LMFDB - Embedded newform 196.10.e.i.177.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,10,Mod(165,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.165"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$100.947023888$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 23330 x^{18} + 430207983 x^{16} + 2419104777826 x^{14} + \cdots + 51\!\cdots\!44 $ x^20 + 23330x^18 + 430207983x^16 + 2419104777826x^14 + 10155737523417645x^12 + 12378541469555078612x^10 + 11090234329554477355996x^8 + 3248019376171617626693136x^6 + 690294487094356142747874960x^4 + 70817323577129541319110129792*x^2 + 5189477088488972821260012831744
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{8}\cdot 7^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.7
Root			$65.2870 + 113.080i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.10.e.i.165.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(35.1890 + 60.9492i) q^{3} +(-81.3880 + 140.968i) q^{5} +(7364.96 - 12756.5i) q^{9} +(-45434.4 - 78694.7i) q^{11} -167897. q^{13} -11455.9 q^{15} +(-4913.47 - 8510.38i) q^{17} +(-237764. + 411820. i) q^{19} +(110522. - 191430. i) q^{23} +(963314. + 1.66851e6i) q^{25} +2.42191e6 q^{27} +820028. q^{29} +(1.41587e6 + 2.45236e6i) q^{31} +(3.19758e6 - 5.53838e6i) q^{33} +(1.35653e6 - 2.34957e6i) q^{37} +(-5.90813e6 - 1.02332e7i) q^{39} -1.90289e7 q^{41} +2.58212e7 q^{43} +(1.19884e6 + 2.07645e6i) q^{45} +(-1.75526e7 + 3.04019e7i) q^{47} +(345801. - 598944. i) q^{51} +(4.10462e7 + 7.10941e7i) q^{53} +1.47913e7 q^{55} -3.34668e7 q^{57} +(6.69928e7 + 1.16035e8i) q^{59} +(5.08262e7 - 8.80335e7i) q^{61} +(1.36648e7 - 2.36681e7i) q^{65} +(-7.40102e7 - 1.28190e8i) q^{67} +1.55567e7 q^{69} +1.94170e8 q^{71} +(-3.10493e7 - 5.37790e7i) q^{73} +(-6.77962e7 + 1.17426e8i) q^{75} +(-2.00722e8 + 3.47660e8i) q^{79} +(-5.97398e7 - 1.03472e8i) q^{81} -1.49637e8 q^{83} +1.59959e6 q^{85} +(2.88560e7 + 4.99801e7i) q^{87} +(-3.27085e8 + 5.66527e8i) q^{89} +(-9.96462e7 + 1.72592e8i) q^{93} +(-3.87023e7 - 6.70344e7i) q^{95} +1.51683e9 q^{97} -1.33849e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 93550 q^{9} - 27740 q^{11} + 1824176 q^{15} + 2921096 q^{23} - 3484998 q^{25} - 1671496 q^{29} + 31928756 q^{37} + 4930944 q^{39} + 26828680 q^{43} - 206013028 q^{51} - 137301788 q^{53} + 144492664 q^{57}+ \cdots + 10632134024 q^{99}+O(q^{100}) $ 20 * q - 93550 * q^9 - 27740 * q^11 + 1824176 * q^15 + 2921096 * q^23 - 3484998 * q^25 - 1671496 * q^29 + 31928756 * q^37 + 4930944 * q^39 + 26828680 * q^43 - 206013028 * q^51 - 137301788 * q^53 + 144492664 * q^57 - 519063672 * q^65 + 342262536 * q^67 - 1062072816 * q^71 - 462186584 * q^79 - 2495014982 * q^81 + 2473207168 * q^85 - 5733362712 * q^93 - 2984918936 * q^95 + 10632134024 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	35.1890	+	60.9492i	0.250820	+	0.434432i	0.963752	−	0.266801i	$-0.0859665\pi$
$3$	35.1890	+	60.9492i	0.250820	+	0.434432i	−0.712932	+	0.701233i	$0.752633\pi$
$4$		0			0
$5$	−81.3880	+	140.968i	−0.0582365	+	0.100869i	−0.893674	−	0.448717i	$-0.851881\pi$
$5$	−81.3880	+	140.968i	−0.0582365	+	0.100869i	0.835437	+	0.549586i	$0.185214\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	7364.96	−	12756.5i	0.374179	−	0.648097i
$10$		0			0
$11$	−45434.4	−	78694.7i	−0.935659	−	1.62061i	−0.773454	−	0.633852i	$-0.781473\pi$
$11$	−45434.4	−	78694.7i	−0.935659	−	1.62061i	−0.162205	−	0.986757i	$-0.551860\pi$
$12$		0			0
$13$	−167897.			−1.63041			−0.815206	−	0.579171i	$-0.803377\pi$
$13$	−167897.			−1.63041			−0.815206	+	0.579171i	$0.803377\pi$
$14$		0			0
$15$	−11455.9			−0.0584275
$16$		0			0
$17$	−4913.47	−	8510.38i	−0.0142682	−	0.0247132i	0.858803	−	0.512306i	$-0.171209\pi$
$17$	−4913.47	−	8510.38i	−0.0142682	−	0.0247132i	−0.873071	+	0.487593i	$0.837875\pi$
$18$		0			0
$19$	−237764.	+	411820.i	−0.418558	+	0.724963i	−0.995795	−	0.0916137i	$-0.970798\pi$
$19$	−237764.	+	411820.i	−0.418558	+	0.724963i	0.577237	+	0.816577i	$0.304131\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	110522.	−	191430.i	0.0823519	−	0.142638i	−0.821908	−	0.569621i	$-0.807090\pi$
$23$	110522.	−	191430.i	0.0823519	−	0.142638i	0.904260	+	0.426983i	$0.140424\pi$
$24$		0			0
$25$	963314.	+	1.66851e6i	0.493217	+	0.854277i
$26$		0			0
$27$	2.42191e6			0.877045
$28$		0			0
$29$	820028.			0.215297			0.107648	−	0.994189i	$-0.465668\pi$
$29$	820028.			0.215297			0.107648	+	0.994189i	$0.465668\pi$
$30$		0			0
$31$	1.41587e6	+	2.45236e6i	0.275357	+	0.476932i	0.970225	−	0.242205i	$-0.0778707\pi$
$31$	1.41587e6	+	2.45236e6i	0.275357	+	0.476932i	−0.694868	+	0.719137i	$0.744537\pi$
$32$		0			0
$33$	3.19758e6	−	5.53838e6i	0.469363	−	0.812961i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.35653e6	−	2.34957e6i	0.118993	−	0.206102i	−0.800376	−	0.599498i	$-0.795367\pi$
$37$	1.35653e6	−	2.34957e6i	0.118993	−	0.206102i	0.919369	+	0.393397i	$0.128700\pi$
$38$		0			0
$39$	−5.90813e6	−	1.02332e7i	−0.408940	−	0.708304i
$40$		0			0
$41$	−1.90289e7			−1.05169			−0.525845	−	0.850581i	$-0.676251\pi$
$41$	−1.90289e7			−1.05169			−0.525845	+	0.850581i	$0.676251\pi$
$42$		0			0
$43$	2.58212e7			1.15178			0.575889	−	0.817528i	$-0.304656\pi$
$43$	2.58212e7			1.15178			0.575889	+	0.817528i	$0.304656\pi$
$44$		0			0
$45$	1.19884e6	+	2.07645e6i	0.0435818	+	0.0754858i
$46$		0			0
$47$	−1.75526e7	+	3.04019e7i	−0.524687	+	0.908784i	0.474900	+	0.880040i	$0.342484\pi$
$47$	−1.75526e7	+	3.04019e7i	−0.524687	+	0.908784i	−0.999587	+	0.0287443i	$0.990849\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	345801.	−	598944.i	0.00715748	−	0.0123971i
$52$		0			0
$53$	4.10462e7	+	7.10941e7i	0.714549	+	1.23763i	0.963133	+	0.269024i	$0.0867012\pi$
$53$	4.10462e7	+	7.10941e7i	0.714549	+	1.23763i	−0.248585	+	0.968610i	$0.579965\pi$
$54$		0			0
$55$	1.47913e7			0.217958
$56$		0			0
$57$	−3.34668e7			−0.419930
$58$		0			0
$59$	6.69928e7	+	1.16035e8i	0.719770	+	1.24668i	0.961091	+	0.276233i	$0.0890861\pi$
$59$	6.69928e7	+	1.16035e8i	0.719770	+	1.24668i	−0.241321	+	0.970445i	$0.577581\pi$
$60$		0			0
$61$	5.08262e7	−	8.80335e7i	0.470006	−	0.814074i	−0.529406	−	0.848369i	$-0.677585\pi$
$61$	5.08262e7	−	8.80335e7i	0.470006	−	0.814074i	0.999412	+	0.0342948i	$0.0109185\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.36648e7	−	2.36681e7i	0.0949496	−	0.164457i
$66$		0			0
$67$	−7.40102e7	−	1.28190e8i	−0.448699	−	0.777170i	0.549603	−	0.835426i	$-0.314779\pi$
$67$	−7.40102e7	−	1.28190e8i	−0.448699	−	0.777170i	−0.998302	+	0.0582566i	$0.981446\pi$
$68$		0			0
$69$	1.55567e7			0.0826219
$70$		0			0
