Properties

Label 300.2.e.e.251.8
Level $300$
Weight $2$
Character 300.251
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4521217600.1
Defining polynomial: \(x^{8} + x^{6} - 2 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.8
Root \(-1.29437 + 0.569745i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.e.251.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +O(q^{10})\) \(q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +3.36131 q^{11} +(3.40201 - 0.652949i) q^{12} -3.70156 q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636i q^{17} +(-0.222237 - 4.23682i) q^{18} -0.440172i q^{19} +(3.70156 + 2.27898i) q^{21} +(4.35078 + 1.91509i) q^{22} -5.17748 q^{23} +(4.77547 + 1.09312i) q^{24} +(-4.79119 - 2.10895i) q^{26} +(-5.17748 - 0.440172i) q^{27} +(-3.70156 + 3.39001i) q^{28} -2.27898i q^{29} +3.39001i q^{31} +(-2.72424 + 4.95767i) q^{32} +(3.05234 - 4.95767i) q^{33} +(4.35078 - 9.88427i) q^{34} +(2.12625 - 5.61062i) q^{36} -7.40312 q^{37} +(0.250786 - 0.569745i) q^{38} +(-3.36131 + 5.45951i) q^{39} +3.07840i q^{41} +(3.49275 + 5.05879i) q^{42} +8.40935i q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} +3.63232 q^{47} +(5.55842 + 4.13570i) q^{48} +0.701562 q^{49} +(-11.2630 - 6.93443i) q^{51} +(-5.00000 - 5.45951i) q^{52} +2.27898i q^{53} +(-6.45078 - 3.51959i) q^{54} +(-6.72263 + 2.27898i) q^{56} +(-0.649219 - 0.399712i) q^{57} +(1.29844 - 2.94984i) q^{58} -5.70156 q^{61} +(-1.93144 + 4.38793i) q^{62} +(6.72263 - 3.39001i) q^{63} +(-6.35078 + 4.86493i) q^{64} +(6.77547 - 4.67800i) q^{66} -5.45951i q^{67} +(11.2630 - 10.3151i) q^{68} +(-4.70156 + 7.63636i) q^{69} +12.4421 q^{71} +(5.94877 - 6.05079i) q^{72} +1.29844 q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579i q^{77} +(-7.46131 + 5.15153i) q^{78} -5.01934i q^{79} +(-5.35078 + 7.23665i) q^{81} +(-1.75391 + 3.98459i) q^{82} +1.81616 q^{83} +(1.63869 + 8.53791i) q^{84} +(-4.79119 + 10.8848i) q^{86} +(-3.36131 - 2.06950i) q^{87} +(3.05234 + 9.00393i) q^{88} -5.35738i q^{89} -9.28970i q^{91} +(-6.99364 - 7.63636i) q^{92} +(5.00000 + 3.07840i) q^{93} +(4.70156 + 2.06950i) q^{94} +(4.83834 + 8.52000i) q^{96} +11.1047 q^{97} +(0.908080 + 0.399712i) q^{98} +(-4.54040 - 9.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} + O(q^{10}) \) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} + 11q^{12} - 4q^{13} + 10q^{16} - 7q^{18} + 4q^{21} + 22q^{22} + 13q^{24} - 4q^{28} - 14q^{33} + 22q^{34} - 21q^{36} - 8q^{37} - 36q^{42} - 28q^{46} + 15q^{48} - 20q^{49} - 40q^{52} - 28q^{54} - 18q^{57} + 36q^{58} - 20q^{61} - 38q^{64} + 29q^{66} - 12q^{69} + 51q^{72} + 36q^{73} + 18q^{76} - 22q^{78} - 30q^{81} + 50q^{82} + 40q^{84} - 14q^{88} + 40q^{93} + 12q^{94} - 39q^{96} + 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29437 + 0.569745i 0.915257 + 0.402871i
\(3\) 0.908080 1.47492i 0.524280 0.851546i
\(4\) 1.35078 + 1.47492i 0.675391 + 0.737460i
\(5\) 0 0
\(6\) 2.01572 1.39172i 0.822914 0.568166i
\(7\) 2.50967i 0.948566i 0.880373 + 0.474283i \(0.157293\pi\)
−0.880373 + 0.474283i \(0.842707\pi\)
\(8\) 0.908080 + 2.67869i 0.321055 + 0.947061i
\(9\) −1.35078 2.67869i −0.450260 0.892897i
\(10\) 0 0
\(11\) 3.36131 1.01347 0.506737 0.862101i \(-0.330851\pi\)
0.506737 + 0.862101i \(0.330851\pi\)
\(12\) 3.40201 0.652949i 0.982075 0.188490i
\(13\) −3.70156 −1.02663 −0.513314 0.858201i \(-0.671582\pi\)
−0.513314 + 0.858201i \(0.671582\pi\)
\(14\) −1.42987 + 3.24844i −0.382149 + 0.868181i
\(15\) 0 0
\(16\) −0.350781 + 3.98459i −0.0876953 + 0.996147i
\(17\) 7.63636i 1.85209i −0.377413 0.926045i \(-0.623186\pi\)
0.377413 0.926045i \(-0.376814\pi\)
\(18\) −0.222237 4.23682i −0.0523818 0.998627i
\(19\) 0.440172i 0.100982i −0.998725 0.0504912i \(-0.983921\pi\)
0.998725 0.0504912i \(-0.0160787\pi\)
\(20\) 0 0
\(21\) 3.70156 + 2.27898i 0.807747 + 0.497314i
\(22\) 4.35078 + 1.91509i 0.927590 + 0.408299i
\(23\) −5.17748 −1.07958 −0.539789 0.841800i \(-0.681496\pi\)
−0.539789 + 0.841800i \(0.681496\pi\)
\(24\) 4.77547 + 1.09312i 0.974788 + 0.223132i
\(25\) 0 0
\(26\) −4.79119 2.10895i −0.939629 0.413599i
\(27\) −5.17748 0.440172i −0.996406 0.0847112i
\(28\) −3.70156 + 3.39001i −0.699529 + 0.640652i
\(29\) 2.27898i 0.423196i −0.977357 0.211598i \(-0.932133\pi\)
0.977357 0.211598i \(-0.0678668\pi\)
\(30\) 0 0
\(31\) 3.39001i 0.608864i 0.952534 + 0.304432i \(0.0984667\pi\)
−0.952534 + 0.304432i \(0.901533\pi\)
\(32\) −2.72424 + 4.95767i −0.481582 + 0.876401i
\(33\) 3.05234 4.95767i 0.531345 0.863020i
\(34\) 4.35078 9.88427i 0.746153 1.69514i
\(35\) 0 0
\(36\) 2.12625 5.61062i 0.354375 0.935104i
\(37\) −7.40312 −1.21707 −0.608533 0.793529i \(-0.708242\pi\)
−0.608533 + 0.793529i \(0.708242\pi\)
\(38\) 0.250786 0.569745i 0.0406828 0.0924249i
\(39\) −3.36131 + 5.45951i −0.538241 + 0.874221i
\(40\) 0 0
\(41\) 3.07840i 0.480766i 0.970678 + 0.240383i \(0.0772730\pi\)
−0.970678 + 0.240383i \(0.922727\pi\)
\(42\) 3.49275 + 5.05879i 0.538943 + 0.780588i
