Properties

Label 670.2.e.d.431.1
Level 670
Weight 2
Character 670.431
Analytic conductor 5.350
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 670.e (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(5.34997693543\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 431.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 670.431
Dual form 670.2.e.d.171.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} -2.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(2.00000 - 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} -6.00000 q^{22} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{24} +1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +1.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} -2.00000 q^{42} +8.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +2.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.00000 + 5.19615i) q^{51} +2.00000 q^{52} -3.00000 q^{53} +(-2.50000 + 4.33013i) q^{54} +(3.00000 + 5.19615i) q^{55} +(1.00000 + 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{57} +6.00000 q^{58} -6.00000 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} -5.00000 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} -6.00000 q^{66} +(2.50000 + 7.79423i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +2.00000 q^{72} +(2.00000 - 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +1.00000 q^{75} -4.00000 q^{76} +(-6.00000 + 10.3923i) q^{77} +(1.00000 + 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} -3.00000 q^{82} +(7.50000 - 12.9904i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +(4.00000 - 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +9.00000 q^{89} +(1.00000 - 1.73205i) q^{90} +4.00000 q^{91} -6.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -6.00000 q^{94} +(-2.00000 + 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +(5.00000 - 8.66025i) q^{97} +(-1.50000 - 2.59808i) q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 2q^{3} - q^{4} - 2q^{5} + q^{6} - 2q^{7} - 2q^{8} - 4q^{9} + O(q^{10}) \) \( 2q + q^{2} + 2q^{3} - q^{4} - 2q^{5} + q^{6} - 2q^{7} - 2q^{8} - 4q^{9} - q^{10} - 6q^{11} - q^{12} - 2q^{13} - 4q^{14} - 2q^{15} - q^{16} - 6q^{17} - 2q^{18} + 4q^{19} + q^{20} - 2q^{21} - 12q^{22} + 6q^{23} - 2q^{24} + 2q^{25} + 2q^{26} - 10q^{27} - 2q^{28} + 6q^{29} - q^{30} - 5q^{31} + q^{32} - 6q^{33} + 6q^{34} + 2q^{35} + 2q^{36} + 7q^{37} - 4q^{38} - 2q^{39} + 2q^{40} - 3q^{41} - 4q^{42} + 16q^{43} - 6q^{44} + 4q^{45} - 6q^{46} - 6q^{47} - q^{48} + 3q^{49} + q^{50} - 6q^{51} + 4q^{52} - 6q^{53} - 5q^{54} + 6q^{55} + 2q^{56} + 4q^{57} + 12q^{58} - 12q^{59} + q^{60} - 8q^{61} - 10q^{62} + 4q^{63} + 2q^{64} + 2q^{65} - 12q^{66} + 5q^{67} + 12q^{68} + 6q^{69} + 4q^{70} + 15q^{71} + 4q^{72} + 4q^{73} - 7q^{74} + 2q^{75} - 8q^{76} - 12q^{77} + 2q^{78} - 8q^{79} + q^{80} + 2q^{81} - 6q^{82} + 15q^{83} - 2q^{84} + 6q^{85} + 8q^{86} + 6q^{87} + 6q^{88} + 18q^{89} + 2q^{90} + 8q^{91} - 12q^{92} - 5q^{93} - 12q^{94} - 4q^{95} + q^{96} + 10q^{97} - 3q^{98} + 12q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).

\(n\) \(471\) \(537\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −2.00000 −0.534522
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) −1.00000 + 1.73205i −0.235702 + 0.408248i
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) −1.00000 1.73205i −0.218218 0.377964i
\(22\) −6.00000 −1.27920
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) −5.00000 −0.962250
\(28\) −1.00000 + 1.73205i −0.188982 + 0.327327i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) 3.00000 + 5.19615i 0.514496 + 0.891133i
\(35\) 1.00000 + 1.73205i 0.169031 + 0.292770i
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) 1.00000 0.158114
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) −2.00000 −0.308607
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) 2.00000 0.298142
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 2.00000 0.277350
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 2.00000 3.46410i 0.264906 0.458831i
\(58\) 6.00000 0.787839
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −5.00000 −0.635001
\(63\) 2.00000 + 3.46410i 0.251976 + 0.436436i
