Properties

Label 75.9.f.d.43.3
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 43.3
Root \(8.37625 - 8.37625i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.9.f.d.7.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.10647 + 3.10647i) q^{2} +(-33.0681 - 33.0681i) q^{3} +236.700i q^{4} +205.450 q^{6} +(974.502 - 974.502i) q^{7} +(-1530.56 - 1530.56i) q^{8} +2187.00i q^{9} +O(q^{10})\) \(q+(-3.10647 + 3.10647i) q^{2} +(-33.0681 - 33.0681i) q^{3} +236.700i q^{4} +205.450 q^{6} +(974.502 - 974.502i) q^{7} +(-1530.56 - 1530.56i) q^{8} +2187.00i q^{9} -4996.30 q^{11} +(7827.21 - 7827.21i) q^{12} +(-14944.9 - 14944.9i) q^{13} +6054.51i q^{14} -51085.9 q^{16} +(11795.2 - 11795.2i) q^{17} +(-6793.84 - 6793.84i) q^{18} +52539.8i q^{19} -64449.9 q^{21} +(15520.8 - 15520.8i) q^{22} +(245594. + 245594. i) q^{23} +101225. i q^{24} +92851.4 q^{26} +(72320.0 - 72320.0i) q^{27} +(230664. + 230664. i) q^{28} -1.02151e6i q^{29} -165534. q^{31} +(550519. - 550519. i) q^{32} +(165218. + 165218. i) q^{33} +73282.9i q^{34} -517662. q^{36} +(2.47866e6 - 2.47866e6i) q^{37} +(-163213. - 163213. i) q^{38} +988397. i q^{39} +3.10533e6 q^{41} +(200211. - 200211. i) q^{42} +(1.63711e6 + 1.63711e6i) q^{43} -1.18262e6i q^{44} -1.52586e6 q^{46} +(5.87036e6 - 5.87036e6i) q^{47} +(1.68931e6 + 1.68931e6i) q^{48} +3.86549e6i q^{49} -780091. q^{51} +(3.53744e6 - 3.53744e6i) q^{52} +(8.41070e6 + 8.41070e6i) q^{53} +449319. i q^{54} -2.98306e6 q^{56} +(1.73739e6 - 1.73739e6i) q^{57} +(3.17328e6 + 3.17328e6i) q^{58} +9.42589e6i q^{59} +3.74107e6 q^{61} +(514226. - 514226. i) q^{62} +(2.13123e6 + 2.13123e6i) q^{63} -9.65765e6i q^{64} -1.02649e6 q^{66} +(1.23693e7 - 1.23693e7i) q^{67} +(2.79193e6 + 2.79193e6i) q^{68} -1.62427e7i q^{69} +1.38777e7 q^{71} +(3.34732e6 - 3.34732e6i) q^{72} +(-2.14552e7 - 2.14552e7i) q^{73} +1.53998e7i q^{74} -1.24361e7 q^{76} +(-4.86890e6 + 4.86890e6i) q^{77} +(-3.07042e6 - 3.07042e6i) q^{78} -4.04271e7i q^{79} -4.78297e6 q^{81} +(-9.64661e6 + 9.64661e6i) q^{82} +(-1.85669e7 - 1.85669e7i) q^{83} -1.52553e7i q^{84} -1.01712e7 q^{86} +(-3.37794e7 + 3.37794e7i) q^{87} +(7.64712e6 + 7.64712e6i) q^{88} +5.33621e7i q^{89} -2.91276e7 q^{91} +(-5.81321e7 + 5.81321e7i) q^{92} +(5.47390e6 + 5.47390e6i) q^{93} +3.64722e7i q^{94} -3.64092e7 q^{96} +(-8.55969e7 + 8.55969e7i) q^{97} +(-1.20080e7 - 1.20080e7i) q^{98} -1.09269e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2268 q^{6}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.10647 + 3.10647i −0.194154 + 0.194154i −0.797488 0.603334i \(-0.793838\pi\)
0.603334 + 0.797488i \(0.293838\pi\)
\(3\) −33.0681 33.0681i −0.408248 0.408248i
\(4\) 236.700i 0.924608i
\(5\) 0 0
\(6\) 205.450 0.158526
\(7\) 974.502 974.502i 0.405873 0.405873i −0.474424 0.880297i \(-0.657343\pi\)
0.880297 + 0.474424i \(0.157343\pi\)
\(8\) −1530.56 1530.56i −0.373671 0.373671i
\(9\) 2187.00i 0.333333i
\(10\) 0 0
\(11\) −4996.30 −0.341254 −0.170627 0.985336i \(-0.554579\pi\)
−0.170627 + 0.985336i \(0.554579\pi\)
\(12\) 7827.21 7827.21i 0.377470 0.377470i
\(13\) −14944.9 14944.9i −0.523261 0.523261i 0.395294 0.918555i \(-0.370643\pi\)
−0.918555 + 0.395294i \(0.870643\pi\)
\(14\) 6054.51i 0.157604i
\(15\) 0 0
\(16\) −51085.9 −0.779509
\(17\) 11795.2 11795.2i 0.141225 0.141225i −0.632960 0.774185i \(-0.718160\pi\)
0.774185 + 0.632960i \(0.218160\pi\)
\(18\) −6793.84 6793.84i −0.0647181 0.0647181i
\(19\) 52539.8i 0.403157i 0.979472 + 0.201578i \(0.0646070\pi\)
−0.979472 + 0.201578i \(0.935393\pi\)
\(20\) 0 0
\(21\) −64449.9 −0.331394
\(22\) 15520.8 15520.8i 0.0662559 0.0662559i
\(23\) 245594. + 245594.i 0.877620 + 0.877620i 0.993288 0.115668i \(-0.0369008\pi\)
−0.115668 + 0.993288i \(0.536901\pi\)
\(24\) 101225.i 0.305101i
\(25\) 0 0
\(26\) 92851.4 0.203187
\(27\) 72320.0 72320.0i 0.136083 0.136083i
\(28\) 230664. + 230664.i 0.375274 + 0.375274i
\(29\) 1.02151e6i 1.44428i −0.691749 0.722138i \(-0.743159\pi\)
0.691749 0.722138i \(-0.256841\pi\)
\(30\) 0 0
\(31\) −165534. −0.179242 −0.0896211 0.995976i \(-0.528566\pi\)
−0.0896211 + 0.995976i \(0.528566\pi\)
\(32\) 550519. 550519.i 0.525016 0.525016i
\(33\) 165218. + 165218.i 0.139316 + 0.139316i
\(34\) 73282.9i 0.0548387i
\(35\) 0 0
\(36\) −517662. −0.308203
\(37\) 2.47866e6 2.47866e6i 1.32255 1.32255i 0.410837 0.911709i \(-0.365236\pi\)
0.911709 0.410837i \(-0.134764\pi\)
\(38\) −163213. 163213.i −0.0782745 0.0782745i
\(39\) 988397.i 0.427241i
\(40\) 0 0
\(41\) 3.10533e6 1.09894 0.549468 0.835515i \(-0.314830\pi\)
0.549468 + 0.835515i \(0.314830\pi\)
\(42\) 200211. 200211.i 0.0643415 0.0643415i
\(43\) 1.63711e6 + 1.63711e6i 0.478854 + 0.478854i 0.904765 0.425911i \(-0.140046\pi\)
−0.425911 + 0.904765i \(0.640046\pi\)
\(44\) 1.18262e6i 0.315526i
\(45\) 0 0
\(46\) −1.52586e6 −0.340787
\(47\) 5.87036e6 5.87036e6i 1.20302 1.20302i 0.229779 0.973243i \(-0.426200\pi\)
0.973243 0.229779i \(-0.0738004\pi\)
\(48\) 1.68931e6 + 1.68931e6i 0.318233 + 0.318233i
\(49\) 3.86549e6i 0.670534i
\(50\) 0 0
\(51\) −780091. −0.115309
\(52\) 3.53744e6 3.53744e6i 0.483812 0.483812i
\(53\) 8.41070e6 + 8.41070e6i 1.06593 + 1.06593i 0.997667 + 0.0682627i \(0.0217456\pi\)
0.0682627 + 0.997667i \(0.478254\pi\)
\(54\) 449319.i 0.0528421i
\(55\) 0 0
\(56\) −2.98306e6 −0.303326
\(57\) 1.73739e6 1.73739e6i 0.164588 0.164588i
\(58\) 3.17328e6 + 3.17328e6i 0.280412 + 0.280412i
\(59\) 9.42589e6i 0.777883i 0.921262 + 0.388942i \(0.127159\pi\)
−0.921262 + 0.388942i \(0.872841\pi\)
\(60\) 0 0
\(61\) 3.74107e6 0.270194 0.135097 0.990832i \(-0.456865\pi\)
0.135097 + 0.990832i \(0.456865\pi\)
\(62\) 514226. 514226.i 0.0348006 0.0348006i
\(63\) 2.13123e6 + 2.13123e6i 0.135291 + 0.135291i
\(64\) 9.65765e6i 0.575641i
\(65\) 0 0
\(66\) −1.02649e6 −0.0540977
\(67\) 1.23693e7 1.23693e7i 0.613827 0.613827i −0.330114 0.943941i \(-0.607087\pi\)
0.943941 + 0.330114i \(0.107087\pi\)
\(68\) 2.79193e6 + 2.79193e6i 0.130577 + 0.130577i
\(69\) 1.62427e7i 0.716574i
\(70\) 0 0
\(71\) 1.38777e7 0.546116 0.273058 0.961998i \(-0.411965\pi\)
0.273058 + 0.961998i \(0.411965\pi\)
\(72\) 3.34732e6 3.34732e6i 0.124557 0.124557i
\(73\) −2.14552e7 2.14552e7i −0.755511 0.755511i 0.219991 0.975502i \(-0.429397\pi\)
−0.975502 + 0.219991i \(0.929397\pi\)
\(74\) 1.53998e7i 0.513556i
\(75\) 0 0
\(76\) −1.24361e7 −0.372762
