LMFDB - Embedded newform 36.13.d.d.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,13,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	36.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.9037774219$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1570 x^{10} - 4077 x^{9} + 1884069 x^{8} - 3551868 x^{7} + 881574992 x^{6} + \cdots + 104882177440000 $ x^12 - 3x^11 + 1570x^10 - 4077x^9 + 1884069x^8 - 3551868x^7 + 881574992x^6 + 2167220880x^5 + 304613421264x^4 + 27792635520x^3 + 5806366144000x^2 + 1120796928000*x + 104882177440000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{63}\cdot 3^{27} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.12
Root			$14.6572 + 25.3870i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.13.d.d.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(62.3881 + 14.2733i) q^{2} +(3688.55 + 1780.96i) q^{4} +21622.0 q^{5} -155240. i q^{7} +(204701. + 163759. i) q^{8} +O(q^{10})$	\(q+(62.3881 + 14.2733i) q^{2} +(3688.55 + 1780.96i) q^{4} +21622.0 q^{5} -155240. i q^{7} +(204701. + 163759. i) q^{8} +(1.34896e6 + 308617. i) q^{10} -3.12388e6i q^{11} +1.10272e6 q^{13} +(2.21578e6 - 9.68513e6i) q^{14} +(1.04336e7 + 1.31383e7i) q^{16} -3.10754e7 q^{17} +2.82999e7i q^{19} +(7.97538e7 + 3.85080e7i) q^{20} +(4.45879e7 - 1.94893e8i) q^{22} -1.30643e8i q^{23} +2.23371e8 q^{25} +(6.87969e7 + 1.57395e7i) q^{26} +(2.76477e8 - 5.72610e8i) q^{28} +7.45018e8 q^{29} +3.42331e8i q^{31} +(4.63403e8 + 9.68597e8i) q^{32} +(-1.93873e9 - 4.43547e8i) q^{34} -3.35660e9i q^{35} +1.27314e9 q^{37} +(-4.03931e8 + 1.76557e9i) q^{38} +(4.42605e9 + 3.54079e9i) q^{40} +8.57107e8 q^{41} +6.63854e9i q^{43} +(5.56351e9 - 1.15226e10i) q^{44} +(1.86470e9 - 8.15056e9i) q^{46} +7.75614e9i q^{47} -1.02582e10 q^{49} +(1.39357e10 + 3.18823e9i) q^{50} +(4.06745e9 + 1.96391e9i) q^{52} +1.80788e10 q^{53} -6.75445e10i q^{55} +(2.54219e10 - 3.17778e10i) q^{56} +(4.64803e10 + 1.06338e10i) q^{58} +6.86310e9i q^{59} +2.30252e10 q^{61} +(-4.88618e9 + 2.13574e10i) q^{62} +(1.50858e10 + 6.70432e10i) q^{64} +2.38431e10 q^{65} +1.09125e11i q^{67} +(-1.14623e11 - 5.53441e10i) q^{68} +(4.79097e10 - 2.09412e11i) q^{70} -2.98952e10i q^{71} -2.57691e11 q^{73} +(7.94288e10 + 1.81719e10i) q^{74} +(-5.04010e10 + 1.04385e11i) q^{76} -4.84951e11 q^{77} +3.42810e11i q^{79} +(2.25594e11 + 2.84077e11i) q^{80} +(5.34733e10 + 1.22337e10i) q^{82} +5.68292e10i q^{83} -6.71912e11 q^{85} +(-9.47536e10 + 4.14166e11i) q^{86} +(5.11561e11 - 6.39462e11i) q^{88} -6.63679e11 q^{89} -1.71187e11i q^{91} +(2.32670e11 - 4.81883e11i) q^{92} +(-1.10705e11 + 4.83891e11i) q^{94} +6.11900e11i q^{95} -9.94906e11 q^{97} +(-6.39989e11 - 1.46418e11i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 90 q^{2} - 4692 q^{4} + 10296 q^{5} + 648000 q^{8}+O(q^{10}) $ 12 * q + 90 * q^2 - 4692 * q^4 + 10296 * q^5 + 648000 * q^8	$ 12 q + 90 q^{2} - 4692 q^{4} + 10296 q^{5} + 648000 q^{8} + 923028 q^{10} + 2094840 q^{13} - 15389208 q^{14} - 61526928 q^{16} + 12097800 q^{17} + 377644248 q^{20} + 482545560 q^{22} + 1058748132 q^{25} - 243358236 q^{26} - 185369520 q^{28} - 1997608680 q^{29} - 1733536800 q^{32} - 7816269348 q^{34} - 960170280 q^{37} + 8280525240 q^{38} + 3985807104 q^{40} - 5806392696 q^{41} - 4989496464 q^{44} + 4149450240 q^{46} - 60479071668 q^{49} - 68552901522 q^{50} - 31090133640 q^{52} - 42482511720 q^{53} + 38053468224 q^{56} + 159666562500 q^{58} + 137368568088 q^{61} + 27876030840 q^{62} + 188355529344 q^{64} + 328250713392 q^{65} - 77938316280 q^{68} - 454939318704 q^{70} - 804477880680 q^{73} + 502785766548 q^{74} + 143972453808 q^{76} - 1383727360320 q^{77} + 417712547808 q^{80} + 460673773020 q^{82} + 1437981718224 q^{85} - 1255416205464 q^{86} + 47622991680 q^{88} + 1422946205928 q^{89} + 3462722444160 q^{92} + 847910842896 q^{94} - 4056673857000 q^{97} - 1702751294790 q^{98}+O(q^{100}) $ 12 * q + 90 * q^2 - 4692 * q^4 + 10296 * q^5 + 648000 * q^8 + 923028 * q^10 + 2094840 * q^13 - 15389208 * q^14 - 61526928 * q^16 + 12097800 * q^17 + 377644248 * q^20 + 482545560 * q^22 + 1058748132 * q^25 - 243358236 * q^26 - 185369520 * q^28 - 1997608680 * q^29 - 1733536800 * q^32 - 7816269348 * q^34 - 960170280 * q^37 + 8280525240 * q^38 + 3985807104 * q^40 - 5806392696 * q^41 - 4989496464 * q^44 + 4149450240 * q^46 - 60479071668 * q^49 - 68552901522 * q^50 - 31090133640 * q^52 - 42482511720 * q^53 + 38053468224 * q^56 + 159666562500 * q^58 + 137368568088 * q^61 + 27876030840 * q^62 + 188355529344 * q^64 + 328250713392 * q^65 - 77938316280 * q^68 - 454939318704 * q^70 - 804477880680 * q^73 + 502785766548 * q^74 + 143972453808 * q^76 - 1383727360320 * q^77 + 417712547808 * q^80 + 460673773020 * q^82 + 1437981718224 * q^85 - 1255416205464 * q^86 + 47622991680 * q^88 + 1422946205928 * q^89 + 3462722444160 * q^92 + 847910842896 * q^94 - 4056673857000 * q^97 - 1702751294790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	62.3881	+	14.2733i	0.974814	+	0.223020i
$2$	62.3881	+	14.2733i	0.974814	+	0.223020i
$3$		0			0
$3$		0			0
$4$	3688.55	+	1780.96i	0.900524	+	0.434805i
$5$	21622.0			1.38381			0.691904	−	0.721989i	$-0.256772\pi$
$5$	21622.0			1.38381			0.691904	+	0.721989i	$0.256772\pi$
$6$		0			0
$7$		−	155240.i		−	1.31952i	−0.751477	−	0.659759i	$-0.770658\pi$
$7$		−	155240.i		−	1.31952i	0.751477	−	0.659759i	$-0.229342\pi$
$8$	204701.	+	163759.i	0.780874	+	0.624689i
$9$		0			0
$10$	1.34896e6	+	308617.i	1.34896	+	0.308617i
$11$		−	3.12388e6i		−	1.76335i	−0.471860	−	0.881673i	$-0.656417\pi$
$11$		−	3.12388e6i		−	1.76335i	0.471860	−	0.881673i	$-0.343583\pi$
$12$		0			0
$13$	1.10272e6			0.228458			0.114229	−	0.993454i	$-0.463560\pi$
$13$	1.10272e6			0.228458			0.114229	+	0.993454i	$0.463560\pi$
$14$	2.21578e6	−	9.68513e6i	0.294279	−	1.28629i
$15$		0			0
$16$	1.04336e7	+	1.31383e7i	0.621888	+	0.783106i
$17$	−3.10754e7			−1.28743			−0.643714	−	0.765267i	$-0.722607\pi$
$17$	−3.10754e7			−1.28743			−0.643714	+	0.765267i	$0.722607\pi$
$18$		0			0
$19$			2.82999e7i			0.601537i	0.953697	+	0.300769i	$0.0972432\pi$
$19$			2.82999e7i			0.601537i	−0.953697	+	0.300769i	$0.902757\pi$
$20$	7.97538e7	+	3.85080e7i	1.24615	+	0.601688i
$21$		0			0
$22$	4.45879e7	−	1.94893e8i	0.393261	−	1.71893i
$23$		−	1.30643e8i		−	0.882508i	−0.897382	−	0.441254i	$-0.854534\pi$
$23$		−	1.30643e8i		−	0.882508i	0.897382	−	0.441254i	$-0.145466\pi$
$24$		0			0
$25$	2.23371e8			0.914926
$26$	6.87969e7	+	1.57395e7i	0.222704	+	0.0509507i
$27$		0			0
$28$	2.76477e8	−	5.72610e8i	0.573734	−	1.18826i
$29$	7.45018e8			1.25250			0.626252	−	0.779621i	$-0.284588\pi$
$29$	7.45018e8			1.25250			0.626252	+	0.779621i	$0.284588\pi$
$30$		0			0
$31$			3.42331e8i			0.385724i	0.981226	+	0.192862i	$0.0617769\pi$
$31$			3.42331e8i			0.385724i	−0.981226	+	0.192862i	$0.938223\pi$
$32$	4.63403e8	+	9.68597e8i	0.431577	+	0.902076i
$33$		0			0
$34$	−1.93873e9	−	4.43547e8i	−1.25500	−	0.287122i
$35$		−	3.35660e9i		−	1.82596i
$36$		0			0
$37$	1.27314e9			0.496211			0.248105	−	0.968733i	$-0.420192\pi$
$37$	1.27314e9			0.496211			0.248105	+	0.968733i	$0.420192\pi$
$38$	−4.03931e8	+	1.76557e9i	−0.134155	+	0.586387i
$39$		0			0
$40$	4.42605e9	+	3.54079e9i	1.08058	+	0.864450i
$41$	8.57107e8			0.180440			0.0902199	−	0.995922i	$-0.471243\pi$
$41$	8.57107e8			0.180440			0.0902199	+	0.995922i	$0.471243\pi$
$42$		0			0
$43$			6.63854e9i			1.05018i	0.851048	+	0.525088i	$0.175967\pi$
$43$			6.63854e9i			1.05018i	−0.851048	+	0.525088i	$0.824033\pi$