\(64\) 1.00000 0.125000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) −6.00000 −0.738549
\(67\) 2.50000 + 7.79423i 0.305424 + 0.952217i
\(68\) 6.00000 0.727607
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) 2.00000 0.239046
\(71\) 7.50000 + 12.9904i 0.890086 + 1.54167i 0.839771 + 0.542941i \(0.182689\pi\)
0.0503155 + 0.998733i \(0.483977\pi\)
\(72\) 2.00000 0.235702
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) −6.00000 + 10.3923i −0.683763 + 1.18431i
\(78\) 1.00000 + 1.73205i 0.113228 + 0.196116i
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 1.00000 0.111111
\(82\) −3.00000 −0.331295
\(83\) 7.50000 12.9904i 0.823232 1.42588i −0.0800311 0.996792i \(-0.525502\pi\)
0.903263 0.429087i \(-0.141165\pi\)
\(84\) −1.00000 + 1.73205i −0.109109 + 0.188982i
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) 1.00000 1.73205i 0.105409 0.182574i
\(91\) 4.00000 0.419314
\(92\) −6.00000 −0.625543
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −6.00000 −0.618853
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −1.50000 2.59808i −0.151523 0.262445i
\(99\) 6.00000 + 10.3923i 0.603023 + 1.04447i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 3.00000 + 5.19615i 0.297044 + 0.514496i
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 1.00000 + 1.73205i 0.0975900 + 0.169031i
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 6.00000 0.572078
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.00000 0.188982
\(113\) 9.00000 + 15.5885i 0.846649 + 1.46644i 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) −3.00000 + 5.19615i −0.276172 + 0.478345i
\(119\) 12.0000 1.10004
\(120\) 1.00000 0.0912871
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 4.00000 + 6.92820i 0.362143 + 0.627250i
\(123\) −1.50000 2.59808i −0.135250 0.234261i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) 4.00000 0.356348
\(127\) −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 8.00000 0.704361
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −3.00000 + 5.19615i −0.261116 + 0.452267i
\(133\) −8.00000 −0.693688
\(134\) 8.00000 + 1.73205i 0.691095 + 0.149626i
\(135\) 5.00000 0.430331
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −3.00000 5.19615i −0.255377 0.442326i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 1.00000 1.73205i 0.0845154 0.146385i
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) 15.0000 1.25877
\(143\) 12.0000 1.00349
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) −7.00000 −0.575396
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i \(-0.552039\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) 6.00000 + 10.3923i 0.483494 + 0.837436i
\(155\) 2.50000 + 4.33013i 0.200805 + 0.347804i
\(156\) 2.00000 0.160128
\(157\) 11.0000 19.0526i 0.877896 1.52056i 0.0242497 0.999706i \(-0.492280\pi\)
0.853646 0.520854i \(-0.174386\pi\)
\(158\) −8.00000 −0.636446
\(159\) −3.00000 −0.237915
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −12.0000 −0.945732
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 3.00000 + 5.19615i 0.233550 + 0.404520i
\(166\) −7.50000 12.9904i −0.582113 1.00825i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 1.00000 + 1.73205i 0.0771517 + 0.133631i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) −4.00000 + 6.92820i −0.305888 + 0.529813i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i \(-0.796953\pi\)
0.917397 + 0.397974i \(0.130287\pi\)
\(174\) 6.00000 0.454859
\(175\) −1.00000 1.73205i −0.0755929 0.130931i
\(176\) 6.00000 0.452267
\(177\) −6.00000 −0.450988
\(178\) 4.50000 7.79423i 0.337289 0.584202i
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) 2.00000 3.46410i 0.148250 0.256776i
\(183\) −4.00000 + 6.92820i −0.295689 + 0.512148i
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) −5.00000 −0.366618
\(187\) 36.0000 2.63258
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) 5.00000 + 8.66025i 0.363696 + 0.629941i
\(190\) 2.00000 + 3.46410i 0.145095 + 0.251312i
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 1.00000 0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 1.00000 1.73205i 0.0716115 0.124035i
\(196\) −3.00000 −0.214286
