LMFDB - Embedded newform 75.10.e.g.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.2
Character	$\chi$	$=$	75.32
Dual form			75.10.e.g.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-29.6409 + 29.6409i) q^{2} +(-70.8607 - 121.086i) q^{3} -1245.17i q^{4} +(5689.47 + 1488.72i) q^{6} +(7257.95 + 7257.95i) q^{7} +(21731.7 + 21731.7i) q^{8} +(-9640.52 + 17160.4i) q^{9} +O(q^{10})$	\(q+(-29.6409 + 29.6409i) q^{2} +(-70.8607 - 121.086i) q^{3} -1245.17i q^{4} +(5689.47 + 1488.72i) q^{6} +(7257.95 + 7257.95i) q^{7} +(21731.7 + 21731.7i) q^{8} +(-9640.52 + 17160.4i) q^{9} -16142.7i q^{11} +(-150772. + 88233.3i) q^{12} +(118985. - 118985. i) q^{13} -430265. q^{14} -650770. q^{16} +(-199725. + 199725. i) q^{17} +(-222897. - 794405. i) q^{18} -49424.8i q^{19} +(364531. - 1.39314e6i) q^{21} +(478484. + 478484. i) q^{22} +(435451. + 435451. i) q^{23} +(1.09148e6 - 4.17133e6i) q^{24} +7.05363e6i q^{26} +(2.76102e6 - 48670.6i) q^{27} +(9.03736e6 - 9.03736e6i) q^{28} +99055.3 q^{29} -7.60465e6 q^{31} +(8.16277e6 - 8.16277e6i) q^{32} +(-1.95465e6 + 1.14388e6i) q^{33} -1.18401e7i q^{34} +(2.13676e7 + 1.20041e7i) q^{36} +(735873. + 735873. i) q^{37} +(1.46500e6 + 1.46500e6i) q^{38} +(-2.28387e7 - 5.97601e6i) q^{39} -2.84743e7i q^{41} +(3.04888e7 + 5.20989e7i) q^{42} +(4.64166e6 - 4.64166e6i) q^{43} -2.01003e7 q^{44} -2.58143e7 q^{46} +(-2.19202e7 + 2.19202e7i) q^{47} +(4.61140e7 + 7.87990e7i) q^{48} +6.50022e7i q^{49} +(3.83366e7 + 1.00312e7i) q^{51} +(-1.48156e8 - 1.48156e8i) q^{52} +(4.34796e7 + 4.34796e7i) q^{53} +(-8.03965e7 + 8.32818e7i) q^{54} +3.15455e8i q^{56} +(-5.98464e6 + 3.50228e6i) q^{57} +(-2.93609e6 + 2.93609e6i) q^{58} +1.37704e8 q^{59} +7.42651e7 q^{61} +(2.25409e8 - 2.25409e8i) q^{62} +(-1.94520e8 + 5.45792e7i) q^{63} +1.50710e8i q^{64} +(2.40319e7 - 9.18432e7i) q^{66} +(4.34208e7 + 4.34208e7i) q^{67} +(2.48691e8 + 2.48691e8i) q^{68} +(2.18705e7 - 8.35832e7i) q^{69} +2.05196e8i q^{71} +(-5.82431e8 + 1.63421e8i) q^{72} +(-1.81205e8 + 1.81205e8i) q^{73} -4.36239e7 q^{74} -6.15421e7 q^{76} +(1.17163e8 - 1.17163e8i) q^{77} +(8.54094e8 - 4.99825e8i) q^{78} -2.98683e7i q^{79} +(-2.01541e8 - 3.30871e8i) q^{81} +(8.44004e8 + 8.44004e8i) q^{82} +(-2.00783e8 - 2.00783e8i) q^{83} +(-1.73469e9 - 4.53902e8i) q^{84} +2.75166e8i q^{86} +(-7.01913e6 - 1.19942e7i) q^{87} +(3.50808e8 - 3.50808e8i) q^{88} +3.63380e8 q^{89} +1.72717e9 q^{91} +(5.42209e8 - 5.42209e8i) q^{92} +(5.38871e8 + 9.20815e8i) q^{93} -1.29947e9i q^{94} +(-1.56682e9 - 4.09976e8i) q^{96} +(6.54780e8 + 6.54780e8i) q^{97} +(-1.92672e9 - 1.92672e9i) q^{98} +(2.77016e8 + 1.55624e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10788 q^{6}+O(q^{10}) $ 48 * q + 10788 * q^6	$ 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) $ 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−29.6409	+	29.6409i	−1.30996	+	1.30996i	−0.388511	+	0.921444i	$0.627011\pi$
$2$	−29.6409	+	29.6409i	−1.30996	+	1.30996i	−0.921444	+	0.388511i	$0.872989\pi$
$3$	−70.8607	−	121.086i	−0.505080	−	0.863073i
$3$	−70.8607	−	121.086i	−0.505080	−	0.863073i
$4$		−	1245.17i		−	2.43197i
$5$		0			0
$5$		0			0
$6$	5689.47	+	1488.72i	1.79222	+	0.468955i
$7$	7257.95	+	7257.95i	1.14254	+	1.14254i	0.987983	+	0.154561i	$0.0493963\pi$
$7$	7257.95	+	7257.95i	1.14254	+	1.14254i	0.154561	+	0.987983i	$0.450604\pi$
$8$	21731.7	+	21731.7i	1.87581	+	1.87581i
$9$	−9640.52	+	17160.4i	−0.489789	+	0.871841i
$10$		0			0
$11$		−	16142.7i		−	0.332436i	−0.986089	−	0.166218i	$-0.946844\pi$
$11$		−	16142.7i		−	0.332436i	0.986089	−	0.166218i	$-0.0531556\pi$
$12$	−150772.	+	88233.3i	−2.09896	+	1.22834i
$13$	118985.	−	118985.i	1.15544	−	1.15544i	0.169990	−	0.985446i	$-0.445626\pi$
$13$	118985.	−	118985.i	1.15544	−	1.15544i	0.985446	−	0.169990i	$-0.0543736\pi$
$14$	−430265.			−2.99336
$15$		0			0
$16$	−650770.			−2.48249
$17$	−199725.	+	199725.i	−0.579980	+	0.579980i	−0.934898	−	0.354918i	$-0.884509\pi$
$17$	−199725.	+	199725.i	−0.579980	+	0.579980i	0.354918	+	0.934898i	$0.384509\pi$
$18$	−222897.	−	794405.i	−0.500470	−	1.78367i
$19$		−	49424.8i		−	0.0870070i	−0.999053	−	0.0435035i	$-0.986148\pi$
$19$		−	49424.8i		−	0.0870070i	0.999053	−	0.0435035i	$-0.0138520\pi$
$20$		0			0
$21$	364531.	−	1.39314e6i	0.409023	−	1.56317i
$22$	478484.	+	478484.i	0.435477	+	0.435477i
$23$	435451.	+	435451.i	0.324462	+	0.324462i	0.850476	−	0.526014i	$-0.176314\pi$
$23$	435451.	+	435451.i	0.324462	+	0.324462i	−0.526014	+	0.850476i	$0.676314\pi$
$24$	1.09148e6	−	4.17133e6i	0.671528	−	2.56639i
$25$		0			0
$26$			7.05363e6i			3.02714i
$27$	2.76102e6	−	48670.6i	0.999845	−	0.0176250i
$28$	9.03736e6	−	9.03736e6i	2.77863	−	2.77863i
$29$	99055.3			0.0260068			0.0130034	−	0.999915i	$-0.495861\pi$
$29$	99055.3			0.0260068			0.0130034	+	0.999915i	$0.495861\pi$
$30$		0			0
$31$	−7.60465e6			−1.47894			−0.739472	−	0.673188i	$-0.764925\pi$
$31$	−7.60465e6			−1.47894			−0.739472	+	0.673188i	$0.764925\pi$
$32$	8.16277e6	−	8.16277e6i	1.37614	−	1.37614i
$33$	−1.95465e6	+	1.14388e6i	−0.286917	+	0.167907i
$34$		−	1.18401e7i		−	1.51950i
$35$		0			0
$36$	2.13676e7	+	1.20041e7i	2.12029	+	1.19115i
$37$	735873.	+	735873.i	0.0645499	+	0.0645499i	0.738645	−	0.674095i	$-0.235466\pi$
$37$	735873.	+	735873.i	0.0645499	+	0.0645499i	−0.674095	+	0.738645i	$0.735466\pi$
$38$	1.46500e6	+	1.46500e6i	0.113975	+	0.113975i
$39$	−2.28387e7	−	5.97601e6i	−1.58081	−	0.413638i
$40$		0			0
$41$		−	2.84743e7i		−	1.57371i	−0.617136	−	0.786857i	$-0.711707\pi$
$41$		−	2.84743e7i		−	1.57371i	0.617136	−	0.786857i	$-0.288293\pi$
$42$	3.04888e7	+	5.20989e7i	1.51189	+	2.58349i
$43$	4.64166e6	−	4.64166e6i	0.207045	−	0.207045i	−0.595965	−	0.803010i	$-0.703230\pi$
$43$	4.64166e6	−	4.64166e6i	0.207045	−	0.207045i	0.803010	+	0.595965i	$0.203230\pi$
$44$	−2.01003e7			−0.808474
$45$		0			0
$46$	−2.58143e7			−0.850061
$47$	−2.19202e7	+	2.19202e7i	−0.655247	+	0.655247i	−0.954252	−	0.299005i	$-0.903345\pi$
$47$	−2.19202e7	+	2.19202e7i	−0.655247	+	0.655247i	0.299005	+	0.954252i	$0.403345\pi$
$48$	4.61140e7	+	7.87990e7i	1.25386	+	2.14257i
$49$			6.50022e7i			1.61081i
$50$		0			0
$51$	3.83366e7	+	1.00312e7i	0.793501	+	0.207629i
$52$	−1.48156e8	−	1.48156e8i	−2.80998	−	2.80998i
$53$	4.34796e7	+	4.34796e7i	0.756911	+	0.756911i	0.975759	−	0.218848i	$-0.0702300\pi$
$53$	4.34796e7	+	4.34796e7i	0.756911	+	0.756911i	−0.218848	+	0.975759i	$0.570230\pi$
$54$	−8.03965e7	+	8.32818e7i	−1.28666	+	1.33284i
$55$		0			0
$56$			3.15455e8i			4.28639i
$57$	−5.98464e6	+	3.50228e6i	−0.0750933	+	0.0439454i
$58$	−2.93609e6	+	2.93609e6i	−0.0340677	+	0.0340677i
$59$	1.37704e8			1.47949			0.739744	−	0.672889i	$-0.234947\pi$
$59$	1.37704e8			1.47949			0.739744	+	0.672889i	$0.234947\pi$
$60$		0			0
$61$	7.42651e7			0.686753			0.343376	−	0.939198i	$-0.388429\pi$
$61$	7.42651e7			0.686753			0.343376	+	0.939198i	$0.388429\pi$
$62$	2.25409e8	−	2.25409e8i	1.93735	−	1.93735i
$63$	−1.94520e8	+	5.45792e7i	−1.55572	+	0.436511i
$64$			1.50710e8i			1.12288i
$65$		0			0
$66$	2.40319e7	−	9.18432e7i	0.155898	−	0.595799i
$67$	4.34208e7	+	4.34208e7i	0.263246	+	0.263246i	0.826371	−	0.563126i	$-0.190401\pi$
$67$	4.34208e7	+	4.34208e7i	0.263246	+	0.263246i	−0.563126	+	0.826371i	$0.690401\pi$
$68$	2.48691e8	+	2.48691e8i	1.41049	+	1.41049i
$69$	2.18705e7	−	8.35832e7i	0.116155	−	0.443913i
$70$		0			0
$71$			2.05196e8i			0.958313i	0.877730	+	0.479156i	$0.159057\pi$
$71$			2.05196e8i			0.958313i	−0.877730	+	0.479156i	$0.840943\pi$
$72$	−5.82431e8	+	1.63421e8i	−2.55416	+	0.716656i
$73$	−1.81205e8	+	1.81205e8i	−0.746822	+	0.746822i	−0.973881	−	0.227059i	$-0.927089\pi$
$73$	−1.81205e8	+	1.81205e8i	−0.746822	+	0.746822i	0.227059	+	0.973881i	$0.427089\pi$
$74$	−4.36239e7			−0.169115
$75$		0			0
$76$	−6.15421e7			−0.211598
$77$	1.17163e8	−	1.17163e8i	0.379823	−	0.379823i
$78$	8.54094e8	−	4.99825e8i	2.61264	−	1.52895i
$79$		−	2.98683e7i		−	0.0862756i	−0.999069	−	0.0431378i	$-0.986265\pi$
$79$		−	2.98683e7i		−	0.0862756i	0.999069	−	0.0431378i	$-0.0137355\pi$
$80$		0			0
$81$	−2.01541e8	−	3.30871e8i	−0.520213	−	0.854037i
$82$	8.44004e8	+	8.44004e8i	2.06149	+	2.06149i