\(43\) 8.40935i 1.28241i 0.767368 + 0.641207i \(0.221566\pi\)
−0.767368 + 0.641207i \(0.778434\pi\)
\(44\) 4.54040 + 4.95767i 0.684491 + 0.747397i
\(45\) 0 0
\(46\) −6.70156 2.94984i −0.988091 0.434930i
\(47\) 3.63232 0.529828 0.264914 0.964272i \(-0.414656\pi\)
0.264914 + 0.964272i \(0.414656\pi\)
\(48\) 5.55842 + 4.13570i 0.802288 + 0.596937i
\(49\) 0.701562 0.100223
\(50\) 0 0
\(51\) −11.2630 6.93443i −1.57714 0.971014i
\(52\) −5.00000 5.45951i −0.693375 0.757098i
\(53\) 2.27898i 0.313042i 0.987675 + 0.156521i \(0.0500279\pi\)
−0.987675 + 0.156521i \(0.949972\pi\)
\(54\) −6.45078 3.51959i −0.877839 0.478955i
\(55\) 0 0
\(56\) −6.72263 + 2.27898i −0.898349 + 0.304542i
\(57\) −0.649219 0.399712i −0.0859911 0.0529431i
\(58\) 1.29844 2.94984i 0.170493 0.387333i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −5.70156 −0.730010 −0.365005 0.931006i \(-0.618933\pi\)
−0.365005 + 0.931006i \(0.618933\pi\)
\(62\) −1.93144 + 4.38793i −0.245294 + 0.557267i
\(63\) 6.72263 3.39001i 0.846972 0.427102i
\(64\) −6.35078 + 4.86493i −0.793848 + 0.608117i
\(65\) 0 0
\(66\) 6.77547 4.67800i 0.834002 0.575822i
\(67\) 5.45951i 0.666985i −0.942753 0.333493i \(-0.891773\pi\)
0.942753 0.333493i \(-0.108227\pi\)
\(68\) 11.2630 10.3151i 1.36584 1.25088i
\(69\) −4.70156 + 7.63636i −0.566002 + 0.919310i
\(70\) 0 0
\(71\) 12.4421 1.47661 0.738304 0.674468i \(-0.235627\pi\)
0.738304 + 0.674468i \(0.235627\pi\)
\(72\) 5.94877 6.05079i 0.701070 0.713093i
\(73\) 1.29844 0.151971 0.0759853 0.997109i \(-0.475790\pi\)
0.0759853 + 0.997109i \(0.475790\pi\)
\(74\) −9.58237 4.21789i −1.11393 0.490320i
\(75\) 0 0
\(76\) 0.649219 0.594576i 0.0744705 0.0682026i
\(77\) 8.43579i 0.961347i
\(78\) −7.46131 + 5.15153i −0.844827 + 0.583296i
\(79\) 5.01934i 0.564720i −0.959309 0.282360i \(-0.908883\pi\)
0.959309 0.282360i \(-0.0911172\pi\)
\(80\) 0 0
\(81\) −5.35078 + 7.23665i −0.594531 + 0.804073i
\(82\) −1.75391 + 3.98459i −0.193686 + 0.440024i
\(83\) 1.81616 0.199349 0.0996747 0.995020i \(-0.468220\pi\)
0.0996747 + 0.995020i \(0.468220\pi\)
\(84\) 1.63869 + 8.53791i 0.178795 + 0.931563i
\(85\) 0 0
\(86\) −4.79119 + 10.8848i −0.516647 + 1.17374i
\(87\) −3.36131 2.06950i −0.360371 0.221873i
\(88\) 3.05234 + 9.00393i 0.325381 + 0.959822i
\(89\) 5.35738i 0.567882i −0.958842 0.283941i \(-0.908358\pi\)
0.958842 0.283941i \(-0.0916419\pi\)
\(90\) 0 0
\(91\) 9.28970i 0.973825i
\(92\) −6.99364 7.63636i −0.729137 0.796146i
\(93\) 5.00000 + 3.07840i 0.518476 + 0.319216i
\(94\) 4.70156 + 2.06950i 0.484929 + 0.213452i
\(95\) 0 0
\(96\) 4.83834 + 8.52000i 0.493811 + 0.869569i
\(97\) 11.1047 1.12751 0.563755 0.825942i \(-0.309356\pi\)
0.563755 + 0.825942i \(0.309356\pi\)
\(98\) 0.908080 + 0.399712i 0.0917299 + 0.0403770i
\(99\) −4.54040 9.00393i −0.456327 0.904929i
\(100\) 0 0
\(101\) 17.5517i 1.74646i −0.487308 0.873230i \(-0.662021\pi\)
0.487308 0.873230i \(-0.337979\pi\)
\(102\) −10.6277 15.3928i −1.05229 1.52411i
\(103\) 10.9190i 1.07588i −0.842982 0.537941i \(-0.819202\pi\)
0.842982 0.537941i \(-0.180798\pi\)
\(104\) −3.36131 9.91534i −0.329604 0.972280i
\(105\) 0 0
\(106\) −1.29844 + 2.94984i −0.126115 + 0.286514i
\(107\) 6.45162 0.623702 0.311851 0.950131i \(-0.399051\pi\)
0.311851 + 0.950131i \(0.399051\pi\)
\(108\) −6.34442 8.23094i −0.610492 0.792023i
\(109\) 2.29844 0.220150 0.110075 0.993923i \(-0.464891\pi\)
0.110075 + 0.993923i \(0.464891\pi\)
\(110\) 0 0
\(111\) −6.72263 + 10.9190i −0.638084 + 1.03639i
\(112\) −10.0000 0.880344i −0.944911 0.0831847i
\(113\) 0.799423i 0.0752034i −0.999293 0.0376017i \(-0.988028\pi\)
0.999293 0.0376017i \(-0.0119718\pi\)
\(114\) −0.612595 0.887263i −0.0573748 0.0830998i
\(115\) 0 0
\(116\) 3.36131 3.07840i 0.312090 0.285823i
\(117\) 5.00000 + 9.91534i 0.462250 + 0.916674i
\(118\) 0 0
\(119\) 19.1647 1.75683
\(120\) 0 0
\(121\) 0.298438 0.0271307
\(122\) −7.37992 3.24844i −0.668147 0.294100i
\(123\) 4.54040 + 2.79544i 0.409394 + 0.252056i
\(124\) −5.00000 + 4.57917i −0.449013 + 0.411221i
\(125\) 0 0
\(126\) 10.6330 0.557742i 0.947263 0.0496876i
\(127\) 12.6797i 1.12514i 0.826749 + 0.562571i \(0.190188\pi\)
−0.826749 + 0.562571i \(0.809812\pi\)
\(128\) −10.9920 + 2.67869i −0.971567 + 0.236765i
\(129\) 12.4031 + 7.63636i 1.09203 + 0.672344i
\(130\) 0 0
\(131\) −5.71949 −0.499714 −0.249857 0.968283i \(-0.580384\pi\)
−0.249857 + 0.968283i \(0.580384\pi\)
\(132\) 11.4352 2.19477i 0.995308 0.191030i
\(133\) 1.10469 0.0957885
\(134\) 3.11053 7.06662i 0.268709 0.610463i
\(135\) 0 0
\(136\) 20.4555 6.93443i 1.75404 0.594623i
\(137\) 9.91534i 0.847125i 0.905867 + 0.423563i \(0.139221\pi\)
−0.905867 + 0.423563i \(0.860779\pi\)
\(138\) −10.4363 + 7.20558i −0.888400 + 0.613380i
\(139\) 2.94984i 0.250202i 0.992144 + 0.125101i \(0.0399255\pi\)
−0.992144 + 0.125101i \(0.960074\pi\)
\(140\) 0 0
\(141\) 3.29844 5.35738i 0.277779 0.451173i
\(142\) 16.1047 + 7.08883i 1.35148 + 0.594882i
\(143\) −12.4421 −1.04046
\(144\) 11.1473 4.44267i 0.928943 0.370223i