$44$	5.56351e9	−	1.15226e10i	0.766713	−	1.58794i
$45$		0			0
$46$	1.86470e9	−	8.15056e9i	0.196817	−	0.860282i
$47$			7.75614e9i			0.719546i	0.933040	+	0.359773i	$0.117146\pi$
$47$			7.75614e9i			0.719546i	−0.933040	+	0.359773i	$0.882854\pi$
$48$		0			0
$49$	−1.02582e10			−0.741130
$50$	1.39357e10	+	3.18823e9i	0.891882	+	0.204046i
$51$		0			0
$52$	4.06745e9	+	1.96391e9i	0.205732	+	0.0993350i
$53$	1.80788e10			0.815669			0.407834	−	0.913056i	$-0.366284\pi$
$53$	1.80788e10			0.815669			0.407834	+	0.913056i	$0.366284\pi$
$54$		0			0
$55$		−	6.75445e10i		−	2.44013i
$56$	2.54219e10	−	3.17778e10i	0.824289	−	1.03038i
$57$		0			0
$58$	4.64803e10	+	1.06338e10i	1.22096	+	0.279333i
$59$			6.86310e9i			0.162708i	0.996685	+	0.0813539i	$0.0259244\pi$
$59$			6.86310e9i			0.162708i	−0.996685	+	0.0813539i	$0.974076\pi$
$60$		0			0
$61$	2.30252e10			0.446914			0.223457	−	0.974714i	$-0.428266\pi$
$61$	2.30252e10			0.446914			0.223457	+	0.974714i	$0.428266\pi$
$62$	−4.88618e9	+	2.13574e10i	−0.0860240	+	0.376009i
$63$		0			0
$64$	1.50858e10	+	6.70432e10i	0.219527	+	0.975606i
$65$	2.38431e10			0.316143
$66$		0			0
$67$			1.09125e11i			1.20636i	0.797605	+	0.603180i	$0.206100\pi$
$67$			1.09125e11i			1.20636i	−0.797605	+	0.603180i	$0.793900\pi$
$68$	−1.14623e11	−	5.53441e10i	−1.15936	−	0.559780i
$69$		0			0
$70$	4.79097e10	−	2.09412e11i	0.407225	−	1.77997i
$71$		−	2.98952e10i		−	0.233374i	−0.993169	−	0.116687i	$-0.962773\pi$
$71$		−	2.98952e10i		−	0.233374i	0.993169	−	0.116687i	$-0.0372274\pi$
$72$		0			0
$73$	−2.57691e11			−1.70279			−0.851396	−	0.524524i	$-0.824243\pi$
$73$	−2.57691e11			−1.70279			−0.851396	+	0.524524i	$0.824243\pi$
$74$	7.94288e10	+	1.81719e10i	0.483713	+	0.110665i
$75$		0			0
$76$	−5.04010e10	+	1.04385e11i	−0.261552	+	0.541699i
$77$	−4.84951e11			−2.32677
$78$		0			0
$79$			3.42810e11i			1.41023i	0.709091	+	0.705117i	$0.249105\pi$
$79$			3.42810e11i			1.41023i	−0.709091	+	0.705117i	$0.750895\pi$
$80$	2.25594e11	+	2.84077e11i	0.860574	+	1.08367i
$81$		0			0
$82$	5.34733e10	+	1.22337e10i	0.175895	+	0.0402416i
$83$			5.68292e10i			0.173821i	0.996216	+	0.0869107i	$0.0276995\pi$
$83$			5.68292e10i			0.173821i	−0.996216	+	0.0869107i	$0.972301\pi$
$84$		0			0
$85$	−6.71912e11			−1.78155
$86$	−9.47536e10	+	4.14166e11i	−0.234210	+	1.02373i
$87$		0			0
$88$	5.11561e11	−	6.39462e11i	1.10154	−	1.37695i
$89$	−6.63679e11			−1.33542			−0.667711	−	0.744421i	$-0.732726\pi$
$89$	−6.63679e11			−1.33542			−0.667711	+	0.744421i	$0.732726\pi$
$90$		0			0
$91$		−	1.71187e11i		−	0.301455i
$92$	2.32670e11	−	4.81883e11i	0.383720	−	0.794720i
$93$		0			0
$94$	−1.10705e11	+	4.83891e11i	−0.160473	+	0.701423i
$95$			6.11900e11i			0.832413i
$96$		0			0
$97$	−9.94906e11			−1.19440			−0.597202	−	0.802091i	$-0.703721\pi$
$97$	−9.94906e11			−1.19440			−0.597202	+	0.802091i	$0.703721\pi$
$98$	−6.39989e11	−	1.46418e11i	−0.722464	−	0.165287i
$99$		0			0
$100$	8.23913e11	+	3.97815e11i	0.823913	+	0.397815i
$101$	7.57925e11			0.713999			0.357000	−	0.934105i	$-0.383800\pi$
$101$	7.57925e11			0.713999			0.357000	+	0.934105i	$0.383800\pi$
$102$		0			0
$103$			3.13209e11i			0.262308i	0.991362	+	0.131154i	$0.0418682\pi$
$103$			3.13209e11i			0.262308i	−0.991362	+	0.131154i	$0.958132\pi$
$104$	2.25729e11	+	1.80581e11i	0.178397	+	0.142715i
$105$		0			0
$106$	1.12790e12	+	2.58043e11i	0.795125	+	0.181910i
$107$		−	1.36140e12i		−	0.907155i	−0.891217	−	0.453578i	$-0.850147\pi$
$107$		−	1.36140e12i		−	0.907155i	0.891217	−	0.453578i	$-0.149853\pi$
$108$		0			0
$109$	1.69639e12			1.01150			0.505751	−	0.862679i	$-0.331215\pi$
$109$	1.69639e12			1.01150			0.505751	+	0.862679i	$0.331215\pi$
$110$	9.64080e11	−	4.21397e12i	0.544198	−	2.37868i
$111$		0			0
$112$	2.03960e12	−	1.61971e12i	1.03332	−	0.820593i
$113$	3.69787e11			0.177616			0.0888079	−	0.996049i	$-0.471694\pi$
$113$	3.69787e11			0.177616			0.0888079	+	0.996049i	$0.471694\pi$
$114$		0			0
$115$		−	2.82476e12i		−	1.22122i
$116$	2.74804e12	+	1.32685e12i	1.12791	+	0.544595i
$117$		0			0
$118$	−9.79588e10	+	4.28176e11i	−0.0362870	+	0.158610i
$119$			4.82414e12i			1.69878i
$120$		0			0
$121$	−6.62018e12			−2.10939
$122$	1.43650e12	+	3.28645e11i	0.435658	+	0.0996707i
$123$		0			0
$124$	−6.09679e11	+	1.26271e12i	−0.167715	+	0.347354i
$125$	−4.49091e11			−0.117726
$126$		0			0
$127$			2.65797e12i			0.633473i	0.948514	+	0.316737i	$0.102587\pi$
$127$			2.65797e12i			0.633473i	−0.948514	+	0.316737i	$0.897413\pi$
$128$	−1.57521e10	+	4.39802e12i	−0.00358161	+	0.999994i
$129$		0			0
$130$	1.48753e12	+	3.40319e11i	0.308180	+	0.0705060i
$131$		−	9.09404e12i		−	1.79941i	−0.436502	−	0.899703i	$-0.643783\pi$
$131$		−	9.09404e12i		−	1.79941i	0.436502	−	0.899703i	$-0.356217\pi$
$132$		0			0
$133$	4.39327e12			0.793740
$134$	−1.55758e12	+	6.80813e12i	−0.269042	+	1.17598i
$135$		0			0
$136$	−6.36117e12	−	5.08885e12i	−1.00532	−	0.804242i
$137$	−2.21070e12			−0.334354			−0.167177	−	0.985927i	$-0.553465\pi$
$137$	−2.21070e12			−0.334354			−0.167177	+	0.985927i	$0.553465\pi$
$138$		0			0
$139$			9.74834e12i			1.35158i	0.737094	+	0.675790i	$0.236198\pi$
$139$			9.74834e12i			1.35158i	−0.737094	+	0.675790i	$0.763802\pi$
$140$	5.97798e12	−	1.23810e13i	0.793938	−	1.64432i
$141$		0			0
$142$	4.26702e11	−	1.86511e12i	0.0520469	−	0.227496i
$143$		−	3.44478e12i		−	0.402851i
$144$		0			0
$145$	1.61088e13			1.73323
$146$	−1.60768e13	−	3.67809e12i	−1.65990	−	0.379756i
$147$		0			0
$148$	4.69604e12	+	2.26742e12i	0.446850	+	0.215755i
$149$	1.68556e13			1.54038			0.770190	−	0.637815i	$-0.220162\pi$
$149$	1.68556e13			1.54038			0.770190	+	0.637815i	$0.220162\pi$
$150$		0			0
$151$		−	9.56339e12i		−	0.806770i	−0.915030	−	0.403385i	$-0.867833\pi$
$151$		−	9.56339e12i		−	0.806770i	0.915030	−	0.403385i	$-0.132167\pi$
$152$	−4.63434e12	+	5.79302e12i	−0.375774	+	0.469725i
$153$		0			0
$154$	−3.02552e13	−	6.92183e12i	−2.26817	−	0.518915i
$155$			7.40189e12i			0.533768i
$156$		0			0
$157$	5.63319e12			0.376146			0.188073	−	0.982155i	$-0.439776\pi$
$157$	5.63319e12			0.376146			0.188073	+	0.982155i	$0.439776\pi$
$158$	−4.89302e12	+	2.13873e13i	−0.314510	+	1.37472i
$159$		0			0
$160$	1.00197e13	+	2.09430e13i	0.597220	+	1.24830i
$161$	−2.02810e13			−1.16449
$162$		0			0
$163$		−	1.62012e13i		−	0.863816i	−0.901918	−	0.431908i	$-0.857841\pi$
$163$		−	1.62012e13i		−	0.863816i	0.901918	−	0.431908i	$-0.142159\pi$
$164$	3.16148e12	+	1.52648e12i	0.162490	+	0.0784562i
$165$		0			0
$166$	−8.11138e11	+	3.54547e12i	−0.0387656	+	0.169443i
$167$			1.19637e13i			0.551528i	0.961225	+	0.275764i	$0.0889309\pi$
$167$			1.19637e13i			0.551528i	−0.961225	+	0.275764i	$0.911069\pi$
$168$		0			0
$169$	−2.20821e13			−0.947807
$170$	−4.19193e13	−	9.59037e12i	−1.73668	−	0.397321i
$171$		0			0
$172$	−1.18230e13	+	2.44866e13i	−0.456622	+	0.945709i
$173$	7.29594e11			0.0272148			0.0136074	−	0.999907i	$-0.495669\pi$
$173$	7.29594e11			0.0272148			0.0136074	+	0.999907i	$0.495669\pi$
$174$		0			0
$175$		−	3.46761e13i		−	1.20726i
$176$	4.10425e13	−	3.25931e13i	1.38089	−	1.09660i
$177$		0			0
$178$	−4.14057e13	−	9.47287e12i	−1.30179	−	0.297825i
$179$			4.27727e13i			1.30032i	0.759799	+	0.650158i	$0.225297\pi$
$179$			4.27727e13i			1.30032i	−0.759799	+	0.650158i	$0.774703\pi$
$180$		0			0
$181$	6.35840e13			1.80833			0.904163	−	0.427188i	$-0.140496\pi$
$181$	6.35840e13			1.80833			0.904163	+	0.427188i	$0.140496\pi$
$182$	2.44340e12	−	1.06800e13i	0.0672304	−	0.293863i
$183$		0			0
