Properties

Label 882.4.g.z.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \(x^{4} - x^{3} + 49 x^{2} + 48 x + 2304\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(3.72311 - 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.z.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.22311 + 9.04669i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.22311 + 9.04669i) q^{5} +8.00000 q^{8} +(-10.4462 - 18.0934i) q^{10} +(-30.5618 - 52.9346i) q^{11} +59.2311 q^{13} +(-8.00000 + 13.8564i) q^{16} +(10.2311 + 17.7208i) q^{17} +(-40.1693 + 69.5753i) q^{19} +41.7849 q^{20} +122.247 q^{22} +(79.1236 - 137.046i) q^{23} +(7.93822 + 13.7494i) q^{25} +(-59.2311 + 102.591i) q^{26} -85.1236 q^{29} +(121.747 + 210.872i) q^{31} +(-16.0000 - 27.7128i) q^{32} -40.9244 q^{34} +(-145.185 + 251.468i) q^{37} +(-80.3387 - 139.151i) q^{38} +(-41.7849 + 72.3735i) q^{40} +168.000 q^{41} +7.62934 q^{43} +(-122.247 + 211.738i) q^{44} +(158.247 + 274.092i) q^{46} +(-84.6453 + 146.610i) q^{47} -31.7529 q^{50} +(-118.462 - 205.183i) q^{52} +(125.056 + 216.603i) q^{53} +638.510 q^{55} +(85.1236 - 147.438i) q^{58} +(-402.610 - 697.341i) q^{59} +(16.5858 - 28.7274i) q^{61} -486.988 q^{62} +64.0000 q^{64} +(-309.371 + 535.846i) q^{65} +(138.691 + 240.220i) q^{67} +(40.9244 - 70.8832i) q^{68} -631.506 q^{71} +(-384.142 - 665.353i) q^{73} +(-290.371 - 502.937i) q^{74} +321.355 q^{76} +(209.365 - 362.631i) q^{79} +(-83.5698 - 144.747i) q^{80} +(-168.000 + 290.985i) q^{82} +761.714 q^{83} -213.753 q^{85} +(-7.62934 + 13.2144i) q^{86} +(-244.494 - 423.476i) q^{88} +(-786.048 + 1361.48i) q^{89} -632.988 q^{92} +(-169.291 - 293.220i) q^{94} +(-419.618 - 726.799i) q^{95} -1045.16 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} - 7q^{5} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} - 7q^{5} + 32q^{8} - 14q^{10} - 25q^{11} + 98q^{13} - 32q^{16} - 98q^{17} - 119q^{19} + 56q^{20} + 100q^{22} + 122q^{23} + 129q^{25} - 98q^{26} - 146q^{29} + 98q^{31} - 64q^{32} + 392q^{34} - 289q^{37} - 238q^{38} - 56q^{40} + 672q^{41} + 614q^{43} - 100q^{44} + 244q^{46} - 672q^{47} - 516q^{50} - 196q^{52} - 375q^{53} + 1526q^{55} + 146q^{58} - 763q^{59} - 406q^{61} - 392q^{62} + 256q^{64} - 654q^{65} + 1041q^{67} - 392q^{68} - 3304q^{71} - 189q^{73} - 578q^{74} + 952q^{76} - 524q^{79} - 112q^{80} - 672q^{82} + 574q^{83} - 1244q^{85} - 614q^{86} - 200q^{88} - 2394q^{89} - 976q^{92} - 1344q^{94} - 706q^{95} + 126q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −5.22311 + 9.04669i −0.467169 + 0.809161i −0.999296 0.0375035i \(-0.988059\pi\)
0.532127 + 0.846664i \(0.321393\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −10.4462 18.0934i −0.330339 0.572163i
\(11\) −30.5618 52.9346i −0.837702 1.45094i −0.891811 0.452407i \(-0.850565\pi\)
0.0541093 0.998535i \(-0.482768\pi\)
\(12\) 0 0
\(13\) 59.2311 1.26367 0.631837 0.775102i \(-0.282301\pi\)
0.631837 + 0.775102i \(0.282301\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 10.2311 + 17.7208i 0.145965 + 0.252819i 0.929733 0.368235i \(-0.120038\pi\)
−0.783767 + 0.621054i \(0.786705\pi\)
\(18\) 0 0
\(19\) −40.1693 + 69.5753i −0.485025 + 0.840088i −0.999852 0.0172061i \(-0.994523\pi\)
0.514827 + 0.857294i \(0.327856\pi\)
\(20\) 41.7849 0.467169
\(21\) 0 0
\(22\) 122.247 1.18469
\(23\) 79.1236 137.046i 0.717322 1.24244i −0.244735 0.969590i \(-0.578701\pi\)
0.962057 0.272848i \(-0.0879656\pi\)
\(24\) 0 0
\(25\) 7.93822 + 13.7494i 0.0635058 + 0.109995i
\(26\) −59.2311 + 102.591i −0.446776 + 0.773839i
\(27\) 0 0
\(28\) 0 0
\(29\) −85.1236 −0.545071 −0.272535 0.962146i \(-0.587862\pi\)
−0.272535 + 0.962146i \(0.587862\pi\)
\(30\) 0 0
\(31\) 121.747 + 210.872i 0.705369 + 1.22173i 0.966558 + 0.256447i \(0.0825518\pi\)
−0.261190 + 0.965287i \(0.584115\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −40.9244 −0.206426
\(35\) 0 0
\(36\) 0 0
\(37\) −145.185 + 251.468i −0.645090 + 1.11733i 0.339191 + 0.940718i \(0.389847\pi\)
−0.984281 + 0.176611i \(0.943487\pi\)
\(38\) −80.3387 139.151i −0.342965 0.594032i
\(39\) 0 0
\(40\) −41.7849 + 72.3735i −0.165169 + 0.286082i
\(41\) 168.000 0.639932 0.319966 0.947429i \(-0.396329\pi\)
0.319966 + 0.947429i \(0.396329\pi\)
\(42\) 0 0
\(43\) 7.62934 0.0270573 0.0135286 0.999908i \(-0.495694\pi\)
0.0135286 + 0.999908i \(0.495694\pi\)
\(44\) −122.247 + 211.738i −0.418851 + 0.725471i
\(45\) 0 0
