Properties

Label 128.4.g.a.17.7
Level $128$
Weight $4$
Character 128.17
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 17.7
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +O(q^{10})\) \(q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +(-11.7977 - 28.4821i) q^{11} +(-12.9230 - 5.35288i) q^{13} -49.1278i q^{15} -72.9239i q^{17} +(143.136 + 59.2889i) q^{19} +(6.17043 + 14.8967i) q^{21} +(-83.6411 - 83.6411i) q^{23} +(162.441 - 162.441i) q^{25} +(113.737 - 47.1114i) q^{27} +(-39.6554 + 95.7367i) q^{29} +29.0324 q^{31} -80.4149 q^{33} +(-44.5534 + 107.562i) q^{35} +(-267.681 + 110.877i) q^{37} +(-25.7996 + 25.7996i) q^{39} +(-124.918 - 124.918i) q^{41} +(27.0156 + 65.2215i) q^{43} +(351.421 + 145.564i) q^{45} +282.627i q^{47} +304.789i q^{49} +(-175.738 - 72.7931i) q^{51} +(-51.4343 - 124.173i) q^{53} +(-410.570 - 410.570i) q^{55} +(285.759 - 285.759i) q^{57} +(222.476 - 92.1524i) q^{59} +(-226.809 + 547.566i) q^{61} -124.842 q^{63} -263.447 q^{65} +(-356.015 + 859.496i) q^{67} +(-285.056 + 118.074i) q^{69} +(-690.837 + 690.837i) q^{71} +(223.345 + 223.345i) q^{73} +(-229.314 - 553.612i) q^{75} +(176.062 + 72.9275i) q^{77} -698.000i q^{79} +224.174i q^{81} +(915.116 + 379.053i) q^{83} +(-525.601 - 1268.91i) q^{85} +(191.130 + 191.130i) q^{87} +(-163.738 + 163.738i) q^{89} +(79.8837 - 33.0889i) q^{91} +(28.9803 - 69.9647i) q^{93} +2917.97 q^{95} -839.460 q^{97} +(238.266 - 575.225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 0.998206 2.40988i 0.192105 0.463782i −0.798252 0.602324i \(-0.794242\pi\)
0.990357 + 0.138542i \(0.0442415\pi\)
\(4\) 0 0
\(5\) 17.4005 7.20752i 1.55635 0.644661i 0.571898 0.820325i \(-0.306207\pi\)
0.984450 + 0.175664i \(0.0562073\pi\)
\(6\) 0 0
\(7\) −4.37099 + 4.37099i −0.236012 + 0.236012i −0.815196 0.579185i \(-0.803371\pi\)
0.579185 + 0.815196i \(0.303371\pi\)
\(8\) 0 0
\(9\) 14.2808 + 14.2808i 0.528917 + 0.528917i
\(10\) 0 0
\(11\) −11.7977 28.4821i −0.323375 0.780697i −0.999053 0.0435002i \(-0.986149\pi\)
0.675678 0.737197i \(-0.263851\pi\)
\(12\) 0 0
\(13\) −12.9230 5.35288i −0.275707 0.114202i 0.240546 0.970638i \(-0.422674\pi\)
−0.516253 + 0.856436i \(0.672674\pi\)
\(14\) 0 0
\(15\) 49.1278i 0.845649i
\(16\) 0 0
\(17\) 72.9239i 1.04039i −0.854047 0.520195i \(-0.825859\pi\)
0.854047 0.520195i \(-0.174141\pi\)
\(18\) 0 0
\(19\) 143.136 + 59.2889i 1.72830 + 0.715884i 0.999515 + 0.0311397i \(0.00991368\pi\)
0.728783 + 0.684745i \(0.240086\pi\)
\(20\) 0 0
\(21\) 6.17043 + 14.8967i 0.0641190 + 0.154797i
\(22\) 0 0
\(23\) −83.6411 83.6411i −0.758278 0.758278i 0.217731 0.976009i \(-0.430134\pi\)
−0.976009 + 0.217731i \(0.930134\pi\)
\(24\) 0 0
\(25\) 162.441 162.441i 1.29953 1.29953i
\(26\) 0 0
\(27\) 113.737 47.1114i 0.810692 0.335800i
\(28\) 0 0
\(29\) −39.6554 + 95.7367i −0.253925 + 0.613030i −0.998514 0.0544937i \(-0.982646\pi\)
0.744589 + 0.667523i \(0.232646\pi\)
\(30\) 0 0
\(31\) 29.0324 0.168206 0.0841029 0.996457i \(-0.473198\pi\)
0.0841029 + 0.996457i \(0.473198\pi\)
\(32\) 0 0
\(33\) −80.4149 −0.424195
\(34\) 0 0
\(35\) −44.5534 + 107.562i −0.215169 + 0.519463i
\(36\) 0 0
\(37\) −267.681 + 110.877i −1.18936 + 0.492650i −0.887547 0.460716i \(-0.847593\pi\)
−0.301815 + 0.953366i \(0.597593\pi\)
\(38\) 0 0
\(39\) −25.7996 + 25.7996i −0.105929 + 0.105929i
\(40\) 0 0
\(41\) −124.918 124.918i −0.475827 0.475827i 0.427968 0.903794i \(-0.359230\pi\)
−0.903794 + 0.427968i \(0.859230\pi\)
\(42\) 0 0
\(43\) 27.0156 + 65.2215i 0.0958103 + 0.231306i 0.964517 0.264020i \(-0.0850485\pi\)
−0.868707 + 0.495326i \(0.835048\pi\)
\(44\) 0 0
\(45\) 351.421 + 145.564i 1.16415 + 0.482207i
\(46\) 0 0
\(47\) 282.627i 0.877136i 0.898698 + 0.438568i \(0.144514\pi\)
−0.898698 + 0.438568i \(0.855486\pi\)
\(48\) 0 0
\(49\) 304.789i 0.888597i
\(50\) 0 0
\(51\) −175.738 72.7931i −0.482515 0.199864i
\(52\) 0 0
\(53\) −51.4343 124.173i −0.133303 0.321821i 0.843107 0.537745i \(-0.180724\pi\)
−0.976410 + 0.215924i \(0.930724\pi\)
\(54\) 0 0
\(55\) −410.570 410.570i −1.00657 1.00657i
\(56\) 0 0
\(57\) 285.759 285.759i 0.664029 0.664029i
\(58\) 0 0
