LMFDB - Embedded newform 80.10.c.c.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,10,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, 10, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
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:	$41.2028668931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.49740556.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 45x^{2} + 304 $ x^4 + 45*x^2 + 304
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.4
Root			$6.05982i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.10.c.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} +O(q^{10})$	\(q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} -44557.8 q^{11} +21430.4i q^{13} +(228880. - 101873. i) q^{15} +300220. i q^{17} +565385. q^{19} +1.56192e6 q^{21} +950727. i q^{23} +(-1.30722e6 + 1.45116e6i) q^{25} +1.29622e6i q^{27} +803167. q^{29} +1.99843e6 q^{31} -7.98755e6i q^{33} +(-1.11246e7 + 4.95149e6i) q^{35} +9.53656e6i q^{37} -3.84168e6 q^{39} -2.54355e7 q^{41} -2.32830e7i q^{43} +(7.07642e6 + 1.58987e7i) q^{45} +3.77353e7i q^{47} -3.55626e7 q^{49} -5.38183e7 q^{51} +4.79297e7i q^{53} +(2.53216e7 + 5.68906e7i) q^{55} +1.01353e8i q^{57} +7.00069e7 q^{59} +1.26942e8 q^{61} +1.08496e8i q^{63} +(2.73620e7 - 1.21787e7i) q^{65} +2.66595e8i q^{67} -1.70430e8 q^{69} -6.59169e7 q^{71} -1.47516e7i q^{73} +(-2.60139e8 - 2.34337e8i) q^{75} +3.88231e8i q^{77} -4.66498e7 q^{79} -4.77460e8 q^{81} +2.01840e8i q^{83} +(3.83316e8 - 1.70611e8i) q^{85} +1.43978e8i q^{87} -5.54039e8 q^{89} +1.86723e8 q^{91} +3.58244e8i q^{93} +(-3.21301e8 - 7.21874e8i) q^{95} +3.39489e8i q^{97} +5.54841e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1140 q^{5} + 11628 q^{9}+O(q^{10}) $ 4 * q + 1140 * q^5 + 11628 * q^9	$ 4 q + 1140 q^{5} + 11628 q^{9} - 109968 q^{11} + 396720 q^{15} + 636880 q^{19} + 3523968 q^{21} - 1337900 q^{25} - 3531720 q^{29} + 10587712 q^{31} - 13629840 q^{35} - 1686816 q^{39} - 16788552 q^{41} + 55737180 q^{45} - 46921028 q^{49} - 84017088 q^{51} + 26907120 q^{55} + 460829040 q^{59} + 360490568 q^{61} + 183895680 q^{65} - 286524864 q^{69} + 47611872 q^{71} - 659239200 q^{75} + 728043520 q^{79} - 343387836 q^{81} + 1275419840 q^{85} - 1582700760 q^{89} - 473322528 q^{91} - 1204791600 q^{95} + 728787024 q^{99}+O(q^{100}) $ 4 * q + 1140 * q^5 + 11628 * q^9 - 109968 * q^11 + 396720 * q^15 + 636880 * q^19 + 3523968 * q^21 - 1337900 * q^25 - 3531720 * q^29 + 10587712 * q^31 - 13629840 * q^35 - 1686816 * q^39 - 16788552 * q^41 + 55737180 * q^45 - 46921028 * q^49 - 84017088 * q^51 + 26907120 * q^55 + 460829040 * q^59 + 360490568 * q^61 + 183895680 * q^65 - 286524864 * q^69 + 47611872 * q^71 - 659239200 * q^75 + 728043520 * q^79 - 343387836 * q^81 + 1275419840 * q^85 - 1582700760 * q^89 - 473322528 * q^91 - 1204791600 * q^95 + 728787024 * 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
$3$			179.263i			1.27775i	0.769312	+	0.638873i	$0.220599\pi$
$3$			179.263i			1.27775i	−0.769312	+	0.638873i	$0.779401\pi$
$4$		0			0
$5$	−568.288	−	1276.78i	−0.406634	−	0.913591i
$5$	−568.288	−	1276.78i	−0.406634	−	0.913591i
$6$		0			0
$7$		−	8712.99i		−	1.37160i	−0.727792	−	0.685798i	$-0.759453\pi$
$7$		−	8712.99i		−	1.37160i	0.727792	−	0.685798i	$-0.240547\pi$
$8$		0			0
$9$	−12452.2			−0.632636
$10$		0			0
$11$	−44557.8			−0.917606			−0.458803	−	0.888538i	$-0.651722\pi$
$11$	−44557.8			−0.917606			−0.458803	+	0.888538i	$0.651722\pi$
$12$		0			0
$13$			21430.4i			0.208107i	0.994572	+	0.104053i	$0.0331813\pi$
$13$			21430.4i			0.208107i	−0.994572	+	0.104053i	$0.966819\pi$
$14$		0			0
$15$	228880.	−	101873.i	1.16734	−	0.519575i
$16$		0			0
$17$			300220.i			0.871805i	0.899994	+	0.435903i	$0.143571\pi$
$17$			300220.i			0.871805i	−0.899994	+	0.435903i	$0.856429\pi$
$18$		0			0
$19$	565385.			0.995298			0.497649	−	0.867379i	$-0.334197\pi$
$19$	565385.			0.995298			0.497649	+	0.867379i	$0.334197\pi$
$20$		0			0
$21$	1.56192e6			1.75255
$22$		0			0
$23$			950727.i			0.708403i	0.935169	+	0.354202i	$0.115247\pi$
$23$			950727.i			0.708403i	−0.935169	+	0.354202i	$0.884753\pi$
$24$		0			0
$25$	−1.30722e6	+	1.45116e6i	−0.669298	+	0.742994i
$26$		0			0
$27$			1.29622e6i			0.469398i
$28$		0			0
$29$	803167.			0.210870			0.105435	−	0.994426i	$-0.466377\pi$
$29$	803167.			0.210870			0.105435	+	0.994426i	$0.466377\pi$
$30$		0			0
$31$	1.99843e6			0.388652			0.194326	−	0.980937i	$-0.437748\pi$
$31$	1.99843e6			0.388652			0.194326	+	0.980937i	$0.437748\pi$
$32$		0			0
$33$		−	7.98755e6i		−	1.17247i
$34$		0			0
$35$	−1.11246e7	+	4.95149e6i	−1.25308	+	0.557737i
$36$		0			0
$37$			9.53656e6i			0.836535i	0.908324	+	0.418267i	$0.137363\pi$
$37$			9.53656e6i			0.836535i	−0.908324	+	0.418267i	$0.862637\pi$
$38$		0			0
$39$	−3.84168e6			−0.265908
$40$		0			0
$41$	−2.54355e7			−1.40576			−0.702882	−	0.711306i	$-0.748104\pi$
$41$	−2.54355e7			−1.40576			−0.702882	+	0.711306i	$0.748104\pi$
$42$		0			0
$43$		−	2.32830e7i		−	1.03856i	−0.854605	−	0.519279i	$-0.826200\pi$
$43$		−	2.32830e7i		−	1.03856i	0.854605	−	0.519279i	$-0.173800\pi$
$44$		0			0
$45$	7.07642e6	+	1.58987e7i	0.257251	+	0.577971i
$46$		0			0
$47$			3.77353e7i			1.12800i	0.825776	+	0.563998i	$0.190738\pi$
$47$			3.77353e7i			1.12800i	−0.825776	+	0.563998i	$0.809262\pi$
$48$		0			0
$49$	−3.55626e7			−0.881274
$50$		0			0
$51$	−5.38183e7			−1.11395
$52$		0			0
$53$			4.79297e7i			0.834379i	0.908819	+	0.417190i	$0.136985\pi$
$53$			4.79297e7i			0.834379i	−0.908819	+	0.417190i	$0.863015\pi$
$54$		0			0
$55$	2.53216e7	+	5.68906e7i	0.373129	+	0.838317i
$56$		0			0
$57$			1.01353e8i			1.27174i
$58$		0			0
$59$	7.00069e7			0.752154			0.376077	−	0.926588i	$-0.377273\pi$
$59$	7.00069e7			0.752154			0.376077	+	0.926588i	$0.377273\pi$
$60$		0			0
$61$	1.26942e8			1.17387			0.586936	−	0.809633i	$-0.300334\pi$
$61$	1.26942e8			1.17387			0.586936	+	0.809633i	$0.300334\pi$
$62$		0			0
$63$			1.08496e8i			0.867721i
$64$		0			0
$65$	2.73620e7	−	1.21787e7i	0.190124	−	0.0846231i