$83$	−2.00783e8	−	2.00783e8i	−0.464382	−	0.464382i	0.435707	−	0.900089i	$-0.356499\pi$
$83$	−2.00783e8	−	2.00783e8i	−0.464382	−	0.464382i	−0.900089	+	0.435707i	$0.856499\pi$
$84$	−1.73469e9	−	4.53902e8i	−3.80159	−	0.994730i
$85$		0			0
$86$			2.75166e8i			0.542440i
$87$	−7.01913e6	−	1.19942e7i	−0.0131355	−	0.0224458i
$88$	3.50808e8	−	3.50808e8i	0.623588	−	0.623588i
$89$	3.63380e8			0.613912			0.306956	−	0.951724i	$-0.400690\pi$
$89$	3.63380e8			0.613912			0.306956	+	0.951724i	$0.400690\pi$
$90$		0			0
$91$	1.72717e9			2.64027
$92$	5.42209e8	−	5.42209e8i	0.789080	−	0.789080i
$93$	5.38871e8	+	9.20815e8i	0.746984	+	1.27644i
$94$		−	1.29947e9i		−	1.71669i
$95$		0			0
$96$	−1.56682e9	−	4.09976e8i	−1.88277	−	0.492649i
$97$	6.54780e8	+	6.54780e8i	0.750971	+	0.750971i	0.974660	−	0.223690i	$-0.0718103\pi$
$97$	6.54780e8	+	6.54780e8i	0.750971	+	0.750971i	−0.223690	+	0.974660i	$0.571810\pi$
$98$	−1.92672e9	−	1.92672e9i	−2.11009	−	2.11009i
$99$	2.77016e8	+	1.55624e8i	0.289832	+	0.162824i
$100$		0			0
$101$		−	5.14458e8i		−	0.491931i	−0.969279	−	0.245965i	$-0.920895\pi$
$101$		−	5.14458e8i		−	0.491931i	0.969279	−	0.245965i	$-0.0791049\pi$
$102$	−1.43366e9	+	8.38996e8i	−1.31144	+	0.767466i
$103$	−2.93840e8	+	2.93840e8i	−0.257243	+	0.257243i	−0.823932	−	0.566689i	$-0.808224\pi$
$103$	−2.93840e8	+	2.93840e8i	−0.257243	+	0.257243i	0.566689	+	0.823932i	$0.308224\pi$
$104$	5.17148e9			4.33476
$105$		0			0
$106$	−2.57755e9			−1.98304
$107$	1.65113e9	−	1.65113e9i	1.21774	−	1.21774i	0.249322	−	0.968421i	$-0.419792\pi$
$107$	1.65113e9	−	1.65113e9i	1.21774	−	1.21774i	0.968421	−	0.249322i	$-0.0802077\pi$
$108$	−6.06029e7	−	3.43793e9i	−0.0428634	−	2.43159i
$109$			4.23843e7i			0.0287598i	0.999897	+	0.0143799i	$0.00457742\pi$
$109$			4.23843e7i			0.0287598i	−0.999897	+	0.0143799i	$0.995423\pi$
$110$		0			0
$111$	3.69593e7	−	1.41248e8i	0.0231084	−	0.0883140i
$112$	−4.72326e9	−	4.72326e9i	−2.83635	−	2.83635i
$113$	1.23716e9	+	1.23716e9i	0.713792	+	0.713792i	0.967326	−	0.253534i	$-0.0815930\pi$
$113$	1.23716e9	+	1.23716e9i	0.713792	+	0.713792i	−0.253534	+	0.967326i	$0.581593\pi$
$114$	7.35796e7	−	2.81201e8i	0.0408024	−	0.155935i
$115$		0			0
$116$		−	1.23340e8i		−	0.0632476i
$117$	8.94755e8	+	3.18890e9i	0.441436	+	1.57328i
$118$	−4.08166e9	+	4.08166e9i	−1.93806	+	1.93806i
$119$	−2.89919e9			−1.32531
$120$		0			0
$121$	2.09736e9			0.889486
$122$	−2.20128e9	+	2.20128e9i	−0.899615	+	0.899615i
$123$	−3.44783e9	+	2.01771e9i	−1.35823	+	0.794850i
$124$			9.46905e9i			3.59674i
$125$		0			0
$126$	4.14798e9	−	7.38353e9i	1.46612	−	2.60974i
$127$	1.46251e9	+	1.46251e9i	0.498862	+	0.498862i	0.911084	−	0.412221i	$-0.135247\pi$
$127$	1.46251e9	+	1.46251e9i	0.498862	+	0.498862i	−0.412221	+	0.911084i	$0.635247\pi$
$128$	−2.87833e8	−	2.87833e8i	−0.0947754	−	0.0947754i
$129$	−8.90951e8	−	2.33128e8i	−0.283270	−	0.0741209i
$130$		0			0
$131$			2.88634e8i			0.0856300i	0.999083	+	0.0428150i	$0.0136326\pi$
$131$			2.88634e8i			0.0856300i	−0.999083	+	0.0428150i	$0.986367\pi$
$132$	1.42432e9	+	2.43386e9i	0.408344	+	0.697772i
$133$	3.58723e8	−	3.58723e8i	0.0994093	−	0.0994093i
$134$	−2.57406e9			−0.689680
$135$		0			0
$136$	−8.68075e9			−2.17586
$137$	−2.24990e9	+	2.24990e9i	−0.545658	+	0.545658i	−0.925182	−	0.379524i	$-0.876088\pi$
$137$	−2.24990e9	+	2.24990e9i	−0.545658	+	0.545658i	0.379524	+	0.925182i	$0.376088\pi$
$138$	1.82922e9	+	3.12575e9i	0.429349	+	0.733665i
$139$		−	1.15289e9i		−	0.261952i	−0.991386	−	0.130976i	$-0.958189\pi$
$139$		−	1.15289e9i		−	0.261952i	0.991386	−	0.130976i	$-0.0418110\pi$
$140$		0			0
$141$	4.20751e9	+	1.10095e9i	0.896477	+	0.234574i
$142$	−6.08221e9	−	6.08221e9i	−1.25535	−	1.25535i
$143$	−1.92073e9	−	1.92073e9i	−0.384109	−	0.384109i
$144$	6.27376e9	−	1.11675e10i	1.21590	−	2.16434i
$145$		0			0
$146$		−	1.07422e10i		−	1.95661i
$147$	7.87084e9	−	4.60610e9i	1.39025	−	0.813589i
$148$	9.16285e8	−	9.16285e8i	0.156983	−	0.156983i
$149$	1.18662e10			1.97230			0.986152	−	0.165843i	$-0.0530344\pi$
$149$	1.18662e10			1.97230			0.986152	+	0.165843i	$0.0530344\pi$
$150$		0			0
$151$	4.78585e9			0.749140			0.374570	−	0.927199i	$-0.377790\pi$
$151$	4.78585e9			0.749140			0.374570	+	0.927199i	$0.377790\pi$
$152$	1.07409e9	−	1.07409e9i	0.163209	−	0.163209i
$153$	−1.50192e9	−	5.35283e9i	−0.221582	−	0.789718i
$154$			6.94562e9i			0.995103i
$155$		0			0
$156$	−7.44113e9	+	2.84380e10i	−1.00595	+	3.84448i
$157$	5.43469e9	+	5.43469e9i	0.713882	+	0.713882i	0.967345	−	0.253463i	$-0.0815696\pi$
$157$	5.43469e9	+	5.43469e9i	0.713882	+	0.713882i	−0.253463	+	0.967345i	$0.581570\pi$
$158$	8.85322e8	+	8.85322e8i	0.113017	+	0.113017i
$159$	2.18377e9	−	8.34576e9i	0.270969	−	1.03557i
$160$		0			0
$161$			6.32096e9i			0.741424i
$162$	1.57812e10	+	3.83347e9i	1.80021	+	0.437295i
$163$	1.37006e9	−	1.37006e9i	0.152018	−	0.152018i	−0.627001	−	0.779019i	$-0.715718\pi$
$163$	1.37006e9	−	1.37006e9i	0.152018	−	0.152018i	0.779019	+	0.627001i	$0.215718\pi$
$164$	−3.54552e10			−3.82722
$165$		0			0
$166$	1.19028e10			1.21664
$167$	8.50234e9	−	8.50234e9i	0.845891	−	0.845891i	−0.143726	−	0.989617i	$-0.545908\pi$
$167$	8.50234e9	−	8.50234e9i	0.845891	−	0.845891i	0.989617	+	0.143726i	$0.0459085\pi$
$168$	3.81972e10	−	2.23534e10i	3.69947	−	2.16497i
$169$		−	1.77102e10i		−	1.67006i
$170$		0			0
$171$	8.48152e8	+	4.76481e8i	0.0758562	+	0.0426151i
$172$	−5.77964e9	−	5.77964e9i	−0.503527	−	0.503527i
$173$	4.78858e9	+	4.78858e9i	0.406443	+	0.406443i	0.880496	−	0.474053i	$-0.157210\pi$
$173$	4.78858e9	+	4.78858e9i	0.406443	+	0.406443i	−0.474053	+	0.880496i	$0.657210\pi$
$174$	5.63572e8	+	1.47465e8i	0.0466099	+	0.0121960i
$175$		0			0
$176$			1.05052e10i			0.825270i
$177$	−9.75777e9	−	1.66739e10i	−0.747259	−	1.27691i
$178$	−1.07709e10	+	1.07709e10i	−0.804198	+	0.804198i
$179$	−7.99954e9			−0.582407			−0.291203	−	0.956661i	$-0.594056\pi$
$179$	−7.99954e9			−0.582407			−0.291203	+	0.956661i	$0.594056\pi$
$180$		0			0
$181$	−1.61751e10			−1.12019			−0.560096	−	0.828428i	$-0.689236\pi$
$181$	−1.61751e10			−1.12019			−0.560096	+	0.828428i	$0.689236\pi$
$182$	−5.11949e10	+	5.11949e10i	−3.45864	+	3.45864i
$183$	−5.26247e9	−	8.99244e9i	−0.346865	−	0.592717i
$184$			1.89262e10i			1.21726i
$185$		0			0
$186$	−4.32664e10	−	1.13212e10i	−2.65059	−	0.693558i
$187$	3.22410e9	+	3.22410e9i	0.192806	+	0.192806i
$188$	2.72943e10	+	2.72943e10i	1.59354	+	1.59354i
$189$	2.03926e10	+	1.96861e10i	1.16250	+	1.12223i
$190$		0			0
$191$			3.24773e9i			0.176575i	0.996095	+	0.0882877i	$0.0281395\pi$
$191$			3.24773e9i			0.176575i	−0.996095	+	0.0882877i	$0.971861\pi$
$192$	1.82488e10	−	1.06794e10i	0.969123	−	0.567141i
$193$	−4.66059e9	+	4.66059e9i	−0.241787	+	0.241787i	−0.817589	−	0.575802i	$-0.804690\pi$
$193$	−4.66059e9	+	4.66059e9i	−0.241787	+	0.241787i	0.575802	+	0.817589i	$0.304690\pi$
$194$	−3.88166e10			−1.96748
$195$		0			0
$196$	8.09385e10			3.91744
$197$	1.61845e10	−	1.61845e10i	0.765600	−	0.765600i	−0.211728	−	0.977329i	$-0.567909\pi$
$197$	1.61845e10	−	1.61845e10i	0.765600	−	0.765600i	0.977329	+	0.211728i	$0.0679091\pi$
$198$	−1.28238e10	+	3.59816e9i	−0.592958	+	0.166375i
$199$			1.77236e10i			0.801150i	0.916264	+	0.400575i	$0.131190\pi$
$199$			1.77236e10i			0.801150i	−0.916264	+	0.400575i	$0.868810\pi$
$200$		0			0
$201$	2.18081e9	−	8.33446e9i	0.0942401	−	0.360160i
$202$	1.52490e10	+	1.52490e10i	0.644407	+	0.644407i
$203$	7.18939e8	+	7.18939e8i	0.0297139	+	0.0297139i
$204$	1.24905e10	−	4.77354e10i	0.504946	−	1.92977i
$205$		0			0
$206$		−	1.74194e10i		−	0.673953i
$207$	−1.16705e10	+	3.27455e9i	−0.441797	+	0.123961i
$208$	−7.74316e10	+	7.74316e10i	−2.86836	+	2.86836i
$209$	−7.97849e8			−0.0289243
$210$		0			0
$211$	−3.86728e9			−0.134318			−0.0671591	−	0.997742i	$-0.521393\pi$
$211$	−3.86728e9			−0.134318			−0.0671591	+	0.997742i	$0.521393\pi$
$212$	5.41394e10	−	5.41394e10i	1.84078	−	1.84078i
$213$	2.48464e10	−	1.45404e10i	0.827094	−	0.484024i
$214$			9.78822e10i			3.19038i
$215$		0			0
$216$	6.10594e10	+	5.89440e10i	1.90858	+	1.84246i
$217$	−5.51942e10	−	5.51942e10i	−1.68976	−	1.68976i
