Properties

Label 6.11.b.a.5.2
Level $6$
Weight $11$
Character 6.5
Analytic conductor $3.812$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.81214351604\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{85})\)
Defining polynomial: \(x^{4} - 2 x^{3} - 37 x^{2} + 38 x + 531\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(5.10977 + 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.11.b.a.5.4

$q$-expansion

\(f(q)\) \(=\) \(q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} +O(q^{10})\) \(q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} -109028. q^{10} +233268. i q^{11} +(-124042. + 9642.73i) q^{12} +307781. q^{13} -15172.4i q^{14} +(-90747.4 - 1.16735e6i) q^{15} +262144. q^{16} +672324. i q^{17} +(-206487. - 1.32007e6i) q^{18} -1.55119e6 q^{19} +2.46703e6i q^{20} +(162449. - 12628.4i) q^{21} +5.27826e6 q^{22} +5.57551e6i q^{23} +(218190. + 2.80674e6i) q^{24} -1.34515e7 q^{25} -6.96428e6i q^{26} +(1.39620e7 - 3.30957e6i) q^{27} -343311. q^{28} -2.97313e7i q^{29} +(-2.64142e7 + 2.05338e6i) q^{30} +3.09368e7 q^{31} -5.93164e6i q^{32} +(4.39325e6 + 5.65137e7i) q^{33} +1.52130e7 q^{34} -3.23089e6i q^{35} +(-2.98699e7 + 4.67227e6i) q^{36} -8.56690e7 q^{37} +3.50994e7i q^{38} +(7.45657e7 - 5.79657e6i) q^{39} +5.58225e7 q^{40} +3.59054e7i q^{41} +(-285748. - 3.67579e6i) q^{42} -3.66253e7 q^{43} -1.19433e8i q^{44} +(-4.39706e7 - 2.81104e8i) q^{45} +1.26159e8 q^{46} +3.28877e7i q^{47} +(6.35094e7 - 4.93708e6i) q^{48} -2.82026e8 q^{49} +3.04372e8i q^{50} +(1.26622e7 + 1.62883e8i) q^{51} -1.57584e8 q^{52} +4.59194e8i q^{53} +(-7.48870e7 - 3.15924e8i) q^{54} +1.12398e9 q^{55} +7.76824e6i q^{56} +(-3.75805e8 + 2.92143e7i) q^{57} -6.72743e8 q^{58} -4.88657e8i q^{59} +(4.64627e7 + 5.97684e8i) q^{60} -6.12928e7 q^{61} -7.00020e8i q^{62} +(3.91184e7 - 6.11894e6i) q^{63} -1.34218e8 q^{64} -1.48301e9i q^{65} +(1.27876e9 - 9.94079e7i) q^{66} -6.70776e8 q^{67} -3.44230e8i q^{68} +(1.05006e8 + 1.35077e9i) q^{69} -7.31067e7 q^{70} +1.23330e9i q^{71} +(1.05721e8 + 6.75878e8i) q^{72} +1.08126e9 q^{73} +1.93847e9i q^{74} +(-3.25888e9 + 2.53338e8i) q^{75} +7.94209e8 q^{76} +1.56413e8i q^{77} +(-1.31161e8 - 1.68723e9i) q^{78} -1.86628e9 q^{79} -1.26312e9i q^{80} +(3.32023e9 - 1.06476e9i) q^{81} +8.12446e8 q^{82} -1.09562e9i q^{83} +(-8.31737e7 + 6.46574e6i) q^{84} +3.23953e9 q^{85} +8.28736e8i q^{86} +(-5.59944e8 - 7.20298e9i) q^{87} -2.70247e9 q^{88} +5.19876e9i q^{89} +(-6.36066e9 + 9.94940e8i) q^{90} +2.06376e8 q^{91} -2.85466e9i q^{92} +(7.49503e9 - 5.82647e8i) q^{93} +7.44163e8 q^{94} +7.47427e9i q^{95} +(-1.11713e8 - 1.43705e9i) q^{96} -1.07471e10 q^{97} +6.38151e9i q^{98} +(2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 84q^{3} - 2048q^{4} + 5376q^{6} - 45112q^{7} + 159012q^{9} + O(q^{10}) \) \( 4q + 84q^{3} - 2048q^{4} + 5376q^{6} - 45112q^{7} + 159012q^{9} - 53760q^{10} - 43008q^{12} + 275240q^{13} - 1180800q^{15} + 1048576q^{16} - 2907648q^{18} - 1568728q^{19} + 9628008q^{21} + 7730688q^{22} - 2752512q^{24} - 33732380q^{25} + 34619508q^{27} + 23097344q^{28} - 85731840q^{30} - 21785848q^{31} + 25974144q^{33} + 151087104q^{34} - 81414144q^{36} - 71014168q^{37} + 217287240q^{39} + 27525120q^{40} - 145233408q^{42} - 470688664q^{43} + 312318720q^{45} + 188814336q^{46} + 22020096q^{48} - 50058420q^{49} - 708576768q^{51} - 140922880q^{52} + 481662720q^{54} + 2701359360q^{55} - 1058753208q^{57} - 1564177920q^{58} + 604569600q^{60} - 1184038744q^{61} - 905007096q^{63} - 536870912q^{64} + 3123445248q^{66} - 297365848q^{67} + 596268288q^{69} - 3962250240q^{70} + 1488715776q^{72} + 6534269000q^{73} - 5150031180q^{75} + 803188736q^{76} - 1322135040q^{78} + 199282568q^{79} + 1458964548q^{81} + 8378668032q^{82} - 4929540096q^{84} - 12880512000q^{85} + 210268800q^{87} - 3958112256q^{88} - 9243763200q^{90} + 8317232080q^{91} + 31744468392q^{93} + 8505477120q^{94} + 1409286144q^{96} - 39176355064q^{97} - 2626912512q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.6274i 0.707107i
\(3\) 242.269 18.8335i 0.996992 0.0775039i
\(4\) −512.000 −0.500000
\(5\) 4818.41i 1.54189i −0.636900 0.770946i \(-0.719784\pi\)
0.636900 0.770946i \(-0.280216\pi\)
\(6\) −426.153 5481.92i −0.0548036 0.704980i
\(7\) 670.530 0.0398959 0.0199479 0.999801i \(-0.493650\pi\)
0.0199479 + 0.999801i \(0.493650\pi\)
\(8\) 11585.2i 0.353553i
\(9\) 58339.6 9125.53i 0.987986 0.154542i
\(10\) −109028. −1.09028
\(11\) 233268.i 1.44841i 0.689583 + 0.724206i \(0.257794\pi\)
−0.689583 + 0.724206i \(0.742206\pi\)
\(12\) −124042. + 9642.73i −0.498496 + 0.0387520i
\(13\) 307781. 0.828943 0.414471 0.910062i \(-0.363967\pi\)
0.414471 + 0.910062i \(0.363967\pi\)
\(14\) 15172.4i 0.0282106i
\(15\) −90747.4 1.16735e6i −0.119503 1.53725i
\(16\) 262144. 0.250000
\(17\) 672324.i 0.473515i 0.971569 + 0.236758i \(0.0760847\pi\)
−0.971569 + 0.236758i \(0.923915\pi\)
\(18\) −206487. 1.32007e6i −0.109277 0.698612i
\(19\) −1.55119e6 −0.626465 −0.313233 0.949676i \(-0.601412\pi\)
−0.313233 + 0.949676i \(0.601412\pi\)
\(20\) 2.46703e6i 0.770946i
\(21\) 162449. 12628.4i 0.0397758 0.00309209i
\(22\) 5.27826e6 1.02418
\(23\) 5.57551e6i 0.866255i 0.901333 + 0.433127i \(0.142590\pi\)
−0.901333 + 0.433127i \(0.857410\pi\)
\(24\) 218190. + 2.80674e6i 0.0274018 + 0.352490i
\(25\) −1.34515e7 −1.37743
\(26\) 6.96428e6i 0.586151i
\(27\) 1.39620e7 3.30957e6i 0.973037 0.230650i
