LMFDB - Embedded newform 13.13.d.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,13,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	13.d (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:	$11.8819196246$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.4
Character	$\chi$	$=$	13.8
Dual form			13.13.d.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-51.8539 - 51.8539i) q^{2} +843.934 q^{3} +1281.66i q^{4} +(16935.0 + 16935.0i) q^{5} +(-43761.3 - 43761.3i) q^{6} +(-94929.1 + 94929.1i) q^{7} +(-145935. + 145935. i) q^{8} +180783. q^{9} +O(q^{10})$	\(q+(-51.8539 - 51.8539i) q^{2} +843.934 q^{3} +1281.66i q^{4} +(16935.0 + 16935.0i) q^{5} +(-43761.3 - 43761.3i) q^{6} +(-94929.1 + 94929.1i) q^{7} +(-145935. + 145935. i) q^{8} +180783. q^{9} -1.75629e6i q^{10} +(-2.04572e6 + 2.04572e6i) q^{11} +1.08163e6i q^{12} +(4.28593e6 + 2.22010e6i) q^{13} +9.84489e6 q^{14} +(1.42920e7 + 1.42920e7i) q^{15} +2.03842e7 q^{16} +2.06419e7i q^{17} +(-9.37433e6 - 9.37433e6i) q^{18} +(-2.58794e7 - 2.58794e7i) q^{19} +(-2.17048e7 + 2.17048e7i) q^{20} +(-8.01139e7 + 8.01139e7i) q^{21} +2.12157e8 q^{22} -1.86479e8i q^{23} +(-1.23159e8 + 1.23159e8i) q^{24} +3.29445e8i q^{25} +(-1.07122e8 - 3.37363e8i) q^{26} -2.95932e8 q^{27} +(-1.21667e8 - 1.21667e8i) q^{28} +8.92300e8 q^{29} -1.48219e9i q^{30} +(1.90989e8 + 1.90989e8i) q^{31} +(-4.59254e8 - 4.59254e8i) q^{32} +(-1.72645e9 + 1.72645e9i) q^{33} +(1.07037e9 - 1.07037e9i) q^{34} -3.21524e9 q^{35} +2.31703e8i q^{36} +(1.72176e9 - 1.72176e9i) q^{37} +2.68390e9i q^{38} +(3.61705e9 + 1.87362e9i) q^{39} -4.94280e9 q^{40} +(2.69861e9 + 2.69861e9i) q^{41} +8.30844e9 q^{42} -2.83397e9i q^{43} +(-2.62192e9 - 2.62192e9i) q^{44} +(3.06156e9 + 3.06156e9i) q^{45} +(-9.66965e9 + 9.66965e9i) q^{46} +(-2.62705e8 + 2.62705e8i) q^{47} +1.72030e10 q^{48} -4.18177e9i q^{49} +(1.70830e10 - 1.70830e10i) q^{50} +1.74204e10i q^{51} +(-2.84541e9 + 5.49310e9i) q^{52} -5.14362e9 q^{53} +(1.53452e10 + 1.53452e10i) q^{54} -6.92885e10 q^{55} -2.77069e10i q^{56} +(-2.18405e10 - 2.18405e10i) q^{57} +(-4.62693e10 - 4.62693e10i) q^{58} +(9.14926e9 - 9.14926e9i) q^{59} +(-1.83174e10 + 1.83174e10i) q^{60} +2.46392e10 q^{61} -1.98070e10i q^{62} +(-1.71616e10 + 1.71616e10i) q^{63} -3.58656e10i q^{64} +(3.49848e10 + 1.10179e11i) q^{65} +1.79047e11 q^{66} +(-6.30909e10 - 6.30909e10i) q^{67} -2.64559e10 q^{68} -1.57376e11i q^{69} +(1.66723e11 + 1.66723e11i) q^{70} +(1.17072e11 + 1.17072e11i) q^{71} +(-2.63826e10 + 2.63826e10i) q^{72} +(-1.14366e11 + 1.14366e11i) q^{73} -1.78560e11 q^{74} +2.78030e11i q^{75} +(3.31686e10 - 3.31686e10i) q^{76} -3.88397e11i q^{77} +(-9.04036e10 - 2.84712e11i) q^{78} -4.27225e10 q^{79} +(3.45206e11 + 3.45206e11i) q^{80} -3.45823e11 q^{81} -2.79867e11i q^{82} +(3.34180e11 + 3.34180e11i) q^{83} +(-1.02679e11 - 1.02679e11i) q^{84} +(-3.49570e11 + 3.49570e11i) q^{85} +(-1.46953e11 + 1.46953e11i) q^{86} +7.53043e11 q^{87} -5.97084e11i q^{88} +(3.70908e10 - 3.70908e10i) q^{89} -3.17508e11i q^{90} +(-6.17612e11 + 1.96108e11i) q^{91} +2.39002e11 q^{92} +(1.61182e11 + 1.61182e11i) q^{93} +2.72446e10 q^{94} -8.76534e11i q^{95} +(-3.87580e11 - 3.87580e11i) q^{96} +(-2.34681e11 - 2.34681e11i) q^{97} +(-2.16841e11 + 2.16841e11i) q^{98} +(-3.69833e11 + 3.69833e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 4 q^{3} + 5146 q^{5} + 64736 q^{6} - 114402 q^{7} - 262080 q^{8} + 3897230 q^{9}+O(q^{10}) $ 26 * q - 2 * q^2 - 4 * q^3 + 5146 * q^5 + 64736 * q^6 - 114402 * q^7 - 262080 * q^8 + 3897230 * q^9	\( 26 q - 2 q^{2} - 4 q^{3} + 5146 q^{5} + 64736 q^{6} - 114402 q^{7} - 262080 q^{8} + 3897230 q^{9} - 1360946 q^{11} - 2904122 q^{13} - 33341620 q^{14} - 26612356 q^{15} - 42212844 q^{16} + 76072094 q^{18} - 41603538 q^{19} + 60982508 q^{20} - 77526388 q^{21} + 648561056 q^{22} - 1131540696 q^{24} + 912969070 q^{26} - 159769528 q^{27} - 311272132 q^{28} + 2981804 q^{29} - 1023774130 q^{31} + 1476108268 q^{32} + 2381658236 q^{33} + 1983101640 q^{34} - 3650085364 q^{35} - 3167118502 q^{37} + 16292940092 q^{39} - 3968093508 q^{40} + 28381274530 q^{41} - 49639312388 q^{42} - 18960178772 q^{44} - 10665692290 q^{45} + 37450277124 q^{46} + 20752786078 q^{47} - 71636180764 q^{48} - 48656842882 q^{50} + 117857606620 q^{52} - 58773364924 q^{53} + 213216359816 q^{54} - 136697226052 q^{55} - 114945046324 q^{57} + 92279424116 q^{58} + 155389424110 q^{59} + 136735907884 q^{60} + 141369458276 q^{61} - 464360668726 q^{63} + 114397918882 q^{65} - 206611171952 q^{66} + 100234053918 q^{67} - 417926231820 q^{68} + 153062962568 q^{70} + 230837239150 q^{71} - 118991496780 q^{72} + 146516995818 q^{73} - 1012588063096 q^{74} + 606168045784 q^{76} + 359416070936 q^{78} + 434995822940 q^{79} + 237895101520 q^{80} + 1613859489074 q^{81} - 637194158642 q^{83} - 981969825256 q^{84} - 213215637336 q^{85} - 2637756396288 q^{86} + 744567460312 q^{87} + 1456251648226 q^{89} - 3121537204578 q^{91} + 1179602583480 q^{92} - 3143065458004 q^{93} + 5250023559428 q^{94} + 948734423984 q^{96} + 1538416432538 q^{97} + 25933667758 q^{98} - 1934327641798 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 4 * q^3 + 5146 * q^5 + 64736 * q^6 - 114402 * q^7 - 262080 * q^8 + 3897230 * q^9 - 1360946 * q^11 - 2904122 * q^13 - 33341620 * q^14 - 26612356 * q^15 - 42212844 * q^16 + 76072094 * q^18 - 41603538 * q^19 + 60982508 * q^20 - 77526388 * q^21 + 648561056 * q^22 - 1131540696 * q^24 + 912969070 * q^26 - 159769528 * q^27 - 311272132 * q^28 + 2981804 * q^29 - 1023774130 * q^31 + 1476108268 * q^32 + 2381658236 * q^33 + 1983101640 * q^34 - 3650085364 * q^35 - 3167118502 * q^37 + 16292940092 * q^39 - 3968093508 * q^40 + 28381274530 * q^41 - 49639312388 * q^42 - 18960178772 * q^44 - 10665692290 * q^45 + 37450277124 * q^46 + 20752786078 * q^47 - 71636180764 * q^48 - 48656842882 * q^50 + 117857606620 * q^52 - 58773364924 * q^53 + 213216359816 * q^54 - 136697226052 * q^55 - 114945046324 * q^57 + 92279424116 * q^58 + 155389424110 * q^59 + 136735907884 * q^60 + 141369458276 * q^61 - 464360668726 * q^63 + 114397918882 * q^65 - 206611171952 * q^66 + 100234053918 * q^67 - 417926231820 * q^68 + 153062962568 * q^70 + 230837239150 * q^71 - 118991496780 * q^72 + 146516995818 * q^73 - 1012588063096 * q^74 + 606168045784 * q^76 + 359416070936 * q^78 + 434995822940 * q^79 + 237895101520 * q^80 + 1613859489074 * q^81 - 637194158642 * q^83 - 981969825256 * q^84 - 213215637336 * q^85 - 2637756396288 * q^86 + 744567460312 * q^87 + 1456251648226 * q^89 - 3121537204578 * q^91 + 1179602583480 * q^92 - 3143065458004 * q^93 + 5250023559428 * q^94 + 948734423984 * q^96 + 1538416432538 * q^97 + 25933667758 * q^98 - 1934327641798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

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 $

$2$	−51.8539	−	51.8539i	−0.810217	−	0.810217i	0.174449	−	0.984666i	$-0.444186\pi$
$2$	−51.8539	−	51.8539i	−0.810217	−	0.810217i	−0.984666	+	0.174449i	$0.944186\pi$
$3$	843.934			1.15766			0.578830	−	0.815448i	$-0.303510\pi$
$3$	843.934			1.15766			0.578830	+	0.815448i	$0.303510\pi$
$4$			1281.66i			0.312905i
$5$	16935.0	+	16935.0i	1.08384	+	1.08384i	0.996148	+	0.0876896i	$0.0279484\pi$
$5$	16935.0	+	16935.0i	1.08384	+	1.08384i	0.0876896	+	0.996148i	$0.472052\pi$
$6$	−43761.3	−	43761.3i	−0.937956	−	0.937956i
$7$	−94929.1	+	94929.1i	−0.806884	+	0.806884i	−0.984161	−	0.177277i	$-0.943271\pi$
$7$	−94929.1	+	94929.1i	−0.806884	+	0.806884i	0.177277	+	0.984161i	$0.443271\pi$
$8$	−145935.	+	145935.i	−0.556697	+	0.556697i
$9$	180783.			0.340176
$10$		−	1.75629e6i		−	1.75629i
$11$	−2.04572e6	+	2.04572e6i	−1.15476	+	1.15476i	−0.169170	+	0.985587i	$0.554109\pi$
$11$	−2.04572e6	+	2.04572e6i	−1.15476	+	1.15476i	−0.985587	+	0.169170i	$0.945891\pi$
$12$			1.08163e6i			0.362237i
$13$	4.28593e6	+	2.22010e6i	0.887944	+	0.459952i
$13$	4.28593e6	+	2.22010e6i	0.887944	+	0.459952i
$14$	9.84489e6			1.30750
$15$	1.42920e7	+	1.42920e7i	1.25471	+	1.25471i
$16$	2.03842e7			1.21500
$17$			2.06419e7i			0.855179i	0.903973	+	0.427589i	$0.140637\pi$
$17$			2.06419e7i			0.855179i	−0.903973	+	0.427589i	$0.859363\pi$
$18$	−9.37433e6	−	9.37433e6i	−0.275617	−	0.275617i
$19$	−2.58794e7	−	2.58794e7i	−0.550089	−	0.550089i	0.376378	−	0.926466i	$-0.377170\pi$
$19$	−2.58794e7	−	2.58794e7i	−0.550089	−	0.550089i	−0.926466	+	0.376378i	$0.877170\pi$
$20$	−2.17048e7	+	2.17048e7i	−0.339138	+	0.339138i
$21$	−8.01139e7	+	8.01139e7i	−0.934097	+	0.934097i
$22$	2.12157e8			1.87121
$23$		−	1.86479e8i		−	1.25969i	−0.776723	−	0.629843i	$-0.783119\pi$
$23$		−	1.86479e8i		−	1.25969i	0.776723	−	0.629843i	$-0.216881\pi$
$24$	−1.23159e8	+	1.23159e8i	−0.644465	+	0.644465i
$25$			3.29445e8i			1.34941i
$26$	−1.07122e8	−	3.37363e8i	−0.346766	−	1.09209i
$27$	−2.95932e8			−0.763852
$28$	−1.21667e8	−	1.21667e8i	−0.252478	−	0.252478i
$29$	8.92300e8			1.50011			0.750055	−	0.661376i	$-0.230027\pi$
$29$	8.92300e8			1.50011			0.750055	+	0.661376i	$0.230027\pi$
$30$		−	1.48219e9i		−	2.03318i
$31$	1.90989e8	+	1.90989e8i	0.215198	+	0.215198i	0.806471	−	0.591273i	$-0.201375\pi$
$31$	1.90989e8	+	1.90989e8i	0.215198	+	0.215198i	−0.591273	+	0.806471i	$0.701375\pi$
$32$	−4.59254e8	−	4.59254e8i	−0.427714	−	0.427714i
$33$	−1.72645e9	+	1.72645e9i	−1.33682	+	1.33682i
$34$	1.07037e9	−	1.07037e9i	0.692881	−	0.692881i
$35$	−3.21524e9			−1.74906
$36$			2.31703e8i			0.106443i
$37$	1.72176e9	−	1.72176e9i	0.671062	−	0.671062i	−0.286899	−	0.957961i	$-0.592624\pi$
