Properties

Label 75.9.d.b.74.4
Level $75$
Weight $9$
Character 75.74
Analytic conductor $30.553$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{14})\)
Defining polynomial: \( x^{4} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.4
Root \(1.87083 - 1.87083i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.b.74.3

$q$-expansion

\(f(q)\) \(=\) \(q+22.4499 q^{2} +(67.3498 + 45.0000i) q^{3} +248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00i q^{7} -179.600 q^{8} +(2511.00 + 6061.48i) q^{9} +O(q^{10})\) \(q+22.4499 q^{2} +(67.3498 + 45.0000i) q^{3} +248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00i q^{7} -179.600 q^{8} +(2511.00 + 6061.48i) q^{9} +6959.48i q^{11} +(16702.8 + 11160.0i) q^{12} +25730.0i q^{13} +39287.4i q^{14} -67520.0 q^{16} +74893.0 q^{17} +(56371.8 + 136080. i) q^{18} -18938.0 q^{19} +(-78750.0 + 117862. i) q^{21} +156240. i q^{22} +470461. q^{23} +(-12096.0 - 8081.98i) q^{24} +577637. i q^{26} +(-103651. + 521235. i) q^{27} +434000. i q^{28} -460897. i q^{29} -351478. q^{31} -1.46984e6 q^{32} +(-313177. + 468720. i) q^{33} +1.68134e6 q^{34} +(622728. + 1.50325e6i) q^{36} -1.33517e6i q^{37} -425157. q^{38} +(-1.15785e6 + 1.73291e6i) q^{39} +1.87547e6i q^{41} +(-1.76793e6 + 2.64600e6i) q^{42} -3.52615e6i q^{43} +1.72595e6i q^{44} +1.05618e7 q^{46} -4.08104e6 q^{47} +(-4.54746e6 - 3.03840e6i) q^{48} +2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.38104e6i q^{52} +6.60177e6 q^{53} +(-2.32697e6 + 1.17017e7i) q^{54} -314299. i q^{56} +(-1.27547e6 - 852210. i) q^{57} -1.03471e7i q^{58} -1.37149e7i q^{59} +753602. q^{61} -7.89066e6 q^{62} +(-1.06076e7 + 4.39425e6i) q^{63} -1.57128e7 q^{64} +(-7.03080e6 + 1.05227e7i) q^{66} -2.26889e6i q^{67} +1.85735e7 q^{68} +(3.16855e7 + 2.11707e7i) q^{69} +1.70220e7i q^{71} +(-450974. - 1.08864e6i) q^{72} +2.76728e7i q^{73} -2.99745e7i q^{74} -4.69662e6 q^{76} -1.21791e7 q^{77} +(-2.59937e7 + 3.89038e7i) q^{78} +2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} +4.21042e7i q^{82} +4.63952e7 q^{83} +(-1.95300e7 + 2.92298e7i) q^{84} -7.91619e7i q^{86} +(2.07404e7 - 3.10414e7i) q^{87} -1.24992e6i q^{88} -7.26152e7i q^{89} -4.50275e7 q^{91} +1.16674e8 q^{92} +(-2.36720e7 - 1.58165e7i) q^{93} -9.16191e7 q^{94} +(-9.89937e7 - 6.61429e7i) q^{96} -1.47271e8i q^{97} +6.06665e7 q^{98} +(-4.21848e7 + 1.74753e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 992 q^{4} + 6048 q^{6} + 10044 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 992 q^{4} + 6048 q^{6} + 10044 q^{9} - 270080 q^{16} - 75752 q^{19} - 315000 q^{21} - 48384 q^{24} - 1405912 q^{31} + 6725376 q^{34} + 2490912 q^{36} - 4631400 q^{39} + 42247296 q^{46} + 10809204 q^{49} + 20176128 q^{51} - 9307872 q^{54} + 3014408 q^{61} - 62851072 q^{64} - 28123200 q^{66} + 126741888 q^{69} - 18786496 q^{76} + 91923928 q^{79} - 121745916 q^{81} - 78120000 q^{84} - 180110000 q^{91} - 366476544 q^{94} - 395974656 q^{96} - 168739200 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.4499 1.40312 0.701561 0.712610i \(-0.252487\pi\)
0.701561 + 0.712610i \(0.252487\pi\)
\(3\) 67.3498 + 45.0000i 0.831479 + 0.555556i
\(4\) 248.000 0.968750
\(5\) 0 0
\(6\) 1512.00 + 1010.25i 1.16667 + 0.779512i
\(7\) 1750.00i 0.728863i 0.931230 + 0.364431i \(0.118737\pi\)
−0.931230 + 0.364431i \(0.881263\pi\)
\(8\) −179.600 −0.0438475
\(9\) 2511.00 + 6061.48i 0.382716 + 0.923866i
\(10\) 0 0
\(11\) 6959.48i 0.475342i 0.971346 + 0.237671i \(0.0763840\pi\)
−0.971346 + 0.237671i \(0.923616\pi\)
\(12\) 16702.8 + 11160.0i 0.805496 + 0.538194i
\(13\) 25730.0i 0.900879i 0.892807 + 0.450439i \(0.148733\pi\)
−0.892807 + 0.450439i \(0.851267\pi\)
\(14\) 39287.4i 1.02268i
\(15\) 0 0
\(16\) −67520.0 −1.03027
\(17\) 74893.0 0.896697 0.448348 0.893859i \(-0.352012\pi\)
0.448348 + 0.893859i \(0.352012\pi\)
\(18\) 56371.8 + 136080.i 0.536997 + 1.29630i
\(19\) −18938.0 −0.145318 −0.0726590 0.997357i \(-0.523148\pi\)
−0.0726590 + 0.997357i \(0.523148\pi\)
\(20\) 0 0
\(21\) −78750.0 + 117862.i −0.404924 + 0.606035i
\(22\) 156240.i 0.666963i
\(23\) 470461. 1.68117 0.840586 0.541678i \(-0.182211\pi\)
0.840586 + 0.541678i \(0.182211\pi\)
\(24\) −12096.0 8081.98i −0.0364583 0.0243597i
\(25\) 0 0
\(26\) 577637.i 1.26404i
\(27\) −103651. + 521235.i −0.195038 + 0.980796i
\(28\) 434000.i 0.706086i
\(29\) 460897.i 0.651647i −0.945431 0.325823i \(-0.894359\pi\)
0.945431 0.325823i \(-0.105641\pi\)
\(30\) 0 0
\(31\) −351478. −0.380585 −0.190292 0.981727i \(-0.560944\pi\)
−0.190292 + 0.981727i \(0.560944\pi\)
\(32\) −1.46984e6 −1.40175
\(33\) −313177. + 468720.i −0.264079 + 0.395237i
\(34\) 1.68134e6 1.25817
\(35\) 0 0
\(36\) 622728. + 1.50325e6i 0.370756 + 0.894995i
