LMFDB - Embedded newform 630.6.b.b.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,6,Mod(251,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("630.251");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	630.b (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:	$101.041806482$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	630.251
Dual form			630.6.b.b.251.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -16.0000 q^{4} +25.0000 q^{5} +(-121.533 - 45.1314i) q^{7} +64.0000i q^{8} -100.000i q^{10} +183.141i q^{11} +827.120i q^{13} +(-180.526 + 486.130i) q^{14} +256.000 q^{16} +371.677 q^{17} +2101.08i q^{19} -400.000 q^{20} +732.564 q^{22} -2585.70i q^{23} +625.000 q^{25} +3308.48 q^{26} +(1944.52 + 722.103i) q^{28} -6062.60i q^{29} -2884.00i q^{31} -1024.00i q^{32} -1486.71i q^{34} +(-3038.31 - 1128.29i) q^{35} -8977.29 q^{37} +8404.32 q^{38} +1600.00i q^{40} +2028.23 q^{41} +3324.34 q^{43} -2930.25i q^{44} -10342.8 q^{46} +8242.15 q^{47} +(12733.3 + 10969.9i) q^{49} -2500.00i q^{50} -13233.9i q^{52} +19163.9i q^{53} +4578.52i q^{55} +(2888.41 - 7778.08i) q^{56} -24250.4 q^{58} -5260.44 q^{59} -39384.4i q^{61} -11536.0 q^{62} -4096.00 q^{64} +20678.0i q^{65} -18191.5 q^{67} -5946.83 q^{68} +(-4513.14 + 12153.3i) q^{70} -16316.5i q^{71} -29817.8i q^{73} +35909.2i q^{74} -33617.3i q^{76} +(8265.41 - 22257.6i) q^{77} +8556.65 q^{79} +6400.00 q^{80} -8112.91i q^{82} +6848.74 q^{83} +9291.93 q^{85} -13297.4i q^{86} -11721.0 q^{88} -48923.4 q^{89} +(37329.1 - 100522. i) q^{91} +41371.2i q^{92} -32968.6i q^{94} +52527.0i q^{95} +32875.6i q^{97} +(43879.5 - 50933.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 384 q^{4} + 600 q^{5} - 196 q^{7} + 6144 q^{16} - 9600 q^{20} + 15000 q^{25} - 3872 q^{26} + 3136 q^{28} - 4900 q^{35} - 33512 q^{37} - 10208 q^{38} + 44968 q^{41} + 8016 q^{43} - 1312 q^{46} + 47240 q^{47}+ \cdots + 257936 q^{98}+O(q^{100}) $ 24 * q - 384 * q^4 + 600 * q^5 - 196 * q^7 + 6144 * q^16 - 9600 * q^20 + 15000 * q^25 - 3872 * q^26 + 3136 * q^28 - 4900 * q^35 - 33512 * q^37 - 10208 * q^38 + 44968 * q^41 + 8016 * q^43 - 1312 * q^46 + 47240 * q^47 - 31724 * q^49 + 35168 * q^58 - 110400 * q^59 + 20320 * q^62 - 98304 * q^64 - 92032 * q^67 + 107212 * q^77 + 90632 * q^79 + 153600 * q^80 - 211664 * q^83 + 286888 * q^89 - 173684 * q^91 + 257936 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−16.0000			−0.500000
$5$	25.0000			0.447214
$5$	25.0000			0.447214
$6$		0			0
$7$	−121.533	−	45.1314i	−0.937448	−	0.348124i
$7$	−121.533	−	45.1314i	−0.937448	−	0.348124i
$8$			64.0000i			0.353553i
$9$		0			0
$10$		−	100.000i		−	0.316228i
$11$			183.141i			0.456356i	0.973619	+	0.228178i	$0.0732768\pi$
$11$			183.141i			0.456356i	−0.973619	+	0.228178i	$0.926723\pi$
$12$		0			0
$13$			827.120i			1.35741i	0.734412	+	0.678703i	$0.237458\pi$
$13$			827.120i			1.35741i	−0.734412	+	0.678703i	$0.762542\pi$
$14$	−180.526	+	486.130i	−0.246161	+	0.662876i
$15$		0			0
$16$	256.000			0.250000
$17$	371.677			0.311920			0.155960	−	0.987763i	$-0.450153\pi$
$17$	371.677			0.311920			0.155960	+	0.987763i	$0.450153\pi$
$18$		0			0
$19$			2101.08i			1.33524i	0.744503	+	0.667619i	$0.232686\pi$
$19$			2101.08i			1.33524i	−0.744503	+	0.667619i	$0.767314\pi$
$20$	−400.000			−0.223607
$21$		0			0
$22$	732.564			0.322692
$23$		−	2585.70i		−	1.01920i	−0.860412	−	0.509599i	$-0.829794\pi$
$23$		−	2585.70i		−	1.01920i	0.860412	−	0.509599i	$-0.170206\pi$
$24$		0			0
$25$	625.000			0.200000
$26$	3308.48			0.959832
$27$		0			0
$28$	1944.52	+	722.103i	0.468724	+	0.174062i
$29$		−	6062.60i		−	1.33864i	−0.742974	−	0.669320i	$-0.766586\pi$
$29$		−	6062.60i		−	1.33864i	0.742974	−	0.669320i	$-0.233414\pi$
$30$		0			0
$31$		−	2884.00i		−	0.539002i	−0.963000	−	0.269501i	$-0.913141\pi$
$31$		−	2884.00i		−	0.539002i	0.963000	−	0.269501i	$-0.0868588\pi$
$32$		−	1024.00i		−	0.176777i
$33$		0			0
$34$		−	1486.71i		−	0.220561i
$35$	−3038.31	−	1128.29i	−0.419240	−	0.155686i
$36$		0			0
$37$	−8977.29			−1.07805			−0.539027	−	0.842288i	$-0.681208\pi$
$37$	−8977.29			−1.07805			−0.539027	+	0.842288i	$0.681208\pi$
$38$	8404.32			0.944156
$39$		0			0
$40$			1600.00i			0.158114i
$41$	2028.23			0.188433			0.0942166	−	0.995552i	$-0.469965\pi$
$41$	2028.23			0.188433			0.0942166	+	0.995552i	$0.469965\pi$
$42$		0			0
$43$	3324.34			0.274179			0.137090	−	0.990559i	$-0.456225\pi$
$43$	3324.34			0.274179			0.137090	+	0.990559i	$0.456225\pi$
$44$		−	2930.25i		−	0.228178i
$45$		0			0
$46$	−10342.8			−0.720681
$47$	8242.15			0.544246			0.272123	−	0.962262i	$-0.412274\pi$
$47$	8242.15			0.544246			0.272123	+	0.962262i	$0.412274\pi$
$48$		0			0
$49$	12733.3	+	10969.9i	0.757619	+	0.652697i
$50$		−	2500.00i		−	0.141421i
$51$		0			0
$52$		−	13233.9i		−	0.678703i
$53$			19163.9i			0.937120i	0.883432	+	0.468560i	$0.155227\pi$
$53$			19163.9i			0.937120i	−0.883432	+	0.468560i	$0.844773\pi$
$54$		0			0
$55$			4578.52i			0.204089i
$56$	2888.41	−	7778.08i	0.123080	−	0.331438i
$57$		0			0
$58$	−24250.4			−0.946561
$59$	−5260.44			−0.196740			−0.0983699	−	0.995150i	$-0.531363\pi$
$59$	−5260.44			−0.196740			−0.0983699	+	0.995150i	$0.531363\pi$
$60$		0			0
$61$		−	39384.4i		−	1.35519i	−0.735435	−	0.677595i	$-0.763022\pi$
$61$		−	39384.4i		−	1.35519i	0.735435	−	0.677595i	$-0.236978\pi$
$62$	−11536.0			−0.381132
$63$		0			0
$64$	−4096.00			−0.125000
$65$			20678.0i			0.607051i
$66$		0			0
$67$	−18191.5			−0.495086			−0.247543	−	0.968877i	$-0.579623\pi$
$67$	−18191.5			−0.495086			−0.247543	+	0.968877i	$0.579623\pi$
$68$	−5946.83			−0.155960
$69$		0			0
$70$	−4513.14	+	12153.3i	−0.110086	+	0.296447i
$71$		−	16316.5i		−	0.384133i	−0.981382	−	0.192067i	$-0.938481\pi$
$71$		−	16316.5i		−	0.384133i	0.981382	−	0.192067i	$-0.0615190\pi$
$72$		0			0
$73$		−	29817.8i		−	0.654891i	−0.944870	−	0.327445i	$-0.893812\pi$
$73$		−	29817.8i		−	0.654891i	0.944870	−	0.327445i	$-0.106188\pi$
$74$			35909.2i			0.762300i
$75$		0			0
$76$		−	33617.3i		−	0.667619i
