LMFDB - Embedded newform 162.13.d.h.107.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,13,Mod(53,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.53"); S:= CuspForms(chi, 13); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 13, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,24576,0,0,220224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$148.066998399$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.9
Character	$\chi$	$=$	162.107
Dual form			162.13.d.h.53.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(16377.2 - 9455.38i) q^{5} +(14783.7 - 25606.1i) q^{7} +92681.9i q^{8} +855803. q^{10} +(-718832. - 415018. i) q^{11} +(826208. + 1.43103e6i) q^{13} +(1.15880e6 - 669032. i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -1.17626e7i q^{17} -8.78398e7 q^{19} +(3.35405e7 + 1.93646e7i) q^{20} +(-1.87816e7 - 3.25306e7i) q^{22} +(-5.37313e7 + 3.10218e7i) q^{23} +(5.67381e7 - 9.82733e7i) q^{25} +7.47798e7i q^{26} +6.05539e7 q^{28} +(-5.49475e8 - 3.17239e8i) q^{29} +(2.63601e8 + 4.56570e8i) q^{31} +(-1.64382e8 + 9.49063e7i) q^{32} +(2.66157e8 - 4.60998e8i) q^{34} -5.59141e8i q^{35} -1.94886e9 q^{37} +(-3.44260e9 - 1.98759e9i) q^{38} +(8.76343e8 + 1.51787e9i) q^{40} +(-1.36774e9 + 7.89668e8i) q^{41} +(-2.72113e8 + 4.71314e8i) q^{43} -1.69991e9i q^{44} -2.80777e9 q^{46} +(-1.09421e10 - 6.31741e9i) q^{47} +(6.48353e9 + 1.12298e10i) q^{49} +(4.44734e9 - 2.56767e9i) q^{50} +(-1.69207e9 + 2.93076e9i) q^{52} -1.19968e10i q^{53} -1.56966e10 q^{55} +(2.37322e9 + 1.37018e9i) q^{56} +(-1.43566e10 - 2.48664e10i) q^{58} +(-2.94269e10 + 1.69896e10i) q^{59} +(-2.86722e10 + 4.96616e10i) q^{61} +2.38584e10i q^{62} -8.58993e9 q^{64} +(2.70619e10 + 1.56242e10i) q^{65} +(1.52909e10 + 2.64847e10i) q^{67} +(2.08624e10 - 1.20449e10i) q^{68} +(1.26519e10 - 2.19137e10i) q^{70} +1.90857e11i q^{71} +2.47145e11 q^{73} +(-7.63796e10 - 4.40978e10i) q^{74} +(-8.99480e10 - 1.55795e11i) q^{76} +(-2.12539e10 + 1.22710e10i) q^{77} +(-9.12931e10 + 1.58124e11i) q^{79} +7.93175e10i q^{80} -7.14726e10 q^{82} +(3.50846e11 + 2.02561e11i) q^{83} +(-1.11220e11 - 1.92638e11i) q^{85} +(-2.13292e10 + 1.23144e10i) q^{86} +(3.84646e10 - 6.66227e10i) q^{88} -6.25344e11i q^{89} +4.88575e10 q^{91} +(-1.10042e11 - 6.35326e10i) q^{92} +(-2.85893e11 - 4.95182e11i) q^{94} +(-1.43857e12 + 8.30559e11i) q^{95} +(-1.35491e11 + 2.34677e11i) q^{97} +5.86822e11i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24576 q^{4} + 220224 q^{7} + 758016 q^{10} + 2372808 q^{13} - 50331648 q^{16} + 285339360 q^{19} - 70253568 q^{22} + 727623852 q^{25} + 902037504 q^{28} - 577374720 q^{31} - 2238076800 q^{34} - 6056330712 q^{37}+ \cdots + 2570481096384 q^{97}+O(q^{100}) $ 24 * q + 24576 * q^4 + 220224 * q^7 + 758016 * q^10 + 2372808 * q^13 - 50331648 * q^16 + 285339360 * q^19 - 70253568 * q^22 + 727623852 * q^25 + 902037504 * q^28 - 577374720 * q^31 - 2238076800 * q^34 - 6056330712 * q^37 + 776208384 * q^40 - 33702957168 * q^43 - 49846440960 * q^46 - 72166762836 * q^49 - 4859510784 * q^52 - 316402444512 * q^55 + 21247000704 * q^58 - 213044029980 * q^61 - 206158430208 * q^64 - 70227468528 * q^67 + 251325402624 * q^70 + 99306462720 * q^73 + 292187504640 * q^76 + 696725200560 * q^79 + 1471123266048 * q^82 + 271807264548 * q^85 + 143879307264 * q^88 + 1458470433408 * q^91 - 1211537346048 * q^94 + 2570481096384 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	39.1918	+	22.6274i	0.612372	+	0.353553i
$2$	39.1918	+	22.6274i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1024.00	+	1773.62i	0.250000	+	0.433013i
$5$	16377.2	−	9455.38i	1.04814	−	0.605144i	0.126012	−	0.992029i	$-0.459782\pi$
$5$	16377.2	−	9455.38i	1.04814	−	0.605144i	0.922128	+	0.386884i	$0.126449\pi$
$6$		0			0
$7$	14783.7	−	25606.1i	0.125659	−	0.217648i	−0.796331	−	0.604861i	$-0.793229\pi$
$7$	14783.7	−	25606.1i	0.125659	−	0.217648i	0.921990	+	0.387213i	$0.126562\pi$
$8$			92681.9i			0.353553i
$9$		0			0
$10$	855803.			0.855803
$11$	−718832.	−	415018.i	−0.405762	−	0.234267i	0.283205	−	0.959059i	$-0.408602\pi$
$11$	−718832.	−	415018.i	−0.405762	−	0.234267i	−0.688967	+	0.724793i	$0.741936\pi$
$12$		0			0
$13$	826208.	+	1.43103e6i	0.171171	+	0.296476i	0.938829	−	0.344383i	$-0.111912\pi$
$13$	826208.	+	1.43103e6i	0.171171	+	0.296476i	−0.767659	+	0.640859i	$0.778578\pi$
$14$	1.15880e6	−	669032.i	0.153900	−	0.0888544i
$15$		0			0
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$		−	1.17626e7i		−	0.487315i	−0.969861	−	0.243657i	$-0.921653\pi$
$17$		−	1.17626e7i		−	0.487315i	0.969861	−	0.243657i	$-0.0783473\pi$
$18$		0			0
$19$	−8.78398e7			−1.86711			−0.933555	−	0.358434i	$-0.883311\pi$
$19$	−8.78398e7			−1.86711			−0.933555	+	0.358434i	$0.883311\pi$
$20$	3.35405e7	+	1.93646e7i	0.524070	+	0.302572i
$21$		0			0
$22$	−1.87816e7	−	3.25306e7i	−0.165652	−	0.286917i
$23$	−5.37313e7	+	3.10218e7i	−0.362961	+	0.209556i	−0.670379	−	0.742019i	$-0.733868\pi$
$23$	−5.37313e7	+	3.10218e7i	−0.362961	+	0.209556i	0.307418	+	0.951575i	$0.400535\pi$
$24$		0			0
$25$	5.67381e7	−	9.82733e7i	0.232399	−	0.402527i
$26$			7.47798e7i			0.242072i
$27$		0			0
$28$	6.05539e7			0.125659
$29$	−5.49475e8	−	3.17239e8i	−0.923762	−	0.533334i	−0.0389284	−	0.999242i	$-0.512394\pi$
$29$	−5.49475e8	−	3.17239e8i	−0.923762	−	0.533334i	−0.884833	+	0.465908i	$0.845728\pi$
$30$		0			0
$31$	2.63601e8	+	4.56570e8i	0.297014	+	0.514443i	0.975451	−	0.220215i	$-0.0706760\pi$
$31$	2.63601e8	+	4.56570e8i	0.297014	+	0.514443i	−0.678438	+	0.734658i	$0.737343\pi$
$32$	−1.64382e8	+	9.49063e7i	−0.153093	+	0.0883883i
$33$		0			0
$34$	2.66157e8	−	4.60998e8i	0.172292	−	0.298418i
$35$		−	5.59141e8i		−	0.304167i
$36$		0			0
$37$	−1.94886e9			−0.759576			−0.379788	−	0.925074i	$-0.624003\pi$
$37$	−1.94886e9			−0.759576			−0.379788	+	0.925074i	$0.624003\pi$
$38$	−3.44260e9	−	1.98759e9i	−1.14337	−	0.660123i
$39$		0			0
$40$	8.76343e8	+	1.51787e9i	0.213951	+	0.370574i
$41$	−1.36774e9	+	7.89668e8i	−0.287940	+	0.166242i	−0.637012	−	0.770854i	$-0.719830\pi$
$41$	−1.36774e9	+	7.89668e8i	−0.287940	+	0.166242i	0.349073	+	0.937096i	$0.386497\pi$
$42$		0			0
$43$	−2.72113e8	+	4.71314e8i	−0.0430466	+	0.0745589i	−0.886746	−	0.462257i	$-0.847040\pi$
$43$	−2.72113e8	+	4.71314e8i	−0.0430466	+	0.0745589i	0.843699	+	0.536816i	$0.180373\pi$
$44$		−	1.69991e9i		−	0.234267i
$45$		0			0
$46$	−2.80777e9			−0.296357
$47$	−1.09421e10	−	6.31741e9i	−1.01511	−	0.586073i	−0.102425	−	0.994741i	$-0.532660\pi$
$47$	−1.09421e10	−	6.31741e9i	−1.01511	−	0.586073i	−0.912683	+	0.408668i	$0.865993\pi$
$48$		0			0
$49$	6.48353e9	+	1.12298e10i	0.468420	+	0.811327i
$50$	4.44734e9	−	2.56767e9i	0.284630	−	0.164331i
$51$		0			0
$52$	−1.69207e9	+	2.93076e9i	−0.0855853	+	0.148238i
$53$		−	1.19968e10i		−	0.541263i	−0.962683	−	0.270632i	$-0.912767\pi$
$53$		−	1.19968e10i		−	0.541263i	0.962683	−	0.270632i	$-0.0872326\pi$
$54$		0			0
$55$	−1.56966e10			−0.567061
$56$	2.37322e9	+	1.37018e9i	0.0769501	+	0.0444272i
$57$		0			0
$58$	−1.43566e10	−	2.48664e10i	−0.377124	−	0.653198i
$59$	−2.94269e10	+	1.69896e10i	−0.697642	+	0.402784i	−0.806469	−	0.591277i	$-0.798624\pi$
$59$	−2.94269e10	+	1.69896e10i	−0.697642	+	0.402784i	0.108826	+	0.994061i	$0.465291\pi$
$60$		0			0
$61$	−2.86722e10	+	4.96616e10i	−0.556521	+	0.963922i	0.441263	+	0.897378i	$0.354531\pi$
$61$	−2.86722e10	+	4.96616e10i	−0.556521	+	0.963922i	−0.997783	+	0.0665442i	$0.978803\pi$
$62$			2.38584e10i			0.420041i
$63$		0			0
$64$	−8.58993e9			−0.125000
$65$	2.70619e10	+	1.56242e10i	0.358822	+	0.207166i
$66$		0			0
$67$	1.52909e10	+	2.64847e10i	0.169038	+	0.292783i	0.938082	−	0.346413i	$-0.112601\pi$
$67$	1.52909e10	+	2.64847e10i	0.169038	+	0.292783i	−0.769044	+	0.639196i	$0.779267\pi$
$68$	2.08624e10	−	1.20449e10i	0.211014	−	0.121829i