\(59\) 222.476 92.1524i 0.490913 0.203343i −0.123474 0.992348i \(-0.539404\pi\)
0.614387 + 0.789005i \(0.289404\pi\)
\(60\) 0 0
\(61\) −226.809 + 547.566i −0.476065 + 1.14932i 0.485374 + 0.874306i \(0.338683\pi\)
−0.961440 + 0.275016i \(0.911317\pi\)
\(62\) 0 0
\(63\) −124.842 −0.249661
\(64\) 0 0
\(65\) −263.447 −0.502717
\(66\) 0 0
\(67\) −356.015 + 859.496i −0.649166 + 1.56723i 0.164808 + 0.986326i \(0.447299\pi\)
−0.813975 + 0.580900i \(0.802701\pi\)
\(68\) 0 0
\(69\) −285.056 + 118.074i −0.497344 + 0.206007i
\(70\) 0 0
\(71\) −690.837 + 690.837i −1.15475 + 1.15475i −0.169163 + 0.985588i \(0.554106\pi\)
−0.985588 + 0.169163i \(0.945894\pi\)
\(72\) 0 0
\(73\) 223.345 + 223.345i 0.358089 + 0.358089i 0.863108 0.505019i \(-0.168515\pi\)
−0.505019 + 0.863108i \(0.668515\pi\)
\(74\) 0 0
\(75\) −229.314 553.612i −0.353052 0.852342i
\(76\) 0 0
\(77\) 176.062 + 72.9275i 0.260574 + 0.107933i
\(78\) 0 0
\(79\) 698.000i 0.994065i −0.867732 0.497033i \(-0.834423\pi\)
0.867732 0.497033i \(-0.165577\pi\)
\(80\) 0 0
\(81\) 224.174i 0.307509i
\(82\) 0 0
\(83\) 915.116 + 379.053i 1.21020 + 0.501283i 0.894283 0.447502i \(-0.147686\pi\)
0.315922 + 0.948785i \(0.397686\pi\)
\(84\) 0 0
\(85\) −525.601 1268.91i −0.670699 1.61921i
\(86\) 0 0
\(87\) 191.130 + 191.130i 0.235532 + 0.235532i
\(88\) 0 0
\(89\) −163.738 + 163.738i −0.195014 + 0.195014i −0.797859 0.602845i \(-0.794034\pi\)
0.602845 + 0.797859i \(0.294034\pi\)
\(90\) 0 0
\(91\) 79.8837 33.0889i 0.0920229 0.0381171i
\(92\) 0 0
\(93\) 28.9803 69.9647i 0.0323131 0.0780108i
\(94\) 0 0
\(95\) 2917.97 3.15134
\(96\) 0 0
\(97\) −839.460 −0.878704 −0.439352 0.898315i \(-0.644792\pi\)
−0.439352 + 0.898315i \(0.644792\pi\)
\(98\) 0 0
\(99\) 238.266 575.225i 0.241885 0.583963i
\(100\) 0 0
\(101\) 1561.02 646.594i 1.53789 0.637015i 0.556814 0.830637i \(-0.312024\pi\)
0.981076 + 0.193622i \(0.0620235\pi\)
\(102\) 0 0
\(103\) 80.1481 80.1481i 0.0766721 0.0766721i −0.667731 0.744403i \(-0.732734\pi\)
0.744403 + 0.667731i \(0.232734\pi\)
\(104\) 0 0
\(105\) 214.737 + 214.737i 0.199583 + 0.199583i
\(106\) 0 0
\(107\) −552.814 1334.61i −0.499463 1.20581i −0.949773 0.312939i \(-0.898687\pi\)
0.450310 0.892872i \(-0.351313\pi\)
\(108\) 0 0
\(109\) 490.666 + 203.241i 0.431168 + 0.178596i 0.587703 0.809077i \(-0.300032\pi\)
−0.156535 + 0.987672i \(0.550032\pi\)
\(110\) 0 0
\(111\) 755.757i 0.646246i
\(112\) 0 0
\(113\) 109.197i 0.0909060i 0.998966 + 0.0454530i \(0.0144731\pi\)
−0.998966 + 0.0454530i \(0.985527\pi\)
\(114\) 0 0
\(115\) −2058.24 852.552i −1.66898 0.691312i
\(116\) 0 0
\(117\) −108.107 260.993i −0.0854230 0.206229i
\(118\) 0 0
\(119\) 318.750 + 318.750i 0.245544 + 0.245544i
\(120\) 0 0
\(121\) 269.116 269.116i 0.202191 0.202191i
\(122\) 0 0
\(123\) −425.731 + 176.344i −0.312088 + 0.129271i
\(124\) 0 0
\(125\) 754.814 1822.28i 0.540101 1.30392i
\(126\) 0 0
\(127\) −1519.49 −1.06167 −0.530837 0.847474i \(-0.678122\pi\)
−0.530837 + 0.847474i \(0.678122\pi\)
\(128\) 0 0
\(129\) 184.143 0.125681
\(130\) 0 0
\(131\) −386.047 + 932.000i −0.257474 + 0.621597i −0.998770 0.0495811i \(-0.984211\pi\)
0.741296 + 0.671178i \(0.234211\pi\)
\(132\) 0 0
\(133\) −884.798 + 366.495i −0.576855 + 0.238941i
\(134\) 0 0
\(135\) 1639.52 1639.52i 1.04524 1.04524i
\(136\) 0 0
\(137\) 121.798 + 121.798i 0.0759557 + 0.0759557i 0.744064 0.668108i \(-0.232896\pi\)
−0.668108 + 0.744064i \(0.732896\pi\)
\(138\) 0 0
\(139\) 2.36667 + 5.71364i 0.00144416 + 0.00348651i 0.924600 0.380939i \(-0.124399\pi\)
−0.923156 + 0.384426i \(0.874399\pi\)
\(140\) 0 0
\(141\) 681.098 + 282.120i 0.406800 + 0.168502i
\(142\) 0 0
\(143\) 431.225i 0.252174i
\(144\) 0 0
\(145\) 1951.68i 1.11778i
\(146\) 0 0
\(147\) 734.505 + 304.242i 0.412115 + 0.170704i
\(148\) 0 0
\(149\) 311.513 + 752.060i 0.171276 + 0.413497i 0.986087 0.166229i \(-0.0531592\pi\)
−0.814811 + 0.579727i \(0.803159\pi\)
\(150\) 0 0
\(151\) −571.254 571.254i −0.307868 0.307868i 0.536214 0.844082i \(-0.319854\pi\)
−0.844082 + 0.536214i \(0.819854\pi\)
\(152\) 0 0
\(153\) 1041.41 1041.41i 0.550281 0.550281i
\(154\) 0 0
\(155\) 505.179 209.252i 0.261787 0.108436i
\(156\) 0 0
