Properties

Label 150.11.b.a.149.4
Level $150$
Weight $11$
Character 150.149
Analytic conductor $95.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 150.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(95.3035879011\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3421020160000.10
Defining polynomial: \(x^{8} + 967 x^{4} + 194481\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{26}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.4
Root \(2.90605 + 2.90605i\) of defining polynomial
Character \(\chi\) \(=\) 150.149
Dual form 150.11.b.a.149.3

$q$-expansion

\(f(q)\) \(=\) \(q-22.6274 q^{2} +(18.8335 + 242.269i) q^{3} +512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530i q^{7} -11585.2 q^{8} +(-58339.6 + 9125.53i) q^{9} +O(q^{10})\) \(q-22.6274 q^{2} +(18.8335 + 242.269i) q^{3} +512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530i q^{7} -11585.2 q^{8} +(-58339.6 + 9125.53i) q^{9} +233268. i q^{11} +(9642.73 + 124042. i) q^{12} +307781. i q^{13} +15172.4i q^{14} +262144. q^{16} +672324. q^{17} +(1.32007e6 - 206487. i) q^{18} +1.55119e6 q^{19} +(162449. - 12628.4i) q^{21} -5.27826e6i q^{22} -5.57551e6 q^{23} +(-218190. - 2.80674e6i) q^{24} -6.96428e6i q^{26} +(-3.30957e6 - 1.39620e7i) q^{27} -343311. i q^{28} +2.97313e7i q^{29} +3.09368e7 q^{31} -5.93164e6 q^{32} +(-5.65137e7 + 4.39325e6i) q^{33} -1.52130e7 q^{34} +(-2.98699e7 + 4.67227e6i) q^{36} +8.56690e7i q^{37} -3.50994e7 q^{38} +(-7.45657e7 + 5.79657e6i) q^{39} +3.59054e7i q^{41} +(-3.67579e6 + 285748. i) q^{42} -3.66253e7i q^{43} +1.19433e8i q^{44} +1.26159e8 q^{46} +3.28877e7 q^{47} +(4.93708e6 + 6.35094e7i) q^{48} +2.82026e8 q^{49} +(1.26622e7 + 1.62883e8i) q^{51} +1.57584e8i q^{52} -4.59194e8 q^{53} +(7.48870e7 + 3.15924e8i) q^{54} +7.76824e6i q^{56} +(2.92143e7 + 3.75805e8i) q^{57} -6.72743e8i q^{58} +4.88657e8i q^{59} -6.12928e7 q^{61} -7.00020e8 q^{62} +(6.11894e6 + 3.91184e7i) q^{63} +1.34218e8 q^{64} +(1.27876e9 - 9.94079e7i) q^{66} +6.70776e8i q^{67} +3.44230e8 q^{68} +(-1.05006e8 - 1.35077e9i) q^{69} +1.23330e9i q^{71} +(6.75878e8 - 1.05721e8i) q^{72} +1.08126e9i q^{73} -1.93847e9i q^{74} +7.94209e8 q^{76} +1.56413e8 q^{77} +(1.68723e9 - 1.31161e8i) q^{78} +1.86628e9 q^{79} +(3.32023e9 - 1.06476e9i) q^{81} -8.12446e8i q^{82} +1.09562e9 q^{83} +(8.31737e7 - 6.46574e6i) q^{84} +8.28736e8i q^{86} +(-7.20298e9 + 5.59944e8i) q^{87} -2.70247e9i q^{88} -5.19876e9i q^{89} +2.06376e8 q^{91} -2.85466e9 q^{92} +(5.82647e8 + 7.49503e9i) q^{93} -7.44163e8 q^{94} +(-1.11713e8 - 1.43705e9i) q^{96} +1.07471e10i q^{97} -6.38151e9 q^{98} +(-2.12870e9 - 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + O(q^{10}) \) \( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.6274 −0.707107
\(3\) 18.8335 + 242.269i 0.0775039 + 0.996992i
\(4\) 512.000 0.500000
\(5\) 0 0
\(6\) −426.153 5481.92i −0.0548036 0.704980i
\(7\) 670.530i 0.0398959i −0.999801 0.0199479i \(-0.993650\pi\)
0.999801 0.0199479i \(-0.00635004\pi\)
\(8\) −11585.2 −0.353553
\(9\) −58339.6 + 9125.53i −0.987986 + 0.154542i
\(10\) 0 0
\(11\) 233268.i 1.44841i 0.689583 + 0.724206i \(0.257794\pi\)
−0.689583 + 0.724206i \(0.742206\pi\)
\(12\) 9642.73 + 124042.i 0.0387520 + 0.498496i
\(13\) 307781.i 0.828943i 0.910062 + 0.414471i \(0.136033\pi\)
−0.910062 + 0.414471i \(0.863967\pi\)
\(14\) 15172.4i 0.0282106i
\(15\) 0 0
\(16\) 262144. 0.250000
\(17\) 672324. 0.473515 0.236758 0.971569i \(-0.423915\pi\)
0.236758 + 0.971569i \(0.423915\pi\)
\(18\) 1.32007e6 206487.i 0.698612 0.109277i
\(19\) 1.55119e6 0.626465 0.313233 0.949676i \(-0.398588\pi\)
0.313233 + 0.949676i \(0.398588\pi\)
\(20\) 0 0
\(21\) 162449. 12628.4i 0.0397758 0.00309209i
\(22\) 5.27826e6i 1.02418i
\(23\) −5.57551e6 −0.866255 −0.433127 0.901333i \(-0.642590\pi\)
−0.433127 + 0.901333i \(0.642590\pi\)
\(24\) −218190. 2.80674e6i −0.0274018 0.352490i
\(25\) 0 0
\(26\) 6.96428e6i 0.586151i
\(27\) −3.30957e6 1.39620e7i −0.230650 0.973037i
\(28\) 343311.i 0.0199479i
\(29\) 2.97313e7i 1.44952i 0.689001 + 0.724760i \(0.258049\pi\)
−0.689001 + 0.724760i \(0.741951\pi\)
\(30\) 0 0
\(31\) 3.09368e7 1.08061 0.540303 0.841471i \(-0.318310\pi\)
0.540303 + 0.841471i \(0.318310\pi\)
\(32\) −5.93164e6 −0.176777
\(33\) −5.65137e7 + 4.39325e6i −1.44406 + 0.112258i
\(34\) −1.52130e7 −0.334826
\(35\) 0 0
\(36\) −2.98699e7 + 4.67227e6i −0.493993 + 0.0772708i
\(37\) 8.56690e7i 1.23542i 0.786406 + 0.617711i \(0.211940\pi\)
−0.786406 + 0.617711i \(0.788060\pi\)
\(38\) −3.50994e7 −0.442978
\(39\) −7.45657e7 + 5.79657e6i −0.826449 + 0.0642463i
\(40\) 0 0
\(41\) 3.59054e7i 0.309913i 0.987921 + 0.154957i \(0.0495238\pi\)
−0.987921 + 0.154957i \(0.950476\pi\)
\(42\) −3.67579e6 + 285748.i −0.0281258 + 0.00218644i