$69$		0			0
$70$	1.26519e10	−	2.19137e10i	0.107539	−	0.186264i
$71$			1.90857e11i			1.48990i	0.667121	+	0.744950i	$0.267527\pi$
$71$			1.90857e11i			1.48990i	−0.667121	+	0.744950i	$0.732473\pi$
$72$		0			0
$73$	2.47145e11			1.63311			0.816553	−	0.577270i	$-0.195882\pi$
$73$	2.47145e11			1.63311			0.816553	+	0.577270i	$0.195882\pi$
$74$	−7.63796e10	−	4.40978e10i	−0.465143	−	0.268551i
$75$		0			0
$76$	−8.99480e10	−	1.55795e11i	−0.466778	−	0.808482i
$77$	−2.12539e10	+	1.22710e10i	−0.101975	+	0.0588755i
$78$		0			0
$79$	−9.12931e10	+	1.58124e11i	−0.375557	+	0.650483i	−0.990410	−	0.138158i	$-0.955882\pi$
$79$	−9.12931e10	+	1.58124e11i	−0.375557	+	0.650483i	0.614854	+	0.788641i	$0.289215\pi$
$80$			7.93175e10i			0.302572i
$81$		0			0
$82$	−7.14726e10			−0.235102
$83$	3.50846e11	+	2.02561e11i	1.07312	+	0.619566i	0.929032	−	0.369998i	$-0.120642\pi$
$83$	3.50846e11	+	2.02561e11i	1.07312	+	0.619566i	0.144088	+	0.989565i	$0.453975\pi$
$84$		0			0
$85$	−1.11220e11	−	1.92638e11i	−0.294896	−	0.510775i
$86$	−2.13292e10	+	1.23144e10i	−0.0527211	+	0.0304386i
$87$		0			0
$88$	3.84646e10	−	6.66227e10i	0.0828258	−	0.143459i
$89$		−	6.25344e11i		−	1.25829i	−0.777290	−	0.629143i	$-0.783406\pi$
$89$		−	6.25344e11i		−	1.25829i	0.777290	−	0.629143i	$-0.216594\pi$
$90$		0			0
$91$	4.88575e10			0.0860365
$92$	−1.10042e11	−	6.35326e10i	−0.181481	−	0.104778i
$93$		0			0
$94$	−2.85893e11	−	4.95182e11i	−0.414416	−	0.717790i
$95$	−1.43857e12	+	8.30559e11i	−1.95699	+	1.12987i
$96$		0			0
$97$	−1.35491e11	+	2.34677e11i	−0.162660	+	0.281735i	−0.935822	−	0.352474i	$-0.885341\pi$
$97$	−1.35491e11	+	2.34677e11i	−0.162660	+	0.281735i	0.773162	+	0.634209i	$0.218674\pi$
$98$			5.86822e11i			0.662445i
$99$		0			0
$100$	2.32399e11			0.232399
$101$	−1.41495e12	−	8.16920e11i	−1.33294	−	0.769576i	−0.347195	−	0.937793i	$-0.612866\pi$
$101$	−1.41495e12	−	8.16920e11i	−1.33294	−	0.769576i	−0.985750	+	0.168217i	$0.946199\pi$
$102$		0			0
$103$	2.53750e11	+	4.39508e11i	0.212512	+	0.368081i	0.952500	−	0.304539i	$-0.0985022\pi$
$103$	2.53750e11	+	4.39508e11i	0.212512	+	0.368081i	−0.739988	+	0.672620i	$0.765169\pi$
$104$	−1.32631e11	+	7.65745e10i	−0.104820	+	0.0605179i
$105$		0			0
$106$	2.71456e11	−	4.70175e11i	0.191366	−	0.331455i
$107$		−	2.77702e11i		−	0.185045i	−0.995711	−	0.0925224i	$-0.970507\pi$
$107$		−	2.77702e11i		−	0.185045i	0.995711	−	0.0925224i	$-0.0294930\pi$
$108$		0			0
$109$	1.84057e11			0.109747			0.0548736	−	0.998493i	$-0.482524\pi$
$109$	1.84057e11			0.109747			0.0548736	+	0.998493i	$0.482524\pi$
$110$	−6.15179e11	−	3.55174e11i	−0.347252	−	0.200486i
$111$		0			0
$112$	6.20072e10	+	1.07400e11i	0.0314148	+	0.0544120i
$113$	−1.87701e12	+	1.08369e12i	−0.901565	+	0.520519i	−0.877708	−	0.479197i	$-0.840928\pi$
$113$	−1.87701e12	+	1.08369e12i	−0.901565	+	0.520519i	−0.0238573	+	0.999715i	$0.507595\pi$
$114$		0			0
$115$	−5.86646e11	+	1.01610e12i	−0.253623	+	0.439288i
$116$		−	1.29941e12i		−	0.533334i
$117$		0			0
$118$	−1.53773e12			−0.569623
$119$	−3.01194e11	−	1.73894e11i	−0.106063	−	0.0612355i
$120$		0			0
$121$	−1.22473e12	−	2.12130e12i	−0.390238	−	0.675912i
$122$	−2.24743e12	+	1.29755e12i	−0.681596	+	0.393520i
$123$		0			0
$124$	−5.39854e11	+	9.35055e11i	−0.148507	+	0.257221i
$125$			2.47096e12i			0.647748i
$126$		0			0
$127$	−1.70097e12			−0.405391			−0.202695	−	0.979242i	$-0.564970\pi$
$127$	−1.70097e12			−0.405391			−0.202695	+	0.979242i	$0.564970\pi$
$128$	−3.36655e11	−	1.94368e11i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	7.07071e11	+	1.22468e12i	0.146488	+	0.253725i
$131$	9.53531e11	−	5.50521e11i	0.188672	−	0.108930i	−0.402689	−	0.915337i	$-0.631924\pi$
$131$	9.53531e11	−	5.50521e11i	0.188672	−	0.108930i	0.591361	+	0.806407i	$0.298591\pi$
$132$		0			0
$133$	−1.29859e12	+	2.24923e12i	−0.234619	+	0.406373i
$134$			1.38398e12i			0.239056i
$135$		0			0
$136$	1.09018e12			0.172292
$137$	2.16098e12	+	1.24764e12i	0.326834	+	0.188698i	0.654435	−	0.756119i	$-0.272907\pi$
$137$	2.16098e12	+	1.24764e12i	0.326834	+	0.188698i	−0.327601	+	0.944816i	$0.606240\pi$
$138$		0			0
$139$	−4.88547e12	−	8.46189e12i	−0.677357	−	1.17322i	−0.975774	−	0.218782i	$-0.929792\pi$
$139$	−4.88547e12	−	8.46189e12i	−0.677357	−	1.17322i	0.298416	−	0.954436i	$-0.403542\pi$
$140$	9.91703e11	−	5.72560e11i	0.131708	−	0.0760419i
$141$		0			0
$142$	−4.31859e12	+	7.48002e12i	−0.526759	+	0.912373i
$143$		−	1.37156e12i		−	0.160398i
$144$		0			0
$145$	−1.19985e13			−1.29098
$146$	9.68606e12	+	5.59225e12i	1.00007	+	0.577390i
$147$		0			0
$148$	−1.99564e12	−	3.45654e12i	−0.189894	−	0.328906i
$149$	−1.09012e12	+	6.29378e11i	−0.0996219	+	0.0575167i	−0.548983	−	0.835833i	$-0.684985\pi$
$149$	−1.09012e12	+	6.29378e11i	−0.0996219	+	0.0575167i	0.449361	+	0.893350i	$0.351652\pi$
$150$		0			0
$151$	−4.95794e12	+	8.58740e12i	−0.418253	+	0.724436i	−0.995764	−	0.0919472i	$-0.970691\pi$
$151$	−4.95794e12	+	8.58740e12i	−0.418253	+	0.724436i	0.577511	+	0.816383i	$0.304024\pi$
$152$		−	8.14116e12i		−	0.660123i
$153$		0			0
$154$	−1.11064e12			−0.0832625
$155$	8.63408e12	+	4.98489e12i	0.622624	+	0.359472i
$156$		0			0
$157$	−5.70646e12	−	9.88388e12i	−0.381039	−	0.659978i	0.610172	−	0.792269i	$-0.291100\pi$
$157$	−5.70646e12	−	9.88388e12i	−0.381039	−	0.659978i	−0.991211	+	0.132290i	$0.957767\pi$
$158$	−7.15589e12	+	4.13145e12i	−0.459961	+	0.265559i
$159$		0			0
$160$	−1.79475e12	+	3.10860e12i	−0.106975	+	0.185287i
$161$			1.83446e12i			0.105330i
$162$		0			0
$163$	−1.55506e13			−0.829130			−0.414565	−	0.910020i	$-0.636066\pi$
$163$	−1.55506e13			−0.829130			−0.414565	+	0.910020i	$0.636066\pi$
$164$	−2.80114e12	−	1.61724e12i	−0.143970	−	0.0831211i
$165$		0			0
$166$	9.16688e12	+	1.58775e13i	0.438100	+	0.758811i
$167$	5.50310e12	−	3.17721e12i	0.253693	−	0.146470i	−0.367761	−	0.929920i	$-0.619876\pi$
$167$	5.50310e12	−	3.17721e12i	0.253693	−	0.146470i	0.621454	+	0.783451i	$0.286542\pi$
$168$		0			0
$169$	1.02838e13	−	1.78121e13i	0.441401	−	0.764529i
$170$		−	1.00665e13i		−	0.417046i
$171$		0			0
$172$	−1.11458e12			−0.0430466
$173$	2.53666e13	+	1.46454e13i	0.946206	+	0.546292i	0.891900	−	0.452232i	$-0.149372\pi$
$173$	2.53666e13	+	1.46454e13i	0.946206	+	0.546292i	0.0543058	+	0.998524i	$0.482705\pi$
$174$		0			0
$175$	−1.67759e12	−	2.90568e12i	−0.0584061	−	0.101162i
$176$	3.01500e12	−	1.74071e12i	0.101440	−	0.0585667i
$177$		0			0
$178$	1.41499e13	−	2.45084e13i	0.444871	−	0.770539i
$179$		−	5.08183e13i		−	1.54491i	−0.635072	−	0.772453i	$-0.719030\pi$
$179$		−	5.08183e13i		−	1.54491i	0.635072	−	0.772453i	$-0.280970\pi$
$180$		0			0
$181$	−6.96319e13			−1.98033			−0.990163	−	0.139920i	$-0.955315\pi$
$181$	−6.96319e13			−1.98033			−0.990163	+	0.139920i	$0.955315\pi$
$182$	1.91482e12	+	1.10552e12i	0.0526864	+	0.0304185i
$183$		0			0
$184$	−2.87516e12	−	4.97992e12i	−0.0740892	−	0.128326i
$185$	−3.19169e13	+	1.84272e13i	−0.796142	+	0.459653i
$186$		0			0
$187$	−4.88169e12	+	8.45533e12i	−0.114162	+	0.197734i
$188$		−	2.58761e13i		−	0.586073i
$189$		0			0
$190$	−7.51736e13			−1.59788
$191$	1.95670e13	+	1.12970e13i	0.403018	+	0.232683i	0.687785	−	0.725914i	$-0.258583\pi$
$191$	1.95670e13	+	1.12970e13i	0.403018	+	0.232683i	−0.284767	+	0.958597i	$0.591916\pi$
$192$		0			0
$193$	−1.83548e13	−	3.17915e13i	−0.355146	−	0.615130i	0.631997	−	0.774971i	$-0.282235\pi$
$193$	−1.83548e13	−	3.17915e13i	−0.355146	−	0.615130i	−0.987143	+	0.159840i	$0.948902\pi$
$194$	−1.06203e13	+	6.13163e12i	−0.199217	+	0.115018i
$195$		0			0
$196$	−1.32783e13	+	2.29986e13i	−0.234210	+	0.405663i
$197$		−	1.03587e14i		−	1.77217i	−0.463520	−	0.886087i	$-0.653414\pi$
$197$		−	1.03587e14i		−	1.77217i	0.463520	−	0.886087i	$-0.346586\pi$
$198$		0			0
$199$	−1.02536e14			−1.65104			−0.825519	−	0.564374i	$-0.809118\pi$
