Properties

Label 108.4.i.a.25.3
Level 108
Weight 4
Character 108.25
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 25.3
Character \(\chi\) \(=\) 108.25
Dual form 108.4.i.a.13.3

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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 −0.353631 + 0.935385i \(0.615053\pi\)
−0.982582 + 0.185831i \(0.940502\pi\)
\(6\) 0 0
\(7\) 23.5233 8.56177i 1.27014 0.462292i 0.382978 0.923757i \(-0.374898\pi\)
0.887158 + 0.461465i \(0.152676\pi\)
\(8\) 0 0
\(9\) 11.7572 24.3057i 0.435453 0.900211i
\(10\) 0 0
\(11\) −39.5319 33.1712i −1.08358 0.909227i −0.0873623 0.996177i \(-0.527844\pi\)
−0.996213 + 0.0869492i \(0.972288\pi\)
\(12\) 0 0
\(13\) −10.2025 57.8615i −0.217668 1.23445i −0.876217 0.481917i \(-0.839941\pi\)
0.658550 0.752537i \(-0.271170\pi\)
\(14\) 0 0
\(15\) 31.1578 96.4258i 0.536327 1.65980i
\(16\) 0 0
\(17\) −3.52013 6.09704i −0.0502210 0.0869853i 0.839822 0.542862i \(-0.182659\pi\)
−0.890043 + 0.455876i \(0.849326\pi\)
\(18\) 0 0
\(19\) −42.6669 + 73.9012i −0.515182 + 0.892321i 0.484663 + 0.874701i \(0.338942\pi\)
−0.999845 + 0.0176203i \(0.994391\pi\)
\(20\) 0 0
\(21\) −79.9157 + 102.630i −0.830431 + 1.06646i
\(22\) 0 0
\(23\) 32.2883 + 11.7520i 0.292721 + 0.106542i 0.484206 0.874954i \(-0.339108\pi\)
−0.191486 + 0.981495i \(0.561331\pi\)
\(24\) 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 −0.600417 0.799687i \(-0.704999\pi\)
0.837717 0.546105i \(-0.183890\pi\)
\(30\) 0 0
\(31\) −133.967 48.7600i −0.776168 0.282502i −0.0765940 0.997062i \(-0.524405\pi\)
−0.699574 + 0.714560i \(0.746627\pi\)
\(32\) 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 0.683702 0.729761i \(-0.260369\pi\)
−0.973843 + 0.227223i \(0.927035\pi\)
\(38\) 0 0
\(39\) 204.650 + 226.547i 0.840263 + 0.930168i
\(40\) 0 0
\(41\) −8.52460 48.3454i −0.0324712 0.184153i 0.964258 0.264964i \(-0.0853601\pi\)
−0.996729 + 0.0808109i \(0.974249\pi\)
\(42\) 0 0
\(43\) 126.716 + 106.327i 0.449394 + 0.377086i 0.839211 0.543806i \(-0.183017\pi\)
−0.389817 + 0.920892i \(0.627462\pi\)
\(44\) 0 0
\(45\) 129.041 + 510.494i 0.427473 + 1.69111i
\(46\) 0 0
\(47\) −470.489 + 171.244i −1.46017 + 0.531458i −0.945412 0.325878i \(-0.894340\pi\)
−0.514757 + 0.857336i \(0.672118\pi\)
\(48\) 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 −0.812954 0.582329i \(-0.802142\pi\)
0.432314 + 0.901723i \(0.357697\pi\)
\(60\) 0 0
\(61\) −577.795 + 210.300i −1.21277 + 0.441413i −0.867664 0.497150i \(-0.834380\pi\)
−0.345107 + 0.938563i \(0.612158\pi\)
\(62\) 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 −0.664353 0.747419i \(-0.731293\pi\)
0.368656 0.929566i \(-0.379818\pi\)
\(68\) 0 0
\(69\) −174.580 + 37.4043i −0.304594 + 0.0652601i
\(70\) 0 0
\(71\) 46.7209 + 80.9229i 0.0780950 + 0.135265i 0.902428 0.430841i \(-0.141783\pi\)
−0.824333 + 0.566105i \(0.808450\pi\)
\(72\) 0 0
\(73\) −133.977 + 232.055i −0.214806 + 0.372055i −0.953213 0.302301i \(-0.902245\pi\)
0.738406 + 0.674356i \(0.235579\pi\)
