e16i	−1.56147	−	0.642582i
$906$		0			0
$907$			1.34560e16i			0.727908i	0.931417	+	0.363954i	$0.118573\pi$
$907$			1.34560e16i			0.727908i	−0.931417	+	0.363954i	$0.881427\pi$
$908$		0			0
$909$	−1.48278e15			−0.0792458
$910$		0			0
$911$	3.04149e16			1.60596			0.802981	−	0.596005i	$-0.203246\pi$
$911$	3.04149e16			1.60596			0.802981	+	0.596005i	$0.203246\pi$
$912$		0			0
$913$		−	1.20235e16i		−	0.627253i
$914$		0			0
$915$	4.86908e15	−	1.18318e16i	0.250975	−	0.609867i
$916$		0			0
$917$		−	8.87619e15i		−	0.452059i
$918$		0			0
$919$	−7.19016e15			−0.361829			−0.180914	−	0.983499i	$-0.557906\pi$
$919$	−7.19016e15			−0.361829			−0.180914	+	0.983499i	$0.557906\pi$
$920$		0			0
$921$	−2.03938e16			−1.01408
$922$		0			0
$923$		−	9.83949e15i		−	0.483463i
$924$		0			0
$925$	−1.97668e16	+	1.99493e16i	−0.959749	+	0.968610i
$926$		0			0
$927$			1.66066e15i			0.0796789i
$928$		0			0
$929$	3.70391e16			1.75620			0.878100	−	0.478476i	$-0.158811\pi$
$929$	3.70391e16			1.75620			0.878100	+	0.478476i	$0.158811\pi$
$930$		0			0
$931$	−2.04592e16			−0.958662
$932$		0			0
$933$		−	6.84934e15i		−	0.317176i
$934$		0			0
$935$	−4.58730e15	+	1.11471e16i	−0.209939	+	0.510150i
$936$		0			0
$937$			1.82228e15i			0.0824228i	0.999150	+	0.0412114i	$0.0131217\pi$
$937$			1.82228e15i			0.0824228i	−0.999150	+	0.0412114i	$0.986878\pi$
$938$		0			0
$939$	1.96963e16			0.880490
$940$		0			0
$941$	3.23703e16			1.43022			0.715111	−	0.699011i	$-0.246376\pi$
$941$	3.23703e16			1.43022			0.715111	+	0.699011i	$0.246376\pi$
$942$		0			0
$943$			3.97175e16i			1.73447i
$944$		0			0
$945$	2.54572e16	+	1.04763e16i	1.09884	+	0.452200i
$946$		0			0
$947$		−	4.09209e16i		−	1.74590i	−0.487806	−	0.872952i	$-0.662203\pi$
$947$		−	4.09209e16i		−	1.74590i	0.487806	−	0.872952i	$-0.337797\pi$
$948$		0			0
$949$	3.85276e16			1.62483
$950$		0			0
$951$	−2.65409e15			−0.110643
$952$		0			0
$953$		−	7.24102e15i		−	0.298393i	−0.988808	−	0.149197i	$-0.952331\pi$
$953$		−	7.24102e15i		−	0.298393i	0.988808	−	0.149197i	$-0.0476687\pi$
$954$		0			0
$955$	−1.18212e16	−	4.86472e15i	−0.481552	−	0.198171i
$956$		0			0
$957$		−	4.40637e15i		−	0.177446i
$958$		0			0
$959$	5.26965e16			2.09787
$960$		0			0
$961$	−2.47194e16			−0.972881
$962$		0			0
$963$		−	2.08912e15i		−	0.0812868i
$964$		0			0
$965$	−1.46569e16	+	3.56162e16i	−0.563824	+	1.37009i
$966$		0			0
$967$			1.81444e15i			0.0690076i	0.999405	+	0.0345038i	$0.0109851\pi$
$967$			1.81444e15i			0.0690076i	−0.999405	+	0.0345038i	$0.989015\pi$
$968$		0			0
$969$	3.36820e16			1.26654
$970$		0			0
$971$	2.90679e16			1.08071			0.540353	−	0.841438i	$-0.318291\pi$
$971$	2.90679e16			1.08071			0.540353	+	0.841438i	$0.318291\pi$
$972$		0			0
$973$		−	6.59178e16i		−	2.42316i
$974$		0			0
$975$	−1.87227e16	−	1.85515e16i	−0.680524	−	0.674299i
$976$		0			0
$977$			2.11637e16i			0.760627i	0.924858	+	0.380314i	$0.124184\pi$
$977$			2.11637e16i			0.760627i	−0.924858	+	0.380314i	$0.875816\pi$
$978$		0			0
$979$	−3.85028e16			−1.36832
$980$		0			0
$981$	4.56789e15			0.160522
$982$		0			0
$983$		−	4.76831e16i		−	1.65699i	−0.559997	−	0.828495i	$-0.689198\pi$
$983$		−	4.76831e16i		−	1.65699i	0.559997	−	0.828495i	$-0.310802\pi$
$984$		0			0
$985$	6.02531e14	−	1.46414e15i	0.0207052	−	0.0503135i
$986$		0			0
$987$			3.30685e16i			1.12375i
$988$		0			0
$989$	−5.81867e16			−1.95544
$990$		0			0
$991$	−2.68163e16			−0.891238			−0.445619	−	0.895223i	$-0.647016\pi$
$991$	−2.68163e16			−0.891238			−0.445619	+	0.895223i	$0.647016\pi$