\(77\) −4.86890e6 + 4.86890e6i −0.138506 + 0.138506i
\(78\) −3.07042e6 3.07042e6i −0.0829506 0.0829506i
\(79\) 4.04271e7i 1.03792i −0.854798 0.518961i \(-0.826319\pi\)
0.854798 0.518961i \(-0.173681\pi\)
\(80\) 0 0
\(81\) −4.78297e6 −0.111111
\(82\) −9.64661e6 + 9.64661e6i −0.213363 + 0.213363i
\(83\) −1.85669e7 1.85669e7i −0.391225 0.391225i 0.483899 0.875124i \(-0.339220\pi\)
−0.875124 + 0.483899i \(0.839220\pi\)
\(84\) 1.52553e7i 0.306410i
\(85\) 0 0
\(86\) −1.01712e7 −0.185943
\(87\) −3.37794e7 + 3.37794e7i −0.589623 + 0.589623i
\(88\) 7.64712e6 + 7.64712e6i 0.127517 + 0.127517i
\(89\) 5.33621e7i 0.850497i 0.905077 + 0.425248i \(0.139813\pi\)
−0.905077 + 0.425248i \(0.860187\pi\)
\(90\) 0 0
\(91\) −2.91276e7 −0.424755
\(92\) −5.81321e7 + 5.81321e7i −0.811455 + 0.811455i
\(93\) 5.47390e6 + 5.47390e6i 0.0731753 + 0.0731753i
\(94\) 3.64722e7i 0.467143i
\(95\) 0 0
\(96\) −3.64092e7 −0.428673
\(97\) −8.55969e7 + 8.55969e7i −0.966877 + 0.966877i −0.999469 0.0325916i \(-0.989624\pi\)
0.0325916 + 0.999469i \(0.489624\pi\)
\(98\) −1.20080e7 1.20080e7i −0.130187 0.130187i
\(99\) 1.09269e7i 0.113751i
\(100\) 0 0
\(101\) 1.76856e8 1.69955 0.849774 0.527147i \(-0.176738\pi\)
0.849774 + 0.527147i \(0.176738\pi\)
\(102\) 2.42333e6 2.42333e6i 0.0223878 0.0223878i
\(103\) −7.41794e7 7.41794e7i −0.659074 0.659074i 0.296087 0.955161i \(-0.404318\pi\)
−0.955161 + 0.296087i \(0.904318\pi\)
\(104\) 4.57479e7i 0.391055i
\(105\) 0 0
\(106\) −5.22551e7 −0.413910
\(107\) −4.71593e7 + 4.71593e7i −0.359776 + 0.359776i −0.863730 0.503955i \(-0.831878\pi\)
0.503955 + 0.863730i \(0.331878\pi\)
\(108\) 1.71181e7 + 1.71181e7i 0.125823 + 0.125823i
\(109\) 1.75445e7i 0.124290i −0.998067 0.0621449i \(-0.980206\pi\)
0.998067 0.0621449i \(-0.0197941\pi\)
\(110\) 0 0
\(111\) −1.63929e8 −1.07985
\(112\) −4.97833e7 + 4.97833e7i −0.316382 + 0.316382i
\(113\) −1.15312e8 1.15312e8i −0.707229 0.707229i 0.258722 0.965952i \(-0.416699\pi\)
−0.965952 + 0.258722i \(0.916699\pi\)
\(114\) 1.07943e7i 0.0639109i
\(115\) 0 0
\(116\) 2.41791e8 1.33539
\(117\) 3.26844e7 3.26844e7i 0.174420 0.174420i
\(118\) −2.92812e7 2.92812e7i −0.151029 0.151029i
\(119\) 2.29889e7i 0.114639i
\(120\) 0 0
\(121\) −1.89396e8 −0.883546
\(122\) −1.16215e7 + 1.16215e7i −0.0524594 + 0.0524594i
\(123\) −1.02687e8 1.02687e8i −0.448639 0.448639i
\(124\) 3.91819e7i 0.165729i
\(125\) 0 0
\(126\) −1.32412e7 −0.0525347
\(127\) 1.05771e8 1.05771e8i 0.406585 0.406585i −0.473961 0.880546i \(-0.657176\pi\)
0.880546 + 0.473961i \(0.157176\pi\)
\(128\) 1.70934e8 + 1.70934e8i 0.636779 + 0.636779i
\(129\) 1.08272e8i 0.390983i
\(130\) 0 0
\(131\) 4.98885e8 1.69401 0.847004 0.531587i \(-0.178404\pi\)
0.847004 + 0.531587i \(0.178404\pi\)
\(132\) −3.91071e7 + 3.91071e7i −0.128813 + 0.128813i
\(133\) 5.12001e7 + 5.12001e7i 0.163630 + 0.163630i
\(134\) 7.68496e7i 0.238354i
\(135\) 0 0
\(136\) −3.61065e7 −0.105543
\(137\) 1.96007e8 1.96007e8i 0.556403 0.556403i −0.371879 0.928281i \(-0.621286\pi\)
0.928281 + 0.371879i \(0.121286\pi\)
\(138\) 5.04573e7 + 5.04573e7i 0.139126 + 0.139126i
\(139\) 3.18232e8i 0.852480i −0.904610 0.426240i \(-0.859838\pi\)
0.904610 0.426240i \(-0.140162\pi\)
\(140\) 0 0
\(141\) −3.88244e8 −0.982263
\(142\) −4.31107e7 + 4.31107e7i −0.106031 + 0.106031i
\(143\) 7.46690e7 + 7.46690e7i 0.178565 + 0.178565i
\(144\) 1.11725e8i 0.259836i
\(145\) 0 0
\(146\) 1.33300e8 0.293371
\(147\) 1.27825e8 1.27825e8i 0.273744 0.273744i
\(148\) 5.86699e8 + 5.86699e8i 1.22284 + 1.22284i
\(149\) 7.86775e8i 1.59627i 0.602481 + 0.798134i \(0.294179\pi\)
−0.602481 + 0.798134i \(0.705821\pi\)
\(150\) 0 0
\(151\) −7.06754e8 −1.35944 −0.679721 0.733471i \(-0.737899\pi\)
−0.679721 + 0.733471i \(0.737899\pi\)
\(152\) 8.04150e7 8.04150e7i 0.150648 0.150648i
\(153\) 2.57961e7 + 2.57961e7i 0.0470749 + 0.0470749i
\(154\) 3.02502e7i 0.0537830i
\(155\) 0 0
\(156\) −2.33953e8 −0.395031
\(157\) 7.32328e8 7.32328e8i 1.20533 1.20533i 0.232811 0.972522i \(-0.425208\pi\)
0.972522 0.232811i \(-0.0747922\pi\)
\(158\) 1.25586e8 + 1.25586e8i 0.201517 + 0.201517i
\(159\) 5.56252e8i 0.870328i
\(160\) 0 0
\(161\) 4.78664e8 0.712405
\(162\) 1.48581e7 1.48581e7i 0.0215727 0.0215727i
\(163\) 3.22135e7 + 3.22135e7i 0.0456339 + 0.0456339i 0.729555 0.683922i \(-0.239727\pi\)
−0.683922 + 0.729555i \(0.739727\pi\)
\(164\) 7.35031e8i 1.01609i
\(165\) 0 0
\(166\) 1.15355e8 0.151916
\(167\) 7.92458e8 7.92458e8i 1.01885 1.01885i 0.0190311 0.999819i \(-0.493942\pi\)
0.999819 0.0190311i \(-0.00605815\pi\)
\(168\) 9.86441e7 + 9.86441e7i 0.123832 + 0.123832i
\(169\) 3.69033e8i 0.452395i
\(170\) 0 0
\(171\) −1.14904e8 −0.134386
\(172\) −3.87503e8 + 3.87503e8i −0.442752 + 0.442752i
\(173\) −6.76294e8 6.76294e8i −0.755008 0.755008i 0.220402 0.975409i \(-0.429263\pi\)
−0.975409 + 0.220402i \(0.929263\pi\)
\(174\) 2.09869e8i 0.228956i
\(175\) 0 0
\(176\) 2.55241e8 0.266011
\(177\) 3.11697e8 3.11697e8i 0.317570 0.317570i
\(178\) −1.65767e8 1.65767e8i −0.165127 0.165127i
\(179\) 8.49985e8i 0.827940i 0.910290 + 0.413970i \(0.135858\pi\)
−0.910290 + 0.413970i \(0.864142\pi\)
\(180\) 0 0
\(181\) 1.37723e8 0.128319 0.0641596 0.997940i \(-0.479563\pi\)
0.0641596 + 0.997940i \(0.479563\pi\)
\(182\) 9.04839e7 9.04839e7i 0.0824680 0.0824680i
\(183\) −1.23710e8 1.23710e8i −0.110306 0.110306i
\(184\) 7.51791e8i 0.655882i
\(185\) 0 0
\(186\) −3.40090e7 −0.0284146
\(187\) −5.89325e7 + 5.89325e7i −0.0481935 + 0.0481935i
\(188\) 1.38951e9 + 1.38951e9i 1.11232 + 1.11232i
\(189\) 1.40952e8i 0.110465i
\(190\) 0 0
\(191\) 1.83102e9 1.37581 0.687905 0.725800i \(-0.258530\pi\)
0.687905 + 0.725800i \(0.258530\pi\)
\(192\) −3.19360e8 + 3.19360e8i −0.235004 + 0.235004i
\(193\) −4.47959e8 4.47959e8i −0.322856 0.322856i 0.527006 0.849862i \(-0.323315\pi\)
−0.849862 + 0.527006i \(0.823315\pi\)
\(194\) 5.31808e8i 0.375446i
\(195\) 0 0
\(196\) −9.14961e8 −0.619981
\(197\) −1.01717e9 + 1.01717e9i −0.675351 + 0.675351i −0.958945 0.283594i \(-0.908473\pi\)
0.283594 + 0.958945i \(0.408473\pi\)
\(198\) 3.39441e7 + 3.39441e7i 0.0220853 + 0.0220853i
\(199\) 4.81408e8i 0.306973i 0.988151 + 0.153487i \(0.0490502\pi\)
−0.988151 + 0.153487i \(0.950950\pi\)
\(200\) 0 0
\(201\) −8.18059e8 −0.501187
\(202\) −5.49396e8 + 5.49396e8i −0.329974 + 0.329974i
\(203\) −9.95463e8 9.95463e8i −0.586193 0.586193i
\(204\) 1.84647e8i 0.106616i
