Properties

Label 75.9.f.d.43.2
Level $75$
Weight $9$
Character 75.43
Analytic conductor $30.553$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(7,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.7");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.f (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: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 192 x^{9} + 27713 x^{8} - 24384 x^{7} + 18432 x^{6} - 2072064 x^{5} + 128589064 x^{4} - 223046400 x^{3} + 184320000 x^{2} + 558720000 x + 846810000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{18}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.2
Root \(-0.782794 + 0.782794i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.9.f.d.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-15.2792 + 15.2792i) q^{2} +(33.0681 + 33.0681i) q^{3} -210.909i q^{4} -1010.51 q^{6} +(1776.62 - 1776.62i) q^{7} +(-688.952 - 688.952i) q^{8} +2187.00i q^{9} +O(q^{10})\) \(q+(-15.2792 + 15.2792i) q^{2} +(33.0681 + 33.0681i) q^{3} -210.909i q^{4} -1010.51 q^{6} +(1776.62 - 1776.62i) q^{7} +(-688.952 - 688.952i) q^{8} +2187.00i q^{9} +4477.64 q^{11} +(6974.37 - 6974.37i) q^{12} +(-18402.3 - 18402.3i) q^{13} +54290.9i q^{14} +75046.1 q^{16} +(-40628.0 + 40628.0i) q^{17} +(-33415.7 - 33415.7i) q^{18} +161124. i q^{19} +117499. q^{21} +(-68414.9 + 68414.9i) q^{22} +(208665. + 208665. i) q^{23} -45564.7i q^{24} +562344. q^{26} +(-72320.0 + 72320.0i) q^{27} +(-374706. - 374706. i) q^{28} +1.08625e6i q^{29} +1.33249e6 q^{31} +(-970274. + 970274. i) q^{32} +(148067. + 148067. i) q^{33} -1.24153e6i q^{34} +461259. q^{36} +(-778701. + 778701. i) q^{37} +(-2.46185e6 - 2.46185e6i) q^{38} -1.21706e6i q^{39} -3.79519e6 q^{41} +(-1.79530e6 + 1.79530e6i) q^{42} +(-3.70334e6 - 3.70334e6i) q^{43} -944377. i q^{44} -6.37648e6 q^{46} +(-3.40201e6 + 3.40201e6i) q^{47} +(2.48163e6 + 2.48163e6i) q^{48} -547985. i q^{49} -2.68698e6 q^{51} +(-3.88121e6 + 3.88121e6i) q^{52} +(3.98610e6 + 3.98610e6i) q^{53} -2.20999e6i q^{54} -2.44802e6 q^{56} +(-5.32806e6 + 5.32806e6i) q^{57} +(-1.65971e7 - 1.65971e7i) q^{58} +4.53528e6i q^{59} -4.88819e6 q^{61} +(-2.03595e7 + 2.03595e7i) q^{62} +(3.88548e6 + 3.88548e6i) q^{63} -1.04383e7i q^{64} -4.52471e6 q^{66} +(1.35112e7 - 1.35112e7i) q^{67} +(8.56883e6 + 8.56883e6i) q^{68} +1.38003e7i q^{69} +4.27542e7 q^{71} +(1.50674e6 - 1.50674e6i) q^{72} +(-3.74805e7 - 3.74805e7i) q^{73} -2.37959e7i q^{74} +3.39825e7 q^{76} +(7.95509e6 - 7.95509e6i) q^{77} +(1.85957e7 + 1.85957e7i) q^{78} +6.47257e7i q^{79} -4.78297e6 q^{81} +(5.79876e7 - 5.79876e7i) q^{82} +(4.04525e7 + 4.04525e7i) q^{83} -2.47817e7i q^{84} +1.13168e8 q^{86} +(-3.59203e7 + 3.59203e7i) q^{87} +(-3.08488e6 - 3.08488e6i) q^{88} +9.02203e7i q^{89} -6.53878e7 q^{91} +(4.40094e7 - 4.40094e7i) q^{92} +(4.40630e7 + 4.40630e7i) q^{93} -1.03960e8i q^{94} -6.41702e7 q^{96} +(1.44242e7 - 1.44242e7i) q^{97} +(8.37278e6 + 8.37278e6i) q^{98} +9.79261e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2268 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2268 q^{6} - 88920 q^{11} - 485796 q^{16} + 79704 q^{21} - 4055976 q^{26} + 5658696 q^{31} + 5065092 q^{36} + 1798056 q^{41} - 10882464 q^{46} + 4329936 q^{51} + 7268040 q^{56} + 33649848 q^{61} - 141361848 q^{66} + 335506464 q^{71} - 395386536 q^{76} - 57395628 q^{81} + 489958560 q^{86} - 216875664 q^{91} - 710311356 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.2792 + 15.2792i −0.954951 + 0.954951i −0.999028 0.0440768i \(-0.985965\pi\)
0.0440768 + 0.999028i \(0.485965\pi\)
\(3\) 33.0681 + 33.0681i 0.408248 + 0.408248i
\(4\) 210.909i 0.823864i
\(5\) 0 0
\(6\) −1010.51 −0.779715
\(7\) 1776.62 1776.62i 0.739952 0.739952i −0.232617 0.972568i \(-0.574729\pi\)
0.972568 + 0.232617i \(0.0747288\pi\)
\(8\) −688.952 688.952i −0.168201 0.168201i
\(9\) 2187.00i 0.333333i
\(10\) 0 0
\(11\) 4477.64 0.305829 0.152915 0.988239i \(-0.451134\pi\)
0.152915 + 0.988239i \(0.451134\pi\)
\(12\) 6974.37 6974.37i 0.336341 0.336341i
\(13\) −18402.3 18402.3i −0.644314 0.644314i 0.307299 0.951613i \(-0.400575\pi\)
−0.951613 + 0.307299i \(0.900575\pi\)
\(14\) 54290.9i 1.41324i
\(15\) 0 0
\(16\) 75046.1 1.14511
\(17\) −40628.0 + 40628.0i −0.486441 + 0.486441i −0.907181 0.420740i \(-0.861770\pi\)
0.420740 + 0.907181i \(0.361770\pi\)
\(18\) −33415.7 33415.7i −0.318317 0.318317i
\(19\) 161124.i 1.23636i 0.786036 + 0.618181i \(0.212130\pi\)
−0.786036 + 0.618181i \(0.787870\pi\)
\(20\) 0 0
\(21\) 117499. 0.604168
\(22\) −68414.9 + 68414.9i −0.292052 + 0.292052i
\(23\) 208665. + 208665.i 0.745656 + 0.745656i 0.973660 0.228004i \(-0.0732199\pi\)
−0.228004 + 0.973660i \(0.573220\pi\)
\(24\) 45564.7i 0.137336i
\(25\) 0 0
\(26\) 562344. 1.23058
\(27\) −72320.0 + 72320.0i −0.136083 + 0.136083i
\(28\) −374706. 374706.i −0.609620 0.609620i
\(29\) 1.08625e6i 1.53581i 0.640561 + 0.767907i \(0.278702\pi\)
−0.640561 + 0.767907i \(0.721298\pi\)
\(30\) 0 0
\(31\) 1.33249e6 1.44284 0.721420 0.692498i \(-0.243490\pi\)
0.721420 + 0.692498i \(0.243490\pi\)
\(32\) −970274. + 970274.i −0.925325 + 0.925325i
\(33\) 148067. + 148067.i 0.124854 + 0.124854i
\(34\) 1.24153e6i 0.929055i
\(35\) 0 0
\(36\) 461259. 0.274621
\(37\) −778701. + 778701.i −0.415493 + 0.415493i −0.883647 0.468154i \(-0.844919\pi\)
0.468154 + 0.883647i \(0.344919\pi\)
\(38\) −2.46185e6 2.46185e6i −1.18066 1.18066i
\(39\) 1.21706e6i 0.526080i
\(40\) 0 0
\(41\) −3.79519e6 −1.34307 −0.671535 0.740973i \(-0.734365\pi\)
−0.671535 + 0.740973i \(0.734365\pi\)
\(42\) −1.79530e6 + 1.79530e6i −0.576951 + 0.576951i
\(43\) −3.70334e6 3.70334e6i −1.08323 1.08323i −0.996206 0.0870210i \(-0.972265\pi\)
−0.0870210 0.996206i \(-0.527735\pi\)
\(44\) 944377.i 0.251962i
\(45\) 0 0
\(46\) −6.37648e6 −1.42413
\(47\) −3.40201e6 + 3.40201e6i −0.697179 + 0.697179i −0.963801 0.266622i \(-0.914092\pi\)
0.266622 + 0.963801i \(0.414092\pi\)
\(48\) 2.48163e6 + 2.48163e6i 0.467490 + 0.467490i
\(49\) 547985.i 0.0950570i
\(50\) 0 0
\(51\) −2.68698e6 −0.397177
\(52\) −3.88121e6 + 3.88121e6i −0.530827 + 0.530827i
\(53\) 3.98610e6 + 3.98610e6i 0.505178 + 0.505178i 0.913042 0.407865i \(-0.133726\pi\)
−0.407865 + 0.913042i \(0.633726\pi\)
\(54\) 2.20999e6i 0.259905i
\(55\) 0 0
\(56\) −2.44802e6 −0.248921
\(57\) −5.32806e6 + 5.32806e6i −0.504742 + 0.504742i
\(58\) −1.65971e7 1.65971e7i −1.46663 1.46663i
\(59\) 4.53528e6i 0.374279i 0.982333 + 0.187140i \(0.0599217\pi\)
