Properties

Label 690.3.k.a.277.4
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.4
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.90173 + 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 + 2.37572i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.90173 + 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 + 2.37572i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-6.52595 + 2.72250i) q^{10} -8.18971 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.42310 + 7.42310i) q^{13} +4.75145i q^{14} +(-3.33436 - 7.99262i) q^{15} -4.00000 q^{16} +(8.23366 + 8.23366i) q^{17} +(3.00000 - 3.00000i) q^{18} -2.11038i q^{19} +(-9.24845 - 3.80345i) q^{20} -5.81931 q^{21} +(-8.18971 - 8.18971i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-17.7669 - 17.5880i) q^{25} -14.8462 q^{26} +(3.67423 + 3.67423i) q^{27} +(-4.75145 + 4.75145i) q^{28} -15.8463i q^{29} +(4.65826 - 11.3270i) q^{30} -15.0787 q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.0303 - 10.0303i) q^{33} +16.4673i q^{34} +(-15.5039 + 6.46790i) q^{35} +6.00000 q^{36} +(-14.2154 - 14.2154i) q^{37} +(2.11038 - 2.11038i) q^{38} -18.1828i q^{39} +(-5.44499 - 13.0519i) q^{40} +7.01600 q^{41} +(-5.81931 - 5.81931i) q^{42} +(-3.12385 + 3.12385i) q^{43} -16.3794i q^{44} +(13.8727 + 5.70518i) q^{45} -6.78233 q^{46} +(29.7144 + 29.7144i) q^{47} +(4.89898 - 4.89898i) q^{48} -37.7119i q^{49} +(-0.178849 - 35.3549i) q^{50} -20.1683 q^{51} +(-14.8462 - 14.8462i) q^{52} +(17.6122 - 17.6122i) q^{53} +7.34847i q^{54} +(15.5746 - 37.8710i) q^{55} -9.50289 q^{56} +(2.58468 + 2.58468i) q^{57} +(15.8463 - 15.8463i) q^{58} +26.4258i q^{59} +(15.9852 - 6.66872i) q^{60} -28.1753 q^{61} +(-15.0787 - 15.0787i) q^{62} +(7.12717 - 7.12717i) q^{63} -8.00000i q^{64} +(-20.2094 - 48.4428i) q^{65} +20.0606 q^{66} +(-66.9478 - 66.9478i) q^{67} +(-16.4673 + 16.4673i) q^{68} -8.30662i q^{69} +(-21.9717 - 9.03595i) q^{70} -67.4077 q^{71} +(6.00000 + 6.00000i) q^{72} +(16.9909 - 16.9909i) q^{73} -28.4307i q^{74} +(43.3007 - 0.219044i) q^{75} +4.22077 q^{76} +(-19.4565 - 19.4565i) q^{77} +(18.1828 - 18.1828i) q^{78} -75.5612i q^{79} +(7.60691 - 18.4969i) q^{80} -9.00000 q^{81} +(7.01600 + 7.01600i) q^{82} +(-53.8232 + 53.8232i) q^{83} -11.6386i q^{84} +(-53.7325 + 22.4161i) q^{85} -6.24770 q^{86} +(19.4077 + 19.4077i) q^{87} +(16.3794 - 16.3794i) q^{88} +76.6024i q^{89} +(8.16749 + 19.5778i) q^{90} -35.2705 q^{91} +(-6.78233 - 6.78233i) q^{92} +(18.4675 - 18.4675i) q^{93} +59.4288i q^{94} +(9.75888 + 4.01337i) q^{95} +9.79796 q^{96} +(34.7900 + 34.7900i) q^{97} +(37.7119 - 37.7119i) q^{98} +24.5691i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −1.90173 + 4.62422i −0.380345 + 0.924845i
\(6\) −2.44949 −0.408248
\(7\) 2.37572 + 2.37572i 0.339389 + 0.339389i 0.856137 0.516748i \(-0.172858\pi\)
−0.516748 + 0.856137i \(0.672858\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.52595 + 2.72250i −0.652595 + 0.272250i
\(11\) −8.18971 −0.744519 −0.372260 0.928129i \(-0.621417\pi\)
−0.372260 + 0.928129i \(0.621417\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.42310 + 7.42310i −0.571008 + 0.571008i −0.932410 0.361402i \(-0.882298\pi\)
0.361402 + 0.932410i \(0.382298\pi\)
\(14\) 4.75145i 0.339389i
\(15\) −3.33436 7.99262i −0.222291 0.532842i
\(16\) −4.00000 −0.250000
\(17\) 8.23366 + 8.23366i 0.484333 + 0.484333i 0.906512 0.422179i \(-0.138735\pi\)
−0.422179 + 0.906512i \(0.638735\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 2.11038i 0.111073i −0.998457 0.0555364i \(-0.982313\pi\)
0.998457 0.0555364i \(-0.0176869\pi\)
\(20\) −9.24845 3.80345i −0.462422 0.190173i
\(21\) −5.81931 −0.277110
\(22\) −8.18971 8.18971i −0.372260 0.372260i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −17.7669 17.5880i −0.710675 0.703521i
\(26\) −14.8462 −0.571008
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −4.75145 + 4.75145i −0.169695 + 0.169695i
\(29\) 15.8463i 0.546424i −0.961954 0.273212i \(-0.911914\pi\)
0.961954 0.273212i \(-0.0880860\pi\)
\(30\) 4.65826 11.3270i 0.155275 0.377566i
\(31\) −15.0787 −0.486409 −0.243204 0.969975i \(-0.578199\pi\)
−0.243204 + 0.969975i \(0.578199\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 10.0303 10.0303i 0.303949 0.303949i
\(34\) 16.4673i 0.484333i
\(35\) −15.5039 + 6.46790i −0.442967 + 0.184797i
\(36\) 6.00000 0.166667
\(37\) −14.2154 14.2154i −0.384199 0.384199i 0.488413 0.872612i \(-0.337576\pi\)
−0.872612 + 0.488413i \(0.837576\pi\)
\(38\) 2.11038 2.11038i 0.0555364 0.0555364i
\(39\) 18.1828i 0.466226i
\(40\) −5.44499 13.0519i −0.136125 0.326297i
\(41\) 7.01600 0.171122 0.0855609 0.996333i \(-0.472732\pi\)
0.0855609 + 0.996333i \(0.472732\pi\)
\(42\) −5.81931 5.81931i −0.138555 0.138555i
\(43\) −3.12385 + 3.12385i −0.0726476 + 0.0726476i −0.742497 0.669849i \(-0.766359\pi\)
0.669849 + 0.742497i \(0.266359\pi\)
\(44\) 16.3794i 0.372260i
\(45\) 13.8727 + 5.70518i 0.308282 + 0.126782i
\(46\) −6.78233 −0.147442
\(47\) 29.7144 + 29.7144i 0.632221 + 0.632221i 0.948625 0.316404i \(-0.102475\pi\)
−0.316404 + 0.948625i \(0.602475\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 37.7119i 0.769630i
\(50\) −0.178849 35.3549i −0.00357698 0.707098i
\(51\) −20.1683 −0.395456
\(52\) −14.8462 14.8462i −0.285504 0.285504i
\(53\) 17.6122 17.6122i 0.332306 0.332306i −0.521155 0.853462i \(-0.674499\pi\)
