LMFDB - Embedded newform 90.12.c.d.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,12,Mod(19,90)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 12, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("90.19"); S:= CuspForms(chi, 12); N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12288,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$69.1508862504$
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} + 2686231540547x^{8} + 128219731460991388255453x^{4} + 14060999354420335522970873124 $ x^12 + 2686231540547x^8 + 128219731460991388255453x^4 + 14060999354420335522970873124
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{16}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Root			$-901.131 - 901.131i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.12.c.d.19.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-32.0000i q^{2} -1024.00 q^{4} +(6895.58 + 1130.97i) q^{5} +14383.7i q^{7} +32768.0i q^{8} +(36191.1 - 220659. i) q^{10} -493678. q^{11} +984091. i q^{13} +460278. q^{14} +1.04858e6 q^{16} -9.98110e6i q^{17} -9.97709e6 q^{19} +(-7.06107e6 - 1.15812e6i) q^{20} +1.57977e7i q^{22} -4.66489e6i q^{23} +(4.62699e7 + 1.55974e7i) q^{25} +3.14909e7 q^{26} -1.47289e7i q^{28} +4.31977e7 q^{29} +1.06016e8 q^{31} -3.35544e7i q^{32} -3.19395e8 q^{34} +(-1.62675e7 + 9.91838e7i) q^{35} +1.33767e8i q^{37} +3.19267e8i q^{38} +(-3.70597e7 + 2.25954e8i) q^{40} +1.24554e9 q^{41} -1.57980e9i q^{43} +5.05526e8 q^{44} -1.49277e8 q^{46} +3.78538e8i q^{47} +1.77044e9 q^{49} +(4.99117e8 - 1.48064e9i) q^{50} -1.00771e9i q^{52} -3.54353e9i q^{53} +(-3.40419e9 - 5.58336e8i) q^{55} -4.71324e8 q^{56} -1.38233e9i q^{58} +6.43548e9 q^{59} +2.83608e8 q^{61} -3.39251e9i q^{62} -1.07374e9 q^{64} +(-1.11298e9 + 6.78588e9i) q^{65} -7.62962e9i q^{67} +1.02207e10i q^{68} +(3.17388e9 + 5.20561e8i) q^{70} -1.48476e9 q^{71} -1.24759e10i q^{73} +4.28053e9 q^{74} +1.02165e10 q^{76} -7.10090e9i q^{77} -3.51048e10 q^{79} +(7.23054e9 + 1.18591e9i) q^{80} -3.98573e10i q^{82} +9.64068e9i q^{83} +(1.12884e10 - 6.88255e10i) q^{85} -5.05536e10 q^{86} -1.61768e10i q^{88} -4.39019e10 q^{89} -1.41548e10 q^{91} +4.77685e9i q^{92} +1.21132e10 q^{94} +(-6.87978e10 - 1.12838e10i) q^{95} -1.45178e11i q^{97} -5.66540e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12288 q^{4} + 56448 q^{10} + 12582912 q^{16} - 489648 q^{19} - 125575548 q^{25} + 47933952 q^{31} + 341743872 q^{34} - 57802752 q^{40} + 3346675200 q^{46} - 6178917036 q^{49} - 11944070688 q^{55}+ \cdots - 10041254400 q^{94}+O(q^{100}) $ 12 * q - 12288 * q^4 + 56448 * q^10 + 12582912 * q^16 - 489648 * q^19 - 125575548 * q^25 + 47933952 * q^31 + 341743872 * q^34 - 57802752 * q^40 + 3346675200 * q^46 - 6178917036 * q^49 - 11944070688 * q^55 + 39086224824 * q^61 - 12884901888 * q^64 - 20035144704 * q^70 + 501399552 * q^76 - 15150606048 * q^79 - 9988044312 * q^85 - 62442252096 * q^91 - 10041254400 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	32.0000i		−	0.707107i
$2$		−	32.0000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1024.00			−0.500000
$5$	6895.58	+	1130.97i	0.986815	+	0.161852i
$5$	6895.58	+	1130.97i	0.986815	+	0.161852i
$6$		0			0
$7$			14383.7i			0.323467i	0.986834	+	0.161734i	$0.0517086\pi$
$7$			14383.7i			0.323467i	−0.986834	+	0.161734i	$0.948291\pi$
$8$			32768.0i			0.353553i
$9$		0			0
$10$	36191.1	−	220659.i	0.114446	−	0.697784i
$11$	−493678.			−0.924238			−0.462119	−	0.886818i	$-0.652911\pi$
$11$	−493678.			−0.924238			−0.462119	+	0.886818i	$0.652911\pi$
$12$		0			0
$13$			984091.i			0.735101i	0.930004	+	0.367550i	$0.119803\pi$
$13$			984091.i			0.735101i	−0.930004	+	0.367550i	$0.880197\pi$
$14$	460278.			0.228726
$15$		0			0
$16$	1.04858e6			0.250000
$17$		−	9.98110e6i		−	1.70494i	−0.522775	−	0.852471i	$-0.675103\pi$
$17$		−	9.98110e6i		−	1.70494i	0.522775	−	0.852471i	$-0.324897\pi$
$18$		0			0
$19$	−9.97709e6			−0.924398			−0.462199	−	0.886776i	$-0.652940\pi$
$19$	−9.97709e6			−0.924398			−0.462199	+	0.886776i	$0.652940\pi$
$20$	−7.06107e6	−	1.15812e6i	−0.493408	−	0.0809258i
$21$		0			0
$22$			1.57977e7i			0.653535i
$23$		−	4.66489e6i		−	0.151126i	−0.997141	−	0.0755629i	$-0.975925\pi$
$23$		−	4.66489e6i		−	0.151126i	0.997141	−	0.0755629i	$-0.0240754\pi$
$24$		0			0
$25$	4.62699e7	+	1.55974e7i	0.947608	+	0.319435i
$26$	3.14909e7			0.519795
$27$		0			0
$28$		−	1.47289e7i		−	0.161734i
$29$	4.31977e7			0.391085			0.195543	−	0.980695i	$-0.437353\pi$
$29$	4.31977e7			0.391085			0.195543	+	0.980695i	$0.437353\pi$
$30$		0			0
$31$	1.06016e8			0.665092			0.332546	−	0.943087i	$-0.392092\pi$
$31$	1.06016e8			0.665092			0.332546	+	0.943087i	$0.392092\pi$
$32$		−	3.35544e7i		−	0.176777i
$33$		0			0
$34$	−3.19395e8			−1.20558
$35$	−1.62675e7	+	9.91838e7i	−0.0523537	+	0.319203i
$36$		0			0
$37$			1.33767e8i			0.317131i	0.987348	+	0.158565i	$0.0506868\pi$
$37$			1.33767e8i			0.317131i	−0.987348	+	0.158565i	$0.949313\pi$
$38$			3.19267e8i			0.653648i
$39$		0			0
$40$	−3.70597e7	+	2.25954e8i	−0.0572232	+	0.348892i
$41$	1.24554e9			1.67899			0.839493	−	0.543371i	$-0.182852\pi$
$41$	1.24554e9			1.67899			0.839493	+	0.543371i	$0.182852\pi$
$42$		0			0
$43$		−	1.57980e9i		−	1.63880i	−0.573224	−	0.819399i	$-0.694307\pi$
$43$		−	1.57980e9i		−	1.63880i	0.573224	−	0.819399i	$-0.305693\pi$
$44$	5.05526e8			0.462119
$45$		0			0
$46$	−1.49277e8			−0.106862
$47$			3.78538e8i			0.240753i	0.992728	+	0.120376i	$0.0384101\pi$
$47$			3.78538e8i			0.240753i	−0.992728	+	0.120376i	$0.961590\pi$
$48$		0			0
$49$	1.77044e9			0.895369
$50$	4.99117e8	−	1.48064e9i	0.225875	−	0.670060i
$51$		0			0
$52$		−	1.00771e9i		−	0.367550i
$53$		−	3.54353e9i		−	1.16391i	−0.813222	−	0.581954i	$-0.802288\pi$
$53$		−	3.54353e9i		−	1.16391i	0.813222	−	0.581954i	$-0.197712\pi$
$54$		0			0
$55$	−3.40419e9	−	5.58336e8i	−0.912052	−	0.149589i
$56$	−4.71324e8			−0.114363
$57$		0			0
$58$		−	1.38233e9i		−	0.276539i
$59$	6.43548e9			1.17191			0.585956	−	0.810343i	$-0.300719\pi$
$59$	6.43548e9			1.17191			0.585956	+	0.810343i	$0.300719\pi$
$60$		0			0
$61$	2.83608e8			0.0429937			0.0214969	−	0.999769i	$-0.493157\pi$
$61$	2.83608e8			0.0429937			0.0214969	+	0.999769i	$0.493157\pi$
$62$		−	3.39251e9i		−	0.470291i
$63$		0			0
$64$	−1.07374e9			−0.125000
$65$	−1.11298e9	+	6.78588e9i	−0.118977	+	0.725408i
$66$		0			0
$67$		−	7.62962e9i		−	0.690385i	−0.938532	−	0.345192i	$-0.887814\pi$
