LMFDB - Embedded newform 342.7.d.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,7,Mod(37,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, 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("342.37");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	342.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:	$78.6784965980$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 5050x^{8} + 7354489x^{6} + 2475755792x^{4} + 232626987584x^{2} + 2900002611200 $ x^10 + 5050x^8 + 7354489x^6 + 2475755792x^4 + 232626987584x^2 + 2900002611200
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.6
Root			$-3.82791i$ of defining polynomial
Character	$\chi$	$=$	342.37
Dual form			342.7.d.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -32.0000 q^{4} -146.942 q^{5} -183.624 q^{7} -181.019i q^{8} +O(q^{10})$	\(q+5.65685i q^{2} -32.0000 q^{4} -146.942 q^{5} -183.624 q^{7} -181.019i q^{8} -831.227i q^{10} -1718.09 q^{11} -4162.60i q^{13} -1038.74i q^{14} +1024.00 q^{16} +5344.58 q^{17} +(5783.77 - 3686.99i) q^{19} +4702.13 q^{20} -9719.01i q^{22} -17446.9 q^{23} +5966.81 q^{25} +23547.2 q^{26} +5875.98 q^{28} -21286.1i q^{29} +51794.2i q^{31} +5792.62i q^{32} +30233.5i q^{34} +26982.0 q^{35} -81389.5i q^{37} +(20856.8 + 32717.9i) q^{38} +26599.3i q^{40} -98459.1i q^{41} -65509.9 q^{43} +54979.0 q^{44} -98694.3i q^{46} +17280.8 q^{47} -83931.1 q^{49} +33753.4i q^{50} +133203. i q^{52} +39630.4i q^{53} +252459. q^{55} +33239.5i q^{56} +120412. q^{58} +293899. i q^{59} -80661.6 q^{61} -292992. q^{62} -32768.0 q^{64} +611659. i q^{65} +351602. i q^{67} -171026. q^{68} +152633. i q^{70} -98918.1i q^{71} -325874. q^{73} +460409. q^{74} +(-185081. + 117984. i) q^{76} +315484. q^{77} -137910. i q^{79} -150468. q^{80} +556969. q^{82} +142009. q^{83} -785340. q^{85} -370580. i q^{86} +311008. i q^{88} -379704. i q^{89} +764355. i q^{91} +558299. q^{92} +97755.2i q^{94} +(-849875. + 541773. i) q^{95} +329181. i q^{97} -474786. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7}+O(q^{10}) $ 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7	$ 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7} - 3644 q^{11} + 10240 q^{16} + 10420 q^{17} - 17230 q^{19} - 3584 q^{20} - 37712 q^{23} - 52078 q^{25} + 7104 q^{26} + 7168 q^{28} + 161720 q^{35} - 25152 q^{38} + 6308 q^{43} + 116608 q^{44} - 322220 q^{47} - 235770 q^{49} - 377880 q^{55} + 445920 q^{58} + 426304 q^{61} - 59424 q^{62} - 327680 q^{64} - 333440 q^{68} - 786076 q^{73} + 293280 q^{74} + 551360 q^{76} - 2303716 q^{77} + 114688 q^{80} - 455136 q^{82} + 101500 q^{83} - 1261380 q^{85} + 1206784 q^{92} - 3106292 q^{95}+O(q^{100}) $ 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7 - 3644 * q^11 + 10240 * q^16 + 10420 * q^17 - 17230 * q^19 - 3584 * q^20 - 37712 * q^23 - 52078 * q^25 + 7104 * q^26 + 7168 * q^28 + 161720 * q^35 - 25152 * q^38 + 6308 * q^43 + 116608 * q^44 - 322220 * q^47 - 235770 * q^49 - 377880 * q^55 + 445920 * q^58 + 426304 * q^61 - 59424 * q^62 - 327680 * q^64 - 333440 * q^68 - 786076 * q^73 + 293280 * q^74 + 551360 * q^76 - 2303716 * q^77 + 114688 * q^80 - 455136 * q^82 + 101500 * q^83 - 1261380 * q^85 + 1206784 * q^92 - 3106292 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$-1$

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 $

$2$			5.65685i			0.707107i
$2$			5.65685i			0.707107i
$3$		0			0
$3$		0			0
$4$	−32.0000			−0.500000
$5$	−146.942			−1.17553			−0.587766	−	0.809031i	$-0.699992\pi$
$5$	−146.942			−1.17553			−0.587766	+	0.809031i	$0.699992\pi$
$6$		0			0
$7$	−183.624			−0.535348			−0.267674	−	0.963510i	$-0.586255\pi$
$7$	−183.624			−0.535348			−0.267674	+	0.963510i	$0.586255\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$		−	831.227i		−	0.831227i
$11$	−1718.09			−1.29083			−0.645415	−	0.763832i	$-0.723316\pi$
$11$	−1718.09			−1.29083			−0.645415	+	0.763832i	$0.723316\pi$
$12$		0			0
$13$		−	4162.60i		−	1.89468i	−0.320235	−	0.947338i	$-0.603762\pi$
$13$		−	4162.60i		−	1.89468i	0.320235	−	0.947338i	$-0.396238\pi$
$14$		−	1038.74i		−	0.378548i
$15$		0			0
$16$	1024.00			0.250000
$17$	5344.58			1.08784			0.543922	−	0.839136i	$-0.316939\pi$
$17$	5344.58			1.08784			0.543922	+	0.839136i	$0.316939\pi$
$18$		0			0
$19$	5783.77	−	3686.99i	0.843238	−	0.537541i
$19$	5783.77	−	3686.99i	0.843238	−	0.537541i
$20$	4702.13			0.587766
$21$		0			0
$22$		−	9719.01i		−	0.912755i
$23$	−17446.9			−1.43395			−0.716974	−	0.697100i	$-0.754473\pi$
$23$	−17446.9			−1.43395			−0.716974	+	0.697100i	$0.754473\pi$
$24$		0			0
$25$	5966.81			0.381876
$26$	23547.2			1.33974
$27$		0			0
$28$	5875.98			0.267674
$29$		−	21286.1i		−	0.872775i	−0.899759	−	0.436387i	$-0.856258\pi$
$29$		−	21286.1i		−	0.872775i	0.899759	−	0.436387i	$-0.143742\pi$
$30$		0			0
$31$			51794.2i			1.73859i	0.494298	+	0.869293i	$0.335425\pi$
$31$			51794.2i			1.73859i	−0.494298	+	0.869293i	$0.664575\pi$
$32$			5792.62i			0.176777i
$33$		0			0
$34$			30233.5i			0.769222i
$35$	26982.0			0.629318
$36$		0			0
$37$		−	81389.5i		−	1.60681i	−0.595436	−	0.803403i	$-0.703021\pi$
$37$		−	81389.5i		−	1.60681i	0.595436	−	0.803403i	$-0.296979\pi$
$38$	20856.8	+	32717.9i	0.380099	+	0.596259i
$39$		0			0
$40$			26599.3i			0.415613i
$41$		−	98459.1i		−	1.42858i	−0.699850	−	0.714289i	$-0.746750\pi$
$41$		−	98459.1i		−	1.42858i	0.699850	−	0.714289i	$-0.253250\pi$
$42$		0			0
$43$	−65509.9			−0.823951			−0.411975	−	0.911195i	$-0.635161\pi$
$43$	−65509.9			−0.823951			−0.411975	+	0.911195i	$0.635161\pi$
$44$	54979.0			0.645415
$45$		0			0
$46$		−	98694.3i		−	1.01395i
$47$	17280.8			0.166445			0.0832226	−	0.996531i	$-0.473479\pi$
$47$	17280.8			0.166445			0.0832226	+	0.996531i	$0.473479\pi$
$48$		0			0
$49$	−83931.1			−0.713403
$50$			33753.4i			0.270027i
$51$		0			0
$52$			133203.i			0.947338i
$53$			39630.4i			0.266195i	0.991103	+	0.133098i	$0.0424924\pi$
$53$			39630.4i			0.266195i	−0.991103	+	0.133098i	$0.957508\pi$
$54$		0			0
$55$	252459.			1.51741
$56$			33239.5i			0.189274i
$57$		0			0
$58$	120412.			0.617145
$59$			293899.i			1.43101i	0.698609	+	0.715503i	$0.253803\pi$