\(37\) 1.33517e6i 0.712409i −0.934408 0.356205i \(-0.884071\pi\)
0.934408 0.356205i \(-0.115929\pi\)
\(38\) −425157. −0.203899
\(39\) −1.15785e6 + 1.73291e6i −0.500488 + 0.749062i
\(40\) 0 0
\(41\) 1.87547e6i 0.663704i 0.943331 + 0.331852i \(0.107673\pi\)
−0.943331 + 0.331852i \(0.892327\pi\)
\(42\) −1.76793e6 + 2.64600e6i −0.568157 + 0.850340i
\(43\) 3.52615e6i 1.03140i −0.856769 0.515700i \(-0.827532\pi\)
0.856769 0.515700i \(-0.172468\pi\)
\(44\) 1.72595e6i 0.460488i
\(45\) 0 0
\(46\) 1.05618e7 2.35889
\(47\) −4.08104e6 −0.836333 −0.418167 0.908370i \(-0.637327\pi\)
−0.418167 + 0.908370i \(0.637327\pi\)
\(48\) −4.54746e6 3.03840e6i −0.856651 0.572374i
\(49\) 2.70230e6 0.468759
\(50\) 0 0
\(51\) 5.04403e6 + 3.37019e6i 0.745585 + 0.498165i
\(52\) 6.38104e6i 0.872726i
\(53\) 6.60177e6 0.836675 0.418337 0.908292i \(-0.362613\pi\)
0.418337 + 0.908292i \(0.362613\pi\)
\(54\) −2.32697e6 + 1.17017e7i −0.273663 + 1.37618i
\(55\) 0 0
\(56\) 314299.i 0.0319589i
\(57\) −1.27547e6 852210.i −0.120829 0.0807323i
\(58\) 1.03471e7i 0.914340i
\(59\) 1.37149e7i 1.13184i −0.824461 0.565919i \(-0.808521\pi\)
0.824461 0.565919i \(-0.191479\pi\)
\(60\) 0 0
\(61\) 753602. 0.0544280 0.0272140 0.999630i \(-0.491336\pi\)
0.0272140 + 0.999630i \(0.491336\pi\)
\(62\) −7.89066e6 −0.534007
\(63\) −1.06076e7 + 4.39425e6i −0.673372 + 0.278948i
\(64\) −1.57128e7 −0.936554
\(65\) 0 0
\(66\) −7.03080e6 + 1.05227e7i −0.370535 + 0.554566i
\(67\) 2.26889e6i 0.112594i −0.998414 0.0562969i \(-0.982071\pi\)
0.998414 0.0562969i \(-0.0179293\pi\)
\(68\) 1.85735e7 0.868675
\(69\) 3.16855e7 + 2.11707e7i 1.39786 + 0.933985i
\(70\) 0 0
\(71\) 1.70220e7i 0.669849i 0.942245 + 0.334925i \(0.108711\pi\)
−0.942245 + 0.334925i \(0.891289\pi\)
\(72\) −450974. 1.08864e6i −0.0167812 0.0405093i
\(73\) 2.76728e7i 0.974454i 0.873275 + 0.487227i \(0.161992\pi\)
−0.873275 + 0.487227i \(0.838008\pi\)
\(74\) 2.99745e7i 0.999597i
\(75\) 0 0
\(76\) −4.69662e6 −0.140777
\(77\) −1.21791e7 −0.346459
\(78\) −2.59937e7 + 3.89038e7i −0.702246 + 1.05103i
\(79\) 2.29810e7 0.590011 0.295006 0.955496i \(-0.404678\pi\)
0.295006 + 0.955496i \(0.404678\pi\)
\(80\) 0 0
\(81\) −3.04365e7 + 3.04408e7i −0.707057 + 0.707157i
\(82\) 4.21042e7i 0.931257i
\(83\) 4.63952e7 0.977599 0.488799 0.872396i \(-0.337435\pi\)
0.488799 + 0.872396i \(0.337435\pi\)
\(84\) −1.95300e7 + 2.92298e7i −0.392270 + 0.587096i
\(85\) 0 0
\(86\) 7.91619e7i 1.44718i
\(87\) 2.07404e7 3.10414e7i 0.362026 0.541831i
\(88\) 1.24992e6i 0.0208426i
\(89\) 7.26152e7i 1.15736i −0.815555 0.578679i \(-0.803568\pi\)
0.815555 0.578679i \(-0.196432\pi\)
\(90\) 0 0
\(91\) −4.50275e7 −0.656617
\(92\) 1.16674e8 1.62864
\(93\) −2.36720e7 1.58165e7i −0.316448 0.211436i
\(94\) −9.16191e7 −1.17348
\(95\) 0 0
\(96\) −9.89937e7 6.61429e7i −1.16553 0.778751i
\(97\) 1.47271e8i 1.66353i −0.555129 0.831764i \(-0.687331\pi\)
0.555129 0.831764i \(-0.312669\pi\)
\(98\) 6.06665e7 0.657726
\(99\) −4.21848e7 + 1.74753e7i −0.439152 + 0.181921i
\(100\) 0 0
\(101\) 1.03545e8i 0.995045i −0.867451 0.497522i \(-0.834243\pi\)
0.867451 0.497522i \(-0.165757\pi\)
\(102\) 1.13238e8 + 7.56605e7i 1.04615 + 0.698986i
\(103\) 1.66064e8i 1.47545i −0.675100 0.737726i \(-0.735899\pi\)
0.675100 0.737726i \(-0.264101\pi\)
\(104\) 4.62110e6i 0.0395013i
\(105\) 0 0
\(106\) 1.48209e8 1.17396
\(107\) −2.25540e7 −0.172063 −0.0860316 0.996292i \(-0.527419\pi\)
−0.0860316 + 0.996292i \(0.527419\pi\)
\(108\) −2.57055e7 + 1.29266e8i −0.188943 + 0.950146i
\(109\) 1.09975e8 0.779091 0.389546 0.921007i \(-0.372632\pi\)
0.389546 + 0.921007i \(0.372632\pi\)
\(110\) 0 0
\(111\) 6.00826e7 8.99235e7i 0.395783 0.592354i
\(112\) 1.18160e8i 0.750928i
\(113\) −2.87748e8 −1.76481 −0.882405 0.470490i \(-0.844077\pi\)
−0.882405 + 0.470490i \(0.844077\pi\)
\(114\) −2.86343e7 1.91321e7i −0.169538 0.113277i
\(115\) 0 0
\(116\) 1.14303e8i 0.631283i
\(117\) −1.55962e8 + 6.46080e7i −0.832291 + 0.344781i
\(118\) 3.07899e8i 1.58811i
\(119\) 1.31063e8i 0.653569i
\(120\) 0 0
\(121\) 1.65924e8 0.774050
\(122\) 1.69183e7 0.0763692
\(123\) −8.43961e7 + 1.26312e8i −0.368724 + 0.551856i
\(124\) −8.71665e7 −0.368691
\(125\) 0 0
\(126\) −2.38140e8 + 9.86507e7i −0.944822 + 0.391397i
\(127\) 2.75994e8i 1.06092i −0.847708 0.530462i \(-0.822018\pi\)
0.847708 0.530462i \(-0.177982\pi\)
\(128\) 2.35290e7 0.0876523
\(129\) 1.58677e8 2.37486e8i 0.573000 0.857588i
\(130\) 0 0
\(131\) 2.89118e8i 0.981725i 0.871237 + 0.490862i \(0.163318\pi\)
−0.871237 + 0.490862i \(0.836682\pi\)
\(132\) −7.76678e7 + 1.16243e8i −0.255826 + 0.382886i
\(133\) 3.31415e7i 0.105917i
\(134\) 5.09365e7i 0.157983i
\(135\) 0 0
\(136\) −1.34508e7 −0.0393180
\(137\) −2.07562e8 −0.589205 −0.294602 0.955620i \(-0.595187\pi\)
−0.294602 + 0.955620i \(0.595187\pi\)
