LMFDB - Embedded newform 90.12.c.a.19.1

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)

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);

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")

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 = [4,0,0,-4096,-4950] 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:	$4$
Coefficient field:	$\Q(i, \sqrt{1129})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 565x^{2} + 79524 $ x^4 + 565*x^2 + 79524
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$16.3003i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.12.c.a.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-32.0000i q^{2} -1024.00 q^{4} +(-6697.60 - 1992.57i) q^{5} -10004.9i q^{7} +32768.0i q^{8} +(-63762.1 + 214323. i) q^{10} +133341. q^{11} -152929. i q^{13} -320158. q^{14} +1.04858e6 q^{16} +8.14793e6i q^{17} +9.95950e6 q^{19} +(6.85834e6 + 2.04039e6i) q^{20} -4.26692e6i q^{22} +1.88677e7i q^{23} +(4.08875e7 + 2.66908e7i) q^{25} -4.89374e6 q^{26} +1.02450e7i q^{28} -1.92191e8 q^{29} +1.47585e8 q^{31} -3.35544e7i q^{32} +2.60734e8 q^{34} +(-1.99355e7 + 6.70090e7i) q^{35} -3.96277e8i q^{37} -3.18704e8i q^{38} +(6.52924e7 - 2.19467e8i) q^{40} -1.20670e8 q^{41} -7.63359e8i q^{43} -1.36542e8 q^{44} +6.03767e8 q^{46} +1.46495e9i q^{47} +1.87723e9 q^{49} +(8.54106e8 - 1.30840e9i) q^{50} +1.56600e8i q^{52} -3.22312e9i q^{53} +(-8.93067e8 - 2.65692e8i) q^{55} +3.27842e8 q^{56} +6.15010e9i q^{58} +8.47873e9 q^{59} -4.24657e9 q^{61} -4.72271e9i q^{62} -1.07374e9 q^{64} +(-3.04722e8 + 1.02426e9i) q^{65} -1.37284e10i q^{67} -8.34348e9i q^{68} +(2.14429e9 + 6.37936e8i) q^{70} +1.36888e9 q^{71} -6.85115e9i q^{73} -1.26809e10 q^{74} -1.01985e10 q^{76} -1.33407e9i q^{77} -1.88528e10 q^{79} +(-7.02294e9 - 2.08936e9i) q^{80} +3.86145e9i q^{82} -4.90531e10i q^{83} +(1.62353e10 - 5.45716e10i) q^{85} -2.44275e10 q^{86} +4.36933e9i q^{88} -5.69604e10 q^{89} -1.53005e9 q^{91} -1.93205e10i q^{92} +4.68785e10 q^{94} +(-6.67047e10 - 1.98450e10i) q^{95} +2.16070e10i q^{97} -6.00713e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4096 q^{4} - 4950 q^{5} + 228800 q^{10} + 452052 q^{11} - 1775232 q^{14} + 4194304 q^{16} + 36378480 q^{19} + 5068800 q^{20} + 55440000 q^{25} + 56098944 q^{26} - 257619420 q^{29} - 300753272 q^{31}+ \cdots - 63907668000 q^{95}+O(q^{100}) $ 4 * q - 4096 * q^4 - 4950 * q^5 + 228800 * q^10 + 452052 * q^11 - 1775232 * q^14 + 4194304 * q^16 + 36378480 * q^19 + 5068800 * q^20 + 55440000 * q^25 + 56098944 * q^26 - 257619420 * q^29 - 300753272 * q^31 + 253100672 * q^34 + 157589100 * q^35 - 234291200 * q^40 - 875749968 * q^41 - 462901248 * q^44 - 270485504 * q^46 + 7080186228 * q^49 + 4717440000 * q^50 - 1003393600 * q^55 + 1817837568 * q^56 + 15671542860 * q^59 - 361352152 * q^61 - 4294967296 * q^64 - 12072791700 * q^65 - 503718400 * q^70 - 422314488 * q^71 + 3000094848 * q^74 - 37251563520 * q^76 - 1904696280 * q^79 - 5190451200 * q^80 + 79162796900 * q^85 + 49155623424 * q^86 + 67118824440 * q^89 + 33451420248 * q^91 + 201866497792 * q^94 - 63907668000 * 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
$5$	−6697.60	−	1992.57i	−0.958482	−	0.285153i
$5$	−6697.60	−	1992.57i	−0.958482	−	0.285153i
$6$		0			0
$7$		−	10004.9i		−	0.224996i	−0.993652	−	0.112498i	$-0.964115\pi$
$7$		−	10004.9i		−	0.224996i	0.993652	−	0.112498i	$-0.0358852\pi$
$8$			32768.0i			0.353553i
$9$		0			0
$10$	−63762.1	+	214323.i	−0.201634	+	0.677749i
$11$	133341.			0.249635			0.124817	−	0.992180i	$-0.460165\pi$
$11$	133341.			0.249635			0.124817	+	0.992180i	$0.460165\pi$
$12$		0			0
$13$		−	152929.i		−	0.114236i	−0.998367	−	0.0571180i	$-0.981809\pi$
$13$		−	152929.i		−	0.114236i	0.998367	−	0.0571180i	$-0.0181911\pi$
$14$	−320158.			−0.159096
$15$		0			0
$16$	1.04858e6			0.250000
$17$			8.14793e6i			1.39180i	0.718137	+	0.695902i	$0.244995\pi$
$17$			8.14793e6i			1.39180i	−0.718137	+	0.695902i	$0.755005\pi$
$18$		0			0
$19$	9.95950e6			0.922768			0.461384	−	0.887200i	$-0.347353\pi$
$19$	9.95950e6			0.922768			0.461384	+	0.887200i	$0.347353\pi$
$20$	6.85834e6	+	2.04039e6i	0.479241	+	0.142576i
$21$		0			0
$22$		−	4.26692e6i		−	0.176518i
$23$			1.88677e7i			0.611246i	0.952153	+	0.305623i	$0.0988648\pi$
$23$			1.88677e7i			0.611246i	−0.952153	+	0.305623i	$0.901135\pi$
$24$		0			0
$25$	4.08875e7	+	2.66908e7i	0.837376	+	0.546628i
$26$	−4.89374e6			−0.0807770
$27$		0			0
$28$			1.02450e7i			0.112498i
$29$	−1.92191e8			−1.73998			−0.869989	−	0.493072i	$-0.835874\pi$
$29$	−1.92191e8			−1.73998			−0.869989	+	0.493072i	$0.835874\pi$
$30$		0			0
$31$	1.47585e8			0.925874			0.462937	−	0.886391i	$-0.346796\pi$
$31$	1.47585e8			0.925874			0.462937	+	0.886391i	$0.346796\pi$
$32$		−	3.35544e7i		−	0.176777i
$33$		0			0
$34$	2.60734e8			0.984154
$35$	−1.99355e7	+	6.70090e7i	−0.0641583	+	0.215655i
$36$		0			0
$37$		−	3.96277e8i		−	0.939485i	−0.882804	−	0.469742i	$-0.844347\pi$
$37$		−	3.96277e8i		−	0.939485i	0.882804	−	0.469742i	$-0.155653\pi$
$38$		−	3.18704e8i		−	0.652496i
$39$		0			0
$40$	6.52924e7	−	2.19467e8i	0.100817	−	0.338875i
$41$	−1.20670e8			−0.162663			−0.0813315	−	0.996687i	$-0.525917\pi$
$41$	−1.20670e8			−0.162663			−0.0813315	+	0.996687i	$0.525917\pi$
$42$		0			0
$43$		−	7.63359e8i		−	0.791868i	−0.918279	−	0.395934i	$-0.870421\pi$
$43$		−	7.63359e8i		−	0.791868i	0.918279	−	0.395934i	$-0.129579\pi$
$44$	−1.36542e8			−0.124817
$45$		0			0
$46$	6.03767e8			0.432216
$47$			1.46495e9i			0.931720i	0.884858	+	0.465860i	$0.154255\pi$
$47$			1.46495e9i			0.931720i	−0.884858	+	0.465860i	$0.845745\pi$
$48$		0			0
$49$	1.87723e9			0.949377
$50$	8.54106e8	−	1.30840e9i	0.386524	−	0.592114i
$51$		0			0
$52$			1.56600e8i			0.0571180i
$53$		−	3.22312e9i		−	1.05867i	−0.848414	−	0.529333i	$-0.822442\pi$
$53$		−	3.22312e9i		−	1.05867i	0.848414	−	0.529333i	$-0.177558\pi$
$54$		0			0
$55$	−8.93067e8	−	2.65692e8i	−0.239270	−	0.0711841i
$56$	3.27842e8			0.0795481
$57$		0			0
$58$			6.15010e9i			1.23035i
$59$	8.47873e9			1.54399			0.771996	−	0.635628i	$-0.219259\pi$
$59$	8.47873e9			1.54399			0.771996	+	0.635628i	$0.219259\pi$
$60$		0			0
$61$	−4.24657e9			−0.643761			−0.321880	−	0.946780i	$-0.604315\pi$
$61$	−4.24657e9			−0.643761			−0.321880	+	0.946780i	$0.604315\pi$
$62$		−	4.72271e9i		−	0.654692i
$63$		0			0
$64$	−1.07374e9			−0.125000
$65$	−3.04722e8	+	1.02426e9i	−0.0325747	+	0.109493i
$66$		0			0
$67$		−	1.37284e10i		−	1.24225i	−0.783710	−	0.621127i	$-0.786675\pi$
$67$		−	1.37284e10i		−	1.24225i	0.783710	−	0.621127i	$-0.213325\pi$
