Properties

Label 252.4.x.a.41.14
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 41.14
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.316211 + 5.18652i) q^{3} +(5.49690 - 9.52092i) q^{5} +(6.85688 - 17.2042i) q^{7} +(-26.8000 + 3.28007i) q^{9} +O(q^{10})\) \(q+(0.316211 + 5.18652i) q^{3} +(5.49690 - 9.52092i) q^{5} +(6.85688 - 17.2042i) q^{7} +(-26.8000 + 3.28007i) q^{9} +(13.8268 - 7.98293i) q^{11} +(-77.4289 - 44.7036i) q^{13} +(51.1186 + 25.4992i) q^{15} -106.953 q^{17} -8.31634i q^{19} +(91.3980 + 30.1232i) q^{21} +(-123.893 - 71.5294i) q^{23} +(2.06812 + 3.58208i) q^{25} +(-25.4866 - 137.962i) q^{27} +(129.721 - 74.8943i) q^{29} +(-37.1952 - 21.4747i) q^{31} +(45.7759 + 69.1890i) q^{33} +(-126.108 - 159.853i) q^{35} +390.706 q^{37} +(207.372 - 415.722i) q^{39} +(172.486 - 298.755i) q^{41} +(28.5593 + 49.4661i) q^{43} +(-116.088 + 273.191i) q^{45} +(8.13282 + 14.0864i) q^{47} +(-248.966 - 235.934i) q^{49} +(-33.8198 - 554.714i) q^{51} +445.230i q^{53} -175.526i q^{55} +(43.1329 - 2.62972i) q^{57} +(193.350 - 334.892i) q^{59} +(-420.857 + 242.982i) q^{61} +(-127.334 + 483.563i) q^{63} +(-851.238 + 491.463i) q^{65} +(-251.821 + 436.167i) q^{67} +(331.813 - 665.190i) q^{69} -751.418i q^{71} +507.533i q^{73} +(-17.9246 + 11.8590i) q^{75} +(-42.5306 - 292.617i) q^{77} +(381.570 + 660.899i) q^{79} +(707.482 - 175.812i) q^{81} +(-607.241 - 1051.77i) q^{83} +(-587.911 + 1018.29i) q^{85} +(429.460 + 649.117i) q^{87} +425.727 q^{89} +(-1300.01 + 1025.57i) q^{91} +(99.6173 - 199.704i) q^{93} +(-79.1792 - 45.7141i) q^{95} +(494.582 - 285.547i) q^{97} +(-344.375 + 259.296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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
\(3\) 0.316211 + 5.18652i 0.0608549 + 0.998147i
\(4\) 0 0
\(5\) 5.49690 9.52092i 0.491658 0.851577i −0.508296 0.861182i \(-0.669724\pi\)
0.999954 + 0.00960594i \(0.00305771\pi\)
\(6\) 0 0
\(7\) 6.85688 17.2042i 0.370237 0.928937i
\(8\) 0 0
\(9\) −26.8000 + 3.28007i −0.992593 + 0.121484i
\(10\) 0 0
\(11\) 13.8268 7.98293i 0.378996 0.218813i −0.298386 0.954445i \(-0.596448\pi\)
0.677381 + 0.735632i \(0.263115\pi\)
\(12\) 0 0
\(13\) −77.4289 44.7036i −1.65192 0.953734i −0.976283 0.216496i \(-0.930537\pi\)
−0.675633 0.737238i \(-0.736130\pi\)
\(14\) 0 0
\(15\) 51.1186 + 25.4992i 0.879918 + 0.438924i
\(16\) 0 0
\(17\) −106.953 −1.52588 −0.762939 0.646471i \(-0.776244\pi\)
−0.762939 + 0.646471i \(0.776244\pi\)
\(18\) 0 0
\(19\) 8.31634i 0.100416i −0.998739 0.0502079i \(-0.984012\pi\)
0.998739 0.0502079i \(-0.0159884\pi\)
\(20\) 0 0
\(21\) 91.3980 + 30.1232i 0.949746 + 0.313020i
\(22\) 0 0
\(23\) −123.893 71.5294i −1.12319 0.648474i −0.180977 0.983487i \(-0.557926\pi\)
−0.942214 + 0.335013i \(0.891259\pi\)
\(24\) 0 0
\(25\) 2.06812 + 3.58208i 0.0165449 + 0.0286567i
\(26\) 0 0
\(27\) −25.4866 137.962i −0.181663 0.983361i
\(28\) 0 0
\(29\) 129.721 74.8943i 0.830639 0.479570i −0.0234322 0.999725i \(-0.507459\pi\)
0.854072 + 0.520156i \(0.174126\pi\)
\(30\) 0 0
\(31\) −37.1952 21.4747i −0.215499 0.124418i 0.388366 0.921505i \(-0.373040\pi\)
−0.603864 + 0.797087i \(0.706373\pi\)
\(32\) 0 0
\(33\) 45.7759 + 69.1890i 0.241471 + 0.364977i
\(34\) 0 0
\(35\) −126.108 159.853i −0.609031 0.772004i
\(36\) 0 0
\(37\) 390.706 1.73599 0.867997 0.496570i \(-0.165407\pi\)
0.867997 + 0.496570i \(0.165407\pi\)
\(38\) 0 0
\(39\) 207.372 415.722i 0.851440 1.70689i
\(40\) 0 0
\(41\) 172.486 298.755i 0.657021 1.13799i −0.324363 0.945933i \(-0.605150\pi\)
0.981383 0.192060i \(-0.0615169\pi\)
\(42\) 0 0
\(43\) 28.5593 + 49.4661i 0.101285 + 0.175430i 0.912214 0.409714i \(-0.134371\pi\)
−0.810929 + 0.585144i \(0.801038\pi\)
\(44\) 0 0
\(45\) −116.088 + 273.191i −0.384563 + 0.904998i
\(46\) 0 0
\(47\) 8.13282 + 14.0864i 0.0252403 + 0.0437174i 0.878370 0.477982i \(-0.158632\pi\)
−0.853129 + 0.521699i \(0.825298\pi\)
\(48\) 0 0
\(49\) −248.966 235.934i −0.725849 0.687854i
\(50\) 0 0
\(51\) −33.8198 554.714i −0.0928571 1.52305i
\(52\) 0 0
\(53\) 445.230i 1.15391i 0.816777 + 0.576954i \(0.195759\pi\)
−0.816777 + 0.576954i \(0.804241\pi\)
\(54\) 0 0
\(55\) 175.526i 0.430325i
\(56\) 0 0
\(57\) 43.1329 2.62972i 0.100230 0.00611079i
\(58\) 0 0
