Properties

Label 128.3.h.a.47.1
Level $128$
Weight $3$
Character 128.47
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 47.1
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.10187 + 5.07436i) q^{3} +(1.74699 + 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +O(q^{10})\) \(q+(-2.10187 + 5.07436i) q^{3} +(1.74699 + 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +(-2.90924 - 7.02353i) q^{11} +(-4.50555 + 10.8774i) q^{13} -25.0737 q^{15} +10.5402i q^{17} +(1.88707 + 0.781651i) q^{19} +(-2.81580 + 1.16634i) q^{21} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(61.7400 - 25.5735i) q^{27} +(0.741814 + 0.307270i) q^{29} +47.6947i q^{31} +41.7548 q^{33} +(-0.969419 + 2.34038i) q^{35} +(14.5080 + 35.0255i) q^{37} +(-45.7256 - 45.7256i) q^{39} +(-11.3365 - 11.3365i) q^{41} +(14.6421 + 35.3493i) q^{43} +(36.9787 - 89.2744i) q^{45} +80.5164 q^{47} -48.6921i q^{49} +(-53.4849 - 22.1542i) q^{51} +(-66.6128 + 27.5919i) q^{53} +(24.5401 - 24.5401i) q^{55} +(-7.93277 + 7.93277i) q^{57} +(-65.0706 + 26.9531i) q^{59} +(87.4322 + 36.2156i) q^{61} -11.7457i q^{63} -53.7476 q^{65} +(7.12379 - 17.1984i) q^{67} +(1.32411 + 3.19668i) q^{69} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(8.74326 + 21.1081i) q^{75} +(1.61436 - 3.89741i) q^{77} +36.2398 q^{79} +176.540i q^{81} +(-27.0868 - 11.2197i) q^{83} +(-44.4545 + 18.4137i) q^{85} +(-3.11840 + 3.11840i) q^{87} +(-56.4944 + 56.4944i) q^{89} +(-6.03592 + 2.50016i) q^{91} +(-242.020 - 100.248i) q^{93} +9.32448i q^{95} +158.579 q^{97} +(-61.5800 + 148.667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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
\(3\) −2.10187 + 5.07436i −0.700624 + 1.69145i 0.0215732 + 0.999767i \(0.493133\pi\)
−0.722197 + 0.691688i \(0.756867\pi\)
\(4\) 0 0
\(5\) 1.74699 + 4.21761i 0.349399 + 0.843523i 0.996691 + 0.0812812i \(0.0259012\pi\)
−0.647293 + 0.762242i \(0.724099\pi\)
\(6\) 0 0
\(7\) 0.392379 + 0.392379i 0.0560541 + 0.0560541i 0.734578 0.678524i \(-0.237380\pi\)
−0.678524 + 0.734578i \(0.737380\pi\)
\(8\) 0 0
\(9\) −14.9674 14.9674i −1.66304 1.66304i
\(10\) 0 0
\(11\) −2.90924 7.02353i −0.264477 0.638503i 0.734729 0.678361i \(-0.237309\pi\)
−0.999205 + 0.0398581i \(0.987309\pi\)
\(12\) 0 0
\(13\) −4.50555 + 10.8774i −0.346581 + 0.836720i 0.650438 + 0.759559i \(0.274585\pi\)
−0.997019 + 0.0771604i \(0.975415\pi\)
\(14\) 0 0
\(15\) −25.0737 −1.67158
\(16\) 0 0
\(17\) 10.5402i 0.620012i 0.950735 + 0.310006i \(0.100331\pi\)
−0.950735 + 0.310006i \(0.899669\pi\)
\(18\) 0 0
\(19\) 1.88707 + 0.781651i 0.0993196 + 0.0411395i 0.431790 0.901974i \(-0.357882\pi\)
−0.332470 + 0.943114i \(0.607882\pi\)
\(20\) 0 0
\(21\) −2.81580 + 1.16634i −0.134086 + 0.0555401i
\(22\) 0 0
\(23\) 0.445453 0.445453i 0.0193675 0.0193675i −0.697357 0.716724i \(-0.745641\pi\)
0.716724 + 0.697357i \(0.245641\pi\)
\(24\) 0 0
\(25\) 2.94139 2.94139i 0.117656 0.117656i
\(26\) 0 0
\(27\) 61.7400 25.5735i 2.28667 0.947168i
\(28\) 0 0
\(29\) 0.741814 + 0.307270i 0.0255798 + 0.0105955i 0.395437 0.918493i \(-0.370593\pi\)
−0.369857 + 0.929089i \(0.620593\pi\)
\(30\) 0 0
\(31\) 47.6947i 1.53854i 0.638924 + 0.769270i \(0.279380\pi\)
−0.638924 + 0.769270i \(0.720620\pi\)
\(32\) 0 0
\(33\) 41.7548 1.26530
\(34\) 0 0
\(35\) −0.969419 + 2.34038i −0.0276977 + 0.0668681i
\(36\) 0 0
\(37\) 14.5080 + 35.0255i 0.392109 + 0.946635i 0.989480 + 0.144670i \(0.0462120\pi\)
−0.597371 + 0.801965i \(0.703788\pi\)
\(38\) 0 0
\(39\) −45.7256 45.7256i −1.17245 1.17245i
\(40\) 0 0
\(41\) −11.3365 11.3365i −0.276501 0.276501i 0.555209 0.831711i \(-0.312638\pi\)
−0.831711 + 0.555209i \(0.812638\pi\)
\(42\) 0 0
\(43\) 14.6421 + 35.3493i 0.340515 + 0.822076i 0.997664 + 0.0683149i \(0.0217622\pi\)
−0.657149 + 0.753761i \(0.728238\pi\)
\(44\) 0 0
\(45\) 36.9787 89.2744i 0.821748 1.98388i
\(46\) 0 0
\(47\) 80.5164 1.71312 0.856558 0.516051i \(-0.172598\pi\)
0.856558 + 0.516051i \(0.172598\pi\)
\(48\) 0 0
\(49\) 48.6921i 0.993716i
\(50\) 0 0
\(51\) −53.4849 22.1542i −1.04872 0.434395i
\(52\) 0 0
\(53\) −66.6128 + 27.5919i −1.25685 + 0.520602i −0.908940 0.416927i \(-0.863107\pi\)
−0.347905 + 0.937530i \(0.613107\pi\)
\(54\) 0 0
\(55\) 24.5401 24.5401i 0.446184 0.446184i
