Properties

Label 147.6.c.c.146.10
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.10
Root \(-1.84692 - 1.06632i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.c.146.8

$q$-expansion

\(f(q)\) \(=\) \(q+2.13264i q^{2} +(9.16236 + 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 + 19.5400i) q^{6} +126.790i q^{8} +(-75.1022 + 231.103i) q^{9} +O(q^{10})\) \(q+2.13264i q^{2} +(9.16236 + 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 + 19.5400i) q^{6} +126.790i q^{8} +(-75.1022 + 231.103i) q^{9} +202.713i q^{10} +130.679i q^{11} +(251.524 + 346.210i) q^{12} -14.6710i q^{13} +(870.905 + 1198.76i) q^{15} +608.062 q^{16} -640.492 q^{17} +(-492.860 - 160.166i) q^{18} -542.677i q^{19} +2609.37 q^{20} -278.692 q^{22} -4094.31i q^{23} +(-1599.01 + 1161.69i) q^{24} +5909.98 q^{25} +31.2880 q^{26} +(-3602.68 + 1170.29i) q^{27} -3594.70i q^{29} +(-2556.52 + 1857.33i) q^{30} +2900.94i q^{31} +5354.04i q^{32} +(-1648.06 + 1197.33i) q^{33} -1365.94i q^{34} +(-2061.69 + 6344.20i) q^{36} -4342.05 q^{37} +1157.34 q^{38} +(185.024 - 134.421i) q^{39} +12051.7i q^{40} -10945.3 q^{41} +20541.6 q^{43} +3587.38i q^{44} +(-7138.66 + 21966.9i) q^{45} +8731.70 q^{46} -8816.03 q^{47} +(5571.28 + 7668.60i) q^{48} +12603.9i q^{50} +(-5868.42 - 8077.60i) q^{51} -402.745i q^{52} +6977.45i q^{53} +(-2495.82 - 7683.23i) q^{54} +12421.4i q^{55} +(6844.00 - 4972.20i) q^{57} +7666.22 q^{58} -40020.1 q^{59} +(23908.0 + 32908.1i) q^{60} -33210.2i q^{61} -6186.66 q^{62} +8039.72 q^{64} -1394.51i q^{65} +(-2553.47 - 3514.73i) q^{66} +6436.18 q^{67} -17582.7 q^{68} +(51635.6 - 37513.6i) q^{69} +32493.9i q^{71} +(-29301.5 - 9522.18i) q^{72} +12737.8i q^{73} -9260.03i q^{74} +(54149.3 + 74533.9i) q^{75} -14897.5i q^{76} +(286.672 + 394.590i) q^{78} +8597.89 q^{79} +57797.8 q^{80} +(-47768.3 - 34712.7i) q^{81} -23342.3i q^{82} -31669.6 q^{83} -60880.4 q^{85} +43807.8i q^{86} +(45334.8 - 32936.0i) q^{87} -16568.7 q^{88} +31945.9 q^{89} +(-46847.6 - 15224.2i) q^{90} -112396. i q^{92} +(-36585.3 + 26579.4i) q^{93} -18801.4i q^{94} -51582.8i q^{95} +(-67522.8 + 49055.7i) q^{96} +143107. i q^{97} +(-30200.3 - 9814.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13264i 0.377001i 0.982073 + 0.188501i \(0.0603628\pi\)
−0.982073 + 0.188501i \(0.939637\pi\)
\(3\) 9.16236 + 12.6115i 0.587766 + 0.809031i
\(4\) 27.4518 0.857870
\(5\) 95.0525 1.70035 0.850175 0.526500i \(-0.176496\pi\)
0.850175 + 0.526500i \(0.176496\pi\)
\(6\) −26.8959 + 19.5400i −0.305006 + 0.221589i
\(7\) 0 0
\(8\) 126.790i 0.700420i
\(9\) −75.1022 + 231.103i −0.309063 + 0.951042i
\(10\) 202.713i 0.641035i
\(11\) 130.679i 0.325630i 0.986657 + 0.162815i \(0.0520573\pi\)
−0.986657 + 0.162815i \(0.947943\pi\)
\(12\) 251.524 + 346.210i 0.504227 + 0.694043i
\(13\) 14.6710i 0.0240769i −0.999928 0.0120385i \(-0.996168\pi\)
0.999928 0.0120385i \(-0.00383205\pi\)
\(14\) 0 0
\(15\) 870.905 + 1198.76i 0.999408 + 1.37564i
\(16\) 608.062 0.593811
\(17\) −640.492 −0.537516 −0.268758 0.963208i \(-0.586613\pi\)
−0.268758 + 0.963208i \(0.586613\pi\)
\(18\) −492.860 160.166i −0.358544 0.116517i
\(19\) 542.677i 0.344872i −0.985021 0.172436i \(-0.944836\pi\)
0.985021 0.172436i \(-0.0551637\pi\)
\(20\) 2609.37 1.45868
\(21\) 0 0
\(22\) −278.692 −0.122763
\(23\) 4094.31i 1.61384i −0.590659 0.806922i \(-0.701132\pi\)
0.590659 0.806922i \(-0.298868\pi\)
\(24\) −1599.01 + 1161.69i −0.566661 + 0.411683i
\(25\) 5909.98 1.89119
\(26\) 31.2880 0.00907703
\(27\) −3602.68 + 1170.29i −0.951079 + 0.308948i
\(28\) 0 0
\(29\) 3594.70i 0.793721i −0.917879 0.396861i \(-0.870100\pi\)
0.917879 0.396861i \(-0.129900\pi\)
\(30\) −2556.52 + 1857.33i −0.518617 + 0.376778i
\(31\) 2900.94i 0.542168i 0.962556 + 0.271084i \(0.0873821\pi\)
−0.962556 + 0.271084i \(0.912618\pi\)
\(32\) 5354.04i 0.924287i
\(33\) −1648.06 + 1197.33i −0.263445 + 0.191394i
\(34\) 1365.94i 0.202644i
\(35\) 0 0
\(36\) −2061.69 + 6344.20i −0.265136 + 0.815870i
\(37\) −4342.05 −0.521423 −0.260712 0.965417i \(-0.583957\pi\)
−0.260712 + 0.965417i \(0.583957\pi\)
\(38\) 1157.34 0.130017
\(39\) 185.024 134.421i 0.0194790 0.0141516i
\(40\) 12051.7i 1.19096i
\(41\) −10945.3 −1.01687 −0.508436 0.861100i \(-0.669776\pi\)
−0.508436 + 0.861100i \(0.669776\pi\)
\(42\) 0 0
\(43\) 20541.6 1.69419 0.847096 0.531440i \(-0.178349\pi\)
0.847096 + 0.531440i \(0.178349\pi\)
\(44\) 3587.38i 0.279348i
\(45\) −7138.66 + 21966.9i −0.525515 + 1.61710i
\(46\) 8731.70 0.608421
\(47\) −8816.03 −0.582141 −0.291071 0.956702i \(-0.594011\pi\)
−0.291071 + 0.956702i \(0.594011\pi\)
\(48\) 5571.28 + 7668.60i 0.349022 + 0.480411i
\(49\) 0 0
\(50\) 12603.9i 0.712982i
