LMFDB - Embedded newform 207.7.d.e.91.7

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			91.7
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.36312 q^{2} -23.5107 q^{4} -60.2242i q^{5} +233.613i q^{7} +556.841 q^{8} +O(q^{10})$	\(q-6.36312 q^{2} -23.5107 q^{4} -60.2242i q^{5} +233.613i q^{7} +556.841 q^{8} +383.214i q^{10} -1397.49i q^{11} -1285.15 q^{13} -1486.51i q^{14} -2038.57 q^{16} -2821.93i q^{17} +10185.1i q^{19} +1415.91i q^{20} +8892.40i q^{22} +(3980.90 + 11497.3i) q^{23} +11998.1 q^{25} +8177.54 q^{26} -5492.39i q^{28} -5523.92 q^{29} -27306.5 q^{31} -22666.2 q^{32} +17956.3i q^{34} +14069.1 q^{35} +39765.7i q^{37} -64809.3i q^{38} -33535.3i q^{40} +18455.9 q^{41} -30920.7i q^{43} +32855.9i q^{44} +(-25330.9 - 73158.9i) q^{46} -62793.6 q^{47} +63074.0 q^{49} -76345.1 q^{50} +30214.6 q^{52} +56165.6i q^{53} -84162.6 q^{55} +130085. i q^{56} +35149.4 q^{58} +159966. q^{59} -333535. i q^{61} +173755. q^{62} +274696. q^{64} +77396.8i q^{65} -244298. i q^{67} +66345.4i q^{68} -89523.7 q^{70} -437275. q^{71} +494935. q^{73} -253034. i q^{74} -239459. i q^{76} +326471. q^{77} -571913. i q^{79} +122771. i q^{80} -117437. q^{82} -720923. i q^{83} -169948. q^{85} +196752. i q^{86} -778179. i q^{88} -785492. i q^{89} -300226. i q^{91} +(-93593.5 - 270310. i) q^{92} +399563. q^{94} +613392. q^{95} -274434. i q^{97} -401348. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.36312			−0.795390			−0.397695	−	0.917518i	$-0.630190\pi$
$2$	−6.36312			−0.795390			−0.397695	+	0.917518i	$0.630190\pi$
$3$		0			0
$3$		0			0
$4$	−23.5107			−0.367354
$5$		−	60.2242i		−	0.481793i	−0.970551	−	0.240897i	$-0.922559\pi$
$5$		−	60.2242i		−	0.481793i	0.970551	−	0.240897i	$-0.0774415\pi$
$6$		0			0
$7$			233.613i			0.681087i	0.940229	+	0.340544i	$0.110611\pi$
$7$			233.613i			0.681087i	−0.940229	+	0.340544i	$0.889389\pi$
$8$	556.841			1.08758
$9$		0			0
$10$			383.214i			0.383214i
$11$		−	1397.49i		−	1.04995i	−0.851116	−	0.524977i	$-0.824074\pi$
$11$		−	1397.49i		−	1.04995i	0.851116	−	0.524977i	$-0.175926\pi$
$12$		0			0
$13$	−1285.15			−0.584955			−0.292477	−	0.956272i	$-0.594480\pi$
$13$	−1285.15			−0.584955			−0.292477	+	0.956272i	$0.594480\pi$
$14$		−	1486.51i		−	0.541730i
$15$		0			0
$16$	−2038.57			−0.497697
$17$		−	2821.93i		−	0.574379i	−0.957874	−	0.287190i	$-0.907279\pi$
$17$		−	2821.93i		−	0.574379i	0.957874	−	0.287190i	$-0.0927210\pi$
$18$		0			0
$19$			10185.1i			1.48493i	0.669884	+	0.742466i	$0.266344\pi$
$19$			10185.1i			1.48493i	−0.669884	+	0.742466i	$0.733656\pi$
$20$			1415.91i			0.176989i
$21$		0			0
$22$			8892.40i			0.835123i
$23$	3980.90	+	11497.3i	0.327188	+	0.944959i
$23$	3980.90	+	11497.3i	0.327188	+	0.944959i
$24$		0			0
$25$	11998.1			0.767875
$26$	8177.54			0.465267
$27$		0			0
$28$		−	5492.39i		−	0.250200i
$29$	−5523.92			−0.226492			−0.113246	−	0.993567i	$-0.536125\pi$
$29$	−5523.92			−0.226492			−0.113246	+	0.993567i	$0.536125\pi$
$30$		0			0
$31$	−27306.5			−0.916603			−0.458301	−	0.888797i	$-0.651542\pi$
$31$	−27306.5			−0.916603			−0.458301	+	0.888797i	$0.651542\pi$
$32$	−22666.2			−0.691717
$33$		0			0
$34$			17956.3i			0.456856i
$35$	14069.1			0.328143
$36$		0			0
$37$			39765.7i			0.785060i	0.919739	+	0.392530i	$0.128400\pi$
$37$			39765.7i			0.785060i	−0.919739	+	0.392530i	$0.871600\pi$
$38$		−	64809.3i		−	1.18110i
$39$		0			0
$40$		−	33535.3i		−	0.523989i
$41$	18455.9			0.267784			0.133892	−	0.990996i	$-0.457252\pi$
$41$	18455.9			0.267784			0.133892	+	0.990996i	$0.457252\pi$
$42$		0			0
$43$		−	30920.7i		−	0.388906i	−0.980912	−	0.194453i	$-0.937707\pi$
$43$		−	30920.7i		−	0.388906i	0.980912	−	0.194453i	$-0.0622931\pi$
$44$			32855.9i			0.385705i
$45$		0			0
$46$	−25330.9	−	73158.9i	−0.260242	−	0.751612i
$47$	−62793.6			−0.604814			−0.302407	−	0.953179i	$-0.597790\pi$
$47$	−62793.6			−0.604814			−0.302407	+	0.953179i	$0.597790\pi$
$48$		0			0
$49$	63074.0			0.536120
$50$	−76345.1			−0.610761
$51$		0			0
$52$	30214.6			0.214885
$53$			56165.6i			0.377262i	0.982048	+	0.188631i	$0.0604050\pi$
$53$			56165.6i			0.377262i	−0.982048	+	0.188631i	$0.939595\pi$
$54$		0			0
$55$	−84162.6			−0.505861
$56$			130085.i			0.740737i
$57$		0			0
$58$	35149.4			0.180150
$59$	159966.			0.778880			0.389440	−	0.921052i	$-0.372669\pi$
$59$	159966.			0.778880			0.389440	+	0.921052i	$0.372669\pi$
$60$		0			0
$61$		−	333535.i		−	1.46944i	−0.678372	−	0.734719i	$-0.737314\pi$
$61$		−	333535.i		−	1.46944i	0.678372	−	0.734719i	$-0.262686\pi$
$62$	173755.			0.729057
$63$		0			0
$64$	274696.			1.04788
$65$			77396.8i			0.281827i
$66$		0			0
$67$		−	244298.i		−	0.812260i	−0.913815	−	0.406130i	$-0.866878\pi$
$67$		−	244298.i		−	0.812260i	0.913815	−	0.406130i	$-0.133122\pi$
$68$			66345.4i			0.211001i
$69$		0			0
$70$	−89523.7			−0.261002
$71$	−437275.			−1.22174			−0.610871	−	0.791731i	$-0.709180\pi$
$71$	−437275.			−1.22174			−0.610871	+	0.791731i	$0.709180\pi$
$72$		0			0
$73$	494935.			1.27227			0.636135	−	0.771578i	$-0.280532\pi$
$73$	494935.			1.27227			0.636135	+	0.771578i	$0.280532\pi$
$74$		−	253034.i		−	0.624429i
$75$		0			0
$76$		−	239459.i		−	0.545496i
$77$	326471.			0.715110
$78$		0			0
$79$		−	571913.i		−	1.15998i	−0.814625	−	0.579988i	$-0.803057\pi$
$79$		−	571913.i		−	1.15998i	0.814625	−	0.579988i	$-0.196943\pi$
$80$			122771.i			0.239787i
$81$		0			0
$82$	−117437.			−0.212993
$83$		−	720923.i		−	1.26082i	−0.776261	−	0.630412i	$-0.782886\pi$
$83$		−	720923.i		−	1.26082i	0.776261	−	0.630412i	$-0.217114\pi$
$84$		0			0
$85$	−169948.			−0.276732
$86$			196752.i			0.309332i
$87$		0			0
$88$		−	778179.i		−	1.14191i
$89$		−	785492.i		−	1.11422i	−0.830438	−	0.557111i	$-0.811910\pi$
