Properties

Label 1512.2.c.f.757.7
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.7
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.796644 - 1.16849i) q^{2} +(-0.730716 + 1.86173i) q^{4} +2.52623i q^{5} +1.00000 q^{7} +(2.75753 - 0.629309i) q^{8} +O(q^{10})\) \(q+(-0.796644 - 1.16849i) q^{2} +(-0.730716 + 1.86173i) q^{4} +2.52623i q^{5} +1.00000 q^{7} +(2.75753 - 0.629309i) q^{8} +(2.95186 - 2.01251i) q^{10} -5.70432i q^{11} +3.06046i q^{13} +(-0.796644 - 1.16849i) q^{14} +(-2.93211 - 2.72080i) q^{16} -5.49926 q^{17} -7.28486i q^{19} +(-4.70317 - 1.84596i) q^{20} +(-6.66541 + 4.54431i) q^{22} +0.539732 q^{23} -1.38184 q^{25} +(3.57610 - 2.43809i) q^{26} +(-0.730716 + 1.86173i) q^{28} -8.35116i q^{29} +6.74848 q^{31} +(-0.843365 + 5.59363i) q^{32} +(4.38095 + 6.42580i) q^{34} +2.52623i q^{35} +10.2711i q^{37} +(-8.51226 + 5.80345i) q^{38} +(1.58978 + 6.96615i) q^{40} +5.58370 q^{41} -3.98332i q^{43} +(10.6199 + 4.16824i) q^{44} +(-0.429975 - 0.630669i) q^{46} +4.83840 q^{47} +1.00000 q^{49} +(1.10083 + 1.61466i) q^{50} +(-5.69776 - 2.23632i) q^{52} -11.1320i q^{53} +14.4104 q^{55} +(2.75753 - 0.629309i) q^{56} +(-9.75821 + 6.65291i) q^{58} -10.1647i q^{59} +4.14075i q^{61} +(-5.37614 - 7.88550i) q^{62} +(7.20794 - 3.47068i) q^{64} -7.73142 q^{65} +5.96348i q^{67} +(4.01839 - 10.2382i) q^{68} +(2.95186 - 2.01251i) q^{70} -4.93014 q^{71} +8.66798 q^{73} +(12.0016 - 8.18239i) q^{74} +(13.5625 + 5.32317i) q^{76} -5.70432i q^{77} +12.0532 q^{79} +(6.87336 - 7.40718i) q^{80} +(-4.44823 - 6.52448i) q^{82} +5.83393i q^{83} -13.8924i q^{85} +(-4.65445 + 3.17329i) q^{86} +(-3.58978 - 15.7298i) q^{88} +9.28810 q^{89} +3.06046i q^{91} +(-0.394391 + 1.00484i) q^{92} +(-3.85449 - 5.65360i) q^{94} +18.4032 q^{95} +12.3500 q^{97} +(-0.796644 - 1.16849i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.796644 1.16849i −0.563313 0.826244i
\(3\) 0 0
\(4\) −0.730716 + 1.86173i −0.365358 + 0.930867i
\(5\) 2.52623i 1.12976i 0.825172 + 0.564882i \(0.191078\pi\)
−0.825172 + 0.564882i \(0.808922\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.75753 0.629309i 0.974934 0.222494i
\(9\) 0 0
\(10\) 2.95186 2.01251i 0.933461 0.636410i
\(11\) 5.70432i 1.71992i −0.510364 0.859958i \(-0.670489\pi\)
0.510364 0.859958i \(-0.329511\pi\)
\(12\) 0 0
\(13\) 3.06046i 0.848818i 0.905471 + 0.424409i \(0.139518\pi\)
−0.905471 + 0.424409i \(0.860482\pi\)
\(14\) −0.796644 1.16849i −0.212912 0.312291i
\(15\) 0 0
\(16\) −2.93211 2.72080i −0.733027 0.680199i
\(17\) −5.49926 −1.33377 −0.666883 0.745163i \(-0.732372\pi\)
−0.666883 + 0.745163i \(0.732372\pi\)
\(18\) 0 0
\(19\) 7.28486i 1.67126i −0.549291 0.835631i \(-0.685102\pi\)
0.549291 0.835631i \(-0.314898\pi\)
\(20\) −4.70317 1.84596i −1.05166 0.412768i
\(21\) 0 0
\(22\) −6.66541 + 4.54431i −1.42107 + 0.968851i
\(23\) 0.539732 0.112542 0.0562710 0.998416i \(-0.482079\pi\)
0.0562710 + 0.998416i \(0.482079\pi\)
\(24\) 0 0
\(25\) −1.38184 −0.276367
\(26\) 3.57610 2.43809i 0.701331 0.478150i
\(27\) 0 0
\(28\) −0.730716 + 1.86173i −0.138092 + 0.351835i
\(29\) 8.35116i 1.55077i −0.631488 0.775386i \(-0.717555\pi\)
0.631488 0.775386i \(-0.282445\pi\)
\(30\) 0 0
\(31\) 6.74848 1.21206 0.606032 0.795441i \(-0.292761\pi\)
0.606032 + 0.795441i \(0.292761\pi\)
\(32\) −0.843365 + 5.59363i −0.149087 + 0.988824i
\(33\) 0 0
\(34\) 4.38095 + 6.42580i 0.751327 + 1.10202i
\(35\) 2.52623i 0.427011i
\(36\) 0 0
\(37\) 10.2711i 1.68855i 0.535908 + 0.844277i \(0.319969\pi\)
−0.535908 + 0.844277i \(0.680031\pi\)
\(38\) −8.51226 + 5.80345i −1.38087 + 0.941443i
\(39\) 0 0
\(40\) 1.58978 + 6.96615i 0.251366 + 1.10145i
\(41\) 5.58370 0.872028 0.436014 0.899940i \(-0.356390\pi\)
0.436014 + 0.899940i \(0.356390\pi\)
\(42\) 0 0
\(43\) 3.98332i 0.607451i −0.952760 0.303725i \(-0.901770\pi\)
0.952760 0.303725i \(-0.0982305\pi\)
\(44\) 10.6199 + 4.16824i 1.60101 + 0.628385i
\(45\) 0 0
\(46\) −0.429975 0.630669i −0.0633963 0.0929871i
\(47\) 4.83840 0.705754 0.352877 0.935670i \(-0.385203\pi\)
0.352877 + 0.935670i \(0.385203\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.10083 + 1.61466i 0.155681 + 0.228347i
\(51\) 0 0
\(52\) −5.69776 2.23632i −0.790137 0.310122i
\(53\) 11.1320i 1.52910i −0.644562 0.764552i \(-0.722960\pi\)
0.644562 0.764552i \(-0.277040\pi\)
\(54\) 0 0