−0.982333 + 0.187140i \(0.940078\pi\)
\(60\) 0 0
\(61\) −4.88819e6 −0.353044 −0.176522 0.984297i \(-0.556485\pi\)
−0.176522 + 0.984297i \(0.556485\pi\)
\(62\) −2.03595e7 + 2.03595e7i −1.37784 + 1.37784i
\(63\) 3.88548e6 + 3.88548e6i 0.246651 + 0.246651i
\(64\) 1.04383e7i 0.622169i
\(65\) 0 0
\(66\) −4.52471e6 −0.238459
\(67\) 1.35112e7 1.35112e7i 0.670492 0.670492i −0.287337 0.957829i \(-0.592770\pi\)
0.957829 + 0.287337i \(0.0927700\pi\)
\(68\) 8.56883e6 + 8.56883e6i 0.400761 + 0.400761i
\(69\) 1.38003e7i 0.608826i
\(70\) 0 0
\(71\) 4.27542e7 1.68246 0.841232 0.540675i \(-0.181831\pi\)
0.841232 + 0.540675i \(0.181831\pi\)
\(72\) 1.50674e6 1.50674e6i 0.0560670 0.0560670i
\(73\) −3.74805e7 3.74805e7i −1.31982 1.31982i −0.913917 0.405902i \(-0.866957\pi\)
−0.405902 0.913917i \(-0.633043\pi\)
\(74\) 2.37959e7i 0.793552i
\(75\) 0 0
\(76\) 3.39825e7 1.01859
\(77\) 7.95509e6 7.95509e6i 0.226299 0.226299i
\(78\) 1.85957e7 + 1.85957e7i 0.502381 + 0.502381i
\(79\) 6.47257e7i 1.66176i 0.556451 + 0.830880i \(0.312163\pi\)
−0.556451 + 0.830880i \(0.687837\pi\)
\(80\) 0 0
\(81\) −4.78297e6 −0.111111
\(82\) 5.79876e7 5.79876e7i 1.28257 1.28257i
\(83\) 4.04525e7 + 4.04525e7i 0.852379 + 0.852379i 0.990426 0.138047i \(-0.0440825\pi\)
−0.138047 + 0.990426i \(0.544083\pi\)
\(84\) 2.47817e7i 0.497752i
\(85\) 0 0
\(86\) 1.13168e8 2.06886
\(87\) −3.59203e7 + 3.59203e7i −0.626993 + 0.626993i
\(88\) −3.08488e6 3.08488e6i −0.0514408 0.0514408i
\(89\) 9.02203e7i 1.43795i 0.695035 + 0.718976i \(0.255389\pi\)
−0.695035 + 0.718976i \(0.744611\pi\)
\(90\) 0 0
\(91\) −6.53878e7 −0.953523
\(92\) 4.40094e7 4.40094e7i 0.614320 0.614320i
\(93\) 4.40630e7 + 4.40630e7i 0.589037 + 0.589037i
\(94\) 1.03960e8i 1.33154i
\(95\) 0 0
\(96\) −6.41702e7 −0.755525
\(97\) 1.44242e7 1.44242e7i 0.162932 0.162932i −0.620932 0.783864i \(-0.713246\pi\)
0.783864 + 0.620932i \(0.213246\pi\)
\(98\) 8.37278e6 + 8.37278e6i 0.0907748 + 0.0907748i
\(99\) 9.79261e6i 0.101943i
\(100\) 0 0
\(101\) −1.42466e8 −1.36907 −0.684535 0.728980i \(-0.739995\pi\)
−0.684535 + 0.728980i \(0.739995\pi\)
\(102\) 4.10550e7 4.10550e7i 0.379285 0.379285i
\(103\) 7.31307e7 + 7.31307e7i 0.649756 + 0.649756i 0.952934 0.303178i \(-0.0980476\pi\)
−0.303178 + 0.952934i \(0.598048\pi\)
\(104\) 2.53565e7i 0.216749i
\(105\) 0 0
\(106\) −1.21809e8 −0.964840
\(107\) 5.10438e7 5.10438e7i 0.389411 0.389411i −0.485067 0.874477i \(-0.661205\pi\)
0.874477 + 0.485067i \(0.161205\pi\)
\(108\) 1.52529e7 + 1.52529e7i 0.112114 + 0.112114i
\(109\) 5.91324e7i 0.418909i −0.977818 0.209454i \(-0.932831\pi\)
0.977818 0.209454i \(-0.0671688\pi\)
\(110\) 0 0
\(111\) −5.15004e7 −0.339249
\(112\) 1.33329e8 1.33329e8i 0.847328 0.847328i
\(113\) 5.36434e7 + 5.36434e7i 0.329005 + 0.329005i 0.852208 0.523203i \(-0.175263\pi\)
−0.523203 + 0.852208i \(0.675263\pi\)
\(114\) 1.62817e8i 0.964009i
\(115\) 0 0
\(116\) 2.29101e8 1.26530
\(117\) 4.02457e7 4.02457e7i 0.214771 0.214771i
\(118\) −6.92955e7 6.92955e7i −0.357419 0.357419i
\(119\) 1.44361e8i 0.719886i
\(120\) 0 0
\(121\) −1.94310e8 −0.906469
\(122\) 7.46877e7 7.46877e7i 0.337140 0.337140i
\(123\) −1.25500e8 1.25500e8i −0.548306 0.548306i
\(124\) 2.81035e8i 1.18870i
\(125\) 0 0
\(126\) −1.18734e8 −0.471079
\(127\) −1.38129e8 + 1.38129e8i −0.530969 + 0.530969i −0.920861 0.389892i \(-0.872512\pi\)
0.389892 + 0.920861i \(0.372512\pi\)
\(128\) −8.89015e7 8.89015e7i −0.331184 0.331184i
\(129\) 2.44925e8i 0.884452i
\(130\) 0 0
\(131\) 2.43973e8 0.828432 0.414216 0.910179i \(-0.364056\pi\)
0.414216 + 0.910179i \(0.364056\pi\)
\(132\) 3.12288e7 3.12288e7i 0.102863 0.102863i
\(133\) 2.86256e8 + 2.86256e8i 0.914848 + 0.914848i
\(134\) 4.12880e8i 1.28058i
\(135\) 0 0
\(136\) 5.59815e7 0.163640
\(137\) −2.63122e8 + 2.63122e8i −0.746920 + 0.746920i −0.973900 0.226979i \(-0.927115\pi\)
0.226979 + 0.973900i \(0.427115\pi\)
\(138\) −2.10858e8 2.10858e8i −0.581399 0.581399i
\(139\) 1.08062e8i 0.289477i 0.989470 + 0.144739i \(0.0462341\pi\)
−0.989470 + 0.144739i \(0.953766\pi\)
\(140\) 0 0
\(141\) −2.24996e8 −0.569244
\(142\) −6.53251e8 + 6.53251e8i −1.60667 + 1.60667i
\(143\) −8.23988e7 8.23988e7i −0.197050 0.197050i
\(144\) 1.64126e8i 0.381704i
\(145\) 0 0
\(146\) 1.14535e9 2.52073
\(147\) 1.81208e7 1.81208e7i 0.0388069 0.0388069i
\(148\) 1.64235e8 + 1.64235e8i 0.342310 + 0.342310i
\(149\) 2.55974e8i 0.519340i 0.965697 + 0.259670i \(0.0836138\pi\)
−0.965697 + 0.259670i \(0.916386\pi\)
\(150\) 0 0
\(151\) 3.02108e8 0.581105 0.290553 0.956859i \(-0.406161\pi\)
0.290553 + 0.956859i \(0.406161\pi\)
\(152\) 1.11007e8 1.11007e8i 0.207957 0.207957i
\(153\) −8.88535e7 8.88535e7i −0.162147 0.162147i
\(154\) 2.43095e8i 0.432209i
\(155\) 0 0
\(156\) −2.56688e8 −0.433419
\(157\) −1.07682e8 + 1.07682e8i −0.177233 + 0.177233i −0.790148 0.612916i \(-0.789996\pi\)
0.612916 + 0.790148i \(0.289996\pi\)
\(158\) −9.88958e8 9.88958e8i −1.58690 1.58690i
\(159\) 2.63625e8i 0.412476i
\(160\) 0 0
\(161\) 7.41439e8 1.10350
\(162\) 7.30800e7 7.30800e7i 0.106106 0.106106i
\(163\) 7.20616e8 + 7.20616e8i 1.02083 + 1.02083i 0.999778 + 0.0210510i \(0.00670125\pi\)
0.0210510 + 0.999778i \(0.493299\pi\)
\(164\) 8.00442e8i 1.10651i
\(165\) 0 0
\(166\) −1.23616e9 −1.62796
\(167\) −4.94776e8 + 4.94776e8i −0.636125 + 0.636125i −0.949597 0.313472i \(-0.898508\pi\)
0.313472 + 0.949597i \(0.398508\pi\)
\(168\) −8.09513e7 8.09513e7i −0.101622 0.101622i
\(169\) 1.38445e8i 0.169718i
\(170\) 0 0
\(171\) −3.52378e8 −0.412120
\(172\) −7.81068e8 + 7.81068e8i −0.892432 + 0.892432i
\(173\) −3.67823e8 3.67823e8i −0.410634 0.410634i 0.471325 0.881959i \(-0.343776\pi\)
−0.881959 + 0.471325i \(0.843776\pi\)
\(174\) 1.09767e9i 1.19750i
\(175\) 0 0
\(176\) 3.36030e8 0.350209
\(177\) −1.49973e8 + 1.49973e8i −0.152799 + 0.152799i
\(178\) −1.37850e9 1.37850e9i −1.37317 1.37317i
\(179\) 1.47156e9i 1.43340i −0.697383 0.716699i \(-0.745652\pi\)
0.697383 0.716699i \(-0.254348\pi\)
\(180\) 0 0
\(181\) −1.08757e9 −1.01331 −0.506654 0.862149i \(-0.669118\pi\)
−0.506654 + 0.862149i \(0.669118\pi\)
\(182\) 9.99074e8 9.99074e8i 0.910568 0.910568i
\(183\) −1.61643e8 1.61643e8i −0.144130 0.144130i
\(184\) 2.87521e8i 0.250840i
\(185\) 0 0
\(186\) −1.34650e9 −1.12500
\(187\) −1.81918e8 + 1.81918e8i −0.148768 + 0.148768i
\(188\) 7.17516e8 + 7.17516e8i 0.574381 + 0.574381i
\(189\) 2.56971e8i 0.201389i
\(190\) 0 0
\(191\) 4.78708e8 0.359698 0.179849 0.983694i \(-0.442439\pi\)