\(46\) 158.247 + 274.092i 0.507223 + 0.878536i
\(47\) −84.6453 + 146.610i −0.262698 + 0.455006i −0.966958 0.254936i \(-0.917946\pi\)
0.704260 + 0.709942i \(0.251279\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −31.7529 −0.0898107
\(51\) 0 0
\(52\) −118.462 205.183i −0.315918 0.547187i
\(53\) 125.056 + 216.603i 0.324109 + 0.561373i 0.981332 0.192324i \(-0.0616023\pi\)
−0.657223 + 0.753696i \(0.728269\pi\)
\(54\) 0 0
\(55\) 638.510 1.56539
\(56\) 0 0
\(57\) 0 0
\(58\) 85.1236 147.438i 0.192712 0.333786i
\(59\) −402.610 697.341i −0.888395 1.53875i −0.841772 0.539833i \(-0.818487\pi\)
−0.0466235 0.998913i \(-0.514846\pi\)
\(60\) 0 0
\(61\) 16.5858 28.7274i 0.0348130 0.0602978i −0.848094 0.529846i \(-0.822250\pi\)
0.882907 + 0.469548i \(0.155583\pi\)
\(62\) −486.988 −0.997542
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −309.371 + 535.846i −0.590349 + 1.02252i
\(66\) 0 0
\(67\) 138.691 + 240.220i 0.252893 + 0.438023i 0.964321 0.264736i \(-0.0852847\pi\)
−0.711428 + 0.702759i \(0.751951\pi\)
\(68\) 40.9244 70.8832i 0.0729826 0.126410i
\(69\) 0 0
\(70\) 0 0
\(71\) −631.506 −1.05558 −0.527788 0.849376i \(-0.676979\pi\)
−0.527788 + 0.849376i \(0.676979\pi\)
\(72\) 0 0
\(73\) −384.142 665.353i −0.615896 1.06676i −0.990227 0.139468i \(-0.955461\pi\)
0.374331 0.927295i \(-0.377872\pi\)
\(74\) −290.371 502.937i −0.456147 0.790070i
\(75\) 0 0
\(76\) 321.355 0.485025
\(77\) 0 0
\(78\) 0 0
\(79\) 209.365 362.631i 0.298169 0.516445i −0.677548 0.735479i \(-0.736957\pi\)
0.975717 + 0.219034i \(0.0702906\pi\)
\(80\) −83.5698 144.747i −0.116792 0.202290i
\(81\) 0 0
\(82\) −168.000 + 290.985i −0.226250 + 0.391876i
\(83\) 761.714 1.00734 0.503668 0.863897i \(-0.331983\pi\)
0.503668 + 0.863897i \(0.331983\pi\)
\(84\) 0 0
\(85\) −213.753 −0.272762
\(86\) −7.62934 + 13.2144i −0.00956619 + 0.0165691i
\(87\) 0 0
\(88\) −244.494 423.476i −0.296172 0.512986i
\(89\) −786.048 + 1361.48i −0.936190 + 1.62153i −0.163692 + 0.986511i \(0.552340\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −632.988 −0.717322
\(93\) 0 0
\(94\) −169.291 293.220i −0.185755 0.321738i
\(95\) −419.618 726.799i −0.453178 0.784927i
\(96\) 0 0
\(97\) −1045.16 −1.09402 −0.547012 0.837125i \(-0.684235\pi\)
−0.547012 + 0.837125i \(0.684235\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 31.7529 54.9976i 0.0317529 0.0549976i
\(101\) 487.961 + 845.173i 0.480732 + 0.832652i 0.999756 0.0221078i \(-0.00703770\pi\)
−0.519024 + 0.854760i \(0.673704\pi\)
\(102\) 0 0
\(103\) −321.572 + 556.979i −0.307626 + 0.532823i −0.977842 0.209342i \(-0.932868\pi\)
0.670217 + 0.742165i \(0.266201\pi\)
\(104\) 473.849 0.446776
\(105\) 0 0
\(106\) −500.224 −0.458359
\(107\) 155.797 269.849i 0.140762 0.243806i −0.787022 0.616925i \(-0.788378\pi\)
0.927784 + 0.373119i \(0.121712\pi\)
\(108\) 0 0
\(109\) 932.915 + 1615.86i 0.819790 + 1.41992i 0.905837 + 0.423626i \(0.139243\pi\)
−0.0860476 + 0.996291i \(0.527424\pi\)
\(110\) −638.510 + 1105.93i −0.553451 + 0.958604i
\(111\) 0 0
\(112\) 0 0
\(113\) −1720.49 −1.43231 −0.716153 0.697944i \(-0.754099\pi\)
−0.716153 + 0.697944i \(0.754099\pi\)
\(114\) 0 0
\(115\) 826.542 + 1431.61i 0.670221 + 1.16086i
\(116\) 170.247 + 294.877i 0.136268 + 0.236022i
\(117\) 0 0
\(118\) 1610.44 1.25638
\(119\) 0 0
\(120\) 0 0
\(121\) −1202.54 + 2082.87i −0.903489 + 1.56489i
\(122\) 33.1715 + 57.4548i 0.0246165 + 0.0426370i
\(123\) 0 0
\(124\) 486.988 843.489i 0.352684 0.610867i
\(125\) −1471.63 −1.05301
\(126\) 0 0
\(127\) 142.236 0.0993808 0.0496904 0.998765i \(-0.484177\pi\)
0.0496904 + 0.998765i \(0.484177\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −618.741 1071.69i −0.417440 0.723027i
\(131\) −1243.26 + 2153.38i −0.829189 + 1.43620i 0.0694870 + 0.997583i \(0.477864\pi\)
−0.898676 + 0.438614i \(0.855470\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −554.764 −0.357644
\(135\) 0 0
\(136\) 81.8489 + 141.766i 0.0516065 + 0.0893851i
\(137\) −1298.61 2249.25i −0.809835 1.40268i −0.912978 0.408009i \(-0.866223\pi\)
0.103143 0.994667i \(-0.467110\pi\)
\(138\) 0 0
\(139\) −1600.52 −0.976651 −0.488325 0.872662i \(-0.662392\pi\)
−0.488325 + 0.872662i \(0.662392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 631.506 1093.80i 0.373203 0.646406i
\(143\) −1810.21 3135.37i −1.05858 1.83352i
\(144\) 0 0
\(145\) 444.610 770.087i 0.254640 0.441050i
\(146\) 1536.57 0.871008
\(147\) 0 0
\(148\) 1161.48 0.645090
