LMFDB - Embedded newform 5.11.c.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,11,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	5.c (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:	$3.17678626337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1334x^{6} + 456089x^{4} + 43159076x^{2} + 31360000 $ x^8 + 1334x^6 + 456089x^4 + 43159076*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.4
Root			$-29.3902i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.11.c.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(37.4391 + 37.4391i) q^{2} +(246.218 - 246.218i) q^{3} +1779.37i q^{4} +(-3025.01 + 784.185i) q^{5} +18436.4 q^{6} +(-8610.35 - 8610.35i) q^{7} +(-28280.5 + 28280.5i) q^{8} -62197.5i q^{9} +O(q^{10})$	\(q+(37.4391 + 37.4391i) q^{2} +(246.218 - 246.218i) q^{3} +1779.37i q^{4} +(-3025.01 + 784.185i) q^{5} +18436.4 q^{6} +(-8610.35 - 8610.35i) q^{7} +(-28280.5 + 28280.5i) q^{8} -62197.5i q^{9} +(-142613. - 83894.5i) q^{10} +67511.6 q^{11} +(438114. + 438114. i) q^{12} +(8342.81 - 8342.81i) q^{13} -644728. i q^{14} +(-551731. + 937892. i) q^{15} -295517. q^{16} +(-693251. - 693251. i) q^{17} +(2.32862e6 - 2.32862e6i) q^{18} +4.48290e6i q^{19} +(-1.39536e6 - 5.38262e6i) q^{20} -4.24004e6 q^{21} +(2.52757e6 + 2.52757e6i) q^{22} +(1.04763e6 - 1.04763e6i) q^{23} +1.39263e7i q^{24} +(8.53573e6 - 4.74433e6i) q^{25} +624695. q^{26} +(-775217. - 775217. i) q^{27} +(1.53210e7 - 1.53210e7i) q^{28} -1.05625e7i q^{29} +(-5.57701e7 + 1.44575e7i) q^{30} -2.77763e7 q^{31} +(1.78954e7 + 1.78954e7i) q^{32} +(1.66226e7 - 1.66226e7i) q^{33} -5.19094e7i q^{34} +(3.27985e7 + 1.92943e7i) q^{35} +1.10673e8 q^{36} +(3.89172e7 + 3.89172e7i) q^{37} +(-1.67836e8 + 1.67836e8i) q^{38} -4.10830e6i q^{39} +(6.33717e7 - 1.07726e8i) q^{40} -7.21297e7 q^{41} +(-1.58743e8 - 1.58743e8i) q^{42} +(1.47395e8 - 1.47395e8i) q^{43} +1.20128e8i q^{44} +(4.87743e7 + 1.88148e8i) q^{45} +7.84449e7 q^{46} +(-1.85551e8 - 1.85551e8i) q^{47} +(-7.27616e7 + 7.27616e7i) q^{48} -1.34199e8i q^{49} +(4.97194e8 + 1.41947e8i) q^{50} -3.41382e8 q^{51} +(1.48450e7 + 1.48450e7i) q^{52} +(-2.40411e8 + 2.40411e8i) q^{53} -5.80468e7i q^{54} +(-2.04223e8 + 5.29416e7i) q^{55} +4.87011e8 q^{56} +(1.10377e9 + 1.10377e9i) q^{57} +(3.95450e8 - 3.95450e8i) q^{58} -8.16660e8i q^{59} +(-1.66886e9 - 9.81736e8i) q^{60} -1.84744e8 q^{61} +(-1.03992e9 - 1.03992e9i) q^{62} +(-5.35542e8 + 5.35542e8i) q^{63} +1.64258e9i q^{64} +(-1.86948e7 + 3.17794e7i) q^{65} +1.24467e9 q^{66} +(1.74545e8 + 1.74545e8i) q^{67} +(1.23355e9 - 1.23355e9i) q^{68} -5.15892e8i q^{69} +(5.05586e8 + 1.95031e9i) q^{70} -7.65409e8 q^{71} +(1.75898e9 + 1.75898e9i) q^{72} +(1.80198e9 - 1.80198e9i) q^{73} +2.91405e9i q^{74} +(9.33510e8 - 3.26979e9i) q^{75} -7.97676e9 q^{76} +(-5.81298e8 - 5.81298e8i) q^{77} +(1.53811e8 - 1.53811e8i) q^{78} +1.02265e9i q^{79} +(8.93942e8 - 2.31740e8i) q^{80} +3.29096e9 q^{81} +(-2.70047e9 - 2.70047e9i) q^{82} +(-3.18619e9 + 3.18619e9i) q^{83} -7.54462e9i q^{84} +(2.64073e9 + 1.55345e9i) q^{85} +1.10367e10 q^{86} +(-2.60067e9 - 2.60067e9i) q^{87} +(-1.90926e9 + 1.90926e9i) q^{88} +6.88808e9i q^{89} +(-5.21803e9 + 8.87016e9i) q^{90} -1.43669e8 q^{91} +(1.86413e9 + 1.86413e9i) q^{92} +(-6.83903e9 + 6.83903e9i) q^{93} -1.38937e10i q^{94} +(-3.51543e9 - 1.35608e10i) q^{95} +8.81232e9 q^{96} +(1.10095e10 + 1.10095e10i) q^{97} +(5.02429e9 - 5.02429e9i) q^{98} -4.19905e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8}+O(q^{10}) $ 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} - 161290 q^{10} - 233784 q^{11} + 863160 q^{12} + 433520 q^{13} - 3188580 q^{15} - 1193992 q^{16} + 1045440 q^{17} + 12804210 q^{18} - 16739820 q^{20} - 20777784 q^{21} + 25939360 q^{22} + 24737580 q^{23} - 35382400 q^{25} - 34440684 q^{26} + 27386640 q^{27} + 89876920 q^{28} - 115784880 q^{30} + 258616 q^{31} - 11664120 q^{32} + 11269320 q^{33} + 113638860 q^{35} + 66085308 q^{36} + 92216120 q^{37} - 435848520 q^{38} + 432590700 q^{40} + 115357416 q^{41} - 609152160 q^{42} - 262653700 q^{43} + 593742420 q^{45} + 1023085816 q^{46} - 669481140 q^{47} - 618046320 q^{48} + 944762850 q^{50} - 768258984 q^{51} - 70856500 q^{52} - 1321976040 q^{53} + 2597320 q^{55} + 852915600 q^{56} + 2367269280 q^{57} + 2687784720 q^{58} - 4237774440 q^{60} - 3143200184 q^{61} - 1373690040 q^{62} + 2578662540 q^{63} - 1924527480 q^{65} + 766734432 q^{66} + 4912566140 q^{67} + 6614874660 q^{68} - 8299690440 q^{70} - 4375053384 q^{71} + 808889220 q^{72} - 786968920 q^{73} + 5379002700 q^{75} - 5577898800 q^{76} + 7522045800 q^{77} + 4109901000 q^{78} + 47717760 q^{80} - 2499208992 q^{81} - 19442731040 q^{82} - 11064240660 q^{83} + 15814282160 q^{85} + 36286046616 q^{86} + 2020273920 q^{87} - 13252572960 q^{88} + 9489047670 q^{90} - 12917794184 q^{91} - 25757138760 q^{92} - 40141724280 q^{93} + 14671558800 q^{95} + 38082222816 q^{96} + 24688294760 q^{97} + 13744332030 q^{98}+O(q^{100}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8 - 161290 * q^10 - 233784 * q^11 + 863160 * q^12 + 433520 * q^13 - 3188580 * q^15 - 1193992 * q^16 + 1045440 * q^17 + 12804210 * q^18 - 16739820 * q^20 - 20777784 * q^21 + 25939360 * q^22 + 24737580 * q^23 - 35382400 * q^25 - 34440684 * q^26 + 27386640 * q^27 + 89876920 * q^28 - 115784880 * q^30 + 258616 * q^31 - 11664120 * q^32 + 11269320 * q^33 + 113638860 * q^35 + 66085308 * q^36 + 92216120 * q^37 - 435848520 * q^38 + 432590700 * q^40 + 115357416 * q^41 - 609152160 * q^42 - 262653700 * q^43 + 593742420 * q^45 + 1023085816 * q^46 - 669481140 * q^47 - 618046320 * q^48 + 944762850 * q^50 - 768258984 * q^51 - 70856500 * q^52 - 1321976040 * q^53 + 2597320 * q^55 + 852915600 * q^56 + 2367269280 * q^57 + 2687784720 * q^58 - 4237774440 * q^60 - 3143200184 * q^61 - 1373690040 * q^62 + 2578662540 * q^63 - 1924527480 * q^65 + 766734432 * q^66 + 4912566140 * q^67 + 6614874660 * q^68 - 8299690440 * q^70 - 4375053384 * q^71 + 808889220 * q^72 - 786968920 * q^73 + 5379002700 * q^75 - 5577898800 * q^76 + 7522045800 * q^77 + 4109901000 * q^78 + 47717760 * q^80 - 2499208992 * q^81 - 19442731040 * q^82 - 11064240660 * q^83 + 15814282160 * q^85 + 36286046616 * q^86 + 2020273920 * q^87 - 13252572960 * q^88 + 9489047670 * q^90 - 12917794184 * q^91 - 25757138760 * q^92 - 40141724280 * q^93 + 14671558800 * q^95 + 38082222816 * q^96 + 24688294760 * q^97 + 13744332030 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	37.4391	+	37.4391i	1.16997	+	1.16997i	0.982216	+	0.187757i	$0.0601216\pi$
$2$	37.4391	+	37.4391i	1.16997	+	1.16997i	0.187757	+	0.982216i	$0.439878\pi$
$3$	246.218	−	246.218i	1.01324	−	1.01324i	0.0133312	−	0.999911i	$-0.495756\pi$
$3$	246.218	−	246.218i	1.01324	−	1.01324i	0.999911	−	0.0133312i	$-0.00424358\pi$
$4$			1779.37i			1.73767i
$5$	−3025.01	+	784.185i	−0.968003	+	0.250939i
$5$	−3025.01	+	784.185i	−0.968003	+	0.250939i
$6$	18436.4			2.37093
$7$	−8610.35	−	8610.35i	−0.512307	−	0.512307i	0.402926	−	0.915233i	$-0.367993\pi$
$7$	−8610.35	−	8610.35i	−0.512307	−	0.512307i	−0.915233	+	0.402926i	$0.867993\pi$
$8$	−28280.5	+	28280.5i	−0.863053	+	0.863053i
$9$		−	62197.5i		−	1.05332i
$10$	−142613.	−	83894.5i	−1.42613	−	0.838945i
$11$	67511.6			0.419194			0.209597	−	0.977788i	$-0.432785\pi$
$11$	67511.6			0.419194			0.209597	+	0.977788i	$0.432785\pi$
$12$	438114.	+	438114.i	1.76068	+	1.76068i
$13$	8342.81	−	8342.81i	0.0224696	−	0.0224696i	−0.695783	−	0.718252i	$-0.744942\pi$
$13$	8342.81	−	8342.81i	0.0224696	−	0.0224696i	0.718252	+	0.695783i	$0.244942\pi$
$14$		−	644728.i		−	1.19877i
$15$	−551731.	+	937892.i	−0.726559	+	1.23508i
$16$	−295517.			−0.281827
$17$	−693251.	−	693251.i	−0.488254	−	0.488254i	0.419501	−	0.907755i	$-0.362205\pi$
$17$	−693251.	−	693251.i	−0.488254	−	0.488254i	−0.907755	+	0.419501i	$0.862205\pi$
$18$	2.32862e6	−	2.32862e6i	1.23236	−	1.23236i
$19$			4.48290e6i			1.81047i	0.424911	+	0.905235i	$0.360305\pi$
$19$			4.48290e6i			1.81047i	−0.424911	+	0.905235i	$0.639695\pi$
$20$	−1.39536e6	−	5.38262e6i	−0.436050	−	1.68207i
$21$	−4.24004e6			−1.03818
$22$	2.52757e6	+	2.52757e6i	0.490445	+	0.490445i
$23$	1.04763e6	−	1.04763e6i	0.162768	−	0.162768i	−0.621024	−	0.783792i	$-0.713283\pi$
$23$	1.04763e6	−	1.04763e6i	0.162768	−	0.162768i	0.783792	+	0.621024i	$0.213283\pi$
$24$			1.39263e7i			1.74896i
$25$	8.53573e6	−	4.74433e6i	0.874059	−	0.485820i
$26$	624695.			0.0525776
$27$	−775217.	−	775217.i	−0.0540262	−	0.0540262i
$28$	1.53210e7	−	1.53210e7i	0.890221	−	0.890221i
$29$		−	1.05625e7i		−	0.514963i	−0.966283	−	0.257482i	$-0.917107\pi$
$29$		−	1.05625e7i		−	0.514963i	0.966283	−	0.257482i	$-0.0828926\pi$
$30$	−5.57701e7	+	1.44575e7i	−2.29507	+	0.594959i
$31$	−2.77763e7			−0.970212			−0.485106	−	0.874455i	$-0.661219\pi$
$31$	−2.77763e7			−0.970212			−0.485106	+	0.874455i	$0.661219\pi$
$32$	1.78954e7	+	1.78954e7i	0.533324	+	0.533324i
$33$	1.66226e7	−	1.66226e7i	0.424745	−	0.424745i
$34$		−	5.19094e7i		−	1.14249i
$35$	3.27985e7	+	1.92943e7i	0.624473	+	0.367357i
$36$	1.10673e8			1.83032
$37$	3.89172e7	+	3.89172e7i	0.561220	+	0.561220i	0.929654	−	0.368434i	$-0.120106\pi$
$37$	3.89172e7	+	3.89172e7i	0.561220	+	0.561220i	−0.368434	+	0.929654i	$0.620106\pi$
$38$	−1.67836e8	+	1.67836e8i	−2.11820	+	2.11820i
$39$		−	4.10830e6i		−	0.0455343i
$40$	6.33717e7	−	1.07726e8i	0.618864	−	1.05201i
$41$	−7.21297e7			−0.622580			−0.311290	−	0.950315i	$-0.600761\pi$
$41$	−7.21297e7			−0.622580			−0.311290	+	0.950315i	$0.600761\pi$
$42$	−1.58743e8	−	1.58743e8i	−1.21465	−	1.21465i
$43$	1.47395e8	−	1.47395e8i	1.00263	−	1.00263i	0.00263511	−	0.999997i	$-0.499161\pi$
