LMFDB - Embedded newform 207.7.d.e.91.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("207.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.6211953093$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.16
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.73591 q^{2} -41.5712 q^{4} +38.4146i q^{5} +655.803i q^{7} -499.975 q^{8} +O(q^{10})$	\(q+4.73591 q^{2} -41.5712 q^{4} +38.4146i q^{5} +655.803i q^{7} -499.975 q^{8} +181.928i q^{10} -589.638i q^{11} -3173.89 q^{13} +3105.82i q^{14} +292.721 q^{16} -909.300i q^{17} -3910.57i q^{19} -1596.94i q^{20} -2792.47i q^{22} +(-2677.23 + 11868.8i) q^{23} +14149.3 q^{25} -15031.3 q^{26} -27262.5i q^{28} +38085.2 q^{29} -12573.1 q^{31} +33384.7 q^{32} -4306.36i q^{34} -25192.4 q^{35} -80835.5i q^{37} -18520.1i q^{38} -19206.4i q^{40} -35231.0 q^{41} -46800.8i q^{43} +24512.0i q^{44} +(-12679.1 + 56209.5i) q^{46} -147162. q^{47} -312428. q^{49} +67009.8 q^{50} +131943. q^{52} -254361. i q^{53} +22650.7 q^{55} -327885. i q^{56} +180368. q^{58} +98850.5 q^{59} -149261. i q^{61} -59545.0 q^{62} +139373. q^{64} -121924. i q^{65} -331116. i q^{67} +37800.7i q^{68} -119309. q^{70} -371128. q^{71} +31506.8 q^{73} -382829. i q^{74} +162567. i q^{76} +386686. q^{77} +242806. i q^{79} +11244.8i q^{80} -166851. q^{82} +827839. i q^{83} +34930.4 q^{85} -221644. i q^{86} +294804. i q^{88} +1.03994e6i q^{89} -2.08145e6i q^{91} +(111295. - 493400. i) q^{92} -696944. q^{94} +150223. q^{95} +833514. i q^{97} -1.47963e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	4.73591			0.591988			0.295994	−	0.955190i	$-0.404349\pi$
$2$	4.73591			0.591988			0.295994	+	0.955190i	$0.404349\pi$
$3$		0			0
$3$		0			0
$4$	−41.5712			−0.649550
$5$			38.4146i			0.307317i	0.988124	+	0.153659i	$0.0491056\pi$
$5$			38.4146i			0.307317i	−0.988124	+	0.153659i	$0.950894\pi$
$6$		0			0
$7$			655.803i			1.91196i	0.293429	+	0.955981i	$0.405203\pi$
$7$			655.803i			1.91196i	−0.293429	+	0.955981i	$0.594797\pi$
$8$	−499.975			−0.976514
$9$		0			0
$10$			181.928i			0.181928i
$11$		−	589.638i		−	0.443004i	−0.975160	−	0.221502i	$-0.928904\pi$
$11$		−	589.638i		−	0.443004i	0.975160	−	0.221502i	$-0.0710959\pi$
$12$		0			0
$13$	−3173.89			−1.44465			−0.722325	−	0.691554i	$-0.756926\pi$
$13$	−3173.89			−1.44465			−0.722325	+	0.691554i	$0.756926\pi$
$14$			3105.82i			1.13186i
$15$		0			0
$16$	292.721			0.0714650
$17$		−	909.300i		−	0.185080i	−0.995709	−	0.0925402i	$-0.970501\pi$
$17$		−	909.300i		−	0.185080i	0.995709	−	0.0925402i	$-0.0294987\pi$
$18$		0			0
$19$		−	3910.57i		−	0.570138i	−0.958507	−	0.285069i	$-0.907984\pi$
$19$		−	3910.57i		−	0.570138i	0.958507	−	0.285069i	$-0.0920165\pi$
$20$		−	1596.94i		−	0.199618i
$21$		0			0
$22$		−	2792.47i		−	0.262253i
$23$	−2677.23	+	11868.8i	−0.220040	+	0.975491i
$23$	−2677.23	+	11868.8i	−0.220040	+	0.975491i
$24$		0			0
$25$	14149.3			0.905556
$26$	−15031.3			−0.855216
$27$		0			0
$28$		−	27262.5i		−	1.24191i
$29$	38085.2			1.56157			0.780786	−	0.624799i	$-0.214819\pi$
$29$	38085.2			1.56157			0.780786	+	0.624799i	$0.214819\pi$
$30$		0			0
$31$	−12573.1			−0.422044			−0.211022	−	0.977481i	$-0.567679\pi$
$31$	−12573.1			−0.422044			−0.211022	+	0.977481i	$0.567679\pi$
$32$	33384.7			1.01882
$33$		0			0
$34$		−	4306.36i		−	0.109565i
$35$	−25192.4			−0.587579
$36$		0			0
$37$		−	80835.5i		−	1.59587i	−0.602745	−	0.797934i	$-0.705927\pi$
$37$		−	80835.5i		−	1.59587i	0.602745	−	0.797934i	$-0.294073\pi$
$38$		−	18520.1i		−	0.337515i
$39$		0			0
$40$		−	19206.4i		−	0.300100i
$41$	−35231.0			−0.511179			−0.255589	−	0.966785i	$-0.582270\pi$
$41$	−35231.0			−0.511179			−0.255589	+	0.966785i	$0.582270\pi$
$42$		0			0
$43$		−	46800.8i		−	0.588637i	−0.955707	−	0.294318i	$-0.904907\pi$
$43$		−	46800.8i		−	0.588637i	0.955707	−	0.294318i	$-0.0950926\pi$
$44$			24512.0i			0.287753i
$45$		0			0
$46$	−12679.1	+	56209.5i	−0.130261	+	0.577479i
$47$	−147162.			−1.41743			−0.708714	−	0.705495i	$-0.750725\pi$
$47$	−147162.			−1.41743			−0.708714	+	0.705495i	$0.750725\pi$
$48$		0			0
$49$	−312428.			−2.65560
$50$	67009.8			0.536079
$51$		0			0
$52$	131943.			0.938372
$53$		−	254361.i		−	1.70853i	−0.519836	−	0.854266i	$-0.674007\pi$
$53$		−	254361.i		−	1.70853i	0.519836	−	0.854266i	$-0.325993\pi$
$54$		0			0
$55$	22650.7			0.136143
$56$		−	327885.i		−	1.86706i
$57$		0			0
$58$	180368.			0.924432
$59$	98850.5			0.481308			0.240654	−	0.970611i	$-0.422638\pi$
$59$	98850.5			0.481308			0.240654	+	0.970611i	$0.422638\pi$
$60$		0			0
$61$		−	149261.i		−	0.657591i	−0.944401	−	0.328796i	$-0.893357\pi$
$61$		−	149261.i		−	0.657591i	0.944401	−	0.328796i	$-0.106643\pi$
$62$	−59545.0			−0.249845
$63$		0			0
$64$	139373.			0.531665
$65$		−	121924.i		−	0.443966i
$66$		0			0
$67$		−	331116.i		−	1.10092i	−0.834861	−	0.550460i	$-0.814452\pi$
$67$		−	331116.i		−	1.10092i	0.834861	−	0.550460i	$-0.185548\pi$
$68$			37800.7i			0.120219i
$69$		0			0
$70$	−119309.			−0.347840
$71$	−371128.			−1.03693			−0.518464	−	0.855100i	$-0.673496\pi$
$71$	−371128.			−1.03693			−0.518464	+	0.855100i	$0.673496\pi$
$72$		0			0
$73$	31506.8			0.0809907			0.0404954	−	0.999180i	$-0.487106\pi$
$73$	31506.8			0.0809907			0.0404954	+	0.999180i	$0.487106\pi$
$74$		−	382829.i		−	0.944735i
$75$		0			0
$76$			162567.i			0.370333i
$77$	386686.			0.847006
$78$		0			0
$79$			242806.i			0.492469i	0.969210	+	0.246234i	$0.0791933\pi$
$79$			242806.i			0.492469i	−0.969210	+	0.246234i	$0.920807\pi$
$80$			11244.8i			0.0219624i
$81$		0			0
$82$	−166851.			−0.302612
$83$			827839.i			1.44781i	0.689900	+	0.723905i	$0.257655\pi$
$83$			827839.i			1.44781i	−0.689900	+	0.723905i	$0.742345\pi$
$84$		0			0
$85$	34930.4			0.0568784
$86$		−	221644.i		−	0.348466i
$87$		0			0
