LMFDB - Embedded newform 90.12.c.b.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 = [6,0,0,-6144,-530] 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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 198x^{3} + 3568321x^{2} - 6762620x + 6408200 $ x^6 - 2x^5 + 2x^4 + 198x^3 + 3568321x^2 - 6762620*x + 6408200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{2}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.5
Root			$-30.7073 - 30.7073i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.12.c.b.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+32.0000i q^{2} -1024.00 q^{4} +(-1594.62 + 6803.33i) q^{5} +24477.0i q^{7} -32768.0i q^{8} +(-217707. - 51027.9i) q^{10} +669055. q^{11} +579245. i q^{13} -783265. q^{14} +1.04858e6 q^{16} +7.85051e6i q^{17} +1.81223e7 q^{19} +(1.63289e6 - 6.96661e6i) q^{20} +2.14098e7i q^{22} +1.97203e7i q^{23} +(-4.37425e7 - 2.16975e7i) q^{25} -1.85358e7 q^{26} -2.50645e7i q^{28} +2.02707e8 q^{29} +1.02789e8 q^{31} +3.35544e7i q^{32} -2.51216e8 q^{34} +(-1.66525e8 - 3.90316e7i) q^{35} -5.02591e8i q^{37} +5.79913e8i q^{38} +(2.22932e8 + 5.22525e7i) q^{40} -3.44964e8 q^{41} +1.43221e9i q^{43} -6.85112e8 q^{44} -6.31051e8 q^{46} +1.38179e9i q^{47} +1.37820e9 q^{49} +(6.94319e8 - 1.39976e9i) q^{50} -5.93147e8i q^{52} +2.89531e8i q^{53} +(-1.06689e9 + 4.55180e9i) q^{55} +8.02063e8 q^{56} +6.48664e9i q^{58} -2.47487e9 q^{59} +9.16284e7 q^{61} +3.28926e9i q^{62} -1.07374e9 q^{64} +(-3.94079e9 - 9.23676e8i) q^{65} +3.09287e7i q^{67} -8.03893e9i q^{68} +(1.24901e9 - 5.32881e9i) q^{70} -2.42503e10 q^{71} -3.55008e9i q^{73} +1.60829e10 q^{74} -1.85572e10 q^{76} +1.63765e10i q^{77} +1.16350e10 q^{79} +(-1.67208e9 + 7.13381e9i) q^{80} -1.10389e10i q^{82} -2.33729e10i q^{83} +(-5.34096e10 - 1.25186e10i) q^{85} -4.58307e10 q^{86} -2.19236e10i q^{88} -1.02379e11 q^{89} -1.41782e10 q^{91} -2.01936e10i q^{92} -4.42174e10 q^{94} +(-2.88982e10 + 1.23292e11i) q^{95} -5.87705e10i q^{97} +4.41025e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6144 q^{4} - 530 q^{5} - 385920 q^{10} + 642728 q^{11} + 2125952 q^{14} + 6291456 q^{16} - 24109080 q^{19} + 542720 q^{20} - 181718850 q^{25} - 89251584 q^{26} + 256409820 q^{29} + 458481792 q^{31}+ \cdots - 104896380600 q^{95}+O(q^{100}) $ 6 * q - 6144 * q^4 - 530 * q^5 - 385920 * q^10 + 642728 * q^11 + 2125952 * q^14 + 6291456 * q^16 - 24109080 * q^19 + 542720 * q^20 - 181718850 * q^25 - 89251584 * q^26 + 256409820 * q^29 + 458481792 * q^31 - 225288192 * q^34 + 697136360 * q^35 + 395182080 * q^40 + 164768948 * q^41 - 658153472 * q^44 - 2956208256 * q^46 - 675514158 * q^49 - 3912262400 * q^50 + 3688644360 * q^55 - 2176974848 * q^56 - 17663962360 * q^59 - 5020792428 * q^61 - 6442450944 * q^64 + 19996916880 * q^65 + 24956826240 * q^70 - 56788418832 * q^71 + 64135292672 * q^74 + 24687697920 * q^76 + 2602550880 * q^79 - 555745280 * q^80 - 85024210560 * q^85 - 111995790464 * q^86 - 249448412540 * q^89 - 184446766128 * q^91 - 337749482112 * q^94 - 104896380600 * q^95

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
$5$	−1594.62	+	6803.33i	−0.228204	+	0.973613i
$5$	−1594.62	+	6803.33i	−0.228204	+	0.973613i
$6$		0			0
$7$			24477.0i			0.550452i	0.961380	+	0.275226i	$0.0887527\pi$
$7$			24477.0i			0.550452i	−0.961380	+	0.275226i	$0.911247\pi$
$8$		−	32768.0i		−	0.353553i
$9$		0			0
$10$	−217707.	−	51027.9i	−0.688449	−	0.161364i
$11$	669055.			1.25257			0.626285	−	0.779594i	$-0.284575\pi$
$11$	669055.			1.25257			0.626285	+	0.779594i	$0.284575\pi$
$12$		0			0
$13$			579245.i			0.432687i	0.976317	+	0.216343i	$0.0694131\pi$
$13$			579245.i			0.432687i	−0.976317	+	0.216343i	$0.930587\pi$
$14$	−783265.			−0.389228
$15$		0			0
$16$	1.04858e6			0.250000
$17$			7.85051e6i			1.34100i	0.741909	+	0.670500i	$0.233920\pi$
$17$			7.85051e6i			1.34100i	−0.741909	+	0.670500i	$0.766080\pi$
$18$		0			0
$19$	1.81223e7			1.67907			0.839534	−	0.543307i	$-0.182828\pi$
$19$	1.81223e7			1.67907			0.839534	+	0.543307i	$0.182828\pi$
$20$	1.63289e6	−	6.96661e6i	0.114102	−	0.486807i
$21$		0			0
$22$			2.14098e7i			0.885701i
$23$			1.97203e7i			0.638868i	0.947609	+	0.319434i	$0.103493\pi$
$23$			1.97203e7i			0.638868i	−0.947609	+	0.319434i	$0.896507\pi$
$24$		0			0
$25$	−4.37425e7	−	2.16975e7i	−0.895846	−	0.444364i
$26$	−1.85358e7			−0.305956
$27$		0			0
$28$		−	2.50645e7i		−	0.275226i
$29$	2.02707e8			1.83519			0.917594	−	0.397518i	$-0.130128\pi$
$29$	2.02707e8			1.83519			0.917594	+	0.397518i	$0.130128\pi$
$30$		0			0
$31$	1.02789e8			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$31$	1.02789e8			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$32$			3.35544e7i			0.176777i
$33$		0			0
$34$	−2.51216e8			−0.948231
$35$	−1.66525e8	−	3.90316e7i	−0.535928	−	0.125615i
$36$		0			0
$37$		−	5.02591e8i		−	1.19153i	−0.803158	−	0.595766i	$-0.796849\pi$
$37$		−	5.02591e8i		−	1.19153i	0.803158	−	0.595766i	$-0.203151\pi$
$38$			5.79913e8i			1.18728i
$39$		0			0
$40$	2.22932e8	+	5.22525e7i	0.344224	+	0.0806821i
$41$	−3.44964e8			−0.465011			−0.232505	−	0.972595i	$-0.574692\pi$
$41$	−3.44964e8			−0.465011			−0.232505	+	0.972595i	$0.574692\pi$
$42$		0			0
$43$			1.43221e9i			1.48570i	0.669460	+	0.742848i	$0.266526\pi$
$43$			1.43221e9i			1.48570i	−0.669460	+	0.742848i	$0.733474\pi$
$44$	−6.85112e8			−0.626285
$45$		0			0
$46$	−6.31051e8			−0.451748
$47$			1.38179e9i			0.878830i	0.898284	+	0.439415i	$0.144814\pi$
$47$			1.38179e9i			0.878830i	−0.898284	+	0.439415i	$0.855186\pi$
$48$		0			0
$49$	1.37820e9			0.697003
$50$	6.94319e8	−	1.39976e9i	0.314213	−	0.633459i
$51$		0			0
$52$		−	5.93147e8i		−	0.216343i
$53$			2.89531e8i			0.0950995i	0.998869	+	0.0475497i	$0.0151413\pi$
$53$			2.89531e8i			0.0950995i	−0.998869	+	0.0475497i	$0.984859\pi$
$54$		0			0
$55$	−1.06689e9	+	4.55180e9i	−0.285841	+	1.21952i
$56$	8.02063e8			0.194614
$57$		0			0
$58$			6.48664e9i			1.29767i
$59$	−2.47487e9			−0.450678			−0.225339	−	0.974280i	$-0.572349\pi$
$59$	−2.47487e9			−0.450678			−0.225339	+	0.974280i	$0.572349\pi$
$60$		0			0
$61$	9.16284e7			0.0138904			0.00694522	−	0.999976i	$-0.497789\pi$
$61$	9.16284e7			0.0138904			0.00694522	+	0.999976i	$0.497789\pi$
$62$			3.28926e9i			0.455977i
$63$		0			0
$64$	−1.07374e9			−0.125000
$65$	−3.94079e9	−	9.23676e8i	−0.421270	−	0.0987406i
$66$		0			0
$67$			3.09287e7i			0.00279866i	0.999999	+	0.00139933i	$0.000445421\pi$
$67$			3.09287e7i			0.00279866i	−0.999999	+	0.00139933i	$0.999555\pi$
$68$		−	8.03893e9i		−	0.670500i
