Properties

Label 75.9.d.c.74.17
Level $75$
Weight $9$
Character 75.74
Analytic conductor $30.553$
Analytic rank $0$
Dimension $20$
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(74,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.74");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not 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: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + 3390679484573 x^{8} + 32981662033730 x^{6} + \cdots + 336685801 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{28}\cdot 3^{22}\cdot 5^{32} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.17
Root \(2.23448i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.c.74.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+23.7888 q^{2} +(-10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 - 1911.92i) q^{6} +692.753i q^{7} +1282.36 q^{8} +(-6357.89 + 1619.88i) q^{9} +O(q^{10})\) \(q+23.7888 q^{2} +(-10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 - 1911.92i) q^{6} +692.753i q^{7} +1282.36 q^{8} +(-6357.89 + 1619.88i) q^{9} -15881.8i q^{11} +(-3123.09 - 24907.4i) q^{12} -48870.9i q^{13} +16479.8i q^{14} -48830.2 q^{16} -41025.6 q^{17} +(-151246. + 38534.9i) q^{18} +108213. q^{19} +(55677.0 - 6981.24i) q^{21} -377809. i q^{22} -433886. q^{23} +(-12923.0 - 103064. i) q^{24} -1.16258e6i q^{26} +(194262. + 494663. i) q^{27} +214688. i q^{28} +377879. i q^{29} -408921. q^{31} -1.48989e6 q^{32} +(-1.27643e6 + 160049. i) q^{33} -975949. q^{34} +(-1.97035e6 + 502009. i) q^{36} -2.31002e6i q^{37} +2.57425e6 q^{38} +(-3.92778e6 + 492497. i) q^{39} +2.15170e6i q^{41} +(1.32449e6 - 166075. i) q^{42} -2.42811e6i q^{43} -4.92187e6i q^{44} -1.03216e7 q^{46} +8.18110e6 q^{47} +(492087. + 3.92451e6i) q^{48} +5.28489e6 q^{49} +(413437. + 3.29725e6i) q^{51} -1.51454e7i q^{52} +1.36324e7 q^{53} +(4.62126e6 + 1.17674e7i) q^{54} +888360. i q^{56} +(-1.09052e6 - 8.69714e6i) q^{57} +8.98929e6i q^{58} -1.23667e7i q^{59} -1.15129e6 q^{61} -9.72773e6 q^{62} +(-1.12217e6 - 4.40445e6i) q^{63} -2.29423e7 q^{64} +(-3.03647e7 + 3.80738e6i) q^{66} +1.55586e7i q^{67} -1.27141e7 q^{68} +(4.37250e6 + 3.48717e7i) q^{69} -2.52525e7i q^{71} +(-8.15311e6 + 2.07727e6i) q^{72} -2.29182e7i q^{73} -5.49526e7i q^{74} +3.35358e7 q^{76} +1.10022e7 q^{77} +(-9.34372e7 + 1.17159e7i) q^{78} -4.49938e7 q^{79} +(3.77987e7 - 2.05980e7i) q^{81} +5.11864e7i q^{82} +2.12119e7 q^{83} +(1.72547e7 - 2.16353e6i) q^{84} -5.77618e7i q^{86} +(3.03704e7 - 3.80809e6i) q^{87} -2.03662e7i q^{88} +4.87898e7i q^{89} +3.38555e7 q^{91} -1.34464e8 q^{92} +(4.12091e6 + 3.28652e7i) q^{93} +1.94618e8 q^{94} +(1.50145e7 + 1.19744e8i) q^{96} -2.91619e7i q^{97} +1.25721e8 q^{98} +(2.57265e7 + 1.00975e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.7888 1.48680 0.743399 0.668848i \(-0.233212\pi\)
0.743399 + 0.668848i \(0.233212\pi\)
\(3\) −10.0775 80.3707i −0.124414 0.992230i
\(4\) 309.906 1.21057
\(5\) 0 0
\(6\) −239.732 1911.92i −0.184978 1.47525i
\(7\) 692.753i 0.288527i 0.989539 + 0.144263i \(0.0460813\pi\)
−0.989539 + 0.144263i \(0.953919\pi\)
\(8\) 1282.36 0.313077
\(9\) −6357.89 + 1619.88i −0.969042 + 0.246895i
\(10\) 0 0
\(11\) 15881.8i 1.08475i −0.840137 0.542374i \(-0.817525\pi\)
0.840137 0.542374i \(-0.182475\pi\)
\(12\) −3123.09 24907.4i −0.150612 1.20117i
\(13\) 48870.9i 1.71110i −0.517716 0.855552i \(-0.673218\pi\)
0.517716 0.855552i \(-0.326782\pi\)
\(14\) 16479.8i 0.428982i
\(15\) 0 0
\(16\) −48830.2 −0.745089
\(17\) −41025.6 −0.491201 −0.245600 0.969371i \(-0.578985\pi\)
−0.245600 + 0.969371i \(0.578985\pi\)
\(18\) −151246. + 38534.9i −1.44077 + 0.367083i
\(19\) 108213. 0.830356 0.415178 0.909740i \(-0.363719\pi\)
0.415178 + 0.909740i \(0.363719\pi\)
\(20\) 0 0
\(21\) 55677.0 6981.24i 0.286285 0.0358968i
\(22\) 377809.i 1.61280i
\(23\) −433886. −1.55047 −0.775237 0.631671i \(-0.782369\pi\)
−0.775237 + 0.631671i \(0.782369\pi\)
\(24\) −12923.0 103064.i −0.0389511 0.310644i
\(25\) 0 0
\(26\) 1.16258e6i 2.54407i
\(27\) 194262. + 494663.i 0.365539 + 0.930796i
\(28\) 214688.i 0.349282i
\(29\) 377879.i 0.534270i 0.963659 + 0.267135i \(0.0860770\pi\)
−0.963659 + 0.267135i \(0.913923\pi\)
\(30\) 0 0
\(31\) −408921. −0.442784 −0.221392 0.975185i \(-0.571060\pi\)
−0.221392 + 0.975185i \(0.571060\pi\)
\(32\) −1.48989e6 −1.42087
\(33\) −1.27643e6 + 160049.i −1.07632 + 0.134958i
\(34\) −975949. −0.730317
\(35\) 0 0
\(36\) −1.97035e6 + 502009.i −1.17309 + 0.298883i
\(37\) 2.31002e6i 1.23256i −0.787526 0.616282i \(-0.788638\pi\)
0.787526 0.616282i \(-0.211362\pi\)
\(38\) 2.57425e6 1.23457
\(39\) −3.92778e6 + 492497.i −1.69781 + 0.212885i
\(40\) 0 0
\(41\) 2.15170e6i 0.761460i 0.924686 + 0.380730i \(0.124327\pi\)
−0.924686 + 0.380730i \(0.875673\pi\)
\(42\) 1.32449e6 166075.i 0.425649 0.0533713i
\(43\) 2.42811e6i 0.710223i −0.934824 0.355111i \(-0.884443\pi\)
0.934824 0.355111i \(-0.115557\pi\)
\(44\) 4.92187e6i 1.31317i
\(45\) 0 0
\(46\) −1.03216e7 −2.30524
\(47\) 8.18110e6 1.67656 0.838282 0.545237i \(-0.183560\pi\)
0.838282 + 0.545237i \(0.183560\pi\)
\(48\) 492087. + 3.92451e6i 0.0926994 + 0.739300i
\(49\) 5.28489e6 0.916752
\(50\) 0 0
\(51\) 413437. + 3.29725e6i 0.0611122 + 0.487385i
\(52\) 1.51454e7i 2.07141i
\(53\) 1.36324e7 1.72770 0.863850 0.503748i \(-0.168046\pi\)
0.863850 + 0.503748i \(0.168046\pi\)
\(54\) 4.62126e6 + 1.17674e7i 0.543482 + 1.38391i
\(55\) 0 0
\(56\) 888360.i 0.0903310i
\(57\) −1.09052e6 8.69714e6i −0.103308 0.823904i
\(58\) 8.98929e6i 0.794353i
\(59\) 1.23667e7i 1.02057i −0.860004 0.510287i \(-0.829539\pi\)
0.860004 0.510287i \(-0.170461\pi\)
\(60\) 0 0
\(61\) −1.15129e6 −0.0831509 −0.0415755 0.999135i \(-0.513238\pi\)
−0.0415755 + 0.999135i \(0.513238\pi\)
\(62\) −9.72773e6 −0.658331
\(63\) −1.12217e6 4.40445e6i −0.0712357 0.279595i
\(64\) −2.29423e7 −1.36746
\(65\) 0 0
\(66\) −3.03647e7 + 3.80738e6i −1.60027 + 0.200655i
\(67\) 1.55586e7i 0.772096i 0.922479 + 0.386048i \(0.126160\pi\)
−0.922479 + 0.386048i \(0.873840\pi\)