0.853462 + 0.521155i \(0.174499\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 15.5746 37.8710i 0.283174 0.688565i
\(56\) −9.50289 −0.169695
\(57\) 2.58468 + 2.58468i 0.0453453 + 0.0453453i
\(58\) 15.8463 15.8463i 0.273212 0.273212i
\(59\) 26.4258i 0.447895i 0.974601 + 0.223947i \(0.0718944\pi\)
−0.974601 + 0.223947i \(0.928106\pi\)
\(60\) 15.9852 6.66872i 0.266421 0.111145i
\(61\) −28.1753 −0.461889 −0.230945 0.972967i \(-0.574182\pi\)
−0.230945 + 0.972967i \(0.574182\pi\)
\(62\) −15.0787 15.0787i −0.243204 0.243204i
\(63\) 7.12717 7.12717i 0.113130 0.113130i
\(64\) 8.00000i 0.125000i
\(65\) −20.2094 48.4428i −0.310913 0.745273i
\(66\) 20.0606 0.303949
\(67\) −66.9478 66.9478i −0.999221 0.999221i 0.000778970 1.00000i \(-0.499752\pi\)
−1.00000 0.000778970i \(0.999752\pi\)
\(68\) −16.4673 + 16.4673i −0.242166 + 0.242166i
\(69\) 8.30662i 0.120386i
\(70\) −21.9717 9.03595i −0.313882 0.129085i
\(71\) −67.4077 −0.949405 −0.474702 0.880146i \(-0.657444\pi\)
−0.474702 + 0.880146i \(0.657444\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 16.9909 16.9909i 0.232752 0.232752i −0.581089 0.813840i \(-0.697373\pi\)
0.813840 + 0.581089i \(0.197373\pi\)
\(74\) 28.4307i 0.384199i
\(75\) 43.3007 0.219044i 0.577343 0.00292059i
\(76\) 4.22077 0.0555364
\(77\) −19.4565 19.4565i −0.252682 0.252682i
\(78\) 18.1828 18.1828i 0.233113 0.233113i
\(79\) 75.5612i 0.956471i −0.878232 0.478235i \(-0.841277\pi\)
0.878232 0.478235i \(-0.158723\pi\)
\(80\) 7.60691 18.4969i 0.0950864 0.231211i
\(81\) −9.00000 −0.111111
\(82\) 7.01600 + 7.01600i 0.0855609 + 0.0855609i
\(83\) −53.8232 + 53.8232i −0.648473 + 0.648473i −0.952624 0.304151i \(-0.901627\pi\)
0.304151 + 0.952624i \(0.401627\pi\)
\(84\) 11.6386i 0.138555i
\(85\) −53.7325 + 22.4161i −0.632147 + 0.263719i
\(86\) −6.24770 −0.0726476
\(87\) 19.4077 + 19.4077i 0.223076 + 0.223076i
\(88\) 16.3794 16.3794i 0.186130 0.186130i
\(89\) 76.6024i 0.860701i 0.902662 + 0.430351i \(0.141610\pi\)
−0.902662 + 0.430351i \(0.858390\pi\)
\(90\) 8.16749 + 19.5778i 0.0907498 + 0.217532i
\(91\) −35.2705 −0.387587
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 18.4675 18.4675i 0.198576 0.198576i
\(94\) 59.4288i 0.632221i
\(95\) 9.75888 + 4.01337i 0.102725 + 0.0422460i
\(96\) 9.79796 0.102062
\(97\) 34.7900 + 34.7900i 0.358660 + 0.358660i 0.863319 0.504659i \(-0.168382\pi\)
−0.504659 + 0.863319i \(0.668382\pi\)
\(98\) 37.7119 37.7119i 0.384815 0.384815i
\(99\) 24.5691i 0.248173i
\(100\) 35.1760 35.5337i 0.351760 0.355337i
\(101\) −0.567660 −0.00562040 −0.00281020 0.999996i \(-0.500895\pi\)
−0.00281020 + 0.999996i \(0.500895\pi\)
\(102\) −20.1683 20.1683i −0.197728 0.197728i
\(103\) −12.3289 + 12.3289i −0.119698 + 0.119698i −0.764418 0.644720i \(-0.776974\pi\)
0.644720 + 0.764418i \(0.276974\pi\)
\(104\) 29.6924i 0.285504i
\(105\) 11.0667 26.9098i 0.105398 0.256284i
\(106\) 35.2245 0.332306
\(107\) 31.8401 + 31.8401i 0.297571 + 0.297571i 0.840062 0.542491i \(-0.182519\pi\)
−0.542491 + 0.840062i \(0.682519\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 178.228i 1.63512i 0.575844 + 0.817559i \(0.304673\pi\)
−0.575844 + 0.817559i \(0.695327\pi\)
\(110\) 53.4456 22.2965i 0.485870 0.202695i
\(111\) 34.8204 0.313697
\(112\) −9.50289 9.50289i −0.0848473 0.0848473i
\(113\) −73.7395 + 73.7395i −0.652562 + 0.652562i −0.953609 0.301047i \(-0.902664\pi\)
0.301047 + 0.953609i \(0.402664\pi\)
\(114\) 5.16936i 0.0453453i
\(115\) −9.23243 22.1306i −0.0802820 0.192440i
\(116\) 31.6926 0.273212
\(117\) 22.2693 + 22.2693i 0.190336 + 0.190336i
\(118\) −26.4258 + 26.4258i −0.223947 + 0.223947i
\(119\) 39.1218i 0.328755i
\(120\) 22.6540 + 9.31652i 0.188783 + 0.0776377i
\(121\) −53.9286 −0.445691
\(122\) −28.1753 28.1753i −0.230945 0.230945i
\(123\) −8.59281 + 8.59281i −0.0698602 + 0.0698602i
\(124\) 30.1573i 0.243204i
\(125\) 115.119 48.7103i 0.920949 0.389683i
\(126\) 14.2543 0.113130
\(127\) 11.2783 + 11.2783i 0.0888056 + 0.0888056i 0.750114 0.661308i \(-0.229999\pi\)
−0.661308 + 0.750114i \(0.729999\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 7.65183i 0.0593165i
\(130\) 28.2334 68.6521i 0.217180 0.528093i
\(131\) −125.767 −0.960057 −0.480028 0.877253i \(-0.659374\pi\)
−0.480028 + 0.877253i \(0.659374\pi\)
\(132\) 20.0606 + 20.0606i 0.151974 + 0.151974i
\(133\) 5.01369 5.01369i 0.0376969 0.0376969i
\(134\) 133.896i 0.999221i
\(135\) −23.9779 + 10.0031i −0.177614 + 0.0740969i
\(136\) −32.9346 −0.242166
\(137\) 89.3505 + 89.3505i 0.652194 + 0.652194i 0.953521 0.301327i \(-0.0974296\pi\)
−0.301327 + 0.953521i \(0.597430\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 61.2074i 0.440341i 0.975461 + 0.220170i \(0.0706613\pi\)
−0.975461 + 0.220170i \(0.929339\pi\)
\(140\) −12.9358 31.0077i −0.0923985 0.221484i
\(141\) −72.7851 −0.516206
\(142\) −67.4077 67.4077i −0.474702 0.474702i
\(143\) 60.7930 60.7930i 0.425126 0.425126i
\(144\) 12.0000i 0.0833333i
\(145\) 73.2767 + 30.1353i 0.505357 + 0.207830i
\(146\) 33.9817 0.232752
\(147\) 46.1874 + 46.1874i 0.314200 + 0.314200i
\(148\) 28.4307 28.4307i 0.192099 0.192099i
\(149\) 245.889i 1.65026i 0.564943 + 0.825130i \(0.308898\pi\)
−0.564943 + 0.825130i \(0.691102\pi\)
\(150\) 43.5198 + 43.0817i 0.290132 + 0.287211i
\(151\) −8.23880 −0.0545616 −0.0272808 0.999628i \(-0.508685\pi\)
−0.0272808 + 0.999628i \(0.508685\pi\)
\(152\) 4.22077 + 4.22077i 0.0277682 + 0.0277682i
\(153\) 24.7010 24.7010i 0.161444 0.161444i
