Properties

Label 300.2.e.e.251.2
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 251.2
Root \(1.29437 + 0.569745i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.e.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29437 + 0.569745i) q^{2} +(-0.908080 + 1.47492i) q^{3} +(1.35078 - 1.47492i) q^{4} +(0.335062 - 2.42647i) q^{6} -2.50967i q^{7} +(-0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +O(q^{10})\) \(q+(-1.29437 + 0.569745i) q^{2} +(-0.908080 + 1.47492i) q^{3} +(1.35078 - 1.47492i) q^{4} +(0.335062 - 2.42647i) q^{6} -2.50967i q^{7} +(-0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} -3.36131 q^{11} +(0.948773 + 3.33164i) q^{12} -3.70156 q^{13} +(1.42987 + 3.24844i) q^{14} +(-0.350781 - 3.98459i) q^{16} -7.63636i q^{17} +(3.27458 + 2.69761i) q^{18} +0.440172i q^{19} +(3.70156 + 2.27898i) q^{21} +(4.35078 - 1.91509i) q^{22} +5.17748 q^{23} +(-3.12625 - 3.77181i) 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} +(-5.77547 - 1.62603i) q^{36} -7.40312 q^{37} +(-0.250786 - 0.569745i) q^{38} +(3.36131 - 5.45951i) q^{39} +3.07840i q^{41} +(-6.08962 - 0.840894i) q^{42} -8.40935i q^{43} +(-4.54040 + 4.95767i) q^{44} +(-6.70156 + 2.94984i) q^{46} -3.63232 q^{47} +(6.19549 + 3.10095i) q^{48} +0.701562 q^{49} +(11.2630 + 6.93443i) q^{51} +(-5.00000 + 5.45951i) q^{52} +2.27898i q^{53} +(-6.95235 + 2.38010i) 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} +(-1.12625 + 8.15611i) q^{66} +5.45951i q^{67} +(-11.2630 - 10.3151i) q^{68} +(-4.70156 + 7.63636i) q^{69} -12.4421 q^{71} +(8.40201 - 1.18586i) q^{72} +1.29844 q^{73} +(9.58237 - 4.21789i) q^{74} +(0.649219 + 0.594576i) q^{76} +8.43579i q^{77} +(-1.24025 + 8.98171i) q^{78} +5.01934i q^{79} +(-5.35078 + 7.23665i) q^{81} +(-1.75391 - 3.98459i) q^{82} -1.81616 q^{83} +(8.36131 - 2.38111i) 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} +(-9.78600 - 0.483926i) 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
\(6\) 0.335062 2.42647i 0.136788 0.990600i
\(7\) 2.50967i 0.948566i −0.880373 0.474283i \(-0.842707\pi\)
0.880373 0.474283i \(-0.157293\pi\)
\(8\) −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 \(-0.669149\pi\)
−0.506737 + 0.862101i \(0.669149\pi\)
\(12\) 0.948773 + 3.33164i 0.273887 + 0.961762i
\(13\) −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 \(-0.376814\pi\)
\(18\) 3.27458 + 2.69761i 0.771826 + 0.635834i
\(19\) 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
\(22\) 4.35078 1.91509i 0.927590 0.408299i
\(23\) 5.17748 1.07958 0.539789 0.841800i \(-0.318504\pi\)
0.539789 + 0.841800i \(0.318504\pi\)
\(24\) −3.12625 3.77181i −0.638143 0.769918i
\(25\) 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 \(-0.901533\pi\)
0.952534 0.304432i \(-0.0984667\pi\)
\(32\) 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
\(36\) −5.77547 1.62603i −0.962578 0.271005i
\(37\) −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 \(0.922727\pi\)
\(42\) −6.08962 0.840894i −0.939649 0.129753i
\(43\) 8.40935i 1.28241i −0.767368 0.641207i \(-0.778434\pi\)
0.767368 0.641207i \(-0.221566\pi\)
\(44\) −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 \(-0.585344\pi\)
−0.264914 + 0.964272i \(0.585344\pi\)
\(48\) 6.19549 + 3.10095i 0.894242 + 0.447584i
\(49\) 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 \(0.949972\pi\)
\(54\) −6.95235 + 2.38010i −0.946095 + 0.323890i
\(55\) 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
\(66\) −1.12625 + 8.15611i −0.138632 + 1.00395i
\(67\) 5.45951i 0.666985i 0.942753 + 0.333493i \(0.108227\pi\)
−0.942753 + 0.333493i \(0.891773\pi\)
\(68\) −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 \(-0.764373\pi\)
−0.738304 + 0.674468i \(0.764373\pi\)
\(72\) 8.40201 1.18586i 0.990186 0.139755i
\(73\) 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
\(78\) −1.24025 + 8.98171i −0.140431 + 1.01698i
\(79\) 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
