Properties

Label 252.4.x.a.41.6
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 41.6
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.09692 + 3.19613i) q^{3} +(3.53447 - 6.12188i) q^{5} +(10.8305 + 15.0234i) q^{7} +(6.56950 - 26.1886i) q^{9} +O(q^{10})\) \(q+(-4.09692 + 3.19613i) q^{3} +(3.53447 - 6.12188i) q^{5} +(10.8305 + 15.0234i) q^{7} +(6.56950 - 26.1886i) q^{9} +(7.40072 - 4.27281i) q^{11} +(-45.3367 - 26.1752i) q^{13} +(5.08588 + 36.3774i) q^{15} +38.9547 q^{17} -66.4008i q^{19} +(-92.3881 - 26.9339i) q^{21} +(173.899 + 100.401i) q^{23} +(37.5151 + 64.9781i) q^{25} +(56.7874 + 128.289i) q^{27} +(52.9622 - 30.5777i) q^{29} +(116.401 + 67.2041i) q^{31} +(-16.6637 + 41.1590i) q^{33} +(130.251 - 13.2032i) q^{35} +298.967 q^{37} +(269.400 - 37.6645i) q^{39} +(-221.278 + 383.265i) q^{41} +(26.1371 + 45.2708i) q^{43} +(-137.104 - 132.780i) q^{45} +(137.682 + 238.472i) q^{47} +(-108.402 + 325.420i) q^{49} +(-159.594 + 124.504i) q^{51} +136.637i q^{53} -60.4084i q^{55} +(212.226 + 272.039i) q^{57} +(191.268 - 331.286i) q^{59} +(261.714 - 151.100i) q^{61} +(464.591 - 184.938i) q^{63} +(-320.482 + 185.030i) q^{65} +(318.940 - 552.420i) q^{67} +(-1033.34 + 144.470i) q^{69} -228.249i q^{71} -1241.68i q^{73} +(-361.375 - 146.307i) q^{75} +(144.345 + 64.9072i) q^{77} +(-100.694 - 174.407i) q^{79} +(-642.683 - 344.092i) q^{81} +(323.452 + 560.235i) q^{83} +(137.684 - 238.476i) q^{85} +(-119.251 + 294.549i) q^{87} +826.042 q^{89} +(-97.7786 - 964.598i) q^{91} +(-691.679 + 96.7027i) q^{93} +(-406.497 - 234.691i) q^{95} +(-17.0700 + 9.85534i) q^{97} +(-63.2797 - 221.885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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 −0.663545 0.748136i \(-0.730949\pi\)
0.979678 + 0.200579i \(0.0642823\pi\)
\(6\) 0 0
\(7\) 10.8305 + 15.0234i 0.584790 + 0.811185i
\(8\) 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 −0.0688473 0.997627i \(-0.521932\pi\)
−0.898394 + 0.439190i \(0.855265\pi\)
\(14\) 0 0
\(15\) 5.08588 + 36.3774i 0.0875447 + 0.626174i
\(16\) 0 0
\(17\) 38.9547 0.555759 0.277879 0.960616i \(-0.410368\pi\)
0.277879 + 0.960616i \(0.410368\pi\)
\(18\) 0 0
\(19\) 66.4008i 0.801757i −0.916131 0.400879i \(-0.868705\pi\)
0.916131 0.400879i \(-0.131295\pi\)
\(20\) 0 0
\(21\) −92.3881 26.9339i −0.960035 0.279879i
\(22\) 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 0.797740 0.603002i \(-0.206029\pi\)
−0.123345 + 0.992364i \(0.539362\pi\)
\(32\) 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 \(0.485805\pi\)
−0.887455 + 0.460895i \(0.847528\pi\)
\(42\) 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 0.996632 0.0820049i \(-0.0261323\pi\)
−0.569334 + 0.822106i \(0.692799\pi\)
\(48\) 0 0
\(49\) −108.402 + 325.420i −0.316042 + 0.948745i
\(50\) 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 −0.574089 0.818793i \(-0.694644\pi\)
0.996140 + 0.0877790i \(0.0279769\pi\)
\(60\) 0 0
\(61\) 261.714 151.100i 0.549328 0.317155i −0.199523 0.979893i \(-0.563939\pi\)
0.748851 + 0.662739i \(0.230606\pi\)
\(62\) 0 0
\(63\) 464.591 184.938i 0.929095 0.369842i
\(64\) 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 \(-0.530560\pi\)
0.0958607 0.995395i \(-0.469440\pi\)
\(74\) 0 0
\(75\) −361.375 146.307i −0.556373 0.225254i
\(76\) 0 0
\(77\) 144.345 + 64.9072i 0.213632 + 0.0960632i
\(78\) 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 0.996673 0.0815036i \(-0.0259722\pi\)
−0.568921 + 0.822392i \(0.692639\pi\)
\(84\) 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 \(-0.336298\pi\)
0.491912 + 0.870645i \(0.336298\pi\)
\(90\) 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 −0.508907 0.860821i \(-0.669950\pi\)