\(59\) 193.350 334.892i 0.426644 0.738969i −0.569928 0.821695i \(-0.693029\pi\)
0.996572 + 0.0827250i \(0.0263623\pi\)
\(60\) 0 0
\(61\) −420.857 + 242.982i −0.883365 + 0.510011i −0.871766 0.489922i \(-0.837025\pi\)
−0.0115982 + 0.999933i \(0.503692\pi\)
\(62\) 0 0
\(63\) −127.334 + 483.563i −0.254643 + 0.967035i
\(64\) 0 0
\(65\) −851.238 + 491.463i −1.62436 + 0.937822i
\(66\) 0 0
\(67\) −251.821 + 436.167i −0.459177 + 0.795318i −0.998918 0.0465137i \(-0.985189\pi\)
0.539741 + 0.841831i \(0.318522\pi\)
\(68\) 0 0
\(69\) 331.813 665.190i 0.578921 1.16057i
\(70\) 0 0
\(71\) 751.418i 1.25601i −0.778208 0.628007i \(-0.783871\pi\)
0.778208 0.628007i \(-0.216129\pi\)
\(72\) 0 0
\(73\) 507.533i 0.813729i 0.913489 + 0.406865i \(0.133378\pi\)
−0.913489 + 0.406865i \(0.866622\pi\)
\(74\) 0 0
\(75\) −17.9246 + 11.8590i −0.0275967 + 0.0182582i
\(76\) 0 0
\(77\) −42.5306 292.617i −0.0629456 0.433076i
\(78\) 0 0
\(79\) 381.570 + 660.899i 0.543418 + 0.941228i 0.998705 + 0.0508826i \(0.0162034\pi\)
−0.455287 + 0.890345i \(0.650463\pi\)
\(80\) 0 0
\(81\) 707.482 175.812i 0.970483 0.241169i
\(82\) 0 0
\(83\) −607.241 1051.77i −0.803052 1.39093i −0.917598 0.397509i \(-0.869875\pi\)
0.114546 0.993418i \(-0.463459\pi\)
\(84\) 0 0
\(85\) −587.911 + 1018.29i −0.750210 + 1.29940i
\(86\) 0 0
\(87\) 429.460 + 649.117i 0.529229 + 0.799916i
\(88\) 0 0
\(89\) 425.727 0.507045 0.253523 0.967329i \(-0.418411\pi\)
0.253523 + 0.967329i \(0.418411\pi\)
\(90\) 0 0
\(91\) −1300.01 + 1025.57i −1.49756 + 1.18142i
\(92\) 0 0
\(93\) 99.6173 199.704i 0.111073 0.222671i
\(94\) 0 0
\(95\) −79.1792 45.7141i −0.0855117 0.0493702i
\(96\) 0 0
\(97\) 494.582 285.547i 0.517703 0.298896i −0.218291 0.975884i \(-0.570048\pi\)
0.735994 + 0.676988i \(0.236715\pi\)
\(98\) 0 0
\(99\) −344.375 + 259.296i −0.349606 + 0.263234i
\(100\) 0 0
\(101\) 353.385 + 612.081i 0.348150 + 0.603013i 0.985921 0.167213i \(-0.0534768\pi\)
−0.637771 + 0.770226i \(0.720143\pi\)
\(102\) 0 0
\(103\) −217.607 125.635i −0.208169 0.120187i 0.392291 0.919841i \(-0.371683\pi\)
−0.600460 + 0.799655i \(0.705016\pi\)
\(104\) 0 0
\(105\) 789.207 704.608i 0.733511 0.654883i
\(106\) 0 0
\(107\) 739.962i 0.668549i −0.942476 0.334275i \(-0.891509\pi\)
0.942476 0.334275i \(-0.108491\pi\)
\(108\) 0 0
\(109\) 1497.38 1.31580 0.657902 0.753104i \(-0.271444\pi\)
0.657902 + 0.753104i \(0.271444\pi\)
\(110\) 0 0
\(111\) 123.546 + 2026.41i 0.105644 + 1.73278i
\(112\) 0 0
\(113\) −861.916 497.627i −0.717542 0.414273i 0.0963056 0.995352i \(-0.469297\pi\)
−0.813847 + 0.581079i \(0.802631\pi\)
\(114\) 0 0
\(115\) −1362.05 + 786.380i −1.10445 + 0.637655i
\(116\) 0 0
\(117\) 2221.73 + 944.085i 1.75554 + 0.745989i
\(118\) 0 0
\(119\) −733.365 + 1840.04i −0.564936 + 1.41744i
\(120\) 0 0
\(121\) −538.046 + 931.922i −0.404242 + 0.700167i
\(122\) 0 0
\(123\) 1604.04 + 800.135i 1.17587 + 0.586550i
\(124\) 0 0
\(125\) 1419.70 1.01585
\(126\) 0 0
\(127\) 2469.41 1.72539 0.862696 0.505724i \(-0.168774\pi\)
0.862696 + 0.505724i \(0.168774\pi\)
\(128\) 0 0
\(129\) −247.526 + 163.765i −0.168942 + 0.111773i
\(130\) 0 0
\(131\) 769.787 1333.31i 0.513409 0.889251i −0.486470 0.873697i \(-0.661716\pi\)
0.999879 0.0155535i \(-0.00495103\pi\)
\(132\) 0 0
\(133\) −143.076 57.0242i −0.0932800 0.0371776i
\(134\) 0 0
\(135\) −1453.62 515.706i −0.926723 0.328777i
\(136\) 0 0
\(137\) −1419.80 + 819.722i −0.885414 + 0.511194i −0.872440 0.488722i \(-0.837463\pi\)
−0.0129744 + 0.999916i \(0.504130\pi\)
\(138\) 0 0
\(139\) −899.533 519.345i −0.548902 0.316909i 0.199777 0.979841i \(-0.435978\pi\)
−0.748679 + 0.662933i \(0.769312\pi\)
\(140\) 0 0
\(141\) −70.4880 + 46.6353i −0.0421004 + 0.0278539i
\(142\) 0 0
\(143\) −1427.46 −0.834759
\(144\) 0 0
\(145\) 1646.75i 0.943137i
\(146\) 0 0
\(147\) 1144.95 1365.87i 0.642407 0.766363i
\(148\) 0 0
\(149\) −1523.17 879.401i −0.837468 0.483512i 0.0189346 0.999821i \(-0.493973\pi\)
−0.856403 + 0.516308i \(0.827306\pi\)
\(150\) 0 0
\(151\) 352.401 + 610.376i 0.189920 + 0.328952i 0.945223 0.326424i \(-0.105844\pi\)
−0.755303 + 0.655376i \(0.772510\pi\)
\(152\) 0 0
\(153\) 2866.34 350.814i 1.51458 0.185370i
\(154\) 0 0
\(155\) −408.917 + 236.088i −0.211903 + 0.122342i
\(156\) 0 0
\(157\) 579.051 + 334.315i 0.294352 + 0.169944i 0.639903 0.768456i \(-0.278975\pi\)