$89$		−	785492.i		−	1.11422i	0.830438	−	0.557111i	$-0.188090\pi$
$90$		0			0
$91$		−	300226.i		−	0.398405i
$92$	−93593.5	−	270310.i	−0.120194	−	0.347135i
$93$		0			0
$94$	399563.			0.481063
$95$	613392.			0.715430
$96$		0			0
$97$		−	274434.i		−	0.300692i	−0.988633	−	0.150346i	$-0.951961\pi$
$97$		−	274434.i		−	0.300692i	0.988633	−	0.150346i	$-0.0480388\pi$
$98$	−401348.			−0.426425
$99$		0			0
$100$	−282082.			−0.282082
$101$	999436.			0.970043			0.485021	−	0.874502i	$-0.338812\pi$
$101$	999436.			0.970043			0.485021	+	0.874502i	$0.338812\pi$
$102$		0			0
$103$			359691.i			0.329168i	0.986363	+	0.164584i	$0.0526282\pi$
$103$			359691.i			0.329168i	−0.986363	+	0.164584i	$0.947372\pi$
$104$	−715622.			−0.636185
$105$		0			0
$106$		−	357389.i		−	0.300070i
$107$		−	2.15412e6i		−	1.75841i	−0.476447	−	0.879203i	$-0.658076\pi$
$107$		−	2.15412e6i		−	1.75841i	0.476447	−	0.879203i	$-0.341924\pi$
$108$		0			0
$109$			1.90465e6i			1.47074i	0.677668	+	0.735368i	$0.262991\pi$
$109$			1.90465e6i			1.47074i	−0.677668	+	0.735368i	$0.737009\pi$
$110$	535537.			0.402357
$111$		0			0
$112$		−	476235.i		−	0.338975i
$113$		−	2.60669e6i		−	1.80657i	−0.429041	−	0.903285i	$-0.641149\pi$
$113$		−	2.60669e6i		−	1.80657i	0.429041	−	0.903285i	$-0.358851\pi$
$114$		0			0
$115$	692416.	−	239746.i	0.455275	−	0.157637i
$116$	129871.			0.0832028
$117$		0			0
$118$	−1.01788e6			−0.619514
$119$	659238.			0.391202
$120$		0			0
$121$	−181415.			−0.102404
$122$			2.12232e6i			1.16878i
$123$		0			0
$124$	641994.			0.336718
$125$		−	1.66357e6i		−	0.851750i
$126$		0			0
$127$	1.00672e6			0.491473			0.245736	−	0.969337i	$-0.420970\pi$
$127$	1.00672e6			0.491473			0.245736	+	0.969337i	$0.420970\pi$
$128$	−297289.			−0.141758
$129$		0			0
$130$		−	492485.i		−	0.224163i
$131$	1.48663e6			0.661284			0.330642	−	0.943756i	$-0.392735\pi$
$131$	1.48663e6			0.661284			0.330642	+	0.943756i	$0.392735\pi$
$132$		0			0
$133$	−2.37938e6			−1.01137
$134$			1.55450e6i			0.646064i
$135$		0			0
$136$		−	1.57136e6i		−	0.624684i
$137$			933505.i			0.363041i	0.983387	+	0.181520i	$0.0581018\pi$
$137$			933505.i			0.363041i	−0.983387	+	0.181520i	$0.941898\pi$
$138$		0			0
$139$	2.57479e6			0.958734			0.479367	−	0.877615i	$-0.340866\pi$
$139$	2.57479e6			0.958734			0.479367	+	0.877615i	$0.340866\pi$
$140$	−330775.			−0.120545
$141$		0			0
$142$	2.78243e6			0.971761
$143$			1.79598e6i			0.614176i
$144$		0			0
$145$			332673.i			0.109122i
$146$	−3.14933e6			−1.01195
$147$		0			0
$148$		−	934917.i		−	0.288395i
$149$			665234.i			0.201102i	0.994932	+	0.100551i	$0.0320605\pi$
$149$			665234.i			0.201102i	−0.994932	+	0.100551i	$0.967940\pi$
$150$		0			0
$151$	−385234.			−0.111891			−0.0559453	−	0.998434i	$-0.517817\pi$
$151$	−385234.			−0.111891			−0.0559453	+	0.998434i	$0.517817\pi$
$152$			5.67151e6i			1.61498i
$153$		0			0
$154$	−2.07738e6			−0.568792
$155$			1.64451e6i			0.441613i
$156$		0			0
$157$		−	2.55515e6i		−	0.660263i	−0.943935	−	0.330132i	$-0.892907\pi$
$157$		−	2.55515e6i		−	0.660263i	0.943935	−	0.330132i	$-0.107093\pi$
$158$			3.63916e6i			0.922634i
$159$		0			0
$160$			1.36505e6i			0.333265i
$161$	−2.68592e6	+	929989.i	−0.643599	+	0.222844i
$162$		0			0
$163$	−4.76008e6			−1.09914			−0.549568	−	0.835449i	$-0.685208\pi$
$163$	−4.76008e6			−1.09914			−0.549568	+	0.835449i	$0.685208\pi$
$164$	−433911.			−0.0983715
$165$		0			0
$166$			4.58732e6i			1.00285i
$167$	−3.47396e6			−0.745892			−0.372946	−	0.927853i	$-0.621652\pi$
$167$	−3.47396e6			−0.745892			−0.372946	+	0.927853i	$0.621652\pi$
$168$		0			0
$169$	−3.17521e6			−0.657828
$170$	1.08140e6			0.220110
$171$		0			0
$172$			726967.i			0.142866i
$173$	−3.58125e6			−0.691666			−0.345833	−	0.938296i	$-0.612404\pi$
$173$	−3.58125e6			−0.691666			−0.345833	+	0.938296i	$0.612404\pi$
$174$		0			0
$175$			2.80290e6i			0.522990i
$176$			2.84887e6i			0.522559i
$177$		0			0
$178$			4.99818e6i			0.886242i
$179$	1.81514e6			0.316483			0.158241	−	0.987400i	$-0.449418\pi$
$179$	1.81514e6			0.316483			0.158241	+	0.987400i	$0.449418\pi$
$180$		0			0
$181$			5.36160e6i			0.904188i	0.891970	+	0.452094i	$0.149323\pi$
$181$			5.36160e6i			0.904188i	−0.891970	+	0.452094i	$0.850677\pi$
$182$			1.91038e6i			0.316888i
$183$		0			0
$184$	2.21673e6	+	6.40218e6i	0.355843	+	1.02772i
$185$	2.39485e6			0.378237
$186$		0			0
$187$	−3.94361e6			−0.603072
$188$	1.47632e6			0.222181
$189$		0			0
$190$	−3.90309e6			−0.569046
$191$		−	6.26268e6i		−	0.898794i	−0.893332	−	0.449397i	$-0.851639\pi$
$191$		−	6.26268e6i		−	0.898794i	0.893332	−	0.449397i	$-0.148361\pi$
$192$		0			0
$193$	1.28599e7			1.78882			0.894408	−	0.447252i	$-0.147597\pi$
$193$	1.28599e7			1.78882			0.894408	+	0.447252i	$0.147597\pi$
$194$			1.74626e6i			0.239168i
$195$		0			0
$196$	−1.48291e6			−0.196946
$197$	−9.53336e6			−1.24694			−0.623472	−	0.781845i	$-0.714279\pi$
$197$	−9.53336e6			−1.24694			−0.623472	+	0.781845i	$0.714279\pi$
$198$		0			0
$199$		−	1.75998e6i		−	0.223331i	−0.993746	−	0.111665i	$-0.964382\pi$
$199$		−	1.75998e6i		−	0.223331i	0.993746	−	0.111665i	$-0.0356185\pi$
$200$	6.68101e6			0.835126
$201$		0			0
$202$	−6.35954e6			−0.771563
$203$		−	1.29046e6i		−	0.154261i
$204$		0			0
$205$		−	1.11149e6i		−	0.129017i
$206$		−	2.28876e6i		−	0.261817i
$207$		0			0
$208$	2.61985e6			0.291130
$209$	1.42336e7			1.55911
$210$		0			0
$211$	−1.02042e6			−0.108626			−0.0543128	−	0.998524i	$-0.517297\pi$
$211$	−1.02042e6			−0.108626			−0.0543128	+	0.998524i	$0.517297\pi$
$212$		−	1.32049e6i		−	0.138589i
$213$		0			0
$214$			1.37069e7i			1.39862i
$215$	−1.86218e6			−0.187372
$216$		0			0
$217$		−	6.37915e6i		−	0.624286i
$218$		−	1.21195e7i		−	1.16981i
$219$		0			0
$220$	1.97872e6			0.185830
$221$			3.62659e6i			0.335986i