\(43\) 3.66253e7i 0.249137i −0.992211 0.124569i \(-0.960245\pi\)
0.992211 0.124569i \(-0.0397547\pi\)
\(44\) 1.19433e8i 0.724206i
\(45\) 0 0
\(46\) 1.26159e8 0.612535
\(47\) 3.28877e7 0.143398 0.0716992 0.997426i \(-0.477158\pi\)
0.0716992 + 0.997426i \(0.477158\pi\)
\(48\) 4.93708e6 + 6.35094e7i 0.0193760 + 0.249248i
\(49\) 2.82026e8 0.998408
\(50\) 0 0
\(51\) 1.26622e7 + 1.62883e8i 0.0366993 + 0.472091i
\(52\) 1.57584e8i 0.414471i
\(53\) −4.59194e8 −1.09804 −0.549019 0.835810i \(-0.684998\pi\)
−0.549019 + 0.835810i \(0.684998\pi\)
\(54\) 7.48870e7 + 3.15924e8i 0.163094 + 0.688041i
\(55\) 0 0
\(56\) 7.76824e6i 0.0141053i
\(57\) 2.92143e7 + 3.75805e8i 0.0485535 + 0.624581i
\(58\) 6.72743e8i 1.02497i
\(59\) 4.88657e8i 0.683508i 0.939789 + 0.341754i \(0.111021\pi\)
−0.939789 + 0.341754i \(0.888979\pi\)
\(60\) 0 0
\(61\) −6.12928e7 −0.0725705 −0.0362852 0.999341i \(-0.511552\pi\)
−0.0362852 + 0.999341i \(0.511552\pi\)
\(62\) −7.00020e8 −0.764103
\(63\) 6.11894e6 + 3.91184e7i 0.00616557 + 0.0394166i
\(64\) 1.34218e8 0.125000
\(65\) 0 0
\(66\) 1.27876e9 9.94079e7i 1.02110 0.0793782i
\(67\) 6.70776e8i 0.496825i 0.968654 + 0.248413i \(0.0799089\pi\)
−0.968654 + 0.248413i \(0.920091\pi\)
\(68\) 3.44230e8 0.236758
\(69\) −1.05006e8 1.35077e9i −0.0671382 0.863649i
\(70\) 0 0
\(71\) 1.23330e9i 0.683561i 0.939780 + 0.341781i \(0.111030\pi\)
−0.939780 + 0.341781i \(0.888970\pi\)
\(72\) 6.75878e8 1.05721e8i 0.349306 0.0546387i
\(73\) 1.08126e9i 0.521573i 0.965396 + 0.260787i \(0.0839819\pi\)
−0.965396 + 0.260787i \(0.916018\pi\)
\(74\) 1.93847e9i 0.873575i
\(75\) 0 0
\(76\) 7.94209e8 0.313233
\(77\) 1.56413e8 0.0577857
\(78\) 1.68723e9 1.31161e8i 0.584388 0.0454290i
\(79\) 1.86628e9 0.606515 0.303258 0.952909i \(-0.401926\pi\)
0.303258 + 0.952909i \(0.401926\pi\)
\(80\) 0 0
\(81\) 3.32023e9 1.06476e9i 0.952234 0.305370i
\(82\) 8.12446e8i 0.219142i
\(83\) 1.09562e9 0.278145 0.139072 0.990282i \(-0.455588\pi\)
0.139072 + 0.990282i \(0.455588\pi\)
\(84\) 8.31737e7 6.46574e6i 0.0198879 0.00154604i
\(85\) 0 0
\(86\) 8.28736e8i 0.176167i
\(87\) −7.20298e9 + 5.59944e8i −1.44516 + 0.112344i
\(88\) 2.70247e9i 0.512091i
\(89\) 5.19876e9i 0.931000i −0.885048 0.465500i \(-0.845874\pi\)
0.885048 0.465500i \(-0.154126\pi\)
\(90\) 0 0
\(91\) 2.06376e8 0.0330714
\(92\) −2.85466e9 −0.433127
\(93\) 5.82647e8 + 7.49503e9i 0.0837512 + 1.07735i
\(94\) −7.44163e8 −0.101398
\(95\) 0 0
\(96\) −1.11713e8 1.43705e9i −0.0137009 0.176245i
\(97\) 1.07471e10i 1.25150i 0.780024 + 0.625750i \(0.215207\pi\)
−0.780024 + 0.625750i \(0.784793\pi\)
\(98\) −6.38151e9 −0.705981
\(99\) −2.12870e9 1.36088e10i −0.223840 1.43101i
\(100\) 0 0
\(101\) 1.08154e10i 1.02905i −0.857475 0.514525i \(-0.827968\pi\)
0.857475 0.514525i \(-0.172032\pi\)
\(102\) −2.86513e8 3.68563e9i −0.0259503 0.333819i
\(103\) 2.83446e9i 0.244503i −0.992499 0.122251i \(-0.960989\pi\)
0.992499 0.122251i \(-0.0390114\pi\)
\(104\) 3.56571e9i 0.293075i
\(105\) 0 0
\(106\) 1.03904e10 0.776430
\(107\) −2.41202e10 −1.71974 −0.859869 0.510515i \(-0.829455\pi\)
−0.859869 + 0.510515i \(0.829455\pi\)
\(108\) −1.69450e9 7.14855e9i −0.115325 0.486518i
\(109\) 5.43424e9 0.353188 0.176594 0.984284i \(-0.443492\pi\)
0.176594 + 0.984284i \(0.443492\pi\)
\(110\) 0 0
\(111\) −2.07549e10 + 1.61344e9i −1.23170 + 0.0957500i
\(112\) 1.75775e8i 0.00997396i
\(113\) −1.39305e10 −0.756092 −0.378046 0.925787i \(-0.623404\pi\)
−0.378046 + 0.925787i \(0.623404\pi\)
\(114\) −6.61043e8 8.50350e9i −0.0343325 0.441645i
\(115\) 0 0
\(116\) 1.52224e10i 0.724760i
\(117\) −2.80866e9 1.79558e10i −0.128106 0.818984i
\(118\) 1.10570e10i 0.483313i
\(119\) 4.50813e8i 0.0188913i
\(120\) 0 0
\(121\) −2.84767e10 −1.09790
\(122\) 1.38690e9 0.0513151
\(123\) −8.69877e9 + 6.76223e8i −0.308981 + 0.0240195i
\(124\) 1.58396e10 0.540303
\(125\) 0 0
\(126\) −1.38456e8 8.85149e8i −0.00435972 0.0278717i
\(127\) 4.08412e10i 1.23617i −0.786110 0.618087i \(-0.787908\pi\)
0.786110 0.618087i \(-0.212092\pi\)
\(128\) −3.03700e9 −0.0883883
\(129\) 8.87317e9 6.89781e8i 0.248388 0.0193091i
\(130\) 0 0
\(131\) 4.15498e10i 1.07699i 0.842628 + 0.538495i \(0.181007\pi\)
−0.842628 + 0.538495i \(0.818993\pi\)
\(132\) −2.89350e10 + 2.24934e9i −0.722028 + 0.0561289i
\(133\) 1.04012e9i 0.0249934i
\(134\) 1.51779e10i 0.351308i
\(135\) 0 0
\(136\) −7.78903e9 −0.167413
\(137\) −9.25532e10 −1.91773 −0.958867 0.283854i \(-0.908387\pi\)
−0.958867 + 0.283854i \(0.908387\pi\)
\(138\) 2.37602e9 + 3.05645e10i 0.0474739 + 0.610692i
\(139\) −7.95575e10 −1.53323 −0.766615 0.642107i \(-0.778061\pi\)
−0.766615 + 0.642107i \(0.778061\pi\)
\(140\) 0 0
\(141\) 6.19389e8 + 7.96767e9i 0.0111139 + 0.142967i
\(142\) 2.79064e10i 0.483351i
\(143\) −7.17955e10 −1.20065
\(144\) −1.52934e10 + 2.39220e9i −0.246997 + 0.0386354i
