Properties

Label 966.2.i.l.277.1
Level $966$
Weight $2$
Character 966.277
Analytic conductor $7.714$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1768034304.4
Defining polynomial: \( x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 277.1
Root \(-0.885685 + 1.90520i\) of defining polynomial
Character \(\chi\) \(=\) 966.277
Dual form 966.2.i.l.415.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.914214 - 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 - 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.914214 - 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 - 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.914214 + 1.58346i) q^{10} +(-2.07397 + 3.59222i) q^{11} +(-0.500000 - 0.866025i) q^{12} -2.18558 q^{13} +(-0.840244 + 2.50878i) q^{14} +1.82843 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.67858 - 2.90738i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.66676 + 6.35102i) q^{19} +1.82843 q^{20} +(2.59279 - 0.526718i) q^{21} +4.14794 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.828427 - 1.43488i) q^{25} +(1.09279 + 1.89277i) q^{26} +1.00000 q^{27} +(2.59279 - 0.526718i) q^{28} +5.18558 q^{29} +(-0.914214 - 1.58346i) q^{30} +(-5.25955 + 9.10981i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.07397 - 3.59222i) q^{33} -3.35716 q^{34} +(-1.53633 + 4.58713i) q^{35} +1.00000 q^{36} +(0.518822 + 0.898626i) q^{37} +(3.66676 - 6.35102i) q^{38} +(1.09279 - 1.89277i) q^{39} +(-0.914214 - 1.58346i) q^{40} +7.33352 q^{41} +(-1.75255 - 1.98206i) q^{42} +5.36098 q^{43} +(-2.07397 - 3.59222i) q^{44} +(-0.914214 + 1.58346i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-3.61161 - 6.25550i) q^{47} +1.00000 q^{48} +(-0.857156 + 6.94732i) q^{49} -1.65685 q^{50} +(1.67858 + 2.90738i) q^{51} +(1.09279 - 1.89277i) q^{52} +(-2.27137 + 3.93413i) q^{53} +(-0.500000 - 0.866025i) q^{54} +7.58420 q^{55} +(-1.75255 - 1.98206i) q^{56} -7.33352 q^{57} +(-2.59279 - 4.49085i) q^{58} +(0.235636 - 0.408133i) q^{59} +(-0.914214 + 1.58346i) q^{60} +(7.37117 + 12.7672i) q^{61} +10.5191 q^{62} +(-0.840244 + 2.50878i) q^{63} +1.00000 q^{64} +(1.99809 + 3.46079i) q^{65} +(-2.07397 + 3.59222i) q^{66} +(-6.70249 + 11.6091i) q^{67} +(1.67858 + 2.90738i) q^{68} +1.00000 q^{69} +(4.74073 - 0.963066i) q^{70} +14.1856 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.75955 + 9.97584i) q^{73} +(0.518822 - 0.898626i) q^{74} +(0.828427 + 1.43488i) q^{75} -7.33352 q^{76} +(10.7547 - 2.18480i) q^{77} -2.18558 q^{78} +(2.59279 + 4.49085i) q^{79} +(-0.914214 + 1.58346i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.66676 - 6.35102i) q^{82} +5.80479 q^{83} +(-0.840244 + 2.50878i) q^{84} -6.13831 q^{85} +(-2.68049 - 4.64274i) q^{86} +(-2.59279 + 4.49085i) q^{87} +(-2.07397 + 3.59222i) q^{88} +(-3.34725 - 5.79761i) q^{89} +1.82843 q^{90} +(3.83034 + 4.33197i) q^{91} +1.00000 q^{92} +(-5.25955 - 9.10981i) q^{93} +(-3.61161 + 6.25550i) q^{94} +(6.70441 - 11.6124i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.47127 q^{97} +(6.44514 - 2.73134i) q^{98} +4.14794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.914214 1.58346i −0.408849 0.708147i 0.585912 0.810374i \(-0.300736\pi\)
−0.994761 + 0.102228i \(0.967403\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.75255 1.98206i −0.662401 0.749150i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.914214 + 1.58346i −0.289100 + 0.500735i
\(11\) −2.07397 + 3.59222i −0.625325 + 1.08310i 0.363153 + 0.931730i \(0.381700\pi\)
−0.988478 + 0.151366i \(0.951633\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −2.18558 −0.606172 −0.303086 0.952963i \(-0.598017\pi\)
−0.303086 + 0.952963i \(0.598017\pi\)
\(14\) −0.840244 + 2.50878i −0.224565 + 0.670500i
\(15\) 1.82843 0.472098
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.67858 2.90738i 0.407115 0.705144i −0.587450 0.809260i \(-0.699868\pi\)
0.994565 + 0.104117i \(0.0332015\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 3.66676 + 6.35102i 0.841213 + 1.45702i 0.888870 + 0.458159i \(0.151491\pi\)
−0.0476575 + 0.998864i \(0.515176\pi\)
\(20\) 1.82843 0.408849
\(21\) 2.59279 0.526718i 0.565793 0.114939i
\(22\) 4.14794 0.884344
\(23\) −0.500000 0.866025i −0.104257 0.180579i
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0.828427 1.43488i 0.165685 0.286976i
\(26\) 1.09279 + 1.89277i 0.214314 + 0.371203i
\(27\) 1.00000 0.192450
\(28\) 2.59279 0.526718i 0.489992 0.0995404i
\(29\) 5.18558 0.962939 0.481469 0.876463i \(-0.340103\pi\)
0.481469 + 0.876463i \(0.340103\pi\)
\(30\) −0.914214 1.58346i −0.166912 0.289100i
\(31\) −5.25955 + 9.10981i −0.944643 + 1.63617i −0.188180 + 0.982135i \(0.560259\pi\)
−0.756463 + 0.654036i \(0.773074\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.07397 3.59222i −0.361032 0.625325i
\(34\) −3.35716 −0.575747
\(35\) −1.53633 + 4.58713i −0.259686 + 0.775366i
\(36\) 1.00000 0.166667
\(37\) 0.518822 + 0.898626i 0.0852938 + 0.147733i 0.905516 0.424311i \(-0.139484\pi\)
−0.820223 + 0.572045i \(0.806150\pi\)
\(38\) 3.66676 6.35102i 0.594827 1.03027i
\(39\) 1.09279 1.89277i 0.174987 0.303086i
\(40\) −0.914214 1.58346i −0.144550 0.250368i
\(41\) 7.33352 1.14530 0.572652 0.819799i \(-0.305915\pi\)
0.572652 + 0.819799i \(0.305915\pi\)
\(42\) −1.75255 1.98206i −0.270424 0.305839i
\(43\) 5.36098 0.817541 0.408771 0.912637i \(-0.365958\pi\)
0.408771 + 0.912637i \(0.365958\pi\)
\(44\) −2.07397 3.59222i −0.312663 0.541548i
\(45\) −0.914214 + 1.58346i −0.136283 + 0.236049i
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) −3.61161 6.25550i −0.526808 0.912458i −0.999512 0.0312369i \(-0.990055\pi\)