\(205\) 0 0
\(206\) 4.60871e8 0.255924
\(207\) −5.37114e8 + 5.37114e8i −0.292540 + 0.292540i
\(208\) 7.63472e8 + 7.63472e8i 0.407887 + 0.407887i
\(209\) 2.62505e8i 0.137579i
\(210\) 0 0
\(211\) 5.57618e7 0.0281324 0.0140662 0.999901i \(-0.495522\pi\)
0.0140662 + 0.999901i \(0.495522\pi\)
\(212\) −1.99081e9 + 1.99081e9i −0.985568 + 0.985568i
\(213\) −4.58910e8 4.58910e8i −0.222951 0.222951i
\(214\) 2.92997e8i 0.139704i
\(215\) 0 0
\(216\) −2.21379e8 −0.101700
\(217\) −1.61313e8 + 1.61313e8i −0.0727496 + 0.0727496i
\(218\) 5.45015e7 + 5.45015e7i 0.0241314 + 0.0241314i
\(219\) 1.41897e9i 0.616872i
\(220\) 0 0
\(221\) −3.52556e8 −0.147795
\(222\) 5.09241e8 5.09241e8i 0.209658 0.209658i
\(223\) −3.04995e9 3.04995e9i −1.23331 1.23331i −0.962684 0.270629i \(-0.912768\pi\)
−0.270629 0.962684i \(-0.587232\pi\)
\(224\) 1.07296e9i 0.426180i
\(225\) 0 0
\(226\) 7.16425e8 0.274623
\(227\) −6.19777e8 + 6.19777e8i −0.233417 + 0.233417i −0.814117 0.580701i \(-0.802779\pi\)
0.580701 + 0.814117i \(0.302779\pi\)
\(228\) 4.11240e8 + 4.11240e8i 0.152179 + 0.152179i
\(229\) 3.01662e9i 1.09693i 0.836173 + 0.548465i \(0.184788\pi\)
−0.836173 + 0.548465i \(0.815212\pi\)
\(230\) 0 0
\(231\) 3.22011e8 0.113090
\(232\) −1.56348e9 + 1.56348e9i −0.539684 + 0.539684i
\(233\) −2.53460e9 2.53460e9i −0.859974 0.859974i 0.131361 0.991335i \(-0.458065\pi\)
−0.991335 + 0.131361i \(0.958065\pi\)
\(234\) 2.03066e8i 0.0677289i
\(235\) 0 0
\(236\) −2.23111e9 −0.719238
\(237\) −1.33685e9 + 1.33685e9i −0.423730 + 0.423730i
\(238\) 7.14143e7 + 7.14143e7i 0.0222576 + 0.0222576i
\(239\) 2.93731e9i 0.900240i −0.892968 0.450120i \(-0.851381\pi\)
0.892968 0.450120i \(-0.148619\pi\)
\(240\) 0 0
\(241\) −2.48664e9 −0.737132 −0.368566 0.929602i \(-0.620151\pi\)
−0.368566 + 0.929602i \(0.620151\pi\)
\(242\) 5.88352e8 5.88352e8i 0.171544 0.171544i
\(243\) 1.58164e8 + 1.58164e8i 0.0453609 + 0.0453609i
\(244\) 8.85510e8i 0.249824i
\(245\) 0 0
\(246\) 6.37990e8 0.174210
\(247\) 7.85200e8 7.85200e8i 0.210956 0.210956i
\(248\) 2.53359e8 + 2.53359e8i 0.0669776 + 0.0669776i
\(249\) 1.22794e9i 0.319434i
\(250\) 0 0
\(251\) −2.67826e9 −0.674772 −0.337386 0.941366i \(-0.609543\pi\)
−0.337386 + 0.941366i \(0.609543\pi\)
\(252\) −5.04463e8 + 5.04463e8i −0.125091 + 0.125091i
\(253\) −1.22706e9 1.22706e9i −0.299492 0.299492i
\(254\) 6.57147e8i 0.157880i
\(255\) 0 0
\(256\) 1.41036e9 0.328374
\(257\) 1.40231e9 1.40231e9i 0.321449 0.321449i −0.527874 0.849323i \(-0.677011\pi\)
0.849323 + 0.527874i \(0.177011\pi\)
\(258\) 3.36344e8 + 3.36344e8i 0.0759109 + 0.0759109i
\(259\) 4.83092e9i 1.07357i
\(260\) 0 0
\(261\) 2.23404e9 0.481426
\(262\) −1.54977e9 + 1.54977e9i −0.328899 + 0.328899i
\(263\) 3.19839e9 + 3.19839e9i 0.668510 + 0.668510i 0.957371 0.288861i \(-0.0932766\pi\)
−0.288861 + 0.957371i \(0.593277\pi\)
\(264\) 5.05751e8i 0.104117i
\(265\) 0 0
\(266\) −3.18103e8 −0.0635391
\(267\) 1.76458e9 1.76458e9i 0.347214 0.347214i
\(268\) 2.92781e9 + 2.92781e9i 0.567549 + 0.567549i
\(269\) 2.77450e9i 0.529877i −0.964265 0.264939i \(-0.914648\pi\)
0.964265 0.264939i \(-0.0853517\pi\)
\(270\) 0 0
\(271\) 9.95720e9 1.84612 0.923060 0.384656i \(-0.125680\pi\)
0.923060 + 0.384656i \(0.125680\pi\)
\(272\) −6.02569e8 + 6.02569e8i −0.110086 + 0.110086i
\(273\) 9.63194e8 + 9.63194e8i 0.173406 + 0.173406i
\(274\) 1.21778e9i 0.216056i
\(275\) 0 0
\(276\) 3.84464e9 0.662550
\(277\) 2.87012e9 2.87012e9i 0.487508 0.487508i −0.420011 0.907519i \(-0.637974\pi\)
0.907519 + 0.420011i \(0.137974\pi\)
\(278\) 9.88577e8 + 9.88577e8i 0.165513 + 0.165513i
\(279\) 3.62023e8i 0.0597474i
\(280\) 0 0
\(281\) −1.02942e10 −1.65108 −0.825540 0.564344i \(-0.809129\pi\)
−0.825540 + 0.564344i \(0.809129\pi\)
\(282\) 1.20607e9 1.20607e9i 0.190711 0.190711i
\(283\) 3.13540e9 + 3.13540e9i 0.488818 + 0.488818i 0.907933 0.419115i \(-0.137660\pi\)
−0.419115 + 0.907933i \(0.637660\pi\)
\(284\) 3.28486e9i 0.504944i
\(285\) 0 0
\(286\) −4.63914e8 −0.0693383
\(287\) 3.02615e9 3.02615e9i 0.446029 0.446029i
\(288\) 1.20398e9 + 1.20398e9i 0.175005 + 0.175005i
\(289\) 6.69750e9i 0.960111i
\(290\) 0 0
\(291\) 5.66106e9 0.789452
\(292\) 5.07844e9 5.07844e9i 0.698552 0.698552i
\(293\) 2.31877e9 + 2.31877e9i 0.314620 + 0.314620i 0.846697 0.532076i \(-0.178588\pi\)
−0.532076 + 0.846697i \(0.678588\pi\)
\(294\) 7.94166e8i 0.106297i
\(295\) 0 0
\(296\) −7.58747e9 −0.988393
\(297\) −3.61332e8 + 3.61332e8i −0.0464388 + 0.0464388i
\(298\) −2.44409e9 2.44409e9i −0.309922 0.309922i
\(299\) 7.34074e9i 0.918449i
\(300\) 0 0
\(301\) 3.19073e9 0.388708
\(302\) 2.19551e9 2.19551e9i 0.263941 0.263941i
\(303\) −5.84828e9 5.84828e9i −0.693838 0.693838i
\(304\) 2.68404e9i 0.314264i
\(305\) 0 0
\(306\) −1.60270e8 −0.0182796
\(307\) 7.65906e9 7.65906e9i 0.862228 0.862228i −0.129368 0.991597i \(-0.541295\pi\)
0.991597 + 0.129368i \(0.0412950\pi\)
\(308\) −1.15247e9 1.15247e9i −0.128064 0.128064i
\(309\) 4.90594e9i 0.538132i
\(310\) 0 0
\(311\) −9.30214e9 −0.994355 −0.497178 0.867649i \(-0.665630\pi\)
−0.497178 + 0.867649i \(0.665630\pi\)
\(312\) 1.51280e9 1.51280e9i 0.159647 0.159647i
\(313\) 6.96927e9 + 6.96927e9i 0.726122 + 0.726122i 0.969845 0.243723i \(-0.0783686\pi\)
−0.243723 + 0.969845i \(0.578369\pi\)
\(314\) 4.54990e9i 0.468041i
\(315\) 0 0
\(316\) 9.56909e9 0.959671
\(317\) 5.65467e9 5.65467e9i 0.559977 0.559977i −0.369324 0.929301i \(-0.620411\pi\)
0.929301 + 0.369324i \(0.120411\pi\)
\(318\) 1.72798e9 + 1.72798e9i 0.168978 + 0.168978i
\(319\) 5.10377e9i 0.492865i
\(320\) 0 0
\(321\) 3.11894e9 0.293756
\(322\) −1.48695e9 + 1.48695e9i −0.138316 + 0.138316i
\(323\) 6.19718e8 + 6.19718e8i 0.0569356 + 0.0569356i
\(324\) 1.13213e9i 0.102734i
\(325\) 0 0
\(326\) −2.00140e8 −0.0177200
\(327\) −5.80164e8 + 5.80164e8i −0.0507411 + 0.0507411i
\(328\) −4.75288e9 4.75288e9i −0.410640 0.410640i
\(329\) 1.14414e10i 0.976549i
\(330\) 0 0
\(331\) −1.43122e10 −1.19232 −0.596160 0.802865i \(-0.703308\pi\)
−0.596160 + 0.802865i \(0.703308\pi\)
\(332\) 4.39477e9 4.39477e9i 0.361730 0.361730i
\(333\) 5.42084e9 + 5.42084e9i 0.440849 + 0.440849i
\(334\) 4.92349e9i 0.395628i
\(335\) 0 0
\(336\) 3.29248e9 0.258325
\(337\) −1.43343e10 + 1.43343e10i −1.11136 + 1.11136i −0.118399 + 0.992966i \(0.537776\pi\)
−0.992966 + 0.118399i \(0.962224\pi\)
\(338\) 1.14639e9 + 1.14639e9i 0.0878345 + 0.0878345i