\(145\) 0 0
\(146\) 2.44661e10i 0.368808i
\(147\) 5.31152e9 + 6.83261e10i 0.0773806 + 0.995405i
\(148\) 4.38625e10i 0.617711i
\(149\) 8.07804e10i 1.09995i −0.835180 0.549977i \(-0.814636\pi\)
0.835180 0.549977i \(-0.185364\pi\)
\(150\) 0 0
\(151\) 3.08654e10 0.393176 0.196588 0.980486i \(-0.437014\pi\)
0.196588 + 0.980486i \(0.437014\pi\)
\(152\) −1.79709e10 −0.221489
\(153\) −3.92231e10 + 6.13531e9i −0.467827 + 0.0731778i
\(154\) −3.53923e9 −0.0408606
\(155\) 0 0
\(156\) −3.81776e10 + 2.96785e9i −0.413225 + 0.0321232i
\(157\) 9.71322e10i 1.01828i −0.860685 0.509138i \(-0.829964\pi\)
0.860685 0.509138i \(-0.170036\pi\)
\(158\) −4.22291e10 −0.428871
\(159\) −8.64822e9 1.11249e11i −0.0851023 1.09473i
\(160\) 0 0
\(161\) 3.73855e9i 0.0345600i
\(162\) −7.51283e10 + 2.40928e10i −0.673331 + 0.215929i
\(163\) 1.39440e11i 1.21185i −0.795520 0.605927i \(-0.792802\pi\)
0.795520 0.605927i \(-0.207198\pi\)
\(164\) 1.83836e10i 0.154957i
\(165\) 0 0
\(166\) −2.47911e10 −0.196678
\(167\) −1.25840e11 −0.968804 −0.484402 0.874845i \(-0.660963\pi\)
−0.484402 + 0.874845i \(0.660963\pi\)
\(168\) −1.88201e9 + 1.46303e8i −0.0140629 + 0.00109322i
\(169\) 4.31296e10 0.312854
\(170\) 0 0
\(171\) −9.04958e10 + 1.41554e10i −0.618939 + 0.0968149i
\(172\) 1.87521e10i 0.124569i
\(173\) 1.26257e11 0.814750 0.407375 0.913261i \(-0.366444\pi\)
0.407375 + 0.913261i \(0.366444\pi\)
\(174\) 1.62985e11 1.26701e10i 1.02188 0.0794389i
\(175\) 0 0
\(176\) 6.11499e10i 0.362103i
\(177\) −1.18386e11 + 9.20310e9i −0.681452 + 0.0529746i
\(178\) 1.17635e11i 0.658317i
\(179\) 2.96543e11i 1.61370i −0.590758 0.806848i \(-0.701171\pi\)
0.590758 0.806848i \(-0.298829\pi\)
\(180\) 0 0
\(181\) 2.48451e11 1.27893 0.639466 0.768819i \(-0.279155\pi\)
0.639466 + 0.768819i \(0.279155\pi\)
\(182\) −4.66976e9 −0.0233850
\(183\) −1.15435e9 1.48493e10i −0.00562450 0.0723522i
\(184\) 6.45936e10 0.306267
\(185\) 0 0
\(186\) −1.31838e10 1.69593e11i −0.0592210 0.761805i
\(187\) 1.56832e11i 0.685846i
\(188\) 1.68385e10 0.0716992
\(189\) −9.36194e9 + 2.21916e9i −0.0388201 + 0.00920196i
\(190\) 0 0
\(191\) 1.58050e11i 0.621769i −0.950448 0.310884i \(-0.899375\pi\)
0.950448 0.310884i \(-0.100625\pi\)
\(192\) 2.52778e9 + 3.25168e10i 0.00968799 + 0.124624i
\(193\) 3.78369e11i 1.41296i −0.707734 0.706479i \(-0.750283\pi\)
0.707734 0.706479i \(-0.249717\pi\)
\(194\) 2.43178e11i 0.884944i
\(195\) 0 0
\(196\) 1.44397e11 0.499204
\(197\) −1.89406e11 −0.638356 −0.319178 0.947695i \(-0.603407\pi\)
−0.319178 + 0.947695i \(0.603407\pi\)
\(198\) 4.81669e10 + 3.07932e11i 0.158279 + 1.01188i
\(199\) −5.02942e10 −0.161158 −0.0805791 0.996748i \(-0.525677\pi\)
−0.0805791 + 0.996748i \(0.525677\pi\)
\(200\) 0 0
\(201\) −1.62508e11 + 1.26330e10i −0.495331 + 0.0385059i
\(202\) 2.44725e11i 0.727648i
\(203\) 1.99357e10 0.0578298
\(204\) 6.48304e9 + 8.33962e10i 0.0183496 + 0.236045i
\(205\) 0 0
\(206\) 6.41365e10i 0.172890i
\(207\) 3.25273e11 5.08795e10i 0.855848 0.133872i
\(208\) 8.06828e10i 0.207236i
\(209\) 3.61843e11i 0.907380i
\(210\) 0 0
\(211\) 4.74970e11 1.13567 0.567837 0.823141i \(-0.307780\pi\)
0.567837 + 0.823141i \(0.307780\pi\)
\(212\) −2.35108e11 −0.549019
\(213\) −2.98791e11 + 2.32273e10i −0.681505 + 0.0529787i
\(214\) 5.45778e11 1.21604
\(215\) 0 0
\(216\) 3.83422e10 + 1.61753e11i 0.0815470 + 0.344020i
\(217\) 2.07440e10i 0.0431117i
\(218\) −1.22963e11 −0.249742
\(219\) −2.61955e11 + 2.03638e10i −0.520004 + 0.0404240i
\(220\) 0 0
\(221\) 2.06928e11i 0.392517i
\(222\) 4.69631e11 3.65081e10i 0.870947 0.0677055i
\(223\) 2.35580e11i 0.427183i −0.976923 0.213592i \(-0.931484\pi\)
0.976923 0.213592i \(-0.0685162\pi\)
\(224\) 3.97734e9i 0.00705266i
\(225\) 0 0
\(226\) 3.15211e11 0.534638
\(227\) 4.27026e11 0.708475 0.354238 0.935155i \(-0.384740\pi\)
0.354238 + 0.935155i \(0.384740\pi\)
\(228\) 1.49577e10 + 1.92412e11i 0.0242768 + 0.312290i
\(229\) −1.03671e12 −1.64619 −0.823096 0.567902i \(-0.807755\pi\)
−0.823096 + 0.567902i \(0.807755\pi\)
\(230\) 0 0
\(231\) 2.94580e9 + 3.78941e10i 0.00447862 + 0.0576119i
\(232\) 3.44444e11i 0.512483i
\(233\) 1.03766e12 1.51103 0.755516 0.655130i \(-0.227386\pi\)
0.755516 + 0.655130i \(0.227386\pi\)
\(234\) 6.35527e10 + 4.06293e11i 0.0905847 + 0.579109i
\(235\) 0 0
\(236\) 2.50192e11i 0.341754i
\(237\) 3.51485e10 + 4.52142e11i 0.0470073 + 0.604691i
\(238\) 1.02007e10i 0.0133582i
\(239\) 1.23687e12i 1.58612i 0.609144 + 0.793060i \(0.291513\pi\)
−0.609144 + 0.793060i \(0.708487\pi\)
\(240\) 0 0
\(241\) −1.03912e12 −1.27814 −0.639072 0.769147i \(-0.720682\pi\)
−0.639072 + 0.769147i \(0.720682\pi\)
\(242\) 6.44354e11 0.776333
\(243\) 3.20490e11 + 7.84337e11i 0.378253 + 0.925702i
\(244\) −3.13819e10 −0.0362852
\(245\) 0 0
\(246\) 1.96831e11 1.53012e10i 0.218483 0.0169844i