$71$	1.94170e8			0.906816			0.453408	−	0.891303i	$-0.350208\pi$
$71$	1.94170e8			0.906816			0.453408	+	0.891303i	$0.350208\pi$
$72$		0			0
$73$	−3.10493e7	−	5.37790e7i	−0.127967	−	0.221646i	0.794922	−	0.606712i	$-0.207512\pi$
$73$	−3.10493e7	−	5.37790e7i	−0.127967	−	0.221646i	−0.922889	+	0.385066i	$0.874179\pi$
$74$		0			0
$75$	−6.77962e7	+	1.17426e8i	−0.247417	+	0.428539i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.00722e8	+	3.47660e8i	−0.579793	+	1.00423i	0.415710	+	0.909497i	$0.363533\pi$
$79$	−2.00722e8	+	3.47660e8i	−0.579793	+	1.00423i	−0.995503	+	0.0947332i	$0.969800\pi$
$80$		0			0
$81$	−5.97398e7	−	1.03472e8i	−0.154199	−	0.267080i
$82$		0			0
$83$	−1.49637e8			−0.346088			−0.173044	−	0.984914i	$-0.555360\pi$
$83$	−1.49637e8			−0.346088			−0.173044	+	0.984914i	$0.555360\pi$
$84$		0			0
$85$	1.59959e6			0.00332372
$86$		0			0
$87$	2.88560e7	+	4.99801e7i	0.0540007	+	0.0935320i
$88$		0			0
$89$	−3.27085e8	+	5.66527e8i	−0.552593	+	0.957119i	0.445494	+	0.895285i	$0.353028\pi$
$89$	−3.27085e8	+	5.66527e8i	−0.552593	+	0.957119i	−0.998086	+	0.0618336i	$0.980305\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.96462e7	+	1.72592e8i	−0.138130	+	0.239248i
$94$		0			0
$95$	−3.87023e7	−	6.70344e7i	−0.0487507	−	0.0844386i
$96$		0			0
$97$	1.51683e9			1.73966			0.869830	−	0.493352i	$-0.164229\pi$
$97$	1.51683e9			1.73966			0.869830	+	0.493352i	$0.164229\pi$
$98$		0			0
$99$	−1.33849e9			−1.40042
$100$		0			0
$101$	8.29097e8	+	1.43604e9i	0.792792	+	1.37316i	0.924232	+	0.381831i	$0.124706\pi$
$101$	8.29097e8	+	1.43604e9i	0.792792	+	1.37316i	−0.131441	+	0.991324i	$0.541960\pi$
$102$		0			0
$103$	2.62915e8	−	4.55382e8i	0.230169	−	0.398665i	−0.727688	−	0.685908i	$-0.759405\pi$
$103$	2.62915e8	−	4.55382e8i	0.230169	−	0.398665i	0.957858	+	0.287243i	$0.0927386\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.63007e8	+	4.55542e8i	−0.193973	+	0.335971i	−0.946563	−	0.322518i	$-0.895471\pi$
$107$	−2.63007e8	+	4.55542e8i	−0.193973	+	0.335971i	0.752590	+	0.658489i	$0.228804\pi$
$108$		0			0
$109$	−9.93973e8	−	1.72161e9i	−0.674459	−	1.16820i	−0.976627	−	0.214942i	$-0.931044\pi$
$109$	−9.93973e8	−	1.72161e9i	−0.674459	−	1.16820i	0.302168	−	0.953255i	$-0.402290\pi$
$110$		0			0
$111$	1.90940e8			0.119383
$112$		0			0
$113$	1.09466e9			0.631577			0.315789	−	0.948830i	$-0.397731\pi$
$113$	1.09466e9			0.631577			0.315789	+	0.948830i	$0.397731\pi$
$114$		0			0
$115$	1.79903e7	+	3.11602e7i	0.00959178	+	0.0166134i
$116$		0			0
$117$	−1.23655e9	+	2.14178e9i	−0.610066	+	1.05667i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.94959e9	+	5.10885e9i	−1.25092	+	2.16665i
$122$		0			0
$123$	−6.69610e8	−	1.15980e9i	−0.263784	−	0.456888i
$124$		0			0
$125$	−6.31531e8			−0.231366
$126$		0			0
$127$	3.18245e9			1.08554			0.542769	−	0.839882i	$-0.317376\pi$
$127$	3.18245e9			1.08554			0.542769	+	0.839882i	$0.317376\pi$
$128$		0			0
$129$	9.08624e8	+	1.57378e9i	0.288889	+	0.500370i
$130$		0			0
$131$	−1.23548e9	+	2.13991e9i	−0.366534	+	0.634856i	−0.989021	−	0.147774i	$-0.952789\pi$
$131$	−1.23548e9	+	2.13991e9i	−0.366534	+	0.634856i	0.622487	+	0.782630i	$0.286122\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.97115e8	+	3.41413e8i	−0.0510761	+	0.0884663i
$136$		0			0
$137$	−5.13765e8	−	8.89867e8i	−0.124601	−	0.215816i	0.796976	−	0.604011i	$-0.206432\pi$
$137$	−5.13765e8	−	8.89867e8i	−0.124601	−	0.215816i	−0.921577	+	0.388196i	$0.873098\pi$
$138$		0			0
$139$	6.01240e9			1.36610			0.683048	−	0.730373i	$-0.260654\pi$
$139$	6.01240e9			1.36610			0.683048	+	0.730373i	$0.260654\pi$
$140$		0			0
$141$	−2.47063e9			−0.526407
$142$		0			0
$143$	7.62829e9	+	1.32126e10i	1.52551	+	2.64226i
$144$		0			0
$145$	−6.67405e7	+	1.15598e8i	−0.0125381	+	0.0217167i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.50531e9	+	2.60727e9i	−0.250200	+	0.433359i	−0.963581	−	0.267418i	$-0.913830\pi$
$149$	−1.50531e9	+	2.60727e9i	−0.250200	+	0.433359i	0.713381	+	0.700777i	$0.247163\pi$
$150$		0			0
$151$	−2.29534e9	−	3.97565e9i	−0.359295	−	0.622317i	0.628548	−	0.777771i	$-0.283649\pi$
$151$	−2.29534e9	−	3.97565e9i	−0.359295	−	0.622317i	−0.987843	+	0.155453i	$0.950316\pi$
$152$		0			0
$153$	−1.44750e8			−0.0213554
$154$		0			0
$155$	−4.60939e8			−0.0641433
$156$		0			0
$157$	4.14966e9	+	7.18742e9i	0.545085	+	0.944115i	0.998602	+	0.0528670i	$0.0168359\pi$
$157$	4.14966e9	+	7.18742e9i	0.545085	+	0.944115i	−0.453517	+	0.891248i	$0.649831\pi$
$158$		0			0
$159$	−2.88875e9	+	5.00347e9i	−0.358446	+	0.620846i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.15907e9	+	1.06678e10i	−0.683393	+	1.18367i	0.290546	+	0.956861i	$0.406163\pi$
$163$	−6.15907e9	+	1.06678e10i	−0.683393	+	1.18367i	−0.973939	+	0.226811i	$0.927170\pi$
$164$		0			0
$165$	5.20490e8	+	9.01515e8i	0.0546682	+	0.0946881i
$166$		0			0
$167$	1.95830e9			0.194830			0.0974150	−	0.995244i	$-0.468943\pi$
$167$	1.95830e9			0.194830			0.0974150	+	0.995244i	$0.468943\pi$
$168$		0			0
$169$	1.75849e10			1.65825
$170$		0			0
$171$	3.50225e9	+	6.06607e9i	0.313231	+	0.542532i
$172$		0			0
$173$	−7.51032e9	+	1.30083e10i	−0.637457	+	1.10411i	0.348531	+	0.937297i	$0.386680\pi$
$173$	−7.51032e9	+	1.30083e10i	−0.637457	+	1.10411i	−0.985989	+	0.166811i	$0.946653\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.71482e9	+	8.16631e9i	−0.361065	+	0.625383i
$178$		0			0
$179$	−1.06544e10	−	1.84539e10i	−0.775692	−	1.34354i	−0.934405	−	0.356213i	$-0.884068\pi$
$179$	−1.06544e10	−	1.84539e10i	−0.775692	−	1.34354i	0.158713	−	0.987325i	$-0.449266\pi$
$180$		0			0
$181$	6.65134e9			0.460634			0.230317	−	0.973116i	$-0.426024\pi$
$181$	6.65134e9			0.460634			0.230317	+	0.973116i	$0.426024\pi$
$182$		0			0
$183$	7.15409e9			0.471547
$184$		0			0
$185$	2.20810e8	+	3.82454e8i	0.0138595	+	0.0240053i
$186$		0			0
$187$	−4.46481e8	+	7.73328e8i	−0.0267003	+	0.0462463i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.91524e9	+	1.54417e10i	−0.484711	+	0.839544i	−0.999846	−	0.0175649i	$-0.994409\pi$
$191$	−8.91524e9	+	1.54417e10i	−0.484711	+	0.839544i	0.515134	+	0.857109i	$0.327742\pi$
$192$		0			0
$193$	−2.20117e8	−	3.81254e8i	−0.0114195	−	0.0197791i	0.860259	−	0.509857i	$-0.170302\pi$
$193$	−2.20117e8	−	3.81254e8i	−0.0114195	−	0.0197791i	−0.871679	+	0.490078i	$0.836968\pi$
$194$		0			0
$195$	1.92340e9			0.0952609
$196$		0			0
$197$	−2.01458e10			−0.952988			−0.476494	−	0.879178i	$-0.658093\pi$
$197$	−2.01458e10			−0.952988			−0.476494	+	0.879178i	$0.658093\pi$
$198$		0			0
$199$	1.61733e10	+	2.80130e10i	0.731071	+	1.26625i	0.956426	+	0.291975i	$0.0943125\pi$