\(28\) −343311. −0.0199479
\(29\) 2.97313e7i 1.44952i −0.689001 0.724760i \(-0.741951\pi\)
0.689001 0.724760i \(-0.258049\pi\)
\(30\) −2.64142e7 + 2.05338e6i −1.08700 + 0.0845012i
\(31\) 3.09368e7 1.08061 0.540303 0.841471i \(-0.318310\pi\)
0.540303 + 0.841471i \(0.318310\pi\)
\(32\) 5.93164e6i 0.176777i
\(33\) 4.39325e6 + 5.65137e7i 0.112258 + 1.44406i
\(34\) 1.52130e7 0.334826
\(35\) 3.23089e6i 0.0615151i
\(36\) −2.98699e7 + 4.67227e6i −0.493993 + 0.0772708i
\(37\) −8.56690e7 −1.23542 −0.617711 0.786406i \(-0.711940\pi\)
−0.617711 + 0.786406i \(0.711940\pi\)
\(38\) 3.50994e7i 0.442978i
\(39\) 7.45657e7 5.79657e6i 0.826449 0.0642463i
\(40\) 5.58225e7 0.545141
\(41\) 3.59054e7i 0.309913i 0.987921 + 0.154957i \(0.0495238\pi\)
−0.987921 + 0.154957i \(0.950476\pi\)
\(42\) −285748. 3.67579e6i −0.00218644 0.0281258i
\(43\) −3.66253e7 −0.249137 −0.124569 0.992211i \(-0.539755\pi\)
−0.124569 + 0.992211i \(0.539755\pi\)
\(44\) 1.19433e8i 0.724206i
\(45\) −4.39706e7 2.81104e8i −0.238287 1.52337i
\(46\) 1.26159e8 0.612535
\(47\) 3.28877e7i 0.143398i 0.997426 + 0.0716992i \(0.0228421\pi\)
−0.997426 + 0.0716992i \(0.977158\pi\)
\(48\) 6.35094e7 4.93708e6i 0.249248 0.0193760i
\(49\) −2.82026e8 −0.998408
\(50\) 3.04372e8i 0.973991i
\(51\) 1.26622e7 + 1.62883e8i 0.0366993 + 0.472091i
\(52\) −1.57584e8 −0.414471
\(53\) 4.59194e8i 1.09804i 0.835810 + 0.549019i \(0.184998\pi\)
−0.835810 + 0.549019i \(0.815002\pi\)
\(54\) −7.48870e7 3.15924e8i −0.163094 0.688041i
\(55\) 1.12398e9 2.23330
\(56\) 7.76824e6i 0.0141053i
\(57\) −3.75805e8 + 2.92143e7i −0.624581 + 0.0485535i
\(58\) −6.72743e8 −1.02497
\(59\) 4.88657e8i 0.683508i −0.939789 0.341754i \(-0.888979\pi\)
0.939789 0.341754i \(-0.111021\pi\)
\(60\) 4.64627e7 + 5.97684e8i 0.0597514 + 0.768627i
\(61\) −6.12928e7 −0.0725705 −0.0362852 0.999341i \(-0.511552\pi\)
−0.0362852 + 0.999341i \(0.511552\pi\)
\(62\) 7.00020e8i 0.764103i
\(63\) 3.91184e7 6.11894e6i 0.0394166 0.00616557i
\(64\) −1.34218e8 −0.125000
\(65\) 1.48301e9i 1.27814i
\(66\) 1.27876e9 9.94079e7i 1.02110 0.0793782i
\(67\) −6.70776e8 −0.496825 −0.248413 0.968654i \(-0.579909\pi\)
−0.248413 + 0.968654i \(0.579909\pi\)
\(68\) 3.44230e8i 0.236758i
\(69\) 1.05006e8 + 1.35077e9i 0.0671382 + 0.863649i
\(70\) −7.31067e7 −0.0434977
\(71\) 1.23330e9i 0.683561i 0.939780 + 0.341781i \(0.111030\pi\)
−0.939780 + 0.341781i \(0.888970\pi\)
\(72\) 1.05721e8 + 6.75878e8i 0.0546387 + 0.349306i
\(73\) 1.08126e9 0.521573 0.260787 0.965396i \(-0.416018\pi\)
0.260787 + 0.965396i \(0.416018\pi\)
\(74\) 1.93847e9i 0.873575i
\(75\) −3.25888e9 + 2.53338e8i −1.37329 + 0.106756i
\(76\) 7.94209e8 0.313233
\(77\) 1.56413e8i 0.0577857i
\(78\) −1.31161e8 1.68723e9i −0.0454290 0.584388i
\(79\) −1.86628e9 −0.606515 −0.303258 0.952909i \(-0.598074\pi\)
−0.303258 + 0.952909i \(0.598074\pi\)
\(80\) 1.26312e9i 0.385473i
\(81\) 3.32023e9 1.06476e9i 0.952234 0.305370i
\(82\) 8.12446e8 0.219142
\(83\) 1.09562e9i 0.278145i −0.990282 0.139072i \(-0.955588\pi\)
0.990282 0.139072i \(-0.0444121\pi\)
\(84\) −8.31737e7 + 6.46574e6i −0.0198879 + 0.00154604i
\(85\) 3.23953e9 0.730109
\(86\) 8.28736e8i 0.176167i
\(87\) −5.59944e8 7.20298e9i −0.112344 1.44516i
\(88\) −2.70247e9 −0.512091
\(89\) 5.19876e9i 0.931000i 0.885048 + 0.465500i \(0.154126\pi\)
−0.885048 + 0.465500i \(0.845874\pi\)
\(90\) −6.36066e9 + 9.94940e8i −1.07718 + 0.168494i
\(91\) 2.06376e8 0.0330714
\(92\) 2.85466e9i 0.433127i
\(93\) 7.49503e9 5.82647e8i 1.07735 0.0837512i
\(94\) 7.44163e8 0.101398
\(95\) 7.47427e9i 0.965941i
\(96\) −1.11713e8 1.43705e9i −0.0137009 0.176245i
\(97\) −1.07471e10 −1.25150 −0.625750 0.780024i \(-0.715207\pi\)
−0.625750 + 0.780024i \(0.715207\pi\)
\(98\) 6.38151e9i 0.705981i
\(99\) 2.12870e9 + 1.36088e10i 0.223840 + 1.43101i
\(100\) 6.88716e9 0.688716
\(101\) 1.08154e10i 1.02905i −0.857475 0.514525i \(-0.827968\pi\)
0.857475 0.514525i \(-0.172032\pi\)
\(102\) 3.68563e9 2.86513e8i 0.333819 0.0259503i
\(103\) −2.83446e9 −0.244503 −0.122251 0.992499i \(-0.539011\pi\)
−0.122251 + 0.992499i \(0.539011\pi\)
\(104\) 3.56571e9i 0.293075i
\(105\) −6.08488e7 7.82744e8i −0.00476766 0.0613301i
\(106\) 1.03904e10 0.776430
\(107\) 2.41202e10i 1.71974i −0.510515 0.859869i \(-0.670545\pi\)
0.510515 0.859869i \(-0.329455\pi\)
\(108\) −7.14855e9 + 1.69450e9i −0.486518 + 0.115325i
\(109\) −5.43424e9 −0.353188 −0.176594 0.984284i \(-0.556508\pi\)
−0.176594 + 0.984284i \(0.556508\pi\)
\(110\) 2.54328e10i 1.57918i
\(111\) −2.07549e10 + 1.61344e9i −1.23170 + 0.0957500i
\(112\) 1.75775e8 0.00997396
\(113\) 1.39305e10i 0.756092i 0.925787 + 0.378046i \(0.123404\pi\)
−0.925787 + 0.378046i \(0.876596\pi\)
\(114\) 6.61043e8 + 8.50350e9i 0.0343325 + 0.441645i
\(115\) 2.68651e10 1.33567
\(116\) 1.52224e10i 0.724760i
\(117\) 1.79558e10 2.80866e9i 0.818984 0.128106i
\(118\) −1.10570e10 −0.483313
\(119\) 4.50813e8i 0.0188913i
\(120\) 1.35241e10 1.05133e9i 0.543501 0.0422506i
\(121\) −2.84767e10 −1.09790
\(122\) 1.38690e9i 0.0513151i
\(123\) 6.76223e8 + 8.69877e9i 0.0240195 + 0.308981i
\(124\) −1.58396e10 −0.540303
\(125\) 1.77600e10i 0.581958i
\(126\) −1.38456e8 8.85149e8i −0.00435972 0.0278717i
\(127\) 4.08412e10 1.23617 0.618087 0.786110i \(-0.287908\pi\)
0.618087 + 0.786110i \(0.287908\pi\)
\(128\) 3.03700e9i 0.0883883i
\(129\) −8.87317e9 + 6.89781e8i −0.248388 + 0.0193091i