\(339\) 7.62629e9i 0.577450i
\(340\) 0 0
\(341\) 8.27058e8 0.0611672
\(342\) 3.56947e8 3.56947e8i 0.0260915 0.0260915i
\(343\) 9.38474e9 + 9.38474e9i 0.678025 + 0.678025i
\(344\) 5.01137e9i 0.357868i
\(345\) 0 0
\(346\) 4.20177e9 0.293176
\(347\) −1.41952e10 + 1.41952e10i −0.979092 + 0.979092i −0.999786 0.0206935i \(-0.993413\pi\)
0.0206935 + 0.999786i \(0.493413\pi\)
\(348\) −7.99557e9 7.99557e9i −0.545171 0.545171i
\(349\) 1.42593e9i 0.0961159i −0.998845 0.0480579i \(-0.984697\pi\)
0.998845 0.0480579i \(-0.0153032\pi\)
\(350\) 0 0
\(351\) −2.16162e9 −0.142414
\(352\) −2.75056e9 + 2.75056e9i −0.179164 + 0.179164i
\(353\) −6.11946e9 6.11946e9i −0.394107 0.394107i 0.482041 0.876149i \(-0.339896\pi\)
−0.876149 + 0.482041i \(0.839896\pi\)
\(354\) 1.93655e9i 0.123315i
\(355\) 0 0
\(356\) −1.26308e10 −0.786376
\(357\) −7.60200e8 + 7.60200e8i −0.0468010 + 0.0468010i
\(358\) −2.64045e9 2.64045e9i −0.160748 0.160748i
\(359\) 2.72763e10i 1.64213i −0.570833 0.821066i \(-0.693380\pi\)
0.570833 0.821066i \(-0.306620\pi\)
\(360\) 0 0
\(361\) 1.42231e10 0.837465
\(362\) −4.27831e8 + 4.27831e8i −0.0249137 + 0.0249137i
\(363\) 6.26296e9 + 6.26296e9i 0.360706 + 0.360706i
\(364\) 6.89449e9i 0.392732i
\(365\) 0 0
\(366\) 7.68603e8 0.0428329
\(367\) −4.35880e9 + 4.35880e9i −0.240271 + 0.240271i −0.816962 0.576691i \(-0.804344\pi\)
0.576691 + 0.816962i \(0.304344\pi\)
\(368\) −1.25464e10 1.25464e10i −0.684113 0.684113i
\(369\) 6.79136e9i 0.366312i
\(370\) 0 0
\(371\) 1.63925e10 0.865265
\(372\) −1.29567e9 + 1.29567e9i −0.0676585 + 0.0676585i
\(373\) −8.61815e9 8.61815e9i −0.445224 0.445224i 0.448539 0.893763i \(-0.351945\pi\)
−0.893763 + 0.448539i \(0.851945\pi\)
\(374\) 3.66144e8i 0.0187139i
\(375\) 0 0
\(376\) −1.79698e10 −0.899068
\(377\) −1.52663e10 + 1.52663e10i −0.755734 + 0.755734i
\(378\) 4.37862e8 + 4.37862e8i 0.0214472 + 0.0214472i
\(379\) 1.62972e10i 0.789873i 0.918708 + 0.394936i \(0.129233\pi\)
−0.918708 + 0.394936i \(0.870767\pi\)
\(380\) 0 0
\(381\) −6.99528e9 −0.331975
\(382\) −5.68799e9 + 5.68799e9i −0.267119 + 0.267119i
\(383\) 9.04711e8 + 9.04711e8i 0.0420450 + 0.0420450i 0.727817 0.685772i \(-0.240535\pi\)
−0.685772 + 0.727817i \(0.740535\pi\)
\(384\) 1.13049e10i 0.519928i
\(385\) 0 0
\(386\) 2.78314e9 0.125368
\(387\) −3.58035e9 + 3.58035e9i −0.159618 + 0.159618i
\(388\) −2.02608e10 2.02608e10i −0.893983 0.893983i
\(389\) 1.38210e10i 0.603591i 0.953373 + 0.301795i \(0.0975860\pi\)
−0.953373 + 0.301795i \(0.902414\pi\)
\(390\) 0 0
\(391\) 5.79367e9 0.247883
\(392\) 5.91635e9 5.91635e9i 0.250559 0.250559i
\(393\) −1.64972e10 1.64972e10i −0.691576 0.691576i
\(394\) 6.31962e9i 0.262244i
\(395\) 0 0
\(396\) 2.58640e9 0.105175
\(397\) −1.18087e10 + 1.18087e10i −0.475378 + 0.475378i −0.903650 0.428272i \(-0.859122\pi\)
0.428272 + 0.903650i \(0.359122\pi\)
\(398\) −1.49548e9 1.49548e9i −0.0596002 0.0596002i
\(399\) 3.38618e9i 0.133604i
\(400\) 0 0
\(401\) 2.44172e10 0.944319 0.472160 0.881513i \(-0.343475\pi\)
0.472160 + 0.881513i \(0.343475\pi\)
\(402\) 2.54127e9 2.54127e9i 0.0973076 0.0973076i
\(403\) 2.47388e9 + 2.47388e9i 0.0937905 + 0.0937905i
\(404\) 4.18617e10i 1.57142i
\(405\) 0 0
\(406\) 6.18474e9 0.227624
\(407\) −1.23842e10 + 1.23842e10i −0.451324 + 0.451324i
\(408\) 1.19397e9 + 1.19397e9i 0.0430877 + 0.0430877i
\(409\) 1.20856e9i 0.0431894i 0.999767 + 0.0215947i \(0.00687433\pi\)
−0.999767 + 0.0215947i \(0.993126\pi\)
\(410\) 0 0
\(411\) −1.29632e10 −0.454301
\(412\) 1.75582e10 1.75582e10i 0.609385 0.609385i
\(413\) 9.18555e9 + 9.18555e9i 0.315722 + 0.315722i
\(414\) 3.33706e9i 0.113596i
\(415\) 0 0
\(416\) −1.64549e10 −0.549441
\(417\) −1.05233e10 + 1.05233e10i −0.348024 + 0.348024i
\(418\) 8.15462e8 + 8.15462e8i 0.0267115 + 0.0267115i
\(419\) 2.99061e10i 0.970296i 0.874432 + 0.485148i \(0.161234\pi\)
−0.874432 + 0.485148i \(0.838766\pi\)
\(420\) 0 0
\(421\) −3.13382e10 −0.997574 −0.498787 0.866725i \(-0.666221\pi\)
−0.498787 + 0.866725i \(0.666221\pi\)
\(422\) −1.73222e8 + 1.73222e8i −0.00546203 + 0.00546203i
\(423\) 1.28385e10 + 1.28385e10i 0.401007 + 0.401007i
\(424\) 2.57461e10i 0.796614i
\(425\) 0 0
\(426\) 2.85118e9 0.0865737
\(427\) 3.64568e9 3.64568e9i 0.109665 0.109665i
\(428\) −1.11626e10 1.11626e10i −0.332652 0.332652i
\(429\) 4.93833e9i 0.145798i
\(430\) 0 0
\(431\) 1.97968e10 0.573701 0.286850 0.957975i \(-0.407392\pi\)
0.286850 + 0.957975i \(0.407392\pi\)
\(432\) −3.69453e9 + 3.69453e9i −0.106078 + 0.106078i
\(433\) 2.04786e10 + 2.04786e10i 0.582570 + 0.582570i 0.935609 0.353039i \(-0.114852\pi\)
−0.353039 + 0.935609i \(0.614852\pi\)
\(434\) 1.00223e9i 0.0282493i
\(435\) 0 0
\(436\) 4.15278e9 0.114919
\(437\) −1.29035e10 + 1.29035e10i −0.353818 + 0.353818i
\(438\) −4.40797e9 4.40797e9i −0.119768 0.119768i
\(439\) 1.52813e10i 0.411435i −0.978611 0.205717i \(-0.934047\pi\)
0.978611 0.205717i \(-0.0659528\pi\)
\(440\) 0 0
\(441\) −8.45384e9 −0.223511
\(442\) 1.09520e9 1.09520e9i 0.0286950 0.0286950i
\(443\) 4.19068e10 + 4.19068e10i 1.08810 + 1.08810i 0.995724 + 0.0923778i \(0.0294468\pi\)
0.0923778 + 0.995724i \(0.470553\pi\)
\(444\) 3.88021e10i 0.998442i
\(445\) 0 0
\(446\) 1.89491e10 0.478906
\(447\) 2.60172e10 2.60172e10i 0.651673 0.651673i
\(448\) −9.41140e9 9.41140e9i −0.233637 0.233637i
\(449\) 3.76958e9i 0.0927487i 0.998924 + 0.0463743i \(0.0147667\pi\)
−0.998924 + 0.0463743i \(0.985233\pi\)
\(450\) 0 0
\(451\) −1.55152e10 −0.375017
\(452\) 2.72943e10 2.72943e10i 0.653910 0.653910i
\(453\) 2.33710e10 + 2.33710e10i 0.554990 + 0.554990i
\(454\) 3.85063e9i 0.0906377i
\(455\) 0 0
\(456\) −5.31835e9 −0.123003
\(457\) 1.58058e10 1.58058e10i 0.362370 0.362370i −0.502315 0.864685i \(-0.667518\pi\)
0.864685 + 0.502315i \(0.167518\pi\)
\(458\) −9.37104e9 9.37104e9i −0.212974 0.212974i
\(459\) 1.70606e9i 0.0384365i
\(460\) 0 0
\(461\) 5.93819e10 1.31477 0.657386 0.753554i \(-0.271662\pi\)
0.657386 + 0.753554i \(0.271662\pi\)
\(462\) −1.00032e9 + 1.00032e9i −0.0219568 + 0.0219568i
\(463\) 3.75293e9 + 3.75293e9i 0.0816670 + 0.0816670i 0.746760 0.665093i \(-0.231608\pi\)
−0.665093 + 0.746760i \(0.731608\pi\)
\(464\) 5.21847e10i 1.12583i
\(465\) 0 0
\(466\) 1.57473e10 0.333935
\(467\) 6.17134e10 6.17134e10i 1.29751 1.29751i 0.367484 0.930030i \(-0.380219\pi\)
0.930030 0.367484i \(-0.119781\pi\)
