LMFDB - Embedded newform 90.12.c.d.19.5

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			19.5
Root			$12.8677 + 12.8677i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.12.c.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)

$f(q)$	$=$	\(q-32.0000i q^{2} -1024.00 q^{4} +(3091.89 + 6266.44i) q^{5} -73452.1i q^{7} +32768.0i q^{8} +(200526. - 98940.6i) q^{10} +7526.04 q^{11} -1.55212e6i q^{13} -2.35047e6 q^{14} +1.04858e6 q^{16} +7.69810e6i q^{17} +1.25808e7 q^{19} +(-3.16610e6 - 6.41684e6i) q^{20} -240833. i q^{22} -81143.4i q^{23} +(-2.97085e7 + 3.87504e7i) q^{25} -4.96678e7 q^{26} +7.52149e7i q^{28} +5.08338e7 q^{29} -3.12711e7 q^{31} -3.35544e7i q^{32} +2.46339e8 q^{34} +(4.60283e8 - 2.27106e8i) q^{35} -6.52001e8i q^{37} -4.02586e8i q^{38} +(-2.05339e8 + 1.01315e8i) q^{40} -1.26492e7 q^{41} -1.47070e8i q^{43} -7.70667e6 q^{44} -2.59659e6 q^{46} -2.34643e9i q^{47} -3.41788e9 q^{49} +(1.24001e9 + 9.50672e8i) q^{50} +1.58937e9i q^{52} -4.42169e8i q^{53} +(2.32697e7 + 4.71615e7i) q^{55} +2.40688e9 q^{56} -1.62668e9i q^{58} -1.02170e10 q^{59} +2.42801e8 q^{61} +1.00068e9i q^{62} -1.07374e9 q^{64} +(9.72626e9 - 4.79899e9i) q^{65} -2.47307e9i q^{67} -7.88285e9i q^{68} +(-7.26739e9 - 1.47291e10i) q^{70} +2.58822e10 q^{71} -1.06223e10i q^{73} -2.08640e10 q^{74} -1.28827e10 q^{76} -5.52803e8i q^{77} -2.10021e10 q^{79} +(3.24209e9 + 6.57084e9i) q^{80} +4.04774e8i q^{82} +3.03743e10i q^{83} +(-4.82397e10 + 2.38017e10i) q^{85} -4.70625e9 q^{86} +2.46613e8i q^{88} -7.74179e10 q^{89} -1.14006e11 q^{91} +8.30909e7i q^{92} -7.50857e10 q^{94} +(3.88985e10 + 7.88369e10i) q^{95} -1.50020e11i q^{97} +1.09372e11i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3091.89	+	6266.44i	0.442476	+	0.896780i
$5$	3091.89	+	6266.44i	0.442476	+	0.896780i
$6$		0			0
$7$		−	73452.1i		−	1.65183i	−0.563796	−	0.825914i	$-0.690660\pi$
$7$		−	73452.1i		−	1.65183i	0.563796	−	0.825914i	$-0.309340\pi$
$8$			32768.0i			0.353553i
$9$		0			0
$10$	200526.	−	98940.6i	0.634119	−	0.312878i
$11$	7526.04			0.0140899			0.00704493	−	0.999975i	$-0.497758\pi$
$11$	7526.04			0.0140899			0.00704493	+	0.999975i	$0.497758\pi$
$12$		0			0
$13$		−	1.55212e6i		−	1.15941i	−0.814827	−	0.579704i	$-0.803168\pi$
$13$		−	1.55212e6i		−	1.15941i	0.814827	−	0.579704i	$-0.196832\pi$
$14$	−2.35047e6			−1.16802
$15$		0			0
$16$	1.04858e6			0.250000
$17$			7.69810e6i			1.31497i	0.753470	+	0.657483i	$0.228379\pi$
$17$			7.69810e6i			1.31497i	−0.753470	+	0.657483i	$0.771621\pi$
$18$		0			0
$19$	1.25808e7			1.16564			0.582819	−	0.812602i	$-0.301950\pi$
$19$	1.25808e7			1.16564			0.582819	+	0.812602i	$0.301950\pi$
$20$	−3.16610e6	−	6.41684e6i	−0.221238	−	0.448390i
$21$		0			0
$22$		−	240833.i		−	0.00996304i
$23$		−	81143.4i		−	0.00262876i	−0.999999	−	0.00131438i	$-0.999582\pi$
$23$		−	81143.4i		−	0.00262876i	0.999999	−	0.00131438i	$-0.000418380\pi$
$24$		0			0
$25$	−2.97085e7	+	3.87504e7i	−0.608430	+	0.793607i
$26$	−4.96678e7			−0.819826
$27$		0			0
$28$			7.52149e7i			0.825914i
$29$	5.08338e7			0.460218			0.230109	−	0.973165i	$-0.426092\pi$
$29$	5.08338e7			0.460218			0.230109	+	0.973165i	$0.426092\pi$
$30$		0			0
$31$	−3.12711e7			−0.196180			−0.0980898	−	0.995178i	$-0.531273\pi$
$31$	−3.12711e7			−0.196180			−0.0980898	+	0.995178i	$0.531273\pi$
$32$		−	3.35544e7i		−	0.176777i
$33$		0			0
$34$	2.46339e8			0.929821
$35$	4.60283e8	−	2.27106e8i	1.48133	−	0.730894i
$36$		0			0
$37$		−	6.52001e8i		−	1.54575i	−0.634560	−	0.772874i	$-0.718819\pi$
$37$		−	6.52001e8i		−	1.54575i	0.634560	−	0.772874i	$-0.281181\pi$
$38$		−	4.02586e8i		−	0.824230i
$39$		0			0
$40$	−2.05339e8	+	1.01315e8i	−0.317060	+	0.156439i
$41$	−1.26492e7			−0.0170511			−0.00852553	−	0.999964i	$-0.502714\pi$
$41$	−1.26492e7			−0.0170511			−0.00852553	+	0.999964i	$0.502714\pi$
$42$		0			0
$43$		−	1.47070e8i		−	0.152563i	−0.997086	−	0.0762814i	$-0.975695\pi$
$43$		−	1.47070e8i		−	0.152563i	0.997086	−	0.0762814i	$-0.0243047\pi$
$44$	−7.70667e6			−0.00704493
$45$		0			0
$46$	−2.59659e6			−0.00185881
$47$		−	2.34643e9i		−	1.49235i	−0.665753	−	0.746173i	$-0.731889\pi$
$47$		−	2.34643e9i		−	1.49235i	0.665753	−	0.746173i	$-0.268111\pi$
$48$		0			0
$49$	−3.41788e9			−1.72854
$50$	1.24001e9	+	9.50672e8i	0.561165	+	0.430225i
$51$		0			0
$52$			1.58937e9i			0.579704i
$53$		−	4.42169e8i		−	0.145235i	−0.997360	−	0.0726174i	$-0.976865\pi$
$53$		−	4.42169e8i		−	0.145235i	0.997360	−	0.0726174i	$-0.0231352\pi$
$54$		0			0
$55$	2.32697e7	+	4.71615e7i	0.00623443	+	0.0126355i
$56$	2.40688e9			0.584009
$57$		0			0
$58$		−	1.62668e9i		−	0.325423i
$59$	−1.02170e10			−1.86054			−0.930268	−	0.366881i	$-0.880426\pi$
$59$	−1.02170e10			−1.86054			−0.930268	+	0.366881i	$0.880426\pi$
$60$		0			0
$61$	2.42801e8			0.0368075			0.0184037	−	0.999831i	$-0.494142\pi$
$61$	2.42801e8			0.0368075			0.0184037	+	0.999831i	$0.494142\pi$
$62$			1.00068e9i			0.138720i
$63$		0			0
$64$	−1.07374e9			−0.125000
$65$	9.72626e9	−	4.79899e9i	1.03973	−	0.513010i
$66$		0			0
$67$		−	2.47307e9i		−	0.223782i	−0.993720	−	0.111891i	$-0.964309\pi$
$67$		−	2.47307e9i		−	0.223782i	0.993720	−	0.111891i	$-0.0356907\pi$
$68$		−	7.88285e9i		−	0.657483i
$69$		0			0
$70$	−7.26739e9	−	1.47291e10i	−0.516820	−	1.04746i
$71$	2.58822e10			1.70247			0.851236	−	0.524783i	$-0.175853\pi$
$71$	2.58822e10			1.70247			0.851236	+	0.524783i	$0.175853\pi$
$72$		0			0
$73$		−	1.06223e10i		−	0.599710i	−0.953985	−	0.299855i	$-0.903062\pi$
$73$		−	1.06223e10i		−	0.599710i	0.953985	−	0.299855i	$-0.0969384\pi$
$74$	−2.08640e10			−1.09301
$75$		0			0
$76$	−1.28827e10			−0.582819
$77$		−	5.52803e8i		−	0.0232740i
$78$		0			0
$79$	−2.10021e10			−0.767915			−0.383957	−	0.923351i	$-0.625439\pi$
$79$	−2.10021e10			−0.767915			−0.383957	+	0.923351i	$0.625439\pi$
$80$	3.24209e9	+	6.57084e9i	0.110619	+	0.224195i
$81$		0			0
$82$			4.04774e8i			0.0120569i
$83$			3.03743e10i			0.846401i	0.906036	+	0.423201i	$0.139093\pi$
$83$			3.03743e10i			0.846401i	−0.906036	+	0.423201i	$0.860907\pi$
$84$		0			0
$85$	−4.82397e10	+	2.38017e10i	−1.17923	+	0.581840i
$86$	−4.70625e9			−0.107878
$87$		0			0
$88$			2.46613e8i			0.00498152i
$89$	−7.74179e10			−1.46959			−0.734796	−	0.678289i	$-0.762722\pi$