\(51\) −5868.42 8077.60i −0.315934 0.434867i
\(52\) 402.745i 0.0206549i
\(53\) 6977.45i 0.341198i 0.985341 + 0.170599i \(0.0545703\pi\)
−0.985341 + 0.170599i \(0.945430\pi\)
\(54\) −2495.82 7683.23i −0.116474 0.358558i
\(55\) 12421.4i 0.553685i
\(56\) 0 0
\(57\) 6844.00 4972.20i 0.279012 0.202704i
\(58\) 7666.22 0.299234
\(59\) −40020.1 −1.49675 −0.748373 0.663278i \(-0.769165\pi\)
−0.748373 + 0.663278i \(0.769165\pi\)
\(60\) 23908.0 + 32908.1i 0.857362 + 1.18012i
\(61\) 33210.2i 1.14274i −0.820693 0.571370i \(-0.806412\pi\)
0.820693 0.571370i \(-0.193588\pi\)
\(62\) −6186.66 −0.204398
\(63\) 0 0
\(64\) 8039.72 0.245353
\(65\) 1394.51i 0.0409392i
\(66\) −2553.47 3514.73i −0.0721558 0.0993190i
\(67\) 6436.18 0.175163 0.0875813 0.996157i \(-0.472086\pi\)
0.0875813 + 0.996157i \(0.472086\pi\)
\(68\) −17582.7 −0.461119
\(69\) 51635.6 37513.6i 1.30565 0.948562i
\(70\) 0 0
\(71\) 32493.9i 0.764990i 0.923958 + 0.382495i \(0.124935\pi\)
−0.923958 + 0.382495i \(0.875065\pi\)
\(72\) −29301.5 9522.18i −0.666128 0.216474i
\(73\) 12737.8i 0.279761i 0.990168 + 0.139880i \(0.0446718\pi\)
−0.990168 + 0.139880i \(0.955328\pi\)
\(74\) 9260.03i 0.196577i
\(75\) 54149.3 + 74533.9i 1.11158 + 1.53003i
\(76\) 14897.5i 0.295855i
\(77\) 0 0
\(78\) 286.672 + 394.590i 0.00533517 + 0.00734360i
\(79\) 8597.89 0.154997 0.0774986 0.996992i \(-0.475307\pi\)
0.0774986 + 0.996992i \(0.475307\pi\)
\(80\) 57797.8 1.00969
\(81\) −47768.3 34712.7i −0.808960 0.587863i
\(82\) 23342.3i 0.383362i
\(83\) −31669.6 −0.504601 −0.252300 0.967649i \(-0.581187\pi\)
−0.252300 + 0.967649i \(0.581187\pi\)
\(84\) 0 0
\(85\) −60880.4 −0.913966
\(86\) 43807.8i 0.638713i
\(87\) 45334.8 32936.0i 0.642145 0.466522i
\(88\) −16568.7 −0.228077
\(89\) 31945.9 0.427504 0.213752 0.976888i \(-0.431432\pi\)
0.213752 + 0.976888i \(0.431432\pi\)
\(90\) −46847.6 15224.2i −0.609651 0.198120i
\(91\) 0 0
\(92\) 112396.i 1.38447i
\(93\) −36585.3 + 26579.4i −0.438631 + 0.318668i
\(94\) 18801.4i 0.219468i
\(95\) 51582.8i 0.586403i
\(96\) −67522.8 + 49055.7i −0.747777 + 0.543264i
\(97\) 143107.i 1.54430i 0.635441 + 0.772149i \(0.280818\pi\)
−0.635441 + 0.772149i \(0.719182\pi\)
\(98\) 0 0
\(99\) −30200.3 9814.28i −0.309687 0.100640i
\(100\) 162240. 1.62240
\(101\) 53587.7 0.522711 0.261355 0.965243i \(-0.415831\pi\)
0.261355 + 0.965243i \(0.415831\pi\)
\(102\) 17226.6 12515.2i 0.163946 0.119107i
\(103\) 153816.i 1.42860i −0.699842 0.714298i \(-0.746746\pi\)
0.699842 0.714298i \(-0.253254\pi\)
\(104\) 1860.13 0.0168639
\(105\) 0 0
\(106\) −14880.4 −0.128632
\(107\) 153413.i 1.29540i −0.761897 0.647698i \(-0.775732\pi\)
0.761897 0.647698i \(-0.224268\pi\)
\(108\) −98900.2 + 32126.7i −0.815902 + 0.265038i
\(109\) −127739. −1.02981 −0.514907 0.857246i \(-0.672174\pi\)
−0.514907 + 0.857246i \(0.672174\pi\)
\(110\) −26490.3 −0.208740
\(111\) −39783.4 54759.9i −0.306475 0.421847i
\(112\) 0 0
\(113\) 90418.2i 0.666131i −0.942904 0.333066i \(-0.891917\pi\)
0.942904 0.333066i \(-0.108083\pi\)
\(114\) 10603.9 + 14595.8i 0.0764196 + 0.105188i
\(115\) 389175.i 2.74410i
\(116\) 98681.2i 0.680910i
\(117\) 3390.51 + 1101.82i 0.0228981 + 0.00744128i
\(118\) 85348.6i 0.564276i
\(119\) 0 0
\(120\) −151990. + 110422.i −0.963523 + 0.700005i
\(121\) 143974. 0.893965
\(122\) 70825.5 0.430814
\(123\) −100284. 138037.i −0.597683 0.822681i
\(124\) 79636.0i 0.465110i
\(125\) 264719. 1.51534
\(126\) 0 0
\(127\) 132321. 0.727982 0.363991 0.931402i \(-0.381414\pi\)
0.363991 + 0.931402i \(0.381414\pi\)
\(128\) 188475.i 1.01679i
\(129\) 188209. + 259061.i 0.995788 + 1.37065i
\(130\) 2974.00 0.0154341
\(131\) 147778. 0.752368 0.376184 0.926545i \(-0.377236\pi\)
0.376184 + 0.926545i \(0.377236\pi\)
\(132\) −45242.4 + 32868.8i −0.226001 + 0.164191i
\(133\) 0 0
\(134\) 13726.1i 0.0660366i
\(135\) −342444. + 111239.i −1.61717 + 0.525321i
\(136\) 81207.7i 0.376487i
\(137\) 226682.i 1.03185i 0.856634 + 0.515925i \(0.172552\pi\)
−0.856634 + 0.515925i \(0.827448\pi\)
\(138\) 80003.0 + 110120.i 0.357609 + 0.492232i
\(139\) 230678.i 1.01267i −0.862335 0.506337i \(-0.830999\pi\)
0.862335 0.506337i \(-0.169001\pi\)
\(140\) 0 0
\(141\) −80775.7 111184.i −0.342163 0.470971i
\(142\) −69297.8 −0.288402
\(143\) 1917.19 0.00784016
\(144\) −45666.8 + 140525.i −0.183525 + 0.564739i
\(145\) 341685.i 1.34960i
\(146\) −27165.1 −0.105470
\(147\) 0 0
\(148\) −119197. −0.447313
\(149\) 9357.83i 0.0345310i 0.999851 + 0.0172655i \(0.00549605\pi\)
−0.999851 + 0.0172655i \(0.994504\pi\)
\(150\) −158954. + 115481.i −0.576825 + 0.419067i
\(151\) 138457. 0.494166 0.247083 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(152\) 68805.8 0.241555