\(197\) −3.00000 5.19615i −0.213741 0.370211i 0.739141 0.673550i \(-0.235232\pi\)
−0.952882 + 0.303340i \(0.901898\pi\)
\(198\) 12.0000 0.852803
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.50000 + 7.79423i 0.176336 + 0.549762i
\(202\) −12.0000 −0.844317
\(203\) 6.00000 10.3923i 0.421117 0.729397i
\(204\) 6.00000 0.420084
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) 4.00000 0.278693
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) −24.0000 −1.66011
\(210\) 2.00000 0.138013
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 7.50000 + 12.9904i 0.513892 + 0.890086i
\(214\) −4.50000 + 7.79423i −0.307614 + 0.532803i
\(215\) −8.00000 −0.545595
\(216\) 5.00000 0.340207
\(217\) −5.00000 + 8.66025i −0.339422 + 0.587896i
\(218\) −2.00000 + 3.46410i −0.135457 + 0.234619i
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) −3.50000 6.06218i −0.234905 0.406867i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) −2.00000 −0.133333
\(226\) 18.0000 1.19734
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) −4.00000 −0.264906
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 3.00000 + 5.19615i 0.197814 + 0.342624i
\(231\) −6.00000 + 10.3923i −0.394771 + 0.683763i
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 6.00000 + 10.3923i 0.393073 + 0.680823i 0.992853 0.119342i \(-0.0380786\pi\)
−0.599780 + 0.800165i \(0.704745\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) −4.00000 6.92820i −0.259828 0.450035i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 12.5000 + 21.6506i 0.803530 + 1.39176i
\(243\) 16.0000 1.02640
\(244\) 8.00000 0.512148
\(245\) −1.50000 + 2.59808i −0.0958315 + 0.165985i
\(246\) −3.00000 −0.191273
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 2.50000 + 4.33013i 0.158750 + 0.274963i
\(249\) 7.50000 12.9904i 0.475293 0.823232i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 2.00000 3.46410i 0.125988 0.218218i
\(253\) −36.0000 −2.26330
\(254\) −8.00000 −0.501965
\(255\) 3.00000 5.19615i 0.187867 0.325396i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.0000 20.7846i −0.748539 1.29651i −0.948523 0.316709i \(-0.897422\pi\)
0.199983 0.979799i \(-0.435911\pi\)
\(258\) 4.00000 6.92820i 0.249029 0.431331i
\(259\) −14.0000 −0.869918
\(260\) −2.00000 −0.124035
\(261\) −6.00000 10.3923i −0.371391 0.643268i
\(262\) −6.00000 + 10.3923i −0.370681 + 0.642039i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 3.00000 0.184289
\(266\) −4.00000 + 6.92820i −0.245256 + 0.424795i
\(267\) 9.00000 0.550791
\(268\) 5.50000 6.06218i 0.335966 0.370306i
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 2.50000 4.33013i 0.152145 0.263523i
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) −3.00000 5.19615i −0.181902 0.315063i
\(273\) 4.00000 0.242091
\(274\) −3.00000 + 5.19615i −0.181237 + 0.313911i
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) −6.00000 −0.361158
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −5.00000 + 8.66025i −0.299880 + 0.519408i
\(279\) 5.00000 + 8.66025i 0.299342 + 0.518476i
\(280\) −1.00000 1.73205i −0.0597614 0.103510i
\(281\) −16.5000 + 28.5788i −0.984307 + 1.70487i −0.339333 + 0.940666i \(0.610201\pi\)
−0.644974 + 0.764204i \(0.723132\pi\)
\(282\) −6.00000 −0.357295
\(283\) 32.0000 1.90220 0.951101 0.308879i \(-0.0999539\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) 7.50000 12.9904i 0.445043 0.770837i
\(285\) −2.00000 + 3.46410i −0.118470 + 0.205196i
\(286\) 6.00000 10.3923i 0.354787 0.614510i
\(287\) −3.00000 + 5.19615i −0.177084 + 0.306719i
\(288\) −1.00000 1.73205i −0.0589256 0.102062i
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −6.00000 −0.352332
\(291\) 5.00000 8.66025i 0.293105 0.507673i
\(292\) −4.00000 −0.234082
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) −1.50000 2.59808i −0.0874818 0.151523i
\(295\) 6.00000 0.349334
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 15.0000 + 25.9808i 0.870388 + 1.50756i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) −9.50000 16.4545i −0.546664 0.946849i
\(303\) −6.00000 10.3923i −0.344691 0.597022i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 4.00000 6.92820i 0.229039 0.396708i
\(306\) −6.00000 10.3923i −0.342997 0.594089i