0.491039 + 0.871137i \(0.336617\pi\)
\(98\) 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 \(0.129685\pi\)
−0.115921 + 0.993258i \(0.536982\pi\)
\(102\) 0 0
\(103\) −644.110 371.877i −0.616175 0.355749i 0.159203 0.987246i \(-0.449107\pi\)
−0.775378 + 0.631497i \(0.782441\pi\)
\(104\) 0 0
\(105\) −491.429 + 470.391i −0.456748 + 0.437195i
\(106\) 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
\(119\) 421.897 + 585.230i 0.325002 + 0.450823i
\(120\) 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 −0.968519 0.248941i \(-0.919917\pi\)
0.699849 + 0.714291i \(0.253251\pi\)
\(132\) 0 0
\(133\) 997.563 719.151i 0.650373 0.468859i
\(134\) 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 0.715028 0.699096i \(-0.246414\pi\)
−0.247921 + 0.968780i \(0.579747\pi\)
\(140\) 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
\(147\) −595.968 1679.69i −0.334385 0.942437i
\(148\) 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 0.197736 0.980255i \(-0.436641\pi\)
−0.750058 + 0.661372i \(0.769975\pi\)
\(158\) 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 \(0.354079\pi\)
−0.997877 + 0.0651274i \(0.979255\pi\)
\(168\) 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 0.862512 0.506036i \(-0.168890\pi\)
−0.869496 + 0.493939i \(0.835556\pi\)
\(174\) 0 0
\(175\) −569.883 + 1267.34i −0.246166 + 0.547441i
\(176\) 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 \(-0.743196\pi\)
0.691831 0.722059i \(-0.256804\pi\)
\(182\) 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
\(189\) −1312.31 + 2242.57i −0.505059 + 0.863085i
\(190\) 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 \(0.149053\pi\)
−0.892353 + 0.451338i \(0.850947\pi\)
\(200\) 0 0
\(201\) 458.935 + 3282.59i 0.161049 + 1.15192i
\(202\) 0 0
\(203\) 1032.98 + 464.499i 0.357149 + 0.160598i
\(204\) 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 −0.0696418 0.997572i \(-0.522186\pi\)
0.829102 + 0.559098i \(0.188852\pi\)
\(224\) 0 0
\(225\) 1948.14 555.593i 0.577226 0.164620i
\(226\) 0 0
\(227\) 390.119 + 675.705i 0.114066 + 0.197569i 0.917406 0.397952i \(-0.130279\pi\)
−0.803340 + 0.595521i \(0.796946\pi\)
\(228\) 0 0
\(229\) −2843.34 1641.61i −0.820495 0.473713i 0.0300919 0.999547i \(-0.490420\pi\)
−0.850587 + 0.525834i \(0.823753\pi\)
\(230\) 0 0
\(231\) −798.822 + 195.426i −0.227527 + 0.0556628i
\(232\) 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 −0.977947 0.208852i \(-0.933027\pi\)
−0.308103 + 0.951353i \(0.599694\pi\)
\(242\) 0 0
\(243\) 3732.78 644.382i 0.985425 0.170112i
\(244\) 0 0
\(245\) 1609.03 + 1813.81i 0.419581 + 0.472980i
\(246\) 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 \(-0.539114\pi\)
−0.122572 + 0.992460i \(0.539114\pi\)
\(252\) 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 \(-0.634798\pi\)
0.994992 0.0999520i \(-0.0318689\pi\)
\(258\) 0 0
\(259\) 3237.95 + 4491.49i 0.776821 + 1.07756i
\(260\) 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 \(-0.576228\pi\)
−0.237194 + 0.971462i \(0.576228\pi\)
\(270\) 0 0
\(271\) 5006.83i 1.12230i 0.827714 + 0.561150i \(0.189641\pi\)
−0.827714 + 0.561150i \(0.810359\pi\)
\(272\) 0 0
\(273\) 3483.57 + 3639.37i 0.772291 + 0.806830i
\(274\) 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 0.855195 0.518307i \(-0.173437\pi\)
−0.0212695 + 0.999774i \(0.506771\pi\)
\(284\) 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 −0.601560 0.798828i \(-0.705454\pi\)
0.992585 + 0.121552i \(0.0387873\pi\)
\(294\) 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
\(301\) −397.043 + 882.971i −0.0760304 + 0.169082i
\(302\) 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 \(0.268431\pi\)
−0.665000 + 0.746843i \(0.731569\pi\)
