Properties

Label 105.2.i.b.46.1
Level 105
Weight 2
Character 105.46
Analytic conductor 0.838
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
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 46.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 105.46
Dual form 105.2.i.b.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{12} -3.00000 q^{13} +(-5.00000 + 1.73205i) q^{14} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} +2.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +12.0000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} +1.00000 q^{27} +(-4.00000 - 3.46410i) q^{28} -8.00000 q^{29} +(1.00000 + 1.73205i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(3.00000 + 5.19615i) q^{33} +8.00000 q^{34} +(2.50000 - 0.866025i) q^{35} +2.00000 q^{36} +(-3.50000 - 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{38} +(1.50000 - 2.59808i) q^{39} -6.00000 q^{41} +(1.00000 - 5.19615i) q^{42} +1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(-1.00000 - 1.73205i) q^{47} -4.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -2.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(1.00000 + 1.73205i) q^{54} -6.00000 q^{55} +1.00000 q^{57} +(-8.00000 - 13.8564i) q^{58} +(4.00000 - 6.92820i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(7.00000 + 12.1244i) q^{61} -2.00000 q^{62} +(2.50000 - 0.866025i) q^{63} -8.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{66} +(-3.50000 + 6.06218i) q^{67} +(4.00000 + 6.92820i) q^{68} -4.00000 q^{69} +(4.00000 + 3.46410i) q^{70} +6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(7.00000 - 12.1244i) q^{74} +(-0.500000 - 0.866025i) q^{75} +2.00000 q^{76} +(12.0000 + 10.3923i) q^{77} +6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} +2.00000 q^{83} +(5.00000 - 1.73205i) q^{84} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(4.00000 - 6.92820i) q^{87} +(6.00000 + 10.3923i) q^{89} -2.00000 q^{90} +(1.50000 - 7.79423i) q^{91} -8.00000 q^{92} +(-0.500000 - 0.866025i) q^{93} +(2.00000 - 3.46410i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(-4.00000 - 6.92820i) q^{96} -6.00000 q^{97} +(-2.00000 - 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - q^{3} - 2q^{4} - q^{5} - 4q^{6} - q^{7} - q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - q^{3} - 2q^{4} - q^{5} - 4q^{6} - q^{7} - q^{9} + 2q^{10} + 6q^{11} - 2q^{12} - 6q^{13} - 10q^{14} + 2q^{15} + 4q^{16} + 4q^{17} + 2q^{18} - q^{19} + 4q^{20} - 4q^{21} + 24q^{22} + 4q^{23} - q^{25} - 6q^{26} + 2q^{27} - 8q^{28} - 16q^{29} + 2q^{30} - q^{31} - 8q^{32} + 6q^{33} + 16q^{34} + 5q^{35} + 4q^{36} - 7q^{37} + 2q^{38} + 3q^{39} - 12q^{41} + 2q^{42} + 2q^{43} + 12q^{44} - q^{45} - 8q^{46} - 2q^{47} - 8q^{48} - 13q^{49} - 4q^{50} + 4q^{51} + 6q^{52} - 4q^{53} + 2q^{54} - 12q^{55} + 2q^{57} - 16q^{58} + 8q^{59} - 2q^{60} + 14q^{61} - 4q^{62} + 5q^{63} - 16q^{64} + 3q^{65} - 12q^{66} - 7q^{67} + 8q^{68} - 8q^{69} + 8q^{70} + 12q^{71} - q^{73} + 14q^{74} - q^{75} + 4q^{76} + 24q^{77} + 12q^{78} + q^{79} + 4q^{80} - q^{81} - 12q^{82} + 4q^{83} + 10q^{84} - 8q^{85} + 2q^{86} + 8q^{87} + 12q^{89} - 4q^{90} + 3q^{91} - 16q^{92} - q^{93} + 4q^{94} - q^{95} - 8q^{96} - 12q^{97} - 4q^{98} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −2.00000 −0.816497
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) −1.00000 1.73205i −0.288675 0.500000i
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −5.00000 + 1.73205i −1.33631 + 0.462910i
\(15\) 1.00000 0.258199
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 1.00000 1.73205i 0.235702 0.408248i
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 2.00000 0.447214
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 12.0000 2.55841
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.00000 5.19615i −0.588348 1.01905i
\(27\) 1.00000 0.192450
\(28\) −4.00000 3.46410i −0.755929 0.654654i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 1.00000 + 1.73205i 0.182574 + 0.316228i
\(31\) −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i \(-0.861957\pi\)
0.817625 + 0.575751i \(0.195290\pi\)
\(32\) −4.00000 + 6.92820i −0.707107 + 1.22474i
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 8.00000 1.37199
\(35\) 2.50000 0.866025i 0.422577 0.146385i
\(36\) 2.00000 0.333333
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 1.50000 2.59808i 0.240192 0.416025i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 1.00000 5.19615i 0.154303 0.801784i
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 6.00000 + 10.3923i 0.904534 + 1.56670i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −4.00000 + 6.92820i −0.589768 + 1.02151i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) −4.00000 −0.577350
