Properties

Label 128.4.g.a.113.6
Level $128$
Weight $4$
Character 128.113
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 113.6
Character \(\chi\) \(=\) 128.113
Dual form 128.4.g.a.17.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +O(q^{10})\) \(q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +(20.1053 - 48.5384i) q^{11} +(37.8086 - 15.6609i) q^{13} -22.0920i q^{15} -53.0615i q^{17} +(32.4427 - 13.4382i) q^{19} +(-12.1781 + 29.4006i) q^{21} +(-32.1343 + 32.1343i) q^{23} +(132.981 + 132.981i) q^{25} +(60.4929 + 25.0570i) q^{27} +(-52.0634 - 125.692i) q^{29} +53.3354 q^{31} +65.5976 q^{33} +(-172.576 - 416.634i) q^{35} +(-57.3789 - 23.7671i) q^{37} +(36.1309 + 36.1309i) q^{39} +(240.383 - 240.383i) q^{41} +(-56.3244 + 135.979i) q^{43} +(-415.879 + 172.263i) q^{45} +314.904i q^{47} +306.601i q^{49} +(61.2086 - 25.3534i) q^{51} +(-177.524 + 428.580i) q^{53} +(-657.312 + 657.312i) q^{55} +(31.0031 + 31.0031i) q^{57} +(133.963 + 55.4894i) q^{59} +(-191.454 - 462.211i) q^{61} +648.422 q^{63} -724.089 q^{65} +(55.4766 + 133.932i) q^{67} +(-52.4224 - 21.7141i) q^{69} +(-191.132 - 191.132i) q^{71} +(-175.452 + 175.452i) q^{73} +(-89.8593 + 216.940i) q^{75} +(1237.11 - 512.428i) q^{77} -1222.08i q^{79} -605.154i q^{81} +(-896.581 + 371.376i) q^{83} +(-359.282 + 867.384i) q^{85} +(120.115 - 120.115i) q^{87} +(883.293 + 883.293i) q^{89} +(963.639 + 399.152i) q^{91} +(25.4843 + 61.5246i) q^{93} -621.324 q^{95} -682.976 q^{97} +(-511.499 - 1234.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0.477813 + 1.15354i 0.0919551 + 0.221999i 0.963165 0.268912i \(-0.0866640\pi\)
−0.871210 + 0.490911i \(0.836664\pi\)
\(4\) 0 0
\(5\) −16.3468 6.77105i −1.46210 0.605621i −0.497057 0.867718i \(-0.665586\pi\)
−0.965042 + 0.262096i \(0.915586\pi\)
\(6\) 0 0
\(7\) 18.0222 + 18.0222i 0.973108 + 0.973108i 0.999648 0.0265394i \(-0.00844875\pi\)
−0.0265394 + 0.999648i \(0.508449\pi\)
\(8\) 0 0
\(9\) 17.9895 17.9895i 0.666279 0.666279i
\(10\) 0 0
\(11\) 20.1053 48.5384i 0.551088 1.33044i −0.365575 0.930782i \(-0.619128\pi\)
0.916663 0.399662i \(-0.130872\pi\)
\(12\) 0 0
\(13\) 37.8086 15.6609i 0.806633 0.334118i 0.0590233 0.998257i \(-0.481201\pi\)
0.747610 + 0.664138i \(0.231201\pi\)
\(14\) 0 0
\(15\) 22.0920i 0.380275i
\(16\) 0 0
\(17\) 53.0615i 0.757018i −0.925598 0.378509i \(-0.876437\pi\)
0.925598 0.378509i \(-0.123563\pi\)
\(18\) 0 0
\(19\) 32.4427 13.4382i 0.391730 0.162260i −0.178120 0.984009i \(-0.557001\pi\)
0.569850 + 0.821749i \(0.307001\pi\)
\(20\) 0 0
\(21\) −12.1781 + 29.4006i −0.126547 + 0.305512i
\(22\) 0 0
\(23\) −32.1343 + 32.1343i −0.291324 + 0.291324i −0.837603 0.546279i \(-0.816044\pi\)
0.546279 + 0.837603i \(0.316044\pi\)
\(24\) 0 0
\(25\) 132.981 + 132.981i 1.06385 + 1.06385i
\(26\) 0 0
\(27\) 60.4929 + 25.0570i 0.431180 + 0.178601i
\(28\) 0 0
\(29\) −52.0634 125.692i −0.333377 0.804842i −0.998320 0.0579483i \(-0.981544\pi\)
0.664943 0.746894i \(-0.268456\pi\)
\(30\) 0 0
\(31\) 53.3354 0.309010 0.154505 0.987992i \(-0.450622\pi\)
0.154505 + 0.987992i \(0.450622\pi\)
\(32\) 0 0
\(33\) 65.5976 0.346033
\(34\) 0 0
\(35\) −172.576 416.634i −0.833446 2.01212i
\(36\) 0 0
\(37\) −57.3789 23.7671i −0.254947 0.105602i 0.251550 0.967844i \(-0.419060\pi\)
−0.506497 + 0.862242i \(0.669060\pi\)
\(38\) 0 0
\(39\) 36.1309 + 36.1309i 0.148348 + 0.148348i
\(40\) 0 0
\(41\) 240.383 240.383i 0.915647 0.915647i −0.0810624 0.996709i \(-0.525831\pi\)
0.996709 + 0.0810624i \(0.0258313\pi\)
\(42\) 0 0
\(43\) −56.3244 + 135.979i −0.199753 + 0.482247i −0.991736 0.128297i \(-0.959049\pi\)
0.791983 + 0.610544i \(0.209049\pi\)
\(44\) 0 0
\(45\) −415.879 + 172.263i −1.37768 + 0.570653i
\(46\) 0 0
\(47\) 314.904i 0.977309i 0.872477 + 0.488655i \(0.162512\pi\)
−0.872477 + 0.488655i \(0.837488\pi\)
\(48\) 0 0
\(49\) 306.601i 0.893880i
\(50\) 0 0
\(51\) 61.2086 25.3534i 0.168057 0.0696116i
\(52\) 0 0
\(53\) −177.524 + 428.580i −0.460089 + 1.11075i 0.508271 + 0.861197i \(0.330285\pi\)
−0.968360 + 0.249557i \(0.919715\pi\)
\(54\) 0 0
\(55\) −657.312 + 657.312i −1.61149 + 1.61149i
\(56\) 0 0
\(57\) 31.0031 + 31.0031i 0.0720431 + 0.0720431i
\(58\) 0 0