$69$		0			0
$70$	1.24901e9	−	5.32881e9i	0.0888233	−	0.378958i
$71$	−2.42503e10			−1.59513			−0.797565	−	0.603233i	$-0.793879\pi$
$71$	−2.42503e10			−1.59513			−0.797565	+	0.603233i	$0.793879\pi$
$72$		0			0
$73$		−	3.55008e9i		−	0.200430i	−0.994966	−	0.100215i	$-0.968047\pi$
$73$		−	3.55008e9i		−	0.200430i	0.994966	−	0.100215i	$-0.0319531\pi$
$74$	1.60829e10			0.842540
$75$		0			0
$76$	−1.85572e10			−0.839534
$77$			1.63765e10i			0.689480i
$78$		0			0
$79$	1.16350e10			0.425419			0.212709	−	0.977116i	$-0.431771\pi$
$79$	1.16350e10			0.425419			0.212709	+	0.977116i	$0.431771\pi$
$80$	−1.67208e9	+	7.13381e9i	−0.0570509	+	0.243403i
$81$		0			0
$82$		−	1.10389e10i		−	0.328812i
$83$		−	2.33729e10i		−	0.651302i	−0.945490	−	0.325651i	$-0.894417\pi$
$83$		−	2.33729e10i		−	0.651302i	0.945490	−	0.325651i	$-0.105583\pi$
$84$		0			0
$85$	−5.34096e10	−	1.25186e10i	−1.30562	−	0.306021i
$86$	−4.58307e10			−1.05055
$87$		0			0
$88$		−	2.19236e10i		−	0.442851i
$89$	−1.02379e11			−1.94342			−0.971710	−	0.236175i	$-0.924106\pi$
$89$	−1.02379e11			−1.94342			−0.971710	+	0.236175i	$0.924106\pi$
$90$		0			0
$91$	−1.41782e10			−0.238173
$92$		−	2.01936e10i		−	0.319434i
$93$		0			0
$94$	−4.42174e10			−0.621426
$95$	−2.88982e10	+	1.23292e11i	−0.383169	+	1.63476i
$96$		0			0
$97$		−	5.87705e10i		−	0.694888i	−0.937701	−	0.347444i	$-0.887050\pi$
$97$		−	5.87705e10i		−	0.694888i	0.937701	−	0.347444i	$-0.112950\pi$
$98$			4.41025e10i			0.492855i
$99$		0			0
$100$	4.47923e10	+	2.22182e10i	0.447923	+	0.222182i
$101$	−3.48576e9			−0.0330012			−0.0165006	−	0.999864i	$-0.505253\pi$
$101$	−3.48576e9			−0.0330012			−0.0165006	+	0.999864i	$0.505253\pi$
$102$		0			0
$103$			8.04437e10i			0.683734i	0.939748	+	0.341867i	$0.111059\pi$
$103$			8.04437e10i			0.683734i	−0.939748	+	0.341867i	$0.888941\pi$
$104$	1.89807e10			0.152978
$105$		0			0
$106$	−9.26500e9			−0.0672455
$107$		−	1.62166e11i		−	1.11776i	−0.829249	−	0.558880i	$-0.811231\pi$
$107$		−	1.62166e11i		−	1.11776i	0.829249	−	0.558880i	$-0.188769\pi$
$108$		0			0
$109$	−1.55539e11			−0.968266			−0.484133	−	0.874994i	$-0.660865\pi$
$109$	−1.55539e11			−0.968266			−0.484133	+	0.874994i	$0.660865\pi$
$110$	−1.45658e11	−	3.41405e10i	−0.862330	−	0.202120i
$111$		0			0
$112$			2.56660e10i			0.137613i
$113$			1.26270e11i			0.644717i	0.946618	+	0.322359i	$0.104476\pi$
$113$			1.26270e11i			0.644717i	−0.946618	+	0.322359i	$0.895524\pi$
$114$		0			0
$115$	−1.34164e11	−	3.14464e10i	−0.622010	−	0.145792i
$116$	−2.07572e11			−0.917594
$117$		0			0
$118$		−	7.91958e10i		−	0.318677i
$119$	−1.92157e11			−0.738157
$120$		0			0
$121$	1.62323e11			0.568933
$122$			2.93211e9i			0.00982202i
$123$		0			0
$124$	−1.05256e11			−0.322425
$125$	2.17368e11	−	2.62995e11i	0.637074	−	0.770803i
$126$		0			0
$127$			4.06263e11i			1.09116i	0.838060	+	0.545578i	$0.183690\pi$
$127$			4.06263e11i			1.09116i	−0.838060	+	0.545578i	$0.816310\pi$
$128$		−	3.43597e10i		−	0.0883883i
$129$		0			0
$130$	2.95576e10	−	1.26105e11i	0.0698202	−	0.297883i
$131$	−4.67394e11			−1.05850			−0.529251	−	0.848466i	$-0.677527\pi$
$131$	−4.67394e11			−1.05850			−0.529251	+	0.848466i	$0.677527\pi$
$132$		0			0
$133$			4.43580e11i			0.924247i
$134$	−9.89718e8			−0.00197895
$135$		0			0
$136$	2.57246e11			0.474115
$137$			5.88796e11i			1.04232i	0.853459	+	0.521161i	$0.174501\pi$
$137$			5.88796e11i			1.04232i	−0.853459	+	0.521161i	$0.825499\pi$
$138$		0			0
$139$	2.38206e11			0.389378			0.194689	−	0.980865i	$-0.437630\pi$
$139$	2.38206e11			0.389378			0.194689	+	0.980865i	$0.437630\pi$
$140$	1.70522e11	+	3.99683e10i	0.267964	+	0.0628076i
$141$		0			0
$142$		−	7.76010e11i		−	1.12793i
$143$			3.87547e11i			0.541971i
$144$		0			0
$145$	−3.23242e11	+	1.37909e12i	−0.418797	+	1.78676i
$146$	1.13603e11			0.141725
$147$		0			0
$148$			5.14653e11i			0.595766i
$149$	1.19618e12			1.33436			0.667179	−	0.744897i	$-0.267501\pi$
$149$	1.19618e12			1.33436			0.667179	+	0.744897i	$0.267501\pi$
$150$		0			0
$151$	−4.69044e10			−0.0486229			−0.0243114	−	0.999704i	$-0.507739\pi$
$151$	−4.69044e10			−0.0486229			−0.0243114	+	0.999704i	$0.507739\pi$
$152$		−	5.93831e11i		−	0.593640i
$153$		0			0
$154$	−5.24047e11			−0.487536
$155$	−1.63910e11	+	6.99309e11i	−0.147157	+	0.627834i
$156$		0			0
$157$		−	1.12550e12i		−	0.941665i	−0.882223	−	0.470833i	$-0.843954\pi$
$157$		−	1.12550e12i		−	0.941665i	0.882223	−	0.470833i	$-0.156046\pi$
$158$			3.72319e11i			0.300816i
$159$		0			0
$160$	−2.28282e11	−	5.35066e10i	−0.172112	−	0.0403411i
$161$	−4.82695e11			−0.351666
$162$		0			0
$163$		−	1.26983e12i		−	0.864396i	−0.901779	−	0.432198i	$-0.857738\pi$
$163$		−	1.26983e12i		−	0.864396i	0.901779	−	0.432198i	$-0.142262\pi$
$164$	3.53244e11			0.232505
$165$		0			0
$166$	7.47932e11			0.460540
$167$			6.55303e11i			0.390393i	0.980764	+	0.195196i	$0.0625344\pi$
$167$			6.55303e11i			0.390393i	−0.980764	+	0.195196i	$0.937466\pi$
$168$		0			0
$169$	1.45664e12			0.812782
$170$	4.00595e11	−	1.70911e12i	0.216390	−	0.923210i
$171$		0			0
$172$		−	1.46658e12i		−	0.742848i
$173$		−	2.29440e12i		−	1.12568i	−0.826565	−	0.562842i	$-0.809708\pi$
$173$		−	2.29440e12i		−	1.12568i	0.826565	−	0.562842i	$-0.190292\pi$
$174$		0			0
$175$	5.31089e11	−	1.07069e12i	0.244601	−	0.493120i
$176$	7.01555e11			0.313143
$177$		0			0
$178$		−	3.27614e12i		−	1.37421i
$179$	2.90384e12			1.18108			0.590542	−	0.807007i	$-0.298914\pi$
$179$	2.90384e12			1.18108			0.590542	+	0.807007i	$0.298914\pi$
$180$		0			0
$181$	2.57501e12			0.985250			0.492625	−	0.870242i	$-0.336037\pi$
$181$	2.57501e12			0.985250			0.492625	+	0.870242i	$0.336037\pi$
$182$		−	4.53702e11i		−	0.168414i
$183$		0			0
$184$	6.46196e11			0.225874
$185$	3.41929e12	+	8.01442e11i	1.16009	+	0.271912i
$186$		0			0
$187$			5.25243e12i			1.67970i
$188$		−	1.41496e12i		−	0.439415i
$189$		0			0
$190$	−3.94534e12	−	9.24742e11i	−1.15595	−	0.270942i
$191$	−2.23479e11			−0.0636140			−0.0318070	−	0.999494i	$-0.510126\pi$
$191$	−2.23479e11			−0.0636140			−0.0318070	+	0.999494i	$0.510126\pi$
$192$		0			0
$193$			3.24295e12i			0.871716i	0.900015	+	0.435858i	$0.143555\pi$
$193$			3.24295e12i			0.871716i	−0.900015	+	0.435858i	$0.856445\pi$
$194$	1.88066e12			0.491360
$195$		0			0
$196$	−1.41128e12			−0.348501
$197$		−	5.15178e12i		−	1.23707i	−0.785758	−	0.618534i	$-0.787727\pi$
$197$		−	5.15178e12i		−	1.23707i	0.785758	−	0.618534i	$-0.212273\pi$
$198$		0			0
$199$	6.92866e11			0.157383			0.0786914	−	0.996899i	$-0.474926\pi$
