Properties

Label 10.19.c.b.7.5
Level $10$
Weight $19$
Character 10.7
Analytic conductor $20.539$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [10,19,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 19, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 19);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 10.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: \(20.5386137710\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 15200484 x^{8} + 52963214026118 x^{6} + \cdots + 20\!\cdots\!04 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{22}\cdot 3^{8}\cdot 5^{17} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.5
Root \(2026.71i\) of defining polynomial
Character \(\chi\) \(=\) 10.7
Dual form 10.19.c.b.3.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-256.000 - 256.000i) q^{2} +(21673.0 - 21673.0i) q^{3} +131072. i q^{4} +(839560. + 1.76347e6i) q^{5} -1.10966e7 q^{6} +(-2.81596e7 - 2.81596e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -5.52014e8i q^{9} +O(q^{10})\) \(q+(-256.000 - 256.000i) q^{2} +(21673.0 - 21673.0i) q^{3} +131072. i q^{4} +(839560. + 1.76347e6i) q^{5} -1.10966e7 q^{6} +(-2.81596e7 - 2.81596e7i) q^{7} +(3.35544e7 - 3.35544e7i) q^{8} -5.52014e8i q^{9} +(2.36522e8 - 6.66376e8i) q^{10} -2.01016e9 q^{11} +(2.84072e9 + 2.84072e9i) q^{12} +(8.61354e9 - 8.61354e9i) q^{13} +1.44177e10i q^{14} +(5.64154e10 + 2.00239e10i) q^{15} -1.71799e10 q^{16} +(-1.24094e11 - 1.24094e11i) q^{17} +(-1.41316e11 + 1.41316e11i) q^{18} -4.61669e11i q^{19} +(-2.31142e11 + 1.10043e11i) q^{20} -1.22060e12 q^{21} +(5.14600e11 + 5.14600e11i) q^{22} +(-9.96769e11 + 9.96769e11i) q^{23} -1.45445e12i q^{24} +(-2.40498e12 + 2.96108e12i) q^{25} -4.41013e12 q^{26} +(-3.56723e12 - 3.56723e12i) q^{27} +(3.69094e12 - 3.69094e12i) q^{28} -1.38376e13i q^{29} +(-9.31622e12 - 1.95685e13i) q^{30} -2.65717e13 q^{31} +(4.39805e12 + 4.39805e12i) q^{32} +(-4.35660e13 + 4.35660e13i) q^{33} +6.35364e13i q^{34} +(2.60170e13 - 7.33004e13i) q^{35} +7.23536e13 q^{36} +(1.40030e14 + 1.40030e14i) q^{37} +(-1.18187e14 + 1.18187e14i) q^{38} -3.73362e14i q^{39} +(8.73433e13 + 3.10014e13i) q^{40} -8.98236e13 q^{41} +(3.12475e14 + 3.12475e14i) q^{42} +(3.06959e13 - 3.06959e13i) q^{43} -2.63475e14i q^{44} +(9.73461e14 - 4.63449e14i) q^{45} +5.10346e14 q^{46} +(7.03769e14 + 7.03769e14i) q^{47} +(-3.72339e14 + 3.72339e14i) q^{48} -4.24859e13i q^{49} +(1.37371e15 - 1.42363e14i) q^{50} -5.37899e15 q^{51} +(1.12899e15 + 1.12899e15i) q^{52} +(-1.18441e15 + 1.18441e15i) q^{53} +1.82642e15i q^{54} +(-1.68765e15 - 3.54486e15i) q^{55} -1.88976e15 q^{56} +(-1.00057e16 - 1.00057e16i) q^{57} +(-3.54243e15 + 3.54243e15i) q^{58} -1.13913e16i q^{59} +(-2.62458e15 + 7.39448e15i) q^{60} +1.79758e16 q^{61} +(6.80234e15 + 6.80234e15i) q^{62} +(-1.55445e16 + 1.55445e16i) q^{63} -2.25180e15i q^{64} +(2.24213e16 + 7.95816e15i) q^{65} +2.23058e16 q^{66} +(-3.42502e16 - 3.42502e16i) q^{67} +(1.62653e16 - 1.62653e16i) q^{68} +4.32059e16i q^{69} +(-2.54253e16 + 1.21045e16i) q^{70} +1.84976e16 q^{71} +(-1.85225e16 - 1.85225e16i) q^{72} +(5.63444e16 - 5.63444e16i) q^{73} -7.16955e16i q^{74} +(1.20525e16 + 1.16298e17i) q^{75} +6.05118e16 q^{76} +(5.66052e16 + 5.66052e16i) q^{77} +(-9.55806e16 + 9.55806e16i) q^{78} +4.85160e16i q^{79} +(-1.44235e16 - 3.02962e16i) q^{80} +5.92368e16 q^{81} +(2.29948e16 + 2.29948e16i) q^{82} +(-1.33052e16 + 1.33052e16i) q^{83} -1.59987e17i q^{84} +(1.14652e17 - 3.23022e17i) q^{85} -1.57163e16 q^{86} +(-2.99902e17 - 2.99902e17i) q^{87} +(-6.74497e16 + 6.74497e16i) q^{88} +4.56446e17i q^{89} +(-3.67849e17 - 1.30563e17i) q^{90} -4.85108e17 q^{91} +(-1.30649e17 - 1.30649e17i) q^{92} +(-5.75886e17 + 5.75886e17i) q^{93} -3.60330e17i q^{94} +(8.14140e17 - 3.87598e17i) q^{95} +1.90637e17 q^{96} +(6.31856e17 + 6.31856e17i) q^{97} +(-1.08764e16 + 1.08764e16i) q^{98} +1.10963e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2560 q^{2} + 3230 q^{3} - 1436130 q^{5} - 1653760 q^{6} - 71828530 q^{7} + 335544320 q^{8} + 280000000 q^{10} - 4684617380 q^{11} + 423362560 q^{12} - 11858528670 q^{13} + 132580211870 q^{15} - 171798691840 q^{16} + 57425096770 q^{17} - 314336842240 q^{18} + 44876431360 q^{20} + 2599949895020 q^{21} + 1199262049280 q^{22} - 2409849379970 q^{23} - 9628701268750 q^{25} + 6071566679040 q^{26} + 10319468097200 q^{27} + 9414709084160 q^{28} - 42920067333120 q^{30} + 44076891672220 q^{31} + 43980465111040 q^{32} - 91028207725540 q^{33} - 92680242801650 q^{35} + 160940463226880 q^{36} + 285126548071770 q^{37} - 268015571763200 q^{38} - 59676892856320 q^{40} + 223001245455820 q^{41} - 665587173125120 q^{42} - 674098663802370 q^{43} + 13\!\cdots\!80 q^{45}+ \cdots + 14\!\cdots\!40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −256.000 256.000i −0.500000 0.500000i
\(3\) 21673.0 21673.0i 1.10110 1.10110i 0.106822 0.994278i \(-0.465932\pi\)
0.994278 0.106822i \(-0.0340676\pi\)
\(4\) 131072.i 0.500000i
\(5\) 839560. + 1.76347e6i 0.429855 + 0.902898i
\(6\) −1.10966e7 −1.10110
\(7\) −2.81596e7 2.81596e7i −0.697821 0.697821i 0.266119 0.963940i \(-0.414259\pi\)
−0.963940 + 0.266119i \(0.914259\pi\)
\(8\) 3.35544e7 3.35544e7i 0.250000 0.250000i
\(9\) 5.52014e8i 1.42484i
\(10\) 2.36522e8 6.66376e8i 0.236522 0.666376i
\(11\) −2.01016e9 −0.852502 −0.426251 0.904605i \(-0.640166\pi\)
−0.426251 + 0.904605i \(0.640166\pi\)
\(12\) 2.84072e9 + 2.84072e9i 0.550550 + 0.550550i
\(13\) 8.61354e9 8.61354e9i 0.812253 0.812253i −0.172718 0.984971i \(-0.555255\pi\)
0.984971 + 0.172718i \(0.0552549\pi\)
\(14\) 1.44177e10i 0.697821i
\(15\) 5.64154e10 + 2.00239e10i 1.46749 + 0.520868i
\(16\) −1.71799e10 −0.250000
\(17\) −1.24094e11 1.24094e11i −1.04643 1.04643i −0.998868 0.0475664i \(-0.984853\pi\)
−0.0475664 0.998868i \(-0.515147\pi\)
\(18\) −1.41316e11 + 1.41316e11i −0.712422 + 0.712422i
\(19\) 4.61669e11i 1.43070i −0.698767 0.715349i \(-0.746268\pi\)
0.698767 0.715349i \(-0.253732\pi\)
\(20\) −2.31142e11 + 1.10043e11i −0.451449 + 0.214927i
\(21\) −1.22060e12 −1.53674
\(22\) 5.14600e11 + 5.14600e11i 0.426251 + 0.426251i
\(23\) −9.96769e11 + 9.96769e11i −0.553406 + 0.553406i −0.927422 0.374016i \(-0.877981\pi\)
0.374016 + 0.927422i \(0.377981\pi\)
\(24\) 1.45445e12i 0.550550i
\(25\) −2.40498e12 + 2.96108e12i −0.630450 + 0.776230i
\(26\) −4.41013e12 −0.812253
\(27\) −3.56723e12 3.56723e12i −0.467796 0.467796i
\(28\) 3.69094e12 3.69094e12i 0.348911 0.348911i
\(29\) 1.38376e13i 0.953848i −0.878944 0.476924i \(-0.841752\pi\)
0.878944 0.476924i \(-0.158248\pi\)
\(30\) −9.31622e12 1.95685e13i −0.473313 0.994181i
\(31\) −2.65717e13 −1.00499 −0.502497 0.864579i \(-0.667585\pi\)
−0.502497 + 0.864579i \(0.667585\pi\)
\(32\) 4.39805e12 + 4.39805e12i 0.125000 + 0.125000i
\(33\) −4.35660e13 + 4.35660e13i −0.938691 + 0.938691i
\(34\) 6.35364e13i 1.04643i
\(35\) 2.60170e13 7.33004e13i 0.330100 0.930024i
\(36\) 7.23536e13 0.712422
\(37\) 1.40030e14 + 1.40030e14i 1.07747 + 1.07747i 0.996735 + 0.0807371i \(0.0257274\pi\)
0.0807371 + 0.996735i \(0.474273\pi\)
\(38\) −1.18187e14 + 1.18187e14i −0.715349 + 0.715349i
\(39\) 3.73362e14i 1.78875i
\(40\) 8.73433e13 + 3.10014e13i 0.333188 + 0.118261i
\(41\) −8.98236e13 −0.274370 −0.137185 0.990545i \(-0.543805\pi\)
−0.137185 + 0.990545i \(0.543805\pi\)
\(42\) 3.12475e14 + 3.12475e14i 0.768372 + 0.768372i
\(43\) 3.06959e13 3.06959e13i 0.0610752 0.0610752i −0.675909 0.736985i \(-0.736249\pi\)
0.736985 + 0.675909i \(0.236249\pi\)
\(44\) 2.63475e14i 0.426251i
\(45\) 9.73461e14 4.63449e14i 1.28649 0.612476i
\(46\) 5.10346e14 0.553406
\(47\) 7.03769e14 + 7.03769e14i 0.628853 + 0.628853i 0.947780 0.318926i \(-0.103322\pi\)
−0.318926 + 0.947780i \(0.603322\pi\)