$89$	−7.74179e10			−1.46959			−0.734796	+	0.678289i	$0.762722\pi$
$90$		0			0
$91$	−1.14006e11			−1.91514
$92$			8.30909e7i			0.00131438i
$93$		0			0
$94$	−7.50857e10			−1.05525
$95$	3.88985e10	+	7.88369e10i	0.515767	+	1.04532i
$96$		0			0
$97$		−	1.50020e11i		−	1.77381i	−0.461957	−	0.886903i	$-0.652852\pi$
$97$		−	1.50020e11i		−	1.77381i	0.461957	−	0.886903i	$-0.347148\pi$
$98$			1.09372e11i			1.22226i
$99$		0			0
$100$	3.04215e10	−	3.96804e10i	0.304215	−	0.396804i
$101$	−1.24779e11			−1.18133			−0.590667	−	0.806915i	$-0.701135\pi$
$101$	−1.24779e11			−1.18133			−0.590667	+	0.806915i	$0.701135\pi$
$102$		0			0
$103$		−	1.62826e11i		−	1.38395i	−0.721922	−	0.691975i	$-0.756741\pi$
$103$		−	1.62826e11i		−	1.38395i	0.721922	−	0.691975i	$-0.243259\pi$
$104$	5.08598e10			0.409913
$105$		0			0
$106$	−1.41494e10			−0.102697
$107$		−	9.85560e10i		−	0.679317i	−0.940549	−	0.339658i	$-0.889689\pi$
$107$		−	9.85560e10i		−	0.679317i	0.940549	−	0.339658i	$-0.110311\pi$
$108$		0			0
$109$	−2.91563e11			−1.81504			−0.907522	−	0.420005i	$-0.862028\pi$
$109$	−2.91563e11			−1.81504			−0.907522	+	0.420005i	$0.862028\pi$
$110$	1.50917e9	−	7.44631e8i	0.00893466	−	0.00440841i
$111$		0			0
$112$		−	7.70201e10i		−	0.412957i
$113$		−	1.84740e11i		−	0.943254i	−0.881798	−	0.471627i	$-0.843667\pi$
$113$		−	1.84740e11i		−	0.943254i	0.881798	−	0.471627i	$-0.156333\pi$
$114$		0			0
$115$	5.08481e8	−	2.50887e8i	0.00235742	−	0.00116316i
$116$	−5.20538e10			−0.230109
$117$		0			0
$118$			3.26945e11i			1.31560i
$119$	5.65441e11			2.17210
$120$		0			0
$121$	−2.85255e11			−0.999801
$122$		−	7.76963e9i		−	0.0260268i
$123$		0			0
$124$	3.20216e10			0.0980898
$125$	−3.34683e11	−	6.63546e10i	−0.980907	−	0.194476i
$126$		0			0
$127$			5.68121e11i			1.52588i	0.646470	+	0.762939i	$0.276245\pi$
$127$			5.68121e11i			1.52588i	−0.646470	+	0.762939i	$0.723755\pi$
$128$			3.43597e10i			0.0883883i
$129$		0			0
$130$	−1.53568e11	−	3.11240e11i	−0.362753	−	0.735204i
$131$	3.55666e11			0.805472			0.402736	−	0.915316i	$-0.368059\pi$
$131$	3.55666e11			0.805472			0.402736	+	0.915316i	$0.368059\pi$
$132$		0			0
$133$		−	9.24086e11i		−	1.92543i
$134$	−7.91382e10			−0.158238
$135$		0			0
$136$	−2.52251e11			−0.464910
$137$		−	8.53191e11i		−	1.51037i	−0.655512	−	0.755184i	$-0.727547\pi$
$137$		−	8.53191e11i		−	1.51037i	0.655512	−	0.755184i	$-0.272453\pi$
$138$		0			0
$139$	−4.72251e9			−0.00771954			−0.00385977	−	0.999993i	$-0.501229\pi$
$139$	−4.72251e9			−0.00771954			−0.00385977	+	0.999993i	$0.501229\pi$
$140$	−4.71330e11	+	2.32557e11i	−0.740663	+	0.365447i
$141$		0			0
$142$		−	8.28230e11i		−	1.20383i
$143$		−	1.16813e10i		−	0.0163359i
$144$		0			0
$145$	1.57173e11	+	3.18547e11i	0.203635	+	0.412714i
$146$	−3.39913e11			−0.424059
$147$		0			0
$148$			6.67649e11i			0.772874i
$149$	7.08422e11			0.790256			0.395128	−	0.918626i	$-0.370700\pi$
$149$	7.08422e11			0.790256			0.395128	+	0.918626i	$0.370700\pi$
$150$		0			0
$151$	1.05336e12			1.09195			0.545977	−	0.837800i	$-0.316159\pi$
$151$	1.05336e12			1.09195			0.545977	+	0.837800i	$0.316159\pi$
$152$			4.12248e11i			0.412115i
$153$		0			0
$154$	−1.76897e10			−0.0164572
$155$	−9.66870e10	−	1.95959e11i	−0.0868048	−	0.175930i
$156$		0			0
$157$			6.60161e11i			0.552334i	0.961110	+	0.276167i	$0.0890643\pi$
$157$			6.60161e11i			0.552334i	−0.961110	+	0.276167i	$0.910936\pi$
$158$			6.72066e11i			0.542998i
$159$		0			0
$160$	2.10267e11	−	1.03747e11i	0.158530	−	0.0782194i
$161$	−5.96015e9			−0.00434225
$162$		0			0
$163$			7.70358e11i			0.524397i	0.965014	+	0.262199i	$0.0844476\pi$
$163$			7.70358e11i			0.524397i	−0.965014	+	0.262199i	$0.915552\pi$
$164$	1.29528e10			0.00852553
$165$		0			0
$166$	9.71977e11			0.598496
$167$		−	2.02077e12i		−	1.20386i	−0.798548	−	0.601932i	$-0.794398\pi$
$167$		−	2.02077e12i		−	1.20386i	0.798548	−	0.601932i	$-0.205602\pi$
$168$		0			0
$169$	−6.16912e11			−0.344228
$170$	7.61654e11	+	1.54367e12i	0.411423	+	0.833845i
$171$		0			0
$172$			1.50600e11i			0.0762814i
$173$		−	3.17723e11i		−	0.155882i	−0.996958	−	0.0779409i	$-0.975165\pi$
$173$		−	3.17723e11i		−	0.155882i	0.996958	−	0.0779409i	$-0.0248346\pi$
$174$		0			0
$175$	2.84629e12	+	2.18215e12i	1.31090	+	1.00502i
$176$	7.89163e9			0.00352247
$177$		0			0
$178$			2.47737e12i			1.03916i
$179$	−3.06145e12			−1.24519			−0.622594	−	0.782545i	$-0.713921\pi$
$179$	−3.06145e12			−1.24519			−0.622594	+	0.782545i	$0.713921\pi$
$180$		0			0
$181$	4.56365e12			1.74614			0.873071	−	0.487592i	$-0.162125\pi$
$181$	4.56365e12			1.74614			0.873071	+	0.487592i	$0.162125\pi$
$182$			3.64820e12i			1.35421i
$183$		0			0
$184$	2.65891e9			0.000929406
$185$	4.08572e12	−	2.01592e12i	1.38620	−	0.683956i
$186$		0			0
$187$			5.79362e10i			0.0185277i
$188$			2.40274e12i			0.746173i
$189$		0			0
$190$	2.52278e12	−	1.24475e12i	0.739154	−	0.364702i
$191$	7.03056e11			0.200127			0.100064	−	0.994981i	$-0.468095\pi$
$191$	7.03056e11			0.200127			0.100064	+	0.994981i	$0.468095\pi$
$192$		0			0
$193$		−	2.53512e12i		−	0.681449i	−0.940163	−	0.340725i	$-0.889328\pi$
$193$		−	2.53512e12i		−	0.681449i	0.940163	−	0.340725i	$-0.110672\pi$
$194$	−4.80065e12			−1.25427
$195$		0			0
$196$	3.49991e12			0.864268
$197$			4.35291e12i			1.04524i	0.852566	+	0.522619i	$0.175045\pi$
$197$			4.35291e12i			1.04524i	−0.852566	+	0.522619i	$0.824955\pi$
$198$		0			0
$199$	3.47856e12			0.790146			0.395073	−	0.918650i	$-0.370719\pi$
$199$	3.47856e12			0.790146			0.395073	+	0.918650i	$0.370719\pi$
$200$	−1.26977e12	−	9.73488e11i	−0.280583	−	0.215113i
$201$		0			0
$202$			3.99292e12i			0.835329i
$203$		−	3.73385e12i		−	0.760200i
$204$		0			0
$205$	−3.91100e10	−	7.92654e10i	−0.00754468	−	0.0152911i
$206$	−5.21045e12			−0.978600
$207$		0			0
$208$		−	1.62751e12i		−	0.289852i
$209$	9.46837e10			0.0164237
$210$		0			0
$211$	−2.13191e12			−0.350926			−0.175463	−	0.984486i	$-0.556142\pi$
$211$	−2.13191e12			−0.350926			−0.175463	+	0.984486i	$0.556142\pi$
$212$			4.52781e11i			0.0726174i
$213$		0			0
$214$	−3.15379e12			−0.480350
$215$	9.21608e11	−	4.54726e11i	0.136815	−	0.0675054i
$216$		0			0
$217$			2.29693e12i			0.324055i
$218$			9.33003e12i			1.28343i
$219$		0			0
$220$	−2.38282e10	−	4.82934e10i	−0.00311721	−	0.00631776i
$221$	1.19484e13			1.52458