$66$		0			0
$67$			2.66595e8i			1.61628i	0.588993	+	0.808138i	$0.299525\pi$
$67$			2.66595e8i			1.61628i	−0.588993	+	0.808138i	$0.700475\pi$
$68$		0			0
$69$	−1.70430e8			−0.905160
$70$		0			0
$71$	−6.59169e7			−0.307846			−0.153923	−	0.988083i	$-0.549191\pi$
$71$	−6.59169e7			−0.307846			−0.153923	+	0.988083i	$0.549191\pi$
$72$		0			0
$73$		−	1.47516e7i		−	0.0607977i	−0.999538	−	0.0303989i	$-0.990322\pi$
$73$		−	1.47516e7i		−	0.0607977i	0.999538	−	0.0303989i	$-0.00967775\pi$
$74$		0			0
$75$	−2.60139e8	−	2.34337e8i	−0.949358	−	0.855193i
$76$		0			0
$77$			3.88231e8i			1.25858i
$78$		0			0
$79$	−4.66498e7			−0.134750			−0.0673748	−	0.997728i	$-0.521462\pi$
$79$	−4.66498e7			−0.134750			−0.0673748	+	0.997728i	$0.521462\pi$
$80$		0			0
$81$	−4.77460e8			−1.23241
$82$		0			0
$83$			2.01840e8i			0.466826i	0.972378	+	0.233413i	$0.0749895\pi$
$83$			2.01840e8i			0.466826i	−0.972378	+	0.233413i	$0.925011\pi$
$84$		0			0
$85$	3.83316e8	−	1.70611e8i	0.796474	−	0.354505i
$86$		0			0
$87$			1.43978e8i			0.269438i
$88$		0			0
$89$	−5.54039e8			−0.936020			−0.468010	−	0.883723i	$-0.655029\pi$
$89$	−5.54039e8			−0.936020			−0.468010	+	0.883723i	$0.655029\pi$
$90$		0			0
$91$	1.86723e8			0.285438
$92$		0			0
$93$			3.58244e8i			0.496599i
$94$		0			0
$95$	−3.21301e8	−	7.21874e8i	−0.404722	−	0.909295i
$96$		0			0
$97$			3.39489e8i			0.389361i	0.980867	+	0.194681i	$0.0623670\pi$
$97$			3.39489e8i			0.389361i	−0.980867	+	0.194681i	$0.937633\pi$
$98$		0			0
$99$	5.54841e8			0.580511
$100$		0			0
$101$	1.33921e9			1.28056			0.640282	−	0.768140i	$-0.278817\pi$
$101$	1.33921e9			1.28056			0.640282	+	0.768140i	$0.278817\pi$
$102$		0			0
$103$		−	3.84306e8i		−	0.336442i	−0.985749	−	0.168221i	$-0.946198\pi$
$103$		−	3.84306e8i		−	0.336442i	0.985749	−	0.168221i	$-0.0538022\pi$
$104$		0			0
$105$	−8.87618e8	−	1.99423e9i	−0.712646	−	1.60112i
$106$		0			0
$107$			7.97379e8i			0.588082i	0.955793	+	0.294041i	$0.0950002\pi$
$107$			7.97379e8i			0.588082i	−0.955793	+	0.294041i	$0.905000\pi$
$108$		0			0
$109$	6.63230e8			0.450034			0.225017	−	0.974355i	$-0.427756\pi$
$109$	6.63230e8			0.450034			0.225017	+	0.974355i	$0.427756\pi$
$110$		0			0
$111$	−1.70955e9			−1.06888
$112$		0			0
$113$		−	1.48164e9i		−	0.854847i	−0.904051	−	0.427424i	$-0.859421\pi$
$113$		−	1.48164e9i		−	0.854847i	0.904051	−	0.427424i	$-0.140579\pi$
$114$		0			0
$115$	1.21387e9	−	5.40286e8i	0.647191	−	0.288060i
$116$		0			0
$117$		−	2.66856e8i		−	0.131656i
$118$		0			0
$119$	2.61581e9			1.19576
$120$		0			0
$121$	−3.72554e8			−0.157999
$122$		0			0
$123$		−	4.55964e9i		−	1.79621i
$124$		0			0
$125$	2.59569e9	+	8.44363e8i	0.950952	+	0.309339i
$126$		0			0
$127$			2.28772e9i			0.780344i	0.920742	+	0.390172i	$0.127584\pi$
$127$			2.28772e9i			0.780344i	−0.920742	+	0.390172i	$0.872416\pi$
$128$		0			0
$129$	4.17378e9			1.32701
$130$		0			0
$131$	3.83999e9			1.13922			0.569612	−	0.821914i	$-0.307094\pi$
$131$	3.83999e9			1.13922			0.569612	+	0.821914i	$0.307094\pi$
$132$		0			0
$133$		−	4.92619e9i		−	1.36515i
$134$		0			0
$135$	1.65499e9	−	7.36625e8i	0.428838	−	0.190873i
$136$		0			0
$137$			5.82666e9i			1.41311i	0.707657	+	0.706556i	$0.249752\pi$
$137$			5.82666e9i			1.41311i	−0.707657	+	0.706556i	$0.750248\pi$
$138$		0			0
$139$	−5.89895e9			−1.34032			−0.670159	−	0.742217i	$-0.733774\pi$
$139$	−5.89895e9			−1.34032			−0.670159	+	0.742217i	$0.733774\pi$
$140$		0			0
$141$	−6.76455e9			−1.44129
$142$		0			0
$143$		−	9.54892e8i		−	0.190960i
$144$		0			0
$145$	−4.56430e8	−	1.02547e9i	−0.0857468	−	0.192649i
$146$		0			0
$147$		−	6.37505e9i		−	1.12604i
$148$		0			0
$149$	−5.39333e9			−0.896436			−0.448218	−	0.893924i	$-0.647941\pi$
$149$	−5.39333e9			−0.896436			−0.448218	+	0.893924i	$0.647941\pi$
$150$		0			0
$151$	−7.92204e8			−0.124005			−0.0620027	−	0.998076i	$-0.519749\pi$
$151$	−7.92204e8			−0.124005			−0.0620027	+	0.998076i	$0.519749\pi$
$152$		0			0
$153$		−	3.73839e9i		−	0.551536i
$154$		0			0
$155$	−1.13568e9	−	2.55156e9i	−0.158039	−	0.355069i
$156$		0			0
$157$		−	1.18606e10i		−	1.55797i	−0.627042	−	0.778985i	$-0.715735\pi$
$157$		−	1.18606e10i		−	1.55797i	0.627042	−	0.778985i	$-0.284265\pi$
$158$		0			0
$159$	−8.59202e9			−1.06613
$160$		0			0
$161$	8.28367e9			0.971642
$162$		0			0
$163$			3.99906e9i			0.443724i	0.975078	+	0.221862i	$0.0712135\pi$
$163$			3.99906e9i			0.443724i	−0.975078	+	0.221862i	$0.928787\pi$
$164$		0			0
$165$	−1.01984e10	+	4.53923e9i	−1.07116	+	0.476765i
$166$		0			0
$167$			1.09118e10i			1.08560i	0.839861	+	0.542802i	$0.182637\pi$
$167$			1.09118e10i			1.08560i	−0.839861	+	0.542802i	$0.817363\pi$
$168$		0			0
$169$	1.01452e10			0.956692
$170$		0			0
$171$	−7.04028e9			−0.629662
$172$		0			0
$173$			1.89328e10i			1.60696i	0.595329	+	0.803482i	$0.297022\pi$
$173$			1.89328e10i			1.60696i	−0.595329	+	0.803482i	$0.702978\pi$
$174$		0			0
$175$	1.26439e10	+	1.13898e10i	1.01909	+	0.918006i
$176$		0			0
$177$			1.25496e10i			0.961062i
$178$		0			0
$179$	2.09763e10			1.52718			0.763592	−	0.645699i	$-0.223434\pi$
$179$	2.09763e10			1.52718			0.763592	+	0.645699i	$0.223434\pi$
$180$		0			0
$181$	−7.16950e9			−0.496518			−0.248259	−	0.968694i	$-0.579858\pi$
$181$	−7.16950e9			−0.496518			−0.248259	+	0.968694i	$0.579858\pi$
$182$		0			0
$183$			2.27560e10i			1.49991i
$184$		0			0
$185$	1.21761e10	−	5.41951e9i	0.764251	−	0.340163i
$186$		0			0
$187$		−	1.33771e10i		−	0.799974i
$188$		0			0
$189$	1.12939e10			0.643824
$190$		0			0
$191$	−1.75301e10			−0.953091			−0.476545	−	0.879150i	$-0.658111\pi$
$191$	−1.75301e10			−0.953091			−0.476545	+	0.879150i	$0.658111\pi$
$192$		0			0
$193$			3.13528e10i			1.62655i	0.581877	+	0.813277i	$0.302319\pi$
$193$			3.13528e10i			1.62655i	−0.581877	+	0.813277i	$0.697681\pi$
$194$		0			0
$195$	2.18318e9	+	4.90499e9i	0.108127	+	0.242931i
$196$		0			0
$197$		−	1.85971e10i		−	0.879725i	−0.898065	−	0.439862i	$-0.855027\pi$
$197$		−	1.85971e10i		−	0.879725i	0.898065	−	0.439862i	$-0.144973\pi$