$199$	1.61733e10	+	2.80130e10i	0.731071	+	1.26625i	−0.225355	+	0.974277i	$0.572354\pi$
$200$		0			0
$201$	5.20870e9	−	9.02173e9i	0.225085	−	0.389859i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.54873e9	−	2.68248e9i	0.0612467	−	0.106082i
$206$		0			0
$207$	−1.62798e9	−	2.81975e9i	−0.0616287	−	0.106744i
$208$		0			0
$209$	4.32107e10			1.56651
$210$		0			0
$211$	−3.85763e10			−1.33983			−0.669915	−	0.742438i	$-0.733670\pi$
$211$	−3.85763e10			−1.33983			−0.669915	+	0.742438i	$0.733670\pi$
$212$		0			0
$213$	6.83265e9	+	1.18345e10i	0.227447	+	0.393950i
$214$		0			0
$215$	−2.10154e9	+	3.63997e9i	−0.0670755	+	0.116178i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.18519e9	−	3.78486e9i	0.0641935	−	0.111186i
$220$		0			0
$221$	8.24957e8	+	1.42887e9i	0.0232630	+	0.0402927i
$222$		0			0
$223$	−3.40626e10			−0.922371			−0.461186	−	0.887304i	$-0.652576\pi$
$223$	−3.40626e10			−0.922371			−0.461186	+	0.887304i	$0.652576\pi$
$224$		0			0
$225$	2.83791e10			0.738206
$226$		0			0
$227$	−3.46901e10	−	6.00851e10i	−0.867141	−	1.50193i	−0.864905	−	0.501935i	$-0.832622\pi$
$227$	−3.46901e10	−	6.00851e10i	−0.867141	−	1.50193i	−0.00223565	−	0.999998i	$-0.500712\pi$
$228$		0			0
$229$	−3.53379e10	+	6.12070e10i	−0.849142	+	1.47076i	0.0328320	+	0.999461i	$0.489547\pi$
$229$	−3.53379e10	+	6.12070e10i	−0.849142	+	1.47076i	−0.881975	+	0.471297i	$0.843786\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.66624e10	+	4.61806e10i	−0.592649	+	1.02650i	0.401225	+	0.915979i	$0.368584\pi$
$233$	−2.66624e10	+	4.61806e10i	−0.592649	+	1.02650i	−0.993874	+	0.110518i	$0.964749\pi$
$234$		0			0
$235$	−2.85714e9	−	4.94870e9i	−0.0611119	−	0.105849i
$236$		0			0
$237$	−2.82528e10			−0.581694
$238$		0			0
$239$	2.61227e10			0.517878			0.258939	−	0.965894i	$-0.416627\pi$
$239$	2.61227e10			0.517878			0.258939	+	0.965894i	$0.416627\pi$
$240$		0			0
$241$	−1.21886e10	−	2.11112e10i	−0.232743	−	0.403122i	0.725872	−	0.687830i	$-0.241437\pi$
$241$	−1.21886e10	−	2.11112e10i	−0.232743	−	0.403122i	−0.958614	+	0.284708i	$0.908103\pi$
$242$		0			0
$243$	2.80396e10	−	4.85661e10i	0.515875	−	0.893521i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.99199e10	−	6.91432e10i	0.682422	−	1.18199i
$248$		0			0
$249$	−5.26557e9	−	9.12024e9i	−0.0868058	−	0.150352i
$250$		0			0
$251$	6.65520e9			0.105835			0.0529175	−	0.998599i	$-0.483148\pi$
$251$	6.65520e9			0.105835			0.0529175	+	0.998599i	$0.483148\pi$
$252$		0			0
$253$	−2.00860e10			−0.308213
$254$		0			0
$255$	5.62880e7	+	9.74938e7i	0.000833653	+	0.00144393i
$256$		0			0
$257$	6.10651e10	−	1.05768e11i	0.873160	−	1.51236i	0.0144509	−	0.999896i	$-0.495400\pi$
$257$	6.10651e10	−	1.05768e11i	0.873160	−	1.51236i	0.858710	−	0.512463i	$-0.171267\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	6.03948e9	−	1.04607e10i	0.0805596	−	0.139533i
$262$		0			0
$263$	1.56994e10	+	2.71922e10i	0.202340	+	0.350463i	0.949282	−	0.314426i	$-0.101812\pi$
$263$	1.56994e10	+	2.71922e10i	0.202340	+	0.350463i	−0.746942	+	0.664889i	$0.768479\pi$
$264$		0			0
$265$	−1.33627e10			−0.166451
$266$		0			0
$267$	−4.60392e10			−0.554405
$268$		0			0
$269$	−6.34832e9	−	1.09956e10i	−0.0739220	−	0.128037i	0.826695	−	0.562650i	$-0.190218\pi$
$269$	−6.34832e9	−	1.09956e10i	−0.0739220	−	0.128037i	−0.900617	+	0.434614i	$0.856885\pi$
$270$		0			0
$271$	−3.21118e9	+	5.56193e9i	−0.0361662	+	0.0626417i	−0.883542	−	0.468352i	$-0.844848\pi$
$271$	−3.21118e9	+	5.56193e9i	−0.0361662	+	0.0626417i	0.847376	+	0.530994i	$0.178181\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.75352e10	−	1.51615e11i	0.922966	−	1.59862i
$276$		0			0
$277$	7.71451e10	+	1.33619e11i	0.787317	+	1.36367i	0.927605	+	0.373562i	$0.121864\pi$
$277$	7.71451e10	+	1.33619e11i	0.787317	+	1.36367i	−0.140288	+	0.990111i	$0.544803\pi$
$278$		0			0
$279$	4.17113e10			0.412131
$280$		0			0
$281$	6.22022e10			0.595151			0.297576	−	0.954698i	$-0.403822\pi$
$281$	6.22022e10			0.595151			0.297576	+	0.954698i	$0.403822\pi$
$282$		0			0
$283$	−2.60820e10	−	4.51753e10i	−0.241714	−	0.418661i	0.719489	−	0.694504i	$-0.244376\pi$
$283$	−2.60820e10	−	4.51753e10i	−0.241714	−	0.418661i	−0.961203	+	0.275843i	$0.911043\pi$
$284$		0			0
$285$	2.72379e9	−	4.71775e9i	0.0244553	−	0.0423577i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.92457e10	−	1.02616e11i	0.499593	−	0.865320i
$290$		0			0
$291$	5.33758e10	+	9.24496e10i	0.436341	+	0.755765i
$292$		0			0
$293$	−1.98645e11			−1.57461			−0.787307	−	0.616561i	$-0.788525\pi$
$293$	−1.98645e11			−1.57461			−0.787307	+	0.616561i	$0.788525\pi$
$294$		0			0
$295$	−2.18096e10			−0.167668
$296$		0			0
$297$	−1.10038e11	−	1.90592e11i	−0.820615	−	1.42135i
$298$		0			0
$299$	−1.85563e10	+	3.21405e10i	−0.134268	+	0.232558i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−5.83502e10	+	1.01066e11i	−0.397695	+	0.688829i
$304$		0			0
$305$	8.27328e9	+	1.43297e10i	0.0547430	+	0.0948177i
$306$		0			0
$307$	−1.72725e11			−1.10977			−0.554885	−	0.831927i	$-0.687238\pi$
$307$	−1.72725e11			−1.10977			−0.554885	+	0.831927i	$0.687238\pi$
$308$		0			0
$309$	3.70069e10			0.230924
$310$		0			0
$311$	−6.52862e9	−	1.13079e10i	−0.0395731	−	0.0685426i	0.845560	−	0.533880i	$-0.179266\pi$
$311$	−6.52862e9	−	1.13079e10i	−0.0395731	−	0.0685426i	−0.885134	+	0.465337i	$0.845933\pi$
$312$		0			0
$313$	8.42354e10	−	1.45900e11i	0.496072	−	0.859223i	−0.503917	−	0.863752i	$-0.668108\pi$
$313$	8.42354e10	−	1.45900e11i	0.496072	−	0.859223i	0.999990	+	0.00452927i	$0.00144171\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.62020e11	−	2.80626e11i	0.901157	−	1.56085i	0.0751637	−	0.997171i	$-0.476052\pi$
$317$	1.62020e11	−	2.80626e11i	0.901157	−	1.56085i	0.825994	−	0.563679i	$-0.190615\pi$
$318$		0			0
$319$	−3.72575e10	−	6.45319e10i	−0.201445	−	0.348912i
$320$		0			0
$321$	−3.70199e10			−0.194609
$322$		0			0
$323$	4.67299e9			0.0238882
$324$		0			0
$325$	−1.61738e11	−	2.80138e11i	−0.804147	−	1.39282i
$326$		0			0
$327$	6.99539e10	−	1.21164e11i	0.338335	−	0.586014i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.12778e10	−	7.14952e10i	0.189012	−	0.327379i	−0.755909	−	0.654677i	$-0.772805\pi$
$331$	4.12778e10	−	7.14952e10i	0.189012	−	0.327379i	0.944921	+	0.327298i	$0.106138\pi$
$332$		0			0
$333$	−1.99816e10	−	3.46091e10i	−0.0890492	−	0.154238i
$334$		0			0
$335$	2.40942e10			0.104523
$336$		0			0
$337$	−5.14965e10			−0.217492			−0.108746	−	0.994070i	$-0.534683\pi$
$337$	−5.14965e10			−0.217492			−0.108746	+	0.994070i	$0.534683\pi$
$338$		0			0
$339$	3.85201e10	+	6.67187e10i	0.158412	+	0.274378i