$68$		−	8.34348e9i		−	0.695902i
$69$		0			0
$70$	2.14429e9	+	6.37936e8i	0.152491	+	0.0453668i
$71$	1.36888e9			0.0900419			0.0450209	−	0.998986i	$-0.485665\pi$
$71$	1.36888e9			0.0900419			0.0450209	+	0.998986i	$0.485665\pi$
$72$		0			0
$73$		−	6.85115e9i		−	0.386801i	−0.981120	−	0.193401i	$-0.938048\pi$
$73$		−	6.85115e9i		−	0.386801i	0.981120	−	0.193401i	$-0.0619517\pi$
$74$	−1.26809e10			−0.664316
$75$		0			0
$76$	−1.01985e10			−0.461384
$77$		−	1.33407e9i		−	0.0561668i
$78$		0			0
$79$	−1.88528e10			−0.689330			−0.344665	−	0.938726i	$-0.612007\pi$
$79$	−1.88528e10			−0.689330			−0.344665	+	0.938726i	$0.612007\pi$
$80$	−7.02294e9	−	2.08936e9i	−0.239621	−	0.0712882i
$81$		0			0
$82$			3.86145e9i			0.115020i
$83$		−	4.90531e10i		−	1.36690i	−0.729997	−	0.683451i	$-0.760478\pi$
$83$		−	4.90531e10i		−	1.36690i	0.729997	−	0.683451i	$-0.239522\pi$
$84$		0			0
$85$	1.62353e10	−	5.45716e10i	0.396877	−	1.33402i
$86$	−2.44275e10			−0.559935
$87$		0			0
$88$			4.36933e9i			0.0882592i
$89$	−5.69604e10			−1.08125			−0.540627	−	0.841262i	$-0.681813\pi$
$89$	−5.69604e10			−1.08125			−0.540627	+	0.841262i	$0.681813\pi$
$90$		0			0
$91$	−1.53005e9			−0.0257026
$92$		−	1.93205e10i		−	0.305623i
$93$		0			0
$94$	4.68785e10			0.658826
$95$	−6.67047e10	−	1.98450e10i	−0.884457	−	0.263130i
$96$		0			0
$97$			2.16070e10i			0.255476i	0.991808	+	0.127738i	$0.0407717\pi$
$97$			2.16070e10i			0.255476i	−0.991808	+	0.127738i	$0.959228\pi$
$98$		−	6.00713e10i		−	0.671311i
$99$		0			0
$100$	−4.18688e10	−	2.73314e10i	−0.418688	−	0.273314i
$101$	−3.38954e10			−0.320902			−0.160451	−	0.987044i	$-0.551295\pi$
$101$	−3.38954e10			−0.320902			−0.160451	+	0.987044i	$0.551295\pi$
$102$		0			0
$103$			1.21228e10i			0.103038i	0.998672	+	0.0515192i	$0.0164063\pi$
$103$			1.21228e10i			0.103038i	−0.998672	+	0.0515192i	$0.983594\pi$
$104$	5.01119e9			0.0403885
$105$		0			0
$106$	−1.03140e11			−0.748589
$107$		−	2.00015e11i		−	1.37865i	−0.724454	−	0.689323i	$-0.757908\pi$
$107$		−	2.00015e11i		−	1.37865i	0.724454	−	0.689323i	$-0.242092\pi$
$108$		0			0
$109$	2.71994e8			0.00169322			0.000846612	−	1.00000i	$-0.499731\pi$
$109$	2.71994e8			0.00169322			0.000846612		1.00000i	$0.499731\pi$
$110$	−8.50213e9	+	2.85781e10i	−0.0503348	+	0.169190i
$111$		0			0
$112$		−	1.04909e10i		−	0.0562490i
$113$		−	1.93061e11i		−	0.985741i	−0.870103	−	0.492871i	$-0.835948\pi$
$113$		−	1.93061e11i		−	0.985741i	0.870103	−	0.492871i	$-0.164052\pi$
$114$		0			0
$115$	3.75952e10	−	1.26368e11i	0.174299	−	0.585869i
$116$	1.96803e11			0.869989
$117$		0			0
$118$		−	2.71319e11i		−	1.09177i
$119$	8.15195e10			0.313151
$120$		0			0
$121$	−2.67532e11			−0.937682
$122$			1.35890e11i			0.455208i
$123$		0			0
$124$	−1.51127e11			−0.462937
$125$	−2.20665e11	−	2.60235e11i	−0.646737	−	0.762713i
$126$		0			0
$127$			1.00806e11i			0.270747i	0.990795	+	0.135374i	$0.0432235\pi$
$127$			1.00806e11i			0.270747i	−0.990795	+	0.135374i	$0.956777\pi$
$128$			3.43597e10i			0.0883883i
$129$		0			0
$130$	3.27763e10	+	9.75111e9i	0.0774233	+	0.0230338i
$131$	8.29795e11			1.87922			0.939612	−	0.342242i	$-0.111186\pi$
$131$	8.29795e11			1.87922			0.939612	+	0.342242i	$0.111186\pi$
$132$		0			0
$133$		−	9.96441e10i		−	0.207619i
$134$	−4.39310e11			−0.878406
$135$		0			0
$136$	−2.66991e11			−0.492077
$137$		−	2.74370e11i		−	0.485705i	−0.970063	−	0.242853i	$-0.921917\pi$
$137$		−	2.74370e11i		−	0.485705i	0.970063	−	0.242853i	$-0.0780832\pi$
$138$		0			0
$139$	7.50277e11			1.22642			0.613212	−	0.789919i	$-0.289877\pi$
$139$	7.50277e11			1.22642			0.613212	+	0.789919i	$0.289877\pi$
$140$	2.04139e10	−	6.86172e10i	0.0320791	−	0.107827i
$141$		0			0
$142$		−	4.38042e10i		−	0.0636692i
$143$		−	2.03918e10i		−	0.0285173i
$144$		0			0
$145$	1.28722e12	+	3.82953e11i	1.66774	+	0.496160i
$146$	−2.19237e11			−0.273510
$147$		0			0
$148$			4.05788e11i			0.469742i
$149$	2.90981e11			0.324594			0.162297	−	0.986742i	$-0.448110\pi$
$149$	2.90981e11			0.324594			0.162297	+	0.986742i	$0.448110\pi$
$150$		0			0
$151$	2.93157e11			0.303897			0.151949	−	0.988388i	$-0.451445\pi$
$151$	2.93157e11			0.303897			0.151949	+	0.988388i	$0.451445\pi$
$152$			3.26353e11i			0.326248i
$153$		0			0
$154$	−4.26903e10			−0.0397160
$155$	−9.88462e11	−	2.94072e11i	−0.887433	−	0.264016i
$156$		0			0
$157$			4.63080e11i			0.387443i	0.981057	+	0.193722i	$0.0620559\pi$
$157$			4.63080e11i			0.387443i	−0.981057	+	0.193722i	$0.937944\pi$
$158$			6.03290e11i			0.487430i
$159$		0			0
$160$	−6.68595e10	+	2.24734e11i	−0.0504084	+	0.169437i
$161$	1.88770e11			0.137528
$162$		0			0
$163$		−	2.40344e12i		−	1.63607i	−0.575168	−	0.818036i	$-0.695063\pi$
$163$		−	2.40344e12i		−	1.63607i	0.575168	−	0.818036i	$-0.304937\pi$
$164$	1.23566e11			0.0813315
$165$		0			0
$166$	−1.56970e12			−0.966545
$167$			2.59189e12i			1.54410i	0.635560	+	0.772052i	$0.280769\pi$
$167$			2.59189e12i			1.54410i	−0.635560	+	0.772052i	$0.719231\pi$
$168$		0			0
$169$	1.76877e12			0.986950
$170$	−1.74629e12	−	5.19529e11i	−0.943294	−	0.280635i
$171$		0			0
$172$			7.81680e11i			0.395934i
$173$			3.57767e12i			1.75528i	0.479318	+	0.877641i	$0.340884\pi$
$173$			3.57767e12i			1.75528i	−0.479318	+	0.877641i	$0.659116\pi$
$174$		0			0
$175$	2.67040e11	−	4.09076e11i	0.122989	−	0.188406i
$176$	1.39819e11			0.0624087
$177$		0			0
$178$			1.82273e12i			0.764562i
$179$	1.36064e12			0.553414			0.276707	−	0.960954i	$-0.410757\pi$
$179$	1.36064e12			0.553414			0.276707	+	0.960954i	$0.410757\pi$
$180$		0			0
$181$	−4.47871e12			−1.71364			−0.856822	−	0.515613i	$-0.827564\pi$
$181$	−4.47871e12			−1.71364			−0.856822	+	0.515613i	$0.827564\pi$
$182$			4.89616e10i			0.0181745i
$183$		0			0
$184$	−6.18257e11			−0.216108
$185$	−7.89609e11	+	2.65411e12i	−0.267897	+	0.900479i
$186$		0			0
$187$			1.08646e12i			0.347443i
$188$		−	1.50011e12i		−	0.465860i
$189$		0			0
$190$	−6.35039e11	+	2.13455e12i	−0.186061	+	0.625405i
$191$	6.69223e12			1.90497			0.952483	−	0.304592i	$-0.0985202\pi$
$191$	6.69223e12			1.90497			0.952483	+	0.304592i	$0.0985202\pi$
$192$		0			0
$193$			5.04342e12i			1.35569i	0.735206	+	0.677844i	$0.237086\pi$
$193$			5.04342e12i			1.35569i	−0.735206	+	0.677844i	$0.762914\pi$
$194$	6.91424e11			0.180649
$195$		0			0
$196$	−1.92228e12			−0.474688
$197$		−	2.74461e12i		−	0.659048i	−0.944147	−	0.329524i	$-0.893112\pi$
$197$		−	2.74461e12i		−	0.659048i	0.944147	−	0.329524i	$-0.106888\pi$
$198$		0			0
$199$	4.80817e12			1.09216			0.546082	−	0.837732i	$-0.316119\pi$
