LMFDB - Embedded newform 80.20.c.d.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,20,Mod(49,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	80.c (of order $2$, degree $1$, not 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:	$183.053357245$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	80.49
Dual form			80.20.c.d.49.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41425.1i q^{3} +(-4.36383e6 - 174471. i) q^{5} -4.72501e7i q^{7} -5.53775e8 q^{9} +O(q^{10})$	\(q-41425.1i q^{3} +(-4.36383e6 - 174471. i) q^{5} -4.72501e7i q^{7} -5.53775e8 q^{9} +2.05736e9 q^{11} +5.51413e10i q^{13} +(-7.22748e9 + 1.80772e11i) q^{15} +5.78616e11i q^{17} +6.40705e11 q^{19} -1.95734e12 q^{21} -9.37674e12i q^{23} +(1.90126e13 + 1.52273e12i) q^{25} -2.52066e13i q^{27} -7.47829e13 q^{29} +2.06622e14 q^{31} -8.52264e13i q^{33} +(-8.24379e12 + 2.06192e14i) q^{35} -3.85056e14i q^{37} +2.28423e15 q^{39} -2.89464e15 q^{41} -3.27312e14i q^{43} +(2.41658e15 + 9.66177e13i) q^{45} -5.69262e15i q^{47} +9.16632e15 q^{49} +2.39692e16 q^{51} +5.87089e15i q^{53} +(-8.97799e15 - 3.58951e14i) q^{55} -2.65413e16i q^{57} -7.38344e16 q^{59} +1.34094e17 q^{61} +2.61659e16i q^{63} +(9.62057e15 - 2.40628e17i) q^{65} -1.67656e17i q^{67} -3.88432e17 q^{69} -5.28564e17 q^{71} -4.64646e17i q^{73} +(6.30791e16 - 7.87598e17i) q^{75} -9.72107e16i q^{77} +1.26302e18 q^{79} -1.68782e18 q^{81} -6.29142e17i q^{83} +(1.00952e17 - 2.52498e18i) q^{85} +3.09788e18i q^{87} +1.81512e18 q^{89} +2.60544e18 q^{91} -8.55934e18i q^{93} +(-2.79593e18 - 1.11785e17i) q^{95} -3.16283e18i q^{97} -1.13931e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) $ 28 * q - 3935164 * q^5 - 10352560732 * q^9	$ 28 q - 3935164 q^{5} - 10352560732 q^{9} - 18570995888 q^{11} - 79041415120 q^{15} + 1685869130672 q^{19} + 140419722832 q^{21} - 29558822439924 q^{25} + 160448197635496 q^{29} - 64251929934720 q^{31} + 88899634227664 q^{35} - 45\!\cdots\!04 q^{39}+ \cdots + 24\!\cdots\!92 q^{99}+O(q^{100}) $ 28 * q - 3935164 * q^5 - 10352560732 * q^9 - 18570995888 * q^11 - 79041415120 * q^15 + 1685869130672 * q^19 + 140419722832 * q^21 - 29558822439924 * q^25 + 160448197635496 * q^29 - 64251929934720 * q^31 + 88899634227664 * q^35 - 4563253596731104 * q^39 + 87868042694936 * q^41 + 3557698140217852 * q^45 - 28923781405647564 * q^49 - 14937379593456000 * q^51 - 28335039172010704 * q^55 + 83879503376835216 * q^59 + 2336306250785000 * q^61 + 23503427909569568 * q^65 - 46927873937137712 * q^69 - 104881848512783264 * q^71 - 1094024007292275040 * q^75 + 795721739900308672 * q^79 + 3593102866196377132 * q^81 + 834124526841485952 * q^85 + 1582238786752844568 * q^89 - 11017818924975052064 * q^91 - 30914057837649668144 * q^95 + 24571127463084047792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	41425.1i		−	1.21510i	−0.794282	−	0.607549i	$-0.792153\pi$
$3$		−	41425.1i		−	1.21510i	0.794282	−	0.607549i	$-0.207847\pi$
$4$		0			0
$5$	−4.36383e6	−	174471.i	−0.999202	−	0.0399493i
$5$	−4.36383e6	−	174471.i	−0.999202	−	0.0399493i
$6$		0			0
$7$		−	4.72501e7i		−	0.442560i	−0.975210	−	0.221280i	$-0.928977\pi$
$7$		−	4.72501e7i		−	0.442560i	0.975210	−	0.221280i	$-0.0710234\pi$
$8$		0			0
$9$	−5.53775e8			−0.476463
$10$		0			0
$11$	2.05736e9			0.263075			0.131538	−	0.991311i	$-0.458009\pi$
$11$	2.05736e9			0.263075			0.131538	+	0.991311i	$0.458009\pi$
$12$		0			0
$13$			5.51413e10i			1.44217i	0.692849	+	0.721083i	$0.256355\pi$
$13$			5.51413e10i			1.44217i	−0.692849	+	0.721083i	$0.743645\pi$
$14$		0			0
$15$	−7.22748e9	+	1.80772e11i	−0.0485423	+	1.21413i
$16$		0			0
$17$			5.78616e11i			1.18338i	0.806164	+	0.591692i	$0.201540\pi$
$17$			5.78616e11i			1.18338i	−0.806164	+	0.591692i	$0.798460\pi$
$18$		0			0
$19$	6.40705e11			0.455511			0.227756	−	0.973718i	$-0.426861\pi$
$19$	6.40705e11			0.455511			0.227756	+	0.973718i	$0.426861\pi$
$20$		0			0
$21$	−1.95734e12			−0.537753
$22$		0			0
$23$		−	9.37674e12i		−	1.08552i	−0.839888	−	0.542760i	$-0.817379\pi$
$23$		−	9.37674e12i		−	1.08552i	0.839888	−	0.542760i	$-0.182621\pi$
$24$		0			0
$25$	1.90126e13	+	1.52273e12i	0.996808	+	0.0798347i
$26$		0			0
$27$		−	2.52066e13i		−	0.636149i
$28$		0			0
$29$	−7.47829e13			−0.957240			−0.478620	−	0.878022i	$-0.658863\pi$
$29$	−7.47829e13			−0.957240			−0.478620	+	0.878022i	$0.658863\pi$
$30$		0			0
$31$	2.06622e14			1.40359			0.701796	−	0.712378i	$-0.252382\pi$
$31$	2.06622e14			1.40359			0.701796	+	0.712378i	$0.252382\pi$
$32$		0			0
$33$		−	8.52264e13i		−	0.319662i
$34$		0			0
$35$	−8.24379e12	+	2.06192e14i	−0.0176799	+	0.442206i
$36$		0			0
$37$		−	3.85056e14i		−	0.487088i	−0.969890	−	0.243544i	$-0.921690\pi$
$37$		−	3.85056e14i		−	0.487088i	0.969890	−	0.243544i	$-0.0783100\pi$
$38$		0			0
$39$	2.28423e15			1.75237
$40$		0			0
$41$	−2.89464e15			−1.38085			−0.690427	−	0.723402i	$-0.742577\pi$
$41$	−2.89464e15			−1.38085			−0.690427	+	0.723402i	$0.742577\pi$
$42$		0			0
$43$		−	3.27312e14i		−	0.0993142i	−0.998766	−	0.0496571i	$-0.984187\pi$
$43$		−	3.27312e14i		−	0.0993142i	0.998766	−	0.0496571i	$-0.0158128\pi$
$44$		0			0
$45$	2.41658e15	+	9.66177e13i	0.476083	+	0.0190343i
$46$		0			0
$47$		−	5.69262e15i		−	0.741964i	−0.928640	−	0.370982i	$-0.879021\pi$
$47$		−	5.69262e15i		−	0.741964i	0.928640	−	0.370982i	$-0.120979\pi$
$48$		0			0
$49$	9.16632e15			0.804141
$50$		0			0
$51$	2.39692e16			1.43793
$52$		0			0
$53$			5.87089e15i			0.244390i	0.992506	+	0.122195i	$0.0389933\pi$
$53$			5.87089e15i			0.244390i	−0.992506	+	0.122195i	$0.961007\pi$
$54$		0			0
$55$	−8.97799e15	−	3.58951e14i	−0.262865	−	0.0105097i
$56$		0			0
$57$		−	2.65413e16i		−	0.553491i
$58$		0			0
$59$	−7.38344e16			−1.10959			−0.554797	−	0.831985i	$-0.687204\pi$
$59$	−7.38344e16			−1.10959			−0.554797	+	0.831985i	$0.687204\pi$
$60$		0			0
$61$	1.34094e17			1.46817			0.734083	−	0.679059i	$-0.237612\pi$
$61$	1.34094e17			1.46817			0.734083	+	0.679059i	$0.237612\pi$
$62$		0			0
$63$			2.61659e16i			0.210863i