\(157\) −219.641 + 530.260i −0.111651 + 0.269550i −0.969822 0.243814i \(-0.921601\pi\)
0.858171 + 0.513365i \(0.171601\pi\)
\(158\) 0 0
\(159\) −350.585 −0.174863
\(160\) 0 0
\(161\) 731.190 0.357924
\(162\) 0 0
\(163\) 570.638 1377.64i 0.274207 0.661995i −0.725447 0.688278i \(-0.758367\pi\)
0.999655 + 0.0262826i \(0.00836698\pi\)
\(164\) 0 0
\(165\) −1399.26 + 579.593i −0.660196 + 0.273462i
\(166\) 0 0
\(167\) −642.374 + 642.374i −0.297655 + 0.297655i −0.840095 0.542440i \(-0.817501\pi\)
0.542440 + 0.840095i \(0.317501\pi\)
\(168\) 0 0
\(169\) −1415.16 1415.16i −0.644134 0.644134i
\(170\) 0 0
\(171\) 1197.40 + 2890.78i 0.535483 + 1.29277i
\(172\) 0 0
\(173\) −1861.21 770.937i −0.817948 0.338805i −0.0658275 0.997831i \(-0.520969\pi\)
−0.752120 + 0.659026i \(0.770969\pi\)
\(174\) 0 0
\(175\) 1420.06i 0.613406i
\(176\) 0 0
\(177\) 628.127i 0.266740i
\(178\) 0 0
\(179\) 317.221 + 131.397i 0.132459 + 0.0548664i 0.447928 0.894069i \(-0.352162\pi\)
−0.315469 + 0.948936i \(0.602162\pi\)
\(180\) 0 0
\(181\) 532.578 + 1285.76i 0.218708 + 0.528008i 0.994710 0.102722i \(-0.0327553\pi\)
−0.776002 + 0.630731i \(0.782755\pi\)
\(182\) 0 0
\(183\) 1093.17 + 1093.17i 0.441581 + 0.441581i
\(184\) 0 0
\(185\) −3858.63 + 3858.63i −1.53347 + 1.53347i
\(186\) 0 0
\(187\) −2077.02 + 860.331i −0.812230 + 0.336437i
\(188\) 0 0
\(189\) −291.220 + 703.067i −0.112080 + 0.270585i
\(190\) 0 0
\(191\) −3161.63 −1.19773 −0.598867 0.800848i \(-0.704382\pi\)
−0.598867 + 0.800848i \(0.704382\pi\)
\(192\) 0 0
\(193\) −1428.55 −0.532796 −0.266398 0.963863i \(-0.585834\pi\)
−0.266398 + 0.963863i \(0.585834\pi\)
\(194\) 0 0
\(195\) −262.975 + 634.877i −0.0965744 + 0.233151i
\(196\) 0 0
\(197\) 1377.48 570.573i 0.498181 0.206353i −0.119421 0.992844i \(-0.538104\pi\)
0.617603 + 0.786490i \(0.288104\pi\)
\(198\) 0 0
\(199\) −1207.72 + 1207.72i −0.430217 + 0.430217i −0.888702 0.458485i \(-0.848392\pi\)
0.458485 + 0.888702i \(0.348392\pi\)
\(200\) 0 0
\(201\) 1715.91 + 1715.91i 0.602143 + 0.602143i
\(202\) 0 0
\(203\) −245.131 591.798i −0.0847528 0.204611i
\(204\) 0 0
\(205\) −3073.98 1273.28i −1.04730 0.433805i
\(206\) 0 0
\(207\) 2388.92i 0.802132i
\(208\) 0 0
\(209\) 4776.28i 1.58078i
\(210\) 0 0
\(211\) 627.654 + 259.983i 0.204784 + 0.0848245i 0.482718 0.875776i \(-0.339650\pi\)
−0.277934 + 0.960600i \(0.589650\pi\)
\(212\) 0 0
\(213\) 975.239 + 2354.43i 0.313720 + 0.757386i
\(214\) 0 0
\(215\) 940.170 + 940.170i 0.298228 + 0.298228i
\(216\) 0 0
\(217\) −126.901 + 126.901i −0.0396985 + 0.0396985i
\(218\) 0 0
\(219\) 761.178 315.290i 0.234866 0.0972846i
\(220\) 0 0
\(221\) −390.353 + 942.394i −0.118814 + 0.286843i
\(222\) 0 0
\(223\) −1684.85 −0.505946 −0.252973 0.967473i \(-0.581408\pi\)
−0.252973 + 0.967473i \(0.581408\pi\)
\(224\) 0 0
\(225\) 4639.56 1.37468
\(226\) 0 0
\(227\) 1751.96 4229.60i 0.512254 1.23669i −0.430315 0.902679i \(-0.641598\pi\)
0.942569 0.334011i \(-0.108402\pi\)
\(228\) 0 0
\(229\) 1072.62 444.292i 0.309521 0.128208i −0.222515 0.974929i \(-0.571427\pi\)
0.532037 + 0.846721i \(0.321427\pi\)
\(230\) 0 0
\(231\) 351.493 351.493i 0.100115 0.100115i
\(232\) 0 0
\(233\) −224.008 224.008i −0.0629840 0.0629840i 0.674913 0.737897i \(-0.264181\pi\)
−0.737897 + 0.674913i \(0.764181\pi\)
\(234\) 0 0
\(235\) 2037.04 + 4917.85i 0.565455 + 1.36513i
\(236\) 0 0
\(237\) −1682.10 696.748i −0.461030 0.190965i
\(238\) 0 0
\(239\) 5695.35i 1.54143i −0.637181 0.770714i \(-0.719899\pi\)
0.637181 0.770714i \(-0.280101\pi\)
\(240\) 0 0
\(241\) 5864.62i 1.56752i −0.621061 0.783762i \(-0.713298\pi\)
0.621061 0.783762i \(-0.286702\pi\)
\(242\) 0 0
\(243\) 3611.13 + 1495.78i 0.953309 + 0.394874i
\(244\) 0 0
\(245\) 2196.77 + 5303.48i 0.572844 + 1.38297i
\(246\) 0 0
\(247\) −1532.38 1532.38i −0.394749 0.394749i
\(248\) 0 0
\(249\) 1826.95 1826.95i 0.464972 0.464972i
\(250\) 0 0
\(251\) −1284.55 + 532.079i −0.323029 + 0.133803i −0.538305 0.842750i \(-0.680935\pi\)
0.215276 + 0.976553i \(0.430935\pi\)
\(252\) 0 0
\(253\) −1395.50 + 3369.04i −0.346777 + 0.837193i
\(254\) 0 0
\(255\) −3582.59 −0.879805
\(256\) 0 0
\(257\) 6068.35 1.47289 0.736446 0.676497i \(-0.236503\pi\)