$77$	8265.41	−	22257.6i	0.158868	−	0.427810i
$78$		0			0
$79$	8556.65			0.154254			0.0771270	−	0.997021i	$-0.475425\pi$
$79$	8556.65			0.154254			0.0771270	+	0.997021i	$0.475425\pi$
$80$	6400.00			0.111803
$81$		0			0
$82$		−	8112.91i		−	0.133242i
$83$	6848.74			0.109123			0.0545614	−	0.998510i	$-0.482624\pi$
$83$	6848.74			0.109123			0.0545614	+	0.998510i	$0.482624\pi$
$84$		0			0
$85$	9291.93			0.139495
$86$		−	13297.4i		−	0.193874i
$87$		0			0
$88$	−11721.0			−0.161346
$89$	−48923.4			−0.654699			−0.327350	−	0.944903i	$-0.606155\pi$
$89$	−48923.4			−0.654699			−0.327350	+	0.944903i	$0.606155\pi$
$90$		0			0
$91$	37329.1	−	100522.i	0.472546	−	1.27250i
$92$			41371.2i			0.509599i
$93$		0			0
$94$		−	32968.6i		−	0.384840i
$95$			52527.0i			0.597137i
$96$		0			0
$97$			32875.6i			0.354768i	0.984142	+	0.177384i	$0.0567634\pi$
$97$			32875.6i			0.354768i	−0.984142	+	0.177384i	$0.943237\pi$
$98$	43879.5	−	50933.2i	0.461526	−	0.535718i
$99$		0			0
$100$	−10000.0			−0.100000
$101$	−32191.6			−0.314007			−0.157003	−	0.987598i	$-0.550183\pi$
$101$	−32191.6			−0.314007			−0.157003	+	0.987598i	$0.550183\pi$
$102$		0			0
$103$		−	166091.i		−	1.54260i	−0.636474	−	0.771298i	$-0.719608\pi$
$103$		−	166091.i		−	1.54260i	0.636474	−	0.771298i	$-0.280392\pi$
$104$	−52935.7			−0.479916
$105$		0			0
$106$	76655.8			0.662644
$107$		−	110522.i		−	0.933228i	−0.884461	−	0.466614i	$-0.845474\pi$
$107$		−	110522.i		−	0.933228i	0.884461	−	0.466614i	$-0.154526\pi$
$108$		0			0
$109$	−149577.			−1.20586			−0.602931	−	0.797793i	$-0.706001\pi$
$109$	−149577.			−1.20586			−0.602931	+	0.797793i	$0.706001\pi$
$110$	18314.1			0.144312
$111$		0			0
$112$	−31112.3	−	11553.6i	−0.234362	−	0.0870310i
$113$		−	26508.9i		−	0.195297i	−0.995221	−	0.0976484i	$-0.968868\pi$
$113$		−	26508.9i		−	0.195297i	0.995221	−	0.0976484i	$-0.0311321\pi$
$114$		0			0
$115$		−	64642.4i		−	0.455799i
$116$			97001.5i			0.669320i
$117$		0			0
$118$			21041.8i			0.139116i
$119$	−45170.8	−	16774.3i	−0.292409	−	0.108587i
$120$		0			0
$121$	127510.			0.791739
$122$	−157538.			−0.958264
$123$		0			0
$124$			46144.0i			0.269501i
$125$	15625.0			0.0894427
$126$		0			0
$127$	−305347.			−1.67990			−0.839951	−	0.542663i	$-0.817416\pi$
$127$	−305347.			−1.67990			−0.839951	+	0.542663i	$0.817416\pi$
$128$			16384.0i			0.0883883i
$129$		0			0
$130$	82712.0			0.429250
$131$	63340.6			0.322481			0.161240	−	0.986915i	$-0.448451\pi$
$131$	63340.6			0.322481			0.161240	+	0.986915i	$0.448451\pi$
$132$		0			0
$133$	94824.8	−	255350.i	0.464828	−	1.25172i
$134$			72765.8i			0.350078i
$135$		0			0
$136$			23787.3i			0.110280i
$137$			181687.i			0.827034i	0.910496	+	0.413517i	$0.135700\pi$
$137$			181687.i			0.827034i	−0.910496	+	0.413517i	$0.864300\pi$
$138$		0			0
$139$		−	120615.i		−	0.529498i	−0.964317	−	0.264749i	$-0.914711\pi$
$139$		−	120615.i		−	0.529498i	0.964317	−	0.264749i	$-0.0852891\pi$
$140$	48613.0	+	18052.6i	0.209620	+	0.0778429i
$141$		0			0
$142$	−65266.1			−0.271623
$143$	−151479.			−0.619461
$144$		0			0
$145$		−	151565.i		−	0.598658i
$146$	−119271.			−0.463078
$147$		0			0
$148$	143637.			0.539027
$149$			100788.i			0.371916i	0.982558	+	0.185958i	$0.0595388\pi$
$149$			100788.i			0.371916i	−0.982558	+	0.185958i	$0.940461\pi$
$150$		0			0
$151$	−311412.			−1.11146			−0.555728	−	0.831364i	$-0.687560\pi$
$151$	−311412.			−1.11146			−0.555728	+	0.831364i	$0.687560\pi$
$152$	−134469.			−0.472078
$153$		0			0
$154$	−89030.3	−	33061.6i	−0.302507	−	0.112337i
$155$		−	72100.0i		−	0.241049i
$156$		0			0
$157$		−	189643.i		−	0.614026i	−0.951705	−	0.307013i	$-0.900670\pi$
$157$		−	189643.i		−	0.614026i	0.951705	−	0.307013i	$-0.0993295\pi$
$158$		−	34226.6i		−	0.109074i
$159$		0			0
$160$		−	25600.0i		−	0.0790569i
$161$	−116696.	+	314246.i	−0.354807	+	0.955445i
$162$		0			0
$163$	−201107.			−0.592868			−0.296434	−	0.955053i	$-0.595797\pi$
$163$	−201107.			−0.592868			−0.296434	+	0.955053i	$0.595797\pi$
$164$	−32451.7			−0.0942166
$165$		0			0
$166$		−	27395.0i		−	0.0771615i
$167$	−207804.			−0.576583			−0.288291	−	0.957543i	$-0.593087\pi$
$167$	−207804.			−0.576583			−0.288291	+	0.957543i	$0.593087\pi$
$168$		0			0
$169$	−312834.			−0.842554
$170$		−	37167.7i		−	0.0986378i
$171$		0			0
$172$	−53189.5			−0.137090
$173$	−632112.			−1.60575			−0.802876	−	0.596146i	$-0.796698\pi$
$173$	−632112.			−1.60575			−0.802876	+	0.596146i	$0.796698\pi$
$174$		0			0
$175$	−75957.8	−	28207.1i	−0.187490	−	0.0696248i
$176$			46884.1i			0.114089i
$177$		0			0
$178$			195694.i			0.462942i
$179$		−	285847.i		−	0.666809i	−0.942784	−	0.333404i	$-0.891803\pi$
$179$		−	285847.i		−	0.666809i	0.942784	−	0.333404i	$-0.108197\pi$
$180$		0			0
$181$		−	386767.i		−	0.877513i	−0.898606	−	0.438756i	$-0.855419\pi$
$181$		−	386767.i		−	0.877513i	0.898606	−	0.438756i	$-0.144581\pi$
$182$	−402088.	−	149316.i	−0.899793	−	0.334140i
$183$		0			0
$184$	165485.			0.360341
$185$	−224432.			−0.482121
$186$		0			0
$187$			68069.3i			0.142347i
$188$	−131874.			−0.272123
$189$		0			0
$190$	210108.			0.422239
$191$		−	580661.i		−	1.15170i	−0.817555	−	0.575850i	$-0.804671\pi$
$191$		−	580661.i		−	1.15170i	0.817555	−	0.575850i	$-0.195329\pi$
$192$		0			0
$193$	415215.			0.802379			0.401190	−	0.915995i	$-0.368597\pi$
$193$	415215.			0.802379			0.401190	+	0.915995i	$0.368597\pi$
$194$	131502.			0.250859
$195$		0			0
$196$	−203733.	−	175518.i	−0.378810	−	0.326348i
$197$			463173.i			0.850310i	0.905120	+	0.425155i	$0.139780\pi$
$197$			463173.i			0.850310i	−0.905120	+	0.425155i	$0.860220\pi$
$198$		0			0
$199$		−	748029.i		−	1.33902i	−0.742805	−	0.669508i	$-0.766505\pi$
$199$		−	748029.i		−	1.33902i	0.742805	−	0.669508i	$-0.233495\pi$
$200$			40000.0i			0.0707107i
$201$		0			0
$202$			128766.i			0.222036i
$203$	−273614.	+	736803.i	−0.466013	+	1.25491i
$204$		0			0
$205$	50705.7			0.0842699
$206$	−664363.			−1.09078
$207$		0			0
$208$			211743.i			0.339352i
$209$	−384794.			−0.609344
$210$		0			0
$211$	494413.			0.764510			0.382255	−	0.924057i	$-0.375148\pi$
