Properties

Label 930.2.i.c.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.c.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} +(-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

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

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
\(13\) −2.00000 3.46410i −0.554700 0.960769i −0.997927 0.0643593i \(-0.979500\pi\)
0.443227 0.896410i \(-0.353834\pi\)
\(14\) −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
\(23\) 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 −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 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 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) 1.50000 + 2.59808i 0.231455 + 0.400892i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 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 0.950464 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
\(58\) −1.00000 −0.131306
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 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 0.722599 0.691268i \(-0.242948\pi\)
−0.959955 + 0.280155i \(0.909614\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −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 −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 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 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) −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 −0.985329 0.170664i \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) 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 −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) −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 0.997102 + 0.0760733i \(0.0242383\pi\)
−0.432670 + 0.901553i \(0.642428\pi\)
\(114\) 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 −0.419064 0.907957i \(-0.637642\pi\)
0.995846 0.0910585i \(-0.0290250\pi\)
\(128\) −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 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 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 0.973910 + 0.226935i \(0.0728704\pi\)
−0.290424 + 0.956898i \(0.593796\pi\)
\(138\) −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 0.154668 + 0.987967i \(0.450569\pi\)
−0.932938 + 0.360037i \(0.882764\pi\)
\(150\) −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 −0.902120 0.431486i \(-0.857990\pi\)
0.824737 + 0.565516i \(0.191323\pi\)
\(168\) 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 0.884407 0.466717i \(-0.154563\pi\)
−0.846392 + 0.532560i \(0.821230\pi\)
\(174\) −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 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) 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 0.999972 + 0.00752447i \(0.00239513\pi\)
−0.493469 + 0.869763i \(0.664272\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −10.5000 + 18.1865i −0.755807 + 1.30910i 0.189166 + 0.981945i \(0.439422\pi\)
−0.944972 + 0.327150i \(0.893912\pi\)
\(194\) −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 0.985160 + 0.171639i \(0.0549062\pi\)
−0.343937 + 0.938993i \(0.611761\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i \(-0.0391815\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 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 −0.970229 0.242190i \(-0.922134\pi\)
0.694857 + 0.719148i \(0.255467\pi\)
\(212\) 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 −0.976440 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
\(226\) −6.00000 10.3923i −0.399114 0.691286i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) −11.0000 + 19.0526i −0.726900 + 1.25903i 0.231287 + 0.972886i \(0.425707\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) −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 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 1.00000 0.0645497
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) −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 0.666880 0.745165i \(-0.267629\pi\)
−0.978772 + 0.204953i \(0.934296\pi\)
\(258\) −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 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) 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 0.377244 + 0.926114i \(0.376872\pi\)
−0.990660 + 0.136355i \(0.956461\pi\)
\(294\) 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 −0.729010 0.684503i \(-0.760019\pi\)
0.957302 + 0.289090i \(0.0933526\pi\)
\(308\) 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 0.400262 + 0.916401i \(0.368919\pi\)
−0.993757 + 0.111563i \(0.964414\pi\)
\(314\) −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 −0.988788 0.149323i \(-0.952290\pi\)
0.623712 + 0.781654i \(0.285624\pi\)
\(318\) −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 0.902320 + 0.431066i \(0.141863\pi\)
−0.0778456 + 0.996965i \(0.524804\pi\)
\(332\) −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 0.489946 + 0.871753i \(0.337016\pi\)
−0.999933 + 0.0115703i \(0.996317\pi\)
\(348\) 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 −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 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 −0.924932 0.380131i \(-0.875879\pi\)
0.133263 0.991081i \(-0.457455\pi\)
\(360\) −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 −0.893873 0.448320i \(-0.852022\pi\)
0.0586798 0.998277i \(-0.481311\pi\)
\(368\) 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 −0.536776 0.843725i \(-0.680358\pi\)