0.472704 0.881221i \(-0.343278\pi\)
\(48\) 1.00000 0.144338
\(49\) −0.857156 + 6.94732i −0.122451 + 0.992475i
\(50\) −1.65685 −0.234315
\(51\) 1.67858 + 2.90738i 0.235048 + 0.407115i
\(52\) 1.09279 1.89277i 0.151543 0.262480i
\(53\) −2.27137 + 3.93413i −0.311997 + 0.540394i −0.978794 0.204845i \(-0.934331\pi\)
0.666798 + 0.745239i \(0.267664\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 7.58420 1.02265
\(56\) −1.75255 1.98206i −0.234194 0.264864i
\(57\) −7.33352 −0.971349
\(58\) −2.59279 4.49085i −0.340450 0.589677i
\(59\) 0.235636 0.408133i 0.0306771 0.0531344i −0.850279 0.526332i \(-0.823567\pi\)
0.880956 + 0.473197i \(0.156900\pi\)
\(60\) −0.914214 + 1.58346i −0.118024 + 0.204424i
\(61\) 7.37117 + 12.7672i 0.943781 + 1.63468i 0.758174 + 0.652053i \(0.226092\pi\)
0.185608 + 0.982624i \(0.440575\pi\)
\(62\) 10.5191 1.33593
\(63\) −0.840244 + 2.50878i −0.105861 + 0.316077i
\(64\) 1.00000 0.125000
\(65\) 1.99809 + 3.46079i 0.247833 + 0.429259i
\(66\) −2.07397 + 3.59222i −0.255288 + 0.442172i
\(67\) −6.70249 + 11.6091i −0.818840 + 1.41827i 0.0876974 + 0.996147i \(0.472049\pi\)
−0.906537 + 0.422125i \(0.861284\pi\)
\(68\) 1.67858 + 2.90738i 0.203557 + 0.352572i
\(69\) 1.00000 0.120386
\(70\) 4.74073 0.963066i 0.566626 0.115108i
\(71\) 14.1856 1.68352 0.841759 0.539853i \(-0.181520\pi\)
0.841759 + 0.539853i \(0.181520\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −5.75955 + 9.97584i −0.674105 + 1.16758i 0.302625 + 0.953110i \(0.402137\pi\)
−0.976730 + 0.214474i \(0.931196\pi\)
\(74\) 0.518822 0.898626i 0.0603118 0.104463i
\(75\) 0.828427 + 1.43488i 0.0956585 + 0.165685i
\(76\) −7.33352 −0.841213
\(77\) 10.7547 2.18480i 1.22562 0.248981i
\(78\) −2.18558 −0.247469
\(79\) 2.59279 + 4.49085i 0.291712 + 0.505260i 0.974215 0.225623i \(-0.0724418\pi\)
−0.682503 + 0.730883i \(0.739109\pi\)
\(80\) −0.914214 + 1.58346i −0.102212 + 0.177037i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.66676 6.35102i −0.404926 0.701352i
\(83\) 5.80479 0.637159 0.318579 0.947896i \(-0.396794\pi\)
0.318579 + 0.947896i \(0.396794\pi\)
\(84\) −0.840244 + 2.50878i −0.0916782 + 0.273731i
\(85\) −6.13831 −0.665794
\(86\) −2.68049 4.64274i −0.289044 0.500640i
\(87\) −2.59279 + 4.49085i −0.277976 + 0.481469i
\(88\) −2.07397 + 3.59222i −0.221086 + 0.382932i
\(89\) −3.34725 5.79761i −0.354808 0.614545i 0.632277 0.774742i \(-0.282120\pi\)
−0.987085 + 0.160197i \(0.948787\pi\)
\(90\) 1.82843 0.192733
\(91\) 3.83034 + 4.33197i 0.401528 + 0.454113i
\(92\) 1.00000 0.104257
\(93\) −5.25955 9.10981i −0.545390 0.944643i
\(94\) −3.61161 + 6.25550i −0.372509 + 0.645205i
\(95\) 6.70441 11.6124i 0.687857 1.19140i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −4.47127 −0.453989 −0.226994 0.973896i \(-0.572890\pi\)
−0.226994 + 0.973896i \(0.572890\pi\)
\(98\) 6.44514 2.73134i 0.651057 0.275907i
\(99\) 4.14794 0.416884
\(100\) 0.828427 + 1.43488i 0.0828427 + 0.143488i
\(101\) −7.65303 + 13.2554i −0.761505 + 1.31897i 0.180569 + 0.983562i \(0.442206\pi\)
−0.942075 + 0.335404i \(0.891127\pi\)
\(102\) 1.67858 2.90738i 0.166204 0.287874i
\(103\) −3.70249 6.41291i −0.364818 0.631883i 0.623929 0.781481i \(-0.285535\pi\)
−0.988747 + 0.149598i \(0.952202\pi\)
\(104\) −2.18558 −0.214314
\(105\) −3.20441 3.62406i −0.312718 0.353672i
\(106\) 4.54274 0.441230
\(107\) 2.75064 + 4.76424i 0.265914 + 0.460577i 0.967803 0.251710i \(-0.0809929\pi\)
−0.701889 + 0.712287i \(0.747660\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 9.34753 16.1904i 0.895331 1.55076i 0.0619370 0.998080i \(-0.480272\pi\)
0.833394 0.552679i \(-0.186394\pi\)
\(110\) −3.79210 6.56811i −0.361563 0.626245i
\(111\) −1.03764 −0.0984888
\(112\) −0.840244 + 2.50878i −0.0793956 + 0.237058i
\(113\) 5.28187 0.496876 0.248438 0.968648i \(-0.420083\pi\)
0.248438 + 0.968648i \(0.420083\pi\)
\(114\) 3.66676 + 6.35102i 0.343424 + 0.594827i
\(115\) −0.914214 + 1.58346i −0.0852509 + 0.147659i
\(116\) −2.59279 + 4.49085i −0.240735 + 0.416965i
\(117\) 1.09279 + 1.89277i 0.101029 + 0.174987i
\(118\) −0.471271 −0.0433840
\(119\) −8.70441 + 1.76828i −0.797932 + 0.162098i
\(120\) 1.82843 0.166912
\(121\) −3.10270 5.37403i −0.282063 0.488548i
\(122\) 7.37117 12.7672i 0.667354 1.15589i
\(123\) −3.66676 + 6.35102i −0.330621 + 0.572652i
\(124\) −5.25955 9.10981i −0.472322 0.818085i
\(125\) −12.1716 −1.08866
\(126\) 2.59279 0.526718i 0.230984 0.0469238i
\(127\) 6.49108 0.575991 0.287995 0.957632i \(-0.407011\pi\)
0.287995 + 0.957632i \(0.407011\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.68049 + 4.64274i −0.236004 + 0.408771i
\(130\) 1.99809 3.46079i 0.175244 0.303532i
\(131\) 2.20441 + 3.81814i 0.192600 + 0.333593i 0.946111 0.323842i \(-0.104975\pi\)
−0.753511 + 0.657435i \(0.771641\pi\)
\(132\) 4.14794 0.361032
\(133\) 6.16195 18.3982i 0.534309 1.59533i
\(134\) 13.4050 1.15801
\(135\) −0.914214 1.58346i −0.0786830 0.136283i
\(136\) 1.67858 2.90738i 0.143937 0.249306i
\(137\) −0.840244 + 1.45535i −0.0717869 + 0.124339i −0.899685 0.436541i \(-0.856203\pi\)
0.827898 + 0.560879i \(0.189537\pi\)
\(138\) −0.500000 0.866025i −0.0425628 0.0737210i
\(139\) −13.3137 −1.12925 −0.564627 0.825346i \(-0.690980\pi\)
−0.564627 + 0.825346i \(0.690980\pi\)
\(140\) −3.20441 3.62406i −0.270822 0.306289i
\(141\) 7.22323 0.608305
\(142\) −7.09279 12.2851i −0.595214 1.03094i
\(143\) 4.53283 7.85110i 0.379054 0.656542i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −4.74073 8.21119i −0.393696 0.681902i
\(146\) 11.5191 0.953328
\(147\) −5.58798 4.21598i −0.460889 0.347728i
\(148\) −1.03764 −0.0852938
\(149\) −9.67886 16.7643i −0.792923 1.37338i −0.924150 0.382031i \(-0.875225\pi\)