$340$		0			0
$341$	1.28658e11	−	2.22843e11i	0.515280	−	0.892491i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.26613e9	+	2.19299e9i	−0.00481161	+	0.00833396i
$346$		0			0
$347$	1.99939e11	+	3.46305e11i	0.740312	+	1.28226i	0.952353	+	0.304998i	$0.0986557\pi$
$347$	1.99939e11	+	3.46305e11i	0.740312	+	1.28226i	−0.212041	+	0.977261i	$0.568011\pi$
$348$		0			0
$349$	5.32897e11			1.92278			0.961388	−	0.275195i	$-0.0887426\pi$
$349$	5.32897e11			1.92278			0.961388	+	0.275195i	$0.0887426\pi$
$350$		0			0
$351$	−4.06632e11			−1.42995
$352$		0			0
$353$	−1.41693e10	−	2.45420e10i	−0.0485694	−	0.0841246i	0.840719	−	0.541472i	$-0.182133\pi$
$353$	−1.41693e10	−	2.45420e10i	−0.0485694	−	0.0841246i	−0.889288	+	0.457348i	$0.848800\pi$
$354$		0			0
$355$	−1.58031e10	+	2.73718e10i	−0.0528098	+	0.0914693i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.66155e10	−	4.60993e10i	0.0845686	−	0.146477i	−0.820639	−	0.571447i	$-0.806382\pi$
$359$	2.66155e10	−	4.60993e10i	0.0845686	−	0.146477i	0.905207	+	0.424970i	$0.139715\pi$
$360$		0			0
$361$	4.82803e10	+	8.36239e10i	0.149619	+	0.259148i
$362$		0			0
$363$	−4.15173e11			−1.25502
$364$		0			0
$365$	1.01082e10			0.0298095
$366$		0			0
$367$	−2.58064e11	−	4.46980e11i	−0.742557	−	1.28615i	−0.951327	−	0.308182i	$-0.900279\pi$
$367$	−2.58064e11	−	4.46980e11i	−0.742557	−	1.28615i	0.208770	−	0.977965i	$-0.433054\pi$
$368$		0			0
$369$	−1.40148e11	+	2.42743e11i	−0.393520	+	0.681597i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.75926e11	+	3.04712e11i	−0.470586	+	0.815079i	−0.999434	−	0.0336374i	$-0.989291\pi$
$373$	−1.75926e11	+	3.04712e11i	−0.470586	+	0.815079i	0.528848	+	0.848717i	$0.322624\pi$
$374$		0			0
$375$	−2.22230e10	−	3.84913e10i	−0.0580312	−	0.100513i
$376$		0			0
$377$	−1.37680e11			−0.351023
$378$		0			0
$379$	3.25484e11			0.810313			0.405157	−	0.914247i	$-0.367217\pi$
$379$	3.25484e11			0.810313			0.405157	+	0.914247i	$0.367217\pi$
$380$		0			0
$381$	1.11987e11	+	1.93968e11i	0.272274	+	0.471593i
$382$		0			0
$383$	−3.82566e11	+	6.62624e11i	−0.908473	+	1.57352i	−0.0922870	+	0.995732i	$0.529418\pi$
$383$	−3.82566e11	+	6.62624e11i	−0.908473	+	1.57352i	−0.816186	+	0.577789i	$0.803916\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.90172e11	−	3.29388e11i	0.430971	−	0.746464i
$388$		0			0
$389$	−3.92948e11	−	6.80606e11i	−0.870085	−	1.50703i	−0.861908	−	0.507065i	$-0.830730\pi$
$389$	−3.92948e11	−	6.80606e11i	−0.870085	−	1.50703i	−0.00817710	−	0.999967i	$-0.502603\pi$
$390$		0			0
$391$	−2.17219e9			−0.00470005
$392$		0			0
$393$	−1.73901e11			−0.367736
$394$		0			0
$395$	−3.26727e10	−	5.65908e10i	−0.0675302	−	0.116966i
$396$		0			0
$397$	3.69607e11	−	6.40178e11i	0.746763	−	1.29343i	−0.202603	−	0.979261i	$-0.564940\pi$
$397$	3.69607e11	−	6.40178e11i	0.746763	−	1.29343i	0.949366	−	0.314171i	$-0.101727\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.64793e11	+	2.85430e11i	−0.318266	+	0.551252i	−0.980126	−	0.198375i	$-0.936434\pi$
$401$	−1.64793e11	+	2.85430e11i	−0.318266	+	0.551252i	0.661861	+	0.749627i	$0.269767\pi$
$402$		0			0
$403$	−2.37720e11	−	4.11743e11i	−0.448945	−	0.777596i
$404$		0			0
$405$	1.94484e10			0.0359200
$406$		0			0
$407$	−2.46532e11			−0.445347
$408$		0			0
$409$	4.57022e11	+	7.91584e11i	0.807573	+	1.39876i	0.914540	+	0.404495i	$0.132553\pi$
$409$	4.57022e11	+	7.91584e11i	0.807573	+	1.39876i	−0.106967	+	0.994263i	$0.534114\pi$
$410$		0			0
$411$	3.61578e10	−	6.26271e10i	0.0625048	−	0.108262i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.21786e10	−	2.10940e10i	0.0201550	−	0.0349094i
$416$		0			0
$417$	2.11571e11	+	3.66451e11i	0.342644	+	0.593477i
$418$		0			0
$419$	6.65088e11			1.05418			0.527092	−	0.849808i	$-0.323282\pi$
$419$	6.65088e11			1.05418			0.527092	+	0.849808i	$0.323282\pi$
$420$		0			0
$421$	8.13818e11			1.26258			0.631288	−	0.775548i	$-0.282527\pi$
$421$	8.13818e11			1.26258			0.631288	+	0.775548i	$0.282527\pi$
$422$		0			0
$423$	2.58548e11	+	4.47818e11i	0.392653	+	0.680096i
$424$		0			0
$425$	9.46644e9	−	1.63964e10i	0.0140746	−	0.0243779i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−5.36864e11	+	9.29876e11i	−0.765256	+	1.32546i
$430$		0			0
$431$	2.80790e11	+	4.86342e11i	0.391953	+	0.678882i	0.992707	−	0.120552i	$-0.0384664\pi$
$431$	2.80790e11	+	4.86342e11i	0.391953	+	0.678882i	−0.600755	+	0.799434i	$0.705133\pi$
$432$		0			0
$433$	5.13223e11			0.701633			0.350817	−	0.936444i	$-0.385904\pi$
$433$	5.13223e11			0.701633			0.350817	+	0.936444i	$0.385904\pi$
$434$		0			0
$435$	−9.39413e9			−0.0125793
$436$		0			0
$437$	5.25564e10	+	9.10303e10i	0.0689380	+	0.119404i
$438$		0			0
$439$	−5.17800e11	+	8.96855e11i	−0.665382	+	1.15248i	0.313799	+	0.949489i	$0.398398\pi$
$439$	−5.17800e11	+	8.96855e11i	−0.665382	+	1.15248i	−0.979181	+	0.202987i	$0.934935\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.28658e11	+	5.69252e11i	−0.405441	+	0.702244i	−0.994373	−	0.105939i	$-0.966215\pi$
$443$	−3.28658e11	+	5.69252e11i	−0.405441	+	0.702244i	0.588932	+	0.808183i	$0.299549\pi$
$444$		0			0
$445$	−5.32415e10	−	9.22171e10i	−0.0643622	−	0.111479i
$446$		0			0
$447$	−2.11881e11			−0.251020
$448$		0			0
$449$	2.82701e11			0.328260			0.164130	−	0.986439i	$-0.447518\pi$
$449$	2.82701e11			0.328260			0.164130	+	0.986439i	$0.447518\pi$
$450$		0			0
$451$	8.64569e11	+	1.49748e12i	0.984023	+	1.70438i
$452$		0			0
$453$	1.61542e11	−	2.79798e11i	0.180237	−	0.312179i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.99859e10	−	5.19372e10i	0.0321584	−	0.0557000i	−0.849498	−	0.527591i	$-0.823095\pi$
$457$	2.99859e10	−	5.19372e10i	0.0321584	−	0.0557000i	0.881657	+	0.471891i	$0.156429\pi$
$458$		0			0
$459$	−1.19000e10	−	2.06114e10i	−0.0125138	−	0.0216746i
$460$		0			0
$461$	5.38434e11			0.555237			0.277618	−	0.960691i	$-0.410455\pi$
$461$	5.38434e11			0.555237			0.277618	+	0.960691i	$0.410455\pi$
$462$		0			0
$463$	4.90683e10			0.0496234			0.0248117	−	0.999692i	$-0.492101\pi$
$463$	4.90683e10			0.0496234			0.0248117	+	0.999692i	$0.492101\pi$
$464$		0			0
$465$	−1.62200e10	−	2.80939e10i	−0.0160884	−	0.0278659i
$466$		0			0
$467$	−7.57287e11	+	1.31166e12i	−0.736774	+	1.27613i	0.217166	+	0.976135i	$0.430319\pi$
$467$	−7.57287e11	+	1.31166e12i	−0.736774	+	1.27613i	−0.953941	+	0.299996i	$0.903015\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.92045e11	+	5.05837e11i	−0.273436	+	0.473605i
$472$		0			0
$473$	−1.17317e12	−	2.03199e12i	−1.07767	−	1.86658i
$474$		0			0
$475$	−9.16167e11			−0.825759
$476$		0			0
$477$	1.20922e12			1.06948
$478$		0			0