$88$			294804.i			0.432599i
$89$			1.03994e6i			1.47515i	0.675265	+	0.737576i	$0.264029\pi$
$89$			1.03994e6i			1.47515i	−0.675265	+	0.737576i	$0.735971\pi$
$90$		0			0
$91$		−	2.08145e6i		−	2.76211i
$92$	111295.	−	493400.i	0.142927	−	0.633630i
$93$		0			0
$94$	−696944.			−0.839101
$95$	150223.			0.175213
$96$		0			0
$97$			833514.i			0.913267i	0.889655	+	0.456633i	$0.150945\pi$
$97$			833514.i			0.913267i	−0.889655	+	0.456633i	$0.849055\pi$
$98$	−1.47963e6			−1.57208
$99$		0			0
$100$	−588204.			−0.588204
$101$	365591.			0.354839			0.177420	−	0.984135i	$-0.443225\pi$
$101$	365591.			0.354839			0.177420	+	0.984135i	$0.443225\pi$
$102$		0			0
$103$		−	1.37353e6i		−	1.25698i	−0.777819	−	0.628489i	$-0.783674\pi$
$103$		−	1.37353e6i		−	1.25698i	0.777819	−	0.628489i	$-0.216326\pi$
$104$	1.58687e6			1.41072
$105$		0			0
$106$		−	1.20463e6i		−	1.01143i
$107$		−	1.26985e6i		−	1.03657i	−0.855207	−	0.518287i	$-0.826570\pi$
$107$		−	1.26985e6i		−	1.03657i	0.855207	−	0.518287i	$-0.173430\pi$
$108$		0			0
$109$		−	1.06233e6i		−	0.820315i	−0.912015	−	0.410157i	$-0.865474\pi$
$109$		−	1.06233e6i		−	0.820315i	0.912015	−	0.410157i	$-0.134526\pi$
$110$	107272.			0.0805949
$111$		0			0
$112$			191967.i			0.136638i
$113$			1.24438e6i			0.862415i	0.902253	+	0.431207i	$0.141912\pi$
$113$			1.24438e6i			0.862415i	−0.902253	+	0.431207i	$0.858088\pi$
$114$		0			0
$115$	−455936.	−	102845.i	−0.299785	−	0.0676220i
$116$	−1.58325e6			−1.01432
$117$		0			0
$118$	468147.			0.284928
$119$	596321.			0.353867
$120$		0			0
$121$	1.42389e6			0.803748
$122$		−	706885.i		−	0.389286i
$123$		0			0
$124$	522679.			0.274138
$125$			1.14377e6i			0.585610i
$126$		0			0
$127$	−874087.			−0.426721			−0.213360	−	0.976974i	$-0.568441\pi$
$127$	−874087.			−0.426721			−0.213360	+	0.976974i	$0.568441\pi$
$128$	−1.47657e6			−0.704081
$129$		0			0
$130$		−	577421.i		−	0.262822i
$131$	1.81535e6			0.807509			0.403754	−	0.914867i	$-0.367705\pi$
$131$	1.81535e6			0.807509			0.403754	+	0.914867i	$0.367705\pi$
$132$		0			0
$133$	2.56457e6			1.09008
$134$		−	1.56814e6i		−	0.651732i
$135$		0			0
$136$			454627.i			0.180734i
$137$			269246.i			0.104710i	0.998629	+	0.0523549i	$0.0166727\pi$
$137$			269246.i			0.104710i	−0.998629	+	0.0523549i	$0.983327\pi$
$138$		0			0
$139$	−1.01592e6			−0.378282			−0.189141	−	0.981950i	$-0.560570\pi$
$139$	−1.01592e6			−0.378282			−0.189141	+	0.981950i	$0.560570\pi$
$140$	1.04728e6			0.381662
$141$		0			0
$142$	−1.75763e6			−0.613849
$143$			1.87145e6i			0.639985i
$144$		0			0
$145$			1.46303e6i			0.479898i
$146$	149213.			0.0479456
$147$		0			0
$148$			3.36043e6i			1.03660i
$149$		−	5.31546e6i		−	1.60688i	−0.595388	−	0.803438i	$-0.703002\pi$
$149$		−	5.31546e6i		−	1.60688i	0.595388	−	0.803438i	$-0.296998\pi$
$150$		0			0
$151$	−4.02808e6			−1.16995			−0.584975	−	0.811051i	$-0.698896\pi$
$151$	−4.02808e6			−1.16995			−0.584975	+	0.811051i	$0.698896\pi$
$152$			1.95519e6i			0.556748i
$153$		0			0
$154$	1.83131e6			0.501418
$155$		−	482991.i		−	0.129701i
$156$		0			0
$157$		−	2.80608e6i		−	0.725107i	−0.931963	−	0.362553i	$-0.881905\pi$
$157$		−	2.80608e6i		−	0.725107i	0.931963	−	0.362553i	$-0.118095\pi$
$158$			1.14991e6i			0.291536i
$159$		0			0
$160$			1.28246e6i			0.313101i
$161$	−7.78359e6	−	1.75573e6i	−1.86510	−	0.420708i
$162$		0			0
$163$	−1.69615e6			−0.391652			−0.195826	−	0.980639i	$-0.562739\pi$
$163$	−1.69615e6			−0.391652			−0.195826	+	0.980639i	$0.562739\pi$
$164$	1.46459e6			0.332036
$165$		0			0
$166$			3.92057e6i			0.857087i
$167$	−4.14358e6			−0.889665			−0.444832	−	0.895614i	$-0.646737\pi$
$167$	−4.14358e6			−0.889665			−0.444832	+	0.895614i	$0.646737\pi$
$168$		0			0
$169$	5.24680e6			1.08701
$170$	165427.			0.0336713
$171$		0			0
$172$			1.94556e6i			0.382349i
$173$	3.49007e6			0.674056			0.337028	−	0.941495i	$-0.390578\pi$
$173$	3.49007e6			0.674056			0.337028	+	0.941495i	$0.390578\pi$
$174$		0			0
$175$			9.27916e6i			1.73139i
$176$		−	172599.i		−	0.0316593i
$177$		0			0
$178$			4.92504e6i			0.873272i
$179$	4.02563e6			0.701899			0.350949	−	0.936394i	$-0.385859\pi$
$179$	4.02563e6			0.701899			0.350949	+	0.936394i	$0.385859\pi$
$180$		0			0
$181$			9.09130e6i			1.53317i	0.642143	+	0.766585i	$0.278046\pi$
$181$			9.09130e6i			1.53317i	−0.642143	+	0.766585i	$0.721954\pi$
$182$		−	9.85755e6i		−	1.63514i
$183$		0			0
$184$	1.33855e6	−	5.93411e6i	0.214872	−	0.952581i
$185$	3.10527e6			0.490437
$186$		0			0
$187$	−536158.			−0.0819913
$188$	6.11769e6			0.920691
$189$		0			0
$190$	711444.			0.103724
$191$			91981.9i			0.0132009i	0.999978	+	0.00660043i	$0.00210100\pi$
$191$			91981.9i			0.0132009i	−0.999978	+	0.00660043i	$0.997899\pi$
$192$		0			0
$193$	1.89895e6			0.264145			0.132073	−	0.991240i	$-0.457837\pi$
$193$	1.89895e6			0.264145			0.132073	+	0.991240i	$0.457837\pi$
$194$			3.94744e6i			0.540643i
$195$		0			0
$196$	1.29880e7			1.72494
$197$	2.32424e6			0.304006			0.152003	−	0.988380i	$-0.451428\pi$
$197$	2.32424e6			0.304006			0.152003	+	0.988380i	$0.451428\pi$
$198$		0			0
$199$		−	6.58139e6i		−	0.835138i	−0.908645	−	0.417569i	$-0.862882\pi$
$199$		−	6.58139e6i		−	0.835138i	0.908645	−	0.417569i	$-0.137118\pi$
$200$	−7.07431e6			−0.884288
$201$		0			0
$202$	1.73141e6			0.210061
$203$			2.49764e7i			2.98566i
$204$		0			0
$205$		−	1.35339e6i		−	0.157094i
$206$		−	6.50492e6i		−	0.744116i
$207$		0			0
$208$	−929065.			−0.103242
$209$	−2.30582e6			−0.252573
$210$		0			0
$211$	−9.49872e6			−1.01115			−0.505577	−	0.862781i	$-0.668720\pi$
$211$	−9.49872e6			−1.01115			−0.505577	+	0.862781i	$0.668720\pi$
$212$			1.05741e7i			1.10978i
$213$		0			0
$214$		−	6.01388e6i		−	0.613639i
$215$	1.79783e6			0.180898
$216$		0			0
$217$		−	8.24547e6i		−	0.806931i