0.131226 0.991352i \(-0.458108\pi\)
\(150\) 0.828427 1.43488i 0.0676408 0.117157i
\(151\) −2.79210 + 4.83606i −0.227218 + 0.393553i −0.956983 0.290145i \(-0.906296\pi\)
0.729765 + 0.683699i \(0.239630\pi\)
\(152\) 3.66676 + 6.35102i 0.297414 + 0.515135i
\(153\) −3.35716 −0.271410
\(154\) −7.26946 8.22148i −0.585790 0.662506i
\(155\) 19.2334 1.54487
\(156\) 1.09279 + 1.89277i 0.0874933 + 0.151543i
\(157\) 11.3951 19.7369i 0.909427 1.57517i 0.0945641 0.995519i \(-0.469854\pi\)
0.814862 0.579654i \(-0.196812\pi\)
\(158\) 2.59279 4.49085i 0.206271 0.357273i
\(159\) −2.27137 3.93413i −0.180131 0.311997i
\(160\) 1.82843 0.144550
\(161\) −0.840244 + 2.50878i −0.0662205 + 0.197720i
\(162\) 1.00000 0.0785674
\(163\) 12.7184 + 22.0289i 0.996183 + 1.72544i 0.573685 + 0.819076i \(0.305513\pi\)
0.422498 + 0.906364i \(0.361153\pi\)
\(164\) −3.66676 + 6.35102i −0.286326 + 0.495931i
\(165\) −3.79210 + 6.56811i −0.295215 + 0.511327i
\(166\) −2.90240 5.02710i −0.225270 0.390178i
\(167\) −22.1185 −1.71158 −0.855791 0.517323i \(-0.826929\pi\)
−0.855791 + 0.517323i \(0.826929\pi\)
\(168\) 2.59279 0.526718i 0.200038 0.0406372i
\(169\) −8.22323 −0.632556
\(170\) 3.06916 + 5.31594i 0.235394 + 0.407714i
\(171\) 3.66676 6.35102i 0.280404 0.485674i
\(172\) −2.68049 + 4.64274i −0.204385 + 0.354006i
\(173\) 6.84244 + 11.8514i 0.520221 + 0.901049i 0.999724 + 0.0235086i \(0.00748371\pi\)
−0.479503 + 0.877540i \(0.659183\pi\)
\(174\) 5.18558 0.393118
\(175\) −4.29588 + 0.872696i −0.324738 + 0.0659696i
\(176\) 4.14794 0.312663
\(177\) 0.235636 + 0.408133i 0.0177115 + 0.0306771i
\(178\) −3.34725 + 5.79761i −0.250887 + 0.434549i
\(179\) 1.38839 2.40476i 0.103773 0.179740i −0.809463 0.587170i \(-0.800242\pi\)
0.913236 + 0.407431i \(0.133575\pi\)
\(180\) −0.914214 1.58346i −0.0681415 0.118024i
\(181\) −20.9629 −1.55816 −0.779081 0.626923i \(-0.784314\pi\)
−0.779081 + 0.626923i \(0.784314\pi\)
\(182\) 1.83642 5.48315i 0.136125 0.406438i
\(183\) −14.7423 −1.08978
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) 0.948628 1.64307i 0.0697445 0.120801i
\(186\) −5.25955 + 9.10981i −0.385649 + 0.667964i
\(187\) 6.96264 + 12.0596i 0.509159 + 0.881888i
\(188\) 7.22323 0.526808
\(189\) −1.75255 1.98206i −0.127479 0.144174i
\(190\) −13.4088 −0.972777
\(191\) 4.48118 + 7.76163i 0.324247 + 0.561612i 0.981360 0.192180i \(-0.0615559\pi\)
−0.657113 + 0.753792i \(0.728223\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −5.81951 + 10.0797i −0.418898 + 0.725552i −0.995829 0.0912408i \(-0.970917\pi\)
0.576931 + 0.816793i \(0.304250\pi\)
\(194\) 2.23564 + 3.87223i 0.160509 + 0.278010i
\(195\) −3.99618 −0.286172
\(196\) −5.58798 4.21598i −0.399141 0.301141i
\(197\) 9.58157 0.682658 0.341329 0.939944i \(-0.389123\pi\)
0.341329 + 0.939944i \(0.389123\pi\)
\(198\) −2.07397 3.59222i −0.147391 0.255288i
\(199\) 4.97637 8.61932i 0.352765 0.611007i −0.633968 0.773360i \(-0.718575\pi\)
0.986733 + 0.162352i \(0.0519081\pi\)
\(200\) 0.828427 1.43488i 0.0585786 0.101461i
\(201\) −6.70249 11.6091i −0.472758 0.818840i
\(202\) 15.3061 1.07693
\(203\) −9.08798 10.2782i −0.637851 0.721385i
\(204\) −3.35716 −0.235048
\(205\) −6.70441 11.6124i −0.468256 0.811043i
\(206\) −3.70249 + 6.41291i −0.257965 + 0.446809i
\(207\) −0.500000 + 0.866025i −0.0347524 + 0.0601929i
\(208\) 1.09279 + 1.89277i 0.0757715 + 0.131240i
\(209\) −30.4190 −2.10413
\(210\) −1.53633 + 4.58713i −0.106017 + 0.316542i
\(211\) 0.303519 0.0208951 0.0104476 0.999945i \(-0.496674\pi\)
0.0104476 + 0.999945i \(0.496674\pi\)
\(212\) −2.27137 3.93413i −0.155998 0.270197i
\(213\) −7.09279 + 12.2851i −0.485990 + 0.841759i
\(214\) 2.75064 4.76424i 0.188030 0.325677i
\(215\) −4.90108 8.48892i −0.334251 0.578939i
\(216\) 1.00000 0.0680414
\(217\) 27.2738 5.54061i 1.85147 0.376121i
\(218\) −18.6951 −1.26619
\(219\) −5.75955 9.97584i −0.389194 0.674105i
\(220\) −3.79210 + 6.56811i −0.255663 + 0.442822i
\(221\) −3.66867 + 6.35433i −0.246782 + 0.427438i
\(222\) 0.518822 + 0.898626i 0.0348211 + 0.0603118i
\(223\) −16.9375 −1.13422 −0.567111 0.823642i \(-0.691939\pi\)
−0.567111 + 0.823642i \(0.691939\pi\)
\(224\) 2.59279 0.526718i 0.173238 0.0351929i
\(225\) −1.65685 −0.110457
\(226\) −2.64093 4.57423i −0.175672 0.304273i
\(227\) 10.7685 18.6515i 0.714728 1.23795i −0.248336 0.968674i \(-0.579884\pi\)
0.963064 0.269272i \(-0.0867830\pi\)
\(228\) 3.66676 6.35102i 0.242837 0.420606i
\(229\) 0.333239 + 0.577187i 0.0220211 + 0.0381416i 0.876826 0.480808i \(-0.159657\pi\)
−0.854805 + 0.518950i \(0.826323\pi\)
\(230\) 1.82843 0.120563
\(231\) −3.48528 + 10.4063i −0.229315 + 0.684683i
\(232\) 5.18558 0.340450
\(233\) 0.838334 + 1.45204i 0.0549211 + 0.0951261i 0.892179 0.451682i \(-0.149176\pi\)
−0.837258 + 0.546808i \(0.815843\pi\)
\(234\) 1.09279 1.89277i 0.0714380 0.123734i
\(235\) −6.60357 + 11.4377i −0.430770 + 0.746115i
\(236\) 0.235636 + 0.408133i 0.0153386 + 0.0265672i
\(237\) −5.18558 −0.336840
\(238\) 5.88357 + 6.65410i 0.381375 + 0.431321i
\(239\) 10.7220 0.693546 0.346773 0.937949i \(-0.387278\pi\)
0.346773 + 0.937949i \(0.387278\pi\)
\(240\) −0.914214 1.58346i −0.0590122 0.102212i
\(241\) −9.10171 + 15.7646i −0.586292 + 1.01549i 0.408420 + 0.912794i \(0.366080\pi\)
−0.994713 + 0.102694i \(0.967254\pi\)
\(242\) −3.10270 + 5.37403i −0.199449 + 0.345456i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −14.7423 −0.943781
\(245\) 11.7845 4.99406i 0.752882 0.319059i
\(246\) 7.33352 0.467568
\(247\) −8.01401 13.8807i −0.509919 0.883206i
\(248\) −5.25955 + 9.10981i −0.333982 + 0.578474i
\(249\) −2.90240 + 5.02710i −0.183932 + 0.318579i
\(250\) 6.08579 + 10.5409i 0.384899 + 0.666665i