$184$	2.13939e13	−	2.67428e13i	0.551293	−	0.689127i
$185$	2.75279e13			0.686660
$186$		0			0
$187$			9.70756e13i			2.27018i
$188$	−1.38134e13	+	2.86089e13i	−0.312862	+	0.647968i
$189$		0			0
$190$	−8.73381e12	+	3.81753e13i	−0.185644	+	0.811447i
$191$		−	6.97546e13i		−	1.43672i	−0.695671	−	0.718360i	$-0.744893\pi$
$191$		−	6.97546e13i		−	1.43672i	0.695671	−	0.718360i	$-0.255107\pi$
$192$		0			0
$193$	−1.49999e13			−0.290231			−0.145115	−	0.989415i	$-0.546355\pi$
$193$	−1.49999e13			−0.290231			−0.145115	+	0.989415i	$0.546355\pi$
$194$	−6.20703e13	−	1.42005e13i	−1.16432	−	0.266376i
$195$		0			0
$196$	−3.78378e13	−	1.82695e13i	−0.667405	−	0.322247i
$197$	9.65977e12			0.165261			0.0826303	−	0.996580i	$-0.473668\pi$
$197$	9.65977e12			0.165261			0.0826303	+	0.996580i	$0.473668\pi$
$198$		0			0
$199$		−	5.59437e13i		−	0.900809i	−0.892825	−	0.450404i	$-0.851280\pi$
$199$		−	5.59437e13i		−	0.900809i	0.892825	−	0.450404i	$-0.148720\pi$
$200$	4.57242e13	+	3.65788e13i	0.714441	+	0.571544i
$201$		0			0
$202$	4.72855e13	+	1.08181e13i	0.696016	+	0.159236i
$203$		−	1.15657e14i		−	1.65270i
$204$		0			0
$205$	1.85324e13			0.249694
$206$	−4.47052e12	+	1.95405e13i	−0.0584998	+	0.255701i
$207$		0			0
$208$	1.15053e13	+	1.44880e13i	0.142076	+	0.178907i
$209$	8.84053e13			1.06072
$210$		0			0
$211$			5.22608e12i			0.0592218i	0.999562	+	0.0296109i	$0.00942681\pi$
$211$			5.22608e12i			0.0592218i	−0.999562	+	0.0296109i	$0.990573\pi$
$212$	6.66844e13	+	3.21976e13i	0.734530	+	0.354657i
$213$		0			0
$214$	1.94316e13	−	8.49349e13i	0.202314	−	0.884308i
$215$			1.43539e14i			1.45324i
$216$		0			0
$217$	5.31435e13			0.508970
$218$	1.05835e14	+	2.42130e13i	0.986027	+	0.225585i
$219$		0			0
$220$	1.20294e14	−	2.49141e14i	1.06098	−	2.19740i
$221$	−3.42676e13			−0.294123
$222$		0			0
$223$		−	5.52974e13i		−	0.449651i	−0.974399	−	0.224826i	$-0.927819\pi$
$223$		−	5.52974e13i		−	0.449651i	0.974399	−	0.224826i	$-0.0721812\pi$
$224$	1.50365e14	−	7.19387e13i	1.19031	−	0.569474i
$225$		0			0
$226$	2.30703e13	+	5.27807e12i	0.173142	+	0.0396118i
$227$		−	1.51944e14i		−	1.11052i	−0.831676	−	0.555261i	$-0.812618\pi$
$227$		−	1.51944e14i		−	1.11052i	0.831676	−	0.555261i	$-0.187382\pi$
$228$		0			0
$229$	−2.14686e14			−1.48864			−0.744321	−	0.667822i	$-0.767227\pi$
$229$	−2.14686e14			−1.48864			−0.744321	+	0.667822i	$0.767227\pi$
$230$	4.03186e13	−	1.76232e14i	0.272357	−	1.19046i
$231$		0			0
$232$	1.52506e14	+	1.22003e14i	0.978047	+	0.782425i
$233$	−2.19897e14			−1.37431			−0.687154	−	0.726511i	$-0.741140\pi$
$233$	−2.19897e14			−1.37431			−0.687154	+	0.726511i	$0.741140\pi$
$234$		0			0
$235$			1.67703e14i			0.995713i
$236$	−1.22229e13	+	2.53149e13i	−0.0707462	+	0.146522i
$237$		0			0
$238$	−6.88562e13	+	3.00969e14i	−0.378862	+	1.65600i
$239$			2.85373e14i			1.53118i	0.643330	+	0.765589i	$0.277552\pi$
$239$			2.85373e14i			1.53118i	−0.643330	+	0.765589i	$0.722448\pi$
$240$		0			0
$241$	−2.33917e14			−1.19388			−0.596939	−	0.802287i	$-0.703616\pi$
$241$	−2.33917e14			−1.19388			−0.596939	+	0.802287i	$0.703616\pi$
$242$	−4.13020e14	−	9.44915e13i	−2.05626	−	0.470436i
$243$		0			0
$244$	8.49296e13	+	4.10070e13i	0.402457	+	0.194321i
$245$	−2.21803e14			−1.02558
$246$		0			0
$247$			3.12070e13i			0.137426i
$248$	−5.60597e13	+	7.00756e13i	−0.240957	+	0.301201i
$249$		0			0
$250$	−2.80179e13	−	6.40999e12i	−0.114761	−	0.0262553i
$251$			5.28817e13i			0.211477i	0.994394	+	0.105738i	$0.0337206\pi$
$251$			5.28817e13i			0.211477i	−0.994394	+	0.105738i	$0.966279\pi$
$252$		0			0
$253$	−4.08112e14			−1.55617
$254$	−3.79379e13	+	1.65826e14i	−0.141277	+	0.617518i
$255$		0			0
$256$	−6.37568e13	+	2.74159e14i	−0.226510	+	0.974009i
$257$	1.70736e14			0.592553			0.296276	−	0.955102i	$-0.404255\pi$
$257$	1.70736e14			0.592553			0.296276	+	0.955102i	$0.404255\pi$
$258$		0			0
$259$		−	1.97642e14i		−	0.654759i
$260$	8.79465e13	+	4.24637e13i	0.284694	+	0.137461i
$261$		0			0
$262$	1.29802e14	−	5.67360e14i	0.401303	−	1.75409i
$263$			3.87597e14i			1.17124i	0.810586	+	0.585620i	$0.199149\pi$
$263$			3.87597e14i			1.17124i	−0.810586	+	0.585620i	$0.800851\pi$
$264$		0			0
$265$	3.90899e14			1.12873
$266$	2.74088e14	+	6.27063e13i	0.773749	+	0.177020i
$267$		0			0
$268$	−1.94348e14	+	4.02514e14i	−0.524532	+	1.08636i
$269$	−1.89974e14			−0.501395			−0.250697	−	0.968065i	$-0.580660\pi$
$269$	−1.89974e14			−0.501395			−0.250697	+	0.968065i	$0.580660\pi$
$270$		0			0
$271$		−	1.94076e14i		−	0.489954i	−0.969529	−	0.244977i	$-0.921220\pi$
$271$		−	1.94076e14i		−	0.489954i	0.969529	−	0.244977i	$-0.0787804\pi$
$272$	−3.24226e14	−	4.08279e14i	−0.800636	−	1.00819i
$273$		0			0
$274$	−1.37921e14	−	3.15539e13i	−0.325933	−	0.0745676i
$275$		−	6.97782e14i		−	1.61333i
$276$		0			0
$277$	−2.96454e14			−0.656263			−0.328132	−	0.944632i	$-0.606419\pi$
$277$	−2.96454e14			−0.656263			−0.328132	+	0.944632i	$0.606419\pi$
$278$	−1.39141e14	+	6.08181e14i	−0.301429	+	1.31754i
$279$		0			0
$280$	5.49672e14	−	6.87101e14i	1.14066	−	1.42584i
$281$	−7.37011e13			−0.149705			−0.0748525	−	0.997195i	$-0.523849\pi$
$281$	−7.37011e13			−0.149705			−0.0748525	+	0.997195i	$0.523849\pi$
$282$		0			0
$283$			7.45699e14i			1.45159i	0.687909	+	0.725797i	$0.258529\pi$
$283$			7.45699e14i			1.45159i	−0.687909	+	0.725797i	$0.741471\pi$
$284$	5.32423e13	−	1.10270e14i	0.101472	−	0.210159i
$285$		0			0
$286$	4.91682e13	−	2.14913e14i	0.0898438	−	0.392705i
$287$		−	1.33057e14i		−	0.238094i
$288$		0			0
$289$	3.83056e14			0.657468
$290$	1.00500e15	+	2.29925e14i	1.68957	+	0.386543i
$291$		0			0
$292$	−9.50504e14	−	4.58937e14i	−1.53340	−	0.740383i
$293$	1.68548e14			0.266390			0.133195	−	0.991090i	$-0.457476\pi$
$293$	1.68548e14			0.266390			0.133195	+	0.991090i	$0.457476\pi$
$294$		0			0
$295$			1.48394e14i			0.225156i
$296$	2.60614e14	+	2.08488e14i	0.387478	+	0.309977i
$297$		0			0
$298$	1.05159e15	+	2.40585e14i	1.50158	+	0.343535i
$299$		−	1.44063e14i		−	0.201616i
$300$		0			0
$301$	1.03057e15			1.38573
$302$	1.36501e14	−	5.96641e14i	0.179926	−	0.786451i
$303$		0			0
$304$	−3.71813e14	+	2.95268e14i	−0.471067	+	0.374089i
$305$	4.97851e14			0.618444
$306$		0			0
$307$		−	3.50499e13i		−	0.0418655i	−0.999781	−	0.0209327i	$-0.993336\pi$
$307$		−	3.50499e13i		−	0.0418655i	0.999781	−	0.0209327i	$-0.00666359\pi$
$308$	−1.78876e15	−	8.63679e14i	−2.09531	−	1.01169i
$309$		0			0
$310$	−1.05649e14	+	4.61790e14i	−0.119041	+	0.520324i
$311$		−	2.44497e14i		−	0.270216i	−0.990831	−	0.135108i	$-0.956862\pi$
$311$		−	2.44497e14i		−	0.270216i	0.990831	−	0.135108i	$-0.0431382\pi$
$312$		0			0
$313$	6.42648e14			0.683451			0.341725	−	0.939800i	$-0.388989\pi$
$313$	6.42648e14			0.683451			0.341725	+	0.939800i	$0.388989\pi$
$314$	3.51444e14	+	8.04040e13i	0.366672	+	0.0838880i
$315$		0			0
$316$	−6.10532e14	+	1.26447e15i	−0.613177	+	1.26995i
$317$	9.70968e14			0.956862			0.478431	−	0.878125i	$-0.341206\pi$
$317$	9.70968e14			0.956862			0.478431	+	0.878125i	$0.341206\pi$
$318$		0			0
$319$		−	2.32735e15i		−	2.20860i
$320$	3.26185e14	+	1.44961e15i	0.303783	+	1.35005i
$321$		0			0
$322$	−1.26529e15	−	2.89476e14i	−1.13516	−	0.259703i
$323$		−	8.79428e14i		−	0.774436i
$324$		0			0
$325$	2.46316e14			0.209022
$326$	2.31244e14	−	1.01076e15i	0.192648	−	0.842060i
$327$		0			0
$328$	1.75451e14	+	1.40359e14i	0.140901	+	0.112719i
$329$	1.20406e15			0.949454
$330$		0			0
$331$			8.82907e14i			0.671347i	0.941978	+	0.335673i	$0.108964\pi$
$331$			8.82907e14i			0.671347i	−0.941978	+	0.335673i	$0.891036\pi$