$37$	1.72176e9	−	1.72176e9i	0.671062	−	0.671062i	0.957961	+	0.286899i	$0.0926243\pi$
$38$			2.68390e9i			0.891383i
$39$	3.61705e9	+	1.87362e9i	1.02794	+	0.532468i
$40$	−4.94280e9			−1.20674
$41$	2.69861e9	+	2.69861e9i	0.568117	+	0.568117i	0.931601	−	0.363484i	$-0.118413\pi$
$41$	2.69861e9	+	2.69861e9i	0.568117	+	0.568117i	−0.363484	+	0.931601i	$0.618413\pi$
$42$	8.30844e9			1.51364
$43$		−	2.83397e9i		−	0.448317i	−0.974553	−	0.224158i	$-0.928037\pi$
$43$		−	2.83397e9i		−	0.448317i	0.974553	−	0.224158i	$-0.0719633\pi$
$44$	−2.62192e9	−	2.62192e9i	−0.361329	−	0.361329i
$45$	3.06156e9	+	3.06156e9i	0.368695	+	0.368695i
$46$	−9.66965e9	+	9.66965e9i	−1.02062	+	1.02062i
$47$	−2.62705e8	+	2.62705e8i	−0.0243715	+	0.0243715i	−0.719188	−	0.694816i	$-0.755486\pi$
$47$	−2.62705e8	+	2.62705e8i	−0.0243715	+	0.0243715i	0.694816	+	0.719188i	$0.255486\pi$
$48$	1.72030e10			1.40655
$49$		−	4.18177e9i		−	0.302123i
$50$	1.70830e10	−	1.70830e10i	1.09331	−	1.09331i
$51$			1.74204e10i			0.990006i
$52$	−2.84541e9	+	5.49310e9i	−0.143921	+	0.277842i
$53$	−5.14362e9			−0.232067			−0.116034	−	0.993245i	$-0.537018\pi$
$53$	−5.14362e9			−0.232067			−0.116034	+	0.993245i	$0.537018\pi$
$54$	1.53452e10	+	1.53452e10i	0.618886	+	0.618886i
$55$	−6.92885e10			−2.50314
$56$		−	2.77069e10i		−	0.898379i
$57$	−2.18405e10	−	2.18405e10i	−0.636816	−	0.636816i
$58$	−4.62693e10	−	4.62693e10i	−1.21542	−	1.21542i
$59$	9.14926e9	−	9.14926e9i	0.216907	−	0.216907i	−0.590287	−	0.807194i	$-0.700985\pi$
$59$	9.14926e9	−	9.14926e9i	0.216907	−	0.216907i	0.807194	+	0.590287i	$0.200985\pi$
$60$	−1.83174e10	+	1.83174e10i	−0.392606	+	0.392606i
$61$	2.46392e10			0.478242			0.239121	−	0.970990i	$-0.423141\pi$
$61$	2.46392e10			0.478242			0.239121	+	0.970990i	$0.423141\pi$
$62$		−	1.98070e10i		−	0.348714i
$63$	−1.71616e10	+	1.71616e10i	−0.274483	+	0.274483i
$64$		−	3.58656e10i		−	0.521913i
$65$	3.49848e10	+	1.10179e11i	0.463873	+	1.46090i
$66$	1.79047e11			2.16622
$67$	−6.30909e10	−	6.30909e10i	−0.697458	−	0.697458i	0.266404	−	0.963862i	$-0.414165\pi$
$67$	−6.30909e10	−	6.30909e10i	−0.697458	−	0.697458i	−0.963862	+	0.266404i	$0.914165\pi$
$68$	−2.64559e10			−0.267589
$69$		−	1.57376e11i		−	1.45829i
$70$	1.66723e11	+	1.66723e11i	1.41712	+	1.41712i
$71$	1.17072e11	+	1.17072e11i	0.913911	+	0.913911i	0.996577	−	0.0826663i	$-0.0263436\pi$
$71$	1.17072e11	+	1.17072e11i	0.913911	+	0.913911i	−0.0826663	+	0.996577i	$0.526344\pi$
$72$	−2.63826e10	+	2.63826e10i	−0.189375	+	0.189375i
$73$	−1.14366e11	+	1.14366e11i	−0.755720	+	0.755720i	−0.975540	−	0.219820i	$-0.929453\pi$
$73$	−1.14366e11	+	1.14366e11i	−0.755720	+	0.755720i	0.219820	+	0.975540i	$0.429453\pi$
$74$	−1.78560e11			−1.08741
$75$			2.78030e11i			1.56215i
$76$	3.31686e10	−	3.31686e10i	0.172125	−	0.172125i
$77$		−	3.88397e11i		−	1.86351i
$78$	−9.04036e10	−	2.84712e11i	−0.401437	−	1.26427i
$79$	−4.27225e10			−0.175749			−0.0878747	−	0.996132i	$-0.528007\pi$
$79$	−4.27225e10			−0.175749			−0.0878747	+	0.996132i	$0.528007\pi$
$80$	3.45206e11	+	3.45206e11i	1.31686	+	1.31686i
$81$	−3.45823e11			−1.22446
$82$		−	2.79867e11i		−	0.920596i
$83$	3.34180e11	+	3.34180e11i	1.02214	+	1.02214i	0.999749	+	0.0223952i	$0.00712920\pi$
$83$	3.34180e11	+	3.34180e11i	1.02214	+	1.02214i	0.0223952	+	0.999749i	$0.492871\pi$
$84$	−1.02679e11	−	1.02679e11i	−0.292283	−	0.292283i
$85$	−3.49570e11	+	3.49570e11i	−0.926875	+	0.926875i
$86$	−1.46953e11	+	1.46953e11i	−0.363234	+	0.363234i
$87$	7.53043e11			1.73662
$88$		−	5.97084e11i		−	1.28570i
$89$	3.70908e10	−	3.70908e10i	0.0746322	−	0.0746322i	−0.668805	−	0.743438i	$-0.733194\pi$
$89$	3.70908e10	−	3.70908e10i	0.0746322	−	0.0746322i	0.743438	+	0.668805i	$0.233194\pi$
$90$		−	3.17508e11i		−	0.597447i
$91$	−6.17612e11	+	1.96108e11i	−1.08760	+	0.345340i
$92$	2.39002e11			0.394162
$93$	1.61182e11	+	1.61182e11i	0.249126	+	0.249126i
$94$	2.72446e10			0.0394924
$95$		−	8.76534e11i		−	1.19241i
$96$	−3.87580e11	−	3.87580e11i	−0.495147	−	0.495147i
$97$	−2.34681e11	−	2.34681e11i	−0.281739	−	0.281739i	0.552063	−	0.833802i	$-0.313841\pi$
$97$	−2.34681e11	−	2.34681e11i	−0.281739	−	0.281739i	−0.833802	+	0.552063i	$0.813841\pi$
$98$	−2.16841e11	+	2.16841e11i	−0.244785	+	0.244785i
$99$	−3.69833e11	+	3.69833e11i	−0.392821	+	0.392821i
$100$	−4.22236e11			−0.422236
$101$		−	2.00937e11i		−	0.189292i	−0.995511	−	0.0946461i	$-0.969828\pi$
$101$		−	2.00937e11i		−	0.189292i	0.995511	−	0.0946461i	$-0.0301719\pi$
$102$	9.03317e11	−	9.03317e11i	0.802120	−	0.802120i
$103$			1.20146e12i			1.00621i	0.864226	+	0.503103i	$0.167809\pi$
$103$			1.20146e12i			1.00621i	−0.864226	+	0.503103i	$0.832191\pi$
$104$	−9.49456e11	+	3.01477e11i	−0.750369	+	0.238262i
$105$	−2.71345e12			−2.02482
$106$	2.66717e11	+	2.66717e11i	0.188025	+	0.188025i
$107$	1.74152e12			1.16045			0.580223	−	0.814458i	$-0.302965\pi$
$107$	1.74152e12			1.16045			0.580223	+	0.814458i	$0.302965\pi$
$108$		−	3.79283e11i		−	0.239013i
$109$	−4.08507e9	−	4.08507e9i	−0.00243580	−	0.00243580i	0.705888	−	0.708324i	$-0.250548\pi$
$109$	−4.08507e9	−	4.08507e9i	−0.00243580	−	0.00243580i	−0.708324	+	0.705888i	$0.750548\pi$
$110$	3.59288e12	+	3.59288e12i	2.02809	+	2.02809i
$111$	1.45305e12	−	1.45305e12i	0.776862	−	0.776862i
$112$	−1.93506e12	+	1.93506e12i	−0.980360	+	0.980360i
$113$	2.86341e12			1.37535			0.687674	−	0.726019i	$-0.258632\pi$
$113$	2.86341e12			1.37535			0.687674	+	0.726019i	$0.258632\pi$
$114$			2.26503e12i			1.03192i
$115$	3.15801e12	−	3.15801e12i	1.36529	−	1.36529i
$116$			1.14362e12i			0.469392i
$117$	7.74826e11	+	4.01358e11i	0.302057	+	0.156465i
$118$	−9.48850e11			−0.351484
$119$	−1.95952e12	−	1.95952e12i	−0.690030	−	0.690030i
$120$	−4.17139e12			−1.39699
$121$		−	5.23153e12i		−	1.66693i
$122$	−1.27764e12	−	1.27764e12i	−0.387480	−	0.387480i
$123$	2.27745e12	+	2.27745e12i	0.657686	+	0.657686i
$124$	−2.44782e11	+	2.44782e11i	−0.0673364	+	0.0673364i
$125$	−1.44463e12	+	1.44463e12i	−0.378701	+	0.378701i
$126$	1.77979e12			0.444781
$127$			4.45683e12i			1.06219i	0.847311	+	0.531097i	$0.178220\pi$
$127$			4.45683e12i			1.06219i	−0.847311	+	0.531097i	$0.821780\pi$
$128$	−3.74088e12	+	3.74088e12i	−0.850577	+	0.850577i
$129$		−	2.39168e12i		−	0.518998i
$130$	3.89914e12	−	7.52734e12i	0.807808	−	1.55949i
$131$	−5.84056e12			−1.15565			−0.577825	−	0.816160i	$-0.696099\pi$
$131$	−5.84056e12			−1.15565			−0.577825	+	0.816160i	$0.696099\pi$
$132$	−2.21272e12	−	2.21272e12i	−0.418296	−	0.418296i
$133$	4.91342e12			0.887716
$134$			6.54302e12i			1.13019i
$135$	−5.01159e12	−	5.01159e12i	−0.827891	−	0.827891i
$136$	−3.01237e12	−	3.01237e12i	−0.476075	−	0.476075i
$137$	5.68603e12	−	5.68603e12i	0.859975	−	0.859975i	−0.131359	−	0.991335i	$-0.541934\pi$
$137$	5.68603e12	−	5.68603e12i	0.859975	−	0.859975i	0.991335	+	0.131359i	$0.0419342\pi$
$138$	−8.16055e12	+	8.16055e12i	−1.18153	+	1.18153i
$139$	−3.67590e12			−0.509654			−0.254827	−	0.966987i	$-0.582018\pi$
$139$	−3.67590e12			−0.509654			−0.254827	+	0.966987i	$0.582018\pi$
$140$		−	4.12084e12i		−	0.547290i
$141$	−2.21706e11	+	2.21706e11i	−0.0282139	+	0.0282139i
$142$		−	1.21413e13i		−	1.48093i
$143$	−1.33095e13	+	4.22612e12i	−1.55649	+	0.494226i
$144$	3.68513e12			0.413312
$145$	1.51111e13	+	1.51111e13i	1.62588	+	1.62588i
$146$	1.18607e13			1.22460
$147$		−	3.52914e12i		−	0.349756i
$148$	2.20671e12	+	2.20671e12i	0.209979	+	0.209979i
$149$	6.08344e12	+	6.08344e12i	0.555945	+	0.555945i	0.928150	−	0.372206i	$-0.121398\pi$
$149$	6.08344e12	+	6.08344e12i	0.555945	+	0.555945i	−0.372206	+	0.928150i	$0.621398\pi$
$150$	1.44169e13	−	1.44169e13i	1.26568	−	1.26568i
$151$	4.40742e12	−	4.40742e12i	0.371811	−	0.371811i	−0.496325	−	0.868137i	$-0.665318\pi$
$151$	4.40742e12	−	4.40742e12i	0.371811	−	0.371811i	0.868137	+	0.496325i	$0.165318\pi$
$152$	7.55341e12			0.612465
$153$			3.73172e12i			0.290911i
$154$	−2.01399e13	+	2.01399e13i	−1.50985	+	1.50985i
$155$			6.46878e12i			0.466479i
$156$	−2.40134e12	+	4.63582e12i	−0.166612	+	0.321646i
$157$	−1.07138e13			−0.715394			−0.357697	−	0.933838i	$-0.616438\pi$
$157$	−1.07138e13			−0.715394			−0.357697	+	0.933838i	$0.616438\pi$
$158$	2.21533e12	+	2.21533e12i	0.142395	+	0.142395i
$159$	−4.34088e12			−0.268655
$160$		−	1.55549e13i		−	0.927145i
$161$	1.77022e13	+	1.77022e13i	1.01642	+	1.01642i
$162$	1.79323e13	+	1.79323e13i	0.992076	+	0.992076i
$163$	−1.08099e13	+	1.08099e13i	−0.576362	+	0.576362i	−0.933899	−	0.357537i	$-0.883617\pi$
$163$	−1.08099e13	+	1.08099e13i	−0.576362	+	0.576362i	0.357537	+	0.933899i	$0.383617\pi$
$164$	−3.45870e12	+	3.45870e12i	−0.177766	+	0.177766i
$165$	−5.84749e13			−2.89778
$166$		−	3.46571e13i		−	1.65632i
$167$	2.80856e13	−	2.80856e13i	1.29475	−	1.29475i	0.362933	−	0.931815i	$-0.381775\pi$
$167$	2.80856e13	−	2.80856e13i	1.29475	−	1.29475i	0.931815	−	0.362933i	$-0.118225\pi$
$168$		−	2.33828e13i		−	1.04002i
$169$	1.34404e13	+	1.90304e13i	0.576888	+	0.816823i
$170$	3.62532e13			1.50194
$171$	−4.67857e12	−	4.67857e12i	−0.187127	−	0.187127i
$172$	3.63218e12			0.140280
$173$			4.51740e13i			1.68505i	0.538659	+	0.842524i	$0.318931\pi$
$173$			4.51740e13i			1.68505i	−0.538659	+	0.842524i	$0.681069\pi$
$174$	−3.90482e13	−	3.90482e13i	−1.40704	−	1.40704i
$175$	−3.12739e13	−	3.12739e13i	−1.08881	−	1.08881i
$176$	−4.17005e13	+	4.17005e13i	−1.40302	+	1.40302i
$177$	7.72137e12	−	7.72137e12i	0.251105	−	0.251105i
$178$	−3.84661e12			−0.120937
$179$		−	2.00323e13i		−	0.608995i	−0.952513	−	0.304497i	$-0.901512\pi$
$179$		−	2.00323e13i		−	0.608995i	0.952513	−	0.304497i	$-0.0984884\pi$
