Properties

Label 210.2.i.d.121.1
Level $210$
Weight $2$
Character 210.121
Analytic conductor $1.677$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 210.121
Dual form 210.2.i.d.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} -1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} +1.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(-0.500000 - 2.59808i) q^{35} +1.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} -11.0000 q^{41} +(2.00000 - 1.73205i) q^{42} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.50000 + 6.06218i) q^{46} +(2.50000 - 4.33013i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +3.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +2.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} -7.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} -6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} +(0.500000 - 0.866025i) q^{75} -3.00000 q^{76} +(2.50000 + 0.866025i) q^{77} +1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.50000 + 9.52628i) q^{82} +8.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} +1.00000 q^{90} +(2.00000 - 1.73205i) q^{91} +7.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-2.50000 - 4.33013i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(-0.500000 + 0.866025i) q^{96} -16.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} - q^{14} + 2q^{15} - q^{16} + q^{18} + 3q^{19} - 2q^{20} + 5q^{21} + 2q^{22} - 7q^{23} - q^{24} - q^{25} + q^{26} - 2q^{27} - 5q^{28} - 16q^{29} + q^{30} + 2q^{31} + q^{32} - q^{33} - q^{35} + 2q^{36} - 11q^{37} - 3q^{38} + q^{39} - q^{40} - 22q^{41} + 4q^{42} + 16q^{43} + q^{44} + q^{45} + 7q^{46} + 5q^{47} - 2q^{48} + 2q^{49} - 2q^{50} - q^{52} + 11q^{53} - q^{54} + 2q^{55} - 4q^{56} + 6q^{57} - 8q^{58} - 4q^{59} - q^{60} + 4q^{62} + q^{63} + 2q^{64} + q^{65} + q^{66} - 14q^{69} - 5q^{70} - 12q^{71} + q^{72} + 6q^{73} + 11q^{74} + q^{75} - 6q^{76} + 5q^{77} + 2q^{78} + 8q^{79} + q^{80} - q^{81} - 11q^{82} + 16q^{83} - q^{84} + 8q^{86} - 8q^{87} - q^{88} + 10q^{89} + 2q^{90} + 4q^{91} + 14q^{92} - 2q^{93} - 5q^{94} - 3q^{95} - q^{96} - 32q^{97} - 11q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 1.00000 0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 1.00000 0.213201
\(23\) −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i \(0.427054\pi\)
−0.956967 + 0.290196i \(0.906280\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −2.50000 0.866025i −0.472456 0.163663i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 0 0
\(35\) −0.500000 2.59808i −0.0845154 0.439155i
\(36\) 1.00000 0.166667
\(37\) −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i \(0.526194\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −1.50000 2.59808i −0.243332 0.421464i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 2.00000 1.73205i 0.308607 0.267261i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 3.50000 + 6.06218i 0.516047 + 0.893819i
\(47\) 2.50000 4.33013i 0.364662 0.631614i −0.624059 0.781377i \(-0.714518\pi\)
0.988722 + 0.149763i \(0.0478510\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i \(0.105931\pi\)
−0.189651 + 0.981852i \(0.560736\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 1.00000 0.134840
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 3.00000 0.397360
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 2.00000 0.254000
\(63\) 0.500000 + 2.59808i 0.0629941 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.842701
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i \(-0.0524664\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) 5.50000 + 9.52628i 0.639362 + 1.10741i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) −3.00000 −0.344124
\(77\) 2.50000 + 0.866025i 0.284901 + 0.0986928i
\(78\) 1.00000 0.113228