\(68\) −1.27141e7 −0.594634
\(69\) 4.37250e6 + 3.48717e7i 0.192900 + 1.53843i
\(70\) 0 0
\(71\) 2.52525e7i 0.993735i −0.867826 0.496868i \(-0.834483\pi\)
0.867826 0.496868i \(-0.165517\pi\)
\(72\) −8.15311e6 + 2.07727e6i −0.303384 + 0.0772969i
\(73\) 2.29182e7i 0.807030i −0.914973 0.403515i \(-0.867788\pi\)
0.914973 0.403515i \(-0.132212\pi\)
\(74\) 5.49526e7i 1.83257i
\(75\) 0 0
\(76\) 3.35358e7 1.00520
\(77\) 1.10022e7 0.312979
\(78\) −9.34372e7 + 1.17159e7i −2.52430 + 0.316518i
\(79\) −4.49938e7 −1.15517 −0.577583 0.816332i \(-0.696004\pi\)
−0.577583 + 0.816332i \(0.696004\pi\)
\(80\) 0 0
\(81\) 3.77987e7 2.05980e7i 0.878086 0.478503i
\(82\) 5.11864e7i 1.13214i
\(83\) 2.12119e7 0.446957 0.223479 0.974709i \(-0.428259\pi\)
0.223479 + 0.974709i \(0.428259\pi\)
\(84\) 1.72547e7 2.16353e6i 0.346569 0.0434556i
\(85\) 0 0
\(86\) 5.77618e7i 1.05596i
\(87\) 3.03704e7 3.80809e6i 0.530119 0.0664707i
\(88\) 2.03662e7i 0.339609i
\(89\) 4.87898e7i 0.777622i 0.921317 + 0.388811i \(0.127114\pi\)
−0.921317 + 0.388811i \(0.872886\pi\)
\(90\) 0 0
\(91\) 3.38555e7 0.493700
\(92\) −1.34464e8 −1.87696
\(93\) 4.12091e6 + 3.28652e7i 0.0550885 + 0.439344i
\(94\) 1.94618e8 2.49271
\(95\) 0 0
\(96\) 1.50145e7 + 1.19744e8i 0.176777 + 1.40983i
\(97\) 2.91619e7i 0.329404i −0.986343 0.164702i \(-0.947334\pi\)
0.986343 0.164702i \(-0.0526662\pi\)
\(98\) 1.25721e8 1.36303
\(99\) 2.57265e7 + 1.00975e8i 0.267818 + 1.05117i
\(100\) 0 0
\(101\) 6.31995e7i 0.607335i 0.952778 + 0.303667i \(0.0982111\pi\)
−0.952778 + 0.303667i \(0.901789\pi\)
\(102\) 9.83515e6 + 7.84377e7i 0.0908616 + 0.724643i
\(103\) 6.94350e7i 0.616921i −0.951237 0.308461i \(-0.900186\pi\)
0.951237 0.308461i \(-0.0998138\pi\)
\(104\) 6.26701e7i 0.535707i
\(105\) 0 0
\(106\) 3.24298e8 2.56874
\(107\) 2.16211e8 1.64946 0.824732 0.565523i \(-0.191326\pi\)
0.824732 + 0.565523i \(0.191326\pi\)
\(108\) 6.02031e7 + 1.53299e8i 0.442510 + 1.12679i
\(109\) −7.00475e7 −0.496234 −0.248117 0.968730i \(-0.579812\pi\)
−0.248117 + 0.968730i \(0.579812\pi\)
\(110\) 0 0
\(111\) −1.85658e8 + 2.32793e7i −1.22299 + 0.153348i
\(112\) 3.38272e7i 0.214978i
\(113\) 4.56013e7 0.279681 0.139841 0.990174i \(-0.455341\pi\)
0.139841 + 0.990174i \(0.455341\pi\)
\(114\) −2.59421e7 2.06894e8i −0.153598 1.22498i
\(115\) 0 0
\(116\) 1.17107e8i 0.646772i
\(117\) 7.91647e7 + 3.10715e8i 0.422462 + 1.65813i
\(118\) 2.94188e8i 1.51739i
\(119\) 2.84206e7i 0.141725i
\(120\) 0 0
\(121\) −3.78728e7 −0.176679
\(122\) −2.73879e7 −0.123629
\(123\) 1.72934e8 2.16839e7i 0.755544 0.0947362i
\(124\) −1.26727e8 −0.536022
\(125\) 0 0
\(126\) −2.66951e7 1.04776e8i −0.105913 0.415701i
\(127\) 1.07871e7i 0.0414660i −0.999785 0.0207330i \(-0.993400\pi\)
0.999785 0.0207330i \(-0.00659998\pi\)
\(128\) −1.64355e8 −0.612271
\(129\) −1.95149e8 + 2.44694e7i −0.704705 + 0.0883616i
\(130\) 0 0
\(131\) 2.88284e8i 0.978894i 0.872033 + 0.489447i \(0.162801\pi\)
−0.872033 + 0.489447i \(0.837199\pi\)
\(132\) −3.95574e8 + 4.96003e7i −1.30296 + 0.163376i
\(133\) 7.49648e7i 0.239580i
\(134\) 3.70120e8i 1.14795i
\(135\) 0 0
\(136\) −5.26097e7 −0.153784
\(137\) −7.39800e7 −0.210006 −0.105003 0.994472i \(-0.533485\pi\)
−0.105003 + 0.994472i \(0.533485\pi\)
\(138\) 1.04016e8 + 8.29555e8i 0.286804 + 2.28733i
\(139\) 4.00966e7 0.107411 0.0537054 0.998557i \(-0.482897\pi\)
0.0537054 + 0.998557i \(0.482897\pi\)
\(140\) 0 0
\(141\) −8.24452e7 6.57520e8i −0.208588 1.66354i
\(142\) 6.00726e8i 1.47748i
\(143\) −7.76158e8 −1.85612
\(144\) 3.10457e8 7.90987e7i 0.722023 0.183958i
\(145\) 0 0
\(146\) 5.45197e8i 1.19989i
\(147\) −5.32587e7 4.24750e8i −0.114057 0.909629i
\(148\) 7.15890e8i 1.49211i
\(149\) 1.80649e8i 0.366515i 0.983065 + 0.183257i \(0.0586641\pi\)
−0.983065 + 0.183257i \(0.941336\pi\)
\(150\) 0 0
\(151\) −4.33011e7 −0.0832898 −0.0416449 0.999132i \(-0.513260\pi\)
−0.0416449 + 0.999132i \(0.513260\pi\)
\(152\) 1.38768e8 0.259965
\(153\) 2.60836e8 6.64563e7i 0.475995 0.121275i
\(154\) 2.61728e8 0.465337
\(155\) 0 0
\(156\) −1.21724e9 + 1.52628e8i −2.05532 + 0.257713i
\(157\) 9.98639e7i 0.164365i −0.996617 0.0821826i \(-0.973811\pi\)
0.996617 0.0821826i \(-0.0261891\pi\)
\(158\) −1.07035e9 −1.71750
\(159\) −1.37381e8 1.09564e9i −0.214950 1.71428i
\(160\) 0 0
\(161\) 3.00576e8i 0.447353i
\(162\) 8.99186e8 4.90000e8i 1.30554 0.711437i
\(163\) 4.15495e8i 0.588594i −0.955714 0.294297i \(-0.904915\pi\)
0.955714 0.294297i \(-0.0950854\pi\)
\(164\) 6.66826e8i 0.921801i
\(165\) 0 0
\(166\) 5.04604e8 0.664536
\(167\) −2.00570e8 −0.257869 −0.128935 0.991653i \(-0.541156\pi\)
−0.128935 + 0.991653i \(0.541156\pi\)
\(168\) 7.13981e7 8.95247e6i 0.0896292 0.0112384i
\(169\) −1.57263e9 −1.92788
\(170\) 0 0
\(171\) −6.88005e8 + 1.75291e8i −0.804650 + 0.205010i
\(172\) 7.52487e8i 0.859775i
\(173\) 1.07943e9 1.20507 0.602534 0.798093i \(-0.294158\pi\)
0.602534 + 0.798093i \(0.294158\pi\)
\(174\) 7.22475e8 9.05898e7i 0.788181 0.0988285i
\(175\) 0 0
\(176\) 7.75511e8i 0.808234i
\(177\) −9.93918e8 + 1.24626e8i −1.01265 + 0.126974i
\(178\) 1.16065e9i 1.15617i
\(179\) 4.03427e8i 0.392964i 0.980507 + 0.196482i \(0.0629517\pi\)
−0.980507 + 0.196482i \(0.937048\pi\)
\(180\) 0 0
\(181\) −9.48830e8 −0.884045 −0.442022 0.897004i \(-0.645739\pi\)
−0.442022 + 0.897004i \(0.645739\pi\)
\(182\) 8.05380e8 0.734032
\(183\) 1.16022e7 + 9.25303e7i 0.0103451 + 0.0825049i
\(184\) −5.56399e8 −0.485417
\(185\) 0 0
\(186\) 9.80314e7 + 7.81824e8i 0.0819056 + 0.653216i
\(187\) 6.51560e8i 0.532830i
\(188\) 2.53537e9 2.02960
\(189\) −3.42680e8 + 1.34576e8i −0.268560 + 0.105468i
\(190\) 0 0
\(191\) 1.09216e9i 0.820643i 0.911941 + 0.410322i \(0.134584\pi\)
−0.911941 + 0.410322i \(0.865416\pi\)
\(192\) 2.31201e8 + 1.84388e9i 0.170132 + 1.35684i
\(193\) 2.66289e9i 1.91921i −0.281342 0.959607i \(-0.590780\pi\)
0.281342 0.959607i \(-0.409220\pi\)
\(194\) 6.93725e8i 0.489757i
\(195\) 0 0
\(196\) 1.63782e9 1.10979
\(197\) −2.31610e9 −1.53777 −0.768886 0.639386i \(-0.779189\pi\)