$218$		−	5.03110e6i		−	0.485617i
$219$		0			0
$220$	−941618.			−0.0884315
$221$			2.88602e6i			0.267376i
$222$		0			0
$223$	−1.00094e7			−0.902596			−0.451298	−	0.892373i	$-0.649039\pi$
$223$	−1.00094e7			−0.902596			−0.451298	+	0.892373i	$0.649039\pi$
$224$			2.18938e7i			1.94795i
$225$		0			0
$226$			5.89324e6i			0.510539i
$227$			1.06382e7i			0.909479i	0.890625	+	0.454739i	$0.150268\pi$
$227$			1.06382e7i			0.909479i	−0.890625	+	0.454739i	$0.849732\pi$
$228$		0			0
$229$			1.56747e7i			1.30525i	0.757682	+	0.652624i	$0.226332\pi$
$229$			1.56747e7i			1.30525i	−0.757682	+	0.652624i	$0.773668\pi$
$230$	−2.15927e6	−	487063.i	−0.177469	−	0.0400314i
$231$		0			0
$232$	−1.90416e7			−1.52490
$233$	1.75407e7			1.38669			0.693345	−	0.720605i	$-0.256136\pi$
$233$	1.75407e7			1.38669			0.693345	+	0.720605i	$0.256136\pi$
$234$		0			0
$235$		−	5.65317e6i		−	0.435600i
$236$	−4.10933e6			−0.312633
$237$		0			0
$238$	2.82412e6			0.209485
$239$	−1.76748e7			−1.29468			−0.647339	−	0.762202i	$-0.724118\pi$
$239$	−1.76748e7			−1.29468			−0.647339	+	0.762202i	$0.724118\pi$
$240$		0			0
$241$		−	1.74693e7i		−	1.24803i	−0.781413	−	0.624015i	$-0.785501\pi$
$241$		−	1.74693e7i		−	1.24803i	0.781413	−	0.624015i	$-0.214499\pi$
$242$	6.74340e6			0.475809
$243$		0			0
$244$			6.20495e6i			0.427138i
$245$		−	1.20018e7i		−	0.816110i
$246$		0			0
$247$			1.24118e7i			0.823649i
$248$	6.28624e6			0.412132
$249$		0			0
$250$			5.41679e6i			0.346674i
$251$		−	2.77630e7i		−	1.75568i	−0.478957	−	0.877839i	$-0.658985\pi$
$251$		−	2.77630e7i		−	1.75568i	0.478957	−	0.877839i	$-0.341015\pi$
$252$		0			0
$253$	6.99829e6	+	1.57859e6i	0.432146	+	0.0974785i
$254$	−4.13960e6			−0.252614
$255$		0			0
$256$	−1.59127e7			−0.948473
$257$	−2.30184e7			−1.35605			−0.678026	−	0.735038i	$-0.737164\pi$
$257$	−2.30184e7			−1.35605			−0.678026	+	0.735038i	$0.737164\pi$
$258$		0			0
$259$	5.30121e7			3.05124
$260$			5.06853e6i			0.288378i
$261$		0			0
$262$	8.59734e6			0.478036
$263$			1.22401e7i			0.672849i	0.941710	+	0.336424i	$0.109218\pi$
$263$			1.22401e7i			0.672849i	−0.941710	+	0.336424i	$0.890782\pi$
$264$		0			0
$265$	9.77119e6			0.525061
$266$	1.21455e7			0.645315
$267$		0			0
$268$			1.37649e7i			0.715103i
$269$	2.04992e7			1.05312			0.526562	−	0.850136i	$-0.323481\pi$
$269$	2.04992e7			1.05312			0.526562	+	0.850136i	$0.323481\pi$
$270$		0			0
$271$	−1.50443e7			−0.755898			−0.377949	−	0.925826i	$-0.623371\pi$
$271$	−1.50443e7			−0.755898			−0.377949	+	0.925826i	$0.623371\pi$
$272$		−	266171.i		−	0.0132268i
$273$		0			0
$274$			1.27512e6i			0.0619870i
$275$		−	8.34297e6i		−	0.401165i
$276$		0			0
$277$	−3.89399e7			−1.83213			−0.916063	−	0.401034i	$-0.868651\pi$
$277$	−3.89399e7			−1.83213			−0.916063	+	0.401034i	$0.868651\pi$
$278$	−4.81131e6			−0.223939
$279$		0			0
$280$	1.25956e7			0.573779
$281$		−	2.98207e7i		−	1.34400i	−0.740553	−	0.671998i	$-0.765436\pi$
$281$		−	2.98207e7i		−	1.34400i	0.740553	−	0.671998i	$-0.234564\pi$
$282$		0			0
$283$		−	8.12480e6i		−	0.358470i	−0.983806	−	0.179235i	$-0.942638\pi$
$283$		−	8.12480e6i		−	0.358470i	0.983806	−	0.179235i	$-0.0573623\pi$
$284$	1.54282e7			0.673536
$285$		0			0
$286$			8.86301e6i			0.378864i
$287$		−	2.31046e7i		−	0.977355i
$288$		0			0
$289$	2.33107e7			0.965745
$290$			6.92876e6i			0.284094i
$291$		0			0
$292$	−1.30977e6			−0.0526075
$293$			3.59566e6i			0.142947i	0.997442	+	0.0714736i	$0.0227702\pi$
$293$			3.59566e6i			0.142947i	−0.997442	+	0.0714736i	$0.977230\pi$
$294$		0			0
$295$			3.79731e6i			0.147914i
$296$			4.04157e7i			1.55839i
$297$		0			0
$298$		−	2.51735e7i		−	0.951252i
$299$	8.49723e6	−	3.76703e7i	0.317881	−	1.40924i
$300$		0			0
$301$	3.06921e7			1.12545
$302$	−1.90766e7			−0.692597
$303$		0			0
$304$		−	1.14471e6i		−	0.0407449i
$305$	5.73380e6			0.202089
$306$		0			0
$307$	−3.56413e7			−1.23179			−0.615897	−	0.787826i	$-0.711206\pi$
$307$	−3.56413e7			−1.23179			−0.615897	+	0.787826i	$0.711206\pi$
$308$	−1.60750e7			−0.550173
$309$		0			0
$310$		−	2.28740e6i		−	0.0767816i
$311$	−2.80618e7			−0.932899			−0.466450	−	0.884548i	$-0.654467\pi$
$311$	−2.80618e7			−0.932899			−0.466450	+	0.884548i	$0.654467\pi$
$312$		0			0
$313$		−	1.51413e7i		−	0.493777i	−0.969044	−	0.246889i	$-0.920592\pi$
$313$		−	1.51413e7i		−	0.493777i	0.969044	−	0.246889i	$-0.0794082\pi$
$314$		−	1.32894e7i		−	0.429255i
$315$		0			0
$316$		−	1.00938e7i		−	0.319883i
$317$	−2.13859e7			−0.671351			−0.335676	−	0.941978i	$-0.608965\pi$
$317$	−2.13859e7			−0.671351			−0.335676	+	0.941978i	$0.608965\pi$
$318$		0			0
$319$		−	2.24565e7i		−	0.691782i
$320$			5.35395e6i			0.163390i
$321$		0			0
$322$	−3.68624e7	−	8.31498e6i	−1.10412	−	0.249054i
$323$	−3.55589e6			−0.105521
$324$		0			0
$325$	−4.49084e7			−1.30821
$326$	−8.03279e6			−0.231853
$327$		0			0
$328$	1.76146e7			0.499174
$329$		−	9.65091e7i		−	2.71007i
$330$		0			0
$331$	−2.67122e7			−0.736591			−0.368295	−	0.929709i	$-0.620059\pi$
$331$	−2.67122e7			−0.736591			−0.368295	+	0.929709i	$0.620059\pi$
$332$		−	3.44143e7i		−	0.940425i
$333$		0			0
$334$	−1.96236e7			−0.526671
$335$	1.27197e7			0.338332
$336$		0			0
$337$		−	4.34797e7i		−	1.13605i	−0.823011	−	0.568025i	$-0.807708\pi$
$337$		−	4.34797e7i		−	1.13605i	0.823011	−	0.568025i	$-0.192292\pi$
$338$	2.48484e7			0.643498
$339$		0			0
$340$	−1.45210e6			−0.0369453
$341$			7.41358e6i			0.186967i
$342$		0			0
$343$		−	1.27737e8i		−	3.16544i
$344$			2.33992e7i			0.574812i
$345$		0			0
$346$	1.65286e7			0.399033
$347$	−1.79683e7			−0.430049			−0.215024	−	0.976609i	$-0.568983\pi$
$347$	−1.79683e7			−0.430049			−0.215024	+	0.976609i	$0.568983\pi$
$348$		0			0
$349$	−1.98878e7			−0.467855			−0.233927	−	0.972254i	$-0.575158\pi$