\(251\) −0.794604 −0.0501549 −0.0250775 0.999686i \(-0.507983\pi\)
−0.0250775 + 0.999686i \(0.507983\pi\)
\(252\) −1.75255 1.98206i −0.110400 0.124858i
\(253\) 4.14794 0.260779
\(254\) −3.24554 5.62144i −0.203643 0.352721i
\(255\) 3.06916 5.31594i 0.192198 0.332897i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.295595 + 0.511985i 0.0184387 + 0.0319368i 0.875098 0.483947i \(-0.160797\pi\)
−0.856659 + 0.515883i \(0.827464\pi\)
\(258\) 5.36098 0.333760
\(259\) 0.871874 2.60322i 0.0541756 0.161756i
\(260\) −3.99618 −0.247833
\(261\) −2.59279 4.49085i −0.160490 0.277976i
\(262\) 2.20441 3.81814i 0.136189 0.235886i
\(263\) −1.43363 + 2.48312i −0.0884012 + 0.153115i −0.906835 0.421485i \(-0.861509\pi\)
0.818434 + 0.574600i \(0.194842\pi\)
\(264\) −2.07397 3.59222i −0.127644 0.221086i
\(265\) 8.30607 0.510238
\(266\) −19.0143 + 3.86270i −1.16584 + 0.236837i
\(267\) 6.69450 0.409697
\(268\) −6.70249 11.6091i −0.409420 0.709136i
\(269\) 3.58897 6.21628i 0.218823 0.379013i −0.735625 0.677389i \(-0.763111\pi\)
0.954449 + 0.298376i \(0.0964448\pi\)
\(270\) −0.914214 + 1.58346i −0.0556373 + 0.0963666i
\(271\) 5.25955 + 9.10981i 0.319495 + 0.553382i 0.980383 0.197103i \(-0.0631534\pi\)
−0.660888 + 0.750485i \(0.729820\pi\)
\(272\) −3.35716 −0.203557
\(273\) −5.66676 + 1.15119i −0.342968 + 0.0696730i
\(274\) 1.68049 0.101522
\(275\) 3.43627 + 5.95179i 0.207215 + 0.358906i
\(276\) −0.500000 + 0.866025i −0.0300965 + 0.0521286i
\(277\) 15.4642 26.7848i 0.929156 1.60935i 0.144419 0.989517i \(-0.453869\pi\)
0.784737 0.619829i \(-0.212798\pi\)
\(278\) 6.65685 + 11.5300i 0.399252 + 0.691524i
\(279\) 10.5191 0.629762
\(280\) −1.53633 + 4.58713i −0.0918130 + 0.274133i
\(281\) −2.09949 −0.125245 −0.0626225 0.998037i \(-0.519946\pi\)
−0.0626225 + 0.998037i \(0.519946\pi\)
\(282\) −3.61161 6.25550i −0.215068 0.372509i
\(283\) −10.1738 + 17.6215i −0.604768 + 1.04749i 0.387321 + 0.921945i \(0.373401\pi\)
−0.992088 + 0.125543i \(0.959933\pi\)
\(284\) −7.09279 + 12.2851i −0.420880 + 0.728985i
\(285\) 6.70441 + 11.6124i 0.397135 + 0.687857i
\(286\) −9.06566 −0.536064
\(287\) −12.8523 14.5355i −0.758650 0.858004i
\(288\) 1.00000 0.0589256
\(289\) 2.86475 + 4.96190i 0.168515 + 0.291876i
\(290\) −4.74073 + 8.21119i −0.278385 + 0.482177i
\(291\) 2.23564 3.87223i 0.131055 0.226994i
\(292\) −5.75955 9.97584i −0.337052 0.583792i
\(293\) −31.4853 −1.83939 −0.919695 0.392634i \(-0.871564\pi\)
−0.919695 + 0.392634i \(0.871564\pi\)
\(294\) −0.857156 + 6.94732i −0.0499903 + 0.405176i
\(295\) −0.861685 −0.0501693
\(296\) 0.518822 + 0.898626i 0.0301559 + 0.0522316i
\(297\) −2.07397 + 3.59222i −0.120344 + 0.208442i
\(298\) −9.67886 + 16.7643i −0.560681 + 0.971129i
\(299\) 1.09279 + 1.89277i 0.0631978 + 0.109462i
\(300\) −1.65685 −0.0956585
\(301\) −9.39537 10.6258i −0.541540 0.612461i
\(302\) 5.58420 0.321335
\(303\) −7.65303 13.2554i −0.439655 0.761505i
\(304\) 3.66676 6.35102i 0.210303 0.364256i
\(305\) 13.4776 23.3440i 0.771727 1.33667i
\(306\) 1.67858 + 2.90738i 0.0959579 + 0.166204i
\(307\) 1.64865 0.0940933 0.0470466 0.998893i \(-0.485019\pi\)
0.0470466 + 0.998893i \(0.485019\pi\)
\(308\) −3.48528 + 10.4063i −0.198592 + 0.592953i
\(309\) 7.40499 0.421255
\(310\) −9.61671 16.6566i −0.546192 0.946033i
\(311\) −6.08897 + 10.5464i −0.345274 + 0.598032i −0.985403 0.170235i \(-0.945547\pi\)
0.640130 + 0.768267i \(0.278881\pi\)
\(312\) 1.09279 1.89277i 0.0618671 0.107157i
\(313\) −6.28347 10.8833i −0.355163 0.615160i 0.631983 0.774982i \(-0.282241\pi\)
−0.987146 + 0.159822i \(0.948908\pi\)
\(314\) −22.7902 −1.28612
\(315\) 4.74073 0.963066i 0.267110 0.0542626i
\(316\) −5.18558 −0.291712
\(317\) 4.58897 + 7.94833i 0.257742 + 0.446423i 0.965637 0.259895i \(-0.0836881\pi\)
−0.707894 + 0.706318i \(0.750355\pi\)
\(318\) −2.27137 + 3.93413i −0.127372 + 0.220615i
\(319\) −10.7547 + 18.6278i −0.602150 + 1.04295i
\(320\) −0.914214 1.58346i −0.0511061 0.0885183i
\(321\) −5.50127 −0.307051
\(322\) 2.59279 0.526718i 0.144491 0.0293529i
\(323\) 24.6198 1.36988
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −1.81060 + 3.13604i −0.100434 + 0.173956i
\(326\) 12.7184 22.0289i 0.704408 1.22007i
\(327\) 9.34753 + 16.1904i 0.516920 + 0.895331i
\(328\) 7.33352 0.404926
\(329\) −6.06927 + 18.1215i −0.334610 + 0.999071i
\(330\) 7.58420 0.417497
\(331\) 14.6948 + 25.4521i 0.807698 + 1.39897i 0.914454 + 0.404689i \(0.132620\pi\)
−0.106756 + 0.994285i \(0.534046\pi\)
\(332\) −2.90240 + 5.02710i −0.159290 + 0.275898i
\(333\) 0.518822 0.898626i 0.0284313 0.0492444i
\(334\) 11.0593 + 19.1552i 0.605135 + 1.04813i
\(335\) 24.5100 1.33913
\(336\) −1.75255 1.98206i −0.0956093 0.108130i
\(337\) 8.12048 0.442351 0.221175 0.975234i \(-0.429011\pi\)
0.221175 + 0.975234i \(0.429011\pi\)
\(338\) 4.11161 + 7.12152i 0.223642 + 0.387360i
\(339\) −2.64093 + 4.57423i −0.143436 + 0.248438i
\(340\) 3.06916 5.31594i 0.166448 0.288297i
\(341\) −21.8163 37.7869i −1.18142 2.04628i
\(342\) −7.33352 −0.396551
\(343\) 15.2722 10.4766i 0.824624 0.565682i
\(344\) 5.36098 0.289044
\(345\) −0.914214 1.58346i −0.0492196 0.0852509i
\(346\) 6.84244 11.8514i 0.367852 0.637138i
\(347\) −14.1307 + 24.4751i −0.758577 + 1.31389i 0.185000 + 0.982739i \(0.440772\pi\)
−0.943576 + 0.331155i \(0.892562\pi\)
\(348\) −2.59279 4.49085i −0.138988 0.240735i
\(349\) 24.1307 1.29169 0.645843 0.763471i \(-0.276506\pi\)
0.645843 + 0.763471i \(0.276506\pi\)
\(350\) 2.90372 + 3.28399i 0.155210 + 0.175537i
\(351\) −2.18558 −0.116658
\(352\) −2.07397 3.59222i −0.110543 0.191466i
\(353\) −6.70441 + 11.6124i −0.356839 + 0.618064i −0.987431 0.158051i \(-0.949479\pi\)