−0.345551 + 0.938400i \(0.612308\pi\)
\(158\) 0 0
\(159\) −2309.20 + 140.787i −1.15177 + 0.0702209i
\(160\) 0 0
\(161\) −2080.12 + 1641.00i −1.01824 + 0.803285i
\(162\) 0 0
\(163\) −3926.19 −1.88665 −0.943323 0.331877i \(-0.892318\pi\)
−0.943323 + 0.331877i \(0.892318\pi\)
\(164\) 0 0
\(165\) 910.368 55.5032i 0.429527 0.0261874i
\(166\) 0 0
\(167\) −966.800 + 1674.55i −0.447984 + 0.775930i −0.998255 0.0590557i \(-0.981191\pi\)
0.550271 + 0.834986i \(0.314524\pi\)
\(168\) 0 0
\(169\) 2898.32 + 5020.04i 1.31922 + 2.28495i
\(170\) 0 0
\(171\) 27.2782 + 222.878i 0.0121989 + 0.0996720i
\(172\) 0 0
\(173\) −850.018 1472.27i −0.373559 0.647023i 0.616551 0.787315i \(-0.288529\pi\)
−0.990110 + 0.140292i \(0.955196\pi\)
\(174\) 0 0
\(175\) 75.8075 11.0183i 0.0327458 0.00475945i
\(176\) 0 0
\(177\) 1798.06 + 896.917i 0.763563 + 0.380884i
\(178\) 0 0
\(179\) 1175.15i 0.490697i −0.969435 0.245349i \(-0.921098\pi\)
0.969435 0.245349i \(-0.0789024\pi\)
\(180\) 0 0
\(181\) 3506.89i 1.44014i 0.693902 + 0.720070i \(0.255890\pi\)
−0.693902 + 0.720070i \(0.744110\pi\)
\(182\) 0 0
\(183\) −1393.31 2105.95i −0.562823 0.850691i
\(184\) 0 0
\(185\) 2147.68 3719.88i 0.853515 1.47833i
\(186\) 0 0
\(187\) −1478.82 + 853.799i −0.578301 + 0.333882i
\(188\) 0 0
\(189\) −2548.27 507.511i −0.980739 0.195323i
\(190\) 0 0
\(191\) 1228.14 709.068i 0.465263 0.268620i −0.248992 0.968506i \(-0.580099\pi\)
0.714255 + 0.699886i \(0.246766\pi\)
\(192\) 0 0
\(193\) 746.819 1293.53i 0.278535 0.482436i −0.692486 0.721431i \(-0.743485\pi\)
0.971021 + 0.238995i \(0.0768179\pi\)
\(194\) 0 0
\(195\) −2818.15 4259.56i −1.03493 1.56427i
\(196\) 0 0
\(197\) 2384.42i 0.862351i −0.902268 0.431175i \(-0.858099\pi\)
0.902268 0.431175i \(-0.141901\pi\)
\(198\) 0 0
\(199\) 4960.24i 1.76695i −0.468482 0.883473i \(-0.655199\pi\)
0.468482 0.883473i \(-0.344801\pi\)
\(200\) 0 0
\(201\) −2341.82 1168.15i −0.821787 0.409927i
\(202\) 0 0
\(203\) −399.014 2745.28i −0.137957 0.949166i
\(204\) 0 0
\(205\) −1896.28 3284.46i −0.646059 1.11901i
\(206\) 0 0
\(207\) 3554.94 + 1510.61i 1.19365 + 0.507221i
\(208\) 0 0
\(209\) −66.3888 114.989i −0.0219723 0.0380571i
\(210\) 0 0
\(211\) 1973.64 3418.45i 0.643939 1.11534i −0.340606 0.940206i \(-0.610632\pi\)
0.984545 0.175129i \(-0.0560343\pi\)
\(212\) 0 0
\(213\) 3897.25 237.607i 1.25369 0.0764345i
\(214\) 0 0
\(215\) 627.950 0.199190
\(216\) 0 0
\(217\) −624.497 + 492.663i −0.195362 + 0.154121i
\(218\) 0 0
\(219\) −2632.33 + 160.488i −0.812221 + 0.0495194i
\(220\) 0 0
\(221\) 8281.26 + 4781.19i 2.52062 + 1.45528i
\(222\) 0 0
\(223\) −1397.46 + 806.825i −0.419646 + 0.242283i −0.694926 0.719082i \(-0.744563\pi\)
0.275280 + 0.961364i \(0.411229\pi\)
\(224\) 0 0
\(225\) −67.1750 89.2163i −0.0199037 0.0264345i
\(226\) 0 0
\(227\) 1749.96 + 3031.01i 0.511668 + 0.886235i 0.999909 + 0.0135262i \(0.00430565\pi\)
−0.488240 + 0.872709i \(0.662361\pi\)
\(228\) 0 0
\(229\) −1654.24 955.078i −0.477360 0.275604i 0.241956 0.970287i \(-0.422211\pi\)
−0.719316 + 0.694683i \(0.755544\pi\)
\(230\) 0 0
\(231\) 1504.22 313.115i 0.428443 0.0891837i
\(232\) 0 0
\(233\) 4408.26i 1.23946i −0.784814 0.619731i \(-0.787242\pi\)
0.784814 0.619731i \(-0.212758\pi\)
\(234\) 0 0
\(235\) 178.821 0.0496383
\(236\) 0 0
\(237\) −3307.11 + 2188.01i −0.906413 + 0.599689i
\(238\) 0 0
\(239\) 3715.64 + 2145.23i 1.00563 + 0.580599i 0.909908 0.414809i \(-0.136152\pi\)
0.0957187 + 0.995408i \(0.469485\pi\)
\(240\) 0 0
\(241\) −1413.43 + 816.047i −0.377790 + 0.218117i −0.676856 0.736115i \(-0.736658\pi\)
0.299066 + 0.954232i \(0.403325\pi\)
\(242\) 0 0
\(243\) 1135.57 + 3613.78i 0.299780 + 0.954008i
\(244\) 0 0
\(245\) −3614.85 + 1073.48i −0.942630 + 0.279927i
\(246\) 0 0
\(247\) −371.770 + 643.925i −0.0957700 + 0.165878i
\(248\) 0 0
\(249\) 5263.02 3482.05i 1.33948 0.886209i
\(250\) 0 0
\(251\) −3912.60 −0.983908 −0.491954 0.870621i \(-0.663717\pi\)
−0.491954 + 0.870621i \(0.663717\pi\)
\(252\) 0 0
\(253\) −2284.06 −0.567579
\(254\) 0 0
\(255\) −5467.29 2727.22i −1.34265 0.669745i
\(256\) 0 0
\(257\) 1054.61 1826.64i 0.255971 0.443356i −0.709187 0.705020i \(-0.750938\pi\)
0.965159 + 0.261664i \(0.0842714\pi\)
\(258\) 0 0
\(259\) 2679.03 6721.78i 0.642729 1.61263i