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.50000 + 9.52628i −0.607373 + 1.05200i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) 0 0
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) 1.00000 0.105409
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) 7.00000 0.729800
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) −2.50000 4.33013i −0.257855 0.446619i
\(95\) −1.50000 2.59808i −0.153897 0.266557i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) −1.00000 −0.100504
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) 11.0000 1.06841
\(107\) 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i \(-0.672747\pi\)
0.999818 + 0.0190994i \(0.00607989\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) −11.0000 −1.04407
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.50000 2.59808i 0.140488 0.243332i
\(115\) 3.50000 + 6.06218i 0.326377 + 0.565301i
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) −5.50000 9.52628i −0.495918 0.858956i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −1.00000 −0.0894427
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −17.0000 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 4.00000 + 6.92820i 0.352180 + 0.609994i
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) 2.50000 4.33013i 0.218426 0.378325i −0.735901 0.677089i \(-0.763241\pi\)
0.954327 + 0.298764i \(0.0965744\pi\)
\(132\) 1.00000 0.0870388
\(133\) −1.50000 7.79423i −0.130066 0.675845i
\(134\) 0 0
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) −3.50000 + 6.06218i −0.297940 + 0.516047i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −2.00000 + 1.73205i −0.169031 + 0.146385i
\(141\) 5.00000 0.421076
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 0.500000 + 0.866025i 0.0418121 + 0.0724207i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 6.00000 0.496564
\(147\) 6.50000 2.59808i 0.536111 0.214286i
\(148\) 11.0000 0.904194
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) −1.50000 + 2.59808i −0.121666 + 0.210732i
\(153\) 0 0
\(154\) 2.00000 1.73205i 0.161165 0.139573i
\(155\) 2.00000 0.160644
\(156\) 0.500000 0.866025i 0.0400320 0.0693375i
\(157\) 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i \(-0.0765542\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) −5.50000 + 9.52628i −0.436178 + 0.755483i
\(160\) 1.00000 0.0790569
\(161\) 3.50000 + 18.1865i 0.275839 + 1.43330i
\(162\) −1.00000 −0.0785674
\(163\) −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i \(0.382224\pi\)
−0.988227 + 0.152992i \(0.951109\pi\)
\(164\) 5.50000 + 9.52628i 0.429478 + 0.743877i
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) −2.50000 0.866025i −0.192879 0.0668153i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 1.50000 + 2.59808i 0.114708 + 0.198680i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) −8.00000 −0.606478
\(175\) −2.50000 0.866025i −0.188982 0.0654654i
\(176\) −1.00000 −0.0753778
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) −5.00000 8.66025i −0.374766 0.649113i
\(179\) 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −24.0000 −1.78391 −0.891953 0.452128i \(-0.850665\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(182\) −0.500000 2.59808i −0.0370625 0.192582i
\(183\) 0 0
\(184\) 3.50000 6.06218i 0.258023 0.446910i
\(185\) 5.50000 + 9.52628i 0.404368 + 0.700386i
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 0 0
\(188\) −5.00000 −0.364662
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) −3.00000 −0.217643
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i \(-0.875812\pi\)
0.133056 0.991109i \(-0.457521\pi\)
\(194\) −8.00000 + 13.8564i −0.574367 + 0.994832i
\(195\) 1.00000 0.0716115
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −1.00000 −0.0712470 −0.0356235 0.999365i \(-0.511342\pi\)