\(59\) 133.963 + 55.4894i 0.295602 + 0.122442i 0.525556 0.850759i \(-0.323857\pi\)
−0.229954 + 0.973202i \(0.573857\pi\)
\(60\) 0 0
\(61\) −191.454 462.211i −0.401855 0.970164i −0.987216 0.159391i \(-0.949047\pi\)
0.585360 0.810773i \(-0.300953\pi\)
\(62\) 0 0
\(63\) 648.422 1.29672
\(64\) 0 0
\(65\) −724.089 −1.38173
\(66\) 0 0
\(67\) 55.4766 + 133.932i 0.101157 + 0.244216i 0.966353 0.257218i \(-0.0828060\pi\)
−0.865196 + 0.501434i \(0.832806\pi\)
\(68\) 0 0
\(69\) −52.4224 21.7141i −0.0914625 0.0378850i
\(70\) 0 0
\(71\) −191.132 191.132i −0.319482 0.319482i 0.529086 0.848568i \(-0.322535\pi\)
−0.848568 + 0.529086i \(0.822535\pi\)
\(72\) 0 0
\(73\) −175.452 + 175.452i −0.281302 + 0.281302i −0.833628 0.552326i \(-0.813740\pi\)
0.552326 + 0.833628i \(0.313740\pi\)
\(74\) 0 0
\(75\) −89.8593 + 216.940i −0.138347 + 0.334000i
\(76\) 0 0
\(77\) 1237.11 512.428i 1.83093 0.758398i
\(78\) 0 0
\(79\) 1222.08i 1.74043i −0.492668 0.870217i \(-0.663978\pi\)
0.492668 0.870217i \(-0.336022\pi\)
\(80\) 0 0
\(81\) 605.154i 0.830116i
\(82\) 0 0
\(83\) −896.581 + 371.376i −1.18569 + 0.491131i −0.886351 0.463015i \(-0.846768\pi\)
−0.299344 + 0.954145i \(0.596768\pi\)
\(84\) 0 0
\(85\) −359.282 + 867.384i −0.458466 + 1.10684i
\(86\) 0 0
\(87\) 120.115 120.115i 0.148019 0.148019i
\(88\) 0 0
\(89\) 883.293 + 883.293i 1.05201 + 1.05201i 0.998571 + 0.0534390i \(0.0170183\pi\)
0.0534390 + 0.998571i \(0.482982\pi\)
\(90\) 0 0
\(91\) 963.639 + 399.152i 1.11007 + 0.459808i
\(92\) 0 0
\(93\) 25.4843 + 61.5246i 0.0284151 + 0.0686001i
\(94\) 0 0
\(95\) −621.324 −0.671016
\(96\) 0 0
\(97\) −682.976 −0.714904 −0.357452 0.933932i \(-0.616354\pi\)
−0.357452 + 0.933932i \(0.616354\pi\)
\(98\) 0 0
\(99\) −511.499 1234.87i −0.519268 1.25362i
\(100\) 0 0
\(101\) 919.967 + 381.063i 0.906338 + 0.375417i 0.786654 0.617395i \(-0.211812\pi\)
0.119684 + 0.992812i \(0.461812\pi\)
\(102\) 0 0
\(103\) 188.265 + 188.265i 0.180100 + 0.180100i 0.791400 0.611299i \(-0.209353\pi\)
−0.611299 + 0.791400i \(0.709353\pi\)
\(104\) 0 0
\(105\) 398.146 398.146i 0.370049 0.370049i
\(106\) 0 0
\(107\) 48.3932 116.832i 0.0437229 0.105556i −0.900509 0.434837i \(-0.856806\pi\)
0.944232 + 0.329280i \(0.106806\pi\)
\(108\) 0 0
\(109\) 394.289 163.320i 0.346477 0.143516i −0.202657 0.979250i \(-0.564958\pi\)
0.549134 + 0.835734i \(0.314958\pi\)
\(110\) 0 0
\(111\) 77.5452i 0.0663087i
\(112\) 0 0
\(113\) 914.060i 0.760952i −0.924791 0.380476i \(-0.875760\pi\)
0.924791 0.380476i \(-0.124240\pi\)
\(114\) 0 0
\(115\) 742.874 307.709i 0.602377 0.249513i
\(116\) 0 0
\(117\) 398.428 961.891i 0.314827 0.760059i
\(118\) 0 0
\(119\) 956.286 956.286i 0.736660 0.736660i
\(120\) 0 0
\(121\) −1010.60 1010.60i −0.759276 0.759276i
\(122\) 0 0
\(123\) 392.150 + 162.434i 0.287471 + 0.119074i
\(124\) 0 0
\(125\) −427.009 1030.89i −0.305543 0.737645i
\(126\) 0 0
\(127\) 2159.36 1.50876 0.754379 0.656439i \(-0.227938\pi\)
0.754379 + 0.656439i \(0.227938\pi\)
\(128\) 0 0
\(129\) −183.770 −0.125427
\(130\) 0 0
\(131\) 896.246 + 2163.73i 0.597751 + 1.44310i 0.875867 + 0.482552i \(0.160290\pi\)
−0.278116 + 0.960547i \(0.589710\pi\)
\(132\) 0 0
\(133\) 826.876 + 342.503i 0.539092 + 0.223299i
\(134\) 0 0
\(135\) −819.201 819.201i −0.522264 0.522264i
\(136\) 0 0
\(137\) −118.307 + 118.307i −0.0737786 + 0.0737786i −0.743033 0.669255i \(-0.766614\pi\)
0.669255 + 0.743033i \(0.266614\pi\)
\(138\) 0 0
\(139\) −924.203 + 2231.22i −0.563956 + 1.36151i 0.342623 + 0.939473i \(0.388685\pi\)
−0.906579 + 0.422037i \(0.861315\pi\)
\(140\) 0 0
\(141\) −363.255 + 150.465i −0.216962 + 0.0898686i
\(142\) 0 0
\(143\) 2150.04i 1.25731i
\(144\) 0 0
\(145\) 2407.18i 1.37866i
\(146\) 0 0
\(147\) −353.677 + 146.498i −0.198441 + 0.0821968i
\(148\) 0 0
\(149\) 366.708 885.311i 0.201623 0.486762i −0.790434 0.612547i \(-0.790145\pi\)
0.992058 + 0.125785i \(0.0401450\pi\)
\(150\) 0 0
\(151\) −1212.74 + 1212.74i −0.653584 + 0.653584i −0.953854 0.300270i \(-0.902923\pi\)
0.300270 + 0.953854i \(0.402923\pi\)
\(152\) 0 0
\(153\) −954.551 954.551i −0.504385 0.504385i
\(154\) 0 0
\(155\) −871.861 361.137i −0.451804 0.187143i
\(156\) 0 0
\(157\) 896.752 + 2164.95i 0.455851 + 1.10052i 0.970062 + 0.242858i \(0.0780848\pi\)