$64$		0			0
$65$	9.62057e15	−	2.40628e17i	0.0576135	−	1.44101i
$66$		0			0
$67$		−	1.67656e17i		−	0.752848i	−0.926448	−	0.376424i	$-0.877154\pi$
$67$		−	1.67656e17i		−	0.752848i	0.926448	−	0.376424i	$-0.122846\pi$
$68$		0			0
$69$	−3.88432e17			−1.31901
$70$		0			0
$71$	−5.28564e17			−1.36818			−0.684090	−	0.729398i	$-0.739800\pi$
$71$	−5.28564e17			−1.36818			−0.684090	+	0.729398i	$0.739800\pi$
$72$		0			0
$73$		−	4.64646e17i		−	0.923751i	−0.886945	−	0.461875i	$-0.847177\pi$
$73$		−	4.64646e17i		−	0.923751i	0.886945	−	0.461875i	$-0.152823\pi$
$74$		0			0
$75$	6.30791e16	−	7.87598e17i	0.0970070	−	1.21122i
$76$		0			0
$77$		−	9.72107e16i		−	0.116427i
$78$		0			0
$79$	1.26302e18			1.18564			0.592822	−	0.805333i	$-0.298014\pi$
$79$	1.26302e18			1.18564			0.592822	+	0.805333i	$0.298014\pi$
$80$		0			0
$81$	−1.68782e18			−1.24945
$82$		0			0
$83$		−	6.29142e17i		−	0.369408i	−0.982794	−	0.184704i	$-0.940867\pi$
$83$		−	6.29142e17i		−	0.369408i	0.982794	−	0.184704i	$-0.0591327\pi$
$84$		0			0
$85$	1.00952e17	−	2.52498e18i	0.0472753	−	1.18244i
$86$		0			0
$87$			3.09788e18i			1.16314i
$88$		0			0
$89$	1.81512e18			0.549163			0.274582	−	0.961564i	$-0.411461\pi$
$89$	1.81512e18			0.549163			0.274582	+	0.961564i	$0.411461\pi$
$90$		0			0
$91$	2.60544e18			0.638244
$92$		0			0
$93$		−	8.55934e18i		−	1.70550i
$94$		0			0
$95$	−2.79593e18	−	1.11785e17i	−0.455148	−	0.0181973i
$96$		0			0
$97$		−	3.16283e18i		−	0.422420i	−0.977441	−	0.211210i	$-0.932260\pi$
$97$		−	3.16283e18i		−	0.422420i	0.977441	−	0.211210i	$-0.0677404\pi$
$98$		0			0
$99$	−1.13931e18			−0.125346
$100$		0			0
$101$	5.16924e18			0.470298			0.235149	−	0.971959i	$-0.424442\pi$
$101$	5.16924e18			0.470298			0.235149	+	0.971959i	$0.424442\pi$
$102$		0			0
$103$			1.99600e18i			0.150733i	0.997156	+	0.0753663i	$0.0240126\pi$
$103$			1.99600e18i			0.150733i	−0.997156	+	0.0753663i	$0.975987\pi$
$104$		0			0
$105$	8.54151e18	+	3.41500e17i	0.537324	+	0.0214828i
$106$		0			0
$107$			3.00887e19i			1.58218i	0.611697	+	0.791092i	$0.290487\pi$
$107$			3.00887e19i			1.58218i	−0.611697	+	0.791092i	$0.709513\pi$
$108$		0			0
$109$	5.57195e18			0.245728			0.122864	−	0.992423i	$-0.460792\pi$
$109$	5.57195e18			0.245728			0.122864	+	0.992423i	$0.460792\pi$
$110$		0			0
$111$	−1.59510e19			−0.591859
$112$		0			0
$113$		−	1.98941e19i		−	0.622987i	−0.950248	−	0.311494i	$-0.899171\pi$
$113$		−	1.98941e19i		−	0.622987i	0.950248	−	0.311494i	$-0.100829\pi$
$114$		0			0
$115$	−1.63597e18	+	4.09186e19i	−0.0433657	+	1.08465i
$116$		0			0
$117$		−	3.05359e19i		−	0.687139i
$118$		0			0
$119$	2.73397e19			0.523718
$120$		0			0
$121$	−5.69264e19			−0.930791
$122$		0			0
$123$			1.19911e20i			1.67787i
$124$		0			0
$125$	−8.27022e19	−	9.96208e18i	−0.992823	−	0.119593i
$126$		0			0
$127$			1.14335e20i			1.18044i	0.807242	+	0.590221i	$0.200959\pi$
$127$			1.14335e20i			1.18044i	−0.807242	+	0.590221i	$0.799041\pi$
$128$		0			0
$129$	−1.35589e19			−0.120676
$130$		0			0
$131$	5.55523e19			0.427193			0.213597	−	0.976922i	$-0.431482\pi$
$131$	5.55523e19			0.427193			0.213597	+	0.976922i	$0.431482\pi$
$132$		0			0
$133$		−	3.02734e19i		−	0.201591i
$134$		0			0
$135$	−4.39783e18	+	1.09997e20i	−0.0254137	+	0.635641i
$136$		0			0
$137$		−	7.78996e18i		−	0.0391462i	−0.999808	−	0.0195731i	$-0.993769\pi$
$137$		−	7.78996e18i		−	0.0391462i	0.999808	−	0.0195731i	$-0.00623072\pi$
$138$		0			0
$139$	−2.20539e20			−0.965705			−0.482853	−	0.875702i	$-0.660399\pi$
$139$	−2.20539e20			−0.965705			−0.482853	+	0.875702i	$0.660399\pi$
$140$		0			0
$141$	−2.35817e20			−0.901558
$142$		0			0
$143$			1.13446e20i			0.379398i
$144$		0			0
$145$	3.26340e20	+	1.30475e19i	0.956476	+	0.0382410i
$146$		0			0
$147$		−	3.79715e20i		−	0.977110i
$148$		0			0
$149$	5.43845e20			1.23085			0.615426	−	0.788195i	$-0.288984\pi$
$149$	5.43845e20			1.23085			0.615426	+	0.788195i	$0.288984\pi$
$150$		0			0
$151$	3.83571e20			0.764829			0.382415	−	0.923991i	$-0.375093\pi$
$151$	3.83571e20			0.764829			0.382415	+	0.923991i	$0.375093\pi$
$152$		0			0
$153$		−	3.20423e20i		−	0.563838i
$154$		0			0
$155$	−9.01665e20	−	3.60496e19i	−1.40247	−	0.0560725i
$156$		0			0
$157$		−	9.22384e20i		−	1.27018i	−0.772438	−	0.635090i	$-0.780963\pi$
$157$		−	9.22384e20i		−	1.27018i	0.772438	−	0.635090i	$-0.219037\pi$
$158$		0			0
$159$	2.43202e20			0.296958
$160$		0			0
$161$	−4.43053e20			−0.480407
$162$		0			0
$163$		−	1.06320e21i		−	1.02526i	−0.858609	−	0.512631i	$-0.828671\pi$
$163$		−	1.06320e21i		−	1.02526i	0.858609	−	0.512631i	$-0.171329\pi$
$164$		0			0
$165$	−1.48695e19	+	3.71914e20i	−0.0127703	+	0.319407i
$166$		0			0
$167$		−	8.13821e20i		−	0.623336i	−0.950191	−	0.311668i	$-0.899112\pi$
$167$		−	8.13821e20i		−	0.623336i	0.950191	−	0.311668i	$-0.100888\pi$
$168$		0			0
$169$	−1.57864e21			−1.07984
$170$		0			0
$171$	−3.54806e20			−0.217034
$172$		0			0
$173$			1.33541e21i			0.731438i	0.930725	+	0.365719i	$0.119177\pi$
$173$			1.33541e21i			0.731438i	−0.930725	+	0.365719i	$0.880823\pi$
$174$		0			0
$175$	7.19491e19	−	8.98348e20i	0.0353316	−	0.441147i
$176$		0			0
$177$			3.05859e21i			1.34827i
$178$		0			0
$179$	−2.77503e21			−1.09942			−0.549711	−	0.835355i	$-0.685262\pi$
$179$	−2.77503e21			−1.09942			−0.549711	+	0.835355i	$0.685262\pi$
$180$		0			0
$181$	−5.08876e21			−1.81412			−0.907059	−	0.421004i	$-0.861678\pi$
$181$	−5.08876e21			−1.81412			−0.907059	+	0.421004i	$0.861678\pi$
$182$		0			0
$183$		−	5.55484e21i		−	1.78397i
$184$		0			0
$185$	−6.71812e19	+	1.68032e21i	−0.0194588	+	0.486699i
$186$		0			0
$187$			1.19042e21i			0.311319i
$188$		0			0
$189$	−1.19102e21			−0.281534
$190$		0			0
$191$	5.13750e21			1.09884			0.549420	−	0.835546i	$-0.314849\pi$
$191$	5.13750e21			1.09884			0.549420	+	0.835546i	$0.314849\pi$
$192$		0			0
$193$		−	4.29802e21i		−	0.832672i	−0.909211	−	0.416336i	$-0.863314\pi$
$193$		−	4.29802e21i		−	0.832672i	0.909211	−	0.416336i	$-0.136686\pi$
$194$		0			0
$195$	−9.96801e21	−	3.98533e20i	−1.75097	−	0.0700060i
