Properties

Label 252.4.x.a.41.19
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.19
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.19

$q$-expansion

\(f(q)\) \(=\) \(q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +O(q^{10})\) \(q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +(7.40072 - 4.27281i) q^{11} +(45.3367 + 26.1752i) q^{13} +(5.08588 + 36.3774i) q^{15} -38.9547 q^{17} +66.4008i q^{19} +(85.1039 + 44.9258i) q^{21} +(173.899 + 100.401i) q^{23} +(37.5151 + 64.9781i) q^{25} +(-56.7874 - 128.289i) q^{27} +(52.9622 - 30.5777i) q^{29} +(-116.401 - 67.2041i) q^{31} +(16.6637 - 41.1590i) q^{33} +(-130.251 - 13.2032i) q^{35} +298.967 q^{37} +(269.400 - 37.6645i) q^{39} +(221.278 - 383.265i) q^{41} +(26.1371 + 45.2708i) q^{43} +(137.104 + 132.780i) q^{45} +(-137.682 - 238.472i) q^{47} +(-227.620 + 256.589i) q^{49} +(-159.594 + 124.504i) q^{51} +136.637i q^{53} +60.4084i q^{55} +(212.226 + 272.039i) q^{57} +(-191.268 + 331.286i) q^{59} +(-261.714 + 151.100i) q^{61} +(492.253 - 87.9458i) q^{63} +(-320.482 + 185.030i) q^{65} +(318.940 - 552.420i) q^{67} +(1033.34 - 144.470i) q^{69} -228.249i q^{71} +1241.68i q^{73} +(361.375 + 146.307i) q^{75} +(128.384 + 92.5530i) q^{77} +(-100.694 - 174.407i) q^{79} +(-642.683 - 344.092i) q^{81} +(-323.452 - 560.235i) q^{83} +(137.684 - 238.476i) q^{85} +(119.251 - 294.549i) q^{87} -826.042 q^{89} +(-97.7786 + 964.598i) q^{91} +(-691.679 + 96.7027i) q^{93} +(-406.497 - 234.691i) q^{95} +(17.0700 - 9.85534i) q^{97} +(-63.2797 - 221.885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.09692 3.19613i 0.788453 0.615096i
\(4\) 0 0
\(5\) −3.53447 + 6.12188i −0.316132 + 0.547557i −0.979678 0.200579i \(-0.935718\pi\)
0.663545 + 0.748136i \(0.269051\pi\)
\(6\) 0 0
\(7\) 7.59538 + 16.8911i 0.410112 + 0.912035i
\(8\) 0 0
\(9\) 6.56950 26.1886i 0.243315 0.969947i
\(10\) 0 0
\(11\) 7.40072 4.27281i 0.202855 0.117118i −0.395132 0.918625i \(-0.629301\pi\)
0.597986 + 0.801506i \(0.295968\pi\)
\(12\) 0 0
\(13\) 45.3367 + 26.1752i 0.967241 + 0.558437i 0.898394 0.439190i \(-0.144735\pi\)
0.0688473 + 0.997627i \(0.478068\pi\)
\(14\) 0 0
\(15\) 5.08588 + 36.3774i 0.0875447 + 0.626174i
\(16\) 0 0
\(17\) −38.9547 −0.555759 −0.277879 0.960616i \(-0.589632\pi\)
−0.277879 + 0.960616i \(0.589632\pi\)
\(18\) 0 0
\(19\) 66.4008i 0.801757i 0.916131 + 0.400879i \(0.131295\pi\)
−0.916131 + 0.400879i \(0.868705\pi\)
\(20\) 0 0
\(21\) 85.1039 + 44.9258i 0.884343 + 0.466839i
\(22\) 0 0
\(23\) 173.899 + 100.401i 1.57654 + 0.910217i 0.995337 + 0.0964590i \(0.0307517\pi\)
0.581204 + 0.813758i \(0.302582\pi\)
\(24\) 0 0
\(25\) 37.5151 + 64.9781i 0.300121 + 0.519824i
\(26\) 0 0
\(27\) −56.7874 128.289i −0.404768 0.914419i
\(28\) 0 0
\(29\) 52.9622 30.5777i 0.339132 0.195798i −0.320756 0.947162i \(-0.603937\pi\)
0.659888 + 0.751364i \(0.270604\pi\)
\(30\) 0 0
\(31\) −116.401 67.2041i −0.674395 0.389362i 0.123345 0.992364i \(-0.460638\pi\)
−0.797740 + 0.603002i \(0.793971\pi\)
\(32\) 0 0
\(33\) 16.6637 41.1590i 0.0879024 0.217117i
\(34\) 0 0
\(35\) −130.251 13.2032i −0.629041 0.0637641i
\(36\) 0 0
\(37\) 298.967 1.32838 0.664188 0.747565i \(-0.268777\pi\)
0.664188 + 0.747565i \(0.268777\pi\)
\(38\) 0 0
\(39\) 269.400 37.6645i 1.10612 0.154645i
\(40\) 0 0
\(41\) 221.278 383.265i 0.842874 1.45990i −0.0445802 0.999006i \(-0.514195\pi\)
0.887455 0.460895i \(-0.152472\pi\)
\(42\) 0 0
\(43\) 26.1371 + 45.2708i 0.0926947 + 0.160552i 0.908644 0.417571i \(-0.137119\pi\)
−0.815949 + 0.578123i \(0.803785\pi\)
\(44\) 0 0
\(45\) 137.104 + 132.780i 0.454182 + 0.439861i
\(46\) 0 0
\(47\) −137.682 238.472i −0.427298 0.740101i 0.569334 0.822106i \(-0.307201\pi\)
−0.996632 + 0.0820049i \(0.973868\pi\)
\(48\) 0 0
\(49\) −227.620 + 256.589i −0.663617 + 0.748073i
\(50\) 0 0
\(51\) −159.594 + 124.504i −0.438189 + 0.341845i
\(52\) 0 0
\(53\) 136.637i 0.354123i 0.984200 + 0.177061i \(0.0566591\pi\)
−0.984200 + 0.177061i \(0.943341\pi\)
\(54\) 0 0
\(55\) 60.4084i 0.148099i
\(56\) 0 0
\(57\) 212.226 + 272.039i 0.493157 + 0.632147i
\(58\) 0 0
\(59\) −191.268 + 331.286i −0.422051 + 0.731014i −0.996140 0.0877790i \(-0.972023\pi\)
0.574089 + 0.818793i \(0.305356\pi\)
\(60\) 0 0