\(56\) 0 0
\(57\) −7.93277 + 7.93277i −0.139171 + 0.139171i
\(58\) 0 0
\(59\) −65.0706 + 26.9531i −1.10289 + 0.456833i −0.858484 0.512840i \(-0.828594\pi\)
−0.244408 + 0.969673i \(0.578594\pi\)
\(60\) 0 0
\(61\) 87.4322 + 36.2156i 1.43331 + 0.593698i 0.958168 0.286208i \(-0.0923948\pi\)
0.475147 + 0.879906i \(0.342395\pi\)
\(62\) 0 0
\(63\) 11.7457i 0.186440i
\(64\) 0 0
\(65\) −53.7476 −0.826887
\(66\) 0 0
\(67\) 7.12379 17.1984i 0.106325 0.256692i −0.861759 0.507319i \(-0.830637\pi\)
0.968084 + 0.250627i \(0.0806367\pi\)
\(68\) 0 0
\(69\) 1.32411 + 3.19668i 0.0191900 + 0.0463287i
\(70\) 0 0
\(71\) 14.8103 + 14.8103i 0.208596 + 0.208596i 0.803671 0.595074i \(-0.202877\pi\)
−0.595074 + 0.803671i \(0.702877\pi\)
\(72\) 0 0
\(73\) 18.6720 + 18.6720i 0.255781 + 0.255781i 0.823336 0.567555i \(-0.192110\pi\)
−0.567555 + 0.823336i \(0.692110\pi\)
\(74\) 0 0
\(75\) 8.74326 + 21.1081i 0.116577 + 0.281441i
\(76\) 0 0
\(77\) 1.61436 3.89741i 0.0209657 0.0506157i
\(78\) 0 0
\(79\) 36.2398 0.458732 0.229366 0.973340i \(-0.426335\pi\)
0.229366 + 0.973340i \(0.426335\pi\)
\(80\) 0 0
\(81\) 176.540i 2.17951i
\(82\) 0 0
\(83\) −27.0868 11.2197i −0.326347 0.135177i 0.213494 0.976944i \(-0.431516\pi\)
−0.539841 + 0.841767i \(0.681516\pi\)
\(84\) 0 0
\(85\) −44.4545 + 18.4137i −0.522994 + 0.216631i
\(86\) 0 0
\(87\) −3.11840 + 3.11840i −0.0358436 + 0.0358436i
\(88\) 0 0
\(89\) −56.4944 + 56.4944i −0.634769 + 0.634769i −0.949260 0.314491i \(-0.898166\pi\)
0.314491 + 0.949260i \(0.398166\pi\)
\(90\) 0 0
\(91\) −6.03592 + 2.50016i −0.0663288 + 0.0274743i
\(92\) 0 0
\(93\) −242.020 100.248i −2.60237 1.07794i
\(94\) 0 0
\(95\) 9.32448i 0.0981525i
\(96\) 0 0
\(97\) 158.579 1.63484 0.817419 0.576043i \(-0.195404\pi\)
0.817419 + 0.576043i \(0.195404\pi\)
\(98\) 0 0
\(99\) −61.5800 + 148.667i −0.622021 + 1.50169i
\(100\) 0 0
\(101\) −53.8420 129.986i −0.533089 1.28699i −0.929468 0.368903i \(-0.879733\pi\)
0.396379 0.918087i \(-0.370267\pi\)
\(102\) 0 0
\(103\) −9.94607 9.94607i −0.0965638 0.0965638i 0.657175 0.753738i \(-0.271751\pi\)
−0.753738 + 0.657175i \(0.771751\pi\)
\(104\) 0 0
\(105\) −9.83837 9.83837i −0.0936987 0.0936987i
\(106\) 0 0
\(107\) −68.8129 166.129i −0.643111 1.55261i −0.822461 0.568822i \(-0.807399\pi\)
0.179350 0.983785i \(-0.442601\pi\)
\(108\) 0 0
\(109\) 3.61301 8.72257i 0.0331469 0.0800236i −0.906439 0.422336i \(-0.861210\pi\)
0.939586 + 0.342313i \(0.111210\pi\)
\(110\) 0 0
\(111\) −208.226 −1.87591
\(112\) 0 0
\(113\) 85.8345i 0.759598i −0.925069 0.379799i \(-0.875993\pi\)
0.925069 0.379799i \(-0.124007\pi\)
\(114\) 0 0
\(115\) 2.65695 + 1.10055i 0.0231039 + 0.00956997i
\(116\) 0 0
\(117\) 230.241 95.3691i 1.96788 0.815121i
\(118\) 0 0
\(119\) −4.13575 + 4.13575i −0.0347542 + 0.0347542i
\(120\) 0 0
\(121\) 44.6936 44.6936i 0.369369 0.369369i
\(122\) 0 0
\(123\) 81.3537 33.6978i 0.661412 0.273966i
\(124\) 0 0
\(125\) 122.985 + 50.9419i 0.983877 + 0.407535i
\(126\) 0 0
\(127\) 17.2873i 0.136120i 0.997681 + 0.0680601i \(0.0216810\pi\)
−0.997681 + 0.0680601i \(0.978319\pi\)
\(128\) 0 0
\(129\) −210.151 −1.62908
\(130\) 0 0
\(131\) 40.2223 97.1053i 0.307041 0.741262i −0.692758 0.721171i \(-0.743604\pi\)
0.999798 0.0200911i \(-0.00639562\pi\)
\(132\) 0 0
\(133\) 0.433744 + 1.04715i 0.00326123 + 0.00787331i
\(134\) 0 0
\(135\) 215.719 + 215.719i 1.59792 + 1.59792i
\(136\) 0 0
\(137\) 25.5351 + 25.5351i 0.186387 + 0.186387i 0.794132 0.607745i \(-0.207926\pi\)
−0.607745 + 0.794132i \(0.707926\pi\)
\(138\) 0 0
\(139\) 52.2202 + 126.071i 0.375685 + 0.906984i 0.992764 + 0.120083i \(0.0383160\pi\)
−0.617079 + 0.786901i \(0.711684\pi\)
\(140\) 0 0
\(141\) −169.235 + 408.570i −1.20025 + 2.89766i
\(142\) 0 0
\(143\) 89.5052 0.625910
\(144\) 0 0
\(145\) 3.66548i 0.0252792i
\(146\) 0 0
\(147\) 247.081 + 102.344i 1.68083 + 0.696221i
\(148\) 0 0
\(149\) 151.298 62.6697i 1.01542 0.420602i 0.187993 0.982170i \(-0.439802\pi\)
0.827430 + 0.561569i \(0.189802\pi\)
\(150\) 0 0
\(151\) 123.292 123.292i 0.816505 0.816505i −0.169095 0.985600i \(-0.554084\pi\)
0.985600 + 0.169095i \(0.0540845\pi\)
\(152\) 0 0
\(153\) 157.759 157.759i 1.03111 1.03111i
\(154\) 0 0
\(155\) −201.158 + 83.3223i −1.29779 + 0.537563i
\(156\) 0 0