\(48\) −3.72339e14 + 3.72339e14i −0.275275 + 0.275275i
\(49\) 4.24859e13i 0.0260904i
\(50\) 1.37371e15 1.42363e14i 0.703340 0.0728901i
\(51\) −5.37899e15 −2.30446
\(52\) 1.12899e15 + 1.12899e15i 0.406127 + 0.406127i
\(53\) −1.18441e15 + 1.18441e15i −0.358939 + 0.358939i −0.863422 0.504483i \(-0.831683\pi\)
0.504483 + 0.863422i \(0.331683\pi\)
\(54\) 1.82642e15i 0.467796i
\(55\) −1.68765e15 3.54486e15i −0.366452 0.769723i
\(56\) −1.88976e15 −0.348911
\(57\) −1.00057e16 1.00057e16i −1.57534 1.57534i
\(58\) −3.54243e15 + 3.54243e15i −0.476924 + 0.476924i
\(59\) 1.13913e16i 1.31494i −0.753481 0.657470i \(-0.771627\pi\)
0.753481 0.657470i \(-0.228373\pi\)
\(60\) −2.62458e15 + 7.39448e15i −0.260434 + 0.733747i
\(61\) 1.79758e16 1.53716 0.768579 0.639754i \(-0.220964\pi\)
0.768579 + 0.639754i \(0.220964\pi\)
\(62\) 6.80234e15 + 6.80234e15i 0.502497 + 0.502497i
\(63\) −1.55445e16 + 1.55445e16i −0.994287 + 0.994287i
\(64\) 2.25180e15i 0.125000i
\(65\) 2.24213e16 + 7.95816e15i 1.08253 + 0.384231i
\(66\) 2.23058e16 0.938691
\(67\) −3.42502e16 3.42502e16i −1.25890 1.25890i −0.951620 0.307276i \(-0.900583\pi\)
−0.307276 0.951620i \(-0.599417\pi\)
\(68\) 1.62653e16 1.62653e16i 0.523217 0.523217i
\(69\) 4.32059e16i 1.21871i
\(70\) −2.54253e16 + 1.21045e16i −0.630062 + 0.299962i
\(71\) 1.84976e16 0.403451 0.201726 0.979442i \(-0.435345\pi\)
0.201726 + 0.979442i \(0.435345\pi\)
\(72\) −1.85225e16 1.85225e16i −0.356211 0.356211i
\(73\) 5.63444e16 5.63444e16i 0.957074 0.957074i −0.0420421 0.999116i \(-0.513386\pi\)
0.999116 + 0.0420421i \(0.0133864\pi\)
\(74\) 7.16955e16i 1.07747i
\(75\) 1.20525e16 + 1.16298e17i 0.160519 + 1.54890i
\(76\) 6.05118e16 0.715349
\(77\) 5.66052e16 + 5.66052e16i 0.594895 + 0.594895i
\(78\) −9.55806e16 + 9.55806e16i −0.894373 + 0.894373i
\(79\) 4.85160e16i 0.404801i 0.979303 + 0.202400i \(0.0648742\pi\)
−0.979303 + 0.202400i \(0.935126\pi\)
\(80\) −1.44235e16 3.02962e16i −0.107464 0.225725i
\(81\) 5.92368e16 0.394663
\(82\) 2.29948e16 + 2.29948e16i 0.137185 + 0.137185i
\(83\) −1.33052e16 + 1.33052e16i −0.0711738 + 0.0711738i −0.741798 0.670624i \(-0.766026\pi\)
0.670624 + 0.741798i \(0.266026\pi\)
\(84\) 1.59987e17i 0.768372i
\(85\) 1.14652e17 3.23022e17i 0.495009 1.39464i
\(86\) −1.57163e16 −0.0610752
\(87\) −2.99902e17 2.99902e17i −1.05028 1.05028i
\(88\) −6.74497e16 + 6.74497e16i −0.213126 + 0.213126i
\(89\) 4.56446e17i 1.30280i 0.758733 + 0.651402i \(0.225819\pi\)
−0.758733 + 0.651402i \(0.774181\pi\)
\(90\) −3.67849e17 1.30563e17i −0.949483 0.337007i
\(91\) −4.85108e17 −1.13362
\(92\) −1.30649e17 1.30649e17i −0.276703 0.276703i
\(93\) −5.75886e17 + 5.75886e17i −1.10660 + 1.10660i
\(94\) 3.60330e17i 0.628853i
\(95\) 8.14140e17 3.87598e17i 1.29177 0.614992i
\(96\) 1.90637e17 0.275275
\(97\) 6.31856e17 + 6.31856e17i 0.831136 + 0.831136i 0.987672 0.156536i \(-0.0500327\pi\)
−0.156536 + 0.987672i \(0.550033\pi\)
\(98\) −1.08764e16 + 1.08764e16i −0.0130452 + 0.0130452i
\(99\) 1.10963e18i 1.21468i
\(100\) −3.88115e17 3.15225e17i −0.388115 0.315225i
\(101\) −4.70951e17 −0.430609 −0.215305 0.976547i \(-0.569074\pi\)
−0.215305 + 0.976547i \(0.569074\pi\)
\(102\) 1.37702e18 + 1.37702e18i 1.15223 + 1.15223i
\(103\) 1.00486e18 1.00486e18i 0.770145 0.770145i −0.207987 0.978132i \(-0.566691\pi\)
0.978132 + 0.207987i \(0.0666911\pi\)
\(104\) 5.78045e17i 0.406127i
\(105\) −1.02477e18 2.15250e18i −0.660576 1.38752i
\(106\) 6.06419e17 0.358939
\(107\) −2.70418e17 2.70418e17i −0.147089 0.147089i 0.629727 0.776816i \(-0.283167\pi\)
−0.776816 + 0.629727i \(0.783167\pi\)
\(108\) 4.67563e17 4.67563e17i 0.233898 0.233898i
\(109\) 7.79245e17i 0.358786i −0.983777 0.179393i \(-0.942587\pi\)
0.983777 0.179393i \(-0.0574134\pi\)
\(110\) −4.75446e17 + 1.33952e18i −0.201635 + 0.568088i
\(111\) 6.06974e18 2.37281
\(112\) 4.83778e17 + 4.83778e17i 0.174455 + 0.174455i
\(113\) −1.20994e17 + 1.20994e17i −0.0402772 + 0.0402772i −0.726959 0.686681i \(-0.759067\pi\)
0.686681 + 0.726959i \(0.259067\pi\)
\(114\) 5.12293e18i 1.57534i
\(115\) −2.59462e18 9.20928e17i −0.737554 0.261785i
\(116\) 1.81372e18 0.476924
\(117\) −4.75479e18 4.75479e18i −1.15733 1.15733i
\(118\) −2.91618e18 + 2.91618e18i −0.657470 + 0.657470i
\(119\) 6.98890e18i 1.46045i
\(120\) 2.56488e18 1.22110e18i 0.497091 0.236657i
\(121\) −1.51919e18 −0.273240
\(122\) −4.60180e18 4.60180e18i −0.768579 0.768579i
\(123\) −1.94674e18 + 1.94674e18i −0.302108 + 0.302108i
\(124\) 3.48280e18i 0.502497i
\(125\) −7.24091e18 1.75510e18i −0.971858 0.235566i
\(126\) 7.95878e18 0.994287
\(127\) −8.83476e18 8.83476e18i −1.02792 1.02792i −0.999599 0.0283254i \(-0.990983\pi\)
−0.0283254 0.999599i \(-0.509017\pi\)
\(128\) −5.76461e17 + 5.76461e17i −0.0625000 + 0.0625000i
\(129\) 1.33054e18i 0.134500i
\(130\) −3.70257e18 7.77715e18i −0.349151 0.733382i
\(131\) 1.51094e19 1.32986 0.664931 0.746905i \(-0.268461\pi\)
0.664931 + 0.746905i \(0.268461\pi\)
\(132\) −5.71029e18 5.71029e18i −0.469345 0.469345i
\(133\) −1.30004e19 + 1.30004e19i −0.998372 + 0.998372i
\(134\) 1.75361e19i 1.25890i
\(135\) 3.29581e18 9.28561e18i 0.221288 0.623457i
\(136\) −8.32784e18 −0.523217
\(137\) 2.18638e19 + 2.18638e19i 1.28600 + 1.28600i 0.937195 + 0.348806i \(0.113413\pi\)
0.348806 + 0.937195i \(0.386587\pi\)
\(138\) 1.10607e19 1.10607e19i 0.609356 0.609356i
\(139\) 9.45473e18i 0.488108i −0.969762 0.244054i \(-0.921523\pi\)
0.969762 0.244054i \(-0.0784774\pi\)
\(140\) 9.60763e18 + 3.41010e18i 0.465012 + 0.165050i
\(141\) 3.05055e19 1.38486
\(142\) −4.73540e18 4.73540e18i −0.201726 0.201726i
\(143\) −1.73146e19 + 1.73146e19i −0.692448 + 0.692448i
\(144\) 9.48353e18i 0.356211i
\(145\) 2.44023e19 1.16175e19i 0.861228 0.410016i
\(146\) −2.88484e19 −0.957074
\(147\) −9.20796e17 9.20796e17i −0.0287281 0.0287281i
\(148\) −1.83540e19 + 1.83540e19i −0.538736 + 0.538736i
\(149\) 7.57728e18i 0.209333i −0.994507 0.104666i \(-0.966623\pi\)
0.994507 0.104666i \(-0.0333775\pi\)
\(150\) 2.66869e19 3.28578e19i 0.694189 0.854707i
\(151\) 4.54551e19 1.11376 0.556878 0.830594i \(-0.311999\pi\)
0.556878 + 0.830594i \(0.311999\pi\)
\(152\) −1.54910e19 1.54910e19i −0.357674 0.357674i
\(153\) −6.85019e19 + 6.85019e19i −1.49101 + 1.49101i
\(154\) 2.89819e19i 0.594895i
\(155\) −2.23085e19 4.68584e19i −0.432001 0.907407i
\(156\) 4.89373e19 0.894373
\(157\) 3.39679e19 + 3.39679e19i 0.586099 + 0.586099i 0.936573 0.350473i \(-0.113979\pi\)
−0.350473 + 0.936573i \(0.613979\pi\)
\(158\) 1.24201e19 1.24201e19i 0.202400 0.202400i
\(159\) 5.13395e19i 0.790455i
\(160\) −4.06341e18 + 1.14483e19i −0.0591304 + 0.166594i
\(161\) 5.61373e19 0.772358
\(162\) −1.51646e19 1.51646e19i −0.197332 0.197332i
\(163\) 2.84690e19 2.84690e19i 0.350497 0.350497i −0.509798 0.860294i \(-0.670280\pi\)
0.860294 + 0.509798i \(0.170280\pi\)
\(164\) 1.17734e19i 0.137185i
\(165\) −1.13404e20 4.02512e19i −1.25104 0.444041i
\(166\) 6.81229e18 0.0711738
\(167\) −3.24829e19 3.24829e19i −0.321519 0.321519i 0.527831 0.849350i \(-0.323006\pi\)
−0.849350 + 0.527831i \(0.823006\pi\)
\(168\) −4.09567e19 + 4.09567e19i −0.384186 + 0.384186i
\(169\) 3.59308e19i 0.319511i
\(170\) −1.12045e20 + 5.33426e19i −0.944824 + 0.449815i
\(171\) −2.54847e20 −2.03852
\(172\) 4.02338e18 + 4.02338e18i 0.0305376 + 0.0305376i
\(173\) 4.31333e19 4.31333e19i 0.310741 0.310741i −0.534456 0.845196i \(-0.679483\pi\)
0.845196 + 0.534456i \(0.179483\pi\)
\(174\) 1.53550e20i 1.05028i
\(175\) 1.51106e20 1.56598e19i 0.981611 0.101729i
\(176\) 3.45342e19 0.213126
\(177\) −2.46884e20 2.46884e20i −1.44788 1.44788i
\(178\) 1.16850e20 1.16850e20i 0.651402 0.651402i
\(179\) 6.14185e19i 0.325553i 0.986663 + 0.162777i \(0.0520450\pi\)
−0.986663 + 0.162777i \(0.947955\pi\)