0.630592 + 0.776115i \(0.282812\pi\)
\(354\) 0.235636 0.408133i 0.0125239 0.0216920i
\(355\) −12.9687 22.4624i −0.688305 1.19218i
\(356\) 6.69450 0.354808
\(357\) 2.82083 8.42237i 0.149294 0.445759i
\(358\) −2.77677 −0.146757
\(359\) 1.94254 + 3.36458i 0.102523 + 0.177576i 0.912724 0.408577i \(-0.133975\pi\)
−0.810200 + 0.586153i \(0.800642\pi\)
\(360\) −0.914214 + 1.58346i −0.0481833 + 0.0834559i
\(361\) −17.3903 + 30.1208i −0.915277 + 1.58531i
\(362\) 10.4815 + 18.1544i 0.550893 + 0.954175i
\(363\) 6.20540 0.325699
\(364\) −5.66676 + 1.15119i −0.297019 + 0.0603386i
\(365\) 21.0618 1.10243
\(366\) 7.37117 + 12.7672i 0.385297 + 0.667354i
\(367\) 0.718724 1.24487i 0.0375171 0.0649815i −0.846657 0.532139i \(-0.821388\pi\)
0.884174 + 0.467157i \(0.154722\pi\)
\(368\) −0.500000 + 0.866025i −0.0260643 + 0.0451447i
\(369\) −3.66676 6.35102i −0.190884 0.330621i
\(370\) −1.89726 −0.0986337
\(371\) 11.7784 2.39274i 0.611503 0.124225i
\(372\) 10.5191 0.545390
\(373\) −9.14794 15.8447i −0.473662 0.820407i 0.525883 0.850557i \(-0.323735\pi\)
−0.999545 + 0.0301497i \(0.990402\pi\)
\(374\) 6.96264 12.0596i 0.360029 0.623589i
\(375\) 6.08579 10.5409i 0.314269 0.544329i
\(376\) −3.61161 6.25550i −0.186255 0.322603i
\(377\) −11.3335 −0.583706
\(378\) −0.840244 + 2.50878i −0.0432175 + 0.129038i
\(379\) −5.97637 −0.306985 −0.153493 0.988150i \(-0.549052\pi\)
−0.153493 + 0.988150i \(0.549052\pi\)
\(380\) 6.70441 + 11.6124i 0.343929 + 0.595702i
\(381\) −3.24554 + 5.62144i −0.166274 + 0.287995i
\(382\) 4.48118 7.76163i 0.229277 0.397119i
\(383\) 2.94863 + 5.10717i 0.150668 + 0.260964i 0.931473 0.363810i \(-0.118524\pi\)
−0.780805 + 0.624774i \(0.785191\pi\)
\(384\) 1.00000 0.0510310
\(385\) −13.2917 15.0324i −0.677407 0.766121i
\(386\) 11.6390 0.592411
\(387\) −2.68049 4.64274i −0.136257 0.236004i
\(388\) 2.23564 3.87223i 0.113497 0.196583i
\(389\) 8.55675 14.8207i 0.433844 0.751441i −0.563356 0.826214i \(-0.690490\pi\)
0.997201 + 0.0747736i \(0.0238234\pi\)
\(390\) 1.99809 + 3.46079i 0.101177 + 0.175244i
\(391\) −3.35716 −0.169779
\(392\) −0.857156 + 6.94732i −0.0432929 + 0.350893i
\(393\) −4.40881 −0.222395
\(394\) −4.79078 8.29788i −0.241356 0.418041i
\(395\) 4.74073 8.21119i 0.238532 0.413150i
\(396\) −2.07397 + 3.59222i −0.104221 + 0.180516i
\(397\) 6.42249 + 11.1241i 0.322336 + 0.558302i 0.980970 0.194162i \(-0.0621987\pi\)
−0.658634 + 0.752464i \(0.728865\pi\)
\(398\) −9.95273 −0.498885
\(399\) 12.8523 + 14.5355i 0.643422 + 0.727686i
\(400\) −1.65685 −0.0828427
\(401\) −8.71650 15.0974i −0.435281 0.753930i 0.562037 0.827112i \(-0.310018\pi\)
−0.997319 + 0.0731824i \(0.976684\pi\)
\(402\) −6.70249 + 11.6091i −0.334290 + 0.579007i
\(403\) 11.4952 19.9102i 0.572616 0.991800i
\(404\) −7.65303 13.2554i −0.380753 0.659483i
\(405\) 1.82843 0.0908553
\(406\) −4.35716 + 13.0095i −0.216242 + 0.645651i
\(407\) −4.30408 −0.213346
\(408\) 1.67858 + 2.90738i 0.0831020 + 0.143937i
\(409\) 4.53382 7.85281i 0.224183 0.388297i −0.731891 0.681422i \(-0.761362\pi\)
0.956074 + 0.293125i \(0.0946953\pi\)
\(410\) −6.70441 + 11.6124i −0.331107 + 0.573494i
\(411\) −0.840244 1.45535i −0.0414462 0.0717869i
\(412\) 7.40499 0.364818
\(413\) −1.22191 + 0.248227i −0.0601262 + 0.0122145i
\(414\) 1.00000 0.0491473
\(415\) −5.30682 9.19168i −0.260502 0.451202i
\(416\) 1.09279 1.89277i 0.0535785 0.0928007i
\(417\) 6.65685 11.5300i 0.325988 0.564627i
\(418\) 15.2095 + 26.3436i 0.743921 + 1.28851i
\(419\) −6.63902 −0.324338 −0.162169 0.986763i \(-0.551849\pi\)
−0.162169 + 0.986763i \(0.551849\pi\)
\(420\) 4.74073 0.963066i 0.231324 0.0469928i
\(421\) −0.942543 −0.0459367 −0.0229684 0.999736i \(-0.507312\pi\)
−0.0229684 + 0.999736i \(0.507312\pi\)
\(422\) −0.151760 0.262855i −0.00738754 0.0127956i
\(423\) −3.61161 + 6.25550i −0.175603 + 0.304153i
\(424\) −2.27137 + 3.93413i −0.110307 + 0.191058i
\(425\) −2.78116 4.81711i −0.134906 0.233664i
\(426\) 14.1856 0.687294
\(427\) 12.3872 36.9853i 0.599457 1.78984i
\(428\) −5.50127 −0.265914
\(429\) 4.53283 + 7.85110i 0.218847 + 0.379054i
\(430\) −4.90108 + 8.48892i −0.236351 + 0.409372i
\(431\) 17.6849 30.6311i 0.851850 1.47545i −0.0276860 0.999617i \(-0.508814\pi\)
0.879536 0.475832i \(-0.157853\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 32.7627 1.57448 0.787238 0.616650i \(-0.211510\pi\)
0.787238 + 0.616650i \(0.211510\pi\)
\(434\) −18.4352 20.8495i −0.884919 1.00081i
\(435\) 9.48146 0.454601
\(436\) 9.34753 + 16.1904i 0.447666 + 0.775380i
\(437\) 3.66676 6.35102i 0.175405 0.303810i
\(438\) −5.75955 + 9.97584i −0.275202 + 0.476664i
\(439\) 9.65817 + 16.7284i 0.460959 + 0.798405i 0.999009 0.0445080i \(-0.0141720\pi\)
−0.538050 + 0.842913i \(0.680839\pi\)
\(440\) 7.58420 0.361563
\(441\) 6.44514 2.73134i 0.306911 0.130064i
\(442\) 7.33734 0.349002
\(443\) −7.20441 12.4784i −0.342292 0.592866i 0.642566 0.766230i \(-0.277870\pi\)
−0.984858 + 0.173364i \(0.944536\pi\)
\(444\) 0.518822 0.898626i 0.0246222 0.0426469i
\(445\) −6.12020 + 10.6005i −0.290125 + 0.502512i
\(446\) 8.46877 + 14.6683i 0.401008 + 0.694566i
\(447\) 19.3577 0.915589
\(448\) −1.75255 1.98206i −0.0828001 0.0936437i
\(449\) −11.0580 −0.521860 −0.260930 0.965358i \(-0.584029\pi\)
−0.260930 + 0.965358i \(0.584029\pi\)
\(450\) 0.828427 + 1.43488i 0.0390524 + 0.0676408i
\(451\) −15.2095 + 26.3436i −0.716187 + 1.24047i
\(452\) −2.64093 + 4.57423i −0.124219 + 0.215154i
\(453\) −2.79210 4.83606i −0.131184 0.227218i
\(454\) −21.5369 −1.01078
\(455\) 3.35777 10.0255i 0.157415 0.470005i
\(456\) −7.33352 −0.343424
\(457\) 12.9225 + 22.3824i 0.604489 + 1.04701i 0.992132 + 0.125196i \(0.0399559\pi\)