$196$		0			0
$197$			1.06113e22i			1.69177i	0.533367	+	0.845884i	$0.320926\pi$
$197$			1.06113e22i			1.69177i	−0.533367	+	0.845884i	$0.679074\pi$
$198$		0			0
$199$	−9.06131e21			−1.31246			−0.656231	−	0.754560i	$-0.727850\pi$
$199$	−9.06131e21			−1.31246			−0.656231	+	0.754560i	$0.727850\pi$
$200$		0			0
$201$	−6.94514e21			−0.914784
$202$		0			0
$203$			3.53350e21i			0.423636i
$204$		0			0
$205$	1.26317e22	+	5.05031e20i	1.37975	+	0.0551641i
$206$		0			0
$207$			5.19260e21i			0.517210i
$208$		0			0
$209$	1.31816e21			0.119834
$210$		0			0
$211$	1.09514e20			0.00909469			0.00454735	−	0.999990i	$-0.498553\pi$
$211$	1.09514e20			0.00909469			0.00454735	+	0.999990i	$0.498553\pi$
$212$		0			0
$213$			2.18958e22i			1.66247i
$214$		0			0
$215$	−5.71065e19	+	1.42833e21i	−0.00396753	+	0.0992349i
$216$		0			0
$217$		−	9.76293e21i		−	0.621173i
$218$		0			0
$219$	−1.92480e22			−1.12245
$220$		0			0
$221$	−3.19056e22			−1.70663
$222$		0			0
$223$			2.29806e22i			1.12841i	0.825636	+	0.564203i	$0.190816\pi$
$223$			2.29806e22i			1.12841i	−0.825636	+	0.564203i	$0.809184\pi$
$224$		0			0
$225$	−1.05287e22	−	8.43247e20i	−0.474942	−	0.0380383i
$226$		0			0
$227$		−	2.60179e22i		−	1.07901i	−0.841982	−	0.539506i	$-0.818611\pi$
$227$		−	2.60179e22i		−	1.07901i	0.841982	−	0.539506i	$-0.181389\pi$
$228$		0			0
$229$	−2.13463e22			−0.814490			−0.407245	−	0.913319i	$-0.633510\pi$
$229$	−2.13463e22			−0.814490			−0.407245	+	0.913319i	$0.633510\pi$
$230$		0			0
$231$	−4.02696e21			−0.141470
$232$		0			0
$233$		−	2.63161e22i		−	0.851805i	−0.904769	−	0.425902i	$-0.859957\pi$
$233$		−	2.63161e22i		−	0.851805i	0.904769	−	0.425902i	$-0.140043\pi$
$234$		0			0
$235$	−9.93198e20	+	2.48417e22i	−0.0296409	+	0.741371i
$236$		0			0
$237$		−	5.23209e22i		−	1.44067i
$238$		0			0
$239$	−1.97593e22			−0.502332			−0.251166	−	0.967944i	$-0.580814\pi$
$239$	−1.97593e22			−0.502332			−0.251166	+	0.967944i	$0.580814\pi$
$240$		0			0
$241$	−5.91708e22			−1.38978			−0.694889	−	0.719117i	$-0.744547\pi$
$241$	−5.91708e22			−1.38978			−0.694889	+	0.719117i	$0.744547\pi$
$242$		0			0
$243$			4.06212e22i			0.882051i
$244$		0			0
$245$	−4.00003e22	−	1.59926e21i	−0.803499	−	0.0321248i
$246$		0			0
$247$			3.53293e22i			0.656923i
$248$		0			0
$249$	−2.60622e22			−0.448867
$250$		0			0
$251$	−7.40817e22			−1.18253			−0.591263	−	0.806479i	$-0.701371\pi$
$251$	−7.40817e22			−1.18253			−0.591263	+	0.806479i	$0.701371\pi$
$252$		0			0
$253$		−	1.92914e22i		−	0.285574i
$254$		0			0
$255$	−1.04598e23	−	4.18193e21i	−1.43678	−	0.0574441i
$256$		0			0
$257$		−	1.42769e23i		−	1.82082i	−0.413703	−	0.910412i	$-0.635765\pi$
$257$		−	1.42769e23i		−	1.82082i	0.413703	−	0.910412i	$-0.364235\pi$
$258$		0			0
$259$	−1.81939e22			−0.215565
$260$		0			0
$261$	4.14128e22			0.456090
$262$		0			0
$263$		−	9.94150e22i		−	1.01829i	−0.860680	−	0.509146i	$-0.829961\pi$
$263$		−	9.94150e22i		−	1.01829i	0.860680	−	0.509146i	$-0.170039\pi$
$264$		0			0
$265$	1.02430e21	−	2.56196e22i	0.00976320	−	0.244195i
$266$		0			0
$267$		−	7.51917e22i		−	0.667287i
$268$		0			0
$269$	−7.72835e22			−0.638911			−0.319455	−	0.947601i	$-0.603500\pi$
$269$	−7.72835e22			−0.638911			−0.319455	+	0.947601i	$0.603500\pi$
$270$		0			0
$271$	−4.16950e22			−0.321274			−0.160637	−	0.987014i	$-0.551355\pi$
$271$	−4.16950e22			−0.321274			−0.160637	+	0.987014i	$0.551355\pi$
$272$		0			0
$273$		−	1.07930e23i		−	0.775530i
$274$		0			0
$275$	3.91158e22	+	3.13280e21i	0.262236	+	0.0210026i
$276$		0			0
$277$			2.43019e23i			1.52083i	0.649435	+	0.760417i	$0.275005\pi$
$277$			2.43019e23i			1.52083i	−0.649435	+	0.760417i	$0.724995\pi$
$278$		0			0
$279$	−1.14422e23			−0.668760
$280$		0			0
$281$	4.83756e22			0.264190			0.132095	−	0.991237i	$-0.457830\pi$
$281$	4.83756e22			0.264190			0.132095	+	0.991237i	$0.457830\pi$
$282$		0			0
$283$			2.64901e23i			1.35242i	0.736708	+	0.676210i	$0.236379\pi$
$283$			2.64901e23i			1.35242i	−0.736708	+	0.676210i	$0.763621\pi$
$284$		0			0
$285$	−4.63069e21	+	1.15822e23i	−0.0221116	+	0.553049i
$286$		0			0
$287$			1.36772e23i			0.611111i
$288$		0			0
$289$	−9.57236e22			−0.400396
$290$		0			0
$291$	−1.31020e23			−0.513282
$292$		0			0
$293$			3.99176e23i			1.46528i	0.680614	+	0.732642i	$0.261713\pi$
$293$			3.99176e23i			1.46528i	−0.680614	+	0.732642i	$0.738287\pi$
$294$		0			0
$295$	3.22201e23	+	1.28820e22i	1.10871	+	0.0443275i
$296$		0			0
$297$		−	5.18591e22i		−	0.167355i
$298$		0			0
$299$	5.17046e23			1.56550
$300$		0			0
$301$	−1.54655e22			−0.0439524
$302$		0			0
$303$		−	2.14136e23i		−	0.571459i
$304$		0			0
$305$	−5.85163e23	−	2.33955e22i	−1.46699	−	0.0586522i
$306$		0			0
$307$		−	7.91594e23i		−	1.86504i	−0.361118	−	0.932520i	$-0.617605\pi$
$307$		−	7.91594e23i		−	1.86504i	0.361118	−	0.932520i	$-0.382395\pi$
$308$		0			0
$309$	8.26845e22			0.183155
$310$		0			0
$311$	−8.30419e23			−1.73011			−0.865054	−	0.501678i	$-0.832716\pi$
$311$	−8.30419e23			−1.73011			−0.865054	+	0.501678i	$0.832716\pi$
$312$		0			0
$313$			5.09497e23i			0.998782i	0.866377	+	0.499391i	$0.166443\pi$
$313$			5.09497e23i			0.998782i	−0.866377	+	0.499391i	$0.833557\pi$
$314$		0			0
$315$	4.56520e21	−	1.14184e23i	0.00842383	−	0.210695i
$316$		0			0
$317$			4.54209e23i			0.789210i	0.918851	+	0.394605i	$0.129119\pi$
$317$			4.54209e23i			0.789210i	−0.918851	+	0.394605i	$0.870881\pi$
$318$		0			0
$319$	−1.53855e23			−0.251826
$320$		0			0
$321$	1.24642e24			1.92251
$322$		0			0
$323$			3.70722e23i			0.539044i
$324$		0			0
$325$	−8.39652e22	+	1.04838e24i	−0.115135	+	1.43756i
$326$		0			0
$327$		−	2.30818e23i		−	0.298584i
$328$		0			0
$329$	−2.68977e23			−0.328363
$330$		0			0
$331$	7.27473e23			0.838400			0.419200	−	0.907894i	$-0.362311\pi$
$331$	7.27473e23			0.838400			0.419200	+	0.907894i	$0.362311\pi$
$332$		0			0
$333$			2.13234e23i			0.232079i
$334$		0			0
$335$	−2.92511e22	+	7.31621e23i	−0.0300757	+	0.752247i
$336$		0			0
$337$		−	2.03449e24i		−	1.97684i	−0.151754	−	0.988418i	$-0.548492\pi$