0.179849 + 0.983694i \(0.442439\pi\)
\(192\) 3.45174e8 3.45174e8i 0.253999 0.253999i
\(193\) 1.58182e9 + 1.58182e9i 1.14006 + 1.14006i 0.988438 + 0.151624i \(0.0484503\pi\)
0.151624 + 0.988438i \(0.451550\pi\)
\(194\) 4.40782e8i 0.311184i
\(195\) 0 0
\(196\) −1.15575e8 −0.0783141
\(197\) −1.05458e9 + 1.05458e9i −0.700185 + 0.700185i −0.964450 0.264265i \(-0.914871\pi\)
0.264265 + 0.964450i \(0.414871\pi\)
\(198\) −1.49623e8 1.49623e8i −0.0973507 0.0973507i
\(199\) 2.81932e9i 1.79776i −0.438190 0.898882i \(-0.644380\pi\)
0.438190 0.898882i \(-0.355620\pi\)
\(200\) 0 0
\(201\) 8.93578e8 0.547455
\(202\) 2.17677e9 2.17677e9i 1.30740 1.30740i
\(203\) 1.92986e9 + 1.92986e9i 1.13643 + 1.13643i
\(204\) 5.66710e8i 0.327220i
\(205\) 0 0
\(206\) −2.23476e9 −1.24097
\(207\) −4.56351e8 + 4.56351e8i −0.248552 + 0.248552i
\(208\) −1.38102e9 1.38102e9i −0.737812 0.737812i
\(209\) 7.21455e8i 0.378115i
\(210\) 0 0
\(211\) 1.35002e9 0.681100 0.340550 0.940226i \(-0.389387\pi\)
0.340550 + 0.940226i \(0.389387\pi\)
\(212\) 8.40704e8 8.40704e8i 0.416198 0.416198i
\(213\) 1.41380e9 + 1.41380e9i 0.686863 + 0.686863i
\(214\) 1.55982e9i 0.743737i
\(215\) 0 0
\(216\) 9.96499e7 0.0457785
\(217\) 2.36734e9 2.36734e9i 1.06763 1.06763i
\(218\) 9.03497e8 + 9.03497e8i 0.400038 + 0.400038i
\(219\) 2.47882e9i 1.07763i
\(220\) 0 0
\(221\) 1.49530e9 0.626842
\(222\) 7.86885e8 7.86885e8i 0.323966 0.323966i
\(223\) −9.94179e8 9.94179e8i −0.402018 0.402018i 0.476926 0.878944i \(-0.341751\pi\)
−0.878944 + 0.476926i \(0.841751\pi\)
\(224\) 3.44762e9i 1.36939i
\(225\) 0 0
\(226\) −1.63926e9 −0.628367
\(227\) −8.75761e7 + 8.75761e7i −0.0329824 + 0.0329824i −0.723406 0.690423i \(-0.757424\pi\)
0.690423 + 0.723406i \(0.257424\pi\)
\(228\) 1.12374e9 + 1.12374e9i 0.415839 + 0.415839i
\(229\) 2.09791e9i 0.762859i 0.924398 + 0.381430i \(0.124568\pi\)
−0.924398 + 0.381430i \(0.875432\pi\)
\(230\) 0 0
\(231\) 5.26120e8 0.184772
\(232\) 7.48375e8 7.48375e8i 0.258326 0.258326i
\(233\) 2.74740e8 + 2.74740e8i 0.0932178 + 0.0932178i 0.752178 0.658960i \(-0.229003\pi\)
−0.658960 + 0.752178i \(0.729003\pi\)
\(234\) 1.22985e9i 0.410192i
\(235\) 0 0
\(236\) 9.56532e8 0.308355
\(237\) −2.14036e9 + 2.14036e9i −0.678411 + 0.678411i
\(238\) −2.20573e9 2.20573e9i −0.687456 0.687456i
\(239\) 5.48652e8i 0.168153i 0.996459 + 0.0840767i \(0.0267941\pi\)
−0.996459 + 0.0840767i \(0.973206\pi\)
\(240\) 0 0
\(241\) 5.12166e9 1.51825 0.759123 0.650947i \(-0.225628\pi\)
0.759123 + 0.650947i \(0.225628\pi\)
\(242\) 2.96890e9 2.96890e9i 0.865633 0.865633i
\(243\) −1.58164e8 1.58164e8i −0.0453609 0.0453609i
\(244\) 1.03096e9i 0.290860i
\(245\) 0 0
\(246\) 3.83508e9 1.04721
\(247\) 2.96504e9 2.96504e9i 0.796605 0.796605i
\(248\) −9.18023e8 9.18023e8i −0.242687 0.242687i
\(249\) 2.67537e9i 0.695964i
\(250\) 0 0
\(251\) −5.04785e8 −0.127178 −0.0635889 0.997976i \(-0.520255\pi\)
−0.0635889 + 0.997976i \(0.520255\pi\)
\(252\) 8.19483e8 8.19483e8i 0.203207 0.203207i
\(253\) 9.34329e8 + 9.34329e8i 0.228043 + 0.228043i
\(254\) 4.22100e9i 1.01410i
\(255\) 0 0
\(256\) 5.38889e9 1.25470
\(257\) −1.17418e9 + 1.17418e9i −0.269155 + 0.269155i −0.828760 0.559605i \(-0.810953\pi\)
0.559605 + 0.828760i \(0.310953\pi\)
\(258\) 3.74226e9 + 3.74226e9i 0.844608 + 0.844608i
\(259\) 2.76692e9i 0.614890i
\(260\) 0 0
\(261\) −2.37563e9 −0.511938
\(262\) −3.72772e9 + 3.72772e9i −0.791112 + 0.791112i
\(263\) 3.37767e9 + 3.37767e9i 0.705982 + 0.705982i 0.965688 0.259706i \(-0.0836255\pi\)
−0.259706 + 0.965688i \(0.583626\pi\)
\(264\) 2.04022e8i 0.0420012i
\(265\) 0 0
\(266\) −8.74755e9 −1.74727
\(267\) −2.98341e9 + 2.98341e9i −0.587041 + 0.587041i
\(268\) −2.84963e9 2.84963e9i −0.552395 0.552395i
\(269\) 5.72780e9i 1.09390i −0.837165 0.546951i \(-0.815788\pi\)
0.837165 0.546951i \(-0.184212\pi\)
\(270\) 0 0
\(271\) −6.27185e9 −1.16284 −0.581418 0.813605i \(-0.697502\pi\)
−0.581418 + 0.813605i \(0.697502\pi\)
\(272\) −3.04897e9 + 3.04897e9i −0.557029 + 0.557029i
\(273\) −2.16225e9 2.16225e9i −0.389274 0.389274i
\(274\) 8.04059e9i 1.42654i
\(275\) 0 0
\(276\) 2.91062e9 0.501590
\(277\) 3.19244e8 3.19244e8i 0.0542254 0.0542254i −0.679474 0.733700i \(-0.737792\pi\)
0.733700 + 0.679474i \(0.237792\pi\)
\(278\) −1.65111e9 1.65111e9i −0.276437 0.276437i
\(279\) 2.91416e9i 0.480947i
\(280\) 0 0
\(281\) −8.35532e9 −1.34010 −0.670051 0.742315i \(-0.733728\pi\)
−0.670051 + 0.742315i \(0.733728\pi\)
\(282\) 3.43777e9 3.43777e9i 0.543601 0.543601i
\(283\) 1.34940e7 + 1.34940e7i 0.00210375 + 0.00210375i 0.708158 0.706054i \(-0.249526\pi\)
−0.706054 + 0.708158i \(0.749526\pi\)
\(284\) 9.01726e9i 1.38612i
\(285\) 0 0
\(286\) 2.51798e9 0.376346
\(287\) −6.74263e9 + 6.74263e9i −0.993807 + 0.993807i
\(288\) −2.12199e9 2.12199e9i −0.308442 0.308442i
\(289\) 3.67448e9i 0.526750i
\(290\) 0 0
\(291\) 9.53964e8 0.133033
\(292\) −7.90499e9 + 7.90499e9i −1.08735 + 1.08735i
\(293\) −5.13714e9 5.13714e9i −0.697029 0.697029i 0.266740 0.963769i \(-0.414054\pi\)
−0.963769 + 0.266740i \(0.914054\pi\)
\(294\) 5.53744e8i 0.0741173i
\(295\) 0 0
\(296\) 1.07298e9 0.139773
\(297\) −3.23823e8 + 3.23823e8i −0.0416181 + 0.0416181i
\(298\) −3.91109e9 3.91109e9i −0.495944 0.495944i
\(299\) 7.67982e9i 0.960874i
\(300\) 0 0
\(301\) −1.31589e10 −1.60307
\(302\) −4.61598e9 + 4.61598e9i −0.554927 + 0.554927i
\(303\) −4.71108e9 4.71108e9i −0.558920 0.558920i
\(304\) 1.20917e10i 1.41577i
\(305\) 0 0
\(306\) 2.71523e9 0.309685
\(307\) 2.16091e9 2.16091e9i 0.243267 0.243267i −0.574933 0.818200i \(-0.694972\pi\)
0.818200 + 0.574933i \(0.194972\pi\)
\(308\) −1.67780e9 1.67780e9i −0.186439 0.186439i
\(309\) 4.83659e9i 0.530524i
\(310\) 0 0
\(311\) −6.44045e9 −0.688454 −0.344227 0.938887i \(-0.611859\pi\)
−0.344227 + 0.938887i \(0.611859\pi\)
\(312\) −8.38493e8 + 8.38493e8i −0.0884873 + 0.0884873i
\(313\) 1.04720e10 + 1.04720e10i 1.09107 + 1.09107i 0.995415 + 0.0956506i \(0.0304931\pi\)
0.0956506 + 0.995415i \(0.469507\pi\)
\(314\) 3.29059e9i 0.338497i
\(315\) 0 0
\(316\) 1.36513e10 1.36907
\(317\) 1.01318e10 1.01318e10i 1.00334 1.00334i 0.00334628 0.999994i \(-0.498935\pi\)
0.999994 0.00334628i \(-0.00106516\pi\)
\(318\) −4.02799e9 4.02799e9i −0.393894 0.393894i
\(319\) 4.86385e9i 0.469697i
\(320\) 0 0
\(321\) 3.37584e9 0.317953
\(322\) −1.13286e10 + 1.13286e10i −1.05379 + 1.05379i
\(323\) −6.54615e9 6.54615e9i −0.601417 0.601417i
\(324\) 1.00877e9i 0.0915405i