\(307\) 3.50000 6.06218i 0.199756 0.345987i −0.748694 0.662916i \(-0.769319\pi\)
0.948449 + 0.316929i \(0.102652\pi\)
\(308\) 12.0000 0.683763
\(309\) 2.00000 + 3.46410i 0.113776 + 0.197066i
\(310\) 5.00000 0.283981
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −11.0000 19.0526i −0.620766 1.07520i
\(315\) −2.00000 3.46410i −0.112687 0.195180i
\(316\) −4.00000 + 6.92820i −0.225018 + 0.389742i
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) −1.50000 + 2.59808i −0.0841158 + 0.145693i
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) −1.00000 −0.0559017
\(321\) −9.00000 −0.502331
\(322\) −6.00000 + 10.3923i −0.334367 + 0.579141i
\(323\) 12.0000 + 20.7846i 0.667698 + 1.15649i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 19.0000 1.05231
\(327\) −4.00000 −0.221201
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) 6.00000 0.330289
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −15.0000 −0.823232
\(333\) −7.00000 + 12.1244i −0.383598 + 0.664411i
\(334\) −12.0000 −0.656611
\(335\) −2.50000 7.79423i −0.136590 0.425844i
\(336\) 2.00000 0.109109
\(337\) −10.0000 + 17.3205i −0.544735 + 0.943508i 0.453889 + 0.891058i \(0.350036\pi\)
−0.998624 + 0.0524499i \(0.983297\pi\)
\(338\) 9.00000 0.489535
\(339\) 9.00000 + 15.5885i 0.488813 + 0.846649i
\(340\) −6.00000 −0.325396
\(341\) −15.0000 + 25.9808i −0.812296 + 1.40694i
\(342\) 4.00000 + 6.92820i 0.216295 + 0.374634i
\(343\) −20.0000 −1.07990
\(344\) −8.00000 −0.431331
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) −1.50000 2.59808i −0.0806405 0.139673i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −2.00000 −0.106904
\(351\) 5.00000 8.66025i 0.266880 0.462250i
\(352\) 3.00000 5.19615i 0.159901 0.276956i
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) −7.50000 12.9904i −0.398059 0.689458i
\(356\) −4.50000 7.79423i −0.238500 0.413093i
\(357\) 12.0000 0.635107
\(358\) −3.00000 + 5.19615i −0.158555 + 0.274625i
\(359\) −27.0000 −1.42501 −0.712503 0.701669i \(-0.752438\pi\)
−0.712503 + 0.701669i \(0.752438\pi\)
\(360\) −2.00000 −0.105409
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −2.00000 −0.105118
\(363\) −12.5000 + 21.6506i −0.656080 + 1.13636i
\(364\) −2.00000 3.46410i −0.104828 0.181568i
\(365\) −2.00000 + 3.46410i −0.104685 + 0.181319i
\(366\) 4.00000 + 6.92820i 0.209083 + 0.362143i
\(367\) −7.00000 12.1244i −0.365397 0.632886i 0.623443 0.781869i \(-0.285733\pi\)
−0.988840 + 0.148983i \(0.952400\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 3.50000 + 6.06218i 0.181956 + 0.315158i
\(371\) 3.00000 + 5.19615i 0.155752 + 0.269771i
\(372\) −2.50000 + 4.33013i −0.129619 + 0.224507i
\(373\) −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 18.0000 31.1769i 0.930758 1.61212i
\(375\) −1.00000 −0.0516398
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) −12.0000 −0.618031
\(378\) 10.0000 0.514344
\(379\) −19.0000 + 32.9090i −0.975964 + 1.69042i −0.299249 + 0.954175i \(0.596736\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(380\) 4.00000 0.205196
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 1.50000 + 2.59808i 0.0767467 + 0.132929i
\(383\) −3.00000 + 5.19615i −0.153293 + 0.265511i −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) 7.00000 12.1244i 0.356291 0.617113i
\(387\) −16.0000 −0.813326
\(388\) −10.0000 −0.507673
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) −1.00000 1.73205i −0.0506370 0.0877058i
\(391\) 18.0000 + 31.1769i 0.910299 + 1.57668i
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) 5.00000 0.250943 0.125471 0.992097i \(-0.459956\pi\)
0.125471 + 0.992097i \(0.459956\pi\)
\(398\) −3.50000 6.06218i −0.175439 0.303870i
\(399\) −8.00000 −0.400501
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 8.00000 + 1.73205i 0.399004 + 0.0863868i
\(403\) 10.0000 0.498135
\(404\) −6.00000 + 10.3923i −0.298511 + 0.517036i
\(405\) −1.00000 −0.0496904
\(406\) −6.00000 10.3923i −0.297775 0.515761i
\(407\) −42.0000 −2.08186
\(408\) 3.00000 5.19615i 0.148522 0.257248i
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 3.00000 0.148159
\(411\) −6.00000 −0.295958
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) 6.00000 + 10.3923i 0.295241 + 0.511372i