\(82\) −1.75391 3.98459i −0.193686 0.440024i
\(83\) −1.81616 −0.199349 −0.0996747 0.995020i \(-0.531780\pi\)
−0.0996747 + 0.995020i \(0.531780\pi\)
\(84\) 8.36131 2.38111i 0.912294 0.259800i
\(85\) 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
\(96\) −9.78600 0.483926i −0.998780 0.0493905i
\(97\) 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 \(-0.337979\pi\)
\(102\) −18.5294 2.55865i −1.83468 0.253344i
\(103\) 10.9190i 1.07588i 0.842982 + 0.537941i \(0.180798\pi\)
−0.842982 + 0.537941i \(0.819202\pi\)
\(104\) 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 \(-0.600949\pi\)
−0.311851 + 0.950131i \(0.600949\pi\)
\(108\) 7.64285 7.04179i 0.735434 0.677596i
\(109\) 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 \(-0.0119718\pi\)
\(114\) 1.06806 + 0.147485i 0.100033 + 0.0138132i
\(115\) 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
\(126\) 6.77012 8.21811i 0.603130 0.732128i
\(127\) 12.6797i 1.12514i −0.826749 0.562571i \(-0.809812\pi\)
0.826749 0.562571i \(-0.190188\pi\)
\(128\) 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 \(-0.419616\pi\)
0.249857 + 0.968283i \(0.419616\pi\)
\(132\) −3.18913 11.1987i −0.277578 0.974721i
\(133\) 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 \(0.860779\pi\)
\(138\) 1.73477 12.5630i 0.147674 1.06943i
\(139\) 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
\(142\) 16.1047 7.08883i 1.35148 0.594882i
\(143\) 12.4421 1.04046
\(144\) −10.1997 + 6.32194i −0.849972 + 0.526829i
\(145\) 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 \(-0.711911\pi\)
0.617641 0.786460i \(-0.288089\pi\)
\(152\) −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
\(156\) −3.51194 12.3323i −0.281180 0.987372i
\(157\) 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
\(162\) 2.80284 12.4155i 0.220212 0.975452i
\(163\) 0.440172i 0.0344769i −0.999851 0.0172385i \(-0.994513\pi\)
0.999851 0.0172385i \(-0.00548745\pi\)
\(164\) 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 \(-0.705218\pi\)
−0.600968 + 0.799273i \(0.705218\pi\)
\(168\) −9.46600 + 7.84585i −0.730318 + 0.605320i
\(169\) 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 \(0.896088\pi\)
\(174\) −5.52987 0.763599i −0.419218 0.0578883i
\(175\) 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 \(-0.389788\pi\)
0.339365 + 0.940655i \(0.389788\pi\)
\(180\) 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
\(186\) −8.22575 1.13586i −0.603141 0.0832856i
\(187\) 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 \(-0.648626\pi\)
−0.450140 + 0.892958i \(0.648626\pi\)
\(192\) 12.9424 4.94915i 0.934038 0.357174i
\(193\) 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 \(-0.124660\pi\)
\(198\) −11.0069 9.06753i −0.782226 0.644401i
\(199\) 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
\(202\) 10.0000 + 22.7184i 0.703598 + 1.59846i
\(203\) −5.71949 −0.401429
\(204\) 25.4416 7.24518i 1.78127 0.507264i
\(205\) 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 \(0.214647\pi\)
−0.781123 + 0.624378i \(0.785353\pi\)
\(212\) 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
\(216\) −5.88065 + 13.4691i −0.400127 + 0.916460i
\(217\) −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
\(222\) −2.48050 + 17.9634i −0.166481 + 1.20563i
\(223\) 21.0891i 1.41223i 0.708098 + 0.706114i \(0.249553\pi\)
−0.708098 + 0.706114i \(0.750447\pi\)
\(224\) 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 \(-0.235506\pi\)
0.738560 + 0.674188i \(0.235506\pi\)
\(228\) −1.46650 + 0.417624i −0.0971210 + 0.0276578i
\(229\) 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 \(0.910884\pi\)
\(234\) −12.1211 9.98539i −0.792379 0.652765i
\(235\) 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 \(-0.184158\pi\)
0.837258 + 0.546809i \(0.184158\pi\)
\(240\) 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
\(246\) 7.46964 + 1.03146i 0.476247 + 0.0657632i