\(308\) 0 0
\(309\) 3827.43 535.109i 0.704644 0.0985154i
\(310\) 0 0
\(311\) −2215.47 + 3837.30i −0.403947 + 0.699657i −0.994198 0.107563i \(-0.965695\pi\)
0.590251 + 0.807220i \(0.299029\pi\)
\(312\) 0 0
\(313\) −5126.22 + 2959.63i −0.925723 + 0.534467i −0.885456 0.464722i \(-0.846154\pi\)
−0.0402668 + 0.999189i \(0.512821\pi\)
\(314\) 0 0
\(315\) 509.912 3497.83i 0.0912073 0.625651i
\(316\) 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
\(329\) −2091.49 + 4651.21i −0.350480 + 0.779421i
\(330\) 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 −0.502357 0.864660i \(-0.667534\pi\)
0.497640 + 0.867384i \(0.334200\pi\)
\(350\) 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 \(-0.897165\pi\)
0.199191 0.979961i \(-0.436168\pi\)
\(354\) 0 0
\(355\) −1397.31 806.740i −0.208906 0.120612i
\(356\) 0 0
\(357\) −3598.95 1049.20i −0.533548 0.155545i
\(358\) 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 −0.961717 0.274044i \(-0.911639\pi\)
−0.243530 + 0.969893i \(0.578305\pi\)
\(368\) 0 0
\(369\) 8583.48 + 8312.82i 1.21094 + 1.17276i
\(370\) 0 0
\(371\) −2052.74 + 1479.84i −0.287259 + 0.207087i
\(372\) 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 \(-0.502896\pi\)
0.870539 0.492100i \(-0.163770\pi\)
\(384\) 0 0
\(385\) 907.537 654.251i 0.120136 0.0866070i
\(386\) 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 \(0.100419\pi\)
−0.950648 + 0.310270i \(0.899581\pi\)
\(398\) 0 0
\(399\) −1788.43 + 6134.64i −0.224395 + 0.769715i
\(400\) 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 0.525268 0.850937i \(-0.323965\pi\)
−0.474299 + 0.880364i \(0.657299\pi\)
\(410\) 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 \(0.445065\pi\)
−0.939024 + 0.343851i \(0.888268\pi\)
\(420\) 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
\(427\) 5104.51 + 2295.33i 0.578512 + 0.260138i
\(428\) 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 \(-0.897648\pi\)
0.948747 0.316036i \(-0.102352\pi\)
\(434\) 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 −0.992316 0.123726i \(-0.960516\pi\)
−0.389008 + 0.921234i \(0.627182\pi\)
\(440\) 0 0
\(441\) 7810.13 + 4976.75i 0.843335 + 0.537388i
\(442\) 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
\(455\) −6250.75 2810.75i −0.644043 0.289605i
\(456\) 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 \(0.0716146\pi\)
−0.294197 + 0.955745i \(0.595052\pi\)
\(462\) 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 \(-0.714424\pi\)
−0.623828 + 0.781561i \(0.714424\pi\)
\(468\) 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 0.712165 0.702012i \(-0.247715\pi\)
−0.964043 + 0.265747i \(0.914382\pi\)
\(480\) 0 0
\(481\) −13554.2 7825.52i −1.28486 0.741815i
\(482\) 0 0
\(483\) −13362.0 13959.6i −1.25878 1.31508i
\(484\) 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
\(497\) 3429.07 2472.05i 0.309487 0.223111i
\(498\) 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 \(-0.777293\pi\)
−0.765065 + 0.643953i \(0.777293\pi\)
\(504\) 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 \(-0.640389\pi\)
0.996594 0.0824613i \(-0.0262781\pi\)
\(510\) 0 0
\(511\) 18654.2 13448.0i 1.61490 1.16419i
\(512\) 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 \(-0.320374\pi\)
0.534835 + 0.844956i \(0.320374\pi\)
\(522\) 0 0
\(523\) 1352.20i 0.113055i 0.998401 + 0.0565274i \(0.0180028\pi\)
−0.998401 + 0.0565274i \(0.981997\pi\)
\(524\) 0 0
\(525\) −1715.83 7013.63i −0.142638 0.583047i
\(526\) 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
\(553\) 1529.61 3401.66i 0.117623 0.261579i
\(554\) 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 −0.995431 0.0954828i \(-0.969561\pi\)
0.580406 + 0.814327i \(0.302894\pi\)