\(414\) 6.00000 + 10.3923i 0.294884 + 0.510754i
\(415\) −7.50000 + 12.9904i −0.368161 + 0.637673i
\(416\) −2.00000 −0.0980581
\(417\) −10.0000 −0.489702
\(418\) −12.0000 + 20.7846i −0.586939 + 1.01661i
\(419\) 12.0000 20.7846i 0.586238 1.01539i −0.408481 0.912767i \(-0.633942\pi\)
0.994720 0.102628i \(-0.0327251\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) 14.0000 24.2487i 0.682318 1.18181i −0.291953 0.956433i \(-0.594305\pi\)
0.974272 0.225377i \(-0.0723615\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) 6.00000 + 10.3923i 0.291730 + 0.505291i
\(424\) 3.00000 0.145693
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 15.0000 0.726752
\(427\) 16.0000 0.774294
\(428\) 4.50000 + 7.79423i 0.217516 + 0.376748i
\(429\) 12.0000 0.579365
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 16.5000 + 28.5788i 0.794777 + 1.37659i 0.922981 + 0.384846i \(0.125746\pi\)
−0.128204 + 0.991748i \(0.540921\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 8.00000 + 13.8564i 0.384455 + 0.665896i 0.991693 0.128624i \(-0.0410559\pi\)
−0.607238 + 0.794520i \(0.707723\pi\)
\(434\) 5.00000 + 8.66025i 0.240008 + 0.415705i
\(435\) −3.00000 5.19615i −0.143839 0.249136i
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) −12.0000 20.7846i −0.574038 0.994263i
\(438\) −2.00000 3.46410i −0.0955637 0.165521i
\(439\) 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i \(-0.683541\pi\)
0.998595 + 0.0529862i \(0.0168739\pi\)
\(440\) −3.00000 5.19615i −0.143019 0.247717i
\(441\) −3.00000 + 5.19615i −0.142857 + 0.247436i
\(442\) −12.0000 −0.570782
\(443\) −13.5000 23.3827i −0.641404 1.11094i −0.985119 0.171871i \(-0.945019\pi\)
0.343715 0.939074i \(-0.388315\pi\)
\(444\) −7.00000 −0.332205
\(445\) −9.00000 −0.426641
\(446\) 10.0000 17.3205i 0.473514 0.820150i
\(447\) 6.00000 0.283790
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) −10.5000 18.1865i −0.495526 0.858276i 0.504461 0.863434i \(-0.331691\pi\)
−0.999987 + 0.00515887i \(0.998358\pi\)
\(450\) −1.00000 + 1.73205i −0.0471405 + 0.0816497i
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 9.50000 16.4545i 0.446349 0.773099i
\(454\) 3.00000 0.140797
\(455\) −4.00000 −0.187523
\(456\) −2.00000 + 3.46410i −0.0936586 + 0.162221i
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) 15.0000 25.9808i 0.700140 1.21268i
\(460\) 6.00000 0.279751
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 6.00000 + 10.3923i 0.279145 + 0.483494i
\(463\) 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i \(-0.803704\pi\)
0.908750 + 0.417340i \(0.137038\pi\)
\(464\) −6.00000 −0.278543
\(465\) 2.50000 + 4.33013i 0.115935 + 0.200805i
\(466\) 12.0000 0.555889
\(467\) 16.5000 28.5788i 0.763529 1.32247i −0.177492 0.984122i \(-0.556798\pi\)
0.941021 0.338349i \(-0.109868\pi\)
\(468\) −4.00000 −0.184900
\(469\) 11.0000 12.1244i 0.507933 0.559851i
\(470\) 6.00000 0.276759
\(471\) 11.0000 19.0526i 0.506853 0.877896i
\(472\) 6.00000 0.276172
\(473\) −24.0000 41.5692i −1.10352 1.91135i
\(474\) −8.00000 −0.367452
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) −6.00000 10.3923i −0.275010 0.476331i
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) 7.00000 + 12.1244i 0.319173 + 0.552823i
\(482\) −6.50000 + 11.2583i −0.296067 + 0.512803i
\(483\) −12.0000 −0.546019
\(484\) 25.0000 1.13636
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 8.00000 13.8564i 0.362887 0.628539i
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) 4.00000 6.92820i 0.181071 0.313625i
\(489\) 9.50000 + 16.4545i 0.429605 + 0.744097i
\(490\) 1.50000 + 2.59808i 0.0677631 + 0.117369i
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) −1.50000 + 2.59808i −0.0676252 + 0.117130i
\(493\) −36.0000 −1.62136
\(494\) 8.00000 0.359937
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) 5.00000 0.224507
\(497\) 15.0000 25.9808i 0.672842 1.16540i
\(498\) −7.50000 12.9904i −0.336083 0.582113i
\(499\) 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) 15.0000 + 25.9808i 0.668817 + 1.15842i 0.978235 + 0.207499i \(0.0665323\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(504\) −2.00000 3.46410i −0.0890871 0.154303i