\(325\) 0 0
\(326\) −2.20209e10 −1.94968
\(327\) 1.95540e9 1.95540e9i 0.171019 0.171019i
\(328\) 2.61471e9 + 2.61471e9i 0.225906 + 0.225906i
\(329\) 1.20882e10i 1.03176i
\(330\) 0 0
\(331\) 2.15436e10 1.79476 0.897378 0.441262i \(-0.145469\pi\)
0.897378 + 0.441262i \(0.145469\pi\)
\(332\) 8.53180e9 8.53180e9i 0.702244 0.702244i
\(333\) −1.70302e9 1.70302e9i −0.138498 0.138498i
\(334\) 1.51196e10i 1.21494i
\(335\) 0 0
\(336\) 8.81785e9 0.691840
\(337\) −4.14231e9 + 4.14231e9i −0.321161 + 0.321161i −0.849213 0.528051i \(-0.822923\pi\)
0.528051 + 0.849213i \(0.322923\pi\)
\(338\) 2.11533e9 + 2.11533e9i 0.162073 + 0.162073i
\(339\) 3.54777e9i 0.268631i
\(340\) 0 0
\(341\) 5.96643e9 0.441262
\(342\) 5.38406e9 5.38406e9i 0.393555 0.393555i
\(343\) 9.26832e9 + 9.26832e9i 0.669614 + 0.669614i
\(344\) 5.10284e9i 0.364400i
\(345\) 0 0
\(346\) 1.12401e10 0.784271
\(347\) −1.35085e10 + 1.35085e10i −0.931730 + 0.931730i −0.997814 0.0660836i \(-0.978950\pi\)
0.0660836 + 0.997814i \(0.478950\pi\)
\(348\) 7.57592e9 + 7.57592e9i 0.516557 + 0.516557i
\(349\) 7.36977e9i 0.496766i 0.968662 + 0.248383i \(0.0798992\pi\)
−0.968662 + 0.248383i \(0.920101\pi\)
\(350\) 0 0
\(351\) 2.66170e9 0.175360
\(352\) −4.34454e9 + 4.34454e9i −0.282991 + 0.282991i
\(353\) −1.28656e10 1.28656e10i −0.828576 0.828576i 0.158743 0.987320i \(-0.449256\pi\)
−0.987320 + 0.158743i \(0.949256\pi\)
\(354\) 4.58295e9i 0.291831i
\(355\) 0 0
\(356\) 1.90283e10 1.18468
\(357\) −4.77376e9 + 4.77376e9i −0.293892 + 0.293892i
\(358\) 2.24843e10 + 2.24843e10i 1.36882 + 1.36882i
\(359\) 2.68477e9i 0.161633i 0.996729 + 0.0808165i \(0.0257528\pi\)
−0.996729 + 0.0808165i \(0.974247\pi\)
\(360\) 0 0
\(361\) −8.97733e9 −0.528589
\(362\) 1.66172e10 1.66172e10i 0.967660 0.967660i
\(363\) −6.42545e9 6.42545e9i −0.370064 0.370064i
\(364\) 1.37909e10i 0.785573i
\(365\) 0 0
\(366\) 4.93957e9 0.275273
\(367\) 2.10778e10 2.10778e10i 1.16188 1.16188i 0.177817 0.984064i \(-0.443096\pi\)
0.984064 0.177817i \(-0.0569036\pi\)
\(368\) 1.56595e10 + 1.56595e10i 0.853860 + 0.853860i
\(369\) 8.30009e9i 0.447690i
\(370\) 0 0
\(371\) 1.41636e10 0.747614
\(372\) 9.29330e9 9.29330e9i 0.485286 0.485286i
\(373\) −2.95974e9 2.95974e9i −0.152904 0.152904i 0.626510 0.779414i \(-0.284483\pi\)
−0.779414 + 0.626510i \(0.784483\pi\)
\(374\) 5.55913e9i 0.284132i
\(375\) 0 0
\(376\) 4.68764e9 0.234532
\(377\) 1.99895e10 1.99895e10i 0.989547 0.989547i
\(378\) −3.92631e9 3.92631e9i −0.192317 0.192317i
\(379\) 8.01600e9i 0.388509i −0.980951 0.194254i \(-0.937771\pi\)
0.980951 0.194254i \(-0.0622287\pi\)
\(380\) 0 0
\(381\) −9.13531e9 −0.433534
\(382\) −7.31429e9 + 7.31429e9i −0.343494 + 0.343494i
\(383\) −1.37328e10 1.37328e10i −0.638210 0.638210i 0.311904 0.950114i \(-0.399033\pi\)
−0.950114 + 0.311904i \(0.899033\pi\)
\(384\) 5.87961e9i 0.270411i
\(385\) 0 0
\(386\) −4.83380e10 −2.17741
\(387\) 8.09920e9 8.09920e9i 0.361076 0.361076i
\(388\) −3.04220e9 3.04220e9i −0.134234 0.134234i
\(389\) 1.23902e10i 0.541102i −0.962706 0.270551i \(-0.912794\pi\)
0.962706 0.270551i \(-0.0872059\pi\)
\(390\) 0 0
\(391\) −1.69553e10 −0.725436
\(392\) −3.77535e8 + 3.77535e8i −0.0159887 + 0.0159887i
\(393\) 8.06773e9 + 8.06773e9i 0.338206 + 0.338206i
\(394\) 3.22262e10i 1.33729i
\(395\) 0 0
\(396\) 2.06535e9 0.0839872
\(397\) 3.17968e10 3.17968e10i 1.28003 1.28003i 0.339385 0.940647i \(-0.389781\pi\)
0.940647 0.339385i \(-0.110219\pi\)
\(398\) 4.30771e10 + 4.30771e10i 1.71678 + 1.71678i
\(399\) 1.89319e10i 0.746970i
\(400\) 0 0
\(401\) −1.45051e10 −0.560976 −0.280488 0.959857i \(-0.590496\pi\)
−0.280488 + 0.959857i \(0.590496\pi\)
\(402\) −1.36532e10 + 1.36532e10i −0.522793 + 0.522793i
\(403\) −2.45209e10 2.45209e10i −0.929642 0.929642i
\(404\) 3.00474e10i 1.12793i
\(405\) 0 0
\(406\) −5.89736e10 −2.17047
\(407\) −3.48675e9 + 3.48675e9i −0.127070 + 0.127070i
\(408\) 1.85120e9 + 1.85120e9i 0.0668057 + 0.0668057i
\(409\) 4.43639e9i 0.158539i 0.996853 + 0.0792696i \(0.0252588\pi\)
−0.996853 + 0.0792696i \(0.974741\pi\)
\(410\) 0 0
\(411\) −1.74019e10 −0.609858
\(412\) 1.54239e10 1.54239e10i 0.535311 0.535311i
\(413\) 8.05749e9 + 8.05749e9i 0.276949 + 0.276949i
\(414\) 1.39454e10i 0.474710i
\(415\) 0 0
\(416\) 3.57105e10 1.19240
\(417\) −3.57341e9 + 3.57341e9i −0.118179 + 0.118179i
\(418\) −1.10233e10 1.10233e10i −0.361082 0.361082i
\(419\) 4.69093e10i 1.52196i −0.648777 0.760979i \(-0.724719\pi\)
0.648777 0.760979i \(-0.275281\pi\)
\(420\) 0 0
\(421\) 2.56171e10 0.815457 0.407728 0.913103i \(-0.366321\pi\)
0.407728 + 0.913103i \(0.366321\pi\)
\(422\) −2.06273e10 + 2.06273e10i −0.650417 + 0.650417i
\(423\) −7.44020e9 7.44020e9i −0.232393 0.232393i
\(424\) 5.49245e9i 0.169943i
\(425\) 0 0
\(426\) −4.32036e10 −1.31184
\(427\) −8.68448e9 + 8.68448e9i −0.261235 + 0.261235i
\(428\) −1.07656e10 1.07656e10i −0.320822 0.320822i
\(429\) 5.44954e9i 0.160891i
\(430\) 0 0
\(431\) 5.60467e10 1.62420 0.812102 0.583515i \(-0.198323\pi\)
0.812102 + 0.583515i \(0.198323\pi\)
\(432\) −5.42733e9 + 5.42733e9i −0.155830 + 0.155830i
\(433\) −4.29249e9 4.29249e9i −0.122112 0.122112i 0.643410 0.765522i \(-0.277519\pi\)
−0.765522 + 0.643410i \(0.777519\pi\)
\(434\) 7.23422e10i 2.03907i
\(435\) 0 0
\(436\) −1.24716e10 −0.345124
\(437\) −3.36209e10 + 3.36209e10i −0.921901 + 0.921901i
\(438\) 3.78744e10 + 3.78744e10i 1.02908 + 1.02908i
\(439\) 3.37587e10i 0.908925i 0.890766 + 0.454463i \(0.150169\pi\)
−0.890766 + 0.454463i \(0.849831\pi\)
\(440\) 0 0
\(441\) 1.19844e9 0.0316857
\(442\) −2.28469e10 + 2.28469e10i −0.598603 + 0.598603i
\(443\) 1.41248e10 + 1.41248e10i 0.366749 + 0.366749i 0.866290 0.499541i \(-0.166498\pi\)
−0.499541 + 0.866290i \(0.666498\pi\)
\(444\) 1.08619e10i 0.279495i
\(445\) 0 0
\(446\) 3.03806e10 0.767815
\(447\) −8.46459e9 + 8.46459e9i −0.212020 + 0.212020i
\(448\) −1.85449e10 1.85449e10i −0.460375 0.460375i
\(449\) 7.48403e10i 1.84141i −0.390260 0.920705i \(-0.627615\pi\)
0.390260 0.920705i \(-0.372385\pi\)
\(450\) 0 0
\(451\) −1.69935e10 −0.410750
\(452\) 1.13139e10 1.13139e10i 0.271055 0.271055i
\(453\) 9.99015e9 + 9.99015e9i 0.237235 + 0.237235i
\(454\) 2.67619e9i 0.0629932i
\(455\) 0 0
\(456\) 7.34155e9 0.169796
\(457\) 1.71094e10 1.71094e10i 0.392256 0.392256i −0.483235 0.875491i \(-0.660538\pi\)
0.875491 + 0.483235i \(0.160538\pi\)
\(458\) −3.20544e10 3.20544e10i −0.728493 0.728493i
\(459\) 5.87644e9i 0.132392i
\(460\) 0 0
