Properties

Label 950.2.e.j.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 201.1
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.j.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} -3.79129 q^{11} +2.79129 q^{12} +(-0.104356 - 0.180750i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} -4.79129 q^{18} +(-3.50000 - 2.59808i) q^{19} +(-1.39564 + 2.41733i) q^{21} +(-1.89564 + 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(1.39564 - 2.41733i) q^{24} -0.208712 q^{26} +5.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-3.39564 - 5.88143i) q^{29} -4.79129 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +(0.395644 + 0.685275i) q^{34} +(-2.39564 + 4.14938i) q^{36} -3.58258 q^{37} +(-4.00000 + 1.73205i) q^{38} +0.582576 q^{39} +(5.68693 - 9.85005i) q^{41} +(1.39564 + 2.41733i) q^{42} +(2.89564 - 5.01540i) q^{43} +(1.89564 + 3.28335i) q^{44} +4.58258 q^{46} +(-6.08258 - 10.5353i) q^{47} +(-1.39564 - 2.41733i) q^{48} -6.00000 q^{49} +(-1.10436 - 1.91280i) q^{51} +(-0.104356 + 0.180750i) q^{52} +(-2.29129 - 3.96863i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{56} +(11.1652 - 4.83465i) q^{57} -6.79129 q^{58} +(-2.29129 + 3.96863i) q^{59} +(-0.686932 - 1.18980i) q^{61} +(-2.39564 + 4.14938i) q^{62} +(-2.39564 - 4.14938i) q^{63} +1.00000 q^{64} +(-5.29129 - 9.16478i) q^{66} +(7.79129 + 13.4949i) q^{67} +0.791288 q^{68} -12.7913 q^{69} +(2.29129 - 3.96863i) q^{71} +(2.39564 + 4.14938i) q^{72} +(1.39564 - 2.41733i) q^{73} +(-1.79129 + 3.10260i) q^{74} +(-0.500000 + 4.33013i) q^{76} -3.79129 q^{77} +(0.291288 - 0.504525i) q^{78} +(-7.47822 + 12.9527i) q^{79} +(0.208712 - 0.361500i) q^{81} +(-5.68693 - 9.85005i) q^{82} -3.79129 q^{83} +2.79129 q^{84} +(-2.89564 - 5.01540i) q^{86} +18.9564 q^{87} +3.79129 q^{88} +(-2.29129 - 3.96863i) q^{89} +(-0.104356 - 0.180750i) q^{91} +(2.29129 - 3.96863i) q^{92} +(6.68693 - 11.5821i) q^{93} -12.1652 q^{94} -2.79129 q^{96} +(-6.18693 + 10.7161i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.08258 + 15.7315i) 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
\(3\) −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i \(0.464918\pi\)
−0.915766 + 0.401711i \(0.868416\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 1.39564 + 2.41733i 0.569769 + 0.986869i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.39564 4.14938i −0.798548 1.38313i
\(10\) 0 0
\(11\) −3.79129 −1.14312 −0.571558 0.820562i \(-0.693661\pi\)
−0.571558 + 0.820562i \(0.693661\pi\)
\(12\) 2.79129 0.805775
\(13\) −0.104356 0.180750i −0.0289432 0.0501310i 0.851191 0.524856i \(-0.175881\pi\)
−0.880134 + 0.474725i \(0.842548\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.395644 + 0.685275i −0.0959577 + 0.166204i −0.910008 0.414591i \(-0.863925\pi\)
0.814050 + 0.580795i \(0.197258\pi\)
\(18\) −4.79129 −1.12932
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) 0 0
\(21\) −1.39564 + 2.41733i −0.304554 + 0.527504i
\(22\) −1.89564 + 3.28335i −0.404153 + 0.700013i
\(23\) 2.29129 + 3.96863i 0.477767 + 0.827516i 0.999675 0.0254855i \(-0.00811315\pi\)
−0.521909 + 0.853001i \(0.674780\pi\)
\(24\) 1.39564 2.41733i 0.284885 0.493435i
\(25\) 0 0
\(26\) −0.208712 −0.0409318
\(27\) 5.00000 0.962250
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −3.39564 5.88143i −0.630555 1.09215i −0.987438 0.158005i \(-0.949494\pi\)
0.356883 0.934149i \(-0.383839\pi\)
\(30\) 0 0
\(31\) −4.79129 −0.860541 −0.430270 0.902700i \(-0.641582\pi\)
−0.430270 + 0.902700i \(0.641582\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 5.29129 9.16478i 0.921095 1.59538i
\(34\) 0.395644 + 0.685275i 0.0678524 + 0.117524i
\(35\) 0 0
\(36\) −2.39564 + 4.14938i −0.399274 + 0.691563i
\(37\) −3.58258 −0.588972 −0.294486 0.955656i \(-0.595148\pi\)
−0.294486 + 0.955656i \(0.595148\pi\)
\(38\) −4.00000 + 1.73205i −0.648886 + 0.280976i
\(39\) 0.582576 0.0932868
\(40\) 0 0
\(41\) 5.68693 9.85005i 0.888150 1.53832i 0.0460888 0.998937i \(-0.485324\pi\)
0.842061 0.539383i \(-0.181342\pi\)
\(42\) 1.39564 + 2.41733i 0.215353 + 0.373002i
\(43\) 2.89564 5.01540i 0.441582 0.764842i −0.556225 0.831031i \(-0.687751\pi\)
0.997807 + 0.0661897i \(0.0210843\pi\)
\(44\) 1.89564 + 3.28335i 0.285779 + 0.494984i
\(45\) 0 0
\(46\) 4.58258 0.675664
\(47\) −6.08258 10.5353i −0.887235 1.53674i −0.843131 0.537709i \(-0.819290\pi\)
−0.0441043 0.999027i \(-0.514043\pi\)
\(48\) −1.39564 2.41733i −0.201444 0.348911i
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −1.10436 1.91280i −0.154641 0.267846i
\(52\) −0.104356 + 0.180750i −0.0144716 + 0.0250655i
\(53\) −2.29129 3.96863i −0.314733 0.545133i 0.664648 0.747157i \(-0.268582\pi\)
−0.979381 + 0.202024i \(0.935248\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 11.1652 4.83465i 1.47886 0.640365i
\(58\) −6.79129 −0.891740