\(154\) 38.9130i 0.252682i
\(155\) 28.6755 69.7271i 0.185003 0.449852i
\(156\) 36.3656 0.233113
\(157\) −57.9326 57.9326i −0.368997 0.368997i 0.498114 0.867111i \(-0.334026\pi\)
−0.867111 + 0.498114i \(0.834026\pi\)
\(158\) 75.5612 75.5612i 0.478235 0.478235i
\(159\) 43.1410i 0.271327i
\(160\) 26.1038 10.8900i 0.163149 0.0680624i
\(161\) −16.1129 −0.100080
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −54.9037 + 54.9037i −0.336832 + 0.336832i −0.855174 0.518341i \(-0.826550\pi\)
0.518341 + 0.855174i \(0.326550\pi\)
\(164\) 14.0320i 0.0855609i
\(165\) 27.3075 + 65.4573i 0.165500 + 0.396711i
\(166\) −107.646 −0.648473
\(167\) 40.0337 + 40.0337i 0.239723 + 0.239723i 0.816735 0.577013i \(-0.195782\pi\)
−0.577013 + 0.816735i \(0.695782\pi\)
\(168\) 11.6386 11.6386i 0.0692775 0.0692775i
\(169\) 58.7952i 0.347901i
\(170\) −76.1486 31.3164i −0.447933 0.184214i
\(171\) −6.33115 −0.0370243
\(172\) −6.24770 6.24770i −0.0363238 0.0363238i
\(173\) 72.6221 72.6221i 0.419781 0.419781i −0.465347 0.885128i \(-0.654071\pi\)
0.885128 + 0.465347i \(0.154071\pi\)
\(174\) 38.8153i 0.223076i
\(175\) −0.424896 83.9934i −0.00242798 0.479962i
\(176\) 32.7588 0.186130
\(177\) −32.3649 32.3649i −0.182852 0.182852i
\(178\) −76.6024 + 76.6024i −0.430351 + 0.430351i
\(179\) 294.692i 1.64632i 0.567808 + 0.823161i \(0.307792\pi\)
−0.567808 + 0.823161i \(0.692208\pi\)
\(180\) −11.4104 + 27.7453i −0.0633909 + 0.154141i
\(181\) 15.6531 0.0864813 0.0432407 0.999065i \(-0.486232\pi\)
0.0432407 + 0.999065i \(0.486232\pi\)
\(182\) −35.2705 35.2705i −0.193794 0.193794i
\(183\) 34.5075 34.5075i 0.188566 0.188566i
\(184\) 13.5647i 0.0737210i
\(185\) 92.7687 38.7012i 0.501452 0.209196i
\(186\) 36.9351 0.198576
\(187\) −67.4313 67.4313i −0.360595 0.360595i
\(188\) −59.4288 + 59.4288i −0.316111 + 0.316111i
\(189\) 17.4579i 0.0923700i
\(190\) 5.74551 + 13.7723i 0.0302395 + 0.0724855i
\(191\) 128.180 0.671097 0.335548 0.942023i \(-0.391078\pi\)
0.335548 + 0.942023i \(0.391078\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −29.7003 + 29.7003i −0.153888 + 0.153888i −0.779852 0.625964i \(-0.784706\pi\)
0.625964 + 0.779852i \(0.284706\pi\)
\(194\) 69.5800i 0.358660i
\(195\) 84.0813 + 34.5787i 0.431186 + 0.177327i
\(196\) 75.4238 0.384815
\(197\) 122.742 + 122.742i 0.623057 + 0.623057i 0.946312 0.323255i \(-0.104777\pi\)
−0.323255 + 0.946312i \(0.604777\pi\)
\(198\) −24.5691 + 24.5691i −0.124087 + 0.124087i
\(199\) 10.9495i 0.0550228i −0.999621 0.0275114i \(-0.991242\pi\)
0.999621 0.0275114i \(-0.00875825\pi\)
\(200\) 70.7098 0.357698i 0.353549 0.00178849i
\(201\) 163.988 0.815860
\(202\) −0.567660 0.567660i −0.00281020 0.00281020i
\(203\) 37.6464 37.6464i 0.185450 0.185450i
\(204\) 40.3365i 0.197728i
\(205\) −13.3425 + 32.4435i −0.0650854 + 0.158261i
\(206\) −24.6578 −0.119698
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 29.6924 29.6924i 0.142752 0.142752i
\(209\) 17.2834i 0.0826958i
\(210\) 37.9765 15.8430i 0.180841 0.0754431i
\(211\) −371.360 −1.76000 −0.879999 0.474975i \(-0.842457\pi\)
−0.879999 + 0.474975i \(0.842457\pi\)
\(212\) 35.2245 + 35.2245i 0.166153 + 0.166153i
\(213\) 82.5573 82.5573i 0.387593 0.387593i
\(214\) 63.6802i 0.297571i
\(215\) −8.50466 20.3861i −0.0395566 0.0948190i
\(216\) −14.6969 −0.0680414
\(217\) −35.8228 35.8228i −0.165082 0.165082i
\(218\) −178.228 + 178.228i −0.817559 + 0.817559i
\(219\) 41.6189i 0.190041i
\(220\) 75.7421 + 31.1492i 0.344282 + 0.141587i
\(221\) −122.239 −0.553116
\(222\) 34.8204 + 34.8204i 0.156849 + 0.156849i
\(223\) −75.9931 + 75.9931i −0.340776 + 0.340776i −0.856659 0.515883i \(-0.827464\pi\)
0.515883 + 0.856659i \(0.327464\pi\)
\(224\) 19.0058i 0.0848473i
\(225\) −52.7641 + 53.3006i −0.234507 + 0.236892i
\(226\) −147.479 −0.652562
\(227\) 172.585 + 172.585i 0.760287 + 0.760287i 0.976374 0.216087i \(-0.0693295\pi\)
−0.216087 + 0.976374i \(0.569330\pi\)
\(228\) −5.16936 + 5.16936i −0.0226726 + 0.0226726i
\(229\) 73.4614i 0.320792i 0.987053 + 0.160396i \(0.0512772\pi\)
−0.987053 + 0.160396i \(0.948723\pi\)
\(230\) 12.8981 31.3630i 0.0560789 0.136361i
\(231\) 47.6585 0.206314
\(232\) 31.6926 + 31.6926i 0.136606 + 0.136606i
\(233\) 284.973 284.973i 1.22306 1.22306i 0.256519 0.966539i \(-0.417424\pi\)
0.966539 0.256519i \(-0.0825757\pi\)
\(234\) 44.5386i 0.190336i
\(235\) −193.915 + 80.8973i −0.825168 + 0.344244i
\(236\) −52.8516 −0.223947
\(237\) 92.5432 + 92.5432i 0.390478 + 0.390478i
\(238\) −39.1218 + 39.1218i −0.164377 + 0.164377i
\(239\) 117.112i 0.490009i 0.969522 + 0.245005i \(0.0787895\pi\)
−0.969522 + 0.245005i \(0.921211\pi\)
\(240\) 13.3374 + 31.9705i 0.0555727 + 0.133210i
\(241\) 178.634 0.741219 0.370610 0.928789i \(-0.379149\pi\)
0.370610 + 0.928789i \(0.379149\pi\)
\(242\) −53.9286 53.9286i −0.222846 0.222846i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 56.3505i 0.230945i
\(245\) 174.388 + 71.7177i 0.711788 + 0.292725i
\(246\) −17.1856 −0.0698602
\(247\) 15.6656 + 15.6656i 0.0634234 + 0.0634234i
\(248\) 30.1573 30.1573i 0.121602 0.121602i
\(249\) 131.839i 0.529476i
\(250\) 163.829 + 66.4083i 0.655316 + 0.265633i
\(251\) −350.780 −1.39753 −0.698765 0.715351i \(-0.746267\pi\)
−0.698765 + 0.715351i \(0.746267\pi\)
\(252\) 14.2543 + 14.2543i 0.0565648 + 0.0565648i
\(253\) 27.7727 27.7727i 0.109773 0.109773i
\(254\) 22.5566i 0.0888056i
\(255\) 38.3545 93.2626i 0.150410 0.365736i
\(256\) 16.0000 0.0625000