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −2.00000 −0.282843
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) 3.00000 5.19615i 0.416025 0.720577i
\(53\) −2.00000 + 3.46410i −0.274721 + 0.475831i −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) 1.00000 + 1.73205i 0.136083 + 0.235702i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) −8.00000 13.8564i −1.05045 1.81944i
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) −1.00000 + 1.73205i −0.129099 + 0.223607i
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) −2.00000 −0.254000
\(63\) 2.50000 0.866025i 0.314970 0.109109i
\(64\) −8.00000 −1.00000
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) −6.00000 + 10.3923i −0.738549 + 1.27920i
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 4.00000 + 6.92820i 0.485071 + 0.840168i
\(69\) −4.00000 −0.481543
\(70\) 4.00000 + 3.46410i 0.478091 + 0.414039i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −0.500000 + 0.866025i −0.0585206 + 0.101361i −0.893801 0.448463i \(-0.851972\pi\)
0.835281 + 0.549823i \(0.185305\pi\)
\(74\) 7.00000 12.1244i 0.813733 1.40943i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 2.00000 0.229416
\(77\) 12.0000 + 10.3923i 1.36753 + 1.18431i
\(78\) 6.00000 0.679366
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 2.00000 3.46410i 0.223607 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.00000 10.3923i −0.662589 1.14764i
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 5.00000 1.73205i 0.545545 0.188982i
\(85\) −4.00000 −0.433861
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 4.00000 6.92820i 0.428845 0.742781i
\(88\) 0 0
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) −2.00000 −0.210819
\(91\) 1.50000 7.79423i 0.157243 0.817057i
\(92\) −8.00000 −0.834058
\(93\) −0.500000 0.866025i −0.0518476 0.0898027i
\(94\) 2.00000 3.46410i 0.206284 0.357295i
\(95\) −0.500000 + 0.866025i −0.0512989 + 0.0888523i
\(96\) −4.00000 6.92820i −0.408248 0.707107i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −2.00000 13.8564i −0.202031 1.39971i
\(99\) −6.00000 −0.603023
\(100\) −1.00000 1.73205i −0.100000 0.173205i
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) −4.00000 + 6.92820i −0.396059 + 0.685994i
\(103\) 9.50000 + 16.4545i 0.936063 + 1.62131i 0.772728 + 0.634738i \(0.218892\pi\)
0.163335 + 0.986571i \(0.447775\pi\)
\(104\) 0 0
\(105\) −0.500000 + 2.59808i −0.0487950 + 0.253546i
\(106\) −8.00000 −0.777029
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) −1.00000 + 1.73205i −0.0962250 + 0.166667i
\(109\) 7.50000 12.9904i 0.718370 1.24425i −0.243276 0.969957i \(-0.578222\pi\)
0.961645 0.274296i \(-0.0884447\pi\)
\(110\) −6.00000 10.3923i −0.572078 0.990867i
\(111\) 7.00000 0.664411
\(112\) −10.0000 + 3.46410i −0.944911 + 0.327327i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 2.00000 3.46410i 0.186501 0.323029i
\(116\) 8.00000 13.8564i 0.742781 1.28654i
\(117\) 1.50000 + 2.59808i 0.138675 + 0.240192i
\(118\) 16.0000 1.47292
\(119\) 8.00000 + 6.92820i 0.733359 + 0.635107i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −14.0000 + 24.2487i −1.26750 + 2.19538i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 4.00000 + 3.46410i 0.356348 + 0.308607i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0 0
\(129\) −0.500000 + 0.866025i −0.0440225 + 0.0762493i
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i \(-0.194513\pi\)
−0.906399 + 0.422423i \(0.861180\pi\)
\(132\) −12.0000 −1.04447
\(133\) 2.50000 0.866025i 0.216777 0.0750939i
\(134\) −14.0000 −1.20942
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 0 0
\(137\) −4.00000 + 6.92820i −0.341743 + 0.591916i −0.984757 0.173939i \(-0.944351\pi\)
0.643013 + 0.765855i \(0.277684\pi\)
\(138\) −4.00000 6.92820i −0.340503 0.589768i
\(139\) 21.0000 1.78120 0.890598 0.454791i \(-0.150286\pi\)
0.890598 + 0.454791i \(0.150286\pi\)
\(140\) −1.00000 + 5.19615i −0.0845154 + 0.439155i
\(141\) 2.00000 0.168430
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −9.00000 + 15.5885i −0.752618 + 1.30357i
\(144\) 2.00000 3.46410i 0.166667 0.288675i
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) −2.00000 −0.165521
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) 14.0000 1.15079
\(149\) 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i \(-0.114277\pi\)
−0.772399 + 0.635138i \(0.780943\pi\)
\(150\) 1.00000 1.73205i 0.0816497 0.141421i
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) −6.00000 + 31.1769i −0.483494 + 2.51231i
\(155\) 1.00000 0.0803219
\(156\) 3.00000 + 5.19615i 0.240192 + 0.416025i
