Properties

Label 950.2.e.j.201.2
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
Defining polynomial: \(x^{4} - x^{3} - x^{2} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.2
Root \(-0.895644 + 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.j.501.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.895644 - 1.55130i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.895644 - 1.55130i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.895644 - 1.55130i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.895644 - 1.55130i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.104356 - 0.180750i) q^{9} +0.791288 q^{11} -1.79129 q^{12} +(-2.39564 - 4.14938i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.89564 - 3.28335i) q^{17} -0.208712 q^{18} +(-3.50000 - 2.59808i) q^{19} +(0.895644 - 1.55130i) q^{21} +(0.395644 - 0.685275i) q^{22} +(-2.29129 - 3.96863i) q^{23} +(-0.895644 + 1.55130i) q^{24} -4.79129 q^{26} +5.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-1.10436 - 1.91280i) q^{29} -0.208712 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.708712 - 1.22753i) q^{33} +(-1.89564 - 3.28335i) q^{34} +(-0.104356 + 0.180750i) q^{36} +5.58258 q^{37} +(-4.00000 + 1.73205i) q^{38} -8.58258 q^{39} +(-1.18693 + 2.05583i) q^{41} +(-0.895644 - 1.55130i) q^{42} +(0.604356 - 1.04678i) q^{43} +(-0.395644 - 0.685275i) q^{44} -4.58258 q^{46} +(3.08258 + 5.33918i) q^{47} +(0.895644 + 1.55130i) q^{48} -6.00000 q^{49} +(-3.39564 - 5.88143i) q^{51} +(-2.39564 + 4.14938i) q^{52} +(2.29129 + 3.96863i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{56} +(-7.16515 + 3.10260i) q^{57} -2.20871 q^{58} +(2.29129 - 3.96863i) q^{59} +(6.18693 + 10.7161i) q^{61} +(-0.104356 + 0.180750i) q^{62} +(-0.104356 - 0.180750i) q^{63} +1.00000 q^{64} +(-0.708712 - 1.22753i) q^{66} +(3.20871 + 5.55765i) q^{67} -3.79129 q^{68} -8.20871 q^{69} +(-2.29129 + 3.96863i) q^{71} +(0.104356 + 0.180750i) q^{72} +(-0.895644 + 1.55130i) q^{73} +(2.79129 - 4.83465i) q^{74} +(-0.500000 + 4.33013i) q^{76} +0.791288 q^{77} +(-4.29129 + 7.43273i) q^{78} +(3.97822 - 6.89048i) q^{79} +(4.79129 - 8.29875i) q^{81} +(1.18693 + 2.05583i) q^{82} +0.791288 q^{83} -1.79129 q^{84} +(-0.604356 - 1.04678i) q^{86} -3.95644 q^{87} -0.791288 q^{88} +(2.29129 + 3.96863i) q^{89} +(-2.39564 - 4.14938i) q^{91} +(-2.29129 + 3.96863i) q^{92} +(-0.186932 + 0.323775i) q^{93} +6.16515 q^{94} +1.79129 q^{96} +(0.686932 - 1.18980i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-0.0825757 - 0.143025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - q^{3} - 2q^{4} + q^{6} + 4q^{7} - 4q^{8} - 5q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - q^{3} - 2q^{4} + q^{6} + 4q^{7} - 4q^{8} - 5q^{9} - 6q^{11} + 2q^{12} - 5q^{13} + 2q^{14} - 2q^{16} + 3q^{17} - 10q^{18} - 14q^{19} - q^{21} - 3q^{22} + q^{24} - 10q^{26} + 20q^{27} - 2q^{28} - 9q^{29} - 10q^{31} + 2q^{32} + 12q^{33} - 3q^{34} - 5q^{36} + 4q^{37} - 16q^{38} - 16q^{39} + 9q^{41} + q^{42} + 7q^{43} + 3q^{44} - 6q^{47} - q^{48} - 24q^{49} - 9q^{51} - 5q^{52} + 10q^{54} - 4q^{56} + 8q^{57} - 18q^{58} + 11q^{61} - 5q^{62} - 5q^{63} + 4q^{64} - 12q^{66} + 22q^{67} - 6q^{68} - 42q^{69} + 5q^{72} + q^{73} + 2q^{74} - 2q^{76} - 6q^{77} - 8q^{78} - 7q^{79} + 10q^{81} - 9q^{82} - 6q^{83} + 2q^{84} - 7q^{86} + 30q^{87} + 6q^{88} - 5q^{91} + 13q^{93} - 12q^{94} - 2q^{96} - 11q^{97} - 12q^{98} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.895644 1.55130i 0.517100 0.895644i −0.482703 0.875784i \(-0.660345\pi\)
0.999803 0.0198595i \(-0.00632191\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.895644 1.55130i −0.365645 0.633316i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.104356 0.180750i −0.0347854 0.0602500i
\(10\) 0 0
\(11\) 0.791288 0.238582 0.119291 0.992859i \(-0.461938\pi\)
0.119291 + 0.992859i \(0.461938\pi\)
\(12\) −1.79129 −0.517100
\(13\) −2.39564 4.14938i −0.664432 1.15083i −0.979439 0.201741i \(-0.935340\pi\)
0.315007 0.949089i \(-0.397993\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.89564 3.28335i 0.459761 0.796330i −0.539187 0.842186i \(-0.681268\pi\)
0.998948 + 0.0458564i \(0.0146017\pi\)
\(18\) −0.208712 −0.0491939
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) 0 0
\(21\) 0.895644 1.55130i 0.195446 0.338522i
\(22\) 0.395644 0.685275i 0.0843516 0.146101i
\(23\) −2.29129 3.96863i −0.477767 0.827516i 0.521909 0.853001i \(-0.325220\pi\)
−0.999675 + 0.0254855i \(0.991887\pi\)
\(24\) −0.895644 + 1.55130i −0.182823 + 0.316658i
\(25\) 0 0
\(26\) −4.79129 −0.939649
\(27\) 5.00000 0.962250
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −1.10436 1.91280i −0.205074 0.355198i 0.745082 0.666972i \(-0.232410\pi\)
−0.950156 + 0.311774i \(0.899077\pi\)
\(30\) 0 0
\(31\) −0.208712 −0.0374858 −0.0187429 0.999824i \(-0.505966\pi\)
−0.0187429 + 0.999824i \(0.505966\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.708712 1.22753i 0.123371 0.213685i
\(34\) −1.89564 3.28335i −0.325100 0.563090i
\(35\) 0 0