$199$	−1.02536e14			−1.65104			−0.825519	+	0.564374i	$0.809118\pi$
$200$	9.10816e12	+	5.25860e12i	0.142315	+	0.0821656i
$201$		0			0
$202$	−3.69696e13	−	6.40332e13i	−0.544172	−	0.942534i
$203$	−1.62465e13	+	9.37992e12i	−0.232158	+	0.134036i
$204$		0			0
$205$	−1.49332e13	+	2.58651e13i	−0.201201	+	0.348490i
$206$			2.29669e13i			0.300537i
$207$		0			0
$208$	−6.93073e12			−0.0855853
$209$	6.31421e13	+	3.64551e13i	0.757602	+	0.437402i
$210$		0			0
$211$	2.27403e13	+	3.93874e13i	0.257693	+	0.446337i	0.965623	−	0.259945i	$-0.0837044\pi$
$211$	2.27403e13	+	3.93874e13i	0.257693	+	0.446337i	−0.707931	+	0.706282i	$0.750371\pi$
$212$	2.12777e13	−	1.22847e13i	0.234374	−	0.135316i
$213$		0			0
$214$	6.28369e12	−	1.08837e13i	0.0654232	−	0.113316i
$215$			1.02917e13i			0.104198i
$216$		0			0
$217$	1.55879e13			0.149290
$218$	7.21353e12	+	4.16474e12i	0.0672062	+	0.0388015i
$219$		0			0
$220$	−1.60733e13	−	2.78398e13i	−0.141765	−	0.245545i
$221$	1.68327e13	−	9.71835e12i	0.144477	−	0.0834140i
$222$		0			0
$223$	−8.74629e13	+	1.51490e14i	−0.711205	+	1.23184i	0.253200	+	0.967414i	$0.418517\pi$
$223$	−8.74629e13	+	1.51490e14i	−0.711205	+	1.23184i	−0.964405	+	0.264429i	$0.914816\pi$
$224$			5.61225e12i			0.0444272i
$225$		0			0
$226$	−9.80849e13			−0.736125
$227$	2.05904e14	+	1.18879e14i	1.50491	+	0.868858i	0.999984	+	0.00569263i	$0.00181203\pi$
$227$	2.05904e14	+	1.18879e14i	1.50491	+	0.868858i	0.504922	+	0.863165i	$0.331521\pi$
$228$		0			0
$229$	−8.78297e13	−	1.52125e14i	−0.609016	−	1.05485i	−0.991403	−	0.130844i	$-0.958231\pi$
$229$	−8.78297e13	−	1.52125e14i	−0.609016	−	1.05485i	0.382387	−	0.924002i	$-0.375102\pi$
$230$	−4.59834e13	+	2.65485e13i	−0.310624	+	0.179339i
$231$		0			0
$232$	2.94024e13	−	5.09264e13i	0.188562	−	0.326599i
$233$		−	3.46732e13i		−	0.216700i	−0.994113	−	0.108350i	$-0.965443\pi$
$233$		−	3.46732e13i		−	0.216700i	0.994113	−	0.108350i	$-0.0345567\pi$
$234$		0			0
$235$	−2.38934e14			−1.41863
$236$	−6.02663e13	−	3.47948e13i	−0.348821	−	0.201392i
$237$		0			0
$238$	−7.86955e12	−	1.36305e13i	−0.0433001	−	0.0749979i
$239$	−6.47209e13	+	3.73666e13i	−0.347262	+	0.200492i	−0.663479	−	0.748195i	$-0.730921\pi$
$239$	−6.47209e13	+	3.73666e13i	−0.347262	+	0.200492i	0.316217	+	0.948687i	$0.397587\pi$
$240$		0			0
$241$	−1.62988e14	+	2.82303e14i	−0.831866	+	1.44083i	0.0646909	+	0.997905i	$0.479394\pi$
$241$	−1.62988e14	+	2.82303e14i	−0.831866	+	1.44083i	−0.896557	+	0.442929i	$0.853939\pi$
$242$		−	1.10850e14i		−	0.551880i
$243$		0			0
$244$	−1.17441e14			−0.556521
$245$	2.12364e14	+	1.22608e14i	0.981939	+	0.566923i
$246$		0			0
$247$	−7.25740e13	−	1.25702e14i	−0.319594	−	0.553554i
$248$	−4.23158e13	+	2.44310e13i	−0.181883	+	0.105010i
$249$		0			0
$250$	−5.59115e13	+	9.68416e13i	−0.229014	+	0.396663i
$251$			1.46645e14i			0.586442i	0.956045	+	0.293221i	$0.0947271\pi$
$251$			1.46645e14i			0.586442i	−0.956045	+	0.293221i	$0.905273\pi$
$252$		0			0
$253$	5.14984e13			0.196368
$254$	−6.66641e13	−	3.84885e13i	−0.248250	−	0.143327i
$255$		0			0
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	−4.41906e14	+	2.55135e14i	−1.53367	+	0.885464i	−0.534481	+	0.845181i	$0.679493\pi$
$257$	−4.41906e14	+	2.55135e14i	−1.53367	+	0.885464i	−0.999188	+	0.0402835i	$0.987174\pi$
$258$		0			0
$259$	−2.88113e13	+	4.99027e13i	−0.0954476	+	0.165320i
$260$			6.39968e13i			0.207166i
$261$		0			0
$262$	4.98275e13			0.154050
$263$	−3.21514e14	−	1.85626e14i	−0.971550	−	0.560925i	−0.0718417	−	0.997416i	$-0.522888\pi$
$263$	−3.21514e14	−	1.85626e14i	−0.971550	−	0.560925i	−0.899708	+	0.436491i	$0.856221\pi$
$264$		0			0
$265$	−1.13434e14	−	1.96473e14i	−0.327543	−	0.567320i
$266$	−1.01789e14	+	5.87677e13i	−0.287349	+	0.165901i
$267$		0			0
$268$	−3.13158e13	+	5.42406e13i	−0.0845191	+	0.146391i
$269$		−	2.33102e14i		−	0.615223i	−0.951512	−	0.307612i	$-0.900470\pi$
$269$		−	2.33102e14i		−	0.615223i	0.951512	−	0.307612i	$-0.0995298\pi$
$270$		0			0
$271$	−4.66343e14			−1.17731			−0.588653	−	0.808386i	$-0.700342\pi$
$271$	−4.66343e14			−1.17731			−0.588653	+	0.808386i	$0.700342\pi$
$272$	4.27262e13	+	2.46680e13i	0.105507	+	0.0609144i
$273$		0			0
$274$	5.64618e13	+	9.77948e13i	0.133429	+	0.231107i
$275$	−8.15704e13	+	4.70947e13i	−0.188598	+	0.108887i
$276$		0			0
$277$	2.96336e14	−	5.13270e14i	0.656004	−	1.13623i	−0.325637	−	0.945495i	$-0.605579\pi$
$277$	2.96336e14	−	5.13270e14i	0.656004	−	1.13623i	0.981641	−	0.190737i	$-0.0610878\pi$
$278$		−	4.42183e14i		−	0.957928i
$279$		0			0
$280$	5.18222e13			0.107539
$281$	−1.60974e14	−	9.29382e13i	−0.326977	−	0.188780i	0.327521	−	0.944844i	$-0.393787\pi$
$281$	−1.60974e14	−	9.29382e13i	−0.326977	−	0.188780i	−0.654498	+	0.756064i	$0.727120\pi$
$282$		0			0
$283$	−3.28265e14	−	5.68572e14i	−0.639008	−	1.10679i	−0.985651	−	0.168798i	$-0.946012\pi$
$283$	−3.28265e14	−	5.68572e14i	−0.639008	−	1.10679i	0.346642	−	0.937997i	$-0.387322\pi$
$284$	−3.38507e14	+	1.95437e14i	−0.645145	+	0.372475i
$285$		0			0
$286$	3.10350e13	−	5.37541e13i	0.0567094	−	0.0982235i
$287$			4.66967e13i			0.0835593i
$288$		0			0
$289$	4.44264e14			0.762524
$290$	−4.70242e14	−	2.71495e14i	−0.790558	−	0.456429i
$291$		0			0
$292$	2.53076e14	+	4.38341e14i	0.408277	+	0.707156i
$293$	−6.93493e13	+	4.00388e13i	−0.109607	+	0.0632814i	−0.553801	−	0.832649i	$-0.686823\pi$
$293$	−6.93493e13	+	4.00388e13i	−0.109607	+	0.0632814i	0.444195	+	0.895930i	$0.353490\pi$
$294$		0			0
$295$	−3.21287e14	+	5.56486e14i	−0.487485	+	0.844349i
$296$		−	1.80624e14i		−	0.268551i
$297$		0			0
$298$	−5.69648e13			−0.0813410
$299$	−8.87865e13	−	5.12609e13i	−0.124257	−	0.0717396i
$300$		0			0
$301$	8.04566e12	+	1.39355e13i	0.0108184	+	0.0187380i
$302$	−3.88621e14	+	2.24371e14i	−0.512254	+	0.295750i
$303$		0			0
$304$	1.84214e14	−	3.19067e14i	0.233389	−	0.404241i
$305$			1.08442e15i			1.34710i
$306$		0			0
$307$	1.24425e15			1.48621			0.743103	−	0.669177i	$-0.233353\pi$
$307$	1.24425e15			1.48621			0.743103	+	0.669177i	$0.233353\pi$
$308$	−4.35281e13	−	2.51309e13i	−0.0509877	−	0.0294377i
$309$		0			0
$310$	2.25590e14	+	3.90734e14i	0.254185	+	0.440262i
$311$	1.46078e15	−	8.43379e14i	1.61444	−	0.932096i	0.626112	−	0.779733i	$-0.284645\pi$
$311$	1.46078e15	−	8.43379e14i	1.61444	−	0.932096i	0.988325	−	0.152363i	$-0.0486882\pi$
$312$		0			0
$313$	5.14755e14	−	8.91583e14i	0.547438	−	0.948190i	−0.451011	−	0.892518i	$-0.648937\pi$
$313$	5.14755e14	−	8.91583e14i	0.547438	−	0.948190i	0.998449	−	0.0556721i	$-0.0177301\pi$
$314$		−	5.16490e14i		−	0.538870i
$315$		0			0
$316$	−3.73937e14			−0.375557
$317$	1.44024e15	+	8.31523e14i	1.41932	+	0.819443i	0.996239	−	0.0866502i	$-0.0276163\pi$
$317$	1.44024e15	+	8.31523e14i	1.41932	+	0.819443i	0.423078	+	0.906093i	$0.360950\pi$
$318$		0			0
$319$	2.63320e14	+	4.56084e14i	0.249885	+	0.432813i
$320$	−1.40679e14	+	8.12211e13i	−0.131018	+	0.0756430i
$321$		0			0
$322$	−4.15091e13	+	7.18959e13i	−0.0372399	+	0.0645014i
$323$			1.03322e15i			0.909871i
$324$		0			0
$325$	1.87510e14			0.159120
$326$	−6.09458e14	−	3.51871e14i	−0.507736	−	0.293142i
$327$		0			0
$328$	−7.31879e13	−	1.26765e14i	−0.0587755	−	0.101802i
$329$	−3.23528e14	+	1.86789e14i	−0.255115	+	0.147291i
$330$		0			0
$331$	−1.15887e15	+	2.00721e15i	−0.881181	+	1.52625i	−0.0311515	+	0.999515i	$0.509917\pi$
$331$	−1.15887e15	+	2.00721e15i	−0.881181	+	1.52625i	−0.850029	+	0.526735i	$0.823416\pi$
$332$			8.29691e14i			0.619566i
$333$		0			0
$334$	2.87569e14			0.207139
$335$	5.00845e14	+	2.89163e14i	0.354352	+	0.204585i
$336$		0			0
$337$	−7.15896e14	−	1.23997e15i	−0.488732	−	0.846508i	0.511184	−	0.859471i	$-0.329207\pi$
$337$	−7.15896e14	−	1.23997e15i	−0.488732	−	0.846508i	−0.999916	+	0.0129631i	$0.995874\pi$
$338$	8.06082e14	−	4.65392e14i	0.540604	−	0.312118i
$339$		0			0
$340$	2.27778e14	−	3.94523e14i	0.147448	−	0.255387i