\(61\) −261.714 + 151.100i −0.549328 + 0.317155i −0.748851 0.662739i \(-0.769394\pi\)
0.199523 + 0.979893i \(0.436061\pi\)
\(62\) 0 0
\(63\) 492.253 87.9458i 0.984412 0.175875i
\(64\) 0 0
\(65\) −320.482 + 185.030i −0.611552 + 0.353080i
\(66\) 0 0
\(67\) 318.940 552.420i 0.581563 1.00730i −0.413732 0.910399i \(-0.635775\pi\)
0.995294 0.0968972i \(-0.0308918\pi\)
\(68\) 0 0
\(69\) 1033.34 144.470i 1.80290 0.252061i
\(70\) 0 0
\(71\) 228.249i 0.381524i −0.981636 0.190762i \(-0.938904\pi\)
0.981636 0.190762i \(-0.0610959\pi\)
\(72\) 0 0
\(73\) 1241.68i 1.99079i 0.0958607 + 0.995395i \(0.469440\pi\)
−0.0958607 + 0.995395i \(0.530560\pi\)
\(74\) 0 0
\(75\) 361.375 + 146.307i 0.556373 + 0.225254i
\(76\) 0 0
\(77\) 128.384 + 92.5530i 0.190009 + 0.136979i
\(78\) 0 0
\(79\) −100.694 174.407i −0.143404 0.248383i 0.785372 0.619024i \(-0.212472\pi\)
−0.928776 + 0.370641i \(0.879138\pi\)
\(80\) 0 0
\(81\) −642.683 344.092i −0.881596 0.472005i
\(82\) 0 0
\(83\) −323.452 560.235i −0.427752 0.740889i 0.568921 0.822392i \(-0.307361\pi\)
−0.996673 + 0.0815036i \(0.974028\pi\)
\(84\) 0 0
\(85\) 137.684 238.476i 0.175693 0.304310i
\(86\) 0 0
\(87\) 119.251 294.549i 0.146955 0.362976i
\(88\) 0 0
\(89\) −826.042 −0.983824 −0.491912 0.870645i \(-0.663702\pi\)
−0.491912 + 0.870645i \(0.663702\pi\)
\(90\) 0 0
\(91\) −97.7786 + 964.598i −0.112637 + 1.11118i
\(92\) 0 0
\(93\) −691.679 + 96.7027i −0.771223 + 0.107824i
\(94\) 0 0
\(95\) −406.497 234.691i −0.439008 0.253461i
\(96\) 0 0
\(97\) 17.0700 9.85534i 0.0178679 0.0103161i −0.491039 0.871137i \(-0.663383\pi\)
0.508907 + 0.860821i \(0.330050\pi\)
\(98\) 0 0
\(99\) −63.2797 221.885i −0.0642409 0.225255i
\(100\) 0 0
\(101\) −814.290 1410.39i −0.802226 1.38950i −0.918148 0.396239i \(-0.870315\pi\)
0.115921 0.993258i \(-0.463018\pi\)
\(102\) 0 0
\(103\) 644.110 + 371.877i 0.616175 + 0.355749i 0.775378 0.631497i \(-0.217559\pi\)
−0.159203 + 0.987246i \(0.550893\pi\)
\(104\) 0 0
\(105\) −575.827 + 362.207i −0.535190 + 0.336645i
\(106\) 0 0
\(107\) 836.505i 0.755775i 0.925851 + 0.377888i \(0.123349\pi\)
−0.925851 + 0.377888i \(0.876651\pi\)
\(108\) 0 0
\(109\) −1564.06 −1.37440 −0.687202 0.726467i \(-0.741161\pi\)
−0.687202 + 0.726467i \(0.741161\pi\)
\(110\) 0 0
\(111\) 1224.85 955.539i 1.04736 0.817079i
\(112\) 0 0
\(113\) −1801.80 1040.27i −1.49999 0.866021i −0.499993 0.866029i \(-0.666664\pi\)
−1.00000 7.94493e-6i \(0.999997\pi\)
\(114\) 0 0
\(115\) −1229.28 + 709.725i −0.996791 + 0.575498i
\(116\) 0 0
\(117\) 983.330 1015.35i 0.776999 0.802297i
\(118\) 0 0
\(119\) −295.875 657.988i −0.227923 0.506871i
\(120\) 0 0
\(121\) −628.986 + 1089.44i −0.472567 + 0.818509i
\(122\) 0 0
\(123\) −318.406 2277.44i −0.233412 1.66951i
\(124\) 0 0
\(125\) −1414.00 −1.01178
\(126\) 0 0
\(127\) 774.362 0.541051 0.270526 0.962713i \(-0.412803\pi\)
0.270526 + 0.962713i \(0.412803\pi\)
\(128\) 0 0
\(129\) 251.773 + 101.933i 0.171840 + 0.0695715i
\(130\) 0 0
\(131\) 402.834 697.729i 0.268670 0.465350i −0.699849 0.714291i \(-0.746749\pi\)
0.968519 + 0.248941i \(0.0800826\pi\)
\(132\) 0 0
\(133\) −1121.58 + 504.339i −0.731231 + 0.328810i
\(134\) 0 0
\(135\) 986.085 + 105.790i 0.628657 + 0.0674439i
\(136\) 0 0
\(137\) 1587.40 916.484i 0.989930 0.571537i 0.0846770 0.996408i \(-0.473014\pi\)
0.905254 + 0.424872i \(0.139681\pi\)
\(138\) 0 0
\(139\) −765.487 441.954i −0.467106 0.269684i 0.247921 0.968780i \(-0.420253\pi\)
−0.715028 + 0.699096i \(0.753586\pi\)
\(140\) 0 0
\(141\) −1326.26 536.952i −0.792137 0.320706i
\(142\) 0 0
\(143\) 447.366 0.261613
\(144\) 0 0
\(145\) 432.304i 0.247592i
\(146\) 0 0
\(147\) −112.451 + 1778.73i −0.0630938 + 0.998008i
\(148\) 0 0
\(149\) −1396.08 806.025i −0.767590 0.443169i 0.0644239 0.997923i \(-0.479479\pi\)
−0.832014 + 0.554754i \(0.812812\pi\)
\(150\) 0 0
\(151\) −575.071 996.052i −0.309925 0.536805i 0.668421 0.743783i \(-0.266970\pi\)
−0.978346 + 0.206978i \(0.933637\pi\)
\(152\) 0 0
\(153\) −255.913 + 1020.17i −0.135224 + 0.539057i
\(154\) 0 0
\(155\) 822.831 475.061i 0.426396 0.246180i
\(156\) 0 0
\(157\) 1086.53 + 627.309i 0.552322 + 0.318883i 0.750058 0.661372i \(-0.230025\pi\)
−0.197736 + 0.980255i \(0.563359\pi\)
\(158\) 0 0
\(159\) 436.709 + 559.790i 0.217819 + 0.279209i