\(257\) 108.104 + 108.104i 0.420639 + 0.420639i 0.885424 0.464785i \(-0.153868\pi\)
−0.464785 + 0.885424i \(0.653868\pi\)
\(258\) 7.65183 7.65183i 0.0296583 0.0296583i
\(259\) 67.5435i 0.260786i
\(260\) 96.8855 40.4187i 0.372637 0.155457i
\(261\) −47.5388 −0.182141
\(262\) −125.767 125.767i −0.480028 0.480028i
\(263\) 78.3826 78.3826i 0.298033 0.298033i −0.542210 0.840243i \(-0.682412\pi\)
0.840243 + 0.542210i \(0.182412\pi\)
\(264\) 40.1212i 0.151974i
\(265\) 47.9492 + 114.937i 0.180941 + 0.433723i
\(266\) 10.0274 0.0376969
\(267\) −93.8184 93.8184i −0.351380 0.351380i
\(268\) 133.896 133.896i 0.499610 0.499610i
\(269\) 326.796i 1.21485i 0.794376 + 0.607427i \(0.207798\pi\)
−0.794376 + 0.607427i \(0.792202\pi\)
\(270\) −33.9810 13.9748i −0.125855 0.0517585i
\(271\) −312.784 −1.15419 −0.577093 0.816679i \(-0.695813\pi\)
−0.577093 + 0.816679i \(0.695813\pi\)
\(272\) −32.9346 32.9346i −0.121083 0.121083i
\(273\) 43.1973 43.1973i 0.158232 0.158232i
\(274\) 178.701i 0.652194i
\(275\) 145.506 + 144.041i 0.529111 + 0.523785i
\(276\) 16.6132 0.0601929
\(277\) −64.9224 64.9224i −0.234377 0.234377i 0.580140 0.814517i \(-0.302998\pi\)
−0.814517 + 0.580140i \(0.802998\pi\)
\(278\) −61.2074 + 61.2074i −0.220170 + 0.220170i
\(279\) 45.2360i 0.162136i
\(280\) 18.0719 43.9435i 0.0645425 0.156941i
\(281\) −222.033 −0.790154 −0.395077 0.918648i \(-0.629282\pi\)
−0.395077 + 0.918648i \(0.629282\pi\)
\(282\) −72.7851 72.7851i −0.258103 0.258103i
\(283\) −264.201 + 264.201i −0.933574 + 0.933574i −0.997927 0.0643532i \(-0.979502\pi\)
0.0643532 + 0.997927i \(0.479502\pi\)
\(284\) 134.815i 0.474702i
\(285\) −16.8675 + 7.03678i −0.0591842 + 0.0246905i
\(286\) 121.586 0.425126
\(287\) 16.6681 + 16.6681i 0.0580769 + 0.0580769i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 153.414i 0.530843i
\(290\) 43.1414 + 103.412i 0.148764 + 0.356593i
\(291\) −85.2178 −0.292845
\(292\) 33.9817 + 33.9817i 0.116376 + 0.116376i
\(293\) 150.293 150.293i 0.512945 0.512945i −0.402483 0.915428i \(-0.631853\pi\)
0.915428 + 0.402483i \(0.131853\pi\)
\(294\) 92.3749i 0.314200i
\(295\) −122.199 50.2546i −0.414233 0.170355i
\(296\) 56.8614 0.192099
\(297\) −30.0909 30.0909i −0.101316 0.101316i
\(298\) −245.889 + 245.889i −0.825130 + 0.825130i
\(299\) 50.3459i 0.168381i
\(300\) 0.438089 + 86.6014i 0.00146030 + 0.288671i
\(301\) −14.8428 −0.0493116
\(302\) −8.23880 8.23880i −0.0272808 0.0272808i
\(303\) 0.695239 0.695239i 0.00229452 0.00229452i
\(304\) 8.44153i 0.0277682i
\(305\) 53.5816 130.289i 0.175678 0.427176i
\(306\) 49.4020 0.161444
\(307\) −371.701 371.701i −1.21075 1.21075i −0.970780 0.239971i \(-0.922862\pi\)
−0.239971 0.970780i \(-0.577138\pi\)
\(308\) 38.9130 38.9130i 0.126341 0.126341i
\(309\) 30.1995i 0.0977331i
\(310\) 98.4027 41.0516i 0.317428 0.132425i
\(311\) 24.8526 0.0799118 0.0399559 0.999201i \(-0.487278\pi\)
0.0399559 + 0.999201i \(0.487278\pi\)
\(312\) 36.3656 + 36.3656i 0.116556 + 0.116556i
\(313\) 159.376 159.376i 0.509189 0.509189i −0.405088 0.914277i \(-0.632759\pi\)
0.914277 + 0.405088i \(0.132759\pi\)
\(314\) 115.865i 0.368997i
\(315\) 19.4037 + 46.5116i 0.0615990 + 0.147656i
\(316\) 151.122 0.478235
\(317\) 161.728 + 161.728i 0.510182 + 0.510182i 0.914582 0.404400i \(-0.132520\pi\)
−0.404400 + 0.914582i \(0.632520\pi\)
\(318\) −43.1410 + 43.1410i −0.135664 + 0.135664i
\(319\) 129.776i 0.406823i
\(320\) 36.9938 + 15.2138i 0.115606 + 0.0475432i
\(321\) −77.9920 −0.242966
\(322\) −16.1129 16.1129i −0.0500402 0.0500402i
\(323\) 17.3762 17.3762i 0.0537962 0.0537962i
\(324\) 18.0000i 0.0555556i
\(325\) 262.443 1.32761i 0.807516 0.00408497i
\(326\) −109.807 −0.336832
\(327\) −218.284 218.284i −0.667534 0.667534i
\(328\) −14.0320 + 14.0320i −0.0427805 + 0.0427805i
\(329\) 141.186i 0.429138i
\(330\) −38.1498 + 92.7647i −0.115606 + 0.281105i
\(331\) −404.107 −1.22087 −0.610434 0.792067i \(-0.709005\pi\)
−0.610434 + 0.792067i \(0.709005\pi\)
\(332\) −107.646 107.646i −0.324236 0.324236i
\(333\) −42.6461 + 42.6461i −0.128066 + 0.128066i
\(334\) 80.0673i 0.239723i
\(335\) 436.898 182.265i 1.30417 0.544075i
\(336\) 23.2772 0.0692775
\(337\) −49.6359 49.6359i −0.147288 0.147288i 0.629618 0.776905i \(-0.283212\pi\)
−0.776905 + 0.629618i \(0.783212\pi\)
\(338\) −58.7952 + 58.7952i −0.173950 + 0.173950i
\(339\) 180.624i 0.532815i
\(340\) −44.8322 107.465i −0.131859 0.316073i
\(341\) 123.490 0.362141
\(342\) −6.33115 6.33115i −0.0185121 0.0185121i
\(343\) 206.003 206.003i 0.600593 0.600593i
\(344\) 12.4954i 0.0363238i
\(345\) 38.4117 + 15.7969i 0.111338 + 0.0457882i
\(346\) 145.244 0.419781
\(347\) −37.8258 37.8258i −0.109008 0.109008i 0.650499 0.759507i \(-0.274560\pi\)
−0.759507 + 0.650499i \(0.774560\pi\)
\(348\) −38.8153 + 38.8153i −0.111538 + 0.111538i
\(349\) 608.019i 1.74217i 0.491129 + 0.871087i \(0.336584\pi\)
−0.491129 + 0.871087i \(0.663416\pi\)
\(350\) 83.5685 84.4183i 0.238767 0.241195i
\(351\) −54.5484 −0.155409
\(352\) 32.7588 + 32.7588i 0.0930649 + 0.0930649i
\(353\) 102.065 102.065i 0.289135 0.289135i −0.547603 0.836738i \(-0.684460\pi\)
0.836738 + 0.547603i \(0.184460\pi\)
\(354\) 64.7297i 0.182852i
\(355\) 128.191 311.708i 0.361102 0.878052i
\(356\) −153.205 −0.430351
\(357\) −47.9142 47.9142i −0.134214 0.134214i
\(358\) −294.692 + 294.692i −0.823161 + 0.823161i
\(359\) 392.739i 1.09398i −0.837139 0.546990i \(-0.815773\pi\)
