LMFDB - Embedded newform 207.7.d.e.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,7,Mod(91,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("207.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	207.d (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:	$47.6211953093$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.5405 q^{2} +119.346 q^{4} -141.090i q^{5} +238.919i q^{7} -749.409 q^{8} +O(q^{10})$	\(q-13.5405 q^{2} +119.346 q^{4} -141.090i q^{5} +238.919i q^{7} -749.409 q^{8} +1910.43i q^{10} +253.900i q^{11} +572.457 q^{13} -3235.09i q^{14} +2509.27 q^{16} +197.610i q^{17} -12138.1i q^{19} -16838.4i q^{20} -3437.93i q^{22} +(-9464.20 + 7646.22i) q^{23} -4281.27 q^{25} -7751.37 q^{26} +28513.9i q^{28} +6501.32 q^{29} +4462.15 q^{31} +13985.4 q^{32} -2675.74i q^{34} +33709.0 q^{35} -44851.3i q^{37} +164356. i q^{38} +105734. i q^{40} +56540.9 q^{41} +119698. i q^{43} +30301.8i q^{44} +(128150. - 103534. i) q^{46} +60673.0 q^{47} +60566.7 q^{49} +57970.6 q^{50} +68320.3 q^{52} +10068.8i q^{53} +35822.6 q^{55} -179048. i q^{56} -88031.2 q^{58} -48463.2 q^{59} +169937. i q^{61} -60419.8 q^{62} -349963. q^{64} -80767.8i q^{65} -551441. i q^{67} +23583.9i q^{68} -456437. q^{70} +256818. q^{71} -723758. q^{73} +607310. i q^{74} -1.44863e6i q^{76} -60661.4 q^{77} -430503. i q^{79} -354032. i q^{80} -765593. q^{82} +90097.3i q^{83} +27880.7 q^{85} -1.62077e6i q^{86} -190275. i q^{88} -868016. i q^{89} +136771. i q^{91} +(-1.12951e6 + 912544. i) q^{92} -821544. q^{94} -1.71256e6 q^{95} +1.17710e6i q^{97} -820105. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$1$

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 $

$2$	−13.5405			−1.69257			−0.846283	−	0.532734i	$-0.821164\pi$
$2$	−13.5405			−1.69257			−0.846283	+	0.532734i	$0.821164\pi$
$3$		0			0
$3$		0			0
$4$	119.346			1.86478
$5$		−	141.090i		−	1.12872i	−0.825530	−	0.564358i	$-0.809124\pi$
$5$		−	141.090i		−	1.12872i	0.825530	−	0.564358i	$-0.190876\pi$
$6$		0			0
$7$			238.919i			0.696557i	0.937391	+	0.348278i	$0.113234\pi$
$7$			238.919i			0.696557i	−0.937391	+	0.348278i	$0.886766\pi$
$8$	−749.409			−1.46369
$9$		0			0
$10$			1910.43i			1.91043i
$11$			253.900i			0.190759i	0.995441	+	0.0953793i	$0.0304064\pi$
$11$			253.900i			0.190759i	−0.995441	+	0.0953793i	$0.969594\pi$
$12$		0			0
$13$	572.457			0.260563			0.130282	−	0.991477i	$-0.458412\pi$
$13$	572.457			0.260563			0.130282	+	0.991477i	$0.458412\pi$
$14$		−	3235.09i		−	1.17897i
$15$		0			0
$16$	2509.27			0.612615
$17$			197.610i			0.0402218i	0.999798	+	0.0201109i	$0.00640193\pi$
$17$			197.610i			0.0402218i	−0.999798	+	0.0201109i	$0.993598\pi$
$18$		0			0
$19$		−	12138.1i		−	1.76966i	−0.465913	−	0.884831i	$-0.654274\pi$
$19$		−	12138.1i		−	1.76966i	0.465913	−	0.884831i	$-0.345726\pi$
$20$		−	16838.4i		−	2.10480i
$21$		0			0
$22$		−	3437.93i		−	0.322871i
$23$	−9464.20	+	7646.22i	−0.777859	+	0.628439i
$23$	−9464.20	+	7646.22i	−0.777859	+	0.628439i
$24$		0			0
$25$	−4281.27			−0.274001
$26$	−7751.37			−0.441020
$27$		0			0
$28$			28513.9i			1.29892i
$29$	6501.32			0.266568			0.133284	−	0.991078i	$-0.457448\pi$
$29$	6501.32			0.266568			0.133284	+	0.991078i	$0.457448\pi$
$30$		0			0
$31$	4462.15			0.149782			0.0748909	−	0.997192i	$-0.476139\pi$
$31$	4462.15			0.149782			0.0748909	+	0.997192i	$0.476139\pi$
$32$	13985.4			0.426800
$33$		0			0
$34$		−	2675.74i		−	0.0680780i
$35$	33709.0			0.786215
$36$		0			0
$37$		−	44851.3i		−	0.885462i	−0.896654	−	0.442731i	$-0.854010\pi$
$37$		−	44851.3i		−	0.885462i	0.896654	−	0.442731i	$-0.145990\pi$
$38$			164356.i			2.99527i
$39$		0			0
$40$			105734.i			1.65209i
$41$	56540.9			0.820372			0.410186	−	0.912002i	$-0.365464\pi$
$41$	56540.9			0.820372			0.410186	+	0.912002i	$0.365464\pi$
$42$		0			0
$43$			119698.i			1.50550i	0.658307	+	0.752750i	$0.271273\pi$
$43$			119698.i			1.50550i	−0.658307	+	0.752750i	$0.728727\pi$
$44$			30301.8i			0.355722i
$45$		0			0
$46$	128150.	−	103534.i	1.31658	−	1.06367i
$47$	60673.0			0.584389			0.292195	−	0.956359i	$-0.405615\pi$
$47$	60673.0			0.584389			0.292195	+	0.956359i	$0.405615\pi$
$48$		0			0
$49$	60566.7			0.514809
$50$	57970.6			0.463765
$51$		0			0
$52$	68320.3			0.485892
$53$			10068.8i			0.0676318i	0.999428	+	0.0338159i	$0.0107660\pi$
$53$			10068.8i			0.0676318i	−0.999428	+	0.0338159i	$0.989234\pi$
$54$		0			0
$55$	35822.6			0.215312
$56$		−	179048.i		−	1.01954i
$57$		0			0
$58$	−88031.2			−0.451183
$59$	−48463.2			−0.235970			−0.117985	−	0.993015i	$-0.537643\pi$
$59$	−48463.2			−0.235970			−0.117985	+	0.993015i	$0.537643\pi$
$60$		0			0
$61$			169937.i			0.748682i	0.927291	+	0.374341i	$0.122131\pi$
$61$			169937.i			0.748682i	−0.927291	+	0.374341i	$0.877869\pi$
$62$	−60419.8			−0.253515
$63$		0			0
$64$	−349963.			−1.33500
$65$		−	80767.8i		−	0.294102i
$66$		0			0
$67$		−	551441.i		−	1.83347i	−0.399493	−	0.916736i	$-0.630814\pi$
$67$		−	551441.i		−	1.83347i	0.399493	−	0.916736i	$-0.369186\pi$
$68$			23583.9i			0.0750046i
$69$		0			0
$70$	−456437.			−1.33072
$71$	256818.			0.717548			0.358774	−	0.933424i	$-0.383195\pi$
$71$	256818.			0.717548			0.358774	+	0.933424i	$0.383195\pi$
$72$		0			0
$73$	−723758.			−1.86048			−0.930240	−	0.366953i	$-0.880401\pi$
$73$	−723758.			−1.86048			−0.930240	+	0.366953i	$0.880401\pi$
$74$			607310.i			1.49870i
$75$		0			0
$76$		−	1.44863e6i		−	3.30002i
$77$	−60661.4			−0.132874
$78$		0			0
$79$		−	430503.i		−	0.873162i	−0.899665	−	0.436581i	$-0.856189\pi$
$79$		−	430503.i		−	0.873162i	0.899665	−	0.436581i	$-0.143811\pi$
$80$		−	354032.i		−	0.691468i
$81$		0			0
$82$	−765593.			−1.38853
$83$			90097.3i			0.157571i	0.996892	+	0.0787857i	$0.0251043\pi$
$83$			90097.3i			0.157571i	−0.996892	+	0.0787857i	$0.974896\pi$