$199$	4.80817e12			1.09216			0.546082	+	0.837732i	$0.316119\pi$
$200$	−8.74605e11	+	1.33980e12i	−0.193262	+	0.296057i
$201$		0			0
$202$			1.08465e12i			0.226912i
$203$			1.92286e12i			0.391488i
$204$		0			0
$205$	8.08200e11	+	2.40443e11i	0.155910	+	0.0463838i
$206$	3.87930e11			0.0728591
$207$		0			0
$208$		−	1.60358e11i		−	0.0285590i
$209$	1.32801e12			0.230355
$210$		0			0
$211$	−9.13618e11			−0.150387			−0.0751936	−	0.997169i	$-0.523957\pi$
$211$	−9.13618e11			−0.150387			−0.0751936	+	0.997169i	$0.523957\pi$
$212$			3.30047e12i			0.529333i
$213$		0			0
$214$	−6.40049e12			−0.974850
$215$	−1.52104e12	+	5.11267e12i	−0.225803	+	0.758991i
$216$		0			0
$217$		−	1.47657e12i		−	0.208318i
$218$		−	8.70382e9i		−	0.00119729i
$219$		0			0
$220$	9.14500e11	+	2.72068e11i	0.119635	+	0.0355921i
$221$	1.24606e12			0.158994
$222$		0			0
$223$		−	5.18336e12i		−	0.629412i	−0.949189	−	0.314706i	$-0.898094\pi$
$223$		−	5.18336e12i		−	0.629412i	0.949189	−	0.314706i	$-0.101906\pi$
$224$	−3.35710e11			−0.0397741
$225$		0			0
$226$	−6.17795e12			−0.697024
$227$		−	9.06537e11i		−	0.0998259i	−0.998754	−	0.0499130i	$-0.984106\pi$
$227$		−	9.06537e11i		−	0.0998259i	0.998754	−	0.0499130i	$-0.0158944\pi$
$228$		0			0
$229$	1.49006e13			1.56354			0.781770	−	0.623566i	$-0.214317\pi$
$229$	1.49006e13			1.56354			0.781770	+	0.623566i	$0.214317\pi$
$230$	−4.04379e12	−	1.20305e12i	−0.414272	−	0.123248i
$231$		0			0
$232$		−	6.29771e12i		−	0.615175i
$233$		−	1.84683e13i		−	1.76186i	−0.473251	−	0.880928i	$-0.656919\pi$
$233$		−	1.84683e13i		−	1.76186i	0.473251	−	0.880928i	$-0.343081\pi$
$234$		0			0
$235$	2.91902e12	−	9.81167e12i	0.265683	−	0.893037i
$236$	−8.68222e12			−0.771996
$237$		0			0
$238$		−	2.60862e12i		−	0.221431i
$239$	1.12464e13			0.932879			0.466439	−	0.884553i	$-0.345537\pi$
$239$	1.12464e13			0.932879			0.466439	+	0.884553i	$0.345537\pi$
$240$		0			0
$241$	2.45061e13			1.94170			0.970848	−	0.239696i	$-0.0770477\pi$
$241$	2.45061e13			1.94170			0.970848	+	0.239696i	$0.0770477\pi$
$242$			8.56102e12i			0.663042i
$243$		0			0
$244$	4.34849e12			0.321880
$245$	−1.25729e13	−	3.74050e12i	−0.909961	−	0.270718i
$246$		0			0
$247$		−	1.52310e12i		−	0.105413i
$248$			4.83605e12i			0.327346i
$249$		0			0
$250$	−8.32753e12	+	7.06127e12i	−0.539320	+	0.457312i
$251$	−1.31965e13			−0.836089			−0.418045	−	0.908426i	$-0.637284\pi$
$251$	−1.31965e13			−0.836089			−0.418045	+	0.908426i	$0.637284\pi$
$252$		0			0
$253$			2.51585e12i			0.152588i
$254$	3.22578e12			0.191447
$255$		0			0
$256$	1.09951e12			0.0625000
$257$		−	3.29792e13i		−	1.83488i	−0.397872	−	0.917441i	$-0.630251\pi$
$257$		−	3.29792e13i		−	1.83488i	0.397872	−	0.917441i	$-0.369749\pi$
$258$		0			0
$259$	−3.96473e12			−0.211380
$260$	3.12036e11	−	1.04884e12i	0.0162874	−	0.0547465i
$261$		0			0
$262$		−	2.65534e13i		−	1.32881i
$263$		−	3.11055e11i		−	0.0152433i	−0.999971	−	0.00762167i	$-0.997574\pi$
$263$		−	3.11055e11i		−	0.0152433i	0.999971	−	0.00762167i	$-0.00242608\pi$
$264$		0			0
$265$	−6.42227e12	+	2.15871e13i	−0.301881	+	1.01471i
$266$	−3.18861e12			−0.146809
$267$		0			0
$268$			1.40579e13i			0.621127i
$269$	2.65722e13			1.15024			0.575122	−	0.818068i	$-0.304955\pi$
$269$	2.65722e13			1.15024			0.575122	+	0.818068i	$0.304955\pi$
$270$		0			0
$271$	−1.08661e13			−0.451589			−0.225794	−	0.974175i	$-0.572498\pi$
$271$	−1.08661e13			−0.451589			−0.225794	+	0.974175i	$0.572498\pi$
$272$			8.54372e12i			0.347951i
$273$		0			0
$274$	−8.77983e12			−0.343446
$275$	5.45199e12	+	3.55899e12i	0.209038	+	0.136457i
$276$		0			0
$277$			1.23183e13i			0.453849i	0.973912	+	0.226924i	$0.0728671\pi$
$277$			1.23183e13i			0.453849i	−0.973912	+	0.226924i	$0.927133\pi$
$278$		−	2.40089e13i		−	0.867212i
$279$		0			0
$280$	−2.19575e12	−	6.53246e11i	−0.0762454	−	0.0226834i
$281$	−3.20934e13			−1.09278			−0.546389	−	0.837532i	$-0.683998\pi$
$281$	−3.20934e13			−1.09278			−0.546389	+	0.837532i	$0.683998\pi$
$282$		0			0
$283$		−	5.33416e13i		−	1.74679i	−0.487012	−	0.873395i	$-0.661913\pi$
$283$		−	5.33416e13i		−	1.74679i	0.487012	−	0.873395i	$-0.338087\pi$
$284$	−1.40173e12			−0.0450209
$285$		0			0
$286$	−6.52538e11			−0.0201648
$287$			1.20730e12i			0.0365985i
$288$		0			0
$289$	−3.21169e13			−0.937120
$290$	1.22545e13	−	4.11909e13i	0.350838	−	1.17927i
$291$		0			0
$292$			7.01558e12i			0.193401i
$293$		−	2.13927e13i		−	0.578752i	−0.957215	−	0.289376i	$-0.906552\pi$
$293$		−	2.13927e13i		−	0.578752i	0.957215	−	0.289376i	$-0.0934479\pi$
$294$		0			0
$295$	−5.67871e13	−	1.68944e13i	−1.47989	−	0.440274i
$296$	1.29852e13			0.332158
$297$		0			0
$298$		−	9.31140e12i		−	0.229523i
$299$	2.88543e12			0.0698263
$300$		0			0
$301$	−7.63736e12			−0.178167
$302$		−	9.38101e12i		−	0.214888i
$303$		0			0
$304$	1.04433e13			0.230692
$305$	2.84418e13	+	8.46158e12i	0.617033	+	0.183570i
$306$		0			0
$307$			5.17532e13i			1.08312i	0.840662	+	0.541560i	$0.182166\pi$
$307$			5.17532e13i			1.08312i	−0.840662	+	0.541560i	$0.817834\pi$
$308$			1.36609e12i			0.0280834i
$309$		0			0
$310$	−9.41031e12	+	3.16308e13i	−0.186687	+	0.627510i
$311$	−7.46747e13			−1.45543			−0.727715	−	0.685880i	$-0.759418\pi$
$311$	−7.46747e13			−1.45543			−0.727715	+	0.685880i	$0.759418\pi$
$312$		0			0
$313$		−	7.06455e13i		−	1.32920i	−0.747199	−	0.664601i	$-0.768602\pi$
$313$		−	7.06455e13i		−	1.32920i	0.747199	−	0.664601i	$-0.231398\pi$
$314$	1.48186e13			0.273964
$315$		0			0
$316$	1.93053e13			0.344665
$317$		−	4.23136e13i		−	0.742427i	−0.928548	−	0.371213i	$-0.878942\pi$
$317$		−	4.23136e13i		−	0.742427i	0.928548	−	0.371213i	$-0.121058\pi$
$318$		0			0
$319$	−2.56270e13			−0.434359
$320$	7.19149e12	+	2.13950e12i	0.119810	+	0.0356441i
$321$		0			0
$322$		−	6.04065e12i		−	0.0972470i
$323$			8.11493e13i			1.28431i
$324$		0			0
$325$	4.08181e12	−	6.25290e12i	0.0624446	−	0.0956584i
$326$	−7.69102e13			−1.15688
$327$		0			0
$328$		−	3.95412e12i		−	0.0575101i
$329$	1.46568e13			0.209633
$330$		0			0
$331$	8.65899e13			1.19788			0.598940	−	0.800794i	$-0.295589\pi$
$331$	8.65899e13			1.19788			0.598940	+	0.800794i	$0.295589\pi$
$332$			5.02304e13i			0.683451i
$333$		0			0
$334$	8.29405e13			1.09185
$335$	−2.73549e13	+	9.19476e13i	−0.354232	+	1.19068i
$336$		0			0
$337$			1.16110e14i			1.45514i	0.686035	+	0.727568i	$0.259349\pi$
$337$			1.16110e14i			1.45514i	−0.686035	+	0.727568i	$0.740651\pi$
$338$		−	5.66007e13i		−	0.697879i
$339$		0			0
$340$	−1.66249e13	+	5.58813e13i	−0.198439	+	0.667010i
$341$	1.96791e13			0.231130