\(247\) 4.77426e11i 0.519304i
\(248\) −3.58410e11 −0.382052
\(249\) 2.06344e10 + 2.65436e11i 0.0215573 + 0.277308i
\(250\) 0 0
\(251\) 5.66781e11i 0.568914i 0.958689 + 0.284457i \(0.0918133\pi\)
−0.958689 + 0.284457i \(0.908187\pi\)
\(252\) 3.13290e9 + 2.00286e10i 0.00308279 + 0.0197083i
\(253\) 1.30059e12i 1.25469i
\(254\) 9.24130e11i 0.874107i
\(255\) 0 0
\(256\) 6.87195e10 0.0625000
\(257\) 1.27943e12 1.14117 0.570584 0.821239i \(-0.306717\pi\)
0.570584 + 0.821239i \(0.306717\pi\)
\(258\) −2.00777e11 + 1.56080e10i −0.175637 + 0.0136536i
\(259\) 5.74436e10 0.0492882
\(260\) 0 0
\(261\) −2.71314e11 1.73451e12i −0.224011 1.43211i
\(262\) 9.40164e11i 0.761548i
\(263\) −1.68583e12 −1.33978 −0.669892 0.742459i \(-0.733660\pi\)
−0.669892 + 0.742459i \(0.733660\pi\)
\(264\) 6.54725e11 5.08968e10i 0.510551 0.0396891i
\(265\) 0 0
\(266\) 2.35352e10i 0.0176730i
\(267\) 1.25950e12 9.79107e10i 0.928200 0.0721562i
\(268\) 3.43437e11i 0.248413i
\(269\) 1.34023e12i 0.951523i 0.879574 + 0.475761i \(0.157827\pi\)
−0.879574 + 0.475761i \(0.842173\pi\)
\(270\) 0 0
\(271\) −1.75349e12 −1.19966 −0.599829 0.800129i \(-0.704765\pi\)
−0.599829 + 0.800129i \(0.704765\pi\)
\(272\) 1.76246e11 0.118379
\(273\) 3.88677e9 + 4.99985e10i 0.00256316 + 0.0329719i
\(274\) 2.09424e12 1.35604
\(275\) 0 0
\(276\) −5.37632e10 6.91597e11i −0.0335691 0.431825i
\(277\) 1.69580e12i 1.03986i −0.854209 0.519930i \(-0.825958\pi\)
0.854209 0.519930i \(-0.174042\pi\)
\(278\) 1.80018e12 1.08416
\(279\) −1.80484e12 + 2.82315e11i −1.06762 + 0.166999i
\(280\) 0 0
\(281\) 2.44175e11i 0.139370i 0.997569 + 0.0696851i \(0.0221995\pi\)
−0.997569 + 0.0696851i \(0.977801\pi\)
\(282\) −1.40152e10 1.80288e11i −0.00785874 0.101093i
\(283\) 9.96409e11i 0.548916i −0.961599 0.274458i \(-0.911502\pi\)
0.961599 0.274458i \(-0.0884984\pi\)
\(284\) 6.31450e11i 0.341781i
\(285\) 0 0
\(286\) 1.62455e12 0.848989
\(287\) 2.40756e10 0.0123643
\(288\) 3.46050e11 5.41294e10i 0.174653 0.0273194i
\(289\) −1.56397e12 −0.775783
\(290\) 0 0
\(291\) −2.60368e12 + 2.02404e11i −1.24774 + 0.0969962i
\(292\) 5.53604e11i 0.260787i
\(293\) 1.57571e12 0.729690 0.364845 0.931068i \(-0.381122\pi\)
0.364845 + 0.931068i \(0.381122\pi\)
\(294\) −1.20186e11 1.54604e12i −0.0547163 0.703858i
\(295\) 0 0
\(296\) 9.92496e11i 0.436787i
\(297\) 3.25690e12 7.72018e11i 1.40936 0.334076i
\(298\) 1.82785e12i 0.777786i
\(299\) 1.71603e12i 0.718076i
\(300\) 0 0
\(301\) −2.45583e10 −0.00993955
\(302\) −6.98405e11 −0.278018
\(303\) 2.62024e12 2.03692e11i 1.02595 0.0797554i
\(304\) 4.06635e11 0.156616
\(305\) 0 0
\(306\) 8.87518e11 1.38826e11i 0.330803 0.0517445i
\(307\) 3.29823e12i 1.20945i 0.796434 + 0.604726i \(0.206717\pi\)
−0.796434 + 0.604726i \(0.793283\pi\)
\(308\) 8.00836e10 0.0288928
\(309\) 6.86702e11 5.33827e10i 0.243768 0.0189499i
\(310\) 0 0
\(311\) 1.67301e12i 0.575038i 0.957775 + 0.287519i \(0.0928304\pi\)
−0.957775 + 0.287519i \(0.907170\pi\)
\(312\) 8.63862e11 6.71547e10i 0.292194 0.0227145i
\(313\) 1.73318e12i 0.576930i 0.957490 + 0.288465i \(0.0931449\pi\)
−0.957490 + 0.288465i \(0.906855\pi\)
\(314\) 2.19785e12i 0.720029i
\(315\) 0 0
\(316\) 9.55536e11 0.303258
\(317\) −1.33100e12 −0.415798 −0.207899 0.978150i \(-0.566663\pi\)
−0.207899 + 0.978150i \(0.566663\pi\)
\(318\) 1.95687e11 + 2.51727e12i 0.0601764 + 0.774094i
\(319\) −6.93538e12 −2.09950
\(320\) 0 0
\(321\) −4.54267e11 5.84358e12i −0.133286 1.71456i
\(322\) 8.45937e10i 0.0244376i
\(323\) 1.04290e12 0.296641
\(324\) 1.69996e12 5.45157e11i 0.476117 0.152685i
\(325\) 0 0
\(326\) 3.15518e12i 0.856911i
\(327\) 1.02345e11 + 1.31655e12i 0.0273735 + 0.352126i
\(328\) 4.15973e11i 0.109571i
\(329\) 2.20522e10i 0.00572100i
\(330\) 0 0
\(331\) 4.71961e12 1.18786 0.593931 0.804516i \(-0.297575\pi\)
0.593931 + 0.804516i \(0.297575\pi\)
\(332\) 5.60959e11 0.139072
\(333\) −7.81775e11 4.99789e12i −0.190924 1.22058i
\(334\) 2.84743e12 0.685048
\(335\) 0 0
\(336\) 4.25849e10 3.31046e9i 0.00994396 0.000773022i
\(337\) 4.15283e12i 0.955422i −0.878517 0.477711i \(-0.841467\pi\)
0.878517 0.477711i \(-0.158533\pi\)
\(338\) −9.75911e11 −0.221221
\(339\) −2.62360e11 3.37493e12i −0.0586001 0.753818i
\(340\) 0 0
\(341\) 7.21658e12i 1.56516i
\(342\) 2.04769e12 3.20301e11i 0.437656 0.0684585i
\(343\) 3.78515e11i 0.0797282i
\(344\) 4.24313e11i 0.0880833i
\(345\) 0 0
\(346\) −2.85687e12 −0.576115
\(347\) −4.39939e12 −0.874470 −0.437235 0.899347i \(-0.644042\pi\)
−0.437235 + 0.899347i \(0.644042\pi\)
\(348\) −3.68793e12 + 2.86691e11i −0.722580 + 0.0561718i
\(349\) 9.24002e12 1.78462 0.892310 0.451423i \(-0.149083\pi\)
0.892310 + 0.451423i \(0.149083\pi\)
\(350\) 0 0
\(351\) 4.29724e12 1.01862e12i 0.806592 0.191195i
\(352\) 1.38366e12i 0.256046i
