Properties

Label 108.3.k.a.41.5
Level 108
Weight 3
Character 108.41
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 41.5
Character \(\chi\) \(=\) 108.41
Dual form 108.3.k.a.29.5

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 −0.0192785 + 0.999814i \(0.506137\pi\)
−0.981277 + 0.192602i \(0.938308\pi\)
\(6\) 0 0
\(7\) −3.39388 1.23527i −0.484840 0.176467i 0.0880231 0.996118i \(-0.471945\pi\)
−0.572863 + 0.819651i \(0.694167\pi\)
\(8\) 0 0
\(9\) −4.51349 + 7.78642i −0.501499 + 0.865158i
\(10\) 0 0
\(11\) 2.59766 + 3.09577i 0.236151 + 0.281434i 0.871085 0.491133i \(-0.163417\pi\)
−0.634934 + 0.772567i \(0.718973\pi\)
\(12\) 0 0
\(13\) 2.31163 13.1099i 0.177818 1.00846i −0.757023 0.653389i \(-0.773347\pi\)
0.934841 0.355067i \(-0.115542\pi\)
\(14\) 0 0
\(15\) −22.9906 4.07439i −1.53271 0.271626i
\(16\) 0 0
\(17\) 20.7679 + 11.9904i 1.22164 + 0.705316i 0.965268 0.261262i \(-0.0841385\pi\)
0.256375 + 0.966577i \(0.417472\pi\)
\(18\) 0 0
\(19\) 13.5983 + 23.5530i 0.715701 + 1.23963i 0.962688 + 0.270612i \(0.0872261\pi\)
−0.246987 + 0.969019i \(0.579441\pi\)
\(20\) 0 0
\(21\) −1.87225 10.6721i −0.0891548 0.508195i
\(22\) 0 0
\(23\) 3.97128 + 10.9110i 0.172665 + 0.474392i 0.995596 0.0937489i \(-0.0298851\pi\)
−0.822931 + 0.568141i \(0.807663\pi\)
\(24\) 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 0.235106 0.971970i \(-0.424456\pi\)
0.553361 + 0.832942i \(0.313345\pi\)
\(30\) 0 0
\(31\) −3.81297 + 1.38781i −0.122999 + 0.0447680i −0.402786 0.915294i \(-0.631958\pi\)
0.279787 + 0.960062i \(0.409736\pi\)
\(32\) 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 0.224074 0.974572i \(-0.428064\pi\)
0.731967 0.681340i \(-0.238602\pi\)
\(38\) 0 0
\(39\) 37.5399 13.6266i 0.962560 0.349400i
\(40\) 0 0
\(41\) −43.0852 7.59708i −1.05086 0.185295i −0.378561 0.925576i \(-0.623581\pi\)
−0.672297 + 0.740282i \(0.734692\pi\)
\(42\) 0 0
\(43\) 35.3804 29.6877i 0.822801 0.690412i −0.130825 0.991405i \(-0.541763\pi\)
0.953626 + 0.300994i \(0.0973183\pi\)
\(44\) 0 0
\(45\) −23.8433 65.8635i −0.529851 1.46363i
\(46\) 0 0
\(47\) −28.3557 + 77.9066i −0.603312 + 1.65759i 0.141203 + 0.989981i \(0.454903\pi\)
−0.744515 + 0.667606i \(0.767319\pi\)
\(48\) 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 \(-0.911864\pi\)
0.961911 0.273363i \(-0.0881361\pi\)
\(54\) 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 −0.398972 0.916963i \(-0.630633\pi\)
0.972313 + 0.233681i \(0.0750772\pi\)
\(60\) 0 0
\(61\) 4.08794 + 1.48789i 0.0670155 + 0.0243916i 0.375310 0.926899i \(-0.377536\pi\)
−0.308295 + 0.951291i \(0.599758\pi\)
\(62\) 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 0.0374978 + 0.999297i \(0.488061\pi\)
−0.377016 + 0.926207i \(0.623050\pi\)
\(68\) 0 0
\(69\) −22.4138 + 26.6648i −0.324838 + 0.386447i
\(70\) 0 0
\(71\) −60.4484 34.8999i −0.851386 0.491548i 0.00973220 0.999953i \(-0.496902\pi\)
−0.861118 + 0.508405i \(0.830235\pi\)
\(72\) 0 0
\(73\) 65.4584 + 113.377i 0.896690 + 1.55311i 0.831699 + 0.555226i \(0.187368\pi\)
0.0649905 + 0.997886i \(0.479298\pi\)
\(74\) 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 0.946509 0.322677i \(-0.104583\pi\)
−0.999790 + 0.0205075i \(0.993472\pi\)
