Properties

Label 108.4.i.a.13.2
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.40571 - 2.75494i) q^{3} +(8.18465 + 6.86774i) q^{5} +(-24.4722 - 8.90714i) q^{7} +(11.8206 + 24.2749i) q^{9} +O(q^{10})\) \(q+(-4.40571 - 2.75494i) q^{3} +(8.18465 + 6.86774i) q^{5} +(-24.4722 - 8.90714i) q^{7} +(11.8206 + 24.2749i) q^{9} +(0.555929 - 0.466480i) q^{11} +(-12.2754 + 69.6174i) q^{13} +(-17.1390 - 52.8055i) q^{15} +(-42.6108 + 73.8041i) q^{17} +(75.7224 + 131.155i) q^{19} +(83.2788 + 106.662i) q^{21} +(-156.978 + 57.1353i) q^{23} +(-1.88334 - 10.6810i) q^{25} +(14.7977 - 139.514i) q^{27} +(-42.3122 - 239.964i) q^{29} +(57.5825 - 20.9583i) q^{31} +(-3.73439 + 0.523626i) q^{33} +(-139.124 - 240.970i) q^{35} +(7.30212 - 12.6477i) q^{37} +(245.874 - 272.896i) q^{39} +(-13.2323 + 75.0441i) q^{41} +(-152.644 + 128.083i) q^{43} +(-69.9662 + 279.863i) q^{45} +(252.257 + 91.8142i) q^{47} +(256.797 + 215.478i) q^{49} +(391.057 - 207.770i) q^{51} -52.6859 q^{53} +7.75374 q^{55} +(27.7129 - 786.442i) q^{57} +(-575.596 - 482.982i) q^{59} +(-34.9282 - 12.7128i) q^{61} +(-73.0561 - 699.349i) q^{63} +(-578.584 + 485.490i) q^{65} +(-88.9446 + 504.430i) q^{67} +(849.003 + 180.743i) q^{69} +(298.140 - 516.394i) q^{71} +(187.698 + 325.103i) q^{73} +(-21.1280 + 52.2458i) q^{75} +(-17.7598 + 6.46403i) q^{77} +(61.3493 + 347.929i) q^{79} +(-449.546 + 573.890i) q^{81} +(14.6810 + 83.2603i) q^{83} +(-855.622 + 311.421i) q^{85} +(-474.672 + 1173.78i) q^{87} +(-351.204 - 608.304i) q^{89} +(920.499 - 1594.35i) q^{91} +(-311.431 - 66.2999i) q^{93} +(-280.977 + 1593.50i) q^{95} +(10.3720 - 8.70312i) q^{97} +(17.8952 + 7.98106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.40571 2.75494i −0.847880 0.530188i
\(4\) 0 0
\(5\) 8.18465 + 6.86774i 0.732057 + 0.614269i 0.930692 0.365805i \(-0.119206\pi\)
−0.198634 + 0.980074i \(0.563651\pi\)
\(6\) 0 0
\(7\) −24.4722 8.90714i −1.32137 0.480941i −0.417475 0.908688i \(-0.637085\pi\)
−0.903898 + 0.427748i \(0.859307\pi\)
\(8\) 0 0
\(9\) 11.8206 + 24.2749i 0.437801 + 0.899072i
\(10\) 0 0
\(11\) 0.555929 0.466480i 0.0152381 0.0127863i −0.635137 0.772400i \(-0.719056\pi\)
0.650375 + 0.759613i \(0.274612\pi\)
\(12\) 0 0
\(13\) −12.2754 + 69.6174i −0.261892 + 1.48526i 0.515851 + 0.856678i \(0.327476\pi\)
−0.777742 + 0.628583i \(0.783635\pi\)
\(14\) 0 0
\(15\) −17.1390 52.8055i −0.295019 0.908954i
\(16\) 0 0
\(17\) −42.6108 + 73.8041i −0.607920 + 1.05295i 0.383662 + 0.923473i \(0.374663\pi\)
−0.991583 + 0.129475i \(0.958671\pi\)
\(18\) 0 0
\(19\) 75.7224 + 131.155i 0.914311 + 1.58363i 0.807907 + 0.589310i \(0.200600\pi\)
0.106404 + 0.994323i \(0.466066\pi\)
\(20\) 0 0
\(21\) 83.2788 + 106.662i 0.865377 + 1.10836i
\(22\) 0 0
\(23\) −156.978 + 57.1353i −1.42314 + 0.517979i −0.934956 0.354764i \(-0.884561\pi\)
−0.488180 + 0.872743i \(0.662339\pi\)
\(24\) 0 0
\(25\) −1.88334 10.6810i −0.0150668 0.0854478i
\(26\) 0 0
\(27\) 14.7977 139.514i 0.105475 0.994422i
\(28\) 0 0
\(29\) −42.3122 239.964i −0.270937 1.53656i −0.751578 0.659644i \(-0.770707\pi\)
0.480641 0.876918i \(-0.340404\pi\)
\(30\) 0 0
\(31\) 57.5825 20.9583i 0.333617 0.121427i −0.169780 0.985482i \(-0.554306\pi\)
0.503397 + 0.864055i \(0.332083\pi\)
\(32\) 0 0
\(33\) −3.73439 + 0.523626i −0.0196992 + 0.00276217i
\(34\) 0 0
\(35\) −139.124 240.970i −0.671894 1.16375i
\(36\) 0 0
\(37\) 7.30212 12.6477i 0.0324449 0.0561962i −0.849347 0.527835i \(-0.823004\pi\)
0.881792 + 0.471639i \(0.156337\pi\)
\(38\) 0 0
\(39\) 245.874 272.896i 1.00952 1.12047i
\(40\) 0 0
\(41\) −13.2323 + 75.0441i −0.0504034 + 0.285852i −0.999583 0.0288839i \(-0.990805\pi\)
0.949179 + 0.314735i \(0.101916\pi\)
\(42\) 0 0
\(43\) −152.644 + 128.083i −0.541348 + 0.454245i −0.871999 0.489508i \(-0.837176\pi\)
0.330650 + 0.943753i \(0.392732\pi\)
\(44\) 0 0
\(45\) −69.9662 + 279.863i −0.231777 + 0.927100i
\(46\) 0 0
\(47\) 252.257 + 91.8142i 0.782884 + 0.284946i 0.702375 0.711807i \(-0.252123\pi\)
0.0805091 + 0.996754i \(0.474345\pi\)
\(48\) 0 0
\(49\) 256.797 + 215.478i 0.748679 + 0.628216i
\(50\) 0 0
\(51\) 391.057 207.770i 1.07370 0.570462i
\(52\) 0 0
\(53\) −52.6859 −0.136546 −0.0682732 0.997667i \(-0.521749\pi\)
−0.0682732 + 0.997667i \(0.521749\pi\)
\(54\) 0 0
\(55\) 7.75374 0.0190093
\(56\) 0 0
\(57\) 27.7129 786.442i 0.0643975 1.82749i
\(58\) 0 0