$222$		0			0
$223$			1.23875e13i			1.50420i	0.659048	+	0.752101i	$0.270959\pi$
$223$			1.23875e13i			1.50420i	−0.659048	+	0.752101i	$0.729041\pi$
$224$	−2.46464e12			−0.292005
$225$		0			0
$226$	−5.91167e12			−0.666981
$227$		−	1.67475e13i		−	1.84420i	−0.386947	−	0.922102i	$-0.626470\pi$
$227$		−	1.67475e13i		−	1.84420i	0.386947	−	0.922102i	$-0.373530\pi$
$228$		0			0
$229$	−1.51109e13			−1.58561			−0.792804	−	0.609477i	$-0.791379\pi$
$229$	−1.51109e13			−1.58561			−0.792804	+	0.609477i	$0.791379\pi$
$230$	−8.02838e9	−	1.62714e10i	−0.000822479	−	0.00166695i
$231$		0			0
$232$			1.66572e12i			0.162712i
$233$		−	1.41596e13i		−	1.35080i	−0.737450	−	0.675402i	$-0.763970\pi$
$233$		−	1.41596e13i		−	1.35080i	0.737450	−	0.675402i	$-0.236030\pi$
$234$		0			0
$235$	1.47038e13	−	7.25491e12i	1.33831	−	0.660327i
$236$	1.04622e13			0.930268
$237$		0			0
$238$		−	1.80941e13i		−	1.53590i
$239$	1.07836e13			0.894486			0.447243	−	0.894413i	$-0.352406\pi$
$239$	1.07836e13			0.894486			0.447243	+	0.894413i	$0.352406\pi$
$240$		0			0
$241$	8.28234e12			0.656235			0.328117	−	0.944637i	$-0.393586\pi$
$241$	8.28234e12			0.656235			0.328117	+	0.944637i	$0.393586\pi$
$242$			9.12816e12i			0.706966i
$243$		0			0
$244$	−2.48628e11			−0.0184037
$245$	−1.05677e13	−	2.14179e13i	−0.764835	−	1.55012i
$246$		0			0
$247$		−	1.95269e13i		−	1.35145i
$248$		−	1.02469e12i		−	0.0693600i
$249$		0			0
$250$	−2.12335e12	+	1.07098e13i	−0.137515	+	0.693606i
$251$	−1.19447e13			−0.756778			−0.378389	−	0.925647i	$-0.623522\pi$
$251$	−1.19447e13			−0.756778			−0.378389	+	0.925647i	$0.623522\pi$
$252$		0			0
$253$		−	6.10689e8i		−	3.70388e-5i
$254$	1.81799e13			1.07896
$255$		0			0
$256$	1.09951e12			0.0625000
$257$			9.52996e12i			0.530223i	0.964218	+	0.265112i	$0.0854088\pi$
$257$			9.52996e12i			0.530223i	−0.964218	+	0.265112i	$0.914591\pi$
$258$		0			0
$259$	−4.78908e13			−2.55331
$260$	−9.95969e12	+	4.91416e12i	−0.519867	+	0.256505i
$261$		0			0
$262$		−	1.13813e13i		−	0.569555i
$263$			1.71489e13i			0.840387i	0.907435	+	0.420194i	$0.138038\pi$
$263$			1.71489e13i			0.840387i	−0.907435	+	0.420194i	$0.861962\pi$
$264$		0			0
$265$	2.77083e12	−	1.36714e12i	0.130244	−	0.0642629i
$266$	−2.95708e13			−1.36149
$267$		0			0
$268$			2.53242e12i			0.111891i
$269$	2.83124e13			1.22557			0.612786	−	0.790249i	$-0.290049\pi$
$269$	2.83124e13			1.22557			0.612786	+	0.790249i	$0.290049\pi$
$270$		0			0
$271$	−2.55352e13			−1.06123			−0.530614	−	0.847614i	$-0.678039\pi$
$271$	−2.55352e13			−1.06123			−0.530614	+	0.847614i	$0.678039\pi$
$272$			8.07204e12i			0.328741i
$273$		0			0
$274$	−2.73021e13			−1.06799
$275$	−2.23587e11	+	2.91637e11i	−0.00857270	+	0.0111818i
$276$		0			0
$277$			3.03063e12i			0.111659i	0.998440	+	0.0558295i	$0.0177803\pi$
$277$			3.03063e12i			0.111659i	−0.998440	+	0.0558295i	$0.982220\pi$
$278$			1.51120e11i			0.00545854i
$279$		0			0
$280$	7.44181e12	+	1.50826e13i	0.258410	+	0.523728i
$281$	−2.92771e13			−0.996882			−0.498441	−	0.866924i	$-0.666094\pi$
$281$	−2.92771e13			−0.996882			−0.498441	+	0.866924i	$0.666094\pi$
$282$		0			0
$283$		−	2.10195e12i		−	0.0688331i	−0.999408	−	0.0344165i	$-0.989043\pi$
$283$		−	2.10195e12i		−	0.0688331i	0.999408	−	0.0344165i	$-0.0109573\pi$
$284$	−2.65034e13			−0.851236
$285$		0			0
$286$	−3.73802e11			−0.0115512
$287$			9.29109e11i			0.0281654i
$288$		0			0
$289$	−2.49888e13			−0.729133
$290$	1.01935e13	−	5.02952e12i	0.291833	−	0.143992i
$291$		0			0
$292$			1.08772e13i			0.299855i
$293$			5.65820e13i			1.53076i	0.643580	+	0.765379i	$0.277448\pi$
$293$			5.65820e13i			1.53076i	−0.643580	+	0.765379i	$0.722552\pi$
$294$		0			0
$295$	−3.15899e13	−	6.40244e13i	−0.823242	−	1.66849i
$296$	2.13648e13			0.546504
$297$		0			0
$298$		−	2.26695e13i		−	0.558795i
$299$	−1.25944e11			−0.00304780
$300$		0			0
$301$	−1.08026e13			−0.252007
$302$		−	3.37076e13i		−	0.772128i
$303$		0			0
$304$	1.31919e13			0.291409
$305$	7.50715e11	+	1.52150e12i	0.0162864	+	0.0330082i
$306$		0			0
$307$		−	1.15587e13i		−	0.241906i	−0.992658	−	0.120953i	$-0.961405\pi$
$307$		−	1.15587e13i		−	0.241906i	0.992658	−	0.120953i	$-0.0385950\pi$
$308$			5.66071e11i			0.0116370i
$309$		0			0
$310$	−6.27068e12	+	3.09398e12i	−0.124401	+	0.0613802i
$311$	5.01602e13			0.977637			0.488818	−	0.872386i	$-0.337428\pi$
$311$	5.01602e13			0.977637			0.488818	+	0.872386i	$0.337428\pi$
$312$		0			0
$313$		−	1.99446e13i		−	0.375260i	−0.982240	−	0.187630i	$-0.939919\pi$
$313$		−	1.99446e13i		−	0.375260i	0.982240	−	0.187630i	$-0.0600806\pi$
$314$	2.11252e13			0.390559
$315$		0			0
$316$	2.15061e13			0.383957
$317$		−	5.04299e13i		−	0.884834i	−0.896809	−	0.442417i	$-0.854121\pi$
$317$		−	5.04299e13i		−	0.884834i	0.896809	−	0.442417i	$-0.145879\pi$
$318$		0			0
$319$	3.82577e11			0.00648441
$320$	−3.31990e12	−	6.72854e12i	−0.0553095	−	0.112098i
$321$		0			0
$322$			1.90725e11i			0.00307044i
$323$			9.68482e13i			1.53277i
$324$		0			0
$325$	6.01452e13	+	4.61111e13i	0.920115	+	0.705419i
$326$	2.46514e13			0.370805
$327$		0			0
$328$		−	4.14489e11i		−	0.00602846i
$329$	−1.72350e14			−2.46510
$330$		0			0
$331$	9.34003e13			1.29209			0.646047	−	0.763297i	$-0.276421\pi$
$331$	9.34003e13			1.29209			0.646047	+	0.763297i	$0.276421\pi$
$332$		−	3.11033e13i		−	0.423201i
$333$		0			0
$334$	−6.46648e13			−0.851260
$335$	1.54973e13	−	7.64647e12i	0.200683	−	0.0990180i
$336$		0			0
$337$			9.67398e13i			1.21239i	0.795318	+	0.606193i	$0.207304\pi$
$337$			9.67398e13i			1.21239i	−0.795318	+	0.606193i	$0.792696\pi$
$338$			1.97412e13i			0.243406i
$339$		0			0
$340$	4.93974e13	−	2.43729e13i	0.589617	−	0.290920i
$341$	−2.35348e11			−0.00276415
$342$		0			0
$343$			1.05812e14i			1.20342i
$344$	4.81920e12			0.0539391
$345$		0			0
$346$	−1.01671e13			−0.110225
$347$			2.98797e13i			0.318833i	0.987211	+	0.159417i	$0.0509613\pi$
$347$			2.98797e13i			0.318833i	−0.987211	+	0.159417i	$0.949039\pi$
$348$		0			0
$349$	8.29449e13			0.857531			0.428765	−	0.903416i	$-0.358949\pi$
$349$	8.29449e13			0.857531			0.428765	+	0.903416i	$0.358949\pi$
$350$	6.98288e13	−	9.10814e13i	0.710658	−	0.926948i
$351$		0			0
$352$		−	2.52532e11i		−	0.00249076i
$353$			2.77862e13i			0.269816i	0.990858	+	0.134908i	$0.0430739\pi$