\(36\) −0.104356 + 0.180750i −0.0173927 + 0.0301250i
\(37\) 5.58258 0.917770 0.458885 0.888496i \(-0.348249\pi\)
0.458885 + 0.888496i \(0.348249\pi\)
\(38\) −4.00000 + 1.73205i −0.648886 + 0.280976i
\(39\) −8.58258 −1.37431
\(40\) 0 0
\(41\) −1.18693 + 2.05583i −0.185368 + 0.321066i −0.943700 0.330802i \(-0.892681\pi\)
0.758333 + 0.651868i \(0.226014\pi\)
\(42\) −0.895644 1.55130i −0.138201 0.239371i
\(43\) 0.604356 1.04678i 0.0921634 0.159632i −0.816258 0.577688i \(-0.803955\pi\)
0.908421 + 0.418056i \(0.137288\pi\)
\(44\) −0.395644 0.685275i −0.0596456 0.103309i
\(45\) 0 0
\(46\) −4.58258 −0.675664
\(47\) 3.08258 + 5.33918i 0.449640 + 0.778799i 0.998362 0.0572054i \(-0.0182190\pi\)
−0.548723 + 0.836005i \(0.684886\pi\)
\(48\) 0.895644 + 1.55130i 0.129275 + 0.223911i
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −3.39564 5.88143i −0.475485 0.823565i
\(52\) −2.39564 + 4.14938i −0.332216 + 0.575415i
\(53\) 2.29129 + 3.96863i 0.314733 + 0.545133i 0.979381 0.202024i \(-0.0647518\pi\)
−0.664648 + 0.747157i \(0.731418\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −7.16515 + 3.10260i −0.949047 + 0.410950i
\(58\) −2.20871 −0.290018
\(59\) 2.29129 3.96863i 0.298300 0.516671i −0.677447 0.735572i \(-0.736914\pi\)
0.975747 + 0.218900i \(0.0702470\pi\)
\(60\) 0 0
\(61\) 6.18693 + 10.7161i 0.792155 + 1.37205i 0.924630 + 0.380867i \(0.124374\pi\)
−0.132474 + 0.991186i \(0.542292\pi\)
\(62\) −0.104356 + 0.180750i −0.0132532 + 0.0229553i
\(63\) −0.104356 0.180750i −0.0131476 0.0227724i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.708712 1.22753i −0.0872364 0.151098i
\(67\) 3.20871 + 5.55765i 0.392007 + 0.678975i 0.992714 0.120494i \(-0.0384477\pi\)
−0.600708 + 0.799469i \(0.705114\pi\)
\(68\) −3.79129 −0.459761
\(69\) −8.20871 −0.988213
\(70\) 0 0
\(71\) −2.29129 + 3.96863i −0.271926 + 0.470989i −0.969355 0.245664i \(-0.920994\pi\)
0.697429 + 0.716654i \(0.254327\pi\)
\(72\) 0.104356 + 0.180750i 0.0122985 + 0.0213016i
\(73\) −0.895644 + 1.55130i −0.104827 + 0.181566i −0.913668 0.406462i \(-0.866762\pi\)
0.808840 + 0.588028i \(0.200096\pi\)
\(74\) 2.79129 4.83465i 0.324481 0.562017i
\(75\) 0 0
\(76\) −0.500000 + 4.33013i −0.0573539 + 0.496700i
\(77\) 0.791288 0.0901756
\(78\) −4.29129 + 7.43273i −0.485893 + 0.841591i
\(79\) 3.97822 6.89048i 0.447585 0.775239i −0.550644 0.834740i \(-0.685618\pi\)
0.998228 + 0.0595011i \(0.0189510\pi\)
\(80\) 0 0
\(81\) 4.79129 8.29875i 0.532365 0.922084i
\(82\) 1.18693 + 2.05583i 0.131075 + 0.227028i
\(83\) 0.791288 0.0868551 0.0434276 0.999057i \(-0.486172\pi\)
0.0434276 + 0.999057i \(0.486172\pi\)
\(84\) −1.79129 −0.195446
\(85\) 0 0
\(86\) −0.604356 1.04678i −0.0651694 0.112877i
\(87\) −3.95644 −0.424175
\(88\) −0.791288 −0.0843516
\(89\) 2.29129 + 3.96863i 0.242876 + 0.420674i 0.961532 0.274692i \(-0.0885758\pi\)
−0.718656 + 0.695365i \(0.755243\pi\)
\(90\) 0 0
\(91\) −2.39564 4.14938i −0.251132 0.434973i
\(92\) −2.29129 + 3.96863i −0.238883 + 0.413758i
\(93\) −0.186932 + 0.323775i −0.0193839 + 0.0335739i
\(94\) 6.16515 0.635887
\(95\) 0 0
\(96\) 1.79129 0.182823
\(97\) 0.686932 1.18980i 0.0697474 0.120806i −0.829043 0.559185i \(-0.811114\pi\)
0.898790 + 0.438379i \(0.144447\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) −0.0825757 0.143025i −0.00829917 0.0143746i
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −6.79129 −0.672438
\(103\) 13.1652 1.29720 0.648600 0.761129i \(-0.275355\pi\)
0.648600 + 0.761129i \(0.275355\pi\)
\(104\) 2.39564 + 4.14938i 0.234912 + 0.406880i
\(105\) 0 0
\(106\) 4.58258 0.445099
\(107\) 3.95644 0.382483 0.191242 0.981543i \(-0.438749\pi\)
0.191242 + 0.981543i \(0.438749\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) −7.87386 + 13.6379i −0.754179 + 1.30628i 0.191602 + 0.981473i \(0.438632\pi\)
−0.945781 + 0.324804i \(0.894702\pi\)
\(110\) 0 0
\(111\) 5.00000 8.66025i 0.474579 0.821995i
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) 8.37386 0.787747 0.393873 0.919165i \(-0.371135\pi\)
0.393873 + 0.919165i \(0.371135\pi\)
\(114\) −0.895644 + 7.75650i −0.0838847 + 0.726463i
\(115\) 0 0
\(116\) −1.10436 + 1.91280i −0.102537 + 0.177599i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) −2.29129 3.96863i −0.210930 0.365342i
\(119\) 1.89564 3.28335i 0.173773 0.300984i
\(120\) 0 0
\(121\) −10.3739 −0.943079
\(122\) 12.3739 1.12028
\(123\) 2.12614 + 3.68258i 0.191707 + 0.332047i
\(124\) 0.104356 + 0.180750i 0.00937145 + 0.0162318i
\(125\) 0 0
\(126\) −0.208712 −0.0185936
\(127\) 8.18693 + 14.1802i 0.726473 + 1.25829i 0.958365 + 0.285546i \(0.0921750\pi\)
−0.231892 + 0.972741i \(0.574492\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.08258 1.87508i −0.0953155 0.165091i
\(130\) 0 0
\(131\) 10.2695 17.7873i 0.897251 1.55408i 0.0662573 0.997803i \(-0.478894\pi\)
0.830994 0.556282i \(-0.187772\pi\)
\(132\) −1.41742 −0.123371
\(133\) −3.50000 2.59808i −0.303488 0.225282i
\(134\) 6.41742 0.554381
\(135\) 0 0
\(136\) −1.89564 + 3.28335i −0.162550 + 0.281545i
\(137\) −10.6652 18.4726i −0.911185 1.57822i −0.812392 0.583111i \(-0.801835\pi\)