\(157\) −5.00000 + 8.66025i −0.399043 + 0.691164i −0.993608 0.112884i \(-0.963991\pi\)
0.594565 + 0.804048i \(0.297324\pi\)
\(158\) −1.00000 + 1.73205i −0.0795557 + 0.137795i
\(159\) −2.00000 3.46410i −0.158610 0.274721i
\(160\) 8.00000 0.632456
\(161\) −10.0000 + 3.46410i −0.788110 + 0.273009i
\(162\) −2.00000 −0.157135
\(163\) 6.00000 + 10.3923i 0.469956 + 0.813988i 0.999410 0.0343508i \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) 6.00000 10.3923i 0.468521 0.811503i
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) −10.0000 −0.773823 −0.386912 0.922117i \(-0.626458\pi\)
−0.386912 + 0.922117i \(0.626458\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) −4.00000 6.92820i −0.306786 0.531369i
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −12.0000 20.7846i −0.912343 1.58022i −0.810745 0.585399i \(-0.800938\pi\)
−0.101598 0.994826i \(-0.532395\pi\)
\(174\) 16.0000 1.21296
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 24.0000 1.80907
\(177\) 4.00000 + 6.92820i 0.300658 + 0.520756i
\(178\) −12.0000 + 20.7846i −0.899438 + 1.55787i
\(179\) −9.00000 + 15.5885i −0.672692 + 1.16514i 0.304446 + 0.952529i \(0.401529\pi\)
−0.977138 + 0.212607i \(0.931805\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) 15.0000 5.19615i 1.11187 0.385164i
\(183\) −14.0000 −1.03491
\(184\) 0 0
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) −12.0000 20.7846i −0.877527 1.51992i
\(188\) 4.00000 0.291730
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) −2.00000 −0.145095
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) 4.00000 6.92820i 0.288675 0.500000i
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) −3.00000 −0.214834
\(196\) 11.0000 8.66025i 0.785714 0.618590i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) −6.00000 10.3923i −0.426401 0.738549i
\(199\) −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i \(-0.924846\pi\)
0.688705 + 0.725042i \(0.258180\pi\)
\(200\) 0 0
\(201\) −3.50000 6.06218i −0.246871 0.427593i
\(202\) 20.0000 1.40720
\(203\) 4.00000 20.7846i 0.280745 1.45879i
\(204\) −8.00000 −0.560112
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) −19.0000 + 32.9090i −1.32379 + 2.29288i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) −6.00000 10.3923i −0.416025 0.720577i
\(209\) −6.00000 −0.415029
\(210\) −5.00000 + 1.73205i −0.345033 + 0.119523i
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −4.00000 6.92820i −0.274721 0.475831i
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) 12.0000 20.7846i 0.820303 1.42081i
\(215\) −0.500000 0.866025i −0.0340997 0.0590624i
\(216\) 0 0
\(217\) −2.00000 1.73205i −0.135769 0.117579i
\(218\) 30.0000 2.03186
\(219\) −0.500000 0.866025i −0.0337869 0.0585206i
\(220\) 6.00000 10.3923i 0.404520 0.700649i
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 7.00000 + 12.1244i 0.469809 + 0.813733i
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) −16.0000 13.8564i −1.06904 0.925820i
\(225\) 1.00000 0.0666667
\(226\) −6.00000 10.3923i −0.399114 0.691286i
\(227\) 5.00000 8.66025i 0.331862 0.574801i −0.651015 0.759065i \(-0.725657\pi\)
0.982877 + 0.184263i \(0.0589899\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i \(-0.307988\pi\)
−0.996832 + 0.0795401i \(0.974655\pi\)
\(230\) 8.00000 0.527504
\(231\) −15.0000 + 5.19615i −0.986928 + 0.341882i
\(232\) 0 0
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) −1.00000 + 1.73205i −0.0652328 + 0.112987i
\(236\) 8.00000 + 13.8564i 0.520756 + 0.901975i
\(237\) −1.00000 −0.0649570
\(238\) −4.00000 + 20.7846i −0.259281 + 1.34727i
\(239\) 14.0000 0.905585 0.452792 0.891616i \(-0.350428\pi\)
0.452792 + 0.891616i \(0.350428\pi\)
\(240\) 2.00000 + 3.46410i 0.129099 + 0.223607i
\(241\) 9.00000 15.5885i 0.579741 1.00414i −0.415768 0.909471i \(-0.636487\pi\)
0.995509 0.0946700i \(-0.0301796\pi\)
\(242\) 25.0000 43.3013i 1.60706 2.78351i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −28.0000 −1.79252
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 12.0000 0.765092
\(247\) 1.50000 + 2.59808i 0.0954427 + 0.165312i
\(248\) 0 0
\(249\) −1.00000 + 1.73205i −0.0633724 + 0.109764i
\(250\) 1.00000 + 1.73205i 0.0632456 + 0.109545i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −1.00000 + 5.19615i −0.0629941 + 0.327327i
\(253\) 24.0000 1.50887
\(254\) 5.00000 + 8.66025i 0.313728 + 0.543393i
\(255\) 2.00000 3.46410i 0.125245 0.216930i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) −2.00000 −0.124515
\(259\) 17.5000 6.06218i 1.08740 0.376685i
\(260\) −6.00000 −0.372104
\(261\) 4.00000 + 6.92820i 0.247594 + 0.428845i
\(262\) 2.00000 3.46410i 0.123560 0.214013i
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 4.00000 + 3.46410i 0.245256 + 0.212398i