$222$		0			0
$223$	−5.16861e6			−0.466078			−0.233039	−	0.972467i	$-0.574867\pi$
$223$	−5.16861e6			−0.466078			−0.233039	+	0.972467i	$0.574867\pi$
$224$		−	5.29511e6i		−	0.471119i
$225$		0			0
$226$			1.65867e7i			1.43693i
$227$			7.01786e6i			0.599967i	0.953944	+	0.299983i	$0.0969812\pi$
$227$			7.01786e6i			0.599967i	−0.953944	+	0.299983i	$0.903019\pi$
$228$		0			0
$229$		−	1.15614e7i		−	0.962731i	−0.876520	−	0.481366i	$-0.840141\pi$
$229$		−	1.15614e7i		−	0.962731i	0.876520	−	0.481366i	$-0.159859\pi$
$230$	−4.40593e6	+	1.52553e6i	−0.362121	+	0.125383i
$231$		0			0
$232$	−3.07594e6			−0.246328
$233$	1.34263e7			1.06143			0.530713	−	0.847552i	$-0.321924\pi$
$233$	1.34263e7			1.06143			0.530713	+	0.847552i	$0.321924\pi$
$234$		0			0
$235$			3.78169e6i			0.291395i
$236$	−3.76090e6			−0.286125
$237$		0			0
$238$	−4.19481e6			−0.311159
$239$	−7.65228e6			−0.560528			−0.280264	−	0.959923i	$-0.590422\pi$
$239$	−7.65228e6			−0.560528			−0.280264	+	0.959923i	$0.590422\pi$
$240$		0			0
$241$		−	9.36770e6i		−	0.669240i	−0.942353	−	0.334620i	$-0.891392\pi$
$241$		−	9.36770e6i		−	0.669240i	0.942353	−	0.334620i	$-0.108608\pi$
$242$	1.15436e6			0.0814510
$243$		0			0
$244$			7.84162e6i			0.539804i
$245$		−	3.79858e6i		−	0.258299i
$246$		0			0
$247$		−	1.30894e7i		−	0.868618i
$248$	−1.52054e7			−0.996879
$249$		0			0
$250$			1.05855e7i			0.677474i
$251$			109973.i			0.00695448i	0.999994	+	0.00347724i	$0.00110684\pi$
$251$			109973.i			0.00695448i	−0.999994	+	0.00347724i	$0.998893\pi$
$252$		0			0
$253$	1.60674e7	−	5.56326e6i	0.992164	−	0.343533i
$254$	−6.40591e6			−0.390913
$255$		0			0
$256$	−1.56889e7			−0.935129
$257$	−5.24170e6			−0.308797			−0.154398	−	0.988009i	$-0.549344\pi$
$257$	−5.24170e6			−0.308797			−0.154398	+	0.988009i	$0.549344\pi$
$258$		0			0
$259$	−9.28977e6			−0.534694
$260$		−	1.81965e6i		−	0.103530i
$261$		0			0
$262$	−9.45959e6			−0.525979
$263$		−	2.01529e7i		−	1.10782i	−0.832576	−	0.553911i	$-0.813135\pi$
$263$		−	2.01529e7i		−	1.10782i	0.832576	−	0.553911i	$-0.186865\pi$
$264$		0			0
$265$	3.38253e6			0.181762
$266$	1.51403e7			0.804432
$267$		0			0
$268$			5.74360e6i			0.298387i
$269$	3.23774e7			1.66336			0.831678	−	0.555258i	$-0.187380\pi$
$269$	3.23774e7			1.66336			0.831678	+	0.555258i	$0.187380\pi$
$270$		0			0
$271$	1.93637e7			0.972929			0.486465	−	0.873700i	$-0.338286\pi$
$271$	1.93637e7			0.972929			0.486465	+	0.873700i	$0.338286\pi$
$272$			5.75268e6i			0.285867i
$273$		0			0
$274$		−	5.94001e6i		−	0.288759i
$275$		−	1.67671e7i		−	0.806234i
$276$		0			0
$277$	3.05629e7			1.43799			0.718994	−	0.695016i	$-0.244603\pi$
$277$	3.05629e7			1.43799			0.718994	+	0.695016i	$0.244603\pi$
$278$	−1.63837e7			−0.762568
$279$		0			0
$280$	7.83427e6			0.356882
$281$			1.20980e7i			0.545249i	0.962120	+	0.272625i	$0.0878917\pi$
$281$			1.20980e7i			0.545249i	−0.962120	+	0.272625i	$0.912108\pi$
$282$		0			0
$283$		−	3.45135e7i		−	1.52275i	−0.648310	−	0.761377i	$-0.724524\pi$
$283$		−	3.45135e7i		−	1.52275i	0.648310	−	0.761377i	$-0.275476\pi$
$284$	1.02806e7			0.448812
$285$		0			0
$286$		−	1.14280e7i		−	0.488509i
$287$			4.31154e6i			0.182384i
$288$		0			0
$289$	1.61743e7			0.670088
$290$		−	2.11684e6i		−	0.0867949i
$291$		0			0
$292$	−1.16362e7			−0.467373
$293$			3.33872e7i			1.32733i	0.748032	+	0.663663i	$0.230999\pi$
$293$			3.33872e7i			1.32733i	−0.748032	+	0.663663i	$0.769001\pi$
$294$		0			0
$295$		−	9.63379e6i		−	0.375259i
$296$			2.21432e7i			0.853816i
$297$		0			0
$298$		−	4.23296e6i		−	0.159954i
$299$	−5.11603e6	−	1.47757e7i	−0.191390	−	0.552758i
$300$		0			0
$301$	7.22348e6			0.264879
$302$	2.45129e6			0.0889968
$303$		0			0
$304$		−	2.07631e7i		−	0.739046i
$305$	−2.00868e7			−0.707965
$306$		0			0
$307$	−5.47778e7			−1.89317			−0.946585	−	0.322455i	$-0.895492\pi$
$307$	−5.47778e7			−1.89317			−0.946585	+	0.322455i	$0.895492\pi$
$308$	−7.67556e6			−0.262699
$309$		0			0
$310$		−	1.04642e7i		−	0.351255i
$311$	−2.86189e7			−0.951418			−0.475709	−	0.879603i	$-0.657808\pi$
$311$	−2.86189e7			−0.951418			−0.475709	+	0.879603i	$0.657808\pi$
$312$		0			0
$313$		−	3.59059e7i		−	1.17094i	−0.810695	−	0.585468i	$-0.800911\pi$
$313$		−	3.59059e7i		−	1.17094i	0.810695	−	0.585468i	$-0.199089\pi$
$314$			1.62587e7i			0.525167i
$315$		0			0
$316$			1.34461e7i			0.426122i
$317$	−3.22286e7			−1.01173			−0.505865	−	0.862613i	$-0.668826\pi$
$317$	−3.22286e7			−1.01173			−0.505865	+	0.862613i	$0.668826\pi$
$318$		0			0
$319$			7.71962e6i			0.237806i
$320$		−	1.65433e7i		−	0.504862i
$321$		0			0
$322$	1.70908e7	−	5.91763e6i	0.511913	−	0.177248i
$323$	2.87417e7			0.852914
$324$		0			0
$325$	−1.54192e7			−0.449172
$326$	3.02890e7			0.874242
$327$		0			0
$328$	1.02770e7			0.291237
$329$		−	1.46694e7i		−	0.411931i
$330$		0			0
$331$	3.35391e7			0.924842			0.462421	−	0.886661i	$-0.346981\pi$
$331$	3.35391e7			0.924842			0.462421	+	0.886661i	$0.346981\pi$
$332$			1.69494e7i			0.463169i
$333$		0			0
$334$	2.21053e7			0.593275
$335$	−1.47126e7			−0.391341
$336$		0			0
$337$		−	5.76754e7i		−	1.50696i	−0.657472	−	0.753479i	$-0.728374\pi$
$337$		−	5.76754e7i		−	1.50696i	0.657472	−	0.753479i	$-0.271626\pi$
$338$	2.02043e7			0.523230
$339$		0			0
$340$	3.99559e6			0.101659
$341$			3.81606e7i			0.962391i
$342$		0			0
$343$			4.22192e7i			1.04623i
$344$		−	1.72179e7i		−	0.422966i
$345$		0			0
$346$	2.27879e7			0.550144
$347$	2.70139e7			0.646545			0.323272	−	0.946306i	$-0.395217\pi$
$347$	2.70139e7			0.646545			0.323272	+	0.946306i	$0.395217\pi$
$348$		0			0
$349$	3.28000e6			0.0771609			0.0385804	−	0.999255i	$-0.487716\pi$
$349$	3.28000e6			0.0771609			0.0385804	+	0.999255i	$0.487716\pi$
$350$		−	1.78352e7i		−	0.415981i