\(138\) 7.11337e8 + 4.75282e8i 1.96137 + 1.31049i
\(139\) 1.42668e8 0.382180 0.191090 0.981573i \(-0.438798\pi\)
0.191090 + 0.981573i \(0.438798\pi\)
\(140\) 0 0
\(141\) −2.74857e8 1.83647e8i −0.695394 0.464630i
\(142\) 3.82143e8i 0.939880i
\(143\) −1.79067e8 −0.428226
\(144\) −1.69543e8 4.09271e8i −0.394302 0.951835i
\(145\) 0 0
\(146\) 6.21252e8i 1.36728i
\(147\) 1.82000e8 + 1.21604e8i 0.389763 + 0.260422i
\(148\) 3.31122e8i 0.690147i
\(149\) 8.19236e8i 1.66213i 0.556179 + 0.831063i \(0.312267\pi\)
−0.556179 + 0.831063i \(0.687733\pi\)
\(150\) 0 0
\(151\) 4.23861e8 0.815296 0.407648 0.913139i \(-0.366349\pi\)
0.407648 + 0.913139i \(0.366349\pi\)
\(152\) 3.40126e6 0.00637184
\(153\) 1.88056e8 + 4.53963e8i 0.343180 + 0.828428i
\(154\) −2.73420e8 −0.486124
\(155\) 0 0
\(156\) −2.87147e8 + 4.29762e8i −0.484848 + 0.725654i
\(157\) 7.59851e8i 1.25063i 0.780371 + 0.625316i \(0.215030\pi\)
−0.780371 + 0.625316i \(0.784970\pi\)
\(158\) 5.15922e8 0.827857
\(159\) 4.44628e8 + 2.97079e8i 0.695678 + 0.464819i
\(160\) 0 0
\(161\) 8.23307e8i 1.22534i
\(162\) −6.83297e8 + 6.83394e8i −0.992087 + 0.992227i
\(163\) 6.68160e8i 0.946520i 0.880923 + 0.473260i \(0.156923\pi\)
−0.880923 + 0.473260i \(0.843077\pi\)
\(164\) 4.65116e8i 0.642963i
\(165\) 0 0
\(166\) 1.04157e9 1.37169
\(167\) 1.96306e8 0.252387 0.126194 0.992006i \(-0.459724\pi\)
0.126194 + 0.992006i \(0.459724\pi\)
\(168\) 1.41435e7 2.11680e7i 0.0177549 0.0265731i
\(169\) 1.53698e8 0.188417
\(170\) 0 0
\(171\) −4.75533e7 1.14792e8i −0.0556156 0.134254i
\(172\) 8.74485e8i 0.999168i
\(173\) −1.02319e9 −1.14228 −0.571141 0.820852i \(-0.693499\pi\)
−0.571141 + 0.820852i \(0.693499\pi\)
\(174\) 4.65620e8 6.96877e8i 0.507966 0.760255i
\(175\) 0 0
\(176\) 4.69904e8i 0.489732i
\(177\) 6.17170e8 9.23696e8i 0.628799 0.941100i
\(178\) 1.63021e9i 1.62391i
\(179\) 1.28895e9i 1.25552i 0.778408 + 0.627759i \(0.216028\pi\)
−0.778408 + 0.627759i \(0.783972\pi\)
\(180\) 0 0
\(181\) 4.71707e8 0.439499 0.219749 0.975556i \(-0.429476\pi\)
0.219749 + 0.975556i \(0.429476\pi\)
\(182\) −1.01086e9 −0.921314
\(183\) 5.07550e7 + 3.39121e7i 0.0452558 + 0.0302378i
\(184\) −8.44946e7 −0.0737153
\(185\) 0 0
\(186\) −5.31435e8 3.55080e8i −0.444016 0.296670i
\(187\) 5.21217e8i 0.426238i
\(188\) −1.01210e9 −0.810198
\(189\) −9.12161e8 1.81390e8i −0.714866 0.142156i
\(190\) 0 0
\(191\) 1.61787e8i 0.121565i −0.998151 0.0607827i \(-0.980640\pi\)
0.998151 0.0607827i \(-0.0193597\pi\)
\(192\) −1.05825e9 7.07075e8i −0.778725 0.520308i
\(193\) 1.58840e9i 1.14480i −0.819974 0.572401i \(-0.806012\pi\)
0.819974 0.572401i \(-0.193988\pi\)
\(194\) 3.30623e9i 2.33413i
\(195\) 0 0
\(196\) 6.70171e8 0.454110
\(197\) −5.37769e8 −0.357052 −0.178526 0.983935i \(-0.557133\pi\)
−0.178526 + 0.983935i \(0.557133\pi\)
\(198\) −9.47046e8 + 3.92319e8i −0.616184 + 0.255257i
\(199\) −6.47586e8 −0.412938 −0.206469 0.978453i \(-0.566197\pi\)
−0.206469 + 0.978453i \(0.566197\pi\)
\(200\) 0 0
\(201\) 1.02100e8 1.52809e8i 0.0625521 0.0936194i
\(202\) 2.32457e9i 1.39617i
\(203\) 8.06570e8 0.474961
\(204\) 1.25092e9 + 8.35806e8i 0.722285 + 0.482597i
\(205\) 0 0
\(206\) 3.72812e9i 2.07024i
\(207\) 1.18133e9 + 2.85169e9i 0.643412 + 1.55318i
\(208\) 1.73729e9i 0.928152i
\(209\) 1.31799e8i 0.0690758i
\(210\) 0 0
\(211\) 5.81104e7 0.0293173 0.0146586 0.999893i \(-0.495334\pi\)
0.0146586 + 0.999893i \(0.495334\pi\)
\(212\) 1.63724e9 0.810529
\(213\) −7.65990e8 + 1.14643e9i −0.372139 + 0.556966i
\(214\) −5.06336e8 −0.241426
\(215\) 0 0
\(216\) 1.86157e7 9.36136e7i 0.00855195 0.0430055i
\(217\) 6.15086e8i 0.277394i
\(218\) 2.46893e9 1.09316
\(219\) −1.24527e9 + 1.86376e9i −0.541363 + 0.810238i
\(220\) 0 0
\(221\) 1.92700e9i 0.807815i
\(222\) 1.34885e9 2.01878e9i 0.555332 0.831144i
\(223\) 4.40200e9i 1.78004i 0.455920 + 0.890021i \(0.349310\pi\)
−0.455920 + 0.890021i \(0.650690\pi\)
\(224\) 2.57222e9i 1.02168i
\(225\) 0 0
\(226\) −6.45992e9 −2.47624
\(227\) 3.53592e9 1.33168 0.665839 0.746095i \(-0.268074\pi\)
0.665839 + 0.746095i \(0.268074\pi\)
\(228\) −3.16317e8 2.11348e8i −0.117053 0.0782094i
\(229\) 1.86569e9 0.678420 0.339210 0.940711i \(-0.389840\pi\)
0.339210 + 0.940711i \(0.389840\pi\)
\(230\) 0 0
\(231\) −8.20260e8 5.48059e8i −0.288074 0.192477i
\(232\) 8.27770e7i 0.0285731i
\(233\) 2.72132e9 0.923328 0.461664 0.887055i \(-0.347253\pi\)
0.461664 + 0.887055i \(0.347253\pi\)
\(234\) −3.50134e9 + 1.45045e9i −1.16781 + 0.483769i
\(235\) 0 0
\(236\) 3.40129e9i 1.09647i
\(237\) 1.54777e9 + 1.03414e9i 0.490582 + 0.327784i
\(238\) 2.94235e9i 0.917037i
\(239\) 2.27461e9i 0.697132i 0.937284 + 0.348566i \(0.113331\pi\)
−0.937284 + 0.348566i \(0.886669\pi\)
\(240\) 0 0