\(80\) 0 0
\(81\) −40.2568 70.2879i −0.496997 0.867752i
\(82\) 0 0
\(83\) −41.0021 + 7.22978i −0.494002 + 0.0871058i −0.415098 0.909776i \(-0.636253\pi\)
−0.0789031 + 0.996882i \(0.525142\pi\)
\(84\) 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 0.0542015 0.998530i \(-0.482739\pi\)
0.891853 + 0.452325i \(0.149405\pi\)
\(90\) 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 −0.430087 0.902787i \(-0.641517\pi\)
0.814388 + 0.580320i \(0.197073\pi\)
\(98\) 0 0
\(99\) −35.8295 + 6.25375i −0.361914 + 0.0631692i
\(100\) 0 0
\(101\) 12.9628 35.6149i 0.128344 0.352623i −0.858832 0.512257i \(-0.828809\pi\)
0.987176 + 0.159635i \(0.0510316\pi\)
\(102\) 0 0
\(103\) 11.7726 + 9.87837i 0.114297 + 0.0959065i 0.698145 0.715957i \(-0.254009\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(104\) 0 0
\(105\) 72.9943 + 42.2276i 0.695184 + 0.402168i
\(106\) 0 0
\(107\) 116.068i 1.08475i −0.840138 0.542373i \(-0.817526\pi\)
0.840138 0.542373i \(-0.182474\pi\)
\(108\) 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 −0.888096 0.459658i \(-0.847972\pi\)
0.606891 + 0.794785i \(0.292416\pi\)
\(114\) 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 0.965430 0.260662i \(-0.0839407\pi\)
−0.708455 + 0.705756i \(0.750607\pi\)
\(128\) 0 0
\(129\) 130.160 + 47.5022i 1.00900 + 0.368234i
\(130\) 0 0
\(131\) −6.91556 19.0003i −0.0527905 0.145041i 0.910495 0.413520i \(-0.135701\pi\)
−0.963285 + 0.268480i \(0.913479\pi\)
\(132\) 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 −0.0195449 0.999809i \(-0.506222\pi\)
0.323589 + 0.946198i \(0.395111\pi\)
\(138\) 0 0
\(139\) 82.7509 30.1189i 0.595330 0.216682i −0.0267421 0.999642i \(-0.508513\pi\)
0.622072 + 0.782960i \(0.286291\pi\)
\(140\) 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 −0.578308 0.815818i \(-0.696287\pi\)
−0.822458 + 0.568826i \(0.807398\pi\)
\(150\) 0 0
\(151\) −135.180 + 113.429i −0.895229 + 0.751186i −0.969252 0.246070i \(-0.920861\pi\)
0.0740229 + 0.997257i \(0.476416\pi\)
\(152\) 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 0.629004 0.777402i \(-0.283463\pi\)
−0.656366 + 0.754443i \(0.727907\pi\)
\(158\) 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 0.222249 0.974990i \(-0.428660\pi\)
0.921585 0.388178i \(-0.126895\pi\)
\(168\) 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 0.961753 0.273918i \(-0.0883197\pi\)
−0.436763 + 0.899577i \(0.643875\pi\)
\(174\) 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 0.860976 0.508646i \(-0.169854\pi\)
−0.0100121 + 0.999950i \(0.503187\pi\)
\(180\) 0 0
\(181\) −120.554 208.805i −0.666042 1.15362i −0.979002 0.203853i \(-0.934654\pi\)
0.312959 0.949767i \(-0.398680\pi\)
\(182\) 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 −0.575113 0.818074i \(-0.695042\pi\)
−0.260632 + 0.965438i \(0.583931\pi\)
\(192\) 0 0
\(193\) −13.5380 + 4.92744i −0.0701452 + 0.0255308i −0.376854 0.926272i \(-0.622994\pi\)
0.306709 + 0.951803i \(0.400772\pi\)
\(194\) 0 0
\(195\) −106.561 + 291.986i −0.546465 + 1.49737i
\(196\) 0 0
\(197\) −188.497 + 108.829i −0.956838 + 0.552431i −0.895199 0.445668i \(-0.852966\pi\)
−0.0616399 + 0.998098i \(0.519633\pi\)
