LMFDB - Embedded newform 240.8.h.b.191.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,8,Mod(191,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("240.191");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	240.h (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:	$74.9724061162$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.19
Character	$\chi$	$=$	240.191
Dual form			240.8.h.b.191.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.89558 - 46.0940i) q^{3} -125.000i q^{5} -1350.65i q^{7} +(-2062.32 - 727.879i) q^{9} -5196.14 q^{11} +5879.53 q^{13} +(-5761.75 - 986.948i) q^{15} -34471.9i q^{17} +4137.04i q^{19} +(-62256.9 - 10664.2i) q^{21} -70821.0 q^{23} -15625.0 q^{25} +(-49834.1 + 89313.6i) q^{27} +36075.8i q^{29} -48178.2i q^{31} +(-41026.5 + 239511. i) q^{33} -168831. q^{35} +337011. q^{37} +(46422.3 - 271011. i) q^{39} -728822. i q^{41} +495437. i q^{43} +(-90984.8 + 257790. i) q^{45} +558564. q^{47} -1.00071e6 q^{49} +(-1.58895e6 - 272176. i) q^{51} -337164. i q^{53} +649517. i q^{55} +(190693. + 32664.4i) q^{57} -1.71716e6 q^{59} +2.22966e6 q^{61} +(-983109. + 2.78547e6i) q^{63} -734941. i q^{65} -1.37032e6i q^{67} +(-559173. + 3.26442e6i) q^{69} -1.34294e6 q^{71} -34540.7 q^{73} +(-123369. + 720219. i) q^{75} +7.01816e6i q^{77} -6.07870e6i q^{79} +(3.72335e6 + 3.00224e6i) q^{81} +7.21089e6 q^{83} -4.30899e6 q^{85} +(1.66288e6 + 284839. i) q^{87} +5.78395e6i q^{89} -7.94119e6i q^{91} +(-2.22073e6 - 380395. i) q^{93} +517131. q^{95} +4.38168e6 q^{97} +(1.07161e7 + 3.78216e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3324 q^{9} - 432 q^{13} - 22032 q^{21} - 562500 q^{25} - 386232 q^{33} + 1200048 q^{37} - 1710000 q^{45} - 3237972 q^{49} - 9331200 q^{57} + 11262360 q^{61} - 11352552 q^{69} + 37210296 q^{73} - 12564252 q^{81}+ \cdots + 94537320 q^{97}+O(q^{100}) $ 36 * q + 3324 * q^9 - 432 * q^13 - 22032 * q^21 - 562500 * q^25 - 386232 * q^33 + 1200048 * q^37 - 1710000 * q^45 - 3237972 * q^49 - 9331200 * q^57 + 11262360 * q^61 - 11352552 * q^69 + 37210296 * q^73 - 12564252 * q^81 + 5271000 * q^85 + 5594400 * q^93 + 94537320 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	7.89558	−	46.0940i	0.168834	−	0.985645i
$3$	7.89558	−	46.0940i	0.168834	−	0.985645i
$4$		0			0
$5$		−	125.000i		−	0.447214i
$5$		−	125.000i		−	0.447214i
$6$		0			0
$7$		−	1350.65i		−	1.48833i	−0.667995	−	0.744166i	$-0.732847\pi$
$7$		−	1350.65i		−	1.48833i	0.667995	−	0.744166i	$-0.267153\pi$
$8$		0			0
$9$	−2062.32	−	727.879i	−0.942990	−	0.332821i
$10$		0			0
$11$	−5196.14			−1.17708			−0.588540	−	0.808468i	$-0.700297\pi$
$11$	−5196.14			−1.17708			−0.588540	+	0.808468i	$0.700297\pi$
$12$		0			0
$13$	5879.53			0.742234			0.371117	−	0.928586i	$-0.378975\pi$
$13$	5879.53			0.742234			0.371117	+	0.928586i	$0.378975\pi$
$14$		0			0
$15$	−5761.75	−	986.948i	−0.440794	−	0.0755049i
$16$		0			0
$17$		−	34471.9i		−	1.70174i	−0.525374	−	0.850871i	$-0.676075\pi$
$17$		−	34471.9i		−	1.70174i	0.525374	−	0.850871i	$-0.323925\pi$
$18$		0			0
$19$			4137.04i			0.138373i	0.997604	+	0.0691867i	$0.0220404\pi$
$19$			4137.04i			0.138373i	−0.997604	+	0.0691867i	$0.977960\pi$
$20$		0			0
$21$	−62256.9	−	10664.2i	−1.46697	−	0.251281i
$22$		0			0
$23$	−70821.0			−1.21371			−0.606854	−	0.794813i	$-0.707569\pi$
$23$	−70821.0			−1.21371			−0.606854	+	0.794813i	$0.707569\pi$
$24$		0			0
$25$	−15625.0			−0.200000
$26$		0			0
$27$	−49834.1	+	89313.6i	−0.487252	+	0.873262i
$28$		0			0
$29$			36075.8i			0.274677i	0.990524	+	0.137339i	$0.0438549\pi$
$29$			36075.8i			0.274677i	−0.990524	+	0.137339i	$0.956145\pi$
$30$		0			0
$31$		−	48178.2i		−	0.290459i	−0.989398	−	0.145229i	$-0.953608\pi$
$31$		−	48178.2i		−	0.290459i	0.989398	−	0.145229i	$-0.0463920\pi$
$32$		0			0
$33$	−41026.5	+	239511.i	−0.198731	+	1.16018i
$34$		0			0
$35$	−168831.			−0.665602
$36$		0			0
$37$	337011.			1.09380			0.546901	−	0.837198i	$-0.315808\pi$
$37$	337011.			1.09380			0.546901	+	0.837198i	$0.315808\pi$
$38$		0			0
$39$	46422.3	−	271011.i	0.125314	−	0.731579i
$40$		0			0
$41$		−	728822.i		−	1.65150i	−0.564037	−	0.825749i	$-0.690753\pi$
$41$		−	728822.i		−	1.65150i	0.564037	−	0.825749i	$-0.309247\pi$
$42$		0			0
$43$			495437.i			0.950274i	0.879912	+	0.475137i	$0.157602\pi$
$43$			495437.i			0.950274i	−0.879912	+	0.475137i	$0.842398\pi$
$44$		0			0
$45$	−90984.8	+	257790.i	−0.148842	+	0.421718i
$46$		0			0
$47$	558564.			0.784749			0.392374	−	0.919806i	$-0.371654\pi$
$47$	558564.			0.784749			0.392374	+	0.919806i	$0.371654\pi$
$48$		0			0
$49$	−1.00071e6			−1.21513
$50$		0			0
$51$	−1.58895e6	−	272176.i	−1.67731	−	0.287312i
$52$		0			0
$53$		−	337164.i		−	0.311082i	−0.987829	−	0.155541i	$-0.950288\pi$
$53$		−	337164.i		−	0.311082i	0.987829	−	0.155541i	$-0.0497122\pi$
$54$		0			0
$55$			649517.i			0.526406i
$56$		0			0
$57$	190693.	+	32664.4i	0.136387	+	0.0233621i
$58$		0			0
$59$	−1.71716e6			−1.08850			−0.544251	−	0.838923i	$-0.683186\pi$
$59$	−1.71716e6			−1.08850			−0.544251	+	0.838923i	$0.683186\pi$
$60$		0			0
$61$	2.22966e6			1.25772			0.628861	−	0.777518i	$-0.283521\pi$
$61$	2.22966e6			1.25772			0.628861	+	0.777518i	$0.283521\pi$
$62$		0			0
$63$	−983109.	+	2.78547e6i	−0.495347	+	1.40348i
$64$		0			0
$65$		−	734941.i		−	0.331937i
$66$		0			0
$67$		−	1.37032e6i		−	0.556622i	−0.960491	−	0.278311i	$-0.910225\pi$
$67$		−	1.37032e6i		−	0.556622i	0.960491	−	0.278311i	$-0.0897746\pi$
$68$		0			0
$69$	−559173.	+	3.26442e6i	−0.204915	+	1.19629i
$70$		0			0
$71$	−1.34294e6			−0.445301			−0.222650	−	0.974898i	$-0.571471\pi$
$71$	−1.34294e6			−0.445301			−0.222650	+	0.974898i	$0.571471\pi$
$72$		0			0
$73$	−34540.7			−0.0103921			−0.00519603	−	0.999987i	$-0.501654\pi$
$73$	−34540.7			−0.0103921			−0.00519603	+	0.999987i	$0.501654\pi$
$74$		0			0
$75$	−123369.	+	720219.i	−0.0337668	+	0.197129i
$76$		0			0
$77$			7.01816e6i			1.75189i
$78$		0			0