$211$	494413.			0.764510			0.382255	+	0.924057i	$0.375148\pi$
$212$		−	306623.i		−	0.468560i
$213$		0			0
$214$	−442086.			−0.659892
$215$	83108.5			0.122617
$216$		0			0
$217$	−130159.	+	350500.i	−0.187640	+	0.505287i
$218$			598306.i			0.852673i
$219$		0			0
$220$		−	73256.4i		−	0.102044i
$221$			307421.i			0.423403i
$222$		0			0
$223$			473758.i			0.637961i	0.947761	+	0.318981i	$0.103340\pi$
$223$			473758.i			0.637961i	−0.947761	+	0.318981i	$0.896660\pi$
$224$	−46214.6	+	124449.i	−0.0615402	+	0.165719i
$225$		0			0
$226$	−106035.			−0.138096
$227$	86127.3			0.110937			0.0554684	−	0.998460i	$-0.482335\pi$
$227$	86127.3			0.110937			0.0554684	+	0.998460i	$0.482335\pi$
$228$		0			0
$229$		−	436159.i		−	0.549612i	−0.961500	−	0.274806i	$-0.911386\pi$
$229$		−	436159.i		−	0.549612i	0.961500	−	0.274806i	$-0.0886136\pi$
$230$	−258570.			−0.322298
$231$		0			0
$232$	388006.			0.473281
$233$			798546.i			0.963630i	0.876273	+	0.481815i	$0.160022\pi$
$233$			798546.i			0.963630i	−0.876273	+	0.481815i	$0.839978\pi$
$234$		0			0
$235$	206054.			0.243394
$236$	84167.1			0.0983699
$237$		0			0
$238$	−67097.3	+	180683.i	−0.0767825	+	0.206764i
$239$			572680.i			0.648511i	0.945970	+	0.324256i	$0.105114\pi$
$239$			572680.i			0.648511i	−0.945970	+	0.324256i	$0.894886\pi$
$240$		0			0
$241$			1.03499e6i			1.14788i	0.818898	+	0.573939i	$0.194585\pi$
$241$			1.03499e6i			1.14788i	−0.818898	+	0.573939i	$0.805415\pi$
$242$		−	510042.i		−	0.559844i
$243$		0			0
$244$			630151.i			0.677595i
$245$	318333.	+	274247.i	0.338818	+	0.291895i
$246$		0			0
$247$	−1.73785e6			−1.81246
$248$	184576.			0.190566
$249$		0			0
$250$		−	62500.0i		−	0.0632456i
$251$	−137874.			−0.138133			−0.0690664	−	0.997612i	$-0.522002\pi$
$251$	−137874.			−0.138133			−0.0690664	+	0.997612i	$0.522002\pi$
$252$		0			0
$253$	473547.			0.465117
$254$			1.22139e6i			1.18787i
$255$		0			0
$256$	65536.0			0.0625000
$257$	−269351.			−0.254382			−0.127191	−	0.991878i	$-0.540596\pi$
$257$	−269351.			−0.254382			−0.127191	+	0.991878i	$0.540596\pi$
$258$		0			0
$259$	1.09103e6	+	405158.i	1.01062	+	0.375297i
$260$		−	330848.i		−	0.303525i
$261$		0			0
$262$		−	253362.i		−	0.228028i
$263$		−	933002.i		−	0.831750i	−0.909422	−	0.415875i	$-0.863475\pi$
$263$		−	933002.i		−	0.831750i	0.909422	−	0.415875i	$-0.136525\pi$
$264$		0			0
$265$			479099.i			0.419093i
$266$	−1.02140e6	−	379299.i	−0.885097	−	0.328683i
$267$		0			0
$268$	291063.			0.247543
$269$	−1.85311e6			−1.56142			−0.780710	−	0.624894i	$-0.785142\pi$
$269$	−1.85311e6			−1.56142			−0.780710	+	0.624894i	$0.785142\pi$
$270$		0			0
$271$		−	1.87458e6i		−	1.55053i	−0.631633	−	0.775267i	$-0.717615\pi$
$271$		−	1.87458e6i		−	1.55053i	0.631633	−	0.775267i	$-0.282385\pi$
$272$	95149.3			0.0779800
$273$		0			0
$274$	726750.			0.584801
$275$			114463.i			0.0912712i
$276$		0			0
$277$	758979.			0.594333			0.297167	−	0.954826i	$-0.403958\pi$
$277$	758979.			0.594333			0.297167	+	0.954826i	$0.403958\pi$
$278$	−482460.			−0.374411
$279$		0			0
$280$	72210.3	−	194452.i	0.0550432	−	0.148224i
$281$		−	2.08335e6i		−	1.57397i	−0.616975	−	0.786983i	$-0.711642\pi$
$281$		−	2.08335e6i		−	1.57397i	0.616975	−	0.786983i	$-0.288358\pi$
$282$		0			0
$283$		−	2.37135e6i		−	1.76007i	−0.474909	−	0.880035i	$-0.657519\pi$
$283$		−	2.37135e6i		−	1.76007i	0.474909	−	0.880035i	$-0.342481\pi$
$284$			261065.i			0.192067i
$285$		0			0
$286$			605918.i			0.438025i
$287$	−246496.	−	91536.9i	−0.176646	−	0.0655981i
$288$		0			0
$289$	−1.28171e6			−0.902706
$290$	−606260.			−0.423315
$291$		0			0
$292$			477085.i			0.327445i
$293$	717721.			0.488412			0.244206	−	0.969723i	$-0.421473\pi$
$293$	717721.			0.488412			0.244206	+	0.969723i	$0.421473\pi$
$294$		0			0
$295$	−131511.			−0.0879847
$296$		−	574546.i		−	0.381150i
$297$		0			0
$298$	403153.			0.262984
$299$	2.13868e6			1.38347
$300$		0			0
$301$	−404016.	−	150032.i	−0.257029	−	0.0954484i
$302$			1.24565e6i			0.785918i
$303$		0			0
$304$			537877.i			0.333809i
$305$		−	984611.i		−	0.606059i
$306$		0			0
$307$		−	1.25243e6i		−	0.758416i	−0.925311	−	0.379208i	$-0.876196\pi$
$307$		−	1.25243e6i		−	0.758416i	0.925311	−	0.379208i	$-0.123804\pi$
$308$	−132247.	+	356121.i	−0.0794342	+	0.213905i
$309$		0			0
$310$	−288400.			−0.170448
$311$	−2.90633e6			−1.70390			−0.851950	−	0.523623i	$-0.824580\pi$
$311$	−2.90633e6			−1.70390			−0.851950	+	0.523623i	$0.824580\pi$
$312$		0			0
$313$		−	653093.i		−	0.376803i	−0.982092	−	0.188401i	$-0.939669\pi$
$313$		−	653093.i		−	0.376803i	0.982092	−	0.188401i	$-0.0603306\pi$
$314$	−758570.			−0.434182
$315$		0			0
$316$	−136906.			−0.0771270
$317$			1.42372e6i			0.795749i	0.917440	+	0.397875i	$0.130252\pi$
$317$			1.42372e6i			0.795749i	−0.917440	+	0.397875i	$0.869748\pi$
$318$		0			0
$319$	1.11031e6			0.610896
$320$	−102400.			−0.0559017
$321$		0			0
$322$	1.25699e6	+	466785.i	0.675601	+	0.250886i
$323$			780923.i			0.416488i
$324$		0			0
$325$			516950.i			0.271481i
$326$			804427.i			0.419221i
$327$		0			0
$328$			129807.i			0.0666212i
$329$	−1.00169e6	−	371980.i	−0.510203	−	0.189465i
$330$		0			0
$331$	−493994.			−0.247829			−0.123914	−	0.992293i	$-0.539545\pi$
$331$	−493994.			−0.247829			−0.123914	+	0.992293i	$0.539545\pi$
$332$	−109580.			−0.0545614
$333$		0			0
$334$			831214.i			0.407706i
$335$	−454786.			−0.221409
$336$		0			0
$337$	−3.83194e6			−1.83799			−0.918996	−	0.394267i	$-0.870998\pi$
$337$	−3.83194e6			−1.83799			−0.918996	+	0.394267i	$0.870998\pi$
$338$			1.25134e6i			0.595775i
$339$		0			0
$340$	−148671.			−0.0697475
$341$	528178.			0.245977
$342$		0			0
$343$	−1.05243e6	−	1.90787e6i	−0.483010	−	0.875615i
$344$			212758.i			0.0969370i
$345$		0			0
$346$			2.52845e6i			1.13544i
$347$			1.86398e6i			0.831033i	0.909586	+	0.415517i	$0.136399\pi$
$347$			1.86398e6i			0.831033i	−0.909586	+	0.415517i	$0.863601\pi$
$348$		0			0
$349$		−	1.02765e6i		−	0.451629i	−0.974170	−	0.225815i	$-0.927496\pi$
$349$		−	1.02765e6i		−	0.451629i	0.974170	−	0.225815i	$-0.0725043\pi$
