Properties

Label 930.2.i.i.811.1
Level $930$
Weight $2$
Character 930.811
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 811.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 930.811
Dual form 930.2.i.i.211.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{22} -4.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} -5.00000 q^{29} +1.00000 q^{30} +(5.50000 + 0.866025i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +(2.00000 - 3.46410i) q^{34} +3.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} +2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(4.00000 - 6.92820i) q^{43} +(1.50000 + 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} -4.00000 q^{46} -8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(1.00000 + 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} -1.00000 q^{54} +(-1.50000 + 2.59808i) q^{55} +(1.50000 - 2.59808i) q^{56} -5.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +1.00000 q^{60} -8.00000 q^{61} +(5.50000 + 0.866025i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +3.00000 q^{66} +(5.00000 + 8.66025i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-2.00000 + 3.46410i) q^{69} +3.00000 q^{70} +(4.00000 + 6.92820i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(3.00000 - 5.19615i) q^{74} +(0.500000 + 0.866025i) q^{75} +9.00000 q^{77} +2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +(4.50000 + 7.79423i) q^{83} +(-1.50000 - 2.59808i) q^{84} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.50000 + 2.59808i) q^{88} -8.00000 q^{89} +(0.500000 - 0.866025i) q^{90} +6.00000 q^{91} -4.00000 q^{92} +(3.50000 - 4.33013i) q^{93} -8.00000 q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-1.00000 - 1.73205i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} - q^{18} + q^{20} - 3 q^{21} + 3 q^{22} - 8 q^{23} + q^{24} - q^{25} + 2 q^{26} - 2 q^{27} + 3 q^{28} - 10 q^{29} + 2 q^{30} + 11 q^{31} + 2 q^{32} + 6 q^{33} + 4 q^{34} + 6 q^{35} - q^{36} + 6 q^{37} + 4 q^{39} + q^{40} + 2 q^{41} - 3 q^{42} + 8 q^{43} + 3 q^{44} + q^{45} - 8 q^{46} - 16 q^{47} + q^{48} - 2 q^{49} - q^{50} - 4 q^{51} + 2 q^{52} + 3 q^{53} - 2 q^{54} - 3 q^{55} + 3 q^{56} - 10 q^{58} - 3 q^{59} + 2 q^{60} - 16 q^{61} + 11 q^{62} - 6 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} + 10 q^{67} + 4 q^{68} - 4 q^{69} + 6 q^{70} + 8 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + q^{75} + 18 q^{77} + 4 q^{78} - 8 q^{79} + q^{80} - q^{81} + 2 q^{82} + 9 q^{83} - 3 q^{84} + 8 q^{85} + 8 q^{86} - 5 q^{87} + 3 q^{88} - 16 q^{89} + q^{90} + 12 q^{91} - 8 q^{92} + 7 q^{93} - 16 q^{94} + q^{96} - 14 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 1.00000 0.500000
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i \(-0.641458\pi\)
0.996866 0.0791130i \(-0.0252088\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) −1.50000 2.59808i −0.327327 0.566947i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 1.50000 2.59808i 0.283473 0.490990i
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 1.00000 0.182574
\(31\) 5.50000 + 0.866025i 0.987829 + 0.155543i
\(32\) 1.00000 0.176777
\(33\) 3.00000 0.522233
\(34\) 2.00000 3.46410i 0.342997 0.594089i
\(35\) 3.00000 0.507093
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) −1.50000 2.59808i −0.231455 0.400892i
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) −4.00000 −0.589768
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.50000 + 2.59808i −0.202260 + 0.350325i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 1.00000 0.129099
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 5.50000 + 0.866025i 0.698501 + 0.109985i
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 3.00000 0.369274
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 3.00000 0.358569
\(71\) 4.00000 + 6.92820i 0.474713 + 0.822226i 0.999581 0.0289572i \(-0.00921865\pi\)
−0.524868 + 0.851184i \(0.675885\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 9.00000 1.02565
\(78\) 2.00000 0.226455
\(79\) −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