$332$	−1.01211e14	+	2.09617e14i	−0.0755785	+	0.156530i
$333$		0			0
$334$	−1.70762e14	+	7.46395e14i	−0.123002	+	0.537638i
$335$			2.35951e15i			1.66937i
$336$		0			0
$337$	3.61078e14			0.246502			0.123251	−	0.992376i	$-0.460668\pi$
$337$	3.61078e14			0.246502			0.123251	+	0.992376i	$0.460668\pi$
$338$	−1.37766e15	−	3.15183e14i	−0.923935	−	0.211380i
$339$		0			0
$340$	−2.47838e15	−	1.19665e15i	−1.60433	−	0.774629i
$341$	1.06940e15			0.680165
$342$		0			0
$343$		−	5.56240e14i		−	0.341584i
$344$	−1.08712e15	+	1.35892e15i	−0.656033	+	0.820054i
$345$		0			0
$346$	4.55180e13	+	1.04137e13i	0.0265293	+	0.00606943i
$347$			2.72152e15i			1.55896i	0.626428	+	0.779479i	$0.284516\pi$
$347$			2.72152e15i			1.55896i	−0.626428	+	0.779479i	$0.715484\pi$
$348$		0			0
$349$	−6.72483e14			−0.372159			−0.186080	−	0.982535i	$-0.559578\pi$
$349$	−6.72483e14			−0.372159			−0.186080	+	0.982535i	$0.559578\pi$
$350$	4.94940e14	−	2.16337e15i	0.269243	−	1.17686i
$351$		0			0
$352$	3.02578e15	−	1.44761e15i	1.59067	−	0.761021i
$353$	−1.85307e15			−0.957733			−0.478866	−	0.877888i	$-0.658952\pi$
$353$	−1.85307e15			−0.957733			−0.478866	+	0.877888i	$0.658952\pi$
$354$		0			0
$355$		−	6.46394e14i		−	0.322944i
$356$	−2.44801e15	−	1.18199e15i	−1.20258	−	0.580649i
$357$		0			0
$358$	−6.10507e14	+	2.66851e15i	−0.289996	+	1.26757i
$359$		−	3.72749e15i		−	1.74120i	−0.491988	−	0.870602i	$-0.663730\pi$
$359$		−	3.72749e15i		−	1.74120i	0.491988	−	0.870602i	$-0.336270\pi$
$360$		0			0
$361$	1.41243e15			0.638153
$362$	3.96689e15	+	9.07552e14i	1.76278	+	0.403292i
$363$		0			0
$364$	3.04878e14	−	6.31432e14i	0.131074	−	0.271468i
$365$	−5.57179e15			−2.35634
$366$		0			0
$367$			4.23753e15i			1.73427i	0.498074	+	0.867134i	$0.334041\pi$
$367$			4.23753e15i			1.73427i	−0.498074	+	0.867134i	$0.665959\pi$
$368$	1.71643e15	−	1.36307e15i	0.691098	−	0.548822i
$369$		0			0
$370$	1.71741e15	+	3.92912e14i	0.669366	+	0.153139i
$371$		−	2.80655e15i		−	1.07629i
$372$		0			0
$373$	2.04505e15			0.759366			0.379683	−	0.925117i	$-0.376033\pi$
$373$	2.04505e15			0.759366			0.379683	+	0.925117i	$0.376033\pi$
$374$	−1.38559e15	+	6.05636e15i	−0.506295	+	2.21300i
$375$		0			0
$376$	−1.27013e15	+	1.58769e15i	−0.449492	+	0.561874i
$377$	8.21550e14			0.286145
$378$		0			0
$379$		−	3.15278e15i		−	1.06380i	−0.846809	−	0.531898i	$-0.821479\pi$
$379$		−	3.15278e15i		−	1.06380i	0.846809	−	0.531898i	$-0.178521\pi$
$380$	−1.08977e15	+	2.25702e15i	−0.361938	+	0.749608i
$381$		0			0
$382$	9.95625e14	−	4.35185e15i	0.320417	−	1.40054i
$383$		−	7.17868e14i		−	0.227432i	−0.993513	−	0.113716i	$-0.963725\pi$
$383$		−	7.17868e14i		−	0.227432i	0.993513	−	0.113716i	$-0.0362754\pi$
$384$		0			0
$385$	−1.04856e16			−3.21980
$386$	−9.35813e14	−	2.14097e14i	−0.282921	−	0.0647272i
$387$		0			0
$388$	−3.66976e15	−	1.77189e15i	−1.07559	−	0.519334i
$389$	2.06072e15			0.594734			0.297367	−	0.954763i	$-0.403892\pi$
$389$	2.06072e15			0.594734			0.297367	+	0.954763i	$0.403892\pi$
$390$		0			0
$391$			4.05978e15i			1.13617i
$392$	−2.09986e15	−	1.67987e15i	−0.578729	−	0.462976i
$393$		0			0
$394$	6.02654e14	+	1.37876e14i	0.161098	+	0.0368564i
$395$			7.41224e15i			1.95149i
$396$		0			0
$397$	4.88827e15			1.24857			0.624283	−	0.781198i	$-0.285391\pi$
$397$	4.88827e15			1.24857			0.624283	+	0.781198i	$0.285391\pi$
$398$	7.98499e14	−	3.49022e15i	0.200898	−	0.878121i
$399$		0			0
$400$	2.33055e15	+	2.93472e15i	0.568982	+	0.716484i
$401$	2.60313e14			0.0626081			0.0313040	−	0.999510i	$-0.490034\pi$
$401$	2.60313e14			0.0626081			0.0313040	+	0.999510i	$0.490034\pi$
$402$		0			0
$403$			3.77497e14i			0.0881218i
$404$	2.79564e15	+	1.34984e15i	0.642974	+	0.310451i
$405$		0			0
$406$	1.65080e15	−	7.21560e15i	0.368585	−	1.61108i
$407$		−	3.97713e15i		−	0.874991i
$408$		0			0
$409$	−3.88078e15			−0.829047			−0.414523	−	0.910039i	$-0.636052\pi$
$409$	−3.88078e15			−0.829047			−0.414523	+	0.910039i	$0.636052\pi$
$410$	1.15620e15	+	2.64518e14i	0.243405	+	0.0556867i
$411$		0			0
$412$	−5.57814e14	+	1.15529e15i	−0.114053	+	0.236215i
$413$	1.06543e15			0.214696
$414$		0			0
$415$			1.22876e15i			0.240535i
$416$	5.11006e14	+	1.06810e15i	0.0985975	+	0.206087i
$417$		0			0
$418$	5.51543e15	+	1.26183e15i	1.03400	+	0.236561i
$419$			3.16498e15i			0.584908i	0.956280	+	0.292454i	$0.0944718\pi$
$419$			3.16498e15i			0.584908i	−0.956280	+	0.292454i	$0.905528\pi$
$420$		0			0
$421$	−7.49878e15			−1.34678			−0.673392	−	0.739286i	$-0.735163\pi$
$421$	−7.49878e15			−1.34678			−0.673392	+	0.739286i	$0.735163\pi$
$422$	−7.45932e13	+	3.26045e14i	−0.0132076	+	0.0577302i
$423$		0			0
$424$	3.70075e15	+	2.96055e15i	0.636934	+	0.509540i
$425$	−6.94132e15			−1.17790
$426$		0			0
$427$		−	3.57443e15i		−	0.589712i
$428$	2.42460e15	−	5.02157e15i	0.394436	−	0.816916i
$429$		0			0
$430$	−2.04876e15	+	8.95510e15i	−0.324102	+	1.41664i
$431$		−	9.32416e14i		−	0.145461i	−0.997352	−	0.0727304i	$-0.976829\pi$
$431$		−	9.32416e14i		−	0.145461i	0.997352	−	0.0727304i	$-0.0231713\pi$
$432$		0			0
$433$	8.97281e15			1.36145			0.680724	−	0.732540i	$-0.261665\pi$
$433$	8.97281e15			1.36145			0.680724	+	0.732540i	$0.261665\pi$
$434$	3.31552e15	+	7.58531e14i	0.496151	+	0.113510i
$435$		0			0
$436$	6.25722e15	+	3.02121e15i	0.910883	+	0.439807i
$437$	3.69718e15			0.530862
$438$		0			0
$439$		−	8.16317e15i		−	1.14044i	−0.821492	−	0.570219i	$-0.806858\pi$
$439$		−	8.16317e15i		−	1.14044i	0.821492	−	0.570219i	$-0.193142\pi$
$440$	1.10610e16	−	1.38264e16i	1.52433	−	1.90544i
$441$		0			0
$442$	−2.13789e15	−	4.89110e14i	−0.286716	−	0.0655953i
$443$			8.55402e12i			0.00113174i	1.00000		0.000565871i	$0.000180122\pi$
$443$			8.55402e12i			0.00113174i	−1.00000		0.000565871i	$0.999820\pi$
$444$		0			0
$445$	−1.43501e16			−1.84797
$446$	7.89275e14	−	3.44990e15i	0.100281	−	0.438326i
$447$		0			0
$448$	1.04078e16	−	2.34192e15i	1.28733	−	0.289670i
$449$	5.23064e15			0.638376			0.319188	−	0.947691i	$-0.396590\pi$
$449$	5.23064e15			0.638376			0.319188	+	0.947691i	$0.396590\pi$
$450$		0			0
$451$		−	2.67750e15i		−	0.318178i
$452$	1.36398e15	+	6.58578e14i	0.159947	+	0.0772283i
$453$		0			0
$454$	2.16873e15	−	9.47947e15i	0.247668	−	1.08255i
$455$		−	3.70141e15i		−	0.417156i
$456$		0			0
$457$	9.16769e15			1.00638			0.503191	−	0.864175i	$-0.332159\pi$
$457$	9.16769e15			1.00638			0.503191	+	0.864175i	$0.332159\pi$
$458$	−1.33938e16	−	3.06426e15i	−1.45115	−	0.331996i
$459$		0			0
$460$	5.03080e15	−	1.04193e16i	0.530994	−	1.09974i
$461$	−5.58085e15			−0.581426			−0.290713	−	0.956810i	$-0.593892\pi$
$461$	−5.58085e15			−0.581426			−0.290713	+	0.956810i	$0.593892\pi$
$462$		0			0
$463$			9.59067e15i			0.973561i	0.873524	+	0.486780i	$0.161829\pi$
$463$			9.59067e15i			0.973561i	−0.873524	+	0.486780i	$0.838171\pi$
$464$	7.77319e15	+	9.78830e15i	0.778917	+	0.980843i
$465$		0			0
$466$	−1.37190e16	−	3.13865e15i	−1.33970	−	0.306498i
$467$		−	2.47121e15i		−	0.238236i	−0.992880	−	0.119118i	$-0.961993\pi$
$467$		−	2.47121e15i		−	0.238236i	0.992880	−	0.119118i	$-0.0380067\pi$
$468$		0			0
$469$	1.69406e16			1.59182
$470$	−2.39367e15	+	1.04627e16i	−0.222064	+	0.970635i
$471$		0			0
$472$	−1.12389e15	+	1.40489e15i	−0.101642	+	0.127054i
$473$	2.07380e16			1.85182
$474$		0			0
$475$			6.32135e15i			0.550362i
$476$	−8.59162e15	+	1.77941e16i	−0.738641	+	1.52980i
$477$		0			0
$478$	−4.07321e15	+	1.78039e16i	−0.341483	+	1.49261i
$479$			1.04803e16i			0.867680i	0.900990	+	0.433840i	$0.142842\pi$