\(157\) 107.069 + 44.3494i 0.681968 + 0.282480i 0.696649 0.717412i \(-0.254673\pi\)
−0.0146813 + 0.999892i \(0.504673\pi\)
\(158\) 0 0
\(159\) 396.012i 2.49064i
\(160\) 0 0
\(161\) 0.349573 0.00217126
\(162\) 0 0
\(163\) 48.6441 117.437i 0.298430 0.720474i −0.701539 0.712631i \(-0.747503\pi\)
0.999969 0.00784306i \(-0.00249655\pi\)
\(164\) 0 0
\(165\) 72.9453 + 176.106i 0.442093 + 1.06731i
\(166\) 0 0
\(167\) −88.6392 88.6392i −0.530774 0.530774i 0.390029 0.920803i \(-0.372465\pi\)
−0.920803 + 0.390029i \(0.872465\pi\)
\(168\) 0 0
\(169\) 21.4841 + 21.4841i 0.127125 + 0.127125i
\(170\) 0 0
\(171\) −16.5452 39.9437i −0.0967558 0.233589i
\(172\) 0 0
\(173\) 87.2836 210.721i 0.504530 1.21804i −0.442463 0.896787i \(-0.645895\pi\)
0.946993 0.321255i \(-0.104105\pi\)
\(174\) 0 0
\(175\) 2.30827 0.0131901
\(176\) 0 0
\(177\) 386.844i 2.18556i
\(178\) 0 0
\(179\) 5.53118 + 2.29109i 0.0309005 + 0.0127994i 0.398080 0.917351i \(-0.369677\pi\)
−0.367180 + 0.930150i \(0.619677\pi\)
\(180\) 0 0
\(181\) −273.836 + 113.427i −1.51291 + 0.626666i −0.976155 0.217075i \(-0.930348\pi\)
−0.536751 + 0.843741i \(0.680348\pi\)
\(182\) 0 0
\(183\) −367.542 + 367.542i −2.00843 + 2.00843i
\(184\) 0 0
\(185\) −122.379 + 122.379i −0.661506 + 0.661506i
\(186\) 0 0
\(187\) 74.0295 30.6640i 0.395880 0.163979i
\(188\) 0 0
\(189\) 34.2600 + 14.1909i 0.181270 + 0.0750843i
\(190\) 0 0
\(191\) 140.503i 0.735620i 0.929901 + 0.367810i \(0.119892\pi\)
−0.929901 + 0.367810i \(0.880108\pi\)
\(192\) 0 0
\(193\) −159.719 −0.827560 −0.413780 0.910377i \(-0.635792\pi\)
−0.413780 + 0.910377i \(0.635792\pi\)
\(194\) 0 0
\(195\) 112.971 272.735i 0.579336 1.39864i
\(196\) 0 0
\(197\) −23.3511 56.3745i −0.118533 0.286165i 0.853466 0.521149i \(-0.174496\pi\)
−0.971999 + 0.234984i \(0.924496\pi\)
\(198\) 0 0
\(199\) −138.741 138.741i −0.697191 0.697191i 0.266613 0.963804i \(-0.414096\pi\)
−0.963804 + 0.266613i \(0.914096\pi\)
\(200\) 0 0
\(201\) 72.2974 + 72.2974i 0.359689 + 0.359689i
\(202\) 0 0
\(203\) 0.170506 + 0.411638i 0.000839931 + 0.00202777i
\(204\) 0 0
\(205\) 28.0083 67.6180i 0.136626 0.329844i
\(206\) 0 0
\(207\) −13.3345 −0.0644180
\(208\) 0 0
\(209\) 15.5279i 0.0742963i
\(210\) 0 0
\(211\) 194.276 + 80.4718i 0.920740 + 0.381383i 0.792158 0.610316i \(-0.208957\pi\)
0.128582 + 0.991699i \(0.458957\pi\)
\(212\) 0 0
\(213\) −106.283 + 44.0237i −0.498979 + 0.206684i
\(214\) 0 0
\(215\) −123.510 + 123.510i −0.574464 + 0.574464i
\(216\) 0 0
\(217\) −18.7144 + 18.7144i −0.0862414 + 0.0862414i
\(218\) 0 0
\(219\) −133.995 + 55.5025i −0.611849 + 0.253436i
\(220\) 0 0
\(221\) −114.650 47.4894i −0.518776 0.214884i
\(222\) 0 0
\(223\) 285.957i 1.28232i 0.767408 + 0.641160i \(0.221546\pi\)
−0.767408 + 0.641160i \(0.778454\pi\)
\(224\) 0 0
\(225\) −88.0496 −0.391332
\(226\) 0 0
\(227\) −8.02885 + 19.3834i −0.0353694 + 0.0853893i −0.940577 0.339580i \(-0.889715\pi\)
0.905208 + 0.424969i \(0.139715\pi\)
\(228\) 0 0
\(229\) −66.9028 161.518i −0.292152 0.705317i 0.707848 0.706365i \(-0.249666\pi\)
−0.999999 + 0.00104819i \(0.999666\pi\)
\(230\) 0 0
\(231\) 16.3837 + 16.3837i 0.0709251 + 0.0709251i
\(232\) 0 0
\(233\) 282.286 + 282.286i 1.21153 + 1.21153i 0.970525 + 0.241001i \(0.0774758\pi\)
0.241001 + 0.970525i \(0.422524\pi\)
\(234\) 0 0
\(235\) 140.662 + 339.587i 0.598560 + 1.44505i
\(236\) 0 0
\(237\) −76.1714 + 183.894i −0.321398 + 0.775925i
\(238\) 0 0
\(239\) −13.1618 −0.0550704 −0.0275352 0.999621i \(-0.508766\pi\)
−0.0275352 + 0.999621i \(0.508766\pi\)
\(240\) 0 0
\(241\) 231.745i 0.961599i 0.876830 + 0.480800i \(0.159654\pi\)
−0.876830 + 0.480800i \(0.840346\pi\)
\(242\) 0 0
\(243\) −340.169 140.903i −1.39987 0.579847i
\(244\) 0 0
\(245\) 205.364 85.0647i 0.838222 0.347203i
\(246\) 0 0
\(247\) −17.0046 + 17.0046i −0.0688445 + 0.0688445i
\(248\) 0 0
\(249\) 113.866 113.866i 0.457293 0.457293i
\(250\) 0 0
\(251\) −131.701 + 54.5521i −0.524703 + 0.217339i −0.629281 0.777177i \(-0.716651\pi\)
0.104578 + 0.994517i \(0.466651\pi\)
\(252\) 0 0
\(253\) −4.42459 1.83272i −0.0174885 0.00724397i
\(254\) 0 0
\(255\) 264.282i 1.03640i
\(256\) 0 0
\(257\) −70.0955 −0.272745 −0.136373 0.990658i \(-0.543544\pi\)
−0.136373 + 0.990658i \(0.543544\pi\)
