Properties

Label 108.3.k.a.29.5
Level 108
Weight 3
Character 108.29
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.5
Character \(\chi\) \(=\) 108.29
Dual form 108.3.k.a.41.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.49775 - 2.59937i) q^{3} +(-5.00278 - 5.96208i) q^{5} +(-3.39388 + 1.23527i) q^{7} +(-4.51349 - 7.78642i) q^{9} +O(q^{10})\) \(q+(1.49775 - 2.59937i) q^{3} +(-5.00278 - 5.96208i) q^{5} +(-3.39388 + 1.23527i) q^{7} +(-4.51349 - 7.78642i) q^{9} +(2.59766 - 3.09577i) q^{11} +(2.31163 + 13.1099i) q^{13} +(-22.9906 + 4.07439i) q^{15} +(20.7679 - 11.9904i) q^{17} +(13.5983 - 23.5530i) q^{19} +(-1.87225 + 10.6721i) q^{21} +(3.97128 - 10.9110i) q^{23} +(-6.17739 + 35.0337i) q^{25} +(-26.9999 + 0.0701370i) q^{27} +(22.8656 + 4.03181i) q^{29} +(-3.81297 - 1.38781i) q^{31} +(-4.15642 - 11.3890i) q^{33} +(24.3436 + 14.0548i) q^{35} +(35.3735 + 61.2687i) q^{37} +(37.5399 + 13.6266i) q^{39} +(-43.0852 + 7.59708i) q^{41} +(35.3804 + 29.6877i) q^{43} +(-23.8433 + 65.8635i) q^{45} +(-28.3557 - 77.9066i) q^{47} +(-27.5437 + 23.1119i) q^{49} +(-0.0622940 - 71.9422i) q^{51} +28.9765i q^{53} -31.4528 q^{55} +(-40.8561 - 70.6236i) q^{57} +(33.8272 + 40.3136i) q^{59} +(4.08794 - 1.48789i) q^{61} +(24.9366 + 20.8508i) q^{63} +(66.5978 - 79.3682i) q^{65} +(-22.7477 - 129.009i) q^{67} +(-22.4138 - 26.6648i) q^{69} +(-60.4484 + 34.8999i) q^{71} +(65.4584 - 113.377i) q^{73} +(81.8135 + 68.5291i) q^{75} +(-4.99203 + 13.7155i) q^{77} +(-4.20918 + 23.8714i) q^{79} +(-40.2568 + 70.2879i) q^{81} +(-41.0021 - 7.22978i) q^{83} +(-175.385 - 63.8349i) q^{85} +(44.7271 - 53.3975i) q^{87} +(84.1989 + 48.6122i) q^{89} +(-24.0397 - 41.6380i) q^{91} +(-9.31831 + 7.83275i) q^{93} +(-208.454 + 36.7561i) q^{95} +(37.2772 + 31.2793i) q^{97} +(-35.8295 - 6.25375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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
\(3\) 1.49775 2.59937i 0.499250 0.866458i
\(4\) 0 0
\(5\) −5.00278 5.96208i −1.00056 1.19242i −0.981277 0.192602i \(-0.938308\pi\)
−0.0192785 0.999814i \(-0.506137\pi\)
\(6\) 0 0
\(7\) −3.39388 + 1.23527i −0.484840 + 0.176467i −0.572863 0.819651i \(-0.694167\pi\)
0.0880231 + 0.996118i \(0.471945\pi\)
\(8\) 0 0
\(9\) −4.51349 7.78642i −0.501499 0.865158i
\(10\) 0 0
\(11\) 2.59766 3.09577i 0.236151 0.281434i −0.634934 0.772567i \(-0.718973\pi\)
0.871085 + 0.491133i \(0.163417\pi\)
\(12\) 0 0
\(13\) 2.31163 + 13.1099i 0.177818 + 1.00846i 0.934841 + 0.355067i \(0.115542\pi\)
−0.757023 + 0.653389i \(0.773347\pi\)
\(14\) 0 0
\(15\) −22.9906 + 4.07439i −1.53271 + 0.271626i
\(16\) 0 0
\(17\) 20.7679 11.9904i 1.22164 0.705316i 0.256375 0.966577i \(-0.417472\pi\)
0.965268 + 0.261262i \(0.0841385\pi\)
\(18\) 0 0
\(19\) 13.5983 23.5530i 0.715701 1.23963i −0.246987 0.969019i \(-0.579441\pi\)
0.962688 0.270612i \(-0.0872261\pi\)
\(20\) 0 0
\(21\) −1.87225 + 10.6721i −0.0891548 + 0.508195i
\(22\) 0 0
\(23\) 3.97128 10.9110i 0.172665 0.474392i −0.822931 0.568141i \(-0.807663\pi\)
0.995596 + 0.0937489i \(0.0298851\pi\)
\(24\) 0 0
\(25\) −6.17739 + 35.0337i −0.247096 + 1.40135i
\(26\) 0 0
\(27\) −26.9999 + 0.0701370i −0.999997 + 0.00259767i
\(28\) 0 0
\(29\) 22.8656 + 4.03181i 0.788467 + 0.139028i 0.553361 0.832942i \(-0.313345\pi\)
0.235106 + 0.971970i \(0.424456\pi\)
\(30\) 0 0
\(31\) −3.81297 1.38781i −0.122999 0.0447680i 0.279787 0.960062i \(-0.409736\pi\)
−0.402786 + 0.915294i \(0.631958\pi\)
\(32\) 0 0
\(33\) −4.15642 11.3890i −0.125952 0.345121i
\(34\) 0 0
\(35\) 24.3436 + 14.0548i 0.695532 + 0.401565i
\(36\) 0 0
\(37\) 35.3735 + 61.2687i 0.956041 + 1.65591i 0.731967 + 0.681340i \(0.238602\pi\)
0.224074 + 0.974572i \(0.428064\pi\)
\(38\) 0 0
\(39\) 37.5399 + 13.6266i 0.962560 + 0.349400i
\(40\) 0 0
\(41\) −43.0852 + 7.59708i −1.05086 + 0.185295i −0.672297 0.740282i \(-0.734692\pi\)
−0.378561 + 0.925576i \(0.623581\pi\)
\(42\) 0 0
\(43\) 35.3804 + 29.6877i 0.822801 + 0.690412i 0.953626 0.300994i \(-0.0973183\pi\)
−0.130825 + 0.991405i \(0.541763\pi\)
\(44\) 0 0
\(45\) −23.8433 + 65.8635i −0.529851 + 1.46363i
\(46\) 0 0
\(47\) −28.3557 77.9066i −0.603312 1.65759i −0.744515 0.667606i \(-0.767319\pi\)
0.141203 0.989981i \(-0.454903\pi\)
\(48\) 0 0
\(49\) −27.5437 + 23.1119i −0.562115 + 0.471671i
\(50\) 0 0
\(51\) −0.0622940 71.9422i −0.00122145 1.41063i
\(52\) 0 0