$198$		0			0
$199$	−1.26662e10			−0.572544			−0.286272	−	0.958148i	$-0.592416\pi$
$199$	−1.26662e10			−0.572544			−0.286272	+	0.958148i	$0.592416\pi$
$200$		0			0
$201$	−4.77906e10			−2.06519
$202$		0			0
$203$		−	6.99798e9i		−	0.289228i
$204$		0			0
$205$	1.44547e10	+	3.24756e10i	0.571631	+	1.28429i
$206$		0			0
$207$		−	1.18386e10i		−	0.448161i
$208$		0			0
$209$	−2.51923e10			−0.913291
$210$		0			0
$211$	6.20579e9			0.215539			0.107770	−	0.994176i	$-0.465629\pi$
$211$	6.20579e9			0.215539			0.107770	+	0.994176i	$0.465629\pi$
$212$		0			0
$213$		−	1.18164e10i		−	0.393350i
$214$		0			0
$215$	−2.97273e10	+	1.32314e10i	−0.948818	+	0.422313i
$216$		0			0
$217$		−	1.74123e10i		−	0.533074i
$218$		0			0
$219$	2.64442e9			0.0776841
$220$		0			0
$221$	−6.43385e9			−0.181428
$222$		0			0
$223$			4.30855e10i			1.16670i	0.812221	+	0.583350i	$0.198258\pi$
$223$			4.30855e10i			1.16670i	−0.812221	+	0.583350i	$0.801742\pi$
$224$		0			0
$225$	1.62778e10	−	1.80701e10i	0.423422	−	0.470045i
$226$		0			0
$227$		−	2.28857e10i		−	0.572068i	−0.958219	−	0.286034i	$-0.907663\pi$
$227$		−	2.28857e10i		−	0.572068i	0.958219	−	0.286034i	$-0.0923371\pi$
$228$		0			0
$229$	5.26747e9			0.126573			0.0632867	−	0.997995i	$-0.479842\pi$
$229$	5.26747e9			0.126573			0.0632867	+	0.997995i	$0.479842\pi$
$230$		0			0
$231$	−6.95955e10			−1.60815
$232$		0			0
$233$		−	3.55179e10i		−	0.789488i	−0.918791	−	0.394744i	$-0.870833\pi$
$233$		−	3.55179e10i		−	0.789488i	0.918791	−	0.394744i	$-0.129167\pi$
$234$		0			0
$235$	4.81798e10	−	2.14445e10i	1.03053	−	0.458681i
$236$		0			0
$237$		−	8.36257e9i		−	0.172176i
$238$		0			0
$239$	5.72471e10			1.13491			0.567457	−	0.823403i	$-0.307927\pi$
$239$	5.72471e10			1.13491			0.567457	+	0.823403i	$0.307927\pi$
$240$		0			0
$241$	3.89830e10			0.744386			0.372193	−	0.928155i	$-0.378606\pi$
$241$	3.89830e10			0.744386			0.372193	+	0.928155i	$0.378606\pi$
$242$		0			0
$243$		−	6.00774e10i		−	1.10531i
$244$		0			0
$245$	2.02098e10	+	4.54057e10i	0.358356	+	0.805124i
$246$		0			0
$247$			1.21164e10i			0.207128i
$248$		0			0
$249$	−3.61824e10			−0.596486
$250$		0			0
$251$	−4.56895e10			−0.726581			−0.363291	−	0.931676i	$-0.618347\pi$
$251$	−4.56895e10			−0.726581			−0.363291	+	0.931676i	$0.618347\pi$
$252$		0			0
$253$		−	4.23622e10i		−	0.650035i
$254$		0			0
$255$	3.05843e10	+	6.87143e10i	0.452968	+	1.01769i
$256$		0			0
$257$		−	1.29955e10i		−	0.185821i	−0.995674	−	0.0929104i	$-0.970383\pi$
$257$		−	1.29955e10i		−	0.185821i	0.995674	−	0.0929104i	$-0.0296170\pi$
$258$		0			0
$259$	8.30920e10			1.14739
$260$		0			0
$261$	−1.00012e10			−0.133404
$262$		0			0
$263$		−	4.80103e10i		−	0.618776i	−0.950936	−	0.309388i	$-0.899876\pi$
$263$		−	4.80103e10i		−	0.618776i	0.950936	−	0.309388i	$-0.100124\pi$
$264$		0			0
$265$	6.11958e10	−	2.72379e10i	0.762282	−	0.339287i
$266$		0			0
$267$		−	9.93185e10i		−	1.19600i
$268$		0			0
$269$	9.98823e10			1.16306			0.581531	−	0.813524i	$-0.302454\pi$
$269$	9.98823e10			1.16306			0.581531	+	0.813524i	$0.302454\pi$
$270$		0			0
$271$	4.80217e10			0.540849			0.270424	−	0.962741i	$-0.412836\pi$
$271$	4.80217e10			0.540849			0.270424	+	0.962741i	$0.412836\pi$
$272$		0			0
$273$			3.34725e10i			0.364718i
$274$		0			0
$275$	5.82469e10	−	6.46604e10i	0.614152	−	0.681776i
$276$		0			0
$277$			1.77838e10i			0.181495i	0.995874	+	0.0907477i	$0.0289257\pi$
$277$			1.77838e10i			0.181495i	−0.995874	+	0.0907477i	$0.971074\pi$
$278$		0			0
$279$	−2.48848e10			−0.245875
$280$		0			0
$281$	−1.52044e11			−1.45476			−0.727379	−	0.686236i	$-0.759262\pi$
$281$	−1.52044e11			−1.45476			−0.727379	+	0.686236i	$0.759262\pi$
$282$		0			0
$283$		−	1.86733e11i		−	1.73055i	−0.501301	−	0.865273i	$-0.667145\pi$
$283$		−	1.86733e11i		−	1.73055i	0.501301	−	0.865273i	$-0.332855\pi$
$284$		0			0
$285$	1.29405e11	−	5.75974e10i	1.16185	−	0.517132i
$286$		0			0
$287$			2.21619e11i			1.92814i
$288$		0			0
$289$	2.84558e10			0.239955
$290$		0			0
$291$	−6.08577e10			−0.497505
$292$		0			0
$293$		−	1.28928e11i		−	1.02198i	−0.859586	−	0.510991i	$-0.829278\pi$
$293$		−	1.28928e11i		−	1.02198i	0.859586	−	0.510991i	$-0.170722\pi$
$294$		0			0
$295$	−3.97841e10	−	8.93836e10i	−0.305851	−	0.687161i
$296$		0			0
$297$		−	5.77565e10i		−	0.430722i
$298$		0			0
$299$	−2.03745e10			−0.147423
$300$		0			0
$301$	−2.02865e11			−1.42448
$302$		0			0
$303$			2.40070e11i			1.63624i
$304$		0			0
$305$	−7.21396e10	−	1.62077e11i	−0.477336	−	1.07244i
$306$		0			0
$307$		−	8.78331e10i		−	0.564333i	−0.959365	−	0.282167i	$-0.908947\pi$
$307$		−	8.78331e10i		−	0.564333i	0.959365	−	0.282167i	$-0.0910531\pi$
$308$		0			0
$309$	6.88919e10			0.429887
$310$		0			0
$311$	−2.76204e11			−1.67420			−0.837101	−	0.547049i	$-0.815751\pi$
$311$	−2.76204e11			−1.67420			−0.837101	+	0.547049i	$0.815751\pi$
$312$		0			0
$313$			1.84107e11i			1.08423i	0.840304	+	0.542115i	$0.182376\pi$
$313$			1.84107e11i			1.08423i	−0.840304	+	0.542115i	$0.817624\pi$
$314$		0			0
$315$	1.38525e11	−	6.16568e10i	0.792742	−	0.352845i
$316$		0			0
$317$			3.48865e11i			1.94040i	0.242313	+	0.970198i	$0.422094\pi$
$317$			3.48865e11i			1.94040i	−0.242313	+	0.970198i	$0.577906\pi$
$318$		0			0
$319$	−3.57873e10			−0.193496
$320$		0			0
$321$	−1.42940e11			−0.751419
$322$		0			0
$323$			1.69740e11i			0.867706i
$324$		0			0
$325$	−3.10990e10	−	2.80144e10i	−0.154622	−	0.139285i
$326$		0			0
$327$			1.18893e11i			0.575029i
$328$		0			0
$329$	3.28788e11			1.54716
$330$		0			0
$331$	−2.88744e11			−1.32217			−0.661084	−	0.750312i	$-0.729903\pi$
$331$	−2.88744e11			−1.32217			−0.661084	+	0.750312i	$0.729903\pi$
$332$		0			0
$333$		−	1.18751e11i		−	0.529222i
$334$		0			0
$335$	3.40384e11	−	1.51503e11i	1.47662	−	0.657232i
$336$		0			0
$337$		−	1.25882e11i		−	0.531654i	−0.964021	−	0.265827i	$-0.914355\pi$
$337$		−	1.25882e11i		−	0.531654i	0.964021	−	0.265827i	$-0.0856450\pi$
$338$		0			0
$339$	2.65602e11			1.09228
$340$		0			0
$341$	−8.90455e10			−0.356630
$342$		0			0
$343$		−	4.17441e10i		−	0.162844i
