Properties

Label 108.4.i.a.13.3
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.3
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +O(q^{10})\) \(q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +(-39.5319 + 33.1712i) q^{11} +(-10.2025 + 57.8615i) q^{13} +(31.1578 + 96.4258i) q^{15} +(-3.52013 + 6.09704i) q^{17} +(-42.6669 - 73.9012i) q^{19} +(-79.9157 - 102.630i) q^{21} +(32.2883 - 11.7520i) q^{23} +(44.3365 + 251.445i) q^{25} +(15.3437 - 139.455i) q^{27} +(37.0590 + 210.172i) q^{29} +(-133.967 + 48.7600i) q^{31} +(265.599 - 36.8883i) q^{33} +(-244.095 - 422.784i) q^{35} +(-65.2996 + 113.102i) q^{37} +(204.650 - 226.547i) q^{39} +(-8.52460 + 48.3454i) q^{41} +(126.716 - 106.327i) q^{43} +(129.041 - 510.494i) q^{45} +(-470.489 - 171.244i) q^{47} +(217.287 + 182.325i) q^{49} +(32.3280 - 17.1219i) q^{51} -347.277 q^{53} +1006.40 q^{55} +(-16.1935 + 443.112i) q^{57} +(-172.501 - 144.746i) q^{59} +(-577.795 - 210.300i) q^{61} +(68.4686 + 672.412i) q^{63} +(877.746 - 736.517i) q^{65} +(-162.166 + 919.690i) q^{67} +(-174.580 - 37.4043i) q^{69} +(46.7209 - 80.9229i) q^{71} +(-133.977 - 232.055i) q^{73} +(498.985 - 1229.29i) q^{75} +(-1213.92 + 441.832i) q^{77} +(-155.815 - 883.669i) q^{79} +(-452.535 + 571.536i) q^{81} +(6.17283 + 35.0079i) q^{83} +(129.018 - 46.9588i) q^{85} +(417.081 - 1027.51i) q^{87} +(361.721 + 626.519i) q^{89} +(-735.394 + 1273.74i) q^{91} +(724.350 + 155.194i) q^{93} +(-288.980 + 1638.89i) q^{95} +(-1214.37 + 1018.98i) q^{97} +(-1271.04 - 570.850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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
\(3\) −4.40211 2.76069i −0.847187 0.531294i
\(4\) 0 0
\(5\) −14.9393 12.5356i −1.33621 1.12122i −0.982582 0.185831i \(-0.940502\pi\)
−0.353631 0.935385i \(-0.615053\pi\)
\(6\) 0 0
\(7\) 23.5233 + 8.56177i 1.27014 + 0.462292i 0.887158 0.461465i \(-0.152676\pi\)
0.382978 + 0.923757i \(0.374898\pi\)
\(8\) 0 0
\(9\) 11.7572 + 24.3057i 0.435453 + 0.900211i
\(10\) 0 0
\(11\) −39.5319 + 33.1712i −1.08358 + 0.909227i −0.996213 0.0869492i \(-0.972288\pi\)
−0.0873623 + 0.996177i \(0.527844\pi\)
\(12\) 0 0
\(13\) −10.2025 + 57.8615i −0.217668 + 1.23445i 0.658550 + 0.752537i \(0.271170\pi\)
−0.876217 + 0.481917i \(0.839941\pi\)
\(14\) 0 0
\(15\) 31.1578 + 96.4258i 0.536327 + 1.65980i
\(16\) 0 0
\(17\) −3.52013 + 6.09704i −0.0502210 + 0.0869853i −0.890043 0.455876i \(-0.849326\pi\)
0.839822 + 0.542862i \(0.182659\pi\)
\(18\) 0 0
\(19\) −42.6669 73.9012i −0.515182 0.892321i −0.999845 0.0176203i \(-0.994391\pi\)
0.484663 0.874701i \(-0.338942\pi\)
\(20\) 0 0
\(21\) −79.9157 102.630i −0.830431 1.06646i
\(22\) 0 0
\(23\) 32.2883 11.7520i 0.292721 0.106542i −0.191486 0.981495i \(-0.561331\pi\)
0.484206 + 0.874954i \(0.339108\pi\)
\(24\) 0 0
\(25\) 44.3365 + 251.445i 0.354692 + 2.01156i
\(26\) 0 0
\(27\) 15.3437 139.455i 0.109367 0.994001i
\(28\) 0 0
\(29\) 37.0590 + 210.172i 0.237300 + 1.34579i 0.837717 + 0.546105i \(0.183890\pi\)
−0.600417 + 0.799687i \(0.704999\pi\)
\(30\) 0 0
\(31\) −133.967 + 48.7600i −0.776168 + 0.282502i −0.699574 0.714560i \(-0.746627\pi\)
−0.0765940 + 0.997062i \(0.524405\pi\)
\(32\) 0 0
\(33\) 265.599 36.8883i 1.40106 0.194589i
\(34\) 0 0
\(35\) −244.095 422.784i −1.17884 2.04182i
\(36\) 0 0
\(37\) −65.2996 + 113.102i −0.290140 + 0.502538i −0.973843 0.227223i \(-0.927035\pi\)
0.683702 + 0.729761i \(0.260369\pi\)
\(38\) 0 0
\(39\) 204.650 226.547i 0.840263 0.930168i
\(40\) 0 0
\(41\) −8.52460 + 48.3454i −0.0324712 + 0.184153i −0.996729 0.0808109i \(-0.974249\pi\)
0.964258 + 0.264964i \(0.0853601\pi\)
\(42\) 0 0
\(43\) 126.716 106.327i 0.449394 0.377086i −0.389817 0.920892i \(-0.627462\pi\)
0.839211 + 0.543806i \(0.183017\pi\)
\(44\) 0 0
\(45\) 129.041 510.494i 0.427473 1.69111i
\(46\) 0 0
\(47\) −470.489 171.244i −1.46017 0.531458i −0.514757 0.857336i \(-0.672118\pi\)
−0.945412 + 0.325878i \(0.894340\pi\)
\(48\) 0 0
\(49\) 217.287 + 182.325i 0.633489 + 0.531560i
\(50\) 0 0
\(51\) 32.3280 17.1219i 0.0887613 0.0470107i
\(52\) 0 0
\(53\) −347.277 −0.900042 −0.450021 0.893018i \(-0.648584\pi\)
−0.450021 + 0.893018i \(0.648584\pi\)
\(54\) 0 0
\(55\) 1006.40 2.46733
\(56\) 0 0
\(57\) −16.1935 + 443.112i −0.0376295 + 1.02968i
\(58\) 0 0
\(59\) −172.501 144.746i −0.380640 0.319395i 0.432314 0.901723i \(-0.357697\pi\)