$180$	−3.92387e12	+	3.92387e12i	−0.115367	+	0.115367i
$181$		−	3.22355e13i		−	0.916776i	−0.888752	−	0.458388i	$-0.848427\pi$
$181$		−	3.22355e13i		−	0.916776i	0.888752	−	0.458388i	$-0.151573\pi$
$182$	4.21946e13	+	2.18566e13i	1.16099	+	0.601389i
$183$	2.07939e13			0.553642
$184$	2.72137e13	+	2.72137e13i	0.701263	+	0.701263i
$185$	5.83159e13			1.45464
$186$		−	1.67158e13i		−	0.403692i
$187$	−4.22277e13	−	4.22277e13i	−0.987523	−	0.987523i
$188$	−3.36698e11	−	3.36698e11i	−0.00762595	−	0.00762595i
$189$	2.80925e13	−	2.80925e13i	0.616340	−	0.616340i
$190$	−4.54517e13	+	4.54517e13i	−0.966115	+	0.966115i
$191$	−1.07582e13			−0.221584			−0.110792	−	0.993844i	$-0.535339\pi$
$191$	−1.07582e13			−0.221584			−0.110792	+	0.993844i	$0.535339\pi$
$192$		−	3.02682e13i		−	0.604197i
$193$	−3.84443e13	+	3.84443e13i	−0.743855	+	0.743855i	−0.973317	−	0.229463i	$-0.926303\pi$
$193$	−3.84443e13	+	3.84443e13i	−0.743855	+	0.743855i	0.229463	+	0.973317i	$0.426303\pi$
$194$			2.43382e13i			0.456540i
$195$	2.95249e13	+	9.29842e13i	0.537008	+	1.69122i
$196$	5.35960e12			0.0945358
$197$	−6.38296e13	−	6.38296e13i	−1.09201	−	1.09201i	−0.995314	−	0.0966906i	$-0.969174\pi$
$197$	−6.38296e13	−	6.38296e13i	−1.09201	−	1.09201i	−0.0966906	−	0.995314i	$-0.530826\pi$
$198$	3.83546e13			0.636540
$199$		−	2.60427e13i		−	0.419342i	−0.977772	−	0.209671i	$-0.932761\pi$
$199$		−	2.60427e13i		−	0.419342i	0.977772	−	0.209671i	$-0.0672392\pi$
$200$	−4.80775e13	−	4.80775e13i	−0.751210	−	0.751210i
$201$	−5.32446e13	−	5.32446e13i	−0.807419	−	0.807419i
$202$	−1.04194e13	+	1.04194e13i	−0.153368	+	0.153368i
$203$	−8.47052e13	+	8.47052e13i	−1.21041	+	1.21041i
$204$	−2.23270e13			−0.309778
$205$			9.14018e13i			1.23149i
$206$	6.23006e13	−	6.23006e13i	0.815246	−	0.815246i
$207$		−	3.37123e13i		−	0.428515i
$208$	8.73655e13	+	4.52551e13i	1.07885	+	0.558840i
$209$	1.05884e14			1.27044
$210$	1.40703e14	+	1.40703e14i	1.64054	+	1.64054i
$211$	1.27525e14			1.44511			0.722553	−	0.691316i	$-0.242969\pi$
$211$	1.27525e14			1.44511			0.722553	+	0.691316i	$0.242969\pi$
$212$		−	6.59236e12i		−	0.0726150i
$213$	9.88012e13	+	9.88012e13i	1.05800	+	1.05800i
$214$	−9.03044e13	−	9.03044e13i	−0.940214	−	0.940214i
$215$	4.79932e13	−	4.79932e13i	0.485902	−	0.485902i
$216$	4.31867e13	−	4.31867e13i	0.425234	−	0.425234i
$217$	−3.62608e13			−0.347279
$218$			4.23654e11i			0.00394705i
$219$	−9.65176e13	+	9.65176e13i	−0.874867	+	0.874867i
$220$		−	8.88041e13i		−	0.783244i
$221$	−4.58272e13	+	8.84700e13i	−0.393341	+	0.759351i
$222$	−1.50693e14			−1.25885
$223$	−5.58183e13	−	5.58183e13i	−0.453886	−	0.453886i	0.442756	−	0.896642i	$-0.354001\pi$
$223$	−5.58183e13	−	5.58183e13i	−0.453886	−	0.453886i	−0.896642	+	0.442756i	$0.854001\pi$
$224$	8.71932e13			0.690231
$225$			5.95582e13i			0.459036i
$226$	−1.48479e14	−	1.48479e14i	−1.11433	−	1.11433i
$227$	1.29809e14	+	1.29809e14i	0.948745	+	0.948745i	0.998749	−	0.0500044i	$-0.0159235\pi$
$227$	1.29809e14	+	1.29809e14i	0.948745	+	0.948745i	−0.0500044	+	0.998749i	$0.515924\pi$
$228$	2.79921e13	−	2.79921e13i	0.199263	−	0.199263i
$229$	8.30898e13	−	8.30898e13i	0.576149	−	0.576149i	−0.357691	−	0.933840i	$-0.616436\pi$
$229$	8.30898e13	−	8.30898e13i	0.576149	−	0.576149i	0.933840	+	0.357691i	$0.116436\pi$
$230$	−3.27510e14			−2.21237
$231$		−	3.27781e14i		−	2.15731i
$232$	−1.30218e14	+	1.30218e14i	−0.835106	+	0.835106i
$233$		−	2.69861e14i		−	1.68657i	−0.537466	−	0.843285i	$-0.680618\pi$
$233$		−	2.69861e14i		−	1.68657i	0.537466	−	0.843285i	$-0.319382\pi$
$234$	−1.93658e13	−	6.09897e13i	−0.117962	−	0.371502i
$235$	−8.89780e12			−0.0528294
$236$	1.17262e13	+	1.17262e13i	0.0678713	+	0.0678713i
$237$	−3.60549e13			−0.203458
$238$			2.03218e14i			1.11815i
$239$	−1.48426e14	−	1.48426e14i	−0.796383	−	0.796383i	0.186140	−	0.982523i	$-0.440402\pi$
$239$	−1.48426e14	−	1.48426e14i	−0.796383	−	0.796383i	−0.982523	+	0.186140i	$0.940402\pi$
$240$	2.91331e14	+	2.91331e14i	1.52447	+	1.52447i
$241$	7.34349e13	−	7.34349e13i	0.374801	−	0.374801i	−0.494422	−	0.869222i	$-0.664620\pi$
$241$	7.34349e13	−	7.34349e13i	0.374801	−	0.374801i	0.869222	+	0.494422i	$0.164620\pi$
$242$	−2.71275e14	+	2.71275e14i	−1.35057	+	1.35057i
$243$	−1.34581e14			−0.653652
$244$			3.15790e13i			0.149644i
$245$	7.08182e13	−	7.08182e13i	0.327452	−	0.327452i
$246$		−	2.36190e14i		−	1.06574i
$247$	−5.34626e13	−	1.68372e14i	−0.235433	−	0.741463i
$248$	−5.57438e13			−0.239600
$249$	2.82026e14	+	2.82026e14i	1.18330	+	1.18330i
$250$	1.49819e14			0.613660
$251$		−	1.96658e14i		−	0.786447i	−0.919443	−	0.393223i	$-0.871360\pi$
$251$		−	1.96658e14i		−	0.786447i	0.919443	−	0.393223i	$-0.128640\pi$
$252$	−2.19953e13	−	2.19953e13i	−0.0858869	−	0.0858869i
$253$	3.81484e14	+	3.81484e14i	1.45463	+	1.45463i
$254$	2.31104e14	−	2.31104e14i	0.860608	−	0.860608i
$255$	−2.95014e14	+	2.95014e14i	−1.07301	+	1.07301i
$256$	2.41053e14			0.856392
$257$		−	1.87742e14i		−	0.651574i	−0.945443	−	0.325787i	$-0.894371\pi$
$257$		−	1.87742e14i		−	0.651574i	0.945443	−	0.325787i	$-0.105629\pi$
$258$	−1.24018e14	+	1.24018e14i	−0.420501	+	0.420501i
$259$			3.26891e14i			1.08294i
$260$	−1.41212e14	+	4.48386e13i	−0.457123	+	0.145148i
$261$	1.61313e14			0.510301
$262$	3.02856e14	+	3.02856e14i	0.936328	+	0.936328i
$263$	1.80689e14			0.546006			0.273003	−	0.962013i	$-0.411983\pi$
$263$	1.80689e14			0.546006			0.273003	+	0.962013i	$0.411983\pi$
$264$		−	5.03899e14i		−	1.48840i
$265$	−8.71070e13	−	8.71070e13i	−0.251523	−	0.251523i
$266$	−2.54780e14	−	2.54780e14i	−0.719243	−	0.719243i
$267$	3.13022e13	−	3.13022e13i	0.0863987	−	0.0863987i
$268$	8.08610e13	−	8.08610e13i	0.218238	−	0.218238i
$269$	2.23350e14			0.589485			0.294743	−	0.955577i	$-0.404766\pi$
$269$	2.23350e14			0.589485			0.294743	+	0.955577i	$0.404766\pi$
$270$			5.19741e14i			1.34154i
$271$	3.43120e14	−	3.43120e14i	0.866225	−	0.866225i	−0.125827	−	0.992052i	$-0.540158\pi$
$271$	3.43120e14	−	3.43120e14i	0.866225	−	0.866225i	0.992052	+	0.125827i	$0.0401585\pi$
$272$			4.20770e14i			1.03904i
$273$	−5.21224e14	+	1.65502e14i	−1.25907	+	0.399786i
$274$	−5.89686e14			−1.39353
$275$	−6.73953e14	−	6.73953e14i	−1.55824	−	1.55824i
$276$	2.01702e14			0.456305
$277$			6.48174e14i			1.43487i	0.696624	+	0.717436i	$0.254684\pi$
$277$			6.48174e14i			1.43487i	−0.696624	+	0.717436i	$0.745316\pi$
$278$	1.90610e14	+	1.90610e14i	0.412930	+	0.412930i
$279$	3.45276e13	+	3.45276e13i	0.0732051	+	0.0732051i
$280$	4.69215e14	−	4.69215e14i	0.973697	−	0.973697i
$281$	−5.30289e14	+	5.30289e14i	−1.07715	+	1.07715i	−0.0803820	+	0.996764i	$0.525614\pi$
$281$	−5.30289e14	+	5.30289e14i	−1.07715	+	1.07715i	−0.996764	+	0.0803820i	$0.974386\pi$
$282$	2.29926e13			0.0457187
$283$			4.57519e13i			0.0890617i	0.999008	+	0.0445308i	$0.0141793\pi$
$283$			4.57519e13i			0.0890617i	−0.999008	+	0.0445308i	$0.985821\pi$
$284$	−1.50047e14	+	1.50047e14i	−0.285967	+	0.285967i
$285$		−	7.39737e14i		−	1.38041i
$286$	9.09293e14	+	4.71011e14i	1.66153	+	0.860666i
$287$	−5.12354e14			−0.916808
$288$	−8.30256e13	−	8.30256e13i	−0.145498	−	0.145498i
$289$	1.56533e14			0.268670
$290$		−	1.56714e15i		−	2.63463i
$291$	−1.98055e14	−	1.98055e14i	−0.326158	−	0.326158i
$292$	−1.46579e14	−	1.46579e14i	−0.236468	−	0.236468i
$293$	−7.60388e14	+	7.60388e14i	−1.20179	+	1.20179i	−0.228172	+	0.973621i	$0.573275\pi$
$293$	−7.60388e14	+	7.60388e14i	−1.20179	+	1.20179i	−0.973621	+	0.228172i	$0.926725\pi$
$294$	−1.83000e14	+	1.83000e14i	−0.283378	+	0.283378i
$295$	3.09885e14			0.470184
$296$			5.02530e14i			0.747156i
$297$	6.05394e14	−	6.05394e14i	0.882063	−	0.882063i
$298$		−	6.30900e14i		−	0.900872i
$299$	4.14001e14	−	7.99235e14i	0.579395	−	1.11853i
$300$	−3.56339e14			−0.488806
$301$	2.69026e14	+	2.69026e14i	0.361739	+	0.361739i
$302$	−4.57084e14			−0.602496
$303$		−	1.69578e14i		−	0.219136i
$304$	−5.27532e14	−	5.27532e14i	−0.668355	−	0.668355i
$305$	4.17264e14	+	4.17264e14i	0.518337	+	0.518337i
$306$	1.93504e14	−	1.93504e14i	0.235701	−	0.235701i
$307$	−4.63148e14	+	4.63148e14i	−0.553209	+	0.553209i	−0.927366	−	0.374157i	$-0.877932\pi$
$307$	−4.63148e14	+	4.63148e14i	−0.553209	+	0.553209i	0.374157	+	0.927366i	$0.377932\pi$
$308$	4.97792e14			0.583101
$309$			1.01396e15i			1.16485i
$310$	3.35431e14	−	3.35431e14i	0.377949	−	0.377949i
$311$			4.14025e14i			0.457577i	0.973476	+	0.228788i	$0.0734764\pi$
$311$			4.14025e14i			0.457577i	−0.973476	+	0.228788i	$0.926524\pi$
$312$	−8.01278e14	+	2.54427e14i	−0.868672	+	0.275826i
$313$	5.48409e14			0.583229			0.291614	−	0.956536i	$-0.405808\pi$
$313$	5.48409e14			0.583229			0.291614	+	0.956536i	$0.405808\pi$
$314$	5.55552e14	+	5.55552e14i	0.579625	+	0.579625i
$315$	−5.81262e14			−0.594989
$316$		−	5.47556e13i		−	0.0549928i
$317$	1.89737e14	+	1.89737e14i	0.186980	+	0.186980i	0.794389	−	0.607409i	$-0.207791\pi$
$317$	1.89737e14	+	1.89737e14i	0.186980	+	0.186980i	−0.607409	+	0.794389i	$0.707791\pi$
$318$	2.25092e14	+	2.25092e14i	0.217669	+	0.217669i
$319$	−1.82540e15	+	1.82540e15i	−1.73226	+	1.73226i
$320$	6.07382e14	−	6.07382e14i	0.565669	−	0.565669i
$321$	1.46972e15			1.34340
$322$		−	1.83586e15i		−	1.64704i
$323$	5.34201e14	−	5.34201e14i	0.470424	−	0.470424i
$324$		−	4.43226e14i		−	0.383138i
$325$	−7.31401e14	+	1.41198e15i	−0.620663	+	1.19820i
$326$	1.12107e15			0.933957
$327$	−3.44753e12	−	3.44753e12i	−0.00281982	−	0.00281982i
$328$	−7.87643e14			−0.632537
$329$		−	4.98767e13i		−	0.0393299i
$330$	3.03215e15	+	3.03215e15i	2.34783	+	2.34783i
$331$	−1.17098e15	−	1.17098e15i	−0.890393	−	0.890393i	0.104166	−	0.994560i	$-0.466783\pi$