\(461\) 8.67176e10 1.92001 0.960006 0.279981i \(-0.0903281\pi\)
0.960006 + 0.279981i \(0.0903281\pi\)
\(462\) −8.03870e9 + 8.03870e9i −0.176448 + 0.176448i
\(463\) −5.15336e10 5.15336e10i −1.12142 1.12142i −0.991529 0.129888i \(-0.958538\pi\)
−0.129888 0.991529i \(-0.541462\pi\)
\(464\) 8.15189e10i 1.75868i
\(465\) 0 0
\(466\) −8.39564e9 −0.178037
\(467\) 6.73199e9 6.73199e9i 0.141539 0.141539i −0.632787 0.774326i \(-0.718089\pi\)
0.774326 + 0.632787i \(0.218089\pi\)
\(468\) −8.48820e9 8.48820e9i −0.176942 0.176942i
\(469\) 4.80085e10i 0.992264i
\(470\) 0 0
\(471\) −7.12166e9 −0.144710
\(472\) 3.12459e9 3.12459e9i 0.0629542 0.0629542i
\(473\) −1.65822e10 1.65822e10i −0.331283 0.331283i
\(474\) 6.54060e10i 1.29570i
\(475\) 0 0
\(476\) 3.04472e10 0.593088
\(477\) −8.71759e9 + 8.71759e9i −0.168393 + 0.168393i
\(478\) −8.38298e9 8.38298e9i −0.160578 0.160578i
\(479\) 2.02194e10i 0.384084i 0.981387 + 0.192042i \(0.0615111\pi\)
−0.981387 + 0.192042i \(0.938489\pi\)
\(480\) 0 0
\(481\) 2.86597e10 0.535416
\(482\) −7.82549e10 + 7.82549e10i −1.44985 + 1.44985i
\(483\) 2.45180e10 + 2.45180e10i 0.450502 + 0.450502i
\(484\) 4.09817e10i 0.746807i
\(485\) 0 0
\(486\) 4.83324e9 0.0866349
\(487\) −5.31073e10 + 5.31073e10i −0.944145 + 0.944145i −0.998521 0.0543755i \(-0.982683\pi\)
0.0543755 + 0.998521i \(0.482683\pi\)
\(488\) 3.36773e9 + 3.36773e9i 0.0593824 + 0.0593824i
\(489\) 4.76588e10i 0.833504i
\(490\) 0 0
\(491\) 2.28584e10 0.393296 0.196648 0.980474i \(-0.436994\pi\)
0.196648 + 0.980474i \(0.436994\pi\)
\(492\) −2.64691e10 + 2.64691e10i −0.451730 + 0.451730i
\(493\) −4.41323e10 4.41323e10i −0.747083 0.747083i
\(494\) 9.06071e10i 1.52144i
\(495\) 0 0
\(496\) 9.99983e10 1.65221
\(497\) 7.59582e10 7.59582e10i 1.24494 1.24494i
\(498\) −4.08776e10 4.08776e10i −0.664612 0.664612i
\(499\) 5.00108e10i 0.806606i −0.915066 0.403303i \(-0.867862\pi\)
0.915066 0.403303i \(-0.132138\pi\)
\(500\) 0 0
\(501\) −3.27226e10 −0.519394
\(502\) 7.71272e9 7.71272e9i 0.121449 0.121449i
\(503\) 1.48953e10 + 1.48953e10i 0.232689 + 0.232689i 0.813814 0.581125i \(-0.197387\pi\)
−0.581125 + 0.813814i \(0.697387\pi\)
\(504\) 5.35381e9i 0.0829738i
\(505\) 0 0
\(506\) −2.85516e10 −0.435541
\(507\) 4.57810e9 4.57810e9i 0.0692873 0.0692873i
\(508\) 2.91326e10 + 2.91326e10i 0.437446 + 0.437446i
\(509\) 5.21786e10i 0.777358i 0.921373 + 0.388679i \(0.127068\pi\)
−0.921373 + 0.388679i \(0.872932\pi\)
\(510\) 0 0
\(511\) −1.33178e11 −1.95320
\(512\) −5.95792e10 + 5.95792e10i −0.866992 + 0.866992i
\(513\) −1.16525e10 1.16525e10i −0.168247 0.168247i
\(514\) 3.58812e10i 0.514060i
\(515\) 0 0
\(516\) −5.16569e10 −0.728668
\(517\) −1.52330e10 + 1.52330e10i −0.213218 + 0.213218i
\(518\) −4.22764e10 4.22764e10i −0.587190 0.587190i
\(519\) 2.43264e10i 0.335281i
\(520\) 0 0
\(521\) 9.76185e9 0.132489 0.0662447 0.997803i \(-0.478898\pi\)
0.0662447 + 0.997803i \(0.478898\pi\)
\(522\) 3.62978e10 3.62978e10i 0.488876 0.488876i
\(523\) 3.56960e10 + 3.56960e10i 0.477104 + 0.477104i 0.904204 0.427100i \(-0.140465\pi\)
−0.427100 + 0.904204i \(0.640465\pi\)
\(524\) 5.14562e10i 0.682515i
\(525\) 0 0
\(526\) −1.03216e11 −1.34836
\(527\) −5.41366e10 + 5.41366e10i −0.701856 + 0.701856i
\(528\) 1.11119e10 + 1.11119e10i 0.142972 + 0.142972i
\(529\) 8.77137e9i 0.112007i
\(530\) 0 0
\(531\) −9.91866e9 −0.124760
\(532\) 6.03741e10 6.03741e10i 0.753710 0.753710i
\(533\) 6.98402e10 + 6.98402e10i 0.865359 + 0.865359i
\(534\) 9.11685e10i 1.12119i
\(535\) 0 0
\(536\) −1.86171e10 −0.225555
\(537\) 4.86618e10 4.86618e10i 0.585182 0.585182i
\(538\) 8.75163e10 + 8.75163e10i 1.04462 + 1.04462i
\(539\) 2.45368e9i 0.0290712i
\(540\) 0 0
\(541\) −5.06153e10 −0.590871 −0.295436 0.955363i \(-0.595465\pi\)
−0.295436 + 0.955363i \(0.595465\pi\)
\(542\) 9.58290e10 9.58290e10i 1.11045 1.11045i
\(543\) −3.59638e10 3.59638e10i −0.413681 0.413681i
\(544\) 7.88406e10i 0.900232i
\(545\) 0 0
\(546\) 6.60750e10 0.743476
\(547\) −1.06937e11 + 1.06937e11i −1.19448 + 1.19448i −0.218683 + 0.975796i \(0.570176\pi\)
−0.975796 + 0.218683i \(0.929824\pi\)
\(548\) 5.54948e10 + 5.54948e10i 0.615361 + 0.615361i
\(549\) 1.06905e10i 0.117681i
\(550\) 0 0
\(551\) −1.75021e11 −1.89882
\(552\) 9.50776e9 9.50776e9i 0.102405 0.102405i
\(553\) 1.14993e11 + 1.14993e11i 1.22962 + 1.22962i
\(554\) 9.75559e9i 0.103565i
\(555\) 0 0
\(556\) 2.27913e10 0.238490
\(557\) 9.95647e10 9.95647e10i 1.03439 1.03439i 0.0350030 0.999387i \(-0.488856\pi\)
0.999387 0.0350030i \(-0.0111441\pi\)
\(558\) −4.45261e10 4.45261e10i −0.459281 0.459281i
\(559\) 1.36300e11i 1.39588i
\(560\) 0 0
\(561\) −1.20314e10 −0.121468
\(562\) 1.27663e11 1.27663e11i 1.27973 1.27973i
\(563\) −1.21355e11 1.21355e11i −1.20788 1.20788i −0.971713 0.236166i \(-0.924109\pi\)
−0.236166 0.971713i \(-0.575891\pi\)
\(564\) 4.74538e10i 0.468980i
\(565\) 0 0
\(566\) −4.12355e8 −0.00401796
\(567\) −8.49754e9 + 8.49754e9i −0.0822169 + 0.0822169i
\(568\) −2.94556e10 2.94556e10i −0.282992 0.282992i
\(569\) 1.62563e11i 1.55086i −0.631436 0.775428i \(-0.717534\pi\)
0.631436 0.775428i \(-0.282466\pi\)
\(570\) 0 0
\(571\) 7.54958e10 0.710197 0.355098 0.934829i \(-0.384447\pi\)
0.355098 + 0.934829i \(0.384447\pi\)
\(572\) −1.73787e10 + 1.73787e10i −0.162343 + 0.162343i
\(573\) 1.58300e10 + 1.58300e10i 0.146846 + 0.146846i
\(574\) 2.06044e11i 1.89807i
\(575\) 0 0
\(576\) 2.28285e10 0.207390
\(577\) −1.95276e10 + 1.95276e10i −0.176175 + 0.176175i −0.789686 0.613511i \(-0.789757\pi\)
0.613511 + 0.789686i \(0.289757\pi\)
\(578\) −5.61432e10 5.61432e10i −0.503021 0.503021i
\(579\) 1.04616e11i 0.930857i
\(580\) 0 0
\(581\) 1.43738e11 1.26144
\(582\) −1.45758e10 + 1.45758e10i −0.127040 + 0.127040i
\(583\) 1.78483e10 + 1.78483e10i 0.154498 + 0.154498i
\(584\) 5.16445e10i 0.443990i
\(585\) 0 0
\(586\) 1.56983e11 1.33126
\(587\) 1.15917e11 1.15917e11i 0.976322 0.976322i −0.0234041 0.999726i \(-0.507450\pi\)
0.999726 + 0.0234041i \(0.00745043\pi\)
\(588\) −3.82185e9 3.82185e9i −0.0319716 0.0319716i
\(589\) 2.14696e11i 1.78387i
\(590\) 0 0
\(591\) −6.97457e10 −0.571699
\(592\) −5.84385e10 + 5.84385e10i −0.475786 + 0.475786i
\(593\) 8.32677e10 + 8.32677e10i 0.673377 + 0.673377i 0.958493 0.285116i \(-0.0920322\pi\)
−0.285116 + 0.958493i \(0.592032\pi\)
\(594\) 9.89553e9i 0.0794865i
\(595\) 0 0
\(596\) 5.39874e10 0.427866
\(597\) 9.32297e10 9.32297e10i 0.733934 0.733934i
\(598\) 1.17342e11 + 1.17342e11i 0.917588 + 0.917588i