\(241\) −1.74667e9 −0.517778 −0.258889 0.965907i \(-0.583356\pi\)
−0.258889 + 0.965907i \(0.583356\pi\)
\(242\) 3.72500e9 1.08609
\(243\) −3.41973e9 + 6.80540e8i −0.980768 + 0.195177i
\(244\) 1.86893e8 0.0527272
\(245\) 0 0
\(246\) −1.89469e9 + 2.83571e9i −0.517365 + 0.774321i
\(247\) 4.87275e8i 0.130914i
\(248\) 6.31253e7 0.0166877
\(249\) 3.12471e9 + 2.08778e9i 0.812853 + 0.543110i
\(250\) 0 0
\(251\) 1.37549e9i 0.346547i 0.984874 + 0.173274i \(0.0554345\pi\)
−0.984874 + 0.173274i \(0.944566\pi\)
\(252\) −2.63068e9 + 1.08977e9i −0.652329 + 0.270230i
\(253\) 3.27417e9i 0.799132i
\(254\) 6.19605e9i 1.48861i
\(255\) 0 0
\(256\) 4.55069e9 1.05954
\(257\) −7.93672e9 −1.81932 −0.909659 0.415356i \(-0.863657\pi\)
−0.909659 + 0.415356i \(0.863657\pi\)
\(258\) 3.56228e9 5.33154e9i 0.803988 1.20330i
\(259\) 2.33655e9 0.519249
\(260\) 0 0
\(261\) 2.79372e9 1.15731e9i 0.602034 0.249396i
\(262\) 6.49068e9i 1.37748i
\(263\) −3.22555e8 −0.0674187 −0.0337093 0.999432i \(-0.510732\pi\)
−0.0337093 + 0.999432i \(0.510732\pi\)
\(264\) 5.62464e7 8.41819e7i 0.0115792 0.0173302i
\(265\) 0 0
\(266\) 7.44025e8i 0.148614i
\(267\) 3.26769e9 4.89062e9i 0.642977 0.962319i
\(268\) 5.62685e8i 0.109075i
\(269\) 3.47314e9i 0.663304i −0.943402 0.331652i \(-0.892394\pi\)
0.943402 0.331652i \(-0.107606\pi\)
\(270\) 0 0
\(271\) −1.44216e9 −0.267385 −0.133693 0.991023i \(-0.542683\pi\)
−0.133693 + 0.991023i \(0.542683\pi\)
\(272\) −5.05678e9 −0.923843
\(273\) −3.03259e9 2.02624e9i −0.545964 0.364787i
\(274\) −4.65976e9 −0.826726
\(275\) 0 0
\(276\) 7.85800e9 + 5.25035e9i 1.35418 + 0.904798i
\(277\) 3.38046e9i 0.574192i −0.957902 0.287096i \(-0.907310\pi\)
0.957902 0.287096i \(-0.0926899\pi\)
\(278\) 3.20289e9 0.536245
\(279\) −8.82561e8 2.13048e9i −0.145656 0.351609i
\(280\) 0 0
\(281\) 4.02262e9i 0.645184i 0.946538 + 0.322592i \(0.104554\pi\)
−0.946538 + 0.322592i \(0.895446\pi\)
\(282\) −6.17053e9 4.12286e9i −0.975722 0.651932i
\(283\) 1.04253e10i 1.62533i −0.582730 0.812666i \(-0.698016\pi\)
0.582730 0.812666i \(-0.301984\pi\)
\(284\) 4.22146e9i 0.648917i
\(285\) 0 0
\(286\) −4.02006e9 −0.600853
\(287\) −3.28207e9 −0.483749
\(288\) −3.69078e9 8.90943e9i −0.536473 1.29503i
\(289\) −1.36679e9 −0.195935
\(290\) 0 0
\(291\) 6.62720e9 9.91868e9i 0.924183 1.38319i
\(292\) 6.86285e9i 0.944002i
\(293\) −1.03927e10 −1.41012 −0.705061 0.709146i \(-0.749081\pi\)
−0.705061 + 0.709146i \(0.749081\pi\)
\(294\) 4.08588e9 + 2.72999e9i 0.546885 + 0.365403i
\(295\) 0 0
\(296\) 2.39796e8i 0.0312374i
\(297\) −3.62753e9 7.21360e8i −0.466213 0.0927099i
\(298\) 1.83918e10i 2.33216i
\(299\) 1.21050e10i 1.51453i
\(300\) 0 0
\(301\) 6.17076e9 0.751749
\(302\) 9.51565e9 1.14396
\(303\) 4.65951e9 6.97372e9i 0.552803 0.827359i
\(304\) 1.27869e9 0.149717
\(305\) 0 0
\(306\) 4.22185e9 + 1.01914e10i 0.481524 + 1.16238i
\(307\) 2.99309e9i 0.336951i 0.985706 + 0.168476i \(0.0538844\pi\)
−0.985706 + 0.168476i \(0.946116\pi\)
\(308\) −3.02042e9 −0.335632
\(309\) 7.47286e9 1.11843e10i 0.819696 1.22681i
\(310\) 0 0
\(311\) 6.44832e9i 0.689295i 0.938732 + 0.344647i \(0.112002\pi\)
−0.938732 + 0.344647i \(0.887998\pi\)
\(312\) 2.07949e8 3.11230e8i 0.0219452 0.0328445i
\(313\) 3.27737e7i 0.00341467i 0.999999 + 0.00170733i \(0.000543462\pi\)
−0.999999 + 0.00170733i \(0.999457\pi\)
\(314\) 1.70586e10i 1.75479i
\(315\) 0 0
\(316\) 5.69928e9 0.571573
\(317\) −1.17797e10 −1.16653 −0.583264 0.812282i \(-0.698225\pi\)
−0.583264 + 0.812282i \(0.698225\pi\)
\(318\) 9.98187e9 + 6.66942e9i 0.976120 + 0.652198i
\(319\) 3.20761e9 0.309755
\(320\) 0 0
\(321\) −1.51901e9 1.01493e9i −0.143067 0.0955907i
\(322\) 1.84832e10i 1.71931i
\(323\) −1.41832e9 −0.130306
\(324\) −7.54825e9 + 7.54931e9i −0.684961 + 0.685058i
\(325\) 0 0
\(326\) 1.50002e10i 1.32808i
\(327\) 7.40680e9 + 4.94888e9i 0.647798 + 0.432829i
\(328\) 3.36833e8i 0.0291018i
\(329\) 7.14182e9i 0.609573i
\(330\) 0 0
\(331\) −1.20100e10 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(332\) 1.15060e10 0.947049
\(333\) 8.09311e9 3.35261e9i 0.658171 0.272651i
\(334\) 4.40705e9 0.354130
\(335\) 0 0
\(336\) 5.31720e9 7.95806e9i 0.417182 0.624381i
\(337\) 1.59214e10i 1.23441i −0.786801 0.617207i \(-0.788264\pi\)
0.786801 0.617207i \(-0.211736\pi\)
\(338\) 3.45051e9 0.264372
\(339\) −1.93798e10 1.29486e10i −1.46740 0.980451i
\(340\) 0 0
\(341\) 2.44611e9i 0.180908i
\(342\) −1.06757e9 2.57708e9i −0.0780354 0.188375i
\(343\) 1.48174e10i 1.07052i
\(344\) 6.33295e8i 0.0452243i
\(345\) 0 0
\(346\) −2.29706e10 −1.60276
\(347\) −4.94792e9 −0.341275 −0.170638 0.985334i \(-0.554583\pi\)
−0.170638 + 0.985334i \(0.554583\pi\)
\(348\) 5.14361e9 7.69826e9i 0.350713 0.524899i
\(349\) 7.29567e9 0.491772 0.245886 0.969299i \(-0.420921\pi\)