\(468\) 7.73639e9 + 7.73639e9i 0.161271 + 0.161271i
\(469\) 2.41078e10i 0.498272i
\(470\) 0 0
\(471\) −4.84334e10 −0.984150
\(472\) 1.44269e10 1.44269e10i 0.290672 0.290672i
\(473\) −8.17948e9 8.17948e9i −0.163411 0.163411i
\(474\) 8.30575e9i 0.164538i
\(475\) 0 0
\(476\) 5.44147e9 0.105996
\(477\) −1.83942e10 + 1.83942e10i −0.355310 + 0.355310i
\(478\) 9.12466e9 + 9.12466e9i 0.174785 + 0.174785i
\(479\) 2.65972e9i 0.0505235i −0.999681 0.0252617i \(-0.991958\pi\)
0.999681 0.0252617i \(-0.00804191\pi\)
\(480\) 0 0
\(481\) −7.40866e10 −1.38407
\(482\) 7.72467e9 7.72467e9i 0.143117 0.143117i
\(483\) −1.58285e10 1.58285e10i −0.290838 0.290838i
\(484\) 4.48299e10i 0.816934i
\(485\) 0 0
\(486\) −9.82661e8 −0.0176140
\(487\) 4.38176e10 4.38176e10i 0.778991 0.778991i −0.200668 0.979659i \(-0.564311\pi\)
0.979659 + 0.200668i \(0.0643114\pi\)
\(488\) −5.72591e9 5.72591e9i −0.100964 0.100964i
\(489\) 2.13048e9i 0.0372599i
\(490\) 0 0
\(491\) 6.09667e10 1.04898 0.524490 0.851417i \(-0.324256\pi\)
0.524490 + 0.851417i \(0.324256\pi\)
\(492\) 2.43061e10 2.43061e10i 0.414815 0.414815i
\(493\) −1.20489e10 1.20489e10i −0.203967 0.203967i
\(494\) 4.87839e9i 0.0819161i
\(495\) 0 0
\(496\) 8.45645e9 0.139721
\(497\) 1.35239e10 1.35239e10i 0.221654 0.221654i
\(498\) −3.81456e9 3.81456e9i −0.0620194 0.0620194i
\(499\) 6.14633e10i 0.991319i 0.868517 + 0.495660i \(0.165074\pi\)
−0.868517 + 0.495660i \(0.834926\pi\)
\(500\) 0 0
\(501\) −5.24102e10 −0.831888
\(502\) 8.31992e9 8.31992e9i 0.131010 0.131010i
\(503\) 4.56188e10 + 4.56188e10i 0.712642 + 0.712642i 0.967087 0.254445i \(-0.0818927\pi\)
−0.254445 + 0.967087i \(0.581893\pi\)
\(504\) 6.52395e9i 0.101109i
\(505\) 0 0
\(506\) 7.62366e9 0.116295
\(507\) −1.22032e10 + 1.22032e10i −0.184690 + 0.184690i
\(508\) 2.50359e10 + 2.50359e10i 0.375931 + 0.375931i
\(509\) 9.24908e10i 1.37793i −0.724794 0.688966i \(-0.758065\pi\)
0.724794 0.688966i \(-0.241935\pi\)
\(510\) 0 0
\(511\) −4.18162e10 −0.613284
\(512\) −4.81403e10 + 4.81403e10i −0.700534 + 0.700534i
\(513\) 3.79967e9 + 3.79967e9i 0.0548627 + 0.0548627i
\(514\) 8.71248e9i 0.124821i
\(515\) 0 0
\(516\) 2.56280e10 0.361506
\(517\) −2.93301e10 + 2.93301e10i −0.410536 + 0.410536i
\(518\) 1.50071e10 + 1.50071e10i 0.208438 + 0.208438i
\(519\) 4.47276e10i 0.616461i
\(520\) 0 0
\(521\) 8.59534e10 1.16657 0.583287 0.812266i \(-0.301766\pi\)
0.583287 + 0.812266i \(0.301766\pi\)
\(522\) −6.93997e9 + 6.93997e9i −0.0934708 + 0.0934708i
\(523\) 1.53299e10 + 1.53299e10i 0.204896 + 0.204896i 0.802094 0.597198i \(-0.203719\pi\)
−0.597198 + 0.802094i \(0.703719\pi\)
\(524\) 1.18086e11i 1.56629i
\(525\) 0 0
\(526\) −1.98714e10 −0.259588
\(527\) −1.95251e9 + 1.95251e9i −0.0253134 + 0.0253134i
\(528\) −8.44032e9 8.44032e9i −0.108598 0.108598i
\(529\) 4.23220e10i 0.540435i
\(530\) 0 0
\(531\) −2.06144e10 −0.259294
\(532\) −1.21190e10 + 1.21190e10i −0.151294 + 0.151294i
\(533\) −4.64088e10 4.64088e10i −0.575031 0.575031i
\(534\) 1.09632e10i 0.134826i
\(535\) 0 0
\(536\) −3.78638e10 −0.458738
\(537\) 2.81074e10 2.81074e10i 0.338005 0.338005i
\(538\) 8.61889e9 + 8.61889e9i 0.102878 + 0.102878i
\(539\) 1.93132e10i 0.228822i
\(540\) 0 0
\(541\) −1.92085e9 −0.0224236 −0.0112118 0.999937i \(-0.503569\pi\)
−0.0112118 + 0.999937i \(0.503569\pi\)
\(542\) −3.09317e10 + 3.09317e10i −0.358432 + 0.358432i
\(543\) −4.55423e9 4.55423e9i −0.0523861 0.0523861i
\(544\) 1.29870e10i 0.148290i
\(545\) 0 0
\(546\) −5.98426e9 −0.0673349
\(547\) −4.24260e10 + 4.24260e10i −0.473896 + 0.473896i −0.903173 0.429277i \(-0.858768\pi\)
0.429277 + 0.903173i \(0.358768\pi\)
\(548\) 4.63948e10 + 4.63948e10i 0.514454 + 0.514454i
\(549\) 8.18172e9i 0.0900648i
\(550\) 0 0
\(551\) 5.36699e10 0.582270
\(552\) −2.48603e10 + 2.48603e10i −0.267763 + 0.267763i
\(553\) −3.93963e10 3.93963e10i −0.421265 0.421265i
\(554\) 1.78319e10i 0.189303i
\(555\) 0 0
\(556\) 7.53254e10 0.788210
\(557\) −7.68174e10 + 7.68174e10i −0.798066 + 0.798066i −0.982790 0.184725i \(-0.940861\pi\)
0.184725 + 0.982790i \(0.440861\pi\)
\(558\) 1.12461e9 + 1.12461e9i 0.0116002 + 0.0116002i
\(559\) 4.89327e10i 0.501132i
\(560\) 0 0
\(561\) 3.89757e9 0.0393498
\(562\) 3.19786e10 3.19786e10i 0.320564 0.320564i
\(563\) −1.20218e11 1.20218e11i −1.19657 1.19657i −0.975188 0.221377i \(-0.928945\pi\)
−0.221377 0.975188i \(-0.571055\pi\)
\(564\) 9.18972e10i 0.908209i
\(565\) 0 0
\(566\) −1.94800e10 −0.189812
\(567\) −4.66101e9 + 4.66101e9i −0.0450970 + 0.0450970i
\(568\) −2.12406e10 2.12406e10i −0.204068 0.204068i
\(569\) 1.12597e11i 1.07418i −0.843525 0.537090i \(-0.819523\pi\)
0.843525 0.537090i \(-0.180477\pi\)
\(570\) 0 0
\(571\) −7.88582e9 −0.0741827 −0.0370913 0.999312i \(-0.511809\pi\)
−0.0370913 + 0.999312i \(0.511809\pi\)
\(572\) −1.76741e10 + 1.76741e10i −0.165103 + 0.165103i
\(573\) −6.05483e10 6.05483e10i −0.561672 0.561672i
\(574\) 1.88013e10i 0.173197i
\(575\) 0 0
\(576\) 2.11213e10 0.191880
\(577\) −1.35022e11 + 1.35022e11i −1.21815 + 1.21815i −0.249872 + 0.968279i \(0.580389\pi\)
−0.968279 + 0.249872i \(0.919611\pi\)
\(578\) −2.08056e10 2.08056e10i −0.186410 0.186410i
\(579\) 2.96263e10i 0.263611i
\(580\) 0 0
\(581\) −3.61869e10 −0.317575
\(582\) −1.75859e10 + 1.75859e10i −0.153275 + 0.153275i
\(583\) −4.20224e10 4.20224e10i −0.363753 0.363753i
\(584\) 6.56767e10i 0.564625i
\(585\) 0 0
\(586\) −1.44064e10 −0.122170
\(587\) 1.24270e11 1.24270e11i 1.04668 1.04668i 0.0478229 0.998856i \(-0.484772\pi\)
0.998856 0.0478229i \(-0.0152283\pi\)
\(588\) 3.02560e10 + 3.02560e10i 0.253106 + 0.253106i
\(589\) 8.69712e9i 0.0722627i
\(590\) 0 0
\(591\) 6.72719e10 0.551422
\(592\) −1.26625e11 + 1.26625e11i −1.03094 + 1.03094i
\(593\) −6.87856e10 6.87856e10i −0.556261 0.556261i 0.371980 0.928241i \(-0.378679\pi\)
−0.928241 + 0.371980i \(0.878679\pi\)
\(594\) 2.24493e9i 0.0180326i
\(595\) 0 0
\(596\) −1.86229e11 −1.47592
\(597\) 1.59192e10 1.59192e10i 0.125321 0.125321i
\(598\) 2.28038e10 + 2.28038e10i 0.178321 + 0.178321i
\(599\) 4.22834e10i 0.328445i −0.986423 0.164222i \(-0.947489\pi\)
0.986423 0.164222i \(-0.0525115\pi\)
\(600\) 0 0
\(601\) 1.67538e11 1.28415 0.642075 0.766642i \(-0.278074\pi\)
0.642075 + 0.766642i \(0.278074\pi\)
\(602\) −9.91189e9 + 9.91189e9i −0.0754693 + 0.0754693i
\(603\) 2.70517e10 + 2.70517e10i 0.204609 + 0.204609i