\(505\) 6.00000 + 10.3923i 0.266996 + 0.462451i
\(506\) −18.0000 + 31.1769i −0.800198 + 1.38598i
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) −4.00000 + 6.92820i −0.177471 + 0.307389i
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) −3.00000 5.19615i −0.132842 0.230089i
\(511\) −8.00000 −0.353899
\(512\) −1.00000 −0.0441942
\(513\) −10.0000 + 17.3205i −0.441511 + 0.764719i
\(514\) −24.0000 −1.05859
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) −18.0000 + 31.1769i −0.791639 + 1.37116i
\(518\) −7.00000 + 12.1244i −0.307562 + 0.532714i
\(519\) 1.50000 2.59808i 0.0658427 0.114043i
\(520\) −1.00000 + 1.73205i −0.0438529 + 0.0759555i
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) −12.0000 −0.525226
\(523\) −2.50000 + 4.33013i −0.109317 + 0.189343i −0.915494 0.402332i \(-0.868200\pi\)
0.806177 + 0.591675i \(0.201533\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) −1.00000 1.73205i −0.0436436 0.0755929i
\(526\) 0 0
\(527\) 30.0000 1.30682
\(528\) 6.00000 0.261116
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 1.50000 2.59808i 0.0651558 0.112853i
\(531\) 12.0000 0.520756
\(532\) 4.00000 + 6.92820i 0.173422 + 0.300376i
\(533\) 6.00000 0.259889
\(534\) 4.50000 7.79423i 0.194734 0.337289i
\(535\) 9.00000 0.389104
\(536\) −2.50000 7.79423i −0.107984 0.336659i
\(537\) −6.00000 −0.258919
\(538\) −9.00000 + 15.5885i −0.388018 + 0.672066i
\(539\) −18.0000 −0.775315
\(540\) −2.50000 4.33013i −0.107583 0.186339i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −6.50000 + 11.2583i −0.279199 + 0.483587i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) −6.00000 −0.257248
\(545\) 4.00000 0.171341
\(546\) 2.00000 3.46410i 0.0855921 0.148250i
\(547\) 12.5000 + 21.6506i 0.534461 + 0.925714i 0.999189 + 0.0402607i \(0.0128188\pi\)
−0.464728 + 0.885454i \(0.653848\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 8.00000 13.8564i 0.341432 0.591377i
\(550\) −6.00000 −0.255841
\(551\) 24.0000 1.02243
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) −8.00000 + 13.8564i −0.340195 + 0.589234i
\(554\) 8.50000 14.7224i 0.361130 0.625496i
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) 5.00000 + 8.66025i 0.212047 + 0.367277i
\(557\) −19.5000 33.7750i −0.826242 1.43109i −0.900967 0.433888i \(-0.857141\pi\)
0.0747252 0.997204i \(-0.476192\pi\)
\(558\) 10.0000 0.423334
\(559\) −8.00000 + 13.8564i −0.338364 + 0.586064i
\(560\) −2.00000 −0.0845154
\(561\) 36.0000 1.51992
\(562\) 16.5000 + 28.5788i 0.696010 + 1.20553i
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 16.0000 27.7128i 0.672530 1.16486i
\(567\) −1.00000 1.73205i −0.0419961 0.0727393i
\(568\) −7.50000 12.9904i −0.314693 0.545064i
\(569\) 13.5000 + 23.3827i 0.565949 + 0.980253i 0.996961 + 0.0779066i \(0.0248236\pi\)
−0.431011 + 0.902347i \(0.641843\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) −6.00000 10.3923i −0.250873 0.434524i
\(573\) −1.50000 + 2.59808i −0.0626634 + 0.108536i
\(574\) 3.00000 + 5.19615i 0.125218 + 0.216883i
\(575\) 3.00000 5.19615i 0.125109 0.216695i
\(576\) −2.00000 −0.0833333
\(577\) 8.00000 + 13.8564i 0.333044 + 0.576850i 0.983107 0.183031i \(-0.0585908\pi\)
−0.650063 + 0.759880i \(0.725257\pi\)
\(578\) −19.0000 −0.790296
\(579\) 14.0000 0.581820
\(580\) −3.00000 + 5.19615i −0.124568 + 0.215758i
\(581\) −30.0000 −1.24461
\(582\) −5.00000 8.66025i −0.207257 0.358979i
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) −2.00000 + 3.46410i −0.0826898 + 0.143223i
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i \(-0.594867\pi\)
0.974668 0.223659i \(-0.0718001\pi\)
\(588\) −3.00000 −0.123718
\(589\) −20.0000 −0.824086
\(590\) 3.00000 5.19615i 0.123508 0.213922i
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 30.0000 1.23091
\(595\) −12.0000 −0.491952
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 3.50000 6.06218i 0.143245 0.248108i
\(598\) 12.0000 0.490716
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 5.00000 8.66025i 0.203954 0.353259i −0.745845 0.666120i \(-0.767954\pi\)
0.949799 + 0.312861i \(0.101287\pi\)
\(602\) −16.0000 −0.652111
\(603\) −5.00000 15.5885i −0.203616 0.634811i
\(604\) −19.0000 −0.773099
\(605\) 12.5000 21.6506i 0.508197 0.880223i