$67$		−	7.62962e9i		−	0.690385i	0.938532	−	0.345192i	$-0.112186\pi$
$68$			1.02207e10i			0.852471i
$69$		0			0
$70$	3.17388e9	+	5.20561e8i	0.225710	+	0.0370197i
$71$	−1.48476e9			−0.0976641			−0.0488320	−	0.998807i	$-0.515550\pi$
$71$	−1.48476e9			−0.0976641			−0.0488320	+	0.998807i	$0.515550\pi$
$72$		0			0
$73$		−	1.24759e10i		−	0.704362i	−0.935932	−	0.352181i	$-0.885440\pi$
$73$		−	1.24759e10i		−	0.704362i	0.935932	−	0.352181i	$-0.114560\pi$
$74$	4.28053e9			0.224245
$75$		0			0
$76$	1.02165e10			0.462199
$77$		−	7.10090e9i		−	0.298961i
$78$		0			0
$79$	−3.51048e10			−1.28357			−0.641783	−	0.766887i	$-0.721805\pi$
$79$	−3.51048e10			−1.28357			−0.641783	+	0.766887i	$0.721805\pi$
$80$	7.23054e9	+	1.18591e9i	0.246704	+	0.0404629i
$81$		0			0
$82$		−	3.98573e10i		−	1.18722i
$83$			9.64068e9i			0.268645i	0.990938	+	0.134322i	$0.0428858\pi$
$83$			9.64068e9i			0.268645i	−0.990938	+	0.134322i	$0.957114\pi$
$84$		0			0
$85$	1.12884e10	−	6.88255e10i	0.275948	−	1.68246i
$86$	−5.05536e10			−1.15881
$87$		0			0
$88$		−	1.61768e10i		−	0.326767i
$89$	−4.39019e10			−0.833370			−0.416685	−	0.909051i	$-0.636808\pi$
$89$	−4.39019e10			−0.833370			−0.416685	+	0.909051i	$0.636808\pi$
$90$		0			0
$91$	−1.41548e10			−0.237781
$92$			4.77685e9i			0.0755629i
$93$		0			0
$94$	1.21132e10			0.170238
$95$	−6.87978e10	−	1.12838e10i	−0.912210	−	0.149615i
$96$		0			0
$97$		−	1.45178e11i		−	1.71655i	−0.513186	−	0.858277i	$-0.671535\pi$
$97$		−	1.45178e11i		−	1.71655i	0.513186	−	0.858277i	$-0.328465\pi$
$98$		−	5.66540e10i		−	0.633121i
$99$		0			0
$100$	−4.73804e10	−	1.59718e10i	−0.473804	−	0.159718i
$101$	6.96131e10			0.659058			0.329529	−	0.944146i	$-0.393110\pi$
$101$	6.96131e10			0.659058			0.329529	+	0.944146i	$0.393110\pi$
$102$		0			0
$103$		−	2.08189e11i		−	1.76951i	−0.466060	−	0.884753i	$-0.654327\pi$
$103$		−	2.08189e11i		−	1.76951i	0.466060	−	0.884753i	$-0.345673\pi$
$104$	−3.22467e10			−0.259897
$105$		0			0
$106$	−1.13393e11			−0.823007
$107$		−	1.16130e11i		−	0.800449i	−0.916417	−	0.400224i	$-0.868932\pi$
$107$		−	1.16130e11i		−	0.800449i	0.916417	−	0.400224i	$-0.131068\pi$
$108$		0			0
$109$	8.68795e10			0.540844			0.270422	−	0.962742i	$-0.412837\pi$
$109$	8.68795e10			0.540844			0.270422	+	0.962742i	$0.412837\pi$
$110$	−1.78667e10	+	1.08934e11i	−0.105776	+	0.644918i
$111$		0			0
$112$			1.50824e10i			0.0808669i
$113$			1.99548e11i			1.01887i	0.860511	+	0.509433i	$0.170145\pi$
$113$			1.99548e11i			1.01887i	−0.860511	+	0.509433i	$0.829855\pi$
$114$		0			0
$115$	5.27586e9	−	3.21671e10i	0.0244599	−	0.149133i
$116$	−4.42344e10			−0.195543
$117$		0			0
$118$		−	2.05935e11i		−	0.828667i
$119$	1.43565e11			0.551493
$120$		0			0
$121$	−4.15941e10			−0.145785
$122$		−	9.07547e9i		−	0.0304012i
$123$		0			0
$124$	−1.08560e11			−0.332546
$125$	3.01418e11	+	1.59883e11i	0.883413	+	0.468595i
$126$		0			0
$127$		−	2.85605e11i		−	0.767089i	−0.923522	−	0.383544i	$-0.874703\pi$
$127$		−	2.85605e11i		−	0.767089i	0.923522	−	0.383544i	$-0.125297\pi$
$128$			3.43597e10i			0.0883883i
$129$		0			0
$130$	2.17148e11	+	3.56153e10i	0.512941	+	0.0841296i
$131$	4.06182e11			0.919875			0.459937	−	0.887951i	$-0.347872\pi$
$131$	4.06182e11			0.919875			0.459937	+	0.887951i	$0.347872\pi$
$132$		0			0
$133$		−	1.43507e11i		−	0.299013i
$134$	−2.44148e11			−0.488176
$135$		0			0
$136$	3.27061e11			0.602788
$137$		−	6.27707e11i		−	1.11120i	−0.831448	−	0.555602i	$-0.812488\pi$
$137$		−	6.27707e11i		−	1.11120i	0.831448	−	0.555602i	$-0.187512\pi$
$138$		0			0
$139$	−7.74832e11			−1.26656			−0.633281	−	0.773922i	$-0.718292\pi$
$139$	−7.74832e11			−1.26656			−0.633281	+	0.773922i	$0.718292\pi$
$140$	1.66580e10	−	1.01564e11i	0.0261769	−	0.159601i
$141$		0			0
$142$			4.75123e10i			0.0690589i
$143$		−	4.85824e11i		−	0.679408i
$144$		0			0
$145$	2.97873e11	+	4.88554e10i	0.385929	+	0.0632978i
$146$	−3.99229e11			−0.498059
$147$		0			0
$148$		−	1.36977e11i		−	0.158565i
$149$	8.83059e11			0.985066			0.492533	−	0.870294i	$-0.336071\pi$
$149$	8.83059e11			0.985066			0.492533	+	0.870294i	$0.336071\pi$
$150$		0			0
$151$	2.46968e10			0.0256016			0.0128008	−	0.999918i	$-0.495925\pi$
$151$	2.46968e10			0.0256016			0.0128008	+	0.999918i	$0.495925\pi$
$152$		−	3.26929e11i		−	0.326824i
$153$		0			0
$154$	−2.27229e11			−0.211397
$155$	7.31041e11	+	1.19901e11i	0.656323	+	0.107646i
$156$		0			0
$157$			3.99502e11i			0.334250i	0.985936	+	0.167125i	$0.0534483\pi$
$157$			3.99502e11i			0.334250i	−0.985936	+	0.167125i	$0.946552\pi$
$158$			1.12335e12i			0.907618i
$159$		0			0
$160$	3.79491e10	−	2.31377e11i	0.0286116	−	0.174446i
$161$	6.70983e10			0.0488843
$162$		0			0
$163$			2.83368e12i			1.92894i	0.264187	+	0.964472i	$0.414896\pi$
$163$			2.83368e12i			1.92894i	−0.264187	+	0.964472i	$0.585104\pi$
$164$	−1.27543e12			−0.839493
$165$		0			0
$166$	3.08502e11			0.189960
$167$			1.28445e12i			0.765205i	0.923913	+	0.382602i	$0.124972\pi$
$167$			1.28445e12i			0.765205i	−0.923913	+	0.382602i	$0.875028\pi$
$168$		0			0
$169$	8.23725e11			0.459627
$170$	−2.20242e12	−	3.61227e11i	−1.18968	−	0.195124i
$171$		0			0
$172$			1.61771e12i			0.819399i
$173$			2.21074e10i			0.0108464i	0.999985	+	0.00542319i	$0.00172626\pi$
$173$			2.21074e10i			0.0108464i	−0.999985	+	0.00542319i	$0.998274\pi$
$174$		0			0
$175$	−2.24348e11	+	6.65532e11i	−0.103327	+	0.306520i
$176$	−5.17659e11			−0.231059
$177$		0			0
$178$			1.40486e12i			0.589282i
$179$	1.10893e12			0.451039			0.225520	−	0.974239i	$-0.427592\pi$
$179$	1.10893e12			0.451039			0.225520	+	0.974239i	$0.427592\pi$
$180$		0			0
$181$	2.61788e12			1.00165			0.500827	−	0.865548i	$-0.333029\pi$
$181$	2.61788e12			1.00165			0.500827	+	0.865548i	$0.333029\pi$
$182$			4.52955e11i			0.168137i
$183$		0			0
$184$	1.52859e11			0.0534310
$185$	−1.51286e11	+	9.22398e11i	−0.0513281	+	0.312949i
$186$		0			0
$187$			4.92745e12i			1.57577i
$188$		−	3.87623e11i		−	0.120376i
$189$		0			0
$190$	−3.61082e11	+	2.20153e12i	−0.105794	+	0.645030i
$191$	1.12739e12			0.320915			0.160457	−	0.987043i	$-0.448703\pi$
$191$	1.12739e12			0.320915			0.160457	+	0.987043i	$0.448703\pi$
$192$		0			0
$193$			2.88477e12i			0.775436i	0.921778	+	0.387718i	$0.126737\pi$
$193$			2.88477e12i			0.775436i	−0.921778	+	0.387718i	$0.873263\pi$
$194$	−4.64571e12			−1.21379
$195$		0			0
$196$	−1.81293e12			−0.447684
$197$		−	4.39441e12i		−	1.05520i	−0.849492	−	0.527601i	$-0.823092\pi$
$197$		−	4.39441e12i		−	1.05520i	0.849492	−	0.527601i	$-0.176908\pi$