$351$		0			0
$352$			3.16757e7i			0.726271i
$353$	4.41288e7			1.00323			0.501613	−	0.865092i	$-0.332740\pi$
$353$	4.41288e7			1.00323			0.501613	+	0.865092i	$0.332740\pi$
$354$		0			0
$355$			2.63345e7i			0.588627i
$356$			1.84674e7i			0.409314i
$357$		0			0
$358$	−1.15499e7			−0.251728
$359$		−	3.84523e7i		−	0.831073i	−0.909576	−	0.415537i	$-0.863594\pi$
$359$		−	3.84523e7i		−	0.831073i	0.909576	−	0.415537i	$-0.136406\pi$
$360$		0			0
$361$	−5.66913e7			−1.20502
$362$		−	3.41165e7i		−	0.719182i
$363$		0			0
$364$			7.05852e6i			0.146356i
$365$		−	2.98070e7i		−	0.612971i
$366$		0			0
$367$			1.90097e7i			0.384571i	0.981339	+	0.192286i	$0.0615900\pi$
$367$			1.90097e7i			0.384571i	−0.981339	+	0.192286i	$0.938410\pi$
$368$	−8.11533e6	−	2.34380e7i	−0.162841	−	0.470303i
$369$		0			0
$370$	−1.52387e7			−0.300846
$371$	−1.31210e7			−0.256948
$372$		0			0
$373$		−	6.82339e7i		−	1.31484i	−0.753523	−	0.657421i	$-0.771647\pi$
$373$		−	6.82339e7i		−	1.31484i	0.753523	−	0.657421i	$-0.228353\pi$
$374$	2.50937e7			0.479678
$375$		0			0
$376$	−3.49660e7			−0.657783
$377$	7.09904e6			0.132488
$378$		0			0
$379$			5.18792e7i			0.952961i	0.879185	+	0.476481i	$0.158088\pi$
$379$			5.18792e7i			0.952961i	−0.879185	+	0.476481i	$0.841912\pi$
$380$	−1.44212e7			−0.262816
$381$		0			0
$382$			3.98502e7i			0.714892i
$383$		−	1.02080e8i		−	1.81696i	−0.417931	−	0.908479i	$-0.637245\pi$
$383$		−	1.02080e8i		−	1.81696i	0.417931	−	0.908479i	$-0.362755\pi$
$384$		0			0
$385$		−	1.96615e7i		−	0.344535i
$386$	−8.18291e7			−1.42281
$387$		0			0
$388$			6.45212e6i			0.110461i
$389$		−	2.97488e7i		−	0.505383i	−0.967547	−	0.252691i	$-0.918684\pi$
$389$		−	2.97488e7i		−	0.505383i	0.967547	−	0.252691i	$-0.0813157\pi$
$390$		0			0
$391$	3.24446e7	−	1.12338e7i	0.542765	−	0.187930i
$392$	3.51222e7			0.583074
$393$		0			0
$394$	6.06619e7			0.991808
$395$	−3.44430e7			−0.558869
$396$		0			0
$397$	−5.08435e6			−0.0812576			−0.0406288	−	0.999174i	$-0.512936\pi$
$397$	−5.08435e6			−0.0812576			−0.0406288	+	0.999174i	$0.512936\pi$
$398$			1.11990e7i			0.177635i
$399$		0			0
$400$	−2.44588e7			−0.382169
$401$			8.46941e7i			1.31347i	0.754122	+	0.656735i	$0.228063\pi$
$401$			8.46941e7i			1.31347i	−0.754122	+	0.656735i	$0.771937\pi$
$402$		0			0
$403$	3.50928e7			0.536171
$404$	−2.34974e7			−0.356349
$405$		0			0
$406$			8.21134e6i			0.122698i
$407$	5.55721e7			0.824277
$408$		0			0
$409$	1.01530e7			0.148397			0.0741985	−	0.997243i	$-0.476360\pi$
$409$	1.01530e7			0.148397			0.0741985	+	0.997243i	$0.476360\pi$
$410$			7.07257e6i			0.102618i
$411$		0			0
$412$		−	8.45657e6i		−	0.120921i
$413$			3.73700e7i			0.530485i
$414$		0			0
$415$	−4.34170e7			−0.607456
$416$	2.91293e7			0.404623
$417$		0			0
$418$	−9.05703e7			−1.24010
$419$		−	2.98259e7i		−	0.405464i	−0.979234	−	0.202732i	$-0.935018\pi$
$419$		−	2.98259e7i		−	0.405464i	0.979234	−	0.202732i	$-0.0649820\pi$
$420$		0			0
$421$		−	8.63872e7i		−	1.15772i	−0.815427	−	0.578860i	$-0.803498\pi$
$421$		−	8.63872e7i		−	1.15772i	0.815427	−	0.578860i	$-0.196502\pi$
$422$	6.49306e6			0.0863997
$423$		0			0
$424$			3.12753e7i			0.410303i
$425$		−	3.38576e7i		−	0.441052i
$426$		0			0
$427$	7.79179e7			1.00082
$428$			5.06449e7i			0.645958i
$429$		0			0
$430$	1.18492e7			0.149034
$431$			4.07286e7i			0.508707i	0.967111	+	0.254353i	$0.0818626\pi$
$431$			4.07286e7i			0.508707i	−0.967111	+	0.254353i	$0.918137\pi$
$432$		0			0
$433$			1.05183e8i			1.29563i	0.761798	+	0.647814i	$0.224317\pi$
$433$			1.05183e8i			1.29563i	−0.761798	+	0.647814i	$0.775683\pi$
$434$			4.05913e7i			0.496551i
$435$		0			0
$436$		−	4.47795e7i		−	0.540281i
$437$	−1.17102e8	+	4.05460e7i	−1.40320	+	0.485852i
$438$		0			0
$439$	−5.25897e7			−0.621594			−0.310797	−	0.950476i	$-0.600596\pi$
$439$	−5.25897e7			−0.621594			−0.310797	+	0.950476i	$0.600596\pi$
$440$	−4.68652e7			−0.550164
$441$		0			0
$442$		−	2.30764e7i		−	0.267240i
$443$	1.46092e8			1.68041			0.840207	−	0.542266i	$-0.182434\pi$
$443$	1.46092e8			1.68041			0.840207	+	0.542266i	$0.182434\pi$
$444$		0			0
$445$	−4.73056e7			−0.536825
$446$	3.28885e7			0.370714
$447$		0			0
$448$			6.41725e7i			0.713699i
$449$	−3.09669e7			−0.342104			−0.171052	−	0.985262i	$-0.554717\pi$
$449$	−3.09669e7			−0.342104			−0.171052	+	0.985262i	$0.554717\pi$
$450$		0			0
$451$		−	2.57920e7i		−	0.281161i
$452$			6.12851e7i			0.663651i
$453$		0			0
$454$		−	4.46555e7i		−	0.477208i
$455$	−1.80809e7			−0.191949
$456$		0			0
$457$		−	3.64508e7i		−	0.381908i	−0.981599	−	0.190954i	$-0.938842\pi$
$457$		−	3.64508e7i		−	0.381908i	0.981599	−	0.190954i	$-0.0611581\pi$
$458$			7.35668e7i			0.765747i
$459$		0			0
$460$	−1.62792e7	+	5.63659e6i	−0.167247	+	0.0579086i
$461$	−3.26518e7			−0.333276			−0.166638	−	0.986018i	$-0.553291\pi$
$461$	−3.26518e7			−0.333276			−0.166638	+	0.986018i	$0.553291\pi$
$462$		0			0
$463$	1.67599e8			1.68860			0.844302	−	0.535868i	$-0.180016\pi$
$463$	1.67599e8			1.68860			0.844302	+	0.535868i	$0.180016\pi$
$464$	1.12609e7			0.112724
$465$		0			0
$466$	−8.54334e7			−0.844248
$467$			3.58074e7i			0.351578i	0.984428	+	0.175789i	$0.0562477\pi$
$467$			3.58074e7i			0.351578i	−0.984428	+	0.175789i	$0.943752\pi$
$468$		0			0
$469$	5.70711e7			0.553220
$470$		−	2.40634e7i		−	0.231773i
$471$		0			0
$472$	8.90754e7			0.847094
$473$	−4.32114e7			−0.408333
$474$		0			0
$475$			1.22202e8i			1.14024i
$476$	−1.54991e7			−0.143710
$477$		0			0
$478$	4.86924e7			0.445838
$479$		−	4.01741e7i		−	0.365544i	−0.983155	−	0.182772i	$-0.941493\pi$
$479$		−	4.01741e7i		−	0.365544i	0.983155	−	0.182772i	$-0.0585070\pi$
$480$		0			0
$481$		−	5.11047e7i		−	0.459225i
$482$			5.96078e7i			0.532307i
$483$		0			0
$484$	4.26518e6			0.0376185