$43$	1.47395e8	−	1.47395e8i	1.00263	−	1.00263i	0.999997	−	0.00263511i	$-0.000838783\pi$
$44$			1.20128e8i			0.728421i
$45$	4.87743e7	+	1.88148e8i	0.264319	+	1.01962i
$46$	7.84449e7			0.380869
$47$	−1.85551e8	−	1.85551e8i	−0.809046	−	0.809046i	0.175444	−	0.984489i	$-0.443864\pi$
$47$	−1.85551e8	−	1.85551e8i	−0.809046	−	0.809046i	−0.984489	+	0.175444i	$0.943864\pi$
$48$	−7.27616e7	+	7.27616e7i	−0.285559	+	0.285559i
$49$		−	1.34199e8i		−	0.475083i
$50$	4.97194e8	+	1.41947e8i	1.59102	+	0.454229i
$51$	−3.41382e8			−0.989439
$52$	1.48450e7	+	1.48450e7i	0.0390448	+	0.0390448i
$53$	−2.40411e8	+	2.40411e8i	−0.574877	+	0.574877i	−0.933487	−	0.358610i	$-0.883251\pi$
$53$	−2.40411e8	+	2.40411e8i	−0.574877	+	0.574877i	0.358610	+	0.933487i	$0.383251\pi$
$54$		−	5.80468e7i		−	0.126418i
$55$	−2.04223e8	+	5.29416e7i	−0.405781	+	0.105192i
$56$	4.87011e8			0.884297
$57$	1.10377e9	+	1.10377e9i	1.83445	+	1.83445i
$58$	3.95450e8	−	3.95450e8i	0.602492	−	0.602492i
$59$		−	8.16660e8i		−	1.14230i	−0.820845	−	0.571152i	$-0.806497\pi$
$59$		−	8.16660e8i		−	1.14230i	0.820845	−	0.571152i	$-0.193503\pi$
$60$	−1.66886e9	−	9.81736e8i	−2.14617	−	1.26252i
$61$	−1.84744e8			−0.218736			−0.109368	−	0.994001i	$-0.534883\pi$
$61$	−1.84744e8			−0.218736			−0.109368	+	0.994001i	$0.534883\pi$
$62$	−1.03992e9	−	1.03992e9i	−1.13512	−	1.13512i
$63$	−5.35542e8	+	5.35542e8i	−0.539624	+	0.539624i
$64$			1.64258e9i			1.52977i
$65$	−1.86948e7	+	3.17794e7i	−0.0161121	+	0.0273891i
$66$	1.24467e9			0.993880
$67$	1.74545e8	+	1.74545e8i	0.129281	+	0.129281i	0.768786	−	0.639506i	$-0.220861\pi$
$67$	1.74545e8	+	1.74545e8i	0.129281	+	0.129281i	−0.639506	+	0.768786i	$0.720861\pi$
$68$	1.23355e9	−	1.23355e9i	0.848424	−	0.848424i
$69$		−	5.15892e8i		−	0.329848i
$70$	5.05586e8	+	1.95031e9i	0.300819	+	1.16041i
$71$	−7.65409e8			−0.424230			−0.212115	−	0.977245i	$-0.568035\pi$
$71$	−7.65409e8			−0.424230			−0.212115	+	0.977245i	$0.568035\pi$
$72$	1.75898e9	+	1.75898e9i	0.909072	+	0.909072i
$73$	1.80198e9	−	1.80198e9i	0.869234	−	0.869234i	−0.123154	−	0.992388i	$-0.539301\pi$
$73$	1.80198e9	−	1.80198e9i	0.869234	−	0.869234i	0.992388	+	0.123154i	$0.0393008\pi$
$74$			2.91405e9i			1.31322i
$75$	9.33510e8	−	3.26979e9i	0.393380	−	1.37789i
$76$	−7.97676e9			−3.14600
$77$	−5.81298e8	−	5.81298e8i	−0.214756	−	0.214756i
$78$	1.53811e8	−	1.53811e8i	0.0532739	−	0.0532739i
$79$			1.02265e9i			0.332348i	0.986096	+	0.166174i	$0.0531414\pi$
$79$			1.02265e9i			0.332348i	−0.986096	+	0.166174i	$0.946859\pi$
$80$	8.93942e8	−	2.31740e8i	0.272809	−	0.0707215i
$81$	3.29096e9			0.943837
$82$	−2.70047e9	−	2.70047e9i	−0.728401	−	0.728401i
$83$	−3.18619e9	+	3.18619e9i	−0.808874	+	0.808874i	−0.984464	−	0.175589i	$-0.943817\pi$
$83$	−3.18619e9	+	3.18619e9i	−0.808874	+	0.808874i	0.175589	+	0.984464i	$0.443817\pi$
$84$		−	7.54462e9i		−	1.80402i
$85$	2.64073e9	+	1.55345e9i	0.595153	+	0.350109i
$86$	1.10367e10			2.34610
$87$	−2.60067e9	−	2.60067e9i	−0.521782	−	0.521782i
$88$	−1.90926e9	+	1.90926e9i	−0.361787	+	0.361787i
$89$			6.88808e9i			1.23353i	0.787149	+	0.616763i	$0.211556\pi$
$89$			6.88808e9i			1.23353i	−0.787149	+	0.616763i	$0.788444\pi$
$90$	−5.21803e9	+	8.87016e9i	−0.883677	+	1.50217i
$91$	−1.43669e8			−0.0230227
$92$	1.86413e9	+	1.86413e9i	0.282838	+	0.282838i
$93$	−6.83903e9	+	6.83903e9i	−0.983060	+	0.983060i
$94$		−	1.38937e10i		−	1.89312i
$95$	−3.51543e9	−	1.35608e10i	−0.454318	−	1.75254i
$96$	8.81232e9			1.08077
$97$	1.10095e10	+	1.10095e10i	1.28207	+	1.28207i	0.939490	+	0.342577i	$0.111300\pi$
$97$	1.10095e10	+	1.10095e10i	1.28207	+	1.28207i	0.342577	+	0.939490i	$0.388700\pi$
$98$	5.02429e9	−	5.02429e9i	0.555833	−	0.555833i
$99$		−	4.19905e9i		−	0.441545i
$100$	8.44194e9	+	1.51883e10i	0.844194	+	1.51883i
$101$	−1.83601e10			−1.74690			−0.873450	−	0.486914i	$-0.838123\pi$
$101$	−1.83601e10			−1.74690			−0.873450	+	0.486914i	$0.838123\pi$
$102$	−1.27810e10	−	1.27810e10i	−1.15762	−	1.15762i
$103$	−3.44134e9	+	3.44134e9i	−0.296853	+	0.296853i	−0.839780	−	0.542927i	$-0.817316\pi$
$103$	−3.44134e9	+	3.44134e9i	−0.296853	+	0.296853i	0.542927	+	0.839780i	$0.317316\pi$
$104$			4.71878e8i			0.0387849i
$105$	1.28262e10	−	3.32498e9i	1.00496	−	0.260521i
$106$	−1.80015e10			−1.34518
$107$	−2.17316e9	−	2.17316e9i	−0.154944	−	0.154944i	0.625378	−	0.780322i	$-0.284945\pi$
$107$	−2.17316e9	−	2.17316e9i	−0.154944	−	0.154944i	−0.780322	+	0.625378i	$0.784945\pi$
$108$	1.37940e9	−	1.37940e9i	0.0938797	−	0.0938797i
$109$		−	1.12073e10i		−	0.728398i	−0.931321	−	0.364199i	$-0.881343\pi$
$109$		−	1.12073e10i		−	0.728398i	0.931321	−	0.364199i	$-0.118657\pi$
$110$	−9.62802e9	−	5.66385e9i	−0.597824	−	0.351680i
$111$	1.91642e10			1.13730
$112$	2.54451e9	+	2.54451e9i	0.144382	+	0.144382i
$113$	1.27884e10	−	1.27884e10i	0.694103	−	0.694103i	−0.269029	−	0.963132i	$-0.586703\pi$
$113$	1.27884e10	−	1.27884e10i	0.694103	−	0.694103i	0.963132	+	0.269029i	$0.0867028\pi$
$114$			8.26484e10i			4.29250i
$115$	−2.34756e9	+	3.99064e9i	−0.116715	+	0.198405i
$116$	1.87946e10			0.894836
$117$	−5.18902e8	−	5.18902e8i	−0.0236677	−	0.0236677i
$118$	3.05750e10	−	3.05750e10i	1.33646	−	1.33646i
$119$			1.19383e10i			0.500272i
$120$	−1.09208e10	−	4.21273e10i	−0.438884	−	1.69300i
$121$	−2.13796e10			−0.824276
$122$	−6.91663e9	−	6.91663e9i	−0.255915	−	0.255915i
$123$	−1.77596e10	+	1.77596e10i	−0.630824	+	0.630824i
$124$		−	4.94245e10i		−	1.68591i
$125$	−2.21002e10	+	2.10452e10i	−0.724180	+	0.689611i
$126$	−4.01004e10			−1.26269
$127$	2.98601e10	+	2.98601e10i	0.903800	+	0.903800i	0.995762	−	0.0919628i	$-0.0293141\pi$
$127$	2.98601e10	+	2.98601e10i	0.903800	+	0.903800i	−0.0919628	+	0.995762i	$0.529314\pi$
$128$	−4.31720e10	+	4.31720e10i	−1.25647	+	1.25647i
$129$		−	7.25827e10i		−	2.03182i
$130$	−1.88971e9	+	4.89876e8i	−0.0508953	+	0.0131938i
$131$	3.75358e10			0.972947			0.486473	−	0.873695i	$-0.338283\pi$
$131$	3.75358e10			0.972947			0.486473	+	0.873695i	$0.338283\pi$
$132$	2.95778e10	+	2.95778e10i	0.738067	+	0.738067i
$133$	3.85994e10	−	3.85994e10i	0.927517	−	0.927517i
$134$			1.30696e10i			0.302510i
$135$	2.95295e9	+	1.73712e9i	0.0658548	+	0.0387402i
$136$	3.92110e10			0.842779
$137$	3.52622e9	+	3.52622e9i	0.0730645	+	0.0730645i	0.742695	−	0.669630i	$-0.233547\pi$
$137$	3.52622e9	+	3.52622e9i	0.0730645	+	0.0730645i	−0.669630	+	0.742695i	$0.733547\pi$
$138$	1.93145e10	−	1.93145e10i	0.385912	−	0.385912i
$139$			3.36099e10i			0.647730i	0.946103	+	0.323865i	$0.104982\pi$
$139$			3.36099e10i			0.647730i	−0.946103	+	0.323865i	$0.895018\pi$
$140$	−3.43317e10	+	5.83608e10i	−0.638345	+	1.08513i
$141$	−9.13718e10			−1.63952
$142$	−2.86562e10	−	2.86562e10i	−0.496338	−	0.496338i
$143$	5.63236e8	−	5.63236e8i	0.00941912	−	0.00941912i
$144$			1.83804e10i			0.296854i
$145$	8.28294e9	+	3.19516e10i	0.129224	+	0.498486i
$146$	1.34929e11			2.03396
$147$	−3.30422e10	−	3.30422e10i	−0.481374	−	0.481374i
$148$	−6.92483e10	+	6.92483e10i	−0.975216	+	0.975216i
$149$		−	1.59826e10i		−	0.217629i	−0.994062	−	0.108815i	$-0.965295\pi$
$149$		−	1.59826e10i		−	0.217629i	0.994062	−	0.108815i	$-0.0347055\pi$
$150$	1.57368e11	−	8.74682e10i	2.07233	−	1.15184i
$151$	−3.89076e10			−0.495621			−0.247811	−	0.968809i	$-0.579711\pi$
$151$	−3.89076e10			−0.495621			−0.247811	+	0.968809i	$0.579711\pi$
$152$	−1.26779e11	−	1.26779e11i	−1.56253	−	1.56253i
$153$	−4.31185e10	+	4.31185e10i	−0.514288	+	0.514288i
$154$		−	4.35266e10i		−	0.502517i
$155$	8.40237e10	−	2.17818e10i	0.939168	−	0.243464i
$156$	7.31020e9			0.0791236
$157$	−4.03814e9	−	4.03814e9i	−0.0423334	−	0.0423334i	0.685623	−	0.727957i	$-0.259530\pi$
$157$	−4.03814e9	−	4.03814e9i	−0.0423334	−	0.0423334i	−0.727957	+	0.685623i	$0.759530\pi$
$158$	−3.82873e10	+	3.82873e10i	−0.388838	+	0.388838i
$159$			1.18387e11i			1.16498i
$160$	−6.81669e10	−	4.01004e10i	−0.650091	−	0.382427i
$161$	−1.80410e10			−0.166775
$162$	1.23210e11	+	1.23210e11i	1.10426	+	1.10426i
$163$	9.87404e9	−	9.87404e9i	0.0858137	−	0.0858137i	−0.662897	−	0.748711i	$-0.730673\pi$
$163$	9.87404e9	−	9.87404e9i	0.0858137	−	0.0858137i	0.748711	+	0.662897i	$0.230673\pi$
$164$		−	1.28346e11i		−	1.08184i
$165$	−3.72482e10	+	6.33186e10i	−0.304569	+	0.517740i
$166$	−2.38576e11			−1.89272
$167$	−4.83455e10	−	4.83455e10i	−0.372198	−	0.372198i	0.496079	−	0.868277i	$-0.334772\pi$
$167$	−4.83455e10	−	4.83455e10i	−0.372198	−	0.372198i	−0.868277	+	0.496079i	$0.834772\pi$
$168$	1.19911e11	−	1.19911e11i	0.896007	−	0.896007i
$169$			1.37719e11i			0.998990i
$170$	4.07066e10	+	1.57026e11i	0.286695	+	1.10593i
$171$	2.78825e11			1.90700
$172$	2.62271e11	+	2.62271e11i	1.74224	+	1.74224i
$173$	1.63798e11	−	1.63798e11i	1.05701	−	1.05701i	0.0587356	−	0.998274i	$-0.481293\pi$
$173$	1.63798e11	−	1.63798e11i	1.05701	−	1.05701i	0.998274	−	0.0587356i	$-0.0187069\pi$
$174$		−	1.94734e11i		−	1.22094i
$175$	−1.14346e11	−	3.26453e10i	−0.696676	−	0.198898i
$176$	−1.99508e10			−0.118140
$177$	−2.01076e11	−	2.01076e11i	−1.15743	−	1.15743i
$178$	−2.57883e11	+	2.57883e11i	−1.44319	+	1.44319i
$179$		−	1.40902e11i		−	0.766748i	−0.923593	−	0.383374i	$-0.874762\pi$
$179$		−	1.40902e11i		−	0.766748i	0.923593	−	0.383374i	$-0.125238\pi$
$180$	−3.34786e11	+	8.67878e10i	−1.77176	+	0.459300i
$181$	3.19842e11			1.64643			0.823214	−	0.567731i	$-0.192179\pi$
$181$	3.19842e11			1.64643			0.823214	+	0.567731i	$0.192179\pi$
$182$	−5.37884e9	−	5.37884e9i	−0.0269359	−	0.0269359i
$183$	−4.54872e10	+	4.54872e10i	−0.221632	+	0.221632i
$184$			5.92552e10i			0.280956i
$185$	−1.48243e11	−	8.72067e10i	−0.684095	−	0.402431i
$186$	−5.12094e11			−2.30030
$187$	−4.68025e10	−	4.68025e10i	−0.204673	−	0.204673i