$79$		−	6.07870e6i		−	1.38713i	−0.720396	−	0.693563i	$-0.756040\pi$
$79$		−	6.07870e6i		−	1.38713i	0.720396	−	0.693563i	$-0.243960\pi$
$80$		0			0
$81$	3.72335e6	+	3.00224e6i	0.778461	+	0.627693i
$82$		0			0
$83$	7.21089e6			1.38425			0.692127	−	0.721776i	$-0.256674\pi$
$83$	7.21089e6			1.38425			0.692127	+	0.721776i	$0.256674\pi$
$84$		0			0
$85$	−4.30899e6			−0.761042
$86$		0			0
$87$	1.66288e6	+	284839.i	0.270734	+	0.0463749i
$88$		0			0
$89$			5.78395e6i			0.869679i	0.900508	+	0.434840i	$0.143195\pi$
$89$			5.78395e6i			0.869679i	−0.900508	+	0.434840i	$0.856805\pi$
$90$		0			0
$91$		−	7.94119e6i		−	1.10469i
$92$		0			0
$93$	−2.22073e6	−	380395.i	−0.286289	−	0.0490393i
$94$		0			0
$95$	517131.			0.0618825
$96$		0			0
$97$	4.38168e6			0.487461			0.243730	−	0.969843i	$-0.421629\pi$
$97$	4.38168e6			0.487461			0.243730	+	0.969843i	$0.421629\pi$
$98$		0			0
$99$	1.07161e7	+	3.78216e6i	1.10998	+	0.391757i
$100$		0			0
$101$			1.52429e7i			1.47212i	0.676917	+	0.736059i	$0.263316\pi$
$101$			1.52429e7i			1.47212i	−0.676917	+	0.736059i	$0.736684\pi$
$102$		0			0
$103$			1.94855e7i			1.75704i	0.477705	+	0.878520i	$0.341469\pi$
$103$			1.94855e7i			1.75704i	−0.477705	+	0.878520i	$0.658531\pi$
$104$		0			0
$105$	−1.33302e6	+	7.78211e6i	−0.112376	+	0.656047i
$106$		0			0
$107$	−1.68239e7			−1.32765			−0.663824	−	0.747889i	$-0.731068\pi$
$107$	−1.68239e7			−1.32765			−0.663824	+	0.747889i	$0.731068\pi$
$108$		0			0
$109$	1.18569e7			0.876955			0.438477	−	0.898742i	$-0.355518\pi$
$109$	1.18569e7			0.876955			0.438477	+	0.898742i	$0.355518\pi$
$110$		0			0
$111$	2.66090e6	−	1.55342e7i	0.184671	−	1.07810i
$112$		0			0
$113$			2.72608e7i			1.77731i	0.458573	+	0.888657i	$0.348361\pi$
$113$			2.72608e7i			1.77731i	−0.458573	+	0.888657i	$0.651639\pi$
$114$		0			0
$115$			8.85262e6i			0.542787i
$116$		0			0
$117$	−1.21255e7	−	4.27958e6i	−0.699919	−	0.247031i
$118$		0			0
$119$	−4.65595e7			−2.53276
$120$		0			0
$121$	7.51265e6			0.385518
$122$		0			0
$123$	−3.35944e7	−	5.75448e6i	−1.62779	−	0.278829i
$124$		0			0
$125$			1.95312e6i			0.0894427i
$126$		0			0
$127$			8.24161e6i			0.357025i	0.983938	+	0.178513i	$0.0571286\pi$
$127$			8.24161e6i			0.357025i	−0.983938	+	0.178513i	$0.942871\pi$
$128$		0			0
$129$	2.28367e7	+	3.91177e6i	0.936633	+	0.160439i
$130$		0			0
$131$	−8.10126e6			−0.314850			−0.157425	−	0.987531i	$-0.550319\pi$
$131$	−8.10126e6			−0.314850			−0.157425	+	0.987531i	$0.550319\pi$
$132$		0			0
$133$	5.58770e6			0.205946
$134$		0			0
$135$	1.11642e7	+	6.22926e6i	0.390534	+	0.217906i
$136$		0			0
$137$			3.17682e7i			1.05553i	0.849391	+	0.527764i	$0.176970\pi$
$137$			3.17682e7i			1.05553i	−0.849391	+	0.527764i	$0.823030\pi$
$138$		0			0
$139$		−	1.91926e7i		−	0.606154i	−0.952966	−	0.303077i	$-0.901986\pi$
$139$		−	1.91926e7i		−	0.606154i	0.952966	−	0.303077i	$-0.0980139\pi$
$140$		0			0
$141$	4.41019e6	−	2.57465e7i	0.132492	−	0.773483i
$142$		0			0
$143$	−3.05508e7			−0.873669
$144$		0			0
$145$	4.50947e6			0.122839
$146$		0			0
$147$	−7.90121e6	+	4.61269e7i	−0.205155	+	1.19769i
$148$		0			0
$149$		−	1.09057e7i		−	0.270086i	−0.990840	−	0.135043i	$-0.956883\pi$
$149$		−	1.09057e7i		−	0.270086i	0.990840	−	0.135043i	$-0.0431173\pi$
$150$		0			0
$151$			5.82575e7i			1.37700i	0.725239	+	0.688498i	$0.241729\pi$
$151$			5.82575e7i			1.37700i	−0.725239	+	0.688498i	$0.758271\pi$
$152$		0			0
$153$	−2.50914e7	+	7.10920e7i	−0.566375	+	1.60473i
$154$		0			0
$155$	−6.02227e6			−0.129897
$156$		0			0
$157$	−4.61596e7			−0.951948			−0.475974	−	0.879459i	$-0.657904\pi$
$157$	−4.61596e7			−0.951948			−0.475974	+	0.879459i	$0.657904\pi$
$158$		0			0
$159$	−1.55412e7	−	2.66211e6i	−0.306617	−	0.0525213i
$160$		0			0
$161$			9.56544e7i			1.80640i
$162$		0			0
$163$		−	1.01728e8i		−	1.83985i	−0.392095	−	0.919925i	$-0.628250\pi$
$163$		−	1.01728e8i		−	1.83985i	0.392095	−	0.919925i	$-0.371750\pi$
$164$		0			0
$165$	2.99389e7	+	5.12832e6i	0.518849	+	0.0888753i
$166$		0			0
$167$	1.04307e7			0.173303			0.0866516	−	0.996239i	$-0.472383\pi$
$167$	1.04307e7			0.173303			0.0866516	+	0.996239i	$0.472383\pi$
$168$		0			0
$169$	−2.81796e7			−0.449089
$170$		0			0
$171$	3.01127e6	−	8.53191e6i	0.0460535	−	0.130485i
$172$		0			0
$173$		−	1.21364e8i		−	1.78208i	−0.453924	−	0.891040i	$-0.649976\pi$
$173$		−	1.21364e8i		−	1.78208i	0.453924	−	0.891040i	$-0.350024\pi$
$174$		0			0
$175$			2.11039e7i			0.297666i
$176$		0			0
$177$	−1.35580e7	+	7.91509e7i	−0.183776	+	1.07288i
$178$		0			0
$179$	3.02122e7			0.393728			0.196864	−	0.980431i	$-0.436924\pi$
$179$	3.02122e7			0.393728			0.196864	+	0.980431i	$0.436924\pi$
$180$		0			0
$181$	−3.75415e7			−0.470584			−0.235292	−	0.971925i	$-0.575605\pi$
$181$	−3.75415e7			−0.470584			−0.235292	+	0.971925i	$0.575605\pi$
$182$		0			0
$183$	1.76045e7	−	1.02774e8i	0.212346	−	1.23967i
$184$		0			0
$185$		−	4.21264e7i		−	0.489163i
$186$		0			0
$187$			1.79121e8i			2.00309i
$188$		0			0
$189$	1.20631e8	+	6.73084e7i	1.29970	+	0.725192i
$190$		0			0
$191$	−1.55793e8			−1.61782			−0.808910	−	0.587932i	$-0.799942\pi$
$191$	−1.55793e8			−1.61782			−0.808910	+	0.587932i	$0.799942\pi$
$192$		0			0
$193$	1.72336e8			1.72554			0.862772	−	0.505593i	$-0.168726\pi$
$193$	1.72336e8			1.72554			0.862772	+	0.505593i	$0.168726\pi$
$194$		0			0
$195$	−3.38764e7	−	5.80279e6i	−0.327172	−	0.0560423i
$196$		0			0
$197$		−	2.40835e6i		−	0.0224434i	−0.999937	−	0.0112217i	$-0.996428\pi$
$197$		−	2.40835e6i		−	0.0224434i	0.999937	−	0.0112217i	$-0.00357205\pi$
$198$		0			0
$199$		−	1.98476e8i		−	1.78535i	−0.450703	−	0.892674i	$-0.648827\pi$
$199$		−	1.98476e8i		−	1.78535i	0.450703	−	0.892674i	$-0.351173\pi$
$200$		0			0
$201$	−6.31636e7	−	1.08195e7i	−0.548631	−	0.0939767i
$202$		0			0
$203$	4.87258e7			0.408811
$204$		0			0
$205$	−9.11028e7			−0.738573
$206$		0			0
$207$	1.46055e8	+	5.15491e7i	1.14452	+	0.403947i
$208$		0			0