\(180\) 6.07452e19 + 1.27594e20i 0.306238 + 0.643245i
\(181\) −1.18309e20 −0.567430 −0.283715 0.958909i \(-0.591567\pi\)
−0.283715 + 0.958909i \(0.591567\pi\)
\(182\) 1.24188e20 + 1.24188e20i 0.566808 + 0.566808i
\(183\) 3.89588e20 3.89588e20i 1.69257 1.69257i
\(184\) 6.68921e19i 0.276703i
\(185\) −1.29376e20 + 3.64503e20i −0.509691 + 1.43600i
\(186\) 2.94854e20 1.10660
\(187\) 2.49449e20 + 2.49449e20i 0.892088 + 0.892088i
\(188\) −9.22444e19 + 9.22444e19i −0.314427 + 0.314427i
\(189\) 2.00903e20i 0.652877i
\(190\) −3.07645e20 1.09195e20i −0.953383 0.338391i
\(191\) 3.91502e20 1.15727 0.578634 0.815588i \(-0.303586\pi\)
0.578634 + 0.815588i \(0.303586\pi\)
\(192\) −4.88032e19 4.88032e19i −0.137638 0.137638i
\(193\) −1.22942e20 + 1.22942e20i −0.330891 + 0.330891i −0.852925 0.522034i \(-0.825174\pi\)
0.522034 + 0.852925i \(0.325174\pi\)
\(194\) 3.23510e20i 0.831136i
\(195\) 6.58413e20 3.13460e20i 1.61505 0.768901i
\(196\) 5.56872e18 0.0130452
\(197\) 1.46541e20 + 1.46541e20i 0.327917 + 0.327917i 0.851794 0.523877i \(-0.175515\pi\)
−0.523877 + 0.851794i \(0.675515\pi\)
\(198\) 2.84066e20 2.84066e20i 0.607342 0.607342i
\(199\) 6.13745e20i 1.25404i −0.779005 0.627018i \(-0.784275\pi\)
0.779005 0.627018i \(-0.215725\pi\)
\(200\) 1.86599e19 + 1.80055e20i 0.0364450 + 0.351670i
\(201\) −1.48461e21 −2.77234
\(202\) 1.20563e20 + 1.20563e20i 0.215305 + 0.215305i
\(203\) −3.89662e20 + 3.89662e20i −0.665616 + 0.665616i
\(204\) 7.05035e20i 1.15223i
\(205\) −7.54123e19 1.58402e20i −0.117939 0.247728i
\(206\) −5.14491e20 −0.770145
\(207\) 5.50231e20 + 5.50231e20i 0.788518 + 0.788518i
\(208\) −1.47979e20 + 1.47979e20i −0.203063 + 0.203063i
\(209\) 9.28026e20i 1.21967i
\(210\) −2.88699e20 + 8.13382e20i −0.363473 + 1.02405i
\(211\) −3.98223e20 −0.480379 −0.240190 0.970726i \(-0.577210\pi\)
−0.240190 + 0.970726i \(0.577210\pi\)
\(212\) −1.55243e20 1.55243e20i −0.179469 0.179469i
\(213\) 4.00899e20 4.00899e20i 0.444241 0.444241i
\(214\) 1.38454e20i 0.147089i
\(215\) 7.99025e19 + 2.83604e19i 0.0813981 + 0.0288912i
\(216\) −2.39392e20 −0.233898
\(217\) 7.48247e20 + 7.48247e20i 0.701306 + 0.701306i
\(218\) −1.99487e20 + 1.99487e20i −0.179393 + 0.179393i
\(219\) 2.44230e21i 2.10767i
\(220\) 4.64631e20 2.21203e20i 0.384861 0.183226i
\(221\) −2.13779e21 −1.69994
\(222\) −1.55385e21 1.55385e21i −1.18641 1.18641i
\(223\) −1.16848e20 + 1.16848e20i −0.0856793 + 0.0856793i −0.748648 0.662968i \(-0.769296\pi\)
0.662968 + 0.748648i \(0.269296\pi\)
\(224\) 2.47695e20i 0.174455i
\(225\) 1.63456e21 + 1.32758e21i 1.10601 + 0.898293i
\(226\) 6.19491e19 0.0402772
\(227\) 7.21268e20 + 7.21268e20i 0.450676 + 0.450676i 0.895579 0.444903i \(-0.146762\pi\)
−0.444903 + 0.895579i \(0.646762\pi\)
\(228\) 1.31147e21 1.31147e21i 0.787671 0.787671i
\(229\) 3.25492e21i 1.87941i −0.341987 0.939705i \(-0.611100\pi\)
0.341987 0.939705i \(-0.388900\pi\)
\(230\) 4.28466e20 + 8.99981e20i 0.237884 + 0.499670i
\(231\) 2.45361e21 1.31008
\(232\) −4.64313e20 4.64313e20i −0.238462 0.238462i
\(233\) −2.39551e21 + 2.39551e21i −1.18357 + 1.18357i −0.204759 + 0.978812i \(0.565641\pi\)
−0.978812 + 0.204759i \(0.934359\pi\)
\(234\) 2.43445e21i 1.15733i
\(235\) −6.50221e20 + 1.83193e21i −0.297475 + 0.838106i
\(236\) 1.49308e21 0.657470
\(237\) 1.05149e21 + 1.05149e21i 0.445726 + 0.445726i
\(238\) 1.78916e21 1.78916e21i 0.730224 0.730224i
\(239\) 2.96344e21i 1.16470i 0.812937 + 0.582351i \(0.197867\pi\)
−0.812937 + 0.582351i \(0.802133\pi\)
\(240\) −9.69210e20 3.44008e20i −0.366874 0.130217i
\(241\) 3.77663e20 0.137705 0.0688527 0.997627i \(-0.478066\pi\)
0.0688527 + 0.997627i \(0.478066\pi\)
\(242\) 3.88912e20 + 3.88912e20i 0.136620 + 0.136620i
\(243\) 2.66585e21 2.66585e21i 0.902360 0.902360i
\(244\) 2.35612e21i 0.768579i
\(245\) 7.49228e19 3.56695e19i 0.0235570 0.0112151i
\(246\) 9.96733e20 0.302108
\(247\) −3.97660e21 3.97660e21i −1.16209 1.16209i
\(248\) −8.91597e20 + 8.91597e20i −0.251248 + 0.251248i
\(249\) 5.76728e20i 0.156739i
\(250\) 1.40437e21 + 2.30298e21i 0.368146 + 0.603712i
\(251\) 8.95398e20 0.226440 0.113220 0.993570i \(-0.463884\pi\)
0.113220 + 0.993570i \(0.463884\pi\)
\(252\) −2.03745e21 2.03745e21i −0.497143 0.497143i
\(253\) 2.00366e21 2.00366e21i 0.471780 0.471780i
\(254\) 4.52339e21i 1.02792i
\(255\) −4.51598e21 9.48570e21i −0.990583 2.08069i
\(256\) 2.95148e20 0.0625000
\(257\) 2.44830e21 + 2.44830e21i 0.500571 + 0.500571i 0.911615 0.411044i \(-0.134836\pi\)
−0.411044 + 0.911615i \(0.634836\pi\)
\(258\) −3.40619e20 + 3.40619e20i −0.0672499 + 0.0672499i
\(259\) 7.88639e21i 1.50377i
\(260\) −1.04309e21 + 2.93881e21i −0.192116 + 0.541266i
\(261\) −7.63856e21 −1.35909
\(262\) −3.86801e21 3.86801e21i −0.664931 0.664931i
\(263\) −4.66735e21 + 4.66735e21i −0.775298 + 0.775298i −0.979027 0.203729i \(-0.934694\pi\)
0.203729 + 0.979027i \(0.434694\pi\)
\(264\) 2.92367e21i 0.469345i
\(265\) −3.08307e21 1.09429e21i −0.478377 0.169794i
\(266\) 6.65621e21 0.998372
\(267\) 9.89253e21 + 9.89253e21i 1.43452 + 1.43452i
\(268\) 4.48924e21 4.48924e21i 0.629448 0.629448i
\(269\) 1.31883e21i 0.178821i −0.995995 0.0894107i \(-0.971502\pi\)
0.995995 0.0894107i \(-0.0284984\pi\)
\(270\) −3.22084e21 + 1.53339e21i −0.422372 + 0.201084i
\(271\) 6.33690e20 0.0803810 0.0401905 0.999192i \(-0.487204\pi\)
0.0401905 + 0.999192i \(0.487204\pi\)
\(272\) 2.13193e21 + 2.13193e21i 0.261609 + 0.261609i
\(273\) −1.05137e22 + 1.05137e22i −1.24822 + 1.24822i
\(274\) 1.11943e22i 1.28600i
\(275\) 4.83438e21 5.95224e21i 0.537460 0.661738i
\(276\) −5.66308e21 −0.609356
\(277\) −6.90617e20 6.90617e20i −0.0719315 0.0719315i 0.670226 0.742157i \(-0.266197\pi\)
−0.742157 + 0.670226i \(0.766197\pi\)
\(278\) −2.42041e21 + 2.42041e21i −0.244054 + 0.244054i
\(279\) 1.46679e22i 1.43196i
\(280\) −1.58657e21 3.33254e21i −0.149981 0.315031i
\(281\) −4.40026e21 −0.402830 −0.201415 0.979506i \(-0.564554\pi\)
−0.201415 + 0.979506i \(0.564554\pi\)
\(282\) −7.80941e21 7.80941e21i −0.692431 0.692431i
\(283\) −5.52989e21 + 5.52989e21i −0.474939 + 0.474939i −0.903509 0.428569i \(-0.859018\pi\)
0.428569 + 0.903509i \(0.359018\pi\)
\(284\) 2.42452e21i 0.201726i
\(285\) 9.24442e21 2.60452e22i 0.745205 2.09954i
\(286\) 8.86506e21 0.692448
\(287\) 2.52940e21 + 2.52940e21i 0.191461 + 0.191461i
\(288\) 2.42778e21 2.42778e21i 0.178106 0.178106i
\(289\) 1.67358e22i 1.19005i
\(290\) −9.22106e21 3.27290e21i −0.635622 0.225606i
\(291\) 2.73884e22 1.83033
\(292\) 7.38518e21 + 7.38518e21i 0.478537 + 0.478537i
\(293\) 7.93653e21 7.93653e21i 0.498680 0.498680i −0.412347 0.911027i \(-0.635291\pi\)
0.911027 + 0.412347i \(0.135291\pi\)
\(294\) 4.71448e20i 0.0287281i
\(295\) 2.00883e22 9.56370e21i 1.18726 0.565233i
\(296\) 9.39727e21 0.538736
\(297\) 7.17068e21 + 7.17068e21i 0.398797 + 0.398797i
\(298\) −1.93978e21 + 1.93978e21i −0.104666 + 0.104666i
\(299\) 1.71714e22i 0.899012i
\(300\) −1.52435e22 + 1.57974e21i −0.774448 + 0.0802593i
\(301\) −1.72877e21 −0.0852392
\(302\) −1.16365e22 1.16365e22i −0.556878 0.556878i
\(303\) −1.02069e22 + 1.02069e22i −0.474144 + 0.474144i
\(304\) 7.93141e21i 0.357674i
\(305\) 1.50917e22 + 3.16998e22i 0.660755 + 1.38790i
\(306\) 3.50730e22 1.49101
\(307\) −2.17651e22 2.17651e22i −0.898495 0.898495i 0.0968085 0.995303i \(-0.469137\pi\)
−0.995303 + 0.0968085i \(0.969137\pi\)
\(308\) −7.41936e21 + 7.41936e21i −0.297447 + 0.297447i
\(309\) 4.35568e22i 1.69601i
\(310\) −6.28477e21 + 1.77067e22i −0.237703 + 0.669704i
\(311\) −1.64905e22 −0.605885 −0.302943 0.953009i \(-0.597969\pi\)
−0.302943 + 0.953009i \(0.597969\pi\)
\(312\) −1.25279e22 1.25279e22i −0.447186 0.447186i
\(313\) 8.39391e21 8.39391e21i 0.291116 0.291116i −0.546405 0.837521i \(-0.684004\pi\)