\(267\) −12.0000 −0.734388
\(268\) −7.00000 12.1244i −0.427593 0.740613i
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 1.00000 1.73205i 0.0608581 0.105409i
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 16.0000 0.970143
\(273\) 6.00000 + 5.19615i 0.363137 + 0.314485i
\(274\) −16.0000 −0.966595
\(275\) 3.00000 + 5.19615i 0.180907 + 0.313340i
\(276\) 4.00000 6.92820i 0.240772 0.417029i
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 21.0000 + 36.3731i 1.25950 + 2.18151i
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 2.00000 + 3.46410i 0.119098 + 0.206284i
\(283\) 3.50000 6.06218i 0.208053 0.360359i −0.743048 0.669238i \(-0.766621\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) −0.500000 0.866025i −0.0296174 0.0512989i
\(286\) −36.0000 −2.12872
\(287\) 3.00000 15.5885i 0.177084 0.920158i
\(288\) 8.00000 0.471405
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −8.00000 + 13.8564i −0.469776 + 0.813676i
\(291\) 3.00000 5.19615i 0.175863 0.304604i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −16.0000 −0.934730 −0.467365 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) 13.0000 + 5.19615i 0.758175 + 0.303046i
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 3.00000 5.19615i 0.174078 0.301511i
\(298\) −4.00000 + 6.92820i −0.231714 + 0.401340i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 2.00000 0.115470
\(301\) −0.500000 + 2.59808i −0.0288195 + 0.149751i
\(302\) −16.0000 −0.920697
\(303\) 5.00000 + 8.66025i 0.287242 + 0.497519i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 7.00000 12.1244i 0.400819 0.694239i
\(306\) −4.00000 6.92820i −0.228665 0.396059i
\(307\) 3.00000 0.171219 0.0856095 0.996329i \(-0.472716\pi\)
0.0856095 + 0.996329i \(0.472716\pi\)
\(308\) −30.0000 + 10.3923i −1.70941 + 0.592157i
\(309\) −19.0000 −1.08087
\(310\) 1.00000 + 1.73205i 0.0567962 + 0.0983739i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) −5.50000 9.52628i −0.310878 0.538457i 0.667674 0.744453i \(-0.267290\pi\)
−0.978553 + 0.205996i \(0.933957\pi\)
\(314\) −20.0000 −1.12867
\(315\) −2.00000 1.73205i −0.112687 0.0975900i
\(316\) −2.00000 −0.112509
\(317\) −10.0000 17.3205i −0.561656 0.972817i −0.997352 0.0727229i \(-0.976831\pi\)
0.435696 0.900094i \(-0.356502\pi\)
\(318\) 4.00000 6.92820i 0.224309 0.388514i
\(319\) −24.0000 + 41.5692i −1.34374 + 2.32743i
\(320\) 4.00000 + 6.92820i 0.223607 + 0.387298i
\(321\) 12.0000 0.669775
\(322\) −16.0000 13.8564i −0.891645 0.772187i
\(323\) −4.00000 −0.222566
\(324\) −1.00000 1.73205i −0.0555556 0.0962250i
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) −12.0000 + 20.7846i −0.664619 + 1.15115i
\(327\) 7.50000 + 12.9904i 0.414751 + 0.718370i
\(328\) 0 0
\(329\) 5.00000 1.73205i 0.275659 0.0954911i
\(330\) 12.0000 0.660578
\(331\) 4.50000 + 7.79423i 0.247342 + 0.428410i 0.962788 0.270259i \(-0.0871094\pi\)
−0.715445 + 0.698669i \(0.753776\pi\)
\(332\) −2.00000 + 3.46410i −0.109764 + 0.190117i
\(333\) −3.50000 + 6.06218i −0.191799 + 0.332205i
\(334\) −10.0000 17.3205i −0.547176 0.947736i
\(335\) 7.00000 0.382451
\(336\) 2.00000 10.3923i 0.109109 0.566947i
\(337\) 25.0000 1.36184 0.680918 0.732359i \(-0.261581\pi\)
0.680918 + 0.732359i \(0.261581\pi\)
\(338\) −4.00000 6.92820i −0.217571 0.376845i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 4.00000 6.92820i 0.216930 0.375735i
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) −2.00000 −0.108148
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 2.00000 + 3.46410i 0.107676 + 0.186501i
\(346\) 24.0000 41.5692i 1.29025 2.23478i
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) 8.00000 + 13.8564i 0.428845 + 0.742781i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 1.00000 5.19615i 0.0534522 0.277746i
\(351\) −3.00000 −0.160128
\(352\) 24.0000 + 41.5692i 1.27920 + 2.21565i
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) −8.00000 + 13.8564i −0.425195 + 0.736460i
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) −24.0000 −1.27200
\(357\) −10.0000 + 3.46410i −0.529256 + 0.183340i
\(358\) −36.0000 −1.90266
\(359\) 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 13.0000 + 22.5167i 0.683265 + 1.18345i
\(363\) 25.0000 1.31216
\(364\) 12.0000 + 10.3923i 0.628971 + 0.544705i
\(365\) 1.00000 0.0523424
\(366\) −14.0000 24.2487i −0.731792 1.26750i
\(367\) −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i \(-0.998494\pi\)
0.504093 + 0.863649i \(0.331827\pi\)
\(368\) −8.00000 + 13.8564i −0.417029 + 0.722315i
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) −14.0000 −0.727825
\(371\) −8.00000 6.92820i −0.415339 0.359694i
\(372\) 2.00000 0.103695