\(74\) 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 0.646608 + 0.762822i \(0.276187\pi\)
−0.868514 + 0.495665i \(0.834924\pi\)
\(80\) 0 0
\(81\) −452.535 571.536i −0.620761 0.784000i
\(82\) 0 0
\(83\) 6.17283 35.0079i 0.00816333 0.0462966i −0.980454 0.196748i \(-0.936962\pi\)
0.988617 + 0.150452i \(0.0480729\pi\)
\(84\) 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 −0.566131 0.824315i \(-0.691560\pi\)
0.996943 + 0.0781261i \(0.0248937\pi\)
\(90\) 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 −0.994401 0.105673i \(-0.966300\pi\)
−0.276744 0.960944i \(-0.589255\pi\)
\(98\) 0 0
\(99\) −1271.04 + 570.850i −1.29034 + 0.579521i
\(100\) 0 0
\(101\) 1643.15 598.056i 1.61880 0.589196i 0.635649 0.771978i \(-0.280732\pi\)
0.983153 + 0.182782i \(0.0585103\pi\)
\(102\) 0 0
\(103\) 717.798 602.304i 0.686667 0.576182i −0.231279 0.972888i \(-0.574291\pi\)
0.917946 + 0.396705i \(0.129846\pi\)
\(104\) 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 −0.866836 0.498593i \(-0.833850\pi\)
0.340493 + 0.940247i \(0.389406\pi\)
\(114\) 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 0.135722 + 0.990747i \(0.456665\pi\)
−0.925873 + 0.377835i \(0.876669\pi\)
\(128\) 0 0
\(129\) −851.352 118.242i −0.581065 0.0807024i
\(130\) 0 0
\(131\) 1343.42 + 488.966i 0.895996 + 0.326116i 0.748647 0.662969i \(-0.230704\pi\)
0.147349 + 0.989085i \(0.452926\pi\)
\(132\) 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 −0.789354 0.613938i \(-0.789584\pi\)
0.951729 0.306938i \(-0.0993046\pi\)
\(138\) 0 0
\(139\) −54.1508 19.7093i −0.0330433 0.0120268i 0.325446 0.945561i \(-0.394486\pi\)
−0.358489 + 0.933534i \(0.616708\pi\)
\(140\) 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 −0.978124 0.208022i \(-0.933297\pi\)
0.847988 0.530015i \(-0.177814\pi\)
\(150\) 0 0
\(151\) 897.782 + 753.329i 0.483844 + 0.405993i 0.851814 0.523844i \(-0.175503\pi\)
−0.367970 + 0.929838i \(0.619947\pi\)
\(152\) 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 −0.856420 0.516280i \(-0.827316\pi\)
0.359721 + 0.933060i \(0.382872\pi\)
\(158\) 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 −0.539177 0.842193i \(-0.681264\pi\)
0.735771 + 0.677231i \(0.236820\pi\)
\(168\) 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 0.753523 0.657421i \(-0.228353\pi\)
−0.516586 + 0.856235i \(0.672797\pi\)
\(174\) 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 0.717410 0.696651i \(-0.245327\pi\)
−0.962023 + 0.272970i \(0.911994\pi\)
\(180\) 0 0
\(181\) −386.512 + 669.458i −0.158725 + 0.274919i −0.934409 0.356202i \(-0.884072\pi\)
0.775684 + 0.631121i \(0.217405\pi\)
\(182\) 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 −0.997789 0.0664597i \(-0.978830\pi\)
0.960346 + 0.278812i \(0.0899407\pi\)
\(192\) 0 0
\(193\) −4565.75 1661.80i −1.70285 0.619787i −0.706705 0.707509i \(-0.749819\pi\)
−0.996145 + 0.0877221i \(0.972041\pi\)
\(194\) 0 0
\(195\) −5897.23 819.049i −2.16569 0.300786i
\(196\) 0 0
\(197\) −946.267 + 1638.98i −0.342227 + 0.592754i −0.984846 0.173431i \(-0.944514\pi\)