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00000 + 1.73205i 0.110432 + 0.191273i
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) −1.50000 2.59808i −0.163663 0.283473i
\(85\) 4.00000 0.433861
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) −2.50000 + 4.33013i −0.268028 + 0.464238i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) 6.00000 0.628971
\(92\) −4.00000 −0.417029
\(93\) 3.50000 4.33013i 0.362933 0.449013i
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) 1.50000 2.59808i 0.150756 0.261116i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 11.0000 1.09454 0.547270 0.836956i \(-0.315667\pi\)
0.547270 + 0.836956i \(0.315667\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 1.50000 2.59808i 0.146385 0.253546i
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −7.50000 + 12.9904i −0.725052 + 1.25583i 0.233900 + 0.972261i \(0.424851\pi\)
−0.958952 + 0.283567i \(0.908482\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) −3.00000 5.19615i −0.284747 0.493197i
\(112\) 1.50000 2.59808i 0.141737 0.245495i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) −5.00000 −0.464238
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) −1.50000 + 2.59808i −0.138086 + 0.239172i
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) 1.00000 0.0912871
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −8.00000 −0.724286
\(123\) 2.00000 0.180334
\(124\) 5.50000 + 0.866025i 0.493915 + 0.0777714i
\(125\) −1.00000 −0.0894427
\(126\) −3.00000 −0.267261
\(127\) 0.500000 0.866025i 0.0443678 0.0768473i −0.842989 0.537931i \(-0.819206\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 5.00000 + 8.66025i 0.431934 + 0.748132i
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i \(-0.0261741\pi\)
−0.569442 + 0.822031i \(0.692841\pi\)
\(138\) −2.00000 + 3.46410i −0.170251 + 0.294884i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 3.00000 0.253546
\(141\) −4.00000 + 6.92820i −0.336861 + 0.583460i
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −2.50000 4.33013i −0.207614 0.359597i
\(146\) −7.00000 12.1244i −0.579324 1.00342i
\(147\) −2.00000 −0.164957
\(148\) 3.00000 5.19615i 0.246598 0.427121i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −9.00000 −0.732410 −0.366205 0.930534i \(-0.619343\pi\)
−0.366205 + 0.930534i \(0.619343\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 9.00000 0.725241
\(155\) 2.00000 + 5.19615i 0.160644 + 0.417365i
\(156\) 2.00000 0.160128
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 3.00000 0.237915
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) −6.00000 + 10.3923i −0.472866 + 0.819028i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 1.50000 + 2.59808i 0.116775 + 0.202260i
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −1.00000 + 1.73205i −0.0773823 + 0.134030i −0.902120 0.431486i \(-0.857990\pi\)
0.824737 + 0.565516i \(0.191323\pi\)
\(168\) −1.50000 2.59808i −0.115728 0.200446i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) 6.50000 + 11.2583i 0.494186 + 0.855955i 0.999978 0.00670064i \(-0.00213290\pi\)
−0.505792 + 0.862656i \(0.668800\pi\)
\(174\) −2.50000 + 4.33013i −0.189525 + 0.328266i
\(175\) 1.50000 + 2.59808i 0.113389 + 0.196396i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 1.50000 + 2.59808i 0.112747 + 0.195283i
\(178\) −8.00000 −0.599625
\(179\) −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 8.00000 + 13.8564i 0.594635 + 1.02994i 0.993598 + 0.112972i \(0.0360369\pi\)
−0.398963 + 0.916967i \(0.630630\pi\)
\(182\) 6.00000 0.444750
\(183\) −4.00000 + 6.92820i −0.295689 + 0.512148i
\(184\) −4.00000 −0.294884
\(185\) 6.00000 0.441129
\(186\) 3.50000 4.33013i 0.256632 0.317500i
\(187\) 12.0000 0.877527
\(188\) −8.00000 −0.583460
\(189\) −1.50000 + 2.59808i −0.109109 + 0.188982i
\(190\) 0 0
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) −7.00000 −0.502571
\(195\) 1.00000 + 1.73205i 0.0716115 + 0.124035i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) −3.00000 5.19615i −0.213741 0.370211i 0.739141 0.673550i \(-0.235232\pi\)