\(59\) −2.29129 + 3.96863i −0.298300 + 0.516671i −0.975747 0.218900i \(-0.929753\pi\)
0.677447 + 0.735572i \(0.263086\pi\)
\(60\) 0 0
\(61\) −0.686932 1.18980i −0.0879526 0.152338i 0.818693 0.574232i \(-0.194699\pi\)
−0.906646 + 0.421893i \(0.861366\pi\)
\(62\) −2.39564 + 4.14938i −0.304247 + 0.526971i
\(63\) −2.39564 4.14938i −0.301823 0.522772i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.29129 9.16478i −0.651313 1.12811i
\(67\) 7.79129 + 13.4949i 0.951857 + 1.64867i 0.741401 + 0.671062i \(0.234162\pi\)
0.210456 + 0.977603i \(0.432505\pi\)
\(68\) 0.791288 0.0959577
\(69\) −12.7913 −1.53989
\(70\) 0 0
\(71\) 2.29129 3.96863i 0.271926 0.470989i −0.697429 0.716654i \(-0.745673\pi\)
0.969355 + 0.245664i \(0.0790061\pi\)
\(72\) 2.39564 + 4.14938i 0.282329 + 0.489009i
\(73\) 1.39564 2.41733i 0.163348 0.282927i −0.772720 0.634748i \(-0.781104\pi\)
0.936067 + 0.351821i \(0.114437\pi\)
\(74\) −1.79129 + 3.10260i −0.208233 + 0.360670i
\(75\) 0 0
\(76\) −0.500000 + 4.33013i −0.0573539 + 0.496700i
\(77\) −3.79129 −0.432057
\(78\) 0.291288 0.504525i 0.0329819 0.0571262i
\(79\) −7.47822 + 12.9527i −0.841365 + 1.45729i 0.0473751 + 0.998877i \(0.484914\pi\)
−0.888741 + 0.458411i \(0.848419\pi\)
\(80\) 0 0
\(81\) 0.208712 0.361500i 0.0231902 0.0401667i
\(82\) −5.68693 9.85005i −0.628017 1.08776i
\(83\) −3.79129 −0.416148 −0.208074 0.978113i \(-0.566719\pi\)
−0.208074 + 0.978113i \(0.566719\pi\)
\(84\) 2.79129 0.304554
\(85\) 0 0
\(86\) −2.89564 5.01540i −0.312245 0.540825i
\(87\) 18.9564 2.03234
\(88\) 3.79129 0.404153
\(89\) −2.29129 3.96863i −0.242876 0.420674i 0.718656 0.695365i \(-0.244757\pi\)
−0.961532 + 0.274692i \(0.911424\pi\)
\(90\) 0 0
\(91\) −0.104356 0.180750i −0.0109395 0.0189478i
\(92\) 2.29129 3.96863i 0.238883 0.413758i
\(93\) 6.68693 11.5821i 0.693403 1.20101i
\(94\) −12.1652 −1.25474
\(95\) 0 0
\(96\) −2.79129 −0.284885
\(97\) −6.18693 + 10.7161i −0.628188 + 1.08805i 0.359727 + 0.933057i \(0.382870\pi\)
−0.987915 + 0.154996i \(0.950464\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 9.08258 + 15.7315i 0.912833 + 1.58107i
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −2.20871 −0.218695
\(103\) −5.16515 −0.508937 −0.254469 0.967081i \(-0.581901\pi\)
−0.254469 + 0.967081i \(0.581901\pi\)
\(104\) 0.104356 + 0.180750i 0.0102330 + 0.0177240i
\(105\) 0 0
\(106\) −4.58258 −0.445099
\(107\) −18.9564 −1.83259 −0.916294 0.400506i \(-0.868834\pi\)
−0.916294 + 0.400506i \(0.868834\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) 5.87386 10.1738i 0.562614 0.974476i −0.434653 0.900598i \(-0.643129\pi\)
0.997267 0.0738783i \(-0.0235376\pi\)
\(110\) 0 0
\(111\) 5.00000 8.66025i 0.474579 0.821995i
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) −5.37386 −0.505531 −0.252765 0.967528i \(-0.581340\pi\)
−0.252765 + 0.967528i \(0.581340\pi\)
\(114\) 1.39564 12.0866i 0.130714 1.13202i
\(115\) 0 0
\(116\) −3.39564 + 5.88143i −0.315278 + 0.546077i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 2.29129 + 3.96863i 0.210930 + 0.365342i
\(119\) −0.395644 + 0.685275i −0.0362686 + 0.0628191i
\(120\) 0 0
\(121\) 3.37386 0.306715
\(122\) −1.37386 −0.124384
\(123\) 15.8739 + 27.4943i 1.43130 + 2.47908i
\(124\) 2.39564 + 4.14938i 0.215135 + 0.372625i
\(125\) 0 0
\(126\) −4.79129 −0.426842
\(127\) 1.31307 + 2.27430i 0.116516 + 0.201812i 0.918385 0.395689i \(-0.129494\pi\)
−0.801869 + 0.597500i \(0.796161\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 8.08258 + 13.9994i 0.711631 + 1.23258i
\(130\) 0 0
\(131\) −5.76951 + 9.99308i −0.504084 + 0.873099i 0.495905 + 0.868377i \(0.334837\pi\)
−0.999989 + 0.00472247i \(0.998497\pi\)
\(132\) −10.5826 −0.921095
\(133\) −3.50000 2.59808i −0.303488 0.225282i
\(134\) 15.5826 1.34613
\(135\) 0 0
\(136\) 0.395644 0.685275i 0.0339262 0.0587619i
\(137\) 7.66515 + 13.2764i 0.654878 + 1.13428i 0.981924 + 0.189274i \(0.0606134\pi\)
−0.327046 + 0.945008i \(0.606053\pi\)
\(138\) −6.39564 + 11.0776i −0.544433 + 0.942986i
\(139\) 6.10436 + 10.5731i 0.517765 + 0.896795i 0.999787 + 0.0206359i \(0.00656907\pi\)
−0.482022 + 0.876159i \(0.660098\pi\)
\(140\) 0 0
\(141\) 33.9564 2.85965
\(142\) −2.29129 3.96863i −0.192281 0.333040i
\(143\) 0.395644 + 0.685275i 0.0330854 + 0.0573056i
\(144\) 4.79129 0.399274
\(145\) 0 0
\(146\) −1.39564 2.41733i −0.115504 0.200059i
\(147\) 8.37386 14.5040i 0.690665 1.19627i
\(148\) 1.79129 + 3.10260i 0.147243 + 0.255032i
\(149\) 11.3739 19.7001i 0.931783 1.61390i 0.151511 0.988456i \(-0.451586\pi\)
0.780272 0.625440i \(-0.215081\pi\)
\(150\) 0 0
\(151\) 15.7477 1.28153 0.640766 0.767736i \(-0.278617\pi\)
0.640766 + 0.767736i \(0.278617\pi\)
\(152\) 3.50000 + 2.59808i 0.283887 + 0.210732i
\(153\) 3.79129 0.306507
\(154\) −1.89564 + 3.28335i −0.152755 + 0.264580i
\(155\) 0 0