\(53\) 28.9765i 0.546726i 0.961911 + 0.273363i \(0.0881361\pi\)
−0.961911 + 0.273363i \(0.911864\pi\)
\(54\) 0 0
\(55\) −31.4528 −0.571868
\(56\) 0 0
\(57\) −40.8561 70.6236i −0.716774 1.23901i
\(58\) 0 0
\(59\) 33.8272 + 40.3136i 0.573342 + 0.683282i 0.972313 0.233681i \(-0.0750772\pi\)
−0.398972 + 0.916963i \(0.630633\pi\)
\(60\) 0 0
\(61\) 4.08794 1.48789i 0.0670155 0.0243916i −0.308295 0.951291i \(-0.599758\pi\)
0.375310 + 0.926899i \(0.377536\pi\)
\(62\) 0 0
\(63\) 24.9366 + 20.8508i 0.395819 + 0.330965i
\(64\) 0 0
\(65\) 66.5978 79.3682i 1.02458 1.22105i
\(66\) 0 0
\(67\) −22.7477 129.009i −0.339518 1.92550i −0.377016 0.926207i \(-0.623050\pi\)
0.0374978 0.999297i \(-0.488061\pi\)
\(68\) 0 0
\(69\) −22.4138 26.6648i −0.324838 0.386447i
\(70\) 0 0
\(71\) −60.4484 + 34.8999i −0.851386 + 0.491548i −0.861118 0.508405i \(-0.830235\pi\)
0.00973220 + 0.999953i \(0.496902\pi\)
\(72\) 0 0
\(73\) 65.4584 113.377i 0.896690 1.55311i 0.0649905 0.997886i \(-0.479298\pi\)
0.831699 0.555226i \(-0.187368\pi\)
\(74\) 0 0
\(75\) 81.8135 + 68.5291i 1.09085 + 0.913721i
\(76\) 0 0
\(77\) −4.99203 + 13.7155i −0.0648316 + 0.178123i
\(78\) 0 0
\(79\) −4.20918 + 23.8714i −0.0532807 + 0.302170i −0.999790 0.0205075i \(-0.993472\pi\)
0.946509 + 0.322677i \(0.104583\pi\)
\(80\) 0 0
\(81\) −40.2568 + 70.2879i −0.496997 + 0.867752i
\(82\) 0 0
\(83\) −41.0021 7.22978i −0.494002 0.0871058i −0.0789031 0.996882i \(-0.525142\pi\)
−0.415098 + 0.909776i \(0.636253\pi\)
\(84\) 0 0
\(85\) −175.385 63.8349i −2.06335 0.750998i
\(86\) 0 0
\(87\) 44.7271 53.3975i 0.514104 0.613764i
\(88\) 0 0
\(89\) 84.1989 + 48.6122i 0.946055 + 0.546205i 0.891853 0.452325i \(-0.149405\pi\)
0.0542015 + 0.998530i \(0.482739\pi\)
\(90\) 0 0
\(91\) −24.0397 41.6380i −0.264173 0.457561i
\(92\) 0 0
\(93\) −9.31831 + 7.83275i −0.100197 + 0.0842231i
\(94\) 0 0
\(95\) −208.454 + 36.7561i −2.19425 + 0.386906i
\(96\) 0 0
\(97\) 37.2772 + 31.2793i 0.384301 + 0.322467i 0.814388 0.580320i \(-0.197073\pi\)
−0.430087 + 0.902787i \(0.641517\pi\)
\(98\) 0 0
\(99\) −35.8295 6.25375i −0.361914 0.0631692i
\(100\) 0 0
\(101\) 12.9628 + 35.6149i 0.128344 + 0.352623i 0.987176 0.159635i \(-0.0510316\pi\)
−0.858832 + 0.512257i \(0.828809\pi\)
\(102\) 0 0
\(103\) 11.7726 9.87837i 0.114297 0.0959065i −0.583848 0.811863i \(-0.698454\pi\)
0.698145 + 0.715957i \(0.254009\pi\)
\(104\) 0 0
\(105\) 72.9943 42.2276i 0.695184 0.402168i
\(106\) 0 0
\(107\) 116.068i 1.08475i 0.840138 + 0.542373i \(0.182474\pi\)
−0.840138 + 0.542373i \(0.817526\pi\)
\(108\) 0 0
\(109\) 108.821 0.998362 0.499181 0.866498i \(-0.333634\pi\)
0.499181 + 0.866498i \(0.333634\pi\)
\(110\) 0 0
\(111\) 212.241 0.183778i 1.91208 0.00165565i
\(112\) 0 0
\(113\) −31.7762 37.8694i −0.281205 0.335127i 0.606891 0.794785i \(-0.292416\pi\)
−0.888096 + 0.459658i \(0.847972\pi\)
\(114\) 0 0
\(115\) −84.9198 + 30.9083i −0.738433 + 0.268768i
\(116\) 0 0
\(117\) 91.6459 77.1709i 0.783298 0.659580i
\(118\) 0 0
\(119\) −55.6725 + 66.3479i −0.467836 + 0.557545i
\(120\) 0 0
\(121\) 18.1755 + 103.078i 0.150210 + 0.851886i
\(122\) 0 0
\(123\) −44.7832 + 123.373i −0.364091 + 1.00303i
\(124\) 0 0
\(125\) 71.2723 41.1491i 0.570178 0.329192i
\(126\) 0 0
\(127\) 32.6359 56.5270i 0.256975 0.445095i −0.708455 0.705756i \(-0.750607\pi\)
0.965430 + 0.260662i \(0.0839407\pi\)
\(128\) 0 0
\(129\) 130.160 47.5022i 1.00900 0.368234i
\(130\) 0 0
\(131\) −6.91556 + 19.0003i −0.0527905 + 0.145041i −0.963285 0.268480i \(-0.913479\pi\)
0.910495 + 0.413520i \(0.135701\pi\)
\(132\) 0 0
\(133\) −17.0567 + 96.7336i −0.128246 + 0.727320i
\(134\) 0 0
\(135\) 135.493 + 160.625i 1.00365 + 1.18981i
\(136\) 0 0
\(137\) 41.6540 + 7.34472i 0.304044 + 0.0536111i 0.323589 0.946198i \(-0.395111\pi\)
−0.0195449 + 0.999809i \(0.506222\pi\)
\(138\) 0 0
\(139\) 82.7509 + 30.1189i 0.595330 + 0.216682i 0.622072 0.782960i \(-0.286291\pi\)
−0.0267421 + 0.999642i \(0.508513\pi\)
\(140\) 0 0
\(141\) −244.978 42.9775i −1.73743 0.304805i
\(142\) 0 0
\(143\) 46.5902 + 26.8989i 0.325805 + 0.188104i
\(144\) 0 0
\(145\) −90.3533 156.497i −0.623126 1.07929i
\(146\) 0 0
\(147\) 18.8229 + 106.212i 0.128047 + 0.722531i
\(148\) 0 0
\(149\) −208.714 + 36.8019i −1.40077 + 0.246993i −0.822458 0.568826i \(-0.807398\pi\)
−0.578308 + 0.815818i \(0.696287\pi\)
\(150\) 0 0
\(151\) −135.180 113.429i −0.895229 0.751186i 0.0740229 0.997257i \(-0.476416\pi\)