$209$		−	2.14966e7i		−	0.162877i
$210$		0			0
$211$			1.08223e8i			0.793106i	0.918012	+	0.396553i	$0.129794\pi$
$211$			1.08223e8i			0.793106i	−0.918012	+	0.396553i	$0.870206\pi$
$212$		0			0
$213$	−1.06033e7	+	6.19017e7i	−0.0751819	+	0.438908i
$214$		0			0
$215$	6.19296e7			0.424976
$216$		0			0
$217$	−6.50719e7			−0.432299
$218$		0			0
$219$	−272719.	+	1.59212e6i	−0.00175453	+	0.0102429i
$220$		0			0
$221$		−	2.02678e8i		−	1.26309i
$222$		0			0
$223$		−	2.35504e7i		−	0.142210i	−0.997469	−	0.0711052i	$-0.977347\pi$
$223$		−	2.35504e7i		−	0.142210i	0.997469	−	0.0711052i	$-0.0226526\pi$
$224$		0			0
$225$	3.22237e7	+	1.13731e7i	0.188598	+	0.0665641i
$226$		0			0
$227$	2.10202e8			1.19274			0.596371	−	0.802709i	$-0.296609\pi$
$227$	2.10202e8			1.19274			0.596371	+	0.802709i	$0.296609\pi$
$228$		0			0
$229$	−8.01798e7			−0.441206			−0.220603	−	0.975364i	$-0.570802\pi$
$229$	−8.01798e7			−0.441206			−0.220603	+	0.975364i	$0.570802\pi$
$230$		0			0
$231$	3.23495e8	+	5.54125e7i	1.72674	+	0.295778i
$232$		0			0
$233$		−	1.64931e8i		−	0.854196i	−0.904205	−	0.427098i	$-0.859536\pi$
$233$		−	1.64931e8i		−	0.854196i	0.904205	−	0.427098i	$-0.140464\pi$
$234$		0			0
$235$		−	6.98205e7i		−	0.350950i
$236$		0			0
$237$	−2.80192e8	−	4.79949e7i	−1.36721	−	0.234194i
$238$		0			0
$239$	−1.73746e7			−0.0823231			−0.0411616	−	0.999153i	$-0.513106\pi$
$239$	−1.73746e7			−0.0823231			−0.0411616	+	0.999153i	$0.513106\pi$
$240$		0			0
$241$	2.97495e8			1.36905			0.684527	−	0.728987i	$-0.260009\pi$
$241$	2.97495e8			1.36905			0.684527	+	0.728987i	$0.260009\pi$
$242$		0			0
$243$	1.67783e8	−	1.47920e8i	0.750113	−	0.661310i
$244$		0			0
$245$			1.25089e8i			0.543423i
$246$		0			0
$247$			2.43239e7i			0.102705i
$248$		0			0
$249$	5.69342e7	−	3.32379e8i	0.233709	−	1.36438i
$250$		0			0
$251$	1.10527e8			0.441174			0.220587	−	0.975367i	$-0.429203\pi$
$251$	1.10527e8			0.441174			0.220587	+	0.975367i	$0.429203\pi$
$252$		0			0
$253$	3.67995e8			1.42863
$254$		0			0
$255$	−3.40220e7	+	1.98619e8i	−0.128490	+	0.750117i
$256$		0			0
$257$		−	1.20153e8i		−	0.441539i	−0.975326	−	0.220769i	$-0.929143\pi$
$257$		−	1.20153e8i		−	0.441539i	0.975326	−	0.220769i	$-0.0708568\pi$
$258$		0			0
$259$		−	4.55184e8i		−	1.62794i
$260$		0			0
$261$	2.62588e7	−	7.43998e7i	0.0914183	−	0.259018i
$262$		0			0
$263$	−4.59590e8			−1.55785			−0.778924	−	0.627118i	$-0.784234\pi$
$263$	−4.59590e8			−1.55785			−0.778924	+	0.627118i	$0.784234\pi$
$264$		0			0
$265$	−4.21455e7			−0.139120
$266$		0			0
$267$	2.66605e8	+	4.56676e7i	0.857195	+	0.146831i
$268$		0			0
$269$		−	1.06178e8i		−	0.332584i	−0.986077	−	0.166292i	$-0.946821\pi$
$269$		−	1.06178e8i		−	0.332584i	0.986077	−	0.166292i	$-0.0531794\pi$
$270$		0			0
$271$		−	8.03828e7i		−	0.245341i	−0.992447	−	0.122671i	$-0.960854\pi$
$271$		−	8.03828e7i		−	0.245341i	0.992447	−	0.122671i	$-0.0391459\pi$
$272$		0			0
$273$	−3.66041e8	−	6.27003e7i	−1.08883	−	0.186509i
$274$		0			0
$275$	8.11896e7			0.235416
$276$		0			0
$277$	−6.34111e8			−1.79261			−0.896305	−	0.443438i	$-0.853759\pi$
$277$	−6.34111e8			−1.79261			−0.896305	+	0.443438i	$0.853759\pi$
$278$		0			0
$279$	−3.50679e7	+	9.93588e7i	−0.0966707	+	0.273900i
$280$		0			0
$281$		−	6.15999e8i		−	1.65618i	−0.560594	−	0.828091i	$-0.689427\pi$
$281$		−	6.15999e8i		−	1.65618i	0.560594	−	0.828091i	$-0.310573\pi$
$282$		0			0
$283$			5.51808e8i			1.44722i	0.690207	+	0.723612i	$0.257519\pi$
$283$			5.51808e8i			1.44722i	−0.690207	+	0.723612i	$0.742481\pi$
$284$		0			0
$285$	4.08305e6	−	2.38366e7i	0.0104479	−	0.0609941i
$286$		0			0
$287$	−9.84384e8			−2.45798
$288$		0			0
$289$	−7.77972e8			−1.89593
$290$		0			0
$291$	3.45959e7	−	2.01969e8i	0.0823000	−	0.480463i
$292$		0			0
$293$		−	4.71303e8i		−	1.09462i	−0.836930	−	0.547310i	$-0.815652\pi$
$293$		−	4.71303e8i		−	1.09462i	0.836930	−	0.547310i	$-0.184348\pi$
$294$		0			0
$295$			2.14645e8i			0.486793i
$296$		0			0
$297$	2.58945e8	−	4.64085e8i	0.573534	−	1.02790i
$298$		0			0
$299$	−4.16394e8			−0.900856
$300$		0			0
$301$	6.69162e8			1.41432
$302$		0			0
$303$	7.02607e8	+	1.20352e8i	1.45099	+	0.248544i
$304$		0			0
$305$		−	2.78708e8i		−	0.562470i
$306$		0			0
$307$			7.04863e7i			0.139034i	0.997581	+	0.0695169i	$0.0221458\pi$
$307$			7.04863e7i			0.139034i	−0.997581	+	0.0695169i	$0.977854\pi$
$308$		0			0
$309$	8.98166e8	+	1.53850e8i	1.73182	+	0.296648i
$310$		0			0
$311$	2.13561e7			0.0402588			0.0201294	−	0.999797i	$-0.493592\pi$
$311$	2.13561e7			0.0402588			0.0201294	+	0.999797i	$0.493592\pi$
$312$		0			0
$313$	−7.44792e8			−1.37287			−0.686435	−	0.727191i	$-0.740825\pi$
$313$	−7.44792e8			−1.37287			−0.686435	+	0.727191i	$0.740825\pi$
$314$		0			0
$315$	3.48184e8	+	1.22889e8i	0.627656	+	0.221526i
$316$		0			0
$317$		−	5.46558e8i		−	0.963670i	−0.876262	−	0.481835i	$-0.839970\pi$
$317$		−	5.46558e8i		−	0.963670i	0.876262	−	0.481835i	$-0.160030\pi$
$318$		0			0
$319$		−	1.87455e8i		−	0.323317i
$320$		0			0
$321$	−1.32834e8	+	7.75480e8i	−0.224152	+	1.30859i
$322$		0			0
$323$	1.42612e8			0.235476
$324$		0			0
$325$	−9.18677e7			−0.148447
$326$		0			0
$327$	9.36169e7	−	5.46531e8i	0.148060	−	0.864365i
$328$		0			0
$329$		−	7.54425e8i		−	1.16797i
$330$		0			0
$331$		−	8.38601e8i		−	1.27103i	−0.772087	−	0.635517i	$-0.780787\pi$
$331$		−	8.38601e8i		−	1.27103i	0.772087	−	0.635517i	$-0.219213\pi$
$332$		0			0
$333$	−6.95025e8	−	2.45303e8i	−1.03144	−	0.364040i
$334$		0			0
$335$	−1.71290e8			−0.248929
$336$		0			0
$337$	8.75298e8			1.24581			0.622904	−	0.782298i	$-0.285953\pi$
$337$	8.75298e8			1.24581			0.622904	+	0.782298i	$0.285953\pi$
$338$		0			0
$339$	1.25656e9	+	2.15240e8i	1.75180	+	0.300071i
$340$		0			0
$341$			2.50340e8i			0.341893i
$342$		0			0
$343$			2.39294e8i			0.320187i
$344$		0			0
$345$	4.08053e8	+	6.98966e7i	0.534995	+	0.0916409i
$346$		0			0
$347$	1.03353e9			1.32792			0.663960	−	0.747768i	$-0.268875\pi$