$188$	3.30164e11	−	3.30164e11i	1.40585	−	1.40585i
$189$			1.33498e10i			0.0553560i
$190$	3.76091e11	−	6.39320e11i	1.51888	−	2.58196i
$191$	−1.30037e11			−0.511565			−0.255782	−	0.966734i	$-0.582333\pi$
$191$	−1.30037e11			−0.511565			−0.255782	+	0.966734i	$0.582333\pi$
$192$	4.04433e11	+	4.04433e11i	1.55003	+	1.55003i
$193$	−9.29833e10	+	9.29833e10i	−0.347231	+	0.347231i	−0.859077	−	0.511846i	$-0.828962\pi$
$193$	−9.29833e10	+	9.29833e10i	−0.347231	+	0.347231i	0.511846	+	0.859077i	$0.328962\pi$
$194$			8.24375e11i			2.99997i
$195$	3.22166e9	+	1.24276e10i	0.0114263	+	0.0440773i
$196$	2.38790e11			0.825537
$197$	2.08308e11	+	2.08308e11i	0.702061	+	0.702061i	0.964853	−	0.262791i	$-0.0846431\pi$
$197$	2.08308e11	+	2.08308e11i	0.702061	+	0.702061i	−0.262791	+	0.964853i	$0.584643\pi$
$198$	1.57209e11	−	1.57209e11i	0.516596	−	0.516596i
$199$			1.32389e11i			0.424214i	0.977246	+	0.212107i	$0.0680326\pi$
$199$			1.32389e11i			0.424214i	−0.977246	+	0.212107i	$0.931967\pi$
$200$	−1.07223e11	+	3.75567e11i	−0.335071	+	1.17365i
$201$	8.59523e10			0.261986
$202$	−6.87386e11	−	6.87386e11i	−2.04382	−	2.04382i
$203$	−9.09467e10	+	9.09467e10i	−0.263819	+	0.263819i
$204$		−	6.07446e11i		−	1.71932i
$205$	2.18193e11	−	5.65631e10i	0.602659	−	0.156230i
$206$	−2.57681e11			−0.694619
$207$	−6.51601e10	−	6.51601e10i	−0.171447	−	0.171447i
$208$	−2.46544e9	+	2.46544e9i	−0.00633254	+	0.00633254i
$209$			3.02648e11i			0.758938i
$210$	6.04685e11	+	3.55716e11i	1.48058	+	0.870978i
$211$	−1.91903e11			−0.458849			−0.229425	−	0.973326i	$-0.573684\pi$
$211$	−1.91903e11			−0.458849			−0.229425	+	0.973326i	$0.573684\pi$
$212$	−4.27781e11	−	4.27781e11i	−0.998946	−	0.998946i
$213$	−1.88457e11	+	1.88457e11i	−0.429848	+	0.429848i
$214$		−	1.62723e11i		−	0.362559i
$215$	−3.30287e11	+	5.61457e11i	−0.718951	+	1.22215i
$216$	4.38471e10			0.0932550
$217$	2.39164e11	+	2.39164e11i	0.497047	+	0.497047i
$218$	4.19592e11	−	4.19592e11i	0.852206	−	0.852206i
$219$		−	8.87362e11i		−	1.76149i
$220$	−9.42029e10	−	3.63389e11i	−0.182789	−	0.705113i
$221$	−1.15673e10			−0.0219418
$222$	7.17492e11	+	7.17492e11i	1.33061	+	1.33061i
$223$	1.03263e11	−	1.03263e11i	0.187249	−	0.187249i	−0.607257	−	0.794506i	$-0.707730\pi$
$223$	1.03263e11	−	1.03263e11i	0.187249	−	0.187249i	0.794506	+	0.607257i	$0.207730\pi$
$224$		−	3.08171e11i		−	0.546451i
$225$	−2.95086e11	−	5.30901e11i	−0.511724	−	0.920664i
$226$	9.57572e11			1.62416
$227$	−3.82762e11	−	3.82762e11i	−0.635037	−	0.635037i	0.314290	−	0.949327i	$-0.398234\pi$
$227$	−3.82762e11	−	3.82762e11i	−0.635037	−	0.635037i	−0.949327	+	0.314290i	$0.898234\pi$
$228$	−1.96402e12	+	1.96402e12i	−3.18766	+	3.18766i
$229$			3.31161e11i			0.525850i	0.964816	+	0.262925i	$0.0846871\pi$
$229$			3.31161e11i			0.525850i	−0.964816	+	0.262925i	$0.915313\pi$
$230$	−2.37296e11	+	6.15153e10i	−0.368682	+	0.0955749i
$231$	−2.86252e11			−0.435200
$232$	2.98713e11	+	2.98713e11i	0.444441	+	0.444441i
$233$	3.33476e11	−	3.33476e11i	0.485607	−	0.485607i	−0.421310	−	0.906917i	$-0.638429\pi$
$233$	3.33476e11	−	3.33476e11i	0.485607	−	0.485607i	0.906917	+	0.421310i	$0.138429\pi$
$234$		−	3.88544e10i		−	0.0553811i
$235$	7.06798e11	+	4.15786e11i	0.986180	+	0.580137i
$236$	1.45314e12			1.98495
$237$	2.51796e11	+	2.51796e11i	0.336749	+	0.336749i
$238$	−4.46958e11	+	4.46958e11i	−0.585305	+	0.585305i
$239$		−	7.88192e11i		−	1.01075i	−0.862901	−	0.505374i	$-0.831355\pi$
$239$		−	7.88192e11i		−	1.01075i	0.862901	−	0.505374i	$-0.168645\pi$
$240$	1.63046e11	−	2.77163e11i	0.204764	−	0.348080i
$241$	1.59486e11			0.196172			0.0980862	−	0.995178i	$-0.468728\pi$
$241$	1.59486e11			0.196172			0.0980862	+	0.995178i	$0.468728\pi$
$242$	−8.00434e11	−	8.00434e11i	−0.964381	−	0.964381i
$243$	8.56068e11	−	8.56068e11i	1.01036	−	1.01036i
$244$		−	3.28728e11i		−	0.380091i
$245$	1.05237e11	+	4.05953e11i	0.119217	+	0.459881i
$246$	−1.32981e12			−1.47609
$247$	3.74000e10	+	3.74000e10i	0.0406806	+	0.0406806i
$248$	7.85530e11	−	7.85530e11i	0.837345	−	0.837345i
$249$			1.56899e12i			1.63917i
$250$	−1.61533e12	−	3.94978e10i	−1.65410	−	0.0404458i
$251$	−1.09708e12			−1.10121			−0.550607	−	0.834765i	$-0.685604\pi$
$251$	−1.09708e12			−1.10121			−0.550607	+	0.834765i	$0.685604\pi$
$252$	−9.52930e11	−	9.52930e11i	−0.937688	−	0.937688i
$253$	7.07274e10	−	7.07274e10i	0.0682315	−	0.0682315i
$254$			2.23587e12i			2.11484i
$255$	1.03268e12	−	2.67706e11i	0.957780	−	0.248289i
$256$	−1.55064e12			−1.41030
$257$	−6.73234e10	−	6.73234e10i	−0.0600483	−	0.0600483i	0.676445	−	0.736493i	$-0.263520\pi$
$257$	−6.73234e10	−	6.73234e10i	−0.0600483	−	0.0600483i	−0.736493	+	0.676445i	$0.763520\pi$
$258$	2.71743e12	−	2.71743e12i	2.37717	−	2.37717i
$259$		−	6.70182e11i		−	0.575034i
$260$	−5.65474e10	−	3.32650e10i	−0.0475933	−	0.0279976i
$261$	−6.56960e11			−0.542421
$262$	1.40531e12	+	1.40531e12i	1.13832	+	1.13832i
$263$	−1.59542e12	+	1.59542e12i	−1.26794	+	1.26794i	−0.320782	+	0.947153i	$0.603946\pi$
$263$	−1.59542e12	+	1.59542e12i	−1.26794	+	1.26794i	−0.947153	+	0.320782i	$0.896054\pi$
$264$			9.40190e11i			0.733155i
$265$	5.38719e11	−	9.15772e11i	0.412223	−	0.700742i
$266$	2.89025e12			2.17034
$267$	1.69597e12	+	1.69597e12i	1.24986	+	1.24986i
$268$	−3.10581e11	+	3.10581e11i	−0.224647	+	0.224647i
$269$		−	1.90944e12i		−	1.35564i	−0.735229	−	0.677819i	$-0.762925\pi$
$269$		−	1.90944e12i		−	1.35564i	0.735229	−	0.677819i	$-0.237075\pi$
$270$	4.55195e10	+	1.75592e11i	0.0317233	+	0.122373i
$271$	−2.32642e12			−1.59163			−0.795816	−	0.605539i	$-0.792958\pi$
$271$	−2.32642e12			−1.59163			−0.795816	+	0.605539i	$0.792958\pi$
$272$	2.04868e11	+	2.04868e11i	0.137603	+	0.137603i
$273$	−3.53739e10	+	3.53739e10i	−0.0233276	+	0.0233276i
$274$			2.64037e11i			0.170967i
$275$	5.76261e11	−	3.20298e11i	0.366400	−	0.203653i
$276$	9.17965e11			0.573166
$277$	−3.52534e11	−	3.52534e11i	−0.216173	−	0.216173i	0.590710	−	0.806884i	$-0.298848\pi$
$277$	−3.52534e11	−	3.52534e11i	−0.216173	−	0.216173i	−0.806884	+	0.590710i	$0.798848\pi$
$278$	−1.25833e12	+	1.25833e12i	−0.757826	+	0.757826i
$279$			1.72762e12i			1.02194i
$280$	−1.47321e12	+	3.81906e11i	−0.856002	+	0.221905i
$281$	1.15816e12			0.661055			0.330527	−	0.943796i	$-0.392773\pi$
$281$	1.15816e12			0.661055			0.330527	+	0.943796i	$0.392773\pi$
$282$	−3.42088e12	−	3.42088e12i	−1.91819	−	1.91819i
$283$	3.01879e11	−	3.01879e11i	0.166303	−	0.166303i	−0.619049	−	0.785352i	$-0.712482\pi$
$283$	3.01879e11	−	3.01879e11i	0.166303	−	0.166303i	0.785352	+	0.619049i	$0.212482\pi$
$284$		−	1.36195e12i		−	0.737172i
$285$	−4.20448e12	−	2.47336e12i	−2.23608	−	1.31541i
$286$	4.21741e10			0.0220402
$287$	6.21062e11	+	6.21062e11i	0.318952	+	0.318952i
$288$	1.11305e12	−	1.11305e12i	0.561760	−	0.561760i
$289$		−	1.05480e12i		−	0.523216i
$290$	−8.86134e11	+	1.50635e12i	−0.432025	+	0.734403i
$291$	5.42149e12			2.59809
$292$	3.20640e12	+	3.20640e12i	1.51044	+	1.51044i
$293$	−5.49090e11	+	5.49090e11i	−0.254276	+	0.254276i	−0.822721	−	0.568445i	$-0.807545\pi$
$293$	−5.49090e11	+	5.49090e11i	−0.254276	+	0.254276i	0.568445	+	0.822721i	$0.307545\pi$
$294$		−	2.47414e12i		−	1.12639i
$295$	6.40413e11	+	2.47041e12i	0.286649	+	1.10575i
$296$	−2.20120e12			−0.968726
$297$	−5.23361e10	−	5.23361e10i	−0.0226474	−	0.0226474i
$298$	5.98376e11	−	5.98376e11i	0.254620	−	0.254620i
$299$		−	1.74804e10i		−	0.00731468i
$300$	5.81818e12	+	1.66106e12i	2.39431	+	0.683566i
$301$	−2.53825e12			−1.02731
$302$	−1.45667e12	−	1.45667e12i	−0.579863	−	0.579863i
$303$	−4.52058e12	+	4.52058e12i	−1.77003	+	1.77003i
$304$		−	1.32478e12i		−	0.510240i
$305$	5.58851e11	−	1.44873e11i	0.211737	−	0.0548894i
$306$	−3.22863e12			−1.20340
$307$	−2.51692e12	−	2.51692e12i	−0.922949	−	0.922949i	0.0742874	−	0.997237i	$-0.476332\pi$
$307$	−2.51692e12	−	2.51692e12i	−0.922949	−	0.922949i	−0.997237	+	0.0742874i	$0.976332\pi$
$308$	1.03435e12	−	1.03435e12i	0.373175	−	0.373175i
$309$			1.69464e12i			0.601568i
$310$	3.96126e12	+	2.33028e12i	1.38365	+	0.813954i
$311$	3.03323e12			1.04257			0.521283	−	0.853384i	$-0.325453\pi$
$311$	3.03323e12			1.04257			0.521283	+	0.853384i	$0.325453\pi$
$312$	1.16185e11	+	1.16185e11i	0.0392985	+	0.0392985i
$313$	2.16128e12	−	2.16128e12i	0.719432	−	0.719432i	−0.249057	−	0.968489i	$-0.580121\pi$
$313$	2.16128e12	−	2.16128e12i	0.719432	−	0.719432i	0.968489	+	0.249057i	$0.0801205\pi$
$314$		−	3.02369e11i		−	0.0990579i
$315$	1.20006e12	−	2.03998e12i	0.386944	−	0.657770i
$316$	−1.81968e12			−0.577512
$317$	2.35241e12	+	2.35241e12i	0.734881	+	0.734881i	0.971582	−	0.236702i	$-0.0760664\pi$
$317$	2.35241e12	+	2.35241e12i	0.734881	+	0.734881i	−0.236702	+	0.971582i	$0.576066\pi$
$318$	−4.43230e12	+	4.43230e12i	−1.36299	+	1.36299i
$319$		−	7.13090e11i		−	0.215869i
$320$	−1.28809e12	−	4.96883e12i	−0.383880	−	1.48083i
$321$	−1.07014e12			−0.313991
$322$	−6.75438e11	−	6.75438e11i	−0.195122	−	0.195122i
$323$	3.10778e12	−	3.10778e12i	0.883970	−	0.883970i
$324$			5.85584e12i			1.64008i
$325$	3.16309e10	−	1.10793e11i	0.00872358	−	0.0305559i
$326$	7.39350e11			0.200799
$327$	−2.75944e12	−	2.75944e12i	−0.738044	−	0.738044i
$328$	2.03987e12	−	2.03987e12i	0.537320	−	0.537320i
$329$			3.19531e12i			0.828960i
$330$	−3.76513e12	+	9.76050e11i	−0.962078	+	0.249403i
$331$	2.06031e12			0.518553			0.259277	−	0.965803i	$-0.416516\pi$
$331$	2.06031e12			0.518553			0.259277	+	0.965803i	$0.416516\pi$
$332$	−5.66942e12	−	5.66942e12i	−1.40556	−	1.40556i
$333$	2.42055e12	−	2.42055e12i	0.591145	−	0.591145i
$334$		−	3.62003e12i		−	0.870922i
$335$	−6.64877e11	−	3.91125e11i	−0.157586	−	0.0927026i
$336$	1.25301e12			0.292588