0.736446 + 0.676497i \(0.236503\pi\)
\(258\) 0 0
\(259\) 685.388 1654.67i 0.164432 0.396974i
\(260\) 0 0
\(261\) −1933.50 + 800.883i −0.458547 + 0.189937i
\(262\) 0 0
\(263\) 1919.51 1919.51i 0.450046 0.450046i −0.445324 0.895370i \(-0.646911\pi\)
0.895370 + 0.445324i \(0.146911\pi\)
\(264\) 0 0
\(265\) −1789.97 1789.97i −0.414931 0.414931i
\(266\) 0 0
\(267\) 231.146 + 558.035i 0.0529808 + 0.127907i
\(268\) 0 0
\(269\) 3969.40 + 1644.18i 0.899697 + 0.372667i 0.784103 0.620630i \(-0.213123\pi\)
0.115593 + 0.993297i \(0.463123\pi\)
\(270\) 0 0
\(271\) 4538.69i 1.01736i 0.860954 + 0.508682i \(0.169867\pi\)
−0.860954 + 0.508682i \(0.830133\pi\)
\(272\) 0 0
\(273\) 225.540i 0.0500011i
\(274\) 0 0
\(275\) −6543.07 2710.23i −1.43477 0.594301i
\(276\) 0 0
\(277\) −1889.91 4562.63i −0.409940 0.989683i −0.985153 0.171679i \(-0.945081\pi\)
0.575213 0.818004i \(-0.304919\pi\)
\(278\) 0 0
\(279\) 414.605 + 414.605i 0.0889669 + 0.0889669i
\(280\) 0 0
\(281\) −30.7223 + 30.7223i −0.00652220 + 0.00652220i −0.710360 0.703838i \(-0.751468\pi\)
0.703838 + 0.710360i \(0.251468\pi\)
\(282\) 0 0
\(283\) 5549.45 2298.66i 1.16565 0.482830i 0.285901 0.958259i \(-0.407707\pi\)
0.879754 + 0.475429i \(0.157707\pi\)
\(284\) 0 0
\(285\) 2912.73 7031.95i 0.605387 1.46153i
\(286\) 0 0
\(287\) 1092.03 0.224601
\(288\) 0 0
\(289\) −404.895 −0.0824130
\(290\) 0 0
\(291\) −837.954 + 2023.00i −0.168803 + 0.407527i
\(292\) 0 0
\(293\) 2663.79 1103.38i 0.531128 0.220000i −0.100969 0.994890i \(-0.532194\pi\)
0.632097 + 0.774889i \(0.282194\pi\)
\(294\) 0 0
\(295\) 3207.00 3207.00i 0.632944 0.632944i
\(296\) 0 0
\(297\) −2683.66 2683.66i −0.524316 0.524316i
\(298\) 0 0
\(299\) 633.173 + 1528.61i 0.122466 + 0.295659i
\(300\) 0 0
\(301\) −403.168 166.998i −0.0772033 0.0319787i
\(302\) 0 0
\(303\) 4407.30i 0.835620i
\(304\) 0 0
\(305\) 11162.7i 2.09565i
\(306\) 0 0
\(307\) −401.539 166.323i −0.0746484 0.0309204i 0.345047 0.938585i \(-0.387863\pi\)
−0.419695 + 0.907665i \(0.637863\pi\)
\(308\) 0 0
\(309\) −113.143 273.152i −0.0208301 0.0502883i
\(310\) 0 0
\(311\) 5345.11 + 5345.11i 0.974577 + 0.974577i 0.999685 0.0251081i \(-0.00799300\pi\)
−0.0251081 + 0.999685i \(0.507993\pi\)
\(312\) 0 0
\(313\) −1787.53 + 1787.53i −0.322803 + 0.322803i −0.849841 0.527039i \(-0.823302\pi\)
0.527039 + 0.849841i \(0.323302\pi\)
\(314\) 0 0
\(315\) −2172.32 + 899.804i −0.388560 + 0.160947i
\(316\) 0 0
\(317\) 2370.77 5723.55i 0.420050 1.01409i −0.562282 0.826945i \(-0.690077\pi\)
0.982332 0.187145i \(-0.0599234\pi\)
\(318\) 0 0
\(319\) 3194.62 0.560703
\(320\) 0 0
\(321\) −3768.08 −0.655183
\(322\) 0 0
\(323\) 4323.58 10438.0i 0.744800 1.79811i
\(324\) 0 0
\(325\) −2968.74 + 1229.69i −0.506696 + 0.209880i
\(326\) 0 0
\(327\) 979.572 979.572i 0.165659 0.165659i
\(328\) 0 0
\(329\) −1235.36 1235.36i −0.207014 0.207014i
\(330\) 0 0
\(331\) −1696.86 4096.57i −0.281775 0.680265i 0.718102 0.695938i \(-0.245011\pi\)
−0.999877 + 0.0156724i \(0.995011\pi\)
\(332\) 0 0
\(333\) −5406.09 2239.28i −0.889646 0.368503i
\(334\) 0 0
\(335\) 17521.6i 2.85764i
\(336\) 0 0
\(337\) 927.470i 0.149918i −0.997187 0.0749592i \(-0.976117\pi\)
0.997187 0.0749592i \(-0.0238826\pi\)
\(338\) 0 0
\(339\) 263.152 + 109.001i 0.0421606 + 0.0174635i
\(340\) 0 0
\(341\) −342.515 826.904i −0.0543936 0.131318i
\(342\) 0 0
\(343\) −2831.48 2831.48i −0.445731 0.445731i
\(344\) 0 0
\(345\) −4109.10 + 4109.10i −0.641237 + 0.641237i
\(346\) 0 0
\(347\) −3765.13 + 1559.57i −0.582487 + 0.241274i −0.654415 0.756136i \(-0.727085\pi\)
0.0719277 + 0.997410i \(0.477085\pi\)
\(348\) 0 0
\(349\) −1631.14 + 3937.93i −0.250181 + 0.603990i −0.998218 0.0596662i \(-0.980996\pi\)
0.748037 + 0.663657i \(0.230996\pi\)
\(350\) 0 0
\(351\) −1722.00 −0.261862
\(352\) 0 0
\(353\) −11289.2 −1.70216 −0.851080 0.525037i \(-0.824052\pi\)
−0.851080 + 0.525037i \(0.824052\pi\)
\(354\) 0 0
\(355\) −7041.69 + 17000.1i −1.05277 + 2.54162i
\(356\) 0 0
\(357\) 1086.33 449.972i 0.161049 0.0667088i
\(358\) 0 0
\(359\) −2970.97 + 2970.97i −0.436774 + 0.436774i −0.890925 0.454151i \(-0.849943\pi\)
0.454151 + 0.890925i \(0.349943\pi\)