−0.0356235 + 0.999365i \(0.511342\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 0 0
\(203\) −16.0000 + 13.8564i −1.12298 + 0.972529i
\(204\) 0 0
\(205\) −5.50000 + 9.52628i −0.384137 + 0.665344i
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) −3.50000 6.06218i −0.243267 0.421350i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) 3.00000 0.207514
\(210\) −0.500000 2.59808i −0.0345033 0.179284i
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 5.50000 9.52628i 0.377742 0.654268i
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) −5.00000 8.66025i −0.341793 0.592003i
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) 1.00000 0.0680414
\(217\) 5.00000 + 1.73205i 0.339422 + 0.117579i
\(218\) −6.00000 −0.406371
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) −0.500000 0.866025i −0.0337100 0.0583874i
\(221\) 0 0
\(222\) −5.50000 + 9.52628i −0.369136 + 0.639362i
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 1.00000 0.0666667
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252136i \(0.918867\pi\)
\(228\) −1.50000 2.59808i −0.0993399 0.172062i
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 7.00000 0.461566
\(231\) 0.500000 + 2.59808i 0.0328976 + 0.170941i
\(232\) 8.00000 0.525226
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) −2.50000 4.33013i −0.163082 0.282466i
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) −5.00000 8.66025i −0.321412 0.556702i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) −11.0000 −0.701334
\(247\) 1.50000 2.59808i 0.0954427 0.165312i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 13.0000 0.820553 0.410276 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 2.00000 1.73205i 0.125988 0.109109i
\(253\) −7.00000 −0.440086
\(254\) −8.50000 + 14.7224i −0.533337 + 0.923768i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.0000 17.3205i 0.623783 1.08042i −0.364992 0.931011i \(-0.618928\pi\)
0.988775 0.149413i \(-0.0477384\pi\)
\(258\) 8.00000 0.498058
\(259\) 5.50000 + 28.5788i 0.341753 + 1.77580i
\(260\) −1.00000 −0.0620174
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −2.50000 4.33013i −0.154451 0.267516i
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 11.0000 0.675725
\(266\) −7.50000 2.59808i −0.459855 0.159298i
\(267\) 10.0000 0.611990
\(268\) 0 0
\(269\) −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i \(-0.957952\pi\)
0.381577 0.924337i \(-0.375381\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −16.0000 + 27.7128i −0.971931 + 1.68343i −0.282218 + 0.959350i \(0.591070\pi\)
−0.689713 + 0.724083i \(0.742263\pi\)
\(272\) 0 0
\(273\) 2.50000 + 0.866025i 0.151307 + 0.0524142i
\(274\) 18.0000 1.08742
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 3.50000 + 6.06218i 0.210675 + 0.364900i
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 10.0000 17.3205i 0.599760 1.03882i
\(279\) −2.00000 −0.119737
\(280\) 0.500000 + 2.59808i 0.0298807 + 0.155265i
\(281\) −1.00000 −0.0596550 −0.0298275 0.999555i \(-0.509496\pi\)
−0.0298275 + 0.999555i \(0.509496\pi\)
\(282\) 2.50000 4.33013i 0.148873 0.257855i
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 1.50000 2.59808i 0.0888523 0.153897i
\(286\) 1.00000 0.0591312
\(287\) −22.0000 + 19.0526i −1.29862 + 1.12464i
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 4.00000 + 6.92820i 0.234888 + 0.406838i
\(291\) −8.00000 13.8564i −0.468968 0.812277i
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) 27.0000 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(294\) 1.00000 6.92820i 0.0583212 0.404061i
\(295\) −4.00000 −0.232889
\(296\) 5.50000 9.52628i 0.319681 0.553704i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 0 0
\(299\) −3.50000 + 6.06218i −0.202410 + 0.350585i
\(300\) −1.00000 −0.0577350
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) −6.00000 −0.345261