\(353\) −9.20733e11 −0.167981 −0.0839905 0.996467i \(-0.526767\pi\)
−0.0839905 + 0.996467i \(0.526767\pi\)
\(354\) 2.67878e12 2.08242e11i 0.481860 0.0374587i
\(355\) 0 0
\(356\) 2.66177e12i 0.465500i
\(357\) 1.09218e11 8.49037e9i 0.0188345 0.00146415i
\(358\) 6.70999e12i 1.14106i
\(359\) 6.17595e12i 1.03569i 0.855473 + 0.517847i \(0.173267\pi\)
−0.855473 + 0.517847i \(0.826733\pi\)
\(360\) 0 0
\(361\) −3.72488e12 −0.607542
\(362\) −5.62180e12 −0.904342
\(363\) −5.36315e11 6.89902e12i −0.0850916 1.09460i
\(364\) 1.05665e11 0.0165357
\(365\) 0 0
\(366\) 2.61201e10 + 3.36002e11i 0.00397712 + 0.0511607i
\(367\) 8.19379e12i 1.23071i 0.788252 + 0.615353i \(0.210987\pi\)
−0.788252 + 0.615353i \(0.789013\pi\)
\(368\) −1.46159e12 −0.216564
\(369\) −3.27656e11 2.09471e12i −0.0478945 0.306190i
\(370\) 0 0
\(371\) 3.07903e11i 0.0438072i
\(372\) 2.98315e11 + 3.83746e12i 0.0418756 + 0.538677i
\(373\) 9.07322e12i 1.25666i −0.777947 0.628329i \(-0.783739\pi\)
0.777947 0.628329i \(-0.216261\pi\)
\(374\) 3.54870e12i 0.484966i
\(375\) 0 0
\(376\) −3.81012e11 −0.0506990
\(377\) −9.15072e12 −1.20157
\(378\) 2.11837e11 5.02140e10i 0.0274500 0.00650677i
\(379\) −1.17817e13 −1.50665 −0.753324 0.657650i \(-0.771551\pi\)
−0.753324 + 0.657650i \(0.771551\pi\)
\(380\) 0 0
\(381\) 9.89455e12 7.69180e11i 1.23246 0.0958083i
\(382\) 3.57627e12i 0.439657i
\(383\) −6.82336e12 −0.827950 −0.413975 0.910288i \(-0.635860\pi\)
−0.413975 + 0.910288i \(0.635860\pi\)
\(384\) −5.71972e10 7.35771e11i −0.00685045 0.0881225i
\(385\) 0 0
\(386\) 8.56152e12i 0.999112i
\(387\) 3.34225e11 + 2.13670e12i 0.0385021 + 0.246144i
\(388\) 5.50249e12i 0.625750i
\(389\) 7.07814e11i 0.0794642i −0.999210 0.0397321i \(-0.987350\pi\)
0.999210 0.0397321i \(-0.0126504\pi\)
\(390\) 0 0
\(391\) −3.74855e12 −0.410185
\(392\) −3.26733e12 −0.352991
\(393\) −1.00662e13 + 7.82526e11i −1.07375 + 0.0834710i
\(394\) 4.28577e12 0.451386
\(395\) 0 0
\(396\) −1.08989e12 6.96770e12i −0.111920 0.715506i
\(397\) 1.26553e12i 0.128328i −0.997939 0.0641639i \(-0.979562\pi\)
0.997939 0.0641639i \(-0.0204380\pi\)
\(398\) 1.13803e12 0.113956
\(399\) 2.51989e11 1.95890e10i 0.0249182 0.00193708i
\(400\) 0 0
\(401\) 1.50259e13i 1.44917i 0.689187 + 0.724583i \(0.257968\pi\)
−0.689187 + 0.724583i \(0.742032\pi\)
\(402\) 3.67714e12 2.85853e11i 0.350252 0.0272278i
\(403\) 9.52175e12i 0.895760i
\(404\) 5.53749e12i 0.514525i
\(405\) 0 0
\(406\) −4.51094e11 −0.0408919
\(407\) −1.99839e13 −1.78940
\(408\) −1.46694e11 1.88704e12i −0.0129752 0.166909i
\(409\) 1.70362e12 0.148852 0.0744261 0.997227i \(-0.476288\pi\)
0.0744261 + 0.997227i \(0.476288\pi\)
\(410\) 0 0
\(411\) −1.74310e12 2.24228e13i −0.148632 1.91197i
\(412\) 1.45124e12i 0.122251i
\(413\) 3.27659e11 0.0272692
\(414\) −7.36009e12 + 1.15127e12i −0.605176 + 0.0946621i
\(415\) 0 0
\(416\) 1.82564e12i 0.146538i
\(417\) −1.49834e12 1.92743e13i −0.118831 1.52862i
\(418\) 8.18758e12i 0.641615i
\(419\) 2.22448e13i 1.72250i −0.508185 0.861248i \(-0.669683\pi\)
0.508185 0.861248i \(-0.330317\pi\)
\(420\) 0 0
\(421\) 1.82948e11 0.0138330 0.00691650 0.999976i \(-0.497798\pi\)
0.00691650 + 0.999976i \(0.497798\pi\)
\(422\) −1.07473e13 −0.803043
\(423\) −1.91865e12 + 3.00118e11i −0.141676 + 0.0221610i
\(424\) 5.31988e12 0.388215
\(425\) 0 0
\(426\) 6.76086e12 5.25574e11i 0.481897 0.0374616i
\(427\) 4.10986e10i 0.00289526i
\(428\) −1.23495e13 −0.859869
\(429\) −1.35216e12 1.73938e13i −0.0930552 1.19704i
\(430\) 0 0
\(431\) 6.64491e12i 0.446789i 0.974728 + 0.223395i \(0.0717139\pi\)
−0.974728 + 0.223395i \(0.928286\pi\)
\(432\) −8.67584e11 3.66006e12i −0.0576624 0.243259i
\(433\) 7.28337e12i 0.478512i 0.970956 + 0.239256i \(0.0769036\pi\)
−0.970956 + 0.239256i \(0.923096\pi\)
\(434\) 4.69384e11i 0.0304846i
\(435\) 0 0
\(436\) 2.78233e12 0.176594
\(437\) −8.64868e12 −0.542678
\(438\) 5.92738e12 4.60781e11i 0.367699 0.0285841i
\(439\) 1.52600e13 0.935907 0.467954 0.883753i \(-0.344991\pi\)
0.467954 + 0.883753i \(0.344991\pi\)
\(440\) 0 0
\(441\) −1.64533e13 + 2.57363e12i −0.986414 + 0.154296i
\(442\) 4.68225e12i 0.277551i
\(443\) 1.83304e13 1.07437 0.537184 0.843465i \(-0.319488\pi\)
0.537184 + 0.843465i \(0.319488\pi\)
\(444\) −1.06265e13 + 8.26083e11i −0.615852 + 0.0478750i
\(445\) 0 0
\(446\) 5.33057e12i 0.302064i
\(447\) 1.95706e13 1.52138e12i 1.09665 0.0852508i
\(448\) 8.99970e10i 0.00498698i
\(449\) 8.33876e12i 0.456951i −0.973550 0.228475i \(-0.926626\pi\)
0.973550 0.228475i \(-0.0733741\pi\)
\(450\) 0 0
\(451\) −8.37559e12 −0.448883
\(452\) −7.13242e12 −0.378046
\(453\) 5.81303e11 + 7.47774e12i 0.0304727 + 0.391994i
\(454\) −9.66249e12 −0.500968
\(455\) 0 0
\(456\) −3.38454e11 4.35379e12i −0.0171663 0.220823i
\(457\) 4.12288e11i 0.0206833i −0.999947 0.0103416i \(-0.996708\pi\)
