Properties

Label 300.2.h.c.299.8
Level $300$
Weight $2$
Character 300.299
Analytic conductor $2.396$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + 1514 x^{6} + 1102 x^{5} + 249 x^{4} - 1056 x^{3} + 392 x^{2} - 280 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.8
Root \(-1.77516 - 0.994127i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.c.299.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} +2.50967 q^{7} +(2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +O(q^{10})\) \(q+(-0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} +2.50967 q^{7} +(2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} -3.36131 q^{11} +(-3.33164 - 0.948773i) q^{12} -3.70156i q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} +7.63636 q^{17} +(2.69761 + 3.27458i) q^{18} +0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(1.91509 - 4.35078i) q^{22} +5.17748i q^{23} +(3.12625 - 3.77181i) q^{24} +(4.79119 + 2.10895i) q^{26} +(-0.440172 - 5.17748i) q^{27} +(-3.39001 - 3.70156i) q^{28} -2.27898i q^{29} +3.39001i q^{31} +(-4.95767 - 2.72424i) q^{32} +(-4.95767 + 3.05234i) q^{33} +(-4.35078 + 9.88427i) q^{34} +(-5.77547 + 1.62603i) q^{36} +7.40312i q^{37} +(-0.569745 - 0.250786i) q^{38} +(-3.36131 - 5.45951i) q^{39} -3.07840i q^{41} +(0.840894 + 6.08962i) q^{42} -8.40935 q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} +3.63232i q^{47} +(3.10095 + 6.19549i) q^{48} -0.701562 q^{49} +(11.2630 - 6.93443i) q^{51} +(-5.45951 + 5.00000i) q^{52} +2.27898 q^{53} +(6.95235 + 2.38010i) q^{54} +(6.72263 - 2.27898i) q^{56} +(0.399712 + 0.649219i) q^{57} +(2.94984 + 1.29844i) q^{58} -5.70156 q^{61} +(-4.38793 - 1.93144i) q^{62} +(3.39001 - 6.72263i) q^{63} +(6.35078 - 4.86493i) q^{64} +(-1.12625 - 8.15611i) q^{66} -5.45951 q^{67} +(-10.3151 - 11.2630i) q^{68} +(4.70156 + 7.63636i) q^{69} -12.4421 q^{71} +(1.18586 - 8.40201i) q^{72} +1.29844i q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} -8.43579 q^{77} +(8.98171 - 1.24025i) q^{78} +5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(3.98459 + 1.75391i) q^{82} -1.81616i q^{83} +(-8.36131 - 2.38111i) q^{84} +(4.79119 - 10.8848i) q^{86} +(-2.06950 - 3.36131i) q^{87} +(-9.00393 + 3.05234i) q^{88} -5.35738i q^{89} -9.28970i q^{91} +(7.63636 - 6.99364i) q^{92} +(3.07840 + 5.00000i) q^{93} +(-4.70156 - 2.06950i) q^{94} +(-9.78600 + 0.483926i) q^{96} -11.1047i q^{97} +(0.399712 - 0.908080i) q^{98} +(-4.54040 + 9.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{4} + 6q^{6} - 4q^{9} + O(q^{10}) \) \( 16q + 4q^{4} + 6q^{6} - 4q^{9} + 20q^{16} + 8q^{21} - 26q^{24} - 44q^{34} - 42q^{36} - 56q^{46} + 40q^{49} + 56q^{54} - 40q^{61} + 76q^{64} + 58q^{66} + 24q^{69} + 36q^{76} - 60q^{81} - 80q^{84} - 24q^{94} - 78q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.569745 + 1.29437i −0.402871 + 0.915257i
\(3\) 1.47492 0.908080i 0.851546 0.524280i
\(4\) −1.35078 1.47492i −0.675391 0.737460i
\(5\) 0 0
\(6\) 0.335062 + 2.42647i 0.136788 + 0.990600i
\(7\) 2.50967 0.948566 0.474283 0.880373i \(-0.342707\pi\)
0.474283 + 0.880373i \(0.342707\pi\)
\(8\) 2.67869 0.908080i 0.947061 0.321055i
\(9\) 1.35078 2.67869i 0.450260 0.892897i
\(10\) 0 0
\(11\) −3.36131 −1.01347 −0.506737 0.862101i \(-0.669149\pi\)
−0.506737 + 0.862101i \(0.669149\pi\)
\(12\) −3.33164 0.948773i −0.961762 0.273887i
\(13\) 3.70156i 1.02663i −0.858201 0.513314i \(-0.828418\pi\)
0.858201 0.513314i \(-0.171582\pi\)
\(14\) −1.42987 + 3.24844i −0.382149 + 0.868181i
\(15\) 0 0
\(16\) −0.350781 + 3.98459i −0.0876953 + 0.996147i
\(17\) 7.63636 1.85209 0.926045 0.377413i \(-0.123186\pi\)
0.926045 + 0.377413i \(0.123186\pi\)
\(18\) 2.69761 + 3.27458i 0.635834 + 0.771826i
\(19\) 0.440172i 0.100982i 0.998725 + 0.0504912i \(0.0160787\pi\)
−0.998725 + 0.0504912i \(0.983921\pi\)
\(20\) 0 0
\(21\) 3.70156 2.27898i 0.807747 0.497314i
\(22\) 1.91509 4.35078i 0.408299 0.927590i
\(23\) 5.17748i 1.07958i 0.841800 + 0.539789i \(0.181496\pi\)
−0.841800 + 0.539789i \(0.818504\pi\)
\(24\) 3.12625 3.77181i 0.638143 0.769918i
\(25\) 0 0
\(26\) 4.79119 + 2.10895i 0.939629 + 0.413599i
\(27\) −0.440172 5.17748i −0.0847112 0.996406i
\(28\) −3.39001 3.70156i −0.640652 0.699529i
\(29\) 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 \(0.901533\pi\)
\(32\) −4.95767 2.72424i −0.876401 0.481582i
\(33\) −4.95767 + 3.05234i −0.863020 + 0.531345i
\(34\) −4.35078 + 9.88427i −0.746153 + 1.69514i
\(35\) 0 0
\(36\) −5.77547 + 1.62603i −0.962578 + 0.271005i
\(37\) 7.40312i 1.21707i 0.793529 + 0.608533i \(0.208242\pi\)
−0.793529 + 0.608533i \(0.791758\pi\)
\(38\) −0.569745 0.250786i −0.0924249 0.0406828i
\(39\) −3.36131 5.45951i −0.538241 0.874221i
\(40\) 0 0
\(41\) 3.07840i 0.480766i −0.970678 0.240383i \(-0.922727\pi\)