−0.514211 + 0.857664i \(0.671915\pi\)
\(158\) 0 0
\(159\) −579.208 −0.288894
\(160\) 0 0
\(161\) −1158.26 −0.566980
\(162\) 0 0
\(163\) −363.960 878.678i −0.174893 0.422229i 0.811989 0.583673i \(-0.198385\pi\)
−0.986882 + 0.161444i \(0.948385\pi\)
\(164\) 0 0
\(165\) −1072.31 444.165i −0.505934 0.209565i
\(166\) 0 0
\(167\) −800.950 800.950i −0.371134 0.371134i 0.496756 0.867890i \(-0.334524\pi\)
−0.867890 + 0.496756i \(0.834524\pi\)
\(168\) 0 0
\(169\) −369.282 + 369.282i −0.168085 + 0.168085i
\(170\) 0 0
\(171\) 341.882 825.376i 0.152891 0.369112i
\(172\) 0 0
\(173\) 217.486 90.0857i 0.0955790 0.0395901i −0.334382 0.942438i \(-0.608527\pi\)
0.429961 + 0.902848i \(0.358527\pi\)
\(174\) 0 0
\(175\) 4793.23i 2.07048i
\(176\) 0 0
\(177\) 181.046i 0.0768826i
\(178\) 0 0
\(179\) 1959.23 811.539i 0.818099 0.338868i 0.0659185 0.997825i \(-0.479002\pi\)
0.752180 + 0.658957i \(0.229002\pi\)
\(180\) 0 0
\(181\) −468.260 + 1130.48i −0.192295 + 0.464242i −0.990392 0.138287i \(-0.955840\pi\)
0.798097 + 0.602529i \(0.205840\pi\)
\(182\) 0 0
\(183\) 441.700 441.700i 0.178423 0.178423i
\(184\) 0 0
\(185\) 777.031 + 777.031i 0.308803 + 0.308803i
\(186\) 0 0
\(187\) −2575.52 1066.82i −1.00717 0.417183i
\(188\) 0 0
\(189\) 638.634 + 1541.80i 0.245787 + 0.593383i
\(190\) 0 0
\(191\) −5115.66 −1.93799 −0.968996 0.247078i \(-0.920530\pi\)
−0.968996 + 0.247078i \(0.920530\pi\)
\(192\) 0 0
\(193\) 4101.82 1.52982 0.764910 0.644137i \(-0.222783\pi\)
0.764910 + 0.644137i \(0.222783\pi\)
\(194\) 0 0
\(195\) −345.979 835.267i −0.127057 0.306742i
\(196\) 0 0
\(197\) −2365.10 979.657i −0.855363 0.354303i −0.0884706 0.996079i \(-0.528198\pi\)
−0.766892 + 0.641776i \(0.778198\pi\)
\(198\) 0 0
\(199\) 3419.40 + 3419.40i 1.21807 + 1.21807i 0.968309 + 0.249757i \(0.0803506\pi\)
0.249757 + 0.968309i \(0.419649\pi\)
\(200\) 0 0
\(201\) −127.989 + 127.989i −0.0449138 + 0.0449138i
\(202\) 0 0
\(203\) 1326.95 3203.55i 0.458787 1.10761i
\(204\) 0 0
\(205\) −5557.13 + 2301.84i −1.89330 + 0.784231i
\(206\) 0 0
\(207\) 1156.16i 0.388206i
\(208\) 0 0
\(209\) 1844.90i 0.610594i
\(210\) 0 0
\(211\) −4175.73 + 1729.64i −1.36241 + 0.564330i −0.939720 0.341944i \(-0.888915\pi\)
−0.422692 + 0.906273i \(0.638915\pi\)
\(212\) 0 0
\(213\) 129.154 311.805i 0.0415468 0.100303i
\(214\) 0 0
\(215\) 1841.44 1841.44i 0.584118 0.584118i
\(216\) 0 0
\(217\) 961.222 + 961.222i 0.300701 + 0.300701i
\(218\) 0 0
\(219\) −286.224 118.558i −0.0883160 0.0365817i
\(220\) 0 0
\(221\) −830.988 2006.18i −0.252934 0.610636i
\(222\) 0 0
\(223\) −717.256 −0.215386 −0.107693 0.994184i \(-0.534346\pi\)
−0.107693 + 0.994184i \(0.534346\pi\)
\(224\) 0 0
\(225\) 4784.54 1.41764
\(226\) 0 0
\(227\) 2316.16 + 5591.71i 0.677221 + 1.63496i 0.769056 + 0.639181i \(0.220727\pi\)
−0.0918358 + 0.995774i \(0.529273\pi\)
\(228\) 0 0
\(229\) −197.065 81.6271i −0.0568665 0.0235549i 0.354069 0.935219i \(-0.384798\pi\)
−0.410935 + 0.911664i \(0.634798\pi\)
\(230\) 0 0
\(231\) 1182.21 + 1182.21i 0.336727 + 0.336727i
\(232\) 0 0
\(233\) −4600.59 + 4600.59i −1.29354 + 1.29354i −0.360955 + 0.932583i \(0.617549\pi\)
−0.932583 + 0.360955i \(0.882451\pi\)
\(234\) 0 0
\(235\) 2132.23 5147.67i 0.591879 1.42892i
\(236\) 0 0
\(237\) 1409.72 583.924i 0.386375 0.160042i
\(238\) 0 0
\(239\) 1366.19i 0.369755i 0.982762 + 0.184878i \(0.0591889\pi\)
−0.982762 + 0.184878i \(0.940811\pi\)
\(240\) 0 0
\(241\) 1568.87i 0.419336i −0.977773 0.209668i \(-0.932762\pi\)
0.977773 0.209668i \(-0.0672382\pi\)
\(242\) 0 0
\(243\) 2331.38 965.689i 0.615465 0.254934i
\(244\) 0 0
\(245\) 2076.01 5011.93i 0.541353 1.30694i
\(246\) 0 0
\(247\) 1016.16 1016.16i 0.261768 0.261768i
\(248\) 0 0
\(249\) −856.796 856.796i −0.218061 0.218061i
\(250\) 0 0
\(251\) −1774.13 734.870i −0.446144 0.184799i 0.148289 0.988944i \(-0.452623\pi\)
−0.594433 + 0.804145i \(0.702623\pi\)
\(252\) 0 0
\(253\) 913.678 + 2205.81i 0.227045 + 0.548136i
\(254\) 0 0
\(255\) −1172.23 −0.287875
\(256\) 0 0
\(257\) 805.660 0.195547 0.0977737 0.995209i \(-0.468828\pi\)
0.0977737 + 0.995209i \(0.468828\pi\)
\(258\) 0 0
\(259\) −605.759 1462.43i −0.145328 0.350854i
\(260\) 0 0