−0.387643 + 0.921809i \(0.626711\pi\)
\(458\) 0.333239 0.577187i 0.0155712 0.0269702i
\(459\) 1.67858 2.90738i 0.0783493 0.135705i
\(460\) −0.914214 1.58346i −0.0426254 0.0738294i
\(461\) −39.3341 −1.83197 −0.915986 0.401211i \(-0.868589\pi\)
−0.915986 + 0.401211i \(0.868589\pi\)
\(462\) 10.7547 2.18480i 0.500356 0.101646i
\(463\) 25.0778 1.16547 0.582733 0.812664i \(-0.301983\pi\)
0.582733 + 0.812664i \(0.301983\pi\)
\(464\) −2.59279 4.49085i −0.120367 0.208482i
\(465\) −9.61671 + 16.6566i −0.445964 + 0.772433i
\(466\) 0.838334 1.45204i 0.0388351 0.0672643i
\(467\) 11.4815 + 19.8865i 0.531299 + 0.920236i 0.999333 + 0.0365258i \(0.0116291\pi\)
−0.468034 + 0.883710i \(0.655038\pi\)
\(468\) −2.18558 −0.101029
\(469\) 34.7563 7.06066i 1.60490 0.326031i
\(470\) 13.2071 0.609200
\(471\) 11.3951 + 19.7369i 0.525058 + 0.909427i
\(472\) 0.235636 0.408133i 0.0108460 0.0187858i
\(473\) −11.1185 + 19.2578i −0.511229 + 0.885475i
\(474\) 2.59279 + 4.49085i 0.119091 + 0.206271i
\(475\) 12.1506 0.557507
\(476\) 2.82083 8.42237i 0.129293 0.386039i
\(477\) 4.54274 0.207998
\(478\) −5.36098 9.28548i −0.245205 0.424708i
\(479\) 8.30578 14.3860i 0.379501 0.657315i −0.611489 0.791253i \(-0.709429\pi\)
0.990990 + 0.133938i \(0.0427624\pi\)
\(480\) −0.914214 + 1.58346i −0.0417279 + 0.0722749i
\(481\) −1.13393 1.96402i −0.0517027 0.0895517i
\(482\) 18.2034 0.829143
\(483\) −1.75255 1.98206i −0.0797437 0.0901870i
\(484\) 6.20540 0.282063
\(485\) 4.08770 + 7.08010i 0.185613 + 0.321491i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 7.41131 12.8368i 0.335839 0.581690i −0.647807 0.761805i \(-0.724314\pi\)
0.983646 + 0.180115i \(0.0576470\pi\)
\(488\) 7.37117 + 12.7672i 0.333677 + 0.577946i
\(489\) −25.4368 −1.15029
\(490\) −10.2172 7.70861i −0.461567 0.348240i
\(491\) 22.2466 1.00398 0.501988 0.864875i \(-0.332602\pi\)
0.501988 + 0.864875i \(0.332602\pi\)
\(492\) −3.66676 6.35102i −0.165310 0.286326i
\(493\) 8.70441 15.0765i 0.392027 0.679010i
\(494\) −8.01401 + 13.8807i −0.360567 + 0.624521i
\(495\) −3.79210 6.56811i −0.170442 0.295215i
\(496\) 10.5191 0.472322
\(497\) −24.8609 28.1167i −1.11516 1.26121i
\(498\) 5.80479 0.260119
\(499\) 5.64284 + 9.77369i 0.252608 + 0.437531i 0.964243 0.265019i \(-0.0853782\pi\)
−0.711635 + 0.702550i \(0.752045\pi\)
\(500\) 6.08579 10.5409i 0.272165 0.471403i
\(501\) 11.0593 19.1552i 0.494091 0.855791i
\(502\) 0.397302 + 0.688147i 0.0177325 + 0.0307135i
\(503\) 27.1339 1.20984 0.604920 0.796286i \(-0.293205\pi\)
0.604920 + 0.796286i \(0.293205\pi\)
\(504\) −0.840244 + 2.50878i −0.0374274 + 0.111750i
\(505\) 27.9860 1.24536
\(506\) −2.07397 3.59222i −0.0921992 0.159694i
\(507\) 4.11161 7.12152i 0.182603 0.316278i
\(508\) −3.24554 + 5.62144i −0.143998 + 0.249411i
\(509\) 19.3976 + 33.5976i 0.859783 + 1.48919i 0.872136 + 0.489264i \(0.162734\pi\)
−0.0123530 + 0.999924i \(0.503932\pi\)
\(510\) −6.13831 −0.271809
\(511\) 29.8666 6.06733i 1.32122 0.268403i
\(512\) 1.00000 0.0441942
\(513\) 3.66676 + 6.35102i 0.161891 + 0.280404i
\(514\) 0.295595 0.511985i 0.0130381 0.0225827i
\(515\) −6.76974 + 11.7255i −0.298310 + 0.516689i
\(516\) −2.68049 4.64274i −0.118002 0.204385i
\(517\) 29.9615 1.31771
\(518\) −2.69039 + 0.546546i −0.118209 + 0.0240139i
\(519\) −13.6849 −0.600699
\(520\) 1.99809 + 3.46079i 0.0876220 + 0.151766i
\(521\) −0.764956 + 1.32494i −0.0335133 + 0.0580468i −0.882296 0.470696i \(-0.844003\pi\)
0.848782 + 0.528743i \(0.177336\pi\)
\(522\) −2.59279 + 4.49085i −0.113483 + 0.196559i
\(523\) −4.21141 7.29438i −0.184152 0.318961i 0.759138 0.650929i \(-0.225621\pi\)
−0.943290 + 0.331968i \(0.892287\pi\)
\(524\) −4.40881 −0.192600
\(525\) 1.39216 4.15669i 0.0607589 0.181413i
\(526\) 2.86725 0.125018
\(527\) 17.6571 + 30.5831i 0.769157 + 1.33222i
\(528\) −2.07397 + 3.59222i −0.0902579 + 0.156331i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) −4.15303 7.19326i −0.180396 0.312455i
\(531\) −0.471271 −0.0204514
\(532\) 12.8523 + 14.5355i 0.557220 + 0.630194i
\(533\) −16.0280 −0.694251
\(534\) −3.34725 5.79761i −0.144850 0.250887i
\(535\) 5.02934 8.71107i 0.217437 0.376612i
\(536\) −6.70249 + 11.6091i −0.289504 + 0.501435i
\(537\) 1.38839 + 2.40476i 0.0599133 + 0.103773i
\(538\) −7.17794 −0.309463
\(539\) −23.1786 17.4876i −0.998373 0.753245i
\(540\) 1.82843 0.0786830
\(541\) 2.82692 + 4.89636i 0.121539 + 0.210511i 0.920375 0.391038i \(-0.127884\pi\)
−0.798836 + 0.601549i \(0.794551\pi\)
\(542\) 5.25955 9.10981i 0.225917 0.391300i
\(543\) 10.4815 18.1544i 0.449803 0.779081i
\(544\) 1.67858 + 2.90738i 0.0719684 + 0.124653i
\(545\) −34.1826 −1.46422
\(546\) 3.83034 + 4.33197i 0.163923 + 0.185391i
\(547\) −26.2480 −1.12229 −0.561143 0.827719i \(-0.689638\pi\)
−0.561143 + 0.827719i \(0.689638\pi\)
\(548\) −0.840244 1.45535i −0.0358935 0.0621693i
\(549\) 7.37117 12.7672i 0.314594 0.544892i
\(550\) 3.43627 5.95179i 0.146523 0.253785i
\(551\) 19.0143 + 32.9337i 0.810036 + 1.40302i
\(552\) 1.00000 0.0425628
\(553\) 4.35716 13.0095i 0.185285 0.553220i
\(554\) −30.9285 −1.31403
\(555\) 0.948628 + 1.64307i 0.0402670 + 0.0697445i
\(556\) 6.65685 11.5300i 0.282314 0.488981i
\(557\) −18.6211 + 32.2527i −0.789001 + 1.36659i 0.137578 + 0.990491i \(0.456068\pi\)
−0.926579 + 0.376099i \(0.877265\pi\)
\(558\) −5.25955 9.10981i −0.222655 0.385649i
\(559\) −11.7169 −0.495570
\(560\) 4.74073 0.963066i 0.200332 0.0406970i
\(561\) −13.9253 −0.587926
\(562\) 1.04974 + 1.81821i 0.0442808 + 0.0766965i
\(563\) −6.74483 + 11.6824i −0.284261 + 0.492354i −0.972430 0.233196i \(-0.925082\pi\)
0.688169 + 0.725551i \(0.258415\pi\)
\(564\) −3.61161 + 6.25550i −0.152076 + 0.263404i