\(604\) 1.67288e11i 1.25695i
\(605\) 0 0
\(606\) 3.63350e10 0.269423
\(607\) 7.21743e10 7.21743e10i 0.531653 0.531653i −0.389411 0.921064i \(-0.627322\pi\)
0.921064 + 0.389411i \(0.127322\pi\)
\(608\) 2.89241e10 + 2.89241e10i 0.211664 + 0.211664i
\(609\) 6.58361e10i 0.478625i
\(610\) 0 0
\(611\) −1.75464e11 −1.25899
\(612\) −6.10594e9 + 6.10594e9i −0.0435258 + 0.0435258i
\(613\) −1.16637e11 1.16637e11i −0.826024 0.826024i 0.160940 0.986964i \(-0.448548\pi\)
−0.986964 + 0.160940i \(0.948548\pi\)
\(614\) 4.75853e10i 0.334810i
\(615\) 0 0
\(616\) 1.49043e10 0.103511
\(617\) −1.32769e11 + 1.32769e11i −0.916126 + 0.916126i −0.996745 0.0806194i \(-0.974310\pi\)
0.0806194 + 0.996745i \(0.474310\pi\)
\(618\) −1.52401e10 1.52401e10i −0.104480 0.104480i
\(619\) 2.20817e11i 1.50408i 0.659118 + 0.752040i \(0.270930\pi\)
−0.659118 + 0.752040i \(0.729070\pi\)
\(620\) 0 0
\(621\) 3.55227e10 0.238858
\(622\) 2.88968e10 2.88968e10i 0.193058 0.193058i
\(623\) 5.20014e10 + 5.20014e10i 0.345194 + 0.345194i
\(624\) 5.04931e10i 0.333038i
\(625\) 0 0
\(626\) −4.32996e10 −0.281959
\(627\) −8.68053e9 + 8.68053e9i −0.0561663 + 0.0561663i
\(628\) 1.73342e11 + 1.73342e11i 1.11446 + 1.11446i
\(629\) 5.84728e10i 0.373552i
\(630\) 0 0
\(631\) −5.85541e10 −0.369352 −0.184676 0.982800i \(-0.559123\pi\)
−0.184676 + 0.982800i \(0.559123\pi\)
\(632\) −6.18760e10 + 6.18760e10i −0.387841 + 0.387841i
\(633\) −1.84394e9 1.84394e9i −0.0114850 0.0114850i
\(634\) 3.51321e10i 0.217444i
\(635\) 0 0
\(636\) 1.31665e11 0.804713
\(637\) 5.77693e10 5.77693e10i 0.350864 0.350864i
\(638\) −1.58547e10 1.58547e10i −0.0956919 0.0956919i
\(639\) 3.03506e10i 0.182039i
\(640\) 0 0
\(641\) −9.71973e10 −0.575734 −0.287867 0.957670i \(-0.592946\pi\)
−0.287867 + 0.957670i \(0.592946\pi\)
\(642\) −9.68887e9 + 9.68887e9i −0.0570339 + 0.0570339i
\(643\) 1.13687e11 + 1.13687e11i 0.665071 + 0.665071i 0.956571 0.291500i \(-0.0941543\pi\)
−0.291500 + 0.956571i \(0.594154\pi\)
\(644\) 1.13300e11i 0.658696i
\(645\) 0 0
\(646\) −3.85027e9 −0.0221086
\(647\) 1.17592e11 1.17592e11i 0.671061 0.671061i −0.286899 0.957961i \(-0.592625\pi\)
0.957961 + 0.286899i \(0.0926246\pi\)
\(648\) 7.32060e9 + 7.32060e9i 0.0415190 + 0.0415190i
\(649\) 4.70946e10i 0.265456i
\(650\) 0 0
\(651\) 1.06686e10 0.0593998
\(652\) −7.62492e9 + 7.62492e9i −0.0421935 + 0.0421935i
\(653\) 2.53561e10 + 2.53561e10i 0.139454 + 0.139454i 0.773387 0.633934i \(-0.218561\pi\)
−0.633934 + 0.773387i \(0.718561\pi\)
\(654\) 3.60452e9i 0.0197032i
\(655\) 0 0
\(656\) −1.58639e11 −0.856631
\(657\) 4.69225e10 4.69225e10i 0.251837 0.251837i
\(658\) 3.55422e10 + 3.55422e10i 0.189601 + 0.189601i
\(659\) 2.75271e11i 1.45955i −0.683689 0.729774i \(-0.739625\pi\)
0.683689 0.729774i \(-0.260375\pi\)
\(660\) 0 0
\(661\) 6.27595e10 0.328756 0.164378 0.986397i \(-0.447438\pi\)
0.164378 + 0.986397i \(0.447438\pi\)
\(662\) 4.44602e10 4.44602e10i 0.231494 0.231494i
\(663\) 1.16584e10 + 1.16584e10i 0.0603369 + 0.0603369i
\(664\) 5.68353e10i 0.292379i
\(665\) 0 0
\(666\) −3.36793e10 −0.171185
\(667\) 2.50877e11 2.50877e11i 1.26753 1.26753i
\(668\) 1.87575e11 + 1.87575e11i 0.942037 + 0.942037i
\(669\) 2.01712e11i 1.00700i
\(670\) 0 0
\(671\) −1.86915e10 −0.0922050
\(672\) −3.54809e10 + 3.54809e10i −0.173987 + 0.173987i
\(673\) −2.01482e11 2.01482e11i −0.982147 0.982147i 0.0176962 0.999843i \(-0.494367\pi\)
−0.999843 + 0.0176962i \(0.994367\pi\)
\(674\) 8.90580e10i 0.431552i
\(675\) 0 0
\(676\) 8.73500e10 0.418289
\(677\) 4.34668e10 4.34668e10i 0.206920 0.206920i −0.596037 0.802957i \(-0.703259\pi\)
0.802957 + 0.596037i \(0.203259\pi\)
\(678\) −2.36908e10 2.36908e10i −0.112114 0.112114i
\(679\) 1.66829e11i 0.784859i
\(680\) 0 0
\(681\) 4.09897e10 0.190584
\(682\) −2.56923e9 + 2.56923e9i −0.0118759 + 0.0118759i
\(683\) 1.33784e10 + 1.33784e10i 0.0614780 + 0.0614780i 0.737177 0.675699i \(-0.236158\pi\)
−0.675699 + 0.737177i \(0.736158\pi\)
\(684\) 2.71979e10i 0.124254i
\(685\) 0 0
\(686\) −5.83068e10 −0.263283
\(687\) 9.97540e10 9.97540e10i 0.447820 0.447820i
\(688\) −8.36331e10 8.36331e10i −0.373271 0.373271i
\(689\) 2.51394e11i 1.11552i
\(690\) 0 0
\(691\) 2.54479e11 1.11619 0.558097 0.829775i \(-0.311532\pi\)
0.558097 + 0.829775i \(0.311532\pi\)
\(692\) 1.60079e11 1.60079e11i 0.698086 0.698086i
\(693\) −1.06483e10 1.06483e10i −0.0461686 0.0461686i
\(694\) 8.81938e10i 0.380190i
\(695\) 0 0
\(696\) 1.03402e11 0.440650
\(697\) 3.66281e10 3.66281e10i 0.155197 0.155197i
\(698\) 4.42959e9 + 4.42959e9i 0.0186613 + 0.0186613i
\(699\) 1.67629e11i 0.702166i
\(700\) 0 0
\(701\) 1.18657e11 0.491384 0.245692 0.969348i \(-0.420985\pi\)
0.245692 + 0.969348i \(0.420985\pi\)
\(702\) 6.71501e9 6.71501e9i 0.0276502 0.0276502i
\(703\) 1.30228e11 + 1.30228e11i 0.533193 + 0.533193i
\(704\) 4.82525e10i 0.196440i
\(705\) 0 0
\(706\) 3.80198e10 0.153035
\(707\) 1.72346e11 1.72346e11i 0.689801 0.689801i
\(708\) 7.37785e10 + 7.37785e10i 0.293627 + 0.293627i
\(709\) 3.20598e11i 1.26875i 0.773025 + 0.634375i \(0.218743\pi\)
−0.773025 + 0.634375i \(0.781257\pi\)
\(710\) 0 0
\(711\) 8.84141e10 0.345974
\(712\) 8.16736e10 8.16736e10i 0.317806 0.317806i
\(713\) −4.06542e10 4.06542e10i −0.157307 0.157307i
\(714\) 4.72307e9i 0.0181732i
\(715\) 0 0
\(716\) −2.01191e11 −0.765520
\(717\) −9.71313e10 + 9.71313e10i −0.367521 + 0.367521i
\(718\) 8.47330e10 + 8.47330e10i 0.318827 + 0.318827i
\(719\) 4.23512e11i 1.58471i −0.610059 0.792356i \(-0.708854\pi\)
0.610059 0.792356i \(-0.291146\pi\)
\(720\) 0 0
\(721\) −1.44576e11 −0.535001
\(722\) −4.41837e10 + 4.41837e10i −0.162597 + 0.162597i
\(723\) 8.22286e10 + 8.22286e10i 0.300933 + 0.300933i
\(724\) 3.25990e10i 0.118645i
\(725\) 0 0
\(726\) −3.89114e10 −0.140065
\(727\) 9.00351e10 9.00351e10i 0.322310 0.322310i −0.527342 0.849653i \(-0.676811\pi\)
0.849653 + 0.527342i \(0.176811\pi\)
\(728\) 4.45814e10 + 4.45814e10i 0.158719 + 0.158719i
\(729\) 1.04604e10i 0.0370370i
\(730\) 0 0
\(731\) 3.86201e10 0.135252
\(732\) 2.92821e10 2.92821e10i 0.101990 0.101990i
\(733\) −1.38110e10 1.38110e10i −0.0478421 0.0478421i 0.682781 0.730623i \(-0.260770\pi\)
−0.730623 + 0.682781i \(0.760770\pi\)
\(734\) 2.70809e10i 0.0932994i
\(735\) 0 0
\(736\) 2.70408e11 0.921529
\(737\) −6.18007e10 + 6.18007e10i −0.209471 + 0.209471i
\(738\) −2.10971e10 2.10971e10i −0.0711210 0.0711210i