\(260\) 0 0
\(261\) −3230.86 + 2432.66i −0.766227 + 0.576927i
\(262\) 0 0
\(263\) 3827.74 2209.95i 0.897448 0.518142i 0.0210765 0.999778i \(-0.493291\pi\)
0.876371 + 0.481636i \(0.159957\pi\)
\(264\) 0 0
\(265\) 4239.00 + 2447.39i 0.982641 + 0.567328i
\(266\) 0 0
\(267\) 134.620 + 2208.04i 0.0308562 + 0.506105i
\(268\) 0 0
\(269\) −4557.94 −1.03309 −0.516547 0.856259i \(-0.672783\pi\)
−0.516547 + 0.856259i \(0.672783\pi\)
\(270\) 0 0
\(271\) 128.189i 0.0287341i 0.999897 + 0.0143671i \(0.00457334\pi\)
−0.999897 + 0.0143671i \(0.995427\pi\)
\(272\) 0 0
\(273\) −5730.23 6418.23i −1.27036 1.42289i
\(274\) 0 0
\(275\) 57.1910 + 33.0193i 0.0125409 + 0.00724050i
\(276\) 0 0
\(277\) 1020.01 + 1766.71i 0.221251 + 0.383218i 0.955188 0.296000i \(-0.0956527\pi\)
−0.733937 + 0.679217i \(0.762319\pi\)
\(278\) 0 0
\(279\) 1067.27 + 453.518i 0.229017 + 0.0973170i
\(280\) 0 0
\(281\) 1506.57 869.820i 0.319838 0.184659i −0.331482 0.943462i \(-0.607549\pi\)
0.651321 + 0.758803i \(0.274215\pi\)
\(282\) 0 0
\(283\) 1080.52 + 623.836i 0.226961 + 0.131036i 0.609169 0.793040i \(-0.291503\pi\)
−0.382208 + 0.924076i \(0.624836\pi\)
\(284\) 0 0
\(285\) 212.060 425.120i 0.0440749 0.0883576i
\(286\) 0 0
\(287\) −3957.11 5016.01i −0.813871 1.03166i
\(288\) 0 0
\(289\) 6525.95 1.32830
\(290\) 0 0
\(291\) 1637.39 + 2474.87i 0.329847 + 0.498554i
\(292\) 0 0
\(293\) −2395.59 + 4149.28i −0.477651 + 0.827316i −0.999672 0.0256168i \(-0.991845\pi\)
0.522021 + 0.852933i \(0.325178\pi\)
\(294\) 0 0
\(295\) −2125.65 3681.74i −0.419526 0.726640i
\(296\) 0 0
\(297\) −1453.74 1704.12i −0.284022 0.332939i
\(298\) 0 0
\(299\) 6395.24 + 11076.9i 1.23694 + 2.14245i
\(300\) 0 0
\(301\) 1046.85 152.155i 0.200463 0.0291364i
\(302\) 0 0
\(303\) −3062.83 + 2026.39i −0.580709 + 0.384201i
\(304\) 0 0
\(305\) 5342.59i 1.00300i
\(306\) 0 0
\(307\) 4679.41i 0.869929i −0.900448 0.434965i \(-0.856761\pi\)
0.900448 0.434965i \(-0.143239\pi\)
\(308\) 0 0
\(309\) 582.801 1168.35i 0.107296 0.215097i
\(310\) 0 0
\(311\) 919.164 1592.04i 0.167592 0.290277i −0.769981 0.638067i \(-0.779734\pi\)
0.937573 + 0.347790i \(0.113068\pi\)
\(312\) 0 0
\(313\) 5160.13 2979.20i 0.931846 0.538001i 0.0444510 0.999012i \(-0.485846\pi\)
0.887395 + 0.461010i \(0.152513\pi\)
\(314\) 0 0
\(315\) 3904.02 + 3870.43i 0.698307 + 0.692299i
\(316\) 0 0
\(317\) −8986.17 + 5188.17i −1.59216 + 0.919232i −0.599220 + 0.800584i \(0.704523\pi\)
−0.992936 + 0.118648i \(0.962144\pi\)
\(318\) 0 0
\(319\) 1195.75 2071.10i 0.209872 0.363510i
\(320\) 0 0
\(321\) 3837.83 233.984i 0.667310 0.0406845i
\(322\) 0 0
\(323\) 889.458i 0.153222i
\(324\) 0 0
\(325\) 369.809i 0.0631179i
\(326\) 0 0
\(327\) 473.487 + 7766.17i 0.0800731 + 1.31337i
\(328\) 0 0
\(329\) 298.111 43.3291i 0.0499557 0.00726083i
\(330\) 0 0
\(331\) −2421.65 4194.42i −0.402132 0.696514i 0.591851 0.806048i \(-0.298398\pi\)
−0.993983 + 0.109534i \(0.965064\pi\)
\(332\) 0 0
\(333\) −10470.9 + 1281.55i −1.72314 + 0.210896i
\(334\) 0 0
\(335\) 2768.47 + 4795.13i 0.451516 + 0.782048i
\(336\) 0 0
\(337\) −559.013 + 968.240i −0.0903602 + 0.156509i −0.907663 0.419700i \(-0.862135\pi\)
0.817302 + 0.576209i \(0.195469\pi\)
\(338\) 0 0
\(339\) 2308.41 4627.70i 0.369839 0.741422i
\(340\) 0 0
\(341\) −685.723 −0.108897
\(342\) 0 0
\(343\) −5766.18 + 2665.49i −0.907709 + 0.419600i
\(344\) 0 0
\(345\) −4509.27 6815.64i −0.703685 1.06360i
\(346\) 0 0
\(347\) 3834.85 + 2214.05i 0.593273 + 0.342526i 0.766391 0.642375i \(-0.222051\pi\)
−0.173118 + 0.984901i \(0.555384\pi\)
\(348\) 0 0
\(349\) 1980.13 1143.23i 0.303707 0.175345i −0.340400 0.940281i \(-0.610562\pi\)
0.644107 + 0.764935i \(0.277229\pi\)
\(350\) 0 0
\(351\) −4193.98 + 11821.6i −0.637773 + 1.79769i
\(352\) 0 0
\(353\) 4027.88 + 6976.50i 0.607316 + 1.05190i 0.991681 + 0.128721i \(0.0410873\pi\)
−0.384364 + 0.923181i \(0.625579\pi\)
\(354\) 0 0
\(355\) −7154.19 4130.47i −1.06959 0.617529i
\(356\) 0 0
\(357\) −9775.29 3221.77i −1.44920 0.477631i
\(358\) 0 0
\(359\) 5537.25i 0.814053i 0.913416 + 0.407027i \(0.133434\pi\)
−0.913416 + 0.407027i \(0.866566\pi\)
\(360\) 0 0
\(361\) 6789.84 0.989917
\(362\) 0 0
\(363\) −5003.57 2495.90i −0.723469 0.360884i
\(364\) 0 0
\(365\) 4832.18 + 2789.86i 0.692953 + 0.400076i