$337$		−	2.03449e24i		−	1.97684i	0.151754	−	0.988418i	$-0.451508\pi$
$338$		0			0
$339$	−8.24115e23			−0.756991
$340$		0			0
$341$	4.25097e23			0.369250
$342$		0			0
$343$		−	9.71709e23i		−	0.798440i
$344$		0			0
$345$	1.69505e24	+	6.77703e22i	1.31796	+	0.0526936i
$346$		0			0
$347$		−	1.46414e24i		−	1.07759i	−0.842437	−	0.538795i	$-0.818880\pi$
$347$		−	1.46414e24i		−	1.07759i	0.842437	−	0.538795i	$-0.181120\pi$
$348$		0			0
$349$	1.42518e24			0.993184			0.496592	−	0.867984i	$-0.334585\pi$
$349$	1.42518e24			0.993184			0.496592	+	0.867984i	$0.334585\pi$
$350$		0			0
$351$	1.38993e24			0.917432
$352$		0			0
$353$		−	2.82016e24i		−	1.76365i	−0.471572	−	0.881827i	$-0.656313\pi$
$353$		−	2.82016e24i		−	1.76365i	0.471572	−	0.881827i	$-0.343687\pi$
$354$		0			0
$355$	2.30657e24	+	9.22192e22i	1.36709	+	0.0546578i
$356$		0			0
$357$		−	1.13255e24i		−	0.636368i
$358$		0			0
$359$	3.50727e24			1.86884			0.934419	−	0.356177i	$-0.115920\pi$
$359$	3.50727e24			1.86884			0.934419	+	0.356177i	$0.115920\pi$
$360$		0			0
$361$	−1.56792e24			−0.792509
$362$		0			0
$363$			2.35818e24i			1.13100i
$364$		0			0
$365$	−8.10673e22	+	2.02764e24i	−0.0369032	+	0.923013i
$366$		0			0
$367$		−	1.95892e24i		−	0.846623i	−0.905984	−	0.423311i	$-0.860868\pi$
$367$		−	1.95892e24i		−	0.846623i	0.905984	−	0.423311i	$-0.139132\pi$
$368$		0			0
$369$	1.60298e24			0.657926
$370$		0			0
$371$	2.77401e23			0.108157
$372$		0			0
$373$			7.87258e22i			0.0291664i	0.999894	+	0.0145832i	$0.00464214\pi$
$373$			7.87258e22i			0.0291664i	−0.999894	+	0.0145832i	$0.995358\pi$
$374$		0			0
$375$	−4.12680e23	+	3.42594e24i	−0.145317	+	1.20638i
$376$		0			0
$377$		−	4.12362e24i		−	1.38050i
$378$		0			0
$379$	7.16827e23			0.228214			0.114107	−	0.993468i	$-0.463599\pi$
$379$	7.16827e23			0.228214			0.114107	+	0.993468i	$0.463599\pi$
$380$		0			0
$381$	4.73634e24			1.43435
$382$		0			0
$383$			1.25313e24i			0.361085i	0.983567	+	0.180542i	$0.0577853\pi$
$383$			1.25313e24i			0.361085i	−0.983567	+	0.180542i	$0.942215\pi$
$384$		0			0
$385$	−1.69605e22	+	4.24211e23i	−0.00465116	+	0.116334i
$386$		0			0
$387$			1.81257e23i			0.0473195i
$388$		0			0
$389$	−4.08051e24			−1.01436			−0.507181	−	0.861839i	$-0.669312\pi$
$389$	−4.08051e24			−1.01436			−0.507181	+	0.861839i	$0.669312\pi$
$390$		0			0
$391$	5.42553e24			1.28459
$392$		0			0
$393$		−	2.30126e24i		−	0.519082i
$394$		0			0
$395$	−5.51163e24	−	2.20361e23i	−1.18470	−	0.0473656i
$396$		0			0
$397$		−	3.11126e24i		−	0.637420i	−0.947852	−	0.318710i	$-0.896750\pi$
$397$		−	3.11126e24i		−	0.637420i	0.947852	−	0.318710i	$-0.103250\pi$
$398$		0			0
$399$	−1.25408e24			−0.244953
$400$		0			0
$401$	−4.03816e24			−0.752162			−0.376081	−	0.926587i	$-0.622729\pi$
$401$	−4.03816e24			−0.752162			−0.376081	+	0.926587i	$0.622729\pi$
$402$		0			0
$403$			1.13934e25i			2.02421i
$404$		0			0
$405$	7.36535e24	+	2.94475e23i	1.24845	+	0.0499144i
$406$		0			0
$407$		−	7.92199e23i		−	0.128141i
$408$		0			0
$409$	1.23897e25			1.91289			0.956447	−	0.291906i	$-0.0942894\pi$
$409$	1.23897e25			1.91289			0.956447	+	0.291906i	$0.0942894\pi$
$410$		0			0
$411$	−3.22700e23			−0.0475665
$412$		0			0
$413$			3.48868e24i			0.491062i
$414$		0			0
$415$	−1.09767e23	+	2.74547e24i	−0.0147576	+	0.369113i
$416$		0			0
$417$			9.13584e24i			1.17343i
$418$		0			0
$419$	−3.53232e24			−0.433538			−0.216769	−	0.976223i	$-0.569552\pi$
$419$	−3.53232e24			−0.433538			−0.216769	+	0.976223i	$0.569552\pi$
$420$		0			0
$421$	−9.12440e24			−1.07035			−0.535173	−	0.844742i	$-0.679754\pi$
$421$	−9.12440e24			−1.07035			−0.535173	+	0.844742i	$0.679754\pi$
$422$		0			0
$423$			3.15243e24i			0.353518i
$424$		0			0
$425$	−8.81074e23	+	1.10010e25i	−0.0944751	+	1.17961i
$426$		0			0
$427$		−	6.33595e24i		−	0.649751i
$428$		0			0
$429$	4.69949e24			0.461006
$430$		0			0
$431$	1.66484e25			1.56256			0.781281	−	0.624180i	$-0.214567\pi$
$431$	1.66484e25			1.56256			0.781281	+	0.624180i	$0.214567\pi$
$432$		0			0
$433$			9.74593e24i			0.875363i	0.899130	+	0.437682i	$0.144200\pi$
$433$			9.74593e24i			0.875363i	−0.899130	+	0.437682i	$0.855800\pi$
$434$		0			0
$435$	5.40492e23	−	1.35187e25i	0.0464666	−	1.16221i
$436$		0			0
$437$		−	6.00773e24i		−	0.494467i
$438$		0			0
$439$	−1.28172e24			−0.101013			−0.0505067	−	0.998724i	$-0.516084\pi$
$439$	−1.28172e24			−0.101013			−0.0505067	+	0.998724i	$0.516084\pi$
$440$		0			0
$441$	−5.07607e24			−0.383143
$442$		0			0
$443$		−	4.78908e24i		−	0.346272i	−0.984898	−	0.173136i	$-0.944610\pi$
$443$		−	4.78908e24i		−	0.346272i	0.984898	−	0.173136i	$-0.0553900\pi$
$444$		0			0
$445$	−7.92090e24	−	3.16687e23i	−0.548725	−	0.0219387i
$446$		0			0
$447$		−	2.25288e25i		−	1.49561i
$448$		0			0
$449$	−1.24413e25			−0.791638			−0.395819	−	0.918329i	$-0.629539\pi$
$449$	−1.24413e25			−0.791638			−0.395819	+	0.918329i	$0.629539\pi$
$450$		0			0
$451$	−5.95532e24			−0.363269
$452$		0			0
$453$		−	1.58894e25i		−	0.929342i
$454$		0			0
$455$	−1.13697e25	−	4.54573e23i	−0.637735	−	0.0254974i
$456$		0			0
$457$		−	1.44589e25i		−	0.777914i	−0.921256	−	0.388957i	$-0.872835\pi$
$457$		−	1.44589e25i		−	0.777914i	0.921256	−	0.388957i	$-0.127165\pi$
$458$		0			0
$459$	1.45849e25			0.752808
$460$		0			0
$461$	−4.34578e24			−0.215233			−0.107617	−	0.994192i	$-0.534322\pi$
$461$	−4.34578e24			−0.215233			−0.107617	+	0.994192i	$0.534322\pi$
$462$		0			0
$463$			9.90443e24i			0.470771i	0.971902	+	0.235386i	$0.0756353\pi$
$463$			9.90443e24i			0.470771i	−0.971902	+	0.235386i	$0.924365\pi$
$464$		0			0
$465$	−1.49336e24	+	3.73515e25i	−0.0681335	+	1.70414i
$466$		0			0
$467$		−	3.16461e25i		−	1.38615i	−0.720867	−	0.693074i	$-0.756256\pi$
$467$		−	3.16461e25i		−	1.38615i	0.720867	−	0.693074i	$-0.243744\pi$
$468$		0			0
$469$	−7.92175e24			−0.333180
$470$		0			0
$471$	−3.82098e25			−1.54339
$472$		0			0
$473$		−	6.73399e23i		−	0.0261271i
$474$		0			0
$475$	1.21815e25	+	9.75619e23i	0.454057	+	0.0363656i
$476$		0			0