\(198\) 0 0
\(199\) 20.5152 35.5335i 0.103092 0.178560i −0.809865 0.586616i \(-0.800460\pi\)
0.912957 + 0.408056i \(0.133793\pi\)
\(200\) 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 0.389883 0.920864i \(-0.372515\pi\)
−0.839172 + 0.543867i \(0.816960\pi\)
\(212\) 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 0.828140 0.560521i \(-0.189399\pi\)
0.274096 + 0.961702i \(0.411621\pi\)
\(224\) 0 0
\(225\) 300.669 + 110.025i 1.33631 + 0.488998i
\(226\) 0 0
\(227\) 53.1278 + 63.3153i 0.234043 + 0.278922i 0.870264 0.492585i \(-0.163948\pi\)
−0.636221 + 0.771507i \(0.719503\pi\)
\(228\) 0 0
\(229\) 23.0046 130.466i 0.100457 0.569719i −0.892481 0.451084i \(-0.851037\pi\)
0.992938 0.118634i \(-0.0378516\pi\)
\(230\) 0 0
\(231\) 28.1749 33.5185i 0.121969 0.145102i
\(232\) 0 0
\(233\) −355.363 205.169i −1.52516 0.880553i −0.999555 0.0298260i \(-0.990505\pi\)
−0.525608 0.850727i \(-0.676162\pi\)
\(234\) 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 0.993982 0.109539i \(-0.0349375\pi\)
−0.831845 + 0.555008i \(0.812715\pi\)
\(240\) 0 0
\(241\) −18.3989 104.345i −0.0763439 0.432968i −0.998891 0.0470832i \(-0.985007\pi\)
0.922547 0.385885i \(-0.126104\pi\)
\(242\) 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 −0.526966 0.849886i \(-0.676671\pi\)
0.472540 + 0.881309i \(0.343337\pi\)
\(252\) 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 0.707566 0.706647i \(-0.249793\pi\)
0.423207 + 0.906033i \(0.360904\pi\)
\(258\) 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 −0.951568 0.307437i \(-0.900529\pi\)
0.926560 + 0.376146i \(0.122751\pi\)
\(264\) 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 \(-0.884939\pi\)
0.935376 0.353654i \(-0.115061\pi\)
\(270\) 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 0.445751 0.895157i \(-0.352937\pi\)
−0.233930 + 0.972253i \(0.575159\pi\)
\(278\) 0 0
\(279\) 6.40375 35.9533i 0.0229525 0.128865i
\(280\) 0 0
\(281\) −163.665 195.048i −0.582437 0.694122i 0.391696 0.920095i \(-0.371888\pi\)
−0.974134 + 0.225973i \(0.927444\pi\)
\(282\) 0 0
\(283\) 37.8599 214.714i 0.133781 0.758707i −0.841921 0.539602i \(-0.818575\pi\)
0.975701 0.219106i \(-0.0703140\pi\)
\(284\) 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 0.994698 + 0.102838i \(0.0327924\pi\)
−0.695880 + 0.718158i \(0.744985\pi\)
\(294\) 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 −0.420509 0.907288i \(-0.638148\pi\)
0.995989 0.0894730i \(-0.0285183\pi\)
\(308\) 0 0
\(309\) −8.04520 + 45.3967i −0.0260362 + 0.146915i
\(310\) 0 0
\(311\) −47.8256 8.43294i −0.153780 0.0271156i 0.0962281 0.995359i \(-0.469322\pi\)
−0.250008 + 0.968244i \(0.580433\pi\)
\(312\) 0 0
\(313\) −50.3641 + 42.2605i −0.160908 + 0.135018i −0.719687 0.694299i \(-0.755714\pi\)
0.558779 + 0.829317i \(0.311270\pi\)
\(314\) 0 0
\(315\) −0.438116 + 252.986i −0.00139085 + 0.803130i
\(316\) 0 0
\(317\) 174.159 478.499i 0.549398 1.50946i −0.285127 0.958490i \(-0.592036\pi\)
0.834525 0.550970i \(-0.185742\pi\)
\(318\) 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 −0.377687 0.925933i \(-0.623280\pi\)
−0.884504 + 0.466534i \(0.845503\pi\)