\(247\) 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 \(-0.248281\pi\)
0.710916 + 0.703277i \(0.248281\pi\)
\(252\) −4.08080 + 14.4945i −0.257066 + 0.913068i
\(253\) −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 \(-0.0454044\pi\)
\(258\) −20.4050 2.81765i −1.27036 0.175419i
\(259\) 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 \(-0.694673\pi\)
−0.574164 + 0.818741i \(0.694673\pi\)
\(264\) 10.5083 + 12.6783i 0.646741 + 0.780292i
\(265\) 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 \(0.0897260\pi\)
−0.960533 + 0.278165i \(0.910274\pi\)
\(272\) −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
\(276\) 4.91225 + 17.2495i 0.295683 + 1.03830i
\(277\) −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 \(0.824617\pi\)
\(282\) −1.21705 + 8.81370i −0.0724744 + 0.524848i
\(283\) 16.3785i 0.973603i −0.873513 0.486801i \(-0.838164\pi\)
0.873513 0.486801i \(-0.161836\pi\)
\(284\) −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
\(288\) 9.60022 13.9941i 0.565699 0.824612i
\(289\) −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 \(-0.215294\pi\)
\(294\) 0.235067 1.70232i 0.0137094 0.0992811i
\(295\) 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
\(306\) 20.6000 25.0059i 1.17762 1.42949i
\(307\) 26.4172i 1.50771i −0.657041 0.753855i \(-0.728192\pi\)
0.657041 0.753855i \(-0.271808\pi\)
\(308\) 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 \(-0.375509\pi\)
0.381205 + 0.924490i \(0.375509\pi\)
\(312\) 11.5720 + 13.9616i 0.655136 + 0.790420i
\(313\) 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 \(-0.157118\pi\)
\(318\) 5.52987 + 0.763599i 0.310100 + 0.0428205i
\(319\) 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
\(324\) 3.44575 + 17.6671i 0.191431 + 0.981506i
\(325\) 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 \(0.156001\pi\)
−0.882290 + 0.470707i \(0.843999\pi\)
\(332\) −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
\(336\) 7.78236 15.5486i 0.424563 0.848247i
\(337\) −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
\(342\) −1.18741 + 1.44138i −0.0642080 + 0.0779409i
\(343\) 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 \(-0.325304\pi\)
0.521683 + 0.853139i \(0.325304\pi\)
\(348\) 7.59274 2.16224i 0.407014 0.115908i
\(349\) 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 \(-0.434646\pi\)
0.203875 + 0.978997i \(0.434646\pi\)
\(360\) 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
\(366\) −1.91038 + 13.8346i −0.0998569 + 0.723148i
\(367\) 2.50967i 0.131004i −0.997852 0.0655018i \(-0.979135\pi\)
0.997852 0.0655018i \(-0.0208648\pi\)
\(368\) −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
\(372\) 11.2943 3.21635i 0.585582 0.166760i
\(373\) −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
\(378\) 5.97325 + 17.4481i 0.307231 + 0.897433i
\(379\) 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
\(382\) 16.1047 7.08883i 0.823987 0.362696i
\(383\) 7.26464 0.371206 0.185603 0.982625i \(-0.440576\pi\)
0.185603 + 0.982625i \(0.440576\pi\)
\(384\) −13.9325 + 13.7799i −0.710990 + 0.703202i
\(385\) 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
\(396\) 19.4132 + 5.46560i 0.975548 + 0.274657i
\(397\) −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 \(-0.0740663\pi\)
\(402\) 13.2473 + 1.82927i 0.660716 + 0.0912359i
\(403\) 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
\(408\) −28.8029 + 23.8732i −1.42596 + 1.18190i
\(409\) 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
\(414\) 16.9541 + 13.9668i 0.833247 + 0.686432i
\(415\) 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 \(-0.174076\pi\)
0.854154 + 0.520021i \(0.174076\pi\)
\(420\) 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
\(426\) −4.16888 + 30.1904i −0.201983 + 1.46273i
\(427\) 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 \(-0.456013\pi\)
0.137749 + 0.990467i \(0.456013\pi\)
\(432\) −0.0622549 20.7845i −0.00299524 0.999996i
