Properties

Label 390.2.f.b.259.4
Level $390$
Weight $2$
Character 390.259
Analytic conductor $3.114$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 259.4
Root \(0.403032 + 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 390.259
Dual form 390.2.f.b.259.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.00000i q^{6} -4.15633 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.00000i q^{6} -4.15633 q^{7} +1.00000 q^{8} -1.00000 q^{9} +(-1.48119 + 1.67513i) q^{10} +5.35026i q^{11} +1.00000i q^{12} +(3.28726 + 1.48119i) q^{13} -4.15633 q^{14} +(-1.67513 - 1.48119i) q^{15} +1.00000 q^{16} -1.19394i q^{17} -1.00000 q^{18} +2.80606i q^{19} +(-1.48119 + 1.67513i) q^{20} -4.15633i q^{21} +5.35026i q^{22} +0.806063i q^{23} +1.00000i q^{24} +(-0.612127 - 4.96239i) q^{25} +(3.28726 + 1.48119i) q^{26} -1.00000i q^{27} -4.15633 q^{28} +7.50659 q^{29} +(-1.67513 - 1.48119i) q^{30} -7.92478i q^{31} +1.00000 q^{32} -5.35026 q^{33} -1.19394i q^{34} +(6.15633 - 6.96239i) q^{35} -1.00000 q^{36} -7.35026 q^{37} +2.80606i q^{38} +(-1.48119 + 3.28726i) q^{39} +(-1.48119 + 1.67513i) q^{40} -3.61213i q^{41} -4.15633i q^{42} +6.57452i q^{43} +5.35026i q^{44} +(1.48119 - 1.67513i) q^{45} +0.806063i q^{46} +12.3127 q^{47} +1.00000i q^{48} +10.2750 q^{49} +(-0.612127 - 4.96239i) q^{50} +1.19394 q^{51} +(3.28726 + 1.48119i) q^{52} +5.53690i q^{53} -1.00000i q^{54} +(-8.96239 - 7.92478i) q^{55} -4.15633 q^{56} -2.80606 q^{57} +7.50659 q^{58} +12.8872i q^{59} +(-1.67513 - 1.48119i) q^{60} +6.31265 q^{61} -7.92478i q^{62} +4.15633 q^{63} +1.00000 q^{64} +(-7.35026 + 3.31265i) q^{65} -5.35026 q^{66} -4.57452 q^{67} -1.19394i q^{68} -0.806063 q^{69} +(6.15633 - 6.96239i) q^{70} -8.96239i q^{71} -1.00000 q^{72} +4.08110 q^{73} -7.35026 q^{74} +(4.96239 - 0.612127i) q^{75} +2.80606i q^{76} -22.2374i q^{77} +(-1.48119 + 3.28726i) q^{78} -12.4387 q^{79} +(-1.48119 + 1.67513i) q^{80} +1.00000 q^{81} -3.61213i q^{82} +10.0508 q^{83} -4.15633i q^{84} +(2.00000 + 1.76845i) q^{85} +6.57452i q^{86} +7.50659i q^{87} +5.35026i q^{88} -5.03761i q^{89} +(1.48119 - 1.67513i) q^{90} +(-13.6629 - 6.15633i) q^{91} +0.806063i q^{92} +7.92478 q^{93} +12.3127 q^{94} +(-4.70052 - 4.15633i) q^{95} +1.00000i q^{96} +2.93207 q^{97} +10.2750 q^{98} -5.35026i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 6 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 6 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - 6 q^{9} + 2 q^{10} + 8 q^{13} - 4 q^{14} + 6 q^{16} - 6 q^{18} + 2 q^{20} - 2 q^{25} + 8 q^{26} - 4 q^{28} + 4 q^{29} + 6 q^{32} - 12 q^{33} + 16 q^{35} - 6 q^{36} - 24 q^{37} + 2 q^{39} + 2 q^{40} - 2 q^{45} + 32 q^{47} - 2 q^{49} - 2 q^{50} + 8 q^{51} + 8 q^{52} - 32 q^{55} - 4 q^{56} - 16 q^{57} + 4 q^{58} - 4 q^{61} + 4 q^{63} + 6 q^{64} - 24 q^{65} - 12 q^{66} - 4 q^{67} - 4 q^{69} + 16 q^{70} - 6 q^{72} - 40 q^{73} - 24 q^{74} + 8 q^{75} + 2 q^{78} - 16 q^{79} + 2 q^{80} + 6 q^{81} + 12 q^{85} - 2 q^{90} - 20 q^{91} + 4 q^{93} + 32 q^{94} + 12 q^{95} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) −1.48119 + 1.67513i −0.662410 + 0.749141i
\(6\) 1.00000i 0.408248i
\(7\) −4.15633 −1.57094 −0.785472 0.618898i \(-0.787580\pi\)
−0.785472 + 0.618898i \(0.787580\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) −1.48119 + 1.67513i −0.468395 + 0.529723i
\(11\) 5.35026i 1.61316i 0.591122 + 0.806582i \(0.298685\pi\)
−0.591122 + 0.806582i \(0.701315\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.28726 + 1.48119i 0.911721 + 0.410809i
\(14\) −4.15633 −1.11082
\(15\) −1.67513 1.48119i −0.432517 0.382443i
\(16\) 1.00000 0.250000
\(17\) 1.19394i 0.289572i −0.989463 0.144786i \(-0.953751\pi\)
0.989463 0.144786i \(-0.0462494\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.80606i 0.643755i 0.946781 + 0.321878i \(0.104314\pi\)
−0.946781 + 0.321878i \(0.895686\pi\)
\(20\) −1.48119 + 1.67513i −0.331205 + 0.374571i
\(21\) 4.15633i 0.906985i
\(22\) 5.35026i 1.14068i
\(23\) 0.806063i 0.168076i 0.996463 + 0.0840379i \(0.0267817\pi\)
−0.996463 + 0.0840379i \(0.973218\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −0.612127 4.96239i −0.122425 0.992478i
\(26\) 3.28726 + 1.48119i 0.644684 + 0.290486i
\(27\) 1.00000i 0.192450i
\(28\) −4.15633 −0.785472
\(29\) 7.50659 1.39394 0.696969 0.717101i \(-0.254531\pi\)
0.696969 + 0.717101i \(0.254531\pi\)
\(30\) −1.67513 1.48119i −0.305836 0.270428i
\(31\) 7.92478i 1.42333i −0.702518 0.711666i \(-0.747941\pi\)
0.702518 0.711666i \(-0.252059\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.35026 −0.931361
\(34\) 1.19394i 0.204758i
\(35\) 6.15633 6.96239i 1.04061 1.17686i
\(36\) −1.00000 −0.166667
\(37\) −7.35026 −1.20838 −0.604188 0.796842i \(-0.706502\pi\)
−0.604188 + 0.796842i \(0.706502\pi\)
\(38\) 2.80606i 0.455204i