$344$		0			0
$345$	9.68533e10	+	2.17602e11i	0.368068	+	0.826946i
$346$		0			0
$347$			2.95822e11i			1.09534i	0.836695	+	0.547669i	$0.184485\pi$
$347$			2.95822e11i			1.09534i	−0.836695	+	0.547669i	$0.815515\pi$
$348$		0			0
$349$	−3.73474e11			−1.34755			−0.673777	−	0.738934i	$-0.735329\pi$
$349$	−3.73474e11			−1.34755			−0.673777	+	0.738934i	$0.735329\pi$
$350$		0			0
$351$	−2.77785e10			−0.0976848
$352$		0			0
$353$			4.89872e11i			1.67918i	0.543223	+	0.839589i	$0.317204\pi$
$353$			4.89872e11i			1.67918i	−0.543223	+	0.839589i	$0.682796\pi$
$354$		0			0
$355$	3.74598e10	+	8.41615e10i	0.125181	+	0.281246i
$356$		0			0
$357$			4.68918e11i			1.52788i
$358$		0			0
$359$	−4.27559e11			−1.35854			−0.679268	−	0.733891i	$-0.737702\pi$
$359$	−4.27559e11			−1.35854			−0.679268	+	0.733891i	$0.737702\pi$
$360$		0			0
$361$	−3.02753e9			−0.00938223
$362$		0			0
$363$		−	6.67851e10i		−	0.201883i
$364$		0			0
$365$	−1.88346e10	+	8.38317e9i	−0.0555443	+	0.0247224i
$366$		0			0
$367$		−	2.54403e10i		−	0.0732023i	−0.999330	−	0.0366012i	$-0.988347\pi$
$367$		−	2.54403e10i		−	0.0732023i	0.999330	−	0.0366012i	$-0.0116531\pi$
$368$		0			0
$369$	3.16727e11			0.889337
$370$		0			0
$371$	4.17611e11			1.14443
$372$		0			0
$373$		−	7.26003e11i		−	1.94200i	−0.239087	−	0.970998i	$-0.576848\pi$
$373$		−	7.26003e11i		−	1.94200i	0.239087	−	0.970998i	$-0.423152\pi$
$374$		0			0
$375$	−1.51363e11	+	4.65312e11i	−0.395256	+	1.21508i
$376$		0			0
$377$			1.72122e10i			0.0438834i
$378$		0			0
$379$	−2.76699e11			−0.688859			−0.344430	−	0.938812i	$-0.611928\pi$
$379$	−2.76699e11			−0.688859			−0.344430	+	0.938812i	$0.611928\pi$
$380$		0			0
$381$	−4.10103e11			−0.997082
$382$		0			0
$383$		−	1.71143e11i		−	0.406410i	−0.979136	−	0.203205i	$-0.934864\pi$
$383$		−	1.71143e11i		−	0.406410i	0.979136	−	0.203205i	$-0.0651358\pi$
$384$		0			0
$385$	4.95687e11	−	2.20627e11i	1.14983	−	0.511783i
$386$		0			0
$387$			2.89924e11i			0.657030i
$388$		0			0
$389$	−3.92384e10			−0.0868837			−0.0434419	−	0.999056i	$-0.513832\pi$
$389$	−3.92384e10			−0.0868837			−0.0434419	+	0.999056i	$0.513832\pi$
$390$		0			0
$391$	−2.85427e11			−0.617590
$392$		0			0
$393$			6.88367e11i			1.45564i
$394$		0			0
$395$	2.65105e10	+	5.95616e10i	0.0547937	+	0.123106i
$396$		0			0
$397$		−	3.91381e11i		−	0.790756i	−0.918519	−	0.395378i	$-0.870614\pi$
$397$		−	3.91381e11i		−	0.790756i	0.918519	−	0.395378i	$-0.129386\pi$
$398$		0			0
$399$	8.83084e11			1.74431
$400$		0			0
$401$	−5.04969e11			−0.975248			−0.487624	−	0.873054i	$-0.662136\pi$
$401$	−5.04969e11			−0.975248			−0.487624	+	0.873054i	$0.662136\pi$
$402$		0			0
$403$			4.28272e10i			0.0808811i
$404$		0			0
$405$	2.71335e11	+	6.09613e11i	0.501138	+	1.12592i
$406$		0			0
$407$		−	4.24928e11i		−	0.767609i
$408$		0			0
$409$	−9.44998e9			−0.0166985			−0.00834923	−	0.999965i	$-0.502658\pi$
$409$	−9.44998e9			−0.0166985			−0.00834923	+	0.999965i	$0.502658\pi$
$410$		0			0
$411$	−1.04450e12			−1.80560
$412$		0			0
$413$		−	6.09969e11i		−	1.03165i
$414$		0			0
$415$	2.57706e11	−	1.14703e11i	0.426488	−	0.189827i
$416$		0			0
$417$		−	1.05746e12i		−	1.71259i
$418$		0			0
$419$	−5.77328e10			−0.0915081			−0.0457541	−	0.998953i	$-0.514569\pi$
$419$	−5.77328e10			−0.0915081			−0.0457541	+	0.998953i	$0.514569\pi$
$420$		0			0
$421$	4.38976e9			0.00681038			0.00340519	−	0.999994i	$-0.498916\pi$
$421$	4.38976e9			0.00681038			0.00340519	+	0.999994i	$0.498916\pi$
$422$		0			0
$423$		−	4.69887e11i		−	0.713612i
$424$		0			0
$425$	−4.35667e11	−	3.92455e11i	−0.647746	−	0.583498i
$426$		0			0
$427$		−	1.10604e12i		−	1.61008i
$428$		0			0
$429$	1.71177e11			0.243998
$430$		0			0
$431$	−9.94476e11			−1.38818			−0.694091	−	0.719887i	$-0.744193\pi$
$431$	−9.94476e11			−1.38818			−0.694091	+	0.719887i	$0.744193\pi$
$432$		0			0
$433$		−	1.91618e11i		−	0.261963i	−0.991385	−	0.130982i	$-0.958187\pi$
$433$		−	1.91618e11i		−	0.261963i	0.991385	−	0.130982i	$-0.0418129\pi$
$434$		0			0
$435$	1.83829e11	−	8.18209e10i	0.246157	−	0.109563i
$436$		0			0
$437$			5.37527e11i			0.705072i
$438$		0			0
$439$	1.38202e12			1.77592			0.887962	−	0.459917i	$-0.152121\pi$
$439$	1.38202e12			1.77592			0.887962	+	0.459917i	$0.152121\pi$
$440$		0			0
$441$	4.42832e11			0.557526
$442$		0			0
$443$			3.05660e11i			0.377070i	0.982066	+	0.188535i	$0.0603740\pi$
$443$			3.05660e11i			0.377070i	−0.982066	+	0.188535i	$0.939626\pi$
$444$		0			0
$445$	3.14853e11	+	7.07387e11i	0.380617	+	0.855139i
$446$		0			0
$447$		−	9.66825e11i		−	1.14542i
$448$		0			0
$449$	−1.49518e12			−1.73614			−0.868069	−	0.496444i	$-0.834639\pi$
$449$	−1.49518e12			−1.73614			−0.868069	+	0.496444i	$0.834639\pi$
$450$		0			0
$451$	1.13335e12			1.28994
$452$		0			0
$453$		−	1.42013e11i		−	0.158447i
$454$		0			0
$455$	−1.06112e11	−	2.38405e11i	−0.116069	−	0.260774i
$456$		0			0
$457$		−	1.17977e12i		−	1.26525i	−0.774459	−	0.632624i	$-0.781978\pi$
$457$		−	1.17977e12i		−	1.26525i	0.774459	−	0.632624i	$-0.218022\pi$
$458$		0			0
$459$	−3.89151e11			−0.409223
$460$		0			0
$461$	1.54415e12			1.59234			0.796170	−	0.605074i	$-0.206856\pi$
$461$	1.54415e12			1.59234			0.796170	+	0.605074i	$0.206856\pi$
$462$		0			0
$463$			4.55769e11i			0.460926i	0.973081	+	0.230463i	$0.0740240\pi$
$463$			4.55769e11i			0.460926i	−0.973081	+	0.230463i	$0.925976\pi$
$464$		0			0
$465$	4.57400e11	−	2.03586e11i	0.453689	−	0.201934i
$466$		0			0
$467$			6.97342e11i			0.678454i	0.940705	+	0.339227i	$0.110165\pi$
$467$			6.97342e11i			0.678454i	−0.940705	+	0.339227i	$0.889835\pi$
$468$		0			0
$469$	2.32284e12			2.21688
$470$		0			0
$471$	2.12617e12			1.99069
$472$		0			0
$473$			1.03744e12i			0.952987i
$474$		0			0
$475$	−7.39084e11	+	8.20464e11i	−0.666151	+	0.739500i
$476$		0			0
$477$		−	5.96829e11i		−	0.527858i
$478$		0			0
$479$	2.43471e11			0.211318			0.105659	−	0.994402i	$-0.466305\pi$
$479$	2.43471e11			0.211318			0.105659	+	0.994402i	$0.466305\pi$
$480$		0			0
$481$	−2.04373e11			−0.174088
$482$		0			0