$59$			293899.i			1.43101i	−0.698609	+	0.715503i	$0.746197\pi$
$60$		0			0
$61$	−80661.6			−0.355367			−0.177683	−	0.984088i	$-0.556860\pi$
$61$	−80661.6			−0.355367			−0.177683	+	0.984088i	$0.556860\pi$
$62$	−292992.			−1.22937
$63$		0			0
$64$	−32768.0			−0.125000
$65$			611659.i			2.22725i
$66$		0			0
$67$			351602.i			1.16903i	0.811381	+	0.584517i	$0.198716\pi$
$67$			351602.i			1.16903i	−0.811381	+	0.584517i	$0.801284\pi$
$68$	−171026.			−0.543922
$69$		0			0
$70$			152633.i			0.444995i
$71$		−	98918.1i		−	0.276376i	−0.990406	−	0.138188i	$-0.955872\pi$
$71$		−	98918.1i		−	0.276376i	0.990406	−	0.138188i	$-0.0441278\pi$
$72$		0			0
$73$	−325874.			−0.837685			−0.418843	−	0.908059i	$-0.637564\pi$
$73$	−325874.			−0.837685			−0.418843	+	0.908059i	$0.637564\pi$
$74$	460409.			1.13618
$75$		0			0
$76$	−185081.	+	117984.i	−0.421619	+	0.268771i
$77$	315484.			0.691043
$78$		0			0
$79$		−	137910.i		−	0.279714i	−0.990172	−	0.139857i	$-0.955336\pi$
$79$		−	137910.i		−	0.279714i	0.990172	−	0.139857i	$-0.0446643\pi$
$80$	−150468.			−0.293883
$81$		0			0
$82$	556969.			1.01016
$83$	142009.			0.248360			0.124180	−	0.992260i	$-0.460370\pi$
$83$	142009.			0.248360			0.124180	+	0.992260i	$0.460370\pi$
$84$		0			0
$85$	−785340.			−1.27880
$86$		−	370580.i		−	0.582621i
$87$		0			0
$88$			311008.i			0.456377i
$89$		−	379704.i		−	0.538610i	−0.963055	−	0.269305i	$-0.913206\pi$
$89$		−	379704.i		−	0.538610i	0.963055	−	0.269305i	$-0.0867940\pi$
$90$		0			0
$91$			764355.i			1.01431i
$92$	558299.			0.716974
$93$		0			0
$94$			97755.2i			0.117695i
$95$	−849875.	+	541773.i	−0.991253	+	0.631897i
$96$		0			0
$97$			329181.i			0.360678i	0.983604	+	0.180339i	$0.0577195\pi$
$97$			329181.i			0.360678i	−0.983604	+	0.180339i	$0.942280\pi$
$98$		−	474786.i		−	0.504452i
$99$		0			0
$100$	−190938.			−0.190938
$101$	1.17948e6			1.14480			0.572398	−	0.819976i	$-0.306013\pi$
$101$	1.17948e6			1.14480			0.572398	+	0.819976i	$0.306013\pi$
$102$		0			0
$103$			1.38891e6i			1.27105i	0.772081	+	0.635524i	$0.219216\pi$
$103$			1.38891e6i			1.27105i	−0.772081	+	0.635524i	$0.780784\pi$
$104$	−753512.			−0.669869
$105$		0			0
$106$	−224183.			−0.188229
$107$		−	65991.3i		−	0.0538685i	−0.999637	−	0.0269343i	$-0.991426\pi$
$107$		−	65991.3i		−	0.0538685i	0.999637	−	0.0269343i	$-0.00857448\pi$
$108$		0			0
$109$		−	836576.i		−	0.645990i	−0.946401	−	0.322995i	$-0.895310\pi$
$109$		−	836576.i		−	0.645990i	0.946401	−	0.322995i	$-0.104690\pi$
$110$			1.42813e6i			1.07297i
$111$		0			0
$112$	−188031.			−0.133837
$113$		−	7470.62i		−	0.00517752i	−0.999997	−	0.00258876i	$-0.999176\pi$
$113$		−	7470.62i		−	0.00517752i	0.999997	−	0.00258876i	$-0.000824028\pi$
$114$		0			0
$115$	2.56367e6			1.68565
$116$			681155.i			0.436387i
$117$		0			0
$118$	−1.66254e6			−1.01187
$119$	−981394.			−0.582375
$120$		0			0
$121$	1.18029e6			0.666242
$122$		−	456291.i		−	0.251282i
$123$		0			0
$124$		−	1.65741e6i		−	0.869293i
$125$	1.41919e6			0.726625
$126$		0			0
$127$			1.21723e6i			0.594239i	0.954840	+	0.297119i	$0.0960260\pi$
$127$			1.21723e6i			0.594239i	−0.954840	+	0.297119i	$0.903974\pi$
$128$		−	185364.i		−	0.0883883i
$129$		0			0
$130$	−3.46007e6			−1.57491
$131$	−1.72205e6			−0.766007			−0.383003	−	0.923747i	$-0.625110\pi$
$131$	−1.72205e6			−0.766007			−0.383003	+	0.923747i	$0.625110\pi$
$132$		0			0
$133$	−1.06204e6	+	677022.i	−0.451425	+	0.287771i
$134$	−1.98896e6			−0.826632
$135$		0			0
$136$		−	967472.i		−	0.384611i
$137$	−2.87455e6			−1.11791			−0.558957	−	0.829197i	$-0.688798\pi$
$137$	−2.87455e6			−1.11791			−0.558957	+	0.829197i	$0.688798\pi$
$138$		0			0
$139$	−3.94916e6			−1.47048			−0.735241	−	0.677805i	$-0.762931\pi$
$139$	−3.94916e6			−1.47048			−0.735241	+	0.677805i	$0.762931\pi$
$140$	−863425.			−0.314659
$141$		0			0
$142$	559565.			0.195427
$143$			7.15175e6i			2.44571i
$144$		0			0
$145$			3.12781e6i			1.02597i
$146$		−	1.84342e6i		−	0.592333i
$147$		0			0
$148$			2.60447e6i			0.803403i
$149$	−183584.			−0.0554978			−0.0277489	−	0.999615i	$-0.508834\pi$
$149$	−183584.			−0.0554978			−0.0277489	+	0.999615i	$0.508834\pi$
$150$		0			0
$151$			3.51046e6i			1.01961i	0.860291	+	0.509804i	$0.170282\pi$
$151$			3.51046e6i			1.01961i	−0.860291	+	0.509804i	$0.829718\pi$
$152$	−667417.	−	1.04697e6i	−0.190049	−	0.298129i
$153$		0			0
$154$			1.78465e6i			0.488641i
$155$		−	7.61072e6i		−	2.04376i
$156$		0			0
$157$	3.21864e6			0.831714			0.415857	−	0.909430i	$-0.363482\pi$
$157$	3.21864e6			0.831714			0.415857	+	0.909430i	$0.363482\pi$
$158$	780137.			0.197788
$159$		0			0
$160$		−	851176.i		−	0.207807i
$161$	3.20366e6			0.767661
$162$		0			0
$163$	1.57947e6			0.364711			0.182356	−	0.983233i	$-0.441628\pi$
$163$	1.57947e6			0.364711			0.182356	+	0.983233i	$0.441628\pi$
$164$			3.15069e6i			0.714289i
$165$		0			0
$166$			803323.i			0.175617i
$167$		−	961133.i		−	0.206364i	−0.994662	−	0.103182i	$-0.967098\pi$
$167$		−	961133.i		−	0.206364i	0.994662	−	0.103182i	$-0.0329024\pi$
$168$		0			0
$169$	−1.25005e7			−2.58980
$170$		−	4.44256e6i		−	0.904245i
$171$		0			0
$172$	2.09632e6			0.411975
$173$			7.05698e6i			1.36295i	0.731840	+	0.681476i	$0.238662\pi$
$173$			7.05698e6i			1.36295i	−0.731840	+	0.681476i	$0.761338\pi$
$174$		0			0
$175$	−1.09565e6			−0.204436
$176$	−1.75933e6			−0.322707
$177$		0			0
$178$	2.14793e6			0.380855
$179$		−	2.56000e6i		−	0.446356i	−0.974778	−	0.223178i	$-0.928357\pi$
$179$		−	2.56000e6i		−	0.446356i	0.974778	−	0.223178i	$-0.0716431\pi$
$180$		0			0
$181$			1.09680e6i			0.184966i	0.995714	+	0.0924828i	$0.0294803\pi$
$181$			1.09680e6i			0.184966i	−0.995714	+	0.0924828i	$0.970520\pi$
$182$	−4.32385e6			−0.717226
$183$		0			0
$184$			3.15822e6i			0.506977i
$185$			1.19595e7i			1.88885i
$186$		0			0
$187$	−9.18249e6			−1.40422
$188$	−552987.			−0.0832226
$189$		0			0
$190$	−3.06473e6	−	4.80762e6i	−0.446819	−	0.700922i
$191$	526703.			0.0755903			0.0377951	−	0.999286i	$-0.487967\pi$
$191$	526703.			0.0755903			0.0377951	+	0.999286i	$0.487967\pi$
$192$		0			0
$193$		−	1.69440e6i		−	0.235691i	−0.993032	−	0.117846i	$-0.962401\pi$