\(360\) 0 0
\(361\) 12122.7 + 12122.7i 1.76742 + 1.76742i
\(362\) 0 0
\(363\) −379.904 917.170i −0.0549306 0.132614i
\(364\) 0 0
\(365\) 5496.07 + 2276.55i 0.788157 + 0.326465i
\(366\) 0 0
\(367\) 12266.5i 1.74470i −0.488882 0.872350i \(-0.662595\pi\)
0.488882 0.872350i \(-0.337405\pi\)
\(368\) 0 0
\(369\) 3567.84i 0.503346i
\(370\) 0 0
\(371\) 767.581 + 317.942i 0.107415 + 0.0444926i
\(372\) 0 0
\(373\) −905.804 2186.80i −0.125739 0.303561i 0.848457 0.529265i \(-0.177532\pi\)
−0.974196 + 0.225703i \(0.927532\pi\)
\(374\) 0 0
\(375\) −3638.03 3638.03i −0.500979 0.500979i
\(376\) 0 0
\(377\) 1024.93 1024.93i 0.140018 0.140018i
\(378\) 0 0
\(379\) −6881.62 + 2850.46i −0.932679 + 0.386328i −0.796694 0.604383i \(-0.793420\pi\)
−0.135985 + 0.990711i \(0.543420\pi\)
\(380\) 0 0
\(381\) −1516.76 + 3661.78i −0.203953 + 0.492385i
\(382\) 0 0
\(383\) 2433.37 0.324645 0.162323 0.986738i \(-0.448101\pi\)
0.162323 + 0.986738i \(0.448101\pi\)
\(384\) 0 0
\(385\) 3589.20 0.475124
\(386\) 0 0
\(387\) −545.609 + 1317.22i −0.0716663 + 0.173018i
\(388\) 0 0
\(389\) 4253.32 1761.78i 0.554375 0.229630i −0.0878663 0.996132i \(-0.528005\pi\)
0.642241 + 0.766503i \(0.278005\pi\)
\(390\) 0 0
\(391\) −6099.44 + 6099.44i −0.788905 + 0.788905i
\(392\) 0 0
\(393\) 1860.66 + 1860.66i 0.238824 + 0.238824i
\(394\) 0 0
\(395\) −5030.85 12145.6i −0.640835 1.54711i
\(396\) 0 0
\(397\) −306.541 126.974i −0.0387528 0.0160519i 0.363223 0.931702i \(-0.381676\pi\)
−0.401976 + 0.915650i \(0.631676\pi\)
\(398\) 0 0
\(399\) 2498.10i 0.313437i
\(400\) 0 0
\(401\) 10975.6i 1.36682i 0.730036 + 0.683409i \(0.239503\pi\)
−0.730036 + 0.683409i \(0.760497\pi\)
\(402\) 0 0
\(403\) −375.186 155.407i −0.0463755 0.0192094i
\(404\) 0 0
\(405\) 1615.74 + 3900.74i 0.198239 + 0.478591i
\(406\) 0 0
\(407\) 6316.01 + 6316.01i 0.769221 + 0.769221i
\(408\) 0 0
\(409\) 8384.88 8384.88i 1.01371 1.01371i 0.0138007 0.999905i \(-0.495607\pi\)
0.999905 0.0138007i \(-0.00439304\pi\)
\(410\) 0 0
\(411\) 415.100 171.940i 0.0498184 0.0206355i
\(412\) 0 0
\(413\) −569.642 + 1375.24i −0.0678698 + 0.163852i
\(414\) 0 0
\(415\) 18655.5 2.20666
\(416\) 0 0
\(417\) 16.1316 0.00189441
\(418\) 0 0
\(419\) −533.639 + 1288.32i −0.0622195 + 0.150211i −0.951931 0.306311i \(-0.900905\pi\)
0.889712 + 0.456522i \(0.150905\pi\)
\(420\) 0 0
\(421\) 1963.49 813.303i 0.227303 0.0941520i −0.266125 0.963938i \(-0.585744\pi\)
0.493428 + 0.869786i \(0.335744\pi\)
\(422\) 0 0
\(423\) −4036.13 + 4036.13i −0.463932 + 0.463932i
\(424\) 0 0
\(425\) −11845.8 11845.8i −1.35201 1.35201i
\(426\) 0 0
\(427\) −1402.03 3384.79i −0.158897 0.383610i
\(428\) 0 0
\(429\) 1039.20 + 430.451i 0.116954 + 0.0484438i
\(430\) 0 0
\(431\) 4521.29i 0.505297i −0.967558 0.252649i \(-0.918698\pi\)
0.967558 0.252649i \(-0.0813016\pi\)
\(432\) 0 0
\(433\) 2122.80i 0.235601i 0.993037 + 0.117801i \(0.0375844\pi\)
−0.993037 + 0.117801i \(0.962416\pi\)
\(434\) 0 0
\(435\) 4703.33 + 1948.18i 0.518408 + 0.214732i
\(436\) 0 0
\(437\) −7013.07 16931.1i −0.767691 1.85337i
\(438\) 0 0
\(439\) −8028.12 8028.12i −0.872805 0.872805i 0.119972 0.992777i \(-0.461719\pi\)
−0.992777 + 0.119972i \(0.961719\pi\)
\(440\) 0 0
\(441\) −4352.62 + 4352.62i −0.469994 + 0.469994i
\(442\) 0 0
\(443\) −3136.09 + 1299.01i −0.336343 + 0.139318i −0.544462 0.838786i \(-0.683266\pi\)
0.208119 + 0.978104i \(0.433266\pi\)
\(444\) 0 0
\(445\) −1668.98 + 4029.28i −0.177792 + 0.429227i
\(446\) 0 0
\(447\) 2123.33 0.224676
\(448\) 0 0
\(449\) −16955.9 −1.78218 −0.891088 0.453832i \(-0.850057\pi\)
−0.891088 + 0.453832i \(0.850057\pi\)
\(450\) 0 0
\(451\) −2084.18 + 5031.66i −0.217606 + 0.525347i
\(452\) 0 0
\(453\) −1946.88 + 806.426i −0.201926 + 0.0836406i
\(454\) 0 0
\(455\) 1151.53 1151.53i 0.118647 0.118647i
\(456\) 0 0
\(457\) 6223.46 + 6223.46i 0.637027 + 0.637027i 0.949821 0.312794i \(-0.101265\pi\)
−0.312794 + 0.949821i \(0.601265\pi\)
\(458\) 0 0
\(459\) −3435.55 8294.14i −0.349363 0.843437i
\(460\) 0 0
\(461\) 10872.5 + 4503.54i 1.09844 + 0.454991i 0.856944 0.515410i \(-0.172360\pi\)
0.241501 + 0.970401i \(0.422360\pi\)
\(462\) 0 0
