LMFDB - Embedded newform 20.18.c.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,18,Mod(9,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("20.9");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	20.c (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:	$36.6444174689$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 10513788 x^{6} + 47438777752 x^{5} - 249513269598475 x^{4} + \cdots + 12\!\cdots\!68 $ x^8 - x^7 - 10513788x^6 + 47438777752x^5 - 249513269598475x^4 + 2482001120988967319x^3 + 4452658897796563124186x^2 - 53508982948055868249424962x + 129749232836567172546933042968
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{35}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.5
Root			$-1102.18 - 4980.24i$ of defining polynomial
Character	$\chi$	$=$	20.9
Dual form			20.18.c.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4988.24i q^{3} +(-60861.6 + 871341. i) q^{5} -8.73679e6i q^{7} +1.04258e8 q^{9} +6.61458e8 q^{11} -3.36520e7i q^{13} +(-4.34646e9 - 3.03592e8i) q^{15} +2.31403e9i q^{17} +6.14052e10 q^{19} +4.35812e10 q^{21} +7.01987e9i q^{23} +(-7.55531e11 - 1.06062e11i) q^{25} +1.16424e12i q^{27} -1.13007e12 q^{29} +3.64909e12 q^{31} +3.29951e12i q^{33} +(7.61272e12 + 5.31735e11i) q^{35} +3.38698e13i q^{37} +1.67864e11 q^{39} -2.80398e13 q^{41} +9.56968e13i q^{43} +(-6.34529e12 + 9.08440e13i) q^{45} +2.08854e14i q^{47} +1.56299e14 q^{49} -1.15429e13 q^{51} +5.01273e14i q^{53} +(-4.02574e13 + 5.76355e14i) q^{55} +3.06304e14i q^{57} -7.12609e14 q^{59} +1.49205e15 q^{61} -9.10877e14i q^{63} +(2.93224e13 + 2.04812e12i) q^{65} -5.73469e14i q^{67} -3.50168e13 q^{69} -6.67771e15 q^{71} -1.14580e16i q^{73} +(5.29065e14 - 3.76877e15i) q^{75} -5.77902e15i q^{77} +1.20012e16 q^{79} +7.65632e15 q^{81} -2.56333e16i q^{83} +(-2.01631e15 - 1.40835e14i) q^{85} -5.63707e15i q^{87} -4.90595e16 q^{89} -2.94011e14 q^{91} +1.82025e16i q^{93} +(-3.73722e15 + 5.35048e16i) q^{95} +2.20754e16i q^{97} +6.89620e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 1276800 q^{5} - 376848248 q^{9} - 396200640 q^{11} + 5677983200 q^{15} + 11821646592 q^{19} - 420670059472 q^{21} + 1642212165000 q^{25} + 1543712861232 q^{29} - 13722543013312 q^{31} - 13325691076800 q^{35}+ \cdots - 23\!\cdots\!60 q^{99}+O(q^{100}) $ 8 * q + 1276800 * q^5 - 376848248 * q^9 - 396200640 * q^11 + 5677983200 * q^15 + 11821646592 * q^19 - 420670059472 * q^21 + 1642212165000 * q^25 + 1543712861232 * q^29 - 13722543013312 * q^31 - 13325691076800 * q^35 - 79298226023808 * q^39 + 29824965017568 * q^41 - 238216983006800 * q^45 - 535615080275736 * q^49 - 764079320419264 * q^51 + 339212427988000 * q^55 + 94539545151744 * q^59 - 3380827226969024 * q^61 + 130929936568800 * q^65 + 5559752175554416 * q^69 + 20155606060098624 * q^71 + 938454087760000 * q^75 - 3634057920126144 * q^79 + 15949137882627512 * q^81 + 3575192471022400 * q^85 + 103487949043655568 * q^89 - 69783870139121088 * q^91 + 67219016711959200 * q^95 - 239420571619653760 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$			4988.24i			0.438952i	0.975618	+	0.219476i	$0.0704347\pi$
$3$			4988.24i			0.438952i	−0.975618	+	0.219476i	$0.929565\pi$
$4$		0			0
$5$	−60861.6	+	871341.i	−0.0696784	+	0.997570i
$5$	−60861.6	+	871341.i	−0.0696784	+	0.997570i
$6$		0			0
$7$		−	8.73679e6i		−	0.572820i	−0.958107	−	0.286410i	$-0.907538\pi$
$7$		−	8.73679e6i		−	0.572820i	0.958107	−	0.286410i	$-0.0924620\pi$
$8$		0			0
$9$	1.04258e8			0.807322
$10$		0			0
$11$	6.61458e8			0.930389			0.465194	−	0.885209i	$-0.345984\pi$
$11$	6.61458e8			0.930389			0.465194	+	0.885209i	$0.345984\pi$
$12$		0			0
$13$		−	3.36520e7i		−	0.0114418i	−0.999984	−	0.00572088i	$-0.998179\pi$
$13$		−	3.36520e7i		−	0.0114418i	0.999984	−	0.00572088i	$-0.00182102\pi$
$14$		0			0
$15$	−4.34646e9	−	3.03592e8i	−0.437885	−	0.0305855i
$16$		0			0
$17$			2.31403e9i			0.0804550i	0.999191	+	0.0402275i	$0.0128083\pi$
$17$			2.31403e9i			0.0804550i	−0.999191	+	0.0402275i	$0.987192\pi$
$18$		0			0
$19$	6.14052e10			0.829467			0.414734	−	0.909943i	$-0.363875\pi$
$19$	6.14052e10			0.829467			0.414734	+	0.909943i	$0.363875\pi$
$20$		0			0
$21$	4.35812e10			0.251440
$22$		0			0
$23$			7.01987e9i			0.0186914i	0.999956	+	0.00934571i	$0.00297487\pi$
$23$			7.01987e9i			0.0186914i	−0.999956	+	0.00934571i	$0.997025\pi$
$24$		0			0
$25$	−7.55531e11	−	1.06062e11i	−0.990290	−	0.139018i
$26$		0			0
$27$			1.16424e12i			0.793327i
$28$		0			0
$29$	−1.13007e12			−0.419491			−0.209746	−	0.977756i	$-0.567264\pi$
$29$	−1.13007e12			−0.419491			−0.209746	+	0.977756i	$0.567264\pi$
$30$		0			0
$31$	3.64909e12			0.768440			0.384220	−	0.923242i	$-0.374470\pi$
$31$	3.64909e12			0.768440			0.384220	+	0.923242i	$0.374470\pi$
$32$		0			0
$33$			3.29951e12i			0.408396i
$34$		0			0
$35$	7.61272e12	+	5.31735e11i	0.571428	+	0.0399132i
$36$		0			0
$37$			3.38698e13i			1.58525i	0.609709	+	0.792625i	$0.291286\pi$
$37$			3.38698e13i			1.58525i	−0.609709	+	0.792625i	$0.708714\pi$
$38$		0			0
$39$	1.67864e11			0.00502238
$40$		0			0
$41$	−2.80398e13			−0.548419			−0.274209	−	0.961670i	$-0.588416\pi$
$41$	−2.80398e13			−0.548419			−0.274209	+	0.961670i	$0.588416\pi$
$42$		0			0
$43$			9.56968e13i			1.24858i	0.781194	+	0.624288i	$0.214611\pi$
$43$			9.56968e13i			1.24858i	−0.781194	+	0.624288i	$0.785389\pi$
$44$		0			0
$45$	−6.34529e12	+	9.08440e13i	−0.0562529	+	0.805359i
$46$		0			0
$47$			2.08854e14i			1.27941i	0.768619	+	0.639707i	$0.220944\pi$
$47$			2.08854e14i			1.27941i	−0.768619	+	0.639707i	$0.779056\pi$
$48$		0			0
$49$	1.56299e14			0.671877
$50$		0			0
$51$	−1.15429e13			−0.0353158
$52$		0			0
$53$			5.01273e14i			1.10593i	0.833203	+	0.552967i	$0.186505\pi$
$53$			5.01273e14i			1.10593i	−0.833203	+	0.552967i	$0.813495\pi$
$54$		0			0
$55$	−4.02574e13	+	5.76355e14i	−0.0648280	+	0.928127i
$56$		0			0
$57$			3.06304e14i			0.364096i
$58$		0			0
$59$	−7.12609e14			−0.631843			−0.315922	−	0.948785i	$-0.602314\pi$
$59$	−7.12609e14			−0.631843			−0.315922	+	0.948785i	$0.602314\pi$