$479$	7.20659e11	+	1.24822e12i	0.625490	+	1.08338i	0.988446	+	0.151574i	$0.0484341\pi$
$479$	7.20659e11	+	1.24822e12i	0.625490	+	1.08338i	−0.362956	+	0.931806i	$0.618233\pi$
$480$		0			0
$481$	−2.27757e11	+	3.94486e11i	−0.194007	+	0.336031i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.23452e11	+	2.13825e11i	−0.101312	+	0.175477i
$486$		0			0
$487$	−3.76261e11	−	6.51703e11i	−0.303116	−	0.525012i	0.673724	−	0.738983i	$-0.264694\pi$
$487$	−3.76261e11	−	6.51703e11i	−0.303116	−	0.525012i	−0.976840	+	0.213971i	$0.931360\pi$
$488$		0			0
$489$	−8.66926e11			−0.685634
$490$		0			0
$491$	−1.05719e12			−0.820896			−0.410448	−	0.911884i	$-0.634628\pi$
$491$	−1.05719e12			−0.820896			−0.410448	+	0.911884i	$0.634628\pi$
$492$		0			0
$493$	−4.02919e9	−	6.97876e9i	−0.00307189	−	0.00532068i
$494$		0			0
$495$	1.08937e11	−	1.88685e11i	0.0815553	−	0.141258i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.55433e11	+	7.88833e11i	−0.328830	+	0.569551i	−0.982280	−	0.187419i	$-0.939988\pi$
$499$	−4.55433e11	+	7.88833e11i	−0.328830	+	0.569551i	0.653450	+	0.756970i	$0.273321\pi$
$500$		0			0
$501$	6.89108e10	+	1.19357e11i	0.0488672	+	0.0846404i
$502$		0			0
$503$	7.10909e11			0.495174			0.247587	−	0.968866i	$-0.420362\pi$
$503$	7.10909e11			0.495174			0.247587	+	0.968866i	$0.420362\pi$
$504$		0			0
$505$	−2.69914e11			−0.184678
$506$		0			0
$507$	6.18794e11	+	1.07178e12i	0.415921	+	0.720396i
$508$		0			0
$509$	6.10984e11	−	1.05826e12i	0.403459	−	0.698812i	−0.590681	−	0.806905i	$-0.701141\pi$
$509$	6.10984e11	−	1.05826e12i	0.403459	−	0.698812i	0.994141	+	0.108093i	$0.0344744\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−5.75845e11	+	9.97392e11i	−0.367094	+	0.635825i
$514$		0			0
$515$	4.27962e10	+	7.41253e10i	0.0268085	+	0.0464338i
$516$		0			0
$517$	3.18996e12			1.96371
$518$		0			0
$519$	−1.05712e12			−0.639547
$520$		0			0
$521$	−3.22589e11	−	5.58740e11i	−0.191814	−	0.332231i	0.754038	−	0.656831i	$-0.228104\pi$
$521$	−3.22589e11	−	5.58740e11i	−0.191814	−	0.332231i	−0.945851	+	0.324600i	$0.894770\pi$
$522$		0			0
$523$	−1.28063e12	+	2.21812e12i	−0.748456	+	1.29636i	0.200106	+	0.979774i	$0.435871\pi$
$523$	−1.28063e12	+	2.21812e12i	−0.748456	+	1.29636i	−0.948563	+	0.316590i	$0.897462\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.39137e10	−	2.40992e10i	0.00785768	−	0.0136099i
$528$		0			0
$529$	8.76146e11	+	1.51753e12i	0.486436	+	0.842532i
$530$		0			0
$531$	1.97360e12			1.07729
$532$		0			0
$533$	3.19490e12			1.71469
$534$		0			0
$535$	−4.28113e10	−	7.41514e10i	−0.0225926	−	0.0391316i
$536$		0			0
$537$	7.49834e11	−	1.29875e12i	0.389118	−	0.673971i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	3.81287e10	−	6.60408e10i	0.0191366	−	0.0331455i	−0.856299	−	0.516481i	$-0.827242\pi$
$541$	3.81287e10	−	6.60408e10i	0.0191366	−	0.0331455i	0.875435	+	0.483336i	$0.160575\pi$
$542$		0			0
$543$	2.34054e11	+	4.05394e11i	0.115536	+	0.200114i
$544$		0			0
$545$	3.23590e11			0.157113
$546$		0			0
$547$	−3.32708e12			−1.58899			−0.794494	−	0.607272i	$-0.792264\pi$
$547$	−3.32708e12			−1.58899			−0.794494	+	0.607272i	$0.792264\pi$
$548$		0			0
$549$	−7.48666e11	−	1.29673e12i	−0.351733	−	0.609219i
$550$		0			0
$551$	−1.94973e11	+	3.37704e11i	−0.0901142	+	0.156082i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.55402e10	+	2.69164e10i	−0.00695245	+	0.0120420i
$556$		0			0
$557$	−8.26743e11	−	1.43196e12i	−0.363933	−	0.630351i	0.624671	−	0.780888i	$-0.285233\pi$
$557$	−8.26743e11	−	1.43196e12i	−0.363933	−	0.630351i	−0.988604	+	0.150537i	$0.951900\pi$
$558$		0			0
$559$	−4.33530e12			−1.87787
$560$		0			0
$561$	−6.28450e10			−0.0267878
$562$		0			0
$563$	−7.21635e11	−	1.24991e12i	−0.302712	−	0.524313i	0.674037	−	0.738697i	$-0.264559\pi$
$563$	−7.21635e11	−	1.24991e12i	−0.302712	−	0.524313i	−0.976749	+	0.214385i	$0.931225\pi$
$564$		0			0
$565$	−8.90923e10	+	1.54312e11i	−0.0367809	+	0.0637063i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.83240e11	+	1.70302e12i	−0.393237	+	0.681107i	−0.992874	−	0.119165i	$-0.961978\pi$
$569$	−9.83240e11	+	1.70302e12i	−0.393237	+	0.681107i	0.599637	+	0.800272i	$0.295312\pi$
$570$		0			0
$571$	−1.77482e12	−	3.07408e12i	−0.698701	−	1.21019i	−0.968917	−	0.247386i	$-0.920428\pi$
$571$	−1.77482e12	−	3.07408e12i	−0.698701	−	1.21019i	0.270216	−	0.962800i	$-0.412905\pi$
$572$		0			0
$573$	−1.25488e12			−0.486300
$574$		0			0
$575$	4.25870e11			0.162469
$576$		0			0
$577$	1.65508e11	+	2.86669e11i	0.0621625	+	0.107669i	0.895432	−	0.445199i	$-0.146867\pi$
$577$	1.65508e11	+	2.86669e11i	0.0621625	+	0.107669i	−0.833269	+	0.552867i	$0.813534\pi$
$578$		0			0
$579$	1.54914e10	−	2.68319e10i	0.00572845	−	0.00992197i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.72982e12	−	6.46024e12i	1.33715	−	2.31601i
$584$		0			0
$585$	−2.01281e11	−	3.48630e11i	−0.0710563	−	0.123073i
$586$		0			0
$587$	−3.23387e12			−1.12422			−0.562109	−	0.827063i	$-0.690010\pi$
$587$	−3.23387e12			−1.12422			−0.562109	+	0.827063i	$0.690010\pi$
$588$		0			0
$589$	−1.34657e12			−0.461011
$590$		0			0
$591$	−7.08912e11	−	1.22787e12i	−0.239028	−	0.414009i
$592$		0			0
$593$	1.64086e12	−	2.84205e12i	0.544911	−	0.943814i	−0.453702	−	0.891154i	$-0.649897\pi$
$593$	1.64086e12	−	2.84205e12i	0.544911	−	0.943814i	0.998613	−	0.0526598i	$-0.0167699\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.13824e12	+	1.97150e12i	−0.366734	+	0.635202i
$598$		0			0
$599$	2.41478e12	+	4.18251e12i	0.766401	+	1.32745i	0.939503	+	0.342542i	$0.111288\pi$
$599$	2.41478e12	+	4.18251e12i	0.766401	+	1.32745i	−0.173101	+	0.984904i	$0.555379\pi$
$600$		0			0
$601$	2.74359e12			0.857797			0.428898	−	0.903353i	$-0.358902\pi$
$601$	2.74359e12			0.857797			0.428898	+	0.903353i	$0.358902\pi$
$602$		0			0
$603$	−2.18033e12			−0.671575
$604$		0			0
$605$	−4.80123e11	−	8.31598e11i	−0.145698	−	0.252356i
$606$		0			0
$607$	−2.94896e11	+	5.10775e11i	−0.0881698	+	0.152715i	−0.906738	−	0.421695i	$-0.861435\pi$
$607$	−2.94896e11	+	5.10775e11i	−0.0881698	+	0.152715i	0.818568	+	0.574410i	$0.194768\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.94702e12	−	5.10439e12i	0.855456	−	1.48169i
$612$		0			0
$613$	2.46640e12	+	4.27193e12i	0.705491	+	1.22195i	0.966514	+	0.256614i	$0.0826069\pi$
$613$	2.46640e12	+	4.27193e12i	0.705491	+	1.22195i	−0.261023	+	0.965333i	$0.584060\pi$
$614$		0			0
$615$	2.17993e11			0.0614475
$616$		0			0
$617$	4.74933e12			1.31932			0.659658	−	0.751566i	$-0.270701\pi$
$617$	4.74933e12			1.31932			0.659658	+	0.751566i	$0.270701\pi$
$618$		0			0