−0.952882 + 0.303340i \(0.901898\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 10.0000 0.705346
\(202\) 11.0000 0.773957
\(203\) −7.50000 + 12.9904i −0.526397 + 0.911746i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) −0.500000 0.866025i −0.0348367 0.0603388i
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) 0 0
\(210\) 1.50000 2.59808i 0.103510 0.179284i
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 8.00000 0.548151
\(214\) −7.50000 + 12.9904i −0.512689 + 0.888004i
\(215\) 8.00000 0.545595
\(216\) −1.00000 −0.0680414
\(217\) 10.5000 12.9904i 0.712786 0.881845i
\(218\) −16.0000 −1.08366
\(219\) −14.0000 −0.946032
\(220\) −1.50000 + 2.59808i −0.101130 + 0.175162i
\(221\) 8.00000 0.538138
\(222\) −3.00000 5.19615i −0.201347 0.348743i
\(223\) −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i \(-0.930768\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 1.00000 0.0666667
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) 10.5000 + 18.1865i 0.696909 + 1.20708i 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) −2.00000 3.46410i −0.131876 0.228416i
\(231\) 4.50000 7.79423i 0.296078 0.512823i
\(232\) −5.00000 −0.328266
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 4.00000 + 6.92820i 0.259828 + 0.450035i
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 1.00000 0.0645497
\(241\) −1.50000 + 2.59808i −0.0966235 + 0.167357i −0.910285 0.413982i \(-0.864138\pi\)
0.813662 + 0.581339i \(0.197471\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −8.00000 −0.512148
\(245\) 1.00000 1.73205i 0.0638877 0.110657i
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 5.50000 + 0.866025i 0.349250 + 0.0549927i
\(249\) 9.00000 0.570352
\(250\) −1.00000 −0.0632456
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) −3.00000 −0.188982
\(253\) −6.00000 10.3923i −0.377217 0.653359i
\(254\) 0.500000 0.866025i 0.0313728 0.0543393i
\(255\) 2.00000 3.46410i 0.125245 0.216930i
\(256\) 1.00000 0.0625000
\(257\) 10.0000 + 17.3205i 0.623783 + 1.08042i 0.988775 + 0.149413i \(0.0477384\pi\)
−0.364992 + 0.931011i \(0.618928\pi\)
\(258\) −4.00000 6.92820i −0.249029 0.431331i
\(259\) −9.00000 15.5885i −0.559233 0.968620i
\(260\) −1.00000 + 1.73205i −0.0620174 + 0.107417i
\(261\) 2.50000 + 4.33013i 0.154746 + 0.268028i
\(262\) 0 0
\(263\) −30.0000 −1.84988 −0.924940 0.380114i \(-0.875885\pi\)
−0.924940 + 0.380114i \(0.875885\pi\)
\(264\) 3.00000 0.184637
\(265\) −1.50000 + 2.59808i −0.0921443 + 0.159599i
\(266\) 0 0
\(267\) −4.00000 + 6.92820i −0.244796 + 0.423999i
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −29.0000 −1.76162 −0.880812 0.473466i \(-0.843003\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) 2.00000 3.46410i 0.121268 0.210042i
\(273\) 3.00000 5.19615i 0.181568 0.314485i
\(274\) 5.00000 + 8.66025i 0.302061 + 0.523185i
\(275\) −3.00000 −0.180907
\(276\) −2.00000 + 3.46410i −0.120386 + 0.208514i
\(277\) 12.0000 0.721010 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) −14.0000 −0.839664
\(279\) −2.00000 5.19615i −0.119737 0.311086i
\(280\) 3.00000 0.179284
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) −4.00000 + 6.92820i −0.238197 + 0.412568i
\(283\) 18.0000 1.06999 0.534994 0.844856i \(-0.320314\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 0 0
\(286\) −3.00000 + 5.19615i −0.177394 + 0.307255i
\(287\) 6.00000 0.354169
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −2.50000 4.33013i −0.146805 0.254274i
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) −2.00000 −0.116642
\(295\) −3.00000 −0.174667
\(296\) 3.00000 5.19615i 0.174371 0.302020i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) −0.500000 + 0.866025i −0.0289642 + 0.0501675i
\(299\) −4.00000 6.92820i −0.231326 0.400668i
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) −9.00000 −0.517892
\(303\) 5.50000 9.52628i 0.315967 0.547270i
\(304\) 0 0
\(305\) −4.00000 6.92820i −0.229039 0.396708i
\(306\) −4.00000 −0.228665