$331$	−1.17098e15	−	1.17098e15i	−0.890393	−	0.890393i	−0.994560	+	0.104166i	$0.966783\pi$
$332$	−4.28305e14	+	4.28305e14i	−0.319834	+	0.319834i
$333$	3.11266e14	−	3.11266e14i	0.228279	−	0.228279i
$334$	−2.91270e15			−2.09806
$335$		−	2.13688e15i		−	1.51186i
$336$	−1.63306e15	+	1.63306e15i	−1.13492	+	1.13492i
$337$			1.74287e15i			1.18983i	0.803789	+	0.594915i	$0.202814\pi$
$337$			1.74287e15i			1.18983i	−0.803789	+	0.594915i	$0.797186\pi$
$338$	2.89865e14	−	1.68374e15i	0.194399	−	1.12921i
$339$	2.41653e15			1.59219
$340$	−4.48030e14	−	4.48030e14i	−0.290023	−	0.290023i
$341$	−7.81420e14			−0.497002
$342$			4.85204e14i			0.303227i
$343$	−9.16969e14	−	9.16969e14i	−0.563106	−	0.563106i
$344$	4.13575e14	+	4.13575e14i	0.249576	+	0.249576i
$345$	2.66515e15	−	2.66515e15i	1.58055	−	1.58055i
$346$	2.34245e15	−	2.34245e15i	1.36526	−	1.36526i
$347$	−3.67884e14			−0.210733			−0.105367	−	0.994433i	$-0.533602\pi$
$347$	−3.67884e14			−0.210733			−0.105367	+	0.994433i	$0.533602\pi$
$348$			9.65143e14i			0.543396i
$349$	6.11464e14	−	6.11464e14i	0.338391	−	0.338391i	−0.517371	−	0.855761i	$-0.673089\pi$
$349$	6.11464e14	−	6.11464e14i	0.338391	−	0.338391i	0.855761	+	0.517371i	$0.173089\pi$
$350$			3.24335e15i			1.76435i
$351$	−1.26834e15	−	6.56998e14i	−0.678257	−	0.351335i
$352$	1.87901e15			0.987811
$353$	5.31588e14	+	5.31588e14i	0.274743	+	0.274743i	0.831006	−	0.556263i	$-0.187765\pi$
$353$	5.31588e14	+	5.31588e14i	0.274743	+	0.274743i	−0.556263	+	0.831006i	$0.687765\pi$
$354$	−8.00767e14			−0.406899
$355$			3.96523e15i			1.98106i
$356$	4.75377e13	+	4.75377e13i	0.0233528	+	0.0233528i
$357$	−1.65371e15	−	1.65371e15i	−0.798820	−	0.798820i
$358$	−1.03876e15	+	1.03876e15i	−0.493418	+	0.493418i
$359$	8.37655e14	−	8.37655e14i	0.391290	−	0.391290i	−0.483857	−	0.875147i	$-0.660765\pi$
$359$	8.37655e14	−	8.37655e14i	0.391290	−	0.391290i	0.875147	+	0.483857i	$0.160765\pi$
$360$	−8.93576e14			−0.410503
$361$		−	8.73827e14i		−	0.394804i
$362$	−1.67154e15	+	1.67154e15i	−0.742788	+	0.742788i
$363$		−	4.41507e15i		−	1.92973i
$364$	−2.51343e14	−	7.91567e14i	−0.108058	−	0.340314i
$365$	−3.87358e15			−1.63816
$366$	−1.07824e15	−	1.07824e15i	−0.448570	−	0.448570i
$367$	−8.16634e14			−0.334219			−0.167109	−	0.985938i	$-0.553443\pi$
$367$	−8.16634e14			−0.334219			−0.167109	+	0.985938i	$0.553443\pi$
$368$		−	3.80123e15i		−	1.53051i
$369$	4.87865e14	+	4.87865e14i	0.193260	+	0.193260i
$370$	−3.02391e15	−	3.02391e15i	−1.17858	−	1.17858i
$371$	4.88279e14	−	4.88279e14i	0.187251	−	0.187251i
$372$	−2.06580e14	+	2.06580e14i	−0.0779527	+	0.0779527i
$373$	8.70453e14			0.323216			0.161608	−	0.986855i	$-0.448332\pi$
$373$	8.70453e14			0.323216			0.161608	+	0.986855i	$0.448332\pi$
$374$			4.37934e15i			1.60022i
$375$	−1.21917e15	+	1.21917e15i	−0.438406	+	0.438406i
$376$		−	7.66756e13i		−	0.0271350i
$377$	3.82434e15	+	1.98100e15i	1.33201	+	0.689979i
$378$	−2.91342e15			−0.998738
$379$	−2.29220e15	−	2.29220e15i	−0.773422	−	0.773422i	0.205281	−	0.978703i	$-0.434189\pi$
$379$	−2.29220e15	−	2.29220e15i	−0.773422	−	0.773422i	−0.978703	+	0.205281i	$0.934189\pi$
$380$	1.12342e15			0.373112
$381$			3.76127e15i			1.22966i
$382$	5.57855e14	+	5.57855e14i	0.179532	+	0.179532i
$383$	3.18773e15	+	3.18773e15i	1.00993	+	1.00993i	0.999950	+	0.00997502i	$0.00317520\pi$
$383$	3.18773e15	+	3.18773e15i	1.00993	+	1.00993i	0.00997502	+	0.999950i	$0.496825\pi$
$384$	−3.15705e15	+	3.15705e15i	−0.984678	+	0.984678i
$385$	6.57749e15	−	6.57749e15i	2.01974	−	2.01974i
$386$	3.98698e15			1.20537
$387$		−	5.12335e14i		−	0.152507i
$388$	3.00780e14	−	3.00780e14i	0.0881574	−	0.0881574i
$389$			3.71689e15i			1.07271i	0.843993	+	0.536354i	$0.180199\pi$
$389$			3.71689e15i			1.07271i	−0.843993	+	0.536354i	$0.819801\pi$
$390$	3.29061e15	−	6.35257e15i	0.935167	−	1.80535i
$391$	3.84928e15			1.07726
$392$	6.10266e14	+	6.10266e14i	0.168191	+	0.168191i
$393$	−4.92905e15			−1.33785
$394$			6.61963e15i			1.76952i
$395$	−7.23503e14	−	7.23503e14i	−0.190484	−	0.190484i
$396$	−4.73999e14	−	4.73999e14i	−0.122915	−	0.122915i
$397$	5.21741e14	−	5.21741e14i	0.133264	−	0.133264i	−0.637329	−	0.770592i	$-0.719961\pi$
$397$	5.21741e14	−	5.21741e14i	0.133264	−	0.133264i	0.770592	+	0.637329i	$0.219961\pi$
$398$	−1.35042e15	+	1.35042e15i	−0.339758	+	0.339758i
$399$	4.14660e15			1.02767
$400$			6.71549e15i			1.63952i
$401$	2.48347e15	−	2.48347e15i	0.597299	−	0.597299i	−0.342294	−	0.939593i	$-0.611204\pi$
$401$	2.48347e15	−	2.48347e15i	0.597299	−	0.597299i	0.939593	+	0.342294i	$0.111204\pi$
$402$			5.52188e15i			1.30837i
$403$	3.94551e14	+	1.24258e15i	0.0921029	+	0.290064i
$404$	2.57533e14			0.0592304
$405$	−5.85649e15	−	5.85649e15i	−1.32711	−	1.32711i
$406$	8.78460e15			1.96140
$407$			7.04449e15i			1.54983i
$408$	−2.54224e15	−	2.54224e15i	−0.551133	−	0.551133i
$409$	−4.85317e15	−	4.85317e15i	−1.03678	−	1.03678i	−0.999297	−	0.0374800i	$-0.988067\pi$
$409$	−4.85317e15	−	4.85317e15i	−1.03678	−	1.03678i	−0.0374800	−	0.999297i	$-0.511933\pi$
$410$	4.73954e15	−	4.73954e15i	0.997777	−	0.997777i
$411$	4.79864e15	−	4.79864e15i	0.995559	−	0.995559i
$412$	−1.53987e15			−0.314847
$413$			1.73706e15i			0.350038i
$414$	−1.74811e15	+	1.74811e15i	−0.347190	+	0.347190i
$415$			1.13187e16i			2.21568i
$416$	−9.48743e14	−	2.98792e15i	−0.183058	−	0.576514i
$417$	−3.10222e15			−0.590006
$418$	−5.49051e15	−	5.49051e15i	−1.02933	−	1.02933i
$419$	−2.64877e15			−0.489509			−0.244755	−	0.969585i	$-0.578707\pi$
$419$	−2.64877e15			−0.489509			−0.244755	+	0.969585i	$0.578707\pi$
$420$		−	3.47772e15i		−	0.633575i
$421$	3.22641e14	+	3.22641e14i	0.0579465	+	0.0579465i	0.735486	−	0.677540i	$-0.236954\pi$
$421$	3.22641e14	+	3.22641e14i	0.0579465	+	0.0579465i	−0.677540	+	0.735486i	$0.736954\pi$
$422$	−6.61266e15	−	6.61266e15i	−1.17085	−	1.17085i
$423$	−4.74928e13	+	4.74928e13i	−0.00829059	+	0.00829059i
$424$	7.50633e14	−	7.50633e14i	0.129191	−	0.129191i
$425$	−6.80038e15			−1.15398
$426$		−	1.02465e16i		−	1.71442i
$427$	−2.33898e15	+	2.33898e15i	−0.385886	+	0.385886i
$428$			2.23203e15i			0.363109i
$429$	−1.12324e16	+	3.56657e15i	−1.80189	+	0.572146i
$430$	−4.97727e15			−0.787373
$431$	5.61497e15	+	5.61497e15i	0.875959	+	0.875959i	0.993114	−	0.117155i	$-0.0373773\pi$
$431$	5.61497e15	+	5.61497e15i	0.875959	+	0.875959i	−0.117155	+	0.993114i	$0.537377\pi$
$432$	−6.03234e15			−0.928076
$433$		−	1.05767e16i		−	1.60481i	−0.596777	−	0.802407i	$-0.703552\pi$
$433$		−	1.05767e16i		−	1.60481i	0.596777	−	0.802407i	$-0.296448\pi$
$434$	1.88026e15	+	1.88026e15i	0.281372	+	0.281372i
$435$	1.27527e16	+	1.27527e16i	1.88221	+	1.88221i
$436$	5.23567e12	−	5.23567e12i	0.000762172	−	0.000762172i
$437$	−4.82596e15	+	4.82596e15i	−0.692939	+	0.692939i
$438$	1.00096e16			1.41766
$439$		−	8.12433e15i		−	1.13501i	−0.823369	−	0.567506i	$-0.807908\pi$
$439$		−	8.12433e15i		−	1.13501i	0.823369	−	0.567506i	$-0.192092\pi$
$440$	1.01116e16	−	1.01116e16i	1.39349	−	1.39349i
$441$		−	7.55996e14i		−	0.102775i
$442$	6.96383e15	−	2.21120e15i	0.933931	−	0.296547i
$443$	1.22445e15			0.162001			0.0810007	−	0.996714i	$-0.474188\pi$
$443$	1.22445e15			0.162001			0.0810007	+	0.996714i	$0.474188\pi$
$444$	1.86232e15	+	1.86232e15i	0.243084	+	0.243084i
$445$	1.25626e15			0.161778
$446$			5.78879e15i			0.735493i
$447$	5.13402e15	+	5.13402e15i	0.643595	+	0.643595i
$448$	3.40469e15	+	3.40469e15i	0.421123	+	0.421123i
$449$	−3.33406e15	+	3.33406e15i	−0.406907	+	0.406907i	−0.880658	−	0.473752i	$-0.842899\pi$
$449$	−3.33406e15	+	3.33406e15i	−0.406907	+	0.406907i	0.473752	+	0.880658i	$0.342899\pi$
$450$	3.08833e15	−	3.08833e15i	0.371919	−	0.371919i
$451$	−1.10412e16			−1.31207
$452$			3.66991e15i			0.430353i
$453$	3.71957e15	−	3.71957e15i	0.430431	−	0.430431i
$454$		−	1.34622e16i		−	1.53738i
$455$	−1.37803e16	−	7.13816e15i	−1.55307	−	0.804485i
$456$	6.37458e15			0.709026
$457$	1.65059e15	+	1.65059e15i	0.181193	+	0.181193i	0.791876	−	0.610682i	$-0.209105\pi$
$457$	1.65059e15	+	1.65059e15i	0.181193	+	0.181193i	−0.610682	+	0.791876i	$0.709105\pi$
$458$	−8.61706e15			−0.933612
$459$		−	6.10860e15i		−	0.653230i
$460$	4.04749e15	+	4.04749e15i	0.427207	+	0.427207i
$461$	−1.46372e15	−	1.46372e15i	−0.152494	−	0.152494i	0.626737	−	0.779231i	$-0.284390\pi$
$461$	−1.46372e15	−	1.46372e15i	−0.152494	−	0.152494i	−0.779231	+	0.626737i	$0.784390\pi$
$462$	−1.69968e16	+	1.69968e16i	−1.74789	+	1.74789i
$463$	−1.41288e15	+	1.41288e15i	−0.143424	+	0.143424i	−0.775173	−	0.631749i	$-0.782337\pi$
$463$	−1.41288e15	+	1.41288e15i	−0.143424	+	0.143424i	0.631749	+	0.775173i	$0.282337\pi$
$464$	1.81889e16			1.82263
$465$			5.45922e15i			0.540024i
$466$	−1.39933e16	+	1.39933e16i	−1.36649	+	1.36649i
$467$		−	1.07926e16i		−	1.04046i	−0.854025	−	0.520232i	$-0.825846\pi$
$467$		−	1.07926e16i		−	1.04046i	0.854025	−	0.520232i	$-0.174154\pi$
$468$	−5.14403e14	+	9.93062e14i	−0.0489585	+	0.0945151i
$469$	1.19783e16			1.12553
$470$	4.61386e14	+	4.61386e14i	0.0428033	+	0.0428033i
$471$	−9.04174e15			−0.828183
$472$			2.67039e15i			0.241503i
$473$	5.79752e15	+	5.79752e15i	0.517697	+	0.517697i
$474$	1.86959e15	+	1.86959e15i	0.164845	+	0.164845i
$475$	8.52585e15	−	8.52585e15i	0.742294	−	0.742294i
$476$	2.51143e15	−	2.51143e15i	0.215914	−	0.215914i
$477$	−9.29882e14			−0.0789437
$478$			1.53929e16i			1.29049i
$479$	4.76168e15	−	4.76168e15i	0.394227	−	0.394227i	−0.481964	−	0.876191i	$-0.660076\pi$
$479$	4.76168e15	−	4.76168e15i	0.394227	−	0.394227i	0.876191	+	0.481964i	$0.160076\pi$