\(599\) 1.05049e11i 0.815991i −0.912984 0.407995i \(-0.866228\pi\)
0.912984 0.407995i \(-0.133772\pi\)
\(600\) 0 0
\(601\) −6.20830e10 −0.475855 −0.237928 0.971283i \(-0.576468\pi\)
−0.237928 + 0.971283i \(0.576468\pi\)
\(602\) 2.01057e11 2.01057e11i 1.53086 1.53086i
\(603\) 2.95489e10 + 2.95489e10i 0.223497 + 0.223497i
\(604\) 6.37174e10i 0.478752i
\(605\) 0 0
\(606\) 1.43963e11 1.06748
\(607\) −8.59912e10 + 8.59912e10i −0.633431 + 0.633431i −0.948927 0.315496i \(-0.897829\pi\)
0.315496 + 0.948927i \(0.397829\pi\)
\(608\) −1.56334e11 1.56334e11i −1.14404 1.14404i
\(609\) 1.27634e11i 0.927890i
\(610\) 0 0
\(611\) 1.25209e11 0.898405
\(612\) −1.87400e10 + 1.87400e10i −0.133587 + 0.133587i
\(613\) 9.83687e10 + 9.83687e10i 0.696651 + 0.696651i 0.963687 0.267036i \(-0.0860442\pi\)
−0.267036 + 0.963687i \(0.586044\pi\)
\(614\) 6.60340e10i 0.464616i
\(615\) 0 0
\(616\) −1.09613e10 −0.0761274
\(617\) −2.02120e11 + 2.02120e11i −1.39466 + 1.39466i −0.580166 + 0.814498i \(0.697012\pi\)
−0.814498 + 0.580166i \(0.802988\pi\)
\(618\) −7.38993e10 7.38993e10i −0.506625 0.506625i
\(619\) 1.10074e11i 0.749758i 0.927074 + 0.374879i \(0.122316\pi\)
−0.927074 + 0.374879i \(0.877684\pi\)
\(620\) 0 0
\(621\) −3.01813e10 −0.202942
\(622\) 9.84051e10 9.84051e10i 0.657440 0.657440i
\(623\) 1.60288e11 + 1.60288e11i 1.06401 + 1.06401i
\(624\) 9.13352e10i 0.602421i
\(625\) 0 0
\(626\) −3.20007e11 −2.08383
\(627\) −2.38572e10 + 2.38572e10i −0.154365 + 0.154365i
\(628\) 2.27111e10 + 2.27111e10i 0.146016 + 0.146016i
\(629\) 6.32742e10i 0.404226i
\(630\) 0 0
\(631\) 2.25703e11 1.42371 0.711854 0.702328i \(-0.247856\pi\)
0.711854 + 0.702328i \(0.247856\pi\)
\(632\) 4.45929e10 4.45929e10i 0.279510 0.279510i
\(633\) 4.46427e10 + 4.46427e10i 0.278058 + 0.278058i
\(634\) 3.09611e11i 1.91628i
\(635\) 0 0
\(636\) 5.56010e10 0.339824
\(637\) −1.00842e10 + 1.00842e10i −0.0612466 + 0.0612466i
\(638\) −7.43159e10 7.43159e10i −0.448537 0.448537i
\(639\) 9.35035e10i 0.560821i
\(640\) 0 0
\(641\) −8.36281e9 −0.0495359 −0.0247679 0.999693i \(-0.507885\pi\)
−0.0247679 + 0.999693i \(0.507885\pi\)
\(642\) −5.15803e10 + 5.15803e10i −0.303629 + 0.303629i
\(643\) −9.94984e10 9.94984e10i −0.582066 0.582066i 0.353405 0.935471i \(-0.385024\pi\)
−0.935471 + 0.353405i \(0.885024\pi\)
\(644\) 1.56376e11i 0.909134i
\(645\) 0 0
\(646\) 2.00040e11 1.14865
\(647\) −1.64550e11 + 1.64550e11i −0.939035 + 0.939035i −0.998245 0.0592109i \(-0.981142\pi\)
0.0592109 + 0.998245i \(0.481142\pi\)
\(648\) 3.29523e9 + 3.29523e9i 0.0186890 + 0.0186890i
\(649\) 2.03074e10i 0.114466i
\(650\) 0 0
\(651\) 1.56567e11 0.871718
\(652\) 1.51984e11 1.51984e11i 0.841025 0.841025i
\(653\) 6.64536e10 + 6.64536e10i 0.365482 + 0.365482i 0.865826 0.500344i \(-0.166793\pi\)
−0.500344 + 0.865826i \(0.666793\pi\)
\(654\) 5.97539e10i 0.326629i
\(655\) 0 0
\(656\) −2.84814e11 −1.53797
\(657\) 8.19699e10 8.19699e10i 0.439940 0.439940i
\(658\) −1.84698e11 1.84698e11i −0.985278 0.985278i
\(659\) 5.17280e10i 0.274273i 0.990552 + 0.137137i \(0.0437900\pi\)
−0.990552 + 0.137137i \(0.956210\pi\)
\(660\) 0 0
\(661\) −1.89964e11 −0.995095 −0.497547 0.867437i \(-0.665766\pi\)
−0.497547 + 0.867437i \(0.665766\pi\)
\(662\) −3.29169e11 + 3.29169e11i −1.71391 + 1.71391i
\(663\) 4.94466e10 + 4.94466e10i 0.255907 + 0.255907i
\(664\) 5.57396e10i 0.286742i
\(665\) 0 0
\(666\) 5.20416e10 0.264517
\(667\) −2.26663e11 + 2.26663e11i −1.14519 + 1.14519i
\(668\) 1.04353e11 + 1.04353e11i 0.524081 + 0.524081i
\(669\) 6.57512e10i 0.328246i
\(670\) 0 0
\(671\) −2.18876e10 −0.107971
\(672\) −1.14006e11 + 1.14006e11i −0.559052 + 0.559052i
\(673\) −1.70060e11 1.70060e11i −0.828978 0.828978i 0.158397 0.987375i \(-0.449367\pi\)
−0.987375 + 0.158397i \(0.949367\pi\)
\(674\) 1.26583e11i 0.613387i
\(675\) 0 0
\(676\) −2.91992e10 −0.139825
\(677\) 2.18049e11 2.18049e11i 1.03801 1.03801i 0.0387581 0.999249i \(-0.487660\pi\)
0.999249 0.0387581i \(-0.0123402\pi\)
\(678\) −5.42072e10 5.42072e10i −0.256530 0.256530i
\(679\) 5.12529e10i 0.241123i
\(680\) 0 0
\(681\) −5.79195e9 −0.0269300
\(682\) −9.11624e10 + 9.11624e10i −0.421384 + 0.421384i
\(683\) −1.05222e11 1.05222e11i −0.483530 0.483530i 0.422727 0.906257i \(-0.361073\pi\)
−0.906257 + 0.422727i \(0.861073\pi\)
\(684\) 7.43197e10i 0.339531i
\(685\) 0 0
\(686\) −2.83225e11 −1.27890
\(687\) −6.93738e10 + 6.93738e10i −0.311436 + 0.311436i
\(688\) −2.77921e11 2.77921e11i −1.24042 1.24042i
\(689\) 1.46706e11i 0.650986i
\(690\) 0 0
\(691\) −3.02900e11 −1.32858 −0.664290 0.747475i \(-0.731266\pi\)
−0.664290 + 0.747475i \(0.731266\pi\)
\(692\) −7.75773e10 + 7.75773e10i −0.338307 + 0.338307i
\(693\) 1.73978e10 + 1.73978e10i 0.0754329 + 0.0754329i
\(694\) 4.12800e11i 1.77951i
\(695\) 0 0
\(696\) 4.94947e10 0.210922
\(697\) 1.54191e11 1.54191e11i 0.653324 0.653324i
\(698\) −1.12604e11 1.12604e11i −0.474388 0.474388i
\(699\) 1.81703e10i 0.0761120i
\(700\) 0 0
\(701\) −3.79525e11 −1.57170 −0.785849 0.618419i \(-0.787773\pi\)
−0.785849 + 0.618419i \(0.787773\pi\)
\(702\) −4.06687e10 + 4.06687e10i −0.167460 + 0.167460i
\(703\) −1.25467e11 1.25467e11i −0.513700 0.513700i
\(704\) 4.67388e10i 0.190277i
\(705\) 0 0
\(706\) 3.93154e11 1.58250
\(707\) −2.53108e11 + 2.53108e11i −1.01305 + 1.01305i
\(708\) 3.16307e10 + 3.16307e10i 0.125886 + 0.125886i
\(709\) 2.85486e11i 1.12980i −0.825160 0.564899i \(-0.808915\pi\)
0.825160 0.564899i \(-0.191085\pi\)
\(710\) 0 0
\(711\) −1.41555e11 −0.553920
\(712\) 6.21574e10 6.21574e10i 0.241865 0.241865i
\(713\) 2.78045e11 + 2.78045e11i 1.07586 + 1.07586i
\(714\) 1.45879e11i 0.561305i
\(715\) 0 0
\(716\) −3.10366e11 −1.18092
\(717\) −1.81429e10 + 1.81429e10i −0.0686483 + 0.0686483i
\(718\) −4.10213e10 4.10213e10i −0.154352 0.154352i
\(719\) 2.09894e11i 0.785389i −0.919669 0.392695i \(-0.871543\pi\)
0.919669 0.392695i \(-0.128457\pi\)
\(720\) 0 0
\(721\) 2.59851e11 0.961577
\(722\) 1.37167e11 1.37167e11i 0.504777 0.504777i
\(723\) 1.69364e11 + 1.69364e11i 0.619822 + 0.619822i
\(724\) 2.29378e11i 0.834829i
\(725\) 0 0
\(726\) 1.96352e11 0.706787
\(727\) 7.80140e10 7.80140e10i 0.279277 0.279277i −0.553543 0.832820i \(-0.686725\pi\)
0.832820 + 0.553543i \(0.186725\pi\)
\(728\) 4.50490e10 + 4.50490e10i 0.160384 + 0.160384i
\(729\) 1.04604e10i 0.0370370i
\(730\) 0 0
\(731\) 3.00919e11 1.05385
\(732\) −3.40921e10 + 3.40921e10i −0.118743 + 0.118743i
\(733\) 6.83172e10 + 6.83172e10i 0.236654 + 0.236654i 0.815463 0.578809i \(-0.196482\pi\)