\(156\) −0.291288 0.504525i −0.0233217 0.0403944i
\(157\) −3.97822 + 6.89048i −0.317496 + 0.549920i −0.979965 0.199170i \(-0.936176\pi\)
0.662469 + 0.749090i \(0.269509\pi\)
\(158\) 7.47822 + 12.9527i 0.594935 + 1.03046i
\(159\) 12.7913 1.01442
\(160\) 0 0
\(161\) 2.29129 + 3.96863i 0.180579 + 0.312772i
\(162\) −0.208712 0.361500i −0.0163980 0.0284021i
\(163\) 14.5826 1.14220 0.571098 0.820882i \(-0.306518\pi\)
0.571098 + 0.820882i \(0.306518\pi\)
\(164\) −11.3739 −0.888150
\(165\) 0 0
\(166\) −1.89564 + 3.28335i −0.147131 + 0.254838i
\(167\) 5.76951 + 9.99308i 0.446458 + 0.773288i 0.998152 0.0607584i \(-0.0193519\pi\)
−0.551695 + 0.834046i \(0.686019\pi\)
\(168\) 1.39564 2.41733i 0.107676 0.186501i
\(169\) 6.47822 11.2206i 0.498325 0.863124i
\(170\) 0 0
\(171\) −2.39564 + 20.7469i −0.183199 + 1.58655i
\(172\) −5.79129 −0.441582
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 9.47822 16.4168i 0.718542 1.24455i
\(175\) 0 0
\(176\) 1.89564 3.28335i 0.142890 0.247492i
\(177\) −6.39564 11.0776i −0.480726 0.832642i
\(178\) −4.58258 −0.343479
\(179\) −16.7477 −1.25178 −0.625892 0.779910i \(-0.715265\pi\)
−0.625892 + 0.779910i \(0.715265\pi\)
\(180\) 0 0
\(181\) 3.81307 + 6.60443i 0.283423 + 0.490903i 0.972226 0.234046i \(-0.0751966\pi\)
−0.688802 + 0.724949i \(0.741863\pi\)
\(182\) −0.208712 −0.0154708
\(183\) 3.83485 0.283480
\(184\) −2.29129 3.96863i −0.168916 0.292571i
\(185\) 0 0
\(186\) −6.68693 11.5821i −0.490310 0.849241i
\(187\) 1.50000 2.59808i 0.109691 0.189990i
\(188\) −6.08258 + 10.5353i −0.443617 + 0.768368i
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) 15.9564 1.15457 0.577284 0.816544i \(-0.304113\pi\)
0.577284 + 0.816544i \(0.304113\pi\)
\(192\) −1.39564 + 2.41733i −0.100722 + 0.174455i
\(193\) −1.37386 + 2.37960i −0.0988929 + 0.171287i −0.911227 0.411905i \(-0.864863\pi\)
0.812334 + 0.583193i \(0.198197\pi\)
\(194\) 6.18693 + 10.7161i 0.444196 + 0.769370i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −20.2087 −1.43981 −0.719906 0.694072i \(-0.755815\pi\)
−0.719906 + 0.694072i \(0.755815\pi\)
\(198\) 18.1652 1.29094
\(199\) −1.79129 3.10260i −0.126981 0.219938i 0.795525 0.605921i \(-0.207195\pi\)
−0.922506 + 0.385984i \(0.873862\pi\)
\(200\) 0 0
\(201\) −43.4955 −3.06793
\(202\) 0 0
\(203\) −3.39564 5.88143i −0.238327 0.412795i
\(204\) −1.10436 + 1.91280i −0.0773204 + 0.133923i
\(205\) 0 0
\(206\) −2.58258 + 4.47315i −0.179937 + 0.311659i
\(207\) 10.9782 19.0148i 0.763039 1.32162i
\(208\) 0.208712 0.0144716
\(209\) 13.2695 + 9.85005i 0.917871 + 0.681343i
\(210\) 0 0
\(211\) −11.9782 + 20.7469i −0.824615 + 1.42827i 0.0775988 + 0.996985i \(0.475275\pi\)
−0.902213 + 0.431290i \(0.858059\pi\)
\(212\) −2.29129 + 3.96863i −0.157366 + 0.272566i
\(213\) 6.39564 + 11.0776i 0.438222 + 0.759023i
\(214\) −9.47822 + 16.4168i −0.647918 + 1.12223i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) −4.79129 −0.325254
\(218\) −5.87386 10.1738i −0.397828 0.689059i
\(219\) 3.89564 + 6.74745i 0.263243 + 0.455951i
\(220\) 0 0
\(221\) 0.165151 0.0111093
\(222\) −5.00000 8.66025i −0.335578 0.581238i
\(223\) 9.60436 16.6352i 0.643155 1.11398i −0.341569 0.939857i \(-0.610958\pi\)
0.984724 0.174121i \(-0.0557084\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) −2.68693 + 4.65390i −0.178732 + 0.309573i
\(227\) −7.74773 −0.514235 −0.257117 0.966380i \(-0.582773\pi\)
−0.257117 + 0.966380i \(0.582773\pi\)
\(228\) −9.76951 7.25198i −0.647001 0.480274i
\(229\) −25.3303 −1.67387 −0.836937 0.547300i \(-0.815656\pi\)
−0.836937 + 0.547300i \(0.815656\pi\)
\(230\) 0 0
\(231\) 5.29129 9.16478i 0.348141 0.602998i
\(232\) 3.39564 + 5.88143i 0.222935 + 0.386135i
\(233\) 4.58258 7.93725i 0.300215 0.519987i −0.675970 0.736929i \(-0.736275\pi\)
0.976184 + 0.216942i \(0.0696084\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) 0 0
\(236\) 4.58258 0.298300
\(237\) −20.8739 36.1546i −1.35590 2.34849i
\(238\) 0.395644 + 0.685275i 0.0256458 + 0.0444198i
\(239\) 16.5826 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(240\) 0 0
\(241\) 8.39564 + 14.5417i 0.540811 + 0.936712i 0.998858 + 0.0477840i \(0.0152159\pi\)
−0.458047 + 0.888928i \(0.651451\pi\)
\(242\) 1.68693 2.92185i 0.108440 0.187824i
\(243\) 8.08258 + 13.9994i 0.518497 + 0.898064i
\(244\) −0.686932 + 1.18980i −0.0439763 + 0.0761692i
\(245\) 0 0
\(246\) 31.7477 2.02416
\(247\) −0.104356 + 0.903750i −0.00664002 + 0.0575042i
\(248\) 4.79129 0.304247
\(249\) 5.29129 9.16478i 0.335322 0.580794i
\(250\) 0 0
\(251\) −6.56080 11.3636i −0.414114 0.717266i 0.581221 0.813746i \(-0.302575\pi\)
−0.995335 + 0.0964796i \(0.969242\pi\)
\(252\) −2.39564 + 4.14938i −0.150911 + 0.261386i
\(253\) −8.68693 15.0462i −0.546143 0.945947i
\(254\) 2.62614 0.164778
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.60436 9.70703i −0.349590 0.605508i 0.636587 0.771205i \(-0.280346\pi\)