$341$		−	4.37596e14i		−	0.278322i
$342$		0			0
$343$	7.92651e14			0.486763
$344$	−4.36823e13	−	2.52200e13i	−0.0263606	−	0.0152193i
$345$		0			0
$346$	6.62776e14	+	1.14796e15i	0.386287	+	0.669069i
$347$	1.97496e15	−	1.14024e15i	1.13131	−	0.653161i	0.187044	−	0.982351i	$-0.440109\pi$
$347$	1.97496e15	−	1.14024e15i	1.13131	−	0.653161i	0.944263	+	0.329191i	$0.106776\pi$
$348$		0			0
$349$	5.05015e14	−	8.74711e14i	0.279481	−	0.484074i	−0.691775	−	0.722113i	$-0.743171\pi$
$349$	5.05015e14	−	8.74711e14i	0.279481	−	0.484074i	0.971256	+	0.238038i	$0.0765044\pi$
$350$		−	1.51838e14i		−	0.0825988i
$351$		0			0
$352$	1.57551e14			0.0828258
$353$	1.44115e14	+	8.32049e13i	0.0744837	+	0.0430032i	0.536779	−	0.843723i	$-0.319641\pi$
$353$	1.44115e14	+	8.32049e13i	0.0744837	+	0.0430032i	−0.462296	+	0.886726i	$0.652974\pi$
$354$		0			0
$355$	1.80462e15	+	3.12570e15i	0.901604	+	1.56162i
$356$	1.10912e15	−	6.40353e14i	0.544854	−	0.314571i
$357$		0			0
$358$	1.14989e15	−	1.99166e15i	0.546206	−	0.946057i
$359$			2.67054e15i			1.24747i	0.781634	+	0.623737i	$0.214387\pi$
$359$			2.67054e15i			1.24747i	−0.781634	+	0.623737i	$0.785613\pi$
$360$		0			0
$361$	5.50252e15			2.48610
$362$	−2.72900e15	−	1.57559e15i	−1.21270	−	0.700151i
$363$		0			0
$364$	5.00301e13	+	8.66546e13i	0.0215091	+	0.0372549i
$365$	4.04754e15	−	2.33685e15i	1.71173	−	0.988265i
$366$		0			0
$367$	8.30314e14	−	1.43815e15i	0.339818	−	0.588581i	−0.644581	−	0.764536i	$-0.722968\pi$
$367$	8.30314e14	−	1.43815e15i	0.339818	−	0.588581i	0.984398	+	0.175955i	$0.0563013\pi$
$368$		−	2.60230e14i		−	0.104778i
$369$		0			0
$370$	−1.66784e15			−0.650048
$371$	−3.07190e14	−	1.77356e14i	−0.117805	−	0.0680146i
$372$		0			0
$373$	1.78176e15	+	3.08610e15i	0.661602	+	1.14593i	0.980195	+	0.198037i	$0.0634566\pi$
$373$	1.78176e15	+	3.08610e15i	0.661602	+	1.14593i	−0.318592	+	0.947892i	$0.603210\pi$
$374$	−3.82645e14	+	2.20920e14i	−0.139819	+	0.0807245i
$375$		0			0
$376$	5.85509e14	−	1.01413e15i	0.207208	−	0.358895i
$377$		−	1.04842e15i		−	0.365164i
$378$		0			0
$379$	−5.39727e14			−0.182112			−0.0910561	−	0.995846i	$-0.529024\pi$
$379$	−5.39727e14			−0.182112			−0.0910561	+	0.995846i	$0.529024\pi$
$380$	−2.94619e15	−	1.70099e15i	−0.978497	−	0.564936i
$381$		0			0
$382$	5.11245e14	+	8.85503e14i	0.164532	+	0.284977i
$383$	1.01931e15	−	5.88501e14i	0.322935	−	0.186447i	−0.329765	−	0.944063i	$-0.606970\pi$
$383$	1.01931e15	−	5.88501e14i	0.322935	−	0.186447i	0.652700	+	0.757616i	$0.273636\pi$
$384$		0			0
$385$	−2.32053e14	+	4.01928e14i	−0.0712563	+	0.123420i
$386$		−	1.66129e15i		−	0.502252i
$387$		0			0
$388$	−5.54971e14			−0.162660
$389$	2.35299e15	+	1.35850e15i	0.679082	+	0.392068i	0.799509	−	0.600654i	$-0.205093\pi$
$389$	2.35299e15	+	1.35850e15i	0.679082	+	0.392068i	−0.120427	+	0.992722i	$0.538426\pi$
$390$		0			0
$391$	3.64897e14	+	6.32020e14i	0.102120	+	0.176877i
$392$	−1.04080e15	+	6.00906e14i	−0.286847	+	0.165611i
$393$		0			0
$394$	2.34390e15	−	4.05975e15i	0.626558	−	1.08523i
$395$			3.45284e15i			0.909064i
$396$		0			0
$397$	2.67431e15			0.683075			0.341538	−	0.939868i	$-0.389052\pi$
$397$	2.67431e15			0.683075			0.341538	+	0.939868i	$0.389052\pi$
$398$	−4.01857e15	−	2.32012e15i	−1.01105	−	0.583730i
$399$		0			0
$400$	2.37977e14	+	4.12188e14i	0.0580998	+	0.100632i
$401$	−1.27208e15	+	7.34434e14i	−0.305948	+	0.176639i	−0.645112	−	0.764088i	$-0.723189\pi$
$401$	−1.27208e15	+	7.34434e14i	−0.305948	+	0.176639i	0.339164	+	0.940727i	$0.389856\pi$
$402$		0			0
$403$	−4.35578e14	+	7.54443e14i	−0.101680	+	0.176115i
$404$		−	3.34611e15i		−	0.769576i
$405$		0			0
$406$	−8.48974e14			−0.189556
$407$	1.40091e15	+	8.08813e14i	0.308207	+	0.177943i
$408$		0			0
$409$	−1.01600e15	−	1.75976e15i	−0.217046	−	0.375935i	0.736857	−	0.676048i	$-0.236309\pi$
$409$	−1.01600e15	−	1.75976e15i	−0.217046	−	0.375935i	−0.953904	+	0.300113i	$0.902976\pi$
$410$	−1.17052e15	+	6.75800e14i	−0.246420	+	0.142271i
$411$		0			0
$412$	−5.19681e14	+	9.00113e14i	−0.106256	+	0.184041i
$413$			1.00468e15i			0.202454i
$414$		0			0
$415$	7.66118e15			1.49971
$416$	−2.71628e14	−	1.56825e14i	−0.0524101	−	0.0302590i
$417$		0			0
$418$	1.64977e15	+	2.85749e15i	0.309290	+	0.535706i
$419$	4.32416e14	−	2.49655e14i	0.0799130	−	0.0461378i	−0.459511	−	0.888172i	$-0.651975\pi$
$419$	4.32416e14	−	2.49655e14i	0.0799130	−	0.0461378i	0.539424	+	0.842034i	$0.318642\pi$
$420$		0			0
$421$	3.98785e15	−	6.90716e15i	0.716220	−	1.24053i	−0.246268	−	0.969202i	$-0.579204\pi$
$421$	3.98785e15	−	6.90716e15i	0.716220	−	1.24053i	0.962487	−	0.271327i	$-0.0874624\pi$
$422$			2.05822e15i			0.364433i
$423$		0			0
$424$	1.11188e15			0.191366
$425$	−1.15595e15	−	6.67388e14i	−0.196158	−	0.113252i
$426$		0			0
$427$	8.47759e14	+	1.46836e15i	0.139864	+	0.242251i
$428$	4.92539e14	−	2.84367e14i	0.0801268	−	0.0462612i
$429$		0			0
$430$	−2.32875e14	+	4.03352e14i	−0.0368394	+	0.0638078i
$431$			4.35987e15i			0.680158i	0.940397	+	0.340079i	$0.110454\pi$
$431$			4.35987e15i			0.680158i	−0.940397	+	0.340079i	$0.889546\pi$
$432$		0			0
$433$	6.19698e15			0.940271			0.470135	−	0.882594i	$-0.344205\pi$
$433$	6.19698e15			0.940271			0.470135	+	0.882594i	$0.344205\pi$
$434$	6.10920e14	+	3.52715e14i	0.0914210	+	0.0527819i
$435$		0			0
$436$	1.88474e14	+	3.26447e14i	0.0274368	+	0.0475219i
$437$	4.71975e15	−	2.72495e15i	0.677689	−	0.391264i
$438$		0			0
$439$	−4.26484e15	+	7.38692e15i	−0.595821	+	1.03199i	0.397610	+	0.917555i	$0.369840\pi$
$439$	−4.26484e15	+	7.38692e15i	−0.595821	+	1.03199i	−0.993431	+	0.114437i	$0.963494\pi$
$440$		−	1.45479e15i		−	0.200486i
$441$		0			0
$442$	8.79605e14			0.117965
$443$	4.61085e15	+	2.66208e15i	0.610041	+	0.352207i	0.772981	−	0.634429i	$-0.218765\pi$
$443$	4.61085e15	+	2.66208e15i	0.610041	+	0.352207i	−0.162941	+	0.986636i	$0.552098\pi$
$444$		0			0
$445$	−5.91287e15	−	1.02414e16i	−0.761444	−	1.31886i
$446$	−6.85566e15	+	3.95812e15i	−0.871045	+	0.502898i
$447$		0			0
$448$	−1.26991e14	+	2.19954e14i	−0.0157074	+	0.0272060i
$449$			1.20214e16i			1.46716i	0.679601	+	0.733582i	$0.262153\pi$
$449$			1.20214e16i			1.46716i	−0.679601	+	0.733582i	$0.737847\pi$
$450$		0			0
$451$	1.31090e15			0.155780
$452$	−3.84413e15	−	2.21941e15i	−0.450782	−	0.260259i
$453$		0			0
$454$	5.37983e15	+	9.31814e15i	0.614375	+	1.06413i
$455$	8.00149e14	−	4.61966e14i	0.0901784	−	0.0520645i
$456$		0			0
$457$	−4.96133e15	+	8.59328e15i	−0.544630	+	0.943326i	0.454001	+	0.891001i	$0.349996\pi$
$457$	−4.96133e15	+	8.59328e15i	−0.544630	+	0.943326i	−0.998630	+	0.0523247i	$0.983337\pi$
$458$		−	7.94944e15i		−	0.861278i
$459$		0			0
$460$	−2.40290e15			−0.253623
$461$	1.10260e16	+	6.36584e15i	1.14871	+	0.663208i	0.948573	−	0.316559i	$-0.102528\pi$
$461$	1.10260e16	+	6.36584e15i	1.14871	+	0.663208i	0.200138	+	0.979768i	$0.435861\pi$
$462$		0			0
$463$	−9.37743e15	−	1.62422e16i	−0.951914	−	1.64876i	−0.741277	−	0.671199i	$-0.765780\pi$
$463$	−9.37743e15	−	1.62422e16i	−0.951914	−	1.64876i	−0.210636	−	0.977564i	$-0.567554\pi$
$464$	2.30466e15	−	1.33060e15i	0.230940	−	0.133333i
$465$		0			0
$466$	7.84565e14	−	1.35891e15i	0.0766149	−	0.132701i
$467$			3.36371e15i			0.324278i	0.986768	+	0.162139i	$0.0518393\pi$
$467$			3.36371e15i			0.324278i	−0.986768	+	0.162139i	$0.948161\pi$
$468$		0			0
$469$	9.04224e14			0.0849647
$470$	−9.36426e15	−	5.40646e15i	−0.868733	−	0.501563i
$471$		0			0
$472$	−1.57463e15	−	2.72734e15i	−0.142406	−	0.246654i
$473$	3.91208e14	−	2.25864e14i	0.0349334	−	0.0201688i
$474$		0			0
$475$	−4.98387e15	+	8.63231e15i	−0.433915	+	0.751563i
$476$		−	7.12271e14i		−	0.0612355i
$477$		0			0
$478$	−3.38204e15			−0.283538
$479$	−7.37545e15	−	4.25822e15i	−0.610626	−	0.352545i	0.162584	−	0.986695i	$-0.448017\pi$