0.970678 0.240383i \(-0.0772730\pi\)
\(42\) 0.840894 + 6.08962i 0.129753 + 0.939649i
\(43\) −8.40935 −1.28241 −0.641207 0.767368i \(-0.721566\pi\)
−0.641207 + 0.767368i \(0.721566\pi\)
\(44\) 4.54040 + 4.95767i 0.684491 + 0.747397i
\(45\) 0 0
\(46\) −6.70156 2.94984i −0.988091 0.434930i
\(47\) 3.63232i 0.529828i 0.964272 + 0.264914i \(0.0853436\pi\)
−0.964272 + 0.264914i \(0.914656\pi\)
\(48\) 3.10095 + 6.19549i 0.447584 + 0.894242i
\(49\) −0.701562 −0.100223
\(50\) 0 0
\(51\) 11.2630 6.93443i 1.57714 0.971014i
\(52\) −5.45951 + 5.00000i −0.757098 + 0.693375i
\(53\) 2.27898 0.313042 0.156521 0.987675i \(-0.449972\pi\)
0.156521 + 0.987675i \(0.449972\pi\)
\(54\) 6.95235 + 2.38010i 0.946095 + 0.323890i
\(55\) 0 0
\(56\) 6.72263 2.27898i 0.898349 0.304542i
\(57\) 0.399712 + 0.649219i 0.0529431 + 0.0859911i
\(58\) 2.94984 + 1.29844i 0.387333 + 0.170493i
\(59\) 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 \(0.618933\pi\)
\(62\) −4.38793 1.93144i −0.557267 0.245294i
\(63\) 3.39001 6.72263i 0.427102 0.846972i
\(64\) 6.35078 4.86493i 0.793848 0.608117i
\(65\) 0 0
\(66\) −1.12625 8.15611i −0.138632 1.00395i
\(67\) −5.45951 −0.666985 −0.333493 0.942753i \(-0.608227\pi\)
−0.333493 + 0.942753i \(0.608227\pi\)
\(68\) −10.3151 11.2630i −1.25088 1.36584i
\(69\) 4.70156 + 7.63636i 0.566002 + 0.919310i
\(70\) 0 0
\(71\) −12.4421 −1.47661 −0.738304 0.674468i \(-0.764373\pi\)
−0.738304 + 0.674468i \(0.764373\pi\)
\(72\) 1.18586 8.40201i 0.139755 0.990186i
\(73\) 1.29844i 0.151971i 0.997109 + 0.0759853i \(0.0242102\pi\)
−0.997109 + 0.0759853i \(0.975790\pi\)
\(74\) −9.58237 4.21789i −1.11393 0.490320i
\(75\) 0 0
\(76\) 0.649219 0.594576i 0.0744705 0.0682026i
\(77\) −8.43579 −0.961347
\(78\) 8.98171 1.24025i 1.01698 0.140431i
\(79\) 5.01934i 0.564720i 0.959309 + 0.282360i \(0.0911172\pi\)
−0.959309 + 0.282360i \(0.908883\pi\)
\(80\) 0 0
\(81\) −5.35078 7.23665i −0.594531 0.804073i
\(82\) 3.98459 + 1.75391i 0.440024 + 0.193686i
\(83\) 1.81616i 0.199349i −0.995020 0.0996747i \(-0.968220\pi\)
0.995020 0.0996747i \(-0.0317802\pi\)
\(84\) −8.36131 2.38111i −0.912294 0.259800i
\(85\) 0 0
\(86\) 4.79119 10.8848i 0.516647 1.17374i
\(87\) −2.06950 3.36131i −0.221873 0.360371i
\(88\) −9.00393 + 3.05234i −0.959822 + 0.325381i
\(89\) 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
\(92\) 7.63636 6.99364i 0.796146 0.729137i
\(93\) 3.07840 + 5.00000i 0.319216 + 0.518476i
\(94\) −4.70156 2.06950i −0.484929 0.213452i
\(95\) 0 0
\(96\) −9.78600 + 0.483926i −0.998780 + 0.0493905i
\(97\) 11.1047i 1.12751i −0.825942 0.563755i \(-0.809356\pi\)
0.825942 0.563755i \(-0.190644\pi\)
\(98\) 0.399712 0.908080i 0.0403770 0.0917299i
\(99\) −4.54040 + 9.00393i −0.456327 + 0.904929i
\(100\) 0 0
\(101\) 17.5517i 1.74646i 0.487308 + 0.873230i \(0.337979\pi\)
−0.487308 + 0.873230i \(0.662021\pi\)
\(102\) 2.55865 + 18.5294i 0.253344 + 1.83468i
\(103\) 10.9190 1.07588 0.537941 0.842982i \(-0.319202\pi\)
0.537941 + 0.842982i \(0.319202\pi\)
\(104\) −3.36131 9.91534i −0.329604 0.972280i
\(105\) 0 0
\(106\) −1.29844 + 2.94984i −0.126115 + 0.286514i
\(107\) 6.45162i 0.623702i 0.950131 + 0.311851i \(0.100949\pi\)
−0.950131 + 0.311851i \(0.899051\pi\)
\(108\) −7.04179 + 7.64285i −0.677596 + 0.735434i
\(109\) −2.29844 −0.220150 −0.110075 0.993923i \(-0.535109\pi\)
−0.110075 + 0.993923i \(0.535109\pi\)
\(110\) 0 0
\(111\) 6.72263 + 10.9190i 0.638084 + 1.03639i
\(112\) −0.880344 + 10.0000i −0.0831847 + 0.944911i
\(113\) −0.799423 −0.0752034 −0.0376017 0.999293i \(-0.511972\pi\)
−0.0376017 + 0.999293i \(0.511972\pi\)
\(114\) −1.06806 + 0.147485i −0.100033 + 0.0138132i
\(115\) 0 0
\(116\) −3.36131 + 3.07840i −0.312090 + 0.285823i
\(117\) −9.91534 5.00000i −0.916674 0.462250i
\(118\) 0 0
\(119\) 19.1647 1.75683
\(120\) 0 0
\(121\) 0.298438 0.0271307
\(122\) 3.24844 7.37992i 0.294100 0.668147i
\(123\) −2.79544 4.54040i −0.252056 0.409394i
\(124\) 5.00000 4.57917i 0.449013 0.411221i
\(125\) 0 0
\(126\) 6.77012 + 8.21811i 0.603130 + 0.732128i
\(127\) 12.6797 1.12514 0.562571 0.826749i \(-0.309812\pi\)
0.562571 + 0.826749i \(0.309812\pi\)
\(128\) 2.67869 + 10.9920i 0.236765 + 0.971567i
\(129\) −12.4031 + 7.63636i −1.09203 + 0.672344i
\(130\) 0 0
\(131\) 5.71949 0.499714 0.249857 0.968283i \(-0.419616\pi\)
0.249857 + 0.968283i \(0.419616\pi\)
\(132\) 11.1987 + 3.18913i 0.974721 + 0.277578i
\(133\) 1.10469i 0.0957885i
\(134\) 3.11053 7.06662i 0.268709 0.610463i
\(135\) 0 0
\(136\) 20.4555 6.93443i 1.75404 0.594623i
\(137\) −9.91534 −0.847125 −0.423563 0.905867i \(-0.639221\pi\)
−0.423563 + 0.905867i \(0.639221\pi\)
\(138\) −12.5630 + 1.73477i −1.06943 + 0.147674i
\(139\) 2.94984i 0.250202i −0.992144 0.125101i \(-0.960074\pi\)
0.992144 0.125101i \(-0.0399255\pi\)
\(140\) 0 0
\(141\) 3.29844 + 5.35738i 0.277779 + 0.451173i