\(59\) −575.596 482.982i −1.27010 1.06574i −0.994529 0.104465i \(-0.966687\pi\)
−0.275576 0.961279i \(-0.588869\pi\)
\(60\) 0 0
\(61\) −34.9282 12.7128i −0.0733130 0.0266838i 0.305103 0.952319i \(-0.401309\pi\)
−0.378416 + 0.925636i \(0.623531\pi\)
\(62\) 0 0
\(63\) −73.0561 699.349i −0.146098 1.39857i
\(64\) 0 0
\(65\) −578.584 + 485.490i −1.10407 + 0.926424i
\(66\) 0 0
\(67\) −88.9446 + 504.430i −0.162184 + 0.919790i 0.789737 + 0.613445i \(0.210217\pi\)
−0.951921 + 0.306344i \(0.900894\pi\)
\(68\) 0 0
\(69\) 849.003 + 180.743i 1.48128 + 0.315346i
\(70\) 0 0
\(71\) 298.140 516.394i 0.498349 0.863165i −0.501649 0.865071i \(-0.667273\pi\)
0.999998 + 0.00190566i \(0.000606591\pi\)
\(72\) 0 0
\(73\) 187.698 + 325.103i 0.300937 + 0.521239i 0.976349 0.216203i \(-0.0693672\pi\)
−0.675411 + 0.737441i \(0.736034\pi\)
\(74\) 0 0
\(75\) −21.1280 + 52.2458i −0.0325286 + 0.0804377i
\(76\) 0 0
\(77\) −17.7598 + 6.46403i −0.0262846 + 0.00956682i
\(78\) 0 0
\(79\) 61.3493 + 347.929i 0.0873714 + 0.495508i 0.996820 + 0.0796906i \(0.0253932\pi\)
−0.909448 + 0.415817i \(0.863496\pi\)
\(80\) 0 0
\(81\) −449.546 + 573.890i −0.616661 + 0.787229i
\(82\) 0 0
\(83\) 14.6810 + 83.2603i 0.0194151 + 0.110109i 0.992975 0.118322i \(-0.0377516\pi\)
−0.973560 + 0.228431i \(0.926641\pi\)
\(84\) 0 0
\(85\) −855.622 + 311.421i −1.09183 + 0.397392i
\(86\) 0 0
\(87\) −474.672 + 1173.78i −0.584945 + 1.44647i
\(88\) 0 0
\(89\) −351.204 608.304i −0.418287 0.724495i 0.577480 0.816405i \(-0.304036\pi\)
−0.995767 + 0.0919098i \(0.970703\pi\)
\(90\) 0 0
\(91\) 920.499 1594.35i 1.06038 1.83663i
\(92\) 0 0
\(93\) −311.431 66.2999i −0.347246 0.0739246i
\(94\) 0 0
\(95\) −280.977 + 1593.50i −0.303449 + 1.72094i
\(96\) 0 0
\(97\) 10.3720 8.70312i 0.0108569 0.00910998i −0.637343 0.770580i \(-0.719967\pi\)
0.648200 + 0.761470i \(0.275522\pi\)
\(98\) 0 0
\(99\) 17.8952 + 7.98106i 0.0181670 + 0.00810229i
\(100\) 0 0
\(101\) 1713.61 + 623.703i 1.68822 + 0.614463i 0.994400 0.105683i \(-0.0337028\pi\)
0.693823 + 0.720146i \(0.255925\pi\)
\(102\) 0 0
\(103\) 547.583 + 459.477i 0.523834 + 0.439549i 0.865966 0.500103i \(-0.166704\pi\)
−0.342132 + 0.939652i \(0.611149\pi\)
\(104\) 0 0
\(105\) −50.9167 + 1444.92i −0.0473234 + 1.34295i
\(106\) 0 0
\(107\) −1919.61 −1.73435 −0.867175 0.498004i \(-0.834066\pi\)
−0.867175 + 0.498004i \(0.834066\pi\)
\(108\) 0 0
\(109\) −49.6874 −0.0436623 −0.0218311 0.999762i \(-0.506950\pi\)
−0.0218311 + 0.999762i \(0.506950\pi\)
\(110\) 0 0
\(111\) −67.0146 + 35.6050i −0.0573040 + 0.0304458i
\(112\) 0 0
\(113\) 1232.86 + 1034.49i 1.02635 + 0.861208i 0.990412 0.138146i \(-0.0441144\pi\)
0.0359359 + 0.999354i \(0.488559\pi\)
\(114\) 0 0
\(115\) −1677.20 610.450i −1.36000 0.494998i
\(116\) 0 0
\(117\) −1835.06 + 524.936i −1.45001 + 0.414790i
\(118\) 0 0
\(119\) 1700.16 1426.61i 1.30970 1.09896i
\(120\) 0 0
\(121\) −231.034 + 1310.26i −0.173579 + 0.984418i
\(122\) 0 0
\(123\) 265.040 294.169i 0.194291 0.215645i
\(124\) 0 0
\(125\) 725.708 1256.96i 0.519275 0.899410i
\(126\) 0 0
\(127\) 410.415 + 710.860i 0.286760 + 0.496682i 0.973034 0.230660i \(-0.0740886\pi\)
−0.686275 + 0.727342i \(0.740755\pi\)
\(128\) 0 0
\(129\) 1025.37 143.774i 0.699834 0.0981289i
\(130\) 0 0
\(131\) −586.240 + 213.374i −0.390993 + 0.142310i −0.530033 0.847977i \(-0.677820\pi\)
0.139040 + 0.990287i \(0.455598\pi\)
\(132\) 0 0
\(133\) −684.875 3884.12i −0.446513 2.53230i
\(134\) 0 0
\(135\) 1079.26 1040.24i 0.688056 0.663184i
\(136\) 0 0
\(137\) 211.268 + 1198.16i 0.131751 + 0.747194i 0.977068 + 0.212929i \(0.0683004\pi\)
−0.845317 + 0.534265i \(0.820588\pi\)
\(138\) 0 0
\(139\) −26.9027 + 9.79178i −0.0164162 + 0.00597502i −0.350215 0.936669i \(-0.613892\pi\)
0.333799 + 0.942644i \(0.391669\pi\)
\(140\) 0 0
\(141\) −858.432 1099.46i −0.512716 0.656676i
\(142\) 0 0
\(143\) 25.6508 + 44.4286i 0.0150002 + 0.0259811i
\(144\) 0 0
\(145\) 1301.70 2254.61i 0.745520 1.29128i
\(146\) 0 0
\(147\) −537.744 1656.79i −0.301717 0.929593i
\(148\) 0 0
\(149\) −154.781 + 877.807i −0.0851017 + 0.482636i 0.912233 + 0.409672i \(0.134357\pi\)
−0.997335 + 0.0729639i \(0.976754\pi\)
\(150\) 0 0
\(151\) −222.292 + 186.525i −0.119800 + 0.100525i −0.700720 0.713437i \(-0.747138\pi\)
0.580919 + 0.813961i \(0.302693\pi\)
\(152\) 0 0
\(153\) −2295.28 161.964i −1.21282 0.0855820i
\(154\) 0 0