$337$	−4.99903e11	−	4.99903e11i	−0.115010	−	0.115010i	0.647259	−	0.762270i	$-0.275915\pi$
$337$	−4.99903e11	−	4.99903e11i	−0.115010	−	0.115010i	−0.762270	+	0.647259i	$0.775915\pi$
$338$	−5.15609e12	+	5.15609e12i	−1.16879	+	1.16879i
$339$		−	6.29746e12i		−	1.40659i
$340$	−2.76417e12	+	4.69884e12i	−0.608374	+	1.03418i
$341$	−1.87522e12			−0.406707
$342$	1.04390e13	+	1.04390e13i	2.23114	+	2.23114i
$343$	−3.58771e12	+	3.58771e12i	−0.755695	+	0.755695i
$344$			8.33684e12i			1.73065i
$345$	4.04555e11	+	1.56058e12i	0.0827717	+	0.319293i
$346$	1.22649e13			2.47334
$347$	1.60915e12	+	1.60915e12i	0.319851	+	0.319851i	0.848710	−	0.528859i	$-0.177380\pi$
$347$	1.60915e12	+	1.60915e12i	0.319851	+	0.319851i	−0.528859	+	0.848710i	$0.677380\pi$
$348$	4.62757e12	−	4.62757e12i	0.906686	−	0.906686i
$349$			1.51410e12i			0.292433i	0.989253	+	0.146216i	$0.0467096\pi$
$349$			1.51410e12i			0.292433i	−0.989253	+	0.146216i	$0.953290\pi$
$350$	−3.05880e12	−	5.50322e12i	−0.582386	−	1.04780i
$351$	−1.29350e10			−0.00242789
$352$	1.20814e12	+	1.20814e12i	0.223566	+	0.223566i
$353$	3.71799e12	−	3.71799e12i	0.678320	−	0.678320i	−0.281300	−	0.959620i	$-0.590766\pi$
$353$	3.71799e12	−	3.71799e12i	0.678320	−	0.678320i	0.959620	+	0.281300i	$0.0907656\pi$
$354$		−	1.50562e13i		−	2.70832i
$355$	2.31537e12	−	6.00222e11i	0.410656	−	0.106456i
$356$	−1.22565e13			−2.14346
$357$	2.93941e12	+	2.93941e12i	0.506897	+	0.506897i
$358$	5.27526e12	−	5.27526e12i	0.897074	−	0.897074i
$359$			4.60918e12i			0.772950i	0.922300	+	0.386475i	$0.126307\pi$
$359$			4.60918e12i			0.772950i	−0.922300	+	0.386475i	$0.873693\pi$
$360$	−6.70029e12	−	3.94156e12i	−1.10811	−	0.651862i
$361$	−1.39654e13			−2.27780
$362$	1.19746e13	+	1.19746e13i	1.92628	+	1.92628i
$363$	−5.26404e12	+	5.26404e12i	−0.835192	+	0.835192i
$364$		−	2.55641e11i		−	0.0400058i
$365$	−4.03793e12	+	6.86411e12i	−0.623296	+	1.05955i
$366$	−3.40600e12			−0.518608
$367$	−7.24691e12	−	7.24691e12i	−1.08849	−	1.08849i	−0.995685	−	0.0928008i	$-0.970418\pi$
$367$	−7.24691e12	−	7.24691e12i	−1.08849	−	1.08849i	−0.0928008	−	0.995685i	$-0.529582\pi$
$368$	−3.09593e11	+	3.09593e11i	−0.0458725	+	0.0458725i
$369$			4.48629e12i			0.655776i
$370$	−2.28516e12	−	8.81504e12i	−0.329539	−	1.27120i
$371$	4.14004e12			0.589027
$372$	−1.21692e13	−	1.21692e13i	−1.70823	−	1.70823i
$373$	8.04695e12	−	8.04695e12i	1.11452	−	1.11452i	0.121986	−	0.992532i	$-0.461074\pi$
$373$	8.04695e12	−	8.04695e12i	1.11452	−	1.11452i	0.992532	−	0.121986i	$-0.0389263\pi$
$374$		−	3.50449e12i		−	0.478924i
$375$	−2.59757e11	+	1.06232e13i	−0.0350276	+	1.43251i
$376$	1.04949e13			1.39650
$377$	−8.81208e10	−	8.81208e10i	−0.0115710	−	0.0115710i
$378$	−4.99803e11	+	4.99803e11i	−0.0647650	+	0.0647650i
$379$			6.54391e12i			0.836838i	0.908254	+	0.418419i	$0.137416\pi$
$379$			6.54391e12i			0.836838i	−0.908254	+	0.418419i	$0.862584\pi$
$380$	2.41298e13	−	6.25526e12i	3.04534	−	0.789455i
$381$	1.47042e13			1.83154
$382$	−4.86847e12	−	4.86847e12i	−0.598516	−	0.598516i
$383$	5.48794e9	−	5.48794e9i	0.000665910	−	0.000665910i	−0.706774	−	0.707440i	$-0.749850\pi$
$383$	5.48794e9	−	5.48794e9i	0.000665910	−	0.000665910i	0.707440	+	0.706774i	$0.249850\pi$
$384$			2.12594e13i			2.54622i
$385$	2.21428e12	+	1.30259e12i	0.261775	+	0.153994i
$386$	−6.96243e12			−0.812501
$387$	−9.16762e12	−	9.16762e12i	−1.05609	−	1.05609i
$388$	−1.95901e13	+	1.95901e13i	−2.22781	+	2.22781i
$389$		−	9.12906e12i		−	1.02489i	−0.858719	−	0.512446i	$-0.828739\pi$
$389$		−	9.12906e12i		−	1.02489i	0.858719	−	0.512446i	$-0.171261\pi$
$390$	−3.44663e11	+	5.85896e11i	−0.0382008	+	0.0649378i
$391$	−1.45254e12			−0.158945
$392$	3.79522e12	+	3.79522e12i	0.410022	+	0.410022i
$393$	9.24198e12	−	9.24198e12i	0.985831	−	0.985831i
$394$			1.55977e13i			1.64278i
$395$	−8.01950e11	−	3.09354e12i	−0.0833992	−	0.321714i
$396$	7.47169e12			0.767260
$397$	6.30755e12	+	6.30755e12i	0.639600	+	0.639600i	0.950457	−	0.310857i	$-0.100616\pi$
$397$	6.30755e12	+	6.30755e12i	0.639600	+	0.639600i	−0.310857	+	0.950457i	$0.600616\pi$
$398$	−4.95651e12	+	4.95651e12i	−0.496319	+	0.496319i
$399$		−	1.90077e13i		−	1.87960i
$400$	−2.52246e12	+	1.40203e12i	−0.246334	+	0.136917i
$401$	−1.34167e13			−1.29397			−0.646984	−	0.762503i	$-0.723970\pi$
$401$	−1.34167e13			−1.29397			−0.646984	+	0.762503i	$0.723970\pi$
$402$	3.21798e12	+	3.21798e12i	0.306516	+	0.306516i
$403$	−2.31733e11	+	2.31733e11i	−0.0218003	+	0.0218003i
$404$		−	3.26695e13i		−	3.03554i
$405$	−9.95517e12	+	2.58072e12i	−0.913637	+	0.236846i
$406$	−6.80992e12			−0.617323
$407$	2.62736e12	+	2.62736e12i	0.235260	+	0.235260i
$408$	9.65445e12	−	9.65445e12i	0.853939	−	0.853939i
$409$			1.60038e13i			1.39832i	0.714965	+	0.699160i	$0.246443\pi$
$409$			1.60038e13i			1.39832i	−0.714965	+	0.699160i	$0.753557\pi$
$410$	1.02866e13	+	6.05128e12i	0.887879	+	0.522310i
$411$	1.73644e12			0.148064
$412$	−6.12343e12	−	6.12343e12i	−0.515832	−	0.515832i
$413$	−7.03173e12	+	7.03173e12i	−0.585210	+	0.585210i
$414$		−	4.87908e12i		−	0.401177i
$415$	7.13969e12	−	1.21368e13i	0.580014	−	0.985971i
$416$	2.98595e11			0.0239671
$417$	8.27537e12	+	8.27537e12i	0.656307	+	0.656307i
$418$	−1.13309e13	+	1.13309e13i	−0.887937	+	0.887937i
$419$		−	2.18901e13i		−	1.69503i	−0.530770	−	0.847516i	$-0.678097\pi$
$419$		−	2.18901e13i		−	1.69503i	0.530770	−	0.847516i	$-0.321903\pi$
$420$	5.91638e12	+	2.28226e13i	0.452699	+	1.74630i
$421$	2.36341e13			1.78701			0.893507	−	0.449049i	$-0.148237\pi$
$421$	2.36341e13			1.78701			0.893507	+	0.449049i	$0.148237\pi$
$422$	−7.18469e12	−	7.18469e12i	−0.536841	−	0.536841i
$423$	−1.15408e13	+	1.15408e13i	−0.852184	+	0.852184i
$424$		−	1.35979e13i		−	0.992299i
$425$	−9.20642e12	−	2.62839e12i	−0.663966	−	0.189559i
$426$	−1.41114e13			−1.00582
$427$	1.59071e12	+	1.59071e12i	0.112060	+	0.112060i
$428$	3.86687e12	−	3.86687e12i	0.269241	−	0.269241i
$429$		−	2.77358e11i		−	0.0190877i
$430$	−3.33861e13	+	8.65481e12i	−2.27103	+	0.588729i
$431$	7.88987e12			0.530498			0.265249	−	0.964180i	$-0.414546\pi$
$431$	7.88987e12			0.530498			0.265249	+	0.964180i	$0.414546\pi$
$432$	2.29090e11	+	2.29090e11i	0.0152260	+	0.0152260i
$433$	1.40802e12	−	1.40802e12i	0.0925057	−	0.0925057i	−0.659340	−	0.751845i	$-0.729164\pi$
$433$	1.40802e12	−	1.40802e12i	0.0925057	−	0.0925057i	0.751845	+	0.659340i	$0.229164\pi$
$434$			1.79082e13i			1.16306i
$435$	9.90647e12	+	5.82765e12i	0.636022	+	0.374151i
$436$	1.99420e13			1.26572
$437$	4.69644e12	+	4.69644e12i	0.294687	+	0.294687i
$438$	3.32220e13	−	3.32220e13i	2.06089	−	2.06089i
$439$			2.27572e13i			1.39571i	0.716239	+	0.697855i	$0.245862\pi$
$439$			2.27572e13i			1.39571i	−0.716239	+	0.697855i	$0.754138\pi$
$440$	4.27832e12	−	7.27276e12i	0.259424	−	0.440997i
$441$	−8.34685e12			−0.500414
$442$	−4.33070e11	−	4.33070e11i	−0.0256712	−	0.0256712i
$443$	−7.19188e12	+	7.19188e12i	−0.421526	+	0.421526i	−0.885729	−	0.464203i	$-0.846341\pi$
$443$	−7.19188e12	+	7.19188e12i	−0.421526	+	0.421526i	0.464203	+	0.885729i	$0.346341\pi$
$444$			3.41004e13i			1.97626i
$445$	−5.40153e12	−	2.08365e13i	−0.309540	−	1.19406i
$446$	7.73212e12			0.438151
$447$	−3.93521e12	−	3.93521e12i	−0.220511	−	0.220511i
$448$	1.41432e13	−	1.41432e13i	0.783715	−	0.783715i
$449$			2.04767e13i			1.12209i	0.827785	+	0.561045i	$0.189601\pi$
$449$			2.04767e13i			1.12209i	−0.827785	+	0.561045i	$0.810399\pi$
$450$	8.82872e12	−	3.09242e13i	0.478449	−	1.67585i
$451$	−4.86959e12			−0.260982
$452$	2.27553e13	+	2.27553e13i	1.20612	+	1.20612i
$453$	−9.57975e12	+	9.57975e12i	−0.502184	+	0.502184i
$454$		−	2.86605e13i		−	1.48595i
$455$	4.34600e11	−	1.12663e11i	0.0222860	−	0.00577729i
$456$	−6.24305e13			−3.16645
$457$	−2.49102e13	−	2.49102e13i	−1.24967	−	1.24967i	−0.955864	−	0.293810i	$-0.905077\pi$
$457$	−2.49102e13	−	2.49102e13i	−1.24967	−	1.24967i	−0.293810	−	0.955864i	$-0.594923\pi$
$458$	−1.23984e13	+	1.23984e13i	−0.615230	+	0.615230i
$459$			1.07484e12i			0.0527570i
$460$	−7.10084e12	−	4.17719e12i	−0.344763	−	0.202813i
$461$	−1.56709e13			−0.752643			−0.376322	−	0.926489i	$-0.622811\pi$
$461$	−1.56709e13			−0.752643			−0.376322	+	0.926489i	$0.622811\pi$
$462$	−1.07170e13	−	1.07170e13i	−0.509172	−	0.509172i
$463$	8.83350e12	−	8.83350e12i	0.415172	−	0.415172i	−0.468364	−	0.883536i	$-0.655156\pi$
$463$	8.83350e12	−	8.83350e12i	0.415172	−	0.415172i	0.883536	+	0.468364i	$0.155156\pi$
$464$			3.12140e12i			0.145131i
$465$	1.53251e13	−	2.60512e13i	0.704916	−	1.19829i
$466$	2.49701e13			1.13629
$467$	−8.00884e12	−	8.00884e12i	−0.360566	−	0.360566i	0.503455	−	0.864021i	$-0.332062\pi$
$467$	−8.00884e12	−	8.00884e12i	−0.360566	−	0.360566i	−0.864021	+	0.503455i	$0.832062\pi$
$468$	9.23320e11	−	9.23320e11i	0.0411266	−	0.0411266i
$469$		−	3.00579e12i		−	0.132463i
$470$	1.08952e13	+	4.20286e13i	0.475059	+	1.83255i
$471$	−1.98853e12			−0.0857880
$472$	2.30956e13	+	2.30956e13i	0.985869	+	0.985869i
$473$	9.95089e12	−	9.95089e12i	0.420297	−	0.420297i
$474$			1.88540e13i			0.787975i
$475$	2.12684e13	+	3.82649e13i	0.879562	+	1.58246i
$476$	−2.12426e13			−0.869308
$477$	1.49530e13	+	1.49530e13i	0.605529	+	0.605529i
$478$	2.95092e13	−	2.95092e13i	1.18255	−	1.18255i
$479$			3.87093e12i			0.153511i	0.997050	+	0.0767553i	$0.0244560\pi$
$479$			3.87093e12i			0.153511i	−0.997050	+	0.0767553i	$0.975544\pi$
$480$	−2.66573e13	+	6.91049e12i	−1.04619	+	0.271208i
$481$	6.49358e11			0.0252208
$482$	5.97102e12	+	5.97102e12i	0.229516	+	0.229516i
$483$	−4.44201e12	+	4.44201e12i	−0.168983	+	0.168983i
$484$		−	3.80423e13i		−	1.43232i
$485$	−4.19375e13	−	2.46705e13i	−1.56277	−	0.919324i
$486$	6.41008e13			2.36419