\(258\) 0 0
\(259\) −8.05061 + 19.4359i −0.0310834 + 0.0750420i
\(260\) 0 0
\(261\) −6.50399 15.7020i −0.0249195 0.0601610i
\(262\) 0 0
\(263\) 245.883 + 245.883i 0.934916 + 0.934916i 0.998008 0.0630921i \(-0.0200962\pi\)
−0.0630921 + 0.998008i \(0.520096\pi\)
\(264\) 0 0
\(265\) −232.744 232.744i −0.878280 0.878280i
\(266\) 0 0
\(267\) −167.929 405.417i −0.628949 1.51842i
\(268\) 0 0
\(269\) 7.33716 17.7135i 0.0272757 0.0658493i −0.909655 0.415365i \(-0.863654\pi\)
0.936931 + 0.349516i \(0.113654\pi\)
\(270\) 0 0
\(271\) −327.600 −1.20886 −0.604429 0.796659i \(-0.706599\pi\)
−0.604429 + 0.796659i \(0.706599\pi\)
\(272\) 0 0
\(273\) 35.8835i 0.131441i
\(274\) 0 0
\(275\) −29.2161 12.1017i −0.106240 0.0440063i
\(276\) 0 0
\(277\) −31.9345 + 13.2277i −0.115287 + 0.0477535i −0.439581 0.898203i \(-0.644873\pi\)
0.324294 + 0.945956i \(0.394873\pi\)
\(278\) 0 0
\(279\) 713.864 713.864i 2.55865 2.55865i
\(280\) 0 0
\(281\) −263.413 + 263.413i −0.937413 + 0.937413i −0.998154 0.0607409i \(-0.980654\pi\)
0.0607409 + 0.998154i \(0.480654\pi\)
\(282\) 0 0
\(283\) 268.113 111.056i 0.947397 0.392425i 0.145145 0.989410i \(-0.453635\pi\)
0.802252 + 0.596986i \(0.203635\pi\)
\(284\) 0 0
\(285\) −47.3158 19.5989i −0.166020 0.0687679i
\(286\) 0 0
\(287\) 8.89644i 0.0309980i
\(288\) 0 0
\(289\) 177.904 0.615585
\(290\) 0 0
\(291\) −333.313 + 804.689i −1.14541 + 2.76526i
\(292\) 0 0
\(293\) 44.7772 + 108.102i 0.152823 + 0.368948i 0.981687 0.190503i \(-0.0610120\pi\)
−0.828863 + 0.559451i \(0.811012\pi\)
\(294\) 0 0
\(295\) −227.356 227.356i −0.770698 0.770698i
\(296\) 0 0
\(297\) −359.233 359.233i −1.20954 1.20954i
\(298\) 0 0
\(299\) 2.83834 + 6.85237i 0.00949279 + 0.0229176i
\(300\) 0 0
\(301\) −8.12503 + 19.6155i −0.0269934 + 0.0651679i
\(302\) 0 0
\(303\) 772.765 2.55038
\(304\) 0 0
\(305\) 432.024i 1.41647i
\(306\) 0 0
\(307\) −430.497 178.318i −1.40227 0.580839i −0.451930 0.892054i \(-0.649264\pi\)
−0.950340 + 0.311215i \(0.899264\pi\)
\(308\) 0 0
\(309\) 71.3754 29.5646i 0.230988 0.0956784i
\(310\) 0 0
\(311\) 61.3250 61.3250i 0.197187 0.197187i −0.601606 0.798793i \(-0.705472\pi\)
0.798793 + 0.601606i \(0.205472\pi\)
\(312\) 0 0
\(313\) 129.308 129.308i 0.413124 0.413124i −0.469701 0.882826i \(-0.655638\pi\)
0.882826 + 0.469701i \(0.155638\pi\)
\(314\) 0 0
\(315\) 49.5390 20.5197i 0.157267 0.0651420i
\(316\) 0 0
\(317\) −286.711 118.760i −0.904452 0.374636i −0.118522 0.992951i \(-0.537816\pi\)
−0.785930 + 0.618315i \(0.787816\pi\)
\(318\) 0 0
\(319\) 6.10408i 0.0191350i
\(320\) 0 0
\(321\) 987.635 3.07674
\(322\) 0 0
\(323\) −8.23877 + 19.8901i −0.0255070 + 0.0615794i
\(324\) 0 0
\(325\) 18.7420 + 45.2471i 0.0576676 + 0.139222i
\(326\) 0 0
\(327\) 36.6674 + 36.6674i 0.112133 + 0.112133i
\(328\) 0 0
\(329\) 31.5929 + 31.5929i 0.0960271 + 0.0960271i
\(330\) 0 0
\(331\) −123.164 297.345i −0.372098 0.898324i −0.993395 0.114748i \(-0.963394\pi\)
0.621297 0.783575i \(-0.286606\pi\)
\(332\) 0 0
\(333\) 307.092 741.386i 0.922198 2.22638i
\(334\) 0 0
\(335\) 84.9812 0.253675
\(336\) 0 0
\(337\) 263.653i 0.782354i 0.920315 + 0.391177i \(0.127932\pi\)
−0.920315 + 0.391177i \(0.872068\pi\)
\(338\) 0 0
\(339\) 435.556 + 180.413i 1.28483 + 0.532192i
\(340\) 0 0
\(341\) 334.985 138.755i 0.982362 0.406908i
\(342\) 0 0
\(343\) 38.3323 38.3323i 0.111756 0.111756i
\(344\) 0 0
\(345\) −11.1691 + 11.1691i −0.0323743 + 0.0323743i
\(346\) 0 0
\(347\) 388.417 160.888i 1.11936 0.463653i 0.255208 0.966886i \(-0.417856\pi\)
0.864151 + 0.503233i \(0.167856\pi\)
\(348\) 0 0
\(349\) 448.277 + 185.683i 1.28446 + 0.532042i 0.917330 0.398127i \(-0.130340\pi\)
0.367132 + 0.930169i \(0.380340\pi\)
\(350\) 0 0
\(351\) 786.791i 2.24157i
\(352\) 0 0
\(353\) −106.951 −0.302976 −0.151488 0.988459i \(-0.548407\pi\)
−0.151488 + 0.988459i \(0.548407\pi\)
\(354\) 0 0
\(355\) −36.5908 + 88.3379i −0.103073 + 0.248839i
\(356\) 0 0
\(357\) −12.2935 29.6791i −0.0344356 0.0831348i
\(358\) 0 0
\(359\) 208.761 + 208.761i 0.581508 + 0.581508i 0.935317 0.353810i \(-0.115114\pi\)
−0.353810 + 0.935317i \(0.615114\pi\)
\(360\) 0 0
\(361\) −252.315 252.315i −0.698935 0.698935i
\(362\) 0 0
\(363\) 132.852 + 320.732i 0.365982 + 0.883559i
\(364\) 0 0