0.642619 + 0.766186i \(0.277848\pi\)
\(198\) 0 0
\(199\) 1950.36 + 3378.12i 0.694759 + 1.20336i 0.970262 + 0.242058i \(0.0778225\pi\)
−0.275502 + 0.961300i \(0.588844\pi\)
\(200\) 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 −0.437011 0.899456i \(-0.643963\pi\)
0.809906 + 0.586560i \(0.199518\pi\)
\(212\) 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 −0.614545 0.788882i \(-0.710660\pi\)
0.0363147 + 0.999340i \(0.488438\pi\)
\(224\) 0 0
\(225\) −5590.27 4033.92i −1.65638 1.19524i
\(226\) 0 0
\(227\) −1243.19 1043.16i −0.363496 0.305009i 0.442686 0.896677i \(-0.354026\pi\)
−0.806182 + 0.591667i \(0.798470\pi\)
\(228\) 0 0
\(229\) 651.857 + 3696.86i 0.188104 + 1.06679i 0.921901 + 0.387425i \(0.126635\pi\)
−0.733797 + 0.679369i \(0.762254\pi\)
\(230\) 0 0
\(231\) 6563.59 1406.27i 1.86949 0.400544i
\(232\) 0 0
\(233\) −48.1965 83.4788i −0.0135513 0.0234716i 0.859170 0.511690i \(-0.170980\pi\)
−0.872722 + 0.488218i \(0.837647\pi\)
\(234\) 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 −0.298626 0.954370i \(-0.596528\pi\)
−0.842218 + 0.539137i \(0.818751\pi\)
\(240\) 0 0
\(241\) 420.948 2387.32i 0.112513 0.638093i −0.875438 0.483330i \(-0.839427\pi\)
0.987952 0.154764i \(-0.0494616\pi\)
\(242\) 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 −0.976536 0.215352i \(-0.930910\pi\)
0.674769 + 0.738029i \(0.264243\pi\)
\(252\) 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 0.975902 0.218209i \(-0.0700214\pi\)
−0.991680 + 0.128729i \(0.958910\pi\)
\(258\) 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 −0.744267 0.667882i \(-0.767201\pi\)
−0.140835 + 0.990033i \(0.544979\pi\)
\(264\) 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 −0.739022 0.673681i \(-0.764712\pi\)
−0.133090 + 0.991104i \(0.542490\pi\)
\(278\) 0 0
\(279\) −2760.23 + 2682.88i −0.592296 + 0.575699i
\(280\) 0 0
\(281\) −3809.81 3196.81i −0.808805 0.678668i 0.141517 0.989936i \(-0.454802\pi\)
−0.950322 + 0.311268i \(0.899246\pi\)
\(282\) 0 0
\(283\) −185.085 1049.67i −0.0388770 0.220482i 0.959180 0.282798i \(-0.0912626\pi\)
−0.998056 + 0.0623156i \(0.980151\pi\)
\(284\) 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 0.884045 0.467402i \(-0.154810\pi\)
0.376778 + 0.926304i \(0.377032\pi\)
\(294\) 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 0.824379 0.566038i \(-0.191524\pi\)
−0.902393 + 0.430915i \(0.858191\pi\)
\(308\) 0 0
\(309\) −1497.06 + 4633.03i −0.275614 + 0.852957i
\(310\) 0 0
\(311\) −782.999 4440.61i −0.142765 0.809658i −0.969135 0.246531i \(-0.920709\pi\)
0.826370 0.563127i \(-0.190402\pi\)
\(312\) 0 0
\(313\) 3326.13 + 2790.96i 0.600652 + 0.504007i 0.891655 0.452715i \(-0.149545\pi\)
−0.291003 + 0.956722i \(0.593989\pi\)
\(314\) 0 0
\(315\) 7406.20 + 10903.7i 1.32474 + 1.95032i
\(316\) 0 0
\(317\) −8805.07 + 3204.78i −1.56007 + 0.567819i −0.970752 0.240083i \(-0.922825\pi\)
−0.589317 + 0.807902i \(0.700603\pi\)
\(318\) 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 0.318077 0.948065i \(-0.396963\pi\)