$84$		0			0
$85$	27880.7			0.0453990
$86$		−	1.62077e6i		−	2.54816i
$87$		0			0
$88$		−	190275.i		−	0.279211i
$89$		−	868016.i		−	1.23128i	−0.788027	−	0.615641i	$-0.788897\pi$
$89$		−	868016.i		−	1.23128i	0.788027	−	0.615641i	$-0.211103\pi$
$90$		0			0
$91$			136771.i			0.181497i
$92$	−1.12951e6	+	912544.i	−1.45053	+	1.17190i
$93$		0			0
$94$	−821544.			−0.989116
$95$	−1.71256e6			−1.99745
$96$		0			0
$97$			1.17710e6i			1.28973i	0.764295	+	0.644866i	$0.223087\pi$
$97$			1.17710e6i			1.28973i	−0.764295	+	0.644866i	$0.776913\pi$
$98$	−820105.			−0.871347
$99$		0			0
$100$	−510951.			−0.510951
$101$	−1.69582e6			−1.64594			−0.822971	−	0.568083i	$-0.807685\pi$
$101$	−1.69582e6			−1.64594			−0.822971	+	0.568083i	$0.807685\pi$
$102$		0			0
$103$			276829.i			0.253338i	0.991945	+	0.126669i	$0.0404286\pi$
$103$			276829.i			0.253338i	−0.991945	+	0.126669i	$0.959571\pi$
$104$	−429005.			−0.381384
$105$		0			0
$106$		−	136337.i		−	0.114471i
$107$		−	961315.i		−	0.784719i	−0.919812	−	0.392360i	$-0.871659\pi$
$107$		−	961315.i		−	0.784719i	0.919812	−	0.392360i	$-0.128341\pi$
$108$		0			0
$109$		−	1.68124e6i		−	1.29822i	−0.760693	−	0.649112i	$-0.775141\pi$
$109$		−	1.68124e6i		−	1.29822i	0.760693	−	0.649112i	$-0.224859\pi$
$110$	−485057.			−0.364430
$111$		0			0
$112$			599512.i			0.426721i
$113$		−	1.63576e6i		−	1.13366i	−0.823833	−	0.566832i	$-0.808169\pi$
$113$		−	1.63576e6i		−	1.13366i	0.823833	−	0.566832i	$-0.191831\pi$
$114$		0			0
$115$	1.07880e6	+	1.33530e6i	0.709330	+	0.877982i
$116$	775904.			0.497089
$117$		0			0
$118$	656217.			0.399394
$119$	−47212.7			−0.0280168
$120$		0			0
$121$	1.70710e6			0.963611
$122$		−	2.30103e6i		−	1.26719i
$123$		0			0
$124$	532538.			0.279309
$125$		−	1.60048e6i		−	0.819447i
$126$		0			0
$127$	1.31698e6			0.642937			0.321469	−	0.946920i	$-0.395824\pi$
$127$	1.31698e6			0.642937			0.321469	+	0.946920i	$0.395824\pi$
$128$	3.84361e6			1.83278
$129$		0			0
$130$			1.09364e6i			0.497787i
$131$	−2.67613e6			−1.19040			−0.595201	−	0.803577i	$-0.702928\pi$
$131$	−2.67613e6			−1.19040			−0.595201	+	0.803577i	$0.702928\pi$
$132$		0			0
$133$	2.90002e6			1.23267
$134$			7.46679e6i			3.10327i
$135$		0			0
$136$		−	148090.i		−	0.0588722i
$137$		−	593938.i		−	0.230983i	−0.993308	−	0.115491i	$-0.963156\pi$
$137$		−	593938.i		−	0.230983i	0.993308	−	0.115491i	$-0.0368442\pi$
$138$		0			0
$139$	−2.89029e6			−1.07621			−0.538105	−	0.842878i	$-0.680860\pi$
$139$	−2.89029e6			−1.07621			−0.538105	+	0.842878i	$0.680860\pi$
$140$	4.02302e6			1.46612
$141$		0			0
$142$	−3.47746e6			−1.21450
$143$			145347.i			0.0497047i
$144$		0			0
$145$		−	917268.i		−	0.300879i
$146$	9.80006e6			3.14898
$147$		0			0
$148$		−	5.35281e6i		−	1.65119i
$149$		−	655168.i		−	0.198059i	−0.995085	−	0.0990293i	$-0.968426\pi$
$149$		−	655168.i		−	0.198059i	0.995085	−	0.0990293i	$-0.0315738\pi$
$150$		0			0
$151$	−3.79265e6			−1.10157			−0.550785	−	0.834647i	$-0.685672\pi$
$151$	−3.79265e6			−1.10157			−0.550785	+	0.834647i	$0.685672\pi$
$152$			9.09641e6i			2.59024i
$153$		0			0
$154$	821387.			0.224898
$155$		−	629562.i		−	0.169061i
$156$		0			0
$157$			1.45090e6i			0.374920i	0.982272	+	0.187460i	$0.0600255\pi$
$157$			1.45090e6i			0.374920i	−0.982272	+	0.187460i	$0.939974\pi$
$158$			5.82923e6i			1.47788i
$159$		0			0
$160$		−	1.97319e6i		−	0.481737i
$161$	−1.82683e6	−	2.26118e6i	−0.437744	−	0.541823i
$162$		0			0
$163$	81239.0			0.0187587			0.00937933	−	0.999956i	$-0.497014\pi$
$163$	81239.0			0.0187587			0.00937933	+	0.999956i	$0.497014\pi$
$164$	6.74791e6			1.52981
$165$		0			0
$166$		−	1.21996e6i		−	0.266700i
$167$	−6.77934e6			−1.45559			−0.727794	−	0.685796i	$-0.759454\pi$
$167$	−6.77934e6			−1.45559			−0.727794	+	0.685796i	$0.759454\pi$
$168$		0			0
$169$	−4.49910e6			−0.932107
$170$	−377519.			−0.0768407
$171$		0			0
$172$			1.42854e7i			2.80742i
$173$	2.80563e6			0.541866			0.270933	−	0.962598i	$-0.412668\pi$
$173$	2.80563e6			0.541866			0.270933	+	0.962598i	$0.412668\pi$
$174$		0			0
$175$		−	1.02288e6i		−	0.190857i
$176$			637103.i			0.116861i
$177$		0			0
$178$			1.17534e7i			2.08403i
$179$	−5.34710e6			−0.932307			−0.466153	−	0.884704i	$-0.654361\pi$
$179$	−5.34710e6			−0.932307			−0.466153	+	0.884704i	$0.654361\pi$
$180$		0			0
$181$		−	4.19704e6i		−	0.707795i	−0.935284	−	0.353897i	$-0.884856\pi$
$181$		−	4.19704e6i		−	0.707795i	0.935284	−	0.353897i	$-0.115144\pi$
$182$		−	1.85195e6i		−	0.307196i
$183$		0			0
$184$	7.09256e6	−	5.73015e6i	1.13854	−	0.919841i
$185$	−6.32805e6			−0.999436
$186$		0			0
$187$	−50173.0			−0.00767265
$188$	7.24106e6			1.08975
$189$		0			0
$190$	2.31890e7			3.38081
$191$			1.00876e7i			1.44773i	0.689940	+	0.723866i	$0.257637\pi$
$191$			1.00876e7i			1.44773i	−0.689940	+	0.723866i	$0.742363\pi$
$192$		0			0
$193$	−3.27393e6			−0.455405			−0.227703	−	0.973731i	$-0.573121\pi$
$193$	−3.27393e6			−0.455405			−0.227703	+	0.973731i	$0.573121\pi$
$194$		−	1.59386e7i		−	2.18296i
$195$		0			0
$196$	7.22838e6			0.960003
$197$	−493897.			−0.0646007			−0.0323004	−	0.999478i	$-0.510283\pi$
$197$	−493897.			−0.0646007			−0.0323004	+	0.999478i	$0.510283\pi$
$198$		0			0
$199$			1.17855e7i			1.49551i	0.663973	+	0.747756i	$0.268869\pi$
$199$			1.17855e7i			1.49551i	−0.663973	+	0.747756i	$0.731131\pi$
$200$	3.20842e6			0.401053
$201$		0			0
$202$	2.29622e7			2.78586
$203$			1.55329e6i			0.185680i
$204$		0			0
$205$		−	7.97733e6i		−	0.925968i
$206$		−	3.74841e6i		−	0.428791i
$207$		0			0
$208$	1.43645e6			0.159625
$209$	3.08186e6			0.337578
$210$		0			0
$211$	−1.60917e7			−1.71299			−0.856497	−	0.516152i	$-0.827364\pi$
$211$	−1.60917e7			−1.71299			−0.856497	+	0.516152i	$0.827364\pi$