$218$	−1.25631e9	−	1.25631e9i	−0.0376740	−	0.0376740i
$219$	3.47816e10	+	9.10103e9i	1.02177	+	0.267357i
$220$		0			0
$221$			4.75285e10i			1.34026i
$222$	3.09122e9	+	5.28223e9i	0.0854164	+	0.145958i
$223$	4.34667e9	−	4.34667e9i	0.117702	−	0.117702i	−0.645802	−	0.763505i	$-0.723477\pi$
$223$	4.34667e9	−	4.34667e9i	0.117702	−	0.117702i	0.763505	+	0.645802i	$0.223477\pi$
$224$	1.18490e11			3.14460
$225$		0			0
$226$	−7.33409e10			−1.87007
$227$	−2.74323e10	+	2.74323e10i	−0.685719	+	0.685719i	−0.961283	−	0.275564i	$-0.911136\pi$
$227$	−2.74323e10	+	2.74323e10i	−0.685719	+	0.685719i	0.275564	+	0.961283i	$0.411136\pi$
$228$	4.36092e9	+	7.45188e9i	0.106874	+	0.182624i
$229$		−	2.09342e10i		−	0.503033i	−0.967853	−	0.251517i	$-0.919071\pi$
$229$		−	2.09342e10i		−	0.503033i	0.967853	−	0.251517i	$-0.0809293\pi$
$230$		0			0
$231$	−2.24890e10	−	5.88451e9i	−0.519656	−	0.135974i
$232$	2.15264e9	+	2.15264e9i	0.0487838	+	0.0487838i
$233$	−3.13849e10	−	3.13849e10i	−0.697621	−	0.697621i	0.266276	−	0.963897i	$-0.414207\pi$
$233$	−3.13849e10	−	3.13849e10i	−0.697621	−	0.697621i	−0.963897	+	0.266276i	$0.914207\pi$
$234$	−1.21043e11	−	6.80007e10i	−2.63918	−	1.48266i
$235$		0			0
$236$		−	1.71464e11i		−	3.59806i
$237$	−3.61662e9	+	2.11649e9i	−0.0744621	+	0.0435760i
$238$	8.59347e10	−	8.59347e10i	1.73609	−	1.73609i
$239$	5.44824e10			1.08010			0.540052	−	0.841632i	$-0.318405\pi$
$239$	5.44824e10			1.08010			0.540052	+	0.841632i	$0.318405\pi$
$240$		0			0
$241$	−8.54614e10			−1.63190			−0.815949	−	0.578124i	$-0.803785\pi$
$241$	−8.54614e10			−1.63190			−0.815949	+	0.578124i	$0.803785\pi$
$242$	−6.21677e10	+	6.21677e10i	−1.16519	+	1.16519i
$243$	−2.57825e10	+	4.78495e10i	−0.474347	+	0.880338i
$244$		−	9.24723e10i		−	1.67016i
$245$		0			0
$246$	4.23902e10	−	1.62004e11i	0.738001	−	2.82044i
$247$	−5.88080e9	−	5.88080e9i	−0.100531	−	0.100531i
$248$	−1.65262e11	−	1.65262e11i	−2.77422	−	2.77422i
$249$	−1.00843e10	+	3.85396e10i	−0.166246	+	0.635345i
$250$		0			0
$251$			8.72214e10i			1.38705i	0.720434	+	0.693523i	$0.243943\pi$
$251$			8.72214e10i			1.38705i	−0.720434	+	0.693523i	$0.756057\pi$
$252$	6.79602e10	+	2.42210e11i	1.06158	+	3.78346i
$253$	7.02934e9	−	7.02934e9i	0.107863	−	0.107863i
$254$	−8.67000e10			−1.30697
$255$		0			0
$256$	−6.01001e10			−0.874572
$257$	4.98619e10	−	4.98619e10i	0.712968	−	0.712968i	−0.254187	−	0.967155i	$-0.581808\pi$
$257$	4.98619e10	−	4.98619e10i	0.712968	−	0.712968i	0.967155	+	0.254187i	$0.0818080\pi$
$258$	3.33187e10	−	1.94985e10i	0.468166	−	0.273976i
$259$			1.06819e10i			0.147502i
$260$		0			0
$261$	−9.54945e8	+	1.69983e9i	−0.0127379	+	0.0226738i
$262$	−8.55536e9	−	8.55536e9i	−0.112172	−	0.112172i
$263$	9.63527e10	+	9.63527e10i	1.24183	+	1.24183i	0.959240	+	0.282592i	$0.0911944\pi$
$263$	9.63527e10	+	9.63527e10i	1.24183	+	1.24183i	0.282592	+	0.959240i	$0.408806\pi$
$264$	−6.73364e10	−	1.76194e10i	−0.853163	−	0.223240i
$265$		0			0
$266$			2.12658e10i			0.260443i
$267$	−2.57494e10	−	4.40002e10i	−0.310075	−	0.529851i
$268$	5.40661e10	−	5.40661e10i	0.640204	−	0.640204i
$269$	5.37045e10			0.625353			0.312676	−	0.949860i	$-0.398774\pi$
$269$	5.37045e10			0.625353			0.312676	+	0.949860i	$0.398774\pi$
$270$		0			0
$271$	8.75000e10			0.985477			0.492738	−	0.870178i	$-0.335996\pi$
$271$	8.75000e10			0.985477			0.492738	+	0.870178i	$0.335996\pi$
$272$	1.29975e11	−	1.29975e11i	1.43979	−	1.43979i
$273$	−1.22388e11	−	2.09136e11i	−1.33355	−	2.27875i
$274$		−	1.33378e11i		−	1.42958i
$275$		0			0
$276$	−1.04075e11	−	2.72325e10i	−1.07958	−	0.282485i
$277$	−1.06315e11	−	1.06315e11i	−1.08502	−	1.08502i	−0.996033	−	0.0889863i	$-0.971637\pi$
$277$	−1.06315e11	−	1.06315e11i	−1.08502	−	1.08502i	−0.0889863	−	0.996033i	$-0.528363\pi$
$278$	3.41727e10	+	3.41727e10i	0.343145	+	0.343145i
$279$	7.33128e10	−	1.30499e11i	0.724371	−	1.28940i
$280$		0			0
$281$			1.67658e11i			1.60415i	0.597221	+	0.802077i	$0.296272\pi$
$281$			1.67658e11i			1.60415i	−0.597221	+	0.802077i	$0.703728\pi$
$282$	−1.57347e11	+	9.20814e10i	−1.48163	+	0.867064i
$283$	7.72903e10	−	7.72903e10i	0.716285	−	0.716285i	−0.251557	−	0.967842i	$-0.580943\pi$
$283$	7.72903e10	−	7.72903e10i	0.716285	−	0.716285i	0.967842	+	0.251557i	$0.0809427\pi$
$284$	2.55504e11			2.33058
$285$		0			0
$286$	1.13864e11			1.00633
$287$	2.06665e11	−	2.06665e11i	1.79804	−	1.79804i
$288$	6.13834e10	+	2.18770e11i	0.525757	+	1.87379i
$289$			3.88075e10i			0.327247i
$290$		0			0
$291$	3.28864e10	−	1.25683e11i	0.268842	−	1.02744i
$292$	2.25630e11	+	2.25630e11i	1.81625	+	1.81625i
$293$	9.19242e10	+	9.19242e10i	0.728661	+	0.728661i	0.970353	−	0.241692i	$-0.0777024\pi$
$293$	9.19242e10	+	9.19242e10i	0.728661	+	0.728661i	−0.241692	+	0.970353i	$0.577702\pi$
$294$	−9.67698e10	+	3.69828e11i	−0.755400	+	2.88693i
$295$		0			0
$296$			3.19836e10i			0.242167i
$297$	−7.85673e8	−	4.45703e10i	−0.00585920	−	0.332385i
$298$	−3.51725e11	+	3.51725e11i	−2.58363	+	2.58363i
$299$	1.03624e11			0.749790
$300$		0			0
$301$	6.73780e10			0.473117
$302$	−1.41857e11	+	1.41857e11i	−0.981340	+	0.981340i
$303$	−6.22936e10	+	3.64549e10i	−0.424572	+	0.248464i
$304$			3.21642e10i			0.215994i
$305$		0			0
$306$	2.03181e11	+	1.14145e11i	1.32476	+	0.744233i
$307$	2.04830e11	+	2.04830e11i	1.31605	+	1.31605i	0.916877	+	0.399170i	$0.130702\pi$
$307$	2.04830e11	+	2.04830e11i	1.31605	+	1.31605i	0.399170	+	0.916877i	$0.369298\pi$
$308$	−1.45887e11	−	1.45887e11i	−0.923717	−	0.923717i
$309$	5.64015e10	+	1.47581e10i	0.351947	+	0.0920912i
$310$		0			0
$311$		−	8.87365e10i		−	0.537874i	−0.963158	−	0.268937i	$-0.913328\pi$
$311$		−	8.87365e10i		−	0.537874i	0.963158	−	0.268937i	$-0.0866723\pi$
$312$	−3.66455e11	−	6.26193e11i	−2.18940	−	3.74121i
$313$	−1.06735e11	+	1.06735e11i	−0.628575	+	0.628575i	−0.947709	−	0.319135i	$-0.896608\pi$
$313$	−1.06735e11	+	1.06735e11i	−0.628575	+	0.628575i	0.319135	+	0.947709i	$0.396608\pi$
$314$	−3.22178e11			−1.87031
$315$		0			0
$316$	−3.71909e10			−0.209819
$317$	−1.76406e11	+	1.76406e11i	−0.981176	+	0.981176i	−0.999826	−	0.0186500i	$-0.994063\pi$
$317$	−1.76406e11	+	1.76406e11i	−0.981176	+	0.981176i	0.0186500	+	0.999826i	$0.494063\pi$
$318$	1.82647e11	+	3.12105e11i	1.00159	+	1.71151i
$319$		−	1.59902e9i		−	0.00864560i
$320$		0			0
$321$	−3.16929e11	−	8.29283e10i	−1.66606	−	0.435944i
$322$	−1.87359e11	−	1.87359e11i	−0.971232	−	0.971232i
$323$	9.87139e9	+	9.87139e9i	0.0504623	+	0.0504623i
$324$	−4.11990e11	+	2.50952e11i	−2.07699	+	1.26514i
$325$		0			0
$326$			8.12197e10i			0.398274i
$327$	5.13213e9	−	3.00338e9i	0.0248218	−	0.0145260i
$328$	6.18795e11	−	6.18795e11i	2.95199	−	2.95199i
$329$	−3.18192e11			−1.49730
$330$		0			0
$331$	2.33530e11			1.06934			0.534671	−	0.845060i	$-0.320435\pi$
$331$	2.33530e11			1.06934			0.534671	+	0.845060i	$0.320435\pi$
$332$	−2.50008e11	+	2.50008e11i	−1.12936	+	1.12936i
$333$	−1.97221e10	+	5.53371e9i	−0.0878930	+	0.0246614i
$334$			5.04034e11i			2.21616i
$335$		0			0
$336$	−2.37226e11	+	9.06613e11i	−1.01540	+	3.88057i
$337$	1.70740e11	+	1.70740e11i	0.721108	+	0.721108i	0.968831	−	0.247723i	$-0.0796822\pi$
$337$	1.70740e11	+	1.70740e11i	0.721108	+	0.721108i	−0.247723	+	0.968831i	$0.579682\pi$
$338$	5.24946e11	+	5.24946e11i	2.18771	+	2.18771i
$339$	6.21363e10	−	2.37468e11i	0.255533	−	0.976577i
$340$		0			0
$341$			1.22759e11i			0.491654i
$342$	−3.92633e10	+	1.10167e10i	−0.155192	+	0.0435444i
$343$	−1.78898e11	+	1.78898e11i	−0.697882	+	0.697882i
$344$	2.01743e11			0.776756
$345$		0			0
$346$	−2.83876e11			−1.06484
$347$	8.14081e10	−	8.14081e10i	0.301429	−	0.301429i	−0.540144	−	0.841573i	$-0.681630\pi$
$347$	8.14081e10	−	8.14081e10i	0.301429	−	0.301429i	0.841573	+	0.540144i	$0.181630\pi$
$348$	−1.49348e10	+	8.73998e9i	−0.0545873	+	0.0319451i
$349$		−	2.07506e11i		−	0.748714i	−0.927285	−	0.374357i	$-0.877863\pi$
$349$		−	2.07506e11i		−	0.748714i	0.927285	−	0.374357i	$-0.122137\pi$
$350$		0			0
$351$	3.22728e11	−	3.34310e11i	1.13489	−	1.17562i
$352$	−1.31769e11	−	1.31769e11i	−0.457479	−	0.457479i
$353$	−1.74023e11	−	1.74023e11i	−0.596513	−	0.596513i	0.342870	−	0.939383i	$-0.388601\pi$