0.999947 0.0103416i \(-0.00329191\pi\)
\(458\) 2.34581e13 1.16403
\(459\) −2.22510e12 9.38700e12i −0.109216 0.460748i
\(460\) 0 0
\(461\) 1.66247e11i 0.00798453i 0.999992 + 0.00399226i \(0.00127078\pi\)
−0.999992 + 0.00399226i \(0.998729\pi\)
\(462\) −6.66559e10 8.57446e11i −0.00316686 0.0407377i
\(463\) 1.27323e13i 0.598416i 0.954188 + 0.299208i \(0.0967224\pi\)
−0.954188 + 0.299208i \(0.903278\pi\)
\(464\) 7.79389e12i 0.362380i
\(465\) 0 0
\(466\) −2.34795e13 −1.06846
\(467\) −2.26689e13 −1.02058 −0.510288 0.860004i \(-0.670461\pi\)
−0.510288 + 0.860004i \(0.670461\pi\)
\(468\) −1.43803e12 9.19337e12i −0.0640531 0.409492i
\(469\) 4.49775e11 0.0198213
\(470\) 0 0
\(471\) 2.35321e13 1.82934e12i 1.01521 0.0789203i
\(472\) 5.66120e12i 0.241657i
\(473\) 8.54352e12 0.360854
\(474\) −7.95321e11 1.02308e13i −0.0332392 0.427581i
\(475\) 0 0
\(476\) 2.30816e11i 0.00944565i
\(477\) 2.67892e13 4.19039e12i 1.08485 0.169693i
\(478\) 2.79873e13i 1.12156i
\(479\) 2.39654e13i 0.950402i 0.879877 + 0.475201i \(0.157625\pi\)
−0.879877 + 0.475201i \(0.842375\pi\)
\(480\) 0 0
\(481\) −2.63673e13 −1.02409
\(482\) 2.35126e13 0.903785
\(483\) −9.05734e11 + 7.04098e10i −0.0344560 + 0.00267853i
\(484\) −1.45801e13 −0.548950
\(485\) 0 0
\(486\) −7.25186e12 1.77475e13i −0.267466 0.654570i
\(487\) 1.13824e13i 0.415516i 0.978180 + 0.207758i \(0.0666167\pi\)
−0.978180 + 0.207758i \(0.933383\pi\)
\(488\) 7.10091e11 0.0256575
\(489\) 3.37821e13 2.62615e12i 1.20821 0.0939235i
\(490\) 0 0
\(491\) 3.59512e13i 1.25981i 0.776672 + 0.629906i \(0.216906\pi\)
−0.776672 + 0.629906i \(0.783094\pi\)
\(492\) −4.45377e12 + 3.46226e11i −0.154491 + 0.0120098i
\(493\) 1.99891e13i 0.686370i
\(494\) 1.08029e13i 0.367203i
\(495\) 0 0
\(496\) 8.10990e12 0.270151
\(497\) 8.26965e11 0.0272713
\(498\) −4.66903e11 6.00612e12i −0.0152433 0.196086i
\(499\) 1.33630e13 0.431917 0.215958 0.976403i \(-0.430712\pi\)
0.215958 + 0.976403i \(0.430712\pi\)
\(500\) 0 0
\(501\) −2.37000e12 3.04871e13i −0.0750862 0.965890i
\(502\) 1.28248e13i 0.402283i
\(503\) −3.54934e13 −1.10232 −0.551160 0.834399i \(-0.685815\pi\)
−0.551160 + 0.834399i \(0.685815\pi\)
\(504\) −7.08893e10 4.53196e11i −0.00217986 0.0139359i
\(505\) 0 0
\(506\) 2.94290e13i 0.887203i
\(507\) 8.12280e11 + 1.04490e13i 0.0242474 + 0.311913i
\(508\) 2.09107e13i 0.618087i
\(509\) 6.07337e13i 1.77763i 0.458269 + 0.888813i \(0.348470\pi\)
−0.458269 + 0.888813i \(0.651530\pi\)
\(510\) 0 0
\(511\) 7.25016e11 0.0208086
\(512\) −1.55494e12 −0.0441942
\(513\) −5.13377e12 2.16577e13i −0.144494 0.609574i
\(514\) −2.89501e13 −0.806928
\(515\) 0 0
\(516\) 4.54307e12 3.53168e11i 0.124194 0.00965456i
\(517\) 7.67166e12i 0.207700i
\(518\) −1.29980e12 −0.0348520
\(519\) 2.37785e12 + 3.05881e13i 0.0631464 + 0.812299i
\(520\) 0 0
\(521\) 2.06244e13i 0.537270i −0.963242 0.268635i \(-0.913427\pi\)
0.963242 0.268635i \(-0.0865726\pi\)
\(522\) 6.13914e12 + 3.92476e13i 0.158400 + 1.01265i
\(523\) 5.24376e13i 1.34009i 0.742320 + 0.670045i \(0.233725\pi\)
−0.742320 + 0.670045i \(0.766275\pi\)
\(524\) 2.12735e13i 0.538495i
\(525\) 0 0
\(526\) 3.81460e13 0.947370
\(527\) 2.07996e13 0.511683
\(528\) −1.48147e13 + 1.15166e12i −0.361014 + 0.0280644i
\(529\) −1.03402e13 −0.249603
\(530\) 0 0
\(531\) −4.45925e12 2.85080e13i −0.105631 0.675297i
\(532\) 5.32541e11i 0.0124967i
\(533\) −1.10510e13 −0.256900
\(534\) −2.84992e13 + 2.21547e12i −0.656337 + 0.0510221i
\(535\) 0 0
\(536\) 7.77110e12i 0.175654i
\(537\) 7.18431e13 5.58492e12i 1.60884 0.125068i
\(538\) 3.03260e13i 0.672828i
\(539\) 6.57877e13i 1.44611i
\(540\) 0 0
\(541\) 8.20249e13 1.76994 0.884972 0.465645i \(-0.154178\pi\)
0.884972 + 0.465645i \(0.154178\pi\)
\(542\) 3.96770e13 0.848286
\(543\) 4.67919e12 + 6.01919e13i 0.0991223 + 1.27509i
\(544\) −3.98798e12 −0.0837064
\(545\) 0 0
\(546\) −8.79477e10 1.13134e12i −0.00181243 0.0233147i
\(547\) 1.62332e13i 0.331488i 0.986169 + 0.165744i \(0.0530025\pi\)
−0.986169 + 0.165744i \(0.946997\pi\)
\(548\) −4.73872e13 −0.958867
\(549\) 3.57580e12 5.59329e11i 0.0716987 0.0112152i
\(550\) 0 0
\(551\) 4.61189e13i 0.908074i
\(552\) 1.21652e12 + 1.56490e13i 0.0237369 + 0.305346i
\(553\) 1.25140e12i 0.0241974i
\(554\) 3.83715e13i 0.735292i
\(555\) 0 0
\(556\) −4.07335e13 −0.766615
\(557\) −1.12168e13 −0.209215 −0.104608 0.994514i \(-0.533359\pi\)
−0.104608 + 0.994514i \(0.533359\pi\)
\(558\) 4.08389e13 6.38805e12i 0.754924 0.118086i
\(559\) 1.12726e13 0.206521
\(560\) 0 0
\(561\) −3.79955e13 + 2.95369e12i −0.683783 + 0.0531557i
\(562\) 5.52506e12i 0.0985497i
\(563\) 7.98522e13 1.41171 0.705854 0.708357i \(-0.250563\pi\)
0.705854 + 0.708357i \(0.250563\pi\)
\(564\) 3.17127e11 + 4.07945e12i 0.00555697 + 0.0714835i
\(565\) 0 0
\(566\) 2.25462e13i 0.388142i