\(55\) 14.4104 1.94310
\(56\) 2.75753 0.629309i 0.368490 0.0840950i
\(57\) 0 0
\(58\) −9.75821 + 6.65291i −1.28132 + 0.873569i
\(59\) 10.1647i 1.32333i −0.749798 0.661666i \(-0.769850\pi\)
0.749798 0.661666i \(-0.230150\pi\)
\(60\) 0 0
\(61\) 4.14075i 0.530169i 0.964225 + 0.265084i \(0.0853998\pi\)
−0.964225 + 0.265084i \(0.914600\pi\)
\(62\) −5.37614 7.88550i −0.682770 1.00146i
\(63\) 0 0
\(64\) 7.20794 3.47068i 0.900993 0.433835i
\(65\) −7.73142 −0.958964
\(66\) 0 0
\(67\) 5.96348i 0.728555i 0.931290 + 0.364278i \(0.118684\pi\)
−0.931290 + 0.364278i \(0.881316\pi\)
\(68\) 4.01839 10.2382i 0.487302 1.24156i
\(69\) 0 0
\(70\) 2.95186 2.01251i 0.352815 0.240541i
\(71\) −4.93014 −0.585100 −0.292550 0.956250i \(-0.594504\pi\)
−0.292550 + 0.956250i \(0.594504\pi\)
\(72\) 0 0
\(73\) 8.66798 1.01451 0.507255 0.861796i \(-0.330660\pi\)
0.507255 + 0.861796i \(0.330660\pi\)
\(74\) 12.0016 8.18239i 1.39516 0.951183i
\(75\) 0 0
\(76\) 13.5625 + 5.32317i 1.55572 + 0.610609i
\(77\) 5.70432i 0.650067i
\(78\) 0 0
\(79\) 12.0532 1.35609 0.678044 0.735021i \(-0.262828\pi\)
0.678044 + 0.735021i \(0.262828\pi\)
\(80\) 6.87336 7.40718i 0.768465 0.828148i
\(81\) 0 0
\(82\) −4.44823 6.52448i −0.491224 0.720508i
\(83\) 5.83393i 0.640357i 0.947357 + 0.320178i \(0.103743\pi\)
−0.947357 + 0.320178i \(0.896257\pi\)
\(84\) 0 0
\(85\) 13.8924i 1.50684i
\(86\) −4.65445 + 3.17329i −0.501902 + 0.342185i
\(87\) 0 0
\(88\) −3.58978 15.7298i −0.382672 1.67681i
\(89\) 9.28810 0.984537 0.492268 0.870444i \(-0.336168\pi\)
0.492268 + 0.870444i \(0.336168\pi\)
\(90\) 0 0
\(91\) 3.06046i 0.320823i
\(92\) −0.394391 + 1.00484i −0.0411181 + 0.104762i
\(93\) 0 0
\(94\) −3.85449 5.65360i −0.397560 0.583125i
\(95\) 18.4032 1.88813
\(96\) 0 0
\(97\) 12.3500 1.25395 0.626974 0.779040i \(-0.284293\pi\)
0.626974 + 0.779040i \(0.284293\pi\)
\(98\) −0.796644 1.16849i −0.0804732 0.118035i
\(99\) 0 0
\(100\) 1.00973 2.57261i 0.100973 0.257261i
\(101\) 9.33719i 0.929085i −0.885551 0.464542i \(-0.846219\pi\)
0.885551 0.464542i \(-0.153781\pi\)
\(102\) 0 0
\(103\) −7.28802 −0.718110 −0.359055 0.933316i \(-0.616901\pi\)
−0.359055 + 0.933316i \(0.616901\pi\)
\(104\) 1.92597 + 8.43930i 0.188857 + 0.827541i
\(105\) 0 0
\(106\) −13.0076 + 8.86828i −1.26341 + 0.861364i
\(107\) 7.31179i 0.706858i 0.935461 + 0.353429i \(0.114984\pi\)
−0.935461 + 0.353429i \(0.885016\pi\)
\(108\) 0 0
\(109\) 15.9330i 1.52611i −0.646336 0.763053i \(-0.723700\pi\)
0.646336 0.763053i \(-0.276300\pi\)
\(110\) −11.4800 16.8384i −1.09457 1.60548i
\(111\) 0 0
\(112\) −2.93211 2.72080i −0.277058 0.257091i
\(113\) −6.91459 −0.650470 −0.325235 0.945633i \(-0.605443\pi\)
−0.325235 + 0.945633i \(0.605443\pi\)
\(114\) 0 0
\(115\) 1.36349i 0.127146i
\(116\) 15.5476 + 6.10233i 1.44356 + 0.566587i
\(117\) 0 0
\(118\) −11.8773 + 8.09766i −1.09340 + 0.745450i
\(119\) −5.49926 −0.504116
\(120\) 0 0
\(121\) −21.5393 −1.95811
\(122\) 4.83840 3.29870i 0.438049 0.298651i
\(123\) 0 0
\(124\) −4.93122 + 12.5639i −0.442837 + 1.12827i
\(125\) 9.14031i 0.817534i
\(126\) 0 0
\(127\) −17.6103 −1.56267 −0.781333 0.624115i \(-0.785460\pi\)
−0.781333 + 0.624115i \(0.785460\pi\)
\(128\) −9.79760 5.65748i −0.865994 0.500055i
\(129\) 0 0
\(130\) 6.15919 + 9.03405i 0.540196 + 0.792338i
\(131\) 10.7551i 0.939675i 0.882753 + 0.469838i \(0.155688\pi\)
−0.882753 + 0.469838i \(0.844312\pi\)
\(132\) 0 0
\(133\) 7.28486i 0.631678i
\(134\) 6.96824 4.75077i 0.601964 0.410404i
\(135\) 0 0
\(136\) −15.1644 + 3.46073i −1.30033 + 0.296755i
\(137\) −1.56413 −0.133633 −0.0668164 0.997765i \(-0.521284\pi\)
−0.0668164 + 0.997765i \(0.521284\pi\)
\(138\) 0 0
\(139\) 11.2728i 0.956149i −0.878319 0.478074i \(-0.841335\pi\)
0.878319 0.478074i \(-0.158665\pi\)
\(140\) −4.70317 1.84596i −0.397490 0.156012i
\(141\) 0 0
\(142\) 3.92757 + 5.76080i 0.329594 + 0.483436i
\(143\) 17.4578 1.45990
\(144\) 0 0
\(145\) 21.0970 1.75201
\(146\) −6.90529 10.1284i −0.571486 0.838233i
\(147\) 0 0
\(148\) −19.1220 7.50523i −1.57182 0.616926i
\(149\) 6.48749i 0.531476i 0.964045 + 0.265738i \(0.0856156\pi\)
−0.964045 + 0.265738i \(0.914384\pi\)
\(150\) 0 0
\(151\) −0.383325 −0.0311945 −0.0155973 0.999878i \(-0.504965\pi\)
−0.0155973 + 0.999878i \(0.504965\pi\)
\(152\) −4.58443 20.0882i −0.371846 1.62937i
\(153\) 0 0