$480$		−	1.31273e16i		−	1.07332i
$481$	1.12018e16	−	3.55688e15i	0.904522	−	0.287209i
$482$	−7.61578e15			−0.607340
$483$	1.49395e16	+	1.49395e16i	1.17667	+	1.17667i
$484$	6.70503e15			0.521589
$485$		−	7.94861e15i		−	0.610718i
$486$	6.97856e15	+	6.97856e15i	0.529600	+	0.529600i
$487$	−6.08961e15	−	6.08961e15i	−0.456473	−	0.456473i	0.441023	−	0.897496i	$-0.354616\pi$
$487$	−6.08961e15	−	6.08961e15i	−0.456473	−	0.456473i	−0.897496	+	0.441023i	$0.854616\pi$
$488$	−3.59572e15	+	3.59572e15i	−0.266236	+	0.266236i
$489$	−9.12283e15	+	9.12283e15i	−0.667231	+	0.667231i
$490$	−7.34440e15			−0.530615
$491$		−	1.55983e15i		−	0.111324i	−0.998450	−	0.0556621i	$-0.982273\pi$
$491$		−	1.55983e15i		−	0.111324i	0.998450	−	0.0556621i	$-0.0177270\pi$
$492$	−2.91891e15	+	2.91891e15i	−0.205793	+	0.205793i
$493$			1.84188e16i			1.28286i
$494$	−5.95852e15	+	1.15030e16i	−0.409994	+	0.791498i
$495$	−1.25262e16			−0.851507
$496$	3.89316e15	+	3.89316e15i	0.261464	+	0.261464i
$497$	−2.22271e16			−1.47484
$498$		−	2.92483e16i		−	1.91745i
$499$	−6.42767e15	−	6.42767e15i	−0.416342	−	0.416342i	0.467599	−	0.883941i	$-0.345119\pi$
$499$	−6.42767e15	−	6.42767e15i	−0.416342	−	0.416342i	−0.883941	+	0.467599i	$0.845119\pi$
$500$	−1.85152e15	−	1.85152e15i	−0.118497	−	0.118497i
$501$	2.37024e16	−	2.37024e16i	1.49888	−	1.49888i
$502$	−1.01975e16	+	1.01975e16i	−0.637193	+	0.637193i
$503$	1.38722e16			0.856521			0.428261	−	0.903655i	$-0.359127\pi$
$503$	1.38722e16			0.856521			0.428261	+	0.903655i	$0.359127\pi$
$504$		−	5.00895e15i		−	0.305607i
$505$	3.40287e15	−	3.40287e15i	0.205162	−	0.205162i
$506$		−	3.95628e16i		−	2.35713i
$507$	1.13428e16	+	1.60604e16i	0.667840	+	0.945603i
$508$	−5.71213e15			−0.332366
$509$	−1.59319e16	−	1.59319e16i	−0.916135	−	0.916135i	0.0806103	−	0.996746i	$-0.474313\pi$
$509$	−1.59319e16	−	1.59319e16i	−0.916135	−	0.916135i	−0.996746	+	0.0806103i	$0.974313\pi$
$510$	3.05953e16			1.73874
$511$		−	2.17134e16i		−	1.21956i
$512$	2.82310e15	+	2.82310e15i	0.156713	+	0.156713i
$513$	7.65854e15	+	7.65854e15i	0.420186	+	0.420186i
$514$	−9.73518e15	+	9.73518e15i	−0.527917	+	0.527917i
$515$	−2.03467e16	+	2.03467e16i	−1.09056	+	1.09056i
$516$	3.06532e15			0.162397
$517$		−	1.07484e15i		−	0.0562862i
$518$	1.69506e16	−	1.69506e16i	0.877416	−	0.877416i
$519$			3.81239e16i			1.95071i
$520$	−2.11845e16	−	1.09735e16i	−1.07151	−	0.555041i
$521$	2.69885e16			1.34943			0.674717	−	0.738076i	$-0.264266\pi$
$521$	2.69885e16			1.34943			0.674717	+	0.738076i	$0.264266\pi$
$522$	−8.36472e15	−	8.36472e15i	−0.413455	−	0.413455i
$523$	−1.05945e16			−0.517693			−0.258846	−	0.965918i	$-0.583342\pi$
$523$	−1.05945e16			−0.517693			−0.258846	+	0.965918i	$0.583342\pi$
$524$		−	7.48560e15i		−	0.361609i
$525$	−2.63931e16	−	2.63931e16i	−1.26048	−	1.26048i
$526$	−9.36943e15	−	9.36943e15i	−0.442383	−	0.442383i
$527$	−3.94238e15	+	3.94238e15i	−0.184033	+	0.184033i
$528$	−3.51925e16	+	3.51925e16i	−1.62422	+	1.62422i
$529$	−1.28597e16			−0.586808
$530$			9.03368e15i			0.407577i
$531$	1.65404e15	−	1.65404e15i	0.0737866	−	0.0737866i
$532$			6.29732e15i			0.277770i
$533$	5.57489e15	+	1.75573e16i	0.243149	+	0.765762i
$534$	−3.24628e15			−0.140003
$535$	2.94925e16	+	2.94925e16i	1.25773	+	1.25773i
$536$	1.84143e16			0.776545
$537$		−	1.69060e16i		−	0.705008i
$538$	−1.15816e16	−	1.15816e16i	−0.477611	−	0.477611i
$539$	8.55475e15	+	8.55475e15i	0.348879	+	0.348879i
$540$	6.42315e15	−	6.42315e15i	0.259051	−	0.259051i
$541$	8.94079e15	−	8.94079e15i	0.356609	−	0.356609i	−0.505953	−	0.862561i	$-0.668859\pi$
$541$	8.94079e15	−	8.94079e15i	0.356609	−	0.356609i	0.862561	+	0.505953i	$0.168859\pi$
$542$	−3.55843e16			−1.40366
$543$		−	2.72047e16i		−	1.06131i
$544$	9.47990e15	−	9.47990e15i	0.365772	−	0.365772i
$545$		−	1.38361e14i		−	0.00528001i
$546$	3.56094e16	+	1.84456e16i	1.34403	+	0.696203i
$547$	−5.96302e15			−0.222609			−0.111304	−	0.993786i	$-0.535503\pi$
$547$	−5.96302e15			−0.222609			−0.111304	+	0.993786i	$0.535503\pi$
$548$	7.28755e15	+	7.28755e15i	0.269090	+	0.269090i
$549$	4.45436e15			0.162686
$550$			6.98942e16i			2.52502i
$551$	−2.30922e16	−	2.30922e16i	−0.825194	−	0.825194i
$552$	2.29666e16	+	2.29666e16i	0.811824	+	0.811824i
$553$	4.05560e15	−	4.05560e15i	0.141809	−	0.141809i
$554$	3.36104e16	−	3.36104e16i	1.16256	−	1.16256i
$555$	4.92148e16			1.68398
$556$		−	4.71125e15i		−	0.159473i
$557$	−1.16008e16	+	1.16008e16i	−0.388468	+	0.388468i	−0.874141	−	0.485673i	$-0.838575\pi$
$557$	−1.16008e16	+	1.16008e16i	−0.388468	+	0.388468i	0.485673	+	0.874141i	$0.338575\pi$
$558$		−	3.58079e15i		−	0.118624i
$559$	6.29170e15	−	1.21462e16i	0.206204	−	0.398080i
$560$	−6.55402e16			−2.12510
$561$	−3.56374e16	−	3.56374e16i	−1.14322	−	1.14322i
$562$	5.49951e16			1.74545
$563$			5.70742e16i			1.79221i	0.443841	+	0.896105i	$0.353615\pi$
$563$			5.70742e16i			1.79221i	−0.443841	+	0.896105i	$0.646385\pi$
$564$	−2.84151e14	−	2.84151e14i	−0.00882825	−	0.00882825i
$565$	4.84917e16	+	4.84917e16i	1.49065	+	1.49065i
$566$	2.37242e15	−	2.37242e15i	0.0721593	−	0.0721593i
$567$	3.28286e16	−	3.28286e16i	0.987994	−	0.987994i
$568$	−3.41698e16			−1.01754
$569$		−	2.59495e16i		−	0.764637i	−0.924031	−	0.382319i	$-0.875126\pi$
$569$		−	2.59495e16i		−	0.764637i	0.924031	−	0.382319i	$-0.124874\pi$
$570$	−3.83582e16	+	3.83582e16i	−1.11843	+	1.11843i
$571$		−	3.40969e16i		−	0.983781i	−0.870657	−	0.491890i	$-0.836306\pi$
$571$		−	3.40969e16i		−	0.983781i	0.870657	−	0.491890i	$-0.163694\pi$
$572$	−5.41644e15	−	1.70583e16i	−0.154646	−	0.487034i
$573$	−9.07921e15			−0.256519
$574$	2.65676e16	+	2.65676e16i	0.742814	+	0.742814i
$575$	6.14345e16			1.69983
$576$		−	6.48390e15i		−	0.177542i
$577$	−1.26136e16	−	1.26136e16i	−0.341811	−	0.341811i	0.515237	−	0.857048i	$-0.327704\pi$
$577$	−1.26136e16	−	1.26136e16i	−0.341811	−	0.341811i	−0.857048	+	0.515237i	$0.827704\pi$
$578$	−8.11684e15	−	8.11684e15i	−0.217681	−	0.217681i
$579$	−3.24444e16	+	3.24444e16i	−0.861131	+	0.861131i
$580$	−1.93672e16	+	1.93672e16i	−0.508744	+	0.508744i
$581$	−6.34468e16			−1.64950
$582$			2.05399e16i			0.528518i
$583$	1.05224e16	−	1.05224e16i	0.267981	−	0.267981i
$584$		−	3.33800e16i		−	0.841414i
$585$	6.32468e15	+	1.99186e16i	0.157799	+	0.496963i
$586$	7.88582e16			1.94743
$587$	4.03426e16	+	4.03426e16i	0.986133	+	0.986133i	0.999905	−	0.0137723i	$-0.00438398\pi$
$587$	4.03426e16	+	4.03426e16i	0.986133	+	0.986133i	−0.0137723	+	0.999905i	$0.504384\pi$
$588$	4.52315e15			0.109440
$589$		−	9.88536e15i		−	0.236756i
$590$	−1.60687e16	−	1.60687e16i	−0.380952	−	0.380952i
$591$	−5.38680e16	−	5.38680e16i	−1.26417	−	1.26417i
$592$	3.50968e16	−	3.50968e16i	0.815337	−	0.815337i
$593$	−5.61169e16	+	5.61169e16i	−1.29052	+	1.29052i	−0.356058	+	0.934464i	$0.615879\pi$
$593$	−5.61169e16	+	5.61169e16i	−1.29052	+	1.29052i	−0.934464	+	0.356058i	$0.884121\pi$
$594$	−6.27841e16			−1.42933
$595$		−	6.63688e16i		−	1.49576i
$596$	−7.79689e15	+	7.79689e15i	−0.173958	+	0.173958i
$597$		−	2.19783e16i		−	0.485455i
$598$	−6.29111e16	+	1.99759e16i	−1.37569	+	0.436817i
$599$	−3.87878e16			−0.839720			−0.419860	−	0.907589i	$-0.637921\pi$
$599$	−3.87878e16			−0.839720			−0.419860	+	0.907589i	$0.637921\pi$
$600$	−4.05742e16	−	4.05742e16i	−0.869646	−	0.869646i
$601$	−1.20406e16			−0.255506			−0.127753	−	0.991806i	$-0.540776\pi$
$601$	−1.20406e16			−0.255506			−0.127753	+	0.991806i	$0.540776\pi$
$602$		−	2.79001e16i		−	0.586175i
$603$	−1.14058e16	−	1.14058e16i	−0.237258	−	0.237258i
$604$	5.64881e15	+	5.64881e15i	0.116342	+	0.116342i
$605$	8.85958e16	−	8.85958e16i	1.80668	−	1.80668i
$606$	−8.79328e15	+	8.79328e15i	−0.177548	+	0.177548i
$607$	−7.89726e15			−0.157886			−0.0789432	−	0.996879i	$-0.525155\pi$
$607$	−7.89726e15			−0.157886			−0.0789432	+	0.996879i	$0.525155\pi$
$608$			2.37705e16i			0.470561i
$609$	−7.14856e16	+	7.14856e16i	−1.40125	+	1.40125i
$610$		−	4.32736e16i		−	0.839931i
$611$	−1.70917e15	+	5.42705e14i	−0.0328502	+	0.0104308i
$612$	−4.78279e15			−0.0910275
$613$	7.54913e15	+	7.54913e15i	0.142277	+	0.142277i	0.774658	−	0.632381i	$-0.217922\pi$
$613$	7.54913e15	+	7.54913e15i	0.142277	+	0.142277i	−0.632381	+	0.774658i	$0.717922\pi$
$614$	4.80320e16			0.896439
$615$			7.71371e16i			1.42565i
$616$	5.66806e16	+	5.66806e16i	1.03741	+	1.03741i
$617$	−7.26232e16	−	7.26232e16i	−1.31633	−	1.31633i	−0.916659	−	0.399670i	$-0.869125\pi$
$617$	−7.26232e16	−	7.26232e16i	−1.31633	−	1.31633i	−0.399670	−	0.916659i	$-0.630875\pi$
$618$	5.25776e16	−	5.25776e16i	0.943778	−	0.943778i
$619$	1.42031e16	−	1.42031e16i	0.252487	−	0.252487i	−0.569503	−	0.821989i	$-0.692864\pi$
$619$	1.42031e16	−	1.42031e16i	0.252487	−	0.252487i	0.821989	+	0.569503i	$0.192864\pi$
$620$	−8.29076e15			−0.145963
$621$			5.51850e16i			0.962213i
$622$	2.14688e16	−	2.14688e16i	0.370737	−	0.370737i
$623$			7.04199e15i			0.120439i
$624$	7.37307e16	+	3.81923e16i	1.24894	+	0.646946i
$625$	3.15015e16			0.528507
$626$	−2.84372e16	−	2.84372e16i	−0.472542	−	0.472542i
$627$	8.93593e16			1.47073
$628$		−	1.37314e16i		−	0.223850i
$629$	3.55405e16	+	3.55405e16i	0.573878	+	0.573878i
$630$	3.01407e16	+	3.01407e16i	0.482070	+	0.482070i
$631$	−7.98791e16	+	7.98791e16i	−1.26548	+	1.26548i	−0.317089	+	0.948396i	$0.602705\pi$
$631$	−7.98791e16	+	7.98791e16i	−1.26548	+	1.26548i	−0.948396	+	0.317089i	$0.897295\pi$
$632$	6.23469e15	−	6.23469e15i	0.0978390	−	0.0978390i
$633$	1.07622e17			1.67294
$634$		−	1.96772e16i		−	0.302989i
$635$	−7.54763e16	+	7.54763e16i	−1.15125	+	1.15125i
$636$		−	5.56352e15i		−	0.0840634i