\(149\) −1468.85 + 2544.13i −0.807605 + 1.39881i 0.106913 + 0.994268i \(0.465903\pi\)
−0.914518 + 0.404545i \(0.867430\pi\)
\(150\) 0 0
\(151\) −911.662 1579.05i −0.491325 0.850999i 0.508625 0.860988i \(-0.330154\pi\)
−0.999950 + 0.00998867i \(0.996820\pi\)
\(152\) −321.355 + 556.603i −0.171482 + 0.297016i
\(153\) 0 0
\(154\) 0 0
\(155\) −2543.59 −1.31811
\(156\) 0 0
\(157\) 316.824 + 548.755i 0.161053 + 0.278952i 0.935247 0.353997i \(-0.115178\pi\)
−0.774194 + 0.632949i \(0.781844\pi\)
\(158\) 418.730 + 725.261i 0.210838 + 0.365182i
\(159\) 0 0
\(160\) 334.279 0.165169
\(161\) 0 0
\(162\) 0 0
\(163\) 672.853 1165.42i 0.323325 0.560015i −0.657847 0.753151i \(-0.728533\pi\)
0.981172 + 0.193137i \(0.0618660\pi\)
\(164\) −336.000 581.969i −0.159983 0.277098i
\(165\) 0 0
\(166\) −761.714 + 1319.33i −0.356147 + 0.616865i
\(167\) −387.922 −0.179750 −0.0898751 0.995953i \(-0.528647\pi\)
−0.0898751 + 0.995953i \(0.528647\pi\)
\(168\) 0 0
\(169\) 1311.32 0.596870
\(170\) 213.753 370.231i 0.0964359 0.167032i
\(171\) 0 0
\(172\) −15.2587 26.4288i −0.00676432 0.0117161i
\(173\) −311.330 + 539.239i −0.136821 + 0.236980i −0.926291 0.376808i \(-0.877022\pi\)
0.789471 + 0.613788i \(0.210355\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 977.977 0.418851
\(177\) 0 0
\(178\) −1572.10 2722.95i −0.661986 1.14659i
\(179\) 224.965 + 389.651i 0.0939368 + 0.162703i 0.909164 0.416437i \(-0.136721\pi\)
−0.815228 + 0.579141i \(0.803388\pi\)
\(180\) 0 0
\(181\) −184.353 −0.0757063 −0.0378532 0.999283i \(-0.512052\pi\)
−0.0378532 + 0.999283i \(0.512052\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 632.988 1096.37i 0.253612 0.439268i
\(185\) −1516.64 2626.89i −0.602732 1.04396i
\(186\) 0 0
\(187\) 625.362 1083.16i 0.244551 0.423574i
\(188\) 677.163 0.262698
\(189\) 0 0
\(190\) 1678.47 0.640890
\(191\) −175.483 + 303.945i −0.0664789 + 0.115145i −0.897349 0.441321i \(-0.854510\pi\)
0.830870 + 0.556466i \(0.187843\pi\)
\(192\) 0 0
\(193\) −764.129 1323.51i −0.284991 0.493619i 0.687616 0.726074i \(-0.258657\pi\)
−0.972607 + 0.232456i \(0.925324\pi\)
\(194\) 1045.16 1810.28i 0.386796 0.669950i
\(195\) 0 0
\(196\) 0 0
\(197\) 2874.65 1.03965 0.519823 0.854274i \(-0.325998\pi\)
0.519823 + 0.854274i \(0.325998\pi\)
\(198\) 0 0
\(199\) 2474.35 + 4285.70i 0.881418 + 1.52666i 0.849765 + 0.527162i \(0.176744\pi\)
0.0316529 + 0.999499i \(0.489923\pi\)
\(200\) 63.5058 + 109.995i 0.0224527 + 0.0388892i
\(201\) 0 0
\(202\) −1951.84 −0.679858
\(203\) 0 0
\(204\) 0 0
\(205\) −877.483 + 1519.84i −0.298956 + 0.517808i
\(206\) −643.144 1113.96i −0.217524 0.376763i
\(207\) 0 0
\(208\) −473.849 + 820.730i −0.157959 + 0.273593i
\(209\) 4910.58 1.62523
\(210\) 0 0
\(211\) −5280.90 −1.72299 −0.861497 0.507762i \(-0.830473\pi\)
−0.861497 + 0.507762i \(0.830473\pi\)
\(212\) 500.224 866.413i 0.162054 0.280686i
\(213\) 0 0
\(214\) 311.595 + 539.698i 0.0995335 + 0.172397i
\(215\) −39.8489 + 69.0203i −0.0126403 + 0.0218937i
\(216\) 0 0
\(217\) 0 0
\(218\) −3731.66 −1.15936
\(219\) 0 0
\(220\) −1277.02 2211.86i −0.391349 0.677836i
\(221\) 606.000 + 1049.62i 0.184452 + 0.319481i
\(222\) 0 0
\(223\) −3996.57 −1.20013 −0.600067 0.799950i \(-0.704859\pi\)
−0.600067 + 0.799950i \(0.704859\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1720.49 2979.98i 0.506396 0.877104i
\(227\) 269.296 + 466.434i 0.0787392 + 0.136380i 0.902706 0.430257i \(-0.141577\pi\)
−0.823967 + 0.566638i \(0.808244\pi\)
\(228\) 0 0
\(229\) 2085.80 3612.72i 0.601895 1.04251i −0.390639 0.920544i \(-0.627746\pi\)
0.992534 0.121968i \(-0.0389206\pi\)
\(230\) −3306.17 −0.947836
\(231\) 0 0
\(232\) −680.988 −0.192712
\(233\) 769.865 1333.45i 0.216461 0.374922i −0.737262 0.675607i \(-0.763882\pi\)
0.953724 + 0.300684i \(0.0972151\pi\)
\(234\) 0 0
\(235\) −884.224 1531.52i −0.245449 0.425129i
\(236\) −1610.44 + 2789.36i −0.444198 + 0.769373i
\(237\) 0 0
\(238\) 0 0
\(239\) −3132.67 −0.847848 −0.423924 0.905698i \(-0.639348\pi\)
−0.423924 + 0.905698i \(0.639348\pi\)
\(240\) 0 0
\(241\) 1303.35 + 2257.46i 0.348365 + 0.603386i 0.985959 0.166987i \(-0.0534037\pi\)
−0.637594 + 0.770372i \(0.720070\pi\)
\(242\) −2405.09 4165.74i −0.638863 1.10654i
\(243\) 0 0
\(244\) −132.686 −0.0348130
\(245\) 0 0
\(246\) 0 0
\(247\) −2379.27 + 4121.02i −0.612913 + 1.06160i
\(248\) 973.977 + 1686.98i 0.249385 + 0.431948i
\(249\) 0 0
\(250\) 1471.63 2548.93i 0.372295 0.644834i