$479$	−7.37545e15	−	4.25822e15i	−0.610626	−	0.352545i	−0.773211	+	0.634149i	$0.781350\pi$
$480$		0			0
$481$	−1.61017e15	−	2.78889e15i	−0.130017	−	0.225196i
$482$	−1.27756e16	+	7.37599e15i	−1.01882	+	0.588218i
$483$		0			0
$484$	2.50826e15	−	4.34443e15i	0.195119	−	0.337956i
$485$			5.12448e15i			0.393731i
$486$		0			0
$487$	−5.71851e15			−0.428656			−0.214328	−	0.976762i	$-0.568756\pi$
$487$	−5.71851e15			−0.428656			−0.214328	+	0.976762i	$0.568756\pi$
$488$	−4.60273e15	−	2.65739e15i	−0.340798	−	0.196760i
$489$		0			0
$490$	5.54863e15	+	9.61050e15i	0.400875	+	0.694336i
$491$	−7.34386e15	+	4.23998e15i	−0.524126	+	0.302604i	−0.738621	−	0.674121i	$-0.764523\pi$
$491$	−7.34386e15	+	4.23998e15i	−0.524126	+	0.302604i	0.214495	+	0.976725i	$0.431189\pi$
$492$		0			0
$493$	−3.73156e15	+	6.46325e15i	−0.259902	+	0.450163i
$494$		−	6.56865e15i		−	0.451975i
$495$		0			0
$496$	−2.21124e15			−0.148507
$497$	4.88708e15	+	2.82156e15i	0.324273	+	0.187219i
$498$		0			0
$499$	−3.76570e15	−	6.52238e15i	−0.243917	−	0.422477i	0.717910	−	0.696136i	$-0.245099\pi$
$499$	−3.76570e15	−	6.52238e15i	−0.243917	−	0.422477i	−0.961827	+	0.273660i	$0.911766\pi$
$500$	−4.38255e15	+	2.53027e15i	−0.280483	+	0.161937i
$501$		0			0
$502$	−3.31820e15	+	5.74729e15i	−0.207338	+	0.359121i
$503$		−	1.61669e16i		−	0.998200i	−0.866544	−	0.499100i	$-0.833664\pi$
$503$		−	1.61669e16i		−	0.998200i	0.866544	−	0.499100i	$-0.166336\pi$
$504$		0			0
$505$	−3.08972e16			−1.86282
$506$	2.01832e15	+	1.16528e15i	0.120250	+	0.0694265i
$507$		0			0
$508$	−1.74179e15	−	3.01687e15i	−0.101348	−	0.175539i
$509$	−1.82686e16	+	1.05474e16i	−1.05051	+	0.606511i	−0.922791	−	0.385300i	$-0.874098\pi$
$509$	−1.82686e16	+	1.05474e16i	−1.05051	+	0.606511i	−0.127716	+	0.991811i	$0.540765\pi$
$510$		0			0
$511$	3.65371e15	−	6.32841e15i	0.205215	−	0.355442i
$512$		−	7.96131e14i		−	0.0441942i
$513$		0			0
$514$	−2.30922e16			−1.25224
$515$	8.31144e15	+	4.79861e15i	0.445485	+	0.257201i
$516$		0			0
$517$	5.24367e15	+	9.08231e15i	0.274595	+	0.475612i
$518$	−2.25834e15	+	1.30385e15i	−0.116899	+	0.0674916i
$519$		0			0
$520$	−1.44808e15	+	2.50815e15i	−0.0732442	+	0.126863i
$521$		−	1.13146e16i		−	0.565734i	−0.959159	−	0.282867i	$-0.908715\pi$
$521$		−	1.13146e16i		−	0.565734i	0.959159	−	0.282867i	$-0.0912855\pi$
$522$		0			0
$523$	−1.21737e16			−0.594856			−0.297428	−	0.954744i	$-0.596129\pi$
$523$	−1.21737e16			−0.594856			−0.297428	+	0.954744i	$0.596129\pi$
$524$	1.95283e15	+	1.12747e15i	0.0943359	+	0.0544649i
$525$		0			0
$526$	−8.40048e15	−	1.45501e16i	−0.396634	−	0.686990i
$527$	5.37045e15	−	3.10063e15i	0.250696	−	0.144739i
$528$		0			0
$529$	−9.03261e15	+	1.56449e16i	−0.412173	+	0.713904i
$530$		−	1.02669e16i		−	0.463215i
$531$		0			0
$532$	−5.31904e15			−0.234619
$533$	−2.26008e15	−	1.30486e15i	−0.0985737	−	0.0569115i
$534$		0			0
$535$	−2.62578e15	−	4.54799e15i	−0.111979	−	0.193953i
$536$	−2.45465e15	+	1.41719e15i	−0.103514	+	0.0597641i
$537$		0			0
$538$	5.27450e15	−	9.13570e15i	0.217514	−	0.376746i
$539$		−	1.07631e16i		−	0.438941i
$540$		0			0
$541$	8.25555e15			0.329278			0.164639	−	0.986354i	$-0.447354\pi$
$541$	8.25555e15			0.329278			0.164639	+	0.986354i	$0.447354\pi$
$542$	−1.82768e16	−	1.05521e16i	−0.720950	−	0.416241i
$543$		0			0
$544$	1.11634e15	+	1.93356e15i	0.0430730	+	0.0746046i
$545$	3.01434e15	−	1.74033e15i	0.115031	−	0.0664129i
$546$		0			0
$547$	1.05892e16	−	1.83410e16i	0.395311	−	0.684699i	−0.597830	−	0.801623i	$-0.703970\pi$
$547$	1.05892e16	−	1.83410e16i	0.395311	−	0.684699i	0.993141	+	0.116924i	$0.0373035\pi$
$548$			5.11034e15i			0.188698i
$549$		0			0
$550$	−4.26252e15			−0.153989
$551$	4.82658e16	+	2.78663e16i	1.72476	+	0.995793i
$552$		0			0
$553$	2.69929e15	+	4.67531e15i	0.0943842	+	0.163478i
$554$	2.32279e16	−	1.34107e16i	0.803437	−	0.463865i
$555$		0			0
$556$	1.00055e16	−	1.73299e16i	0.338679	−	0.586609i
$557$		−	2.16781e16i		−	0.725922i	−0.931804	−	0.362961i	$-0.881766\pi$
$557$		−	2.16781e16i		−	0.725922i	0.931804	−	0.362961i	$-0.118234\pi$
$558$		0			0
$559$	−8.99289e14			−0.0294733
$560$	2.03101e15	+	1.17260e15i	0.0658542	+	0.0380209i
$561$		0			0
$562$	−4.20590e15	−	7.28484e15i	−0.133488	−	0.231208i
$563$	−8.69551e15	+	5.02036e15i	−0.273052	+	0.157646i	−0.630274	−	0.776373i	$-0.717057\pi$
$563$	−8.69551e15	+	5.02036e15i	−0.273052	+	0.157646i	0.357222	+	0.934020i	$0.383724\pi$
$564$		0			0
$565$	−2.04935e16	+	3.54958e16i	−0.629978	+	1.09115i
$566$		−	2.97112e16i		−	0.903694i
$567$		0			0
$568$	−1.76889e16			−0.526759
$569$	4.34888e16	+	2.51083e16i	1.28146	+	0.739849i	0.977114	−	0.212714i	$-0.0682303\pi$
$569$	4.34888e16	+	2.51083e16i	1.28146	+	0.739849i	0.304341	+	0.952563i	$0.401564\pi$
$570$		0			0
$571$	−1.28741e16	−	2.22986e16i	−0.371450	−	0.643370i	0.618339	−	0.785911i	$-0.287806\pi$
$571$	−1.28741e16	−	2.22986e16i	−0.371450	−	0.643370i	−0.989789	+	0.142542i	$0.954473\pi$
$572$	2.43263e15	−	1.40448e15i	0.0694545	−	0.0400996i
$573$		0			0
$574$	−1.05663e15	+	1.83013e15i	−0.0295427	+	0.0511694i
$575$			7.04047e15i			0.194803i
$576$		0			0
$577$	−5.52293e16			−1.49663			−0.748315	−	0.663343i	$-0.769137\pi$
$577$	−5.52293e16			−1.49663			−0.748315	+	0.663343i	$0.769137\pi$
$578$	1.74115e16	+	1.00525e16i	0.466949	+	0.269593i
$579$		0			0
$580$	−1.22864e16	−	2.12807e16i	−0.322744	−	0.559009i
$581$	1.03736e16	−	5.98919e15i	0.269695	−	0.155708i
$582$		0			0
$583$	−4.97887e15	+	8.62366e15i	−0.126800	+	0.219624i
$584$			2.29059e16i			0.577390i
$585$		0			0
$586$	−3.62390e15			−0.0894934
$587$	4.55835e16	+	2.63176e16i	1.11424	+	0.643307i	0.939924	−	0.341383i	$-0.110895\pi$
$587$	4.55835e16	+	2.63176e16i	1.11424	+	0.643307i	0.174316	+	0.984690i	$0.444229\pi$
$588$		0			0
$589$	−2.31546e16	−	4.01050e16i	−0.554557	−	0.960521i
$590$	−2.51837e16	+	1.45398e16i	−0.597045	+	0.344704i
$591$		0			0
$592$	4.08706e15	−	7.07900e15i	0.0949470	−	0.164453i
$593$		−	2.05457e16i		−	0.472491i	−0.971693	−	0.236246i	$-0.924083\pi$
$593$		−	2.05457e16i		−	0.472491i	0.971693	−	0.236246i	$-0.0759170\pi$
$594$		0			0
$595$	−6.57694e15			−0.148225
$596$	−2.23256e15	−	1.28897e15i	−0.0498110	−	0.0287584i
$597$		0			0
$598$	−2.31980e15	−	4.01802e15i	−0.0507276	−	0.0878627i
$599$	−2.73072e16	+	1.57658e16i	−0.591174	+	0.341315i	−0.765562	−	0.643362i	$-0.777539\pi$
$599$	−2.73072e16	+	1.57658e16i	−0.591174	+	0.341315i	0.174387	+	0.984677i	$0.444205\pi$
$600$		0			0
$601$	−1.05207e16	+	1.82224e16i	−0.223253	+	0.386685i	−0.955794	−	0.294038i	$-0.905001\pi$
$601$	−1.05207e16	+	1.82224e16i	−0.223253	+	0.386685i	0.732541	+	0.680723i	$0.238334\pi$
$602$			7.28210e14i			0.0152995i
$603$		0			0
$604$	−2.03077e16			−0.418253
$605$	−4.01154e16	−	2.31607e16i	−0.818049	−	0.472301i
$606$		0			0
$607$	1.69260e16	+	2.93167e16i	0.338394	+	0.586115i	0.984131	−	0.177445i	$-0.0567832\pi$
$607$	1.69260e16	+	2.93167e16i	0.338394	+	0.586115i	−0.645737	+	0.763560i	$0.723450\pi$
$608$	1.44393e16	−	8.33655e15i	0.285842	−	0.165031i
$609$		0			0
$610$	−2.45377e16	+	4.25006e16i	−0.476272	+	0.824928i
$611$		−	2.08780e16i		−	0.401274i
$612$		0			0
$613$	−2.15758e16			−0.406634			−0.203317	−	0.979113i	$-0.565172\pi$
$613$	−2.15758e16			−0.406634			−0.203317	+	0.979113i	$0.565172\pi$
$614$	4.87646e16	+	2.81543e16i	0.910111	+	0.525453i
$615$		0			0
$616$	−1.13730e15	−	1.96986e15i	−0.0208156	−	0.0360537i
$617$	7.88954e16	−	4.55503e16i	1.43001	−	0.825619i	0.432894	−	0.901445i	$-0.357493\pi$
$617$	7.88954e16	−	4.55503e16i	1.43001	−	0.825619i	0.997121	+	0.0758257i	$0.0241593\pi$
$618$		0			0
$619$	4.48100e16	−	7.76131e16i	0.796582	−	1.37972i	−0.125247	−	0.992126i	$-0.539972\pi$
$619$	4.48100e16	−	7.76131e16i	0.796582	−	1.37972i	0.921829	−	0.387596i	$-0.126694\pi$
$620$			2.04181e16i			0.359472i
$621$		0			0
$622$	7.63340e16			1.31818