$199$	6.92866e11			0.157383			0.0786914	+	0.996899i	$0.474926\pi$
$200$	−7.10982e11	+	1.43335e12i	−0.157106	+	0.316729i
$201$		0			0
$202$		−	1.11544e11i		−	0.0233354i
$203$			4.96168e12i			1.01018i
$204$		0			0
$205$	5.50087e11	−	2.34691e12i	0.106117	−	0.452741i
$206$	−2.57420e12			−0.483473
$207$		0			0
$208$			6.07382e11i			0.108172i
$209$	1.21248e13			2.10315
$210$		0			0
$211$	7.15534e12			1.17781			0.588907	−	0.808201i	$-0.299558\pi$
$211$	7.15534e12			1.17781			0.588907	+	0.808201i	$0.299558\pi$
$212$		−	2.96480e11i		−	0.0475497i
$213$		0			0
$214$	5.18930e12			0.790375
$215$	−9.74380e12	−	2.28383e12i	−1.44649	−	0.339041i
$216$		0			0
$217$			2.51598e12i			0.354959i
$218$		−	4.97726e12i		−	0.684667i
$219$		0			0
$220$	1.09249e12	−	4.66105e12i	0.142921	−	0.609760i
$221$	−4.54737e12			−0.580233
$222$		0			0
$223$			7.85354e12i			0.953650i	0.878998	+	0.476825i	$0.158212\pi$
$223$			7.85354e12i			0.953650i	−0.878998	+	0.476825i	$0.841788\pi$
$224$	−8.21313e11			−0.0973071
$225$		0			0
$226$	−4.04065e12			−0.455884
$227$			5.24834e12i			0.577936i	0.957339	+	0.288968i	$0.0933121\pi$
$227$			5.24834e12i			0.577936i	−0.957339	+	0.288968i	$0.906688\pi$
$228$		0			0
$229$	−2.54851e12			−0.267419			−0.133709	−	0.991021i	$-0.542689\pi$
$229$	−2.54851e12			−0.267419			−0.133709	+	0.991021i	$0.542689\pi$
$230$	1.00629e12	−	4.29325e12i	0.103090	−	0.439828i
$231$		0			0
$232$		−	6.64232e12i		−	0.648837i
$233$			1.29244e13i			1.23297i	0.787368	+	0.616483i	$0.211443\pi$
$233$			1.29244e13i			1.23297i	−0.787368	+	0.616483i	$0.788557\pi$
$234$		0			0
$235$	−9.40079e12	−	2.20344e12i	−0.855640	−	0.200552i
$236$	2.53427e12			0.225339
$237$		0			0
$238$		−	6.14903e12i		−	0.521955i
$239$	−3.04646e12			−0.252701			−0.126350	−	0.991986i	$-0.540326\pi$
$239$	−3.04646e12			−0.252701			−0.126350	+	0.991986i	$0.540326\pi$
$240$		0			0
$241$	−1.51377e13			−1.19940			−0.599701	−	0.800224i	$-0.704714\pi$
$241$	−1.51377e13			−1.19940			−0.599701	+	0.800224i	$0.704714\pi$
$242$			5.19434e12i			0.402296i
$243$		0			0
$244$	−9.38275e10			−0.00694522
$245$	−2.19771e12	+	9.37636e12i	−0.159058	+	0.678611i
$246$		0			0
$247$			1.04972e13i			0.726511i
$248$		−	3.36820e12i		−	0.227989i
$249$		0			0
$250$	8.41585e12	+	6.95577e12i	0.545040	+	0.450479i
$251$	5.88554e12			0.372890			0.186445	−	0.982465i	$-0.440303\pi$
$251$	5.88554e12			0.372890			0.186445	+	0.982465i	$0.440303\pi$
$252$		0			0
$253$			1.31940e13i			0.800227i
$254$	−1.30004e13			−0.771564
$255$		0			0
$256$	1.09951e12			0.0625000
$257$			1.26568e13i			0.704194i	0.935964	+	0.352097i	$0.114531\pi$
$257$			1.26568e13i			0.704194i	−0.935964	+	0.352097i	$0.885469\pi$
$258$		0			0
$259$	1.23019e13			0.655881
$260$	4.03537e12	+	9.45844e11i	0.210635	+	0.0493703i
$261$		0			0
$262$		−	1.49566e13i		−	0.748473i
$263$		−	1.94934e13i		−	0.955280i	−0.878556	−	0.477640i	$-0.841492\pi$
$263$		−	1.94934e13i		−	0.955280i	0.878556	−	0.477640i	$-0.158508\pi$
$264$		0			0
$265$	−1.96978e12	−	4.61693e11i	−0.0925901	−	0.0217020i
$266$	−1.41946e13			−0.653541
$267$		0			0
$268$		−	3.16710e10i		−	0.00139933i
$269$	−4.34447e12			−0.188061			−0.0940306	−	0.995569i	$-0.529975\pi$
$269$	−4.34447e12			−0.188061			−0.0940306	+	0.995569i	$0.529975\pi$
$270$		0			0
$271$	2.67882e12			0.111330			0.0556650	−	0.998449i	$-0.482272\pi$
$271$	2.67882e12			0.111330			0.0556650	+	0.998449i	$0.482272\pi$
$272$			8.23186e12i			0.335250i
$273$		0			0
$274$	−1.88415e13			−0.737032
$275$	−2.92661e13	−	1.45168e13i	−1.12211	−	0.556597i
$276$		0			0
$277$			1.30102e13i			0.479343i	0.970854	+	0.239672i	$0.0770398\pi$
$277$			1.30102e13i			0.479343i	−0.970854	+	0.239672i	$0.922960\pi$
$278$			7.62260e12i			0.275332i
$279$		0			0
$280$	−1.27899e12	+	5.45670e12i	−0.0444116	+	0.189479i
$281$	−2.90772e13			−0.990075			−0.495037	−	0.868872i	$-0.664846\pi$
$281$	−2.90772e13			−0.990075			−0.495037	+	0.868872i	$0.664846\pi$
$282$		0			0
$283$		−	8.21076e12i		−	0.268880i	−0.990922	−	0.134440i	$-0.957076\pi$
$283$		−	8.21076e12i		−	0.268880i	0.990922	−	0.134440i	$-0.0429235\pi$
$284$	2.48323e13			0.797565
$285$		0			0
$286$	−1.24015e13			−0.383231
$287$		−	8.44371e12i		−	0.255966i
$288$		0			0
$289$	−2.73587e13			−0.798283
$290$	−4.41308e13	−	1.03437e13i	−1.26343	−	0.296134i
$291$		0			0
$292$			3.63529e12i			0.100215i
$293$			8.70497e12i			0.235502i	0.993043	+	0.117751i	$0.0375685\pi$
$293$			8.70497e12i			0.235502i	−0.993043	+	0.117751i	$0.962431\pi$
$294$		0			0
$295$	3.94648e12	−	1.68374e13i	0.102846	−	0.438786i
$296$	−1.64689e13			−0.421270
$297$		0			0
$298$			3.82778e13i			0.943534i
$299$	−1.14229e13			−0.276430
$300$		0			0
$301$	−3.50562e13			−0.817805
$302$		−	1.50094e12i		−	0.0343816i
$303$		0			0
$304$	1.90026e13			0.419767
$305$	−1.46112e11	+	6.23378e11i	−0.00316985	+	0.0135239i
$306$		0			0
$307$		−	6.59577e13i		−	1.38040i	−0.723620	−	0.690199i	$-0.757523\pi$
$307$		−	6.59577e13i		−	1.38040i	0.723620	−	0.690199i	$-0.242477\pi$
$308$		−	1.67695e13i		−	0.344740i
$309$		0			0
$310$	−2.23779e13	−	5.24512e12i	−0.443946	−	0.104056i
$311$	2.13842e13			0.416783			0.208392	−	0.978045i	$-0.433177\pi$
$311$	2.13842e13			0.416783			0.208392	+	0.978045i	$0.433177\pi$
$312$		0			0
$313$		−	2.84379e13i		−	0.535062i	−0.963549	−	0.267531i	$-0.913792\pi$
$313$		−	2.84379e13i		−	0.535062i	0.963549	−	0.267531i	$-0.0862078\pi$
$314$	3.60159e13			0.665858
$315$		0			0
$316$	−1.19142e13			−0.212709
$317$		−	1.06352e14i		−	1.86603i	−0.359833	−	0.933017i	$-0.617166\pi$
$317$		−	1.06352e14i		−	1.86603i	0.359833	−	0.933017i	$-0.382834\pi$
$318$		0			0
$319$	1.35622e14			2.29870
$320$	1.71221e12	−	7.30502e12i	0.0285254	−	0.121702i
$321$		0			0
$322$		−	1.54462e13i		−	0.248666i
$323$			1.42269e14i			2.25163i
$324$		0			0
$325$	1.25681e13	−	2.53376e13i	0.192270	−	0.387621i
$326$	4.06344e13			0.611220
$327$		0			0
$328$			1.13038e13i			0.164406i
$329$	−3.38222e13			−0.483754
$330$		0			0
$331$	−1.23331e14			−1.70616			−0.853079	−	0.521781i	$-0.825268\pi$
$331$	−1.23331e14			−1.70616			−0.853079	+	0.521781i	$0.825268\pi$
$332$			2.39338e13i			0.325651i
$333$		0			0
$334$	−2.09697e13			−0.276049
$335$	−2.10418e11	−	4.93195e10i	−0.00272481	−	0.000638664i
$336$		0			0
$337$			4.55439e13i			0.570776i	0.958412	+	0.285388i	$0.0921225\pi$
$337$			4.55439e13i			0.570776i	−0.958412	+	0.285388i	$0.907877\pi$
$338$			4.66124e13i			0.574724i
$339$		0			0
$340$	5.46915e13	+	1.28190e13i	0.652808	+	0.153011i
$341$	6.87717e13			0.807719
$342$		0			0