$483$			1.48495e12i			1.24151i
$484$		0			0
$485$	4.33453e11	−	1.92927e11i	0.355717	−	0.158327i
$486$		0			0
$487$		−	1.56961e12i		−	1.26448i	−0.774773	−	0.632239i	$-0.782136\pi$
$487$		−	1.56961e12i		−	1.26448i	0.774773	−	0.632239i	$-0.217864\pi$
$488$		0			0
$489$	−7.16882e11			−0.566967
$490$		0			0
$491$	−6.52870e11			−0.506944			−0.253472	−	0.967343i	$-0.581573\pi$
$491$	−6.52870e11			−0.506944			−0.253472	+	0.967343i	$0.581573\pi$
$492$		0			0
$493$			2.41127e11i			0.183838i
$494$		0			0
$495$	−3.15309e11	−	7.08412e11i	−0.236055	−	0.530350i
$496$		0			0
$497$			5.74333e11i			0.422241i
$498$		0			0
$499$	−7.51465e11			−0.542571			−0.271285	−	0.962499i	$-0.587449\pi$
$499$	−7.51465e11			−0.542571			−0.271285	+	0.962499i	$0.587449\pi$
$500$		0			0
$501$	−1.95608e12			−1.38713
$502$		0			0
$503$		−	1.31120e12i		−	0.913299i	−0.889647	−	0.456649i	$-0.849049\pi$
$503$		−	1.31120e12i		−	0.913299i	0.889647	−	0.456649i	$-0.150951\pi$
$504$		0			0
$505$	−7.61055e11	−	1.70988e12i	−0.520721	−	1.16991i
$506$		0			0
$507$			1.81866e12i			1.22241i
$508$		0			0
$509$	−1.78629e12			−1.17957			−0.589783	−	0.807561i	$-0.700787\pi$
$509$	−1.78629e12			−1.17957			−0.589783	+	0.807561i	$0.700787\pi$
$510$		0			0
$511$	−1.28531e11			−0.0833899
$512$		0			0
$513$			7.32862e11i			0.467191i
$514$		0			0
$515$	−4.90676e11	+	2.18397e11i	−0.307370	+	0.136809i
$516$		0			0
$517$		−	1.68140e12i		−	1.03506i
$518$		0			0
$519$	−3.39394e12			−2.05329
$520$		0			0
$521$	5.88627e11			0.350002			0.175001	−	0.984568i	$-0.444007\pi$
$521$	5.88627e11			0.350002			0.175001	+	0.984568i	$0.444007\pi$
$522$		0			0
$523$		−	6.01202e11i		−	0.351369i	−0.984447	−	0.175684i	$-0.943786\pi$
$523$		−	6.01202e11i		−	0.351369i	0.984447	−	0.175684i	$-0.0562138\pi$
$524$		0			0
$525$	−2.04177e12	+	2.26659e12i	−1.17298	+	1.30213i
$526$		0			0
$527$			5.99968e11i			0.338829i
$528$		0			0
$529$	8.97272e11			0.498165
$530$		0			0
$531$	−8.71739e11			−0.475840
$532$		0			0
$533$		−	5.45093e11i		−	0.292549i
$534$		0			0
$535$	1.01808e12	−	4.53141e11i	0.537266	−	0.239134i
$536$		0			0
$537$			3.76028e12i			1.95135i
$538$		0			0
$539$	1.58459e12			0.808662
$540$		0			0
$541$	1.40863e12			0.706982			0.353491	−	0.935438i	$-0.384995\pi$
$541$	1.40863e12			0.706982			0.353491	+	0.935438i	$0.384995\pi$
$542$		0			0
$543$		−	1.28522e12i		−	0.634424i
$544$		0			0
$545$	−3.76905e11	−	8.46800e11i	−0.182999	−	0.411147i
$546$		0			0
$547$		−	8.05933e10i		−	0.0384907i	−0.999815	−	0.0192454i	$-0.993874\pi$
$547$		−	8.05933e10i		−	0.0384907i	0.999815	−	0.0192454i	$-0.00612636\pi$
$548$		0			0
$549$	−1.58070e12			−0.742635
$550$		0			0
$551$	4.54098e11			0.209878
$552$		0			0
$553$			4.06459e11i			0.184822i
$554$		0			0
$555$	9.71517e11	+	2.18273e12i	0.434642	+	0.976519i
$556$		0			0
$557$			3.92066e12i			1.72588i	0.505305	+	0.862941i	$0.331380\pi$
$557$			3.92066e12i			1.72588i	−0.505305	+	0.862941i	$0.668620\pi$
$558$		0			0
$559$	4.98965e11			0.216131
$560$		0			0
$561$	2.39802e12			1.02216
$562$		0			0
$563$			3.86627e12i			1.62182i	0.585168	+	0.810912i	$0.301029\pi$
$563$			3.86627e12i			1.62182i	−0.585168	+	0.810912i	$0.698971\pi$
$564$		0			0
$565$	−1.89173e12	+	8.41996e11i	−0.780981	+	0.347610i
$566$		0			0
$567$			4.16010e12i			1.69036i
$568$		0			0
$569$	1.87990e12			0.751849			0.375924	−	0.926650i	$-0.377325\pi$
$569$	1.87990e12			0.751849			0.375924	+	0.926650i	$0.377325\pi$
$570$		0			0
$571$	3.44726e12			1.35710			0.678550	−	0.734554i	$-0.262609\pi$
$571$	3.44726e12			1.35710			0.678550	+	0.734554i	$0.262609\pi$
$572$		0			0
$573$		−	3.14250e12i		−	1.21781i
$574$		0			0
$575$	−1.37966e12	−	1.24281e12i	−0.526339	−	0.474133i
$576$		0			0
$577$			1.68433e12i			0.632608i	0.948658	+	0.316304i	$0.102442\pi$
$577$			1.68433e12i			0.632608i	−0.948658	+	0.316304i	$0.897558\pi$
$578$		0			0
$579$	−5.62039e12			−2.07832
$580$		0			0
$581$	1.75863e12			0.640297
$582$		0			0
$583$		−	2.13564e12i		−	0.765631i
$584$		0			0
$585$	−3.40717e11	+	1.51651e11i	−0.120280	+	0.0535357i
$586$		0			0
$587$			5.04715e12i			1.75458i	0.479956	+	0.877292i	$0.340652\pi$
$587$			5.04715e12i			1.75458i	−0.479956	+	0.877292i	$0.659348\pi$
$588$		0			0
$589$	1.12988e12			0.386825
$590$		0			0
$591$	3.33377e12			1.12407
$592$		0			0
$593$		−	6.66924e11i		−	0.221478i	−0.993850	−	0.110739i	$-0.964678\pi$
$593$		−	6.66924e11i		−	0.221478i	0.993850	−	0.110739i	$-0.0353217\pi$
$594$		0			0
$595$	−1.48654e12	−	3.33983e12i	−0.486238	−	1.09244i
$596$		0			0
$597$		−	2.27059e12i		−	0.731566i
$598$		0			0
$599$	3.36479e12			1.06792			0.533958	−	0.845511i	$-0.320704\pi$
$599$	3.36479e12			1.06792			0.533958	+	0.845511i	$0.320704\pi$
$600$		0			0
$601$	−2.79891e12			−0.875092			−0.437546	−	0.899196i	$-0.644152\pi$
$601$	−2.79891e12			−0.875092			−0.437546	+	0.899196i	$0.644152\pi$
$602$		0			0
$603$		−	3.31969e12i		−	1.02251i
$604$		0			0
$605$	2.11718e11	+	4.75671e11i	0.0642478	+	0.144347i
$606$		0			0
$607$		−	3.38683e12i		−	1.01261i	−0.862353	−	0.506307i	$-0.831010\pi$
$607$		−	3.38683e12i		−	1.01261i	0.862353	−	0.506307i	$-0.168990\pi$
$608$		0			0
$609$	1.25448e12			0.369560
$610$		0			0
$611$	−8.08685e11			−0.234744
$612$		0			0
$613$		−	7.53866e11i		−	0.215636i	−0.994171	−	0.107818i	$-0.965614\pi$
$613$		−	7.53866e11i		−	0.215636i	0.994171	−	0.107818i	$-0.0343864\pi$
$614$		0			0
$615$	−5.82166e12	+	2.59119e12i	−1.64100	+	0.730399i
$616$		0			0
$617$		−	1.42132e11i		−	0.0394827i	−0.999805	−	0.0197414i	$-0.993716\pi$
$617$		−	1.42132e11i		−	0.0394827i	0.999805	−	0.0197414i	$-0.00628428\pi$
$618$		0			0
$619$	−1.03073e12			−0.282186			−0.141093	−	0.989996i	$-0.545062\pi$
$619$	−1.03073e12			−0.282186			−0.141093	+	0.989996i	$0.545062\pi$
$620$		0			0
$621$	−1.23235e12			−0.332523
$622$		0			0
$623$			4.82733e12i			1.28384i
$624$		0			0
$625$	−3.97033e11	−	3.79398e12i	−0.104080	−	0.994569i
$626$		0			0
$627$		−	4.51604e12i		−	1.16695i
$628$		0			0
$629$	−2.86307e12			−0.729296
$630$		0			0