−0.768886 + 0.639386i \(0.779189\pi\)
\(198\) 6.12003e8 + 2.40207e9i 0.398192 + 1.56287i
\(199\) 9.37508e8 0.597809 0.298905 0.954283i \(-0.403379\pi\)
0.298905 + 0.954283i \(0.403379\pi\)
\(200\) 0 0
\(201\) 1.25046e9 1.56792e8i 0.766097 0.0960595i
\(202\) 1.50344e9i 0.902984i
\(203\) −2.61777e8 −0.154151
\(204\) 1.28127e8 + 1.02184e9i 0.0739807 + 0.590014i
\(205\) 0 0
\(206\) 1.65177e9i 0.917238i
\(207\) 2.75860e9 7.02841e8i 1.50247 0.382803i
\(208\) 2.38637e9i 1.27493i
\(209\) 1.71861e9i 0.900727i
\(210\) 0 0
\(211\) 2.14693e9 1.08315 0.541575 0.840652i \(-0.317828\pi\)
0.541575 + 0.840652i \(0.317828\pi\)
\(212\) 4.22476e9 2.09150
\(213\) −2.02956e9 + 2.54483e8i −0.986014 + 0.123634i
\(214\) 5.14340e9 2.45242
\(215\) 0 0
\(216\) 2.49114e8 + 6.34337e8i 0.114442 + 0.291411i
\(217\) 2.83281e8i 0.127755i
\(218\) −1.66634e9 −0.737800
\(219\) −1.84195e9 + 2.30959e8i −0.800759 + 0.100406i
\(220\) 0 0
\(221\) 2.00496e9i 0.840496i
\(222\) −4.41658e9 + 5.53787e8i −1.81834 + 0.227998i
\(223\) 3.70772e9i 1.49929i −0.661838 0.749647i \(-0.730223\pi\)
0.661838 0.749647i \(-0.269777\pi\)
\(224\) 1.03213e9i 0.409960i
\(225\) 0 0
\(226\) 1.08480e9 0.415830
\(227\) −3.97024e9 −1.49525 −0.747624 0.664122i \(-0.768806\pi\)
−0.747624 + 0.664122i \(0.768806\pi\)
\(228\) −3.37958e8 2.69530e9i −0.125061 0.997395i
\(229\) −2.84129e9 −1.03317 −0.516587 0.856235i \(-0.672798\pi\)
−0.516587 + 0.856235i \(0.672798\pi\)
\(230\) 0 0
\(231\) −1.10875e8 8.84252e8i −0.0389390 0.310547i
\(232\) 4.84578e8i 0.167268i
\(233\) −3.80946e8 −0.129253 −0.0646264 0.997910i \(-0.520586\pi\)
−0.0646264 + 0.997910i \(0.520586\pi\)
\(234\) 1.88323e9 + 7.39154e9i 0.628117 + 2.46531i
\(235\) 0 0
\(236\) 3.83251e9i 1.23548i
\(237\) 4.53426e8 + 3.61618e9i 0.143719 + 1.14619i
\(238\) 6.76092e8i 0.210716i
\(239\) 3.08542e9i 0.945633i −0.881161 0.472817i \(-0.843237\pi\)
0.881161 0.472817i \(-0.156763\pi\)
\(240\) 0 0
\(241\) −1.83623e9 −0.544326 −0.272163 0.962251i \(-0.587739\pi\)
−0.272163 + 0.962251i \(0.587739\pi\)
\(242\) −9.00948e8 −0.262687
\(243\) −2.03639e9 2.83033e9i −0.584031 0.811731i
\(244\) −3.56793e8 −0.100660
\(245\) 0 0
\(246\) 4.11389e9 5.15833e8i 1.12334 0.140854i
\(247\) 5.28845e9i 1.42083i
\(248\) −5.24384e8 −0.138625
\(249\) −2.13763e8 1.70481e9i −0.0556077 0.443485i
\(250\) 0 0
\(251\) 4.14381e9i 1.04401i −0.852942 0.522005i \(-0.825184\pi\)
0.852942 0.522005i \(-0.174816\pi\)
\(252\) −3.47769e8 1.36497e9i −0.0862359 0.338469i
\(253\) 6.89089e9i 1.68187i
\(254\) 2.56613e8i 0.0616515i
\(255\) 0 0
\(256\) 1.96340e9 0.457141
\(257\) 1.12642e9 0.258207 0.129104 0.991631i \(-0.458790\pi\)
0.129104 + 0.991631i \(0.458790\pi\)
\(258\) −4.64235e9 + 5.82096e8i −1.04775 + 0.131376i
\(259\) 1.60028e9 0.355628
\(260\) 0 0
\(261\) −6.12117e8 2.40251e9i −0.131908 0.517731i
\(262\) 6.85793e9i 1.45542i
\(263\) 6.91865e9 1.44610 0.723050 0.690796i \(-0.242740\pi\)
0.723050 + 0.690796i \(0.242740\pi\)
\(264\) −1.63685e9 + 2.05241e8i −0.336971 + 0.0422521i
\(265\) 0 0
\(266\) 1.78332e9i 0.356207i
\(267\) 3.92127e9 4.91680e8i 0.771581 0.0967470i
\(268\) 4.82171e9i 0.934677i
\(269\) 1.04065e9i 0.198744i 0.995050 + 0.0993720i \(0.0316834\pi\)
−0.995050 + 0.0993720i \(0.968317\pi\)
\(270\) 0 0
\(271\) −4.30357e9 −0.797906 −0.398953 0.916971i \(-0.630626\pi\)
−0.398953 + 0.916971i \(0.630626\pi\)
\(272\) 2.00329e9 0.365988
\(273\) −3.41179e8 2.72099e9i −0.0614231 0.489864i
\(274\) −1.75989e9 −0.312237
\(275\) 0 0
\(276\) 1.35506e9 + 1.08070e10i 0.233520 + 1.86237i
\(277\) 1.01360e10i 1.72166i 0.508889 + 0.860832i \(0.330056\pi\)
−0.508889 + 0.860832i \(0.669944\pi\)
\(278\) 9.53848e8 0.159698
\(279\) 2.59987e9 6.62400e8i 0.429077 0.109321i
\(280\) 0 0
\(281\) 8.82598e9i 1.41559i 0.706418 + 0.707795i \(0.250310\pi\)
−0.706418 + 0.707795i \(0.749690\pi\)
\(282\) −1.96127e9 1.56416e10i −0.310128 2.47335i
\(283\) 1.58051e9i 0.246405i 0.992382 + 0.123203i \(0.0393165\pi\)
−0.992382 + 0.123203i \(0.960683\pi\)
\(284\) 7.82590e9i 1.20299i
\(285\) 0 0
\(286\) −1.84638e10 −2.75967
\(287\) −1.49060e9 −0.219702
\(288\) 9.47258e9 2.41344e9i 1.37689 0.350806i
\(289\) −5.29266e9 −0.758722
\(290\) 0 0
\(291\) −2.34376e9 + 2.93880e8i −0.326844 + 0.0409824i
\(292\) 7.10250e9i 0.976967i
\(293\) 7.30987e8 0.0991835 0.0495917 0.998770i \(-0.484208\pi\)
0.0495917 + 0.998770i \(0.484208\pi\)
\(294\) −1.26696e9 1.01043e10i −0.169579 1.35244i
\(295\) 0 0
\(296\) 2.96228e9i 0.385887i
\(297\) 7.85614e9 3.08523e9i 1.00968 0.396517i
\(298\) 4.29743e9i 0.544934i
\(299\) 2.12044e10i 2.65302i
\(300\) 0 0
\(301\) 1.68208e9 0.204918
\(302\) −1.03008e9 −0.123835
\(303\) 5.07938e9 6.36894e8i 0.602616 0.0755609i
\(304\) −5.28405e9 −0.618689
\(305\) 0 0
\(306\) 6.20497e9 1.58092e9i 0.707708 0.180311i
\(307\) 8.05460e9i 0.906757i −0.891318 0.453378i \(-0.850219\pi\)
0.891318 0.453378i \(-0.149781\pi\)
\(308\) 3.40964e9 0.378884
\(309\) −5.58054e9 + 6.99733e8i −0.612128 + 0.0767536i
\(310\) 0 0
\(311\) 2.28173e9i 0.243906i 0.992536 + 0.121953i \(0.0389157\pi\)
−0.992536 + 0.121953i \(0.961084\pi\)
\(312\) −5.03684e9 + 6.31560e8i −0.531545 + 0.0666494i
\(313\) 3.40795e9i 0.355072i 0.984114 + 0.177536i \(0.0568126\pi\)
−0.984114 + 0.177536i \(0.943187\pi\)
\(314\) 2.37564e9i 0.244378i
\(315\) 0 0
\(316\) −1.39439e10 −1.39841
\(317\) 2.80342e9 0.277620 0.138810 0.990319i \(-0.455672\pi\)
0.138810 + 0.990319i \(0.455672\pi\)
\(318\) −3.26812e9 2.60640e10i −0.319587 2.54879i
\(319\) 6.00140e9 0.579549
\(320\) 0 0
\(321\) −2.17887e9 1.73770e10i −0.205216 1.63665i
\(322\) 7.15034e9i 0.665125i
\(323\) −4.43950e9 −0.407872
\(324\) 1.17141e10 6.38344e9i 1.06299 0.579261i
\(325\) 0 0
\(326\) 9.88412e9i 0.875120i
\(327\) 7.05906e8 + 5.62976e9i 0.0617384 + 0.492379i
\(328\) 2.75926e9i 0.238395i
\(329\) 5.66748e9i 0.483734i
\(330\) 0 0
\(331\) −3.85817e9 −0.321417 −0.160709 0.987002i \(-0.551378\pi\)
−0.160709 + 0.987002i \(0.551378\pi\)
\(332\) 6.57368e9 0.541074
\(333\) 3.74195e9 + 1.46869e10i 0.304313 + 1.19441i