\(261\) −3197.74 1324.55i −0.758371 0.314128i
\(262\) 0 0
\(263\) −2159.44 2159.44i −0.506300 0.506300i 0.407089 0.913389i \(-0.366544\pi\)
−0.913389 + 0.407089i \(0.866544\pi\)
\(264\) 0 0
\(265\) 5803.87 5803.87i 1.34539 1.34539i
\(266\) 0 0
\(267\) −596.867 + 1440.96i −0.136808 + 0.330283i
\(268\) 0 0
\(269\) 2403.35 995.499i 0.544738 0.225638i −0.0933062 0.995637i \(-0.529744\pi\)
0.638045 + 0.769999i \(0.279744\pi\)
\(270\) 0 0
\(271\) 363.916i 0.0815731i 0.999168 + 0.0407866i \(0.0129864\pi\)
−0.999168 + 0.0407866i \(0.987014\pi\)
\(272\) 0 0
\(273\) 1302.32i 0.288717i
\(274\) 0 0
\(275\) 9128.32 3781.08i 2.00167 0.829118i
\(276\) 0 0
\(277\) 236.874 571.865i 0.0513805 0.124043i −0.896105 0.443842i \(-0.853615\pi\)
0.947486 + 0.319798i \(0.103615\pi\)
\(278\) 0 0
\(279\) 959.479 959.479i 0.205887 0.205887i
\(280\) 0 0
\(281\) −5905.54 5905.54i −1.25372 1.25372i −0.954040 0.299680i \(-0.903120\pi\)
−0.299680 0.954040i \(-0.596880\pi\)
\(282\) 0 0
\(283\) 2127.03 + 881.046i 0.446781 + 0.185063i 0.594719 0.803934i \(-0.297264\pi\)
−0.147938 + 0.988997i \(0.547264\pi\)
\(284\) 0 0
\(285\) −296.877 716.723i −0.0617033 0.148965i
\(286\) 0 0
\(287\) 8664.47 1.78205
\(288\) 0 0
\(289\) 2097.48 0.426924
\(290\) 0 0
\(291\) −326.334 787.841i −0.0657391 0.158708i
\(292\) 0 0
\(293\) 1783.51 + 738.755i 0.355610 + 0.147299i 0.553335 0.832959i \(-0.313355\pi\)
−0.197724 + 0.980258i \(0.563355\pi\)
\(294\) 0 0
\(295\) −1814.14 1814.14i −0.358046 0.358046i
\(296\) 0 0
\(297\) 2432.45 2432.45i 0.475237 0.475237i
\(298\) 0 0
\(299\) −711.703 + 1718.20i −0.137655 + 0.332329i
\(300\) 0 0
\(301\) −3465.74 + 1435.56i −0.663660 + 0.274897i
\(302\) 0 0
\(303\) 1243.30i 0.235728i
\(304\) 0 0
\(305\) 8852.00i 1.66185i
\(306\) 0 0
\(307\) −6622.54 + 2743.14i −1.23117 + 0.509966i −0.900943 0.433937i \(-0.857124\pi\)
−0.330223 + 0.943903i \(0.607124\pi\)
\(308\) 0 0
\(309\) −127.216 + 307.128i −0.0234210 + 0.0565433i
\(310\) 0 0
\(311\) −777.649 + 777.649i −0.141789 + 0.141789i −0.774438 0.632649i \(-0.781967\pi\)
0.632649 + 0.774438i \(0.281967\pi\)
\(312\) 0 0
\(313\) 3478.96 + 3478.96i 0.628251 + 0.628251i 0.947628 0.319377i \(-0.103474\pi\)
−0.319377 + 0.947628i \(0.603474\pi\)
\(314\) 0 0
\(315\) −10599.6 4390.50i −1.89594 0.785323i
\(316\) 0 0
\(317\) 2639.41 + 6372.11i 0.467648 + 1.12900i 0.965187 + 0.261560i \(0.0842369\pi\)
−0.497540 + 0.867441i \(0.665763\pi\)
\(318\) 0 0
\(319\) −7147.64 −1.25452
\(320\) 0 0
\(321\) 157.893 0.0274540
\(322\) 0 0
\(323\) −713.052 1721.46i −0.122834 0.296547i
\(324\) 0 0
\(325\) 7110.44 + 2945.24i 1.21359 + 0.502685i
\(326\) 0 0
\(327\) 376.792 + 376.792i 0.0637207 + 0.0637207i
\(328\) 0 0
\(329\) −5675.28 + 5675.28i −0.951028 + 0.951028i
\(330\) 0 0
\(331\) −1414.82 + 3415.68i −0.234941 + 0.567198i −0.996746 0.0806085i \(-0.974314\pi\)
0.761805 + 0.647807i \(0.224314\pi\)
\(332\) 0 0
\(333\) −1459.78 + 604.660i −0.240226 + 0.0995050i
\(334\) 0 0
\(335\) 2565.00i 0.418331i
\(336\) 0 0
\(337\) 5963.90i 0.964018i −0.876166 0.482009i \(-0.839907\pi\)
0.876166 0.482009i \(-0.160093\pi\)
\(338\) 0 0
\(339\) 1054.41 436.750i 0.168931 0.0699734i
\(340\) 0 0
\(341\) 1072.32 2588.82i 0.170292 0.411121i
\(342\) 0 0
\(343\) 655.996 655.996i 0.103267 0.103267i
\(344\) 0 0
\(345\) 709.909 + 709.909i 0.110783 + 0.110783i
\(346\) 0 0
\(347\) 11609.9 + 4808.98i 1.79612 + 0.743975i 0.987901 + 0.155086i \(0.0495656\pi\)
0.808214 + 0.588889i \(0.200434\pi\)
\(348\) 0 0
\(349\) −3007.79 7261.44i −0.461327 1.11374i −0.967853 0.251518i \(-0.919070\pi\)
0.506525 0.862225i \(-0.330930\pi\)
\(350\) 0 0
\(351\) 2679.57 0.407478
\(352\) 0 0
\(353\) −4646.74 −0.700627 −0.350313 0.936633i \(-0.613925\pi\)
−0.350313 + 0.936633i \(0.613925\pi\)
\(354\) 0 0
\(355\) 1830.23 + 4418.57i 0.273630 + 0.660600i
\(356\) 0 0
\(357\) 1560.04 + 646.190i 0.231278 + 0.0957983i
\(358\) 0 0
\(359\) −1380.53 1380.53i −0.202957 0.202957i 0.598309 0.801266i \(-0.295840\pi\)
−0.801266 + 0.598309i \(0.795840\pi\)
\(360\) 0 0
\(361\) −3978.10 + 3978.10i −0.579983 + 0.579983i
\(362\) 0 0
\(363\) 682.890 1648.64i 0.0987394 0.238378i
\(364\) 0 0
\(365\) 4056.06 1680.07i 0.581654 0.240929i
\(366\) 0 0