\(365\) −46.1315 + 111.371i −0.126388 + 0.305127i
\(366\) 0 0
\(367\) −711.002 −1.93734 −0.968668 0.248361i \(-0.920108\pi\)
−0.968668 + 0.248361i \(0.920108\pi\)
\(368\) 0 0
\(369\) 339.356i 0.919665i
\(370\) 0 0
\(371\) −36.9639 15.3110i −0.0996332 0.0412694i
\(372\) 0 0
\(373\) −587.430 + 243.321i −1.57488 + 0.652336i −0.987592 0.157043i \(-0.949804\pi\)
−0.587287 + 0.809379i \(0.699804\pi\)
\(374\) 0 0
\(375\) −516.995 + 516.995i −1.37865 + 1.37865i
\(376\) 0 0
\(377\) −6.68456 + 6.68456i −0.0177309 + 0.0177309i
\(378\) 0 0
\(379\) 34.5203 14.2988i 0.0910825 0.0377276i −0.336677 0.941620i \(-0.609303\pi\)
0.427759 + 0.903893i \(0.359303\pi\)
\(380\) 0 0
\(381\) −87.7220 36.3356i −0.230241 0.0953691i
\(382\) 0 0
\(383\) 347.623i 0.907631i −0.891096 0.453815i \(-0.850063\pi\)
0.891096 0.453815i \(-0.149937\pi\)
\(384\) 0 0
\(385\) 19.2580 0.0500209
\(386\) 0 0
\(387\) 309.931 748.239i 0.800855 1.93343i
\(388\) 0 0
\(389\) −60.7529 146.670i −0.156177 0.377045i 0.826352 0.563154i \(-0.190412\pi\)
−0.982529 + 0.186109i \(0.940412\pi\)
\(390\) 0 0
\(391\) 4.69517 + 4.69517i 0.0120081 + 0.0120081i
\(392\) 0 0
\(393\) 408.205 + 408.205i 1.03869 + 1.03869i
\(394\) 0 0
\(395\) 63.3107 + 152.846i 0.160280 + 0.386951i
\(396\) 0 0
\(397\) 179.460 433.255i 0.452041 1.09132i −0.519505 0.854468i \(-0.673883\pi\)
0.971545 0.236855i \(-0.0761165\pi\)
\(398\) 0 0
\(399\) −6.22529 −0.0156022
\(400\) 0 0
\(401\) 680.550i 1.69713i −0.529089 0.848566i \(-0.677466\pi\)
0.529089 0.848566i \(-0.322534\pi\)
\(402\) 0 0
\(403\) −518.792 214.891i −1.28733 0.533228i
\(404\) 0 0
\(405\) −744.578 + 308.414i −1.83847 + 0.761517i
\(406\) 0 0
\(407\) 203.795 203.795i 0.500725 0.500725i
\(408\) 0 0
\(409\) 239.915 239.915i 0.586589 0.586589i −0.350117 0.936706i \(-0.613858\pi\)
0.936706 + 0.350117i \(0.113858\pi\)
\(410\) 0 0
\(411\) −183.246 + 75.9028i −0.445853 + 0.184678i
\(412\) 0 0
\(413\) −36.1082 14.9565i −0.0874289 0.0362143i
\(414\) 0 0
\(415\) 133.843i 0.322512i
\(416\) 0 0
\(417\) −749.489 −1.79734
\(418\) 0 0
\(419\) −33.5102 + 80.9009i −0.0799767 + 0.193081i −0.958810 0.284048i \(-0.908322\pi\)
0.878833 + 0.477129i \(0.158322\pi\)
\(420\) 0 0
\(421\) 37.2975 + 90.0441i 0.0885926 + 0.213882i 0.961966 0.273170i \(-0.0880723\pi\)
−0.873373 + 0.487052i \(0.838072\pi\)
\(422\) 0 0
\(423\) −1205.12 1205.12i −2.84898 2.84898i
\(424\) 0 0
\(425\) 31.0028 + 31.0028i 0.0729479 + 0.0729479i
\(426\) 0 0
\(427\) 20.0963 + 48.5167i 0.0470639 + 0.113622i
\(428\) 0 0
\(429\) −188.128 + 454.182i −0.438527 + 1.05870i
\(430\) 0 0
\(431\) 509.094 1.18119 0.590596 0.806967i \(-0.298893\pi\)
0.590596 + 0.806967i \(0.298893\pi\)
\(432\) 0 0
\(433\) 66.0083i 0.152444i 0.997091 + 0.0762220i \(0.0242858\pi\)
−0.997091 + 0.0762220i \(0.975714\pi\)
\(434\) 0 0
\(435\) −18.6000 7.70438i −0.0427586 0.0177112i
\(436\) 0 0
\(437\) 1.18879 0.492414i 0.00272035 0.00112681i
\(438\) 0 0
\(439\) 39.8501 39.8501i 0.0907747 0.0907747i −0.660261 0.751036i \(-0.729554\pi\)
0.751036 + 0.660261i \(0.229554\pi\)
\(440\) 0 0
\(441\) −728.792 + 728.792i −1.65259 + 1.65259i
\(442\) 0 0
\(443\) 193.778 80.2656i 0.437423 0.181187i −0.153094 0.988212i \(-0.548924\pi\)
0.590517 + 0.807025i \(0.298924\pi\)
\(444\) 0 0
\(445\) −336.967 139.576i −0.757229 0.313655i
\(446\) 0 0
\(447\) 899.465i 2.01223i
\(448\) 0 0
\(449\) 124.217 0.276652 0.138326 0.990387i \(-0.455828\pi\)
0.138326 + 0.990387i \(0.455828\pi\)
\(450\) 0 0
\(451\) −46.6418 + 112.603i −0.103419 + 0.249675i
\(452\) 0 0
\(453\) 366.485 + 884.774i 0.809019 + 1.95314i
\(454\) 0 0
\(455\) −21.0894 21.0894i −0.0463504 0.0463504i
\(456\) 0 0
\(457\) −573.100 573.100i −1.25405 1.25405i −0.953889 0.300159i \(-0.902960\pi\)
−0.300159 0.953889i \(-0.597040\pi\)
\(458\) 0 0
\(459\) 269.550 + 650.752i 0.587256 + 1.41776i
\(460\) 0 0
\(461\) −86.0707 + 207.793i −0.186704 + 0.450744i −0.989321 0.145750i \(-0.953440\pi\)
0.802617 + 0.596495i \(0.203440\pi\)
\(462\) 0 0
\(463\) 555.587 1.19997 0.599986 0.800010i \(-0.295173\pi\)
0.599986 + 0.800010i \(0.295173\pi\)
\(464\) 0 0
\(465\) 1195.88i 2.57179i
\(466\) 0 0
\(467\) 319.806 + 132.468i 0.684809 + 0.283657i 0.697835 0.716258i \(-0.254147\pi\)
−0.0130269 + 0.999915i \(0.504147\pi\)