\(155\) 615.229 + 223.925i 0.318815 + 0.116039i
\(156\) 0 0
\(157\) −1213.97 1018.64i −0.617104 0.517812i 0.279788 0.960062i \(-0.409736\pi\)
−0.896892 + 0.442250i \(0.854180\pi\)
\(158\) 0 0
\(159\) 232.119 + 145.146i 0.115775 + 0.0723953i
\(160\) 0 0
\(161\) 4350.50 2.12961
\(162\) 0 0
\(163\) 3469.70 1.66729 0.833643 0.552304i \(-0.186251\pi\)
0.833643 + 0.552304i \(0.186251\pi\)
\(164\) 0 0
\(165\) −34.1608 21.3611i −0.0161176 0.0100785i
\(166\) 0 0
\(167\) −1868.59 1567.93i −0.865843 0.726529i 0.0973754 0.995248i \(-0.468955\pi\)
−0.963219 + 0.268719i \(0.913400\pi\)
\(168\) 0 0
\(169\) −2631.39 957.749i −1.19772 0.435935i
\(170\) 0 0
\(171\) −2288.69 + 3388.49i −1.02351 + 1.51535i
\(172\) 0 0
\(173\) 2917.03 2447.68i 1.28195 1.07569i 0.288981 0.957335i \(-0.406684\pi\)
0.992972 0.118351i \(-0.0377608\pi\)
\(174\) 0 0
\(175\) −49.0475 + 278.162i −0.0211865 + 0.120155i
\(176\) 0 0
\(177\) 1205.32 + 3713.61i 0.511851 + 1.57702i
\(178\) 0 0
\(179\) −157.552 + 272.889i −0.0657878 + 0.113948i −0.897043 0.441943i \(-0.854289\pi\)
0.831255 + 0.555891i \(0.187623\pi\)
\(180\) 0 0
\(181\) −1920.99 3327.25i −0.788873 1.36637i −0.926658 0.375906i \(-0.877331\pi\)
0.137785 0.990462i \(-0.456002\pi\)
\(182\) 0 0
\(183\) 118.860 + 152.234i 0.0480132 + 0.0614943i
\(184\) 0 0
\(185\) 146.626 53.3675i 0.0582711 0.0212090i
\(186\) 0 0
\(187\) 10.7395 + 60.9069i 0.00419974 + 0.0238179i
\(188\) 0 0
\(189\) −1604.80 + 3282.39i −0.617629 + 1.26328i
\(190\) 0 0
\(191\) 436.206 + 2473.85i 0.165250 + 0.937180i 0.948806 + 0.315859i \(0.102293\pi\)
−0.783556 + 0.621321i \(0.786596\pi\)
\(192\) 0 0
\(193\) 3588.62 1306.15i 1.33842 0.487144i 0.429104 0.903255i \(-0.358829\pi\)
0.909314 + 0.416111i \(0.136607\pi\)
\(194\) 0 0
\(195\) 3886.57 544.965i 1.42730 0.200132i
\(196\) 0 0
\(197\) −1819.27 3151.06i −0.657957 1.13961i −0.981144 0.193279i \(-0.938088\pi\)
0.323187 0.946335i \(-0.395246\pi\)
\(198\) 0 0
\(199\) −1745.94 + 3024.05i −0.621941 + 1.07723i 0.367183 + 0.930149i \(0.380322\pi\)
−0.989124 + 0.147085i \(0.953011\pi\)
\(200\) 0 0
\(201\) 1781.54 1977.34i 0.625174 0.693883i
\(202\) 0 0
\(203\) −1101.93 + 6249.33i −0.380986 + 2.16068i
\(204\) 0 0
\(205\) −623.685 + 523.334i −0.212488 + 0.178299i
\(206\) 0 0
\(207\) −3242.53 3135.25i −1.08875 1.05273i
\(208\) 0 0
\(209\) 103.277 + 37.5899i 0.0341811 + 0.0124409i
\(210\) 0 0
\(211\) 3627.33 + 3043.69i 1.18349 + 0.993062i 0.999950 + 0.0100489i \(0.00319870\pi\)
0.183536 + 0.983013i \(0.441246\pi\)
\(212\) 0 0
\(213\) −2736.16 + 1453.73i −0.880180 + 0.467642i
\(214\) 0 0
\(215\) −2128.98 −0.675327
\(216\) 0 0
\(217\) −1595.85 −0.499232
\(218\) 0 0
\(219\) 68.6938 1949.41i 0.0211959 0.601501i
\(220\) 0 0
\(221\) −4614.99 3872.43i −1.40469 1.17868i
\(222\) 0 0
\(223\) 590.712 + 215.002i 0.177386 + 0.0645631i 0.429186 0.903216i \(-0.358800\pi\)
−0.251800 + 0.967779i \(0.581023\pi\)
\(224\) 0 0
\(225\) 237.018 171.974i 0.0702275 0.0509552i
\(226\) 0 0
\(227\) −994.390 + 834.392i −0.290749 + 0.243967i −0.776481 0.630140i \(-0.782997\pi\)
0.485732 + 0.874108i \(0.338553\pi\)
\(228\) 0 0
\(229\) 101.719 576.874i 0.0293526 0.166467i −0.966608 0.256260i \(-0.917510\pi\)
0.995960 + 0.0897934i \(0.0286207\pi\)
\(230\) 0 0
\(231\) 96.0525 + 20.4484i 0.0273584 + 0.00582428i
\(232\) 0 0
\(233\) −423.007 + 732.669i −0.118936 + 0.206003i −0.919346 0.393449i \(-0.871282\pi\)
0.800410 + 0.599453i \(0.204615\pi\)
\(234\) 0 0
\(235\) 1434.08 + 2483.90i 0.398082 + 0.689498i
\(236\) 0 0
\(237\) 688.236 1701.89i 0.188632 0.466454i
\(238\) 0 0
\(239\) 3912.58 1424.06i 1.05893 0.385419i 0.246903 0.969040i \(-0.420587\pi\)
0.812026 + 0.583621i \(0.198365\pi\)
\(240\) 0 0
\(241\) 982.311 + 5570.96i 0.262557 + 1.48903i 0.775903 + 0.630852i \(0.217295\pi\)
−0.513346 + 0.858182i \(0.671594\pi\)
\(242\) 0 0
\(243\) 3561.60 1289.92i 0.940234 0.340530i
\(244\) 0 0
\(245\) 621.945 + 3527.23i 0.162182 + 0.919780i
\(246\) 0 0
\(247\) −10060.2 + 3661.61i −2.59156 + 0.943251i
\(248\) 0 0
\(249\) 164.697 407.266i 0.0419166 0.103652i
\(250\) 0 0
\(251\) −185.584 321.441i −0.0466692 0.0808334i 0.841747 0.539872i \(-0.181527\pi\)
−0.888416 + 0.459039i \(0.848194\pi\)
\(252\) 0 0
\(253\) −60.6160 + 104.990i −0.0150628 + 0.0260896i
\(254\) 0 0
\(255\) 4627.57 + 985.154i 1.13643 + 0.241932i
\(256\) 0 0