$623$	−1.60126e16	−	9.24488e15i	−0.273863	−	0.158115i
$624$		0			0
$625$	3.72160e16	+	6.44600e16i	0.624380	+	1.08146i
$626$	4.03484e16	−	2.32952e16i	0.670472	−	0.387097i
$627$		0			0
$628$	1.16868e16	−	2.02422e16i	0.190519	−	0.329989i
$629$			2.29237e16i			0.370153i
$630$		0			0
$631$	−2.78001e16			−0.440423			−0.220212	−	0.975452i	$-0.570675\pi$
$631$	−2.78001e16			−0.440423			−0.220212	+	0.975452i	$0.570675\pi$
$632$	−1.46553e16	−	8.46122e15i	−0.229981	−	0.132779i
$633$		0			0
$634$	3.76304e16	+	6.51778e16i	0.579434	+	1.00361i
$635$	−2.78571e16	+	1.60833e16i	−0.424907	+	0.245320i
$636$		0			0
$637$	−1.07135e16	+	1.85563e16i	−0.160359	+	0.277751i
$638$			2.38330e16i			0.353391i
$639$		0			0
$640$	−7.35129e15			−0.106975
$641$	−1.15223e17	−	6.65239e16i	−1.66108	−	0.959024i	−0.972202	−	0.234145i	$-0.924771\pi$
$641$	−1.15223e17	−	6.65239e16i	−1.66108	−	0.959024i	−0.688876	−	0.724879i	$-0.741896\pi$
$642$		0			0
$643$	1.52893e15	+	2.64818e15i	0.0216332	+	0.0374699i	0.876639	−	0.481148i	$-0.159780\pi$
$643$	1.52893e15	+	2.64818e15i	0.0216332	+	0.0374699i	−0.855006	+	0.518618i	$0.826447\pi$
$644$	−3.25364e15	+	1.87849e15i	−0.0456094	+	0.0263326i
$645$		0			0
$646$	−2.33792e16	+	4.04940e16i	−0.321688	+	0.557180i
$647$		−	2.59063e16i		−	0.353167i	−0.984286	−	0.176584i	$-0.943495\pi$
$647$		−	2.59063e16i		−	0.353167i	0.984286	−	0.176584i	$-0.0565046\pi$
$648$		0			0
$649$	2.82040e16			0.377436
$650$	7.34886e15	+	4.24286e15i	0.0974405	+	0.0562573i
$651$		0			0
$652$	−1.59239e16	−	2.75809e16i	−0.207283	−	0.359024i
$653$	−7.30712e16	+	4.21877e16i	−0.942469	+	0.544135i	−0.890733	−	0.454526i	$-0.849809\pi$
$653$	−7.30712e16	+	4.21877e16i	−0.942469	+	0.544135i	−0.0517357	+	0.998661i	$0.516475\pi$
$654$		0			0
$655$	1.04108e16	−	1.80320e16i	0.131836	−	0.228347i
$656$		−	6.62421e15i		−	0.0831211i
$657$		0			0
$658$	−1.69062e16			−0.208301
$659$	−7.89816e16	−	4.56001e16i	−0.964303	−	0.556741i	−0.0668085	−	0.997766i	$-0.521282\pi$
$659$	−7.89816e16	−	4.56001e16i	−0.964303	−	0.556741i	−0.897495	+	0.441025i	$0.854615\pi$
$660$		0			0
$661$	−1.19936e16	−	2.07735e16i	−0.143794	−	0.249058i	0.785128	−	0.619333i	$-0.212597\pi$
$661$	−1.19936e16	−	2.07735e16i	−0.143794	−	0.249058i	−0.928922	+	0.370275i	$0.879264\pi$
$662$	−9.08361e16	+	5.24443e16i	−1.07922	+	0.623089i
$663$		0			0
$664$	−1.87738e16	+	3.25171e16i	−0.219050	+	0.379405i
$665$			4.91148e16i			0.567914i
$666$		0			0
$667$	3.93653e16			0.447053
$668$	1.12703e16	+	6.50694e15i	0.126846	+	0.0732348i
$669$		0			0
$670$	1.30860e16	+	2.26657e16i	0.144664	+	0.250565i
$671$	4.12209e16	−	2.37989e16i	0.451630	−	0.260749i
$672$		0			0
$673$	4.73486e16	−	8.20101e16i	0.509585	−	0.882627i	−0.490353	−	0.871524i	$-0.663132\pi$
$673$	4.73486e16	−	8.20101e16i	0.509585	−	0.882627i	0.999938	−	0.0111033i	$-0.00353435\pi$
$674$		−	6.47955e16i		−	0.691171i
$675$		0			0
$676$	4.21225e16			0.441401
$677$	−5.03760e16	−	2.90846e16i	−0.523229	−	0.302086i	0.215026	−	0.976608i	$-0.431016\pi$
$677$	−5.03760e16	−	2.90846e16i	−0.523229	−	0.302086i	−0.738255	+	0.674522i	$0.764350\pi$
$678$		0			0
$679$	4.00611e15	+	6.93878e15i	0.0408793	+	0.0708051i
$680$	1.78541e16	−	1.03081e16i	0.180586	−	0.104261i
$681$		0			0
$682$	9.90167e15	−	1.71502e16i	0.0984016	−	0.170437i
$683$		−	2.07602e16i		−	0.204507i	−0.994758	−	0.102253i	$-0.967395\pi$
$683$		−	2.07602e16i		−	0.204507i	0.994758	−	0.102253i	$-0.0326052\pi$
$684$		0			0
$685$	4.71877e16			0.456757
$686$	3.10654e16	+	1.79356e16i	0.298080	+	0.172097i
$687$		0			0
$688$	−1.14133e15	−	1.97683e15i	−0.0107617	−	0.0186397i
$689$	1.71678e16	−	9.91182e15i	0.160472	−	0.0926484i
$690$		0			0
$691$	−3.62946e16	+	6.28641e16i	−0.333406	+	0.577477i	−0.983177	−	0.182653i	$-0.941531\pi$
$691$	−3.62946e16	+	6.28641e16i	−0.333406	+	0.577477i	0.649771	+	0.760130i	$0.274865\pi$
$692$			5.99876e16i			0.546292i
$693$		0			0
$694$	1.03203e17			0.923709
$695$	−1.60021e17	−	9.23880e16i	−1.41993	−	0.819798i
$696$		0			0
$697$	9.28854e15	+	1.60882e16i	0.0810123	+	0.140317i
$698$	3.95849e16	−	2.28544e16i	0.342292	−	0.197623i
$699$		0			0
$700$	3.43571e15	−	5.95083e15i	0.0292031	−	0.0505812i
$701$			1.74918e17i			1.47410i	0.675838	+	0.737050i	$0.263782\pi$
$701$			1.74918e17i			1.47410i	−0.675838	+	0.737050i	$0.736218\pi$
$702$		0			0
$703$	1.71188e17			1.41821
$704$	6.17472e15	+	3.56498e15i	0.0507202	+	0.0292833i
$705$		0			0
$706$	3.76542e15	+	6.52191e15i	0.0304079	+	0.0526679i
$707$	−4.18362e16	+	2.41541e16i	−0.334993	+	0.193408i
$708$		0			0
$709$	2.86875e16	−	4.96883e16i	0.225848	−	0.391180i	−0.730726	−	0.682671i	$-0.760818\pi$
$709$	2.86875e16	−	4.96883e16i	0.225848	−	0.391180i	0.956573	+	0.291491i	$0.0941515\pi$
$710$			1.63336e17i			1.27506i
$711$		0			0
$712$	5.79581e16			0.444871
$713$	−2.83272e16	−	1.63547e16i	−0.215609	−	0.124482i
$714$		0			0
$715$	−1.29687e16	−	2.24624e16i	−0.0970641	−	0.168120i
$716$	9.01323e16	−	5.20379e16i	0.668964	−	0.386226i
$717$		0			0
$718$	−6.04273e16	+	1.04663e17i	−0.441049	+	0.763919i
$719$		−	4.90100e16i		−	0.354741i	−0.984144	−	0.177370i	$-0.943241\pi$
$719$		−	4.90100e16i		−	0.354741i	0.984144	−	0.177370i	$-0.0567591\pi$
$720$		0			0
$721$	1.50054e16			0.106816
$722$	2.15654e17	+	1.24508e17i	1.52242	+	0.878969i
$723$		0			0
$724$	−7.13030e16	−	1.23500e17i	−0.495081	−	0.857506i
$725$	−6.23523e16	+	3.59991e16i	−0.429363	+	0.247893i
$726$		0			0
$727$	1.15805e17	−	2.00580e17i	0.784368	−	1.35856i	−0.145009	−	0.989430i	$-0.546321\pi$
$727$	1.15805e17	−	2.00580e17i	0.784368	−	1.35856i	0.929376	−	0.369134i	$-0.120346\pi$
$728$			4.52821e15i			0.0304185i
$729$		0			0
$730$	2.11507e17			1.39762
$731$	5.54388e15	+	3.20076e15i	0.0363337	+	0.0209773i
$732$		0			0
$733$	7.53058e16	+	1.30434e17i	0.485517	+	0.840941i	0.999861	−	0.0166433i	$-0.00529796\pi$
$733$	7.53058e16	+	1.30434e17i	0.485517	+	0.840941i	−0.514344	+	0.857584i	$0.671965\pi$
$734$	6.50830e16	−	3.75757e16i	0.416190	−	0.240287i
$735$		0			0
$736$	5.88832e15	−	1.01989e16i	0.0370446	−	0.0641631i
$737$		−	2.53840e16i		−	0.158400i
$738$		0			0
$739$	3.92960e16			0.241258			0.120629	−	0.992698i	$-0.461509\pi$
$739$	3.92960e16			0.241258			0.120629	+	0.992698i	$0.461509\pi$
$740$	−6.53659e16	−	3.77390e16i	−0.398071	−	0.229827i
$741$		0			0
$742$	−8.02622e15	−	1.39018e16i	−0.0480936	−	0.0833006i
$743$	3.69092e15	−	2.13096e15i	0.0219383	−	0.0126661i	−0.488991	−	0.872289i	$-0.662635\pi$
$743$	3.69092e15	−	2.13096e15i	0.0219383	−	0.0126661i	0.510929	+	0.859623i	$0.329301\pi$
$744$		0			0
$745$	−1.19020e16	+	2.06149e16i	−0.0696119	+	0.120571i
$746$			1.61267e17i			0.935647i
$747$		0			0
$748$	−1.99954e16			−0.114162
$749$	−7.11086e15	−	4.10546e15i	−0.0402746	−	0.0232526i
$750$		0			0
$751$	1.31112e17	+	2.27092e17i	0.730806	+	1.26579i	0.956539	+	0.291604i	$0.0941888\pi$
$751$	1.31112e17	+	2.27092e17i	0.730806	+	1.26579i	−0.225733	+	0.974189i	$0.572478\pi$
$752$	4.58944e16	−	2.64971e16i	0.253777	−	0.146518i
$753$		0			0
$754$	2.37231e16	−	4.10896e16i	0.129105	−	0.223617i
$755$			1.87517e17i			1.01241i
$756$		0			0
$757$	3.06475e17			1.62862			0.814309	−	0.580432i	$-0.197116\pi$
$757$	3.06475e17			1.62862			0.814309	+	0.580432i	$0.197116\pi$
$758$	−2.11529e16	−	1.22126e16i	−0.111520	−	0.0643864i
$759$		0			0
$760$	−7.69778e16	−	1.33329e17i	−0.399470	−	0.691902i
$761$	−6.37043e15	+	3.67797e15i	−0.0327990	+	0.0189365i	−0.516310	−	0.856402i	$-0.672695\pi$
$761$	−6.37043e15	+	3.67797e15i	−0.0327990	+	0.0189365i	0.483511	+	0.875338i	$0.339361\pi$
$762$		0			0
$763$	2.72104e15	−	4.71297e15i	0.0137907	−	0.0238862i
$764$			4.62726e16i			0.232683i
$765$		0			0
$766$	5.32650e16			0.263675
$767$	−4.86255e16	−	2.80740e16i	−0.238832	−	0.137890i
$768$		0			0
$769$	4.18161e16	+	7.24275e16i	0.202202	+	0.350224i	0.949238	−	0.314560i	$-0.101857\pi$