$479$			1.04803e16i			0.867680i	−0.900990	+	0.433840i	$0.857158\pi$
$480$		0			0
$481$	1.40392e15			0.113363
$482$	−1.45936e16	−	3.33876e15i	−1.16381	−	0.266258i
$483$		0			0
$484$	−2.44188e16	−	1.17903e16i	−1.89956	−	0.917175i
$485$	−2.15119e16			−1.65283
$486$		0			0
$487$		−	1.46081e15i		−	0.109501i	−0.998500	−	0.0547507i	$-0.982564\pi$
$487$		−	1.46081e15i		−	0.109501i	0.998500	−	0.0547507i	$-0.0174364\pi$
$488$	4.71329e15	+	3.77057e15i	0.348984	+	0.279183i
$489$		0			0
$490$	−1.38378e16	−	3.16585e15i	−0.999751	−	0.228725i
$491$		−	9.29150e15i		−	0.663128i	−0.943433	−	0.331564i	$-0.892424\pi$
$491$		−	9.29150e15i		−	0.663128i	0.943433	−	0.331564i	$-0.107576\pi$
$492$		0			0
$493$	−2.31517e16			−1.61251
$494$	−4.45425e14	+	1.94694e15i	−0.0306488	+	0.133965i
$495$		0			0
$496$	−4.49766e15	+	3.57173e15i	−0.302063	+	0.239877i
$497$	−4.64093e15			−0.307941
$498$		0			0
$499$		−	4.55680e15i		−	0.295160i	−0.989050	−	0.147580i	$-0.952852\pi$
$499$		−	4.55680e15i		−	0.295160i	0.989050	−	0.147580i	$-0.0471483\pi$
$500$	−1.65649e15	−	7.99814e14i	−0.106016	−	0.0511881i
$501$		0			0
$502$	−7.54794e14	+	3.29919e15i	−0.0471635	+	0.206151i
$503$		−	7.93408e15i		−	0.489879i	−0.969538	−	0.244939i	$-0.921232\pi$
$503$		−	7.93408e15i		−	0.489879i	0.969538	−	0.244939i	$-0.0787681\pi$
$504$		0			0
$505$	1.63879e16			0.988038
$506$	−2.54613e16	−	5.82509e15i	−1.51697	−	0.347056i
$507$		0			0
$508$	−4.73375e15	+	9.80406e15i	−0.275438	+	0.570458i
$509$	−1.89940e15			−0.109222			−0.0546110	−	0.998508i	$-0.517392\pi$
$509$	−1.89940e15			−0.109222			−0.0546110	+	0.998508i	$0.517392\pi$
$510$		0			0
$511$			4.00039e16i			2.24686i
$512$	−7.89081e15	+	1.61942e16i	−0.438028	+	0.898961i
$513$		0			0
$514$	1.06519e16	+	2.43696e15i	0.577629	+	0.132151i
$515$			6.77221e15i			0.362984i
$516$		0			0
$517$	2.42292e16			1.26881
$518$	2.82100e15	−	1.23305e16i	0.146024	−	0.638268i
$519$		0			0
$520$	4.88072e15	+	3.90451e15i	0.246867	+	0.197491i
$521$	5.48607e14			0.0274306			0.0137153	−	0.999906i	$-0.495634\pi$
$521$	5.48607e14			0.0274306			0.0137153	+	0.999906i	$0.495634\pi$
$522$		0			0
$523$		−	3.85719e16i		−	1.88478i	−0.334515	−	0.942390i	$-0.608573\pi$
$523$		−	3.85719e16i		−	1.88478i	0.334515	−	0.942390i	$-0.391427\pi$
$524$	1.61962e16	−	3.35438e16i	0.782392	−	1.62041i
$525$		0			0
$526$	−5.53227e15	+	2.41814e16i	−0.261209	+	1.14174i
$527$		−	1.06381e16i		−	0.496591i
$528$		0			0
$529$	4.84705e15			0.221179
$530$	2.43875e16	+	5.57941e15i	1.10030	+	0.251729i
$531$		0			0
$532$	1.62048e16	+	7.82426e15i	0.714782	+	0.345122i
$533$	9.45154e14			0.0412230
$534$		0			0
$535$		−	2.94361e16i		−	1.25533i
$536$	−1.78702e16	+	2.23381e16i	−0.753601	+	0.942015i
$537$		0			0
$538$	−1.18521e16	−	2.71155e15i	−0.488767	−	0.111821i
$539$			3.20453e16i			1.30687i
$540$		0			0
$541$	−2.86737e16			−1.14367			−0.571835	−	0.820369i	$-0.693768\pi$
$541$	−2.86737e16			−1.14367			−0.571835	+	0.820369i	$0.693768\pi$
$542$	2.77009e15	−	1.21080e16i	0.109269	−	0.477614i
$543$		0			0
$544$	−1.44004e16	−	3.00995e16i	−0.555624	−	1.16136i
$545$	3.66794e16			1.39973
$546$		0			0
$547$		−	1.66195e16i		−	0.620433i	−0.950666	−	0.310216i	$-0.899598\pi$
$547$		−	1.66195e16i		−	0.620433i	0.950666	−	0.310216i	$-0.100402\pi$
$548$	−8.15428e15	−	3.93718e15i	−0.301094	−	0.145379i
$549$		0			0
$550$	9.95963e15	−	4.35333e16i	0.359805	−	1.57270i
$551$			2.10839e16i			0.753428i
$552$		0			0
$553$	5.32179e16			1.86083
$554$	−1.84952e16	−	4.23136e15i	−0.639734	−	0.146360i
$555$		0			0
$556$	−1.73614e16	+	3.59572e16i	−0.587675	+	1.21713i
$557$	−9.18623e15			−0.307614			−0.153807	−	0.988101i	$-0.549153\pi$
$557$	−9.18623e15			−0.307614			−0.153807	+	0.988101i	$0.549153\pi$
$558$		0			0
$559$			7.32048e15i			0.239921i
$560$	4.41002e16	−	3.50213e16i	1.42992	−	1.13554i
$561$		0			0
$562$	−4.59807e15	−	1.05196e15i	−0.145934	−	0.0333872i
$563$		−	7.64499e15i		−	0.240064i	−0.992770	−	0.120032i	$-0.961700\pi$
$563$		−	7.64499e15i		−	0.240064i	0.992770	−	0.120032i	$-0.0382997\pi$
$564$		0			0
$565$	7.99554e15			0.245786
$566$	−1.06436e16	+	4.65227e16i	−0.323734	+	1.41503i
$567$		0			0
$568$	4.89560e15	−	6.11959e15i	0.145786	−	0.182235i
$569$	6.01416e16			1.77215			0.886076	−	0.463539i	$-0.153421\pi$
$569$	6.01416e16			1.77215			0.886076	+	0.463539i	$0.153421\pi$
$570$		0			0
$571$			2.90031e16i			0.836812i	0.908260	+	0.418406i	$0.137411\pi$
$571$			2.90031e16i			0.836812i	−0.908260	+	0.418406i	$0.862589\pi$
$572$	6.13502e15	−	1.27062e16i	0.175162	−	0.362777i
$573$		0			0
$574$	1.89916e15	−	8.30120e15i	0.0530996	−	0.232097i
$575$		−	2.91818e16i		−	0.807430i
$576$		0			0
$577$	−3.08072e16			−0.834827			−0.417414	−	0.908717i	$-0.637063\pi$
$577$	−3.08072e16			−0.834827			−0.417414	+	0.908717i	$0.637063\pi$
$578$	2.38981e16	+	5.46746e15i	0.640909	+	0.146628i
$579$		0			0
$580$	5.94181e16	+	2.86892e16i	1.56081	+	0.753616i
$581$	8.82217e15			0.229361
$582$		0			0
$583$		−	5.64759e16i		−	1.43831i
$584$	−5.27496e16	−	4.21990e16i	−1.32966	−	1.06372i
$585$		0			0
$586$	1.05154e16	+	2.40573e15i	0.259681	+	0.0594103i
$587$		−	6.49747e16i		−	1.58824i	−0.607763	−	0.794119i	$-0.707933\pi$
$587$		−	6.49747e16i		−	1.58824i	0.607763	−	0.794119i	$-0.292067\pi$
$588$		0			0
$589$	−9.68792e15			−0.232027
$590$	−2.11807e15	+	9.25802e15i	−0.0502143	+	0.219486i
$591$		0			0
$592$	1.32834e16	+	1.67269e16i	0.308588	+	0.388585i
$593$	−2.90149e16			−0.667256			−0.333628	−	0.942705i	$-0.608273\pi$
$593$	−2.90149e16			−0.667256			−0.333628	+	0.942705i	$0.608273\pi$
$594$		0			0
$595$			1.04308e17i			2.35079i
$596$	6.21728e16	+	3.00193e16i	1.38715	+	0.669765i
$597$		0			0
$598$	2.05625e15	−	8.98783e15i	0.0449644	−	0.196539i
$599$		−	2.11300e16i		−	0.457445i	−0.973492	−	0.228723i	$-0.926545\pi$
$599$		−	2.11300e16i		−	0.457445i	0.973492	−	0.228723i	$-0.0734549\pi$
$600$		0			0
$601$	−1.62140e16			−0.344067			−0.172033	−	0.985091i	$-0.555034\pi$
$601$	−1.62140e16			−0.344067			−0.172033	+	0.985091i	$0.555034\pi$
$602$	6.42951e16	+	1.47096e16i	1.35083	+	0.309044i
$603$		0			0
$604$	1.70320e16	−	3.52750e16i	0.350788	−	0.726516i
$605$	−1.43141e17			−2.91899
$606$		0			0
$607$		−	1.90567e16i		−	0.380991i	−0.981688	−	0.190496i	$-0.938991\pi$
$607$		−	1.90567e16i		−	0.380991i	0.981688	−	0.190496i	$-0.0610095\pi$
$608$	−2.74111e16	+	1.31142e16i	−0.542632	+	0.259610i
$609$		0			0
$610$	3.10600e16	+	7.10596e15i	0.602868	+	0.137925i
$611$			8.55288e15i			0.164386i
$612$		0			0
$613$	−7.71443e16			−1.45392			−0.726961	−	0.686679i	$-0.759068\pi$
$613$	−7.71443e16			−1.45392			−0.726961	+	0.686679i	$0.759068\pi$
$614$	5.00276e14	−	2.18670e15i	0.00933683	−	0.0408111i
$615$		0			0
$616$	−9.92701e16	−	7.94148e16i	−1.81691	−	1.45351i
$617$	3.22878e16			0.585232			0.292616	−	0.956230i	$-0.405474\pi$
$617$	3.22878e16			0.585232			0.292616	+	0.956230i	$0.405474\pi$
$618$		0			0
$619$			9.72802e16i			1.72934i	0.502340	+	0.864670i	$0.332473\pi$
$619$			9.72802e16i			1.72934i	−0.502340	+	0.864670i	$0.667527\pi$
$620$	−1.31825e16	+	2.73022e16i	−0.232085	+	0.480671i
$621$		0			0
$622$	3.48977e15	−	1.52537e16i	0.0602635	−	0.263411i
$623$			1.03030e17i			1.76211i
$624$		0			0
$625$	−6.42441e16			−1.07784
$626$	4.00936e16	+	9.17269e15i	0.666237	+	0.152423i
$627$		0			0
$628$	2.07783e16	+	1.00325e16i	0.338729	+	0.163550i
$629$	−3.95633e16			−0.638835
$630$		0			0
$631$			1.75094e16i			0.277392i	0.990335	+	0.138696i	$0.0442911\pi$