$60$		0			0
$61$	1.49205e15			0.996507			0.498254	−	0.867031i	$-0.333975\pi$
$61$	1.49205e15			0.996507			0.498254	+	0.867031i	$0.333975\pi$
$62$		0			0
$63$		−	9.10877e14i		−	0.462450i
$64$		0			0
$65$	2.93224e13	+	2.04812e12i	0.0114139	+	0.000797243i
$66$		0			0
$67$		−	5.73469e14i		−	0.172534i	−0.996272	−	0.0862669i	$-0.972506\pi$
$67$		−	5.73469e14i		−	0.172534i	0.996272	−	0.0862669i	$-0.0274938\pi$
$68$		0			0
$69$	−3.50168e13			−0.00820463
$70$		0			0
$71$	−6.67771e15			−1.22725			−0.613623	−	0.789599i	$-0.710288\pi$
$71$	−6.67771e15			−1.22725			−0.613623	+	0.789599i	$0.710288\pi$
$72$		0			0
$73$		−	1.14580e16i		−	1.66290i	−0.555600	−	0.831450i	$-0.687511\pi$
$73$		−	1.14580e16i		−	1.66290i	0.555600	−	0.831450i	$-0.312489\pi$
$74$		0			0
$75$	5.29065e14	−	3.76877e15i	0.0610222	−	0.434689i
$76$		0			0
$77$		−	5.77902e15i		−	0.532946i
$78$		0			0
$79$	1.20012e16			0.890005			0.445003	−	0.895529i	$-0.353203\pi$
$79$	1.20012e16			0.890005			0.445003	+	0.895529i	$0.353203\pi$
$80$		0			0
$81$	7.65632e15			0.459090
$82$		0			0
$83$		−	2.56333e16i		−	1.24923i	−0.780934	−	0.624614i	$-0.785256\pi$
$83$		−	2.56333e16i		−	1.24923i	0.780934	−	0.624614i	$-0.214744\pi$
$84$		0			0
$85$	−2.01631e15	−	1.40835e14i	−0.0802594	−	0.00560598i
$86$		0			0
$87$		−	5.63707e15i		−	0.184136i
$88$		0			0
$89$	−4.90595e16			−1.32102			−0.660508	−	0.750819i	$-0.729659\pi$
$89$	−4.90595e16			−1.32102			−0.660508	+	0.750819i	$0.729659\pi$
$90$		0			0
$91$	−2.94011e14			−0.00655407
$92$		0			0
$93$			1.82025e16i			0.337308i
$94$		0			0
$95$	−3.73722e15	+	5.35048e16i	−0.0577960	+	0.827451i
$96$		0			0
$97$			2.20754e16i			0.285988i	0.989724	+	0.142994i	$0.0456730\pi$
$97$			2.20754e16i			0.285988i	−0.989724	+	0.142994i	$0.954327\pi$
$98$		0			0
$99$	6.89620e16			0.751123
$100$		0			0
$101$	4.35640e16			0.400310			0.200155	−	0.979764i	$-0.435855\pi$
$101$	4.35640e16			0.400310			0.200155	+	0.979764i	$0.435855\pi$
$102$		0			0
$103$			1.09433e17i			0.851198i	0.904912	+	0.425599i	$0.139937\pi$
$103$			1.09433e17i			0.851198i	−0.904912	+	0.425599i	$0.860063\pi$
$104$		0			0
$105$	−2.65242e15	+	3.79741e16i	−0.0175200	+	0.250829i
$106$		0			0
$107$			1.96661e17i			1.10651i	0.833011	+	0.553256i	$0.186615\pi$
$107$			1.96661e17i			1.10651i	−0.833011	+	0.553256i	$0.813385\pi$
$108$		0			0
$109$	7.27689e16			0.349801			0.174900	−	0.984586i	$-0.444040\pi$
$109$	7.27689e16			0.349801			0.174900	+	0.984586i	$0.444040\pi$
$110$		0			0
$111$	−1.68951e17			−0.695848
$112$		0			0
$113$			1.81697e17i			0.642957i	0.946917	+	0.321479i	$0.104180\pi$
$113$			1.81697e17i			0.642957i	−0.946917	+	0.321479i	$0.895820\pi$
$114$		0			0
$115$	−6.11670e15	−	4.27240e14i	−0.0186460	−	0.00130239i
$116$		0			0
$117$		−	3.50848e15i		−	0.00923718i
$118$		0			0
$119$	2.02172e16			0.0460862
$120$		0			0
$121$	−6.79205e16			−0.134377
$122$		0			0
$123$		−	1.39869e17i		−	0.240729i
$124$		0			0
$125$	1.38399e17	−	6.51870e17i	0.207682	−	0.978196i
$126$		0			0
$127$		−	2.79786e17i		−	0.366855i	−0.983033	−	0.183428i	$-0.941281\pi$
$127$		−	2.79786e17i		−	0.366855i	0.983033	−	0.183428i	$-0.0587193\pi$
$128$		0			0
$129$	−4.77358e17			−0.548065
$130$		0			0
$131$	8.37934e17			0.844119			0.422060	−	0.906568i	$-0.361307\pi$
$131$	8.37934e17			0.844119			0.422060	+	0.906568i	$0.361307\pi$
$132$		0			0
$133$		−	5.36484e17i		−	0.475136i
$134$		0			0
$135$	−1.01445e18	−	7.08578e16i	−0.791398	−	0.0552777i
$136$		0			0
$137$		−	2.45426e18i		−	1.68965i	−0.535046	−	0.844823i	$-0.679706\pi$
$137$		−	2.45426e18i		−	1.68965i	0.535046	−	0.844823i	$-0.320294\pi$
$138$		0			0
$139$	1.17108e18			0.712786			0.356393	−	0.934336i	$-0.384006\pi$
$139$	1.17108e18			0.712786			0.356393	+	0.934336i	$0.384006\pi$
$140$		0			0
$141$	−1.04181e18			−0.561600
$142$		0			0
$143$		−	2.22594e16i		−	0.0106453i
$144$		0			0
$145$	6.87780e16	−	9.84678e17i	0.0292295	−	0.418472i
$146$		0			0
$147$			7.79657e17i			0.294921i
$148$		0			0
$149$	2.93908e18			0.991124			0.495562	−	0.868573i	$-0.334962\pi$
$149$	2.93908e18			0.991124			0.495562	+	0.868573i	$0.334962\pi$
$150$		0			0
$151$	−2.52716e18			−0.760902			−0.380451	−	0.924801i	$-0.624231\pi$
$151$	−2.52716e18			−0.760902			−0.380451	+	0.924801i	$0.624231\pi$
$152$		0			0
$153$			2.41255e17i			0.0649530i
$154$		0			0
$155$	−2.22089e17	+	3.17960e18i	−0.0535437	+	0.766572i
$156$		0			0
$157$			5.25673e17i			0.113650i	0.998384	+	0.0568248i	$0.0180977\pi$
$157$			5.25673e17i			0.113650i	−0.998384	+	0.0568248i	$0.981902\pi$
$158$		0			0
$159$	−2.50047e18			−0.485452
$160$		0			0
$161$	6.13311e16			0.0107068
$162$		0			0
$163$			5.49012e18i			0.862953i	0.902124	+	0.431476i	$0.142007\pi$
$163$			5.49012e18i			0.862953i	−0.902124	+	0.431476i	$0.857993\pi$
$164$		0			0
$165$	−2.87500e18	−	2.00813e17i	−0.407403	−	0.0284564i
$166$		0			0
$167$			1.54439e19i			1.97546i	0.156175	+	0.987729i	$0.450083\pi$
$167$			1.54439e19i			1.97546i	−0.156175	+	0.987729i	$0.549917\pi$
$168$		0			0
$169$	8.64928e18			0.999869
$170$		0			0
$171$	6.40196e18			0.669647
$172$		0			0
$173$		−	6.59357e18i		−	0.624782i	−0.949954	−	0.312391i	$-0.898870\pi$
$173$		−	6.59357e18i		−	0.624782i	0.949954	−	0.312391i	$-0.101130\pi$
$174$		0			0
$175$	−9.26645e17	+	6.60092e18i	−0.0796324	+	0.567258i
$176$		0			0
$177$		−	3.55466e18i		−	0.277349i
$178$		0			0
$179$	1.38246e19			0.980400			0.490200	−	0.871610i	$-0.336924\pi$
$179$	1.38246e19			0.980400			0.490200	+	0.871610i	$0.336924\pi$
$180$		0			0
$181$	−1.27920e19			−0.825413			−0.412707	−	0.910864i	$-0.635417\pi$
$181$	−1.27920e19			−0.825413			−0.412707	+	0.910864i	$0.635417\pi$
$182$		0			0
$183$			7.44271e18i			0.437418i
$184$		0			0
$185$	−2.95121e19	−	2.06137e18i	−1.58140	−	0.110458i
$186$		0			0
$187$			1.53063e18i			0.0748544i
$188$		0			0
$189$	1.01718e19			0.454434
$190$		0			0
$191$	−1.69147e19			−0.691004			−0.345502	−	0.938418i	$-0.612291\pi$
$191$	−1.69147e19			−0.691004			−0.345502	+	0.938418i	$0.612291\pi$