−0.812954 + 0.582329i \(0.802142\pi\)
\(60\) 0 0
\(61\) −577.795 210.300i −1.21277 0.441413i −0.345107 0.938563i \(-0.612158\pi\)
−0.867664 + 0.497150i \(0.834380\pi\)
\(62\) 0 0
\(63\) 68.4686 + 672.412i 0.136924 + 1.34470i
\(64\) 0 0
\(65\) 877.746 736.517i 1.67494 1.40544i
\(66\) 0 0
\(67\) −162.166 + 919.690i −0.295698 + 1.67698i 0.368656 + 0.929566i \(0.379818\pi\)
−0.664353 + 0.747419i \(0.731293\pi\)
\(68\) 0 0
\(69\) −174.580 37.4043i −0.304594 0.0652601i
\(70\) 0 0
\(71\) 46.7209 80.9229i 0.0780950 0.135265i −0.824333 0.566105i \(-0.808450\pi\)
0.902428 + 0.430841i \(0.141783\pi\)
\(72\) 0 0
\(73\) −133.977 232.055i −0.214806 0.372055i 0.738406 0.674356i \(-0.235579\pi\)
−0.953213 + 0.302301i \(0.902245\pi\)
\(74\) 0 0
\(75\) 498.985 1229.29i 0.768238 1.89261i
\(76\) 0 0
\(77\) −1213.92 + 441.832i −1.79662 + 0.653915i
\(78\) 0 0
\(79\) −155.815 883.669i −0.221905 1.25849i −0.868514 0.495665i \(-0.834924\pi\)
0.646608 0.762822i \(-0.276187\pi\)
\(80\) 0 0
\(81\) −452.535 + 571.536i −0.620761 + 0.784000i
\(82\) 0 0
\(83\) 6.17283 + 35.0079i 0.00816333 + 0.0462966i 0.988617 0.150452i \(-0.0480729\pi\)
−0.980454 + 0.196748i \(0.936962\pi\)
\(84\) 0 0
\(85\) 129.018 46.9588i 0.164635 0.0599223i
\(86\) 0 0
\(87\) 417.081 1027.51i 0.513975 1.26621i
\(88\) 0 0
\(89\) 361.721 + 626.519i 0.430813 + 0.746189i 0.996943 0.0781261i \(-0.0248937\pi\)
−0.566131 + 0.824315i \(0.691560\pi\)
\(90\) 0 0
\(91\) −735.394 + 1273.74i −0.847146 + 1.46730i
\(92\) 0 0
\(93\) 724.350 + 155.194i 0.807651 + 0.173041i
\(94\) 0 0
\(95\) −288.980 + 1638.89i −0.312092 + 1.76996i
\(96\) 0 0
\(97\) −1214.37 + 1018.98i −1.27114 + 1.06662i −0.276744 + 0.960944i \(0.589255\pi\)
−0.994401 + 0.105673i \(0.966300\pi\)
\(98\) 0 0
\(99\) −1271.04 570.850i −1.29034 0.579521i
\(100\) 0 0
\(101\) 1643.15 + 598.056i 1.61880 + 0.589196i 0.983153 0.182782i \(-0.0585103\pi\)
0.635649 + 0.771978i \(0.280732\pi\)
\(102\) 0 0
\(103\) 717.798 + 602.304i 0.686667 + 0.576182i 0.917946 0.396705i \(-0.129846\pi\)
−0.231279 + 0.972888i \(0.574291\pi\)
\(104\) 0 0
\(105\) −92.6420 + 2535.01i −0.0861041 + 2.35611i
\(106\) 0 0
\(107\) −16.1019 −0.0145480 −0.00727398 0.999974i \(-0.502315\pi\)
−0.00727398 + 0.999974i \(0.502315\pi\)
\(108\) 0 0
\(109\) 1665.12 1.46321 0.731603 0.681731i \(-0.238772\pi\)
0.731603 + 0.681731i \(0.238772\pi\)
\(110\) 0 0
\(111\) 599.696 317.617i 0.512799 0.271594i
\(112\) 0 0
\(113\) −632.247 530.518i −0.526343 0.441654i 0.340493 0.940247i \(-0.389406\pi\)
−0.866836 + 0.498593i \(0.833850\pi\)
\(114\) 0 0
\(115\) −629.683 229.186i −0.510593 0.185841i
\(116\) 0 0
\(117\) −1526.32 + 432.311i −1.20605 + 0.341600i
\(118\) 0 0
\(119\) −135.006 + 113.284i −0.104000 + 0.0872664i
\(120\) 0 0
\(121\) 231.317 1311.87i 0.173792 0.985625i
\(122\) 0 0
\(123\) 170.993 189.288i 0.125349 0.138761i
\(124\) 0 0
\(125\) 1270.78 2201.05i 0.909295 1.57495i
\(126\) 0 0
\(127\) −1130.88 1958.74i −0.790151 1.36858i −0.925873 0.377835i \(-0.876669\pi\)
0.135722 0.990747i \(-0.456665\pi\)
\(128\) 0 0
\(129\) −851.352 + 118.242i −0.581065 + 0.0807024i
\(130\) 0 0
\(131\) 1343.42 488.966i 0.895996 0.326116i 0.147349 0.989085i \(-0.452926\pi\)
0.748647 + 0.662969i \(0.230704\pi\)
\(132\) 0 0
\(133\) −370.939 2103.70i −0.241839 1.37153i
\(134\) 0 0
\(135\) −1977.37 + 1891.01i −1.26063 + 1.20557i
\(136\) 0 0
\(137\) 260.376 + 1476.67i 0.162375 + 0.920877i 0.951729 + 0.306938i \(0.0993046\pi\)
−0.789354 + 0.613938i \(0.789584\pi\)
\(138\) 0 0
\(139\) −54.1508 + 19.7093i −0.0330433 + 0.0120268i −0.358489 0.933534i \(-0.616708\pi\)
0.325446 + 0.945561i \(0.394486\pi\)
\(140\) 0 0
\(141\) 1598.40 + 2052.71i 0.954676 + 1.22602i
\(142\) 0 0
\(143\) −1516.01 2625.81i −0.886540 1.53553i
\(144\) 0 0
\(145\) 2080.99 3604.38i 1.19184 2.06433i
\(146\) 0 0
\(147\) −453.178 1402.48i −0.254269 0.786900i
\(148\) 0 0
\(149\) −236.688 + 1342.32i −0.130136 + 0.738037i 0.847988 + 0.530015i \(0.177814\pi\)
−0.978124 + 0.208022i \(0.933297\pi\)
\(150\) 0 0
\(151\) 897.782 753.329i 0.483844 0.405993i −0.367970 0.929838i \(-0.619947\pi\)
0.851814 + 0.523844i \(0.175503\pi\)
\(152\) 0 0
\(153\) −189.580 13.8749i −0.100174 0.00733150i
\(154\) 0 0
\(155\) 2612.61 + 950.913i 1.35387 + 0.492769i
\(156\) 0 0