\(142\) 7.08883 16.1047i 0.594882 1.35148i
\(143\) 12.4421i 1.04046i
\(144\) 10.1997 + 6.32194i 0.849972 + 0.526829i
\(145\) 0 0
\(146\) −1.68066 0.739779i −0.139092 0.0612245i
\(147\) −1.03475 + 0.637075i −0.0853446 + 0.0525450i
\(148\) 10.9190 10.0000i 0.897538 0.821995i
\(149\) 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 \(0.711911\pi\)
\(152\) 0.399712 + 1.17909i 0.0324209 + 0.0956365i
\(153\) 10.3151 20.4555i 0.833923 1.65373i
\(154\) 4.80625 10.9190i 0.387299 0.879880i
\(155\) 0 0
\(156\) −3.51194 + 12.3323i −0.281180 + 0.987372i
\(157\) 11.1047i 0.886250i −0.896460 0.443125i \(-0.853870\pi\)
0.896460 0.443125i \(-0.146130\pi\)
\(158\) −6.49687 2.85974i −0.516864 0.227509i
\(159\) 3.36131 2.06950i 0.266570 0.164122i
\(160\) 0 0
\(161\) 12.9937i 1.02405i
\(162\) 12.4155 2.80284i 0.975452 0.220212i
\(163\) −0.440172 −0.0344769 −0.0172385 0.999851i \(-0.505487\pi\)
−0.0172385 + 0.999851i \(0.505487\pi\)
\(164\) −4.54040 + 4.15825i −0.354546 + 0.324705i
\(165\) 0 0
\(166\) 2.35078 + 1.03475i 0.182456 + 0.0803120i
\(167\) 15.5324i 1.20194i 0.799273 + 0.600968i \(0.205218\pi\)
−0.799273 + 0.600968i \(0.794782\pi\)
\(168\) 7.84585 9.46600i 0.605320 0.730318i
\(169\) −0.701562 −0.0539663
\(170\) 0 0
\(171\) 1.17909 + 0.594576i 0.0901669 + 0.0454684i
\(172\) 11.3592 + 12.4031i 0.866130 + 0.945729i
\(173\) 8.43579 0.641361 0.320681 0.947187i \(-0.396088\pi\)
0.320681 + 0.947187i \(0.396088\pi\)
\(174\) 5.52987 0.763599i 0.419218 0.0578883i
\(175\) 0 0
\(176\) 1.17909 13.3935i 0.0888769 1.00957i
\(177\) 0 0
\(178\) 6.93443 + 3.05234i 0.519758 + 0.228783i
\(179\) −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 \(0.372295\pi\)
\(182\) 12.0243 + 5.29276i 0.891300 + 0.392325i
\(183\) −8.40935 + 5.17748i −0.621637 + 0.382730i
\(184\) 4.70156 + 13.8689i 0.346604 + 1.02243i
\(185\) 0 0
\(186\) −8.22575 + 1.13586i −0.603141 + 0.0832856i
\(187\) −25.6682 −1.87705
\(188\) 5.35738 4.90647i 0.390727 0.357841i
\(189\) −1.10469 12.9937i −0.0803541 0.945156i
\(190\) 0 0
\(191\) −12.4421 −0.900280 −0.450140 0.892958i \(-0.648626\pi\)
−0.450140 + 0.892958i \(0.648626\pi\)
\(192\) 4.94915 12.9424i 0.357174 0.934038i
\(193\) 19.8062i 1.42568i 0.701324 + 0.712842i \(0.252593\pi\)
−0.701324 + 0.712842i \(0.747407\pi\)
\(194\) 14.3736 + 6.32684i 1.03196 + 0.454241i
\(195\) 0 0
\(196\) 0.947657 + 1.03475i 0.0676898 + 0.0739106i
\(197\) 10.7148 0.763396 0.381698 0.924287i \(-0.375340\pi\)
0.381698 + 0.924287i \(0.375340\pi\)
\(198\) −9.06753 11.0069i −0.644401 0.782226i
\(199\) 21.0891i 1.49496i −0.664282 0.747482i \(-0.731263\pi\)
0.664282 0.747482i \(-0.268737\pi\)
\(200\) 0 0
\(201\) −8.05234 + 4.95767i −0.567968 + 0.349687i
\(202\) −22.7184 10.0000i −1.59846 0.703598i
\(203\) 5.71949i 0.401429i
\(204\) −25.4416 7.24518i −1.78127 0.507264i
\(205\) 0 0
\(206\) −6.22106 + 14.1332i −0.433442 + 0.984709i
\(207\) 13.8689 + 6.99364i 0.963952 + 0.486091i
\(208\) 14.7492 + 1.29844i 1.02267 + 0.0900305i
\(209\) 1.47956i 0.102343i
\(210\) 0 0
\(211\) 18.1392i 1.24876i −0.781123 0.624378i \(-0.785353\pi\)
0.781123 0.624378i \(-0.214647\pi\)
\(212\) −3.07840 3.36131i −0.211426 0.230856i
\(213\) −18.3511 + 11.2984i −1.25740 + 0.774156i
\(214\) −8.35078 3.67578i −0.570848 0.251271i
\(215\) 0 0
\(216\) −5.88065 13.4691i −0.400127 0.916460i
\(217\) 8.50781i 0.577548i
\(218\) 1.30952 2.97503i 0.0886921 0.201494i
\(219\) 1.17909 + 1.91509i 0.0796752 + 0.129410i
\(220\) 0 0
\(221\) 28.2665i 1.90141i
\(222\) −17.9634 + 2.48050i −1.20563 + 0.166481i
\(223\) 21.0891 1.41223 0.706114 0.708098i \(-0.250447\pi\)
0.706114 + 0.708098i \(0.250447\pi\)
\(224\) −12.4421 6.83694i −0.831324 0.456812i
\(225\) 0 0
\(226\) 0.455467 1.03475i 0.0302972 0.0688304i
\(227\) 22.2551i 1.47712i −0.674188 0.738560i \(-0.735506\pi\)
0.674188 0.738560i \(-0.264494\pi\)
\(228\) 0.417624 1.46650i 0.0276578 0.0971210i
\(229\) −2.29844 −0.151885 −0.0759425 0.997112i \(-0.524197\pi\)
−0.0759425 + 0.997112i \(0.524197\pi\)
\(230\) 0 0
\(231\) −12.4421 + 7.66037i −0.818631 + 0.504015i
\(232\) −2.06950 6.10469i −0.135869 0.400792i
\(233\) 8.43579 0.552647 0.276323 0.961065i \(-0.410884\pi\)
0.276323 + 0.961065i \(0.410884\pi\)
\(234\) 12.1211 9.98539i 0.792379 0.652765i
\(235\) 0 0
\(236\) 0 0
\(237\) 4.55796 + 7.40312i 0.296071 + 0.480885i
\(238\) −10.9190 + 24.8062i −0.707775 + 1.60795i
\(239\) −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 \(0.427613\pi\)
\(242\) −0.170034 + 0.386289i −0.0109302 + 0.0248316i
\(243\) −14.4634 5.81455i −0.927830 0.373004i
\(244\) 7.70156 + 8.40935i 0.493042 + 0.538354i
\(245\) 0 0
\(246\) 7.46964 1.03146i 0.476247 0.0657632i
\(247\) 1.62932 0.103671
\(248\) 3.07840 + 9.08080i 0.195479 + 0.576631i
\(249\) −1.64922 2.67869i −0.104515 0.169755i