$353$			2.77862e13i			0.269816i	−0.990858	+	0.134908i	$0.956926\pi$
$354$		0			0
$355$	8.00250e13	+	1.62189e14i	0.753303	+	1.52674i
$356$	7.92760e13			0.734796
$357$		0			0
$358$			9.79663e13i			0.880481i
$359$	−6.00448e13			−0.531442			−0.265721	−	0.964050i	$-0.585610\pi$
$359$	−6.00448e13			−0.531442			−0.265721	+	0.964050i	$0.585610\pi$
$360$		0			0
$361$	4.17864e13			0.358711
$362$		−	1.46037e14i		−	1.23471i
$363$		0			0
$364$	1.16742e14			0.957572
$365$	6.65639e13	−	3.28429e13i	0.537809	−	0.265357i
$366$		0			0
$367$		−	1.58072e14i		−	1.23934i	−0.784861	−	0.619672i	$-0.787266\pi$
$367$		−	1.58072e14i		−	1.23934i	0.784861	−	0.619672i	$-0.212734\pi$
$368$		−	8.50851e10i		−	0.000657189i
$369$		0			0
$370$	−6.45093e13	−	1.30743e14i	−0.483630	−	0.980189i
$371$	−3.24782e13			−0.239903
$372$		0			0
$373$		−	1.82296e14i		−	1.30731i	−0.756793	−	0.653655i	$-0.773235\pi$
$373$		−	1.82296e14i		−	1.30731i	0.756793	−	0.653655i	$-0.226765\pi$
$374$	1.85396e12			0.0131011
$375$		0			0
$376$	7.68878e13			0.527624
$377$		−	7.89000e13i		−	0.533580i
$378$		0			0
$379$	1.32427e14			0.869885			0.434942	−	0.900458i	$-0.356769\pi$
$379$	1.32427e14			0.869885			0.434942	+	0.900458i	$0.356769\pi$
$380$	−3.98321e13	−	8.07290e13i	−0.257883	−	0.522661i
$381$		0			0
$382$		−	2.24978e13i		−	0.141511i
$383$			2.66390e14i			1.65167i	0.563910	+	0.825836i	$0.309297\pi$
$383$			2.66390e14i			1.65167i	−0.563910	+	0.825836i	$0.690703\pi$
$384$		0			0
$385$	3.46411e12	−	1.70921e12i	0.0208717	−	0.0102982i
$386$	−8.11238e13			−0.481857
$387$		0			0
$388$			1.53621e14i			0.886903i
$389$	3.31443e14			1.88663			0.943314	−	0.331903i	$-0.107691\pi$
$389$	3.31443e14			1.88663			0.943314	+	0.331903i	$0.107691\pi$
$390$		0			0
$391$	6.24650e11			0.00345672
$392$		−	1.11997e14i		−	0.611130i
$393$		0			0
$394$	1.39293e14			0.739095
$395$	−6.49362e13	−	1.31608e14i	−0.339784	−	0.688651i
$396$		0			0
$397$			2.66173e14i			1.35461i	0.735700	+	0.677307i	$0.236853\pi$
$397$			2.66173e14i			1.35461i	−0.735700	+	0.677307i	$0.763147\pi$
$398$		−	1.11314e14i		−	0.558718i
$399$		0			0
$400$	−3.11516e13	+	4.06327e13i	−0.152108	+	0.198402i
$401$	−5.83506e13			−0.281029			−0.140514	−	0.990079i	$-0.544876\pi$
$401$	−5.83506e13			−0.281029			−0.140514	+	0.990079i	$0.544876\pi$
$402$		0			0
$403$			4.85365e13i			0.227452i
$404$	1.27773e14			0.590667
$405$		0			0
$406$	−1.19483e14			−0.537543
$407$		−	4.90699e12i		−	0.0217794i
$408$		0			0
$409$	1.50629e14			0.650774			0.325387	−	0.945581i	$-0.394505\pi$
$409$	1.50629e14			0.650774			0.325387	+	0.945581i	$0.394505\pi$
$410$	−2.53649e12	+	1.25152e12i	−0.0108124	+	0.00533490i
$411$		0			0
$412$			1.66734e14i			0.691975i
$413$			7.50461e14i			3.07328i
$414$		0			0
$415$	−1.90339e14	+	9.39140e13i	−0.759036	+	0.374512i
$416$	−5.20805e13			−0.204956
$417$		0			0
$418$		−	3.02988e12i		−	0.0116133i
$419$	−1.12162e14			−0.424296			−0.212148	−	0.977238i	$-0.568046\pi$
$419$	−1.12162e14			−0.424296			−0.212148	+	0.977238i	$0.568046\pi$
$420$		0			0
$421$	−2.61767e14			−0.964635			−0.482318	−	0.875996i	$-0.660205\pi$
$421$	−2.61767e14			−0.964635			−0.482318	+	0.875996i	$0.660205\pi$
$422$			6.82211e13i			0.248142i
$423$		0			0
$424$	1.44890e13			0.0513483
$425$	−2.98304e14	−	2.28699e14i	−1.04357	−	0.800064i
$426$		0			0
$427$		−	1.78342e13i		−	0.0607996i
$428$			1.00921e14i			0.339658i
$429$		0			0
$430$	−1.45512e13	−	2.94915e13i	−0.0477335	−	0.0967430i
$431$	−5.44798e14			−1.76446			−0.882228	−	0.470822i	$-0.843957\pi$
$431$	−5.44798e14			−1.76446			−0.882228	+	0.470822i	$0.843957\pi$
$432$		0			0
$433$		−	3.95370e14i		−	1.24830i	−0.781303	−	0.624152i	$-0.785444\pi$
$433$		−	3.95370e14i		−	1.24830i	0.781303	−	0.624152i	$-0.214556\pi$
$434$	7.35017e13			0.229141
$435$		0			0
$436$	2.98561e14			0.907522
$437$		−	1.02085e12i		−	0.00306418i
$438$		0			0
$439$	1.61637e14			0.473135			0.236567	−	0.971615i	$-0.423978\pi$
$439$	1.61637e14			0.473135			0.236567	+	0.971615i	$0.423978\pi$
$440$	−1.54539e12	+	7.62503e11i	−0.00446733	+	0.00220420i
$441$		0			0
$442$		−	3.82347e14i		−	1.07804i
$443$			3.75361e14i			1.04527i	0.852556	+	0.522635i	$0.175051\pi$
$443$			3.75361e14i			1.04527i	−0.852556	+	0.522635i	$0.824949\pi$
$444$		0			0
$445$	−2.39368e14	−	4.85135e14i	−0.650259	−	1.31790i
$446$	3.96399e14			1.06363
$447$		0			0
$448$			7.88686e13i			0.206478i
$449$	9.66467e13			0.249938			0.124969	−	0.992161i	$-0.460117\pi$
$449$	9.66467e13			0.249938			0.124969	+	0.992161i	$0.460117\pi$
$450$		0			0
$451$	−9.51983e10			−0.000240247
$452$			1.89173e14i			0.471627i
$453$		0			0
$454$	−5.35921e14			−1.30405
$455$	−3.52496e14	−	7.14414e14i	−0.847405	−	1.71746i
$456$		0			0
$457$			1.18646e14i			0.278430i	0.990262	+	0.139215i	$0.0444579\pi$
$457$			1.18646e14i			0.278430i	−0.990262	+	0.139215i	$0.955542\pi$
$458$			4.83549e14i			1.12119i
$459$		0			0
$460$	−5.20684e11	+	2.56908e11i	−0.00117871	+	0.000581581i
$461$	6.78976e14			1.51879			0.759397	−	0.650627i	$-0.225494\pi$
$461$	6.78976e14			1.51879			0.759397	+	0.650627i	$0.225494\pi$
$462$		0			0
$463$			1.56158e14i			0.341090i	0.985350	+	0.170545i	$0.0545529\pi$
$463$			1.56158e14i			0.341090i	−0.985350	+	0.170545i	$0.945447\pi$
$464$	5.33031e13			0.115054
$465$		0			0
$466$	−4.53106e14			−0.955163
$467$			3.48325e14i			0.725675i	0.931852	+	0.362837i	$0.118192\pi$
$467$			3.48325e14i			0.725675i	−0.931852	+	0.362837i	$0.881808\pi$
$468$		0			0
$469$	−1.81652e14			−0.369649
$470$	−2.32157e14	−	4.70521e14i	−0.466922	−	0.946325i
$471$		0			0
$472$		−	3.34791e14i		−	0.657799i
$473$		−	1.10686e12i		−	0.00214959i
$474$		0			0
$475$	−3.73757e14	+	4.87511e14i	−0.709209	+	0.925059i
$476$	−5.79012e14			−1.08605
$477$		0			0
$478$		−	3.45074e14i		−	0.632497i
$479$	2.00750e13			0.0363756			0.0181878	−	0.999835i	$-0.494210\pi$
$479$	2.00750e13			0.0363756			0.0181878	+	0.999835i	$0.494210\pi$
$480$		0			0
$481$	−1.01198e15			−1.79215
$482$		−	2.65035e14i		−	0.464028i
$483$		0			0
$484$	2.92101e14			0.499901
$485$	9.40095e14	−	4.63847e14i	1.59071	−	0.784866i
$486$		0			0
$487$		−	7.97827e14i		−	1.31977i	−0.751365	−	0.659887i	$-0.770604\pi$
$487$		−	7.97827e14i		−	1.31977i	0.751365	−	0.659887i	$-0.229396\pi$