\(334\) −4.77131e9 −0.383400
\(335\) 0 0
\(336\) −2.71872e9 + 3.40895e8i −0.213308 + 0.0267463i
\(337\) 4.33270e9i 0.335922i −0.985794 0.167961i \(-0.946282\pi\)
0.985794 0.167961i \(-0.0537183\pi\)
\(338\) −3.74110e10 −2.86637
\(339\) −4.59548e8 3.66500e9i −0.0347962 0.277508i
\(340\) 0 0
\(341\) 6.49440e9i 0.480310i
\(342\) −1.63668e10 + 4.16997e9i −1.19635 + 0.304809i
\(343\) 7.65471e9i 0.553035i
\(344\) 3.11372e9i 0.222354i
\(345\) 0 0
\(346\) 2.56784e10 1.79169
\(347\) 1.49997e9 0.103458 0.0517291 0.998661i \(-0.483527\pi\)
0.0517291 + 0.998661i \(0.483527\pi\)
\(348\) 9.41198e9 1.18015e9i 0.641747 0.0804675i
\(349\) 1.91502e10 1.29084 0.645418 0.763830i \(-0.276683\pi\)
0.645418 + 0.763830i \(0.276683\pi\)
\(350\) 0 0
\(351\) 2.41746e10 9.49376e9i 1.59269 0.625475i
\(352\) 2.36622e10i 1.54129i
\(353\) −2.74321e10 −1.76669 −0.883345 0.468723i \(-0.844714\pi\)
−0.883345 + 0.468723i \(0.844714\pi\)
\(354\) −2.36441e10 + 2.96469e9i −1.50560 + 0.188784i
\(355\) 0 0
\(356\) 1.51202e10i 0.941367i
\(357\) −2.28418e9 + 2.86410e8i −0.140624 + 0.0176325i
\(358\) 9.59704e9i 0.584258i
\(359\) 7.34907e9i 0.442440i 0.975224 + 0.221220i \(0.0710039\pi\)
−0.975224 + 0.221220i \(0.928996\pi\)
\(360\) 0 0
\(361\) −5.27355e9 −0.310509
\(362\) −2.25715e10 −1.31440
\(363\) 3.81664e8 + 3.04386e9i 0.0219814 + 0.175307i
\(364\) 1.04920e10 0.597659
\(365\) 0 0
\(366\) 2.76002e8 + 2.20118e9i 0.0153811 + 0.122668i
\(367\) 6.53522e9i 0.360243i 0.983644 + 0.180122i \(0.0576492\pi\)
−0.983644 + 0.180122i \(0.942351\pi\)
\(368\) 2.11867e10 1.15524
\(369\) −3.48549e9 1.36803e10i −0.188000 0.737887i
\(370\) 0 0
\(371\) 9.44388e9i 0.498488i
\(372\) 1.27710e9 + 1.01851e10i 0.0666886 + 0.531857i
\(373\) 3.22724e10i 1.66723i −0.552346 0.833615i \(-0.686267\pi\)
0.552346 0.833615i \(-0.313733\pi\)
\(374\) 1.54998e10i 0.792210i
\(375\) 0 0
\(376\) 1.04911e10 0.524893
\(377\) 1.84673e10 0.914193
\(378\) −8.15193e9 + 3.20139e9i −0.399294 + 0.156809i
\(379\) 2.00937e10 0.973875 0.486938 0.873437i \(-0.338114\pi\)
0.486938 + 0.873437i \(0.338114\pi\)
\(380\) 0 0
\(381\) −8.66970e8 + 1.08708e8i −0.0411438 + 0.00515894i
\(382\) 2.59813e10i 1.22013i
\(383\) 2.64566e10 1.22953 0.614765 0.788711i \(-0.289251\pi\)
0.614765 + 0.788711i \(0.289251\pi\)
\(384\) 1.65630e9 + 1.32093e10i 0.0761751 + 0.607514i
\(385\) 0 0
\(386\) 6.33469e10i 2.85349i
\(387\) 3.93324e9 + 1.54377e10i 0.175350 + 0.688236i
\(388\) 9.03744e9i 0.398766i
\(389\) 2.69010e10i 1.17482i −0.809291 0.587408i \(-0.800149\pi\)
0.809291 0.587408i \(-0.199851\pi\)
\(390\) 0 0
\(391\) 1.78004e10 0.761594
\(392\) 6.77715e9 0.287014
\(393\) 2.31696e10 2.90519e9i 0.971288 0.121788i
\(394\) −5.50971e10 −2.28636
\(395\) 0 0
\(396\) 7.97281e9 + 3.12927e10i 0.324213 + 1.27251i
\(397\) 2.18233e10i 0.878533i −0.898357 0.439266i \(-0.855238\pi\)
0.898357 0.439266i \(-0.144762\pi\)
\(398\) 2.23022e10 0.888822
\(399\) 6.02497e9 7.55460e8i 0.237719 0.0298071i
\(400\) 0 0
\(401\) 3.86361e10i 1.49422i 0.664698 + 0.747112i \(0.268560\pi\)
−0.664698 + 0.747112i \(0.731440\pi\)
\(402\) 2.97468e10 3.72990e9i 1.13903 0.142821i
\(403\) 1.99843e10i 0.757651i
\(404\) 1.95859e10i 0.735222i
\(405\) 0 0
\(406\) −6.22736e9 −0.229192
\(407\) −3.66873e10 −1.33702
\(408\) 5.30175e8 + 4.22827e9i 0.0191328 + 0.152589i
\(409\) 1.02245e10 0.365385 0.182692 0.983170i \(-0.441519\pi\)
0.182692 + 0.983170i \(0.441519\pi\)
\(410\) 0 0
\(411\) 7.45535e8 + 5.94582e9i 0.0261277 + 0.208375i
\(412\) 2.15183e10i 0.746827i
\(413\) 8.56705e9 0.294463
\(414\) 6.56237e10 1.67197e10i 2.23388 0.569152i
\(415\) 0 0
\(416\) 7.28124e10i 2.43126i
\(417\) −4.04074e8 3.22259e9i −0.0133634 0.106576i
\(418\) 4.08838e10i 1.33920i
\(419\) 3.03535e10i 0.984812i −0.870366 0.492406i \(-0.836118\pi\)
0.870366 0.492406i \(-0.163882\pi\)
\(420\) 0 0
\(421\) 3.94064e10 1.25441 0.627203 0.778856i \(-0.284200\pi\)
0.627203 + 0.778856i \(0.284200\pi\)
\(422\) 5.10729e10 1.61043
\(423\) −5.20145e10 + 1.32524e10i −1.62466 + 0.413934i
\(424\) 1.74817e10 0.540903
\(425\) 0 0
\(426\) −4.82807e10 + 6.05383e9i −1.46600 + 0.183820i
\(427\) 7.97563e8i 0.0239913i
\(428\) 6.70052e10 1.99679
\(429\) 7.82175e9 + 6.23803e10i 0.230927 + 1.84170i
\(430\) 0 0
\(431\) 2.00931e10i 0.582288i −0.956679 0.291144i \(-0.905964\pi\)
0.956679 0.291144i \(-0.0940358\pi\)
\(432\) −9.48585e9 2.41545e10i −0.272359 0.693526i
\(433\) 4.76129e10i 1.35448i 0.735761 + 0.677241i \(0.236824\pi\)
−0.735761 + 0.677241i \(0.763176\pi\)
\(434\) 6.73891e9i 0.189946i
\(435\) 0 0
\(436\) −2.17082e10 −0.600727
\(437\) −4.69520e10 −1.28744
\(438\) −4.38178e10 + 5.49423e9i −1.19057 + 0.149283i
\(439\) 2.80845e10 0.756151 0.378076 0.925775i \(-0.376586\pi\)
0.378076 + 0.925775i \(0.376586\pi\)
\(440\) 0 0
\(441\) −3.36008e10 + 8.56087e9i −0.888372 + 0.226341i
\(442\) 4.76955e10i 1.24965i
\(443\) −3.22901e9 −0.0838407 −0.0419204 0.999121i \(-0.513348\pi\)
−0.0419204 + 0.999121i \(0.513348\pi\)
\(444\) −5.75366e10 + 7.21440e9i −1.48051 + 0.185639i
\(445\) 0 0
\(446\) 8.82020e10i 2.22915i
\(447\) 1.45189e10 1.82050e9i 0.363667 0.0455995i
\(448\) 1.58933e10i 0.394551i
\(449\) 4.21051e10i 1.03598i −0.855388 0.517988i \(-0.826681\pi\)
0.855388 0.517988i \(-0.173319\pi\)
\(450\) 0 0
\(451\) 3.41729e10 0.825993
\(452\) 1.41321e10 0.338574
\(453\) 4.36368e8 + 3.48014e9i 0.0103624 + 0.0826426i
\(454\) −9.44472e10 −2.22313
\(455\) 0 0
\(456\) −1.39844e9 1.11529e10i −0.0323433 0.257945i
\(457\) 4.14329e10i 0.949905i −0.880011 0.474952i \(-0.842465\pi\)
0.880011 0.474952i \(-0.157535\pi\)
\(458\) −6.75908e10 −1.53612
\(459\) −7.96972e9 2.02939e10i −0.179553 0.457208i
\(460\) 0 0
\(461\) 7.44199e10i 1.64773i −0.566789 0.823863i \(-0.691814\pi\)
0.566789 0.823863i \(-0.308186\pi\)
\(462\) −2.63757e9 2.10353e10i −0.0578944 0.461722i
\(463\) 4.57191e10i 0.994887i −0.867496 0.497444i \(-0.834272\pi\)
0.867496 0.497444i \(-0.165728\pi\)
\(464\) 1.84519e10i 0.398079i
\(465\) 0 0
\(466\) −9.06225e9 −0.192173