\(153\) 48102.4 148020.i 0.166126 0.511200i
\(154\) 0 0
\(155\) 275741.i 0.921876i
\(156\) 5079.24 3690.10i 0.0167104 0.0121402i
\(157\) 15464.9i 0.0500724i 0.999687 + 0.0250362i \(0.00797010\pi\)
−0.999687 + 0.0250362i \(0.992030\pi\)
\(158\) 18336.2i 0.0584342i
\(159\) −87996.4 + 63929.9i −0.276040 + 0.200545i
\(160\) 508915.i 1.57161i
\(161\) 0 0
\(162\) 74029.8 101873.i 0.221625 0.304979i
\(163\) 289645. 0.853880 0.426940 0.904280i \(-0.359592\pi\)
0.426940 + 0.904280i \(0.359592\pi\)
\(164\) −300467. −0.872344
\(165\) −156653. + 113809.i −0.447948 + 0.325437i
\(166\) 67540.0i 0.190235i
\(167\) −347837. −0.965128 −0.482564 0.875861i \(-0.660294\pi\)
−0.482564 + 0.875861i \(0.660294\pi\)
\(168\) 0 0
\(169\) 371078. 0.999420
\(170\) 129836.i 0.344567i
\(171\) 125414. + 40756.3i 0.327987 + 0.106587i
\(172\) 563904. 1.45340
\(173\) −508138. −1.29082 −0.645411 0.763836i \(-0.723314\pi\)
−0.645411 + 0.763836i \(0.723314\pi\)
\(174\) 70240.7 + 96682.9i 0.175880 + 0.242090i
\(175\) 0 0
\(176\) 79460.9i 0.193362i
\(177\) −366679. 504716.i −0.879736 1.21091i
\(178\) 68129.1i 0.161169i
\(179\) 400409.i 0.934053i −0.884243 0.467026i \(-0.845325\pi\)
0.884243 0.467026i \(-0.154675\pi\)
\(180\) −195969. + 603032.i −0.450824 + 1.38727i
\(181\) 10694.7i 0.0242646i 0.999926 + 0.0121323i \(0.00386192\pi\)
−0.999926 + 0.0121323i \(0.996138\pi\)
\(182\) 0 0
\(183\) 418832. 304284.i 0.924511 0.671663i
\(184\) 519116. 1.13037
\(185\) −412722. −0.886602
\(186\) −56684.4 78023.3i −0.120138 0.165364i
\(187\) 83698.9i 0.175031i
\(188\) −242016. −0.499402
\(189\) 0 0
\(190\) 110008. 0.221075
\(191\) 197252.i 0.391236i 0.980680 + 0.195618i \(0.0626712\pi\)
−0.980680 + 0.195618i \(0.937329\pi\)
\(192\) 73662.9 + 101393.i 0.144210 + 0.198498i
\(193\) −125511. −0.242542 −0.121271 0.992619i \(-0.538697\pi\)
−0.121271 + 0.992619i \(0.538697\pi\)
\(194\) −305196. −0.582203
\(195\) 17587.0 12777.0i 0.0331211 0.0240627i
\(196\) 0 0
\(197\) 631690.i 1.15968i 0.814730 + 0.579841i \(0.196885\pi\)
−0.814730 + 0.579841i \(0.803115\pi\)
\(198\) 20930.4 64406.5i 0.0379414 0.116753i
\(199\) 622380.i 1.11410i 0.830480 + 0.557049i \(0.188066\pi\)
−0.830480 + 0.557049i \(0.811934\pi\)
\(200\) 749323.i 1.32463i
\(201\) 58970.6 + 81170.2i 0.102955 + 0.141712i
\(202\) 114283.i 0.197063i
\(203\) 0 0
\(204\) −161099. 221745.i −0.271030 0.373060i
\(205\) −1.04037e6 −1.72904
\(206\) 328035. 0.538583
\(207\) 946208. + 307492.i 1.53483 + 0.498779i
\(208\) 8920.87i 0.0142971i
\(209\) 70916.5 0.112300
\(210\) 0 0
\(211\) −271742. −0.420195 −0.210098 0.977680i \(-0.567378\pi\)
−0.210098 + 0.977680i \(0.567378\pi\)
\(212\) 191544.i 0.292704i
\(213\) −409798. + 297721.i −0.618900 + 0.449635i
\(214\) 327175. 0.488366
\(215\) 1.95253e6 2.88072
\(216\) −148381. 456782.i −0.216394 0.666154i
\(217\) 0 0
\(218\) 272423.i 0.388241i
\(219\) −160643. + 116708.i −0.226335 + 0.164434i
\(220\) 340989.i 0.474989i
\(221\) 9396.65i 0.0129417i
\(222\) 116783. 84843.8i 0.159037 0.115541i
\(223\) 256397.i 0.345264i 0.984986 + 0.172632i \(0.0552271\pi\)
−0.984986 + 0.172632i \(0.944773\pi\)
\(224\) 0 0
\(225\) −443852. + 1.36581e6i −0.584497 + 1.79860i
\(226\) 192830. 0.251133
\(227\) 117895. 0.151856 0.0759278 0.997113i \(-0.475808\pi\)
0.0759278 + 0.997113i \(0.475808\pi\)
\(228\) 187880. 136496.i 0.239356 0.173893i
\(229\) 373781.i 0.471008i 0.971873 + 0.235504i \(0.0756741\pi\)
−0.971873 + 0.235504i \(0.924326\pi\)
\(230\) 829970. 1.03453
\(231\) 0 0
\(232\) 455771. 0.555938
\(233\) 1.26480e6i 1.52627i −0.646240 0.763134i \(-0.723660\pi\)
0.646240 0.763134i \(-0.276340\pi\)
\(234\) −2349.80 + 7230.74i −0.00280537 + 0.00863264i
\(235\) −837986. −0.989845
\(236\) −1.09863e6 −1.28401
\(237\) 78776.9 + 108433.i 0.0911021 + 0.125398i
\(238\) 0 0
\(239\) 520817.i 0.589780i −0.955531 0.294890i \(-0.904717\pi\)
0.955531 0.294890i \(-0.0952830\pi\)
\(240\) 529564. + 728920.i 0.593459 + 0.816868i
\(241\) 954289.i 1.05837i −0.848507 0.529185i \(-0.822498\pi\)
0.848507 0.529185i \(-0.177502\pi\)
\(242\) 307045.i 0.337026i
\(243\) 110.689 920483.i 0.000120251 1.00000i
\(244\) 911681.i 0.980321i
\(245\) 0 0
\(246\) 294383. 213871.i 0.310152 0.225327i
\(247\) −7961.60 −0.00830344
\(248\) −367808. −0.379745
\(249\) −290169. 399403.i −0.296587 0.408238i
\(250\) 564551.i 0.571285i
\(251\) 789792. 0.791277 0.395638 0.918406i \(-0.370523\pi\)
0.395638 + 0.918406i \(0.370523\pi\)
\(252\) 0 0
\(253\) 535040. 0.525515
\(254\) 282194.i 0.274450i
\(255\) −557808. 767796.i −0.537198 0.739427i
\(256\) −144679. −0.137977