−0.986177 + 0.165697i \(0.947012\pi\)
\(258\) 16.1652 1.00640
\(259\) −3.58258 −0.222610
\(260\) 0 0
\(261\) −16.2695 + 28.1796i −1.00706 + 1.74427i
\(262\) 5.76951 + 9.99308i 0.356441 + 0.617375i
\(263\) −9.70871 + 16.8160i −0.598665 + 1.03692i 0.394354 + 0.918959i \(0.370969\pi\)
−0.993018 + 0.117959i \(0.962365\pi\)
\(264\) −5.29129 + 9.16478i −0.325656 + 0.564053i
\(265\) 0 0
\(266\) −4.00000 + 1.73205i −0.245256 + 0.106199i
\(267\) 12.7913 0.782814
\(268\) 7.79129 13.4949i 0.475929 0.824333i
\(269\) −6.56080 + 11.3636i −0.400019 + 0.692853i −0.993728 0.111827i \(-0.964330\pi\)
0.593709 + 0.804680i \(0.297663\pi\)
\(270\) 0 0
\(271\) 8.56080 14.8277i 0.520031 0.900721i −0.479698 0.877434i \(-0.659254\pi\)
0.999729 0.0232867i \(-0.00741305\pi\)
\(272\) −0.395644 0.685275i −0.0239894 0.0415509i
\(273\) 0.582576 0.0352591
\(274\) 15.3303 0.926137
\(275\) 0 0
\(276\) 6.39564 + 11.0776i 0.384973 + 0.666792i
\(277\) 8.74773 0.525600 0.262800 0.964850i \(-0.415354\pi\)
0.262800 + 0.964850i \(0.415354\pi\)
\(278\) 12.2087 0.732230
\(279\) 11.4782 + 19.8809i 0.687183 + 1.19024i
\(280\) 0 0
\(281\) −5.29129 9.16478i −0.315652 0.546725i 0.663924 0.747800i \(-0.268890\pi\)
−0.979576 + 0.201075i \(0.935556\pi\)
\(282\) 16.9782 29.4071i 1.01104 1.75117i
\(283\) 10.5608 18.2918i 0.627774 1.08734i −0.360223 0.932866i \(-0.617299\pi\)
0.987997 0.154471i \(-0.0493672\pi\)
\(284\) −4.58258 −0.271926
\(285\) 0 0
\(286\) 0.791288 0.0467898
\(287\) 5.68693 9.85005i 0.335689 0.581430i
\(288\) 2.39564 4.14938i 0.141165 0.244504i
\(289\) 8.18693 + 14.1802i 0.481584 + 0.834128i
\(290\) 0 0
\(291\) −17.2695 29.9117i −1.01236 1.75345i
\(292\) −2.79129 −0.163348
\(293\) −24.9564 −1.45797 −0.728985 0.684529i \(-0.760008\pi\)
−0.728985 + 0.684529i \(0.760008\pi\)
\(294\) −8.37386 14.5040i −0.488374 0.845888i
\(295\) 0 0
\(296\) 3.58258 0.208233
\(297\) −18.9564 −1.09996
\(298\) −11.3739 19.7001i −0.658870 1.14120i
\(299\) 0.478220 0.828301i 0.0276562 0.0479019i
\(300\) 0 0
\(301\) 2.89564 5.01540i 0.166902 0.289083i
\(302\) 7.87386 13.6379i 0.453090 0.784775i
\(303\) 0 0
\(304\) 4.00000 1.73205i 0.229416 0.0993399i
\(305\) 0 0
\(306\) 1.89564 3.28335i 0.108367 0.187697i
\(307\) −17.2477 + 29.8739i −0.984380 + 1.70500i −0.339719 + 0.940527i \(0.610332\pi\)
−0.644661 + 0.764469i \(0.723001\pi\)
\(308\) 1.89564 + 3.28335i 0.108014 + 0.187086i
\(309\) 7.20871 12.4859i 0.410089 0.710296i
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) −0.582576 −0.0329819
\(313\) −5.87386 10.1738i −0.332010 0.575059i 0.650896 0.759167i \(-0.274394\pi\)
−0.982906 + 0.184108i \(0.941060\pi\)
\(314\) 3.97822 + 6.89048i 0.224504 + 0.388852i
\(315\) 0 0
\(316\) 14.9564 0.841365
\(317\) −4.58258 7.93725i −0.257383 0.445801i 0.708157 0.706055i \(-0.249527\pi\)
−0.965540 + 0.260254i \(0.916194\pi\)
\(318\) 6.39564 11.0776i 0.358650 0.621200i
\(319\) 12.8739 + 22.2982i 0.720798 + 1.24846i
\(320\) 0 0
\(321\) 26.4564 45.8239i 1.47665 2.55764i
\(322\) 4.58258 0.255377
\(323\) 3.16515 1.37055i 0.176114 0.0762595i
\(324\) −0.417424 −0.0231902
\(325\) 0 0
\(326\) 7.29129 12.6289i 0.403827 0.699449i
\(327\) 16.3956 + 28.3981i 0.906681 + 1.57042i
\(328\) −5.68693 + 9.85005i −0.314008 + 0.543878i
\(329\) −6.08258 10.5353i −0.335343 0.580832i
\(330\) 0 0
\(331\) −17.9129 −0.984581 −0.492290 0.870431i \(-0.663840\pi\)
−0.492290 + 0.870431i \(0.663840\pi\)
\(332\) 1.89564 + 3.28335i 0.104037 + 0.180197i
\(333\) 8.58258 + 14.8655i 0.470322 + 0.814622i
\(334\) 11.5390 0.631387
\(335\) 0 0
\(336\) −1.39564 2.41733i −0.0761386 0.131876i
\(337\) 11.6652 20.2046i 0.635441 1.10062i −0.350980 0.936383i \(-0.614152\pi\)
0.986421 0.164234i \(-0.0525151\pi\)
\(338\) −6.47822 11.2206i −0.352369 0.610320i
\(339\) 7.50000 12.9904i 0.407344 0.705541i
\(340\) 0 0
\(341\) 18.1652 0.983698
\(342\) 16.7695 + 12.4481i 0.906791 + 0.673118i
\(343\) −13.0000 −0.701934
\(344\) −2.89564 + 5.01540i −0.156123 + 0.270412i
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 1.81307 3.14033i 0.0973306 0.168582i −0.813248 0.581917i \(-0.802303\pi\)
0.910579 + 0.413335i \(0.135636\pi\)
\(348\) −9.47822 16.4168i −0.508086 0.880031i
\(349\) −5.41742 −0.289988 −0.144994 0.989433i \(-0.546316\pi\)
−0.144994 + 0.989433i \(0.546316\pi\)
\(350\) 0 0
\(351\) −0.521780 0.903750i −0.0278506 0.0482386i
\(352\) −1.89564 3.28335i −0.101038 0.175003i
\(353\) 13.7477 0.731718 0.365859 0.930670i \(-0.380775\pi\)
0.365859 + 0.930670i \(0.380775\pi\)
\(354\) −12.7913 −0.679849
\(355\) 0 0
\(356\) −2.29129 + 3.96863i −0.121438 + 0.210337i
\(357\) −1.10436 1.91280i −0.0584487 0.101236i
\(358\) −8.37386 + 14.5040i −0.442572 + 0.766558i
\(359\) 17.8521 30.9207i 0.942197 1.63193i 0.180928 0.983496i \(-0.442090\pi\)