\(250\) 0 0
\(251\) 22.5261 1.42183 0.710916 0.703277i \(-0.248281\pi\)
0.710916 + 0.703277i \(0.248281\pi\)
\(252\) −14.4945 + 4.08080i −0.913068 + 0.257066i
\(253\) 17.4031i 1.09413i
\(254\) −7.22420 + 16.4122i −0.453287 + 1.02979i
\(255\) 0 0
\(256\) −15.7539 2.79544i −0.984619 0.174715i
\(257\) 4.55796 0.284318 0.142159 0.989844i \(-0.454596\pi\)
0.142159 + 0.989844i \(0.454596\pi\)
\(258\) −2.81765 20.4050i −0.175419 1.27036i
\(259\) 18.5794i 1.15447i
\(260\) 0 0
\(261\) −6.10469 3.07840i −0.377871 0.190548i
\(262\) −3.25865 + 7.40312i −0.201320 + 0.457367i
\(263\) 18.6227i 1.14833i −0.818741 0.574164i \(-0.805327\pi\)
0.818741 0.574164i \(-0.194673\pi\)
\(264\) −10.5083 + 12.6783i −0.646741 + 0.780292i
\(265\) 0 0
\(266\) −1.42987 0.629390i −0.0876710 0.0385904i
\(267\) −4.86493 7.90172i −0.297729 0.483577i
\(268\) 7.37460 + 8.05234i 0.450476 + 0.491875i
\(269\) 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 \(-0.0897260\pi\)
\(272\) −2.67869 + 30.4278i −0.162420 + 1.84495i
\(273\) −8.43579 13.7016i −0.510557 0.829256i
\(274\) 5.64922 12.8341i 0.341282 0.775337i
\(275\) 0 0
\(276\) 4.91225 17.2495i 0.295683 1.03830i
\(277\) 8.89531i 0.534468i 0.963632 + 0.267234i \(0.0861096\pi\)
−0.963632 + 0.267234i \(0.913890\pi\)
\(278\) 3.81818 + 1.68066i 0.228999 + 0.100799i
\(279\) 9.08080 + 4.57917i 0.543653 + 0.274147i
\(280\) 0 0
\(281\) 17.5517i 1.04705i −0.852011 0.523524i \(-0.824617\pi\)
0.852011 0.523524i \(-0.175383\pi\)
\(282\) −8.81370 + 1.21705i −0.524848 + 0.0724744i
\(283\) −16.3785 −0.973603 −0.486801 0.873513i \(-0.661836\pi\)
−0.486801 + 0.873513i \(0.661836\pi\)
\(284\) 16.8066 + 18.3511i 0.997287 + 1.08894i
\(285\) 0 0
\(286\) −16.1047 7.08883i −0.952290 0.419172i
\(287\) 7.72577i 0.456038i
\(288\) −13.9941 + 9.60022i −0.824612 + 0.565699i
\(289\) 41.3141 2.43024
\(290\) 0 0
\(291\) −10.0839 16.3785i −0.591131 0.960126i
\(292\) 1.91509 1.75391i 0.112072 0.102640i
\(293\) −21.4295 −1.25193 −0.625963 0.779852i \(-0.715294\pi\)
−0.625963 + 0.779852i \(0.715294\pi\)
\(294\) −0.235067 1.70232i −0.0137094 0.0992811i
\(295\) 0 0
\(296\) 6.72263 + 19.8307i 0.390745 + 1.15264i
\(297\) 1.47956 + 17.4031i 0.0858526 + 1.00983i
\(298\) −19.7685 8.70156i −1.14516 0.504068i
\(299\) 19.1647 1.10833
\(300\) 0 0
\(301\) −21.1047 −1.21645
\(302\) −25.0180 11.0122i −1.43963 0.633683i
\(303\) 15.9384 + 25.8874i 0.915635 + 1.48719i
\(304\) −1.75391 0.154404i −0.100593 0.00885568i
\(305\) 0 0
\(306\) 20.6000 + 25.0059i 1.17762 + 1.42949i
\(307\) 26.4172 1.50771 0.753855 0.657041i \(-0.228192\pi\)
0.753855 + 0.657041i \(0.228192\pi\)
\(308\) 11.3949 + 12.4421i 0.649285 + 0.708955i
\(309\) 16.1047 9.91534i 0.916164 0.564064i
\(310\) 0 0
\(311\) 13.4453 0.762411 0.381205 0.924490i \(-0.375509\pi\)
0.381205 + 0.924490i \(0.375509\pi\)
\(312\) −13.9616 11.5720i −0.790420 0.655136i
\(313\) 16.2984i 0.921242i 0.887597 + 0.460621i \(0.152373\pi\)
−0.887597 + 0.460621i \(0.847627\pi\)
\(314\) 14.3736 + 6.32684i 0.811147 + 0.357044i
\(315\) 0 0
\(316\) 7.40312 6.78003i 0.416458 0.381406i
\(317\) 16.8716 0.947602 0.473801 0.880632i \(-0.342882\pi\)
0.473801 + 0.880632i \(0.342882\pi\)
\(318\) 0.763599 + 5.52987i 0.0428205 + 0.310100i
\(319\) 7.66037i 0.428898i
\(320\) 0 0
\(321\) 5.85859 + 9.51563i 0.326995 + 0.531111i
\(322\) −16.8187 7.40312i −0.937270 0.412560i
\(323\) 3.36131i 0.187029i
\(324\) −3.44575 + 17.6671i −0.191431 + 0.981506i
\(325\) 0 0
\(326\) 0.250786 0.569745i 0.0138897 0.0315553i
\(327\) −3.39001 + 2.08717i −0.187468 + 0.115421i
\(328\) −2.79544 8.24609i −0.154352 0.455314i
\(329\) 9.11592i 0.502577i
\(330\) 0 0
\(331\) 17.1275i 0.941413i −0.882290 0.470707i \(-0.843999\pi\)
0.882290 0.470707i \(-0.156001\pi\)
\(332\) −2.67869 + 2.45323i −0.147012 + 0.134639i
\(333\) 19.8307 + 10.0000i 1.08672 + 0.547997i
\(334\) −20.1047 8.84952i −1.10008 0.484224i
\(335\) 0 0
\(336\) 7.78236 + 15.5486i 0.424563 + 0.848247i
\(337\) 12.4031i 0.675641i 0.941211 + 0.337821i \(0.109690\pi\)
−0.941211 + 0.337821i \(0.890310\pi\)
\(338\) 0.399712 0.908080i 0.0217414 0.0493930i
\(339\) −1.17909 + 0.725940i −0.0640391 + 0.0394277i
\(340\) 0 0
\(341\) 11.3949i 0.617069i
\(342\) −1.44138 + 1.18741i −0.0779409 + 0.0642080i
\(343\) −19.3284 −1.04363
\(344\) −22.5261 + 7.63636i −1.21452 + 0.411725i
\(345\) 0 0
\(346\) −4.80625 + 10.9190i −0.258386 + 0.587010i
\(347\) 19.4358i 1.04337i −0.853139 0.521683i \(-0.825304\pi\)
0.853139 0.521683i \(-0.174696\pi\)
\(348\) −2.16224 + 7.59274i −0.115908 + 0.407014i
\(349\) −26.2094 −1.40296 −0.701478 0.712691i \(-0.747476\pi\)
−0.701478 + 0.712691i \(0.747476\pi\)
\(350\) 0 0
\(351\) −19.1647 + 1.62932i −1.02294 + 0.0869669i
\(352\) 16.6643 + 9.15703i 0.888210 + 0.488071i