$619$	−1.77433e12	−	3.07324e12i	−0.485766	−	0.841372i	0.514100	−	0.857730i	$-0.328126\pi$
$619$	−1.77433e12	−	3.07324e12i	−0.485766	−	0.841372i	−0.999866	+	0.0163586i	$0.994793\pi$
$620$		0			0
$621$	2.67675e11	−	4.63627e11i	0.0722263	−	0.125100i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.83007e12	+	3.16978e12i	−0.479743	+	0.830939i
$626$		0			0
$627$	1.52054e12	+	2.63366e12i	0.392911	+	0.680542i
$628$		0			0
$629$	−2.66610e10			−0.00679124
$630$		0			0
$631$	1.34343e11			0.0337351			0.0168676	−	0.999858i	$-0.494631\pi$
$631$	1.34343e11			0.0337351			0.0168676	+	0.999858i	$0.494631\pi$
$632$		0			0
$633$	−1.35746e12	−	2.35120e12i	−0.336056	−	0.582066i
$634$		0			0
$635$	−2.59013e11	+	4.48624e11i	−0.0632179	+	0.109497i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.43005e12	−	2.47693e12i	0.339311	−	0.587705i
$640$		0			0
$641$	1.91377e12	+	3.31475e12i	0.447743	+	0.775514i	0.998239	−	0.0593244i	$-0.0188946\pi$
$641$	1.91377e12	+	3.31475e12i	0.447743	+	0.775514i	−0.550496	+	0.834838i	$0.685561\pi$
$642$		0			0
$643$	−1.30004e12			−0.299921			−0.149960	−	0.988692i	$-0.547915\pi$
$643$	−1.30004e12			−0.299921			−0.149960	+	0.988692i	$0.547915\pi$
$644$		0			0
$645$	−2.95804e11			−0.0672955
$646$		0			0
$647$	1.13102e12	+	1.95899e12i	0.253747	+	0.439503i	0.964554	−	0.263884i	$-0.0850035\pi$
$647$	1.13102e12	+	1.95899e12i	0.253747	+	0.439503i	−0.710807	+	0.703387i	$0.751670\pi$
$648$		0			0
$649$	6.08755e12	−	1.05439e13i	1.34692	−	2.33293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.02541e12	−	6.97222e12i	0.866365	−	1.50059i	0.000680147	−	1.00000i	$-0.499784\pi$
$653$	4.02541e12	−	6.97222e12i	0.866365	−	1.50059i	0.865685	−	0.500589i	$-0.166883\pi$
$654$		0			0
$655$	−2.01106e11	−	3.48326e11i	−0.0426913	−	0.0739436i
$656$		0			0
$657$	−9.14709e11			−0.191531
$658$		0			0
$659$	−3.50688e12			−0.724330			−0.362165	−	0.932114i	$-0.617962\pi$
$659$	−3.50688e12			−0.724330			−0.362165	+	0.932114i	$0.617962\pi$
$660$		0			0
$661$	−3.43112e12	−	5.94287e12i	−0.699084	−	1.21085i	−0.968784	−	0.247905i	$-0.920258\pi$
$661$	−3.43112e12	−	5.94287e12i	−0.699084	−	1.21085i	0.269701	−	0.962944i	$-0.413075\pi$
$662$		0			0
$663$	−5.80588e10	+	1.00561e11i	−0.0116696	+	0.0202124i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.06312e10	−	1.56978e11i	0.0177301	−	0.0307095i
$668$		0			0
$669$	−1.19863e12	−	2.07609e12i	−0.231349	−	0.400708i
$670$		0			0
$671$	−9.23702e12			−1.75906
$672$		0			0
$673$	8.29182e12			1.55805			0.779026	−	0.626991i	$-0.215714\pi$
$673$	8.29182e12			1.55805			0.779026	+	0.626991i	$0.215714\pi$
$674$		0			0
$675$	2.33307e12	+	4.04099e12i	0.432574	+	0.749239i
$676$		0			0
$677$	−2.00277e12	+	3.46889e12i	−0.366422	+	0.634661i	−0.989003	−	0.147894i	$-0.952751\pi$
$677$	−2.00277e12	+	3.46889e12i	−0.366422	+	0.634661i	0.622582	+	0.782555i	$0.286084\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.44142e12	−	4.22867e12i	0.434992	−	0.753428i
$682$		0			0
$683$	−2.18361e12	−	3.78213e12i	−0.383957	−	0.665033i	0.607667	−	0.794192i	$-0.292106\pi$
$683$	−2.18361e12	−	3.78213e12i	−0.383957	−	0.665033i	−0.991624	+	0.129159i	$0.958772\pi$
$684$		0			0
$685$	1.67257e11			0.0290254
$686$		0			0
$687$	−4.97402e12			−0.851927
$688$		0			0
$689$	−6.89153e12	−	1.19365e13i	−1.16501	−	2.01786i
$690$		0			0
$691$	2.30265e11	−	3.98831e11i	0.0384218	−	0.0665485i	−0.846175	−	0.532905i	$-0.821100\pi$
$691$	2.30265e11	−	3.98831e11i	0.0384218	−	0.0665485i	0.884597	+	0.466357i	$0.154434\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.89338e11	+	8.47558e11i	−0.0795567	+	0.137796i
$696$		0			0
$697$	9.34982e10	+	1.61944e11i	0.0150057	+	0.0259906i
$698$		0			0
$699$	−3.75289e12			−0.594592
$700$		0			0
$701$	−8.47672e11			−0.132586			−0.0662928	−	0.997800i	$-0.521117\pi$
$701$	−8.47672e11			−0.132586			−0.0662928	+	0.997800i	$0.521117\pi$
$702$		0			0
$703$	6.45067e11	+	1.11729e12i	0.0996107	+	0.172531i
$704$		0			0
$705$	2.01080e11	−	3.48280e11i	0.0306561	−	0.0530979i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2.88463e12	−	4.99633e12i	0.428728	−	0.742580i	−0.568032	−	0.823006i	$-0.692295\pi$
$709$	2.88463e12	−	4.99633e12i	0.428728	−	0.742580i	0.996761	+	0.0804269i	$0.0256284\pi$
$710$		0			0
$711$	2.95662e12	+	5.12101e12i	0.433892	+	0.751524i
$712$		0			0
$713$	6.25940e11			0.0907046
$714$		0			0
$715$	−2.48341e12			−0.355362
$716$		0			0
$717$	9.19232e11	+	1.59216e12i	0.129894	+	0.224983i
$718$		0			0
$719$	−3.76918e12	+	6.52842e12i	−0.525978	+	0.911020i	0.473564	+	0.880759i	$0.342967\pi$
$719$	−3.76918e12	+	6.52842e12i	−0.525978	+	0.911020i	−0.999542	+	0.0302608i	$0.990366\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.57808e11	−	1.48577e12i	0.116753	−	0.202222i
$724$		0			0
$725$	7.89945e11	+	1.36823e12i	0.106188	+	0.183923i
$726$		0			0
$727$	9.73268e12			1.29219			0.646097	−	0.763255i	$-0.276400\pi$
$727$	9.73268e12			1.29219			0.646097	+	0.763255i	$0.276400\pi$
$728$		0			0
$729$	1.59504e12			0.209169
$730$		0			0
$731$	−1.26872e11	−	2.19748e11i	−0.0164338	−	0.0284641i
$732$		0			0
$733$	4.17735e12	−	7.23539e12i	0.534482	−	0.925750i	−0.464706	−	0.885465i	$-0.653840\pi$
$733$	4.17735e12	−	7.23539e12i	0.534482	−	0.925750i	0.999188	−	0.0402852i	$-0.0128267\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.72522e12	+	1.16484e13i	−0.839659	+	1.45433i
$738$		0			0
$739$	7.13682e12	+	1.23613e13i	0.880248	+	1.52463i	0.851066	+	0.525059i	$0.175957\pi$
$739$	7.13682e12	+	1.23613e13i	0.880248	+	1.52463i	0.0291821	+	0.999574i	$0.490710\pi$
$740$		0			0
$741$	5.61896e12			0.684659
$742$		0			0
$743$	−1.54557e13			−1.86054			−0.930271	−	0.366873i	$-0.880428\pi$
$743$	−1.54557e13			−1.86054			−0.930271	+	0.366873i	$0.880428\pi$
$744$		0			0
$745$	−2.45028e11	−	4.24401e11i	−0.0291415	−	0.0504746i
$746$		0			0
$747$	−1.10207e12	+	1.90884e12i	−0.129499	+	0.224299i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.92223e12	+	3.32940e12i	−0.220509	+	0.381932i	−0.954963	−	0.296726i	$-0.904105\pi$
$751$	−1.92223e12	+	3.32940e12i	−0.220509	+	0.381932i	0.734454	+	0.678659i	$0.237438\pi$
$752$		0			0
$753$	2.34190e11	+	4.05629e11i	0.0265455	+	0.0459781i
$754$		0			0
$755$	7.47253e11			0.0836964
$756$		0			0
$757$	5.43161e12			0.601169			0.300585	−	0.953755i	$-0.402818\pi$
$757$	5.43161e12			0.601169			0.300585	+	0.953755i	$0.402818\pi$
$758$		0			0
$759$	−7.06807e11	−	1.22423e12i	−0.0773059	−	0.133898i
$760$		0			0
$761$	4.20380e12	−	7.28119e12i	0.454371	−	0.786994i	−0.544281	−	0.838903i	$-0.683197\pi$