−0.969252 + 0.246070i \(0.920861\pi\)
\(152\) 0 0
\(153\) −187.098 107.589i −1.22286 0.703199i
\(154\) 0 0
\(155\) 10.8012 + 29.6761i 0.0696854 + 0.191459i
\(156\) 0 0
\(157\) −4.29582 + 3.60462i −0.0273619 + 0.0229594i −0.656366 0.754443i \(-0.727907\pi\)
0.629004 + 0.777402i \(0.283463\pi\)
\(158\) 0 0
\(159\) 75.3208 + 43.3995i 0.473715 + 0.272953i
\(160\) 0 0
\(161\) 41.9363i 0.260474i
\(162\) 0 0
\(163\) 176.753 1.08437 0.542186 0.840258i \(-0.317597\pi\)
0.542186 + 0.840258i \(0.317597\pi\)
\(164\) 0 0
\(165\) −47.1084 + 81.7575i −0.285505 + 0.495500i
\(166\) 0 0
\(167\) 191.020 + 227.649i 1.14383 + 1.36317i 0.921585 + 0.388178i \(0.126895\pi\)
0.222249 + 0.974990i \(0.428660\pi\)
\(168\) 0 0
\(169\) −7.71852 + 2.80931i −0.0456717 + 0.0166232i
\(170\) 0 0
\(171\) −244.769 + 0.423887i −1.43140 + 0.00247887i
\(172\) 0 0
\(173\) 90.8233 108.239i 0.524990 0.625659i −0.436763 0.899577i \(-0.643875\pi\)
0.961753 + 0.273918i \(0.0883197\pi\)
\(174\) 0 0
\(175\) −22.3108 126.531i −0.127490 0.723034i
\(176\) 0 0
\(177\) 155.455 27.5497i 0.878276 0.155648i
\(178\) 0 0
\(179\) 152.323 87.9435i 0.850964 0.491304i −0.0100121 0.999950i \(-0.503187\pi\)
0.860976 + 0.508646i \(0.169854\pi\)
\(180\) 0 0
\(181\) −120.554 + 208.805i −0.666042 + 1.15362i 0.312959 + 0.949767i \(0.398680\pi\)
−0.979002 + 0.203853i \(0.934654\pi\)
\(182\) 0 0
\(183\) 2.25513 12.8546i 0.0123231 0.0702436i
\(184\) 0 0
\(185\) 188.323 517.414i 1.01796 2.79683i
\(186\) 0 0
\(187\) 16.8286 95.4397i 0.0899925 0.510373i
\(188\) 0 0
\(189\) 91.5478 33.5902i 0.484380 0.177726i
\(190\) 0 0
\(191\) −159.627 28.1466i −0.835745 0.147364i −0.260632 0.965438i \(-0.583931\pi\)
−0.575113 + 0.818074i \(0.695042\pi\)
\(192\) 0 0
\(193\) −13.5380 4.92744i −0.0701452 0.0255308i 0.306709 0.951803i \(-0.400772\pi\)
−0.376854 + 0.926272i \(0.622994\pi\)
\(194\) 0 0
\(195\) −106.561 291.986i −0.546465 1.49737i
\(196\) 0 0
\(197\) −188.497 108.829i −0.956838 0.552431i −0.0616399 0.998098i \(-0.519633\pi\)
−0.895199 + 0.445668i \(0.852966\pi\)
\(198\) 0 0
\(199\) 20.5152 + 35.5335i 0.103092 + 0.178560i 0.912957 0.408056i \(-0.133793\pi\)
−0.809865 + 0.586616i \(0.800460\pi\)
\(200\) 0 0
\(201\) −369.412 134.093i −1.83787 0.667129i
\(202\) 0 0
\(203\) −82.5833 + 14.5617i −0.406814 + 0.0717324i
\(204\) 0 0
\(205\) 260.840 + 218.871i 1.27239 + 1.06766i
\(206\) 0 0
\(207\) −102.882 + 18.3247i −0.497015 + 0.0885249i
\(208\) 0 0
\(209\) −37.5908 103.280i −0.179860 0.494163i
\(210\) 0 0
\(211\) −94.7998 + 79.5465i −0.449288 + 0.376998i −0.839172 0.543867i \(-0.816960\pi\)
0.389883 + 0.920864i \(0.372515\pi\)
\(212\) 0 0
\(213\) 0.181317 + 209.399i 0.000851253 + 0.983096i
\(214\) 0 0
\(215\) 359.462i 1.67192i
\(216\) 0 0
\(217\) 14.6551 0.0675350
\(218\) 0 0
\(219\) −196.670 339.961i −0.898034 1.55234i
\(220\) 0 0
\(221\) 205.201 + 244.549i 0.928510 + 1.10656i
\(222\) 0 0
\(223\) 245.799 89.4634i 1.10224 0.401181i 0.274096 0.961702i \(-0.411621\pi\)
0.828140 + 0.560521i \(0.189399\pi\)
\(224\) 0 0
\(225\) 300.669 110.025i 1.33631 0.488998i
\(226\) 0 0
\(227\) 53.1278 63.3153i 0.234043 0.278922i −0.636221 0.771507i \(-0.719503\pi\)
0.870264 + 0.492585i \(0.163948\pi\)
\(228\) 0 0
\(229\) 23.0046 + 130.466i 0.100457 + 0.569719i 0.992938 + 0.118634i \(0.0378516\pi\)
−0.892481 + 0.451084i \(0.851037\pi\)
\(230\) 0 0
\(231\) 28.1749 + 33.5185i 0.121969 + 0.145102i
\(232\) 0 0
\(233\) −355.363 + 205.169i −1.52516 + 0.880553i −0.525608 + 0.850727i \(0.676162\pi\)
−0.999555 + 0.0298260i \(0.990505\pi\)
\(234\) 0 0
\(235\) −322.628 + 558.808i −1.37288 + 2.37791i
\(236\) 0 0
\(237\) 55.7465 + 46.6946i 0.235217 + 0.197024i
\(238\) 0 0
\(239\) 38.7508 106.467i 0.162137 0.445469i −0.831845 0.555008i \(-0.812715\pi\)
0.993982 + 0.109539i \(0.0349375\pi\)
\(240\) 0 0
\(241\) −18.3989 + 104.345i −0.0763439 + 0.432968i 0.922547 + 0.385885i \(0.126104\pi\)
−0.998891 + 0.0470832i \(0.985007\pi\)
\(242\) 0 0
\(243\) 122.410 + 209.916i 0.503745 + 0.863853i
\(244\) 0 0
\(245\) 275.590 + 48.5939i 1.12486 + 0.198342i
\(246\) 0 0
\(247\) 340.212 + 123.827i 1.37738 + 0.501324i
\(248\) 0 0
\(249\) −80.2038 + 95.7515i −0.322104 + 0.384544i
\(250\) 0 0
\(251\) −13.6611 7.88725i −0.0544267 0.0314233i 0.472540 0.881309i \(-0.343337\pi\)
−0.526966 + 0.849886i \(0.676671\pi\)
\(252\) 0 0
