Properties

Label 16.4.e.a.5.5
Level 16
Weight 4
Character 16.5
Analytic conductor 0.944
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.944030560092\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{10} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.5
Root \(-1.56339 + 1.24732i\)
Character \(\chi\) = 16.5
Dual form 16.4.e.a.13.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.81071 - 0.316066i) q^{2} +(-3.27139 + 3.27139i) q^{3} +(7.80020 - 1.77674i) q^{4} +(-12.6449 - 12.6449i) q^{5} +(-8.16095 + 10.2289i) q^{6} +13.8754i q^{7} +(21.3626 - 7.45928i) q^{8} +5.59607i q^{9} +O(q^{10})\) \(q+(2.81071 - 0.316066i) q^{2} +(-3.27139 + 3.27139i) q^{3} +(7.80020 - 1.77674i) q^{4} +(-12.6449 - 12.6449i) q^{5} +(-8.16095 + 10.2289i) q^{6} +13.8754i q^{7} +(21.3626 - 7.45928i) q^{8} +5.59607i q^{9} +(-39.5378 - 31.5445i) q^{10} +(1.54694 + 1.54694i) q^{11} +(-19.7051 + 31.3299i) q^{12} +(32.7875 - 32.7875i) q^{13} +(4.38553 + 38.9997i) q^{14} +82.7326 q^{15} +(57.6864 - 27.7179i) q^{16} +18.6531 q^{17} +(1.76873 + 15.7289i) q^{18} +(-86.4042 + 86.4042i) q^{19} +(-121.099 - 76.1661i) q^{20} +(-45.3917 - 45.3917i) q^{21} +(4.83695 + 3.85908i) q^{22} -134.006i q^{23} +(-45.4830 + 94.2874i) q^{24} +194.786i q^{25} +(81.7932 - 102.519i) q^{26} +(-106.634 - 106.634i) q^{27} +(24.6529 + 108.231i) q^{28} +(-59.7949 + 59.7949i) q^{29} +(232.538 - 26.1489i) q^{30} -31.5391 q^{31} +(153.379 - 96.1396i) q^{32} -10.1213 q^{33} +(52.4284 - 5.89559i) q^{34} +(175.453 - 175.453i) q^{35} +(9.94276 + 43.6505i) q^{36} +(89.1866 + 89.1866i) q^{37} +(-215.548 + 270.167i) q^{38} +214.521i q^{39} +(-364.449 - 175.805i) q^{40} -210.504i q^{41} +(-141.930 - 113.236i) q^{42} +(119.402 + 119.402i) q^{43} +(14.8150 + 9.31796i) q^{44} +(70.7617 - 70.7617i) q^{45} +(-42.3547 - 376.652i) q^{46} -182.902 q^{47} +(-98.0386 + 279.390i) q^{48} +150.474 q^{49} +(61.5653 + 547.489i) q^{50} +(-61.0213 + 61.0213i) q^{51} +(197.494 - 314.004i) q^{52} +(-26.1644 - 26.1644i) q^{53} +(-333.422 - 266.015i) q^{54} -39.1219i q^{55} +(103.500 + 296.414i) q^{56} -565.323i q^{57} +(-149.167 + 186.965i) q^{58} +(441.584 + 441.584i) q^{59} +(645.331 - 146.994i) q^{60} +(-174.485 + 174.485i) q^{61} +(-88.6475 + 9.96844i) q^{62} -77.6476 q^{63} +(400.718 - 318.699i) q^{64} -829.188 q^{65} +(-28.4480 + 3.19899i) q^{66} +(91.7562 - 91.7562i) q^{67} +(145.498 - 33.1416i) q^{68} +(438.385 + 438.385i) q^{69} +(437.692 - 548.601i) q^{70} +348.360i q^{71} +(41.7427 + 119.546i) q^{72} -299.436i q^{73} +(278.867 + 222.489i) q^{74} +(-637.222 - 637.222i) q^{75} +(-520.453 + 827.488i) q^{76} +(-21.4644 + 21.4644i) q^{77} +(67.8027 + 602.957i) q^{78} -943.487 q^{79} +(-1079.93 - 378.949i) q^{80} +546.590 q^{81} +(-66.5330 - 591.666i) q^{82} +(313.272 - 313.272i) q^{83} +(-434.714 - 273.415i) q^{84} +(-235.866 - 235.866i) q^{85} +(373.343 + 297.865i) q^{86} -391.224i q^{87} +(44.5858 + 21.5076i) q^{88} +1412.35i q^{89} +(176.525 - 221.256i) q^{90} +(454.939 + 454.939i) q^{91} +(-238.094 - 1045.27i) q^{92} +(103.177 - 103.177i) q^{93} +(-514.085 + 57.8091i) q^{94} +2185.14 q^{95} +(-187.253 + 816.272i) q^{96} +1515.29 q^{97} +(422.939 - 47.5596i) q^{98} +(-8.65680 + 8.65680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} - 68q^{10} + 18q^{11} + 100q^{12} - 2q^{13} + 188q^{14} - 124q^{15} + 280q^{16} - 4q^{17} + 174q^{18} - 26q^{19} - 196q^{20} + 52q^{21} - 588q^{22} - 848q^{24} - 264q^{26} + 184q^{27} + 280q^{28} - 202q^{29} + 1236q^{30} + 368q^{31} + 968q^{32} - 4q^{33} + 436q^{34} + 476q^{35} - 596q^{36} - 10q^{37} - 1232q^{38} - 1336q^{40} - 680q^{42} - 838q^{43} + 868q^{44} + 194q^{45} + 1132q^{46} - 944q^{47} + 1768q^{48} + 94q^{49} + 726q^{50} - 1500q^{51} - 236q^{52} - 378q^{53} - 1376q^{54} - 488q^{56} + 8q^{58} + 1706q^{59} - 192q^{60} + 910q^{61} - 80q^{62} + 2628q^{63} + 512q^{64} - 492q^{65} - 428q^{66} + 1942q^{67} - 880q^{68} + 580q^{69} + 160q^{70} + 1092q^{72} - 452q^{74} - 2954q^{75} - 1228q^{76} - 268q^{77} - 772q^{78} - 4416q^{79} - 2648q^{80} + 482q^{81} - 704q^{82} - 2562q^{83} + 1960q^{84} - 12q^{85} + 3764q^{86} + 1528q^{88} + 1896q^{90} + 3332q^{91} + 632q^{92} - 2192q^{93} - 3248q^{94} + 6900q^{95} - 4432q^{96} - 4q^{97} + 314q^{98} + 4958q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.81071 0.316066i 0.993737 0.111746i
\(3\) −3.27139 + 3.27139i −0.629578 + 0.629578i −0.947962 0.318384i \(-0.896860\pi\)
0.318384 + 0.947962i \(0.396860\pi\)
\(4\) 7.80020 1.77674i 0.975026 0.222092i
\(5\) −12.6449 12.6449i −1.13099 1.13099i −0.990012 0.140981i \(-0.954974\pi\)
−0.140981 0.990012i \(-0.545026\pi\)
\(6\) −8.16095 + 10.2289i −0.555282 + 0.695988i
\(7\) 13.8754i 0.749200i 0.927187 + 0.374600i \(0.122220\pi\)
−0.927187 + 0.374600i \(0.877780\pi\)
\(8\) 21.3626 7.45928i 0.944101 0.329657i
\(9\) 5.59607i 0.207262i
\(10\) −39.5378 31.5445i −1.25029 0.997526i
\(11\) 1.54694 + 1.54694i 0.0424019 + 0.0424019i 0.727990 0.685588i \(-0.240455\pi\)
−0.685588 + 0.727990i \(0.740455\pi\)
\(12\) −19.7051 + 31.3299i −0.474031 + 0.753680i
\(13\) 32.7875 32.7875i 0.699509 0.699509i −0.264796 0.964304i \(-0.585305\pi\)
0.964304 + 0.264796i \(0.0853046\pi\)
\(14\) 4.38553 + 38.9997i 0.0837202 + 0.744508i
\(15\) 82.7326 1.42410
\(16\) 57.6864 27.7179i 0.901350 0.433092i
\(17\) 18.6531 0.266119 0.133060 0.991108i \(-0.457520\pi\)
0.133060 + 0.991108i \(0.457520\pi\)
\(18\) 1.76873 + 15.7289i 0.0231607 + 0.205964i
\(19\) −86.4042 + 86.4042i −1.04329 + 1.04329i −0.0442688 + 0.999020i \(0.514096\pi\)
−0.999020 + 0.0442688i \(0.985904\pi\)
\(20\) −121.099 76.1661i −1.35393 0.851562i
\(21\) −45.3917 45.3917i −0.471680 0.471680i
\(22\) 4.83695 + 3.85908i 0.0468746 + 0.0373981i
\(23\) 134.006i 1.21488i −0.794367 0.607438i \(-0.792197\pi\)
0.794367 0.607438i \(-0.207803\pi\)
\(24\) −45.4830 + 94.2874i −0.386841 + 0.801930i
\(25\) 194.786i 1.55829i
\(26\) 81.7932 102.519i 0.616960 0.773295i