\(39\) −1.48119 + 3.28726i −0.237181 + 0.526383i
\(40\) −1.48119 + 1.67513i −0.234197 + 0.264861i
\(41\) 3.61213i 0.564119i −0.959397 0.282060i \(-0.908982\pi\)
0.959397 0.282060i \(-0.0910176\pi\)
\(42\) 4.15633i 0.641335i
\(43\) 6.57452i 1.00260i 0.865272 + 0.501302i \(0.167145\pi\)
−0.865272 + 0.501302i \(0.832855\pi\)
\(44\) 5.35026i 0.806582i
\(45\) 1.48119 1.67513i 0.220803 0.249714i
\(46\) 0.806063i 0.118848i
\(47\) 12.3127 1.79598 0.897992 0.440011i \(-0.145026\pi\)
0.897992 + 0.440011i \(0.145026\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 10.2750 1.46786
\(50\) −0.612127 4.96239i −0.0865678 0.701788i
\(51\) 1.19394 0.167185
\(52\) 3.28726 + 1.48119i 0.455861 + 0.205405i
\(53\) 5.53690i 0.760552i 0.924873 + 0.380276i \(0.124171\pi\)
−0.924873 + 0.380276i \(0.875829\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −8.96239 7.92478i −1.20849 1.06858i
\(56\) −4.15633 −0.555412
\(57\) −2.80606 −0.371672
\(58\) 7.50659 0.985663
\(59\) 12.8872i 1.67777i 0.544312 + 0.838883i \(0.316791\pi\)
−0.544312 + 0.838883i \(0.683209\pi\)
\(60\) −1.67513 1.48119i −0.216258 0.191221i
\(61\) 6.31265 0.808252 0.404126 0.914703i \(-0.367576\pi\)
0.404126 + 0.914703i \(0.367576\pi\)
\(62\) 7.92478i 1.00645i
\(63\) 4.15633 0.523648
\(64\) 1.00000 0.125000
\(65\) −7.35026 + 3.31265i −0.911688 + 0.410884i
\(66\) −5.35026 −0.658572
\(67\) −4.57452 −0.558866 −0.279433 0.960165i \(-0.590146\pi\)
−0.279433 + 0.960165i \(0.590146\pi\)
\(68\) 1.19394i 0.144786i
\(69\) −0.806063 −0.0970386
\(70\) 6.15633 6.96239i 0.735822 0.832165i
\(71\) 8.96239i 1.06364i −0.846857 0.531820i \(-0.821508\pi\)
0.846857 0.531820i \(-0.178492\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.08110 0.477657 0.238828 0.971062i \(-0.423237\pi\)
0.238828 + 0.971062i \(0.423237\pi\)
\(74\) −7.35026 −0.854451
\(75\) 4.96239 0.612127i 0.573007 0.0706823i
\(76\) 2.80606i 0.321878i
\(77\) 22.2374i 2.53419i
\(78\) −1.48119 + 3.28726i −0.167712 + 0.372209i
\(79\) −12.4387 −1.39946 −0.699729 0.714408i \(-0.746696\pi\)
−0.699729 + 0.714408i \(0.746696\pi\)
\(80\) −1.48119 + 1.67513i −0.165603 + 0.187285i
\(81\) 1.00000 0.111111
\(82\) 3.61213i 0.398893i
\(83\) 10.0508 1.10322 0.551609 0.834103i \(-0.314014\pi\)
0.551609 + 0.834103i \(0.314014\pi\)
\(84\) 4.15633i 0.453492i
\(85\) 2.00000 + 1.76845i 0.216930 + 0.191816i
\(86\) 6.57452i 0.708948i
\(87\) 7.50659i 0.804791i
\(88\) 5.35026i 0.570340i
\(89\) 5.03761i 0.533986i −0.963699 0.266993i \(-0.913970\pi\)
0.963699 0.266993i \(-0.0860300\pi\)
\(90\) 1.48119 1.67513i 0.156132 0.176574i
\(91\) −13.6629 6.15633i −1.43226 0.645358i
\(92\) 0.806063i 0.0840379i
\(93\) 7.92478 0.821761
\(94\) 12.3127 1.26995
\(95\) −4.70052 4.15633i −0.482264 0.426430i
\(96\) 1.00000i 0.102062i
\(97\) 2.93207 0.297707 0.148853 0.988859i \(-0.452442\pi\)
0.148853 + 0.988859i \(0.452442\pi\)
\(98\) 10.2750 1.03794
\(99\) 5.35026i 0.537722i
\(100\) −0.612127 4.96239i −0.0612127 0.496239i
\(101\) 5.89446 0.586521 0.293260 0.956033i \(-0.405260\pi\)
0.293260 + 0.956033i \(0.405260\pi\)
\(102\) 1.19394 0.118217
\(103\) 3.29948i 0.325107i 0.986700 + 0.162554i \(0.0519730\pi\)
−0.986700 + 0.162554i \(0.948027\pi\)
\(104\) 3.28726 + 1.48119i 0.322342 + 0.145243i
\(105\) 6.96239 + 6.15633i 0.679460 + 0.600796i
\(106\) 5.53690i 0.537792i
\(107\) 19.7889i 1.91307i 0.291622 + 0.956534i \(0.405805\pi\)
−0.291622 + 0.956534i \(0.594195\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 9.43136i 0.903361i −0.892180 0.451680i \(-0.850825\pi\)
0.892180 0.451680i \(-0.149175\pi\)
\(110\) −8.96239 7.92478i −0.854530 0.755598i
\(111\) 7.35026i 0.697656i
\(112\) −4.15633 −0.392736
\(113\) 4.41819i 0.415628i 0.978168 + 0.207814i \(0.0666349\pi\)
−0.978168 + 0.207814i \(0.933365\pi\)
\(114\) −2.80606 −0.262812
\(115\) −1.35026 1.19394i −0.125913 0.111335i
\(116\) 7.50659 0.696969
\(117\) −3.28726 1.48119i −0.303907 0.136936i
\(118\) 12.8872i 1.18636i
\(119\) 4.96239i 0.454901i
\(120\) −1.67513 1.48119i −0.152918 0.135214i
\(121\) −17.6253 −1.60230
\(122\) 6.31265 0.571521
\(123\) 3.61213 0.325695
\(124\) 7.92478i 0.711666i
\(125\) 9.21933 + 6.32487i 0.824602 + 0.565713i
\(126\) 4.15633 0.370275
\(127\) 18.1622i 1.61164i −0.592164 0.805818i \(-0.701726\pi\)
0.592164 0.805818i \(-0.298274\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.57452 −0.578854
\(130\) −7.35026 + 3.31265i −0.644661 + 0.290539i
\(131\) −9.81924 −0.857911 −0.428955 0.903326i \(-0.641118\pi\)
−0.428955 + 0.903326i \(0.641118\pi\)
\(132\) −5.35026 −0.465681
\(133\) 11.6629i 1.01130i
\(134\) −4.57452 −0.395178
\(135\) 1.67513 + 1.48119i 0.144172 + 0.127481i
\(136\) 1.19394i 0.102379i
\(137\) 0.911603 0.0778835 0.0389418 0.999241i \(-0.487601\pi\)
0.0389418 + 0.999241i \(0.487601\pi\)
\(138\) −0.806063 −0.0686167