\(307\) 13.0000 22.5167i 0.741949 1.28509i −0.209657 0.977775i \(-0.567235\pi\)
0.951607 0.307319i \(-0.0994318\pi\)
\(308\) 9.00000 0.512823
\(309\) −1.00000 −0.0568880
\(310\) 2.00000 + 5.19615i 0.113592 + 0.295122i
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 2.00000 0.113228
\(313\) 10.5000 18.1865i 0.593495 1.02796i −0.400262 0.916401i \(-0.631081\pi\)
0.993757 0.111563i \(-0.0355857\pi\)
\(314\) 4.00000 0.225733
\(315\) −1.50000 2.59808i −0.0845154 0.146385i
\(316\) −4.00000 + 6.92820i −0.225018 + 0.389742i
\(317\) −0.500000 + 0.866025i −0.0280828 + 0.0486408i −0.879725 0.475482i \(-0.842274\pi\)
0.851642 + 0.524123i \(0.175607\pi\)
\(318\) 3.00000 0.168232
\(319\) −7.50000 12.9904i −0.419919 0.727322i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 7.50000 + 12.9904i 0.418609 + 0.725052i
\(322\) −6.00000 + 10.3923i −0.334367 + 0.579141i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −2.00000 −0.110940
\(326\) −4.00000 −0.221540
\(327\) −8.00000 + 13.8564i −0.442401 + 0.766261i
\(328\) 1.00000 + 1.73205i 0.0552158 + 0.0956365i
\(329\) −12.0000 + 20.7846i −0.661581 + 1.14589i
\(330\) 1.50000 + 2.59808i 0.0825723 + 0.143019i
\(331\) −12.0000 20.7846i −0.659580 1.14243i −0.980725 0.195395i \(-0.937401\pi\)
0.321145 0.947030i \(-0.395932\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) −6.00000 −0.328798
\(334\) −1.00000 + 1.73205i −0.0547176 + 0.0947736i
\(335\) −5.00000 + 8.66025i −0.273179 + 0.473160i
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) −5.00000 −0.272367 −0.136184 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) −6.00000 −0.325875
\(340\) 4.00000 0.216930
\(341\) 6.00000 + 15.5885i 0.324918 + 0.844162i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) −4.00000 −0.215353
\(346\) 6.50000 + 11.2583i 0.349442 + 0.605252i
\(347\) 11.5000 19.9186i 0.617352 1.06929i −0.372615 0.927986i \(-0.621539\pi\)
0.989967 0.141299i \(-0.0451280\pi\)
\(348\) −2.50000 + 4.33013i −0.134014 + 0.232119i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 1.50000 + 2.59808i 0.0801784 + 0.138873i
\(351\) −1.00000 1.73205i −0.0533761 0.0924500i
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 1.50000 + 2.59808i 0.0797241 + 0.138086i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) −8.00000 −0.423999
\(357\) −12.0000 −0.635107
\(358\) −9.50000 + 16.4545i −0.502091 + 0.869646i
\(359\) −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) 8.00000 + 13.8564i 0.420471 + 0.728277i
\(363\) −1.00000 1.73205i −0.0524864 0.0909091i
\(364\) 6.00000 0.314485
\(365\) 7.00000 12.1244i 0.366397 0.634618i
\(366\) −4.00000 + 6.92820i −0.209083 + 0.362143i
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) −4.00000 −0.208514
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 6.00000 0.311925
\(371\) 9.00000 0.467257
\(372\) 3.50000 4.33013i 0.181467 0.224507i
\(373\) 24.0000 1.24267 0.621336 0.783544i \(-0.286590\pi\)
0.621336 + 0.783544i \(0.286590\pi\)
\(374\) 12.0000 0.620505
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) −8.00000 −0.412568
\(377\) −5.00000 8.66025i −0.257513 0.446026i
\(378\) −1.50000 + 2.59808i −0.0771517 + 0.133631i
\(379\) 18.0000 31.1769i 0.924598 1.60145i 0.132391 0.991198i \(-0.457734\pi\)
0.792207 0.610253i \(-0.208932\pi\)
\(380\) 0 0
\(381\) −0.500000 0.866025i −0.0256158 0.0443678i
\(382\) −5.00000 8.66025i −0.255822 0.443097i
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 4.50000 + 7.79423i 0.229341 + 0.397231i
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) −8.00000 −0.406663
\(388\) −7.00000 −0.355371
\(389\) 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) 1.00000 + 1.73205i 0.0506370 + 0.0877058i
\(391\) −8.00000 + 13.8564i −0.404577 + 0.700749i
\(392\) −1.00000 1.73205i −0.0505076 0.0874818i
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) −8.00000 −0.402524
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 14.0000 24.2487i 0.702640 1.21701i −0.264897 0.964277i \(-0.585338\pi\)
0.967537 0.252731i \(-0.0813288\pi\)