\(157\) −977.108 819.891i −0.496699 0.416780i 0.359721 0.933060i \(-0.382872\pi\)
−0.856420 + 0.516280i \(0.827316\pi\)
\(158\) 0 0
\(159\) 1528.76 + 958.724i 0.762504 + 0.478187i
\(160\) 0 0
\(161\) 860.144 0.421049
\(162\) 0 0
\(163\) 1616.42 0.776736 0.388368 0.921504i \(-0.373039\pi\)
0.388368 + 0.921504i \(0.373039\pi\)
\(164\) 0 0
\(165\) −4430.29 2778.35i −2.09029 1.31088i
\(166\) 0 0
\(167\) 424.273 + 356.007i 0.196594 + 0.164962i 0.735771 0.677231i \(-0.236820\pi\)
−0.539177 + 0.842193i \(0.681264\pi\)
\(168\) 0 0
\(169\) −1179.36 429.252i −0.536805 0.195381i
\(170\) 0 0
\(171\) 1294.58 1905.92i 0.578940 0.852337i
\(172\) 0 0
\(173\) 539.141 452.393i 0.236937 0.198814i −0.516586 0.856235i \(-0.672797\pi\)
0.753523 + 0.657421i \(0.228353\pi\)
\(174\) 0 0
\(175\) −1109.87 + 6294.40i −0.479420 + 2.71892i
\(176\) 0 0
\(177\) 359.773 + 1113.41i 0.152781 + 0.472819i
\(178\) 0 0
\(179\) −585.812 + 1014.66i −0.244612 + 0.423681i −0.962023 0.272970i \(-0.911994\pi\)
0.717410 + 0.696651i \(0.245327\pi\)
\(180\) 0 0
\(181\) −386.512 669.458i −0.158725 0.274919i 0.775684 0.631121i \(-0.217405\pi\)
−0.934409 + 0.356202i \(0.884072\pi\)
\(182\) 0 0
\(183\) 1962.95 + 2520.88i 0.792925 + 1.01830i
\(184\) 0 0
\(185\) 2393.33 871.102i 0.951143 0.346188i
\(186\) 0 0
\(187\) −63.0889 357.795i −0.0246712 0.139917i
\(188\) 0 0
\(189\) 1554.91 3149.06i 0.598430 1.21196i
\(190\) 0 0
\(191\) −98.8386 560.541i −0.0374435 0.212353i 0.960346 0.278812i \(-0.0899407\pi\)
−0.997789 + 0.0664597i \(0.978830\pi\)
\(192\) 0 0
\(193\) −4565.75 + 1661.80i −1.70285 + 0.619787i −0.996145 0.0877221i \(-0.972041\pi\)
−0.706705 + 0.707509i \(0.749819\pi\)
\(194\) 0 0
\(195\) −5897.23 + 819.049i −2.16569 + 0.300786i
\(196\) 0 0
\(197\) −946.267 1638.98i −0.342227 0.592754i 0.642619 0.766186i \(-0.277848\pi\)
−0.984846 + 0.173431i \(0.944514\pi\)
\(198\) 0 0
\(199\) 1950.36 3378.12i 0.694759 1.20336i −0.275502 0.961300i \(-0.588844\pi\)
0.970262 0.242058i \(-0.0778225\pi\)
\(200\) 0 0
\(201\) 3252.85 3600.89i 1.14148 1.26362i
\(202\) 0 0
\(203\) −927.696 + 5261.22i −0.320746 + 1.81904i
\(204\) 0 0
\(205\) 733.389 615.386i 0.249864 0.209661i
\(206\) 0 0
\(207\) 665.261 + 646.619i 0.223376 + 0.217117i
\(208\) 0 0
\(209\) 4138.10 + 1506.15i 1.36956 + 0.498480i
\(210\) 0 0
\(211\) 1142.91 + 959.011i 0.372895 + 0.312896i 0.809906 0.586560i \(-0.199518\pi\)
−0.437011 + 0.899456i \(0.643963\pi\)
\(212\) 0 0
\(213\) −429.073 + 227.250i −0.138026 + 0.0731030i
\(214\) 0 0
\(215\) −3225.91 −1.02328
\(216\) 0 0
\(217\) −3568.81 −1.11644
\(218\) 0 0
\(219\) −50.8488 + 1391.40i −0.0156897 + 0.429326i
\(220\) 0 0
\(221\) −316.870 265.885i −0.0964478 0.0809293i
\(222\) 0 0
\(223\) −1925.56 700.848i −0.578230 0.210459i 0.0363147 0.999340i \(-0.488438\pi\)
−0.614545 + 0.788882i \(0.710660\pi\)
\(224\) 0 0
\(225\) −5590.27 + 4033.92i −1.65638 + 1.19524i
\(226\) 0 0
\(227\) −1243.19 + 1043.16i −0.363496 + 0.305009i −0.806182 0.591667i \(-0.798470\pi\)
0.442686 + 0.896677i \(0.354026\pi\)
\(228\) 0 0
\(229\) 651.857 3696.86i 0.188104 1.06679i −0.733797 0.679369i \(-0.762254\pi\)
0.921901 0.387425i \(-0.126635\pi\)
\(230\) 0 0
\(231\) 6563.59 + 1406.27i 1.86949 + 0.400544i
\(232\) 0 0
\(233\) −48.1965 + 83.4788i −0.0135513 + 0.0234716i −0.872722 0.488218i \(-0.837647\pi\)
0.859170 + 0.511690i \(0.170980\pi\)
\(234\) 0 0
\(235\) 4882.15 + 8456.12i 1.35522 + 2.34731i
\(236\) 0 0
\(237\) −1753.62 + 4320.17i −0.480632 + 1.18407i
\(238\) 0 0
\(239\) −4215.25 + 1534.22i −1.14084 + 0.415233i −0.842218 0.539137i \(-0.818751\pi\)
−0.298626 + 0.954370i \(0.596528\pi\)
\(240\) 0 0
\(241\) 420.948 + 2387.32i 0.112513 + 0.638093i 0.987952 + 0.154764i \(0.0494616\pi\)
−0.875438 + 0.483330i \(0.839427\pi\)
\(242\) 0 0
\(243\) 3569.94 1266.66i 0.942436 0.334388i
\(244\) 0 0
\(245\) −960.563 5447.62i −0.250482 1.42055i
\(246\) 0 0
\(247\) 4711.35 1714.79i 1.21367 0.441739i
\(248\) 0 0
\(249\) 69.4722 171.150i 0.0176812 0.0435590i
\(250\) 0 0
\(251\) −1200.00 2078.47i −0.301767 0.522677i 0.674769 0.738029i \(-0.264243\pi\)
−0.976536 + 0.215352i \(0.930910\pi\)
\(252\) 0 0
\(253\) −886.591 + 1535.62i −0.220314 + 0.381595i
\(254\) 0 0
\(255\) −697.591 149.461i −0.171313 0.0367043i
\(256\) 0 0