$487$	2.06496e13	+	2.06496e13i	0.753819	+	0.753819i	0.975190	−	0.221371i	$-0.0710531\pi$
$487$	2.06496e13	+	2.06496e13i	0.753819	+	0.753819i	−0.221371	+	0.975190i	$0.571053\pi$
$488$	5.22465e12	−	5.22465e12i	0.188781	−	0.188781i
$489$		−	4.86233e12i		−	0.173900i
$490$	−1.12586e13	+	1.91385e13i	−0.398568	+	0.677529i
$491$	1.15907e13			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	1.15907e13			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$	−3.16010e13	−	3.16010e13i	−1.09616	−	1.09616i
$493$	−7.32245e12	+	7.32245e12i	−0.251433	+	0.251433i
$494$			2.80045e12i			0.0951902i
$495$	3.29283e12	+	1.27022e13i	0.110801	+	0.427417i
$496$	8.20838e12			0.273432
$497$	6.59044e12	+	6.59044e12i	0.217336	+	0.217336i
$498$	−5.87417e13	+	5.87417e13i	−1.91779	+	1.91779i
$499$			1.50505e12i			0.0486460i	0.999704	+	0.0243230i	$0.00774302\pi$
$499$			1.50505e12i			0.0486460i	−0.999704	+	0.0243230i	$0.992257\pi$
$500$	−3.74474e13	−	3.93246e13i	−1.19832	−	1.25839i
$501$	−2.38071e13			−0.754253
$502$	−4.10739e13	−	4.10739e13i	−1.28839	−	1.28839i
$503$	4.66282e12	−	4.66282e12i	0.144813	−	0.144813i	−0.630983	−	0.775797i	$-0.717348\pi$
$503$	4.66282e12	−	4.66282e12i	0.144813	−	0.144813i	0.775797	+	0.630983i	$0.217348\pi$
$504$		−	3.02908e13i		−	0.931448i
$505$	5.55395e13	−	1.43977e13i	1.69100	−	0.438366i
$506$	5.29594e12			0.159658
$507$	3.39090e13	+	3.39090e13i	1.01222	+	1.01222i
$508$	−5.31322e13	+	5.31322e13i	−1.57051	+	1.57051i
$509$		−	3.78988e13i		−	1.10927i	−0.832095	−	0.554634i	$-0.812858\pi$
$509$		−	3.78988e13i		−	1.10927i	0.832095	−	0.554634i	$-0.187142\pi$
$510$	4.86854e13	+	2.86400e13i	1.41107	+	0.830085i
$511$	−3.10314e13			−0.890630
$512$	−1.38463e13	−	1.38463e13i	−0.393537	−	0.393537i
$513$	3.47522e12	−	3.47522e12i	0.0978128	−	0.0978128i
$514$		−	5.04106e12i		−	0.140510i
$515$	7.71143e12	−	1.31087e13i	0.212862	−	0.361847i
$516$	1.29152e14			3.53063
$517$	−1.25268e13	−	1.25268e13i	−0.339147	−	0.339147i
$518$	2.50910e13	−	2.50910e13i	0.672774	−	0.672774i
$519$		−	8.06601e13i		−	2.14201i
$520$	−3.70040e11	−	1.42744e12i	−0.00973266	−	0.0375439i
$521$	1.99065e13			0.518569			0.259284	−	0.965801i	$-0.416513\pi$
$521$	1.99065e13			0.518569			0.259284	+	0.965801i	$0.416513\pi$
$522$	−2.45960e13	−	2.45960e13i	−0.634617	−	0.634617i
$523$	−3.05808e13	+	3.05808e13i	−0.781521	+	0.781521i	−0.980087	−	0.198566i	$-0.936371\pi$
$523$	−3.05808e13	+	3.05808e13i	−0.781521	+	0.781521i	0.198566	+	0.980087i	$0.436371\pi$
$524$			6.67902e13i			1.69066i
$525$	−3.61919e13	+	2.01162e13i	−0.907433	+	0.504370i
$526$	−1.19462e14			−2.96690
$527$	1.92560e13	+	1.92560e13i	0.473710	+	0.473710i
$528$	−4.91225e12	+	4.91225e12i	−0.119705	+	0.119705i
$529$			3.92314e13i			0.947013i
$530$	5.44548e13	−	1.41165e13i	1.30214	−	0.337558i
$531$	−5.07942e13			−1.20321
$532$	6.86827e13	+	6.86827e13i	1.61172	+	1.61172i
$533$	−6.01764e11	+	6.01764e11i	−0.0139891	+	0.0139891i
$534$			1.26991e14i			2.92460i
$535$	8.27800e12	+	4.86968e12i	0.188867	+	0.111104i
$536$	−9.87247e12			−0.223153
$537$	−3.46927e13	−	3.46927e13i	−0.776902	−	0.776902i
$538$	7.14876e13	−	7.14876e13i	1.58606	−	1.58606i
$539$		−	9.05999e12i		−	0.199152i
$540$	−3.09099e12	+	5.25440e12i	−0.0673177	+	0.114434i
$541$	2.58612e13			0.558037			0.279018	−	0.960286i	$-0.409991\pi$
$541$	2.58612e13			0.558037			0.279018	+	0.960286i	$0.409991\pi$
$542$	−8.70993e13	−	8.70993e13i	−1.86216	−	1.86216i
$543$	7.87509e13	−	7.87509e13i	1.66823	−	1.66823i
$544$		−	2.48120e13i		−	0.520795i
$545$	8.78860e12	+	3.39022e13i	0.182784	+	0.705091i
$546$	−2.64873e12			−0.0545852
$547$	−8.28003e12	−	8.28003e12i	−0.169081	−	0.169081i	0.617494	−	0.786575i	$-0.288148\pi$
$547$	−8.28003e12	−	8.28003e12i	−0.169081	−	0.169081i	−0.786575	+	0.617494i	$0.788148\pi$
$548$	−6.27446e12	+	6.27446e12i	−0.126962	+	0.126962i
$549$			1.14906e13i			0.230399i
$550$	3.35664e13	+	9.58304e12i	0.666946	+	0.190410i
$551$	4.73506e13			0.932325
$552$	1.45897e13	+	1.45897e13i	0.284676	+	0.284676i
$553$	8.80541e12	−	8.80541e12i	0.170264	−	0.170264i
$554$		−	2.63971e13i		−	0.505833i
$555$	−5.79720e13	+	1.50283e13i	−1.10091	+	0.285394i
$556$	−5.98047e13			−1.12554
$557$	3.64196e13	+	3.64196e13i	0.679296	+	0.679296i	0.959841	−	0.280545i	$-0.0905152\pi$
$557$	3.64196e13	+	3.64196e13i	0.679296	+	0.679296i	−0.280545	+	0.959841i	$0.590515\pi$
$558$	−6.46805e13	+	6.46805e13i	−1.19565	+	1.19565i
$559$		−	2.45938e12i		−	0.0450575i
$560$	−9.69252e12	−	5.70179e12i	−0.175993	−	0.103531i
$561$	−2.30472e13			−0.414767
$562$	4.33605e13	+	4.33605e13i	0.773415	+	0.773415i
$563$	−3.65138e13	+	3.65138e13i	−0.645527	+	0.645527i	−0.951909	−	0.306381i	$-0.900882\pi$
$563$	−3.65138e13	+	3.65138e13i	−0.645527	+	0.645527i	0.306381	+	0.951909i	$0.400882\pi$
$564$		−	1.62585e14i		−	2.84894i
$565$	−2.86565e13	+	4.87135e13i	−0.497716	+	0.846071i
$566$	2.26042e13			0.389140
$567$	−2.83363e13	−	2.83363e13i	−0.483534	−	0.483534i
$568$	2.16462e13	−	2.16462e13i	0.366133	−	0.366133i
$569$			8.10982e13i			1.35972i	0.733342	+	0.679860i	$0.237960\pi$
$569$			8.10982e13i			1.35972i	−0.733342	+	0.679860i	$0.762040\pi$
$570$	−6.48117e13	−	2.50012e14i	−1.07716	−	4.15515i
$571$	−6.86458e13			−1.13092			−0.565462	−	0.824774i	$-0.691302\pi$
$571$	−6.86458e13			−1.13092			−0.565462	+	0.824774i	$0.691302\pi$
$572$	1.00221e12	+	1.00221e12i	0.0163673	+	0.0163673i
$573$	−3.20175e13	+	3.20175e13i	−0.518339	+	0.518339i
$574$			4.65040e13i			0.746330i
$575$	3.97199e12	−	1.39126e13i	0.0631931	−	0.221345i
$576$	1.02165e14			1.61134
$577$	1.89504e13	+	1.89504e13i	0.296305	+	0.296305i	0.839565	−	0.543260i	$-0.182810\pi$
$577$	1.89504e13	+	1.89504e13i	0.296305	+	0.296305i	−0.543260	+	0.839565i	$0.682810\pi$
$578$	3.94908e13	−	3.94908e13i	0.612148	−	0.612148i
$579$			4.57883e13i			0.703658i
$580$	−5.68539e13	+	1.47385e13i	−0.866204	+	0.224549i
$581$	5.48684e13			0.828784
$582$	2.02976e14	+	2.02976e14i	3.03969	+	3.03969i
$583$	−1.62305e13	+	1.62305e13i	−0.240985	+	0.240985i
$584$			1.01922e14i			1.50039i
$585$	1.97660e12	+	1.16277e12i	0.0288495	+	0.0169712i
$586$	−4.11149e13			−0.594991
$587$	−6.92959e13	−	6.92959e13i	−0.994299	−	0.994299i	0.00568494	−	0.999984i	$-0.498190\pi$
$587$	−6.92959e13	−	6.92959e13i	−0.994299	−	0.994299i	−0.999984	+	0.00568494i	$0.998190\pi$
$588$	5.87945e13	−	5.87945e13i	0.836469	−	0.836469i
$589$		−	1.24519e14i		−	1.75654i
$590$	−6.85133e13	+	1.16466e14i	−0.958329	+	1.62907i
$591$	1.02578e14			1.42272
$592$	−1.15007e13	−	1.15007e13i	−0.158167	−	0.158167i
$593$	2.26363e13	−	2.26363e13i	0.308696	−	0.308696i	−0.535707	−	0.844404i	$-0.679955\pi$
$593$	2.26363e13	−	2.26363e13i	0.308696	−	0.308696i	0.844404	+	0.535707i	$0.179955\pi$
$594$		−	3.91883e12i		−	0.0529938i
$595$	−9.36181e12	−	3.61134e13i	−0.125538	−	0.484265i
$596$	2.84391e13			0.378168
$597$	3.25964e13	+	3.25964e13i	0.429832	+	0.429832i
$598$	6.54451e11	−	6.54451e11i	0.00855797	−	0.00855797i
$599$			4.01937e13i			0.521224i	0.965444	+	0.260612i	$0.0839243\pi$
$599$			4.01937e13i			0.521224i	−0.965444	+	0.260612i	$0.916076\pi$
$600$	6.60712e13	+	1.18872e14i	0.849682	+	1.52870i
$601$	4.86719e13			0.620734			0.310367	−	0.950617i	$-0.399548\pi$
$601$	4.86719e13			0.620734			0.310367	+	0.950617i	$0.399548\pi$
$602$	−9.50298e13	−	9.50298e13i	−1.20193	−	1.20193i
$603$	1.08563e13	−	1.08563e13i	0.136174	−	0.136174i
$604$		−	6.92312e13i		−	0.861226i
$605$	6.46735e13	−	1.67656e13i	0.797902	−	0.206843i
$606$	−3.38493e14			−4.14178
$607$	−1.01626e14	−	1.01626e14i	−1.23328	−	1.23328i	−0.962696	−	0.270585i	$-0.912783\pi$
$607$	−1.01626e14	−	1.01626e14i	−1.23328	−	1.23328i	−0.270585	−	0.962696i	$-0.587217\pi$
$608$	−8.02232e13	+	8.02232e13i	−0.965567	+	0.965567i
$609$			4.47854e13i			0.534626i
$610$	2.63468e13	+	1.54990e13i	0.311945	+	0.183507i
$611$	−3.09603e12			−0.0363579
$612$	−7.67239e13	−	7.67239e13i	−0.893663	−	0.893663i
$613$	4.15916e13	−	4.15916e13i	0.480511	−	0.480511i	−0.424784	−	0.905295i	$-0.639650\pi$
$613$	4.15916e13	−	4.15916e13i	0.480511	−	0.480511i	0.905295	+	0.424784i	$0.139650\pi$
$614$		−	1.88463e14i		−	2.15965i
$615$	3.97962e13	−	6.76499e13i	0.452341	−	0.768938i
$616$	3.28789e13			0.370692
$617$	−6.03617e13	−	6.03617e13i	−0.675050	−	0.675050i	0.283826	−	0.958876i	$-0.408396\pi$
$617$	−6.03617e13	−	6.03617e13i	−0.675050	−	0.675050i	−0.958876	+	0.283826i	$0.908396\pi$
$618$	−6.34458e13	+	6.34458e13i	−0.703818	+	0.703818i
$619$			1.48954e14i			1.63908i	0.573024	+	0.819538i	$0.305770\pi$
$619$			1.48954e14i			1.63908i	−0.573024	+	0.819538i	$0.694230\pi$
$620$	3.87579e13	+	1.49510e14i	0.423060	+	1.63196i
$621$	−1.62428e12			−0.0175875
$622$	1.13562e14	+	1.13562e14i	1.21977	+	1.21977i
$623$	5.93087e13	−	5.93087e13i	0.631944	−	0.631944i
$624$			1.21407e12i			0.0128328i
$625$	5.03500e13	−	8.09927e13i	0.527958	−	0.849270i
$626$	1.61833e14			1.68343
$627$	7.45174e13	+	7.45174e13i	0.768988	+	0.768988i
$628$	7.18537e12	−	7.18537e12i	0.0735615	−	0.0735615i
$629$		−	5.39588e13i		−	0.548036i
$630$	1.21304e14	−	3.14462e13i	1.22229	−	0.316858i
$631$	1.75259e13			0.175200			0.0876001	−	0.996156i	$-0.472080\pi$
$631$	1.75259e13			0.175200			0.0876001	+	0.996156i	$0.472080\pi$
$632$	−2.89212e13	−	2.89212e13i	−0.286834	−	0.286834i
$633$	−4.72500e13	+	4.72500e13i	−0.464926	+	0.464926i
$634$			1.76144e14i			1.71958i
$635$	−1.13743e14	−	6.69111e13i	−1.10168	−	0.648082i
$636$	−2.10655e14			−2.02435
$637$	−1.11960e12	−	1.11960e12i	−0.0106749	−	0.0106749i
$638$	2.66975e13	−	2.66975e13i	0.252561	−	0.252561i
$639$			4.76065e13i			0.446850i
$640$	9.67408e13	−	1.64450e14i	0.900969	−	1.53156i
$641$	−1.22676e14			−1.13363			−0.566815	−	0.823845i	$-0.691824\pi$