0.999075 + 0.0429994i \(0.0136914\pi\)
\(380\) 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 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) −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 −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 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 −0.712843 0.701324i \(-0.752593\pi\)
0.963786 + 0.266678i \(0.0859261\pi\)
\(398\) −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 −0.659374 0.751815i \(-0.729178\pi\)
0.980778 + 0.195127i \(0.0625118\pi\)
\(410\) 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 0.899192 + 0.437555i \(0.144155\pi\)
−0.0706626 + 0.997500i \(0.522511\pi\)
\(422\) 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 −0.166491 0.986043i \(-0.553244\pi\)
0.937184 0.348836i \(-0.113423\pi\)
\(432\) −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 0.899599 0.436717i \(-0.143859\pi\)
−0.828008 + 0.560717i \(0.810526\pi\)
\(440\) 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 −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) −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 −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) −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 −0.981374 0.192109i \(-0.938467\pi\)
0.324316 0.945949i \(-0.394866\pi\)
\(488\) 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 0.996761 0.0804264i \(-0.0256282\pi\)
−0.568032 + 0.823007i \(0.692295\pi\)
\(492\) 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 −0.999962 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
\(502\) 0 0
\(503\) −7.00000 + 12.1244i −0.312115 + 0.540598i −0.978820 0.204723i \(-0.934371\pi\)
0.666705 + 0.745321i \(0.267704\pi\)
\(504\) 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 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) −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 −0.473821 0.880621i \(-0.657126\pi\)
0.999551 0.0299693i \(-0.00954094\pi\)
\(522\) 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 −0.953262 0.302144i \(-0.902298\pi\)
0.738296 + 0.674477i \(0.235631\pi\)
\(542\) −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 0.739111 0.673583i \(-0.235246\pi\)
−0.952896 + 0.303298i \(0.901912\pi\)
\(548\) 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 0.515178 0.857083i \(-0.327726\pi\)
−0.999845 + 0.0176152i \(0.994393\pi\)
\(564\) 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 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(570\) 0 0
\(571\) −11.0000 19.0526i −0.460336 0.797325i 0.538642 0.842535i \(-0.318938\pi\)
−0.998978 + 0.0452101i \(0.985604\pi\)
\(572\) 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 −0.457639 0.889138i \(-0.651305\pi\)
0.998836 0.0482425i \(-0.0153620\pi\)
\(578\) −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 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −21.0000 + 36.3731i −0.856608 + 1.48369i 0.0185374 + 0.999828i \(0.494099\pi\)
−0.875145 + 0.483860i \(0.839234\pi\)
\(602\) −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 −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 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 −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) −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 0.0398207 + 0.999207i \(0.487321\pi\)
−0.885249 + 0.465118i \(0.846012\pi\)
\(618\) 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 −0.908541 0.417796i \(-0.862803\pi\)
0.0924489 0.995717i \(-0.470531\pi\)
\(632\) −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 0.947713 0.319123i \(-0.103388\pi\)
−0.750225 + 0.661182i \(0.770055\pi\)
\(642\) 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 0.688301 + 0.725426i \(0.258357\pi\)
0.284087 + 0.958799i \(0.408310\pi\)
\(662\) −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 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) −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 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) −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 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 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 −0.688917 0.724840i \(-0.741914\pi\)
0.972188 + 0.234200i \(0.0752470\pi\)
\(702\) −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 −0.826319 0.563202i \(-0.809569\pi\)
0.900907 + 0.434013i \(0.142903\pi\)
\(720\) 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 −0.892500 0.451047i \(-0.851051\pi\)
0.836868 + 0.547404i \(0.184384\pi\)
\(728\) 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 0.650564 0.759452i \(-0.274533\pi\)
−0.982986 + 0.183679i \(0.941199\pi\)
\(734\) 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 0.680534 0.732717i \(-0.261748\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 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 −0.748056 0.663636i \(-0.769012\pi\)
0.948753 + 0.316017i \(0.102346\pi\)
\(752\) 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 0.755779 + 0.654827i \(0.227258\pi\)
0.189207 + 0.981937i \(0.439408\pi\)
\(758\) −9.00000 + 15.5885i −0.326895 + 0.566198i
\(759\) 6.00000 0.217786
\(760\) 0 0
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 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 0.100534 + 0.994934i \(0.467945\pi\)
−0.911905 + 0.410402i \(0.865388\pi\)
\(770\) −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 + 22.5