$631$	4.61780e12			1.15959			0.579793	−	0.814764i	$-0.303133\pi$
$631$	4.61780e12			1.15959			0.579793	+	0.814764i	$0.303133\pi$
$632$		0			0
$633$			1.11247e12i			0.275404i
$634$		0			0
$635$	2.92092e12	−	1.30008e12i	0.712916	−	0.317314i
$636$		0			0
$637$		−	7.62122e11i		−	0.183399i
$638$		0			0
$639$	8.20809e11			0.194755
$640$		0			0
$641$	7.51099e12			1.75726			0.878630	−	0.477503i	$-0.158458\pi$
$641$	7.51099e12			1.75726			0.878630	+	0.477503i	$0.158458\pi$
$642$		0			0
$643$		−	4.42841e12i		−	1.02164i	−0.859687	−	0.510821i	$-0.829341\pi$
$643$		−	4.42841e12i		−	1.02164i	0.859687	−	0.510821i	$-0.170659\pi$
$644$		0			0
$645$	−2.37191e12	−	5.32901e12i	−0.539609	−	1.21235i
$646$		0			0
$647$		−	1.09396e12i		−	0.245432i	−0.992442	−	0.122716i	$-0.960840\pi$
$647$		−	1.09396e12i		−	0.245432i	0.992442	−	0.122716i	$-0.0391604\pi$
$648$		0			0
$649$	−3.11935e12			−0.690181
$650$		0			0
$651$	3.12138e12			0.681133
$652$		0			0
$653$			8.24881e12i			1.77534i	0.460477	+	0.887671i	$0.347678\pi$
$653$			8.24881e12i			1.77534i	−0.460477	+	0.887671i	$0.652322\pi$
$654$		0			0
$655$	−2.18222e12	−	4.90283e12i	−0.463247	−	1.04078i
$656$		0			0
$657$			1.83690e11i			0.0384628i
$658$		0			0
$659$	−2.64086e12			−0.545458			−0.272729	−	0.962091i	$-0.587926\pi$
$659$	−2.64086e12			−0.545458			−0.272729	+	0.962091i	$0.587926\pi$
$660$		0			0
$661$	8.94654e12			1.82284			0.911420	−	0.411478i	$-0.134987\pi$
$661$	8.94654e12			1.82284			0.911420	+	0.411478i	$0.134987\pi$
$662$		0			0
$663$		−	1.15335e12i		−	0.231820i
$664$		0			0
$665$	−6.28968e12	+	2.79950e12i	−1.24719	+	0.555114i
$666$		0			0
$667$			7.63592e11i			0.149381i
$668$		0			0
$669$	−7.72362e12			−1.49075
$670$		0			0
$671$	−5.65625e12			−1.07715
$672$		0			0
$673$		−	6.40541e12i		−	1.20359i	−0.798650	−	0.601796i	$-0.794452\pi$
$673$		−	6.40541e12i		−	1.20359i	0.798650	−	0.601796i	$-0.205548\pi$
$674$		0			0
$675$	−1.88102e12	−	1.69445e12i	−0.348760	−	0.314167i
$676$		0			0
$677$		−	6.41491e12i		−	1.17366i	−0.809711	−	0.586829i	$-0.800376\pi$
$677$		−	6.41491e12i		−	1.17366i	0.809711	−	0.586829i	$-0.199624\pi$
$678$		0			0
$679$	2.95796e12			0.534046
$680$		0			0
$681$	4.10256e12			0.730958
$682$		0			0
$683$		−	2.15592e12i		−	0.379088i	−0.981872	−	0.189544i	$-0.939299\pi$
$683$		−	2.15592e12i		−	0.379088i	0.981872	−	0.189544i	$-0.0607009\pi$
$684$		0			0
$685$	7.43937e12	−	3.31122e12i	1.29101	−	0.574619i
$686$		0			0
$687$			9.44262e11i			0.161729i
$688$		0			0
$689$	−1.02715e12			−0.173640
$690$		0			0
$691$	4.58074e12			0.764336			0.382168	−	0.924093i	$-0.375178\pi$
$691$	4.58074e12			0.764336			0.382168	+	0.924093i	$0.375178\pi$
$692$		0			0
$693$		−	4.83433e12i		−	0.796226i
$694$		0			0
$695$	3.35230e12	+	7.53168e12i	0.545019	+	1.22450i
$696$		0			0
$697$		−	7.63624e12i		−	1.22555i
$698$		0			0
$699$	6.36704e12			1.00877
$700$		0			0
$701$	−1.22474e12			−0.191564			−0.0957819	−	0.995402i	$-0.530535\pi$
$701$	−1.22474e12			−0.191564			−0.0957819	+	0.995402i	$0.530535\pi$
$702$		0			0
$703$			5.39183e12i			0.832601i
$704$		0			0
$705$	3.84421e12	+	8.63686e12i	0.586079	+	1.31675i
$706$		0			0
$707$		−	1.16685e13i		−	1.75642i
$708$		0			0
$709$	5.65887e12			0.841049			0.420525	−	0.907281i	$-0.361846\pi$
$709$	5.65887e12			0.841049			0.420525	+	0.907281i	$0.361846\pi$
$710$		0			0
$711$	5.80891e11			0.0852475
$712$		0			0
$713$			1.89996e12i			0.275322i
$714$		0			0
$715$	−1.21919e12	+	5.42653e11i	−0.174459	+	0.0776507i
$716$		0			0
$717$			1.02623e13i			1.45013i
$718$		0			0
$719$	−6.02904e12			−0.841333			−0.420667	−	0.907215i	$-0.638204\pi$
$719$	−6.02904e12			−0.841333			−0.420667	+	0.907215i	$0.638204\pi$
$720$		0			0
$721$	−3.34846e12			−0.461462
$722$		0			0
$723$			6.98820e12i			0.951137i
$724$		0			0
$725$	−1.04992e12	+	1.16552e12i	−0.141135	+	0.156675i
$726$		0			0
$727$			2.63469e12i			0.349805i	0.984586	+	0.174902i	$0.0559609\pi$
$727$			2.63469e12i			0.349805i	−0.984586	+	0.174902i	$0.944039\pi$
$728$		0			0
$729$	1.37180e12			0.179894
$730$		0			0
$731$	6.99002e12			0.905421
$732$		0			0
$733$			5.28609e12i			0.676343i	0.941085	+	0.338171i	$0.109808\pi$
$733$			5.28609e12i			0.676343i	−0.941085	+	0.338171i	$0.890192\pi$
$734$		0			0
$735$	−8.13955e12	+	3.62286e12i	−1.02874	+	0.457888i
$736$		0			0
$737$		−	1.18789e13i		−	1.48310i
$738$		0			0
$739$	2.51810e12			0.310580			0.155290	−	0.987869i	$-0.450369\pi$
$739$	2.51810e12			0.310580			0.155290	+	0.987869i	$0.450369\pi$
$740$		0			0
$741$	−2.17203e12			−0.264657
$742$		0			0
$743$		−	7.02537e11i		−	0.0845706i	−0.999106	−	0.0422853i	$-0.986536\pi$
$743$		−	7.02537e11i		−	0.0845706i	0.999106	−	0.0422853i	$-0.0134638\pi$
$744$		0			0
$745$	3.06497e12	+	6.88612e12i	0.364521	+	0.818976i
$746$		0			0
$747$		−	2.51335e12i		−	0.295331i
$748$		0			0
$749$	6.94755e12			0.806610
$750$		0			0
$751$	−4.60108e12			−0.527813			−0.263907	−	0.964548i	$-0.585011\pi$
$751$	−4.60108e12			−0.527813			−0.263907	+	0.964548i	$0.585011\pi$
$752$		0			0
$753$		−	8.19042e12i		−	0.928387i
$754$		0			0
$755$	4.50200e11	+	1.01147e12i	0.0504248	+	0.113290i
$756$		0			0
$757$			3.05764e12i			0.338419i	0.985580	+	0.169210i	$0.0541215\pi$
$757$			3.05764e12i			0.338419i	−0.985580	+	0.169210i	$0.945878\pi$
$758$		0			0
$759$	7.59398e12			0.830580
$760$		0			0
$761$	−9.86753e12			−1.06654			−0.533270	−	0.845945i	$-0.679037\pi$
$761$	−9.86753e12			−1.06654			−0.533270	+	0.845945i	$0.679037\pi$
$762$		0			0
$763$		−	5.77872e12i		−	0.617264i
$764$		0			0
$765$	−4.77312e12	+	2.12448e12i	−0.503878	+	0.224273i
$766$		0			0
$767$			1.50028e12i			0.156528i
$768$		0			0
$769$	−1.65694e13			−1.70859			−0.854294	−	0.519790i	$-0.826010\pi$
$769$	−1.65694e13			−1.70859			−0.854294	+	0.519790i	$0.826010\pi$
$770$		0			0
$771$	2.32961e12			0.237432
$772$		0			0
$773$			1.10674e13i			1.11490i	0.830210	+	0.557451i	$0.188221\pi$
$773$			1.10674e13i			1.11490i	−0.830210	+	0.557451i	$0.811779\pi$
$774$		0			0
$775$	−2.61239e12	+	2.90004e12i	−0.260124	+	0.288766i