\(253\) −23.4620 40.6373i −0.0927350 0.160622i
\(254\) 0 0
\(255\) −428.613 + 360.282i −1.68084 + 1.41287i
\(256\) 0 0
\(257\) 290.609 51.2422i 1.13077 0.199386i 0.423207 0.906033i \(-0.360904\pi\)
0.707566 + 0.706647i \(0.249793\pi\)
\(258\) 0 0
\(259\) −195.737 164.243i −0.755741 0.634142i
\(260\) 0 0
\(261\) −71.8101 196.238i −0.275134 0.751871i
\(262\) 0 0
\(263\) −6.57712 18.0705i −0.0250080 0.0687090i 0.926560 0.376146i \(-0.122751\pi\)
−0.951568 + 0.307437i \(0.900529\pi\)
\(264\) 0 0
\(265\) 172.760 144.963i 0.651925 0.547030i
\(266\) 0 0
\(267\) 252.470 146.055i 0.945581 0.547024i
\(268\) 0 0
\(269\) 190.266i 0.707309i 0.935376 + 0.353654i \(0.115061\pi\)
−0.935376 + 0.353654i \(0.884939\pi\)
\(270\) 0 0
\(271\) −121.179 −0.447154 −0.223577 0.974686i \(-0.571773\pi\)
−0.223577 + 0.974686i \(0.571773\pi\)
\(272\) 0 0
\(273\) −144.238 + 0.124895i −0.528345 + 0.000457489i
\(274\) 0 0
\(275\) 92.4096 + 110.129i 0.336035 + 0.400471i
\(276\) 0 0
\(277\) 58.6745 21.3558i 0.211821 0.0770966i −0.233930 0.972253i \(-0.575159\pi\)
0.445751 + 0.895157i \(0.352937\pi\)
\(278\) 0 0
\(279\) 6.40375 + 35.9533i 0.0229525 + 0.128865i
\(280\) 0 0
\(281\) −163.665 + 195.048i −0.582437 + 0.694122i −0.974134 0.225973i \(-0.927444\pi\)
0.391696 + 0.920095i \(0.371888\pi\)
\(282\) 0 0
\(283\) 37.8599 + 214.714i 0.133781 + 0.758707i 0.975701 + 0.219106i \(0.0703140\pi\)
−0.841921 + 0.539602i \(0.818575\pi\)
\(284\) 0 0
\(285\) −216.669 + 596.902i −0.760243 + 2.09439i
\(286\) 0 0
\(287\) 136.841 79.0055i 0.476800 0.275280i
\(288\) 0 0
\(289\) 143.038 247.749i 0.494941 0.857262i
\(290\) 0 0
\(291\) 137.139 50.0489i 0.471267 0.171989i
\(292\) 0 0
\(293\) 87.5538 240.552i 0.298818 0.820997i −0.695880 0.718158i \(-0.744985\pi\)
0.994698 0.102838i \(-0.0327924\pi\)
\(294\) 0 0
\(295\) 71.1233 403.360i 0.241096 1.36732i
\(296\) 0 0
\(297\) −69.9195 + 83.7677i −0.235419 + 0.282046i
\(298\) 0 0
\(299\) 152.223 + 26.8410i 0.509106 + 0.0897692i
\(300\) 0 0
\(301\) −156.749 57.0521i −0.520762 0.189542i
\(302\) 0 0
\(303\) 111.991 + 19.6471i 0.369609 + 0.0648421i
\(304\) 0 0
\(305\) −29.3220 16.9291i −0.0961377 0.0555051i
\(306\) 0 0
\(307\) 176.673 + 306.006i 0.575480 + 0.996761i 0.995989 + 0.0894730i \(0.0285183\pi\)
−0.420509 + 0.907288i \(0.638148\pi\)
\(308\) 0 0
\(309\) −8.04520 45.3967i −0.0260362 0.146915i
\(310\) 0 0
\(311\) −47.8256 + 8.43294i −0.153780 + 0.0271156i −0.250008 0.968244i \(-0.580433\pi\)
0.0962281 + 0.995359i \(0.469322\pi\)
\(312\) 0 0
\(313\) −50.3641 42.2605i −0.160908 0.135018i 0.558779 0.829317i \(-0.311270\pi\)
−0.719687 + 0.694299i \(0.755714\pi\)
\(314\) 0 0
\(315\) −0.438116 252.986i −0.00139085 0.803130i
\(316\) 0 0
\(317\) 174.159 + 478.499i 0.549398 + 1.50946i 0.834525 + 0.550970i \(0.185742\pi\)
−0.285127 + 0.958490i \(0.592036\pi\)
\(318\) 0 0
\(319\) 71.8785 60.3132i 0.225325 0.189070i
\(320\) 0 0
\(321\) 301.703 + 173.840i 0.939886 + 0.541559i
\(322\) 0 0
\(323\) 652.196i 2.01918i
\(324\) 0 0
\(325\) −473.569 −1.45714
\(326\) 0 0
\(327\) 162.987 282.868i 0.498432 0.865038i
\(328\) 0 0
\(329\) 192.471 + 229.379i 0.585020 + 0.697199i
\(330\) 0 0
\(331\) −417.785 + 152.061i −1.26219 + 0.459400i −0.884504 0.466534i \(-0.845503\pi\)
−0.377687 + 0.925933i \(0.623280\pi\)
\(332\) 0 0
\(333\) 317.406 551.969i 0.953172 1.65757i
\(334\) 0 0
\(335\) −655.358 + 781.026i −1.95629 + 2.33142i
\(336\) 0 0
\(337\) 61.5963 + 349.330i 0.182778 + 1.03659i 0.928777 + 0.370639i \(0.120861\pi\)
−0.745999 + 0.665948i \(0.768027\pi\)
\(338\) 0 0
\(339\) −146.029 + 25.8793i −0.430765 + 0.0763402i
\(340\) 0 0
\(341\) −14.2011 + 8.19903i −0.0416456 + 0.0240441i
\(342\) 0 0
\(343\) 153.417 265.726i 0.447279 0.774711i
\(344\) 0 0
\(345\) −46.8464 + 267.031i −0.135787 + 0.774003i
\(346\) 0 0
\(347\) 156.901 431.082i 0.452164 1.24231i −0.479034 0.877797i \(-0.659013\pi\)
0.931198 0.364514i \(-0.118765\pi\)
\(348\) 0 0
\(349\) 72.6326 411.920i 0.208116 1.18029i −0.684343 0.729160i \(-0.739911\pi\)
0.892460 0.451127i \(-0.148978\pi\)
\(350\) 0 0
\(351\) −63.3334 353.805i −0.180437 1.00799i
\(352\) 0 0
\(353\) −625.536 110.299i −1.77206 0.312462i −0.810229 0.586114i \(-0.800657\pi\)
−0.961829 + 0.273652i \(0.911768\pi\)
\(354\) 0 0
\(355\) 510.486 + 185.802i 1.43799 + 0.523385i
\(356\) 0 0
\(357\) 89.0795 + 244.086i 0.249522 + 0.683715i