−0.0987932 0.995108i \(-0.531498\pi\)
\(138\) −4.10436 + 7.10895i −0.349386 + 0.605154i
\(139\) 8.39564 + 14.5417i 0.712109 + 1.23341i 0.964064 + 0.265670i \(0.0855933\pi\)
−0.251955 + 0.967739i \(0.581073\pi\)
\(140\) 0 0
\(141\) 11.0436 0.930036
\(142\) 2.29129 + 3.96863i 0.192281 + 0.333040i
\(143\) −1.89564 3.28335i −0.158522 0.274568i
\(144\) 0.208712 0.0173927
\(145\) 0 0
\(146\) 0.895644 + 1.55130i 0.0741240 + 0.128387i
\(147\) −5.37386 + 9.30780i −0.443229 + 0.767695i
\(148\) −2.79129 4.83465i −0.229442 0.397406i
\(149\) −2.37386 + 4.11165i −0.194474 + 0.336840i −0.946728 0.322034i \(-0.895633\pi\)
0.752254 + 0.658874i \(0.228967\pi\)
\(150\) 0 0
\(151\) −11.7477 −0.956016 −0.478008 0.878355i \(-0.658641\pi\)
−0.478008 + 0.878355i \(0.658641\pi\)
\(152\) 3.50000 + 2.59808i 0.283887 + 0.210732i
\(153\) −0.791288 −0.0639718
\(154\) 0.395644 0.685275i 0.0318819 0.0552211i
\(155\) 0 0
\(156\) 4.29129 + 7.43273i 0.343578 + 0.595095i
\(157\) 7.47822 12.9527i 0.596827 1.03373i −0.396459 0.918052i \(-0.629761\pi\)
0.993286 0.115682i \(-0.0369054\pi\)
\(158\) −3.97822 6.89048i −0.316490 0.548177i
\(159\) 8.20871 0.650993
\(160\) 0 0
\(161\) −2.29129 3.96863i −0.180579 0.312772i
\(162\) −4.79129 8.29875i −0.376439 0.652012i
\(163\) 5.41742 0.424325 0.212163 0.977234i \(-0.431949\pi\)
0.212163 + 0.977234i \(0.431949\pi\)
\(164\) 2.37386 0.185368
\(165\) 0 0
\(166\) 0.395644 0.685275i 0.0307079 0.0531877i
\(167\) −10.2695 17.7873i −0.794678 1.37642i −0.923043 0.384696i \(-0.874306\pi\)
0.128365 0.991727i \(-0.459027\pi\)
\(168\) −0.895644 + 1.55130i −0.0691004 + 0.119685i
\(169\) −4.97822 + 8.62253i −0.382940 + 0.663271i
\(170\) 0 0
\(171\) −0.104356 + 0.903750i −0.00798031 + 0.0691115i
\(172\) −1.20871 −0.0921634
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) −1.97822 + 3.42638i −0.149968 + 0.259753i
\(175\) 0 0
\(176\) −0.395644 + 0.685275i −0.0298228 + 0.0516546i
\(177\) −4.10436 7.10895i −0.308502 0.534342i
\(178\) 4.58258 0.343479
\(179\) 10.7477 0.803323 0.401661 0.915788i \(-0.368433\pi\)
0.401661 + 0.915788i \(0.368433\pi\)
\(180\) 0 0
\(181\) 10.6869 + 18.5103i 0.794353 + 1.37586i 0.923249 + 0.384202i \(0.125523\pi\)
−0.128896 + 0.991658i \(0.541143\pi\)
\(182\) −4.79129 −0.355154
\(183\) 22.1652 1.63850
\(184\) 2.29129 + 3.96863i 0.168916 + 0.292571i
\(185\) 0 0
\(186\) 0.186932 + 0.323775i 0.0137065 + 0.0237404i
\(187\) 1.50000 2.59808i 0.109691 0.189990i
\(188\) 3.08258 5.33918i 0.224820 0.389400i
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −6.95644 −0.503350 −0.251675 0.967812i \(-0.580981\pi\)
−0.251675 + 0.967812i \(0.580981\pi\)
\(192\) 0.895644 1.55130i 0.0646375 0.111955i
\(193\) 12.3739 21.4322i 0.890690 1.54272i 0.0516406 0.998666i \(-0.483555\pi\)
0.839050 0.544055i \(-0.183112\pi\)
\(194\) −0.686932 1.18980i −0.0493188 0.0854227i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −24.7913 −1.76631 −0.883153 0.469085i \(-0.844584\pi\)
−0.883153 + 0.469085i \(0.844584\pi\)
\(198\) −0.165151 −0.0117368
\(199\) 2.79129 + 4.83465i 0.197869 + 0.342719i 0.947837 0.318755i \(-0.103265\pi\)
−0.749968 + 0.661474i \(0.769931\pi\)
\(200\) 0 0
\(201\) 11.4955 0.810827
\(202\) 0 0
\(203\) −1.10436 1.91280i −0.0775106 0.134252i
\(204\) −3.39564 + 5.88143i −0.237743 + 0.411782i
\(205\) 0 0
\(206\) 6.58258 11.4014i 0.458630 0.794370i
\(207\) −0.478220 + 0.828301i −0.0332386 + 0.0575709i
\(208\) 4.79129 0.332216
\(209\) −2.76951 2.05583i −0.191571 0.142204i
\(210\) 0 0
\(211\) −0.521780 + 0.903750i −0.0359208 + 0.0622167i −0.883427 0.468569i \(-0.844770\pi\)
0.847506 + 0.530786i \(0.178103\pi\)
\(212\) 2.29129 3.96863i 0.157366 0.272566i
\(213\) 4.10436 + 7.10895i 0.281226 + 0.487097i
\(214\) 1.97822 3.42638i 0.135228 0.234222i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) −0.208712 −0.0141683
\(218\) 7.87386 + 13.6379i 0.533285 + 0.923677i
\(219\) 1.60436 + 2.77883i 0.108412 + 0.187776i
\(220\) 0 0
\(221\) −18.1652 −1.22192
\(222\) −5.00000 8.66025i −0.335578 0.581238i
\(223\) 11.8956 20.6039i 0.796591 1.37974i −0.125233 0.992127i \(-0.539968\pi\)
0.921824 0.387609i \(-0.126699\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 4.18693 7.25198i 0.278511 0.482394i
\(227\) 19.7477 1.31070 0.655351 0.755324i \(-0.272521\pi\)
0.655351 + 0.755324i \(0.272521\pi\)
\(228\) 6.26951 + 4.65390i 0.415208 + 0.308212i
\(229\) 11.3303 0.748727 0.374364 0.927282i \(-0.377861\pi\)
0.374364 + 0.927282i \(0.377861\pi\)
\(230\) 0 0
\(231\) 0.708712 1.22753i 0.0466298 0.0807652i
\(232\) 1.10436 + 1.91280i 0.0725045 + 0.125582i
\(233\) −4.58258 + 7.93725i −0.300215 + 0.519987i −0.976184 0.216942i \(-0.930392\pi\)
0.675970 + 0.736929i \(0.263725\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) 0 0
\(236\) −4.58258 −0.298300
\(237\) −7.12614 12.3428i −0.462892 0.801753i
\(238\) −1.89564 3.28335i −0.122876 0.212828i
\(239\) 7.41742 0.479793 0.239897 0.970798i \(-0.422886\pi\)
0.239897 + 0.970798i \(0.422886\pi\)
\(240\) 0 0