\(154\) −6.66541 + 4.54431i −0.537114 + 0.366191i
\(155\) 17.0482i 1.36935i
\(156\) 0 0
\(157\) 8.66658i 0.691669i −0.938296 0.345834i \(-0.887596\pi\)
0.938296 0.345834i \(-0.112404\pi\)
\(158\) −9.60210 14.0840i −0.763902 1.12046i
\(159\) 0 0
\(160\) −14.1308 2.13053i −1.11714 0.168433i
\(161\) 0.539732 0.0425369
\(162\) 0 0
\(163\) 25.0771i 1.96419i −0.188382 0.982096i \(-0.560324\pi\)
0.188382 0.982096i \(-0.439676\pi\)
\(164\) −4.08010 + 10.3954i −0.318602 + 0.811742i
\(165\) 0 0
\(166\) 6.81686 4.64756i 0.529091 0.360721i
\(167\) 8.75411 0.677414 0.338707 0.940892i \(-0.390011\pi\)
0.338707 + 0.940892i \(0.390011\pi\)
\(168\) 0 0
\(169\) 3.63361 0.279508
\(170\) −16.2330 + 11.0673i −1.24502 + 0.848822i
\(171\) 0 0
\(172\) 7.41588 + 2.91067i 0.565456 + 0.221937i
\(173\) 9.29760i 0.706883i 0.935457 + 0.353442i \(0.114989\pi\)
−0.935457 + 0.353442i \(0.885011\pi\)
\(174\) 0 0
\(175\) −1.38184 −0.104457
\(176\) −15.5203 + 16.7257i −1.16989 + 1.26075i
\(177\) 0 0
\(178\) −7.39931 10.8530i −0.554602 0.813467i
\(179\) 7.65495i 0.572158i 0.958206 + 0.286079i \(0.0923520\pi\)
−0.958206 + 0.286079i \(0.907648\pi\)
\(180\) 0 0
\(181\) 2.50424i 0.186138i 0.995660 + 0.0930692i \(0.0296678\pi\)
−0.995660 + 0.0930692i \(0.970332\pi\)
\(182\) 3.57610 2.43809i 0.265078 0.180724i
\(183\) 0 0
\(184\) 1.48833 0.339658i 0.109721 0.0250400i
\(185\) −25.9471 −1.90767
\(186\) 0 0
\(187\) 31.3695i 2.29397i
\(188\) −3.53550 + 9.00782i −0.257853 + 0.656963i
\(189\) 0 0
\(190\) −14.6608 21.5039i −1.06361 1.56006i
\(191\) 3.20627 0.231997 0.115999 0.993249i \(-0.462993\pi\)
0.115999 + 0.993249i \(0.462993\pi\)
\(192\) 0 0
\(193\) 10.9544 0.788518 0.394259 0.918999i \(-0.371001\pi\)
0.394259 + 0.918999i \(0.371001\pi\)
\(194\) −9.83853 14.4308i −0.706365 1.03607i
\(195\) 0 0
\(196\) −0.730716 + 1.86173i −0.0521940 + 0.132981i
\(197\) 7.87749i 0.561248i −0.959818 0.280624i \(-0.909459\pi\)
0.959818 0.280624i \(-0.0905414\pi\)
\(198\) 0 0
\(199\) 1.00753 0.0714217 0.0357109 0.999362i \(-0.488630\pi\)
0.0357109 + 0.999362i \(0.488630\pi\)
\(200\) −3.81046 + 0.869603i −0.269440 + 0.0614902i
\(201\) 0 0
\(202\) −10.9104 + 7.43842i −0.767651 + 0.523365i
\(203\) 8.35116i 0.586137i
\(204\) 0 0
\(205\) 14.1057i 0.985186i
\(206\) 5.80596 + 8.51594i 0.404520 + 0.593334i
\(207\) 0 0
\(208\) 8.32688 8.97359i 0.577365 0.622206i
\(209\) −41.5552 −2.87443
\(210\) 0 0
\(211\) 16.2709i 1.12014i −0.828446 0.560069i \(-0.810775\pi\)
0.828446 0.560069i \(-0.189225\pi\)
\(212\) 20.7249 + 8.13436i 1.42339 + 0.558670i
\(213\) 0 0
\(214\) 8.54372 5.82490i 0.584037 0.398182i
\(215\) 10.0628 0.686276
\(216\) 0 0
\(217\) 6.74848 0.458117
\(218\) −18.6175 + 12.6929i −1.26094 + 0.859674i
\(219\) 0 0
\(220\) −10.5299 + 26.8284i −0.709927 + 1.80877i
\(221\) 16.8302i 1.13212i
\(222\) 0 0
\(223\) 2.78339 0.186390 0.0931949 0.995648i \(-0.470292\pi\)
0.0931949 + 0.995648i \(0.470292\pi\)
\(224\) −0.843365 + 5.59363i −0.0563497 + 0.373740i
\(225\) 0 0
\(226\) 5.50847 + 8.07959i 0.366418 + 0.537447i
\(227\) 11.4440i 0.759565i −0.925076 0.379782i \(-0.875999\pi\)
0.925076 0.379782i \(-0.124001\pi\)
\(228\) 0 0
\(229\) 4.54391i 0.300270i −0.988666 0.150135i \(-0.952029\pi\)
0.988666 0.150135i \(-0.0479708\pi\)
\(230\) 1.59322 1.08621i 0.105054 0.0716229i
\(231\) 0 0
\(232\) −5.25546 23.0286i −0.345038 1.51190i
\(233\) 16.0188 1.04943 0.524715 0.851278i \(-0.324172\pi\)
0.524715 + 0.851278i \(0.324172\pi\)
\(234\) 0 0
\(235\) 12.2229i 0.797335i
\(236\) 18.9240 + 7.42752i 1.23185 + 0.483490i
\(237\) 0 0
\(238\) 4.38095 + 6.42580i 0.283975 + 0.416523i
\(239\) 19.2968 1.24821 0.624104 0.781341i \(-0.285464\pi\)
0.624104 + 0.781341i \(0.285464\pi\)
\(240\) 0 0
\(241\) −22.1358 −1.42589 −0.712947 0.701218i \(-0.752640\pi\)
−0.712947 + 0.701218i \(0.752640\pi\)
\(242\) 17.1591 + 25.1683i 1.10303 + 1.61788i
\(243\) 0 0
\(244\) −7.70897 3.02571i −0.493516 0.193701i
\(245\) 2.52623i 0.161395i
\(246\) 0 0
\(247\) 22.2950 1.41860
\(248\) 18.6091 4.24688i 1.18168 0.269677i
\(249\) 0 0
\(250\) 10.6803 7.28158i 0.675483 0.460527i
\(251\) 7.94172i 0.501277i 0.968081 + 0.250638i \(0.0806405\pi\)
−0.968081 + 0.250638i \(0.919360\pi\)
\(252\) 0 0
\(253\) 3.07881i 0.193563i
\(254\) 14.0292 + 20.5774i 0.880269 + 1.29114i
\(255\) 0 0
\(256\) 1.19452 + 15.9553i 0.0746576 + 0.997209i