$485$	−1.65275e7			−0.144872
$486$		0			0
$487$	−1.60417e8			−1.38888			−0.694439	−	0.719552i	$-0.744347\pi$
$487$	−1.60417e8			−1.38888			−0.694439	+	0.719552i	$0.744347\pi$
$488$		−	1.85726e8i		−	1.59813i
$489$		0			0
$490$			2.41708e7i			0.205449i
$491$	7.40765e7			0.625800			0.312900	−	0.949786i	$-0.398699\pi$
$491$	7.40765e7			0.625800			0.312900	+	0.949786i	$0.398699\pi$
$492$		0			0
$493$			1.55881e7i			0.130092i
$494$			8.32894e7i			0.690890i
$495$		0			0
$496$	5.56661e7			0.456190
$497$		−	1.02153e8i		−	0.832112i
$498$		0			0
$499$	−1.97181e8			−1.58695			−0.793474	−	0.608604i	$-0.791730\pi$
$499$	−1.97181e8			−1.58695			−0.793474	+	0.608604i	$0.791730\pi$
$500$			3.91117e7i			0.312894i
$501$		0			0
$502$		−	699772.i		−	0.00553153i
$503$			6.73802e6i			0.0529454i	0.999650	+	0.0264727i	$0.00842750\pi$
$503$			6.73802e6i			0.0529454i	−0.999650	+	0.0264727i	$0.991572\pi$
$504$		0			0
$505$		−	6.01902e7i		−	0.467360i
$506$	−1.02239e8	+	3.53997e7i	−0.789158	+	0.273242i
$507$		0			0
$508$	−2.36688e7			−0.180544
$509$	−2.39743e7			−0.181799			−0.0908997	−	0.995860i	$-0.528974\pi$
$509$	−2.39743e7			−0.181799			−0.0908997	+	0.995860i	$0.528974\pi$
$510$		0			0
$511$			1.15623e8i			0.866526i
$512$	1.18857e8			0.885551
$513$		0			0
$514$	3.33536e7			0.245614
$515$	2.16621e7			0.158591
$516$		0			0
$517$			8.77533e7i			0.635027i
$518$	5.91119e7			0.425291
$519$		0			0
$520$			4.30977e7i			0.306510i
$521$			1.14966e8i			0.812933i	0.913666	+	0.406467i	$0.133239\pi$
$521$			1.14966e8i			0.812933i	−0.913666	+	0.406467i	$0.866761\pi$
$522$		0			0
$523$			2.70926e8i			1.89385i	0.321456	+	0.946925i	$0.395828\pi$
$523$			2.70926e8i			1.89385i	−0.321456	+	0.946925i	$0.604172\pi$
$524$	−3.49516e7			−0.242926
$525$		0			0
$526$			1.28235e8i			0.881152i
$527$			7.70570e7i			0.526478i
$528$		0			0
$529$	−1.16341e8	+	9.15393e7i	−0.785896	+	0.618359i
$530$	−2.15234e7			−0.144572
$531$		0			0
$532$	5.59408e7			0.371530
$533$	−2.37186e7			−0.156641
$534$		0			0
$535$	−1.29730e8			−0.847188
$536$		−	1.36035e8i		−	0.883398i
$537$		0			0
$538$	−2.06021e8			−1.32302
$539$		−	8.81453e7i		−	0.562902i
$540$		0			0
$541$	1.43573e8			0.906739			0.453370	−	0.891323i	$-0.350222\pi$
$541$	1.43573e8			0.906739			0.453370	+	0.891323i	$0.350222\pi$
$542$	−1.23214e8			−0.773859
$543$		0			0
$544$			6.39623e7i			0.397308i
$545$	1.14706e8			0.708591
$546$		0			0
$547$	2.07872e8			1.27009			0.635045	−	0.772475i	$-0.280982\pi$
$547$	2.07872e8			1.27009			0.635045	+	0.772475i	$0.280982\pi$
$548$		−	2.19473e7i		−	0.133364i
$549$		0			0
$550$			1.06691e8i			0.641271i
$551$		−	5.62619e7i		−	0.336325i
$552$		0			0
$553$	1.33606e8			0.790044
$554$	−1.94475e8			−1.14376
$555$		0			0
$556$	−6.05351e7			−0.352195
$557$			2.03427e8i			1.17718i	0.808431	+	0.588591i	$0.200317\pi$
$557$			2.03427e8i			1.17718i	−0.808431	+	0.588591i	$0.799683\pi$
$558$		0			0
$559$			3.97376e7i			0.227492i
$560$	−2.86809e7			−0.163316
$561$		0			0
$562$		−	7.69812e7i		−	0.433686i
$563$			4.02092e7i			0.225320i	0.993634	+	0.112660i	$0.0359371\pi$
$563$			4.02092e7i			0.225320i	−0.993634	+	0.112660i	$0.964063\pi$
$564$		0			0
$565$	−1.56986e8			−0.870393
$566$			2.19614e8i			1.21118i
$567$		0			0
$568$	−2.43492e8			−1.32874
$569$		−	2.17982e8i		−	1.18327i	−0.806205	−	0.591636i	$-0.798482\pi$
$569$		−	2.17982e8i		−	1.18327i	0.806205	−	0.591636i	$-0.201518\pi$
$570$		0			0
$571$		−	1.53635e8i		−	0.825243i	−0.910903	−	0.412621i	$-0.864613\pi$
$571$		−	1.53635e8i		−	0.825243i	0.910903	−	0.412621i	$-0.135387\pi$
$572$		−	4.22246e7i		−	0.225620i
$573$		0			0
$574$		−	2.74349e7i		−	0.145067i
$575$	4.77630e7	+	1.37945e8i	0.251240	+	0.725611i
$576$		0			0
$577$	4.00536e7			0.208504			0.104252	−	0.994551i	$-0.466755\pi$
$577$	4.00536e7			0.208504			0.104252	+	0.994551i	$0.466755\pi$
$578$	−1.02919e8			−0.532982
$579$		0			0
$580$		−	7.82137e6i		−	0.0400866i
$581$	1.68417e8			0.858731
$582$		0			0
$583$	7.84908e7			0.396108
$584$	2.75600e8			1.38370
$585$		0			0
$586$		−	2.12447e8i		−	1.05574i
$587$	1.79154e8			0.885750			0.442875	−	0.896583i	$-0.353958\pi$
$587$	1.79154e8			0.885750			0.442875	+	0.896583i	$0.353958\pi$
$588$		0			0
$589$		−	2.78121e8i		−	1.36109i
$590$			6.13010e7i			0.298477i
$591$		0			0
$592$		−	8.10649e7i		−	0.390722i
$593$	−3.94002e8			−1.88944			−0.944722	−	0.327872i	$-0.893669\pi$
$593$	−3.94002e8			−1.88944			−0.944722	+	0.327872i	$0.893669\pi$
$594$		0			0
$595$		−	3.97021e7i		−	0.188479i
$596$		−	1.56401e7i		−	0.0738755i
$597$		0			0
$598$	3.25539e7	+	9.40198e7i	0.152230	+	0.439659i
$599$	−3.26132e8			−1.51745			−0.758723	−	0.651413i	$-0.774177\pi$
$599$	−3.26132e8			−1.51745			−0.758723	+	0.651413i	$0.774177\pi$
$600$		0			0
$601$	3.34444e8			1.54064			0.770318	−	0.637659i	$-0.220097\pi$
$601$	3.34444e8			1.54064			0.770318	+	0.637659i	$0.220097\pi$
$602$	−4.59639e7			−0.210682
$603$		0			0
$604$	9.05711e6			0.0411035
$605$			1.09255e7i			0.0493375i
$606$		0			0
$607$	−2.70163e8			−1.20798			−0.603991	−	0.796991i	$-0.706424\pi$
$607$	−2.70163e8			−1.20798			−0.603991	+	0.796991i	$0.706424\pi$
$608$		−	2.30858e8i		−	1.02715i
$609$		0			0
$610$	1.27815e8			0.563109
$611$	8.06989e7			0.353789
$612$		0			0
$613$		−	1.66910e8i		−	0.724606i	−0.932060	−	0.362303i	$-0.881991\pi$
$613$		−	1.66910e8i		−	0.724606i	0.932060	−	0.362303i	$-0.118009\pi$
$614$	3.48558e8			1.50581
$615$		0			0
$616$	1.81793e8			0.777740
$617$			3.40980e6i			0.0145169i	0.999974	+	0.00725843i	$0.00231045\pi$
$617$			3.40980e6i			0.0145169i	−0.999974	+	0.00725843i	$0.997690\pi$
$618$		0			0
$619$		−	7.78890e7i		−	0.328401i	−0.986427	−	0.164200i	$-0.947496\pi$
$619$		−	7.78890e7i		−	0.328401i	0.986427	−	0.164200i	$-0.0525043\pi$