0.837521 + 0.546405i \(0.184004\pi\)
\(314\) 1.73915e22i 0.586099i
\(315\) −4.04628e22 1.43618e22i −1.32514 0.470341i
\(316\) −6.35909e21 −0.202400
\(317\) −1.53965e22 1.53965e22i −0.476310 0.476310i 0.427640 0.903949i \(-0.359345\pi\)
−0.903949 + 0.427640i \(0.859345\pi\)
\(318\) 1.31429e22 1.31429e22i 0.395228 0.395228i
\(319\) 2.78158e22i 0.813158i
\(320\) 3.97099e21 1.89052e21i 0.112862 0.0537318i
\(321\) −1.17215e22 −0.323921
\(322\) −1.43711e22 1.43711e22i −0.386179 0.386179i
\(323\) −5.72905e22 + 5.72905e22i −1.49713 + 1.49713i
\(324\) 7.76429e21i 0.197332i
\(325\) 4.79005e21 + 4.62208e22i 0.118410 + 1.14258i
\(326\) −1.45761e22 −0.350497
\(327\) −1.68885e22 1.68885e22i −0.395059 0.395059i
\(328\) −3.01398e21 + 3.01398e21i −0.0685924 + 0.0685924i
\(329\) 3.96357e22i 0.877655i
\(330\) 1.87271e22 + 3.93357e22i 0.403501 + 0.847542i
\(331\) −2.29878e22 −0.481998 −0.240999 0.970525i \(-0.577475\pi\)
−0.240999 + 0.970525i \(0.577475\pi\)
\(332\) −1.74395e21 1.74395e21i −0.0355869 0.0355869i
\(333\) 7.72986e22 7.72986e22i 1.53523 1.53523i
\(334\) 1.66312e22i 0.321519i
\(335\) 3.16442e22 8.91544e22i 0.595513 1.67780i
\(336\) 2.09698e22 0.384186
\(337\) 6.20976e22 + 6.20976e22i 1.10766 + 1.10766i 0.993458 + 0.114201i \(0.0364308\pi\)
0.114201 + 0.993458i \(0.463569\pi\)
\(338\) −9.19827e21 + 9.19827e21i −0.159756 + 0.159756i
\(339\) 5.24461e21i 0.0886985i
\(340\) 4.23391e22 + 1.50277e22i 0.697319 + 0.247504i
\(341\) 5.34132e22 0.856760
\(342\) 6.52410e22 + 6.52410e22i 1.01926 + 1.01926i
\(343\) −4.70519e22 + 4.70519e22i −0.716028 + 0.716028i
\(344\) 2.05997e21i 0.0305376i
\(345\) −7.61924e22 + 3.62739e22i −1.10037 + 0.523869i
\(346\) −2.20843e22 −0.310741
\(347\) −3.20550e22 3.20550e22i −0.439471 0.439471i 0.452363 0.891834i \(-0.350581\pi\)
−0.891834 + 0.452363i \(0.850581\pi\)
\(348\) 3.93088e22 3.93088e22i 0.525141 0.525141i
\(349\) 1.42412e23i 1.85403i −0.375020 0.927017i \(-0.622364\pi\)
0.375020 0.927017i \(-0.377636\pi\)
\(350\) −4.26921e22 3.46743e22i −0.541670 0.439941i
\(351\) −6.14529e22 −0.759938
\(352\) −8.84076e21 8.84076e21i −0.106563 0.106563i
\(353\) 9.43648e22 9.43648e22i 1.10876 1.10876i 0.115447 0.993314i \(-0.463170\pi\)
0.993314 0.115447i \(-0.0368301\pi\)
\(354\) 1.26404e23i 1.44788i
\(355\) 1.55299e22 + 3.26201e22i 0.173426 + 0.364276i
\(356\) −5.98272e22 −0.651402
\(357\) 1.51470e23 + 1.51470e23i 1.60810 + 1.60810i
\(358\) 1.57231e22 1.57231e22i 0.162777 0.162777i
\(359\) 5.14231e21i 0.0519168i −0.999663 0.0259584i \(-0.991736\pi\)
0.999663 0.0259584i \(-0.00826374\pi\)
\(360\) 1.71132e22 4.82147e22i 0.168503 0.474741i
\(361\) −1.09011e23 −1.04690
\(362\) 3.02872e22 + 3.02872e22i 0.283715 + 0.283715i
\(363\) −3.29253e22 + 3.29253e22i −0.300864 + 0.300864i
\(364\) 6.35841e22i 0.566808i
\(365\) 1.46666e23 + 5.20574e22i 1.27554 + 0.452737i
\(366\) −1.99469e23 −1.69257
\(367\) 1.00104e23 + 1.00104e23i 0.828817 + 0.828817i 0.987353 0.158536i \(-0.0506775\pi\)
−0.158536 + 0.987353i \(0.550678\pi\)
\(368\) 1.71244e22 1.71244e22i 0.138352 0.138352i
\(369\) 4.95839e22i 0.390934i
\(370\) 1.26433e23 6.01926e22i 0.972848 0.463157i
\(371\) 6.67052e22 0.500950
\(372\) −7.54826e22 7.54826e22i −0.553299 0.553299i
\(373\) −8.80250e22 + 8.80250e22i −0.629835 + 0.629835i −0.948026 0.318192i \(-0.896924\pi\)
0.318192 + 0.948026i \(0.396924\pi\)
\(374\) 1.27718e23i 0.892088i
\(375\) −1.94970e23 + 1.18894e23i −1.32950 + 0.810732i
\(376\) 4.72291e22 0.314427
\(377\) −1.19191e23 1.19191e23i −0.774767 0.774767i
\(378\) 5.14313e22 5.14313e22i 0.326438 0.326438i
\(379\) 2.05289e22i 0.127237i 0.997974 + 0.0636185i \(0.0202641\pi\)
−0.997974 + 0.0636185i \(0.979736\pi\)
\(380\) 5.08033e22 + 1.06711e23i 0.307496 + 0.645887i
\(381\) −3.82951e23 −2.26370
\(382\) −1.00225e23 1.00225e23i −0.578634 0.578634i
\(383\) 2.34489e23 2.34489e23i 1.32231 1.32231i 0.410414 0.911899i \(-0.365384\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(384\) 2.49872e22i 0.137638i
\(385\) −5.22983e22 + 1.47345e23i −0.281411 + 0.792847i
\(386\) 6.29464e22 0.330891
\(387\) −1.69446e22 1.69446e22i −0.0870226 0.0870226i
\(388\) −8.28186e22 + 8.28186e22i −0.415568 + 0.415568i
\(389\) 1.96355e23i 0.962710i −0.876526 0.481355i \(-0.840145\pi\)
0.876526 0.481355i \(-0.159855\pi\)
\(390\) −2.48800e23 8.83082e22i −1.19198 0.423077i
\(391\) 2.47387e23 1.15821
\(392\) −1.42559e21 1.42559e21i −0.00652260 0.00652260i
\(393\) 3.27466e23 3.27466e23i 1.46431 1.46431i
\(394\) 7.50292e22i 0.327917i
\(395\) −8.55566e22 + 4.07321e22i −0.365494 + 0.174005i
\(396\) −1.45442e23 −0.607342
\(397\) −1.56434e23 1.56434e23i −0.638581 0.638581i 0.311625 0.950205i \(-0.399127\pi\)
−0.950205 + 0.311625i \(0.899127\pi\)
\(398\) −1.57119e23 + 1.57119e23i −0.627018 + 0.627018i
\(399\) 5.63515e23i 2.19862i
\(400\) 4.13172e22 5.08710e22i 0.157612 0.194057i
\(401\) 2.24216e23 0.836309 0.418154 0.908376i \(-0.362677\pi\)
0.418154 + 0.908376i \(0.362677\pi\)
\(402\) 3.80059e23 + 3.80059e23i 1.38617 + 1.38617i
\(403\) −2.28876e23 + 2.28876e23i −0.816310 + 0.816310i
\(404\) 6.17285e22i 0.215305i
\(405\) 4.97328e22 + 1.04462e23i 0.169648 + 0.356340i
\(406\) 1.99507e23 0.665616
\(407\) −2.81483e23 2.81483e23i −0.918548 0.918548i
\(408\) −1.80489e23 + 1.80489e23i −0.576115 + 0.576115i
\(409\) 1.24937e23i 0.390104i 0.980793 + 0.195052i \(0.0624876\pi\)
−0.980793 + 0.195052i \(0.937512\pi\)
\(410\) −2.12452e22 + 5.98563e22i −0.0648943 + 0.182833i
\(411\) 9.47708e23 2.83203
\(412\) 1.31710e23 + 1.31710e23i 0.385072 + 0.385072i
\(413\) −3.20775e23 + 3.20775e23i −0.917594 + 0.917594i
\(414\) 2.81718e23i 0.788518i
\(415\) −3.46340e22 1.22929e22i −0.0948571 0.0336683i
\(416\) 7.57655e22 0.203063
\(417\) −2.04912e23 2.04912e23i −0.537456 0.537456i
\(418\) 2.37575e23 2.37575e23i 0.609837 0.609837i
\(419\) 4.44206e23i 1.11599i −0.829846 0.557993i \(-0.811572\pi\)
0.829846 0.557993i \(-0.188428\pi\)
\(420\) 2.82133e23 1.34319e23i 0.693761 0.330288i
\(421\) −3.69953e23 −0.890446 −0.445223 0.895420i \(-0.646876\pi\)
−0.445223 + 0.895420i \(0.646876\pi\)
\(422\) 1.01945e23 + 1.01945e23i 0.240190 + 0.240190i
\(423\) 3.88490e23 3.88490e23i 0.896018 0.896018i
\(424\) 7.94846e22i 0.179469i
\(425\) 6.65898e23 6.90098e22i 1.47200 0.152549i
\(426\) −2.05260e23 −0.444241
\(427\) −5.06191e23 5.06191e23i −1.07266 1.07266i
\(428\) 3.54442e22 3.54442e22i 0.0735447 0.0735447i
\(429\) 7.50516e23i 1.52491i
\(430\) −1.31948e22 2.77153e22i −0.0262535 0.0551447i
\(431\) −3.27398e23 −0.637942 −0.318971 0.947765i \(-0.603337\pi\)
−0.318971 + 0.947765i \(0.603337\pi\)
\(432\) 6.12845e22 + 6.12845e22i 0.116949 + 0.116949i
\(433\) −3.28782e23 + 3.28782e23i −0.614493 + 0.614493i −0.944113 0.329621i \(-0.893079\pi\)
0.329621 + 0.944113i \(0.393079\pi\)
\(434\) 3.83103e23i 0.701306i
\(435\) 2.77083e23 7.80655e23i 0.496829 1.39977i
\(436\) 1.02137e23 0.179393
\(437\) 4.60177e23 + 4.60177e23i 0.791757 + 0.791757i
\(438\) −6.25229e23 + 6.25229e23i −1.05383 + 1.05383i
\(439\) 2.94245e23i 0.485880i −0.970041 0.242940i \(-0.921888\pi\)
0.970041 0.242940i \(-0.0781118\pi\)
\(440\) −1.75574e23 6.23176e22i −0.284044 0.100818i
\(441\) −2.34528e22 −0.0371747
\(442\) 5.47273e23 + 5.47273e23i 0.849970 + 0.849970i
\(443\) −8.40443e23 + 8.40443e23i −1.27901 + 1.27901i −0.337792 + 0.941221i \(0.609680\pi\)
−0.941221 + 0.337792i \(0.890320\pi\)
\(444\) 7.95573e23i 1.18641i
\(445\) −8.04929e23 + 3.83213e23i −1.17630 + 0.560016i
\(446\) 5.98259e22 0.0856793
\(447\) −1.64222e23 1.64222e23i −0.230496 0.230496i
\(448\) −6.34098e22 + 6.34098e22i −0.0872277 + 0.0872277i
\(449\) 4.24066e23i 0.571764i −0.958265 0.285882i \(-0.907714\pi\)
0.958265 0.285882i \(-0.0922865\pi\)