\(160\) 0 0
\(161\) −375.051 + 3699.93i −0.183591 + 1.81115i
\(162\) 0 0
\(163\) 1005.42 0.483131 0.241565 0.970385i \(-0.422339\pi\)
0.241565 + 0.970385i \(0.422339\pi\)
\(164\) 0 0
\(165\) 193.073 + 247.488i 0.0910953 + 0.116769i
\(166\) 0 0
\(167\) 1198.49 2075.84i 0.555340 0.961878i −0.442536 0.896750i \(-0.645921\pi\)
0.997877 0.0651274i \(-0.0207454\pi\)
\(168\) 0 0
\(169\) 271.778 + 470.733i 0.123704 + 0.214262i
\(170\) 0 0
\(171\) 1738.94 + 436.220i 0.777662 + 0.195080i
\(172\) 0 0
\(173\) 15.8922 + 27.5262i 0.00698419 + 0.0120970i 0.869496 0.493939i \(-0.164444\pi\)
−0.862512 + 0.506036i \(0.831110\pi\)
\(174\) 0 0
\(175\) −812.611 + 1127.21i −0.351015 + 0.486907i
\(176\) 0 0
\(177\) 275.224 + 1968.57i 0.116876 + 0.835972i
\(178\) 0 0
\(179\) 1553.05i 0.648494i −0.945972 0.324247i \(-0.894889\pi\)
0.945972 0.324247i \(-0.105111\pi\)
\(180\) 0 0
\(181\) 3516.58i 1.44412i 0.691831 + 0.722059i \(0.256804\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(182\) 0 0
\(183\) −589.283 + 1455.52i −0.238039 + 0.587950i
\(184\) 0 0
\(185\) −1056.69 + 1830.24i −0.419943 + 0.727362i
\(186\) 0 0
\(187\) −288.293 + 166.446i −0.112738 + 0.0650895i
\(188\) 0 0
\(189\) 1735.63 1933.61i 0.667983 0.744177i
\(190\) 0 0
\(191\) 1971.02 1137.97i 0.746692 0.431103i −0.0778056 0.996969i \(-0.524791\pi\)
0.824497 + 0.565866i \(0.191458\pi\)
\(192\) 0 0
\(193\) 795.313 1377.52i 0.296621 0.513763i −0.678740 0.734379i \(-0.737473\pi\)
0.975361 + 0.220616i \(0.0708068\pi\)
\(194\) 0 0
\(195\) −721.608 + 1782.36i −0.265002 + 0.654550i
\(196\) 0 0
\(197\) 1715.67i 0.620490i 0.950657 + 0.310245i \(0.100411\pi\)
−0.950657 + 0.310245i \(0.899589\pi\)
\(198\) 0 0
\(199\) 2534.03i 0.902676i −0.892353 0.451338i \(-0.850947\pi\)
0.892353 0.451338i \(-0.149053\pi\)
\(200\) 0 0
\(201\) −458.935 3282.59i −0.161049 1.15192i
\(202\) 0 0
\(203\) 918.760 + 662.342i 0.317657 + 0.229001i
\(204\) 0 0
\(205\) 1564.20 + 2709.27i 0.532920 + 0.923044i
\(206\) 0 0
\(207\) 3771.78 3894.59i 1.26646 1.30769i
\(208\) 0 0
\(209\) 283.718 + 491.414i 0.0939004 + 0.162640i
\(210\) 0 0
\(211\) 2149.79 3723.55i 0.701411 1.21488i −0.266560 0.963818i \(-0.585887\pi\)
0.967971 0.251061i \(-0.0807795\pi\)
\(212\) 0 0
\(213\) −729.515 935.120i −0.234674 0.300814i
\(214\) 0 0
\(215\) −369.523 −0.117215
\(216\) 0 0
\(217\) 251.044 2476.58i 0.0785345 0.774753i
\(218\) 0 0
\(219\) 3968.57 + 5087.06i 1.22453 + 1.56964i
\(220\) 0 0
\(221\) −1766.08 1019.64i −0.537553 0.310356i
\(222\) 0 0
\(223\) −2529.08 + 1460.16i −0.759460 + 0.438474i −0.829102 0.559098i \(-0.811148\pi\)
0.0696418 + 0.997572i \(0.477814\pi\)
\(224\) 0 0
\(225\) 1948.14 555.593i 0.577226 0.164620i
\(226\) 0 0
\(227\) −390.119 675.705i −0.114066 0.197569i 0.803340 0.595521i \(-0.203054\pi\)
−0.917406 + 0.397952i \(0.869721\pi\)
\(228\) 0 0
\(229\) 2843.34 + 1641.61i 0.820495 + 0.473713i 0.850587 0.525834i \(-0.176247\pi\)
−0.0300919 + 0.999547i \(0.509580\pi\)
\(230\) 0 0
\(231\) 821.790 31.1495i 0.234068 0.00887223i
\(232\) 0 0
\(233\) 5223.64i 1.46872i 0.678759 + 0.734361i \(0.262518\pi\)
−0.678759 + 0.734361i \(0.737482\pi\)
\(234\) 0 0
\(235\) 1946.53 0.540330
\(236\) 0 0
\(237\) −969.960 392.699i −0.265847 0.107631i
\(238\) 0 0
\(239\) −896.500 517.595i −0.242635 0.140085i 0.373752 0.927529i \(-0.378071\pi\)
−0.616387 + 0.787443i \(0.711404\pi\)
\(240\) 0 0
\(241\) 4811.53 2777.94i 1.28605 0.742501i 0.308103 0.951353i \(-0.400306\pi\)
0.977947 + 0.208852i \(0.0669726\pi\)
\(242\) 0 0
\(243\) −3732.78 + 644.382i −0.985425 + 0.170112i
\(244\) 0 0
\(245\) −766.289 2300.37i −0.199822 0.599858i
\(246\) 0 0
\(247\) −1738.05 + 3010.39i −0.447731 + 0.775493i
\(248\) 0 0
\(249\) −3115.74 1261.44i −0.792980 0.321047i
\(250\) 0 0
\(251\) 974.838 0.245144 0.122572 0.992460i \(-0.460886\pi\)
0.122572 + 0.992460i \(0.460886\pi\)
\(252\) 0 0
\(253\) 1715.97 0.426412
\(254\) 0 0
\(255\) −198.119 1417.07i −0.0486537 0.348002i
\(256\) 0 0
\(257\) −2406.33 + 4167.88i −0.584057 + 1.01162i 0.410935 + 0.911665i \(0.365202\pi\)
−0.994992 + 0.0999520i \(0.968131\pi\)
\(258\) 0 0
\(259\) 2270.77 + 5049.90i 0.544783 + 1.21153i
\(260\) 0 0
\(261\) −452.852 1587.89i −0.107398 0.376581i
\(262\) 0 0
