Properties

Label 252.4.x.a.41.11
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 41.11
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.316211 - 5.18652i) q^{3} +(-5.49690 + 9.52092i) q^{5} +(-18.3277 - 2.66385i) q^{7} +(-26.8000 + 3.28007i) q^{9} +O(q^{10})\) \(q+(-0.316211 - 5.18652i) q^{3} +(-5.49690 + 9.52092i) q^{5} +(-18.3277 - 2.66385i) q^{7} +(-26.8000 + 3.28007i) q^{9} +(13.8268 - 7.98293i) q^{11} +(77.4289 + 44.7036i) q^{13} +(51.1186 + 25.4992i) q^{15} +106.953 q^{17} +8.31634i q^{19} +(-8.02068 + 95.8993i) q^{21} +(-123.893 - 71.5294i) q^{23} +(2.06812 + 3.58208i) q^{25} +(25.4866 + 137.962i) q^{27} +(129.721 - 74.8943i) q^{29} +(37.1952 + 21.4747i) q^{31} +(-45.7759 - 69.1890i) q^{33} +(126.108 - 159.853i) q^{35} +390.706 q^{37} +(207.372 - 415.722i) q^{39} +(-172.486 + 298.755i) q^{41} +(28.5593 + 49.4661i) q^{43} +(116.088 - 273.191i) q^{45} +(-8.13282 - 14.0864i) q^{47} +(328.808 + 97.6442i) q^{49} +(-33.8198 - 554.714i) q^{51} +445.230i q^{53} +175.526i q^{55} +(43.1329 - 2.62972i) q^{57} +(-193.350 + 334.892i) q^{59} +(420.857 - 242.982i) q^{61} +(499.920 + 11.2750i) q^{63} +(-851.238 + 491.463i) q^{65} +(-251.821 + 436.167i) q^{67} +(-331.813 + 665.190i) q^{69} -751.418i q^{71} -507.533i q^{73} +(17.9246 - 11.8590i) q^{75} +(-274.679 + 109.476i) q^{77} +(381.570 + 660.899i) q^{79} +(707.482 - 175.812i) q^{81} +(607.241 + 1051.77i) q^{83} +(-587.911 + 1018.29i) q^{85} +(-429.460 - 649.117i) q^{87} -425.727 q^{89} +(-1300.01 - 1025.57i) q^{91} +(99.6173 - 199.704i) q^{93} +(-79.1792 - 45.7141i) q^{95} +(-494.582 + 285.547i) q^{97} +(-344.375 + 259.296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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 −0.999954 0.00960594i \(-0.996942\pi\)
0.508296 + 0.861182i \(0.330276\pi\)
\(6\) 0 0
\(7\) −18.3277 2.66385i −0.989602 0.143834i
\(8\) 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 \(0.0694629\pi\)
0.675633 + 0.737238i \(0.263870\pi\)
\(14\) 0 0
\(15\) 51.1186 + 25.4992i 0.879918 + 0.438924i
\(16\) 0 0
\(17\) 106.953 1.52588 0.762939 0.646471i \(-0.223756\pi\)
0.762939 + 0.646471i \(0.223756\pi\)
\(18\) 0 0
\(19\) 8.31634i 0.100416i 0.998739 + 0.0502079i \(0.0159884\pi\)
−0.998739 + 0.0502079i \(0.984012\pi\)
\(20\) 0 0
\(21\) −8.02068 + 95.8993i −0.0833455 + 0.996521i
\(22\) 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 0.603864 0.797087i \(-0.293627\pi\)
−0.388366 + 0.921505i \(0.626960\pi\)
\(32\) 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 \(0.394850\pi\)
−0.981383 + 0.192060i \(0.938483\pi\)
\(42\) 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 0.853129 0.521699i \(-0.174702\pi\)
−0.878370 + 0.477982i \(0.841368\pi\)
\(48\) 0 0
\(49\) 328.808 + 97.6442i 0.958623 + 0.284677i
\(50\) 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 −0.996572 0.0827250i \(-0.973638\pi\)
0.569928 + 0.821695i \(0.306971\pi\)
\(60\) 0 0
\(61\) 420.857 242.982i 0.883365 0.510011i 0.0115982 0.999933i \(-0.496308\pi\)
0.871766 + 0.489922i \(0.162975\pi\)
\(62\) 0 0
\(63\) 499.920 + 11.2750i 0.999746 + 0.0225479i
\(64\) 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 \(-0.866622\pi\)
0.913489 0.406865i \(-0.133378\pi\)
\(74\) 0 0
\(75\) 17.9246 11.8590i 0.0275967 0.0182582i
\(76\) 0 0
\(77\) −274.679 + 109.476i −0.406528 + 0.162025i
\(78\) 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 \(0.130125\pi\)
−0.114546 + 0.993418i \(0.536541\pi\)
\(84\) 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 \(-0.581589\pi\)
−0.253523 + 0.967329i \(0.581589\pi\)
\(90\) 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 −0.735994 0.676988i \(-0.763285\pi\)
0.218291 + 0.975884i \(0.429952\pi\)
\(98\) 0 0