$347$	1.03353e9			1.32792			0.663960	+	0.747768i	$0.268875\pi$
$348$		0			0
$349$	2.55964e7			0.0322322			0.0161161	−	0.999870i	$-0.494870\pi$
$349$	2.55964e7			0.0322322			0.0161161	+	0.999870i	$0.494870\pi$
$350$		0			0
$351$	−2.93001e8	+	5.25122e8i	−0.361655	+	0.648164i
$352$		0			0
$353$			9.32132e8i			1.12789i	0.825813	+	0.563944i	$0.190717\pi$
$353$			9.32132e8i			1.12789i	−0.825813	+	0.563944i	$0.809283\pi$
$354$		0			0
$355$			1.67868e8i			0.199145i
$356$		0			0
$357$	−3.67614e8	+	2.14611e9i	−0.427616	+	2.49640i
$358$		0			0
$359$	−1.83930e8			−0.209808			−0.104904	−	0.994482i	$-0.533453\pi$
$359$	−1.83930e8			−0.209808			−0.104904	+	0.994482i	$0.533453\pi$
$360$		0			0
$361$	8.76757e8			0.980853
$362$		0			0
$363$	5.93168e7	−	3.46288e8i	0.0650885	−	0.379983i
$364$		0			0
$365$			4.31759e6i			0.00464747i
$366$		0			0
$367$		−	8.07499e8i		−	0.852729i	−0.904552	−	0.426364i	$-0.859794\pi$
$367$		−	8.07499e8i		−	0.852729i	0.904552	−	0.426364i	$-0.140206\pi$
$368$		0			0
$369$	−5.30494e8	+	1.50306e9i	−0.549653	+	1.55735i
$370$		0			0
$371$	−4.55391e8			−0.462994
$372$		0			0
$373$	7.97292e8			0.795494			0.397747	−	0.917495i	$-0.369792\pi$
$373$	7.97292e8			0.795494			0.397747	+	0.917495i	$0.369792\pi$
$374$		0			0
$375$	9.00274e7	+	1.54211e7i	0.0881587	+	0.0151010i
$376$		0			0
$377$			2.12109e8i			0.203875i
$378$		0			0
$379$			8.62959e8i			0.814241i	0.913374	+	0.407120i	$0.133467\pi$
$379$			8.62959e8i			0.814241i	−0.913374	+	0.407120i	$0.866533\pi$
$380$		0			0
$381$	3.79889e8	+	6.50723e7i	0.351900	+	0.0602780i
$382$		0			0
$383$	−7.09139e8			−0.644964			−0.322482	−	0.946576i	$-0.604517\pi$
$383$	−7.09139e8			−0.644964			−0.322482	+	0.946576i	$0.604517\pi$
$384$		0			0
$385$	8.77270e8			0.783467
$386$		0			0
$387$	3.60618e8	−	1.02175e9i	0.316271	−	0.896099i
$388$		0			0
$389$		−	3.74248e8i		−	0.322356i	−0.986925	−	0.161178i	$-0.948471\pi$
$389$		−	3.74248e8i		−	0.322356i	0.986925	−	0.161178i	$-0.0515293\pi$
$390$		0			0
$391$			2.44133e9i			2.06542i
$392$		0			0
$393$	−6.39642e7	+	3.73420e8i	−0.0531573	+	0.310330i
$394$		0			0
$395$	−7.59838e8			−0.620342
$396$		0			0
$397$	−2.26270e9			−1.81493			−0.907466	−	0.420124i	$-0.861986\pi$
$397$	−2.26270e9			−1.81493			−0.907466	+	0.420124i	$0.861986\pi$
$398$		0			0
$399$	4.41182e7	−	2.57560e8i	0.0347706	−	0.202989i
$400$		0			0
$401$		−	2.16218e9i		−	1.67451i	−0.546816	−	0.837253i	$-0.684160\pi$
$401$		−	2.16218e9i		−	1.67451i	0.546816	−	0.837253i	$-0.315840\pi$
$402$		0			0
$403$		−	2.83265e8i		−	0.215588i
$404$		0			0
$405$	3.75280e8	−	4.65419e8i	0.280713	−	0.348138i
$406$		0			0
$407$	−1.75116e9			−1.28749
$408$		0			0
$409$	−1.29551e9			−0.936286			−0.468143	−	0.883653i	$-0.655077\pi$
$409$	−1.29551e9			−0.936286			−0.468143	+	0.883653i	$0.655077\pi$
$410$		0			0
$411$	1.46432e9	+	2.50828e8i	1.04038	+	0.178209i
$412$		0			0
$413$			2.31928e9i			1.62005i
$414$		0			0
$415$		−	9.01361e8i		−	0.619057i
$416$		0			0
$417$	−8.84666e8	−	1.51537e8i	−0.597452	−	0.102339i
$418$		0			0
$419$	−1.39379e9			−0.925652			−0.462826	−	0.886449i	$-0.653165\pi$
$419$	−1.39379e9			−0.925652			−0.462826	+	0.886449i	$0.653165\pi$
$420$		0			0
$421$	9.40084e8			0.614016			0.307008	−	0.951707i	$-0.400672\pi$
$421$	9.40084e8			0.614016			0.307008	+	0.951707i	$0.400672\pi$
$422$		0			0
$423$	−1.15194e9	−	4.06567e8i	−0.740010	−	0.261181i
$424$		0			0
$425$			5.38623e8i			0.340348i
$426$		0			0
$427$		−	3.01149e9i		−	1.87191i
$428$		0			0
$429$	−2.41217e8	+	1.40821e9i	−0.147505	+	0.861127i
$430$		0			0
$431$	−1.96356e9			−1.18134			−0.590668	−	0.806915i	$-0.701136\pi$
$431$	−1.96356e9			−1.18134			−0.590668	+	0.806915i	$0.701136\pi$
$432$		0			0
$433$	−7.55538e8			−0.447248			−0.223624	−	0.974675i	$-0.571789\pi$
$433$	−7.55538e8			−0.447248			−0.223624	+	0.974675i	$0.571789\pi$
$434$		0			0
$435$	3.56049e7	−	2.07860e8i	0.0207395	−	0.121076i
$436$		0			0
$437$		−	2.92990e8i		−	0.167945i
$438$		0			0
$439$			1.05923e9i			0.597537i	0.954326	+	0.298769i	$0.0965759\pi$
$439$			1.05923e9i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$440$		0			0
$441$	2.06379e9	+	7.28397e8i	1.14586	+	0.404421i
$442$		0			0
$443$	−7.83328e8			−0.428085			−0.214043	−	0.976824i	$-0.568663\pi$
$443$	−7.83328e8			−0.428085			−0.214043	+	0.976824i	$0.568663\pi$
$444$		0			0
$445$	7.22993e8			0.388932
$446$		0			0
$447$	−5.02688e8	−	8.61070e7i	−0.266209	−	0.0455997i
$448$		0			0
$449$			2.73310e9i			1.42493i	0.701708	+	0.712465i	$0.252421\pi$
$449$			2.73310e9i			1.42493i	−0.701708	+	0.712465i	$0.747579\pi$
$450$		0			0
$451$			3.78706e9i			1.94395i
$452$		0			0
$453$	2.68532e9	+	4.59977e8i	1.35723	+	0.232484i
$454$		0			0
$455$	−9.92648e8			−0.494033
$456$		0			0
$457$	4.98698e8			0.244417			0.122208	−	0.992504i	$-0.461002\pi$
$457$	4.98698e8			0.244417			0.122208	+	0.992504i	$0.461002\pi$
$458$		0			0
$459$	3.07881e9	+	1.71787e9i	1.48607	+	0.829177i
$460$		0			0
$461$			3.66061e9i			1.74020i	0.492873	+	0.870101i	$0.335947\pi$
$461$			3.66061e9i			1.74020i	−0.492873	+	0.870101i	$0.664053\pi$
$462$		0			0
$463$		−	4.77840e8i		−	0.223743i	−0.993723	−	0.111871i	$-0.964316\pi$
$463$		−	4.77840e8i		−	0.223743i	0.993723	−	0.111871i	$-0.0356844\pi$
$464$		0			0
$465$	−4.75494e7	+	2.77591e8i	−0.0219311	+	0.128032i
$466$		0			0
$467$	−3.82209e9			−1.73657			−0.868283	−	0.496069i	$-0.834776\pi$
$467$	−3.82209e9			−1.73657			−0.868283	+	0.496069i	$0.834776\pi$
$468$		0			0
$469$	−1.85082e9			−0.828438
$470$		0			0
$471$	−3.64457e8	+	2.12768e9i	−0.160721	+	0.938282i
$472$		0			0
$473$		−	2.57436e9i		−	1.11855i
$474$		0			0
$475$		−	6.46413e7i		−	0.0276747i
$476$		0			0
$477$	−2.45414e8	+	6.95340e8i	−0.103535	+	0.293348i
$478$		0			0
$479$	−3.37672e9			−1.40385			−0.701924	−	0.712251i	$-0.747676\pi$
$479$	−3.37672e9			−1.40385			−0.701924	+	0.712251i	$0.747676\pi$
$480$		0			0
$481$	1.98147e9			0.811857