$477$		−	3.25115e24i		−	0.116443i
$478$		0			0
$479$	−5.41912e25			−1.86527			−0.932634	−	0.360824i	$-0.882495\pi$
$479$	−5.41912e25			−1.86527			−0.932634	+	0.360824i	$0.882495\pi$
$480$		0			0
$481$	2.12325e25			0.702462
$482$		0			0
$483$			1.83535e25i			0.583742i
$484$		0			0
$485$	−5.51823e23	+	1.38021e25i	−0.0168754	+	0.422083i
$486$		0			0
$487$		−	5.55923e25i		−	1.63489i	−0.576004	−	0.817447i	$-0.695389\pi$
$487$		−	5.55923e25i		−	1.63489i	0.576004	−	0.817447i	$-0.304611\pi$
$488$		0			0
$489$	−4.40433e25			−1.24579
$490$		0			0
$491$	−5.15322e25			−1.40218			−0.701091	−	0.713072i	$-0.747303\pi$
$491$	−5.15322e25			−1.40218			−0.701091	+	0.713072i	$0.747303\pi$
$492$		0			0
$493$		−	4.32705e25i		−	1.13278i
$494$		0			0
$495$	4.97178e24	+	1.98778e23i	0.125246	+	0.00500747i
$496$		0			0
$497$			2.49747e25i			0.605501i
$498$		0			0
$499$	−1.48174e25			−0.345793			−0.172897	−	0.984940i	$-0.555313\pi$
$499$	−1.48174e25			−0.345793			−0.172897	+	0.984940i	$0.555313\pi$
$500$		0			0
$501$	−3.37126e25			−0.757415
$502$		0			0
$503$			4.49294e25i			0.971930i	0.873978	+	0.485965i	$0.161532\pi$
$503$			4.49294e25i			0.971930i	−0.873978	+	0.485965i	$0.838468\pi$
$504$		0			0
$505$	−2.25577e25	−	9.01883e23i	−0.469923	−	0.0187881i
$506$		0			0
$507$			6.53954e25i			1.31211i
$508$		0			0
$509$	−1.71856e25			−0.332158			−0.166079	−	0.986112i	$-0.553111\pi$
$509$	−1.71856e25			−0.332158			−0.166079	+	0.986112i	$0.553111\pi$
$510$		0			0
$511$	−2.19546e25			−0.408815
$512$		0			0
$513$		−	1.61500e25i		−	0.289773i
$514$		0			0
$515$	3.48245e23	−	8.71022e24i	0.00602166	−	0.150612i
$516$		0			0
$517$		−	1.17118e25i		−	0.195192i
$518$		0			0
$519$	5.53196e25			0.888769
$520$		0			0
$521$	−1.05727e25			−0.163768			−0.0818841	−	0.996642i	$-0.526094\pi$
$521$	−1.05727e25			−0.163768			−0.0818841	+	0.996642i	$0.526094\pi$
$522$		0			0
$523$			7.74027e25i			1.15609i	0.816007	+	0.578043i	$0.196183\pi$
$523$			7.74027e25i			1.15609i	−0.816007	+	0.578043i	$0.803817\pi$
$524$		0			0
$525$	−3.72141e25	−	2.98049e24i	−0.536037	−	0.0429314i
$526$		0			0
$527$			1.19555e26i			1.66099i
$528$		0			0
$529$	−1.33079e25			−0.178353
$530$		0			0
$531$	4.08876e25			0.528681
$532$		0			0
$533$		−	1.59614e26i		−	1.99142i
$534$		0			0
$535$	5.24961e24	−	1.31302e26i	0.0632071	−	1.58092i
$536$		0			0
$537$			1.14956e26i			1.33591i
$538$		0			0
$539$	1.88584e25			0.211550
$540$		0			0
$541$	1.20337e26			1.30325			0.651623	−	0.758543i	$-0.274089\pi$
$541$	1.20337e26			1.30325			0.651623	+	0.758543i	$0.274089\pi$
$542$		0			0
$543$			2.10802e26i			2.20433i
$544$		0			0
$545$	−2.43151e25	−	9.72145e23i	−0.245532	−	0.00981667i
$546$		0			0
$547$		−	1.63557e25i		−	0.159511i	−0.996814	−	0.0797553i	$-0.974586\pi$
$547$		−	1.63557e25i		−	0.159511i	0.996814	−	0.0797553i	$-0.0254139\pi$
$548$		0			0
$549$	−7.42577e25			−0.699527
$550$		0			0
$551$	−4.79138e25			−0.436034
$552$		0			0
$553$		−	5.96781e25i		−	0.524718i
$554$		0			0
$555$	6.96074e25	+	2.78298e24i	0.591387	+	0.0236443i
$556$		0			0
$557$			1.06967e26i			0.878263i	0.898423	+	0.439131i	$0.144714\pi$
$557$			1.06967e26i			0.878263i	−0.898423	+	0.439131i	$0.855286\pi$
$558$		0			0
$559$	1.80484e25			0.143228
$560$		0			0
$561$	4.93133e25			0.378283
$562$		0			0
$563$		−	1.20153e26i		−	0.891059i	−0.895267	−	0.445529i	$-0.853015\pi$
$563$		−	1.20153e26i		−	0.891059i	0.895267	−	0.445529i	$-0.146985\pi$
$564$		0			0
$565$	−3.47095e24	+	8.68146e25i	−0.0248879	+	0.622490i
$566$		0			0
$567$			7.97496e25i			0.552954i
$568$		0			0
$569$	1.54406e26			1.03538			0.517689	−	0.855569i	$-0.326793\pi$
$569$	1.54406e26			1.03538			0.517689	+	0.855569i	$0.326793\pi$
$570$		0			0
$571$	−2.57573e26			−1.67054			−0.835271	−	0.549838i	$-0.814690\pi$
$571$	−2.57573e26			−1.67054			−0.835271	+	0.549838i	$0.814690\pi$
$572$		0			0
$573$		−	2.12821e26i		−	1.33520i
$574$		0			0
$575$	1.42782e25	−	1.78276e26i	0.0866622	−	1.08205i
$576$		0			0
$577$		−	7.03753e25i		−	0.413286i	−0.978416	−	0.206643i	$-0.933746\pi$
$577$		−	7.03753e25i		−	0.413286i	0.978416	−	0.206643i	$-0.0662538\pi$
$578$		0			0
$579$	−1.78046e26			−1.01178
$580$		0			0
$581$	−2.97270e25			−0.163485
$582$		0			0
$583$			1.20786e25i			0.0642930i
$584$		0			0
$585$	−5.32763e24	+	1.33253e26i	−0.0274507	+	0.686590i
$586$		0			0
$587$		−	1.31622e26i		−	0.656546i	−0.944583	−	0.328273i	$-0.893533\pi$
$587$		−	1.31622e26i		−	0.656546i	0.944583	−	0.328273i	$-0.106467\pi$
$588$		0			0
$589$	1.32384e26			0.639352
$590$		0			0
$591$	4.39575e26			2.05566
$592$		0			0
$593$		−	3.84184e26i		−	1.73988i	−0.493157	−	0.869940i	$-0.664157\pi$
$593$		−	3.84184e26i		−	1.73988i	0.493157	−	0.869940i	$-0.335843\pi$
$594$		0			0
$595$	−1.19306e26	−	4.76999e24i	−0.523300	−	0.0209221i
$596$		0			0
$597$			3.75365e26i			1.59477i
$598$		0			0
$599$	1.79598e26			0.739174			0.369587	−	0.929196i	$-0.379499\pi$
$599$	1.79598e26			0.739174			0.369587	+	0.929196i	$0.379499\pi$
$600$		0			0
$601$	−2.49891e26			−0.996422			−0.498211	−	0.867056i	$-0.666010\pi$
$601$	−2.49891e26			−0.996422			−0.498211	+	0.867056i	$0.666010\pi$
$602$		0			0
$603$			9.28434e25i			0.358704i
$604$		0			0
$605$	2.48417e26	+	9.93201e24i	0.930048	+	0.0371844i
$606$		0			0
$607$		−	3.78133e26i		−	1.37199i	−0.727604	−	0.685997i	$-0.759366\pi$
$607$		−	3.78133e26i		−	1.37199i	0.727604	−	0.685997i	$-0.240634\pi$
$608$		0			0
$609$	1.46376e26			0.514759
$610$		0			0
$611$	3.13899e26			1.07003
$612$		0			0
$613$			7.14877e25i			0.236242i	0.992999	+	0.118121i	$0.0376870\pi$
$613$			7.14877e25i			0.236242i	−0.992999	+	0.118121i	$0.962313\pi$
$614$		0			0
$615$	2.09210e25	−	5.23270e26i	0.0670298	−	1.67653i
$616$		0			0
$617$			1.67720e26i			0.521044i	0.965468	+	0.260522i	$0.0838947\pi$
$617$			1.67720e26i			0.521044i	−0.965468	+	0.260522i	$0.916105\pi$
$618$		0			0
$619$	3.39604e26			1.02308			0.511542	−	0.859258i	$-0.329074\pi$
$619$	3.39604e26			1.02308			0.511542	+	0.859258i	$0.329074\pi$
$620$		0			0