\(565\) −4.82875 8.36365i −0.203147 0.351861i
\(566\) 20.3475 0.855271
\(567\) 2.59279 0.526718i 0.108887 0.0221201i
\(568\) 14.1856 0.595214
\(569\) 8.36897 + 14.4955i 0.350846 + 0.607682i 0.986398 0.164375i \(-0.0525609\pi\)
−0.635552 + 0.772058i \(0.719228\pi\)
\(570\) 6.70441 11.6124i 0.280817 0.486389i
\(571\) 13.0836 22.6614i 0.547530 0.948350i −0.450913 0.892568i \(-0.648901\pi\)
0.998443 0.0557822i \(-0.0177652\pi\)
\(572\) 4.53283 + 7.85110i 0.189527 + 0.328271i
\(573\) −8.96236 −0.374408
\(574\) −6.16195 + 18.3982i −0.257195 + 0.767926i
\(575\) −1.65685 −0.0690956
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −9.89858 + 17.1448i −0.412083 + 0.713749i −0.995117 0.0986987i \(-0.968532\pi\)
0.583034 + 0.812448i \(0.301865\pi\)
\(578\) 2.86475 4.96190i 0.119158 0.206388i
\(579\) −5.81951 10.0797i −0.241851 0.418898i
\(580\) 9.48146 0.393696
\(581\) −10.1732 11.5055i −0.422054 0.477327i
\(582\) −4.47127 −0.185340
\(583\) −9.42150 16.3185i −0.390199 0.675844i
\(584\) −5.75955 + 9.97584i −0.238332 + 0.412803i
\(585\) 1.99809 3.46079i 0.0826108 0.143086i
\(586\) 15.7426 + 27.2671i 0.650322 + 1.12639i
\(587\) −3.20078 −0.132110 −0.0660551 0.997816i \(-0.521041\pi\)
−0.0660551 + 0.997816i \(0.521041\pi\)
\(588\) 6.44514 2.73134i 0.265793 0.112639i
\(589\) −77.1421 −3.17858
\(590\) 0.430843 + 0.746241i 0.0177375 + 0.0307223i
\(591\) −4.79078 + 8.29788i −0.197066 + 0.341329i
\(592\) 0.518822 0.898626i 0.0213235 0.0369333i
\(593\) 16.0517 + 27.8023i 0.659162 + 1.14170i 0.980833 + 0.194851i \(0.0624224\pi\)
−0.321670 + 0.946852i \(0.604244\pi\)
\(594\) 4.14794 0.170192
\(595\) 10.7577 + 12.1665i 0.441022 + 0.498779i
\(596\) 19.3577 0.792923
\(597\) 4.97637 + 8.61932i 0.203669 + 0.352765i
\(598\) 1.09279 1.89277i 0.0446876 0.0774011i
\(599\) −22.5921 + 39.1306i −0.923087 + 1.59883i −0.128479 + 0.991712i \(0.541009\pi\)
−0.794608 + 0.607122i \(0.792324\pi\)
\(600\) 0.828427 + 1.43488i 0.0338204 + 0.0585786i
\(601\) 15.5166 0.632934 0.316467 0.948604i \(-0.397503\pi\)
0.316467 + 0.948604i \(0.397503\pi\)
\(602\) −4.50453 + 13.4495i −0.183591 + 0.548162i
\(603\) 13.4050 0.545893
\(604\) −2.79210 4.83606i −0.113609 0.196777i
\(605\) −5.67306 + 9.82602i −0.230643 + 0.399485i
\(606\) −7.65303 + 13.2554i −0.310883 + 0.538466i
\(607\) −2.43113 4.21083i −0.0986763 0.170912i 0.812461 0.583016i \(-0.198128\pi\)
−0.911137 + 0.412104i \(0.864794\pi\)
\(608\) −7.33352 −0.297414
\(609\) 13.4451 2.73134i 0.544824 0.110680i
\(610\) −26.9553 −1.09139
\(611\) 7.89348 + 13.6719i 0.319336 + 0.553106i
\(612\) 1.67858 2.90738i 0.0678525 0.117524i
\(613\) −3.40499 + 5.89761i −0.137526 + 0.238202i −0.926560 0.376148i \(-0.877248\pi\)
0.789033 + 0.614350i \(0.210582\pi\)
\(614\) −0.824324 1.42777i −0.0332670 0.0576201i
\(615\) 13.4088 0.540695
\(616\) 10.7547 2.18480i 0.433321 0.0880279i
\(617\) 7.70087 0.310025 0.155013 0.987912i \(-0.450458\pi\)
0.155013 + 0.987912i \(0.450458\pi\)
\(618\) −3.70249 6.41291i −0.148936 0.257965i
\(619\) −1.56828 + 2.71635i −0.0630346 + 0.109179i −0.895820 0.444416i \(-0.853411\pi\)
0.832786 + 0.553595i \(0.186745\pi\)
\(620\) −9.61671 + 16.6566i −0.386216 + 0.668946i
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 12.1779 0.488291
\(623\) −5.62501 + 16.7950i −0.225361 + 0.672879i
\(624\) −2.18558 −0.0874933
\(625\) 6.98528 + 12.0989i 0.279411 + 0.483954i
\(626\) −6.28347 + 10.8833i −0.251138 + 0.434984i
\(627\) 15.2095 26.3436i 0.607409 1.05206i
\(628\) 11.3951 + 19.7369i 0.454713 + 0.787587i
\(629\) 3.48353 0.138898
\(630\) −3.20441 3.62406i −0.127667 0.144386i
\(631\) −22.1045 −0.879966 −0.439983 0.898006i \(-0.645016\pi\)
−0.439983 + 0.898006i \(0.645016\pi\)
\(632\) 2.59279 + 4.49085i 0.103136 + 0.178636i
\(633\) −0.151760 + 0.262855i −0.00603190 + 0.0104476i
\(634\) 4.58897 7.94833i 0.182251 0.315669i
\(635\) −5.93424 10.2784i −0.235493 0.407886i
\(636\) 4.54274 0.180131
\(637\) 1.87339 15.1839i 0.0742262 0.601610i
\(638\) 21.5095 0.851568
\(639\) −7.09279 12.2851i −0.280586 0.485990i
\(640\) −0.914214 + 1.58346i −0.0361375 + 0.0625919i
\(641\) 9.27415 16.0633i 0.366307 0.634462i −0.622678 0.782478i \(-0.713955\pi\)
0.988985 + 0.148016i \(0.0472886\pi\)
\(642\) 2.75064 + 4.76424i 0.108559 + 0.188030i
\(643\) −12.4114 −0.489456 −0.244728 0.969592i \(-0.578699\pi\)
−0.244728 + 0.969592i \(0.578699\pi\)
\(644\) −1.75255 1.98206i −0.0690600 0.0781043i
\(645\) 9.80216 0.385959
\(646\) −12.3099 21.3214i −0.484326 0.838877i
\(647\) −18.9101 + 32.7532i −0.743432 + 1.28766i 0.207492 + 0.978237i \(0.433470\pi\)
−0.950924 + 0.309425i \(0.899863\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0.977402 + 1.69291i 0.0383664 + 0.0664525i
\(650\) 3.62119 0.142035
\(651\) −8.83862 + 26.3901i −0.346413 + 1.03431i
\(652\) −25.4368 −0.996183
\(653\) −9.75474 16.8957i −0.381732 0.661180i 0.609578 0.792726i \(-0.291339\pi\)
−0.991310 + 0.131546i \(0.958006\pi\)
\(654\) 9.34753 16.1904i 0.365517 0.633095i
\(655\) 4.03059 6.98119i 0.157488 0.272778i
\(656\) −3.66676 6.35102i −0.143163 0.247966i
\(657\) 11.5191 0.449403
\(658\) 18.7283 3.80461i 0.730106 0.148319i
\(659\) −33.6772 −1.31188 −0.655939 0.754814i \(-0.727727\pi\)
−0.655939 + 0.754814i \(0.727727\pi\)
\(660\) −3.79210 6.56811i −0.147607 0.255663i
\(661\) −13.6983 + 23.7262i −0.532803 + 0.922842i 0.466463 + 0.884541i \(0.345528\pi\)
−0.999266 + 0.0383011i \(0.987805\pi\)
\(662\) 14.6948 25.4521i 0.571129 0.989224i
\(663\) −3.66867 6.35433i −0.142479 0.246782i
\(664\) 5.80479 0.225270
\(665\) −34.7662 + 7.06267i −1.34818 + 0.273879i
\(666\) −1.03764 −0.0402079
\(667\) −2.59279 4.49085i −0.100393 0.173886i