\(564\) 0 0
\(565\) −12736.8 + 7353.60i −0.948392 + 0.547555i
\(566\) 0 0
\(567\) −1791.14 13381.9i −0.132664 0.991161i
\(568\) 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 \(-0.809926\pi\)
0.826950 0.562275i \(-0.190074\pi\)
\(578\) 0 0
\(579\) 1144.41 + 8185.52i 0.0821415 + 0.587528i
\(580\) 0 0
\(581\) −4913.48 + 10926.9i −0.350853 + 0.780250i
\(582\) 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 \(0.166310\pi\)
−0.00111897 + 0.999999i \(0.500356\pi\)
\(588\) 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 \(-0.165154\pi\)
0.868392 + 0.495878i \(0.165154\pi\)
\(594\) 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 −0.0530857 0.998590i \(-0.516906\pi\)
0.838261 + 0.545269i \(0.183572\pi\)
\(602\) 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 0.145402 0.989373i \(-0.453552\pi\)
−0.784121 + 0.620608i \(0.786886\pi\)
\(608\) 0 0
\(609\) −5716.66 + 1398.54i −0.380379 + 0.0930569i
\(610\) 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 −0.327697 0.944783i \(-0.606273\pi\)
0.654357 + 0.756186i \(0.272939\pi\)
\(620\) 0 0
\(621\) −3005.08 + 28010.9i −0.194186 + 1.81005i
\(622\) 0 0
\(623\) 8946.42 + 12409.9i 0.575330 + 0.798063i
\(624\) 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
\(637\) 13432.5 11916.0i 0.835503 0.741176i
\(638\) 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 0.874836 0.484419i \(-0.160969\pi\)
0.0178986 + 0.999840i \(0.494302\pi\)
\(644\) 0 0
\(645\) −1513.91 + 1181.04i −0.0924186 + 0.0720985i
\(646\) 0 0
\(647\) 14607.3 0.887595 0.443798 0.896127i \(-0.353631\pi\)
0.443798 + 0.896127i \(0.353631\pi\)
\(648\) 0 0
\(649\) 3269.01i 0.197720i
\(650\) 0 0
\(651\) −8943.99 9344.00i −0.538468 0.562550i
\(652\) 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 −0.464247 0.885706i \(-0.653675\pi\)
−0.999167 + 0.0408035i \(0.987008\pi\)
\(662\) 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 \(-0.960249\pi\)
0.388236 0.921560i \(-0.373084\pi\)
\(678\) 0 0
\(679\) −332.936 149.710i −0.0188172 0.00846148i
\(680\) 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 −0.277014 0.960866i \(-0.589345\pi\)
0.693627 + 0.720334i \(0.256011\pi\)
\(692\) 0 0
\(693\) 2648.10 3353.79i 0.145156 0.183838i
\(694\) 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
\(707\) −12369.7 + 27508.6i −0.658005 + 1.46332i
\(708\) 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 \(-0.288743\pi\)
0.616023 + 0.787728i \(0.288743\pi\)
\(720\) 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 0.223150 0.974784i \(-0.428366\pi\)
0.955763 + 0.294139i \(0.0950327\pi\)
\(728\) 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 −0.470531 0.882383i \(-0.655938\pi\)
−0.999432 + 0.0337000i \(0.989271\pi\)
\(734\) 0 0
\(735\) −12389.3 2288.35i −0.621748 0.114840i
\(736\) 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
\(749\) −12567.1 + 9059.73i −0.613074 + 0.441970i
\(750\) 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 \(-0.605565\pi\)
0.981633 0.190779i \(-0.0611012\pi\)
\(762\) 0 0
\(763\) −16939.5 23497.5i −0.803737 1.11490i
\(764\) 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 0.723970 0.689832i \(-0.242315\pi\)
−0.235427 + 0.971892i \(0.575649\pi\)
\(770\) 0 0
\(771\) 3462.56 + 24766.4i 0.161740 + 1.15686i
\(772\) 0 0
\(773\) −20325.9 −0.945758 −0.472879 0.881127i \(-0.656785\pi\)
−0.472879 + 0.881127i \(0.656785\pi\)
\(774\) 0 0
\(775\) 10084.7i 0.467422i
\(776\) 0 0
\(777\) −27621.0 8052.37i −1.27529 0.371785i
\(778\) 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 0.919046 0.394151i \(-0.128961\pi\)
0.118178 + 0.992992i \(0.462295\pi\)
\(788\) 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