$350$	−112829.	+	303831.i	−0.0492322	+	0.132575i
$351$		0			0
$352$	187536.			0.0806731
$353$	3.74842e6			1.60108			0.800538	−	0.599282i	$-0.204547\pi$
$353$	3.74842e6			1.60108			0.800538	+	0.599282i	$0.204547\pi$
$354$		0			0
$355$		−	407913.i		−	0.171790i
$356$	782775.			0.327350
$357$		0			0
$358$	−1.14339e6			−0.471505
$359$		−	483437.i		−	0.197972i	−0.995089	−	0.0989860i	$-0.968440\pi$
$359$		−	483437.i		−	0.197972i	0.995089	−	0.0989860i	$-0.0315599\pi$
$360$		0			0
$361$	−1.93844e6			−0.782860
$362$	−1.54707e6			−0.620495
$363$		0			0
$364$	−597266.	+	1.60835e6i	−0.236273	+	0.636250i
$365$		−	745446.i		−	0.292876i
$366$		0			0
$367$		−	2.13555e6i		−	0.827647i	−0.910357	−	0.413823i	$-0.864193\pi$
$367$		−	2.13555e6i		−	0.827647i	0.910357	−	0.413823i	$-0.135807\pi$
$368$		−	661939.i		−	0.254799i
$369$		0			0
$370$			897729.i			0.340911i
$371$	864896.	−	2.32904e6i	0.326234	−	0.878502i
$372$		0			0
$373$	−334566.			−0.124511			−0.0622557	−	0.998060i	$-0.519829\pi$
$373$	−334566.			−0.124511			−0.0622557	+	0.998060i	$0.519829\pi$
$374$	272277.			0.100654
$375$		0			0
$376$			527497.i			0.192420i
$377$	5.01449e6			1.81708
$378$		0			0
$379$	3.03557e6			1.08553			0.542766	−	0.839884i	$-0.317377\pi$
$379$	3.03557e6			1.08553			0.542766	+	0.839884i	$0.317377\pi$
$380$		−	840432.i		−	0.298568i
$381$		0			0
$382$	−2.32265e6			−0.814375
$383$	4.28661e6			1.49320			0.746598	−	0.665275i	$-0.231686\pi$
$383$	4.28661e6			1.49320			0.746598	+	0.665275i	$0.231686\pi$
$384$		0			0
$385$	206635.	−	556439.i	0.0710481	−	0.191322i
$386$		−	1.66086e6i		−	0.567368i
$387$		0			0
$388$		−	526009.i		−	0.177384i
$389$		−	15926.2i		−	0.00533627i	−0.999996	−	0.00266814i	$-0.999151\pi$
$389$		−	15926.2i		−	0.00533627i	0.999996	−	0.00266814i	$-0.000849295\pi$
$390$		0			0
$391$		−	961045.i		−	0.317908i
$392$	−702072.	+	814932.i	−0.230763	+	0.267859i
$393$		0			0
$394$	1.85269e6			0.601260
$395$	213916.			0.0689844
$396$		0			0
$397$			441407.i			0.140560i	0.997527	+	0.0702802i	$0.0223893\pi$
$397$			441407.i			0.140560i	−0.997527	+	0.0702802i	$0.977611\pi$
$398$	−2.99212e6			−0.946828
$399$		0			0
$400$	160000.			0.0500000
$401$		−	4.55692e6i		−	1.41518i	−0.706626	−	0.707588i	$-0.749784\pi$
$401$		−	4.55692e6i		−	1.41518i	0.706626	−	0.707588i	$-0.250216\pi$
$402$		0			0
$403$	2.38541e6			0.731646
$404$	515066.			0.157003
$405$		0			0
$406$	2.94721e6	+	1.09445e6i	0.887352	+	0.329521i
$407$		−	1.64411e6i		−	0.491977i
$408$		0			0
$409$		−	6.26979e6i		−	1.85330i	−0.375931	−	0.926648i	$-0.622677\pi$
$409$		−	6.26979e6i		−	1.85330i	0.375931	−	0.926648i	$-0.377323\pi$
$410$		−	202823.i		−	0.0595878i
$411$		0			0
$412$			2.65745e6i			0.771298i
$413$	639315.	+	237411.i	0.184433	+	0.0684898i
$414$		0			0
$415$	171218.			0.0488012
$416$	846971.			0.239958
$417$		0			0
$418$			1.53917e6i			0.430871i
$419$	6.15452e6			1.71261			0.856306	−	0.516468i	$-0.172754\pi$
$419$	6.15452e6			1.71261			0.856306	+	0.516468i	$0.172754\pi$
$420$		0			0
$421$	1.97389e6			0.542773			0.271387	−	0.962470i	$-0.412518\pi$
$421$	1.97389e6			0.542773			0.271387	+	0.962470i	$0.412518\pi$
$422$		−	1.97765e6i		−	0.540590i
$423$		0			0
$424$	−1.22649e6			−0.331322
$425$	232298.			0.0623840
$426$		0			0
$427$	−1.77748e6	+	4.78649e6i	−0.471774	+	1.27042i
$428$			1.76834e6i			0.466614i
$429$		0			0
$430$		−	332434.i		−	0.0867031i
$431$		−	2.62571e6i		−	0.680853i	−0.940271	−	0.340427i	$-0.889428\pi$
$431$		−	2.62571e6i		−	0.680853i	0.940271	−	0.340427i	$-0.110572\pi$
$432$		0			0
$433$			7.38978e6i			1.89414i	0.321031	+	0.947069i	$0.395971\pi$
$433$			7.38978e6i			1.89414i	−0.321031	+	0.947069i	$0.604029\pi$
$434$	1.40200e6	+	520636.i	0.357292	+	0.132681i
$435$		0			0
$436$	2.39323e6			0.602931
$437$	5.43276e6			1.36087
$438$		0			0
$439$			1.26097e6i			0.312279i	0.987735	+	0.156140i	$0.0499050\pi$
$439$			1.26097e6i			0.312279i	−0.987735	+	0.156140i	$0.950095\pi$
$440$	−293025.			−0.0721562
$441$		0			0
$442$	1.22969e6			0.299391
$443$		−	5.09227e6i		−	1.23283i	−0.787423	−	0.616413i	$-0.788585\pi$
$443$		−	5.09227e6i		−	1.23283i	0.787423	−	0.616413i	$-0.211415\pi$
$444$		0			0
$445$	−1.22309e6			−0.292790
$446$	1.89503e6			0.451107
$447$		0			0
$448$	497797.	+	184858.i	0.117181	+	0.0435155i
$449$			2.77353e6i			0.649259i	0.945841	+	0.324629i	$0.105240\pi$
$449$			2.77353e6i			0.649259i	−0.945841	+	0.324629i	$0.894760\pi$
$450$		0			0
$451$			371452.i			0.0859926i
$452$			424142.i			0.0976484i
$453$		0			0
$454$		−	344509.i		−	0.0784442i
$455$	933227.	−	2.51305e6i	0.211329	−	0.569079i
$456$		0			0
$457$	1.86529e6			0.417788			0.208894	−	0.977938i	$-0.433014\pi$
$457$	1.86529e6			0.417788			0.208894	+	0.977938i	$0.433014\pi$
$458$	−1.74464e6			−0.388634
$459$		0			0
$460$			1.03428e6i			0.227899i
$461$	5.92597e6			1.29870			0.649348	−	0.760492i	$-0.275042\pi$
$461$	5.92597e6			1.29870			0.649348	+	0.760492i	$0.275042\pi$
$462$		0			0
$463$	2.20120e6			0.477207			0.238604	−	0.971117i	$-0.423310\pi$
$463$	2.20120e6			0.477207			0.238604	+	0.971117i	$0.423310\pi$
$464$		−	1.55202e6i		−	0.334660i
$465$		0			0
$466$	3.19418e6			0.681389
$467$	5.26273e6			1.11666			0.558328	−	0.829620i	$-0.311443\pi$
$467$	5.26273e6			1.11666			0.558328	+	0.829620i	$0.311443\pi$
$468$		0			0
$469$	2.21085e6	+	821006.i	0.464117	+	0.172351i
$470$		−	824215.i		−	0.172106i
$471$		0			0
$472$		−	336668.i		−	0.0695580i
$473$			608823.i			0.125123i
$474$		0			0
$475$			1.31318e6i			0.267048i
$476$	722734.	+	268389.i	0.146205	+	0.0542934i
$477$		0			0
$478$	2.29072e6			0.458567
$479$	8.19922e6			1.63280			0.816401	−	0.577485i	$-0.195966\pi$
$479$	8.19922e6			1.63280			0.816401	+	0.577485i	$0.195966\pi$
$480$		0			0
$481$		−	7.42529e6i		−	1.46336i
$482$	4.13998e6			0.811672
$483$		0			0
$484$	−2.04017e6			−0.395870
$485$			821890.i			0.158657i
$486$		0			0
$487$	−1.03249e7			−1.97271			−0.986356	−	0.164624i	$-0.947359\pi$
$487$	−1.03249e7			−1.97271			−0.986356	+	0.164624i	$0.947359\pi$