\(251\) −3426.24 −0.861603 −0.430801 0.902447i \(-0.641769\pi\)
−0.430801 + 0.902447i \(0.641769\pi\)
\(252\) 0 0
\(253\) −9672.63 −2.40361
\(254\) −142.236 + 246.359i −0.0351364 + 0.0608581i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −2928.72 + 5072.69i −0.710850 + 1.23123i 0.253688 + 0.967286i \(0.418356\pi\)
−0.964538 + 0.263943i \(0.914977\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2474.97 0.590349
\(261\) 0 0
\(262\) −2486.51 4306.76i −0.586325 1.01554i
\(263\) −542.965 940.443i −0.127303 0.220495i 0.795328 0.606180i \(-0.207299\pi\)
−0.922631 + 0.385684i \(0.873965\pi\)
\(264\) 0 0
\(265\) −2612.73 −0.605654
\(266\) 0 0
\(267\) 0 0
\(268\) 554.764 960.880i 0.126446 0.219012i
\(269\) 2789.73 + 4831.95i 0.632315 + 1.09520i 0.987077 + 0.160245i \(0.0512283\pi\)
−0.354763 + 0.934956i \(0.615438\pi\)
\(270\) 0 0
\(271\) −280.164 + 485.258i −0.0627997 + 0.108772i −0.895716 0.444627i \(-0.853336\pi\)
0.832916 + 0.553399i \(0.186670\pi\)
\(272\) −327.396 −0.0729826
\(273\) 0 0
\(274\) 5194.42 1.14528
\(275\) 485.212 840.413i 0.106398 0.184286i
\(276\) 0 0
\(277\) 2254.04 + 3904.11i 0.488924 + 0.846842i 0.999919 0.0127421i \(-0.00405606\pi\)
−0.510994 + 0.859584i \(0.670723\pi\)
\(278\) 1600.52 2772.19i 0.345298 0.598074i
\(279\) 0 0
\(280\) 0 0
\(281\) 4329.75 0.919186 0.459593 0.888130i \(-0.347995\pi\)
0.459593 + 0.888130i \(0.347995\pi\)
\(282\) 0 0
\(283\) −435.526 754.353i −0.0914817 0.158451i 0.816653 0.577129i \(-0.195827\pi\)
−0.908135 + 0.418678i \(0.862494\pi\)
\(284\) 1263.01 + 2187.60i 0.263894 + 0.457078i
\(285\) 0 0
\(286\) 7240.83 1.49706
\(287\) 0 0
\(288\) 0 0
\(289\) 2247.15 3892.18i 0.457388 0.792220i
\(290\) 889.220 + 1540.17i 0.180058 + 0.311869i
\(291\) 0 0
\(292\) −1536.57 + 2661.41i −0.307948 + 0.533381i
\(293\) 1651.91 0.329372 0.164686 0.986346i \(-0.447339\pi\)
0.164686 + 0.986346i \(0.447339\pi\)
\(294\) 0 0
\(295\) 8411.50 1.66012
\(296\) −1161.48 + 2011.75i −0.228074 + 0.395035i
\(297\) 0 0
\(298\) −2937.71 5088.26i −0.571063 0.989110i
\(299\) 4686.58 8117.39i 0.906460 1.57004i
\(300\) 0 0
\(301\) 0 0
\(302\) 3646.65 0.694838
\(303\) 0 0
\(304\) −642.709 1113.21i −0.121256 0.210022i
\(305\) 173.259 + 300.093i 0.0325271 + 0.0563386i
\(306\) 0 0
\(307\) −1016.42 −0.188958 −0.0944791 0.995527i \(-0.530119\pi\)
−0.0944791 + 0.995527i \(0.530119\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2543.59 4405.64i 0.466021 0.807172i
\(311\) 4596.53 + 7961.42i 0.838087 + 1.45161i 0.891492 + 0.453037i \(0.149659\pi\)
−0.0534049 + 0.998573i \(0.517007\pi\)
\(312\) 0 0
\(313\) −3346.30 + 5795.97i −0.604295 + 1.04667i 0.387868 + 0.921715i \(0.373212\pi\)
−0.992162 + 0.124954i \(0.960122\pi\)
\(314\) −1267.30 −0.227763
\(315\) 0 0
\(316\) −1674.92 −0.298169
\(317\) 3526.25 6107.64i 0.624775 1.08214i −0.363809 0.931473i \(-0.618524\pi\)
0.988584 0.150669i \(-0.0481426\pi\)
\(318\) 0 0
\(319\) 2601.53 + 4505.98i 0.456607 + 0.790866i
\(320\) −334.279 + 578.988i −0.0583962 + 0.101145i
\(321\) 0 0
\(322\) 0 0
\(323\) −1643.91 −0.283187
\(324\) 0 0
\(325\) 470.190 + 814.393i 0.0802506 + 0.138998i
\(326\) 1345.71 + 2330.83i 0.228625 + 0.395990i
\(327\) 0 0
\(328\) 1344.00 0.226250
\(329\) 0 0
\(330\) 0 0
\(331\) −1570.19 + 2719.64i −0.260741 + 0.451616i −0.966439 0.256896i \(-0.917300\pi\)
0.705698 + 0.708513i \(0.250633\pi\)
\(332\) −1523.43 2638.65i −0.251834 0.436190i
\(333\) 0 0
\(334\) 387.922 671.900i 0.0635513 0.110074i
\(335\) −2897.60 −0.472575
\(336\) 0 0
\(337\) 2743.87 0.443526 0.221763 0.975101i \(-0.428819\pi\)
0.221763 + 0.975101i \(0.428819\pi\)
\(338\) −1311.32 + 2271.28i −0.211026 + 0.365507i
\(339\) 0 0
\(340\) 427.506 + 740.462i 0.0681905 + 0.118109i
\(341\) 7441.62 12889.3i 1.18178 2.04690i
\(342\) 0 0
\(343\) 0 0
\(344\) 61.0347 0.00956619
\(345\) 0 0
\(346\) −622.660 1078.48i −0.0967468 0.167570i
\(347\) 5218.45 + 9038.62i 0.807323 + 1.39832i 0.914712 + 0.404107i \(0.132418\pi\)
−0.107389 + 0.994217i \(0.534249\pi\)
\(348\) 0 0
\(349\) 2257.01 0.346175 0.173087 0.984906i \(-0.444626\pi\)
0.173087 + 0.984906i \(0.444626\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −977.977 + 1693.91i −0.148086 + 0.256493i
\(353\) −2808.22 4863.98i −0.423418 0.733381i 0.572854 0.819658i \(-0.305836\pi\)
−0.996271 + 0.0862770i \(0.972503\pi\)
\(354\) 0 0
\(355\) 3298.42 5713.04i 0.493133 0.854131i
\(356\) 6288.38 0.936190