\(257\) −1.10769e6 −1.04613 −0.523064 0.852293i \(-0.675211\pi\)
−0.523064 + 0.852293i \(0.675211\pi\)
\(258\) −552485. + 401383.i −0.516739 + 0.375414i
\(259\) 0 0
\(260\) 38281.9i 0.0351205i
\(261\) 830747. + 269970.i 0.754862 + 0.245310i
\(262\) 315157.i 0.283644i
\(263\) 1.05399e6i 0.939608i −0.882771 0.469804i \(-0.844325\pi\)
0.882771 0.469804i \(-0.155675\pi\)
\(264\) −151809. 208957.i −0.134056 0.184522i
\(265\) 663224.i 0.580157i
\(266\) 0 0
\(267\) 292700. + 402887.i 0.251272 + 0.345864i
\(268\) 176685. 0.150267
\(269\) 459896. 0.387507 0.193753 0.981050i \(-0.437934\pi\)
0.193753 + 0.981050i \(0.437934\pi\)
\(270\) −237234. 730310.i −0.198047 0.609675i
\(271\) 885691.i 0.732586i −0.930499 0.366293i \(-0.880627\pi\)
0.930499 0.366293i \(-0.119373\pi\)
\(272\) −389459. −0.319183
\(273\) 0 0
\(274\) −483433. −0.389009
\(275\) 772310.i 0.615828i
\(276\) 1.41749e6 1.02982e6i 1.12008 0.813743i
\(277\) −770456. −0.603321 −0.301660 0.953415i \(-0.597541\pi\)
−0.301660 + 0.953415i \(0.597541\pi\)
\(278\) 491955. 0.381780
\(279\) −670415. 217867.i −0.515624 0.167564i
\(280\) 0 0
\(281\) 2.25084e6i 1.70051i −0.526374 0.850253i \(-0.676449\pi\)
0.526374 0.850253i \(-0.323551\pi\)
\(282\) 237115. 172266.i 0.177557 0.128996i
\(283\) 5068.25i 0.00376177i −0.999998 0.00188088i \(-0.999401\pi\)
0.999998 0.00188088i \(-0.000598704\pi\)
\(284\) 892016.i 0.656262i
\(285\) 650539. 472620.i 0.474418 0.344667i
\(286\) 4088.68i 0.00295575i
\(287\) 0 0
\(288\) −1.23734e6 402101.i −0.879036 0.285663i
\(289\) −1.00963e6 −0.711076
\(290\) 728693. 0.508803
\(291\) −1.80480e6 + 1.31120e6i −1.24939 + 0.907686i
\(292\) 349675.i 0.239998i
\(293\) −2.51767e6 −1.71329 −0.856643 0.515909i \(-0.827454\pi\)
−0.856643 + 0.515909i \(0.827454\pi\)
\(294\) 0 0
\(295\) −3.80401e6 −2.54499
\(296\) 550526.i 0.365215i
\(297\) −152933. 470795.i −0.100603 0.309699i
\(298\) −19956.9 −0.0130182
\(299\) −60067.6 −0.0388564
\(300\) 1.48650e6 + 2.04609e6i 0.953589 + 1.31257i
\(301\) 0 0
\(302\) 295280.i 0.186301i
\(303\) 490989. + 675823.i 0.307231 + 0.422889i
\(304\) 329981.i 0.204788i
\(305\) 3.15671e6i 1.94306i
\(306\) 315673. + 102585.i 0.192723 + 0.0626299i
\(307\) 2.31011e6i 1.39890i −0.714681 0.699451i \(-0.753428\pi\)
0.714681 0.699451i \(-0.246572\pi\)
\(308\) 0 0
\(309\) 1.93986e6 1.40932e6i 1.15578 0.839680i
\(310\) −588057. −0.347549
\(311\) 2.35286e6 1.37941 0.689707 0.724089i \(-0.257739\pi\)
0.689707 + 0.724089i \(0.257739\pi\)
\(312\) 17043.2 + 23459.1i 0.00991205 + 0.0136435i
\(313\) 1.99117e6i 1.14881i 0.818572 + 0.574404i \(0.194766\pi\)
−0.818572 + 0.574404i \(0.805234\pi\)
\(314\) −32981.1 −0.0188774
\(315\) 0 0
\(316\) 236028. 0.132967
\(317\) 2.09384e6i 1.17029i 0.810927 + 0.585147i \(0.198963\pi\)
−0.810927 + 0.585147i \(0.801037\pi\)
\(318\) −136340. 187665.i −0.0756056 0.104068i
\(319\) 469752. 0.258459
\(320\) 764196. 0.417186
\(321\) 1.93478e6 1.40563e6i 1.04802 0.761390i
\(322\) 0 0
\(323\) 347581.i 0.185374i
\(324\) −1.31133e6 952928.i −0.693983 0.504310i
\(325\) 86705.1i 0.0455341i
\(326\) 617709.i 0.321914i
\(327\) −1.17040e6 1.61099e6i −0.605289 0.833152i
\(328\) 1.38774e6i 0.712237i
\(329\) 0 0
\(330\) −242714. 334084.i −0.122690 0.168877i
\(331\) 275243. 0.138085 0.0690426 0.997614i \(-0.478006\pi\)
0.0690426 + 0.997614i \(0.478006\pi\)
\(332\) −869390. −0.432882
\(333\) 326097. 1.00346e6i 0.161152 0.495895i
\(334\) 741812.i 0.363855i
\(335\) 611775. 0.297838
\(336\) 0 0
\(337\) 455651. 0.218553 0.109277 0.994011i \(-0.465147\pi\)
0.109277 + 0.994011i \(0.465147\pi\)
\(338\) 791376.i 0.376783i
\(339\) 1.14031e6 828445.i 0.538921 0.391529i
\(340\) −1.67128e6 −0.784064
\(341\) −379091. −0.176546
\(342\) −86918.5 + 267464.i −0.0401834 + 0.123652i
\(343\) 0 0
\(344\) 2.60446e6i 1.18665i
\(345\) 4.90809e6 3.56576e6i 2.22006 1.61289i
\(346\) 1.08368e6i 0.486642i
\(347\) 1.71199e6i 0.763271i 0.924313 + 0.381636i \(0.124639\pi\)
−0.924313 + 0.381636i \(0.875361\pi\)
\(348\) 1.24452e6 904153.i 0.550877 0.400215i
\(349\) 1.94736e6i 0.855822i 0.903821 + 0.427911i \(0.140750\pi\)
−0.903821 + 0.427911i \(0.859250\pi\)
\(350\) 0 0
\(351\) 17169.4 + 52854.9i 0.00743852 + 0.0228990i
\(352\) −699661. −0.300975
\(353\) −3.59350e6 −1.53490 −0.767452 0.641106i \(-0.778476\pi\)
−0.767452 + 0.641106i \(0.778476\pi\)
\(354\) 1.07638e6 781995.i 0.456517 0.331662i
\(355\) 3.08862e6i 1.30075i
\(356\) 876973. 0.366742
\(357\) 0 0
\(358\) 853930. 0.352139
\(359\) 2.58351e6i 1.05797i −0.848630 0.528987i \(-0.822572\pi\)
0.848630 0.528987i \(-0.177428\pi\)
\(360\) −2.78518e6 905107.i −1.13265 0.368081i
\(361\) 2.18160e6 0.881064
\(362\) −22808.0 −0.00914779