−0.578809 + 0.815463i \(0.696482\pi\)
\(734\) 6.44106e11i 2.21908i
\(735\) 0 0
\(736\) −4.04925e11 −1.37995
\(737\) 6.04982e10 6.04982e10i 0.205056 0.205056i
\(738\) 1.26819e11 + 1.26819e11i 0.427522 + 0.427522i
\(739\) 1.68021e11i 0.563358i 0.959509 + 0.281679i \(0.0908914\pi\)
−0.959509 + 0.281679i \(0.909109\pi\)
\(740\) 0 0
\(741\) 1.96097e11 0.650425
\(742\) −2.16409e11 + 2.16409e11i −0.713935 + 0.713935i
\(743\) −4.02895e11 4.02895e11i −1.32201 1.32201i −0.912143 0.409872i \(-0.865573\pi\)
−0.409872 0.912143i \(-0.634427\pi\)
\(744\) 6.07146e10i 0.198153i
\(745\) 0 0
\(746\) 9.04450e10 0.292031
\(747\) −8.84695e10 + 8.84695e10i −0.284126 + 0.284126i
\(748\) 3.83682e10 + 3.83682e10i 0.122564 + 0.122564i
\(749\) 1.81371e11i 0.576290i
\(750\) 0 0
\(751\) 1.15049e11 0.361678 0.180839 0.983513i \(-0.442119\pi\)
0.180839 + 0.983513i \(0.442119\pi\)
\(752\) −2.55307e11 + 2.55307e11i −0.798348 + 0.798348i
\(753\) −1.66923e10 1.66923e10i −0.0519201 0.0519201i
\(754\) 6.10848e11i 1.88994i
\(755\) 0 0
\(756\) 5.41975e10 0.165917
\(757\) 1.32371e11 1.32371e11i 0.403096 0.403096i −0.476227 0.879323i \(-0.657996\pi\)
0.879323 + 0.476227i \(0.157996\pi\)
\(758\) 1.22478e11 + 1.22478e11i 0.371007 + 0.371007i
\(759\) 6.17930e10i 0.186197i
\(760\) 0 0
\(761\) 2.75577e11 0.821683 0.410841 0.911707i \(-0.365235\pi\)
0.410841 + 0.911707i \(0.365235\pi\)
\(762\) 1.39580e11 1.39580e11i 0.414004 0.414004i
\(763\) −1.05056e11 1.05056e11i −0.309972 0.309972i
\(764\) 1.00964e11i 0.296342i
\(765\) 0 0
\(766\) 4.19652e11 1.21892
\(767\) 8.34594e10 8.34594e10i 0.241154 0.241154i
\(768\) 1.78200e11 + 1.78200e11i 0.512228 + 0.512228i
\(769\) 6.27339e10i 0.179390i 0.995969 + 0.0896948i \(0.0285892\pi\)
−0.995969 + 0.0896948i \(0.971411\pi\)
\(770\) 0 0
\(771\) −7.76559e10 −0.219764
\(772\) 3.33621e11 3.33621e11i 0.939257 0.939257i
\(773\) 2.75539e11 + 2.75539e11i 0.771730 + 0.771730i 0.978409 0.206679i \(-0.0662655\pi\)
−0.206679 + 0.978409i \(0.566265\pi\)
\(774\) 2.47499e11i 0.689620i
\(775\) 0 0
\(776\) −1.98752e10 −0.0548106
\(777\) −9.14968e10 + 9.14968e10i −0.251028 + 0.251028i
\(778\) 1.89312e11 + 1.89312e11i 0.516726 + 0.516726i
\(779\) 6.11496e11i 1.66052i
\(780\) 0 0
\(781\) 1.91438e11 0.514546
\(782\) 2.59064e11 2.59064e11i 0.692756 0.692756i
\(783\) −7.85577e10 7.85577e10i −0.208998 0.208998i
\(784\) 4.11241e10i 0.108851i
\(785\) 0 0
\(786\) −2.46537e11 −0.645940
\(787\) −2.59480e11 + 2.59480e11i −0.676402 + 0.676402i −0.959184 0.282782i \(-0.908743\pi\)
0.282782 + 0.959184i \(0.408743\pi\)
\(788\) 2.22420e11 + 2.22420e11i 0.576858 + 0.576858i
\(789\) 2.23386e11i 0.576432i
\(790\) 0 0
\(791\) 1.90608e11 0.486895
\(792\) 6.74663e9 6.74663e9i 0.0171469 0.0171469i
\(793\) 8.99537e10 + 8.99537e10i 0.227471 + 0.227471i
\(794\) 9.71660e11i 2.44474i
\(795\) 0 0
\(796\) −5.94622e11 −1.48111
\(797\) 2.57815e11 2.57815e11i 0.638961 0.638961i −0.311338 0.950299i \(-0.600777\pi\)
0.950299 + 0.311338i \(0.100777\pi\)
\(798\) −2.89265e11 2.89265e11i −0.713320 0.713320i
\(799\) 2.76434e11i 0.678273i
\(800\) 0 0
\(801\) −1.97312e11 −0.479317
\(802\) 2.21627e11 2.21627e11i 0.535705 0.535705i
\(803\) −1.67824e11 1.67824e11i −0.403639 0.403639i
\(804\) 1.88464e11i 0.451028i
\(805\) 0 0
\(806\) 7.49320e11 1.77553
\(807\) 1.89407e11 1.89407e11i 0.446584 0.446584i
\(808\) 9.81522e10 + 9.81522e10i 0.230279 + 0.230279i
\(809\) 4.40964e11i 1.02946i 0.857353 + 0.514729i \(0.172108\pi\)
−0.857353 + 0.514729i \(0.827892\pi\)
\(810\) 0 0
\(811\) 3.14945e11 0.728033 0.364016 0.931393i \(-0.381405\pi\)
0.364016 + 0.931393i \(0.381405\pi\)
\(812\) 4.07026e11 4.07026e11i 0.936262 0.936262i
\(813\) −2.07398e11 2.07398e11i −0.474726 0.474726i
\(814\) 1.06550e11i 0.242691i
\(815\) 0 0
\(816\) −2.01648e11 −0.454813
\(817\) 5.96696e11 5.96696e11i 1.33926 1.33926i
\(818\) −6.77846e10 6.77846e10i −0.151397 0.151397i
\(819\) 1.43003e11i 0.317841i
\(820\) 0 0
\(821\) 2.96960e11 0.653621 0.326810 0.945090i \(-0.394026\pi\)
0.326810 + 0.945090i \(0.394026\pi\)
\(822\) 2.65887e11 2.65887e11i 0.582385 0.582385i
\(823\) 1.54849e11 + 1.54849e11i 0.337526 + 0.337526i 0.855436 0.517909i \(-0.173289\pi\)
−0.517909 + 0.855436i \(0.673289\pi\)
\(824\) 1.00767e11i 0.218579i
\(825\) 0 0
\(826\) −2.46224e11 −0.528945
\(827\) 4.19074e10 4.19074e10i 0.0895919 0.0895919i −0.660890 0.750482i \(-0.729821\pi\)
0.750482 + 0.660890i \(0.229821\pi\)
\(828\) 9.62486e10 + 9.62486e10i 0.204773 + 0.204773i
\(829\) 6.56756e10i 0.139055i −0.997580 0.0695274i \(-0.977851\pi\)
0.997580 0.0695274i \(-0.0221491\pi\)
\(830\) 0 0
\(831\) 2.11136e10 0.0442749
\(832\) −1.92088e11 + 1.92088e11i −0.400872 + 0.400872i
\(833\) 2.22635e10 + 2.22635e10i 0.0462396 + 0.0462396i
\(834\) 1.09198e11i 0.225710i
\(835\) 0 0
\(836\) 1.52162e11 0.311516
\(837\) −9.63658e10 + 9.63658e10i −0.196346 + 0.196346i
\(838\) 7.16737e11 + 7.16737e11i 1.45340 + 1.45340i
\(839\) 7.98678e11i 1.61185i −0.592020 0.805924i \(-0.701669\pi\)
0.592020 0.805924i \(-0.298331\pi\)
\(840\) 0 0
\(841\) −6.79697e11 −1.35872
\(842\) −3.91409e11 + 3.91409e11i −0.778721 + 0.778721i
\(843\) −2.76295e11 2.76295e11i −0.547094 0.547094i
\(844\) 2.84732e11i 0.561134i
\(845\) 0 0
\(846\) 2.27361e11 0.443848
\(847\) −3.45215e11 + 3.45215e11i −0.670743 + 0.670743i
\(848\) 2.99141e11 + 2.99141e11i 0.578485 + 0.578485i
\(849\) 8.92440e8i 0.00171770i
\(850\) 0 0
\(851\) −3.24976e11 −0.619630
\(852\) 2.98184e11 2.98184e11i 0.565882 0.565882i
\(853\) 1.87598e11 + 1.87598e11i 0.354350 + 0.354350i 0.861725 0.507375i \(-0.169384\pi\)
−0.507375 + 0.861725i \(0.669384\pi\)
\(854\) 2.65384e11i 0.498934i
\(855\) 0 0
\(856\) −7.03334e10 −0.130999
\(857\) 4.78106e11 4.78106e11i 0.886342 0.886342i −0.107828 0.994170i \(-0.534390\pi\)
0.994170 + 0.107828i \(0.0343896\pi\)
\(858\) 8.32648e10 + 8.32648e10i 0.153643 + 0.153643i
\(859\) 2.92378e11i 0.536996i 0.963280 + 0.268498i \(0.0865273\pi\)
−0.963280 + 0.268498i \(0.913473\pi\)
\(860\) 0 0
\(861\) −4.45932e11 −0.811440
\(862\) −8.56349e11 + 8.56349e11i −1.55104 + 1.55104i
\(863\) −8.69978e10 8.69978e10i −0.156843 0.156843i 0.624323 0.781166i \(-0.285375\pi\)
−0.781166 + 0.624323i \(0.785375\pi\)
\(864\) 1.40340e11i 0.251842i
\(865\) 0 0
\(866\) 1.31172e11 0.233222
\(867\) −1.21508e11 + 1.21508e11i −0.215045 + 0.215045i
\(868\) −4.99294e11 4.99294e11i −0.879584 0.879584i