\(463\) 13182.5i 1.32320i 0.749858 + 0.661599i \(0.230122\pi\)
−0.749858 + 0.661599i \(0.769878\pi\)
\(464\) 0 0
\(465\) 1426.30i 0.142243i
\(466\) 0 0
\(467\) −7043.25 2917.41i −0.697907 0.289083i 0.00538305 0.999986i \(-0.498287\pi\)
−0.703290 + 0.710903i \(0.748287\pi\)
\(468\) 0 0
\(469\) −2200.71 5312.99i −0.216673 0.523094i
\(470\) 0 0
\(471\) 1058.62 + 1058.62i 0.103564 + 0.103564i
\(472\) 0 0
\(473\) 1538.92 1538.92i 0.149598 0.149598i
\(474\) 0 0
\(475\) 32882.1 13620.2i 3.17628 1.31566i
\(476\) 0 0
\(477\) 1038.77 2507.81i 0.0997107 0.240723i
\(478\) 0 0
\(479\) −4612.37 −0.439968 −0.219984 0.975503i \(-0.570601\pi\)
−0.219984 + 0.975503i \(0.570601\pi\)
\(480\) 0 0
\(481\) 4052.74 0.384177
\(482\) 0 0
\(483\) 729.878 1762.08i 0.0687590 0.165999i
\(484\) 0 0
\(485\) −14607.0 + 6050.43i −1.36757 + 0.566466i
\(486\) 0 0
\(487\) 10988.9 10988.9i 1.02249 1.02249i 0.0227515 0.999741i \(-0.492757\pi\)
0.999741 0.0227515i \(-0.00724266\pi\)
\(488\) 0 0
\(489\) −2750.34 2750.34i −0.254345 0.254345i
\(490\) 0 0
\(491\) 7836.91 + 18920.0i 0.720316 + 1.73900i 0.672451 + 0.740142i \(0.265242\pi\)
0.0478645 + 0.998854i \(0.484758\pi\)
\(492\) 0 0
\(493\) 6981.49 + 2891.83i 0.637790 + 0.264181i
\(494\) 0 0
\(495\) 11726.5i 1.06478i
\(496\) 0 0
\(497\) 6039.29i 0.545069i
\(498\) 0 0
\(499\) 6404.45 + 2652.81i 0.574554 + 0.237988i 0.650990 0.759086i \(-0.274354\pi\)
−0.0764356 + 0.997075i \(0.524354\pi\)
\(500\) 0 0
\(501\) 906.824 + 2189.27i 0.0808661 + 0.195228i
\(502\) 0 0
\(503\) −2553.60 2553.60i −0.226361 0.226361i 0.584810 0.811171i \(-0.301169\pi\)
−0.811171 + 0.584810i \(0.801169\pi\)
\(504\) 0 0
\(505\) 22502.1 22502.1i 1.98283 1.98283i
\(506\) 0 0
\(507\) −4823.00 + 1997.75i −0.422479 + 0.174997i
\(508\) 0 0
\(509\) 3141.82 7585.02i 0.273593 0.660511i −0.726039 0.687654i \(-0.758641\pi\)
0.999632 + 0.0271425i \(0.00864080\pi\)
\(510\) 0 0
\(511\) −1952.48 −0.169026
\(512\) 0 0
\(513\) 19073.0 1.64151
\(514\) 0 0
\(515\) 816.948 1972.29i 0.0699010 0.168756i
\(516\) 0 0
\(517\) 8049.80 3334.34i 0.684777 0.283644i
\(518\) 0 0
\(519\) −3715.74 + 3715.74i −0.314263 + 0.314263i
\(520\) 0 0
\(521\) −7065.05 7065.05i −0.594099 0.594099i 0.344637 0.938736i \(-0.388002\pi\)
−0.938736 + 0.344637i \(0.888002\pi\)
\(522\) 0 0
\(523\) 111.041 + 268.077i 0.00928391 + 0.0224134i 0.928454 0.371449i \(-0.121139\pi\)
−0.919170 + 0.393862i \(0.871139\pi\)
\(524\) 0 0
\(525\) 3422.17 + 1417.51i 0.284487 + 0.117838i
\(526\) 0 0
\(527\) 2117.16i 0.175000i
\(528\) 0 0
\(529\) 1824.68i 0.149970i
\(530\) 0 0
\(531\) 4493.13 + 1861.11i 0.367204 + 0.152101i
\(532\) 0 0
\(533\) 945.642 + 2282.98i 0.0768486 + 0.185529i
\(534\) 0 0
\(535\) −19238.5 19238.5i −1.55468 1.55468i
\(536\) 0 0
\(537\) 633.304 633.304i 0.0508921 0.0508921i
\(538\) 0 0
\(539\) 8681.02 3595.79i 0.693725 0.287350i
\(540\) 0 0
\(541\) −8420.37 + 20328.6i −0.669168 + 1.61552i 0.113837 + 0.993499i \(0.463686\pi\)
−0.783005 + 0.622016i \(0.786314\pi\)
\(542\) 0 0
\(543\) 3630.14 0.286896
\(544\) 0 0
\(545\) 10002.7 0.786181
\(546\) 0 0
\(547\) −646.357 + 1560.44i −0.0505233 + 0.121974i −0.947126 0.320862i \(-0.896028\pi\)
0.896603 + 0.442836i \(0.146028\pi\)
\(548\) 0 0
\(549\) −11058.7 + 4580.65i −0.859696 + 0.356098i
\(550\) 0 0
\(551\) −11352.2 + 11352.2i −0.877717 + 0.877717i
\(552\) 0 0
\(553\) 3050.95 + 3050.95i 0.234611 + 0.234611i
\(554\) 0 0
\(555\) 5447.14 + 13150.5i 0.416609 + 1.00578i
\(556\) 0 0
\(557\) −6482.01 2684.93i −0.493091 0.204245i 0.122260 0.992498i \(-0.460986\pi\)
−0.615351 + 0.788253i \(0.710986\pi\)
\(558\) 0 0
\(559\) 987.467i 0.0747145i
\(560\) 0 0
\(561\) 5864.17i 0.441329i
\(562\) 0 0
\(563\) 945.289 + 391.551i 0.0707623 + 0.0293107i 0.417784 0.908546i \(-0.362807\pi\)
−0.347022 + 0.937857i \(0.612807\pi\)
\(564\) 0 0
\(565\) 787.039 + 1900.08i 0.0586035 + 0.141481i
\(566\) 0 0
\(567\) −979.862 979.862i −0.0725756 0.0725756i
\(568\) 0 0
\(569\) −3760.45 + 3760.45i −0.277058 + 0.277058i −0.831934 0.554875i \(-0.812766\pi\)
0.554875 + 0.831934i \(0.312766\pi\)
\(570\) 0 0
\(571\) −2056.20 + 851.705i −0.150699 + 0.0624216i −0.456758 0.889591i \(-0.650990\pi\)