0.837139 0.546990i \(-0.184227\pi\)
\(360\) −39.1557 + 16.3350i −0.108766 + 0.0453749i
\(361\) 356.546 0.987663
\(362\) 15.6531 + 15.6531i 0.0432407 + 0.0432407i
\(363\) 66.0488 66.0488i 0.181953 0.181953i
\(364\) 70.5409i 0.193794i
\(365\) 46.2575 + 110.882i 0.126733 + 0.303785i
\(366\) 69.0150 0.188566
\(367\) 41.5309 + 41.5309i 0.113163 + 0.113163i 0.761421 0.648258i \(-0.224502\pi\)
−0.648258 + 0.761421i \(0.724502\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 21.0480i 0.0570406i
\(370\) 131.470 + 54.0675i 0.355324 + 0.146128i
\(371\) 83.6836 0.225562
\(372\) 36.9351 + 36.9351i 0.0992878 + 0.0992878i
\(373\) −188.716 + 188.716i −0.505941 + 0.505941i −0.913278 0.407337i \(-0.866457\pi\)
0.407337 + 0.913278i \(0.366457\pi\)
\(374\) 134.863i 0.360595i
\(375\) −81.3332 + 200.649i −0.216889 + 0.535063i
\(376\) −118.858 −0.316111
\(377\) 117.629 + 117.629i 0.312012 + 0.312012i
\(378\) −17.4579 + 17.4579i −0.0461850 + 0.0461850i
\(379\) 143.699i 0.379152i −0.981866 0.189576i \(-0.939289\pi\)
0.981866 0.189576i \(-0.0607113\pi\)
\(380\) −8.02675 + 19.5178i −0.0211230 + 0.0513625i
\(381\) −27.6261 −0.0725095
\(382\) 128.180 + 128.180i 0.335548 + 0.335548i
\(383\) 98.2112 98.2112i 0.256426 0.256426i −0.567173 0.823599i \(-0.691963\pi\)
0.823599 + 0.567173i \(0.191963\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 126.972 52.9702i 0.329798 0.137585i
\(386\) −59.4006 −0.153888
\(387\) 9.37154 + 9.37154i 0.0242159 + 0.0242159i
\(388\) −69.5800 + 69.5800i −0.179330 + 0.179330i
\(389\) 244.042i 0.627357i −0.949529 0.313678i \(-0.898439\pi\)
0.949529 0.313678i \(-0.101561\pi\)
\(390\) 49.5026 + 118.660i 0.126930 + 0.304257i
\(391\) −55.8434 −0.142822
\(392\) 75.4238 + 75.4238i 0.192408 + 0.192408i
\(393\) 154.033 154.033i 0.391941 0.391941i
\(394\) 245.484i 0.623057i
\(395\) 349.412 + 143.697i 0.884587 + 0.363789i
\(396\) −49.1383 −0.124087
\(397\) −168.912 168.912i −0.425470 0.425470i 0.461612 0.887082i \(-0.347271\pi\)
−0.887082 + 0.461612i \(0.847271\pi\)
\(398\) 10.9495 10.9495i 0.0275114 0.0275114i
\(399\) 12.2810i 0.0307794i
\(400\) 71.0675 + 70.3521i 0.177669 + 0.175880i
\(401\) −226.855 −0.565724 −0.282862 0.959161i \(-0.591284\pi\)
−0.282862 + 0.959161i \(0.591284\pi\)
\(402\) 163.988 + 163.988i 0.407930 + 0.407930i
\(403\) 111.930 111.930i 0.277743 0.277743i
\(404\) 1.13532i 0.00281020i
\(405\) 17.1155 41.6180i 0.0422606 0.102761i
\(406\) 75.2928 0.185450
\(407\) 116.420 + 116.420i 0.286043 + 0.286043i
\(408\) 40.3365 40.3365i 0.0988641 0.0988641i
\(409\) 193.056i 0.472021i 0.971751 + 0.236010i \(0.0758399\pi\)
−0.971751 + 0.236010i \(0.924160\pi\)
\(410\) −45.7860 + 19.1010i −0.111673 + 0.0465878i
\(411\) −218.863 −0.532514
\(412\) −24.6578 24.6578i −0.0598490 0.0598490i
\(413\) −62.7804 + 62.7804i −0.152011 + 0.152011i
\(414\) 20.3470i 0.0491473i
\(415\) −146.533 351.248i −0.353093 0.846380i
\(416\) 59.3848 0.142752
\(417\) −74.9634 74.9634i −0.179768 0.179768i
\(418\) −17.2834 + 17.2834i −0.0413479 + 0.0413479i
\(419\) 418.810i 0.999546i −0.866156 0.499773i \(-0.833417\pi\)
0.866156 0.499773i \(-0.166583\pi\)
\(420\) 53.8196 + 22.1335i 0.128142 + 0.0526988i
\(421\) 781.367 1.85598 0.927989 0.372607i \(-0.121536\pi\)
0.927989 + 0.372607i \(0.121536\pi\)
\(422\) −371.360 371.360i −0.879999 0.879999i
\(423\) 89.1432 89.1432i 0.210740 0.210740i
\(424\) 70.4490i 0.166153i
\(425\) −1.47258 291.100i −0.00346490 0.684942i
\(426\) 165.115 0.387593
\(427\) −66.9366 66.9366i −0.156760 0.156760i
\(428\) −63.6802 + 63.6802i −0.148785 + 0.148785i
\(429\) 148.912i 0.347114i
\(430\) 11.8814 28.8907i 0.0276312 0.0671878i
\(431\) −127.925 −0.296809 −0.148404 0.988927i \(-0.547414\pi\)
−0.148404 + 0.988927i \(0.547414\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 219.940 219.940i 0.507945 0.507945i −0.405950 0.913895i \(-0.633059\pi\)
0.913895 + 0.405950i \(0.133059\pi\)
\(434\) 71.6455i 0.165082i
\(435\) −126.653 + 52.8372i −0.291157 + 0.121465i
\(436\) −356.456 −0.817559
\(437\) 7.15666 + 7.15666i 0.0163768 + 0.0163768i
\(438\) −41.6189 + 41.6189i −0.0950204 + 0.0950204i
\(439\) 159.575i 0.363496i 0.983345 + 0.181748i \(0.0581754\pi\)
−0.983345 + 0.181748i \(0.941825\pi\)
\(440\) 44.5929 + 106.891i 0.101348 + 0.242935i
\(441\) −113.136 −0.256543
\(442\) −122.239 122.239i −0.276558 0.276558i
\(443\) 0.230949 0.230949i 0.000521329 0.000521329i −0.706846 0.707367i \(-0.749883\pi\)
0.707367 + 0.706846i \(0.249883\pi\)
\(444\) 69.6407i 0.156849i
\(445\) −354.227 145.677i −0.796015 0.327364i
\(446\) −151.986 −0.340776
\(447\) −301.151 301.151i −0.673716 0.673716i
\(448\) 19.0058 19.0058i 0.0424236 0.0424236i
\(449\) 717.728i 1.59850i 0.600997 + 0.799251i \(0.294770\pi\)
−0.600997 + 0.799251i \(0.705230\pi\)
\(450\) −106.065 + 0.536547i −0.235699 + 0.00119233i
\(451\) −57.4590 −0.127404
\(452\) −147.479 147.479i −0.326281 0.326281i
\(453\) 10.0904 10.0904i 0.0222747 0.0222747i
\(454\) 345.170i 0.760287i
\(455\) 67.0748 163.098i 0.147417 0.358458i
\(456\) −10.3387 −0.0226726
\(457\) 46.2379 + 46.2379i 0.101177 + 0.101177i 0.755883 0.654706i \(-0.227208\pi\)
−0.654706 + 0.755883i \(0.727208\pi\)
\(458\) −73.4614 + 73.4614i −0.160396 + 0.160396i
\(459\) 60.5048i 0.131819i
\(460\) 44.2611 18.4649i 0.0962199 0.0401410i
\(461\) −88.2710 −0.191477 −0.0957386 0.995407i \(-0.530521\pi\)
−0.0957386 + 0.995407i \(0.530521\pi\)
\(462\) 47.6585 + 47.6585i 0.103157 + 0.103157i