$482$		0			0
$483$	4.40910e9	+	7.55247e8i	1.78047	+	0.304982i
$484$		0			0
$485$		−	5.47710e8i		−	0.217999i
$486$		0			0
$487$		−	1.21677e9i		−	0.477372i	−0.971097	−	0.238686i	$-0.923283\pi$
$487$		−	1.21677e9i		−	0.477372i	0.971097	−	0.238686i	$-0.0767166\pi$
$488$		0			0
$489$	−4.68904e9	−	8.03199e8i	−1.81344	−	0.310629i
$490$		0			0
$491$	1.56009e9			0.594789			0.297395	−	0.954755i	$-0.403882\pi$
$491$	1.56009e9			0.594789			0.297395	+	0.954755i	$0.403882\pi$
$492$		0			0
$493$	1.24360e9			0.467430
$494$		0			0
$495$	4.72769e8	−	1.33951e9i	0.175199	−	0.496396i
$496$		0			0
$497$			1.81385e9i			0.662755i
$498$		0			0
$499$		−	1.24349e9i		−	0.448011i	−0.974588	−	0.224006i	$-0.928087\pi$
$499$		−	1.24349e9i		−	0.448011i	0.974588	−	0.224006i	$-0.0719134\pi$
$500$		0			0
$501$	8.23567e7	−	4.80794e8i	0.0292595	−	0.170815i
$502$		0			0
$503$	−4.22042e9			−1.47866			−0.739330	−	0.673344i	$-0.764857\pi$
$503$	−4.22042e9			−1.47866			−0.739330	+	0.673344i	$0.764857\pi$
$504$		0			0
$505$	1.90536e9			0.658351
$506$		0			0
$507$	−2.22495e8	+	1.29891e9i	−0.0758214	+	0.442642i
$508$		0			0
$509$		−	5.82245e8i		−	0.195701i	−0.995201	−	0.0978507i	$-0.968803\pi$
$509$		−	5.82245e8i		−	0.195701i	0.995201	−	0.0978507i	$-0.0311968\pi$
$510$		0			0
$511$			4.66524e7i			0.0154668i
$512$		0			0
$513$	−3.69494e8	−	2.06166e8i	−0.120836	−	0.0674227i
$514$		0			0
$515$	2.43569e9			0.785773
$516$		0			0
$517$	−2.90238e9			−0.923712
$518$		0			0
$519$	−5.59414e9	−	9.58237e8i	−1.75650	−	0.300876i
$520$		0			0
$521$		−	1.00581e7i		−	0.00311589i	−0.999999	−	0.00155794i	$-0.999504\pi$
$521$		−	1.00581e7i		−	0.00311589i	0.999999	−	0.00155794i	$-0.000495909\pi$
$522$		0			0
$523$		−	1.69033e9i		−	0.516673i	−0.966055	−	0.258337i	$-0.916826\pi$
$523$		−	1.69033e9i		−	0.516673i	0.966055	−	0.258337i	$-0.0831744\pi$
$524$		0			0
$525$	9.72764e8	+	1.66628e8i	0.293393	+	0.0502562i
$526$		0			0
$527$	−1.66079e9			−0.494286
$528$		0			0
$529$	1.61079e9			0.473089
$530$		0			0
$531$	3.54134e9	+	1.24989e9i	1.02645	+	0.362276i
$532$		0			0
$533$		−	4.28513e9i		−	1.22580i
$534$		0			0
$535$			2.10298e9i			0.593742i
$536$		0			0
$537$	2.38543e8	−	1.39260e9i	0.0664747	−	0.388076i
$538$		0			0
$539$	5.19984e9			1.43031
$540$		0			0
$541$	5.04328e9			1.36938			0.684688	−	0.728836i	$-0.259938\pi$
$541$	5.04328e9			1.36938			0.684688	+	0.728836i	$0.259938\pi$
$542$		0			0
$543$	−2.96412e8	+	1.73044e9i	−0.0794505	+	0.463828i
$544$		0			0
$545$		−	1.48211e9i		−	0.392186i
$546$		0			0
$547$		−	7.31685e9i		−	1.91147i	−0.294222	−	0.955737i	$-0.595060\pi$
$547$		−	7.31685e9i		−	1.91147i	0.294222	−	0.955737i	$-0.404940\pi$
$548$		0			0
$549$	−4.59828e9	−	1.62292e9i	−1.18602	−	0.418596i
$550$		0			0
$551$	−1.49247e8			−0.0380080
$552$		0			0
$553$	−8.21020e9			−2.06450
$554$		0			0
$555$	−1.94178e9	−	3.32613e8i	−0.482141	−	0.0825873i
$556$		0			0
$557$		−	1.09682e9i		−	0.268931i	−0.990918	−	0.134466i	$-0.957068\pi$
$557$		−	1.09682e9i		−	0.268931i	0.990918	−	0.134466i	$-0.0429318\pi$
$558$		0			0
$559$			2.91294e9i			0.705326i
$560$		0			0
$561$	8.25639e9	+	1.41426e9i	1.97433	+	0.338189i
$562$		0			0
$563$	4.01062e9			0.947178			0.473589	−	0.880746i	$-0.342958\pi$
$563$	4.01062e9			0.947178			0.473589	+	0.880746i	$0.342958\pi$
$564$		0			0
$565$	3.40760e9			0.794839
$566$		0			0
$567$	4.05497e9	−	5.02895e9i	0.934216	−	1.15861i
$568$		0			0
$569$			4.04252e9i			0.919941i	0.887934	+	0.459970i	$0.152140\pi$
$569$			4.04252e9i			0.919941i	−0.887934	+	0.459970i	$0.847860\pi$
$570$		0			0
$571$			2.49867e9i			0.561673i	0.959756	+	0.280836i	$0.0906118\pi$
$571$			2.49867e9i			0.561673i	−0.959756	+	0.280836i	$0.909388\pi$
$572$		0			0
$573$	−1.23007e9	+	7.18111e9i	−0.273143	+	1.59460i
$574$		0			0
$575$	1.10658e9			0.242742
$576$		0			0
$577$	−5.59645e9			−1.21282			−0.606412	−	0.795151i	$-0.707392\pi$
$577$	−5.59645e9			−1.21282			−0.606412	+	0.795151i	$0.707392\pi$
$578$		0			0
$579$	1.36070e9	−	7.94367e9i	0.291331	−	1.70077i
$580$		0			0
$581$		−	9.73939e9i		−	2.06023i
$582$		0			0
$583$			1.75195e9i			0.366169i
$584$		0			0
$585$	−5.34948e8	+	1.51568e9i	−0.110476	+	0.313013i
$586$		0			0
$587$	5.95277e9			1.21475			0.607373	−	0.794416i	$-0.292223\pi$
$587$	5.95277e9			1.21475			0.607373	+	0.794416i	$0.292223\pi$
$588$		0			0
$589$	1.99315e8			0.0401918
$590$		0			0
$591$	−1.11011e8	−	1.90154e7i	−0.0221212	−	0.00378921i
$592$		0			0
$593$			3.99539e9i			0.786806i	0.919366	+	0.393403i	$0.128702\pi$
$593$			3.99539e9i			0.786806i	−0.919366	+	0.393403i	$0.871298\pi$
$594$		0			0
$595$			5.81993e9i			1.13268i
$596$		0			0
$597$	−9.14857e9	−	1.56709e9i	−1.75972	−	0.301427i
$598$		0			0
$599$	7.68215e9			1.46046			0.730228	−	0.683203i	$-0.239414\pi$
$599$	7.68215e9			1.46046			0.730228	+	0.683203i	$0.239414\pi$
$600$		0			0
$601$	8.42836e9			1.58374			0.791868	−	0.610693i	$-0.209109\pi$
$601$	8.42836e9			1.58374			0.791868	+	0.610693i	$0.209109\pi$
$602$		0			0
$603$	−9.97427e8	+	2.82604e9i	−0.185255	+	0.524889i
$604$		0			0
$605$		−	9.39081e8i		−	0.172409i
$606$		0			0
$607$		−	1.38208e9i		−	0.250826i	−0.992105	−	0.125413i	$-0.959974\pi$
$607$		−	1.38208e9i		−	0.250826i	0.992105	−	0.125413i	$-0.0400257\pi$
$608$		0			0
$609$	3.84718e8	−	2.24597e9i	0.0690212	−	0.402942i
$610$		0			0
$611$	3.28409e9			0.582467
$612$		0			0
$613$	−4.50316e9			−0.789598			−0.394799	−	0.918768i	$-0.629186\pi$
$613$	−4.50316e9			−0.789598			−0.394799	+	0.918768i	$0.629186\pi$
$614$		0			0
$615$	−7.19310e8	+	4.19930e9i	−0.124696	+	0.727970i
$616$		0			0
$617$			1.00952e9i			0.173029i	0.996251	+	0.0865144i	$0.0275729\pi$
$617$			1.00952e9i			0.173029i	−0.996251	+	0.0865144i	$0.972427\pi$
$618$		0			0
$619$		−	1.88930e9i		−	0.320172i	−0.987103	−	0.160086i	$-0.948823\pi$
$619$		−	1.88930e9i		−	0.320172i	0.987103	−	0.160086i	$-0.0511771\pi$
$620$		0			0
$621$	3.52930e9	−	6.32528e9i	0.591382	−	1.05989i