0.306059 + 0.952013i \(0.400990\pi\)
\(572\) 0 0
\(573\) −3155.95 + 7619.15i −0.230091 + 0.555488i
\(574\) 0 0
\(575\) −27173.5 −1.97080
\(576\) 0 0
\(577\) −23621.3 −1.70427 −0.852137 0.523318i \(-0.824694\pi\)
−0.852137 + 0.523318i \(0.824694\pi\)
\(578\) 0 0
\(579\) −1425.99 + 3442.65i −0.102353 + 0.247101i
\(580\) 0 0
\(581\) −5656.80 + 2343.13i −0.403931 + 0.167314i
\(582\) 0 0
\(583\) −2929.91 + 2929.91i −0.208138 + 0.208138i
\(584\) 0 0
\(585\) −3762.23 3762.23i −0.265896 0.265896i
\(586\) 0 0
\(587\) −7316.12 17662.7i −0.514427 1.24194i −0.941283 0.337617i \(-0.890379\pi\)
0.426857 0.904319i \(-0.359621\pi\)
\(588\) 0 0
\(589\) 4155.59 + 1721.30i 0.290710 + 0.120416i
\(590\) 0 0
\(591\) 3889.13i 0.270689i
\(592\) 0 0
\(593\) 16542.0i 1.14553i −0.819720 0.572764i \(-0.805871\pi\)
0.819720 0.572764i \(-0.194129\pi\)
\(594\) 0 0
\(595\) 7843.81 + 3249.01i 0.540445 + 0.223860i
\(596\) 0 0
\(597\) 1704.91 + 4116.02i 0.116880 + 0.282174i
\(598\) 0 0
\(599\) 8579.81 + 8579.81i 0.585244 + 0.585244i 0.936340 0.351095i \(-0.114191\pi\)
−0.351095 + 0.936340i \(0.614191\pi\)
\(600\) 0 0
\(601\) −13633.8 + 13633.8i −0.925346 + 0.925346i −0.997401 0.0720542i \(-0.977045\pi\)
0.0720542 + 0.997401i \(0.477045\pi\)
\(602\) 0 0
\(603\) −17358.4 + 7190.09i −1.17229 + 0.485578i
\(604\) 0 0
\(605\) 2743.09 6622.41i 0.184335 0.445023i
\(606\) 0 0
\(607\) 23984.1 1.60376 0.801881 0.597484i \(-0.203833\pi\)
0.801881 + 0.597484i \(0.203833\pi\)
\(608\) 0 0
\(609\) −1670.86 −0.111176
\(610\) 0 0
\(611\) 1512.87 3652.38i 0.100170 0.241833i
\(612\) 0 0
\(613\) 18072.9 7486.04i 1.19080 0.493244i 0.302782 0.953060i \(-0.402085\pi\)
0.888014 + 0.459816i \(0.152085\pi\)
\(614\) 0 0
\(615\) −6136.93 + 6136.93i −0.402382 + 0.402382i
\(616\) 0 0
\(617\) 18674.2 + 18674.2i 1.21847 + 1.21847i 0.968168 + 0.250301i \(0.0805297\pi\)
0.250301 + 0.968168i \(0.419470\pi\)
\(618\) 0 0
\(619\) −3214.09 7759.51i −0.208700 0.503846i 0.784519 0.620105i \(-0.212910\pi\)
−0.993219 + 0.116258i \(0.962910\pi\)
\(620\) 0 0
\(621\) −13453.5 5572.64i −0.869359 0.360100i
\(622\) 0 0
\(623\) 1431.40i 0.0920511i
\(624\) 0 0
\(625\) 8433.25i 0.539728i
\(626\) 0 0
\(627\) −11510.3 4767.71i −0.733136 0.303675i
\(628\) 0 0
\(629\) 8085.58 + 19520.3i 0.512549 + 1.23740i
\(630\) 0 0
\(631\) 20023.0 + 20023.0i 1.26324 + 1.26324i 0.949515 + 0.313722i \(0.101576\pi\)
0.313722 + 0.949515i \(0.398424\pi\)
\(632\) 0 0
\(633\) 1253.06 1253.06i 0.0786801 0.0786801i
\(634\) 0 0
\(635\) −26439.8 + 10951.7i −1.65233 + 0.684419i
\(636\) 0 0
\(637\) 1631.50 3938.78i 0.101479 0.244992i
\(638\) 0 0
\(639\) −19731.4 −1.22154
\(640\) 0 0
\(641\) 8637.88 0.532255 0.266128 0.963938i \(-0.414256\pi\)
0.266128 + 0.963938i \(0.414256\pi\)
\(642\) 0 0
\(643\) −5274.73 + 12734.3i −0.323507 + 0.781015i 0.675538 + 0.737325i \(0.263911\pi\)
−0.999045 + 0.0436901i \(0.986089\pi\)
\(644\) 0 0
\(645\) 3204.18 1327.22i 0.195604 0.0810219i
\(646\) 0 0
\(647\) 14785.3 14785.3i 0.898406 0.898406i −0.0968891 0.995295i \(-0.530889\pi\)
0.995295 + 0.0968891i \(0.0308892\pi\)
\(648\) 0 0
\(649\) −5249.38 5249.38i −0.317498 0.317498i
\(650\) 0 0
\(651\) 179.143 + 432.488i 0.0107852 + 0.0260377i
\(652\) 0 0
\(653\) −25046.7 10374.7i −1.50100 0.621733i −0.527321 0.849666i \(-0.676803\pi\)
−0.973677 + 0.227933i \(0.926803\pi\)
\(654\) 0 0
\(655\) 18999.7i 1.13340i
\(656\) 0 0
\(657\) 6379.06i 0.378799i
\(658\) 0 0
\(659\) 23962.3 + 9925.50i 1.41645 + 0.586711i 0.953965 0.299918i \(-0.0969594\pi\)
0.462481 + 0.886629i \(0.346959\pi\)
\(660\) 0 0
\(661\) −398.063 961.010i −0.0234234 0.0565491i 0.911735 0.410779i \(-0.134743\pi\)
−0.935158 + 0.354230i \(0.884743\pi\)
\(662\) 0 0
\(663\) 1881.41 + 1881.41i 0.110208 + 0.110208i
\(664\) 0 0
\(665\) −12754.4 + 12754.4i −0.743752 + 0.743752i
\(666\) 0 0
\(667\) 11324.4 4690.70i 0.657392 0.272301i
\(668\) 0 0
\(669\) −1681.83 + 4060.30i −0.0971948 + 0.234649i
\(670\) 0 0
\(671\) 18271.6 1.05122
\(672\) 0 0
\(673\) −15307.7 −0.876775 −0.438387 0.898786i \(-0.644450\pi\)
−0.438387 + 0.898786i \(0.644450\pi\)
\(674\) 0 0
\(675\) 10822.7 26128.3i 0.617135 1.48990i