$637$	9.28396e15	−	1.79228e16i	0.138962	−	0.268268i
$638$	1.89308e17			2.80702
$639$	2.11647e16	+	2.11647e16i	0.310891	+	0.310891i
$640$	−1.26703e17			−1.84377
$641$			9.43281e16i			1.35986i	0.733279	+	0.679928i	$0.237989\pi$
$641$			9.43281e16i			1.35986i	−0.733279	+	0.679928i	$0.762011\pi$
$642$	−7.62110e16	−	7.62110e16i	−1.08845	−	1.08845i
$643$	7.12523e15	+	7.12523e15i	0.100817	+	0.100817i	0.755716	−	0.654899i	$-0.227289\pi$
$643$	7.12523e15	+	7.12523e15i	0.100817	+	0.100817i	−0.654899	+	0.755716i	$0.727289\pi$
$644$	−2.26882e16	+	2.26882e16i	−0.318043	+	0.318043i
$645$	4.05031e16	−	4.05031e16i	0.562509	−	0.562509i
$646$	−5.54008e16			−0.762292
$647$			1.51447e16i			0.206460i	0.994658	+	0.103230i	$0.0329177\pi$
$647$			1.51447e16i			0.206460i	−0.994658	+	0.103230i	$0.967082\pi$
$648$	5.04675e16	−	5.04675e16i	0.681651	−	0.681651i
$649$			3.74337e16i			0.500950i
$650$	1.11143e17	−	3.52907e16i	1.47367	−	0.467929i
$651$	−3.06017e16			−0.402031
$652$	−1.38546e16	−	1.38546e16i	−0.180346	−	0.180346i
$653$	−1.19858e17			−1.54592			−0.772959	−	0.634456i	$-0.781224\pi$
$653$	−1.19858e17			−1.54592			−0.772959	+	0.634456i	$0.781224\pi$
$654$			3.57536e14i			0.00456934i
$655$	−9.89096e16	−	9.89096e16i	−1.25254	−	1.25254i
$656$	5.50092e16	+	5.50092e16i	0.690259	+	0.690259i
$657$	−2.06755e16	+	2.06755e16i	−0.257078	+	0.257078i
$658$	−2.58630e15	+	2.58630e15i	−0.0318658	+	0.0318658i
$659$	−9.30427e16			−1.13598			−0.567989	−	0.823036i	$-0.692278\pi$
$659$	−9.30427e16			−1.13598			−0.567989	+	0.823036i	$0.692278\pi$
$660$		−	7.49448e16i		−	0.906730i
$661$	5.03132e16	−	5.03132e16i	0.603217	−	0.603217i	−0.337948	−	0.941165i	$-0.609733\pi$
$661$	5.03132e16	−	5.03132e16i	0.603217	−	0.603217i	0.941165	+	0.337948i	$0.109733\pi$
$662$			1.21440e17i			1.44282i
$663$	−3.86751e16	+	7.46628e16i	−0.455355	+	0.879069i
$664$	−9.75370e16			−1.13805
$665$	8.32085e16	+	8.32085e16i	0.962140	+	0.962140i
$666$	−3.22807e16			−0.369912
$667$		−	1.66395e17i		−	1.88967i
$668$	3.59962e16	+	3.59962e16i	0.405133	+	0.405133i
$669$	−4.71069e16	−	4.71069e16i	−0.525446	−	0.525446i
$670$	−1.10806e17	+	1.10806e17i	−1.22494	+	1.22494i
$671$	−5.04050e16	+	5.04050e16i	−0.552253	+	0.552253i
$672$	7.35853e16			0.799053
$673$			4.15580e16i			0.447264i	0.974674	+	0.223632i	$0.0717914\pi$
$673$			4.15580e16i			0.447264i	−0.974674	+	0.223632i	$0.928209\pi$
$674$	9.03745e16	−	9.03745e16i	0.964021	−	0.964021i
$675$		−	9.74933e16i		−	1.03075i
$676$	−2.43905e16	+	1.72260e16i	−0.255588	+	0.180511i
$677$	1.41850e17			1.47333			0.736663	−	0.676260i	$-0.236401\pi$
$677$	1.41850e17			1.47333			0.736663	+	0.676260i	$0.236401\pi$
$678$	−1.25306e17	−	1.25306e17i	−1.29002	−	1.29002i
$679$	4.45560e16			0.454661
$680$		−	1.02029e17i		−	1.03198i
$681$	1.09550e17	+	1.09550e17i	1.09832	+	1.09832i
$682$	4.05197e16	+	4.05197e16i	0.402680	+	0.402680i
$683$	2.66495e16	−	2.66495e16i	0.262521	−	0.262521i	−0.563556	−	0.826078i	$-0.690567\pi$
$683$	2.66495e16	−	2.66495e16i	0.262521	−	0.262521i	0.826078	+	0.563556i	$0.190567\pi$
$684$	5.99633e15	−	5.99633e15i	0.0585529	−	0.0585529i
$685$	1.92586e17			1.86415
$686$			9.50968e16i			0.912476i
$687$	7.01223e16	−	7.01223e16i	0.666985	−	0.666985i
$688$		−	5.77684e16i		−	0.544703i
$689$	−2.20452e16	−	1.14194e16i	−0.206063	−	0.106740i
$690$	−2.76397e17			−2.56117
$691$	6.75434e16	+	6.75434e16i	0.620461	+	0.620461i	0.945649	−	0.325188i	$-0.105428\pi$
$691$	6.75434e16	+	6.75434e16i	0.620461	+	0.620461i	−0.325188	+	0.945649i	$0.605428\pi$
$692$	−5.78976e16			−0.527259
$693$		−	7.02158e16i		−	0.633921i
$694$	1.90762e16	+	1.90762e16i	0.170740	+	0.170740i
$695$	−6.22513e16	−	6.22513e16i	−0.552382	−	0.552382i
$696$	−1.09895e17	+	1.09895e17i	−0.966769	+	0.966769i
$697$	−5.57046e16	+	5.57046e16i	−0.485841	+	0.485841i
$698$	−6.34137e16			−0.548340
$699$		−	2.27745e17i		−	1.95247i
$700$	4.00825e16	−	4.00825e16i	0.340695	−	0.340695i
$701$			9.07455e16i			0.764746i	0.924008	+	0.382373i	$0.124893\pi$
$701$			9.07455e16i			0.764746i	−0.924008	+	0.382373i	$0.875107\pi$
$702$	3.17007e16	+	9.98366e16i	0.264878	+	0.834194i
$703$	−8.91164e16			−0.738288
$704$	7.33710e16	+	7.33710e16i	0.602682	+	0.602682i
$705$	−7.50916e15			−0.0611585
$706$		−	5.51299e16i		−	0.445204i
$707$	1.90748e16	+	1.90748e16i	0.152737	+	0.152737i
$708$	9.89616e15	+	9.89616e15i	0.0785719	+	0.0785719i
$709$	5.52164e16	−	5.52164e16i	0.434701	−	0.434701i	−0.455523	−	0.890224i	$-0.650548\pi$
$709$	5.52164e16	−	5.52164e16i	0.434701	−	0.434701i	0.890224	+	0.455523i	$0.150548\pi$
$710$	2.05613e17	−	2.05613e17i	1.60509	−	1.60509i
$711$	−7.72351e15			−0.0597857
$712$			1.08257e16i			0.0830950i
$713$	3.56153e16	−	3.56153e16i	0.271082	−	0.271082i
$714$			1.71502e17i			1.29444i
$715$	−2.96966e17	−	1.53827e17i	−2.22265	−	1.15132i
$716$	2.56746e16			0.190557
$717$	−1.25262e17	−	1.25262e17i	−0.921941	−	0.921941i
$718$	−8.68714e16			−0.634059
$719$		−	1.02007e17i		−	0.738344i	−0.929361	−	0.369172i	$-0.879641\pi$
$719$		−	1.02007e17i		−	0.738344i	0.929361	−	0.369172i	$-0.120359\pi$
$720$	6.24076e16	+	6.24076e16i	0.447963	+	0.447963i
$721$	−1.14054e17	−	1.14054e17i	−0.811892	−	0.811892i
$722$	−4.53113e16	+	4.53113e16i	−0.319877	+	0.319877i
$723$	6.19742e16	−	6.19742e16i	0.433892	−	0.433892i
$724$	4.13149e16			0.286864
$725$			2.93964e17i			2.02426i
$726$	−2.28939e17	+	2.28939e17i	−1.56350	+	1.56350i
$727$			1.93159e17i			1.30830i	0.756363	+	0.654152i	$0.226974\pi$
$727$			1.93159e17i			1.30830i	−0.756363	+	0.654152i	$0.773026\pi$
$728$	6.15121e16	−	1.18750e17i	0.413211	−	0.797710i
$729$	7.02067e16			0.467750
$730$	2.00860e17	+	2.00860e17i	1.32726	+	1.32726i
$731$	5.84987e16			0.383391
$732$			2.66506e16i			0.173237i
$733$	1.08593e17	+	1.08593e17i	0.700132	+	0.700132i	0.964439	−	0.264307i	$-0.0851432\pi$
$733$	1.08593e17	+	1.08593e17i	0.700132	+	0.700132i	−0.264307	+	0.964439i	$0.585143\pi$
$734$	4.23457e16	+	4.23457e16i	0.270790	+	0.270790i
$735$	5.97659e16	−	5.97659e16i	0.379078	−	0.379078i
$736$	−8.56411e16	+	8.56411e16i	−0.538785	+	0.538785i
$737$	2.58133e17			1.61079
$738$		−	5.05954e16i		−	0.313165i
$739$	1.06384e17	−	1.06384e17i	0.653143	−	0.653143i	−0.300605	−	0.953749i	$-0.597189\pi$
$739$	1.06384e17	−	1.06384e17i	0.653143	−	0.653143i	0.953749	+	0.300605i	$0.0971887\pi$
$740$			7.47411e16i			0.455165i
$741$	−4.51189e16	−	1.42095e17i	−0.272552	−	0.858361i
$742$	−5.06384e16			−0.303429
$743$	−2.00749e17	−	2.00749e17i	−1.19322	−	1.19322i	−0.976157	−	0.217066i	$-0.930351\pi$
$743$	−2.00749e17	−	2.00749e17i	−1.19322	−	1.19322i	−0.217066	−	0.976157i	$-0.569649\pi$
$744$	−4.70441e16			−0.277375
$745$			2.06046e17i			1.20511i
$746$	−4.51364e16	−	4.51364e16i	−0.261875	−	0.261875i
$747$	6.04143e16	+	6.04143e16i	0.347709	+	0.347709i
$748$	5.41214e16	−	5.41214e16i	0.309001	−	0.309001i
$749$	−1.65321e17	+	1.65321e17i	−0.936345	+	0.936345i
$750$	1.26438e17			0.710409
$751$			1.44618e17i			0.806088i	0.915181	+	0.403044i	$0.132048\pi$
$751$			1.44618e17i			0.806088i	−0.915181	+	0.403044i	$0.867952\pi$
$752$	−5.35505e15	+	5.35505e15i	−0.0296112	+	0.0296112i
$753$		−	1.65966e17i		−	0.910438i
$754$	−9.55846e16	−	3.01030e17i	−0.520188	−	1.63825i
$755$	1.49279e17			0.805966
$756$	3.60050e16	+	3.60050e16i	0.192856	+	0.192856i
$757$	1.63171e17			0.867094			0.433547	−	0.901131i	$-0.357262\pi$
$757$	1.63171e17			0.867094			0.433547	+	0.901131i	$0.357262\pi$
$758$			2.37719e17i			1.25328i
$759$	3.21947e17	+	3.21947e17i	1.68397	+	1.68397i
$760$	1.27917e17	+	1.27917e17i	0.663813	+	0.663813i
$761$	3.34659e16	−	3.34659e16i	0.172304	−	0.172304i	−0.615687	−	0.787991i	$-0.711121\pi$
$761$	3.34659e16	−	3.34659e16i	0.172304	−	0.172304i	0.787991	+	0.615687i	$0.211121\pi$
$762$	1.95037e17	−	1.95037e17i	0.996291	−	0.996291i
$763$	7.75585e14			0.00393081
$764$		−	1.37883e16i		−	0.0693348i
$765$	−6.31965e16	+	6.31965e16i	−0.315300	+	0.315300i
$766$		−	3.30593e17i		−	1.63652i
$767$	5.95254e16	−	1.89009e16i	0.292368	−	0.0928345i
$768$	2.03433e17			0.991410
$769$	−1.62692e17	−	1.62692e17i	−0.786699	−	0.786699i	0.194252	−	0.980952i	$-0.437772\pi$
$769$	−1.62692e17	−	1.62692e17i	−0.786699	−	0.786699i	−0.980952	+	0.194252i	$0.937772\pi$
$770$	−6.82137e17			−3.27286
$771$		−	1.58442e17i		−	0.754301i
$772$	−4.92724e16	−	4.92724e16i	−0.232756	−	0.232756i
$773$	−1.20466e16	−	1.20466e16i	−0.0564661	−	0.0564661i	0.678310	−	0.734776i	$-0.262713\pi$
$773$	−1.20466e16	−	1.20466e16i	−0.0564661	−	0.0564661i	−0.734776	+	0.678310i	$0.762713\pi$
$774$	−2.65666e16	+	2.65666e16i	−0.123563	+	0.123563i
$775$	−6.29203e16	+	6.29203e16i	−0.290389	+	0.290389i
$776$	6.84961e16			0.313686
$777$			2.75874e17i			1.25367i
$778$	1.92735e17	−	1.92735e17i	0.869127	−	0.869127i
$779$		−	1.39677e17i		−	0.625029i
$780$	−1.19174e17	+	3.78408e16i	−0.529192	+	0.168032i
$781$	−4.78995e17			−2.11069
$782$	−1.99600e17	−	1.99600e17i	−0.872812	−	0.872812i
$783$	−2.64060e17			−1.14586
$784$		−	8.52423e16i		−	0.367078i
$785$	−1.81438e17	−	1.81438e17i	−0.775371	−	0.775371i
$786$	2.55590e17	+	2.55590e17i	1.08395	+	1.08395i
$787$	−1.86515e16	+	1.86515e16i	−0.0784992	+	0.0784992i	−0.745266	−	0.666767i	$-0.767678\pi$
$787$	−1.86515e16	+	1.86515e16i	−0.0784992	+	0.0784992i	0.666767	+	0.745266i	$0.267678\pi$
$788$	8.18077e16	−	8.18077e16i	0.341694	−	0.341694i
$789$	1.52490e17			0.632089
$790$			7.50329e16i			0.308666i
$791$	−2.71821e17	+	2.71821e17i	−1.10975	+	1.10975i
$792$		−	1.07943e17i		−	0.437364i
$793$	1.05602e17	+	5.47015e16i	0.424652	+	0.219968i