\(263\) 2132.47 1231.18i 0.499976 0.288661i −0.228728 0.973490i \(-0.573457\pi\)
0.728704 + 0.684829i \(0.240123\pi\)
\(264\) 0 0
\(265\) −836.473 482.938i −0.193902 0.111950i
\(266\) 0 0
\(267\) −3384.23 + 2640.14i −0.775698 + 0.605146i
\(268\) 0 0
\(269\) 2092.97 0.474389 0.237194 0.971462i \(-0.423772\pi\)
0.237194 + 0.971462i \(0.423772\pi\)
\(270\) 0 0
\(271\) 5006.83i 1.12230i −0.827714 0.561150i \(-0.810359\pi\)
0.827714 0.561150i \(-0.189641\pi\)
\(272\) 0 0
\(273\) 2682.39 + 4264.39i 0.594673 + 0.945395i
\(274\) 0 0
\(275\) 555.278 + 320.590i 0.121762 + 0.0702992i
\(276\) 0 0
\(277\) −4158.94 7203.49i −0.902117 1.56251i −0.824742 0.565510i \(-0.808680\pi\)
−0.0773748 0.997002i \(-0.524654\pi\)
\(278\) 0 0
\(279\) −2524.68 + 2606.88i −0.541751 + 0.559390i
\(280\) 0 0
\(281\) 4024.77 2323.70i 0.854440 0.493311i −0.00770671 0.999970i \(-0.502453\pi\)
0.862146 + 0.506659i \(0.169120\pi\)
\(282\) 0 0
\(283\) −3970.15 2292.17i −0.833925 0.481467i 0.0212695 0.999774i \(-0.493229\pi\)
−0.855195 + 0.518307i \(0.826563\pi\)
\(284\) 0 0
\(285\) −2415.49 + 337.707i −0.502040 + 0.0701895i
\(286\) 0 0
\(287\) 8154.47 + 826.595i 1.67715 + 0.170008i
\(288\) 0 0
\(289\) −3395.53 −0.691132
\(290\) 0 0
\(291\) 38.4353 94.9343i 0.00774266 0.0191242i
\(292\) 0 0
\(293\) −1961.13 + 3396.77i −0.391025 + 0.677275i −0.992585 0.121552i \(-0.961213\pi\)
0.601560 + 0.798828i \(0.294546\pi\)
\(294\) 0 0
\(295\) −1352.06 2341.84i −0.266848 0.462194i
\(296\) 0 0
\(297\) −968.424 706.793i −0.189204 0.138089i
\(298\) 0 0
\(299\) 5256.01 + 9103.67i 1.01660 + 1.76080i
\(300\) 0 0
\(301\) −566.154 + 785.334i −0.108414 + 0.150385i
\(302\) 0 0
\(303\) −7843.88 3175.68i −1.48719 0.602107i
\(304\) 0 0
\(305\) 2136.24i 0.401051i
\(306\) 0 0
\(307\) 8034.65i 1.49369i −0.665000 0.746843i \(-0.731569\pi\)
0.665000 0.746843i \(-0.268431\pi\)
\(308\) 0 0
\(309\) 3827.43 535.109i 0.704644 0.0985154i
\(310\) 0 0
\(311\) 2215.47 3837.30i 0.403947 0.699657i −0.590251 0.807220i \(-0.700971\pi\)
0.994198 + 0.107563i \(0.0343047\pi\)
\(312\) 0 0
\(313\) 5126.22 2959.63i 0.925723 0.534467i 0.0402668 0.999189i \(-0.487179\pi\)
0.885456 + 0.464722i \(0.153846\pi\)
\(314\) 0 0
\(315\) −1201.46 + 3324.35i −0.214903 + 0.594622i
\(316\) 0 0
\(317\) 458.040 264.450i 0.0811549 0.0468548i −0.458873 0.888502i \(-0.651747\pi\)
0.540028 + 0.841647i \(0.318414\pi\)
\(318\) 0 0
\(319\) 261.306 452.595i 0.0458630 0.0794371i
\(320\) 0 0
\(321\) 2673.58 + 3427.09i 0.464874 + 0.595893i
\(322\) 0 0
\(323\) 2586.62i 0.445583i
\(324\) 0 0
\(325\) 3927.85i 0.670394i
\(326\) 0 0
\(327\) −6407.84 + 4998.95i −1.08365 + 0.845390i
\(328\) 0 0
\(329\) 2982.32 4136.89i 0.499759 0.693235i
\(330\) 0 0
\(331\) 1824.88 + 3160.78i 0.303035 + 0.524871i 0.976822 0.214054i \(-0.0686669\pi\)
−0.673787 + 0.738925i \(0.735334\pi\)
\(332\) 0 0
\(333\) 1964.07 7829.53i 0.323214 1.28846i
\(334\) 0 0
\(335\) 2254.56 + 3905.02i 0.367701 + 0.636878i
\(336\) 0 0
\(337\) −3284.70 + 5689.26i −0.530946 + 0.919625i 0.468402 + 0.883516i \(0.344830\pi\)
−0.999348 + 0.0361099i \(0.988503\pi\)
\(338\) 0 0
\(339\) −10706.7 + 1496.89i −1.71536 + 0.239822i
\(340\) 0 0
\(341\) −1148.60 −0.182405
\(342\) 0 0
\(343\) −6062.94 1895.88i −0.954426 0.298448i
\(344\) 0 0
\(345\) −2767.89 + 6836.63i −0.431937 + 1.06687i
\(346\) 0 0
\(347\) −10270.0 5929.38i −1.58882 0.917307i −0.993501 0.113820i \(-0.963691\pi\)
−0.595321 0.803488i \(-0.702975\pi\)
\(348\) 0 0
\(349\) 30.7558 17.7568i 0.00471724 0.00272350i −0.497640 0.867384i \(-0.665800\pi\)
0.502357 + 0.864660i \(0.332466\pi\)
\(350\) 0 0
\(351\) 783.446 7302.64i 0.119137 1.11050i
\(352\) 0 0
\(353\) 4968.07 + 8604.94i 0.749075 + 1.29744i 0.948266 + 0.317475i \(0.102835\pi\)
−0.199191 + 0.979961i \(0.563832\pi\)
\(354\) 0 0
\(355\) 1397.31 + 806.740i 0.208906 + 0.120612i
\(356\) 0 0
\(357\) −3315.19 1750.07i −0.491481 0.259450i
\(358\) 0 0
\(359\) 10087.1i 1.48295i 0.670983 + 0.741473i \(0.265872\pi\)
−0.670983 + 0.741473i \(0.734128\pi\)
\(360\) 0 0
\(361\) 2449.94 0.357186
\(362\) 0 0
\(363\) 905.073 + 6473.65i 0.130865 + 0.936030i
\(364\) 0 0
\(365\) −7601.41 4388.68i −1.09007 0.629353i
\(366\) 0 0
\(367\) 8473.74 4892.32i 1.20525 0.695850i 0.243530 0.969893i \(-0.421695\pi\)