$488$	2.52060e6			0.479132
$489$		0			0
$490$	1.09699e6	−	1.27333e6i	0.206401	−	0.239580i
$491$			4.13669e6i			0.774370i	0.922002	+	0.387185i	$0.126553\pi$
$491$			4.13669e6i			0.774370i	−0.922002	+	0.387185i	$0.873447\pi$
$492$		0			0
$493$		−	2.25333e6i		−	0.417549i
$494$			6.95138e6i			1.28160i
$495$		0			0
$496$		−	738303.i		−	0.134751i
$497$	−736389.	+	1.98299e6i	−0.133726	+	0.360105i
$498$		0			0
$499$	−2.49758e6			−0.449022			−0.224511	−	0.974472i	$-0.572078\pi$
$499$	−2.49758e6			−0.449022			−0.224511	+	0.974472i	$0.572078\pi$
$500$	−250000.			−0.0447214
$501$		0			0
$502$			551495.i			0.0976747i
$503$	−7.82815e6			−1.37956			−0.689778	−	0.724021i	$-0.742292\pi$
$503$	−7.82815e6			−1.37956			−0.689778	+	0.724021i	$0.742292\pi$
$504$		0			0
$505$	−804790.			−0.140428
$506$		−	1.89419e6i		−	0.328887i
$507$		0			0
$508$	4.88555e6			0.839951
$509$	5.65690e6			0.967797			0.483899	−	0.875124i	$-0.339220\pi$
$509$	5.65690e6			0.967797			0.483899	+	0.875124i	$0.339220\pi$
$510$		0			0
$511$	−1.34572e6	+	3.62383e6i	−0.227983	+	0.613926i
$512$		−	262144.i		−	0.0441942i
$513$		0			0
$514$			1.07740e6i			0.179875i
$515$		−	4.15227e6i		−	0.689870i
$516$		0			0
$517$			1.50947e6i			0.248370i
$518$	1.62063e6	−	4.36413e6i	0.265375	−	0.714617i
$519$		0			0
$520$	−1.32339e6			−0.214625
$521$	−8.37669e6			−1.35201			−0.676003	−	0.736899i	$-0.736289\pi$
$521$	−8.37669e6			−1.35201			−0.676003	+	0.736899i	$0.736289\pi$
$522$		0			0
$523$			1.22788e6i			0.196291i	0.995172	+	0.0981454i	$0.0312910\pi$
$523$			1.22788e6i			0.196291i	−0.995172	+	0.0981454i	$0.968709\pi$
$524$	−1.01345e6			−0.161240
$525$		0			0
$526$	−3.73201e6			−0.588136
$527$		−	1.07192e6i		−	0.168126i
$528$		0			0
$529$	−249490.			−0.0387627
$530$	1.91639e6			0.296343
$531$		0			0
$532$	−1.51720e6	+	4.08559e6i	−0.232414	+	0.625858i
$533$			1.67759e6i			0.255780i
$534$		0			0
$535$		−	2.76304e6i		−	0.417352i
$536$		−	1.16425e6i		−	0.175039i
$537$		0			0
$538$			7.41243e6i			1.10409i
$539$	−2.00903e6	+	2.33199e6i	−0.297862	+	0.345744i
$540$		0			0
$541$	1.32681e7			1.94902			0.974509	−	0.224350i	$-0.0720258\pi$
$541$	1.32681e7			1.94902			0.974509	+	0.224350i	$0.0720258\pi$
$542$	−7.49833e6			−1.09639
$543$		0			0
$544$		−	380597.i		−	0.0551402i
$545$	−3.73942e6			−0.539278
$546$		0			0
$547$	−4.94583e6			−0.706758			−0.353379	−	0.935480i	$-0.614967\pi$
$547$	−4.94583e6			−0.706758			−0.353379	+	0.935480i	$0.614967\pi$
$548$		−	2.90700e6i		−	0.413517i
$549$		0			0
$550$	457852.			0.0645385
$551$	1.27380e7			1.78740
$552$		0			0
$553$	−1.03991e6	−	386174.i	−0.144605	−	0.0536995i
$554$		−	3.03591e6i		−	0.420257i
$555$		0			0
$556$			1.92984e6i			0.264749i
$557$		−	5.16886e6i		−	0.705922i	−0.935638	−	0.352961i	$-0.885175\pi$
$557$		−	5.16886e6i		−	0.705922i	0.935638	−	0.352961i	$-0.114825\pi$
$558$		0			0
$559$			2.74963e6i			0.372173i
$560$	−777808.	−	288841.i	−0.104810	−	0.0389214i
$561$		0			0
$562$	−8.33338e6			−1.11296
$563$	2.12993e6			0.283201			0.141601	−	0.989924i	$-0.454775\pi$
$563$	2.12993e6			0.283201			0.141601	+	0.989924i	$0.454775\pi$
$564$		0			0
$565$		−	662722.i		−	0.0873394i
$566$	−9.48541e6			−1.24456
$567$		0			0
$568$	1.04426e6			0.135812
$569$			1.16292e7i			1.50581i	0.658131	+	0.752903i	$0.271347\pi$
$569$			1.16292e7i			1.50581i	−0.658131	+	0.752903i	$0.728653\pi$
$570$		0			0
$571$	1.36578e7			1.75304			0.876518	−	0.481370i	$-0.159861\pi$
$571$	1.36578e7			1.75304			0.876518	+	0.481370i	$0.159861\pi$
$572$	2.42367e6			0.309730
$573$		0			0
$574$	−366147.	+	985983.i	−0.0463849	+	0.124908i
$575$		−	1.61606e6i		−	0.203839i
$576$		0			0
$577$			6.92755e6i			0.866244i	0.901335	+	0.433122i	$0.142588\pi$
$577$			6.92755e6i			0.866244i	−0.901335	+	0.433122i	$0.857412\pi$
$578$			5.12685e6i			0.638309i
$579$		0			0
$580$			2.42504e6i			0.299329i
$581$	−832345.	−	309093.i	−0.102297	−	0.0379883i
$582$		0			0
$583$	−3.50970e6			−0.427660
$584$	1.90834e6			0.231539
$585$		0			0
$586$		−	2.87088e6i		−	0.345359i
$587$	−1.63952e7			−1.96391			−0.981957	−	0.189102i	$-0.939442\pi$
$587$	−1.63952e7			−1.96391			−0.981957	+	0.189102i	$0.939442\pi$
$588$		0			0
$589$	6.05951e6			0.719697
$590$			526044.i			0.0622146i
$591$		0			0
$592$	−2.29819e6			−0.269514
$593$	7.49183e6			0.874885			0.437443	−	0.899246i	$-0.355884\pi$
$593$	7.49183e6			0.874885			0.437443	+	0.899246i	$0.355884\pi$
$594$		0			0
$595$	−1.12927e6	−	419358.i	−0.130769	−	0.0485615i
$596$		−	1.61261e6i		−	0.185958i
$597$		0			0
$598$		−	8.55473e6i		−	0.978258i
$599$			5.00561e6i			0.570019i	0.958525	+	0.285010i	$0.0919968\pi$
$599$			5.00561e6i			0.570019i	−0.958525	+	0.285010i	$0.908003\pi$
$600$		0			0
$601$		−	1.38113e6i		−	0.155972i	−0.996954	−	0.0779862i	$-0.975151\pi$
$601$		−	1.38113e6i		−	0.155972i	0.996954	−	0.0779862i	$-0.0248490\pi$
$602$	−600129.	+	1.61606e6i	−0.0674922	+	0.181747i
$603$		0			0
$604$	4.98259e6			0.555728
$605$	3.18776e6			0.354077
$606$		0			0
$607$		−	171358.i		−	0.0188770i	−0.999955	−	0.00943851i	$-0.996996\pi$
$607$		−	171358.i		−	0.0188770i	0.999955	−	0.00943851i	$-0.00300441\pi$
$608$	2.15151e6			0.236039
$609$		0			0
$610$	−3.93844e6			−0.428549
$611$			6.81724e6i			0.738764i
$612$		0			0
$613$	−8.89098e6			−0.955649			−0.477824	−	0.878455i	$-0.658574\pi$
$613$	−8.89098e6			−0.955649			−0.477824	+	0.878455i	$0.658574\pi$
$614$	−5.00972e6			−0.536281
$615$		0			0
$616$	1.42448e6	+	528986.i	0.151254	+	0.0561685i
$617$		−	1.77883e7i		−	1.88115i	−0.339592	−	0.940573i	$-0.610289\pi$
$617$		−	1.77883e7i		−	1.88115i	0.339592	−	0.940573i	$-0.389711\pi$
$618$		0			0
$619$			8.80341e6i			0.923473i	0.887017	+	0.461737i	$0.152773\pi$
$619$			8.80341e6i			0.923473i	−0.887017	+	0.461737i	$0.847227\pi$
$620$			1.15360e6i			0.120525i
$621$		0			0
$622$			1.16253e7i			1.20484i
$623$	5.94579e6	+	2.20798e6i	0.613747	+	0.227917i
$624$		0			0
$625$	390625.			0.0400000
$626$	−2.61237e6			−0.266440
$627$		0			0
$628$			3.03428e6i			0.307013i
$629$	−3.33665e6			−0.336267
$630$		0			0
