Properties

Label 930.2.i.c.211.1
Level $930$
Weight $2$
Character 930.211
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 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 930.211
Dual form 930.2.i.c.811.1

$q$-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} +(-2.00000 + 3.46410i) 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} +2.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +1.00000 q^{29} -1.00000 q^{30} +(-3.50000 + 4.33013i) 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} -4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-2.00000 - 3.46410i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} -2.00000 q^{46} +4.00000 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} +(-2.00000 + 3.46410i) q^{52} +(1.50000 - 2.59808i) q^{53} +1.00000 q^{54} +(-1.50000 - 2.59808i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.00000 q^{58} +(4.50000 + 7.79423i) q^{59} +1.00000 q^{60} -2.00000 q^{61} +(3.50000 - 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} -3.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +(1.00000 + 1.73205i) q^{69} -3.00000 q^{70} +(-2.00000 + 3.46410i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} +9.00000 q^{77} +4.00000 q^{78} +(2.00000 + 3.46410i) 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} +(2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{87} +(-1.50000 + 2.59808i) q^{88} +10.0000 q^{89} +(-0.500000 - 0.866025i) q^{90} -12.0000 q^{91} +2.00000 q^{92} +(-5.50000 - 0.866025i) q^{93} -4.00000 q^{94} +(-0.500000 - 0.866025i) q^{96} +11.0000 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 \( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - q^{6} + 3 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} - 4 q^{13} - 3 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} + q^{18} + q^{20} - 3 q^{21} - 3 q^{22} + 4 q^{23} - q^{24} - q^{25} + 4 q^{26} - 2 q^{27} + 3 q^{28} + 2 q^{29} - 2 q^{30} - 7 q^{31} - 2 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} + 6 q^{37} - 8 q^{39} - q^{40} + 2 q^{41} + 3 q^{42} - 4 q^{43} + 3 q^{44} + q^{45} - 4 q^{46} + 8 q^{47} + q^{48} - 2 q^{49} + q^{50} - 4 q^{51} - 4 q^{52} + 3 q^{53} + 2 q^{54} - 3 q^{55} - 3 q^{56} - 2 q^{58} + 9 q^{59} + 2 q^{60} - 4 q^{61} + 7 q^{62} - 6 q^{63} + 2 q^{64} + 4 q^{65} - 6 q^{66} - 2 q^{67} + 4 q^{68} + 2 q^{69} - 6 q^{70} - 4 q^{71} + q^{72} - 2 q^{73} - 6 q^{74} + q^{75} + 18 q^{77} + 8 q^{78} + 4 q^{79} + q^{80} - q^{81} - 2 q^{82} - 9 q^{83} - 3 q^{84} + 8 q^{85} + 4 q^{86} + q^{87} - 3 q^{88} + 20 q^{89} - q^{90} - 24 q^{91} + 4 q^{92} - 11 q^{93} - 8 q^{94} - q^{96} + 22 q^{97} + 2 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) −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 −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) −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 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 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
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.00000 3.46410i 0.392232 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 1.50000 + 2.59808i 0.283473 + 0.490990i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) −1.00000 −0.182574
\(31\) −3.50000 + 4.33013i −0.628619 + 0.777714i
\(32\) −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 0.999969 0.00783774i \(-0.00249486\pi\)
−0.506772 + 0.862080i \(0.669162\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) 1.50000 2.59808i 0.231455 0.400892i
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) −2.00000 −0.294884
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 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
\(52\) −2.00000 + 3.46410i −0.277350 + 0.480384i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 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
\(58\) −1.00000 −0.131306
\(59\) 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) 1.00000 0.129099
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 3.50000 4.33013i 0.444500 0.549927i
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) −3.00000 −0.369274
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 1.00000 + 1.73205i 0.120386 + 0.208514i