\(257\) −523.583 + 2969.39i −0.127083 + 0.720721i 0.852967 + 0.521965i \(0.174801\pi\)
−0.980049 + 0.198755i \(0.936310\pi\)
\(258\) 0 0
\(259\) −291.353 + 244.474i −0.0698989 + 0.0586521i
\(260\) 0 0
\(261\) 5324.97 3863.66i 1.26286 0.916300i
\(262\) 0 0
\(263\) −3971.62 1445.55i −0.931182 0.338922i −0.168504 0.985701i \(-0.553894\pi\)
−0.762678 + 0.646778i \(0.776116\pi\)
\(264\) 0 0
\(265\) −431.215 361.832i −0.0999598 0.0838762i
\(266\) 0 0
\(267\) −128.534 + 3647.56i −0.0294612 + 0.836056i
\(268\) 0 0
\(269\) −1948.75 −0.441700 −0.220850 0.975308i \(-0.570883\pi\)
−0.220850 + 0.975308i \(0.570883\pi\)
\(270\) 0 0
\(271\) 6235.43 1.39769 0.698847 0.715271i \(-0.253697\pi\)
0.698847 + 0.715271i \(0.253697\pi\)
\(272\) 0 0
\(273\) −8447.79 + 4488.34i −1.87283 + 0.995042i
\(274\) 0 0
\(275\) −6.02946 5.05932i −0.00132215 0.00110941i
\(276\) 0 0
\(277\) 2656.36 + 966.836i 0.576192 + 0.209717i 0.613646 0.789582i \(-0.289702\pi\)
−0.0374534 + 0.999298i \(0.511925\pi\)
\(278\) 0 0
\(279\) 1189.42 + 1150.07i 0.255229 + 0.246785i
\(280\) 0 0
\(281\) −1579.35 + 1325.24i −0.335290 + 0.281341i −0.794851 0.606805i \(-0.792451\pi\)
0.459561 + 0.888146i \(0.348007\pi\)
\(282\) 0 0
\(283\) −1178.94 + 6686.12i −0.247636 + 1.40441i 0.566656 + 0.823955i \(0.308237\pi\)
−0.814291 + 0.580457i \(0.802874\pi\)
\(284\) 0 0
\(285\) 5627.90 6246.43i 1.16971 1.29827i
\(286\) 0 0
\(287\) 992.252 1718.63i 0.204079 0.353476i
\(288\) 0 0
\(289\) −1174.87 2034.93i −0.239134 0.414192i
\(290\) 0 0
\(291\) −69.6725 + 9.76931i −0.0140353 + 0.00196800i
\(292\) 0 0
\(293\) 4133.18 1504.35i 0.824105 0.299950i 0.104668 0.994507i \(-0.466622\pi\)
0.719437 + 0.694557i \(0.244400\pi\)
\(294\) 0 0
\(295\) −1394.05 7906.08i −0.275136 1.56037i
\(296\) 0 0
\(297\) −56.8538 84.4624i −0.0111077 0.0165017i
\(298\) 0 0
\(299\) −2050.64 11629.8i −0.396627 2.24938i
\(300\) 0 0
\(301\) 4876.39 1774.86i 0.933788 0.339871i
\(302\) 0 0
\(303\) −5831.41 7468.74i −1.10563 1.41607i
\(304\) 0 0
\(305\) −198.567 343.927i −0.0372783 0.0645679i
\(306\) 0 0
\(307\) 489.447 847.746i 0.0909909 0.157601i −0.816937 0.576726i \(-0.804330\pi\)
0.907928 + 0.419125i \(0.137663\pi\)
\(308\) 0 0
\(309\) −1146.66 3532.88i −0.211105 0.650416i
\(310\) 0 0
\(311\) 571.383 3240.47i 0.104181 0.590837i −0.887364 0.461070i \(-0.847466\pi\)
0.991544 0.129767i \(-0.0414231\pi\)
\(312\) 0 0
\(313\) −591.666 + 496.467i −0.106847 + 0.0896549i −0.694646 0.719352i \(-0.744439\pi\)
0.587799 + 0.809007i \(0.299994\pi\)
\(314\) 0 0
\(315\) 4205.00 6225.65i 0.752143 1.11357i
\(316\) 0 0
\(317\) 657.562 + 239.333i 0.116506 + 0.0424046i 0.399615 0.916683i \(-0.369144\pi\)
−0.283109 + 0.959088i \(0.591366\pi\)
\(318\) 0 0
\(319\) −135.461 113.665i −0.0237754 0.0199500i
\(320\) 0 0
\(321\) 8457.24 + 5288.40i 1.47052 + 0.919532i
\(322\) 0 0
\(323\) −12906.4 −2.22331
\(324\) 0 0
\(325\) 766.701 0.130858
\(326\) 0 0
\(327\) 218.908 + 136.886i 0.0370204 + 0.0231492i
\(328\) 0 0
\(329\) −5355.49 4493.79i −0.897439 0.753041i
\(330\) 0 0
\(331\) 5019.41 + 1826.92i 0.833509 + 0.303373i 0.723298 0.690536i \(-0.242625\pi\)
0.110211 + 0.993908i \(0.464847\pi\)
\(332\) 0 0
\(333\) 393.337 + 27.7555i 0.0647289 + 0.00456754i
\(334\) 0 0
\(335\) −4192.27 + 3517.73i −0.683726 + 0.573714i
\(336\) 0 0
\(337\) 571.369 3240.40i 0.0923575 0.523785i −0.903168 0.429288i \(-0.858765\pi\)
0.995525 0.0944973i \(-0.0301244\pi\)
\(338\) 0 0
\(339\) −2581.66 7954.10i −0.413617 1.27436i
\(340\) 0 0
\(341\) 22.2351 38.5124i 0.00353109 0.00611602i
\(342\) 0 0
\(343\) 101.247 + 175.365i 0.0159383 + 0.0276059i
\(344\) 0 0
\(345\) 5707.50 + 7310.05i 0.890671 + 1.14075i
\(346\) 0 0
\(347\) 4481.59 1631.16i 0.693326 0.252350i 0.0287674 0.999586i \(-0.490842\pi\)
0.664559 + 0.747236i \(0.268620\pi\)
\(348\) 0 0
\(349\) 2217.09 + 12573.7i 0.340052 + 1.92853i 0.370122 + 0.928983i \(0.379316\pi\)
−0.0300695 + 0.999548i \(0.509573\pi\)
\(350\) 0 0
\(351\) 9530.93 + 2742.76i 1.44935 + 0.417088i
\(352\) 0 0
\(353\) −337.891 1916.28i −0.0509465 0.288932i 0.948681 0.316236i \(-0.102419\pi\)
−0.999627 + 0.0273036i \(0.991308\pi\)
\(354\) 0 0
\(355\) 5986.63 2178.96i 0.895035 0.325766i
\(356\) 0 0
\(357\) −11420.6 + 1601.37i −1.69312 + 0.237405i
\(358\) 0 0
\(359\) 3268.90 + 5661.90i 0.480573 + 0.832378i 0.999752 0.0222884i \(-0.00709521\pi\)
−0.519178 + 0.854666i \(0.673762\pi\)