\(398\) −3.50000 6.06218i −0.175439 0.303870i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 10.0000 0.498755
\(403\) 4.00000 + 10.3923i 0.199254 + 0.517678i
\(404\) 11.0000 0.547270
\(405\) −1.00000 −0.0496904
\(406\) −7.50000 + 12.9904i −0.372219 + 0.644702i
\(407\) 18.0000 0.892227
\(408\) −2.00000 3.46410i −0.0990148 0.171499i
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) −1.00000 + 1.73205i −0.0493865 + 0.0855399i
\(411\) 10.0000 0.493264
\(412\) −0.500000 0.866025i −0.0246332 0.0426660i
\(413\) 4.50000 + 7.79423i 0.221431 + 0.383529i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) −7.00000 + 12.1244i −0.342791 + 0.593732i
\(418\) 0 0
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 1.50000 2.59808i 0.0731925 0.126773i
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) −10.0000 + 17.3205i −0.486792 + 0.843149i
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 8.00000 0.387601
\(427\) −12.0000 + 20.7846i −0.580721 + 1.00584i
\(428\) −7.50000 + 12.9904i −0.362526 + 0.627914i
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 8.00000 0.385794
\(431\) 1.00000 1.73205i 0.0481683 0.0834300i −0.840936 0.541135i \(-0.817995\pi\)
0.889104 + 0.457705i \(0.151328\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 10.5000 12.9904i 0.504016 0.623558i
\(435\) −5.00000 −0.239732
\(436\) −16.0000 −0.766261
\(437\) 0 0
\(438\) −14.0000 −0.668946
\(439\) −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i \(-0.283193\pi\)
−0.987619 + 0.156871i \(0.949859\pi\)
\(440\) −1.50000 + 2.59808i −0.0715097 + 0.123858i
\(441\) −1.00000 + 1.73205i −0.0476190 + 0.0824786i
\(442\) 8.00000 0.380521
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) −3.00000 5.19615i −0.142374 0.246598i
\(445\) −4.00000 6.92820i −0.189618 0.328428i
\(446\) −4.50000 + 7.79423i −0.213081 + 0.369067i
\(447\) 0.500000 + 0.866025i 0.0236492 + 0.0409616i
\(448\) 1.50000 2.59808i 0.0708683 0.122748i
\(449\) −40.0000 −1.88772 −0.943858 0.330350i \(-0.892833\pi\)
−0.943858 + 0.330350i \(0.892833\pi\)
\(450\) 1.00000 0.0471405
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −4.50000 + 7.79423i −0.211428 + 0.366205i
\(454\) 10.5000 + 18.1865i 0.492789 + 0.853536i
\(455\) 3.00000 + 5.19615i 0.140642 + 0.243599i
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 7.00000 12.1244i 0.327089 0.566534i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) −2.00000 3.46410i −0.0932505 0.161515i
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 4.50000 7.79423i 0.209359 0.362620i
\(463\) −5.00000 −0.232370 −0.116185 0.993228i \(-0.537067\pi\)
−0.116185 + 0.993228i \(0.537067\pi\)
\(464\) −5.00000 −0.232119
\(465\) 5.50000 + 0.866025i 0.255056 + 0.0401610i
\(466\) −18.0000 −0.833834
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 1.00000 1.73205i 0.0462250 0.0800641i
\(469\) 30.0000 1.38527
\(470\) −4.00000 6.92820i −0.184506 0.319574i
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 24.0000 1.10352
\(474\) 4.00000 + 6.92820i 0.183726 + 0.318223i
\(475\) 0 0
\(476\) −6.00000 10.3923i −0.275010 0.476331i
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 1.00000 0.0456435
\(481\) 12.0000 0.547153
\(482\) −1.50000 + 2.59808i −0.0683231 + 0.118339i
\(483\) 6.00000 + 10.3923i 0.273009 + 0.472866i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −3.50000 6.06218i −0.158927 0.275269i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 15.5000 + 26.8468i 0.702372 + 1.21654i 0.967632 + 0.252367i \(0.0812090\pi\)
−0.265260 + 0.964177i \(0.585458\pi\)
\(488\) −8.00000 −0.362143
\(489\) −2.00000 + 3.46410i −0.0904431 + 0.156652i
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −20.5000 35.5070i −0.925152 1.60241i −0.791316 0.611407i \(-0.790604\pi\)
−0.133836 0.991004i \(-0.542729\pi\)
\(492\) 2.00000 0.0901670
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) 5.50000 + 0.866025i 0.246957 + 0.0388857i
\(497\) 24.0000 1.07655
\(498\) 9.00000 0.403300
\(499\) −11.0000 + 19.0526i −0.492428 + 0.852910i −0.999962 0.00872186i \(-0.997224\pi\)