$631$			1.75094e16i			0.277392i	−0.990335	+	0.138696i	$0.955709\pi$
$632$	−5.61381e16	+	7.01737e16i	−0.880957	+	1.10121i
$633$		0			0
$634$	6.05768e16	+	1.38589e16i	0.932762	+	0.213399i
$635$			5.74707e16i			0.876605i
$636$		0			0
$637$	−1.13120e16			−0.169317
$638$	3.32188e16	−	1.45199e17i	0.492561	−	2.15297i
$639$		0			0
$640$	−3.40592e14	+	9.50940e16i	−0.00495627	+	1.38380i
$641$	−8.75867e16			−1.26267			−0.631335	−	0.775510i	$-0.717493\pi$
$641$	−8.75867e16			−1.26267			−0.631335	+	0.775510i	$0.717493\pi$
$642$		0			0
$643$		−	5.14892e16i		−	0.728534i	−0.931294	−	0.364267i	$-0.881320\pi$
$643$		−	5.14892e16i		−	0.728534i	0.931294	−	0.364267i	$-0.118680\pi$
$644$	−7.48075e16	−	3.61197e16i	−1.04865	−	0.506325i
$645$		0			0
$646$	1.25523e16	−	5.48658e16i	0.172714	−	0.754931i
$647$			5.41943e16i			0.738802i	0.929270	+	0.369401i	$0.120437\pi$
$647$			5.41943e16i			0.738802i	−0.929270	+	0.369401i	$0.879563\pi$
$648$		0			0
$649$	2.14395e16			0.286910
$650$	1.53672e16	+	3.51574e15i	0.203758	+	0.0466161i
$651$		0			0
$652$	2.88537e16	−	5.97588e16i	0.375592	−	0.777887i
$653$	1.37006e17			1.76709			0.883546	−	0.468344i	$-0.155149\pi$
$653$	1.37006e17			1.76709			0.883546	+	0.468344i	$0.155149\pi$
$654$		0			0
$655$		−	1.96631e17i		−	2.49003i
$656$	8.94268e15	+	1.12610e16i	0.112213	+	0.141303i
$657$		0			0
$658$	7.51192e16	+	1.71859e16i	0.925541	+	0.211747i
$659$		−	1.47626e17i		−	1.80240i	−0.433405	−	0.901199i	$-0.642688\pi$
$659$		−	1.47626e17i		−	1.80240i	0.433405	−	0.901199i	$-0.357312\pi$
$660$		0			0
$661$	1.07423e16			0.128792			0.0643962	−	0.997924i	$-0.479488\pi$
$661$	1.07423e16			0.128792			0.0643962	+	0.997924i	$0.479488\pi$
$662$	−1.26020e16	+	5.50829e16i	−0.149724	+	0.654438i
$663$		0			0
$664$	−9.30627e15	+	1.16330e16i	−0.108584	+	0.135732i
$665$	9.49913e16			1.09838
$666$		0			0
$667$		−	9.73314e16i		−	1.10534i
$668$	−2.13070e16	+	4.41288e16i	−0.239808	+	0.496665i
$669$		0			0
$670$	−3.36779e16	+	1.47205e17i	−0.372303	+	1.62733i
$671$		−	7.19279e16i		−	0.788065i
$672$		0			0
$673$	3.81076e16			0.410129			0.205065	−	0.978748i	$-0.434260\pi$
$673$	3.81076e16			0.410129			0.205065	+	0.978748i	$0.434260\pi$
$674$	2.25269e16	+	5.15375e15i	0.240294	+	0.0549749i
$675$		0			0
$676$	−8.14508e16	−	3.93274e16i	−0.853523	−	0.412112i
$677$	−1.27844e17			−1.32785			−0.663925	−	0.747799i	$-0.731111\pi$
$677$	−1.27844e17			−1.32785			−0.663925	+	0.747799i	$0.731111\pi$
$678$		0			0
$679$			1.54449e17i			1.57604i
$680$	−1.37541e17	−	1.10031e17i	−1.39117	−	1.11292i
$681$		0			0
$682$	6.67178e16	+	1.52638e16i	0.663034	+	0.151690i
$683$			1.30569e17i			1.28622i	0.765773	+	0.643111i	$0.222357\pi$
$683$			1.30569e17i			1.28622i	−0.765773	+	0.643111i	$0.777643\pi$
$684$		0			0
$685$	−4.77998e16			−0.462682
$686$	7.93937e15	−	3.47028e16i	0.0761800	−	0.332981i
$687$		0			0
$688$	−8.72194e16	+	6.92636e16i	−0.822399	+	0.653092i
$689$	1.99359e16			0.186346
$690$		0			0
$691$			1.43495e17i			1.31816i	0.752072	+	0.659081i	$0.229055\pi$
$691$			1.43495e17i			1.31816i	−0.752072	+	0.659081i	$0.770945\pi$
$692$	2.69114e15	+	1.29938e15i	0.0245076	+	0.0118331i
$693$		0			0
$694$	−3.88450e16	+	1.69790e17i	−0.347678	+	1.51969i
$695$			2.10779e17i			1.87033i
$696$		0			0
$697$	−2.66349e16			−0.232303
$698$	−4.19549e16	−	9.59852e15i	−0.362786	−	0.0829988i
$699$		0			0
$700$	6.17568e16	−	1.27904e17i	0.524924	−	1.08717i
$701$	−9.83348e16			−0.828703			−0.414352	−	0.910117i	$-0.635992\pi$
$701$	−9.83348e16			−0.828703			−0.414352	+	0.910117i	$0.635992\pi$
$702$		0			0
$703$			3.60297e16i			0.298489i
$704$	2.09435e17	−	4.71261e16i	1.72033	−	0.387102i
$705$		0			0
$706$	−1.15610e17	−	2.64494e16i	−0.933611	−	0.213593i
$707$		−	1.17660e17i		−	0.942135i
$708$		0			0
$709$	2.30903e17			1.81782			0.908911	−	0.416990i	$-0.136915\pi$
$709$	2.30903e17			1.81782			0.908911	+	0.416990i	$0.136915\pi$
$710$	9.22616e15	−	4.03273e16i	0.0720229	−	0.314811i
$711$		0			0
$712$	−1.35856e17	−	1.08683e17i	−1.04280	−	0.834223i
$713$	4.47231e16			0.340404
$714$		0			0
$715$		−	7.44830e16i		−	0.557469i
$716$	−7.61767e16	+	1.57769e17i	−0.565385	+	1.17097i
$717$		0			0
$718$	5.32034e16	−	2.32551e17i	0.388323	−	1.69735i
$719$		−	2.49508e17i		−	1.80597i	−0.429669	−	0.902986i	$-0.641370\pi$
$719$		−	2.49508e17i		−	1.80597i	0.429669	−	0.902986i	$-0.358630\pi$
$720$		0			0
$721$	4.86226e16			0.346120
$722$	8.81190e16	+	2.01600e16i	0.622080	+	0.142321i
$723$		0			0
$724$	2.34533e17	+	1.13241e17i	1.62844	+	0.786270i
$725$	1.66415e17			1.14595
$726$		0			0
$727$			9.48578e15i			0.0642490i	0.999484	+	0.0321245i	$0.0102273\pi$
$727$			9.48578e15i			0.0642490i	−0.999484	+	0.0321245i	$0.989773\pi$
$728$	2.80333e16	−	3.50422e16i	0.188316	−	0.235398i
$729$		0			0
$730$	−3.47613e17	−	7.95276e16i	−2.29699	−	0.525510i
$731$		−	2.06295e17i		−	1.35202i
$732$		0			0
$733$	−1.66228e17			−1.07172			−0.535858	−	0.844308i	$-0.680012\pi$
$733$	−1.66228e17			−1.07172			−0.535858	+	0.844308i	$0.680012\pi$
$734$	−6.04834e16	+	2.64371e17i	−0.386776	+	1.69059i
$735$		0			0
$736$	1.26540e17	−	6.05403e16i	0.796090	−	0.380871i
$737$	3.40894e17			2.12723
$738$		0			0
$739$		−	1.22508e17i		−	0.752139i	−0.926592	−	0.376069i	$-0.877275\pi$
$739$		−	1.22508e17i		−	0.752139i	0.926592	−	0.376069i	$-0.122725\pi$
$740$	1.01538e17	+	4.90261e16i	0.618354	+	0.298564i
$741$		0			0
$742$	4.00586e16	−	1.75095e17i	0.240034	−	1.04918i
$743$			2.69909e17i			1.60430i	0.597125	+	0.802148i	$0.296310\pi$
$743$			2.69909e17i			1.60430i	−0.597125	+	0.802148i	$0.703690\pi$
$744$		0			0
$745$	3.64453e17			2.13159
$746$	1.27587e17	+	2.91896e16i	0.740241	+	0.169354i
$747$		0			0
$748$	−1.72888e17	+	3.58068e17i	−0.987087	+	2.04435i
$749$	−2.11343e17			−1.19701
$750$		0			0
$751$			8.47181e16i			0.472212i	0.971727	+	0.236106i	$0.0758712\pi$
$751$			8.47181e16i			0.472212i	−0.971727	+	0.236106i	$0.924129\pi$
$752$	−1.01903e17	+	8.09241e16i	−0.563480	+	0.447477i
$753$		0			0
$754$	5.12550e16	+	1.17262e16i	0.278938	+	0.0638160i
$755$		−	2.06780e17i		−	1.11642i
$756$		0			0
$757$	1.65174e17			0.877740			0.438870	−	0.898550i	$-0.355379\pi$
$757$	1.65174e17			0.877740			0.438870	+	0.898550i	$0.355379\pi$
$758$	4.50004e16	−	1.96696e17i	0.237247	−	1.03700i
$759$		0			0
$760$	−1.00204e17	+	1.25257e17i	−0.519999	+	0.650009i
$761$	2.79189e17			1.43744			0.718722	−	0.695298i	$-0.244728\pi$
$761$	2.79189e17			1.43744			0.718722	+	0.695298i	$0.244728\pi$
$762$		0			0
$763$		−	2.63348e17i		−	1.33470i
$764$	1.24230e17	−	2.57293e17i	0.624694	−	1.29380i
$765$		0			0
$766$	1.02463e16	−	4.47864e16i	0.0507219	−	0.221704i
$767$			7.56811e15i			0.0371719i
$768$		0			0
$769$	1.33836e17			0.647167			0.323583	−	0.946200i	$-0.395112\pi$
$769$	1.33836e17			0.647167			0.323583	+	0.946200i	$0.395112\pi$
$770$	−6.54177e17	−	1.49664e17i	−3.13871	−	0.718080i
$771$		0			0
$772$	−5.53277e16	−	2.67142e16i	−0.261360	−	0.126194i
$773$	−2.23145e17			−1.04595			−0.522975	−	0.852348i	$-0.675178\pi$
$773$	−2.23145e17			−1.04595			−0.522975	+	0.852348i	$0.675178\pi$
$774$		0			0
$775$			7.64667e16i			0.352909i
$776$	−2.03658e17	−	1.62924e17i	−0.932679	−	0.746132i
$777$		0			0
$778$	1.28565e17	+	2.94133e16i	0.579755	+	0.132637i
$779$			2.42560e16i			0.108541i
$780$		0			0
$781$	−9.33889e16			−0.411518
$782$	−5.79462e16	+	2.53282e17i	−0.253387	+	1.10755i
$783$		0			0
$784$	−1.07029e17	−	1.34776e17i	−0.460900	−	0.580383i
$785$	1.21801e17			0.520514
$786$		0			0
$787$			2.88562e17i			1.21448i	0.794519	+	0.607240i	$0.207723\pi$