\(332\) 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 −0.745999 0.665948i \(-0.768027\pi\)
0.928777 0.370639i \(-0.120861\pi\)
\(338\) 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 0.931198 + 0.364514i \(0.118765\pi\)
−0.479034 + 0.877797i \(0.659013\pi\)
\(348\) 0 0
\(349\) 72.6326 + 411.920i 0.208116 + 1.18029i 0.892460 + 0.451127i \(0.148978\pi\)
−0.684343 + 0.729160i \(0.739911\pi\)
\(350\) 0 0
\(351\) −63.3334 + 353.805i −0.180437 + 1.00799i
\(352\) 0 0
\(353\) −625.536 + 110.299i −1.77206 + 0.312462i −0.961829 0.273652i \(-0.911768\pi\)
−0.810229 + 0.586114i \(0.800657\pi\)
\(354\) 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 −0.930780 0.365579i \(-0.880871\pi\)
−0.148789 + 0.988869i \(0.547538\pi\)
\(360\) 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 −0.191767 + 0.981440i \(0.561422\pi\)
−0.999830 + 0.0184287i \(0.994134\pi\)
\(368\) 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 0.841450 0.540335i \(-0.181702\pi\)
−0.386010 + 0.922495i \(0.626147\pi\)
\(374\) 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 −0.304716 0.952443i \(-0.598562\pi\)
0.990887 + 0.134697i \(0.0430060\pi\)
\(384\) 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 0.987251 0.159169i \(-0.0508814\pi\)
−0.328185 + 0.944613i \(0.606437\pi\)
\(390\) 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 0.986155 0.165827i \(-0.0530293\pi\)
−0.636688 + 0.771122i \(0.719696\pi\)
\(398\) 0 0
\(399\) 225.900 189.220i 0.566166 0.474235i
\(400\) 0 0
\(401\) 49.8939 + 137.082i 0.124424 + 0.341851i 0.986228 0.165389i \(-0.0528880\pi\)
−0.861805 + 0.507240i \(0.830666\pi\)
\(402\) 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 −0.469624 0.882866i \(-0.655611\pi\)
0.207743 + 0.978184i \(0.433388\pi\)
\(410\) 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 0.749464 0.662045i \(-0.230311\pi\)
0.477833 + 0.878451i \(0.341422\pi\)
\(420\) 0 0
\(421\) −302.908 + 254.170i −0.719495 + 0.603728i −0.927246 0.374454i \(-0.877830\pi\)
0.207750 + 0.978182i \(0.433386\pi\)
\(422\) 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 \(-0.777161\pi\)
0.764797 0.644272i \(-0.222839\pi\)
\(432\) 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 0.640244 0.768171i \(-0.278833\pi\)
−0.00331548 + 0.999995i \(0.501055\pi\)
\(440\) 0 0
\(441\) 304.277 110.151i 0.689970 0.249776i
\(442\) 0 0
\(443\) 64.0510 + 76.3330i 0.144585 + 0.172309i 0.833477 0.552555i \(-0.186347\pi\)
−0.688892 + 0.724864i \(0.741903\pi\)
\(444\) 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 −0.0548032 0.998497i \(-0.517453\pi\)
−0.892126 + 0.451788i \(0.850786\pi\)
\(450\) 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 0.954960 0.296736i \(-0.0958980\pi\)
−0.998858 + 0.0477752i \(0.984787\pi\)
\(458\) 0 0
\(459\) −559.891 325.195i −1.21981 0.708487i
\(460\) 0 0
\(461\) −113.395 + 19.9947i −0.245977 + 0.0433724i −0.295277 0.955412i \(-0.595412\pi\)
0.0493001 + 0.998784i \(0.484301\pi\)
\(462\) 0 0
\(463\) −42.9280 + 15.6245i −0.0927171 + 0.0337463i −0.387962 0.921675i \(-0.626821\pi\)
0.295245 + 0.955422i \(0.404599\pi\)
\(464\) 0 0
\(465\) 93.3169 16.3710i 0.200682 0.0352064i
\(466\) 0 0
\(467\) 343.979 198.596i 0.736571 0.425259i −0.0842504 0.996445i \(-0.526850\pi\)