0.245886 + 0.969299i \(0.420921\pi\)
\(350\) 0 0
\(351\) −1.34114e10 2.66695e9i −0.883578 0.175706i
\(352\) 1.02293e10i 0.666311i
\(353\) 6.93875e9 0.446871 0.223436 0.974719i \(-0.428273\pi\)
0.223436 + 0.974719i \(0.428273\pi\)
\(354\) 1.38554e10 2.07369e10i 0.882282 1.32048i
\(355\) 0 0
\(356\) 1.80086e10i 1.12119i
\(357\) −5.89782e9 + 8.82706e9i −0.363094 + 0.543429i
\(358\) 2.89368e10i 1.76164i
\(359\) 1.60096e10i 0.963838i −0.876216 0.481919i \(-0.839940\pi\)
0.876216 0.481919i \(-0.160060\pi\)
\(360\) 0 0
\(361\) −1.66249e10 −0.978883
\(362\) 1.05898e10 0.616670
\(363\) 1.11750e10 + 7.46660e9i 0.643607 + 0.430028i
\(364\) −1.11668e10 −0.636098
\(365\) 0 0
\(366\) 1.13945e9 + 7.61325e8i 0.0634994 + 0.0424273i
\(367\) 1.36364e10i 0.751686i −0.926683 0.375843i \(-0.877353\pi\)
0.926683 0.375843i \(-0.122647\pi\)
\(368\) −3.17655e10 −1.73207
\(369\) −1.13681e10 + 4.70930e9i −0.613173 + 0.254010i
\(370\) 0 0
\(371\) 1.15531e10i 0.609821i
\(372\) −5.87065e9 3.92249e9i −0.306559 0.204829i
\(373\) 2.44062e10i 1.26085i −0.776248 0.630427i \(-0.782880\pi\)
0.776248 0.630427i \(-0.217120\pi\)
\(374\) 1.17013e10i 0.598063i
\(375\) 0 0
\(376\) 7.32953e8 0.0366712
\(377\) 1.18589e10 0.587055
\(378\) −2.04780e10 4.07219e9i −1.00304 0.199463i
\(379\) 1.98392e10 0.961542 0.480771 0.876846i \(-0.340357\pi\)
0.480771 + 0.876846i \(0.340357\pi\)
\(380\) 0 0
\(381\) 1.24197e10 1.85881e10i 0.589403 0.882137i
\(382\) 3.63211e9i 0.170571i
\(383\) 1.51133e10 0.702366 0.351183 0.936307i \(-0.385780\pi\)
0.351183 + 0.936307i \(0.385780\pi\)
\(384\) 1.58467e9 + 1.05880e9i 0.0728811 + 0.0486957i
\(385\) 0 0
\(386\) 3.56594e10i 1.60630i
\(387\) 2.13737e10 8.85416e9i 0.952875 0.394733i
\(388\) 3.65232e10i 1.61154i
\(389\) 1.79991e10i 0.786056i 0.919527 + 0.393028i \(0.128572\pi\)
−0.919527 + 0.393028i \(0.871428\pi\)
\(390\) 0 0
\(391\) 3.52342e10 1.50750
\(392\) −4.85332e8 −0.0205539
\(393\) −1.30103e10 + 1.94720e10i −0.545403 + 0.816284i
\(394\) −1.20729e10 −0.500987
\(395\) 0 0
\(396\) −1.04618e10 + 4.33386e9i −0.425429 + 0.176236i
\(397\) 2.35673e10i 0.948739i 0.880326 + 0.474370i \(0.157324\pi\)
−0.880326 + 0.474370i \(0.842676\pi\)
\(398\) −1.45383e10 −0.579403
\(399\) 1.49137e9 2.23207e9i 0.0588428 0.0880678i
\(400\) 0 0
\(401\) 1.37692e10i 0.532515i 0.963902 + 0.266257i \(0.0857871\pi\)
−0.963902 + 0.266257i \(0.914213\pi\)
\(402\) 2.29214e9 3.43056e9i 0.0877682 0.131359i
\(403\) 9.04353e9i 0.342861i
\(404\) 2.56791e10i 0.963950i
\(405\) 0 0
\(406\) 1.81075e10 0.666428
\(407\) 9.29209e9 0.338638
\(408\) −9.05906e8 6.05284e8i −0.0326921 0.0218433i
\(409\) −3.58480e10 −1.28107 −0.640533 0.767931i \(-0.721286\pi\)
−0.640533 + 0.767931i \(0.721286\pi\)
\(410\) 0 0
\(411\) −1.39793e10 9.34031e9i −0.489912 0.327336i
\(412\) 4.11838e10i 1.42934i
\(413\) 2.40011e10 0.824955
\(414\) 2.65207e10 + 6.40203e10i 0.902785 + 2.17930i
\(415\) 0 0
\(416\) 3.78191e10i 1.26281i
\(417\) 9.60868e9 + 6.42007e9i 0.317775 + 0.212322i
\(418\) 2.95887e9i 0.0969217i
\(419\) 2.23996e10i 0.726750i −0.931643 0.363375i \(-0.881624\pi\)
0.931643 0.363375i \(-0.118376\pi\)
\(420\) 0 0
\(421\) −1.49535e10 −0.476008 −0.238004 0.971264i \(-0.576493\pi\)
−0.238004 + 0.971264i \(0.576493\pi\)
\(422\) 1.30457e9 0.0411357
\(423\) −1.02475e10 2.47372e10i −0.320078 0.772660i
\(424\) −1.18567e9 −0.0366861
\(425\) 0 0
\(426\) −1.71964e10 + 2.57373e10i −0.522156 + 0.781491i
\(427\) 1.31880e9i 0.0396706i
\(428\) −5.59339e9 −0.166686
\(429\) −1.20602e10 8.05804e9i −0.356061 0.237903i
\(430\) 0 0
\(431\) 6.40436e10i 1.85595i −0.372640 0.927976i \(-0.621547\pi\)
0.372640 0.927976i \(-0.378453\pi\)
\(432\) 6.99854e9 3.51938e10i 0.200943 1.01049i
\(433\) 5.22954e9i 0.148769i −0.997230 0.0743843i \(-0.976301\pi\)
0.997230 0.0743843i \(-0.0236992\pi\)
\(434\) 1.38087e10i 0.389218i
\(435\) 0 0
\(436\) 2.72738e10 0.754745
\(437\) −8.90959e9 −0.244305
\(438\) −2.79563e10 + 4.18412e10i −0.759598 + 1.13686i
\(439\) −4.34801e10 −1.17066 −0.585332 0.810793i \(-0.699036\pi\)
−0.585332 + 0.810793i \(0.699036\pi\)
\(440\) 0 0
\(441\) 6.78548e9 + 1.63800e10i 0.179402 + 0.433070i
\(442\) 4.32610e10i 1.13346i
\(443\) 3.78737e10 0.983383 0.491691 0.870770i \(-0.336379\pi\)
0.491691 + 0.870770i \(0.336379\pi\)
\(444\) 1.49005e10 2.23010e10i 0.383415 0.573843i
\(445\) 0 0
\(446\) 9.88246e10i 2.49761i
\(447\) −3.68656e10 + 5.51754e10i −0.923403 + 1.38202i
\(448\) 2.74973e10i 0.682620i
\(449\) 2.95505e10i 0.727076i −0.931579 0.363538i \(-0.881569\pi\)
0.931579 0.363538i \(-0.118431\pi\)
\(450\) 0 0
\(451\) −1.30523e10 −0.315486
\(452\) −7.13614e10 −1.70966
\(453\) 2.85469e10 + 1.90737e10i 0.677902 + 0.452942i
\(454\) 7.93813e10 1.86851
\(455\) 0 0
\(456\) 2.29074e8 + 1.53057e8i 0.00529806 + 0.00353991i