$342$		0			0
$343$		−	3.85646e13i		−	0.438602i
$344$	2.50138e13			0.279967
$345$		0			0
$346$	1.14486e14			1.24117
$347$			6.39053e13i			0.681906i	0.940080	+	0.340953i	$0.110750\pi$
$347$			6.39053e13i			0.681906i	−0.940080	+	0.340953i	$0.889250\pi$
$348$		0			0
$349$	4.75085e13			0.491170			0.245585	−	0.969375i	$-0.421020\pi$
$349$	4.75085e13			0.491170			0.245585	+	0.969375i	$0.421020\pi$
$350$	−1.30904e13	−	8.54527e12i	−0.133223	−	0.0869665i
$351$		0			0
$352$		−	4.47419e12i		−	0.0441296i
$353$			5.02444e13i			0.487895i	0.969788	+	0.243948i	$0.0784425\pi$
$353$			5.02444e13i			0.487895i	−0.969788	+	0.243948i	$0.921558\pi$
$354$		0			0
$355$	−9.16821e12	−	2.72759e12i	−0.0863035	−	0.0256757i
$356$	5.83274e13			0.540627
$357$		0			0
$358$		−	4.35404e13i		−	0.391323i
$359$	1.32835e14			1.17569			0.587844	−	0.808974i	$-0.299977\pi$
$359$	1.32835e14			1.17569			0.587844	+	0.808974i	$0.299977\pi$
$360$		0			0
$361$	−1.72986e13			−0.148499
$362$			1.43319e14i			1.21173i
$363$		0			0
$364$	1.56677e12			0.0128513
$365$	−1.36514e13	+	4.58863e13i	−0.110298	+	0.370742i
$366$		0			0
$367$			7.45502e13i			0.584501i	0.956342	+	0.292251i	$0.0944041\pi$
$367$			7.45502e13i			0.584501i	−0.956342	+	0.292251i	$0.905596\pi$
$368$			1.97842e13i			0.152812i
$369$		0			0
$370$	8.49314e13	+	2.52675e13i	0.636735	+	0.189432i
$371$	−3.22471e13			−0.238195
$372$		0			0
$373$			2.87139e13i			0.205918i	0.994686	+	0.102959i	$0.0328310\pi$
$373$			2.87139e13i			0.205918i	−0.994686	+	0.102959i	$0.967169\pi$
$374$	3.47666e13			0.245679
$375$		0			0
$376$	−4.80036e13			−0.329413
$377$			2.93916e13i			0.198768i
$378$		0			0
$379$	−1.20853e14			−0.793855			−0.396927	−	0.917850i	$-0.629923\pi$
$379$	−1.20853e14			−0.793855			−0.396927	+	0.917850i	$0.629923\pi$
$380$	6.83056e13	+	2.03212e13i	0.442228	+	0.131565i
$381$		0			0
$382$		−	2.14151e14i		−	1.34701i
$383$		−	1.60437e14i		−	0.994745i	−0.867537	−	0.497372i	$-0.834298\pi$
$383$		−	1.60437e14i		−	0.994745i	0.867537	−	0.497372i	$-0.165702\pi$
$384$		0			0
$385$	−2.65823e12	+	8.93507e12i	−0.0160161	+	0.0538349i
$386$	1.61389e14			0.958616
$387$		0			0
$388$		−	2.21256e13i		−	0.127738i
$389$	−2.80107e14			−1.59441			−0.797207	−	0.603706i	$-0.793690\pi$
$389$	−2.80107e14			−1.59441			−0.797207	+	0.603706i	$0.793690\pi$
$390$		0			0
$391$	−1.53733e14			−0.850735
$392$			6.15130e13i			0.335655i
$393$		0			0
$394$	−8.78276e13			−0.466017
$395$	1.26268e14	+	3.75655e13i	0.660710	+	0.196564i
$396$		0			0
$397$			2.94199e14i			1.49725i	0.662995	+	0.748624i	$0.269285\pi$
$397$			2.94199e14i			1.49725i	−0.662995	+	0.748624i	$0.730715\pi$
$398$		−	1.53861e14i		−	0.772276i
$399$		0			0
$400$	4.28736e13	+	2.79874e13i	0.209344	+	0.136657i
$401$	2.74046e14			1.31986			0.659932	−	0.751325i	$-0.270585\pi$
$401$	2.74046e14			1.31986			0.659932	+	0.751325i	$0.270585\pi$
$402$		0			0
$403$		−	2.25700e13i		−	0.105768i
$404$	3.47089e13			0.160451
$405$		0			0
$406$	6.15314e13			0.276824
$407$		−	5.28402e13i		−	0.234528i
$408$		0			0
$409$	−3.71472e13			−0.160490			−0.0802451	−	0.996775i	$-0.525570\pi$
$409$	−3.71472e13			−0.160490			−0.0802451	+	0.996775i	$0.525570\pi$
$410$	7.69419e12	−	2.58624e13i	0.0327983	−	0.110245i
$411$		0			0
$412$		−	1.24138e13i		−	0.0515192i
$413$		−	8.48291e13i		−	0.347392i
$414$		0			0
$415$	−9.77416e13	+	3.28538e14i	−0.389776	+	1.31015i
$416$	−5.13146e12			−0.0201943
$417$		0			0
$418$		−	4.24964e13i		−	0.162886i
$419$	−3.33663e14			−1.26221			−0.631104	−	0.775698i	$-0.717398\pi$
$419$	−3.33663e14			−1.26221			−0.631104	+	0.775698i	$0.717398\pi$
$420$		0			0
$421$	−2.75493e14			−1.01522			−0.507609	−	0.861588i	$-0.669470\pi$
$421$	−2.75493e14			−1.01522			−0.507609	+	0.861588i	$0.669470\pi$
$422$			2.92358e13i			0.106340i
$423$		0			0
$424$	1.05615e14			0.374295
$425$	−2.17475e14	+	3.33148e14i	−0.760799	+	1.16546i
$426$		0			0
$427$			4.24867e13i			0.144844i
$428$			2.04816e14i			0.689323i
$429$		0			0
$430$	1.63606e14	+	4.86734e13i	0.536688	+	0.159667i
$431$	6.62478e13			0.214559			0.107280	−	0.994229i	$-0.465786\pi$
$431$	6.62478e13			0.214559			0.107280	+	0.994229i	$0.465786\pi$
$432$		0			0
$433$		−	5.22063e14i		−	1.64831i	−0.566363	−	0.824156i	$-0.691650\pi$
$433$		−	5.22063e14i		−	1.64831i	0.566363	−	0.824156i	$-0.308350\pi$
$434$	−4.72504e13			−0.147303
$435$		0			0
$436$	−2.78522e11			−0.000846612
$437$			1.87913e14i			0.564039i
$438$		0			0
$439$	9.25027e13			0.270769			0.135385	−	0.990793i	$-0.456773\pi$
$439$	9.25027e13			0.270769			0.135385	+	0.990793i	$0.456773\pi$
$440$	8.70618e12	−	2.92640e13i	0.0251674	−	0.0845949i
$441$		0			0
$442$		−	3.98739e13i		−	0.112426i
$443$		−	3.10271e14i		−	0.864014i	−0.901870	−	0.432007i	$-0.857806\pi$
$443$		−	3.10271e14i		−	0.864014i	0.901870	−	0.432007i	$-0.142194\pi$
$444$		0			0
$445$	3.81497e14	+	1.13497e14i	1.03636	+	0.308323i
$446$	−1.65868e14			−0.445061
$447$		0			0
$448$			1.07427e13i			0.0281245i
$449$	−2.72361e14			−0.704353			−0.352177	−	0.935934i	$-0.614558\pi$
$449$	−2.72361e14			−0.704353			−0.352177	+	0.935934i	$0.614558\pi$
$450$		0			0
$451$	−1.60903e13			−0.0406063
$452$			1.97694e14i			0.492871i
$453$		0			0
$454$	−2.90092e13			−0.0705876
$455$	1.02477e13	+	3.04872e12i	0.0246355	+	0.00732918i
$456$		0			0
$457$		−	4.48576e14i		−	1.05268i	−0.850274	−	0.526341i	$-0.823564\pi$
$457$		−	4.48576e14i		−	1.05268i	0.850274	−	0.526341i	$-0.176436\pi$
$458$		−	4.76820e14i		−	1.10559i
$459$		0			0
$460$	−3.84975e13	+	1.29401e14i	−0.0871493	+	0.292934i
$461$	2.08873e14			0.467227			0.233613	−	0.972330i	$-0.424945\pi$
$461$	2.08873e14			0.467227			0.233613	+	0.972330i	$0.424945\pi$
$462$		0			0
$463$		−	5.50658e14i		−	1.20278i	−0.798956	−	0.601390i	$-0.794614\pi$
$463$		−	5.50658e14i		−	1.20278i	0.798956	−	0.601390i	$-0.205386\pi$
$464$	−2.01527e14			−0.434994
$465$		0			0
$466$	−5.90987e14			−1.24582
$467$		−	8.79949e14i		−	1.83322i	−0.399782	−	0.916610i	$-0.630914\pi$
$467$		−	8.79949e14i		−	1.83322i	0.399782	−	0.916610i	$-0.369086\pi$
$468$		0			0
$469$	−1.37352e14			−0.279502
$470$	−3.13973e14	−	9.34086e13i	−0.631473	−	0.187866i
$471$		0			0
$472$			2.77831e14i			0.545883i
$473$		−	1.01787e14i		−	0.197678i
$474$		0			0
$475$	4.07219e14	+	2.65827e14i	0.772704	+	0.504411i
$476$	−8.34760e13			−0.156575
$477$		0			0
$478$		−	3.59885e14i		−	0.659645i
$479$	−4.87950e14			−0.884157			−0.442079	−	0.896976i	$-0.645759\pi$
$479$	−4.87950e14			−0.884157			−0.442079	+	0.896976i	$0.645759\pi$
$480$		0			0