\(27\) −106.634 106.634i −0.760066 0.760066i
\(28\) 24.6529 + 108.231i 0.166392 + 0.730489i
\(29\) −59.7949 + 59.7949i −0.382884 + 0.382884i −0.872140 0.489256i \(-0.837268\pi\)
0.489256 + 0.872140i \(0.337268\pi\)
\(30\) 232.538 26.1489i 1.41518 0.159137i
\(31\) −31.5391 −0.182729 −0.0913645 0.995818i \(-0.529123\pi\)
−0.0913645 + 0.995818i \(0.529123\pi\)
\(32\) 153.379 96.1396i 0.847308 0.531101i
\(33\) −10.1213 −0.0533906
\(34\) 52.4284 5.89559i 0.264453 0.0297378i
\(35\) 175.453 175.453i 0.847340 0.847340i
\(36\) 9.94276 + 43.6505i 0.0460313 + 0.202086i
\(37\) 89.1866 + 89.1866i 0.396275 + 0.396275i 0.876917 0.480642i \(-0.159596\pi\)
−0.480642 + 0.876917i \(0.659596\pi\)
\(38\) −215.548 + 270.167i −0.920171 + 1.15334i
\(39\) 214.521i 0.880791i
\(40\) −364.449 175.805i −1.44061 0.694932i
\(41\) 210.504i 0.801834i −0.916114 0.400917i \(-0.868692\pi\)
0.916114 0.400917i \(-0.131308\pi\)
\(42\) −141.930 113.236i −0.521434 0.416018i
\(43\) 119.402 + 119.402i 0.423456 + 0.423456i 0.886392 0.462936i \(-0.153204\pi\)
−0.462936 + 0.886392i \(0.653204\pi\)
\(44\) 14.8150 + 9.31796i 0.0507601 + 0.0319258i
\(45\) 70.7617 70.7617i 0.234412 0.234412i
\(46\) −42.3547 376.652i −0.135758 1.20727i
\(47\) −182.902 −0.567638 −0.283819 0.958878i \(-0.591602\pi\)
−0.283819 + 0.958878i \(0.591602\pi\)
\(48\) −98.0386 + 279.390i −0.294805 + 0.840136i
\(49\) 150.474 0.438699
\(50\) 61.5653 + 547.489i 0.174133 + 1.54853i
\(51\) −61.0213 + 61.0213i −0.167543 + 0.167543i
\(52\) 197.494 314.004i 0.526683 0.837394i
\(53\) −26.1644 26.1644i −0.0678104 0.0678104i 0.672388 0.740199i \(-0.265269\pi\)
−0.740199 + 0.672388i \(0.765269\pi\)
\(54\) −333.422 266.015i −0.840240 0.670371i
\(55\) 39.1219i 0.0959125i
\(56\) 103.500 + 296.414i 0.246979 + 0.707320i
\(57\) 565.323i 1.31366i
\(58\) −149.167 + 186.965i −0.337700 + 0.423272i
\(59\) 441.584 + 441.584i 0.974395 + 0.974395i 0.999680 0.0252856i \(-0.00804951\pi\)
−0.0252856 + 0.999680i \(0.508050\pi\)
\(60\) 645.331 146.994i 1.38853 0.316281i
\(61\) −174.485 + 174.485i −0.366238 + 0.366238i −0.866103 0.499865i \(-0.833383\pi\)
0.499865 + 0.866103i \(0.333383\pi\)
\(62\) −88.6475 + 9.96844i −0.181585 + 0.0204192i
\(63\) −77.6476 −0.155281
\(64\) 400.718 318.699i 0.782653 0.622458i
\(65\) −829.188 −1.58228
\(66\) −28.4480 + 3.19899i −0.0530563 + 0.00596620i
\(67\) 91.7562 91.7562i 0.167311 0.167311i −0.618486 0.785796i \(-0.712253\pi\)
0.785796 + 0.618486i \(0.212253\pi\)
\(68\) 145.498 33.1416i 0.259473 0.0591031i
\(69\) 438.385 + 438.385i 0.764860 + 0.764860i
\(70\) 437.692 548.601i 0.747346 0.936720i
\(71\) 348.360i 0.582291i 0.956679 + 0.291146i \(0.0940364\pi\)
−0.956679 + 0.291146i \(0.905964\pi\)
\(72\) 41.7427 + 119.546i 0.0683253 + 0.195676i
\(73\) 299.436i 0.480087i −0.970762 0.240043i \(-0.922838\pi\)
0.970762 0.240043i \(-0.0771617\pi\)
\(74\) 278.867 + 222.489i 0.438076 + 0.349511i
\(75\) −637.222 637.222i −0.981067 0.981067i
\(76\) −520.453 + 827.488i −0.785526 + 1.24894i
\(77\) −21.4644 + 21.4644i −0.0317675 + 0.0317675i
\(78\) 67.8027 + 602.957i 0.0984250 + 0.875275i
\(79\) −943.487 −1.34368 −0.671839 0.740697i \(-0.734495\pi\)
−0.671839 + 0.740697i \(0.734495\pi\)
\(80\) −1079.93 378.949i −1.50924 0.529597i
\(81\) 546.590 0.749781
\(82\) −66.5330 591.666i −0.0896018 0.796812i
\(83\) 313.272 313.272i 0.414290 0.414290i −0.468940 0.883230i \(-0.655364\pi\)
0.883230 + 0.468940i \(0.155364\pi\)
\(84\) −434.714 273.415i −0.564657 0.355144i
\(85\) −235.866 235.866i −0.300979 0.300979i
\(86\) 373.343 + 297.865i 0.468123 + 0.373484i
\(87\) 391.224i 0.482111i
\(88\) 44.5858 + 21.5076i 0.0540097 + 0.0260536i
\(89\) 1412.35i 1.68212i 0.540942 + 0.841060i \(0.318068\pi\)
−0.540942 + 0.841060i \(0.681932\pi\)
\(90\) 176.525 221.256i 0.206749 0.259138i
\(91\) 454.939 + 454.939i 0.524072 + 0.524072i
\(92\) −238.094 1045.27i −0.269815 1.18454i
\(93\) 103.177 103.177i 0.115042 0.115042i
\(94\) −514.085 + 57.8091i −0.564083 + 0.0634314i
\(95\) 2185.14 2.35990
\(96\) −187.253 + 816.272i −0.199077 + 0.867817i
\(97\) 1515.29 1.58613 0.793063 0.609140i \(-0.208485\pi\)
0.793063 + 0.609140i \(0.208485\pi\)
\(98\) 422.939 47.5596i 0.435952 0.0490229i
\(99\) −8.65680 + 8.65680i −0.00878830 + 0.00878830i
\(100\) 346.085 + 1519.37i 0.346085 + 1.51937i
\(101\) −573.202 573.202i −0.564711 0.564711i 0.365931 0.930642i \(-0.380751\pi\)
−0.930642 + 0.365931i \(0.880751\pi\)
\(102\) −152.227 + 190.800i −0.147771 + 0.185216i
\(103\) 1021.00i 0.976717i −0.872643 0.488359i \(-0.837596\pi\)
0.872643 0.488359i \(-0.162404\pi\)
\(104\) 455.854 944.996i 0.429809 0.891004i
\(105\) 1147.95i 1.06693i
\(106\) −81.8101 65.2708i −0.0749632 0.0598081i
\(107\) −1240.79 1240.79i −1.12105 1.12105i −0.991584 0.129462i \(-0.958675\pi\)
−0.129462 0.991584i \(-0.541325\pi\)
\(108\) −1021.23 642.308i −0.909889 0.572279i
\(109\) −108.629 + 108.629i −0.0954565 + 0.0954565i −0.753222 0.657766i \(-0.771502\pi\)
0.657766 + 0.753222i \(0.271502\pi\)
\(110\) −12.3651 109.960i −0.0107179 0.0953118i
\(111\) −583.528 −0.498973
\(112\) 384.596 + 800.421i 0.324472 + 0.675291i
\(113\) −1722.22 −1.43374 −0.716870 0.697207i \(-0.754426\pi\)
−0.716870 + 0.697207i \(0.754426\pi\)
\(114\) −178.679 1588.96i −0.146797 1.30544i
\(115\) −1694.49 + 1694.49i −1.37402 + 1.37402i
\(116\) −360.173 + 572.653i −0.288286 + 0.458357i
\(117\) 183.481 + 183.481i 0.144981 + 0.144981i
\(118\) 1380.73 + 1101.59i 1.07718 + 0.859407i
\(119\) 258.818i 0.199377i
\(120\) 1767.38 617.126i 1.34449 0.469463i
\(121\) 1326.21i 0.996404i
\(122\) −435.278 + 545.576i −0.323018 + 0.404870i
\(123\) 688.639 + 688.639i 0.504817 + 0.504817i
\(124\) −246.012 + 56.0368i −0.178165 + 0.0405827i
\(125\) 882.442 882.442i 0.631424 0.631424i
\(126\) −218.245 + 24.5417i −0.154308 + 0.0173520i
\(127\) 699.127 0.488484 0.244242 0.969714i \(-0.421461\pi\)
0.244242 + 0.969714i \(0.421461\pi\)