0.761269 0.648437i \(-0.224577\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 7.62614 0.400821
\(363\) −4.70871 + 8.15573i −0.247143 + 0.428065i
\(364\) −0.104356 + 0.180750i −0.00546974 + 0.00947388i
\(365\) 0 0
\(366\) 1.91742 3.32108i 0.100225 0.173595i
\(367\) 4.39564 + 7.61348i 0.229451 + 0.397420i 0.957645 0.287950i \(-0.0929737\pi\)
−0.728195 + 0.685370i \(0.759640\pi\)
\(368\) −4.58258 −0.238883
\(369\) −54.4955 −2.83692
\(370\) 0 0
\(371\) −2.29129 3.96863i −0.118958 0.206041i
\(372\) −13.3739 −0.693403
\(373\) 21.3739 1.10670 0.553348 0.832950i \(-0.313350\pi\)
0.553348 + 0.832950i \(0.313350\pi\)
\(374\) −1.50000 2.59808i −0.0775632 0.134343i
\(375\) 0 0
\(376\) 6.08258 + 10.5353i 0.313685 + 0.543318i
\(377\) −0.708712 + 1.22753i −0.0365005 + 0.0632208i
\(378\) 2.50000 4.33013i 0.128586 0.222718i
\(379\) 4.83485 0.248349 0.124175 0.992260i \(-0.460372\pi\)
0.124175 + 0.992260i \(0.460372\pi\)
\(380\) 0 0
\(381\) −7.33030 −0.375543
\(382\) 7.97822 13.8187i 0.408201 0.707025i
\(383\) 2.29129 3.96863i 0.117079 0.202787i −0.801530 0.597955i \(-0.795980\pi\)
0.918609 + 0.395168i \(0.129313\pi\)
\(384\) 1.39564 + 2.41733i 0.0712212 + 0.123359i
\(385\) 0 0
\(386\) 1.37386 + 2.37960i 0.0699278 + 0.121119i
\(387\) −27.7477 −1.41050
\(388\) 12.3739 0.628188
\(389\) −9.31307 16.1307i −0.472191 0.817859i 0.527302 0.849678i \(-0.323204\pi\)
−0.999494 + 0.0318184i \(0.989870\pi\)
\(390\) 0 0
\(391\) −3.62614 −0.183382
\(392\) 6.00000 0.303046
\(393\) −16.1044 27.8936i −0.812357 1.40704i
\(394\) −10.1044 + 17.5013i −0.509050 + 0.881701i
\(395\) 0 0
\(396\) 9.08258 15.7315i 0.456417 0.790537i
\(397\) −5.70871 + 9.88778i −0.286512 + 0.496253i −0.972975 0.230912i \(-0.925829\pi\)
0.686463 + 0.727165i \(0.259163\pi\)
\(398\) −3.58258 −0.179578
\(399\) 11.1652 4.83465i 0.558957 0.242035i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) −21.7477 + 37.6682i −1.08468 + 1.87872i
\(403\) 0.500000 + 0.866025i 0.0249068 + 0.0431398i
\(404\) 0 0
\(405\) 0 0
\(406\) −6.79129 −0.337046
\(407\) 13.5826 0.673263
\(408\) 1.10436 + 1.91280i 0.0546738 + 0.0946978i
\(409\) 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
\(411\) −42.7913 −2.11074
\(412\) 2.58258 + 4.47315i 0.127234 + 0.220376i
\(413\) −2.29129 + 3.96863i −0.112747 + 0.195283i
\(414\) −10.9782 19.0148i −0.539550 0.934528i
\(415\) 0 0
\(416\) 0.104356 0.180750i 0.00511648 0.00886200i
\(417\) −34.0780 −1.66881
\(418\) 15.1652 6.56670i 0.741752 0.321188i
\(419\) −22.7477 −1.11130 −0.555650 0.831417i \(-0.687530\pi\)
−0.555650 + 0.831417i \(0.687530\pi\)
\(420\) 0 0
\(421\) −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i \(-0.995377\pi\)
0.512524 + 0.858673i \(0.328710\pi\)
\(422\) 11.9782 + 20.7469i 0.583091 + 1.00994i
\(423\) −29.1434 + 50.4778i −1.41700 + 2.45431i
\(424\) 2.29129 + 3.96863i 0.111275 + 0.192734i
\(425\) 0 0
\(426\) 12.7913 0.619740
\(427\) −0.686932 1.18980i −0.0332430 0.0575785i
\(428\) 9.47822 + 16.4168i 0.458147 + 0.793534i
\(429\) −2.20871 −0.106638
\(430\) 0 0
\(431\) −4.10436 7.10895i −0.197700 0.342426i 0.750082 0.661344i \(-0.230014\pi\)
−0.947782 + 0.318918i \(0.896680\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 3.45644 + 5.98673i 0.166106 + 0.287704i 0.937047 0.349202i \(-0.113547\pi\)
−0.770942 + 0.636906i \(0.780214\pi\)
\(434\) −2.39564 + 4.14938i −0.114995 + 0.199176i
\(435\) 0 0
\(436\) −11.7477 −0.562614
\(437\) 2.29129 19.8431i 0.109607 0.949226i
\(438\) 7.79129 0.372282
\(439\) 12.6652 21.9367i 0.604475 1.04698i −0.387660 0.921803i \(-0.626716\pi\)
0.992134 0.125178i \(-0.0399503\pi\)
\(440\) 0 0
\(441\) 14.3739 + 24.8963i 0.684470 + 1.18554i
\(442\) 0.0825757 0.143025i 0.00392773 0.00680302i
\(443\) −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
\(446\) −9.60436 16.6352i −0.454779 0.787701i
\(447\) 31.7477 + 54.9887i 1.50162 + 2.60088i
\(448\) 1.00000 0.0472456
\(449\) 3.33030 0.157167 0.0785834 0.996908i \(-0.474960\pi\)
0.0785834 + 0.996908i \(0.474960\pi\)
\(450\) 0 0
\(451\) −21.5608 + 37.3444i −1.01526 + 1.75848i
\(452\) 2.68693 + 4.65390i 0.126383 + 0.218901i
\(453\) −21.9782 + 38.0674i −1.03263 + 1.78856i
\(454\) −3.87386 + 6.70973i −0.181809 + 0.314903i
\(455\) 0 0
\(456\) −11.1652 + 4.83465i −0.522856 + 0.226403i
\(457\) 20.7477 0.970538 0.485269 0.874365i \(-0.338722\pi\)
0.485269 + 0.874365i \(0.338722\pi\)
\(458\) −12.6652 + 21.9367i −0.591804 + 1.02503i
\(459\) −1.97822 + 3.42638i −0.0923354 + 0.159930i
\(460\) 0 0
\(461\) −6.39564 + 11.0776i −0.297875 + 0.515934i −0.975650 0.219335i \(-0.929611\pi\)
0.677775 + 0.735270i \(0.262944\pi\)
\(462\) −5.29129 9.16478i −0.246173 0.426384i
\(463\) −17.9564 −0.834507 −0.417253 0.908790i \(-0.637007\pi\)
−0.417253 + 0.908790i \(0.637007\pi\)
\(464\) 6.79129 0.315278
\(465\) 0 0
\(466\) −4.58258 7.93725i −0.212284 0.367686i