\(353\) −26.6676 −1.41937 −0.709687 0.704517i \(-0.751164\pi\)
−0.709687 + 0.704517i \(0.751164\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.90172 + 7.23665i −0.418790 + 0.383542i
\(357\) 28.2665 17.4031i 1.49602 0.921071i
\(358\) 5.17374 11.7539i 0.273441 0.621213i
\(359\) −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
\(362\) −5.98677 + 13.6010i −0.314658 + 0.714852i
\(363\) 0.440172 0.271006i 0.0231030 0.0142241i
\(364\) −13.7016 + 12.5483i −0.718157 + 0.657712i
\(365\) 0 0
\(366\) −1.91038 13.8346i −0.0998569 0.723148i
\(367\) 2.50967 0.131004 0.0655018 0.997852i \(-0.479135\pi\)
0.0655018 + 0.997852i \(0.479135\pi\)
\(368\) −20.6301 1.81616i −1.07542 0.0946739i
\(369\) −8.24609 4.15825i −0.429275 0.216470i
\(370\) 0 0
\(371\) 5.71949 0.296941
\(372\) 3.21635 11.2943i 0.166760 0.585582i
\(373\) 23.7016i 1.22722i −0.789609 0.613610i \(-0.789717\pi\)
0.789609 0.613610i \(-0.210283\pi\)
\(374\) 14.6243 33.2241i 0.756207 1.71798i
\(375\) 0 0
\(376\) 3.29844 + 9.72987i 0.170104 + 0.501780i
\(377\) −8.43579 −0.434465
\(378\) 17.4481 + 5.97325i 0.897433 + 0.307231i
\(379\) 13.1199i 0.673923i −0.941518 0.336961i \(-0.890601\pi\)
0.941518 0.336961i \(-0.109399\pi\)
\(380\) 0 0
\(381\) 18.7016 11.5142i 0.958110 0.589890i
\(382\) 7.08883 16.1047i 0.362696 0.823987i
\(383\) 7.26464i 0.371206i 0.982625 + 0.185603i \(0.0594238\pi\)
−0.982625 + 0.185603i \(0.940576\pi\)
\(384\) 13.9325 + 13.7799i 0.710990 + 0.703202i
\(385\) 0 0
\(386\) −25.6366 11.2845i −1.30487 0.574367i
\(387\) −11.3592 + 22.5261i −0.577420 + 1.14506i
\(388\) −16.3785 + 15.0000i −0.831494 + 0.761510i
\(389\) 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
\(392\) −1.87927 + 0.637075i −0.0949174 + 0.0321771i
\(393\) 8.43579 5.19375i 0.425529 0.261990i
\(394\) −6.10469 + 13.8689i −0.307550 + 0.698703i
\(395\) 0 0
\(396\) 19.4132 5.46560i 0.975548 0.274657i
\(397\) 15.9109i 0.798547i 0.916832 + 0.399273i \(0.130738\pi\)
−0.916832 + 0.399273i \(0.869262\pi\)
\(398\) 27.2970 + 12.0154i 1.36828 + 0.602277i
\(399\) 1.00314 + 1.62932i 0.0502200 + 0.0815683i
\(400\) 0 0
\(401\) 9.23521i 0.461184i 0.973050 + 0.230592i \(0.0740663\pi\)
−0.973050 + 0.230592i \(0.925934\pi\)
\(402\) −1.82927 13.2473i −0.0912359 0.660716i
\(403\) 12.5483 0.625078
\(404\) 25.8874 23.7085i 1.28795 1.17954i
\(405\) 0 0
\(406\) 7.40312 + 3.25865i 0.367411 + 0.161724i
\(407\) 24.8842i 1.23347i
\(408\) 23.8732 28.8029i 1.18190 1.42596i
\(409\) −11.2094 −0.554268 −0.277134 0.960831i \(-0.589385\pi\)
−0.277134 + 0.960831i \(0.589385\pi\)
\(410\) 0 0
\(411\) −14.6243 + 9.00393i −0.721366 + 0.444131i
\(412\) −14.7492 16.1047i −0.726641 0.793421i
\(413\) 0 0
\(414\) −16.9541 + 13.9668i −0.833247 + 0.686432i
\(415\) 0 0
\(416\) −10.0839 + 18.3511i −0.494406 + 0.899738i
\(417\) −2.67869 4.35078i −0.131176 0.213059i
\(418\) 1.91509 + 0.842970i 0.0936702 + 0.0412310i
\(419\) −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 \(0.612549\pi\)
\(422\) 23.4788 + 10.3347i 1.14293 + 0.503087i
\(423\) 9.72987 + 4.90647i 0.473082 + 0.238561i
\(424\) 6.10469 2.06950i 0.296470 0.100504i
\(425\) 0 0
\(426\) −4.16888 30.1904i −0.201983 1.46273i
\(427\) −14.3090 −0.692463
\(428\) 9.51563 8.71473i 0.459955 0.421242i
\(429\) 11.2984 + 18.3511i 0.545494 + 0.886001i
\(430\) 0 0
\(431\) 5.71949 0.275498 0.137749 0.990467i \(-0.456013\pi\)
0.137749 + 0.990467i \(0.456013\pi\)
\(432\) 20.7845 + 0.0622549i 0.999996 + 0.00299524i
\(433\) 7.20937i 0.346460i −0.984881 0.173230i \(-0.944580\pi\)
0.984881 0.173230i \(-0.0554205\pi\)
\(434\) −11.0122 4.84728i −0.528605 0.232677i
\(435\) 0 0
\(436\) 3.10469 + 3.39001i 0.148688 + 0.162352i
\(437\) −2.27898 −0.109018
\(438\) −3.15061 + 0.435057i −0.150542 + 0.0207878i
\(439\) 23.4674i 1.12004i −0.828480 0.560018i \(-0.810794\pi\)
0.828480 0.560018i \(-0.189206\pi\)
\(440\) 0 0
\(441\) −0.947657 + 1.87927i −0.0451265 + 0.0894890i
\(442\) 36.5872 + 16.1047i 1.74028 + 0.766022i
\(443\) 29.7907i 1.41540i −0.706514 0.707699i \(-0.749733\pi\)
0.706514 0.707699i \(-0.250267\pi\)
\(444\) 7.02389 24.6645i 0.333339 1.17053i
\(445\) 0 0
\(446\) −12.0154 + 27.2970i −0.568945 + 1.29255i
\(447\) 13.8689 + 22.5261i 0.655975 + 1.06545i
\(448\) 15.9384 12.2094i 0.753017 0.576839i
\(449\) 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
\(452\) 1.07985 + 1.17909i 0.0507917 + 0.0554595i
\(453\) 17.5517 + 28.5078i 0.824651 + 1.33941i
\(454\) 28.8062 + 12.6797i 1.35194 + 0.595088i
\(455\) 0 0
\(456\) 1.66025 + 1.37609i 0.0777482 + 0.0644412i
\(457\) 36.1047i 1.68891i −0.535630 0.844453i \(-0.679926\pi\)
0.535630 0.844453i \(-0.320074\pi\)
\(458\) 1.30952 2.97503i 0.0611900 0.139014i
\(459\) −3.36131 39.5371i −0.156893 1.84543i
\(460\) 0 0
\(461\) 17.5517i 0.817465i 0.912654 + 0.408732i \(0.134029\pi\)