\(358\) 0 0
\(359\) −387.565 223.761i −1.07957 0.623290i −0.148789 0.988869i \(-0.547538\pi\)
−0.930780 + 0.365579i \(0.880871\pi\)
\(360\) 0 0
\(361\) −189.329 327.927i −0.524456 0.908385i
\(362\) 0 0
\(363\) 295.161 + 107.141i 0.813116 + 0.295153i
\(364\) 0 0
\(365\) −1003.44 + 176.933i −2.74914 + 0.484748i
\(366\) 0 0
\(367\) −437.316 366.952i −1.19160 0.999869i −0.999830 0.0184287i \(-0.994134\pi\)
−0.191767 0.981440i \(-0.561422\pi\)
\(368\) 0 0
\(369\) 253.619 + 301.190i 0.687314 + 0.816234i
\(370\) 0 0
\(371\) −35.7938 98.3427i −0.0964793 0.265075i
\(372\) 0 0
\(373\) 169.879 142.546i 0.455440 0.382160i −0.386010 0.922495i \(-0.626147\pi\)
0.841450 + 0.540335i \(0.181702\pi\)
\(374\) 0 0
\(375\) −0.213783 246.894i −0.000570089 0.658385i
\(376\) 0 0
\(377\) 309.086i 0.819856i
\(378\) 0 0
\(379\) −523.969 −1.38250 −0.691252 0.722614i \(-0.742941\pi\)
−0.691252 + 0.722614i \(0.742941\pi\)
\(380\) 0 0
\(381\) −98.0545 169.496i −0.257361 0.444872i
\(382\) 0 0
\(383\) 262.803 + 313.197i 0.686171 + 0.817746i 0.990887 0.134697i \(-0.0430060\pi\)
−0.304716 + 0.952443i \(0.598562\pi\)
\(384\) 0 0
\(385\) 106.747 38.8527i 0.277265 0.100916i
\(386\) 0 0
\(387\) 71.4718 409.482i 0.184682 1.05809i
\(388\) 0 0
\(389\) 256.377 305.538i 0.659066 0.785445i −0.328185 0.944613i \(-0.606437\pi\)
0.987251 + 0.159169i \(0.0508814\pi\)
\(390\) 0 0
\(391\) −48.3517 274.216i −0.123662 0.701320i
\(392\) 0 0
\(393\) 39.0312 + 46.4339i 0.0993160 + 0.118152i
\(394\) 0 0
\(395\) 163.381 94.3280i 0.413622 0.238805i
\(396\) 0 0
\(397\) 138.738 240.302i 0.349467 0.605295i −0.636688 0.771122i \(-0.719696\pi\)
0.986155 + 0.165827i \(0.0530293\pi\)
\(398\) 0 0
\(399\) 225.900 + 189.220i 0.566166 + 0.474235i
\(400\) 0 0
\(401\) 49.8939 137.082i 0.124424 0.341851i −0.861805 0.507240i \(-0.830666\pi\)
0.986228 + 0.165389i \(0.0528880\pi\)
\(402\) 0 0
\(403\) 9.37987 53.1959i 0.0232751 0.132000i
\(404\) 0 0
\(405\) 620.458 111.621i 1.53199 0.275606i
\(406\) 0 0
\(407\) 281.562 + 49.6471i 0.691800 + 0.121983i
\(408\) 0 0
\(409\) −107.110 38.9847i −0.261882 0.0953171i 0.207743 0.978184i \(-0.433388\pi\)
−0.469624 + 0.882866i \(0.655611\pi\)
\(410\) 0 0
\(411\) 81.4789 97.2738i 0.198246 0.236676i
\(412\) 0 0
\(413\) −164.604 95.0339i −0.398556 0.230106i
\(414\) 0 0
\(415\) 162.020 + 280.627i 0.390410 + 0.676209i
\(416\) 0 0
\(417\) 202.230 169.990i 0.484965 0.407650i
\(418\) 0 0
\(419\) 514.237 90.6739i 1.22730 0.216406i 0.477833 0.878451i \(-0.341422\pi\)
0.749464 + 0.662045i \(0.230311\pi\)
\(420\) 0 0
\(421\) −302.908 254.170i −0.719495 0.603728i 0.207750 0.978182i \(-0.433386\pi\)
−0.927246 + 0.374454i \(0.877830\pi\)
\(422\) 0 0
\(423\) −478.630 + 572.420i −1.13151 + 1.35324i
\(424\) 0 0
\(425\) 291.776 + 801.647i 0.686531 + 1.88623i
\(426\) 0 0
\(427\) −12.0360 + 10.0994i −0.0281874 + 0.0236521i
\(428\) 0 0
\(429\) 139.701 80.8176i 0.325642 0.188386i
\(430\) 0 0
\(431\) 555.362i 1.28854i 0.764797 + 0.644272i \(0.222839\pi\)
−0.764797 + 0.644272i \(0.777161\pi\)
\(432\) 0 0
\(433\) 13.3027 0.0307222 0.0153611 0.999882i \(-0.495110\pi\)
0.0153611 + 0.999882i \(0.495110\pi\)
\(434\) 0 0
\(435\) −542.120 + 0.469416i −1.24625 + 0.00107912i
\(436\) 0 0
\(437\) −202.984 241.907i −0.464495 0.553563i
\(438\) 0 0
\(439\) 279.612 101.770i 0.636929 0.231823i −0.00331548 0.999995i \(-0.501055\pi\)
0.640244 + 0.768171i \(0.278833\pi\)
\(440\) 0 0
\(441\) 304.277 + 110.151i 0.689970 + 0.249776i
\(442\) 0 0
\(443\) 64.0510 76.3330i 0.144585 0.172309i −0.688892 0.724864i \(-0.741903\pi\)
0.833477 + 0.552555i \(0.186347\pi\)
\(444\) 0 0
\(445\) −131.398 745.196i −0.295277 1.67460i
\(446\) 0 0
\(447\) −216.940 + 597.646i −0.485324 + 1.33702i
\(448\) 0 0
\(449\) −425.171 + 245.473i −0.946929 + 0.546710i −0.892126 0.451788i \(-0.850786\pi\)
−0.0548032 + 0.998497i \(0.517453\pi\)
\(450\) 0 0
\(451\) −88.4019 + 153.117i −0.196013 + 0.339505i
\(452\) 0 0
\(453\) −497.310 + 181.494i −1.09781 + 0.400649i
\(454\) 0 0
\(455\) −127.984 + 351.633i −0.281283 + 0.772819i
\(456\) 0 0
\(457\) −20.0616 + 113.775i −0.0438984 + 0.248960i −0.998858 0.0477752i \(-0.984787\pi\)
0.954960 + 0.296736i \(0.0958980\pi\)
\(458\) 0 0
\(459\) −559.891 + 325.195i −1.21981 + 0.708487i
\(460\) 0 0
\(461\) −113.395 19.9947i −0.245977 0.0433724i 0.0493001 0.998784i \(-0.484301\pi\)