$212$			1.20167e6i			0.126118i
$213$		0			0
$214$			1.30167e7i			1.32819i
$215$	1.68881e7			1.69928
$216$		0			0
$217$			1.06609e6i			0.104331i
$218$			2.27648e7i			2.19733i
$219$		0			0
$220$	4.27527e6			0.401509
$221$			113123.i			0.0104803i
$222$		0			0
$223$	−1.69138e7			−1.52520			−0.762600	−	0.646870i	$-0.776078\pi$
$223$	−1.69138e7			−1.52520			−0.762600	+	0.646870i	$0.776078\pi$
$224$			3.34138e6i			0.297291i
$225$		0			0
$226$			2.21491e7i			1.91880i
$227$		−	1.34846e7i		−	1.15281i	−0.817163	−	0.576407i	$-0.804454\pi$
$227$		−	1.34846e7i		−	1.15281i	0.817163	−	0.576407i	$-0.195546\pi$
$228$		0			0
$229$		−	1.85356e7i		−	1.54347i	−0.635942	−	0.771737i	$-0.719388\pi$
$229$		−	1.85356e7i		−	1.54347i	0.635942	−	0.771737i	$-0.280612\pi$
$230$	−1.46075e7	−	1.80807e7i	−1.20059	−	1.48604i
$231$		0			0
$232$	−4.87215e6			−0.390172
$233$	1.21229e7			0.958384			0.479192	−	0.877710i	$-0.340930\pi$
$233$	1.21229e7			0.958384			0.479192	+	0.877710i	$0.340930\pi$
$234$		0			0
$235$		−	8.56033e6i		−	0.659610i
$236$	−5.78388e6			−0.440031
$237$		0			0
$238$	639284.			0.0474202
$239$	−1.72709e7			−1.26509			−0.632545	−	0.774524i	$-0.717990\pi$
$239$	−1.72709e7			−1.26509			−0.632545	+	0.774524i	$0.717990\pi$
$240$		0			0
$241$		−	2.31843e7i		−	1.65632i	−0.560493	−	0.828159i	$-0.689388\pi$
$241$		−	2.31843e7i		−	1.65632i	0.560493	−	0.828159i	$-0.310612\pi$
$242$	−2.31150e7			−1.63097
$243$		0			0
$244$			2.02812e7i			1.39612i
$245$		−	8.54533e6i		−	0.581073i
$246$		0			0
$247$		−	6.94855e6i		−	0.461109i
$248$	−3.34398e6			−0.219234
$249$		0			0
$250$			2.16714e7i			1.38697i
$251$		−	2.88945e7i		−	1.82724i	−0.406574	−	0.913618i	$-0.633277\pi$
$251$		−	2.88945e7i		−	1.82724i	0.406574	−	0.913618i	$-0.366723\pi$
$252$		0			0
$253$	−1.94137e6	−	2.40296e6i	−0.119880	−	0.148383i
$254$	−1.78326e7			−1.08821
$255$		0			0
$256$	−2.96469e7			−1.76709
$257$	1.39430e6			0.0821404			0.0410702	−	0.999156i	$-0.486923\pi$
$257$	1.39430e6			0.0821404			0.0410702	+	0.999156i	$0.486923\pi$
$258$		0			0
$259$	1.07158e7			0.616775
$260$		−	9.63928e6i		−	0.548434i
$261$		0			0
$262$	3.62362e7			2.01483
$263$			1.79725e7i			0.987963i	0.869472	+	0.493981i	$0.164459\pi$
$263$			1.79725e7i			0.987963i	−0.869472	+	0.493981i	$0.835541\pi$
$264$		0			0
$265$	1.42061e6			0.0763372
$266$	−3.92678e7			−2.08637
$267$		0			0
$268$		−	6.58121e7i		−	3.41902i
$269$	−6.33003e6			−0.325199			−0.162599	−	0.986692i	$-0.551988\pi$
$269$	−6.33003e6			−0.325199			−0.162599	+	0.986692i	$0.551988\pi$
$270$		0			0
$271$	3.25661e6			0.163628			0.0818140	−	0.996648i	$-0.473929\pi$
$271$	3.25661e6			0.163628			0.0818140	+	0.996648i	$0.473929\pi$
$272$			495856.i			0.0246404i
$273$		0			0
$274$			8.04223e6i			0.390953i
$275$		−	1.08701e6i		−	0.0522681i
$276$		0			0
$277$	−3.85959e7			−1.81594			−0.907970	−	0.419036i	$-0.862368\pi$
$277$	−3.85959e7			−1.81594			−0.907970	+	0.419036i	$0.862368\pi$
$278$	3.91360e7			1.82156
$279$		0			0
$280$	−2.52618e7			−1.15078
$281$		−	239914.i		−	0.0108128i	−0.999985	−	0.00540638i	$-0.998279\pi$
$281$		−	239914.i		−	0.0108128i	0.999985	−	0.00540638i	$-0.00172091\pi$
$282$		0			0
$283$		−	7.89480e6i		−	0.348323i	−0.984717	−	0.174161i	$-0.944279\pi$
$283$		−	7.89480e6i		−	0.348323i	0.984717	−	0.174161i	$-0.0557214\pi$
$284$	3.06502e7			1.33807
$285$		0			0
$286$		−	1.96807e6i		−	0.0841284i
$287$			1.35087e7i			0.571436i
$288$		0			0
$289$	2.40985e7			0.998382
$290$			1.24203e7i			0.509258i
$291$		0			0
$292$	−8.63774e7			−3.46938
$293$		−	9.50811e6i		−	0.378000i	−0.981977	−	0.189000i	$-0.939475\pi$
$293$		−	9.50811e6i		−	0.378000i	0.981977	−	0.189000i	$-0.0605245\pi$
$294$		0			0
$295$			6.83766e6i			0.266343i
$296$			3.36120e7i			1.29604i
$297$		0			0
$298$			8.87131e6i			0.335227i
$299$	−5.41785e6	+	4.37714e6i	−0.202681	+	0.163748i
$300$		0			0
$301$	−2.85981e7			−1.04867
$302$	5.13545e7			1.86448
$303$		0			0
$304$		−	3.04578e7i		−	1.08412i
$305$	2.39763e7			0.845050
$306$		0			0
$307$	2.98407e7			1.03132			0.515661	−	0.856793i	$-0.327547\pi$
$307$	2.98407e7			1.03132			0.515661	+	0.856793i	$0.327547\pi$
$308$	−7.23968e6			−0.247781
$309$		0			0
$310$			8.52460e6i			0.286147i
$311$	−4.08440e7			−1.35783			−0.678917	−	0.734215i	$-0.737550\pi$
$311$	−4.08440e7			−1.35783			−0.678917	+	0.734215i	$0.737550\pi$
$312$		0			0
$313$			1.25566e7i			0.409487i	0.978816	+	0.204743i	$0.0656360\pi$
$313$			1.25566e7i			0.409487i	−0.978816	+	0.204743i	$0.934364\pi$
$314$		−	1.96460e7i		−	0.634577i
$315$		0			0
$316$		−	5.13787e7i		−	1.62825i
$317$	4.07702e7			1.27987			0.639934	−	0.768430i	$-0.278962\pi$
$317$	4.07702e7			1.27987			0.639934	+	0.768430i	$0.278962\pi$
$318$		0			0
$319$			1.65068e6i			0.0508501i
$320$			4.93761e7i			1.50684i
$321$		0			0
$322$	2.47362e7	+	3.06175e7i	0.740910	+	0.917070i
$323$	2.39861e6			0.0711789
$324$		0			0
$325$	−2.45084e6			−0.0713946
$326$	−1.10002e6			−0.0317503
$327$		0			0
$328$	−4.23723e7			−1.20077
$329$			1.44959e7i			0.407060i
$330$		0			0
$331$	3.18323e7			0.877776			0.438888	−	0.898542i	$-0.355372\pi$
$331$	3.18323e7			0.877776			0.438888	+	0.898542i	$0.355372\pi$
$332$			1.07527e7i			0.293835i
$333$		0			0
$334$	9.17958e7			2.46368
$335$	−7.78025e7			−2.06947
$336$		0			0
$337$			1.01907e7i			0.266264i	0.991098	+	0.133132i	$0.0425034\pi$
$337$			1.01907e7i			0.266264i	−0.991098	+	0.133132i	$0.957497\pi$
$338$	6.09202e7			1.57765
$339$		0			0
$340$	3.32744e6			0.0846590
$341$			1.13294e6i			0.0285721i
$342$		0			0
$343$			4.25791e7i			1.05515i
$344$		−	8.97026e7i		−	2.20358i
$345$		0			0
$346$	−3.79897e7			−0.917143
$347$	5.41650e7			1.29637			0.648187	−	0.761481i	$-0.275527\pi$
$347$	5.41650e7			1.29637			0.648187	+	0.761481i	$0.275527\pi$