\(257\) −7.02501 −0.438208 −0.219104 0.975701i \(-0.570313\pi\)
−0.219104 + 0.975701i \(0.570313\pi\)
\(258\) 0 0
\(259\) 10.2711i 0.638213i
\(260\) 5.64947 14.3938i 0.350365 0.892668i
\(261\) 0 0
\(262\) 12.5671 8.56797i 0.776401 0.529331i
\(263\) −19.4695 −1.20054 −0.600270 0.799798i \(-0.704940\pi\)
−0.600270 + 0.799798i \(0.704940\pi\)
\(264\) 0 0
\(265\) 28.1221 1.72753
\(266\) −8.51226 + 5.80345i −0.521920 + 0.355832i
\(267\) 0 0
\(268\) −11.1024 4.35761i −0.678188 0.266184i
\(269\) 15.4258i 0.940526i −0.882526 0.470263i \(-0.844159\pi\)
0.882526 0.470263i \(-0.155841\pi\)
\(270\) 0 0
\(271\) 7.28198 0.442349 0.221174 0.975234i \(-0.429011\pi\)
0.221174 + 0.975234i \(0.429011\pi\)
\(272\) 16.1244 + 14.9624i 0.977686 + 0.907227i
\(273\) 0 0
\(274\) 1.24606 + 1.82766i 0.0752770 + 0.110413i
\(275\) 7.88244i 0.475329i
\(276\) 0 0
\(277\) 2.43449i 0.146275i −0.997322 0.0731373i \(-0.976699\pi\)
0.997322 0.0731373i \(-0.0233011\pi\)
\(278\) −13.1721 + 8.98043i −0.790012 + 0.538611i
\(279\) 0 0
\(280\) 1.58978 + 6.96615i 0.0950075 + 0.416307i
\(281\) −18.1555 −1.08307 −0.541534 0.840679i \(-0.682156\pi\)
−0.541534 + 0.840679i \(0.682156\pi\)
\(282\) 0 0
\(283\) 31.2909i 1.86005i −0.367496 0.930025i \(-0.619785\pi\)
0.367496 0.930025i \(-0.380215\pi\)
\(284\) 3.60253 9.17862i 0.213771 0.544651i
\(285\) 0 0
\(286\) −13.9077 20.3992i −0.822378 1.20623i
\(287\) 5.58370 0.329596
\(288\) 0 0
\(289\) 13.2418 0.778931
\(290\) −16.8068 24.6515i −0.986928 1.44759i
\(291\) 0 0
\(292\) −6.33383 + 16.1375i −0.370659 + 0.944374i
\(293\) 18.3419i 1.07155i 0.844362 + 0.535773i \(0.179980\pi\)
−0.844362 + 0.535773i \(0.820020\pi\)
\(294\) 0 0
\(295\) 25.6784 1.49505
\(296\) 6.46368 + 28.3228i 0.375694 + 1.64623i
\(297\) 0 0
\(298\) 7.58053 5.16822i 0.439129 0.299387i
\(299\) 1.65183i 0.0955276i
\(300\) 0 0
\(301\) 3.98332i 0.229595i
\(302\) 0.305373 + 0.447909i 0.0175723 + 0.0257743i
\(303\) 0 0
\(304\) −19.8206 + 21.3600i −1.13679 + 1.22508i
\(305\) −10.4605 −0.598966
\(306\) 0 0
\(307\) 24.5811i 1.40292i 0.712709 + 0.701460i \(0.247468\pi\)
−0.712709 + 0.701460i \(0.752532\pi\)
\(308\) 10.6199 + 4.16824i 0.605126 + 0.237507i
\(309\) 0 0
\(310\) 19.9206 13.5814i 1.13141 0.771370i
\(311\) −6.95251 −0.394240 −0.197120 0.980379i \(-0.563159\pi\)
−0.197120 + 0.980379i \(0.563159\pi\)
\(312\) 0 0
\(313\) −9.81498 −0.554775 −0.277388 0.960758i \(-0.589469\pi\)
−0.277388 + 0.960758i \(0.589469\pi\)
\(314\) −10.1268 + 6.90418i −0.571487 + 0.389626i
\(315\) 0 0
\(316\) −8.80745 + 22.4398i −0.495458 + 1.26234i
\(317\) 6.69289i 0.375910i −0.982178 0.187955i \(-0.939814\pi\)
0.982178 0.187955i \(-0.0601860\pi\)
\(318\) 0 0
\(319\) −47.6377 −2.66720
\(320\) 8.76773 + 18.2089i 0.490131 + 1.01791i
\(321\) 0 0
\(322\) −0.429975 0.630669i −0.0239616 0.0351458i
\(323\) 40.0613i 2.22907i
\(324\) 0 0
\(325\) 4.22905i 0.234586i
\(326\) −29.3022 + 19.9775i −1.62290 + 1.10645i
\(327\) 0 0
\(328\) 15.3972 3.51388i 0.850170 0.194021i
\(329\) 4.83840 0.266750
\(330\) 0 0
\(331\) 2.10916i 0.115930i 0.998319 + 0.0579651i \(0.0184612\pi\)
−0.998319 + 0.0579651i \(0.981539\pi\)
\(332\) −10.8612 4.26294i −0.596087 0.233959i
\(333\) 0 0
\(334\) −6.97391 10.2291i −0.381596 0.559709i
\(335\) −15.0651 −0.823096
\(336\) 0 0
\(337\) −5.53954 −0.301758 −0.150879 0.988552i \(-0.548210\pi\)
−0.150879 + 0.988552i \(0.548210\pi\)
\(338\) −2.89469 4.24582i −0.157451 0.230942i
\(339\) 0 0
\(340\) 25.8639 + 10.1514i 1.40267 + 0.550536i
\(341\) 38.4955i 2.08465i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −2.50674 10.9841i −0.135154 0.592224i
\(345\) 0 0
\(346\) 10.8641 7.40688i 0.584058 0.398196i
\(347\) 9.63790i 0.517389i −0.965959 0.258695i \(-0.916708\pi\)
0.965959 0.258695i \(-0.0832924\pi\)
\(348\) 0 0
\(349\) 8.04565i 0.430674i −0.976540 0.215337i \(-0.930915\pi\)
0.976540 0.215337i \(-0.0690850\pi\)
\(350\) 1.10083 + 1.61466i 0.0588420 + 0.0863070i
\(351\) 0 0
\(352\) 31.9079 + 4.81082i 1.70070 + 0.256418i
\(353\) 27.2775 1.45184 0.725918 0.687782i \(-0.241415\pi\)
0.725918 + 0.687782i \(0.241415\pi\)
\(354\) 0 0
\(355\) 12.4547i 0.661025i
\(356\) −6.78696 + 17.2920i −0.359708 + 0.916473i
\(357\) 0 0
\(358\) 8.94470 6.09827i 0.472742 0.322304i
\(359\) −7.36413 −0.388664 −0.194332 0.980936i \(-0.562254\pi\)