$641$	−1.22676e14			−1.13363			−0.566815	+	0.823845i	$0.691824\pi$
$642$	−4.00652e13	−	4.00652e13i	−0.367361	−	0.367361i
$643$	−4.61206e13	+	4.61206e13i	−0.419604	+	0.419604i	−0.885067	−	0.465463i	$-0.845888\pi$
$643$	−4.61206e13	+	4.61206e13i	−0.419604	+	0.419604i	0.465463	+	0.885067i	$0.345888\pi$
$644$		−	3.21016e13i		−	0.289800i
$645$	5.69183e13	+	2.19563e14i	0.509863	+	1.96681i
$646$	2.32705e14			2.06844
$647$	1.40259e13	+	1.40259e13i	0.123711	+	0.123711i	0.766252	−	0.642541i	$-0.222120\pi$
$647$	1.40259e13	+	1.40259e13i	0.123711	+	0.123711i	−0.642541	+	0.766252i	$0.722120\pi$
$648$	−9.30700e13	+	9.30700e13i	−0.814582	+	0.814582i
$649$		−	5.51340e13i		−	0.478847i
$650$	5.33223e12	−	2.96376e12i	0.0459559	−	0.0255432i
$651$	1.17773e14			1.00726
$652$	1.75696e13	+	1.75696e13i	0.149116	+	0.149116i
$653$	−5.59590e13	+	5.59590e13i	−0.471307	+	0.471307i	−0.902337	−	0.431031i	$-0.858150\pi$
$653$	−5.59590e13	+	5.59590e13i	−0.471307	+	0.471307i	0.431031	+	0.902337i	$0.358150\pi$
$654$		−	2.06622e14i		−	1.72698i
$655$	−1.13546e14	+	2.94350e13i	−0.941815	+	0.244150i
$656$	2.13156e13			0.175460
$657$	−1.12079e14	−	1.12079e14i	−0.915582	−	0.915582i
$658$	−1.19630e14	+	1.19630e14i	−0.969860	+	0.969860i
$659$			8.78505e13i			0.706833i	0.935466	+	0.353417i	$0.114980\pi$
$659$			8.78505e13i			0.706833i	−0.935466	+	0.353417i	$0.885020\pi$
$660$	−1.12667e14	−	6.62785e13i	−0.899661	−	0.529241i
$661$	2.10365e14			1.66711			0.833557	−	0.552433i	$-0.186300\pi$
$661$	2.10365e14			1.66711			0.833557	+	0.552433i	$0.186300\pi$
$662$	7.71363e13	+	7.71363e13i	0.606693	+	0.606693i
$663$	−2.84808e12	+	2.84808e12i	−0.0222323	+	0.0222323i
$664$		−	1.80214e14i		−	1.39620i
$665$	−8.64944e13	+	1.47032e14i	−0.665089	+	1.13059i
$666$	1.81247e14			1.38325
$667$	−1.10656e13	−	1.10656e13i	−0.0838197	−	0.0838197i
$668$	8.60247e13	−	8.60247e13i	0.646757	−	0.646757i
$669$		−	5.08502e13i		−	0.379457i
$670$	−1.02490e13	−	3.95358e13i	−0.0759116	−	0.292830i
$671$	−1.24723e13			−0.0916928
$672$	−7.58771e13	−	7.58771e13i	−0.553687	−	0.553687i
$673$	−7.19154e12	+	7.19154e12i	−0.0520891	+	0.0520891i	−0.732672	−	0.680582i	$-0.761727\pi$
$673$	−7.19154e12	+	7.19154e12i	−0.0520891	+	0.0520891i	0.680582	+	0.732672i	$0.261727\pi$
$674$		−	3.74319e13i		−	0.269118i
$675$	−1.02949e13	−	2.93916e12i	−0.0734690	−	0.0209751i
$676$	−2.45054e14			−1.73592
$677$	1.12233e14	+	1.12233e14i	0.789184	+	0.789184i	0.981360	−	0.192176i	$-0.0615546\pi$
$677$	1.12233e14	+	1.12233e14i	0.789184	+	0.789184i	−0.192176	+	0.981360i	$0.561555\pi$
$678$	2.35771e14	−	2.35771e14i	1.64567	−	1.64567i
$679$		−	1.89592e14i		−	1.31362i
$680$	−1.18614e14	+	3.07487e13i	−0.815812	+	0.211486i
$681$	−1.88486e14			−1.28689
$682$	−7.02068e13	−	7.02068e13i	−0.475836	−	0.475836i
$683$	2.00246e14	−	2.00246e14i	1.34729	−	1.34729i	0.458695	−	0.888594i	$-0.348317\pi$
$683$	2.00246e14	−	2.00246e14i	1.34729	−	1.34729i	0.888594	−	0.458695i	$-0.151683\pi$
$684$			4.96135e14i			3.31375i
$685$	−1.34320e13	−	7.90163e12i	−0.0890614	−	0.0523919i
$686$	−2.68641e14			−1.76829
$687$	8.15377e13	+	8.15377e13i	0.532813	+	0.532813i
$688$	−4.35578e13	+	4.35578e13i	−0.282569	+	0.282569i
$689$			4.01140e12i			0.0258345i
$690$	−4.32805e13	+	7.35728e13i	−0.276724	+	0.470405i
$691$	−9.77575e13			−0.620526			−0.310263	−	0.950651i	$-0.600417\pi$
$691$	−9.77575e13			−0.620526			−0.310263	+	0.950651i	$0.600417\pi$
$692$	2.91458e14	+	2.91458e14i	1.83673	+	1.83673i
$693$	−3.61553e13	+	3.61553e13i	−0.226207	+	0.226207i
$694$			1.20490e14i			0.748435i
$695$	−2.63564e13	−	1.01670e14i	−0.162541	−	0.627004i
$696$	1.47097e14			0.900652
$697$	5.00040e13	+	5.00040e13i	0.303977	+	0.303977i
$698$	−5.66864e13	+	5.66864e13i	−0.342138	+	0.342138i
$699$		−	1.64215e14i		−	0.984075i
$700$	5.80881e13	−	2.03464e14i	0.345619	−	1.21059i
$701$	−2.74859e14			−1.62375			−0.811875	−	0.583831i	$-0.801553\pi$
$701$	−2.74859e14			−1.62375			−0.811875	+	0.583831i	$0.801553\pi$
$702$	−4.84274e11	−	4.84274e11i	−0.00284057	−	0.00284057i
$703$	−1.74462e14	+	1.74462e14i	−1.01607	+	1.01607i
$704$			1.10893e14i			0.641272i
$705$	2.76400e14	−	7.16524e13i	1.58706	−	0.411420i
$706$	2.78396e14			1.58723
$707$	1.58087e14	+	1.58087e14i	0.894950	+	0.894950i
$708$	3.57790e14	−	3.57790e14i	2.01123	−	2.01123i
$709$		−	2.13844e14i		−	1.19362i	−0.802383	−	0.596810i	$-0.796435\pi$
$709$		−	2.13844e14i		−	1.19362i	0.802383	−	0.596810i	$-0.203565\pi$
$710$	1.09157e14	+	6.42136e13i	0.605007	+	0.355906i
$711$	6.36065e13			0.350069
$712$	−1.94799e14	−	1.94799e14i	−1.06460	−	1.06460i
$713$	−2.90994e13	+	2.90994e13i	−0.157920	+	0.157920i
$714$			2.20098e14i			1.18611i
$715$	−1.26211e12	+	2.14548e12i	−0.00675411	+	0.0114814i
$716$	2.50718e14			1.33236
$717$	−1.94067e14	−	1.94067e14i	−1.02413	−	1.02413i
$718$	−1.72563e14	+	1.72563e14i	−0.904330	+	0.904330i
$719$			3.58501e14i			1.86572i	0.360242	+	0.932859i	$0.382694\pi$
$719$			3.58501e14i			1.86572i	−0.360242	+	0.932859i	$0.617306\pi$
$720$	−1.44137e13	−	5.56010e13i	−0.0744923	−	0.287356i
$721$	5.92623e13			0.304160
$722$	−5.22851e14	−	5.22851e14i	−2.66497	−	2.66497i
$723$	3.92683e13	−	3.92683e13i	0.198770	−	0.198770i
$724$			5.69119e14i			2.86095i
$725$	−5.01119e13	−	9.01585e13i	−0.250179	−	0.450108i
$726$	−3.94162e14			−1.95430
$727$	1.93743e14	+	1.93743e14i	0.954014	+	0.954014i	0.998988	−	0.0449742i	$-0.0143206\pi$
$727$	1.93743e14	+	1.93743e14i	0.954014	+	0.954014i	−0.0449742	+	0.998988i	$0.514321\pi$
$728$	4.06303e12	−	4.06303e12i	0.0198698	−	0.0198698i
$729$		−	2.27231e14i		−	1.10365i
$730$	−4.08163e14	+	1.05810e14i	−1.96888	+	0.510400i
$731$	−2.04364e14			−0.979078
$732$	−8.09387e13	−	8.09387e13i	−0.385124	−	0.385124i
$733$	1.25217e14	−	1.25217e14i	0.591755	−	0.591755i	−0.346350	−	0.938105i	$-0.612579\pi$
$733$	1.25217e14	−	1.25217e14i	0.591755	−	0.591755i	0.938105	+	0.346350i	$0.112579\pi$
$734$		−	5.42636e14i		−	2.54700i
$735$	1.25864e14	+	7.40418e13i	0.586767	+	0.345176i
$736$	3.74956e13			0.173616
$737$	1.17838e13	+	1.17838e13i	0.0541937	+	0.0541937i
$738$	−1.67963e14	+	1.67963e14i	−0.767240	+	0.767240i
$739$			2.23292e14i			1.01310i	0.862211	+	0.506549i	$0.169079\pi$
$739$			2.23292e14i			1.01310i	−0.862211	+	0.506549i	$0.830921\pi$
$740$	1.55173e14	−	2.63780e14i	0.699292	−	1.18873i
$741$	1.84171e13			0.0824385
$742$	1.55000e14	+	1.55000e14i	0.689145	+	0.689145i
$743$	2.74839e14	−	2.74839e14i	1.21376	−	1.21376i	0.243983	−	0.969779i	$-0.421546\pi$
$743$	2.74839e14	−	2.74839e14i	1.21376	−	1.21376i	0.969779	−	0.243983i	$-0.0784543\pi$
$744$		−	3.86823e14i		−	1.69687i
$745$	1.25334e13	+	4.83476e13i	0.0546117	+	0.210666i
$746$	6.02541e14			2.60791
$747$	1.98173e14	+	1.98173e14i	0.852004	+	0.852004i
$748$	8.32791e13	−	8.32791e13i	0.355654	−	0.355654i
$749$			3.74234e13i			0.158757i
$750$	−4.07448e14	+	3.87998e14i	−1.71698	+	1.63502i
$751$	−1.59492e14			−0.667635			−0.333817	−	0.942638i	$-0.608337\pi$
$751$	−1.59492e14			−0.667635			−0.333817	+	0.942638i	$0.608337\pi$
$752$	5.48334e13	+	5.48334e13i	0.228011	+	0.228011i
$753$	−2.70122e14	+	2.70122e14i	−1.11580	+	1.11580i
$754$		−	6.59833e12i		−	0.0270755i
$755$	1.17696e14	−	3.05108e13i	0.479763	−	0.124371i
$756$	−2.37542e13			−0.0961905
$757$	−2.26272e14	−	2.26272e14i	−0.910231	−	0.910231i	0.0860591	−	0.996290i	$-0.472573\pi$
$757$	−2.26272e14	−	2.26272e14i	−0.910231	−	0.910231i	−0.996290	+	0.0860591i	$0.972573\pi$
$758$	−2.44998e14	+	2.44998e14i	−0.979077	+	0.979077i
$759$		−	3.48287e13i		−	0.138270i
$760$	4.82926e14	+	2.84089e14i	1.90464	+	1.12044i
$761$	3.21294e14			1.25886			0.629432	−	0.777055i	$-0.283287\pi$
$761$	3.21294e14			1.25886			0.629432	+	0.777055i	$0.283287\pi$
$762$	5.50511e14	+	5.50511e14i	2.14285	+	2.14285i
$763$	−9.64988e13	+	9.64988e13i	−0.373164	+	0.373164i
$764$		−	2.31385e14i		−	0.888930i
$765$	9.66209e13	−	1.64247e14i	0.368777	−	0.626887i
$766$	4.10927e11			0.00155819
$767$	−6.81324e12	−	6.81324e12i	−0.0256671	−	0.0256671i
$768$	−3.81795e14	+	3.81795e14i	−1.42897	+	1.42897i
$769$		−	3.20477e14i		−	1.19169i	−0.803098	−	0.595847i	$-0.796816\pi$
$769$		−	3.20477e14i		−	1.19169i	0.803098	−	0.595847i	$-0.203184\pi$
$770$	3.41329e13	+	1.31668e14i	0.126101	+	0.486438i
$771$	−3.31524e13			−0.121687
$772$	−1.65452e14	−	1.65452e14i	−0.603373	−	0.603373i
$773$	−7.88431e13	+	7.88431e13i	−0.285671	+	0.285671i	−0.835366	−	0.549695i	$-0.814744\pi$
$773$	−7.88431e13	+	7.88431e13i	−0.285671	+	0.285671i	0.549695	+	0.835366i	$0.314744\pi$
$774$		−	6.86455e14i		−	2.47120i
$775$	−2.37091e14	+	1.31780e14i	−0.848022	+	0.471348i
$776$	−6.22712e14			−2.21298
$777$	−1.65011e14	−	1.65011e14i	−0.582649	−	0.582649i
$778$	3.41784e14	−	3.41784e14i	1.19910	−	1.19910i
$779$		−	3.23351e14i		−	1.12716i
$780$	−2.21134e13	+	5.73255e12i	−0.0765919	+	0.0198552i
$781$	−5.16740e13			−0.177835
$782$	−5.43820e13	−	5.43820e13i	−0.185961	−	0.185961i
$783$	−8.18821e12	+	8.18821e12i	−0.0278215	+	0.0278215i
$784$			3.96581e13i			0.133891i
$785$	1.53821e13	+	9.04877e12i	0.0516020	+	0.0303558i
$786$	6.92023e14			2.30679
$787$	−8.71811e13	−	8.71811e13i	−0.288768	−	0.288768i	0.547825	−	0.836593i	$-0.315456\pi$
$787$	−8.71811e13	−	8.71811e13i	−0.288768	−	0.288768i	−0.836593	+	0.547825i	$0.815456\pi$
$788$	−3.70658e14	+	3.70658e14i	−1.21995	+	1.21995i
$789$			7.85643e14i			2.56945i
$790$	8.57950e13	−	1.45844e14i	0.278822	−	0.473971i
$791$	−2.20225e14			−0.711188
$792$	1.18751e14	+	1.18751e14i	0.381077	+	0.381077i
$793$	−1.54128e12	+	1.54128e12i	−0.00491491	+	0.00491491i
$794$			4.72298e14i			1.49663i
$795$	−9.28373e13	−	3.58122e14i	−0.292339	−	1.12770i