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 24.0000 41.5692i 1.24101 2.14949i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) −5.00000 + 1.73205i −0.257172 + 0.0890871i
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) −1.00000 1.73205i −0.0512989 0.0888523i
\(381\) −2.50000 + 4.33013i −0.128079 + 0.221839i
\(382\) 10.0000 17.3205i 0.511645 0.886194i
\(383\) −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i \(-0.912926\pi\)
0.247451 0.968900i \(-0.420407\pi\)
\(384\) 0 0
\(385\) 3.00000 15.5885i 0.152894 0.794461i
\(386\) 18.0000 0.916176
\(387\) −0.500000 0.866025i −0.0254164 0.0440225i
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) −3.00000 5.19615i −0.151911 0.263117i
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 0.500000 0.866025i 0.0251577 0.0435745i
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) 18.5000 + 32.0429i 0.928488 + 1.60819i 0.785853 + 0.618414i \(0.212224\pi\)
0.142636 + 0.989775i \(0.454442\pi\)
\(398\) −16.0000 −0.802008
\(399\) −0.500000 + 2.59808i −0.0250313 + 0.130066i
\(400\) −4.00000 −0.200000
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 7.00000 12.1244i 0.349128 0.604708i
\(403\) 1.50000 2.59808i 0.0747203 0.129419i
\(404\) 10.0000 + 17.3205i 0.497519 + 0.861727i
\(405\) 1.00000 0.0496904
\(406\) 40.0000 13.8564i 1.98517 0.687682i
\(407\) −42.0000 −2.08186
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) −4.00000 6.92820i −0.197305 0.341743i
\(412\) −38.0000 −1.87213
\(413\) 16.0000 + 13.8564i 0.787309 + 0.681829i
\(414\) 8.00000 0.393179
\(415\) −1.00000 1.73205i −0.0490881 0.0850230i
\(416\) 12.0000 20.7846i 0.588348 1.01905i
\(417\) −10.5000 + 18.1865i −0.514187 + 0.890598i
\(418\) −6.00000 10.3923i −0.293470 0.508304i
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) −4.00000 3.46410i −0.195180 0.169031i
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) −20.0000 34.6410i −0.973585 1.68630i
\(423\) −1.00000 + 1.73205i −0.0486217 + 0.0842152i
\(424\) 0 0
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) −12.0000 −0.581402
\(427\) −35.0000 + 12.1244i −1.69377 + 0.586739i
\(428\) 24.0000 1.16008
\(429\) −9.00000 15.5885i −0.434524 0.752618i
\(430\) 1.00000 1.73205i 0.0482243 0.0835269i
\(431\) 1.00000 1.73205i 0.0481683 0.0834300i −0.840936 0.541135i \(-0.817995\pi\)
0.889104 + 0.457705i \(0.151328\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) −5.00000 −0.240285 −0.120142 0.992757i \(-0.538335\pi\)
−0.120142 + 0.992757i \(0.538335\pi\)
\(434\) 1.00000 5.19615i 0.0480015 0.249423i
\(435\) −8.00000 −0.383571
\(436\) 15.0000 + 25.9808i 0.718370 + 1.24425i
\(437\) 2.00000 3.46410i 0.0956730 0.165710i
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) −24.0000 −1.14156
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) −7.00000 + 12.1244i −0.332205 + 0.575396i
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) −24.0000 41.5692i −1.13643 1.96836i
\(447\) −4.00000 −0.189194
\(448\) 4.00000 20.7846i 0.188982 0.981981i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 1.00000 + 1.73205i 0.0471405 + 0.0816497i
\(451\) −18.0000 + 31.1769i −0.847587 + 1.46806i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 20.0000 0.938647
\(455\) −7.50000 + 2.59808i −0.351605 + 0.121800i
\(456\) 0 0
\(457\) 7.50000 + 12.9904i 0.350835 + 0.607664i 0.986396 0.164386i \(-0.0525644\pi\)
−0.635561 + 0.772051i \(0.719231\pi\)
\(458\) 13.0000 22.5167i 0.607450 1.05213i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 4.00000 + 6.92820i 0.186501 + 0.323029i
\(461\) −8.00000 −0.372597 −0.186299 0.982493i \(-0.559649\pi\)
−0.186299 + 0.982493i \(0.559649\pi\)
\(462\) −24.0000 20.7846i −1.11658 0.966988i
\(463\) 3.00000 0.139422 0.0697109 0.997567i \(-0.477792\pi\)
0.0697109 + 0.997567i \(0.477792\pi\)
\(464\) −16.0000 27.7128i −0.742781 1.28654i
\(465\) −0.500000 + 0.866025i −0.0231869 + 0.0401610i
\(466\) 6.00000 10.3923i 0.277945 0.481414i
\(467\) −11.0000 19.0526i −0.509019 0.881647i −0.999945 0.0104461i \(-0.996675\pi\)
0.490926 0.871201i \(-0.336658\pi\)
\(468\) −6.00000 −0.277350
\(469\) −14.0000 12.1244i −0.646460 0.559851i
\(470\) −4.00000 −0.184506
\(471\) −5.00000 8.66025i −0.230388 0.399043i
\(472\) 0 0
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) −1.00000 1.73205i −0.0459315 0.0795557i
\(475\) 1.00000 0.0458831
\(476\) −20.0000 + 6.92820i −0.916698 + 0.317554i
\(477\) 4.00000 0.183147
\(478\) 14.0000 + 24.2487i 0.640345 + 1.10911i
\(479\) 2.00000 3.46410i 0.0913823 0.158279i −0.816711 0.577047i \(-0.804205\pi\)
0.908093 + 0.418769i \(0.137538\pi\)
\(480\) −4.00000 + 6.92820i −0.182574 + 0.316228i