\(70\) −3.00000 −0.358569
\(71\) −2.00000 + 3.46410i −0.237356 + 0.411113i −0.959955 0.280155i \(-0.909614\pi\)
0.722599 + 0.691268i \(0.242948\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −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
\(78\) 4.00000 0.452911
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 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 \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) −1.50000 + 2.59808i −0.163663 + 0.283473i
\(85\) 4.00000 0.433861
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 0.500000 + 0.866025i 0.0536056 + 0.0928477i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) −12.0000 −1.25794
\(92\) 2.00000 0.208514
\(93\) −5.50000 0.866025i −0.570323 0.0898027i
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 11.0000 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(98\) 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
\(101\) −19.0000 −1.89057 −0.945285 0.326245i \(-0.894217\pi\)
−0.945285 + 0.326245i \(0.894217\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i \(0.387925\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 2.00000 3.46410i 0.196116 0.339683i
\(105\) 1.50000 + 2.59808i 0.146385 + 0.253546i
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 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
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 0 0
\(115\) 1.00000 1.73205i 0.0932505 0.161515i
\(116\) 1.00000 0.0928477
\(117\) −2.00000 3.46410i −0.184900 0.320256i
\(118\) −4.50000 7.79423i −0.414259 0.717517i
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 2.00000 0.181071
\(123\) 2.00000 0.180334
\(124\) −3.50000 + 4.33013i −0.314309 + 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) 3.00000 0.267261
\(127\) 6.50000 + 11.2583i 0.576782 + 0.999015i 0.995846 + 0.0910585i \(0.0290250\pi\)
−0.419064 + 0.907957i \(0.637642\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) −2.00000 3.46410i −0.175412 0.303822i
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) −1.00000 1.73205i −0.0851257 0.147442i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 3.00000 0.253546
\(141\) 2.00000 + 3.46410i 0.168430 + 0.291730i
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0.500000 0.866025i 0.0415227 0.0719195i
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) −2.00000 −0.164957
\(148\) 3.00000 + 5.19615i 0.246598 + 0.427121i
\(149\) −9.50000 16.4545i −0.778270 1.34800i −0.932938 0.360037i \(-0.882764\pi\)
0.154668 0.987967i \(-0.450569\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) −9.00000 −0.725241
\(155\) 2.00000 + 5.19615i 0.160644 + 0.417365i
\(156\) −4.00000 −0.320256
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) 3.00000 0.237915
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 3.00000 + 5.19615i 0.236433 + 0.409514i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 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 0.824737 0.565516i \(-0.191323\pi\)
−0.902120 + 0.431486i \(0.857990\pi\)
\(168\) 1.50000 2.59808i 0.115728 0.200446i
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) −0.500000 0.866025i −0.0379049 0.0656532i
\(175\) 1.50000 2.59808i 0.113389 0.196396i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) −10.0000 −0.749532
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 12.0000 0.889499
\(183\) −1.00000 1.73205i −0.0739221 0.128037i
\(184\) −2.00000 −0.147442
\(185\) 6.00000 0.441129
\(186\) 5.50000 + 0.866025i 0.403280 + 0.0635001i
\(187\) 12.0000 0.877527
\(188\) 4.00000 0.291730
\(189\) −1.50000 2.59808i −0.109109 0.188982i
\(190\) 0 0
\(191\) 7.00000 12.1244i 0.506502 0.877288i −0.493469 0.869763i \(-0.664272\pi\)
0.999972 0.00752447i \(-0.00239513\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −10.5000 18.1865i −0.755807 1.30910i −0.944972 0.327150i \(-0.893912\pi\)
0.189166 0.981945i \(-0.439422\pi\)
\(194\) −11.0000 −0.789754
\(195\) −2.00000 + 3.46410i −0.143223 + 0.248069i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 9.00000 15.5885i 0.641223 1.11063i −0.343937 0.938993i \(-0.611761\pi\)
0.985160 0.171639i \(-0.0549062\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i \(-0.705848\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −2.00000 −0.141069