\(367\) 8418.93i 1.19745i −0.800954 0.598725i \(-0.795674\pi\)
0.800954 0.598725i \(-0.204326\pi\)
\(368\) 0 0
\(369\) 8648.75i 1.22015i
\(370\) 0 0
\(371\) −10923.3 + 4524.59i −1.52860 + 0.633167i
\(372\) 0 0
\(373\) −2147.40 + 5184.27i −0.298091 + 0.719655i 0.701882 + 0.712293i \(0.252343\pi\)
−0.999973 + 0.00736187i \(0.997657\pi\)
\(374\) 0 0
\(375\) 985.145 985.145i 0.135660 0.135660i
\(376\) 0 0
\(377\) −3936.89 3936.89i −0.537825 0.537825i
\(378\) 0 0
\(379\) 7606.92 + 3150.89i 1.03098 + 0.427046i 0.833066 0.553173i \(-0.186583\pi\)
0.197914 + 0.980219i \(0.436583\pi\)
\(380\) 0 0
\(381\) 1031.77 + 2490.91i 0.138738 + 0.334943i
\(382\) 0 0
\(383\) −12379.9 −1.65166 −0.825828 0.563922i \(-0.809292\pi\)
−0.825828 + 0.563922i \(0.809292\pi\)
\(384\) 0 0
\(385\) −23692.5 −3.13631
\(386\) 0 0
\(387\) 1432.95 + 3459.45i 0.188220 + 0.454402i
\(388\) 0 0
\(389\) −2056.29 851.744i −0.268016 0.111016i 0.244629 0.969617i \(-0.421334\pi\)
−0.512644 + 0.858601i \(0.671334\pi\)
\(390\) 0 0
\(391\) 1705.09 + 1705.09i 0.220538 + 0.220538i
\(392\) 0 0
\(393\) −2067.72 + 2067.72i −0.265401 + 0.265401i
\(394\) 0 0
\(395\) −8274.74 + 19977.0i −1.05404 + 2.54469i
\(396\) 0 0
\(397\) 10550.8 4370.29i 1.33383 0.552490i 0.402083 0.915603i \(-0.368286\pi\)
0.931745 + 0.363114i \(0.118286\pi\)
\(398\) 0 0
\(399\) 1117.49i 0.140212i
\(400\) 0 0
\(401\) 3711.66i 0.462224i 0.972927 + 0.231112i \(0.0742363\pi\)
−0.972927 + 0.231112i \(0.925764\pi\)
\(402\) 0 0
\(403\) 2016.54 835.278i 0.249258 0.103246i
\(404\) 0 0
\(405\) −4097.53 + 9892.32i −0.502736 + 1.21371i
\(406\) 0 0
\(407\) −2307.24 + 2307.24i −0.280996 + 0.280996i
\(408\) 0 0
\(409\) 6598.84 + 6598.84i 0.797780 + 0.797780i 0.982745 0.184965i \(-0.0592173\pi\)
−0.184965 + 0.982745i \(0.559217\pi\)
\(410\) 0 0
\(411\) −193.001 79.9436i −0.0231631 0.00959447i
\(412\) 0 0
\(413\) 1414.27 + 3414.36i 0.168503 + 0.406803i
\(414\) 0 0
\(415\) 17170.8 2.03104
\(416\) 0 0
\(417\) −3015.41 −0.354113
\(418\) 0 0
\(419\) −866.138 2091.04i −0.100987 0.243804i 0.865308 0.501240i \(-0.167123\pi\)
−0.966296 + 0.257435i \(0.917123\pi\)
\(420\) 0 0
\(421\) −5360.95 2220.58i −0.620610 0.257065i 0.0501475 0.998742i \(-0.484031\pi\)
−0.670757 + 0.741677i \(0.734031\pi\)
\(422\) 0 0
\(423\) 5664.98 + 5664.98i 0.651161 + 0.651161i
\(424\) 0 0
\(425\) 7056.18 7056.18i 0.805353 0.805353i
\(426\) 0 0
\(427\) 4879.64 11780.5i 0.553026 1.33512i
\(428\) 0 0
\(429\) 2480.16 1027.31i 0.279122 0.115616i
\(430\) 0 0
\(431\) 3632.29i 0.405943i −0.979185 0.202971i \(-0.934940\pi\)
0.979185 0.202971i \(-0.0650599\pi\)
\(432\) 0 0
\(433\) 4662.59i 0.517482i 0.965947 + 0.258741i \(0.0833076\pi\)
−0.965947 + 0.258741i \(0.916692\pi\)
\(434\) 0 0
\(435\) −2776.79 + 1150.18i −0.306061 + 0.126775i
\(436\) 0 0
\(437\) −610.696 + 1474.35i −0.0668502 + 0.161391i
\(438\) 0 0
\(439\) −8537.50 + 8537.50i −0.928184 + 0.928184i −0.997589 0.0694048i \(-0.977890\pi\)
0.0694048 + 0.997589i \(0.477890\pi\)
\(440\) 0 0
\(441\) 5515.60 + 5515.60i 0.595573 + 0.595573i
\(442\) 0 0
\(443\) −4536.01 1878.88i −0.486484 0.201508i 0.125940 0.992038i \(-0.459805\pi\)
−0.612424 + 0.790530i \(0.709805\pi\)
\(444\) 0 0
\(445\) −8458.16 20419.8i −0.901023 2.17526i
\(446\) 0 0
\(447\) 1196.46 0.126601
\(448\) 0 0
\(449\) 17669.7 1.85720 0.928602 0.371077i \(-0.121011\pi\)
0.928602 + 0.371077i \(0.121011\pi\)
\(450\) 0 0
\(451\) −6834.84 16500.8i −0.713615 1.72282i
\(452\) 0 0
\(453\) −1978.41 819.482i −0.205196 0.0849948i
\(454\) 0 0
\(455\) −13049.7 13049.7i −1.34457 1.34457i
\(456\) 0 0
\(457\) 10783.5 10783.5i 1.10378 1.10378i 0.109833 0.993950i \(-0.464968\pi\)
0.993950 0.109833i \(-0.0350317\pi\)
\(458\) 0 0
\(459\) 1329.56 3209.84i 0.135204 0.326411i
\(460\) 0 0
\(461\) −96.4913 + 39.9680i −0.00974847 + 0.00403795i −0.387552 0.921848i \(-0.626679\pi\)
0.377804 + 0.925886i \(0.376679\pi\)
\(462\) 0 0
\(463\) 16514.0i 1.65761i −0.559539 0.828804i \(-0.689022\pi\)
0.559539 0.828804i \(-0.310978\pi\)
\(464\) 0 0
\(465\) 1178.28i 0.117509i
\(466\) 0 0
\(467\) 4949.67 2050.22i 0.490457 0.203154i −0.123728 0.992316i \(-0.539485\pi\)
0.614185 + 0.789162i \(0.289485\pi\)
\(468\) 0 0