\(467\) 2.76952e9 0.0582286 0.0291143 0.999576i \(-0.490731\pi\)
0.0291143 + 0.999576i \(0.490731\pi\)
\(468\) 2.45336e10 + 9.62926e10i 0.511421 + 2.00729i
\(469\) −1.07783e10 −0.222771
\(470\) 0 0
\(471\) −8.02613e9 + 1.00638e9i −0.163088 + 0.0204493i
\(472\) 1.58586e10i 0.319518i
\(473\) −3.85628e10 −0.770413
\(474\) 1.07865e10 + 8.60245e10i 0.213681 + 1.70415i
\(475\) 0 0
\(476\) 8.80772e9i 0.171568i
\(477\) −8.66732e10 + 2.20828e10i −1.67422 + 0.426560i
\(478\) 7.33984e10i 1.40597i
\(479\) 3.82055e10i 0.725744i 0.931839 + 0.362872i \(0.118204\pi\)
−0.931839 + 0.362872i \(0.881796\pi\)
\(480\) 0 0
\(481\) −1.12893e11 −2.10905
\(482\) −4.36817e10 −0.809303
\(483\) −2.41575e10 + 3.02906e9i −0.443878 + 0.0556570i
\(484\) −1.17370e10 −0.213883
\(485\) 0 0
\(486\) −4.84432e10 6.73302e10i −0.868336 1.20688i
\(487\) 2.79097e10i 0.496179i −0.968737 0.248090i \(-0.920197\pi\)
0.968737 0.248090i \(-0.0798028\pi\)
\(488\) −1.47638e9 −0.0260326
\(489\) −3.33936e10 + 4.18716e9i −0.584021 + 0.0732292i
\(490\) 0 0
\(491\) 3.62482e10i 0.623677i 0.950135 + 0.311839i \(0.100945\pi\)
−0.950135 + 0.311839i \(0.899055\pi\)
\(492\) 5.35933e10 6.71996e9i 0.914639 0.114685i
\(493\) 1.55027e10i 0.262434i
\(494\) 1.25806e11i 2.11248i
\(495\) 0 0
\(496\) 1.99677e10 0.329914
\(497\) 1.74937e10 0.286719
\(498\) −5.08516e9 4.05554e10i −0.0826775 0.659373i
\(499\) 1.31298e10 0.211765 0.105883 0.994379i \(-0.466233\pi\)
0.105883 + 0.994379i \(0.466233\pi\)
\(500\) 0 0
\(501\) 2.02125e9 + 1.61199e10i 0.0320825 + 0.255866i
\(502\) 9.85762e10i 1.55223i
\(503\) −1.84778e10 −0.288654 −0.144327 0.989530i \(-0.546102\pi\)
−0.144327 + 0.989530i \(0.546102\pi\)
\(504\) −1.43903e9 5.64809e9i −0.0223022 0.0875346i
\(505\) 0 0
\(506\) 1.63926e11i 2.50061i
\(507\) 1.58482e10 + 1.26393e11i 0.239855 + 1.91290i
\(508\) 3.34300e9i 0.0501975i
\(509\) 7.39108e10i 1.10112i 0.834794 + 0.550562i \(0.185587\pi\)
−0.834794 + 0.550562i \(0.814413\pi\)
\(510\) 0 0
\(511\) 1.58767e10 0.232850
\(512\) 8.87820e10 1.29195
\(513\) 2.10217e10 + 5.35289e10i 0.303527 + 0.772892i
\(514\) 2.67962e10 0.383902
\(515\) 0 0
\(516\) −6.04778e10 + 7.58320e9i −0.853095 + 0.106968i
\(517\) 1.29931e11i 1.81865i
\(518\) 3.80686e10 0.528747
\(519\) −1.08780e10 8.67548e10i −0.149927 1.19571i
\(520\) 0 0
\(521\) 7.94911e10i 1.07887i −0.842029 0.539433i \(-0.818639\pi\)
0.842029 0.539433i \(-0.181361\pi\)
\(522\) −1.45615e10 5.71529e10i −0.196121 0.769761i
\(523\) 3.03522e10i 0.405680i 0.979212 + 0.202840i \(0.0650171\pi\)
−0.979212 + 0.202840i \(0.934983\pi\)
\(524\) 8.93410e10i 1.18502i
\(525\) 0 0
\(526\) 1.64586e11 2.15006
\(527\) 1.67762e10 0.217496
\(528\) 6.23283e10 7.81523e9i 0.801955 0.100556i
\(529\) 1.09946e11 1.40397
\(530\) 0 0
\(531\) 2.00325e10 + 7.86259e10i 0.251974 + 0.988980i
\(532\) 2.32320e10i 0.290029i
\(533\) 1.05156e11 1.30294
\(534\) 9.32821e10 1.16965e10i 1.14719 0.143843i
\(535\) 0 0
\(536\) 1.99518e10i 0.241725i
\(537\) 3.24237e10 4.06555e9i 0.389911 0.0488902i
\(538\) 2.47557e10i 0.295492i
\(539\) 8.39336e10i 0.994446i
\(540\) 0 0
\(541\) −3.53261e10 −0.412389 −0.206195 0.978511i \(-0.566108\pi\)
−0.206195 + 0.978511i \(0.566108\pi\)
\(542\) −1.02377e11 −1.18633
\(543\) 9.56187e9 + 7.62581e10i 0.109987 + 0.877176i
\(544\) 6.11238e10 0.697935
\(545\) 0 0
\(546\) −8.11624e9 6.47289e10i −0.0913239 0.728329i
\(547\) 1.62586e11i 1.81607i 0.418891 + 0.908036i \(0.362419\pi\)
−0.418891 + 0.908036i \(0.637581\pi\)
\(548\) −2.29269e10 −0.254227
\(549\) 7.31980e9 1.86495e9i 0.0805768 0.0205295i
\(550\) 0 0
\(551\) 4.08914e10i 0.443635i
\(552\) 5.60712e9 + 4.47181e10i 0.0603926 + 0.481645i
\(553\) 3.11696e10i 0.333296i
\(554\) 2.41124e11i 2.55977i
\(555\) 0 0
\(556\) 1.24262e10 0.130028
\(557\) 1.81639e11 1.88707 0.943535 0.331273i \(-0.107478\pi\)
0.943535 + 0.331273i \(0.107478\pi\)
\(558\) 6.18478e10 1.57577e10i 0.637951 0.162538i
\(559\) −1.18664e11 −1.21527
\(560\) 0 0
\(561\) 5.23663e10 6.56612e9i 0.528690 0.0662914i
\(562\) 2.09959e11i 2.10470i
\(563\) 6.38376e10 0.635394 0.317697 0.948192i \(-0.397090\pi\)
0.317697 + 0.948192i \(0.397090\pi\)
\(564\) −2.55503e10 2.03770e11i −0.252510 2.01383i
\(565\) 0 0
\(566\) 3.75983e10i 0.366355i
\(567\) 1.42693e10 + 2.61852e10i 0.138061 + 0.253352i
\(568\) 3.23828e10i 0.311115i
\(569\) 1.31605e10i 0.125552i 0.998028 + 0.0627760i \(0.0199954\pi\)
−0.998028 + 0.0627760i \(0.980005\pi\)
\(570\) 0 0
\(571\) 7.09445e10 0.667382 0.333691 0.942683i \(-0.391706\pi\)
0.333691 + 0.942683i \(0.391706\pi\)
\(572\) −2.40536e11 −2.24696
\(573\) 8.77780e10 1.10063e10i 0.814267 0.102099i
\(574\) −3.54596e10 −0.326652
\(575\) 0 0
\(576\) 1.45864e11 3.71636e10i 1.32513 0.337620i
\(577\) 1.05284e11i 0.949859i −0.880024 0.474929i \(-0.842474\pi\)
0.880024 0.474929i \(-0.157526\pi\)
\(578\) −1.25906e11 −1.12807
\(579\) −2.14018e11 + 2.68353e10i −1.90430 + 0.238777i
\(580\) 0 0
\(581\) 1.46946e10i 0.128959i
\(582\) −5.57552e10 + 6.99104e9i −0.485952 + 0.0609326i
\(583\) 2.16507e11i 1.87412i
\(584\) 2.93895e10i 0.252662i
\(585\) 0 0
\(586\) 1.73893e10 0.147466
\(587\) −3.67507e10 −0.309538 −0.154769 0.987951i \(-0.549463\pi\)
−0.154769 + 0.987951i \(0.549463\pi\)
\(588\) −1.65052e10 1.31633e11i −0.138074 1.10117i
\(589\) −4.42505e10 −0.367669
\(590\) 0 0
\(591\) 2.33405e10 + 1.86146e11i 0.191320 + 1.52582i
\(592\) 1.12799e11i 0.918370i
\(593\) −2.06347e11 −1.66870 −0.834351 0.551234i \(-0.814157\pi\)
−0.834351 + 0.551234i \(0.814157\pi\)
\(594\) 1.86888e11 7.33940e10i 1.50119 0.589542i
\(595\) 0 0
\(596\) 5.59843e10i 0.443692i
\(597\) −9.44776e9 7.53481e10i −0.0743758 0.593164i
\(598\) 5.04427e11i 3.94451i
\(599\) 1.66792e11i 1.29559i 0.761813 + 0.647797i \(0.224310\pi\)
−0.761813 + 0.647797i \(0.775690\pi\)
\(600\) 0 0
\(601\) −1.53051e11 −1.17311 −0.586555 0.809909i \(-0.699516\pi\)
−0.586555 + 0.809909i \(0.699516\pi\)
\(602\) 4.00147e10 0.304673
\(603\) −2.52030e10 9.89199e10i −0.190626 0.748194i
\(604\) −1.34193e10 −0.100828