$622$		0			0
$623$	7.81209e9			1.29437
$624$		0			0
$625$	2.44141e8			0.0400000
$626$		0			0
$627$	−9.90867e8	−	1.69729e8i	−0.160538	−	0.0274991i
$628$		0			0
$629$		−	1.16174e10i		−	1.86137i
$630$		0			0
$631$		−	8.07412e9i		−	1.27936i	−0.768642	−	0.639680i	$-0.779067\pi$
$631$		−	8.07412e9i		−	1.27936i	0.768642	−	0.639680i	$-0.220933\pi$
$632$		0			0
$633$	4.98844e9	+	8.54485e8i	0.781721	+	0.133903i
$634$		0			0
$635$	1.03020e9			0.159667
$636$		0			0
$637$	−5.88372e9			−0.901912
$638$		0			0
$639$	2.76958e9	+	9.77500e8i	0.419914	+	0.148205i
$640$		0			0
$641$		−	5.93182e9i		−	0.889579i	−0.895635	−	0.444789i	$-0.853278\pi$
$641$		−	5.93182e9i		−	0.889579i	0.895635	−	0.444789i	$-0.146722\pi$
$642$		0			0
$643$			5.47689e8i			0.0812448i	0.999175	+	0.0406224i	$0.0129341\pi$
$643$			5.47689e8i			0.0812448i	−0.999175	+	0.0406224i	$0.987066\pi$
$644$		0			0
$645$	4.88971e8	−	2.85459e9i	0.0717503	−	0.418875i
$646$		0			0
$647$	−4.07837e9			−0.591999			−0.296000	−	0.955188i	$-0.595653\pi$
$647$	−4.07837e9			−0.591999			−0.296000	+	0.955188i	$0.595653\pi$
$648$		0			0
$649$	8.92260e9			1.28125
$650$		0			0
$651$	−5.13781e8	+	2.99943e9i	−0.0729868	+	0.426093i
$652$		0			0
$653$		−	1.23204e10i		−	1.73152i	−0.500456	−	0.865762i	$-0.666834\pi$
$653$		−	1.23204e10i		−	1.73152i	0.500456	−	0.865762i	$-0.333166\pi$
$654$		0			0
$655$			1.01266e9i			0.140805i
$656$		0			0
$657$	7.12340e7	+	2.51415e7i	0.00979960	+	0.00345869i
$658$		0			0
$659$	−4.58602e9			−0.624219			−0.312109	−	0.950046i	$-0.601036\pi$
$659$	−4.58602e9			−0.624219			−0.312109	+	0.950046i	$0.601036\pi$
$660$		0			0
$661$	6.61798e8			0.0891293			0.0445647	−	0.999007i	$-0.485810\pi$
$661$	6.61798e8			0.0891293			0.0445647	+	0.999007i	$0.485810\pi$
$662$		0			0
$663$	−9.34227e9	−	1.60027e9i	−1.24496	−	0.213253i
$664$		0			0
$665$		−	6.98462e8i		−	0.0921016i
$666$		0			0
$667$		−	2.55492e9i		−	0.333378i
$668$		0			0
$669$	−1.08553e9	−	1.85944e8i	−0.140169	−	0.0240100i
$670$		0			0
$671$	−1.15856e10			−1.48044
$672$		0			0
$673$	−1.17729e10			−1.48878			−0.744389	−	0.667746i	$-0.767259\pi$
$673$	−1.17729e10			−1.48878			−0.744389	+	0.667746i	$0.767259\pi$
$674$		0			0
$675$	7.78657e8	−	1.39552e9i	0.0974503	−	0.174652i
$676$		0			0
$677$		−	1.01101e9i		−	0.125226i	−0.998038	−	0.0626131i	$-0.980057\pi$
$677$		−	1.01101e9i		−	0.125226i	0.998038	−	0.0626131i	$-0.0199434\pi$
$678$		0			0
$679$		−	5.91812e9i		−	0.725504i
$680$		0			0
$681$	1.65967e9	−	9.68906e9i	0.201375	−	1.17562i
$682$		0			0
$683$	−2.59887e9			−0.312114			−0.156057	−	0.987748i	$-0.549878\pi$
$683$	−2.59887e9			−0.312114			−0.156057	+	0.987748i	$0.549878\pi$
$684$		0			0
$685$	3.97102e9			0.472047
$686$		0			0
$687$	−6.33067e8	+	3.69581e9i	−0.0744905	+	0.434872i
$688$		0			0
$689$		−	1.98237e9i		−	0.230896i
$690$		0			0
$691$			1.19545e10i			1.37835i	0.724597	+	0.689173i	$0.242026\pi$
$691$			1.19545e10i			1.37835i	−0.724597	+	0.689173i	$0.757974\pi$
$692$		0			0
$693$	5.10837e9	−	1.44737e10i	0.583064	−	1.65201i
$694$		0			0
$695$	−2.39908e9			−0.271080
$696$		0			0
$697$	−2.51239e10			−2.81043
$698$		0			0
$699$	−7.60235e9	−	1.30223e9i	−0.841934	−	0.144217i
$700$		0			0
$701$			1.68159e10i			1.84377i	0.387465	+	0.921884i	$0.373351\pi$
$701$			1.68159e10i			1.84377i	−0.387465	+	0.921884i	$0.626649\pi$
$702$		0			0
$703$			1.39423e9i			0.151353i
$704$		0			0
$705$	−3.21831e9	−	5.51274e8i	−0.345912	−	0.0592523i
$706$		0			0
$707$	2.05878e10			2.19100
$708$		0			0
$709$	−8.91920e9			−0.939862			−0.469931	−	0.882703i	$-0.655721\pi$
$709$	−8.91920e9			−0.939862			−0.469931	+	0.882703i	$0.655721\pi$
$710$		0			0
$711$	−4.42456e9	+	1.25362e10i	−0.461664	+	1.30805i
$712$		0			0
$713$			3.41203e9i			0.352532i
$714$		0			0
$715$			3.81885e9i			0.390717i
$716$		0			0
$717$	−1.37182e8	+	8.00865e8i	−0.0138989	+	0.0811413i
$718$		0			0
$719$	−1.20751e10			−1.21155			−0.605775	−	0.795636i	$-0.707137\pi$
$719$	−1.20751e10			−1.21155			−0.605775	+	0.795636i	$0.707137\pi$
$720$		0			0
$721$	2.63181e10			2.61506
$722$		0			0
$723$	2.34890e9	−	1.37128e10i	0.231143	−	1.34940i
$724$		0			0
$725$		−	5.63684e8i		−	0.0549355i
$726$		0			0
$727$			1.52930e10i			1.47612i	0.674735	+	0.738060i	$0.264258\pi$
$727$			1.52930e10i			1.47612i	−0.674735	+	0.738060i	$0.735742\pi$
$728$		0			0
$729$	−5.49348e9	−	8.90172e9i	−0.525172	−	0.850996i
$730$		0			0
$731$	1.70787e10			1.61712
$732$		0			0
$733$	1.34809e10			1.26431			0.632157	−	0.774841i	$-0.282170\pi$
$733$	1.34809e10			1.26431			0.632157	+	0.774841i	$0.282170\pi$
$734$		0			0
$735$	5.76586e9	+	9.87652e8i	0.535622	+	0.0917483i
$736$		0			0
$737$			7.12037e9i			0.655189i
$738$		0			0
$739$		−	1.06341e10i		−	0.969268i	−0.874717	−	0.484634i	$-0.838953\pi$
$739$		−	1.06341e10i		−	0.969268i	0.874717	−	0.484634i	$-0.161047\pi$
$740$		0			0
$741$	1.12119e9	+	1.92051e8i	0.101231	+	0.0173402i
$742$		0			0
$743$	6.62660e9			0.592693			0.296346	−	0.955081i	$-0.404232\pi$
$743$	6.62660e9			0.592693			0.296346	+	0.955081i	$0.404232\pi$
$744$		0			0
$745$	−1.36321e9			−0.120786
$746$		0			0
$747$	−1.48712e10	−	5.24865e9i	−1.30534	−	0.460708i
$748$		0			0
$749$			2.27232e10i			1.97598i
$750$		0			0
$751$			6.65260e9i			0.573128i	0.958061	+	0.286564i	$0.0925131\pi$
$751$			6.65260e9i			0.573128i	−0.958061	+	0.286564i	$0.907487\pi$
$752$		0			0
$753$	8.72675e8	−	5.09463e9i	0.0744852	−	0.434841i
$754$		0			0
$755$	7.28219e9			0.615811
$756$		0			0
$757$	−4.95809e9			−0.415411			−0.207706	−	0.978191i	$-0.566600\pi$
$757$	−4.95809e9			−0.415411			−0.207706	+	0.978191i	$0.566600\pi$
$758$		0			0
$759$	2.90554e9	−	1.69624e10i	0.241202	−	1.40812i
$760$		0			0
$761$			1.11170e10i			0.914411i	0.889361	+	0.457206i	$0.151150\pi$
$761$			1.11170e10i			0.914411i	−0.889361	+	0.457206i	$0.848850\pi$
$762$		0			0
$763$		−	1.60145e10i		−	1.30520i
$764$		0			0