\(257\) −65.0046 + 368.659i −0.0157777 + 0.0894799i −0.991680 0.128729i \(-0.958910\pi\)
0.975902 + 0.218209i \(0.0700214\pi\)
\(258\) 0 0
\(259\) −2504.42 + 2101.45i −0.600837 + 0.504162i
\(260\) 0 0
\(261\) −4672.67 + 3371.79i −1.10816 + 0.799649i
\(262\) 0 0
\(263\) −3775.09 1374.02i −0.885102 0.322151i −0.140835 0.990033i \(-0.544979\pi\)
−0.744267 + 0.667882i \(0.767201\pi\)
\(264\) 0 0
\(265\) 5188.09 + 4353.32i 1.20265 + 1.00914i
\(266\) 0 0
\(267\) 137.285 3756.60i 0.0314670 0.861050i
\(268\) 0 0
\(269\) 3102.46 0.703198 0.351599 0.936151i \(-0.385638\pi\)
0.351599 + 0.936151i \(0.385638\pi\)
\(270\) 0 0
\(271\) −146.797 −0.0329050 −0.0164525 0.999865i \(-0.505237\pi\)
−0.0164525 + 0.999865i \(0.505237\pi\)
\(272\) 0 0
\(273\) 6753.69 3576.96i 1.49726 0.792994i
\(274\) 0 0
\(275\) −10093.4 8469.40i −2.21330 1.85718i
\(276\) 0 0
\(277\) −4020.61 1463.38i −0.872111 0.317423i −0.133090 0.991104i \(-0.542490\pi\)
−0.739022 + 0.673681i \(0.764712\pi\)
\(278\) 0 0
\(279\) −2760.23 2682.88i −0.592296 0.575699i
\(280\) 0 0
\(281\) −3809.81 + 3196.81i −0.808805 + 0.678668i −0.950322 0.311268i \(-0.899246\pi\)
0.141517 + 0.989936i \(0.454802\pi\)
\(282\) 0 0
\(283\) −185.085 + 1049.67i −0.0388770 + 0.220482i −0.998056 0.0623156i \(-0.980151\pi\)
0.959180 + 0.282798i \(0.0912626\pi\)
\(284\) 0 0
\(285\) 5796.58 6416.79i 1.20477 1.33368i
\(286\) 0 0
\(287\) −614.448 + 1064.26i −0.126375 + 0.218889i
\(288\) 0 0
\(289\) 2431.72 + 4211.86i 0.494956 + 0.857288i
\(290\) 0 0
\(291\) 8158.90 1133.17i 1.64358 0.228273i
\(292\) 0 0
\(293\) 6323.47 2301.56i 1.26082 0.458902i 0.376778 0.926304i \(-0.377032\pi\)
0.884045 + 0.467402i \(0.154810\pi\)
\(294\) 0 0
\(295\) 762.579 + 4324.80i 0.150505 + 0.853559i
\(296\) 0 0
\(297\) 4019.31 + 6021.88i 0.785266 + 1.17651i
\(298\) 0 0
\(299\) 350.565 + 1988.15i 0.0678049 + 0.384541i
\(300\) 0 0
\(301\) 3891.11 1416.25i 0.745116 0.271200i
\(302\) 0 0
\(303\) −5582.27 7168.92i −1.05839 1.35922i
\(304\) 0 0
\(305\) 5995.63 + 10384.7i 1.12560 + 1.94960i
\(306\) 0 0
\(307\) −419.639 + 726.835i −0.0780132 + 0.135123i −0.902393 0.430915i \(-0.858191\pi\)
0.824379 + 0.566038i \(0.191524\pi\)
\(308\) 0 0
\(309\) −1497.06 4633.03i −0.275614 0.852957i
\(310\) 0 0
\(311\) −782.999 + 4440.61i −0.142765 + 0.809658i 0.826370 + 0.563127i \(0.190402\pi\)
−0.969135 + 0.246531i \(0.920709\pi\)
\(312\) 0 0
\(313\) 3326.13 2790.96i 0.600652 0.504007i −0.291003 0.956722i \(-0.593989\pi\)
0.891655 + 0.452715i \(0.149545\pi\)
\(314\) 0 0
\(315\) 7406.20 10903.7i 1.32474 1.95032i
\(316\) 0 0
\(317\) −8805.07 3204.78i −1.56007 0.567819i −0.589317 0.807902i \(-0.700603\pi\)
−0.970752 + 0.240083i \(0.922825\pi\)
\(318\) 0 0
\(319\) −8436.68 7079.22i −1.48076 1.24251i
\(320\) 0 0
\(321\) 70.8825 + 44.4524i 0.0123249 + 0.00772925i
\(322\) 0 0
\(323\) 600.772 0.103492
\(324\) 0 0
\(325\) −15001.3 −2.56038
\(326\) 0 0
\(327\) −7330.05 4596.87i −1.23961 0.777393i
\(328\) 0 0
\(329\) −9601.29 8056.44i −1.60893 1.35005i
\(330\) 0 0
\(331\) 7052.64 + 2566.95i 1.17114 + 0.426261i 0.853066 0.521804i \(-0.174741\pi\)
0.318077 + 0.948065i \(0.396963\pi\)
\(332\) 0 0
\(333\) −3516.77 257.384i −0.578733 0.0423561i
\(334\) 0 0
\(335\) 13951.5 11706.7i 2.27538 1.90927i
\(336\) 0 0
\(337\) 595.457 3377.01i 0.0962511 0.545867i −0.898106 0.439780i \(-0.855057\pi\)
0.994357 0.106087i \(-0.0338323\pi\)
\(338\) 0 0
\(339\) 1318.63 + 4080.84i 0.211263 + 0.653807i
\(340\) 0 0
\(341\) 3678.55 6371.43i 0.584178 1.01183i
\(342\) 0 0
\(343\) −742.883 1286.71i −0.116944 0.202553i
\(344\) 0 0
\(345\) 2139.23 + 2747.26i 0.333832 + 0.428717i
\(346\) 0 0
\(347\) 10147.3 3693.32i 1.56984 0.571377i 0.596880 0.802331i \(-0.296407\pi\)
0.972965 + 0.230954i \(0.0741848\pi\)
\(348\) 0 0
\(349\) −221.987 1258.95i −0.0340479 0.193095i 0.963040 0.269359i \(-0.0868119\pi\)
−0.997088 + 0.0762641i \(0.975701\pi\)
\(350\) 0 0
\(351\) 7912.51 + 2310.60i 1.20324 + 0.351370i
\(352\) 0 0
\(353\) 1599.06 + 9068.74i 0.241104 + 1.36737i 0.829370 + 0.558700i \(0.188699\pi\)
−0.588267 + 0.808667i \(0.700189\pi\)
\(354\) 0 0
\(355\) −1712.39 + 623.260i −0.256012 + 0.0931809i
\(356\) 0 0
\(357\) 907.054 125.978i 0.134472 0.0186764i
\(358\) 0 0
\(359\) −331.332 573.884i −0.0487104 0.0843689i 0.840642 0.541591i \(-0.182178\pi\)
−0.889353 + 0.457222i \(0.848844\pi\)