\(130\) −3.35568e10 −0.903782
\(131\) 4.15498e10i 1.07699i 0.842628 + 0.538495i \(0.181007\pi\)
−0.842628 + 0.538495i \(0.818993\pi\)
\(132\) −2.24934e9 2.89350e10i −0.0561289 0.722028i
\(133\) −1.04012e9 −0.0249934
\(134\) 1.51779e10i 0.351308i
\(135\) −1.59469e10 6.72748e10i −0.355637 1.50032i
\(136\) −7.78903e9 −0.167413
\(137\) 9.25532e10i 1.91773i −0.283854 0.958867i \(-0.591613\pi\)
0.283854 0.958867i \(-0.408387\pi\)
\(138\) 3.05645e10 2.37602e9i 0.610692 0.0474739i
\(139\) 7.95575e10 1.53323 0.766615 0.642107i \(-0.221939\pi\)
0.766615 + 0.642107i \(0.221939\pi\)
\(140\) 1.65421e9i 0.0307576i
\(141\) 6.19389e8 + 7.96767e9i 0.0111139 + 0.142967i
\(142\) 2.79064e10 0.483351
\(143\) 7.17955e10i 1.20065i
\(144\) 1.52934e10 2.39220e9i 0.246997 0.0386354i
\(145\) −1.43258e11 −2.23500
\(146\) 2.44661e10i 0.368808i
\(147\) −6.83261e10 + 5.31152e9i −0.995405 + 0.0773806i
\(148\) 4.38625e10 0.617711
\(149\) 8.07804e10i 1.09995i 0.835180 + 0.549977i \(0.185364\pi\)
−0.835180 + 0.549977i \(0.814636\pi\)
\(150\) 5.73238e9 + 7.37400e10i 0.0754881 + 0.971061i
\(151\) 3.08654e10 0.393176 0.196588 0.980486i \(-0.437014\pi\)
0.196588 + 0.980486i \(0.437014\pi\)
\(152\) 1.79709e10i 0.221489i
\(153\) 6.13531e9 + 3.92231e10i 0.0731778 + 0.467827i
\(154\) 3.53923e9 0.0408606
\(155\) 1.49066e11i 1.66618i
\(156\) −3.81776e10 + 2.96785e9i −0.413225 + 0.0321232i
\(157\) 9.71322e10 1.01828 0.509138 0.860685i \(-0.329964\pi\)
0.509138 + 0.860685i \(0.329964\pi\)
\(158\) 4.22291e10i 0.428871i
\(159\) 8.64822e9 + 1.11249e11i 0.0851023 + 1.09473i
\(160\) −2.85811e10 −0.272571
\(161\) 3.73855e9i 0.0345600i
\(162\) −2.40928e10 7.51283e10i −0.215929 0.673331i
\(163\) −1.39440e11 −1.21185 −0.605927 0.795520i \(-0.707198\pi\)
−0.605927 + 0.795520i \(0.707198\pi\)
\(164\) 1.83836e10i 0.154957i
\(165\) 2.72306e11 2.11685e10i 2.22658 0.173089i
\(166\) −2.47911e10 −0.196678
\(167\) 1.25840e11i 0.968804i −0.874845 0.484402i \(-0.839037\pi\)
0.874845 0.484402i \(-0.160963\pi\)
\(168\) 1.46303e8 + 1.88201e9i 0.00109322 + 0.0140629i
\(169\) −4.31296e10 −0.312854
\(170\) 7.33023e10i 0.516265i
\(171\) −9.04958e10 + 1.41554e10i −0.618939 + 0.0968149i
\(172\) 1.87521e10 0.124569
\(173\) 1.26257e11i 0.814750i −0.913261 0.407375i \(-0.866444\pi\)
0.913261 0.407375i \(-0.133556\pi\)
\(174\) −1.62985e11 + 1.26701e10i −1.02188 + 0.0794389i
\(175\) −9.01961e9 −0.0549538
\(176\) 6.11499e10i 0.362103i
\(177\) −9.20310e9 1.18386e11i −0.0529746 0.681452i
\(178\) 1.17635e11 0.658317
\(179\) 2.96543e11i 1.61370i 0.590758 + 0.806848i \(0.298829\pi\)
−0.590758 + 0.806848i \(0.701171\pi\)
\(180\) 2.25129e10 + 1.43925e11i 0.119143 + 0.761684i
\(181\) 2.48451e11 1.27893 0.639466 0.768819i \(-0.279155\pi\)
0.639466 + 0.768819i \(0.279155\pi\)
\(182\) 4.66976e9i 0.0233850i
\(183\) −1.48493e10 + 1.15435e9i −0.0723522 + 0.00562450i
\(184\) −6.45936e10 −0.306267
\(185\) 4.12789e11i 1.90489i
\(186\) −1.31838e10 1.69593e11i −0.0592210 0.761805i
\(187\) −1.56832e11 −0.685846
\(188\) 1.68385e10i 0.0716992i
\(189\) 9.36194e9 2.21916e9i 0.0388201 0.00920196i
\(190\) 1.69123e11 0.683024
\(191\) 1.58050e11i 0.621769i −0.950448 0.310884i \(-0.899375\pi\)
0.950448 0.310884i \(-0.100625\pi\)
\(192\) −3.25168e10 + 2.52778e9i −0.124624 + 0.00968799i
\(193\) −3.78369e11 −1.41296 −0.706479 0.707734i \(-0.749717\pi\)
−0.706479 + 0.707734i \(0.749717\pi\)
\(194\) 2.43178e11i 0.884944i
\(195\) −2.79303e10 3.59288e11i −0.0990609 1.27430i
\(196\) 1.44397e11 0.499204
\(197\) 1.89406e11i 0.638356i −0.947695 0.319178i \(-0.896593\pi\)
0.947695 0.319178i \(-0.103407\pi\)
\(198\) 3.07932e11 4.81669e10i 1.01188 0.158279i
\(199\) 5.02942e10 0.161158 0.0805791 0.996748i \(-0.474323\pi\)
0.0805791 + 0.996748i \(0.474323\pi\)
\(200\) 1.55839e11i 0.486996i
\(201\) −1.62508e11 + 1.26330e10i −0.495331 + 0.0385059i
\(202\) −2.44725e11 −0.727648
\(203\) 1.99357e10i 0.0578298i
\(204\) −6.48304e9 8.33962e10i −0.0183496 0.236045i
\(205\) 1.73007e11 0.477853
\(206\) 6.41365e10i 0.172890i
\(207\) 5.08795e10 + 3.25273e11i 0.133872 + 0.855848i
\(208\) 8.06828e10 0.207236
\(209\) 3.61843e11i 0.907380i
\(210\) −1.77115e10 + 1.37685e9i −0.0433669 + 0.00337125i
\(211\) 4.74970e11 1.13567 0.567837 0.823141i \(-0.307780\pi\)
0.567837 + 0.823141i \(0.307780\pi\)
\(212\) 2.35108e11i 0.549019i
\(213\) 2.32273e10 + 2.98791e11i 0.0529787 + 0.681505i
\(214\) −5.45778e11 −1.21604
\(215\) 1.76476e11i 0.384143i
\(216\) 3.83422e10 + 1.61753e11i 0.0815470 + 0.344020i
\(217\) 2.07440e10 0.0431117
\(218\) 1.22963e11i 0.249742i
\(219\) 2.61955e11 2.03638e10i 0.520004 0.0404240i
\(220\) −5.75479e11 −1.11665
\(221\) 2.06928e11i 0.392517i
\(222\) 3.65081e10 + 4.69631e11i 0.0677055 + 0.870947i
\(223\) −2.35580e11 −0.427183 −0.213592 0.976923i \(-0.568516\pi\)
−0.213592 + 0.976923i \(0.568516\pi\)
\(224\) 3.97734e9i 0.00705266i
\(225\) −7.84754e11 + 1.22752e11i −1.36088 + 0.212870i
\(226\) 3.15211e11 0.534638
\(227\) 4.27026e11i 0.708475i 0.935155 + 0.354238i \(0.115260\pi\)
−0.935155 + 0.354238i \(0.884740\pi\)
\(228\) 1.92412e11 1.49577e10i 0.312290 0.0242768i
\(229\) 1.03671e12 1.64619 0.823096 0.567902i \(-0.192245\pi\)
0.823096 + 0.567902i \(0.192245\pi\)
\(230\) 6.07888e11i 0.944462i
\(231\) 2.94580e9 + 3.78941e10i 0.00447862 + 0.0576119i
\(232\) 3.44444e11 0.512483
\(233\) 1.03766e12i 1.51103i −0.655130 0.755516i \(-0.727386\pi\)