$348$		0			0
$349$	2.80302e7			0.659401			0.329700	−	0.944086i	$-0.393052\pi$
$349$	2.80302e7			0.659401			0.329700	+	0.944086i	$0.393052\pi$
$350$			1.38503e7i			0.323039i
$351$		0			0
$352$			3.55089e6i			0.0814158i
$353$	4.48916e7			1.02057			0.510283	−	0.860007i	$-0.329541\pi$
$353$	4.48916e7			1.02057			0.510283	+	0.860007i	$0.329541\pi$
$354$		0			0
$355$		−	3.62344e7i		−	0.809909i
$356$		−	1.03594e8i		−	2.29607i
$357$		0			0
$358$	7.24025e7			1.57799
$359$		−	3.75717e7i		−	0.812041i	−0.913864	−	0.406021i	$-0.866916\pi$
$359$		−	3.75717e7i		−	0.812041i	0.913864	−	0.406021i	$-0.133084\pi$
$360$		0			0
$361$	−1.00288e8			−2.13170
$362$			5.68301e7i			1.19799i
$363$		0			0
$364$			1.63230e7i			0.338451i
$365$			1.02115e8i			2.09995i
$366$		0			0
$367$		−	4.13968e6i		−	0.0837469i	−0.999123	−	0.0418734i	$-0.986667\pi$
$367$		−	4.13968e6i		−	0.0837469i	0.999123	−	0.0418734i	$-0.0133326\pi$
$368$	−2.37482e7	+	1.91864e7i	−0.476527	+	0.384991i
$369$		0			0
$370$	8.56851e7			1.69161
$371$	−2.40563e6			−0.0471094
$372$		0			0
$373$		−	4.93256e6i		−	0.0950486i	−0.998870	−	0.0475243i	$-0.984867\pi$
$373$		−	4.93256e6i		−	0.0950486i	0.998870	−	0.0475243i	$-0.0151332\pi$
$374$	679369.			0.0129865
$375$		0			0
$376$	−4.54689e7			−0.855365
$377$	3.72173e6			0.0694577
$378$		0			0
$379$			9.46295e7i			1.73824i	0.494605	+	0.869118i	$0.335313\pi$
$379$			9.46295e7i			1.73824i	−0.494605	+	0.869118i	$0.664687\pi$
$380$	−2.04387e8			−3.72479
$381$		0			0
$382$		−	1.36592e8i		−	2.45038i
$383$			8.36066e7i			1.48814i	0.668101	+	0.744071i	$0.267107\pi$
$383$			8.36066e7i			1.48814i	−0.668101	+	0.744071i	$0.732893\pi$
$384$		0			0
$385$			8.55870e6i			0.149977i
$386$	4.43308e7			0.770803
$387$		0			0
$388$			1.40482e8i			2.40506i
$389$		−	6.95859e7i		−	1.18215i	−0.806616	−	0.591075i	$-0.798704\pi$
$389$		−	6.95859e7i		−	1.18215i	0.806616	−	0.591075i	$-0.201296\pi$
$390$		0			0
$391$	−1.51097e6	−	1.87022e6i	−0.0252769	−	0.0312869i
$392$	−4.53893e7			−0.753520
$393$		0			0
$394$	6.68762e6			0.109341
$395$	−6.07395e7			−0.985553
$396$		0			0
$397$	−1.14324e7			−0.182711			−0.0913555	−	0.995818i	$-0.529120\pi$
$397$	−1.14324e7			−0.182711			−0.0913555	+	0.995818i	$0.529120\pi$
$398$		−	1.59582e8i		−	2.53125i
$399$		0			0
$400$	−1.07429e7			−0.167857
$401$		−	5.36802e7i		−	0.832494i	−0.909252	−	0.416247i	$-0.863345\pi$
$401$		−	5.36802e7i		−	0.832494i	0.909252	−	0.416247i	$-0.136655\pi$
$402$		0			0
$403$	2.55439e6			0.0390276
$404$	−2.02388e8			−3.06931
$405$		0			0
$406$		−	2.10323e7i		−	0.314275i
$407$	1.13877e7			0.168909
$408$		0			0
$409$	−3.37689e7			−0.493567			−0.246784	−	0.969071i	$-0.579374\pi$
$409$	−3.37689e7			−0.493567			−0.246784	+	0.969071i	$0.579374\pi$
$410$			1.08017e8i			1.56726i
$411$		0			0
$412$			3.30384e7i			0.472418i
$413$		−	1.15788e7i		−	0.164366i
$414$		0			0
$415$	1.27118e7			0.177853
$416$	8.00604e6			0.111208
$417$		0			0
$418$	−4.17300e7			−0.571373
$419$		−	8.71527e7i		−	1.18478i	−0.805650	−	0.592391i	$-0.798184\pi$
$419$		−	8.71527e7i		−	1.18478i	0.805650	−	0.592391i	$-0.201816\pi$
$420$		0			0
$421$		−	1.36836e8i		−	1.83381i	−0.399100	−	0.916907i	$-0.630677\pi$
$421$		−	1.36836e8i		−	1.83381i	0.399100	−	0.916907i	$-0.369323\pi$
$422$	2.17891e8			2.89935
$423$		0			0
$424$		−	7.54567e6i		−	0.0989921i
$425$		−	846020.i		−	0.0110208i
$426$		0			0
$427$	−4.06011e7			−0.521499
$428$		−	1.14729e8i		−	1.46333i
$429$		0			0
$430$	−2.28674e8			−2.87615
$431$			7.28953e7i			0.910474i	0.890370	+	0.455237i	$0.150445\pi$
$431$			7.28953e7i			0.910474i	−0.890370	+	0.455237i	$0.849555\pi$
$432$		0			0
$433$		−	1.53479e8i		−	1.89054i	−0.326288	−	0.945270i	$-0.605798\pi$
$433$		−	1.53479e8i		−	1.89054i	0.326288	−	0.945270i	$-0.394202\pi$
$434$		−	1.44354e7i		−	0.176588i
$435$		0			0
$436$		−	2.00648e8i		−	2.42090i
$437$	9.28107e7	+	1.14878e8i	1.11212	+	1.37655i
$438$		0			0
$439$	1.12591e8			1.33079			0.665394	−	0.746493i	$-0.268264\pi$
$439$	1.12591e8			1.33079			0.665394	+	0.746493i	$0.268264\pi$
$440$	−2.68458e7			−0.315151
$441$		0			0
$442$		−	1.53174e6i		−	0.0177386i
$443$	−9.25522e7			−1.06457			−0.532286	−	0.846564i	$-0.678667\pi$
$443$	−9.25522e7			−1.06457			−0.532286	+	0.846564i	$0.678667\pi$
$444$		0			0
$445$	−1.22468e8			−1.38977
$446$	2.29022e8			2.58150
$447$		0			0
$448$		−	8.36127e7i		−	0.929905i
$449$	−7.69119e7			−0.849678			−0.424839	−	0.905269i	$-0.639669\pi$
$449$	−7.69119e7			−0.849678			−0.424839	+	0.905269i	$0.639669\pi$
$450$		0			0
$451$			1.43557e7i			0.156493i
$452$		−	1.95221e8i		−	2.11403i
$453$		0			0
$454$			1.82588e8i			1.95121i
$455$	1.92969e7			0.204859
$456$		0			0
$457$			6.01115e7i			0.629809i	0.949123	+	0.314905i	$0.101973\pi$
$457$			6.01115e7i			0.629809i	−0.949123	+	0.314905i	$0.898027\pi$
$458$			2.50981e8i			2.61243i
$459$		0			0
$460$	1.28750e8	+	1.59362e8i	1.32274	+	1.63724i
$461$	−3.14343e7			−0.320849			−0.160425	−	0.987048i	$-0.551286\pi$
$461$	−3.14343e7			−0.320849			−0.160425	+	0.987048i	$0.551286\pi$
$462$		0			0
$463$	−1.26683e7			−0.127637			−0.0638185	−	0.997962i	$-0.520328\pi$
$463$	−1.26683e7			−0.127637			−0.0638185	+	0.997962i	$0.520328\pi$
$464$	1.63136e7			0.163303
$465$		0			0
$466$	−1.64151e8			−1.62213
$467$			4.47112e7i			0.439001i	0.975612	+	0.219500i	$0.0704427\pi$
$467$			4.47112e7i			0.439001i	−0.975612	+	0.219500i	$0.929557\pi$
$468$		0			0
$469$	1.31750e8			1.27712
$470$			1.15911e8i			1.11643i
$471$		0			0
$472$	3.63188e7			0.345387
$473$	−3.03912e7			−0.287187
$474$		0			0
$475$			5.19665e7i			0.484890i
$476$	−5.63463e6			−0.0522450
$477$		0			0
$478$	2.33857e8			2.14125
$479$		−	1.84293e8i		−	1.67688i	−0.544994	−	0.838440i	$-0.683468\pi$