\(145\) 0 0
\(146\) 1.68066 + 0.739779i 0.139092 + 0.0612245i
\(147\) 0.637075 1.03475i 0.0525450 0.0853446i
\(148\) −10.0000 10.9190i −0.821995 0.897538i
\(149\) 15.2727i 1.25119i 0.780148 + 0.625595i \(0.215144\pi\)
−0.780148 + 0.625595i \(0.784856\pi\)
\(150\) 0 0
\(151\) 19.3284i 1.57292i 0.617641 + 0.786460i \(0.288089\pi\)
−0.617641 + 0.786460i \(0.711911\pi\)
\(152\) 1.17909 0.399712i 0.0956365 0.0324209i
\(153\) −20.4555 + 10.3151i −1.65373 + 0.833923i
\(154\) −4.80625 + 10.9190i −0.387299 + 0.879880i
\(155\) 0 0
\(156\) −12.5927 + 2.41693i −1.00823 + 0.193509i
\(157\) 11.1047 0.886250 0.443125 0.896460i \(-0.353870\pi\)
0.443125 + 0.896460i \(0.353870\pi\)
\(158\) 2.85974 6.49687i 0.227509 0.516864i
\(159\) 3.36131 + 2.06950i 0.266570 + 0.164122i
\(160\) 0 0
\(161\) 12.9937i 1.02405i
\(162\) −11.0489 + 6.31832i −0.868086 + 0.496414i
\(163\) 0.440172i 0.0344769i 0.999851 + 0.0172385i \(0.00548745\pi\)
−0.999851 + 0.0172385i \(0.994513\pi\)
\(164\) −4.54040 + 4.15825i −0.354546 + 0.324705i
\(165\) 0 0
\(166\) 2.35078 + 1.03475i 0.182456 + 0.0803120i
\(167\) 15.5324 1.20194 0.600968 0.799273i \(-0.294782\pi\)
0.600968 + 0.799273i \(0.294782\pi\)
\(168\) −2.74337 + 11.9848i −0.211656 + 0.924651i
\(169\) 0.701562 0.0539663
\(170\) 0 0
\(171\) −1.17909 + 0.594576i −0.0901669 + 0.0454684i
\(172\) −12.4031 + 11.3592i −0.945729 + 0.866130i
\(173\) 8.43579i 0.641361i 0.947187 + 0.320681i \(0.103912\pi\)
−0.947187 + 0.320681i \(0.896088\pi\)
\(174\) −3.17170 4.59378i −0.240446 0.348254i
\(175\) 0 0
\(176\) −1.17909 + 13.3935i −0.0888769 + 1.00957i
\(177\) 0 0
\(178\) 3.05234 6.93443i 0.228783 0.519758i
\(179\) −9.08080 −0.678731 −0.339365 0.940655i \(-0.610212\pi\)
−0.339365 + 0.940655i \(0.610212\pi\)
\(180\) 0 0
\(181\) 10.5078 0.781039 0.390520 0.920595i \(-0.372295\pi\)
0.390520 + 0.920595i \(0.372295\pi\)
\(182\) 5.29276 12.0243i 0.392325 0.891300i
\(183\) −5.17748 + 8.40935i −0.382730 + 0.621637i
\(184\) −4.70156 13.8689i −0.346604 1.02243i
\(185\) 0 0
\(186\) 4.71794 + 6.83331i 0.345936 + 0.501043i
\(187\) 25.6682i 1.87705i
\(188\) 4.90647 + 5.35738i 0.357841 + 0.390727i
\(189\) 1.10469 12.9937i 0.0803541 0.945156i
\(190\) 0 0
\(191\) 12.4421 0.900280 0.450140 0.892958i \(-0.351374\pi\)
0.450140 + 0.892958i \(0.351374\pi\)
\(192\) 1.40837 + 13.7846i 0.101641 + 0.994821i
\(193\) 19.8062 1.42568 0.712842 0.701324i \(-0.247407\pi\)
0.712842 + 0.701324i \(0.247407\pi\)
\(194\) 14.3736 + 6.32684i 1.03196 + 0.454241i
\(195\) 0 0
\(196\) 0.947657 + 1.03475i 0.0676898 + 0.0739106i
\(197\) 10.7148i 0.763396i −0.924287 0.381698i \(-0.875340\pi\)
0.924287 0.381698i \(-0.124660\pi\)
\(198\) −0.747009 14.2413i −0.0530876 1.01208i
\(199\) 21.0891i 1.49496i 0.664282 + 0.747482i \(0.268737\pi\)
−0.664282 + 0.747482i \(0.731263\pi\)
\(200\) 0 0
\(201\) −8.05234 4.95767i −0.567968 0.349687i
\(202\) 10.0000 22.7184i 0.703598 1.59846i
\(203\) 5.71949 0.401429
\(204\) −4.98615 25.9790i −0.349101 1.81889i
\(205\) 0 0
\(206\) 6.22106 14.1332i 0.433442 0.984709i
\(207\) 6.99364 + 13.8689i 0.486091 + 0.963952i
\(208\) 1.29844 14.7492i 0.0900305 1.02267i
\(209\) 1.47956i 0.102343i
\(210\) 0 0
\(211\) 18.1392i 1.24876i −0.781123 0.624378i \(-0.785353\pi\)
0.781123 0.624378i \(-0.214647\pi\)
\(212\) −3.36131 + 3.07840i −0.230856 + 0.211426i
\(213\) 11.2984 18.3511i 0.774156 1.25740i
\(214\) 8.35078 + 3.67578i 0.570848 + 0.251271i
\(215\) 0 0
\(216\) −3.52248 14.2686i −0.239674 0.970853i
\(217\) −8.50781 −0.577548
\(218\) 2.97503 + 1.30952i 0.201494 + 0.0886921i
\(219\) 1.17909 1.91509i 0.0796752 0.129410i
\(220\) 0 0
\(221\) 28.2665i 1.90141i
\(222\) −14.9226 + 10.3031i −1.00154 + 0.691496i
\(223\) 21.0891i 1.41223i −0.708098 0.706114i \(-0.750447\pi\)
0.708098 0.706114i \(-0.249553\pi\)
\(224\) −12.4421 6.83694i −0.831324 0.456812i
\(225\) 0 0
\(226\) 0.455467 1.03475i 0.0302972 0.0688304i
\(227\) −22.2551 −1.47712 −0.738560 0.674188i \(-0.764494\pi\)
−0.738560 + 0.674188i \(0.764494\pi\)
\(228\) −0.287410 1.49747i −0.0190342 0.0991723i
\(229\) 2.29844 0.151885 0.0759425 0.997112i \(-0.475803\pi\)
0.0759425 + 0.997112i \(0.475803\pi\)
\(230\) 0 0
\(231\) 12.4421 + 7.66037i 0.818631 + 0.504015i
\(232\) 6.10469 2.06950i 0.400792 0.135869i
\(233\) 8.43579i 0.552647i 0.961065 + 0.276323i \(0.0891161\pi\)
−0.961065 + 0.276323i \(0.910884\pi\)
\(234\) 0.822625 + 15.6828i 0.0537767 + 1.02522i
\(235\) 0 0
\(236\) 0 0
\(237\) −7.40312 4.55796i −0.480885 0.296071i
\(238\) 24.8062 + 10.9190i 1.60795 + 0.707775i
\(239\) −25.8874 −1.67452 −0.837258 0.546809i \(-0.815842\pi\)
−0.837258 + 0.546809i \(0.815842\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 0.386289 + 0.170034i 0.0248316 + 0.0109302i
\(243\) 5.81455 + 14.4634i 0.373004 + 0.927830i
\(244\) −7.70156 8.40935i −0.493042 0.538354i
\(245\) 0 0
\(246\) 4.28427 + 6.20520i 0.273155 + 0.395629i
\(247\) 1.62932i 0.103671i
\(248\) −9.08080 + 3.07840i −0.576631 + 0.195479i