\(241\) 6.10436 + 10.5731i 0.393216 + 0.681070i 0.992872 0.119188i \(-0.0380291\pi\)
−0.599656 + 0.800258i \(0.704696\pi\)
\(242\) −5.18693 + 8.98403i −0.333429 + 0.577515i
\(243\) −1.08258 1.87508i −0.0694473 0.120286i
\(244\) 6.18693 10.7161i 0.396078 0.686027i
\(245\) 0 0
\(246\) 4.25227 0.271115
\(247\) −2.39564 + 20.7469i −0.152431 + 1.32009i
\(248\) 0.208712 0.0132532
\(249\) 0.708712 1.22753i 0.0449128 0.0777913i
\(250\) 0 0
\(251\) 14.0608 + 24.3540i 0.887510 + 1.53721i 0.842810 + 0.538211i \(0.180900\pi\)
0.0446995 + 0.999000i \(0.485767\pi\)
\(252\) −0.104356 + 0.180750i −0.00657381 + 0.0113862i
\(253\) −1.81307 3.14033i −0.113987 0.197431i
\(254\) 16.3739 1.02739
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.89564 13.6757i −0.492517 0.853064i 0.507446 0.861683i \(-0.330590\pi\)
−0.999963 + 0.00861948i \(0.997256\pi\)
\(258\) −2.16515 −0.134796
\(259\) 5.58258 0.346884
\(260\) 0 0
\(261\) −0.230493 + 0.399225i −0.0142671 + 0.0247114i
\(262\) −10.2695 17.7873i −0.634452 1.09890i
\(263\) −14.2913 + 24.7532i −0.881239 + 1.52635i −0.0312735 + 0.999511i \(0.509956\pi\)
−0.849965 + 0.526839i \(0.823377\pi\)
\(264\) −0.708712 + 1.22753i −0.0436182 + 0.0755490i
\(265\) 0 0
\(266\) −4.00000 + 1.73205i −0.245256 + 0.106199i
\(267\) 8.20871 0.502365
\(268\) 3.20871 5.55765i 0.196003 0.339488i
\(269\) 14.0608 24.3540i 0.857302 1.48489i −0.0171912 0.999852i \(-0.505472\pi\)
0.874493 0.485038i \(-0.161194\pi\)
\(270\) 0 0
\(271\) −12.0608 + 20.8899i −0.732641 + 1.26897i 0.223109 + 0.974793i \(0.428379\pi\)
−0.955751 + 0.294178i \(0.904954\pi\)
\(272\) 1.89564 + 3.28335i 0.114940 + 0.199082i
\(273\) −8.58258 −0.519441
\(274\) −21.3303 −1.28861
\(275\) 0 0
\(276\) 4.10436 + 7.10895i 0.247053 + 0.427909i
\(277\) −18.7477 −1.12644 −0.563221 0.826306i \(-0.690438\pi\)
−0.563221 + 0.826306i \(0.690438\pi\)
\(278\) 16.7913 1.00707
\(279\) 0.0217804 + 0.0377247i 0.00130396 + 0.00225852i
\(280\) 0 0
\(281\) −0.708712 1.22753i −0.0422782 0.0732280i 0.844112 0.536167i \(-0.180128\pi\)
−0.886390 + 0.462939i \(0.846795\pi\)
\(282\) 5.52178 9.56400i 0.328817 0.569528i
\(283\) −10.0608 + 17.4258i −0.598052 + 1.03586i 0.395056 + 0.918657i \(0.370725\pi\)
−0.993108 + 0.117200i \(0.962608\pi\)
\(284\) 4.58258 0.271926
\(285\) 0 0
\(286\) −3.79129 −0.224184
\(287\) −1.18693 + 2.05583i −0.0700624 + 0.121352i
\(288\) 0.104356 0.180750i 0.00614924 0.0106508i
\(289\) 1.31307 + 2.27430i 0.0772393 + 0.133782i
\(290\) 0 0
\(291\) −1.23049 2.13128i −0.0721327 0.124938i
\(292\) 1.79129 0.104827
\(293\) −2.04356 −0.119386 −0.0596930 0.998217i \(-0.519012\pi\)
−0.0596930 + 0.998217i \(0.519012\pi\)
\(294\) 5.37386 + 9.30780i 0.313410 + 0.542842i
\(295\) 0 0
\(296\) −5.58258 −0.324481
\(297\) 3.95644 0.229576
\(298\) 2.37386 + 4.11165i 0.137514 + 0.238182i
\(299\) −10.9782 + 19.0148i −0.634887 + 1.09966i
\(300\) 0 0
\(301\) 0.604356 1.04678i 0.0348345 0.0603351i
\(302\) −5.87386 + 10.1738i −0.338003 + 0.585438i
\(303\) 0 0
\(304\) 4.00000 1.73205i 0.229416 0.0993399i
\(305\) 0 0
\(306\) −0.395644 + 0.685275i −0.0226175 + 0.0391746i
\(307\) 10.2477 17.7496i 0.584869 1.01302i −0.410023 0.912075i \(-0.634479\pi\)
0.994892 0.100947i \(-0.0321873\pi\)
\(308\) −0.395644 0.685275i −0.0225439 0.0390472i
\(309\) 11.7913 20.4231i 0.670783 1.16183i
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 8.58258 0.485893
\(313\) 7.87386 + 13.6379i 0.445057 + 0.770861i 0.998056 0.0623204i \(-0.0198501\pi\)
−0.552999 + 0.833182i \(0.686517\pi\)
\(314\) −7.47822 12.9527i −0.422020 0.730961i
\(315\) 0 0
\(316\) −7.95644 −0.447585
\(317\) 4.58258 + 7.93725i 0.257383 + 0.445801i 0.965540 0.260254i \(-0.0838064\pi\)
−0.708157 + 0.706055i \(0.750473\pi\)
\(318\) 4.10436 7.10895i 0.230161 0.398650i
\(319\) −0.873864 1.51358i −0.0489270 0.0847440i
\(320\) 0 0
\(321\) 3.54356 6.13763i 0.197782 0.342569i
\(322\) −4.58258 −0.255377
\(323\) −15.1652 + 6.56670i −0.843812 + 0.365381i
\(324\) −9.58258 −0.532365
\(325\) 0 0
\(326\) 2.70871 4.69163i 0.150022 0.259845i
\(327\) 14.1044 + 24.4295i 0.779973 + 1.35095i
\(328\) 1.18693 2.05583i 0.0655373 0.113514i
\(329\) 3.08258 + 5.33918i 0.169948 + 0.294358i
\(330\) 0 0
\(331\) 27.9129 1.53423 0.767115 0.641509i \(-0.221691\pi\)
0.767115 + 0.641509i \(0.221691\pi\)
\(332\) −0.395644 0.685275i −0.0217138 0.0376094i
\(333\) −0.582576 1.00905i −0.0319250 0.0552956i
\(334\) −20.5390 −1.12384
\(335\) 0 0
\(336\) 0.895644 + 1.55130i 0.0488614 + 0.0846304i
\(337\) −6.66515 + 11.5444i −0.363074 + 0.628862i −0.988465 0.151449i \(-0.951606\pi\)
0.625391 + 0.780311i \(0.284939\pi\)
\(338\) 4.97822 + 8.62253i 0.270779 + 0.469004i
\(339\) 7.50000 12.9904i 0.407344 0.705541i
\(340\) 0 0
\(341\) −0.165151 −0.00894345
\(342\) 0.730493 + 0.542250i 0.0395005 + 0.0293215i
\(343\) −13.0000 −0.701934
\(344\) −0.604356 + 1.04678i −0.0325847 + 0.0564383i
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 8.68693 15.0462i 0.466339 0.807723i −0.532922 0.846164i \(-0.678906\pi\)
0.999261 + 0.0384417i \(0.0122394\pi\)