$353$	−1.74023e11	−	1.74023e11i	−0.596513	−	0.596513i	−0.939383	+	0.342870i	$0.888601\pi$
$354$	7.83460e11	+	2.05002e11i	2.65156	+	0.693813i
$355$		0			0
$356$		−	4.52469e11i		−	1.49301i
$357$	2.05439e11	+	3.51051e11i	0.669385	+	1.14383i
$358$	2.37114e11	−	2.37114e11i	0.762927	−	0.762927i
$359$	−5.85721e11			−1.86108			−0.930542	−	0.366186i	$-0.880663\pi$
$359$	−5.85721e11			−1.86108			−0.930542	+	0.366186i	$0.880663\pi$
$360$		0			0
$361$	3.20245e11			0.992430
$362$	4.79443e11	−	4.79443e11i	1.46740	−	1.46740i
$363$	−1.48620e11	−	2.53961e11i	−0.449261	−	0.767691i
$364$		−	2.15061e12i		−	6.42105i
$365$		0			0
$366$	4.22529e11	+	1.10560e11i	1.23081	+	0.322056i
$367$	3.32031e11	+	3.32031e11i	0.955393	+	0.955393i	0.999047	−	0.0436540i	$-0.0138999\pi$
$367$	3.32031e11	+	3.32031e11i	0.955393	+	0.955393i	−0.0436540	+	0.999047i	$0.513900\pi$
$368$	−2.83378e11	−	2.83378e11i	−0.805474	−	0.805474i
$369$	4.88632e11	+	2.74507e11i	1.37203	+	0.770788i
$370$		0			0
$371$			6.31146e11i			1.72961i
$372$	1.14657e12	−	6.70983e11i	3.10425	−	1.81664i
$373$	4.41482e11	−	4.41482e11i	1.18093	−	1.18093i	0.201424	−	0.979504i	$-0.435443\pi$
$373$	4.41482e11	−	4.41482e11i	1.18093	−	1.18093i	0.979504	−	0.201424i	$-0.0645570\pi$
$374$	−1.91131e11			−0.505136
$375$		0			0
$376$	−9.52728e11			−2.45824
$377$	1.17861e10	−	1.17861e10i	0.0300492	−	0.0300492i
$378$	−1.18797e12	+	2.09412e10i	−2.99290	+	0.0527581i
$379$			2.10839e11i			0.524898i	0.964946	+	0.262449i	$0.0845301\pi$
$379$			2.10839e11i			0.524898i	−0.964946	+	0.262449i	$0.915470\pi$
$380$		0			0
$381$	7.34544e10	−	2.80723e11i	0.178589	−	0.682520i
$382$	−9.62657e10	−	9.62657e10i	−0.231306	−	0.231306i
$383$	3.86785e11	+	3.86785e11i	0.918491	+	0.918491i	0.996920	−	0.0784289i	$-0.0249904\pi$
$383$	3.86785e11	+	3.86785e11i	0.918491	+	0.918491i	−0.0784289	+	0.996920i	$0.524990\pi$
$384$	−1.44564e10	+	5.52485e10i	−0.0339290	+	0.129667i
$385$		0			0
$386$		−	2.76288e11i		−	0.633460i
$387$	3.49049e10	+	1.24401e11i	0.0791020	+	0.281919i
$388$	8.15311e11	−	8.15311e11i	1.82633	−	1.82633i
$389$	6.94915e10			0.153871			0.0769357	−	0.997036i	$-0.475486\pi$
$389$	6.94915e10			0.153871			0.0769357	+	0.997036i	$0.475486\pi$
$390$		0			0
$391$	−1.73941e11			−0.376363
$392$	−1.41261e12	+	1.41261e12i	−3.02158	+	3.02158i
$393$	3.49494e10	−	2.04528e10i	0.0739050	−	0.0432500i
$394$			9.59448e11i			2.00580i
$395$		0			0
$396$	1.93778e11	−	3.44930e11i	0.395982	−	0.704860i
$397$	−6.23636e11	−	6.23636e11i	−1.26001	−	1.26001i	−0.951088	−	0.308922i	$-0.900032\pi$
$397$	−6.23636e11	−	6.23636e11i	−1.26001	−	1.26001i	−0.308922	−	0.951088i	$-0.599968\pi$
$398$	−5.25344e11	−	5.25344e11i	−1.04947	−	1.04947i
$399$	−6.88556e10	−	1.80169e10i	−0.136007	−	0.0355879i
$400$		0			0
$401$		−	5.07588e11i		−	0.980306i	−0.871636	−	0.490153i	$-0.836941\pi$
$401$		−	5.07588e11i		−	0.980306i	0.871636	−	0.490153i	$-0.163059\pi$
$402$	1.82400e11	+	3.11682e11i	0.348343	+	0.595244i
$403$	−9.04836e11	+	9.04836e11i	−1.70882	+	1.70882i
$404$	−6.40586e11			−1.19636
$405$		0			0
$406$	−4.26200e10			−0.0778478
$407$	1.18790e10	−	1.18790e10i	0.0214587	−	0.0214587i
$408$	6.15124e11	+	1.05111e12i	1.09898	+	1.87793i
$409$		−	5.94486e11i		−	1.05048i	−0.850955	−	0.525238i	$-0.823976\pi$
$409$		−	5.94486e11i		−	1.05048i	0.850955	−	0.525238i	$-0.176024\pi$
$410$		0			0
$411$	4.31860e11	+	1.13001e11i	0.746544	+	0.195342i
$412$	3.65880e11	+	3.65880e11i	0.625606	+	0.625606i
$413$	9.99446e11	+	9.99446e11i	1.69038	+	1.69038i
$414$	2.48863e11	−	4.42985e11i	0.416351	−	0.741118i
$415$		0			0
$416$		−	1.94249e12i		−	3.18009i
$417$	−1.39599e11	+	8.16946e10i	−0.226083	+	0.132306i
$418$	2.36490e10	−	2.36490e10i	0.0378895	−	0.0378895i
$419$	−5.67328e11			−0.899231			−0.449615	−	0.893222i	$-0.648439\pi$
$419$	−5.67328e11			−0.899231			−0.449615	+	0.893222i	$0.648439\pi$
$420$		0			0
$421$	5.63710e10			0.0874553			0.0437276	−	0.999043i	$-0.486077\pi$
$421$	5.63710e10			0.0874553			0.0437276	+	0.999043i	$0.486077\pi$
$422$	1.14630e11	−	1.14630e11i	0.175951	−	0.175951i
$423$	−1.64838e11	−	5.87483e11i	−0.250338	−	0.892204i
$424$			1.88977e12i			2.83964i
$425$		0			0
$426$	−3.05479e11	+	1.16746e12i	−0.449406	+	1.71751i
$427$	5.39012e11	+	5.39012e11i	0.784645	+	0.784645i
$428$	−2.05594e12	−	2.05594e12i	−2.96151	−	2.96151i
$429$	−9.64689e10	+	3.68678e11i	−0.137508	+	0.525520i
$430$		0			0
$431$		−	1.93049e11i		−	0.269476i	−0.990881	−	0.134738i	$-0.956981\pi$
$431$		−	1.93049e11i		−	0.269476i	0.990881	−	0.134738i	$-0.0430193\pi$
$432$	−1.79679e12	+	3.16733e10i	−2.48210	+	0.0437539i
$433$	−5.37694e11	+	5.37694e11i	−0.735088	+	0.735088i	−0.971623	−	0.236535i	$-0.923988\pi$
$433$	−5.37694e11	+	5.37694e11i	−0.735088	+	0.735088i	0.236535	+	0.971623i	$0.423988\pi$
$434$	3.27201e12			4.42701
$435$		0			0
$436$	5.27755e10			0.0699428
$437$	2.15221e10	−	2.15221e10i	0.0282304	−	0.0282304i
$438$	−1.30072e12	+	7.61197e11i	−1.68869	+	0.988242i
$439$			6.94162e11i			0.892012i	0.895030	+	0.446006i	$0.147154\pi$
$439$			6.94162e11i			0.892012i	−0.895030	+	0.446006i	$0.852846\pi$
$440$		0			0
$441$	−1.11547e12	−	6.26655e11i	−1.40437	−	0.788960i
$442$	−1.40879e12	−	1.40879e12i	−1.75568	−	1.75568i
$443$	−1.65910e11	−	1.65910e11i	−0.204671	−	0.204671i	0.597327	−	0.801998i	$-0.296230\pi$
$443$	−1.65910e11	−	1.65910e11i	−0.204671	−	0.204671i	−0.801998	+	0.597327i	$0.796230\pi$
$444$	−1.75878e11	−	4.60205e10i	−0.214777	−	0.0561989i
$445$		0			0
$446$			2.57678e11i			0.308369i
$447$	−8.40848e11	−	1.43683e12i	−0.996171	−	1.70224i
$448$	−1.09384e12	+	1.09384e12i	−1.28293	+	1.28293i
$449$	7.23937e11			0.840606			0.420303	−	0.907384i	$-0.361924\pi$
$449$	7.23937e11			0.840606			0.420303	+	0.907384i	$0.361924\pi$
$450$		0			0
$451$	−4.59651e11			−0.523160
$452$	1.54047e12	−	1.54047e12i	1.73592	−	1.73592i
$453$	−3.39129e11	−	5.79499e11i	−0.378375	−	0.646563i
$454$		−	1.62624e12i		−	1.79652i
$455$		0			0
$456$	−2.06167e11	−	5.39461e10i	−0.223294	−	0.0584276i
$457$	−8.04589e10	−	8.04589e10i	−0.0862882	−	0.0862882i	0.662645	−	0.748933i	$-0.269434\pi$
$457$	−8.04589e10	−	8.04589e10i	−0.0862882	−	0.0862882i	−0.748933	+	0.662645i	$0.769434\pi$
$458$	6.20509e11	+	6.20509e11i	0.658951	+	0.658951i
$459$	−5.41725e11	+	5.61166e11i	−0.569668	+	0.590112i
$460$		0			0
$461$			1.23002e12i			1.26840i	0.773168	+	0.634201i	$0.218671\pi$
$461$			1.23002e12i			1.26840i	−0.773168	+	0.634201i	$0.781329\pi$
$462$	8.41016e11	−	4.92172e11i	0.858846	−	0.502606i
$463$	9.42317e11	−	9.42317e11i	0.952977	−	0.952977i	−0.0459659	−	0.998943i	$-0.514637\pi$
$463$	9.42317e11	−	9.42317e11i	0.952977	−	0.952977i	0.998943	+	0.0459659i	$0.0146366\pi$
$464$	−6.44622e10			−0.0645616
$465$		0			0
$466$	1.86056e12			1.82770
$467$	−1.15861e12	+	1.15861e12i	−1.12723	+	1.12723i	−0.136600	+	0.990626i	$0.543617\pi$
$467$	−1.15861e12	+	1.15861e12i	−1.12723	+	1.12723i	−0.990626	+	0.136600i	$0.956383\pi$
$468$	3.97072e12	−	1.11412e12i	3.82615	−	1.07356i
$469$			6.30292e11i			0.601539i
$470$		0			0
$471$	2.72958e11	−	1.04317e12i	0.255565	−	0.976699i
$472$	2.99253e12	+	2.99253e12i	2.77524	+	2.77524i
$473$	−7.49289e10	−	7.49289e10i	−0.0688294	−	0.0688294i
$474$	4.44654e10	−	1.69934e11i	0.0404594	−	0.154625i
$475$		0			0
$476$			3.60998e12i			3.22310i
$477$	−1.16530e12	+	3.26963e11i	−1.03063	+	0.289179i
$478$	−1.61491e12	+	1.61491e12i	−1.41489	+	1.41489i
$479$	−1.36419e12			−1.18403			−0.592017	−	0.805926i	$-0.701668\pi$
$479$	−1.36419e12			−1.18403			−0.592017	+	0.805926i	$0.701668\pi$
$480$		0			0
$481$	1.75115e11			0.149166
$482$	2.53315e12	−	2.53315e12i	2.13771	−	2.13771i
$483$	7.65379e11	−	4.47908e11i	0.639903	−	0.374478i
$484$		−	2.61156e12i		−	2.16320i
$485$		0			0
$486$	−6.54088e11	−	2.18252e12i	−0.531830	−	1.77458i
$487$	3.70322e11	+	3.70322e11i	0.298332	+	0.298332i	0.840360	−	0.542028i	$-0.182344\pi$
$487$	3.70322e11	+	3.70322e11i	0.298332	+	0.298332i	−0.542028	+	0.840360i	$0.682344\pi$
$488$	1.61391e12	+	1.61391e12i	1.28822	+	1.28822i
$489$	−2.62978e11	−	6.88114e10i	−0.207984	−	0.0544215i
$490$		0			0