$193$		−	1.69440e6i		−	0.235691i	0.993032	−	0.117846i	$-0.0375988\pi$
$194$	−1.86213e6			−0.255038
$195$		0			0
$196$	2.68580e6			0.356701
$197$	−2.22350e6			−0.290830			−0.145415	−	0.989371i	$-0.546452\pi$
$197$	−2.22350e6			−0.290830			−0.145415	+	0.989371i	$0.546452\pi$
$198$		0			0
$199$	7.32774e6			0.929846			0.464923	−	0.885351i	$-0.346082\pi$
$199$	7.32774e6			0.929846			0.464923	+	0.885351i	$0.346082\pi$
$200$		−	1.08011e6i		−	0.135014i
$201$		0			0
$202$			6.67217e6i			0.809493i
$203$			3.90864e6i			0.467238i
$204$		0			0
$205$			1.44677e7i			1.67934i
$206$	−7.85685e6			−0.898766
$207$		0			0
$208$		−	4.26251e6i		−	0.473669i
$209$	−9.93706e6	+	6.33461e6i	−1.08848	+	0.693874i
$210$		0			0
$211$		−	1.58228e7i		−	1.68437i	−0.539192	−	0.842183i	$-0.681270\pi$
$211$		−	1.58228e7i		−	1.68437i	0.539192	−	0.842183i	$-0.318730\pi$
$212$		−	1.26817e6i		−	0.133098i
$213$		0			0
$214$	373303.			0.0380908
$215$	9.62612e6			0.968581
$216$		0			0
$217$		−	9.51067e6i		−	0.930748i
$218$	4.73239e6			0.456784
$219$		0			0
$220$	−8.07870e6			−0.758706
$221$		−	2.22474e7i		−	2.06111i
$222$		0			0
$223$			9.02405e6i			0.813743i	0.913485	+	0.406871i	$0.133380\pi$
$223$			9.02405e6i			0.813743i	−0.913485	+	0.406871i	$0.866620\pi$
$224$		−	1.06367e6i		−	0.0946370i
$225$		0			0
$226$	42260.2			0.00366106
$227$		−	1.04551e7i		−	0.893819i	−0.894579	−	0.446909i	$-0.852525\pi$
$227$		−	1.04551e7i		−	0.893819i	0.894579	−	0.446909i	$-0.147475\pi$
$228$		0			0
$229$	2.28936e7			1.90637			0.953185	−	0.302387i	$-0.0977835\pi$
$229$	2.28936e7			1.90637			0.953185	+	0.302387i	$0.0977835\pi$
$230$			1.45023e7i			1.19194i
$231$		0			0
$232$	−3.85320e6			−0.308572
$233$	1.82578e7			1.44338			0.721689	−	0.692218i	$-0.243366\pi$
$233$	1.82578e7			1.44338			0.721689	+	0.692218i	$0.243366\pi$
$234$		0			0
$235$	−2.53927e6			−0.195662
$236$		−	9.40476e6i		−	0.715503i
$237$		0			0
$238$		−	5.55160e6i		−	0.411801i
$239$	7.13532e6			0.522660			0.261330	−	0.965249i	$-0.415839\pi$
$239$	7.13532e6			0.522660			0.261330	+	0.965249i	$0.415839\pi$
$240$		0			0
$241$			2.74824e7i			1.96338i	0.190495	+	0.981688i	$0.438991\pi$
$241$			2.74824e7i			1.96338i	−0.190495	+	0.981688i	$0.561009\pi$
$242$			6.67672e6i			0.471104i
$243$		0			0
$244$	2.58117e6			0.177683
$245$	1.23330e7			0.838628
$246$		0			0
$247$	−1.53475e7	−	2.40755e7i	−1.01847	−	1.59766i
$248$	9.37575e6			0.614683
$249$		0			0
$250$			8.02814e6i			0.513801i
$251$	9.86492e6			0.623839			0.311919	−	0.950109i	$-0.399028\pi$
$251$	9.86492e6			0.623839			0.311919	+	0.950109i	$0.399028\pi$
$252$		0			0
$253$	2.99753e7			1.85098
$254$	−6.88569e6			−0.420190
$255$		0			0
$256$	1.04858e6			0.0625000
$257$			1.06898e7i			0.629751i	0.949133	+	0.314876i	$0.101963\pi$
$257$			1.06898e7i			0.629751i	−0.949133	+	0.314876i	$0.898037\pi$
$258$		0			0
$259$			1.49451e7i			0.860200i
$260$		−	1.95731e7i		−	1.11363i
$261$		0			0
$262$		−	9.74140e6i		−	0.541649i
$263$	−1.67268e6			−0.0919485			−0.0459742	−	0.998943i	$-0.514639\pi$
$263$	−1.67268e6			−0.0919485			−0.0459742	+	0.998943i	$0.514639\pi$
$264$		0			0
$265$		−	5.82335e6i		−	0.312921i
$266$	−3.82981e6	−	6.00780e6i	−0.203485	−	0.319206i
$267$		0			0
$268$		−	1.12513e7i		−	0.584517i
$269$			1.91376e6i			0.0983177i	0.998791	+	0.0491588i	$0.0156541\pi$
$269$			1.91376e6i			0.0983177i	−0.998791	+	0.0491588i	$0.984346\pi$
$270$		0			0
$271$	−8.66253e6			−0.435248			−0.217624	−	0.976033i	$-0.569831\pi$
$271$	−8.66253e6			−0.435248			−0.217624	+	0.976033i	$0.569831\pi$
$272$	5.47285e6			0.271961
$273$		0			0
$274$		−	1.62609e7i		−	0.790484i
$275$	−1.02516e7			−0.492937
$276$		0			0
$277$	3.50325e7			1.64828			0.824142	−	0.566384i	$-0.191658\pi$
$277$	3.50325e7			1.64828			0.824142	+	0.566384i	$0.191658\pi$
$278$		−	2.23398e7i		−	1.03979i
$279$		0			0
$280$		−	4.88427e6i		−	0.222498i
$281$		−	5.99966e6i		−	0.270401i	−0.990818	−	0.135200i	$-0.956832\pi$
$281$		−	5.99966e6i		−	0.270401i	0.990818	−	0.135200i	$-0.0431678\pi$
$282$		0			0
$283$	2.33721e6			0.103119			0.0515594	−	0.998670i	$-0.483581\pi$
$283$	2.33721e6			0.103119			0.0515594	+	0.998670i	$0.483581\pi$
$284$			3.16538e6i			0.138188i
$285$		0			0
$286$	−4.04564e7			−1.72937
$287$			1.80795e7i			0.764786i
$288$		0			0
$289$	4.42695e6			0.183405
$290$	−1.76936e7			−0.725474
$291$		0			0
$292$	1.04280e7			0.418843
$293$			1.96602e7i			0.781603i	0.920475	+	0.390801i	$0.127802\pi$
$293$			1.96602e7i			0.781603i	−0.920475	+	0.390801i	$0.872198\pi$
$294$		0			0
$295$		−	4.31859e7i		−	1.68219i
$296$	−1.47331e7			−0.568092
$297$		0			0
$298$		−	1.03851e6i		−	0.0392429i
$299$			7.26243e7i			2.71687i
$300$		0			0
$301$	1.20292e7			0.441100
$302$	−1.98581e7			−0.720971
$303$		0			0
$304$	5.92258e6	−	3.77548e6i	0.210809	−	0.134385i
$305$	1.18525e7			0.417745
$306$		0			0
$307$		−	1.81733e7i		−	0.628087i	−0.949409	−	0.314043i	$-0.898316\pi$
$307$		−	1.81733e7i		−	0.628087i	0.949409	−	0.314043i	$-0.101684\pi$
$308$	−1.00955e7			−0.345521
$309$		0			0
$310$	4.30527e7			1.44516
$311$	4.39266e7			1.46031			0.730157	−	0.683280i	$-0.239447\pi$
$311$	4.39266e7			1.46031			0.730157	+	0.683280i	$0.239447\pi$
$312$		0			0
$313$	−1.83265e6			−0.0597650			−0.0298825	−	0.999553i	$-0.509513\pi$
$313$	−1.83265e6			−0.0597650			−0.0298825	+	0.999553i	$0.509513\pi$
$314$			1.82074e7i			0.588111i
$315$		0			0
$316$			4.41312e6i			0.139857i
$317$		−	4.42788e6i		−	0.139001i	−0.997582	−	0.0695005i	$-0.977859\pi$
$317$		−	4.42788e6i		−	0.139001i	0.997582	−	0.0695005i	$-0.0221406\pi$
$318$		0			0
$319$			3.65715e7i			1.12660i
$320$	4.81498e6			0.146942
$321$		0			0
$322$			1.81227e7i			0.542818i
$323$	3.09118e7	−	1.97054e7i	0.917311	−	0.584761i
$324$		0			0
$325$		−	2.48375e7i		−	0.723532i
$326$			8.93484e6i			0.257890i
$327$		0			0
$328$	−1.78230e7			−0.505079
$329$	−3.17318e6			−0.0891061
$330$		0			0
$331$			1.52513e7i			0.420556i	0.977642	+	0.210278i	$0.0674369\pi$
$331$			1.52513e7i			0.420556i	−0.977642	+	0.210278i	$0.932563\pi$
$332$	−4.54428e6			−0.124180
$333$		0			0
$334$	5.43699e6			0.145921
$335$		−	5.16650e7i		−	1.37424i
$336$		0			0