0.961717 + 0.274044i \(0.0883612\pi\)
\(368\) 0 0
\(369\) −8583.48 8312.82i −1.21094 1.17276i
\(370\) 0 0
\(371\) −2307.95 + 1037.81i −0.322972 + 0.145230i
\(372\) 0 0
\(373\) 3884.31 6727.82i 0.539201 0.933923i −0.459747 0.888050i \(-0.652060\pi\)
0.998947 0.0458729i \(-0.0146069\pi\)
\(374\) 0 0
\(375\) −5793.04 + 4519.33i −0.797737 + 0.622339i
\(376\) 0 0
\(377\) 3201.51 0.437364
\(378\) 0 0
\(379\) −10683.1 −1.44789 −0.723947 0.689856i \(-0.757674\pi\)
−0.723947 + 0.689856i \(0.757674\pi\)
\(380\) 0 0
\(381\) 3172.50 2474.96i 0.426593 0.332798i
\(382\) 0 0
\(383\) −6456.89 + 11183.7i −0.861440 + 1.49206i 0.00909866 + 0.999959i \(0.497104\pi\)
−0.870539 + 0.492100i \(0.836230\pi\)
\(384\) 0 0
\(385\) −1020.37 + 458.825i −0.135072 + 0.0607373i
\(386\) 0 0
\(387\) 1357.29 387.087i 0.178281 0.0508443i
\(388\) 0 0
\(389\) 9760.56 5635.26i 1.27218 0.734496i 0.296786 0.954944i \(-0.404085\pi\)
0.975399 + 0.220448i \(0.0707518\pi\)
\(390\) 0 0
\(391\) −6774.18 3911.07i −0.876176 0.505861i
\(392\) 0 0
\(393\) −579.654 4146.05i −0.0744012 0.532164i
\(394\) 0 0
\(395\) 1423.59 0.181339
\(396\) 0 0
\(397\) 4908.58i 0.620540i −0.950648 0.310270i \(-0.899581\pi\)
0.950648 0.310270i \(-0.100419\pi\)
\(398\) 0 0
\(399\) −2983.11 + 5650.97i −0.374291 + 0.709028i
\(400\) 0 0
\(401\) −4193.64 2421.20i −0.522246 0.301519i 0.215607 0.976480i \(-0.430827\pi\)
−0.737853 + 0.674961i \(0.764160\pi\)
\(402\) 0 0
\(403\) −3518.16 6093.63i −0.434868 0.753214i
\(404\) 0 0
\(405\) 4378.03 2718.25i 0.537151 0.333508i
\(406\) 0 0
\(407\) 2212.58 1277.43i 0.269468 0.155577i
\(408\) 0 0
\(409\) −421.586 243.403i −0.0509684 0.0294266i 0.474299 0.880364i \(-0.342701\pi\)
−0.525268 + 0.850937i \(0.676035\pi\)
\(410\) 0 0
\(411\) 3574.24 8828.29i 0.428964 1.05953i
\(412\) 0 0
\(413\) −7048.56 714.492i −0.839799 0.0851280i
\(414\) 0 0
\(415\) 4572.92 0.540905
\(416\) 0 0
\(417\) −4548.68 + 635.946i −0.534173 + 0.0746820i
\(418\) 0 0
\(419\) 6580.88 11398.4i 0.767296 1.32900i −0.171728 0.985144i \(-0.554935\pi\)
0.939024 0.343851i \(-0.111732\pi\)
\(420\) 0 0
\(421\) −848.070 1468.90i −0.0981767 0.170047i 0.812753 0.582608i \(-0.197968\pi\)
−0.910930 + 0.412561i \(0.864634\pi\)
\(422\) 0 0
\(423\) −7149.75 + 2039.05i −0.821827 + 0.234378i
\(424\) 0 0
\(425\) −1461.39 2531.20i −0.166795 0.288897i
\(426\) 0 0
\(427\) −4540.07 3272.97i −0.514542 0.370937i
\(428\) 0 0
\(429\) 1832.82 1429.84i 0.206269 0.160917i
\(430\) 0 0
\(431\) 3662.97i 0.409372i 0.978828 + 0.204686i \(0.0656173\pi\)
−0.978828 + 0.204686i \(0.934383\pi\)
\(432\) 0 0
\(433\) 5695.06i 0.632071i 0.948747 + 0.316036i \(0.102352\pi\)
−0.948747 + 0.316036i \(0.897648\pi\)
\(434\) 0 0
\(435\) 1381.70 + 1771.11i 0.152293 + 0.195215i
\(436\) 0 0
\(437\) −6666.68 + 11547.0i −0.729773 + 1.26400i
\(438\) 0 0
\(439\) 12705.5 7335.54i 1.38132 0.797508i 0.389008 0.921234i \(-0.372818\pi\)
0.992316 + 0.123726i \(0.0394845\pi\)
\(440\) 0 0
\(441\) 5224.35 + 7646.72i 0.564124 + 0.825690i
\(442\) 0 0
\(443\) 3537.20 2042.20i 0.379362 0.219025i −0.298179 0.954510i \(-0.596379\pi\)
0.677541 + 0.735485i \(0.263046\pi\)
\(444\) 0 0
\(445\) 2919.62 5056.93i 0.311018 0.538700i
\(446\) 0 0
\(447\) −8295.77 + 1159.82i −0.877800 + 0.122724i
\(448\) 0 0
\(449\) 17057.8i 1.79289i 0.443160 + 0.896443i \(0.353857\pi\)
−0.443160 + 0.896443i \(0.646143\pi\)
\(450\) 0 0
\(451\) 3781.92i 0.394864i
\(452\) 0 0
\(453\) −5539.53 2242.74i −0.574547 0.232612i
\(454\) 0 0
\(455\) −5559.56 4007.93i −0.572826 0.412955i
\(456\) 0 0
\(457\) −1850.19 3204.63i −0.189384 0.328022i 0.755661 0.654963i \(-0.227316\pi\)
−0.945045 + 0.326940i \(0.893982\pi\)
\(458\) 0 0
\(459\) 2212.13 + 4997.48i 0.224953 + 0.508196i
\(460\) 0 0
\(461\) −6736.65 11668.2i −0.680601 1.17884i −0.974798 0.223091i \(-0.928385\pi\)
0.294197 0.955745i \(-0.404948\pi\)
\(462\) 0 0
\(463\) −1550.96 + 2686.34i −0.155678 + 0.269643i −0.933306 0.359082i \(-0.883090\pi\)
0.777627 + 0.628725i \(0.216423\pi\)
\(464\) 0 0
\(465\) 1852.71 4576.16i 0.184769 0.456375i
\(466\) 0 0
\(467\) 12591.3 1.24766 0.623828 0.781561i \(-0.285576\pi\)
0.623828 + 0.781561i \(0.285576\pi\)
\(468\) 0 0
\(469\) 11753.5 + 1191.41i 1.15720 + 0.117302i