\(360\) 0 0
\(361\) −8038.26 + 13922.7i −1.17193 + 2.02984i
\(362\) 0 0
\(363\) 4627.56 5136.15i 0.669101 0.742639i
\(364\) 0 0
\(365\) −696.477 + 3949.91i −0.0998774 + 0.566433i
\(366\) 0 0
\(367\) 4978.80 4177.71i 0.708150 0.594209i −0.215929 0.976409i \(-0.569278\pi\)
0.924079 + 0.382200i \(0.124834\pi\)
\(368\) 0 0
\(369\) −1978.10 + 565.855i −0.279068 + 0.0798299i
\(370\) 0 0
\(371\) 1289.34 + 469.280i 0.180429 + 0.0656707i
\(372\) 0 0
\(373\) −7933.62 6657.10i −1.10131 0.924106i −0.103794 0.994599i \(-0.533098\pi\)
−0.997512 + 0.0704931i \(0.977543\pi\)
\(374\) 0 0
\(375\) −6660.12 + 3538.54i −0.917139 + 0.487278i
\(376\) 0 0
\(377\) 17225.1 2.35315
\(378\) 0 0
\(379\) −12857.0 −1.74254 −0.871268 0.490807i \(-0.836702\pi\)
−0.871268 + 0.490807i \(0.836702\pi\)
\(380\) 0 0
\(381\) 150.204 4262.51i 0.0201973 0.573163i
\(382\) 0 0
\(383\) −1960.38 1644.96i −0.261543 0.219461i 0.502581 0.864530i \(-0.332384\pi\)
−0.764124 + 0.645070i \(0.776828\pi\)
\(384\) 0 0
\(385\) −189.751 69.0637i −0.0251184 0.00914236i
\(386\) 0 0
\(387\) −4913.56 2191.39i −0.645402 0.287842i
\(388\) 0 0
\(389\) −8568.05 + 7189.45i −1.11675 + 0.937068i −0.998436 0.0559072i \(-0.982195\pi\)
−0.118319 + 0.992976i \(0.537750\pi\)
\(390\) 0 0
\(391\) 2472.14 14020.2i 0.319748 1.81338i
\(392\) 0 0
\(393\) 3170.64 + 674.991i 0.406966 + 0.0866381i
\(394\) 0 0
\(395\) −1887.36 + 3269.01i −0.240414 + 0.416410i
\(396\) 0 0
\(397\) −1143.34 1980.33i −0.144541 0.250352i 0.784661 0.619926i \(-0.212837\pi\)
−0.929202 + 0.369573i \(0.879504\pi\)
\(398\) 0 0
\(399\) −7683.15 + 18999.1i −0.964006 + 2.38382i
\(400\) 0 0
\(401\) 12492.1 4546.76i 1.55568 0.566220i 0.585935 0.810358i \(-0.300727\pi\)
0.969740 + 0.244138i \(0.0785050\pi\)
\(402\) 0 0
\(403\) 752.214 + 4266.02i 0.0929788 + 0.527309i
\(404\) 0 0
\(405\) −7620.70 + 1609.73i −0.935001 + 0.197501i
\(406\) 0 0
\(407\) −1.84041 10.4375i −0.000224142 0.00127117i
\(408\) 0 0
\(409\) 4155.16 1512.36i 0.502346 0.182839i −0.0784028 0.996922i \(-0.524982\pi\)
0.580749 + 0.814083i \(0.302760\pi\)
\(410\) 0 0
\(411\) 2370.07 5860.77i 0.284445 0.703384i
\(412\) 0 0
\(413\) 9784.09 + 16946.5i 1.16572 + 2.01909i
\(414\) 0 0
\(415\) −451.651 + 782.282i −0.0534233 + 0.0925318i
\(416\) 0 0
\(417\) 145.501 + 30.9755i 0.0170869 + 0.00363759i
\(418\) 0 0
\(419\) −1861.24 + 10555.6i −0.217011 + 1.23073i 0.660373 + 0.750938i \(0.270398\pi\)
−0.877383 + 0.479790i \(0.840713\pi\)
\(420\) 0 0
\(421\) −3381.05 + 2837.04i −0.391406 + 0.328429i −0.817161 0.576410i \(-0.804453\pi\)
0.425754 + 0.904839i \(0.360009\pi\)
\(422\) 0 0
\(423\) 753.057 + 7208.84i 0.0865600 + 0.828619i
\(424\) 0 0
\(425\) 868.551 + 316.127i 0.0991316 + 0.0360809i
\(426\) 0 0
\(427\) 741.533 + 622.220i 0.0840406 + 0.0705184i
\(428\) 0 0
\(429\) 9.38769 266.406i 0.00105651 0.0299818i
\(430\) 0 0
\(431\) 12301.2 1.37477 0.687385 0.726293i \(-0.258758\pi\)
0.687385 + 0.726293i \(0.258758\pi\)
\(432\) 0 0
\(433\) −8467.47 −0.939770 −0.469885 0.882728i \(-0.655705\pi\)
−0.469885 + 0.882728i \(0.655705\pi\)
\(434\) 0 0
\(435\) −11946.2 + 6347.07i −1.31673 + 0.699584i
\(436\) 0 0
\(437\) −19380.3 16262.0i −2.12148 1.78013i
\(438\) 0 0
\(439\) −1628.97 592.898i −0.177100 0.0644590i 0.251948 0.967741i \(-0.418929\pi\)
−0.429048 + 0.903282i \(0.641151\pi\)
\(440\) 0 0
\(441\) −2195.22 + 8780.82i −0.237039 + 0.948150i
\(442\) 0 0
\(443\) 6356.76 5333.96i 0.681758 0.572063i −0.234761 0.972053i \(-0.575431\pi\)
0.916519 + 0.399990i \(0.130986\pi\)
\(444\) 0 0
\(445\) 1303.19 7390.73i 0.138825 0.787313i
\(446\) 0 0
\(447\) 3100.23 3440.95i 0.328044 0.364097i
\(448\) 0 0
\(449\) −7397.73 + 12813.2i −0.777551 + 1.34676i 0.155799 + 0.987789i \(0.450205\pi\)
−0.933350 + 0.358968i \(0.883129\pi\)
\(450\) 0 0
\(451\) 27.6503 + 47.8918i 0.00288692 + 0.00500030i
\(452\) 0 0
\(453\) 1493.22 209.376i 0.154873 0.0217159i
\(454\) 0 0
\(455\) 18483.5 6727.46i 1.90444 0.693161i
\(456\) 0 0
\(457\) −1618.87 9181.09i −0.165706 0.939767i −0.948333 0.317276i \(-0.897232\pi\)
0.782627 0.622491i \(-0.213879\pi\)
\(458\) 0 0
\(459\) 9666.13 + 7036.92i 0.982955 + 0.715589i
\(460\) 0 0
\(461\) −889.156 5042.65i −0.0898311 0.509457i −0.996209 0.0869899i \(-0.972275\pi\)
0.906378 0.422467i \(-0.138836\pi\)
\(462\) 0 0