$337$		−	4.46345e7i		−	1.16622i	−0.812393	−	0.583111i	$-0.801835\pi$
$337$		−	4.46345e7i		−	1.16622i	0.812393	−	0.583111i	$-0.198165\pi$
$338$		−	7.07133e7i		−	1.83126i
$339$		0			0
$340$	2.51309e7			0.639398
$341$		−	8.89873e7i		−	2.24422i
$342$		0			0
$343$	3.70150e7			0.917266
$344$			1.18586e7i			0.291311i
$345$		0			0
$346$	−3.99203e7			−0.963753
$347$	2.82394e7			0.675876			0.337938	−	0.941168i	$-0.390271\pi$
$347$	2.82394e7			0.675876			0.337938	+	0.941168i	$0.390271\pi$
$348$		0			0
$349$	−1.29030e6			−0.0303539			−0.0151769	−	0.999885i	$-0.504831\pi$
$349$	−1.29030e6			−0.0303539			−0.0151769	+	0.999885i	$0.504831\pi$
$350$		−	6.19794e6i		−	0.144558i
$351$		0			0
$352$		−	9.95227e6i		−	0.228189i
$353$	4.60022e7			1.04581			0.522907	−	0.852390i	$-0.324848\pi$
$353$	4.60022e7			1.04581			0.522907	+	0.852390i	$0.324848\pi$
$354$		0			0
$355$			1.45352e7i			0.324889i
$356$			1.21505e7i			0.269305i
$357$		0			0
$358$	1.44816e7			0.315621
$359$	−4.28733e7			−0.926623			−0.463312	−	0.886195i	$-0.653339\pi$
$359$	−4.28733e7			−0.926623			−0.463312	+	0.886195i	$0.653339\pi$
$360$		0			0
$361$	1.98580e7	−	4.26494e7i	0.422099	−	0.906550i
$362$	−6.20443e6			−0.130790
$363$		0			0
$364$		−	2.44594e7i		−	0.507155i
$365$	4.78844e7			0.984726
$366$		0			0
$367$	−1.41368e7			−0.285991			−0.142995	−	0.989723i	$-0.545673\pi$
$367$	−1.41368e7			−0.285991			−0.142995	+	0.989723i	$0.545673\pi$
$368$	−1.78656e7			−0.358487
$369$		0			0
$370$	−6.76532e7			−1.33562
$371$		−	7.27710e6i		−	0.142507i
$372$		0			0
$373$			3.96596e7i			0.764226i	0.924116	+	0.382113i	$0.124803\pi$
$373$			3.96596e7i			0.764226i	−0.924116	+	0.382113i	$0.875197\pi$
$374$		−	5.19440e7i		−	0.992935i
$375$		0			0
$376$		−	3.12817e6i		−	0.0588473i
$377$	−8.86056e7			−1.65363
$378$		0			0
$379$		−	2.72051e7i		−	0.499727i	−0.968281	−	0.249863i	$-0.919614\pi$
$379$		−	2.72051e7i		−	0.499727i	0.968281	−	0.249863i	$-0.0803857\pi$
$380$	2.71960e7	−	1.73367e7i	0.495626	−	0.315948i
$381$		0			0
$382$			2.97948e6i			0.0534504i
$383$		−	2.60602e7i		−	0.463854i	−0.972733	−	0.231927i	$-0.925497\pi$
$383$		−	2.60602e7i		−	0.463854i	0.972733	−	0.231927i	$-0.0745031\pi$
$384$		0			0
$385$	−4.63577e7			−0.812343
$386$	9.58497e6			0.166659
$387$		0			0
$388$		−	1.05338e7i		−	0.180339i
$389$	−3.80804e7			−0.646923			−0.323461	−	0.946241i	$-0.604847\pi$
$389$	−3.80804e7			−0.646923			−0.323461	+	0.946241i	$0.604847\pi$
$390$		0			0
$391$	−9.32461e7			−1.55991
$392$			1.51932e7i			0.252226i
$393$		0			0
$394$		−	1.25780e7i		−	0.205648i
$395$			2.02647e7i			0.328813i
$396$		0			0
$397$	−3.09038e6			−0.0493901			−0.0246951	−	0.999695i	$-0.507861\pi$
$397$	−3.09038e6			−0.0493901			−0.0246951	+	0.999695i	$0.507861\pi$
$398$			4.14520e7i			0.657500i
$399$		0			0
$400$	6.11002e6			0.0954690
$401$			4.93134e7i			0.764772i	0.924003	+	0.382386i	$0.124898\pi$
$401$			4.93134e7i			0.764772i	−0.924003	+	0.382386i	$0.875102\pi$
$402$		0			0
$403$	2.15599e8			3.29406
$404$	−3.77435e7			−0.572398
$405$		0			0
$406$	−2.21106e7			−0.330387
$407$			1.39835e8i			2.07411i
$408$		0			0
$409$		−	6.10251e7i		−	0.891947i	−0.895046	−	0.445973i	$-0.852858\pi$
$409$		−	6.10251e7i		−	0.891947i	0.895046	−	0.445973i	$-0.147142\pi$
$410$	−8.18418e7			−1.18747
$411$		0			0
$412$		−	4.44450e7i		−	0.635524i
$413$		−	5.39669e7i		−	0.766086i
$414$		0			0
$415$	−2.08670e7			−0.291955
$416$	2.41124e7			0.334935
$417$		0			0
$418$	−3.58339e7	−	5.62125e7i	−0.490643	−	0.769669i
$419$	6.74617e6			0.0917097			0.0458549	−	0.998948i	$-0.485399\pi$
$419$	6.74617e6			0.0917097			0.0458549	+	0.998948i	$0.485399\pi$
$420$		0			0
$421$			5.49198e7i			0.736009i	0.929824	+	0.368004i	$0.119959\pi$
$421$			5.49198e7i			0.736009i	−0.929824	+	0.368004i	$0.880041\pi$
$422$	8.95074e7			1.19103
$423$		0			0
$424$	7.17386e6			0.0941143
$425$	3.18901e7			0.415422
$426$		0			0
$427$	1.48114e7			0.190245
$428$			2.11172e6i			0.0269343i
$429$		0			0
$430$			5.44536e7i			0.684890i
$431$		−	1.14851e8i		−	1.43451i	−0.696812	−	0.717254i	$-0.745399\pi$
$431$		−	1.14851e8i		−	1.43451i	0.696812	−	0.717254i	$-0.254601\pi$
$432$		0			0
$433$			9.64970e6i			0.118864i	0.998232	+	0.0594320i	$0.0189289\pi$
$433$			9.64970e6i			0.118864i	−0.998232	+	0.0594320i	$0.981071\pi$
$434$	5.38005e7			0.658138
$435$		0			0
$436$			2.67704e7i			0.322995i
$437$	−1.00909e8	+	6.43264e7i	−1.20916	+	0.770806i
$438$		0			0
$439$		−	7.17354e7i		−	0.847891i	−0.905688	−	0.423945i	$-0.860645\pi$
$439$		−	7.17354e7i		−	0.847891i	0.905688	−	0.423945i	$-0.139355\pi$
$440$		−	4.57000e7i		−	0.536486i
$441$		0			0
$442$	1.25850e8			1.45743
$443$	−9.91448e7			−1.14040			−0.570202	−	0.821504i	$-0.693135\pi$
$443$	−9.91448e7			−1.14040			−0.570202	+	0.821504i	$0.693135\pi$
$444$		0			0
$445$			5.57942e7i			0.633154i
$446$	−5.10478e7			−0.575403
$447$		0			0
$448$	6.01700e6			0.0669185
$449$			1.47824e8i			1.63307i	0.577296	+	0.816535i	$0.304108\pi$
$449$			1.47824e8i			1.63307i	−0.577296	+	0.816535i	$0.695892\pi$
$450$		0			0
$451$			1.69162e8i			1.84405i
$452$			239060.i			0.00258876i
$453$		0			0
$454$	5.91428e7			0.632025
$455$		−	1.12316e8i		−	1.19235i
$456$		0			0
$457$	−1.25418e8			−1.31405			−0.657023	−	0.753870i	$-0.728185\pi$
$457$	−1.25418e8			−1.31405			−0.657023	+	0.753870i	$0.728185\pi$
$458$			1.29506e8i			1.34801i
$459$		0			0
$460$	−8.20373e7			−0.842826
$461$	5.25946e7			0.536831			0.268416	−	0.963303i	$-0.413500\pi$
$461$	5.25946e7			0.536831			0.268416	+	0.963303i	$0.413500\pi$
$462$		0			0
$463$	4.14145e7			0.417262			0.208631	−	0.977994i	$-0.433099\pi$
$463$	4.14145e7			0.417262			0.208631	+	0.977994i	$0.433099\pi$
$464$		−	2.17970e7i		−	0.218194i
$465$		0			0
$466$			1.03282e8i			1.02062i
$467$	−6.02070e7			−0.591148			−0.295574	−	0.955320i	$-0.595511\pi$
$467$	−6.02070e7			−0.591148			−0.295574	+	0.955320i	$0.595511\pi$
$468$		0			0
$469$		−	6.45627e7i		−	0.625840i
$470$		−	1.43643e7i		−	0.138354i
$471$		0			0
$472$	5.32013e7			0.505937
$473$	1.12552e8			1.06358
$474$		0			0
$475$	3.45107e7	−	2.19996e7i	0.322012	−	0.205274i
$476$	3.14046e7			0.291187
$477$		0			0