\(249\) 1.64922 2.67869i 0.104515 0.169755i
\(250\) 0 0
\(251\) −22.5261 −1.42183 −0.710916 0.703277i \(-0.751719\pi\)
−0.710916 + 0.703277i \(0.751719\pi\)
\(252\) 14.0808 + 5.33618i 0.887007 + 0.336148i
\(253\) −17.4031 −1.09413
\(254\) −7.22420 + 16.4122i −0.453287 + 1.02979i
\(255\) 0 0
\(256\) −15.7539 2.79544i −0.984619 0.174715i
\(257\) 4.55796i 0.284318i −0.989844 0.142159i \(-0.954596\pi\)
0.989844 0.142159i \(-0.0454044\pi\)
\(258\) 11.7034 + 16.9509i 0.728624 + 1.05532i
\(259\) 18.5794i 1.15447i
\(260\) 0 0
\(261\) −6.10469 + 3.07840i −0.377871 + 0.190548i
\(262\) −7.40312 3.25865i −0.457367 0.201320i
\(263\) 18.6227 1.14833 0.574164 0.818741i \(-0.305327\pi\)
0.574164 + 0.818741i \(0.305327\pi\)
\(264\) 16.0518 + 3.67432i 0.987923 + 0.226139i
\(265\) 0 0
\(266\) 1.42987 + 0.629390i 0.0876710 + 0.0385904i
\(267\) −7.90172 4.86493i −0.483577 0.297729i
\(268\) 8.05234 7.37460i 0.491875 0.450476i
\(269\) 8.43579i 0.514339i −0.966366 0.257170i \(-0.917210\pi\)
0.966366 0.257170i \(-0.0827899\pi\)
\(270\) 0 0
\(271\) 9.15833i 0.556329i −0.960533 0.278165i \(-0.910274\pi\)
0.960533 0.278165i \(-0.0897260\pi\)
\(272\) 30.4278 + 2.67869i 1.84495 + 0.162420i
\(273\) −13.7016 8.43579i −0.829256 0.510557i
\(274\) −5.64922 + 12.8341i −0.341282 + 0.775337i
\(275\) 0 0
\(276\) −17.6138 + 3.38063i −1.06023 + 0.203490i
\(277\) −8.89531 −0.534468 −0.267234 0.963632i \(-0.586110\pi\)
−0.267234 + 0.963632i \(0.586110\pi\)
\(278\) −1.68066 + 3.81818i −0.100799 + 0.228999i
\(279\) 9.08080 4.57917i 0.543653 0.274147i
\(280\) 0 0
\(281\) 17.5517i 1.04705i 0.852011 + 0.523524i \(0.175383\pi\)
−0.852011 + 0.523524i \(0.824617\pi\)
\(282\) 7.32174 5.05516i 0.436003 0.301030i
\(283\) 16.3785i 0.973603i 0.873513 + 0.486801i \(0.161836\pi\)
−0.873513 + 0.486801i \(0.838164\pi\)
\(284\) 16.8066 + 18.3511i 0.997287 + 1.08894i
\(285\) 0 0
\(286\) −16.1047 7.08883i −0.952290 0.419172i
\(287\) −7.72577 −0.456038
\(288\) 16.9599 + 0.600671i 0.999373 + 0.0353949i
\(289\) −41.3141 −2.43024
\(290\) 0 0
\(291\) 10.0839 16.3785i 0.591131 0.960126i
\(292\) 1.75391 + 1.91509i 0.102640 + 0.112072i
\(293\) 21.4295i 1.25193i −0.779852 0.625963i \(-0.784706\pi\)
0.779852 0.625963i \(-0.215294\pi\)
\(294\) 1.41415 0.976376i 0.0824750 0.0569434i
\(295\) 0 0
\(296\) −6.72263 19.8307i −0.390745 1.15264i
\(297\) −17.4031 1.47956i −1.00983 0.0858526i
\(298\) −8.70156 + 19.7685i −0.504068 + 1.14516i
\(299\) 19.1647 1.10833
\(300\) 0 0
\(301\) −21.1047 −1.21645
\(302\) −11.0122 + 25.0180i −0.633683 + 1.43963i
\(303\) −25.8874 15.9384i −1.48719 0.915635i
\(304\) 1.75391 + 0.154404i 0.100593 + 0.00885568i
\(305\) 0 0
\(306\) −32.3539 + 1.69708i −1.84955 + 0.0970159i
\(307\) 26.4172i 1.50771i 0.657041 + 0.753855i \(0.271808\pi\)
−0.657041 + 0.753855i \(0.728192\pi\)
\(308\) −12.4421 + 11.3949i −0.708955 + 0.649285i
\(309\) −16.1047 9.91534i −0.916164 0.564064i
\(310\) 0 0
\(311\) −13.4453 −0.762411 −0.381205 0.924490i \(-0.624491\pi\)
−0.381205 + 0.924490i \(0.624491\pi\)
\(312\) −17.6767 4.04625i −1.00075 0.229074i
\(313\) 16.2984 0.921242 0.460621 0.887597i \(-0.347627\pi\)
0.460621 + 0.887597i \(0.347627\pi\)
\(314\) 14.3736 + 6.32684i 0.811147 + 0.357044i
\(315\) 0 0
\(316\) 7.40312 6.78003i 0.416458 0.381406i
\(317\) 16.8716i 0.947602i −0.880632 0.473801i \(-0.842882\pi\)
0.880632 0.473801i \(-0.157118\pi\)
\(318\) 3.17170 + 4.59378i 0.177860 + 0.257607i
\(319\) 7.66037i 0.428898i
\(320\) 0 0
\(321\) 5.85859 9.51563i 0.326995 0.531111i
\(322\) 7.40312 16.8187i 0.412560 0.937270i
\(323\) −3.36131 −0.187029
\(324\) −17.9012 + 1.88316i −0.994512 + 0.104620i
\(325\) 0 0
\(326\) −0.250786 + 0.569745i −0.0138897 + 0.0315553i
\(327\) 2.08717 3.39001i 0.115421 0.187468i
\(328\) −8.24609 + 2.79544i −0.455314 + 0.154352i
\(329\) 9.11592i 0.502577i
\(330\) 0 0
\(331\) 17.1275i 0.941413i −0.882290 0.470707i \(-0.843999\pi\)
0.882290 0.470707i \(-0.156001\pi\)
\(332\) 2.45323 + 2.67869i 0.134639 + 0.147012i
\(333\) 10.0000 + 19.8307i 0.547997 + 1.08672i
\(334\) 20.1047 + 8.84952i 1.10008 + 0.484224i
\(335\) 0 0
\(336\) −10.3792 + 13.9498i −0.566234 + 0.761023i
\(337\) −12.4031 −0.675641 −0.337821 0.941211i \(-0.609690\pi\)
−0.337821 + 0.941211i \(0.609690\pi\)
\(338\) 0.908080 + 0.399712i 0.0493930 + 0.0217414i
\(339\) −1.17909 0.725940i −0.0640391 0.0394277i
\(340\) 0 0
\(341\) 11.3949i 0.617069i
\(342\) −1.86493 + 0.0978226i −0.100844 + 0.00528964i
\(343\) 19.3284i 1.04363i
\(344\) −22.5261 + 7.63636i −1.21452 + 0.411725i
\(345\) 0 0
\(346\) −4.80625 + 10.9190i −0.258386 + 0.587010i
\(347\) −19.4358 −1.04337 −0.521683 0.853139i \(-0.674696\pi\)
−0.521683 + 0.853139i \(0.674696\pi\)
\(348\) −1.48806 7.75311i −0.0797682 0.415610i
\(349\) 26.2094 1.40296 0.701478 0.712691i \(-0.252524\pi\)
0.701478 + 0.712691i \(0.252524\pi\)
\(350\) 0 0
\(351\) 19.1647 + 1.62932i 1.02294 + 0.0869669i
\(352\) −9.15703 + 16.6643i −0.488071 + 0.888210i
\(353\) 26.6676i 1.41937i −0.704517 0.709687i \(-0.748836\pi\)