\(668\) 11.0593 19.1552i 0.427895 0.741136i
\(669\) 8.46877 14.6683i 0.327422 0.567111i
\(670\) −12.2550 21.2263i −0.473453 0.820044i
\(671\) −61.1503 −2.36068
\(672\) −0.840244 + 2.50878i −0.0324131 + 0.0967784i
\(673\) 7.79715 0.300558 0.150279 0.988644i \(-0.451983\pi\)
0.150279 + 0.988644i \(0.451983\pi\)
\(674\) −4.06024 7.03255i −0.156395 0.270884i
\(675\) 0.828427 1.43488i 0.0318862 0.0552285i
\(676\) 4.11161 7.12152i 0.158139 0.273905i
\(677\) 0.0283290 + 0.0490673i 0.00108877 + 0.00188581i 0.866569 0.499057i \(-0.166320\pi\)
−0.865481 + 0.500943i \(0.832987\pi\)
\(678\) 5.28187 0.202849
\(679\) 7.83611 + 8.86235i 0.300722 + 0.340106i
\(680\) −6.13831 −0.235394
\(681\) 10.7685 + 18.6515i 0.412649 + 0.714728i
\(682\) −21.8163 + 37.7869i −0.835389 + 1.44694i
\(683\) 17.9817 31.1453i 0.688052 1.19174i −0.284415 0.958701i \(-0.591799\pi\)
0.972467 0.233040i \(-0.0748674\pi\)
\(684\) 3.66676 + 6.35102i 0.140202 + 0.242837i
\(685\) 3.07265 0.117400
\(686\) −16.7091 7.98786i −0.637956 0.304978i
\(687\) −0.666478 −0.0254277
\(688\) −2.68049 4.64274i −0.102193 0.177003i
\(689\) 4.96427 8.59836i 0.189123 0.327571i
\(690\) −0.914214 + 1.58346i −0.0348035 + 0.0602815i
\(691\) 11.0181 + 19.0839i 0.419149 + 0.725987i 0.995854 0.0909653i \(-0.0289952\pi\)
−0.576705 + 0.816952i \(0.695662\pi\)
\(692\) −13.6849 −0.520221
\(693\) −7.26946 8.22148i −0.276144 0.312308i
\(694\) 28.2614 1.07279
\(695\) 12.1716 + 21.0818i 0.461694 + 0.799678i
\(696\) −2.59279 + 4.49085i −0.0982795 + 0.170225i
\(697\) 12.3099 21.3214i 0.466270 0.807604i
\(698\) −12.0653 20.8978i −0.456680 0.790992i
\(699\) −1.67667 −0.0634174
\(700\) 1.39216 4.15669i 0.0526188 0.157108i
\(701\) 37.5337 1.41763 0.708814 0.705396i \(-0.249231\pi\)
0.708814 + 0.705396i \(0.249231\pi\)
\(702\) 1.09279 + 1.89277i 0.0412448 + 0.0714380i
\(703\) −3.80479 + 6.59009i −0.143500 + 0.248550i
\(704\) −2.07397 + 3.59222i −0.0781657 + 0.135387i
\(705\) −6.60357 11.4377i −0.248705 0.430770i
\(706\) 13.4088 0.504647
\(707\) 39.6854 8.06199i 1.49252 0.303202i
\(708\) −0.471271 −0.0177115
\(709\) −20.4894 35.4887i −0.769495 1.33280i −0.937837 0.347076i \(-0.887175\pi\)
0.168342 0.985729i \(-0.446159\pi\)
\(710\) −12.9687 + 22.4624i −0.486705 + 0.842998i
\(711\) 2.59279 4.49085i 0.0972373 0.168420i
\(712\) −3.34725 5.79761i −0.125443 0.217274i
\(713\) 10.5191 0.393944
\(714\) −8.70441 + 1.76828i −0.325754 + 0.0661761i
\(715\) −16.5759 −0.619904
\(716\) 1.38839 + 2.40476i 0.0518864 + 0.0898699i
\(717\) −5.36098 + 9.28548i −0.200209 + 0.346773i
\(718\) 1.94254 3.36458i 0.0724950 0.125565i
\(719\) −8.86985 15.3630i −0.330789 0.572944i 0.651877 0.758324i \(-0.273982\pi\)
−0.982667 + 0.185380i \(0.940648\pi\)
\(720\) 1.82843 0.0681415
\(721\) −6.22200 + 18.5775i −0.231719 + 0.691863i
\(722\) 34.7805 1.29440
\(723\) −9.10171 15.7646i −0.338496 0.586292i
\(724\) 10.4815 18.1544i 0.389540 0.674704i
\(725\) 4.29588 7.44068i 0.159545 0.276340i
\(726\) −3.10270 5.37403i −0.115152 0.199449i
\(727\) 14.4240 0.534957 0.267478 0.963564i \(-0.413810\pi\)
0.267478 + 0.963564i \(0.413810\pi\)
\(728\) 3.83034 + 4.33197i 0.141962 + 0.160553i
\(729\) 1.00000 0.0370370
\(730\) −10.5309 18.2401i −0.389767 0.675096i
\(731\) 8.99882 15.5864i 0.332833 0.576484i
\(732\) 7.37117 12.7672i 0.272446 0.471891i
\(733\) 15.8427 + 27.4404i 0.585164 + 1.01353i 0.994855 + 0.101310i \(0.0323033\pi\)
−0.409691 + 0.912224i \(0.634363\pi\)
\(734\) −1.43745 −0.0530572
\(735\) −1.56725 + 12.7027i −0.0578088 + 0.468545i
\(736\) 1.00000 0.0368605
\(737\) −27.8015 48.1537i −1.02408 1.77376i
\(738\) −3.66676 + 6.35102i −0.134975 + 0.233784i
\(739\) 2.10011 3.63749i 0.0772536 0.133807i −0.824810 0.565409i \(-0.808718\pi\)
0.902064 + 0.431602i \(0.142052\pi\)
\(740\) 0.948628 + 1.64307i 0.0348723 + 0.0604005i
\(741\) 16.0280 0.588804
\(742\) −7.96136 9.00400i −0.292271 0.330547i
\(743\) −42.3168 −1.55245 −0.776227 0.630454i \(-0.782869\pi\)
−0.776227 + 0.630454i \(0.782869\pi\)
\(744\) −5.25955 9.10981i −0.192825 0.333982i
\(745\) −17.6971 + 30.6523i −0.648371 + 1.12301i
\(746\) −9.14794 + 15.8447i −0.334930 + 0.580115i
\(747\) −2.90240 5.02710i −0.106193 0.183932i
\(748\) −13.9253 −0.509159
\(749\) 4.62241 13.8015i 0.168899 0.504296i
\(750\) −12.1716 −0.444443
\(751\) −8.22219 14.2413i −0.300032 0.519671i 0.676111 0.736800i \(-0.263664\pi\)
−0.976143 + 0.217129i \(0.930331\pi\)
\(752\) −3.61161 + 6.25550i −0.131702 + 0.228115i
\(753\) 0.397302 0.688147i 0.0144785 0.0250775i
\(754\) 5.66676 + 9.81512i 0.206371 + 0.357446i
\(755\) 10.2103 0.371591
\(756\) 2.59279 0.526718i 0.0942989 0.0191566i
\(757\) 45.4215 1.65087 0.825437 0.564494i \(-0.190929\pi\)
0.825437 + 0.564494i \(0.190929\pi\)
\(758\) 2.98818 + 5.17568i 0.108536 + 0.187989i
\(759\) −2.07397 + 3.59222i −0.0752803 + 0.130389i
\(760\) 6.70441 11.6124i 0.243194 0.421225i
\(761\) −7.82107 13.5465i −0.283513 0.491060i 0.688734 0.725014i \(-0.258167\pi\)
−0.972248 + 0.233954i \(0.924833\pi\)
\(762\) 6.49108 0.235147
\(763\) −48.4724 + 9.84704i −1.75482 + 0.356487i
\(764\) −8.96236 −0.324247
\(765\) 3.06916 + 5.31594i 0.110966 + 0.192198i
\(766\) 2.94863 5.10717i 0.106538 0.184530i
\(767\) −0.515001 + 0.892008i −0.0185956 + 0.0322086i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −14.1205 −0.509198 −0.254599 0.967047i \(-0.581943\pi\)
−0.254599 + 0.967047i \(0.581943\pi\)
\(770\) −6.37258 + 19.0271i −0.229652 + 0.685690i
\(771\) −0.591190 −0.0212912
\(772\) −5.81951 10.0797i −0.209449 0.362776i
\(773\) −8.80260 + 15.2466i −0.316608 + 0.548380i −0.979778 0.200088i \(-0.935877\pi\)
0.663170 + 0.748468i \(0.269210\pi\)
\(774\) −2.68049 +