\(139\) 0.836381 0.0709409 0.0354704 0.999371i \(-0.488707\pi\)
0.0354704 + 0.999371i \(0.488707\pi\)
\(140\) 6.15633 6.96239i 0.520304 0.588429i
\(141\) 12.3127i 1.03691i
\(142\) 8.96239i 0.752107i
\(143\) −7.92478 + 17.5877i −0.662703 + 1.47076i
\(144\) −1.00000 −0.0833333
\(145\) −11.1187 + 12.5745i −0.923359 + 1.04426i
\(146\) 4.08110 0.337754
\(147\) 10.2750i 0.847471i
\(148\) −7.35026 −0.604188
\(149\) 10.8872i 0.891911i −0.895055 0.445956i \(-0.852864\pi\)
0.895055 0.445956i \(-0.147136\pi\)
\(150\) 4.96239 0.612127i 0.405177 0.0499799i
\(151\) 17.7889i 1.44764i 0.689988 + 0.723821i \(0.257616\pi\)
−0.689988 + 0.723821i \(0.742384\pi\)
\(152\) 2.80606i 0.227602i
\(153\) 1.19394i 0.0965241i
\(154\) 22.2374i 1.79194i
\(155\) 13.2750 + 11.7381i 1.06628 + 0.942830i
\(156\) −1.48119 + 3.28726i −0.118590 + 0.263191i
\(157\) 10.7757i 0.859998i −0.902829 0.429999i \(-0.858514\pi\)
0.902829 0.429999i \(-0.141486\pi\)
\(158\) −12.4387 −0.989567
\(159\) −5.53690 −0.439105
\(160\) −1.48119 + 1.67513i −0.117099 + 0.132431i
\(161\) 3.35026i 0.264038i
\(162\) 1.00000 0.0785674
\(163\) −12.0508 −0.943890 −0.471945 0.881628i \(-0.656448\pi\)
−0.471945 + 0.881628i \(0.656448\pi\)
\(164\) 3.61213i 0.282060i
\(165\) 7.92478 8.96239i 0.616943 0.697721i
\(166\) 10.0508 0.780092
\(167\) 1.61213 0.124750 0.0623751 0.998053i \(-0.480133\pi\)
0.0623751 + 0.998053i \(0.480133\pi\)
\(168\) 4.15633i 0.320667i
\(169\) 8.61213 + 9.73813i 0.662471 + 0.749087i
\(170\) 2.00000 + 1.76845i 0.153393 + 0.135634i
\(171\) 2.80606i 0.214585i
\(172\) 6.57452i 0.501302i
\(173\) 1.22425i 0.0930783i 0.998916 + 0.0465391i \(0.0148192\pi\)
−0.998916 + 0.0465391i \(0.985181\pi\)
\(174\) 7.50659i 0.569073i
\(175\) 2.54420 + 20.6253i 0.192323 + 1.55913i
\(176\) 5.35026i 0.403291i
\(177\) −12.8872 −0.968659
\(178\) 5.03761i 0.377585i
\(179\) −1.25457 −0.0937710 −0.0468855 0.998900i \(-0.514930\pi\)
−0.0468855 + 0.998900i \(0.514930\pi\)
\(180\) 1.48119 1.67513i 0.110402 0.124857i
\(181\) 5.47627 0.407048 0.203524 0.979070i \(-0.434761\pi\)
0.203524 + 0.979070i \(0.434761\pi\)
\(182\) −13.6629 6.15633i −1.01276 0.456337i
\(183\) 6.31265i 0.466645i
\(184\) 0.806063i 0.0594238i
\(185\) 10.8872 12.3127i 0.800440 0.905244i
\(186\) 7.92478 0.581073
\(187\) 6.38787 0.467128
\(188\) 12.3127 0.897992
\(189\) 4.15633i 0.302328i
\(190\) −4.70052 4.15633i −0.341012 0.301532i
\(191\) −10.2374 −0.740754 −0.370377 0.928881i \(-0.620772\pi\)
−0.370377 + 0.928881i \(0.620772\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 9.06793 0.652724 0.326362 0.945245i \(-0.394177\pi\)
0.326362 + 0.945245i \(0.394177\pi\)
\(194\) 2.93207 0.210510
\(195\) −3.31265 7.35026i −0.237224 0.526363i
\(196\) 10.2750 0.733931
\(197\) 3.14903 0.224359 0.112180 0.993688i \(-0.464217\pi\)
0.112180 + 0.993688i \(0.464217\pi\)
\(198\) 5.35026i 0.380227i
\(199\) 14.1114 1.00033 0.500166 0.865930i \(-0.333272\pi\)
0.500166 + 0.865930i \(0.333272\pi\)
\(200\) −0.612127 4.96239i −0.0432839 0.350894i
\(201\) 4.57452i 0.322661i
\(202\) 5.89446 0.414733
\(203\) −31.1998 −2.18980
\(204\) 1.19394 0.0835923
\(205\) 6.05079 + 5.35026i 0.422605 + 0.373678i
\(206\) 3.29948i 0.229885i
\(207\) 0.806063i 0.0560253i
\(208\) 3.28726 + 1.48119i 0.227930 + 0.102702i
\(209\) −15.0132 −1.03848
\(210\) 6.96239 + 6.15633i 0.480450 + 0.424827i
\(211\) −17.4617 −1.20211 −0.601056 0.799207i \(-0.705253\pi\)
−0.601056 + 0.799207i \(0.705253\pi\)
\(212\) 5.53690i 0.380276i
\(213\) 8.96239 0.614093
\(214\) 19.7889i 1.35274i
\(215\) −11.0132 9.73813i −0.751092 0.664135i
\(216\) 1.00000i 0.0680414i
\(217\) 32.9380i 2.23597i
\(218\) 9.43136i 0.638773i
\(219\) 4.08110i 0.275775i
\(220\) −8.96239 7.92478i −0.604244 0.534288i
\(221\) 1.76845 3.92478i 0.118959 0.264009i
\(222\) 7.35026i 0.493317i
\(223\) 19.6326 1.31470 0.657348 0.753587i \(-0.271678\pi\)
0.657348 + 0.753587i \(0.271678\pi\)
\(224\) −4.15633 −0.277706
\(225\) 0.612127 + 4.96239i 0.0408085 + 0.330826i
\(226\) 4.41819i 0.293894i
\(227\) −4.77575 −0.316977 −0.158489 0.987361i \(-0.550662\pi\)
−0.158489 + 0.987361i \(0.550662\pi\)
\(228\) −2.80606 −0.185836
\(229\) 19.5672i 1.29304i −0.762898 0.646519i \(-0.776224\pi\)
0.762898 0.646519i \(-0.223776\pi\)
\(230\) −1.35026 1.19394i −0.0890336 0.0787258i
\(231\) 22.2374 1.46312
\(232\) 7.50659 0.492832
\(233\) 2.74543i 0.179859i 0.995948 + 0.0899295i \(0.0286642\pi\)
−0.995948 + 0.0899295i \(0.971336\pi\)
\(234\) −3.28726 1.48119i −0.214895 0.0968287i
\(235\) −18.2374 + 20.6253i −1.18968 + 1.34545i
\(236\) 12.8872i 0.838883i
\(237\) 12.4387i 0.807978i
\(238\) 4.96239i 0.321664i
\(239\) 5.29948i 0.342795i 0.985202 + 0.171397i \(0.0548282\pi\)
−0.985202 + 0.171397i \(0.945172\pi\)
\(240\) −1.67513 1.48119i −0.108129 0.0956107i
\(241\) 12.9380i 0.833407i 0.909043 + 0.416703i \(0.136815\pi\)