\(469\) −1413.95 + 3413.57i −0.139211 + 0.336086i
\(470\) 0 0
\(471\) −2068.88 + 2068.88i −0.202397 + 0.202397i
\(472\) 0 0
\(473\) 5467.80 + 5467.80i 0.531521 + 0.531521i
\(474\) 0 0
\(475\) 6101.30 + 2527.24i 0.589362 + 0.244122i
\(476\) 0 0
\(477\) 4516.38 + 10903.5i 0.433524 + 1.04662i
\(478\) 0 0
\(479\) 19166.1 1.82823 0.914114 0.405456i \(-0.132887\pi\)
0.914114 + 0.405456i \(0.132887\pi\)
\(480\) 0 0
\(481\) −2541.63 −0.240932
\(482\) 0 0
\(483\) −553.432 1336.10i −0.0521367 0.125869i
\(484\) 0 0
\(485\) 11164.4 + 4624.46i 1.04526 + 0.432961i
\(486\) 0 0
\(487\) 3738.42 + 3738.42i 0.347852 + 0.347852i 0.859309 0.511457i \(-0.170894\pi\)
−0.511457 + 0.859309i \(0.670894\pi\)
\(488\) 0 0
\(489\) 839.687 839.687i 0.0776523 0.0776523i
\(490\) 0 0
\(491\) 1743.88 4210.09i 0.160285 0.386963i −0.823250 0.567679i \(-0.807842\pi\)
0.983535 + 0.180716i \(0.0578416\pi\)
\(492\) 0 0
\(493\) −6669.41 + 2762.56i −0.609280 + 0.252372i
\(494\) 0 0
\(495\) 23649.5i 2.14740i
\(496\) 0 0
\(497\) 6889.26i 0.621782i
\(498\) 0 0
\(499\) 6509.03 2696.13i 0.583936 0.241874i −0.0711034 0.997469i \(-0.522652\pi\)
0.655039 + 0.755595i \(0.272652\pi\)
\(500\) 0 0
\(501\) 541.225 1306.63i 0.0482638 0.116519i
\(502\) 0 0
\(503\) −3534.14 + 3534.14i −0.313280 + 0.313280i −0.846179 0.532899i \(-0.821103\pi\)
0.532899 + 0.846179i \(0.321103\pi\)
\(504\) 0 0
\(505\) −12458.3 12458.3i −1.09780 1.09780i
\(506\) 0 0
\(507\) −602.430 249.535i −0.0527710 0.0218584i
\(508\) 0 0
\(509\) −4345.28 10490.4i −0.378391 0.913518i −0.992268 0.124115i \(-0.960391\pi\)
0.613876 0.789402i \(-0.289609\pi\)
\(510\) 0 0
\(511\) −6324.05 −0.547475
\(512\) 0 0
\(513\) 2299.28 0.197886
\(514\) 0 0
\(515\) −1802.78 4352.28i −0.154252 0.372397i
\(516\) 0 0
\(517\) 15285.0 + 6331.24i 1.30026 + 0.538583i
\(518\) 0 0
\(519\) 207.835 + 207.835i 0.0175779 + 0.0175779i
\(520\) 0 0
\(521\) −8864.19 + 8864.19i −0.745388 + 0.745388i −0.973609 0.228221i \(-0.926709\pi\)
0.228221 + 0.973609i \(0.426709\pi\)
\(522\) 0 0
\(523\) −1505.26 + 3634.02i −0.125852 + 0.303833i −0.974230 0.225558i \(-0.927579\pi\)
0.848378 + 0.529391i \(0.177579\pi\)
\(524\) 0 0
\(525\) −5529.20 + 2290.27i −0.459645 + 0.190391i
\(526\) 0 0
\(527\) 2830.06i 0.233926i
\(528\) 0 0
\(529\) 10101.8i 0.830260i
\(530\) 0 0
\(531\) 3408.16 1411.71i 0.278534 0.115373i
\(532\) 0 0
\(533\) 5323.95 12853.2i 0.432657 1.04453i
\(534\) 0 0
\(535\) −1582.15 + 1582.15i −0.127854 + 0.127854i
\(536\) 0 0
\(537\) 1872.29 + 1872.29i 0.150457 + 0.150457i
\(538\) 0 0
\(539\) 14881.9 + 6164.29i 1.18926 + 0.492606i
\(540\) 0 0
\(541\) −4671.40 11277.8i −0.371237 0.896245i −0.993541 0.113470i \(-0.963804\pi\)
0.622305 0.782775i \(-0.286196\pi\)
\(542\) 0 0
\(543\) −1527.80 −0.120744
\(544\) 0 0
\(545\) −7551.19 −0.593500
\(546\) 0 0
\(547\) −6749.10 16293.8i −0.527552 1.27362i −0.933122 0.359559i \(-0.882927\pi\)
0.405571 0.914064i \(-0.367073\pi\)
\(548\) 0 0
\(549\) −11759.1 4870.79i −0.914148 0.378652i
\(550\) 0 0
\(551\) −3378.15 3378.15i −0.261187 0.261187i
\(552\) 0 0
\(553\) 22024.5 22024.5i 1.69363 1.69363i
\(554\) 0 0
\(555\) −525.063 + 1267.61i −0.0401580 + 0.0969499i
\(556\) 0 0
\(557\) −2590.39 + 1072.98i −0.197053 + 0.0816220i −0.479028 0.877800i \(-0.659011\pi\)
0.281975 + 0.959422i \(0.409011\pi\)
\(558\) 0 0
\(559\) 6023.28i 0.455738i
\(560\) 0 0
\(561\) 3480.71i 0.261953i
\(562\) 0 0
\(563\) 7377.58 3055.89i 0.552270 0.228758i −0.0890556 0.996027i \(-0.528385\pi\)
0.641325 + 0.767269i \(0.278385\pi\)
\(564\) 0 0
\(565\) −6189.15 + 14941.9i −0.460849 + 1.11259i
\(566\) 0 0
\(567\) 10906.2 10906.2i 0.807792 0.807792i
\(568\) 0 0
\(569\) 16799.5 + 16799.5i 1.23773 + 1.23773i 0.960925 + 0.276810i \(0.0892773\pi\)
0.276810 + 0.960925i \(0.410723\pi\)
\(570\) 0 0
\(571\) −8801.25 3645.60i −0.645045 0.267186i 0.0360851 0.999349i \(-0.488511\pi\)
−0.681130 + 0.732162i \(0.738511\pi\)
\(572\) 0 0
\(573\) −2444.33 5901.13i −0.178208 0.430232i
\(574\) 0 0
\(575\) −8546.51 −0.619851
\(576\) 0 0
\(577\) 11551.9 0.833472 0.416736 0.909028i \(-0.363174\pi\)
0.416736 + 0.909028i \(0.363174\pi\)
\(578\) 0 0
\(579\) 1959.90 + 4731.62i 0.140675 + 0.339619i
\(580\) 0 0