$491$		−	5.50619e10i		−	0.0427547i	−0.999771	−	0.0213774i	$-0.993195\pi$
$491$		−	5.50619e10i		−	0.0427547i	0.999771	−	0.0213774i	$-0.00680515\pi$
$492$	2.51238e12	+	4.29312e12i	1.93305	+	3.30317i
$493$	−1.97839e10	+	1.97839e10i	−0.0150834	+	0.0150834i
$494$	3.48624e11			0.263382
$495$		0			0
$496$	4.94888e12			3.67146
$497$	−1.48931e12	+	1.48931e12i	−1.09491	+	1.09491i
$498$	−8.43439e11	−	1.44126e12i	−0.614500	−	1.05005i
$499$			6.37228e11i			0.460089i	0.973180	+	0.230045i	$0.0738872\pi$
$499$			6.37228e11i			0.460089i	−0.973180	+	0.230045i	$0.926113\pi$
$500$		0			0
$501$	−1.63199e12	−	4.27031e11i	−1.15731	−	0.302823i
$502$	−2.58532e12	−	2.58532e12i	−1.81697	−	1.81697i
$503$	1.13493e12	+	1.13493e12i	0.790519	+	0.790519i	0.981579	−	0.191059i	$-0.0611922\pi$
$503$	1.13493e12	+	1.13493e12i	0.790519	+	0.790519i	−0.191059	+	0.981579i	$0.561192\pi$
$504$	−5.41336e12	−	3.04116e12i	−3.73705	−	2.09943i
$505$		0			0
$506$			4.16712e11i			0.282591i
$507$	−2.14445e12	+	1.25496e12i	−1.44139	+	0.843516i
$508$	1.82106e12	−	1.82106e12i	1.21322	−	1.21322i
$509$	−1.91690e12			−1.26581			−0.632905	−	0.774229i	$-0.718138\pi$
$509$	−1.91690e12			−1.26581			−0.632905	+	0.774229i	$0.718138\pi$
$510$		0			0
$511$	−2.63035e12			−1.70655
$512$	1.92879e12	−	1.92879e12i	1.24043	−	1.24043i
$513$	−2.40553e9	−	1.36463e11i	−0.00153350	−	0.0869934i
$514$			2.95590e12i			1.86791i
$515$		0			0
$516$	−2.90283e11	+	1.10938e12i	−0.180259	+	0.688902i
$517$	3.53851e11	+	3.53851e11i	0.217828	+	0.217828i
$518$	−3.16620e11	−	3.16620e11i	−0.193221	−	0.193221i
$519$	2.40507e11	−	9.19151e11i	0.145504	−	0.556075i
$520$		0			0
$521$		−	1.18855e12i		−	0.706722i	−0.935487	−	0.353361i	$-0.885039\pi$
$521$		−	1.18855e12i		−	0.706722i	0.935487	−	0.353361i	$-0.114961\pi$
$522$	−2.20792e10	−	7.86900e10i	−0.0130156	−	0.0463877i
$523$	1.26576e12	−	1.26576e12i	0.739766	−	0.739766i	−0.232767	−	0.972533i	$-0.574778\pi$
$523$	1.26576e12	−	1.26576e12i	0.739766	−	0.739766i	0.972533	+	0.232767i	$0.0747780\pi$
$524$	3.59397e11			0.208249
$525$		0			0
$526$	−5.71196e12			−3.25349
$527$	1.51884e12	−	1.51884e12i	0.857757	−	0.857757i
$528$	1.27203e12	−	7.44404e11i	0.712268	−	0.416827i
$529$		−	1.42192e12i		−	0.789449i
$530$		0			0
$531$	−1.32753e12	+	2.36305e12i	−0.724637	+	1.28988i
$532$	−4.46670e11	−	4.46670e11i	−0.241760	−	0.241760i
$533$	−3.38800e12	−	3.38800e12i	−1.81833	−	1.81833i
$534$	2.06744e12	+	5.40970e11i	1.10026	+	0.287897i
$535$		0			0
$536$			1.88722e12i			0.987598i
$537$	5.66853e11	+	9.68631e11i	0.294162	+	0.502659i
$538$	−1.59185e12	+	1.59185e12i	−0.819184	+	0.819184i
$539$	1.04931e12			0.535493
$540$		0			0
$541$	1.79636e12			0.901583			0.450791	−	0.892629i	$-0.351142\pi$
$541$	1.79636e12			0.901583			0.450791	+	0.892629i	$0.351142\pi$
$542$	−2.59358e12	+	2.59358e12i	−1.29093	+	1.29093i
$543$	1.14618e12	+	1.95857e12i	0.565786	+	0.966807i
$544$			3.26063e12i			1.59627i
$545$		0			0
$546$	9.82668e12	+	2.57127e12i	4.73195	+	1.23817i
$547$	−1.44906e12	−	1.44906e12i	−0.692060	−	0.692060i	0.270625	−	0.962685i	$-0.412770\pi$
$547$	−1.44906e12	−	1.44906e12i	−0.692060	−	0.692060i	−0.962685	+	0.270625i	$0.912770\pi$
$548$	2.80150e12	+	2.80150e12i	1.32702	+	1.32702i
$549$	−7.15954e11	+	1.27442e12i	−0.336364	+	0.598739i
$550$		0			0
$551$		−	4.89579e9i		−	0.00226277i
$552$	2.29169e12	−	1.34112e12i	1.05058	−	0.614812i
$553$	2.16782e11	−	2.16782e11i	0.0985737	−	0.0985737i
$554$	6.30257e12			2.84265
$555$		0			0
$556$	−1.43554e12			−0.637057
$557$	2.59623e12	−	2.59623e12i	1.14286	−	1.14286i	0.154940	−	0.987924i	$-0.450482\pi$
$557$	2.59623e12	−	2.59623e12i	1.14286	−	1.14286i	0.987924	−	0.154940i	$-0.0495183\pi$
$558$	1.69505e12	+	6.04117e12i	0.740167	+	2.63795i
$559$		−	1.10457e12i		−	0.478455i
$560$		0			0
$561$	1.61931e11	−	6.18855e11i	0.0690234	−	0.263789i
$562$	−4.96954e12	−	4.96954e12i	−2.10137	−	2.10137i
$563$	−1.42368e11	−	1.42368e11i	−0.0597208	−	0.0597208i	0.676616	−	0.736336i	$-0.263446\pi$
$563$	−1.42368e11	−	1.42368e11i	−0.0597208	−	0.0597208i	−0.736336	+	0.676616i	$0.763446\pi$
$564$	1.37086e12	−	5.23905e12i	0.570476	−	2.18020i
$565$		0			0
$566$			4.58191e12i			1.87660i
$567$	9.38673e11	−	3.86422e12i	0.381409	−	1.57014i
$568$	−4.45927e12	+	4.45927e12i	−1.79761	+	1.79761i
$569$	1.01867e11			0.0407406			0.0203703	−	0.999793i	$-0.493515\pi$
$569$	1.01867e11			0.0407406			0.0203703	+	0.999793i	$0.493515\pi$
$570$		0			0
$571$	3.03156e12			1.19345			0.596724	−	0.802447i	$-0.296469\pi$
$571$	3.03156e12			1.19345			0.596724	+	0.802447i	$0.296469\pi$
$572$	−2.39163e12	+	2.39163e12i	−0.934140	+	0.934140i
$573$	3.93254e11	−	2.30137e11i	0.152397	−	0.0891846i
$574$			1.22515e13i			4.71070i
$575$		0			0
$576$	−2.58625e12	−	1.45292e12i	−0.978968	−	0.549972i
$577$	2.34160e11	+	2.34160e11i	0.0879471	+	0.0879471i	0.749712	−	0.661765i	$-0.230192\pi$
$577$	2.34160e11	+	2.34160e11i	0.0879471	+	0.0879471i	−0.661765	+	0.749712i	$0.730192\pi$
$578$	−1.15029e12	−	1.15029e12i	−0.428678	−	0.428678i
$579$	8.94584e11	+	2.34078e11i	0.330801	+	0.0865581i
$580$		0			0
$581$		−	2.91455e12i		−	1.06115i
$582$	2.75057e12	+	4.70013e12i	0.993732	+	1.69807i
$583$	7.01878e11	−	7.01878e11i	0.251625	−	0.251625i
$584$	−7.87579e12			−2.80179
$585$		0			0
$586$	−5.44943e12			−1.90903
$587$	−3.57135e12	+	3.57135e12i	−1.24154	+	1.24154i	−0.282178	+	0.959362i	$0.591057\pi$
$587$	−3.57135e12	+	3.57135e12i	−1.24154	+	1.24154i	−0.959362	+	0.282178i	$0.908943\pi$
$588$	−5.73536e12	−	9.80050e12i	−1.97862	−	3.38104i
$589$			3.75858e11i			0.128678i
$590$		0			0
$591$	−3.10656e12	−	8.12869e11i	−1.04746	−	0.274080i
$592$	−4.78884e11	−	4.78884e11i	−0.160244	−	0.160244i
$593$	3.71726e11	+	3.71726e11i	0.123446	+	0.123446i	0.766131	−	0.642685i	$-0.222180\pi$
$593$	3.71726e11	+	3.71726e11i	0.123446	+	0.123446i	−0.642685	+	0.766131i	$0.722180\pi$
$594$	1.34439e12	+	1.29781e12i	0.443084	+	0.427734i
$595$		0			0
$596$		−	1.47754e13i		−	4.79658i
$597$	2.14608e12	−	1.25591e12i	0.691450	−	0.404644i
$598$	−3.07151e12	+	3.07151e12i	−0.982191	+	0.982191i
$599$	2.49239e12			0.791033			0.395517	−	0.918459i	$-0.370566\pi$
$599$	2.49239e12			0.791033			0.395517	+	0.918459i	$0.370566\pi$
$600$		0			0
$601$	1.11178e12			0.347605			0.173802	−	0.984781i	$-0.444395\pi$
$601$	1.11178e12			0.347605			0.173802	+	0.984781i	$0.444395\pi$
$602$	−1.99714e12	+	1.99714e12i	−0.619762	+	0.619762i
$603$	−1.16372e12	+	3.26521e11i	−0.358443	+	0.100573i
$604$		−	5.95918e12i		−	1.82188i
$605$		0			0
$606$	7.65882e11	−	2.92699e12i	0.230693	−	0.881647i
$607$	1.92756e12	+	1.92756e12i	0.576315	+	0.576315i	0.933886	−	0.357571i	$-0.116395\pi$
$607$	1.92756e12	+	1.92756e12i	0.576315	+	0.576315i	−0.357571	+	0.933886i	$0.616395\pi$
$608$	−4.03444e11	−	4.03444e11i	−0.119734	−	0.119734i
$609$	3.61088e10	−	1.37998e11i	0.0106374	−	0.0406532i
$610$		0			0
$611$			5.21634e12i			1.51419i
$612$	−6.66517e12	+	1.87014e12i	−1.92057	+	0.538880i
$613$	−2.53070e12	+	2.53070e12i	−0.723883	+	0.723883i	−0.969394	−	0.245511i	$-0.921044\pi$
$613$	−2.53070e12	+	2.53070e12i	−0.723883	+	0.723883i	0.245511	+	0.969394i	$0.421044\pi$
$614$	−1.21427e13			−3.44793
$615$		0			0
$616$	5.09230e12			1.42495
$617$	3.90361e11	−	3.90361e11i	0.108438	−	0.108438i	−0.650806	−	0.759244i	$-0.725569\pi$
$617$	3.90361e11	−	3.90361e11i	0.108438	−	0.108438i	0.759244	+	0.650806i	$0.225569\pi$
$618$	−2.10924e12	+	1.23435e12i	−0.581671	+	0.340400i
$619$		−	2.28134e12i		−	0.624571i	−0.949988	−	0.312285i	$-0.898905\pi$
$619$		−	2.28134e12i		−	0.624571i	0.949988	−	0.312285i	$-0.101095\pi$
$620$		0			0
$621$	1.22348e12	+	1.18109e12i	0.330130	+	0.318693i
$622$	2.63023e12	+	2.63023e12i	0.704591	+	0.704591i
$623$	2.63740e12	+	2.63740e12i	0.701422	+	0.701422i
$624$	1.48627e13	+	3.88901e12i	3.92435	+	1.02685i
$625$		0			0
$626$		−	6.32744e12i		−	1.64681i
$627$	5.65361e10	+	9.66082e10i	0.0146091	+	0.0249638i
$628$	6.76710e12	−	6.76710e12i	1.73614	−	1.73614i
$629$	−2.93945e11			−0.0748752
$630$		0			0
$631$	6.24192e12			1.56742			0.783711	−	0.621125i	$-0.213324\pi$
$631$	6.24192e12			1.56742			0.783711	+	0.621125i	$0.213324\pi$