−0.909043 + 0.416703i \(0.863185\pi\)
\(242\) −17.6253 −1.13300
\(243\) 1.00000i 0.0641500i
\(244\) 6.31265 0.404126
\(245\) −15.2193 + 17.2120i −0.972327 + 1.09964i
\(246\) 3.61213 0.230301
\(247\) −4.15633 + 9.22425i −0.264461 + 0.586925i
\(248\) 7.92478i 0.503224i
\(249\) 10.0508i 0.636943i
\(250\) 9.21933 + 6.32487i 0.583082 + 0.400020i
\(251\) 8.10554 0.511617 0.255809 0.966727i \(-0.417658\pi\)
0.255809 + 0.966727i \(0.417658\pi\)
\(252\) 4.15633 0.261824
\(253\) −4.31265 −0.271134
\(254\) 18.1622i 1.13960i
\(255\) −1.76845 + 2.00000i −0.110745 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 12.0567i 0.752074i −0.926605 0.376037i \(-0.877287\pi\)
0.926605 0.376037i \(-0.122713\pi\)
\(258\) −6.57452 −0.409311
\(259\) 30.5501 1.89829
\(260\) −7.35026 + 3.31265i −0.455844 + 0.205442i
\(261\) −7.50659 −0.464646
\(262\) −9.81924 −0.606635
\(263\) 4.28233i 0.264060i 0.991246 + 0.132030i \(0.0421495\pi\)
−0.991246 + 0.132030i \(0.957850\pi\)
\(264\) −5.35026 −0.329286
\(265\) −9.27504 8.20123i −0.569761 0.503798i
\(266\) 11.6629i 0.715099i
\(267\) 5.03761 0.308297
\(268\) −4.57452 −0.279433
\(269\) −19.8799 −1.21210 −0.606049 0.795428i \(-0.707246\pi\)
−0.606049 + 0.795428i \(0.707246\pi\)
\(270\) 1.67513 + 1.48119i 0.101945 + 0.0901426i
\(271\) 5.01317i 0.304529i −0.988340 0.152264i \(-0.951344\pi\)
0.988340 0.152264i \(-0.0486565\pi\)
\(272\) 1.19394i 0.0723930i
\(273\) 6.15633 13.6629i 0.372598 0.826917i
\(274\) 0.911603 0.0550720
\(275\) 26.5501 3.27504i 1.60103 0.197492i
\(276\) −0.806063 −0.0485193
\(277\) 8.55008i 0.513724i 0.966448 + 0.256862i \(0.0826887\pi\)
−0.966448 + 0.256862i \(0.917311\pi\)
\(278\) 0.836381 0.0501628
\(279\) 7.92478i 0.474444i
\(280\) 6.15633 6.96239i 0.367911 0.416082i
\(281\) 25.5125i 1.52195i −0.648783 0.760973i \(-0.724722\pi\)
0.648783 0.760973i \(-0.275278\pi\)
\(282\) 12.3127i 0.733208i
\(283\) 23.7235i 1.41022i −0.709099 0.705109i \(-0.750898\pi\)
0.709099 0.705109i \(-0.249102\pi\)
\(284\) 8.96239i 0.531820i
\(285\) 4.15633 4.70052i 0.246199 0.278435i
\(286\) −7.92478 + 17.5877i −0.468602 + 1.03998i
\(287\) 15.0132i 0.886200i
\(288\) −1.00000 −0.0589256
\(289\) 15.5745 0.916148
\(290\) −11.1187 + 12.5745i −0.652913 + 0.738401i
\(291\) 2.93207i 0.171881i
\(292\) 4.08110 0.238828
\(293\) −23.9248 −1.39770 −0.698850 0.715268i \(-0.746305\pi\)
−0.698850 + 0.715268i \(0.746305\pi\)
\(294\) 10.2750i 0.599252i
\(295\) −21.5877 19.0884i −1.25688 1.11137i
\(296\) −7.35026 −0.427225
\(297\) 5.35026 0.310454
\(298\) 10.8872i 0.630677i
\(299\) −1.19394 + 2.64974i −0.0690471 + 0.153238i
\(300\) 4.96239 0.612127i 0.286504 0.0353412i
\(301\) 27.3258i 1.57503i
\(302\) 17.7889i 1.02364i
\(303\) 5.89446i 0.338628i
\(304\) 2.80606i 0.160939i
\(305\) −9.35026 + 10.5745i −0.535394 + 0.605495i
\(306\) 1.19394i 0.0682528i
\(307\) 33.5125 1.91266 0.956329 0.292293i \(-0.0944183\pi\)
0.956329 + 0.292293i \(0.0944183\pi\)
\(308\) 22.2374i 1.26710i
\(309\) −3.29948 −0.187701
\(310\) 13.2750 + 11.7381i 0.753972 + 0.666681i
\(311\) −5.76257 −0.326766 −0.163383 0.986563i \(-0.552241\pi\)
−0.163383 + 0.986563i \(0.552241\pi\)
\(312\) −1.48119 + 3.28726i −0.0838561 + 0.186104i
\(313\) 12.6253i 0.713624i 0.934176 + 0.356812i \(0.116136\pi\)
−0.934176 + 0.356812i \(0.883864\pi\)
\(314\) 10.7757i 0.608111i
\(315\) −6.15633 + 6.96239i −0.346870 + 0.392286i
\(316\) −12.4387 −0.699729
\(317\) −3.73813 −0.209955 −0.104977 0.994475i \(-0.533477\pi\)
−0.104977 + 0.994475i \(0.533477\pi\)
\(318\) −5.53690 −0.310494
\(319\) 40.1622i 2.24865i
\(320\) −1.48119 + 1.67513i −0.0828013 + 0.0936427i
\(321\) −19.7889 −1.10451
\(322\) 3.35026i 0.186703i
\(323\) 3.35026 0.186414
\(324\) 1.00000 0.0555556
\(325\) 5.33804 17.2193i 0.296101 0.955157i
\(326\) −12.0508 −0.667431
\(327\) 9.43136 0.521556
\(328\) 3.61213i 0.199446i
\(329\) −51.1754 −2.82139
\(330\) 7.92478 8.96239i 0.436245 0.493363i
\(331\) 1.81924i 0.0999943i 0.998749 + 0.0499972i \(0.0159212\pi\)
−0.998749 + 0.0499972i \(0.984079\pi\)
\(332\) 10.0508 0.551609
\(333\) 7.35026 0.402792
\(334\) 1.61213 0.0882117
\(335\) 6.77575 7.66291i 0.370199 0.418670i
\(336\) 4.15633i 0.226746i
\(337\) 8.83638i 0.481348i −0.970606 0.240674i \(-0.922631\pi\)
0.970606 0.240674i \(-0.0773685\pi\)
\(338\) 8.61213 + 9.73813i 0.468438 + 0.529685i
\(339\) −4.41819 −0.239963
\(340\) 2.00000 + 1.76845i 0.108465 + 0.0959078i
\(341\) 42.3996 2.29607
\(342\) 2.80606i 0.151735i
\(343\) −13.6121 −0.734986
\(344\) 6.57452i 0.354474i
\(345\) 1.19394 1.35026i 0.0642794 0.0726956i
\(346\) 1.22425i 0.0658163i
\(347\) 2.13586i 0.114659i 0.998355 + 0.0573294i \(0.0182585\pi\)
−0.998355 + 0.0573294i \(0.981741\pi\)
\(348\) 7.50659i 0.402395i
\(349\) 16.4934i 0.882872i −0.897293 0.441436i \(-0.854469\pi\)
0.897293 0.441436i \(-0.145531\pi\)