$343$			8.21334e13i			0.934119i
$344$	4.69307e13			0.525273
$345$		0			0
$346$	7.34209e13			0.795978
$347$		−	8.36511e13i		−	0.892605i	−0.894882	−	0.446303i	$-0.852741\pi$
$347$		−	8.36511e13i		−	0.892605i	0.894882	−	0.446303i	$-0.147259\pi$
$348$		0			0
$349$	−6.38318e13			−0.659929			−0.329965	−	0.943993i	$-0.607037\pi$
$349$	−6.38318e13			−0.659929			−0.329965	+	0.943993i	$0.607037\pi$
$350$	3.42620e13	+	1.69949e13i	0.348689	+	0.172959i
$351$		0			0
$352$			2.24498e13i			0.221425i
$353$		−	3.55388e13i		−	0.345097i	−0.985001	−	0.172549i	$-0.944800\pi$
$353$		−	3.55388e13i		−	0.345097i	0.985001	−	0.172549i	$-0.0552002\pi$
$354$		0			0
$355$	3.86700e13	−	1.64983e14i	0.364014	−	1.55304i
$356$	1.04836e14			0.971710
$357$		0			0
$358$			9.29229e13i			0.835153i
$359$	1.40868e14			1.24679			0.623393	−	0.781909i	$-0.285754\pi$
$359$	1.40868e14			1.24679			0.623393	+	0.781909i	$0.285754\pi$
$360$		0			0
$361$	2.11927e14			1.81927
$362$			8.24003e13i			0.696677i
$363$		0			0
$364$	1.45185e13			0.119087
$365$	2.41524e13	+	5.66104e12i	0.195141	+	0.0457388i
$366$		0			0
$367$		−	5.21259e13i		−	0.408686i	−0.978899	−	0.204343i	$-0.934494\pi$
$367$		−	5.21259e13i		−	0.408686i	0.978899	−	0.204343i	$-0.0655058\pi$
$368$			2.06783e13i			0.159717i
$369$		0			0
$370$	−2.56462e13	+	1.09417e14i	−0.192271	+	0.820308i
$371$	−7.08687e12			−0.0523477
$372$		0			0
$373$			1.12302e14i			0.805355i	0.915342	+	0.402677i	$0.131920\pi$
$373$			1.12302e14i			0.805355i	−0.915342	+	0.402677i	$0.868080\pi$
$374$	−1.68078e14			−1.18773
$375$		0			0
$376$	4.52786e13			0.310713
$377$			1.17417e14i			0.794062i
$378$		0			0
$379$	8.23254e13			0.540777			0.270388	−	0.962751i	$-0.412848\pi$
$379$	8.23254e13			0.540777			0.270388	+	0.962751i	$0.412848\pi$
$380$	2.95917e13	−	1.26251e14i	0.191585	−	0.817382i
$381$		0			0
$382$		−	7.15132e12i		−	0.0449819i
$383$		−	1.86623e14i		−	1.15710i	−0.815645	−	0.578552i	$-0.803618\pi$
$383$		−	1.86623e14i		−	1.15710i	0.815645	−	0.578552i	$-0.196382\pi$
$384$		0			0
$385$	−1.11415e14	−	2.61143e13i	−0.671287	−	0.157342i
$386$	−1.03774e14			−0.616396
$387$		0			0
$388$			6.01810e13i			0.347444i
$389$	1.33809e14			0.761660			0.380830	−	0.924645i	$-0.375638\pi$
$389$	1.33809e14			0.761660			0.380830	+	0.924645i	$0.375638\pi$
$390$		0			0
$391$	−1.54815e14			−0.856722
$392$		−	4.51609e13i		−	0.246428i
$393$		0			0
$394$	1.64857e14			0.874739
$395$	−1.85534e13	+	7.91566e13i	−0.0970820	+	0.414193i
$396$		0			0
$397$		−	3.34373e14i		−	1.70170i	−0.525406	−	0.850851i	$-0.676087\pi$
$397$		−	3.34373e14i		−	1.70170i	0.525406	−	0.850851i	$-0.323913\pi$
$398$			2.21717e13i			0.111286i
$399$		0			0
$400$	−4.58673e13	−	2.27514e13i	−0.223962	−	0.111091i
$401$	1.88539e14			0.908043			0.454021	−	0.890991i	$-0.349989\pi$
$401$	1.88539e14			0.908043			0.454021	+	0.890991i	$0.349989\pi$
$402$		0			0
$403$			5.95401e13i			0.279018i
$404$	3.56942e12			0.0165006
$405$		0			0
$406$	−1.58774e14			−0.714308
$407$		−	3.36261e14i		−	1.49248i
$408$		0			0
$409$	−3.34993e14			−1.44730			−0.723649	−	0.690168i	$-0.757537\pi$
$409$	−3.34993e14			−1.44730			−0.723649	+	0.690168i	$0.757537\pi$
$410$	7.51010e13	+	1.76028e13i	0.320136	+	0.0750361i
$411$		0			0
$412$		−	8.23744e13i		−	0.341867i
$413$		−	6.05774e13i		−	0.248077i
$414$		0			0
$415$	1.59013e14	+	3.72709e13i	0.634117	+	0.148629i
$416$	−1.94362e13			−0.0764889
$417$		0			0
$418$			3.87994e14i			1.48715i
$419$	−1.56423e14			−0.591729			−0.295864	−	0.955230i	$-0.595608\pi$
$419$	−1.56423e14			−0.591729			−0.295864	+	0.955230i	$0.595608\pi$
$420$		0			0
$421$	5.29550e14			1.95144			0.975721	−	0.219015i	$-0.0702845\pi$
$421$	5.29550e14			1.95144			0.975721	+	0.219015i	$0.0702845\pi$
$422$			2.28971e14i			0.832840i
$423$		0			0
$424$	9.48736e12			0.0336227
$425$	1.70336e14	−	3.43401e14i	0.595892	−	1.20133i
$426$		0			0
$427$			2.24279e12i			0.00764602i
$428$			1.66058e14i			0.558880i
$429$		0			0
$430$	7.30826e13	−	3.11802e14i	0.239738	−	1.02283i
$431$	−8.37388e13			−0.271208			−0.135604	−	0.990763i	$-0.543297\pi$
$431$	−8.37388e13			−0.271208			−0.135604	+	0.990763i	$0.543297\pi$
$432$		0			0
$433$			9.93342e13i			0.313628i	0.987628	+	0.156814i	$0.0501224\pi$
$433$			9.93342e13i			0.313628i	−0.987628	+	0.156814i	$0.949878\pi$
$434$	−8.05112e13			−0.250994
$435$		0			0
$436$	1.59272e14			0.484133
$437$			3.57378e14i			1.07270i
$438$		0			0
$439$	−5.35579e14			−1.56772			−0.783860	−	0.620938i	$-0.786752\pi$
$439$	−5.35579e14			−1.56772			−0.783860	+	0.620938i	$0.786752\pi$
$440$	1.49154e14	+	3.49598e13i	0.431165	+	0.101060i
$441$		0			0
$442$		−	1.45516e14i		−	0.410287i
$443$			4.64925e14i			1.29468i	0.762201	+	0.647341i	$0.224119\pi$
$443$			4.64925e14i			1.29468i	−0.762201	+	0.647341i	$0.775881\pi$
$444$		0			0
$445$	1.63256e14	−	6.96520e14i	0.443496	−	1.89214i
$446$	−2.51313e14			−0.674332
$447$		0			0
$448$		−	2.62820e13i		−	0.0688065i
$449$	−5.07045e14			−1.31127			−0.655634	−	0.755079i	$-0.727599\pi$
$449$	−5.07045e14			−1.31127			−0.655634	+	0.755079i	$0.727599\pi$
$450$		0			0
$451$	−2.30800e14			−0.582459
$452$		−	1.29301e14i		−	0.322359i
$453$		0			0
$454$	−1.67947e14			−0.408662
$455$	2.26088e13	−	9.64589e13i	0.0543520	−	0.231889i
$456$		0			0
$457$			5.05346e14i			1.18591i	0.805237	+	0.592953i	$0.202038\pi$
$457$			5.05346e14i			1.18591i	−0.805237	+	0.592953i	$0.797962\pi$
$458$		−	8.15524e13i		−	0.189094i
$459$		0			0
$460$	1.37384e14	+	3.22012e13i	0.311005	+	0.0728960i
$461$	−7.16573e14			−1.60290			−0.801448	−	0.598064i	$-0.795937\pi$
$461$	−7.16573e14			−1.60290			−0.801448	+	0.598064i	$0.795937\pi$
$462$		0			0
$463$			1.12357e14i			0.245418i	0.992443	+	0.122709i	$0.0391581\pi$
$463$			1.12357e14i			0.245418i	−0.992443	+	0.122709i	$0.960842\pi$
$464$	2.12554e14			0.458797
$465$		0			0
$466$	−4.13579e14			−0.871839
$467$		−	2.21056e14i		−	0.460532i	−0.973128	−	0.230266i	$-0.926040\pi$
$467$		−	2.21056e14i		−	0.460532i	0.973128	−	0.230266i	$-0.0739597\pi$
$468$		0			0
$469$	−7.57042e11			−0.00154053
$470$	7.05099e13	−	3.00825e14i	0.141812	−	0.605029i
$471$		0			0
$472$			8.10965e13i			0.159339i
$473$			9.58227e14i			1.86094i
$474$		0			0
$475$	−7.92714e14	−	3.93208e14i	−1.50419	−	0.746118i
$476$	1.96769e14			0.369078
$477$		0			0
$478$		−	9.74866e13i		−	0.178686i
$479$	−9.23603e14			−1.67356			−0.836778	−	0.547543i	$-0.815563\pi$
$479$	−9.23603e14			−1.67356			−0.836778	+	0.547543i	$0.815563\pi$
$480$		0			0
$481$	2.91123e14			0.515560
$482$		−	4.84405e14i		−	0.848106i