0.655130 0.755516i \(-0.272614\pi\)
\(234\) −6.35527e10 4.06293e11i −0.0905847 0.579109i
\(235\) 1.58466e11 0.221105
\(236\) 2.50192e11i 0.341754i
\(237\) −4.52142e11 + 3.51485e10i −0.604691 + 0.0470073i
\(238\) 1.02007e10 0.0133582
\(239\) 1.23687e12i 1.58612i −0.609144 0.793060i \(-0.708487\pi\)
0.609144 0.793060i \(-0.291513\pi\)
\(240\) −2.37889e10 3.06014e11i −0.0298757 0.384314i
\(241\) −1.03912e12 −1.27814 −0.639072 0.769147i \(-0.720682\pi\)
−0.639072 + 0.769147i \(0.720682\pi\)
\(242\) 6.44354e11i 0.776333i
\(243\) 7.84337e11 3.20490e11i 0.925702 0.378253i
\(244\) 3.13819e10 0.0362852
\(245\) 1.35892e12i 1.53944i
\(246\) 1.96831e11 1.53012e10i 0.218483 0.0169844i
\(247\) −4.77426e11 −0.519304
\(248\) 3.58410e11i 0.382052i
\(249\) −2.06344e10 2.65436e11i −0.0215573 0.277308i
\(250\) 4.01862e11 0.411507
\(251\) 5.66781e11i 0.568914i 0.958689 + 0.284457i \(0.0918133\pi\)
−0.958689 + 0.284457i \(0.908187\pi\)
\(252\) −2.00286e10 + 3.13290e9i −0.0197083 + 0.00308279i
\(253\) −1.30059e12 −1.25469
\(254\) 9.24130e11i 0.874107i
\(255\) 7.84839e11 6.10116e10i 0.727913 0.0565864i
\(256\) 6.87195e10 0.0625000
\(257\) 1.27943e12i 1.14117i 0.821239 + 0.570584i \(0.193283\pi\)
−0.821239 + 0.570584i \(0.806717\pi\)
\(258\) 1.56080e10 + 2.00777e11i 0.0136536 + 0.175637i
\(259\) −5.74436e10 −0.0492882
\(260\) 7.59303e11i 0.639070i
\(261\) −2.71314e11 1.73451e12i −0.224011 1.43211i
\(262\) 9.40164e11 0.761548
\(263\) 1.68583e12i 1.33978i 0.742459 + 0.669892i \(0.233660\pi\)
−0.742459 + 0.669892i \(0.766340\pi\)
\(264\) −6.54725e11 + 5.08968e10i −0.510551 + 0.0396891i
\(265\) 2.21259e12 1.69306
\(266\) 2.35352e10i 0.0176730i
\(267\) 9.79107e10 + 1.25950e12i 0.0721562 + 0.928200i
\(268\) 3.43437e11 0.248413
\(269\) 1.34023e12i 0.951523i −0.879574 0.475761i \(-0.842173\pi\)
0.879574 0.475761i \(-0.157827\pi\)
\(270\) −1.52225e12 + 3.60837e11i −1.06088 + 0.251473i
\(271\) −1.75349e12 −1.19966 −0.599829 0.800129i \(-0.704765\pi\)
−0.599829 + 0.800129i \(0.704765\pi\)
\(272\) 1.76246e11i 0.118379i
\(273\) 4.99985e10 3.88677e9i 0.0329719 0.00256316i
\(274\) −2.09424e12 −1.35604
\(275\) 3.13780e12i 1.99509i
\(276\) −5.37632e10 6.91597e11i −0.0335691 0.431825i
\(277\) 1.69580e12 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(278\) 1.80018e12i 1.08416i
\(279\) 1.80484e12 2.82315e11i 1.06762 0.166999i
\(280\) 3.74306e10 0.0217489
\(281\) 2.44175e11i 0.139370i 0.997569 + 0.0696851i \(0.0221995\pi\)
−0.997569 + 0.0696851i \(0.977801\pi\)
\(282\) 1.80288e11 1.40152e10i 0.101093 0.00785874i
\(283\) −9.96409e11 −0.548916 −0.274458 0.961599i \(-0.588498\pi\)
−0.274458 + 0.961599i \(0.588498\pi\)
\(284\) 6.31450e11i 0.341781i
\(285\) 1.40766e11 + 1.81078e12i 0.0748643 + 0.963036i
\(286\) 1.62455e12 0.848989
\(287\) 2.40756e10i 0.0123643i
\(288\) −5.41294e10 3.46050e11i −0.0273194 0.174653i
\(289\) 1.56397e12 0.775783
\(290\) 3.24155e12i 1.58039i
\(291\) −2.60368e12 + 2.02404e11i −1.24774 + 0.0969962i
\(292\) −5.53604e11 −0.260787
\(293\) 1.57571e12i 0.729690i −0.931068 0.364845i \(-0.881122\pi\)
0.931068 0.364845i \(-0.118878\pi\)
\(294\) 1.20186e11 + 1.54604e12i 0.0547163 + 0.703858i
\(295\) −2.35455e12 −1.05390
\(296\) 9.92496e11i 0.436787i
\(297\) 7.72018e11 + 3.25690e12i 0.334076 + 1.40936i
\(298\) 1.82785e12 0.777786
\(299\) 1.71603e12i 0.718076i
\(300\) 1.66854e12 1.29709e11i 0.686644 0.0533782i
\(301\) −2.45583e10 −0.00993955
\(302\) 6.98405e11i 0.278018i
\(303\) −2.03692e11 2.62024e12i −0.0797554 1.02595i
\(304\) −4.06635e11 −0.156616
\(305\) 2.95334e11i 0.111896i
\(306\) 8.87518e11 1.38826e11i 0.330803 0.0517445i
\(307\) −3.29823e12 −1.20945 −0.604726 0.796434i \(-0.706717\pi\)
−0.604726 + 0.796434i \(0.706717\pi\)
\(308\) 8.00836e10i 0.0288928i
\(309\) −6.86702e11 + 5.33827e10i −0.243768 + 0.0189499i
\(310\) −3.37299e12 −1.17816
\(311\) 1.67301e12i 0.575038i 0.957775 + 0.287519i \(0.0928304\pi\)
−0.957775 + 0.287519i \(0.907170\pi\)
\(312\) 6.71547e10 + 8.63862e11i 0.0227145 + 0.292194i
\(313\) 1.73318e12 0.576930 0.288465 0.957490i \(-0.406855\pi\)
0.288465 + 0.957490i \(0.406855\pi\)
\(314\) 2.19785e12i 0.720029i
\(315\) −2.94836e10 1.88489e11i −0.00950664 0.0607761i
\(316\) 9.55536e11 0.303258
\(317\) 1.33100e12i 0.415798i −0.978150 0.207899i \(-0.933337\pi\)
0.978150 0.207899i \(-0.0666625\pi\)
\(318\) 2.51727e12 1.95687e11i 0.774094 0.0601764i
\(319\) 6.93538e12 2.09950
\(320\) 6.46716e11i 0.192737i
\(321\) −4.54267e11 5.84358e12i −0.133286 1.71456i
\(322\) 8.45937e10 0.0244376
\(323\) 1.04290e12i 0.296641i
\(324\) −1.69996e12 + 5.45157e11i −0.476117 + 0.152685i
\(325\) −4.14010e12 −1.14181
\(326\) 3.15518e12i 0.856911i
\(327\) −1.31655e12 + 1.02345e11i −0.352126 + 0.0273735i
\(328\) −4.15973e11 −0.109571
\(329\) 2.20522e10i 0.00572100i
\(330\) −4.78988e11 6.16159e12i −0.122393 1.57443i
\(331\) 4.71961e12 1.18786 0.593931 0.804516i \(-0.297575\pi\)
0.593931 + 0.804516i \(0.297575\pi\)
\(332\) 5.60959e11i 0.139072i
\(333\) −4.99789e12 + 7.81775e11i −1.22058 + 0.190924i
\(334\) −2.84743e12 −0.685048
\(335\) 3.23208e12i 0.766051i
\(336\) 4.25849e10 3.31046e9i 0.00994396 0.000773022i
\(337\) 4.15283e12 0.955422 0.477711 0.878517i \(-0.341467\pi\)
0.477711 + 0.878517i \(0.341467\pi\)
\(338\) 9.75911e11i 0.221221i
\(339\) 2.62360e11 + 3.37493e12i 0.0586001 + 0.753818i