\(363\) 1.31914e6 + 1.81574e6i 0.525442 + 0.723246i
\(364\) 0 0
\(365\) 1.21076e6i 0.475691i
\(366\) 648929. + 893219.i 0.253218 + 0.348542i
\(367\) 3.76563e6i 1.45939i 0.683772 + 0.729696i \(0.260338\pi\)
−0.683772 + 0.729696i \(0.739662\pi\)
\(368\) 2.48960e6i 0.958317i
\(369\) 822014. 2.52948e6i 0.314277 0.967088i
\(370\) 880189.i 0.334250i
\(371\) 0 0
\(372\) −1.00433e6 + 729654.i −0.376288 + 0.273376i
\(373\) −1.93722e6 −0.720952 −0.360476 0.932768i \(-0.617386\pi\)
−0.360476 + 0.932768i \(0.617386\pi\)
\(374\) 178500. 0.0659870
\(375\) 2.42545e6 + 3.33852e6i 0.890665 + 1.22596i
\(376\) 1.11778e6i 0.407743i
\(377\) −52737.8 −0.0191104
\(378\) 0 0
\(379\) 2.04113e6 0.729917 0.364959 0.931024i \(-0.381083\pi\)
0.364959 + 0.931024i \(0.381083\pi\)
\(380\) 1.41604e6i 0.503057i
\(381\) 1.21238e6 + 1.66878e6i 0.427883 + 0.588960i
\(382\) −420668. −0.147496
\(383\) 470701. 0.163964 0.0819819 0.996634i \(-0.473875\pi\)
0.0819819 + 0.996634i \(0.473875\pi\)
\(384\) −2.37696e6 + 1.72688e6i −0.822611 + 0.597632i
\(385\) 0 0
\(386\) 267670.i 0.0914388i
\(387\) −1.54272e6 + 4.74722e6i −0.523612 + 1.61125i
\(388\) 3.92855e6i 1.32481i
\(389\) 4.59134e6i 1.53839i 0.639017 + 0.769193i \(0.279341\pi\)
−0.639017 + 0.769193i \(0.720659\pi\)
\(390\) 27248.8 + 37506.7i 0.00907166 + 0.0124867i
\(391\) 2.62238e6i 0.867467i
\(392\) 0 0
\(393\) 1.35399e6 + 1.86371e6i 0.442216 + 0.608690i
\(394\) −1.34717e6 −0.437202
\(395\) 817250. 0.263550
\(396\) −829054. 269420.i −0.265671 0.0863360i
\(397\) 4.55566e6i 1.45069i 0.688384 + 0.725346i \(0.258320\pi\)
−0.688384 + 0.725346i \(0.741680\pi\)
\(398\) −1.32731e6 −0.420016
\(399\) 0 0
\(400\) 3.59363e6 1.12301
\(401\) 2.41750e6i 0.750766i 0.926870 + 0.375383i \(0.122489\pi\)
−0.926870 + 0.375383i \(0.877511\pi\)
\(402\) −173107. + 125763.i −0.0534256 + 0.0388140i
\(403\) 42559.6 0.0130537
\(404\) 1.47108e6 0.448418
\(405\) −4.54050e6 3.29953e6i −1.37552 0.999573i
\(406\) 0 0
\(407\) 567414.i 0.169791i
\(408\) 1.02415e6 744054.i 0.304590 0.221286i
\(409\) 64985.1i 0.0192090i −0.999954 0.00960452i \(-0.996943\pi\)
0.999954 0.00960452i \(-0.00305726\pi\)
\(410\) 2.21875e6i 0.651851i
\(411\) −2.85882e6 + 2.07695e6i −0.834798 + 0.606486i
\(412\) 4.22254e6i 1.22555i
\(413\) 0 0
\(414\) −655771. + 2.01792e6i −0.188040 + 0.578634i
\(415\) −3.01028e6 −0.857998
\(416\) 78549.1 0.0222540
\(417\) 2.90921e6 2.11356e6i 0.819285 0.595216i
\(418\) 151239.i 0.0423374i
\(419\) 4.52870e6 1.26020 0.630098 0.776515i \(-0.283015\pi\)
0.630098 + 0.776515i \(0.283015\pi\)
\(420\) 0 0
\(421\) −3.77935e6 −1.03923 −0.519615 0.854401i \(-0.673925\pi\)
−0.519615 + 0.854401i \(0.673925\pi\)
\(422\) 579529.i 0.158414i
\(423\) 662104. 2.03741e6i 0.179918 0.553641i
\(424\) −884667. −0.238982
\(425\) −3.78529e6 −1.01655
\(426\) −634932. 873953.i −0.169513 0.233326i
\(427\) 0 0
\(428\) 4.21147e6i 1.11128i
\(429\) 17566.0 + 24178.7i 0.00460818 + 0.00634293i
\(430\) 4.16404e6i 1.08604i
\(431\) 6.61895e6i 1.71631i 0.513391 + 0.858155i \(0.328389\pi\)
−0.513391 + 0.858155i \(0.671611\pi\)
\(432\) −2.19065e6 + 711612.i −0.564761 + 0.183457i
\(433\) 5.25855e6i 1.34786i 0.738794 + 0.673932i \(0.235396\pi\)
−0.738794 + 0.673932i \(0.764604\pi\)
\(434\) 0 0
\(435\) 4.30918e6 3.13065e6i 1.09187 0.793251i
\(436\) −3.50668e6 −0.883446
\(437\) −2.22189e6 −0.556569
\(438\) −248897. 342594.i −0.0619917 0.0853286i
\(439\) 416451.i 0.103134i −0.998670 0.0515671i \(-0.983578\pi\)
0.998670 0.0515671i \(-0.0164216\pi\)
\(440\) −1.57490e6 −0.387812
\(441\) 0 0
\(442\) −20039.7 −0.00487905
\(443\) 7.00727e6i 1.69644i −0.529641 0.848222i \(-0.677673\pi\)
0.529641 0.848222i \(-0.322327\pi\)
\(444\) −1.09213e6 1.50326e6i −0.262915 0.361890i
\(445\) 3.03653e6 0.726906
\(446\) −546803. −0.130165
\(447\) −118017. + 85739.8i −0.0279367 + 0.0202961i
\(448\) 0 0
\(449\) 1.63032e6i 0.381643i 0.981625 + 0.190822i \(0.0611152\pi\)
−0.981625 + 0.190822i \(0.938885\pi\)
\(450\) −2.91279e6 946579.i −0.678076 0.220356i
\(451\) 1.43032e6i 0.331124i
\(452\) 2.48215e6i 0.571454i
\(453\) 1.26860e6 + 1.74616e6i 0.290454 + 0.399796i
\(454\) 251428.i 0.0572498i
\(455\) 0 0
\(456\) 630423. + 867747.i 0.141978 + 0.195425i
\(457\) 8.38895e6 1.87896 0.939479 0.342606i \(-0.111310\pi\)
0.939479 + 0.342606i \(0.111310\pi\)
\(458\) −797141. −0.177571
\(459\) 2.30749e6 749565.i 0.511220 0.166065i
\(460\) 1.06836e7i 2.35408i
\(461\) 186426. 0.0408560 0.0204280 0.999791i \(-0.493497\pi\)
0.0204280 + 0.999791i \(0.493497\pi\)
\(462\) 0 0
\(463\) −5.23908e6 −1.13580 −0.567901 0.823097i \(-0.692244\pi\)
−0.567901 + 0.823097i \(0.692244\pi\)