$483$		0			0
$484$	−1.66219e14			−0.284466
$485$	3.99835e14	+	9.37167e13i	0.676552	+	0.158576i
$486$		0			0
$487$		−	4.58584e14i		−	0.758594i	−0.925275	−	0.379297i	$-0.876166\pi$
$487$		−	4.58584e14i		−	0.758594i	0.925275	−	0.379297i	$-0.123834\pi$
$488$		−	3.00248e12i		−	0.00491101i
$489$		0			0
$490$	−3.00044e14	−	7.03267e13i	−0.479850	−	0.112471i
$491$	2.27335e14			0.359516			0.179758	−	0.983711i	$-0.442469\pi$
$491$	2.27335e14			0.359516			0.179758	+	0.983711i	$0.442469\pi$
$492$		0			0
$493$			1.59136e15i			2.46099i
$494$	−3.35912e14			−0.513721
$495$		0			0
$496$	1.07782e14			0.161212
$497$		−	5.93575e14i		−	0.878043i
$498$		0			0
$499$	6.20100e14			0.897240			0.448620	−	0.893723i	$-0.351916\pi$
$499$	6.20100e14			0.897240			0.448620	+	0.893723i	$0.351916\pi$
$500$	−2.22585e14	+	2.69307e14i	−0.318537	+	0.385401i
$501$		0			0
$502$			1.88337e14i			0.263673i
$503$			3.45337e14i			0.478211i	0.970994	+	0.239105i	$0.0768541\pi$
$503$			3.45337e14i			0.478211i	−0.970994	+	0.239105i	$0.923146\pi$
$504$		0			0
$505$	5.55847e12	−	2.37148e13i	0.00753100	−	0.0321304i
$506$	−4.22208e14			−0.565846
$507$		0			0
$508$		−	4.16013e14i		−	0.545578i
$509$	1.29592e14			0.168125			0.0840624	−	0.996460i	$-0.473210\pi$
$509$	1.29592e14			0.168125			0.0840624	+	0.996460i	$0.473210\pi$
$510$		0			0
$511$	8.68955e13			0.110327
$512$			3.51844e13i			0.0441942i
$513$		0			0
$514$	−4.05018e14			−0.497940
$515$	−5.47285e14	−	1.28277e14i	−0.665693	−	0.156031i
$516$		0			0
$517$			9.24496e14i			1.10080i
$518$			3.93662e14i			0.463778i
$519$		0			0
$520$	−3.02670e13	+	1.29132e14i	−0.0349101	+	0.148941i
$521$	−8.63535e14			−0.985536			−0.492768	−	0.870161i	$-0.664015\pi$
$521$	−8.63535e14			−0.985536			−0.492768	+	0.870161i	$0.664015\pi$
$522$		0			0
$523$			1.76403e15i			1.97128i	0.168870	+	0.985638i	$0.445988\pi$
$523$			1.76403e15i			1.97128i	−0.168870	+	0.985638i	$0.554012\pi$
$524$	4.78612e14			0.529251
$525$		0			0
$526$	6.23789e14			0.675485
$527$			8.06948e14i			0.864744i
$528$		0			0
$529$	5.63918e14			0.591848
$530$	1.47742e13	−	6.30329e13i	0.0153457	−	0.0654711i
$531$		0			0
$532$		−	4.54226e14i		−	0.462123i
$533$		−	1.99819e14i		−	0.201204i
$534$		0			0
$535$	1.10327e15	+	2.58593e14i	1.08827	+	0.255077i
$536$	1.01347e12			0.000989475
$537$		0			0
$538$		−	1.39023e14i		−	0.132979i
$539$	9.22093e14			0.873045
$540$		0			0
$541$	−5.96542e14			−0.553421			−0.276711	−	0.960953i	$-0.589244\pi$
$541$	−5.96542e14			−0.553421			−0.276711	+	0.960953i	$0.589244\pi$
$542$			8.57223e13i			0.0787223i
$543$		0			0
$544$	−2.63419e14			−0.237058
$545$	2.48026e14	−	1.05819e15i	0.220962	−	0.942717i
$546$		0			0
$547$		−	1.72805e15i		−	1.50878i	−0.656426	−	0.754390i	$-0.727933\pi$
$547$		−	1.72805e15i		−	1.50878i	0.656426	−	0.754390i	$-0.272067\pi$
$548$		−	6.02927e14i		−	0.521161i
$549$		0			0
$550$	4.64538e14	−	9.36517e14i	0.393574	−	0.793452i
$551$	3.67352e15			3.08141
$552$		0			0
$553$			2.84790e14i			0.234173i
$554$	−4.16328e14			−0.338947
$555$		0			0
$556$	−2.43923e14			−0.194689
$557$			1.11647e15i			0.882353i	0.897420	+	0.441177i	$0.145439\pi$
$557$			1.11647e15i			0.882353i	−0.897420	+	0.441177i	$0.854561\pi$
$558$		0			0
$559$	−8.29600e14			−0.642841
$560$	−1.74614e14	−	4.09276e13i	−0.133982	−	0.0314038i
$561$		0			0
$562$		−	9.30471e14i		−	0.700089i
$563$		−	3.81802e13i		−	0.0284474i	−0.999899	−	0.0142237i	$-0.995472\pi$
$563$		−	3.81802e13i		−	0.0284474i	0.999899	−	0.0142237i	$-0.00452769\pi$
$564$		0			0
$565$	−8.59058e14	−	2.01353e14i	−0.627705	−	0.147127i
$566$	2.62744e14			0.190127
$567$		0			0
$568$			7.94634e14i			0.563964i
$569$	−8.00530e14			−0.562678			−0.281339	−	0.959608i	$-0.590779\pi$
$569$	−8.00530e14			−0.562678			−0.281339	+	0.959608i	$0.590779\pi$
$570$		0			0
$571$	−1.20542e12			−0.000831073			−0.000415536	−	1.00000i	$-0.500132\pi$
$571$	−1.20542e12			−0.000831073			−0.000415536		1.00000i	$0.500132\pi$
$572$		−	3.96848e14i		−	0.270985i
$573$		0			0
$574$	2.70199e14			0.180995
$575$	4.27881e14	−	8.62616e14i	0.283890	−	0.572327i
$576$		0			0
$577$		−	1.11237e15i		−	0.724075i	−0.932163	−	0.362038i	$-0.882081\pi$
$577$		−	1.11237e15i		−	0.724075i	0.932163	−	0.362038i	$-0.117919\pi$
$578$		−	8.75477e14i		−	0.564471i
$579$		0			0
$580$	3.30999e14	−	1.41218e15i	0.209398	−	0.893382i
$581$	5.72099e14			0.358511
$582$		0			0
$583$			1.93712e14i			0.119119i
$584$	−1.16329e14			−0.0708627
$585$		0			0
$586$	−2.78559e14			−0.166525
$587$		−	1.41072e15i		−	0.835474i	−0.908568	−	0.417737i	$-0.862823\pi$
$587$		−	1.41072e15i		−	0.835474i	0.908568	−	0.417737i	$-0.137177\pi$
$588$		0			0
$589$	1.86278e15			1.08275
$590$	5.38795e14	+	1.26287e14i	0.310268	+	0.0727233i
$591$		0			0
$592$		−	5.27005e14i		−	0.297883i
$593$			2.95927e15i			1.65723i	0.559816	+	0.828617i	$0.310872\pi$
$593$			2.95927e15i			1.65723i	−0.559816	+	0.828617i	$0.689128\pi$
$594$		0			0
$595$	3.06418e14	−	1.30731e15i	0.168450	−	0.718679i
$596$	−1.22489e15			−0.667179
$597$		0			0
$598$		−	3.65533e14i		−	0.195465i
$599$	7.61671e14			0.403571			0.201785	−	0.979430i	$-0.435326\pi$
$599$	7.61671e14			0.403571			0.201785	+	0.979430i	$0.435326\pi$
$600$		0			0
$601$	−5.33224e14			−0.277396			−0.138698	−	0.990335i	$-0.544292\pi$
$601$	−5.33224e14			−0.277396			−0.138698	+	0.990335i	$0.544292\pi$
$602$		−	1.12180e15i		−	0.578275i
$603$		0			0
$604$	4.80301e13			0.0243114
$605$	−2.58844e14	+	1.10434e15i	−0.129832	+	0.553921i
$606$		0			0
$607$		−	2.82058e15i		−	1.38931i	−0.719341	−	0.694657i	$-0.755556\pi$
$607$		−	2.82058e15i		−	1.38931i	0.719341	−	0.694657i	$-0.244444\pi$
$608$			6.08083e14i			0.296820i
$609$		0			0
$610$	−1.99481e13	−	4.67560e12i	−0.00956285	−	0.00224142i
$611$	−8.00396e14			−0.380258
$612$		0			0
$613$			3.94879e15i			1.84260i	0.388850	+	0.921301i	$0.372873\pi$
$613$			3.94879e15i			1.84260i	−0.388850	+	0.921301i	$0.627127\pi$
$614$	2.11065e15			0.976089
$615$		0			0
$616$	5.36625e14			0.243768
$617$		−	4.71962e14i		−	0.212490i	−0.994340	−	0.106245i	$-0.966117\pi$
$617$		−	4.71962e14i		−	0.212490i	0.994340	−	0.106245i	$-0.0338828\pi$
$618$		0			0
$619$	−6.15999e14			−0.272447			−0.136223	−	0.990678i	$-0.543496\pi$
$619$	−6.15999e14			−0.272447			−0.136223	+	0.990678i	$0.543496\pi$
$620$	1.67844e14	−	7.16093e14i	0.0735785	−	0.313917i
$621$		0			0
$622$			6.84293e14i			0.294710i
$623$		−	2.50594e15i		−	1.06976i
$624$		0			0
$625$	1.44263e15	+	1.89820e15i	0.605081	+	0.796164i
$626$	9.10014e14			0.378346
$627$		0			0