−0.912654 + 0.408732i \(0.865971\pi\)
\(462\) −2.82651 20.4691i −0.131501 0.952311i
\(463\) −5.01934 −0.233268 −0.116634 0.993175i \(-0.537211\pi\)
−0.116634 + 0.993175i \(0.537211\pi\)
\(464\) 9.08080 + 0.799423i 0.421566 + 0.0371123i
\(465\) 0 0
\(466\) −4.80625 + 10.9190i −0.222645 + 0.505814i
\(467\) 29.5197i 1.36601i 0.730414 + 0.683004i \(0.239327\pi\)
−0.730414 + 0.683004i \(0.760673\pi\)
\(468\) 6.01886 + 21.3783i 0.278222 + 0.988210i
\(469\) −13.7016 −0.632679
\(470\) 0 0
\(471\) −10.0839 16.3785i −0.464644 0.754683i
\(472\) 0 0
\(473\) 28.2665 1.29969
\(474\) −12.1792 + 1.68179i −0.559411 + 0.0772471i
\(475\) 0 0
\(476\) −25.8874 28.2665i −1.18655 1.29559i
\(477\) 3.07840 6.10469i 0.140950 0.279514i
\(478\) 14.7492 33.5078i 0.674613 1.53261i
\(479\) 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
\(482\) −3.98822 + 9.06058i −0.181658 + 0.412698i
\(483\) 11.7994 + 19.1647i 0.536890 + 0.872026i
\(484\) −0.403124 0.440172i −0.0183238 0.0200078i
\(485\) 0 0
\(486\) 15.7666 15.4082i 0.715189 0.698931i
\(487\) 0.131364 0.00595267 0.00297634 0.999996i \(-0.499053\pi\)
0.00297634 + 0.999996i \(0.499053\pi\)
\(488\) −15.2727 + 5.17748i −0.691364 + 0.234373i
\(489\) −0.649219 + 0.399712i −0.0293587 + 0.0180756i
\(490\) 0 0
\(491\) 13.4453 0.606776 0.303388 0.952867i \(-0.401882\pi\)
0.303388 + 0.952867i \(0.401882\pi\)
\(492\) −2.92071 + 10.2561i −0.131676 + 0.462382i
\(493\) 17.4031i 0.783797i
\(494\) −0.928300 + 2.10895i −0.0417662 + 0.0948860i
\(495\) 0 0
\(496\) −13.5078 1.18915i −0.606519 0.0533945i
\(497\) −31.2256 −1.40066
\(498\) 4.40685 0.608526i 0.197476 0.0272687i
\(499\) 40.2861i 1.80345i 0.432308 + 0.901726i \(0.357699\pi\)
−0.432308 + 0.901726i \(0.642301\pi\)
\(500\) 0 0
\(501\) 14.1047 + 22.9091i 0.630151 + 1.02350i
\(502\) −12.8341 + 29.1570i −0.572814 + 1.30134i
\(503\) 12.9841i 0.578934i −0.957188 0.289467i \(-0.906522\pi\)
0.957188 0.289467i \(-0.0934780\pi\)
\(504\) 2.97611 21.0863i 0.132567 0.939257i
\(505\) 0 0
\(506\) 22.5261 + 9.91534i 1.00141 + 0.440791i
\(507\) −1.03475 + 0.637075i −0.0459548 + 0.0282935i
\(508\) −17.1275 18.7016i −0.759910 0.829748i
\(509\) 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
\(512\) 12.5940 18.7987i 0.556583 0.830792i
\(513\) 2.27898 0.193752i 0.100619 0.00855434i
\(514\) −2.59688 + 5.89968i −0.114543 + 0.260224i
\(515\) 0 0
\(516\) 28.0169 + 7.97857i 1.23338 + 0.351237i
\(517\) 12.2094i 0.536968i
\(518\) −24.0486 10.5855i −1.05663 0.465101i
\(519\) 12.4421 7.66037i 0.546148 0.336253i
\(520\) 0 0
\(521\) 3.07840i 0.134867i 0.997724 + 0.0674337i \(0.0214811\pi\)
−0.997724 + 0.0674337i \(0.978519\pi\)
\(522\) 7.46270 6.14781i 0.326634 0.269082i
\(523\) −14.0002 −0.612187 −0.306094 0.952001i \(-0.599022\pi\)
−0.306094 + 0.952001i \(0.599022\pi\)
\(524\) −7.72577 8.43579i −0.337502 0.368519i
\(525\) 0 0
\(526\) 24.1047 + 10.6102i 1.05101 + 0.462627i
\(527\) 25.8874i 1.12767i
\(528\) −10.4233 20.8250i −0.453615 0.906291i
\(529\) −3.80625 −0.165489
\(530\) 0 0
\(531\) 0 0
\(532\) 1.62932 1.49219i 0.0706402 0.0646946i
\(533\) −11.3949 −0.493568
\(534\) 12.9995 1.79505i 0.562544 0.0776796i
\(535\) 0 0
\(536\) −14.6243 + 4.95767i −0.631676 + 0.214139i
\(537\) −13.3935 + 8.24609i −0.577970 + 0.355845i
\(538\) 10.9190 + 4.80625i 0.470752 + 0.207212i
\(539\) 2.35817 0.101574
\(540\) 0 0
\(541\) −25.7016 −1.10500 −0.552498 0.833514i \(-0.686325\pi\)
−0.552498 + 0.833514i \(0.686325\pi\)
\(542\) 11.8543 + 5.21791i 0.509184 + 0.224129i
\(543\) 15.4982 9.54193i 0.665091 0.409484i
\(544\) −37.8586 20.8033i −1.62317 0.891934i
\(545\) 0 0
\(546\) 22.5411 3.11262i 0.964671 0.133208i
\(547\) 4.71053 0.201408 0.100704 0.994916i \(-0.467891\pi\)
0.100704 + 0.994916i \(0.467891\pi\)
\(548\) 13.3935 + 14.6243i 0.572140 + 0.624721i
\(549\) −7.70156 + 15.2727i −0.328695 + 0.651824i
\(550\) 0 0
\(551\) 1.00314 0.0427354
\(552\) 19.5285 + 16.1861i 0.831187 + 0.688925i
\(553\) 12.5969i 0.535674i
\(554\) −11.5138 5.06806i −0.489175 0.215321i
\(555\) 0 0
\(556\) −4.35078 + 3.98459i −0.184514 + 0.168984i
\(557\) −36.7023 −1.55512 −0.777562 0.628806i \(-0.783544\pi\)
−0.777562 + 0.628806i \(0.783544\pi\)
\(558\) −11.1009 + 9.14495i −0.469937 + 0.387137i
\(559\) 31.1277i 1.31656i
\(560\) 0 0
\(561\) −37.8586 + 23.3088i −1.59839 + 0.984098i
\(562\) 22.7184 + 10.0000i 0.958317 + 0.421825i
\(563\) 23.3391i 0.983625i 0.870701 + 0.491812i \(0.163665\pi\)
−0.870701 + 0.491812i \(0.836335\pi\)
\(564\) 3.44625 12.1016i 0.145113 0.509569i
\(565\) 0 0
\(566\) 9.33159 21.1999i 0.392236 0.891096i
\(567\) −13.4287 18.1616i −0.563952 0.762716i
\(568\) −33.3286 + 11.2984i −1.39844 + 0.474072i
\(569\) 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 \(0.884594\pi\)