$349$	−1.98878e7			−0.467855			−0.233927	+	0.972254i	$0.575158\pi$
$350$			4.39452e7i			1.02496i
$351$		0			0
$352$		−	1.96849e7i		−	0.451341i
$353$	−2.64567e7			−0.601467			−0.300733	−	0.953708i	$-0.597231\pi$
$353$	−2.64567e7			−0.601467			−0.300733	+	0.953708i	$0.597231\pi$
$354$		0			0
$355$		−	1.42567e7i		−	0.318665i
$356$		−	4.32314e7i		−	0.958184i
$357$		0			0
$358$	1.90650e7			0.415516
$359$			5.31179e7i			1.14804i	0.818841	+	0.574020i	$0.194617\pi$
$359$			5.31179e7i			1.14804i	−0.818841	+	0.574020i	$0.805383\pi$
$360$		0			0
$361$	3.17533e7			0.674943
$362$			4.30555e7i			0.907618i
$363$		0			0
$364$			8.65283e7i			1.79413i
$365$			1.21032e6i			0.0248898i
$366$		0			0
$367$			1.02909e7i			0.208188i	0.994567	+	0.104094i	$0.0331942\pi$
$367$			1.02909e7i			0.208188i	−0.994567	+	0.104094i	$0.966806\pi$
$368$	−783679.	+	3.47424e6i	−0.0157252	+	0.0697135i
$369$		0			0
$370$	1.47062e7			0.290333
$371$	1.66811e8			3.26665
$372$		0			0
$373$			2.28746e7i			0.440785i	0.975411	+	0.220392i	$0.0707338\pi$
$373$			2.28746e7i			0.440785i	−0.975411	+	0.220392i	$0.929266\pi$
$374$	−2.53919e6			−0.0485379
$375$		0			0
$376$	7.35772e7			1.38414
$377$	−1.20878e8			−2.25592
$378$		0			0
$379$		−	8.53493e7i		−	1.56777i	−0.620906	−	0.783885i	$-0.713235\pi$
$379$		−	8.53493e7i		−	1.56777i	0.620906	−	0.783885i	$-0.286765\pi$
$380$	−6.24496e6			−0.113810
$381$		0			0
$382$			435618.i			0.00781475i
$383$			5.06708e7i			0.901906i	0.892548	+	0.450953i	$0.148916\pi$
$383$			5.06708e7i			0.901906i	−0.892548	+	0.450953i	$0.851084\pi$
$384$		0			0
$385$			1.48544e7i			0.260300i
$386$	8.99327e6			0.156371
$387$		0			0
$388$		−	3.46502e7i		−	0.593212i
$389$		−	4.61864e7i		−	0.784630i	−0.919831	−	0.392315i	$-0.871674\pi$
$389$		−	4.61864e7i		−	0.784630i	0.919831	−	0.392315i	$-0.128326\pi$
$390$		0			0
$391$	1.07923e7	+	2.43440e6i	0.180544	+	0.0407251i
$392$	1.56206e8			2.59323
$393$		0			0
$394$	1.10074e7			0.179968
$395$	−9.32732e6			−0.151344
$396$		0			0
$397$	−6.30551e7			−1.00774			−0.503870	−	0.863779i	$-0.668091\pi$
$397$	−6.30551e7			−1.00774			−0.503870	+	0.863779i	$0.668091\pi$
$398$		−	3.11688e7i		−	0.494392i
$399$		0			0
$400$	4.14180e6			0.0647156
$401$			6.06571e7i			0.940695i	0.882481	+	0.470347i	$0.155871\pi$
$401$			6.06571e7i			0.940695i	−0.882481	+	0.470347i	$0.844129\pi$
$402$		0			0
$403$	3.99057e7			0.609705
$404$	−1.51981e7			−0.230486
$405$		0			0
$406$			1.18286e8i			1.76748i
$407$	−4.76637e7			−0.706975
$408$		0			0
$409$	−8.56293e7			−1.25156			−0.625781	−	0.779998i	$-0.715220\pi$
$409$	−8.56293e7			−1.25156			−0.625781	+	0.779998i	$0.715220\pi$
$410$		−	6.40950e6i		−	0.0929978i
$411$		0			0
$412$			5.70994e7i			0.816470i
$413$			6.48264e7i			0.920242i
$414$		0			0
$415$	−3.18011e7			−0.444937
$416$	−1.05960e8			−1.47184
$417$		0			0
$418$	−1.09202e7			−0.149520
$419$		−	4.27680e7i		−	0.581403i	−0.956814	−	0.290701i	$-0.906111\pi$
$419$		−	4.27680e7i		−	0.581403i	0.956814	−	0.290701i	$-0.0938886\pi$
$420$		0			0
$421$			1.37696e7i			0.184534i	0.995734	+	0.0922668i	$0.0294113\pi$
$421$			1.37696e7i			0.184534i	−0.995734	+	0.0922668i	$0.970589\pi$
$422$	−4.49850e7			−0.598592
$423$		0			0
$424$			1.27174e8i			1.66841i
$425$		−	1.28660e7i		−	0.167601i
$426$		0			0
$427$	9.78856e7			1.25729
$428$			5.27891e7i			0.673306i
$429$		0			0
$430$	8.51437e6			0.107090
$431$		−	1.76722e7i		−	0.220729i	−0.993891	−	0.110365i	$-0.964798\pi$
$431$		−	1.76722e7i		−	0.220729i	0.993891	−	0.110365i	$-0.0352018\pi$
$432$		0			0
$433$		−	6.14430e7i		−	0.756848i	−0.925632	−	0.378424i	$-0.876466\pi$
$433$		−	6.14430e7i		−	0.756848i	0.925632	−	0.378424i	$-0.123534\pi$
$434$		−	3.90498e7i		−	0.477694i
$435$		0			0
$436$			4.41624e7i			0.532835i
$437$	4.64138e7	+	1.04695e7i	0.556164	+	0.125453i
$438$		0			0
$439$	−4.41260e7			−0.521556			−0.260778	−	0.965399i	$-0.583979\pi$
$439$	−4.41260e7			−0.521556			−0.260778	+	0.965399i	$0.583979\pi$
$440$	−1.13248e7			−0.132945
$441$		0			0
$442$			1.36679e7i			0.158284i
$443$	−3.93587e7			−0.452719			−0.226360	−	0.974044i	$-0.572682\pi$
$443$	−3.93587e7			−0.452719			−0.226360	+	0.974044i	$0.572682\pi$
$444$		0			0
$445$	−3.99488e7			−0.453339
$446$	−4.74036e7			−0.534326
$447$		0			0
$448$			9.14010e7i			1.01652i
$449$	9.04011e7			0.998699			0.499349	−	0.866401i	$-0.333572\pi$
$449$	9.04011e7			0.998699			0.499349	+	0.866401i	$0.333572\pi$
$450$		0			0
$451$			2.07735e7i			0.226454i
$452$		−	5.17302e7i		−	0.560181i
$453$		0			0
$454$			5.03817e7i			0.538401i
$455$	7.99581e7			0.848845
$456$		0			0
$457$			4.88645e7i			0.511970i	0.966681	+	0.255985i	$0.0823998\pi$
$457$			4.88645e7i			0.511970i	−0.966681	+	0.255985i	$0.917600\pi$
$458$			7.42340e7i			0.772692i
$459$		0			0
$460$	1.89538e7	+	4.27538e6i	0.194725	+	0.0439239i
$461$	5.13497e7			0.524125			0.262063	−	0.965051i	$-0.415597\pi$
$461$	5.13497e7			0.524125			0.262063	+	0.965051i	$0.415597\pi$
$462$		0			0
$463$	−9.15812e7			−0.922706			−0.461353	−	0.887217i	$-0.652636\pi$
$463$	−9.15812e7			−0.922706			−0.461353	+	0.887217i	$0.652636\pi$
$464$	1.11483e7			0.111598
$465$		0			0
$466$	8.30712e7			0.820905
$467$			1.65064e8i			1.62070i	0.585948	+	0.810349i	$0.300722\pi$
$467$			1.65064e8i			1.62070i	−0.585948	+	0.810349i	$0.699278\pi$
$468$		0			0
$469$	2.17147e8			2.10492
$470$		−	2.67729e7i		−	0.257870i
$471$		0			0
$472$	−4.94228e7			−0.470004
$473$	−2.75955e7			−0.260768
$474$		0			0
$475$		−	5.53320e7i		−	0.516292i
$476$	−2.47898e7			−0.229854
$477$		0			0
$478$	−8.37064e7			−0.766434
$479$			5.12647e7i			0.466457i	0.972422	+	0.233228i	$0.0749290\pi$
$479$			5.12647e7i			0.466457i	−0.972422	+	0.233228i	$0.925071\pi$
$480$		0			0
$481$			2.56563e8i			2.30547i