\(340\) −1.65864e12 −0.365055
\(341\) 7.21658e12i 1.56516i
\(342\) 3.20301e11 + 2.04769e12i 0.0684585 + 0.437656i
\(343\) −3.78515e11 −0.0797282
\(344\) 4.24313e11i 0.0880833i
\(345\) 6.50859e12 5.05963e11i 1.33165 0.103520i
\(346\) −2.85687e12 −0.576115
\(347\) 4.39939e12i 0.874470i −0.899347 0.437235i \(-0.855958\pi\)
0.899347 0.437235i \(-0.144042\pi\)
\(348\) 2.86691e11 + 3.68793e12i 0.0561718 + 0.722580i
\(349\) −9.24002e12 −1.78462 −0.892310 0.451423i \(-0.850917\pi\)
−0.892310 + 0.451423i \(0.850917\pi\)
\(350\) 2.04091e11i 0.0388582i
\(351\) 4.29724e12 1.01862e12i 0.806592 0.191195i
\(352\) 1.38366e12 0.256046
\(353\) 9.20733e11i 0.167981i 0.996467 + 0.0839905i \(0.0267665\pi\)
−0.996467 + 0.0839905i \(0.973233\pi\)
\(354\) −2.67878e12 + 2.08242e11i −0.481860 + 0.0374587i
\(355\) 5.94255e12 1.05398
\(356\) 2.66177e12i 0.465500i
\(357\) 8.49037e9 + 1.09218e11i 0.00146415 + 0.0188345i
\(358\) 6.70999e12 1.14106
\(359\) 6.17595e12i 1.03569i −0.855473 0.517847i \(-0.826733\pi\)
0.855473 0.517847i \(-0.173267\pi\)
\(360\) 3.25666e12 5.09409e11i 0.538592 0.0842470i
\(361\) −3.72488e12 −0.607542
\(362\) 5.62180e12i 0.904342i
\(363\) −6.89902e12 + 5.36315e11i −1.09460 + 0.0850916i
\(364\) −1.05665e11 −0.0165357
\(365\) 5.20995e12i 0.804209i
\(366\) 2.61201e10 + 3.36002e11i 0.00397712 + 0.0511607i
\(367\) −8.19379e12 −1.23071 −0.615353 0.788252i \(-0.710987\pi\)
−0.615353 + 0.788252i \(0.710987\pi\)
\(368\) 1.46159e12i 0.216564i
\(369\) 3.27656e11 + 2.09471e12i 0.0478945 + 0.306190i
\(370\) 9.34034e12 1.34696
\(371\) 3.07903e11i 0.0438072i
\(372\) −3.83746e12 + 2.98315e11i −0.538677 + 0.0418756i
\(373\) −9.07322e12 −1.25666 −0.628329 0.777947i \(-0.716261\pi\)
−0.628329 + 0.777947i \(0.716261\pi\)
\(374\) 3.54870e12i 0.484966i
\(375\) 3.34481e11 + 4.30269e12i 0.0451041 + 0.580208i
\(376\) −3.81012e11 −0.0506990
\(377\) 9.15072e12i 1.20157i
\(378\) −5.02140e10 2.11837e11i −0.00650677 0.0274500i
\(379\) 1.17817e13 1.50665 0.753324 0.657650i \(-0.228449\pi\)
0.753324 + 0.657650i \(0.228449\pi\)
\(380\) 3.82683e12i 0.482971i
\(381\) 9.89455e12 7.69180e11i 1.23246 0.0958083i
\(382\) −3.57627e12 −0.439657
\(383\) 6.82336e12i 0.827950i 0.910288 + 0.413975i \(0.135860\pi\)
−0.910288 + 0.413975i \(0.864140\pi\)
\(384\) 5.71972e10 + 7.35771e11i 0.00685045 + 0.0881225i
\(385\) 7.53664e11 0.0890993
\(386\) 8.56152e12i 0.999112i
\(387\) −2.13670e12 + 3.34225e11i −0.246144 + 0.0385021i
\(388\) 5.50249e12 0.625750
\(389\) 7.07814e11i 0.0794642i 0.999210 + 0.0397321i \(0.0126504\pi\)
−0.999210 + 0.0397321i \(0.987350\pi\)
\(390\) −8.12977e12 + 6.31990e11i −0.901063 + 0.0700466i
\(391\) −3.74855e12 −0.410185
\(392\) 3.26733e12i 0.352991i
\(393\) 7.82526e11 + 1.00662e13i 0.0834710 + 1.07375i
\(394\) −4.28577e12 −0.451386
\(395\) 8.99251e12i 0.935181i
\(396\) −1.08989e12 6.96770e12i −0.111920 0.715506i
\(397\) 1.26553e12 0.128328 0.0641639 0.997939i \(-0.479562\pi\)
0.0641639 + 0.997939i \(0.479562\pi\)
\(398\) 1.13803e12i 0.113956i
\(399\) −2.51989e11 + 1.95890e10i −0.0249182 + 0.00193708i
\(400\) −3.52622e12 −0.344358
\(401\) 1.50259e13i 1.44917i 0.689187 + 0.724583i \(0.257968\pi\)
−0.689187 + 0.724583i \(0.742032\pi\)
\(402\) 2.85853e11 + 3.67714e12i 0.0272278 + 0.350252i
\(403\) 9.52175e12 0.895760
\(404\) 5.53749e12i 0.514525i
\(405\) −5.13045e12 1.59983e13i −0.470848 1.46824i
\(406\) −4.51094e11 −0.0408919
\(407\) 1.99839e13i 1.78940i
\(408\) −1.88704e12 + 1.46694e11i −0.166909 + 0.0129752i
\(409\) −1.70362e12 −0.148852 −0.0744261 0.997227i \(-0.523712\pi\)
−0.0744261 + 0.997227i \(0.523712\pi\)
\(410\) 3.91470e12i 0.337893i
\(411\) −1.74310e12 2.24228e13i −0.148632 1.91197i
\(412\) 1.45124e12 0.122251
\(413\) 3.27659e11i 0.0272692i
\(414\) 7.36009e12 1.15127e12i 0.605176 0.0946621i
\(415\) −5.27917e12 −0.428869
\(416\) 1.82564e12i 0.146538i
\(417\) 1.92743e13 1.49834e12i 1.52862 0.118831i
\(418\) −8.18758e12 −0.641615
\(419\) 2.22448e13i 1.72250i 0.508185 + 0.861248i \(0.330317\pi\)
−0.508185 + 0.861248i \(0.669683\pi\)
\(420\) 3.11546e10 + 4.00765e11i 0.00238383 + 0.0306650i
\(421\) 1.82948e11 0.0138330 0.00691650 0.999976i \(-0.497798\pi\)
0.00691650 + 0.999976i \(0.497798\pi\)
\(422\) 1.07473e13i 0.803043i
\(423\) 3.00118e11 + 1.91865e12i 0.0221610 + 0.141676i
\(424\) −5.31988e12 −0.388215
\(425\) 9.04375e12i 0.652235i
\(426\) 6.76086e12 5.25574e11i 0.481897 0.0374616i
\(427\) −4.10986e10 −0.00289526
\(428\) 1.23495e13i 0.859869i
\(429\) 1.35216e12 + 1.73938e13i 0.0930552 + 1.19704i
\(430\) 3.99319e12 0.271630
\(431\) 6.64491e12i 0.446789i 0.974728 + 0.223395i \(0.0717139\pi\)
−0.974728 + 0.223395i \(0.928286\pi\)
\(432\) 3.66006e12 8.67584e11i 0.243259 0.0576624i
\(433\) 7.28337e12 0.478512 0.239256 0.970956i \(-0.423096\pi\)
0.239256 + 0.970956i \(0.423096\pi\)
\(434\) 4.69384e11i 0.0304846i
\(435\) −3.47069e13 + 2.69804e12i −2.22828 + 0.173222i
\(436\) 2.78233e12 0.176594
\(437\) 8.64868e12i 0.542678i
\(438\) −4.60781e11 5.92738e12i −0.0285841 0.367699i
\(439\) −1.52600e13 −0.935907 −0.467954 0.883753i \(-0.655009\pi\)
−0.467954 + 0.883753i \(0.655009\pi\)
\(440\) 1.30216e13i 0.789590i
\(441\) −1.64533e13 + 2.57363e12i −0.986414 + 0.154296i
\(442\) 4.68225e12 0.277551
\(443\) 1.83304e13i 1.07437i −0.843465 0.537184i \(-0.819488\pi\)
0.843465 0.537184i \(-0.180512\pi\)
\(444\) 1.06265e13 8.26083e11i 0.615852 0.0478750i