\(467\) 12.3303 0.570578 0.285289 0.958441i \(-0.407910\pi\)
0.285289 + 0.958441i \(0.407910\pi\)
\(468\) 1.00000 0.0462250
\(469\) 7.79129 + 13.4949i 0.359768 + 0.623137i
\(470\) 0 0
\(471\) −11.1044 19.2333i −0.511662 0.886224i
\(472\) 2.29129 3.96863i 0.105465 0.182671i
\(473\) −10.9782 + 19.0148i −0.504779 + 0.874303i
\(474\) −41.7477 −1.91754
\(475\) 0 0
\(476\) 0.791288 0.0362686
\(477\) −10.9782 + 19.0148i −0.502658 + 0.870629i
\(478\) 8.29129 14.3609i 0.379235 0.656854i
\(479\) −15.8739 27.4943i −0.725295 1.25625i −0.958852 0.283905i \(-0.908370\pi\)
0.233557 0.972343i \(-0.424963\pi\)
\(480\) 0 0
\(481\) 0.373864 + 0.647551i 0.0170467 + 0.0295258i
\(482\) 16.7913 0.764822
\(483\) −12.7913 −0.582024
\(484\) −1.68693 2.92185i −0.0766787 0.132811i
\(485\) 0 0
\(486\) 16.1652 0.733266
\(487\) −23.0000 −1.04223 −0.521115 0.853487i \(-0.674484\pi\)
−0.521115 + 0.853487i \(0.674484\pi\)
\(488\) 0.686932 + 1.18980i 0.0310959 + 0.0538597i
\(489\) −20.3521 + 35.2508i −0.920353 + 1.59410i
\(490\) 0 0
\(491\) 15.7087 27.2083i 0.708924 1.22789i −0.256332 0.966589i \(-0.582514\pi\)
0.965257 0.261304i \(-0.0841525\pi\)
\(492\) 15.8739 27.4943i 0.715649 1.23954i
\(493\) 5.37386 0.242027
\(494\) 0.730493 + 0.542250i 0.0328664 + 0.0243970i
\(495\) 0 0
\(496\) 2.39564 4.14938i 0.107568 0.186313i
\(497\) 2.29129 3.96863i 0.102778 0.178017i
\(498\) −5.29129 9.16478i −0.237108 0.410684i
\(499\) 9.66515 16.7405i 0.432672 0.749409i −0.564431 0.825480i \(-0.690904\pi\)
0.997102 + 0.0760712i \(0.0242376\pi\)
\(500\) 0 0
\(501\) −32.2087 −1.43898
\(502\) −13.1216 −0.585645
\(503\) −2.29129 3.96863i −0.102163 0.176952i 0.810412 0.585860i \(-0.199243\pi\)
−0.912576 + 0.408908i \(0.865910\pi\)
\(504\) 2.39564 + 4.14938i 0.106710 + 0.184828i
\(505\) 0 0
\(506\) −17.3739 −0.772362
\(507\) 18.0826 + 31.3199i 0.803075 + 1.39097i
\(508\) 1.31307 2.27430i 0.0582580 0.100906i
\(509\) −11.2087 19.4141i −0.496817 0.860513i 0.503176 0.864184i \(-0.332165\pi\)
−0.999993 + 0.00367102i \(0.998831\pi\)
\(510\) 0 0
\(511\) 1.39564 2.41733i 0.0617397 0.106936i
\(512\) −1.00000 −0.0441942
\(513\) −17.5000 12.9904i −0.772644 0.573539i
\(514\) −11.2087 −0.494395
\(515\) 0 0
\(516\) 8.08258 13.9994i 0.355816 0.616291i
\(517\) 23.0608 + 39.9425i 1.01421 + 1.75667i
\(518\) −1.79129 + 3.10260i −0.0787047 + 0.136320i
\(519\) −29.3085 50.7638i −1.28650 2.22829i
\(520\) 0 0
\(521\) 13.2523 0.580593 0.290296 0.956937i \(-0.406246\pi\)
0.290296 + 0.956937i \(0.406246\pi\)
\(522\) 16.2695 + 28.1796i 0.712097 + 1.23339i
\(523\) −8.87386 15.3700i −0.388027 0.672082i 0.604157 0.796865i \(-0.293510\pi\)
−0.992184 + 0.124783i \(0.960177\pi\)
\(524\) 11.5390 0.504084
\(525\) 0 0
\(526\) 9.70871 + 16.8160i 0.423320 + 0.733212i
\(527\) 1.89564 3.28335i 0.0825755 0.143025i
\(528\) 5.29129 + 9.16478i 0.230274 + 0.398846i
\(529\) 1.00000 1.73205i 0.0434783 0.0753066i
\(530\) 0 0
\(531\) 21.9564 0.952828
\(532\) −0.500000 + 4.33013i −0.0216777 + 0.187735i
\(533\) −2.37386 −0.102823
\(534\) 6.39564 11.0776i 0.276767 0.479374i
\(535\) 0 0
\(536\) −7.79129 13.4949i −0.336532 0.582891i
\(537\) 23.3739 40.4847i 1.00866 1.74704i
\(538\) 6.56080 + 11.3636i 0.282856 + 0.489921i
\(539\) 22.7477 0.979814
\(540\) 0 0
\(541\) 8.56080 + 14.8277i 0.368057 + 0.637494i 0.989262 0.146155i \(-0.0466897\pi\)
−0.621204 + 0.783649i \(0.713356\pi\)
\(542\) −8.56080 14.8277i −0.367718 0.636906i
\(543\) −21.2867 −0.913502
\(544\) −0.791288 −0.0339262
\(545\) 0 0
\(546\) 0.291288 0.504525i 0.0124660 0.0215917i
\(547\) 8.41742 + 14.5794i 0.359903 + 0.623370i 0.987944 0.154810i \(-0.0494764\pi\)
−0.628041 + 0.778180i \(0.716143\pi\)
\(548\) 7.66515 13.2764i 0.327439 0.567141i
\(549\) −3.29129 + 5.70068i −0.140469 + 0.243299i
\(550\) 0 0
\(551\) −3.39564 + 29.4071i −0.144659 + 1.25279i
\(552\) 12.7913 0.544433
\(553\) −7.47822 + 12.9527i −0.318006 + 0.550803i
\(554\) 4.37386 7.57575i 0.185828 0.321863i
\(555\) 0 0
\(556\) 6.10436 10.5731i 0.258882 0.448397i
\(557\) 4.97822 + 8.62253i 0.210934 + 0.365348i 0.952007 0.306076i \(-0.0990162\pi\)
−0.741073 + 0.671424i \(0.765683\pi\)
\(558\) 22.9564 0.971824
\(559\) −1.20871 −0.0511231
\(560\) 0 0
\(561\) 4.18693 + 7.25198i 0.176772 + 0.306179i
\(562\) −10.5826 −0.446399
\(563\) 14.3739 0.605786 0.302893 0.953025i \(-0.402047\pi\)
0.302893 + 0.953025i \(0.402047\pi\)
\(564\) −16.9782 29.4071i −0.714912 1.23826i
\(565\) 0 0
\(566\) −10.5608 18.2918i −0.443903 0.768863i
\(567\) 0.208712 0.361500i 0.00876509 0.0151816i
\(568\) −2.29129 + 3.96863i −0.0961403 + 0.166520i
\(569\) −8.83485 −0.370376 −0.185188 0.982703i \(-0.559289\pi\)
−0.185188 + 0.982703i \(0.559289\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 0.395644 0.685275i 0.0165427 0.0286528i
\(573\) −22.2695 + 38.5719i −0.930322 + 1.61137i