\(463\) −863.470 + 314.277i −0.0866714 + 0.0315458i −0.384992 0.922920i \(-0.625796\pi\)
0.298321 + 0.954466i \(0.403574\pi\)
\(464\) 0 0
\(465\) −2093.62 2681.47i −0.208794 0.267420i
\(466\) 0 0
\(467\) −2802.50 4854.08i −0.277697 0.480985i 0.693115 0.720827i \(-0.256238\pi\)
−0.970812 + 0.239842i \(0.922904\pi\)
\(468\) 0 0
\(469\) 6669.70 11552.3i 0.656669 1.13738i
\(470\) 0 0
\(471\) 2542.11 + 7832.26i 0.248693 + 0.766224i
\(472\) 0 0
\(473\) −25.1108 + 142.411i −0.00244101 + 0.0138436i
\(474\) 0 0
\(475\) 1258.25 1055.80i 0.121542 0.101986i
\(476\) 0 0
\(477\) −622.780 1278.95i −0.0597801 0.122765i
\(478\) 0 0
\(479\) −8793.16 3200.45i −0.838768 0.305286i −0.113315 0.993559i \(-0.536147\pi\)
−0.725452 + 0.688273i \(0.758369\pi\)
\(480\) 0 0
\(481\) 790.860 + 663.610i 0.0749691 + 0.0629065i
\(482\) 0 0
\(483\) −19167.1 11985.4i −1.80566 1.12909i
\(484\) 0 0
\(485\) 144.662 0.0135438
\(486\) 0 0
\(487\) −5274.19 −0.490752 −0.245376 0.969428i \(-0.578911\pi\)
−0.245376 + 0.969428i \(0.578911\pi\)
\(488\) 0 0
\(489\) −15286.5 9558.80i −1.41366 0.883975i
\(490\) 0 0
\(491\) 10145.4 + 8513.01i 0.932497 + 0.782458i 0.976264 0.216584i \(-0.0694915\pi\)
−0.0437671 + 0.999042i \(0.513936\pi\)
\(492\) 0 0
\(493\) 19513.3 + 7102.27i 1.78263 + 0.648824i
\(494\) 0 0
\(495\) 91.6541 + 188.222i 0.00832231 + 0.0170908i
\(496\) 0 0
\(497\) −11895.7 + 9981.71i −1.07364 + 0.900887i
\(498\) 0 0
\(499\) 1209.51 6859.46i 0.108507 0.615374i −0.881254 0.472642i \(-0.843300\pi\)
0.989761 0.142732i \(-0.0455886\pi\)
\(500\) 0 0
\(501\) 3912.91 + 12055.7i 0.348934 + 1.07507i
\(502\) 0 0
\(503\) −297.634 + 515.517i −0.0263834 + 0.0456974i −0.878916 0.476977i \(-0.841732\pi\)
0.852532 + 0.522675i \(0.175066\pi\)
\(504\) 0 0
\(505\) 9741.86 + 16873.4i 0.858430 + 1.48684i
\(506\) 0 0
\(507\) 8954.63 + 11468.9i 0.784397 + 1.00464i
\(508\) 0 0
\(509\) 18230.3 6635.30i 1.58752 0.577809i 0.610695 0.791866i \(-0.290890\pi\)
0.976821 + 0.214057i \(0.0686678\pi\)
\(510\) 0 0
\(511\) −1697.65 9627.83i −0.146966 0.833484i
\(512\) 0 0
\(513\) 19418.4 8623.51i 1.67124 0.742178i
\(514\) 0 0
\(515\) 1326.21 + 7521.31i 0.113475 + 0.643550i
\(516\) 0 0
\(517\) 183.067 66.6308i 0.0155730 0.00566812i
\(518\) 0 0
\(519\) −19594.8 + 2747.53i −1.65726 + 0.232376i
\(520\) 0 0
\(521\) −2437.03 4221.05i −0.204929 0.354948i 0.745181 0.666862i \(-0.232363\pi\)
−0.950110 + 0.311915i \(0.899030\pi\)
\(522\) 0 0
\(523\) 4980.61 8626.67i 0.416419 0.721258i −0.579158 0.815216i \(-0.696618\pi\)
0.995576 + 0.0939573i \(0.0299517\pi\)
\(524\) 0 0
\(525\) 982.408 1090.38i 0.0816682 0.0906439i
\(526\) 0 0
\(527\) −906.828 + 5142.88i −0.0749565 + 0.425099i
\(528\) 0 0
\(529\) 12057.1 10117.1i 0.990970 0.831523i
\(530\) 0 0
\(531\) 4920.46 19681.7i 0.402128 1.60850i
\(532\) 0 0
\(533\) −5061.94 1842.40i −0.411364 0.149724i
\(534\) 0 0
\(535\) −15711.3 13183.4i −1.26964 1.06536i
\(536\) 0 0
\(537\) 1445.92 768.223i 0.116194 0.0617342i
\(538\) 0 0
\(539\) 243.277 0.0194410
\(540\) 0 0
\(541\) −20408.9 −1.62190 −0.810948 0.585118i \(-0.801048\pi\)
−0.810948 + 0.585118i \(0.801048\pi\)
\(542\) 0 0
\(543\) −703.044 + 19951.1i −0.0555626 + 1.57677i
\(544\) 0 0
\(545\) −406.674 341.240i −0.0319633 0.0268204i
\(546\) 0 0
\(547\) −15260.6 5554.42i −1.19287 0.434168i −0.332137 0.943231i \(-0.607770\pi\)
−0.860729 + 0.509064i \(0.829992\pi\)
\(548\) 0 0
\(549\) −104.270 998.153i −0.00810590 0.0775958i
\(550\) 0 0
\(551\) 28268.6 23720.1i 2.18563 1.83396i
\(552\) 0 0
\(553\) 1597.71 9061.04i 0.122860 0.696771i
\(554\) 0 0
\(555\) −793.017 168.824i −0.0606517 0.0129120i
\(556\) 0 0
\(557\) 4689.68 8122.76i 0.356747 0.617904i −0.630668 0.776052i \(-0.717219\pi\)
0.987415 + 0.158149i \(0.0505525\pi\)
\(558\) 0 0
\(559\) −7043.07 12199.0i −0.532898 0.923007i
\(560\) 0 0
\(561\) 120.479 297.925i 0.00906711 0.0224214i
\(562\) 0 0
\(563\) 10092.1 3673.21i 0.755471 0.274969i 0.0645648 0.997914i \(-0.479434\pi\)
0.690906 + 0.722945i \(0.257212\pi\)
\(564\) 0 0
\(565\) 2985.89 + 16933.9i 0.222332 + 1.26091i
\(566\) 0 0
\(567\) 16113.1 10040.2i 1.19345 0.743646i
\(568\) 0 0
\(569\) 13.7609 + 78.0417i 0.00101386 + 0.00574987i 0.985310 0.170773i \(-0.0546263\pi\)
−0.984297 + 0.176522i \(0.943515\pi\)
\(570\) 0 0
\(571\) −17084.1 + 6218.11i −1.25210 + 0.455726i −0.881110 0.472911i \(-0.843203\pi\)
−0.370988 + 0.928638i \(0.620981\pi\)