\(605\) 0 0
\(606\) 1.20832e11 1.51509e10i 0.895969 0.112344i
\(607\) 2.06970e11i 1.52459i 0.647233 + 0.762293i \(0.275926\pi\)
−0.647233 + 0.762293i \(0.724074\pi\)
\(608\) −1.61226e11 −1.17983
\(609\) 2.63807e9 + 2.10392e10i 0.0191786 + 0.152954i
\(610\) 0 0
\(611\) 3.99817e11i 2.86878i
\(612\) 8.08347e10 2.05952e10i 0.576225 0.146812i
\(613\) 1.06596e11i 0.754913i −0.926027 0.377457i \(-0.876799\pi\)
0.926027 0.377457i \(-0.123201\pi\)
\(614\) 1.91609e11i 1.34816i
\(615\) 0 0
\(616\) 1.41088e10 0.0979865
\(617\) 1.06362e11 0.733914 0.366957 0.930238i \(-0.380400\pi\)
0.366957 + 0.930238i \(0.380400\pi\)
\(618\) −1.32754e11 + 1.66458e10i −0.910111 + 0.114117i
\(619\) 1.57576e11 1.07332 0.536659 0.843799i \(-0.319686\pi\)
0.536659 + 0.843799i \(0.319686\pi\)
\(620\) 0 0
\(621\) −8.42877e10 2.14627e11i −0.566758 1.44317i
\(622\) 5.42795e10i 0.362639i
\(623\) −3.37993e10 −0.224365
\(624\) 1.91794e11 2.40487e10i 1.26502 0.158618i
\(625\) 0 0
\(626\) 8.10711e10i 0.527920i
\(627\) −1.38126e11 + 1.73194e10i −0.893729 + 0.112063i
\(628\) 3.09484e10i 0.198976i
\(629\) 9.47701e10i 0.605436i
\(630\) 0 0
\(631\) 2.74992e11 1.73461 0.867306 0.497775i \(-0.165850\pi\)
0.867306 + 0.497775i \(0.165850\pi\)
\(632\) −5.76983e10 −0.361655
\(633\) −2.16358e10 1.72550e11i −0.134759 1.07473i
\(634\) 6.66900e10 0.412766
\(635\) 0 0
\(636\) −4.25752e10 3.39547e11i −0.260212 2.07525i
\(637\) 2.58277e11i 1.56866i
\(638\) 1.42766e11 0.861673
\(639\) 4.09059e10 + 1.60552e11i 0.245348 + 0.962971i
\(640\) 0 0
\(641\) 2.88263e11i 1.70749i 0.520695 + 0.853743i \(0.325673\pi\)
−0.520695 + 0.853743i \(0.674327\pi\)
\(642\) −5.18328e10 4.13379e11i −0.305116 2.43337i
\(643\) 2.34011e11i 1.36896i 0.729030 + 0.684481i \(0.239971\pi\)
−0.729030 + 0.684481i \(0.760029\pi\)
\(644\) 9.31503e10i 0.541553i
\(645\) 0 0
\(646\) −1.05610e11 −0.606423
\(647\) 1.59734e11 0.911551 0.455775 0.890095i \(-0.349362\pi\)
0.455775 + 0.890095i \(0.349362\pi\)
\(648\) 4.84716e10 2.64140e10i 0.274908 0.149808i
\(649\) −1.96405e11 −1.10707
\(650\) 0 0
\(651\) −2.27675e10 + 2.85477e9i −0.126763 + 0.0158945i
\(652\) 1.28765e11i 0.712534i
\(653\) 1.20294e11 0.661596 0.330798 0.943702i \(-0.392682\pi\)
0.330798 + 0.943702i \(0.392682\pi\)
\(654\) 1.67926e10 + 1.33925e11i 0.0917926 + 0.732068i
\(655\) 0 0
\(656\) 1.05068e11i 0.567356i
\(657\) 3.71247e10 + 1.45711e11i 0.199251 + 0.782046i
\(658\) 1.34822e11i 0.719215i
\(659\) 9.51290e10i 0.504396i 0.967676 + 0.252198i \(0.0811534\pi\)
−0.967676 + 0.252198i \(0.918847\pi\)
\(660\) 0 0
\(661\) −3.37799e11 −1.76951 −0.884755 0.466056i \(-0.845674\pi\)
−0.884755 + 0.466056i \(0.845674\pi\)
\(662\) −9.17811e10 −0.477882
\(663\) 1.61140e11 2.02050e10i 0.833966 0.104569i
\(664\) 2.72013e10 0.139932
\(665\) 0 0
\(666\) 8.90164e10 + 3.49383e11i 0.452453 + 1.77584i
\(667\) 1.63957e11i 0.828372i
\(668\) −6.21578e10 −0.312169
\(669\) −2.97992e11 + 3.73646e10i −1.48765 + 0.186533i
\(670\) 0 0
\(671\) 1.82846e10i 0.0901978i
\(672\) −8.29529e10 + 1.04013e10i −0.406775 + 0.0510048i
\(673\) 1.01484e11i 0.494693i −0.968927 0.247347i \(-0.920441\pi\)
0.968927 0.247347i \(-0.0795586\pi\)
\(674\) 1.03070e11i 0.499449i
\(675\) 0 0
\(676\) −4.87368e11 −2.33384
\(677\) −1.58724e11 −0.755595 −0.377797 0.925888i \(-0.623318\pi\)
−0.377797 + 0.925888i \(0.623318\pi\)
\(678\) −1.09321e10 8.71860e10i −0.0517350 0.412599i
\(679\) 2.02020e10 0.0950418
\(680\) 0 0
\(681\) 4.00102e10 + 3.19091e11i 0.186030 + 1.48363i
\(682\) 1.54494e11i 0.714124i
\(683\) 1.30156e11 0.598110 0.299055 0.954236i \(-0.403329\pi\)
0.299055 + 0.954236i \(0.403329\pi\)
\(684\) −2.13217e11 + 5.43238e10i −0.974086 + 0.248180i
\(685\) 0 0
\(686\) 1.82096e11i 0.822251i
\(687\) 2.86332e10 + 2.28356e11i 0.128541 + 1.02515i
\(688\) 1.18565e11i 0.529179i
\(689\) 6.66227e11i 2.95628i
\(690\) 0 0
\(691\) −2.27036e9 −0.00995823 −0.00497912 0.999988i \(-0.501585\pi\)
−0.00497912 + 0.999988i \(0.501585\pi\)
\(692\) 3.34523e11 1.45882
\(693\) −6.99506e10 + 1.78221e10i −0.303290 + 0.0772729i
\(694\) 3.56825e10 0.153821
\(695\) 0 0
\(696\) 3.89459e10 4.88335e9i 0.165968 0.0208104i
\(697\) 8.82750e10i 0.374030i
\(698\) 4.55559e11 1.91921
\(699\) 3.83900e9 + 3.06169e10i 0.0160808 + 0.128249i
\(700\) 0 0
\(701\) 2.75263e11i 1.13993i −0.821671 0.569963i \(-0.806958\pi\)
0.821671 0.569963i \(-0.193042\pi\)
\(702\) 5.75085e11 2.25845e11i 2.36801 0.929955i
\(703\) 2.49974e11i 1.02347i
\(704\) 3.64364e11i 1.48336i
\(705\) 0 0
\(706\) −6.52577e11 −2.62671
\(707\) −4.37816e10 −0.175232
\(708\) −3.08021e11 + 3.86222e10i −1.22588 + 0.153711i
\(709\) −1.38692e11 −0.548865 −0.274433 0.961606i \(-0.588490\pi\)
−0.274433 + 0.961606i \(0.588490\pi\)
\(710\) 0 0
\(711\) 2.86065e11 7.28843e10i 1.11940 0.285204i
\(712\) 6.25661e10i 0.243455i
\(713\) 1.77425e11 0.686525
\(714\) −5.43379e10 + 6.81333e9i −0.209079 + 0.0262160i
\(715\) 0 0
\(716\) 1.25024e11i 0.475711i
\(717\) −2.47977e11 + 3.10934e10i −0.938286 + 0.117650i
\(718\) 1.74825e11i 0.657820i
\(719\) 5.06730e11i 1.89610i −0.318125 0.948049i \(-0.603053\pi\)
0.318125 0.948049i \(-0.396947\pi\)
\(720\) 0 0
\(721\) 4.81013e10 0.177998
\(722\) −1.25451e11 −0.461664
\(723\) 1.85047e10 + 1.47579e11i 0.0677217 + 0.540097i
\(724\) −2.94048e11 −1.07020
\(725\) 0 0
\(726\) 9.07933e9 + 7.24098e10i 0.0326819 + 0.260646i
\(727\) 2.19798e11i 0.786840i −0.919359 0.393420i \(-0.871292\pi\)
0.919359 0.393420i \(-0.128708\pi\)
\(728\) 4.34149e10 0.154566
\(729\) −2.06954e11 + 1.92189e11i −0.732763 + 0.680484i
\(730\) 0 0
\(731\) 9.96147e10i 0.348862i
\(732\) 3.59559e9 + 2.86757e10i 0.0125235 + 0.0998780i
\(733\) 3.34443e11i 1.15853i 0.815140 + 0.579263i \(0.196660\pi\)
−0.815140 + 0.579263i \(0.803340\pi\)
\(734\) 1.55465e11i 0.535609i
\(735\) 0 0
\(736\) 6.46444e11 2.20303
\(737\) 2.47099e11 0.837530
\(738\) −8.29156e10 3.25437e11i −0.279519 1.09709i
\(739\) 4.18860e11 1.40440 0.702201 0.711979i \(-0.252201\pi\)
0.702201 + 0.711979i \(0.252201\pi\)