\(303\) 0 0
\(304\) 1.50000 + 2.59808i 0.0860309 + 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) 16.0000 0.910208
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) 6.00000 10.3923i 0.339140 0.587408i −0.645131 0.764072i \(-0.723197\pi\)
0.984271 + 0.176664i \(0.0565306\pi\)
\(314\) 7.00000 0.395033
\(315\) 2.50000 + 0.866025i 0.140859 + 0.0487950i
\(316\) −8.00000 −0.450035
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 5.50000 + 9.52628i 0.308425 + 0.534207i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 10.0000 0.558146
\(322\) 17.5000 + 6.06218i 0.975237 + 0.337832i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) 8.00000 + 13.8564i 0.443079 + 0.767435i
\(327\) 3.00000 5.19615i 0.165900 0.287348i
\(328\) 11.0000 0.607373
\(329\) −2.50000 12.9904i −0.137829 0.716183i
\(330\) 1.00000 0.0550482
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) −4.00000 6.92820i −0.219529 0.380235i
\(333\) −5.50000 9.52628i −0.301398 0.522037i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −2.00000 + 1.73205i −0.109109 + 0.0944911i
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) 3.00000 0.162221
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −8.00000 −0.431331
\(345\) −3.50000 + 6.06218i −0.188434 + 0.326377i
\(346\) −7.50000 12.9904i −0.403202 0.698367i
\(347\) −7.00000 12.1244i −0.375780 0.650870i 0.614664 0.788789i \(-0.289292\pi\)
−0.990443 + 0.137920i \(0.955958\pi\)
\(348\) −4.00000 + 6.92820i −0.214423 + 0.371391i
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) −2.00000 + 1.73205i −0.106904 + 0.0925820i
\(351\) −1.00000 −0.0533761
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 19.0000 1.00418
\(359\) −2.00000 + 3.46410i −0.105556 + 0.182828i −0.913965 0.405793i \(-0.866996\pi\)
0.808409 + 0.588621i \(0.200329\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) −12.0000 + 20.7846i −0.630706 + 1.09241i
\(363\) 10.0000 0.524864
\(364\) −2.50000 0.866025i −0.131036 0.0453921i
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i \(-0.940389\pi\)
0.330021 0.943974i \(-0.392944\pi\)
\(368\) −3.50000 6.06218i −0.182450 0.316013i
\(369\) 5.50000 9.52628i 0.286319 0.495918i
\(370\) 11.0000 0.571863
\(371\) 27.5000 + 9.52628i 1.42773 + 0.494580i
\(372\) 2.00000 0.103695
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) −2.50000 + 4.33013i −0.128928 + 0.223309i
\(377\) −8.00000 −0.412021
\(378\) 0.500000 + 2.59808i 0.0257172 + 0.133631i
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) −1.50000 + 2.59808i −0.0769484 + 0.133278i
\(381\) −8.50000 14.7224i −0.435468 0.754253i
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) −17.5000 + 30.3109i −0.894208 + 1.54881i −0.0594268 + 0.998233i \(0.518927\pi\)
−0.834781 + 0.550581i \(0.814406\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.00000 1.73205i 0.101929 0.0882735i
\(386\) −22.0000 −1.11977
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264120i \(0.914918\pi\)
\(390\) 0.500000 0.866025i 0.0253185 0.0438529i
\(391\) 0 0
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 5.00000 0.252217
\(394\) −0.500000 + 0.866025i −0.0251896 + 0.0436297i
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 24.0000 1.20301
\(399\) 6.00000 5.19615i 0.300376 0.260133i
\(400\) 1.00000 0.0500000
\(401\) 2.50000 4.33013i 0.124844 0.216236i −0.796828 0.604206i \(-0.793490\pi\)
0.921672 + 0.387970i \(0.126824\pi\)
\(402\) 0 0
\(403\) 1.00000 + 1.73205i 0.0498135 + 0.0862796i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 4.00000 + 20.7846i 0.198517 + 1.03152i
\(407\) −11.0000 −0.545250
\(408\) 0 0
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) 5.50000 + 9.52628i 0.271626 + 0.470469i
\(411\) −9.00000 + 15.5885i −0.443937 + 0.768922i
\(412\) −16.0000 −0.788263