$620$		−	3.86636e7i		−	0.162228i
$621$		0			0
$622$	1.82105e8			0.756748
$623$	1.83501e8			0.758882
$624$		0			0
$625$	8.72821e7			0.357508
$626$			2.28474e8i			0.931352i
$627$		0			0
$628$			6.00732e7i			0.242550i
$629$	1.12216e8			0.450923
$630$		0			0
$631$		−	2.97365e8i		−	1.18359i	−0.806089	−	0.591795i	$-0.798420\pi$
$631$		−	2.97365e8i		−	1.18359i	0.806089	−	0.591795i	$-0.201580\pi$
$632$		−	3.18465e8i		−	1.26157i
$633$		0			0
$634$	2.05075e8			0.804720
$635$		−	6.06291e7i		−	0.236788i
$636$		0			0
$637$	−8.10593e7			−0.313606
$638$		−	4.91209e7i		−	0.189149i
$639$		0			0
$640$			1.79040e7i			0.0682982i
$641$		−	1.39938e8i		−	0.531328i	−0.964066	−	0.265664i	$-0.914409\pi$
$641$		−	1.39938e8i		−	0.531328i	0.964066	−	0.265664i	$-0.0855912\pi$
$642$		0			0
$643$			3.06153e8i			1.15161i	0.817587	+	0.575805i	$0.195311\pi$
$643$			3.06153e8i			1.15161i	−0.817587	+	0.575805i	$0.804689\pi$
$644$	6.31478e7	−	2.18647e7i	0.236429	−	0.0818625i
$645$		0			0
$646$	−1.82887e8			−0.678400
$647$	−2.49111e8			−0.919771			−0.459885	−	0.887978i	$-0.652110\pi$
$647$	−2.49111e8			−0.919771			−0.459885	+	0.887978i	$0.652110\pi$
$648$		0			0
$649$		−	2.23550e8i		−	0.817788i
$650$	9.81145e7			0.357267
$651$		0			0
$652$	1.11913e8			0.403772
$653$	4.16924e8			1.49733			0.748665	−	0.662948i	$-0.230695\pi$
$653$	4.16924e8			1.49733			0.748665	+	0.662948i	$0.230695\pi$
$654$		0			0
$655$		−	8.95309e7i		−	0.318602i
$656$	−3.76237e7			−0.133275
$657$		0			0
$658$			9.33431e7i			0.327646i
$659$		−	2.42010e8i		−	0.845622i	−0.906218	−	0.422811i	$-0.861043\pi$
$659$		−	2.42010e8i		−	0.845622i	0.906218	−	0.422811i	$-0.138957\pi$
$660$		0			0
$661$		−	4.85278e8i		−	1.68030i	−0.542356	−	0.840149i	$-0.682468\pi$
$661$		−	4.85278e8i		−	1.68030i	0.542356	−	0.840149i	$-0.317532\pi$
$662$	−2.13413e8			−0.735610
$663$		0			0
$664$		−	4.01439e8i		−	1.37125i
$665$			1.43296e8i			0.487270i
$666$		0			0
$667$	−2.19902e7	−	6.35102e7i	−0.0741056	−	0.214026i
$668$	8.16752e7			0.274006
$669$		0			0
$670$	9.36183e7			0.311269
$671$	−4.66111e8			−1.54284
$672$		0			0
$673$	−3.54234e8			−1.16211			−0.581053	−	0.813866i	$-0.697359\pi$
$673$	−3.54234e8			−1.16211			−0.581053	+	0.813866i	$0.697359\pi$
$674$			3.66996e8i			1.19862i
$675$		0			0
$676$	7.46513e7			0.241656
$677$		−	1.26295e8i		−	0.407023i	−0.979073	−	0.203512i	$-0.934765\pi$
$677$		−	1.26295e8i		−	0.407023i	0.979073	−	0.203512i	$-0.0652354\pi$
$678$		0			0
$679$	6.41113e7			0.204798
$680$	−9.46341e7			−0.300968
$681$		0			0
$682$		−	2.42820e8i		−	0.765477i
$683$	−2.78165e7			−0.0873054			−0.0436527	−	0.999047i	$-0.513899\pi$
$683$	−2.78165e7			−0.0873054			−0.0436527	+	0.999047i	$0.513899\pi$
$684$		0			0
$685$	5.62196e7			0.174910
$686$		−	2.68646e8i		−	0.832163i
$687$		0			0
$688$			6.30340e7i			0.193557i
$689$		−	7.21810e7i		−	0.220681i
$690$		0			0
$691$	6.07780e8			1.84210			0.921048	−	0.389449i	$-0.127335\pi$
$691$	6.07780e8			1.84210			0.921048	+	0.389449i	$0.127335\pi$
$692$	8.41976e7			0.254086
$693$		0			0
$694$	−1.71893e8			−0.514256
$695$		−	1.55065e8i		−	0.461912i
$696$		0			0
$697$		−	5.20813e7i		−	0.153810i
$698$	−2.08710e7			−0.0613730
$699$		0			0
$700$		−	6.58980e7i		−	0.192122i
$701$			3.75291e8i			1.08947i	0.838609	+	0.544733i	$0.183369\pi$
$701$			3.75291e8i			1.08947i	−0.838609	+	0.544733i	$0.816631\pi$
$702$		0			0
$703$	−4.05019e8			−1.16576
$704$		−	3.83885e8i		−	1.10023i
$705$		0			0
$706$	−2.80797e8			−0.797956
$707$			2.33481e8i			0.660684i
$708$		0			0
$709$		−	4.32348e8i		−	1.21309i	−0.795048	−	0.606547i	$-0.792554\pi$
$709$		−	4.32348e8i		−	1.21309i	0.795048	−	0.606547i	$-0.207446\pi$
$710$		−	1.67570e8i		−	0.468188i
$711$		0			0
$712$		−	4.37394e8i		−	1.21181i
$713$	−1.08704e8	−	3.13952e8i	−0.299902	−	0.866152i
$714$		0			0
$715$	1.08161e8			0.295906
$716$	−4.26751e7			−0.116261
$717$		0			0
$718$			2.44677e8i			0.661028i
$719$	1.83199e8			0.492875			0.246437	−	0.969159i	$-0.420740\pi$
$719$	1.83199e8			0.492875			0.246437	+	0.969159i	$0.420740\pi$
$720$		0			0
$721$	−8.40284e7			−0.224192
$722$	3.60734e8			0.958462
$723$		0			0
$724$		−	1.26055e8i		−	0.332157i
$725$	−6.62763e7			−0.173918
$726$		0			0
$727$			3.32462e8i			0.865244i	0.901575	+	0.432622i	$0.142412\pi$
$727$			3.32462e8i			0.865244i	−0.901575	+	0.432622i	$0.857588\pi$
$728$		−	1.67178e8i		−	0.433297i
$729$		0			0
$730$			1.89666e8i			0.487551i
$731$	−8.72560e7			−0.223380
$732$		0			0
$733$			5.89347e8i			1.49644i	0.663450	+	0.748220i	$0.269091\pi$
$733$			5.89347e8i			1.49644i	−0.663450	+	0.748220i	$0.730909\pi$
$734$		−	1.20961e8i		−	0.305884i
$735$		0			0
$736$	−9.02318e7	−	2.60600e8i	−0.226322	−	0.653644i
$737$	−3.41403e8			−0.852836
$738$		0			0
$739$	5.99727e8			1.48601			0.743003	−	0.669288i	$-0.233401\pi$
$739$	5.99727e8			1.48601			0.743003	+	0.669288i	$0.233401\pi$
$740$	−5.63046e7			−0.138947
$741$		0			0
$742$	8.34906e7			0.204374
$743$			6.45667e7i			0.157414i	0.996898	+	0.0787068i	$0.0250791\pi$
$743$			6.45667e7i			0.157414i	−0.996898	+	0.0787068i	$0.974921\pi$
$744$		0			0
$745$	4.00631e7			0.0968894
$746$			4.34181e8i			1.04581i
$747$		0			0
$748$	9.27169e7			0.221541
$749$	5.03231e8			1.19763
$750$		0			0
$751$			8.08683e7i			0.190923i	0.995433	+	0.0954616i	$0.0304327\pi$
$751$			8.08683e7i			0.190923i	−0.995433	+	0.0954616i	$0.969567\pi$
$752$	1.28009e8			0.301014
$753$		0			0
$754$	−4.51721e7			−0.105379
$755$			2.32004e7i			0.0539082i
$756$		0			0
$757$			6.29360e7i			0.145081i	0.997365	+	0.0725406i	$0.0231107\pi$
$757$			6.29360e7i			0.145081i	−0.997365	+	0.0725406i	$0.976889\pi$
$758$		−	3.30113e8i		−	0.757976i
$759$		0			0
$760$	3.41562e8			0.778088