\(445\) 2.50498e13 1.43550
\(446\) 5.33057e12i 0.302064i
\(447\) 1.52138e12 + 1.95706e13i 0.0852508 + 1.09665i
\(448\) −8.99970e10 −0.00498698
\(449\) 8.33876e12i 0.456951i 0.973550 + 0.228475i \(0.0733741\pi\)
−0.973550 + 0.228475i \(0.926626\pi\)
\(450\) 2.77756e12 + 1.77570e13i 0.150522 + 0.962290i
\(451\) −8.37559e12 −0.448883
\(452\) 7.13242e12i 0.378046i
\(453\) 7.47774e12 5.81303e11i 0.391994 0.0304727i
\(454\) 9.66249e12 0.500968
\(455\) 9.94405e11i 0.0509925i
\(456\) −3.38454e11 4.35379e12i −0.0171663 0.220823i
\(457\) 4.12288e11 0.0206833 0.0103416 0.999947i \(-0.496708\pi\)
0.0103416 + 0.999947i \(0.496708\pi\)
\(458\) 2.34581e13i 1.16403i
\(459\) 2.22510e12 + 9.38700e12i 0.109216 + 0.460748i
\(460\) −1.37549e13 −0.667836
\(461\) 1.66247e11i 0.00798453i 0.999992 + 0.00399226i \(0.00127078\pi\)
−0.999992 + 0.00399226i \(0.998729\pi\)
\(462\) 8.57446e11 6.66559e10i 0.0407377 0.00316686i
\(463\) 1.27323e13 0.598416 0.299208 0.954188i \(-0.403278\pi\)
0.299208 + 0.954188i \(0.403278\pi\)
\(464\) 7.79389e12i 0.362380i
\(465\) −2.80743e12 3.61142e13i −0.129135 1.66116i
\(466\) −2.34795e13 −1.06846
\(467\) 2.26689e13i 1.02058i −0.860004 0.510288i \(-0.829539\pi\)
0.860004 0.510288i \(-0.170461\pi\)
\(468\) −9.19337e12 + 1.43803e12i −0.409492 + 0.0640531i
\(469\) −4.49775e11 −0.0198213
\(470\) 3.58569e12i 0.156345i
\(471\) 2.35321e13 1.82934e12i 1.01521 0.0789203i
\(472\) 5.66120e12 0.241657
\(473\) 8.54352e12i 0.360854i
\(474\) 7.95321e11 + 1.02308e13i 0.0332392 + 0.427581i
\(475\) 2.08658e13 0.862913
\(476\) 2.30816e11i 0.00944565i
\(477\) 4.19039e12 + 2.67892e13i 0.169693 + 1.08485i
\(478\) −2.79873e13 −1.12156
\(479\) 2.39654e13i 0.950402i −0.879877 0.475201i \(-0.842375\pi\)
0.879877 0.475201i \(-0.157625\pi\)
\(480\) −6.92432e12 + 5.38281e11i −0.271751 + 0.0211253i
\(481\) −2.63673e13 −1.02409
\(482\) 2.35126e13i 0.903785i
\(483\) 7.04098e10 + 9.05734e11i 0.00267853 + 0.0344560i
\(484\) 1.45801e13 0.548950
\(485\) 5.17838e13i 1.92968i
\(486\) −7.25186e12 1.77475e13i −0.267466 0.654570i
\(487\) −1.13824e13 −0.415516 −0.207758 0.978180i \(-0.566617\pi\)
−0.207758 + 0.978180i \(0.566617\pi\)
\(488\) 7.10091e11i 0.0256575i
\(489\) −3.37821e13 + 2.62615e12i −1.20821 + 0.0939235i
\(490\) 3.07488e13 1.08855
\(491\) 3.59512e13i 1.25981i 0.776672 + 0.629906i \(0.216906\pi\)
−0.776672 + 0.629906i \(0.783094\pi\)
\(492\) −3.46226e11 4.45377e12i −0.0120098 0.154491i
\(493\) 1.99891e13 0.686370
\(494\) 1.08029e13i 0.367203i
\(495\) 6.55727e13 1.02569e13i 2.20647 0.345137i
\(496\) 8.10990e12 0.270151
\(497\) 8.26965e11i 0.0272713i
\(498\) −6.00612e12 + 4.66903e11i −0.196086 + 0.0152433i
\(499\) −1.33630e13 −0.431917 −0.215958 0.976403i \(-0.569288\pi\)
−0.215958 + 0.976403i \(0.569288\pi\)
\(500\) 9.09310e12i 0.290979i
\(501\) −2.37000e12 3.04871e13i −0.0750862 0.965890i
\(502\) 1.28248e13 0.402283
\(503\) 3.54934e13i 1.10232i 0.834399 + 0.551160i \(0.185815\pi\)
−0.834399 + 0.551160i \(0.814185\pi\)
\(504\) 7.08893e10 + 4.53196e11i 0.00217986 + 0.0139359i
\(505\) −5.21132e13 −1.58668
\(506\) 2.94290e13i 0.887203i
\(507\) −1.04490e13 + 8.12280e11i −0.311913 + 0.0242474i
\(508\) −2.09107e13 −0.618087
\(509\) 6.07337e13i 1.77763i −0.458269 0.888813i \(-0.651530\pi\)
0.458269 0.888813i \(-0.348470\pi\)
\(510\) −1.38054e12 1.77589e13i −0.0400126 0.514712i
\(511\) 7.25016e11 0.0208086
\(512\) 1.55494e12i 0.0441942i
\(513\) −2.16577e13 + 5.13377e12i −0.609574 + 0.144494i
\(514\) 2.89501e13 0.806928
\(515\) 1.36576e13i 0.376997i
\(516\) 4.54307e12 3.53168e11i 0.124194 0.00965456i
\(517\) −7.67166e12 −0.207700
\(518\) 1.29980e12i 0.0348520i
\(519\) −2.37785e12 3.05881e13i −0.0631464 0.812299i
\(520\) 1.71811e13 0.451891
\(521\) 2.06244e13i 0.537270i −0.963242 0.268635i \(-0.913427\pi\)
0.963242 0.268635i \(-0.0865726\pi\)
\(522\) −3.92476e13 + 6.13914e12i −1.01265 + 0.158400i
\(523\) 5.24376e13 1.34009 0.670045 0.742320i \(-0.266275\pi\)
0.670045 + 0.742320i \(0.266275\pi\)
\(524\) 2.12735e13i 0.538495i
\(525\) −2.18517e12 + 1.69871e11i −0.0547885 + 0.00425914i
\(526\) 3.81460e13 0.947370
\(527\) 2.07996e13i 0.511683i
\(528\) 1.15166e12 + 1.48147e13i 0.0280644 + 0.361014i
\(529\) 1.03402e13 0.249603
\(530\) 5.00652e13i 1.19717i
\(531\) −4.45925e12 2.85080e13i −0.105631 0.675297i
\(532\) 5.32541e11 0.0124967
\(533\) 1.10510e13i 0.256900i
\(534\) 2.84992e13 2.21547e12i 0.656337 0.0510221i
\(535\) −1.16221e14 −2.65165
\(536\) 7.77110e12i 0.175654i
\(537\) 5.58492e12 + 7.18431e13i 0.125068 + 1.60884i
\(538\) −3.03260e13 −0.672828
\(539\) 6.57877e13i 1.44611i
\(540\) 8.16480e12 + 3.44447e13i 0.177818 + 0.750159i
\(541\) 8.20249e13 1.76994 0.884972 0.465645i \(-0.154178\pi\)
0.884972 + 0.465645i \(0.154178\pi\)
\(542\) 3.96770e13i 0.848286i
\(543\) 6.01919e13 4.67919e12i 1.27509 0.0991223i
\(544\) 3.98798e12 0.0837064
\(545\) 2.61844e13i 0.544578i
\(546\) −8.79477e10 1.13134e12i −0.00181243 0.0233147i
\(547\) −1.62332e13 −0.331488 −0.165744 0.986169i \(-0.553003\pi\)
−0.165744 + 0.986169i \(0.553003\pi\)
\(548\) 4.73872e13i 0.958867i
\(549\) −3.57580e12 + 5.59329e11i −0.0716987 + 0.0112152i
\(550\) −7.10004e13 −1.41074
\(551\) 4.61189e13i 0.908074i
\(552\) −1.56490e13 + 1.21652e12i −0.305346 + 0.0237369i
\(553\) −1.25140e12 −0.0241974
\(554\) 3.83715e13i 0.735292i
\(555\) 7.77424e12 + 1.00006e14i 0.147636 + 1.89916i