\(360\) 0 0
\(361\) −211.429 + 366.206i −0.0308250 + 0.0533905i
\(362\) 0 0
\(363\) −4639.94 + 5136.39i −0.670891 + 0.742674i
\(364\) 0 0
\(365\) −907.419 + 5146.23i −0.130127 + 0.737989i
\(366\) 0 0
\(367\) −4961.59 + 4163.27i −0.705702 + 0.592155i −0.923390 0.383864i \(-0.874593\pi\)
0.217687 + 0.976019i \(0.430149\pi\)
\(368\) 0 0
\(369\) −1275.29 + 361.211i −0.179916 + 0.0509591i
\(370\) 0 0
\(371\) −8169.10 2973.31i −1.14318 0.416082i
\(372\) 0 0
\(373\) 5459.75 + 4581.27i 0.757896 + 0.635950i 0.937578 0.347775i \(-0.113063\pi\)
−0.179682 + 0.983725i \(0.557507\pi\)
\(374\) 0 0
\(375\) −11670.5 + 6181.07i −1.60710 + 0.851170i
\(376\) 0 0
\(377\) −12539.0 −1.71297
\(378\) 0 0
\(379\) 7451.59 1.00993 0.504964 0.863140i \(-0.331506\pi\)
0.504964 + 0.863140i \(0.331506\pi\)
\(380\) 0 0
\(381\) −429.205 + 11744.6i −0.0577135 + 1.57925i
\(382\) 0 0
\(383\) 10198.1 + 8557.21i 1.36057 + 1.14165i 0.975806 + 0.218637i \(0.0701610\pi\)
0.384762 + 0.923016i \(0.374283\pi\)
\(384\) 0 0
\(385\) 23673.8 + 8616.56i 3.13384 + 1.14063i
\(386\) 0 0
\(387\) 4074.18 + 1829.80i 0.535148 + 0.240346i
\(388\) 0 0
\(389\) −10703.4 + 8981.22i −1.39508 + 1.17061i −0.431839 + 0.901951i \(0.642135\pi\)
−0.963236 + 0.268656i \(0.913420\pi\)
\(390\) 0 0
\(391\) −42.0066 + 238.232i −0.00543316 + 0.0308130i
\(392\) 0 0
\(393\) −7263.79 1556.29i −0.932340 0.199756i
\(394\) 0 0
\(395\) −8749.53 + 15154.6i −1.11452 + 1.93041i
\(396\) 0 0
\(397\) −4359.70 7551.22i −0.551151 0.954622i −0.998192 0.0601082i \(-0.980855\pi\)
0.447041 0.894514i \(-0.352478\pi\)
\(398\) 0 0
\(399\) −4174.74 + 10284.8i −0.523806 + 1.29043i
\(400\) 0 0
\(401\) 12751.4 4641.12i 1.58796 0.577971i 0.611046 0.791595i \(-0.290749\pi\)
0.976916 + 0.213624i \(0.0685267\pi\)
\(402\) 0 0
\(403\) −1454.52 8249.02i −0.179789 1.01963i
\(404\) 0 0
\(405\) 13925.1 2865.56i 1.70850 0.351583i
\(406\) 0 0
\(407\) −1170.32 6637.22i −0.142532 0.808341i
\(408\) 0 0
\(409\) −8465.11 + 3081.05i −1.02341 + 0.372489i −0.798566 0.601907i \(-0.794408\pi\)
−0.224839 + 0.974396i \(0.572186\pi\)
\(410\) 0 0
\(411\) 2930.41 7219.27i 0.351694 0.866424i
\(412\) 0 0
\(413\) −2818.51 4881.81i −0.335811 0.581642i
\(414\) 0 0
\(415\) 346.626 600.374i 0.0410005 0.0710149i
\(416\) 0 0
\(417\) 292.789 + 62.7309i 0.0343836 + 0.00736677i
\(418\) 0 0
\(419\) 769.338 4363.13i 0.0897008 0.508718i −0.906542 0.422115i \(-0.861288\pi\)
0.996243 0.0866031i \(-0.0276012\pi\)
\(420\) 0 0
\(421\) −472.103 + 396.141i −0.0546529 + 0.0458592i −0.669705 0.742627i \(-0.733579\pi\)
0.615052 + 0.788487i \(0.289135\pi\)
\(422\) 0 0
\(423\) −1369.44 13448.9i −0.157410 1.54589i
\(424\) 0 0
\(425\) −1689.14 614.796i −0.192789 0.0701694i
\(426\) 0 0
\(427\) −11791.1 9893.89i −1.33632 1.12131i
\(428\) 0 0
\(429\) −575.376 + 15744.3i −0.0647539 + 1.77190i
\(430\) 0 0
\(431\) 9458.47 1.05707 0.528537 0.848910i \(-0.322741\pi\)
0.528537 + 0.848910i \(0.322741\pi\)
\(432\) 0 0
\(433\) 5691.49 0.631676 0.315838 0.948813i \(-0.397714\pi\)
0.315838 + 0.948813i \(0.397714\pi\)
\(434\) 0 0
\(435\) −19111.3 + 10121.9i −2.10648 + 1.11566i
\(436\) 0 0
\(437\) −2246.13 1884.72i −0.245874 0.206313i
\(438\) 0 0
\(439\) −12777.3 4650.57i −1.38913 0.505602i −0.464198 0.885732i \(-0.653657\pi\)
−0.924933 + 0.380129i \(0.875880\pi\)
\(440\) 0 0
\(441\) −1876.85 + 7424.94i −0.202662 + 0.801743i
\(442\) 0 0
\(443\) −8689.72 + 7291.54i −0.931966 + 0.782013i −0.976169 0.217010i \(-0.930370\pi\)
0.0442031 + 0.999023i \(0.485925\pi\)
\(444\) 0 0
\(445\) 2449.91 13894.1i 0.260982 1.48010i
\(446\) 0 0
\(447\) 4747.67 5255.65i 0.502364 0.556115i
\(448\) 0 0
\(449\) 2603.29 4509.03i 0.273623 0.473930i −0.696163 0.717883i \(-0.745111\pi\)
0.969787 + 0.243954i \(0.0784444\pi\)
\(450\) 0 0
\(451\) −1266.68 2193.96i −0.132252 0.229067i
\(452\) 0 0
\(453\) −6031.84 + 837.745i −0.625609 + 0.0868889i
\(454\) 0 0
\(455\) 26953.3 9810.21i 2.77713 1.01079i
\(456\) 0 0
\(457\) 2794.59 + 15848.9i 0.286051 + 1.62228i 0.701506 + 0.712664i \(0.252512\pi\)
−0.415454 + 0.909614i \(0.636377\pi\)
\(458\) 0 0
\(459\) 796.248 + 584.449i 0.0809710 + 0.0594330i
\(460\) 0 0
\(461\) 2417.98 + 13713.0i 0.244287 + 1.38542i 0.822143 + 0.569282i \(0.192779\pi\)
−0.577855 + 0.816139i \(0.696110\pi\)
\(462\) 0 0