\(572\) 18.3511 16.8066i 0.767299 0.702718i
\(573\) −18.3511 + 11.2984i −0.766630 + 0.471999i
\(574\) 10.0000 + 4.40172i 0.417392 + 0.183724i
\(575\) 0 0
\(576\) −4.45314 23.5832i −0.185548 0.982635i
\(577\) 12.4031i 0.516349i 0.966098 + 0.258174i \(0.0831209\pi\)
−0.966098 + 0.258174i \(0.916879\pi\)
\(578\) −23.5385 + 53.4756i −0.979072 + 2.22429i
\(579\) 17.9857 + 29.2126i 0.747459 + 1.21404i
\(580\) 0 0
\(581\) 4.55796i 0.189096i
\(582\) 26.9451 3.72076i 1.11691 0.154230i
\(583\) −7.66037 −0.317260
\(584\) 1.17909 + 3.47812i 0.0487909 + 0.143925i
\(585\) 0 0
\(586\) 12.2094 27.7377i 0.504365 1.14583i
\(587\) 31.3359i 1.29337i −0.762758 0.646685i \(-0.776155\pi\)
0.762758 0.646685i \(-0.223845\pi\)
\(588\) 2.33735 + 0.665623i 0.0963908 + 0.0274498i
\(589\) −1.49219 −0.0614846
\(590\) 0 0
\(591\) 15.8034 9.72987i 0.650066 0.400233i
\(592\) −29.4984 2.59688i −1.21238 0.106731i
\(593\) 10.5955 0.435104 0.217552 0.976049i \(-0.430193\pi\)
0.217552 + 0.976049i \(0.430193\pi\)
\(594\) −23.3690 8.00025i −0.958843 0.328254i
\(595\) 0 0
\(596\) 22.5261 20.6301i 0.922703 0.845042i
\(597\) −19.1506 31.1047i −0.783780 1.27303i
\(598\) −10.9190 + 24.8062i −0.446512 + 1.01440i
\(599\) 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 \(0.803888\pi\)
\(602\) 12.0243 27.3172i 0.490074 1.11337i
\(603\) −7.37460 + 14.6243i −0.300317 + 0.595549i
\(604\) 28.5078 26.1084i 1.15997 1.06234i
\(605\) 0 0
\(606\) −42.5886 + 5.88091i −1.73004 + 0.238896i
\(607\) −3.25865 −0.132264 −0.0661322 0.997811i \(-0.521066\pi\)
−0.0661322 + 0.997811i \(0.521066\pi\)
\(608\) 1.19913 2.18223i 0.0486313 0.0885011i
\(609\) −5.19375 8.43579i −0.210461 0.341835i
\(610\) 0 0
\(611\) 13.4453 0.543937
\(612\) −44.1036 + 12.4170i −1.78278 + 0.501926i
\(613\) 4.80625i 0.194123i 0.995278 + 0.0970613i \(0.0309443\pi\)
−0.995278 + 0.0970613i \(0.969056\pi\)
\(614\) −15.0511 + 34.1936i −0.607412 + 1.37994i
\(615\) 0 0
\(616\) −22.5969 + 7.66037i −0.910454 + 0.308645i
\(617\) 22.1097 0.890102 0.445051 0.895505i \(-0.353186\pi\)
0.445051 + 0.895505i \(0.353186\pi\)
\(618\) 3.65855 + 26.4946i 0.147168 + 1.06577i
\(619\) 5.15070i 0.207024i −0.994628 0.103512i \(-0.966992\pi\)
0.994628 0.103512i \(-0.0330080\pi\)
\(620\) 0 0
\(621\) 26.8062 2.27898i 1.07570 0.0914523i
\(622\) −7.66037 + 17.4031i −0.307153 + 0.697802i
\(623\) 13.4453i 0.538673i
\(624\) 22.9330 11.4784i 0.918054 0.459502i
\(625\) 0 0
\(626\) −21.0962 9.28595i −0.843173 0.371141i
\(627\) −1.34356 2.18223i −0.0536565 0.0871498i
\(628\) −16.3785 + 15.0000i −0.653574 + 0.598565i
\(629\) 56.5330i 2.25412i
\(630\) 0 0
\(631\) 42.0468i 1.67385i −0.547314 0.836927i \(-0.684350\pi\)
0.547314 0.836927i \(-0.315650\pi\)
\(632\) 4.55796 + 13.4453i 0.181306 + 0.534824i
\(633\) −16.4719 26.7539i −0.654698 1.06337i
\(634\) −9.61250 + 21.8380i −0.381761 + 0.867299i
\(635\) 0 0
\(636\) −7.59274 2.16224i −0.301072 0.0857382i
\(637\) 2.59688i 0.102892i
\(638\) −9.91534 4.36446i −0.392552 0.172791i
\(639\) −16.8066 + 33.3286i −0.664858 + 1.31846i
\(640\) 0 0
\(641\) 12.3136i 0.486359i −0.969981 0.243179i \(-0.921810\pi\)
0.969981 0.243179i \(-0.0781903\pi\)
\(642\) −15.6546 + 2.16169i −0.617839 + 0.0853152i
\(643\) 24.4791 0.965360 0.482680 0.875797i \(-0.339663\pi\)
0.482680 + 0.875797i \(0.339663\pi\)
\(644\) 19.1647 17.5517i 0.755197 0.691634i
\(645\) 0 0
\(646\) −4.35078 1.91509i −0.171179 0.0753483i
\(647\) 10.3550i 0.407095i −0.979065 0.203548i \(-0.934753\pi\)
0.979065 0.203548i \(-0.0652472\pi\)
\(648\) −20.9046 14.5258i −0.821208 0.570628i
\(649\) 0 0
\(650\) 0 0
\(651\) 7.72577 + 12.5483i 0.302797 + 0.491808i
\(652\) 0.594576 + 0.649219i 0.0232854 + 0.0254254i
\(653\) 25.9875 1.01697 0.508485 0.861071i \(-0.330206\pi\)
0.508485 + 0.861071i \(0.330206\pi\)
\(654\) −0.770119 5.57708i −0.0301140 0.218081i
\(655\) 0 0
\(656\) 12.2662 + 1.07985i 0.478914 + 0.0421609i
\(657\) 3.47812 + 1.75391i 0.135694 + 0.0684264i
\(658\) −11.7994 5.19375i −0.459987 0.202474i
\(659\) 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 \(0.613839\pi\)
\(662\) 22.1693 + 9.75831i 0.861635 + 0.379268i
\(663\) −25.6682 41.6908i −0.996871 1.61914i
\(664\) −1.64922 4.86493i −0.0640021 0.188796i
\(665\) 0 0
\(666\) −24.2421 + 19.9708i −0.939363 + 0.773852i
\(667\) 11.7994 0.456873
\(668\) 22.9091 20.9809i 0.886379 0.811776i
\(669\) 31.1047 19.1506i 1.20258 0.740403i
\(670\) 0 0
\(671\) 19.1647 0.739847
\(672\) −24.5596 + 1.21449i −0.947408 + 0.0468501i
\(673\) 24.8062i 0.956211i 0.878303 + 0.478105i \(0.158676\pi\)
−0.878303 + 0.478105i \(0.841324\pi\)
\(674\) −16.0542 7.06662i −0.618385 0.272196i
\(675\) 0 0
\(676\) 0.947657 + 1.03475i 0.0364483 + 0.0397980i
\(677\) −12.9937 −0.499390 −0.249695 0.968324i \(-0.580330\pi\)
−0.249695 + 0.968324i \(0.580330\pi\)