$761$	4.20380e12	−	7.28119e12i	0.454371	−	0.786994i	0.998652	+	0.0519094i	$0.0165307\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.17809e10	−	2.04052e10i	0.00124366	−	0.00215409i
$766$		0			0
$767$	−1.12479e13	−	1.94819e13i	−1.17352	−	2.03260i
$768$		0			0
$769$	−1.01254e12			−0.104411			−0.0522053	−	0.998636i	$-0.516625\pi$
$769$	−1.01254e12			−0.104411			−0.0522053	+	0.998636i	$0.516625\pi$
$770$		0			0
$771$	8.59529e12			0.876023
$772$		0			0
$773$	7.08876e11	+	1.22781e12i	0.0714106	+	0.123687i	0.899520	−	0.436880i	$-0.143917\pi$
$773$	7.08876e11	+	1.22781e12i	0.0714106	+	0.123687i	−0.828109	+	0.560567i	$0.810583\pi$
$774$		0			0
$775$	−2.72786e12	+	4.72479e12i	−0.271621	+	0.470462i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.52440e12	−	7.83649e12i	0.440192	−	0.762436i
$780$		0			0
$781$	−8.82199e12	−	1.52801e13i	−0.848470	−	1.46959i
$782$		0			0
$783$	1.98604e12			0.188825
$784$		0			0
$785$	−1.35093e12			−0.126975
$786$		0			0
$787$	2.95831e12	+	5.12394e12i	0.274889	+	0.476121i	0.970107	−	0.242677i	$-0.0780257\pi$
$787$	2.95831e12	+	5.12394e12i	0.274889	+	0.476121i	−0.695218	+	0.718799i	$0.744692\pi$
$788$		0			0
$789$	−1.10489e12	+	1.91373e12i	−0.101502	+	0.175806i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−8.53356e12	+	1.47806e13i	−0.766303	+	1.32728i
$794$		0			0
$795$	−4.70220e11	−	8.14445e11i	−0.0417493	−	0.0723118i
$796$		0			0
$797$	−3.00078e12			−0.263434			−0.131717	−	0.991287i	$-0.542049\pi$
$797$	−3.00078e12			−0.263434			−0.131717	+	0.991287i	$0.542049\pi$
$798$		0			0
$799$	3.44976e11			0.0299453
$800$		0			0
$801$	4.81793e12	+	8.34491e12i	0.413537	+	0.716267i
$802$		0			0
$803$	−2.82141e12	+	4.88683e12i	−0.239468	+	0.414770i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.46782e11	−	7.73850e11i	0.0370822	−	0.0642282i
$808$		0			0
$809$	−2.66409e12	−	4.61433e12i	−0.218665	−	0.378739i	0.735735	−	0.677270i	$-0.236837\pi$
$809$	−2.66409e12	−	4.61433e12i	−0.218665	−	0.378739i	−0.954400	+	0.298530i	$0.903504\pi$
$810$		0			0
$811$	−1.28093e13			−1.03976			−0.519878	−	0.854241i	$-0.674022\pi$
$811$	−1.28093e13			−1.03976			−0.519878	+	0.854241i	$0.674022\pi$
$812$		0			0
$813$	−4.51993e11			−0.0362848
$814$		0			0
$815$	−1.00255e12	−	1.73646e12i	−0.0795969	−	0.137866i
$816$		0			0
$817$	−6.13936e12	+	1.06337e13i	−0.482085	+	0.834996i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.12246e13	+	1.94416e13i	−0.862237	+	1.49344i	0.00752701	+	0.999972i	$0.497604\pi$
$821$	−1.12246e13	+	1.94416e13i	−0.862237	+	1.49344i	−0.869764	+	0.493467i	$0.835729\pi$
$822$		0			0
$823$	6.73031e12	+	1.16572e13i	0.511371	+	0.885720i	0.999913	+	0.0131801i	$0.00419548\pi$
$823$	6.73031e12	+	1.16572e13i	0.511371	+	0.885720i	−0.488542	+	0.872540i	$0.662471\pi$
$824$		0			0
$825$	1.23211e13			0.925992
$826$		0			0
$827$	1.35017e13			1.00372			0.501861	−	0.864948i	$-0.332649\pi$
$827$	1.35017e13			1.00372			0.501861	+	0.864948i	$0.332649\pi$
$828$		0			0
$829$	9.08459e12	+	1.57350e13i	0.668052	+	1.15710i	0.978448	+	0.206492i	$0.0662048\pi$
$829$	9.08459e12	+	1.57350e13i	0.668052	+	1.15710i	−0.310397	+	0.950607i	$0.600462\pi$
$830$		0			0
$831$	−5.42932e12	+	9.40386e12i	−0.394949	+	0.684072i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.59382e11	+	2.76058e11i	−0.0113462	+	0.0196522i
$836$		0			0
$837$	3.42912e12	+	5.93941e12i	0.241500	+	0.418291i
$838$		0			0
$839$	6.58386e12			0.458724			0.229362	−	0.973341i	$-0.426336\pi$
$839$	6.58386e12			0.458724			0.229362	+	0.973341i	$0.426336\pi$
$840$		0			0
$841$	−1.38347e13			−0.953647
$842$		0			0
$843$	2.18883e12	+	3.79117e12i	0.149276	+	0.258553i
$844$		0			0
$845$	−1.43120e12	+	2.47891e12i	−0.0965705	+	0.167265i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.83560e12	−	3.17935e12i	0.121253	−	0.210017i
$850$		0			0
$851$	−2.99852e11	−	5.19360e11i	−0.0195986	−	0.0339457i
$852$		0			0
$853$	2.09998e13			1.35814			0.679070	−	0.734073i	$-0.262383\pi$
$853$	2.09998e13			1.35814			0.679070	+	0.734073i	$0.262383\pi$
$854$		0			0
$855$	−1.14016e12			−0.0729659
$856$		0			0
$857$	1.25399e13	+	2.17197e13i	0.794108	+	1.37544i	0.923404	+	0.383830i	$0.125395\pi$
$857$	1.25399e13	+	2.17197e13i	0.794108	+	1.37544i	−0.129296	+	0.991606i	$0.541272\pi$
$858$		0			0
$859$	−8.93336e12	+	1.54730e13i	−0.559816	+	0.969630i	0.437695	+	0.899123i	$0.355795\pi$
$859$	−8.93336e12	+	1.54730e13i	−0.559816	+	0.969630i	−0.997511	+	0.0705065i	$0.977538\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.85522e12	+	1.36056e13i	−0.482070	+	0.834969i	−0.999788	−	0.0205819i	$-0.993448\pi$
$863$	−7.85522e12	+	1.36056e13i	−0.482070	+	0.834969i	0.517719	+	0.855551i	$0.326781\pi$
$864$		0			0
$865$	−1.22250e12	−	2.11743e12i	−0.0742466	−	0.128599i
$866$		0			0
$867$	8.33919e12			0.501231
$868$		0			0
$869$	3.64787e13			2.16995
$870$		0			0
$871$	1.24261e13	+	2.15226e13i	0.731565	+	1.26711i
$872$		0			0
$873$	1.11714e13	−	1.93494e13i	0.650944	−	1.12747i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.37494e12	−	1.10417e13i	0.363896	−	0.630287i	−0.624702	−	0.780863i	$-0.714780\pi$
$877$	6.37494e12	−	1.10417e13i	0.363896	−	0.630287i	0.988598	+	0.150576i	$0.0481129\pi$
$878$		0			0
$879$	−6.99014e12	−	1.21073e13i	−0.394944	−	0.684064i
$880$		0			0
$881$	−1.77457e13			−0.992432			−0.496216	−	0.868199i	$-0.665278\pi$
$881$	−1.77457e13			−0.992432			−0.496216	+	0.868199i	$0.665278\pi$
$882$		0			0
$883$	−2.35402e13			−1.30313			−0.651565	−	0.758593i	$-0.725887\pi$
$883$	−2.35402e13			−1.30313			−0.651565	+	0.758593i	$0.725887\pi$
$884$		0			0
$885$	−7.67460e11	−	1.32928e12i	−0.0420543	−	0.0728403i
$886$		0			0
$887$	3.52995e12	−	6.11405e12i	0.191475	−	0.331644i	−0.754264	−	0.656571i	$-0.772006\pi$
$887$	3.52995e12	−	6.11405e12i	0.191475	−	0.331644i	0.945739	+	0.324927i	$0.105340\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.42848e12	+	9.40240e12i	−0.288555	+	0.499792i
$892$		0			0
$893$	−8.34674e12	−	1.44570e13i	−0.439223	−	0.760757i
$894$		0			0
$895$	3.46855e12			0.180694
$896$		0			0
$897$	−2.61191e12			−0.134708
$898$		0			0
$899$	1.16105e12	+	2.01100e12i	0.0592835	+	0.102682i
$900$		0			0
$901$	4.03359e11	−	6.98638e11i	0.0203906	−	0.0353176i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.41340e11	+	9.37628e11i	−0.0268257	+	0.0464635i
$906$		0			0
$907$	−2.34149e12	−	4.05559e12i	−0.114884	−	0.198985i	0.802849	−	0.596182i	$-0.203316\pi$
$907$	−2.34149e12	−	4.05559e12i	−0.114884	−	0.198985i	−0.917733	+	0.397197i	$0.869983\pi$
$908$		0			0
$909$	2.44251e13			1.18658
$910$		0			0
$911$	2.77029e13			1.33258			0.666289	−	0.745694i	$-0.267882\pi$