\(366\) 0 0
\(367\) 4668.87 2695.58i 0.664069 0.383400i −0.129757 0.991546i \(-0.541420\pi\)
0.793825 + 0.608146i \(0.208086\pi\)
\(368\) 0 0
\(369\) −3642.70 + 8572.41i −0.513906 + 1.20938i
\(370\) 0 0
\(371\) 7659.81 + 3052.89i 1.07191 + 0.427219i
\(372\) 0 0
\(373\) 1062.08 1839.58i 0.147433 0.255362i −0.782845 0.622217i \(-0.786232\pi\)
0.930278 + 0.366855i \(0.119566\pi\)
\(374\) 0 0
\(375\) 448.925 + 7363.30i 0.0618196 + 1.01397i
\(376\) 0 0
\(377\) −13392.2 −1.82953
\(378\) 0 0
\(379\) −5358.80 −0.726288 −0.363144 0.931733i \(-0.618297\pi\)
−0.363144 + 0.931733i \(0.618297\pi\)
\(380\) 0 0
\(381\) 780.855 + 12807.6i 0.104998 + 1.72219i
\(382\) 0 0
\(383\) 2729.23 4727.16i 0.364118 0.630670i −0.624517 0.781012i \(-0.714704\pi\)
0.988634 + 0.150341i \(0.0480373\pi\)
\(384\) 0 0
\(385\) −3019.77 1203.56i −0.399745 0.159322i
\(386\) 0 0
\(387\) −927.641 1232.02i −0.121847 0.161827i
\(388\) 0 0
\(389\) 1416.25 817.670i 0.184593 0.106575i −0.404856 0.914380i \(-0.632678\pi\)
0.589449 + 0.807806i \(0.299345\pi\)
\(390\) 0 0
\(391\) 13250.7 + 7650.29i 1.71385 + 0.989493i
\(392\) 0 0
\(393\) 7158.66 + 3570.91i 0.918846 + 0.458342i
\(394\) 0 0
\(395\) 8389.82 1.06870
\(396\) 0 0
\(397\) 7694.41i 0.972724i 0.873757 + 0.486362i \(0.161676\pi\)
−0.873757 + 0.486362i \(0.838324\pi\)
\(398\) 0 0
\(399\) 250.515 760.097i 0.0314322 0.0953695i
\(400\) 0 0
\(401\) 4800.46 + 2771.55i 0.597815 + 0.345148i 0.768181 0.640232i \(-0.221162\pi\)
−0.170367 + 0.985381i \(0.554495\pi\)
\(402\) 0 0
\(403\) 1919.99 + 3325.52i 0.237324 + 0.411057i
\(404\) 0 0
\(405\) 2215.07 7702.30i 0.271772 0.945013i
\(406\) 0 0
\(407\) 5402.24 3118.98i 0.657934 0.379858i
\(408\) 0 0
\(409\) 6361.70 + 3672.93i 0.769109 + 0.444045i 0.832557 0.553940i \(-0.186876\pi\)
−0.0634474 + 0.997985i \(0.520210\pi\)
\(410\) 0 0
\(411\) −4700.46 7104.62i −0.564128 0.852664i
\(412\) 0 0
\(413\) −4435.75 5622.74i −0.528497 0.669920i
\(414\) 0 0
\(415\) −13351.8 −1.57931
\(416\) 0 0
\(417\) 2409.15 4829.67i 0.282918 0.567170i
\(418\) 0 0
\(419\) 1717.45 2974.72i 0.200246 0.346836i −0.748362 0.663291i \(-0.769159\pi\)
0.948608 + 0.316455i \(0.102492\pi\)
\(420\) 0 0
\(421\) −7241.13 12542.0i −0.838269 1.45192i −0.891341 0.453334i \(-0.850235\pi\)
0.0530719 0.998591i \(-0.483099\pi\)
\(422\) 0 0
\(423\) −264.164 350.841i −0.0303643 0.0403274i
\(424\) 0 0
\(425\) −221.191 383.115i −0.0252455 0.0437266i
\(426\) 0 0
\(427\) 1294.53 + 8906.59i 0.146714 + 1.00942i
\(428\) 0 0
\(429\) −451.380 7403.57i −0.0507991 0.833212i
\(430\) 0 0
\(431\) 13632.5i 1.52356i −0.647839 0.761778i \(-0.724327\pi\)
0.647839 0.761778i \(-0.275673\pi\)
\(432\) 0 0
\(433\) 6735.48i 0.747544i 0.927521 + 0.373772i \(0.121936\pi\)
−0.927521 + 0.373772i \(0.878064\pi\)
\(434\) 0 0
\(435\) 8540.89 520.720i 0.941389 0.0573945i
\(436\) 0 0
\(437\) −594.863 + 1030.33i −0.0651170 + 0.112786i
\(438\) 0 0
\(439\) 9181.17 5300.75i 0.998162 0.576289i 0.0904581 0.995900i \(-0.471167\pi\)
0.907704 + 0.419611i \(0.137834\pi\)
\(440\) 0 0
\(441\) 7446.18 + 5506.40i 0.804037 + 0.594580i
\(442\) 0 0
\(443\) −3111.86 + 1796.64i −0.333745 + 0.192688i −0.657503 0.753452i \(-0.728387\pi\)
0.323757 + 0.946140i \(0.395054\pi\)
\(444\) 0 0
\(445\) 2340.18 4053.31i 0.249293 0.431788i
\(446\) 0 0
\(447\) 4079.39 8178.02i 0.431652 0.865340i
\(448\) 0 0
\(449\) 8675.98i 0.911904i 0.890004 + 0.455952i \(0.150701\pi\)
−0.890004 + 0.455952i \(0.849299\pi\)
\(450\) 0 0
\(451\) 5507.79i 0.575059i
\(452\) 0 0
\(453\) −3054.29 + 2020.74i −0.316784 + 0.209587i
\(454\) 0 0
\(455\) 2618.36 + 18014.7i 0.269782 + 1.85614i
\(456\) 0 0
\(457\) −1466.35 2539.79i −0.150094 0.259970i 0.781168 0.624321i \(-0.214624\pi\)
−0.931262 + 0.364351i \(0.881291\pi\)
\(458\) 0 0
\(459\) 2725.87 + 14755.4i 0.277196 + 1.50049i
\(460\) 0 0
\(461\) 3015.81 + 5223.53i 0.304686 + 0.527731i 0.977191 0.212361i \(-0.0681152\pi\)
−0.672506 + 0.740092i \(0.734782\pi\)
\(462\) 0 0
\(463\) 295.638 512.060i 0.0296748 0.0513983i −0.850807 0.525479i \(-0.823886\pi\)
0.880481 + 0.474081i \(0.157219\pi\)
\(464\) 0 0
\(465\) −1353.78 2046.20i −0.135011 0.204065i
\(466\) 0 0
\(467\) 16674.6 1.65227 0.826134 0.563473i \(-0.190535\pi\)
0.826134 + 0.563473i \(0.190535\pi\)