$481$	−6.06025e13			−0.107323
$482$		−	7.84197e14i		−	1.37299i
$483$		0			0
$484$	2.73953e14			0.468841
$485$	4.30534e13	−	1.44715e14i	0.0728497	−	0.244869i
$486$		0			0
$487$			2.80492e14i			0.463993i	0.972717	+	0.231997i	$0.0745258\pi$
$487$			2.80492e14i			0.463993i	−0.972717	+	0.231997i	$0.925474\pi$
$488$		−	1.39152e14i		−	0.227604i
$489$		0			0
$490$	−1.19696e14	+	4.02333e14i	−0.191426	+	0.643439i
$491$	6.28487e14			0.993912			0.496956	−	0.867776i	$-0.334451\pi$
$491$	6.28487e14			0.993912			0.496956	+	0.867776i	$0.334451\pi$
$492$		0			0
$493$		−	1.56596e15i		−	2.42171i
$494$	−4.87392e13			−0.0745385
$495$		0			0
$496$	1.54754e14			0.231468
$497$		−	1.36956e13i		−	0.0202591i
$498$		0			0
$499$	−9.17043e13			−0.132690			−0.0663448	−	0.997797i	$-0.521134\pi$
$499$	−9.17043e13			−0.132690			−0.0663448	+	0.997797i	$0.521134\pi$
$500$	2.25961e14	+	2.66481e14i	0.323368	+	0.381357i
$501$		0			0
$502$			4.22287e14i			0.591204i
$503$		−	5.17206e14i		−	0.716209i	−0.933682	−	0.358104i	$-0.883423\pi$
$503$		−	5.17206e14i		−	0.716209i	0.933682	−	0.358104i	$-0.116577\pi$
$504$		0			0
$505$	2.27018e14	+	6.75388e13i	0.307579	+	0.0915062i
$506$	8.05071e13			0.107896
$507$		0			0
$508$		−	1.03225e14i		−	0.135374i
$509$	7.65954e14			0.993700			0.496850	−	0.867837i	$-0.334490\pi$
$509$	7.65954e14			0.993700			0.496850	+	0.867837i	$0.334490\pi$
$510$		0			0
$511$	−6.85453e13			−0.0870288
$512$		−	3.51844e13i		−	0.0441942i
$513$		0			0
$514$	−1.05533e15			−1.29746
$515$	2.41555e13	−	8.11938e13i	0.0293817	−	0.0987604i
$516$		0			0
$517$			1.95339e14i			0.232590i
$518$			1.26871e14i			0.149469i
$519$		0			0
$520$	−3.35629e13	−	9.98514e12i	−0.0387117	−	0.0115169i
$521$	1.21310e15			1.38449			0.692244	−	0.721664i	$-0.256622\pi$
$521$	1.21310e15			1.38449			0.692244	+	0.721664i	$0.256622\pi$
$522$		0			0
$523$		−	2.78153e14i		−	0.310831i	−0.987849	−	0.155415i	$-0.950328\pi$
$523$		−	2.78153e14i		−	0.310831i	0.987849	−	0.155415i	$-0.0496716\pi$
$524$	−8.49710e14			−0.939612
$525$		0			0
$526$	−9.95375e12			−0.0107787
$527$			1.20251e15i			1.28864i
$528$		0			0
$529$	5.96819e14			0.626378
$530$	6.90788e14	+	2.05513e14i	0.717509	+	0.213462i
$531$		0			0
$532$			1.02036e14i			0.103810i
$533$			1.84540e13i			0.0185820i
$534$		0			0
$535$	−3.98544e14	+	1.33962e15i	−0.393125	+	1.32141i
$536$	4.49854e14			0.439203
$537$		0			0
$538$		−	8.50310e14i		−	0.813345i
$539$	2.50312e14			0.236997
$540$		0			0
$541$	1.36205e15			1.26359			0.631797	−	0.775134i	$-0.282318\pi$
$541$	1.36205e15			1.26359			0.631797	+	0.775134i	$0.282318\pi$
$542$			3.47716e14i			0.319321i
$543$		0			0
$544$	2.73399e14			0.246039
$545$	−1.82171e12	−	5.41967e11i	−0.00162292	−	0.000482828i
$546$		0			0
$547$			2.95444e14i			0.257956i	0.991647	+	0.128978i	$0.0411696\pi$
$547$			2.95444e14i			0.257956i	−0.991647	+	0.128978i	$0.958830\pi$
$548$			2.80955e14i			0.242853i
$549$		0			0
$550$	1.13888e14	−	1.74464e14i	0.0964899	−	0.147812i
$551$	−1.91412e15			−1.60560
$552$		0			0
$553$			1.88621e14i			0.155096i
$554$	3.94185e14			0.320920
$555$		0			0
$556$	−7.68284e14			−0.613212
$557$			9.49495e14i			0.750394i	0.926945	+	0.375197i	$0.122425\pi$
$557$			9.49495e14i			0.750394i	−0.926945	+	0.375197i	$0.877575\pi$
$558$		0			0
$559$	−1.16740e14			−0.0904597
$560$	−2.09039e13	+	7.02640e13i	−0.0160396	+	0.0539137i
$561$		0			0
$562$			1.02699e15i			0.772710i
$563$		−	1.50227e15i		−	1.11931i	−0.828725	−	0.559656i	$-0.810933\pi$
$563$		−	1.50227e15i		−	1.11931i	0.828725	−	0.559656i	$-0.189067\pi$
$564$		0			0
$565$	−3.84687e14	+	1.29304e15i	−0.281087	+	0.944815i
$566$	−1.70693e15			−1.23517
$567$		0			0
$568$			4.48555e13i			0.0318346i
$569$	−1.23558e14			−0.0868467			−0.0434233	−	0.999057i	$-0.513826\pi$
$569$	−1.23558e14			−0.0868467			−0.0434233	+	0.999057i	$0.513826\pi$
$570$		0			0
$571$	1.38364e15			0.953949			0.476974	−	0.878917i	$-0.341733\pi$
$571$	1.38364e15			0.953949			0.476974	+	0.878917i	$0.341733\pi$
$572$			2.08812e13i			0.0142586i
$573$		0			0
$574$	3.86335e13			0.0258791
$575$	−5.03595e14	+	7.71453e14i	−0.334124	+	0.511843i
$576$		0			0
$577$		−	1.31636e15i		−	0.856853i	−0.903577	−	0.428426i	$-0.859068\pi$
$577$		−	1.31636e15i		−	0.856853i	0.903577	−	0.428426i	$-0.140932\pi$
$578$			1.02774e15i			0.662644i
$579$		0			0
$580$	−1.31811e15	−	3.92144e14i	−0.833868	−	0.248080i
$581$	−4.90773e14			−0.307547
$582$		0			0
$583$		−	4.29775e14i		−	0.264280i
$584$	2.24499e14			0.136755
$585$		0			0
$586$	−6.84565e14			−0.409240
$587$			1.80764e15i			1.07054i	0.844682	+	0.535268i	$0.179790\pi$
$587$			1.80764e15i			1.07054i	−0.844682	+	0.535268i	$0.820210\pi$
$588$		0			0
$589$	1.46987e15			0.854367
$590$	−5.40622e14	+	1.81719e15i	−0.311321	+	1.04644i
$591$		0			0
$592$		−	4.15527e14i		−	0.234871i
$593$		−	1.28746e15i		−	0.720996i	−0.932760	−	0.360498i	$-0.882607\pi$
$593$		−	1.28746e15i		−	0.720996i	0.932760	−	0.360498i	$-0.117393\pi$
$594$		0			0
$595$	−5.45985e14	−	1.62433e14i	−0.300149	−	0.0892958i
$596$	−2.97965e14			−0.162297
$597$		0			0
$598$		−	9.23338e13i		−	0.0493746i
$599$	−4.05077e14			−0.214630			−0.107315	−	0.994225i	$-0.534225\pi$
$599$	−4.05077e14			−0.214630			−0.107315	+	0.994225i	$0.534225\pi$
$600$		0			0
$601$	1.40866e15			0.732819			0.366410	−	0.930454i	$-0.380587\pi$
$601$	1.40866e15			0.732819			0.366410	+	0.930454i	$0.380587\pi$
$602$			2.44395e14i			0.125983i
$603$		0			0
$604$	−3.00192e14			−0.151949
$605$	1.79182e15	+	5.33075e14i	0.898752	+	0.267383i
$606$		0			0
$607$			3.28823e15i			1.61966i	0.586664	+	0.809831i	$0.300441\pi$
$607$			3.28823e15i			1.61966i	−0.586664	+	0.809831i	$0.699559\pi$
$608$		−	3.34185e14i		−	0.163124i
$609$		0			0
$610$	2.70771e14	−	9.10139e14i	0.129804	−	0.436308i
$611$	2.24035e14			0.106436
$612$		0			0
$613$		−	1.41333e15i		−	0.659493i	−0.944070	−	0.329746i	$-0.893037\pi$
$613$		−	1.41333e15i		−	0.659493i	0.944070	−	0.329746i	$-0.106963\pi$
$614$	1.65610e15			0.765881
$615$		0			0
$616$	4.37148e13			0.0198580
$617$			1.50170e15i			0.676105i	0.941127	+	0.338052i	$0.109768\pi$
$617$			1.50170e15i			0.676105i	−0.941127	+	0.338052i	$0.890232\pi$
$618$		0			0
$619$	−3.52301e15			−1.55817			−0.779087	−	0.626916i	$-0.784317\pi$
$619$	−3.52301e15			−1.55817			−0.779087	+	0.626916i	$0.784317\pi$
$620$	1.01219e15	+	3.01130e14i	0.443717	+	0.132008i
$621$		0			0
$622$			2.38959e15i			1.02914i
$623$			5.69884e14i			0.243278i
$624$		0			0
$625$	9.59386e14	+	2.18264e15i	0.402396	+	0.915466i
$626$	−2.26066e15			−0.939887