\(128\) 1025.57 1022.42i 0.708194 0.706018i
\(129\) −781.219 −0.533198
\(130\) −2330.61 + 262.078i −1.57237 + 0.176814i
\(131\) 197.970 197.970i 0.132036 0.132036i −0.638000 0.770036i \(-0.720238\pi\)
0.770036 + 0.638000i \(0.220238\pi\)
\(132\) −78.9482 + 17.9829i −0.0520572 + 0.0118577i
\(133\) −1198.89 1198.89i −0.781632 0.781632i
\(134\) 228.899 286.901i 0.147566 0.184959i
\(135\) 2696.76i 1.71926i
\(136\) 398.477 139.138i 0.251244 0.0877281i
\(137\) 271.386i 0.169242i −0.996413 0.0846209i \(-0.973032\pi\)
0.996413 0.0846209i \(-0.0269679\pi\)
\(138\) 1370.73 + 1093.62i 0.845540 + 0.674600i
\(139\) 459.937 + 459.937i 0.280657 + 0.280657i 0.833371 0.552714i \(-0.186408\pi\)
−0.552714 + 0.833371i \(0.686408\pi\)
\(140\) 1056.83 1680.30i 0.637991 1.01437i
\(141\) 598.343 598.343i 0.357373 0.357373i
\(142\) 110.105 + 979.139i 0.0650688 + 0.578644i
\(143\) 101.441 0.0593210
\(144\) 155.111 + 322.817i 0.0897634 + 0.186815i
\(145\) 1512.20 0.866079
\(146\) −94.6415 841.628i −0.0536478 0.477080i
\(147\) −492.258 + 492.258i −0.276196 + 0.276196i
\(148\) 854.135 + 537.213i 0.474389 + 0.298369i
\(149\) 605.772 + 605.772i 0.333066 + 0.333066i 0.853750 0.520684i \(-0.174323\pi\)
−0.520684 + 0.853750i \(0.674323\pi\)
\(150\) −1992.45 1589.64i −1.08455 0.865292i
\(151\) 3534.47i 1.90484i −0.304785 0.952421i \(-0.598585\pi\)
0.304785 0.952421i \(-0.401415\pi\)
\(152\) −1201.30 + 2490.33i −0.641042 + 1.32890i
\(153\) 104.384i 0.0551564i
\(154\) −53.5461 + 67.1145i −0.0280186 + 0.0351184i
\(155\) 398.809 + 398.809i 0.206665 + 0.206665i
\(156\) 381.148 + 1673.31i 0.195617 + 0.858794i
\(157\) −1233.54 + 1233.54i −0.627051 + 0.627051i −0.947325 0.320274i \(-0.896225\pi\)
0.320274 + 0.947325i \(0.396225\pi\)
\(158\) −2651.87 + 298.204i −1.33526 + 0.150151i
\(159\) 171.187 0.0853839
\(160\) −3155.14 723.788i −1.55897 0.357628i
\(161\) 1859.38 0.910186
\(162\) 1536.31 172.758i 0.745085 0.0837851i
\(163\) 2569.36 2569.36i 1.23465 1.23465i 0.272494 0.962158i \(-0.412152\pi\)
0.962158 0.272494i \(-0.0878484\pi\)
\(164\) −374.010 1641.97i −0.178081 0.781808i
\(165\) 127.983 + 127.983i 0.0603845 + 0.0603845i
\(166\) 781.503 979.532i 0.365400 0.457991i
\(167\) 3048.39i 1.41252i 0.707950 + 0.706262i \(0.249620\pi\)
−0.707950 + 0.706262i \(0.750380\pi\)
\(168\) −1308.27 631.094i −0.600806 0.289821i
\(169\) 46.9618i 0.0213754i
\(170\) −737.500 588.402i −0.332727 0.265461i
\(171\) −483.524 483.524i −0.216234 0.216234i
\(172\) 1143.50 + 719.213i 0.506927 + 0.318834i
\(173\) −1522.05 + 1522.05i −0.668898 + 0.668898i −0.957461 0.288563i \(-0.906823\pi\)
0.288563 + 0.957461i \(0.406823\pi\)
\(174\) −123.653 1099.62i −0.0538740 0.479092i
\(175\) −2702.74 −1.16747
\(176\) 132.116 + 46.3596i 0.0565829 + 0.0198550i
\(177\) −2889.18 −1.22692
\(178\) 446.395 + 3969.71i 0.187970 + 1.67158i
\(179\) 302.258 302.258i 0.126211 0.126211i −0.641180 0.767391i \(-0.721555\pi\)
0.767391 + 0.641180i \(0.221555\pi\)
\(180\) 426.231 677.681i 0.176496 0.280619i
\(181\) 1696.94 + 1696.94i 0.696865 + 0.696865i 0.963733 0.266868i \(-0.0859889\pi\)
−0.266868 + 0.963733i \(0.585989\pi\)
\(182\) 1422.49 + 1134.91i 0.579353 + 0.462227i
\(183\) 1141.62i 0.461151i
\(184\) −999.588 2862.71i −0.400492 1.14697i
\(185\) 2255.51i 0.896370i
\(186\) 257.389 322.611i 0.101466 0.127177i
\(187\) 28.8552 + 28.8552i 0.0112840 + 0.0112840i
\(188\) −1426.67 + 324.969i −0.553462 + 0.126068i
\(189\) 1479.59 1479.59i 0.569442 0.569442i
\(190\) 6141.81 690.649i 2.34512 0.263710i
\(191\) −4035.31 −1.52872 −0.764358 0.644792i \(-0.776944\pi\)
−0.764358 + 0.644792i \(0.776944\pi\)
\(192\) −268.318 + 2353.49i −0.100855 + 0.884628i
\(193\) −886.172 −0.330508 −0.165254 0.986251i \(-0.552844\pi\)
−0.165254 + 0.986251i \(0.552844\pi\)
\(194\) 4259.04 478.931i 1.57619 0.177243i
\(195\) 2712.59 2712.59i 0.996169 0.996169i
\(196\) 1173.73 267.353i 0.427743 0.0974318i
\(197\) 3270.12 + 3270.12i 1.18267 + 1.18267i 0.979049 + 0.203624i \(0.0652720\pi\)
0.203624 + 0.979049i \(0.434728\pi\)
\(198\) −21.5957 + 27.0679i −0.00775120 + 0.00971531i
\(199\) 222.513i 0.0792639i 0.999214 + 0.0396319i \(0.0126185\pi\)
−0.999214 + 0.0396319i \(0.987381\pi\)
\(200\) 1452.97 + 4161.14i 0.513701 + 1.47118i
\(201\) 600.340i 0.210670i
\(202\) −1792.28 1429.94i −0.624278 0.498070i
\(203\) −829.677 829.677i −0.286857 0.286857i
\(204\) −367.560 + 584.398i −0.126149 + 0.200569i
\(205\) −2661.80 + 2661.80i −0.906868 + 0.906868i
\(206\) −322.702 2869.73i −0.109144 0.970600i
\(207\) 749.907 0.251798
\(208\) 982.593 2800.19i 0.327551 0.933453i
\(209\) −267.325 −0.0884748
\(210\) 362.827 + 3226.55i 0.119226 + 1.06025i
\(211\) −3527.46 + 3527.46i −1.15090 + 1.15090i −0.164529 + 0.986372i \(0.552610\pi\)
−0.986372 + 0.164529i \(0.947390\pi\)
\(212\) −250.575 157.600i −0.0811770 0.0510567i
\(213\) −1139.62 1139.62i −0.366598 0.366598i
\(214\) −3879.68 3095.34i −1.23930 0.988753i
\(215\) 3019.65i 0.957852i
\(216\) −3073.40 1482.57i −0.968140 0.467018i
\(217\) 437.618i 0.136901i
\(218\) −270.991 + 339.658i −0.0841918 + 0.105526i
\(219\) 979.571 + 979.571i 0.302252 + 0.302252i
\(220\) −69.5093 305.158i −0.0213014 0.0935172i
\(221\) 611.587 611.587i 0.186153 0.186153i
\(222\) −1640.13 + 184.433i −0.495848 + 0.0557583i
\(223\) 5841.90 1.75427 0.877136 0.480242i \(-0.159451\pi\)
0.877136 + 0.480242i \(0.159451\pi\)
\(224\) 1333.97 + 2128.19i 0.397901 + 0.634803i
\(225\) −1090.04 −0.322975
\(226\) −4840.66 + 544.334i −1.42476 + 0.160215i
\(227\) −1129.54 + 1129.54i −0.330265 + 0.330265i −0.852687 0.522422i \(-0.825029\pi\)
0.522422 + 0.852687i \(0.325029\pi\)
\(228\) −1004.43 4409.63i −0.291755 1.28086i
\(229\) −2905.40 2905.40i −0.838403 0.838403i 0.150246 0.988649i \(-0.451994\pi\)
−0.988649 + 0.150246i \(0.951994\pi\)
\(230\) −4227.15 + 5298.29i −1.21187 + 1.51895i
\(231\) 140.437i 0.0400003i
\(232\) −831.346 + 1723.40i −0.235261 + 0.487701i