−0.295277 + 0.955412i \(0.595412\pi\)
\(462\) 0 0
\(463\) −42.9280 15.6245i −0.0927171 0.0337463i 0.295245 0.955422i \(-0.404599\pi\)
−0.387962 + 0.921675i \(0.626821\pi\)
\(464\) 0 0
\(465\) 93.3169 + 16.3710i 0.200682 + 0.0352064i
\(466\) 0 0
\(467\) 343.979 + 198.596i 0.736571 + 0.425259i 0.820821 0.571185i \(-0.193516\pi\)
−0.0842504 + 0.996445i \(0.526850\pi\)
\(468\) 0 0
\(469\) 236.564 + 409.740i 0.504400 + 0.873647i
\(470\) 0 0
\(471\) 2.93569 + 16.5653i 0.00623289 + 0.0351704i
\(472\) 0 0
\(473\) 183.813 32.4111i 0.388610 0.0685225i
\(474\) 0 0
\(475\) 741.146 + 621.896i 1.56031 + 1.30925i
\(476\) 0 0
\(477\) 225.623 130.785i 0.473005 0.274183i
\(478\) 0 0
\(479\) −267.653 735.372i −0.558775 1.53522i −0.821416 0.570329i \(-0.806816\pi\)
0.262641 0.964894i \(-0.415406\pi\)
\(480\) 0 0
\(481\) −721.458 + 605.375i −1.49991 + 1.25858i
\(482\) 0 0
\(483\) 109.008 + 62.8101i 0.225690 + 0.130042i
\(484\) 0 0
\(485\) 378.733i 0.780893i
\(486\) 0 0
\(487\) −505.750 −1.03850 −0.519250 0.854622i \(-0.673789\pi\)
−0.519250 + 0.854622i \(0.673789\pi\)
\(488\) 0 0
\(489\) 264.731 459.446i 0.541373 0.939563i
\(490\) 0 0
\(491\) 592.619 + 706.256i 1.20696 + 1.43840i 0.867250 + 0.497874i \(0.165886\pi\)
0.339714 + 0.940529i \(0.389670\pi\)
\(492\) 0 0
\(493\) 523.213 190.434i 1.06128 0.386276i
\(494\) 0 0
\(495\) 141.962 + 244.904i 0.286791 + 0.494757i
\(496\) 0 0
\(497\) 162.044 193.116i 0.326044 0.388564i
\(498\) 0 0
\(499\) 107.632 + 610.414i 0.215696 + 1.22327i 0.879694 + 0.475540i \(0.157747\pi\)
−0.663998 + 0.747734i \(0.731142\pi\)
\(500\) 0 0
\(501\) 877.845 155.572i 1.75219 0.310522i
\(502\) 0 0
\(503\) 1.70660 0.985304i 0.00339284 0.00195885i −0.498303 0.867003i \(-0.666043\pi\)
0.501695 + 0.865044i \(0.332710\pi\)
\(504\) 0 0
\(505\) 147.489 255.459i 0.292058 0.505859i
\(506\) 0 0
\(507\) −4.25796 + 24.2710i −0.00839835 + 0.0478718i
\(508\) 0 0
\(509\) −4.31115 + 11.8448i −0.00846985 + 0.0232707i −0.943856 0.330359i \(-0.892830\pi\)
0.935386 + 0.353629i \(0.115053\pi\)
\(510\) 0 0
\(511\) −82.1062 + 465.647i −0.160677 + 0.911247i
\(512\) 0 0
\(513\) −365.502 + 636.882i −0.712479 + 1.24149i
\(514\) 0 0
\(515\) −117.791 20.7698i −0.228721 0.0403297i
\(516\) 0 0
\(517\) −314.839 114.592i −0.608974 0.221648i
\(518\) 0 0
\(519\) −145.323 398.198i −0.280006 0.767242i
\(520\) 0 0
\(521\) −227.658 131.438i −0.436964 0.252281i 0.265345 0.964154i \(-0.414514\pi\)
−0.702309 + 0.711872i \(0.747847\pi\)
\(522\) 0 0
\(523\) 134.833 + 233.537i 0.257807 + 0.446534i 0.965654 0.259831i \(-0.0836669\pi\)
−0.707847 + 0.706365i \(0.750334\pi\)
\(524\) 0 0
\(525\) −362.317 131.518i −0.690128 0.250510i
\(526\) 0 0
\(527\) −95.8279 + 16.8970i −0.181837 + 0.0320627i
\(528\) 0 0
\(529\) 301.958 + 253.373i 0.570810 + 0.478966i
\(530\) 0 0
\(531\) 161.220 445.348i 0.303617 0.838696i
\(532\) 0 0
\(533\) −199.194 547.282i −0.373723 1.02680i
\(534\) 0 0
\(535\) 692.005 580.661i 1.29347 1.08535i
\(536\) 0 0
\(537\) −0.456896 527.661i −0.000850831 0.982608i
\(538\) 0 0
\(539\) 145.306i 0.269584i
\(540\) 0 0
\(541\) 986.273 1.82306 0.911528 0.411238i \(-0.134903\pi\)
0.911528 + 0.411238i \(0.134903\pi\)
\(542\) 0 0
\(543\) 362.203 + 626.102i 0.667041 + 1.15304i
\(544\) 0 0
\(545\) −544.409 648.802i −0.998916 1.19046i
\(546\) 0 0
\(547\) −632.979 + 230.385i −1.15718 + 0.421180i −0.848090 0.529852i \(-0.822247\pi\)
−0.309092 + 0.951032i \(0.600025\pi\)
\(548\) 0 0
\(549\) −30.0362 25.1149i −0.0547108 0.0457466i
\(550\) 0 0
\(551\) 405.894 483.726i 0.736651 0.877906i
\(552\) 0 0
\(553\) −15.2022 86.2162i −0.0274905 0.155906i
\(554\) 0 0
\(555\) −1062.89 1264.48i −1.91512 2.27834i
\(556\) 0 0
\(557\) −192.011 + 110.858i −0.344723 + 0.199026i −0.662359 0.749187i \(-0.730445\pi\)
0.317635 + 0.948213i \(0.397111\pi\)
\(558\) 0 0
\(559\) −307.417 + 532.462i −0.549941 + 0.952526i
\(560\) 0 0
\(561\) −222.878 186.689i −0.397288 0.332778i
\(562\) 0 0
\(563\) 34.1283 93.7667i 0.0606187 0.166548i −0.905686 0.423949i \(-0.860644\pi\)
0.966305 + 0.257400i \(0.0828659\pi\)
\(564\) 0 0
\(565\) −66.8110 + 378.904i −0.118250 + 0.670627i
\(566\) 0 0
\(567\) 49.8021 288.277i 0.0878344 0.508425i
\(568\) 0 0
\(569\) 601.483 + 106.058i 1.05709 + 0.186393i 0.675064 0.737760i \(-0.264116\pi\)
0.382024 + 0.924153i \(0.375227\pi\)
\(570\) 0 0
\(571\) −557.549 202.931i −0.976444 0.355397i −0.195987 0.980606i \(-0.562791\pi\)