$911$	2.77029e13			1.33258			0.666289	+	0.745694i	$0.267882\pi$
$912$		0			0
$913$	6.79866e12	+	1.17756e13i	0.323821	+	0.560874i
$914$		0			0
$915$	−5.82257e11	+	1.00850e12i	−0.0274612	+	0.0475643i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.67172e13	+	2.89550e13i	−0.773112	+	1.33907i	0.162737	+	0.986669i	$0.447968\pi$
$919$	−1.67172e13	+	2.89550e13i	−0.773112	+	1.33907i	−0.935849	+	0.352400i	$0.885366\pi$
$920$		0			0
$921$	−6.07803e12	−	1.05275e13i	−0.278352	−	0.482120i
$922$		0			0
$923$	−3.26005e13			−1.47848
$924$		0			0
$925$	5.22705e12			0.234757
$926$		0			0
$927$	−3.87272e12	−	6.70774e12i	−0.172249	−	0.298344i
$928$		0			0
$929$	−1.71914e13	+	2.97764e13i	−0.757252	+	1.31160i	0.186995	+	0.982361i	$0.440125\pi$
$929$	−1.71914e13	+	2.97764e13i	−0.757252	+	1.31160i	−0.944247	+	0.329238i	$0.893208\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.59472e11	−	7.95828e11i	0.0198514	−	0.0343837i
$934$		0			0
$935$	−7.26764e10	−	1.25879e11i	−0.00310986	−	0.00538644i
$936$		0			0
$937$	−2.90342e13			−1.23050			−0.615250	−	0.788332i	$-0.710945\pi$
$937$	−2.90342e13			−1.23050			−0.615250	+	0.788332i	$0.710945\pi$
$938$		0			0
$939$	1.18566e13			0.497699
$940$		0			0
$941$	−1.15681e13	−	2.00365e13i	−0.480958	−	0.833044i	0.518803	−	0.854894i	$-0.326378\pi$
$941$	−1.15681e13	−	2.00365e13i	−0.480958	−	0.833044i	−0.999761	+	0.0218500i	$0.993044\pi$
$942$		0			0
$943$	−2.10312e12	+	3.64271e12i	−0.0866086	+	0.150011i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.92132e12	+	1.19881e13i	−0.279649	+	0.484367i	−0.971298	−	0.237868i	$-0.923552\pi$
$947$	−6.92132e12	+	1.19881e13i	−0.279649	+	0.484367i	0.691648	+	0.722235i	$0.256885\pi$
$948$		0			0
$949$	5.21308e12	+	9.02933e12i	0.208640	+	0.361374i
$950$		0			0
$951$	2.28052e13			0.904112
$952$		0			0
$953$	−1.60424e13			−0.630016			−0.315008	−	0.949089i	$-0.602007\pi$
$953$	−1.60424e13			−0.630016			−0.315008	+	0.949089i	$0.602007\pi$
$954$		0			0
$955$	−1.45119e12	−	2.51353e12i	−0.0564558	−	0.0977843i
$956$		0			0
$957$	2.62211e12	−	4.54163e12i	0.101053	−	0.175028i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	9.21043e12	−	1.59529e13i	0.348357	−	0.603372i
$962$		0			0
$963$	3.87408e12	+	6.71011e12i	0.145161	+	0.251427i
$964$		0			0
$965$	7.16595e10			0.00266012
$966$		0			0
$967$	−2.69595e13			−0.991502			−0.495751	−	0.868465i	$-0.665107\pi$
$967$	−2.69595e13			−0.991502			−0.495751	+	0.868465i	$0.665107\pi$
$968$		0			0
$969$	1.64438e11	+	2.84815e11i	0.00599163	+	0.0103778i
$970$		0			0
$971$	−6.33963e11	+	1.09806e12i	−0.0228864	+	0.0396404i	−0.877242	−	0.480049i	$-0.840619\pi$
$971$	−6.33963e11	+	1.09806e12i	−0.0228864	+	0.0396404i	0.854355	+	0.519689i	$0.173952\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.13828e13	−	1.97155e13i	0.403392	−	0.698695i
$976$		0			0
$977$	1.04355e13	+	1.80748e13i	0.366428	+	0.634671i	0.989004	−	0.147888i	$-0.0472474\pi$
$977$	1.04355e13	+	1.80748e13i	0.366428	+	0.634671i	−0.622577	+	0.782559i	$0.713914\pi$
$978$		0			0
$979$	5.94436e13			2.06815
$980$		0			0
$981$	−2.92823e13			−1.00947
$982$		0			0
$983$	1.31973e13	+	2.28584e13i	0.450811	+	0.780828i	0.998437	−	0.0558955i	$-0.0178014\pi$
$983$	1.31973e13	+	2.28584e13i	0.450811	+	0.780828i	−0.547625	+	0.836724i	$0.684468\pi$
$984$		0			0
$985$	1.63963e12	−	2.83992e12i	0.0554987	−	0.0961265i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.85381e12	−	4.94295e12i	0.0948511	−	0.164287i
$990$		0			0
$991$	1.16642e13	+	2.02029e13i	0.384169	+	0.665400i	0.991654	−	0.128931i	$-0.0411546\pi$
$991$	1.16642e13	+	2.02029e13i	0.384169	+	0.665400i	−0.607484	+	0.794332i	$0.707821\pi$
$992$		0			0
$993$	5.81010e12			0.189632
$994$		0			0
$995$	−5.26525e12			−0.170300
$996$		0			0
$997$	−1.81120e13	−	3.13709e13i	−0.580548	−	1.00554i	−0.995414	−	0.0956566i	$-0.969505\pi$
$997$	−1.81120e13	−	3.13709e13i	−0.580548	−	1.00554i	0.414866	−	0.909882i	$-0.363828\pi$
$998$		0			0
$999$	3.28539e12	−	5.69047e12i	0.104362	−	0.180760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.10.e.i.177.7		20
7.2	even	3		196.10.a.g.1.4	✓	10
7.3	odd	6	inner	196.10.e.i.165.4		20
7.4	even	3	inner	196.10.e.i.165.7		20
7.5	odd	6		196.10.a.g.1.7	yes	10
7.6	odd	2	inner	196.10.e.i.177.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.10.a.g.1.4	✓	10	7.2	even	3
196.10.a.g.1.7	yes	10	7.5	odd	6
196.10.e.i.165.4		20	7.3	odd	6	inner
196.10.e.i.165.7		20	7.4	even	3	inner
196.10.e.i.177.4		20	7.6	odd	2	inner
196.10.e.i.177.7		20	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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(35.1890 + 60.9492i) q^{3} +(-81.3880 + 140.968i) q^{5} +(7364.96 - 12756.5i) q^{9} +(-45434.4 - 78694.7i) q^{11} -167897. q^{13} -11455.9 q^{15} +(-4913.47 - 8510.38i) q^{17} +(-237764. + 411820. i) q^{19} +(110522. - 191430. i) q^{23} +(963314. + 1.66851e6i) q^{25} +2.42191e6 q^{27} +820028. q^{29} +(1.41587e6 + 2.45236e6i) q^{31} +(3.19758e6 - 5.53838e6i) q^{33} +(1.35653e6 - 2.34957e6i) q^{37} +(-5.90813e6 - 1.02332e7i) q^{39} -1.90289e7 q^{41} +2.58212e7 q^{43} +(1.19884e6 + 2.07645e6i) q^{45} +(-1.75526e7 + 3.04019e7i) q^{47} +(345801. - 598944. i) q^{51} +(4.10462e7 + 7.10941e7i) q^{53} +1.47913e7 q^{55} -3.34668e7 q^{57} +(6.69928e7 + 1.16035e8i) q^{59} +(5.08262e7 - 8.80335e7i) q^{61} +(1.36648e7 - 2.36681e7i) q^{65} +(-7.40102e7 - 1.28190e8i) q^{67} +1.55567e7 q^{69} +1.94170e8 q^{71} +(-3.10493e7 - 5.37790e7i) q^{73} +(-6.77962e7 + 1.17426e8i) q^{75} +(-2.00722e8 + 3.47660e8i) q^{79} +(-5.97398e7 - 1.03472e8i) q^{81} -1.49637e8 q^{83} +1.59959e6 q^{85} +(2.88560e7 + 4.99801e7i) q^{87} +(-3.27085e8 + 5.66527e8i) q^{89} +(-9.96462e7 + 1.72592e8i) q^{93} +(-3.87023e7 - 6.70344e7i) q^{95} +1.51683e9 q^{97} -1.33849e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 93550 q^{9} - 27740 q^{11} + 1824176 q^{15} + 2921096 q^{23} - 3484998 q^{25} - 1671496 q^{29} + 31928756 q^{37} + 4930944 q^{39} + 26828680 q^{43} - 206013028 q^{51} - 137301788 q^{53} + 144492664 q^{57}+ \cdots + 10632134024 q^{99}+O(q^{100}) \) 20 * q - 93550 * q^9 - 27740 * q^11 + 1824176 * q^15 + 2921096 * q^23 - 3484998 * q^25 - 1671496 * q^29 + 31928756 * q^37 + 4930944 * q^39 + 26828680 * q^43 - 206013028 * q^51 - 137301788 * q^53 + 144492664 * q^57 - 519063672 * q^65 + 342262536 * q^67 - 1062072816 * q^71 - 462186584 * q^79 - 2495014982 * q^81 + 2473207168 * q^85 - 5733362712 * q^93 - 2984918936 * q^95 + 10632134024 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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