0.853066 + 0.521804i \(0.174741\pi\)
\(332\) 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 0.994357 + 0.106087i \(0.0338323\pi\)
−0.898106 + 0.439780i \(0.855057\pi\)
\(338\) 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 0.972965 0.230954i \(-0.0741848\pi\)
0.596880 + 0.802331i \(0.296407\pi\)
\(348\) 0 0
\(349\) −221.987 + 1258.95i −0.0340479 + 0.193095i −0.997088 0.0762641i \(-0.975701\pi\)
0.963040 + 0.269359i \(0.0868119\pi\)
\(350\) 0 0
\(351\) 7912.51 2310.60i 1.20324 0.351370i
\(352\) 0 0
\(353\) 1599.06 9068.74i 0.241104 1.36737i −0.588267 0.808667i \(-0.700189\pi\)
0.829370 0.558700i \(-0.188699\pi\)
\(354\) 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 −0.889353 0.457222i \(-0.848844\pi\)
0.840642 + 0.541591i \(0.182178\pi\)
\(360\) 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 0.217687 0.976019i \(-0.430149\pi\)
−0.923390 + 0.383864i \(0.874593\pi\)
\(368\) 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 −0.179682 0.983725i \(-0.557507\pi\)
0.937578 + 0.347775i \(0.113063\pi\)
\(374\) 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 0.384762 0.923016i \(-0.374283\pi\)
0.975806 0.218637i \(-0.0701610\pi\)
\(384\) 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 −0.963236 0.268656i \(-0.913420\pi\)
−0.431839 0.901951i \(-0.642135\pi\)
\(390\) 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 0.447041 + 0.894514i \(0.352478\pi\)
−0.998192 + 0.0601082i \(0.980855\pi\)
\(398\) 0 0
\(399\) −4174.74 10284.8i −0.523806 1.29043i
\(400\) 0 0
\(401\) 12751.4 + 4641.12i 1.58796 + 0.577971i 0.976916 0.213624i \(-0.0685267\pi\)
0.611046 + 0.791595i \(0.290749\pi\)
\(402\) 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 −0.224839 0.974396i \(-0.572186\pi\)
−0.798566 + 0.601907i \(0.794408\pi\)
\(410\) 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 0.996243 + 0.0866031i \(0.0276012\pi\)
−0.906542 + 0.422115i \(0.861288\pi\)
\(420\) 0 0
\(421\) −472.103 396.141i −0.0546529 0.0458592i 0.615052 0.788487i \(-0.289135\pi\)
−0.669705 + 0.742627i \(0.733579\pi\)
\(422\) 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 −0.924933 0.380129i \(-0.875880\pi\)
−0.464198 + 0.885732i \(0.653657\pi\)
\(440\) 0 0
\(441\) −1876.85 7424.94i −0.202662 0.801743i
\(442\) 0 0
\(443\) −8689.72 7291.54i −0.931966 0.782013i 0.0442031 0.999023i \(-0.485925\pi\)
−0.976169 + 0.217010i \(0.930370\pi\)
\(444\) 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 0.969787 0.243954i \(-0.0784444\pi\)
−0.696163 + 0.717883i \(0.745111\pi\)
\(450\) 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 −0.415454 0.909614i \(-0.636377\pi\)
0.701506 0.712664i \(-0.252512\pi\)
\(458\) 0 0
\(459\) 796.248 584.449i 0.0809710 0.0594330i
\(460\) 0 0
\(461\) 2417.98 13713.0i 0.244287 1.38542i −0.577855 0.816139i \(-0.696110\pi\)
0.822143 0.569282i \(-0.192779\pi\)
\(462\) 0 0
\(463\) −683.331 248.712i −0.0685898 0.0249646i 0.307497 0.951549i \(-0.400508\pi\)
−0.376087 + 0.926584i \(0.622731\pi\)
