Properties

Label 670.2.e.d.171.1
Level 670
Weight 2
Character 670.171
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 171.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 670.171
Dual form 670.2.e.d.431.1

$q$-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 \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).

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

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 −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −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 −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −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 −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 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 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −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 −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 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 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) −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 −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) −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 −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) −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 −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) −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 0.0503155 0.998733i \(-0.483977\pi\)
0.839771 0.542941i \(-0.182689\pi\)
\(72\) 2.00000 0.235702
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −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 −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 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 0.903263 + 0.429087i \(0.141165\pi\)
−0.0800311 + 0.996792i \(0.525502\pi\)
\(84\) −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 0.999961 + 0.00888289i \(0.00282755\pi\)
−0.492287 + 0.870433i \(0.663839\pi\)
\(98\) −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 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 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 −0.0375328 0.999295i \(-0.511950\pi\)
0.884182 0.467143i \(-0.154717\pi\)
\(114\) −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 −0.987108 0.160055i \(-0.948833\pi\)
0.632166 + 0.774833i \(0.282166\pi\)
\(128\) 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 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −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 0.853646 + 0.520854i \(0.174386\pi\)
0.0242497 + 0.999706i \(0.492280\pi\)
\(158\) −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 −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) −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 −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 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 0.917397 0.397974i \(-0.130287\pi\)
−0.803354 + 0.595502i \(0.796953\pi\)
\(174\) 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 −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 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 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 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 −0.952882 0.303340i \(-0.901898\pi\)
0.739141 + 0.673550i \(0.235232\pi\)
\(198\) 12.0000 0.852803
\(199\) 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i \(-0.0868577\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(200\) −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 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) 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 −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) −4.00000 −0.264906
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 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 −0.599780 0.800165i \(-0.704745\pi\)
0.992853 + 0.119342i \(0.0380786\pi\)
\(234\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 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 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 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 0.199983 + 0.979799i \(0.435911\pi\)
−0.948523 + 0.316709i \(0.897422\pi\)
\(258\) 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 −0.644974 0.764204i \(-0.723132\pi\)
−0.339333 0.940666i \(-0.610201\pi\)
\(282\) −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 0.948449 0.316929i \(-0.102652\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(308\) 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 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) −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 −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −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 −0.998624 0.0524499i \(-0.983297\pi\)
0.453889 0.891058i \(-0.350036\pi\)
\(338\) 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 −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) −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 −0.988840 0.148983i \(-0.952400\pi\)
0.623443 + 0.781869i \(0.285733\pi\)
\(368\) 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 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 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 −0.676715 0.736245i \(-0.736597\pi\)
−0.299249 0.954175i \(-0.596736\pi\)
\(380\) 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 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) 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 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) −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 −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 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 0.994720 + 0.102628i \(0.0327251\pi\)
−0.408481 + 0.912767i \(0.633942\pi\)
\(420\) 1.00000 + 1.73205i 0.0487950 + 0.0845154i
\(421\) 14.0000 + 24.2487i 0.682318 + 1.18181i 0.974272 + 0.225377i \(0.0723615\pi\)
−0.291953 + 0.956433i \(0.594305\pi\)
\(422\) −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 −0.128204 0.991748i \(-0.540921\pi\)
0.922981 0.384846i \(-0.125746\pi\)
\(432\) 2.50000 + 4.33013i 0.120281 + 0.208333i
\(433\) 8.00000 13.8564i 0.384455 0.665896i −0.607238 0.794520i \(-0.707723\pi\)
0.991693 + 0.128624i \(0.0410559\pi\)
\(434\) 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 0.998595 0.0529862i \(-0.0168739\pi\)
−0.545185 + 0.838316i \(0.683541\pi\)
\(440\) −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 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) −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 −0.999987 0.00515887i \(-0.998358\pi\)
0.504461 + 0.863434i \(0.331691\pi\)
\(450\) −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 −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) −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 0.908750 0.417340i \(-0.137038\pi\)
−0.815802 + 0.578331i \(0.803704\pi\)
\(464\) −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 0.941021 + 0.338349i \(0.109868\pi\)
−0.177492 + 0.984122i \(0.556798\pi\)
\(468\) −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 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) −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 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 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 0.833404 + 0.552664i \(0.186389\pi\)
0.0619186 + 0.998081i \(0.480278\pi\)
\(500\) 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 −0.309418 0.950926i \(-0.600134\pi\)
0.978235 0.207499i \(-0.0665323\pi\)
\(504\) −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 0.806177 0.591675i \(-0.201533\pi\)
−0.915494 + 0.402332i \(0.868200\pi\)
\(524\) 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 −0.464728 0.885454i \(-0.653848\pi\)
0.999189 0.0402607i \(-0.0128188\pi\)
\(548\) 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 0.0747252 + 0.997204i \(0.476192\pi\)
−0.900967 + 0.433888i \(0.857141\pi\)
\(558\) 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 −0.431011 0.902347i \(-0.641843\pi\)
0.996961 0.0779066i \(-0.0248236\pi\)
\(570\) 2.00000 3.46410i 0.0837708 0.145095i
\(571\) 20.0000 34.6410i 0.836974 1.44968i −0.0554391 0.998462i \(-0.517656\pi\)
0.892413 0.451219i \(-0.149011\pi\)
\(572\) −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 −0.650063 0.759880i \(-0.725257\pi\)
0.983107 + 0.183031i \(0.0585908\pi\)
\(578\) −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 0.974668 + 0.223659i \(0.0718001\pi\)
−0.293640 + 0.955916i \(0.594867\pi\)
\(588\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 5.00000 + 8.66025i 0.203954 + 0.353259i 0.949799 0.312861i \(-0.101287\pi\)
−0.745845 + 0.666120i \(0.767954\pi\)
\(602\) −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 −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 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 0.863655 + 0.504084i \(0.168170\pi\)
0.00472215 + 0.999989i \(0.498497\pi\)
\(614\) −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 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 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 0.775356 0.631524i \(-0.217570\pi\)
−0.934594 + 0.355716i \(0.884237\pi\)
\(632\) 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 −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −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 0.850794 + 0.525500i \(0.176122\pi\)
0.0296993 + 0.999559i \(0.490545\pi\)
\(654\) −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 −0.635763 0.771885i \(-0.719314\pi\)
0.986353 + 0.164644i \(0.0526477\pi\)
\(660\) 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 −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 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 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 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 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −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 −0.430362 0.902656i \(-0.641614\pi\)
0.996904 0.0786236i \(-0.0250525\pi\)
\(702\) −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 −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) −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 −0.958051 0.286599i \(-0.907475\pi\)
0.230823 0.972996i \(-0.425858\pi\)
\(720\) −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 0.999750 + 0.0223506i \(0.00711500\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(728\) −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 −0.908495 0.417895i \(-0.862768\pi\)
0.816156 + 0.577832i \(0.196101\pi\)
\(734\) −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 0.783028 0.621987i \(-0.213674\pi\)
−0.930170 + 0.367129i \(0.880341\pi\)
\(740\) 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 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 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 0.472493 + 0.881334i \(0.343354\pi\)
−0.999505 + 0.0314762i \(0.989979\pi\)
\(758\) 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 −0.964193 0.265200i \(-0.914562\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(770\) −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 −0.990721 0.135910i \(-0.956604\pi\)
0.613062 + 0.790034i \(0.289937\pi\)
\(774\) −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 0.673820 0.738896i \(-0.264652\pi\)
−0.976812 + 0.214097i \(0.931319\pi\)
\(788\) −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 +