\(99\) −344.375 + 259.296i −0.349606 + 0.263234i
\(100\) 0 0
\(101\) −353.385 612.081i −0.348150 0.603013i 0.637771 0.770226i \(-0.279857\pi\)
−0.985921 + 0.167213i \(0.946523\pi\)
\(102\) 0 0
\(103\) 217.607 + 125.635i 0.208169 + 0.120187i 0.600460 0.799655i \(-0.294984\pi\)
−0.392291 + 0.919841i \(0.628317\pi\)
\(104\) 0 0
\(105\) −868.960 603.513i −0.807636 0.560922i
\(106\) 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
\(119\) −1960.20 284.906i −1.51001 0.219473i
\(120\) 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 \(0.338284\pi\)
−0.999879 + 0.0155535i \(0.995049\pi\)
\(132\) 0 0
\(133\) 22.1534 152.419i 0.0144432 0.0993716i
\(134\) 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 0.748679 0.662933i \(-0.230688\pi\)
−0.199777 + 0.979841i \(0.564022\pi\)
\(140\) 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
\(147\) 402.461 1736.25i 0.225813 0.974171i
\(148\) 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 0.345551 0.938400i \(-0.387692\pi\)
−0.639903 + 0.768456i \(0.721025\pi\)
\(158\) 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 −0.550271 0.834986i \(-0.685476\pi\)
0.998255 + 0.0590557i \(0.0188090\pi\)
\(168\) 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 0.990110 0.140292i \(-0.0448041\pi\)
−0.616551 + 0.787315i \(0.711471\pi\)
\(174\) 0 0
\(175\) −28.3617 71.1604i −0.0122511 0.0307384i
\(176\) 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 \(-0.744110\pi\)
0.693902 0.720070i \(-0.255890\pi\)
\(182\) 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
\(189\) −99.6023 2596.41i −0.0383333 0.999265i
\(190\) 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 \(0.344801\pi\)
−0.468482 + 0.883473i \(0.655199\pi\)
\(200\) 0 0
\(201\) 2341.82 + 1168.15i 0.821787 + 0.409927i
\(202\) 0 0
\(203\) −2576.99 + 1027.08i −0.890981 + 0.355109i
\(204\) 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 −0.275280 0.961364i \(-0.588771\pi\)
0.694926 + 0.719082i \(0.255437\pi\)
\(224\) 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 \(-0.995694\pi\)
0.488240 0.872709i \(-0.337639\pi\)
\(228\) 0 0
\(229\) 1654.24 + 955.078i 0.477360 + 0.275604i 0.719316 0.694683i \(-0.244456\pi\)
−0.241956 + 0.970287i \(0.577789\pi\)
\(230\) 0 0
\(231\) 654.657 + 1390.01i 0.186464 + 0.395914i
\(232\) 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 −0.299066 0.954232i \(-0.596675\pi\)
0.676856 + 0.736115i \(0.263342\pi\)
\(242\) 0 0
\(243\) −1135.57 3613.78i −0.299780 0.954008i
\(244\) 0 0
\(245\) −2737.09 + 2593.81i −0.713739 + 0.676378i
\(246\) 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 \(-0.336283\pi\)
0.491954 + 0.870621i \(0.336283\pi\)
\(252\) 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 −0.965159 0.261664i \(-0.915729\pi\)
0.709187 + 0.705020i \(0.249062\pi\)
\(258\) 0 0
\(259\) −7160.74 1040.78i −1.71794 0.249695i
\(260\) 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 \(-0.327217\pi\)
0.516547 + 0.856259i \(0.327217\pi\)
\(270\) 0 0
\(271\) 128.189i 0.0287341i −0.999897 0.0143671i \(-0.995427\pi\)
0.999897 0.0143671i \(-0.00457334\pi\)
\(272\) 0 0
\(273\) −4908.07 + 7066.82i −1.08810 + 1.56668i
\(274\) 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 0.382208 0.924076i \(-0.375164\pi\)
−0.609169 + 0.793040i \(0.708497\pi\)
\(284\) 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 −0.522021 0.852933i \(-0.674822\pi\)
0.999672 + 0.0256168i \(0.00815497\pi\)
\(294\) 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
\(301\) −391.655 982.676i −0.0749987 0.188175i
\(302\) 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 \(0.143239\pi\)
−0.900448 + 0.434965i \(0.856761\pi\)
\(308\) 0 0
\(309\) 582.801 1168.35i 0.107296 0.215097i