$794$	−5.41086e16			−0.215945
$795$	−7.35126e16	−	7.35126e16i	−0.291178	−	0.291178i
$796$	3.33779e16			0.131214
$797$		−	1.32340e16i		−	0.0516348i	−0.999667	−	0.0258174i	$-0.991781\pi$
$797$		−	1.32340e16i		−	0.0516348i	0.999667	−	0.0258174i	$-0.00821884\pi$
$798$	−2.15017e17	−	2.15017e17i	−0.832638	−	0.832638i
$799$	−5.42274e15	−	5.42274e15i	−0.0208420	−	0.0208420i
$800$	1.51299e17	−	1.51299e17i	0.577160	−	0.577160i
$801$	6.70540e15	−	6.70540e15i	0.0253881	−	0.0253881i
$802$	−2.57555e17			−0.967885
$803$		−	4.67924e17i		−	1.74535i
$804$	6.82413e16	−	6.82413e16i	0.252645	−	0.252645i
$805$			5.99574e17i			2.20327i
$806$	4.39736e16	−	8.48917e16i	0.160392	−	0.309638i
$807$	1.88493e17			0.682423
$808$	2.93237e16	+	2.93237e16i	0.105378	+	0.105378i
$809$	4.76113e17			1.69832			0.849159	−	0.528137i	$-0.177109\pi$
$809$	4.76113e17			1.69832			0.849159	+	0.528137i	$0.177109\pi$
$810$			6.07364e17i			2.15050i
$811$	3.42620e17	+	3.42620e17i	1.20417	+	1.20417i	0.972886	+	0.231284i	$0.0742928\pi$
$811$	3.42620e17	+	3.42620e17i	1.20417	+	1.20417i	0.231284	+	0.972886i	$0.425707\pi$
$812$	−1.08563e17	−	1.08563e17i	−0.378744	−	0.378744i
$813$	2.89571e17	−	2.89571e17i	1.00279	−	1.00279i
$814$	3.65285e17	−	3.65285e17i	1.25570	−	1.25570i
$815$	−3.66130e17			−1.24937
$816$			3.55102e17i			1.20285i
$817$	−7.33415e16	+	7.33415e16i	−0.246614	+	0.246614i
$818$			5.03312e17i			1.68003i
$819$	−1.11654e17	+	3.54530e16i	−0.369974	+	0.117476i
$820$	−1.17146e17			−0.385340
$821$	−2.40910e17	−	2.40910e17i	−0.786676	−	0.786676i	0.194272	−	0.980948i	$-0.437766\pi$
$821$	−2.40910e17	−	2.40910e17i	−0.786676	−	0.786676i	−0.980948	+	0.194272i	$0.937766\pi$
$822$	−4.97656e17			−1.61324
$823$			5.79222e16i			0.186400i	0.995647	+	0.0932001i	$0.0297096\pi$
$823$			5.79222e16i			0.186400i	−0.995647	+	0.0932001i	$0.970290\pi$
$824$	−1.75335e17	−	1.75335e17i	−0.560152	−	0.560152i
$825$	−5.68772e17	−	5.68772e17i	−1.80391	−	1.80391i
$826$	9.00735e16	−	9.00735e16i	0.283607	−	0.283607i
$827$	−3.75542e16	+	3.75542e16i	−0.117388	+	0.117388i	−0.763361	−	0.645972i	$-0.776452\pi$
$827$	−3.75542e16	+	3.75542e16i	−0.117388	+	0.117388i	0.645972	+	0.763361i	$0.276452\pi$
$828$	4.32076e16			0.134084
$829$		−	2.76726e17i		−	0.852556i	−0.904592	−	0.426278i	$-0.859824\pi$
$829$		−	2.76726e17i		−	0.852556i	0.904592	−	0.426278i	$-0.140176\pi$
$830$	5.86917e17	−	5.86917e17i	1.79518	−	1.79518i
$831$			5.47016e17i			1.66109i
$832$	7.96252e16	−	1.53718e17i	0.240055	−	0.463429i
$833$	8.63199e16			0.258369
$834$	1.60862e17	+	1.60862e17i	0.478033	+	0.478033i
$835$	9.51258e17			2.80659
$836$			1.35707e17i			0.397526i
$837$	−5.65197e16	−	5.65197e16i	−0.164379	−	0.164379i
$838$	1.37349e17	+	1.37349e17i	0.396609	+	0.396609i
$839$	−3.73685e17	+	3.73685e17i	−1.07136	+	1.07136i	−0.0741050	+	0.997250i	$0.523610\pi$
$839$	−3.73685e17	+	3.73685e17i	−1.07136	+	1.07136i	−0.997250	+	0.0741050i	$0.976390\pi$
$840$	3.95986e17	−	3.95986e17i	1.12721	−	1.12721i
$841$	4.42385e17			1.25033
$842$		−	3.34604e16i		−	0.0938986i
$843$	−4.47529e17	+	4.47529e17i	−1.24697	+	1.24697i
$844$			1.63443e17i			0.452180i
$845$	−9.46668e16	+	5.49892e17i	−0.260050	+	1.51056i
$846$	4.92537e15			0.0134344
$847$	4.96625e17	+	4.96625e17i	1.34502	+	1.34502i
$848$	−1.04849e17			−0.281961
$849$			3.86116e16i			0.103103i
$850$	3.52627e17	+	3.52627e17i	0.934978	+	0.934978i
$851$	−3.21072e17	−	3.21072e17i	−0.845327	−	0.845327i
$852$	−1.26629e17	+	1.26629e17i	−0.331053	+	0.331053i
$853$	4.57186e17	−	4.57186e17i	1.18686	−	1.18686i	0.208928	−	0.977931i	$-0.433003\pi$
$853$	4.57186e17	−	4.57186e17i	1.18686	−	1.18686i	0.977931	−	0.208928i	$-0.0669974\pi$
$854$	2.42570e17			0.625303
$855$		−	1.58463e17i		−	0.405631i
$856$	−2.54148e17	+	2.54148e17i	−0.646016	+	0.646016i
$857$		−	2.14429e17i		−	0.541250i	−0.962685	−	0.270625i	$-0.912770\pi$
$857$		−	2.14429e17i		−	0.541250i	0.962685	−	0.270625i	$-0.0872304\pi$
$858$	7.67383e17	+	3.97502e17i	1.92348	+	0.996359i
$859$	−5.32813e15			−0.0132622			−0.00663110	−	0.999978i	$-0.502111\pi$
$859$	−5.32813e15			−0.0132622			−0.00663110	+	0.999978i	$0.502111\pi$
$860$	6.15109e16	+	6.15109e16i	0.152041	+	0.152041i
$861$	−4.32393e17			−1.06135
$862$		−	5.82316e17i		−	1.41943i
$863$	−4.73994e17	−	4.73994e17i	−1.14738	−	1.14738i	−0.987066	−	0.160316i	$-0.948749\pi$
$863$	−4.73994e17	−	4.73994e17i	−1.14738	−	1.14738i	−0.160316	−	0.987066i	$-0.551251\pi$
$864$	1.35908e17	+	1.35908e17i	0.326710	+	0.326710i
$865$	−7.65020e17	+	7.65020e17i	−1.82632	+	1.82632i
$866$	−5.48446e17	+	5.48446e17i	−1.30025	+	1.30025i
$867$	1.32103e17			0.311028
$868$		−	4.64739e16i		−	0.108665i
$869$	8.73983e16	−	8.73983e16i	0.202948	−	0.202948i
$870$		−	1.32256e18i		−	3.05000i
$871$	−1.30335e17	−	4.10472e17i	−0.298506	−	0.940101i
$872$	1.19231e15			0.00271200
$873$	−4.24264e16	−	4.24264e16i	−0.0958408	−	0.0958408i
$874$	5.00490e17			1.12286
$875$		−	2.74274e17i		−	0.611135i
$876$	−1.23703e17	−	1.23703e17i	−0.273750	−	0.273750i
$877$	−3.44358e17	−	3.44358e17i	−0.756854	−	0.756854i	0.218894	−	0.975749i	$-0.429755\pi$
$877$	−3.44358e17	−	3.44358e17i	−0.756854	−	0.756854i	−0.975749	+	0.218894i	$0.929755\pi$
$878$	−4.21278e17	+	4.21278e17i	−0.919606	+	0.919606i
$879$	−6.41717e17	+	6.41717e17i	−1.39127	+	1.39127i
$880$	−1.41239e18			−3.04130
$881$			1.91163e17i			0.408836i	0.978884	+	0.204418i	$0.0655302\pi$
$881$			1.91163e17i			0.408836i	−0.978884	+	0.204418i	$0.934470\pi$
$882$	−3.92013e16	+	3.92013e16i	−0.0832701	+	0.0832701i
$883$			7.75562e17i			1.63626i	0.575034	+	0.818130i	$0.304989\pi$
$883$			7.75562e17i			1.63626i	−0.575034	+	0.818130i	$0.695011\pi$
$884$	−1.13388e17	−	5.87348e16i	−0.237604	−	0.123078i
$885$	2.61522e17			0.544313
$886$	−6.34925e16	−	6.34925e16i	−0.131256	−	0.131256i
$887$	8.36526e17			1.71766			0.858831	−	0.512259i	$-0.171191\pi$
$887$	8.36526e17			1.71766			0.858831	+	0.512259i	$0.171191\pi$
$888$			4.24102e17i			0.864953i
$889$	−4.23083e17	−	4.23083e17i	−0.857067	−	0.857067i
$890$	−6.51421e16	−	6.51421e16i	−0.131076	−	0.131076i
$891$	7.07457e17	−	7.07457e17i	1.41395	−	1.41395i
$892$	7.15399e16	−	7.15399e16i	0.142023	−	0.142023i
$893$	1.35973e16			0.0268129
$894$		−	5.32438e17i		−	1.04290i
$895$	3.39247e17	−	3.39247e17i	0.660051	−	0.660051i
$896$		−	7.10236e17i		−	1.37263i
$897$	3.49390e17	−	6.74502e17i	0.670742	−	1.29488i
$898$	3.45768e17			0.659366
$899$	1.70419e17	+	1.70419e17i	0.322820	+	0.322820i
$900$	−7.63333e16			−0.143635
$901$		−	1.06174e17i		−	0.198459i
$902$	5.72531e17	+	5.72531e17i	1.06306	+	1.06306i
$903$	2.27040e17	+	2.27040e17i	0.418771	+	0.418771i
$904$	−4.17871e17	+	4.17871e17i	−0.765652	+	0.765652i
$905$	5.45907e17	−	5.45907e17i	0.993636	−	0.993636i
$906$	−3.85749e17			−0.697486
$907$		−	8.42481e17i		−	1.51327i	−0.653838	−	0.756635i	$-0.726842\pi$
$907$		−	8.42481e17i		−	1.51327i	0.653838	−	0.756635i	$-0.273158\pi$
$908$	−1.66371e17	+	1.66371e17i	−0.296867	+	0.296867i
$909$		−	3.63262e16i		−	0.0643926i
$910$	3.44422e17	+	1.08470e18i	0.606516	+	1.91013i
$911$	4.20754e17			0.736068			0.368034	−	0.929812i	$-0.380031\pi$
$911$	4.20754e17			0.736068			0.368034	+	0.929812i	$0.380031\pi$
$912$	−4.45202e17	−	4.45202e17i	−0.773728	−	0.773728i
$913$	−1.36728e18			−2.36066
$914$		−	1.71179e17i		−	0.293612i
$915$	3.52143e17	+	3.52143e17i	0.600058	+	0.600058i
$916$	1.06493e17	+	1.06493e17i	0.180280	+	0.180280i
$917$	5.54439e17	−	5.54439e17i	0.932476	−	0.932476i
$918$	−3.16755e17	+	3.16755e17i	−0.529258	+	0.529258i
$919$	−8.65405e17			−1.43657			−0.718284	−	0.695750i	$-0.755072\pi$
$919$	−8.65405e17			−1.43657			−0.718284	+	0.695750i	$0.755072\pi$
$920$			9.21726e17i			1.52011i
$921$	−3.90866e17	+	3.90866e17i	−0.640428	+	0.640428i
$922$			1.51799e17i			0.247106i
$923$	2.41852e17	+	7.61676e17i	0.391146	+	1.23186i
$924$	4.20104e17			0.675033
$925$	5.67226e17	+	5.67226e17i	0.905536	+	0.905536i
$926$	1.46527e17			0.232409
$927$			2.17205e17i			0.342287i
$928$	−4.09793e17	−	4.09793e17i	−0.641618	−	0.641618i
$929$	−2.18341e17	−	2.18341e17i	−0.339658	−	0.339658i	0.516581	−	0.856239i	$-0.327205\pi$
$929$	−2.18341e17	−	2.18341e17i	−0.339658	−	0.339658i	−0.856239	+	0.516581i	$0.827205\pi$
$930$	2.83082e17	−	2.83082e17i	0.437537	−	0.437537i
$931$	−1.08222e17	+	1.08222e17i	−0.166195	+	0.166195i
$932$	3.45869e17			0.527736
$933$			3.49410e17i			0.529718i
$934$	−5.59641e17	+	5.59641e17i	−0.843001	+	0.843001i
$935$		−	1.43025e18i		−	2.14063i
$936$	−1.71646e17	+	5.45020e16i	−0.255258	+	0.0810509i
$937$	4.84574e17			0.716016			0.358008	−	0.933719i	$-0.383456\pi$
$937$	4.84574e17			0.716016			0.358008	+	0.933719i	$0.383456\pi$
$938$	−6.21123e17	−	6.21123e17i	−0.911928	−	0.911928i
$939$	4.62821e17			0.675180
$940$		−	1.14039e16i		−	0.0165306i
$941$	3.07029e17	+	3.07029e17i	0.442223	+	0.442223i	0.892758	−	0.450536i	$-0.148767\pi$
$941$	3.07029e17	+	3.07029e17i	0.442223	+	0.442223i	−0.450536	+	0.892758i	$0.648767\pi$
$942$	4.68849e17	+	4.68849e17i	0.671008	+	0.671008i
$943$	5.03234e17	−	5.03234e17i	0.715648	−	0.715648i
$944$	1.86501e17	−	1.86501e17i	0.263541	−	0.263541i
$945$	9.51492e17			1.33602
$946$		−	6.01248e17i		−	0.838894i
$947$	1.73976e16	−	1.73976e16i	0.0241207	−	0.0241207i	−0.694944	−	0.719064i	$-0.744571\pi$
$947$	1.73976e16	−	1.73976e16i	0.0241207	−	0.0241207i	0.719064	+	0.694944i	$0.244571\pi$
$948$		−	4.62101e16i		−	0.0636629i
$949$	−7.44071e17	+	2.36262e17i	−1.01863	+	0.323442i
$950$	−8.84197e17			−1.20284
$951$	1.60125e17	+	1.60125e17i	0.216459	+	0.216459i
$952$	5.71924e17			0.768274