$769$	4.18161e16	+	7.24275e16i	0.202202	+	0.350224i	−0.747036	+	0.664784i	$0.768524\pi$
$770$	−1.81892e16	+	1.05015e16i	−0.0872708	+	0.0503858i
$771$		0			0
$772$	3.75907e16	−	6.51090e16i	0.177573	−	0.307565i
$773$		−	3.28068e17i		−	1.53775i	−0.639397	−	0.768877i	$-0.720816\pi$
$773$		−	3.28068e17i		−	1.53775i	0.639397	−	0.768877i	$-0.279184\pi$
$774$		0			0
$775$	5.98248e16			0.276103
$776$	−2.17503e16	−	1.25576e16i	−0.0996084	−	0.0575089i
$777$		0			0
$778$	6.14786e16	+	1.06484e17i	0.277234	+	0.480184i
$779$	1.20142e17	−	6.93643e16i	0.537616	−	0.310392i
$780$		0			0
$781$	7.92089e16	−	1.37194e17i	0.349034	−	0.604545i
$782$			3.30267e16i			0.144419i
$783$		0			0
$784$	−5.43878e16			−0.234210
$785$	−1.86912e17	−	1.07914e17i	−0.798764	−	0.461167i
$786$		0			0
$787$	1.05244e17	+	1.82287e17i	0.442943	+	0.767200i	0.997906	−	0.0646751i	$-0.0206011\pi$
$787$	1.05244e17	+	1.82287e17i	0.442943	+	0.767200i	−0.554963	+	0.831875i	$0.687268\pi$
$788$	1.83723e17	−	1.06073e17i	0.767374	−	0.443043i
$789$		0			0
$790$	−7.81289e16	+	1.35323e17i	−0.321403	+	0.556686i
$791$			6.40839e16i			0.261632i
$792$		0			0
$793$	−9.47566e16			−0.381040
$794$	1.04811e17	+	6.05127e16i	0.418296	+	0.241504i
$795$		0			0
$796$	−1.04997e17	−	1.81860e17i	−0.412760	−	0.714921i
$797$	1.24332e17	−	7.17832e16i	0.485103	−	0.280074i	−0.237438	−	0.971403i	$-0.576308\pi$
$797$	1.24332e17	−	7.17832e16i	0.485103	−	0.280074i	0.722541	+	0.691329i	$0.242974\pi$
$798$		0			0
$799$	−7.43091e16	+	1.28707e17i	−0.285602	+	0.494677i
$800$			2.15392e16i			0.0821656i
$801$		0			0
$802$	−6.64734e16			−0.249805
$803$	−1.77656e17	−	1.02570e17i	−0.662653	−	0.382583i
$804$		0			0
$805$	1.73455e16	+	3.00434e16i	0.0637401	+	0.110401i
$806$	−3.41422e16	+	1.97120e16i	−0.124532	+	0.0718986i
$807$		0			0
$808$	7.57137e16	−	1.31140e17i	0.272086	−	0.471267i
$809$		−	3.15573e17i		−	1.12566i	−0.826572	−	0.562831i	$-0.809712\pi$
$809$		−	3.15573e17i		−	1.12566i	0.826572	−	0.562831i	$-0.190288\pi$
$810$		0			0
$811$	−4.48547e17			−1.57646			−0.788230	−	0.615381i	$-0.789002\pi$
$811$	−4.48547e17			−1.57646			−0.788230	+	0.615381i	$0.789002\pi$
$812$	−3.32728e16	−	1.92101e16i	−0.116079	−	0.0670182i
$813$		0			0
$814$	3.66027e16	+	6.33978e16i	0.125825	+	0.217935i
$815$	−2.54676e17	+	1.47037e17i	−0.869045	+	0.501743i
$816$		0			0
$817$	2.39024e16	−	4.14002e16i	0.0803728	−	0.139210i
$818$		−	9.19574e16i		−	0.306950i
$819$		0			0
$820$	−6.11664e16			−0.201201
$821$	−5.01232e16	−	2.89386e16i	−0.163674	−	0.0944972i	0.415926	−	0.909399i	$-0.363458\pi$
$821$	−5.01232e16	−	2.89386e16i	−0.163674	−	0.0944972i	−0.579600	+	0.814901i	$0.696791\pi$
$822$		0			0
$823$	1.29235e17	+	2.23841e17i	0.415891	+	0.720345i	0.995522	−	0.0945348i	$-0.0301364\pi$
$823$	1.29235e17	+	2.23841e17i	0.415891	+	0.720345i	−0.579630	+	0.814880i	$0.696803\pi$
$824$	−4.07345e16	+	2.35181e16i	−0.130136	+	0.0751343i
$825$		0			0
$826$	−2.27332e16	+	3.93751e16i	−0.0715782	+	0.123977i
$827$		−	8.14460e16i		−	0.254587i	−0.991865	−	0.127294i	$-0.959371\pi$
$827$		−	8.14460e16i		−	0.254587i	0.991865	−	0.127294i	$-0.0406290\pi$
$828$		0			0
$829$	−4.74541e17			−1.46200			−0.730999	−	0.682378i	$-0.760946\pi$
$829$	−4.74541e17			−1.46200			−0.730999	+	0.682378i	$0.760946\pi$
$830$	3.00256e17	+	1.73353e17i	0.918380	+	0.530227i
$831$		0			0
$832$	−7.09707e15	−	1.22925e16i	−0.0213963	−	0.0370595i
$833$	1.32092e17	−	7.62632e16i	0.395372	−	0.228268i
$834$		0			0
$835$	6.00835e16	−	1.04068e17i	0.177271	−	0.307042i
$836$			1.49320e17i			0.437402i
$837$		0			0
$838$	2.25962e16			0.0652487
$839$	−8.85816e16	−	5.11426e16i	−0.253964	−	0.146626i	0.367614	−	0.929978i	$-0.380175\pi$
$839$	−8.85816e16	−	5.11426e16i	−0.253964	−	0.146626i	−0.621578	+	0.783352i	$0.713508\pi$
$840$		0			0
$841$	2.43744e16	+	4.22177e16i	0.0688902	+	0.119321i
$842$	3.12582e17	−	1.80469e17i	0.877186	−	0.506444i
$843$		0			0
$844$	−4.65722e16	+	8.06655e16i	−0.128846	+	0.223169i
$845$		−	3.88949e17i		−	1.06845i
$846$		0			0
$847$	−7.24242e16			−0.196148
$848$	4.35767e16	+	2.51590e16i	0.117187	+	0.0676579i
$849$		0			0
$850$	−3.02025e16	−	5.23123e16i	−0.0800810	−	0.138704i
$851$	1.04715e17	−	6.04572e16i	0.275697	−	0.159174i
$852$		0			0
$853$	1.96344e17	−	3.40077e17i	0.509710	−	0.882843i	−0.490227	−	0.871595i	$-0.663086\pi$
$853$	1.96344e17	−	3.40077e17i	0.509710	−	0.882843i	0.999937	−	0.0112481i	$-0.00358046\pi$
$854$			7.67304e16i			0.197797i
$855$		0			0
$856$	2.57380e16			0.0654232
$857$	−8.22469e15	−	4.74852e15i	−0.0207603	−	0.0119860i	0.489584	−	0.871956i	$-0.337149\pi$
$857$	−8.22469e15	−	4.74852e15i	−0.0207603	−	0.0119860i	−0.510344	+	0.859970i	$0.670482\pi$
$858$		0			0
$859$	5.25707e16	+	9.10552e16i	0.130853	+	0.226645i	0.924006	−	0.382378i	$-0.124895\pi$
$859$	5.25707e16	+	9.10552e16i	0.130853	+	0.226645i	−0.793152	+	0.609023i	$0.791562\pi$
$860$	−1.82536e16	+	1.05387e16i	−0.0451189	+	0.0260494i
$861$		0			0
$862$	−9.86526e16	+	1.70871e17i	−0.240472	+	0.416510i
$863$			5.06978e17i			1.22722i	0.789608	+	0.613612i	$0.210284\pi$
$863$			5.06978e17i			1.22722i	−0.789608	+	0.613612i	$0.789716\pi$
$864$		0			0
$865$	5.53912e17			1.32234
$866$	2.42871e17	+	1.40222e17i	0.575796	+	0.332436i
$867$		0			0
$868$	1.59620e16	+	2.76471e16i	0.0373224	+	0.0646444i
$869$	1.31249e17	−	7.57765e16i	0.304773	−	0.175961i
$870$		0			0
$871$	−2.52670e16	+	4.37637e16i	−0.0578688	+	0.100232i
$872$			1.70588e16i			0.0388015i
$873$		0			0
$874$	2.46634e17			0.553331
$875$	6.32716e16	+	3.65299e16i	0.140981	+	0.0813954i
$876$		0			0
$877$	−3.12625e17	−	5.41482e17i	−0.687110	−	1.19011i	−0.972769	−	0.231778i	$-0.925546\pi$
$877$	−3.12625e17	−	5.41482e17i	−0.687110	−	1.19011i	0.285659	−	0.958331i	$-0.407788\pi$
$878$	−3.34294e17	+	1.93005e17i	−0.729728	+	0.421309i
$879$		0			0
$880$	3.29182e16	−	5.70160e16i	0.0708826	−	0.122772i
$881$		−	6.69837e16i		−	0.143256i	−0.997431	−	0.0716281i	$-0.977181\pi$
$881$		−	6.69837e16i		−	0.143256i	0.997431	−	0.0716281i	$-0.0228195\pi$
$882$		0			0
$883$	−9.02336e17			−1.90372			−0.951862	−	0.306528i	$-0.900833\pi$
$883$	−9.02336e17			−1.90372			−0.951862	+	0.306528i	$0.900833\pi$
$884$	3.44733e16	+	1.99032e16i	0.0722386	+	0.0417070i
$885$		0			0
$886$	1.20472e17	+	2.08663e17i	0.249048	+	0.431364i
$887$	2.97400e17	−	1.71704e17i	0.610661	−	0.352565i	−0.162563	−	0.986698i	$-0.551976\pi$
$887$	2.97400e17	−	1.71704e17i	0.610661	−	0.352565i	0.773224	+	0.634133i	$0.218643\pi$
$888$		0			0
$889$	−2.51465e16	+	4.35551e16i	−0.0509410	+	0.0882324i
$890$		−	5.35172e17i		−	1.07685i
$891$		0			0
$892$	−3.58248e17			−0.711205
$893$	9.61150e17	+	5.54920e17i	1.89532	+	1.09426i
$894$		0			0
$895$	−4.80506e17	−	8.32261e17i	−0.934891	−	1.61928i
$896$	−9.95400e15	+	5.74694e15i	−0.0192375	+	0.0111068i
$897$		0			0
$898$	−2.72014e17	+	4.71143e17i	−0.518721	+	0.898451i
$899$		−	3.34498e17i		−	0.633630i
$900$		0			0
$901$	−1.41113e17			−0.263766
$902$	5.13768e16	+	2.96624e16i	0.0953954	+	0.0550766i
$903$		0			0
$904$	−1.00439e17	−	1.73965e17i	−0.184031	−	0.318751i
$905$	−1.14037e18	+	6.58396e17i	−2.07566	+	1.19838i
$906$		0			0
$907$	−4.89958e17	+	8.48633e17i	−0.880066	+	1.52432i	−0.0288003	+	0.999585i	$0.509169\pi$
$907$	−4.89958e17	+	8.48633e17i	−0.880066	+	1.52432i	−0.851266	+	0.524734i	$0.824165\pi$
$908$			4.86927e17i			0.868858i
$909$		0			0
$910$	4.18124e16			0.0736303
$911$	4.50307e17	+	2.59985e17i	0.787769	+	0.454819i	0.839176	−	0.543859i	$-0.183037\pi$
$911$	4.50307e17	+	2.59985e17i	0.787769	+	0.454819i	−0.0514076	+	0.998678i	$0.516371\pi$
$912$		0			0
$913$	−1.68133e17	−	2.91215e17i	−0.290288	−	0.502793i
$914$	−3.88888e17	+	2.24524e17i	−0.667032	+	0.385111i
$915$		0			0
$916$	1.79875e17	−	3.11553e17i	0.304508	−	0.527423i
$917$		−	3.25549e16i		−	0.0547520i