\(574\) −5.68693 9.85005i −0.237368 0.411133i
\(575\) 0 0
\(576\) −2.39564 4.14938i −0.0998185 0.172891i
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 16.3739 0.681063
\(579\) −3.83485 6.64215i −0.159371 0.276038i
\(580\) 0 0
\(581\) −3.79129 −0.157289
\(582\) −34.5390 −1.43169
\(583\) 8.68693 + 15.0462i 0.359776 + 0.623150i
\(584\) −1.39564 + 2.41733i −0.0577522 + 0.100030i
\(585\) 0 0
\(586\) −12.4782 + 21.6129i −0.515471 + 0.892821i
\(587\) −4.74773 + 8.22330i −0.195960 + 0.339412i −0.947215 0.320600i \(-0.896116\pi\)
0.751255 + 0.660012i \(0.229449\pi\)
\(588\) −16.7477 −0.690665
\(589\) 16.7695 + 12.4481i 0.690976 + 0.512916i
\(590\) 0 0
\(591\) 28.2042 48.8510i 1.16016 2.00946i
\(592\) 1.79129 3.10260i 0.0736215 0.127516i
\(593\) −5.91742 10.2493i −0.242999 0.420887i 0.718568 0.695457i \(-0.244798\pi\)
−0.961567 + 0.274569i \(0.911465\pi\)
\(594\) −9.47822 + 16.4168i −0.388896 + 0.673588i
\(595\) 0 0
\(596\) −22.7477 −0.931783
\(597\) 10.0000 0.409273
\(598\) −0.478220 0.828301i −0.0195559 0.0338717i
\(599\) 18.5608 + 32.1482i 0.758374 + 1.31354i 0.943680 + 0.330861i \(0.107339\pi\)
−0.185306 + 0.982681i \(0.559328\pi\)
\(600\) 0 0
\(601\) 9.91288 0.404355 0.202177 0.979349i \(-0.435198\pi\)
0.202177 + 0.979349i \(0.435198\pi\)
\(602\) −2.89564 5.01540i −0.118018 0.204413i
\(603\) 37.3303 64.6580i 1.52021 2.63308i
\(604\) −7.87386 13.6379i −0.320383 0.554920i
\(605\) 0 0
\(606\) 0 0
\(607\) 18.2087 0.739069 0.369534 0.929217i \(-0.379517\pi\)
0.369534 + 0.929217i \(0.379517\pi\)
\(608\) 0.500000 4.33013i 0.0202777 0.175610i
\(609\) 18.9564 0.768154
\(610\) 0 0
\(611\) −1.26951 + 2.19885i −0.0513588 + 0.0889560i
\(612\) −1.89564 3.28335i −0.0766269 0.132722i
\(613\) 7.24773 12.5534i 0.292733 0.507028i −0.681722 0.731611i \(-0.738769\pi\)
0.974455 + 0.224583i \(0.0721020\pi\)
\(614\) 17.2477 + 29.8739i 0.696062 + 1.20561i
\(615\) 0 0
\(616\) 3.79129 0.152755
\(617\) −16.5000 28.5788i −0.664265 1.15054i −0.979484 0.201522i \(-0.935411\pi\)
0.315219 0.949019i \(-0.397922\pi\)
\(618\) −7.20871 12.4859i −0.289977 0.502255i
\(619\) −24.3739 −0.979668 −0.489834 0.871816i \(-0.662943\pi\)
−0.489834 + 0.871816i \(0.662943\pi\)
\(620\) 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
\(624\) −0.291288 + 0.504525i −0.0116608 + 0.0201972i
\(625\) 0 0
\(626\) −11.7477 −0.469534
\(627\) −42.3303 + 18.3296i −1.69051 + 0.732012i
\(628\) 7.95644 0.317496
\(629\) 1.41742 2.45505i 0.0565164 0.0978893i
\(630\) 0 0
\(631\) 18.1044 + 31.3577i 0.720723 + 1.24833i 0.960710 + 0.277553i \(0.0895234\pi\)
−0.239987 + 0.970776i \(0.577143\pi\)
\(632\) 7.47822 12.9527i 0.297468 0.515229i
\(633\) −33.4347 57.9105i −1.32891 2.30174i
\(634\) −9.16515 −0.363995
\(635\) 0 0
\(636\) −6.39564 11.0776i −0.253604 0.439255i
\(637\) 0.626136 + 1.08450i 0.0248084 + 0.0429695i
\(638\) 25.7477 1.01936
\(639\) −21.9564 −0.868583
\(640\) 0 0
\(641\) −8.52178 + 14.7602i −0.336590 + 0.582991i −0.983789 0.179330i \(-0.942607\pi\)
0.647199 + 0.762321i \(0.275940\pi\)
\(642\) −26.4564 45.8239i −1.04415 1.80852i
\(643\) 14.7477 25.5438i 0.581594 1.00735i −0.413697 0.910415i \(-0.635763\pi\)
0.995291 0.0969351i \(-0.0309039\pi\)
\(644\) 2.29129 3.96863i 0.0902894 0.156386i
\(645\) 0 0
\(646\) 0.395644 3.42638i 0.0155664 0.134809i
\(647\) −18.7913 −0.738762 −0.369381 0.929278i \(-0.620430\pi\)
−0.369381 + 0.929278i \(0.620430\pi\)
\(648\) −0.208712 + 0.361500i −0.00819899 + 0.0142011i
\(649\) 8.68693 15.0462i 0.340992 0.590615i
\(650\) 0 0
\(651\) 6.68693 11.5821i 0.262082 0.453939i
\(652\) −7.29129 12.6289i −0.285549 0.494585i
\(653\) 27.3303 1.06952 0.534759 0.845005i \(-0.320403\pi\)
0.534759 + 0.845005i \(0.320403\pi\)
\(654\) 32.7913 1.28224
\(655\) 0 0
\(656\) 5.68693 + 9.85005i 0.222037 + 0.384580i
\(657\) −13.3739 −0.521764
\(658\) −12.1652 −0.474247
\(659\) −0.873864 1.51358i −0.0340409 0.0589606i 0.848503 0.529190i \(-0.177504\pi\)
−0.882544 + 0.470230i \(0.844171\pi\)
\(660\) 0 0
\(661\) −23.4347 40.5900i −0.911503 1.57877i −0.811943 0.583737i \(-0.801590\pi\)
−0.0995599 0.995032i \(-0.531744\pi\)
\(662\) −8.95644 + 15.5130i −0.348102 + 0.602930i
\(663\) −0.230493 + 0.399225i −0.00895159 + 0.0155046i
\(664\) 3.79129 0.147131
\(665\) 0 0
\(666\) 17.1652 0.665136
\(667\) 15.5608 26.9521i 0.602516 1.04359i
\(668\) 5.76951 9.99308i 0.223229 0.386644i
\(669\) 26.8085 + 46.4337i 1.03648 + 1.79523i
\(670\) 0 0
\(671\) 2.60436 + 4.51088i 0.100540 + 0.174140i
\(672\) −2.79129 −0.107676
\(673\) −2.79129 −0.107596 −0.0537981 0.998552i \(-0.517133\pi\)
−0.0537981 + 0.998552i \(0.517133\pi\)
\(674\) −11.6652 20.2046i −0.449325 0.778253i
\(675\) 0 0
\(676\) −12.9564 −0.498325
\(677\) 35.2432 1.35451 0.677253 0.735750i \(-0.263170\pi\)
0.677253 + 0.735750i \(0.263170\pi\)
\(678\) −7.50000 12.9904i −0.288036 0.498893i