\(464\) 2.18580e6i 0.471320i
\(465\) −3.47752e6 + 2.52644e6i −0.745826 + 0.541847i
\(466\) 2.69736e6 0.575405
\(467\) −564223. −0.119718 −0.0598589 0.998207i \(-0.519065\pi\)
−0.0598589 + 0.998207i \(0.519065\pi\)
\(468\) 93075.7 + 30247.1i 0.0196436 + 0.00638365i
\(469\) 0 0
\(470\) 1.78712e6i 0.373173i
\(471\) −195036. + 141695.i −0.0405101 + 0.0294308i
\(472\) 5.07413e6i 1.04835i
\(473\) 2.68435e6i 0.551679i
\(474\) −231248. + 168003.i −0.0472751 + 0.0343456i
\(475\) 3.20721e6i 0.652219i
\(476\) 0 0
\(477\) −1.61251e6 524022.i −0.324494 0.105452i
\(478\) 1.11072e6 0.222348
\(479\) −2.69727e6 −0.537137 −0.268568 0.963261i \(-0.586551\pi\)
−0.268568 + 0.963261i \(0.586551\pi\)
\(480\) −6.41821e6 + 4.66286e6i −1.27148 + 0.923740i
\(481\) 63702.1i 0.0125543i
\(482\) 2.03516e6 0.399007
\(483\) 0 0
\(484\) 3.95235e6 0.766906
\(485\) 1.36027e7i 2.62585i
\(486\) 1.96306e6 + 236.061i 0.377001 + 4.53350e-5i
\(487\) −2.84365e6 −0.543317 −0.271658 0.962394i \(-0.587572\pi\)
−0.271658 + 0.962394i \(0.587572\pi\)
\(488\) 4.21071e6 0.800397
\(489\) 2.65383e6 + 3.65287e6i 0.501881 + 0.690815i
\(490\) 0 0
\(491\) 7.38962e6i 1.38331i 0.722229 + 0.691654i \(0.243118\pi\)
−0.722229 + 0.691654i \(0.756882\pi\)
\(492\) −2.75299e6 3.78936e6i −0.512734 0.705754i
\(493\) 2.30238e6i 0.426638i
\(494\) 16979.3i 0.00313041i
\(495\) −2.87062e6 932872.i −0.526577 0.171123i
\(496\) 1.76395e6i 0.321945i
\(497\) 0 0
\(498\) 851784. 618826.i 0.153906 0.111814i
\(499\) 2.13675e6 0.384152 0.192076 0.981380i \(-0.438478\pi\)
0.192076 + 0.981380i \(0.438478\pi\)
\(500\) 7.26702e6 1.29996
\(501\) −3.18701e6 4.38677e6i −0.567269 0.780818i
\(502\) 1.68434e6i 0.298313i
\(503\) −2.60933e6 −0.459842 −0.229921 0.973209i \(-0.573847\pi\)
−0.229921 + 0.973209i \(0.573847\pi\)
\(504\) 0 0
\(505\) 5.09364e6 0.888791
\(506\) 1.14105e6i 0.198120i
\(507\) 3.39995e6 + 4.67986e6i 0.587425 + 0.808562i
\(508\) 3.63246e6 0.624514
\(509\) 5.78866e6 0.990338 0.495169 0.868797i \(-0.335106\pi\)
0.495169 + 0.868797i \(0.335106\pi\)
\(510\) 1.63743e6 1.18961e6i 0.278765 0.202524i
\(511\) 0 0
\(512\) 5.72266e6i 0.964768i
\(513\) 635092. + 1.95509e6i 0.106548 + 0.328000i
\(514\) 2.36231e6i 0.394392i
\(515\) 1.46206e7i 2.42911i
\(516\) 5.16669e6 + 7.11170e6i 0.854257 + 1.17584i
\(517\) 1.15207e6i 0.189563i
\(518\) 0 0
\(519\) −4.65574e6 6.40840e6i −0.758701 1.04431i
\(520\) 176810. 0.0286746
\(521\) 306226. 0.0494250 0.0247125 0.999695i \(-0.492133\pi\)
0.0247125 + 0.999695i \(0.492133\pi\)
\(522\) −575750. + 1.77169e6i −0.0924821 + 0.284584i
\(523\) 7.18513e6i 1.14863i 0.818634 + 0.574315i \(0.194732\pi\)
−0.818634 + 0.574315i \(0.805268\pi\)
\(524\) 4.05677e6 0.645434
\(525\) 0 0
\(526\) 2.24778e6 0.354234
\(527\) 1.85803e6i 0.291424i
\(528\) −1.00213e6 + 728050.i −0.156436 + 0.113652i
\(529\) −1.03270e7 −1.60449
\(530\) −1.41442e6 −0.218720
\(531\) 3.00560e6 9.24877e6i 0.462589 1.42347i
\(532\) 0 0
\(533\) 160578.i 0.0244831i
\(534\) −859214. + 624224.i −0.130391 + 0.0947299i
\(535\) 1.45823e7i 2.20263i
\(536\) 816040.i 0.122687i
\(537\) 5.04978e6 3.66869e6i 0.755678 0.549004i
\(538\) 980795.i 0.146091i
\(539\) 0 0
\(540\) −9.40071e6 + 3.05373e6i −1.38732 + 0.450657i
\(541\) 7.76483e6 1.14061 0.570307 0.821431i \(-0.306824\pi\)
0.570307 + 0.821431i \(0.306824\pi\)
\(542\) 1.88886e6 0.276186
\(543\) −134877. + 97988.9i −0.0196308 + 0.0142619i
\(544\) 3.42922e6i 0.496819i
\(545\) −1.21420e7 −1.75104
\(546\) 0 0
\(547\) −7.87821e6 −1.12580 −0.562898 0.826527i \(-0.690313\pi\)
−0.562898 + 0.826527i \(0.690313\pi\)
\(548\) 6.22285e6i 0.885193i
\(549\) 7.67498e6 + 2.49416e6i 1.08679 + 0.353178i
\(550\) −1.64706e6 −0.232168
\(551\) −1.95076e6 −0.273732
\(552\) 4.75633e6 + 6.54685e6i 0.664391 + 0.914503i
\(553\) 0 0
\(554\) 1.64311e6i 0.227453i
\(555\) −3.78151e6 5.20507e6i −0.521114 0.717289i
\(556\) 6.33255e6i 0.868743i
\(557\) 4.59766e6i 0.627913i 0.949437 + 0.313956i \(0.101655\pi\)
−0.949437 + 0.313956i \(0.898345\pi\)
\(558\) 464632. 1.42976e6i 0.0631719 0.194391i
\(559\) 301365.i 0.0407909i
\(560\) 0 0
\(561\) 1.05557e6 766879.i 0.141606 0.102877i
\(562\) 4.80023e6 0.641094
\(563\) −2.72419e6 −0.362215 −0.181107 0.983463i \(-0.557968\pi\)
−0.181107 + 0.983463i \(0.557968\pi\)
\(564\) −2.21744e6 3.05220e6i −0.293531 0.404031i
\(565\) 8.59448e6i 1.13266i
\(566\) 10808.8 0.00141819
\(567\) 0 0
\(568\) −4.11988e6 −0.535814
\(569\) 8.67813e6i 1.12369i −0.827243 0.561844i \(-0.810092\pi\)
0.827243 0.561844i \(-0.189908\pi\)
\(570\) 1.00793e6 + 1.38737e6i 0.129940 + 0.178856i
\(571\) 1.07384e7 1.37832 0.689161 0.724608i \(-0.257979\pi\)
0.689161 + 0.724608i \(0.257979\pi\)