\(463\) 167.771 167.771i 0.362357 0.362357i −0.502323 0.864680i \(-0.667521\pi\)
0.864680 + 0.502323i \(0.167521\pi\)
\(464\) 63.3851i 0.136606i
\(465\) 50.2778 + 120.518i 0.108124 + 0.259179i
\(466\) 569.945 1.22306
\(467\) −62.5685 62.5685i −0.133980 0.133980i 0.636937 0.770916i \(-0.280201\pi\)
−0.770916 + 0.636937i \(0.780201\pi\)
\(468\) −44.5386 + 44.5386i −0.0951679 + 0.0951679i
\(469\) 318.099i 0.678249i
\(470\) −274.812 113.017i −0.584706 0.240462i
\(471\) 141.905 0.301285
\(472\) −52.8516 52.8516i −0.111974 0.111974i
\(473\) 25.5834 25.5834i 0.0540876 0.0540876i
\(474\) 185.086i 0.390478i
\(475\) −37.1175 + 37.4949i −0.0781420 + 0.0789366i
\(476\) −78.2436 −0.164377
\(477\) −52.8367 52.8367i −0.110769 0.110769i
\(478\) −117.112 + 117.112i −0.245005 + 0.245005i
\(479\) 612.563i 1.27884i −0.768858 0.639419i \(-0.779175\pi\)
0.768858 0.639419i \(-0.220825\pi\)
\(480\) −18.6330 + 45.3079i −0.0388188 + 0.0943915i
\(481\) 211.044 0.438761
\(482\) 178.634 + 178.634i 0.370610 + 0.370610i
\(483\) 19.7342 19.7342i 0.0408576 0.0408576i
\(484\) 107.857i 0.222846i
\(485\) −227.038 + 94.7157i −0.468119 + 0.195290i
\(486\) 22.0454 0.0453609
\(487\) −342.927 342.927i −0.704162 0.704162i 0.261139 0.965301i \(-0.415902\pi\)
−0.965301 + 0.261139i \(0.915902\pi\)
\(488\) 56.3505 56.3505i 0.115472 0.115472i
\(489\) 134.486i 0.275022i
\(490\) 102.670 + 246.106i 0.209531 + 0.502257i
\(491\) −850.889 −1.73297 −0.866486 0.499202i \(-0.833627\pi\)
−0.866486 + 0.499202i \(0.833627\pi\)
\(492\) −17.1856 17.1856i −0.0349301 0.0349301i
\(493\) 130.473 130.473i 0.264651 0.264651i
\(494\) 31.3312i 0.0634234i
\(495\) −113.613 46.7238i −0.229522 0.0943915i
\(496\) 60.3147 0.121602
\(497\) −160.142 160.142i −0.322218 0.322218i
\(498\) 131.839 131.839i 0.264738 0.264738i
\(499\) 782.522i 1.56818i 0.620647 + 0.784090i \(0.286870\pi\)
−0.620647 + 0.784090i \(0.713130\pi\)
\(500\) 97.4207 + 230.237i 0.194841 + 0.460475i
\(501\) −98.0621 −0.195733
\(502\) −350.780 350.780i −0.698765 0.698765i
\(503\) 71.5670 71.5670i 0.142280 0.142280i −0.632379 0.774659i \(-0.717921\pi\)
0.774659 + 0.632379i \(0.217921\pi\)
\(504\) 28.5087i 0.0565648i
\(505\) 1.07953 2.62499i 0.00213769 0.00519799i
\(506\) 55.5453 0.109773
\(507\) −72.0091 72.0091i −0.142030 0.142030i
\(508\) −22.5566 + 22.5566i −0.0444028 + 0.0444028i
\(509\) 451.402i 0.886840i −0.896314 0.443420i \(-0.853765\pi\)
0.896314 0.443420i \(-0.146235\pi\)
\(510\) 131.617 54.9080i 0.258073 0.107663i
\(511\) 80.7312 0.157987
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 7.75404 7.75404i 0.0151151 0.0151151i
\(514\) 216.209i 0.420639i
\(515\) −33.5654 80.4578i −0.0651755 0.156229i
\(516\) 15.3037 0.0296583
\(517\) −243.352 243.352i −0.470701 0.470701i
\(518\) 67.5435 67.5435i 0.130393 0.130393i
\(519\) 177.887i 0.342749i
\(520\) 137.304 + 56.4668i 0.264047 + 0.108590i
\(521\) 595.887 1.14374 0.571869 0.820345i \(-0.306219\pi\)
0.571869 + 0.820345i \(0.306219\pi\)
\(522\) −47.5388 47.5388i −0.0910706 0.0910706i
\(523\) 172.420 172.420i 0.329674 0.329674i −0.522788 0.852463i \(-0.675108\pi\)
0.852463 + 0.522788i \(0.175108\pi\)
\(524\) 251.535i 0.480028i
\(525\) 103.391 + 102.350i 0.196935 + 0.194953i
\(526\) 156.765 0.298033
\(527\) −124.153 124.153i −0.235584 0.235584i
\(528\) −40.1212 + 40.1212i −0.0759872 + 0.0759872i
\(529\) 23.0000i 0.0434783i
\(530\) −66.9873 + 162.886i −0.126391 + 0.307332i
\(531\) 79.2774 0.149298
\(532\) 10.0274 + 10.0274i 0.0188484 + 0.0188484i
\(533\) −52.0804 + 52.0804i −0.0977119 + 0.0977119i
\(534\) 187.637i 0.351380i
\(535\) −207.787 + 86.6845i −0.388387 + 0.162027i
\(536\) 267.791 0.499610
\(537\) −360.922 360.922i −0.672108 0.672108i
\(538\) −326.796 + 326.796i −0.607427 + 0.607427i
\(539\) 308.849i 0.573004i
\(540\) −20.0062 47.9557i −0.0370485 0.0888069i
\(541\) 576.448 1.06552 0.532762 0.846265i \(-0.321154\pi\)
0.532762 + 0.846265i \(0.321154\pi\)
\(542\) −312.784 312.784i −0.577093 0.577093i
\(543\) −19.1711 + 19.1711i −0.0353059 + 0.0353059i
\(544\) 65.8693i 0.121083i
\(545\) −824.166 338.941i −1.51223 0.621910i
\(546\) 86.3946 0.158232
\(547\) −196.463 196.463i −0.359164 0.359164i 0.504341 0.863505i \(-0.331736\pi\)
−0.863505 + 0.504341i \(0.831736\pi\)
\(548\) −178.701 + 178.701i −0.326097 + 0.326097i
\(549\) 84.5258i 0.153963i
\(550\) 1.46472 + 289.546i 0.00266313 + 0.526448i
\(551\) −33.4417 −0.0606928
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 179.512 179.512i 0.324616 0.324616i
\(554\) 129.845i 0.234377i
\(555\) −66.2188 + 161.017i −0.119313 + 0.290121i
\(556\) −122.415 −0.220170
\(557\) −175.913 175.913i −0.315823 0.315823i 0.531337 0.847160i \(-0.321690\pi\)
−0.847160 + 0.531337i \(0.821690\pi\)
\(558\) −45.2360 + 45.2360i −0.0810681 + 0.0810681i
\(559\) 46.3773i 0.0829647i
\(560\) 62.0154 25.8716i 0.110742 0.0461993i
\(561\) 165.172 0.294425
\(562\) −222.033 222.033i −0.395077 0.395077i
\(563\) 385.523 385.523i 0.684765 0.684765i −0.276305 0.961070i \(-0.589110\pi\)
0.961070 + 0.276305i \(0.0891100\pi\)
\(564\) 145.570i 0.258103i
\(565\) −200.755 481.220i −0.355319 0.851717i
\(566\) −528.403 −0.933574
\(567\) −21.3815 21.3815i −0.0377099 0.0377099i
\(568\) 134.815 134.815i 0.237351 0.237351i
\(569\) 133.135i 0.233981i −0.993133 0.116990i \(-0.962675\pi\)
0.993133 0.116990i \(-0.0373247\pi\)
\(570\) −23.9043 9.83072i −0.0419373 0.0172469i