\(463\) −683.331 + 248.712i −0.0685898 + 0.0249646i −0.376087 0.926584i \(-0.622731\pi\)
0.307497 + 0.951549i \(0.400508\pi\)
\(464\) 0 0
\(465\) −8875.84 11398.6i −0.885177 1.13677i
\(466\) 0 0
\(467\) 6275.96 + 10870.3i 0.621877 + 1.07712i 0.989136 + 0.147004i \(0.0469630\pi\)
−0.367259 + 0.930119i \(0.619704\pi\)
\(468\) 0 0
\(469\) −11688.8 + 20245.7i −1.15083 + 1.99330i
\(470\) 0 0
\(471\) 2037.88 + 6306.74i 0.199364 + 0.616984i
\(472\) 0 0
\(473\) −1482.31 + 8406.62i −0.144095 + 0.817203i
\(474\) 0 0
\(475\) 16690.4 14004.9i 1.61222 1.35282i
\(476\) 0 0
\(477\) −4083.02 8440.83i −0.391926 0.810228i
\(478\) 0 0
\(479\) 8706.20 + 3168.80i 0.830472 + 0.302267i 0.722053 0.691838i \(-0.243199\pi\)
0.108420 + 0.994105i \(0.465421\pi\)
\(480\) 0 0
\(481\) −5878.05 4932.27i −0.557206 0.467551i
\(482\) 0 0
\(483\) −3786.45 2374.59i −0.356707 0.223701i
\(484\) 0 0
\(485\) 30915.4 2.89443
\(486\) 0 0
\(487\) −7806.10 −0.726341 −0.363170 0.931723i \(-0.618306\pi\)
−0.363170 + 0.931723i \(0.618306\pi\)
\(488\) 0 0
\(489\) −7115.67 4462.43i −0.658041 0.412675i
\(490\) 0 0
\(491\) −4101.97 3441.96i −0.377025 0.316361i 0.434508 0.900668i \(-0.356922\pi\)
−0.811533 + 0.584306i \(0.801367\pi\)
\(492\) 0 0
\(493\) −1411.88 513.882i −0.128982 0.0469454i
\(494\) 0 0
\(495\) 11832.5 + 24461.3i 1.07440 + 2.22112i
\(496\) 0 0
\(497\) 1791.87 1503.56i 0.161723 0.135702i
\(498\) 0 0
\(499\) 256.588 1455.18i 0.0230190 0.130547i −0.971133 0.238540i \(-0.923331\pi\)
0.994152 + 0.107993i \(0.0344423\pi\)
\(500\) 0 0
\(501\) −884.874 2738.47i −0.0789087 0.244203i
\(502\) 0 0
\(503\) −6261.59 + 10845.4i −0.555051 + 0.961376i 0.442849 + 0.896596i \(0.353968\pi\)
−0.997900 + 0.0647801i \(0.979365\pi\)
\(504\) 0 0
\(505\) −17050.5 29532.3i −1.50245 2.60232i
\(506\) 0 0
\(507\) 4006.65 + 5145.46i 0.350970 + 0.450726i
\(508\) 0 0
\(509\) 980.124 356.736i 0.0853502 0.0310649i −0.298992 0.954256i \(-0.596650\pi\)
0.384342 + 0.923191i \(0.374428\pi\)
\(510\) 0 0
\(511\) −1164.78 6605.78i −0.100835 0.571864i
\(512\) 0 0
\(513\) −10960.5 + 4816.17i −0.943313 + 0.414501i
\(514\) 0 0
\(515\) −3173.18 17996.0i −0.271509 1.53980i
\(516\) 0 0
\(517\) 24279.7 8837.10i 2.06542 0.751751i
\(518\) 0 0
\(519\) −3622.28 + 503.088i −0.306359 + 0.0425493i
\(520\) 0 0
\(521\) 4911.87 + 8507.61i 0.413038 + 0.715403i 0.995220 0.0976552i \(-0.0311342\pi\)
−0.582182 + 0.813058i \(0.697801\pi\)
\(522\) 0 0
\(523\) −904.471 + 1566.59i −0.0756209 + 0.130979i −0.901356 0.433079i \(-0.857427\pi\)
0.825735 + 0.564058i \(0.190761\pi\)
\(524\) 0 0
\(525\) 22262.6 24644.7i 1.85071 2.04873i
\(526\) 0 0
\(527\) 174.289 988.444i 0.0144064 0.0817027i
\(528\) 0 0
\(529\) −8416.04 + 7061.89i −0.691710 + 0.580414i
\(530\) 0 0
\(531\) 1490.01 5894.57i 0.121772 0.481738i
\(532\) 0 0
\(533\) −2710.37 986.492i −0.220261 0.0801683i
\(534\) 0 0
\(535\) 240.552 + 201.847i 0.0194392 + 0.0163114i
\(536\) 0 0
\(537\) 5379.96 2849.39i 0.432332 0.228976i
\(538\) 0 0
\(539\) −14637.7 −1.16974
\(540\) 0 0
\(541\) 5724.91 0.454960 0.227480 0.973783i \(-0.426951\pi\)
0.227480 + 0.973783i \(0.426951\pi\)
\(542\) 0 0
\(543\) −146.694 + 4014.07i −0.0115934 + 0.317238i
\(544\) 0 0
\(545\) −24875.7 20873.2i −1.95516 1.64057i
\(546\) 0 0
\(547\) 6752.26 + 2457.62i 0.527798 + 0.192103i 0.592155 0.805824i \(-0.298277\pi\)
−0.0643567 + 0.997927i \(0.520500\pi\)
\(548\) 0 0
\(549\) −1681.77 16516.3i −0.130740 1.28397i
\(550\) 0 0
\(551\) 13950.8 11706.1i 1.07863 0.905075i
\(552\) 0 0
\(553\) 3900.50 22120.8i 0.299939 1.70104i
\(554\) 0 0
\(555\) −12940.6 2772.55i −0.989723 0.212051i
\(556\) 0 0
\(557\) −800.454 + 1386.43i −0.0608910 + 0.105466i −0.894864 0.446339i \(-0.852728\pi\)
0.833973 + 0.551805i \(0.186061\pi\)
\(558\) 0 0
\(559\) 4859.42 + 8416.77i 0.367677 + 0.636836i
\(560\) 0 0
\(561\) −710.034 + 1749.22i −0.0534361 + 0.131644i
\(562\) 0 0
\(563\) −12290.5 + 4473.39i −0.920042 + 0.334868i −0.758255 0.651958i \(-0.773948\pi\)
−0.161787 + 0.986826i \(0.551726\pi\)
\(564\) 0 0
\(565\) 2794.98 + 15851.1i 0.208117 + 1.18029i
\(566\) 0 0
\(567\) −15538.5 + 9569.88i −1.15089 + 0.708813i
\(568\) 0 0
\(569\) −3956.96 22441.0i −0.291537 1.65339i −0.680955 0.732325i \(-0.738435\pi\)
0.389419 0.921061i \(-0.372676\pi\)
\(570\) 0 0
\(571\) 10197.6 3711.63i 0.747386 0.272026i 0.0598805 0.998206i \(-0.480928\pi\)