$796$	−2.35569e14			−0.737144
$797$	7.22772e13	+	7.22772e13i	0.224755	+	0.224755i	0.810497	−	0.585742i	$-0.199197\pi$
$797$	7.22772e13	+	7.22772e13i	0.224755	+	0.224755i	−0.585742	+	0.810497i	$0.699197\pi$
$798$	7.11632e14	−	7.11632e14i	2.19908	−	2.19908i
$799$			2.57266e14i			0.790040i
$800$	2.37652e14	+	6.78485e13i	0.725255	+	0.207057i
$801$	4.28421e14			1.29930
$802$	−5.02309e14	−	5.02309e14i	−1.51391	−	1.51391i
$803$	1.21655e14	−	1.21655e14i	0.364378	−	0.364378i
$804$			1.52941e14i			0.455245i
$805$	5.45741e13	−	1.41475e13i	0.161438	−	0.0418503i
$806$	−1.73517e13			−0.0510114
$807$	−4.70137e14	−	4.70137e14i	−1.37359	−	1.37359i
$808$	5.19233e14	−	5.19233e14i	1.50767	−	1.50767i
$809$			3.22130e14i			0.929585i	0.885420	+	0.464792i	$0.153871\pi$
$809$			3.22130e14i			0.929585i	−0.885420	+	0.464792i	$0.846129\pi$
$810$	−4.69333e14	−	2.76093e14i	−1.34603	−	0.791827i
$811$	8.83143e11			0.00251725			0.00125863	−	0.999999i	$-0.499599\pi$
$811$	8.83143e11			0.00251725			0.00125863	+	0.999999i	$0.499599\pi$
$812$	−1.61828e14	−	1.61828e14i	−0.458431	−	0.458431i
$813$	−5.72807e14	+	5.72807e14i	−1.61271	+	1.61271i
$814$			1.96732e14i			0.550496i
$815$	−2.21260e13	+	3.76121e13i	−0.0615339	+	0.104602i
$816$	1.00884e14			0.278851
$817$	6.60759e14	+	6.60759e14i	1.81523	+	1.81523i
$818$	−5.99168e14	+	5.99168e14i	−1.63600	+	1.63600i
$819$			8.93585e12i			0.0242503i
$820$	1.00647e14	+	3.88247e14i	0.271476	+	1.04722i
$821$	1.30031e14			0.348604			0.174302	−	0.984692i	$-0.444233\pi$
$821$	1.30031e14			0.348604			0.174302	+	0.984692i	$0.444233\pi$
$822$	6.50106e13	+	6.50106e13i	0.173231	+	0.173231i
$823$	1.63232e14	−	1.63232e14i	0.432321	−	0.432321i	−0.457096	−	0.889417i	$-0.651110\pi$
$823$	1.63232e14	−	1.63232e14i	0.432321	−	0.432321i	0.889417	+	0.457096i	$0.151110\pi$
$824$		−	1.94646e14i		−	0.512400i
$825$	6.30228e13	−	2.20749e14i	0.164903	−	0.577602i
$826$	−5.26523e14			−1.36936
$827$	8.81723e13	+	8.81723e13i	0.227932	+	0.227932i	0.811828	−	0.583897i	$-0.198473\pi$
$827$	8.81723e13	+	8.81723e13i	0.227932	+	0.227932i	−0.583897	+	0.811828i	$0.698473\pi$
$828$	1.15944e14	−	1.15944e14i	0.297919	−	0.297919i
$829$		−	3.84764e14i		−	0.982701i	−0.870962	−	0.491351i	$-0.836503\pi$
$829$		−	3.84764e14i		−	0.982701i	0.870962	−	0.491351i	$-0.163497\pi$
$830$	7.21695e14	−	1.87088e14i	1.83216	−	0.474958i
$831$	−1.73600e14			−0.438072
$832$	1.37038e13	+	1.37038e13i	0.0343734	+	0.0343734i
$833$	−9.30336e13	+	9.30336e13i	−0.231961	+	0.231961i
$834$			6.19645e14i			1.53572i
$835$	1.84157e14	+	1.08334e14i	0.453688	+	0.266889i
$836$	−5.38524e14			−1.31878
$837$	2.15327e13	+	2.15327e13i	0.0524168	+	0.0524168i
$838$	8.19546e14	−	8.19546e14i	1.98314	−	1.98314i
$839$		−	3.40778e13i		−	0.0819713i	−0.999160	−	0.0409856i	$-0.986950\pi$
$839$		−	3.40778e13i		−	0.0819713i	0.999160	−	0.0409856i	$-0.0130498\pi$
$840$	−2.68699e14	+	4.56763e14i	−0.642494	+	1.09218i
$841$	3.09141e14			0.734813
$842$	8.84838e14	+	8.84838e14i	2.09076	+	2.09076i
$843$	2.85160e14	−	2.85160e14i	0.669808	−	0.669808i
$844$		−	3.41468e14i		−	0.797329i
$845$	−1.07997e14	−	4.16602e14i	−0.250686	−	0.967025i
$846$	−8.64153e14			−1.99406
$847$	1.84086e14	+	1.84086e14i	0.422283	+	0.422283i
$848$	7.10456e13	−	7.10456e13i	0.162016	−	0.162016i
$849$		−	1.48656e14i		−	0.337011i
$850$	−2.46275e14	−	4.43085e14i	−0.555043	−	0.998601i
$851$	8.15420e13			0.182698
$852$	−3.35336e14	−	3.35336e14i	−0.746934	−	0.746934i
$853$	−3.41010e14	+	3.41010e14i	−0.755130	+	0.755130i	−0.975432	−	0.220302i	$-0.929296\pi$
$853$	−3.41010e14	+	3.41010e14i	−0.755130	+	0.755130i	0.220302	+	0.975432i	$0.429296\pi$
$854$			1.19109e14i			0.262214i
$855$	−8.43449e14	+	2.18651e14i	−1.84599	+	0.478542i
$856$	1.22917e14			0.267449
$857$	−2.81046e14	−	2.81046e14i	−0.607959	−	0.607959i	0.334454	−	0.942412i	$-0.391448\pi$
$857$	−2.81046e14	−	2.81046e14i	−0.607959	−	0.607959i	−0.942412	+	0.334454i	$0.891448\pi$
$858$	1.03840e13	−	1.03840e13i	0.0223321	−	0.0223321i
$859$		−	8.55745e14i		−	1.82969i	−0.403801	−	0.914847i	$-0.632311\pi$
$859$		−	8.55745e14i		−	1.82969i	0.403801	−	0.914847i	$-0.367689\pi$
$860$	−9.99043e14	−	5.87704e14i	−2.12369	−	1.24930i
$861$	3.05833e14			0.646352
$862$	2.95390e14	+	2.95390e14i	0.620668	+	0.620668i
$863$	1.58686e14	−	1.58686e14i	0.331502	−	0.331502i	−0.521655	−	0.853157i	$-0.674685\pi$
$863$	1.58686e14	−	1.58686e14i	0.331502	−	0.331502i	0.853157	+	0.521655i	$0.174685\pi$
$864$		−	2.77456e13i		−	0.0576269i
$865$	−3.67043e14	+	6.23939e14i	−0.757943	+	1.28843i
$866$	1.05430e14			0.216458
$867$	−2.59711e14	−	2.59711e14i	−0.530145	−	0.530145i
$868$	−4.25562e14	+	4.25562e14i	−0.863703	+	0.863703i
$869$			6.90410e13i			0.139318i
$870$	1.52707e14	+	5.89071e14i	0.306382	+	1.18188i
$871$	2.91240e12			0.00580978
$872$	3.16949e14	+	3.16949e14i	0.628646	+	0.628646i
$873$	6.84766e14	−	6.84766e14i	1.35043	−	1.35043i
$874$			3.51661e14i			0.689552i
$875$	3.71498e14	+	9.08382e12i	0.724295	+	0.0177104i
$876$	1.57895e15			3.06089
$877$	−3.20760e14	−	3.20760e14i	−0.618276	−	0.618276i	0.326813	−	0.945089i	$-0.394025\pi$
$877$	−3.20760e14	−	3.20760e14i	−0.618276	−	0.618276i	−0.945089	+	0.326813i	$0.894025\pi$
$878$	−8.52008e14	+	8.52008e14i	−1.63294	+	1.63294i
$879$			2.70391e14i			0.515286i
$880$	6.03515e13	−	1.56451e13i	0.114360	−	0.0296460i
$881$	1.11571e14			0.210219			0.105110	−	0.994461i	$-0.466481\pi$
$881$	1.11571e14			0.210219			0.105110	+	0.994461i	$0.466481\pi$
$882$	−3.12498e14	−	3.12498e14i	−0.585470	−	0.585470i
$883$	−4.29854e13	+	4.29854e13i	−0.0800788	+	0.0800788i	−0.746012	−	0.665933i	$-0.768034\pi$
$883$	−4.29854e13	+	4.29854e13i	−0.0800788	+	0.0800788i	0.665933	+	0.746012i	$0.268034\pi$
$884$		−	2.05826e13i		−	0.0381275i
$885$	7.65939e14	+	4.50577e14i	1.41084	+	0.829951i
$886$	−5.38515e14			−0.986347
$887$	1.96607e13	+	1.96607e13i	0.0358081	+	0.0358081i	0.724784	−	0.688976i	$-0.241939\pi$
$887$	1.96607e13	+	1.96607e13i	0.0358081	+	0.0358081i	−0.688976	+	0.724784i	$0.741939\pi$
$888$	−5.41975e14	+	5.41975e14i	−0.981554	+	0.981554i
$889$		−	5.14211e14i		−	0.926046i
$890$	5.77872e14	−	9.82328e14i	1.03486	−	1.75917i
$891$	2.22178e14			0.395651
$892$	1.83743e14	+	1.83743e14i	0.325376	+	0.325376i
$893$	8.31806e14	−	8.31806e14i	1.46475	−	1.46475i
$894$		−	2.94662e14i		−	0.515984i
$895$	1.10493e14	+	4.26231e14i	0.192407	+	0.742215i
$896$	7.43452e14			1.28740
$897$	−4.30399e12	−	4.30399e12i	−0.00741154	−	0.00741154i
$898$	−7.66629e14	+	7.66629e14i	−1.31281	+	1.31281i
$899$			2.93387e14i			0.499623i
$900$	9.44672e14	−	5.25068e14i	1.59981	−	0.889207i
$901$	3.33330e14			0.561372
$902$	−1.82313e14	−	1.82313e14i	−0.305341	−	0.305341i
$903$	−6.24963e14	+	6.24963e14i	−1.04091	+	1.04091i
$904$			7.23325e14i			1.19810i
$905$	−9.67525e14	+	2.50815e14i	−1.59375	+	0.413153i
$906$	−7.17315e14			−1.17508
$907$	4.73562e13	+	4.73562e13i	0.0771507	+	0.0771507i	0.744629	−	0.667478i	$-0.232626\pi$
$907$	4.73562e13	+	4.73562e13i	0.0771507	+	0.0771507i	−0.667478	+	0.744629i	$0.732626\pi$
$908$	6.81076e14	−	6.81076e14i	1.10349	−	1.10349i
$909$			1.14195e15i			1.84004i
$910$	2.04890e13	+	1.20530e13i	0.0328333	+	0.0193148i
$911$	−1.17842e15			−1.87805			−0.939025	−	0.343848i	$-0.888270\pi$
$911$	−1.17842e15			−1.87805			−0.939025	+	0.343848i	$0.888270\pi$
$912$	−3.26183e14	−	3.26183e14i	−0.516996	−	0.516996i
$913$	−2.15105e14	+	2.15105e14i	−0.339075	+	0.339075i
$914$		−	1.86523e15i		−	2.92417i
$915$	1.01929e14	−	1.73269e14i	0.158925	−	0.270157i
$916$	−5.89259e14			−0.913753
$917$	−3.23196e14	−	3.23196e14i	−0.498448	−	0.498448i
$918$	−4.02410e13	+	4.02410e13i	−0.0617242	+	0.0617242i
$919$			7.08787e14i			1.08128i	0.841254	+	0.540640i	$0.181818\pi$
$919$			7.08787e14i			1.08128i	−0.841254	+	0.540640i	$0.818182\pi$
$920$	−4.64671e13	−	1.79248e14i	−0.0705028	−	0.271966i
$921$	−1.23942e15			−1.87034
$922$	−5.86704e14	−	5.86704e14i	−0.880572	−	0.880572i
$923$	−6.38566e12	+	6.38566e12i	−0.00953229	+	0.00953229i
$924$		−	5.09350e14i		−	0.756234i
$925$	5.16823e14	+	1.47551e14i	0.763192	+	0.217888i
$926$	6.61437e14			0.971479
$927$	2.14043e14	+	2.14043e14i	0.312681	+	0.312681i
$928$	1.89020e14	−	1.89020e14i	0.274642	−	0.274642i
$929$			5.10820e14i			0.738227i	0.929384	+	0.369113i	$0.120339\pi$
$929$			5.10820e14i			0.738227i	−0.929384	+	0.369113i	$0.879661\pi$
$930$	1.54909e15	−	4.01577e14i	2.22670	−	0.577237i
$931$	6.01601e14			0.860123
$932$	5.93378e14	+	5.93378e14i	0.843825	+	0.843825i
$933$	7.46836e14	−	7.46836e14i	1.05637	−	1.05637i
$934$		−	5.99688e14i		−	0.843705i
$935$	1.78280e14	+	1.04876e14i	0.249485	+	0.146764i
$936$	2.93496e13			0.0408530
$937$	−2.89263e13	−	2.89263e13i	−0.0400493	−	0.0400493i	0.686799	−	0.726848i	$-0.259015\pi$
$937$	−2.89263e13	−	2.89263e13i	−0.0400493	−	0.0400493i	−0.726848	+	0.686799i	$0.759015\pi$
$938$	1.12534e14	−	1.12534e14i	0.154978	−	0.154978i
$939$		−	1.06429e15i		−	1.45792i
$940$	−7.39839e14	+	1.25766e15i	−1.00809	+	1.71366i
$941$	−1.20189e15			−1.62899			−0.814494	−	0.580172i	$-0.802985\pi$
$941$	−1.20189e15			−1.62899			−0.814494	+	0.580172i	$0.802985\pi$
$942$	−7.44486e13	−	7.44486e13i	−0.100370	−	0.100370i
$943$	−7.55655e13	+	7.55655e13i	−0.101336	+	0.101336i
$944$			2.41337e14i			0.321932i
$945$	−1.04687e13	−	4.03832e13i	−0.0138910	−	0.0535848i
$946$	7.45105e14			0.983472
$947$	1.21600e13	+	1.21600e13i	0.0159655	+	0.0159655i	0.715044	−	0.699079i	$-0.246406\pi$
$947$	1.21600e13	+	1.21600e13i	0.0159655	+	0.0159655i	−0.699079	+	0.715044i	$0.746406\pi$
$948$	−4.48039e14	+	4.48039e14i	−0.585159	+	0.585159i
$949$		−	3.00672e13i		−	0.0390627i