\(606\) −12.0000 −0.487467
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 4.00000 0.162221
\(609\) 6.00000 10.3923i 0.243132 0.421117i
\(610\) −4.00000 6.92820i −0.161955 0.280515i
\(611\) 12.0000 0.485468
\(612\) −12.0000 −0.485071
\(613\) 21.5000 37.2391i 0.868377 1.50407i 0.00472215 0.999989i \(-0.498497\pi\)
0.863655 0.504084i \(-0.168170\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 1.50000 + 2.59808i 0.0604858 + 0.104765i
\(616\) 6.00000 10.3923i 0.241747 0.418718i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 4.00000 0.160904
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 2.50000 4.33013i 0.100402 0.173902i
\(621\) −15.0000 + 25.9808i −0.601929 + 1.04257i
\(622\) −10.5000 + 18.1865i −0.421012 + 0.729214i
\(623\) −9.00000 15.5885i −0.360577 0.624538i
\(624\) −1.00000 1.73205i −0.0400320 0.0693375i
\(625\) 1.00000 0.0400000
\(626\) −11.0000 + 19.0526i −0.439648 + 0.761493i
\(627\) −24.0000 −0.958468
\(628\) −22.0000 −0.877896
\(629\) 21.0000 + 36.3731i 0.837325 + 1.45029i
\(630\) −4.00000 −0.159364
\(631\) −4.00000 + 6.92820i −0.159237 + 0.275807i −0.934594 0.355716i \(-0.884237\pi\)
0.775356 + 0.631524i \(0.217570\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) 2.00000 3.46410i 0.0794929 0.137686i
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) 4.00000 + 6.92820i 0.158735 + 0.274937i
\(636\) 1.50000 + 2.59808i 0.0594789 + 0.103020i
\(637\) 3.00000 + 5.19615i 0.118864 + 0.205879i
\(638\) −18.0000 31.1769i −0.712627 1.23431i
\(639\) −15.0000 25.9808i −0.593391 1.02778i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) −4.50000 + 7.79423i −0.177601 + 0.307614i
\(643\) 41.0000 1.61688 0.808441 0.588577i \(-0.200312\pi\)
0.808441 + 0.588577i \(0.200312\pi\)
\(644\) 6.00000 + 10.3923i 0.236433 + 0.409514i
\(645\) −8.00000 −0.315000
\(646\) 24.0000 0.944267
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 18.0000 + 31.1769i 0.706562 + 1.22380i
\(650\) 1.00000 + 1.73205i 0.0392232 + 0.0679366i
\(651\) −5.00000 + 8.66025i −0.195965 + 0.339422i
\(652\) 9.50000 16.4545i 0.372049 0.644407i
\(653\) 22.5000 38.9711i 0.880493 1.52506i 0.0296993 0.999559i \(-0.490545\pi\)
0.850794 0.525500i \(-0.176122\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 12.0000 0.468879
\(656\) 3.00000 0.117130
\(657\) −4.00000 + 6.92820i −0.156055 + 0.270295i
\(658\) 6.00000 + 10.3923i 0.233904 + 0.405134i
\(659\) 9.00000 + 15.5885i 0.350590 + 0.607240i 0.986353 0.164644i \(-0.0526477\pi\)
−0.635763 + 0.771885i \(0.719314\pi\)
\(660\) 3.00000 5.19615i 0.116775 0.202260i
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) −8.00000 −0.310929
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) −7.50000 + 12.9904i −0.291056 + 0.504125i
\(665\) 8.00000 0.310227
\(666\) 7.00000 + 12.1244i 0.271244 + 0.469809i
\(667\) 36.0000 1.39393
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 20.0000 0.773245
\(670\) −8.00000 1.73205i −0.309067 0.0669150i
\(671\) 48.0000 1.85302
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 10.0000 + 17.3205i 0.385186 + 0.667161i
\(675\) −5.00000 −0.192450
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 4.50000 + 7.79423i 0.172949 + 0.299557i 0.939450 0.342687i \(-0.111337\pi\)
−0.766501 + 0.642244i \(0.778004\pi\)
\(678\) 18.0000 0.691286
\(679\) −20.0000 −0.767530
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) 1.50000 + 2.59808i 0.0574801 + 0.0995585i
\(682\) 15.0000 + 25.9808i 0.574380 + 0.994855i
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 8.00000 0.305888
\(685\) 6.00000 0.229248
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 5.00000 8.66025i 0.190762 0.330409i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 3.00000 5.19615i 0.114291 0.197958i
\(690\) 3.00000 + 5.19615i 0.114208 + 0.197814i
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) −3.00000 −0.114043
\(693\) 12.0000 20.7846i 0.455842 0.789542i
\(694\) 12.0000 0.455514
\(695\) 10.0000 0.379322
\(696\) −3.00000 5.19615i −0.113715 0.196960i
\(697\) 18.0000 0.681799
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 6.00000 + 10.3923i 0.226941 + 0.393073i
\(700\) −1.00000 + 1.73205i −0.0377964 + 0.0654654i