0.820821 + 0.571185i \(0.193516\pi\)
\(468\) 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 0.262641 + 0.964894i \(0.415406\pi\)
−0.821416 + 0.570329i \(0.806816\pi\)
\(480\) 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 0.339714 0.940529i \(-0.389670\pi\)
0.867250 0.497874i \(-0.165886\pi\)
\(492\) 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 −0.663998 0.747734i \(-0.731142\pi\)
0.879694 0.475540i \(-0.157747\pi\)
\(500\) 0 0
\(501\) 877.845 + 155.572i 1.75219 + 0.310522i
\(502\) 0 0
\(503\) 1.70660 + 0.985304i 0.00339284 + 0.00195885i 0.501695 0.865044i \(-0.332710\pi\)
−0.498303 + 0.867003i \(0.666043\pi\)
\(504\) 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 0.935386 0.353629i \(-0.115053\pi\)
−0.943856 + 0.330359i \(0.892830\pi\)
\(510\) 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 −0.702309 0.711872i \(-0.747847\pi\)
0.265345 + 0.964154i \(0.414514\pi\)
\(522\) 0 0
\(523\) 134.833 233.537i 0.257807 0.446534i −0.707847 0.706365i \(-0.750334\pi\)
0.965654 + 0.259831i \(0.0836669\pi\)
\(524\) 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 −0.309092 0.951032i \(-0.600025\pi\)
−0.848090 + 0.529852i \(0.822247\pi\)
\(548\) 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 0.317635 0.948213i \(-0.397111\pi\)
−0.662359 + 0.749187i \(0.730445\pi\)
\(558\) 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 0.966305 0.257400i \(-0.0828659\pi\)
−0.905686 + 0.423949i \(0.860644\pi\)
\(564\) 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 0.382024 0.924153i \(-0.375227\pi\)
0.675064 + 0.737760i \(0.264116\pi\)
\(570\) 0 0
\(571\) −557.549 + 202.931i −0.976444 + 0.355397i −0.780457 0.625210i \(-0.785013\pi\)
−0.195987 + 0.980606i \(0.562791\pi\)
\(572\) 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 −0.985948 0.167055i \(-0.946574\pi\)
0.637648 + 0.770328i \(0.279908\pi\)
\(578\) 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 0.764237 + 0.644936i \(0.223116\pi\)
−0.999996 + 0.00280774i \(0.999106\pi\)
\(588\) 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 \(0.108885\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(594\) 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 −0.0829193 + 0.996556i \(0.526424\pi\)
−0.967018 + 0.254710i \(0.918020\pi\)
\(600\) 0 0
\(601\) −289.500 105.369i −0.481698 0.175324i 0.0897464 0.995965i \(-0.471394\pi\)
−0.571444 + 0.820641i \(0.693617\pi\)
\(602\) 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 −0.958933 0.283634i \(-0.908460\pi\)
0.998110 + 0.0614454i \(0.0195710\pi\)
\(608\) 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 0.968895 0.247471i \(-0.0795995\pi\)
−0.698764 + 0.715352i \(0.746266\pi\)
\(614\) 0 0
\(615\) 959.600 + 350.207i 1.56033 + 0.569443i
\(616\) 0 0
\(617\) −167.681 460.699i −0.271768 0.746676i −0.998230 0.0594697i \(-0.981059\pi\)
0.726462 0.687206i \(-0.241163\pi\)
\(618\) 0 0
\(619\) −44.5940 252.905i −0.0720420 0.408571i −0.999408 0.0344143i \(-0.989043\pi\)
0.927366 0.374156i \(-0.122068\pi\)
\(620\) 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 0.491785 + 0.870717i \(0.336345\pi\)