\(202\) 19.0000 1.33684
\(203\) 1.50000 + 2.59808i 0.105279 + 0.182349i
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 6.50000 11.2583i 0.452876 0.784405i
\(207\) −1.00000 + 1.73205i −0.0695048 + 0.120386i
\(208\) −2.00000 + 3.46410i −0.138675 + 0.240192i
\(209\) 0 0
\(210\) −1.50000 2.59808i −0.103510 0.179284i
\(211\) −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i \(-0.255467\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) −4.00000 −0.274075
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) −4.00000 −0.272798
\(216\) 1.00000 0.0680414
\(217\) −16.5000 2.59808i −1.12009 0.176369i
\(218\) 4.00000 0.270914
\(219\) −2.00000 −0.135147
\(220\) −1.50000 2.59808i −0.101130 0.175162i
\(221\) −16.0000 −1.07628
\(222\) 3.00000 5.19615i 0.201347 0.348743i
\(223\) −4.50000 7.79423i −0.301342 0.521940i 0.675098 0.737728i \(-0.264101\pi\)
−0.976440 + 0.215788i \(0.930768\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) 1.00000 0.0666667
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) −11.0000 19.0526i −0.726900 1.25903i −0.958187 0.286143i \(-0.907627\pi\)
0.231287 0.972886i \(-0.425707\pi\)
\(230\) −1.00000 + 1.73205i −0.0659380 + 0.114208i
\(231\) 4.50000 + 7.79423i 0.296078 + 0.512823i
\(232\) −1.00000 −0.0656532
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 2.00000 + 3.46410i 0.130744 + 0.226455i
\(235\) 2.00000 3.46410i 0.130466 0.225973i
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) −2.00000 + 3.46410i −0.129914 + 0.225018i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 1.00000 0.0645497
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) −2.00000 −0.127515
\(247\) 0 0
\(248\) 3.50000 4.33013i 0.222250 0.274963i
\(249\) −9.00000 −0.570352
\(250\) 1.00000 0.0632456
\(251\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) −3.00000 −0.188982
\(253\) 3.00000 5.19615i 0.188608 0.326679i
\(254\) −6.50000 11.2583i −0.407846 0.706410i
\(255\) 2.00000 + 3.46410i 0.125245 + 0.216930i
\(256\) 1.00000 0.0625000
\(257\) −5.00000 + 8.66025i −0.311891 + 0.540212i −0.978772 0.204953i \(-0.934296\pi\)
0.666880 + 0.745165i \(0.267629\pi\)
\(258\) −2.00000 + 3.46410i −0.124515 + 0.215666i
\(259\) −9.00000 + 15.5885i −0.559233 + 0.968620i
\(260\) 2.00000 + 3.46410i 0.124035 + 0.214834i
\(261\) −0.500000 + 0.866025i −0.0309492 + 0.0536056i
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) −3.00000 −0.184637
\(265\) −1.50000 2.59808i −0.0921443 0.159599i
\(266\) 0 0
\(267\) 5.00000 + 8.66025i 0.305995 + 0.529999i
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 1.00000 0.0607457 0.0303728 0.999539i \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) 2.00000 + 3.46410i 0.121268 + 0.210042i
\(273\) −6.00000 10.3923i −0.363137 0.628971i
\(274\) −8.00000 + 13.8564i −0.483298 + 0.837096i
\(275\) −3.00000 −0.180907
\(276\) 1.00000 + 1.73205i 0.0601929 + 0.104257i
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) −4.00000 −0.239904
\(279\) −2.00000 5.19615i −0.119737 0.311086i
\(280\) −3.00000 −0.179284
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) −2.00000 3.46410i −0.119098 0.206284i
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −2.00000 + 3.46410i −0.118678 + 0.205557i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.354787 0.614510i
\(287\) 6.00000 0.354169
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −0.500000 + 0.866025i −0.0293610 + 0.0508548i
\(291\) 5.50000 + 9.52628i 0.322416 + 0.558440i
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −10.5000 18.1865i −0.613417 1.06247i −0.990660 0.136355i \(-0.956461\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(294\) 2.00000 0.116642
\(295\) 9.00000 0.524000
\(296\) −3.00000 5.19615i −0.174371 0.302020i
\(297\) −1.50000 + 2.59808i −0.0870388 + 0.150756i
\(298\) 9.50000 + 16.4545i 0.550320 + 0.953183i
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 6.00000 10.3923i 0.345834 0.599002i
\(302\) −9.00000 −0.517892
\(303\) −9.50000 16.4545i −0.545761 0.945285i
\(304\) 0 0
\(305\) −1.00000 + 1.73205i −0.0572598 + 0.0991769i
\(306\) 4.00000 0.228665