\(567\) −7.13953e11 2.22632e12i −0.0121830 0.0379902i
\(568\) 1.42881e13i 0.241675i
\(569\) 9.95594e11i 0.0166925i 0.999965 + 0.00834624i \(0.00265672\pi\)
−0.999965 + 0.00834624i \(0.997343\pi\)
\(570\) 0 0
\(571\) 1.07836e14 1.77657 0.888283 0.459297i \(-0.151899\pi\)
0.888283 + 0.459297i \(0.151899\pi\)
\(572\) −3.67593e13 −0.600326
\(573\) 3.82907e13 2.97664e12i 0.619899 0.0481895i
\(574\) −5.44769e11 −0.00874285
\(575\) 0 0
\(576\) −7.83021e12 + 1.22481e12i −0.123498 + 0.0193177i
\(577\) 3.31000e13i 0.517546i −0.965938 0.258773i \(-0.916682\pi\)
0.965938 0.258773i \(-0.0833182\pi\)
\(578\) 3.53887e13 0.548562
\(579\) 9.16671e13 7.12600e12i 1.40871 0.109510i
\(580\) 0 0
\(581\) 7.34648e11i 0.0110968i
\(582\) 5.89145e13 4.57989e12i 0.882282 0.0685867i
\(583\) 1.07116e14i 1.59041i
\(584\) 1.25266e13i 0.184404i
\(585\) 0 0
\(586\) −3.56543e13 −0.515969
\(587\) 1.21022e14 1.73650 0.868248 0.496131i \(-0.165246\pi\)
0.868248 + 0.496131i \(0.165246\pi\)
\(588\) 2.71950e12 + 3.49830e13i 0.0386903 + 0.497703i
\(589\) 4.79889e13 0.676961
\(590\) 0 0
\(591\) −3.56717e12 4.58873e13i −0.0494751 0.636436i
\(592\) 2.24576e13i 0.308855i
\(593\) 8.43944e12 0.115091 0.0575453 0.998343i \(-0.481673\pi\)
0.0575453 + 0.998343i \(0.481673\pi\)
\(594\) −7.36952e13 + 1.74688e13i −0.996567 + 0.236227i
\(595\) 0 0
\(596\) 4.13596e13i 0.549977i
\(597\) −9.47213e11 1.21847e13i −0.0124904 0.160673i
\(598\) 3.88294e13i 0.507756i
\(599\) 3.11882e13i 0.404443i −0.979340 0.202221i \(-0.935184\pi\)
0.979340 0.202221i \(-0.0648160\pi\)
\(600\) 0 0
\(601\) 2.87401e13 0.366535 0.183267 0.983063i \(-0.441333\pi\)
0.183267 + 0.983063i \(0.441333\pi\)
\(602\) 5.55692e11 0.00702832
\(603\) −6.12119e12 3.91328e13i −0.0767802 0.490857i
\(604\) 1.58031e13 0.196588
\(605\) 0 0
\(606\) −5.92893e13 + 4.60902e12i −0.725459 + 0.0563956i
\(607\) 4.47536e13i 0.543106i 0.962423 + 0.271553i \(0.0875372\pi\)
−0.962423 + 0.271553i \(0.912463\pi\)
\(608\) −9.20110e12 −0.110744
\(609\) 3.75459e11 + 4.82981e12i 0.00448204 + 0.0576559i
\(610\) 0 0
\(611\) 1.01222e13i 0.118869i
\(612\) −2.00822e13 + 3.14128e12i −0.233913 + 0.0365889i
\(613\) 6.78051e13i 0.783358i 0.920102 + 0.391679i \(0.128106\pi\)
−0.920102 + 0.391679i \(0.871894\pi\)
\(614\) 7.46303e13i 0.855211i
\(615\) 0 0
\(616\) −1.81209e12 −0.0204303
\(617\) −2.48261e12 −0.0277641 −0.0138820 0.999904i \(-0.504419\pi\)
−0.0138820 + 0.999904i \(0.504419\pi\)
\(618\) −1.55383e13 + 1.20791e12i −0.172370 + 0.0133996i
\(619\) −1.64000e13 −0.180464 −0.0902320 0.995921i \(-0.528761\pi\)
−0.0902320 + 0.995921i \(0.528761\pi\)
\(620\) 0 0
\(621\) 1.84526e13 + 7.78454e13i 0.199801 + 0.842898i
\(622\) 3.78559e13i 0.406613i
\(623\) −3.48592e12 −0.0371431
\(624\) −1.95470e13 + 1.51954e12i −0.206612 + 0.0160616i
\(625\) 0 0
\(626\) 3.92175e13i 0.407951i
\(627\) −8.76635e13 + 6.81476e12i −0.904651 + 0.0703255i
\(628\) 4.97317e13i 0.509138i
\(629\) 5.75973e13i 0.584991i
\(630\) 0 0
\(631\) −1.37258e13 −0.137211 −0.0686056 0.997644i \(-0.521855\pi\)
−0.0686056 + 0.997644i \(0.521855\pi\)
\(632\) −2.16213e13 −0.214435
\(633\) 8.94532e12 + 1.15070e14i 0.0880192 + 1.13226i
\(634\) 3.01171e13 0.294014
\(635\) 0 0
\(636\) −4.42789e12 5.69593e13i −0.0425511 0.547367i
\(637\) 8.68020e13i 0.827623i
\(638\) 1.56930e14 1.48457
\(639\) −1.12545e13 7.19503e13i −0.105639 0.675349i
\(640\) 0 0
\(641\) 5.42348e13i 0.501173i −0.968094 0.250587i \(-0.919377\pi\)
0.968094 0.250587i \(-0.0806235\pi\)
\(642\) 1.02789e13 + 1.32225e14i 0.0942477 + 1.21238i
\(643\) 5.54693e13i 0.504659i −0.967641 0.252329i \(-0.918803\pi\)
0.967641 0.252329i \(-0.0811966\pi\)
\(644\) 1.91414e12i 0.0172800i
\(645\) 0 0
\(646\) −2.35982e13 −0.209757
\(647\) 5.56652e13 0.490979 0.245489 0.969399i \(-0.421051\pi\)
0.245489 + 0.969399i \(0.421051\pi\)
\(648\) −3.84657e13 + 1.23355e13i −0.336665 + 0.107965i
\(649\) −1.13988e14 −0.990002
\(650\) 0 0
\(651\) 5.02564e12 3.90682e11i 0.0429820 0.00334132i
\(652\) 7.13935e13i 0.605927i
\(653\) 5.56792e13 0.468951 0.234475 0.972122i \(-0.424663\pi\)
0.234475 + 0.972122i \(0.424663\pi\)
\(654\) −2.31581e12 2.97901e13i −0.0193560 0.248991i
\(655\) 0 0
\(656\) 9.41238e12i 0.0774784i
\(657\) −9.86706e12 6.30802e13i −0.0806048 0.515307i
\(658\) 4.98984e11i 0.00404536i
\(659\) 1.52699e14i 1.22860i −0.789074 0.614298i \(-0.789439\pi\)
0.789074 0.614298i \(-0.210561\pi\)
\(660\) 0 0
\(661\) −2.08036e14 −1.64866 −0.824329 0.566111i \(-0.808447\pi\)
−0.824329 + 0.566111i \(0.808447\pi\)
\(662\) −1.06793e14 −0.839945
\(663\) −5.01323e13 + 3.89717e12i −0.391336 + 0.0304216i
\(664\) −1.26931e13 −0.0983390
\(665\) 0 0
\(666\) 1.76895e13 + 1.13089e14i 0.135004 + 0.863080i
\(667\) 1.65767e14i 1.25565i
\(668\) −6.44300e13 −0.484402