\(464\) 0 0
\(465\) −8875.84 + 11398.6i −0.885177 + 1.13677i
\(466\) 0 0
\(467\) 6275.96 10870.3i 0.621877 1.07712i −0.367259 0.930119i \(-0.619704\pi\)
0.989136 0.147004i \(-0.0469630\pi\)
\(468\) 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 0.108420 0.994105i \(-0.465421\pi\)
0.722053 + 0.691838i \(0.243199\pi\)
\(480\) 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 −0.811533 0.584306i \(-0.801367\pi\)
0.434508 + 0.900668i \(0.356922\pi\)
\(492\) 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 0.994152 0.107993i \(-0.0344423\pi\)
−0.971133 + 0.238540i \(0.923331\pi\)
\(500\) 0 0
\(501\) −884.874 + 2738.47i −0.0789087 + 0.244203i
\(502\) 0 0
\(503\) −6261.59 10845.4i −0.555051 0.961376i −0.997900 0.0647801i \(-0.979365\pi\)
0.442849 0.896596i \(-0.353968\pi\)
\(504\) 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 0.384342 0.923191i \(-0.374428\pi\)
−0.298992 + 0.954256i \(0.596650\pi\)
\(510\) 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 −0.582182 0.813058i \(-0.697801\pi\)
0.995220 + 0.0976552i \(0.0311342\pi\)
\(522\) 0 0
\(523\) −904.471 1566.59i −0.0756209 0.130979i 0.825735 0.564058i \(-0.190761\pi\)
−0.901356 + 0.433079i \(0.857427\pi\)
\(524\) 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 −0.0643567 0.997927i \(-0.520500\pi\)
0.592155 + 0.805824i \(0.298277\pi\)
\(548\) 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 0.833973 0.551805i \(-0.186061\pi\)
−0.894864 + 0.446339i \(0.852728\pi\)
\(558\) 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 −0.161787 0.986826i \(-0.551726\pi\)
−0.758255 + 0.651958i \(0.773948\pi\)
\(564\) 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 0.389419 + 0.921061i \(0.372676\pi\)
−0.680955 + 0.732325i \(0.738435\pi\)
\(570\) 0 0
\(571\) 10197.6 + 3711.63i 0.747386 + 0.272026i 0.687505 0.726179i \(-0.258706\pi\)
0.0598805 + 0.998206i \(0.480928\pi\)
\(572\) 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 −0.928499 0.371335i \(-0.878900\pi\)
0.142664 0.989771i \(-0.454433\pi\)
\(578\) 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 −0.659115 0.752042i \(-0.729069\pi\)
−0.0215079 + 0.999769i \(0.506847\pi\)
\(588\) 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 −0.765590 0.643328i \(-0.777553\pi\)
0.500611 + 0.865672i \(0.333109\pi\)
\(600\) 0 0
\(601\) −6769.34 + 2463.84i −0.459446 + 0.167225i −0.561366 0.827568i \(-0.689724\pi\)
0.101919 + 0.994793i \(0.467502\pi\)
\(602\) 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 0.944426 0.328723i \(-0.106618\pi\)
−0.999900 + 0.0141141i \(0.995507\pi\)
\(608\) 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 −0.391474 0.920189i \(-0.628035\pi\)
0.992644 0.121068i \(-0.0386319\pi\)
\(614\) 0 0
\(615\) −4927.35 684.345i −0.323073 0.0448707i
\(616\) 0 0
\(617\) 9238.38 + 3362.50i 0.602793 + 0.219399i 0.625347 0.780347i \(-0.284958\pi\)
−0.0225540 + 0.999746i \(0.507180\pi\)
\(618\) 0 0
\(619\) −2028.41 + 11503.7i −0.131710 + 0.746966i 0.845384 + 0.534159i \(0.179372\pi\)