\(350\) 2.54420 + 20.6253i 0.135993 + 1.10247i
\(351\) 1.48119 3.28726i 0.0790603 0.175461i
\(352\) 5.35026i 0.285170i
\(353\) 3.86414 0.205668 0.102834 0.994699i \(-0.467209\pi\)
0.102834 + 0.994699i \(0.467209\pi\)
\(354\) −12.8872 −0.684945
\(355\) 15.0132 + 13.2750i 0.796817 + 0.704566i
\(356\) 5.03761i 0.266993i
\(357\) −4.96239 −0.262637
\(358\) −1.25457 −0.0663061
\(359\) 18.5139i 0.977125i −0.872529 0.488563i \(-0.837521\pi\)
0.872529 0.488563i \(-0.162479\pi\)
\(360\) 1.48119 1.67513i 0.0780658 0.0882871i
\(361\) 11.1260 0.585579
\(362\) 5.47627 0.287826
\(363\) 17.6253i 0.925088i
\(364\) −13.6629 6.15633i −0.716131 0.322679i
\(365\) −6.04491 + 6.83638i −0.316405 + 0.357833i
\(366\) 6.31265i 0.329968i
\(367\) 23.7137i 1.23784i −0.785452 0.618922i \(-0.787570\pi\)
0.785452 0.618922i \(-0.212430\pi\)
\(368\) 0.806063i 0.0420190i
\(369\) 3.61213i 0.188040i
\(370\) 10.8872 12.3127i 0.565997 0.640104i
\(371\) 23.0132i 1.19478i
\(372\) 7.92478 0.410881
\(373\) 11.1490i 0.577275i −0.957438 0.288637i \(-0.906798\pi\)
0.957438 0.288637i \(-0.0932022\pi\)
\(374\) 6.38787 0.330309
\(375\) −6.32487 + 9.21933i −0.326615 + 0.476084i
\(376\) 12.3127 0.634976
\(377\) 24.6761 + 11.1187i 1.27088 + 0.572643i
\(378\) 4.15633i 0.213778i
\(379\) 38.7572i 1.99082i −0.0956865 0.995412i \(-0.530505\pi\)
0.0956865 0.995412i \(-0.469495\pi\)
\(380\) −4.70052 4.15633i −0.241132 0.213215i
\(381\) 18.1622 0.930478
\(382\) −10.2374 −0.523792
\(383\) 1.76257 0.0900632 0.0450316 0.998986i \(-0.485661\pi\)
0.0450316 + 0.998986i \(0.485661\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 37.2506 + 32.9380i 1.89847 + 1.67867i
\(386\) 9.06793 0.461545
\(387\) 6.57452i 0.334201i
\(388\) 2.93207 0.148853
\(389\) 34.0567 1.72674 0.863371 0.504570i \(-0.168349\pi\)
0.863371 + 0.504570i \(0.168349\pi\)
\(390\) −3.31265 7.35026i −0.167743 0.372195i
\(391\) 0.962389 0.0486701
\(392\) 10.2750 0.518968
\(393\) 9.81924i 0.495315i
\(394\) 3.14903 0.158646
\(395\) 18.4241 20.8364i 0.927016 1.04839i
\(396\) 5.35026i 0.268861i
\(397\) −15.8134 −0.793650 −0.396825 0.917894i \(-0.629888\pi\)
−0.396825 + 0.917894i \(0.629888\pi\)
\(398\) 14.1114 0.707342
\(399\) 11.6629 0.583876
\(400\) −0.612127 4.96239i −0.0306063 0.248119i
\(401\) 25.0132i 1.24910i 0.780986 + 0.624549i \(0.214717\pi\)
−0.780986 + 0.624549i \(0.785283\pi\)
\(402\) 4.57452i 0.228156i
\(403\) 11.7381 26.0508i 0.584718 1.29768i
\(404\) 5.89446 0.293260
\(405\) −1.48119 + 1.67513i −0.0736011 + 0.0832379i
\(406\) −31.1998 −1.54842
\(407\) 39.3258i 1.94931i
\(408\) 1.19394 0.0591087
\(409\) 34.0263i 1.68249i −0.540651 0.841247i \(-0.681822\pi\)
0.540651 0.841247i \(-0.318178\pi\)
\(410\) 6.05079 + 5.35026i 0.298827 + 0.264231i
\(411\) 0.911603i 0.0449661i
\(412\) 3.29948i 0.162554i
\(413\) 53.5633i 2.63568i
\(414\) 0.806063i 0.0396159i
\(415\) −14.8872 + 16.8364i −0.730782 + 0.826465i
\(416\) 3.28726 + 1.48119i 0.161171 + 0.0726215i
\(417\) 0.836381i 0.0409577i
\(418\) −15.0132 −0.734318
\(419\) −3.73226 −0.182333 −0.0911663 0.995836i \(-0.529059\pi\)
−0.0911663 + 0.995836i \(0.529059\pi\)
\(420\) 6.96239 + 6.15633i 0.339730 + 0.300398i
\(421\) 16.9683i 0.826983i 0.910508 + 0.413491i \(0.135691\pi\)
−0.910508 + 0.413491i \(0.864309\pi\)
\(422\) −17.4617 −0.850021
\(423\) −12.3127 −0.598662
\(424\) 5.53690i 0.268896i
\(425\) −5.92478 + 0.730841i −0.287394 + 0.0354510i
\(426\) 8.96239 0.434229
\(427\) −26.2374 −1.26972
\(428\) 19.7889i 0.956534i
\(429\) −17.5877 7.92478i −0.849142 0.382612i
\(430\) −11.0132 9.73813i −0.531102 0.469615i
\(431\) 20.9986i 1.01147i −0.862690 0.505733i \(-0.831222\pi\)
0.862690 0.505733i \(-0.168778\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 17.3404i 0.833327i 0.909061 + 0.416664i \(0.136801\pi\)
−0.909061 + 0.416664i \(0.863199\pi\)
\(434\) 32.9380i 1.58107i
\(435\) −12.5745 11.1187i −0.602902 0.533102i
\(436\) 9.43136i 0.451680i
\(437\) −2.26187 −0.108200
\(438\) 4.08110i 0.195003i
\(439\) 13.7743 0.657413 0.328706 0.944432i \(-0.393387\pi\)
0.328706 + 0.944432i \(0.393387\pi\)
\(440\) −8.96239 7.92478i −0.427265 0.377799i
\(441\) −10.2750 −0.489288
\(442\) 1.76845 3.92478i 0.0841167 0.186683i
\(443\) 9.61213i 0.456686i −0.973581 0.228343i \(-0.926669\pi\)
0.973581 0.228343i \(-0.0733307\pi\)
\(444\) 7.35026i 0.348828i
\(445\) 8.43866 + 7.46168i 0.400031 + 0.353718i
\(446\) 19.6326 0.929630
\(447\) 10.8872 0.514945
\(448\) −4.15633 −0.196368
\(449\) 25.6629i 1.21111i 0.795804 + 0.605554i \(0.207048\pi\)
−0.795804 + 0.605554i \(0.792952\pi\)
\(450\) 0.612127 + 4.96239i 0.0288559 + 0.233929i
\(451\) 19.3258 0.910018
\(452\) 4.41819i 0.207814i
\(453\) −17.7889 −0.835796
\(454\) −4.77575 −0.224137
\(455\) 30.5501 13.7685i 1.43221 0.645475i
\(456\) −2.80606 −0.131406