\(310\) 0 0
\(311\) −919.164 + 1592.04i −0.167592 + 0.290277i −0.937573 0.347790i \(-0.886932\pi\)
0.769981 + 0.638067i \(0.220266\pi\)
\(312\) 0 0
\(313\) −5160.13 + 2979.20i −0.931846 + 0.538001i −0.887395 0.461010i \(-0.847487\pi\)
−0.0444510 + 0.999012i \(0.514154\pi\)
\(314\) 0 0
\(315\) −2855.36 + 4697.72i −0.510734 + 0.840274i
\(316\) 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
\(329\) 111.532 + 279.837i 0.0186898 + 0.0468933i
\(330\) 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 −0.644107 0.764935i \(-0.722771\pi\)
0.340400 + 0.940281i \(0.389438\pi\)
\(350\) 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 \(-0.958913\pi\)
0.384364 0.923181i \(-0.374421\pi\)
\(354\) 0 0
\(355\) 7154.19 + 4130.47i 1.06959 + 0.617529i
\(356\) 0 0
\(357\) −857.836 + 10256.7i −0.127175 + 1.52057i
\(358\) 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 −0.793825 0.608146i \(-0.791914\pi\)
0.129757 + 0.991546i \(0.458580\pi\)
\(368\) 0 0
\(369\) 3642.70 8572.41i 0.513906 1.20938i
\(370\) 0 0
\(371\) 1186.03 8160.04i 0.165971 1.14191i
\(372\) 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 −0.988634 0.150341i \(-0.951963\pi\)
0.624517 + 0.781012i \(0.285296\pi\)
\(384\) 0 0
\(385\) 467.573 3216.98i 0.0618954 0.425850i
\(386\) 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 \(-0.838324\pi\)
0.873757 0.486362i \(-0.161676\pi\)
\(398\) 0 0
\(399\) −797.531 66.7027i −0.100066 0.00836920i
\(400\) 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 0.0634474 0.997985i \(-0.479790\pi\)
−0.832557 + 0.553940i \(0.813124\pi\)
\(410\) 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 −0.948608 0.316455i \(-0.897508\pi\)
0.748362 + 0.663291i \(0.230841\pi\)
\(420\) 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
\(427\) −8360.60 + 3332.20i −0.947536 + 0.377650i
\(428\) 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 \(-0.878064\pi\)
0.927521 0.373772i \(-0.121936\pi\)
\(434\) 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 −0.907704 0.419611i \(-0.862166\pi\)
−0.0904581 + 0.995900i \(0.528833\pi\)
\(440\) 0 0
\(441\) −9132.34 1538.35i −0.986107 0.166111i
\(442\) 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
\(455\) 16910.4 6739.80i 1.74236 0.694433i
\(456\) 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 0.672506 0.740092i \(-0.265218\pi\)
−0.977191 + 0.212361i \(0.931885\pi\)
\(462\) 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 \(-0.809465\pi\)
−0.826134 + 0.563473i \(0.809465\pi\)
\(468\) 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 \(0.140014\pi\)
−0.0836331 + 0.996497i \(0.526652\pi\)
\(480\) 0 0
\(481\) 30252.0 + 17466.0i 2.86772 + 1.65568i
\(482\) 0 0
\(483\) 7853.32 11307.5i 0.739831 1.06524i
\(484\) 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
\(497\) −2001.66 + 13771.8i −0.180658 + 1.24295i
\(498\) 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 \(-0.424524\pi\)
0.234898 + 0.972020i \(0.424524\pi\)
\(504\) 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 \(0.469247\pi\)
−0.910218 + 0.414129i \(0.864086\pi\)
\(510\) 0 0
\(511\) −1351.99 + 9301.90i −0.117042 + 0.805268i
\(512\) 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 \(-0.376980\pi\)
0.376930 + 0.926242i \(0.376980\pi\)
\(522\) 0 0
\(523\) 20614.1i 1.72350i 0.507330 + 0.861752i \(0.330633\pi\)
−0.507330 + 0.861752i \(0.669367\pi\)
\(524\) 0 0
\(525\) −360.107 + 169.600i −0.0299359 + 0.0140990i
\(526\) 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
\(553\) −5232.77 13129.2i −0.402387 1.00960i
\(554\) 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 −0.517138 0.855902i \(-0.673003\pi\)
0.999802 + 0.0199041i \(0.00633608\pi\)
\(564\) 0 0