\(307\) 4.00000 + 6.92820i 0.228292 + 0.395413i 0.957302 0.289090i \(-0.0933526\pi\)
−0.729010 + 0.684503i \(0.760019\pi\)
\(308\) 9.00000 0.512823
\(309\) −13.0000 −0.739544
\(310\) −2.00000 5.19615i −0.113592 0.295122i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 4.00000 0.226455
\(313\) −10.5000 18.1865i −0.593495 1.02796i −0.993757 0.111563i \(-0.964414\pi\)
0.400262 0.916401i \(-0.368919\pi\)
\(314\) −22.0000 −1.24153
\(315\) −1.50000 + 2.59808i −0.0845154 + 0.146385i
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) −6.50000 11.2583i −0.365076 0.632331i 0.623712 0.781654i \(-0.285624\pi\)
−0.988788 + 0.149323i \(0.952290\pi\)
\(318\) −3.00000 −0.168232
\(319\) 1.50000 2.59808i 0.0839839 0.145464i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −1.50000 + 2.59808i −0.0837218 + 0.145010i
\(322\) −3.00000 5.19615i −0.167183 0.289570i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 4.00000 0.221880
\(326\) 10.0000 0.553849
\(327\) −2.00000 3.46410i −0.110600 0.191565i
\(328\) −1.00000 + 1.73205i −0.0552158 + 0.0956365i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) −1.50000 + 2.59808i −0.0825723 + 0.143019i
\(331\) 15.0000 25.9808i 0.824475 1.42803i −0.0778456 0.996965i \(-0.524804\pi\)
0.902320 0.431066i \(-0.141863\pi\)
\(332\) −4.50000 + 7.79423i −0.246970 + 0.427764i
\(333\) −6.00000 −0.328798
\(334\) 1.00000 + 1.73205i 0.0547176 + 0.0947736i
\(335\) 1.00000 + 1.73205i 0.0546358 + 0.0946320i
\(336\) −1.50000 + 2.59808i −0.0818317 + 0.141737i
\(337\) 25.0000 1.36184 0.680918 0.732359i \(-0.261581\pi\)
0.680918 + 0.732359i \(0.261581\pi\)
\(338\) 1.50000 + 2.59808i 0.0815892 + 0.141317i
\(339\) 12.0000 0.651751
\(340\) 4.00000 0.216930
\(341\) 6.00000 + 15.5885i 0.324918 + 0.844162i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 2.00000 0.107676
\(346\) −0.500000 + 0.866025i −0.0268802 + 0.0465578i
\(347\) −9.50000 16.4545i −0.509987 0.883323i −0.999933 0.0115703i \(-0.996317\pi\)
0.489946 0.871753i \(-0.337016\pi\)
\(348\) 0.500000 + 0.866025i 0.0268028 + 0.0464238i
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) −1.50000 + 2.59808i −0.0801784 + 0.138873i
\(351\) 2.00000 3.46410i 0.106752 0.184900i
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 4.50000 7.79423i 0.239172 0.414259i
\(355\) 2.00000 + 3.46410i 0.106149 + 0.183855i
\(356\) 10.0000 0.529999
\(357\) −12.0000 −0.635107
\(358\) 9.50000 + 16.4545i 0.502091 + 0.869646i
\(359\) −15.0000 + 25.9808i −0.791670 + 1.37121i 0.133263 + 0.991081i \(0.457455\pi\)
−0.924932 + 0.380131i \(0.875879\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) −1.00000 + 1.73205i −0.0524864 + 0.0909091i
\(364\) −12.0000 −0.628971
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) 2.00000 0.104257
\(369\) 1.00000 + 1.73205i 0.0520579 + 0.0901670i
\(370\) −6.00000 −0.311925
\(371\) 9.00000 0.467257
\(372\) −5.50000 0.866025i −0.285162 0.0449013i
\(373\) 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
\(376\) −4.00000 −0.206284
\(377\) −2.00000 + 3.46410i −0.103005 + 0.178410i
\(378\) 1.50000 + 2.59808i 0.0771517 + 0.133631i
\(379\) 9.00000 + 15.5885i 0.462299 + 0.800725i 0.999075 0.0429994i \(-0.0136914\pi\)
−0.536776 + 0.843725i \(0.680358\pi\)
\(380\) 0 0
\(381\) −6.50000 + 11.2583i −0.333005 + 0.576782i
\(382\) −7.00000 + 12.1244i −0.358151 + 0.620336i
\(383\) −3.00000 + 5.19615i −0.153293 + 0.265511i −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 4.50000 7.79423i 0.229341 0.397231i
\(386\) 10.5000 + 18.1865i 0.534436 + 0.925670i
\(387\) 4.00000 0.203331
\(388\) 11.0000 0.558440
\(389\) 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) 2.00000 3.46410i 0.101274 0.175412i
\(391\) 4.00000 + 6.92820i 0.202289 + 0.350374i
\(392\) 1.00000 1.73205i 0.0505076 0.0874818i
\(393\) 6.00000 10.3923i 0.302660 0.524222i
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 4.00000 0.201262
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 5.00000 + 8.66025i 0.250943 + 0.434646i 0.963786 0.266678i \(-0.0859261\pi\)
−0.712843 + 0.701324i \(0.752593\pi\)
\(398\) −5.50000 + 9.52628i −0.275690 + 0.477509i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −8.00000 −0.399501 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 2.00000 0.0997509