$482$		−	8.27330e7i		−	0.738819i
$483$		0			0
$484$	−5.91927e7			−0.522074
$485$	−3.20191e7			−0.280663
$486$		0			0
$487$	1.00852e8			0.873168			0.436584	−	0.899664i	$-0.356188\pi$
$487$	1.00852e8			0.873168			0.436584	+	0.899664i	$0.356188\pi$
$488$			7.46266e7i			0.642147i
$489$		0			0
$490$		−	5.68395e7i		−	0.483128i
$491$	−4.28499e7			−0.361998			−0.180999	−	0.983483i	$-0.557933\pi$
$491$	−4.28499e7			−0.361998			−0.180999	+	0.983483i	$0.557933\pi$
$492$		0			0
$493$		−	3.46308e7i		−	0.289016i
$494$			5.87809e7i			0.487591i
$495$		0			0
$496$	−3.68041e6			−0.0301613
$497$		−	2.43387e8i		−	1.98256i
$498$		0			0
$499$	2.43539e8			1.96005			0.980024	−	0.198877i	$-0.0637295\pi$
$499$	2.43539e8			1.96005			0.980024	+	0.198877i	$0.0637295\pi$
$500$		−	4.75479e7i		−	0.380383i
$501$		0			0
$502$		−	1.31483e8i		−	1.03934i
$503$		−	2.71475e7i		−	0.213317i	−0.994296	−	0.106659i	$-0.965985\pi$
$503$		−	2.71475e7i		−	0.213317i	0.994296	−	0.106659i	$-0.0340152\pi$
$504$		0			0
$505$			1.40441e7i			0.109048i
$506$	3.31433e7	+	7.47607e6i	0.255825	+	0.0577061i
$507$		0			0
$508$	3.63369e7			0.277176
$509$	−1.63613e8			−1.24069			−0.620347	−	0.784327i	$-0.713008\pi$
$509$	−1.63613e8			−1.24069			−0.620347	+	0.784327i	$0.713008\pi$
$510$		0			0
$511$			2.06622e7i			0.154851i
$512$	1.91390e7			0.142597
$513$		0			0
$514$	−1.09013e8			−0.802766
$515$	5.27638e7			0.386291
$516$		0			0
$517$			8.67722e7i			0.627926i
$518$	2.51060e8			1.80630
$519$		0			0
$520$			6.09590e7i			0.433539i
$521$			3.82670e7i			0.270590i	0.990805	+	0.135295i	$0.0431982\pi$
$521$			3.82670e7i			0.270590i	−0.990805	+	0.135295i	$0.956802\pi$
$522$		0			0
$523$		−	1.69427e8i		−	1.18434i	−0.805812	−	0.592172i	$-0.798271\pi$
$523$		−	1.69427e8i		−	1.18434i	0.805812	−	0.592172i	$-0.201729\pi$
$524$	−7.54664e7			−0.524517
$525$		0			0
$526$			5.79679e7i			0.398319i
$527$			1.14327e7i			0.0781120i
$528$		0			0
$529$	−1.33701e8	−	6.35509e7i	−0.903165	−	0.429294i
$530$	4.62754e7			0.310830
$531$		0			0
$532$	−1.06612e8			−0.708062
$533$	1.11819e8			0.738474
$534$		0			0
$535$	4.87807e7			0.318557
$536$			1.65550e8i			1.07506i
$537$		0			0
$538$	9.70822e7			0.623438
$539$			1.84220e8i			1.17644i
$540$		0			0
$541$	−1.41458e8			−0.893378			−0.446689	−	0.894689i	$-0.647397\pi$
$541$	−1.41458e8			−0.893378			−0.446689	+	0.894689i	$0.647397\pi$
$542$	−7.12483e7			−0.447483
$543$		0			0
$544$		−	3.03567e7i		−	0.188564i
$545$	4.08091e7			0.252097
$546$		0			0
$547$	−5.97977e7			−0.365361			−0.182681	−	0.983172i	$-0.558477\pi$
$547$	−5.97977e7			−0.365361			−0.182681	+	0.983172i	$0.558477\pi$
$548$		−	1.11929e7i		−	0.0680142i
$549$		0			0
$550$		−	3.95115e7i		−	0.237485i
$551$		−	1.48935e8i		−	0.890311i
$552$		0			0
$553$	−1.59233e8			−0.941582
$554$	−1.84416e8			−1.08460
$555$		0			0
$556$	4.22331e7			0.245713
$557$		−	3.31067e7i		−	0.191580i	−0.995402	−	0.0957900i	$-0.969462\pi$
$557$		−	3.31067e7i		−	0.191580i	0.995402	−	0.0957900i	$-0.0305377\pi$
$558$		0			0
$559$			1.48541e8i			0.850374i
$560$	−7.37435e6			−0.0419913
$561$		0			0
$562$		−	1.41228e8i		−	0.795630i
$563$			2.07541e8i			1.16299i	0.813548	+	0.581497i	$0.197533\pi$
$563$			2.07541e8i			1.16299i	−0.813548	+	0.581497i	$0.802467\pi$
$564$		0			0
$565$	−4.78022e7			−0.265035
$566$		−	3.84783e7i		−	0.212210i
$567$		0			0
$568$	1.85555e8			1.01257
$569$		−	2.45063e8i		−	1.33027i	−0.746723	−	0.665136i	$-0.768374\pi$
$569$		−	2.45063e8i		−	1.33027i	0.746723	−	0.665136i	$-0.231626\pi$
$570$		0			0
$571$		−	1.57184e8i		−	0.844307i	−0.906524	−	0.422153i	$-0.861274\pi$
$571$		−	1.57184e8i		−	0.844307i	0.906524	−	0.422153i	$-0.138726\pi$
$572$		−	7.77984e7i		−	0.415702i
$573$		0			0
$574$		−	1.09421e8i		−	0.578582i
$575$	−3.78809e7	+	1.67935e8i	−0.199258	+	0.883362i
$576$		0			0
$577$	7.78829e7			0.405429			0.202715	−	0.979238i	$-0.435024\pi$
$577$	7.78829e7			0.405429			0.202715	+	0.979238i	$0.435024\pi$
$578$	1.10397e8			0.571710
$579$		0			0
$580$		−	6.08198e7i		−	0.311717i
$581$	−5.42899e8			−2.76816
$582$		0			0
$583$	−1.49981e8			−0.756886
$584$	−1.57526e7			−0.0790886
$585$		0			0
$586$			1.70287e7i			0.0846231i
$587$	1.75136e7			0.0865888			0.0432944	−	0.999062i	$-0.486215\pi$
$587$	1.75136e7			0.0865888			0.0432944	+	0.999062i	$0.486215\pi$
$588$		0			0
$589$			4.91680e7i			0.240623i
$590$			1.79837e7i			0.0875634i
$591$		0			0
$592$		−	2.36622e7i		−	0.114049i
$593$	3.78225e8			1.81379			0.906893	−	0.421361i	$-0.138447\pi$
$593$	3.78225e8			1.81379			0.906893	+	0.421361i	$0.138447\pi$
$594$		0			0
$595$			2.29075e7i			0.108749i
$596$			2.20970e8i			1.04375i
$597$		0			0
$598$	4.02421e7	−	1.78403e8i	0.188182	−	0.834255i
$599$	6.74384e7			0.313781			0.156891	−	0.987616i	$-0.449853\pi$
$599$	6.74384e7			0.313781			0.156891	+	0.987616i	$0.449853\pi$
$600$		0			0
$601$	−1.98091e8			−0.912516			−0.456258	−	0.889847i	$-0.650811\pi$
$601$	−1.98091e8			−0.912516			−0.456258	+	0.889847i	$0.650811\pi$
$602$	1.45355e8			0.666254
$603$		0			0
$604$	1.67452e8			0.759941
$605$			5.46981e7i			0.247005i
$606$		0			0
$607$	−3.35592e7			−0.150053			−0.0750267	−	0.997182i	$-0.523904\pi$
$607$	−3.35592e7			−0.150053			−0.0750267	+	0.997182i	$0.523904\pi$
$608$		−	1.30553e8i		−	0.580868i
$609$		0			0
$610$	2.71547e7			0.119634
$611$	4.67076e8			2.04769
$612$		0			0
$613$		−	6.44452e7i		−	0.279775i	−0.990167	−	0.139888i	$-0.955326\pi$
$613$		−	6.44452e7i		−	0.279775i	0.990167	−	0.139888i	$-0.0446741\pi$
$614$	−1.68794e8			−0.729208
$615$		0			0
$616$	−1.93334e8			−0.827114
$617$		−	3.01733e8i		−	1.28460i	−0.766453	−	0.642300i	$-0.777980\pi$
$617$		−	3.01733e8i		−	1.28460i	0.766453	−	0.642300i	$-0.222020\pi$
$618$		0			0