\(348\) 1.97822 + 3.42638i 0.106044 + 0.183673i
\(349\) −14.5826 −0.780587 −0.390294 0.920690i \(-0.627627\pi\)
−0.390294 + 0.920690i \(0.627627\pi\)
\(350\) 0 0
\(351\) −11.9782 20.7469i −0.639350 1.10739i
\(352\) 0.395644 + 0.685275i 0.0210879 + 0.0365253i
\(353\) −13.7477 −0.731718 −0.365859 0.930670i \(-0.619225\pi\)
−0.365859 + 0.930670i \(0.619225\pi\)
\(354\) −8.20871 −0.436288
\(355\) 0 0
\(356\) 2.29129 3.96863i 0.121438 0.210337i
\(357\) −3.39564 5.88143i −0.179717 0.311278i
\(358\) 5.37386 9.30780i 0.284018 0.491933i
\(359\) −7.35208 + 12.7342i −0.388028 + 0.672084i −0.992184 0.124782i \(-0.960177\pi\)
0.604156 + 0.796866i \(0.293510\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 21.3739 1.12339
\(363\) −9.29129 + 16.0930i −0.487666 + 0.844663i
\(364\) −2.39564 + 4.14938i −0.125566 + 0.217486i
\(365\) 0 0
\(366\) 11.0826 19.1956i 0.579296 1.00337i
\(367\) 2.10436 + 3.64485i 0.109846 + 0.190260i 0.915708 0.401844i \(-0.131631\pi\)
−0.805861 + 0.592104i \(0.798297\pi\)
\(368\) 4.58258 0.238883
\(369\) 0.495454 0.0257923
\(370\) 0 0
\(371\) 2.29129 + 3.96863i 0.118958 + 0.206041i
\(372\) 0.373864 0.0193839
\(373\) 7.62614 0.394866 0.197433 0.980316i \(-0.436739\pi\)
0.197433 + 0.980316i \(0.436739\pi\)
\(374\) −1.50000 2.59808i −0.0775632 0.134343i
\(375\) 0 0
\(376\) −3.08258 5.33918i −0.158972 0.275347i
\(377\) −5.29129 + 9.16478i −0.272515 + 0.472010i
\(378\) 2.50000 4.33013i 0.128586 0.222718i
\(379\) 23.1652 1.18991 0.594957 0.803758i \(-0.297169\pi\)
0.594957 + 0.803758i \(0.297169\pi\)
\(380\) 0 0
\(381\) 29.3303 1.50264
\(382\) −3.47822 + 6.02445i −0.177961 + 0.308238i
\(383\) −2.29129 + 3.96863i −0.117079 + 0.202787i −0.918609 0.395168i \(-0.870687\pi\)
0.801530 + 0.597955i \(0.204020\pi\)
\(384\) −0.895644 1.55130i −0.0457056 0.0791645i
\(385\) 0 0
\(386\) −12.3739 21.4322i −0.629813 1.09087i
\(387\) −0.252273 −0.0128238
\(388\) −1.37386 −0.0697474
\(389\) −16.1869 28.0366i −0.820710 1.42151i −0.905154 0.425083i \(-0.860245\pi\)
0.0844442 0.996428i \(-0.473089\pi\)
\(390\) 0 0
\(391\) −17.3739 −0.878634
\(392\) 6.00000 0.303046
\(393\) −18.3956 31.8622i −0.927937 1.60723i
\(394\) −12.3956 + 21.4699i −0.624484 + 1.08164i
\(395\) 0 0
\(396\) −0.0825757 + 0.143025i −0.00414958 + 0.00718729i
\(397\) −10.2913 + 17.8250i −0.516505 + 0.894613i 0.483311 + 0.875448i \(0.339434\pi\)
−0.999816 + 0.0191643i \(0.993899\pi\)
\(398\) 5.58258 0.279829
\(399\) −7.16515 + 3.10260i −0.358706 + 0.155324i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 5.74773 9.95536i 0.286671 0.496528i
\(403\) 0.500000 + 0.866025i 0.0249068 + 0.0431398i
\(404\) 0 0
\(405\) 0 0
\(406\) −2.20871 −0.109617
\(407\) 4.41742 0.218964
\(408\) 3.39564 + 5.88143i 0.168109 + 0.291174i
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 0 0
\(411\) −38.2087 −1.88470
\(412\) −6.58258 11.4014i −0.324300 0.561704i
\(413\) 2.29129 3.96863i 0.112747 0.195283i
\(414\) 0.478220 + 0.828301i 0.0235032 + 0.0407088i
\(415\) 0 0
\(416\) 2.39564 4.14938i 0.117456 0.203440i
\(417\) 30.0780 1.47293
\(418\) −3.16515 + 1.37055i −0.154813 + 0.0670358i
\(419\) 4.74773 0.231942 0.115971 0.993253i \(-0.463002\pi\)
0.115971 + 0.993253i \(0.463002\pi\)
\(420\) 0 0
\(421\) −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i \(-0.995377\pi\)
0.512524 + 0.858673i \(0.328710\pi\)
\(422\) 0.521780 + 0.903750i 0.0253999 + 0.0439939i
\(423\) 0.643371 1.11435i 0.0312818 0.0541816i
\(424\) −2.29129 3.96863i −0.111275 0.192734i
\(425\) 0 0
\(426\) 8.20871 0.397713
\(427\) 6.18693 + 10.7161i 0.299407 + 0.518587i
\(428\) −1.97822 3.42638i −0.0956209 0.165620i
\(429\) −6.79129 −0.327886
\(430\) 0 0
\(431\) −6.39564 11.0776i −0.308067 0.533588i 0.669872 0.742476i \(-0.266349\pi\)
−0.977940 + 0.208888i \(0.933016\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −19.4564 33.6995i −0.935017 1.61950i −0.774604 0.632447i \(-0.782051\pi\)
−0.160413 0.987050i \(-0.551283\pi\)
\(434\) −0.104356 + 0.180750i −0.00500925 + 0.00867628i
\(435\) 0 0
\(436\) 15.7477 0.754179
\(437\) −2.29129 + 19.8431i −0.109607 + 0.949226i
\(438\) 3.20871 0.153318
\(439\) −5.66515 + 9.81233i −0.270383 + 0.468317i −0.968960 0.247218i \(-0.920484\pi\)
0.698577 + 0.715535i \(0.253817\pi\)
\(440\) 0 0
\(441\) 0.626136 + 1.08450i 0.0298160 + 0.0516429i
\(442\) −9.08258 + 15.7315i −0.432014 + 0.748270i
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) −11.8956 20.6039i −0.563275 0.975621i
\(447\) 4.25227 + 7.36515i 0.201126 + 0.348360i
\(448\) 1.00000 0.0472456
\(449\) −33.3303 −1.57295 −0.786477 0.617619i \(-0.788097\pi\)
−0.786477 + 0.617619i \(0.788097\pi\)
\(450\) 0 0
\(451\) −0.939205 + 1.62675i −0.0442254 + 0.0766007i
\(452\) −4.18693 7.25198i −0.196937 0.341104i
\(453\) −10.5218 + 18.2243i −0.494356 + 0.856250i
\(454\) 9.87386 17.1020i 0.463403 0.802638i
\(455\) 0 0
\(456\) 7.16515 3.10260i 0.335539 0.145293i
\(457\) −6.74773 −0.315645 −0.157823 0.987467i \(-0.550447\pi\)
−0.157823 + 0.987467i \(0.550447\pi\)
\(458\) 5.66515 9.81233i 0.264715 0.458500i