$198$		0			0
$199$	−7.04590e12			−1.60046			−0.800230	−	0.599694i	$-0.795289\pi$
$199$	−7.04590e12			−1.60046			−0.800230	+	0.599694i	$0.795289\pi$
$200$	−5.11096e11	+	1.51617e12i	−0.112937	+	0.335030i
$201$		0			0
$202$		−	2.22762e12i		−	0.466024i
$203$			6.21341e11i			0.126503i
$204$		0			0
$205$	8.58873e12	+	1.40867e12i	1.65685	+	0.271746i
$206$	−6.66203e12			−1.25123
$207$		0			0
$208$			1.03189e12i			0.183775i
$209$	4.92547e12			0.854364
$210$		0			0
$211$	3.96943e12			0.653394			0.326697	−	0.945129i	$-0.394064\pi$
$211$	3.96943e12			0.653394			0.326697	+	0.945129i	$0.394064\pi$
$212$			3.62857e12i			0.581954i
$213$		0			0
$214$	−3.71616e12			−0.566003
$215$	1.78671e12	−	1.08936e13i	0.265242	−	1.61719i
$216$		0			0
$217$			1.52490e12i			0.215136i
$218$		−	2.78014e12i		−	0.382434i
$219$		0			0
$220$	3.48589e12	+	5.71736e11i	0.456026	+	0.0747947i
$221$	9.82231e12			1.25330
$222$		0			0
$223$		−	9.83562e12i		−	1.19433i	−0.802118	−	0.597166i	$-0.796293\pi$
$223$		−	9.83562e12i		−	1.19433i	0.802118	−	0.597166i	$-0.203707\pi$
$224$	4.82636e11			0.0571815
$225$		0			0
$226$	6.38555e12			0.720446
$227$			1.19389e13i			1.31468i	0.753592	+	0.657342i	$0.228319\pi$
$227$			1.19389e13i			1.31468i	−0.753592	+	0.657342i	$0.771681\pi$
$228$		0			0
$229$	−9.06605e12			−0.951312			−0.475656	−	0.879631i	$-0.657789\pi$
$229$	−9.06605e12			−0.951312			−0.475656	+	0.879631i	$0.657789\pi$
$230$	−1.02935e12	−	1.68828e11i	−0.105453	−	0.0172958i
$231$		0			0
$232$			1.41550e12i			0.138270i
$233$			6.85789e12i			0.654234i	0.944984	+	0.327117i	$0.106077\pi$
$233$			6.85789e12i			0.654234i	−0.944984	+	0.327117i	$0.893923\pi$
$234$		0			0
$235$	−4.28116e11	+	2.61024e12i	−0.0389662	+	0.237578i
$236$	−6.58993e12			−0.585956
$237$		0			0
$238$		−	4.59408e12i		−	0.389965i
$239$	1.60055e13			1.32764			0.663822	−	0.747891i	$-0.268933\pi$
$239$	1.60055e13			1.32764			0.663822	+	0.747891i	$0.268933\pi$
$240$		0			0
$241$	−1.42320e13			−1.12765			−0.563823	−	0.825896i	$-0.690670\pi$
$241$	−1.42320e13			−1.12765			−0.563823	+	0.825896i	$0.690670\pi$
$242$			1.33101e12i			0.103085i
$243$		0			0
$244$	−2.90415e11			−0.0214969
$245$	1.22082e13	+	2.00231e12i	0.883563	+	0.144917i
$246$		0			0
$247$		−	9.81837e12i		−	0.679526i
$248$			3.47393e12i			0.235146i
$249$		0			0
$250$	5.11626e12	−	9.64537e12i	0.331347	−	0.624667i
$251$	1.22090e13			0.773528			0.386764	−	0.922179i	$-0.373593\pi$
$251$	1.22090e13			0.773528			0.386764	+	0.922179i	$0.373593\pi$
$252$		0			0
$253$			2.30295e12i			0.139676i
$254$	−9.13937e12			−0.542414
$255$		0			0
$256$	1.09951e12			0.0625000
$257$		−	1.72148e13i		−	0.957791i	−0.877872	−	0.478896i	$-0.841037\pi$
$257$		−	1.72148e13i		−	0.957791i	0.877872	−	0.478896i	$-0.158963\pi$
$258$		0			0
$259$	−1.92405e12			−0.102581
$260$	1.13969e12	−	6.94874e12i	0.0594886	−	0.362704i
$261$		0			0
$262$		−	1.29978e13i		−	0.650450i
$263$		−	1.28087e13i		−	0.627692i	−0.949474	−	0.313846i	$-0.898382\pi$
$263$		−	1.28087e13i		−	0.627692i	0.949474	−	0.313846i	$-0.101618\pi$
$264$		0			0
$265$	4.00763e12	−	2.44347e13i	0.188380	−	1.14856i
$266$	−4.59223e12			−0.211434
$267$		0			0
$268$			7.81273e12i			0.345192i
$269$	−3.20929e13			−1.38922			−0.694610	−	0.719386i	$-0.744423\pi$
$269$	−3.20929e13			−1.38922			−0.694610	+	0.719386i	$0.744423\pi$
$270$		0			0
$271$	2.91487e13			1.21140			0.605700	−	0.795693i	$-0.292893\pi$
$271$	2.91487e13			1.21140			0.605700	+	0.795693i	$0.292893\pi$
$272$		−	1.04659e13i		−	0.426235i
$273$		0			0
$274$	−2.00866e13			−0.785740
$275$	−2.28424e13	−	7.70010e12i	−0.875815	−	0.295234i
$276$		0			0
$277$		−	4.06501e13i		−	1.49769i	−0.662744	−	0.748846i	$-0.730608\pi$
$277$		−	4.06501e13i		−	1.49769i	0.662744	−	0.748846i	$-0.269392\pi$
$278$			2.47946e13i			0.895594i
$279$		0			0
$280$	−3.25005e12	−	5.33055e11i	−0.112855	−	0.0185098i
$281$	1.20927e13			0.411756			0.205878	−	0.978578i	$-0.433995\pi$
$281$	1.20927e13			0.411756			0.205878	+	0.978578i	$0.433995\pi$
$282$		0			0
$283$		−	4.36486e13i		−	1.42937i	−0.699447	−	0.714685i	$-0.746570\pi$
$283$		−	4.36486e13i		−	1.42937i	0.699447	−	0.714685i	$-0.253430\pi$
$284$	1.52039e12			0.0488320
$285$		0			0
$286$	−1.55464e13			−0.480414
$287$			1.79155e13i			0.543097i
$288$		0			0
$289$	−6.53505e13			−1.90683
$290$	1.56337e12	−	9.53194e12i	0.0447583	−	0.272893i
$291$		0			0
$292$			1.27753e13i			0.352181i
$293$			2.88496e13i			0.780490i	0.920711	+	0.390245i	$0.127610\pi$
$293$			2.88496e13i			0.780490i	−0.920711	+	0.390245i	$0.872390\pi$
$294$		0			0
$295$	4.43764e13	+	7.27835e12i	1.15646	+	0.189676i
$296$	−4.38326e12			−0.112123
$297$		0			0
$298$		−	2.82579e13i		−	0.696547i
$299$	4.59068e12			0.111093
$300$		0			0
$301$	2.27233e13			0.530098
$302$		−	7.90296e11i		−	0.0181031i
$303$		0			0
$304$	−1.04617e13			−0.231100
$305$	1.95564e12	+	3.20753e11i	0.0424269	+	0.00695860i
$306$		0			0
$307$		−	1.43204e13i		−	0.299705i	−0.988708	−	0.149853i	$-0.952120\pi$
$307$		−	1.43204e13i		−	0.299705i	0.988708	−	0.149853i	$-0.0478799\pi$
$308$			7.27132e12i			0.149480i
$309$		0			0
$310$	3.83683e12	−	2.33933e13i	0.0761174	−	0.464090i
$311$	−9.57675e13			−1.86653			−0.933267	−	0.359184i	$-0.883055\pi$
$311$	−9.57675e13			−1.86653			−0.933267	+	0.359184i	$0.883055\pi$
$312$		0			0
$313$			9.23470e12i			0.173752i	0.996219	+	0.0868758i	$0.0276883\pi$
$313$			9.23470e12i			0.173752i	−0.996219	+	0.0868758i	$0.972312\pi$
$314$	1.27841e13			0.236350
$315$		0			0
$316$	3.59473e13			0.641783
$317$		−	3.85697e13i		−	0.676737i	−0.941014	−	0.338369i	$-0.890125\pi$
$317$		−	3.85697e13i		−	0.676737i	0.941014	−	0.338369i	$-0.109875\pi$
$318$		0			0
$319$	−2.13257e13			−0.361456
$320$	−7.40407e12	−	1.21437e12i	−0.123352	−	0.0202314i
$321$		0			0
$322$		−	2.14715e12i		−	0.0345664i
$323$			9.95824e13i			1.57605i
$324$		0			0
$325$	−1.53493e13	+	4.55338e13i	−0.234817	+	0.696587i
$326$	9.06779e13			1.36397
$327$		0			0
$328$			4.08139e13i			0.593611i
$329$	−5.44477e12			−0.0778757
$330$		0			0
$331$	−3.53241e13			−0.488671			−0.244336	−	0.969691i	$-0.578570\pi$
$331$	−3.53241e13			−0.488671			−0.244336	+	0.969691i	$0.578570\pi$
$332$		−	9.87206e12i		−	0.134322i
$333$		0			0
$334$	4.11025e13			0.541082
$335$	8.62888e12	−	5.26106e13i	0.111740	−	0.681282i
$336$		0			0
$337$			1.15113e14i			1.44265i	0.692598	+	0.721324i	$0.256466\pi$
$337$			1.15113e14i			1.44265i	−0.692598	+	0.721324i	$0.743534\pi$