$479$		−	1.84293e8i		−	1.67688i	0.544994	−	0.838440i	$-0.316532\pi$
$480$		0			0
$481$		−	2.56755e7i		−	0.230719i
$482$			3.13928e8i			2.80343i
$483$		0			0
$484$	2.03735e8			1.79692
$485$	1.66077e8			1.45574
$486$		0			0
$487$	1.36691e8			1.18346			0.591731	−	0.806136i	$-0.298445\pi$
$487$	1.36691e8			1.18346			0.591731	+	0.806136i	$0.298445\pi$
$488$		−	1.27352e8i		−	1.09584i
$489$		0			0
$490$			1.15708e8i			0.983504i
$491$	1.51702e8			1.28159			0.640793	−	0.767714i	$-0.278606\pi$
$491$	1.51702e8			1.28159			0.640793	+	0.767714i	$0.278606\pi$
$492$		0			0
$493$			1.28472e6i			0.0107218i
$494$			9.40869e7i			0.780456i
$495$		0			0
$496$	1.11967e7			0.0917585
$497$			6.13588e7i			0.499813i
$498$		0			0
$499$	2.35547e7			0.189572			0.0947862	−	0.995498i	$-0.469783\pi$
$499$	2.35547e7			0.189572			0.0947862	+	0.995498i	$0.469783\pi$
$500$		−	1.91011e8i		−	1.52809i
$501$		0			0
$502$			3.91247e8i			3.09272i
$503$		−	1.77581e8i		−	1.39538i	−0.716401	−	0.697689i	$-0.754212\pi$
$503$		−	1.77581e8i		−	1.39538i	0.716401	−	0.697689i	$-0.245788\pi$
$504$		0			0
$505$			2.39262e8i			1.85780i
$506$	2.62872e7	+	3.25373e7i	0.202905	+	0.251148i
$507$		0			0
$508$	1.57176e8			1.19893
$509$	−6.77590e7			−0.513823			−0.256912	−	0.966435i	$-0.582705\pi$
$509$	−6.77590e7			−0.513823			−0.256912	+	0.966435i	$0.582705\pi$
$510$		0			0
$511$		−	1.72920e8i		−	1.29593i
$512$	1.55443e8			1.15814
$513$		0			0
$514$	−1.88795e7			−0.139028
$515$	3.90577e7			0.285947
$516$		0			0
$517$			1.54049e7i			0.111477i
$518$	−1.45098e8			−1.04393
$519$		0			0
$520$			6.05281e7i			0.430474i
$521$			6.21385e7i			0.439388i	0.975569	+	0.219694i	$0.0705058\pi$
$521$			6.21385e7i			0.439388i	−0.975569	+	0.219694i	$0.929494\pi$
$522$		0			0
$523$			1.91056e8i			1.33554i	0.744369	+	0.667769i	$0.232750\pi$
$523$			1.91056e8i			1.33554i	−0.744369	+	0.667769i	$0.767250\pi$
$524$	−3.19385e8			−2.21983
$525$		0			0
$526$		−	2.43357e8i		−	1.67219i
$527$			881763.i			0.00602449i
$528$		0			0
$529$	3.11064e7	−	1.44731e8i	0.210128	−	0.977674i
$530$	−1.92357e7			−0.129206
$531$		0			0
$532$	3.46105e8			2.29865
$533$	3.23672e7			0.213759
$534$		0			0
$535$	−1.35631e8			−0.885725
$536$			4.13255e8i			2.68364i
$537$		0			0
$538$	8.57119e7			0.550420
$539$			1.53779e7i			0.0982042i
$540$		0			0
$541$	−2.12729e8			−1.34349			−0.671747	−	0.740781i	$-0.734456\pi$
$541$	−2.12729e8			−1.34349			−0.671747	+	0.740781i	$0.734456\pi$
$542$	−4.40962e7			−0.276951
$543$		0			0
$544$			2.76365e6i			0.0171667i
$545$	−2.37205e8			−1.46533
$546$		0			0
$547$	8.50697e7			0.519772			0.259886	−	0.965639i	$-0.416315\pi$
$547$	8.50697e7			0.519772			0.259886	+	0.965639i	$0.416315\pi$
$548$		−	7.08839e7i		−	0.430731i
$549$		0			0
$550$			1.47187e7i			0.0884671i
$551$		−	7.89137e7i		−	0.471734i
$552$		0			0
$553$	1.02855e8			0.608207
$554$	5.22608e8			3.07360
$555$		0			0
$556$	−3.44944e8			−2.00689
$557$		−	3.83860e7i		−	0.222130i	−0.993813	−	0.111065i	$-0.964574\pi$
$557$		−	3.83860e7i		−	0.222130i	0.993813	−	0.111065i	$-0.0354262\pi$
$558$		0			0
$559$			6.85218e7i			0.392278i
$560$	8.45849e7			0.481647
$561$		0			0
$562$			3.24856e6i			0.0183013i
$563$		−	1.57315e8i		−	0.881545i	−0.897619	−	0.440772i	$-0.854705\pi$
$563$		−	1.57315e8i		−	0.881545i	0.897619	−	0.440772i	$-0.145295\pi$
$564$		0			0
$565$	−2.30789e8			−1.27959
$566$			1.06900e8i			0.589559i
$567$		0			0
$568$	−1.92462e8			−1.05027
$569$			2.55454e8i			1.38668i	0.720611	+	0.693340i	$0.243861\pi$
$569$			2.55454e8i			1.38668i	−0.720611	+	0.693340i	$0.756139\pi$
$570$		0			0
$571$		−	6.59181e7i		−	0.354076i	−0.984204	−	0.177038i	$-0.943348\pi$
$571$		−	6.59181e7i		−	0.354076i	0.984204	−	0.177038i	$-0.0566515\pi$
$572$			1.73465e7i			0.0926881i
$573$		0			0
$574$		−	1.82915e8i		−	0.967192i
$575$	4.05188e7	−	3.27355e7i	0.213134	−	0.172193i
$576$		0			0
$577$	−2.76208e7			−0.143783			−0.0718917	−	0.997412i	$-0.522904\pi$
$577$	−2.76208e7			−0.143783			−0.0718917	+	0.997412i	$0.522904\pi$
$578$	−3.26306e8			−1.68983
$579$		0			0
$580$		−	1.09472e8i		−	0.561073i
$581$	−2.15259e7			−0.109757
$582$		0			0
$583$	−2.55647e6			−0.0129014
$584$	5.42391e8			2.72317
$585$		0			0
$586$			1.28745e8i			0.639789i
$587$	−9.86349e7			−0.487659			−0.243830	−	0.969818i	$-0.578404\pi$
$587$	−9.86349e7			−0.487659			−0.243830	+	0.969818i	$0.578404\pi$
$588$		0			0
$589$		−	5.41620e7i		−	0.265063i
$590$		−	9.25854e7i		−	0.450803i
$591$		0			0
$592$		−	1.12544e8i		−	0.542447i
$593$	−1.34617e8			−0.645560			−0.322780	−	0.946474i	$-0.604617\pi$
$593$	−1.34617e8			−0.645560			−0.322780	+	0.946474i	$0.604617\pi$
$594$		0			0
$595$			6.66122e6i			0.0316230i
$596$		−	7.81914e7i		−	0.369335i
$597$		0			0
$598$	7.33605e7	−	5.92687e7i	0.343051	−	0.277154i
$599$	−9.83081e7			−0.457413			−0.228707	−	0.973495i	$-0.573450\pi$
$599$	−9.83081e7			−0.457413			−0.228707	+	0.973495i	$0.573450\pi$
$600$		0			0
$601$	1.26071e8			0.580752			0.290376	−	0.956913i	$-0.406220\pi$
$601$	1.26071e8			0.580752			0.290376	+	0.956913i	$0.406220\pi$
$602$	3.87233e8			1.77493
$603$		0			0
$604$	−4.52637e8			−2.05418
$605$		−	2.40853e8i		−	1.08764i
$606$		0			0
$607$	3.97425e8			1.77701			0.888504	−	0.458869i	$-0.151745\pi$
$607$	3.97425e8			1.77701			0.888504	+	0.458869i	$0.151745\pi$
$608$		−	1.69756e8i		−	0.755292i
$609$		0			0
$610$	−3.24651e8			−1.43030
$611$	3.47327e7			0.152270
$612$		0			0
$613$			2.65834e7i			0.115406i	0.998334	+	0.0577032i	$0.0183777\pi$
$613$			2.65834e7i			0.115406i	−0.998334	+	0.0577032i	$0.981622\pi$
$614$	−4.04059e8			−1.74558
$615$		0			0
$616$	4.54603e7			0.194487
$617$			3.72932e8i			1.58772i	0.608100	+	0.793861i	$0.291932\pi$
$617$			3.72932e8i			1.58772i	−0.608100	+	0.793861i	$0.708068\pi$