\(233\) 734.054i 0.206393i −0.994661 0.103196i \(-0.967093\pi\)
0.994661 0.103196i \(-0.0329070\pi\)
\(234\) 573.705 + 457.720i 0.160275 + 0.127872i
\(235\) 2312.78 + 2312.78i 0.641995 + 0.641995i
\(236\) 4229.02 + 2659.86i 1.16647 + 0.733654i
\(237\) 3086.51 3086.51i 0.845951 0.845951i
\(238\) 81.8036 + 727.463i 0.0222796 + 0.198128i
\(239\) −511.807 −0.138519 −0.0692595 0.997599i \(-0.522064\pi\)
−0.0692595 + 0.997599i \(0.522064\pi\)
\(240\) 4772.55 2293.17i 1.28361 0.616765i
\(241\) 5920.31 1.58241 0.791204 0.611552i \(-0.209455\pi\)
0.791204 + 0.611552i \(0.209455\pi\)
\(242\) −419.171 3727.61i −0.111344 0.990163i
\(243\) 1091.02 1091.02i 0.288020 0.288020i
\(244\) −1051.00 + 1671.03i −0.275753 + 0.438430i
\(245\) −1902.73 1902.73i −0.496166 0.496166i
\(246\) 2153.22 + 1717.91i 0.558067 + 0.445244i
\(247\) 5665.95i 1.45958i
\(248\) −673.757 + 235.259i −0.172515 + 0.0602378i
\(249\) 2049.67i 0.521656i
\(250\) 2201.38 2759.20i 0.556910 0.698029i
\(251\) −309.332 309.332i −0.0777883 0.0777883i 0.667142 0.744930i \(-0.267517\pi\)
−0.744930 + 0.667142i \(0.767517\pi\)
\(252\) −605.667 + 137.960i −0.151403 + 0.0344866i
\(253\) 207.300 207.300i 0.0515131 0.0515131i
\(254\) 1965.05 220.970i 0.485425 0.0545862i
\(255\) 1543.22 0.378980
\(256\) 2559.44 3197.89i 0.624863 0.780734i
\(257\) 323.723 0.0785730 0.0392865 0.999228i \(-0.487491\pi\)
0.0392865 + 0.999228i \(0.487491\pi\)
\(258\) −2195.78 + 246.917i −0.529858 + 0.0595828i
\(259\) −1237.50 + 1237.50i −0.296890 + 0.296890i
\(260\) −6467.84 + 1473.25i −1.54276 + 0.351412i
\(261\) −334.617 334.617i −0.0793573 0.0793573i
\(262\) 493.865 619.009i 0.116455 0.145964i
\(263\) 2689.15i 0.630495i 0.949009 + 0.315248i \(0.102088\pi\)
−0.949009 + 0.315248i \(0.897912\pi\)
\(264\) −216.217 + 75.4976i −0.0504062 + 0.0176006i
\(265\) 661.691i 0.153386i
\(266\) −3748.67 2990.81i −0.864081 0.689392i
\(267\) −4620.34 4620.34i −1.05903 1.05903i
\(268\) 552.691 878.744i 0.125974 0.200291i
\(269\) 4703.78 4703.78i 1.06615 1.06615i 0.0684995 0.997651i \(-0.478179\pi\)
0.997651 0.0684995i \(-0.0218212\pi\)
\(270\) 852.353 + 7579.81i 0.192121 + 1.70849i
\(271\) −2018.97 −0.452561 −0.226280 0.974062i \(-0.572657\pi\)
−0.226280 + 0.974062i \(0.572657\pi\)
\(272\) 1076.03 517.023i 0.239867 0.115254i
\(273\) −2976.56 −0.659889
\(274\) −85.7760 762.789i −0.0189121 0.168182i
\(275\) −301.324 + 301.324i −0.0660745 + 0.0660745i
\(276\) 4198.39 + 2640.60i 0.915628 + 0.575889i
\(277\) −3080.60 3080.60i −0.668215 0.668215i 0.289088 0.957303i \(-0.406648\pi\)
−0.957303 + 0.289088i \(0.906648\pi\)
\(278\) 1438.12 + 1147.38i 0.310262 + 0.247537i
\(279\) 176.495i 0.0378728i
\(280\) 2439.37 5056.87i 0.520643 1.07931i
\(281\) 3893.51i 0.826575i 0.910601 + 0.413287i \(0.135619\pi\)
−0.910601 + 0.413287i \(0.864381\pi\)
\(282\) 1492.65 1870.89i 0.315200 0.395070i
\(283\) 2026.38 + 2026.38i 0.425639 + 0.425639i 0.887140 0.461501i \(-0.152689\pi\)
−0.461501 + 0.887140i \(0.652689\pi\)
\(284\) 618.944 + 2717.28i 0.129323 + 0.567749i
\(285\) −7148.45 + 7148.45i −1.48575 + 1.48575i
\(286\) 285.121 32.0619i 0.0589494 0.00662889i
\(287\) 2920.82 0.600734
\(288\) 538.004 + 858.321i 0.110077 + 0.175615i
\(289\) −4565.06 −0.929180
\(290\) 4250.36 477.955i 0.860654 0.0967809i
\(291\) −4957.09 + 4957.09i −0.998591 + 0.998591i
\(292\) −532.020 2335.66i −0.106624 0.468097i
\(293\) −1001.68 1001.68i −0.199724 0.199724i 0.600158 0.799882i \(-0.295104\pi\)
−0.799882 + 0.600158i \(0.795104\pi\)
\(294\) −1228.01 + 1539.18i −0.243602 + 0.305329i
\(295\) 11167.6i 2.20407i
\(296\) 2570.52 + 1239.99i 0.504759 + 0.243489i
\(297\) 329.914i 0.0644565i
\(298\) 1894.12 + 1511.19i 0.368199 + 0.293761i
\(299\) −4393.72 4393.72i −0.849817 0.849817i
\(300\) −6102.64 3838.28i −1.17445 0.738678i
\(301\) −1656.75 + 1656.75i −0.317253 + 0.317253i
\(302\) −1117.12 9934.38i −0.212859 1.89291i
\(303\) 3750.33 0.711059
\(304\) −2589.41 + 7379.29i −0.488528 + 1.39221i
\(305\) 4412.69 0.828425
\(306\) 32.9921 + 293.393i 0.00616351 + 0.0548110i
\(307\) 2966.54 2966.54i 0.551497 0.551497i −0.375376 0.926873i \(-0.622486\pi\)
0.926873 + 0.375376i \(0.122486\pi\)
\(308\) −129.290 + 205.564i −0.0239188 + 0.0380295i
\(309\) 3340.08 + 3340.08i 0.614920 + 0.614920i
\(310\) 1246.99 + 994.888i 0.228465 + 0.182277i
\(311\) 2911.18i 0.530797i −0.964139 0.265399i \(-0.914496\pi\)
0.964139 0.265399i \(-0.0855036\pi\)
\(312\) 1600.17 + 4582.72i 0.290359 + 0.831556i
\(313\) 8287.74i 1.49665i 0.663333 + 0.748324i \(0.269141\pi\)
−0.663333 + 0.748324i \(0.730859\pi\)
\(314\) −3077.24 + 3857.00i −0.553053 + 0.693194i
\(315\) 981.845 + 981.845i 0.175621 + 0.175621i
\(316\) −7359.39 + 1676.33i −1.31012 + 0.298421i
\(317\) 5742.18 5742.18i 1.01739 1.01739i 0.0175452 0.999846i \(-0.494415\pi\)
0.999846 0.0175452i \(-0.00558510\pi\)
\(318\) 481.158 54.1065i 0.0848491 0.00954132i
\(319\) −184.999 −0.0324700
\(320\) −9096.95 1037.13i −1.58917 0.181179i
\(321\) 8118.23 1.41157
\(322\) 5226.19 587.687i 0.904485 0.101710i
\(323\) −1611.70 + 1611.70i −0.277639 + 0.277639i
\(324\) 4263.51 971.148i 0.731055 0.166521i
\(325\) 6386.56 + 6386.56i 1.09004 + 1.09004i
\(326\) 6409.66 8033.83i 1.08895 1.36489i
\(327\) 710.734i 0.120195i
\(328\) −1570.21 4496.90i −0.264330 0.757012i
\(329\) 2537.84i 0.425275i
\(330\) 400.173 + 319.271i 0.0667540 + 0.0532585i
\(331\) 4499.27 + 4499.27i 0.747136 + 0.747136i 0.973940 0.226804i \(-0.0728278\pi\)
−0.226804 + 0.973940i \(0.572828\pi\)
\(332\) 1886.98 3000.19i 0.311933 0.495954i
\(333\) −499.095 + 499.095i −0.0821328 + 0.0821328i
\(334\) 963.492 + 8568.15i 0.157844 + 1.40368i
\(335\) −2320.50 −0.378454
\(336\) −3876.65 1360.32i −0.629430 0.220868i
\(337\) −5860.06 −0.947234 −0.473617 0.880731i \(-0.657052\pi\)
−0.473617 + 0.880731i \(0.657052\pi\)
\(338\) 14.8430 + 131.996i 0.00238862 + 0.0212416i
\(339\) 5634.04 5634.04i 0.902652 0.902652i
\(340\) −2258.87 1420.73i −0.360308 0.226617i