\(413\) −10.0000 3.46410i −0.492068 0.170457i
\(414\) −7.00000 −0.344031
\(415\) 4.00000 6.92820i 0.196352 0.340092i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 10.0000 + 17.3205i 0.489702 + 0.848189i
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) −2.50000 0.866025i −0.121988 0.0422577i
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 2.50000 4.33013i 0.121698 0.210787i
\(423\) 2.50000 + 4.33013i 0.121554 + 0.210538i
\(424\) −5.50000 9.52628i −0.267104 0.462637i
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) −0.500000 + 0.866025i −0.0241402 + 0.0418121i
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) 4.00000 3.46410i 0.192006 0.166282i
\(435\) −8.00000 −0.383571
\(436\) −3.00000 + 5.19615i −0.143674 + 0.248851i
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 3.00000 + 5.19615i 0.143346 + 0.248282i
\(439\) −16.0000 + 27.7128i −0.763638 + 1.32266i 0.177325 + 0.984152i \(0.443256\pi\)
−0.940963 + 0.338508i \(0.890078\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) −8.00000 + 13.8564i −0.380091 + 0.658338i −0.991075 0.133306i \(-0.957441\pi\)
0.610984 + 0.791643i \(0.290774\pi\)
\(444\) 5.50000 + 9.52628i 0.261018 + 0.452097i
\(445\) −5.00000 8.66025i −0.237023 0.410535i
\(446\) 6.00000 10.3923i 0.284108 0.492090i
\(447\) 0 0
\(448\) 2.00000 1.73205i 0.0944911 0.0818317i
\(449\) 11.0000 0.519122 0.259561 0.965727i \(-0.416422\pi\)
0.259561 + 0.965727i \(0.416422\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) −5.50000 9.52628i −0.258985 0.448575i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 3.00000 5.19615i 0.140952 0.244137i
\(454\) −8.00000 −0.375459
\(455\) −0.500000 2.59808i −0.0234404 0.121800i
\(456\) −3.00000 −0.140488
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) 3.50000 6.06218i 0.163188 0.282650i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 2.50000 + 0.866025i 0.116311 + 0.0402911i
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 1.00000 + 1.73205i 0.0463739 + 0.0803219i
\(466\) 9.00000 + 15.5885i 0.416917 + 0.722121i
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 1.00000 0.0462250
\(469\) 0 0
\(470\) −5.00000 −0.230633
\(471\) −3.50000 + 6.06218i −0.161271 + 0.279330i
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) 4.00000 + 6.92820i 0.183920 + 0.318559i
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) −3.00000 −0.137649
\(476\) 0 0
\(477\) −11.0000 −0.503655
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) −11.0000 19.0526i −0.502603 0.870534i −0.999995 0.00300810i \(-0.999042\pi\)
0.497393 0.867526i \(-0.334291\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −5.50000 + 9.52628i −0.250778 + 0.434361i
\(482\) −7.00000 −0.318841
\(483\) −14.0000 + 12.1244i −0.637022 + 0.551677i
\(484\) −10.0000 −0.454545
\(485\) −8.00000 + 13.8564i −0.363261 + 0.629187i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 0 0
\(489\) −16.0000 −0.723545
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) −5.50000 + 9.52628i −0.247959 + 0.429478i
\(493\) 0 0
\(494\) −1.50000 2.59808i −0.0674882 0.116893i
\(495\) −0.500000 + 0.866025i −0.0224733 + 0.0389249i
\(496\) −2.00000 −0.0898027
\(497\) −12.0000 + 10.3923i −0.538274 + 0.466159i
\(498\) 8.00000 0.358489
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −1.50000 2.59808i −0.0670151 0.116073i
\(502\) 6.50000 11.2583i 0.290109 0.502484i
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) −0.500000 2.59808i −0.0222718 0.115728i
\(505\) 0 0
\(506\) −3.50000 + 6.06218i −0.155594 + 0.269497i
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 8.50000 + 14.7224i 0.377127 + 0.653202i
\(509\) 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i \(-0.561692\pi\)
0.946111 0.323843i \(-0.104975\pi\)
\(510\) 0 0