\(457\) 2.02181e10i 0.463529i 0.972772 + 0.231764i \(0.0744498\pi\)
−0.972772 + 0.231764i \(0.925550\pi\)
\(458\) 4.18847e10 0.951905
\(459\) −7.76277e9 + 3.90369e10i −0.174890 + 0.879476i
\(460\) 0 0
\(461\) 7.01826e10i 1.55391i 0.629556 + 0.776955i \(0.283237\pi\)
−0.629556 + 0.776955i \(0.716763\pi\)
\(462\) −1.84148e10 1.23039e10i −0.404202 0.270069i
\(463\) 4.16009e9i 0.0905271i 0.998975 + 0.0452635i \(0.0144128\pi\)
−0.998975 + 0.0452635i \(0.985587\pi\)
\(464\) 3.11198e10i 0.671374i
\(465\) 0 0
\(466\) 6.10935e10 1.29554
\(467\) 2.88138e10 0.605806 0.302903 0.953021i \(-0.402044\pi\)
0.302903 + 0.953021i \(0.402044\pi\)
\(468\) −3.86786e10 + 1.60228e10i −0.806282 + 0.334006i
\(469\) 3.97056e9 0.0820654
\(470\) 0 0
\(471\) −3.41933e10 + 5.11758e10i −0.694796 + 1.03988i
\(472\) 2.46319e9i 0.0496283i
\(473\) 2.45402e10 0.490268
\(474\) 3.47472e10 + 2.32165e10i 0.688346 + 0.459921i
\(475\) 0 0
\(476\) 3.25036e10i 0.633145i
\(477\) 1.65770e10 + 4.00165e10i 0.320209 + 0.772975i
\(478\) 5.10649e10i 0.978161i
\(479\) 4.47149e10i 0.849395i −0.905335 0.424698i \(-0.860380\pi\)
0.905335 0.424698i \(-0.139620\pi\)
\(480\) 0 0
\(481\) 3.43539e10 0.641795
\(482\) −3.92127e10 −0.726505
\(483\) −3.70488e10 + 5.54496e10i −0.680747 + 1.01885i
\(484\) 4.11493e10 0.749861
\(485\) 0 0
\(486\) −7.67727e10 + 1.52781e10i −1.37614 + 0.273857i
\(487\) 5.72836e10i 1.01839i −0.860651 0.509195i \(-0.829943\pi\)
0.860651 0.509195i \(-0.170057\pi\)
\(488\) −1.35347e8 −0.00238654
\(489\) −3.00672e10 + 4.50005e10i −0.525845 + 0.787012i
\(490\) 0 0
\(491\) 7.25262e10i 1.24787i −0.781477 0.623934i \(-0.785533\pi\)
0.781477 0.623934i \(-0.214467\pi\)
\(492\) −2.09302e10 + 3.13255e10i −0.357202 + 0.534611i
\(493\) 3.45180e10i 0.584330i
\(494\) 1.09393e10i 0.183688i
\(495\) 0 0
\(496\) 2.37318e10 0.392106
\(497\) −2.97885e10 −0.488228
\(498\) 7.01495e10 + 4.68706e10i 1.14053 + 0.762050i
\(499\) 2.64368e10 0.426389 0.213195 0.977010i \(-0.431613\pi\)
0.213195 + 0.977010i \(0.431613\pi\)
\(500\) 0 0
\(501\) 1.32212e10 + 8.83376e9i 0.209855 + 0.140215i
\(502\) 3.08797e10i 0.486248i
\(503\) −7.52828e10 −1.17604 −0.588022 0.808845i \(-0.700093\pi\)
−0.588022 + 0.808845i \(0.700093\pi\)
\(504\) 1.90512e9 7.89205e8i 0.0295257 0.0122312i
\(505\) 0 0
\(506\) 7.35048e10i 1.12128i
\(507\) 1.03515e10 + 6.91640e9i 0.156665 + 0.104676i
\(508\) 6.84465e10i 1.02777i
\(509\) 6.45184e10i 0.961197i 0.876941 + 0.480599i \(0.159581\pi\)
−0.876941 + 0.480599i \(0.840419\pi\)
\(510\) 0 0
\(511\) −4.84273e10 −0.710243
\(512\) 9.61394e10 1.39901
\(513\) 1.96295e9 9.87115e9i 0.0283426 0.142527i
\(514\) −1.78179e11 −2.55272
\(515\) 0 0
\(516\) 3.93518e10 5.88964e10i 0.555094 0.830788i
\(517\) 2.84019e10i 0.397544i
\(518\) 5.24554e10 0.728569
\(519\) −6.89119e10 4.60437e10i −0.949783 0.634601i
\(520\) 0 0
\(521\) 7.65146e10i 1.03847i −0.854632 0.519235i \(-0.826217\pi\)
0.854632 0.519235i \(-0.173783\pi\)
\(522\) 6.27189e10 2.59816e10i 0.844727 0.349932i
\(523\) 8.46771e10i 1.13177i −0.824483 0.565886i \(-0.808534\pi\)
0.824483 0.565886i \(-0.191466\pi\)
\(524\) 7.17012e10i 0.951046i
\(525\) 0 0
\(526\) −7.24133e9 −0.0945966
\(527\) −2.63232e10 −0.341269
\(528\) 2.11457e10 3.16480e10i 0.272073 0.407202i
\(529\) 1.43023e11 1.82634
\(530\) 0 0
\(531\) 8.31326e10 3.44381e10i 1.04567 0.433173i
\(532\) 8.21909e9i 0.102607i
\(533\) −4.82558e10 −0.597917
\(534\) 7.33594e10 1.09794e11i 0.902175 1.35025i
\(535\) 0 0
\(536\) 4.07492e8i 0.00493696i
\(537\) −5.80026e10 + 8.68104e10i −0.697510 + 1.04394i
\(538\) 7.79717e10i 0.930696i
\(539\) 1.88066e10i 0.222821i
\(540\) 0 0
\(541\) 1.43470e11 1.67483 0.837415 0.546568i \(-0.184066\pi\)
0.837415 + 0.546568i \(0.184066\pi\)
\(542\) −3.23765e10 −0.375174
\(543\) 3.17694e10 + 2.12268e10i 0.365434 + 0.244166i
\(544\) −1.10081e11 −1.25695
\(545\) 0 0
\(546\) −6.80816e10 4.54889e10i −0.766053 0.511841i
\(547\) 1.64171e11i 1.83378i −0.399134 0.916892i \(-0.630689\pi\)
0.399134 0.916892i \(-0.369311\pi\)
\(548\) −5.14755e10 −0.570792
\(549\) 1.89229e9 + 4.56795e9i 0.0208305 + 0.0502842i
\(550\) 0 0
\(551\) 8.72847e9i 0.0946961i
\(552\) −5.69070e9 3.80226e9i −0.0612928 0.0409529i
\(553\) 4.02167e10i 0.430037i
\(554\) 7.58912e10i 0.805661i
\(555\) 0 0
\(556\) 3.53817e10 0.370237
\(557\) 1.54420e11 1.60429 0.802145 0.597130i \(-0.203692\pi\)
0.802145 + 0.597130i \(0.203692\pi\)
\(558\) −1.98135e10 4.78291e10i −0.204373 0.493351i
\(559\) 9.07278e10 0.929166
\(560\) 0 0
\(561\) −2.34547e10 + 3.51039e10i −0.236799 + 0.354408i
\(562\) 9.03075e10i 0.905271i
\(563\) −1.54622e11 −1.53900 −0.769500 0.638646i \(-0.779495\pi\)
−0.769500 + 0.638646i \(0.779495\pi\)
\(564\) −6.81646e10 4.55444e10i −0.673663 0.450110i