$621$	−2.36356e26			−0.690552
$622$		0			0
$623$		−	8.57649e25i		−	0.243037i
$624$		0			0
$625$	3.59160e26	+	5.79020e25i	0.987253	+	0.159160i
$626$		0			0
$627$		−	5.46050e25i		−	0.145610i
$628$		0			0
$629$	2.22799e26			0.576412
$630$		0			0
$631$	4.81505e26			1.20871			0.604355	−	0.796715i	$-0.293431\pi$
$631$	4.81505e26			1.20871			0.604355	+	0.796715i	$0.293431\pi$
$632$		0			0
$633$		−	4.53664e24i		−	0.0110509i
$634$		0			0
$635$	1.99482e25	−	4.98940e26i	0.0471578	−	1.17950i
$636$		0			0
$637$			5.05443e26i			1.15970i
$638$		0			0
$639$	2.92705e26			0.651887
$640$		0			0
$641$	6.11577e26			1.32221			0.661104	−	0.750294i	$-0.270088\pi$
$641$	6.11577e26			1.32221			0.661104	+	0.750294i	$0.270088\pi$
$642$		0			0
$643$			6.51238e26i			1.36690i	0.729999	+	0.683448i	$0.239520\pi$
$643$			6.51238e26i			1.36690i	−0.729999	+	0.683448i	$0.760480\pi$
$644$		0			0
$645$	5.91688e25	+	2.36564e24i	0.120580	+	0.00482093i
$646$		0			0
$647$			2.27059e26i			0.449311i	0.974438	+	0.224656i	$0.0721257\pi$
$647$			2.27059e26i			0.449311i	−0.974438	+	0.224656i	$0.927874\pi$
$648$		0			0
$649$	−1.51904e26			−0.291907
$650$		0			0
$651$	−4.04430e26			−0.754786
$652$		0			0
$653$		−	4.30770e25i		−	0.0780855i	−0.999238	−	0.0390428i	$-0.987569\pi$
$653$		−	4.30770e25i		−	0.0780855i	0.999238	−	0.0390428i	$-0.0124309\pi$
$654$		0			0
$655$	−2.42421e26	−	9.69228e24i	−0.426852	−	0.0170661i
$656$		0			0
$657$			2.57309e26i			0.440133i
$658$		0			0
$659$	−3.58337e26			−0.595498			−0.297749	−	0.954644i	$-0.596236\pi$
$659$	−3.58337e26			−0.595498			−0.297749	+	0.954644i	$0.596236\pi$
$660$		0			0
$661$	1.80474e26			0.291408			0.145704	−	0.989328i	$-0.453455\pi$
$661$	1.80474e26			0.291408			0.145704	+	0.989328i	$0.453455\pi$
$662$		0			0
$663$			1.32169e27i			2.07373i
$664$		0			0
$665$	−5.28184e24	+	1.32108e26i	−0.00805341	+	0.201430i
$666$		0			0
$667$			7.01220e26i			1.03910i
$668$		0			0
$669$	9.51973e26			1.37112
$670$		0			0
$671$	2.75880e26			0.386239
$672$		0			0
$673$		−	1.25614e27i		−	1.70960i	−0.518958	−	0.854800i	$-0.673680\pi$
$673$		−	1.25614e27i		−	1.70960i	0.518958	−	0.854800i	$-0.326320\pi$
$674$		0			0
$675$	3.83828e25	−	4.79243e26i	0.0507868	−	0.634118i
$676$		0			0
$677$			9.07536e26i			1.16754i	0.811919	+	0.583770i	$0.198423\pi$
$677$			9.07536e26i			1.16754i	−0.811919	+	0.583770i	$0.801577\pi$
$678$		0			0
$679$	−1.49444e26			−0.186946
$680$		0			0
$681$	−1.07779e27			−1.31110
$682$		0			0
$683$		−	4.15004e26i		−	0.490971i	−0.969400	−	0.245485i	$-0.921053\pi$
$683$		−	4.15004e26i		−	0.490971i	0.969400	−	0.245485i	$-0.0789473\pi$
$684$		0			0
$685$	−1.35912e24	+	3.39941e25i	−0.00156386	+	0.0391150i
$686$		0			0
$687$			8.84272e26i			0.989685i
$688$		0			0
$689$	−3.23729e26			−0.352451
$690$		0			0
$691$	−2.47952e26			−0.262619			−0.131309	−	0.991341i	$-0.541918\pi$
$691$	−2.47952e26			−0.262619			−0.131309	+	0.991341i	$0.541918\pi$
$692$		0			0
$693$			5.38328e25i			0.0554729i
$694$		0			0
$695$	9.62395e26	+	3.84777e25i	0.964935	+	0.0385792i
$696$		0			0
$697$		−	1.67488e27i		−	1.63408i
$698$		0			0
$699$	−1.09015e27			−1.03503
$700$		0			0
$701$	−5.91031e26			−0.546122			−0.273061	−	0.961997i	$-0.588036\pi$
$701$	−5.91031e26			−0.546122			−0.273061	+	0.961997i	$0.588036\pi$
$702$		0			0
$703$		−	2.46707e26i		−	0.221874i
$704$		0			0
$705$	1.02907e27	+	4.11433e25i	0.900839	+	0.0360166i
$706$		0			0
$707$		−	2.44247e26i		−	0.208135i
$708$		0			0
$709$	−2.07358e27			−1.72021			−0.860105	−	0.510117i	$-0.829602\pi$
$709$	−2.07358e27			−1.72021			−0.860105	+	0.510117i	$0.829602\pi$
$710$		0			0
$711$	−6.99431e26			−0.564916
$712$		0			0
$713$		−	1.93744e27i		−	1.52363i
$714$		0			0
$715$	1.97930e25	−	4.95058e26i	0.0151567	−	0.379096i
$716$		0			0
$717$			8.18529e26i			0.610383i
$718$		0			0
$719$	9.72209e26			0.706049			0.353025	−	0.935614i	$-0.385153\pi$
$719$	9.72209e26			0.706049			0.353025	+	0.935614i	$0.385153\pi$
$720$		0			0
$721$	9.43114e25			0.0667082
$722$		0			0
$723$			2.45115e27i			1.68872i
$724$		0			0
$725$	−1.42182e27	−	1.13874e26i	−0.954185	−	0.0764210i
$726$		0			0
$727$		−	1.21670e27i		−	0.795441i	−0.917507	−	0.397720i	$-0.869801\pi$
$727$		−	1.21670e27i		−	0.795441i	0.917507	−	0.397720i	$-0.130199\pi$
$728$		0			0
$729$	−2.78947e26			−0.177668
$730$		0			0
$731$	1.89388e26			0.117527
$732$		0			0
$733$		−	2.04070e27i		−	1.23394i	−0.786989	−	0.616968i	$-0.788361\pi$
$733$		−	2.04070e27i		−	1.23394i	0.786989	−	0.616968i	$-0.211639\pi$
$734$		0			0
$735$	−6.62494e25	+	1.65701e27i	−0.0390348	+	0.976330i
$736$		0			0
$737$		−	3.44928e26i		−	0.198056i
$738$		0			0
$739$	6.44557e26			0.360694			0.180347	−	0.983603i	$-0.442278\pi$
$739$	6.44557e26			0.360694			0.180347	+	0.983603i	$0.442278\pi$
$740$		0			0
$741$	1.46352e27			0.798226
$742$		0			0
$743$		−	2.69694e27i		−	1.43376i	−0.697196	−	0.716881i	$-0.745569\pi$
$743$		−	2.69694e27i		−	1.43376i	0.697196	−	0.716881i	$-0.254431\pi$
$744$		0			0
$745$	−2.37325e27	−	9.48853e25i	−1.22987	−	0.0491716i
$746$		0			0
$747$			3.48403e26i			0.176009i
$748$		0			0
$749$	1.42169e27			0.700211
$750$		0			0
$751$	−3.07338e27			−1.47583			−0.737915	−	0.674893i	$-0.764190\pi$
$751$	−3.07338e27			−1.47583			−0.737915	+	0.674893i	$0.764190\pi$
$752$		0			0
$753$			3.06884e27i			1.43689i
$754$		0			0
$755$	−1.67384e27	−	6.69221e25i	−0.764219	−	0.0305544i
$756$		0			0
$757$		−	2.68835e27i		−	1.19695i	−0.801143	−	0.598473i	$-0.795775\pi$
$757$		−	2.68835e27i		−	1.19695i	0.801143	−	0.598473i	$-0.204225\pi$
$758$		0			0
$759$	−7.99146e26			−0.347000
$760$		0			0
$761$	2.02502e26			0.0857581			0.0428790	−	0.999080i	$-0.486347\pi$
$761$	2.02502e26			0.0857581			0.0428790	+	0.999080i	$0.486347\pi$
$762$		0			0
$763$		−	2.63275e26i		−	0.108749i
$764$		0			0
$765$	−5.59045e25	+	1.39827e27i	−0.0225249	+	0.563388i
$766$		0			0
$767$		−	4.07132e27i		−	1.60022i
$768$		0			0
$769$	3.60146e26			0.138095			0.0690475	−	0.997613i	$-0.478004\pi$