$761$	5.45904e8			1.23869			0.619344	−	0.785119i	$-0.287398\pi$
$761$	5.45904e8			1.23869			0.619344	+	0.785119i	$0.287398\pi$
$762$		0			0
$763$	−4.44950e8			−1.00170
$764$			1.47240e8i			0.330176i
$765$		0			0
$766$			6.49548e8i			1.44519i
$767$	−2.05579e8			−0.455609
$768$		0			0
$769$			1.19089e8i			0.261874i	0.991391	+	0.130937i	$0.0417985\pi$
$769$			1.19089e8i			0.261874i	−0.991391	+	0.130937i	$0.958201\pi$
$770$			1.25108e8i			0.274040i
$771$		0			0
$772$	−3.02345e8			−0.657129
$773$		−	3.69267e8i		−	0.799470i	−0.916631	−	0.399735i	$-0.869102\pi$
$773$		−	3.69267e8i		−	0.799470i	0.916631	−	0.399735i	$-0.130898\pi$
$774$		0			0
$775$	−3.27625e8			−0.703837
$776$		−	1.52816e8i		−	0.327027i
$777$		0			0
$778$			1.89295e8i			0.401977i
$779$			1.87976e8i			0.397641i
$780$		0			0
$781$			6.11086e8i			1.28277i
$782$	−2.06449e8	+	7.14821e7i	−0.431710	+	0.149478i
$783$		0			0
$784$	−1.28581e8			−0.266826
$785$	−1.53882e8			−0.318110
$786$		0			0
$787$			9.26119e8i			1.89995i	0.312324	+	0.949976i	$0.398893\pi$
$787$			9.26119e8i			1.89995i	−0.312324	+	0.949976i	$0.601107\pi$
$788$	2.24136e8			0.458070
$789$		0			0
$790$	2.19165e8			0.444519
$791$	6.08957e8			1.23043
$792$		0			0
$793$			4.28640e8i			0.859555i
$794$	3.23523e7			0.0646315
$795$		0			0
$796$			4.13783e7i			0.0820415i
$797$			7.70727e8i			1.52239i	0.648523	+	0.761195i	$0.275387\pi$
$797$			7.70727e8i			1.52239i	−0.648523	+	0.761195i	$0.724613\pi$
$798$		0			0
$799$			1.77199e8i			0.347393i
$800$	−2.71950e8			−0.531152
$801$		0			0
$802$		−	5.38919e8i		−	1.04472i
$803$		−	6.91666e8i		−	1.33582i
$804$		0			0
$805$	5.60078e7	+	1.61757e8i	0.107365	+	0.310082i
$806$	−2.23300e8			−0.426465
$807$		0			0
$808$	5.56527e8			1.05500
$809$	−5.09249e8			−0.961800			−0.480900	−	0.876775i	$-0.659690\pi$
$809$	−5.09249e8			−0.961800			−0.480900	+	0.876775i	$0.659690\pi$
$810$		0			0
$811$	−9.15685e8			−1.71666			−0.858328	−	0.513101i	$-0.828497\pi$
$811$	−9.15685e8			−1.71666			−0.858328	+	0.513101i	$0.828497\pi$
$812$			3.03395e7i			0.0566684i
$813$		0			0
$814$	−3.53612e8			−0.655622
$815$			2.86672e8i			0.529556i
$816$		0			0
$817$	3.14932e8			0.577498
$818$	−6.46049e7			−0.118034
$819$		0			0
$820$			2.61319e7i			0.0473947i
$821$	−4.22090e8			−0.762738			−0.381369	−	0.924423i	$-0.624547\pi$
$821$	−4.22090e8			−0.762738			−0.381369	+	0.924423i	$0.624547\pi$
$822$		0			0
$823$	−8.84464e8			−1.58665			−0.793324	−	0.608800i	$-0.791651\pi$
$823$	−8.84464e8			−1.58665			−0.793324	+	0.608800i	$0.791651\pi$
$824$			2.00291e8i			0.357997i
$825$		0			0
$826$		−	2.37790e8i		−	0.421943i
$827$			1.06398e9i			1.88111i	0.339636	+	0.940557i	$0.389696\pi$
$827$			1.06398e9i			1.88111i	−0.339636	+	0.940557i	$0.610304\pi$
$828$		0			0
$829$	8.34964e8			1.46556			0.732781	−	0.680465i	$-0.238222\pi$
$829$	8.34964e8			1.46556			0.732781	+	0.680465i	$0.238222\pi$
$830$	2.76267e8			0.483165
$831$		0			0
$832$	−3.53024e8			−0.612963
$833$		−	1.77990e8i		−	0.307937i
$834$		0			0
$835$			2.09217e8i			0.359366i
$836$	−3.34642e8			−0.572745
$837$		0			0
$838$			1.89786e8i			0.322502i
$839$			3.90151e8i			0.660613i	0.943874	+	0.330307i	$0.107152\pi$
$839$			3.90151e8i			0.660613i	−0.943874	+	0.330307i	$0.892848\pi$
$840$		0			0
$841$	−5.64310e8			−0.948701
$842$			5.49693e8i			0.920839i
$843$		0			0
$844$	2.39908e7			0.0399040
$845$			1.91224e8i			0.316937i
$846$		0			0
$847$		−	4.23808e7i		−	0.0697459i
$848$		−	1.14497e8i		−	0.187762i
$849$		0			0
$850$			2.15440e8i			0.350808i
$851$	−4.57198e8	+	1.58303e8i	−0.741850	+	0.256862i
$852$		0			0
$853$	−1.58229e8			−0.254940			−0.127470	−	0.991842i	$-0.540686\pi$
$853$	−1.58229e8			−0.254940			−0.127470	+	0.991842i	$0.540686\pi$
$854$	−4.95802e8			−0.796039
$855$		0			0
$856$		−	1.19950e9i		−	1.91241i
$857$	3.52002e8			0.559245			0.279623	−	0.960110i	$-0.409791\pi$
$857$	3.52002e8			0.559245			0.279623	+	0.960110i	$0.409791\pi$
$858$		0			0
$859$	−5.14413e7			−0.0811582			−0.0405791	−	0.999176i	$-0.512920\pi$
$859$	−5.14413e7			−0.0811582			−0.0405791	+	0.999176i	$0.512920\pi$
$860$	4.37810e7			0.0688319
$861$		0			0
$862$		−	2.59161e8i		−	0.404620i
$863$	−4.96102e8			−0.771861			−0.385930	−	0.922528i	$-0.626119\pi$
$863$	−4.96102e8			−0.771861			−0.385930	+	0.922528i	$0.626119\pi$
$864$		0			0
$865$			2.15678e8i			0.333240i
$866$		−	6.69290e8i		−	1.03053i
$867$		0			0
$868$			1.49978e8i			0.229334i
$869$	−7.99243e8			−1.21792
$870$		0			0
$871$			3.13958e8i			0.475135i
$872$			1.06059e9i			1.59954i
$873$		0			0
$874$	7.45134e8	−	2.57999e8i	1.11609	−	0.386442i
$875$	3.88632e8			0.580116
$876$		0			0
$877$	4.89169e8			0.725203			0.362602	−	0.931944i	$-0.381889\pi$
$877$	4.89169e8			0.725203			0.362602	+	0.931944i	$0.381889\pi$
$878$	3.34635e8			0.494410
$879$		0			0
$880$	1.71571e8			0.251765
$881$			3.68496e8i			0.538896i	0.963015	+	0.269448i	$0.0868412\pi$
$881$			3.68496e8i			0.538896i	−0.963015	+	0.269448i	$0.913159\pi$
$882$		0			0
$883$	7.59012e8			1.10247			0.551235	−	0.834350i	$-0.314157\pi$
$883$	7.59012e8			1.10247			0.551235	+	0.834350i	$0.314157\pi$
$884$		−	8.52634e7i		−	0.123426i
$885$		0			0
$886$	−9.29603e8			−1.33658
$887$	2.70519e8			0.387638			0.193819	−	0.981037i	$-0.437913\pi$
$887$	2.70519e8			0.387638			0.193819	+	0.981037i	$0.437913\pi$
$888$		0			0
$889$			2.35184e8i			0.334736i
$890$	3.01011e8			0.426985
$891$		0			0
$892$	1.21517e8			0.171216
$893$		−	6.39562e8i		−	0.898107i
$894$		0			0
$895$		−	1.09315e8i		−	0.152479i
$896$		−	6.94504e7i		−	0.0965497i
$897$		0			0
$898$	1.97046e8			0.272107
$899$	1.50839e8			0.207603
$900$		0			0
$901$	1.58495e8			0.216691
$902$			1.64117e8i			0.223633i
$903$		0			0
$904$		−	1.45151e9i		−	1.96479i