\(556\) −4.07335e13 −0.766615
\(557\) 1.12168e13i 0.209215i −0.994514 0.104608i \(-0.966641\pi\)
0.994514 0.104608i \(-0.0333587\pi\)
\(558\) −6.38805e12 4.08389e13i −0.118086 0.754924i
\(559\) −1.12726e13 −0.206521
\(560\) 8.46958e11i 0.0153788i
\(561\) −3.79955e13 + 2.95369e12i −0.683783 + 0.0531557i
\(562\) 5.52506e12 0.0985497
\(563\) 7.98522e13i 1.41171i −0.708357 0.705854i \(-0.750563\pi\)
0.708357 0.705854i \(-0.249437\pi\)
\(564\) −3.17127e11 4.07945e12i −0.00555697 0.0714835i
\(565\) 6.71230e13 1.16581
\(566\) 2.25462e13i 0.388142i
\(567\) 2.22632e12 7.13953e11i 0.0379902 0.0121830i
\(568\) −1.42881e13 −0.241675
\(569\) 9.95594e11i 0.0166925i −0.999965 0.00834624i \(-0.997343\pi\)
0.999965 0.00834624i \(-0.00265672\pi\)
\(570\) 4.09734e13 3.18518e12i 0.680969 0.0529370i
\(571\) 1.07836e14 1.77657 0.888283 0.459297i \(-0.151899\pi\)
0.888283 + 0.459297i \(0.151899\pi\)
\(572\) 3.67593e13i 0.600326i
\(573\) −2.97664e12 3.82907e13i −0.0481895 0.619899i
\(574\) 5.44769e11 0.00874285
\(575\) 7.49989e13i 1.19321i
\(576\) −7.83021e12 + 1.22481e12i −0.123498 + 0.0193177i
\(577\) 3.31000e13 0.517546 0.258773 0.965938i \(-0.416682\pi\)
0.258773 + 0.965938i \(0.416682\pi\)
\(578\) 3.53887e13i 0.548562i
\(579\) −9.16671e13 + 7.12600e12i −1.40871 + 0.109510i
\(580\) 7.33480e13 1.11750
\(581\) 7.34648e11i 0.0110968i
\(582\) 4.57989e12 + 5.89145e13i 0.0685867 + 0.882282i
\(583\) −1.07116e14 −1.59041
\(584\) 1.25266e13i 0.184404i
\(585\) −1.35333e13 8.65184e13i −0.197526 1.26278i
\(586\) −3.56543e13 −0.515969
\(587\) 1.21022e14i 1.73650i 0.496131 + 0.868248i \(0.334754\pi\)
−0.496131 + 0.868248i \(0.665246\pi\)
\(588\) 3.49830e13 2.71950e12i 0.497703 0.0386903i
\(589\) −4.79889e13 −0.676961
\(590\) 5.32774e13i 0.745217i
\(591\) −3.56717e12 4.58873e13i −0.0494751 0.636436i
\(592\) −2.24576e13 −0.308855
\(593\) 8.43944e12i 0.115091i −0.998343 0.0575453i \(-0.981673\pi\)
0.998343 0.0575453i \(-0.0183274\pi\)
\(594\) 7.36952e13 1.74688e13i 0.996567 0.236227i
\(595\) 2.17220e12 0.0291283
\(596\) 4.13596e13i 0.549977i
\(597\) 1.21847e13 9.47213e11i 0.160673 0.0124904i
\(598\) 3.88294e13 0.507756
\(599\) 3.11882e13i 0.404443i 0.979340 + 0.202221i \(0.0648160\pi\)
−0.979340 + 0.202221i \(0.935184\pi\)
\(600\) −2.93498e12 3.77549e13i −0.0377441 0.485531i
\(601\) 2.87401e13 0.366535 0.183267 0.983063i \(-0.441333\pi\)
0.183267 + 0.983063i \(0.441333\pi\)
\(602\) 5.55692e11i 0.00702832i
\(603\) −3.91328e13 + 6.12119e12i −0.490857 + 0.0767802i
\(604\) −1.58031e13 −0.196588
\(605\) 1.37212e14i 1.69284i
\(606\) −5.92893e13 + 4.60902e12i −0.725459 + 0.0563956i
\(607\) −4.47536e13 −0.543106 −0.271553 0.962423i \(-0.587537\pi\)
−0.271553 + 0.962423i \(0.587537\pi\)
\(608\) 9.20110e12i 0.110744i
\(609\) −3.75459e11 4.82981e12i −0.00448204 0.0576559i
\(610\) 6.68264e12 0.0791223
\(611\) 1.01222e13i 0.118869i
\(612\) −3.14128e12 2.00822e13i −0.0365889 0.233913i
\(613\) 6.78051e13 0.783358 0.391679 0.920102i \(-0.371894\pi\)
0.391679 + 0.920102i \(0.371894\pi\)
\(614\) 7.46303e13i 0.855211i
\(615\) 4.19143e13 3.25832e12i 0.476416 0.0370355i
\(616\) −1.81209e12 −0.0204303
\(617\) 2.48261e12i 0.0277641i −0.999904 0.0138820i \(-0.995581\pi\)
0.999904 0.0138820i \(-0.00441893\pi\)
\(618\) 1.20791e12 + 1.55383e13i 0.0133996 + 0.172370i
\(619\) 1.64000e13 0.180464 0.0902320 0.995921i \(-0.471239\pi\)
0.0902320 + 0.995921i \(0.471239\pi\)
\(620\) 7.63220e13i 0.833088i
\(621\) 1.84526e13 + 7.78454e13i 0.199801 + 0.842898i
\(622\) 3.78559e13 0.406613
\(623\) 3.48592e12i 0.0371431i
\(624\) 1.95470e13 1.51954e12i 0.206612 0.0160616i
\(625\) −4.57873e13 −0.480114
\(626\) 3.92175e13i 0.407951i
\(627\) −6.81476e12 8.76635e13i −0.0703255 0.904651i
\(628\) −4.97317e13 −0.509138
\(629\) 5.75973e13i 0.584991i
\(630\) −4.26501e12 + 6.67137e11i −0.0429752 + 0.00672221i
\(631\) −1.37258e13 −0.137211 −0.0686056 0.997644i \(-0.521855\pi\)
−0.0686056 + 0.997644i \(0.521855\pi\)
\(632\) 2.16213e13i 0.214435i
\(633\) 1.15070e14 8.94532e12i 1.13226 0.0880192i
\(634\) −3.01171e13 −0.294014
\(635\) 1.96790e14i 1.90605i
\(636\) −4.42789e12 5.69593e13i −0.0425511 0.547367i
\(637\) −8.68020e13 −0.827623
\(638\) 1.56930e14i 1.48457i
\(639\) 1.12545e13 + 7.19503e13i 0.105639 + 0.675349i
\(640\) 1.46335e13 0.136285
\(641\) 5.42348e13i 0.501173i −0.968094 0.250587i \(-0.919377\pi\)
0.968094 0.250587i \(-0.0806235\pi\)
\(642\) −1.32225e14 + 1.02789e13i −1.21238 + 0.0942477i
\(643\) −5.54693e13 −0.504659 −0.252329 0.967641i \(-0.581197\pi\)
−0.252329 + 0.967641i \(0.581197\pi\)
\(644\) 1.91414e12i 0.0172800i
\(645\) 3.32365e12 + 4.27546e13i 0.0297726 + 0.382987i
\(646\) −2.35982e13 −0.209757
\(647\) 5.56652e13i 0.490979i 0.969399 + 0.245489i \(0.0789486\pi\)
−0.969399 + 0.245489i \(0.921051\pi\)
\(648\) 1.23355e13 + 3.84657e13i 0.107965 + 0.336665i
\(649\) 1.13988e14 0.990002
\(650\) 9.36799e13i 0.807383i
\(651\) 5.02564e12 3.90682e11i 0.0429820 0.00334132i
\(652\) 7.13935e13 0.605927
\(653\) 5.56792e13i 0.468951i −0.972122 0.234475i \(-0.924663\pi\)
0.972122 0.234475i \(-0.0753372\pi\)
\(654\) 2.31581e12 + 2.97901e13i 0.0193560 + 0.248991i
\(655\) 2.00204e14 1.66060
\(656\) 9.41238e12i 0.0774784i
\(657\) 6.30802e13 9.86706e12i 0.515307 0.0806048i
\(658\) 4.98984e11 0.00404536
\(659\) 1.52699e14i 1.22860i 0.789074 + 0.614298i \(0.210561\pi\)