$765$	8.88651e9	+	3.13642e9i	0.717655	+	0.253291i
$766$		0			0
$767$	−1.00961e10			−0.807923
$768$		0			0
$769$	−7.24814e9			−0.574757			−0.287379	−	0.957817i	$-0.592784\pi$
$769$	−7.24814e9			−0.574757			−0.287379	+	0.957817i	$0.592784\pi$
$770$		0			0
$771$	−5.53834e9	−	9.48679e8i	−0.435200	−	0.0745468i
$772$		0			0
$773$			1.50778e10i			1.17411i	0.809546	+	0.587057i	$0.199713\pi$
$773$			1.50778e10i			1.17411i	−0.809546	+	0.587057i	$0.800287\pi$
$774$		0			0
$775$			7.52784e8i			0.0580918i
$776$		0			0
$777$	−2.09813e10	−	3.59395e9i	−1.60457	−	0.274851i
$778$		0			0
$779$	3.01517e9			0.228523
$780$		0			0
$781$	6.97811e9			0.524155
$782$		0			0
$783$	−3.22206e9	−	1.79780e9i	−0.239865	−	0.133837i
$784$		0			0
$785$			5.76995e9i			0.425724i
$786$		0			0
$787$			6.39018e9i			0.467306i	0.972320	+	0.233653i	$0.0750680\pi$
$787$			6.39018e9i			0.467306i	−0.972320	+	0.233653i	$0.924932\pi$
$788$		0			0
$789$	−3.62873e9	+	2.11843e10i	−0.263018	+	1.53548i
$790$		0			0
$791$	3.68198e10			2.64523
$792$		0			0
$793$	1.31094e10			0.933524
$794$		0			0
$795$	−3.32763e8	+	1.94266e9i	−0.0234882	+	0.137123i
$796$		0			0
$797$			2.01379e10i			1.40900i	0.709705	+	0.704499i	$0.248828\pi$
$797$			2.01379e10i			1.40900i	−0.709705	+	0.704499i	$0.751172\pi$
$798$		0			0
$799$		−	1.92548e10i		−	1.33544i
$800$		0			0
$801$	4.21001e9	−	1.19283e10i	0.289447	−	0.820099i
$802$		0			0
$803$	1.79478e8			0.0122323
$804$		0			0
$805$	1.19568e10			0.807847
$806$		0			0
$807$	−4.89417e9	−	8.38337e8i	−0.327810	−	0.0561515i
$808$		0			0
$809$		−	2.11237e10i		−	1.40265i	−0.712840	−	0.701326i	$-0.752592\pi$
$809$		−	2.11237e10i		−	1.40265i	0.712840	−	0.701326i	$-0.247408\pi$
$810$		0			0
$811$			1.04253e10i			0.686302i	0.939280	+	0.343151i	$0.111494\pi$
$811$			1.04253e10i			0.686302i	−0.939280	+	0.343151i	$0.888506\pi$
$812$		0			0
$813$	−3.70517e9	−	6.34669e8i	−0.241819	−	0.0414219i
$814$		0			0
$815$	−1.27160e10			−0.822806
$816$		0			0
$817$	−2.04965e9			−0.131493
$818$		0			0
$819$	−5.78022e9	+	1.63773e10i	−0.367664	+	1.04171i
$820$		0			0
$821$		−	1.41564e10i		−	0.892796i	−0.894834	−	0.446398i	$-0.852707\pi$
$821$		−	1.41564e10i		−	0.892796i	0.894834	−	0.446398i	$-0.147293\pi$
$822$		0			0
$823$		−	2.50984e9i		−	0.156945i	−0.996916	−	0.0784723i	$-0.974996\pi$
$823$		−	2.50984e9i		−	0.156945i	0.996916	−	0.0784723i	$-0.0250042\pi$
$824$		0			0
$825$	6.41039e8	−	3.74236e9i	0.0397462	−	0.232037i
$826$		0			0
$827$	5.62711e9			0.345952			0.172976	−	0.984926i	$-0.444662\pi$
$827$	5.62711e9			0.345952			0.172976	+	0.984926i	$0.444662\pi$
$828$		0			0
$829$	−2.36326e10			−1.44069			−0.720345	−	0.693616i	$-0.756016\pi$
$829$	−2.36326e10			−1.44069			−0.720345	+	0.693616i	$0.756016\pi$
$830$		0			0
$831$	−5.00667e9	+	2.92287e10i	−0.302654	+	1.76688i
$832$		0			0
$833$			3.44965e10i			2.06784i
$834$		0			0
$835$		−	1.30384e9i		−	0.0775036i
$836$		0			0
$837$	4.30297e9	+	2.40092e9i	0.253647	+	0.141527i
$838$		0			0
$839$	5.28767e9			0.309099			0.154550	−	0.987985i	$-0.450607\pi$
$839$	5.28767e9			0.309099			0.154550	+	0.987985i	$0.450607\pi$
$840$		0			0
$841$	1.59484e10			0.924552
$842$		0			0
$843$	−2.83939e10	−	4.86367e9i	−1.63241	−	0.279620i
$844$		0			0
$845$			3.52246e9i			0.200839i
$846$		0			0
$847$		−	1.01470e10i		−	0.573778i
$848$		0			0
$849$	2.54351e10	+	4.35685e9i	1.42645	+	0.244340i
$850$		0			0
$851$	−2.38675e10			−1.32756
$852$		0			0
$853$	2.60783e10			1.43866			0.719329	−	0.694669i	$-0.244449\pi$
$853$	2.60783e10			1.43866			0.719329	+	0.694669i	$0.244449\pi$
$854$		0			0
$855$	−1.06649e9	−	3.76408e8i	−0.0583546	−	0.0205958i
$856$		0			0
$857$		−	1.23249e10i		−	0.668882i	−0.942417	−	0.334441i	$-0.891452\pi$
$857$		−	1.23249e10i		−	0.668882i	0.942417	−	0.334441i	$-0.108548\pi$
$858$		0			0
$859$			6.61867e9i			0.356282i	0.984005	+	0.178141i	$0.0570084\pi$
$859$			6.61867e9i			0.356282i	−0.984005	+	0.178141i	$0.942992\pi$
$860$		0			0
$861$	−7.77229e9	+	4.53742e10i	−0.414990	+	2.42269i
$862$		0			0
$863$	−2.81070e9			−0.148859			−0.0744297	−	0.997226i	$-0.523714\pi$
$863$	−2.81070e9			−0.148859			−0.0744297	+	0.997226i	$0.523714\pi$
$864$		0			0
$865$	−1.51705e10			−0.796971
$866$		0			0
$867$	−6.14255e9	+	3.58599e10i	−0.320097	+	1.86871i
$868$		0			0
$869$			3.15858e10i			1.63276i
$870$		0			0
$871$		−	8.05684e9i		−	0.413144i
$872$		0			0
$873$	−9.03643e9	−	3.18933e9i	−0.459671	−	0.162237i
$874$		0			0
$875$	2.63799e9			0.133120
$876$		0			0
$877$	3.20127e8			0.0160260			0.00801298	−	0.999968i	$-0.497449\pi$
$877$	3.20127e8			0.0160260			0.00801298	+	0.999968i	$0.497449\pi$
$878$		0			0
$879$	−2.17243e10	−	3.72121e9i	−1.07891	−	0.184809i
$880$		0			0
$881$		−	1.26151e9i		−	0.0621548i	−0.999517	−	0.0310774i	$-0.990106\pi$
$881$		−	1.26151e9i		−	0.0621548i	0.999517	−	0.0310774i	$-0.00989383\pi$
$882$		0			0
$883$			1.52205e10i			0.743990i	0.928235	+	0.371995i	$0.121326\pi$
$883$			1.52205e10i			0.743990i	−0.928235	+	0.371995i	$0.878674\pi$
$884$		0			0
$885$	9.89386e9	+	1.69475e9i	0.479805	+	0.0821872i
$886$		0			0
$887$	1.67411e10			0.805473			0.402736	−	0.915316i	$-0.368059\pi$
$887$	1.67411e10			0.805473			0.402736	+	0.915316i	$0.368059\pi$
$888$		0			0
$889$	1.11315e10			0.531372
$890$		0			0
$891$	−1.93471e10	−	1.56000e10i	−0.916311	−	0.738845i
$892$		0			0
$893$			2.31080e9i			0.108588i
$894$		0			0
$895$		−	3.77652e9i		−	0.176081i
$896$		0			0
$897$	−3.28767e9	+	1.91933e10i	−0.152095	+	0.887924i
$898$		0			0
$899$	1.73807e9			0.0797824
$900$		0			0
$901$	−1.16227e10			−0.529382
$902$		0			0
$903$	5.28343e9	−	3.08444e10i	0.238786	−	1.39402i
$904$		0			0
$905$			4.69269e9i			0.210451i
$906$		0			0
$907$		−	3.15856e10i		−	1.40560i	−0.711385	−	0.702802i	$-0.751932\pi$
$907$		−	3.15856e10i		−	1.40560i	0.711385	−	0.702802i	$-0.248068\pi$
$908$		0			0
$909$	1.10950e10	−	3.14357e10i	0.489951	−	1.38819i
$910$		0			0