$488$			7.95610e12i			0.0130134i
$489$		0			0
$490$	−6.85374e14	+	3.38167e14i	−1.09610	+	0.540820i
$491$	7.97717e14			1.26154			0.630769	−	0.775970i	$-0.282739\pi$
$491$	7.97717e14			1.26154			0.630769	+	0.775970i	$0.282739\pi$
$492$		0			0
$493$			3.91323e14i			0.605170i
$494$	−6.24861e14			−0.955620
$495$		0			0
$496$	−3.27901e13			−0.0490449
$497$		−	1.90110e15i		−	2.81219i
$498$		0			0
$499$	1.38791e14			0.200820			0.100410	−	0.994946i	$-0.467984\pi$
$499$	1.38791e14			0.200820			0.100410	+	0.994946i	$0.467984\pi$
$500$	3.42715e14	+	6.79471e13i	0.490454	+	0.0972380i
$501$		0			0
$502$			3.82230e14i			0.535123i
$503$			9.58116e14i			1.32677i	0.748280	+	0.663383i	$0.230880\pi$
$503$			9.58116e14i			1.32677i	−0.748280	+	0.663383i	$0.769120\pi$
$504$		0			0
$505$	−3.85802e14	−	7.81918e14i	−0.522712	−	1.05940i
$506$	−1.95421e10			−2.61904e−5
$507$		0			0
$508$		−	5.81755e14i		−	0.762939i
$509$	−5.19145e14			−0.673505			−0.336752	−	0.941593i	$-0.609329\pi$
$509$	−5.19145e14			−0.673505			−0.336752	+	0.941593i	$0.609329\pi$
$510$		0			0
$511$	−7.80228e14			−0.990618
$512$		−	3.51844e13i		−	0.0441942i
$513$		0			0
$514$	3.04959e14			0.374925
$515$	1.02034e15	−	5.03442e14i	1.24110	−	0.612364i
$516$		0			0
$517$		−	1.76593e13i		−	0.0210269i
$518$			1.53251e15i			1.80546i
$519$		0			0
$520$	1.57253e14	+	3.18710e14i	0.181377	+	0.367602i
$521$	−1.16468e15			−1.32922			−0.664612	−	0.747189i	$-0.731403\pi$
$521$	−1.16468e15			−1.32922			−0.664612	+	0.747189i	$0.731403\pi$
$522$		0			0
$523$			2.93884e13i			0.0328410i	0.999865	+	0.0164205i	$0.00522705\pi$
$523$			2.93884e13i			0.0328410i	−0.999865	+	0.0164205i	$0.994773\pi$
$524$	−3.64202e14			−0.402736
$525$		0			0
$526$	5.48764e14			0.594243
$527$		−	2.40728e14i		−	0.257969i
$528$		0			0
$529$	9.52803e14			0.999993
$530$	−4.37485e13	−	8.86664e13i	−0.0454407	−	0.0920962i
$531$		0			0
$532$			9.46264e14i			0.962717i
$533$			1.96330e13i			0.0197691i
$534$		0			0
$535$	6.17596e14	−	3.04725e14i	0.609198	−	0.300581i
$536$	8.10375e13			0.0791188
$537$		0			0
$538$		−	9.05997e14i		−	0.866611i
$539$	−2.57231e13			−0.0243548
$540$		0			0
$541$	1.19815e15			1.11155			0.555773	−	0.831334i	$-0.312422\pi$
$541$	1.19815e15			1.11155			0.555773	+	0.831334i	$0.312422\pi$
$542$			8.17127e14i			0.750401i
$543$		0			0
$544$	2.58305e14			0.232455
$545$	−9.01483e14	−	1.82706e15i	−0.803113	−	1.62770i
$546$		0			0
$547$		−	7.13308e14i		−	0.622797i	−0.950279	−	0.311399i	$-0.899203\pi$
$547$		−	7.13308e14i		−	0.622797i	0.950279	−	0.311399i	$-0.100797\pi$
$548$			8.73667e14i			0.755184i
$549$		0			0
$550$	9.33238e12	+	7.15480e12i	0.00790674	+	0.00606181i
$551$	6.39530e14			0.536447
$552$		0			0
$553$			1.54265e15i			1.26846i
$554$	9.69800e13			0.0789548
$555$		0			0
$556$	4.83585e12			0.00385977
$557$		−	1.18931e15i		−	0.939918i	−0.882688	−	0.469959i	$-0.844269\pi$
$557$		−	1.18931e15i		−	0.939918i	0.882688	−	0.469959i	$-0.155731\pi$
$558$		0			0
$559$	−2.28271e14			−0.176883
$560$	4.82642e14	−	2.38138e14i	0.370332	−	0.182724i
$561$		0			0
$562$			9.36868e14i			0.704902i
$563$			2.16625e15i			1.61403i	0.590529	+	0.807017i	$0.298919\pi$
$563$			2.16625e15i			1.61403i	−0.590529	+	0.807017i	$0.701081\pi$
$564$		0			0
$565$	1.15766e15	−	5.71195e14i	0.845891	−	0.417367i
$566$	−6.72624e13			−0.0486723
$567$		0			0
$568$			8.48108e14i			0.601915i
$569$	−9.56332e13			−0.0672188			−0.0336094	−	0.999435i	$-0.510700\pi$
$569$	−9.56332e13			−0.0672188			−0.0336094	+	0.999435i	$0.510700\pi$
$570$		0			0
$571$	−1.06033e15			−0.731041			−0.365521	−	0.930803i	$-0.619109\pi$
$571$	−1.06033e15			−0.731041			−0.365521	+	0.930803i	$0.619109\pi$
$572$			1.19617e13i			0.00816796i
$573$		0			0
$574$	2.97315e13			0.0199160
$575$	3.14434e12	+	2.41065e12i	0.00208620	+	0.00159941i
$576$		0			0
$577$			2.62145e15i			1.70637i	0.521605	+	0.853187i	$0.325333\pi$
$577$			2.62145e15i			1.70637i	−0.521605	+	0.853187i	$0.674667\pi$
$578$			7.99641e14i			0.515575i
$579$		0			0
$580$	−1.60945e14	−	3.26192e14i	−0.101818	−	0.206357i
$581$	2.23105e15			1.39811
$582$		0			0
$583$		−	3.32778e12i		−	0.00204634i
$584$	3.48071e14			0.212030
$585$		0			0
$586$	1.81062e15			1.08241
$587$		−	1.75497e15i		−	1.03935i	−0.854365	−	0.519674i	$-0.826053\pi$
$587$		−	1.75497e15i		−	1.03935i	0.854365	−	0.519674i	$-0.173947\pi$
$588$		0			0
$589$	−3.93416e14			−0.228674
$590$	−2.04878e15	+	1.01088e15i	−1.17980	+	0.582120i
$591$		0			0
$592$		−	6.83672e14i		−	0.386437i
$593$			1.57877e15i			0.884133i	0.896982	+	0.442066i	$0.145754\pi$
$593$			1.57877e15i			0.884133i	−0.896982	+	0.442066i	$0.854246\pi$
$594$		0			0
$595$	1.74828e15	+	3.54330e15i	0.961100	+	1.94789i
$596$	−7.25424e14			−0.395128
$597$		0			0
$598$			4.03022e12i			0.00215512i
$599$	1.28636e15			0.681577			0.340789	−	0.940140i	$-0.389306\pi$
$599$	1.28636e15			0.681577			0.340789	+	0.940140i	$0.389306\pi$
$600$		0			0
$601$	3.43995e15			1.78955			0.894773	−	0.446522i	$-0.147337\pi$
$601$	3.43995e15			1.78955			0.894773	+	0.446522i	$0.147337\pi$
$602$			3.45684e14i			0.178196i
$603$		0			0
$604$	−1.07864e15			−0.545977
$605$	−8.81978e14	−	1.78753e15i	−0.442388	−	0.896602i
$606$		0			0
$607$		−	3.76439e15i		−	1.85420i	−0.374815	−	0.927100i	$-0.622294\pi$
$607$		−	3.76439e15i		−	1.85420i	0.374815	−	0.927100i	$-0.377706\pi$
$608$		−	4.22142e14i		−	0.206058i
$609$		0			0
$610$	4.86879e13	−	2.40229e13i	0.0233403	−	0.0115162i
$611$	−3.64194e15			−1.73024
$612$		0			0
$613$		−	2.65739e14i		−	0.124000i	−0.998076	−	0.0620001i	$-0.980252\pi$
$613$		−	2.65739e14i		−	0.124000i	0.998076	−	0.0620001i	$-0.0197479\pi$
$614$	−3.69877e14			−0.171053
$615$		0			0
$616$	1.81143e13			0.00822862
$617$		−	1.63882e14i		−	0.0737842i	−0.999319	−	0.0368921i	$-0.988254\pi$
$617$		−	1.63882e14i		−	0.0737842i	0.999319	−	0.0368921i	$-0.0117458\pi$
$618$		0			0
$619$	3.96471e15			1.75353			0.876764	−	0.480920i	$-0.159697\pi$
$619$	3.96471e15			1.75353			0.876764	+	0.480920i	$0.159697\pi$
$620$	9.90074e13	+	2.00662e14i	0.0434024	+	0.0879650i
$621$		0			0
$622$		−	1.60513e15i		−	0.691293i
$623$			5.68651e15i			2.42751i
$624$		0			0
$625$	−6.18996e14	−	2.30243e15i	−0.259626	−	0.965709i
$626$	−6.38228e14			−0.265349
$627$		0			0