−0.789074 + 0.614298i \(0.789439\pi\)
\(660\) −1.39421e14 + 1.08383e13i −1.11329 + 0.0865446i
\(661\) −2.08036e14 −1.64866 −0.824329 0.566111i \(-0.808447\pi\)
−0.824329 + 0.566111i \(0.808447\pi\)
\(662\) 1.06793e14i 0.839945i
\(663\) 3.89717e12 + 5.01323e13i 0.0304216 + 0.391336i
\(664\) 1.26931e13 0.0983390
\(665\) 5.01172e12i 0.0385371i
\(666\) 1.76895e13 + 1.13089e14i 0.135004 + 0.863080i
\(667\) 1.65767e14 1.25565
\(668\) 6.44300e13i 0.484402i
\(669\) −5.70737e13 + 4.43679e12i −0.425898 + 0.0331084i
\(670\) 7.31335e13 0.541680
\(671\) 1.42977e13i 0.105112i
\(672\) −7.49071e10 9.63587e11i −0.000546609 0.00703144i
\(673\) −9.45260e13 −0.684662 −0.342331 0.939579i \(-0.611216\pi\)
−0.342331 + 0.939579i \(0.611216\pi\)
\(674\) 9.39679e13i 0.675585i
\(675\) −1.87810e14 + 4.45186e13i −1.34029 + 0.317704i
\(676\) 2.20824e13 0.156427
\(677\) 1.70106e14i 1.19612i −0.801451 0.598060i \(-0.795938\pi\)
0.801451 0.598060i \(-0.204062\pi\)
\(678\) 7.63660e13 5.93652e12i 0.533030 0.0414366i
\(679\) −7.20622e12 −0.0499297
\(680\) 3.75308e13i 0.258133i
\(681\) 8.04237e12 + 1.03455e14i 0.0549096 + 0.706344i
\(682\) 1.63293e14 1.10674
\(683\) 2.23578e14i 1.50427i 0.659009 + 0.752135i \(0.270976\pi\)
−0.659009 + 0.752135i \(0.729024\pi\)
\(684\) 4.63338e13 7.24758e12i 0.309469 0.0484075i
\(685\) −4.45960e14 −2.95694
\(686\) 8.56481e12i 0.0563764i
\(687\) 2.51163e14 1.95249e13i 1.64124 0.127586i
\(688\) −9.60110e12 −0.0622843
\(689\) 1.41331e14i 0.910210i
\(690\) −1.14486e13 1.47273e14i −0.0731996 0.941622i
\(691\) −1.10134e13 −0.0699090 −0.0349545 0.999389i \(-0.511129\pi\)
−0.0349545 + 0.999389i \(0.511129\pi\)
\(692\) 6.46435e13i 0.407375i
\(693\) 1.42735e12 + 9.12509e12i 0.00893029 + 0.0570915i
\(694\) −9.95468e13 −0.618344
\(695\) 3.83341e14i 2.36408i
\(696\) 8.34482e13 6.48708e12i 0.510941 0.0397194i
\(697\) −2.41401e13 −0.146749
\(698\) 2.09078e14i 1.26192i
\(699\) −1.95426e13 2.51392e14i −0.117111 1.50649i
\(700\) 4.61804e12 0.0274769
\(701\) 1.10962e14i 0.655516i −0.944762 0.327758i \(-0.893707\pi\)
0.944762 0.327758i \(-0.106293\pi\)
\(702\) −2.30488e13 9.72354e13i −0.135195 0.570346i
\(703\) 1.32889e14 0.773948
\(704\) 3.13087e13i 0.181052i
\(705\) 3.83915e13 2.98447e12i 0.220440 0.0171365i
\(706\) 2.08338e13 0.118781
\(707\) 7.25206e12i 0.0410548i
\(708\) 4.71199e12 + 6.06138e13i 0.0264873 + 0.340726i
\(709\) 2.08219e14 1.16222 0.581112 0.813824i \(-0.302618\pi\)
0.581112 + 0.813824i \(0.302618\pi\)
\(710\) 1.34465e14i 0.745275i
\(711\) −1.08878e14 + 1.70308e13i −0.599229 + 0.0937318i
\(712\) −6.02289e13 −0.329158
\(713\) 1.72489e14i 0.936080i
\(714\) 2.47132e12 1.92115e11i 0.0133180 0.00103531i
\(715\) 3.45940e14 1.85127
\(716\) 1.51830e14i 0.806848i
\(717\) −2.32946e13 2.99656e14i −0.122931 1.58135i
\(718\) −1.39746e14 −0.732347
\(719\) 2.74910e14i 1.43069i 0.698771 + 0.715346i \(0.253731\pi\)
−0.698771 + 0.715346i \(0.746269\pi\)
\(720\) −1.15266e13 7.36898e13i −0.0595716 0.380842i
\(721\) −1.90059e12 −0.00975465
\(722\) 8.42844e13i 0.429597i
\(723\) −2.51746e14 + 1.95702e13i −1.27430 + 0.0990613i
\(724\) −1.27207e14 −0.639466
\(725\) 3.99930e14i 1.99661i
\(726\) 1.21354e13 + 1.56107e14i 0.0601688 + 0.773997i
\(727\) −2.99071e14 −1.47266 −0.736330 0.676622i \(-0.763443\pi\)
−0.736330 + 0.676622i \(0.763443\pi\)
\(728\) 2.39092e12i 0.0116925i
\(729\) 1.83985e14 9.24165e13i 0.893602 0.448861i
\(730\) −1.17888e14 −0.568662
\(731\) 2.46241e13i 0.117970i
\(732\) 7.60286e12 5.91030e11i 0.0361761 0.00281225i
\(733\) 1.19922e14 0.566734 0.283367 0.959012i \(-0.408549\pi\)
0.283367 + 0.959012i \(0.408549\pi\)
\(734\) 1.85404e14i 0.870241i
\(735\) 2.55931e13 + 3.29223e14i 0.119313 + 1.53481i
\(736\) 3.30719e13 0.153134
\(737\) 1.56471e14i 0.719608i
\(738\) 4.73978e13 7.41400e12i 0.216509 0.0338666i
\(739\) −7.29345e13 −0.330911 −0.165455 0.986217i \(-0.552909\pi\)
−0.165455 + 0.986217i \(0.552909\pi\)
\(740\) 2.11348e14i 0.952443i
\(741\) −1.15666e14 + 8.99158e12i −0.517742 + 0.0402481i
\(742\) 6.96706e12 0.0309763
\(743\) 1.07061e14i 0.472809i −0.971655 0.236405i \(-0.924031\pi\)
0.971655 0.236405i \(-0.0759691\pi\)
\(744\) 6.75011e12 + 8.68317e13i 0.0296105 + 0.380902i
\(745\) 3.89234e14 1.69601
\(746\) 2.05304e14i 0.888592i
\(747\) −9.99815e12 6.39183e13i −0.0429850 0.274803i
\(748\) 8.02979e13 0.342923
\(749\) 1.61733e13i 0.0686104i
\(750\) 9.73587e13 7.56845e12i 0.410269 0.0318934i
\(751\) 1.83777e14 0.769292 0.384646 0.923064i \(-0.374323\pi\)
0.384646 + 0.923064i \(0.374323\pi\)
\(752\) 8.62131e12i 0.0358496i
\(753\) 1.06744e13 + 1.37313e14i 0.0440931 + 0.567203i
\(754\) −2.07057e14 −0.849638
\(755\) 1.48722e14i 0.606236i
\(756\) −4.79332e12 + 1.13621e12i −0.0194101 + 0.00460098i
\(757\) −1.73049e14 −0.696130 −0.348065 0.937470i \(-0.613161\pi\)
−0.348065 + 0.937470i \(0.613161\pi\)
\(758\) 2.66589e14i 1.06536i
\(759\) −3.15093e14 + 2.44946e13i −1.25092 + 0.0972438i
\(760\) −8.65912e13 −0.341512
\(761\) 1.10156e14i 0.431604i −0.976437 0.215802i \(-0.930764\pi\)
0.976437 0.215802i \(-0.0692365\pi\)
\(762\) −1.74046e13 2.23888e14i −0.0677467 0.871477i
\(763\) −3.64382e12 −0.0140907
\(764\) 8.09218e13i 0.310884i
\(765\) 1.88993e14 2.95625e13i 0.721338 0.112832i
\(766\) 1.54395e14 0.585449
\(767\) 1.50399e14i 0.566589i
\(768\) 1.66486e13 1.29423e12i 0.0623120 0.00484400i
\(769\) 2.30458e14 0.856959