$338$		−	2.63592e13i		−	0.325005i
$339$		0			0
$340$	−1.15593e13	+	7.04773e13i	−0.137974	+	0.841231i
$341$	−5.23377e13			−0.614703
$342$		0			0
$343$			5.39066e13i			0.613090i
$344$	5.17669e13			0.579403
$345$		0			0
$346$	7.07438e11			0.00766955
$347$		−	1.55630e14i		−	1.66067i	−0.557268	−	0.830333i	$-0.688150\pi$
$347$		−	1.55630e14i		−	1.66067i	0.557268	−	0.830333i	$-0.311850\pi$
$348$		0			0
$349$	9.23502e13			0.954768			0.477384	−	0.878695i	$-0.341585\pi$
$349$	9.23502e13			0.954768			0.477384	+	0.878695i	$0.341585\pi$
$350$	2.12970e13	+	7.17914e12i	0.216743	+	0.0730631i
$351$		0			0
$352$			1.65651e13i			0.163384i
$353$			1.37302e14i			1.33326i	0.745387	+	0.666632i	$0.232265\pi$
$353$			1.37302e14i			1.33326i	−0.745387	+	0.666632i	$0.767735\pi$
$354$		0			0
$355$	−1.02383e13	−	1.67922e12i	−0.0963764	−	0.0158071i
$356$	4.49555e13			0.416685
$357$		0			0
$358$		−	3.54859e13i		−	0.318933i
$359$	−1.52572e13			−0.135038			−0.0675189	−	0.997718i	$-0.521508\pi$
$359$	−1.52572e13			−0.135038			−0.0675189	+	0.997718i	$0.521508\pi$
$360$		0			0
$361$	−1.69479e13			−0.145488
$362$		−	8.37721e13i		−	0.708276i
$363$		0			0
$364$	1.44946e13			0.118891
$365$	1.41099e13	−	8.60286e13i	0.114002	−	0.695075i
$366$		0			0
$367$			1.82864e14i			1.43372i	0.697218	+	0.716859i	$0.254421\pi$
$367$			1.82864e14i			1.43372i	−0.697218	+	0.716859i	$0.745579\pi$
$368$		−	4.89149e12i		−	0.0377814i
$369$		0			0
$370$	2.95167e13	+	4.84116e12i	0.221289	+	0.0362944i
$371$	5.09689e13			0.376486
$372$		0			0
$373$			1.75097e14i			1.25568i	0.778340	+	0.627842i	$0.216062\pi$
$373$			1.75097e14i			1.25568i	−0.778340	+	0.627842i	$0.783938\pi$
$374$	1.57678e14			1.11424
$375$		0			0
$376$	−1.24039e13			−0.0851190
$377$			4.25105e13i			0.287487i
$378$		0			0
$379$	2.92435e13			0.192094			0.0960469	−	0.995377i	$-0.469380\pi$
$379$	2.92435e13			0.192094			0.0960469	+	0.995377i	$0.469380\pi$
$380$	7.04490e13	+	1.15546e13i	0.456105	+	0.0748077i
$381$		0			0
$382$		−	3.60764e13i		−	0.226921i
$383$			2.39337e14i			1.48394i	0.670434	+	0.741969i	$0.266108\pi$
$383$			2.39337e14i			1.48394i	−0.670434	+	0.741969i	$0.733892\pi$
$384$		0			0
$385$	8.03092e12	−	4.89648e13i	0.0483873	−	0.295019i
$386$	9.23126e13			0.548316
$387$		0			0
$388$			1.48663e14i			0.858277i
$389$	−1.12715e14			−0.641594			−0.320797	−	0.947148i	$-0.603951\pi$
$389$	−1.12715e14			−0.641594			−0.320797	+	0.947148i	$0.603951\pi$
$390$		0			0
$391$	−4.65608e13			−0.257661
$392$			5.80137e13i			0.316561i
$393$		0			0
$394$	−1.40621e14			−0.746141
$395$	−2.42068e14	−	3.97026e13i	−1.26664	−	0.207747i
$396$		0			0
$397$		−	1.86208e14i		−	0.947656i	−0.880617	−	0.473828i	$-0.842872\pi$
$397$		−	1.86208e14i		−	0.947656i	0.880617	−	0.473828i	$-0.157128\pi$
$398$			2.25469e14i			1.13170i
$399$		0			0
$400$	4.85175e13	+	1.63551e13i	0.236902	+	0.0798588i
$401$	−2.59493e13			−0.124977			−0.0624887	−	0.998046i	$-0.519904\pi$
$401$	−2.59493e13			−0.124977			−0.0624887	+	0.998046i	$0.519904\pi$
$402$		0			0
$403$			1.04329e14i			0.488910i
$404$	−7.12838e13			−0.329529
$405$		0			0
$406$	1.98829e13			0.0894514
$407$		−	6.60376e13i		−	0.293104i
$408$		0			0
$409$	1.47199e14			0.635956			0.317978	−	0.948098i	$-0.396996\pi$
$409$	1.47199e14			0.635956			0.317978	+	0.948098i	$0.396996\pi$
$410$	4.50775e13	−	2.74839e14i	0.192154	−	1.17157i
$411$		0			0
$412$			2.13185e14i			0.884753i
$413$			9.25658e13i			0.379075i
$414$		0			0
$415$	−1.09033e13	+	6.64781e13i	−0.0434806	+	0.265103i
$416$	3.30206e13			0.129949
$417$		0			0
$418$		−	1.57615e14i		−	0.604127i
$419$	−1.89584e14			−0.717172			−0.358586	−	0.933497i	$-0.616741\pi$
$419$	−1.89584e14			−0.717172			−0.358586	+	0.933497i	$0.616741\pi$
$420$		0			0
$421$	1.54796e14			0.570438			0.285219	−	0.958462i	$-0.407934\pi$
$421$	1.54796e14			0.570438			0.285219	+	0.958462i	$0.407934\pi$
$422$		−	1.27022e14i		−	0.462019i
$423$		0			0
$424$	1.16114e14			0.411503
$425$	1.55679e14	−	4.61825e14i	0.544618	−	1.61562i
$426$		0			0
$427$			4.07933e12i			0.0139071i
$428$			1.18917e14i			0.400224i
$429$		0			0
$430$	−3.48596e14	−	5.71747e13i	−1.14353	−	0.187554i
$431$	−3.79771e14			−1.22998			−0.614988	−	0.788536i	$-0.710839\pi$
$431$	−3.79771e14			−1.22998			−0.614988	+	0.788536i	$0.710839\pi$
$432$		0			0
$433$		−	1.22608e14i		−	0.387111i	−0.981089	−	0.193555i	$-0.937998\pi$
$433$		−	1.22608e14i		−	0.387111i	0.981089	−	0.193555i	$-0.0620019\pi$
$434$	4.87968e13			0.152124
$435$		0			0
$436$	−8.89646e13			−0.270422
$437$			4.65421e13i			0.139700i
$438$		0			0
$439$	3.44574e14			1.00862			0.504311	−	0.863522i	$-0.331747\pi$
$439$	3.44574e14			1.00862			0.504311	+	0.863522i	$0.331747\pi$
$440$	1.82955e13	−	1.11549e14i	0.0528878	−	0.322459i
$441$		0			0
$442$		−	3.14314e14i		−	0.886220i
$443$			5.10771e14i			1.42235i	0.703016	+	0.711174i	$0.251836\pi$
$443$			5.10771e14i			1.42235i	−0.703016	+	0.711174i	$0.748164\pi$
$444$		0			0
$445$	−3.02729e14	−	4.96518e13i	−0.822383	−	0.134882i
$446$	−3.14740e14			−0.844520
$447$		0			0
$448$		−	1.54444e13i		−	0.0404334i
$449$	−3.62527e14			−0.937531			−0.468766	−	0.883323i	$-0.655301\pi$
$449$	−3.62527e14			−0.937531			−0.468766	+	0.883323i	$0.655301\pi$
$450$		0			0
$451$	−6.14896e14			−1.55178
$452$		−	2.04338e14i		−	0.509433i
$453$		0			0
$454$	3.82044e14			0.929623
$455$	−9.76059e13	−	1.60087e13i	−0.234646	−	0.0384853i
$456$		0			0
$457$		−	2.71960e14i		−	0.638213i	−0.947719	−	0.319106i	$-0.896617\pi$
$457$		−	2.71960e14i		−	0.638213i	0.947719	−	0.319106i	$-0.103383\pi$
$458$			2.90114e14i			0.672680i
$459$		0			0
$460$	−5.40248e12	+	3.29391e13i	−0.0122300	+	0.0745666i
$461$	5.57568e14			1.24722			0.623610	−	0.781736i	$-0.285665\pi$
$461$	5.57568e14			1.24722			0.623610	+	0.781736i	$0.285665\pi$
$462$		0			0
$463$		−	8.32053e14i		−	1.81742i	−0.417427	−	0.908710i	$-0.637068\pi$
$463$		−	8.32053e14i		−	1.81742i	0.417427	−	0.908710i	$-0.362932\pi$
$464$	4.52961e13			0.0977713
$465$		0			0
$466$	2.19453e14			0.462613
$467$		−	3.67952e14i		−	0.766564i	−0.923631	−	0.383282i	$-0.874794\pi$
$467$		−	3.67952e14i		−	0.766564i	0.923631	−	0.383282i	$-0.125206\pi$
$468$		0			0
$469$	1.09742e14			0.223317
$470$	8.35277e13	+	1.36997e13i	0.167993	+	0.0275533i
$471$		0			0
$472$			2.10878e14i			0.414333i
$473$			7.79912e14i			1.51464i
$474$		0			0
$475$	−4.61639e14	−	1.55617e14i	−0.875967	−	0.295285i
$476$	−1.47011e14			−0.275747