\(565\) 0 0
\(566\) 2.34047e11i 2.28054i
\(567\) −5.32714e10 5.32638e10i −0.515420 0.515348i
\(568\) 3.05714e9i 0.0293712i
\(569\) 1.15380e11i 1.10073i 0.834925 + 0.550364i \(0.185511\pi\)
−0.834925 + 0.550364i \(0.814489\pi\)
\(570\) 0 0
\(571\) −1.63410e11 −1.53722 −0.768608 0.639720i \(-0.779050\pi\)
−0.768608 + 0.639720i \(0.779050\pi\)
\(572\) −4.44087e10 −0.414844
\(573\) 7.28041e9 1.08963e10i 0.0675363 0.101079i
\(574\) −7.36823e10 −0.678759
\(575\) 0 0
\(576\) −3.94548e10 9.52427e10i −0.358434 0.865250i
\(577\) 7.42282e10i 0.669678i −0.942275 0.334839i \(-0.891318\pi\)
0.942275 0.334839i \(-0.108682\pi\)
\(578\) −3.06844e10 −0.274920
\(579\) 7.14779e10 1.06978e11i 0.636001 0.951879i
\(580\) 0 0
\(581\) 8.11916e10i 0.712535i
\(582\) 1.48780e11 2.22674e11i 1.29674 1.94078i
\(583\) 4.59449e10i 0.397707i
\(584\) 4.97002e9i 0.0427274i
\(585\) 0 0
\(586\) −2.33315e11 −1.97857
\(587\) −6.72877e10 −0.566739 −0.283369 0.959011i \(-0.591452\pi\)
−0.283369 + 0.959011i \(0.591452\pi\)
\(588\) 4.51359e10 + 3.01577e10i 0.377583 + 0.252283i
\(589\) 6.65629e9 0.0553059
\(590\) 0 0
\(591\) −3.62187e10 2.41996e10i −0.296881 0.198362i
\(592\) 9.01507e10i 0.733977i
\(593\) 2.36444e10 0.191210 0.0956048 0.995419i \(-0.469521\pi\)
0.0956048 + 0.995419i \(0.469521\pi\)
\(594\) −8.14378e10 1.61945e10i −0.654154 0.130083i
\(595\) 0 0
\(596\) 2.03170e11i 1.61018i
\(597\) −4.36148e10 2.91414e10i −0.343350 0.229410i
\(598\) 2.71756e11i 2.12507i
\(599\) 3.03370e10i 0.235649i −0.993034 0.117825i \(-0.962408\pi\)
0.993034 0.117825i \(-0.0375921\pi\)
\(600\) 0 0
\(601\) 3.37911e10 0.259003 0.129501 0.991579i \(-0.458662\pi\)
0.129501 + 0.991579i \(0.458662\pi\)
\(602\) 1.38533e11 1.05480
\(603\) 1.37528e10 5.69718e9i 0.104022 0.0430914i
\(604\) 1.05117e11 0.789818
\(605\) 0 0
\(606\) 1.04606e11 1.56560e11i 0.775649 1.16089i
\(607\) 3.82366e10i 0.281660i 0.990034 + 0.140830i \(0.0449771\pi\)
−0.990034 + 0.140830i \(0.955023\pi\)
\(608\) 2.78359e10 0.203700
\(609\) 5.43224e10 + 3.62957e10i 0.394920 + 0.263867i
\(610\) 0 0
\(611\) 1.05005e11i 0.753435i
\(612\) 4.66380e10 + 1.12583e11i 0.332456 + 0.802539i
\(613\) 1.08066e11i 0.765330i 0.923887 + 0.382665i \(0.124994\pi\)
−0.923887 + 0.382665i \(0.875006\pi\)
\(614\) 6.71948e10i 0.472783i
\(615\) 0 0
\(616\) 2.18736e9 0.0151914
\(617\) −4.72538e9 −0.0326059 −0.0163029 0.999867i \(-0.505190\pi\)
−0.0163029 + 0.999867i \(0.505190\pi\)
\(618\) 1.67765e11 2.51088e11i 1.15013 1.72136i
\(619\) −2.29845e10 −0.156557 −0.0782786 0.996932i \(-0.524942\pi\)
−0.0782786 + 0.996932i \(0.524942\pi\)
\(620\) 0 0
\(621\) −4.87639e10 + 2.45221e11i −0.327893 + 1.64889i
\(622\) 1.44764e11i 0.967165i
\(623\) 1.27077e11 0.843555
\(624\) 7.81780e10 1.17006e11i 0.515640 0.771739i
\(625\) 0 0
\(626\) 7.35768e8i 0.00479119i
\(627\) 5.93094e9 8.87662e9i 0.0383754 0.0574351i
\(628\) 1.88443e11i 1.21155i
\(629\) 9.99949e10i 0.638815i
\(630\) 0 0
\(631\) −1.01892e11 −0.642722 −0.321361 0.946957i \(-0.604140\pi\)
−0.321361 + 0.946957i \(0.604140\pi\)
\(632\) −4.12737e9 −0.0258705
\(633\) 3.91372e9 + 2.61497e9i 0.0243767 + 0.0162874i
\(634\) −2.64453e11 −1.63678
\(635\) 0 0
\(636\) 1.10268e11 + 7.36757e10i 0.673938 + 0.450294i
\(637\) 6.95302e10i 0.422295i
\(638\) 7.20106e10 0.434624
\(639\) −1.03179e11 + 4.27422e10i −0.618851 + 0.256362i
\(640\) 0 0
\(641\) 1.17803e11i 0.697791i 0.937162 + 0.348896i \(0.113443\pi\)
−0.937162 + 0.348896i \(0.886557\pi\)
\(642\) −3.41016e10 2.27851e10i −0.200740 0.134125i
\(643\) 2.62680e10i 0.153668i −0.997044 0.0768339i \(-0.975519\pi\)
0.997044 0.0768339i \(-0.0244811\pi\)
\(644\) 2.04180e11i 1.18705i
\(645\) 0 0
\(646\) −3.18413e10 −0.182836
\(647\) 3.10527e11 1.77208 0.886038 0.463612i \(-0.153447\pi\)
0.886038 + 0.463612i \(0.153447\pi\)
\(648\) 5.46638e9 5.46715e9i 0.0310027 0.0310071i
\(649\) 9.54486e10 0.538010
\(650\) 0 0
\(651\) 2.76789e10 4.14260e10i 0.154108 0.230648i
\(652\) 1.65704e11i 0.916942i
\(653\) −3.48345e10 −0.191583 −0.0957914 0.995401i \(-0.530538\pi\)
−0.0957914 + 0.995401i \(0.530538\pi\)
\(654\) 1.66282e11 + 1.11102e11i 0.908940 + 0.607311i
\(655\) 0 0
\(656\) 1.26632e11i 0.683796i
\(657\) −1.67738e11 + 6.94863e10i −0.900265 + 0.372939i
\(658\) 1.60333e11i 0.855304i
\(659\) 3.77120e10i 0.199957i −0.994990 0.0999787i \(-0.968123\pi\)
0.994990 0.0999787i \(-0.0318775\pi\)
\(660\) 0 0
\(661\) −1.39619e11 −0.731372 −0.365686 0.930738i \(-0.619166\pi\)
−0.365686 + 0.930738i \(0.619166\pi\)
\(662\) −2.69623e11 −1.40386
\(663\) −8.67149e10 + 1.29783e11i −0.448786 + 0.671682i
\(664\) −8.33256e9 −0.0428653
\(665\) 0 0
\(666\) 1.81690e11 7.52659e10i 0.923494 0.382562i
\(667\) 2.16834e11i 1.09553i
\(668\) 4.86838e10 0.244500