$631$	1.41323e7			1.41299			0.706495	−	0.707718i	$-0.250275\pi$
$631$	1.41323e7			1.41299			0.706495	+	0.707718i	$0.250275\pi$
$632$			547626.i			0.0545370i
$633$		0			0
$634$	5.69488e6			0.562680
$635$	−7.63367e6			−0.751275
$636$		0			0
$637$	−9.07340e6	+	1.05320e7i	−0.885975	+	1.02840i
$638$		−	4.44124e6i		−	0.431969i
$639$		0			0
$640$			409600.i			0.0395285i
$641$		−	1.20651e7i		−	1.15981i	−0.814683	−	0.579906i	$-0.803089\pi$
$641$		−	1.20651e7i		−	1.15981i	0.814683	−	0.579906i	$-0.196911\pi$
$642$		0			0
$643$			2.30489e6i			0.219848i	0.993940	+	0.109924i	$0.0350608\pi$
$643$			2.30489e6i			0.219848i	−0.993940	+	0.109924i	$0.964939\pi$
$644$	1.86714e6	−	5.02794e6i	0.177403	−	0.477722i
$645$		0			0
$646$	3.12369e6			0.294501
$647$	−1.41536e7			−1.32925			−0.664623	−	0.747179i	$-0.731408\pi$
$647$	−1.41536e7			−1.32925			−0.664623	+	0.747179i	$0.731408\pi$
$648$		0			0
$649$		−	963402.i		−	0.0897833i
$650$	2.06780e6			0.191966
$651$		0			0
$652$	3.21771e6			0.296434
$653$			1.15469e7i			1.05969i	0.848093	+	0.529847i	$0.177751\pi$
$653$			1.15469e7i			1.05969i	−0.848093	+	0.529847i	$0.822249\pi$
$654$		0			0
$655$	1.58351e6			0.144218
$656$	519227.			0.0471083
$657$		0			0
$658$	−1.48792e6	+	4.00675e6i	−0.133972	+	0.360768i
$659$		−	5.64678e6i		−	0.506510i	−0.967400	−	0.253255i	$-0.918499\pi$
$659$		−	5.64678e6i		−	0.506510i	0.967400	−	0.253255i	$-0.0815011\pi$
$660$		0			0
$661$		−	7.28300e6i		−	0.648346i	−0.945998	−	0.324173i	$-0.894914\pi$
$661$		−	7.28300e6i		−	0.648346i	0.945998	−	0.324173i	$-0.105086\pi$
$662$			1.97598e6i			0.175241i
$663$		0			0
$664$			438319.i			0.0385807i
$665$	2.37062e6	−	6.38374e6i	0.207878	−	0.559785i
$666$		0			0
$667$	−1.56760e7			−1.36434
$668$	3.32486e6			0.288291
$669$		0			0
$670$			1.81915e6i			0.156560i
$671$	7.21290e6			0.618449
$672$		0			0
$673$	−1.14636e7			−0.975624			−0.487812	−	0.872949i	$-0.662205\pi$
$673$	−1.14636e7			−0.975624			−0.487812	+	0.872949i	$0.662205\pi$
$674$			1.53277e7i			1.29966i
$675$		0			0
$676$	5.00535e6			0.421277
$677$	8.05827e6			0.675725			0.337863	−	0.941195i	$-0.390296\pi$
$677$	8.05827e6			0.675725			0.337863	+	0.941195i	$0.390296\pi$
$678$		0			0
$679$	1.48372e6	−	3.99545e6i	0.123503	−	0.332577i
$680$			594683.i			0.0493189i
$681$		0			0
$682$		−	2.11271e6i		−	0.173932i
$683$			1.51467e6i			0.124241i	0.998069	+	0.0621206i	$0.0197863\pi$
$683$			1.51467e6i			0.124241i	−0.998069	+	0.0621206i	$0.980214\pi$
$684$		0			0
$685$			4.54219e6i			0.369861i
$686$	−7.63147e6	+	4.20970e6i	−0.619153	+	0.341539i
$687$		0			0
$688$	851031.			0.0685448
$689$	−1.58509e7			−1.27205
$690$		0			0
$691$		−	3.15419e6i		−	0.251300i	−0.992075	−	0.125650i	$-0.959898\pi$
$691$		−	3.15419e6i		−	0.251300i	0.992075	−	0.125650i	$-0.0401016\pi$
$692$	1.01138e7			0.802876
$693$		0			0
$694$	7.45594e6			0.587629
$695$		−	3.01537e6i		−	0.236799i
$696$		0			0
$697$	753846.			0.0587761
$698$	−4.11060e6			−0.319350
$699$		0			0
$700$	1.21533e6	+	451314.i	0.0937448	+	0.0348124i
$701$		−	2.71147e6i		−	0.208406i	−0.994556	−	0.104203i	$-0.966771\pi$
$701$		−	2.71147e6i		−	0.208406i	0.994556	−	0.104203i	$-0.0332292\pi$
$702$		0			0
$703$		−	1.88620e7i		−	1.43946i
$704$		−	750145.i		−	0.0570445i
$705$		0			0
$706$		−	1.49937e7i		−	1.13213i
$707$	3.91233e6	+	1.45285e6i	0.294365	+	0.109313i
$708$		0			0
$709$	1.71376e7			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$709$	1.71376e7			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$710$	−1.63165e6			−0.121474
$711$		0			0
$712$		−	3.13110e6i		−	0.231471i
$713$	−7.45715e6			−0.549350
$714$		0			0
$715$	−3.78699e6			−0.277031
$716$			4.57356e6i			0.333404i
$717$		0			0
$718$	−1.93375e6			−0.139987
$719$	9.03240e6			0.651600			0.325800	−	0.945439i	$-0.394366\pi$
$719$	9.03240e6			0.651600			0.325800	+	0.945439i	$0.394366\pi$
$720$		0			0
$721$	−7.49591e6	+	2.01854e7i	−0.537015	+	1.44611i
$722$			7.75376e6i			0.553566i
$723$		0			0
$724$			6.18828e6i			0.438756i
$725$		−	3.78912e6i		−	0.267728i
$726$		0			0
$727$		−	1.44566e7i		−	1.01445i	−0.861813	−	0.507226i	$-0.830671\pi$
$727$		−	1.44566e7i		−	1.01445i	0.861813	−	0.507226i	$-0.169329\pi$
$728$	6.43341e6	+	2.38906e6i	0.449896	+	0.167070i
$729$		0			0
$730$	−2.98178e6			−0.207095
$731$	1.23558e6			0.0855220
$732$		0			0
$733$		−	6.38834e6i		−	0.439165i	−0.975594	−	0.219583i	$-0.929530\pi$
$733$		−	6.38834e6i		−	0.439165i	0.975594	−	0.219583i	$-0.0704695\pi$
$734$	−8.54221e6			−0.585234
$735$		0			0
$736$	−2.64775e6			−0.180170
$737$		−	3.33160e6i		−	0.225935i
$738$		0			0
$739$	1.35024e7			0.909492			0.454746	−	0.890621i	$-0.349730\pi$
$739$	1.35024e7			0.909492			0.454746	+	0.890621i	$0.349730\pi$
$740$	3.59092e6			0.241060
$741$		0			0
$742$	−9.31617e6	−	3.45959e6i	−0.621195	−	0.230682i
$743$			1.97481e7i			1.31236i	0.754605	+	0.656179i	$0.227828\pi$
$743$			1.97481e7i			1.31236i	−0.754605	+	0.656179i	$0.772172\pi$
$744$		0			0
$745$			2.51971e6i			0.166326i
$746$			1.33826e6i			0.0880429i
$747$		0			0
$748$		−	1.08911e6i		−	0.0711733i
$749$	−4.98800e6	+	1.34320e7i	−0.324879	+	0.874853i
$750$		0			0
$751$	−1.76700e7			−1.14324			−0.571618	−	0.820520i	$-0.693684\pi$
$751$	−1.76700e7			−1.14324			−0.571618	+	0.820520i	$0.693684\pi$
$752$	2.10999e6			0.136062
$753$		0			0
$754$		−	2.00580e7i		−	1.28487i
$755$	−7.78529e6			−0.497058
$756$		0			0
$757$	−9.97065e6			−0.632388			−0.316194	−	0.948695i	$-0.602405\pi$
$757$	−9.97065e6			−0.632388			−0.316194	+	0.948695i	$0.602405\pi$
$758$		−	1.21423e7i		−	0.767587i
$759$		0			0
$760$	−3.36173e6			−0.211120
$761$	−1.05836e7			−0.662477			−0.331238	−	0.943547i	$-0.607466\pi$
$761$	−1.05836e7			−0.662477			−0.331238	+	0.943547i	$0.607466\pi$
$762$		0			0
$763$	1.81784e7	+	6.75061e6i	1.13043	+	0.419789i
$764$			9.29058e6i			0.575850i
$765$		0			0
$766$		−	1.71464e7i		−	1.05585i
$767$		−	4.35102e6i		−	0.267056i
$768$		0			0
$769$		−	1.69866e6i		−	0.103584i	−0.998658	−	0.0517918i	$-0.983507\pi$
$769$		−	1.69866e6i		−	0.103584i	0.998658	−	0.0517918i	$-0.0164932\pi$