$477$		0			0
$478$		−	5.12177e14i		−	0.938786i
$479$	8.05880e14			1.46024			0.730122	−	0.683317i	$-0.239463\pi$
$479$	8.05880e14			1.46024			0.730122	+	0.683317i	$0.239463\pi$
$480$		0			0
$481$	−1.31638e14			−0.233123
$482$			4.55425e14i			0.797366i
$483$		0			0
$484$	4.25923e13			0.0728923
$485$	1.64193e14	−	1.00109e15i	0.277827	−	1.69392i
$486$		0			0
$487$		−	6.67016e14i		−	1.10339i	−0.834047	−	0.551693i	$-0.813982\pi$
$487$		−	6.67016e14i		−	1.10339i	0.834047	−	0.551693i	$-0.186018\pi$
$488$			9.29328e12i			0.0152006i
$489$		0			0
$490$	6.40741e13	−	3.90662e14i	0.102472	−	0.624774i
$491$	7.10616e13			0.112379			0.0561897	−	0.998420i	$-0.482105\pi$
$491$	7.10616e13			0.112379			0.0561897	+	0.998420i	$0.482105\pi$
$492$		0			0
$493$		−	4.31161e14i		−	0.666778i
$494$	−3.14188e14			−0.480497
$495$		0			0
$496$	1.11166e14			0.166273
$497$		−	2.13563e13i		−	0.0315912i
$498$		0			0
$499$	−1.65477e14			−0.239434			−0.119717	−	0.992808i	$-0.538199\pi$
$499$	−1.65477e14			−0.239434			−0.119717	+	0.992808i	$0.538199\pi$
$500$	−3.08652e14	−	1.63720e14i	−0.441706	−	0.234298i
$501$		0			0
$502$		−	3.90689e14i		−	0.546967i
$503$			1.03762e15i			1.43686i	0.695599	+	0.718431i	$0.255139\pi$
$503$			1.03762e15i			1.43686i	−0.695599	+	0.718431i	$0.744861\pi$
$504$		0			0
$505$	4.80023e14	+	7.87305e13i	0.650368	+	0.106670i
$506$	7.36945e13			0.0987659
$507$		0			0
$508$			2.92460e14i			0.383544i
$509$	1.20946e15			1.56908			0.784538	−	0.620081i	$-0.212900\pi$
$509$	1.20946e15			1.56908			0.784538	+	0.620081i	$0.212900\pi$
$510$		0			0
$511$	1.79449e14			0.227838
$512$		−	3.51844e13i		−	0.0441942i
$513$		0			0
$514$	−5.50875e14			−0.677261
$515$	2.35455e14	−	1.43558e15i	0.286397	−	1.74618i
$516$		0			0
$517$		−	1.86876e14i		−	0.222513i
$518$			6.15697e13i			0.0725360i
$519$		0			0
$520$	−2.22360e14	−	3.64701e13i	−0.256471	−	0.0420648i
$521$	8.99117e14			1.02614			0.513072	−	0.858345i	$-0.328507\pi$
$521$	8.99117e14			1.02614			0.513072	+	0.858345i	$0.328507\pi$
$522$		0			0
$523$			1.10607e15i			1.23601i	0.786172	+	0.618007i	$0.212060\pi$
$523$			1.10607e15i			1.23601i	−0.786172	+	0.618007i	$0.787940\pi$
$524$	−4.15931e14			−0.459937
$525$		0			0
$526$	−4.09877e14			−0.443846
$527$		−	1.05816e15i		−	1.13394i
$528$		0			0
$529$	9.31049e14			0.977161
$530$	−7.81909e14	−	1.28244e14i	−0.812156	−	0.133205i
$531$		0			0
$532$			1.46951e14i			0.149506i
$533$			1.22573e15i			1.23422i
$534$		0			0
$535$	1.31340e14	−	8.00783e14i	0.129554	−	0.789895i
$536$	2.50007e14			0.244088
$537$		0			0
$538$			1.02697e15i			0.982327i
$539$	−8.74025e14			−0.827534
$540$		0			0
$541$	−1.16749e15			−1.08310			−0.541552	−	0.840668i	$-0.682163\pi$
$541$	−1.16749e15			−1.08310			−0.541552	+	0.840668i	$0.682163\pi$
$542$		−	9.32757e14i		−	0.856589i
$543$		0			0
$544$	−3.34910e14			−0.301394
$545$	5.99085e14	+	9.82583e13i	0.533713	+	0.0875364i
$546$		0			0
$547$			1.47623e15i			1.28891i	0.764640	+	0.644457i	$0.222917\pi$
$547$			1.47623e15i			1.28891i	−0.764640	+	0.644457i	$0.777083\pi$
$548$			6.42772e14i			0.555602i
$549$		0			0
$550$	−2.46403e14	+	7.30958e14i	−0.208762	+	0.619295i
$551$	−4.30987e14			−0.361519
$552$		0			0
$553$		−	5.04936e14i		−	0.415192i
$554$	−1.30080e15			−1.05903
$555$		0			0
$556$	7.93428e14			0.633281
$557$		−	1.46210e15i		−	1.15551i	−0.816212	−	0.577753i	$-0.803930\pi$
$557$		−	1.46210e15i		−	1.15551i	0.816212	−	0.577753i	$-0.196070\pi$
$558$		0			0
$559$	1.55467e15			1.20468
$560$	−1.70577e13	+	1.04002e14i	−0.0130884	+	0.0798006i
$561$		0			0
$562$		−	3.86968e14i		−	0.291155i
$563$			1.82633e15i			1.36076i	0.732858	+	0.680381i	$0.238186\pi$
$563$			1.82633e15i			1.36076i	−0.732858	+	0.680381i	$0.761814\pi$
$564$		0			0
$565$	−2.25684e14	+	1.37600e15i	−0.164905	+	1.00543i
$566$	−1.39675e15			−1.01072
$567$		0			0
$568$		−	4.86526e13i		−	0.0345295i
$569$	2.46241e15			1.73078			0.865391	−	0.501098i	$-0.167070\pi$
$569$	2.46241e15			1.73078			0.865391	+	0.501098i	$0.167070\pi$
$570$		0			0
$571$	4.81918e14			0.332258			0.166129	−	0.986104i	$-0.446873\pi$
$571$	4.81918e14			0.332258			0.166129	+	0.986104i	$0.446873\pi$
$572$			4.97483e14i			0.339704i
$573$		0			0
$574$	5.73295e14			0.384028
$575$	7.27603e13	−	2.15844e14i	0.0482749	−	0.143208i
$576$		0			0
$577$			1.50690e15i			0.980887i	0.871473	+	0.490443i	$0.163165\pi$
$577$			1.50690e15i			0.980887i	−0.871473	+	0.490443i	$0.836835\pi$
$578$			2.09122e15i			1.34833i
$579$		0			0
$580$	−3.05022e14	−	5.00279e13i	−0.192964	−	0.0316489i
$581$	−1.38668e14			−0.0868978
$582$		0			0
$583$			1.74936e15i			1.07573i
$584$	4.08810e14			0.249030
$585$		0			0
$586$	9.23186e14			0.551890
$587$			7.41461e14i			0.439115i	0.975600	+	0.219558i	$0.0704614\pi$
$587$			7.41461e14i			0.439115i	−0.975600	+	0.219558i	$0.929539\pi$
$588$		0			0
$589$	−1.05773e15			−0.614810
$590$	2.32907e14	−	1.42004e15i	0.134121	−	0.817741i
$591$		0			0
$592$			1.40264e14i			0.0792826i
$593$			1.39684e15i			0.782249i	0.920338	+	0.391124i	$0.127914\pi$
$593$			1.39684e15i			0.782249i	−0.920338	+	0.391124i	$0.872086\pi$
$594$		0			0
$595$	9.89964e14	+	1.62368e14i	0.544222	+	0.0892600i
$596$	−9.04253e14			−0.492533
$597$		0			0
$598$		−	1.46902e14i		−	0.0785544i
$599$	−3.31738e15			−1.75771			−0.878856	−	0.477087i	$-0.841693\pi$
$599$	−3.31738e15			−1.75771			−0.878856	+	0.477087i	$0.841693\pi$
$600$		0			0
$601$	−1.75846e15			−0.914792			−0.457396	−	0.889263i	$-0.651218\pi$
$601$	−1.75846e15			−0.914792			−0.457396	+	0.889263i	$0.651218\pi$
$602$		−	7.27146e14i		−	0.374836i
$603$		0			0
$604$	−2.52895e13			−0.0128008
$605$	−2.86815e14	−	4.70417e13i	−0.143862	−	0.0235955i
$606$		0			0
$607$		−	1.71424e14i		−	0.0844371i	−0.999108	−	0.0422186i	$-0.986557\pi$
$607$		−	1.71424e14i		−	0.0844371i	0.999108	−	0.0422186i	$-0.0134426\pi$
$608$			3.34776e14i			0.163412i
$609$		0			0
$610$	1.02641e13	−	6.25806e13i	0.00492048	−	0.0300003i
$611$	−3.72516e14			−0.176978
$612$		0			0
$613$			1.34314e15i			0.626744i	0.949630	+	0.313372i	$0.101459\pi$
$613$			1.34314e15i			0.626744i	−0.949630	+	0.313372i	$0.898541\pi$
$614$	−4.58253e14			−0.211923
$615$		0			0
$616$	2.32682e14			0.105699
$617$		−	3.54108e15i		−	1.59429i	−0.603787	−	0.797146i	$-0.706342\pi$
$617$		−	3.54108e15i		−	1.59429i	0.603787	−	0.797146i	$-0.293658\pi$
$618$		0			0
$619$	−3.30674e15			−1.46252			−0.731259	−	0.682100i	$-0.761067\pi$