$628$			1.15251e15i			0.470833i
$629$	3.94560e15			1.59784
$630$		0			0
$631$	7.19339e14			0.286267			0.143134	−	0.989703i	$-0.454282\pi$
$631$	7.19339e14			0.286267			0.143134	+	0.989703i	$0.454282\pi$
$632$		−	3.81255e14i		−	0.150408i
$633$		0			0
$634$	3.40326e15			1.31949
$635$	−2.76394e15	−	6.47836e14i	−1.06236	−	0.249006i
$636$		0			0
$637$			7.98316e14i			0.301584i
$638$			4.33992e15i			1.62543i
$639$		0			0
$640$	2.33761e14	+	5.47907e13i	0.0860561	+	0.0201705i
$641$	2.58937e15			0.945094			0.472547	−	0.881306i	$-0.343335\pi$
$641$	2.58937e15			0.945094			0.472547	+	0.881306i	$0.343335\pi$
$642$		0			0
$643$			9.64667e14i			0.346112i	0.984912	+	0.173056i	$0.0553642\pi$
$643$			9.64667e14i			0.346112i	−0.984912	+	0.173056i	$0.944636\pi$
$644$	4.94280e14			0.175833
$645$		0			0
$646$	−4.55262e15			−1.59214
$647$		−	1.46486e15i		−	0.507951i	−0.967211	−	0.253976i	$-0.918262\pi$
$647$		−	1.46486e15i		−	0.507951i	0.967211	−	0.253976i	$-0.0817383\pi$
$648$		0			0
$649$	−1.65582e15			−0.564506
$650$	8.10803e14	+	4.02180e14i	0.274089	+	0.135956i
$651$		0			0
$652$			1.30030e15i			0.432198i
$653$		−	6.05527e14i		−	0.199577i	−0.995009	−	0.0997886i	$-0.968183\pi$
$653$		−	6.05527e14i		−	0.199577i	0.995009	−	0.0997886i	$-0.0318166\pi$
$654$		0			0
$655$	7.45317e14	−	3.17984e15i	0.241554	−	1.03057i
$656$	−3.61721e14			−0.116253
$657$		0			0
$658$		−	1.08231e15i		−	0.342065i
$659$	−3.25431e15			−1.01998			−0.509988	−	0.860182i	$-0.670350\pi$
$659$	−3.25431e15			−1.01998			−0.509988	+	0.860182i	$0.670350\pi$
$660$		0			0
$661$	3.71162e15			1.14408			0.572038	−	0.820227i	$-0.306153\pi$
$661$	3.71162e15			1.14408			0.572038	+	0.820227i	$0.306153\pi$
$662$		−	3.94660e15i		−	1.20644i
$663$		0			0
$664$	−7.65882e14			−0.230270
$665$	−3.01782e15	−	7.07342e14i	−0.899859	−	0.210916i
$666$		0			0
$667$			3.99746e15i			1.17244i
$668$		−	6.71031e14i		−	0.195196i
$669$		0			0
$670$	1.57822e12	−	6.73338e12i	0.000451604	−	0.00192673i
$671$	6.13044e13			0.0173987
$672$		0			0
$673$			9.34378e14i			0.260879i	0.991456	+	0.130440i	$0.0416389\pi$
$673$			9.34378e14i			0.260879i	−0.991456	+	0.130440i	$0.958361\pi$
$674$	−1.45741e15			−0.403600
$675$		0			0
$676$	−1.49160e15			−0.406391
$677$			4.76512e15i			1.28776i	0.765125	+	0.643882i	$0.222677\pi$
$677$			4.76512e15i			1.28776i	−0.765125	+	0.643882i	$0.777323\pi$
$678$		0			0
$679$	1.43853e15			0.382503
$680$	−4.10209e14	+	1.75013e15i	−0.108195	+	0.461605i
$681$		0			0
$682$			2.20069e15i			0.571144i
$683$		−	2.09026e14i		−	0.0538130i	−0.999638	−	0.0269065i	$-0.991434\pi$
$683$		−	2.09026e14i		−	0.0538130i	0.999638	−	0.0269065i	$-0.00856564\pi$
$684$		0			0
$685$	−4.00577e15	−	9.38906e14i	−1.01482	−	0.237861i
$686$	−2.62827e15			−0.660522
$687$		0			0
$688$			1.50178e15i			0.371424i
$689$	−1.67709e14			−0.0411483
$690$		0			0
$691$	−3.22483e15			−0.778712			−0.389356	−	0.921087i	$-0.627302\pi$
$691$	−3.22483e15			−0.778712			−0.389356	+	0.921087i	$0.627302\pi$
$692$			2.34947e15i			0.562842i
$693$		0			0
$694$	2.67683e15			0.631167
$695$	−3.79849e14	+	1.62060e15i	−0.0888575	+	0.379104i
$696$		0			0
$697$		−	2.70815e15i		−	0.623580i
$698$		−	2.04262e15i		−	0.466641i
$699$		0			0
$700$	−5.43836e14	+	1.09638e15i	−0.122301	+	0.246560i
$701$	1.50206e13			0.00335149			0.00167575	−	0.999999i	$-0.499467\pi$
$701$	1.50206e13			0.00335149			0.00167575	+	0.999999i	$0.499467\pi$
$702$		0			0
$703$		−	9.10811e15i		−	2.00066i
$704$	−7.18393e14			−0.156571
$705$		0			0
$706$	1.13724e15			0.244021
$707$		−	8.53211e13i		−	0.0181656i
$708$		0			0
$709$	−2.05916e14			−0.0431654			−0.0215827	−	0.999767i	$-0.506871\pi$
$709$	−2.05916e14			−0.0431654			−0.0215827	+	0.999767i	$0.506871\pi$
$710$	5.27945e15	+	1.23744e15i	1.09817	+	0.257397i
$711$		0			0
$712$			3.35476e15i			0.687103i
$713$			2.02704e15i			0.411974i
$714$		0			0
$715$	−2.63661e15	−	6.17990e14i	−0.527670	−	0.123680i
$716$	−2.97353e15			−0.590542
$717$		0			0
$718$			4.50776e15i			0.881611i
$719$	1.06708e15			0.207104			0.103552	−	0.994624i	$-0.466979\pi$
$719$	1.06708e15			0.207104			0.103552	+	0.994624i	$0.466979\pi$
$720$		0			0
$721$	−1.96902e15			−0.376363
$722$			6.78168e15i			1.28642i
$723$		0			0
$724$	−2.63681e15			−0.492625
$725$	−8.86693e15	−	4.39824e15i	−1.64405	−	0.815492i
$726$		0			0
$727$		−	3.85905e15i		−	0.704759i	−0.935857	−	0.352380i	$-0.885373\pi$
$727$		−	3.85905e15i		−	0.704759i	0.935857	−	0.352380i	$-0.114627\pi$
$728$			4.64591e14i			0.0842070i
$729$		0			0
$730$	−1.81153e14	+	7.72876e14i	−0.0323422	+	0.137986i
$731$	−1.12436e16			−1.99232
$732$		0			0
$733$		−	1.09224e15i		−	0.190653i	−0.995446	−	0.0953267i	$-0.969610\pi$
$733$		−	1.09224e15i		−	0.190653i	0.995446	−	0.0953267i	$-0.0303896\pi$
$734$	1.66803e15			0.288985
$735$		0			0
$736$	−6.61704e14			−0.112937
$737$			2.06930e13i			0.00350552i
$738$		0			0
$739$	−4.82140e15			−0.804691			−0.402345	−	0.915488i	$-0.631805\pi$
$739$	−4.82140e15			−0.804691			−0.402345	+	0.915488i	$0.631805\pi$
$740$	−3.50136e15	−	8.20677e14i	−0.580045	−	0.135956i
$741$		0			0
$742$		−	2.26780e14i		−	0.0370154i
$743$			2.51982e15i			0.408255i	0.978944	+	0.204128i	$0.0654357\pi$
$743$			2.51982e15i			0.408255i	−0.978944	+	0.204128i	$0.934564\pi$
$744$		0			0
$745$	−1.90746e15	+	8.13802e15i	−0.304505	+	1.29915i
$746$	−3.59365e15			−0.569472
$747$		0			0
$748$		−	5.37848e15i		−	0.839849i
$749$	3.96934e15			0.615273
$750$		0			0
$751$	7.47268e15			1.14145			0.570725	−	0.821142i	$-0.306662\pi$
$751$	7.47268e15			1.14145			0.570725	+	0.821142i	$0.306662\pi$
$752$			1.44891e15i			0.219707i
$753$		0			0
$754$	−3.75735e15			−0.561487
$755$	7.47948e13	−	3.19106e14i	0.0110959	−	0.0473399i
$756$		0			0
$757$			3.09514e15i			0.452535i	0.974065	+	0.226268i	$0.0726524\pi$
$757$			3.09514e15i			0.452535i	−0.974065	+	0.226268i	$0.927348\pi$
$758$			2.63441e15i			0.382387i
$759$		0			0
$760$	4.04003e15	+	9.46936e14i	0.577976	+	0.135471i
$761$	6.77183e15			0.961812			0.480906	−	0.876772i	$-0.340308\pi$
$761$	6.77183e15			0.961812			0.480906	+	0.876772i	$0.340308\pi$
$762$		0			0
$763$		−	3.80714e15i		−	0.532984i
$764$	2.28842e14			0.0318070
$765$		0			0
$766$	5.97194e15			0.818196
$767$		−	1.43355e15i		−	0.195002i
$768$		0			0
$769$	1.04403e16			1.39997			0.699984	−	0.714159i	$-0.253190\pi$
$769$	1.04403e16			1.39997			0.699984	+	0.714159i	$0.253190\pi$
$770$	8.35657e14	−	3.56527e15i	0.111257	−	0.474672i
$771$		0			0
$772$		−	3.32078e15i		−	0.435858i