\(740\) 0 0
\(741\) −4.25037e11 + 5.32945e10i −1.40979 + 0.176771i
\(742\) 2.24658e11i 0.741152i
\(743\) −1.94993e11 −0.639830 −0.319915 0.947446i \(-0.603654\pi\)
−0.319915 + 0.947446i \(0.603654\pi\)
\(744\) 5.28450e9 + 4.21451e10i 0.0172469 + 0.137548i
\(745\) 0 0
\(746\) 7.67721e11i 2.47884i
\(747\) −1.34863e11 + 3.43606e10i −0.433121 + 0.110351i
\(748\) 2.01923e11i 0.645028i
\(749\) 1.49781e11i 0.475915i
\(750\) 0 0
\(751\) 2.13581e10 0.0671433 0.0335717 0.999436i \(-0.489312\pi\)
0.0335717 + 0.999436i \(0.489312\pi\)
\(752\) −3.99484e11 −1.24919
\(753\) −3.33041e11 + 4.17594e10i −1.03590 + 0.129889i
\(754\) 4.39314e11 1.35922
\(755\) 0 0
\(756\) −1.06199e11 + 4.17059e10i −0.325111 + 0.127676i
\(757\) 9.33494e10i 0.284268i 0.989847 + 0.142134i \(0.0453964\pi\)
−0.989847 + 0.142134i \(0.954604\pi\)
\(758\) 4.78005e11 1.44796
\(759\) 5.53826e11 6.94432e10i 1.66881 0.209248i
\(760\) 0 0
\(761\) 7.19545e10i 0.214546i 0.994230 + 0.107273i \(0.0342118\pi\)
−0.994230 + 0.107273i \(0.965788\pi\)
\(762\) −2.06242e10 + 2.58603e9i −0.0611725 + 0.00767031i
\(763\) 4.85256e10i 0.143177i
\(764\) 3.38468e11i 0.993447i
\(765\) 0 0
\(766\) 6.29370e11 1.82806
\(767\) −6.04370e11 −1.74631
\(768\) −1.97863e10 1.57800e11i −0.0568747 0.453589i
\(769\) 1.60418e11 0.458720 0.229360 0.973342i \(-0.426337\pi\)
0.229360 + 0.973342i \(0.426337\pi\)
\(770\) 0 0
\(771\) −1.13515e10 9.05313e10i −0.0321246 0.256201i
\(772\) 8.25245e11i 2.32335i
\(773\) −3.72166e11 −1.04236 −0.521181 0.853446i \(-0.674508\pi\)
−0.521181 + 0.853446i \(0.674508\pi\)
\(774\) 9.35669e10 + 3.67243e11i 0.260710 + 1.02327i
\(775\) 0 0
\(776\) 3.73961e10i 0.103129i
\(777\) −1.61268e10 1.28615e11i −0.0442451 0.352865i
\(778\) 6.39941e11i 1.74671i
\(779\) 2.32842e11i 0.632283i
\(780\) 0 0
\(781\) −4.01055e11 −1.07795
\(782\) 4.23451e11 1.13234
\(783\) −1.86923e11 + 7.34077e10i −0.497297 + 0.195296i
\(784\) −2.58062e11 −0.683062
\(785\) 0 0
\(786\) 5.51176e11 6.91110e10i 1.44411 0.181074i
\(787\) 5.18916e11i 1.35269i 0.736585 + 0.676345i \(0.236437\pi\)
−0.736585 + 0.676345i \(0.763563\pi\)
\(788\) −7.17773e11 −1.86158
\(789\) −6.97229e10 5.56056e11i −0.179915 1.43486i
\(790\) 0 0
\(791\) 3.15904e10i 0.0806956i
\(792\) 3.29907e10 + 1.29486e11i 0.0838477 + 0.329096i
\(793\) 5.62648e10i 0.142280i
\(794\) 5.19149e11i 1.30620i
\(795\) 0 0
\(796\) 2.90539e11 0.723690
\(797\) 1.05184e11 0.260686 0.130343 0.991469i \(-0.458392\pi\)
0.130343 + 0.991469i \(0.458392\pi\)
\(798\) 1.43327e11 1.79715e10i 0.353440 0.0443172i
\(799\) −3.35634e11 −0.823530
\(800\) 0 0
\(801\) −7.90333e10 3.10200e11i −0.191991 0.753549i
\(802\) 9.19105e11i 2.22161i
\(803\) −3.63983e11 −0.875424
\(804\) 3.87524e11 4.85909e10i 0.927415 0.116287i
\(805\) 0 0
\(806\) 4.75402e11i 1.12647i
\(807\) 8.36375e10 1.04871e10i 0.197200 0.0247265i
\(808\) 8.10446e10i 0.190142i
\(809\) 1.09572e10i 0.0255804i −0.999918 0.0127902i \(-0.995929\pi\)
0.999918 0.0127902i \(-0.00407135\pi\)
\(810\) 0 0
\(811\) 1.31782e11 0.304630 0.152315 0.988332i \(-0.451327\pi\)
0.152315 + 0.988332i \(0.451327\pi\)
\(812\) −8.11263e10 −0.186611
\(813\) 4.33694e10 + 3.45881e11i 0.0992706 + 0.791707i
\(814\) −8.72747e11 −1.98788
\(815\) 0 0
\(816\) −2.01882e10 1.61005e11i −0.0455341 0.363145i
\(817\) 2.62753e11i 0.589738i
\(818\) 2.43229e11 0.543254
\(819\) −2.15249e11 + 5.48416e10i −0.478416 + 0.121892i
\(820\) 0 0
\(821\) 3.65371e10i 0.0804194i −0.999191 0.0402097i \(-0.987197\pi\)
0.999191 0.0402097i \(-0.0128026\pi\)
\(822\) 1.77354e10 + 1.41444e11i 0.0388466 + 0.309811i
\(823\) 4.11792e11i 0.897591i −0.893635 0.448795i \(-0.851853\pi\)
0.893635 0.448795i \(-0.148147\pi\)
\(824\) 8.90408e10i 0.193144i
\(825\) 0 0
\(826\) 2.03800e11 0.437808
\(827\) 1.78687e11 0.382007 0.191004 0.981589i \(-0.438826\pi\)
0.191004 + 0.981589i \(0.438826\pi\)
\(828\) 8.54907e11 2.17815e11i 1.81885 0.463411i
\(829\) 3.65541e11 0.773960 0.386980 0.922088i \(-0.373518\pi\)
0.386980 + 0.922088i \(0.373518\pi\)
\(830\) 0 0
\(831\) 8.14639e11 1.02146e11i 1.70829 0.214199i
\(832\) 1.12121e12i 2.33988i
\(833\) −2.16816e11 −0.450310
\(834\) −9.61243e9 7.66614e10i −0.0198687 0.158457i
\(835\) 0 0
\(836\) 5.32609e11i 1.09039i
\(837\) −7.94378e10 2.02278e11i −0.161855 0.412142i
\(838\) 7.22074e11i 1.46422i
\(839\) 5.20766e11i 1.05098i 0.850799 + 0.525491i \(0.176118\pi\)
−0.850799 + 0.525491i \(0.823882\pi\)
\(840\) 0 0
\(841\) 3.57454e11 0.714555
\(842\) 9.37429e11 1.86505
\(843\) 7.09349e11 8.89440e10i 1.40459 0.176119i
\(844\) 6.65348e11 1.31123
\(845\) 0 0
\(846\) −1.23736e12 + 3.15257e11i −2.41554 + 0.615437i
\(847\) 2.62365e10i 0.0509768i
\(848\) −6.65672e11 −1.28729
\(849\) 1.27026e11 1.59276e10i 0.244491 0.0306563i
\(850\) 0 0
\(851\) 1.00229e12i 1.91106i
\(852\) −6.28973e11 + 7.88657e10i −1.19364 + 0.149668i
\(853\) 5.21152e11i 0.984392i 0.870484 + 0.492196i \(0.163806\pi\)
−0.870484 + 0.492196i \(0.836194\pi\)
\(854\) 1.89731e10i 0.0356702i
\(855\) 0 0
\(856\) 2.77261e11 0.516409
\(857\) −8.67435e11 −1.60810 −0.804051 0.594560i \(-0.797326\pi\)
−0.804051 + 0.594560i \(0.797326\pi\)
\(858\) 1.86070e11 + 1.48395e12i 0.343342 + 2.73823i
\(859\) 6.24921e11 1.14776 0.573882 0.818938i \(-0.305437\pi\)
0.573882 + 0.818938i \(0.305437\pi\)
\(860\) 0 0
\(861\) 1.50216e10 + 1.19801e11i 0.0273340 + 0.217995i
\(862\) 4.77990e11i 0.865745i
\(863\) 8.65555e11 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(864\) −2.89430e11 7.36996e11i −0.519384 1.32254i
\(865\) 0 0
\(866\) 1.13265e12i 2.01384i
\(867\) 5.33369e10 + 4.25374e11i 0.0943955 + 0.752827i
\(868\) 8.77906e10i 0.154657i
\(869\) 7.14583e11i 1.25306i
\(870\) 0 0
\(871\) 7.60363e11 1.32114
\(872\) −8.98262e10 −0.155359
\(873\) 4.72386e10 + 1.85408e11i 0.0813280 + 0.319206i
\(874\) −1.11693e12 −1.91417
\(875\) 0 0
\(876\) −5.70833e11 + 7.15756e10i −0.969376 + 0.121548i
\(877\) 3.45290e10i 0.0583694i −0.999574 0.0291847i \(-0.990709\pi\)
0.999574 0.0291847i \(-0.00929110\pi\)
\(878\) 6.68096e11 1.12424