$627$		0			0
$628$		−	4.74194e14i		−	0.193722i
$629$	3.22884e15			1.30758
$630$		0			0
$631$	−1.01419e14			−0.0403606			−0.0201803	−	0.999796i	$-0.506424\pi$
$631$	−1.01419e14			−0.0403606			−0.0201803	+	0.999796i	$0.506424\pi$
$632$		−	6.17769e14i		−	0.243715i
$633$		0			0
$634$	−1.35403e15			−0.524975
$635$	2.00862e14	−	6.75155e14i	0.0772044	−	0.259506i
$636$		0			0
$637$		−	2.87084e14i		−	0.108453i
$638$			8.20063e14i			0.307138i
$639$		0			0
$640$	6.84641e13	−	2.30128e14i	0.0252042	−	0.0847186i
$641$	6.09730e14			0.222545			0.111273	−	0.993790i	$-0.464507\pi$
$641$	6.09730e14			0.222545			0.111273	+	0.993790i	$0.464507\pi$
$642$		0			0
$643$			1.71169e15i			0.614136i	0.951688	+	0.307068i	$0.0993478\pi$
$643$			1.71169e15i			0.614136i	−0.951688	+	0.307068i	$0.900652\pi$
$644$	−1.93301e14			−0.0687640
$645$		0			0
$646$	2.59678e15			0.908147
$647$			3.62038e15i			1.25540i	0.778457	+	0.627698i	$0.216003\pi$
$647$			3.62038e15i			1.25540i	−0.778457	+	0.627698i	$0.783997\pi$
$648$		0			0
$649$	1.13057e15			0.385434
$650$	−2.00093e14	−	1.30618e14i	−0.0676407	−	0.0441550i
$651$		0			0
$652$			2.46113e15i			0.818036i
$653$		−	1.77012e15i		−	0.583419i	−0.956507	−	0.291709i	$-0.905776\pi$
$653$		−	1.77012e15i		−	0.583419i	0.956507	−	0.291709i	$-0.0942240\pi$
$654$		0			0
$655$	−5.55763e15	−	1.65342e15i	−1.80120	−	0.535866i
$656$	−1.26532e14			−0.0406658
$657$		0			0
$658$		−	4.69016e14i		−	0.148233i
$659$	1.93677e15			0.607029			0.303514	−	0.952827i	$-0.401840\pi$
$659$	1.93677e15			0.607029			0.303514	+	0.952827i	$0.401840\pi$
$660$		0			0
$661$	2.25856e15			0.696184			0.348092	−	0.937460i	$-0.386830\pi$
$661$	2.25856e15			0.696184			0.348092	+	0.937460i	$0.386830\pi$
$662$		−	2.77088e15i		−	0.847029i
$663$		0			0
$664$	1.60737e15			0.483273
$665$	−1.98548e14	+	6.67376e14i	−0.0592032	+	0.198999i
$666$		0			0
$667$		−	3.62620e15i		−	1.06355i
$668$		−	2.65410e15i		−	0.772052i
$669$		0			0
$670$	2.94232e15	+	8.75355e14i	0.841936	+	0.250480i
$671$	−5.66244e14			−0.160705
$672$		0			0
$673$		−	3.47635e15i		−	0.970600i	−0.874348	−	0.485300i	$-0.838710\pi$
$673$		−	3.47635e15i		−	0.970600i	0.874348	−	0.485300i	$-0.161290\pi$
$674$	3.71551e15			1.02894
$675$		0			0
$676$	−1.81122e15			−0.493475
$677$		−	6.11961e15i		−	1.65381i	−0.562340	−	0.826906i	$-0.690099\pi$
$677$		−	6.11961e15i		−	1.65381i	0.562340	−	0.826906i	$-0.309901\pi$
$678$		0			0
$679$	2.16177e14			0.0574811
$680$	1.78820e15	+	5.31998e14i	0.471647	+	0.140317i
$681$		0			0
$682$		−	6.29732e14i		−	0.163434i
$683$			2.12650e15i			0.547459i	0.961807	+	0.273730i	$0.0882574\pi$
$683$			2.12650e15i			0.547459i	−0.961807	+	0.273730i	$0.911743\pi$
$684$		0			0
$685$	−5.46700e14	+	1.83762e15i	−0.138500	+	0.465540i
$686$	−1.23407e15			−0.310139
$687$		0			0
$688$		−	8.00440e14i		−	0.197967i
$689$	−4.92909e14			−0.120938
$690$		0			0
$691$	−3.62175e15			−0.874559			−0.437279	−	0.899326i	$-0.644058\pi$
$691$	−3.62175e15			−0.874559			−0.437279	+	0.899326i	$0.644058\pi$
$692$		−	3.66354e15i		−	0.877641i
$693$		0			0
$694$	2.04497e15			0.482180
$695$	−5.02505e15	−	1.49498e15i	−1.17550	−	0.349718i
$696$		0			0
$697$		−	9.83212e14i		−	0.226395i
$698$		−	1.52027e15i		−	0.347309i
$699$		0			0
$700$	−2.73449e14	+	4.18894e14i	−0.0614946	+	0.0942031i
$701$	−4.26088e15			−0.950714			−0.475357	−	0.879793i	$-0.657681\pi$
$701$	−4.26088e15			−0.950714			−0.475357	+	0.879793i	$0.657681\pi$
$702$		0			0
$703$		−	3.94672e15i		−	0.866927i
$704$	−1.43174e14			−0.0312043
$705$		0			0
$706$	1.60782e15			0.344994
$707$			3.39121e14i			0.0722018i
$708$		0			0
$709$	5.11768e15			1.07280			0.536400	−	0.843964i	$-0.319784\pi$
$709$	5.11768e15			1.07280			0.536400	+	0.843964i	$0.319784\pi$
$710$	−8.72827e13	+	2.93383e14i	−0.0181555	+	0.0610258i
$711$		0			0
$712$		−	1.86648e15i		−	0.382281i
$713$			2.78458e15i			0.565937i
$714$		0			0
$715$	−4.06321e13	+	1.36576e14i	−0.00813178	+	0.0273333i
$716$	−1.39329e15			−0.276707
$717$		0			0
$718$		−	4.25071e15i		−	0.831337i
$719$	−5.59985e15			−1.08684			−0.543422	−	0.839460i	$-0.682872\pi$
$719$	−5.59985e15			−1.08684			−0.543422	+	0.839460i	$0.682872\pi$
$720$		0			0
$721$	1.21288e14			0.0231832
$722$			5.53556e14i			0.105004i
$723$		0			0
$724$	4.58620e15			0.856822
$725$	−7.85820e15	−	5.12973e15i	−1.45701	−	0.951120i
$726$		0			0
$727$		−	7.58938e15i		−	1.38601i	−0.720932	−	0.693006i	$-0.756286\pi$
$727$		−	7.58938e15i		−	1.38601i	0.720932	−	0.693006i	$-0.243714\pi$
$728$		−	5.01366e13i		−	0.00908725i
$729$		0			0
$730$	1.46836e15	+	4.36844e14i	0.262154	+	0.0779921i
$731$	6.21980e15			1.10212
$732$		0			0
$733$			8.96849e15i			1.56548i	0.622349	+	0.782740i	$0.286179\pi$
$733$			8.96849e15i			1.56548i	−0.622349	+	0.782740i	$0.713821\pi$
$734$	2.38561e15			0.413305
$735$		0			0
$736$	6.33095e14			0.108054
$737$		−	1.83057e15i		−	0.310110i
$738$		0			0
$739$	−4.50240e15			−0.751449			−0.375724	−	0.926731i	$-0.622606\pi$
$739$	−4.50240e15			−0.751449			−0.375724	+	0.926731i	$0.622606\pi$
$740$	8.08560e14	−	2.71780e15i	0.133948	−	0.450240i
$741$		0			0
$742$			1.03191e15i			0.168430i
$743$		−	2.94446e15i		−	0.477053i	−0.971136	−	0.238527i	$-0.923336\pi$
$743$		−	2.94446e15i		−	0.477053i	0.971136	−	0.238527i	$-0.0766644\pi$
$744$		0			0
$745$	−1.94887e15	−	5.79800e14i	−0.311118	−	0.0925589i
$746$	9.18846e14			0.145606
$747$		0			0
$748$		−	1.11253e15i		−	0.173721i
$749$	−2.00114e15			−0.310190
$750$		0			0
$751$	−8.50045e15			−1.29844			−0.649221	−	0.760600i	$-0.724905\pi$
$751$	−8.50045e15			−1.29844			−0.649221	+	0.760600i	$0.724905\pi$
$752$			1.53611e15i			0.232930i
$753$		0			0
$754$	9.40532e14			0.140550
$755$	−1.96345e15	−	5.84134e14i	−0.291280	−	0.0866572i
$756$		0			0
$757$			4.72643e15i			0.691044i	0.938411	+	0.345522i	$0.112298\pi$
$757$			4.72643e15i			0.691044i	−0.938411	+	0.345522i	$0.887702\pi$
$758$			3.86729e15i			0.561340i
$759$		0			0
$760$	6.50280e14	−	2.18578e15i	0.0930306	−	0.312703i
$761$	8.74955e15			1.24271			0.621356	−	0.783529i	$-0.286582\pi$
$761$	8.74955e15			1.24271			0.621356	+	0.783529i	$0.286582\pi$
$762$		0			0
$763$		−	2.72129e12i		−	0.000380969i
$764$	−6.85284e15			−0.952483
$765$		0			0
$766$	−5.13399e15			−0.703391
$767$		−	1.29665e15i		−	0.176379i
$768$		0			0
$769$	−4.01783e15			−0.538762			−0.269381	−	0.963034i	$-0.586819\pi$
$769$	−4.01783e15			−0.538762			−0.269381	+	0.963034i	$0.586819\pi$
$770$	2.85922e14	+	8.50632e13i	0.0380670	+	0.0113251i
$771$		0			0
$772$		−	5.16446e15i		−	0.677844i