$619$		−	6.36803e7i		−	0.268493i	−0.990948	−	0.134246i	$-0.957139\pi$
$619$		−	6.36803e7i		−	0.268493i	0.990948	−	0.134246i	$-0.0428614\pi$
$620$			2.00785e7i			0.0842474i
$621$		0			0
$622$	−1.32898e8			−0.552265
$623$	−6.81993e8			−2.82043
$624$		0			0
$625$	1.77146e8			0.725588
$626$		−	7.17080e7i		−	0.292310i
$627$		0			0
$628$			1.16652e8i			0.470993i
$629$	−7.35037e7			−0.295364
$630$		0			0
$631$			1.83010e8i			0.728427i	0.931315	+	0.364214i	$0.118662\pi$
$631$			1.83010e8i			0.728427i	−0.931315	+	0.364214i	$0.881338\pi$
$632$		−	1.21397e8i		−	0.480903i
$633$		0			0
$634$	−1.01282e8			−0.397432
$635$		−	3.35778e7i		−	0.131139i
$636$		0			0
$637$	9.91615e8			3.83641
$638$		−	1.06352e8i		−	0.409527i
$639$		0			0
$640$		−	5.67217e7i		−	0.216376i
$641$		−	3.89706e8i		−	1.47967i	−0.672791	−	0.739833i	$-0.734905\pi$
$641$		−	3.89706e8i		−	1.47967i	0.672791	−	0.739833i	$-0.265095\pi$
$642$		0			0
$643$			2.85643e8i			1.07446i	0.843436	+	0.537230i	$0.180529\pi$
$643$			2.85643e8i			1.07446i	−0.843436	+	0.537230i	$0.819471\pi$
$644$	3.23573e8	+	7.29879e7i	1.21148	+	0.273271i
$645$		0			0
$646$	−1.68403e7			−0.0624674
$647$	4.43292e8			1.63673			0.818365	−	0.574699i	$-0.194881\pi$
$647$	4.43292e8			1.63673			0.818365	+	0.574699i	$0.194881\pi$
$648$		0			0
$649$		−	5.82860e7i		−	0.213221i
$650$	−2.12682e8			−0.774446
$651$		0			0
$652$	7.05108e7			0.254398
$653$	−1.53784e8			−0.552294			−0.276147	−	0.961115i	$-0.589058\pi$
$653$	−1.53784e8			−0.552294			−0.276147	+	0.961115i	$0.589058\pi$
$654$		0			0
$655$			6.97361e7i			0.248161i
$656$	−1.03128e7			−0.0365314
$657$		0			0
$658$		−	4.57058e8i		−	1.60433i
$659$		−	1.40657e8i		−	0.491481i	−0.969336	−	0.245740i	$-0.920969\pi$
$659$		−	1.40657e8i		−	0.491481i	0.969336	−	0.245740i	$-0.0790311\pi$
$660$		0			0
$661$		−	1.20638e8i		−	0.417713i	−0.977946	−	0.208857i	$-0.933026\pi$
$661$		−	1.20638e8i		−	0.417713i	0.977946	−	0.208857i	$-0.0669742\pi$
$662$	−1.26507e8			−0.436053
$663$		0			0
$664$		−	4.13899e8i		−	1.41381i
$665$			9.85169e7i			0.335001i
$666$		0			0
$667$	−1.01963e8	+	4.52025e8i	−0.343608	+	1.52330i
$668$	1.72254e8			0.577882
$669$		0			0
$670$	6.02393e7			0.200288
$671$	−8.80098e7			−0.291315
$672$		0			0
$673$	−4.99233e8			−1.63779			−0.818895	−	0.573943i	$-0.805413\pi$
$673$	−4.99233e8			−1.63779			−0.818895	+	0.573943i	$0.805413\pi$
$674$		−	2.05916e8i		−	0.672528i
$675$		0			0
$676$	−2.18116e8			−0.706069
$677$		−	5.75205e8i		−	1.85377i	−0.375342	−	0.926886i	$-0.622475\pi$
$677$		−	5.75205e8i		−	1.85377i	0.375342	−	0.926886i	$-0.377525\pi$
$678$		0			0
$679$	−5.46621e8			−1.74613
$680$	−1.74644e7			−0.0555425
$681$		0			0
$682$			3.51100e7i			0.110682i
$683$	−3.10528e8			−0.974626			−0.487313	−	0.873227i	$-0.662023\pi$
$683$	−3.10528e8			−0.974626			−0.487313	+	0.873227i	$0.662023\pi$
$684$		0			0
$685$	−1.03430e7			−0.0321791
$686$		−	6.04950e8i		−	1.87390i
$687$		0			0
$688$		−	1.36995e7i		−	0.0420669i
$689$			8.07315e8i			2.46823i
$690$		0			0
$691$	3.16160e7			0.0958237			0.0479119	−	0.998852i	$-0.484743\pi$
$691$	3.16160e7			0.0958237			0.0479119	+	0.998852i	$0.484743\pi$
$692$	−1.45086e8			−0.437833
$693$		0			0
$694$	−8.50960e7			−0.254584
$695$		−	3.90263e7i		−	0.116253i
$696$		0			0
$697$			3.20355e7i			0.0946092i
$698$	−9.41869e7			−0.276964
$699$		0			0
$700$		−	3.85746e8i		−	1.12462i
$701$			6.49293e8i			1.88489i	0.334355	+	0.942447i	$0.391481\pi$
$701$			6.49293e8i			1.88489i	−0.334355	+	0.942447i	$0.608519\pi$
$702$		0			0
$703$	−3.16113e8			−0.909864
$704$		−	8.21795e7i		−	0.235530i
$705$		0			0
$706$	−1.25296e8			−0.356061
$707$			2.39756e8i			0.678439i
$708$		0			0
$709$			2.76124e8i			0.774757i	0.921921	+	0.387379i	$0.126619\pi$
$709$			2.76124e8i			0.774757i	−0.921921	+	0.387379i	$0.873381\pi$
$710$		−	6.75186e7i		−	0.188646i
$711$		0			0
$712$		−	5.19942e8i		−	1.44051i
$713$	3.36610e7	−	1.49228e8i	0.0928664	−	0.411700i
$714$		0			0
$715$	−7.18911e7			−0.196678
$716$	−1.67350e8			−0.455918
$717$		0			0
$718$			2.51561e8i			0.679627i
$719$	1.67972e7			0.0451907			0.0225953	−	0.999745i	$-0.492807\pi$
$719$	1.67972e7			0.0451907			0.0225953	+	0.999745i	$0.492807\pi$
$720$		0			0
$721$	9.00767e8			2.40329
$722$	1.50381e8			0.399558
$723$		0			0
$724$		−	3.77936e8i		−	0.995870i
$725$	5.38879e8			1.41409
$726$		0			0
$727$		−	1.40934e8i		−	0.366786i	−0.983040	−	0.183393i	$-0.941292\pi$
$727$		−	1.40934e8i		−	0.366786i	0.983040	−	0.183393i	$-0.0587082\pi$
$728$			1.04067e9i			2.69724i
$729$		0			0
$730$			5.73197e6i			0.0147345i
$731$	−4.25559e7			−0.108945
$732$		0			0
$733$		−	4.60922e8i		−	1.17035i	−0.810907	−	0.585175i	$-0.801026\pi$
$733$		−	4.60922e8i		−	1.17035i	0.810907	−	0.585175i	$-0.198974\pi$
$734$			4.87367e7i			0.123245i
$735$		0			0
$736$	−8.93784e7	+	3.96236e8i	−0.224181	+	0.993850i
$737$	−1.95239e8			−0.487712
$738$		0			0
$739$	−2.18814e8			−0.542177			−0.271088	−	0.962554i	$-0.587384\pi$
$739$	−2.18814e8			−0.542177			−0.271088	+	0.962554i	$0.587384\pi$
$740$	−1.29090e8			−0.318564
$741$		0			0
$742$	7.90000e8			1.93382
$743$			6.03913e8i			1.47234i	0.676797	+	0.736170i	$0.263368\pi$
$743$			6.03913e8i			1.47234i	−0.676797	+	0.736170i	$0.736632\pi$
$744$		0			0
$745$	2.04192e8			0.493821
$746$			1.08332e8i			0.260939i
$747$		0			0
$748$	2.22887e7			0.0532574
$749$	8.32769e8			1.98189
$750$		0			0
$751$			3.51109e8i			0.828938i	0.910063	+	0.414469i	$0.136033\pi$
$751$			3.51109e8i			0.828938i	−0.910063	+	0.414469i	$0.863967\pi$
$752$	−4.30773e7			−0.101297
$753$		0			0
$754$	−5.72468e8			−1.33548
$755$		−	1.54737e8i		−	0.359546i
$756$		0			0
$757$		−	3.44892e8i		−	0.795051i	−0.917591	−	0.397526i	$-0.869869\pi$
$757$		−	3.44892e8i		−	0.795051i	0.917591	−	0.397526i	$-0.130131\pi$