\(357\) 0 0
\(358\) −899.861 −0.132847
\(359\) −397.795 + 689.002i −0.0584815 + 0.101293i −0.893784 0.448498i \(-0.851959\pi\)
0.835302 + 0.549791i \(0.185293\pi\)
\(360\) 0 0
\(361\) 202.349 + 350.479i 0.0295013 + 0.0510977i
\(362\) 184.353 319.309i 0.0267662 0.0463605i
\(363\) 0 0
\(364\) 0 0
\(365\) 8025.66 1.15091
\(366\) 0 0
\(367\) 4096.99 + 7096.19i 0.582727 + 1.00931i 0.995155 + 0.0983227i \(0.0313477\pi\)
−0.412427 + 0.910990i \(0.635319\pi\)
\(368\) 1265.98 + 2192.74i 0.179330 + 0.310609i
\(369\) 0 0
\(370\) 6066.55 0.852392
\(371\) 0 0
\(372\) 0 0
\(373\) −7038.69 + 12191.4i −0.977076 + 1.69235i −0.304170 + 0.952618i \(0.598379\pi\)
−0.672906 + 0.739728i \(0.734954\pi\)
\(374\) 1250.72 + 2166.32i 0.172923 + 0.299512i
\(375\) 0 0
\(376\) −677.163 + 1172.88i −0.0928777 + 0.160869i
\(377\) −5041.96 −0.688791
\(378\) 0 0
\(379\) 6221.22 0.843173 0.421587 0.906788i \(-0.361473\pi\)
0.421587 + 0.906788i \(0.361473\pi\)
\(380\) −1678.47 + 2907.20i −0.226589 + 0.392463i
\(381\) 0 0
\(382\) −350.965 607.890i −0.0470077 0.0814197i
\(383\) 5350.71 9267.70i 0.713860 1.23644i −0.249537 0.968365i \(-0.580278\pi\)
0.963397 0.268077i \(-0.0863883\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3056.52 0.403038
\(387\) 0 0
\(388\) 2090.33 + 3620.56i 0.273506 + 0.473726i
\(389\) 2110.81 + 3656.03i 0.275121 + 0.476524i 0.970166 0.242443i \(-0.0779487\pi\)
−0.695044 + 0.718967i \(0.744615\pi\)
\(390\) 0 0
\(391\) 3238.09 0.418816
\(392\) 0 0
\(393\) 0 0
\(394\) −2874.65 + 4979.04i −0.367570 + 0.636651i
\(395\) 2187.07 + 3788.12i 0.278591 + 0.482534i
\(396\) 0 0
\(397\) −6037.87 + 10457.9i −0.763305 + 1.32208i 0.177833 + 0.984061i \(0.443091\pi\)
−0.941138 + 0.338023i \(0.890242\pi\)
\(398\) −9897.41 −1.24651
\(399\) 0 0
\(400\) −254.023 −0.0317529
\(401\) −2753.19 + 4768.66i −0.342862 + 0.593855i −0.984963 0.172766i \(-0.944730\pi\)
0.642101 + 0.766620i \(0.278063\pi\)
\(402\) 0 0
\(403\) 7211.22 + 12490.2i 0.891356 + 1.54387i
\(404\) 1951.84 3380.69i 0.240366 0.416326i
\(405\) 0 0
\(406\) 0 0
\(407\) 17748.5 2.16157
\(408\) 0 0
\(409\) 714.089 + 1236.84i 0.0863311 + 0.149530i 0.905958 0.423368i \(-0.139152\pi\)
−0.819627 + 0.572898i \(0.805819\pi\)
\(410\) −1754.97 3039.69i −0.211394 0.366145i
\(411\) 0 0
\(412\) 2572.58 0.307626
\(413\) 0 0
\(414\) 0 0
\(415\) −3978.52 + 6890.99i −0.470597 + 0.815097i
\(416\) −947.698 1641.46i −0.111694 0.193460i
\(417\) 0 0
\(418\) −4910.58 + 8505.38i −0.574604 + 0.995244i
\(419\) 264.960 0.0308929 0.0154465 0.999881i \(-0.495083\pi\)
0.0154465 + 0.999881i \(0.495083\pi\)
\(420\) 0 0
\(421\) −281.066 −0.0325375 −0.0162688 0.999868i \(-0.505179\pi\)
−0.0162688 + 0.999868i \(0.505179\pi\)
\(422\) 5280.90 9146.78i 0.609171 1.05511i
\(423\) 0 0
\(424\) 1000.45 + 1732.83i 0.114590 + 0.198475i
\(425\) −162.434 + 281.343i −0.0185393 + 0.0321110i
\(426\) 0 0
\(427\) 0 0
\(428\) −1246.38 −0.140762
\(429\) 0 0
\(430\) −79.6978 138.041i −0.00893806 0.0154812i
\(431\) −893.189 1547.05i −0.0998223 0.172897i 0.811789 0.583951i \(-0.198494\pi\)
−0.911611 + 0.411054i \(0.865161\pi\)
\(432\) 0 0
\(433\) −184.621 −0.0204904 −0.0102452 0.999948i \(-0.503261\pi\)
−0.0102452 + 0.999948i \(0.503261\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 3731.66 6463.43i 0.409895 0.709959i
\(437\) 6356.68 + 11010.1i 0.695838 + 1.20523i
\(438\) 0 0
\(439\) 5637.32 9764.12i 0.612881 1.06154i −0.377872 0.925858i \(-0.623344\pi\)
0.990752 0.135682i \(-0.0433227\pi\)
\(440\) 5108.08 0.553451
\(441\) 0 0
\(442\) −2424.00 −0.260855
\(443\) 3984.92 6902.09i 0.427380 0.740244i −0.569259 0.822158i \(-0.692770\pi\)
0.996639 + 0.0819142i \(0.0261033\pi\)
\(444\) 0 0
\(445\) −8211.23 14222.3i −0.874718 1.51506i
\(446\) 3996.57 6922.25i 0.424311 0.734929i
\(447\) 0 0
\(448\) 0 0
\(449\) −8850.37 −0.930233 −0.465117 0.885249i \(-0.653988\pi\)
−0.465117 + 0.885249i \(0.653988\pi\)
\(450\) 0 0
\(451\) −5134.38 8893.00i −0.536072 0.928504i
\(452\) 3440.99 + 5959.97i 0.358076 + 0.620206i
\(453\) 0 0
\(454\) −1077.18 −0.111354
\(455\) 0 0
\(456\) 0 0
\(457\) 6513.65 11282.0i 0.666730 1.15481i −0.312083 0.950055i \(-0.601027\pi\)
0.978813 0.204756i \(-0.0656400\pi\)
\(458\) 4171.61 + 7225.44i 0.425604 + 0.737167i
\(459\) 0 0
\(460\) 3306.17 5726.45i 0.335111 0.580429i
\(461\) 1261.05 0.127403 0.0637016 0.997969i \(-0.479709\pi\)
0.0637016 + 0.997969i \(0.479709\pi\)