0.704517 0.709687i \(-0.251164\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.90172 7.23665i 0.418790 0.383542i
\(357\) 17.4031 28.2665i 0.921071 1.49602i
\(358\) −11.7539 5.17374i −0.621213 0.273441i
\(359\) −7.72577 −0.407751 −0.203875 0.978997i \(-0.565354\pi\)
−0.203875 + 0.978997i \(0.565354\pi\)
\(360\) 0 0
\(361\) 18.8062 0.989803
\(362\) 13.6010 + 5.98677i 0.714852 + 0.314658i
\(363\) 0.271006 0.440172i 0.0142241 0.0231030i
\(364\) 13.7016 12.5483i 0.718157 0.657712i
\(365\) 0 0
\(366\) −11.4927 + 7.93496i −0.600736 + 0.414767i
\(367\) 2.50967i 0.131004i 0.997852 + 0.0655018i \(0.0208648\pi\)
−0.997852 + 0.0655018i \(0.979135\pi\)
\(368\) 1.81616 20.6301i 0.0946739 1.07542i
\(369\) 8.24609 4.15825i 0.429275 0.216470i
\(370\) 0 0
\(371\) −5.71949 −0.296941
\(372\) 2.21350 + 11.5329i 0.114765 + 0.597951i
\(373\) −23.7016 −1.22722 −0.613610 0.789609i \(-0.710283\pi\)
−0.613610 + 0.789609i \(0.710283\pi\)
\(374\) 14.6243 33.2241i 0.756207 1.71798i
\(375\) 0 0
\(376\) 3.29844 + 9.72987i 0.170104 + 0.501780i
\(377\) 8.43579i 0.434465i
\(378\) 8.83300 16.1893i 0.454320 0.832688i
\(379\) 13.1199i 0.673923i 0.941518 + 0.336961i \(0.109399\pi\)
−0.941518 + 0.336961i \(0.890601\pi\)
\(380\) 0 0
\(381\) 18.7016 + 11.5142i 0.958110 + 0.589890i
\(382\) 16.1047 + 7.08883i 0.823987 + 0.362696i
\(383\) −7.26464 −0.371206 −0.185603 0.982625i \(-0.559424\pi\)
−0.185603 + 0.982625i \(0.559424\pi\)
\(384\) −6.03078 + 18.6448i −0.307757 + 0.951465i
\(385\) 0 0
\(386\) 25.6366 + 11.2845i 1.30487 + 0.574367i
\(387\) 22.5261 11.3592i 1.14506 0.577420i
\(388\) 15.0000 + 16.3785i 0.761510 + 0.831494i
\(389\) 37.3824i 1.89536i −0.319218 0.947681i \(-0.603420\pi\)
0.319218 0.947681i \(-0.396580\pi\)
\(390\) 0 0
\(391\) 39.5371i 1.99948i
\(392\) 0.637075 + 1.87927i 0.0321771 + 0.0949174i
\(393\) −5.19375 + 8.43579i −0.261990 + 0.425529i
\(394\) 6.10469 13.8689i 0.307550 0.698703i
\(395\) 0 0
\(396\) 7.14699 18.8591i 0.359150 0.947704i
\(397\) −15.9109 −0.798547 −0.399273 0.916832i \(-0.630738\pi\)
−0.399273 + 0.916832i \(0.630738\pi\)
\(398\) −12.0154 + 27.2970i −0.602277 + 1.36828i
\(399\) 1.00314 1.62932i 0.0502200 0.0815683i
\(400\) 0 0
\(401\) 9.23521i 0.461184i −0.973050 0.230592i \(-0.925934\pi\)
0.973050 0.230592i \(-0.0740663\pi\)
\(402\) −7.59809 11.0048i −0.378958 0.548871i
\(403\) 12.5483i 0.625078i
\(404\) 25.8874 23.7085i 1.28795 1.17954i
\(405\) 0 0
\(406\) 7.40312 + 3.25865i 0.367411 + 0.161724i
\(407\) −24.8842 −1.23347
\(408\) 8.34747 36.4672i 0.413261 1.80540i
\(409\) 11.2094 0.554268 0.277134 0.960831i \(-0.410615\pi\)
0.277134 + 0.960831i \(0.410615\pi\)
\(410\) 0 0
\(411\) 14.6243 + 9.00393i 0.721366 + 0.444131i
\(412\) 16.1047 14.7492i 0.793421 0.726641i
\(413\) 0 0
\(414\) 1.15063 + 21.9360i 0.0565503 + 1.07810i
\(415\) 0 0
\(416\) 10.0839 18.3511i 0.494406 0.899738i
\(417\) 4.35078 + 2.67869i 0.213059 + 0.131176i
\(418\) 0.842970 1.91509i 0.0412310 0.0936702i
\(419\) −34.9682 −1.70831 −0.854154 0.520021i \(-0.825924\pi\)
−0.854154 + 0.520021i \(0.825924\pi\)
\(420\) 0 0
\(421\) −14.2094 −0.692522 −0.346261 0.938138i \(-0.612549\pi\)
−0.346261 + 0.938138i \(0.612549\pi\)
\(422\) 10.3347 23.4788i 0.503087 1.14293i
\(423\) −4.90647 9.72987i −0.238561 0.473082i
\(424\) −6.10469 + 2.06950i −0.296470 + 0.100504i
\(425\) 0 0
\(426\) 25.0798 17.3159i 1.21512 0.838958i
\(427\) 14.3090i 0.692463i
\(428\) 8.71473 + 9.51563i 0.421242 + 0.459955i
\(429\) −11.2984 + 18.3511i −0.545494 + 0.886001i
\(430\) 0 0
\(431\) −5.71949 −0.275498 −0.137749 0.990467i \(-0.543987\pi\)
−0.137749 + 0.990467i \(0.543987\pi\)
\(432\) 3.57007 20.4757i 0.171765 0.985138i
\(433\) −7.20937 −0.346460 −0.173230 0.984881i \(-0.555420\pi\)
−0.173230 + 0.984881i \(0.555420\pi\)
\(434\) −11.0122 4.84728i −0.528605 0.232677i
\(435\) 0 0
\(436\) 3.10469 + 3.39001i 0.148688 + 0.162352i
\(437\) 2.27898i 0.109018i
\(438\) 2.61729 1.80706i 0.125059 0.0863446i
\(439\) 23.4674i 1.12004i 0.828480 + 0.560018i \(0.189206\pi\)
−0.828480 + 0.560018i \(0.810794\pi\)
\(440\) 0 0
\(441\) −0.947657 1.87927i −0.0451265 0.0894890i
\(442\) −16.1047 + 36.5872i −0.766022 + 1.74028i
\(443\) 29.7907 1.41540 0.707699 0.706514i \(-0.249733\pi\)
0.707699 + 0.706514i \(0.249733\pi\)
\(444\) −25.1855 + 4.83386i −1.19525 + 0.229405i
\(445\) 0 0
\(446\) 12.0154 27.2970i 0.568945 1.29255i
\(447\) 22.5261 + 13.8689i 1.06545 + 0.655975i
\(448\) −12.2094 15.9384i −0.576839 0.753017i
\(449\) 29.7460i 1.40380i 0.712274 + 0.701901i \(0.247665\pi\)
−0.712274 + 0.701901i \(0.752335\pi\)
\(450\) 0 0
\(451\) 10.3475i 0.487244i
\(452\) 1.17909 1.07985i 0.0554595 0.0507917i
\(453\) 28.5078 + 17.5517i 1.33941 + 0.824651i
\(454\) −28.8062 12.6797i −1.35194 0.595088i
\(455\) 0 0
\(456\) 0.481161 2.10203i 0.0225324 0.0984365i
\(457\) 36.1047 1.68891 0.844453 0.535630i \(-0.179926\pi\)
0.844453 + 0.535630i \(0.179926\pi\)
\(458\) 2.97503 + 1.30952i 0.139014 + 0.0611900i