\(572\) 52630.3 0.00672583
\(573\) −2.48765e6 + 1.80730e6i −0.316522 + 0.229955i
\(574\) 0 0
\(575\) 2.41973e7i 3.05209i
\(576\) −603801. + 1.85801e6i −0.0758294 + 0.233341i
\(577\) 7.06870e6i 0.883894i −0.897041 0.441947i \(-0.854288\pi\)
0.897041 0.441947i \(-0.145712\pi\)
\(578\) 2.15317e6i 0.268077i
\(579\) −1.14997e6 1.58288e6i −0.142558 0.196224i
\(580\) 9.37989e6i 1.15779i
\(581\) 0 0
\(582\) −2.79631e6 3.84899e6i −0.342199 0.471020i
\(583\) −911805. −0.111104
\(584\) −1.61502e6 −0.195950
\(585\) 322276. + 104731.i 0.0389349 + 0.0126528i
\(586\) 5.36929e6i 0.645911i
\(587\) 3.96818e6 0.475331 0.237666 0.971347i \(-0.423618\pi\)
0.237666 + 0.971347i \(0.423618\pi\)
\(588\) 0 0
\(589\) 1.57427e6 0.186978
\(590\) 8.11260e6i 0.959467i
\(591\) −7.96659e6 + 5.78777e6i −0.938218 + 0.681621i
\(592\) −2.64023e6 −0.309626
\(593\) −1.67421e7 −1.95512 −0.977562 0.210649i \(-0.932442\pi\)
−0.977562 + 0.210649i \(0.932442\pi\)
\(594\) 1.00404e6 326151.i 0.116757 0.0379274i
\(595\) 0 0
\(596\) 256889.i 0.0296231i
\(597\) −7.84918e6 + 5.70247e6i −0.901339 + 0.654828i
\(598\) 128103.i 0.0146489i
\(599\) 1.08814e7i 1.23913i −0.784944 0.619567i \(-0.787308\pi\)
0.784944 0.619567i \(-0.212692\pi\)
\(600\) −9.45012e6 + 6.86557e6i −1.07167 + 0.778571i
\(601\) 1.72048e7i 1.94296i 0.237128 + 0.971478i \(0.423794\pi\)
−0.237128 + 0.971478i \(0.576206\pi\)
\(602\) 0 0
\(603\) −483372. + 1.48742e6i −0.0541362 + 0.166587i
\(604\) 3.80090e6 0.423930
\(605\) 1.36851e7 1.52005
\(606\) −1.44129e6 + 1.04711e6i −0.159430 + 0.115827i
\(607\) 5.56535e6i 0.613085i −0.951857 0.306543i \(-0.900828\pi\)
0.951857 0.306543i \(-0.0991722\pi\)
\(608\) 2.90552e6 0.318760
\(609\) 0 0
\(610\) 6.73214e6 0.732535
\(611\) 129340.i 0.0140162i
\(612\) 1.32050e6 4.06341e6i 0.142515 0.438543i
\(613\) −1.18075e7 −1.26914 −0.634568 0.772867i \(-0.718822\pi\)
−0.634568 + 0.772867i \(0.718822\pi\)
\(614\) 4.92664e6 0.527388
\(615\) −9.53229e6 1.31207e7i −1.01627 1.39885i
\(616\) 0 0
\(617\) 5.91582e6i 0.625608i 0.949818 + 0.312804i \(0.101268\pi\)
−0.949818 + 0.312804i \(0.898732\pi\)
\(618\) 3.00558e6 + 4.13703e6i 0.316560 + 0.435730i
\(619\) 2.82876e6i 0.296736i −0.988932 0.148368i \(-0.952598\pi\)
0.988932 0.148368i \(-0.0474020\pi\)
\(620\) 7.56960e6i 0.790849i
\(621\) 4.79155e6 + 1.47505e7i 0.498594 + 1.53489i
\(622\) 5.01780e6i 0.520041i
\(623\) 0 0
\(624\) 112506. 81736.2i 0.0115668 0.00840336i
\(625\) 6.69352e6 0.685416
\(626\) −4.24646e6 −0.433103
\(627\) 649762. + 894366.i 0.0660063 + 0.0908545i
\(628\) 424540.i 0.0429556i
\(629\) 2.78105e6 0.280273
\(630\) 0 0
\(631\) −9.60301e6 −0.960139 −0.480069 0.877231i \(-0.659389\pi\)
−0.480069 + 0.877231i \(0.659389\pi\)
\(632\) 1.09012e6i 0.108563i
\(633\) −2.48980e6 3.42709e6i −0.246976 0.339951i
\(634\) −4.46541e6 −0.441203
\(635\) 1.25775e7 1.23782
\(636\) −2.41566e6 + 1.75499e6i −0.236806 + 0.172041i
\(637\) 0 0
\(638\) 1.00181e6i 0.0974395i
\(639\) −7.50943e6 2.44036e6i −0.727537 0.236430i
\(640\) 1.79150e7i 1.72889i
\(641\) 9.00157e6i 0.865312i 0.901559 + 0.432656i \(0.142424\pi\)
−0.901559 + 0.432656i \(0.857576\pi\)
\(642\) 2.99770e6 + 4.12618e6i 0.287045 + 0.395104i
\(643\) 6.92082e6i 0.660131i −0.943958 0.330065i \(-0.892929\pi\)
0.943958 0.330065i \(-0.107071\pi\)
\(644\) 0 0
\(645\) 1.78898e7 + 2.46244e7i 1.69319 + 2.33059i
\(646\) −741265. −0.0698863
\(647\) 1.66850e6 0.156699 0.0783495 0.996926i \(-0.475035\pi\)
0.0783495 + 0.996926i \(0.475035\pi\)
\(648\) 4.40121e6 6.05652e6i 0.411751 0.566612i
\(649\) 5.22979e6i 0.487385i
\(650\) 184911. 0.0171664
\(651\) 0 0
\(652\) 7.95128e6 0.732518
\(653\) 1.81810e7i 1.66853i 0.551364 + 0.834265i \(0.314108\pi\)
−0.551364 + 0.834265i \(0.685892\pi\)
\(654\) 3.43567e6 2.49603e6i 0.314099 0.228195i
\(655\) 1.40466e7 1.27929
\(656\) −6.65540e6 −0.603830
\(657\) −2.94374e6 956635.i −0.266064 0.0864635i
\(658\) 0 0
\(659\) 5.58660e6i 0.501111i 0.968102 + 0.250556i \(0.0806133\pi\)
−0.968102 + 0.250556i \(0.919387\pi\)
\(660\) −4.30040e6 + 3.12427e6i −0.384281 + 0.279182i
\(661\) 1.30855e7i 1.16489i 0.812870 + 0.582445i \(0.197904\pi\)
−0.812870 + 0.582445i \(0.802096\pi\)
\(662\) 586996.i 0.0520583i
\(663\) −118506. + 86095.5i −0.0104703 + 0.00760671i
\(664\) 4.01538e6i 0.353432i
\(665\) 0 0
\(666\) 2.14002e6 + 695449.i 0.186953 + 0.0607547i
\(667\) −1.47178e7 −1.28094
\(668\) −9.54877e6 −0.827954
\(669\) −3.23356e6 + 2.34920e6i −0.279329 + 0.202934i
\(670\) 1.30470e6i 0.112285i
\(671\) 4.33988e6 0.372110
\(672\) 0 0
\(673\) 9.79316e6 0.833461 0.416730 0.909030i \(-0.363176\pi\)
0.416730 + 0.909030i \(0.363176\pi\)