\(457\) 22.9321 1.07272 0.536359 0.843990i \(-0.319799\pi\)
0.536359 + 0.843990i \(0.319799\pi\)
\(458\) 19.5672i 0.914316i
\(459\) −1.19394 −0.0557282
\(460\) −1.35026 1.19394i −0.0629563 0.0556676i
\(461\) 22.7367i 1.05895i 0.848324 + 0.529477i \(0.177612\pi\)
−0.848324 + 0.529477i \(0.822388\pi\)
\(462\) 22.2374 1.03458
\(463\) −5.08252 −0.236205 −0.118102 0.993001i \(-0.537681\pi\)
−0.118102 + 0.993001i \(0.537681\pi\)
\(464\) 7.50659 0.348485
\(465\) −11.7381 + 13.2750i −0.544343 + 0.615615i
\(466\) 2.74543i 0.127180i
\(467\) 16.4631i 0.761821i −0.924612 0.380911i \(-0.875611\pi\)
0.924612 0.380911i \(-0.124389\pi\)
\(468\) −3.28726 1.48119i −0.151954 0.0684682i
\(469\) 19.0132 0.877947
\(470\) −18.2374 + 20.6253i −0.841230 + 0.951374i
\(471\) 10.7757 0.496520
\(472\) 12.8872i 0.593180i
\(473\) −35.1754 −1.61737
\(474\) 12.4387i 0.571327i
\(475\) 13.9248 1.71767i 0.638913 0.0788120i
\(476\) 4.96239i 0.227451i
\(477\) 5.53690i 0.253517i
\(478\) 5.29948i 0.242392i
\(479\) 8.15045i 0.372403i −0.982512 0.186202i \(-0.940382\pi\)
0.982512 0.186202i \(-0.0596178\pi\)
\(480\) −1.67513 1.48119i −0.0764589 0.0676070i
\(481\) −24.1622 10.8872i −1.10170 0.496412i
\(482\) 12.9380i 0.589308i
\(483\) 3.35026 0.152442
\(484\) −17.6253 −0.801150
\(485\) −4.34297 + 4.91160i −0.197204 + 0.223024i
\(486\) 1.00000i 0.0453609i
\(487\) −35.4215 −1.60510 −0.802551 0.596583i \(-0.796524\pi\)
−0.802551 + 0.596583i \(0.796524\pi\)
\(488\) 6.31265 0.285760
\(489\) 12.0508i 0.544955i
\(490\) −15.2193 + 17.2120i −0.687539 + 0.777560i
\(491\) −35.8046 −1.61584 −0.807921 0.589291i \(-0.799407\pi\)
−0.807921 + 0.589291i \(0.799407\pi\)
\(492\) 3.61213 0.162847
\(493\) 8.96239i 0.403646i
\(494\) −4.15633 + 9.22425i −0.187002 + 0.415019i
\(495\) 8.96239 + 7.92478i 0.402829 + 0.356192i
\(496\) 7.92478i 0.355833i
\(497\) 37.2506i 1.67092i
\(498\) 10.0508i 0.450386i
\(499\) 29.1939i 1.30690i 0.756970 + 0.653450i \(0.226679\pi\)
−0.756970 + 0.653450i \(0.773321\pi\)
\(500\) 9.21933 + 6.32487i 0.412301 + 0.282857i
\(501\) 1.61213i 0.0720245i
\(502\) 8.10554 0.361768
\(503\) 0.806063i 0.0359406i 0.999839 + 0.0179703i \(0.00572043\pi\)
−0.999839 + 0.0179703i \(0.994280\pi\)
\(504\) 4.15633 0.185137
\(505\) −8.73084 + 9.87399i −0.388517 + 0.439387i
\(506\) −4.31265 −0.191721
\(507\) −9.73813 + 8.61213i −0.432486 + 0.382478i
\(508\) 18.1622i 0.805818i
\(509\) 11.9149i 0.528120i 0.964506 + 0.264060i \(0.0850617\pi\)
−0.964506 + 0.264060i \(0.914938\pi\)
\(510\) −1.76845 + 2.00000i −0.0783084 + 0.0885615i
\(511\) −16.9624 −0.750372
\(512\) 1.00000 0.0441942
\(513\) 2.80606 0.123891
\(514\) 12.0567i 0.531797i
\(515\) −5.52705 4.88717i −0.243551 0.215354i
\(516\) −6.57452 −0.289427
\(517\) 65.8759i 2.89722i
\(518\) 30.5501 1.34229
\(519\) −1.22425 −0.0537388
\(520\) −7.35026 + 3.31265i −0.322330 + 0.145269i
\(521\) 16.4485 0.720622 0.360311 0.932832i \(-0.382671\pi\)
0.360311 + 0.932832i \(0.382671\pi\)
\(522\) −7.50659 −0.328554
\(523\) 6.07522i 0.265651i 0.991139 + 0.132825i \(0.0424050\pi\)
−0.991139 + 0.132825i \(0.957595\pi\)
\(524\) −9.81924 −0.428955
\(525\) −20.6253 + 2.54420i −0.900162 + 0.111038i
\(526\) 4.28233i 0.186719i
\(527\) −9.46168 −0.412157
\(528\) −5.35026 −0.232840
\(529\) 22.3503 0.971751
\(530\) −9.27504 8.20123i −0.402882 0.356239i
\(531\) 12.8872i 0.559255i
\(532\) 11.6629i 0.505651i
\(533\) 5.35026 11.8740i 0.231746 0.514320i
\(534\) 5.03761 0.217999
\(535\) −33.1490 29.3112i −1.43316 1.26724i
\(536\) −4.57452 −0.197589
\(537\) 1.25457i 0.0541387i
\(538\) −19.8799 −0.857082
\(539\) 54.9741i 2.36790i
\(540\) 1.67513 + 1.48119i 0.0720862 + 0.0637405i
\(541\) 6.10554i 0.262498i 0.991349 + 0.131249i \(0.0418987\pi\)
−0.991349 + 0.131249i \(0.958101\pi\)
\(542\) 5.01317i 0.215334i
\(543\) 5.47627i 0.235009i
\(544\) 1.19394i 0.0511896i
\(545\) 15.7988 + 13.9697i 0.676745 + 0.598395i
\(546\) 6.15633 13.6629i 0.263466 0.584719i
\(547\) 0.775746i 0.0331685i −0.999862 0.0165843i \(-0.994721\pi\)
0.999862 0.0165843i \(-0.00527918\pi\)
\(548\) 0.911603 0.0389418
\(549\) −6.31265 −0.269417
\(550\) 26.5501 3.27504i 1.13210 0.139648i
\(551\) 21.0640i 0.897355i
\(552\) −0.806063 −0.0343083
\(553\) 51.6991 2.19847
\(554\) 8.55008i 0.363258i
\(555\) 12.3127 + 10.8872i 0.522643 + 0.462134i
\(556\) 0.836381 0.0354704
\(557\) −5.13918 −0.217754 −0.108877 0.994055i \(-0.534725\pi\)
−0.108877 + 0.994055i \(0.534725\pi\)
\(558\) 7.92478i 0.335483i
\(559\) −9.73813 + 21.6121i −0.411879 + 0.914096i
\(560\) 6.15633 6.96239i 0.260152 0.294215i
\(561\) 6.38787i 0.269696i
\(562\) 25.5125i 1.07618i
\(563\) 30.3390i 1.27864i −0.768942 0.639318i \(-0.779217\pi\)
0.768942 0.639318i \(-0.220783\pi\)
\(564\) 12.3127i 0.518456i
\(565\) −7.40105 6.54420i −0.311364 0.275316i
\(566\) 23.7235i 0.997175i
\(567\) −4.15633 −0.174549