$773$		−	1.34162e16i		−	1.74841i	−0.485558	−	0.874204i	$-0.661384\pi$
$773$		−	1.34162e16i		−	1.74841i	0.485558	−	0.874204i	$-0.338616\pi$
$774$		0			0
$775$	−4.49626e15	−	2.23027e15i	−0.577686	−	0.286548i
$776$	−1.92579e15			−0.245680
$777$		0			0
$778$			4.28187e15i			0.538575i
$779$	−6.25155e15			−0.780785
$780$		0			0
$781$	−1.62248e16			−1.99801
$782$		−	4.95407e15i		−	0.605794i
$783$		0			0
$784$	1.44515e15			0.174251
$785$	7.65713e15	+	1.79474e15i	0.916818	+	0.214891i
$786$		0			0
$787$		−	1.58544e16i		−	1.87193i	−0.352097	−	0.935964i	$-0.614531\pi$
$787$		−	1.58544e16i		−	1.87193i	0.352097	−	0.935964i	$-0.385469\pi$
$788$			5.27543e15i			0.618534i
$789$		0			0
$790$	−2.53301e15	−	5.93708e14i	−0.292879	−	0.0686473i
$791$	−3.09072e15			−0.354886
$792$		0			0
$793$			5.30752e13i			0.00601021i
$794$	1.06999e16			1.20329
$795$		0			0
$796$	−7.09495e14			−0.0786914
$797$		−	2.54021e14i		−	0.0279800i	−0.999902	−	0.0139900i	$-0.995547\pi$
$797$		−	2.54021e14i		−	0.0279800i	0.999902	−	0.0139900i	$-0.00445331\pi$
$798$		0			0
$799$	−1.08478e16			−1.17851
$800$	7.28046e14	−	1.46775e15i	0.0785532	−	0.158365i
$801$		0			0
$802$			6.03324e15i			0.642083i
$803$		−	2.37520e15i		−	0.251053i
$804$		0			0
$805$	7.69716e14	−	3.28393e15i	0.0802515	−	0.342387i
$806$	−1.90528e15			−0.197295
$807$		0			0
$808$			1.14221e14i			0.0116677i
$809$	−1.13120e16			−1.14768			−0.573842	−	0.818966i	$-0.694548\pi$
$809$	−1.13120e16			−1.14768			−0.573842	+	0.818966i	$0.694548\pi$
$810$		0			0
$811$	1.05859e16			1.05953			0.529767	−	0.848143i	$-0.322279\pi$
$811$	1.05859e16			1.05953			0.529767	+	0.848143i	$0.322279\pi$
$812$		−	5.08076e15i		−	0.505092i
$813$		0			0
$814$	1.07604e16			1.05534
$815$	8.63905e15	+	2.02489e15i	0.841587	+	0.197258i
$816$		0			0
$817$			2.59549e16i			2.49459i
$818$		−	1.07198e16i		−	1.02339i
$819$		0			0
$820$	−5.63290e14	+	2.40323e15i	−0.0530586	+	0.226370i
$821$	2.04679e16			1.91508			0.957539	−	0.288303i	$-0.0930911\pi$
$821$	2.04679e16			1.91508			0.957539	+	0.288303i	$0.0930911\pi$
$822$		0			0
$823$		−	1.10300e16i		−	1.01830i	−0.860677	−	0.509151i	$-0.829959\pi$
$823$		−	1.10300e16i		−	1.01830i	0.860677	−	0.509151i	$-0.170041\pi$
$824$	2.63598e15			0.241737
$825$		0			0
$826$	1.93848e15			0.175417
$827$		−	8.21173e15i		−	0.738167i	−0.929396	−	0.369083i	$-0.879672\pi$
$827$		−	8.21173e15i		−	0.738167i	0.929396	−	0.369083i	$-0.120328\pi$
$828$		0			0
$829$	−3.82596e15			−0.339383			−0.169691	−	0.985497i	$-0.554277\pi$
$829$	−3.82596e15			−0.339383			−0.169691	+	0.985497i	$0.554277\pi$
$830$	−1.19267e15	+	5.08843e15i	−0.105097	+	0.448388i
$831$		0			0
$832$		−	6.21959e14i		−	0.0540858i
$833$			1.08196e16i			0.934681i
$834$		0			0
$835$	−4.45825e15	−	1.04496e15i	−0.380092	−	0.0890890i
$836$	−1.24158e16			−1.05158
$837$		0			0
$838$		−	5.00553e15i		−	0.418415i
$839$	−2.86284e15			−0.237742			−0.118871	−	0.992910i	$-0.537928\pi$
$839$	−2.86284e15			−0.237742			−0.118871	+	0.992910i	$0.537928\pi$
$840$		0			0
$841$	2.88898e16			2.36792
$842$			1.69456e16i			1.37988i
$843$		0			0
$844$	−7.32707e15			−0.588907
$845$	−2.32278e15	+	9.90998e15i	−0.185480	+	0.791336i
$846$		0			0
$847$			3.97319e15i			0.313170i
$848$			3.03596e14i			0.0237749i
$849$		0			0
$850$	1.09888e16	+	5.45076e15i	0.849469	+	0.421360i
$851$	9.91126e15			0.761231
$852$		0			0
$853$		−	8.25498e15i		−	0.625888i	−0.949772	−	0.312944i	$-0.898685\pi$
$853$		−	8.25498e15i		−	0.625888i	0.949772	−	0.312944i	$-0.101315\pi$
$854$	−7.17693e13			−0.00540655
$855$		0			0
$856$	−5.31385e15			−0.395188
$857$			7.60811e15i			0.562189i	0.959680	+	0.281094i	$0.0906974\pi$
$857$			7.60811e15i			0.562189i	−0.959680	+	0.281094i	$0.909303\pi$
$858$		0			0
$859$	4.89672e15			0.357226			0.178613	−	0.983919i	$-0.442839\pi$
$859$	4.89672e15			0.357226			0.178613	+	0.983919i	$0.442839\pi$
$860$	9.97765e15	+	2.33864e15i	0.723247	+	0.169521i
$861$		0			0
$862$		−	2.67964e15i		−	0.191773i
$863$		−	2.33733e16i		−	1.66212i	−0.556186	−	0.831058i	$-0.687736\pi$
$863$		−	2.33733e16i		−	1.66212i	0.556186	−	0.831058i	$-0.312264\pi$
$864$		0			0
$865$	1.56096e16	+	3.65870e15i	1.09598	+	0.256885i
$866$	−3.17869e15			−0.221769
$867$		0			0
$868$		−	2.57636e15i		−	0.177479i
$869$	7.78444e15			0.532867
$870$		0			0
$871$	−1.79153e13			−0.00121094
$872$			5.09671e15i			0.342334i
$873$		0			0
$874$	−1.14361e16			−0.758516
$875$	6.43735e15	+	5.32052e15i	0.424290	+	0.350679i
$876$		0			0
$877$			2.29255e16i			1.49218i	0.665846	+	0.746089i	$0.268071\pi$
$877$			2.29255e16i			1.49218i	−0.665846	+	0.746089i	$0.731929\pi$
$878$		−	1.71385e16i		−	1.10855i
$879$		0			0
$880$	−1.11871e15	+	4.77291e15i	−0.0714603	+	0.304880i
$881$	4.14708e15			0.263254			0.131627	−	0.991299i	$-0.457980\pi$
$881$	4.14708e15			0.263254			0.131627	+	0.991299i	$0.457980\pi$
$882$		0			0
$883$		−	1.24171e15i		−	0.0778461i	−0.999242	−	0.0389231i	$-0.987607\pi$
$883$		−	1.24171e15i		−	0.0778461i	0.999242	−	0.0389231i	$-0.0123927\pi$
$884$	4.65650e15			0.290117
$885$		0			0
$886$	−1.48776e16			−0.915478
$887$		−	7.53940e15i		−	0.461060i	−0.973065	−	0.230530i	$-0.925954\pi$
$887$		−	7.53940e15i		−	0.461060i	0.973065	−	0.230530i	$-0.0740459\pi$
$888$		0			0
$889$	−9.94412e15			−0.600629
$890$	2.22886e16	+	5.22419e15i	1.33795	+	0.313599i
$891$		0			0
$892$		−	8.04203e15i		−	0.476825i
$893$			2.50413e16i			1.47562i
$894$		0			0
$895$	−4.63052e15	+	1.97558e16i	−0.269528	+	1.14992i
$896$	8.41024e14			0.0486535
$897$		0			0
$898$		−	1.62254e16i		−	0.927207i
$899$	2.08362e16			1.18342
$900$		0			0
$901$	−2.27297e15			−0.127528
$902$		−	7.38561e15i		−	0.411861i
$903$		0			0
$904$	4.13762e15			0.227942
$905$	−4.10616e15	+	1.75186e16i	−0.224838	+	0.959253i
$906$		0			0
$907$		−	1.84213e16i		−	0.996505i	−0.867032	−	0.498253i	$-0.833975\pi$
$907$		−	1.84213e16i		−	0.996505i	0.867032	−	0.498253i	$-0.166025\pi$
$908$		−	5.37430e15i		−	0.288968i
$909$		0			0
$910$	3.08669e15	+	7.23483e14i	0.163970	+	0.0384327i
$911$	1.91486e16			1.01108			0.505539	−	0.862804i	$-0.331294\pi$
$911$	1.91486e16			1.01108			0.505539	+	0.862804i	$0.331294\pi$
$912$		0			0
$913$		−	1.56377e16i		−	0.815802i
$914$	−1.61711e16			−0.838562
$915$		0			0
$916$	2.60968e15			0.133709
$917$		−	1.14404e16i		−	0.582654i
$918$		0			0
$919$	2.24328e16			1.12888			0.564440	−	0.825474i	$-0.309092\pi$
$919$	2.24328e16			1.12888			0.564440	+	0.825474i	$0.309092\pi$
$920$	−1.03044e15	+	4.39628e15i	−0.0515452	+	0.219914i
$921$		0			0
$922$		−	2.29303e16i		−	1.13342i