\(674\) 971740.i 0.0823949i
\(675\) −2.12918e7 + 6.91642e6i −1.79867 + 0.584281i
\(676\) 1.01868e7 0.857373
\(677\) 8.00917e6 0.671608 0.335804 0.941932i \(-0.390992\pi\)
0.335804 + 0.941932i \(0.390992\pi\)
\(678\) 1.76678e6 + 2.43188e6i 0.147607 + 0.203174i
\(679\) 0 0
\(680\) 7.71900e6i 0.640160i
\(681\) 1.08020e6 + 1.48684e6i 0.0892555 + 0.122856i
\(682\) 808466.i 0.0665581i
\(683\) 2.00990e7i 1.64863i 0.566133 + 0.824314i \(0.308439\pi\)
−0.566133 + 0.824314i \(0.691561\pi\)
\(684\) 3.44285e6 + 1.11883e6i 0.281370 + 0.0914377i
\(685\) 2.15467e7i 1.75451i
\(686\) 0 0
\(687\) −4.71395e6 + 3.42471e6i −0.381060 + 0.276842i
\(688\) 1.24906e7 1.00603
\(689\) 102366. 0.00821500
\(690\) 7.60449e6 + 1.04672e7i 0.608061 + 0.836967i
\(691\) 7.78435e6i 0.620193i −0.950705 0.310097i \(-0.899639\pi\)
0.950705 0.310097i \(-0.100361\pi\)
\(692\) −1.39493e7 −1.10736
\(693\) 0 0
\(694\) −3.65107e6 −0.287754
\(695\) 2.19266e7i 1.72190i
\(696\) 4.17594e6 + 5.74797e6i 0.326761 + 0.449771i
\(697\) 7.01036e6 0.546586
\(698\) −4.15303e6 −0.322646
\(699\) 1.59510e7 1.15885e7i 1.23480 0.897088i
\(700\) 0 0
\(701\) 1.12400e7i 0.863912i 0.901895 + 0.431956i \(0.142176\pi\)
−0.901895 + 0.431956i \(0.857824\pi\)
\(702\) −112721. + 36616.1i −0.00863297 + 0.00280433i
\(703\) 2.35633e6i 0.179824i
\(704\) 1.05062e6i 0.0798942i
\(705\) −7.67793e6 1.05683e7i −0.581797 0.800815i
\(706\) 7.66366e6i 0.578661i
\(707\) 0 0
\(708\) −1.00660e7 1.38554e7i −0.754699 1.03881i
\(709\) −1.15696e7 −0.864376 −0.432188 0.901783i \(-0.642258\pi\)
−0.432188 + 0.901783i \(0.642258\pi\)
\(710\) −6.58693e6 −0.490385
\(711\) −645721. + 1.98700e6i −0.0479039 + 0.147409i
\(712\) 4.05040e6i 0.299432i
\(713\) 1.18773e7 0.874974
\(714\) 0 0
\(715\) 182234. 0.0133310
\(716\) 1.09920e7i 0.801296i
\(717\) 6.56830e6 4.77191e6i 0.477150 0.346653i
\(718\) 5.50971e6 0.398857
\(719\) −461291. −0.0332777 −0.0166388 0.999862i \(-0.505297\pi\)
−0.0166388 + 0.999862i \(0.505297\pi\)
\(720\) −4.34075e6 + 1.33573e7i −0.312056 + 0.960254i
\(721\) 0 0
\(722\) 4.65257e6i 0.332162i
\(723\) 1.20351e7 8.74354e6i 0.856254 0.622073i
\(724\) 293590.i 0.0208159i
\(725\) 2.12446e7i 1.50108i
\(726\) −3.87231e6 + 2.81326e6i −0.272665 + 0.198093i
\(727\) 2.83046e6i 0.198619i −0.995057 0.0993096i \(-0.968337\pi\)
0.995057 0.0993096i \(-0.0316634\pi\)
\(728\) 0 0
\(729\) 1.16097e7 8.43240e6i 0.809102 0.587669i
\(730\) −2.58211e6 −0.179336
\(731\) −1.31567e7 −0.910656
\(732\) 1.14977e7 8.35315e6i 0.793111 0.576199i
\(733\) 2.05309e7i 1.41140i 0.708513 + 0.705698i \(0.249366\pi\)
−0.708513 + 0.705698i \(0.750634\pi\)
\(734\) −8.03073e6 −0.550193
\(735\) 0 0
\(736\) 2.19211e7 1.49165
\(737\) 841074.i 0.0570381i
\(738\) 5.39448e6 + 1.75306e6i 0.364594 + 0.118483i
\(739\) −1.51479e7 −1.02033 −0.510167 0.860075i \(-0.670416\pi\)
−0.510167 + 0.860075i \(0.670416\pi\)
\(740\) −1.13300e7 −0.760589
\(741\) −72947.1 100408.i −0.00488048 0.00671774i
\(742\) 0 0
\(743\) 3.14063e6i 0.208711i 0.994540 + 0.104355i \(0.0332779\pi\)
−0.994540 + 0.104355i \(0.966722\pi\)
\(744\) −3.36999e6 4.63863e6i −0.223201 0.307226i
\(745\) 889485.i 0.0587148i
\(746\) 4.13140e6i 0.271800i
\(747\) 2.37846e6 7.31895e6i 0.155953 0.479896i
\(748\) 2.29769e6i 0.150154i
\(749\) 0 0
\(750\) −7.11986e6 + 5.17262e6i −0.462188 + 0.335782i
\(751\) −1.43376e6 −0.0927634 −0.0463817 0.998924i \(-0.514769\pi\)
−0.0463817 + 0.998924i \(0.514769\pi\)
\(752\) −5.36069e6 −0.345682
\(753\) 7.23636e6 + 9.96050e6i 0.465085 + 0.640168i
\(754\) 112471.i 0.00720463i
\(755\) 1.31607e7 0.840256
\(756\) 0 0
\(757\) −6.81110e6 −0.431994 −0.215997 0.976394i \(-0.569300\pi\)
−0.215997 + 0.976394i \(0.569300\pi\)
\(758\) 4.35301e6i 0.275180i
\(759\) 4.90223e6 + 6.74769e6i 0.308880 + 0.425158i
\(760\) 6.54016e6 0.410728
\(761\) −110270. −0.00690235 −0.00345117 0.999994i \(-0.501099\pi\)
−0.00345117 + 0.999994i \(0.501099\pi\)
\(762\) −3.55890e6 + 2.58557e6i −0.222039 + 0.161313i
\(763\) 0 0
\(764\) 5.41493e6i 0.335629i
\(765\) 4.57225e6 1.40696e7i 0.282473 0.869220i
\(766\) 1.00384e6i 0.0618146i
\(767\) 587134.i 0.0360370i
\(768\) −1.32560e6 1.82463e6i −0.0810980 0.111628i
\(769\) 1.61688e7i 0.985968i −0.870038 0.492984i \(-0.835906\pi\)
0.870038 0.492984i \(-0.164094\pi\)
\(770\) 0 0
\(771\) −1.01491e7 1.39697e7i −0.614879 0.846351i
\(772\) −3.44550e6 −0.208070
\(773\) 1.67611e7 1.00892 0.504458 0.863436i \(-0.331692\pi\)
0.504458 + 0.863436i \(0.331692\pi\)
\(774\) −1.01241e7 3.29007e6i −0.607443 0.197402i
\(775\) 1.71445e7i 1.02534i
\(776\) −1.81445e7 −1.08166
\(777\) 0 0
\(778\) −9.79168e6 −0.579974
\(779\) 5.93974e6i 0.350690i
\(780\) 482795.