\(481\) 10.5000 + 18.1865i 0.478759 + 0.829235i
\(482\) 36.0000 1.63976
\(483\) 2.00000 10.3923i 0.0910032 0.472866i
\(484\) 50.0000 2.27273
\(485\) 3.00000 + 5.19615i 0.136223 + 0.235945i
\(486\) 1.00000 1.73205i 0.0453609 0.0785674i
\(487\) 6.50000 11.2583i 0.294543 0.510164i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714992\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) −11.0000 + 8.66025i −0.496929 + 0.391230i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 6.00000 + 10.3923i 0.270501 + 0.468521i
\(493\) −16.0000 + 27.7128i −0.720604 + 1.24812i
\(494\) −3.00000 + 5.19615i −0.134976 + 0.233786i
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) −4.00000 −0.179605
\(497\) −3.00000 + 15.5885i −0.134568 + 0.699238i
\(498\) −4.00000 −0.179244
\(499\) −14.5000 25.1147i −0.649109 1.12429i −0.983336 0.181797i \(-0.941809\pi\)
0.334227 0.942493i \(-0.391525\pi\)
\(500\) −1.00000 + 1.73205i −0.0447214 + 0.0774597i
\(501\) 5.00000 8.66025i 0.223384 0.386912i
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) −2.00000 −0.0891756 −0.0445878 0.999005i \(-0.514197\pi\)
−0.0445878 + 0.999005i \(0.514197\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 24.0000 + 41.5692i 1.06693 + 1.84798i
\(507\) 2.00000 3.46410i 0.0888231 0.153846i
\(508\) −5.00000 + 8.66025i −0.221839 + 0.384237i
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 8.00000 0.354246
\(511\) −2.00000 1.73205i −0.0884748 0.0766214i
\(512\) −32.0000 −1.41421
\(513\) −0.500000 0.866025i −0.0220755 0.0382360i
\(514\) −18.0000 + 31.1769i −0.793946 + 1.37515i
\(515\) 9.50000 16.4545i 0.418620 0.725071i
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) −12.0000 −0.527759
\(518\) 28.0000 + 24.2487i 1.23025 + 1.06543i
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −2.00000 + 3.46410i −0.0876216 + 0.151765i −0.906505 0.422194i \(-0.861260\pi\)
0.818884 + 0.573959i \(0.194593\pi\)
\(522\) −8.00000 + 13.8564i −0.350150 + 0.606478i
\(523\) −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i \(-0.243977\pi\)
−0.960856 + 0.277047i \(0.910644\pi\)
\(524\) 4.00000 0.174741
\(525\) 2.50000 0.866025i 0.109109 0.0377964i
\(526\) −8.00000 −0.348817
\(527\) 2.00000 + 3.46410i 0.0871214 + 0.150899i
\(528\) −12.0000 + 20.7846i −0.522233 + 0.904534i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 4.00000 + 6.92820i 0.173749 + 0.300942i
\(531\) −8.00000 −0.347170
\(532\) −1.00000 + 5.19615i −0.0433555 + 0.225282i
\(533\) 18.0000 0.779667
\(534\) −12.0000 20.7846i −0.519291 0.899438i
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 0 0
\(537\) −9.00000 15.5885i −0.388379 0.672692i
\(538\) 20.0000 0.862261
\(539\) −33.0000 + 25.9808i −1.42141 + 1.11907i
\(540\) 2.00000 0.0860663
\(541\) 1.50000 + 2.59808i 0.0644900 + 0.111700i 0.896468 0.443109i \(-0.146125\pi\)
−0.831978 + 0.554809i \(0.812791\pi\)
\(542\) −24.0000 + 41.5692i −1.03089 + 1.78555i
\(543\) −6.50000 + 11.2583i −0.278942 + 0.483141i
\(544\) 16.0000 + 27.7128i 0.685994 + 1.18818i
\(545\) −15.0000 −0.642529
\(546\) −3.00000 + 15.5885i −0.128388 + 0.667124i
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) −8.00000 13.8564i −0.341743 0.591916i
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) −6.00000 + 10.3923i −0.255841 + 0.443129i
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 0 0
\(553\) −2.50000 + 0.866025i −0.106311 + 0.0368271i
\(554\) 14.0000 0.594803
\(555\) −3.50000 6.06218i −0.148567 0.257325i
\(556\) −21.0000 + 36.3731i −0.890598 + 1.54256i
\(557\) 5.00000 8.66025i 0.211857 0.366947i −0.740439 0.672124i \(-0.765382\pi\)
0.952296 + 0.305177i \(0.0987156\pi\)
\(558\) 1.00000 + 1.73205i 0.0423334 + 0.0733236i
\(559\) −3.00000 −0.126886
\(560\) 8.00000 + 6.92820i 0.338062 + 0.292770i
\(561\) 24.0000 1.01328
\(562\) −12.0000 20.7846i −0.506189 0.876746i
\(563\) 13.0000 22.5167i 0.547885 0.948964i −0.450535 0.892759i \(-0.648767\pi\)
0.998419 0.0562051i \(-0.0179001\pi\)
\(564\) −2.00000 + 3.46410i −0.0842152 + 0.145865i
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 14.0000 0.588464
\(567\) −2.00000 1.73205i −0.0839921 0.0727393i
\(568\) 0 0
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) 1.50000 2.59808i 0.0627730 0.108726i −0.832931 0.553377i \(-0.813339\pi\)
0.895704 + 0.444651i \(0.146672\pi\)
\(572\) −18.0000 31.1769i −0.752618 1.30357i
\(573\) 10.0000 0.417756
\(574\) 30.0000 10.3923i 1.25218 0.433766i
\(575\) −4.00000 −0.166812
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) 14.5000 25.1147i 0.603643 1.04554i −0.388621 0.921397i \(-0.627049\pi\)
0.992264 0.124143i \(-0.0396180\pi\)
\(578\) −1.00000 + 1.73205i −0.0415945 + 0.0720438i
\(579\) 4.50000 + 7.79423i 0.187014 + 0.323917i