\(341\) −48.7893 48.7893i −0.00774806 0.00774806i
\(342\) −1511.87 1206.22i −0.239043 0.190716i
\(343\) 6847.14i 1.07787i
\(344\) 3441.38 + 1660.08i 0.539380 + 0.260190i
\(345\) 11086.7i 1.73010i
\(346\) −3796.98 + 4759.12i −0.589962 + 0.739456i
\(347\) −2029.11 2029.11i −0.313915 0.313915i 0.532509 0.846424i \(-0.321249\pi\)
−0.846424 + 0.532509i \(0.821249\pi\)
\(348\) −695.104 3051.63i −0.107073 0.470071i
\(349\) −1943.26 + 1943.26i −0.298053 + 0.298053i −0.840251 0.542198i \(-0.817592\pi\)
0.542198 + 0.840251i \(0.317592\pi\)
\(350\) −7596.61 + 854.242i −1.16016 + 0.130460i
\(351\) −6992.54 −1.06335
\(352\) 385.991 + 88.5463i 0.0584472 + 0.0134078i
\(353\) −7548.63 −1.13817 −0.569084 0.822280i \(-0.692702\pi\)
−0.569084 + 0.822280i \(0.692702\pi\)
\(354\) −8120.65 + 913.171i −1.21923 + 0.137103i
\(355\) 4404.97 4404.97i 0.658568 0.658568i
\(356\) 2509.38 + 11016.6i 0.373586 + 1.64011i
\(357\) −846.694 846.694i −0.125523 0.125523i
\(358\) 754.026 945.092i 0.111317 0.139524i
\(359\) 5554.15i 0.816537i 0.912862 + 0.408269i \(0.133867\pi\)
−0.912862 + 0.408269i \(0.866133\pi\)
\(360\) 983.820 2039.48i 0.144033 0.298584i
\(361\) 8072.37i 1.17690i
\(362\) 5305.95 + 4233.26i 0.770372 + 0.614628i
\(363\) 4338.56 + 4338.56i 0.627315 + 0.627315i
\(364\) 4356.92 + 2740.31i 0.627376 + 0.394591i
\(365\) −3786.34 + 3786.34i −0.542975 + 0.542975i
\(366\) −360.825 3208.75i −0.0515318 0.458263i
\(367\) −3610.98 −0.513601 −0.256800 0.966464i \(-0.582668\pi\)
−0.256800 + 0.966464i \(0.582668\pi\)
\(368\) −3714.36 7730.32i −0.526153 1.09503i
\(369\) 1177.99 0.166190
\(370\) −712.889 6339.59i −0.100166 0.890756i
\(371\) 363.040 363.040i 0.0508035 0.0508035i
\(372\) 621.481 988.118i 0.0866191 0.137719i
\(373\) 1215.49 + 1215.49i 0.168728 + 0.168728i 0.786420 0.617692i \(-0.211932\pi\)
−0.617692 + 0.786420i \(0.711932\pi\)
\(374\) 90.2238 + 71.9836i 0.0124742 + 0.00995236i
\(375\) 5773.62i 0.795062i
\(376\) −3907.26 + 1364.32i −0.535908 + 0.187126i
\(377\) 3921.05i 0.535661i
\(378\) 3691.06 4626.35i 0.502242 0.629508i
\(379\) −7347.81 7347.81i −0.995861 0.995861i 0.00413018 0.999991i \(-0.498685\pi\)
−0.999991 + 0.00413018i \(0.998685\pi\)
\(380\) 17044.6 3882.43i 2.30097 0.524117i
\(381\) −2287.12 + 2287.12i −0.307539 + 0.307539i
\(382\) −11342.1 + 1275.42i −1.51914 + 0.170828i
\(383\) −7668.98 −1.02315 −0.511575 0.859238i \(-0.670938\pi\)
−0.511575 + 0.859238i \(0.670938\pi\)
\(384\) −10.3064 + 6699.79i −0.00136965 + 0.890357i
\(385\) 542.831 0.0718577
\(386\) −2490.77 + 280.088i −0.328438 + 0.0369330i
\(387\) −668.181 + 668.181i −0.0877663 + 0.0877663i
\(388\) 11819.6 2692.27i 1.54651 0.352267i
\(389\) −200.924 200.924i −0.0261884 0.0261884i 0.693891 0.720080i \(-0.255895\pi\)
−0.720080 + 0.693891i \(0.755895\pi\)
\(390\) 6766.96 8481.68i 0.878612 1.10125i
\(391\) 2499.62i 0.323302i
\(392\) 3214.51 1122.43i 0.414176 0.144620i
\(393\) 1295.27i 0.166254i
\(394\) 10224.9 + 8157.80i 1.30742 + 1.04311i
\(395\) 11930.3 + 11930.3i 1.51969 + 1.51969i
\(396\) −52.1440 + 82.9057i −0.00661700 + 0.0105206i
\(397\) 6512.21 6512.21i 0.823271 0.823271i −0.163305 0.986576i \(-0.552215\pi\)
0.986576 + 0.163305i \(0.0522153\pi\)
\(398\) 70.3286 + 625.419i 0.00885743 + 0.0787674i
\(399\) 7844.07 0.984197
\(400\) 5399.06 + 11236.5i 0.674883 + 1.40457i
\(401\) 5565.10 0.693036 0.346518 0.938043i \(-0.387364\pi\)
0.346518 + 0.938043i \(0.387364\pi\)
\(402\) 189.747 + 1687.38i 0.0235416 + 0.209351i
\(403\) −1034.09 + 1034.09i −0.127820 + 0.127820i
\(404\) −5489.53 3452.67i −0.676025 0.425189i
\(405\) −6911.57 6911.57i −0.847997 0.847997i
\(406\) −2594.22 2069.75i −0.317115 0.253005i
\(407\) 275.933i 0.0336057i
\(408\) −848.397 + 1758.75i −0.102946 + 0.213409i
\(409\) 12077.6i 1.46014i −0.683370 0.730072i \(-0.739486\pi\)
0.683370 0.730072i \(-0.260514\pi\)
\(410\) −6640.24 + 8322.85i −0.799850 + 1.00253i
\(411\) 887.810 + 887.810i 0.106551 + 0.106551i
\(412\) −1814.05 7963.99i −0.216921 0.952324i
\(413\) −6127.14 + 6127.14i −0.730017 + 0.730017i
\(414\) 2107.77 237.020i 0.250221 0.0281374i
\(415\) −7922.58 −0.937119
\(416\) 1876.74 8181.09i 0.221189 0.964209i
\(417\) −3009.26 −0.353391
\(418\) −751.373 + 84.4922i −0.0879207 + 0.00988672i
\(419\) −1453.03 + 1453.03i −0.169415 + 0.169415i −0.786722 0.617307i \(-0.788224\pi\)
0.617307 + 0.786722i \(0.288224\pi\)
\(420\) 2039.60 + 8954.22i 0.236958 + 1.04029i
\(421\) −4822.25 4822.25i −0.558247 0.558247i 0.370561 0.928808i \(-0.379165\pi\)
−0.928808 + 0.370561i \(0.879165\pi\)
\(422\) −8799.76 + 11029.6i −1.01508 + 1.27230i
\(423\) 1023.53i 0.117650i
\(424\) −754.105 363.770i −0.0863740 0.0416657i
\(425\) 3633.36i 0.414692i
\(426\) −3563.34 2842.95i −0.405268 0.323336i
\(427\) −2421.04 2421.04i −0.274385 0.274385i
\(428\) −11883.0 7473.87i −1.34203 0.844073i
\(429\) −331.852 + 331.852i −0.0373472 + 0.0373472i
\(430\) −954.407 8487.36i −0.107036 0.951853i
\(431\) 12519.2 1.39914 0.699571 0.714563i \(-0.253374\pi\)
0.699571 + 0.714563i \(0.253374\pi\)
\(432\) −9107.02 3195.67i −1.01426 0.355907i
\(433\) −2921.40 −0.324235 −0.162117 0.986771i \(-0.551832\pi\)
−0.162117 + 0.986771i \(0.551832\pi\)
\(434\) −138.316 1230.02i −0.0152981 0.136043i
\(435\) −4946.99 + 4946.99i −0.545264 + 0.545264i
\(436\) −654.322 + 1040.33i −0.0718724 + 0.114273i
\(437\) 11578.7 + 11578.7i 1.26747 + 1.26747i
\(438\) 3062.90 + 2443.68i 0.334135 + 0.266584i
\(439\) 1140.50i 0.123993i 0.998076 + 0.0619967i \(0.0197468\pi\)
−0.998076 + 0.0619967i \(0.980253\pi\)
\(440\) −291.821 835.743i −0.0316182 0.0905511i
\(441\) 842.062i 0.0909256i
\(442\) 1525.69 1912.30i 0.164185 0.205789i
\(443\) −1843.05 1843.05i −0.197665 0.197665i 0.601333 0.798999i \(-0.294637\pi\)
−0.798999 + 0.601333i \(0.794637\pi\)
\(444\) −4551.64 + 1036.78i −0.486511 + 0.110818i
\(445\) 17859.0 17859.0i 1.90247 1.90247i
\(446\) 16419.9 1846.42i 1.74328 0.196033i