\(511\) 15.0000 + 5.19615i 0.663561 + 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) −1.50000 + 2.59808i −0.0662266 + 0.114708i
\(514\) −10.0000 17.3205i −0.441081 0.763975i
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) 5.00000 0.219900
\(518\) 27.5000 + 9.52628i 1.20828 + 0.418561i
\(519\) 15.0000 0.658427
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i \(0.0905145\pi\)
−0.236963 + 0.971519i \(0.576152\pi\)
\(522\) −4.00000 6.92820i −0.175075 0.303239i
\(523\) −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i \(-0.847256\pi\)
0.843334 + 0.537390i \(0.180590\pi\)
\(524\) −5.00000 −0.218426
\(525\) −0.500000 2.59808i −0.0218218 0.113389i
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) 5.50000 9.52628i 0.238905 0.413795i
\(531\) 4.00000 0.173585
\(532\) −6.00000 + 5.19615i −0.260133 + 0.225282i
\(533\) −11.0000 −0.476463
\(534\) 5.00000 8.66025i 0.216371 0.374766i
\(535\) −5.00000 8.66025i −0.216169 0.374415i
\(536\) 0 0
\(537\) −9.50000 + 16.4545i −0.409955 + 0.710063i
\(538\) −20.0000 −0.862261
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 1.00000 0.0430331
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) 16.0000 + 27.7128i 0.687259 + 1.19037i
\(543\) −12.0000 20.7846i −0.514969 0.891953i
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 2.00000 1.73205i 0.0855921 0.0741249i
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) 0 0
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) −12.0000 + 20.7846i −0.511217 + 0.885454i
\(552\) 7.00000 0.297940
\(553\) −4.00000 20.7846i −0.170097 0.883852i
\(554\) 22.0000 0.934690
\(555\) −5.50000 + 9.52628i −0.233462 + 0.404368i
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i \(0.0797613\pi\)
−0.269642 + 0.962961i \(0.586905\pi\)
\(558\) −1.00000 + 1.73205i −0.0423334 + 0.0733236i
\(559\) 8.00000 0.338364
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) 0 0
\(562\) −0.500000 + 0.866025i −0.0210912 + 0.0365311i
\(563\) 19.0000 + 32.9090i 0.800755 + 1.38695i 0.919120 + 0.393977i \(0.128901\pi\)
−0.118366 + 0.992970i \(0.537765\pi\)
\(564\) −2.50000 4.33013i −0.105269 0.182331i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 14.0000 0.588464
\(567\) −2.50000 0.866025i −0.104990 0.0363696i
\(568\) 6.00000 0.251754
\(569\) 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i \(-0.772922\pi\)
0.944800 + 0.327647i \(0.106256\pi\)
\(570\) −1.50000 2.59808i −0.0628281 0.108821i
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) 6.00000 0.250654
\(574\) 5.50000 + 28.5788i 0.229566 + 1.19286i
\(575\) 7.00000 0.291920
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) 11.0000 19.0526i 0.457144 0.791797i
\(580\) 8.00000 0.332182
\(581\) 16.0000 13.8564i 0.663792 0.574861i
\(582\) −16.0000 −0.663221
\(583\) −5.50000 + 9.52628i −0.227787 + 0.394538i
\(584\) −3.00000 5.19615i −0.124141 0.215018i
\(585\) 0.500000 + 0.866025i 0.0206725 + 0.0358057i
\(586\) 13.5000 23.3827i 0.557680 0.965930i
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) −5.50000 4.33013i −0.226816 0.178571i
\(589\) 6.00000 0.247226
\(590\) −2.00000 + 3.46410i −0.0823387 + 0.142615i
\(591\) −0.500000 0.866025i −0.0205673 0.0356235i
\(592\) −5.50000 9.52628i −0.226049 0.391528i
\(593\) −8.00000 + 13.8564i −0.328521 + 0.569014i −0.982219 0.187741i \(-0.939883\pi\)
0.653698 + 0.756756i \(0.273217\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 0 0
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) 3.50000 + 6.06218i 0.143126 + 0.247901i
\(599\) −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) −4.00000 20.7846i −0.163028 0.847117i
\(603\) 0 0
\(604\) −3.00000 + 5.19615i −0.122068 + 0.211428i
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) 18.5000 32.0429i 0.750892 1.30058i −0.196499 0.980504i \(-0.562957\pi\)
0.947391 0.320079i \(-0.103709\pi\)
\(608\) 3.00000 0.121666