$787$			2.88562e17i			1.21448i	−0.794519	+	0.607240i	$0.792277\pi$
$788$	3.56305e16	+	1.72037e16i	0.148821	+	0.0718562i
$789$		0			0
$790$	−1.05797e17	+	4.62436e17i	−0.435221	+	1.90234i
$791$		−	5.74058e16i		−	0.234367i
$792$		0			0
$793$	2.53905e16			0.102101
$794$	3.04970e17	+	6.97715e16i	1.21712	+	0.278455i
$795$		0			0
$796$	9.96336e16	−	2.06351e17i	0.391677	−	0.811200i
$797$	−2.67724e17			−1.04457			−0.522285	−	0.852771i	$-0.674920\pi$
$797$	−2.67724e17			−1.04457			−0.522285	+	0.852771i	$0.674920\pi$
$798$		0			0
$799$		−	2.41025e17i		−	0.926362i
$800$	1.03511e17	+	2.16356e17i	0.394861	+	0.825332i
$801$		0			0
$802$	1.62405e16	+	3.71552e15i	0.0610312	+	0.0139628i
$803$			8.04993e17i			3.00261i
$804$		0			0
$805$	−4.38516e17			−1.61143
$806$	−5.38812e15	+	2.35513e16i	−0.0196529	+	0.0859024i
$807$		0			0
$808$	1.55148e17	+	1.24117e17i	0.557543	+	0.446028i
$809$	−4.94956e15			−0.0176553			−0.00882766	−	0.999961i	$-0.502810\pi$
$809$	−4.94956e15			−0.0176553			−0.00882766	+	0.999961i	$0.502810\pi$
$810$		0			0
$811$			9.75802e16i			0.342954i	0.985188	+	0.171477i	$0.0548540\pi$
$811$			9.75802e16i			0.342954i	−0.985188	+	0.171477i	$0.945146\pi$
$812$	2.05980e17	−	4.26605e17i	0.718604	−	1.48830i
$813$		0			0
$814$	5.67667e16	−	2.48126e17i	0.195140	−	0.852954i
$815$		−	3.50302e17i		−	1.19536i
$816$		0			0
$817$	−1.87870e17			−0.631720
$818$	−2.42114e17	−	5.53914e16i	−0.808166	−	0.184894i
$819$		0			0
$820$	6.83576e16	+	3.30055e16i	0.224856	+	0.108568i
$821$	−5.21711e17			−1.70362			−0.851808	−	0.523855i	$-0.824493\pi$
$821$	−5.21711e17			−1.70362			−0.851808	+	0.523855i	$0.824493\pi$
$822$		0			0
$823$		−	6.00186e17i		−	1.93146i	−0.259542	−	0.965732i	$-0.583572\pi$
$823$		−	6.00186e17i		−	1.93146i	0.259542	−	0.965732i	$-0.416428\pi$
$824$	−5.12907e16	+	6.41143e16i	−0.163861	+	0.204829i
$825$		0			0
$826$	6.64700e16	+	1.52071e16i	0.209289	+	0.0478814i
$827$			5.10181e17i			1.59475i	0.603487	+	0.797373i	$0.293778\pi$
$827$			5.10181e17i			1.59475i	−0.603487	+	0.797373i	$0.706222\pi$
$828$		0			0
$829$	−6.30673e17			−1.94302			−0.971510	−	0.237000i	$-0.923836\pi$
$829$	−6.30673e17			−1.94302			−0.971510	+	0.237000i	$0.923836\pi$
$830$	−1.75384e16	+	7.66601e16i	−0.0536442	+	0.234477i
$831$		0			0
$832$	1.66355e16	+	7.39302e16i	0.0501528	+	0.222885i
$833$	3.18777e17			0.954150
$834$		0			0
$835$			2.58680e17i			0.763210i
$836$	3.26087e17	+	1.57447e17i	0.955203	+	0.461206i
$837$		0			0
$838$	−4.51746e16	+	1.97457e17i	−0.130446	+	0.570176i
$839$		−	1.63773e17i		−	0.469538i	−0.972051	−	0.234769i	$-0.924567\pi$
$839$		−	1.63773e17i		−	0.469538i	0.972051	−	0.234769i	$-0.0754333\pi$
$840$		0			0
$841$	2.01238e17			0.568765
$842$	−4.67834e17	−	1.07032e17i	−1.31286	−	0.300359i
$843$		0			0
$844$	−9.30746e15	+	1.92766e16i	−0.0257499	+	0.0533306i
$845$	−4.77459e17			−1.31158
$846$		0			0
$847$			1.02772e18i			2.78338i
$848$	1.88626e17	+	2.37525e17i	0.507255	+	0.638755i
$849$		0			0
$850$	−4.33056e17	−	9.90753e16i	−1.14823	−	0.262695i
$851$		−	1.66327e17i		−	0.437910i
$852$		0			0
$853$	−3.50732e17			−0.910502			−0.455251	−	0.890363i	$-0.650450\pi$
$853$	−3.50732e17			−0.910502			−0.455251	+	0.890363i	$0.650450\pi$
$854$	5.10188e16	−	2.23002e17i	0.131517	−	0.574860i
$855$		0			0
$856$	2.22940e17	−	2.78679e17i	0.566690	−	0.708374i
$857$	−7.54363e17			−1.90412			−0.952062	−	0.305905i	$-0.901041\pi$
$857$	−7.54363e17			−1.90412			−0.952062	+	0.305905i	$0.901041\pi$
$858$		0			0
$859$		−	3.62762e17i		−	0.902947i	−0.892284	−	0.451474i	$-0.850899\pi$
$859$		−	3.62762e17i		−	0.902947i	0.892284	−	0.451474i	$-0.149101\pi$
$860$	−2.55637e17	+	5.29449e17i	−0.631877	+	1.30868i
$861$		0			0
$862$	1.33086e16	−	5.81716e16i	0.0324406	−	0.141797i
$863$		−	6.77574e17i		−	1.64018i	−0.572234	−	0.820090i	$-0.693923\pi$
$863$		−	6.77574e17i		−	1.64018i	0.572234	−	0.820090i	$-0.306077\pi$
$864$		0			0
$865$	1.57753e16			0.0376600
$866$	5.59796e17	+	1.28071e17i	1.32716	+	0.303630i
$867$		0			0
$868$	1.96022e17	+	9.46467e16i	0.458340	+	0.221303i
$869$	1.07090e18			2.48673
$870$		0			0
$871$			1.20335e17i			0.275603i
$872$	3.47254e17	+	2.77799e17i	0.789856	+	0.631875i
$873$		0			0
$874$	2.30660e17	+	5.27708e16i	0.517491	+	0.118393i
$875$			6.97169e16i			0.155342i
$876$		0			0
$877$	5.19244e17			1.14123			0.570616	−	0.821217i	$-0.306705\pi$
$877$	5.19244e17			1.14123			0.570616	+	0.821217i	$0.306705\pi$
$878$	1.16515e17	−	5.09285e17i	0.254340	−	1.11172i
$879$		0			0
$880$	8.87422e17	−	7.04729e17i	1.91088	−	1.51749i
$881$	3.20562e17			0.685577			0.342789	−	0.939413i	$-0.388629\pi$
$881$	3.20562e17			0.685577			0.342789	+	0.939413i	$0.388629\pi$
$882$		0			0
$883$		−	3.58284e17i		−	0.755897i	−0.925827	−	0.377949i	$-0.876630\pi$
$883$		−	3.58284e17i		−	0.755897i	0.925827	−	0.377949i	$-0.123370\pi$
$884$	−1.26398e17	−	6.10293e16i	−0.264865	−	0.127887i
$885$		0			0
$886$	−1.22094e14	+	5.33669e14i	−0.000252401	+	0.00110324i
$887$		−	4.08613e17i		−	0.839017i	−0.907751	−	0.419509i	$-0.862202\pi$
$887$		−	4.08613e17i		−	0.839017i	0.907751	−	0.419509i	$-0.137798\pi$
$888$		0			0
$889$	4.12624e17			0.835880
$890$	−8.95274e17	−	2.04822e17i	−1.80142	−	0.412133i
$891$		0			0
$892$	9.84827e16	−	2.03967e17i	0.195511	−	0.404922i
$893$	−2.19498e17			−0.432834
$894$		0			0
$895$			9.24833e17i			1.79939i
$896$	6.82749e17	+	2.44536e15i	1.31951	+	0.00472601i
$897$		0			0
$898$	3.26330e17	+	7.46583e16i	0.622298	+	0.142370i
$899$			2.55043e17i			0.483120i
$900$		0			0
$901$	−5.61805e17			−1.05011
$902$	3.82166e16	−	1.67044e17i	0.0709599	−	0.310164i
$903$		0			0
$904$	7.56960e16	+	6.05558e16i	0.138695	+	0.110955i
$905$	1.37481e18			2.50238
$906$		0			0
$907$		−	1.70610e17i		−	0.306451i	−0.988191	−	0.153225i	$-0.951034\pi$
$907$		−	1.70610e17i		−	0.306451i	0.988191	−	0.153225i	$-0.0489661\pi$
$908$	2.70606e17	−	5.60451e17i	0.482861	−	1.00005i
$909$		0			0
$910$	5.28312e16	−	2.30924e17i	0.0930340	−	0.406650i
$911$		−	4.75780e17i		−	0.832331i	−0.909289	−	0.416165i	$-0.863374\pi$
$911$		−	4.75780e17i		−	0.832331i	0.909289	−	0.416165i	$-0.136626\pi$
$912$		0			0
$913$	1.77527e17			0.306507
$914$	5.71955e17	+	1.30853e17i	0.981035	+	0.224443i
$915$		0			0
$916$	−7.91878e17	−	3.82347e17i	−1.34056	−	0.647269i
$917$	−1.41176e18			−2.37435
$918$		0			0
$919$		−	8.39899e17i		−	1.39423i	−0.716960	−	0.697114i	$-0.754467\pi$
$919$		−	8.39899e17i		−	1.39423i	0.716960	−	0.697114i	$-0.245533\pi$
$920$	4.62579e17	−	5.78232e17i	0.762885	−	0.953620i
$921$		0			0
$922$	−3.48178e17	−	7.96569e16i	−0.566782	−	0.129669i
$923$		−	3.29662e16i		−	0.0533161i
$924$		0			0
$925$	2.84382e17			0.453996
$926$	−1.36890e17	+	5.98344e17i	−0.217123	+	0.949041i
$927$		0			0
$928$	3.45244e17	+	7.21622e17i	0.540552	+	1.12985i
$929$	−3.96383e17			−0.616625			−0.308313	−	0.951285i	$-0.599764\pi$
$929$	−3.96383e17			−0.616625			−0.308313	+	0.951285i	$0.599764\pi$
$930$		0			0
$931$		−	2.90305e17i		−	0.445817i
$932$	−8.11102e17	−	3.91629e17i	−1.23760	−	0.597557i
$933$		0			0
$934$	3.52722e16	−	1.54174e17i	0.0531314	−	0.232236i
$935$			2.09897e18i			3.14149i
$936$		0			0
$937$	−1.17315e18			−1.73347			−0.866734	−	0.498771i	$-0.833785\pi$
$937$	−1.17315e18			−1.73347			−0.866734	+	0.498771i	$0.833785\pi$
$938$	1.05689e18	+	2.41798e17i	1.55172	+	0.355006i
$939$		0			0
$940$	−2.98673e17	+	6.18581e17i	−0.432942	+	0.896664i
$941$	7.22130e17			1.04011			0.520053	−	0.854134i	$-0.325912\pi$