\(580\) −16.0000 −0.664364
\(581\) −1.00000 + 5.19615i −0.0414870 + 0.215573i
\(582\) 12.0000 0.497416
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) 0 0
\(585\) 1.50000 2.59808i 0.0620174 0.107417i
\(586\) −16.0000 27.7128i −0.660954 1.14481i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 2.00000 + 13.8564i 0.0824786 + 0.571429i
\(589\) 1.00000 0.0412043
\(590\) −8.00000 13.8564i −0.329355 0.570459i
\(591\) −6.00000 + 10.3923i −0.246807 + 0.427482i
\(592\) 14.0000 24.2487i 0.575396 0.996616i
\(593\) 9.00000 + 15.5885i 0.369586 + 0.640141i 0.989501 0.144528i \(-0.0461663\pi\)
−0.619915 + 0.784669i \(0.712833\pi\)
\(594\) 12.0000 0.492366
\(595\) 2.00000 10.3923i 0.0819920 0.426043i
\(596\) −8.00000 −0.327693
\(597\) −4.00000 6.92820i −0.163709 0.283552i
\(598\) 12.0000 20.7846i 0.490716 0.849946i
\(599\) 2.00000 3.46410i 0.0817178 0.141539i −0.822270 0.569097i \(-0.807293\pi\)
0.903988 + 0.427558i \(0.140626\pi\)
\(600\) 0 0
\(601\) −33.0000 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(602\) −5.00000 + 1.73205i −0.203785 + 0.0705931i
\(603\) 7.00000 0.285062
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) −12.5000 + 21.6506i −0.508197 + 0.880223i
\(606\) −10.0000 + 17.3205i −0.406222 + 0.703598i
\(607\) −17.5000 30.3109i −0.710303 1.23028i −0.964743 0.263193i \(-0.915225\pi\)
0.254440 0.967088i \(-0.418109\pi\)
\(608\) 8.00000 0.324443
\(609\) 16.0000 + 13.8564i 0.648353 + 0.561490i
\(610\) 28.0000 1.13369
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 4.00000 6.92820i 0.161690 0.280056i
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 3.00000 + 5.19615i 0.121070 + 0.209700i
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −19.0000 32.9090i −0.764292 1.32379i
\(619\) −1.50000 + 2.59808i −0.0602901 + 0.104425i −0.894595 0.446878i \(-0.852536\pi\)
0.834305 + 0.551303i \(0.185869\pi\)
\(620\) −1.00000 + 1.73205i −0.0401610 + 0.0695608i
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) −12.0000 −0.481156
\(623\) −30.0000 + 10.3923i −1.20192 + 0.416359i
\(624\) 12.0000 0.480384
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 11.0000 19.0526i 0.439648 0.761493i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −10.0000 17.3205i −0.399043 0.691164i
\(629\) −28.0000 −1.11643
\(630\) 1.00000 5.19615i 0.0398410 0.207020i
\(631\) 24.0000 0.955425 0.477712 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) 0 0
\(633\) 10.0000 17.3205i 0.397464 0.688428i
\(634\) 20.0000 34.6410i 0.794301 1.37577i
\(635\) −2.50000 4.33013i −0.0992095 0.171836i
\(636\) 8.00000 0.317221
\(637\) 19.5000 + 7.79423i 0.772618 + 0.308819i
\(638\) −96.0000 −3.80068
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 12.0000 + 20.7846i 0.473602 + 0.820303i
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 4.00000 20.7846i 0.157622 0.819028i
\(645\) 1.00000 0.0393750
\(646\) −4.00000 6.92820i −0.157378 0.272587i
\(647\) −15.0000 + 25.9808i −0.589711 + 1.02141i 0.404559 + 0.914512i \(0.367425\pi\)
−0.994270 + 0.106897i \(0.965908\pi\)
\(648\) 0 0
\(649\) −24.0000 41.5692i −0.942082 1.63173i
\(650\) 6.00000 0.235339
\(651\) 2.50000 0.866025i 0.0979827 0.0339422i
\(652\) −24.0000 −0.939913
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) −15.0000 + 25.9808i −0.586546 + 1.01593i
\(655\) −1.00000 + 1.73205i −0.0390732 + 0.0676768i
\(656\) −12.0000 20.7846i −0.468521 0.811503i
\(657\) 1.00000 0.0390137
\(658\) 8.00000 + 6.92820i 0.311872 + 0.270089i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 6.00000 + 10.3923i 0.233550 + 0.404520i
\(661\) −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i \(-0.980947\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(662\) −9.00000 + 15.5885i −0.349795 + 0.605863i
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) 0 0
\(665\) −2.00000 1.73205i −0.0775567 0.0671660i
\(666\) −14.0000 −0.542489
\(667\) −16.0000 27.7128i −0.619522 1.07304i
\(668\) 10.0000 17.3205i 0.386912 0.670151i
\(669\) 12.0000 20.7846i 0.463947 0.803579i
\(670\) 7.00000 + 12.1244i 0.270434 + 0.468405i
\(671\) 84.0000 3.24278
\(672\) 20.0000 6.92820i 0.771517 0.267261i
\(673\) −37.0000 −1.42625 −0.713123 0.701039i \(-0.752720\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) 25.0000 + 43.3013i 0.962964 + 1.66790i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 4.00000 6.92820i 0.153846 0.266469i
\(677\) −8.00000 13.8564i −0.307465 0.532545i 0.670342 0.742052i \(-0.266147\pi\)
−0.977807 + 0.209507i \(0.932814\pi\)
\(678\) 12.0000 0.460857
\(679\) 3.00000 15.5885i 0.115129 0.598230i
\(680\) 0 0