\(447\) −3963.43 −0.419382
\(448\) 4422.07 + 5560.12i 0.466346 + 0.586364i
\(449\) 1752.13 0.184161 0.0920805 0.995752i \(-0.470648\pi\)
0.0920805 + 0.995752i \(0.470648\pi\)
\(450\) −3063.79 + 344.524i −0.320952 + 0.0360911i
\(451\) 325.637 325.637i 0.0339993 0.0339993i
\(452\) −13433.7 + 3059.93i −1.39793 + 0.318423i
\(453\) 11562.6 + 11562.6i 1.19925 + 1.19925i
\(454\) −2817.80 + 3531.82i −0.291291 + 0.365102i
\(455\) 11505.3i 1.18544i
\(456\) −4216.90 12076.7i −0.433058 1.24023i
\(457\) 12875.6i 1.31794i 0.752171 + 0.658968i \(0.229007\pi\)
−0.752171 + 0.658968i \(0.770993\pi\)
\(458\) −9084.54 7247.95i −0.926840 0.739464i
\(459\) −1989.06 1989.06i −0.202268 0.202268i
\(460\) −10206.7 + 16228.0i −1.03454 + 1.64486i
\(461\) −13679.7 + 13679.7i −1.38205 + 1.38205i −0.541085 + 0.840968i \(0.681986\pi\)
−0.840968 + 0.541085i \(0.818014\pi\)
\(462\) −44.3873 394.727i −0.00446987 0.0397497i
\(463\) 15002.4 1.50588 0.752938 0.658091i \(-0.228636\pi\)
0.752938 + 0.658091i \(0.228636\pi\)
\(464\) −1791.97 + 5106.74i −0.179289 + 0.510936i
\(465\) −2609.32 −0.260224
\(466\) −232.009 2063.22i −0.0230636 0.205100i
\(467\) 9669.42 9669.42i 0.958131 0.958131i −0.0410271 0.999158i \(-0.513063\pi\)
0.999158 + 0.0410271i \(0.0130630\pi\)
\(468\) 1757.19 + 1105.19i 0.173560 + 0.109161i
\(469\) 1273.15 + 1273.15i 0.125349 + 0.125349i
\(470\) 7231.54 + 5769.56i 0.709715 + 0.566234i
\(471\) 8070.75i 0.789555i
\(472\) 12727.3 + 6139.46i 1.24114 + 0.598711i
\(473\) 369.416i 0.0359107i
\(474\) 7699.75 9650.83i 0.746120 0.935184i
\(475\) −16830.4 16830.4i −1.62575 1.62575i
\(476\) 459.853 + 2018.84i 0.0442801 + 0.194397i
\(477\) 146.418 146.418i 0.0140545 0.0140545i
\(478\) −1438.54 + 161.765i −0.137651 + 0.0154789i
\(479\) −3072.68 −0.293099 −0.146550 0.989203i \(-0.546817\pi\)
−0.146550 + 0.989203i \(0.546817\pi\)
\(480\) 12689.5 7953.88i 1.20665 0.756340i
\(481\) 5848.41 0.554396
\(482\) 16640.3 1871.21i 1.57250 0.176828i
\(483\) −6082.76 + 6082.76i −0.573033 + 0.573033i
\(484\) −2356.34 10344.7i −0.221294 0.971520i
\(485\) −19160.7 19160.7i −1.79390 1.79390i
\(486\) 2721.71 3411.38i 0.254031 0.318402i
\(487\) 8689.64i 0.808553i 0.914637 + 0.404276i \(0.132477\pi\)
−0.914637 + 0.404276i \(0.867523\pi\)
\(488\) −2425.91 + 5028.98i −0.225033 + 0.466498i
\(489\) 16810.8i 1.55462i
\(490\) −5949.40 4746.63i −0.548503 0.437614i
\(491\) 11194.3 + 11194.3i 1.02891 + 1.02891i 0.999570 + 0.0293379i \(0.00933987\pi\)
0.0293379 + 0.999570i \(0.490660\pi\)
\(492\) 6595.06 + 4147.99i 0.604326 + 0.380094i
\(493\) −1115.36 + 1115.36i −0.101893 + 0.101893i
\(494\) 1790.81 + 15925.4i 0.163102 + 1.45044i
\(495\) 218.929 0.0198790
\(496\) −1819.38 + 874.198i −0.164703 + 0.0791384i
\(497\) −4833.62 −0.436253
\(498\) 647.830 + 5761.03i 0.0582930 + 0.518389i
\(499\) −1632.72 + 1632.72i −0.146474 + 0.146474i −0.776541 0.630067i \(-0.783027\pi\)
0.630067 + 0.776541i \(0.283027\pi\)
\(500\) 5315.36 8451.10i 0.475420 0.755889i
\(501\) −9972.47 9972.47i −0.889295 0.889295i
\(502\) −967.213 771.674i −0.0859936 0.0686086i
\(503\) 6901.81i 0.611802i −0.952063 0.305901i \(-0.901042\pi\)
0.952063 0.305901i \(-0.0989577\pi\)
\(504\) −1658.75 + 579.195i −0.146601 + 0.0511893i
\(505\) 14496.2i 1.27737i
\(506\) 517.139 648.180i 0.0454341 0.0569468i
\(507\) −153.630 153.630i −0.0134575 0.0134575i
\(508\) 5453.34 1242.17i 0.476285 0.108489i
\(509\) 92.9712 92.9712i 0.00809603 0.00809603i −0.703047 0.711143i \(-0.748178\pi\)
0.711143 + 0.703047i \(0.248178\pi\)
\(510\) 4337.54 487.758i 0.376607 0.0423496i
\(511\) 4154.79 0.359681
\(512\) 6183.11 9797.29i 0.533706 0.845670i
\(513\) 18427.3 1.58594
\(514\) 909.891 102.318i 0.0780809 0.00878023i
\(515\) −12910.4 + 12910.4i −1.10466 + 1.10466i
\(516\) −6093.67 + 1388.02i −0.519881 + 0.118419i
\(517\) −282.939 282.939i −0.0240689 0.0240689i
\(518\) −3087.12 + 3869.38i −0.261854 + 0.328206i
\(519\) 9958.43i 0.842248i
\(520\) −17713.6 + 6185.15i −1.49383 + 0.521609i
\(521\) 11931.3i 1.00330i −0.865071 0.501649i \(-0.832727\pi\)
0.865071 0.501649i \(-0.167273\pi\)
\(522\) −1046.27 834.750i −0.0877281 0.0699924i
\(523\) −9702.46 9702.46i −0.811203 0.811203i 0.173611 0.984814i \(-0.444456\pi\)
−0.984814 + 0.173611i \(0.944456\pi\)
\(524\) 1192.47 1895.95i 0.0994144 0.158063i
\(525\) 8841.69 8841.69i 0.735015 0.735015i
\(526\) 849.949 + 7558.43i 0.0704554 + 0.626546i
\(527\) −588.301 −0.0486277
\(528\) −583.861 + 280.541i −0.0481237 + 0.0231230i
\(529\) −5790.59 −0.475926
\(530\) 209.138 + 1859.82i 0.0171403 + 0.152425i
\(531\) −2471.13 + 2471.13i −0.201955 + 0.201955i
\(532\) −11481.7 7221.48i −0.935706 0.588517i
\(533\) −6901.89 6901.89i −0.560889 0.560889i
\(534\) −14446.8 11526.1i −1.17074 0.934052i
\(535\) 31379.4i 2.53579i
\(536\) 1275.71 2644.58i 0.102803 0.213113i
\(537\) 1977.60i 0.158920i
\(538\) 11734.3 14707.7i 0.940335 1.17861i
\(539\) 232.774 + 232.774i 0.0186017 + 0.0186017i
\(540\) 4791.44 + 21035.3i 0.381834 + 1.67632i
\(541\) −8556.67 + 8556.67i −0.680000 + 0.680000i −0.960000 0.280000i \(-0.909666\pi\)
0.280000 + 0.960000i \(0.409666\pi\)
\(542\) −5674.75 + 638.128i −0.449726 + 0.0505719i
\(543\) −11102.7 −0.877462
\(544\) 2860.99 1793.30i 0.225485 0.141336i
\(545\) 2747.20 0.215921
\(546\) −8366.25 + 940.789i −0.655756 + 0.0737400i
\(547\) −45.1953 + 45.1953i −0.00353274 + 0.00353274i −0.708871 0.705338i \(-0.750795\pi\)
0.705338 + 0.708871i \(0.250795\pi\)
\(548\) −482.183 2116.87i −0.0375873 0.165015i
\(549\) −976.430 976.430i −0.0759071 0.0759071i
\(550\) −751.696 + 942.172i −0.0582771 + 0.0730443i
\(551\) 10333.1i 0.798917i
\(552\) 12635.1 + 6094.99i 0.974247 + 0.469964i
\(553\) 13091.2i 1.00668i
\(554\) −9632.37 7685.02i −0.738700 0.589360i
\(555\) 7378.64 + 7378.64i 0.564335 + 0.564335i
\(556\) 4404.79 + 2770.41i 0.335980 + 0.211316i
\(557\) 4279.60 4279.60i 0.325552 0.325552i −0.525340 0.850892i \(-0.676062\pi\)