−0.780457 + 0.625210i \(0.785013\pi\)
\(572\) 0 0
\(573\) −312.245 + 372.774i −0.544931 + 0.650566i
\(574\) 0 0
\(575\) 357.721 + 206.530i 0.622124 + 0.359183i
\(576\) 0 0
\(577\) −200.969 348.089i −0.348300 0.603273i 0.637648 0.770328i \(-0.279908\pi\)
−0.985948 + 0.167055i \(0.946574\pi\)
\(578\) 0 0
\(579\) −33.0848 + 27.8103i −0.0571413 + 0.0480316i
\(580\) 0 0
\(581\) 148.087 26.1117i 0.254883 0.0449428i
\(582\) 0 0
\(583\) 89.7046 + 75.2711i 0.153867 + 0.129110i
\(584\) 0 0
\(585\) −918.583 160.331i −1.57023 0.274071i
\(586\) 0 0
\(587\) −138.391 380.226i −0.235759 0.647744i −0.999996 0.00280774i \(-0.999106\pi\)
0.764237 0.644936i \(-0.223116\pi\)
\(588\) 0 0
\(589\) −84.5370 + 70.9350i −0.143526 + 0.120433i
\(590\) 0 0
\(591\) −565.209 + 326.976i −0.956360 + 0.553259i
\(592\) 0 0
\(593\) 397.833i 0.670882i −0.942061 0.335441i \(-0.891115\pi\)
0.942061 0.335441i \(-0.108885\pi\)
\(594\) 0 0
\(595\) 674.088 1.13292
\(596\) 0 0
\(597\) 123.091 0.106584i 0.206183 0.000178532i
\(598\) 0 0
\(599\) −628.912 749.508i −1.04994 1.25127i −0.967018 0.254710i \(-0.918020\pi\)
−0.0829193 0.996556i \(-0.526424\pi\)
\(600\) 0 0
\(601\) −289.500 + 105.369i −0.481698 + 0.175324i −0.571444 0.820641i \(-0.693617\pi\)
0.0897464 + 0.995965i \(0.471394\pi\)
\(602\) 0 0
\(603\) −901.845 + 759.403i −1.49560 + 1.25938i
\(604\) 0 0
\(605\) 523.633 624.041i 0.865508 1.03147i
\(606\) 0 0
\(607\) 23.7810 + 134.869i 0.0391779 + 0.222189i 0.998110 0.0614454i \(-0.0195710\pi\)
−0.958933 + 0.283634i \(0.908460\pi\)
\(608\) 0 0
\(609\) −85.8379 + 236.475i −0.140949 + 0.388300i
\(610\) 0 0
\(611\) 955.801 551.832i 1.56432 0.903162i
\(612\) 0 0
\(613\) 165.591 286.811i 0.270132 0.467882i −0.698764 0.715352i \(-0.746266\pi\)
0.968895 + 0.247471i \(0.0795995\pi\)
\(614\) 0 0
\(615\) 959.600 350.207i 1.56033 0.569443i
\(616\) 0 0
\(617\) −167.681 + 460.699i −0.271768 + 0.746676i 0.726462 + 0.687206i \(0.241163\pi\)
−0.998230 + 0.0594697i \(0.981059\pi\)
\(618\) 0 0
\(619\) −44.5940 + 252.905i −0.0720420 + 0.408571i 0.927366 + 0.374156i \(0.122068\pi\)
−0.999408 + 0.0344143i \(0.989043\pi\)
\(620\) 0 0
\(621\) −106.459 + 294.875i −0.171432 + 0.474839i
\(622\) 0 0
\(623\) −345.810 60.9756i −0.555072 0.0978742i
\(624\) 0 0
\(625\) 233.826 + 85.1058i 0.374122 + 0.136169i
\(626\) 0 0
\(627\) −324.765 56.9749i −0.517966 0.0908691i
\(628\) 0 0
\(629\) 1469.27 + 848.283i 2.33588 + 1.34862i
\(630\) 0 0
\(631\) −320.656 555.392i −0.508171 0.880177i −0.999955 0.00946046i \(-0.996989\pi\)
0.491785 0.870717i \(-0.336345\pi\)
\(632\) 0 0
\(633\) 64.7847 + 365.561i 0.102345 + 0.577506i
\(634\) 0 0
\(635\) −500.289 + 88.2144i −0.787856 + 0.138920i
\(636\) 0 0
\(637\) −366.666 307.669i −0.575614 0.482997i
\(638\) 0 0
\(639\) 544.579 + 313.157i 0.852236 + 0.490073i
\(640\) 0 0
\(641\) 296.689 + 815.145i 0.462853 + 1.27168i 0.923330 + 0.384006i \(0.125456\pi\)
−0.460478 + 0.887671i \(0.652322\pi\)
\(642\) 0 0
\(643\) −12.8197 + 10.7570i −0.0199373 + 0.0167294i −0.652702 0.757615i \(-0.726365\pi\)
0.632765 + 0.774344i \(0.281920\pi\)
\(644\) 0 0
\(645\) −934.376 538.384i −1.44864 0.834704i
\(646\) 0 0
\(647\) 96.9735i 0.149882i −0.997188 0.0749409i \(-0.976123\pi\)
0.997188 0.0749409i \(-0.0238768\pi\)
\(648\) 0 0
\(649\) 212.673 0.327694
\(650\) 0 0
\(651\) 21.9497 38.0941i 0.0337168 0.0585162i
\(652\) 0 0
\(653\) −233.975 278.841i −0.358309 0.427015i 0.556535 0.830824i \(-0.312131\pi\)
−0.914843 + 0.403809i \(0.867686\pi\)
\(654\) 0 0
\(655\) 147.878 53.8234i 0.225769 0.0821731i
\(656\) 0 0
\(657\) −1178.25 + 2.04047i −1.79338 + 0.00310574i
\(658\) 0 0
\(659\) −246.864 + 294.201i −0.374604 + 0.446436i −0.920104 0.391675i \(-0.871896\pi\)
0.545499 + 0.838111i \(0.316340\pi\)
\(660\) 0 0
\(661\) 46.2263 + 262.162i 0.0699338 + 0.396614i 0.999602 + 0.0282161i \(0.00898265\pi\)
−0.929668 + 0.368398i \(0.879906\pi\)
\(662\) 0 0
\(663\) 943.013 167.121i 1.42234 0.252067i
\(664\) 0 0
\(665\) 662.064 382.243i 0.995586 0.574802i
\(666\) 0 0
\(667\) 134.797 233.475i 0.202094 0.350037i
\(668\) 0 0
\(669\) 135.596 772.917i 0.202685 1.15533i
\(670\) 0 0
\(671\) 6.01292 16.5204i 0.00896114 0.0246205i
\(672\) 0 0
\(673\) −15.4024 + 87.3511i −0.0228861 + 0.129794i −0.994110 0.108374i \(-0.965436\pi\)
0.971224 + 0.238168i \(0.0765467\pi\)
\(674\) 0 0