\(459\) 9.47822 16.4168i 0.442405 0.766269i
\(460\) 0 0
\(461\) −4.10436 + 7.10895i −0.191159 + 0.331097i −0.945635 0.325231i \(-0.894558\pi\)
0.754476 + 0.656328i \(0.227891\pi\)
\(462\) −0.708712 1.22753i −0.0329723 0.0571097i
\(463\) 4.95644 0.230345 0.115173 0.993345i \(-0.463258\pi\)
0.115173 + 0.993345i \(0.463258\pi\)
\(464\) 2.20871 0.102537
\(465\) 0 0
\(466\) 4.58258 + 7.93725i 0.212284 + 0.367686i
\(467\) −24.3303 −1.12587 −0.562936 0.826500i \(-0.690328\pi\)
−0.562936 + 0.826500i \(0.690328\pi\)
\(468\) 1.00000 0.0462250
\(469\) 3.20871 + 5.55765i 0.148165 + 0.256629i
\(470\) 0 0
\(471\) −13.3956 23.2019i −0.617239 1.06909i
\(472\) −2.29129 + 3.96863i −0.105465 + 0.182671i
\(473\) 0.478220 0.828301i 0.0219886 0.0380853i
\(474\) −14.2523 −0.654629
\(475\) 0 0
\(476\) −3.79129 −0.173773
\(477\) 0.478220 0.828301i 0.0218962 0.0379253i
\(478\) 3.70871 6.42368i 0.169633 0.293812i
\(479\) −2.12614 3.68258i −0.0971457 0.168261i 0.813356 0.581766i \(-0.197638\pi\)
−0.910502 + 0.413504i \(0.864305\pi\)
\(480\) 0 0
\(481\) −13.3739 23.1642i −0.609796 1.05620i
\(482\) 12.2087 0.556092
\(483\) −8.20871 −0.373509
\(484\) 5.18693 + 8.98403i 0.235770 + 0.408365i
\(485\) 0 0
\(486\) −2.16515 −0.0982133
\(487\) −23.0000 −1.04223 −0.521115 0.853487i \(-0.674484\pi\)
−0.521115 + 0.853487i \(0.674484\pi\)
\(488\) −6.18693 10.7161i −0.280069 0.485094i
\(489\) 4.85208 8.40405i 0.219419 0.380044i
\(490\) 0 0
\(491\) 20.2913 35.1455i 0.915733 1.58610i 0.109908 0.993942i \(-0.464944\pi\)
0.805825 0.592154i \(-0.201722\pi\)
\(492\) 2.12614 3.68258i 0.0958536 0.166023i
\(493\) −8.37386 −0.377140
\(494\) 16.7695 + 12.4481i 0.754496 + 0.560068i
\(495\) 0 0
\(496\) 0.104356 0.180750i 0.00468573 0.00811592i
\(497\) −2.29129 + 3.96863i −0.102778 + 0.178017i
\(498\) −0.708712 1.22753i −0.0317582 0.0550067i
\(499\) −8.66515 + 15.0085i −0.387905 + 0.671872i −0.992168 0.124914i \(-0.960135\pi\)
0.604262 + 0.796786i \(0.293468\pi\)
\(500\) 0 0
\(501\) −36.7913 −1.64371
\(502\) 28.1216 1.25513
\(503\) 2.29129 + 3.96863i 0.102163 + 0.176952i 0.912576 0.408908i \(-0.134090\pi\)
−0.810412 + 0.585860i \(0.800757\pi\)
\(504\) 0.104356 + 0.180750i 0.00464839 + 0.00805125i
\(505\) 0 0
\(506\) −3.62614 −0.161201
\(507\) 8.91742 + 15.4454i 0.396037 + 0.685956i
\(508\) 8.18693 14.1802i 0.363236 0.629144i
\(509\) −15.7913 27.3513i −0.699937 1.21233i −0.968488 0.249060i \(-0.919878\pi\)
0.268551 0.963265i \(-0.413455\pi\)
\(510\) 0 0
\(511\) −0.895644 + 1.55130i −0.0396210 + 0.0686255i
\(512\) −1.00000 −0.0441942
\(513\) −17.5000 12.9904i −0.772644 0.573539i
\(514\) −15.7913 −0.696524
\(515\) 0 0
\(516\) −1.08258 + 1.87508i −0.0476577 + 0.0825456i
\(517\) 2.43920 + 4.22483i 0.107276 + 0.185808i
\(518\) 2.79129 4.83465i 0.122642 0.212422i
\(519\) 18.8085 + 32.5773i 0.825603 + 1.42999i
\(520\) 0 0
\(521\) 40.7477 1.78519 0.892595 0.450859i \(-0.148882\pi\)
0.892595 + 0.450859i \(0.148882\pi\)
\(522\) 0.230493 + 0.399225i 0.0100884 + 0.0174736i
\(523\) 4.87386 + 8.44178i 0.213119 + 0.369133i 0.952689 0.303946i \(-0.0983044\pi\)
−0.739570 + 0.673080i \(0.764971\pi\)
\(524\) −20.5390 −0.897251
\(525\) 0 0
\(526\) 14.2913 + 24.7532i 0.623130 + 1.07929i
\(527\) −0.395644 + 0.685275i −0.0172345 + 0.0298511i
\(528\) 0.708712 + 1.22753i 0.0308427 + 0.0534212i
\(529\) 1.00000 1.73205i 0.0434783 0.0753066i
\(530\) 0 0
\(531\) −0.956439 −0.0415059
\(532\) −0.500000 + 4.33013i −0.0216777 + 0.187735i
\(533\) 11.3739 0.492657
\(534\) 4.10436 7.10895i 0.177613 0.307634i
\(535\) 0 0
\(536\) −3.20871 5.55765i −0.138595 0.240054i
\(537\) 9.62614 16.6730i 0.415398 0.719491i
\(538\) −14.0608 24.3540i −0.606204 1.04998i
\(539\) −4.74773 −0.204499
\(540\) 0 0
\(541\) −12.0608 20.8899i −0.518534 0.898127i −0.999768 0.0215352i \(-0.993145\pi\)
0.481234 0.876592i \(-0.340189\pi\)
\(542\) 12.0608 + 20.8899i 0.518056 + 0.897298i
\(543\) 38.2867 1.64304
\(544\) 3.79129 0.162550
\(545\) 0 0
\(546\) −4.29129 + 7.43273i −0.183650 + 0.318091i
\(547\) 17.5826 + 30.4539i 0.751777 + 1.30212i 0.946961 + 0.321349i \(0.104136\pi\)
−0.195184 + 0.980767i \(0.562530\pi\)
\(548\) −10.6652 + 18.4726i −0.455593 + 0.789110i
\(549\) 1.29129 2.23658i 0.0551108 0.0954547i
\(550\) 0 0
\(551\) −1.10436 + 9.56400i −0.0470472 + 0.407440i
\(552\) 8.20871 0.349386
\(553\) 3.97822 6.89048i 0.169171 0.293013i
\(554\) −9.37386 + 16.2360i −0.398257 + 0.689802i
\(555\) 0 0
\(556\) 8.39564 14.5417i 0.356055 0.616705i
\(557\) −6.47822 11.2206i −0.274491 0.475432i 0.695516 0.718511i \(-0.255176\pi\)
−0.970007 + 0.243079i \(0.921843\pi\)
\(558\) 0.0435608 0.00184407
\(559\) −5.79129 −0.244945
\(560\) 0 0
\(561\) −2.68693 4.65390i −0.113442 0.196488i
\(562\) −1.41742 −0.0597904
\(563\) 0.626136 0.0263885 0.0131943 0.999913i \(-0.495800\pi\)
0.0131943 + 0.999913i \(0.495800\pi\)
\(564\) −5.52178 9.56400i −0.232509 0.402717i
\(565\) 0 0
\(566\) 10.0608 + 17.4258i 0.422887 + 0.732461i
\(567\) 4.79129 8.29875i 0.201215 0.348515i
\(568\) 2.29129 3.96863i 0.0961403 0.166520i