\(669\) 5.70737e13 4.43679e12i 0.425898 0.0331084i
\(670\) 0 0
\(671\) 1.42977e13i 0.105112i
\(672\) −9.63587e11 + 7.49071e10i −0.00703144 + 0.000546609i
\(673\) 9.45260e13i 0.684662i −0.939579 0.342331i \(-0.888784\pi\)
0.939579 0.342331i \(-0.111216\pi\)
\(674\) 9.39679e13i 0.675585i
\(675\) 0 0
\(676\) 2.20824e13 0.156427
\(677\) −1.70106e14 −1.19612 −0.598060 0.801451i \(-0.704062\pi\)
−0.598060 + 0.801451i \(0.704062\pi\)
\(678\) 5.93652e12 + 7.63660e13i 0.0414366 + 0.533030i
\(679\) 7.20622e12 0.0499297
\(680\) 0 0
\(681\) 8.04237e12 + 1.03455e14i 0.0549096 + 0.706344i
\(682\) 1.63293e14i 1.10674i
\(683\) −2.23578e14 −1.50427 −0.752135 0.659009i \(-0.770976\pi\)
−0.752135 + 0.659009i \(0.770976\pi\)
\(684\) −4.63338e13 + 7.24758e12i −0.309469 + 0.0484075i
\(685\) 0 0
\(686\) 8.56481e12i 0.0563764i
\(687\) −1.95249e13 2.51163e14i −0.127586 1.64124i
\(688\) 9.60110e12i 0.0622843i
\(689\) 1.41331e14i 0.910210i
\(690\) 0 0
\(691\) −1.10134e13 −0.0699090 −0.0349545 0.999389i \(-0.511129\pi\)
−0.0349545 + 0.999389i \(0.511129\pi\)
\(692\) 6.46435e13 0.407375
\(693\) −9.12509e12 + 1.42735e12i −0.0570915 + 0.00893029i
\(694\) 9.95468e13 0.618344
\(695\) 0 0
\(696\) 8.34482e13 6.48708e12i 0.510941 0.0397194i
\(697\) 2.41401e13i 0.146749i
\(698\) −2.09078e14 −1.26192
\(699\) 1.95426e13 + 2.51392e14i 0.117111 + 1.50649i
\(700\) 0 0
\(701\) 1.10962e14i 0.655516i −0.944762 0.327758i \(-0.893707\pi\)
0.944762 0.327758i \(-0.106293\pi\)
\(702\) −9.72354e13 + 2.30488e13i −0.570346 + 0.135195i
\(703\) 1.32889e14i 0.773948i
\(704\) 3.13087e13i 0.181052i
\(705\) 0 0
\(706\) 2.08338e13 0.118781
\(707\) −7.25206e12 −0.0410548
\(708\) −6.06138e13 + 4.71199e12i −0.340726 + 0.0264873i
\(709\) −2.08219e14 −1.16222 −0.581112 0.813824i \(-0.697382\pi\)
−0.581112 + 0.813824i \(0.697382\pi\)
\(710\) 0 0
\(711\) −1.08878e14 + 1.70308e13i −0.599229 + 0.0937318i
\(712\) 6.02289e13i 0.329158i
\(713\) −1.72489e14 −0.936080
\(714\) −2.47132e12 + 1.92115e11i −0.0133180 + 0.00103531i
\(715\) 0 0
\(716\) 1.51830e14i 0.806848i
\(717\) −2.99656e14 + 2.32946e13i −1.58135 + 0.122931i
\(718\) 1.39746e14i 0.732347i
\(719\) 2.74910e14i 1.43069i −0.698771 0.715346i \(-0.746269\pi\)
0.698771 0.715346i \(-0.253731\pi\)
\(720\) 0 0
\(721\) −1.90059e12 −0.00975465
\(722\) 8.42844e13 0.429597
\(723\) −1.95702e13 2.51746e14i −0.0990613 1.27430i
\(724\) 1.27207e14 0.639466
\(725\) 0 0
\(726\) 1.21354e13 + 1.56107e14i 0.0601688 + 0.773997i
\(727\) 2.99071e14i 1.47266i 0.676622 + 0.736330i \(0.263443\pi\)
−0.676622 + 0.736330i \(0.736557\pi\)
\(728\) −2.39092e12 −0.0116925
\(729\) −1.83985e14 + 9.24165e13i −0.893602 + 0.448861i
\(730\) 0 0
\(731\) 2.46241e13i 0.117970i
\(732\) −5.91030e11 7.60286e12i −0.00281225 0.0361761i
\(733\) 1.19922e14i 0.566734i 0.959012 + 0.283367i \(0.0914514\pi\)
−0.959012 + 0.283367i \(0.908549\pi\)
\(734\) 1.85404e14i 0.870241i
\(735\) 0 0
\(736\) 3.30719e13 0.153134
\(737\) −1.56471e14 −0.719608
\(738\) 7.41400e12 + 4.73978e13i 0.0338666 + 0.216509i
\(739\) 7.29345e13 0.330911 0.165455 0.986217i \(-0.447091\pi\)
0.165455 + 0.986217i \(0.447091\pi\)
\(740\) 0 0
\(741\) −1.15666e14 + 8.99158e12i −0.517742 + 0.0402481i
\(742\) 6.96706e12i 0.0309763i
\(743\) 1.07061e14 0.472809 0.236405 0.971655i \(-0.424031\pi\)
0.236405 + 0.971655i \(0.424031\pi\)
\(744\) −6.75011e12 8.68317e13i −0.0296105 0.380902i
\(745\) 0 0
\(746\) 2.05304e14i 0.888592i
\(747\) −6.39183e13 + 9.99815e12i −0.274803 + 0.0429850i
\(748\) 8.02979e13i 0.342923i
\(749\) 1.61733e13i 0.0686104i
\(750\) 0 0
\(751\) 1.83777e14 0.769292 0.384646 0.923064i \(-0.374323\pi\)
0.384646 + 0.923064i \(0.374323\pi\)
\(752\) 8.62131e12 0.0358496
\(753\) −1.37313e14 + 1.06744e13i −0.567203 + 0.0440931i
\(754\) 2.07057e14 0.849638
\(755\) 0 0
\(756\) −4.79332e12 + 1.13621e12i −0.0194101 + 0.00460098i
\(757\) 1.73049e14i 0.696130i 0.937470 + 0.348065i \(0.113161\pi\)
−0.937470 + 0.348065i \(0.886839\pi\)
\(758\) 2.66589e14 1.06536
\(759\) 3.15093e14 2.44946e13i 1.25092 0.0972438i
\(760\) 0 0
\(761\) 1.10156e14i 0.431604i −0.976437 0.215802i \(-0.930764\pi\)
0.976437 0.215802i \(-0.0692365\pi\)
\(762\) −2.23888e14 + 1.74046e13i −0.871477 + 0.0677467i
\(763\) 3.64382e12i 0.0140907i
\(764\) 8.09218e13i 0.310884i
\(765\) 0 0
\(766\) 1.54395e14 0.585449
\(767\) −1.50399e14 −0.566589
\(768\) 1.29423e12 + 1.66486e13i 0.00484400 + 0.0623120i
\(769\) −2.30458e14 −0.856959 −0.428480 0.903551i \(-0.640951\pi\)
−0.428480 + 0.903551i \(0.640951\pi\)
\(770\) 0 0
\(771\) 2.40960e13 + 3.09965e14i 0.0884451 + 1.13774i
\(772\) 1.93725e14i 0.706479i
\(773\) 1.50965e14 0.546991 0.273495 0.961873i \(-0.411820\pi\)
0.273495 + 0.961873i \(0.411820\pi\)
\(774\) −7.56265e12 4.83481e13i −0.0272251 0.174050i
\(775\) 0