$769$	3.60146e26			0.138095			0.0690475	+	0.997613i	$0.478004\pi$
$770$		0			0
$771$	−5.91420e27			−2.21248
$772$		0			0
$773$			2.73239e26i			0.0997329i	0.998756	+	0.0498664i	$0.0158796\pi$
$773$			2.73239e26i			0.0997329i	−0.998756	+	0.0498664i	$0.984120\pi$
$774$		0			0
$775$	3.92843e27	+	3.14629e26i	1.39911	+	0.112055i
$776$		0			0
$777$			7.53685e26i			0.261933i
$778$		0			0
$779$	−1.85461e27			−0.628995
$780$		0			0
$781$	−1.08745e27			−0.359935
$782$		0			0
$783$			1.88502e27i			0.608947i
$784$		0			0
$785$	−1.60929e26	+	4.02513e27i	−0.0507427	+	1.26917i
$786$		0			0
$787$		−	3.83735e27i		−	1.18106i	−0.807016	−	0.590530i	$-0.798919\pi$
$787$		−	3.83735e27i		−	1.18106i	0.807016	−	0.590530i	$-0.201081\pi$
$788$		0			0
$789$	−4.11827e27			−1.23732
$790$		0			0
$791$	−9.40000e26			−0.275709
$792$		0			0
$793$			7.39411e27i			2.11734i
$794$		0			0
$795$	−1.06129e27	−	4.24318e25i	−0.296721	−	0.0118632i
$796$		0			0
$797$		−	4.40376e26i		−	0.120218i	−0.998192	−	0.0601091i	$-0.980855\pi$
$797$		−	4.40376e26i		−	0.120218i	0.998192	−	0.0601091i	$-0.0191448\pi$
$798$		0			0
$799$	3.29384e27			0.878027
$800$		0			0
$801$	−1.00517e27			−0.261656
$802$		0			0
$803$		−	9.55945e26i		−	0.243016i
$804$		0			0
$805$	1.93341e27	+	7.72999e25i	0.480024	+	0.0191919i
$806$		0			0
$807$			3.20147e27i			0.776339i
$808$		0			0
$809$	−4.39799e27			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$809$	−4.39799e27			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$810$		0			0
$811$	−3.73831e27			−0.864923			−0.432461	−	0.901652i	$-0.642355\pi$
$811$	−3.73831e27			−0.864923			−0.432461	+	0.901652i	$0.642355\pi$
$812$		0			0
$813$			1.72722e27i			0.390380i
$814$		0			0
$815$	−1.85499e26	+	4.63965e27i	−0.0409584	+	1.02444i
$816$		0			0
$817$		−	2.09710e26i		−	0.0452387i
$818$		0			0
$819$	−1.44282e27			−0.304100
$820$		0			0
$821$	−9.57070e27			−1.97099			−0.985494	−	0.169713i	$-0.945716\pi$
$821$	−9.57070e27			−1.97099			−0.985494	+	0.169713i	$0.945716\pi$
$822$		0			0
$823$		−	3.11943e27i		−	0.627735i	−0.949467	−	0.313867i	$-0.898375\pi$
$823$		−	3.11943e27i		−	0.627735i	0.949467	−	0.313867i	$-0.101625\pi$
$824$		0			0
$825$	1.29776e26	−	1.62038e27i	0.0255202	−	0.318642i
$826$		0			0
$827$		−	2.14178e27i		−	0.411597i	−0.978594	−	0.205798i	$-0.934021\pi$
$827$		−	2.14178e27i		−	0.411597i	0.978594	−	0.205798i	$-0.0659791\pi$
$828$		0			0
$829$	5.22490e27			0.981319			0.490660	−	0.871351i	$-0.336756\pi$
$829$	5.22490e27			0.981319			0.490660	+	0.871351i	$0.336756\pi$
$830$		0			0
$831$	1.00671e28			1.84796
$832$		0			0
$833$			5.30377e27i			0.951607i
$834$		0			0
$835$	−1.41988e26	+	3.55138e27i	−0.0249018	+	0.622839i
$836$		0			0
$837$		−	5.20824e27i		−	0.892893i
$838$		0			0
$839$	6.92133e27			1.15998			0.579991	−	0.814623i	$-0.303056\pi$
$839$	6.92133e27			1.15998			0.579991	+	0.814623i	$0.303056\pi$
$840$		0			0
$841$	−5.10787e26			−0.0836908
$842$		0			0
$843$		−	2.00396e27i		−	0.321017i
$844$		0			0
$845$	6.88894e27	+	2.75428e26i	1.07898	+	0.0431389i
$846$		0			0
$847$			2.68978e27i			0.411931i
$848$		0			0
$849$	1.09735e28			1.64332
$850$		0			0
$851$	−3.61057e27			−0.528743
$852$		0			0
$853$		−	1.17732e27i		−	0.168608i	−0.996440	−	0.0843041i	$-0.973133\pi$
$853$		−	1.17732e27i		−	0.168608i	0.996440	−	0.0843041i	$-0.0268667\pi$
$854$		0			0
$855$	1.54832e27	+	6.19035e25i	0.216861	+	0.00867036i
$856$		0			0
$857$			3.51725e27i			0.481820i	0.970547	+	0.240910i	$0.0774459\pi$
$857$			3.51725e27i			0.481820i	−0.970547	+	0.240910i	$0.922554\pi$
$858$		0			0
$859$	−1.39249e28			−1.86577			−0.932883	−	0.360180i	$-0.882715\pi$
$859$	−1.39249e28			−1.86577			−0.932883	+	0.360180i	$0.882715\pi$
$860$		0			0
$861$	5.66580e27			0.742559
$862$		0			0
$863$		−	9.73816e27i		−	1.24846i	−0.781241	−	0.624229i	$-0.785413\pi$
$863$		−	9.73816e27i		−	1.24846i	0.781241	−	0.624229i	$-0.214587\pi$
$864$		0			0
$865$	2.32991e26	−	5.82752e27i	0.0292204	−	0.730855i
$866$		0			0
$867$			3.96536e27i			0.486520i
$868$		0			0
$869$	2.59850e27			0.311914
$870$		0			0
$871$	9.24475e27			1.08573
$872$		0			0
$873$			1.75149e27i			0.201267i
$874$		0			0
$875$	−4.70710e26	+	3.90769e27i	−0.0529269	+	0.439383i
$876$		0			0
$877$		−	1.04968e28i		−	1.15494i	−0.816412	−	0.577470i	$-0.804040\pi$
$877$		−	1.04968e28i		−	1.15494i	0.816412	−	0.577470i	$-0.195960\pi$
$878$		0			0
$879$	1.65359e28			1.78046
$880$		0			0
$881$	−4.39557e25			−0.00463174			−0.00231587	−	0.999997i	$-0.500737\pi$
$881$	−4.39557e25			−0.00463174			−0.00231587	+	0.999997i	$0.500737\pi$
$882$		0			0
$883$			7.69304e27i			0.793362i	0.917957	+	0.396681i	$0.129838\pi$
$883$			7.69304e27i			0.793362i	−0.917957	+	0.396681i	$0.870162\pi$
$884$		0			0
$885$	5.33636e26	−	1.33472e28i	0.0538622	−	1.34719i
$886$		0			0
$887$		−	2.70370e27i		−	0.267106i	−0.991042	−	0.133553i	$-0.957361\pi$
$887$		−	2.70370e27i		−	0.267106i	0.991042	−	0.133553i	$-0.0426386\pi$
$888$		0			0
$889$	5.40235e27			0.522416
$890$		0			0
$891$	−3.47245e27			−0.328699
$892$		0			0
$893$		−	3.64729e27i		−	0.337973i
$894$		0			0
$895$	1.21098e28	+	4.84163e26i	1.09854	+	0.0439211i
$896$		0			0
$897$		−	2.14187e28i		−	1.90224i
$898$		0			0
$899$	−1.54518e28			−1.34357
$900$		0			0
$901$	−3.39699e27			−0.289207
$902$		0			0
$903$			6.40660e26i			0.0534065i
$904$		0			0
$905$	2.22065e28	+	8.87842e26i	1.81267	+	0.0724727i
$906$		0			0
$907$			3.89446e26i			0.0311300i	0.999879	+	0.0155650i	$0.00495469\pi$
$907$			3.89446e26i			0.0311300i	−0.999879	+	0.0155650i	$0.995045\pi$
$908$		0			0
$909$	−2.86259e27			−0.224080
$910$		0			0
$911$	−1.63847e26			−0.0125607			−0.00628033	−	0.999980i	$-0.501999\pi$
$911$	−1.63847e26			−0.0125607			−0.00628033	+	0.999980i	$0.501999\pi$
$912$		0			0
$913$		−	1.29437e27i		−	0.0971822i
$914$		0			0
$915$	−9.69161e26	+	2.42404e28i	−0.0712681	+	1.78254i
$916$		0			0
$917$		−	2.62485e27i		−	0.189059i
$918$		0			0
$919$	1.74062e28			1.22803			0.614013	−	0.789296i	$-0.289554\pi$
$919$	1.74062e28			1.22803			0.614013	+	0.789296i	$0.289554\pi$