$758$		−	4.04206e8i		−	0.928101i
$759$		0			0
$760$	−7.51079e7			−0.171098
$761$	6.29042e8			1.42733			0.713667	−	0.700485i	$-0.247033\pi$
$761$	6.29042e8			1.42733			0.713667	+	0.700485i	$0.247033\pi$
$762$		0			0
$763$	6.96680e8			1.56841
$764$		−	3.82380e6i		−	0.00857462i
$765$		0			0
$766$			2.39972e8i			0.533918i
$767$	−3.13741e8			−0.695321
$768$		0			0
$769$		−	7.77114e6i		−	0.0170886i	−0.999963	−	0.00854428i	$-0.997280\pi$
$769$		−	7.77114e6i		−	0.0170886i	0.999963	−	0.00854428i	$-0.00271976\pi$
$770$			7.03491e7i			0.154094i
$771$		0			0
$772$	−7.89418e7			−0.171575
$773$			3.82987e8i			0.829174i	0.910010	+	0.414587i	$0.136074\pi$
$773$			3.82987e8i			0.829174i	−0.910010	+	0.414587i	$0.863926\pi$
$774$		0			0
$775$	−1.77901e8			−0.382184
$776$		−	4.16736e8i		−	0.891818i
$777$		0			0
$778$		−	2.18734e8i		−	0.464492i
$779$			1.37773e8i			0.291442i
$780$		0			0
$781$			2.18831e8i			0.459363i
$782$	5.11113e7	+	1.15291e7i	0.106880	+	0.0241088i
$783$		0			0
$784$	−9.14542e7			−0.189782
$785$	1.07795e8			0.222838
$786$		0			0
$787$		−	3.06974e8i		−	0.629763i	−0.949131	−	0.314881i	$-0.898035\pi$
$787$		−	3.06974e8i		−	0.629763i	0.949131	−	0.314881i	$-0.101965\pi$
$788$	−9.66215e7			−0.197467
$789$		0			0
$790$	−4.41733e7			−0.0895940
$791$	−8.16065e8			−1.64890
$792$		0			0
$793$			4.73738e8i			0.949989i
$794$	−2.98623e8			−0.596571
$795$		0			0
$796$			2.73596e8i			0.542464i
$797$		−	8.04892e8i		−	1.58987i	−0.606692	−	0.794937i	$-0.707504\pi$
$797$		−	8.04892e8i		−	1.58987i	0.606692	−	0.794937i	$-0.292496\pi$
$798$		0			0
$799$			1.33814e8i			0.262338i
$800$	4.72371e8			0.922599
$801$		0			0
$802$			2.87266e8i			0.556880i
$803$		−	1.85776e7i		−	0.0358792i
$804$		0			0
$805$	6.74458e7	−	2.99004e8i	0.129291	−	0.573178i
$806$	1.88990e8			0.360938
$807$		0			0
$808$	−1.82787e8			−0.346505
$809$	−6.07169e8			−1.14674			−0.573368	−	0.819298i	$-0.694364\pi$
$809$	−6.07169e8			−1.14674			−0.573368	+	0.819298i	$0.694364\pi$
$810$		0			0
$811$	8.35320e8			1.56600			0.782998	−	0.622025i	$-0.213690\pi$
$811$	8.35320e8			1.56600			0.782998	+	0.622025i	$0.213690\pi$
$812$		−	1.03830e9i		−	1.93934i
$813$		0			0
$814$	−2.25731e8			−0.418521
$815$		−	6.51568e7i		−	0.120361i
$816$		0			0
$817$	−1.83018e8			−0.335604
$818$	−4.05532e8			−0.740910
$819$		0			0
$820$			5.62618e7i			0.102040i
$821$	−3.94342e8			−0.712596			−0.356298	−	0.934372i	$-0.615961\pi$
$821$	−3.94342e8			−0.712596			−0.356298	+	0.934372i	$0.615961\pi$
$822$		0			0
$823$	−3.08910e8			−0.554156			−0.277078	−	0.960847i	$-0.589366\pi$
$823$	−3.08910e8			−0.554156			−0.277078	+	0.960847i	$0.589366\pi$
$824$			6.86733e8i			1.22746i
$825$		0			0
$826$			3.07012e8i			0.544772i
$827$		−	9.23533e7i		−	0.163281i	−0.996662	−	0.0816405i	$-0.973984\pi$
$827$		−	9.23533e7i		−	0.163281i	0.996662	−	0.0816405i	$-0.0260159\pi$
$828$		0			0
$829$	−9.68038e8			−1.69914			−0.849569	−	0.527477i	$-0.823138\pi$
$829$	−9.68038e8			−1.69914			−0.849569	+	0.527477i	$0.823138\pi$
$830$	−1.50607e8			−0.263397
$831$		0			0
$832$	−4.42354e8			−0.768069
$833$			2.84091e8i			0.491499i
$834$		0			0
$835$		−	1.59174e8i		−	0.273409i
$836$	9.58558e7			0.164059
$837$		0			0
$838$		−	2.02545e8i		−	0.344184i
$839$		−	3.10762e8i		−	0.526190i	−0.964770	−	0.263095i	$-0.915257\pi$
$839$		−	3.10762e8i		−	0.526190i	0.964770	−	0.263095i	$-0.0847432\pi$
$840$		0			0
$841$	8.55656e8			1.43851
$842$			6.52116e7i			0.109242i
$843$		0			0
$844$	3.94873e8			0.656795
$845$			2.01554e8i			0.334057i
$846$		0			0
$847$			9.33790e8i			1.53673i
$848$		−	7.44568e7i		−	0.122100i
$849$		0			0
$850$		−	6.09320e7i		−	0.0992176i
$851$	9.59420e8	+	2.16415e8i	1.55675	+	0.351154i
$852$		0			0
$853$	−7.92172e8			−1.27636			−0.638179	−	0.769888i	$-0.720312\pi$
$853$	−7.92172e8			−1.27636			−0.638179	+	0.769888i	$0.720312\pi$
$854$	4.63577e8			0.744300
$855$		0			0
$856$			6.34892e8i			1.01223i
$857$	1.82412e8			0.289809			0.144905	−	0.989446i	$-0.453713\pi$
$857$	1.82412e8			0.289809			0.144905	+	0.989446i	$0.453713\pi$
$858$		0			0
$859$	7.83080e8			1.23545			0.617727	−	0.786393i	$-0.288054\pi$
$859$	7.83080e8			1.23545			0.617727	+	0.786393i	$0.288054\pi$
$860$	−7.47381e7			−0.117502
$861$		0			0
$862$		−	8.36940e7i		−	0.130669i
$863$	2.77850e8			0.432293			0.216147	−	0.976361i	$-0.430651\pi$
$863$	2.77850e8			0.432293			0.216147	+	0.976361i	$0.430651\pi$
$864$		0			0
$865$			1.34070e8i			0.207149i
$866$		−	2.90988e8i		−	0.448045i
$867$		0			0
$868$			3.42774e8i			0.524142i
$869$	1.43168e8			0.218166
$870$		0			0
$871$			1.05093e9i			1.59044i
$872$			5.31139e8i			0.801049i
$873$		0			0
$874$	2.19811e8	+	4.95825e7i	0.329243	+	0.0742667i
$875$	−7.50087e8			−1.11966
$876$		0			0
$877$	−3.26734e8			−0.484390			−0.242195	−	0.970228i	$-0.577867\pi$
$877$	−3.26734e8			−0.484390			−0.242195	+	0.970228i	$0.577867\pi$
$878$	−2.08976e8			−0.308755
$879$		0			0
$880$	6.63034e6			0.00972944
$881$			5.55927e8i			0.812999i	0.913651	+	0.406499i	$0.133251\pi$
$881$			5.55927e8i			0.812999i	−0.913651	+	0.406499i	$0.866749\pi$
$882$		0			0
$883$	−1.18410e8			−0.171991			−0.0859953	−	0.996296i	$-0.527407\pi$
$883$	−1.18410e8			−0.171991			−0.0859953	+	0.996296i	$0.527407\pi$
$884$		−	1.19975e8i		−	0.173674i
$885$		0			0
$886$	−1.86399e8			−0.268005
$887$	6.88323e8			0.986327			0.493164	−	0.869937i	$-0.335840\pi$
$887$	6.88323e8			0.986327			0.493164	+	0.869937i	$0.335840\pi$
$888$		0			0
$889$		−	5.73229e8i		−	0.815873i
$890$	−1.89194e8			−0.268372
$891$		0			0
$892$	4.16103e8			0.586281
$893$			5.75487e8i			0.808130i
$894$		0			0
$895$			1.54643e8i			0.215705i
$896$		−	9.68336e8i		−	1.34618i
$897$		0			0
$898$	4.28131e8			0.591218
$899$	−4.78849e8			−0.659051