$632$	6.49088e11	−	6.49088e11i	0.161837	−	0.161837i
$633$	2.74038e11	+	4.68273e11i	0.0678413	+	0.115926i
$634$		−	1.04577e13i		−	2.57059i
$635$		0			0
$636$	−1.03919e13	−	2.71915e12i	−2.51847	−	0.658987i
$637$	7.73426e12	+	7.73426e12i	1.86119	+	1.86119i
$638$	4.73963e10	+	4.73963e10i	0.0113254	+	0.0113254i
$639$	−3.52126e12	−	1.97820e12i	−0.835496	−	0.469371i
$640$		0			0
$641$		−	7.05772e12i		−	1.65121i	−0.564245	−	0.825607i	$-0.690833\pi$
$641$		−	7.05772e12i		−	1.65121i	0.564245	−	0.825607i	$-0.309167\pi$
$642$	1.18521e13	−	6.93600e12i	2.75353	−	1.61139i
$643$	−2.51554e12	+	2.51554e12i	−0.580338	+	0.580338i	−0.934996	−	0.354658i	$-0.884597\pi$
$643$	−2.51554e12	+	2.51554e12i	−0.580338	+	0.580338i	0.354658	+	0.934996i	$0.384597\pi$
$644$	7.87065e12			1.80312
$645$		0			0
$646$	−5.85194e11			−0.132207
$647$	6.62609e11	−	6.62609e11i	0.148658	−	0.148658i	−0.628860	−	0.777518i	$-0.716478\pi$
$647$	6.62609e11	−	6.62609e11i	0.148658	−	0.148658i	0.777518	+	0.628860i	$0.216478\pi$
$648$	2.81057e12	−	1.15702e13i	0.626191	−	2.57783i
$649$		−	2.22291e12i		−	0.491835i
$650$		0			0
$651$	−2.77213e12	+	1.05943e13i	−0.604922	+	2.31185i
$652$	−1.70595e12	−	1.70595e12i	−0.369703	−	0.369703i
$653$	−1.75025e12	−	1.75025e12i	−0.376695	−	0.376695i	0.493213	−	0.869909i	$-0.335822\pi$
$653$	−1.75025e12	−	1.75025e12i	−0.376695	−	0.376695i	−0.869909	+	0.493213i	$0.835822\pi$
$654$	−6.30981e10	+	2.41144e11i	−0.0134870	+	0.0515438i
$655$		0			0
$656$			1.85302e13i			3.90673i
$657$	−1.36265e12	−	4.85647e12i	−0.285324	−	1.01690i
$658$	9.43150e12	−	9.43150e12i	1.96139	−	1.96139i
$659$	3.48214e12			0.719220			0.359610	−	0.933103i	$-0.382910\pi$
$659$	3.48214e12			0.719220			0.359610	+	0.933103i	$0.382910\pi$
$660$		0			0
$661$	3.43147e12			0.699156			0.349578	−	0.936907i	$-0.386325\pi$
$661$	3.43147e12			0.699156			0.349578	+	0.936907i	$0.386325\pi$
$662$	−6.92204e12	+	6.92204e12i	−1.40079	+	1.40079i
$663$	5.75502e12	−	3.36790e12i	1.15674	−	0.676938i
$664$		−	8.72671e12i		−	1.74219i
$665$		0			0
$666$	4.20557e11	−	7.48605e11i	0.0828306	−	0.147441i
$667$	4.31337e10	+	4.31337e10i	0.00843822	+	0.00843822i
$668$	−1.05868e13	−	1.05868e13i	−2.05718	−	2.05718i
$669$	−8.34328e11	−	2.18312e11i	−0.161035	−	0.0421366i
$670$		0			0
$671$		−	1.19884e12i		−	0.228302i
$672$	−8.39629e12	−	1.43475e13i	−1.58827	−	2.71402i
$673$	−5.98934e12	+	5.98934e12i	−1.12541	+	1.12541i	−0.134498	+	0.990914i	$0.542942\pi$
$673$	−5.98934e12	+	5.98934e12i	−1.12541	+	1.12541i	−0.990914	+	0.134498i	$0.957058\pi$
$674$	−1.01218e13			−1.88924
$675$		0			0
$676$	−2.20521e13			−4.06154
$677$	−3.59586e11	+	3.59586e11i	−0.0657891	+	0.0657891i	−0.739236	−	0.673447i	$-0.764813\pi$
$677$	−3.59586e11	+	3.59586e11i	−0.0657891	+	0.0657891i	0.673447	+	0.739236i	$0.264813\pi$
$678$	5.19699e12	+	8.88054e12i	0.944535	+	1.61401i
$679$			9.50473e12i			1.71603i
$680$		0			0
$681$	5.26554e12	+	1.37779e12i	0.938168	+	0.245483i
$682$	−3.63870e12	−	3.63870e12i	−0.644045	−	0.644045i
$683$	−3.60852e12	−	3.60852e12i	−0.634507	−	0.634507i	0.314688	−	0.949195i	$-0.398100\pi$
$683$	−3.60852e12	−	3.60852e12i	−0.634507	−	0.634507i	−0.949195	+	0.314688i	$0.898100\pi$
$684$	5.93298e11	−	1.05609e12i	0.103638	−	0.184480i
$685$		0			0
$686$		−	1.06054e13i		−	1.82839i
$687$	−2.53483e12	+	1.48341e12i	−0.434154	+	0.254072i
$688$	−3.02066e12	+	3.02066e12i	−0.513988	+	0.513988i
$689$	1.03468e13			1.74912
$690$		0			0
$691$	6.84285e12			1.14179			0.570894	−	0.821023i	$-0.306597\pi$
$691$	6.84285e12			1.14179			0.570894	+	0.821023i	$0.306597\pi$
$692$	5.96258e12	−	5.96258e12i	0.988454	−	0.988454i
$693$	8.81055e11	+	3.14008e12i	0.145112	+	0.517179i
$694$			4.82602e12i			0.789717i
$695$		0			0
$696$	1.08117e11	−	4.13192e11i	0.0174643	−	0.0667437i
$697$	5.68704e12	+	5.68704e12i	0.912722	+	0.912722i
$698$	6.15066e12	+	6.15066e12i	0.980782	+	0.980782i
$699$	−1.57631e12	+	6.02423e12i	−0.249744	+	0.954452i
$700$		0			0
$701$		−	9.48280e12i		−	1.48322i	−0.670831	−	0.741610i	$-0.734063\pi$
$701$		−	9.48280e12i		−	1.48322i	0.670831	−	0.741610i	$-0.265937\pi$
$702$	3.43304e11	+	1.94752e13i	0.0533534	+	3.02667i
$703$	3.63704e10	−	3.63704e10i	0.00561629	−	0.00561629i
$704$	2.43286e12			0.373285
$705$		0			0
$706$	1.03164e13			1.56281
$707$	3.73391e12	−	3.73391e12i	0.562053	−	0.562053i
$708$	−2.07618e13	+	1.21500e13i	−3.10539	+	1.81731i
$709$		−	5.73782e12i		−	0.852784i	−0.904538	−	0.426392i	$-0.859784\pi$
$709$		−	5.73782e12i		−	0.852784i	0.904538	−	0.426392i	$-0.140216\pi$
$710$		0			0
$711$	5.12553e11	+	2.87946e11i	0.0752186	+	0.0422569i
$712$	7.89688e12	+	7.89688e12i	1.15158	+	1.15158i
$713$	−3.31145e12	−	3.31145e12i	−0.479861	−	0.479861i
$714$	−1.64949e13	−	4.31608e12i	−2.37524	−	0.621509i
$715$		0			0
$716$			9.96076e12i			1.41639i
$717$	−3.86066e12	−	6.59704e12i	−0.545538	−	0.932208i
$718$	1.73613e13	−	1.73613e13i	2.43794	−	2.43794i
$719$	−8.92648e12			−1.24566			−0.622831	−	0.782356i	$-0.714018\pi$
$719$	−8.92648e12			−1.24566			−0.622831	+	0.782356i	$0.714018\pi$
$720$		0			0
$721$	−4.26535e12			−0.587823
$722$	−9.49235e12	+	9.49235e12i	−1.30004	+	1.30004i
$723$	6.05585e12	+	1.03482e13i	0.824238	+	1.40845i
$724$			2.01406e13i			2.72427i
$725$		0			0
$726$	1.19329e13	+	3.12238e12i	1.59415	+	0.417129i
$727$	−2.71412e12	−	2.71412e12i	−0.360350	−	0.360350i	0.503592	−	0.863942i	$-0.332012\pi$
$727$	−2.71412e12	−	2.71412e12i	−0.360350	−	0.360350i	−0.863942	+	0.503592i	$0.832012\pi$
$728$	3.75344e13	+	3.75344e13i	4.95265	+	4.95265i
$729$	7.62086e12	−	2.68761e11i	0.999379	−	0.0352445i
$730$		0			0
$731$			1.85412e12i			0.240164i
$732$	−1.11971e13	+	6.55265e12i	−1.44147	+	0.843563i
$733$	−8.30621e12	+	8.30621e12i	−1.06276	+	1.06276i	−0.0648652	+	0.997894i	$0.520662\pi$
$733$	−8.30621e12	+	8.30621e12i	−1.06276	+	1.06276i	−0.997894	+	0.0648652i	$0.979338\pi$
$734$	−1.96834e13			−2.50304
$735$		0			0
$736$	7.10897e12			0.893011
$737$	7.00928e11	−	7.00928e11i	0.0875124	−	0.0875124i
$738$	−2.26201e13	+	6.34684e12i	−2.80699	+	0.787597i
$739$		−	1.04457e13i		−	1.28836i	−0.764876	−	0.644178i	$-0.777200\pi$
$739$		−	1.04457e13i		−	1.28836i	0.764876	−	0.644178i	$-0.222800\pi$
$740$		0			0
$741$	−2.95363e11	+	1.12880e12i	−0.0359894	+	0.137542i
$742$	−1.87078e13	−	1.87078e13i	−2.26571	−	2.26571i
$743$	−4.67168e12	−	4.67168e12i	−0.562371	−	0.562371i	0.367609	−	0.929980i	$-0.380176\pi$
$743$	−4.67168e12	−	4.67168e12i	−0.562371	−	0.562371i	−0.929980	+	0.367609i	$0.880176\pi$
$744$	−8.30030e12	+	3.17215e13i	−0.993151	+	3.79555i
$745$		0			0
$746$			2.61719e13i			3.09393i
$747$	5.38118e12	−	1.50987e12i	0.632317	−	0.177418i
$748$	4.01454e12	−	4.01454e12i	0.468899	−	0.468899i
$749$	2.39677e13			2.78265
$750$		0			0
$751$	−9.72404e12			−1.11549			−0.557746	−	0.830011i	$-0.688334\pi$
$751$	−9.72404e12			−1.11549			−0.557746	+	0.830011i	$0.688334\pi$
$752$	1.42650e13	−	1.42650e13i	1.62664	−	1.62664i
$753$	1.05613e13	−	6.18057e12i	1.19712	−	0.700569i
$754$			6.98699e11i			0.0787262i
$755$		0			0
$756$	2.45125e13	−	2.53922e13i	2.72922	−	2.82717i
$757$	−4.23335e12	−	4.23335e12i	−0.468546	−	0.468546i	0.432897	−	0.901443i	$-0.357491\pi$
$757$	−4.23335e12	−	4.23335e12i	−0.468546	−	0.468546i	−0.901443	+	0.432897i	$0.857491\pi$
$758$	−6.24946e12	−	6.24946e12i	−0.687593	−	0.687593i
$759$	−1.34926e12	−	3.53049e11i	−0.147573	−	0.0386142i
$760$		0			0
$761$			4.95819e12i			0.535910i	0.963431	+	0.267955i	$0.0863479\pi$
$761$			4.95819e12i			0.535910i	−0.963431	+	0.267955i	$0.913652\pi$
$762$	6.14362e12	+	1.04981e13i	0.660126	+	1.12801i
$763$	−3.07623e11	+	3.07623e11i	−0.0328593	+	0.0328593i
$764$	4.04397e12			0.429425
$765$		0			0
$766$	−2.29293e13			−2.40636
$767$	1.63846e13	−	1.63846e13i	1.70945	−	1.70945i
$768$	4.25874e12	+	7.27727e12i	0.441728	+	0.754819i
$769$			9.77555e12i			1.00803i	0.863696	+	0.504014i	$0.168144\pi$
$769$			9.77555e12i			1.00803i	−0.863696	+	0.504014i	$0.831856\pi$
$770$		0			0
$771$	−9.57082e12	−	2.50432e12i	−0.975448	−	0.255238i
$772$	5.80321e12	+	5.80321e12i	0.588018	+	0.588018i
$773$	−5.61151e12	−	5.61151e12i	−0.565291	−	0.565291i	0.365515	−	0.930806i	$-0.380893\pi$