\(462\) 0 0
\(463\) −4005.47 −0.402052 −0.201026 0.979586i \(-0.564427\pi\)
−0.201026 + 0.979586i \(0.564427\pi\)
\(464\) 680.988 1179.51i 0.0681338 0.118011i
\(465\) 0 0
\(466\) 1539.73 + 2666.89i 0.153061 + 0.265110i
\(467\) −8548.91 + 14807.1i −0.847101 + 1.46722i 0.0366825 + 0.999327i \(0.488321\pi\)
−0.883784 + 0.467895i \(0.845012\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 3536.90 0.347117
\(471\) 0 0
\(472\) −3220.88 5578.72i −0.314095 0.544029i
\(473\) −233.166 403.856i −0.0226659 0.0392586i
\(474\) 0 0
\(475\) −1275.49 −0.123208
\(476\) 0 0
\(477\) 0 0
\(478\) 3132.67 5425.95i 0.299760 0.519199i
\(479\) −5844.26 10122.6i −0.557477 0.965578i −0.997706 0.0676925i \(-0.978436\pi\)
0.440230 0.897885i \(-0.354897\pi\)
\(480\) 0 0
\(481\) −8599.49 + 14894.8i −0.815183 + 1.41194i
\(482\) −5213.39 −0.492662
\(483\) 0 0
\(484\) 9620.36 0.903489
\(485\) 5459.01 9455.28i 0.511095 0.885242i
\(486\) 0 0
\(487\) 4812.40 + 8335.31i 0.447783 + 0.775583i 0.998241 0.0592793i \(-0.0188803\pi\)
−0.550458 + 0.834863i \(0.685547\pi\)
\(488\) 132.686 229.819i 0.0123082 0.0213185i
\(489\) 0 0
\(490\) 0 0
\(491\) 6320.63 0.580949 0.290475 0.956883i \(-0.406187\pi\)
0.290475 + 0.956883i \(0.406187\pi\)
\(492\) 0 0
\(493\) −870.908 1508.46i −0.0795613 0.137804i
\(494\) −4758.55 8242.05i −0.433395 0.750662i
\(495\) 0 0
\(496\) −3895.91 −0.352684
\(497\) 0 0
\(498\) 0 0
\(499\) 7527.29 13037.6i 0.675286 1.16963i −0.301100 0.953593i \(-0.597354\pi\)
0.976385 0.216037i \(-0.0693130\pi\)
\(500\) 2943.25 + 5097.86i 0.263253 + 0.455967i
\(501\) 0 0
\(502\) 3426.24 5934.42i 0.304623 0.527622i
\(503\) 16559.1 1.46786 0.733930 0.679225i \(-0.237684\pi\)
0.733930 + 0.679225i \(0.237684\pi\)
\(504\) 0 0
\(505\) −10194.7 −0.898333
\(506\) 9672.63 16753.5i 0.849804 1.47190i
\(507\) 0 0
\(508\) −284.471 492.718i −0.0248452 0.0430332i
\(509\) 6669.48 11551.9i 0.580785 1.00595i −0.414601 0.910003i \(-0.636079\pi\)
0.995387 0.0959462i \(-0.0305877\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −5857.44 10145.4i −0.502647 0.870610i
\(515\) −3359.21 5818.33i −0.287426 0.497837i
\(516\) 0 0
\(517\) 10347.6 0.880250
\(518\) 0 0
\(519\) 0 0
\(520\) −2474.97 + 4286.77i −0.208720 + 0.361514i
\(521\) 3591.35 + 6220.40i 0.301996 + 0.523072i 0.976588 0.215118i \(-0.0690138\pi\)
−0.674592 + 0.738191i \(0.735680\pi\)
\(522\) 0 0
\(523\) 4815.07 8339.94i 0.402578 0.697285i −0.591459 0.806335i \(-0.701448\pi\)
0.994036 + 0.109050i \(0.0347810\pi\)
\(524\) 9946.04 0.829189
\(525\) 0 0
\(526\) 2171.86 0.180034
\(527\) −2491.22 + 4314.91i −0.205919 + 0.356661i
\(528\) 0 0
\(529\) −6437.57 11150.2i −0.529101 0.916430i
\(530\) 2612.73 4525.37i 0.214131 0.370886i
\(531\) 0 0
\(532\) 0 0
\(533\) 9950.83 0.808664
\(534\) 0 0
\(535\) 1627.49 + 2818.90i 0.131519 + 0.227798i
\(536\) 1109.53 + 1921.76i 0.0894111 + 0.154865i
\(537\) 0 0
\(538\) −11158.9 −0.894228
\(539\) 0 0
\(540\) 0 0
\(541\) −7774.74 + 13466.2i −0.617860 + 1.07016i 0.372016 + 0.928227i \(0.378667\pi\)
−0.989875 + 0.141938i \(0.954667\pi\)
\(542\) −560.327 970.515i −0.0444061 0.0769136i
\(543\) 0 0
\(544\) 327.396 567.066i 0.0258032 0.0446925i
\(545\) −19490.9 −1.53192
\(546\) 0 0
\(547\) −5917.38 −0.462539 −0.231270 0.972890i \(-0.574288\pi\)
−0.231270 + 0.972890i \(0.574288\pi\)
\(548\) −5194.42 + 8997.01i −0.404918 + 0.701338i
\(549\) 0 0
\(550\) 970.425 + 1680.83i 0.0752346 + 0.130310i
\(551\) 3419.36 5922.50i 0.264373 0.457907i
\(552\) 0 0
\(553\) 0 0
\(554\) −9016.15 −0.691444
\(555\) 0 0
\(556\) 3201.04 + 5544.37i 0.244163 + 0.422902i
\(557\) 1065.93 + 1846.25i 0.0810862 + 0.140445i 0.903717 0.428131i \(-0.140828\pi\)
−0.822631 + 0.568576i \(0.807494\pi\)
\(558\) 0 0
\(559\) 451.894 0.0341916
\(560\) 0 0
\(561\) 0 0
\(562\) −4329.75 + 7499.35i −0.324981 + 0.562884i
\(563\) 3687.95 + 6387.72i 0.276072 + 0.478171i 0.970405 0.241483i \(-0.0776337\pi\)
−0.694333 + 0.719654i \(0.744300\pi\)
\(564\) 0 0
\(565\) 8986.33 15564.8i 0.669129 1.15897i
\(566\) 1742.10 0.129375
\(567\) 0 0
\(568\) −5052.05 −0.373203
\(569\) −6350.42 + 10999.3i −0.467880 + 0.810391i −0.999326 0.0367005i \(-0.988315\pi\)
0.531447 + 0.847092i \(0.321649\pi\)
\(570\) 0 0
\(571\) 3845.06 + 6659.84i 0.281805 + 0.488101i 0.971829 0.235686i \(-0.0757335\pi\)
−0.690024 + 0.723786i \(0.742400\pi\)
\(572\) −7240.83 + 12541.5i −0.529291 + 0.916759i
\(573\) 0 0
\(574\) 0 0