\(681\) 5.00000 + 8.66025i 0.191600 + 0.331862i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) 24.0000 41.5692i 0.918334 1.59060i 0.116390 0.993204i \(-0.462868\pi\)
0.801945 0.597398i \(-0.203799\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) 8.00000 0.305664
\(686\) 37.0000 + 1.73205i 1.41267 + 0.0661300i
\(687\) 13.0000 0.495981
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) −4.00000 + 6.92820i −0.152277 + 0.263752i
\(691\) −13.5000 23.3827i −0.513564 0.889519i −0.999876 0.0157341i \(-0.994991\pi\)
0.486312 0.873785i \(-0.338342\pi\)
\(692\) 48.0000 1.82469
\(693\) 3.00000 15.5885i 0.113961 0.592157i
\(694\) −32.0000 −1.21470
\(695\) −10.5000 18.1865i −0.398288 0.689855i
\(696\) 0 0
\(697\) −12.0000 + 20.7846i −0.454532 + 0.787273i
\(698\) 2.00000 + 3.46410i 0.0757011 + 0.131118i
\(699\) 6.00000 0.226941
\(700\) 5.00000 1.73205i 0.188982 0.0654654i
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) −3.00000 5.19615i −0.113228 0.196116i
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) −24.0000 + 41.5692i −0.904534 + 1.56670i
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) 36.0000 1.35488
\(707\) 20.0000 + 17.3205i 0.752177 + 0.651405i
\(708\) −16.0000 −0.601317
\(709\) 13.0000 + 22.5167i 0.488225 + 0.845631i 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) 6.00000 10.3923i 0.225176 0.390016i
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) −16.0000 13.8564i −0.598785 0.518563i
\(715\) 18.0000 0.673162
\(716\) −18.0000 31.1769i −0.672692 1.16514i
\(717\) −7.00000 + 12.1244i −0.261420 + 0.452792i
\(718\) −24.0000 + 41.5692i −0.895672 + 1.55135i
\(719\) 17.0000 + 29.4449i 0.633993 + 1.09811i 0.986728 + 0.162385i \(0.0519185\pi\)
−0.352735 + 0.935723i \(0.614748\pi\)
\(720\) −4.00000 −0.149071
\(721\) −47.5000 + 16.4545i −1.76899 + 0.612797i
\(722\) 36.0000 1.33978
\(723\) 9.00000 + 15.5885i 0.334714 + 0.579741i
\(724\) −13.0000 + 22.5167i −0.483141 + 0.836825i
\(725\) 4.00000 6.92820i 0.148556 0.257307i
\(726\) 25.0000 + 43.3013i 0.927837 + 1.60706i
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.00000 + 1.73205i 0.0370117 + 0.0641061i
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 14.0000 24.2487i 0.517455 0.896258i
\(733\) 21.5000 + 37.2391i 0.794121 + 1.37546i 0.923396 + 0.383849i \(0.125402\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) −38.0000 −1.40261
\(735\) −6.50000 2.59808i −0.239756 0.0958315i
\(736\) −32.0000 −1.17954
\(737\) 21.0000 + 36.3731i 0.773545 + 1.33982i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) −20.5000 + 35.5070i −0.754105 + 1.30615i 0.191714 + 0.981451i \(0.438596\pi\)
−0.945818 + 0.324697i \(0.894738\pi\)
\(740\) −7.00000 12.1244i −0.257325 0.445700i
\(741\) −3.00000 −0.110208
\(742\) 4.00000 20.7846i 0.146845 0.763027i
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) −1.00000 1.73205i −0.0365881 0.0633724i
\(748\) 48.0000 1.75505
\(749\) 30.0000 10.3923i 1.09618 0.379727i
\(750\) −2.00000 −0.0730297
\(751\) −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i \(-0.989192\pi\)
0.470311 0.882501i \(-0.344142\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) 24.0000 + 41.5692i 0.874028 + 1.51386i
\(755\) 8.00000 0.291150
\(756\) −4.00000 3.46410i −0.145479 0.125988i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 11.0000 + 19.0526i 0.399538 + 0.692020i
\(759\) −12.0000 + 20.7846i −0.435572 + 0.754434i
\(760\) 0 0
\(761\) 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) −10.0000 −0.362262
\(763\) 30.0000 + 25.9808i 1.08607 + 0.940567i
\(764\) 20.0000 0.723575
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 28.0000 48.4974i 1.01168 1.75228i
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) −8.00000 13.8564i −0.288675 0.500000i
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 30.0000 10.3923i 1.08112 0.374513i
\(771\) −18.0000 −0.648254
\(772\) 9.00000 + 15.5885i 0.323917 + 0.561041i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) −0.500000 0.866025i −0.0179605 0.0311086i
\(776\) 0 0
\(777\) −3.50000 + 18.1865i −0.125562 + 0.652438i
\(778\) −12.0000 −0.430221
\(779\) 3.00000 + 5.19615i 0.107486 + 0.186171i
\(780\) 3.00000 5.19615i 0.107417 0.186052i
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 16.0000 + 27.7128i 0.572159 + 0.991008i
\(783\) −8.00000 −0.285897
\(784\) −4.00000 27.7128i −0.142857 0.989743i
\(785\) 10.0000 0.356915
\(786\) 2.00000 + 3.46410i 0.0713376 + 0.123560i
\(787\) 16.0000 27.7128i 0.570338 0.987855i −0.426193 0.904632i \(-0.640145\pi\)
0.996531 0.0832226i \(-0.0265213\pi\)
\(788\) −12.0000 + 20.7846i −0.427482 + 0.740421i
\(789\) −2.00000 3.46410i −0.0712019 0.123325i
\(790\) 2.00000 0.0711568
\(791\) 3.00000 15.5885i 0.106668 0.554262i
\(792\) 0 0