−0.977094 + 0.212807i \(0.931739\pi\)
\(620\) 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 0.641158 0.767409i \(-0.278454\pi\)
−0.985175 + 0.171554i \(0.945121\pi\)
\(632\) 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 0.339676 0.940542i \(-0.389682\pi\)
0.864776 + 0.502158i \(0.167460\pi\)
\(642\) 0 0
\(643\) 6541.99 5489.38i 0.401230 0.336672i −0.419739 0.907645i \(-0.637878\pi\)
0.820969 + 0.570973i \(0.193434\pi\)
\(644\) 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 −0.906721 0.421732i \(-0.861422\pi\)
0.257874 + 0.966179i \(0.416978\pi\)
\(654\) 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 0.385985 0.922505i \(-0.373862\pi\)
−0.841465 + 0.540312i \(0.818306\pi\)
\(660\) 0 0
\(661\) −3544.49 20101.8i −0.208570 1.18286i −0.891723 0.452582i \(-0.850503\pi\)
0.683153 0.730275i \(-0.260608\pi\)
\(662\) 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 −0.870940 0.491389i \(-0.836489\pi\)
0.986481 0.163876i \(-0.0523996\pi\)
\(674\) 0 0
\(675\) 35745.4 + 2324.82i 2.03828 + 0.132566i
\(676\) 0 0
\(677\) −3453.35 + 19584.9i −0.196046 + 1.11183i 0.714876 + 0.699252i \(0.246483\pi\)
−0.910921 + 0.412580i \(0.864628\pi\)
\(678\) 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 −0.973967 0.226690i \(-0.927209\pi\)
0.683303 + 0.730135i \(0.260543\pi\)
\(684\) 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 −0.989655 0.143468i \(-0.954175\pi\)
−0.313140 0.949707i \(-0.601381\pi\)
\(692\) 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 0.254103 0.967177i \(-0.418220\pi\)
0.816344 + 0.577566i \(0.195997\pi\)
\(710\) 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 0.713261 + 0.700899i \(0.247217\pi\)
0.250366 + 0.968151i \(0.419449\pi\)
\(720\) 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 0.828753 + 0.559614i \(0.189051\pi\)
−0.970173 + 0.242415i \(0.922060\pi\)
\(728\) 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 0.978129 0.207998i \(-0.0666948\pi\)
0.615592 + 0.788065i \(0.288917\pi\)
\(734\) 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 0.961869 + 0.273510i \(0.0881845\pi\)
−0.244068 + 0.969758i \(0.578482\pi\)
\(740\) 0 0
\(741\) −25473.9 + 5457.85i −1.26290 + 0.270579i
\(742\) 0 0
\(743\) −1573.69 8924.86i −0.0777028 0.440675i −0.998694 0.0510912i \(-0.983730\pi\)
0.920991 0.389583i \(-0.127381\pi\)
\(744\) 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 −0.524152 0.851625i \(-0.675618\pi\)
0.747668 + 0.664072i \(0.231173\pi\)
\(752\) 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 −0.942128 0.335254i \(-0.891178\pi\)
0.166562 + 0.986031i \(0.446733\pi\)
\(762\) 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 0.995620 0.0934935i \(-0.0298034\pi\)
−0.967553 + 0.252667i \(0.918692\pi\)
\(770\) 0 0
\(771\) 1303.91 + 1443.42i 0.0609068 + 0.0674236i
\(772\) 0 0
\(773\) 9004.85 + 15596.8i 0.418993 + 0.725718i 0.995838 0.0911359i \(-0.0290498\pi\)
−0.576845 + 0.816853i \(0.695716\pi\)
\(774\) 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