\(676\) 0 0
\(677\) −1043.10 + 432.068i −0.0592168 + 0.0245284i −0.412095 0.911141i \(-0.635203\pi\)
0.352878 + 0.935669i \(0.385203\pi\)
\(678\) 0 0
\(679\) 3669.28 3669.28i 0.207384 0.207384i
\(680\) 0 0
\(681\) −8444.03 8444.03i −0.475148 0.475148i
\(682\) 0 0
\(683\) 8946.40 + 21598.5i 0.501207 + 1.21002i 0.948827 + 0.315797i \(0.102272\pi\)
−0.447619 + 0.894224i \(0.647728\pi\)
\(684\) 0 0
\(685\) 2997.22 + 1241.49i 0.167179 + 0.0692479i
\(686\) 0 0
\(687\) 3028.37i 0.168180i
\(688\) 0 0
\(689\) 1880.01i 0.103952i
\(690\) 0 0
\(691\) −19676.4 8150.22i −1.08325 0.448696i −0.231600 0.972811i \(-0.574396\pi\)
−0.851647 + 0.524115i \(0.824396\pi\)
\(692\) 0 0
\(693\) 1472.85 + 3555.77i 0.0807342 + 0.194910i
\(694\) 0 0
\(695\) 82.3624 + 82.3624i 0.00449523 + 0.00449523i
\(696\) 0 0
\(697\) −9109.50 + 9109.50i −0.495046 + 0.495046i
\(698\) 0 0
\(699\) −763.440 + 316.227i −0.0413104 + 0.0171113i
\(700\) 0 0
\(701\) 2739.27 6613.19i 0.147591 0.356315i −0.832744 0.553658i \(-0.813231\pi\)
0.980334 + 0.197343i \(0.0632313\pi\)
\(702\) 0 0
\(703\) −44888.5 −2.40825
\(704\) 0 0
\(705\) 13884.8 0.741749
\(706\) 0 0
\(707\) −3996.93 + 9649.45i −0.212617 + 0.513303i
\(708\) 0 0
\(709\) −2388.26 + 989.248i −0.126506 + 0.0524005i −0.445039 0.895511i \(-0.646810\pi\)
0.318532 + 0.947912i \(0.396810\pi\)
\(710\) 0 0
\(711\) 9967.97 9967.97i 0.525778 0.525778i
\(712\) 0 0
\(713\) −2428.31 2428.31i −0.127547 0.127547i
\(714\) 0 0
\(715\) 3108.06 + 7503.53i 0.162566 + 0.392470i
\(716\) 0 0
\(717\) −13725.1 5685.13i −0.714887 0.296116i
\(718\) 0 0
\(719\) 11843.1i 0.614288i −0.951663 0.307144i \(-0.900627\pi\)
0.951663 0.307144i \(-0.0993734\pi\)
\(720\) 0 0
\(721\) 700.654i 0.0361910i
\(722\) 0 0
\(723\) −14133.0 5854.10i −0.726990 0.301129i
\(724\) 0 0
\(725\) 9109.88 + 21993.2i 0.466665 + 1.12663i
\(726\) 0 0
\(727\) 4691.36 + 4691.36i 0.239330 + 0.239330i 0.816573 0.577243i \(-0.195871\pi\)
−0.577243 + 0.816573i \(0.695871\pi\)
\(728\) 0 0
\(729\) 2929.40 2929.40i 0.148829 0.148829i
\(730\) 0 0
\(731\) 4756.20 1970.08i 0.240649 0.0996801i
\(732\) 0 0
\(733\) 13224.6 31927.0i 0.666386 1.60880i −0.121224 0.992625i \(-0.538682\pi\)
0.787610 0.616174i \(-0.211318\pi\)
\(734\) 0 0
\(735\) 14973.6 0.751441
\(736\) 0 0
\(737\) 28680.4 1.43345
\(738\) 0 0
\(739\) 13199.0 31865.1i 0.657012 1.58617i −0.145383 0.989375i \(-0.546442\pi\)
0.802396 0.596793i \(-0.203558\pi\)
\(740\) 0 0
\(741\) −5222.48 + 2163.22i −0.258911 + 0.107244i
\(742\) 0 0
\(743\) 14307.6 14307.6i 0.706452 0.706452i −0.259335 0.965787i \(-0.583503\pi\)
0.965787 + 0.259335i \(0.0835035\pi\)
\(744\) 0 0
\(745\) 10841.0 + 10841.0i 0.533131 + 0.533131i
\(746\) 0 0
\(747\) 7655.38 + 18481.7i 0.374961 + 0.905235i
\(748\) 0 0
\(749\) 8249.93 + 3417.23i 0.402464 + 0.166706i
\(750\) 0 0
\(751\) 15781.7i 0.766820i 0.923578 + 0.383410i \(0.125250\pi\)
−0.923578 + 0.383410i \(0.874750\pi\)
\(752\) 0 0
\(753\) 3626.75i 0.175519i
\(754\) 0 0
\(755\) −14057.4 5822.78i −0.677619 0.280679i
\(756\) 0 0
\(757\) −15069.9 36382.0i −0.723548 1.74680i −0.662983 0.748635i \(-0.730710\pi\)
−0.0605650 0.998164i \(-0.519290\pi\)
\(758\) 0 0
\(759\) 6726.00 + 6726.00i 0.321658 + 0.321658i
\(760\) 0 0
\(761\) −12120.7 + 12120.7i −0.577363 + 0.577363i −0.934176 0.356813i \(-0.883863\pi\)
0.356813 + 0.934176i \(0.383863\pi\)
\(762\) 0 0
\(763\) −3033.06 + 1256.34i −0.143911 + 0.0596100i
\(764\) 0 0
\(765\) 10615.1 25627.0i 0.501684 1.21117i
\(766\) 0 0
\(767\) −3368.33 −0.158570
\(768\) 0 0
\(769\) 5213.88 0.244496 0.122248 0.992500i \(-0.460990\pi\)
0.122248 + 0.992500i \(0.460990\pi\)
\(770\) 0 0
\(771\) 6057.46 14624.0i 0.282950 0.683101i
\(772\) 0 0
\(773\) 25960.5 10753.2i 1.20793 0.500343i 0.314380 0.949297i \(-0.398203\pi\)
0.893555 + 0.448954i \(0.148203\pi\)
\(774\) 0 0
\(775\) 4716.05 4716.05i 0.218588 0.218588i
\(776\) 0 0
\(777\) −3303.41 3303.41i −0.152521 0.152521i
\(778\) 0 0
\(779\) −10474.0 25286.5i −0.481733 1.16301i
\(780\) 0 0
\(781\) 27826.7 + 11526.2i 1.27493 + 0.528093i
\(782\) 0 0
\(783\) 12757.0i 0.582246i
\(784\) 0 0
\(785\) 10809.9i 0.491491i
\(786\) 0 0