$192$		0			0
$193$		−	3.85104e19i		−	1.43993i	−0.694011	−	0.719964i	$-0.744158\pi$
$193$		−	3.85104e19i		−	1.43993i	0.694011	−	0.719964i	$-0.255842\pi$
$194$		0			0
$195$	−1.02165e16	+	1.46267e17i	−0.000349951	+	0.00501017i
$196$		0			0
$197$		−	5.29078e19i		−	1.66172i	−0.556484	−	0.830858i	$-0.687850\pi$
$197$		−	5.29078e19i		−	1.66172i	0.556484	−	0.830858i	$-0.312150\pi$
$198$		0			0
$199$	5.02252e19			1.44767			0.723837	−	0.689971i	$-0.242377\pi$
$199$	5.02252e19			1.44767			0.723837	+	0.689971i	$0.242377\pi$
$200$		0			0
$201$	2.86060e18			0.0757340
$202$		0			0
$203$			9.87320e18i			0.240293i
$204$		0			0
$205$	1.70655e18	−	2.44322e19i	0.0382130	−	0.547086i
$206$		0			0
$207$			7.31875e17i			0.0150900i
$208$		0			0
$209$	4.06169e19			0.771727
$210$		0			0
$211$	−6.25806e19			−1.09658			−0.548288	−	0.836289i	$-0.684720\pi$
$211$	−6.25806e19			−1.09658			−0.548288	+	0.836289i	$0.684720\pi$
$212$		0			0
$213$		−	3.33100e19i		−	0.538701i
$214$		0			0
$215$	−8.33845e19	−	5.82426e18i	−1.24554	−	0.0869989i
$216$		0			0
$217$		−	3.18813e19i		−	0.440178i
$218$		0			0
$219$	5.71554e19			0.729932
$220$		0			0
$221$	7.78717e16			0.000920546
$222$		0			0
$223$			1.15820e20i			1.26821i	0.773246	+	0.634106i	$0.218632\pi$
$223$			1.15820e20i			1.26821i	−0.773246	+	0.634106i	$0.781368\pi$
$224$		0			0
$225$	−7.87699e19	−	1.10578e19i	−0.799482	−	0.112232i
$226$		0			0
$227$			1.47311e20i			1.38680i	0.720552	+	0.693401i	$0.243888\pi$
$227$			1.47311e20i			1.38680i	−0.720552	+	0.693401i	$0.756112\pi$
$228$		0			0
$229$	1.79644e20			1.56968			0.784841	−	0.619697i	$-0.212744\pi$
$229$	1.79644e20			1.56968			0.784841	+	0.619697i	$0.212744\pi$
$230$		0			0
$231$	2.88271e19			0.233937
$232$		0			0
$233$			3.47360e19i			0.261972i	0.991384	+	0.130986i	$0.0418143\pi$
$233$			3.47360e19i			0.261972i	−0.991384	+	0.130986i	$0.958186\pi$
$234$		0			0
$235$	−1.81983e20	−	1.27112e19i	−1.27630	−	0.0891475i
$236$		0			0
$237$			5.98646e19i			0.390669i
$238$		0			0
$239$	2.75666e20			1.67495			0.837473	−	0.546478i	$-0.184032\pi$
$239$	2.75666e20			1.67495			0.837473	+	0.546478i	$0.184032\pi$
$240$		0			0
$241$	−2.16087e20			−1.22316			−0.611579	−	0.791183i	$-0.709465\pi$
$241$	−2.16087e20			−1.22316			−0.611579	+	0.791183i	$0.709465\pi$
$242$		0			0
$243$			1.88542e20i			0.994845i
$244$		0			0
$245$	−9.51261e18	+	1.36190e20i	−0.0468153	+	0.670244i
$246$		0			0
$247$		−	2.06641e18i		−	0.00949056i
$248$		0			0
$249$	1.27865e20			0.548350
$250$		0			0
$251$	−8.83606e19			−0.354023			−0.177012	−	0.984209i	$-0.556643\pi$
$251$	−8.83606e19			−0.354023			−0.177012	+	0.984209i	$0.556643\pi$
$252$		0			0
$253$			4.64335e18i			0.0173903i
$254$		0			0
$255$	7.02521e17	−	1.00578e19i	0.00246075	−	0.0352300i
$256$		0			0
$257$		−	8.99412e19i		−	0.294800i	−0.989077	−	0.147400i	$-0.952910\pi$
$257$		−	8.99412e19i		−	0.294800i	0.989077	−	0.147400i	$-0.0470904\pi$
$258$		0			0
$259$	2.95913e20			0.908064
$260$		0			0
$261$	−1.17819e20			−0.338664
$262$		0			0
$263$		−	4.85249e20i		−	1.30720i	−0.756841	−	0.653599i	$-0.773258\pi$
$263$		−	4.85249e20i		−	1.30720i	0.756841	−	0.653599i	$-0.226742\pi$
$264$		0			0
$265$	−4.36780e20	−	3.05083e19i	−1.10325	−	0.0770598i
$266$		0			0
$267$		−	2.44721e20i		−	0.579862i
$268$		0			0
$269$	4.15720e20			0.924499			0.462249	−	0.886750i	$-0.347042\pi$
$269$	4.15720e20			0.924499			0.462249	+	0.886750i	$0.347042\pi$
$270$		0			0
$271$	−1.31018e20			−0.273585			−0.136793	−	0.990600i	$-0.543679\pi$
$271$	−1.31018e20			−0.273585			−0.136793	+	0.990600i	$0.543679\pi$
$272$		0			0
$273$		−	1.46660e18i		−	0.00287692i
$274$		0			0
$275$	−4.99752e20	−	7.01558e19i	−0.921354	−	0.129341i
$276$		0			0
$277$		−	3.70408e20i		−	0.642100i	−0.947062	−	0.321050i	$-0.895964\pi$
$277$		−	3.70408e20i		−	0.642100i	0.947062	−	0.321050i	$-0.104036\pi$
$278$		0			0
$279$	3.80445e20			0.620378
$280$		0			0
$281$	−2.18104e20			−0.334704			−0.167352	−	0.985897i	$-0.553522\pi$
$281$	−2.18104e20			−0.334704			−0.167352	+	0.985897i	$0.553522\pi$
$282$		0			0
$283$		−	1.17331e21i		−	1.69523i	−0.530611	−	0.847616i	$-0.678037\pi$
$283$		−	1.17331e21i		−	1.69523i	0.530611	−	0.847616i	$-0.321963\pi$
$284$		0			0
$285$	−2.66895e20	−	1.86421e19i	−0.363211	−	0.0253696i
$286$		0			0
$287$			2.44978e20i			0.314146i
$288$		0			0
$289$	8.21886e20			0.993527
$290$		0			0
$291$	−1.10117e20			−0.125535
$292$		0			0
$293$			4.00436e20i			0.430684i	0.976539	+	0.215342i	$0.0690866\pi$
$293$			4.00436e20i			0.430684i	−0.976539	+	0.215342i	$0.930913\pi$
$294$		0			0
$295$	4.33705e19	−	6.20926e20i	0.0440258	−	0.630307i
$296$		0			0
$297$			7.70098e20i			0.738102i
$298$		0			0
$299$	2.36233e17			0.000213863
$300$		0			0
$301$	8.36082e20			0.715210
$302$		0			0
$303$			2.17308e20i			0.175717i
$304$		0			0
$305$	−9.08087e19	+	1.30009e21i	−0.0694350	+	0.994085i
$306$		0			0
$307$		−	4.64633e20i		−	0.336073i	−0.985781	−	0.168037i	$-0.946257\pi$
$307$		−	4.64633e20i		−	0.336073i	0.985781	−	0.168037i	$-0.0537427\pi$
$308$		0			0
$309$	−5.45877e20			−0.373635
$310$		0			0
$311$	−1.54971e21			−1.00412			−0.502060	−	0.864833i	$-0.667424\pi$
$311$	−1.54971e21			−1.00412			−0.502060	+	0.864833i	$0.667424\pi$
$312$		0			0
$313$			2.22175e21i			1.36323i	0.731713	+	0.681613i	$0.238721\pi$
$313$			2.22175e21i			1.36323i	−0.731713	+	0.681613i	$0.761279\pi$
$314$		0			0
$315$	7.93685e20	+	5.54374e19i	0.461326	+	0.0322228i
$316$		0			0
$317$			1.76769e21i			0.973646i	0.873501	+	0.486823i	$0.161844\pi$
$317$			1.76769e21i			0.973646i	−0.873501	+	0.486823i	$0.838156\pi$
$318$		0			0
$319$	−7.47495e20			−0.390290
$320$		0			0
$321$	−9.80992e20			−0.485705
$322$		0			0
$323$			1.42093e20i			0.0667348i
$324$		0			0
$325$	−3.56921e18	+	2.54252e19i	−0.00159061	+	0.0113307i
$326$		0			0
$327$			3.62989e20i			0.153546i
$328$		0			0
$329$	1.82471e21			0.732874
$330$		0			0
$331$	2.81224e21			1.07279			0.536394	−	0.843967i	$-0.319786\pi$
$331$	2.81224e21			1.07279			0.536394	+	0.843967i	$0.319786\pi$