$905$	3.22898e8			0.435631
$906$		0			0
$907$			1.23189e9i			1.65101i	0.564394	+	0.825505i	$0.309110\pi$
$907$			1.23189e9i			1.65101i	−0.564394	+	0.825505i	$0.690890\pi$
$908$		−	1.64995e8i		−	0.220400i
$909$		0			0
$910$	1.15051e8			0.152674
$911$			1.21327e9i			1.60473i	0.596832	+	0.802366i	$0.296426\pi$
$911$			1.21327e9i			1.60473i	−0.596832	+	0.802366i	$0.703574\pi$
$912$		0			0
$913$	−1.00748e9			−1.32381
$914$			2.31941e8i			0.303766i
$915$		0			0
$916$			2.71817e8i			0.353663i
$917$			3.47295e8i			0.450392i
$918$		0			0
$919$		−	6.64269e8i		−	0.855850i	−0.903814	−	0.427925i	$-0.859245\pi$
$919$		−	6.64269e8i		−	0.855850i	0.903814	−	0.427925i	$-0.140755\pi$
$920$	3.85566e8	−	1.33501e8i	0.495148	−	0.171443i
$921$		0			0
$922$	2.07767e8			0.265084
$923$	5.61961e8			0.714663
$924$		0			0
$925$			4.77110e8i			0.602828i
$926$	−1.06645e9			−1.34310
$927$		0			0
$928$	1.25206e8			0.156669
$929$	9.67171e8			1.20630			0.603151	−	0.797627i	$-0.293912\pi$
$929$	9.67171e8			1.20630			0.603151	+	0.797627i	$0.293912\pi$
$930$		0			0
$931$			6.42418e8i			0.796102i
$932$	−3.15662e8			−0.389919
$933$		0			0
$934$		−	2.27847e8i		−	0.279642i
$935$			2.37501e8i			0.290556i
$936$		0			0
$937$		−	2.93220e8i		−	0.356430i	−0.983992	−	0.178215i	$-0.942968\pi$
$937$		−	2.93220e8i		−	0.356430i	0.983992	−	0.178215i	$-0.0570323\pi$
$938$	−3.63150e8			−0.440026
$939$		0			0
$940$		−	8.89100e7i		−	0.107045i
$941$		−	1.21758e9i		−	1.46127i	−0.682769	−	0.730635i	$-0.739224\pi$
$941$		−	1.21758e9i		−	1.46127i	0.682769	−	0.730635i	$-0.260776\pi$
$942$		0			0
$943$	7.34712e7	+	2.12194e8i	0.0876157	+	0.253045i
$944$	−3.26100e8			−0.387646
$945$		0			0
$946$	2.74959e8			0.324784
$947$	−8.42419e8			−0.991924			−0.495962	−	0.868344i	$-0.665184\pi$
$947$	−8.42419e8			−0.991924			−0.495962	+	0.868344i	$0.665184\pi$
$948$		0			0
$949$	−6.36063e8			−0.744220
$950$		−	7.77586e8i		−	0.906938i
$951$		0			0
$952$	3.67091e8			0.425464
$953$		−	1.79752e8i		−	0.207680i	−0.994594	−	0.103840i	$-0.966887\pi$
$953$		−	1.79752e8i		−	0.207680i	0.994594	−	0.103840i	$-0.0331129\pi$
$954$		0			0
$955$	−3.77165e8			−0.433033
$956$	1.79910e8			0.205912
$957$		0			0
$958$			2.55633e8i			0.290750i
$959$	−2.18079e8			−0.247262
$960$		0			0
$961$	−1.41858e8			−0.159839
$962$			3.25185e8i			0.365263i
$963$		0			0
$964$			2.20241e8i			0.245848i
$965$		−	7.74477e8i		−	0.861839i
$966$		0			0
$967$	1.27323e9			1.40808			0.704039	−	0.710161i	$-0.251378\pi$
$967$	1.27323e9			1.40808			0.704039	+	0.710161i	$0.251378\pi$
$968$	−1.01019e8			−0.111372
$969$		0			0
$970$	1.05167e8			0.115229
$971$			3.28170e7i			0.0358461i	0.999839	+	0.0179230i	$0.00570538\pi$
$971$			3.28170e7i			0.0358461i	−0.999839	+	0.0179230i	$0.994295\pi$
$972$		0			0
$973$			6.01505e8i			0.652981i
$974$	1.02075e9			1.10470
$975$		0			0
$976$			6.79932e8i			0.731335i
$977$		−	7.22268e8i		−	0.774488i	−0.921977	−	0.387244i	$-0.873427\pi$
$977$		−	7.22268e8i		−	0.774488i	0.921977	−	0.387244i	$-0.126573\pi$
$978$		0			0
$979$	−1.09772e9			−1.16988
$980$			8.93071e7i			0.0948873i
$981$		0			0
$982$	−4.71358e8			−0.497756
$983$		−	1.40301e9i		−	1.47706i	−0.674219	−	0.738532i	$-0.735519\pi$
$983$		−	1.40301e9i		−	1.47706i	0.674219	−	0.738532i	$-0.264481\pi$
$984$		0			0
$985$			5.74138e8i			0.600770i
$986$		−	9.91889e7i		−	0.103474i
$987$		0			0
$988$			3.07740e8i			0.319090i
$989$	3.55506e8	−	1.23092e8i	0.367500	−	0.127245i
$990$		0			0
$991$	1.77438e8			0.182316			0.0911581	−	0.995836i	$-0.470943\pi$
$991$	1.77438e8			0.182316			0.0911581	+	0.995836i	$0.470943\pi$
$992$	6.18934e8			0.634030
$993$		0			0
$994$			6.50012e8i			0.661854i
$995$	−1.05993e8			−0.107599
$996$		0			0
$997$	−1.51194e9			−1.52563			−0.762813	−	0.646619i	$-0.776182\pi$
$997$	−1.51194e9			−1.52563			−0.762813	+	0.646619i	$0.776182\pi$
$998$	1.25469e9			1.26224
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.7		24
3.2	odd	2		69.7.d.a.22.18	yes	24
23.22	odd	2	inner	207.7.d.e.91.8		24
69.68	even	2		69.7.d.a.22.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.17	✓	24	69.68	even	2
69.7.d.a.22.18	yes	24	3.2	odd	2
207.7.d.e.91.7		24	1.1	even	1	trivial
207.7.d.e.91.8		24	23.22	odd	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	207.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.36312 q^{2} -23.5107 q^{4} -60.2242i q^{5} +233.613i q^{7} +556.841 q^{8} +O(q^{10})\)	\(q-6.36312 q^{2} -23.5107 q^{4} -60.2242i q^{5} +233.613i q^{7} +556.841 q^{8} +383.214i q^{10} -1397.49i q^{11} -1285.15 q^{13} -1486.51i q^{14} -2038.57 q^{16} -2821.93i q^{17} +10185.1i q^{19} +1415.91i q^{20} +8892.40i q^{22} +(3980.90 + 11497.3i) q^{23} +11998.1 q^{25} +8177.54 q^{26} -5492.39i q^{28} -5523.92 q^{29} -27306.5 q^{31} -22666.2 q^{32} +17956.3i q^{34} +14069.1 q^{35} +39765.7i q^{37} -64809.3i q^{38} -33535.3i q^{40} +18455.9 q^{41} -30920.7i q^{43} +32855.9i q^{44} +(-25330.9 - 73158.9i) q^{46} -62793.6 q^{47} +63074.0 q^{49} -76345.1 q^{50} +30214.6 q^{52} +56165.6i q^{53} -84162.6 q^{55} +130085. i q^{56} +35149.4 q^{58} +159966. q^{59} -333535. i q^{61} +173755. q^{62} +274696. q^{64} +77396.8i q^{65} -244298. i q^{67} +66345.4i q^{68} -89523.7 q^{70} -437275. q^{71} +494935. q^{73} -253034. i q^{74} -239459. i q^{76} +326471. q^{77} -571913. i q^{79} +122771. i q^{80} -117437. q^{82} -720923. i q^{83} -169948. q^{85} +196752. i q^{86} -778179. i q^{88} -785492. i q^{89} -300226. i q^{91} +(-93593.5 - 270310. i) q^{92} +399563. q^{94} +613392. q^{95} -274434. i q^{97} -401348. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 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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