\(869\) 2.89819e11i 0.508215i
\(870\) 0 0
\(871\) −4.97272e11 −0.864015
\(872\) −4.07394e10 + 4.07394e10i −0.0704609 + 0.0704609i
\(873\) 3.15458e10 + 3.15458e10i 0.0543106 + 0.0543106i
\(874\) 1.02740e12i 1.76074i
\(875\) 0 0
\(876\) −5.22806e11 −0.887819
\(877\) 3.39966e11 3.39966e11i 0.574695 0.574695i −0.358742 0.933437i \(-0.616794\pi\)
0.933437 + 0.358742i \(0.116794\pi\)
\(878\) −5.15807e11 5.15807e11i −0.867979 0.867979i
\(879\) 3.39751e11i 0.569122i
\(880\) 0 0
\(881\) 2.22272e11 0.368961 0.184480 0.982836i \(-0.440940\pi\)
0.184480 + 0.982836i \(0.440940\pi\)
\(882\) −1.83113e10 + 1.83113e10i −0.0302583 + 0.0302583i
\(883\) 2.34413e11 + 2.34413e11i 0.385602 + 0.385602i 0.873116 0.487513i \(-0.162096\pi\)
−0.487513 + 0.873116i \(0.662096\pi\)
\(884\) 3.15372e11i 0.516432i
\(885\) 0 0
\(886\) −4.31633e11 −0.700454
\(887\) −7.39337e11 + 7.39337e11i −1.19439 + 1.19439i −0.218574 + 0.975820i \(0.570140\pi\)
−0.975820 + 0.218574i \(0.929860\pi\)
\(888\) 3.54813e10 + 3.54813e10i 0.0570620 + 0.0570620i
\(889\) 4.90806e11i 0.785783i
\(890\) 0 0
\(891\) −2.14164e10 −0.0339810
\(892\) −2.09682e11 + 2.09682e11i −0.331208 + 0.331208i
\(893\) −5.48145e11 5.48145e11i −0.861965 0.861965i
\(894\) 2.58665e11i 0.404937i
\(895\) 0 0
\(896\) −3.15889e11 −0.490120
\(897\) 2.53957e11 2.53957e11i 0.392275 0.392275i
\(898\) 1.14350e12 + 1.14350e12i 1.75846 + 1.75846i
\(899\) 1.44742e12i 2.21593i
\(900\) 0 0
\(901\) −3.23894e11 −0.491478
\(902\) 2.59648e11 2.59648e11i 0.392246 0.392246i
\(903\) −4.35139e11 4.35139e11i −0.654451 0.654451i
\(904\) 7.39154e10i 0.110678i
\(905\) 0 0
\(906\) −3.05284e11 −0.453096
\(907\) 9.79482e10 9.79482e10i 0.144733 0.144733i −0.631027 0.775760i \(-0.717367\pi\)
0.775760 + 0.631027i \(0.217367\pi\)
\(908\) 1.84706e10 + 1.84706e10i 0.0271730 + 0.0271730i
\(909\) 3.11573e11i 0.456357i
\(910\) 0 0
\(911\) −6.30284e10 −0.0915088 −0.0457544 0.998953i \(-0.514569\pi\)
−0.0457544 + 0.998953i \(0.514569\pi\)
\(912\) −3.99850e11 + 3.99850e11i −0.577987 + 0.577987i
\(913\) 1.81132e11 + 1.81132e11i 0.260682 + 0.260682i
\(914\) 5.22836e11i 0.749171i
\(915\) 0 0
\(916\) 4.42468e11 0.628492
\(917\) 4.33449e11 4.33449e11i 0.613000 0.613000i
\(918\) 8.97874e10 + 8.97874e10i 0.126428 + 0.126428i
\(919\) 1.20904e12i 1.69503i −0.530772 0.847515i \(-0.678098\pi\)
0.530772 0.847515i \(-0.321902\pi\)
\(920\) 0 0
\(921\) 1.42914e11 0.198626
\(922\) −1.32498e12 + 1.32498e12i −1.83352 + 1.83352i
\(923\) −7.86774e11 7.86774e11i −1.08403 1.08403i
\(924\) 1.10964e11i 0.152227i
\(925\) 0 0
\(926\) 1.57479e12 2.14180
\(927\) −1.59937e11 + 1.59937e11i −0.216585 + 0.216585i
\(928\) −1.05396e12 1.05396e12i −1.42113 1.42113i
\(929\) 1.37970e12i 1.85234i 0.377106 + 0.926170i \(0.376919\pi\)
−0.377106 + 0.926170i \(0.623081\pi\)
\(930\) 0 0
\(931\) 8.82934e10 0.117525
\(932\) 5.79453e10 5.79453e10i 0.0767988 0.0767988i
\(933\) −2.12974e11 2.12974e11i −0.281060 0.281060i
\(934\) 2.05719e11i 0.270325i
\(935\) 0 0
\(936\) −5.54547e10 −0.0722496
\(937\) 1.57203e11 1.57203e11i 0.203940 0.203940i −0.597746 0.801686i \(-0.703937\pi\)
0.801686 + 0.597746i \(0.203937\pi\)
\(938\) 7.33533e11 + 7.33533e11i 0.947564 + 0.947564i
\(939\) 6.92576e11i 0.890851i
\(940\) 0 0
\(941\) 5.08269e11 0.648239 0.324120 0.946016i \(-0.394932\pi\)
0.324120 + 0.946016i \(0.394932\pi\)
\(942\) 1.08813e11 1.08813e11i 0.138191 0.138191i
\(943\) −7.91925e11 7.91925e11i −1.00147 1.00147i
\(944\) 3.40355e11i 0.428592i
\(945\) 0 0
\(946\) 5.06727e11 0.632717
\(947\) −4.22518e11 + 4.22518e11i −0.525346 + 0.525346i −0.919181 0.393835i \(-0.871148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(948\) 4.51421e11 + 4.51421e11i 0.558918 + 0.558918i
\(949\) 1.37945e12i 1.70076i
\(950\) 0 0
\(951\) 6.70077e11 0.819224
\(952\) 9.94581e10 9.94581e10i 0.121086 0.121086i
\(953\) −5.77256e11 5.77256e11i −0.699837 0.699837i 0.264538 0.964375i \(-0.414781\pi\)
−0.964375 + 0.264538i \(0.914781\pi\)
\(954\) 2.66396e11i 0.321613i
\(955\) 0 0
\(956\) 1.15716e11 0.138536
\(957\) −1.60838e11 + 1.60838e11i −0.191753 + 0.191753i
\(958\) −3.08937e11 3.08937e11i −0.366782 0.366782i
\(959\) 9.34936e11i 1.10537i
\(960\) 0 0
\(961\) 9.22646e11 1.08179
\(962\) −4.37898e11 + 4.37898e11i −0.511297 + 0.511297i
\(963\) 1.11633e11 + 1.11633e11i 0.129804 + 0.129804i
\(964\) 1.08020e12i 1.25083i
\(965\) 0 0
\(966\) −7.49232e11 −0.860415
\(967\) 6.14848e11 6.14848e11i 0.703173 0.703173i −0.261918 0.965090i \(-0.584355\pi\)
0.965090 + 0.261918i \(0.0843549\pi\)
\(968\) 1.33870e11 + 1.33870e11i 0.152469 + 0.152469i
\(969\) 4.32937e11i 0.491055i
\(970\) 0 0
\(971\) −3.74017e11 −0.420741 −0.210370 0.977622i \(-0.567467\pi\)
−0.210370 + 0.977622i \(0.567467\pi\)
\(972\) −3.33582e10 + 3.33582e10i −0.0373712 + 0.0373712i
\(973\) 1.91986e11 + 1.91986e11i 0.214199 + 0.214199i
\(974\) 1.62288e12i 1.80323i
\(975\) 0 0
\(976\) −3.66839e11 −0.404275
\(977\) −5.84649e11 + 5.84649e11i −0.641678 + 0.641678i −0.950968 0.309290i \(-0.899909\pi\)
0.309290 + 0.950968i \(0.399909\pi\)
\(978\) −7.28189e11 7.28189e11i −0.795956 0.795956i
\(979\) 4.03974e11i 0.439767i
\(980\) 0 0
\(981\) 1.29323e11 0.139636
\(982\) −3.49259e11 + 3.49259e11i −0.375579 + 0.375579i
\(983\) 1.87740e11 + 1.87740e11i 0.201068 + 0.201068i 0.800457 0.599390i \(-0.204590\pi\)
−0.599390 + 0.800457i \(0.704590\pi\)
\(984\) 1.72927e11i 0.184451i
\(985\) 0 0
\(986\) 1.34861e12 1.42686
\(987\) −3.99734e11 + 3.99734e11i −0.421213 + 0.421213i
\(988\) −6.25355e11 6.25355e11i −0.656295 0.656295i
\(989\) 1.54552e12i 1.61543i
\(990\) 0 0
\(991\) −3.37718e11 −0.350155 −0.175077 0.984555i \(-0.556018\pi\)
−0.175077 + 0.984555i \(0.556018\pi\)
\(992\) −1.29288e12 + 1.29288e12i −1.33510 + 1.33510i
\(993\) 7.12405e11 + 7.12405e11i 0.732706 + 0.732706i
\(994\) 2.32116e12i 2.37772i
\(995\) 0 0
\(996\) 5.64261e11 0.573380
\(997\) 5.07145e11 5.07145e11i 0.513277 0.513277i −0.402252 0.915529i \(-0.631772\pi\)
0.915529 + 0.402252i \(0.131772\pi\)
\(998\) 7.64126e11 + 7.64126e11i 0.770270 + 0.770270i
\(999\) 1.12631e11i 0.113083i
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 75.9.f.d.43.2 yes 12
5.2 odd 4 inner 75.9.f.d.7.2 12
5.3 odd 4 inner 75.9.f.d.7.5 yes 12
5.4 even 2 inner 75.9.f.d.43.5 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.f.d.7.2 12 5.2 odd 4 inner
75.9.f.d.7.5 yes 12 5.3 odd 4 inner
75.9.f.d.43.2 yes 12 1.1 even 1 trivial
75.9.f.d.43.5 yes 12 5.4 even 2 inner