\(569\) −27.1652 −1.13882 −0.569411 0.822053i \(-0.692829\pi\)
−0.569411 + 0.822053i \(0.692829\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −1.89564 + 3.28335i −0.0792609 + 0.137284i
\(573\) −6.23049 + 10.7915i −0.260283 + 0.450823i
\(574\) 1.18693 + 2.05583i 0.0495416 + 0.0858085i
\(575\) 0 0
\(576\) −0.104356 0.180750i −0.00434817 0.00753125i
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 2.62614 0.109233
\(579\) −22.1652 38.3912i −0.921152 1.59548i
\(580\) 0 0
\(581\) 0.791288 0.0328282
\(582\) −2.46099 −0.102011
\(583\) 1.81307 + 3.14033i 0.0750896 + 0.130059i
\(584\) 0.895644 1.55130i 0.0370620 0.0641933i
\(585\) 0 0
\(586\) −1.02178 + 1.76978i −0.0422094 + 0.0731088i
\(587\) 22.7477 39.4002i 0.938899 1.62622i 0.171370 0.985207i \(-0.445181\pi\)
0.767529 0.641014i \(-0.221486\pi\)
\(588\) 10.7477 0.443229
\(589\) 0.730493 + 0.542250i 0.0300994 + 0.0223430i
\(590\) 0 0
\(591\) −22.2042 + 38.4587i −0.913357 + 1.58198i
\(592\) −2.79129 + 4.83465i −0.114721 + 0.198703i
\(593\) −15.0826 26.1238i −0.619367 1.07278i −0.989601 0.143837i \(-0.954056\pi\)
0.370234 0.928938i \(-0.379277\pi\)
\(594\) 1.97822 3.42638i 0.0811673 0.140586i
\(595\) 0 0
\(596\) 4.74773 0.194474
\(597\) 10.0000 0.409273
\(598\) 10.9782 + 19.0148i 0.448933 + 0.777574i
\(599\) −2.06080 3.56940i −0.0842018 0.145842i 0.820849 0.571145i \(-0.193501\pi\)
−0.905051 + 0.425303i \(0.860167\pi\)
\(600\) 0 0
\(601\) −35.9129 −1.46492 −0.732458 0.680812i \(-0.761627\pi\)
−0.732458 + 0.680812i \(0.761627\pi\)
\(602\) −0.604356 1.04678i −0.0246317 0.0426634i
\(603\) 0.669697 1.15995i 0.0272722 0.0472368i
\(604\) 5.87386 + 10.1738i 0.239004 + 0.413967i
\(605\) 0 0
\(606\) 0 0
\(607\) 22.7913 0.925070 0.462535 0.886601i \(-0.346940\pi\)
0.462535 + 0.886601i \(0.346940\pi\)
\(608\) 0.500000 4.33013i 0.0202777 0.175610i
\(609\) −3.95644 −0.160323
\(610\) 0 0
\(611\) 14.7695 25.5815i 0.597510 1.03492i
\(612\) 0.395644 + 0.685275i 0.0159930 + 0.0277006i
\(613\) −20.2477 + 35.0701i −0.817798 + 1.41647i 0.0895033 + 0.995987i \(0.471472\pi\)
−0.907301 + 0.420481i \(0.861861\pi\)
\(614\) −10.2477 17.7496i −0.413565 0.716315i
\(615\) 0 0
\(616\) −0.791288 −0.0318819
\(617\) −16.5000 28.5788i −0.664265 1.15054i −0.979484 0.201522i \(-0.935411\pi\)
0.315219 0.949019i \(-0.397922\pi\)
\(618\) −11.7913 20.4231i −0.474315 0.821538i
\(619\) −10.6261 −0.427100 −0.213550 0.976932i \(-0.568503\pi\)
−0.213550 + 0.976932i \(0.568503\pi\)
\(620\) 0 0
\(621\) −11.4564 19.8431i −0.459731 0.796278i
\(622\) −7.50000 + 12.9904i −0.300723 + 0.520867i
\(623\) 2.29129 + 3.96863i 0.0917985 + 0.159000i
\(624\) 4.29129 7.43273i 0.171789 0.297547i
\(625\) 0 0
\(626\) 15.7477 0.629406
\(627\) −5.66970 + 2.45505i −0.226426 + 0.0980453i
\(628\) −14.9564 −0.596827
\(629\) 10.5826 18.3296i 0.421955 0.730847i
\(630\) 0 0
\(631\) 20.3956 + 35.3263i 0.811938 + 1.40632i 0.911506 + 0.411287i \(0.134921\pi\)
−0.0995683 + 0.995031i \(0.531746\pi\)
\(632\) −3.97822 + 6.89048i −0.158245 + 0.274089i
\(633\) 0.934659 + 1.61888i 0.0371494 + 0.0643446i
\(634\) 9.16515 0.363995
\(635\) 0 0
\(636\) −4.10436 7.10895i −0.162748 0.281888i
\(637\) 14.3739 + 24.8963i 0.569513 + 0.986426i
\(638\) −1.74773 −0.0691932
\(639\) 0.956439 0.0378362
\(640\) 0 0
\(641\) −19.9782 + 34.6033i −0.789092 + 1.36675i 0.137431 + 0.990511i \(0.456115\pi\)
−0.926524 + 0.376237i \(0.877218\pi\)
\(642\) −3.54356 6.13763i −0.139853 0.242233i
\(643\) −12.7477 + 22.0797i −0.502721 + 0.870739i 0.497274 + 0.867594i \(0.334334\pi\)
−0.999995 + 0.00314512i \(0.998999\pi\)
\(644\) −2.29129 + 3.96863i −0.0902894 + 0.156386i
\(645\) 0 0
\(646\) −1.89564 + 16.4168i −0.0745831 + 0.645909i
\(647\) −14.2087 −0.558602 −0.279301 0.960204i \(-0.590103\pi\)
−0.279301 + 0.960204i \(0.590103\pi\)
\(648\) −4.79129 + 8.29875i −0.188220 + 0.326006i
\(649\) 1.81307 3.14033i 0.0711692 0.123269i
\(650\) 0 0
\(651\) −0.186932 + 0.323775i −0.00732643 + 0.0126898i
\(652\) −2.70871 4.69163i −0.106081 0.183738i
\(653\) −9.33030 −0.365123 −0.182561 0.983194i \(-0.558439\pi\)
−0.182561 + 0.983194i \(0.558439\pi\)
\(654\) 28.2087 1.10305
\(655\) 0 0
\(656\) −1.18693 2.05583i −0.0463419 0.0802665i
\(657\) 0.373864 0.0145858
\(658\) 6.16515 0.240343
\(659\) 12.8739 + 22.2982i 0.501495 + 0.868614i 0.999999 + 0.00172659i \(0.000549590\pi\)
−0.498504 + 0.866887i \(0.666117\pi\)
\(660\) 0 0
\(661\) 10.9347 + 18.9394i 0.425309 + 0.736657i 0.996449 0.0841958i \(-0.0268321\pi\)
−0.571140 + 0.820852i \(0.693499\pi\)
\(662\) 13.9564 24.1733i 0.542432 0.939521i
\(663\) −16.2695 + 28.1796i −0.631855 + 1.09441i
\(664\) −0.791288 −0.0307079
\(665\) 0 0
\(666\) −1.16515 −0.0451487
\(667\) −5.06080 + 8.76555i −0.195955 + 0.339404i
\(668\) −10.2695 + 17.7873i −0.397339 + 0.688212i
\(669\) −21.3085 36.9074i −0.823835 1.42692i
\(670\) 0 0
\(671\) 4.89564 + 8.47950i 0.188994 + 0.327348i
\(672\) 1.79129 0.0691004
\(673\) 1.79129 0.0690491 0.0345245 0.999404i \(-0.489008\pi\)
0.0345245 + 0.999404i \(0.489008\pi\)