\(571\) −296.967 −0.520082 −0.260041 0.965598i \(-0.583736\pi\)
−0.260041 + 0.965598i \(0.583736\pi\)
\(572\) 121.586 + 121.586i 0.212563 + 0.212563i
\(573\) −156.987 + 156.987i −0.273974 + 0.273974i
\(574\) 33.3361i 0.0580769i
\(575\) 119.894 0.606507i 0.208512 0.00105479i
\(576\) −24.0000 −0.0416667
\(577\) −337.682 337.682i −0.585237 0.585237i 0.351101 0.936338i \(-0.385807\pi\)
−0.936338 + 0.351101i \(0.885807\pi\)
\(578\) 153.414 153.414i 0.265422 0.265422i
\(579\) 72.7506i 0.125649i
\(580\) −60.2706 + 146.553i −0.103915 + 0.252678i
\(581\) −255.738 −0.440169
\(582\) −85.2178 85.2178i −0.146422 0.146422i
\(583\) −144.239 + 144.239i −0.247408 + 0.247408i
\(584\) 67.9635i 0.116376i
\(585\) −145.328 + 60.6281i −0.248424 + 0.103638i
\(586\) 300.586 0.512945
\(587\) −389.132 389.132i −0.662916 0.662916i 0.293150 0.956066i \(-0.405296\pi\)
−0.956066 + 0.293150i \(0.905296\pi\)
\(588\) −92.3749 + 92.3749i −0.157100 + 0.157100i
\(589\) 31.8218i 0.0540268i
\(590\) −71.9441 172.453i −0.121939 0.292294i
\(591\) −300.656 −0.508724
\(592\) 56.8614 + 56.8614i 0.0960497 + 0.0960497i
\(593\) −511.328 + 511.328i −0.862273 + 0.862273i −0.991602 0.129329i \(-0.958718\pi\)
0.129329 + 0.991602i \(0.458718\pi\)
\(594\) 60.1818i 0.101316i
\(595\) −180.908 74.3990i −0.304047 0.125040i
\(596\) −491.778 −0.825130
\(597\) 13.4104 + 13.4104i 0.0224630 + 0.0224630i
\(598\) 50.3459 50.3459i 0.0841905 0.0841905i
\(599\) 163.806i 0.273466i 0.990608 + 0.136733i \(0.0436602\pi\)
−0.990608 + 0.136733i \(0.956340\pi\)
\(600\) −86.1633 + 87.0395i −0.143606 + 0.145066i
\(601\) 686.382 1.14207 0.571033 0.820927i \(-0.306543\pi\)
0.571033 + 0.820927i \(0.306543\pi\)
\(602\) −14.8428 14.8428i −0.0246558 0.0246558i
\(603\) −200.843 + 200.843i −0.333074 + 0.333074i
\(604\) 16.4776i 0.0272808i
\(605\) 102.558 249.378i 0.169517 0.412195i
\(606\) 1.39048 0.00229452
\(607\) −153.299 153.299i −0.252553 0.252553i 0.569464 0.822016i \(-0.307151\pi\)
−0.822016 + 0.569464i \(0.807151\pi\)
\(608\) −8.44153 + 8.44153i −0.0138841 + 0.0138841i
\(609\) 92.2144i 0.151419i
\(610\) 183.870 76.7070i 0.301427 0.125749i
\(611\) −441.146 −0.722006
\(612\) 49.4020 + 49.4020i 0.0807222 + 0.0807222i
\(613\) 713.442 713.442i 1.16385 1.16385i 0.180228 0.983625i \(-0.442317\pi\)
0.983625 0.180228i \(-0.0576834\pi\)
\(614\) 743.401i 1.21075i
\(615\) −23.3939 56.0762i −0.0380388 0.0911808i
\(616\) 77.8260 0.126341
\(617\) 232.838 + 232.838i 0.377372 + 0.377372i 0.870153 0.492781i \(-0.164020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(618\) 30.1995 30.1995i 0.0488665 0.0488665i
\(619\) 126.186i 0.203854i 0.994792 + 0.101927i \(0.0325009\pi\)
−0.994792 + 0.101927i \(0.967499\pi\)
\(620\) 139.454 + 57.3510i 0.224926 + 0.0925017i
\(621\) −24.9199 −0.0401286
\(622\) 24.8526 + 24.8526i 0.0399559 + 0.0399559i
\(623\) −181.986 + 181.986i −0.292113 + 0.292113i
\(624\) 72.7312i 0.116556i
\(625\) 6.32319 + 624.968i 0.0101171 + 0.999949i
\(626\) 318.752 0.509189
\(627\) −21.1678 21.1678i −0.0337604 0.0337604i
\(628\) 115.865 115.865i 0.184499 0.184499i
\(629\) 234.089i 0.372160i
\(630\) −27.1079 + 65.9152i −0.0430284 + 0.104627i
\(631\) −632.532 −1.00243 −0.501214 0.865323i \(-0.667113\pi\)
−0.501214 + 0.865323i \(0.667113\pi\)
\(632\) 151.122 + 151.122i 0.239118 + 0.239118i
\(633\) 454.821 454.821i 0.718516 0.718516i
\(634\) 323.455i 0.510182i
\(635\) −73.6017 + 30.7052i −0.115908 + 0.0483546i
\(636\) −86.2820 −0.135664
\(637\) 279.939 + 279.939i 0.439465 + 0.439465i
\(638\) −129.776 + 129.776i −0.203411 + 0.203411i
\(639\) 202.223i 0.316468i
\(640\) 21.7800 + 52.2076i 0.0340312 + 0.0815744i
\(641\) 216.571 0.337864 0.168932 0.985628i \(-0.445968\pi\)
0.168932 + 0.985628i \(0.445968\pi\)
\(642\) −77.9920 77.9920i −0.121483 0.121483i
\(643\) 763.835 763.835i 1.18792 1.18792i 0.210283 0.977641i \(-0.432562\pi\)
0.977641 0.210283i \(-0.0674385\pi\)
\(644\) 32.2259i 0.0500402i
\(645\) 35.3838 + 14.5517i 0.0548586 + 0.0225608i
\(646\) 34.7524 0.0537962
\(647\) 868.923 + 868.923i 1.34300 + 1.34300i 0.893054 + 0.449949i \(0.148558\pi\)
0.449949 + 0.893054i \(0.351442\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 216.420i 0.333466i
\(650\) 263.770 + 261.115i 0.405801 + 0.401716i
\(651\) 87.7475 0.134789
\(652\) −109.807 109.807i −0.168416 0.168416i
\(653\) −441.359 + 441.359i −0.675894 + 0.675894i −0.959069 0.283174i \(-0.908613\pi\)
0.283174 + 0.959069i \(0.408613\pi\)
\(654\) 436.568i 0.667534i
\(655\) 239.175 581.577i 0.365153 0.887903i
\(656\) −28.0640 −0.0427805
\(657\) −50.9726 50.9726i −0.0775839 0.0775839i
\(658\) −141.186 + 141.186i −0.214569 + 0.214569i
\(659\) 333.161i 0.505555i 0.967524 + 0.252778i \(0.0813441\pi\)
−0.967524 + 0.252778i \(0.918656\pi\)
\(660\) −130.915 + 54.6149i −0.198355 + 0.0827499i
\(661\) 1104.51 1.67096 0.835481 0.549520i \(-0.185189\pi\)
0.835481 + 0.549520i \(0.185189\pi\)
\(662\) −404.107 404.107i −0.610434 0.610434i
\(663\) 149.711 149.711i 0.225809 0.225809i
\(664\) 215.293i 0.324236i
\(665\) 13.6497 + 32.7191i 0.0205259 + 0.0492016i
\(666\) −85.2921 −0.128066
\(667\) 53.7374 + 53.7374i 0.0805658 + 0.0805658i
\(668\) −80.0673 + 80.0673i −0.119861 + 0.119861i
\(669\) 186.144i 0.278242i
\(670\) 619.163 + 254.633i 0.924124 + 0.380049i
\(671\) 230.747 0.343886
\(672\) 23.2772 + 23.2772i 0.0346387 + 0.0346387i
\(673\) 166.235 166.235i 0.247005 0.247005i −0.572735 0.819740i \(-0.694118\pi\)