\(572\) 0 0
\(573\) 4893.50 12100.8i 0.356769 0.882230i
\(574\) 0 0
\(575\) 905.904 + 1569.07i 0.0657023 + 0.113800i
\(576\) 0 0
\(577\) −2781.75 + 4818.13i −0.200703 + 0.347628i −0.948755 0.316012i \(-0.897656\pi\)
0.748052 + 0.663640i \(0.230989\pi\)
\(578\) 0 0
\(579\) −19408.8 4131.90i −1.39310 0.296573i
\(580\) 0 0
\(581\) 382.335 2168.33i 0.0273011 0.154832i
\(582\) 0 0
\(583\) −29.2896 + 24.5769i −0.00208070 + 0.00174592i
\(584\) 0 0
\(585\) −18624.5 8306.30i −1.31628 0.587048i
\(586\) 0 0
\(587\) −2307.80 839.972i −0.162271 0.0590619i 0.259607 0.965714i \(-0.416407\pi\)
−0.421879 + 0.906652i \(0.638629\pi\)
\(588\) 0 0
\(589\) 7109.08 + 5965.22i 0.497325 + 0.417305i
\(590\) 0 0
\(591\) −665.815 + 18894.7i −0.0463418 + 1.31510i
\(592\) 0 0
\(593\) −17323.9 −1.19967 −0.599837 0.800122i \(-0.704768\pi\)
−0.599837 + 0.800122i \(0.704768\pi\)
\(594\) 0 0
\(595\) 23712.8 1.63383
\(596\) 0 0
\(597\) 16023.2 8513.16i 1.09847 0.583619i
\(598\) 0 0
\(599\) 1054.57 + 884.892i 0.0719344 + 0.0603601i 0.678046 0.735020i \(-0.262827\pi\)
−0.606112 + 0.795380i \(0.707271\pi\)
\(600\) 0 0
\(601\) 16841.2 + 6129.69i 1.14304 + 0.416032i 0.843010 0.537898i \(-0.180781\pi\)
0.300029 + 0.953930i \(0.403004\pi\)
\(602\) 0 0
\(603\) −13296.4 + 3803.55i −0.897961 + 0.256870i
\(604\) 0 0
\(605\) −10889.5 + 9137.34i −0.731768 + 0.614026i
\(606\) 0 0
\(607\) −4434.77 + 25150.8i −0.296543 + 1.68178i 0.364319 + 0.931274i \(0.381302\pi\)
−0.660862 + 0.750507i \(0.729809\pi\)
\(608\) 0 0
\(609\) 22071.3 24497.0i 1.46859 1.63000i
\(610\) 0 0
\(611\) −9488.44 + 16434.5i −0.628251 + 1.08816i
\(612\) 0 0
\(613\) −6521.06 11294.8i −0.429662 0.744197i 0.567181 0.823593i \(-0.308034\pi\)
−0.996843 + 0.0793963i \(0.974701\pi\)
\(614\) 0 0
\(615\) 4189.53 587.445i 0.274696 0.0385172i
\(616\) 0 0
\(617\) −21565.7 + 7849.26i −1.40713 + 0.512154i −0.930287 0.366833i \(-0.880442\pi\)
−0.476845 + 0.878987i \(0.658220\pi\)
\(618\) 0 0
\(619\) 1776.31 + 10073.9i 0.115341 + 0.654129i 0.986581 + 0.163273i \(0.0522050\pi\)
−0.871240 + 0.490857i \(0.836684\pi\)
\(620\) 0 0
\(621\) 5648.23 + 22746.0i 0.364985 + 1.46983i
\(622\) 0 0
\(623\) 3176.49 + 18014.7i 0.204275 + 1.15850i
\(624\) 0 0
\(625\) 13298.2 4840.15i 0.851085 0.309770i
\(626\) 0 0
\(627\) −351.453 450.133i −0.0223854 0.0286708i
\(628\) 0 0
\(629\) 622.299 + 1077.85i 0.0394478 + 0.0683257i
\(630\) 0 0
\(631\) −3681.07 + 6375.79i −0.232236 + 0.402245i −0.958466 0.285207i \(-0.907937\pi\)
0.726230 + 0.687452i \(0.241271\pi\)
\(632\) 0 0
\(633\) −7595.78 23402.7i −0.476944 1.46947i
\(634\) 0 0
\(635\) −1522.89 + 8636.76i −0.0951720 + 0.539747i
\(636\) 0 0
\(637\) −18153.3 + 15232.5i −1.12914 + 0.947460i
\(638\) 0 0
\(639\) 16059.7 + 1133.24i 0.994225 + 0.0701567i
\(640\) 0 0
\(641\) −27630.6 10056.7i −1.70256 0.619683i −0.706451 0.707762i \(-0.749705\pi\)
−0.996114 + 0.0880788i \(0.971927\pi\)
\(642\) 0 0
\(643\) 15587.5 + 13079.5i 0.956004 + 0.802182i 0.980298 0.197523i \(-0.0632896\pi\)
−0.0242947 + 0.999705i \(0.507734\pi\)
\(644\) 0 0
\(645\) 9379.67 + 5865.21i 0.572596 + 0.358050i
\(646\) 0 0
\(647\) −6586.91 −0.400244 −0.200122 0.979771i \(-0.564134\pi\)
−0.200122 + 0.979771i \(0.564134\pi\)
\(648\) 0 0
\(649\) −545.291 −0.0329808
\(650\) 0 0
\(651\) 7030.85 + 4396.46i 0.423288 + 0.264687i
\(652\) 0 0
\(653\) −15535.4 13035.7i −0.931004 0.781205i 0.0449934 0.998987i \(-0.485673\pi\)
−0.975997 + 0.217782i \(0.930118\pi\)
\(654\) 0 0
\(655\) −6263.56 2279.75i −0.373645 0.135996i
\(656\) 0 0
\(657\) −5673.14 + 8399.28i −0.336880 + 0.498763i
\(658\) 0 0
\(659\) −8105.40 + 6801.23i −0.479122 + 0.402031i −0.850109 0.526607i \(-0.823464\pi\)
0.370987 + 0.928638i \(0.379019\pi\)
\(660\) 0 0
\(661\) −2105.13 + 11938.8i −0.123873 + 0.702518i 0.858098 + 0.513486i \(0.171646\pi\)
−0.981971 + 0.189032i \(0.939465\pi\)
\(662\) 0 0
\(663\) 9663.99 + 29774.8i 0.566091 + 1.74413i
\(664\) 0 0
\(665\) 21069.6 36493.7i 1.22864 2.12807i
\(666\) 0 0
\(667\) 20352.5 + 35251.6i 1.18149 + 2.04640i
\(668\) 0 0
\(669\) −2010.19 2574.61i −0.116171 0.148790i
\(670\) 0 0
\(671\) −25.3478 + 9.22586i −0.00145833 + 0.000530790i
\(672\) 0 0
\(673\) 1997.23 + 11326.8i 0.114395 + 0.648764i 0.987048 + 0.160424i \(0.0512862\pi\)
−0.872654 + 0.488340i \(0.837603\pi\)
\(674\) 0 0
\(675\) −1518.01 + 104.698i −0.0865604 + 0.00597014i