$776$		0			0
$777$			1.48953e13i			1.46607i
$778$		0			0
$779$	−1.43808e13			−1.39915
$780$		0			0
$781$	2.93711e12			0.282482
$782$		0			0
$783$			1.04108e12i			0.0989819i
$784$		0			0
$785$	−1.51434e13	+	6.74025e12i	−1.42335	+	0.633523i
$786$		0			0
$787$		−	1.67201e12i		−	0.155365i	−0.996978	−	0.0776825i	$-0.975248\pi$
$787$		−	1.67201e12i		−	0.155365i	0.996978	−	0.0776825i	$-0.0247520\pi$
$788$		0			0
$789$	8.60646e12			0.790638
$790$		0			0
$791$	−1.29095e13			−1.17250
$792$		0			0
$793$			2.72042e12i			0.244291i
$794$		0			0
$795$	4.88274e12	+	1.09701e13i	0.433522	+	0.974003i
$796$		0			0
$797$		−	6.97864e12i		−	0.612644i	−0.951928	−	0.306322i	$-0.900902\pi$
$797$		−	6.97864e12i		−	0.612644i	0.951928	−	0.306322i	$-0.0990985\pi$
$798$		0			0
$799$	−1.13289e13			−0.983394
$800$		0			0
$801$	6.89899e12			0.592160
$802$		0			0
$803$			6.57300e11i			0.0557884i
$804$		0			0
$805$	−4.70751e12	−	1.05764e13i	−0.395102	−	0.887684i
$806$		0			0
$807$			1.79052e13i			1.48610i
$808$		0			0
$809$	−5.27673e12			−0.433108			−0.216554	−	0.976271i	$-0.569482\pi$
$809$	−5.27673e12			−0.433108			−0.216554	+	0.976271i	$0.569482\pi$
$810$		0			0
$811$	1.43675e12			0.116624			0.0583118	−	0.998298i	$-0.481428\pi$
$811$	1.43675e12			0.116624			0.0583118	+	0.998298i	$0.481428\pi$
$812$		0			0
$813$			8.60851e12i			0.691068i
$814$		0			0
$815$	5.10592e12	−	2.27261e12i	0.405383	−	0.180433i
$816$		0			0
$817$		−	1.31639e13i		−	1.03367i
$818$		0			0
$819$	−2.32511e12			−0.180578
$820$		0			0
$821$	9.44899e12			0.725840			0.362920	−	0.931820i	$-0.381780\pi$
$821$	9.44899e12			0.725840			0.362920	+	0.931820i	$0.381780\pi$
$822$		0			0
$823$			1.20237e13i			0.913562i	0.889579	+	0.456781i	$0.150998\pi$
$823$			1.20237e13i			0.913562i	−0.889579	+	0.456781i	$0.849002\pi$
$824$		0			0
$825$	1.15912e13	+	1.04415e13i	0.871136	+	0.784731i
$826$		0			0
$827$		−	7.86848e12i		−	0.584947i	−0.956274	−	0.292473i	$-0.905522\pi$
$827$		−	7.86848e12i		−	0.584947i	0.956274	−	0.292473i	$-0.0944782\pi$
$828$		0			0
$829$	−4.86184e12			−0.357524			−0.178762	−	0.983892i	$-0.557209\pi$
$829$	−4.86184e12			−0.357524			−0.178762	+	0.983892i	$0.557209\pi$
$830$		0			0
$831$	−3.18798e12			−0.231905
$832$		0			0
$833$		−	1.06766e13i		−	0.768299i
$834$		0			0
$835$	1.39320e13	−	6.20103e12i	0.991798	−	0.441443i
$836$		0			0
$837$			2.59040e12i			0.182432i
$838$		0			0
$839$	1.76025e13			1.22644			0.613218	−	0.789914i	$-0.289875\pi$
$839$	1.76025e13			1.22644			0.613218	+	0.789914i	$0.289875\pi$
$840$		0			0
$841$	−1.38621e13			−0.955534
$842$		0			0
$843$		−	2.72559e13i		−	1.85881i
$844$		0			0
$845$	−5.76541e12	−	1.29533e13i	−0.389023	−	0.874025i
$846$		0			0
$847$			3.24606e12i			0.216711i
$848$		0			0
$849$	3.34744e13			2.21120
$850$		0			0
$851$	−9.06666e12			−0.592604
$852$		0			0
$853$			9.20458e11i			0.0595296i	0.999557	+	0.0297648i	$0.00947584\pi$
$853$			9.20458e11i			0.0595296i	−0.999557	+	0.0297648i	$0.990524\pi$
$854$		0			0
$855$	4.00090e12	+	8.98890e12i	0.256042	+	0.575253i
$856$		0			0
$857$			2.35047e13i			1.48847i	0.667915	+	0.744237i	$0.267187\pi$
$857$			2.35047e13i			1.48847i	−0.667915	+	0.744237i	$0.732813\pi$
$858$		0			0
$859$	−2.02385e13			−1.26826			−0.634132	−	0.773225i	$-0.718643\pi$
$859$	−2.02385e13			−1.26826			−0.634132	+	0.773225i	$0.718643\pi$
$860$		0			0
$861$	−3.97281e13			−2.46367
$862$		0			0
$863$			3.07364e13i			1.88627i	0.332406	+	0.943136i	$0.392140\pi$
$863$			3.07364e13i			1.88627i	−0.332406	+	0.943136i	$0.607860\pi$
$864$		0			0
$865$	2.41730e13	−	1.07593e13i	1.46811	−	0.653446i
$866$		0			0
$867$			5.10107e12i			0.306602i
$868$		0			0
$869$	2.07861e12			0.123647
$870$		0			0
$871$	−5.71325e12			−0.336358
$872$		0			0
$873$		−	4.22737e12i		−	0.246324i
$874$		0			0
$875$	7.35693e12	−	2.26163e13i	0.424288	−	1.30432i
$876$		0			0
$877$			6.65840e12i			0.380077i	0.981777	+	0.190039i	$0.0608613\pi$
$877$			6.65840e12i			0.380077i	−0.981777	+	0.190039i	$0.939139\pi$
$878$		0			0
$879$	2.31120e13			1.30584
$880$		0			0
$881$	3.41842e12			0.191176			0.0955882	−	0.995421i	$-0.469527\pi$
$881$	3.41842e12			0.191176			0.0955882	+	0.995421i	$0.469527\pi$
$882$		0			0
$883$			1.92500e13i			1.06563i	0.846231	+	0.532815i	$0.178866\pi$
$883$			1.92500e13i			1.06563i	−0.846231	+	0.532815i	$0.821134\pi$
$884$		0			0
$885$	1.60232e13	−	7.13181e12i	0.878018	−	0.390800i
$886$		0			0
$887$		−	1.48977e13i		−	0.808095i	−0.914738	−	0.404048i	$-0.867603\pi$
$887$		−	1.48977e13i		−	0.808095i	0.914738	−	0.404048i	$-0.132397\pi$
$888$		0			0
$889$	1.99329e13			1.07032
$890$		0			0
$891$	2.12745e13			1.13086
$892$		0			0
$893$			2.13350e13i			1.12269i
$894$		0			0
$895$	−1.19206e13	−	2.67822e13i	−0.621004	−	1.39522i
$896$		0			0
$897$		−	3.65239e12i		−	0.188370i
$898$		0			0
$899$	1.60507e12			0.0819551
$900$		0			0
$901$	−1.43895e13			−0.727416
$902$		0			0
$903$		−	3.63661e13i		−	1.82013i
$904$		0			0
$905$	4.07434e12	+	9.15389e12i	0.201901	+	0.453615i
$906$		0			0
$907$			1.11529e13i			0.547210i	0.961842	+	0.273605i	$0.0882162\pi$
$907$			1.11529e13i			0.547210i	−0.961842	+	0.273605i	$0.911784\pi$
$908$		0			0
$909$	−1.66760e13			−0.810132
$910$		0			0
$911$	2.25248e12			0.108350			0.0541750	−	0.998531i	$-0.482747\pi$
$911$	2.25248e12			0.108350			0.0541750	+	0.998531i	$0.482747\pi$
$912$		0			0
$913$		−	8.99353e12i		−	0.428363i
$914$		0			0
$915$	2.90545e13	−	1.29320e13i	1.37031	−	0.609915i
$916$		0			0
$917$		−	3.34578e13i		−	1.56255i
$918$		0			0
$919$	1.40633e13			0.650380			0.325190	−	0.945649i	$-0.394572\pi$
$919$	1.40633e13			0.650380			0.325190	+	0.945649i	$0.394572\pi$
$920$		0			0
$921$	1.57452e13			0.721075
$922$		0			0
$923$		−	1.41263e12i		−	0.0640649i
$924$		0			0
$925$	−1.38391e13	−	1.24664e13i	−0.621540	−	0.559891i
$926$		0			0
$927$			4.78545e12i			0.212845i
$928$		0			0
$929$	−1.04912e13			−0.462118			−0.231059	−	0.972940i	$-0.574219\pi$
$929$	−1.04912e13			−0.462118			−0.231059	+	0.972940i	$0.574219\pi$