\(403\) −8.00000 20.7846i −0.398508 1.03536i
\(404\) −19.0000 −0.945285
\(405\) −1.00000 −0.0496904
\(406\) −1.50000 2.59808i −0.0744438 0.128940i
\(407\) 18.0000 0.892227
\(408\) 2.00000 3.46410i 0.0990148 0.171499i
\(409\) 6.50000 + 11.2583i 0.321404 + 0.556689i 0.980778 0.195127i \(-0.0625118\pi\)
−0.659374 + 0.751815i \(0.729178\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) 16.0000 0.789222
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) −13.5000 + 23.3827i −0.664292 + 1.15059i
\(414\) 1.00000 1.73205i 0.0491473 0.0851257i
\(415\) 4.50000 + 7.79423i 0.220896 + 0.382604i
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 0 0
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 1.50000 + 2.59808i 0.0731925 + 0.126773i
\(421\) 17.0000 29.4449i 0.828529 1.43505i −0.0706626 0.997500i \(-0.522511\pi\)
0.899192 0.437555i \(-0.144155\pi\)
\(422\) 4.00000 + 6.92820i 0.194717 + 0.337260i
\(423\) −2.00000 + 3.46410i −0.0972433 + 0.168430i
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 4.00000 0.193801
\(427\) −3.00000 5.19615i −0.145180 0.251459i
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) −6.00000 + 10.3923i −0.289683 + 0.501745i
\(430\) 4.00000 0.192897
\(431\) 16.0000 + 27.7128i 0.770693 + 1.33488i 0.937184 + 0.348836i \(0.113423\pi\)
−0.166491 + 0.986043i \(0.553244\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 16.5000 + 2.59808i 0.792025 + 0.124712i
\(435\) 1.00000 0.0479463
\(436\) −4.00000 −0.191565
\(437\) 0 0
\(438\) 2.00000 0.0955637
\(439\) 1.50000 2.59808i 0.0715911 0.123999i −0.828008 0.560717i \(-0.810526\pi\)
0.899599 + 0.436717i \(0.143859\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) −1.00000 1.73205i −0.0476190 0.0824786i
\(442\) 16.0000 0.761042
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) −3.00000 + 5.19615i −0.142374 + 0.246598i
\(445\) 5.00000 8.66025i 0.237023 0.410535i
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) 9.50000 16.4545i 0.449335 0.778270i
\(448\) 1.50000 + 2.59808i 0.0708683 + 0.122748i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 4.50000 + 7.79423i 0.211428 + 0.366205i
\(454\) −1.50000 + 2.59808i −0.0703985 + 0.121934i
\(455\) −6.00000 + 10.3923i −0.281284 + 0.487199i
\(456\) 0 0
\(457\) −26.0000 −1.21623 −0.608114 0.793849i \(-0.708074\pi\)
−0.608114 + 0.793849i \(0.708074\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 1.00000 1.73205i 0.0466252 0.0807573i
\(461\) −9.00000 −0.419172 −0.209586 0.977790i \(-0.567212\pi\)
−0.209586 + 0.977790i \(0.567212\pi\)
\(462\) −4.50000 7.79423i −0.209359 0.362620i
\(463\) −5.00000 −0.232370 −0.116185 0.993228i \(-0.537067\pi\)
−0.116185 + 0.993228i \(0.537067\pi\)
\(464\) 1.00000 0.0464238
\(465\) −3.50000 + 4.33013i −0.162309 + 0.200805i
\(466\) 6.00000 0.277945
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) −2.00000 3.46410i −0.0924500 0.160128i
\(469\) −6.00000 −0.277054
\(470\) −2.00000 + 3.46410i −0.0922531 + 0.159787i
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) −4.50000 7.79423i −0.207129 0.358758i
\(473\) −12.0000 −0.551761
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) 0 0
\(476\) −6.00000 + 10.3923i −0.275010 + 0.476331i
\(477\) 1.50000 + 2.59808i 0.0686803 + 0.118958i
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −24.0000 −1.09431
\(482\) 7.50000 + 12.9904i 0.341616 + 0.591696i
\(483\) −3.00000 + 5.19615i −0.136505 + 0.236433i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 5.50000 9.52628i 0.249742 0.432566i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −14.5000 + 25.1147i −0.657058 + 1.13806i 0.324316 + 0.945949i \(0.394866\pi\)
−0.981374 + 0.192109i \(0.938467\pi\)
\(488\) 2.00000 0.0905357
\(489\) −5.00000 8.66025i −0.226108 0.391630i
\(490\) −1.00000 1.73205i −0.0451754 0.0782461i
\(491\) 9.50000 16.4545i 0.428729 0.742580i −0.568032 0.823007i \(-0.692295\pi\)
0.996761 + 0.0804264i \(0.0256282\pi\)
\(492\) 2.00000 0.0901670
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) −3.50000 + 4.33013i −0.157155 + 0.194428i
\(497\) −12.0000 −0.538274
\(498\) 9.00000 0.403300
\(499\) −11.0000 19.0526i −0.492428 0.852910i 0.507534 0.861632i \(-0.330557\pi\)