$770$	−2.22576e6	−	826541.i	−0.135285	−	0.0502386i
$771$		0			0
$772$	−6.64344e6			−0.401190
$773$	−2.90176e7			−1.74668			−0.873338	−	0.487114i	$-0.838050\pi$
$773$	−2.90176e7			−1.74668			−0.873338	+	0.487114i	$0.838050\pi$
$774$		0			0
$775$		−	1.80250e6i		−	0.107800i
$776$	−2.10404e6			−0.125429
$777$		0			0
$778$	−63704.7			−0.00377331
$779$			4.26147e6i			0.251603i
$780$		0			0
$781$	2.98822e6			0.175302
$782$	−3.84418e6			−0.224795
$783$		0			0
$784$	3.25973e6	+	2.80829e6i	0.189405	+	0.163174i
$785$		−	4.74106e6i		−	0.274601i
$786$		0			0
$787$			9.36084e6i			0.538738i	0.963037	+	0.269369i	$0.0868152\pi$
$787$			9.36084e6i			0.538738i	−0.963037	+	0.269369i	$0.913185\pi$
$788$		−	7.41076e6i		−	0.425155i
$789$		0			0
$790$		−	855665.i		−	0.0487794i
$791$	−1.19638e6	+	3.22169e6i	−0.0679875	+	0.183081i
$792$		0			0
$793$	3.25756e7			1.83954
$794$	1.76563e6			0.0993912
$795$		0			0
$796$			1.19685e7i			0.669508i
$797$	−3.31540e7			−1.84880			−0.924402	−	0.381421i	$-0.875435\pi$
$797$	−3.31540e7			−1.84880			−0.924402	+	0.381421i	$0.875435\pi$
$798$		0			0
$799$	3.06342e6			0.169761
$800$		−	640000.i		−	0.0353553i
$801$		0			0
$802$	−1.82277e7			−1.00068
$803$	5.46086e6			0.298863
$804$		0			0
$805$	−2.91741e6	+	7.85616e6i	−0.158675	+	0.427288i
$806$		−	9.54165e6i		−	0.517352i
$807$		0			0
$808$		−	2.06026e6i		−	0.111018i
$809$			1.18124e7i			0.634550i	0.948334	+	0.317275i	$0.102768\pi$
$809$			1.18124e7i			0.634550i	−0.948334	+	0.317275i	$0.897232\pi$
$810$		0			0
$811$		−	1.53715e7i		−	0.820660i	−0.911937	−	0.410330i	$-0.865413\pi$
$811$		−	1.53715e7i		−	0.820660i	0.911937	−	0.410330i	$-0.134587\pi$
$812$	4.37782e6	−	1.17888e7i	0.233006	−	0.627453i
$813$		0			0
$814$	−6.57643e6			−0.347880
$815$	−5.02767e6			−0.265139
$816$		0			0
$817$			6.98471e6i			0.366094i
$818$	−2.50792e7			−1.31048
$819$		0			0
$820$	−811291.			−0.0421349
$821$			1.16833e7i			0.604931i	0.953160	+	0.302466i	$0.0978097\pi$
$821$			1.16833e7i			0.604931i	−0.953160	+	0.302466i	$0.902190\pi$
$822$		0			0
$823$	1.40608e7			0.723619			0.361810	−	0.932252i	$-0.382159\pi$
$823$	1.40608e7			0.723619			0.361810	+	0.932252i	$0.382159\pi$
$824$	1.06298e7			0.545390
$825$		0			0
$826$	949645.	−	2.55726e6i	0.0484296	−	0.130414i
$827$			9.92625e6i			0.504686i	0.967638	+	0.252343i	$0.0812012\pi$
$827$			9.92625e6i			0.504686i	−0.967638	+	0.252343i	$0.918799\pi$
$828$		0			0
$829$		−	2.89630e7i		−	1.46372i	−0.681456	−	0.731859i	$-0.738653\pi$
$829$		−	2.89630e7i		−	1.46372i	0.681456	−	0.731859i	$-0.261347\pi$
$830$		−	684874.i		−	0.0345077i
$831$		0			0
$832$		−	3.38788e6i		−	0.169676i
$833$	4.73268e6	+	4.07725e6i	0.236317	+	0.203589i
$834$		0			0
$835$	−5.19509e6			−0.257856
$836$	6.15670e6			0.304672
$837$		0			0
$838$		−	2.46181e7i		−	1.21100i
$839$	−4.40951e6			−0.216265			−0.108132	−	0.994137i	$-0.534487\pi$
$839$	−4.40951e6			−0.216265			−0.108132	+	0.994137i	$0.534487\pi$
$840$		0			0
$841$	−1.62439e7			−0.791956
$842$		−	7.89558e6i		−	0.383799i
$843$		0			0
$844$	−7.91060e6			−0.382255
$845$	−7.82086e6			−0.376801
$846$		0			0
$847$	−1.54967e7	−	5.75473e6i	−0.742215	−	0.275623i
$848$			4.90597e6i			0.234280i
$849$		0			0
$850$		−	929193.i		−	0.0441122i
$851$			2.32126e7i			1.09875i
$852$		0			0
$853$			1.35591e7i			0.638056i	0.947745	+	0.319028i	$0.103356\pi$
$853$			1.35591e7i			0.638056i	−0.947745	+	0.319028i	$0.896644\pi$
$854$	1.91460e7	+	7.10990e6i	0.898323	+	0.333595i
$855$		0			0
$856$	7.07338e6			0.329946
$857$	−2.32431e7			−1.08104			−0.540520	−	0.841331i	$-0.681773\pi$
$857$	−2.32431e7			−1.08104			−0.540520	+	0.841331i	$0.681773\pi$
$858$		0			0
$859$		−	3.66434e7i		−	1.69439i	−0.531284	−	0.847194i	$-0.678290\pi$
$859$		−	3.66434e7i		−	1.69439i	0.531284	−	0.847194i	$-0.321710\pi$
$860$	−1.32974e6			−0.0613083
$861$		0			0
$862$	−1.05028e7			−0.481436
$863$		−	5.42841e6i		−	0.248111i	−0.992275	−	0.124055i	$-0.960410\pi$
$863$		−	5.42841e6i		−	0.248111i	0.992275	−	0.124055i	$-0.0395901\pi$
$864$		0			0
$865$	−1.58028e7			−0.718114
$866$	2.95591e7			1.33936
$867$		0			0
$868$	2.08254e6	−	5.60799e6i	0.0938198	−	0.252644i
$869$			1.56707e6i			0.0703947i
$870$		0			0
$871$		−	1.50465e7i		−	0.672033i
$872$		−	9.57290e6i		−	0.426336i
$873$		0			0
$874$		−	2.17310e7i		−	0.962281i
$875$	−1.89895e6	−	705179.i	−0.0838479	−	0.0311372i
$876$		0			0
$877$	−3.12144e7			−1.37043			−0.685213	−	0.728343i	$-0.740291\pi$
$877$	−3.12144e7			−1.37043			−0.685213	+	0.728343i	$0.740291\pi$
$878$	5.04388e6			0.220815
$879$		0			0
$880$			1.17210e6i			0.0510221i
$881$	−3.33771e7			−1.44880			−0.724400	−	0.689380i	$-0.757883\pi$
$881$	−3.33771e7			−1.44880			−0.724400	+	0.689380i	$0.757883\pi$
$882$		0			0
$883$	−1.66178e7			−0.717254			−0.358627	−	0.933481i	$-0.616755\pi$
$883$	−1.66178e7			−0.717254			−0.358627	+	0.933481i	$0.616755\pi$
$884$		−	4.91874e6i		−	0.211701i
$885$		0			0
$886$	−2.03691e7			−0.871740
$887$	2.94191e7			1.25551			0.627756	−	0.778410i	$-0.283974\pi$
$887$	2.94191e7			1.25551			0.627756	+	0.778410i	$0.283974\pi$
$888$		0			0
$889$	3.71095e7	+	1.37807e7i	1.57482	+	0.584814i
$890$			4.89234e6i			0.207034i
$891$		0			0
$892$		−	7.58013e6i		−	0.318981i
$893$			1.73174e7i			0.726699i
$894$		0			0
$895$		−	7.14618e6i		−	0.298206i
$896$	739433.	−	1.99119e6i	0.0307701	−	0.0828595i
$897$		0			0
$898$	1.10941e7			0.459095
$899$	−1.74845e7			−0.721530
$900$		0			0
$901$			7.12280e6i			0.292307i
$902$	1.48581e6			0.0608059
$903$		0			0
$904$	1.69657e6			0.0690478
$905$		−	9.66919e6i		−	0.392436i
$906$		0			0
$907$	3.03152e6			0.122361			0.0611803	−	0.998127i	$-0.480514\pi$
$907$	3.03152e6			0.122361			0.0611803	+	0.998127i	$0.480514\pi$
$908$	−1.37804e6			−0.0554684
$909$		0			0
$910$	−1.00522e7	−	3.73291e6i	−0.402400	−	0.149432i
$911$		−	7.41523e6i		−	0.296025i	−0.988985	−	0.148013i	$-0.952712\pi$
$911$		−	7.41523e6i		−	0.296025i	0.988985	−	0.148013i	$-0.0472876\pi$
$912$		0			0
$913$			1.25428e6i			0.0497988i