\(468\) 0 0
\(469\) 5777.18 + 7323.12i 0.568796 + 0.721002i
\(470\) 0 0
\(471\) −1550.83 + 3108.98i −0.151717 + 0.304149i
\(472\) 0 0
\(473\) 789.769 + 455.973i 0.0767730 + 0.0443249i
\(474\) 0 0
\(475\) 29.7898 17.1992i 0.00287758 0.00166137i
\(476\) 0 0
\(477\) −1460.39 11932.2i −0.140181 1.14536i
\(478\) 0 0
\(479\) −8608.73 14910.8i −0.821175 1.42232i −0.904808 0.425820i \(-0.859986\pi\)
0.0836331 0.996497i \(-0.473348\pi\)
\(480\) 0 0
\(481\) −30252.0 17466.0i −2.86772 1.65568i
\(482\) 0 0
\(483\) −9168.83 10269.7i −0.863761 0.967468i
\(484\) 0 0
\(485\) 6278.50i 0.587818i
\(486\) 0 0
\(487\) 8745.94 0.813792 0.406896 0.913475i \(-0.366611\pi\)
0.406896 + 0.913475i \(0.366611\pi\)
\(488\) 0 0
\(489\) −1241.51 20363.3i −0.114812 1.88315i
\(490\) 0 0
\(491\) 653.319 + 377.194i 0.0600486 + 0.0346691i 0.529724 0.848170i \(-0.322296\pi\)
−0.469675 + 0.882839i \(0.655629\pi\)
\(492\) 0 0
\(493\) −13874.0 + 8010.17i −1.26745 + 0.731765i
\(494\) 0 0
\(495\) 575.737 + 4704.09i 0.0522777 + 0.427138i
\(496\) 0 0
\(497\) −12927.5 5152.39i −1.16676 0.465022i
\(498\) 0 0
\(499\) −2480.24 + 4295.90i −0.222506 + 0.385392i −0.955568 0.294769i \(-0.904757\pi\)
0.733062 + 0.680162i \(0.238090\pi\)
\(500\) 0 0
\(501\) −8990.79 4484.82i −0.801754 0.399934i
\(502\) 0 0
\(503\) −5299.83 −0.469797 −0.234898 0.972020i \(-0.575476\pi\)
−0.234898 + 0.972020i \(0.575476\pi\)
\(504\) 0 0
\(505\) 7770.09 0.684682
\(506\) 0 0
\(507\) −25120.1 + 16619.6i −2.20044 + 1.45582i
\(508\) 0 0
\(509\) 9344.81 16185.7i 0.813755 1.40947i −0.0964627 0.995337i \(-0.530753\pi\)
0.910218 0.414129i \(-0.135914\pi\)
\(510\) 0 0
\(511\) 8731.68 + 3480.09i 0.755903 + 0.301273i
\(512\) 0 0
\(513\) −1147.34 + 211.956i −0.0987449 + 0.0182418i
\(514\) 0 0
\(515\) −2392.33 + 1381.21i −0.204696 + 0.118181i
\(516\) 0 0
\(517\) 224.902 + 129.847i 0.0191319 + 0.0110458i
\(518\) 0 0
\(519\) 7367.20 4874.19i 0.623091 0.412241i
\(520\) 0 0
\(521\) −8964.93 −0.753859 −0.376930 0.926242i \(-0.623020\pi\)
−0.376930 + 0.926242i \(0.623020\pi\)
\(522\) 0 0
\(523\) 20614.1i 1.72350i −0.507330 0.861752i \(-0.669367\pi\)
0.507330 0.861752i \(-0.330633\pi\)
\(524\) 0 0
\(525\) 81.1178 + 389.693i 0.00674337 + 0.0323955i
\(526\) 0 0
\(527\) 3978.14 + 2296.78i 0.328825 + 0.189847i
\(528\) 0 0
\(529\) 4149.41 + 7186.99i 0.341038 + 0.590695i
\(530\) 0 0
\(531\) −4083.31 + 9609.31i −0.333711 + 0.785327i
\(532\) 0 0
\(533\) −26710.9 + 15421.5i −2.17069 + 1.25325i
\(534\) 0 0
\(535\) −7045.11 4067.50i −0.569321 0.328698i
\(536\) 0 0
\(537\) 6094.94 371.595i 0.489788 0.0298613i
\(538\) 0 0
\(539\) −5325.86 1274.74i −0.425605 0.101868i
\(540\) 0 0
\(541\) 9376.65 0.745164 0.372582 0.927999i \(-0.378473\pi\)
0.372582 + 0.927999i \(0.378473\pi\)
\(542\) 0 0
\(543\) −18188.6 + 1108.92i −1.43747 + 0.0876395i
\(544\) 0 0
\(545\) 8230.93 14256.4i 0.646925 1.12051i
\(546\) 0 0
\(547\) 1172.25 + 2030.40i 0.0916305 + 0.158709i 0.908197 0.418542i \(-0.137459\pi\)
−0.816567 + 0.577251i \(0.804125\pi\)
\(548\) 0 0
\(549\) 10482.0 7892.36i 0.814864 0.613548i
\(550\) 0 0
\(551\) −622.847 1078.80i −0.0481564 0.0834093i
\(552\) 0 0
\(553\) 13986.6 2032.89i 1.07553 0.156324i
\(554\) 0 0
\(555\) 19972.4 + 9962.70i 1.52753 + 0.761969i
\(556\) 0 0
\(557\) 15368.4i 1.16908i −0.811364 0.584541i \(-0.801275\pi\)
0.811364 0.584541i \(-0.198725\pi\)
\(558\) 0 0
\(559\) 5106.81i 0.386395i
\(560\) 0 0
\(561\) −4895.87 7399.97i −0.368456 0.556911i
\(562\) 0 0
\(563\) −6447.73 + 11167.8i −0.482664 + 0.835998i −0.999802 0.0199041i \(-0.993664\pi\)
0.517138 + 0.855902i \(0.326997\pi\)
\(564\) 0 0
\(565\) −9475.73 + 5470.82i −0.705570 + 0.407361i
\(566\) 0 0
\(567\) 1826.42 13377.2i 0.135278 0.990808i
\(568\) 0 0
\(569\) 20989.2 12118.1i 1.54642 0.892824i 0.548005 0.836475i \(-0.315387\pi\)
0.998411 0.0563492i \(-0.0179460\pi\)
\(570\) 0 0
\(571\) −3678.38 + 6371.14i −0.269589 + 0.466942i −0.968756 0.248017i \(-0.920221\pi\)
0.699167 + 0.714959i \(0.253555\pi\)
\(572\) 0 0
\(573\) 4065.95 + 6145.57i 0.296435 + 0.448054i
\(574\) 0 0
\(575\) 591.724i 0.0429158i
\(576\) 0 0
\(577\) 11928.2i 0.860617i −0.902682 0.430308i \(-0.858405\pi\)
0.902682 0.430308i \(-0.141595\pi\)
\(578\) 0 0