$923$		−	1.40469e16i		−	0.690192i
$924$		0			0
$925$	−1.09050e16	+	2.19846e16i	−0.529474	+	1.06743i
$926$	−3.59543e15			−0.173536
$927$		0			0
$928$			6.80173e15i			0.324419i
$929$	−3.69311e16			−1.75108			−0.875540	−	0.483145i	$-0.839494\pi$
$929$	−3.69311e16			−1.75108			−0.875540	+	0.483145i	$0.839494\pi$
$930$		0			0
$931$	2.49762e16			1.17031
$932$		−	1.32345e16i		−	0.616483i
$933$		0			0
$934$	7.07380e15			0.325646
$935$	−3.57340e16	−	8.37563e15i	−1.63538	−	0.383313i
$936$		0			0
$937$		−	2.97721e15i		−	0.134661i	−0.997731	−	0.0673306i	$-0.978552\pi$
$937$		−	2.97721e15i		−	0.134661i	0.997731	−	0.0673306i	$-0.0214482\pi$
$938$		−	2.42254e13i		−	0.00108932i
$939$		0			0
$940$	9.62641e15	+	2.25632e15i	0.427820	+	0.100276i
$941$	1.24483e16			0.550004			0.275002	−	0.961444i	$-0.411321\pi$
$941$	1.24483e16			0.550004			0.275002	+	0.961444i	$0.411321\pi$
$942$		0			0
$943$		−	6.80281e15i		−	0.297081i
$944$	−2.59509e15			−0.112669
$945$		0			0
$946$	−3.06633e16			−1.31588
$947$			3.25711e16i			1.38966i	0.719175	+	0.694829i	$0.244520\pi$
$947$			3.25711e16i			1.38966i	−0.719175	+	0.694829i	$0.755480\pi$
$948$		0			0
$949$	2.05637e15			0.0867234
$950$	1.25827e16	−	2.53669e16i	0.527585	−	1.06362i
$951$		0			0
$952$			6.29661e15i			0.260978i
$953$		−	8.18081e15i		−	0.337121i	−0.985691	−	0.168560i	$-0.946088\pi$
$953$		−	8.18081e15i		−	0.337121i	0.985691	−	0.168560i	$-0.0539118\pi$
$954$		0			0
$955$	3.56364e14	−	1.52040e15i	0.0145169	−	0.0619354i
$956$	3.11957e15			0.126350
$957$		0			0
$958$		−	2.95553e16i		−	1.18338i
$959$	−1.44120e16			−0.573748
$960$		0			0
$961$	−1.48428e16			−0.584169
$962$			9.31594e15i			0.364556i
$963$		0			0
$964$	1.55010e16			0.599701
$965$	−2.20629e16	−	5.17127e15i	−0.848714	−	0.198929i
$966$		0			0
$967$			2.01660e16i			0.766961i	0.923549	+	0.383480i	$0.125275\pi$
$967$			2.01660e16i			0.766961i	−0.923549	+	0.383480i	$0.874725\pi$
$968$		−	5.31900e15i		−	0.201148i
$969$		0			0
$970$	−2.99893e15	+	1.27947e16i	−0.112130	+	0.478395i
$971$	2.84728e16			1.05858			0.529291	−	0.848440i	$-0.322458\pi$
$971$	2.84728e16			1.05858			0.529291	+	0.848440i	$0.322458\pi$
$972$		0			0
$973$			5.83058e15i			0.214334i
$974$	1.46747e16			0.536407
$975$		0			0
$976$	9.60793e13			0.00347261
$977$			1.91832e15i			0.0689448i	0.999406	+	0.0344724i	$0.0109751\pi$
$977$			1.91832e15i			0.0689448i	−0.999406	+	0.0344724i	$0.989025\pi$
$978$		0			0
$979$	−6.84974e16			−2.43427
$980$	2.25045e15	−	9.60139e15i	0.0795292	−	0.339306i
$981$		0			0
$982$			7.27472e15i			0.254216i
$983$		−	2.65744e16i		−	0.923463i	−0.887020	−	0.461732i	$-0.847228\pi$
$983$		−	2.65744e16i		−	0.923463i	0.887020	−	0.461732i	$-0.152772\pi$
$984$		0			0
$985$	3.50493e16	+	8.21514e15i	1.20443	+	0.282303i
$986$	−5.09234e16			−1.74018
$987$		0			0
$988$		−	1.07492e16i		−	0.363255i
$989$	−2.82436e16			−0.949164
$990$		0			0
$991$	−4.40916e16			−1.46538			−0.732690	−	0.680562i	$-0.761736\pi$
$991$	−4.40916e16			−1.46538			−0.732690	+	0.680562i	$0.761736\pi$
$992$			3.44903e15i			0.113994i
$993$		0			0
$994$	1.89944e16			0.620870
$995$	−1.10486e15	+	4.71379e15i	−0.0359153	+	0.153230i
$996$		0			0
$997$			3.52203e16i			1.13232i	0.824295	+	0.566161i	$0.191572\pi$
$997$			3.52203e16i			1.13232i	−0.824295	+	0.566161i	$0.808428\pi$
$998$			1.98432e16i			0.634444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.12.c.b.19.5		6
3.2	odd	2		10.12.b.a.9.1	✓	6
5.4	even	2	inner	90.12.c.b.19.2		6
12.11	even	2		80.12.c.c.49.5		6
15.2	even	4		50.12.a.j.1.1		3
15.8	even	4		50.12.a.i.1.3		3
15.14	odd	2		10.12.b.a.9.6	yes	6
60.59	even	2		80.12.c.c.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.b.a.9.1	✓	6	3.2	odd	2
10.12.b.a.9.6	yes	6	15.14	odd	2
50.12.a.i.1.3		3	15.8	even	4
50.12.a.j.1.1		3	15.2	even	4
80.12.c.c.49.2		6	60.59	even	2
80.12.c.c.49.5		6	12.11	even	2
90.12.c.b.19.2		6	5.4	even	2	inner
90.12.c.b.19.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+32.0000i q^{2} -1024.00 q^{4} +(-1594.62 + 6803.33i) q^{5} +24477.0i q^{7} -32768.0i q^{8} +(-217707. - 51027.9i) q^{10} +669055. q^{11} +579245. i q^{13} -783265. q^{14} +1.04858e6 q^{16} +7.85051e6i q^{17} +1.81223e7 q^{19} +(1.63289e6 - 6.96661e6i) q^{20} +2.14098e7i q^{22} +1.97203e7i q^{23} +(-4.37425e7 - 2.16975e7i) q^{25} -1.85358e7 q^{26} -2.50645e7i q^{28} +2.02707e8 q^{29} +1.02789e8 q^{31} +3.35544e7i q^{32} -2.51216e8 q^{34} +(-1.66525e8 - 3.90316e7i) q^{35} -5.02591e8i q^{37} +5.79913e8i q^{38} +(2.22932e8 + 5.22525e7i) q^{40} -3.44964e8 q^{41} +1.43221e9i q^{43} -6.85112e8 q^{44} -6.31051e8 q^{46} +1.38179e9i q^{47} +1.37820e9 q^{49} +(6.94319e8 - 1.39976e9i) q^{50} -5.93147e8i q^{52} +2.89531e8i q^{53} +(-1.06689e9 + 4.55180e9i) q^{55} +8.02063e8 q^{56} +6.48664e9i q^{58} -2.47487e9 q^{59} +9.16284e7 q^{61} +3.28926e9i q^{62} -1.07374e9 q^{64} +(-3.94079e9 - 9.23676e8i) q^{65} +3.09287e7i q^{67} -8.03893e9i q^{68} +(1.24901e9 - 5.32881e9i) q^{70} -2.42503e10 q^{71} -3.55008e9i q^{73} +1.60829e10 q^{74} -1.85572e10 q^{76} +1.63765e10i q^{77} +1.16350e10 q^{79} +(-1.67208e9 + 7.13381e9i) q^{80} -1.10389e10i q^{82} -2.33729e10i q^{83} +(-5.34096e10 - 1.25186e10i) q^{85} -4.58307e10 q^{86} -2.19236e10i q^{88} -1.02379e11 q^{89} -1.41782e10 q^{91} -2.01936e10i q^{92} -4.42174e10 q^{94} +(-2.88982e10 + 1.23292e11i) q^{95} -5.87705e10i q^{97} +4.41025e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6144 q^{4} - 530 q^{5} - 385920 q^{10} + 642728 q^{11} + 2125952 q^{14} + 6291456 q^{16} - 24109080 q^{19} + 542720 q^{20} - 181718850 q^{25} - 89251584 q^{26} + 256409820 q^{29} + 458481792 q^{31}+ \cdots - 104896380600 q^{95}+O(q^{100}) \) 6 * q - 6144 * q^4 - 530 * q^5 - 385920 * q^10 + 642728 * q^11 + 2125952 * q^14 + 6291456 * q^16 - 24109080 * q^19 + 542720 * q^20 - 181718850 * q^25 - 89251584 * q^26 + 256409820 * q^29 + 458481792 * q^31 - 225288192 * q^34 + 697136360 * q^35 + 395182080 * q^40 + 164768948 * q^41 - 658153472 * q^44 - 2956208256 * q^46 - 675514158 * q^49 - 3912262400 * q^50 + 3688644360 * q^55 - 2176974848 * q^56 - 17663962360 * q^59 - 5020792428 * q^61 - 6442450944 * q^64 + 19996916880 * q^65 + 24956826240 * q^70 - 56788418832 * q^71 + 64135292672 * q^74 + 24687697920 * q^76 + 2602550880 * q^79 - 555745280 * q^80 - 85024210560 * q^85 - 111995790464 * q^86 - 249448412540 * q^89 - 184446766128 * q^91 - 337749482112 * q^94 - 104896380600 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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