−0.999962 + 0.00872186i \(0.997224\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 1.00000 1.73205i 0.0446767 0.0773823i
\(502\) 0 0
\(503\) −7.00000 12.1244i −0.312115 0.540598i 0.666705 0.745321i \(-0.267704\pi\)
−0.978820 + 0.204723i \(0.934371\pi\)
\(504\) 3.00000 0.133631
\(505\) −9.50000 + 16.4545i −0.422744 + 0.732215i
\(506\) −3.00000 + 5.19615i −0.133366 + 0.230997i
\(507\) 1.50000 2.59808i 0.0666173 0.115385i
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i \(-0.725464\pi\)
0.982988 + 0.183669i \(0.0587976\pi\)
\(510\) −2.00000 3.46410i −0.0885615 0.153393i
\(511\) −6.00000 −0.265424
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.00000 8.66025i 0.220541 0.381987i
\(515\) 6.50000 + 11.2583i 0.286424 + 0.496101i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 6.00000 10.3923i 0.263880 0.457053i
\(518\) 9.00000 15.5885i 0.395437 0.684917i
\(519\) 1.00000 0.0438951
\(520\) −2.00000 3.46410i −0.0877058 0.151911i
\(521\) 12.0000 + 20.7846i 0.525730 + 0.910590i 0.999551 + 0.0299693i \(0.00954094\pi\)
−0.473821 + 0.880621i \(0.657126\pi\)
\(522\) 0.500000 0.866025i 0.0218844 0.0379049i
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 3.00000 0.130931
\(526\) 6.00000 0.261612
\(527\) −22.0000 3.46410i −0.958335 0.150899i
\(528\) 3.00000 0.130558
\(529\) −19.0000 −0.826087
\(530\) 1.50000 + 2.59808i 0.0651558 + 0.112853i
\(531\) −9.00000 −0.390567
\(532\) 0 0
\(533\) 4.00000 + 6.92820i 0.173259 + 0.300094i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) 3.00000 0.129701
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 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
\(541\) −5.00000 8.66025i −0.214967 0.372333i 0.738296 0.674477i \(-0.235631\pi\)
−0.953262 + 0.302144i \(0.902298\pi\)
\(542\) −1.00000 −0.0429537
\(543\) −2.00000 −0.0858282
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) −2.00000 + 3.46410i −0.0856706 + 0.148386i
\(546\) 6.00000 + 10.3923i 0.256776 + 0.444750i
\(547\) −5.00000 + 8.66025i −0.213785 + 0.370286i −0.952896 0.303298i \(-0.901912\pi\)
0.739111 + 0.673583i \(0.235246\pi\)
\(548\) 8.00000 13.8564i 0.341743 0.591916i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 3.00000 0.127920
\(551\) 0 0
\(552\) −1.00000 1.73205i −0.0425628 0.0737210i
\(553\) −6.00000 + 10.3923i −0.255146 + 0.441926i
\(554\) 0 0
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) 4.00000 0.169638
\(557\) 11.0000 0.466085 0.233042 0.972467i \(-0.425132\pi\)
0.233042 + 0.972467i \(0.425132\pi\)
\(558\) 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
\(562\) 26.0000 1.09674
\(563\) −11.5000 + 19.9186i −0.484667 + 0.839468i −0.999845 0.0176152i \(-0.994393\pi\)
0.515178 + 0.857083i \(0.327726\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) −6.00000 10.3923i −0.252422 0.437208i
\(566\) 0 0
\(567\) 1.50000 2.59808i 0.0629941 0.109109i
\(568\) 2.00000 3.46410i 0.0839181 0.145350i
\(569\) −2.00000 + 3.46410i −0.0838444 + 0.145223i −0.904898 0.425628i \(-0.860053\pi\)
0.821054 + 0.570851i \(0.193387\pi\)
\(570\) 0 0
\(571\) −11.0000 + 19.0526i −0.460336 + 0.797325i −0.998978 0.0452101i \(-0.985604\pi\)
0.538642 + 0.842535i \(0.318938\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 14.0000 0.584858
\(574\) −6.00000 −0.250435
\(575\) −1.00000 1.73205i −0.0417029 0.0722315i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 13.0000 + 22.5167i 0.541197 + 0.937381i 0.998836 + 0.0482425i \(0.0153620\pi\)
−0.457639 + 0.889138i \(0.651305\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) 10.5000 18.1865i 0.436365 0.755807i
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) −27.0000 −1.12015
\(582\) −5.50000 9.52628i −0.227982 0.394877i
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) 1.00000 1.73205i 0.0413803 0.0716728i
\(585\) −4.00000 −0.165380
\(586\) 10.5000 + 18.1865i 0.433751 + 0.751279i
\(587\) 11.0000 0.454019 0.227009 0.973893i \(-0.427105\pi\)
0.227009 + 0.973893i \(0.427105\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) −9.00000 −0.370524
\(591\) 18.0000 0.740421
\(592\) 3.00000 + 5.19615i 0.123299 + 0.213561i
\(593\) −20.0000 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) 1.50000 2.59808i 0.0615457 0.106600i