\(568\) 8.96239i 0.376053i
\(569\) −7.25060 −0.303961 −0.151981 0.988383i \(-0.548565\pi\)
−0.151981 + 0.988383i \(0.548565\pi\)
\(570\) 4.15633 4.70052i 0.174089 0.196883i
\(571\) 16.3127 0.682663 0.341332 0.939943i \(-0.389122\pi\)
0.341332 + 0.939943i \(0.389122\pi\)
\(572\) −7.92478 + 17.5877i −0.331352 + 0.735378i
\(573\) 10.2374i 0.427675i
\(574\) 15.0132i 0.626638i
\(575\) 4.00000 0.493413i 0.166812 0.0205767i
\(576\) −1.00000 −0.0416667
\(577\) −4.85685 −0.202193 −0.101097 0.994877i \(-0.532235\pi\)
−0.101097 + 0.994877i \(0.532235\pi\)
\(578\) 15.5745 0.647814
\(579\) 9.06793i 0.376850i
\(580\) −11.1187 + 12.5745i −0.461679 + 0.522128i
\(581\) −41.7743 −1.73309
\(582\) 2.93207i 0.121538i
\(583\) −29.6239 −1.22690
\(584\) 4.08110 0.168877
\(585\) 7.35026 3.31265i 0.303896 0.136961i
\(586\) −23.9248 −0.988323
\(587\) −18.8218 −0.776859 −0.388429 0.921479i \(-0.626982\pi\)
−0.388429 + 0.921479i \(0.626982\pi\)
\(588\) 10.2750i 0.423735i
\(589\) 22.2374 0.916277
\(590\) −21.5877 19.0884i −0.888751 0.785857i
\(591\) 3.14903i 0.129534i
\(592\) −7.35026 −0.302094
\(593\) −5.59754 −0.229863 −0.114932 0.993373i \(-0.536665\pi\)
−0.114932 + 0.993373i \(0.536665\pi\)
\(594\) 5.35026 0.219524
\(595\) −8.31265 7.35026i −0.340785 0.301331i
\(596\) 10.8872i 0.445956i
\(597\) 14.1114i 0.577542i
\(598\) −1.19394 + 2.64974i −0.0488237 + 0.108356i
\(599\) 47.9511 1.95923 0.979615 0.200885i \(-0.0643816\pi\)
0.979615 + 0.200885i \(0.0643816\pi\)
\(600\) 4.96239 0.612127i 0.202589 0.0249900i
\(601\) −1.97556 −0.0805849 −0.0402924 0.999188i \(-0.512829\pi\)
−0.0402924 + 0.999188i \(0.512829\pi\)
\(602\) 27.3258i 1.11372i
\(603\) 4.57452 0.186289
\(604\) 17.7889i 0.723821i
\(605\) 26.1065 29.5247i 1.06138 1.20035i
\(606\) 5.89446i 0.239446i
\(607\) 18.1622i 0.737181i −0.929592 0.368591i \(-0.879840\pi\)
0.929592 0.368591i \(-0.120160\pi\)
\(608\) 2.80606i 0.113801i
\(609\) 31.1998i 1.26428i
\(610\) −9.35026 + 10.5745i −0.378581 + 0.428150i
\(611\) 40.4749 + 18.2374i 1.63744 + 0.737807i
\(612\) 1.19394i 0.0482620i
\(613\) −30.6761 −1.23900 −0.619498 0.784998i \(-0.712664\pi\)
−0.619498 + 0.784998i \(0.712664\pi\)
\(614\) 33.5125 1.35245
\(615\) −5.35026 + 6.05079i −0.215743 + 0.243991i
\(616\) 22.2374i 0.895971i
\(617\) 37.3258 1.50268 0.751341 0.659915i \(-0.229408\pi\)
0.751341 + 0.659915i \(0.229408\pi\)
\(618\) −3.29948 −0.132724
\(619\) 17.9814i 0.722735i 0.932423 + 0.361368i \(0.117690\pi\)
−0.932423 + 0.361368i \(0.882310\pi\)
\(620\) 13.2750 + 11.7381i 0.533138 + 0.471415i
\(621\) 0.806063 0.0323462
\(622\) −5.76257 −0.231058
\(623\) 20.9380i 0.838861i
\(624\) −1.48119 + 3.28726i −0.0592952 + 0.131596i
\(625\) −24.2506 + 6.07522i −0.970024 + 0.243009i
\(626\) 12.6253i 0.504609i
\(627\) 15.0132i 0.599568i
\(628\) 10.7757i 0.429999i
\(629\) 8.77575i 0.349912i
\(630\) −6.15633 + 6.96239i −0.245274 + 0.277388i
\(631\) 32.2374i 1.28335i −0.766976 0.641676i \(-0.778239\pi\)
0.766976 0.641676i \(-0.221761\pi\)
\(632\) −12.4387 −0.494783
\(633\) 17.4617i 0.694040i
\(634\) −3.73813 −0.148460
\(635\) 30.4241 + 26.9018i 1.20734 + 1.06756i
\(636\) −5.53690 −0.219553
\(637\) 33.7767 + 15.2193i 1.33828 + 0.603012i
\(638\) 40.1622i 1.59004i
\(639\) 8.96239i 0.354547i
\(640\) −1.48119 + 1.67513i −0.0585493 + 0.0662154i
\(641\) −12.6107 −0.498093 −0.249047 0.968492i \(-0.580117\pi\)
−0.249047 + 0.968492i \(0.580117\pi\)
\(642\) −19.7889 −0.781006
\(643\) 11.0230 0.434706 0.217353 0.976093i \(-0.430258\pi\)
0.217353 + 0.976093i \(0.430258\pi\)
\(644\) 3.35026i 0.132019i
\(645\) 9.73813 11.0132i 0.383439 0.433643i
\(646\) 3.35026 0.131814
\(647\) 29.8046i 1.17174i 0.810404 + 0.585871i \(0.199247\pi\)
−0.810404 + 0.585871i \(0.800753\pi\)
\(648\) 1.00000 0.0392837
\(649\) −68.9497 −2.70651
\(650\) 5.33804 17.2193i 0.209375 0.675398i
\(651\) −32.9380 −1.29094
\(652\) −12.0508 −0.471945
\(653\) 44.8627i 1.75561i 0.479014 + 0.877807i \(0.340994\pi\)
−0.479014 + 0.877807i \(0.659006\pi\)
\(654\) 9.43136 0.368796
\(655\) 14.5442 16.4485i 0.568289 0.642696i
\(656\) 3.61213i 0.141030i
\(657\) −4.08110 −0.159219
\(658\) −51.1754 −1.99502
\(659\) 26.9683 1.05053 0.525267 0.850937i \(-0.323965\pi\)
0.525267 + 0.850937i \(0.323965\pi\)
\(660\) 7.92478 8.96239i 0.308472 0.348861i
\(661\) 42.9537i 1.67070i 0.549715 + 0.835352i \(0.314736\pi\)
−0.549715 + 0.835352i \(0.685264\pi\)
\(662\) 1.81924i 0.0707067i
\(663\) 3.92478 + 1.76845i 0.152426 + 0.0686810i
\(664\) 10.0508 0.390046
\(665\) 19.5369 + 17.2750i 0.757609 + 0.669897i
\(666\) 7.35026 0.284817
\(667\) 6.05079i 0.234287i
\(668\) 1.61213 0.0623751
\(669\) 19.6326i 0.759040i
\(670\) 6.77575 7.66291i 0.261770 0.296044i
\(671\) 33.7743i 1.30384i
\(672\) 4.15633i 0.160334i
\(673\) 14.8627i 0.572916i 0.958093 + 0.286458i \(0.0924779\pi\)