0.850892 + 0.525340i \(0.176062\pi\)
\(558\) −55.7841 496.078i −0.00423213 0.0376355i
\(559\) 7829.77 0.592422
\(560\) 5258.06 14984.4i 0.396774 1.13073i
\(561\) −188.793 −0.0142083
\(562\) 1230.61 + 10943.5i 0.0923665 + 0.821398i
\(563\) 14593.9 14593.9i 1.09247 1.09247i 0.0972023 0.995265i \(-0.469011\pi\)
0.995265 0.0972023i \(-0.0309894\pi\)
\(564\) 3604.10 5730.30i 0.269078 0.427818i
\(565\) 21777.3 + 21777.3i 1.62155 + 1.62155i
\(566\) 6336.05 + 5055.11i 0.470537 + 0.375410i
\(567\) 7584.14i 0.561736i
\(568\) 2598.51 + 7441.86i 0.191956 + 0.549742i
\(569\) 21728.1i 1.60086i −0.599425 0.800431i \(-0.704604\pi\)
0.599425 0.800431i \(-0.295396\pi\)
\(570\) −17832.8 + 22351.6i −1.31041 + 1.64247i
\(571\) 16078.0 + 16078.0i 1.17836 + 1.17836i 0.980161 + 0.198202i \(0.0635102\pi\)
0.198202 + 0.980161i \(0.436490\pi\)
\(572\) 791.259 180.234i 0.0578395 0.0131747i
\(573\) 13201.0 13201.0i 0.962446 0.962446i
\(574\) 8209.59 923.171i 0.596971 0.0671297i
\(575\) 26102.5 1.89313
\(576\) 1783.46 + 2242.45i 0.129012 + 0.162214i
\(577\) −26648.2 −1.92267 −0.961335 0.275383i \(-0.911195\pi\)
−0.961335 + 0.275383i \(0.911195\pi\)
\(578\) −12831.1 + 1442.86i −0.923361 + 0.103832i
\(579\) 2899.01 2899.01i 0.208081 0.208081i
\(580\) 11795.5 2686.79i 0.844449 0.192349i
\(581\) 4346.77 + 4346.77i 0.310386 + 0.310386i
\(582\) −12366.2 + 15499.7i −0.880748 + 1.10393i
\(583\) 80.9495i 0.00575058i
\(584\) −2233.58 6396.72i −0.158264 0.453250i
\(585\) 4640.20i 0.327946i
\(586\) −3132.05 2498.85i −0.220791 0.176154i
\(587\) 1342.62 + 1342.62i 0.0944050 + 0.0944050i 0.752732 0.658327i \(-0.228736\pi\)
−0.658327 + 0.752732i \(0.728736\pi\)
\(588\) −2965.10 + 4714.33i −0.207957 + 0.330639i
\(589\) 2725.11 2725.11i 0.190639 0.190639i
\(590\) −3529.68 31388.8i −0.246296 2.19026i
\(591\) −21395.7 −1.48917
\(592\) 7616.92 + 2672.79i 0.528806 + 0.185559i
\(593\) 4474.79 0.309878 0.154939 0.987924i \(-0.450482\pi\)
0.154939 + 0.987924i \(0.450482\pi\)
\(594\) −104.275 927.295i −0.00720276 0.0640528i
\(595\) 3272.73 3272.73i 0.225494 0.225494i
\(596\) 5801.45 + 3648.85i 0.398719 + 0.250776i
\(597\) −727.925 727.925i −0.0499028 0.0499028i
\(598\) −13738.2 10960.8i −0.939458 0.749531i
\(599\) 12603.8i 0.859725i 0.902894 + 0.429863i \(0.141438\pi\)
−0.902894 + 0.429863i \(0.858562\pi\)
\(600\) −18365.9 8859.47i −1.24964 0.602811i
\(601\) 7220.64i 0.490077i 0.969513 + 0.245038i \(0.0788006\pi\)
−0.969513 + 0.245038i \(0.921199\pi\)
\(602\) −4133.00 + 5180.28i −0.279814 + 0.350718i
\(603\) 513.474 + 513.474i 0.0346771 + 0.0346771i
\(604\) −6279.83 27569.6i −0.423051 1.85727i
\(605\) −16769.8 + 16769.8i −1.12693 + 1.12693i
\(606\) 10541.1 1185.35i 0.706606 0.0794581i
\(607\) −13695.6 −0.915796 −0.457898 0.889005i \(-0.651397\pi\)
−0.457898 + 0.889005i \(0.651397\pi\)
\(608\) −4945.74 + 21559.5i −0.329895 + 1.43808i
\(609\) 5428.39 0.361198
\(610\) 12402.8 1394.70i 0.823236 0.0925733i
\(611\) −5996.90 + 5996.90i −0.397068 + 0.397068i
\(612\) 185.463 + 814.215i 0.0122498 + 0.0537789i
\(613\) −2358.34 2358.34i −0.155387 0.155387i 0.625132 0.780519i \(-0.285045\pi\)
−0.780519 + 0.625132i \(0.785045\pi\)
\(614\) 7400.47 9275.72i 0.486415 0.609670i
\(615\) 17415.5i 1.14189i
\(616\) −298.426 + 618.644i −0.0195194 + 0.0404641i
\(617\) 4186.39i 0.273157i 0.990629 + 0.136579i \(0.0436106\pi\)
−0.990629 + 0.136579i \(0.956389\pi\)
\(618\) 10443.7 + 8332.31i 0.679784 + 0.542354i
\(619\) −4800.50 4800.50i −0.311710 0.311710i 0.533862 0.845572i \(-0.320740\pi\)
−0.845572 + 0.533862i \(0.820740\pi\)
\(620\) 3819.37 + 2402.21i 0.247403 + 0.155605i
\(621\) −14289.6 + 14289.6i −0.923387 + 0.923387i
\(622\) −920.125 8182.50i −0.0593145 0.527473i
\(623\) −19596.9 −1.26024
\(624\) 5946.06 + 12374.9i 0.381463 + 0.793901i
\(625\) 2031.54 0.130018
\(626\) 2619.47 + 23294.5i 0.167245 + 1.48727i
\(627\) 874.522 874.522i 0.0557018 0.0557018i
\(628\) −7430.17 + 11813.5i −0.472127 + 0.750654i
\(629\) 1663.60 + 1663.60i 0.105457 + 0.105457i
\(630\) 3070.01 + 2449.36i 0.194146 + 0.154896i
\(631\) 16106.3i 1.01614i −0.861316 0.508069i \(-0.830360\pi\)
0.861316 0.508069i \(-0.169640\pi\)
\(632\) −20155.3 + 7037.73i −1.26857 + 0.442952i
\(633\) 23079.3i 1.44917i
\(634\) 14324.7 17954.5i 0.897330 1.12471i
\(635\) −8840.39 8840.39i −0.552473 0.552473i
\(636\) 1335.30 304.155i 0.0832515 0.0189631i
\(637\) 4933.66 4933.66i 0.306874 0.306874i
\(638\) −519.978 + 58.4717i −0.0322667 + 0.00362840i
\(639\) −1949.45 −0.120687
\(640\) −25896.7 39.8373i −1.59946 0.00246048i
\(641\) −6682.21 −0.411749 −0.205875 0.978578i \(-0.566004\pi\)
−0.205875 + 0.978578i \(0.566004\pi\)
\(642\) 22818.0 2565.89i 1.40273 0.157738i
\(643\) −4983.47 + 4983.47i −0.305644 + 0.305644i −0.843217 0.537573i \(-0.819341\pi\)
0.537573 + 0.843217i \(0.319341\pi\)
\(644\) 14503.6 3303.64i 0.887455 0.202145i
\(645\) 9878.43 + 9878.43i 0.603043 + 0.603043i
\(646\) −4020.63 + 5039.43i −0.244875 + 0.306926i
\(647\) 5078.45i 0.308585i 0.988025 + 0.154292i \(0.0493098\pi\)
−0.988025 + 0.154292i \(0.950690\pi\)
\(648\) 11676.6 4077.17i 0.707869 0.247170i
\(649\) 1366.21i 0.0826324i
\(650\) 19969.3 + 15932.2i 1.20502 + 0.961404i
\(651\) 1431.62 + 1431.62i 0.0861896 + 0.0861896i
\(652\) 15476.5 24606.7i 0.929610 1.47802i
\(653\) 6189.91 6189.91i 0.370949 0.370949i −0.496874 0.867823i \(-0.665519\pi\)
0.867823 + 0.496874i \(0.165519\pi\)
\(654\) −224.639 1997.67i −0.0134313 0.119442i
\(655\) −5006.62 −0.298664
\(656\) −5834.72 12143.2i −0.347267 0.722733i
\(657\) 1675.67 0.0995037
\(658\) −802.123 7133.12i −0.0475228 0.422611i
\(659\) 5751.19 5751.19i 0.339962 0.339962i −0.516391 0.856353i \(-0.672725\pi\)
0.856353 + 0.516391i \(0.172725\pi\)
\(660\) 1225.68 + 770.899i 0.0722873 + 0.0454655i
\(661\) −6305.38 6305.38i −0.371030 0.371030i 0.496822 0.867852i \(-0.334500\pi\)
−0.867852 + 0.496822i \(0.834500\pi\)
\(662\) 14068.2 + 11224.1i 0.825946 + 0.658967i