$478$			4.03634e7i			0.369577i
$479$	−1.18008e8			−1.07375			−0.536876	−	0.843661i	$-0.680396\pi$
$479$	−1.18008e8			−1.07375			−0.536876	+	0.843661i	$0.680396\pi$
$480$		0			0
$481$	−3.38792e8			−3.04438
$482$	−1.55464e8			−1.38832
$483$		0			0
$484$	−3.77692e7			−0.333121
$485$		−	4.83704e7i		−	0.423989i
$486$		0			0
$487$			8.37555e7i			0.725148i	0.931955	+	0.362574i	$0.118102\pi$
$487$			8.37555e7i			0.725148i	−0.931955	+	0.362574i	$0.881898\pi$
$488$			1.46013e7i			0.125641i
$489$		0			0
$490$			6.97658e7i			0.593000i
$491$	9.11236e7			0.769815			0.384908	−	0.922955i	$-0.374233\pi$
$491$	9.11236e7			0.769815			0.384908	+	0.922955i	$0.374233\pi$
$492$		0			0
$493$		−	1.13765e8i		−	0.949443i
$494$	1.36192e8	−	8.68186e7i	1.12972	−	0.720165i
$495$		0			0
$496$			5.30373e7i			0.434646i
$497$			1.81638e7i			0.147957i
$498$		0			0
$499$	−7.45201e7			−0.599752			−0.299876	−	0.953978i	$-0.596945\pi$
$499$	−7.45201e7			−0.599752			−0.299876	+	0.953978i	$0.596945\pi$
$500$	−4.54140e7			−0.363312
$501$		0			0
$502$			5.58044e7i			0.441121i
$503$	2.21380e8			1.73954			0.869769	−	0.493460i	$-0.164268\pi$
$503$	2.21380e8			1.73954			0.869769	+	0.493460i	$0.164268\pi$
$504$		0			0
$505$	−1.73315e8			−1.34574
$506$			1.69566e8i			1.30884i
$507$		0			0
$508$		−	3.89513e7i		−	0.297119i
$509$		−	1.44062e8i		−	1.09244i	−0.837642	−	0.546220i	$-0.816066\pi$
$509$		−	1.44062e8i		−	1.09244i	0.837642	−	0.546220i	$-0.183934\pi$
$510$		0			0
$511$	5.98383e7			0.448453
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	−6.04705e7			−0.445301
$515$		−	2.04088e8i		−	1.49416i
$516$		0			0
$517$	−2.96901e7			−0.214852
$518$	−8.45422e7			−0.608253
$519$		0			0
$520$	1.10722e8			0.787453
$521$			1.83396e8i			1.29681i	0.761296	+	0.648405i	$0.224564\pi$
$521$			1.83396e8i			1.29681i	−0.761296	+	0.648405i	$0.775436\pi$
$522$		0			0
$523$			2.60056e8i			1.81786i	0.416946	+	0.908931i	$0.363100\pi$
$523$			2.60056e8i			1.81786i	−0.416946	+	0.908931i	$0.636900\pi$
$524$	5.51057e7			0.383003
$525$		0			0
$526$		−	9.46208e6i		−	0.0650174i
$527$			2.76818e8i			1.89131i
$528$		0			0
$529$	1.56357e8			1.05621
$530$	3.29418e7			0.221269
$531$		0			0
$532$	3.39853e7	−	2.16647e7i	0.225713	−	0.143886i
$533$	−4.09846e8			−2.70669
$534$		0			0
$535$			9.69686e6i			0.0633242i
$536$	6.36468e7			0.413316
$537$		0			0
$538$	−1.08259e7			−0.0695211
$539$	1.44202e8			0.920882
$540$		0			0
$541$	2.68741e8			1.69723			0.848617	−	0.529008i	$-0.177436\pi$
$541$	2.68741e8			1.69723			0.848617	+	0.529008i	$0.177436\pi$
$542$		−	4.90027e7i		−	0.307767i
$543$		0			0
$544$			3.09591e7i			0.192305i
$545$			1.22928e8i			0.759382i
$546$		0			0
$547$		−	1.38572e8i		−	0.846671i	−0.905973	−	0.423335i	$-0.860859\pi$
$547$		−	1.38572e8i		−	0.846671i	0.905973	−	0.423335i	$-0.139141\pi$
$548$	9.19856e7			0.558957
$549$		0			0
$550$		−	5.79915e7i		−	0.348559i
$551$	−7.84817e7	−	1.23114e8i	−0.469152	−	0.735956i
$552$		0			0
$553$			2.53236e7i			0.149744i
$554$			1.98174e8i			1.16551i
$555$		0			0
$556$	1.26373e8			0.735241
$557$	1.94423e8			1.12508			0.562538	−	0.826771i	$-0.309825\pi$
$557$	1.94423e8			1.12508			0.562538	+	0.826771i	$0.309825\pi$
$558$		0			0
$559$			2.72692e8i			1.56112i
$560$	2.76296e7			0.157330
$561$		0			0
$562$	3.39392e7			0.191202
$563$			3.21069e8i			1.79917i	0.436744	+	0.899586i	$0.356132\pi$
$563$			3.21069e8i			1.79917i	−0.436744	+	0.899586i	$0.643868\pi$
$564$		0			0
$565$			1.09774e6i			0.00608634i
$566$			1.32212e7i			0.0729160i
$567$		0			0
$568$	−1.79061e7			−0.0977137
$569$		−	1.83897e8i		−	0.998248i	−0.866531	−	0.499124i	$-0.833655\pi$
$569$		−	1.83897e8i		−	0.998248i	0.866531	−	0.499124i	$-0.166345\pi$
$570$		0			0
$571$	9.74111e6			0.0523239			0.0261619	−	0.999658i	$-0.491671\pi$
$571$	9.74111e6			0.0523239			0.0261619	+	0.999658i	$0.491671\pi$
$572$		−	2.28856e8i		−	1.22285i
$573$		0			0
$574$	−1.02273e8			−0.540786
$575$	−1.04102e8			−0.547591
$576$		0			0
$577$	−1.67489e8			−0.871886			−0.435943	−	0.899974i	$-0.643585\pi$
$577$	−1.67489e8			−0.871886			−0.435943	+	0.899974i	$0.643585\pi$
$578$			2.50426e7i			0.129687i
$579$		0			0
$580$		−	1.00090e8i		−	0.512987i
$581$	−2.60763e7			−0.132959
$582$		0			0
$583$		−	6.80887e7i		−	0.343613i
$584$			5.89895e7i			0.296167i
$585$		0			0
$586$	−1.11215e8			−0.552677
$587$	1.87247e8			0.925763			0.462882	−	0.886420i	$-0.346815\pi$
$587$	1.87247e8			0.925763			0.462882	+	0.886420i	$0.346815\pi$
$588$		0			0
$589$	1.90965e8	+	2.99566e8i	0.934561	+	1.46604i
$590$	2.44296e8			1.18949
$591$		0			0
$592$		−	8.33429e7i		−	0.401702i
$593$	−1.56747e8			−0.751683			−0.375842	−	0.926684i	$-0.622646\pi$
$593$	−1.56747e8			−0.751683			−0.375842	+	0.926684i	$0.622646\pi$
$594$		0			0
$595$	1.44208e8			0.684600
$596$	5.87469e6			0.0277489
$597$		0			0
$598$	−4.10825e8			−1.92112
$599$			1.42517e8i			0.663112i	0.943435	+	0.331556i	$0.107574\pi$
$599$			1.42517e8i			0.663112i	−0.943435	+	0.331556i	$0.892426\pi$
$600$		0			0
$601$			1.48027e8i			0.681894i	0.940083	+	0.340947i	$0.110748\pi$
$601$			1.48027e8i			0.681894i	−0.940083	+	0.340947i	$0.889252\pi$
$602$			6.80474e7i			0.311905i
$603$		0			0
$604$		−	1.12335e8i		−	0.509804i
$605$	−1.73433e8			−0.783189
$606$		0			0
$607$		−	7.58253e7i		−	0.339038i	−0.985527	−	0.169519i	$-0.945779\pi$
$607$		−	7.58253e7i		−	0.339038i	0.985527	−	0.169519i	$-0.0542214\pi$
$608$	2.13574e7	+	3.35032e7i	0.0950247	+	0.149065i
$609$		0			0
$610$			6.70480e7i			0.295391i
$611$		−	7.19333e7i		−	0.315360i
$612$		0			0
$613$	−2.23802e8			−0.971589			−0.485794	−	0.874073i	$-0.661470\pi$
$613$	−2.23802e8			−0.971589			−0.485794	+	0.874073i	$0.661470\pi$
$614$	1.02804e8			0.444124
$615$		0			0
$616$		−	5.71087e7i		−	0.244321i
$617$	−1.50027e8			−0.638726			−0.319363	−	0.947633i	$-0.603469\pi$
$617$	−1.50027e8			−0.638726			−0.319363	+	0.947633i	$0.603469\pi$
$618$		0			0
$619$	3.37666e7			0.142369			0.0711844	−	0.997463i	$-0.477322\pi$
$619$	3.37666e7			0.142369			0.0711844	+	0.997463i	$0.477322\pi$
$620$			2.43543e8i			1.02188i
$621$		0			0
$622$			2.48486e8i			1.03260i
$623$			6.97228e7i			0.288344i