$914$		−	7.46117e6i		−	0.295421i
$915$		0			0
$916$			6.97855e6i			0.274806i
$917$	−7.69794e6	−	2.85865e6i	−0.302309	−	0.112263i
$918$		0			0
$919$	6.94938e6			0.271430			0.135715	−	0.990748i	$-0.456667\pi$
$919$	6.94938e6			0.271430			0.135715	+	0.990748i	$0.456667\pi$
$920$	4.13712e6			0.161149
$921$		0			0
$922$		−	2.37039e7i		−	0.918317i
$923$	1.34957e7			0.521425
$924$		0			0
$925$	−5.61081e6			−0.215611
$926$		−	8.80480e6i		−	0.337436i
$927$		0			0
$928$	−6.20810e6			−0.236640
$929$	3.61427e7			1.37398			0.686992	−	0.726665i	$-0.258931\pi$
$929$	3.61427e7			1.37398			0.686992	+	0.726665i	$0.258931\pi$
$930$		0			0
$931$	−2.30486e7	+	2.67537e7i	−0.871505	+	1.01160i
$932$		−	1.27767e7i		−	0.481815i
$933$		0			0
$934$		−	2.10509e7i		−	0.789595i
$935$			1.70173e6i			0.0636593i
$936$		0			0
$937$			2.00541e6i			0.0746199i	0.999304	+	0.0373099i	$0.0118789\pi$
$937$			2.00541e6i			0.0746199i	−0.999304	+	0.0373099i	$0.988121\pi$
$938$	3.28402e6	−	8.84341e6i	0.121871	−	0.328180i
$939$		0			0
$940$	−3.29686e6			−0.121697
$941$	−3.89595e7			−1.43430			−0.717149	−	0.696920i	$-0.754553\pi$
$941$	−3.89595e7			−1.43430			−0.717149	+	0.696920i	$0.754553\pi$
$942$		0			0
$943$		−	5.24439e6i		−	0.192050i
$944$	−1.34667e6			−0.0491849
$945$		0			0
$946$	2.43529e6			0.0884755
$947$		−	4.45403e7i		−	1.61391i	−0.590615	−	0.806954i	$-0.701115\pi$
$947$		−	4.45403e7i		−	1.61391i	0.590615	−	0.806954i	$-0.298885\pi$
$948$		0			0
$949$	2.46629e7			0.888953
$950$	5.25270e6			0.188831
$951$		0			0
$952$	1.07356e6	−	2.89093e6i	0.0383913	−	0.103382i
$953$			4.90366e7i			1.74899i	0.485031	+	0.874497i	$0.338808\pi$
$953$			4.90366e7i			1.74899i	−0.485031	+	0.874497i	$0.661192\pi$
$954$		0			0
$955$		−	1.45165e7i		−	0.515056i
$956$		−	9.16288e6i		−	0.324256i
$957$		0			0
$958$		−	3.27969e7i		−	1.15457i
$959$	8.19981e6	−	2.20809e7i	0.287910	−	0.775302i
$960$		0			0
$961$	2.03117e7			0.709476
$962$	−2.97012e7			−1.03475
$963$		0			0
$964$		−	1.65599e7i		−	0.573939i
$965$	1.03804e7			0.358835
$966$		0			0
$967$	−2.72533e7			−0.937246			−0.468623	−	0.883398i	$-0.655250\pi$
$967$	−2.72533e7			−0.937246			−0.468623	+	0.883398i	$0.655250\pi$
$968$			8.16067e6i			0.279922i
$969$		0			0
$970$	3.28756e6			0.112187
$971$	−3.54321e7			−1.20600			−0.603001	−	0.797740i	$-0.706029\pi$
$971$	−3.54321e7			−1.20600			−0.603001	+	0.797740i	$0.706029\pi$
$972$		0			0
$973$	−5.44352e6	+	1.46586e7i	−0.184331	+	0.496377i
$974$			4.12996e7i			1.39492i
$975$		0			0
$976$		−	1.00824e7i		−	0.338797i
$977$		−	3.61918e7i		−	1.21304i	−0.795069	−	0.606519i	$-0.792565\pi$
$977$		−	3.61918e7i		−	1.21304i	0.795069	−	0.606519i	$-0.207435\pi$
$978$		0			0
$979$		−	8.95988e6i		−	0.298776i
$980$	−5.09332e6	−	4.38795e6i	−0.169409	−	0.145947i
$981$		0			0
$982$	1.65467e7			0.547563
$983$	−1.63741e7			−0.540473			−0.270237	−	0.962794i	$-0.587102\pi$
$983$	−1.63741e7			−0.540473			−0.270237	+	0.962794i	$0.587102\pi$
$984$		0			0
$985$			1.15793e7i			0.380270i
$986$	−9.01331e6			−0.295252
$987$		0			0
$988$	2.78055e7			0.906231
$989$		−	8.59574e6i		−	0.279443i
$990$		0			0
$991$	−4.01953e7			−1.30014			−0.650072	−	0.759873i	$-0.725261\pi$
$991$	−4.01953e7			−1.30014			−0.650072	+	0.759873i	$0.725261\pi$
$992$	−2.95321e6			−0.0952831
$993$		0			0
$994$	7.93196e6	+	2.94555e6i	0.254633	+	0.0945586i
$995$		−	1.87007e7i		−	0.598826i
$996$		0			0
$997$			2.97471e7i			0.947778i	0.880585	+	0.473889i	$0.157150\pi$
$997$			2.97471e7i			0.947778i	−0.880585	+	0.473889i	$0.842850\pi$
$998$			9.99030e6i			0.317506i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.6.b.b.251.2	yes	24
3.2	odd	2		630.6.b.a.251.14	yes	24
7.6	odd	2		630.6.b.a.251.2	✓	24
21.20	even	2	inner	630.6.b.b.251.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.6.b.a.251.2	✓	24	7.6	odd	2
630.6.b.a.251.14	yes	24	3.2	odd	2
630.6.b.b.251.2	yes	24	1.1	even	1	trivial
630.6.b.b.251.14	yes	24	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	630.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -16.0000 q^{4} +25.0000 q^{5} +(-121.533 - 45.1314i) q^{7} +64.0000i q^{8} -100.000i q^{10} +183.141i q^{11} +827.120i q^{13} +(-180.526 + 486.130i) q^{14} +256.000 q^{16} +371.677 q^{17} +2101.08i q^{19} -400.000 q^{20} +732.564 q^{22} -2585.70i q^{23} +625.000 q^{25} +3308.48 q^{26} +(1944.52 + 722.103i) q^{28} -6062.60i q^{29} -2884.00i q^{31} -1024.00i q^{32} -1486.71i q^{34} +(-3038.31 - 1128.29i) q^{35} -8977.29 q^{37} +8404.32 q^{38} +1600.00i q^{40} +2028.23 q^{41} +3324.34 q^{43} -2930.25i q^{44} -10342.8 q^{46} +8242.15 q^{47} +(12733.3 + 10969.9i) q^{49} -2500.00i q^{50} -13233.9i q^{52} +19163.9i q^{53} +4578.52i q^{55} +(2888.41 - 7778.08i) q^{56} -24250.4 q^{58} -5260.44 q^{59} -39384.4i q^{61} -11536.0 q^{62} -4096.00 q^{64} +20678.0i q^{65} -18191.5 q^{67} -5946.83 q^{68} +(-4513.14 + 12153.3i) q^{70} -16316.5i q^{71} -29817.8i q^{73} +35909.2i q^{74} -33617.3i q^{76} +(8265.41 - 22257.6i) q^{77} +8556.65 q^{79} +6400.00 q^{80} -8112.91i q^{82} +6848.74 q^{83} +9291.93 q^{85} -13297.4i q^{86} -11721.0 q^{88} -48923.4 q^{89} +(37329.1 - 100522. i) q^{91} +41371.2i q^{92} -32968.6i q^{94} +52527.0i q^{95} +32875.6i q^{97} +(43879.5 - 50933.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 384 q^{4} + 600 q^{5} - 196 q^{7} + 6144 q^{16} - 9600 q^{20} + 15000 q^{25} - 3872 q^{26} + 3136 q^{28} - 4900 q^{35} - 33512 q^{37} - 10208 q^{38} + 44968 q^{41} + 8016 q^{43} - 1312 q^{46} + 47240 q^{47}+ \cdots + 257936 q^{98}+O(q^{100}) \) 24 * q - 384 * q^4 + 600 * q^5 - 196 * q^7 + 6144 * q^16 - 9600 * q^20 + 15000 * q^25 - 3872 * q^26 + 3136 * q^28 - 4900 * q^35 - 33512 * q^37 - 10208 * q^38 + 44968 * q^41 + 8016 * q^43 - 1312 * q^46 + 47240 * q^47 - 31724 * q^49 + 35168 * q^58 - 110400 * q^59 + 20320 * q^62 - 98304 * q^64 - 92032 * q^67 + 107212 * q^77 + 90632 * q^79 + 153600 * q^80 - 211664 * q^83 + 286888 * q^89 - 173684 * q^91 + 257936 * q^98

Introduction

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