$773$	−5.61151e12	−	5.61151e12i	−0.565291	−	0.565291i	−0.930806	+	0.365515i	$0.880893\pi$
$774$	−4.72197e12	−	2.65275e12i	−0.472922	−	0.265682i
$775$		0			0
$776$			2.84590e13i			2.81736i
$777$	1.29342e12	−	7.56924e11i	0.127305	−	0.0745003i
$778$	−2.05979e12	+	2.05979e12i	−0.201565	+	0.201565i
$779$	−1.40734e12			−0.136924
$780$		0			0
$781$	3.31242e12			0.318578
$782$	5.15577e12	−	5.15577e12i	0.493018	−	0.493018i
$783$	2.73494e11	−	4.82108e9i	0.0260028	−	0.000458370i
$784$		−	4.23015e13i		−	3.99883i
$785$		0			0
$786$	−4.29694e11	+	1.64217e12i	−0.0401567	+	0.153468i
$787$	−8.97702e12	−	8.97702e12i	−0.834153	−	0.834153i	0.153929	−	0.988082i	$-0.450807\pi$
$787$	−8.97702e12	−	8.97702e12i	−0.834153	−	0.834153i	−0.988082	+	0.153929i	$0.950807\pi$
$788$	−2.01524e13	−	2.01524e13i	−1.86191	−	1.86191i
$789$	4.83932e12	−	1.84946e13i	0.444568	−	1.69902i
$790$		0			0
$791$			1.79585e13i			1.63108i
$792$	2.63805e12	+	9.40200e12i	0.238243	+	0.849096i
$793$	8.83640e12	−	8.83640e12i	0.793499	−	0.793499i
$794$	3.69703e13			3.30111
$795$		0			0
$796$	2.20689e13			1.94837
$797$	−9.94850e12	+	9.94850e12i	−0.873364	+	0.873364i	−0.992837	−	0.119473i	$-0.961879\pi$
$797$	−9.94850e12	+	9.94850e12i	−0.873364	+	0.873364i	0.119473	+	0.992837i	$0.461879\pi$
$798$	2.57498e12	−	1.50691e12i	0.224782	−	0.131545i
$799$		−	8.75605e12i		−	0.760060i
$800$		0			0
$801$	−3.50318e12	+	6.23577e12i	−0.300688	+	0.535234i
$802$	1.50454e13	+	1.50454e13i	1.28416	+	1.28416i
$803$	2.92513e12	+	2.92513e12i	0.248271	+	0.248271i
$804$	−1.03778e13	−	2.71547e12i	−0.875897	−	0.229189i
$805$		0			0
$806$		−	5.36403e13i		−	4.47697i
$807$	−3.80554e12	−	6.50285e12i	−0.315853	−	0.539725i
$808$	1.11801e13	−	1.11801e13i	0.922769	−	0.922769i
$809$	−7.44638e11			−0.0611191			−0.0305596	−	0.999533i	$-0.509729\pi$
$809$	−7.44638e11			−0.0611191			−0.0305596	+	0.999533i	$0.509729\pi$
$810$		0			0
$811$	1.89682e13			1.53968			0.769842	−	0.638235i	$-0.220335\pi$
$811$	1.89682e13			1.53968			0.769842	+	0.638235i	$0.220335\pi$
$812$	8.95198e11	−	8.95198e11i	0.0722632	−	0.0722632i
$813$	−6.20031e12	−	1.05950e13i	−0.497744	−	0.850538i
$814$			7.04207e11i			0.0562199i
$815$		0			0
$816$	−2.49483e13	−	6.52802e12i	−1.96986	−	0.515437i
$817$	−2.29413e11	−	2.29413e11i	−0.0180144	−	0.0180144i
$818$	1.76211e13	+	1.76211e13i	1.37608	+	1.37608i
$819$	−1.66508e13	+	2.96390e13i	−1.29318	+	2.30190i
$820$		0			0
$821$		−	1.98177e13i		−	1.52233i	−0.648557	−	0.761166i	$-0.724627\pi$
$821$		−	1.98177e13i		−	1.52233i	0.648557	−	0.761166i	$-0.275373\pi$
$822$	−1.61502e13	+	9.45127e12i	−1.23383	+	0.722050i
$823$	7.61050e12	−	7.61050e12i	0.578248	−	0.578248i	−0.356172	−	0.934420i	$-0.615918\pi$
$823$	7.61050e12	−	7.61050e12i	0.578248	−	0.578248i	0.934420	+	0.356172i	$0.115918\pi$
$824$	−1.27713e13			−0.965078
$825$		0			0
$826$	−5.92490e13			−4.42864
$827$	−9.32693e12	+	9.32693e12i	−0.693368	+	0.693368i	−0.962972	−	0.269603i	$-0.913107\pi$
$827$	−9.32693e12	+	9.32693e12i	−0.693368	+	0.693368i	0.269603	+	0.962972i	$0.413107\pi$
$828$	4.07736e12	+	1.45317e13i	0.301469	+	1.07444i
$829$		−	4.66048e12i		−	0.342716i	−0.985209	−	0.171358i	$-0.945184\pi$
$829$		−	4.66048e12i		−	0.342716i	0.985209	−	0.171358i	$-0.0548155\pi$
$830$		0			0
$831$	−5.33970e12	+	2.04069e13i	−0.388430	+	1.48447i
$832$	1.79321e13	+	1.79321e13i	1.29741	+	1.29741i
$833$	−1.29826e13	−	1.29826e13i	−0.934240	−	0.934240i
$834$	1.71633e12	−	6.55933e12i	0.122844	−	0.469475i
$835$		0			0
$836$			9.93455e11i			0.0703428i
$837$	−2.09966e13	+	3.70122e11i	−1.47871	+	0.0260664i
$838$	1.68161e13	−	1.68161e13i	1.17795	−	1.17795i
$839$	−5.16560e12			−0.359908			−0.179954	−	0.983675i	$-0.557595\pi$
$839$	−5.16560e12			−0.359908			−0.179954	+	0.983675i	$0.557595\pi$
$840$		0			0
$841$	−1.44973e13			−0.999324
$842$	−1.67089e12	+	1.67089e12i	−0.114562	+	0.114562i
$843$	2.03010e13	−	1.18804e13i	1.38450	−	0.810225i
$844$			4.81541e12i			0.326657i
$845$		0			0
$846$	2.22995e13	+	1.25276e13i	1.49668	+	0.840815i
$847$	1.52226e13	+	1.52226e13i	1.01628	+	1.01628i
$848$	−2.82952e13	−	2.82952e13i	−1.87902	−	1.87902i
$849$	−1.48356e13	−	3.88191e12i	−0.979987	−	0.256425i
$850$		0			0
$851$			6.40873e11i			0.0418879i
$852$	−1.81052e13	−	3.09379e13i	−1.17713	−	2.01146i
$853$	1.17400e13	−	1.17400e13i	0.759272	−	0.759272i	−0.216917	−	0.976190i	$-0.569600\pi$
$853$	1.17400e13	−	1.17400e13i	0.759272	−	0.759272i	0.976190	+	0.216917i	$0.0696003\pi$
$854$	−3.19536e13			−2.05570
$855$		0			0
$856$	7.17640e13			4.56851
$857$	3.00769e12	−	3.00769e12i	0.190467	−	0.190467i	−0.605431	−	0.795898i	$-0.706999\pi$
$857$	3.00769e12	−	3.00769e12i	0.190467	−	0.190467i	0.795898	+	0.605431i	$0.206999\pi$
$858$	−8.06851e12	−	1.37874e13i	−0.508277	−	0.868537i
$859$			1.58833e12i			0.0995340i	0.998761	+	0.0497670i	$0.0158479\pi$
$859$			1.58833e12i			0.0995340i	−0.998761	+	0.0497670i	$0.984152\pi$
$860$		0			0
$861$	−3.96686e13	−	1.03798e13i	−2.45999	−	0.643685i
$862$	5.72215e12	+	5.72215e12i	0.353001	+	0.353001i
$863$	1.74132e13	+	1.74132e13i	1.06864	+	1.06864i	0.997464	+	0.0711728i	$0.0226742\pi$
$863$	1.74132e13	+	1.74132e13i	1.06864	+	1.06864i	0.0711728	+	0.997464i	$0.477326\pi$
$864$	2.21403e13	−	2.29349e13i	1.35167	−	1.40018i
$865$		0			0
$866$		−	3.18755e13i		−	1.92586i
$867$	4.69903e12	−	2.74993e12i	0.282438	−	0.165286i
$868$	−6.87259e13	+	6.87259e13i	−4.10943	+	4.10943i
$869$	−4.82154e11			−0.0286811
$870$		0			0
$871$	1.03328e13			0.608327
$872$	−9.21083e11	+	9.21083e11i	−0.0539479	+	0.0539479i
$873$	−1.75488e13	+	4.92390e12i	−1.02254	+	0.286909i
$874$			1.27587e12i			0.0739612i
$875$		0			0
$876$	1.13323e13	−	4.33089e13i	0.650204	−	2.48490i
$877$	9.56744e12	+	9.56744e12i	0.546132	+	0.546132i	0.925320	−	0.379188i	$-0.123797\pi$
$877$	9.56744e12	+	9.56744e12i	0.546132	+	0.546132i	−0.379188	+	0.925320i	$0.623797\pi$
$878$	−2.05756e13	−	2.05756e13i	−1.16850	−	1.16850i
$879$	4.61690e12	−	1.76445e13i	0.260856	−	0.996919i
$880$		0			0
$881$			4.01056e12i			0.224292i	0.993692	+	0.112146i	$0.0357724\pi$
$881$			4.01056e12i			0.224292i	−0.993692	+	0.112146i	$0.964228\pi$
$882$	5.16380e13	−	1.44888e13i	2.87317	−	0.806165i
$883$	−1.70461e13	+	1.70461e13i	−0.943632	+	0.943632i	−0.998494	−	0.0548624i	$-0.982528\pi$
$883$	−1.70461e13	+	1.70461e13i	−0.943632	+	0.943632i	0.0548624	+	0.998494i	$0.482528\pi$
$884$	5.91809e13			3.25946
$885$		0			0
$886$	9.83546e12			0.536220
$887$	−2.20528e13	+	2.20528e13i	−1.19621	+	1.19621i	−0.220918	+	0.975292i	$0.570905\pi$
$887$	−2.20528e13	+	2.20528e13i	−1.19621	+	1.19621i	−0.975292	+	0.220918i	$0.929095\pi$
$888$	3.87275e12	−	2.26638e12i	0.209007	−	0.122313i
$889$			2.12296e13i			1.13994i
$890$		0			0
$891$	−5.34115e12	+	3.25341e12i	−0.283913	+	0.172938i
$892$	−5.41233e12	−	5.41233e12i	−0.286248	−	0.286248i
$893$	1.08340e12	+	1.08340e12i	0.0570110	+	0.0570110i
$894$	6.75124e13	+	1.76654e13i	3.53480	+	0.924922i
$895$		0			0
$896$		−	4.17816e12i		−	0.216570i
$897$	−7.34286e12	−	1.25474e13i	−0.378704	−	0.647123i
$898$	−2.14581e13	+	2.14581e13i	−1.10116	+	1.10116i
$899$	−7.53281e11			−0.0384626
$900$		0			0
$901$	−1.73680e13			−0.877986
$902$	1.36245e13	−	1.36245e13i	0.685316	−	0.685316i
$903$	−4.77445e12	−	8.15851e12i	−0.238962	−	0.408334i
$904$			5.37711e13i			2.67788i
$905$		0			0
$906$	2.72290e13	+	7.12478e12i	1.34262	+	0.351313i
$907$	−1.49337e13	−	1.49337e13i	−0.732716	−	0.732716i	0.238441	−	0.971157i	$-0.423364\pi$
$907$	−1.49337e13	−	1.49337e13i	−0.732716	−	0.732716i	−0.971157	+	0.238441i	$0.923364\pi$
$908$	3.41578e13	+	3.41578e13i	1.66765	+	1.66765i
$909$	8.82833e12	+	4.95965e12i	0.428885	+	0.240942i
$910$		0			0
$911$			4.39447e12i			0.211385i	0.994399	+	0.105692i	$0.0337059\pi$
$911$			4.39447e12i			0.211385i	−0.994399	+	0.105692i	$0.966294\pi$
$912$	3.89463e12	−	2.27918e12i	0.186419	−	0.109094i
$913$	−3.24117e12	+	3.24117e12i	−0.154377	+	0.154377i
$914$	4.76975e12			0.226067
$915$		0			0
$916$	−2.60666e13			−1.22336
$917$	−2.09489e12	+	2.09489e12i	−0.0978361	+	0.0978361i
$918$	−5.76263e11	−	3.26907e13i	−0.0267811	−	1.51926i