\(595\) 6.00000 + 10.3923i 0.245976 + 0.426043i
\(596\) −9.50000 16.4545i −0.389135 0.674002i
\(597\) 11.0000 0.450200
\(598\) 4.00000 6.92820i 0.163572 0.283315i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) −21.0000 36.3731i −0.856608 1.48369i −0.875145 0.483860i \(-0.839234\pi\)
0.0185374 0.999828i \(-0.494099\pi\)
\(602\) −6.00000 + 10.3923i −0.244542 + 0.423559i
\(603\) −1.00000 1.73205i −0.0407231 0.0705346i
\(604\) 9.00000 0.366205
\(605\) 2.00000 0.0813116
\(606\) 9.50000 + 16.4545i 0.385911 + 0.668418i
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 0 0
\(609\) −1.50000 + 2.59808i −0.0607831 + 0.105279i
\(610\) 1.00000 1.73205i 0.0404888 0.0701287i
\(611\) −8.00000 + 13.8564i −0.323645 + 0.560570i
\(612\) −4.00000 −0.161690
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 1.00000 1.73205i 0.0403239 0.0698430i
\(616\) −9.00000 −0.362620
\(617\) −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i \(-0.846012\pi\)
0.0398207 0.999207i \(-0.487321\pi\)
\(618\) 13.0000 0.522937
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) 2.00000 + 5.19615i 0.0803219 + 0.208683i
\(621\) −2.00000 −0.0802572
\(622\) −24.0000 −0.962312
\(623\) 15.0000 + 25.9808i 0.600962 + 1.04090i
\(624\) −4.00000 −0.160128
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 10.5000 + 18.1865i 0.419664 + 0.726880i
\(627\) 0 0
\(628\) 22.0000 0.877896
\(629\) −12.0000 + 20.7846i −0.478471 + 0.828737i
\(630\) 1.50000 2.59808i 0.0597614 0.103510i
\(631\) −20.5000 + 35.5070i −0.816092 + 1.41351i 0.0924489 + 0.995717i \(0.470531\pi\)
−0.908541 + 0.417796i \(0.862803\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) 4.00000 6.92820i 0.158986 0.275371i
\(634\) 6.50000 + 11.2583i 0.258148 + 0.447125i
\(635\) 13.0000 0.515889
\(636\) 3.00000 0.118958
\(637\) −4.00000 6.92820i −0.158486 0.274505i
\(638\) −1.50000 + 2.59808i −0.0593856 + 0.102859i
\(639\) −2.00000 3.46410i −0.0791188 0.137038i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 5.00000 8.66025i 0.197488 0.342059i −0.750225 0.661182i \(-0.770055\pi\)
0.947713 + 0.319123i \(0.103388\pi\)
\(642\) 1.50000 2.59808i 0.0592003 0.102538i
\(643\) −38.0000 −1.49857 −0.749287 0.662246i \(-0.769604\pi\)
−0.749287 + 0.662246i \(0.769604\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) −2.00000 3.46410i −0.0787499 0.136399i
\(646\) 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
\(649\) 27.0000 1.05984
\(650\) −4.00000 −0.156893
\(651\) −6.00000 15.5885i −0.235159 0.610960i
\(652\) −10.0000 −0.391630
\(653\) −29.0000 −1.13486 −0.567429 0.823422i \(-0.692062\pi\)
−0.567429 + 0.823422i \(0.692062\pi\)
\(654\) 2.00000 + 3.46410i 0.0782062 + 0.135457i
\(655\) −12.0000 −0.468879
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) −1.00000 1.73205i −0.0390137 0.0675737i
\(658\) −6.00000 10.3923i −0.233904 0.405134i
\(659\) −37.0000 −1.44132 −0.720658 0.693291i \(-0.756160\pi\)
−0.720658 + 0.693291i \(0.756160\pi\)
\(660\) 1.50000 2.59808i 0.0583874 0.101130i
\(661\) 25.0000 43.3013i 0.972387 1.68422i 0.284087 0.958799i \(-0.408310\pi\)
0.688301 0.725426i \(-0.258357\pi\)
\(662\) −15.0000 + 25.9808i −0.582992 + 1.00977i
\(663\) −8.00000 13.8564i −0.310694 0.538138i
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 2.00000 0.0774403
\(668\) −1.00000 1.73205i −0.0386912 0.0670151i
\(669\) 4.50000 7.79423i 0.173980 0.301342i
\(670\) −1.00000 1.73205i −0.0386334 0.0669150i
\(671\) −3.00000 + 5.19615i −0.115814 + 0.200595i
\(672\) 1.50000 2.59808i 0.0578638 0.100223i
\(673\) 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i \(-0.713993\pi\)
0.988968 + 0.148132i \(0.0473259\pi\)
\(674\) −25.0000 −0.962964
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) −12.0000 −0.460857
\(679\) 16.5000 + 28.5788i 0.633212 + 1.09676i
\(680\) −4.00000 −0.153393
\(681\) 3.00000 0.114960
\(682\) −6.00000 15.5885i −0.229752 0.596913i
\(683\) 23.0000 0.880071 0.440035 0.897980i \(-0.354966\pi\)
0.440035 + 0.897980i \(0.354966\pi\)
\(684\) 0 0
\(685\) −8.00000 13.8564i −0.305664 0.529426i
\(686\) −15.0000 −0.572703
\(687\) 11.0000 19.0526i 0.419676 0.726900i
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) −2.00000 −0.0761387