\(470\) 0 0
\(471\) 6456.39 902.660i 0.631624 0.0883065i
\(472\) 0 0
\(473\) 386.867 + 223.358i 0.0376071 + 0.0217125i
\(474\) 0 0
\(475\) −4314.59 + 2491.03i −0.416773 + 0.240624i
\(476\) 0 0
\(477\) 3578.32 + 897.635i 0.343480 + 0.0861633i
\(478\) 0 0
\(479\) 2640.55 + 4573.56i 0.251878 + 0.436266i 0.964043 0.265747i \(-0.0856184\pi\)
−0.712165 + 0.702012i \(0.752285\pi\)
\(480\) 0 0
\(481\) 13554.2 + 7825.52i 1.28486 + 0.741815i
\(482\) 0 0
\(483\) 10288.9 + 16357.0i 0.969278 + 1.54093i
\(484\) 0 0
\(485\) 139.333i 0.0130450i
\(486\) 0 0
\(487\) 945.042 0.0879341 0.0439671 0.999033i \(-0.486000\pi\)
0.0439671 + 0.999033i \(0.486000\pi\)
\(488\) 0 0
\(489\) 4119.11 3213.44i 0.380926 0.297171i
\(490\) 0 0
\(491\) −1326.45 765.828i −0.121919 0.0703897i 0.437801 0.899072i \(-0.355758\pi\)
−0.559719 + 0.828682i \(0.689091\pi\)
\(492\) 0 0
\(493\) −2063.12 + 1191.15i −0.188476 + 0.108816i
\(494\) 0 0
\(495\) 1582.01 + 396.853i 0.143649 + 0.0360348i
\(496\) 0 0
\(497\) 3855.39 1733.64i 0.347964 0.156468i
\(498\) 0 0
\(499\) −6853.72 + 11871.0i −0.614859 + 1.06497i 0.375550 + 0.926802i \(0.377454\pi\)
−0.990409 + 0.138165i \(0.955879\pi\)
\(500\) 0 0
\(501\) −1724.55 12335.1i −0.153787 1.09998i
\(502\) 0 0
\(503\) 17261.6 1.53013 0.765065 0.643953i \(-0.222707\pi\)
0.765065 + 0.643953i \(0.222707\pi\)
\(504\) 0 0
\(505\) 11512.3 1.01444
\(506\) 0 0
\(507\) 2617.97 + 1059.92i 0.229326 + 0.0928453i
\(508\) 0 0
\(509\) −6542.31 + 11331.6i −0.569711 + 0.986768i 0.426884 + 0.904307i \(0.359611\pi\)
−0.996594 + 0.0824613i \(0.973722\pi\)
\(510\) 0 0
\(511\) −20973.4 + 9431.03i −1.81567 + 0.816446i
\(512\) 0 0
\(513\) 8518.52 3770.73i 0.733142 0.324526i
\(514\) 0 0
\(515\) −4553.17 + 2628.77i −0.389586 + 0.224927i
\(516\) 0 0
\(517\) −2037.89 1176.58i −0.173359 0.100089i
\(518\) 0 0
\(519\) 153.087 + 61.9789i 0.0129475 + 0.00524195i
\(520\) 0 0
\(521\) −12720.6 −1.06967 −0.534835 0.844956i \(-0.679626\pi\)
−0.534835 + 0.844956i \(0.679626\pi\)
\(522\) 0 0
\(523\) 1352.20i 0.113055i −0.998401 0.0565274i \(-0.981997\pi\)
0.998401 0.0565274i \(-0.0180028\pi\)
\(524\) 0 0
\(525\) 273.491 + 7215.28i 0.0227355 + 0.599811i
\(526\) 0 0
\(527\) 4534.36 + 2617.91i 0.374801 + 0.216391i
\(528\) 0 0
\(529\) 14077.1 + 24382.2i 1.15699 + 2.00396i
\(530\) 0 0
\(531\) 7419.38 + 7185.43i 0.606354 + 0.587234i
\(532\) 0 0
\(533\) 20064.0 11584.0i 1.63053 0.941385i
\(534\) 0 0
\(535\) −5120.98 2956.60i −0.413830 0.238925i
\(536\) 0 0
\(537\) −4963.75 6362.72i −0.398886 0.511307i
\(538\) 0 0
\(539\) −588.200 + 2871.52i −0.0470048 + 0.229472i
\(540\) 0 0
\(541\) −8023.06 −0.637594 −0.318797 0.947823i \(-0.603279\pi\)
−0.318797 + 0.947823i \(0.603279\pi\)
\(542\) 0 0
\(543\) 11239.5 + 14407.1i 0.888271 + 1.13862i
\(544\) 0 0
\(545\) 5528.13 9574.99i 0.434493 0.752565i
\(546\) 0 0
\(547\) 966.417 + 1673.88i 0.0755411 + 0.130841i 0.901321 0.433151i \(-0.142598\pi\)
−0.825780 + 0.563992i \(0.809265\pi\)
\(548\) 0 0
\(549\) 2237.78 + 7846.56i 0.173964 + 0.609988i
\(550\) 0 0
\(551\) 2030.39 + 3516.73i 0.156982 + 0.271902i
\(552\) 0 0
\(553\) 2181.12 3025.51i 0.167722 0.232654i
\(554\) 0 0
\(555\) 1520.51 + 10875.7i 0.116292 + 0.831796i
\(556\) 0 0
\(557\) 3185.91i 0.242354i −0.992631 0.121177i \(-0.961333\pi\)
0.992631 0.121177i \(-0.0386669\pi\)
\(558\) 0 0
\(559\) 2736.57i 0.207057i
\(560\) 0 0
\(561\) −649.130 + 1603.34i −0.0488525 + 0.120665i
\(562\) 0 0
\(563\) 5544.17 9602.79i 0.415025 0.718844i −0.580406 0.814327i \(-0.697106\pi\)
0.995431 + 0.0954828i \(0.0304395\pi\)
\(564\) 0 0
\(565\) 12736.8 7353.60i 0.948392 0.547555i
\(566\) 0 0
\(567\) 930.679 13469.2i 0.0689327 0.997621i
\(568\) 0 0
\(569\) 4166.78 2405.69i 0.306995 0.177244i −0.338586 0.940936i \(-0.609949\pi\)
0.645581 + 0.763692i \(0.276615\pi\)
\(570\) 0 0
\(571\) 1711.30 2964.07i 0.125422 0.217237i −0.796476 0.604670i \(-0.793305\pi\)
0.921898 + 0.387433i \(0.126638\pi\)
\(572\) 0 0
\(573\) 4438.02 10961.8i 0.323562 0.799191i
\(574\) 0 0
\(575\) 15066.2i 1.09270i
\(576\) 0 0
\(577\) 15586.3i 1.12455i 0.826950 + 0.562275i \(0.190074\pi\)
−0.826950 + 0.562275i \(0.809926\pi\)
\(578\) 0 0
\(579\) −1144.41 8185.52i −0.0821415 0.587528i
\(580\) 0 0