$332$		0			0
$333$			3.53118e21i			1.27981i
$334$		0			0
$335$	4.99687e20	+	3.49022e19i	0.172114	+	0.0120219i
$336$		0			0
$337$		−	3.43159e21i		−	1.12368i	−0.827247	−	0.561838i	$-0.810094\pi$
$337$		−	3.43159e21i		−	1.12368i	0.827247	−	0.561838i	$-0.189906\pi$
$338$		0			0
$339$	−9.06350e20			−0.282227
$340$		0			0
$341$	2.41372e21			0.714948
$342$		0			0
$343$		−	3.39800e21i		−	0.957685i
$344$		0			0
$345$	2.13118e18	−	3.05116e19i	0.000571686	−	0.00818469i
$346$		0			0
$347$			2.42288e20i			0.0618773i	0.999521	+	0.0309387i	$0.00984965\pi$
$347$			2.42288e20i			0.0618773i	−0.999521	+	0.0309387i	$0.990150\pi$
$348$		0			0
$349$	−7.34788e21			−1.78709			−0.893544	−	0.448976i	$-0.851789\pi$
$349$	−7.34788e21			−1.78709			−0.893544	+	0.448976i	$0.851789\pi$
$350$		0			0
$351$	3.91792e19			0.00907705
$352$		0			0
$353$		−	2.16796e21i		−	0.478592i	−0.970947	−	0.239296i	$-0.923083\pi$
$353$		−	2.16796e21i		−	0.478592i	0.970947	−	0.239296i	$-0.0769167\pi$
$354$		0			0
$355$	4.06416e20	−	5.81856e21i	0.0855125	−	1.22426i
$356$		0			0
$357$			1.00848e20i			0.0202296i
$358$		0			0
$359$	−5.57848e21			−1.06712			−0.533560	−	0.845762i	$-0.679146\pi$
$359$	−5.57848e21			−1.06712			−0.533560	+	0.845762i	$0.679146\pi$
$360$		0			0
$361$	−1.70979e21			−0.311984
$362$		0			0
$363$		−	3.38803e20i		−	0.0589850i
$364$		0			0
$365$	9.98386e21	+	6.97354e20i	1.65886	+	0.115868i
$366$		0			0
$367$		−	5.15562e21i		−	0.817748i	−0.912591	−	0.408874i	$-0.865922\pi$
$367$		−	5.15562e21i		−	0.817748i	0.912591	−	0.408874i	$-0.134078\pi$
$368$		0			0
$369$	−2.92336e21			−0.442750
$370$		0			0
$371$	4.37952e21			0.633502
$372$		0			0
$373$		−	1.16300e22i		−	1.60714i	−0.595209	−	0.803571i	$-0.702931\pi$
$373$		−	1.16300e22i		−	1.60714i	0.595209	−	0.803571i	$-0.297069\pi$
$374$		0			0
$375$	3.25168e21	+	6.90369e20i	0.429381	+	0.0911624i
$376$		0			0
$377$			3.80292e19i			0.00479972i
$378$		0			0
$379$	−4.10676e21			−0.495525			−0.247763	−	0.968821i	$-0.579695\pi$
$379$	−4.10676e21			−0.495525			−0.247763	+	0.968821i	$0.579695\pi$
$380$		0			0
$381$	1.39564e21			0.161032
$382$		0			0
$383$			7.92184e21i			0.874252i	0.899400	+	0.437126i	$0.144004\pi$
$383$			7.92184e21i			0.874252i	−0.899400	+	0.437126i	$0.855996\pi$
$384$		0			0
$385$	5.03550e21	+	3.51720e20i	0.531650	+	0.0371348i
$386$		0			0
$387$			9.97712e21i			1.00800i
$388$		0			0
$389$	−1.41357e22			−1.36693			−0.683466	−	0.729983i	$-0.739528\pi$
$389$	−1.41357e22			−1.36693			−0.683466	+	0.729983i	$0.739528\pi$
$390$		0			0
$391$	−1.62442e19			−0.00150382
$392$		0			0
$393$			4.17982e21i			0.370528i
$394$		0			0
$395$	−7.30409e20	+	1.04571e22i	−0.0620142	+	0.887842i
$396$		0			0
$397$		−	1.01127e22i		−	0.822526i	−0.911517	−	0.411263i	$-0.865088\pi$
$397$		−	1.01127e22i		−	0.822526i	0.911517	−	0.411263i	$-0.134912\pi$
$398$		0			0
$399$	2.67611e21			0.208562
$400$		0			0
$401$	9.77567e21			0.730162			0.365081	−	0.930976i	$-0.381041\pi$
$401$	9.77567e21			0.730162			0.365081	+	0.930976i	$0.381041\pi$
$402$		0			0
$403$		−	1.22799e20i		−	0.00879230i
$404$		0			0
$405$	−4.65976e20	+	6.67127e21i	−0.0319886	+	0.457974i
$406$		0			0
$407$			2.24034e22i			1.47490i
$408$		0			0
$409$	−1.10530e22			−0.697960			−0.348980	−	0.937130i	$-0.613472\pi$
$409$	−1.10530e22			−0.697960			−0.348980	+	0.937130i	$0.613472\pi$
$410$		0			0
$411$	1.22424e22			0.741673
$412$		0			0
$413$			6.22592e21i			0.361933i
$414$		0			0
$415$	2.23354e22	+	1.56009e21i	1.24619	+	0.0870442i
$416$		0			0
$417$			5.84161e21i			0.312879i
$418$		0			0
$419$	−3.43934e22			−1.76871			−0.884353	−	0.466819i	$-0.845400\pi$
$419$	−3.43934e22			−1.76871			−0.884353	+	0.466819i	$0.845400\pi$
$420$		0			0
$421$	−1.69964e21			−0.0839381			−0.0419691	−	0.999119i	$-0.513363\pi$
$421$	−1.69964e21			−0.0839381			−0.0419691	+	0.999119i	$0.513363\pi$
$422$		0			0
$423$			2.17746e22i			1.03290i
$424$		0			0
$425$	2.45431e20	−	1.74832e21i	0.0111847	−	0.0796737i
$426$		0			0
$427$		−	1.30357e22i		−	0.570820i
$428$		0			0
$429$	1.11035e20			0.00467276
$430$		0			0
$431$	−5.25915e21			−0.212745			−0.106372	−	0.994326i	$-0.533924\pi$
$431$	−5.25915e21			−0.212745			−0.106372	+	0.994326i	$0.533924\pi$
$432$		0			0
$433$		−	3.96890e22i		−	1.54356i	−0.635892	−	0.771778i	$-0.719368\pi$
$433$		−	3.96890e22i		−	1.54356i	0.635892	−	0.771778i	$-0.280632\pi$
$434$		0			0
$435$	4.91181e21	+	3.43081e20i	0.183689	+	0.0128303i
$436$		0			0
$437$			4.31056e20i			0.0155039i
$438$		0			0
$439$	−1.16302e21			−0.0402383			−0.0201191	−	0.999798i	$-0.506405\pi$
$439$	−1.16302e21			−0.0402383			−0.0201191	+	0.999798i	$0.506405\pi$
$440$		0			0
$441$	1.62954e22			0.542421
$442$		0			0
$443$			1.32297e22i			0.423757i	0.977296	+	0.211878i	$0.0679581\pi$
$443$			1.32297e22i			0.423757i	−0.977296	+	0.211878i	$0.932042\pi$
$444$		0			0
$445$	2.98584e21	−	4.27476e22i	0.0920464	−	1.31781i
$446$		0			0
$447$			1.46608e22i			0.435055i
$448$		0			0
$449$	3.39299e22			0.969368			0.484684	−	0.874689i	$-0.338935\pi$
$449$	3.39299e22			0.969368			0.484684	+	0.874689i	$0.338935\pi$
$450$		0			0
$451$	−1.85472e22			−0.510243
$452$		0			0
$453$		−	1.26061e22i		−	0.333999i
$454$		0			0
$455$	1.78940e19	−	2.56184e20i	0.000456677	−	0.00653814i
$456$		0			0
$457$		−	7.61346e22i		−	1.87195i	−0.352065	−	0.935976i	$-0.614520\pi$
$457$		−	7.61346e22i		−	1.87195i	0.352065	−	0.935976i	$-0.385480\pi$
$458$		0			0
$459$	−2.69409e21			−0.0638271
$460$		0			0
$461$	−3.05919e22			−0.698471			−0.349235	−	0.937035i	$-0.613559\pi$
$461$	−3.05919e22			−0.698471			−0.349235	+	0.937035i	$0.613559\pi$
$462$		0			0
$463$		−	4.13172e22i		−	0.909270i	−0.890678	−	0.454635i	$-0.849770\pi$
$463$		−	4.13172e22i		−	0.909270i	0.890678	−	0.454635i	$-0.150230\pi$
$464$		0			0
$465$	−1.58606e22	−	1.10783e21i	−0.336488	−	0.0235031i
$466$		0			0
$467$		−	2.41963e22i		−	0.494944i	−0.968895	−	0.247472i	$-0.920400\pi$
$467$		−	2.41963e22i		−	0.494944i	0.968895	−	0.247472i	$-0.0795999\pi$
$468$		0			0
$469$	−5.01028e21			−0.0988309