−0.194332 + 0.980936i \(0.562254\pi\)
\(360\) 0 0
\(361\) −34.0692 −1.79312
\(362\) 2.92616 1.99499i 0.153796 0.104854i
\(363\) 0 0
\(364\) −5.69776 2.23632i −0.298644 0.117215i
\(365\) 21.8973i 1.14616i
\(366\) 0 0
\(367\) 21.8746 1.14185 0.570923 0.821003i \(-0.306585\pi\)
0.570923 + 0.821003i \(0.306585\pi\)
\(368\) −1.58255 1.46850i −0.0824963 0.0765510i
\(369\) 0 0
\(370\) 20.6706 + 30.3188i 1.07461 + 1.57620i
\(371\) 11.1320i 0.577947i
\(372\) 0 0
\(373\) 8.99106i 0.465539i −0.972532 0.232770i \(-0.925221\pi\)
0.972532 0.232770i \(-0.0747788\pi\)
\(374\) 36.6548 24.9903i 1.89538 1.29222i
\(375\) 0 0
\(376\) 13.3420 3.04485i 0.688063 0.157026i
\(377\) 25.5584 1.31632
\(378\) 0 0
\(379\) 28.9165i 1.48534i 0.669656 + 0.742671i \(0.266442\pi\)
−0.669656 + 0.742671i \(0.733558\pi\)
\(380\) −13.4475 + 34.2619i −0.689844 + 1.75760i
\(381\) 0 0
\(382\) −2.55425 3.74647i −0.130687 0.191686i
\(383\) 12.5404 0.640786 0.320393 0.947285i \(-0.396185\pi\)
0.320393 + 0.947285i \(0.396185\pi\)
\(384\) 0 0
\(385\) 14.4104 0.734423
\(386\) −8.72680 12.8001i −0.444182 0.651509i
\(387\) 0 0
\(388\) −9.02431 + 22.9924i −0.458140 + 1.16726i
\(389\) 7.50374i 0.380455i 0.981740 + 0.190227i \(0.0609225\pi\)
−0.981740 + 0.190227i \(0.939077\pi\)
\(390\) 0 0
\(391\) −2.96813 −0.150105
\(392\) 2.75753 0.629309i 0.139276 0.0317849i
\(393\) 0 0
\(394\) −9.20474 + 6.27556i −0.463728 + 0.316158i
\(395\) 30.4491i 1.53206i
\(396\) 0 0
\(397\) 27.6639i 1.38841i 0.719778 + 0.694205i \(0.244244\pi\)
−0.719778 + 0.694205i \(0.755756\pi\)
\(398\) −0.802641 1.17728i −0.0402327 0.0590117i
\(399\) 0 0
\(400\) 4.05170 + 3.75970i 0.202585 + 0.187985i
\(401\) −35.8414 −1.78983 −0.894916 0.446234i \(-0.852765\pi\)
−0.894916 + 0.446234i \(0.852765\pi\)
\(402\) 0 0
\(403\) 20.6534i 1.02882i
\(404\) 17.3834 + 6.82283i 0.864855 + 0.339449i
\(405\) 0 0
\(406\) −9.75821 + 6.65291i −0.484292 + 0.330178i
\(407\) 58.5894 2.90417
\(408\) 0 0
\(409\) 18.4056 0.910097 0.455048 0.890467i \(-0.349622\pi\)
0.455048 + 0.890467i \(0.349622\pi\)
\(410\) 16.4823 11.2372i 0.814004 0.554968i
\(411\) 0 0
\(412\) 5.32547 13.5684i 0.262367 0.668465i
\(413\) 10.1647i 0.500173i
\(414\) 0 0
\(415\) −14.7378 −0.723452
\(416\) −17.1191 2.58108i −0.839331 0.126548i
\(417\) 0 0
\(418\) 33.1047 + 48.5566i 1.61920 + 2.37498i
\(419\) 0.0173724i 0.000848699i 1.00000 0.000424349i \(0.000135075\pi\)
−1.00000 0.000424349i \(0.999865\pi\)
\(420\) 0 0
\(421\) 1.03437i 0.0504121i −0.999682 0.0252060i \(-0.991976\pi\)
0.999682 0.0252060i \(-0.00802418\pi\)
\(422\) −19.0124 + 12.9622i −0.925507 + 0.630988i
\(423\) 0 0
\(424\) −7.00550 30.6970i −0.340217 1.49078i
\(425\) 7.59908 0.368609
\(426\) 0 0
\(427\) 4.14075i 0.200385i
\(428\) −13.6126 5.34284i −0.657991 0.258256i
\(429\) 0 0
\(430\) −8.01646 11.7582i −0.386588 0.567031i
\(431\) 10.1392 0.488390 0.244195 0.969726i \(-0.421476\pi\)
0.244195 + 0.969726i \(0.421476\pi\)
\(432\) 0 0
\(433\) −33.5806 −1.61378 −0.806890 0.590701i \(-0.798851\pi\)
−0.806890 + 0.590701i \(0.798851\pi\)
\(434\) −5.37614 7.88550i −0.258063 0.378516i
\(435\) 0 0
\(436\) 29.6630 + 11.6425i 1.42060 + 0.557575i
\(437\) 3.93188i 0.188087i
\(438\) 0 0
\(439\) −3.92098 −0.187138 −0.0935692 0.995613i \(-0.529828\pi\)
−0.0935692 + 0.995613i \(0.529828\pi\)
\(440\) 39.7372 9.06861i 1.89439 0.432329i
\(441\) 0 0
\(442\) −19.6659 + 13.4077i −0.935411 + 0.637740i
\(443\) 34.6306i 1.64535i 0.568514 + 0.822674i \(0.307519\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(444\) 0 0
\(445\) 23.4639i 1.11229i
\(446\) −2.21737 3.25235i −0.104996 0.154003i
\(447\) 0 0
\(448\) 7.20794 3.47068i 0.340543 0.163974i
\(449\) −17.7862 −0.839383 −0.419691 0.907667i \(-0.637862\pi\)
−0.419691 + 0.907667i \(0.637862\pi\)
\(450\) 0 0
\(451\) 31.8512i 1.49982i
\(452\) 5.05260 12.8731i 0.237654 0.605501i
\(453\) 0 0
\(454\) −13.3721 + 9.11679i −0.627586 + 0.427872i
\(455\) −7.73142 −0.362454
\(456\) 0 0
\(457\) 11.5852 0.541933 0.270966 0.962589i \(-0.412657\pi\)
0.270966 + 0.962589i \(0.412657\pi\)
\(458\) −5.30949 + 3.61988i −0.248096 + 0.169146i
\(459\) 0 0
\(460\) −2.53845 0.996322i −0.118356 0.0464538i
\(461\) 12.5948i 0.586596i 0.956021 + 0.293298i \(0.0947529\pi\)
−0.956021 + 0.293298i \(0.905247\pi\)
\(462\) 0 0