$953$			1.18178e18i			1.57754i	0.614689	+	0.788770i	$0.289282\pi$
$953$			1.18178e18i			1.57754i	−0.614689	+	0.788770i	$0.710718\pi$
$954$	4.82180e16	+	4.82180e16i	0.0639616	+	0.0639616i
$955$	−1.82190e17	−	1.82190e17i	−0.240162	−	0.240162i
$956$	1.90231e17	−	1.90231e17i	0.249192	−	0.249192i
$957$	−1.54052e18	+	1.54052e18i	−2.00537	+	2.00537i
$958$	−4.93823e17			−0.638820
$959$			1.07954e18i			1.38780i
$960$	5.12590e17	−	5.12590e17i	0.654852	−	0.654852i
$961$		−	7.14709e17i		−	0.907380i
$962$	−7.65297e17	−	3.96422e17i	−0.965561	−	0.500158i
$963$	3.14837e17			0.394756
$964$	9.41185e16	+	9.41185e16i	0.117277	+	0.117277i
$965$	−1.30211e18			−1.61244
$966$		−	1.54935e18i		−	1.90671i
$967$	−6.27459e17	−	6.27459e17i	−0.767408	−	0.767408i	0.210241	−	0.977650i	$-0.432575\pi$
$967$	−6.27459e17	−	6.27459e17i	−0.767408	−	0.767408i	−0.977650	+	0.210241i	$0.932575\pi$
$968$	7.63462e17	+	7.63462e17i	0.927973	+	0.927973i
$969$	4.50830e17	−	4.50830e17i	0.544591	−	0.544591i
$970$	−4.12167e17	+	4.12167e17i	−0.494815	+	0.494815i
$971$	1.31364e18			1.56734			0.783669	−	0.621179i	$-0.213346\pi$
$971$	1.31364e18			1.56734			0.783669	+	0.621179i	$0.213346\pi$
$972$		−	1.72487e17i		−	0.204531i
$973$	3.48950e17	−	3.48950e17i	0.411231	−	0.411231i
$974$			6.31540e17i			0.739685i
$975$	−6.17254e17	+	1.19162e18i	−0.718516	+	1.38711i
$976$	5.02252e17			0.581062
$977$	1.14403e18	+	1.14403e18i	1.31543	+	1.31543i	0.917348	+	0.398086i	$0.130325\pi$
$977$	1.14403e18	+	1.14403e18i	1.31543	+	1.31543i	0.398086	+	0.917348i	$0.369675\pi$
$978$	9.46109e17			1.08120
$979$			1.51755e17i			0.172364i
$980$	9.07647e16	+	9.07647e16i	0.102461	+	0.102461i
$981$	−7.38514e14	−	7.38514e14i	−0.000828599	−	0.000828599i
$982$	−8.08835e16	+	8.08835e16i	−0.0901968	+	0.0901968i
$983$	−7.40361e17	+	7.40361e17i	−0.820583	+	0.820583i	−0.986192	−	0.165609i	$-0.947041\pi$
$983$	−7.40361e17	+	7.40361e17i	−0.820583	+	0.820583i	0.165609	+	0.986192i	$0.447041\pi$
$984$	−6.64718e17			−0.732263
$985$		−	2.16190e18i		−	2.36711i
$986$	9.55087e17	−	9.55087e17i	1.03940	−	1.03940i
$987$		−	4.20927e16i		−	0.0455306i
$988$	2.15796e17	−	6.85207e16i	0.232007	−	0.0736683i
$989$	−5.28475e17			−0.564738
$990$	6.49533e17	+	6.49533e17i	0.689906	+	0.689906i
$991$	1.40266e18			1.48084			0.740422	−	0.672142i	$-0.234626\pi$
$991$	1.40266e18			1.48084			0.740422	+	0.672142i	$0.234626\pi$
$992$		−	1.75425e17i		−	0.184086i
$993$	−9.88231e17	−	9.88231e17i	−1.03077	−	1.03077i
$994$	1.15256e18	+	1.15256e18i	1.19494	+	1.19494i
$995$	4.41032e17	−	4.41032e17i	0.454498	−	0.454498i
$996$	−3.61461e17	+	3.61461e17i	−0.370259	+	0.370259i
$997$	1.90391e17			0.193855			0.0969273	−	0.995291i	$-0.469099\pi$
$997$	1.90391e17			0.193855			0.0969273	+	0.995291i	$0.469099\pi$
$998$			6.66600e17i			0.674655i
$999$	−5.09524e17	+	5.09524e17i	−0.512592	+	0.512592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.13.d.a.8.4	yes	26
13.5	odd	4	inner	13.13.d.a.5.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.13.d.a.5.4	✓	26	13.5	odd	4	inner
13.13.d.a.8.4	yes	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-51.8539 - 51.8539i) q^{2} +843.934 q^{3} +1281.66i q^{4} +(16935.0 + 16935.0i) q^{5} +(-43761.3 - 43761.3i) q^{6} +(-94929.1 + 94929.1i) q^{7} +(-145935. + 145935. i) q^{8} +180783. q^{9} +O(q^{10})\)	\(q+(-51.8539 - 51.8539i) q^{2} +843.934 q^{3} +1281.66i q^{4} +(16935.0 + 16935.0i) q^{5} +(-43761.3 - 43761.3i) q^{6} +(-94929.1 + 94929.1i) q^{7} +(-145935. + 145935. i) q^{8} +180783. q^{9} -1.75629e6i q^{10} +(-2.04572e6 + 2.04572e6i) q^{11} +1.08163e6i q^{12} +(4.28593e6 + 2.22010e6i) q^{13} +9.84489e6 q^{14} +(1.42920e7 + 1.42920e7i) q^{15} +2.03842e7 q^{16} +2.06419e7i q^{17} +(-9.37433e6 - 9.37433e6i) q^{18} +(-2.58794e7 - 2.58794e7i) q^{19} +(-2.17048e7 + 2.17048e7i) q^{20} +(-8.01139e7 + 8.01139e7i) q^{21} +2.12157e8 q^{22} -1.86479e8i q^{23} +(-1.23159e8 + 1.23159e8i) q^{24} +3.29445e8i q^{25} +(-1.07122e8 - 3.37363e8i) q^{26} -2.95932e8 q^{27} +(-1.21667e8 - 1.21667e8i) q^{28} +8.92300e8 q^{29} -1.48219e9i q^{30} +(1.90989e8 + 1.90989e8i) q^{31} +(-4.59254e8 - 4.59254e8i) q^{32} +(-1.72645e9 + 1.72645e9i) q^{33} +(1.07037e9 - 1.07037e9i) q^{34} -3.21524e9 q^{35} +2.31703e8i q^{36} +(1.72176e9 - 1.72176e9i) q^{37} +2.68390e9i q^{38} +(3.61705e9 + 1.87362e9i) q^{39} -4.94280e9 q^{40} +(2.69861e9 + 2.69861e9i) q^{41} +8.30844e9 q^{42} -2.83397e9i q^{43} +(-2.62192e9 - 2.62192e9i) q^{44} +(3.06156e9 + 3.06156e9i) q^{45} +(-9.66965e9 + 9.66965e9i) q^{46} +(-2.62705e8 + 2.62705e8i) q^{47} +1.72030e10 q^{48} -4.18177e9i q^{49} +(1.70830e10 - 1.70830e10i) q^{50} +1.74204e10i q^{51} +(-2.84541e9 + 5.49310e9i) q^{52} -5.14362e9 q^{53} +(1.53452e10 + 1.53452e10i) q^{54} -6.92885e10 q^{55} -2.77069e10i q^{56} +(-2.18405e10 - 2.18405e10i) q^{57} +(-4.62693e10 - 4.62693e10i) q^{58} +(9.14926e9 - 9.14926e9i) q^{59} +(-1.83174e10 + 1.83174e10i) q^{60} +2.46392e10 q^{61} -1.98070e10i q^{62} +(-1.71616e10 + 1.71616e10i) q^{63} -3.58656e10i q^{64} +(3.49848e10 + 1.10179e11i) q^{65} +1.79047e11 q^{66} +(-6.30909e10 - 6.30909e10i) q^{67} -2.64559e10 q^{68} -1.57376e11i q^{69} +(1.66723e11 + 1.66723e11i) q^{70} +(1.17072e11 + 1.17072e11i) q^{71} +(-2.63826e10 + 2.63826e10i) q^{72} +(-1.14366e11 + 1.14366e11i) q^{73} -1.78560e11 q^{74} +2.78030e11i q^{75} +(3.31686e10 - 3.31686e10i) q^{76} -3.88397e11i q^{77} +(-9.04036e10 - 2.84712e11i) q^{78} -4.27225e10 q^{79} +(3.45206e11 + 3.45206e11i) q^{80} -3.45823e11 q^{81} -2.79867e11i q^{82} +(3.34180e11 + 3.34180e11i) q^{83} +(-1.02679e11 - 1.02679e11i) q^{84} +(-3.49570e11 + 3.49570e11i) q^{85} +(-1.46953e11 + 1.46953e11i) q^{86} +7.53043e11 q^{87} -5.97084e11i q^{88} +(3.70908e10 - 3.70908e10i) q^{89} -3.17508e11i q^{90} +(-6.17612e11 + 1.96108e11i) q^{91} +2.39002e11 q^{92} +(1.61182e11 + 1.61182e11i) q^{93} +2.72446e10 q^{94} -8.76534e11i q^{95} +(-3.87580e11 - 3.87580e11i) q^{96} +(-2.34681e11 - 2.34681e11i) q^{97} +(-2.16841e11 + 2.16841e11i) q^{98} +(-3.69833e11 + 3.69833e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 4 q^{3} + 5146 q^{5} + 64736 q^{6} - 114402 q^{7} - 262080 q^{8} + 3897230 q^{9}+O(q^{10}) \) 26 * q - 2 * q^2 - 4 * q^3 + 5146 * q^5 + 64736 * q^6 - 114402 * q^7 - 262080 * q^8 + 3897230 * q^9	\( 26 q - 2 q^{2} - 4 q^{3} + 5146 q^{5} + 64736 q^{6} - 114402 q^{7} - 262080 q^{8} + 3897230 q^{9} - 1360946 q^{11} - 2904122 q^{13} - 33341620 q^{14} - 26612356 q^{15} - 42212844 q^{16} + 76072094 q^{18} - 41603538 q^{19} + 60982508 q^{20} - 77526388 q^{21} + 648561056 q^{22} - 1131540696 q^{24} + 912969070 q^{26} - 159769528 q^{27} - 311272132 q^{28} + 2981804 q^{29} - 1023774130 q^{31} + 1476108268 q^{32} + 2381658236 q^{33} + 1983101640 q^{34} - 3650085364 q^{35} - 3167118502 q^{37} + 16292940092 q^{39} - 3968093508 q^{40} + 28381274530 q^{41} - 49639312388 q^{42} - 18960178772 q^{44} - 10665692290 q^{45} + 37450277124 q^{46} + 20752786078 q^{47} - 71636180764 q^{48} - 48656842882 q^{50} + 117857606620 q^{52} - 58773364924 q^{53} + 213216359816 q^{54} - 136697226052 q^{55} - 114945046324 q^{57} + 92279424116 q^{58} + 155389424110 q^{59} + 136735907884 q^{60} + 141369458276 q^{61} - 464360668726 q^{63} + 114397918882 q^{65} - 206611171952 q^{66} + 100234053918 q^{67} - 417926231820 q^{68} + 153062962568 q^{70} + 230837239150 q^{71} - 118991496780 q^{72} + 146516995818 q^{73} - 1012588063096 q^{74} + 606168045784 q^{76} + 359416070936 q^{78} + 434995822940 q^{79} + 237895101520 q^{80} + 1613859489074 q^{81} - 637194158642 q^{83} - 981969825256 q^{84} - 213215637336 q^{85} - 2637756396288 q^{86} + 744567460312 q^{87} + 1456251648226 q^{89} - 3121537204578 q^{91} + 1179602583480 q^{92} - 3143065458004 q^{93} + 5250023559428 q^{94} + 948734423984 q^{96} + 1538416432538 q^{97} + 25933667758 q^{98} - 1934327641798 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 4 * q^3 + 5146 * q^5 + 64736 * q^6 - 114402 * q^7 - 262080 * q^8 + 3897230 * q^9 - 1360946 * q^11 - 2904122 * q^13 - 33341620 * q^14 - 26612356 * q^15 - 42212844 * q^16 + 76072094 * q^18 - 41603538 * q^19 + 60982508 * q^20 - 77526388 * q^21 + 648561056 * q^22 - 1131540696 * q^24 + 912969070 * q^26 - 159769528 * q^27 - 311272132 * q^28 + 2981804 * q^29 - 1023774130 * q^31 + 1476108268 * q^32 + 2381658236 * q^33 + 1983101640 * q^34 - 3650085364 * q^35 - 3167118502 * q^37 + 16292940092 * q^39 - 3968093508 * q^40 + 28381274530 * q^41 - 49639312388 * q^42 - 18960178772 * q^44 - 10665692290 * q^45 + 37450277124 * q^46 + 20752786078 * q^47 - 71636180764 * q^48 - 48656842882 * q^50 + 117857606620 * q^52 - 58773364924 * q^53 + 213216359816 * q^54 - 136697226052 * q^55 - 114945046324 * q^57 + 92279424116 * q^58 + 155389424110 * q^59 + 136735907884 * q^60 + 141369458276 * q^61 - 464360668726 * q^63 + 114397918882 * q^65 - 206611171952 * q^66 + 100234053918 * q^67 - 417926231820 * q^68 + 153062962568 * q^70 + 230837239150 * q^71 - 118991496780 * q^72 + 146516995818 * q^73 - 1012588063096 * q^74 + 606168045784 * q^76 + 359416070936 * q^78 + 434995822940 * q^79 + 237895101520 * q^80 + 1613859489074 * q^81 - 637194158642 * q^83 - 981969825256 * q^84 - 213215637336 * q^85 - 2637756396288 * q^86 + 744567460312 * q^87 + 1456251648226 * q^89 - 3121537204578 * q^91 + 1179602583480 * q^92 - 3143065458004 * q^93 + 5250023559428 * q^94 + 948734423984 * q^96 + 1538416432538 * q^97 + 25933667758 * q^98 - 1934327641798 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more