$470$		0			0
$471$	−2.62218e21			−0.0498867
$472$		0			0
$473$			6.32994e22i			1.16166i
$474$		0			0
$475$	−4.63935e22	−	6.51278e21i	−0.821413	−	0.115311i
$476$		0			0
$477$			5.22616e22i			0.892845i
$478$		0			0
$479$	5.15334e22			0.849644			0.424822	−	0.905277i	$-0.360337\pi$
$479$	5.15334e22			0.849644			0.424822	+	0.905277i	$0.360337\pi$
$480$		0			0
$481$	1.13979e21			0.0181380
$482$		0			0
$483$			3.05934e20i			0.00469978i
$484$		0			0
$485$	−1.92352e22	−	1.34354e21i	−0.285293	−	0.0199272i
$486$		0			0
$487$		−	4.38806e22i		−	0.628458i	−0.949347	−	0.314229i	$-0.898254\pi$
$487$		−	4.38806e22i		−	0.628458i	0.949347	−	0.314229i	$-0.101746\pi$
$488$		0			0
$489$	−2.73860e22			−0.378794
$490$		0			0
$491$	1.04309e23			1.39357			0.696787	−	0.717278i	$-0.254612\pi$
$491$	1.04309e23			1.39357			0.696787	+	0.717278i	$0.254612\pi$
$492$		0			0
$493$		−	2.61502e21i		−	0.0337502i
$494$		0			0
$495$	−4.19714e21	+	6.00895e22i	−0.0523371	+	0.749297i
$496$		0			0
$497$			5.83417e22i			0.702991i
$498$		0			0
$499$	9.97077e22			1.16111			0.580556	−	0.814220i	$-0.302835\pi$
$499$	9.97077e22			1.16111			0.580556	+	0.814220i	$0.302835\pi$
$500$		0			0
$501$	−7.70380e22			−0.867131
$502$		0			0
$503$			7.99430e22i			0.869867i	0.900463	+	0.434933i	$0.143228\pi$
$503$			7.99430e22i			0.869867i	−0.900463	+	0.434933i	$0.856772\pi$
$504$		0			0
$505$	−2.65138e21	+	3.79591e22i	−0.0278930	+	0.399337i
$506$		0			0
$507$			4.31447e22i			0.438894i
$508$		0			0
$509$	1.58395e23			1.55827			0.779133	−	0.626859i	$-0.215660\pi$
$509$	1.58395e23			1.55827			0.779133	+	0.626859i	$0.215660\pi$
$510$		0			0
$511$	−1.00106e23			−0.952543
$512$		0			0
$513$			7.14906e22i			0.658038i
$514$		0			0
$515$	−9.53532e22	−	6.66025e21i	−0.849129	−	0.0593102i
$516$		0			0
$517$			1.38148e23i			1.19035i
$518$		0			0
$519$	3.28903e22			0.274249
$520$		0			0
$521$	−1.45303e23			−1.17261			−0.586306	−	0.810090i	$-0.699418\pi$
$521$	−1.45303e23			−1.17261			−0.586306	+	0.810090i	$0.699418\pi$
$522$		0			0
$523$		−	1.64129e23i		−	1.28210i	−0.767499	−	0.641050i	$-0.778499\pi$
$523$		−	1.64129e23i		−	1.28210i	0.767499	−	0.641050i	$-0.221501\pi$
$524$		0			0
$525$	−3.29270e22	−	4.62233e21i	−0.248999	−	0.0349548i
$526$		0			0
$527$			8.44409e21i			0.0618248i
$528$		0			0
$529$	1.41001e23			0.999651
$530$		0			0
$531$	−7.42949e22			−0.510101
$532$		0			0
$533$			9.43596e20i			0.00627487i
$534$		0			0
$535$	−1.71359e23	−	1.19691e22i	−1.10382	−	0.0771000i
$536$		0			0
$537$			6.89606e22i			0.430348i
$538$		0			0
$539$	1.03385e23			0.625106
$540$		0			0
$541$	2.16545e23			1.26873			0.634367	−	0.773032i	$-0.281261\pi$
$541$	2.16545e23			1.26873			0.634367	+	0.773032i	$0.281261\pi$
$542$		0			0
$543$		−	6.38097e22i		−	0.362317i
$544$		0			0
$545$	−4.42883e21	+	6.34066e22i	−0.0243736	+	0.348951i
$546$		0			0
$547$		−	3.49615e23i		−	1.86508i	−0.361064	−	0.932541i	$-0.617586\pi$
$547$		−	3.49615e23i		−	1.86508i	0.361064	−	0.932541i	$-0.382414\pi$
$548$		0			0
$549$	1.55558e23			0.804502
$550$		0			0
$551$	−6.93922e22			−0.347954
$552$		0			0
$553$		−	1.04852e23i		−	0.509813i
$554$		0			0
$555$	1.02826e22	−	1.47214e23i	0.0484856	−	0.694157i
$556$		0			0
$557$		−	1.56088e22i		−	0.0713839i	−0.999363	−	0.0356919i	$-0.988636\pi$
$557$		−	1.56088e22i		−	0.0713839i	0.999363	−	0.0356919i	$-0.0113635\pi$
$558$		0			0
$559$	3.22039e21			0.0142859
$560$		0			0
$561$	−7.63516e21			−0.0328575
$562$		0			0
$563$		−	1.54986e23i		−	0.647099i	−0.946211	−	0.323550i	$-0.895124\pi$
$563$		−	1.54986e23i		−	0.647099i	0.946211	−	0.323550i	$-0.104876\pi$
$564$		0			0
$565$	−1.58320e23	−	1.10584e22i	−0.641394	−	0.0448002i
$566$		0			0
$567$		−	6.68917e22i		−	0.262976i
$568$		0			0
$569$	−2.22901e23			−0.850468			−0.425234	−	0.905083i	$-0.639808\pi$
$569$	−2.22901e23			−0.850468			−0.425234	+	0.905083i	$0.639808\pi$
$570$		0			0
$571$	−4.79371e22			−0.177527			−0.0887637	−	0.996053i	$-0.528292\pi$
$571$	−4.79371e22			−0.177527			−0.0887637	+	0.996053i	$0.528292\pi$
$572$		0			0
$573$		−	8.43745e22i		−	0.303317i
$574$		0			0
$575$	7.44544e20	−	5.30373e21i	0.00259845	−	0.0185099i
$576$		0			0
$577$		−	8.37199e22i		−	0.283684i	−0.989889	−	0.141842i	$-0.954698\pi$
$577$		−	8.37199e22i		−	0.283684i	0.989889	−	0.141842i	$-0.0453024\pi$
$578$		0			0
$579$	1.92099e23			0.632059
$580$		0			0
$581$	−2.23953e23			−0.715583
$582$		0			0
$583$			3.31571e23i			1.02895i
$584$		0			0
$585$	3.05708e21	+	2.13532e20i	0.00921472	+	0.000643632i
$586$		0			0
$587$		−	3.07053e23i		−	0.899063i	−0.893265	−	0.449531i	$-0.851591\pi$
$587$		−	3.07053e23i		−	0.899063i	0.893265	−	0.449531i	$-0.148409\pi$
$588$		0			0
$589$	2.24073e23			0.637396
$590$		0			0
$591$	2.63917e23			0.729413
$592$		0			0
$593$			1.81111e23i			0.486385i	0.969978	+	0.243193i	$0.0781947\pi$
$593$			1.81111e23i			0.486385i	−0.969978	+	0.243193i	$0.921805\pi$
$594$		0			0
$595$	−1.23045e21	+	1.76161e22i	−0.00321122	+	0.0459742i
$596$		0			0
$597$			2.50535e23i			0.635458i
$598$		0			0
$599$	1.26579e23			0.312057			0.156028	−	0.987753i	$-0.450131\pi$
$599$	1.26579e23			0.312057			0.156028	+	0.987753i	$0.450131\pi$
$600$		0			0
$601$	−2.83226e23			−0.678734			−0.339367	−	0.940654i	$-0.610213\pi$
$601$	−2.83226e23			−0.678734			−0.339367	+	0.940654i	$0.610213\pi$
$602$		0			0
$603$		−	5.97885e22i		−	0.139290i
$604$		0			0
$605$	4.13375e21	−	5.91819e22i	0.00936318	−	0.134050i
$606$		0			0
$607$			7.56311e23i			1.66570i	0.553500	+	0.832849i	$0.313292\pi$
$607$			7.56311e23i			1.66570i	−0.553500	+	0.832849i	$0.686708\pi$
$608$		0			0
$609$	−4.92499e22			−0.105477
$610$		0			0
$611$	7.02836e21			0.0146387
$612$		0			0
$613$			5.21867e23i			1.05717i	0.848880	+	0.528586i	$0.177278\pi$
$613$			5.21867e23i			1.05717i	−0.848880	+	0.528586i	$0.822722\pi$
$614$		0			0
$615$	1.21874e23	+	8.51267e21i	0.240144	+	0.0167736i
$616$		0			0
$617$		−	9.91259e21i		−	0.0190004i	−0.999955	−	0.00950021i	$-0.996976\pi$
$617$		−	9.91259e21i		−	0.0190004i	0.999955	−	0.00950021i	$-0.00302406\pi$