$628$		−	6.76005e14i		−	0.276167i
$629$	5.01916e15			2.03260
$630$		0			0
$631$	−8.76182e14			−0.348685			−0.174342	−	0.984685i	$-0.555780\pi$
$631$	−8.76182e14			−0.348685			−0.174342	+	0.984685i	$0.555780\pi$
$632$		−	6.88196e14i		−	0.271499i
$633$		0			0
$634$	−1.61376e15			−0.625672
$635$	−3.56010e15	+	1.75657e15i	−1.36838	+	0.675165i
$636$		0			0
$637$			5.30496e15i			2.00408i
$638$		−	1.22425e13i		−	0.00458517i
$639$		0			0
$640$	−2.15313e14	+	1.06237e14i	−0.0792649	+	0.0391097i
$641$	4.91614e14			0.179434			0.0897171	−	0.995967i	$-0.471404\pi$
$641$	4.91614e14			0.179434			0.0897171	+	0.995967i	$0.471404\pi$
$642$		0			0
$643$			8.05370e14i			0.288958i	0.989508	+	0.144479i	$0.0461507\pi$
$643$			8.05370e14i			0.288958i	−0.989508	+	0.144479i	$0.953849\pi$
$644$	6.10320e12			0.00217113
$645$		0			0
$646$	3.09914e15			1.08383
$647$		−	1.76423e15i		−	0.611760i	−0.952070	−	0.305880i	$-0.901049\pi$
$647$		−	1.76423e15i		−	0.611760i	0.952070	−	0.305880i	$-0.0989506\pi$
$648$		0			0
$649$	−7.68937e13			−0.0262147
$650$	1.47556e15	−	1.92465e15i	0.498807	−	0.650620i
$651$		0			0
$652$		−	7.88846e14i		−	0.262199i
$653$		−	3.30911e15i		−	1.09066i	−0.838222	−	0.545329i	$-0.816405\pi$
$653$		−	3.30911e15i		−	1.09066i	0.838222	−	0.545329i	$-0.183595\pi$
$654$		0			0
$655$	1.09968e15	+	2.22876e15i	0.356402	+	0.722332i
$656$	−1.32636e13			−0.00426277
$657$		0			0
$658$			5.51520e15i			1.74309i
$659$	−4.08284e15			−1.27966			−0.639828	−	0.768518i	$-0.720994\pi$
$659$	−4.08284e15			−1.27966			−0.639828	+	0.768518i	$0.720994\pi$
$660$		0			0
$661$	−3.94938e15			−1.21737			−0.608683	−	0.793413i	$-0.708302\pi$
$661$	−3.94938e15			−1.21737			−0.608683	+	0.793413i	$0.708302\pi$
$662$		−	2.98881e15i		−	0.913649i
$663$		0			0
$664$	−9.95304e14			−0.299248
$665$	5.79073e15	−	2.85718e15i	1.72669	−	0.851958i
$666$		0			0
$667$		−	4.12483e12i		−	0.00120980i
$668$			2.06927e15i			0.601932i
$669$		0			0
$670$	−2.44687e14	−	4.95915e14i	−0.0700163	−	0.141904i
$671$	1.82733e12			0.000518613
$672$		0			0
$673$		−	4.54748e15i		−	1.26966i	−0.772651	−	0.634831i	$-0.781070\pi$
$673$		−	4.54748e15i		−	1.26966i	0.772651	−	0.634831i	$-0.218930\pi$
$674$	3.09567e15			0.857286
$675$		0			0
$676$	6.31718e14			0.172114
$677$		−	2.25251e14i		−	0.0608735i	−0.999537	−	0.0304368i	$-0.990310\pi$
$677$		−	2.25251e14i		−	0.0608735i	0.999537	−	0.0304368i	$-0.00968982\pi$
$678$		0			0
$679$	−1.10193e16			−2.93002
$680$	−7.79934e14	−	1.58072e15i	−0.205712	−	0.416922i
$681$		0			0
$682$			7.53113e12i			0.00195455i
$683$		−	2.16550e15i		−	0.557499i	−0.960364	−	0.278750i	$-0.910080\pi$
$683$		−	2.16550e15i		−	0.557499i	0.960364	−	0.278750i	$-0.0899199\pi$
$684$		0			0
$685$	5.34647e15	−	2.63798e15i	1.35447	−	0.668302i
$686$	3.38597e15			0.850943
$687$		0			0
$688$		−	1.54214e14i		−	0.0381407i
$689$	−6.86299e14			−0.168387
$690$		0			0
$691$	2.56112e15			0.618445			0.309223	−	0.950990i	$-0.399931\pi$
$691$	2.56112e15			0.618445			0.309223	+	0.950990i	$0.399931\pi$
$692$			3.25349e14i			0.0779409i
$693$		0			0
$694$	9.56149e14			0.225449
$695$	−1.46015e13	−	2.95933e13i	−0.00341571	−	0.00692273i
$696$		0			0
$697$		−	9.73747e13i		−	0.0224216i
$698$		−	2.65424e15i		−	0.606366i
$699$		0			0
$700$	−2.91461e15	−	2.23452e15i	−0.655452	−	0.502511i
$701$	−1.70243e15			−0.379858			−0.189929	−	0.981798i	$-0.560826\pi$
$701$	−1.70243e15			−0.379858			−0.189929	+	0.981798i	$0.560826\pi$
$702$		0			0
$703$		−	8.20269e15i		−	1.80178i
$704$	−8.08103e12			−0.00176123
$705$		0			0
$706$	8.89157e14			0.190789
$707$			9.16525e15i			1.95136i
$708$		0			0
$709$	−6.47024e15			−1.35633			−0.678166	−	0.734909i	$-0.737225\pi$
$709$	−6.47024e15			−1.35633			−0.678166	+	0.734909i	$0.737225\pi$
$710$	5.19006e15	−	2.56080e15i	1.07957	−	0.532666i
$711$		0			0
$712$		−	2.53683e15i		−	0.519579i
$713$			2.53745e12i			0.000515708i
$714$		0			0
$715$	7.32003e13	−	3.61174e13i	0.0146497	−	0.00722825i
$716$	3.13492e15			0.622594
$717$		0			0
$718$			1.92143e15i			0.375786i
$719$	−7.19791e15			−1.39700			−0.698501	−	0.715609i	$-0.746149\pi$
$719$	−7.19791e15			−1.39700			−0.698501	+	0.715609i	$0.746149\pi$
$720$		0			0
$721$	−1.19599e16			−2.28605
$722$		−	1.33716e15i		−	0.253647i
$723$		0			0
$724$	−4.67317e15			−0.873071
$725$	−1.51019e15	+	1.96983e15i	−0.280010	+	0.365232i
$726$		0			0
$727$		−	1.76074e15i		−	0.321556i	−0.986991	−	0.160778i	$-0.948600\pi$
$727$		−	1.76074e15i		−	0.321556i	0.986991	−	0.160778i	$-0.0514003\pi$
$728$		−	3.73576e15i		−	0.677105i
$729$		0			0
$730$	−1.05097e15	−	2.13004e15i	−0.187636	−	0.380288i
$731$	1.13216e15			0.200615
$732$		0			0
$733$		−	5.66913e15i		−	0.989566i	−0.869016	−	0.494783i	$-0.835247\pi$
$733$		−	5.66913e15i		−	0.989566i	0.869016	−	0.494783i	$-0.164753\pi$
$734$	−5.05831e15			−0.876349
$735$		0			0
$736$	−2.72272e12			−0.000464703
$737$		−	1.86124e13i		−	0.00315306i
$738$		0			0
$739$	3.83696e14			0.0640388			0.0320194	−	0.999487i	$-0.489806\pi$
$739$	3.83696e14			0.0640388			0.0320194	+	0.999487i	$0.489806\pi$
$740$	−4.18378e15	+	2.06430e15i	−0.693098	+	0.341978i
$741$		0			0
$742$			1.03930e15i			0.169637i
$743$			9.58748e15i			1.55334i	0.629909	+	0.776669i	$0.283092\pi$
$743$			9.58748e15i			1.55334i	−0.629909	+	0.776669i	$0.716908\pi$
$744$		0			0
$745$	2.19037e15	+	4.43929e15i	0.349669	+	0.708686i
$746$	−5.83347e15			−0.924408
$747$		0			0
$748$		−	5.93267e13i		−	0.00926384i
$749$	−7.23915e15			−1.12211
$750$		0			0
$751$	−7.40637e15			−1.13132			−0.565660	−	0.824638i	$-0.691379\pi$
$751$	−7.40637e15			−1.13132			−0.565660	+	0.824638i	$0.691379\pi$
$752$		−	2.46041e15i		−	0.373086i
$753$		0			0
$754$	−2.52480e15			−0.377298
$755$	3.25688e15	+	6.60083e15i	0.483163	+	0.979242i
$756$		0			0
$757$		−	4.64962e15i		−	0.679813i	−0.940459	−	0.339907i	$-0.889604\pi$
$757$		−	4.64962e15i		−	0.679813i	0.940459	−	0.339907i	$-0.110396\pi$
$758$		−	4.23767e15i		−	0.615101i
$759$		0			0
$760$	−2.58333e15	+	1.27463e15i	−0.369577	+	0.182351i
$761$	1.19479e16			1.69698			0.848490	−	0.529212i	$-0.177512\pi$
$761$	1.19479e16			1.69698			0.848490	+	0.529212i	$0.177512\pi$
$762$		0			0
$763$			2.14159e16i			2.99814i
$764$	−7.19929e14			−0.100064
$765$		0			0
$766$	8.52447e15			1.16791