\(879\) −7.36654e9 5.87499e10i −0.0123398 0.0984129i
\(880\) 0 0
\(881\) 5.74904e10i 0.0954316i −0.998861 0.0477158i \(-0.984806\pi\)
0.998861 0.0477158i \(-0.0151942\pi\)
\(882\) −7.99321e11 + 2.03653e11i −1.32083 + 0.336524i
\(883\) 7.36663e11i 1.21179i 0.795546 + 0.605893i \(0.207184\pi\)
−0.795546 + 0.605893i \(0.792816\pi\)
\(884\) 6.21348e11i 1.01748i
\(885\) 0 0
\(886\) −7.68143e10 −0.124654
\(887\) 1.56687e11 0.253126 0.126563 0.991959i \(-0.459605\pi\)
0.126563 + 0.991959i \(0.459605\pi\)
\(888\) −2.38081e11 + 2.98525e10i −0.382889 + 0.0480097i
\(889\) 7.47283e9 0.0119640
\(890\) 0 0
\(891\) −3.27133e11 6.00312e11i −0.519055 0.952503i
\(892\) 1.14904e12i 1.81500i
\(893\) 8.85300e11 1.39214
\(894\) 3.45387e11 4.33074e10i 0.540700 0.0677973i
\(895\) 0 0
\(896\) 1.13858e11i 0.176657i
\(897\) 1.70421e12 2.13688e11i 2.63241 0.330073i
\(898\) 1.00163e12i 1.54029i
\(899\) 1.54523e11i 0.236567i
\(900\) 0 0
\(901\) −5.59277e11 −0.848648
\(902\) 8.12933e11 1.22809
\(903\) −1.69512e10 1.35190e11i −0.0254947 0.203326i
\(904\) 5.84773e10 0.0875616
\(905\) 0 0
\(906\) 1.03807e10 + 8.27883e10i 0.0154068 + 0.122873i
\(907\) 5.78430e11i 0.854716i −0.904083 0.427358i \(-0.859444\pi\)
0.904083 0.427358i \(-0.140556\pi\)
\(908\) −1.23040e12 −1.81010
\(909\) −1.02375e11 4.01815e11i −0.149948 0.588533i
\(910\) 0 0
\(911\) 8.17142e10i 0.118638i −0.998239 0.0593190i \(-0.981107\pi\)
0.998239 0.0593190i \(-0.0188929\pi\)
\(912\) 5.32501e10 + 4.24682e11i 0.0769735 + 0.613882i
\(913\) 3.36882e11i 0.484836i
\(914\) 9.85637e11i 1.41232i
\(915\) 0 0
\(916\) −8.80533e11 −1.25073
\(917\) −1.99710e11 −0.282437
\(918\) −1.89590e11 4.82766e11i −0.266959 0.679776i
\(919\) 8.52245e11 1.19482 0.597410 0.801936i \(-0.296197\pi\)
0.597410 + 0.801936i \(0.296197\pi\)
\(920\) 0 0
\(921\) −6.47354e11 + 8.11705e10i −0.899711 + 0.112813i
\(922\) 1.77036e12i 2.44984i
\(923\) −1.23411e12 −1.70038
\(924\) −3.43607e10 2.74035e11i −0.0471384 0.375940i
\(925\) 0 0
\(926\) 1.08760e12i 1.47920i
\(927\) 1.12476e11 + 4.41460e11i 0.152314 + 0.597823i
\(928\) 5.63000e11i 0.759131i
\(929\) 4.58591e11i 0.615691i 0.951436 + 0.307845i \(0.0996079\pi\)
−0.951436 + 0.307845i \(0.900392\pi\)
\(930\) 0 0
\(931\) 5.71893e11 0.761231
\(932\) −1.18058e11 −0.156470
\(933\) 1.83384e11 2.29942e10i 0.242011 0.0303453i
\(934\) 6.58834e10 0.0865742
\(935\) 0 0
\(936\) 1.01518e11 + 3.98450e11i 0.132263 + 0.519123i
\(937\) 1.32495e11i 0.171886i 0.996300 + 0.0859432i \(0.0273904\pi\)
−0.996300 + 0.0859432i \(0.972610\pi\)
\(938\) −2.56402e11 −0.331215
\(939\) 2.73899e11 3.43437e10i 0.352313 0.0441759i
\(940\) 0 0
\(941\) 7.82786e11i 0.998354i −0.866500 0.499177i \(-0.833636\pi\)
0.866500 0.499177i \(-0.166364\pi\)
\(942\) −1.90932e11 + 2.39406e10i −0.242479 + 0.0304040i
\(943\) 9.33594e11i 1.18062i
\(944\) 6.03867e11i 0.760419i
\(945\) 0 0
\(946\) −9.17362e11 −1.14545
\(947\) 7.18981e11 0.893959 0.446980 0.894544i \(-0.352500\pi\)
0.446980 + 0.894544i \(0.352500\pi\)
\(948\) 1.40520e11 + 1.12068e12i 0.173982 + 1.38754i
\(949\) −1.12003e12 −1.38091
\(950\) 0 0
\(951\) −2.82516e10 2.25313e11i −0.0345398 0.275463i
\(952\) 3.64455e10i 0.0443707i
\(953\) 3.21954e11 0.390321 0.195160 0.980771i \(-0.437477\pi\)
0.195160 + 0.980771i \(0.437477\pi\)
\(954\) −2.06185e12 + 5.25322e11i −2.48922 + 0.634209i
\(955\) 0 0
\(956\) 9.56191e11i 1.14476i
\(957\) −6.04793e10 4.82337e11i −0.0721040 0.575046i
\(958\) 9.08862e11i 1.07904i
\(959\) 5.12499e10i 0.0605924i
\(960\) 0 0
\(961\) −6.85675e11 −0.803942
\(962\) −2.68558e12 −3.13573
\(963\) −1.37465e12 + 3.50235e11i −1.59840 + 0.407244i
\(964\) −5.69059e11 −0.658945
\(965\) 0 0
\(966\) −5.74677e11 + 7.20577e10i −0.659957 + 0.0827507i
\(967\) 4.20589e11i 0.481008i −0.970648 0.240504i \(-0.922687\pi\)
0.970648 0.240504i \(-0.0773127\pi\)
\(968\) −4.85666e10 −0.0553142
\(969\) 4.47391e10 + 3.56805e11i 0.0507449 + 0.404703i
\(970\) 0 0
\(971\) 8.93768e11i 1.00542i 0.864455 + 0.502710i \(0.167664\pi\)
−0.864455 + 0.502710i \(0.832336\pi\)
\(972\) −6.31090e11 8.77137e11i −0.707011 0.982658i
\(973\) 2.77770e10i 0.0309909i
\(974\) 6.63937e11i 0.737719i
\(975\) 0 0
\(976\) 5.62179e10 0.0619548
\(977\) −8.04509e11 −0.882983 −0.441492 0.897265i \(-0.645551\pi\)
−0.441492 + 0.897265i \(0.645551\pi\)
\(978\) −7.94394e11 + 9.96075e10i −0.868321 + 0.108877i
\(979\) 7.74869e11 0.843525
\(980\) 0 0
\(981\) 4.45354e11 1.13468e11i 0.480872 0.122518i
\(982\) 8.62300e11i 0.927283i
\(983\) 7.12126e11 0.762681 0.381340 0.924435i \(-0.375463\pi\)
0.381340 + 0.924435i \(0.375463\pi\)
\(984\) 2.21764e11 2.78066e10i 0.236543 0.0296597i
\(985\) 0 0
\(986\) 3.68791e11i 0.390187i
\(987\) 4.55499e11 5.71142e10i 0.479975 0.0601832i
\(988\) 1.63892e12i 1.72001i
\(989\) 1.05352e12i 1.10118i
\(990\) 0 0
\(991\) 1.20276e12 1.24705 0.623526 0.781803i \(-0.285700\pi\)
0.623526 + 0.781803i \(0.285700\pi\)
\(992\) 6.09249e11 0.629141
\(993\) 3.88808e10 + 3.10083e11i 0.0399887 + 0.318920i
\(994\) 4.16155e11 0.426294
\(995\) 0 0
\(996\) −6.62465e10 5.28331e11i −0.0673171 0.536870i
\(997\) 2.28898e11i 0.231665i −0.993269 0.115833i \(-0.963046\pi\)
0.993269 0.115833i \(-0.0369536\pi\)
\(998\) 3.12341e11 0.314852
\(999\) 1.14268e12 4.48750e11i 1.14727 0.450550i
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.d.c.74.17 20
3.2 odd 2 inner 75.9.d.c.74.3 20
5.2 odd 4 15.9.c.a.11.9 yes 10
5.3 odd 4 75.9.c.g.26.2 10
5.4 even 2 inner 75.9.d.c.74.4 20
15.2 even 4 15.9.c.a.11.2 10
15.8 even 4 75.9.c.g.26.9 10
15.14 odd 2 inner 75.9.d.c.74.18 20
20.7 even 4 240.9.l.b.161.9 10
60.47 odd 4 240.9.l.b.161.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.9.c.a.11.2 10 15.2 even 4
15.9.c.a.11.9 yes 10 5.2 odd 4
75.9.c.g.26.2 10 5.3 odd 4
75.9.c.g.26.9 10 15.8 even 4
75.9.d.c.74.3 20 3.2 odd 2 inner
75.9.d.c.74.4 20 5.4 even 2 inner
75.9.d.c.74.17 20 1.1 even 1 trivial
75.9.d.c.74.18 20 15.14 odd 2 inner
240.9.l.b.161.9 10 20.7 even 4
240.9.l.b.161.10 10 60.47 odd 4