$624$		0			0
$625$	−3.01769e8			−1.23605
$626$		−	1.03670e7i		−	0.0422602i
$627$		0			0
$628$	−1.02997e8			−0.415857
$629$		−	4.34993e8i		−	1.74795i
$630$		0			0
$631$	−8.02120e7			−0.319265			−0.159633	−	0.987177i	$-0.551031\pi$
$631$	−8.02120e7			−0.319265			−0.159633	+	0.987177i	$0.551031\pi$
$632$	−2.49644e7			−0.0988939
$633$		0			0
$634$	2.50479e7			0.0982886
$635$		−	1.78861e8i		−	0.698547i
$636$		0			0
$637$			3.49372e8i			1.35167i
$638$	−2.06880e8			−0.796629
$639$		0			0
$640$			2.72376e7i			0.103903i
$641$		−	2.30796e8i		−	0.876303i	−0.898901	−	0.438151i	$-0.855633\pi$
$641$		−	2.30796e8i		−	0.876303i	0.898901	−	0.438151i	$-0.144367\pi$
$642$		0			0
$643$	−4.17210e8			−1.56936			−0.784678	−	0.619903i	$-0.787172\pi$
$643$	−4.17210e8			−1.56936			−0.784678	+	0.619903i	$0.787172\pi$
$644$	−1.02517e8			−0.383830
$645$		0			0
$646$	1.11471e8	+	1.74863e8i	0.413488	+	0.648637i
$647$	−2.74624e8			−1.01397			−0.506986	−	0.861954i	$-0.669240\pi$
$647$	−2.74624e8			−1.01397			−0.506986	+	0.861954i	$0.669240\pi$
$648$		0			0
$649$		−	5.04946e8i		−	1.84719i
$650$	1.40502e8			0.511614
$651$		0			0
$652$	−5.05431e7			−0.182356
$653$	−3.30922e8			−1.18847			−0.594233	−	0.804293i	$-0.702544\pi$
$653$	−3.30922e8			−1.18847			−0.594233	+	0.804293i	$0.702544\pi$
$654$		0			0
$655$	2.53041e8			0.900466
$656$		−	1.00822e8i		−	0.357145i
$657$		0			0
$658$		−	1.79502e7i		−	0.0630075i
$659$			4.03864e8i			1.41117i	0.708625	+	0.705585i	$0.249316\pi$
$659$			4.03864e8i			1.41117i	−0.708625	+	0.705585i	$0.750684\pi$
$660$		0			0
$661$		−	2.70497e8i		−	0.936608i	−0.883568	−	0.468304i	$-0.844865\pi$
$661$		−	2.70497e8i		−	0.936608i	0.883568	−	0.468304i	$-0.155135\pi$
$662$	−8.62745e7			−0.297378
$663$		0			0
$664$		−	2.57063e7i		−	0.0878083i
$665$	1.56058e8	−	9.94826e7i	0.530665	−	0.338285i
$666$		0			0
$667$			3.71375e8i			1.25151i
$668$			3.07563e7i			0.103182i
$669$		0			0
$670$	2.92261e8			0.971732
$671$	1.38584e8			0.458718
$672$		0			0
$673$			7.07317e6i			0.0232043i	0.999933	+	0.0116022i	$0.00369317\pi$
$673$			7.07317e6i			0.0232043i	−0.999933	+	0.0116022i	$0.996307\pi$
$674$	2.52491e8			0.824643
$675$		0			0
$676$	4.00015e8			1.29490
$677$			3.47099e8i			1.11863i	0.828955	+	0.559316i	$0.188936\pi$
$677$			3.47099e8i			1.11863i	−0.828955	+	0.559316i	$0.811064\pi$
$678$		0			0
$679$		−	6.04457e7i		−	0.193088i
$680$			1.42162e8i			0.452123i
$681$		0			0
$682$	5.03388e8			1.58690
$683$			4.98305e7i			0.156399i	0.996938	+	0.0781994i	$0.0249171\pi$
$683$			4.98305e7i			0.156399i	−0.996938	+	0.0781994i	$0.975083\pi$
$684$		0			0
$685$	4.22391e8			1.31414
$686$			2.09388e8i			0.648605i
$687$		0			0
$688$	−6.70821e7			−0.205988
$689$	1.64966e8			0.504354
$690$		0			0
$691$	−1.58794e8			−0.481282			−0.240641	−	0.970614i	$-0.577358\pi$
$691$	−1.58794e8			−0.481282			−0.240641	+	0.970614i	$0.577358\pi$
$692$		−	2.25823e8i		−	0.681476i
$693$		0			0
$694$			1.59746e8i			0.477916i
$695$	5.80295e8			1.72860
$696$		0			0
$697$		−	5.26222e8i		−	1.55407i
$698$		−	7.29904e6i		−	0.0214634i
$699$		0			0
$700$	3.50609e7			0.102218
$701$	−5.55496e8			−1.61260			−0.806301	−	0.591506i	$-0.798534\pi$
$701$	−5.55496e8			−1.61260			−0.806301	+	0.591506i	$0.798534\pi$
$702$		0			0
$703$	−3.00083e8	−	4.70738e8i	−0.863724	−	1.35492i
$704$	5.62985e7			0.161354
$705$		0			0
$706$			2.60228e8i			0.739502i
$707$	−2.16582e8			−0.612864
$708$		0			0
$709$	1.67180e7			0.0469080			0.0234540	−	0.999725i	$-0.492534\pi$
$709$	1.67180e7			0.0469080			0.0234540	+	0.999725i	$0.492534\pi$
$710$	−8.22234e7			−0.229731
$711$		0			0
$712$	−6.87337e7			−0.190428
$713$		−	9.03646e8i		−	2.49304i
$714$		0			0
$715$		−	1.05089e9i		−	2.87501i
$716$			8.19201e7i			0.223178i
$717$		0			0
$718$		−	2.42528e8i		−	0.655222i
$719$	−3.04546e8			−0.819344			−0.409672	−	0.912233i	$-0.634357\pi$
$719$	−3.04546e8			−0.819344			−0.409672	+	0.912233i	$0.634357\pi$
$720$		0			0
$721$		−	2.55037e8i		−	0.680452i
$722$	2.41262e8	+	1.12334e8i	0.641027	+	0.298469i
$723$		0			0
$724$		−	3.50975e7i		−	0.0924828i
$725$		−	1.27010e8i		−	0.333292i
$726$		0			0
$727$	−6.18054e7			−0.160851			−0.0804254	−	0.996761i	$-0.525628\pi$
$727$	−6.18054e7			−0.160851			−0.0804254	+	0.996761i	$0.525628\pi$
$728$	1.38363e8			0.358613
$729$		0			0
$730$			2.70875e8i			0.696307i
$731$	−3.50123e8			−0.896330
$732$		0			0
$733$	8.30071e7			0.210767			0.105384	−	0.994432i	$-0.466393\pi$
$733$	8.30071e7			0.210767			0.105384	+	0.994432i	$0.466393\pi$
$734$		−	7.99696e7i		−	0.202226i
$735$		0			0
$736$		−	1.01063e8i		−	0.253489i
$737$		−	6.04086e8i		−	1.50902i
$738$		0			0
$739$	−2.09997e8			−0.520332			−0.260166	−	0.965564i	$-0.583777\pi$
$739$	−2.09997e8			−0.520332			−0.260166	+	0.965564i	$0.583777\pi$
$740$		−	3.82704e8i		−	0.944426i
$741$		0			0
$742$	4.11655e7			0.100768
$743$			5.36457e8i			1.30788i	0.756545	+	0.653941i	$0.226886\pi$
$743$			5.36457e8i			1.30788i	−0.756545	+	0.653941i	$0.773114\pi$
$744$		0			0
$745$	2.69761e7			0.0652395
$746$	−2.24348e8			−0.540389
$747$		0			0
$748$	2.93840e8			0.702111
$749$			1.21176e7i			0.0288384i
$750$		0			0
$751$		−	6.93030e7i		−	0.163618i	−0.996648	−	0.0818092i	$-0.973930\pi$
$751$		−	6.93030e7i		−	0.163618i	0.996648	−	0.0818092i	$-0.0260698\pi$
$752$	1.76956e7			0.0416113
$753$		0			0
$754$		−	5.01229e8i		−	1.16929i
$755$		−	5.15832e8i		−	1.19858i
$756$		0			0
$757$	−1.18269e8			−0.272636			−0.136318	−	0.990665i	$-0.543527\pi$
$757$	−1.18269e8			−0.272636			−0.136318	+	0.990665i	$0.543527\pi$
$758$	1.53895e8			0.353360
$759$		0			0
$760$	9.80713e7	+	1.53844e8i	0.223409	+	0.350461i
$761$	1.69867e8			0.385438			0.192719	−	0.981254i	$-0.438269\pi$
$761$	1.69867e8			0.385438			0.192719	+	0.981254i	$0.438269\pi$
$762$		0			0
$763$			1.53616e8i			0.345829i
$764$	−1.68545e7			−0.0377951
$765$		0			0
$766$	1.47419e8			0.327994
$767$	1.22338e9			2.71129
$768$		0			0
$769$	7.59248e8			1.66957			0.834785	−	0.550577i	$-0.185592\pi$
$769$	7.59248e8			1.66957			0.834785	+	0.550577i	$0.185592\pi$
$770$		−	2.62239e8i		−	0.574413i
$771$		0			0
$772$			5.42208e7i			0.117846i