−0.999955 + 0.00946046i \(0.996989\pi\)
\(632\) 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 −0.460478 0.887671i \(-0.652322\pi\)
0.923330 0.384006i \(-0.125456\pi\)
\(642\) 0 0
\(643\) −12.8197 10.7570i −0.0199373 0.0167294i 0.632765 0.774344i \(-0.281920\pi\)
−0.652702 + 0.757615i \(0.726365\pi\)
\(644\) 0 0
\(645\) −934.376 + 538.384i −1.44864 + 0.834704i
\(646\) 0 0
\(647\) 96.9735i 0.149882i 0.997188 + 0.0749409i \(0.0238768\pi\)
−0.997188 + 0.0749409i \(0.976123\pi\)
\(648\) 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 −0.914843 0.403809i \(-0.867686\pi\)
0.556535 + 0.830824i \(0.312131\pi\)
\(654\) 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 0.545499 0.838111i \(-0.316340\pi\)
−0.920104 + 0.391675i \(0.871896\pi\)
\(660\) 0 0
\(661\) 46.2263 262.162i 0.0699338 0.396614i −0.929668 0.368398i \(-0.879906\pi\)
0.999602 0.0282161i \(-0.00898265\pi\)
\(662\) 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 0.971224 0.238168i \(-0.0765467\pi\)
−0.994110 + 0.108374i \(0.965436\pi\)
\(674\) 0 0
\(675\) 164.332 + 946.340i 0.243454 + 1.40199i
\(676\) 0 0
\(677\) −440.545 + 77.6799i −0.650731 + 0.114741i −0.489262 0.872137i \(-0.662734\pi\)
−0.161468 + 0.986878i \(0.551623\pi\)
\(678\) 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 −0.696930 0.717139i \(-0.745451\pi\)
0.272595 + 0.962129i \(0.412118\pi\)
\(684\) 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 −0.381526 0.924358i \(-0.624601\pi\)
0.844064 + 0.536243i \(0.180157\pi\)
\(692\) 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 \(-0.855788\pi\)
0.899114 0.437714i \(-0.144212\pi\)
\(702\) 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 −0.280600 0.959825i \(-0.590533\pi\)
−0.831916 + 0.554902i \(0.812756\pi\)
\(710\) 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 −0.243879 0.969806i \(-0.578420\pi\)
−0.961816 + 0.273697i \(0.911753\pi\)
\(720\) 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 −0.800488 0.599348i \(-0.795427\pi\)
0.547224 0.836986i \(-0.315685\pi\)
\(728\) 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 −0.106438 0.994319i \(-0.533945\pi\)
0.557600 + 0.830110i \(0.311723\pi\)
\(734\) 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 0.432428 + 0.901669i \(0.357657\pi\)
−0.997082 + 0.0763410i \(0.975676\pi\)
\(740\) 0 0
\(741\) 831.426 + 698.877i 1.12203 + 0.943154i
\(742\) 0 0
\(743\) −132.230 23.3158i −0.177968 0.0313806i 0.0839538 0.996470i \(-0.473245\pi\)
−0.261922 + 0.965089i \(0.584356\pi\)
\(744\) 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 0.472992 0.881066i \(-0.343174\pi\)
−0.785547 + 0.618802i \(0.787618\pi\)
\(752\) 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 −0.816352 0.577554i \(-0.804007\pi\)
0.710538 + 0.703659i \(0.248452\pi\)
\(762\) 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 0.681210 + 0.732088i \(0.261454\pi\)
−0.890517 + 0.454950i \(0.849657\pi\)
\(770\) 0 0
\(771\) 302.062 + 832.149i 0.391779 + 1.07931i
\(772\) 0 0
\(773\) 202.681 + 117.018i 0.262200 + 0.151381i 0.625338 0.780354i \(-0.284961\pi\)
−0.363138 + 0.931736i \(0.618295\pi\)
\(774\) 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