\(663\) 4001.47i 0.234396i
\(664\) 4355.51 9029.08i 0.254558 0.527705i
\(665\) 30319.7i 1.76804i
\(666\) −1245.06 + 1560.56i −0.0724404 + 0.0907964i
\(667\) 8012.87 + 8012.87i 0.465157 + 0.465157i
\(668\) 5416.20 + 23778.1i 0.313711 + 1.37725i
\(669\) −19111.1 + 19111.1i −1.10445 + 1.10445i
\(670\) −6522.24 + 733.429i −0.376084 + 0.0422908i
\(671\) −539.837 −0.0310584
\(672\) −11326.1 2598.20i −0.650169 0.149149i
\(673\) 14664.4 0.839925 0.419963 0.907541i \(-0.362043\pi\)
0.419963 + 0.907541i \(0.362043\pi\)
\(674\) −16471.0 + 1852.16i −0.941302 + 0.105850i
\(675\) 20770.9 20770.9i 1.18440 1.18440i
\(676\) 83.4389 + 366.312i 0.00474732 + 0.0208416i
\(677\) 5795.16 + 5795.16i 0.328990 + 0.328990i 0.852202 0.523212i \(-0.175267\pi\)
−0.523212 + 0.852202i \(0.675267\pi\)
\(678\) 14054.9 17616.4i 0.796131 0.997866i
\(679\) 21025.2i 1.18833i
\(680\) −6798.09 3279.31i −0.383375 0.184935i
\(681\) 7390.32i 0.415855i
\(682\) −152.553 121.712i −0.00856534 0.00683371i
\(683\) −13134.1 13134.1i −0.735816 0.735816i 0.235950 0.971765i \(-0.424180\pi\)
−0.971765 + 0.235950i \(0.924180\pi\)
\(684\) −4630.68 2912.49i −0.258858 0.162810i
\(685\) −3431.65 + 3431.65i −0.191411 + 0.191411i
\(686\) 2164.15 + 19245.3i 0.120448 + 1.07112i
\(687\) 19009.4 1.05568
\(688\) 10197.4 + 3578.30i 0.565077 + 0.198287i
\(689\) −1715.73 −0.0948679
\(690\) −3504.11 31161.4i −0.193332 1.71927i
\(691\) 14324.0 14324.0i 0.788583 0.788583i −0.192679 0.981262i \(-0.561718\pi\)
0.981262 + 0.192679i \(0.0617175\pi\)
\(692\) −9168.02 + 14576.6i −0.503636 + 0.800750i
\(693\) −120.116 120.116i −0.00658419 0.00658419i
\(694\) −6344.58 5061.92i −0.347027 0.276870i
\(695\) 11631.7i 0.634843i
\(696\) −2918.25 8357.56i −0.158931 0.455162i
\(697\) 3926.54i 0.213383i
\(698\) −4847.76 + 6076.15i −0.262880 + 0.329493i
\(699\) 2401.37 + 2401.37i 0.129940 + 0.129940i
\(700\) −21081.9 + 4802.06i −1.13832 + 0.259287i
\(701\) 15987.2 15987.2i 0.861382 0.861382i −0.130117 0.991499i \(-0.541535\pi\)
0.991499 + 0.130117i \(0.0415351\pi\)
\(702\) −19654.0 + 2210.10i −1.05669 + 0.118825i
\(703\) −15412.2 −0.826859
\(704\) 1112.90 + 126.880i 0.0595794 + 0.00679255i
\(705\) −15132.0 −0.808373
\(706\) −21217.0 + 2385.86i −1.13104 + 0.127186i
\(707\) 7953.40 7953.40i 0.423081 0.423081i
\(708\) −22536.2 + 5133.32i −1.19627 + 0.272489i
\(709\) 19580.4 + 19580.4i 1.03718 + 1.03718i 0.999282 + 0.0378960i \(0.0120656\pi\)
0.0378960 + 0.999282i \(0.487934\pi\)
\(710\) 10988.8 13773.4i 0.580851 0.728035i
\(711\) 5279.82i 0.278493i
\(712\) 10535.1 + 30171.4i 0.554522 + 1.58809i
\(713\) 4226.43i 0.221993i
\(714\) −2647.42 2112.20i −0.138764 0.110710i
\(715\) −1282.71 1282.71i −0.0670916 0.0670916i
\(716\) 1820.64 2894.70i 0.0950285 0.151090i
\(717\) 1674.32 1674.32i 0.0872085 0.0872085i
\(718\) 1755.48 + 15611.1i 0.0912448 + 0.811423i
\(719\) −2111.24 −0.109507 −0.0547537 0.998500i \(-0.517437\pi\)
−0.0547537 + 0.998500i \(0.517437\pi\)
\(720\) 2120.62 6043.35i 0.109765 0.312809i
\(721\) 14166.7 0.731757
\(722\) −2551.40 22689.1i −0.131514 1.16953i
\(723\) −19367.6 + 19367.6i −0.996250 + 0.996250i
\(724\) 16251.5 + 10221.5i 0.834229 + 0.524692i
\(725\) −11647.2 11647.2i −0.596645 0.596645i
\(726\) 13565.7 + 10823.2i 0.693486 + 0.553286i
\(727\) 14763.6i 0.753164i −0.926383 0.376582i \(-0.877099\pi\)
0.926383 0.376582i \(-0.122901\pi\)
\(728\) 13112.2 + 6325.14i 0.667541 + 0.322013i
\(729\) 21896.2i 1.11244i
\(730\) −9445.57 + 11839.0i −0.478899 + 0.600250i
\(731\) 2227.21 + 2227.21i 0.112690 + 0.112690i
\(732\) −2028.35 8904.83i −0.102418 0.449634i
\(733\) 3419.77 3419.77i 0.172322 0.172322i −0.615677 0.787999i \(-0.711117\pi\)
0.787999 + 0.615677i \(0.211117\pi\)
\(734\) −10149.4 + 1141.31i −0.510384 + 0.0573929i
\(735\) 12449.1 0.624751
\(736\) −12883.3 20553.7i −0.645223 1.02938i
\(737\) 283.883 0.0141886
\(738\) 3311.00 372.324i 0.165149 0.0185710i
\(739\) −11324.8 + 11324.8i −0.563723 + 0.563723i −0.930363 0.366640i \(-0.880508\pi\)
0.366640 + 0.930363i \(0.380508\pi\)
\(740\) −4007.45 17593.4i −0.199077 0.873984i
\(741\) −18535.5 18535.5i −0.918919 0.918919i
\(742\) 905.657 1135.15i 0.0448083 0.0561625i
\(743\) 20313.3i 1.00299i 0.865160 + 0.501495i \(0.167217\pi\)
−0.865160 + 0.501495i \(0.832783\pi\)
\(744\) 1434.50 2973.74i 0.0706870 0.146536i
\(745\) 15319.9i 0.753391i
\(746\) 3800.57 + 3032.22i 0.186526 + 0.148817i
\(747\) 1753.09 + 1753.09i 0.0858665 + 0.0858665i
\(748\) 276.345 + 173.808i 0.0135082 + 0.00849608i
\(749\) 17216.5 17216.5i 0.839888 0.839888i
\(750\) 1824.84 + 16228.0i 0.0888451 + 0.790083i
\(751\) 28755.3 1.39720 0.698598 0.715514i \(-0.253808\pi\)
0.698598 + 0.715514i \(0.253808\pi\)
\(752\) −10551.0 + 5069.65i −0.511641 + 0.245839i
\(753\) 2023.89 0.0979477
\(754\) 1239.31 + 11020.9i 0.0598581 + 0.532306i
\(755\) −44693.0 + 44693.0i −2.15436 + 2.15436i
\(756\) 8912.27 14170.0i 0.428751 0.681689i
\(757\) −23006.0 23006.0i −1.10458 1.10458i −0.993850 0.110730i \(-0.964681\pi\)
−0.110730 0.993850i \(-0.535319\pi\)
\(758\) −22975.0 18330.2i −1.10091 0.878340i
\(759\) 1356.31i 0.0648631i
\(760\) 46680.3 16299.6i 2.22799 0.777958i
\(761\) 9298.53i 0.442932i −0.975168 0.221466i \(-0.928916\pi\)
0.975168 0.221466i \(-0.0710843\pi\)
\(762\) −5705.54 + 7151.30i −0.271247 + 0.339979i
\(763\) −1507.27 1507.27i −0.0715160 0.0715160i
\(764\) −31476.2 + 7169.69i −1.49054 + 0.339516i
\(765\) 1319.92 1319.92i 0.0623815 0.0623815i
\(766\) −21555.3 + 2423.90i −1.01674 + 0.114333i
\(767\) 28956.8 1.36319
\(768\) 2088.61 + 18834.4i 0.0981329 + 0.884934i
\(769\) −20402.0 −0.956717 −0.478358 0.878165i \(-0.658768\pi\)
−0.478358 + 0.878165i \(0.658768\pi\)
\(770\) 1525.74 171.570i 0.0714076 0.00802981i
\(771\) −1059.02 + 1059.02i −0.0494679 + 0.0494679i
\(772\) −6912.32 + 1574.50i −0.322254 + 0.0734033i
\(773\) 7337.03 + 7337.03i 0.341390 + 0.341390i 0.856890 0.515500i \(-0.172394\pi\)