$930$		0			0
$931$	−2.01066e13			−0.877130
$932$		0			0
$933$		−	4.95131e13i		−	2.13920i
$934$		0			0
$935$	−1.70797e13	+	7.60206e12i	−0.730849	+	0.325296i
$936$		0			0
$937$			3.77841e13i			1.60133i	0.599111	+	0.800666i	$0.295521\pi$
$937$			3.77841e13i			1.60133i	−0.599111	+	0.800666i	$0.704479\pi$
$938$		0			0
$939$	−3.30036e13			−1.38537
$940$		0			0
$941$	1.11142e13			0.462088			0.231044	−	0.972943i	$-0.425786\pi$
$941$	1.11142e13			0.462088			0.231044	+	0.972943i	$0.425786\pi$
$942$		0			0
$943$		−	2.41822e13i		−	0.995847i
$944$		0			0
$945$	−6.41820e12	−	1.44199e13i	−0.261800	−	0.588192i
$946$		0			0
$947$		−	4.96563e12i		−	0.200631i	−0.994956	−	0.100316i	$-0.968015\pi$
$947$		−	4.96563e12i		−	0.200631i	0.994956	−	0.100316i	$-0.0319853\pi$
$948$		0			0
$949$	3.16134e11			0.0126524
$950$		0			0
$951$	−6.25385e13			−2.47933
$952$		0			0
$953$		−	3.02750e13i		−	1.18896i	−0.804111	−	0.594479i	$-0.797358\pi$
$953$		−	3.02750e13i		−	1.18896i	0.804111	−	0.594479i	$-0.202642\pi$
$954$		0			0
$955$	9.96214e12	+	2.23821e13i	0.387559	+	0.870736i
$956$		0			0
$957$		−	6.41533e12i		−	0.247238i
$958$		0			0
$959$	5.07676e13			1.93822
$960$		0			0
$961$	−2.24459e13			−0.848949
$962$		0			0
$963$		−	9.92910e12i		−	0.372042i
$964$		0			0
$965$	4.00307e13	−	1.78174e13i	1.48601	−	0.661412i
$966$		0			0
$967$		−	2.48487e13i		−	0.913869i	−0.889500	−	0.456934i	$-0.848947\pi$
$967$		−	2.48487e13i		−	0.913869i	0.889500	−	0.456934i	$-0.151053\pi$
$968$		0			0
$969$	−3.04281e13			−1.10871
$970$		0			0
$971$	−4.43278e13			−1.60026			−0.800128	−	0.599829i	$-0.795235\pi$
$971$	−4.43278e13			−1.60026			−0.800128	+	0.599829i	$0.795235\pi$
$972$		0			0
$973$			5.13975e13i			1.83837i
$974$		0			0
$975$	5.02193e12	−	5.57489e12i	0.177971	−	0.197568i
$976$		0			0
$977$		−	9.73746e11i		−	0.0341917i	−0.999854	−	0.0170958i	$-0.994558\pi$
$977$		−	9.73746e11i		−	0.0341917i	0.999854	−	0.0170958i	$-0.00544204\pi$
$978$		0			0
$979$	2.46867e13			0.858897
$980$		0			0
$981$	−8.25866e12			−0.284708
$982$		0			0
$983$		−	2.85792e13i		−	0.976247i	−0.872775	−	0.488123i	$-0.837682\pi$
$983$		−	2.85792e13i		−	0.976247i	0.872775	−	0.488123i	$-0.162318\pi$
$984$		0			0
$985$	−2.37444e13	+	1.05685e13i	−0.803709	+	0.357726i
$986$		0			0
$987$			5.89394e13i			1.97687i
$988$		0			0
$989$	2.21358e13			0.735718
$990$		0			0
$991$	3.49036e13			1.14958			0.574789	−	0.818302i	$-0.305084\pi$
$991$	3.49036e13			1.14958			0.574789	+	0.818302i	$0.305084\pi$
$992$		0			0
$993$		−	5.17610e13i		−	1.68940i
$994$		0			0
$995$	7.19807e12	+	1.61720e13i	0.232816	+	0.523071i
$996$		0			0
$997$		−	8.78834e12i		−	0.281695i	−0.990031	−	0.140847i	$-0.955017\pi$
$997$		−	8.78834e12i		−	0.281695i	0.990031	−	0.140847i	$-0.0449827\pi$
$998$		0			0
$999$	−1.23615e13			−0.392668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.10.c.c.49.4		4
4.3	odd	2		5.10.b.a.4.2	✓	4
5.2	odd	4		400.10.a.ba.1.4		4
5.3	odd	4		400.10.a.ba.1.1		4
5.4	even	2	inner	80.10.c.c.49.1		4
12.11	even	2		45.10.b.b.19.3		4
20.3	even	4		25.10.a.e.1.2		4
20.7	even	4		25.10.a.e.1.3		4
20.19	odd	2		5.10.b.a.4.3	yes	4
60.23	odd	4		225.10.a.s.1.3		4
60.47	odd	4		225.10.a.s.1.2		4
60.59	even	2		45.10.b.b.19.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.b.a.4.2	✓	4	4.3	odd	2
5.10.b.a.4.3	yes	4	20.19	odd	2
25.10.a.e.1.2		4	20.3	even	4
25.10.a.e.1.3		4	20.7	even	4
45.10.b.b.19.2		4	60.59	even	2
45.10.b.b.19.3		4	12.11	even	2
80.10.c.c.49.1		4	5.4	even	2	inner
80.10.c.c.49.4		4	1.1	even	1	trivial
225.10.a.s.1.2		4	60.47	odd	4
225.10.a.s.1.3		4	60.23	odd	4
400.10.a.ba.1.1		4	5.3	odd	4
400.10.a.ba.1.4		4	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} +O(q^{10})\)	\(q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} -44557.8 q^{11} +21430.4i q^{13} +(228880. - 101873. i) q^{15} +300220. i q^{17} +565385. q^{19} +1.56192e6 q^{21} +950727. i q^{23} +(-1.30722e6 + 1.45116e6i) q^{25} +1.29622e6i q^{27} +803167. q^{29} +1.99843e6 q^{31} -7.98755e6i q^{33} +(-1.11246e7 + 4.95149e6i) q^{35} +9.53656e6i q^{37} -3.84168e6 q^{39} -2.54355e7 q^{41} -2.32830e7i q^{43} +(7.07642e6 + 1.58987e7i) q^{45} +3.77353e7i q^{47} -3.55626e7 q^{49} -5.38183e7 q^{51} +4.79297e7i q^{53} +(2.53216e7 + 5.68906e7i) q^{55} +1.01353e8i q^{57} +7.00069e7 q^{59} +1.26942e8 q^{61} +1.08496e8i q^{63} +(2.73620e7 - 1.21787e7i) q^{65} +2.66595e8i q^{67} -1.70430e8 q^{69} -6.59169e7 q^{71} -1.47516e7i q^{73} +(-2.60139e8 - 2.34337e8i) q^{75} +3.88231e8i q^{77} -4.66498e7 q^{79} -4.77460e8 q^{81} +2.01840e8i q^{83} +(3.83316e8 - 1.70611e8i) q^{85} +1.43978e8i q^{87} -5.54039e8 q^{89} +1.86723e8 q^{91} +3.58244e8i q^{93} +(-3.21301e8 - 7.21874e8i) q^{95} +3.39489e8i q^{97} +5.54841e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1140 q^{5} + 11628 q^{9}+O(q^{10}) \) 4 * q + 1140 * q^5 + 11628 * q^9	\( 4 q + 1140 q^{5} + 11628 q^{9} - 109968 q^{11} + 396720 q^{15} + 636880 q^{19} + 3523968 q^{21} - 1337900 q^{25} - 3531720 q^{29} + 10587712 q^{31} - 13629840 q^{35} - 1686816 q^{39} - 16788552 q^{41} + 55737180 q^{45} - 46921028 q^{49} - 84017088 q^{51} + 26907120 q^{55} + 460829040 q^{59} + 360490568 q^{61} + 183895680 q^{65} - 286524864 q^{69} + 47611872 q^{71} - 659239200 q^{75} + 728043520 q^{79} - 343387836 q^{81} + 1275419840 q^{85} - 1582700760 q^{89} - 473322528 q^{91} - 1204791600 q^{95} + 728787024 q^{99}+O(q^{100}) \) 4 * q + 1140 * q^5 + 11628 * q^9 - 109968 * q^11 + 396720 * q^15 + 636880 * q^19 + 3523968 * q^21 - 1337900 * q^25 - 3531720 * q^29 + 10587712 * q^31 - 13629840 * q^35 - 1686816 * q^39 - 16788552 * q^41 + 55737180 * q^45 - 46921028 * q^49 - 84017088 * q^51 + 26907120 * q^55 + 460829040 * q^59 + 360490568 * q^61 + 183895680 * q^65 - 286524864 * q^69 + 47611872 * q^71 - 659239200 * q^75 + 728043520 * q^79 - 343387836 * q^81 + 1275419840 * q^85 - 1582700760 * q^89 - 473322528 * q^91 - 1204791600 * q^95 + 728787024 * q^99

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