\(579\) 6945.07 + 3464.37i 0.498493 + 0.248660i
\(580\) 0 0
\(581\) −22258.6 + 3235.19i −1.58940 + 0.231013i
\(582\) 0 0
\(583\) 3554.24 + 6156.13i 0.252490 + 0.437326i
\(584\) 0 0
\(585\) 21201.2 15963.3i 1.49839 1.12821i
\(586\) 0 0
\(587\) −2638.36 4569.77i −0.185514 0.321320i 0.758236 0.651981i \(-0.226062\pi\)
−0.943750 + 0.330661i \(0.892728\pi\)
\(588\) 0 0
\(589\) −178.591 + 309.328i −0.0124935 + 0.0216395i
\(590\) 0 0
\(591\) 12366.9 753.981i 0.860752 0.0524782i
\(592\) 0 0
\(593\) 5290.53 0.366367 0.183184 0.983079i \(-0.441360\pi\)
0.183184 + 0.983079i \(0.441360\pi\)
\(594\) 0 0
\(595\) 13487.6 + 17096.8i 0.929308 + 1.17798i
\(596\) 0 0
\(597\) 25726.4 1568.48i 1.76367 0.107527i
\(598\) 0 0
\(599\) −8568.78 4947.19i −0.584492 0.337457i 0.178424 0.983954i \(-0.442900\pi\)
−0.762917 + 0.646497i \(0.776233\pi\)
\(600\) 0 0
\(601\) 2305.57 1331.12i 0.156483 0.0903454i −0.419714 0.907656i \(-0.637870\pi\)
0.576197 + 0.817311i \(0.304536\pi\)
\(602\) 0 0
\(603\) 5318.15 12515.3i 0.359157 0.845210i
\(604\) 0 0
\(605\) 5915.17 + 10245.4i 0.397497 + 0.688485i
\(606\) 0 0
\(607\) −9797.65 5656.68i −0.655147 0.378249i 0.135278 0.990808i \(-0.456807\pi\)
−0.790425 + 0.612558i \(0.790141\pi\)
\(608\) 0 0
\(609\) 14112.3 2937.58i 0.939012 0.195463i
\(610\) 0 0
\(611\) 1454.26i 0.0962901i
\(612\) 0 0
\(613\) −23984.5 −1.58030 −0.790151 0.612912i \(-0.789998\pi\)
−0.790151 + 0.612912i \(0.789998\pi\)
\(614\) 0 0
\(615\) 16435.3 10873.7i 1.07762 0.712958i
\(616\) 0 0
\(617\) −14063.1 8119.31i −0.917597 0.529775i −0.0347291 0.999397i \(-0.511057\pi\)
−0.882868 + 0.469622i \(0.844390\pi\)
\(618\) 0 0
\(619\) −14971.6 + 8643.88i −0.972150 + 0.561271i −0.899891 0.436115i \(-0.856354\pi\)
−0.0722590 + 0.997386i \(0.523021\pi\)
\(620\) 0 0
\(621\) −6710.71 + 18915.5i −0.433642 + 1.22231i
\(622\) 0 0
\(623\) 2919.16 7324.28i 0.187727 0.471013i
\(624\) 0 0
\(625\) 7545.43 13069.1i 0.482908 0.836421i
\(626\) 0 0
\(627\) 575.399 380.688i 0.0366495 0.0242475i
\(628\) 0 0
\(629\) −41787.2 −2.64891
\(630\) 0 0
\(631\) 348.827 0.0220073 0.0110036 0.999939i \(-0.496497\pi\)
0.0110036 + 0.999939i \(0.496497\pi\)
\(632\) 0 0
\(633\) 18354.0 + 9155.39i 1.15246 + 0.574872i
\(634\) 0 0
\(635\) 13574.1 23511.0i 0.848302 1.46930i
\(636\) 0 0
\(637\) 8730.10 + 29397.8i 0.543013 + 1.82854i
\(638\) 0 0
\(639\) 2464.71 + 20138.0i 0.152586 + 1.24671i
\(640\) 0 0
\(641\) −14508.8 + 8376.64i −0.894013 + 0.516158i −0.875253 0.483666i \(-0.839305\pi\)
−0.0187597 + 0.999824i \(0.505972\pi\)
\(642\) 0 0
\(643\) 10660.5 + 6154.87i 0.653827 + 0.377487i 0.789921 0.613209i \(-0.210122\pi\)
−0.136094 + 0.990696i \(0.543455\pi\)
\(644\) 0 0
\(645\) 198.565 + 3256.88i 0.0121217 + 0.198821i
\(646\) 0 0
\(647\) 32197.6 1.95644 0.978220 0.207570i \(-0.0665555\pi\)
0.978220 + 0.207570i \(0.0665555\pi\)
\(648\) 0 0
\(649\) 6174.00i 0.373422i
\(650\) 0 0
\(651\) −2752.68 3083.18i −0.165724 0.185621i
\(652\) 0 0
\(653\) −15436.6 8912.32i −0.925085 0.534098i −0.0398315 0.999206i \(-0.512682\pi\)
−0.885254 + 0.465108i \(0.846015\pi\)
\(654\) 0 0
\(655\) −8462.89 14658.2i −0.504843 0.874415i
\(656\) 0 0
\(657\) −1664.74 13601.9i −0.0988552 0.807702i
\(658\) 0 0
\(659\) 17782.9 10267.0i 1.05117 0.606895i 0.128196 0.991749i \(-0.459081\pi\)
0.922978 + 0.384853i \(0.125748\pi\)
\(660\) 0 0
\(661\) 8819.60 + 5092.00i 0.518975 + 0.299630i 0.736515 0.676421i \(-0.236470\pi\)
−0.217540 + 0.976051i \(0.569803\pi\)
\(662\) 0 0
\(663\) −22179.1 + 44462.8i −1.29919 + 2.60451i
\(664\) 0 0
\(665\) −1329.40 + 1048.75i −0.0775214 + 0.0611563i
\(666\) 0 0
\(667\) −21428.6 −1.24395
\(668\) 0 0
\(669\) −4626.51 6992.84i −0.267371 0.404124i
\(670\) 0 0
\(671\) −3879.42 + 6719.35i −0.223194 + 0.386584i
\(672\) 0 0
\(673\) 8773.58 + 15196.3i 0.502521 + 0.870392i 0.999996 + 0.00291344i \(0.000927377\pi\)
−0.497475 + 0.867478i \(0.665739\pi\)
\(674\) 0 0
\(675\) 441.481 376.616i 0.0251742 0.0214755i
\(676\) 0 0
\(677\) 4832.83 + 8370.70i 0.274358 + 0.475203i 0.969973 0.243212i \(-0.0782012\pi\)
−0.695615 + 0.718415i \(0.744868\pi\)
\(678\) 0 0
\(679\) −1521.31 10466.8i −0.0859829 0.591576i
\(680\) 0 0
\(681\) −15167.1 + 10034.6i −0.853455 + 0.564652i
\(682\) 0 0
\(683\) 4376.97i 0.245213i 0.992455 + 0.122606i \(0.0391253\pi\)