$773$			1.05343e8i			0.228070i	0.993477	+	0.114035i	$0.0363776\pi$
$773$			1.05343e8i			0.228070i	−0.993477	+	0.114035i	$0.963622\pi$
$774$		0			0
$775$			3.09046e8i			0.663924i
$776$	5.95882e7			0.127519
$777$		0			0
$778$		−	2.15415e8i		−	0.457443i
$779$	−3.63018e8	−	5.69464e8i	−0.767920	−	1.20463i
$780$		0			0
$781$			1.69951e8i			0.356755i
$782$		−	5.27479e8i		−	1.10302i
$783$		0			0
$784$	−8.59455e7			−0.178351
$785$	−4.72952e8			−0.977706
$786$		0			0
$787$			7.32535e7i			0.150281i	0.997173	+	0.0751405i	$0.0239405\pi$
$787$			7.32535e7i			0.150281i	−0.997173	+	0.0751405i	$0.976059\pi$
$788$	7.11521e7			0.145415
$789$		0			0
$790$	−1.14634e8			−0.232506
$791$			1.37179e6i			0.00277177i
$792$		0			0
$793$			3.35762e8i			0.673305i
$794$		−	1.74818e7i		−	0.0349241i
$795$		0			0
$796$	−2.34488e8			−0.464923
$797$			5.46491e8i			1.07946i	0.841837	+	0.539732i	$0.181474\pi$
$797$			5.46491e8i			1.07946i	−0.841837	+	0.539732i	$0.818526\pi$
$798$		0			0
$799$	9.23588e7			0.181066
$800$			3.45635e7i			0.0675068i
$801$		0			0
$802$	−2.78959e8			−0.540775
$803$	5.59882e8			1.08131
$804$		0			0
$805$	−4.70751e8			−0.902410
$806$			1.21961e9i			2.32925i
$807$		0			0
$808$		−	2.13509e8i		−	0.404746i
$809$	−4.63575e8			−0.875536			−0.437768	−	0.899088i	$-0.644231\pi$
$809$	−4.63575e8			−0.875536			−0.437768	+	0.899088i	$0.644231\pi$
$810$		0			0
$811$		−	3.91098e8i		−	0.733201i	−0.930378	−	0.366601i	$-0.880522\pi$
$811$		−	3.91098e8i		−	0.733201i	0.930378	−	0.366601i	$-0.119478\pi$
$812$		−	1.25077e8i		−	0.233619i
$813$		0			0
$814$	−7.91026e8			−1.46662
$815$	−2.32090e8			−0.428730
$816$		0			0
$817$	−3.78894e8	+	2.41535e8i	−0.694786	+	0.442908i
$818$	3.45210e8			0.630702
$819$		0			0
$820$		−	4.62967e8i		−	0.839670i
$821$	−9.37749e8			−1.69456			−0.847281	−	0.531145i	$-0.821762\pi$
$821$	−9.37749e8			−1.69456			−0.847281	+	0.531145i	$0.821762\pi$
$822$		0			0
$823$	8.49232e8			1.52345			0.761723	−	0.647903i	$-0.224354\pi$
$823$	8.49232e8			1.52345			0.761723	+	0.647903i	$0.224354\pi$
$824$	2.51419e8			0.449383
$825$		0			0
$826$	3.05283e8			0.541705
$827$		−	5.72787e8i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$827$		−	5.72787e8i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$828$		0			0
$829$			4.15850e8i			0.729916i	0.931024	+	0.364958i	$0.118917\pi$
$829$			4.15850e8i			0.729916i	−0.931024	+	0.364958i	$0.881083\pi$
$830$		−	1.18041e8i		−	0.206443i
$831$		0			0
$832$			1.36400e8i			0.236835i
$833$	−4.48576e8			−0.776071
$834$		0			0
$835$			1.41230e8i			0.242588i
$836$	3.17986e8	−	2.02707e8i	0.544238	−	0.346937i
$837$		0			0
$838$			3.81621e7i			0.0648486i
$839$		−	2.72831e8i		−	0.461963i	−0.972958	−	0.230982i	$-0.925806\pi$
$839$		−	2.72831e8i		−	0.461963i	0.972958	−	0.230982i	$-0.0741937\pi$
$840$		0			0
$841$	1.41725e8			0.238264
$842$	−3.10674e8			−0.520437
$843$		0			0
$844$			5.06330e8i			0.842183i
$845$	1.83684e9			3.04439
$846$		0			0
$847$	−2.16730e8			−0.356671
$848$			4.05815e7i			0.0665488i
$849$		0			0
$850$			1.80398e8i			0.293747i
$851$			1.41999e9i			2.30408i
$852$		0			0
$853$	2.48260e8			0.400000			0.200000	−	0.979796i	$-0.435906\pi$
$853$	2.48260e8			0.400000			0.200000	+	0.979796i	$0.435906\pi$
$854$			8.37860e7i			0.134523i
$855$		0			0
$856$	−1.19457e7			−0.0190454
$857$			3.79494e8i			0.602923i	0.953478	+	0.301462i	$0.0974745\pi$
$857$			3.79494e8i			0.602923i	−0.953478	+	0.301462i	$0.902525\pi$
$858$		0			0
$859$	−2.67792e8			−0.422491			−0.211245	−	0.977433i	$-0.567752\pi$
$859$	−2.67792e8			−0.422491			−0.211245	+	0.977433i	$0.567752\pi$
$860$	−3.08036e8			−0.484290
$861$		0			0
$862$	6.49695e8			1.01435
$863$			3.57938e7i			0.0556898i	0.999612	+	0.0278449i	$0.00886446\pi$
$863$			3.57938e7i			0.0556898i	−0.999612	+	0.0278449i	$0.991136\pi$
$864$		0			0
$865$		−	1.03696e9i		−	1.60219i
$866$	−5.45869e7			−0.0840495
$867$		0			0
$868$			3.04341e8i			0.465374i
$869$			2.36942e8i			0.361063i
$870$		0			0
$871$	1.46358e9			2.21494
$872$	−1.51436e8			−0.228392
$873$		0			0
$874$	−3.63885e8	−	5.70825e8i	−0.545042	−	0.855005i
$875$	−2.60597e8			−0.388997
$876$		0			0
$877$		−	2.97741e8i		−	0.441407i	−0.975341	−	0.220704i	$-0.929165\pi$
$877$		−	2.97741e8i		−	0.441407i	0.975341	−	0.220704i	$-0.0708353\pi$
$878$	4.05797e8			0.599549
$879$		0			0
$880$	2.58518e8			0.379353
$881$	1.09276e8			0.159807			0.0799036	−	0.996803i	$-0.474539\pi$
$881$	1.09276e8			0.159807			0.0799036	+	0.996803i	$0.474539\pi$
$882$		0			0
$883$	7.36749e8			1.07013			0.535066	−	0.844810i	$-0.320287\pi$
$883$	7.36749e8			1.07013			0.535066	+	0.844810i	$0.320287\pi$
$884$			7.11916e8i			1.03056i
$885$		0			0
$886$		−	5.60848e8i		−	0.806388i
$887$		−	1.02599e9i		−	1.47019i	−0.677966	−	0.735094i	$-0.737138\pi$
$887$		−	1.02599e9i		−	1.47019i	0.677966	−	0.735094i	$-0.262862\pi$
$888$		0			0
$889$		−	2.23513e8i		−	0.318124i
$890$	−3.15620e8			−0.447707
$891$		0			0
$892$		−	2.88770e8i		−	0.406871i
$893$	9.99484e7	−	6.37144e7i	0.140353	−	0.0894711i
$894$		0			0
$895$			3.76171e8i			0.524706i
$896$			3.40373e7i			0.0473185i
$897$		0			0
$898$	−8.36216e8			−1.15475
$899$	1.10250e9			1.51739
$900$		0			0
$901$			2.11808e8i			0.289579i
$902$	−9.56925e8			−1.30394
$903$		0			0
$904$	−1.35233e6			−0.00183053
$905$		−	1.61165e8i		−	0.217433i
$906$		0			0
$907$		−	1.29958e9i		−	1.74174i	−0.491516	−	0.870869i	$-0.663557\pi$
$907$		−	1.29958e9i		−	1.74174i	0.491516	−	0.870869i	$-0.336443\pi$
$908$			3.34562e8i			0.446909i
$909$		0			0
$910$	6.35352e8			0.843122
$911$			7.29839e8i			0.965322i	0.875807	+	0.482661i	$0.160330\pi$
$911$			7.29839e8i			0.965322i	−0.875807	+	0.482661i	$0.839670\pi$
$912$		0			0
$913$	−2.43984e8			−0.320590
$914$		−	7.09470e8i		−	0.929171i
$915$		0			0
$916$	−7.32595e8			−0.953185
$917$	3.16211e8			0.410080
$918$		0			0
$919$	1.07725e9			1.38794			0.693968	−	0.720006i	$-0.255861\pi$
$919$	1.07725e9			1.38794			0.693968	+	0.720006i	$0.255861\pi$
$920$		−	4.64073e8i		−	0.595968i
$921$		0			0
$922$			2.97520e8i			0.379597i
$923$	−4.11757e8			−0.523643
$924$		0			0
$925$		−	4.85636e8i		−	0.613601i
$926$			2.34276e8i			0.295049i