0.507534 + 0.861632i \(0.330557\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 1.00000 + 1.73205i 0.0446767 + 0.0773823i
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −1.00000 + 1.73205i −0.0445878 + 0.0772283i −0.887458 0.460889i \(-0.847531\pi\)
0.842870 + 0.538117i \(0.180864\pi\)
\(504\) −3.00000 −0.133631
\(505\) 5.50000 + 9.52628i 0.244747 + 0.423914i
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) −4.50000 7.79423i −0.199852 0.346154i
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) −42.0000 −1.85797
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.0000 + 17.3205i 0.441081 + 0.763975i
\(515\) 0.500000 0.866025i 0.0220326 0.0381616i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) −9.00000 15.5885i −0.395437 0.684917i
\(519\) 13.0000 0.570637
\(520\) −1.00000 + 1.73205i −0.0438529 + 0.0759555i
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 2.50000 + 4.33013i 0.109422 + 0.189525i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 0 0
\(525\) 3.00000 0.130931
\(526\) −30.0000 −1.30806
\(527\) 14.0000 17.3205i 0.609850 0.754493i
\(528\) 3.00000 0.130558
\(529\) −7.00000 −0.304348
\(530\) −1.50000 + 2.59808i −0.0651558 + 0.112853i
\(531\) 3.00000 0.130189
\(532\) 0 0
\(533\) −2.00000 + 3.46410i −0.0866296 + 0.150047i
\(534\) −4.00000 + 6.92820i −0.173097 + 0.299813i
\(535\) −15.0000 −0.648507
\(536\) 5.00000 + 8.66025i 0.215967 + 0.374066i
\(537\) 9.50000 + 16.4545i 0.409955 + 0.710063i
\(538\) −7.00000 12.1244i −0.301791 0.522718i
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) 10.0000 17.3205i 0.429934 0.744667i −0.566933 0.823764i \(-0.691870\pi\)
0.996867 + 0.0790969i \(0.0252036\pi\)
\(542\) −29.0000 −1.24566
\(543\) 16.0000 0.686626
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) −8.00000 13.8564i −0.342682 0.593543i
\(546\) 3.00000 5.19615i 0.128388 0.222375i
\(547\) 4.00000 + 6.92820i 0.171028 + 0.296229i 0.938779 0.344519i \(-0.111958\pi\)
−0.767752 + 0.640747i \(0.778625\pi\)
\(548\) 5.00000 + 8.66025i 0.213589 + 0.369948i
\(549\) 4.00000 + 6.92820i 0.170716 + 0.295689i
\(550\) −3.00000 −0.127920
\(551\) 0 0
\(552\) −2.00000 + 3.46410i −0.0851257 + 0.147442i
\(553\) 12.0000 + 20.7846i 0.510292 + 0.883852i
\(554\) 12.0000 0.509831
\(555\) 3.00000 5.19615i 0.127343 0.220564i
\(556\) −14.0000 −0.593732
\(557\) −37.0000 −1.56774 −0.783870 0.620925i \(-0.786757\pi\)
−0.783870 + 0.620925i \(0.786757\pi\)
\(558\) −2.00000 5.19615i −0.0846668 0.219971i
\(559\) 16.0000 0.676728
\(560\) 3.00000 0.126773
\(561\) 6.00000 10.3923i 0.253320 0.438763i
\(562\) 16.0000 0.674919
\(563\) 3.50000 + 6.06218i 0.147507 + 0.255490i 0.930306 0.366785i \(-0.119542\pi\)
−0.782798 + 0.622276i \(0.786208\pi\)
\(564\) −4.00000 + 6.92820i −0.168430 + 0.291730i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 18.0000 0.756596
\(567\) 1.50000 + 2.59808i 0.0629941 + 0.109109i
\(568\) 4.00000 + 6.92820i 0.167836 + 0.290701i
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) −10.0000 −0.417756
\(574\) 6.00000 0.250435
\(575\) 2.00000 3.46410i 0.0834058 0.144463i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −5.00000 + 8.66025i −0.208153 + 0.360531i −0.951133 0.308783i \(-0.900078\pi\)
0.742980 + 0.669314i \(0.233412\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −4.50000 7.79423i −0.187014 0.323917i
\(580\) −2.50000 4.33013i −0.103807 0.179799i
\(581\) 27.0000 1.12015
\(582\) −3.50000 + 6.06218i −0.145080 + 0.251285i
\(583\) −4.50000 + 7.79423i −0.186371 + 0.322804i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) 2.00000 0.0826898
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) −7.00000 −0.288921 −0.144460 0.989511i \(-0.546145\pi\)
−0.144460 + 0.989511i \(0.546145\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) −3.00000 −0.123508
\(591\) −6.00000 −0.246807
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) −1.50000 2.59808i −0.0615457 0.106600i
\(595\) 6.00000 10.3923i 0.245976 0.426043i
\(596\) −0.500000 + 0.866025i −0.0204808 + 0.0354738i