−0.958093 + 0.286458i \(0.907522\pi\)
\(674\) 8.83638i 0.340365i
\(675\) −4.96239 + 0.612127i −0.191002 + 0.0235608i
\(676\) 8.61213 + 9.73813i 0.331236 + 0.374544i
\(677\) 0.911603i 0.0350358i −0.999847 0.0175179i \(-0.994424\pi\)
0.999847 0.0175179i \(-0.00557640\pi\)
\(678\) −4.41819 −0.169680
\(679\) −12.1866 −0.467680
\(680\) 2.00000 + 1.76845i 0.0766965 + 0.0678170i
\(681\) 4.77575i 0.183007i
\(682\) 42.3996 1.62357
\(683\) −27.1998 −1.04077 −0.520386 0.853931i \(-0.674212\pi\)
−0.520386 + 0.853931i \(0.674212\pi\)
\(684\) 2.80606i 0.107293i
\(685\) −1.35026 + 1.52705i −0.0515908 + 0.0583458i
\(686\) −13.6121 −0.519713
\(687\) 19.5672 0.746536
\(688\) 6.57452i 0.250651i
\(689\) −8.20123 + 18.2012i −0.312442 + 0.693412i
\(690\) 1.19394 1.35026i 0.0454524 0.0514036i
\(691\) 25.9697i 0.987933i 0.869481 + 0.493967i \(0.164454\pi\)
−0.869481 + 0.493967i \(0.835546\pi\)
\(692\) 1.22425i 0.0465391i
\(693\) 22.2374i 0.844730i
\(694\) 2.13586i 0.0810760i
\(695\) −1.23884 + 1.40105i −0.0469920 + 0.0531447i
\(696\) 7.50659i 0.284536i
\(697\) −4.31265 −0.163353
\(698\) 16.4934i 0.624285i
\(699\) −2.74543 −0.103842
\(700\) 2.54420 + 20.6253i 0.0961617 + 0.779563i
\(701\) −5.20853 −0.196723 −0.0983616 0.995151i \(-0.531360\pi\)
−0.0983616 + 0.995151i \(0.531360\pi\)
\(702\) 1.48119 3.28726i 0.0559041 0.124070i
\(703\) 20.6253i 0.777898i
\(704\) 5.35026i 0.201646i
\(705\) −20.6253 18.2374i −0.776794 0.686861i
\(706\) 3.86414 0.145429
\(707\) −24.4993 −0.921391
\(708\) −12.8872 −0.484329
\(709\) 6.79147i 0.255059i −0.991835 0.127530i \(-0.959295\pi\)
0.991835 0.127530i \(-0.0407048\pi\)
\(710\) 15.0132 + 13.2750i 0.563434 + 0.498203i
\(711\) 12.4387 0.466486
\(712\) 5.03761i 0.188792i
\(713\) 6.38787 0.239228
\(714\) −4.96239 −0.185713
\(715\) −17.7235 39.3258i −0.662823 1.47070i
\(716\) −1.25457 −0.0468855
\(717\) −5.29948 −0.197913
\(718\) 18.5139i 0.690932i
\(719\) −20.9986 −0.783115 −0.391558 0.920154i \(-0.628064\pi\)
−0.391558 + 0.920154i \(0.628064\pi\)
\(720\) 1.48119 1.67513i 0.0552009 0.0624284i
\(721\) 13.7137i 0.510725i
\(722\) 11.1260 0.414067
\(723\) −12.9380 −0.481168
\(724\) 5.47627 0.203524
\(725\) −4.59498 37.2506i −0.170653 1.38345i
\(726\) 17.6253i 0.654136i
\(727\) 21.4763i 0.796511i −0.917275 0.398255i \(-0.869616\pi\)
0.917275 0.398255i \(-0.130384\pi\)
\(728\) −13.6629 6.15633i −0.506381 0.228169i
\(729\) −1.00000 −0.0370370
\(730\) −6.04491 + 6.83638i −0.223732 + 0.253026i
\(731\) 7.84955 0.290326
\(732\) 6.31265i 0.233322i
\(733\) −10.5139 −0.388339 −0.194170 0.980968i \(-0.562201\pi\)
−0.194170 + 0.980968i \(0.562201\pi\)
\(734\) 23.7137i 0.875289i
\(735\) −17.2120 15.2193i −0.634875 0.561373i
\(736\) 0.806063i 0.0297119i
\(737\) 24.4749i 0.901543i
\(738\) 3.61213i 0.132964i
\(739\) 22.7454i 0.836704i −0.908285 0.418352i \(-0.862608\pi\)
0.908285 0.418352i \(-0.137392\pi\)
\(740\) 10.8872 12.3127i 0.400220 0.452622i
\(741\) −9.22425 4.15633i −0.338861 0.152686i
\(742\) 23.0132i 0.844840i
\(743\) 31.9511 1.17217 0.586087 0.810248i \(-0.300668\pi\)
0.586087 + 0.810248i \(0.300668\pi\)
\(744\) 7.92478 0.290536
\(745\) 18.2374 + 16.1260i 0.668168 + 0.590811i
\(746\) 11.1490i 0.408195i
\(747\) −10.0508 −0.367739
\(748\) 6.38787 0.233564
\(749\) 82.2492i 3.00532i
\(750\) −6.32487 + 9.21933i −0.230952 + 0.336642i
\(751\) 11.5975 0.423200 0.211600 0.977356i \(-0.432133\pi\)
0.211600 + 0.977356i \(0.432133\pi\)
\(752\) 12.3127 0.448996
\(753\) 8.10554i 0.295382i
\(754\) 24.6761 + 11.1187i 0.898650 + 0.404920i
\(755\) −29.7988 26.3488i −1.08449 0.958933i
\(756\) 4.15633i 0.151164i
\(757\) 33.5125i 1.21803i −0.793158 0.609016i \(-0.791565\pi\)
0.793158 0.609016i \(-0.208435\pi\)
\(758\) 38.7572i 1.40772i
\(759\) 4.31265i 0.156539i
\(760\) −4.70052 4.15633i −0.170506 0.150766i
\(761\) 36.7123i 1.33082i 0.746478 + 0.665410i \(0.231743\pi\)
−0.746478 + 0.665410i \(0.768257\pi\)
\(762\) 18.1622 0.657947
\(763\) 39.1998i 1.41913i
\(764\) −10.2374 −0.370377
\(765\) −2.00000 1.76845i −0.0723102 0.0639385i
\(766\) 1.76257 0.0636843
\(767\) −19.0884 + 42.3634i −0.689242 + 1.52966i
\(768\) 1.00000i 0.0360844i
\(769\) 45.4010i 1.63720i −0.574361 0.818602i \(-0.694750\pi\)
0.574361 0.818602i \(-0.305250\pi\)
\(770\) 37.2506 + 32.9380i 1.34242 + 1.18700i
\(771\) 12.0567 0.434210
\(772\) 9.06793 0.326362
\(773\) −2.52373 −0.0907723 −0.0453861 0.998970i \(-0.514452\pi\)
−0.0453861 + 0.998970i \(0.514452\pi\)
\(774\) 6.57452i 0.236316i
\(775\) −39.3258 + 4.85097i −1.41263 + 0.174252i
\(776\) 2.93207 0.105255
\(777\) 30.5501i 1.09598i
\(778\) 34.0567 1.22099
\(779\) 10.1359 0.363155
\(780\) −3.31265 7.35026i −0.118612 0.263182i
\(781\) 47.9511 1.71583
\(782\) 0.962389 0.0344149
\(783\) 7.50659i 0.268264i
\(784\) 10.2750 0.366966
\(785\) 18.0508 + 15.9610i 0.644260 + 0.569672i