\(463\) −3.16107 −0.146907 −0.0734537 0.997299i \(-0.523402\pi\)
−0.0734537 + 0.997299i \(0.523402\pi\)
\(464\) −22.7218 + 24.4865i −1.05483 + 1.13676i
\(465\) 0 0
\(466\) −12.7613 18.7178i −0.591157 0.867085i
\(467\) 20.8974i 0.967015i −0.875340 0.483507i \(-0.839363\pi\)
0.875340 0.483507i \(-0.160637\pi\)
\(468\) 0 0
\(469\) 5.96348i 0.275368i
\(470\) 14.2823 9.73732i 0.658794 0.449149i
\(471\) 0 0
\(472\) −6.39674 28.0295i −0.294434 1.29016i
\(473\) −22.7221 −1.04476
\(474\) 0 0
\(475\) 10.0665i 0.461882i
\(476\) 4.01839 10.2382i 0.184183 0.469265i
\(477\) 0 0
\(478\) −15.3727 22.5481i −0.703131 1.03132i
\(479\) 28.2766 1.29199 0.645996 0.763341i \(-0.276442\pi\)
0.645996 + 0.763341i \(0.276442\pi\)
\(480\) 0 0
\(481\) −31.4341 −1.43327
\(482\) 17.6344 + 25.8654i 0.803224 + 1.17814i
\(483\) 0 0
\(484\) 15.7391 40.1004i 0.715412 1.82274i
\(485\) 31.1988i 1.41667i
\(486\) 0 0
\(487\) −26.8879 −1.21841 −0.609203 0.793014i \(-0.708511\pi\)
−0.609203 + 0.793014i \(0.708511\pi\)
\(488\) 2.60581 + 11.4182i 0.117960 + 0.516879i
\(489\) 0 0
\(490\) 2.95186 2.01251i 0.133352 0.0909158i
\(491\) 6.00142i 0.270840i 0.990788 + 0.135420i \(0.0432384\pi\)
−0.990788 + 0.135420i \(0.956762\pi\)
\(492\) 0 0
\(493\) 45.9252i 2.06837i
\(494\) −17.7612 26.0514i −0.799114 1.17211i
\(495\) 0 0
\(496\) −19.7873 18.3613i −0.888475 0.824445i
\(497\) −4.93014 −0.221147
\(498\) 0 0
\(499\) 18.3124i 0.819777i 0.912136 + 0.409888i \(0.134432\pi\)
−0.912136 + 0.409888i \(0.865568\pi\)
\(500\) −17.0168 6.67897i −0.761016 0.298693i
\(501\) 0 0
\(502\) 9.27978 6.32672i 0.414177 0.282375i
\(503\) −6.95874 −0.310275 −0.155137 0.987893i \(-0.549582\pi\)
−0.155137 + 0.987893i \(0.549582\pi\)
\(504\) 0 0
\(505\) 23.5879 1.04965
\(506\) −3.59754 + 2.45271i −0.159930 + 0.109036i
\(507\) 0 0
\(508\) 12.8682 32.7858i 0.570932 1.45463i
\(509\) 15.2426i 0.675618i 0.941215 + 0.337809i \(0.109686\pi\)
−0.941215 + 0.337809i \(0.890314\pi\)
\(510\) 0 0
\(511\) 8.66798 0.383449
\(512\) 17.6920 14.1065i 0.781882 0.623426i
\(513\) 0 0
\(514\) 5.59644 + 8.20862i 0.246848 + 0.362067i
\(515\) 18.4112i 0.811295i
\(516\) 0 0
\(517\) 27.5998i 1.21384i
\(518\) 12.0016 8.18239i 0.527320 0.359513i
\(519\) 0 0
\(520\) −21.3196 + 4.86545i −0.934927 + 0.213364i
\(521\) −13.0764 −0.572887 −0.286444 0.958097i \(-0.592473\pi\)
−0.286444 + 0.958097i \(0.592473\pi\)
\(522\) 0 0
\(523\) 23.9123i 1.04561i 0.852452 + 0.522806i \(0.175115\pi\)
−0.852452 + 0.522806i \(0.824885\pi\)
\(524\) −20.0231 7.85891i −0.874713 0.343318i
\(525\) 0 0
\(526\) 15.5103 + 22.7498i 0.676279 + 0.991939i
\(527\) −37.1116 −1.61661
\(528\) 0 0
\(529\) −22.7087 −0.987334
\(530\) −22.4033 32.8603i −0.973138 1.42736i
\(531\) 0 0
\(532\) 13.5625 + 5.32317i 0.588008 + 0.230789i
\(533\) 17.0887i 0.740193i
\(534\) 0 0
\(535\) −18.4713 −0.798583
\(536\) 3.75287 + 16.4445i 0.162099 + 0.710293i
\(537\) 0 0
\(538\) −18.0248 + 12.2889i −0.777104 + 0.529810i
\(539\) 5.70432i 0.245702i
\(540\) 0 0
\(541\) 13.9717i 0.600689i 0.953831 + 0.300345i \(0.0971017\pi\)
−0.953831 + 0.300345i \(0.902898\pi\)
\(542\) −5.80115 8.50889i −0.249181 0.365488i
\(543\) 0 0
\(544\) 4.63788 30.7608i 0.198847 1.31886i
\(545\) 40.2504 1.72414
\(546\) 0 0
\(547\) 21.5760i 0.922522i −0.887264 0.461261i \(-0.847397\pi\)
0.887264 0.461261i \(-0.152603\pi\)
\(548\) 1.14294 2.91200i 0.0488238 0.124394i
\(549\) 0 0
\(550\) 9.21051 6.27950i 0.392738 0.267759i
\(551\) −60.8371 −2.59175
\(552\) 0 0
\(553\) 12.0532 0.512553
\(554\) −2.84467 + 1.93942i −0.120858 + 0.0823983i
\(555\) 0 0
\(556\) 20.9870 + 8.23723i 0.890047 + 0.349337i
\(557\) 0.679074i 0.0287733i 0.999897 + 0.0143866i \(0.00457957\pi\)
−0.999897 + 0.0143866i \(0.995420\pi\)
\(558\) 0 0
\(559\) 12.1908 0.515615
\(560\) 6.87336 7.40718i 0.290452 0.313010i
\(561\) 0 0
\(562\) 14.4635 + 21.2145i 0.610106 + 0.894878i
\(563\) 15.8429i 0.667698i 0.942626 + 0.333849i \(0.108348\pi\)
−0.942626 + 0.333849i \(0.891652\pi\)
\(564\) 0 0
\(565\) 17.4678i 0.734877i
\(566\) −36.5629 + 24.9277i −1.53686 + 1.04779i
\(567\) 0 0
\(568\) −13.5950 + 3.10258i −0.570434 + 0.130182i
\(569\) −3.24267 −0.135940 −0.0679698 0.997687i \(-0.521652\pi\)
−0.0679698 + 0.997687i \(0.521652\pi\)
\(570\) 0 0
\(571\) 1.38251i 0.0578563i −0.999581 0.0289281i \(-0.990791\pi\)
0.999581 0.0289281i \(-0.00920939\pi\)