\(450\) −7.85866e22 7.58307e23i −0.103857 1.00215i
\(451\) 1.80560e23 0.233901
\(452\) −1.58590e22 1.58590e22i −0.0201386 0.0201386i
\(453\) 9.85146e23 9.85146e23i 1.22636 1.22636i
\(454\) 3.69289e23i 0.450676i
\(455\) −4.07277e23 8.55475e23i −0.487290 1.02354i
\(456\) −6.71473e23 −0.787671
\(457\) −9.31623e23 9.31623e23i −1.07151 1.07151i −0.997238 0.0742673i \(-0.976338\pi\)
−0.0742673 0.997238i \(-0.523662\pi\)
\(458\) −8.33260e23 + 8.33260e23i −0.939705 + 0.939705i
\(459\) 8.85346e23i 0.979036i
\(460\) 1.20708e23 3.40082e23i 0.130893 0.368777i
\(461\) 1.99127e23 0.211749 0.105874 0.994380i \(-0.466236\pi\)
0.105874 + 0.994380i \(0.466236\pi\)
\(462\) −6.28123e23 6.28123e23i −0.655039 0.655039i
\(463\) −1.39613e23 + 1.39613e23i −0.142789 + 0.142789i −0.774888 0.632099i \(-0.782194\pi\)
0.632099 + 0.774888i \(0.282194\pi\)
\(464\) 2.37728e23i 0.238462i
\(465\) −1.49905e24 5.32069e23i −1.47482 0.523469i
\(466\) 1.22650e24 1.18357
\(467\) 8.53068e23 + 8.53068e23i 0.807480 + 0.807480i 0.984252 0.176772i \(-0.0565656\pi\)
−0.176772 + 0.984252i \(0.556566\pi\)
\(468\) 6.23220e23 6.23220e23i 0.578667 0.578667i
\(469\) 1.92895e24i 1.75697i
\(470\) 6.35432e23 3.02518e23i 0.567790 0.270316i
\(471\) 1.47237e24 1.29071
\(472\) −3.82229e23 3.82229e23i −0.328735 0.328735i
\(473\) −6.17036e22 + 6.17036e22i −0.0520668 + 0.0520668i
\(474\) 5.38360e23i 0.445726i
\(475\) 1.36704e24 + 1.11030e24i 1.11055 + 0.901983i
\(476\) −9.16050e23 −0.730224
\(477\) 6.53812e23 + 6.53812e23i 0.511432 + 0.511432i
\(478\) 7.58641e23 7.58641e23i 0.582351 0.582351i
\(479\) 3.14908e22i 0.0237227i 0.999930 + 0.0118614i \(0.00377567\pi\)
−0.999930 + 0.0118614i \(0.996224\pi\)
\(480\) 1.60052e23 + 3.36184e23i 0.118328 + 0.248545i
\(481\) 2.41231e24 1.75036
\(482\) −9.66816e22 9.66816e22i −0.0688527 0.0688527i
\(483\) 1.21666e24 1.21666e24i 0.850443 0.850443i
\(484\) 1.99123e23i 0.136620i
\(485\) −5.83780e23 + 1.64474e24i −0.393164 + 1.10770i
\(486\) −1.36492e24 −0.902360
\(487\) 6.85335e23 + 6.85335e23i 0.444777 + 0.444777i 0.893614 0.448837i \(-0.148161\pi\)
−0.448837 + 0.893614i \(0.648161\pi\)
\(488\) 6.03166e23 6.03166e23i 0.384290 0.384290i
\(489\) 1.23402e24i 0.771864i
\(490\) −2.83116e22 1.00488e22i −0.0173860 0.00617094i
\(491\) 7.58996e23 0.457621 0.228811 0.973471i \(-0.426516\pi\)
0.228811 + 0.973471i \(0.426516\pi\)
\(492\) −2.55164e23 2.55164e23i −0.151054 0.151054i
\(493\) −1.71717e24 + 1.71717e24i −0.998140 + 0.998140i
\(494\) 2.03602e24i 1.16209i
\(495\) −1.95681e24 + 9.31604e23i −1.09674 + 0.522137i
\(496\) 4.56498e23 0.251248
\(497\) −5.20887e23 5.20887e23i −0.281537 0.281537i
\(498\) 1.47642e23 1.47642e23i 0.0783695 0.0783695i
\(499\) 2.27644e24i 1.18673i −0.804934 0.593364i \(-0.797799\pi\)
0.804934 0.593364i \(-0.202201\pi\)
\(500\) 2.30045e23 9.49080e23i 0.117783 0.485929i
\(501\) −1.40800e24 −0.708049
\(502\) −2.29222e23 2.29222e23i −0.113220 0.113220i
\(503\) 1.72617e24 1.72617e24i 0.837474 0.837474i −0.151052 0.988526i \(-0.548266\pi\)
0.988526 + 0.151052i \(0.0482660\pi\)
\(504\) 1.04317e24i 0.497143i
\(505\) −3.95392e23 8.30509e23i −0.185099 0.388796i
\(506\) −1.02588e24 −0.471780
\(507\) −7.78726e23 7.78726e23i −0.351814 0.351814i
\(508\) 1.15799e24 1.15799e24i 0.513962 0.513962i
\(509\) 5.34569e23i 0.233101i −0.993185 0.116550i \(-0.962816\pi\)
0.993185 0.116550i \(-0.0371837\pi\)
\(510\) −1.27225e24 + 3.58443e24i −0.545055 + 1.53564i
\(511\) −3.17328e24 −1.33573
\(512\) −7.55579e22 7.55579e22i −0.0312500 0.0312500i
\(513\) −1.64688e24 + 1.64688e24i −0.669275 + 0.669275i
\(514\) 1.25353e24i 0.500571i
\(515\) 2.61569e24 + 9.28407e23i 1.02641 + 0.364312i
\(516\) 1.74397e23 0.0672499
\(517\) −1.41469e24 1.41469e24i −0.536099 0.536099i
\(518\) −2.01892e24 + 2.01892e24i −0.751883 + 0.751883i
\(519\) 1.86965e24i 0.684313i
\(520\) 1.01937e24 4.85303e23i 0.366691 0.174575i
\(521\) −3.06229e24 −1.08270 −0.541348 0.840798i \(-0.682086\pi\)
−0.541348 + 0.840798i \(0.682086\pi\)
\(522\) 1.95547e24 + 1.95547e24i 0.679543 + 0.679543i
\(523\) 1.53641e24 1.53641e24i 0.524797 0.524797i −0.394219 0.919016i \(-0.628985\pi\)
0.919016 + 0.394219i \(0.128985\pi\)
\(524\) 1.98042e24i 0.664931i
\(525\) 2.93552e24 3.61431e24i 0.968839 1.19287i
\(526\) 2.38968e24 0.775298
\(527\) 3.29739e24 + 3.29739e24i 1.05166 + 1.05166i
\(528\) 7.48459e23 7.48459e23i 0.234673 0.234673i
\(529\) 1.25705e24i 0.387483i
\(530\) 5.09126e23 + 1.06940e24i 0.154292 + 0.324085i
\(531\) −6.28817e24 −1.87359
\(532\) −1.70399e24 1.70399e24i −0.499186 0.499186i
\(533\) −7.73699e23 + 7.73699e23i −0.222858 + 0.222858i
\(534\) 5.06497e24i 1.43452i
\(535\) 2.49843e23 7.03907e23i 0.0695797 0.196034i
\(536\) −2.29849e24 −0.629448
\(537\) 1.33112e24 + 1.33112e24i 0.358467 + 0.358467i
\(538\) −3.37621e23 + 3.37621e23i −0.0894107 + 0.0894107i
\(539\) 8.54034e22i 0.0222421i
\(540\) 1.21708e24 + 4.31988e23i 0.311728 + 0.110644i
\(541\) 4.40201e23 0.110886 0.0554428 0.998462i \(-0.482343\pi\)
0.0554428 + 0.998462i \(0.482343\pi\)
\(542\) −1.62225e23 1.62225e23i −0.0401905 0.0401905i
\(543\) −2.56411e24 + 2.56411e24i −0.624797 + 0.624797i
\(544\) 1.09155e24i 0.261609i
\(545\) 1.37418e24 6.54223e23i 0.323947 0.154226i
\(546\) 5.38303e24 1.24822
\(547\) −1.18120e24 1.18120e24i −0.269424 0.269424i 0.559444 0.828868i \(-0.311015\pi\)
−0.828868 + 0.559444i \(0.811015\pi\)
\(548\) −2.86574e24 + 2.86574e24i −0.643001 + 0.643001i
\(549\) 9.92287e24i 2.19021i
\(550\) −2.76137e24 + 2.86173e23i −0.599599 + 0.0621390i
\(551\) −6.38839e24 −1.36467
\(552\) 1.44975e24 + 1.44975e24i 0.304678 + 0.304678i
\(553\) 1.36619e24 1.36619e24i 0.282478 0.282478i
\(554\) 3.53596e23i 0.0719315i
\(555\) 5.09591e24 + 1.07038e25i 1.01996 + 2.14241i
\(556\) 1.23925e24 0.244054
\(557\) 5.77137e24 + 5.77137e24i 1.11836 + 1.11836i 0.991982 + 0.126380i \(0.0403360\pi\)
0.126380 + 0.991982i \(0.459664\pi\)
\(558\) 3.75499e24 3.75499e24i 0.715980 0.715980i
\(559\) 5.28801e23i 0.0992171i
\(560\) −4.46969e23 + 1.25929e24i −0.0825250 + 0.232506i
\(561\) 1.08126e25 1.96456
\(562\) 1.12647e24 + 1.12647e24i 0.201415 + 0.201415i
\(563\) 3.51547e23 3.51547e23i 0.0618597 0.0618597i −0.675500 0.737360i \(-0.736072\pi\)
0.737360 + 0.675500i \(0.236072\pi\)
\(564\) 3.99842e24i 0.692431i
\(565\) −3.14952e23 1.11788e23i −0.0536795 0.0190529i
\(566\) 2.83130e24 0.474939
\(567\) −1.66809e24 1.66809e24i −0.275404 0.275404i
\(568\) 6.20678e23 6.20678e23i 0.100863 0.100863i
\(569\) 5.74910e24i 0.919580i 0.888028 + 0.459790i \(0.152075\pi\)
−0.888028 + 0.459790i \(0.847925\pi\)
\(570\) −9.03415e24 + 4.30101e24i −1.42237 + 0.677168i
\(571\) −1.10385e25 −1.71075 −0.855375 0.518009i \(-0.826673\pi\)
−0.855375 + 0.518009i \(0.826673\pi\)
\(572\) −2.26945e24 2.26945e24i −0.346224 0.346224i
\(573\) 8.48501e24 8.48501e24i 1.27427 1.27427i
\(574\) 1.29505e24i 0.191461i
\(575\) −5.54311e23 5.34872e24i −0.0806757 0.778466i
\(576\) −1.24302e24 −0.178106
\(577\) 4.10073e24 + 4.10073e24i 0.578467 + 0.578467i 0.934481 0.356014i \(-0.115864\pi\)
−0.356014 + 0.934481i \(0.615864\pi\)
\(578\) 4.28436e24 4.28436e24i 0.595025 0.595025i
\(579\) 5.32904e24i 0.728689i
\(580\) 1.52273e24 + 3.19845e24i 0.205008 + 0.430614i
\(581\) 7.49341e23 0.0993332
\(582\) −7.01142e24 7.01142e24i −0.915165 0.915165i
\(583\) 2.38086e24 2.38086e24i 0.305996 0.305996i
\(584\) 3.78121e24i 0.478537i
\(585\) 4.39301e24 1.23769e25i 0.547469 1.54244i
\(586\) −4.06350e24 −0.498680
\(587\) −2.35372e24 2.35372e24i −0.284454 0.284454i 0.550428 0.834883i \(-0.314465\pi\)
−0.834883 + 0.550428i \(0.814465\pi\)
\(588\) 1.20691e23 1.20691e23i 0.0143641 0.0143641i
\(589\) 1.22673e25i 1.43784i
\(590\) −7.59091e24 2.69429e24i −0.876245 0.311012i