$619$	−3.30674e15			−1.46252			−0.731259	+	0.682100i	$0.761067\pi$
$620$	−7.48586e14	−	1.22779e14i	−0.328162	−	0.0538231i
$621$		0			0
$622$			3.06456e15i			1.31984i
$623$		−	6.31470e14i		−	0.269568i
$624$		0			0
$625$	1.89763e15	+	1.44338e15i	0.795922	+	0.605399i
$626$	2.95510e14			0.122861
$627$		0			0
$628$		−	4.09090e14i		−	0.167125i
$629$	1.33514e15			0.540689
$630$		0			0
$631$	3.53490e15			1.40675			0.703374	−	0.710820i	$-0.251676\pi$
$631$	3.53490e15			1.40675			0.703374	+	0.710820i	$0.251676\pi$
$632$		−	1.15032e15i		−	0.453809i
$633$		0			0
$634$	−1.23423e15			−0.478525
$635$	3.23012e14	−	1.96941e15i	0.124155	−	0.756975i
$636$		0			0
$637$			1.74227e15i			0.658186i
$638$			6.82423e14i			0.255588i
$639$		0			0
$640$	−3.88599e13	+	2.36930e14i	−0.0143058	+	0.0872230i
$641$	2.17674e15			0.794486			0.397243	−	0.917713i	$-0.369967\pi$
$641$	2.17674e15			0.794486			0.397243	+	0.917713i	$0.369967\pi$
$642$		0			0
$643$		−	2.81878e15i		−	1.01135i	−0.862725	−	0.505674i	$-0.831244\pi$
$643$		−	2.81878e15i		−	1.01135i	0.862725	−	0.505674i	$-0.168756\pi$
$644$	−6.87086e13			−0.0244421
$645$		0			0
$646$	3.18664e15			1.11443
$647$			2.43407e15i			0.844032i	0.906588	+	0.422016i	$0.138677\pi$
$647$			2.43407e15i			0.844032i	−0.906588	+	0.422016i	$0.861323\pi$
$648$		0			0
$649$	−3.17705e15			−1.08312
$650$	1.45708e15	+	4.91177e14i	0.492562	+	0.166041i
$651$		0			0
$652$		−	2.90169e15i		−	0.964472i
$653$			2.11894e15i			0.698388i	0.937050	+	0.349194i	$0.113545\pi$
$653$			2.11894e15i			0.698388i	−0.937050	+	0.349194i	$0.886455\pi$
$654$		0			0
$655$	2.80086e15	+	4.59381e14i	0.907746	+	0.148883i
$656$	1.30604e15			0.419746
$657$		0			0
$658$			1.74233e14i			0.0550664i
$659$	−1.95713e15			−0.613408			−0.306704	−	0.951805i	$-0.599226\pi$
$659$	−1.95713e15			−0.613408			−0.306704	+	0.951805i	$0.599226\pi$
$660$		0			0
$661$	−3.99976e14			−0.123289			−0.0616447	−	0.998098i	$-0.519635\pi$
$661$	−3.99976e14			−0.123289			−0.0616447	+	0.998098i	$0.519635\pi$
$662$			1.13037e15i			0.345543i
$663$		0			0
$664$	−3.15906e14			−0.0949802
$665$	1.62303e14	−	9.89566e14i	0.0483957	−	0.295070i
$666$		0			0
$667$		−	2.01513e14i		−	0.0591031i
$668$		−	1.31528e15i		−	0.382602i
$669$		0			0
$670$	−1.68354e15	−	2.76124e14i	−0.481739	−	0.0790120i
$671$	−1.40011e14			−0.0397364
$672$		0			0
$673$			3.45541e15i			0.964756i	0.875963	+	0.482378i	$0.160227\pi$
$673$			3.45541e15i			0.964756i	−0.875963	+	0.482378i	$0.839773\pi$
$674$	3.68362e15			1.02011
$675$		0			0
$676$	−8.43495e14			−0.229814
$677$		−	2.00366e15i		−	0.541486i	−0.962652	−	0.270743i	$-0.912731\pi$
$677$		−	2.00366e15i		−	0.541486i	0.962652	−	0.270743i	$-0.0872694\pi$
$678$		0			0
$679$	2.08820e15			0.555250
$680$	2.25527e15	+	3.69897e14i	0.594840	+	0.0975622i
$681$		0			0
$682$			1.67481e15i			0.434661i
$683$			5.60801e15i			1.44376i	0.692018	+	0.721880i	$0.256722\pi$
$683$			5.60801e15i			1.44376i	−0.692018	+	0.721880i	$0.743278\pi$
$684$		0			0
$685$	7.09919e14	−	4.32841e15i	0.179850	−	1.09655i
$686$	1.72501e15			0.433520
$687$		0			0
$688$		−	1.65654e15i		−	0.409700i
$689$	3.48715e15			0.855589
$690$		0			0
$691$	−7.85512e15			−1.89681			−0.948404	−	0.317064i	$-0.897303\pi$
$691$	−7.85512e15			−1.89681			−0.948404	+	0.317064i	$0.897303\pi$
$692$		−	2.26380e13i		−	0.00542319i
$693$		0			0
$694$	−4.98017e15			−1.17427
$695$	−5.34292e15	−	8.76313e14i	−1.24986	−	0.204995i
$696$		0			0
$697$		−	1.24319e16i		−	2.86257i
$698$		−	2.95521e15i		−	0.675123i
$699$		0			0
$700$	2.29733e14	−	6.81504e14i	0.0516634	−	0.153260i
$701$	4.81649e15			1.07469			0.537343	−	0.843364i	$-0.319428\pi$
$701$	4.81649e15			1.07469			0.537343	+	0.843364i	$0.319428\pi$
$702$		0			0
$703$		−	1.33460e15i		−	0.293155i
$704$	5.30082e14			0.115530
$705$		0			0
$706$	4.39367e15			0.942760
$707$			1.00129e15i			0.213184i
$708$		0			0
$709$	5.47981e15			1.14871			0.574356	−	0.818606i	$-0.305253\pi$
$709$	5.47981e15			1.14871			0.574356	+	0.818606i	$0.305253\pi$
$710$	−5.37351e13	+	3.27625e14i	−0.0111773	+	0.0681484i
$711$		0			0
$712$		−	1.43858e15i		−	0.294641i
$713$		−	4.94553e14i		−	0.100513i
$714$		0			0
$715$	5.49453e14	−	3.35004e15i	0.109963	−	0.670450i
$716$	−1.13555e15			−0.225520
$717$		0			0
$718$			4.88230e14i			0.0954861i
$719$	−6.68977e15			−1.29838			−0.649191	−	0.760626i	$-0.724892\pi$
$719$	−6.68977e15			−1.29838			−0.649191	+	0.760626i	$0.724892\pi$
$720$		0			0
$721$	2.99452e15			0.572378
$722$			5.42332e14i			0.102875i
$723$		0			0
$724$	−2.68071e15			−0.500827
$725$	1.99875e15	+	6.73772e14i	0.370596	+	0.124926i
$726$		0			0
$727$		−	3.18682e14i		−	0.0581993i	−0.999577	−	0.0290997i	$-0.990736\pi$
$727$		−	3.18682e14i		−	0.0581993i	0.999577	−	0.0290997i	$-0.00926401\pi$
$728$		−	4.63826e14i		−	0.0840683i
$729$		0			0
$730$	−2.75291e15	−	4.51517e14i	−0.491493	−	0.0806117i
$731$	−1.57681e16			−2.79406
$732$		0			0
$733$		−	1.01321e16i		−	1.76860i	−0.466922	−	0.884298i	$-0.654637\pi$
$733$		−	1.01321e16i		−	1.76860i	0.466922	−	0.884298i	$-0.345363\pi$
$734$	5.85164e15			1.01379
$735$		0			0
$736$	−1.56528e14			−0.0267155
$737$			3.76657e15i			0.638080i
$738$		0			0
$739$	−5.86926e15			−0.979578			−0.489789	−	0.871841i	$-0.662926\pi$
$739$	−5.86926e15			−0.979578			−0.489789	+	0.871841i	$0.662926\pi$
$740$	1.54917e14	−	9.44536e14i	0.0256640	−	0.156475i
$741$		0			0
$742$		−	1.63101e15i		−	0.266216i
$743$		−	1.01226e16i		−	1.64004i	−0.572338	−	0.820018i	$-0.693964\pi$
$743$		−	1.01226e16i		−	1.64004i	0.572338	−	0.820018i	$-0.306036\pi$
$744$		0			0
$745$	6.08921e15	+	9.98715e14i	0.972078	+	0.159434i
$746$	5.60311e15			0.887903
$747$		0			0
$748$		−	5.04571e15i		−	0.787886i
$749$	1.67038e15			0.258919
$750$		0			0
$751$	−9.02397e15			−1.37841			−0.689204	−	0.724567i	$-0.742040\pi$
$751$	−9.02397e15			−1.37841			−0.689204	+	0.724567i	$0.742040\pi$
$752$			3.96926e14i			0.0601882i
$753$		0			0
$754$	1.36033e15			0.203284
$755$	1.70299e14	+	2.79314e13i	0.0252640	+	0.00414366i
$756$		0			0
$757$			4.97374e15i			0.727203i	0.931555	+	0.363601i	$0.118453\pi$
$757$			4.97374e15i			0.727203i	−0.931555	+	0.363601i	$0.881547\pi$
$758$		−	9.35791e14i		−	0.135831i
$759$		0			0
$760$	3.69748e14	−	2.25437e15i	0.0528970	−	0.322515i
$761$	−6.61472e15			−0.939498			−0.469749	−	0.882800i	$-0.655656\pi$
$761$	−6.61472e15			−0.939498			−0.469749	+	0.882800i	$0.655656\pi$
$762$		0			0
$763$			1.24965e15i			0.174945i
$764$	−1.15444e15			−0.160457