\(581\) 7006.26 9718.66i 0.500290 0.693973i
\(582\) 0 0
\(583\) 583.823 + 1011.21i 0.0414742 + 0.0718354i
\(584\) 0 0
\(585\) 2740.28 + 9608.53i 0.193669 + 0.679083i
\(586\) 0 0
\(587\) −12308.5 21319.0i −0.865465 1.49903i −0.866584 0.499031i \(-0.833690\pi\)
0.00111897 0.999999i \(-0.499644\pi\)
\(588\) 0 0
\(589\) 4462.41 7729.12i 0.312174 0.540701i
\(590\) 0 0
\(591\) 5483.51 + 7028.97i 0.381661 + 0.489227i
\(592\) 0 0
\(593\) −25080.0 −1.73678 −0.868392 0.495878i \(-0.834846\pi\)
−0.868392 + 0.495878i \(0.834846\pi\)
\(594\) 0 0
\(595\) 5073.88 + 514.325i 0.349595 + 0.0354374i
\(596\) 0 0
\(597\) −8099.09 10381.7i −0.555232 0.711718i
\(598\) 0 0
\(599\) 11208.0 + 6470.92i 0.764516 + 0.441394i 0.830915 0.556400i \(-0.187818\pi\)
−0.0663988 + 0.997793i \(0.521151\pi\)
\(600\) 0 0
\(601\) −11568.5 + 6679.10i −0.785176 + 0.453321i −0.838261 0.545269i \(-0.816428\pi\)
0.0530857 + 0.998590i \(0.483094\pi\)
\(602\) 0 0
\(603\) −12371.8 11981.7i −0.835521 0.809175i
\(604\) 0 0
\(605\) −4446.26 7701.15i −0.298787 0.517514i
\(606\) 0 0
\(607\) 9551.96 + 5514.83i 0.638718 + 0.368764i 0.784121 0.620608i \(-0.213114\pi\)
−0.145402 + 0.989373i \(0.546448\pi\)
\(608\) 0 0
\(609\) 5881.02 222.917i 0.391315 0.0148326i
\(610\) 0 0
\(611\) 14415.4i 0.954475i
\(612\) 0 0
\(613\) −9716.71 −0.640219 −0.320109 0.947381i \(-0.603720\pi\)
−0.320109 + 0.947381i \(0.603720\pi\)
\(614\) 0 0
\(615\) 15067.6 + 6100.29i 0.987942 + 0.399980i
\(616\) 0 0
\(617\) 19367.5 + 11181.9i 1.26371 + 0.729602i 0.973790 0.227449i \(-0.0730386\pi\)
0.289918 + 0.957051i \(0.406372\pi\)
\(618\) 0 0
\(619\) −5030.74 + 2904.50i −0.326660 + 0.188597i −0.654357 0.756186i \(-0.727061\pi\)
0.327697 + 0.944783i \(0.393727\pi\)
\(620\) 0 0
\(621\) 3005.08 28010.9i 0.194186 1.81005i
\(622\) 0 0
\(623\) −6274.10 13952.8i −0.403478 0.897282i
\(624\) 0 0
\(625\) 308.348 534.075i 0.0197343 0.0341808i
\(626\) 0 0
\(627\) 2732.99 + 1106.48i 0.174075 + 0.0704764i
\(628\) 0 0
\(629\) −11646.2 −0.738257
\(630\) 0 0
\(631\) −11462.0 −0.723128 −0.361564 0.932347i \(-0.617757\pi\)
−0.361564 + 0.932347i \(0.617757\pi\)
\(632\) 0 0
\(633\) −3093.42 22126.1i −0.194238 1.38931i
\(634\) 0 0
\(635\) −2736.96 + 4740.55i −0.171044 + 0.296257i
\(636\) 0 0
\(637\) −17035.8 + 5674.90i −1.05963 + 0.352979i
\(638\) 0 0
\(639\) −5977.53 1499.49i −0.370058 0.0928306i
\(640\) 0 0
\(641\) −22256.6 + 12849.8i −1.37142 + 0.791791i −0.991107 0.133066i \(-0.957518\pi\)
−0.380315 + 0.924857i \(0.624184\pi\)
\(642\) 0 0
\(643\) −14555.9 8403.85i −0.892735 0.515421i −0.0178986 0.999840i \(-0.505698\pi\)
−0.874836 + 0.484419i \(0.839031\pi\)
\(644\) 0 0
\(645\) −1513.91 + 1181.04i −0.0924186 + 0.0720985i
\(646\) 0 0
\(647\) −14607.3 −0.887595 −0.443798 0.896127i \(-0.646369\pi\)
−0.443798 + 0.896127i \(0.646369\pi\)
\(648\) 0 0
\(649\) 3269.01i 0.197720i
\(650\) 0 0
\(651\) −6886.98 10948.7i −0.414627 0.659163i
\(652\) 0 0
\(653\) −23324.4 13466.4i −1.39779 0.807013i −0.403627 0.914924i \(-0.632251\pi\)
−0.994161 + 0.107911i \(0.965584\pi\)
\(654\) 0 0
\(655\) 2847.61 + 4932.20i 0.169870 + 0.294224i
\(656\) 0 0
\(657\) 32517.8 + 8157.22i 1.93096 + 0.484389i
\(658\) 0 0
\(659\) −21546.5 + 12439.9i −1.27364 + 0.735339i −0.975672 0.219235i \(-0.929644\pi\)
−0.297973 + 0.954574i \(0.596310\pi\)
\(660\) 0 0
\(661\) 24869.6 + 14358.5i 1.46341 + 0.844902i 0.999167 0.0408035i \(-0.0129918\pi\)
0.464247 + 0.885706i \(0.346325\pi\)
\(662\) 0 0
\(663\) −10494.4 + 1467.21i −0.614734 + 0.0859451i
\(664\) 0 0
\(665\) 876.701 8648.77i 0.0511233 0.504338i
\(666\) 0 0
\(667\) 12280.1 0.712874
\(668\) 0 0
\(669\) −5694.56 + 14065.4i −0.329095 + 0.812857i
\(670\) 0 0
\(671\) −1291.25 + 2236.51i −0.0742892 + 0.128673i
\(672\) 0 0
\(673\) −487.441 844.272i −0.0279190 0.0483570i 0.851728 0.523984i \(-0.175555\pi\)
−0.879647 + 0.475627i \(0.842221\pi\)
\(674\) 0 0
\(675\) 6205.62 8502.73i 0.353858 0.484845i
\(676\) 0 0
\(677\) 10639.0 + 18427.4i 0.603976 + 1.04612i 0.992212 + 0.124557i \(0.0397511\pi\)
−0.388236 + 0.921560i \(0.626916\pi\)
\(678\) 0 0
\(679\) 296.121 + 213.476i 0.0167365 + 0.0120655i
\(680\) 0 0
\(681\) −3757.93 1521.44i −0.211460 0.0856120i
\(682\) 0 0
\(683\) 6554.78i 0.367221i −0.982999 0.183610i \(-0.941222\pi\)