$911$	1.19638e9			0.0524271			0.0262136	−	0.999656i	$-0.491655\pi$
$911$	1.19638e9			0.0524271			0.0262136	+	0.999656i	$0.491655\pi$
$912$		0			0
$913$	−3.74688e10			−1.62938
$914$		0			0
$915$	−1.28468e10	−	2.20056e9i	−0.554396	−	0.0949641i
$916$		0			0
$917$			1.09420e10i			0.468601i
$918$		0			0
$919$			1.93525e10i			0.822496i	0.911524	+	0.411248i	$0.134907\pi$
$919$			1.93525e10i			0.822496i	−0.911524	+	0.411248i	$0.865093\pi$
$920$		0			0
$921$	3.24900e9	+	5.56531e8i	0.137038	+	0.0234736i
$922$		0			0
$923$	−7.89587e9			−0.330517
$924$		0			0
$925$	−5.26580e9			−0.218760
$926$		0			0
$927$	1.41831e10	−	4.01854e10i	0.584779	−	1.65687i
$928$		0			0
$929$			2.27011e10i			0.928948i	0.885587	+	0.464474i	$0.153757\pi$
$929$			2.27011e10i			0.928948i	−0.885587	+	0.464474i	$0.846243\pi$
$930$		0			0
$931$		−	4.13999e9i		−	0.168142i
$932$		0			0
$933$	1.68619e8	−	9.84390e8i	0.00679706	−	0.0396809i
$934$		0			0
$935$	2.23901e10			0.895808
$936$		0			0
$937$	8.34496e9			0.331387			0.165694	−	0.986177i	$-0.447014\pi$
$937$	8.34496e9			0.331387			0.165694	+	0.986177i	$0.447014\pi$
$938$		0			0
$939$	−5.88056e9	+	3.43304e10i	−0.231787	+	1.35316i
$940$		0			0
$941$		−	3.06131e10i		−	1.19769i	−0.800865	−	0.598845i	$-0.795627\pi$
$941$		−	3.06131e10i		−	1.19769i	0.800865	−	0.598845i	$-0.204373\pi$
$942$		0			0
$943$			5.16159e10i			2.00444i
$944$		0			0
$945$	8.41355e9	−	1.50789e10i	0.324316	−	0.581245i
$946$		0			0
$947$	−2.53338e10			−0.969339			−0.484670	−	0.874697i	$-0.661060\pi$
$947$	−2.53338e10			−0.969339			−0.484670	+	0.874697i	$0.661060\pi$
$948$		0			0
$949$	−2.03083e8			−0.00771334
$950$		0			0
$951$	−2.51930e10	−	4.31539e9i	−0.949837	−	0.162700i
$952$		0			0
$953$		−	1.92371e10i		−	0.719971i	−0.932958	−	0.359986i	$-0.882782\pi$
$953$		−	1.92371e10i		−	0.719971i	0.932958	−	0.359986i	$-0.117218\pi$
$954$		0			0
$955$			1.94741e10i			0.723511i
$956$		0			0
$957$	−8.64054e9	−	1.48006e9i	−0.318676	−	0.0545869i
$958$		0			0
$959$	4.29077e10			1.57098
$960$		0			0
$961$	2.51915e10			0.915634
$962$		0			0
$963$	3.46962e10	+	1.22457e10i	1.25196	+	0.441869i
$964$		0			0
$965$		−	2.15420e10i		−	0.771687i
$966$		0			0
$967$		−	1.93286e10i		−	0.687399i	−0.939080	−	0.343699i	$-0.888320\pi$
$967$		−	1.93286e10i		−	0.687399i	0.939080	−	0.343699i	$-0.111680\pi$
$968$		0			0
$969$	1.12600e9	−	6.57355e9i	0.0397563	−	0.232096i
$970$		0			0
$971$	−2.56710e10			−0.899861			−0.449931	−	0.893063i	$-0.648551\pi$
$971$	−2.56710e10			−0.899861			−0.449931	+	0.893063i	$0.648551\pi$
$972$		0			0
$973$	−2.59225e10			−0.902158
$974$		0			0
$975$	−7.25349e8	+	4.23455e9i	−0.0250629	+	0.146316i
$976$		0			0
$977$			4.63030e10i			1.58847i	0.607612	+	0.794234i	$0.292128\pi$
$977$			4.63030e10i			1.58847i	−0.607612	+	0.794234i	$0.707872\pi$
$978$		0			0
$979$		−	3.00542e10i		−	1.02368i
$980$		0			0
$981$	−2.44526e10	−	8.63036e9i	−0.826959	−	0.291869i
$982$		0			0
$983$	4.11266e9			0.138097			0.0690487	−	0.997613i	$-0.478004\pi$
$983$	4.11266e9			0.138097			0.0690487	+	0.997613i	$0.478004\pi$
$984$		0			0
$985$	−3.01044e8			−0.0100370
$986$		0			0
$987$	−3.47745e10	−	5.95662e9i	−1.15120	−	0.197192i
$988$		0			0
$989$		−	3.50873e10i		−	1.15336i
$990$		0			0
$991$			2.57081e9i			0.0839098i	0.999120	+	0.0419549i	$0.0133586\pi$
$991$			2.57081e9i			0.0839098i	−0.999120	+	0.0419549i	$0.986641\pi$
$992$		0			0
$993$	−3.86545e10	−	6.62125e9i	−1.25279	−	0.214594i
$994$		0			0
$995$	−2.48095e10			−0.798432
$996$		0			0
$997$	1.05992e10			0.338719			0.169360	−	0.985554i	$-0.445830\pi$
$997$	1.05992e10			0.338719			0.169360	+	0.985554i	$0.445830\pi$
$998$		0			0
$999$	−1.67946e10	+	3.00997e10i	−0.532956	+	0.955175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.8.h.b.191.19	yes	36
3.2	odd	2	inner	240.8.h.b.191.17	✓	36
4.3	odd	2	inner	240.8.h.b.191.18	yes	36
12.11	even	2	inner	240.8.h.b.191.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.8.h.b.191.17	✓	36	3.2	odd	2	inner
240.8.h.b.191.18	yes	36	4.3	odd	2	inner
240.8.h.b.191.19	yes	36	1.1	even	1	trivial
240.8.h.b.191.20	yes	36	12.11	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	240.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.89558 - 46.0940i) q^{3} -125.000i q^{5} -1350.65i q^{7} +(-2062.32 - 727.879i) q^{9} -5196.14 q^{11} +5879.53 q^{13} +(-5761.75 - 986.948i) q^{15} -34471.9i q^{17} +4137.04i q^{19} +(-62256.9 - 10664.2i) q^{21} -70821.0 q^{23} -15625.0 q^{25} +(-49834.1 + 89313.6i) q^{27} +36075.8i q^{29} -48178.2i q^{31} +(-41026.5 + 239511. i) q^{33} -168831. q^{35} +337011. q^{37} +(46422.3 - 271011. i) q^{39} -728822. i q^{41} +495437. i q^{43} +(-90984.8 + 257790. i) q^{45} +558564. q^{47} -1.00071e6 q^{49} +(-1.58895e6 - 272176. i) q^{51} -337164. i q^{53} +649517. i q^{55} +(190693. + 32664.4i) q^{57} -1.71716e6 q^{59} +2.22966e6 q^{61} +(-983109. + 2.78547e6i) q^{63} -734941. i q^{65} -1.37032e6i q^{67} +(-559173. + 3.26442e6i) q^{69} -1.34294e6 q^{71} -34540.7 q^{73} +(-123369. + 720219. i) q^{75} +7.01816e6i q^{77} -6.07870e6i q^{79} +(3.72335e6 + 3.00224e6i) q^{81} +7.21089e6 q^{83} -4.30899e6 q^{85} +(1.66288e6 + 284839. i) q^{87} +5.78395e6i q^{89} -7.94119e6i q^{91} +(-2.22073e6 - 380395. i) q^{93} +517131. q^{95} +4.38168e6 q^{97} +(1.07161e7 + 3.78216e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3324 q^{9} - 432 q^{13} - 22032 q^{21} - 562500 q^{25} - 386232 q^{33} + 1200048 q^{37} - 1710000 q^{45} - 3237972 q^{49} - 9331200 q^{57} + 11262360 q^{61} - 11352552 q^{69} + 37210296 q^{73} - 12564252 q^{81}+ \cdots + 94537320 q^{97}+O(q^{100}) \) 36 * q + 3324 * q^9 - 432 * q^13 - 22032 * q^21 - 562500 * q^25 - 386232 * q^33 + 1200048 * q^37 - 1710000 * q^45 - 3237972 * q^49 - 9331200 * q^57 + 11262360 * q^61 - 11352552 * q^69 + 37210296 * q^73 - 12564252 * q^81 + 5271000 * q^85 + 5594400 * q^93 + 94537320 * q^97

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