\(575\) 2512.40 0.182216
\(576\) 0 0
\(577\) 1547.43 + 2680.23i 0.111647 + 0.193379i 0.916435 0.400185i \(-0.131054\pi\)
−0.804787 + 0.593563i \(0.797721\pi\)
\(578\) 4494.30 + 7784.35i 0.323422 + 0.560184i
\(579\) 0 0
\(580\) −3556.88 −0.254640
\(581\) 0 0
\(582\) 0 0
\(583\) 7643.87 13239.6i 0.543013 0.940526i
\(584\) −3073.13 5322.82i −0.217752 0.377158i
\(585\) 0 0
\(586\) −1651.91 + 2861.20i −0.116450 + 0.201698i
\(587\) −9967.83 −0.700880 −0.350440 0.936585i \(-0.613968\pi\)
−0.350440 + 0.936585i \(0.613968\pi\)
\(588\) 0 0
\(589\) −19562.0 −1.36849
\(590\) −8411.50 + 14569.1i −0.586942 + 1.01661i
\(591\) 0 0
\(592\) −2322.97 4023.49i −0.161272 0.279332i
\(593\) −884.864 + 1532.63i −0.0612766 + 0.106134i −0.895036 0.445993i \(-0.852851\pi\)
0.833760 + 0.552127i \(0.186184\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11750.8 0.807605
\(597\) 0 0
\(598\) 9373.15 + 16234.8i 0.640964 + 1.11018i
\(599\) −3173.66 5496.95i −0.216481 0.374957i 0.737248 0.675622i \(-0.236125\pi\)
−0.953730 + 0.300665i \(0.902791\pi\)
\(600\) 0 0
\(601\) −22005.7 −1.49356 −0.746781 0.665070i \(-0.768401\pi\)
−0.746781 + 0.665070i \(0.768401\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3646.65 + 6316.18i −0.245662 + 0.425500i
\(605\) −12562.0 21758.1i −0.844165 1.46214i
\(606\) 0 0
\(607\) 8853.55 15334.8i 0.592017 1.02540i −0.401943 0.915665i \(-0.631665\pi\)
0.993960 0.109740i \(-0.0350017\pi\)
\(608\) 2570.84 0.171482
\(609\) 0 0
\(610\) −693.035 −0.0460003
\(611\) −5013.64 + 8683.87i −0.331964 + 0.574979i
\(612\) 0 0
\(613\) −7923.32 13723.6i −0.522055 0.904226i −0.999671 0.0256570i \(-0.991832\pi\)
0.477616 0.878569i \(-0.341501\pi\)
\(614\) 1016.42 1760.49i 0.0668068 0.115713i
\(615\) 0 0
\(616\) 0 0
\(617\) −29473.4 −1.92311 −0.961553 0.274621i \(-0.911448\pi\)
−0.961553 + 0.274621i \(0.911448\pi\)
\(618\) 0 0
\(619\) 5763.74 + 9983.08i 0.374255 + 0.648229i 0.990215 0.139548i \(-0.0445650\pi\)
−0.615960 + 0.787778i \(0.711232\pi\)
\(620\) 5087.19 + 8811.27i 0.329527 + 0.570757i
\(621\) 0 0
\(622\) −18386.1 −1.18523
\(623\) 0 0
\(624\) 0 0
\(625\) 6694.19 11594.7i 0.428428 0.742059i
\(626\) −6692.61 11591.9i −0.427301 0.740107i
\(627\) 0 0
\(628\) 1267.30 2195.02i 0.0805265 0.139476i
\(629\) −5941.63 −0.376643
\(630\) 0 0
\(631\) 25846.1 1.63062 0.815308 0.579027i \(-0.196568\pi\)
0.815308 + 0.579027i \(0.196568\pi\)
\(632\) 1674.92 2901.04i 0.105419 0.182591i
\(633\) 0 0
\(634\) 7052.49 + 12215.3i 0.441783 + 0.765190i
\(635\) −742.912 + 1286.76i −0.0464277 + 0.0804151i
\(636\) 0 0
\(637\) 0 0
\(638\) −10406.1 −0.645739
\(639\) 0 0
\(640\) −668.558 1157.98i −0.0412923 0.0715204i
\(641\) 2767.39 + 4793.26i 0.170523 + 0.295355i 0.938603 0.344999i \(-0.112121\pi\)
−0.768080 + 0.640354i \(0.778788\pi\)
\(642\) 0 0
\(643\) −1634.56 −0.100250 −0.0501251 0.998743i \(-0.515962\pi\)
−0.0501251 + 0.998743i \(0.515962\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1643.91 2847.33i 0.100122 0.173416i
\(647\) −3769.00 6528.10i −0.229018 0.396671i 0.728499 0.685047i \(-0.240218\pi\)
−0.957517 + 0.288375i \(0.906885\pi\)
\(648\) 0 0
\(649\) −24608.9 + 42623.9i −1.48842 + 2.57802i
\(650\) −1880.76 −0.113491
\(651\) 0 0
\(652\) −5382.83 −0.323325
\(653\) −6656.09 + 11528.7i −0.398887 + 0.690892i −0.993589 0.113054i \(-0.963937\pi\)
0.594702 + 0.803946i \(0.297270\pi\)
\(654\) 0 0
\(655\) −12987.3 22494.7i −0.774743 1.34189i
\(656\) −1344.00 + 2327.88i −0.0799914 + 0.138549i
\(657\) 0 0
\(658\) 0 0
\(659\) −10962.0 −0.647981 −0.323991 0.946060i \(-0.605025\pi\)
−0.323991 + 0.946060i \(0.605025\pi\)
\(660\) 0 0
\(661\) −11816.3 20466.4i −0.695309 1.20431i −0.970076 0.242800i \(-0.921934\pi\)
0.274767 0.961511i \(-0.411399\pi\)
\(662\) −3140.37 5439.28i −0.184372 0.319341i
\(663\) 0 0
\(664\) 6093.71 0.356147
\(665\) 0 0
\(666\) 0 0
\(667\) −6735.28 + 11665.8i −0.390991 + 0.677216i
\(668\) 775.843 + 1343.80i 0.0449376 + 0.0778341i
\(669\) 0 0
\(670\) 2897.60 5018.78i 0.167080 0.289392i
\(671\) −2027.56 −0.116652
\(672\) 0 0
\(673\) 23483.0 1.34503 0.672513 0.740085i \(-0.265215\pi\)
0.672513 + 0.740085i \(0.265215\pi\)
\(674\) −2743.87 + 4752.53i −0.156810 + 0.271603i
\(675\) 0 0
\(676\) −2622.65 4542.56i −0.149218 0.258452i
\(677\) −12336.2 + 21367.0i −0.700325 + 1.21300i 0.268028 + 0.963411i \(0.413628\pi\)
−0.968352 + 0.249587i \(0.919705\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1710.02 −0.0964359