\(572\) −12.7567 + 32.5018i −0.533385 + 1.35897i
\(573\) 0 0
\(574\) −4.44823 6.52448i −0.185665 0.272326i
\(575\) −0.745822 −0.0311029
\(576\) 0 0
\(577\) −7.57598 −0.315392 −0.157696 0.987488i \(-0.550407\pi\)
−0.157696 + 0.987488i \(0.550407\pi\)
\(578\) −10.5490 15.4729i −0.438782 0.643587i
\(579\) 0 0
\(580\) −15.4159 + 39.2769i −0.640110 + 1.63089i
\(581\) 5.83393i 0.242032i
\(582\) 0 0
\(583\) −63.5007 −2.62993
\(584\) 23.9022 5.45484i 0.989080 0.225723i
\(585\) 0 0
\(586\) 21.4323 14.6120i 0.885358 0.603615i
\(587\) 5.03970i 0.208011i −0.994577 0.104005i \(-0.966834\pi\)
0.994577 0.104005i \(-0.0331659\pi\)
\(588\) 0 0
\(589\) 49.1618i 2.02568i
\(590\) −20.4565 30.0048i −0.842183 1.23528i
\(591\) 0 0
\(592\) 27.9455 30.1159i 1.14855 1.23776i
\(593\) 7.94121 0.326106 0.163053 0.986617i \(-0.447866\pi\)
0.163053 + 0.986617i \(0.447866\pi\)
\(594\) 0 0
\(595\) 13.8924i 0.569532i
\(596\) −12.0780 4.74051i −0.494733 0.194179i
\(597\) 0 0
\(598\) 1.93014 1.31592i 0.0789291 0.0538119i
\(599\) 33.0131 1.34888 0.674439 0.738331i \(-0.264386\pi\)
0.674439 + 0.738331i \(0.264386\pi\)
\(600\) 0 0
\(601\) 40.4038 1.64810 0.824052 0.566513i \(-0.191708\pi\)
0.824052 + 0.566513i \(0.191708\pi\)
\(602\) −4.65445 + 3.17329i −0.189701 + 0.129334i
\(603\) 0 0
\(604\) 0.280101 0.713648i 0.0113972 0.0290379i
\(605\) 54.4131i 2.21221i
\(606\) 0 0
\(607\) 0.544975 0.0221199 0.0110599 0.999939i \(-0.496479\pi\)
0.0110599 + 0.999939i \(0.496479\pi\)
\(608\) 40.7489 + 6.14380i 1.65258 + 0.249164i
\(609\) 0 0
\(610\) 8.33328 + 12.2229i 0.337405 + 0.494892i
\(611\) 14.8077i 0.599056i
\(612\) 0 0
\(613\) 2.75425i 0.111243i −0.998452 0.0556215i \(-0.982286\pi\)
0.998452 0.0556215i \(-0.0177140\pi\)
\(614\) 28.7227 19.5824i 1.15915 0.790283i
\(615\) 0 0
\(616\) −3.58978 15.7298i −0.144636 0.633773i
\(617\) −32.6720 −1.31533 −0.657664 0.753312i \(-0.728455\pi\)
−0.657664 + 0.753312i \(0.728455\pi\)
\(618\) 0 0
\(619\) 10.4789i 0.421183i 0.977574 + 0.210591i \(0.0675389\pi\)
−0.977574 + 0.210591i \(0.932461\pi\)
\(620\) −31.7392 12.4574i −1.27468 0.500301i
\(621\) 0 0
\(622\) 5.53867 + 8.12390i 0.222081 + 0.325739i
\(623\) 9.28810 0.372120
\(624\) 0 0
\(625\) −29.9997 −1.19999
\(626\) 7.81904 + 11.4687i 0.312512 + 0.458380i
\(627\) 0 0
\(628\) 16.1349 + 6.33281i 0.643852 + 0.252707i
\(629\) 56.4832i 2.25213i
\(630\) 0 0
\(631\) −7.94128 −0.316138 −0.158069 0.987428i \(-0.550527\pi\)
−0.158069 + 0.987428i \(0.550527\pi\)
\(632\) 33.2370 7.58518i 1.32210 0.301722i
\(633\) 0 0
\(634\) −7.82055 + 5.33185i −0.310594 + 0.211755i
\(635\) 44.4878i 1.76544i
\(636\) 0 0
\(637\) 3.06046i 0.121260i
\(638\) 37.9503 + 55.6639i 1.50247 + 2.20376i
\(639\) 0 0
\(640\) 14.2921 24.7510i 0.564944 0.978369i
\(641\) −17.5222 −0.692084 −0.346042 0.938219i \(-0.612475\pi\)
−0.346042 + 0.938219i \(0.612475\pi\)
\(642\) 0 0
\(643\) 34.7998i 1.37237i −0.727426 0.686186i \(-0.759284\pi\)
0.727426 0.686186i \(-0.240716\pi\)
\(644\) −0.394391 + 1.00484i −0.0155412 + 0.0395962i
\(645\) 0 0
\(646\) 46.8111 31.9146i 1.84176 1.25566i
\(647\) −24.4054 −0.959474 −0.479737 0.877412i \(-0.659268\pi\)
−0.479737 + 0.877412i \(0.659268\pi\)
\(648\) 0 0
\(649\) −57.9827 −2.27602
\(650\) −4.94158 + 3.36905i −0.193825 + 0.132145i
\(651\) 0 0
\(652\) 46.6869 + 18.3243i 1.82840 + 0.717633i
\(653\) 20.9374i 0.819345i 0.912233 + 0.409673i \(0.134357\pi\)
−0.912233 + 0.409673i \(0.865643\pi\)
\(654\) 0 0
\(655\) −27.1698 −1.06161
\(656\) −16.3720 15.1921i −0.639220 0.593153i
\(657\) 0 0
\(658\) −3.85449 5.65360i −0.150264 0.220400i
\(659\) 27.6061i 1.07538i −0.843143 0.537690i \(-0.819297\pi\)
0.843143 0.537690i \(-0.180703\pi\)
\(660\) 0 0
\(661\) 31.2679i 1.21618i 0.793868 + 0.608090i \(0.208064\pi\)
−0.793868 + 0.608090i \(0.791936\pi\)
\(662\) 2.46453 1.68025i 0.0957865 0.0653049i
\(663\) 0 0
\(664\) 3.67134 + 16.0872i 0.142476 + 0.624305i
\(665\) 18.4032 0.713647
\(666\) 0 0
\(667\) 4.50739i 0.174527i
\(668\) −6.39677 + 16.2978i −0.247498 + 0.630582i
\(669\) 0 0
\(670\) 12.0015 + 17.6034i 0.463660 + 0.680078i
\(671\) 23.6201 0.911846
\(672\) 0 0
\(673\) 18.7023 0.720923 0.360461 0.932774i \(-0.382619\pi\)
0.360461 + 0.932774i \(0.382619\pi\)
\(674\) 4.41304 + 6.47287i 0.169984 + 0.249326i
\(675\) 0 0