\(581\) −22851.4 9465.36i −1.63173 0.675886i
\(582\) 0 0
\(583\) 17233.4 + 17233.4i 1.22425 + 1.22425i
\(584\) 0 0
\(585\) −13026.0 + 13026.0i −0.920615 + 0.920615i
\(586\) 0 0
\(587\) −2507.65 + 6054.00i −0.176323 + 0.425682i −0.987190 0.159549i \(-0.948996\pi\)
0.810867 + 0.585231i \(0.198996\pi\)
\(588\) 0 0
\(589\) 1730.35 716.733i 0.121049 0.0501400i
\(590\) 0 0
\(591\) 3196.34i 0.222470i
\(592\) 0 0
\(593\) 7192.49i 0.498078i −0.968493 0.249039i \(-0.919885\pi\)
0.968493 0.249039i \(-0.0801147\pi\)
\(594\) 0 0
\(595\) −22107.2 + 9157.12i −1.52321 + 0.630933i
\(596\) 0 0
\(597\) −2310.59 + 5578.26i −0.158402 + 0.382417i
\(598\) 0 0
\(599\) −8885.88 + 8885.88i −0.606122 + 0.606122i −0.941930 0.335808i \(-0.890991\pi\)
0.335808 + 0.941930i \(0.390991\pi\)
\(600\) 0 0
\(601\) 1468.96 + 1468.96i 0.0997009 + 0.0997009i 0.755198 0.655497i \(-0.227541\pi\)
−0.655497 + 0.755198i \(0.727541\pi\)
\(602\) 0 0
\(603\) 3407.38 + 1411.38i 0.230115 + 0.0953167i
\(604\) 0 0
\(605\) 9677.19 + 23362.8i 0.650303 + 1.56997i
\(606\) 0 0
\(607\) 1305.90 0.0873225 0.0436613 0.999046i \(-0.486098\pi\)
0.0436613 + 0.999046i \(0.486098\pi\)
\(608\) 0 0
\(609\) 4329.46 0.288076
\(610\) 0 0
\(611\) 4931.67 + 11906.1i 0.326537 + 0.788330i
\(612\) 0 0
\(613\) −15396.4 6377.39i −1.01444 0.420196i −0.187370 0.982289i \(-0.559996\pi\)
−0.827074 + 0.562093i \(0.809996\pi\)
\(614\) 0 0
\(615\) −5310.53 5310.53i −0.348197 0.348197i
\(616\) 0 0
\(617\) −14943.6 + 14943.6i −0.975049 + 0.975049i −0.999696 0.0246473i \(-0.992154\pi\)
0.0246473 + 0.999696i \(0.492154\pi\)
\(618\) 0 0
\(619\) 9902.61 23907.0i 0.643004 1.55235i −0.179604 0.983739i \(-0.557482\pi\)
0.822608 0.568609i \(-0.192518\pi\)
\(620\) 0 0
\(621\) −2749.08 + 1138.71i −0.177644 + 0.0735826i
\(622\) 0 0
\(623\) 31837.8i 2.04744i
\(624\) 0 0
\(625\) 3764.96i 0.240957i
\(626\) 0 0
\(627\) 2128.17 881.515i 0.135551 0.0561472i
\(628\) 0 0
\(629\) −1261.12 + 3044.61i −0.0799429 + 0.192999i
\(630\) 0 0
\(631\) −11209.4 + 11209.4i −0.707191 + 0.707191i −0.965944 0.258753i \(-0.916688\pi\)
0.258753 + 0.965944i \(0.416688\pi\)
\(632\) 0 0
\(633\) −3990.43 3990.43i −0.250561 0.250561i
\(634\) 0 0
\(635\) −35298.5 14621.1i −2.20595 0.913736i
\(636\) 0 0
\(637\) 4801.63 + 11592.2i 0.298662 + 0.721033i
\(638\) 0 0
\(639\) −6876.77 −0.425729
\(640\) 0 0
\(641\) −8922.84 −0.549814 −0.274907 0.961471i \(-0.588647\pi\)
−0.274907 + 0.961471i \(0.588647\pi\)
\(642\) 0 0
\(643\) 7149.00 + 17259.2i 0.438459 + 1.05853i 0.976481 + 0.215603i \(0.0691715\pi\)
−0.538022 + 0.842930i \(0.680828\pi\)
\(644\) 0 0
\(645\) 3004.05 + 1244.32i 0.183386 + 0.0759611i
\(646\) 0 0
\(647\) 15074.6 + 15074.6i 0.915985 + 0.915985i 0.996734 0.0807492i \(-0.0257313\pi\)
−0.0807492 + 0.996734i \(0.525731\pi\)
\(648\) 0 0
\(649\) 5386.73 5386.73i 0.325805 0.325805i
\(650\) 0 0
\(651\) −649.526 + 1568.09i −0.0391043 + 0.0944062i
\(652\) 0 0
\(653\) 717.534 297.212i 0.0430004 0.0178114i −0.361080 0.932535i \(-0.617592\pi\)
0.404080 + 0.914724i \(0.367592\pi\)
\(654\) 0 0
\(655\) 41438.5i 2.47197i
\(656\) 0 0
\(657\) 6312.58i 0.374851i
\(658\) 0 0
\(659\) −6945.56 + 2876.95i −0.410562 + 0.170061i −0.578398 0.815754i \(-0.696322\pi\)
0.167836 + 0.985815i \(0.446322\pi\)
\(660\) 0 0
\(661\) −797.182 + 1924.57i −0.0469089 + 0.113248i −0.945597 0.325340i \(-0.894521\pi\)
0.898688 + 0.438588i \(0.144521\pi\)
\(662\) 0 0
\(663\) 1917.16 1917.16i 0.112302 0.112302i
\(664\) 0 0
\(665\) −11197.6 11197.6i −0.652971 0.652971i
\(666\) 0 0
\(667\) 5712.04 + 2366.01i 0.331591 + 0.137349i
\(668\) 0 0
\(669\) −342.714 827.385i −0.0198058 0.0478155i
\(670\) 0 0
\(671\) −26284.2 −1.51221
\(672\) 0 0
\(673\) 6013.47 0.344431 0.172216 0.985059i \(-0.444907\pi\)
0.172216 + 0.985059i \(0.444907\pi\)
\(674\) 0 0
\(675\) 4712.31 + 11376.5i 0.268707 + 0.648716i
\(676\) 0 0
\(677\) 19577.8 + 8109.41i 1.11143 + 0.460369i 0.861430 0.507877i \(-0.169569\pi\)
0.250000 + 0.968246i \(0.419569\pi\)
\(678\) 0 0
\(679\) −12308.7 12308.7i −0.695679 0.695679i
\(680\) 0 0
\(681\) −5343.58 + 5343.58i −0.300685 + 0.300685i
\(682\) 0 0
\(683\) 5715.60 13798.7i 0.320207 0.773048i −0.679035 0.734106i \(-0.737601\pi\)