$767$			1.58580e16i			2.15712i
$768$		0			0
$769$	4.18830e15			0.561621			0.280810	−	0.959763i	$-0.409397\pi$
$769$	4.18830e15			0.561621			0.280810	+	0.959763i	$0.409397\pi$
$770$	−5.46947e13	−	1.10852e14i	−0.00728193	−	0.0147585i
$771$		0			0
$772$			2.59596e15i			0.340725i
$773$		−	6.97307e15i		−	0.908734i	−0.890815	−	0.454367i	$-0.849865\pi$
$773$		−	6.97307e15i		−	0.908734i	0.890815	−	0.454367i	$-0.150135\pi$
$774$		0			0
$775$	9.29018e14	−	1.21177e15i	0.119362	−	0.155690i
$776$	4.91587e15			0.627135
$777$		0			0
$778$		−	1.06062e16i		−	1.33405i
$779$	−1.59137e14			−0.0198754
$780$		0			0
$781$	1.94790e14			0.0239876
$782$		−	1.99888e13i		−	0.00244427i
$783$		0			0
$784$	−3.58391e15			−0.432134
$785$	−4.13686e15	+	2.04115e15i	−0.495323	+	0.244395i
$786$		0			0
$787$		−	5.88998e15i		−	0.695430i	−0.937600	−	0.347715i	$-0.886958\pi$
$787$		−	5.88998e15i		−	0.695430i	0.937600	−	0.347715i	$-0.113042\pi$
$788$		−	4.45738e15i		−	0.522619i
$789$		0			0
$790$	−4.21147e15	+	2.07796e15i	−0.486950	+	0.240263i
$791$	−1.35695e16			−1.55809
$792$		0			0
$793$		−	3.76856e14i		−	0.0426749i
$794$	8.51753e15			0.957857
$795$		0			0
$796$	−3.56204e15			−0.395073
$797$		−	9.45081e15i		−	1.04099i	−0.853864	−	0.520497i	$-0.825747\pi$
$797$		−	9.45081e15i		−	1.04099i	0.853864	−	0.520497i	$-0.174253\pi$
$798$		0			0
$799$	1.80630e16			1.96238
$800$	1.30025e15	+	9.96852e14i	0.140291	+	0.107556i
$801$		0			0
$802$			1.86722e15i			0.198717i
$803$		−	7.99437e13i		−	0.00844984i
$804$		0			0
$805$	−1.84282e13	−	3.73490e13i	−0.00192134	−	0.00389405i
$806$	1.55317e15			0.160833
$807$		0			0
$808$		−	4.08875e15i		−	0.417665i
$809$	1.45474e16			1.47594			0.737968	−	0.674835i	$-0.235785\pi$
$809$	1.45474e16			1.47594			0.737968	+	0.674835i	$0.235785\pi$
$810$		0			0
$811$	3.44330e15			0.344636			0.172318	−	0.985041i	$-0.444874\pi$
$811$	3.44330e15			0.344636			0.172318	+	0.985041i	$0.444874\pi$
$812$			3.82346e15i			0.380100i
$813$		0			0
$814$	−1.57024e14			−0.0154003
$815$	−4.82740e15	+	2.38186e15i	−0.470269	+	0.232033i
$816$		0			0
$817$		−	1.85026e15i		−	0.177833i
$818$		−	4.82013e15i		−	0.460167i
$819$		0			0
$820$	4.00486e13	+	8.11678e13i	0.00377234	+	0.00764553i
$821$	−1.62433e16			−1.51981			−0.759903	−	0.650037i	$-0.774753\pi$
$821$	−1.62433e16			−1.51981			−0.759903	+	0.650037i	$0.774753\pi$
$822$		0			0
$823$		−	2.70386e15i		−	0.249624i	−0.992180	−	0.124812i	$-0.960167\pi$
$823$		−	2.70386e15i		−	0.249624i	0.992180	−	0.124812i	$-0.0398327\pi$
$824$	5.33550e15			0.489300
$825$		0			0
$826$	2.40148e16			2.17314
$827$			1.18633e16i			1.06641i	0.845985	+	0.533207i	$0.179013\pi$
$827$			1.18633e16i			1.06641i	−0.845985	+	0.533207i	$0.820987\pi$
$828$		0			0
$829$	4.11995e15			0.365462			0.182731	−	0.983163i	$-0.441506\pi$
$829$	4.11995e15			0.365462			0.182731	+	0.983163i	$0.441506\pi$
$830$	3.00525e15	+	6.09084e15i	0.264820	+	0.536720i
$831$		0			0
$832$			1.66657e15i			0.144926i
$833$		−	2.63112e16i		−	2.27296i
$834$		0			0
$835$	1.26631e16	−	6.24802e15i	1.07960	−	0.532681i
$836$	−9.69561e13			−0.00821184
$837$		0			0
$838$			3.58919e15i			0.300023i
$839$	1.47076e16			1.22138			0.610689	−	0.791871i	$-0.290893\pi$
$839$	1.47076e16			1.22138			0.610689	+	0.791871i	$0.290893\pi$
$840$		0			0
$841$	−9.61644e15			−0.788200
$842$			8.37654e15i			0.682100i
$843$		0			0
$844$	2.18308e15			0.175463
$845$	−1.90743e15	−	3.86585e15i	−0.152313	−	0.308697i
$846$		0			0
$847$			2.09526e16i			1.65150i
$848$		−	4.63648e14i		−	0.0363087i
$849$		0			0
$850$	−7.31836e15	+	9.54573e15i	−0.565731	+	0.737913i
$851$	−5.29056e13			−0.00406339
$852$		0			0
$853$			1.02344e16i			0.775969i	0.921666	+	0.387984i	$0.126829\pi$
$853$			1.02344e16i			0.775969i	−0.921666	+	0.387984i	$0.873171\pi$
$854$	−5.70695e14			−0.0429918
$855$		0			0
$856$	3.22948e15			0.240175
$857$		−	1.11509e16i		−	0.823979i	−0.911189	−	0.411989i	$-0.864834\pi$
$857$		−	1.11509e16i		−	0.823979i	0.911189	−	0.411989i	$-0.135166\pi$
$858$		0			0
$859$	−5.22746e15			−0.381354			−0.190677	−	0.981653i	$-0.561068\pi$
$859$	−5.22746e15			−0.381354			−0.190677	+	0.981653i	$0.561068\pi$
$860$	−9.43727e14	+	4.65639e14i	−0.0684077	+	0.0337527i
$861$		0			0
$862$			1.74335e16i			1.24766i
$863$		−	7.43513e15i		−	0.528724i	−0.964424	−	0.264362i	$-0.914839\pi$
$863$		−	7.43513e15i		−	0.528724i	0.964424	−	0.264362i	$-0.0851614\pi$
$864$		0			0
$865$	1.99100e15	−	9.82367e14i	0.139792	−	0.0689740i
$866$	−1.26518e16			−0.882685
$867$		0			0
$868$		−	2.35205e15i		−	0.162027i
$869$	−1.58062e14			−0.0108198
$870$		0			0
$871$	−3.83850e15			−0.259455
$872$		−	9.55395e15i		−	0.641715i
$873$		0			0
$874$	−3.26672e13			−0.00216670
$875$	−4.87388e15	+	2.45831e16i	−0.321241	+	1.62029i
$876$		0			0
$877$			4.20461e15i			0.273671i	0.990594	+	0.136835i	$0.0436931\pi$
$877$			4.20461e15i			0.273671i	−0.990594	+	0.136835i	$0.956307\pi$
$878$		−	5.17237e15i		−	0.334557i
$879$		0			0
$880$	2.44001e13	+	4.94524e13i	0.00155861	+	0.00315888i
$881$	2.08294e16			1.32224			0.661119	−	0.750281i	$-0.270082\pi$
$881$	2.08294e16			1.32224			0.661119	+	0.750281i	$0.270082\pi$
$882$		0			0
$883$			9.97011e15i			0.625052i	0.949909	+	0.312526i	$0.101175\pi$
$883$			9.97011e15i			0.625052i	−0.949909	+	0.312526i	$0.898825\pi$
$884$	−1.22351e16			−0.762291
$885$		0			0
$886$	1.20116e16			0.739118
$887$			9.91209e13i			0.00606157i	0.999995	+	0.00303079i	$0.000964731\pi$
$887$			9.91209e13i			0.00606157i	−0.999995	+	0.00303079i	$0.999035\pi$
$888$		0			0
$889$	4.17296e16			2.52049
$890$	−1.55243e16	+	7.65978e15i	−0.931896	+	0.459802i
$891$		0			0
$892$		−	1.26848e16i		−	0.752101i
$893$		−	2.95200e16i		−	1.73953i
$894$		0			0
$895$	−9.46567e15	−	1.91844e16i	−0.550966	−	1.11666i
$896$	2.52379e15			0.146002
$897$		0			0
$898$		−	3.09269e15i		−	0.176733i
$899$	−1.58963e15			−0.0902853
$900$		0			0
$901$	3.40386e15			0.190979
$902$			3.04635e12i			0.000169880i
$903$		0			0
$904$	6.05355e15			0.333490
$905$	1.41103e16	+	2.85978e16i	0.772626	+	1.56591i
$906$		0			0
$907$		−	2.08572e16i		−	1.12828i	−0.825681	−	0.564138i	$-0.809209\pi$
$907$		−	2.08572e16i		−	1.12828i	0.825681	−	0.564138i	$-0.190791\pi$
$908$			1.71495e16i			0.922102i
$909$		0			0