0.982999 0.183610i \(-0.0587785\pi\)
\(684\) 0 0
\(685\) 12957.1i 0.722725i
\(686\) 0 0
\(687\) 16895.7 2362.17i 0.938301 0.131183i
\(688\) 0 0
\(689\) −3576.49 + 6194.66i −0.197755 + 0.342522i
\(690\) 0 0
\(691\) −7567.47 + 4369.08i −0.416614 + 0.240532i −0.693627 0.720334i \(-0.743989\pi\)
0.277014 + 0.960866i \(0.410655\pi\)
\(692\) 0 0
\(693\) 3267.25 2754.16i 0.179095 0.150970i
\(694\) 0 0
\(695\) 5411.18 3124.15i 0.295335 0.170512i
\(696\) 0 0
\(697\) −8619.82 + 14930.0i −0.468435 + 0.811353i
\(698\) 0 0
\(699\) 16695.4 + 21400.8i 0.903404 + 1.15802i
\(700\) 0 0
\(701\) 9016.22i 0.485789i −0.970053 0.242894i \(-0.921903\pi\)
0.970053 0.242894i \(-0.0780969\pi\)
\(702\) 0 0
\(703\) 19851.7i 1.06504i
\(704\) 0 0
\(705\) 7974.78 6221.36i 0.426025 0.332355i
\(706\) 0 0
\(707\) 17638.3 24466.7i 0.938268 1.30151i
\(708\) 0 0
\(709\) −14131.7 24476.8i −0.748557 1.29654i −0.948515 0.316734i \(-0.897414\pi\)
0.199958 0.979804i \(-0.435919\pi\)
\(710\) 0 0
\(711\) −5228.97 + 1491.26i −0.275811 + 0.0786591i
\(712\) 0 0
\(713\) −13494.7 23373.5i −0.708807 1.22769i
\(714\) 0 0
\(715\) −1581.20 + 2738.72i −0.0827042 + 0.143248i
\(716\) 0 0
\(717\) −5327.19 + 744.788i −0.277472 + 0.0387930i
\(718\) 0 0
\(719\) −23753.1 −1.23205 −0.616023 0.787728i \(-0.711257\pi\)
−0.616023 + 0.787728i \(0.711257\pi\)
\(720\) 0 0
\(721\) −1389.16 + 13704.3i −0.0717548 + 0.707870i
\(722\) 0 0
\(723\) 10833.8 26759.3i 0.557280 1.37647i
\(724\) 0 0
\(725\) 3973.76 + 2294.25i 0.203561 + 0.117526i
\(726\) 0 0
\(727\) −23109.1 + 13342.1i −1.17891 + 0.680645i −0.955763 0.294139i \(-0.904967\pi\)
−0.223150 + 0.974784i \(0.571634\pi\)
\(728\) 0 0
\(729\) −13233.4 + 14570.4i −0.672326 + 0.740255i
\(730\) 0 0
\(731\) −1018.16 1763.51i −0.0515159 0.0892281i
\(732\) 0 0
\(733\) 29171.7 + 16842.3i 1.46996 + 0.848684i 0.999432 0.0337000i \(-0.0107291\pi\)
0.470531 + 0.882383i \(0.344062\pi\)
\(734\) 0 0
\(735\) −10491.7 6975.27i −0.526520 0.350050i
\(736\) 0 0
\(737\) 5451.08i 0.272446i
\(738\) 0 0
\(739\) 1602.94 0.0797905 0.0398952 0.999204i \(-0.487298\pi\)
0.0398952 + 0.999204i \(0.487298\pi\)
\(740\) 0 0
\(741\) 2500.95 + 17888.4i 0.123987 + 0.886836i
\(742\) 0 0
\(743\) −33905.7 19575.5i −1.67413 0.966560i −0.965285 0.261197i \(-0.915883\pi\)
−0.708846 0.705363i \(-0.750784\pi\)
\(744\) 0 0
\(745\) 9868.76 5697.73i 0.485320 0.280200i
\(746\) 0 0
\(747\) −16796.7 + 4790.28i −0.822702 + 0.234628i
\(748\) 0 0
\(749\) −14129.5 + 6353.57i −0.689294 + 0.309952i
\(750\) 0 0
\(751\) 10417.9 18044.4i 0.506199 0.876762i −0.493775 0.869590i \(-0.664383\pi\)
0.999974 0.00717280i \(-0.00228319\pi\)
\(752\) 0 0
\(753\) 3993.83 3115.71i 0.193285 0.150787i
\(754\) 0 0
\(755\) 8130.28 0.391909
\(756\) 0 0
\(757\) 1105.00 0.0530538 0.0265269 0.999648i \(-0.491555\pi\)
0.0265269 + 0.999648i \(0.491555\pi\)
\(758\) 0 0
\(759\) 7030.20 5484.47i 0.336206 0.262284i
\(760\) 0 0
\(761\) −13772.2 + 23854.2i −0.656036 + 1.13629i 0.325597 + 0.945508i \(0.394435\pi\)
−0.981633 + 0.190779i \(0.938899\pi\)
\(762\) 0 0
\(763\) −11879.6 26418.8i −0.563659 1.25350i
\(764\) 0 0
\(765\) −5340.82 5172.41i −0.252415 0.244456i
\(766\) 0 0
\(767\) −17342.9 + 10013.0i −0.816451 + 0.471378i
\(768\) 0 0
\(769\) −10418.2 6014.95i −0.488543 0.282060i 0.235427 0.971892i \(-0.424351\pi\)
−0.723970 + 0.689832i \(0.757685\pi\)
\(770\) 0 0
\(771\) 3462.56 + 24766.4i 0.161740 + 1.15686i
\(772\) 0 0
\(773\) 20325.9 0.945758 0.472879 0.881127i \(-0.343215\pi\)
0.472879 + 0.881127i \(0.343215\pi\)
\(774\) 0 0
\(775\) 10084.7i 0.467422i
\(776\) 0 0
\(777\) 25443.3 + 13431.3i 1.17474 + 0.620138i
\(778\) 0 0
\(779\) 25449.1 + 14693.0i 1.17049 + 0.675780i
\(780\) 0 0
\(781\) −975.266 1689.21i −0.0446834 0.0773940i
\(782\) 0 0
\(783\) −6930.39 5058.06i −0.316311 0.230856i
\(784\) 0 0
\(785\) −7680.61 + 4434.40i −0.349214 + 0.201619i
\(786\) 0 0
\(787\) −22900.0 13221.3i −1.03722 0.598842i −0.118178 0.992992i \(-0.537705\pi\)
−0.919046 + 0.394151i \(0.871039\pi\)
\(788\) 0 0
\(789\) 4801.54 11859.7i 0.216653 0.535129i
\(790\) 0 0
\(791\) 3885.98 38335.7i 0.174677 1.72321i
\(792\) 0 0
\(793\) −15820.3 −0.708443
\(794\) 0 0
\(795\) −4970.49 + 694.919i −0.221742 + 0.0310015i