\(459\) −3.36131 + 39.5371i −0.156893 + 1.84543i
\(460\) 0 0
\(461\) 17.5517i 0.817465i −0.912654 0.408732i \(-0.865971\pi\)
0.912654 0.408732i \(-0.134029\pi\)
\(462\) 11.7402 + 17.0042i 0.546205 + 0.791106i
\(463\) 5.01934i 0.233268i 0.993175 + 0.116634i \(0.0372105\pi\)
−0.993175 + 0.116634i \(0.962789\pi\)
\(464\) 9.08080 + 0.799423i 0.421566 + 0.0371123i
\(465\) 0 0
\(466\) −4.80625 + 10.9190i −0.222645 + 0.505814i
\(467\) 29.5197 1.36601 0.683004 0.730414i \(-0.260673\pi\)
0.683004 + 0.730414i \(0.260673\pi\)
\(468\) −7.87044 + 20.7681i −0.363811 + 0.960004i
\(469\) 13.7016 0.632679
\(470\) 0 0
\(471\) 10.0839 16.3785i 0.464644 0.754683i
\(472\) 0 0
\(473\) 28.2665i 1.29969i
\(474\) −6.98550 10.1176i −0.320855 0.464716i
\(475\) 0 0
\(476\) 25.8874 + 28.2665i 1.18655 + 1.29559i
\(477\) 6.10469 3.07840i 0.279514 0.140950i
\(478\) −33.5078 14.7492i −1.53261 0.674613i
\(479\) 33.6131 1.53582 0.767912 0.640555i \(-0.221296\pi\)
0.767912 + 0.640555i \(0.221296\pi\)
\(480\) 0 0
\(481\) 27.4031 1.24947
\(482\) 9.06058 + 3.98822i 0.412698 + 0.181658i
\(483\) −19.1647 11.7994i −0.872026 0.536890i
\(484\) 0.403124 + 0.440172i 0.0183238 + 0.0200078i
\(485\) 0 0
\(486\) −0.714301 + 22.0338i −0.0324013 + 0.999475i
\(487\) 0.131364i 0.00595267i 0.999996 + 0.00297634i \(0.000947399\pi\)
−0.999996 + 0.00297634i \(0.999053\pi\)
\(488\) −5.17748 15.2727i −0.234373 0.691364i
\(489\) 0.649219 + 0.399712i 0.0293587 + 0.0180756i
\(490\) 0 0
\(491\) −13.4453 −0.606776 −0.303388 0.952867i \(-0.598118\pi\)
−0.303388 + 0.952867i \(0.598118\pi\)
\(492\) 2.01004 + 10.4728i 0.0906196 + 0.472148i
\(493\) −17.4031 −0.783797
\(494\) −0.928300 + 2.10895i −0.0417662 + 0.0948860i
\(495\) 0 0
\(496\) −13.5078 1.18915i −0.606519 0.0533945i
\(497\) 31.2256i 1.40066i
\(498\) 3.66087 2.52758i 0.164047 0.113264i
\(499\) 40.2861i 1.80345i −0.432308 0.901726i \(-0.642301\pi\)
0.432308 0.901726i \(-0.357699\pi\)
\(500\) 0 0
\(501\) 14.1047 22.9091i 0.630151 1.02350i
\(502\) −29.1570 12.8341i −1.30134 0.572814i
\(503\) 12.9841 0.578934 0.289467 0.957188i \(-0.406522\pi\)
0.289467 + 0.957188i \(0.406522\pi\)
\(504\) 15.1855 + 14.9295i 0.676415 + 0.665011i
\(505\) 0 0
\(506\) −22.5261 9.91534i −1.00141 0.440791i
\(507\) 0.637075 1.03475i 0.0282935 0.0459548i
\(508\) −18.7016 + 17.1275i −0.829748 + 0.759910i
\(509\) 2.95911i 0.131160i 0.997847 + 0.0655802i \(0.0208898\pi\)
−0.997847 + 0.0655802i \(0.979110\pi\)
\(510\) 0 0
\(511\) 3.25865i 0.144154i
\(512\) −18.7987 12.5940i −0.830792 0.556583i
\(513\) −0.193752 + 2.27898i −0.00855434 + 0.100619i
\(514\) 2.59688 5.89968i 0.114543 0.260224i
\(515\) 0 0
\(516\) 5.49087 + 28.6087i 0.241722 + 1.25943i
\(517\) 12.2094 0.536968
\(518\) 10.5855 24.0486i 0.465101 1.05663i
\(519\) 12.4421 + 7.66037i 0.546148 + 0.336253i
\(520\) 0 0
\(521\) 3.07840i 0.134867i −0.997724 0.0674337i \(-0.978519\pi\)
0.997724 0.0674337i \(-0.0214811\pi\)
\(522\) −9.65562 + 0.506474i −0.422615 + 0.0221678i
\(523\) 14.0002i 0.612187i 0.952001 + 0.306094i \(0.0990220\pi\)
−0.952001 + 0.306094i \(0.900978\pi\)
\(524\) −7.72577 8.43579i −0.337502 0.368519i
\(525\) 0 0
\(526\) 24.1047 + 10.6102i 1.05101 + 0.462627i
\(527\) 25.8874 1.12767
\(528\) 18.6836 + 13.9014i 0.813099 + 0.604980i
\(529\) 3.80625 0.165489
\(530\) 0 0
\(531\) 0 0
\(532\) 1.49219 + 1.62932i 0.0646946 + 0.0706402i
\(533\) 11.3949i 0.493568i
\(534\) −7.45596 10.7990i −0.322651 0.467318i
\(535\) 0 0
\(536\) 14.6243 4.95767i 0.631676 0.214139i
\(537\) −8.24609 + 13.3935i −0.355845 + 0.577970i
\(538\) 4.80625 10.9190i 0.207212 0.470752i
\(539\) 2.35817 0.101574
\(540\) 0 0
\(541\) −25.7016 −1.10500 −0.552498 0.833514i \(-0.686325\pi\)
−0.552498 + 0.833514i \(0.686325\pi\)
\(542\) 5.21791 11.8543i 0.224129 0.509184i
\(543\) 9.54193 15.4982i 0.409484 0.665091i
\(544\) 37.8586 + 20.8033i 1.62317 + 0.891934i
\(545\) 0 0
\(546\) −12.9286 18.7254i −0.553294 0.801374i
\(547\) 4.71053i 0.201408i 0.994916 + 0.100704i \(0.0321095\pi\)
−0.994916 + 0.100704i \(0.967891\pi\)
\(548\) −14.6243 + 13.3935i −0.624721 + 0.572140i
\(549\) 7.70156 + 15.2727i 0.328695 + 0.651824i
\(550\) 0 0
\(551\) −1.00314 −0.0427354
\(552\) −24.7249 5.65961i −1.05236 0.240889i
\(553\) 12.5969 0.535674
\(554\) −11.5138 5.06806i −0.489175 0.215321i
\(555\) 0 0
\(556\) −4.35078 + 3.98459i −0.184514 + 0.168984i
\(557\) 36.7023i 1.55512i 0.628806 + 0.777562i \(0.283544\pi\)
−0.628806 + 0.777562i \(0.716456\pi\)
\(558\) 14.3629 0.753387i 0.608028 0.0318934i
\(559\) 31.1277i 1.31656i
\(560\) 0 0
\(561\) −37.8586 23.3088i −1.59839 0.984098i
\(562\) −10.0000 + 22.7184i −0.421825 + 0.958317i
\(563\) −23.3391 −0.983625 −0.491812 0.870701i \(-0.663665\pi\)
−0.491812 + 0.870701i \(0.663665\pi\)
\(564\) 12.3572 2.37172i 0.520331 0.0998674i
\(565\) 0 0
\(566\) −9.33159 + 21.1999i −0.392236 + 0.891096i
\(567\) −18.1616 13.4287i −0.762716 0.563952i
\(568\) 11.2984 + 33.3286i 0.474072 + 1.39844i
\(569\) 10.5955i 0.444186i −0.975026 0.222093i \(-0.928711\pi\)