−0.992455 + 0.122606i \(0.960875\pi\)
\(684\) 0 0
\(685\) 18023.7i 1.00533i
\(686\) 0 0
\(687\) 4430.44 8881.77i 0.246043 0.493247i
\(688\) 0 0
\(689\) 19903.4 34473.7i 1.10052 1.90616i
\(690\) 0 0
\(691\) −17526.8 + 10119.1i −0.964905 + 0.557088i −0.897679 0.440649i \(-0.854748\pi\)
−0.0672260 + 0.997738i \(0.521415\pi\)
\(692\) 0 0
\(693\) 2099.63 + 7702.65i 0.115091 + 0.422221i
\(694\) 0 0
\(695\) −9889.29 + 5709.58i −0.539744 + 0.311621i
\(696\) 0 0
\(697\) −18447.9 + 31952.8i −1.00253 + 1.73644i
\(698\) 0 0
\(699\) 22863.5 1393.94i 1.23717 0.0754273i
\(700\) 0 0
\(701\) 33130.3i 1.78504i 0.451004 + 0.892522i \(0.351066\pi\)
−0.451004 + 0.892522i \(0.648934\pi\)
\(702\) 0 0
\(703\) 3249.25i 0.174321i
\(704\) 0 0
\(705\) 56.5453 + 927.460i 0.00302073 + 0.0495463i
\(706\) 0 0
\(707\) 12953.5 1882.73i 0.689059 0.100152i
\(708\) 0 0
\(709\) 17606.6 + 30495.5i 0.932623 + 1.61535i 0.778819 + 0.627249i \(0.215819\pi\)
0.153804 + 0.988101i \(0.450847\pi\)
\(710\) 0 0
\(711\) −12393.9 16460.5i −0.653737 0.868240i
\(712\) 0 0
\(713\) 3072.14 + 5321.10i 0.161364 + 0.279491i
\(714\) 0 0
\(715\) −7846.63 + 13590.8i −0.410416 + 0.710861i
\(716\) 0 0
\(717\) −9951.34 + 19949.6i −0.518326 + 1.03910i
\(718\) 0 0
\(719\) 21789.0 1.13017 0.565086 0.825032i \(-0.308843\pi\)
0.565086 + 0.825032i \(0.308843\pi\)
\(720\) 0 0
\(721\) −3653.55 + 2882.28i −0.188718 + 0.148879i
\(722\) 0 0
\(723\) −4679.39 7072.77i −0.240703 0.363816i
\(724\) 0 0
\(725\) 536.555 + 309.780i 0.0274857 + 0.0158689i
\(726\) 0 0
\(727\) 685.180 395.589i 0.0349545 0.0201810i −0.482421 0.875940i \(-0.660242\pi\)
0.517375 + 0.855759i \(0.326909\pi\)
\(728\) 0 0
\(729\) −18383.9 + 7032.36i −0.933997 + 0.357281i
\(730\) 0 0
\(731\) −3054.50 5290.55i −0.154548 0.267685i
\(732\) 0 0
\(733\) 195.132 + 112.659i 0.00983269 + 0.00567691i 0.504908 0.863173i \(-0.331526\pi\)
−0.495076 + 0.868850i \(0.664860\pi\)
\(734\) 0 0
\(735\) −6710.69 18409.1i −0.336772 0.923848i
\(736\) 0 0
\(737\) 8041.08i 0.401896i
\(738\) 0 0
\(739\) −2564.36 −0.127648 −0.0638238 0.997961i \(-0.520330\pi\)
−0.0638238 + 0.997961i \(0.520330\pi\)
\(740\) 0 0
\(741\) −3457.29 1724.58i −0.171399 0.0854980i
\(742\) 0 0
\(743\) −30419.9 17563.0i −1.50202 0.867190i −0.999997 0.00233421i \(-0.999257\pi\)
−0.502020 0.864856i \(-0.667410\pi\)
\(744\) 0 0
\(745\) −16745.4 + 9667.97i −0.823496 + 0.475446i
\(746\) 0 0
\(747\) 19724.0 + 26195.7i 0.966080 + 1.28307i
\(748\) 0 0
\(749\) −12730.4 5073.83i −0.621041 0.247522i
\(750\) 0 0
\(751\) −5213.77 + 9030.52i −0.253333 + 0.438786i −0.964441 0.264297i \(-0.914860\pi\)
0.711108 + 0.703083i \(0.248194\pi\)
\(752\) 0 0
\(753\) −1237.21 20292.8i −0.0598756 0.982084i
\(754\) 0 0
\(755\) 7748.45 0.373503
\(756\) 0 0
\(757\) −14031.2 −0.673677 −0.336838 0.941562i \(-0.609358\pi\)
−0.336838 + 0.941562i \(0.609358\pi\)
\(758\) 0 0
\(759\) −722.245 11846.3i −0.0345399 0.566527i
\(760\) 0 0
\(761\) 5435.63 9414.79i 0.258924 0.448470i −0.707030 0.707184i \(-0.749965\pi\)
0.965954 + 0.258714i \(0.0832986\pi\)
\(762\) 0 0
\(763\) 10267.3 25761.1i 0.487159 1.22230i
\(764\) 0 0
\(765\) 12415.9 29218.6i 0.586797 1.38092i
\(766\) 0 0
\(767\) −29941.7 + 17286.9i −1.40956 + 0.813811i
\(768\) 0 0
\(769\) 17962.0 + 10370.3i 0.842295 + 0.486299i 0.858044 0.513577i \(-0.171680\pi\)
−0.0157486 + 0.999876i \(0.505013\pi\)
\(770\) 0 0
\(771\) 9807.36 + 4892.15i 0.458111 + 0.228517i
\(772\) 0 0
\(773\) 7445.62 0.346443 0.173221 0.984883i \(-0.444582\pi\)
0.173221 + 0.984883i \(0.444582\pi\)
\(774\) 0 0
\(775\) 177.648i 0.00823396i
\(776\) 0 0
\(777\) 35709.8 + 11769.3i 1.64875 + 0.543401i
\(778\) 0 0
\(779\) −2484.55 1434.46i −0.114272 0.0659752i
\(780\) 0 0
\(781\) −5998.52 10389.7i −0.274832 0.476023i
\(782\) 0 0
\(783\) −13638.7 15987.7i −0.622487 0.729698i
\(784\) 0 0
\(785\) 6365.97 3675.40i 0.289441 0.167109i
\(786\) 0 0
\(787\) −14417.6 8323.99i −0.653025 0.377024i 0.136589 0.990628i \(-0.456386\pi\)
−0.789614 + 0.613603i \(0.789719\pi\)
\(788\) 0 0
\(789\) 12672.3 + 19153.9i 0.571796 + 0.864253i
\(790\) 0 0
\(791\) −14471.3 + 11416.4i −0.650494 + 0.513172i
\(792\) 0 0
\(793\) 43448.7 1.94566
\(794\) 0 0
\(795\) −11353.0 + 22759.6i −0.506478 + 1.01534i