$618$		0			0
$619$		−	1.35110e8i		−	0.569661i	−0.958578	−	0.284831i	$-0.908063\pi$
$619$		−	1.35110e8i		−	0.569661i	0.958578	−	0.284831i	$-0.0919374\pi$
$620$		−	7.51356e7i		−	0.315261i
$621$		0			0
$622$	5.53049e8			2.29822
$623$	2.07385e8			0.857658
$624$		0			0
$625$	−2.92706e8			−1.19892
$626$		−	1.70023e8i		−	0.693083i
$627$		0			0
$628$			1.73159e8i			0.699142i
$629$	8.86305e6			0.0356149
$630$		0			0
$631$		−	1.89677e8i		−	0.754966i	−0.926017	−	0.377483i	$-0.876790\pi$
$631$		−	1.89677e8i		−	0.754966i	0.926017	−	0.377483i	$-0.123210\pi$
$632$			3.22623e8i			1.27804i
$633$		0			0
$634$	−5.52050e8			−2.16626
$635$		−	1.85812e8i		−	0.725694i
$636$		0			0
$637$	3.46719e7			0.134140
$638$		−	2.23511e7i		−	0.0860670i
$639$		0			0
$640$		−	5.42294e8i		−	2.06869i
$641$		−	1.46509e8i		−	0.556274i	−0.960541	−	0.278137i	$-0.910283\pi$
$641$		−	1.46509e8i		−	0.556274i	0.960541	−	0.278137i	$-0.0897170\pi$
$642$		0			0
$643$		−	1.78788e8i		−	0.672519i	−0.941769	−	0.336259i	$-0.890838\pi$
$643$		−	1.78788e8i		−	0.672519i	0.941769	−	0.336259i	$-0.109162\pi$
$644$	−2.18024e8	−	2.69862e8i	−0.816294	−	1.01038i
$645$		0			0
$646$	−3.24784e7			−0.120475
$647$	−1.04538e8			−0.385976			−0.192988	−	0.981201i	$-0.561818\pi$
$647$	−1.04538e8			−0.385976			−0.192988	+	0.981201i	$0.561818\pi$
$648$		0			0
$649$		−	1.23048e7i		−	0.0450132i
$650$	3.31857e7			0.120840
$651$		0			0
$652$	9.69553e6			0.0349807
$653$	8.10405e7			0.291046			0.145523	−	0.989355i	$-0.453513\pi$
$653$	8.10405e7			0.291046			0.145523	+	0.989355i	$0.453513\pi$
$654$		0			0
$655$			3.77575e8i			1.34363i
$656$	1.41876e8			0.502572
$657$		0			0
$658$		−	1.96283e8i		−	0.688976i
$659$			4.66108e8i			1.62866i	0.580401	+	0.814330i	$0.302896\pi$
$659$			4.66108e8i			1.62866i	−0.580401	+	0.814330i	$0.697104\pi$
$660$		0			0
$661$		−	2.04259e7i		−	0.0707256i	−0.999375	−	0.0353628i	$-0.988741\pi$
$661$		−	2.04259e7i		−	0.0707256i	0.999375	−	0.0353628i	$-0.0112587\pi$
$662$	−4.31026e8			−1.48569
$663$		0			0
$664$		−	6.75197e7i		−	0.230636i
$665$		−	4.09163e8i		−	1.39133i
$666$		0			0
$667$	−6.15298e7	+	4.97105e7i	−0.207352	+	0.167522i
$668$	−8.09085e8			−2.71434
$669$		0			0
$670$	1.05349e9			3.50271
$671$	−4.31468e7			−0.142817
$672$		0			0
$673$	−2.07183e8			−0.679688			−0.339844	−	0.940482i	$-0.610374\pi$
$673$	−2.07183e8			−0.679688			−0.339844	+	0.940482i	$0.610374\pi$
$674$		−	1.37987e8i		−	0.450669i
$675$		0			0
$676$	−5.36948e8			−1.73817
$677$		−	2.29791e8i		−	0.740573i	−0.928918	−	0.370287i	$-0.879260\pi$
$677$		−	2.29791e8i		−	0.740573i	0.928918	−	0.370287i	$-0.120740\pi$
$678$		0			0
$679$	−2.81232e8			−0.898372
$680$	−2.08940e7			−0.0664501
$681$		0			0
$682$		−	1.53406e7i		−	0.0483602i
$683$	−4.46167e8			−1.40035			−0.700173	−	0.713973i	$-0.746894\pi$
$683$	−4.46167e8			−1.40035			−0.700173	+	0.713973i	$0.746894\pi$
$684$		0			0
$685$	−8.37984e7			−0.260714
$686$		−	5.76543e8i		−	1.78591i
$687$		0			0
$688$			3.00354e8i			0.922291i
$689$			5.76397e6i			0.0176224i
$690$		0			0
$691$	4.18181e8			1.26745			0.633724	−	0.773559i	$-0.281525\pi$
$691$	4.18181e8			1.26745			0.633724	+	0.773559i	$0.281525\pi$
$692$	3.34840e8			1.01046
$693$		0			0
$694$	−7.33423e8			−2.19420
$695$			4.07790e8i			1.21474i
$696$		0			0
$697$			1.11730e7i			0.0329968i
$698$	−3.79543e8			−1.11608
$699$		0			0
$700$		−	1.22076e8i		−	0.355907i
$701$			4.70754e8i			1.36660i	0.730140	+	0.683298i	$0.239455\pi$
$701$			4.70754e8i			1.36660i	−0.730140	+	0.683298i	$0.760545\pi$
$702$		0			0
$703$	−5.44410e8			−1.56697
$704$		−	8.88554e7i		−	0.254663i
$705$		0			0
$706$	−6.07855e8			−1.72737
$707$		−	4.05163e8i		−	1.14649i
$708$		0			0
$709$		−	1.15724e8i		−	0.324702i	−0.986733	−	0.162351i	$-0.948092\pi$
$709$		−	1.15724e8i		−	0.324702i	0.986733	−	0.162351i	$-0.0519077\pi$
$710$			4.90633e8i			1.37082i
$711$		0			0
$712$			6.50499e8i			1.80222i
$713$	−4.22307e7	+	3.41186e7i	−0.116509	+	0.0941287i
$714$		0			0
$715$	2.05069e7			0.0561025
$716$	−6.38153e8			−1.73854
$717$		0			0
$718$			5.08741e8i			1.37443i
$719$	4.03070e8			1.08441			0.542206	−	0.840246i	$-0.317589\pi$
$719$	4.03070e8			1.08441			0.542206	+	0.840246i	$0.317589\pi$
$720$		0			0
$721$	−6.61397e7			−0.176464
$722$	1.35795e9			3.60804
$723$		0			0
$724$		−	5.00899e8i		−	1.31988i
$725$	−2.78339e7			−0.0730399
$726$		0			0
$727$			7.14412e7i			0.185928i	0.995669	+	0.0929641i	$0.0296342\pi$
$727$			7.14412e7i			0.185928i	−0.995669	+	0.0929641i	$0.970366\pi$
$728$		−	1.02497e8i		−	0.265655i
$729$		0			0
$730$		−	1.38269e9i		−	3.55431i
$731$	−2.36534e7			−0.0605539
$732$		0			0
$733$		−	2.95021e8i		−	0.749102i	−0.927206	−	0.374551i	$-0.877797\pi$
$733$		−	2.95021e8i		−	0.749102i	0.927206	−	0.374551i	$-0.122203\pi$
$734$			5.60534e7i			0.141747i
$735$		0			0
$736$	−1.32361e8	+	1.06935e8i	−0.331990	+	0.268218i
$737$	1.40011e8			0.349751
$738$		0			0
$739$	1.79328e8			0.444340			0.222170	−	0.975008i	$-0.428686\pi$
$739$	1.79328e8			0.444340			0.222170	+	0.975008i	$0.428686\pi$
$740$	−7.55226e8			−1.86372
$741$		0			0
$742$	3.25735e7			0.0797357
$743$			9.30017e7i			0.226738i	0.993553	+	0.113369i	$0.0361642\pi$
$743$			9.30017e7i			0.226738i	−0.993553	+	0.113369i	$0.963836\pi$
$744$		0			0
$745$	−9.24373e7			−0.223552
$746$			6.67894e7i			0.160876i
$747$		0			0
$748$	−5.98793e6			−0.0143078
$749$	2.29676e8			0.546601
$750$		0			0
$751$			1.91991e8i			0.453274i	0.973979	+	0.226637i	$0.0727730\pi$
$751$			1.91991e8i			0.453274i	−0.973979	+	0.226637i	$0.927227\pi$
$752$	1.52245e8			0.358005
$753$		0			0
$754$	−5.03941e7			−0.117562
$755$			5.35104e8i			1.24336i
$756$		0			0
$757$		−	3.88688e8i		−	0.896011i	−0.894031	−	0.448005i	$-0.852135\pi$