\(739\) 3.81206e11i 1.27815i −0.769144 0.639075i \(-0.779317\pi\)
0.769144 0.639075i \(-0.220683\pi\)
\(740\) 0 0
\(741\) −5.19301e10 −0.172245
\(742\) −5.09227e10 + 5.09227e10i −0.167995 + 0.167995i
\(743\) 1.18224e11 + 1.18224e11i 0.387927 + 0.387927i 0.873947 0.486020i \(-0.161552\pi\)
−0.486020 + 0.873947i \(0.661552\pi\)
\(744\) 1.67562e10i 0.0546870i
\(745\) 0 0
\(746\) 5.35440e10 0.172884
\(747\) 4.06058e10 4.06058e10i 0.130408 0.130408i
\(748\) −1.39493e10 1.39493e10i −0.0445601 0.0445601i
\(749\) 9.19135e10i 0.292047i
\(750\) 0 0
\(751\) −4.45619e11 −1.40089 −0.700445 0.713707i \(-0.747015\pi\)
−0.700445 + 0.713707i \(0.747015\pi\)
\(752\) −2.99893e11 + 2.99893e11i −0.937766 + 0.937766i
\(753\) 8.85649e10 + 8.85649e10i 0.275475 + 0.275475i
\(754\) 9.48486e10i 0.293458i
\(755\) 0 0
\(756\) 3.33633e10 0.102137
\(757\) −4.26149e11 + 4.26149e11i −1.29771 + 1.29771i −0.367808 + 0.929902i \(0.619892\pi\)
−0.929902 + 0.367808i \(0.880108\pi\)
\(758\) −5.06268e10 5.06268e10i −0.153357 0.153357i
\(759\) 8.11533e10i 0.244534i
\(760\) 0 0
\(761\) −2.56636e11 −0.765207 −0.382603 0.923913i \(-0.624972\pi\)
−0.382603 + 0.923913i \(0.624972\pi\)
\(762\) 2.17306e10 2.17306e10i 0.0644543 0.0644543i
\(763\) −1.70972e10 1.70972e10i −0.0504459 0.0504459i
\(764\) 4.33401e11i 1.27209i
\(765\) 0 0
\(766\) −5.62091e9 −0.0163264
\(767\) 1.40869e11 1.40869e11i 0.407036 0.407036i
\(768\) −4.66379e10 4.66379e10i −0.134058 0.134058i
\(769\) 5.23066e11i 1.49572i 0.663855 + 0.747861i \(0.268919\pi\)
−0.663855 + 0.747861i \(0.731081\pi\)
\(770\) 0 0
\(771\) −9.27437e10 −0.262462
\(772\) 1.06032e11 1.06032e11i 0.298516 0.298516i
\(773\) −2.31264e11 2.31264e11i −0.647723 0.647723i 0.304719 0.952442i \(-0.401437\pi\)
−0.952442 + 0.304719i \(0.901437\pi\)
\(774\) 2.22445e10i 0.0619810i
\(775\) 0 0
\(776\) 2.62022e11 0.722587
\(777\) −1.59750e11 + 1.59750e11i −0.438284 + 0.438284i
\(778\) −4.29346e10 4.29346e10i −0.117190 0.117190i
\(779\) 1.63153e11i 0.443044i
\(780\) 0 0
\(781\) −6.93373e10 −0.186364
\(782\) −1.79979e10 + 1.79979e10i −0.0481275 + 0.0481275i
\(783\) −7.38755e10 7.38755e10i −0.196541 0.196541i
\(784\) 1.97472e11i 0.522687i
\(785\) 0 0
\(786\) 1.02496e11 0.268545
\(787\) 9.83798e9 9.83798e9i 0.0256453 0.0256453i −0.694168 0.719813i \(-0.744227\pi\)
0.719813 + 0.694168i \(0.244227\pi\)
\(788\) −2.40764e11 2.40764e11i −0.624435 0.624435i
\(789\) 2.11529e11i 0.545836i
\(790\) 0 0
\(791\) −2.24743e11 −0.574091
\(792\) −1.67242e10 + 1.67242e10i −0.0425056 + 0.0425056i
\(793\) −5.59098e10 5.59098e10i −0.141382 0.141382i
\(794\) 7.33665e10i 0.184593i
\(795\) 0 0
\(796\) −1.13949e11 −0.283830
\(797\) −5.12588e11 + 5.12588e11i −1.27038 + 1.27038i −0.324497 + 0.945887i \(0.605195\pi\)
−0.945887 + 0.324497i \(0.894805\pi\)
\(798\) 1.05191e10 + 1.05191e10i 0.0259397 + 0.0259397i
\(799\) 1.38484e11i 0.339793i
\(800\) 0 0
\(801\) −1.16703e11 −0.283499
\(802\) −7.58513e10 + 7.58513e10i −0.183344 + 0.183344i
\(803\) 1.07197e11 + 1.07197e11i 0.257821 + 0.257821i
\(804\) 1.93634e11i 0.463402i
\(805\) 0 0
\(806\) −1.53701e10 −0.0364196
\(807\) −9.17474e10 + 9.17474e10i −0.216322 + 0.216322i
\(808\) −2.70687e11 2.70687e11i −0.635071 0.635071i
\(809\) 2.69111e11i 0.628258i 0.949380 + 0.314129i \(0.101712\pi\)
−0.949380 + 0.314129i \(0.898288\pi\)
\(810\) 0 0
\(811\) 5.11333e11 1.18201 0.591004 0.806669i \(-0.298732\pi\)
0.591004 + 0.806669i \(0.298732\pi\)
\(812\) 2.35626e11 2.35626e11i 0.541999 0.541999i
\(813\) −3.29266e11 3.29266e11i −0.753675 0.753675i
\(814\) 7.69419e10i 0.175253i
\(815\) 0 0
\(816\) 3.98517e10 0.0898847
\(817\) −8.60132e10 + 8.60132e10i −0.193053 + 0.193053i
\(818\) −3.75437e9 3.75437e9i −0.00838539 0.00838539i
\(819\) 6.37020e10i 0.141585i
\(820\) 0 0
\(821\) 1.54755e11 0.340623 0.170311 0.985390i \(-0.445523\pi\)
0.170311 + 0.985390i \(0.445523\pi\)
\(822\) 4.02696e10 4.02696e10i 0.0882044 0.0882044i
\(823\) −9.01212e10 9.01212e10i −0.196439 0.196439i 0.602033 0.798471i \(-0.294358\pi\)
−0.798471 + 0.602033i \(0.794358\pi\)
\(824\) 2.27071e11i 0.492553i
\(825\) 0 0
\(826\) −5.70692e10 −0.122598
\(827\) −2.24761e11 + 2.24761e11i −0.480506 + 0.480506i −0.905293 0.424787i \(-0.860349\pi\)
0.424787 + 0.905293i \(0.360349\pi\)
\(828\) −1.27135e11 1.27135e11i −0.270485 0.270485i
\(829\) 7.91622e11i 1.67610i −0.545594 0.838050i \(-0.683696\pi\)
0.545594 0.838050i \(-0.316304\pi\)
\(830\) 0 0
\(831\) −1.89819e11 −0.398048
\(832\) −1.44332e11 + 1.44332e11i −0.301211 + 0.301211i
\(833\) 4.55944e10 + 4.55944e10i 0.0946959 + 0.0946959i
\(834\) 6.53807e10i 0.135140i
\(835\) 0 0
\(836\) 6.21348e10 0.127207
\(837\) −1.19714e10 + 1.19714e10i −0.0243918 + 0.0243918i
\(838\) −9.29024e10 9.29024e10i −0.188387 0.188387i
\(839\) 3.46532e11i 0.699352i 0.936871 + 0.349676i \(0.113708\pi\)
−0.936871 + 0.349676i \(0.886292\pi\)
\(840\) 0 0
\(841\) −5.43235e11 −1.08593
\(842\) 9.73510e10 9.73510e10i 0.193683 0.193683i
\(843\) 3.40410e11 + 3.40410e11i 0.674051 + 0.674051i
\(844\) 1.31988e10i 0.0260115i
\(845\) 0 0
\(846\) −7.97647e10 −0.155714
\(847\) −1.84567e11 + 1.84567e11i −0.358608 + 0.358608i
\(848\) −4.29668e11 4.29668e11i −0.830902 0.830902i
\(849\) 2.07363e11i 0.399118i
\(850\) 0 0
\(851\) 1.21749e12 2.32139
\(852\) 1.08624e11 1.08624e11i 0.206142 0.206142i
\(853\) 2.32474e11 + 2.32474e11i 0.439114 + 0.439114i 0.891714 0.452600i \(-0.149503\pi\)
−0.452600 + 0.891714i \(0.649503\pi\)
\(854\) 2.26504e10i 0.0425837i
\(855\) 0 0
\(856\) 1.44360e11 0.268875
\(857\) −3.14575e11 + 3.14575e11i −0.583177 + 0.583177i −0.935775 0.352598i \(-0.885298\pi\)
0.352598 + 0.935775i \(0.385298\pi\)
\(858\) 1.53408e10 + 1.53408e10i 0.0283072 + 0.0283072i
\(859\) 4.37243e11i 0.803063i 0.915845 + 0.401532i \(0.131522\pi\)
−0.915845 + 0.401532i \(0.868478\pi\)
\(860\) 0 0
\(861\) −2.00138e11 −0.364181
\(862\) −6.14980e10 + 6.14980e10i −0.111386 + 0.111386i
\(863\) 2.88466e11 + 2.88466e11i 0.520057 + 0.520057i 0.917588 0.397532i \(-0.130133\pi\)
−0.397532 + 0.917588i \(0.630133\pi\)
\(864\) 7.96270e10i 0.142891i
\(865\) 0 0
\(866\) −1.27232e11 −0.226217
\(867\) 2.21474e11 2.21474e11i 0.391964 0.391964i
\(868\) −3.81828e10 3.81828e10i −0.0672649 0.0672649i
\(869\) 2.01986e11i 0.354195i
\(870\) 0 0
\(871\) −3.69715e11 −0.642383
\(872\) −2.68529e10 + 2.68529e10i −0.0464435 + 0.0464435i