$927$		0			0
$928$	1.23302e8			0.154286
$929$	8.99955e7			0.112247			0.0561234	−	0.998424i	$-0.482126\pi$
$929$	8.99955e7			0.112247			0.0561234	+	0.998424i	$0.482126\pi$
$930$		0			0
$931$	−4.85438e8	+	3.09454e8i	−0.601568	+	0.383483i
$932$	−5.84249e8			−0.721689
$933$		0			0
$934$		−	3.40582e8i		−	0.418005i
$935$	1.34929e9			1.65071
$936$		0			0
$937$	−1.92583e8			−0.234099			−0.117050	−	0.993126i	$-0.537344\pi$
$937$	−1.92583e8			−0.234099			−0.117050	+	0.993126i	$0.537344\pi$
$938$	3.65222e8			0.442536
$939$		0			0
$940$	8.12567e7			0.0978309
$941$			9.44507e8i			1.13354i	0.823877	+	0.566769i	$0.191807\pi$
$941$			9.44507e8i			1.13354i	−0.823877	+	0.566769i	$0.808193\pi$
$942$		0			0
$943$			1.71780e9i			2.04851i
$944$			3.00952e8i			0.357752i
$945$		0			0
$946$			6.36691e8i			0.752065i
$947$	5.88012e7			0.0692367			0.0346184	−	0.999401i	$-0.488978\pi$
$947$	5.88012e7			0.0692367			0.0346184	+	0.999401i	$0.488978\pi$
$948$		0			0
$949$			1.35648e9i			1.58714i
$950$	1.24449e8	+	1.95222e8i	0.145151	+	0.227697i
$951$		0			0
$952$			1.77651e8i			0.205901i
$953$			6.20225e8i			0.716589i	0.933609	+	0.358295i	$0.116642\pi$
$953$			6.20225e8i			0.716589i	−0.933609	+	0.358295i	$0.883358\pi$
$954$		0			0
$955$	−7.73946e7			−0.0888588
$956$	−2.28330e8			−0.261330
$957$		0			0
$958$		−	6.67552e8i		−	0.759257i
$959$	5.27837e8			0.598473
$960$		0			0
$961$	−1.79513e9			−2.02268
$962$		−	1.91650e9i		−	2.15270i
$963$		0			0
$964$		−	8.79437e8i		−	0.981688i
$965$			2.48978e8i			0.277063i
$966$		0			0
$967$	−7.24092e8			−0.800782			−0.400391	−	0.916344i	$-0.631126\pi$
$967$	−7.24092e8			−0.800782			−0.400391	+	0.916344i	$0.631126\pi$
$968$		−	2.13655e8i		−	0.235552i
$969$		0			0
$970$	2.73624e8			0.299806
$971$			3.05228e8i			0.333401i	0.986008	+	0.166701i	$0.0533114\pi$
$971$			3.05228e8i			0.333401i	−0.986008	+	0.166701i	$0.946689\pi$
$972$		0			0
$973$	7.25161e8			0.787220
$974$	−4.73793e8			−0.512757
$975$		0			0
$976$	−8.25974e7			−0.0888417
$977$		−	7.55141e8i		−	0.809738i	−0.914375	−	0.404869i	$-0.867317\pi$
$977$		−	7.55141e8i		−	0.809738i	0.914375	−	0.404869i	$-0.132683\pi$
$978$		0			0
$979$			6.52367e8i			0.695254i
$980$	−3.94655e8			−0.419314
$981$		0			0
$982$			5.15473e8i			0.544342i
$983$			9.20545e8i			0.969135i	0.874754	+	0.484568i	$0.161023\pi$
$983$			9.20545e8i			0.969135i	−0.874754	+	0.484568i	$0.838977\pi$
$984$		0			0
$985$	3.26725e8			0.341880
$986$	6.43553e8			0.671357
$987$		0			0
$988$	4.91120e8	+	7.70417e8i	0.509233	+	0.798831i
$989$	1.14294e9			1.18150
$990$		0			0
$991$		−	1.60808e9i		−	1.65229i	−0.563457	−	0.826146i	$-0.690529\pi$
$991$		−	1.60808e9i		−	1.65229i	0.563457	−	0.826146i	$-0.309471\pi$
$992$	−3.00024e8			−0.307341
$993$		0			0
$994$	−1.02750e8			−0.104622
$995$	−1.07675e9			−1.09306
$996$		0			0
$997$	−8.94189e8			−0.902286			−0.451143	−	0.892452i	$-0.648984\pi$
$997$	−8.94189e8			−0.902286			−0.451143	+	0.892452i	$0.648984\pi$
$998$		−	4.21549e8i		−	0.424089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.7.d.a.37.6		10
3.2	odd	2		38.7.b.a.37.3	✓	10
12.11	even	2		304.7.e.e.113.5		10
19.18	odd	2	inner	342.7.d.a.37.1		10
57.56	even	2		38.7.b.a.37.8	yes	10
228.227	odd	2		304.7.e.e.113.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.b.a.37.3	✓	10	3.2	odd	2
38.7.b.a.37.8	yes	10	57.56	even	2
304.7.e.e.113.5		10	12.11	even	2
304.7.e.e.113.6		10	228.227	odd	2
342.7.d.a.37.1		10	19.18	odd	2	inner
342.7.d.a.37.6		10	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	342.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -32.0000 q^{4} -146.942 q^{5} -183.624 q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+5.65685i q^{2} -32.0000 q^{4} -146.942 q^{5} -183.624 q^{7} -181.019i q^{8} -831.227i q^{10} -1718.09 q^{11} -4162.60i q^{13} -1038.74i q^{14} +1024.00 q^{16} +5344.58 q^{17} +(5783.77 - 3686.99i) q^{19} +4702.13 q^{20} -9719.01i q^{22} -17446.9 q^{23} +5966.81 q^{25} +23547.2 q^{26} +5875.98 q^{28} -21286.1i q^{29} +51794.2i q^{31} +5792.62i q^{32} +30233.5i q^{34} +26982.0 q^{35} -81389.5i q^{37} +(20856.8 + 32717.9i) q^{38} +26599.3i q^{40} -98459.1i q^{41} -65509.9 q^{43} +54979.0 q^{44} -98694.3i q^{46} +17280.8 q^{47} -83931.1 q^{49} +33753.4i q^{50} +133203. i q^{52} +39630.4i q^{53} +252459. q^{55} +33239.5i q^{56} +120412. q^{58} +293899. i q^{59} -80661.6 q^{61} -292992. q^{62} -32768.0 q^{64} +611659. i q^{65} +351602. i q^{67} -171026. q^{68} +152633. i q^{70} -98918.1i q^{71} -325874. q^{73} +460409. q^{74} +(-185081. + 117984. i) q^{76} +315484. q^{77} -137910. i q^{79} -150468. q^{80} +556969. q^{82} +142009. q^{83} -785340. q^{85} -370580. i q^{86} +311008. i q^{88} -379704. i q^{89} +764355. i q^{91} +558299. q^{92} +97755.2i q^{94} +(-849875. + 541773. i) q^{95} +329181. i q^{97} -474786. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7}+O(q^{10}) \) 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7	\( 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7} - 3644 q^{11} + 10240 q^{16} + 10420 q^{17} - 17230 q^{19} - 3584 q^{20} - 37712 q^{23} - 52078 q^{25} + 7104 q^{26} + 7168 q^{28} + 161720 q^{35} - 25152 q^{38} + 6308 q^{43} + 116608 q^{44} - 322220 q^{47} - 235770 q^{49} - 377880 q^{55} + 445920 q^{58} + 426304 q^{61} - 59424 q^{62} - 327680 q^{64} - 333440 q^{68} - 786076 q^{73} + 293280 q^{74} + 551360 q^{76} - 2303716 q^{77} + 114688 q^{80} - 455136 q^{82} + 101500 q^{83} - 1261380 q^{85} + 1206784 q^{92} - 3106292 q^{95}+O(q^{100}) \) 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7 - 3644 * q^11 + 10240 * q^16 + 10420 * q^17 - 17230 * q^19 - 3584 * q^20 - 37712 * q^23 - 52078 * q^25 + 7104 * q^26 + 7168 * q^28 + 161720 * q^35 - 25152 * q^38 + 6308 * q^43 + 116608 * q^44 - 322220 * q^47 - 235770 * q^49 - 377880 * q^55 + 445920 * q^58 + 426304 * q^61 - 59424 * q^62 - 327680 * q^64 - 333440 * q^68 - 786076 * q^73 + 293280 * q^74 + 551360 * q^76 - 2303716 * q^77 + 114688 * q^80 - 455136 * q^82 + 101500 * q^83 - 1261380 * q^85 + 1206784 * q^92 - 3106292 * q^95

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