$918$		0			0
$919$	−4.23574e17			−0.703131			−0.351566	−	0.936163i	$-0.614351\pi$
$919$	−4.23574e17			−0.703131			−0.351566	+	0.936163i	$0.614351\pi$
$920$	−9.41741e16	−	5.43714e16i	−0.155312	−	0.0896693i
$921$		0			0
$922$	2.88085e17	+	4.98978e17i	0.468959	+	0.812261i
$923$	−2.73122e17	+	1.57687e17i	−0.441720	+	0.255027i
$924$		0			0
$925$	−1.10575e17	+	1.91521e17i	−0.176525	+	0.305750i
$926$		−	8.48748e17i		−	1.34621i
$927$		0			0
$928$	1.20432e17			0.188562
$929$	2.16408e16	+	1.24943e16i	0.0336650	+	0.0194365i	0.516738	−	0.856144i	$-0.327146\pi$
$929$	2.16408e16	+	1.24943e16i	0.0336650	+	0.0194365i	−0.483073	+	0.875580i	$0.660479\pi$
$930$		0			0
$931$	−5.69512e17	−	9.86424e17i	−0.874591	−	1.51484i
$932$	6.14971e16	−	3.55053e16i	0.0938337	−	0.0541749i
$933$		0			0
$934$	−7.61121e16	+	1.31830e17i	−0.114650	+	0.198579i
$935$			1.84633e17i			0.276337i
$936$		0			0
$937$	−5.29055e17			−0.781741			−0.390871	−	0.920446i	$-0.627826\pi$
$937$	−5.29055e17			−0.781741			−0.390871	+	0.920446i	$0.627826\pi$
$938$	3.54382e16	+	2.04602e16i	0.0520301	+	0.0300396i
$939$		0			0
$940$	−2.44668e17	−	4.23778e17i	−0.354659	−	0.614287i
$941$	3.07927e17	−	1.77782e17i	0.443517	−	0.256065i	−0.261571	−	0.965184i	$-0.584241\pi$
$941$	3.07927e17	−	1.77782e17i	0.443517	−	0.256065i	0.705088	+	0.709119i	$0.250907\pi$
$942$		0			0
$943$	4.89938e16	−	8.48598e16i	0.0696740	−	0.120679i
$944$		−	1.42519e17i		−	0.201392i
$945$		0			0
$946$	2.04429e16			0.0285230
$947$	−3.11884e16	−	1.80066e16i	−0.0432407	−	0.0249651i	0.478224	−	0.878238i	$-0.341281\pi$
$947$	−3.11884e16	−	1.80066e16i	−0.0432407	−	0.0249651i	−0.521465	+	0.853273i	$0.674614\pi$
$948$		0			0
$949$	2.04193e17	+	3.53673e17i	0.279540	+	0.484177i
$950$	−3.90654e17	+	2.25544e17i	−0.531435	+	0.306824i
$951$		0			0
$952$	1.61168e16	−	2.79152e16i	0.0216500	−	0.0374989i
$953$		−	1.18677e17i		−	0.158420i	−0.996858	−	0.0792099i	$-0.974760\pi$
$953$		−	1.18677e17i		−	0.158420i	0.996858	−	0.0792099i	$-0.0252397\pi$
$954$		0			0
$955$	4.27271e17			0.563226
$956$	−1.32548e17	−	7.65269e16i	−0.173631	−	0.100246i
$957$		0			0
$958$	−1.92705e17	−	3.33775e17i	−0.249287	−	0.431778i
$959$	6.38944e16	−	3.68894e16i	0.0821393	−	0.0474231i
$960$		0			0
$961$	2.54861e17	−	4.41432e17i	0.323566	−	0.560432i
$962$		−	1.45736e17i		−	0.183872i
$963$		0			0
$964$	−6.67599e17			−0.831866
$965$	−6.01202e17	−	3.47104e17i	−0.744485	−	0.429829i
$966$		0			0
$967$	7.37615e17	+	1.27759e18i	0.902134	+	1.56254i	0.824719	+	0.565542i	$0.191333\pi$
$967$	7.37615e17	+	1.27759e18i	0.902134	+	1.56254i	0.0774140	+	0.996999i	$0.475334\pi$
$968$	1.96606e17	−	1.13511e17i	0.238971	−	0.137970i
$969$		0			0
$970$	−1.15954e17	+	2.00838e17i	−0.139205	+	0.241110i
$971$		−	5.85570e17i		−	0.698656i	−0.937000	−	0.349328i	$-0.886410\pi$
$971$		−	5.85570e17i		−	0.698656i	0.937000	−	0.349328i	$-0.113590\pi$
$972$		0			0
$973$	−2.88901e17			−0.340464
$974$	−2.24119e17	−	1.29395e17i	−0.262497	−	0.151553i
$975$		0			0
$976$	−1.20260e17	−	2.08296e17i	−0.139130	−	0.240981i
$977$	−1.04426e18	+	6.02903e17i	−1.20072	+	0.693234i	−0.960715	−	0.277538i	$-0.910482\pi$
$977$	−1.04426e18	+	6.02903e17i	−1.20072	+	0.693234i	−0.240002	+	0.970772i	$0.577148\pi$
$978$		0			0
$979$	−2.59529e17	+	4.49518e17i	−0.294775	+	0.510564i
$980$			5.02204e17i			0.566923i
$981$		0			0
$982$	−3.83759e17			−0.427947
$983$	−5.86905e17	−	3.38850e17i	−0.650499	−	0.375566i	0.138148	−	0.990412i	$-0.455885\pi$
$983$	−5.86905e17	−	3.38850e17i	−0.650499	−	0.375566i	−0.788647	+	0.614846i	$0.789218\pi$
$984$		0			0
$985$	−9.79451e17	−	1.69646e18i	−1.07242	−	1.85749i
$986$	−2.92493e17	+	1.68871e17i	−0.318313	+	0.183778i
$987$		0			0
$988$	1.48631e17	−	2.57437e17i	0.159797	−	0.276777i
$989$		−	3.37658e16i		−	0.0360827i
$990$		0			0
$991$	−2.10263e17			−0.221984			−0.110992	−	0.993821i	$-0.535403\pi$
$991$	−2.10263e17			−0.221984			−0.110992	+	0.993821i	$0.535403\pi$
$992$	−8.66627e16	−	5.00347e16i	−0.0909415	−	0.0525051i
$993$		0			0
$994$	1.27689e17	+	2.21164e17i	0.132384	+	0.229296i
$995$	−1.67925e18	+	9.69515e17i	−1.73052	+	0.999117i
$996$		0			0
$997$	−5.51416e17	+	9.55080e17i	−0.561446	+	0.972454i	0.435924	+	0.899983i	$0.356422\pi$
$997$	−5.51416e17	+	9.55080e17i	−0.561446	+	0.972454i	−0.997371	+	0.0724703i	$0.976912\pi$
$998$		−	3.40832e17i		−	0.344951i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.13.d.h.107.9		24
3.2	odd	2	inner	162.13.d.h.107.4		24
9.2	odd	6		162.13.b.a.161.8	yes	12
9.4	even	3	inner	162.13.d.h.53.4		24
9.5	odd	6	inner	162.13.d.h.53.9		24
9.7	even	3		162.13.b.a.161.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.13.b.a.161.5	✓	12	9.7	even	3
162.13.b.a.161.8	yes	12	9.2	odd	6
162.13.d.h.53.4		24	9.4	even	3	inner
162.13.d.h.53.9		24	9.5	odd	6	inner
162.13.d.h.107.4		24	3.2	odd	2	inner
162.13.d.h.107.9		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(16377.2 - 9455.38i) q^{5} +(14783.7 - 25606.1i) q^{7} +92681.9i q^{8} +855803. q^{10} +(-718832. - 415018. i) q^{11} +(826208. + 1.43103e6i) q^{13} +(1.15880e6 - 669032. i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -1.17626e7i q^{17} -8.78398e7 q^{19} +(3.35405e7 + 1.93646e7i) q^{20} +(-1.87816e7 - 3.25306e7i) q^{22} +(-5.37313e7 + 3.10218e7i) q^{23} +(5.67381e7 - 9.82733e7i) q^{25} +7.47798e7i q^{26} +6.05539e7 q^{28} +(-5.49475e8 - 3.17239e8i) q^{29} +(2.63601e8 + 4.56570e8i) q^{31} +(-1.64382e8 + 9.49063e7i) q^{32} +(2.66157e8 - 4.60998e8i) q^{34} -5.59141e8i q^{35} -1.94886e9 q^{37} +(-3.44260e9 - 1.98759e9i) q^{38} +(8.76343e8 + 1.51787e9i) q^{40} +(-1.36774e9 + 7.89668e8i) q^{41} +(-2.72113e8 + 4.71314e8i) q^{43} -1.69991e9i q^{44} -2.80777e9 q^{46} +(-1.09421e10 - 6.31741e9i) q^{47} +(6.48353e9 + 1.12298e10i) q^{49} +(4.44734e9 - 2.56767e9i) q^{50} +(-1.69207e9 + 2.93076e9i) q^{52} -1.19968e10i q^{53} -1.56966e10 q^{55} +(2.37322e9 + 1.37018e9i) q^{56} +(-1.43566e10 - 2.48664e10i) q^{58} +(-2.94269e10 + 1.69896e10i) q^{59} +(-2.86722e10 + 4.96616e10i) q^{61} +2.38584e10i q^{62} -8.58993e9 q^{64} +(2.70619e10 + 1.56242e10i) q^{65} +(1.52909e10 + 2.64847e10i) q^{67} +(2.08624e10 - 1.20449e10i) q^{68} +(1.26519e10 - 2.19137e10i) q^{70} +1.90857e11i q^{71} +2.47145e11 q^{73} +(-7.63796e10 - 4.40978e10i) q^{74} +(-8.99480e10 - 1.55795e11i) q^{76} +(-2.12539e10 + 1.22710e10i) q^{77} +(-9.12931e10 + 1.58124e11i) q^{79} +7.93175e10i q^{80} -7.14726e10 q^{82} +(3.50846e11 + 2.02561e11i) q^{83} +(-1.11220e11 - 1.92638e11i) q^{85} +(-2.13292e10 + 1.23144e10i) q^{86} +(3.84646e10 - 6.66227e10i) q^{88} -6.25344e11i q^{89} +4.88575e10 q^{91} +(-1.10042e11 - 6.35326e10i) q^{92} +(-2.85893e11 - 4.95182e11i) q^{94} +(-1.43857e12 + 8.30559e11i) q^{95} +(-1.35491e11 + 2.34677e11i) q^{97} +5.86822e11i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24576 q^{4} + 220224 q^{7} + 758016 q^{10} + 2372808 q^{13} - 50331648 q^{16} + 285339360 q^{19} - 70253568 q^{22} + 727623852 q^{25} + 902037504 q^{28} - 577374720 q^{31} - 2238076800 q^{34} - 6056330712 q^{37}+ \cdots + 2570481096384 q^{97}+O(q^{100}) \) 24 * q + 24576 * q^4 + 220224 * q^7 + 758016 * q^10 + 2372808 * q^13 - 50331648 * q^16 + 285339360 * q^19 - 70253568 * q^22 + 727623852 * q^25 + 902037504 * q^28 - 577374720 * q^31 - 2238076800 * q^34 - 6056330712 * q^37 + 776208384 * q^40 - 33702957168 * q^43 - 49846440960 * q^46 - 72166762836 * q^49 - 4859510784 * q^52 - 316402444512 * q^55 + 21247000704 * q^58 - 213044029980 * q^61 - 206158430208 * q^64 - 70227468528 * q^67 + 251325402624 * q^70 + 99306462720 * q^73 + 292187504640 * q^76 + 696725200560 * q^79 + 1471123266048 * q^82 + 271807264548 * q^85 + 143879307264 * q^88 + 1458470433408 * q^91 - 1211537346048 * q^94 + 2570481096384 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more