$765$		0			0
$766$	7.65877e15			1.04930
$767$			6.33310e15i			0.861473i
$768$		0			0
$769$	−9.58448e15			−1.28521			−0.642605	−	0.766198i	$-0.722146\pi$
$769$	−9.58448e15			−1.28521			−0.642605	+	0.766198i	$0.722146\pi$
$770$	−1.56687e15	−	2.56989e14i	−0.208610	−	0.0342150i
$771$		0			0
$772$		−	2.95400e15i		−	0.387718i
$773$		−	1.03509e16i		−	1.34893i	−0.738305	−	0.674467i	$-0.764373\pi$
$773$		−	1.03509e16i		−	1.34893i	0.738305	−	0.674467i	$-0.235627\pi$
$774$		0			0
$775$	4.90535e15	+	1.65358e15i	0.630247	+	0.212454i
$776$	4.75721e15			0.606894
$777$		0			0
$778$			3.60689e15i			0.453676i
$779$	−1.24269e16			−1.55205
$780$		0			0
$781$	7.32992e14			0.0902648
$782$			1.48994e15i			0.182194i
$783$		0			0
$784$	1.85644e15			0.223842
$785$	−4.51826e14	+	2.75480e15i	−0.0540989	+	0.329843i
$786$		0			0
$787$			1.15659e15i			0.136558i	0.997666	+	0.0682792i	$0.0217509\pi$
$787$			1.15659e15i			0.136558i	−0.997666	+	0.0682792i	$0.978249\pi$
$788$			4.49987e15i			0.527601i
$789$		0			0
$790$	−1.27048e15	+	7.74618e15i	−0.146899	+	0.895651i
$791$	−2.87024e15			−0.329570
$792$		0			0
$793$			2.79097e14i			0.0316047i
$794$	−5.95866e15			−0.670094
$795$		0			0
$796$	7.21500e15			0.800230
$797$			1.19285e16i			1.31391i	0.753931	+	0.656954i	$0.228155\pi$
$797$			1.19285e16i			1.31391i	−0.753931	+	0.656954i	$0.771845\pi$
$798$		0			0
$799$	3.77823e15			0.410469
$800$	5.23363e14	−	1.55256e15i	0.0564687	−	0.167515i
$801$		0			0
$802$			8.30378e14i			0.0883724i
$803$			6.15907e15i			0.650998i
$804$		0			0
$805$	4.62682e14	+	7.58863e13i	0.0482397	+	0.00791200i
$806$	3.33854e15			0.345711
$807$		0			0
$808$			2.28108e15i			0.233012i
$809$	1.07593e16			1.09161			0.545804	−	0.837913i	$-0.316224\pi$
$809$	1.07593e16			1.09161			0.545804	+	0.837913i	$0.316224\pi$
$810$		0			0
$811$	−8.84760e15			−0.885546			−0.442773	−	0.896634i	$-0.646005\pi$
$811$	−8.84760e15			−0.885546			−0.442773	+	0.896634i	$0.646005\pi$
$812$		−	6.36254e14i		−	0.0632517i
$813$		0			0
$814$	−2.11320e15			−0.207256
$815$	−3.20482e15	+	1.95399e16i	−0.312202	+	1.90351i
$816$		0			0
$817$			1.57618e16i			1.51490i
$818$		−	4.71037e15i		−	0.449689i
$819$		0			0
$820$	−8.79486e15	−	1.44248e15i	−0.828424	−	0.135873i
$821$	1.29958e16			1.21595			0.607973	−	0.793958i	$-0.291983\pi$
$821$	1.29958e16			1.21595			0.607973	+	0.793958i	$0.291983\pi$
$822$		0			0
$823$		−	4.06063e15i		−	0.374882i	−0.982276	−	0.187441i	$-0.939981\pi$
$823$		−	4.06063e15i		−	0.374882i	0.982276	−	0.187441i	$-0.0600193\pi$
$824$	6.82192e15			0.625615
$825$		0			0
$826$	2.96211e15			0.268047
$827$		−	1.24492e16i		−	1.11908i	−0.828802	−	0.559542i	$-0.810977\pi$
$827$		−	1.24492e16i		−	1.11908i	0.828802	−	0.559542i	$-0.189023\pi$
$828$		0			0
$829$	1.96783e16			1.74557			0.872787	−	0.488100i	$-0.162310\pi$
$829$	1.96783e16			1.74557			0.872787	+	0.488100i	$0.162310\pi$
$830$	2.12730e15	+	3.48907e14i	0.187456	+	0.0307454i
$831$		0			0
$832$		−	1.05666e15i		−	0.0918876i
$833$		−	1.76709e16i		−	1.52655i
$834$		0			0
$835$	−1.45268e15	+	8.85705e15i	−0.123850	+	0.755116i
$836$	−5.04368e15			−0.427182
$837$		0			0
$838$			6.06667e15i			0.507117i
$839$	−9.11633e15			−0.757058			−0.378529	−	0.925589i	$-0.623570\pi$
$839$	−9.11633e15			−0.757058			−0.378529	+	0.925589i	$0.623570\pi$
$840$		0			0
$841$	−1.03345e16			−0.847052
$842$		−	4.95347e15i		−	0.403361i
$843$		0			0
$844$	−4.06470e15			−0.326697
$845$	5.68006e15	+	9.31611e14i	0.453567	+	0.0743914i
$846$		0			0
$847$		−	5.98275e14i		−	0.0471566i
$848$		−	3.71566e15i		−	0.290977i
$849$		0			0
$850$	−1.47784e16	−	4.98174e15i	−1.14241	−	0.385103i
$851$	6.24007e14			0.0479266
$852$		0			0
$853$			2.63088e16i			1.99472i	0.0726323	+	0.997359i	$0.476860\pi$
$853$			2.63088e16i			1.99472i	−0.0726323	+	0.997359i	$0.523140\pi$
$854$	1.30539e14			0.00983379
$855$		0			0
$856$	3.80535e15			0.283001
$857$		−	1.82752e15i		−	0.135042i	−0.997718	−	0.0675209i	$-0.978491\pi$
$857$		−	1.82752e15i		−	0.135042i	0.997718	−	0.0675209i	$-0.0215089\pi$
$858$		0			0
$859$	2.22714e16			1.62474			0.812372	−	0.583140i	$-0.198176\pi$
$859$	2.22714e16			1.62474			0.812372	+	0.583140i	$0.198176\pi$
$860$	−1.82959e15	+	1.11551e16i	−0.132621	+	0.808595i
$861$		0			0
$862$			1.21527e16i			0.869725i
$863$		−	2.44153e16i		−	1.73621i	−0.496376	−	0.868107i	$-0.665336\pi$
$863$		−	2.44153e16i		−	1.73621i	0.496376	−	0.868107i	$-0.334664\pi$
$864$		0			0
$865$	−2.50029e13	+	1.52444e14i	−0.00175550	+	0.0107034i
$866$	−3.92346e15			−0.273729
$867$		0			0
$868$		−	1.56150e15i		−	0.107568i
$869$	1.73305e16			1.18632
$870$		0			0
$871$	7.50824e15			0.507502
$872$			2.84687e15i			0.191217i
$873$		0			0
$874$	1.48935e15			0.0987831
$875$	−2.29971e15	+	4.33549e15i	−0.151575	+	0.285755i
$876$		0			0
$877$		−	1.80392e16i		−	1.17414i	−0.809537	−	0.587069i	$-0.800282\pi$
$877$		−	1.80392e16i		−	1.17414i	0.809537	−	0.587069i	$-0.199718\pi$
$878$		−	1.10264e16i		−	0.713203i
$879$		0			0
$880$	−3.56956e15	−	5.85457e14i	−0.228013	−	0.0373973i
$881$	2.62222e16			1.66457			0.832283	−	0.554351i	$-0.187033\pi$
$881$	2.62222e16			1.66457			0.832283	+	0.554351i	$0.187033\pi$
$882$		0			0
$883$			1.03481e16i			0.648747i	0.945929	+	0.324373i	$0.105153\pi$
$883$			1.03481e16i			0.648747i	−0.945929	+	0.324373i	$0.894847\pi$
$884$	−1.00581e16			−0.626652
$885$		0			0
$886$	1.63447e16			1.00575
$887$			1.09642e16i			0.670498i	0.942130	+	0.335249i	$0.108820\pi$
$887$			1.09642e16i			0.670498i	−0.942130	+	0.335249i	$0.891180\pi$
$888$		0			0
$889$	4.10805e15			0.248128
$890$	−1.58886e15	+	9.68733e15i	−0.0953762	+	0.581512i
$891$		0			0
$892$			1.00717e16i			0.597166i
$893$		−	3.77671e15i		−	0.222552i
$894$		0			0
$895$	7.64675e15	+	1.25417e15i	0.445092	+	0.0730014i
$896$	−4.94219e14			−0.0285908
$897$		0			0
$898$			1.16009e16i			0.662935i
$899$	4.57964e15			0.260108
$900$		0			0
$901$	−3.53683e16			−1.98439
$902$			1.96767e16i			1.09728i
$903$		0			0
$904$	−6.53880e15			−0.360223
$905$	1.80518e16	+	2.96075e15i	0.988446	+	0.162119i
$906$		0			0
$907$			3.00845e16i			1.62743i	0.581263	+	0.813716i	$0.302559\pi$
$907$			3.00845e16i			1.62743i	−0.581263	+	0.813716i	$0.697441\pi$
$908$		−	1.22254e16i		−	0.657342i
$909$		0			0
$910$	−5.12280e14	+	3.12339e15i	−0.0272132	+	0.165920i
$911$	−2.27506e16			−1.20127			−0.600636	−	0.799523i	$-0.705086\pi$
$911$	−2.27506e16			−1.20127			−0.600636	+	0.799523i	$0.705086\pi$
$912$		0			0