\(468\) 0 0
\(469\) 9.54349 3.95304i 0.0203486 0.00842866i
\(470\) 0 0
\(471\) −450.090 + 450.090i −0.955606 + 0.955606i
\(472\) 0 0
\(473\) 205.679 205.679i 0.434839 0.434839i
\(474\) 0 0
\(475\) 7.84975 3.25147i 0.0165258 0.00684521i
\(476\) 0 0
\(477\) 1410.00 + 584.039i 2.95597 + 1.22440i
\(478\) 0 0
\(479\) 239.576i 0.500159i −0.968225 0.250079i \(-0.919543\pi\)
0.968225 0.250079i \(-0.0804567\pi\)
\(480\) 0 0
\(481\) −446.351 −0.927965
\(482\) 0 0
\(483\) −0.734757 + 1.77386i −0.00152124 + 0.00367259i
\(484\) 0 0
\(485\) 277.037 + 668.826i 0.571210 + 1.37902i
\(486\) 0 0
\(487\) 269.525 + 269.525i 0.553439 + 0.553439i 0.927432 0.373992i \(-0.122011\pi\)
−0.373992 + 0.927432i \(0.622011\pi\)
\(488\) 0 0
\(489\) 493.676 + 493.676i 1.00956 + 1.00956i
\(490\) 0 0
\(491\) −285.394 689.002i −0.581250 1.40326i −0.891680 0.452666i \(-0.850473\pi\)
0.310430 0.950596i \(-0.399527\pi\)
\(492\) 0 0
\(493\) −3.23869 + 7.81888i −0.00656934 + 0.0158598i
\(494\) 0 0
\(495\) −734.601 −1.48404
\(496\) 0 0
\(497\) 11.6225i 0.0233854i
\(498\) 0 0
\(499\) −581.267 240.769i −1.16486 0.482503i −0.285373 0.958417i \(-0.592117\pi\)
−0.879492 + 0.475914i \(0.842117\pi\)
\(500\) 0 0
\(501\) 636.096 263.479i 1.26965 0.525907i
\(502\) 0 0
\(503\) −204.189 + 204.189i −0.405942 + 0.405942i −0.880321 0.474379i \(-0.842673\pi\)
0.474379 + 0.880321i \(0.342673\pi\)
\(504\) 0 0
\(505\) 454.169 454.169i 0.899345 0.899345i
\(506\) 0 0
\(507\) −154.175 + 63.8615i −0.304093 + 0.125960i
\(508\) 0 0
\(509\) −397.562 164.676i −0.781066 0.323528i −0.0437202 0.999044i \(-0.513921\pi\)
−0.737345 + 0.675516i \(0.763921\pi\)
\(510\) 0 0
\(511\) 14.6530i 0.0286751i
\(512\) 0 0
\(513\) 136.497 0.266077
\(514\) 0 0
\(515\) 24.5730 59.3244i 0.0477145 0.115193i
\(516\) 0 0
\(517\) −234.242 565.510i −0.453079 1.09383i
\(518\) 0 0
\(519\) 885.818 + 885.818i 1.70678 + 1.70678i
\(520\) 0 0
\(521\) −333.835 333.835i −0.640759 0.640759i 0.309983 0.950742i \(-0.399676\pi\)
−0.950742 + 0.309983i \(0.899676\pi\)
\(522\) 0 0
\(523\) 211.672 + 511.022i 0.404727 + 0.977097i 0.986502 + 0.163748i \(0.0523583\pi\)
−0.581775 + 0.813350i \(0.697642\pi\)
\(524\) 0 0
\(525\) −4.85170 + 11.7130i −0.00924132 + 0.0223105i
\(526\) 0 0
\(527\) −502.712 −0.953913
\(528\) 0 0
\(529\) 528.603i 0.999250i
\(530\) 0 0
\(531\) 1377.35 + 570.518i 2.59388 + 1.07442i
\(532\) 0 0
\(533\) 174.389 72.2343i 0.327184 0.135524i
\(534\) 0 0
\(535\) 580.452 580.452i 1.08496 1.08496i
\(536\) 0 0
\(537\) −23.2517 + 23.2517i −0.0432992 + 0.0432992i
\(538\) 0 0
\(539\) −341.990 + 141.657i −0.634490 + 0.262815i
\(540\) 0 0
\(541\) −529.582 219.360i −0.978896 0.405472i −0.164879 0.986314i \(-0.552723\pi\)
−0.814016 + 0.580842i \(0.802723\pi\)
\(542\) 0 0
\(543\) 1627.95i 2.99807i
\(544\) 0 0
\(545\) 43.1003 0.0790832
\(546\) 0 0
\(547\) 68.4960 165.364i 0.125221 0.302311i −0.848820 0.528682i \(-0.822686\pi\)
0.974041 + 0.226371i \(0.0726863\pi\)
\(548\) 0 0
\(549\) −766.577 1850.68i −1.39632 3.37100i
\(550\) 0 0
\(551\) 1.15968 + 1.15968i 0.00210468 + 0.00210468i
\(552\) 0 0
\(553\) 14.2197 + 14.2197i 0.0257138 + 0.0257138i
\(554\) 0 0
\(555\) −363.770 878.217i −0.655441 1.58237i
\(556\) 0 0
\(557\) −308.610 + 745.049i −0.554057 + 1.33761i 0.360351 + 0.932817i \(0.382657\pi\)
−0.914408 + 0.404794i \(0.867343\pi\)
\(558\) 0 0
\(559\) −450.477 −0.805863
\(560\) 0 0
\(561\) 440.104i 0.784500i
\(562\) 0 0
\(563\) 347.195 + 143.813i 0.616687 + 0.255440i 0.669085 0.743186i \(-0.266686\pi\)
−0.0523978 + 0.998626i \(0.516686\pi\)
\(564\) 0 0
\(565\) 362.017 149.952i 0.640738 0.265402i
\(566\) 0 0
\(567\) −69.2706 + 69.2706i −0.122170 + 0.122170i
\(568\) 0 0
\(569\) 717.322 717.322i 1.26067 1.26067i 0.309903 0.950768i \(-0.399703\pi\)
0.950768 0.309903i \(-0.100297\pi\)
\(570\) 0 0
\(571\) 327.041 135.465i 0.572751 0.237241i −0.0774591 0.996996i \(-0.524681\pi\)
0.650210 + 0.759754i \(0.274681\pi\)
\(572\) 0 0
\(573\) −712.966 295.320i −1.24427 0.515393i
\(574\) 0 0
\(575\) 2.62050i 0.00455740i
\(576\) 0 0
\(577\) 531.710 0.921507 0.460754 0.887528i \(-0.347579\pi\)
0.460754 + 0.887528i \(0.347579\pi\)
\(578\) 0 0
\(579\) 335.709 810.473i 0.579808 1.39978i
\(580\) 0 0