\(679\) −6.18693 + 10.7161i −0.237433 + 0.411245i
\(680\) 0 0
\(681\) 10.8131 18.7288i 0.414358 0.717689i
\(682\) 9.08258 15.7315i 0.347790 0.602390i
\(683\) 36.1652 1.38382 0.691911 0.721983i \(-0.256769\pi\)
0.691911 + 0.721983i \(0.256769\pi\)
\(684\) 19.1652 8.29875i 0.732798 0.317311i
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) 35.3521 61.2316i 1.34877 2.33613i
\(688\) 2.89564 + 5.01540i 0.110395 + 0.191210i
\(689\) −0.478220 + 0.828301i −0.0182187 + 0.0315557i
\(690\) 0 0
\(691\) −32.1216 −1.22196 −0.610981 0.791645i \(-0.709225\pi\)
−0.610981 + 0.791645i \(0.709225\pi\)
\(692\) 21.0000 0.798300
\(693\) 9.08258 + 15.7315i 0.345019 + 0.597590i
\(694\) −1.81307 3.14033i −0.0688231 0.119205i
\(695\) 0 0
\(696\) −18.9564 −0.718542
\(697\) 4.50000 + 7.79423i 0.170450 + 0.295227i
\(698\) −2.70871 + 4.69163i −0.102526 + 0.177581i
\(699\) 12.7913 + 22.1552i 0.483811 + 0.837985i
\(700\) 0 0
\(701\) 6.47822 11.2206i 0.244679 0.423796i −0.717362 0.696700i \(-0.754651\pi\)
0.962041 + 0.272904i \(0.0879841\pi\)
\(702\) −1.04356 −0.0393867
\(703\) 12.5390 + 9.30780i 0.472918 + 0.351051i
\(704\) −3.79129 −0.142890
\(705\) 0 0
\(706\) 6.87386 11.9059i 0.258701 0.448084i
\(707\) 0 0
\(708\) −6.39564 + 11.0776i −0.240363 + 0.416321i
\(709\) 13.3739 + 23.1642i 0.502266 + 0.869950i 0.999997 + 0.00261852i \(0.000833501\pi\)
−0.497731 + 0.867332i \(0.665833\pi\)
\(710\) 0 0
\(711\) 71.6606 2.68748
\(712\) 2.29129 + 3.96863i 0.0858696 + 0.148731i
\(713\) −10.9782 19.0148i −0.411138 0.712111i
\(714\) −2.20871 −0.0826590
\(715\) 0 0
\(716\) 8.37386 + 14.5040i 0.312946 + 0.542038i
\(717\) −23.1434 + 40.0855i −0.864305 + 1.49702i
\(718\) −17.8521 30.9207i −0.666234 1.15395i
\(719\) 6.08258 10.5353i 0.226842 0.392902i −0.730029 0.683417i \(-0.760493\pi\)
0.956870 + 0.290515i \(0.0938266\pi\)
\(720\) 0 0
\(721\) −5.16515 −0.192360
\(722\) 18.5000 + 4.33013i 0.688499 + 0.161151i
\(723\) −46.8693 −1.74309
\(724\) 3.81307 6.60443i 0.141712 0.245452i
\(725\) 0 0
\(726\) 4.70871 + 8.15573i 0.174757 + 0.302687i
\(727\) −2.08258 + 3.60713i −0.0772385 + 0.133781i −0.902058 0.431616i \(-0.857944\pi\)
0.824819 + 0.565397i \(0.191277\pi\)
\(728\) 0.104356 + 0.180750i 0.00386769 + 0.00669904i
\(729\) −43.8693 −1.62479
\(730\) 0 0
\(731\) 2.29129 + 3.96863i 0.0847463 + 0.146785i
\(732\) −1.91742 3.32108i −0.0708700 0.122751i
\(733\) −12.7477 −0.470848 −0.235424 0.971893i \(-0.575648\pi\)
−0.235424 + 0.971893i \(0.575648\pi\)
\(734\) 8.79129 0.324492
\(735\) 0 0
\(736\) −2.29129 + 3.96863i −0.0844580 + 0.146286i
\(737\) −29.5390 51.1631i −1.08808 1.88462i
\(738\) −27.2477 + 47.1944i −1.00300 + 1.73725i
\(739\) 17.8739 30.9584i 0.657501 1.13882i −0.323760 0.946139i \(-0.604947\pi\)
0.981261 0.192685i \(-0.0617197\pi\)
\(740\) 0 0
\(741\) −2.03901 1.51358i −0.0749051 0.0556026i
\(742\) −4.58258 −0.168232
\(743\) 9.70871 16.8160i 0.356178 0.616919i −0.631141 0.775668i \(-0.717413\pi\)
0.987319 + 0.158750i \(0.0507463\pi\)
\(744\) −6.68693 + 11.5821i −0.245155 + 0.424621i
\(745\) 0 0
\(746\) 10.6869 18.5103i 0.391276 0.677711i
\(747\) 9.08258 + 15.7315i 0.332314 + 0.575585i
\(748\) −3.00000 −0.109691
\(749\) −18.9564 −0.692653
\(750\) 0 0
\(751\) −10.7913 18.6911i −0.393780 0.682046i 0.599165 0.800626i \(-0.295499\pi\)
−0.992945 + 0.118579i \(0.962166\pi\)
\(752\) 12.1652 0.443617
\(753\) 36.6261 1.33473
\(754\) 0.708712 + 1.22753i 0.0258098 + 0.0447038i
\(755\) 0 0
\(756\) −2.50000 4.33013i −0.0909241 0.157485i
\(757\) 22.8739 39.6187i 0.831365 1.43997i −0.0655915 0.997847i \(-0.520893\pi\)
0.896956 0.442119i \(-0.145773\pi\)
\(758\) 2.41742 4.18710i 0.0878048 0.152082i
\(759\) 48.4955 1.76027
\(760\) 0 0
\(761\) 25.2523 0.915394 0.457697 0.889108i \(-0.348674\pi\)
0.457697 + 0.889108i \(0.348674\pi\)
\(762\) −3.66515 + 6.34823i −0.132774 + 0.229972i
\(763\) 5.87386 10.1738i 0.212648 0.368317i
\(764\) −7.97822 13.8187i −0.288642 0.499942i
\(765\) 0 0
\(766\) −2.29129 3.96863i −0.0827876 0.143392i
\(767\) 0.956439 0.0345350
\(768\) 2.79129 0.100722
\(769\) 11.1652 + 19.3386i 0.402626 + 0.697368i 0.994042 0.108998i \(-0.0347643\pi\)
−0.591416 + 0.806366i \(0.701431\pi\)
\(770\) 0 0
\(771\) 31.2867 1.12676
\(772\) 2.74773 0.0988929
\(773\) −10.6652 18.4726i −0.383599 0.664413i 0.607975 0.793956i \(-0.291982\pi\)
−0.991574 + 0.129544i \(0.958649\pi\)
\(774\) −13.8739 + 24.0302i −0.498686 + 0.863749i
\(775\) 0 0
\(776\) 6.18693 10.7161i 0.222098 0.384685i
\(777\) 5.00000 8.66025i 0.179374 0.310685i
\(778\) −18.6261 −0.667779
\(779\) −45.4955 + 19.7001i −1.63004 + 0.705830i
\(780\) 0 0
\(781\) −8.68693 + 15.0462i −0.310843 + 0.538396i
\(782\) −1.81307 + 3.14033i −0.0648352 + 0.112298i
\(783\) −16.9782 29.4071i −0.606752 1.05093i
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0