$618$		0			0
$619$	−7.36588e23			−1.37358			−0.686790	−	0.726856i	$-0.740981\pi$
$619$	−7.36588e23			−1.37358			−0.686790	+	0.726856i	$0.740981\pi$
$620$		0			0
$621$	−8.17284e21			−0.0148284
$622$		0			0
$623$			4.28623e23i			0.756705i
$624$		0			0
$625$	5.59578e23	+	1.60267e23i	0.961348	+	0.275337i
$626$		0			0
$627$			2.02607e23i			0.338751i
$628$		0			0
$629$	−7.83757e22			−0.127541
$630$		0			0
$631$	6.98066e23			1.10572			0.552862	−	0.833273i	$-0.313536\pi$
$631$	6.98066e23			1.10572			0.552862	+	0.833273i	$0.313536\pi$
$632$		0			0
$633$		−	3.12167e23i		−	0.481344i
$634$		0			0
$635$	2.43789e23	+	1.70282e22i	0.365964	+	0.0255619i
$636$		0			0
$637$		−	5.25978e21i		−	0.00768745i
$638$		0			0
$639$	−6.96202e23			−0.990782
$640$		0			0
$641$	6.23825e23			0.864509			0.432254	−	0.901752i	$-0.357718\pi$
$641$	6.23825e23			0.864509			0.432254	+	0.901752i	$0.357718\pi$
$642$		0			0
$643$			3.46371e23i			0.467465i	0.972301	+	0.233732i	$0.0750939\pi$
$643$			3.46371e23i			0.467465i	−0.972301	+	0.233732i	$0.924906\pi$
$644$		0			0
$645$	2.90528e22	−	4.15942e23i	0.0381883	−	0.546733i
$646$		0			0
$647$			2.47826e23i			0.317293i	0.987335	+	0.158647i	$0.0507131\pi$
$647$			2.47826e23i			0.317293i	−0.987335	+	0.158647i	$0.949287\pi$
$648$		0			0
$649$	−4.71361e23			−0.587860
$650$		0			0
$651$	1.59032e23			0.193217
$652$		0			0
$653$		−	1.24507e24i		−	1.47378i	−0.676011	−	0.736891i	$-0.736293\pi$
$653$		−	1.24507e24i		−	1.47378i	0.676011	−	0.736891i	$-0.263707\pi$
$654$		0			0
$655$	−5.09980e22	+	7.30127e23i	−0.0588169	+	0.842068i
$656$		0			0
$657$		−	1.19459e24i		−	1.34249i
$658$		0			0
$659$	−1.18538e24			−1.29817			−0.649085	−	0.760716i	$-0.724848\pi$
$659$	−1.18538e24			−1.29817			−0.649085	+	0.760716i	$0.724848\pi$
$660$		0			0
$661$	−7.63244e23			−0.814613			−0.407306	−	0.913292i	$-0.633532\pi$
$661$	−7.63244e23			−0.814613			−0.407306	+	0.913292i	$0.633532\pi$
$662$		0			0
$663$			3.88443e20i			0.000404075i
$664$		0			0
$665$	4.67460e23	+	3.26513e22i	0.473981	+	0.0331067i
$666$		0			0
$667$		−	7.93295e21i		−	0.00784089i
$668$		0			0
$669$	−5.77738e23			−0.556684
$670$		0			0
$671$	9.86930e23			0.927139
$672$		0			0
$673$			1.42179e23i			0.130229i	0.997878	+	0.0651144i	$0.0207412\pi$
$673$			1.42179e23i			0.130229i	−0.997878	+	0.0651144i	$0.979259\pi$
$674$		0			0
$675$	1.23483e23	−	8.79623e23i	0.110287	−	0.785623i
$676$		0			0
$677$		−	1.54090e24i		−	1.34205i	−0.741433	−	0.671027i	$-0.765853\pi$
$677$		−	1.54090e24i		−	1.34205i	0.741433	−	0.671027i	$-0.234147\pi$
$678$		0			0
$679$	1.92868e23			0.163820
$680$		0			0
$681$	−7.34821e23			−0.608739
$682$		0			0
$683$		−	2.32059e24i		−	1.87509i	−0.347865	−	0.937545i	$-0.613093\pi$
$683$		−	2.32059e24i		−	1.87509i	0.347865	−	0.937545i	$-0.386907\pi$
$684$		0			0
$685$	2.13850e24	+	1.49370e23i	1.68554	+	0.117732i
$686$		0			0
$687$			8.96109e23i			0.689015i
$688$		0			0
$689$	1.68689e22			0.0126538
$690$		0			0
$691$	3.27287e23			0.239533			0.119766	−	0.992802i	$-0.461785\pi$
$691$	3.27287e23			0.239533			0.119766	+	0.992802i	$0.461785\pi$
$692$		0			0
$693$		−	6.02507e23i		−	0.430258i
$694$		0			0
$695$	−7.12736e22	+	1.02041e24i	−0.0496658	+	0.711054i
$696$		0			0
$697$		−	6.48849e22i		−	0.0441230i
$698$		0			0
$699$	−1.73272e23			−0.114993
$700$		0			0
$701$	5.06478e22			0.0328063			0.0164032	−	0.999865i	$-0.494778\pi$
$701$	5.06478e22			0.0328063			0.0164032	+	0.999865i	$0.494778\pi$
$702$		0			0
$703$			2.07978e24i			1.31491i
$704$		0			0
$705$	6.34064e22	−	9.07775e23i	0.0391314	−	0.560235i
$706$		0			0
$707$		−	3.80610e23i		−	0.229306i
$708$		0			0
$709$	−2.97489e24			−1.74975			−0.874877	−	0.484344i	$-0.839058\pi$
$709$	−2.97489e24			−1.74975			−0.874877	+	0.484344i	$0.839058\pi$
$710$		0			0
$711$	1.25121e24			0.718520
$712$		0			0
$713$			2.56161e22i			0.0143632i
$714$		0			0
$715$	1.93955e22	+	1.35474e21i	0.0106194	+	0.000741746i
$716$		0			0
$717$			1.37509e24i			0.735220i
$718$		0			0
$719$	−2.64437e24			−1.38079			−0.690393	−	0.723435i	$-0.742562\pi$
$719$	−2.64437e24			−1.38079			−0.690393	+	0.723435i	$0.742562\pi$
$720$		0			0
$721$	9.56091e23			0.487584
$722$		0			0
$723$		−	1.07789e24i		−	0.536907i
$724$		0			0
$725$	8.53805e23	+	1.19858e23i	0.415418	+	0.0583169i
$726$		0			0
$727$			3.89057e24i			1.84914i	0.381007	+	0.924572i	$0.375577\pi$
$727$			3.89057e24i			1.84914i	−0.381007	+	0.924572i	$0.624423\pi$
$728$		0			0
$729$	4.82447e22			0.0224009
$730$		0			0
$731$	−2.21445e23			−0.100454
$732$		0			0
$733$			2.92056e24i			1.29444i	0.762304	+	0.647220i	$0.224068\pi$
$733$			2.92056e24i			1.29444i	−0.762304	+	0.647220i	$0.775932\pi$
$734$		0			0
$735$	−6.79347e23	−	4.74512e22i	−0.294205	−	0.0205497i
$736$		0			0
$737$		−	3.79326e23i		−	0.160523i
$738$		0			0
$739$	2.80453e24			1.15980			0.579898	−	0.814689i	$-0.303092\pi$
$739$	2.80453e24			1.15980			0.579898	+	0.814689i	$0.303092\pi$
$740$		0			0
$741$	1.03077e22			0.00416590
$742$		0			0
$743$			3.22775e24i			1.27496i	0.770468	+	0.637478i	$0.220022\pi$
$743$			3.22775e24i			1.27496i	−0.770468	+	0.637478i	$0.779978\pi$
$744$		0			0
$745$	−1.78877e23	+	2.56094e24i	−0.0690599	+	0.988715i
$746$		0			0
$747$		−	2.67247e24i		−	1.00853i
$748$		0			0
$749$	1.71819e24			0.633833
$750$		0			0
$751$	9.11135e23			0.328582			0.164291	−	0.986412i	$-0.447466\pi$
$751$	9.11135e23			0.328582			0.164291	+	0.986412i	$0.447466\pi$
$752$		0			0
$753$		−	4.40764e23i		−	0.155399i
$754$		0			0
$755$	1.53807e23	−	2.20202e24i	0.0530184	−	0.759052i
$756$		0			0
$757$			7.82526e23i			0.263745i	0.991267	+	0.131872i	$0.0420989\pi$
$757$			7.82526e23i			0.263745i	−0.991267	+	0.131872i	$0.957901\pi$
$758$		0			0
$759$	−2.31621e22			−0.00763349
$760$		0			0
$761$	−2.33932e24			−0.753912			−0.376956	−	0.926231i	$-0.623029\pi$
$761$	−2.33932e24			−0.753912			−0.376956	+	0.926231i	$0.623029\pi$
$762$		0			0
$763$		−	6.35767e23i		−	0.200373i
$764$		0			0
$765$	−2.10216e23	−	1.46832e22i	−0.0647952	−	0.00452582i