$900$		0			0
$901$	−2.31291e8			−0.316216
$902$			9.83814e7i			0.134058i
$903$		0			0
$904$		−	6.22157e8i		−	0.842160i
$905$	−3.49239e8			−0.471169
$906$		0			0
$907$			3.43780e8i			0.460743i	0.973103	+	0.230372i	$0.0739942\pi$
$907$			3.43780e8i			0.460743i	−0.973103	+	0.230372i	$0.926006\pi$
$908$		−	4.42245e8i		−	0.590752i
$909$		0			0
$910$	3.78674e8			0.502506
$911$		−	8.52295e8i		−	1.12729i	−0.826018	−	0.563644i	$-0.809399\pi$
$911$		−	8.52295e8i		−	1.12729i	0.826018	−	0.563644i	$-0.190601\pi$
$912$		0			0
$913$	4.88125e8			0.641385
$914$			2.31418e8i			0.303080i
$915$		0			0
$916$		−	6.51617e8i		−	0.847824i
$917$			1.19051e9i			1.54393i
$918$		0			0
$919$			1.19920e9i			1.54505i	0.634982	+	0.772527i	$0.281008\pi$
$919$			1.19920e9i			1.54505i	−0.634982	+	0.772527i	$0.718992\pi$
$920$	2.27957e8	+	5.14198e7i	0.292744	+	0.0660339i
$921$		0			0
$922$	2.43187e8			0.310276
$923$	1.17792e9			1.49800
$924$		0			0
$925$		−	1.14377e9i		−	1.44515i
$926$	−4.33720e8			−0.546231
$927$		0			0
$928$	1.27146e9			1.59096
$929$	−1.19275e8			−0.148765			−0.0743825	−	0.997230i	$-0.523699\pi$
$929$	−1.19275e8			−0.148765			−0.0743825	+	0.997230i	$0.523699\pi$
$930$		0			0
$931$			1.22177e9i			1.51406i
$932$	−7.29189e8			−0.900725
$933$		0			0
$934$			7.81728e8i			0.959434i
$935$		−	2.05963e7i		−	0.0251973i
$936$		0			0
$937$			4.74435e8i			0.576711i	0.957523	+	0.288356i	$0.0931085\pi$
$937$			4.74435e8i			0.576711i	−0.957523	+	0.288356i	$0.906891\pi$
$938$	1.02839e9			1.24609
$939$		0			0
$940$			2.35009e8i			0.282944i
$941$		−	1.43051e9i		−	1.71681i	−0.512975	−	0.858404i	$-0.671457\pi$
$941$		−	1.43051e9i		−	1.71681i	0.512975	−	0.858404i	$-0.328543\pi$
$942$		0			0
$943$	9.43212e7	−	4.18149e8i	0.112480	−	0.498650i
$944$	2.89356e7			0.0343967
$945$		0			0
$946$	−1.30690e8			−0.154372
$947$	−5.63569e8			−0.663586			−0.331793	−	0.943352i	$-0.607654\pi$
$947$	−5.63569e8			−0.663586			−0.331793	+	0.943352i	$0.607654\pi$
$948$		0			0
$949$	−9.99992e7			−0.117003
$950$		−	2.62047e8i		−	0.305639i
$951$		0			0
$952$	−2.98146e8			−0.345556
$953$			1.28750e9i			1.48754i	0.668433	+	0.743772i	$0.266965\pi$
$953$			1.28750e9i			1.48754i	−0.668433	+	0.743772i	$0.733035\pi$
$954$		0			0
$955$	−3.53345e6			−0.00405685
$956$	7.34764e8			0.840958
$957$		0			0
$958$			2.42785e8i			0.276137i
$959$	−1.76572e8			−0.200201
$960$		0			0
$961$	−7.29421e8			−0.821879
$962$			1.21506e9i			1.36481i
$963$		0			0
$964$			7.26220e8i			0.810657i
$965$			7.29477e7i			0.0811763i
$966$		0			0
$967$	−1.14839e9			−1.27002			−0.635010	−	0.772504i	$-0.719004\pi$
$967$	−1.14839e9			−1.27002			−0.635010	+	0.772504i	$0.719004\pi$
$968$	−7.11909e8			−0.784871
$969$		0			0
$970$	−1.51640e8			−0.166149
$971$		−	7.06658e8i		−	0.771883i	−0.922523	−	0.385942i	$-0.873877\pi$
$971$		−	7.06658e8i		−	0.771883i	0.922523	−	0.385942i	$-0.126123\pi$
$972$		0			0
$973$		−	6.66244e8i		−	0.723261i
$974$	4.77626e8			0.516905
$975$		0			0
$976$		−	4.36917e7i		−	0.0469948i
$977$		−	3.80874e8i		−	0.408411i	−0.978928	−	0.204206i	$-0.934539\pi$
$977$		−	3.80874e8i		−	0.408411i	0.978928	−	0.204206i	$-0.0654611\pi$
$978$		0			0
$979$	6.13186e8			0.653498
$980$			4.98930e8i			0.530104i
$981$		0			0
$982$	−2.02933e8			−0.214298
$983$			1.51176e9i			1.59155i	0.605590	+	0.795777i	$0.292937\pi$
$983$			1.51176e9i			1.59155i	−0.605590	+	0.795777i	$0.707063\pi$
$984$		0			0
$985$			8.92849e7i			0.0934264i
$986$		−	1.64008e8i		−	0.171094i
$987$		0			0
$988$		−	5.15971e8i		−	0.535001i
$989$	5.55469e8	+	1.25296e8i	0.574210	+	0.129524i
$990$		0			0
$991$	4.20133e8			0.431684			0.215842	−	0.976428i	$-0.430750\pi$
$991$	4.20133e8			0.431684			0.215842	+	0.976428i	$0.430750\pi$
$992$	−4.19749e8			−0.429987
$993$		0			0
$994$		−	1.15266e9i		−	1.17365i
$995$	2.52822e8			0.256652
$996$		0			0
$997$	−3.88505e8			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$997$	−3.88505e8			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$998$	1.15338e9			1.16033
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.16		24
3.2	odd	2		69.7.d.a.22.9	✓	24
23.22	odd	2	inner	207.7.d.e.91.15		24
69.68	even	2		69.7.d.a.22.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.9	✓	24	3.2	odd	2
69.7.d.a.22.10	yes	24	69.68	even	2
207.7.d.e.91.15		24	23.22	odd	2	inner
207.7.d.e.91.16		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.73591 q^{2} -41.5712 q^{4} +38.4146i q^{5} +655.803i q^{7} -499.975 q^{8} +O(q^{10})\)	\(q+4.73591 q^{2} -41.5712 q^{4} +38.4146i q^{5} +655.803i q^{7} -499.975 q^{8} +181.928i q^{10} -589.638i q^{11} -3173.89 q^{13} +3105.82i q^{14} +292.721 q^{16} -909.300i q^{17} -3910.57i q^{19} -1596.94i q^{20} -2792.47i q^{22} +(-2677.23 + 11868.8i) q^{23} +14149.3 q^{25} -15031.3 q^{26} -27262.5i q^{28} +38085.2 q^{29} -12573.1 q^{31} +33384.7 q^{32} -4306.36i q^{34} -25192.4 q^{35} -80835.5i q^{37} -18520.1i q^{38} -19206.4i q^{40} -35231.0 q^{41} -46800.8i q^{43} +24512.0i q^{44} +(-12679.1 + 56209.5i) q^{46} -147162. q^{47} -312428. q^{49} +67009.8 q^{50} +131943. q^{52} -254361. i q^{53} +22650.7 q^{55} -327885. i q^{56} +180368. q^{58} +98850.5 q^{59} -149261. i q^{61} -59545.0 q^{62} +139373. q^{64} -121924. i q^{65} -331116. i q^{67} +37800.7i q^{68} -119309. q^{70} -371128. q^{71} +31506.8 q^{73} -382829. i q^{74} +162567. i q^{76} +386686. q^{77} +242806. i q^{79} +11244.8i q^{80} -166851. q^{82} +827839. i q^{83} +34930.4 q^{85} -221644. i q^{86} +294804. i q^{88} +1.03994e6i q^{89} -2.08145e6i q^{91} +(111295. - 493400. i) q^{92} -696944. q^{94} +150223. q^{95} +833514. i q^{97} -1.47963e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

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