0.975026 0.222093i \(-0.0712888\pi\)
\(570\) 0 0
\(571\) 16.9501i 0.709338i 0.934992 + 0.354669i \(0.115406\pi\)
−0.934992 + 0.354669i \(0.884594\pi\)
\(572\) −16.8066 18.3511i −0.702718 0.767299i
\(573\) 11.2984 18.3511i 0.471999 0.766630i
\(574\) −10.0000 4.40172i −0.417392 0.183724i
\(575\) 0 0
\(576\) 21.6102 + 10.4403i 0.900424 + 0.435014i
\(577\) −12.4031 −0.516349 −0.258174 0.966098i \(-0.583121\pi\)
−0.258174 + 0.966098i \(0.583121\pi\)
\(578\) −53.4756 23.5385i −2.22429 0.979072i
\(579\) 17.9857 29.2126i 0.747459 1.21404i
\(580\) 0 0
\(581\) 4.55796i 0.189096i
\(582\) 22.3839 15.4546i 0.927844 0.640613i
\(583\) 7.66037i 0.317260i
\(584\) 1.17909 + 3.47812i 0.0487909 + 0.143925i
\(585\) 0 0
\(586\) 12.2094 27.7377i 0.504365 1.14583i
\(587\) −31.3359 −1.29337 −0.646685 0.762758i \(-0.723845\pi\)
−0.646685 + 0.762758i \(0.723845\pi\)
\(588\) 2.38672 0.458084i 0.0984267 0.0188911i
\(589\) 1.49219 0.0614846
\(590\) 0 0
\(591\) −15.8034 9.72987i −0.650066 0.400233i
\(592\) 2.59688 29.4984i 0.106731 1.21238i
\(593\) 10.5955i 0.435104i 0.976049 + 0.217552i \(0.0698072\pi\)
−0.976049 + 0.217552i \(0.930193\pi\)
\(594\) −21.6831 11.8304i −0.889668 0.485409i
\(595\) 0 0
\(596\) −22.5261 + 20.6301i −0.922703 + 0.845042i
\(597\) 31.1047 + 19.1506i 1.27303 + 0.783780i
\(598\) 24.8062 + 10.9190i 1.01440 + 0.446512i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −40.0156 −1.63227 −0.816136 0.577860i \(-0.803888\pi\)
−0.816136 + 0.577860i \(0.803888\pi\)
\(602\) −27.3172 12.0243i −1.11337 0.490074i
\(603\) −14.6243 + 7.37460i −0.595549 + 0.300317i
\(604\) −28.5078 + 26.1084i −1.15997 + 1.06234i
\(605\) 0 0
\(606\) −24.4270 35.3793i −0.992279 1.43719i
\(607\) 3.25865i 0.132264i −0.997811 0.0661322i \(-0.978934\pi\)
0.997811 0.0661322i \(-0.0210659\pi\)
\(608\) 2.18223 + 1.19913i 0.0885011 + 0.0486313i
\(609\) 5.19375 8.43579i 0.210461 0.341835i
\(610\) 0 0
\(611\) −13.4453 −0.543937
\(612\) −42.8447 16.2368i −1.73190 0.656334i
\(613\) 4.80625 0.194123 0.0970613 0.995278i \(-0.469056\pi\)
0.0970613 + 0.995278i \(0.469056\pi\)
\(614\) −15.0511 + 34.1936i −0.607412 + 1.37994i
\(615\) 0 0
\(616\) −22.5969 + 7.66037i −0.910454 + 0.308645i
\(617\) 22.1097i 0.890102i −0.895505 0.445051i \(-0.853186\pi\)
0.895505 0.445051i \(-0.146814\pi\)
\(618\) −15.1962 22.0097i −0.611280 0.885359i
\(619\) 5.15070i 0.207024i 0.994628 + 0.103512i \(0.0330080\pi\)
−0.994628 + 0.103512i \(0.966992\pi\)
\(620\) 0 0
\(621\) 26.8062 + 2.27898i 1.07570 + 0.0914523i
\(622\) −17.4031 7.66037i −0.697802 0.307153i
\(623\) 13.4453 0.538673
\(624\) −20.5748 15.3086i −0.823652 0.612833i
\(625\) 0 0
\(626\) 21.0962 + 9.28595i 0.843173 + 0.371141i
\(627\) −2.18223 1.34356i −0.0871498 0.0536565i
\(628\) 15.0000 + 16.3785i 0.598565 + 0.653574i
\(629\) 56.5330i 2.25412i
\(630\) 0 0
\(631\) 42.0468i 1.67385i −0.547314 0.836927i \(-0.684350\pi\)
0.547314 0.836927i \(-0.315650\pi\)
\(632\) 13.4453 4.55796i 0.534824 0.181306i
\(633\) −26.7539 16.4719i −1.06337 0.654698i
\(634\) 9.61250 21.8380i 0.381761 0.867299i
\(635\) 0 0
\(636\) 1.48806 + 7.75311i 0.0590053 + 0.307431i
\(637\) −2.59688 −0.102892
\(638\) 4.36446 9.91534i 0.172791 0.392552i
\(639\) −16.8066 33.3286i −0.664858 1.31846i
\(640\) 0 0
\(641\) 12.3136i 0.486359i 0.969981 + 0.243179i \(0.0781903\pi\)
−0.969981 + 0.243179i \(0.921810\pi\)
\(642\) 13.0047 8.97883i 0.513253 0.354366i
\(643\) 24.4791i 0.965360i −0.875797 0.482680i \(-0.839663\pi\)
0.875797 0.482680i \(-0.160337\pi\)
\(644\) 19.1647 17.5517i 0.755197 0.691634i
\(645\) 0 0
\(646\) −4.35078 1.91509i −0.171179 0.0753483i
\(647\) −10.3550 −0.407095 −0.203548 0.979065i \(-0.565247\pi\)
−0.203548 + 0.979065i \(0.565247\pi\)
\(648\) −24.2437 7.76163i −0.952383 0.304906i
\(649\) 0 0
\(650\) 0 0
\(651\) −7.72577 + 12.5483i −0.302797 + 0.491808i
\(652\) −0.649219 + 0.594576i −0.0254254 + 0.0232854i
\(653\) 25.9875i 1.01697i 0.861071 + 0.508485i \(0.169794\pi\)
−0.861071 + 0.508485i \(0.830206\pi\)
\(654\) 4.63301 3.19877i 0.181165 0.125082i
\(655\) 0 0
\(656\) −12.2662 1.07985i −0.478914 0.0421609i
\(657\) −1.75391 3.47812i −0.0684264 0.135694i
\(658\) −5.19375 + 11.7994i −0.202474 + 0.459987i
\(659\) 16.8066 0.654691 0.327346 0.944905i \(-0.393846\pi\)
0.327346 + 0.944905i \(0.393846\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 9.75831 22.1693i 0.379268 0.861635i
\(663\) 41.6908 + 25.6682i 1.61914 + 0.996871i
\(664\) 1.64922 + 4.86493i 0.0640021 + 0.188796i
\(665\) 0 0
\(666\) 1.64525 + 31.3657i 0.0637521 + 1.21540i
\(667\) 11.7994i 0.456873i
\(668\) 20.9809 + 22.9091i 0.811776 + 0.886379i
\(669\) −31.1047 19.1506i −1.20258 0.740403i
\(670\) 0 0
\(671\) −19.1647 −0.739847
\(672\) −21.3824 + 12.1426i −0.824843 + 0.468413i
\(673\) 24.8062 0.956211 0.478105 0.878303i \(-0.341324\pi\)
0.478105 + 0.878303i \(0.341324\pi\)
\(674\) −16.0542 7.06662i −0.618385 0.272196i
\(675\) 0 0
\(676\) 0.947657 + 1.03475i 0.0364483 + 0.0397980i