$950$	−6.36333e14	+	2.22887e15i	−0.822369	+	2.88050i
$951$	1.15841e15			1.48922
$952$	−3.37621e14	−	3.37621e14i	−0.431762	−	0.431762i
$953$	−6.49900e14	+	6.49900e14i	−0.826765	+	0.826765i	−0.987068	−	0.160303i	$-0.948753\pi$
$953$	−6.49900e14	+	6.49900e14i	−0.826765	+	0.826765i	0.160303	+	0.987068i	$0.448753\pi$
$954$			1.11965e15i			1.41691i
$955$	3.93363e14	−	1.01973e14i	0.495196	−	0.128372i
$956$	1.40249e15			1.75635
$957$	−1.75576e14	−	1.75576e14i	−0.218728	−	0.218728i
$958$	−1.44924e14	+	1.44924e14i	−0.179603	+	0.179603i
$959$		−	6.07239e13i		−	0.0748629i
$960$	−1.54056e15	−	9.06264e14i	−1.88940	−	1.11147i
$961$	−4.81034e13			−0.0586892
$962$	2.43114e13	+	2.43114e13i	0.0295076	+	0.0295076i
$963$	−1.35165e14	+	1.35165e14i	−0.163205	+	0.163205i
$964$			2.83786e14i			0.340883i
$965$	2.08359e14	−	3.54192e14i	0.248987	−	0.423255i
$966$	−3.32610e14			−0.395412
$967$	−7.60405e14	−	7.60405e14i	−0.899317	−	0.899317i	0.0960585	−	0.995376i	$-0.469376\pi$
$967$	−7.60405e14	−	7.60405e14i	−0.899317	−	0.899317i	−0.995376	+	0.0960585i	$0.969376\pi$
$968$	6.04627e14	−	6.04627e14i	0.711395	−	0.711395i
$969$		−	1.53038e15i		−	1.79135i
$970$	−6.46463e14	−	2.49374e15i	−0.752809	−	2.90398i
$971$	4.42428e14			0.512562			0.256281	−	0.966602i	$-0.417503\pi$
$971$	4.42428e14			0.512562			0.256281	+	0.966602i	$0.417503\pi$
$972$	1.52327e15	+	1.52327e15i	1.75568	+	1.75568i
$973$	2.89393e14	−	2.89393e14i	0.331837	−	0.331837i
$974$			1.54621e15i			1.76389i
$975$	−1.94911e13	−	3.50673e13i	−0.0221215	−	0.0397997i
$976$	5.45949e13			0.0616457
$977$	1.12952e15	+	1.12952e15i	1.26888	+	1.26888i	0.946666	+	0.322217i	$0.104428\pi$
$977$	1.12952e15	+	1.12952e15i	1.26888	+	1.26888i	0.322217	+	0.946666i	$0.395572\pi$
$978$	1.82041e14	−	1.82041e14i	0.203458	−	0.203458i
$979$			4.65025e14i			0.517086i
$980$	−7.22343e14	+	1.87256e14i	−0.799122	+	0.207160i
$981$	−6.97066e14			−0.767236
$982$	4.33944e14	+	4.33944e14i	0.475200	+	0.475200i
$983$	−1.17543e14	+	1.17543e14i	−0.128064	+	0.128064i	−0.768234	−	0.640169i	$-0.778864\pi$
$983$	−1.17543e14	+	1.17543e14i	−0.128064	+	0.128064i	0.640169	+	0.768234i	$0.278864\pi$
$984$		−	1.00450e15i		−	1.08887i
$985$	−7.93486e14	−	4.66782e14i	−0.855772	−	0.503423i
$986$	−5.48292e14			−0.588339
$987$	7.86743e14	+	7.86743e14i	0.839938	+	0.839938i
$988$	−6.65486e13	+	6.65486e13i	−0.0706894	+	0.0706894i
$989$		−	3.08832e14i		−	0.326393i
$990$	−3.52277e14	+	5.98839e14i	−0.370432	+	0.629700i
$991$	1.60275e15			1.67686			0.838431	−	0.545008i	$-0.183473\pi$
$991$	1.60275e15			1.67686			0.838431	+	0.545008i	$0.183473\pi$
$992$	−4.97068e14	−	4.97068e14i	−0.517437	−	0.517437i
$993$	5.07286e14	−	5.07286e14i	0.525420	−	0.525420i
$994$			4.93480e14i			0.508555i
$995$	−1.03817e14	−	4.00477e14i	−0.106452	−	0.410640i
$996$	−2.79183e15			−2.84834
$997$	6.55787e14	+	6.55787e14i	0.665713	+	0.665713i	0.956721	−	0.291008i	$-0.0939905\pi$
$997$	6.55787e14	+	6.55787e14i	0.665713	+	0.665713i	−0.291008	+	0.956721i	$0.593991\pi$
$998$	−5.63476e13	+	5.63476e13i	−0.0569145	+	0.0569145i
$999$		−	6.03386e13i		−	0.0606412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.11.c.a.2.4	✓	8
3.2	odd	2		45.11.g.a.37.1		8
4.3	odd	2		80.11.p.d.17.1		8
5.2	odd	4		25.11.c.a.18.1		8
5.3	odd	4	inner	5.11.c.a.3.4	yes	8
5.4	even	2		25.11.c.a.7.1		8
15.8	even	4		45.11.g.a.28.1		8
20.3	even	4		80.11.p.d.33.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.11.c.a.2.4	✓	8	1.1	even	1	trivial
5.11.c.a.3.4	yes	8	5.3	odd	4	inner
25.11.c.a.7.1		8	5.4	even	2
25.11.c.a.18.1		8	5.2	odd	4
45.11.g.a.28.1		8	15.8	even	4
45.11.g.a.37.1		8	3.2	odd	2
80.11.p.d.17.1		8	4.3	odd	2
80.11.p.d.33.1		8	20.3	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(37.4391 + 37.4391i) q^{2} +(246.218 - 246.218i) q^{3} +1779.37i q^{4} +(-3025.01 + 784.185i) q^{5} +18436.4 q^{6} +(-8610.35 - 8610.35i) q^{7} +(-28280.5 + 28280.5i) q^{8} -62197.5i q^{9} +O(q^{10})\)	\(q+(37.4391 + 37.4391i) q^{2} +(246.218 - 246.218i) q^{3} +1779.37i q^{4} +(-3025.01 + 784.185i) q^{5} +18436.4 q^{6} +(-8610.35 - 8610.35i) q^{7} +(-28280.5 + 28280.5i) q^{8} -62197.5i q^{9} +(-142613. - 83894.5i) q^{10} +67511.6 q^{11} +(438114. + 438114. i) q^{12} +(8342.81 - 8342.81i) q^{13} -644728. i q^{14} +(-551731. + 937892. i) q^{15} -295517. q^{16} +(-693251. - 693251. i) q^{17} +(2.32862e6 - 2.32862e6i) q^{18} +4.48290e6i q^{19} +(-1.39536e6 - 5.38262e6i) q^{20} -4.24004e6 q^{21} +(2.52757e6 + 2.52757e6i) q^{22} +(1.04763e6 - 1.04763e6i) q^{23} +1.39263e7i q^{24} +(8.53573e6 - 4.74433e6i) q^{25} +624695. q^{26} +(-775217. - 775217. i) q^{27} +(1.53210e7 - 1.53210e7i) q^{28} -1.05625e7i q^{29} +(-5.57701e7 + 1.44575e7i) q^{30} -2.77763e7 q^{31} +(1.78954e7 + 1.78954e7i) q^{32} +(1.66226e7 - 1.66226e7i) q^{33} -5.19094e7i q^{34} +(3.27985e7 + 1.92943e7i) q^{35} +1.10673e8 q^{36} +(3.89172e7 + 3.89172e7i) q^{37} +(-1.67836e8 + 1.67836e8i) q^{38} -4.10830e6i q^{39} +(6.33717e7 - 1.07726e8i) q^{40} -7.21297e7 q^{41} +(-1.58743e8 - 1.58743e8i) q^{42} +(1.47395e8 - 1.47395e8i) q^{43} +1.20128e8i q^{44} +(4.87743e7 + 1.88148e8i) q^{45} +7.84449e7 q^{46} +(-1.85551e8 - 1.85551e8i) q^{47} +(-7.27616e7 + 7.27616e7i) q^{48} -1.34199e8i q^{49} +(4.97194e8 + 1.41947e8i) q^{50} -3.41382e8 q^{51} +(1.48450e7 + 1.48450e7i) q^{52} +(-2.40411e8 + 2.40411e8i) q^{53} -5.80468e7i q^{54} +(-2.04223e8 + 5.29416e7i) q^{55} +4.87011e8 q^{56} +(1.10377e9 + 1.10377e9i) q^{57} +(3.95450e8 - 3.95450e8i) q^{58} -8.16660e8i q^{59} +(-1.66886e9 - 9.81736e8i) q^{60} -1.84744e8 q^{61} +(-1.03992e9 - 1.03992e9i) q^{62} +(-5.35542e8 + 5.35542e8i) q^{63} +1.64258e9i q^{64} +(-1.86948e7 + 3.17794e7i) q^{65} +1.24467e9 q^{66} +(1.74545e8 + 1.74545e8i) q^{67} +(1.23355e9 - 1.23355e9i) q^{68} -5.15892e8i q^{69} +(5.05586e8 + 1.95031e9i) q^{70} -7.65409e8 q^{71} +(1.75898e9 + 1.75898e9i) q^{72} +(1.80198e9 - 1.80198e9i) q^{73} +2.91405e9i q^{74} +(9.33510e8 - 3.26979e9i) q^{75} -7.97676e9 q^{76} +(-5.81298e8 - 5.81298e8i) q^{77} +(1.53811e8 - 1.53811e8i) q^{78} +1.02265e9i q^{79} +(8.93942e8 - 2.31740e8i) q^{80} +3.29096e9 q^{81} +(-2.70047e9 - 2.70047e9i) q^{82} +(-3.18619e9 + 3.18619e9i) q^{83} -7.54462e9i q^{84} +(2.64073e9 + 1.55345e9i) q^{85} +1.10367e10 q^{86} +(-2.60067e9 - 2.60067e9i) q^{87} +(-1.90926e9 + 1.90926e9i) q^{88} +6.88808e9i q^{89} +(-5.21803e9 + 8.87016e9i) q^{90} -1.43669e8 q^{91} +(1.86413e9 + 1.86413e9i) q^{92} +(-6.83903e9 + 6.83903e9i) q^{93} -1.38937e10i q^{94} +(-3.51543e9 - 1.35608e10i) q^{95} +8.81232e9 q^{96} +(1.10095e10 + 1.10095e10i) q^{97} +(5.02429e9 - 5.02429e9i) q^{98} -4.19905e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8}+O(q^{10}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} - 161290 q^{10} - 233784 q^{11} + 863160 q^{12} + 433520 q^{13} - 3188580 q^{15} - 1193992 q^{16} + 1045440 q^{17} + 12804210 q^{18} - 16739820 q^{20} - 20777784 q^{21} + 25939360 q^{22} + 24737580 q^{23} - 35382400 q^{25} - 34440684 q^{26} + 27386640 q^{27} + 89876920 q^{28} - 115784880 q^{30} + 258616 q^{31} - 11664120 q^{32} + 11269320 q^{33} + 113638860 q^{35} + 66085308 q^{36} + 92216120 q^{37} - 435848520 q^{38} + 432590700 q^{40} + 115357416 q^{41} - 609152160 q^{42} - 262653700 q^{43} + 593742420 q^{45} + 1023085816 q^{46} - 669481140 q^{47} - 618046320 q^{48} + 944762850 q^{50} - 768258984 q^{51} - 70856500 q^{52} - 1321976040 q^{53} + 2597320 q^{55} + 852915600 q^{56} + 2367269280 q^{57} + 2687784720 q^{58} - 4237774440 q^{60} - 3143200184 q^{61} - 1373690040 q^{62} + 2578662540 q^{63} - 1924527480 q^{65} + 766734432 q^{66} + 4912566140 q^{67} + 6614874660 q^{68} - 8299690440 q^{70} - 4375053384 q^{71} + 808889220 q^{72} - 786968920 q^{73} + 5379002700 q^{75} - 5577898800 q^{76} + 7522045800 q^{77} + 4109901000 q^{78} + 47717760 q^{80} - 2499208992 q^{81} - 19442731040 q^{82} - 11064240660 q^{83} + 15814282160 q^{85} + 36286046616 q^{86} + 2020273920 q^{87} - 13252572960 q^{88} + 9489047670 q^{90} - 12917794184 q^{91} - 25757138760 q^{92} - 40141724280 q^{93} + 14671558800 q^{95} + 38082222816 q^{96} + 24688294760 q^{97} + 13744332030 q^{98}+O(q^{100}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8 - 161290 * q^10 - 233784 * q^11 + 863160 * q^12 + 433520 * q^13 - 3188580 * q^15 - 1193992 * q^16 + 1045440 * q^17 + 12804210 * q^18 - 16739820 * q^20 - 20777784 * q^21 + 25939360 * q^22 + 24737580 * q^23 - 35382400 * q^25 - 34440684 * q^26 + 27386640 * q^27 + 89876920 * q^28 - 115784880 * q^30 + 258616 * q^31 - 11664120 * q^32 + 11269320 * q^33 + 113638860 * q^35 + 66085308 * q^36 + 92216120 * q^37 - 435848520 * q^38 + 432590700 * q^40 + 115357416 * q^41 - 609152160 * q^42 - 262653700 * q^43 + 593742420 * q^45 + 1023085816 * q^46 - 669481140 * q^47 - 618046320 * q^48 + 944762850 * q^50 - 768258984 * q^51 - 70856500 * q^52 - 1321976040 * q^53 + 2597320 * q^55 + 852915600 * q^56 + 2367269280 * q^57 + 2687784720 * q^58 - 4237774440 * q^60 - 3143200184 * q^61 - 1373690040 * q^62 + 2578662540 * q^63 - 1924527480 * q^65 + 766734432 * q^66 + 4912566140 * q^67 + 6614874660 * q^68 - 8299690440 * q^70 - 4375053384 * q^71 + 808889220 * q^72 - 786968920 * q^73 + 5379002700 * q^75 - 5577898800 * q^76 + 7522045800 * q^77 + 4109901000 * q^78 + 47717760 * q^80 - 2499208992 * q^81 - 19442731040 * q^82 - 11064240660 * q^83 + 15814282160 * q^85 + 36286046616 * q^86 + 2020273920 * q^87 - 13252572960 * q^88 + 9489047670 * q^90 - 12917794184 * q^91 - 25757138760 * q^92 - 40141724280 * q^93 + 14671558800 * q^95 + 38082222816 * q^96 + 24688294760 * q^97 + 13744332030 * q^98

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