0.687505 + 0.726179i \(0.258706\pi\)
\(572\) 0 0
\(573\) −1112.38 + 2740.43i −0.0811001 + 0.199796i
\(574\) 0 0
\(575\) 4386.52 + 7597.68i 0.318140 + 0.551035i
\(576\) 0 0
\(577\) −10891.7 + 18865.0i −0.785835 + 1.36111i 0.142664 + 0.989771i \(0.454433\pi\)
−0.928499 + 0.371335i \(0.878900\pi\)
\(578\) 0 0
\(579\) 24686.7 + 5289.18i 1.77192 + 0.379639i
\(580\) 0 0
\(581\) −154.524 + 876.350i −0.0110340 + 0.0625768i
\(582\) 0 0
\(583\) 13728.5 11519.6i 0.975263 0.818343i
\(584\) 0 0
\(585\) 28221.4 + 12674.9i 1.99455 + 0.895796i
\(586\) 0 0
\(587\) −9679.74 3523.14i −0.680623 0.247726i −0.0215079 0.999769i \(-0.506847\pi\)
−0.659115 + 0.752042i \(0.729069\pi\)
\(588\) 0 0
\(589\) 9319.39 + 7819.90i 0.651950 + 0.547051i
\(590\) 0 0
\(591\) −359.139 + 9827.33i −0.0249966 + 0.683997i
\(592\) 0 0
\(593\) 4017.02 0.278178 0.139089 0.990280i \(-0.455583\pi\)
0.139089 + 0.990280i \(0.455583\pi\)
\(594\) 0 0
\(595\) 3436.98 0.236811
\(596\) 0 0
\(597\) −17911.6 + 9486.54i −1.22793 + 0.650349i
\(598\) 0 0
\(599\) −3884.65 3259.61i −0.264979 0.222344i 0.500611 0.865672i \(-0.333109\pi\)
−0.765590 + 0.643328i \(0.777553\pi\)
\(600\) 0 0
\(601\) −6769.34 2463.84i −0.459446 0.167225i 0.101919 0.994793i \(-0.467502\pi\)
−0.561366 + 0.827568i \(0.689724\pi\)
\(602\) 0 0
\(603\) −24260.3 + 6871.44i −1.63840 + 0.464057i
\(604\) 0 0
\(605\) −19900.7 + 16698.7i −1.33732 + 1.12215i
\(606\) 0 0
\(607\) −829.608 + 4704.94i −0.0554741 + 0.314609i −0.999900 0.0141141i \(-0.995507\pi\)
0.944426 + 0.328723i \(0.106618\pi\)
\(608\) 0 0
\(609\) 18608.4 20599.4i 1.23818 1.37066i
\(610\) 0 0
\(611\) 14708.6 25476.1i 0.973892 1.68683i
\(612\) 0 0
\(613\) 9124.06 + 15803.3i 0.601170 + 1.04126i 0.992644 + 0.121068i \(0.0386319\pi\)
−0.391474 + 0.920189i \(0.628035\pi\)
\(614\) 0 0
\(615\) −4927.35 + 684.345i −0.323073 + 0.0448707i
\(616\) 0 0
\(617\) 9238.38 3362.50i 0.602793 0.219399i −0.0225540 0.999746i \(-0.507180\pi\)
0.625347 + 0.780347i \(0.284958\pi\)
\(618\) 0 0
\(619\) −2028.41 11503.7i −0.131710 0.746966i −0.977094 0.212807i \(-0.931739\pi\)
0.845384 0.534159i \(-0.179372\pi\)
\(620\) 0 0
\(621\) −1143.44 4683.07i −0.0738886 0.302617i
\(622\) 0 0
\(623\) 3144.74 + 17834.7i 0.202234 + 1.14692i
\(624\) 0 0
\(625\) −16585.3 + 6036.55i −1.06146 + 0.386339i
\(626\) 0 0
\(627\) −14058.4 18054.2i −0.895436 1.14995i
\(628\) 0 0
\(629\) −459.726 796.269i −0.0291423 0.0504759i
\(630\) 0 0
\(631\) −5452.85 + 9444.62i −0.344017 + 0.595855i −0.985175 0.171554i \(-0.945121\pi\)
0.641158 + 0.767409i \(0.278454\pi\)
\(632\) 0 0
\(633\) −2383.67 7376.88i −0.149672 0.463199i
\(634\) 0 0
\(635\) −7659.36 + 43438.4i −0.478665 + 2.71465i
\(636\) 0 0
\(637\) −12766.5 + 10712.4i −0.794077 + 0.666309i
\(638\) 0 0
\(639\) 2516.20 + 184.155i 0.155773 + 0.0114007i
\(640\) 0 0
\(641\) 19546.8 + 7114.47i 1.20445 + 0.438385i 0.864776 0.502158i \(-0.167460\pi\)
0.339676 + 0.940542i \(0.389682\pi\)
\(642\) 0 0
\(643\) 6541.99 + 5489.38i 0.401230 + 0.336672i 0.820969 0.570973i \(-0.193434\pi\)
−0.419739 + 0.907645i \(0.637878\pi\)
\(644\) 0 0
\(645\) 14200.8 + 8905.73i 0.866911 + 0.543663i
\(646\) 0 0
\(647\) −17690.0 −1.07491 −0.537454 0.843293i \(-0.680614\pi\)
−0.537454 + 0.843293i \(0.680614\pi\)
\(648\) 0 0
\(649\) 11620.7 0.702854
\(650\) 0 0
\(651\) 15710.3 + 9852.38i 0.945832 + 0.593157i
\(652\) 0 0
\(653\) −10827.1 9085.01i −0.648847 0.544447i 0.257874 0.966179i \(-0.416978\pi\)
−0.906721 + 0.421732i \(0.861422\pi\)
\(654\) 0 0
\(655\) −26199.3 9535.77i −1.56289 0.568845i
\(656\) 0 0
\(657\) 4065.07 5984.74i 0.241390 0.355383i
\(658\) 0 0
\(659\) −7705.44 + 6465.63i −0.455480 + 0.382193i −0.841465 0.540312i \(-0.818306\pi\)
0.385985 + 0.922505i \(0.373862\pi\)
\(660\) 0 0
\(661\) −3544.49 + 20101.8i −0.208570 + 1.18286i 0.683153 + 0.730275i \(0.260608\pi\)
−0.891723 + 0.452582i \(0.850503\pi\)
\(662\) 0 0
\(663\) 660.872 + 2045.24i 0.0387121 + 0.119805i
\(664\) 0 0
\(665\) −20829.5 + 36077.8i −1.21464 + 2.10382i
\(666\) 0 0
\(667\) 3666.51 + 6350.58i 0.212845 + 0.368659i
\(668\) 0 0
\(669\) 6541.74 + 8401.09i 0.378054 + 0.485508i
\(670\) 0 0
\(671\) 29817.3 10852.6i 1.71547 0.624381i
\(672\) 0 0
\(673\) 2017.24 + 11440.4i 0.115541 + 0.655265i 0.986481 + 0.163876i \(0.0523996\pi\)