\(581\) −6.22591 15.0307i −0.0107158 0.0258703i
\(582\) 0 0
\(583\) 387.585 + 387.585i 0.664812 + 0.664812i
\(584\) 0 0
\(585\) 804.460 + 804.460i 1.37515 + 1.37515i
\(586\) 0 0
\(587\) −105.581 254.894i −0.179865 0.434232i 0.808073 0.589082i \(-0.200510\pi\)
−0.987938 + 0.154850i \(0.950510\pi\)
\(588\) 0 0
\(589\) −37.2806 + 90.0034i −0.0632948 + 0.152807i
\(590\) 0 0
\(591\) 335.145 0.567082
\(592\) 0 0
\(593\) 405.861i 0.684419i 0.939624 + 0.342210i \(0.111175\pi\)
−0.939624 + 0.342210i \(0.888825\pi\)
\(594\) 0 0
\(595\) −24.6681 10.2179i −0.0414590 0.0171729i
\(596\) 0 0
\(597\) 995.638 412.407i 1.66774 0.690799i
\(598\) 0 0
\(599\) −561.484 + 561.484i −0.937370 + 0.937370i −0.998151 0.0607815i \(-0.980641\pi\)
0.0607815 + 0.998151i \(0.480641\pi\)
\(600\) 0 0
\(601\) −358.762 + 358.762i −0.596941 + 0.596941i −0.939497 0.342556i \(-0.888707\pi\)
0.342556 + 0.939497i \(0.388707\pi\)
\(602\) 0 0
\(603\) −364.038 + 150.790i −0.603712 + 0.250066i
\(604\) 0 0
\(605\) 266.580 + 110.421i 0.440628 + 0.182514i
\(606\) 0 0
\(607\) 571.923i 0.942213i 0.882076 + 0.471107i \(0.156145\pi\)
−0.882076 + 0.471107i \(0.843855\pi\)
\(608\) 0 0
\(609\) −2.44718 −0.00401836
\(610\) 0 0
\(611\) −362.771 + 875.806i −0.593733 + 1.43340i
\(612\) 0 0
\(613\) 401.254 + 968.712i 0.654574 + 1.58028i 0.806068 + 0.591823i \(0.201591\pi\)
−0.151494 + 0.988458i \(0.548409\pi\)
\(614\) 0 0
\(615\) 284.249 + 284.249i 0.462193 + 0.462193i
\(616\) 0 0
\(617\) −151.870 151.870i −0.246143 0.246143i 0.573242 0.819386i \(-0.305685\pi\)
−0.819386 + 0.573242i \(0.805685\pi\)
\(618\) 0 0
\(619\) −146.518 353.725i −0.236701 0.571446i 0.760237 0.649646i \(-0.225083\pi\)
−0.996938 + 0.0781999i \(0.975083\pi\)
\(620\) 0 0
\(621\) 16.1105 38.8941i 0.0259428 0.0626314i
\(622\) 0 0
\(623\) −44.3344 −0.0711628
\(624\) 0 0
\(625\) 503.703i 0.805924i
\(626\) 0 0
\(627\) 78.7944 + 32.6377i 0.125669 + 0.0520537i
\(628\) 0 0
\(629\) −369.176 + 152.918i −0.586925 + 0.243112i
\(630\) 0 0
\(631\) 682.535 682.535i 1.08167 1.08167i 0.0853189 0.996354i \(-0.472809\pi\)
0.996354 0.0853189i \(-0.0271909\pi\)
\(632\) 0 0
\(633\) −816.687 + 816.687i −1.29018 + 1.29018i
\(634\) 0 0
\(635\) −72.9111 + 30.2007i −0.114821 + 0.0475602i
\(636\) 0 0
\(637\) 529.641 + 219.385i 0.831462 + 0.344403i
\(638\) 0 0
\(639\) 443.344i 0.693808i
\(640\) 0 0
\(641\) 38.9310 0.0607348 0.0303674 0.999539i \(-0.490332\pi\)
0.0303674 + 0.999539i \(0.490332\pi\)
\(642\) 0 0
\(643\) −318.631 + 769.243i −0.495538 + 1.19633i 0.456326 + 0.889813i \(0.349165\pi\)
−0.951864 + 0.306522i \(0.900835\pi\)
\(644\) 0 0
\(645\) −367.132 886.335i −0.569197 1.37416i
\(646\) 0 0
\(647\) 157.445 + 157.445i 0.243346 + 0.243346i 0.818233 0.574887i \(-0.194954\pi\)
−0.574887 + 0.818233i \(0.694954\pi\)
\(648\) 0 0
\(649\) 378.612 + 378.612i 0.583378 + 0.583378i
\(650\) 0 0
\(651\) −55.6284 134.299i −0.0854507 0.206296i
\(652\) 0 0
\(653\) −15.6861 + 37.8696i −0.0240216 + 0.0579933i −0.935435 0.353498i \(-0.884992\pi\)
0.911414 + 0.411492i \(0.134992\pi\)
\(654\) 0 0
\(655\) 479.821 0.732551
\(656\) 0 0
\(657\) 558.942i 0.850748i
\(658\) 0 0
\(659\) −187.169 77.5281i −0.284020 0.117645i 0.236125 0.971723i \(-0.424122\pi\)
−0.520146 + 0.854078i \(0.674122\pi\)
\(660\) 0 0
\(661\) 30.1818 12.5017i 0.0456608 0.0189133i −0.359736 0.933054i \(-0.617133\pi\)
0.405397 + 0.914141i \(0.367133\pi\)
\(662\) 0 0
\(663\) 481.957 481.957i 0.726934 0.726934i
\(664\) 0 0
\(665\) −3.65873 + 3.65873i −0.00550184 + 0.00550184i
\(666\) 0 0
\(667\) 0.467318 0.193569i 0.000700627 0.000290209i
\(668\) 0 0
\(669\) −1451.05 601.045i −2.16899 0.898423i
\(670\) 0 0
\(671\) 719.443i 1.07219i
\(672\) 0 0
\(673\) −327.878 −0.487189 −0.243595 0.969877i \(-0.578327\pi\)
−0.243595 + 0.969877i \(0.578327\pi\)
\(674\) 0 0
\(675\) 106.380 256.823i 0.157599 0.380479i
\(676\) 0 0
\(677\) 117.661 + 284.058i 0.173797 + 0.419583i 0.986643 0.162895i \(-0.0520832\pi\)
−0.812846 + 0.582478i \(0.802083\pi\)
\(678\) 0 0
\(679\) 62.2231 + 62.2231i 0.0916393 + 0.0916393i
\(680\) 0 0
\(681\) −81.4826 81.4826i −0.119651 0.119651i
\(682\) 0 0
\(683\) 324.811 + 784.162i 0.475564 + 1.14811i 0.961669 + 0.274213i \(0.0884175\pi\)
−0.486104 + 0.873901i \(0.661583\pi\)