\(609\) −20.0000 6.92820i −0.810441 0.280745i
\(610\) 0 0
\(611\) 2.50000 4.33013i 0.101139 0.175178i
\(612\) 0 0
\(613\) 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i \(0.143847\pi\)
−0.0716275 + 0.997431i \(0.522819\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) −11.0000 −0.443563
\(616\) −2.50000 0.866025i −0.100728 0.0348932i
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 8.00000 13.8564i 0.321807 0.557386i
\(619\) −14.5000 25.1147i −0.582804 1.00945i −0.995145 0.0984169i \(-0.968622\pi\)
0.412341 0.911030i \(-0.364711\pi\)
\(620\) −1.00000 1.73205i −0.0401610 0.0695608i
\(621\) 3.50000 6.06218i 0.140450 0.243267i
\(622\) −12.0000 −0.481156
\(623\) −5.00000 25.9808i −0.200321 1.04090i
\(624\) −1.00000 −0.0400320
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −6.00000 10.3923i −0.239808 0.415360i
\(627\) 1.50000 + 2.59808i 0.0599042 + 0.103757i
\(628\) 3.50000 6.06218i 0.139665 0.241907i
\(629\) 0 0
\(630\) 2.00000 1.73205i 0.0796819 0.0690066i
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 2.50000 + 4.33013i 0.0993661 + 0.172107i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) −8.50000 + 14.7224i −0.337312 + 0.584242i
\(636\) 11.0000 0.436178
\(637\) 1.00000 6.92820i 0.0396214 0.274505i
\(638\) −8.00000 −0.316723
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) 5.00000 8.66025i 0.197334 0.341793i
\(643\) −10.0000 −0.394362 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) 14.0000 12.1244i 0.551677 0.477767i
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i \(-0.0582109\pi\)
−0.649155 + 0.760656i \(0.724878\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 2.00000 3.46410i 0.0785069 0.135978i
\(650\) −1.00000 −0.0392232
\(651\) 1.00000 + 5.19615i 0.0391931 + 0.203653i
\(652\) 16.0000 0.626608
\(653\) −3.50000 + 6.06218i −0.136966 + 0.237231i −0.926347 0.376672i \(-0.877068\pi\)
0.789381 + 0.613904i \(0.210402\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) −2.50000 4.33013i −0.0976831 0.169192i
\(656\) 5.50000 9.52628i 0.214739 0.371939i
\(657\) −6.00000 −0.234082
\(658\) −12.5000 4.33013i −0.487301 0.168806i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) 12.0000 + 20.7846i 0.466746 + 0.808428i 0.999278 0.0379819i \(-0.0120929\pi\)
−0.532533 + 0.846410i \(0.678760\pi\)
\(662\) −6.50000 11.2583i −0.252630 0.437567i
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) −7.50000 2.59808i −0.290838 0.100749i
\(666\) −11.0000 −0.426241
\(667\) 28.0000 48.4974i 1.08416 1.87783i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) 6.00000 + 10.3923i 0.231973 + 0.401790i
\(670\) 0 0
\(671\) 0 0
\(672\) 0.500000 + 2.59808i 0.0192879 + 0.100223i
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) −6.00000 + 10.3923i −0.231111 + 0.400297i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 6.50000 11.2583i 0.249815 0.432693i −0.713659 0.700493i \(-0.752963\pi\)
0.963474 + 0.267800i \(0.0862968\pi\)
\(678\) 6.00000 0.230429
\(679\) −32.0000 + 27.7128i −1.22805 + 1.06352i
\(680\) 0 0
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) −2.00000 3.46410i −0.0765279 0.132550i 0.825222 0.564809i \(-0.191050\pi\)
−0.901750 + 0.432259i \(0.857717\pi\)
\(684\) 1.50000 2.59808i 0.0573539 0.0993399i
\(685\) 18.0000 0.687745
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) −14.0000 −0.534133
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 5.50000 + 9.52628i 0.209533 + 0.362922i
\(690\) 3.50000 + 6.06218i 0.133243 + 0.230783i
\(691\) 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i \(-0.760033\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(692\) −15.0000 −0.570214
\(693\) −2.00000 + 1.73205i −0.0759737 + 0.0657952i
\(694\) −14.0000 −0.531433
\(695\) 10.0000 17.3205i 0.379322 0.657004i
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) 0 0