$757$		−	3.88688e8i		−	0.896011i	0.894031	−	0.448005i	$-0.147865\pi$
$758$		−	1.28133e9i		−	2.94208i
$759$		0			0
$760$	1.28341e9			2.92364
$761$	−1.07515e8			−0.243958			−0.121979	−	0.992533i	$-0.538924\pi$
$761$	−1.07515e8			−0.243958			−0.121979	+	0.992533i	$0.538924\pi$
$762$		0			0
$763$	4.01679e8			0.904286
$764$			1.20391e9i			2.69970i
$765$		0			0
$766$		−	1.13208e9i		−	2.51878i
$767$	−2.77431e7			−0.0614850
$768$		0			0
$769$			1.95497e8i			0.429895i	0.976626	+	0.214947i	$0.0689580\pi$
$769$			1.95497e8i			0.429895i	−0.976626	+	0.214947i	$0.931042\pi$
$770$		−	1.15889e8i		−	0.253846i
$771$		0			0
$772$	−3.90730e8			−0.849229
$773$			5.56140e7i			0.120405i	0.998186	+	0.0602027i	$0.0191747\pi$
$773$			5.56140e7i			0.120405i	−0.998186	+	0.0602027i	$0.980825\pi$
$774$		0			0
$775$	−1.91037e7			−0.0410404
$776$		−	8.82133e8i		−	1.88777i
$777$		0			0
$778$			9.42230e8i			2.00087i
$779$		−	6.86299e8i		−	1.45178i
$780$		0			0
$781$			6.52061e7i			0.136878i
$782$	2.04593e7	+	2.53237e7i	0.0427829	+	0.0529550i
$783$		0			0
$784$	1.51978e8			0.315379
$785$	2.04707e8			0.423179
$786$		0			0
$787$			4.00540e8i			0.821717i	0.911699	+	0.410858i	$0.134771\pi$
$787$			4.00540e8i			0.821717i	−0.911699	+	0.410858i	$0.865229\pi$
$788$	−5.89445e7			−0.120466
$789$		0			0
$790$	8.22444e8			1.66811
$791$	3.90814e8			0.789662
$792$		0			0
$793$			9.72814e7i			0.195079i
$794$	1.54800e8			0.309250
$795$		0			0
$796$			1.40655e9i			2.78880i
$797$		−	6.53711e8i		−	1.29125i	−0.763654	−	0.645626i	$-0.776597\pi$
$797$		−	6.53711e8i		−	1.29125i	0.763654	−	0.645626i	$-0.223403\pi$
$798$		0			0
$799$			1.19896e7i			0.0235052i
$800$	−5.98752e7			−0.116944
$801$		0			0
$802$			7.26858e8i			1.40905i
$803$		−	1.83762e8i		−	0.354902i
$804$		0			0
$805$	−3.19029e8	+	2.57746e8i	−0.611564	+	0.494089i
$806$	−3.45877e7			−0.0660567
$807$		0			0
$808$	1.27086e9			2.40915
$809$	−9.45718e8			−1.78614			−0.893071	−	0.449915i	$-0.851454\pi$
$809$	−9.45718e8			−1.78614			−0.893071	+	0.449915i	$0.851454\pi$
$810$		0			0
$811$	−1.05558e8			−0.197891			−0.0989457	−	0.995093i	$-0.531547\pi$
$811$	−1.05558e8			−0.197891			−0.0989457	+	0.995093i	$0.531547\pi$
$812$			1.85378e8i			0.346251i
$813$		0			0
$814$	−1.54196e8			−0.285890
$815$		−	1.14620e7i		−	0.0211732i
$816$		0			0
$817$	1.45290e9			2.66422
$818$	4.57248e8			0.835395
$819$		0			0
$820$		−	9.52060e8i		−	1.72672i
$821$	1.75537e7			0.0317204			0.0158602	−	0.999874i	$-0.494951\pi$
$821$	1.75537e7			0.0317204			0.0158602	+	0.999874i	$0.494951\pi$
$822$		0			0
$823$	6.22011e8			1.11583			0.557916	−	0.829898i	$-0.311601\pi$
$823$	6.22011e8			1.11583			0.557916	+	0.829898i	$0.311601\pi$
$824$		−	2.07458e8i		−	0.370808i
$825$		0			0
$826$			1.56783e8i			0.278201i
$827$			8.41114e8i			1.48709i	0.668684	+	0.743547i	$0.266858\pi$
$827$			8.41114e8i			1.48709i	−0.668684	+	0.743547i	$0.733142\pi$
$828$		0			0
$829$	1.73280e8			0.304148			0.152074	−	0.988369i	$-0.451405\pi$
$829$	1.73280e8			0.304148			0.152074	+	0.988369i	$0.451405\pi$
$830$	−1.72124e8			−0.301028
$831$		0			0
$832$	−2.00339e8			−0.347852
$833$			1.19686e7i			0.0207065i
$834$		0			0
$835$			9.56495e8i			1.64295i
$836$	3.67807e8			0.629508
$837$		0			0
$838$			1.18009e9i			2.00532i
$839$			4.59114e8i			0.777382i	0.921368	+	0.388691i	$0.127073\pi$
$839$			4.59114e8i			0.777382i	−0.921368	+	0.388691i	$0.872927\pi$
$840$		0			0
$841$	−5.52556e8			−0.928942
$842$			1.85284e9i			3.10385i
$843$		0			0
$844$	−1.92048e9			−3.19435
$845$			6.34776e8i			1.05208i
$846$		0			0
$847$			4.07858e8i			0.671210i
$848$			2.52654e7i			0.0414322i
$849$		0			0
$850$			1.14556e7i			0.0186535i
$851$	3.42943e8	+	4.24482e8i	0.556459	+	0.688764i
$852$		0			0
$853$	7.25042e8			1.16820			0.584098	−	0.811683i	$-0.301448\pi$
$853$	7.25042e8			1.16820			0.584098	+	0.811683i	$0.301448\pi$
$854$	5.49760e8			0.882672
$855$		0			0
$856$			7.20418e8i			1.14859i
$857$	9.49017e8			1.50776			0.753879	−	0.657014i	$-0.228181\pi$
$857$	9.49017e8			1.50776			0.753879	+	0.657014i	$0.228181\pi$
$858$		0			0
$859$	6.95950e8			1.09799			0.548995	−	0.835825i	$-0.315010\pi$
$859$	6.95950e8			1.09799			0.548995	+	0.835825i	$0.315010\pi$
$860$	2.01552e9			3.16878
$861$		0			0
$862$		−	9.87040e8i		−	1.54104i
$863$	1.41244e8			0.219754			0.109877	−	0.993945i	$-0.464954\pi$
$863$	1.41244e8			0.219754			0.109877	+	0.993945i	$0.464954\pi$
$864$		0			0
$865$		−	3.95845e8i		−	0.611613i
$866$			2.07819e9i			3.19986i
$867$		0			0
$868$			1.27233e8i			0.194555i
$869$	1.09305e8			0.166563
$870$		0			0
$871$		−	3.15676e8i		−	0.477735i
$872$			1.25993e9i			1.90020i
$873$		0			0
$874$	−1.25670e9	−	1.55550e9i	−1.88234	−	2.32989i
$875$	3.82386e8			0.570791
$876$		0			0
$877$	4.63597e8			0.687293			0.343646	−	0.939099i	$-0.388338\pi$
$877$	4.63597e8			0.687293			0.343646	+	0.939099i	$0.388338\pi$
$878$	−1.52454e9			−2.25244
$879$		0			0
$880$	8.98885e7			0.131903
$881$			2.21523e8i			0.323960i	0.986794	+	0.161980i	$0.0517881\pi$
$881$			2.21523e8i			0.323960i	−0.986794	+	0.161980i	$0.948212\pi$
$882$		0			0
$883$	3.52515e8			0.512030			0.256015	−	0.966673i	$-0.417590\pi$
$883$	3.52515e8			0.512030			0.256015	+	0.966673i	$0.417590\pi$
$884$			1.35007e7i			0.0195434i
$885$		0			0
$886$	1.25320e9			1.80186
$887$	9.04156e8			1.29560			0.647802	−	0.761808i	$-0.275688\pi$
$887$	9.04156e8			1.29560			0.647802	+	0.761808i	$0.275688\pi$
$888$		0			0
$889$			3.14652e8i			0.447842i
$890$	1.65828e9			2.35227
$891$		0			0
$892$	−2.01859e9			−2.84416
$893$		−	7.36456e8i		−	1.03417i
$894$		0			0
$895$			7.54420e8i			1.05231i
$896$			9.18312e8i			1.27663i
$897$		0			0
$898$	1.04143e9			1.43814
$899$	2.90098e7			0.0399270
$900$		0			0
$901$	−1.98970e6			−0.00272027