\(701\) 15.0000 + 25.9808i 0.566542 + 0.981280i 0.996904 + 0.0786236i \(0.0250525\pi\)
−0.430362 + 0.902656i \(0.641614\pi\)
\(702\) −5.00000 8.66025i −0.188713 0.326860i
\(703\) −14.0000 24.2487i −0.528020 0.914557i
\(704\) −3.00000 5.19615i −0.113067 0.195837i
\(705\) 3.00000 + 5.19615i 0.112987 + 0.195698i
\(706\) 0 0
\(707\) −12.0000 + 20.7846i −0.451306 + 0.781686i
\(708\) 3.00000 + 5.19615i 0.112747 + 0.195283i
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) −15.0000 −0.562940
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) −9.00000 −0.337289
\(713\) −30.0000 −1.12351
\(714\) 6.00000 10.3923i 0.224544 0.388922i
\(715\) −12.0000 −0.448775
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) 0 0
\(718\) −13.5000 + 23.3827i −0.503816 + 0.872634i
\(719\) −19.5000 + 33.7750i −0.727227 + 1.25959i 0.230823 + 0.972996i \(0.425858\pi\)
−0.958051 + 0.286599i \(0.907475\pi\)
\(720\) −1.00000 + 1.73205i −0.0372678 + 0.0645497i
\(721\) 4.00000 6.92820i 0.148968 0.258020i
\(722\) 3.00000 0.111648
\(723\) −13.0000 −0.483475
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 12.5000 + 21.6506i 0.463919 + 0.803530i
\(727\) 14.0000 24.2487i 0.519231 0.899335i −0.480519 0.876984i \(-0.659552\pi\)
0.999750 0.0223506i \(-0.00711500\pi\)
\(728\) −4.00000 −0.148250
\(729\) 13.0000 0.481481
\(730\) 2.00000 + 3.46410i 0.0740233 + 0.128212i
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 8.00000 0.295689
\(733\) −2.50000 4.33013i −0.0923396 0.159937i 0.816156 0.577832i \(-0.196101\pi\)
−0.908495 + 0.417895i \(0.862768\pi\)
\(734\) −14.0000 −0.516749
\(735\) −1.50000 + 2.59808i −0.0553283 + 0.0958315i
\(736\) 6.00000 0.221163
\(737\) 33.0000 36.3731i 1.21557 1.33982i
\(738\) 6.00000 0.220863
\(739\) −4.00000 + 6.92820i −0.147142 + 0.254858i −0.930170 0.367129i \(-0.880341\pi\)
0.783028 + 0.621987i \(0.213674\pi\)
\(740\) 7.00000 0.257325
\(741\) 4.00000 + 6.92820i 0.146944 + 0.254514i
\(742\) 6.00000 0.220267
\(743\) −3.00000 + 5.19615i −0.110059 + 0.190628i −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) 2.50000 + 4.33013i 0.0916544 + 0.158750i
\(745\) −6.00000 −0.219823
\(746\) −23.0000 −0.842090
\(747\) −15.0000 + 25.9808i −0.548821 + 0.950586i
\(748\) −18.0000 31.1769i −0.658145 1.13994i
\(749\) 9.00000 + 15.5885i 0.328853 + 0.569590i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 41.0000 1.49611 0.748056 0.663636i \(-0.230988\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) 6.00000 0.218797
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) −9.50000 + 16.4545i −0.345740 + 0.598840i
\(756\) 5.00000 8.66025i 0.181848 0.314970i
\(757\) −14.5000 25.1147i −0.527011 0.912811i −0.999505 0.0314762i \(-0.989979\pi\)
0.472493 0.881334i \(-0.343354\pi\)
\(758\) 19.0000 + 32.9090i 0.690111 + 1.19531i
\(759\) −36.0000 −1.30672
\(760\) 2.00000 3.46410i 0.0725476 0.125656i
\(761\) 33.0000 1.19625 0.598125 0.801403i \(-0.295913\pi\)
0.598125 + 0.801403i \(0.295913\pi\)
\(762\) −8.00000 −0.289809
\(763\) 4.00000 + 6.92820i 0.144810 + 0.250818i
\(764\) 3.00000 0.108536
\(765\) −6.00000 + 10.3923i −0.216930 + 0.375735i
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) 6.00000 10.3923i 0.216647 0.375244i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) −6.00000 10.3923i −0.216225 0.374513i
\(771\) −12.0000 20.7846i −0.432169 0.748539i
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) −8.00000 + 13.8564i −0.287554 + 0.498058i
\(775\) −2.50000 4.33013i −0.0898027 0.155543i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) −14.0000 −0.502247
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) −12.0000 −0.429945
\(780\) −2.00000 −0.0716115
\(781\) 45.0000 77.9423i 1.61023 2.78899i
\(782\) 36.0000 1.28736
\(783\) −15.0000 25.9808i −0.536056 0.928477i
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) −11.0000 + 19.0526i −0.392607 + 0.680015i
\(786\) −6.00000 + 10.3923i −0.214013 + 0.370681i
\(787\) −8.50000 + 14.7224i −0.302992 + 0.524798i −0.976812 0.214097i \(-0.931319\pi\)
0.673820 + 0.738896i \(0.264652\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) 0 0
\(790\) 8.00000 0.284627
\(791\) 18.0000 31.1769i 0.640006 1.10852i
\(792\) −6.00000 10.3923i