\(591\) 6.35197e24 0.722140
\(592\) −2.40570e24 2.40570e24i −0.269368 0.269368i
\(593\) −9.78054e24 + 9.78054e24i −1.07862 + 1.07862i −0.0819919 + 0.996633i \(0.526128\pi\)
−0.996633 + 0.0819919i \(0.973872\pi\)
\(594\) 3.67139e24i 0.398797i
\(595\) −1.23247e25 + 5.86760e24i −1.31864 + 0.627781i
\(596\) 9.93169e23 0.104666
\(597\) −1.33017e25 1.33017e25i −1.38082 1.38082i
\(598\) 4.39589e24 4.39589e24i 0.449506 0.449506i
\(599\) 3.41830e24i 0.344325i −0.985069 0.172162i \(-0.944925\pi\)
0.985069 0.172162i \(-0.0550754\pi\)
\(600\) 4.30674e24 + 3.49791e24i 0.427354 + 0.347094i
\(601\) −2.54521e23 −0.0248802 −0.0124401 0.999923i \(-0.503960\pi\)
−0.0124401 + 0.999923i \(0.503960\pi\)
\(602\) 4.42566e23 + 4.42566e23i 0.0426196 + 0.0426196i
\(603\) −1.89066e25 + 1.89066e25i −1.79373 + 1.79373i
\(604\) 5.95789e24i 0.556878i
\(605\) −1.27545e24 2.67905e24i −0.117453 0.246707i
\(606\) 5.22593e24 0.474144
\(607\) 3.01333e24 + 3.01333e24i 0.269370 + 0.269370i 0.828846 0.559477i \(-0.188998\pi\)
−0.559477 + 0.828846i \(0.688998\pi\)
\(608\) 2.03044e24 2.03044e24i 0.178837 0.178837i
\(609\) 1.68903e25i 1.46582i
\(610\) 4.25166e24 1.19786e25i 0.363571 1.02433i
\(611\) 1.21239e25 1.02158
\(612\) −8.97868e24 8.97868e24i −0.745503 0.745503i
\(613\) 5.96667e24 5.96667e24i 0.488188 0.488188i −0.419546 0.907734i \(-0.637811\pi\)
0.907734 + 0.419546i \(0.137811\pi\)
\(614\) 1.11437e25i 0.898495i
\(615\) −5.06744e24 1.79862e24i −0.402636 0.142910i
\(616\) 3.79871e24 0.297447
\(617\) 1.05403e25 + 1.05403e25i 0.813371 + 0.813371i 0.985138 0.171767i \(-0.0549476\pi\)
−0.171767 + 0.985138i \(0.554948\pi\)
\(618\) −1.11505e25 + 1.11505e25i −0.848007 + 0.848007i
\(619\) 1.30457e25i 0.977807i −0.872338 0.488903i \(-0.837397\pi\)
0.872338 0.488903i \(-0.162603\pi\)
\(620\) 6.14182e24 2.92402e24i 0.453703 0.216001i
\(621\) 7.11140e24 0.517763
\(622\) 4.22157e24 + 4.22157e24i 0.302943 + 0.302943i
\(623\) 1.28533e25 1.28533e25i 0.909124 0.909124i
\(624\) 6.41431e24i 0.447186i
\(625\) −2.98410e24 1.42427e25i −0.205066 0.978748i
\(626\) −4.29768e24 −0.291116
\(627\) 2.01131e25 + 2.01131e25i 1.34298 + 1.34298i
\(628\) −4.45224e24 + 4.45224e24i −0.293050 + 0.293050i
\(629\) 3.47539e25i 2.25501i
\(630\) 6.68188e24 + 1.40351e25i 0.427399 + 0.897740i
\(631\) −1.23499e25 −0.778755 −0.389378 0.921078i \(-0.627310\pi\)
−0.389378 + 0.921078i \(0.627310\pi\)
\(632\) 1.62793e24 + 1.62793e24i 0.101200 + 0.101200i
\(633\) −8.63067e24 + 8.63067e24i −0.528946 + 0.528946i
\(634\) 7.88302e24i 0.476310i
\(635\) 8.16254e24 2.29972e25i 0.486253 1.36997i
\(636\) −6.72917e24 −0.395228
\(637\) −3.65954e23 3.65954e23i −0.0211920 0.0211920i
\(638\) 7.12084e24 7.12084e24i 0.406579 0.406579i
\(639\) 1.02110e25i 0.574856i
\(640\) −1.50055e24 5.32599e23i −0.0832970 0.0295652i
\(641\) −7.78434e24 −0.426088 −0.213044 0.977043i \(-0.568338\pi\)
−0.213044 + 0.977043i \(0.568338\pi\)
\(642\) 3.00071e24 + 3.00071e24i 0.161960 + 0.161960i
\(643\) −8.62731e23 + 8.62731e23i −0.0459174 + 0.0459174i −0.729693 0.683775i \(-0.760337\pi\)
0.683775 + 0.729693i \(0.260337\pi\)
\(644\) 7.35803e24i 0.386179i
\(645\) 2.34638e24 1.11707e24i 0.121440 0.0578154i
\(646\) 2.93327e25 1.49713
\(647\) −4.00425e24 4.00425e24i −0.201550 0.201550i 0.599114 0.800664i \(-0.295520\pi\)
−0.800664 + 0.599114i \(0.795520\pi\)
\(648\) 1.98766e24 1.98766e24i 0.0986658 0.0986658i
\(649\) 2.28983e25i 1.12099i
\(650\) 1.06063e25 1.30588e25i 0.512085 0.630495i
\(651\) 3.24335e25 1.54442
\(652\) 3.73149e24 + 3.73149e24i 0.175248 + 0.175248i
\(653\) −6.73509e24 + 6.73509e24i −0.311979 + 0.311979i −0.845676 0.533697i \(-0.820802\pi\)
0.533697 + 0.845676i \(0.320802\pi\)
\(654\) 8.64693e24i 0.395059i
\(655\) 1.26853e25 + 2.66451e25i 0.571647 + 1.20073i
\(656\) 1.54316e24 0.0685924
\(657\) −3.11029e25 3.11029e25i −1.36368 1.36368i
\(658\) −1.01467e25 + 1.01467e25i −0.438827 + 0.438827i
\(659\) 1.78789e24i 0.0762730i −0.999273 0.0381365i \(-0.987858\pi\)
0.999273 0.0381365i \(-0.0121422\pi\)
\(660\) 5.27581e24 1.48641e25i 0.222021 0.625521i
\(661\) 1.99846e25 0.829624 0.414812 0.909907i \(-0.363847\pi\)
0.414812 + 0.909907i \(0.363847\pi\)
\(662\) 5.88487e24 + 5.88487e24i 0.240999 + 0.240999i
\(663\) −4.63321e25 + 4.63321e25i −1.87180 + 1.87180i
\(664\) 8.92900e23i 0.0355869i
\(665\) −3.38405e25 1.20112e25i −1.33058 0.472273i
\(666\) −3.95769e25 −1.53523
\(667\) 1.37929e25 + 1.37929e25i 0.527866 + 0.527866i
\(668\) 4.25760e24 4.25760e24i 0.160760 0.160760i
\(669\) 5.06486e24i 0.188683i
\(670\) −3.09244e25 + 1.47226e25i −1.13666 + 0.541143i
\(671\) −3.61341e25 −1.31043
\(672\) −5.36827e24 5.36827e24i −0.192093 0.192093i
\(673\) −5.81796e24 + 5.81796e24i −0.205416 + 0.205416i −0.802316 0.596900i \(-0.796399\pi\)
0.596900 + 0.802316i \(0.296399\pi\)
\(674\) 3.17940e25i 1.10766i
\(675\) 1.91419e25 1.98376e24i 0.658040 0.0681954i
\(676\) 4.70952e24 0.159756
\(677\) −9.58000e24 9.58000e24i −0.320677 0.320677i 0.528350 0.849027i \(-0.322811\pi\)
−0.849027 + 0.528350i \(0.822811\pi\)
\(678\) 1.34262e24 1.34262e24i 0.0443492 0.0443492i
\(679\) 3.55856e25i 1.15997i
\(680\) −6.99172e24 1.46859e25i −0.224907 0.472412i
\(681\) 3.12640e25 0.992479
\(682\) −1.36738e25 1.36738e25i −0.428380 0.428380i
\(683\) 3.34343e25 3.34343e25i 1.03373 1.03373i 0.0343157 0.999411i \(-0.489075\pi\)
0.999411 0.0343157i \(-0.0109252\pi\)
\(684\) 3.34034e25i 1.01926i
\(685\) −2.02003e25 + 5.69123e25i −0.608334 + 1.71392i
\(686\) 2.40906e25 0.716028
\(687\) −7.05438e25 7.05438e25i −2.06942 2.06942i
\(688\) −5.27352e23 + 5.27352e23i −0.0152688 + 0.0152688i
\(689\) 2.04040e25i 0.583098i
\(690\) 2.87914e25 + 1.02191e25i 0.812121 + 0.288252i
\(691\) 2.94336e25 0.819486 0.409743 0.912201i \(-0.365618\pi\)
0.409743 + 0.912201i \(0.365618\pi\)
\(692\) 5.65357e24 + 5.65357e24i 0.155370 + 0.155370i
\(693\) 3.12469e25 3.12469e25i 0.847632 0.847632i
\(694\) 1.64121e25i 0.439471i
\(695\) 1.66732e25 7.93781e24i 0.440712 0.209816i
\(696\) −2.01261e25 −0.525141
\(697\) 1.11466e25 + 1.11466e25i 0.287110 + 0.287110i
\(698\) −3.64575e25 + 3.64575e25i −0.927017 + 0.927017i
\(699\) 1.03836e26i 2.60646i
\(700\) 2.05256e24 + 1.98058e25i 0.0508643 + 0.490806i
\(701\) −4.86804e25 −1.19095 −0.595473 0.803375i \(-0.703035\pi\)
−0.595473 + 0.803375i \(0.703035\pi\)
\(702\) 1.57319e25 + 1.57319e25i 0.379969 + 0.379969i
\(703\) 6.46475e25 6.46475e25i 1.54154 1.54154i
\(704\) 4.52647e24i 0.106563i
\(705\) 2.56112e25 + 5.37956e25i 0.595289 + 1.25039i
\(706\) −4.83148e25 −1.10876
\(707\) 1.32618e25 + 1.32618e25i 0.300488 + 0.300488i
\(708\) 3.23595e25 3.23595e25i 0.723941 0.723941i
\(709\) 2.38652e25i 0.527167i 0.964637 + 0.263584i \(0.0849045\pi\)
−0.964637 + 0.263584i \(0.915095\pi\)
\(710\) 4.37509e24 1.23264e25i 0.0954250 0.268851i
\(711\) 2.67815e25 0.576778
\(712\) 1.53158e25 + 1.53158e25i 0.325701 + 0.325701i
\(713\) 2.64858e25 2.64858e25i 0.556170 0.556170i
\(714\) 7.75528e25i 1.60810i
\(715\) −4.50704e25 1.59971e25i −0.922862 0.327558i
\(716\) −8.05025e24 −0.162777
\(717\) 6.42265e25 + 6.42265e25i 1.28245 + 1.28245i
\(718\) −1.31643e24 + 1.31643e24i −0.0259584 + 0.0259584i
\(719\) 2.39320e25i 0.466035i 0.972473 + 0.233018i \(0.0748600\pi\)
−0.972473 + 0.233018i \(0.925140\pi\)
\(720\) −1.67239e25 + 7.96199e24i −0.321622 + 0.153119i
\(721\) −5.65932e25 −1.07485
\(722\) 2.79067e25 + 2.79067e25i 0.523448 + 0.523448i
\(723\) 8.18507e24 8.18507e24i 0.151627 0.151627i
\(724\) 1.55070e25i 0.283715i
\(725\) 4.09743e25 + 3.32791e25i 0.740406 + 0.601354i
\(726\) 1.68578e25 0.300864
\(727\) −4.32047e25 4.32047e25i −0.761590 0.761590i 0.215020 0.976610i \(-0.431018\pi\)
−0.976610 + 0.215020i \(0.931018\pi\)