$766$		0			0
$767$			2.39807e22i			0.00722939i
$768$		0			0
$769$	3.17224e24			0.935388			0.467694	−	0.883891i	$-0.345085\pi$
$769$	3.17224e24			0.935388			0.467694	+	0.883891i	$0.345085\pi$
$770$		0			0
$771$	4.48648e23			0.129403
$772$		0			0
$773$			1.00492e24i			0.283534i	0.989900	+	0.141767i	$0.0452784\pi$
$773$			1.00492e24i			0.283534i	−0.989900	+	0.141767i	$0.954722\pi$
$774$		0			0
$775$	−2.75700e24	−	3.87031e23i	−0.760978	−	0.106827i
$776$		0			0
$777$			1.47609e24i			0.398596i
$778$		0			0
$779$	−1.72179e24			−0.454895
$780$		0			0
$781$	−4.41702e24			−1.14182
$782$		0			0
$783$		−	1.31568e24i		−	0.332794i
$784$		0			0
$785$	−4.58040e23	−	3.19933e22i	−0.113373	−	0.00791893i
$786$		0			0
$787$		−	8.15000e24i		−	1.97412i	−0.160365	−	0.987058i	$-0.551267\pi$
$787$		−	8.15000e24i		−	1.97412i	0.160365	−	0.987058i	$-0.448733\pi$
$788$		0			0
$789$	2.42054e24			0.573796
$790$		0			0
$791$	1.58745e24			0.368299
$792$		0			0
$793$		−	5.02106e22i		−	0.0114018i
$794$		0			0
$795$	1.52183e23	−	2.17876e24i	0.0338255	−	0.484272i
$796$		0			0
$797$		−	3.83723e24i		−	0.834876i	−0.908705	−	0.417438i	$-0.862928\pi$
$797$		−	3.83723e24i		−	0.834876i	0.908705	−	0.417438i	$-0.137072\pi$
$798$		0			0
$799$	−4.83294e23			−0.102935
$800$		0			0
$801$	−5.11483e24			−1.06649
$802$		0			0
$803$		−	7.57901e24i		−	1.54714i
$804$		0			0
$805$	−3.73271e21	+	5.34403e22i	−0.000746035	+	0.0106808i
$806$		0			0
$807$			2.07371e24i			0.405810i
$808$		0			0
$809$	8.12096e24			1.55613			0.778064	−	0.628185i	$-0.216202\pi$
$809$	8.12096e24			1.55613			0.778064	+	0.628185i	$0.216202\pi$
$810$		0			0
$811$	6.16668e24			1.15711			0.578554	−	0.815644i	$-0.303617\pi$
$811$	6.16668e24			1.15711			0.578554	+	0.815644i	$0.303617\pi$
$812$		0			0
$813$		−	6.53550e23i		−	0.120091i
$814$		0			0
$815$	−4.78376e24	−	3.34137e23i	−0.860855	−	0.0601292i
$816$		0			0
$817$			5.87627e24i			1.03565i
$818$		0			0
$819$	−3.06528e22			−0.00529124
$820$		0			0
$821$	−3.44858e24			−0.583074			−0.291537	−	0.956560i	$-0.594167\pi$
$821$	−3.44858e24			−0.583074			−0.291537	+	0.956560i	$0.594167\pi$
$822$		0			0
$823$		−	5.80386e23i		−	0.0961210i	−0.998844	−	0.0480605i	$-0.984696\pi$
$823$		−	5.80386e23i		−	0.0961210i	0.998844	−	0.0480605i	$-0.0153040\pi$
$824$		0			0
$825$	3.49954e23	−	2.49288e24i	0.0567744	−	0.404430i
$826$		0			0
$827$		−	3.09602e24i		−	0.492048i	−0.969264	−	0.246024i	$-0.920876\pi$
$827$		−	3.09602e24i		−	0.492048i	0.969264	−	0.246024i	$-0.0791242\pi$
$828$		0			0
$829$	3.40942e24			0.530844			0.265422	−	0.964132i	$-0.414489\pi$
$829$	3.40942e24			0.530844			0.265422	+	0.964132i	$0.414489\pi$
$830$		0			0
$831$	1.84768e24			0.281851
$832$		0			0
$833$			3.61680e23i			0.0540558i
$834$		0			0
$835$	−1.34569e25	−	9.39943e23i	−1.97066	−	0.137647i
$836$		0			0
$837$			4.24843e24i			0.609624i
$838$		0			0
$839$	9.38827e24			1.32011			0.660053	−	0.751219i	$-0.270534\pi$
$839$	9.38827e24			1.32011			0.660053	+	0.751219i	$0.270534\pi$
$840$		0			0
$841$	−5.98009e24			−0.824027
$842$		0			0
$843$		−	1.08796e24i		−	0.146919i
$844$		0			0
$845$	−5.26409e23	+	7.53648e24i	−0.0696693	+	0.997439i
$846$		0			0
$847$			5.93407e23i			0.0769739i
$848$		0			0
$849$	5.85276e24			0.744125
$850$		0			0
$851$	−2.37761e23			−0.0296306
$852$		0			0
$853$		−	9.91412e23i		−	0.121112i	−0.998165	−	0.0605560i	$-0.980713\pi$
$853$		−	9.91412e23i		−	0.121112i	0.998165	−	0.0605560i	$-0.0192874\pi$
$854$		0			0
$855$	−3.89633e23	+	5.57829e24i	−0.0466599	+	0.668019i
$856$		0			0
$857$			7.06301e24i			0.829188i	0.910007	+	0.414594i	$0.136076\pi$
$857$			7.06301e24i			0.829188i	−0.910007	+	0.414594i	$0.863924\pi$
$858$		0			0
$859$	1.24591e24			0.143398			0.0716992	−	0.997426i	$-0.477158\pi$
$859$	1.24591e24			0.143398			0.0716992	+	0.997426i	$0.477158\pi$
$860$		0			0
$861$	−1.22201e24			−0.137895
$862$		0			0
$863$			1.46337e25i			1.61906i	0.587082	+	0.809528i	$0.300277\pi$
$863$			1.46337e25i			1.61906i	−0.587082	+	0.809528i	$0.699723\pi$
$864$		0			0
$865$	5.74525e24	+	4.01295e23i	0.623264	+	0.0435338i
$866$		0			0
$867$			4.09976e24i			0.436110i
$868$		0			0
$869$	7.93826e24			0.828051
$870$		0			0
$871$	−1.92984e22			−0.00197409
$872$		0			0
$873$			2.30153e24i			0.230885i
$874$		0			0
$875$	−5.69525e24	−	1.20917e24i	−0.560331	−	0.118965i
$876$		0			0
$877$		−	5.04985e24i		−	0.487284i	−0.969865	−	0.243642i	$-0.921658\pi$
$877$		−	5.04985e24i		−	0.487284i	0.969865	−	0.243642i	$-0.0783422\pi$
$878$		0			0
$879$	−1.99747e24			−0.189049
$880$		0			0
$881$	−1.61016e25			−1.49477			−0.747384	−	0.664393i	$-0.768690\pi$
$881$	−1.61016e25			−1.49477			−0.747384	+	0.664393i	$0.768690\pi$
$882$		0			0
$883$		−	1.06552e25i		−	0.970273i	−0.874438	−	0.485137i	$-0.838770\pi$
$883$		−	1.06552e25i		−	0.970273i	0.874438	−	0.485137i	$-0.161230\pi$
$884$		0			0
$885$	3.09733e24	+	2.16343e23i	0.276674	+	0.0193252i
$886$		0			0
$887$			5.73815e24i			0.502830i	0.967879	+	0.251415i	$0.0808959\pi$
$887$			5.73815e24i			0.502830i	−0.967879	+	0.251415i	$0.919104\pi$
$888$		0			0
$889$	−2.44443e24			−0.210142
$890$		0			0
$891$	5.06433e24			0.427132
$892$		0			0
$893$			1.28247e25i			1.06123i
$894$		0			0
$895$	−8.41390e23	+	1.20460e25i	−0.0683127	+	0.978017i
$896$		0			0
$897$			1.17839e21i			9.38753e-5i
$898$		0			0
$899$	−4.12373e24			−0.322354
$900$		0			0
$901$	−1.15996e24			−0.0889780
$902$		0			0
$903$			4.17058e24i			0.313943i
$904$		0			0
$905$	7.78543e23	−	1.11462e25i	0.0575135	−	0.823407i
$906$		0			0
$907$		−	1.60345e25i		−	1.16250i	−0.813725	−	0.581250i	$-0.802564\pi$
$907$		−	1.60345e25i		−	1.16250i	0.813725	−	0.581250i	$-0.197436\pi$
$908$		0			0
$909$	4.54188e24			0.323179
$910$		0			0
$911$	2.07808e25			1.45130			0.725648	−	0.688066i	$-0.241540\pi$
$911$	2.07808e25			1.45130			0.725648	+	0.688066i	$0.241540\pi$
$912$		0			0
$913$		−	1.69554e25i		−	1.16227i
$914$		0			0
$915$	−6.48514e24	−	4.52975e23i	−0.436355	−	0.0304786i
$916$		0			0
$917$		−	7.32085e24i		−	0.483529i