$902$		−	1.94384e8i		−	0.264875i
$903$		0			0
$904$			1.22586e9i			1.65933i
$905$	−5.92159e8			−0.798900
$906$		0			0
$907$		−	4.35170e8i		−	0.583226i	−0.956536	−	0.291613i	$-0.905808\pi$
$907$		−	4.35170e8i		−	0.583226i	0.956536	−	0.291613i	$-0.0941920\pi$
$908$		−	1.60932e9i		−	2.14974i
$909$		0			0
$910$	−2.61291e8			−0.346737
$911$		−	1.20770e9i		−	1.59736i	−0.601755	−	0.798680i	$-0.705532\pi$
$911$		−	1.20770e9i		−	1.59736i	0.601755	−	0.798680i	$-0.294468\pi$
$912$		0			0
$913$	−2.28757e7			−0.0300581
$914$		−	8.13941e8i		−	1.06599i
$915$		0			0
$916$		−	2.21214e9i		−	2.87823i
$917$		−	6.39379e8i		−	0.829183i
$918$		0			0
$919$			5.47514e8i			0.705422i	0.935732	+	0.352711i	$0.114740\pi$
$919$			5.47514e8i			0.705422i	−0.935732	+	0.352711i	$0.885260\pi$
$920$	−8.08465e8	−	1.00069e9i	−1.03824	−	1.28509i
$921$		0			0
$922$	4.25637e8			0.543058
$923$	1.47018e8			0.186967
$924$		0			0
$925$			1.92021e8i			0.242618i
$926$	1.71536e8			0.216034
$927$		0			0
$928$	9.09235e7			0.113771
$929$	−1.13676e9			−1.41782			−0.708912	−	0.705297i	$-0.750814\pi$
$929$	−1.13676e9			−1.41782			−0.708912	+	0.705297i	$0.750814\pi$
$930$		0			0
$931$		−	7.35165e8i		−	0.911037i
$932$	1.44682e9			1.78717
$933$		0			0
$934$		−	6.05413e8i		−	0.743038i
$935$			7.07889e6i			0.00866025i
$936$		0			0
$937$			1.00875e9i			1.22621i	0.790003	+	0.613103i	$0.210079\pi$
$937$			1.00875e9i			1.22621i	−0.790003	+	0.613103i	$0.789921\pi$
$938$	−1.78396e9			−2.16160
$939$		0			0
$940$		−	1.02164e9i		−	1.23002i
$941$			2.74885e8i			0.329900i	0.986302	+	0.164950i	$0.0527462\pi$
$941$			2.74885e8i			0.329900i	−0.986302	+	0.164950i	$0.947254\pi$
$942$		0			0
$943$	−5.35114e8	+	4.32324e8i	−0.638133	+	0.515554i
$944$	−1.21607e8			−0.144558
$945$		0			0
$946$	4.11513e8			0.486082
$947$	−1.38163e9			−1.62683			−0.813413	−	0.581686i	$-0.802393\pi$
$947$	−1.38163e9			−1.62683			−0.813413	+	0.581686i	$0.802393\pi$
$948$		0			0
$949$	−4.14321e8			−0.484772
$950$		−	7.03654e8i		−	0.820707i
$951$		0			0
$952$	3.53816e7			0.0410078
$953$		−	3.48258e8i		−	0.402367i	−0.979554	−	0.201184i	$-0.935521\pi$
$953$		−	3.48258e8i		−	0.402367i	0.979554	−	0.201184i	$-0.0644788\pi$
$954$		0			0
$955$	1.42326e9			1.63408
$956$	−2.06121e9			−2.35911
$957$		0			0
$958$			2.49542e9i			2.83823i
$959$	1.41903e8			0.160892
$960$		0			0
$961$	−8.67593e8			−0.977565
$962$			3.47659e8i			0.390507i
$963$		0			0
$964$		−	2.76695e9i		−	3.08866i
$965$			4.61918e8i			0.514023i
$966$		0			0
$967$	2.73810e8			0.302809			0.151405	−	0.988472i	$-0.451620\pi$
$967$	2.73810e8			0.302809			0.151405	+	0.988472i	$0.451620\pi$
$968$	−1.27931e9			−1.41043
$969$		0			0
$970$	−2.24877e9			−2.46394
$971$		−	9.58608e8i		−	1.04709i	−0.851998	−	0.523544i	$-0.824609\pi$
$971$		−	9.58608e8i		−	1.04709i	0.851998	−	0.523544i	$-0.175391\pi$
$972$		0			0
$973$		−	6.90545e8i		−	0.749641i
$974$	−1.85087e9			−2.00309
$975$		0			0
$976$			4.26417e8i			0.458653i
$977$		−	1.74901e8i		−	0.187546i	−0.995594	−	0.0937732i	$-0.970107\pi$
$977$		−	1.74901e8i		−	0.187546i	0.995594	−	0.0937732i	$-0.0298929\pi$
$978$		0			0
$979$	2.20389e8			0.234878
$980$		−	1.01985e9i		−	1.08357i
$981$		0			0
$982$	−2.05413e9			−2.16917
$983$			1.37390e9i			1.44642i	0.690629	+	0.723209i	$0.257334\pi$
$983$			1.37390e9i			1.44642i	−0.690629	+	0.723209i	$0.742666\pi$
$984$		0			0
$985$			6.96837e7i			0.0729159i
$986$		−	1.73958e7i		−	0.0181474i
$987$		0			0
$988$		−	8.29279e8i		−	0.859864i
$989$	−9.15236e8	−	1.13284e9i	−0.946115	−	1.17107i
$990$		0			0
$991$	−2.00665e8			−0.206182			−0.103091	−	0.994672i	$-0.532873\pi$
$991$	−2.00665e8			−0.206182			−0.103091	+	0.994672i	$0.532873\pi$
$992$	6.24049e7			0.0639269
$993$		0			0
$994$		−	8.30830e8i		−	0.845966i
$995$	1.66282e9			1.68801
$996$		0			0
$997$	2.15150e8			0.217098			0.108549	−	0.994091i	$-0.465380\pi$
$997$	2.15150e8			0.217098			0.108549	+	0.994091i	$0.465380\pi$
$998$	−3.18942e8			−0.320864
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.2		24
3.2	odd	2		69.7.d.a.22.24	yes	24
23.22	odd	2	inner	207.7.d.e.91.1		24
69.68	even	2		69.7.d.a.22.23	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.23	✓	24	69.68	even	2
69.7.d.a.22.24	yes	24	3.2	odd	2
207.7.d.e.91.1		24	23.22	odd	2	inner
207.7.d.e.91.2		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	207.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-13.5405 q^{2} +119.346 q^{4} -141.090i q^{5} +238.919i q^{7} -749.409 q^{8} +O(q^{10})\)	\(q-13.5405 q^{2} +119.346 q^{4} -141.090i q^{5} +238.919i q^{7} -749.409 q^{8} +1910.43i q^{10} +253.900i q^{11} +572.457 q^{13} -3235.09i q^{14} +2509.27 q^{16} +197.610i q^{17} -12138.1i q^{19} -16838.4i q^{20} -3437.93i q^{22} +(-9464.20 + 7646.22i) q^{23} -4281.27 q^{25} -7751.37 q^{26} +28513.9i q^{28} +6501.32 q^{29} +4462.15 q^{31} +13985.4 q^{32} -2675.74i q^{34} +33709.0 q^{35} -44851.3i q^{37} +164356. i q^{38} +105734. i q^{40} +56540.9 q^{41} +119698. i q^{43} +30301.8i q^{44} +(128150. - 103534. i) q^{46} +60673.0 q^{47} +60566.7 q^{49} +57970.6 q^{50} +68320.3 q^{52} +10068.8i q^{53} +35822.6 q^{55} -179048. i q^{56} -88031.2 q^{58} -48463.2 q^{59} +169937. i q^{61} -60419.8 q^{62} -349963. q^{64} -80767.8i q^{65} -551441. i q^{67} +23583.9i q^{68} -456437. q^{70} +256818. q^{71} -723758. q^{73} +607310. i q^{74} -1.44863e6i q^{76} -60661.4 q^{77} -430503. i q^{79} -354032. i q^{80} -765593. q^{82} +90097.3i q^{83} +27880.7 q^{85} -1.62077e6i q^{86} -190275. i q^{88} -868016. i q^{89} +136771. i q^{91} +(-1.12951e6 + 912544. i) q^{92} -821544. q^{94} -1.71256e6 q^{95} +1.17710e6i q^{97} -820105. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

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