0.819740 + 0.572735i \(0.194118\pi\)
\(674\) 99.2719i 0.147288i
\(675\) −0.657133 129.902i −0.000973531 0.192448i
\(676\) −117.590 −0.173950
\(677\) 56.8084 + 56.8084i 0.0839119 + 0.0839119i 0.747817 0.663905i \(-0.231102\pi\)
−0.663905 + 0.747817i \(0.731102\pi\)
\(678\) 180.624 180.624i 0.266407 0.266407i
\(679\) 165.303i 0.243451i
\(680\) 62.6327 152.297i 0.0921069 0.223966i
\(681\) −422.745 −0.620772
\(682\) 123.490 + 123.490i 0.181070 + 0.181070i
\(683\) −695.233 + 695.233i −1.01791 + 1.01791i −0.0180741 + 0.999837i \(0.505753\pi\)
−0.999837 + 0.0180741i \(0.994247\pi\)
\(684\) 12.6623i 0.0185121i
\(685\) −583.097 + 243.256i −0.851237 + 0.355119i
\(686\) 412.007 0.600593
\(687\) −89.9715 89.9715i −0.130963 0.130963i
\(688\) 12.4954 12.4954i 0.0181619 0.0181619i
\(689\) 261.475i 0.379499i
\(690\) 22.6147 + 54.2086i 0.0327750 + 0.0785632i
\(691\) 667.858 0.966509 0.483255 0.875480i \(-0.339455\pi\)
0.483255 + 0.875480i \(0.339455\pi\)
\(692\) 145.244 + 145.244i 0.209890 + 0.209890i
\(693\) −58.3695 + 58.3695i −0.0842272 + 0.0842272i
\(694\) 75.6516i 0.109008i
\(695\) −283.037 116.400i −0.407247 0.167482i
\(696\) −77.6306 −0.111538
\(697\) 57.7673 + 57.7673i 0.0828800 + 0.0828800i
\(698\) −608.019 + 608.019i −0.871087 + 0.871087i
\(699\) 698.037i 0.998623i
\(700\) 167.987 0.849792i 0.239981 0.00121399i
\(701\) −936.912 −1.33654 −0.668268 0.743920i \(-0.732964\pi\)
−0.668268 + 0.743920i \(0.732964\pi\)
\(702\) −54.5484 54.5484i −0.0777043 0.0777043i
\(703\) −29.9998 + 29.9998i −0.0426740 + 0.0426740i
\(704\) 65.5177i 0.0930649i
\(705\) 138.417 336.574i 0.196337 0.477411i
\(706\) 204.130 0.289135
\(707\) −1.34860 1.34860i −0.00190750 0.00190750i
\(708\) 64.7297 64.7297i 0.0914261 0.0914261i
\(709\) 680.289i 0.959505i −0.877404 0.479753i \(-0.840726\pi\)
0.877404 0.479753i \(-0.159274\pi\)
\(710\) 439.900 183.517i 0.619577 0.258475i
\(711\) −226.684 −0.318824
\(712\) −153.205 153.205i −0.215175 0.215175i
\(713\) 51.1343 51.1343i 0.0717171 0.0717171i
\(714\) 95.8284i 0.134214i
\(715\) 165.509 + 396.732i 0.231481 + 0.554870i
\(716\) −589.383 −0.823161
\(717\) −143.433 143.433i −0.200045 0.200045i
\(718\) 392.739 392.739i 0.546990 0.546990i
\(719\) 872.799i 1.21391i 0.794737 + 0.606953i \(0.207609\pi\)
−0.794737 + 0.606953i \(0.792391\pi\)
\(720\) −55.4907 22.8207i −0.0770704 0.0316955i
\(721\) −58.5801 −0.0812484
\(722\) 356.546 + 356.546i 0.493831 + 0.493831i
\(723\) −218.781 + 218.781i −0.302601 + 0.302601i
\(724\) 31.3062i 0.0432407i
\(725\) −278.705 + 281.539i −0.384420 + 0.388329i
\(726\) 132.098 0.181953
\(727\) 736.548 + 736.548i 1.01313 + 1.01313i 0.999913 + 0.0132213i \(0.00420860\pi\)
0.0132213 + 0.999913i \(0.495791\pi\)
\(728\) 70.5409 70.5409i 0.0968969 0.0968969i
\(729\) 27.0000i 0.0370370i
\(730\) −64.6240 + 157.139i −0.0885260 + 0.215259i
\(731\) −51.4414 −0.0703713
\(732\) 69.0150 + 69.0150i 0.0942828 + 0.0942828i
\(733\) 20.9889 20.9889i 0.0286342 0.0286342i −0.692645 0.721279i \(-0.743555\pi\)
0.721279 + 0.692645i \(0.243555\pi\)
\(734\) 83.0619i 0.113163i
\(735\) −301.417 + 125.745i −0.410091 + 0.171082i
\(736\) 27.1293 0.0368605
\(737\) 548.283 + 548.283i 0.743939 + 0.743939i
\(738\) 21.0480 21.0480i 0.0285203 0.0285203i
\(739\) 799.903i 1.08241i 0.840890 + 0.541206i \(0.182032\pi\)
−0.840890 + 0.541206i \(0.817968\pi\)
\(740\) 77.4025 + 185.537i 0.104598 + 0.250726i
\(741\) −38.3727 −0.0517850
\(742\) 83.6836 + 83.6836i 0.112781 + 0.112781i
\(743\) −293.529 + 293.529i −0.395059 + 0.395059i −0.876486 0.481427i \(-0.840119\pi\)
0.481427 + 0.876486i \(0.340119\pi\)
\(744\) 73.8701i 0.0992878i
\(745\) −1137.04 467.613i −1.52623 0.627669i
\(746\) −377.432 −0.505941
\(747\) 161.470 + 161.470i 0.216158 + 0.216158i
\(748\) 134.863 134.863i 0.180298 0.180298i
\(749\) 151.286i 0.201985i
\(750\) −281.982 + 119.315i −0.375976 + 0.159087i
\(751\) 1348.43 1.79551 0.897757 0.440491i \(-0.145196\pi\)
0.897757 + 0.440491i \(0.145196\pi\)
\(752\) −118.858 118.858i −0.158055 0.158055i
\(753\) 429.616 429.616i 0.570539 0.570539i
\(754\) 235.257i 0.312012i
\(755\) 15.6680 38.0981i 0.0207523 0.0504610i
\(756\) −34.9159 −0.0461850
\(757\) 165.657 + 165.657i 0.218834 + 0.218834i 0.808007 0.589173i \(-0.200546\pi\)
−0.589173 + 0.808007i \(0.700546\pi\)
\(758\) 143.699 143.699i 0.189576 0.189576i
\(759\) 68.0289i 0.0896296i
\(760\) −27.5445 + 11.4910i −0.0362428 + 0.0151198i
\(761\) −650.491 −0.854785 −0.427392 0.904066i \(-0.640568\pi\)
−0.427392 + 0.904066i \(0.640568\pi\)
\(762\) −27.6261 27.6261i −0.0362547 0.0362547i
\(763\) −423.420 + 423.420i −0.554941 + 0.554941i
\(764\) 256.359i 0.335548i
\(765\) 67.2483 + 161.197i 0.0879063 + 0.210716i
\(766\) 196.422 0.256426
\(767\) −196.161 196.161i −0.255751 0.255751i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 774.000i 1.00650i 0.864140 + 0.503251i \(0.167863\pi\)
−0.864140 + 0.503251i \(0.832137\pi\)
\(770\) 179.942 + 74.0019i 0.233691 + 0.0961063i
\(771\) −264.800 −0.343450
\(772\) −59.4006 59.4006i −0.0769438 0.0769438i
\(773\) −534.474 + 534.474i −0.691429 + 0.691429i −0.962546 0.271118i \(-0.912607\pi\)
0.271118 + 0.962546i \(0.412607\pi\)
\(774\) 18.7431i 0.0242159i
\(775\) 267.901 + 265.204i 0.345678 + 0.342199i
\(776\) −139.160 −0.179330
\(777\) 82.7236 + 82.7236i 0.106465 + 0.106465i
\(778\) 244.042 244.042i 0.313678 0.313678i
\(779\) 14.8064i