\(678\) −0.267856 1.93977i −0.0102870 0.0744965i
\(679\) 27.8691i 1.06952i
\(680\) 0 0
\(681\) −20.2094 32.8244i −0.774425 1.25784i
\(682\) 14.7492 + 6.49219i 0.564776 + 0.248599i
\(683\) 11.6291i 0.444975i −0.974936 0.222488i \(-0.928582\pi\)
0.974936 0.222488i \(-0.0714177\pi\)
\(684\) −0.715734 2.54220i −0.0273668 0.0972034i
\(685\) 0 0
\(686\) 11.0122 25.0180i 0.420449 0.955193i
\(687\) −3.39001 + 2.08717i −0.129337 + 0.0796303i
\(688\) 2.94984 33.5078i 0.112462 1.27747i
\(689\) 8.43579i 0.321378i
\(690\) 0 0
\(691\) 1.18915i 0.0452375i −0.999744 0.0226187i \(-0.992800\pi\)
0.999744 0.0226187i \(-0.00720038\pi\)
\(692\) −11.3949 12.4421i −0.433169 0.472978i
\(693\) −11.3949 + 22.5969i −0.432857 + 0.858384i
\(694\) 25.1570 + 11.0734i 0.954948 + 0.420341i
\(695\) 0 0
\(696\) −8.59589 7.12466i −0.325826 0.270059i
\(697\) 23.5078i 0.890422i
\(698\) 14.9327 33.9246i 0.565210 1.28406i
\(699\) 12.4421 7.66037i 0.470604 0.289742i
\(700\) 0 0
\(701\) 11.3949i 0.430380i 0.976572 + 0.215190i \(0.0690370\pi\)
−0.976572 + 0.215190i \(0.930963\pi\)
\(702\) 8.81007 25.7345i 0.332515 0.971288i
\(703\) −3.25865 −0.122902
\(704\) −21.3470 + 16.3526i −0.804544 + 0.616311i
\(705\) 0 0
\(706\) 15.1938 34.5177i 0.571824 1.29909i
\(707\) 44.0490i 1.65663i
\(708\) 0 0
\(709\) 17.7016 0.664796 0.332398 0.943139i \(-0.392142\pi\)
0.332398 + 0.943139i \(0.392142\pi\)
\(710\) 0 0
\(711\) 13.4453 + 6.78003i 0.504237 + 0.254271i
\(712\) −4.86493 14.3508i −0.182321 0.537818i
\(713\) −17.5517 −0.657317
\(714\) 6.42137 + 46.5026i 0.240314 + 1.74032i
\(715\) 0 0
\(716\) 12.2662 + 13.3935i 0.458408 + 0.500537i
\(717\) −38.1818 + 23.5078i −1.42593 + 0.877915i
\(718\) 4.40172 10.0000i 0.164271 0.373197i
\(719\) −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
\(722\) −10.7148 + 24.3422i −0.398762 + 0.905924i
\(723\) 10.3244 6.35656i 0.383970 0.236403i
\(724\) −14.1938 15.4982i −0.527507 0.575986i
\(725\) 0 0
\(726\) 0.0999951 + 0.724149i 0.00371117 + 0.0268757i
\(727\) −40.5488 −1.50387 −0.751936 0.659236i \(-0.770880\pi\)
−0.751936 + 0.659236i \(0.770880\pi\)
\(728\) −8.43579 24.8842i −0.312651 0.922271i
\(729\) −26.6125 + 4.55796i −0.985648 + 0.168813i
\(730\) 0 0
\(731\) −64.2169 −2.37515
\(732\) 18.9956 + 5.40949i 0.702096 + 0.199940i
\(733\) 4.80625i 0.177523i 0.996053 + 0.0887614i \(0.0282909\pi\)
−0.996053 + 0.0887614i \(0.971709\pi\)
\(734\) −1.42987 + 3.24844i −0.0527775 + 0.119902i
\(735\) 0 0
\(736\) 14.1047 25.6682i 0.519906 0.946143i
\(737\) 18.3511 0.675973
\(738\) 10.0805 8.30435i 0.371068 0.305687i
\(739\) 29.2357i 1.07545i −0.843120 0.537726i \(-0.819283\pi\)
0.843120 0.537726i \(-0.180717\pi\)
\(740\) 0 0
\(741\) 2.40312 1.47956i 0.0882810 0.0543529i
\(742\) −3.25865 + 7.40312i −0.119629 + 0.271777i
\(743\) 40.8778i 1.49966i 0.661630 + 0.749830i \(0.269865\pi\)
−0.661630 + 0.749830i \(0.730135\pi\)
\(744\) 12.7865 + 10.5980i 0.468776 + 0.388542i
\(745\) 0 0
\(746\) 30.6786 + 13.5038i 1.12322 + 0.494411i
\(747\) −4.86493 2.45323i −0.177999 0.0897592i
\(748\) 34.6722 + 37.8586i 1.26774 + 1.38425i
\(749\) 16.1914i 0.591622i
\(750\) 0 0
\(751\) 36.2784i 1.32382i −0.749584 0.661909i \(-0.769746\pi\)
0.749584 0.661909i \(-0.230254\pi\)
\(752\) −14.4733 1.27415i −0.527787 0.0464634i
\(753\) 33.2241 20.4555i 1.21076 0.745439i
\(754\) 4.80625 10.9190i 0.175033 0.397647i
\(755\) 0 0
\(756\) −17.6726 + 19.1810i −0.642745 + 0.697607i
\(757\) 35.9109i 1.30521i 0.757700 + 0.652603i \(0.226323\pi\)
−0.757700 + 0.652603i \(0.773677\pi\)
\(758\) 16.9820 + 7.47499i 0.616813 + 0.271504i
\(759\) −15.8034 25.6682i −0.573628 0.931698i
\(760\) 0 0
\(761\) 20.6301i 0.747841i 0.927461 + 0.373920i \(0.121987\pi\)
−0.927461 + 0.373920i \(0.878013\pi\)
\(762\) 4.24849 + 30.7669i 0.153906 + 1.11457i
\(763\) −5.76832 −0.208827
\(764\) 16.8066 + 18.3511i 0.608041 + 0.663921i
\(765\) 0 0
\(766\) −9.40312 4.13899i −0.339749 0.149548i
\(767\) 0 0
\(768\) −25.7742 + 10.1828i −0.930048 + 0.367439i
\(769\) 14.1938 0.511840 0.255920 0.966698i \(-0.417622\pi\)
0.255920 + 0.966698i \(0.417622\pi\)
\(770\) 0 0
\(771\) 6.72263 4.13899i 0.242110 0.149062i
\(772\) 29.2126 26.7539i 1.05139 0.962894i
\(773\) 2.27898 0.0819692 0.0409846 0.999160i \(-0.486951\pi\)
0.0409846 + 0.999160i \(0.486951\pi\)
\(774\) −22.6852 27.5371i −0.815402 0.989800i
\(775\) 0 0
\(776\) −10.0839 29.7460i −0.361993 1.06782i
\(777\) 16.8716 + 27.4031i 0.605264 + 0.983082i
\(778\) 48.3866 + 21.2984i 1.73474 + 0.763586i
\(779\) 1.35503 0.0485489
\(780\) 0 0
\(781\) 41.8219 1.49650
\(782\) −51.1756 22.5261i −1.83003 0.805530i
\(783\) −11.7994 + 1.00314i −0.421675 + 0.0358494i
\(784\) 0.246095 2.79544i 0.00878910 0.0998370i
\(785\) 0 0
\(786\) 1.91638 + 13.8781i 0.0683551 + 0.495017i
\(787\) 18.4480 0.657601