\(433\) −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
\(438\) 0.435057 3.15061i 0.0207878 0.150542i
\(439\) 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
\(442\) −16.1047 36.5872i −0.766022 1.74028i
\(443\) −29.7907 −1.41540 −0.707699 0.706514i \(-0.750267\pi\)
−0.707699 + 0.706514i \(0.750267\pi\)
\(444\) −7.02389 24.6645i −0.333339 1.17053i
\(445\) 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
\(456\) 1.66025 1.37609i 0.0777482 0.0644412i
\(457\) 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 \(-0.134029\pi\)
\(462\) 20.4691 + 2.82651i 0.952311 + 0.131501i
\(463\) 5.01934i 0.233268i −0.993175 0.116634i \(-0.962789\pi\)
0.993175 0.116634i \(-0.0372105\pi\)
\(464\) −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 \(-0.739327\pi\)
−0.683004 + 0.730414i \(0.739327\pi\)
\(468\) 21.3783 + 6.01886i 0.988210 + 0.278222i
\(469\) 13.7016 0.632679
\(470\) 0 0
\(471\) −10.0839 + 16.3785i −0.464644 + 0.754683i
\(472\) 0 0
\(473\) 28.2665i 1.29969i
\(474\) 12.1792 + 1.68179i 0.559411 + 0.0772471i
\(475\) 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 \(-0.778704\pi\)
−0.767912 + 0.640555i \(0.778704\pi\)
\(480\) 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
\(486\) 15.7666 + 15.4082i 0.715189 + 0.698931i
\(487\) 0.131364i 0.00595267i −0.999996 0.00297634i \(-0.999053\pi\)
0.999996 0.00297634i \(-0.000947399\pi\)
\(488\) 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 \(-0.401882\pi\)
0.303388 + 0.952867i \(0.401882\pi\)
\(492\) −10.2561 + 2.92071i −0.462382 + 0.131676i
\(493\) −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
\(498\) −0.608526 + 4.40685i −0.0272687 + 0.197476i
\(499\) 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
\(502\) −29.1570 + 12.8341i −1.30134 + 0.572814i
\(503\) −12.9841 −0.578934 −0.289467 0.957188i \(-0.593478\pi\)
−0.289467 + 0.957188i \(0.593478\pi\)
\(504\) −2.97611 21.0863i −0.132567 0.939257i
\(505\) 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
\(516\) 28.0169 7.97857i 1.23338 0.351237i
\(517\) 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 \(-0.0214811\pi\)
\(522\) 6.14781 7.46270i 0.269082 0.326634i
\(523\) 14.0002i 0.612187i −0.952001 0.306094i \(-0.900978\pi\)
0.952001 0.306094i \(-0.0990220\pi\)
\(524\) 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
\(528\) −20.8250 10.4233i −0.906291 0.453615i
\(529\) 3.80625 0.165489
\(530\) 0 0
\(531\) 0 0
\(532\) 1.49219 1.62932i 0.0646946 0.0706402i
\(533\) 11.3949i 0.493568i
\(534\) −12.9995 1.79505i −0.562544 0.0776796i
\(535\) 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
\(546\) 22.5411 + 3.11262i 0.964671 + 0.133208i
\(547\) 4.71053i 0.201408i −0.994916 0.100704i \(-0.967891\pi\)
0.994916 0.100704i \(-0.0321095\pi\)
\(548\) 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
\(552\) −16.1861 19.5285i −0.688925 0.831187i
\(553\) 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 \(0.716456\pi\)
\(558\) 9.14495 11.1009i 0.387137 0.469937i
\(559\) 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 \(-0.336335\pi\)
0.491812 + 0.870701i \(0.336335\pi\)
\(564\) −3.44625 12.1016i −0.145113 0.509569i
\(565\) 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 \(-0.884594\pi\)
0.934992 0.354669i \(-0.115406\pi\)
\(572\) 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
\(576\) −4.45314 + 23.5832i −0.185548 + 0.982635i
\(577\) −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
\(582\) 3.72076 26.9451i 0.154230 1.11691i
\(583\) 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 \(-0.276155\pi\)
0.646685 + 0.762758i \(0.276155\pi\)
\(588\) 0.665623 + 2.33735i 0.0274498 + 0.0963908i
\(589\) 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 \(0.930193\pi\)
\(594\) 23.3690 8.00025i 0.958843 0.328254i
\(595\) 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
\(606\) −42.5886 5.88091i −1.73004 0.238896i