\(728\) −1.62775e25 + 1.62775e25i −0.283404 + 0.283404i
\(729\) 9.26043e25i 1.59251i
\(730\) −2.42199e25 5.08733e25i −0.411403 0.864140i
\(731\) −7.61839e24 −0.127822
\(732\) 5.10641e25 + 5.10641e25i 0.846283 + 0.846283i
\(733\) 3.46694e24 3.46694e24i 0.0567558 0.0567558i −0.678159 0.734915i \(-0.737222\pi\)
0.734915 + 0.678159i \(0.237222\pi\)
\(734\) 5.12534e25i 0.828817i
\(735\) 8.50735e23 2.39686e24i 0.0135897 0.0382875i
\(736\) −8.76768e24 −0.138352
\(737\) 6.88483e25 + 6.88483e25i 1.07321 + 1.07321i
\(738\) 1.26935e25 1.26935e25i 0.195467 0.195467i
\(739\) 2.57729e25i 0.392069i −0.980597 0.196035i \(-0.937194\pi\)
0.980597 0.196035i \(-0.0628065\pi\)
\(740\) −4.77762e25 1.69575e25i −0.718002 0.254846i
\(741\) −1.72369e26 −2.55915
\(742\) −1.70765e25 1.70765e25i −0.250475 0.250475i
\(743\) −2.88959e25 + 2.88959e25i −0.418733 + 0.418733i −0.884767 0.466034i \(-0.845683\pi\)
0.466034 + 0.884767i \(0.345683\pi\)
\(744\) 3.86471e25i 0.553299i
\(745\) 1.33623e25 6.36158e24i 0.189006 0.0899826i
\(746\) 4.50688e25 0.629835
\(747\) 7.34468e24 + 7.34468e24i 0.101412 + 0.101412i
\(748\) −3.26958e25 + 3.26958e25i −0.446044 + 0.446044i
\(749\) 1.52297e25i 0.205284i
\(750\) 8.03492e25 + 1.94756e25i 1.07011 + 0.259382i
\(751\) 1.19196e26 1.56856 0.784282 0.620404i \(-0.213032\pi\)
0.784282 + 0.620404i \(0.213032\pi\)
\(752\) −1.20907e25 1.20907e25i −0.157213 0.157213i
\(753\) 1.94059e25 1.94059e25i 0.249333 0.249333i
\(754\) 6.10257e25i 0.774767i
\(755\) 3.81623e25 + 8.01588e25i 0.478753 + 1.00561i
\(756\) −2.63328e25 −0.326438
\(757\) −1.26082e25 1.26082e25i −0.154451 0.154451i 0.625652 0.780102i \(-0.284833\pi\)
−0.780102 + 0.625652i \(0.784833\pi\)
\(758\) 5.25540e24 5.25540e24i 0.0636185 0.0636185i
\(759\) 8.68506e25i 1.03896i
\(760\) 1.43124e25 4.03237e25i 0.169196 0.476692i
\(761\) −9.90307e25 −1.15693 −0.578466 0.815706i \(-0.696348\pi\)
−0.578466 + 0.815706i \(0.696348\pi\)
\(762\) 9.80354e25 + 9.80354e25i 1.13185 + 1.13185i
\(763\) −2.19432e25 + 2.19432e25i −0.250369 + 0.250369i
\(764\) 5.13150e25i 0.578634i
\(765\) −1.78313e26 6.32897e25i −1.98714 0.705311i
\(766\) −1.20059e26 −1.32231
\(767\) −9.81196e25 9.81196e25i −1.06806 1.06806i
\(768\) 6.39673e24 6.39673e24i 0.0688188 0.0688188i
\(769\) 1.32343e26i 1.40722i −0.710586 0.703611i \(-0.751570\pi\)
0.710586 0.703611i \(-0.248430\pi\)
\(770\) 5.11087e25 2.43320e25i 0.537129 0.255718i
\(771\) 1.06124e26 1.10236
\(772\) −1.61143e25 1.61143e25i −0.165446 0.165446i
\(773\) 1.20740e24 1.20740e24i 0.0122528 0.0122528i −0.700954 0.713207i \(-0.747242\pi\)
0.713207 + 0.700954i \(0.247242\pi\)
\(774\) 8.67563e24i 0.0870226i
\(775\) 6.39042e25 7.86809e25i 0.633598 0.780106i
\(776\) 4.24031e25 0.415568
\(777\) −1.70921e26 1.70921e26i −1.65580 1.65580i
\(778\) −5.02669e25 + 5.02669e25i −0.481355 + 0.481355i
\(779\) 4.14687e25i 0.392540i
\(780\) 4.10858e25 + 8.62996e25i 0.384450 + 0.807527i
\(781\) −3.71832e25 −0.343943
\(782\) −6.33311e25 6.33311e25i −0.579104 0.579104i
\(783\) −4.93619e25 + 4.93619e25i −0.446207 + 0.446207i
\(784\) 7.29903e23i 0.00652260i
\(785\) −3.13833e25 + 8.84195e25i −0.277250 + 0.781126i
\(786\) −1.67663e26 −1.46431
\(787\) 1.14752e26 + 1.14752e26i 0.990800 + 0.990800i 0.999958 0.00915769i \(-0.00291502\pi\)
−0.00915769 + 0.999958i \(0.502915\pi\)
\(788\) −1.92075e25 + 1.92075e25i −0.163959 + 0.163959i
\(789\) 2.02311e26i 1.70736i
\(790\) 3.23299e25 + 1.14751e25i 0.269750 + 0.0957441i
\(791\) 6.81431e24 0.0562126
\(792\) 3.72331e25 + 3.72331e25i 0.303671 + 0.303671i
\(793\) 1.54835e26 1.54835e26i 1.24856 1.24856i
\(794\) 8.00941e25i 0.638581i
\(795\) −9.05358e25 + 4.31026e25i −0.713701 + 0.339781i
\(796\) 8.04448e25 0.627018
\(797\) 1.36534e26 + 1.36534e26i 1.05224 + 1.05224i 0.998558 + 0.0536868i \(0.0170972\pi\)
0.0536868 + 0.998558i \(0.482903\pi\)
\(798\) 1.44260e26 1.44260e26i 1.09931 1.09931i
\(799\) 1.74668e26i 1.31611i
\(800\) −2.36002e25 + 2.44578e24i −0.175835 + 0.0182225i
\(801\) 2.51964e26 1.85629
\(802\) −5.73992e25 5.73992e25i −0.418154 0.418154i
\(803\) −1.13261e26 + 1.13261e26i −0.815908 + 0.815908i
\(804\) 1.94590e26i 1.38617i
\(805\) 4.71306e25 + 9.89966e25i 0.332002 + 0.697360i
\(806\) 1.17185e26 0.816310
\(807\) −2.85830e25 2.85830e25i −0.196900 0.196900i
\(808\) −1.58025e25 + 1.58025e25i −0.107652 + 0.107652i
\(809\) 1.19623e26i 0.805896i 0.915223 + 0.402948i \(0.132014\pi\)
−0.915223 + 0.402948i \(0.867986\pi\)
\(810\) 1.40108e25 3.94740e25i 0.0933464 0.262994i
\(811\) 2.46399e26 1.62349 0.811747 0.584010i \(-0.198517\pi\)
0.811747 + 0.584010i \(0.198517\pi\)
\(812\) −5.10738e25 5.10738e25i −0.332808 0.332808i
\(813\) 1.37339e25 1.37339e25i 0.0885075 0.0885075i
\(814\) 1.44119e26i 0.918548i
\(815\) 7.41058e25 + 2.63029e25i 0.467125 + 0.165800i
\(816\) 9.24103e25 0.576115
\(817\) −1.41714e25 1.41714e25i −0.0873802 0.0873802i
\(818\) 3.19838e25 3.19838e25i 0.195052 0.195052i
\(819\) 2.67786e26i 1.61523i
\(820\) 2.07620e25 9.88444e24i 0.123864 0.0589695i
\(821\) 1.47376e26 0.869639 0.434819 0.900518i \(-0.356812\pi\)
0.434819 + 0.900518i \(0.356812\pi\)
\(822\) −2.42613e26 2.42613e26i −1.41602 1.41602i
\(823\) −2.13336e26 + 2.13336e26i −1.23159 + 1.23159i −0.268238 + 0.963353i \(0.586442\pi\)
−0.963353 + 0.268238i \(0.913558\pi\)
\(824\) 6.74353e25i 0.385072i
\(825\) −2.42274e25 2.33778e26i −0.136842 1.32044i
\(826\) 1.64237e26 0.917594
\(827\) −1.90505e26 1.90505e26i −1.05283 1.05283i −0.998525 0.0543008i \(-0.982707\pi\)
−0.0543008 0.998525i \(-0.517293\pi\)
\(828\) −7.21198e25 + 7.21198e25i −0.394259 + 0.394259i
\(829\) 2.37733e26i 1.28558i −0.766043 0.642790i \(-0.777777\pi\)
0.766043 0.642790i \(-0.222223\pi\)
\(830\) 5.71932e24 + 1.20133e25i 0.0305944 + 0.0642627i
\(831\) −2.99354e25 −0.158408
\(832\) −1.93960e25 1.93960e25i −0.101532 0.101532i
\(833\) −5.27227e24 + 5.27227e24i −0.0273019 + 0.0273019i
\(834\) 1.04915e26i 0.537456i
\(835\) 3.00114e25 8.45541e25i 0.152092 0.428505i
\(836\) −1.21638e26 −0.609837
\(837\) 9.47871e25 + 9.47871e25i 0.470132 + 0.470132i
\(838\) −1.13717e26 + 1.13717e26i −0.557993 + 0.557993i
\(839\) 5.87426e25i 0.285165i −0.989783 0.142582i \(-0.954459\pi\)
0.989783 0.142582i \(-0.0455406\pi\)
\(840\) −1.06612e26 3.78404e25i −0.512025 0.181737i
\(841\) 1.89776e25 0.0901734
\(842\) 9.47080e25 + 9.47080e25i 0.445223 + 0.445223i
\(843\) −9.53667e25 + 9.53667e25i −0.443556 + 0.443556i
\(844\) 5.21959e25i 0.240190i
\(845\) 6.33629e25 3.01660e25i 0.288486 0.137343i
\(846\) −1.98907e26 −0.896018
\(847\) 4.27798e25 + 4.27798e25i 0.190672 + 0.190672i
\(848\) 2.03481e25 2.03481e25i 0.0897347 0.0897347i
\(849\) 2.39698e26i 1.04591i
\(850\) −1.88136e26 1.52803e26i −0.812274 0.659724i
\(851\) −2.79156e26 −1.19256
\(852\) 5.25466e25 + 5.25466e25i 0.222120 + 0.222120i
\(853\) −9.24585e25 + 9.24585e25i −0.386728 + 0.386728i −0.873519 0.486791i \(-0.838167\pi\)
0.486791 + 0.873519i \(0.338167\pi\)
\(854\) 2.59170e26i 1.07266i
\(855\) −2.13960e26 4.49417e26i −0.876268 1.84058i
\(856\) −1.81474e25 −0.0735447
\(857\) 1.93037e25 + 1.93037e25i 0.0774130 + 0.0774130i 0.744753 0.667340i \(-0.232567\pi\)
−0.667340 + 0.744753i \(0.732567\pi\)
\(858\) 1.92132e26 1.92132e26i 0.762455 0.762455i
\(859\) 2.04874e25i 0.0804541i −0.999191 0.0402270i \(-0.987192\pi\)
0.999191 0.0402270i \(-0.0128081\pi\)
\(860\) −3.71725e24 + 1.04730e25i −0.0144456 + 0.0406991i
\(861\) 1.09639e26 0.421635
\(862\) 8.38140e25 + 8.38140e25i 0.318971 + 0.318971i
\(863\) −1.92698e26 + 1.92698e26i −0.725738 + 0.725738i −0.969768 0.244030i \(-0.921531\pi\)
0.244030 + 0.969768i \(0.421531\pi\)
\(864\) 3.13777e25i 0.116949i
\(865\) 1.12277e26 + 3.98514e25i 0.414140 + 0.146994i
\(866\) 1.68336e26 0.614493