\(698\) 6.00000 10.3923i 0.227103 0.393355i
\(699\) −18.0000 −0.680823
\(700\) 0.500000 + 2.59808i 0.0188982 + 0.0981981i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −0.500000 + 0.866025i −0.0188713 + 0.0326860i
\(703\) 16.5000 + 28.5788i 0.622309 + 1.07787i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 2.50000 4.33013i 0.0941554 0.163082i
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 3.00000 + 5.19615i 0.112588 + 0.195008i
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) −5.00000 + 8.66025i −0.187383 + 0.324557i
\(713\) −14.0000 −0.524304
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 9.50000 16.4545i 0.355032 0.614933i
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) −1.00000 + 1.73205i −0.0372937 + 0.0645946i −0.884070 0.467355i \(-0.845207\pi\)
0.846776 + 0.531949i \(0.178540\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −8.00000 41.5692i −0.297936 1.54812i
\(722\) 10.0000 0.372161
\(723\) 3.50000 6.06218i 0.130166 0.225455i
\(724\) 12.0000 + 20.7846i 0.445976 + 0.772454i
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) 11.0000 0.407967 0.203984 0.978974i \(-0.434611\pi\)
0.203984 + 0.978974i \(0.434611\pi\)
\(728\) −2.00000 + 1.73205i −0.0741249 + 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) −25.0000 −0.922767
\(735\) 1.00000 6.92820i 0.0368856 0.255551i
\(736\) −7.00000 −0.258023
\(737\) 0 0
\(738\) −5.50000 9.52628i −0.202458 0.350667i
\(739\) 9.50000 + 16.4545i 0.349463 + 0.605288i 0.986154 0.165831i \(-0.0530307\pi\)
−0.636691 + 0.771119i \(0.719697\pi\)
\(740\) 5.50000 9.52628i 0.202184 0.350193i
\(741\) 3.00000 0.110208
\(742\) 22.0000 19.0526i 0.807645 0.699441i
\(743\) 49.0000 1.79764 0.898818 0.438322i \(-0.144427\pi\)
0.898818 + 0.438322i \(0.144427\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) 3.00000 + 5.19615i 0.109838 + 0.190245i
\(747\) −4.00000 + 6.92820i −0.146352 + 0.253490i
\(748\) 0 0
\(749\) −5.00000 25.9808i −0.182696 0.949316i
\(750\) −1.00000 −0.0365148
\(751\) −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i \(-0.990660\pi\)
0.525193 + 0.850983i \(0.323993\pi\)
\(752\) 2.50000 + 4.33013i 0.0911656 + 0.157903i
\(753\) 6.50000 + 11.2583i 0.236873 + 0.410276i
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) −6.00000 −0.218362
\(756\) 2.50000 + 0.866025i 0.0909241 + 0.0314970i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −9.50000 + 16.4545i −0.345056 + 0.597654i
\(759\) −3.50000 6.06218i −0.127042 0.220043i
\(760\) 1.50000 + 2.59808i 0.0544107 + 0.0942421i
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) −17.0000 −0.615845
\(763\) −15.0000 5.19615i −0.543036 0.188113i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) 17.5000 + 30.3109i 0.632301 + 1.09518i
\(767\) −2.00000 3.46410i −0.0722158 0.125081i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) −0.500000 2.59808i −0.0180187 0.0936282i
\(771\) 20.0000 0.720282
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i \(-0.964427\pi\)
0.400298 0.916385i \(-0.368907\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) 16.0000 0.574367
\(777\) −22.0000 + 19.0526i −0.789246 + 0.683507i
\(778\) −10.0000 −0.358517
\(779\) −16.5000 + 28.5788i −0.591174 + 1.02394i
\(780\) −0.500000 0.866025i −0.0179029 0.0310087i
\(781\) −3.00000 5.19615i −0.107348 0.185933i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) 7.00000 0.249841
\(786\) 2.50000 4.33013i 0.0891720 0.154451i
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) 0.500000 + 0.866025i 0.0178118 + 0.0308509i
\(789\) 12.0000 20.7846i 0.427211 0.739952i
\(790\) −8.00000 −0.284627
\(791\) 12.0000 10.3923i 0.426671 0.369508i
\(792\) 1.00000 0.0355335
\(793\) 0 0
\(794\) 7.00000 + 12.1244i 0.248421 + 0.430277i
\(795\) 5.50000 + 9.52628i 0.195065 + 0.337862i