$941$	7.22130e17			1.04011			0.520053	+	0.854134i	$0.325912\pi$
$942$		0			0
$943$		−	1.11975e17i		−	0.159240i
$944$	−9.01697e16	+	7.16065e16i	−0.127417	+	0.101186i
$945$		0			0
$946$	1.29380e18	+	2.95999e17i	1.80518	+	0.412993i
$947$		−	4.60861e17i		−	0.638954i	−0.947594	−	0.319477i	$-0.896493\pi$
$947$		−	4.60861e17i		−	0.638954i	0.947594	−	0.319477i	$-0.103507\pi$
$948$		0			0
$949$	−2.84162e17			−0.389017
$950$	−9.02264e16	+	3.94377e17i	−0.122742	+	0.536501i
$951$		0			0
$952$	−7.89994e17	+	9.87508e17i	−1.06121	+	1.32654i
$953$	8.66560e16			0.115675			0.0578377	−	0.998326i	$-0.481579\pi$
$953$	8.66560e16			0.115675			0.0578377	+	0.998326i	$0.481579\pi$
$954$		0			0
$955$		−	1.50823e18i		−	1.98815i
$956$	−5.08239e17	+	1.05261e18i	−0.665765	+	1.37886i
$957$		0			0
$958$	−1.49588e17	+	6.53845e17i	−0.193510	+	0.845827i
$959$			3.43189e17i			0.441186i
$960$		0			0
$961$	6.70472e17			0.851217
$962$	8.75881e16	+	2.00386e16i	0.110508	+	0.0252823i
$963$		0			0
$964$	−8.62814e17	−	4.16598e17i	−1.07512	−	0.519104i
$965$	−3.24327e17			−0.401624
$966$		0			0
$967$			2.58380e17i			0.316009i	0.987438	+	0.158005i	$0.0505061\pi$
$967$			2.58380e17i			0.316009i	−0.987438	+	0.158005i	$0.949494\pi$
$968$	−1.35516e18	−	1.08411e18i	−1.64717	−	1.31771i
$969$		0			0
$970$	−1.34208e18	−	3.07044e17i	−1.61120	−	0.368613i
$971$		−	4.34867e17i		−	0.518849i	−0.965763	−	0.259424i	$-0.916467\pi$
$971$		−	4.34867e17i		−	0.518849i	0.965763	−	0.259424i	$-0.0835329\pi$
$972$		0			0
$973$	1.51333e18			1.78344
$974$	2.08505e16	−	9.11372e16i	0.0244210	−	0.106744i
$975$		0			0
$976$	2.40235e17	+	3.02513e17i	0.277931	+	0.349981i
$977$	−1.10041e17			−0.126528			−0.0632641	−	0.997997i	$-0.520151\pi$
$977$	−1.10041e17			−0.126528			−0.0632641	+	0.997997i	$0.520151\pi$
$978$		0			0
$979$			2.07325e18i			2.35481i
$980$	−8.18130e17	−	3.95022e17i	−0.923561	−	0.445928i
$981$		0			0
$982$	1.32620e17	−	5.79679e17i	0.147891	−	0.646426i
$983$		−	2.65231e17i		−	0.293970i	−0.989139	−	0.146985i	$-0.953043\pi$
$983$		−	2.65231e17i		−	0.293970i	0.989139	−	0.146985i	$-0.0469568\pi$
$984$		0			0
$985$	2.08864e17			0.228689
$986$	−1.44439e18	−	3.30450e17i	−1.57189	−	0.359621i
$987$		0			0
$988$	−5.55784e16	+	1.15108e17i	−0.0597537	+	0.123756i
$989$	8.67278e17			0.926789
$990$		0			0
$991$			1.55644e18i			1.64320i	0.570065	+	0.821600i	$0.306918\pi$
$991$			1.55644e18i			1.64320i	−0.570065	+	0.821600i	$0.693082\pi$
$992$	−3.31581e17	+	1.58637e17i	−0.347952	+	0.166470i
$993$		0			0
$994$	−2.89539e17	−	6.62413e16i	−0.300185	−	0.0686769i
$995$		−	1.20961e18i		−	1.24655i
$996$		0			0
$997$	−5.97707e17			−0.608580			−0.304290	−	0.952579i	$-0.598419\pi$
$997$	−5.97707e17			−0.608580			−0.304290	+	0.952579i	$0.598419\pi$
$998$	6.50404e16	−	2.84290e17i	0.0658264	−	0.287726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.13.d.d.19.12		12
3.2	odd	2		12.13.d.a.7.1	✓	12
4.3	odd	2	inner	36.13.d.d.19.11		12
12.11	even	2		12.13.d.a.7.2	yes	12
24.5	odd	2		192.13.g.e.127.11		12
24.11	even	2		192.13.g.e.127.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.13.d.a.7.1	✓	12	3.2	odd	2
12.13.d.a.7.2	yes	12	12.11	even	2
36.13.d.d.19.11		12	4.3	odd	2	inner
36.13.d.d.19.12		12	1.1	even	1	trivial
192.13.g.e.127.5		12	24.11	even	2
192.13.g.e.127.11		12	24.5	odd	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(62.3881 + 14.2733i) q^{2} +(3688.55 + 1780.96i) q^{4} +21622.0 q^{5} -155240. i q^{7} +(204701. + 163759. i) q^{8} +O(q^{10})\)	\(q+(62.3881 + 14.2733i) q^{2} +(3688.55 + 1780.96i) q^{4} +21622.0 q^{5} -155240. i q^{7} +(204701. + 163759. i) q^{8} +(1.34896e6 + 308617. i) q^{10} -3.12388e6i q^{11} +1.10272e6 q^{13} +(2.21578e6 - 9.68513e6i) q^{14} +(1.04336e7 + 1.31383e7i) q^{16} -3.10754e7 q^{17} +2.82999e7i q^{19} +(7.97538e7 + 3.85080e7i) q^{20} +(4.45879e7 - 1.94893e8i) q^{22} -1.30643e8i q^{23} +2.23371e8 q^{25} +(6.87969e7 + 1.57395e7i) q^{26} +(2.76477e8 - 5.72610e8i) q^{28} +7.45018e8 q^{29} +3.42331e8i q^{31} +(4.63403e8 + 9.68597e8i) q^{32} +(-1.93873e9 - 4.43547e8i) q^{34} -3.35660e9i q^{35} +1.27314e9 q^{37} +(-4.03931e8 + 1.76557e9i) q^{38} +(4.42605e9 + 3.54079e9i) q^{40} +8.57107e8 q^{41} +6.63854e9i q^{43} +(5.56351e9 - 1.15226e10i) q^{44} +(1.86470e9 - 8.15056e9i) q^{46} +7.75614e9i q^{47} -1.02582e10 q^{49} +(1.39357e10 + 3.18823e9i) q^{50} +(4.06745e9 + 1.96391e9i) q^{52} +1.80788e10 q^{53} -6.75445e10i q^{55} +(2.54219e10 - 3.17778e10i) q^{56} +(4.64803e10 + 1.06338e10i) q^{58} +6.86310e9i q^{59} +2.30252e10 q^{61} +(-4.88618e9 + 2.13574e10i) q^{62} +(1.50858e10 + 6.70432e10i) q^{64} +2.38431e10 q^{65} +1.09125e11i q^{67} +(-1.14623e11 - 5.53441e10i) q^{68} +(4.79097e10 - 2.09412e11i) q^{70} -2.98952e10i q^{71} -2.57691e11 q^{73} +(7.94288e10 + 1.81719e10i) q^{74} +(-5.04010e10 + 1.04385e11i) q^{76} -4.84951e11 q^{77} +3.42810e11i q^{79} +(2.25594e11 + 2.84077e11i) q^{80} +(5.34733e10 + 1.22337e10i) q^{82} +5.68292e10i q^{83} -6.71912e11 q^{85} +(-9.47536e10 + 4.14166e11i) q^{86} +(5.11561e11 - 6.39462e11i) q^{88} -6.63679e11 q^{89} -1.71187e11i q^{91} +(2.32670e11 - 4.81883e11i) q^{92} +(-1.10705e11 + 4.83891e11i) q^{94} +6.11900e11i q^{95} -9.94906e11 q^{97} +(-6.39989e11 - 1.46418e11i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 90 q^{2} - 4692 q^{4} + 10296 q^{5} + 648000 q^{8}+O(q^{10}) \) 12 * q + 90 * q^2 - 4692 * q^4 + 10296 * q^5 + 648000 * q^8	\( 12 q + 90 q^{2} - 4692 q^{4} + 10296 q^{5} + 648000 q^{8} + 923028 q^{10} + 2094840 q^{13} - 15389208 q^{14} - 61526928 q^{16} + 12097800 q^{17} + 377644248 q^{20} + 482545560 q^{22} + 1058748132 q^{25} - 243358236 q^{26} - 185369520 q^{28} - 1997608680 q^{29} - 1733536800 q^{32} - 7816269348 q^{34} - 960170280 q^{37} + 8280525240 q^{38} + 3985807104 q^{40} - 5806392696 q^{41} - 4989496464 q^{44} + 4149450240 q^{46} - 60479071668 q^{49} - 68552901522 q^{50} - 31090133640 q^{52} - 42482511720 q^{53} + 38053468224 q^{56} + 159666562500 q^{58} + 137368568088 q^{61} + 27876030840 q^{62} + 188355529344 q^{64} + 328250713392 q^{65} - 77938316280 q^{68} - 454939318704 q^{70} - 804477880680 q^{73} + 502785766548 q^{74} + 143972453808 q^{76} - 1383727360320 q^{77} + 417712547808 q^{80} + 460673773020 q^{82} + 1437981718224 q^{85} - 1255416205464 q^{86} + 47622991680 q^{88} + 1422946205928 q^{89} + 3462722444160 q^{92} + 847910842896 q^{94} - 4056673857000 q^{97} - 1702751294790 q^{98}+O(q^{100}) \) 12 * q + 90 * q^2 - 4692 * q^4 + 10296 * q^5 + 648000 * q^8 + 923028 * q^10 + 2094840 * q^13 - 15389208 * q^14 - 61526928 * q^16 + 12097800 * q^17 + 377644248 * q^20 + 482545560 * q^22 + 1058748132 * q^25 - 243358236 * q^26 - 185369520 * q^28 - 1997608680 * q^29 - 1733536800 * q^32 - 7816269348 * q^34 - 960170280 * q^37 + 8280525240 * q^38 + 3985807104 * q^40 - 5806392696 * q^41 - 4989496464 * q^44 + 4149450240 * q^46 - 60479071668 * q^49 - 68552901522 * q^50 - 31090133640 * q^52 - 42482511720 * q^53 + 38053468224 * q^56 + 159666562500 * q^58 + 137368568088 * q^61 + 27876030840 * q^62 + 188355529344 * q^64 + 328250713392 * q^65 - 77938316280 * q^68 - 454939318704 * q^70 - 804477880680 * q^73 + 502785766548 * q^74 + 143972453808 * q^76 - 1383727360320 * q^77 + 417712547808 * q^80 + 460673773020 * q^82 + 1437981718224 * q^85 - 1255416205464 * q^86 + 47622991680 * q^88 + 1422946205928 * q^89 + 3462722444160 * q^92 + 847910842896 * q^94 - 4056673857000 * q^97 - 1702751294790 * q^98

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