$920$		0			0
$921$	−3.27919e28			−2.26621
$922$		0			0
$923$		−	2.91457e28i		−	1.97314i
$924$		0			0
$925$	5.86335e26	−	7.32091e27i	0.0388865	−	0.485533i
$926$		0			0
$927$		−	1.10533e27i		−	0.0718185i
$928$		0			0
$929$	−4.76947e27			−0.303613			−0.151807	−	0.988410i	$-0.548509\pi$
$929$	−4.76947e27			−0.303613			−0.151807	+	0.988410i	$0.548509\pi$
$930$		0			0
$931$	5.87291e27			0.366295
$932$		0			0
$933$			3.44001e28i			2.10225i
$934$		0			0
$935$	2.07694e26	−	5.19480e27i	0.0124370	−	0.311071i
$936$		0			0
$937$		−	9.11764e27i		−	0.535003i	−0.963557	−	0.267502i	$-0.913802\pi$
$937$		−	9.11764e27i		−	0.535003i	0.963557	−	0.267502i	$-0.0861981\pi$
$938$		0			0
$939$	2.11059e28			1.21362
$940$		0			0
$941$	−6.57656e26			−0.0370593			−0.0185297	−	0.999828i	$-0.505899\pi$
$941$	−6.57656e26			−0.0370593			−0.0185297	+	0.999828i	$0.505899\pi$
$942$		0			0
$943$			2.71423e28i			1.49894i
$944$		0			0
$945$	5.19740e27	+	2.07798e26i	0.281309	+	0.0112471i
$946$		0			0
$947$			6.99014e26i			0.0370818i	0.999828	+	0.0185409i	$0.00590209\pi$
$947$			6.99014e26i			0.0370818i	−0.999828	+	0.0185409i	$0.994098\pi$
$948$		0			0
$949$	2.56212e28			1.33220
$950$		0			0
$951$	1.88156e28			0.958968
$952$		0			0
$953$			3.02275e28i			1.51015i	0.655638	+	0.755075i	$0.272400\pi$
$953$			3.02275e28i			1.51015i	−0.655638	+	0.755075i	$0.727600\pi$
$954$		0			0
$955$	−2.24192e28	−	8.96346e26i	−1.09796	−	0.0438979i
$956$		0			0
$957$			6.37347e27i			0.305994i
$958$		0			0
$959$	−3.68077e26			−0.0173245
$960$		0			0
$961$	2.10221e28			0.970070
$962$		0			0
$963$		−	1.66623e28i		−	0.753852i
$964$		0			0
$965$	−7.49880e26	+	1.87558e28i	−0.0332646	+	0.832007i
$966$		0			0
$967$			2.77170e28i			1.20558i	0.797901	+	0.602789i	$0.205944\pi$
$967$			2.77170e28i			1.20558i	−0.797901	+	0.602789i	$0.794056\pi$
$968$		0			0
$969$	1.53572e28			0.654992
$970$		0			0
$971$	−4.18159e28			−1.74888			−0.874438	−	0.485137i	$-0.838770\pi$
$971$	−4.18159e28			−1.74888			−0.874438	+	0.485137i	$0.838770\pi$
$972$		0			0
$973$			1.04205e28i			0.427382i
$974$		0			0
$975$	4.34292e28	+	3.47826e27i	1.74678	+	0.139900i
$976$		0			0
$977$			3.47774e28i			1.37183i	0.727684	+	0.685913i	$0.240597\pi$
$977$			3.47774e28i			1.37183i	−0.727684	+	0.685913i	$0.759403\pi$
$978$		0			0
$979$	3.73437e27			0.144471
$980$		0			0
$981$	−3.08560e27			−0.117080
$982$		0			0
$983$		−	5.24074e28i		−	1.95045i	−0.221224	−	0.975223i	$-0.571005\pi$
$983$		−	5.24074e28i		−	1.95045i	0.221224	−	0.975223i	$-0.428995\pi$
$984$		0			0
$985$	1.85137e27	−	4.63061e28i	0.0675849	−	1.69042i
$986$		0			0
$987$			1.11424e28i			0.398993i
$988$		0			0
$989$	−3.06912e27			−0.107807
$990$		0			0
$991$	−4.64199e28			−1.59957			−0.799787	−	0.600284i	$-0.795054\pi$
$991$	−4.64199e28			−1.59957			−0.799787	+	0.600284i	$0.795054\pi$
$992$		0			0
$993$		−	3.01356e28i		−	1.01874i
$994$		0			0
$995$	3.95421e28	+	1.58094e27i	1.31141	+	0.0524319i
$996$		0			0
$997$			3.51680e28i			1.14431i	0.820146	+	0.572154i	$0.193892\pi$
$997$			3.51680e28i			1.14431i	−0.820146	+	0.572154i	$0.806108\pi$
$998$		0			0
$999$	−9.70595e27			−0.309860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.d.49.6		28
4.3	odd	2		40.20.c.a.9.23	yes	28
5.4	even	2	inner	80.20.c.d.49.23		28
20.19	odd	2		40.20.c.a.9.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.20.c.a.9.6	✓	28	20.19	odd	2
40.20.c.a.9.23	yes	28	4.3	odd	2
80.20.c.d.49.6		28	1.1	even	1	trivial
80.20.c.d.49.23		28	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-41425.1i q^{3} +(-4.36383e6 - 174471. i) q^{5} -4.72501e7i q^{7} -5.53775e8 q^{9} +O(q^{10})\)	\(q-41425.1i q^{3} +(-4.36383e6 - 174471. i) q^{5} -4.72501e7i q^{7} -5.53775e8 q^{9} +2.05736e9 q^{11} +5.51413e10i q^{13} +(-7.22748e9 + 1.80772e11i) q^{15} +5.78616e11i q^{17} +6.40705e11 q^{19} -1.95734e12 q^{21} -9.37674e12i q^{23} +(1.90126e13 + 1.52273e12i) q^{25} -2.52066e13i q^{27} -7.47829e13 q^{29} +2.06622e14 q^{31} -8.52264e13i q^{33} +(-8.24379e12 + 2.06192e14i) q^{35} -3.85056e14i q^{37} +2.28423e15 q^{39} -2.89464e15 q^{41} -3.27312e14i q^{43} +(2.41658e15 + 9.66177e13i) q^{45} -5.69262e15i q^{47} +9.16632e15 q^{49} +2.39692e16 q^{51} +5.87089e15i q^{53} +(-8.97799e15 - 3.58951e14i) q^{55} -2.65413e16i q^{57} -7.38344e16 q^{59} +1.34094e17 q^{61} +2.61659e16i q^{63} +(9.62057e15 - 2.40628e17i) q^{65} -1.67656e17i q^{67} -3.88432e17 q^{69} -5.28564e17 q^{71} -4.64646e17i q^{73} +(6.30791e16 - 7.87598e17i) q^{75} -9.72107e16i q^{77} +1.26302e18 q^{79} -1.68782e18 q^{81} -6.29142e17i q^{83} +(1.00952e17 - 2.52498e18i) q^{85} +3.09788e18i q^{87} +1.81512e18 q^{89} +2.60544e18 q^{91} -8.55934e18i q^{93} +(-2.79593e18 - 1.11785e17i) q^{95} -3.16283e18i q^{97} -1.13931e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) \) 28 * q - 3935164 * q^5 - 10352560732 * q^9	\( 28 q - 3935164 q^{5} - 10352560732 q^{9} - 18570995888 q^{11} - 79041415120 q^{15} + 1685869130672 q^{19} + 140419722832 q^{21} - 29558822439924 q^{25} + 160448197635496 q^{29} - 64251929934720 q^{31} + 88899634227664 q^{35} - 45\!\cdots\!04 q^{39}+ \cdots + 24\!\cdots\!92 q^{99}+O(q^{100}) \) 28 * q - 3935164 * q^5 - 10352560732 * q^9 - 18570995888 * q^11 - 79041415120 * q^15 + 1685869130672 * q^19 + 140419722832 * q^21 - 29558822439924 * q^25 + 160448197635496 * q^29 - 64251929934720 * q^31 + 88899634227664 * q^35 - 4563253596731104 * q^39 + 87868042694936 * q^41 + 3557698140217852 * q^45 - 28923781405647564 * q^49 - 14937379593456000 * q^51 - 28335039172010704 * q^55 + 83879503376835216 * q^59 + 2336306250785000 * q^61 + 23503427909569568 * q^65 - 46927873937137712 * q^69 - 104881848512783264 * q^71 - 1094024007292275040 * q^75 + 795721739900308672 * q^79 + 3593102866196377132 * q^81 + 834124526841485952 * q^85 + 1582238786752844568 * q^89 - 11017818924975052064 * q^91 - 30914057837649668144 * q^95 + 24571127463084047792 * q^99

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