\(669\) −1.98090e11 + 2.96474e11i −0.988912 + 1.48007i
\(670\) 0 0
\(671\) 5.24468e9i 0.0258719i
\(672\) 1.15750e11 1.73239e11i 0.567603 0.849510i
\(673\) 1.29783e11i 0.632642i −0.948652 0.316321i \(-0.897552\pi\)
0.948652 0.316321i \(-0.102448\pi\)
\(674\) 3.57434e11i 1.73203i
\(675\) 0 0
\(676\) 3.81171e10 0.182529
\(677\) −3.40648e11 −1.62163 −0.810813 0.585306i \(-0.800975\pi\)
−0.810813 + 0.585306i \(0.800975\pi\)
\(678\) −4.35075e11 2.90696e11i −2.05895 1.37569i
\(679\) 2.57724e11 1.21248
\(680\) 0 0
\(681\) 2.38144e11 + 1.59117e11i 1.10726 + 0.739821i
\(682\) 5.49149e10i 0.253836i
\(683\) −1.02876e11 −0.472750 −0.236375 0.971662i \(-0.575959\pi\)
−0.236375 + 0.971662i \(0.575959\pi\)
\(684\) −1.17932e10 2.84685e10i −0.0538776 0.130059i
\(685\) 0 0
\(686\) 3.32650e11i 1.50208i
\(687\) 1.25654e11 + 8.39562e10i 0.564092 + 0.376900i
\(688\) 2.38086e11i 1.06262i
\(689\) 1.69863e11i 0.753742i
\(690\) 0 0
\(691\) 3.58259e11 1.57140 0.785698 0.618611i \(-0.212304\pi\)
0.785698 + 0.618611i \(0.212304\pi\)
\(692\) −2.53752e11 −1.10659
\(693\) −3.05817e10 7.38234e10i −0.132595 0.320082i
\(694\) −1.11081e11 −0.478851
\(695\) 0 0
\(696\) −3.72496e9 + 5.57501e9i −0.0158740 + 0.0237580i
\(697\) 1.40459e11i 0.595141i
\(698\) 1.63787e11 0.690016
\(699\) 1.83280e11 + 1.22459e11i 0.767728 + 0.512960i
\(700\) 0 0
\(701\) 2.49323e11i 1.03250i −0.856438 0.516250i \(-0.827327\pi\)
0.856438 0.516250i \(-0.172673\pi\)
\(702\) −3.01085e11 5.98729e10i −1.23977 0.246537i
\(703\) 2.52854e10i 0.103526i
\(704\) 1.09353e11i 0.445183i
\(705\) 0 0
\(706\) 1.55775e11 0.627015
\(707\) 1.81203e11 0.725251
\(708\) 1.53058e11 2.29077e11i 0.609149 0.911691i
\(709\) 3.88874e11 1.53895 0.769474 0.638678i \(-0.220518\pi\)
0.769474 + 0.638678i \(0.220518\pi\)
\(710\) 0 0
\(711\) 5.77052e10 + 1.39299e11i 0.225807 + 0.545091i
\(712\) 1.30417e10i 0.0507473i
\(713\) −1.65357e11 −0.639829
\(714\) −1.32406e11 + 1.98167e11i −0.509465 + 0.762497i
\(715\) 0 0
\(716\) 3.19659e11i 1.21628i
\(717\) −1.02357e11 + 1.53195e11i −0.387296 + 0.579651i
\(718\) 3.59416e11i 1.35238i
\(719\) 3.35735e10i 0.125626i −0.998025 0.0628132i \(-0.979993\pi\)
0.998025 0.0628132i \(-0.0200072\pi\)
\(720\) 0 0
\(721\) 2.90611e11 1.07540
\(722\) −3.73228e11 −1.37349
\(723\) −1.17638e11 7.86002e10i −0.430521 0.287654i
\(724\) 1.16983e11 0.425764
\(725\) 0 0
\(726\) 2.50878e11 + 1.67625e11i 0.903058 + 0.603381i
\(727\) 2.53113e11i 0.906102i −0.891485 0.453051i \(-0.850336\pi\)
0.891485 0.453051i \(-0.149664\pi\)
\(728\) 8.08692e9 0.0287911
\(729\) −2.60942e11 1.08053e11i −0.923920 0.382586i
\(730\) 0 0
\(731\) 2.64084e11i 0.924853i
\(732\) 1.25872e10 + 8.41020e9i 0.0438416 + 0.0292929i
\(733\) 2.07602e11i 0.719144i 0.933117 + 0.359572i \(0.117077\pi\)
−0.933117 + 0.359572i \(0.882923\pi\)
\(734\) 3.06137e11i 1.05471i
\(735\) 0 0
\(736\) −6.91504e11 −2.35659
\(737\) 1.57903e10 0.0535205
\(738\) −2.55214e11 + 1.05724e11i −0.860357 + 0.356407i
\(739\) −4.15014e11 −1.39151 −0.695753 0.718281i \(-0.744929\pi\)
−0.695753 + 0.718281i \(0.744929\pi\)
\(740\) 0 0
\(741\) 2.19274e10 3.28179e10i 0.0727300 0.108852i
\(742\) 2.59366e11i 0.855653i
\(743\) 3.30690e11 1.08509 0.542545 0.840027i \(-0.317461\pi\)
0.542545 + 0.840027i \(0.317461\pi\)
\(744\) 4.25148e9 + 2.84064e9i 0.0138755 + 0.00927095i
\(745\) 0 0
\(746\) 5.47918e11i 1.76913i
\(747\) 1.16498e11 + 2.81224e11i 0.374143 + 0.903170i
\(748\) 1.29262e11i 0.412918i
\(749\) 3.94695e10i 0.125411i
\(750\) 0 0
\(751\) −4.77978e11 −1.50262 −0.751308 0.659952i \(-0.770577\pi\)
−0.751308 + 0.659952i \(0.770577\pi\)
\(752\) 2.75552e11 0.861652
\(753\) −6.18970e10 + 9.26390e10i −0.192526 + 0.288147i
\(754\) 2.66231e11 0.823709
\(755\) 0 0
\(756\) −2.26216e11 4.49847e10i −0.692526 0.137714i
\(757\) 8.95066e10i 0.272566i 0.990670 + 0.136283i \(0.0435156\pi\)
−0.990670 + 0.136283i \(0.956484\pi\)
\(758\) 4.45390e11 1.34916
\(759\) −1.47337e11 + 2.20514e11i −0.443962 + 0.664462i
\(760\) 0 0
\(761\) 5.71473e11i 1.70395i 0.523581 + 0.851976i \(0.324596\pi\)
−0.523581 + 0.851976i \(0.675404\pi\)
\(762\) 2.78822e11 4.17303e11i 0.827004 1.23775i
\(763\) 1.92456e11i 0.567851i
\(764\) 4.01231e10i 0.117766i
\(765\) 0 0
\(766\) 3.39292e11 0.985504
\(767\) 3.52884e11 1.01965
\(768\) 3.06488e11 + 2.04781e11i 0.880986 + 0.588634i
\(769\) −2.56194e11 −0.732596 −0.366298 0.930498i \(-0.619375\pi\)
−0.366298 + 0.930498i \(0.619375\pi\)
\(770\) 0 0
\(771\) −5.34537e11 3.57152e11i −1.51273 1.01073i
\(772\) 3.93923e11i 1.10903i
\(773\) 1.00523e11 0.281543 0.140772 0.990042i \(-0.455042\pi\)
0.140772 + 0.990042i \(0.455042\pi\)
\(774\) 4.79838e11 1.98775e11i 1.33700 0.553859i
\(775\) 0 0
\(776\) 2.64498e10i 0.0729417i
\(777\)