\(676\) −2.65514 + 6.76481i −0.102121 + 0.260185i
\(677\) 1.58757i 0.0610152i −0.999535 0.0305076i \(-0.990288\pi\)
0.999535 0.0305076i \(-0.00971238\pi\)
\(678\) 0 0
\(679\) 12.3500 0.473948
\(680\) −8.74260 38.3087i −0.335264 1.46907i
\(681\) 0 0
\(682\) −44.9814 + 30.6672i −1.72243 + 1.17431i
\(683\) 34.1798i 1.30785i 0.756557 + 0.653927i \(0.226880\pi\)
−0.756557 + 0.653927i \(0.773120\pi\)
\(684\) 0 0
\(685\) 3.95135i 0.150974i
\(686\) −0.796644 1.16849i −0.0304160 0.0446130i
\(687\) 0 0
\(688\) −10.8378 + 11.6795i −0.413187 + 0.445278i
\(689\) 34.0691 1.29793
\(690\) 0 0
\(691\) 39.5718i 1.50538i −0.658373 0.752692i \(-0.728755\pi\)
0.658373 0.752692i \(-0.271245\pi\)
\(692\) −17.3097 6.79390i −0.658014 0.258265i
\(693\) 0 0
\(694\) −11.2617 + 7.67798i −0.427490 + 0.291452i
\(695\) 28.4778 1.08022
\(696\) 0 0
\(697\) −30.7062 −1.16308
\(698\) −9.40123 + 6.40952i −0.355842 + 0.242604i
\(699\) 0 0
\(700\) 1.00973 2.57261i 0.0381642 0.0972356i
\(701\) 30.2500i 1.14253i −0.820767 0.571263i \(-0.806454\pi\)
0.820767 0.571263i \(-0.193546\pi\)
\(702\) 0 0
\(703\) 74.8233 2.82202
\(704\) −19.7978 41.1164i −0.746159 1.54963i
\(705\) 0 0
\(706\) −21.7305 31.8734i −0.817837 1.19957i
\(707\) 9.33719i 0.351161i
\(708\) 0 0
\(709\) 51.5735i 1.93688i 0.249244 + 0.968441i \(0.419818\pi\)
−0.249244 + 0.968441i \(0.580182\pi\)
\(710\) −14.5531 + 9.92194i −0.546168 + 0.372364i
\(711\) 0 0
\(712\) 25.6122 5.84509i 0.959858 0.219054i
\(713\) 3.64237 0.136408
\(714\) 0 0
\(715\) 44.1025i 1.64934i
\(716\) −14.2515 5.59359i −0.532603 0.209042i
\(717\) 0 0
\(718\) 5.86659 + 8.60488i 0.218939 + 0.321131i
\(719\) −11.2028 −0.417795 −0.208898 0.977938i \(-0.566988\pi\)
−0.208898 + 0.977938i \(0.566988\pi\)
\(720\) 0 0
\(721\) −7.28802 −0.271420
\(722\) 27.1411 + 39.8094i 1.01009 + 1.48155i
\(723\) 0 0
\(724\) −4.66222 1.82989i −0.173270 0.0680072i
\(725\) 11.5399i 0.428583i
\(726\) 0 0
\(727\) −0.814724 −0.0302164 −0.0151082 0.999886i \(-0.504809\pi\)
−0.0151082 + 0.999886i \(0.504809\pi\)
\(728\) 1.92597 + 8.43930i 0.0713813 + 0.312781i
\(729\) 0 0
\(730\) 25.5867 17.4444i 0.947005 0.645645i
\(731\) 21.9053i 0.810197i
\(732\) 0 0
\(733\) 12.7283i 0.470131i −0.971980 0.235066i \(-0.924470\pi\)
0.971980 0.235066i \(-0.0755305\pi\)
\(734\) −17.4263 25.5602i −0.643217 0.943444i
\(735\) 0 0
\(736\) −0.455191 + 3.01906i −0.0167786 + 0.111284i
\(737\) 34.0176 1.25305
\(738\) 0 0
\(739\) 9.13395i 0.335998i −0.985787 0.167999i \(-0.946269\pi\)
0.985787 0.167999i \(-0.0537305\pi\)
\(740\) 18.9599 48.3066i 0.696981 1.77578i
\(741\) 0 0
\(742\) −13.0076 + 8.86828i −0.477525 + 0.325565i
\(743\) −15.4112 −0.565383 −0.282692 0.959211i \(-0.591227\pi\)
−0.282692 + 0.959211i \(0.591227\pi\)
\(744\) 0 0
\(745\) −16.3889 −0.600442
\(746\) −10.5059 + 7.16267i −0.384649 + 0.262244i
\(747\) 0 0
\(748\) −58.4017 22.9222i −2.13538 0.838119i
\(749\) 7.31179i 0.267167i
\(750\) 0 0
\(751\) 40.7526 1.48708 0.743542 0.668690i \(-0.233144\pi\)
0.743542 + 0.668690i \(0.233144\pi\)
\(752\) −14.1867 13.1643i −0.517337 0.480053i
\(753\) 0 0
\(754\) −20.3609 29.8646i −0.741501 1.08760i
\(755\) 0.968366i 0.0352424i
\(756\) 0 0
\(757\) 26.0085i 0.945296i 0.881251 + 0.472648i \(0.156702\pi\)
−0.881251 + 0.472648i \(0.843298\pi\)
\(758\) 33.7885 23.0362i 1.22726 0.836712i
\(759\) 0 0
\(760\) 50.7475 11.5813i 1.84080 0.420099i
\(761\) −10.3686 −0.375861 −0.187931 0.982182i \(-0.560178\pi\)
−0.187931 + 0.982182i \(0.560178\pi\)
\(762\) 0 0
\(763\) 15.9330i 0.576814i
\(764\) −2.34287 + 5.96922i −0.0847620 + 0.215959i
\(765\) 0 0
\(766\) −9.99027 14.6533i −0.360963 0.529446i
\(767\) 31.1086 1.12327
\(768\) 0 0
\(769\) −31.7525 −1.14502 −0.572512 0.819896i \(-0.694031\pi\)
−0.572512 + 0.819896i \(0.694031\pi\)
\(770\) −11.4800 16.8384i −0.413710 0.606813i
\(771\) 0 0
\(772\) −8.00459 + 20.3943i −0.288091 + 0.734006i
\(773\) 16.3614i 0.588478i −0.955732 0.294239i \(-0.904934\pi\)
0.955732 0.294239i \(-0.0950662\pi\)
\(774\) 0 0
\(775\) −9.32530 −0.334975
\(776\) 34.0554 7.77194i 1.22252 0.278997i
\(777\) 0 0
\(778\) 8.76801 5.97781i 0.314348 0.214315i
\(779\) 40.6765i 1.45739i
\(780\) 0 0
\(781\) 28.1231i 1.00632i
\(782\) 2.36454 + 3.46821i 0.0845558 + 0.124023i
\(783\) 0 0
\(784\) −2.93211 2.72080i −0.104718 0.0971713i
\(785\) 21.8938 0.781422
\(786\) 0