$992$		0			0
$993$			5.78893e16i			1.90273i
$994$		0			0
$995$	3.14090e15	+	1.29256e15i	0.102100	+	0.0420168i
$996$		0			0
$997$		−	5.40367e16i		−	1.73726i	−0.495459	−	0.868632i	$-0.665000\pi$
$997$		−	5.40367e16i		−	1.73726i	0.495459	−	0.868632i	$-0.335000\pi$
$998$		0			0
$999$	4.01121e16			1.27546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.12.c.a.9.2	✓	6
3.2	odd	2		180.12.d.a.109.1		6
4.3	odd	2		80.12.c.b.49.5		6
5.2	odd	4		100.12.a.f.1.2		6
5.3	odd	4		100.12.a.f.1.5		6
5.4	even	2	inner	20.12.c.a.9.5	yes	6
15.14	odd	2		180.12.d.a.109.2		6
20.19	odd	2		80.12.c.b.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.12.c.a.9.2	✓	6	1.1	even	1	trivial
20.12.c.a.9.5	yes	6	5.4	even	2	inner
80.12.c.b.49.2		6	20.19	odd	2
80.12.c.b.49.5		6	4.3	odd	2
100.12.a.f.1.2		6	5.2	odd	4
100.12.a.f.1.5		6	5.3	odd	4
180.12.d.a.109.1		6	3.2	odd	2
180.12.d.a.109.2		6	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-444.156i q^{3} +(6461.93 + 2659.24i) q^{5} +56488.4i q^{7} -20127.7 q^{9} +O(q^{10})\)	\(q-444.156i q^{3} +(6461.93 + 2659.24i) q^{5} +56488.4i q^{7} -20127.7 q^{9} +383483. q^{11} -1.21532e6i q^{13} +(1.18112e6 - 2.87011e6i) q^{15} +4.49835e6i q^{17} +1.68581e7 q^{19} +2.50897e7 q^{21} -4.22361e7i q^{23} +(3.46850e7 + 3.43677e7i) q^{25} -6.97411e7i q^{27} +2.58702e7 q^{29} +2.62498e7 q^{31} -1.70326e8i q^{33} +(-1.50216e8 + 3.65024e8i) q^{35} +5.75158e8i q^{37} -5.39793e8 q^{39} -9.40368e8 q^{41} -1.37765e9i q^{43} +(-1.30064e8 - 5.35243e7i) q^{45} +1.31801e9i q^{47} -1.21361e9 q^{49} +1.99797e9 q^{51} +2.71171e9i q^{53} +(2.47804e9 + 1.01977e9i) q^{55} -7.48764e9i q^{57} +6.01808e9 q^{59} +4.12243e9 q^{61} -1.13698e9i q^{63} +(3.23184e9 - 7.85334e9i) q^{65} -1.12629e9i q^{67} -1.87594e10 q^{69} +8.09619e9 q^{71} +3.17015e10i q^{73} +(1.52646e10 - 1.54055e10i) q^{75} +2.16623e10i q^{77} -3.33112e10 q^{79} -3.45415e10 q^{81} -3.13536e10i q^{83} +(-1.19622e10 + 2.90680e10i) q^{85} -1.14904e10i q^{87} -1.00403e11 q^{89} +6.86517e10 q^{91} -1.16590e10i q^{93} +(1.08936e11 + 4.48298e10i) q^{95} -4.33591e10i q^{97} -7.71861e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4126 q^{5} - 501494 q^{9}+O(q^{10}) \) 6 * q - 4126 * q^5 - 501494 * q^9	\( 6 q - 4126 q^{5} - 501494 q^{9} + 1298200 q^{11} - 3310648 q^{15} - 244824 q^{19} - 44518024 q^{21} + 34713726 q^{25} - 138940764 q^{29} + 214450176 q^{31} - 308845352 q^{35} + 542728176 q^{39} + 106601836 q^{41} + 3311255374 q^{45} - 4506920718 q^{49} + 571023872 q^{51} - 1741716600 q^{55} - 14817616328 q^{59} + 13263695412 q^{61} + 22042348848 q^{65} - 57831800072 q^{69} + 983424528 q^{71} + 97974745648 q^{75} - 158406142752 q^{79} + 113598783134 q^{81} + 109785881856 q^{85} - 288677471236 q^{89} + 228887753424 q^{91} + 348434078904 q^{95} - 1006608631000 q^{99}+O(q^{100}) \) 6 * q - 4126 * q^5 - 501494 * q^9 + 1298200 * q^11 - 3310648 * q^15 - 244824 * q^19 - 44518024 * q^21 + 34713726 * q^25 - 138940764 * q^29 + 214450176 * q^31 - 308845352 * q^35 + 542728176 * q^39 + 106601836 * q^41 + 3311255374 * q^45 - 4506920718 * q^49 + 571023872 * q^51 - 1741716600 * q^55 - 14817616328 * q^59 + 13263695412 * q^61 + 22042348848 * q^65 - 57831800072 * q^69 + 983424528 * q^71 + 97974745648 * q^75 - 158406142752 * q^79 + 113598783134 * q^81 + 109785881856 * q^85 - 288677471236 * q^89 + 228887753424 * q^91 + 348434078904 * q^95 - 1006608631000 * q^99

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