\(565\) 9475.73 5470.82i 0.705570 0.407361i
\(566\) 0 0
\(567\) −13434.8 + 1337.60i −0.995080 + 0.0990724i
\(568\) 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 \(0.141595\pi\)
−0.902682 + 0.430308i \(0.858405\pi\)
\(578\) 0 0
\(579\) −6945.07 3464.37i −0.498493 0.248660i
\(580\) 0 0
\(581\) −8327.56 20894.1i −0.594639 1.49197i
\(582\) 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 0.943750 0.330661i \(-0.107272\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(588\) 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 \(-0.558640\pi\)
−0.183184 + 0.983079i \(0.558640\pi\)
\(594\) 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 −0.576197 0.817311i \(-0.695464\pi\)
0.419714 + 0.907656i \(0.362130\pi\)
\(602\) 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 0.790425 0.612558i \(-0.209859\pi\)
−0.135278 + 0.990808i \(0.543193\pi\)
\(608\) 0 0
\(609\) 6141.86 + 13040.8i 0.408671 + 0.867719i
\(610\) 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 0.0722590 0.997386i \(-0.476979\pi\)
0.899891 + 0.436115i \(0.143646\pi\)
\(620\) 0 0
\(621\) 6710.71 18915.5i 0.433642 1.22231i
\(622\) 0 0
\(623\) 7802.60 + 1134.07i 0.501773 + 0.0729304i
\(624\) 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
\(637\) 21094.2 + 22259.4i 1.31206 + 1.38453i
\(638\) 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 0.136094 0.990696i \(-0.456545\pi\)
−0.789921 + 0.613209i \(0.789878\pi\)
\(644\) 0 0
\(645\) 198.565 + 3256.88i 0.0121217 + 0.198821i
\(646\) 0 0
\(647\) −32197.6 −1.95644 −0.978220 0.207570i \(-0.933445\pi\)
−0.978220 + 0.207570i \(0.933445\pi\)
\(648\) 0 0
\(649\) 6174.00i 0.373422i
\(650\) 0 0
\(651\) −2357.74 + 3394.75i −0.141946 + 0.204379i
\(652\) 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 0.217540 0.976051i \(-0.430197\pi\)
−0.736515 + 0.676421i \(0.763530\pi\)
\(662\) 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 0.695615 0.718415i \(-0.255132\pi\)
−0.969973 + 0.243212i \(0.921799\pi\)
\(678\) 0 0
\(679\) 9825.20 3915.93i 0.555311 0.221325i
\(680\) 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 0.0672260 0.997738i \(-0.478585\pi\)
0.897679 + 0.440649i \(0.145252\pi\)
\(692\) 0 0
\(693\) 7002.32 3834.93i 0.383833 0.210212i
\(694\) 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
\(707\) 4846.24 + 12159.4i 0.257796 + 0.646818i
\(708\) 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 \(-0.691157\pi\)
−0.565086 + 0.825032i \(0.691157\pi\)
\(720\) 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 −0.517375 0.855759i \(-0.673091\pi\)
0.482421 + 0.875940i \(0.339758\pi\)
\(728\) 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 0.495076 0.868850i \(-0.335140\pi\)
−0.504908 + 0.863173i \(0.668474\pi\)
\(734\) 0 0
\(735\) 14318.4 + 13375.8i 0.718558 + 0.671255i
\(736\) 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
\(749\) −1971.14 + 13561.8i −0.0961602 + 0.661598i
\(750\) 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 −0.965954 0.258714i \(-0.916701\pi\)
0.707030 + 0.707184i \(0.250035\pi\)
\(762\) 0 0
\(763\) −27443.4 3988.78i −1.30212 0.189258i
\(764\) 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 0.0157486 0.999876i \(-0.494987\pi\)
−0.858044 + 0.513577i \(0.828320\pi\)
\(770\) 0 0
\(771\) 9807.36 + 4892.15i 0.458111 + 0.228517i
\(772\) 0 0
\(773\) −7445.62 −0.346443 −0.173221 0.984883i \(-0.555418\pi\)
−0.173221 + 0.984883i \(0.555418\pi\)
\(774\) 0 0
\(775\) 177.648i 0.00823396i
\(776\) 0 0
\(777\) −3133.73 + 37468.5i −0.144687 + 1.72995i
\(778\) 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 0.789614 0.613603i \(-0.210281\pi\)
−0.136589 + 0.990628i \(0.543614\pi\)
\(788\) 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