\(597\) −7.00000 −0.286491
\(598\) −4.00000 6.92820i −0.163572 0.283315i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) −15.0000 + 25.9808i −0.611863 + 1.05978i 0.379063 + 0.925371i \(0.376246\pi\)
−0.990926 + 0.134407i \(0.957087\pi\)
\(602\) −12.0000 20.7846i −0.489083 0.847117i
\(603\) 5.00000 8.66025i 0.203616 0.352673i
\(604\) −9.00000 −0.366205
\(605\) 2.00000 0.0813116
\(606\) 5.50000 9.52628i 0.223422 0.386979i
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 0 0
\(609\) 7.50000 + 12.9904i 0.303915 + 0.526397i
\(610\) −4.00000 6.92820i −0.161955 0.280515i
\(611\) −8.00000 13.8564i −0.323645 0.560570i
\(612\) −4.00000 −0.161690
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) 13.0000 22.5167i 0.524637 0.908698i
\(615\) 1.00000 + 1.73205i 0.0403239 + 0.0698430i
\(616\) 9.00000 0.362620
\(617\) 18.0000 31.1769i 0.724653 1.25514i −0.234464 0.972125i \(-0.575334\pi\)
0.959117 0.283011i \(-0.0913331\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 2.00000 + 5.19615i 0.0803219 + 0.208683i
\(621\) 4.00000 0.160514
\(622\) 18.0000 0.721734
\(623\) −12.0000 + 20.7846i −0.480770 + 0.832718i
\(624\) 2.00000 0.0800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 10.5000 18.1865i 0.419664 0.726880i
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) −12.0000 20.7846i −0.478471 0.828737i
\(630\) −1.50000 2.59808i −0.0597614 0.103510i
\(631\) 0.500000 + 0.866025i 0.0199047 + 0.0344759i 0.875806 0.482663i \(-0.160330\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 10.0000 + 17.3205i 0.397464 + 0.688428i
\(634\) −0.500000 + 0.866025i −0.0198575 + 0.0343943i
\(635\) 1.00000 0.0396838
\(636\) 3.00000 0.118958
\(637\) 2.00000 3.46410i 0.0792429 0.137253i
\(638\) −7.50000 12.9904i −0.296928 0.514294i
\(639\) 4.00000 6.92820i 0.158238 0.274075i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −16.0000 27.7128i −0.631962 1.09459i −0.987150 0.159795i \(-0.948917\pi\)
0.355188 0.934795i \(-0.384417\pi\)
\(642\) 7.50000 + 12.9904i 0.296001 + 0.512689i
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) −6.00000 + 10.3923i −0.236433 + 0.409514i
\(645\) 4.00000 6.92820i 0.157500 0.272798i
\(646\) 0 0
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −9.00000 −0.353281
\(650\) −2.00000 −0.0784465
\(651\) −6.00000 15.5885i −0.235159 0.610960i
\(652\) −4.00000 −0.156652
\(653\) 31.0000 1.21312 0.606562 0.795036i \(-0.292548\pi\)
0.606562 + 0.795036i \(0.292548\pi\)
\(654\) −8.00000 + 13.8564i −0.312825 + 0.541828i
\(655\) 0 0
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) −7.00000 + 12.1244i −0.273096 + 0.473016i
\(658\) −12.0000 + 20.7846i −0.467809 + 0.810268i
\(659\) 23.0000 0.895953 0.447976 0.894045i \(-0.352145\pi\)
0.447976 + 0.894045i \(0.352145\pi\)
\(660\) 1.50000 + 2.59808i 0.0583874 + 0.101130i
\(661\) −14.0000 24.2487i −0.544537 0.943166i −0.998636 0.0522143i \(-0.983372\pi\)
0.454099 0.890951i \(-0.349961\pi\)
\(662\) −12.0000 20.7846i −0.466393 0.807817i
\(663\) 4.00000 6.92820i 0.155347 0.269069i
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 20.0000 0.774403
\(668\) −1.00000 + 1.73205i −0.0386912 + 0.0670151i
\(669\) 4.50000 + 7.79423i 0.173980 + 0.301342i
\(670\) −5.00000 + 8.66025i −0.193167 + 0.334575i
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) −1.50000 2.59808i −0.0578638 0.100223i
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) −5.00000 −0.192593
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i \(-0.259740\pi\)
−0.973392 + 0.229147i \(0.926406\pi\)
\(678\) −6.00000 −0.230429
\(679\) −10.5000 + 18.1865i −0.402953 + 0.697935i
\(680\) 4.00000 0.153393
\(681\) 21.0000 0.804722
\(682\) 6.00000 + 15.5885i 0.229752 + 0.596913i
\(683\) 5.00000 0.191320 0.0956598 0.995414i \(-0.469504\pi\)
0.0956598 + 0.995414i \(0.469504\pi\)
\(684\) 0 0
\(685\) −5.00000 + 8.66025i −0.191040 + 0.330891i
\(686\) 15.0000 0.572703
\(687\) −7.00000 12.1244i −0.267067 0.462573i
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) −3.00000 + 5.19615i −0.114291 + 0.197958i