$919$		−	1.39737e13i		−	0.646239i	−0.946358	−	0.323119i	$-0.895268\pi$
$919$		−	1.39737e13i		−	0.646239i	0.946358	−	0.323119i	$-0.104732\pi$
$920$		0			0
$921$	1.02876e13	−	3.93164e13i	0.471136	−	1.80055i
$922$	−3.64588e13	−	3.64588e13i	−1.66155	−	1.66155i
$923$	2.44152e13	+	2.44152e13i	1.10727	+	1.10727i
$924$	−7.32719e12	+	2.80025e13i	−0.330684	+	1.26379i
$925$		0			0
$926$			5.58622e13i			2.49671i
$927$	−2.20965e12	−	7.87519e12i	−0.0982800	−	0.350270i
$928$	8.08566e11	−	8.08566e11i	0.0357890	−	0.0357890i
$929$	−2.72495e13			−1.20029			−0.600147	−	0.799889i	$-0.704891\pi$
$929$	−2.72495e13			−1.20029			−0.600147	+	0.799889i	$0.704891\pi$
$930$		0			0
$931$	3.21272e12			0.140152
$932$	−3.90795e13	+	3.90795e13i	−1.69659	+	1.69659i
$933$	−1.07447e13	+	6.28793e12i	−0.464224	+	0.271669i
$934$		−	6.86845e13i		−	2.95323i
$935$		0			0
$936$	−4.98558e13	+	8.87449e13i	−2.12312	+	3.77922i
$937$	−1.07092e13	−	1.07092e13i	−0.453869	−	0.453869i	0.442768	−	0.896636i	$-0.353997\pi$
$937$	−1.07092e13	−	1.07092e13i	−0.453869	−	0.453869i	−0.896636	+	0.442768i	$0.853997\pi$
$938$	−1.86824e13	−	1.86824e13i	−0.787990	−	0.787990i
$939$	2.04874e13	+	5.36077e12i	0.859986	+	0.225025i
$940$		0			0
$941$		−	2.06121e13i		−	0.856978i	−0.903547	−	0.428489i	$-0.859046\pi$
$941$		−	2.06121e13i		−	0.856978i	0.903547	−	0.428489i	$-0.140954\pi$
$942$	2.28298e13	+	3.90112e13i	0.944654	+	1.61421i
$943$	1.23992e13	−	1.23992e13i	0.510610	−	0.510610i
$944$	−8.96134e13			−3.67281
$945$		0			0
$946$	4.44192e12			0.180327
$947$	2.18464e13	−	2.18464e13i	0.882682	−	0.882682i	−0.111125	−	0.993806i	$-0.535445\pi$
$947$	2.18464e13	−	2.18464e13i	0.882682	−	0.882682i	0.993806	+	0.111125i	$0.0354453\pi$
$948$	2.63538e12	+	4.50329e12i	0.105975	+	0.181089i
$949$			4.31212e13i			1.72581i
$950$		0			0
$951$	3.38605e13	+	8.86001e12i	1.34240	+	0.351254i
$952$	−6.30044e13	−	6.30044e13i	−2.48602	−	2.48602i
$953$	−2.19762e13	−	2.19762e13i	−0.863047	−	0.863047i	0.128644	−	0.991691i	$-0.458938\pi$
$953$	−2.19762e13	−	2.19762e13i	−0.863047	−	0.863047i	−0.991691	+	0.128644i	$0.958938\pi$
$954$	2.48490e13	−	4.42319e13i	0.971271	−	1.72889i
$955$		0			0
$956$		−	6.78396e13i		−	2.62677i
$957$	−1.93618e11	+	1.13308e11i	−0.00746179	+	0.00436672i
$958$	4.04357e13	−	4.04357e13i	1.55103	−	1.55103i
$959$	−3.26593e13			−1.24688
$960$		0			0
$961$	3.13910e13			1.18727
$962$	−5.19057e12	+	5.19057e12i	−0.195401	+	0.195401i
$963$	1.24164e13	+	4.42520e13i	0.465240	+	1.65811i
$964$			1.06414e14i			3.96872i
$965$		0			0
$966$	−9.41012e12	+	3.59629e13i	−0.347695	+	1.32879i
$967$	3.76320e13	+	3.76320e13i	1.38401	+	1.38401i	0.837371	+	0.546635i	$0.184092\pi$
$967$	3.76320e13	+	3.76320e13i	1.38401	+	1.38401i	0.546635	+	0.837371i	$0.315908\pi$
$968$	4.55793e13	+	4.55793e13i	1.66851	+	1.66851i
$969$	4.95791e11	−	1.89478e12i	0.0180652	−	0.0690401i
$970$		0			0
$971$			1.13124e13i			0.408385i	0.978931	+	0.204193i	$0.0654569\pi$
$971$			1.13124e13i			0.408385i	−0.978931	+	0.204193i	$0.934543\pi$
$972$	5.95806e13	+	3.21035e13i	2.14095	+	1.15360i
$973$	8.36762e12	−	8.36762e12i	0.299291	−	0.299291i
$974$	−2.19534e13			−0.781602
$975$		0			0
$976$	−4.83295e13			−1.70486
$977$	−8.24471e12	+	8.24471e12i	−0.289501	+	0.289501i	−0.836883	−	0.547382i	$-0.815624\pi$
$977$	−8.24471e12	+	8.24471e12i	−0.289501	+	0.289501i	0.547382	+	0.836883i	$0.315624\pi$
$978$	9.83455e12	−	5.75529e12i	0.343740	−	0.201160i
$979$		−	5.86593e12i		−	0.204087i
$980$		0			0
$981$	−7.27333e11	−	4.08607e11i	−0.0250739	−	0.0140862i
$982$	1.63208e12	+	1.63208e12i	0.0560068	+	0.0560068i
$983$	8.16033e12	+	8.16033e12i	0.278751	+	0.278751i	0.832610	−	0.553859i	$-0.186845\pi$
$983$	8.16033e12	+	8.16033e12i	0.278751	+	0.278751i	−0.553859	+	0.832610i	$0.686845\pi$
$984$	−1.18776e14	−	3.10790e13i	−4.03877	−	1.05679i
$985$		0			0
$986$		−	1.17282e12i		−	0.0395172i
$987$	2.25473e13	+	3.85285e13i	0.756254	+	1.29228i
$988$	−7.32257e12	+	7.32257e12i	−0.244488	+	0.244488i
$989$	4.04243e12			0.134357
$990$		0			0
$991$	1.47608e13			0.486158			0.243079	−	0.970006i	$-0.421842\pi$
$991$	1.47608e13			0.486158			0.243079	+	0.970006i	$0.421842\pi$
$992$	−6.20750e13	+	6.20750e13i	−2.03523	+	2.03523i
$993$	−1.65481e13	−	2.82772e13i	−0.540103	−	0.922920i
$994$		−	8.82888e13i		−	2.86858i
$995$		0			0
$996$	4.79882e13	+	1.25567e13i	1.54514	+	0.404304i
$997$	7.18684e11	+	7.18684e11i	0.0230362	+	0.0230362i	0.718531	−	0.695495i	$-0.244815\pi$
$997$	7.18684e11	+	7.18684e11i	0.0230362	+	0.0230362i	−0.695495	+	0.718531i	$0.744815\pi$
$998$	−1.88880e13	−	1.88880e13i	−0.602697	−	0.602697i
$999$	2.06758e12	+	1.99594e12i	0.0656775	+	0.0634021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.g.32.2	yes	48
3.2	odd	2	inner	75.10.e.g.32.24	yes	48
5.2	odd	4	inner	75.10.e.g.68.1	yes	48
5.3	odd	4	inner	75.10.e.g.68.24	yes	48
5.4	even	2	inner	75.10.e.g.32.23	yes	48
15.2	even	4	inner	75.10.e.g.68.23	yes	48
15.8	even	4	inner	75.10.e.g.68.2	yes	48
15.14	odd	2	inner	75.10.e.g.32.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.g.32.1	✓	48	15.14	odd	2	inner
75.10.e.g.32.2	yes	48	1.1	even	1	trivial
75.10.e.g.32.23	yes	48	5.4	even	2	inner
75.10.e.g.32.24	yes	48	3.2	odd	2	inner
75.10.e.g.68.1	yes	48	5.2	odd	4	inner
75.10.e.g.68.2	yes	48	15.8	even	4	inner
75.10.e.g.68.23	yes	48	15.2	even	4	inner
75.10.e.g.68.24	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-29.6409 + 29.6409i) q^{2} +(-70.8607 - 121.086i) q^{3} -1245.17i q^{4} +(5689.47 + 1488.72i) q^{6} +(7257.95 + 7257.95i) q^{7} +(21731.7 + 21731.7i) q^{8} +(-9640.52 + 17160.4i) q^{9} +O(q^{10})\)	\(q+(-29.6409 + 29.6409i) q^{2} +(-70.8607 - 121.086i) q^{3} -1245.17i q^{4} +(5689.47 + 1488.72i) q^{6} +(7257.95 + 7257.95i) q^{7} +(21731.7 + 21731.7i) q^{8} +(-9640.52 + 17160.4i) q^{9} -16142.7i q^{11} +(-150772. + 88233.3i) q^{12} +(118985. - 118985. i) q^{13} -430265. q^{14} -650770. q^{16} +(-199725. + 199725. i) q^{17} +(-222897. - 794405. i) q^{18} -49424.8i q^{19} +(364531. - 1.39314e6i) q^{21} +(478484. + 478484. i) q^{22} +(435451. + 435451. i) q^{23} +(1.09148e6 - 4.17133e6i) q^{24} +7.05363e6i q^{26} +(2.76102e6 - 48670.6i) q^{27} +(9.03736e6 - 9.03736e6i) q^{28} +99055.3 q^{29} -7.60465e6 q^{31} +(8.16277e6 - 8.16277e6i) q^{32} +(-1.95465e6 + 1.14388e6i) q^{33} -1.18401e7i q^{34} +(2.13676e7 + 1.20041e7i) q^{36} +(735873. + 735873. i) q^{37} +(1.46500e6 + 1.46500e6i) q^{38} +(-2.28387e7 - 5.97601e6i) q^{39} -2.84743e7i q^{41} +(3.04888e7 + 5.20989e7i) q^{42} +(4.64166e6 - 4.64166e6i) q^{43} -2.01003e7 q^{44} -2.58143e7 q^{46} +(-2.19202e7 + 2.19202e7i) q^{47} +(4.61140e7 + 7.87990e7i) q^{48} +6.50022e7i q^{49} +(3.83366e7 + 1.00312e7i) q^{51} +(-1.48156e8 - 1.48156e8i) q^{52} +(4.34796e7 + 4.34796e7i) q^{53} +(-8.03965e7 + 8.32818e7i) q^{54} +3.15455e8i q^{56} +(-5.98464e6 + 3.50228e6i) q^{57} +(-2.93609e6 + 2.93609e6i) q^{58} +1.37704e8 q^{59} +7.42651e7 q^{61} +(2.25409e8 - 2.25409e8i) q^{62} +(-1.94520e8 + 5.45792e7i) q^{63} +1.50710e8i q^{64} +(2.40319e7 - 9.18432e7i) q^{66} +(4.34208e7 + 4.34208e7i) q^{67} +(2.48691e8 + 2.48691e8i) q^{68} +(2.18705e7 - 8.35832e7i) q^{69} +2.05196e8i q^{71} +(-5.82431e8 + 1.63421e8i) q^{72} +(-1.81205e8 + 1.81205e8i) q^{73} -4.36239e7 q^{74} -6.15421e7 q^{76} +(1.17163e8 - 1.17163e8i) q^{77} +(8.54094e8 - 4.99825e8i) q^{78} -2.98683e7i q^{79} +(-2.01541e8 - 3.30871e8i) q^{81} +(8.44004e8 + 8.44004e8i) q^{82} +(-2.00783e8 - 2.00783e8i) q^{83} +(-1.73469e9 - 4.53902e8i) q^{84} +2.75166e8i q^{86} +(-7.01913e6 - 1.19942e7i) q^{87} +(3.50808e8 - 3.50808e8i) q^{88} +3.63380e8 q^{89} +1.72717e9 q^{91} +(5.42209e8 - 5.42209e8i) q^{92} +(5.38871e8 + 9.20815e8i) q^{93} -1.29947e9i q^{94} +(-1.56682e9 - 4.09976e8i) q^{96} +(6.54780e8 + 6.54780e8i) q^{97} +(-1.92672e9 - 1.92672e9i) q^{98} +(2.77016e8 + 1.55624e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10788 q^{6}+O(q^{10}) \) 48 * q + 10788 * q^6	\( 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) \) 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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