\(867\) 3.62714e26 + 3.62714e26i 1.31037 + 1.31037i
\(868\) −9.80743e25 + 9.80743e25i −0.350653 + 0.350653i
\(869\) 9.75247e25i 0.345093i
\(870\) −2.70781e26 + 1.28914e26i −0.948298 + 0.451469i
\(871\) −5.90031e26 −2.04509
\(872\) −2.61471e25 2.61471e25i −0.0896965 0.0896965i
\(873\) 3.48793e26 3.48793e26i 1.18424 1.18424i
\(874\) 2.35611e26i 0.791757i
\(875\) 1.54478e26 + 2.53324e26i 0.513801 + 0.842567i
\(876\) 3.20117e26 1.05383
\(877\) 2.00014e25 + 2.00014e25i 0.0651726 + 0.0651726i 0.738942 0.673769i \(-0.235326\pi\)
−0.673769 + 0.738942i \(0.735326\pi\)
\(878\) −7.53268e25 + 7.53268e25i −0.242940 + 0.242940i
\(879\) 3.44016e26i 1.09819i
\(880\) 2.89936e25 + 6.09002e25i 0.0916131 + 0.192431i
\(881\) −4.19858e26 −1.31316 −0.656582 0.754255i \(-0.727998\pi\)
−0.656582 + 0.754255i \(0.727998\pi\)
\(882\) 6.00392e24 + 6.00392e24i 0.0185874 + 0.0185874i
\(883\) −5.48338e25 + 5.48338e25i −0.168036 + 0.168036i −0.786115 0.618080i \(-0.787911\pi\)
0.618080 + 0.786115i \(0.287911\pi\)
\(884\) 2.80204e26i 0.849970i
\(885\) 2.28099e26 6.42646e26i 0.684911 1.92967i
\(886\) 4.30307e26 1.27901
\(887\) −3.29199e26 3.29199e26i −0.968604 0.968604i 0.0309183 0.999522i \(-0.490157\pi\)
−0.999522 + 0.0309183i \(0.990157\pi\)
\(888\) 2.03667e26 2.03667e26i 0.593203 0.593203i
\(889\) 4.97567e26i 1.43462i
\(890\) 3.04165e26 + 1.07959e26i 0.868158 + 0.308141i
\(891\) −1.19075e26 −0.336451
\(892\) −1.53154e25 1.53154e25i −0.0428396 0.0428396i
\(893\) 3.24908e26 3.24908e26i 0.899699 0.899699i
\(894\) 8.40817e25i 0.230496i
\(895\) −1.08310e26 + 5.15645e25i −0.293941 + 0.139941i
\(896\) 3.24658e25 0.0872277
\(897\) 3.72156e26 + 3.72156e26i 0.989903 + 0.989903i
\(898\) −1.08561e26 + 1.08561e26i −0.285882 + 0.285882i
\(899\) 3.67688e26i 0.958612i
\(900\) −1.74009e26 + 2.14245e26i −0.449146 + 0.553003i
\(901\) 2.93958e26 0.751212
\(902\) −4.62232e25 4.62232e25i −0.116950 0.116950i
\(903\) −3.74676e25 + 3.74676e25i −0.0938569 + 0.0938569i
\(904\) 8.11980e24i 0.0201386i
\(905\) −9.93278e25 2.08635e26i −0.243912 0.512331i
\(906\) −5.04395e26 −1.22636
\(907\) 1.20580e26 + 1.20580e26i 0.290275 + 0.290275i 0.837189 0.546914i \(-0.184197\pi\)
−0.546914 + 0.837189i \(0.684197\pi\)
\(908\) −9.45381e25 + 9.45381e25i −0.225338 + 0.225338i
\(909\) 2.59972e26i 0.613551i
\(910\) −1.14739e26 + 3.23264e26i −0.268125 + 0.755415i
\(911\) 8.14540e26 1.88472 0.942360 0.334600i \(-0.108601\pi\)
0.942360 + 0.334600i \(0.108601\pi\)
\(912\) 1.71897e26 + 1.71897e26i 0.393836 + 0.393836i
\(913\) 2.67456e25 2.67456e25i 0.0606758 0.0606758i
\(914\) 4.76991e26i 1.07151i
\(915\) 1.01411e27 + 3.59945e26i 2.25577 + 0.800657i
\(916\) 4.26629e26 0.939705
\(917\) −4.25476e26 4.25476e26i −0.928006 0.928006i
\(918\) 2.26649e26 2.26649e26i 0.489518 0.489518i
\(919\) 3.19256e26i 0.682809i −0.939917 0.341404i \(-0.889097\pi\)
0.939917 0.341404i \(-0.110903\pi\)
\(920\) −1.17962e26 + 5.61599e25i −0.249835 + 0.118942i
\(921\) −9.43429e26 −1.97867
\(922\) −5.09764e25 5.09764e25i −0.105874 0.105874i
\(923\) 1.59330e26 1.59330e26i 0.327705 0.327705i
\(924\) 3.21599e26i 0.655039i
\(925\) −7.51410e26 + 7.78718e25i −1.51566 + 0.157074i
\(926\) 7.14816e25 0.142789
\(927\) −5.54699e26 5.54699e26i −1.09734 1.09734i
\(928\) 6.08585e25 6.08585e25i 0.119231 0.119231i
\(929\) 6.83658e26i 1.32647i −0.748411 0.663235i \(-0.769183\pi\)
0.748411 0.663235i \(-0.230817\pi\)
\(930\) 2.47547e26 + 5.19967e26i 0.475677 + 0.999146i
\(931\) −1.96144e25 −0.0373275
\(932\) −3.13984e26 3.13984e26i −0.591786 0.591786i
\(933\) −3.57398e26 + 3.57398e26i −0.667141 + 0.667141i
\(934\) 4.36771e26i 0.807480i
\(935\) −2.30469e26 + 6.49325e26i −0.421996 + 1.18893i
\(936\) −3.19089e26 −0.578667
\(937\) 1.72845e26 + 1.72845e26i 0.310456 + 0.310456i 0.845086 0.534630i \(-0.179549\pi\)
−0.534630 + 0.845086i \(0.679549\pi\)
\(938\) 4.93810e26 4.93810e26i 0.878485 0.878485i
\(939\) 3.63842e26i 0.641095i
\(940\) −2.40115e26 8.52258e25i −0.419053 0.148737i
\(941\) 2.95805e26 0.511328 0.255664 0.966766i \(-0.417706\pi\)
0.255664 + 0.966766i \(0.417706\pi\)
\(942\) −3.76926e26 3.76926e26i −0.645354 0.645354i
\(943\) 8.95334e25 8.95334e25i 0.151838 0.151838i
\(944\) 1.95701e26i 0.328735i
\(945\) −3.54288e26 + 1.68670e26i −0.589481 + 0.280642i
\(946\) 3.15923e25 0.0520668
\(947\) 5.46582e26 + 5.46582e26i 0.892288 + 0.892288i 0.994738 0.102450i \(-0.0326681\pi\)
−0.102450 + 0.994738i \(0.532668\pi\)
\(948\) −1.37820e26 + 1.37820e26i −0.222863 + 0.222863i
\(949\) 9.70650e26i 1.55477i
\(950\) −6.57247e25 6.34199e26i −0.104284 1.00627i
\(951\) −6.67376e26 −1.04893
\(952\) 2.34509e26 + 2.34509e26i 0.365112 + 0.365112i
\(953\) −8.99405e25 + 8.99405e25i −0.138714 + 0.138714i −0.773054 0.634340i \(-0.781272\pi\)
0.634340 + 0.773054i \(0.281272\pi\)
\(954\) 3.34752e26i 0.511432i
\(955\) 3.28689e26 + 6.90403e26i 0.497457 + 1.04489i
\(956\) −3.88424e26 −0.582351
\(957\) 6.02850e26 + 6.02850e26i 0.895369 + 0.895369i
\(958\) 8.06165e24 8.06165e24i 0.0118614 0.0118614i
\(959\) 1.23135e27i 1.79480i
\(960\) 4.50899e25 1.27036e26i 0.0651085 0.183437i
\(961\) 6.99912e24 0.0100123
\(962\) −6.17552e26 6.17552e26i −0.875181 0.875181i
\(963\) −1.49274e26 + 1.49274e26i −0.209580 + 0.209580i
\(964\) 4.95010e25i 0.0688527i
\(965\) −3.20023e26 1.13588e26i −0.440996 0.156526i
\(966\) −6.22930e26 −0.850443
\(967\) 3.04683e26 + 3.04683e26i 0.412107 + 0.412107i 0.882472 0.470365i \(-0.155878\pi\)
−0.470365 + 0.882472i \(0.655878\pi\)
\(968\) −5.09755e25 + 5.09755e25i −0.0683099 + 0.0683099i
\(969\) 2.48331e27i 3.29698i
\(970\) 5.70501e26 2.71606e26i 0.750432 0.357268i
\(971\) −1.33377e26 −0.173824 −0.0869119 0.996216i \(-0.527700\pi\)
−0.0869119 + 0.996216i \(0.527700\pi\)
\(972\) 3.49419e26 + 3.49419e26i 0.451180 + 0.451180i
\(973\) −2.66242e26 + 2.66242e26i −0.340612 + 0.340612i
\(974\) 3.50892e26i 0.444777i
\(975\) 1.10556e27 + 8.97926e26i 1.38848 + 1.12771i
\(976\) −3.08821e26 −0.384290
\(977\) 3.39872e26 + 3.39872e26i 0.419048 + 0.419048i 0.884876 0.465827i \(-0.154243\pi\)
−0.465827 + 0.884876i \(0.654243\pi\)
\(978\) −3.15908e26 + 3.15908e26i −0.385932 + 0.385932i
\(979\) 9.17527e26i 1.11064i
\(980\) 4.67527e24 + 9.82028e24i 0.00560754 + 0.0117785i
\(981\) −4.30154e26 −0.511214
\(982\) −1.94303e26 1.94303e26i −0.228811 0.228811i
\(983\) 1.10437e27 1.10437e27i 1.28864 1.28864i 0.353030 0.935612i \(-0.385151\pi\)
0.935612 0.353030i \(-0.114849\pi\)
\(984\) 1.30644e26i 0.151054i
\(985\) −1.35391e26 + 3.81452e26i −0.155119 + 0.437033i
\(986\) 8.79192e26 0.998140
\(987\) −8.59023e26 8.59023e26i −0.966386 0.966386i
\(988\) 5.21221e26 5.21221e26i 0.581045 0.581045i
\(989\) 6.11936e25i 0.0675988i
\(990\) 7.39434e26 + 2.62453e26i 0.809436 + 0.287299i
\(991\) −1.18012e27 −1.28015 −0.640076 0.768311i \(-0.721097\pi\)
−0.640076 + 0.768311i \(0.721097\pi\)
\(992\) −1.16863e26 1.16863e26i −0.125624 0.125624i
\(993\) −4.98213e26 + 4.98213e26i −0.530728 + 0.530728i
\(994\) 2.66694e26i 0.281537i
\(995\) 1.08232e27 5.15276e26i 1.13227 0.539053i
\(996\) −7.55929e25 −0.0783695
\(997\) 8.35834e26 + 8.35834e26i 0.858744 + 0.858744i 0.991190 0.132446i \(-0.0422832\pi\)
−0.132446 + 0.991190i \(0.542283\pi\)
\(998\) −5.82769e26 + 5.82769e26i −0.593364 + 0.593364i
\(999\) 9.99039e26i 1.00808i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 10.19.c.b.7.5 yes 10
3.2 odd 2 90.19.g.b.37.2 10
5.2 odd 4 50.19.c.d.43.1 10
5.3 odd 4 inner 10.19.c.b.3.5 10
5.4 even 2 50.19.c.d.7.1 10
15.8 even 4 90.19.g.b.73.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.19.c.b.3.5 10 5.3 odd 4 inner
10.19.c.b.7.5 yes 10 1.1 even 1 trivial
50.19.c.d.7.1 10 5.4 even 2
50.19.c.d.43.1 10 5.2 odd 4
90.19.g.b.37.2 10 3.2 odd 2
90.19.g.b.73.2 10 15.8 even 4