$773$		−	4.77859e15i		−	0.622749i	−0.950287	−	0.311374i	$-0.899211\pi$
$773$		−	4.77859e15i		−	0.622749i	0.950287	−	0.311374i	$-0.100789\pi$
$774$		0			0
$775$	6.03436e15	+	3.93915e15i	0.775304	+	0.506109i
$776$	−7.08019e14			−0.0903244
$777$		0			0
$778$			8.96342e15i			1.12742i
$779$	−1.20181e15			−0.150100
$780$		0			0
$781$	1.82528e14			0.0224776
$782$			4.91945e15i			0.601561i
$783$		0			0
$784$	1.96842e15			0.237344
$785$	9.22718e14	−	3.10152e15i	0.110481	−	0.371357i
$786$		0			0
$787$			8.20164e15i			0.968366i	0.874967	+	0.484183i	$0.160883\pi$
$787$			8.20164e15i			0.968366i	−0.874967	+	0.484183i	$0.839117\pi$
$788$			2.81048e15i			0.329524i
$789$		0			0
$790$	1.20210e15	−	4.04059e15i	0.138992	−	0.467193i
$791$	−1.93156e15			−0.221788
$792$		0			0
$793$			6.49426e14i			0.0735406i
$794$	9.41437e15			1.05871
$795$		0			0
$796$	−4.92356e15			−0.546082
$797$		−	5.71181e15i		−	0.629148i	−0.949233	−	0.314574i	$-0.898138\pi$
$797$		−	5.71181e15i		−	0.629148i	0.949233	−	0.314574i	$-0.101862\pi$
$798$		0			0
$799$	−1.19363e16			−1.29677
$800$	8.95595e14	−	1.37196e15i	0.0966311	−	0.148028i
$801$		0			0
$802$		−	8.76947e15i		−	0.933285i
$803$		−	9.13542e14i		−	0.0965591i
$804$		0			0
$805$	−1.26431e15	−	3.76137e14i	−0.131818	−	0.0392165i
$806$	−7.22241e14			−0.0747893
$807$		0			0
$808$		−	1.11068e15i		−	0.113456i
$809$	−1.37124e15			−0.139122			−0.0695612	−	0.997578i	$-0.522160\pi$
$809$	−1.37124e15			−0.139122			−0.0695612	+	0.997578i	$0.522160\pi$
$810$		0			0
$811$	−1.59239e16			−1.59380			−0.796900	−	0.604111i	$-0.793528\pi$
$811$	−1.59239e16			−1.59380			−0.796900	+	0.604111i	$0.793528\pi$
$812$		−	1.96900e15i		−	0.195744i
$813$		0			0
$814$	−1.69089e15			−0.165836
$815$	−4.78902e15	+	1.60973e16i	−0.466531	+	1.56814i
$816$		0			0
$817$		−	7.60268e15i		−	0.730710i
$818$			1.18871e15i			0.113484i
$819$		0			0
$820$	−8.27597e14	−	2.46214e14i	−0.0779548	−	0.0231919i
$821$	1.99735e16			1.86882			0.934410	−	0.356199i	$-0.115928\pi$
$821$	1.99735e16			1.86882			0.934410	+	0.356199i	$0.115928\pi$
$822$		0			0
$823$			1.97814e16i			1.82624i	0.407690	+	0.913121i	$0.366335\pi$
$823$			1.97814e16i			1.82624i	−0.407690	+	0.913121i	$0.633665\pi$
$824$	−3.97241e14			−0.0364296
$825$		0			0
$826$	−2.71453e15			−0.245643
$827$		−	1.95434e15i		−	0.175679i	−0.996135	−	0.0878394i	$-0.972004\pi$
$827$		−	1.95434e15i		−	0.175679i	0.996135	−	0.0878394i	$-0.0279962\pi$
$828$		0			0
$829$	8.79807e15			0.780436			0.390218	−	0.920722i	$-0.372400\pi$
$829$	8.79807e15			0.780436			0.390218	+	0.920722i	$0.372400\pi$
$830$	1.05132e16	+	3.12773e15i	0.926416	+	0.275613i
$831$		0			0
$832$			1.64207e14i			0.0142795i
$833$			1.52955e16i			1.32135i
$834$		0			0
$835$	5.16452e15	−	1.73594e16i	0.440306	−	1.48000i
$836$	−1.35989e15			−0.115178
$837$		0			0
$838$			1.06772e16i			0.892516i
$839$	−1.35734e15			−0.112719			−0.0563594	−	0.998411i	$-0.517949\pi$
$839$	−1.35734e15			−0.112719			−0.0563594	+	0.998411i	$0.517949\pi$
$840$		0			0
$841$	2.47368e16			2.02752
$842$			8.81578e15i			0.717867i
$843$		0			0
$844$	9.35544e14			0.0751936
$845$	−1.18465e16	−	3.52440e15i	−0.945974	−	0.281432i
$846$		0			0
$847$			2.67664e15i			0.210975i
$848$		−	3.37968e15i		−	0.264666i
$849$		0			0
$850$	1.06607e16	+	6.95920e15i	0.824107	+	0.537966i
$851$	7.47685e15			0.574257
$852$		0			0
$853$		−	4.31342e15i		−	0.327041i	−0.986540	−	0.163520i	$-0.947715\pi$
$853$		−	4.31342e15i		−	0.327041i	0.986540	−	0.163520i	$-0.0522849\pi$
$854$	1.35957e15			0.102420
$855$		0			0
$856$	6.55410e15			0.487425
$857$			1.15504e16i			0.853496i	0.904370	+	0.426748i	$0.140341\pi$
$857$			1.15504e16i			0.853496i	−0.904370	+	0.426748i	$0.859659\pi$
$858$		0			0
$859$	1.46253e16			1.06694			0.533472	−	0.845818i	$-0.320887\pi$
$859$	1.46253e16			1.06694			0.533472	+	0.845818i	$0.320887\pi$
$860$	1.55755e15	−	5.23538e15i	0.112902	−	0.379495i
$861$		0			0
$862$		−	2.11993e15i		−	0.151716i
$863$			1.43334e16i			1.01927i	0.860391	+	0.509634i	$0.170219\pi$
$863$			1.43334e16i			1.01927i	−0.860391	+	0.509634i	$0.829781\pi$
$864$		0			0
$865$	7.12875e15	−	2.39618e16i	0.500524	−	1.68241i
$866$	−1.67060e16			−1.16553
$867$		0			0
$868$			1.51201e15i			0.104159i
$869$	−2.51386e15			−0.172081
$870$		0			0
$871$	−2.09948e15			−0.141910
$872$			8.91271e12i			0.000598645i
$873$		0			0
$874$	6.01322e15			0.398836
$875$	−2.60364e15	+	2.20773e15i	−0.171607	+	0.145513i
$876$		0			0
$877$			2.69396e16i			1.75345i	0.480990	+	0.876726i	$0.340277\pi$
$877$			2.69396e16i			1.75345i	−0.480990	+	0.876726i	$0.659723\pi$
$878$		−	2.96009e15i		−	0.191463i
$879$		0			0
$880$	−9.36448e14	−	2.78598e14i	−0.0598176	−	0.0177960i
$881$	2.67478e15			0.169793			0.0848965	−	0.996390i	$-0.472944\pi$
$881$	2.67478e15			0.169793			0.0848965	+	0.996390i	$0.472944\pi$
$882$		0			0
$883$			2.97836e16i			1.86721i	0.358305	+	0.933605i	$0.383355\pi$
$883$			2.97836e16i			1.86721i	−0.358305	+	0.933605i	$0.616645\pi$
$884$	−1.27596e15			−0.0794970
$885$		0			0
$886$	−9.92867e15			−0.610950
$887$		−	1.08553e15i		−	0.0663839i	−0.999449	−	0.0331919i	$-0.989433\pi$
$887$		−	1.08553e15i		−	0.0663839i	0.999449	−	0.0331919i	$-0.0105673\pi$
$888$		0			0
$889$	1.00855e15			0.0609171
$890$	3.63191e15	−	1.22079e16i	0.218017	−	0.732819i
$891$		0			0
$892$			5.30776e15i			0.314706i
$893$			1.45902e16i			0.859762i
$894$		0			0
$895$	−9.11299e15	−	2.71116e15i	−0.530438	−	0.157808i
$896$	3.43767e14			0.0198870
$897$		0			0
$898$			8.71556e15i			0.498053i
$899$	−2.83644e16			−1.61100
$900$		0			0
$901$	2.62617e16			1.47345
$902$			5.14891e14i			0.0287130i
$903$		0			0
$904$	6.32622e15			0.348512
$905$	2.99966e16	+	8.92412e15i	1.64250	+	0.488651i
$906$		0			0
$907$		−	2.29571e16i		−	1.24187i	−0.783861	−	0.620936i	$-0.786753\pi$
$907$		−	2.29571e16i		−	1.24187i	0.783861	−	0.620936i	$-0.213247\pi$
$908$			9.28294e14i			0.0499130i
$909$		0			0
$910$	9.75592e13	−	3.27925e14i	0.00518251	−	0.0174199i
$911$	1.78621e16			0.943153			0.471576	−	0.881825i	$-0.343685\pi$
$911$	1.78621e16			0.943153			0.471576	+	0.881825i	$0.343685\pi$
$912$		0			0
$913$		−	6.54081e15i		−	0.341226i
$914$	−1.43544e16			−0.744358
$915$		0			0
$916$	−1.52582e16			−0.781770
$917$		−	8.30204e15i		−	0.422818i
$918$		0			0
$919$	−2.38879e16			−1.20211			−0.601053	−	0.799209i	$-0.705252\pi$
$919$	−2.38879e16			−1.20211			−0.601053	+	0.799209i	$0.705252\pi$
$920$	4.14084e15	+	1.23192e15i	0.207136	+	0.0616239i
$921$		0			0
$922$		−	6.68394e15i		−	0.330379i
$923$		−	2.09342e14i		−	0.0102860i