$913$		−	4.75939e15i		−	0.248292i
$914$	−8.70271e15			−0.451285
$915$		0			0
$916$	9.28364e15			0.475656
$917$			5.84239e15i			0.297550i
$918$		0			0
$919$	7.47065e15			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$919$	7.47065e15			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$920$	1.05405e15	+	1.72879e14i	0.0527265	+	0.00864790i
$921$		0			0
$922$		−	1.78422e16i		−	0.881917i
$923$		−	1.46114e15i		−	0.0717929i
$924$		0			0
$925$	−2.08641e15	+	6.18937e15i	−0.101303	+	0.300515i
$926$	−2.66257e16			−1.28511
$927$		0			0
$928$		−	1.44947e15i		−	0.0691348i
$929$	3.25912e15			0.154531			0.0772653	−	0.997011i	$-0.475381\pi$
$929$	3.25912e15			0.154531			0.0772653	+	0.997011i	$0.475381\pi$
$930$		0			0
$931$	−1.76638e16			−0.827678
$932$		−	7.02248e15i		−	0.327117i
$933$		0			0
$934$	−1.17745e16			−0.542042
$935$	−5.57281e15	+	3.39776e16i	−0.255041	+	1.55500i
$936$		0			0
$937$			9.63223e15i			0.435671i	0.975985	+	0.217836i	$0.0698997\pi$
$937$			9.63223e15i			0.435671i	−0.975985	+	0.217836i	$0.930100\pi$
$938$		−	3.51174e15i		−	0.157909i
$939$		0			0
$940$	4.38391e14	−	2.67289e15i	0.0194831	−	0.118789i
$941$	2.39897e16			1.05994			0.529970	−	0.848016i	$-0.322203\pi$
$941$	2.39897e16			1.05994			0.529970	+	0.848016i	$0.322203\pi$
$942$		0			0
$943$		−	5.81032e15i		−	0.253738i
$944$	6.74809e15			0.292978
$945$		0			0
$946$	2.49572e16			1.07101
$947$		−	1.92352e16i		−	0.820674i	−0.911934	−	0.410337i	$-0.865411\pi$
$947$		−	1.92352e16i		−	0.820674i	0.911934	−	0.410337i	$-0.134589\pi$
$948$		0			0
$949$	1.22774e16			0.517777
$950$	−4.97974e15	+	1.47725e16i	−0.208798	+	0.619403i
$951$		0			0
$952$			4.70434e15i			0.194982i
$953$		−	2.60513e16i		−	1.07354i	−0.843728	−	0.536771i	$-0.819644\pi$
$953$		−	2.60513e16i		−	1.07354i	0.843728	−	0.536771i	$-0.180356\pi$
$954$		0			0
$955$	7.77399e15	+	1.27504e15i	0.316683	+	0.0519405i
$956$	−1.63897e16			−0.663822
$957$		0			0
$958$		−	2.57882e16i		−	1.03255i
$959$	9.02874e15			0.359439
$960$		0			0
$961$	−1.41691e16			−0.557652
$962$			4.21243e15i			0.164843i
$963$		0			0
$964$	1.45736e16			0.563823
$965$	−3.26259e15	+	1.98922e16i	−0.125505	+	0.765212i
$966$		0			0
$967$		−	4.88181e16i		−	1.85667i	−0.371742	−	0.928336i	$-0.621240\pi$
$967$		−	4.88181e16i		−	1.85667i	0.371742	−	0.928336i	$-0.378760\pi$
$968$		−	1.36295e15i		−	0.0515427i
$969$		0			0
$970$	−3.20349e16	−	5.25417e15i	−1.19778	−	0.196453i
$971$	2.90334e15			0.107942			0.0539712	−	0.998542i	$-0.482812\pi$
$971$	2.90334e15			0.107942			0.0539712	+	0.998542i	$0.482812\pi$
$972$		0			0
$973$		−	1.11449e16i		−	0.409691i
$974$	−2.13445e16			−0.780211
$975$		0			0
$976$	2.97385e14			0.0107484
$977$			1.52533e16i			0.548207i	0.961700	+	0.274104i	$0.0883811\pi$
$977$			1.52533e16i			0.548207i	−0.961700	+	0.274104i	$0.911619\pi$
$978$		0			0
$979$	2.16734e16			0.770232
$980$	−1.25012e16	−	2.05037e15i	−0.441782	−	0.0724584i
$981$		0			0
$982$		−	2.27397e15i		−	0.0794642i
$983$		−	3.43490e16i		−	1.19363i	−0.802379	−	0.596814i	$-0.796433\pi$
$983$		−	3.43490e16i		−	1.19363i	0.802379	−	0.596814i	$-0.203567\pi$
$984$		0			0
$985$	4.96995e15	−	3.03020e16i	0.170786	−	1.04129i
$986$	−1.37971e16			−0.471483
$987$		0			0
$988$			1.00540e16i			0.339763i
$989$	−7.36959e15			−0.247665
$990$		0			0
$991$	−4.77614e16			−1.58735			−0.793674	−	0.608343i	$-0.791835\pi$
$991$	−4.77614e16			−1.58735			−0.793674	+	0.608343i	$0.791835\pi$
$992$		−	3.55730e15i		−	0.117573i
$993$		0			0
$994$	−6.83401e14			−0.0223383
$995$	−4.85856e16	−	7.96872e15i	−1.57936	−	0.259037i
$996$		0			0
$997$		−	2.46899e15i		−	0.0793774i	−0.999212	−	0.0396887i	$-0.987363\pi$
$997$		−	2.46899e15i		−	0.0793774i	0.999212	−	0.0396887i	$-0.0126366\pi$
$998$			5.29527e15i			0.169305i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.12.c.d.19.6	yes	12
3.2	odd	2	inner	90.12.c.d.19.7	yes	12
5.4	even	2	inner	90.12.c.d.19.12	yes	12
15.14	odd	2	inner	90.12.c.d.19.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.12.c.d.19.1	✓	12	15.14	odd	2	inner
90.12.c.d.19.6	yes	12	1.1	even	1	trivial
90.12.c.d.19.7	yes	12	3.2	odd	2	inner
90.12.c.d.19.12	yes	12	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-32.0000i q^{2} -1024.00 q^{4} +(6895.58 + 1130.97i) q^{5} +14383.7i q^{7} +32768.0i q^{8} +(36191.1 - 220659. i) q^{10} -493678. q^{11} +984091. i q^{13} +460278. q^{14} +1.04858e6 q^{16} -9.98110e6i q^{17} -9.97709e6 q^{19} +(-7.06107e6 - 1.15812e6i) q^{20} +1.57977e7i q^{22} -4.66489e6i q^{23} +(4.62699e7 + 1.55974e7i) q^{25} +3.14909e7 q^{26} -1.47289e7i q^{28} +4.31977e7 q^{29} +1.06016e8 q^{31} -3.35544e7i q^{32} -3.19395e8 q^{34} +(-1.62675e7 + 9.91838e7i) q^{35} +1.33767e8i q^{37} +3.19267e8i q^{38} +(-3.70597e7 + 2.25954e8i) q^{40} +1.24554e9 q^{41} -1.57980e9i q^{43} +5.05526e8 q^{44} -1.49277e8 q^{46} +3.78538e8i q^{47} +1.77044e9 q^{49} +(4.99117e8 - 1.48064e9i) q^{50} -1.00771e9i q^{52} -3.54353e9i q^{53} +(-3.40419e9 - 5.58336e8i) q^{55} -4.71324e8 q^{56} -1.38233e9i q^{58} +6.43548e9 q^{59} +2.83608e8 q^{61} -3.39251e9i q^{62} -1.07374e9 q^{64} +(-1.11298e9 + 6.78588e9i) q^{65} -7.62962e9i q^{67} +1.02207e10i q^{68} +(3.17388e9 + 5.20561e8i) q^{70} -1.48476e9 q^{71} -1.24759e10i q^{73} +4.28053e9 q^{74} +1.02165e10 q^{76} -7.10090e9i q^{77} -3.51048e10 q^{79} +(7.23054e9 + 1.18591e9i) q^{80} -3.98573e10i q^{82} +9.64068e9i q^{83} +(1.12884e10 - 6.88255e10i) q^{85} -5.05536e10 q^{86} -1.61768e10i q^{88} -4.39019e10 q^{89} -1.41548e10 q^{91} +4.77685e9i q^{92} +1.21132e10 q^{94} +(-6.87978e10 - 1.12838e10i) q^{95} -1.45178e11i q^{97} -5.66540e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12288 q^{4} + 56448 q^{10} + 12582912 q^{16} - 489648 q^{19} - 125575548 q^{25} + 47933952 q^{31} + 341743872 q^{34} - 57802752 q^{40} + 3346675200 q^{46} - 6178917036 q^{49} - 11944070688 q^{55}+ \cdots - 10041254400 q^{94}+O(q^{100}) \) 12 * q - 12288 * q^4 + 56448 * q^10 + 12582912 * q^16 - 489648 * q^19 - 125575548 * q^25 + 47933952 * q^31 + 341743872 * q^34 - 57802752 * q^40 + 3346675200 * q^46 - 6178917036 * q^49 - 11944070688 * q^55 + 39086224824 * q^61 - 12884901888 * q^64 - 20035144704 * q^70 + 501399552 * q^76 - 15150606048 * q^79 - 9988044312 * q^85 - 62442252096 * q^91 - 10041254400 * q^94

Introduction

L-functions

Modular forms

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Database

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