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 0.500000 0.866025i 0.0190071 0.0329213i
\(693\) −4.50000 + 7.79423i −0.170941 + 0.296078i
\(694\) 9.50000 + 16.4545i 0.360615 + 0.624604i
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) −0.500000 0.866025i −0.0189525 0.0328266i
\(697\) 8.00000 0.303022
\(698\) −12.0000 −0.454207
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) 1.50000 2.59808i 0.0566947 0.0981981i
\(701\) 7.50000 + 12.9904i 0.283271 + 0.490640i 0.972188 0.234200i \(-0.0752470\pi\)
−0.688917 + 0.724840i \(0.741914\pi\)
\(702\) −2.00000 + 3.46410i −0.0754851 + 0.130744i
\(703\) 0 0
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 4.00000 0.150649
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) −28.5000 49.3634i −1.07185 1.85650i
\(708\) −4.50000 + 7.79423i −0.169120 + 0.292925i
\(709\) 50.0000 1.87779 0.938895 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) −2.00000 3.46410i −0.0750587 0.130005i
\(711\) −4.00000 −0.150012
\(712\) −10.0000 −0.374766
\(713\) −7.00000 + 8.66025i −0.262152 + 0.324329i
\(714\) 12.0000 0.449089
\(715\) 12.0000 0.448775
\(716\) −9.50000 16.4545i −0.355032 0.614933i
\(717\) 24.0000 0.896296
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 2.00000 + 3.46410i 0.0745874 + 0.129189i 0.900907 0.434013i \(-0.142903\pi\)
−0.826319 + 0.563202i \(0.809569\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −39.0000 −1.45244
\(722\) −9.50000 + 16.4545i −0.353553 + 0.612372i
\(723\) 7.50000 12.9904i 0.278928 0.483117i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −0.500000 0.866025i −0.0185695 0.0321634i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) −1.50000 2.59808i −0.0556319 0.0963573i 0.836868 0.547404i \(-0.184384\pi\)
−0.892500 + 0.451047i \(0.851051\pi\)
\(728\) 12.0000 0.444750
\(729\) 1.00000 0.0370370
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) 8.00000 13.8564i 0.295891 0.512498i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −9.00000 + 15.5885i −0.332423 + 0.575773i −0.982986 0.183679i \(-0.941199\pi\)
0.650564 + 0.759452i \(0.274533\pi\)
\(734\) 16.0000 27.7128i 0.590571 1.02290i
\(735\) −1.00000 + 1.73205i −0.0368856 + 0.0638877i
\(736\) −2.00000 −0.0737210
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) −1.00000 1.73205i −0.0368105 0.0637577i
\(739\) −8.00000 + 13.8564i −0.294285 + 0.509716i −0.974818 0.223001i \(-0.928415\pi\)
0.680534 + 0.732717i \(0.261748\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) −9.00000 −0.330400
\(743\) 50.0000 1.83432 0.917161 0.398517i \(-0.130475\pi\)
0.917161 + 0.398517i \(0.130475\pi\)
\(744\) 5.50000 + 0.866025i 0.201640 + 0.0317500i
\(745\) −19.0000 −0.696106
\(746\) −24.0000 −0.878702
\(747\) −4.50000 7.79423i −0.164646 0.285176i
\(748\) 12.0000 0.438763
\(749\) −4.50000 + 7.79423i −0.164426 + 0.284795i
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) 5.50000 + 9.52628i 0.200698 + 0.347619i 0.948753 0.316017i \(-0.102346\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) 4.00000 0.145865
\(753\) 0 0
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) 4.50000 7.79423i 0.163772 0.283661i
\(756\) −1.50000 2.59808i −0.0545545 0.0944911i
\(757\) 26.0000 45.0333i 0.944986 1.63676i 0.189207 0.981937i \(-0.439408\pi\)
0.755779 0.654827i \(-0.227258\pi\)
\(758\) −9.00000 15.5885i −0.326895 0.566198i
\(759\) 6.00000 0.217786
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 6.50000 11.2583i 0.235470 0.407846i
\(763\) −6.00000 10.3923i −0.217215 0.376227i
\(764\) 7.00000 12.1244i 0.253251 0.438644i
\(765\) −2.00000 + 3.46410i −0.0723102 + 0.125245i
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) −36.0000 −1.29988
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −22.5000 38.9711i −0.811371 1.40534i −0.911905 0.410402i \(-0.865388\pi\)
0.100534 0.994934i \(-0.467945\pi\)
\(770\) −4.50000 + 7.79423i −0.162169 + 0.280885i
\(771\) −10.0000 −0.360141
\(772\) −10.5000 18.1865i −0.377903 0.654548i
\(773\) 14.0000 0.503545 0.251773 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) −4.00000 −0.143777
\(775\) 5.50000 + 0.866025i 0.197566 + 0.0311086i
\(776\) −11.0000 −0.394877
\(777\) −18.0000 −0.645746
\(778\) −13.0000 22.5167i</