$918$		0			0
$919$	1.13639e25			0.736796			0.368398	−	0.929668i	$-0.379906\pi$
$919$	1.13639e25			0.736796			0.368398	+	0.929668i	$0.379906\pi$
$920$		0			0
$921$	2.31770e24			0.147520
$922$		0			0
$923$			2.24718e23i			0.0140418i
$924$		0			0
$925$	3.59231e24	−	2.55897e25i	0.220379	−	1.56986i
$926$		0			0
$927$			1.14092e25i			0.687191i
$928$		0			0
$929$	−1.86032e25			−1.10015			−0.550077	−	0.835114i	$-0.685402\pi$
$929$	−1.86032e25			−1.10015			−0.550077	+	0.835114i	$0.685402\pi$
$930$		0			0
$931$	9.59757e24			0.557300
$932$		0			0
$933$		−	7.73030e24i		−	0.440760i
$934$		0			0
$935$	−1.33370e24	−	9.31567e22i	−0.0746725	−	0.00521574i
$936$		0			0
$937$		−	1.86174e25i		−	1.02360i	−0.859103	−	0.511802i	$-0.828978\pi$
$937$		−	1.86174e25i		−	1.02360i	0.859103	−	0.511802i	$-0.171022\pi$
$938$		0			0
$939$	−1.10826e25			−0.598390
$940$		0			0
$941$	−2.30780e25			−1.22373			−0.611865	−	0.790962i	$-0.709581\pi$
$941$	−2.30780e25			−1.22373			−0.611865	+	0.790962i	$0.709581\pi$
$942$		0			0
$943$		−	1.96836e23i		−	0.0102507i
$944$		0			0
$945$	−6.19069e23	+	8.86307e24i	−0.0316642	+	0.453329i
$946$		0			0
$947$			1.45502e24i			0.0730959i	0.999332	+	0.0365479i	$0.0116362\pi$
$947$			1.45502e24i			0.0730959i	−0.999332	+	0.0365479i	$0.988364\pi$
$948$		0			0
$949$	−3.85586e23			−0.0190265
$950$		0			0
$951$	−8.81764e24			−0.427384
$952$		0			0
$953$		−	1.25990e25i		−	0.599854i	−0.953962	−	0.299927i	$-0.903038\pi$
$953$		−	1.25990e25i		−	0.599854i	0.953962	−	0.299927i	$-0.0969623\pi$
$954$		0			0
$955$	1.02946e24	−	1.47385e25i	0.0481481	−	0.689324i
$956$		0			0
$957$		−	3.72868e24i		−	0.171318i
$958$		0			0
$959$	−2.14424e25			−0.967864
$960$		0			0
$961$	−9.23427e24			−0.409500
$962$		0			0
$963$			2.05034e25i			0.893311i
$964$		0			0
$965$	3.35557e25	+	2.34380e24i	1.43643	+	0.100332i
$966$		0			0
$967$		−	1.96037e24i		−	0.0824543i	−0.999150	−	0.0412271i	$-0.986873\pi$
$967$		−	1.96037e24i		−	0.0824543i	0.999150	−	0.0412271i	$-0.0131267\pi$
$968$		0			0
$969$	−7.08795e23			−0.0292933
$970$		0			0
$971$	4.74466e25			1.92682			0.963411	−	0.268029i	$-0.0863724\pi$
$971$	4.74466e25			1.92682			0.963411	+	0.268029i	$0.0863724\pi$
$972$		0			0
$973$		−	1.02314e25i		−	0.408298i
$974$		0			0
$975$	−1.26827e23	−	1.78041e22i	−0.00497361	−	0.000698201i
$976$		0			0
$977$			1.12147e25i			0.432199i	0.976371	+	0.216099i	$0.0693335\pi$
$977$			1.12147e25i			0.432199i	−0.976371	+	0.216099i	$0.930667\pi$
$978$		0			0
$979$	−3.24508e25			−1.22906
$980$		0			0
$981$	7.58672e24			0.282402
$982$		0			0
$983$			1.85575e25i			0.678912i	0.940622	+	0.339456i	$0.110243\pi$
$983$			1.85575e25i			0.678912i	−0.940622	+	0.339456i	$0.889757\pi$
$984$		0			0
$985$	4.61008e25	+	3.22006e24i	1.65768	+	0.115786i
$986$		0			0
$987$			9.10210e24i			0.321696i
$988$		0			0
$989$	−6.71778e23			−0.0233377
$990$		0			0
$991$	4.41082e24			0.150624			0.0753119	−	0.997160i	$-0.476005\pi$
$991$	4.41082e24			0.150624			0.0753119	+	0.997160i	$0.476005\pi$
$992$		0			0
$993$			1.40281e25i			0.470902i
$994$		0			0
$995$	−3.05679e24	+	4.37633e25i	−0.100872	+	1.44415i
$996$		0			0
$997$		−	6.58711e24i		−	0.213691i	−0.994276	−	0.106845i	$-0.965925\pi$
$997$		−	6.58711e24i		−	0.213691i	0.994276	−	0.106845i	$-0.0340750\pi$
$998$		0			0
$999$	−3.94327e25			−1.25762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.18.c.a.9.5	yes	8
4.3	odd	2		80.18.c.c.49.4		8
5.2	odd	4		100.18.a.f.1.5		8
5.3	odd	4		100.18.a.f.1.4		8
5.4	even	2	inner	20.18.c.a.9.4	✓	8
20.19	odd	2		80.18.c.c.49.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.18.c.a.9.4	✓	8	5.4	even	2	inner
20.18.c.a.9.5	yes	8	1.1	even	1	trivial
80.18.c.c.49.4		8	4.3	odd	2
80.18.c.c.49.5		8	20.19	odd	2
100.18.a.f.1.4		8	5.3	odd	4
100.18.a.f.1.5		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4988.24i q^{3} +(-60861.6 + 871341. i) q^{5} -8.73679e6i q^{7} +1.04258e8 q^{9} +6.61458e8 q^{11} -3.36520e7i q^{13} +(-4.34646e9 - 3.03592e8i) q^{15} +2.31403e9i q^{17} +6.14052e10 q^{19} +4.35812e10 q^{21} +7.01987e9i q^{23} +(-7.55531e11 - 1.06062e11i) q^{25} +1.16424e12i q^{27} -1.13007e12 q^{29} +3.64909e12 q^{31} +3.29951e12i q^{33} +(7.61272e12 + 5.31735e11i) q^{35} +3.38698e13i q^{37} +1.67864e11 q^{39} -2.80398e13 q^{41} +9.56968e13i q^{43} +(-6.34529e12 + 9.08440e13i) q^{45} +2.08854e14i q^{47} +1.56299e14 q^{49} -1.15429e13 q^{51} +5.01273e14i q^{53} +(-4.02574e13 + 5.76355e14i) q^{55} +3.06304e14i q^{57} -7.12609e14 q^{59} +1.49205e15 q^{61} -9.10877e14i q^{63} +(2.93224e13 + 2.04812e12i) q^{65} -5.73469e14i q^{67} -3.50168e13 q^{69} -6.67771e15 q^{71} -1.14580e16i q^{73} +(5.29065e14 - 3.76877e15i) q^{75} -5.77902e15i q^{77} +1.20012e16 q^{79} +7.65632e15 q^{81} -2.56333e16i q^{83} +(-2.01631e15 - 1.40835e14i) q^{85} -5.63707e15i q^{87} -4.90595e16 q^{89} -2.94011e14 q^{91} +1.82025e16i q^{93} +(-3.73722e15 + 5.35048e16i) q^{95} +2.20754e16i q^{97} +6.89620e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1276800 q^{5} - 376848248 q^{9} - 396200640 q^{11} + 5677983200 q^{15} + 11821646592 q^{19} - 420670059472 q^{21} + 1642212165000 q^{25} + 1543712861232 q^{29} - 13722543013312 q^{31} - 13325691076800 q^{35}+ \cdots - 23\!\cdots\!60 q^{99}+O(q^{100}) \) 8 * q + 1276800 * q^5 - 376848248 * q^9 - 396200640 * q^11 + 5677983200 * q^15 + 11821646592 * q^19 - 420670059472 * q^21 + 1642212165000 * q^25 + 1543712861232 * q^29 - 13722543013312 * q^31 - 13325691076800 * q^35 - 79298226023808 * q^39 + 29824965017568 * q^41 - 238216983006800 * q^45 - 535615080275736 * q^49 - 764079320419264 * q^51 + 339212427988000 * q^55 + 94539545151744 * q^59 - 3380827226969024 * q^61 + 130929936568800 * q^65 + 5559752175554416 * q^69 + 20155606060098624 * q^71 + 938454087760000 * q^75 - 3634057920126144 * q^79 + 15949137882627512 * q^81 + 3575192471022400 * q^85 + 103487949043655568 * q^89 - 69783870139121088 * q^91 + 67219016711959200 * q^95 - 239420571619653760 * q^99

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