\(677\) 12.9937i 0.499390i 0.968324 + 0.249695i \(0.0803304\pi\)
−0.968324 + 0.249695i \(0.919670\pi\)
\(678\) −1.11257 1.61141i −0.0427280 0.0618859i
\(679\) 27.8691i 1.06952i
\(680\) 0 0
\(681\) −20.2094 + 32.8244i −0.774425 + 1.25784i
\(682\) −6.49219 + 14.7492i −0.248599 + 0.564776i
\(683\) 11.6291 0.444975 0.222488 0.974936i \(-0.428582\pi\)
0.222488 + 0.974936i \(0.428582\pi\)
\(684\) −2.46964 0.935915i −0.0944290 0.0357856i
\(685\) 0 0
\(686\) −11.0122 + 25.0180i −0.420449 + 0.955193i
\(687\) 2.08717 3.39001i 0.0796303 0.129337i
\(688\) −33.5078 2.94984i −1.27747 0.112462i
\(689\) 8.43579i 0.321378i
\(690\) 0 0
\(691\) 1.18915i 0.0452375i −0.999744 0.0226187i \(-0.992800\pi\)
0.999744 0.0226187i \(-0.00720038\pi\)
\(692\) −12.4421 + 11.3949i −0.472978 + 0.433169i
\(693\) 22.5969 11.3949i 0.858384 0.432857i
\(694\) −25.1570 11.0734i −0.954948 0.420341i
\(695\) 0 0
\(696\) 2.49120 10.8832i 0.0944287 0.412526i
\(697\) 23.5078 0.890422
\(698\) 33.9246 + 14.9327i 1.28406 + 0.565210i
\(699\) 12.4421 + 7.66037i 0.470604 + 0.289742i
\(700\) 0 0
\(701\) 11.3949i 0.430380i −0.976572 0.215190i \(-0.930963\pi\)
0.976572 0.215190i \(-0.0690370\pi\)
\(702\) 23.8779 + 13.0280i 0.901215 + 0.491709i
\(703\) 3.25865i 0.122902i
\(704\) −21.3470 + 16.3526i −0.804544 + 0.616311i
\(705\) 0 0
\(706\) 15.1938 34.5177i 0.571824 1.29909i
\(707\) 44.0490 1.65663
\(708\) 0 0
\(709\) −17.7016 −0.664796 −0.332398 0.943139i \(-0.607858\pi\)
−0.332398 + 0.943139i \(0.607858\pi\)
\(710\) 0 0
\(711\) −13.4453 + 6.78003i −0.504237 + 0.254271i
\(712\) 14.3508 4.86493i 0.537818 0.182321i
\(713\) 17.5517i 0.657317i
\(714\) 38.6307 26.6719i 1.44572 0.998171i
\(715\) 0 0
\(716\) −12.2662 13.3935i −0.458408 0.500537i
\(717\) −23.5078 + 38.1818i −0.877915 + 1.42593i
\(718\) −10.0000 4.40172i −0.373197 0.164271i
\(719\) −44.0490 −1.64275 −0.821375 0.570389i \(-0.806793\pi\)
−0.821375 + 0.570389i \(0.806793\pi\)
\(720\) 0 0
\(721\) 27.4031 1.02055
\(722\) 24.3422 + 10.7148i 0.905924 + 0.398762i
\(723\) 6.35656 10.3244i 0.236403 0.383970i
\(724\) 14.1938 + 15.4982i 0.527507 + 0.575986i
\(725\) 0 0
\(726\) 0.601567 0.415341i 0.0223262 0.0154148i
\(727\) 40.5488i 1.50387i −0.659236 0.751936i \(-0.729120\pi\)
0.659236 0.751936i \(-0.270880\pi\)
\(728\) 24.8842 8.43579i 0.922271 0.312651i
\(729\) 26.6125 + 4.55796i 0.985648 + 0.168813i
\(730\) 0 0
\(731\) 64.2169 2.37515
\(732\) −19.3968 + 3.72283i −0.716925 + 0.137600i
\(733\) 4.80625 0.177523 0.0887614 0.996053i \(-0.471709\pi\)
0.0887614 + 0.996053i \(0.471709\pi\)
\(734\) −1.42987 + 3.24844i −0.0527775 + 0.119902i
\(735\) 0 0
\(736\) 14.1047 25.6682i 0.519906 0.946143i
\(737\) 18.3511i 0.675973i
\(738\) 13.0426 0.684136i 0.480106 0.0251834i
\(739\) 29.2357i 1.07545i 0.843120 + 0.537726i \(0.180717\pi\)
−0.843120 + 0.537726i \(0.819283\pi\)
\(740\) 0 0
\(741\) 2.40312 + 1.47956i 0.0882810 + 0.0543529i
\(742\) −7.40312 3.25865i −0.271777 0.119629i
\(743\) −40.8778 −1.49966 −0.749830 0.661630i \(-0.769865\pi\)
−0.749830 + 0.661630i \(0.769865\pi\)
\(744\) −3.70569 + 16.1889i −0.135857 + 0.593514i
\(745\) 0 0
\(746\) −30.6786 13.5038i −1.12322 0.494411i
\(747\) −2.45323 4.86493i −0.0897592 0.177999i
\(748\) 37.8586 34.6722i 1.38425 1.26774i
\(749\) 16.1914i 0.591622i
\(750\) 0 0
\(751\) 36.2784i 1.32382i −0.749584 0.661909i \(-0.769746\pi\)
0.749584 0.661909i \(-0.230254\pi\)
\(752\) −1.27415 + 14.4733i −0.0464634 + 0.527787i
\(753\) −20.4555 + 33.2241i −0.745439 + 1.21076i
\(754\) −4.80625 + 10.9190i −0.175033 + 0.397647i
\(755\) 0 0
\(756\) 20.6569 15.9224i 0.751285 0.579092i
\(757\) −35.9109 −1.30521 −0.652603 0.757700i \(-0.726323\pi\)
−0.652603 + 0.757700i \(0.726323\pi\)
\(758\) −7.47499 + 16.9820i −0.271504 + 0.616813i
\(759\) −15.8034 + 25.6682i −0.573628 + 0.931698i
\(760\) 0 0
\(761\) 20.6301i 0.747841i −0.927461 0.373920i \(-0.878013\pi\)
0.927461 0.373920i \(-0.121987\pi\)
\(762\) 17.6466 + 25.5587i 0.639268 + 0.925895i
\(763\) 5.76832i 0.208827i
\(764\) 16.8066 + 18.3511i 0.608041 + 0.663921i
\(765\) 0 0
\(766\) −9.40312 4.13899i −0.339749 0.149548i
\(767\) 0 0
\(768\) −18.4289 + 20.6973i −0.664994 + 0.746849i
\(769\) −14.1938 −0.511840 −0.255920 0.966698i \(-0.582378\pi\)
−0.255920 + 0.966698i \(0.582378\pi\)
\(770\) 0 0
\(771\) −6.72263 4.13899i −0.242110 0.149062i
\(772\) 26.7539 + 29.2126i 0.962894 + 1.05139i
\(773\) 2.27898i 0.0819692i 0.999160 + 0.0409846i \(0.0130495\pi\)
−0.999160 + 0.0409846i \(0.986951\pi\)
\(774\) 35.6289 1.86887i 1.28065 0.0671752i
\(775\) 0 0
\(776\) 10.0839 + 29.7460i 0.361993 + 1.06782i
\(777\) −27.4031 16.8716i −0.983082 0.605264i
\(778\) 21.2984 48.3866i 0.763586 1.73474i
\(779\) 1.35503 0.0485489
\(780\) 0 0
\(781\) 41.8219 1.49650
\(782\) −22.5261 + 51.1756i −0.805530 + 1.83003i
\(783\) −1.00314 + 11.7994i −0.0358494 + 0.421675i
\(784\) −0.246095 + 2.79544i −0.00878910 + 0.0998370i
\(785\) 0 0
\(786\) −11.5289 + 7.95991i −0.411221 + 0.283920i