\(681\) 0 0
\(682\) 14883.2 + 25778.5i 0.835643 + 1.44738i
\(683\) 4469.73 + 7741.80i 0.250409 + 0.433721i 0.963638 0.267209i \(-0.0861016\pi\)
−0.713229 + 0.700931i \(0.752768\pi\)
\(684\) 0 0
\(685\) 27131.1 1.51332
\(686\) 0 0
\(687\) 0 0
\(688\) −61.0347 + 105.715i −0.00338216 + 0.00585807i
\(689\) 7407.21 + 12829.7i 0.409568 + 0.709392i
\(690\) 0 0
\(691\) 7555.03 13085.7i 0.415929 0.720410i −0.579597 0.814904i \(-0.696790\pi\)
0.995525 + 0.0944937i \(0.0301232\pi\)
\(692\) 2490.64 0.136821
\(693\) 0 0
\(694\) −20873.8 −1.14173
\(695\) 8359.70 14479.4i 0.456261 0.790268i
\(696\) 0 0
\(697\) 1718.83 + 2977.09i 0.0934077 + 0.161787i
\(698\) −2257.01 + 3909.26i −0.122391 + 0.211988i
\(699\) 0 0
\(700\) 0 0
\(701\) −18353.3 −0.988865 −0.494432 0.869216i \(-0.664624\pi\)
−0.494432 + 0.869216i \(0.664624\pi\)
\(702\) 0 0
\(703\) −11664.0 20202.6i −0.625769 1.08386i
\(704\) −1955.95 3387.81i −0.104713 0.181368i
\(705\) 0 0
\(706\) 11232.9 0.598803
\(707\) 0 0
\(708\) 0 0
\(709\) 5036.85 8724.07i 0.266802 0.462115i −0.701232 0.712933i \(-0.747366\pi\)
0.968034 + 0.250818i \(0.0806997\pi\)
\(710\) 6596.85 + 11426.1i 0.348698 + 0.603962i
\(711\) 0 0
\(712\) −6288.38 + 10891.8i −0.330993 + 0.573297i
\(713\) 38532.3 2.02391
\(714\) 0 0
\(715\) 37819.7 1.97815
\(716\) 899.861 1558.61i 0.0469684 0.0813517i
\(717\) 0 0
\(718\) −795.591 1378.00i −0.0413526 0.0716249i
\(719\) −9944.63 + 17224.6i −0.515817 + 0.893420i 0.484015 + 0.875060i \(0.339178\pi\)
−0.999831 + 0.0183607i \(0.994155\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −809.397 −0.0417211
\(723\) 0 0
\(724\) 368.706 + 638.617i 0.0189266 + 0.0327818i
\(725\) −675.730 1170.40i −0.0346151 0.0599552i
\(726\) 0 0
\(727\) −13403.5 −0.683780 −0.341890 0.939740i \(-0.611067\pi\)
−0.341890 + 0.939740i \(0.611067\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −8025.66 + 13900.9i −0.406908 + 0.704786i
\(731\) 78.0566 + 135.198i 0.00394942 + 0.00684060i
\(732\) 0 0
\(733\) 6627.50 11479.2i 0.333960 0.578435i −0.649325 0.760511i \(-0.724948\pi\)
0.983284 + 0.182076i \(0.0582817\pi\)
\(734\) −16387.9 −0.824101
\(735\) 0 0
\(736\) −5063.91 −0.253612
\(737\) 8477.29 14683.1i 0.423698 0.733866i
\(738\) 0 0
\(739\) −7710.19 13354.4i −0.383794 0.664751i 0.607807 0.794085i \(-0.292049\pi\)
−0.991601 + 0.129334i \(0.958716\pi\)
\(740\) −6066.55 + 10507.6i −0.301366 + 0.521981i
\(741\) 0 0
\(742\) 0 0
\(743\) −943.019 −0.0465626 −0.0232813 0.999729i \(-0.507411\pi\)
−0.0232813 + 0.999729i \(0.507411\pi\)
\(744\) 0 0
\(745\) −15344.0 26576.5i −0.754576 1.30696i
\(746\) −14077.4 24382.7i −0.690897 1.19667i
\(747\) 0 0
\(748\) −5002.89 −0.244551
\(749\) 0 0
\(750\) 0 0
\(751\) 14297.9 24764.7i 0.694726 1.20330i −0.275547 0.961287i \(-0.588859\pi\)
0.970273 0.242013i \(-0.0778076\pi\)
\(752\) −1354.33 2345.76i −0.0656744 0.113751i
\(753\) 0 0
\(754\) 5041.96 8732.94i 0.243524 0.421797i
\(755\) 19046.9 0.918127
\(756\) 0 0
\(757\) −28984.4 −1.39162 −0.695810 0.718226i \(-0.744955\pi\)
−0.695810 + 0.718226i \(0.744955\pi\)
\(758\) −6221.22 + 10775.5i −0.298107 + 0.516336i
\(759\) 0 0
\(760\) −3356.94 5814.39i −0.160222 0.277513i
\(761\) −4465.05 + 7733.70i −0.212691 + 0.368392i −0.952556 0.304364i \(-0.901556\pi\)
0.739865 + 0.672756i \(0.234890\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1403.86 0.0664789
\(765\) 0 0
\(766\) 10701.4 + 18535.4i 0.504776 + 0.874297i
\(767\) −23847.0 41304.3i −1.12264 1.94447i
\(768\) 0 0
\(769\) −2373.15 −0.111285 −0.0556424 0.998451i \(-0.517721\pi\)
−0.0556424 + 0.998451i \(0.517721\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3056.52 + 5294.04i −0.142495 + 0.246809i
\(773\) −13988.5 24228.8i −0.650881 1.12736i −0.982909 0.184089i \(-0.941066\pi\)
0.332029 0.943269i \(-0.392267\pi\)
\(774\) 0 0
\(775\) −1932.91 + 3347.90i −0.0895900 + 0.155174i
\(776\) −8361.32 −0.386796
\(777\) 0 0
\(778\) −8443.23 −0.389080
\(779\) −6748.45 + 11688.7i −0.310383 + 0.537599i
\(780\) 0 0
\(781\) 19299.9 + 33428.5i 0.884259 + 1.53158i
\(782\) −3238.09 + 5608.53i −0.148074 + 0.256471i
\(783\) 0 0
\(784\) 0 0
\(785\) −6619.23 −0.300956
\(786\) 0 0
\(787\) 17180.5 + 29757.4i 0.778167 + 1.34782i 0.932997 + 0.359883i \(0.117183\pi\)
−0.154831 + 0.987941i \(0.549483\pi\)
\(788\) −5749.30 9958.08i −0.259911 0.450180i
\(789\) 0 0
\(790\) −8748.29 −0.393987
\(791\)