\(675\) 164.332 946.340i 0.243454 1.40199i
\(676\) 0 0
\(677\) −440.545 77.6799i −0.650731 0.114741i −0.161468 0.986878i \(-0.551623\pi\)
−0.489262 + 0.872137i \(0.662734\pi\)
\(678\) 0 0
\(679\) −165.153 60.1107i −0.243230 0.0885283i
\(680\) 0 0
\(681\) −85.0079 232.929i −0.124828 0.342040i
\(682\) 0 0
\(683\) −289.821 167.328i −0.424335 0.244990i 0.272595 0.962129i \(-0.412118\pi\)
−0.696930 + 0.717139i \(0.745451\pi\)
\(684\) 0 0
\(685\) −164.596 285.088i −0.240286 0.416187i
\(686\) 0 0
\(687\) 373.584 + 135.607i 0.543790 + 0.197390i
\(688\) 0 0
\(689\) −379.880 + 66.9831i −0.551349 + 0.0972178i
\(690\) 0 0
\(691\) 319.613 + 268.187i 0.462537 + 0.388115i 0.844064 0.536243i \(-0.180157\pi\)
−0.381526 + 0.924358i \(0.624601\pi\)
\(692\) 0 0
\(693\) 129.326 23.0347i 0.186618 0.0332391i
\(694\) 0 0
\(695\) −234.413 644.045i −0.337285 0.926684i
\(696\) 0 0
\(697\) −803.698 + 674.383i −1.15308 + 0.967551i
\(698\) 0 0
\(699\) 1.06592 + 1231.01i 0.00152492 + 1.76111i
\(700\) 0 0
\(701\) 613.675i 0.875428i 0.899114 + 0.437714i \(0.144212\pi\)
−0.899114 + 0.437714i \(0.855788\pi\)
\(702\) 0 0
\(703\) 1924.08 2.73696
\(704\) 0 0
\(705\) 969.335 + 1675.59i 1.37494 + 2.37672i
\(706\) 0 0
\(707\) −87.9882 104.860i −0.124453 0.148317i
\(708\) 0 0
\(709\) −788.773 + 287.090i −1.11252 + 0.404923i −0.831916 0.554902i \(-0.812756\pi\)
−0.280600 + 0.959825i \(0.590533\pi\)
\(710\) 0 0
\(711\) 204.871 74.9690i 0.288145 0.105442i
\(712\) 0 0
\(713\) −30.2848 + 36.0920i −0.0424752 + 0.0506199i
\(714\) 0 0
\(715\) −72.7073 412.343i −0.101688 0.576704i
\(716\) 0 0
\(717\) −218.709 260.189i −0.305033 0.362885i
\(718\) 0 0
\(719\) −866.895 + 500.502i −1.20570 + 0.696108i −0.961816 0.273697i \(-0.911753\pi\)
−0.243879 + 0.969806i \(0.578420\pi\)
\(720\) 0 0
\(721\) −27.7523 + 48.0683i −0.0384914 + 0.0666690i
\(722\) 0 0
\(723\) 243.675 + 204.109i 0.337034 + 0.282308i
\(724\) 0 0
\(725\) −282.499 + 776.159i −0.389654 + 1.07056i
\(726\) 0 0
\(727\) −184.123 + 1044.22i −0.253264 + 1.43633i 0.547224 + 0.836986i \(0.315685\pi\)
−0.800488 + 0.599348i \(0.795427\pi\)
\(728\) 0 0
\(729\) 728.990 3.78739i 0.999987 0.00519532i
\(730\) 0 0
\(731\) 1090.74 + 192.328i 1.49213 + 0.263102i
\(732\) 0 0
\(733\) 330.701 + 120.365i 0.451161 + 0.164209i 0.557600 0.830110i \(-0.311723\pi\)
−0.106438 + 0.994319i \(0.533945\pi\)
\(734\) 0 0
\(735\) 539.078 643.579i 0.733439 0.875618i
\(736\) 0 0
\(737\) −458.472 264.699i −0.622079 0.359158i
\(738\) 0 0
\(739\) −417.279 722.749i −0.564654 0.978010i −0.997082 0.0763410i \(-0.975676\pi\)
0.432428 0.901669i \(-0.357657\pi\)
\(740\) 0 0
\(741\) 831.426 698.877i 1.12203 0.943154i
\(742\) 0 0
\(743\) −132.230 + 23.3158i −0.177968 + 0.0313806i −0.261922 0.965089i \(-0.584356\pi\)
0.0839538 + 0.996470i \(0.473245\pi\)
\(744\) 0 0
\(745\) 1263.57 + 1060.26i 1.69606 + 1.42317i
\(746\) 0 0
\(747\) 128.769 + 351.892i 0.172381 + 0.471073i
\(748\) 0 0
\(749\) −143.375 393.920i −0.191422 0.525928i
\(750\) 0 0
\(751\) −234.728 + 196.960i −0.312554 + 0.262264i −0.785547 0.618802i \(-0.787618\pi\)
0.472992 + 0.881066i \(0.343174\pi\)
\(752\) 0 0
\(753\) −40.9628 + 23.6972i −0.0543995 + 0.0314704i
\(754\) 0 0
\(755\) 1373.41i 1.81909i
\(756\) 0 0
\(757\) 248.812 0.328682 0.164341 0.986404i \(-0.447450\pi\)
0.164341 + 0.986404i \(0.447450\pi\)
\(758\) 0 0
\(759\) −140.772 + 0.121893i −0.185470 + 0.000160597i
\(760\) 0 0
\(761\) −80.5249 95.9658i −0.105815 0.126105i 0.710538 0.703659i \(-0.248452\pi\)
−0.816352 + 0.577554i \(0.804007\pi\)
\(762\) 0 0
\(763\) −369.327 + 134.424i −0.484046 + 0.176178i
\(764\) 0 0
\(765\) 294.553 + 1653.74i 0.385036 + 2.16175i
\(766\) 0 0
\(767\) −450.313 + 536.662i −0.587109 + 0.699690i
\(768\) 0 0
\(769\) −160.957 912.832i −0.209307 1.18704i −0.890517 0.454950i \(-0.849657\pi\)
0.681210 0.732088i \(-0.261454\pi\)
\(770\) 0 0
\(771\) 302.062 832.149i 0.391779 1.07931i
\(772\) 0 0
\(773\) 202.681 117.018i 0.262200 0.151381i −0.363138 0.931736i \(-0.618295\pi\)
0.625338 + 0.780354i \(0.284961\pi\)
\(774\) 0 0
\(775\) 72.1743 125.010i 0.0931281 0.161303i
\(776\) 0 0
\(777\) −720.094 + 262.799i −0.926761 + 0.338223i
\(778\) 0 0
\(779\) −406.952 + 1118.09i −0.522404 + 1.43529i
\(780\) 0 0
\(781\) −48.9823 + 277.793i −0.0627175 + 0.355688i
\(782\) 0 0
\(783\) −617.651 107.255i −0.788826 0.136979i
\(784\)