0.999241 0.0389416i \(-0.0123986\pi\)
\(684\) 0 0
\(685\) 2735.00 1132.88i 0.152553 0.0631897i
\(686\) 0 0
\(687\) 266.325i 0.0147903i
\(688\) 0 0
\(689\) 18984.2i 1.04970i
\(690\) 0 0
\(691\) 8261.06 3421.84i 0.454798 0.188384i −0.143511 0.989649i \(-0.545839\pi\)
0.598310 + 0.801265i \(0.295839\pi\)
\(692\) 0 0
\(693\) 13036.7 31473.4i 0.714608 1.72522i
\(694\) 0 0
\(695\) 30215.5 30215.5i 1.64912 1.64912i
\(696\) 0 0
\(697\) −12755.1 12755.1i −0.693161 0.693161i
\(698\) 0 0
\(699\) −7505.19 3108.75i −0.406112 0.168217i
\(700\) 0 0
\(701\) 8530.14 + 20593.6i 0.459599 + 1.10957i 0.968560 + 0.248780i \(0.0800298\pi\)
−0.508961 + 0.860790i \(0.669970\pi\)
\(702\) 0 0
\(703\) −2180.92 −0.117005
\(704\) 0 0
\(705\) 6956.86 0.371646
\(706\) 0 0
\(707\) 9712.25 + 23447.4i 0.516643 + 1.24729i
\(708\) 0 0
\(709\) 11948.6 + 4949.27i 0.632919 + 0.262163i 0.675993 0.736908i \(-0.263715\pi\)
−0.0430740 + 0.999072i \(0.513715\pi\)
\(710\) 0 0
\(711\) −21984.6 21984.6i −1.15962 1.15962i
\(712\) 0 0
\(713\) −1713.89 + 1713.89i −0.0900222 + 0.0900222i
\(714\) 0 0
\(715\) −14558.0 + 35146.2i −0.761453 + 1.83831i
\(716\) 0 0
\(717\) −1575.96 + 652.783i −0.0820854 + 0.0340009i
\(718\) 0 0
\(719\) 3624.32i 0.187989i 0.995573 + 0.0939947i \(0.0299637\pi\)
−0.995573 + 0.0939947i \(0.970036\pi\)
\(720\) 0 0
\(721\) 6785.92i 0.350514i
\(722\) 0 0
\(723\) 1809.76 749.626i 0.0930921 0.0385600i
\(724\) 0 0
\(725\) 9791.24 23638.1i 0.501569 1.21089i
\(726\) 0 0
\(727\) 24377.4 24377.4i 1.24361 1.24361i 0.285123 0.958491i \(-0.407966\pi\)
0.958491 0.285123i \(-0.0920345\pi\)
\(728\) 0 0
\(729\) −9325.61 9325.61i −0.473790 0.473790i
\(730\) 0 0
\(731\) 7215.26 + 2988.66i 0.365070 + 0.151217i
\(732\) 0 0
\(733\) −2874.93 6940.70i −0.144868 0.349742i 0.834745 0.550637i \(-0.185615\pi\)
−0.979613 + 0.200895i \(0.935615\pi\)
\(734\) 0 0
\(735\) 6773.41 0.339920
\(736\) 0 0
\(737\) 7616.24 0.380662
\(738\) 0 0
\(739\) −9423.24 22749.7i −0.469066 1.13242i −0.964572 0.263820i \(-0.915017\pi\)
0.495506 0.868604i \(-0.334983\pi\)
\(740\) 0 0
\(741\) 1657.72 + 686.650i 0.0821833 + 0.0340414i
\(742\) 0 0
\(743\) 4515.42 + 4515.42i 0.222954 + 0.222954i 0.809741 0.586787i \(-0.199607\pi\)
−0.586787 + 0.809741i \(0.699607\pi\)
\(744\) 0 0
\(745\) −11989.0 + 11989.0i −0.589587 + 0.589587i
\(746\) 0 0
\(747\) −9448.20 + 22810.0i −0.462773 + 1.11723i
\(748\) 0 0
\(749\) 2977.72 1233.41i 0.145265 0.0601707i
\(750\) 0 0
\(751\) 25582.2i 1.24302i 0.783406 + 0.621510i \(0.213481\pi\)
−0.783406 + 0.621510i \(0.786519\pi\)
\(752\) 0 0
\(753\) 2397.67i 0.116037i
\(754\) 0 0
\(755\) 28035.9 11612.8i 1.35143 0.559780i
\(756\) 0 0
\(757\) 7681.53 18544.9i 0.368811 0.890389i −0.625135 0.780517i \(-0.714956\pi\)
0.993946 0.109872i \(-0.0350440\pi\)
\(758\) 0 0
\(759\) −2107.93 + 2107.93i −0.100808 + 0.100808i
\(760\) 0 0
\(761\) −9053.82 9053.82i −0.431276 0.431276i 0.457786 0.889062i \(-0.348642\pi\)
−0.889062 + 0.457786i \(0.848642\pi\)
\(762\) 0 0
\(763\) 10049.3 + 4162.58i 0.476816 + 0.197504i
\(764\) 0 0
\(765\) 9140.51 + 22067.1i 0.431995 + 1.04293i
\(766\) 0 0
\(767\) 5933.98 0.279353
\(768\) 0 0
\(769\) −22171.5 −1.03969 −0.519847 0.854259i \(-0.674011\pi\)
−0.519847 + 0.854259i \(0.674011\pi\)
\(770\) 0 0
\(771\) 384.954 + 929.362i 0.0179816 + 0.0434113i
\(772\) 0 0
\(773\) 4511.27 + 1868.63i 0.209908 + 0.0869469i 0.485160 0.874425i \(-0.338761\pi\)
−0.275252 + 0.961372i \(0.588761\pi\)
\(774\) 0 0
\(775\) 7092.61 + 7092.61i 0.328741 + 0.328741i
\(776\) 0 0
\(777\) 1397.54 1397.54i 0.0645255 0.0645255i
\(778\) 0 0
\(779\) 4568.36 11029.0i 0.210114 0.507259i
\(780\) 0 0
\(781\) −13120.0 + 5434.50i −0.601116 + 0.248991i
\(782\) 0 0
\(783\) 8908.03i 0.406574i
\(784\) 0 0
\(785\) 41461.9i 1.88514i
\(786\) 0 0
\(787\) −23455.4 + 9715.54i −1.06238 + 0.440053i −0.844296 0.535877i \(-0.819981\pi\)
−0.218086 + 0.975930i \(0.569981\pi\)
\(788\) 0 0
\(789\) 1459.20 3522.81i 0.0658413 0.158955i
\(790\) 0 0
\(791\) 16473.4 16473.4i 0.740489 0.740489i
\(792\) 0 0
\(793\) −14477.2 14477.2i −0.648300 0.648300i
\(794\) 0 0
\(795\) 9468.17 + 3921.84i 0.422392 + 0.174960i
\(796\) 0 0
\(797\) −11912.1