$910$	−2.28613e16	+	1.12799e16i	−1.21443	+	0.599206i
$911$	1.77980e16			0.939766			0.469883	−	0.882729i	$-0.344296\pi$
$911$	1.77980e16			0.939766			0.469883	+	0.882729i	$0.344296\pi$
$912$		0			0
$913$			2.28598e14i			0.0119257i
$914$	3.79669e15			0.196880
$915$		0			0
$916$	1.54736e16			0.792804
$917$		−	2.61244e16i		−	1.33050i
$918$		0			0
$919$	3.30314e16			1.66223			0.831116	−	0.556100i	$-0.187703\pi$
$919$	3.30314e16			1.66223			0.831116	+	0.556100i	$0.187703\pi$
$920$	8.22106e12	+	1.66619e13i	0.000411240	+	0.000833473i
$921$		0			0
$922$		−	2.17272e16i		−	1.07395i
$923$		−	4.01722e16i		−	1.97386i
$924$		0			0
$925$	2.52653e16	+	1.93700e16i	1.22672	+	0.940479i
$926$	4.99706e15			0.241187
$927$		0			0
$928$		−	1.70570e15i		−	0.0813558i
$929$	8.55855e15			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$929$	8.55855e15			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$930$		0			0
$931$	−4.29997e16			−2.01485
$932$			1.44994e16i			0.675402i
$933$		0			0
$934$	1.11464e16			0.513130
$935$	−3.63054e14	+	1.79133e14i	−0.0166153	+	0.00819805i
$936$		0			0
$937$			1.12342e16i			0.508132i	0.967187	+	0.254066i	$0.0817680\pi$
$937$			1.12342e16i			0.508132i	−0.967187	+	0.254066i	$0.918232\pi$
$938$			5.81286e15i			0.261381i
$939$		0			0
$940$	−1.50567e16	+	7.42903e15i	−0.669153	+	0.330163i
$941$	7.27902e15			0.321610			0.160805	−	0.986986i	$-0.448591\pi$
$941$	7.27902e15			0.321610			0.160805	+	0.986986i	$0.448591\pi$
$942$		0			0
$943$			1.02640e12i			4.48231e-5i
$944$	−1.07133e16			−0.465134
$945$		0			0
$946$	−3.54195e13			−0.00151999
$947$			3.58374e16i			1.52901i	0.644616	+	0.764506i	$0.277017\pi$
$947$			3.58374e16i			1.52901i	−0.644616	+	0.764506i	$0.722983\pi$
$948$		0			0
$949$	−1.64870e16			−0.695309
$950$	1.56003e16	+	1.19602e16i	0.654115	+	0.501487i
$951$		0			0
$952$			1.85284e16i			0.767952i
$953$		−	2.79333e16i		−	1.15110i	−0.817768	−	0.575548i	$-0.804789\pi$
$953$		−	2.79333e16i		−	1.15110i	0.817768	−	0.575548i	$-0.195211\pi$
$954$		0			0
$955$	2.17378e15	+	4.40566e15i	0.0885515	+	0.179470i
$956$	−1.10424e16			−0.447243
$957$		0			0
$958$		−	6.42400e14i		−	0.0257214i
$959$	−6.26686e16			−2.49487
$960$		0			0
$961$	−2.44306e16			−0.961514
$962$			3.23834e16i			1.26724i
$963$		0			0
$964$	−8.48112e15			−0.328117
$965$	1.58862e16	−	7.83832e15i	0.611110	−	0.301525i
$966$		0			0
$967$			1.61731e16i			0.615103i	0.951531	+	0.307551i	$0.0995096\pi$
$967$			1.61731e16i			0.615103i	−0.951531	+	0.307551i	$0.900490\pi$
$968$		−	9.34724e15i		−	0.353483i
$969$		0			0
$970$	−1.48431e16	−	3.00830e16i	−0.554984	−	1.12480i
$971$	−1.57576e16			−0.585846			−0.292923	−	0.956136i	$-0.594628\pi$
$971$	−1.57576e16			−0.585846			−0.292923	+	0.956136i	$0.594628\pi$
$972$		0			0
$973$			3.46878e14i			0.0127513i
$974$	−2.55305e16			−0.933221
$975$		0			0
$976$	2.54595e14			0.00920187
$977$			6.52441e15i			0.234488i	0.993103	+	0.117244i	$0.0374060\pi$
$977$			6.52441e15i			0.234488i	−0.993103	+	0.117244i	$0.962594\pi$
$978$		0			0
$979$	−5.82651e14			−0.0207063
$980$	1.08213e16	+	2.19320e16i	0.382418	+	0.775058i
$981$		0			0
$982$		−	2.55269e16i		−	0.892042i
$983$			2.21995e16i			0.771434i	0.922617	+	0.385717i	$0.126046\pi$
$983$			2.21995e16i			0.771434i	−0.922617	+	0.385717i	$0.873954\pi$
$984$		0			0
$985$	−2.72773e16	+	1.34587e16i	−0.937349	+	0.462493i
$986$	1.25223e16			0.427920
$987$		0			0
$988$			1.99955e16i			0.675725i
$989$	−1.19338e13			−0.000401050
$990$		0			0
$991$	−4.57252e16			−1.51967			−0.759837	−	0.650114i	$-0.774721\pi$
$991$	−4.57252e16			−1.51967			−0.759837	+	0.650114i	$0.774721\pi$
$992$			1.04928e15i			0.0346800i
$993$		0			0
$994$	−6.08352e16			−1.98852
$995$	1.07553e16	+	2.17982e16i	0.349621	+	0.708587i
$996$		0			0
$997$		−	4.05315e16i		−	1.30308i	−0.758616	−	0.651538i	$-0.774124\pi$
$997$		−	4.05315e16i		−	1.30308i	0.758616	−	0.651538i	$-0.225876\pi$
$998$		−	4.44131e15i		−	0.142001i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.12.c.d.19.5	yes	12
3.2	odd	2	inner	90.12.c.d.19.8	yes	12
5.4	even	2	inner	90.12.c.d.19.11	yes	12
15.14	odd	2	inner	90.12.c.d.19.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.12.c.d.19.2	✓	12	15.14	odd	2	inner
90.12.c.d.19.5	yes	12	1.1	even	1	trivial
90.12.c.d.19.8	yes	12	3.2	odd	2	inner
90.12.c.d.19.11	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)

\(f(q)\)	\(=\)	\(q-32.0000i q^{2} -1024.00 q^{4} +(3091.89 + 6266.44i) q^{5} -73452.1i q^{7} +32768.0i q^{8} +(200526. - 98940.6i) q^{10} +7526.04 q^{11} -1.55212e6i q^{13} -2.35047e6 q^{14} +1.04858e6 q^{16} +7.69810e6i q^{17} +1.25808e7 q^{19} +(-3.16610e6 - 6.41684e6i) q^{20} -240833. i q^{22} -81143.4i q^{23} +(-2.97085e7 + 3.87504e7i) q^{25} -4.96678e7 q^{26} +7.52149e7i q^{28} +5.08338e7 q^{29} -3.12711e7 q^{31} -3.35544e7i q^{32} +2.46339e8 q^{34} +(4.60283e8 - 2.27106e8i) q^{35} -6.52001e8i q^{37} -4.02586e8i q^{38} +(-2.05339e8 + 1.01315e8i) q^{40} -1.26492e7 q^{41} -1.47070e8i q^{43} -7.70667e6 q^{44} -2.59659e6 q^{46} -2.34643e9i q^{47} -3.41788e9 q^{49} +(1.24001e9 + 9.50672e8i) q^{50} +1.58937e9i q^{52} -4.42169e8i q^{53} +(2.32697e7 + 4.71615e7i) q^{55} +2.40688e9 q^{56} -1.62668e9i q^{58} -1.02170e10 q^{59} +2.42801e8 q^{61} +1.00068e9i q^{62} -1.07374e9 q^{64} +(9.72626e9 - 4.79899e9i) q^{65} -2.47307e9i q^{67} -7.88285e9i q^{68} +(-7.26739e9 - 1.47291e10i) q^{70} +2.58822e10 q^{71} -1.06223e10i q^{73} -2.08640e10 q^{74} -1.28827e10 q^{76} -5.52803e8i q^{77} -2.10021e10 q^{79} +(3.24209e9 + 6.57084e9i) q^{80} +4.04774e8i q^{82} +3.03743e10i q^{83} +(-4.82397e10 + 2.38017e10i) q^{85} -4.70625e9 q^{86} +2.46613e8i q^{88} -7.74179e10 q^{89} -1.14006e11 q^{91} +8.30909e7i q^{92} -7.50857e10 q^{94} +(3.88985e10 + 7.88369e10i) q^{95} -1.50020e11i q^{97} +1.09372e11i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12288 q^{4} + 56448 q^{10} + 12582912 q^{16} - 489648 q^{19} - 125575548 q^{25} + 47933952 q^{31} + 341743872 q^{34} - 57802752 q^{40} + 3346675200 q^{46} - 6178917036 q^{49} - 11944070688 q^{55}+ \cdots - 10041254400 q^{94}+O(q^{100}) \) 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

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Database

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