\(676\) 0 0
\(677\) 1826.50 + 10358.6i 0.103690 + 0.588055i 0.991735 + 0.128300i \(0.0409519\pi\)
−0.888045 + 0.459756i \(0.847937\pi\)
\(678\) 0 0
\(679\) −331.345 + 120.600i −0.0187273 + 0.00681619i
\(680\) 0 0
\(681\) 6679.70 936.610i 0.375869 0.0527033i
\(682\) 0 0
\(683\) 2489.30 + 4311.59i 0.139459 + 0.241550i 0.927292 0.374339i \(-0.122130\pi\)
−0.787833 + 0.615889i \(0.788797\pi\)
\(684\) 0 0
\(685\) −6499.49 + 11257.4i −0.362529 + 0.627919i
\(686\) 0 0
\(687\) −2037.40 + 2261.31i −0.113146 + 0.125582i
\(688\) 0 0
\(689\) 646.741 3667.85i 0.0357604 0.202807i
\(690\) 0 0
\(691\) 5474.46 4593.62i 0.301387 0.252893i −0.479534 0.877523i \(-0.659194\pi\)
0.780921 + 0.624630i \(0.214750\pi\)
\(692\) 0 0
\(693\) −366.846 354.709i −0.0201087 0.0194434i
\(694\) 0 0
\(695\) −287.436 104.618i −0.0156879 0.00570993i
\(696\) 0 0
\(697\) −4974.72 4174.29i −0.270346 0.226847i
\(698\) 0 0
\(699\) 3882.11 2062.57i 0.210064 0.111608i
\(700\) 0 0
\(701\) −2134.56 −0.115009 −0.0575044 0.998345i \(-0.518314\pi\)
−0.0575044 + 0.998345i \(0.518314\pi\)
\(702\) 0 0
\(703\) 2211.74 0.118659
\(704\) 0 0
\(705\) 524.845 14894.2i 0.0280380 0.795670i
\(706\) 0 0
\(707\) −36380.3 30526.7i −1.93525 1.62387i
\(708\) 0 0
\(709\) −10970.4 3992.90i −0.581103 0.211504i 0.0347089 0.999397i \(-0.488950\pi\)
−0.615812 + 0.787893i \(0.711172\pi\)
\(710\) 0 0
\(711\) −7720.78 + 5601.99i −0.407246 + 0.295487i
\(712\) 0 0
\(713\) −7841.72 + 6579.98i −0.411886 + 0.345613i
\(714\) 0 0
\(715\) −95.1805 + 539.795i −0.00497839 + 0.0282338i
\(716\) 0 0
\(717\) −21160.9 4504.91i −1.10219 0.234643i
\(718\) 0 0
\(719\) −3341.98 + 5788.48i −0.173345 + 0.300242i −0.939587 0.342310i \(-0.888791\pi\)
0.766242 + 0.642552i \(0.222124\pi\)
\(720\) 0 0
\(721\) −9307.92 16121.8i −0.480784 0.832742i
\(722\) 0 0
\(723\) 11019.9 27250.3i 0.566851 1.40173i
\(724\) 0 0
\(725\) −2483.37 + 903.872i −0.127214 + 0.0463020i
\(726\) 0 0
\(727\) −4870.25 27620.6i −0.248456 1.40907i −0.812327 0.583202i \(-0.801799\pi\)
0.563871 0.825863i \(-0.309312\pi\)
\(728\) 0 0
\(729\) −19245.1 4128.95i −0.977750 0.209772i
\(730\) 0 0
\(731\) −2948.80 16723.5i −0.149200 0.846157i
\(732\) 0 0
\(733\) 27055.3 9847.32i 1.36331 0.496206i 0.446237 0.894915i \(-0.352764\pi\)
0.917078 + 0.398709i \(0.130542\pi\)
\(734\) 0 0
\(735\) 6977.18 17253.4i 0.350146 0.865851i
\(736\) 0 0
\(737\) 185.859 + 321.918i 0.00928930 + 0.0160895i
\(738\) 0 0
\(739\) 2190.75 3794.49i 0.109050 0.188880i −0.806336 0.591458i \(-0.798552\pi\)
0.915386 + 0.402578i \(0.131886\pi\)
\(740\) 0 0
\(741\) 54409.9 + 11583.2i 2.69743 + 0.574251i
\(742\) 0 0
\(743\) −5769.87 + 32722.6i −0.284894 + 1.61571i 0.420770 + 0.907167i \(0.361760\pi\)
−0.705664 + 0.708546i \(0.749351\pi\)
\(744\) 0 0
\(745\) −7295.38 + 6121.55i −0.358768 + 0.301042i
\(746\) 0 0
\(747\) −1847.60 + 1340.57i −0.0904955 + 0.0656612i
\(748\) 0 0
\(749\) 46977.0 + 17098.2i 2.29172 + 0.834119i
\(750\) 0 0
\(751\) −4666.53 3915.68i −0.226743 0.190260i 0.522338 0.852739i \(-0.325060\pi\)
−0.749081 + 0.662479i \(0.769504\pi\)
\(752\) 0 0
\(753\) −67.9200 + 1927.45i −0.00328704 + 0.0932804i
\(754\) 0 0
\(755\) −3100.39 −0.149450
\(756\) 0 0
\(757\) −234.359 −0.0112522 −0.00562610 0.999984i \(-0.501791\pi\)
−0.00562610 + 0.999984i \(0.501791\pi\)
\(758\) 0 0
\(759\) 556.298 295.563i 0.0266039 0.0141347i
\(760\) 0 0
\(761\) 5554.52 + 4660.79i 0.264587 + 0.222015i 0.765423 0.643527i \(-0.222530\pi\)
−0.500836 + 0.865542i \(0.666974\pi\)
\(762\) 0 0
\(763\) 1215.96 + 442.573i 0.0576942 + 0.0209990i
\(764\) 0 0
\(765\) −17673.7 17089.0i −0.835287 0.807651i
\(766\) 0 0
\(767\) 40689.7 34142.7i 1.91554 1.60733i
\(768\) 0 0
\(769\) −2924.93 + 16588.1i −0.137160 + 0.777871i 0.836172 + 0.548467i \(0.184789\pi\)
−0.973331 + 0.229403i \(0.926323\pi\)
\(770\) 0 0
\(771\) 10487.2 11639.8i 0.489868 0.543707i
\(772\) 0 0
\(773\) −95.1463 + 164.798i −0.00442713 + 0.00766802i −0.868230 0.496161i \(-0.834743\pi\)
0.863803 + 0.503829i \(0.168076\pi\)
\(774\) 0 0
\(775\) −332.303 575.566i −0.0154022 0.0266773i
\(776\) 0 0
\(777\) 1957.13 274.424i 0.0903625 0.0126704i
\(778\) 0 0
\(779\) −10844.4 + 3947.04i −0.498769 + 0.181537i
\(780\) 0 0
\(781\) −75.1426 426.155i −0.00344278 0.0195250i
\(782\) 0 0
\(783\) −34104.4 + 2352.21i −1.55657 + 0.107358i