\(607\) 3.25865i 0.132264i 0.997811 + 0.0661322i \(0.0210659\pi\)
−0.997811 + 0.0661322i \(0.978934\pi\)
\(608\) −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
\(612\) −12.4170 + 44.1036i −0.501926 + 1.78278i
\(613\) 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 \(-0.146814\pi\)
\(618\) 26.4946 + 3.65855i 1.06577 + 0.147168i
\(619\) 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
\(622\) −17.4031 + 7.66037i −0.697802 + 0.307153i
\(623\) −13.4453 −0.538673
\(624\) −22.9330 11.4784i −0.918054 0.459502i
\(625\) 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 \(0.315650\pi\)
−0.547314 + 0.836927i \(0.684350\pi\)
\(632\) −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
\(636\) −7.59274 + 2.16224i −0.301072 + 0.0857382i
\(637\) −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 \(0.921810\pi\)
\(642\) −2.16169 + 15.6546i −0.0853152 + 0.617839i
\(643\) 24.4791i 0.965360i 0.875797 + 0.482680i \(0.160337\pi\)
−0.875797 + 0.482680i \(0.839663\pi\)
\(644\) −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 \(-0.434753\pi\)
0.203548 + 0.979065i \(0.434753\pi\)
\(648\) −14.5258 20.9046i −0.570628 0.821208i
\(649\) 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 \(0.830206\pi\)
\(654\) 0.770119 5.57708i 0.0301140 0.218081i
\(655\) 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 \(-0.606154\pi\)
−0.327346 + 0.944905i \(0.606154\pi\)
\(660\) 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
\(666\) −24.2421 19.9708i −0.939363 0.773852i
\(667\) 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
\(672\) −1.21449 + 24.5596i −0.0468501 + 0.947408i
\(673\) 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 \(0.919670\pi\)
\(678\) −1.93977 0.267856i −0.0744965 0.0102870i
\(679\) 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 \(-0.571418\pi\)
−0.222488 + 0.974936i \(0.571418\pi\)
\(684\) 0.715734 2.54220i 0.0273668 0.0972034i
\(685\) 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 \(0.00720038\pi\)
−0.999744 + 0.0226187i \(0.992800\pi\)
\(692\) 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
\(696\) −8.59589 + 7.12466i −0.325826 + 0.270059i
\(697\) 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 \(-0.0690370\pi\)
\(702\) 25.7345 8.81007i 0.971288 0.332515i
\(703\) 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
\(714\) −6.42137 + 46.5026i −0.240314 + 1.74032i
\(715\) 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 \(-0.193207\pi\)
0.821375 + 0.570389i \(0.193207\pi\)
\(720\) 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
\(726\) 0.0999951 0.724149i 0.00371117 0.0268757i
\(727\) 40.5488i 1.50387i 0.659236 + 0.751936i \(0.270880\pi\)
−0.659236 + 0.751936i \(0.729120\pi\)
\(728\) −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
\(732\) −5.40949 18.9956i −0.199940 0.702096i
\(733\) 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
\(738\) −8.30435 + 10.0805i −0.305687 + 0.371068i
\(739\) 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
\(742\) −7.40312 + 3.25865i −0.271777 + 0.119629i
\(743\) 40.8778 1.49966 0.749830 0.661630i \(-0.230135\pi\)
0.749830 + 0.661630i \(0.230135\pi\)
\(744\) −12.7865 + 10.5980i −0.468776 + 0.388542i
\(745\) 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 \(0.230254\pi\)
−0.749584 + 0.661909i \(0.769746\pi\)
\(752\) 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
\(756\) −17.6726 19.1810i −0.642745 0.697607i
\(757\) −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 \(-0.121987\pi\)
\(762\) −30.7669 4.24849i −1.11457 0.153906i
\(763\) 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
\(768\) 10.1828 25.7742i 0.367439 0.930048i
\(769\) −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 \(0.986951\pi\)
\(774\) 22.6852 27.5371i 0.815402 0.989800i
\(775\) 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
\(786\) 1.91638 13.8781i 0.0683551 0.495017i
\(787\)