\(873\) −1.87201e11 1.87201e11i −0.322292 0.322292i
\(874\) 8.01683e10i 0.137391i
\(875\) 0 0
\(876\) −3.35869e11 −0.570365
\(877\) −6.00399e11 + 6.00399e11i −1.01494 + 1.01494i −0.0150556 + 0.999887i \(0.504793\pi\)
−0.999887 + 0.0150556i \(0.995207\pi\)
\(878\) 4.74707e10 + 4.74707e10i 0.0798818 + 0.0798818i
\(879\) 1.53355e11i 0.256887i
\(880\) 0 0
\(881\) 1.08213e12 1.79629 0.898147 0.439694i \(-0.144913\pi\)
0.898147 + 0.439694i \(0.144913\pi\)
\(882\) 2.62616e10 2.62616e10i 0.0433956 0.0433956i
\(883\) 7.01877e11 + 7.01877e11i 1.15456 + 1.15456i 0.985627 + 0.168938i \(0.0540338\pi\)
0.168938 + 0.985627i \(0.445966\pi\)
\(884\) 8.34499e10i 0.136652i
\(885\) 0 0
\(886\) −2.60364e11 −0.422519
\(887\) 4.78658e11 4.78658e11i 0.773270 0.773270i −0.205407 0.978677i \(-0.565852\pi\)
0.978677 + 0.205407i \(0.0658518\pi\)
\(888\) 2.50903e11 + 2.50903e11i 0.403510 + 0.403510i
\(889\) 2.06148e11i 0.330044i
\(890\) 0 0
\(891\) 2.38972e10 0.0379171
\(892\) 7.21922e11 7.21922e11i 1.14033 1.14033i
\(893\) 3.08428e11 + 3.08428e11i 0.485006 + 0.485006i
\(894\) 1.61643e11i 0.253050i
\(895\) 0 0
\(896\) 3.33151e11 0.516903
\(897\) −2.42744e11 + 2.42744e11i −0.374955 + 0.374955i
\(898\) −1.17101e10 1.17101e10i −0.0180075 0.0180075i
\(899\) 1.69095e11i 0.258875i
\(900\) 0 0
\(901\) 1.98412e11 0.301071
\(902\) 4.81974e10 4.81974e10i 0.0728110 0.0728110i
\(903\) −1.05511e11 1.05511e11i −0.158689 0.158689i
\(904\) 3.52982e11i 0.528542i
\(905\) 0 0
\(906\) −1.45203e11 −0.215507
\(907\) 5.94503e11 5.94503e11i 0.878465 0.878465i −0.114911 0.993376i \(-0.536658\pi\)
0.993376 + 0.114911i \(0.0366582\pi\)
\(908\) −1.46701e11 1.46701e11i −0.215819 0.215819i
\(909\) 3.86783e11i 0.566516i
\(910\) 0 0
\(911\) 1.94927e10 0.0283008 0.0141504 0.999900i \(-0.495496\pi\)
0.0141504 + 0.999900i \(0.495496\pi\)
\(912\) −8.87562e10 + 8.87562e10i −0.128298 + 0.128298i
\(913\) 9.27657e10 + 9.27657e10i 0.133507 + 0.133507i
\(914\) 9.82006e10i 0.140711i
\(915\) 0 0
\(916\) −7.14034e11 −1.01423
\(917\) 4.86164e11 4.86164e11i 0.687552 0.687552i
\(918\) 5.29982e9 + 5.29982e9i 0.00746260 + 0.00746260i
\(919\) 5.36385e11i 0.751995i −0.926621 0.375997i \(-0.877300\pi\)
0.926621 0.375997i \(-0.122700\pi\)
\(920\) 0 0
\(921\) −5.06542e11 −0.704006
\(922\) −1.84468e11 + 1.84468e11i −0.255268 + 0.255268i
\(923\) −2.07401e11 2.07401e11i −0.285761 0.285761i
\(924\) 7.62199e10i 0.104564i
\(925\) 0 0
\(926\) −2.33167e10 −0.0317120
\(927\) 1.62230e11 1.62230e11i 0.219691 0.219691i
\(928\) −5.62360e11 5.62360e11i −0.758268 0.758268i
\(929\) 2.91516e11i 0.391381i 0.980666 + 0.195691i \(0.0626948\pi\)
−0.980666 + 0.195691i \(0.937305\pi\)
\(930\) 0 0
\(931\) −2.03092e11 −0.270330
\(932\) 5.99939e11 5.99939e11i 0.795139 0.795139i
\(933\) 3.07604e11 + 3.07604e11i 0.405944 + 0.405944i
\(934\) 3.83421e11i 0.503835i
\(935\) 0 0
\(936\) −1.00051e11 −0.130352
\(937\) 3.52799e11 3.52799e11i 0.457688 0.457688i −0.440208 0.897896i \(-0.645095\pi\)
0.897896 + 0.440208i \(0.145095\pi\)
\(938\) 7.48901e10 + 7.48901e10i 0.0967415 + 0.0967415i
\(939\) 4.60921e11i 0.592876i
\(940\) 0 0
\(941\) −1.96719e9 −0.00250893 −0.00125446 0.999999i \(-0.500399\pi\)
−0.00125446 + 0.999999i \(0.500399\pi\)
\(942\) 1.50457e11 1.50457e11i 0.191077 0.191077i
\(943\) 7.62651e11 + 7.62651e11i 0.964449 + 0.964449i
\(944\) 4.81530e11i 0.606367i
\(945\) 0 0
\(946\) 5.08186e10 0.0634538
\(947\) 2.52474e11 2.52474e11i 0.313918 0.313918i −0.532507 0.846426i \(-0.678750\pi\)
0.846426 + 0.532507i \(0.178750\pi\)
\(948\) −3.16432e11 3.16432e11i −0.391784 0.391784i
\(949\) 6.41290e11i 0.790659i
\(950\) 0 0
\(951\) −3.73978e11 −0.457219
\(952\) −3.51858e10 + 3.51858e10i −0.0428371 + 0.0428371i
\(953\) 1.39641e11 + 1.39641e11i 0.169294 + 0.169294i 0.786669 0.617375i \(-0.211804\pi\)
−0.617375 + 0.786669i \(0.711804\pi\)
\(954\) 1.14282e11i 0.137970i
\(955\) 0 0
\(956\) 6.95260e11 0.832369
\(957\) 1.68772e11 1.68772e11i 0.201211 0.201211i
\(958\) 8.26232e9 + 8.26232e9i 0.00980934 + 0.00980934i
\(959\) 3.82018e11i 0.451658i
\(960\) 0 0
\(961\) −8.25490e11 −0.967872
\(962\) 2.30148e11 2.30148e11i 0.268724 0.268724i
\(963\) −1.03137e11 1.03137e11i −0.119925 0.119925i
\(964\) 5.88587e11i 0.681558i
\(965\) 0 0
\(966\) 9.83415e10 0.112935
\(967\) 1.22373e12 1.22373e12i 1.39953 1.39953i 0.598124 0.801403i \(-0.295913\pi\)
0.801403 0.598124i \(-0.204087\pi\)
\(968\) 2.89881e11 + 2.89881e11i 0.330155 + 0.330155i
\(969\) 4.09858e10i 0.0464877i
\(970\) 0 0
\(971\) 1.85260e11 0.208403 0.104202 0.994556i \(-0.466771\pi\)
0.104202 + 0.994556i \(0.466771\pi\)
\(972\) −3.74373e10 + 3.74373e10i −0.0419411 + 0.0419411i
\(973\) −3.10117e11 3.10117e11i −0.345999 0.345999i
\(974\) 2.72236e11i 0.302489i
\(975\) 0 0
\(976\) −1.91116e11 −0.210619
\(977\) −8.96530e11 + 8.96530e11i −0.983981 + 0.983981i −0.999874 0.0158927i \(-0.994941\pi\)
0.0158927 + 0.999874i \(0.494941\pi\)
\(978\) 6.61826e9 + 6.61826e9i 0.00723417 + 0.00723417i
\(979\) 2.66613e11i 0.290235i
\(980\) 0 0
\(981\) 3.83699e10 0.0414299
\(982\) −1.89391e11 + 1.89391e11i −0.203664 + 0.203664i
\(983\) 7.43264e11 + 7.43264e11i 0.796029 + 0.796029i 0.982467 0.186438i \(-0.0596944\pi\)
−0.186438 + 0.982467i \(0.559694\pi\)
\(984\) 3.14338e11i 0.335286i
\(985\) 0 0
\(986\) 7.48592e10 0.0792022
\(987\) −3.78344e11 + 3.78344e11i −0.398674 + 0.398674i
\(988\) 1.85857e11 + 1.85857e11i 0.195052 + 0.195052i
\(989\) 8.04128e11i 0.840504i
\(990\) 0 0
\(991\) 1.69152e12 1.75381 0.876904 0.480665i \(-0.159605\pi\)
0.876904 + 0.480665i \(0.159605\pi\)
\(992\) −9.11296e10 + 9.11296e10i −0.0941050 + 0.0941050i
\(993\) 4.73276e11 + 4.73276e11i 0.486763 + 0.486763i
\(994\) 8.40229e10i 0.0860701i
\(995\) 0 0
\(996\) −2.90654e11 −0.295351
\(997\) −6.16013e11 + 6.16013e11i −0.623461 + 0.623461i −0.946415 0.322953i \(-0.895324\pi\)
0.322953 + 0.946415i \(0.395324\pi\)
\(998\) −1.90934e11 1.90934e11i −0.192469 0.192469i
\(999\) 3.58514e11i 0.359951i
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.43.3 yes 12
5.2 odd 4 inner 75.9.f.d.7.3 12
5.3 odd 4 inner 75.9.f.d.7.4 yes 12
5.4 even 2 inner 75.9.f.d.43.4 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.f.d.7.3 12 5.2 odd 4 inner
75.9.f.d.7.4 yes 12 5.3 odd 4 inner
75.9.f.d.43.3 yes 12 1.1 even 1 trivial
75.9.f.d.43.4 yes 12 5.4 even 2 inner