−0.870940 + 0.491389i \(0.836489\pi\)
\(674\) 0 0
\(675\) 35745.4 2324.82i 2.03828 0.132566i
\(676\) 0 0
\(677\) −3453.35 19584.9i −0.196046 1.11183i −0.910921 0.412580i \(-0.864628\pi\)
0.714876 0.699252i \(-0.246483\pi\)
\(678\) 0 0
\(679\) −37290.3 + 13572.6i −2.10762 + 0.767109i
\(680\) 0 0
\(681\) 8352.52 1160.06i 0.469999 0.0652768i
\(682\) 0 0
\(683\) −5188.26 8986.33i −0.290664 0.503444i 0.683303 0.730135i \(-0.260543\pi\)
−0.973967 + 0.226690i \(0.927209\pi\)
\(684\) 0 0
\(685\) 14621.0 25324.3i 0.815533 1.41255i
\(686\) 0 0
\(687\) −13075.4 + 14474.4i −0.726141 + 0.803835i
\(688\) 0 0
\(689\) 3543.12 20094.0i 0.195910 1.11106i
\(690\) 0 0
\(691\) −23664.3 + 19856.7i −1.30279 + 1.09317i −0.313140 + 0.949707i \(0.601381\pi\)
−0.989655 + 0.143468i \(0.954175\pi\)
\(692\) 0 0
\(693\) −25011.4 24310.6i −1.37100 1.33259i
\(694\) 0 0
\(695\) 1056.04 + 384.368i 0.0576374 + 0.0209783i
\(696\) 0 0
\(697\) −264.756 222.157i −0.0143879 0.0120729i
\(698\) 0 0
\(699\) 442.625 234.428i 0.0239508 0.0126851i
\(700\) 0 0
\(701\) −28142.8 −1.51632 −0.758158 0.652071i \(-0.773901\pi\)
−0.758158 + 0.652071i \(0.773901\pi\)
\(702\) 0 0
\(703\) 11144.5 0.597900
\(704\) 0 0
\(705\) 1852.94 50702.9i 0.0989866 2.70863i
\(706\) 0 0
\(707\) 33531.7 + 28136.5i 1.78372 + 1.49672i
\(708\) 0 0
\(709\) 20208.5 + 7355.30i 1.07045 + 0.389611i 0.816344 0.577566i \(-0.195997\pi\)
0.254103 + 0.967177i \(0.418220\pi\)
\(710\) 0 0
\(711\) 19646.3 14176.7i 1.03628 0.747774i
\(712\) 0 0
\(713\) −3752.54 + 3148.76i −0.197102 + 0.165388i
\(714\) 0 0
\(715\) −10267.8 + 58231.9i −0.537057 + 3.04580i
\(716\) 0 0
\(717\) 22791.5 + 4883.14i 1.18712 + 0.254343i
\(718\) 0 0
\(719\) 18578.1 32178.3i 0.963626 1.66905i 0.250366 0.968151i \(-0.419449\pi\)
0.713261 0.700899i \(-0.247217\pi\)
\(720\) 0 0
\(721\) 11728.2 + 20313.8i 0.605797 + 1.04927i
\(722\) 0 0
\(723\) 4737.57 11671.3i 0.243696 0.600362i
\(724\) 0 0
\(725\) −51203.6 + 18636.6i −2.62297 + 0.954683i
\(726\) 0 0
\(727\) −2772.11 15721.4i −0.141419 0.802029i −0.970173 0.242415i \(-0.922060\pi\)
0.828753 0.559614i \(-0.189051\pi\)
\(728\) 0 0
\(729\) −19212.1 4279.51i −0.976078 0.217422i
\(730\) 0 0
\(731\) 202.225 + 1146.87i 0.0102320 + 0.0580283i
\(732\) 0 0
\(733\) 31627.8 11511.6i 1.59372 0.580067i 0.615592 0.788065i \(-0.288917\pi\)
0.978129 + 0.207998i \(0.0666948\pi\)
\(734\) 0 0
\(735\) −10810.7 + 26632.9i −0.542527 + 1.33656i
\(736\) 0 0
\(737\) −24096.5 41736.4i −1.20435 2.08600i
\(738\) 0 0
\(739\) 14420.2 24976.5i 0.717801 1.24327i −0.244068 0.969758i \(-0.578482\pi\)
0.961869 0.273510i \(-0.0881845\pi\)
\(740\) 0 0
\(741\) −25473.9 5457.85i −1.26290 0.270579i
\(742\) 0 0
\(743\) −1573.69 + 8924.86i −0.0777028 + 0.440675i 0.920991 + 0.389583i \(0.127381\pi\)
−0.998694 + 0.0510912i \(0.983730\pi\)
\(744\) 0 0
\(745\) 20362.8 17086.4i 1.00139 0.840264i
\(746\) 0 0
\(747\) −778.316 + 561.631i −0.0381219 + 0.0275087i
\(748\) 0 0
\(749\) −378.770 137.861i −0.0184779 0.00672541i
\(750\) 0 0
\(751\) 4600.11 + 3859.95i 0.223516 + 0.187552i 0.747668 0.664072i \(-0.231173\pi\)
−0.524152 + 0.851625i \(0.675618\pi\)
\(752\) 0 0
\(753\) −455.441 + 12462.5i −0.0220414 + 0.603132i
\(754\) 0 0
\(755\) −22855.7 −1.10172
\(756\) 0 0
\(757\) −25006.2 −1.20061 −0.600307 0.799770i \(-0.704955\pi\)
−0.600307 + 0.799770i \(0.704955\pi\)
\(758\) 0 0
\(759\) 8142.24 4312.38i 0.389387 0.206231i
\(760\) 0 0
\(761\) −16281.6 13661.8i −0.775566 0.650777i 0.166562 0.986031i \(-0.446733\pi\)
−0.942128 + 0.335254i \(0.891178\pi\)
\(762\) 0 0
\(763\) 39169.0 + 14256.4i 1.85847 + 0.676429i
\(764\) 0 0
\(765\) 2658.26 + 2583.77i 0.125634 + 0.122113i
\(766\) 0 0
\(767\) 10135.2 8504.41i 0.477131 0.400360i
\(768\) 0 0
\(769\) 598.520 3394.38i 0.0280666 0.159173i −0.967553 0.252667i \(-0.918692\pi\)
0.995620 + 0.0934935i \(0.0298034\pi\)
\(770\) 0 0
\(771\) 1303.91 1443.42i 0.0609068 0.0674236i
\(772\) 0 0
\(773\) 9004.85 15596.8i 0.418993 0.725718i −0.576845 0.816853i \(-0.695716\pi\)
0.995838 + 0.0911359i \(0.0290498\pi\)
\(774\) 0 0
\(775\) −18200.1 31523.5i −0.843569 1.46110i
\(776\) 0 0
\(777\) 16826.2 2336.94i 0.776880 0.107899i
\(778\) 0 0
\(779\) 3936.50 1432.77i 0.181052 0.0658977i
\(780\) 0 0
\(781\) 837.347 + 4748.83i 0.0383644 + 0.217575i
\(782\) 0 0