$924$		0			0
$925$	1.05770e16	−	1.62028e16i	0.513549	−	0.786702i
$926$	−1.76210e16			−0.850494
$927$		0			0
$928$			6.44885e15i			0.307587i
$929$	9.57374e15			0.453936			0.226968	−	0.973902i	$-0.427119\pi$
$929$	9.57374e15			0.453936			0.226968	+	0.973902i	$0.427119\pi$
$930$		0			0
$931$	1.86963e16			0.876055
$932$			1.89116e16i			0.880928i
$933$		0			0
$934$	−2.81584e16			−1.29628
$935$	2.16484e15	−	7.27664e15i	0.0990744	−	0.333018i
$936$		0			0
$937$		−	2.25750e16i		−	1.02108i	−0.859853	−	0.510541i	$-0.829445\pi$
$937$		−	2.25750e16i		−	1.02108i	0.859853	−	0.510541i	$-0.170555\pi$
$938$			4.39527e15i			0.197638i
$939$		0			0
$940$	−2.98907e15	+	1.00471e16i	−0.132841	+	0.446519i
$941$	9.26321e15			0.409278			0.204639	−	0.978837i	$-0.434398\pi$
$941$	9.26321e15			0.409278			0.204639	+	0.978837i	$0.434398\pi$
$942$		0			0
$943$		−	2.27677e15i		−	0.0994272i
$944$	8.89060e15			0.385998
$945$		0			0
$946$	−3.25720e15			−0.139779
$947$		−	1.09295e16i		−	0.466312i	−0.972439	−	0.233156i	$-0.925095\pi$
$947$		−	1.09295e16i		−	0.466312i	0.972439	−	0.233156i	$-0.0749053\pi$
$948$		0			0
$949$	−1.04774e15			−0.0441866
$950$	8.50647e15	−	1.30310e16i	0.356672	−	0.546384i
$951$		0			0
$952$			2.67123e15i			0.110715i
$953$			3.06665e16i			1.26373i	0.775080	+	0.631863i	$0.217709\pi$
$953$			3.06665e16i			1.26373i	−0.775080	+	0.631863i	$0.782291\pi$
$954$		0			0
$955$	−4.48218e16	−	1.33347e16i	−1.82588	−	0.543207i
$956$	−1.15163e16			−0.466439
$957$		0			0
$958$			1.56144e16i			0.625194i
$959$	−2.74505e15			−0.109282
$960$		0			0
$961$	−3.62725e15			−0.142758
$962$			1.93928e15i			0.0758888i
$963$		0			0
$964$	−2.50943e16			−0.970848
$965$	1.00493e16	−	3.37788e16i	0.386578	−	1.29940i
$966$		0			0
$967$			3.64467e16i			1.38616i	0.720862	+	0.693079i	$0.243746\pi$
$967$			3.64467e16i			1.38616i	−0.720862	+	0.693079i	$0.756254\pi$
$968$		−	8.76648e15i		−	0.331521i
$969$		0			0
$970$	−4.63088e15	−	1.37771e15i	−0.173149	−	0.0515125i
$971$	−3.51494e14			−0.0130681			−0.00653405	−	0.999979i	$-0.502080\pi$
$971$	−3.51494e14			−0.0130681			−0.00653405	+	0.999979i	$0.502080\pi$
$972$		0			0
$973$		−	7.50647e15i		−	0.275940i
$974$	8.97575e15			0.328093
$975$		0			0
$976$	−4.45285e15			−0.160940
$977$		−	2.49440e16i		−	0.896490i	−0.893911	−	0.448245i	$-0.852049\pi$
$977$		−	2.49440e16i		−	0.896490i	0.893911	−	0.448245i	$-0.147951\pi$
$978$		0			0
$979$	−7.59517e15			−0.269919
$980$	1.28747e16	+	3.83027e15i	0.454980	+	0.135359i
$981$		0			0
$982$		−	2.01116e16i		−	0.702802i
$983$		−	2.83374e16i		−	0.984725i	−0.870390	−	0.492363i	$-0.836133\pi$
$983$		−	2.83374e16i		−	0.984725i	0.870390	−	0.492363i	$-0.163867\pi$
$984$		0			0
$985$	−5.46882e15	+	1.83823e16i	−0.187929	+	0.631685i
$986$	−5.01106e16			−1.71241
$987$		0			0
$988$			1.55966e15i			0.0527067i
$989$	1.44028e16			0.484026
$990$		0			0
$991$	2.87221e16			0.954577			0.477289	−	0.878747i	$-0.341620\pi$
$991$	2.87221e16			0.954577			0.477289	+	0.878747i	$0.341620\pi$
$992$		−	4.95212e15i		−	0.163673i
$993$		0			0
$994$	−4.38258e14			−0.0143253
$995$	−3.22032e16	−	9.58059e15i	−1.04682	−	0.311434i
$996$		0			0
$997$		−	2.75510e16i		−	0.885755i	−0.896582	−	0.442877i	$-0.853958\pi$
$997$		−	2.75510e16i		−	0.885755i	0.896582	−	0.442877i	$-0.146042\pi$
$998$			2.93454e15i			0.0938257i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.12.c.a.19.1		4
3.2	odd	2		30.12.c.a.19.4	yes	4
5.4	even	2	inner	90.12.c.a.19.3		4
12.11	even	2		240.12.f.a.49.4		4
15.2	even	4		150.12.a.k.1.1		2
15.8	even	4		150.12.a.r.1.2		2
15.14	odd	2		30.12.c.a.19.2	✓	4
60.59	even	2		240.12.f.a.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.c.a.19.2	✓	4	15.14	odd	2
30.12.c.a.19.4	yes	4	3.2	odd	2
90.12.c.a.19.1		4	1.1	even	1	trivial
90.12.c.a.19.3		4	5.4	even	2	inner
150.12.a.k.1.1		2	15.2	even	4
150.12.a.r.1.2		2	15.8	even	4
240.12.f.a.49.2		4	60.59	even	2
240.12.f.a.49.4		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q-32.0000i q^{2} -1024.00 q^{4} +(-6697.60 - 1992.57i) q^{5} -10004.9i q^{7} +32768.0i q^{8} +(-63762.1 + 214323. i) q^{10} +133341. q^{11} -152929. i q^{13} -320158. q^{14} +1.04858e6 q^{16} +8.14793e6i q^{17} +9.95950e6 q^{19} +(6.85834e6 + 2.04039e6i) q^{20} -4.26692e6i q^{22} +1.88677e7i q^{23} +(4.08875e7 + 2.66908e7i) q^{25} -4.89374e6 q^{26} +1.02450e7i q^{28} -1.92191e8 q^{29} +1.47585e8 q^{31} -3.35544e7i q^{32} +2.60734e8 q^{34} +(-1.99355e7 + 6.70090e7i) q^{35} -3.96277e8i q^{37} -3.18704e8i q^{38} +(6.52924e7 - 2.19467e8i) q^{40} -1.20670e8 q^{41} -7.63359e8i q^{43} -1.36542e8 q^{44} +6.03767e8 q^{46} +1.46495e9i q^{47} +1.87723e9 q^{49} +(8.54106e8 - 1.30840e9i) q^{50} +1.56600e8i q^{52} -3.22312e9i q^{53} +(-8.93067e8 - 2.65692e8i) q^{55} +3.27842e8 q^{56} +6.15010e9i q^{58} +8.47873e9 q^{59} -4.24657e9 q^{61} -4.72271e9i q^{62} -1.07374e9 q^{64} +(-3.04722e8 + 1.02426e9i) q^{65} -1.37284e10i q^{67} -8.34348e9i q^{68} +(2.14429e9 + 6.37936e8i) q^{70} +1.36888e9 q^{71} -6.85115e9i q^{73} -1.26809e10 q^{74} -1.01985e10 q^{76} -1.33407e9i q^{77} -1.88528e10 q^{79} +(-7.02294e9 - 2.08936e9i) q^{80} +3.86145e9i q^{82} -4.90531e10i q^{83} +(1.62353e10 - 5.45716e10i) q^{85} -2.44275e10 q^{86} +4.36933e9i q^{88} -5.69604e10 q^{89} -1.53005e9 q^{91} -1.93205e10i q^{92} +4.68785e10 q^{94} +(-6.67047e10 - 1.98450e10i) q^{95} +2.16070e10i q^{97} -6.00713e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4096 q^{4} - 4950 q^{5} + 228800 q^{10} + 452052 q^{11} - 1775232 q^{14} + 4194304 q^{16} + 36378480 q^{19} + 5068800 q^{20} + 55440000 q^{25} + 56098944 q^{26} - 257619420 q^{29} - 300753272 q^{31}+ \cdots - 63907668000 q^{95}+O(q^{100}) \) 4 * q - 4096 * q^4 - 4950 * q^5 + 228800 * q^10 + 452052 * q^11 - 1775232 * q^14 + 4194304 * q^16 + 36378480 * q^19 + 5068800 * q^20 + 55440000 * q^25 + 56098944 * q^26 - 257619420 * q^29 - 300753272 * q^31 + 253100672 * q^34 + 157589100 * q^35 - 234291200 * q^40 - 875749968 * q^41 - 462901248 * q^44 - 270485504 * q^46 + 7080186228 * q^49 + 4717440000 * q^50 - 1003393600 * q^55 + 1817837568 * q^56 + 15671542860 * q^59 - 361352152 * q^61 - 4294967296 * q^64 - 12072791700 * q^65 - 503718400 * q^70 - 422314488 * q^71 + 3000094848 * q^74 - 37251563520 * q^76 - 1904696280 * q^79 - 5190451200 * q^80 + 79162796900 * q^85 + 49155623424 * q^86 + 67118824440 * q^89 + 33451420248 * q^91 + 201866497792 * q^94 - 63907668000 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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