\(684\) 0 0
\(685\) −63.0875 + 152.307i −0.0920985 + 0.222345i
\(686\) 0 0
\(687\) 960.220 1.39770
\(688\) 0 0
\(689\) 848.888i 1.23206i
\(690\) 0 0
\(691\) −826.286 342.259i −1.19578 0.495309i −0.306149 0.951984i \(-0.599041\pi\)
−0.889634 + 0.456674i \(0.849041\pi\)
\(692\) 0 0
\(693\) −82.4966 + 34.1712i −0.119043 + 0.0493091i
\(694\) 0 0
\(695\) −440.490 + 440.490i −0.633798 + 0.633798i
\(696\) 0 0
\(697\) 119.490 119.490i 0.171434 0.171434i
\(698\) 0 0
\(699\) −2025.75 + 839.092i −2.89807 + 1.20042i
\(700\) 0 0
\(701\) 430.597 + 178.359i 0.614260 + 0.254435i 0.668049 0.744117i \(-0.267130\pi\)
−0.0537885 + 0.998552i \(0.517130\pi\)
\(702\) 0 0
\(703\) 77.4359i 0.110151i
\(704\) 0 0
\(705\) −2018.84 −2.86361
\(706\) 0 0
\(707\) 29.8773 72.1301i 0.0422592 0.102023i
\(708\) 0 0
\(709\) −77.1066 186.152i −0.108754 0.262555i 0.860128 0.510078i \(-0.170384\pi\)
−0.968882 + 0.247523i \(0.920384\pi\)
\(710\) 0 0
\(711\) −542.414 542.414i −0.762889 0.762889i
\(712\) 0 0
\(713\) 21.2458 + 21.2458i 0.0297977 + 0.0297977i
\(714\) 0 0
\(715\) 156.365 + 377.498i 0.218692 + 0.527970i
\(716\) 0 0
\(717\) 27.6645 66.7879i 0.0385836 0.0931491i
\(718\) 0 0
\(719\) −809.898 −1.12642 −0.563212 0.826313i \(-0.690434\pi\)
−0.563212 + 0.826313i \(0.690434\pi\)
\(720\) 0 0
\(721\) 7.80525i 0.0108256i
\(722\) 0 0
\(723\) −1175.96 487.099i −1.62650 0.673719i
\(724\) 0 0
\(725\) 3.08576 1.27817i 0.00425623 0.00176299i
\(726\) 0 0
\(727\) −542.456 + 542.456i −0.746156 + 0.746156i −0.973755 0.227599i \(-0.926913\pi\)
0.227599 + 0.973755i \(0.426913\pi\)
\(728\) 0 0
\(729\) 306.489 306.489i 0.420424 0.420424i
\(730\) 0 0
\(731\) −372.588 + 154.331i −0.509697 + 0.211123i
\(732\) 0 0
\(733\) 562.276 + 232.903i 0.767089 + 0.317739i 0.731693 0.681635i \(-0.238731\pi\)
0.0353965 + 0.999373i \(0.488731\pi\)
\(734\) 0 0
\(735\) 1220.89i 1.66107i
\(736\) 0 0
\(737\) −141.518 −0.192019
\(738\) 0 0
\(739\) 305.819 738.312i 0.413828 0.999070i −0.570272 0.821456i \(-0.693162\pi\)
0.984100 0.177614i \(-0.0568378\pi\)
\(740\) 0 0
\(741\) −50.5461 122.029i −0.0682133 0.164681i
\(742\) 0 0
\(743\) −581.334 581.334i −0.782414 0.782414i 0.197823 0.980238i \(-0.436613\pi\)
−0.980238 + 0.197823i \(0.936613\pi\)
\(744\) 0 0
\(745\) 528.633 + 528.633i 0.709574 + 0.709574i
\(746\) 0 0
\(747\) 237.488 + 573.348i 0.317923 + 0.767534i
\(748\) 0 0
\(749\) 38.1847 92.1861i 0.0509810 0.123079i
\(750\) 0 0
\(751\) 187.901 0.250201 0.125100 0.992144i \(-0.460075\pi\)
0.125100 + 0.992144i \(0.460075\pi\)
\(752\) 0 0
\(753\) 782.958i 1.03978i
\(754\) 0 0
\(755\) 735.390 + 304.608i 0.974026 + 0.403455i
\(756\) 0 0
\(757\) −168.645 + 69.8549i −0.222780 + 0.0922786i −0.491282 0.871001i \(-0.663472\pi\)
0.268502 + 0.963279i \(0.413472\pi\)
\(758\) 0 0
\(759\) 18.5998 18.5998i 0.0245057 0.0245057i
\(760\) 0 0
\(761\) 391.406 391.406i 0.514331 0.514331i −0.401520 0.915850i \(-0.631518\pi\)
0.915850 + 0.401520i \(0.131518\pi\)
\(762\) 0 0
\(763\) 4.84022 2.00488i 0.00634367 0.00262763i
\(764\) 0 0
\(765\) 940.971 + 389.763i 1.23003 + 0.509494i
\(766\) 0 0
\(767\) 829.235i 1.08114i
\(768\) 0 0
\(769\) 184.433 0.239835 0.119918 0.992784i \(-0.461737\pi\)
0.119918 + 0.992784i \(0.461737\pi\)
\(770\) 0 0
\(771\) 147.332 355.690i 0.191092 0.461336i
\(772\) 0 0
\(773\) −140.532 339.275i −0.181801 0.438907i 0.806537 0.591184i \(-0.201339\pi\)
−0.988338 + 0.152277i \(0.951339\pi\)
\(774\) 0 0
\(775\) 140.289 + 140.289i 0.181018 + 0.181018i
\(776\) 0 0
\(777\) −81.7035 81.7035i −0.105152 0.105152i
\(778\) 0 0
\(779\) −12.5317 30.2541i −0.0160869 0.0388371i
\(780\) 0 0
\(781\) 60.9340 147.108i 0.0780206 0.188358i
\(782\) 0 0
\(783\) 53.6576 0.0685282
\(784\) 0 0
\(785\) 529.054i 0.673954i
\(786\) 0 0
\(787\) 926.743 + 383.870i 1.17756 + 0.487763i 0.883686 0.468080i \(-0.155054\pi\)
0.293878 + 0.955843i \(0.405054\pi\)
\(788\) 0 0
\(789\) −1764.51 + 730.885i −2.23639 + 0.926344i
\(790\) 0 0
\(791\) 33.6796 33.6796i 0.0425785 0.0425785i
\(792\) 0 0
\(793\) −787.860 + 787.860i −0.993518 + 0.993518i
\(794\) 0 0
\(795\) 1670.23 691.831i 2.10091 0.870227i
\(796\) 0 0
\(797\) −871.860 361.136i −1.09393 0.453119i −0.238553 0.971130i \(-0.576673\pi\)
−0.855374 + 0.518010