\(674\) 6.66515 + 11.5444i 0.256732 + 0.444673i
\(675\) 0 0
\(676\) 9.95644 0.382940
\(677\) −47.2432 −1.81570 −0.907851 0.419292i \(-0.862278\pi\)
−0.907851 + 0.419292i \(0.862278\pi\)
\(678\) −7.50000 12.9904i −0.288036 0.498893i
\(679\) 0.686932 1.18980i 0.0263620 0.0456604i
\(680\) 0 0
\(681\) 17.6869 30.6347i 0.677765 1.17392i
\(682\) −0.0825757 + 0.143025i −0.00316199 + 0.00547672i
\(683\) 17.8348 0.682432 0.341216 0.939985i \(-0.389161\pi\)
0.341216 + 0.939985i \(0.389161\pi\)
\(684\) 0.834849 0.361500i 0.0319212 0.0138223i
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) 10.1479 17.5767i 0.387167 0.670593i
\(688\) 0.604356 + 1.04678i 0.0230409 + 0.0399079i
\(689\) 10.9782 19.0148i 0.418237 0.724407i
\(690\) 0 0
\(691\) 9.12159 0.347002 0.173501 0.984834i \(-0.444492\pi\)
0.173501 + 0.984834i \(0.444492\pi\)
\(692\) 21.0000 0.798300
\(693\) −0.0825757 0.143025i −0.00313679 0.00543308i
\(694\) −8.68693 15.0462i −0.329751 0.571146i
\(695\) 0 0
\(696\) 3.95644 0.149968
\(697\) 4.50000 + 7.79423i 0.170450 + 0.295227i
\(698\) −7.29129 + 12.6289i −0.275979 + 0.478010i
\(699\) 8.20871 + 14.2179i 0.310482 + 0.537771i
\(700\) 0 0
\(701\) −4.97822 + 8.62253i −0.188025 + 0.325668i −0.944592 0.328248i \(-0.893542\pi\)
0.756567 + 0.653916i \(0.226875\pi\)
\(702\) −23.9564 −0.904178
\(703\) −19.5390 14.5040i −0.736928 0.547027i
\(704\) 0.791288 0.0298228
\(705\) 0 0
\(706\) −6.87386 + 11.9059i −0.258701 + 0.448084i
\(707\) 0 0
\(708\) −4.10436 + 7.10895i −0.154251 + 0.267171i
\(709\) −0.373864 0.647551i −0.0140407 0.0243193i 0.858920 0.512110i \(-0.171136\pi\)
−0.872960 + 0.487791i \(0.837803\pi\)
\(710\) 0 0
\(711\) −1.66061 −0.0622776
\(712\) −2.29129 3.96863i −0.0858696 0.148731i
\(713\) 0.478220 + 0.828301i 0.0179095 + 0.0310201i
\(714\) −6.79129 −0.254158
\(715\) 0 0
\(716\) −5.37386 9.30780i −0.200831 0.347849i
\(717\) 6.64337 11.5067i 0.248101 0.429724i
\(718\) 7.35208 + 12.7342i 0.274377 + 0.475235i
\(719\) −3.08258 + 5.33918i −0.114961 + 0.199118i −0.917764 0.397126i \(-0.870008\pi\)
0.802803 + 0.596244i \(0.203341\pi\)
\(720\) 0 0
\(721\) 13.1652 0.490296
\(722\) 18.5000 + 4.33013i 0.688499 + 0.161151i
\(723\) 21.8693 0.813329
\(724\) 10.6869 18.5103i 0.397177 0.687930i
\(725\) 0 0
\(726\) 9.29129 + 16.0930i 0.344832 + 0.597267i
\(727\) 7.08258 12.2674i 0.262678 0.454972i −0.704275 0.709928i \(-0.748728\pi\)
0.966953 + 0.254956i \(0.0820609\pi\)
\(728\) 2.39564 + 4.14938i 0.0887885 + 0.153786i
\(729\) 24.8693 0.921086
\(730\) 0 0
\(731\) −2.29129 3.96863i −0.0847463 0.146785i
\(732\) −11.0826 19.1956i −0.409624 0.709489i
\(733\) 14.7477 0.544720 0.272360 0.962195i \(-0.412196\pi\)
0.272360 + 0.962195i \(0.412196\pi\)
\(734\) 4.20871 0.155346
\(735\) 0 0
\(736\) 2.29129 3.96863i 0.0844580 0.146286i
\(737\) 2.53901 + 4.39770i 0.0935258 + 0.161991i
\(738\) 0.247727 0.429076i 0.00911896 0.0157945i
\(739\) 4.12614 7.14668i 0.151782 0.262895i −0.780100 0.625654i \(-0.784832\pi\)
0.931883 + 0.362760i \(0.118165\pi\)
\(740\) 0 0
\(741\) 30.0390 + 22.2982i 1.10351 + 0.819144i
\(742\) 4.58258 0.168232
\(743\) 14.2913 24.7532i 0.524297 0.908108i −0.475303 0.879822i \(-0.657662\pi\)
0.999600 0.0282862i \(-0.00900498\pi\)
\(744\) 0.186932 0.323775i 0.00685325 0.0118702i
\(745\) 0 0
\(746\) 3.81307 6.60443i 0.139606 0.241805i
\(747\) −0.0825757 0.143025i −0.00302129 0.00523302i
\(748\) −3.00000 −0.109691
\(749\) 3.95644 0.144565
\(750\) 0 0
\(751\) −6.20871 10.7538i −0.226559 0.392412i 0.730227 0.683205i \(-0.239414\pi\)
−0.956786 + 0.290793i \(0.906081\pi\)
\(752\) −6.16515 −0.224820
\(753\) 50.3739 1.83573
\(754\) 5.29129 + 9.16478i 0.192697 + 0.333762i
\(755\) 0 0
\(756\) −2.50000 4.33013i −0.0909241 0.157485i
\(757\) 9.12614 15.8069i 0.331695 0.574513i −0.651149 0.758950i \(-0.725713\pi\)
0.982844 + 0.184437i \(0.0590462\pi\)
\(758\) 11.5826 20.0616i 0.420698 0.728670i
\(759\) −6.49545 −0.235770
\(760\) 0 0
\(761\) 52.7477 1.91210 0.956052 0.293198i \(-0.0947194\pi\)
0.956052 + 0.293198i \(0.0947194\pi\)
\(762\) 14.6652 25.4008i 0.531262 0.920173i
\(763\) −7.87386 + 13.6379i −0.285053 + 0.493726i
\(764\) 3.47822 + 6.02445i 0.125838 + 0.217957i
\(765\) 0 0
\(766\) 2.29129 + 3.96863i 0.0827876 + 0.143392i
\(767\) −21.9564 −0.792801
\(768\) −1.79129 −0.0646375
\(769\) −7.16515 12.4104i −0.258382 0.447531i 0.707427 0.706787i \(-0.249856\pi\)
−0.965809 + 0.259256i \(0.916523\pi\)
\(770\) 0 0
\(771\) −28.2867 −1.01872
\(772\) −24.7477 −0.890690
\(773\) 7.66515 + 13.2764i 0.275696 + 0.477520i 0.970311 0.241862i \(-0.0777582\pi\)
−0.694614 + 0.719382i \(0.744425\pi\)
\(774\) −0.126136 + 0.218475i −0.00453388 + 0.00785291i
\(775\) 0 0
\(776\) −0.686932 + 1.18980i −0.0246594 + 0.0427114i
\(777\) 5.00000 8.66025i 0.179374 0.310685i
\(778\) −32.3739 −1.16066
\(779\) 9.49545 4.11165i 0.340210 0.147315i
\(780\) 0 0
\(781\) −1.81307 + 3.14033i −0.0648767 + 0.112370i
\(782\) −8.68693 + 15.0462i −0.310644 + 0.538051i
\(783\) −5.52178 9.56400i −0.197332 0.341790i
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0