\(690\) −4.00000 −0.152277
\(691\) 17.0000 + 29.4449i 0.646710 + 1.12014i 0.983904 + 0.178700i \(0.0571891\pi\)
−0.337193 + 0.941435i \(0.609478\pi\)
\(692\) 6.50000 + 11.2583i 0.247093 + 0.427977i
\(693\) −4.50000 7.79423i −0.170941 0.296078i
\(694\) 11.5000 19.9186i 0.436534 0.756099i
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) −2.50000 + 4.33013i −0.0947623 + 0.164133i
\(697\) 8.00000 0.303022
\(698\) 0 0
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 1.50000 + 2.59808i 0.0566947 + 0.0981981i
\(701\) −13.5000 + 23.3827i −0.509888 + 0.883152i 0.490046 + 0.871696i \(0.336980\pi\)
−0.999934 + 0.0114555i \(0.996354\pi\)
\(702\) −1.00000 1.73205i −0.0377426 0.0653720i
\(703\) 0 0
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) −8.00000 −0.301297
\(706\) 9.00000 15.5885i 0.338719 0.586679i
\(707\) 16.5000 28.5788i 0.620546 1.07482i
\(708\) 1.50000 + 2.59808i 0.0563735 + 0.0976417i
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 8.00000 0.300023
\(712\) −8.00000 −0.299813
\(713\) −22.0000 3.46410i −0.823906 0.129732i
\(714\) −12.0000 −0.449089
\(715\) −6.00000 −0.224387
\(716\) −9.50000 + 16.4545i −0.355032 + 0.614933i
\(717\) −6.00000 −0.224074
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −7.00000 + 12.1244i −0.261056 + 0.452162i −0.966523 0.256581i \(-0.917404\pi\)
0.705467 + 0.708743i \(0.250737\pi\)
\(720\) 0.500000 0.866025i 0.0186339 0.0322749i
\(721\) −3.00000 −0.111726
\(722\) 9.50000 + 16.4545i 0.353553 + 0.612372i
\(723\) 1.50000 + 2.59808i 0.0557856 + 0.0966235i
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −25.5000 + 44.1673i −0.945743 + 1.63807i −0.191485 + 0.981495i \(0.561330\pi\)
−0.754257 + 0.656579i \(0.772003\pi\)
\(728\) 6.00000 0.222375
\(729\) 1.00000 0.0370370
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) −4.00000 + 6.92820i −0.147844 + 0.256074i
\(733\) 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) 14.0000 + 24.2487i 0.516749 + 0.895036i
\(735\) −1.00000 1.73205i −0.0368856 0.0638877i
\(736\) −4.00000 −0.147442
\(737\) −15.0000 + 25.9808i −0.552532 + 0.957014i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i \(0.0796718\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) 9.00000 0.330400
\(743\) −40.0000 −1.46746 −0.733729 0.679442i \(-0.762222\pi\)
−0.733729 + 0.679442i \(0.762222\pi\)
\(744\) 3.50000 4.33013i 0.128316 0.158750i
\(745\) −1.00000 −0.0366372
\(746\) 24.0000 0.878702
\(747\) 4.50000 7.79423i 0.164646 0.285176i
\(748\) 12.0000 0.438763
\(749\) 22.5000 + 38.9711i 0.822132 + 1.42397i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −21.5000 + 37.2391i −0.784546 + 1.35887i 0.144724 + 0.989472i \(0.453771\pi\)
−0.929270 + 0.369402i \(0.879563\pi\)
\(752\) −8.00000 −0.291730
\(753\) −6.00000 10.3923i −0.218652 0.378717i
\(754\) −5.00000 8.66025i −0.182089 0.315388i
\(755\) −4.50000 7.79423i −0.163772 0.283661i
\(756\) −1.50000 + 2.59808i −0.0545545 + 0.0944911i
\(757\) −10.0000 17.3205i −0.363456 0.629525i 0.625071 0.780568i \(-0.285070\pi\)
−0.988527 + 0.151043i \(0.951737\pi\)
\(758\) 18.0000 31.1769i 0.653789 1.13240i
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) 21.0000 36.3731i 0.761249 1.31852i −0.180957 0.983491i \(-0.557920\pi\)
0.942207 0.335032i \(-0.108747\pi\)
\(762\) −0.500000 0.866025i −0.0181131 0.0313728i
\(763\) −24.0000 + 41.5692i −0.868858 + 1.50491i
\(764\) −5.00000 8.66025i −0.180894 0.313317i
\(765\) −2.00000 3.46410i −0.0723102 0.125245i
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) −6.00000 −0.216647
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −4.50000 + 7.79423i −0.162274 + 0.281067i −0.935684 0.352839i \(-0.885216\pi\)
0.773410 + 0.633906i \(0.218550\pi\)
\(770\) 4.50000 + 7.79423i 0.162169 + 0.280885i
\(771\) 20.0000 0.720282
\(772\) 4.50000 7.79423i 0.161959 0.280520i
\(773\) −10.0000 −0.359675 −0.179838 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) −8.00000 −0.287554
\(775\) −3.50000 + 4.33013i −0.125724 + 0.155543i
\(776\) −7.00000 −0.251285
\(777\) −18.0000 −0.645746