Properties

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

Related objects

Downloads

Learn more

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.e.211.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.00000 + 5.19615i) q^{13} +1.00000 q^{15} +1.00000 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{22} +7.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} +(2.00000 - 5.19615i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(0.500000 - 0.866025i) q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} +(-2.00000 + 3.46410i) q^{38} -6.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.50000 - 6.06218i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} +7.00000 q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{51} +(3.00000 + 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(-2.00000 - 3.46410i) q^{57} +6.00000 q^{58} +(-6.00000 + 10.3923i) q^{59} +1.00000 q^{60} -14.0000 q^{61} +(2.00000 - 5.19615i) q^{62} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} -1.00000 q^{66} +(-2.50000 - 4.33013i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-3.50000 + 6.06218i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-2.00000 + 3.46410i) q^{76} -6.00000 q^{78} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +(-8.00000 - 13.8564i) q^{83} -1.00000 q^{85} +(3.50000 - 6.06218i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(0.500000 + 0.866025i) q^{88} +4.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} +7.00000 q^{92} +(3.50000 + 4.33013i) q^{93} +3.00000 q^{94} +4.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -6.00000 q^{97} +(3.50000 + 6.06218i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + q^{17} - q^{18} - 4 q^{19} - q^{20} + q^{22} + 14 q^{23} - q^{24} - q^{25} + 6 q^{26} + 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 2 q^{33} + q^{34} - q^{36} - 7 q^{37} - 4 q^{38} - 12 q^{39} - q^{40} + 2 q^{41} + 7 q^{43} + q^{44} - q^{45} + 14 q^{46} + 6 q^{47} - q^{48} + 7 q^{49} - q^{50} + q^{51} + 6 q^{52} + 4 q^{53} + 2 q^{54} + q^{55} - 4 q^{57} + 12 q^{58} - 12 q^{59} + 2 q^{60} - 28 q^{61} + 4 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 5 q^{67} + q^{68} - 7 q^{69} - 6 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} - q^{75} - 4 q^{76} - 12 q^{78} - 3 q^{79} - q^{80} - q^{81} + 2 q^{82} - 16 q^{83} - 2 q^{85} + 7 q^{86} - 6 q^{87} + q^{88} + 8 q^{89} - q^{90} + 14 q^{92} + 7 q^{93} + 6 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 7 q^{98} + q^{99}+O(q^{100}) \) 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
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) 7.00000 1.45960 0.729800 0.683660i \(-0.239613\pi\)
0.729800 + 0.683660i \(0.239613\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.00000 5.19615i 0.359211 0.933257i
\(32\) 1.00000 0.176777
\(33\) −1.00000 −0.174078
\(34\) 0.500000 0.866025i 0.0857493 0.148522i
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) −2.00000 + 3.46410i −0.324443 + 0.561951i
\(39\) −6.00000 −0.960769
\(40\) −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 \(0.783417\pi\)
\(42\) 0 0
\(43\) 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i \(-0.654118\pi\)
0.999223 0.0394140i \(-0.0125491\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 7.00000 1.03209
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0.500000 + 0.866025i 0.0700140 + 0.121268i
\(52\) 3.00000 + 5.19615i 0.416025 + 0.720577i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.500000 0.866025i 0.0674200 0.116775i
\(56\) 0 0
\(57\) −2.00000 3.46410i −0.264906 0.458831i
\(58\) 6.00000 0.787839
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 1.00000 0.129099
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 2.00000 5.19615i 0.254000 0.659912i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) −1.00000 −0.123091
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0.500000 0.866025i 0.0606339 0.105021i
\(69\) −3.50000 + 6.06218i −0.421350 + 0.729800i
\(70\) 0 0
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) −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 \(0.870674\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −2.00000 + 3.46410i −0.229416 + 0.397360i
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) −1.50000 + 2.59808i −0.168763 + 0.292306i −0.937985 0.346675i \(-0.887311\pi\)
0.769222 + 0.638982i \(0.220644\pi\)
\(80\) −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
\(83\) −8.00000 13.8564i −0.878114 1.52094i −0.853408 0.521243i \(-0.825468\pi\)
−0.0247060 0.999695i \(-0.507865\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 3.50000 6.06218i 0.377415 0.653701i
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 0 0
\(92\) 7.00000 0.729800
\(93\) 3.50000 + 4.33013i 0.362933 + 0.449013i
\(94\) 3.00000 0.309426
\(95\) 4.00000 0.410391
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 0.500000 0.866025i 0.0502519 0.0870388i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 0.500000 + 0.866025i 0.0495074 + 0.0857493i
\(103\) 1.00000 + 1.73205i 0.0985329 + 0.170664i 0.911078 0.412235i \(-0.135252\pi\)
−0.812545 + 0.582899i \(0.801918\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) 2.00000 + 3.46410i 0.194257 + 0.336463i
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) 1.00000 0.0962250
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) −3.50000 6.06218i −0.332205 0.575396i
\(112\) 0 0
\(113\) −9.50000 16.4545i −0.893685 1.54791i −0.835424 0.549606i \(-0.814778\pi\)
−0.0582609 0.998301i \(-0.518556\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) −3.50000 6.06218i −0.326377 0.565301i
\(116\) 6.00000 0.557086
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) −6.00000 + 10.3923i −0.552345 + 0.956689i
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −14.0000 −1.26750
\(123\) −2.00000 −0.180334
\(124\) 2.00000 5.19615i 0.179605 0.466628i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 9.00000 15.5885i 0.798621 1.38325i −0.121894 0.992543i \(-0.538897\pi\)
0.920514 0.390709i \(-0.127770\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.50000 + 6.06218i 0.308158 + 0.533745i
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i \(-0.819423\pi\)
0.887041 + 0.461690i \(0.152757\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) −2.50000 4.33013i −0.215967 0.374066i
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 0.500000 0.866025i 0.0428746 0.0742611i
\(137\) 3.50000 + 6.06218i 0.299025 + 0.517927i 0.975913 0.218159i \(-0.0700052\pi\)
−0.676888 + 0.736086i \(0.736672\pi\)
\(138\) −3.50000 + 6.06218i −0.297940 + 0.516047i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0 0
\(141\) −1.50000 + 2.59808i −0.126323 + 0.218797i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) −7.00000 −0.577350
\(148\) −3.50000 + 6.06218i −0.287698 + 0.498308i
\(149\) −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i \(0.361067\pi\)
−0.996207 + 0.0870170i \(0.972267\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) −5.50000 + 0.866025i −0.441771 + 0.0695608i
\(156\) −6.00000 −0.480384
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −1.50000 + 2.59808i −0.119334 + 0.206692i
\(159\) −4.00000 −0.317221
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 0 0
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 5.00000 0.391630 0.195815 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) −8.00000 13.8564i −0.620920 1.07547i
\(167\) 12.0000 20.7846i 0.928588 1.60836i 0.142901 0.989737i \(-0.454357\pi\)
0.785687 0.618624i \(-0.212310\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) −1.00000 −0.0766965
\(171\) 4.00000 0.305888
\(172\) 3.50000 6.06218i 0.266872 0.462237i
\(173\) −1.00000 1.73205i −0.0760286 0.131685i 0.825505 0.564396i \(-0.190891\pi\)
−0.901533 + 0.432710i \(0.857557\pi\)
\(174\) −3.00000 + 5.19615i −0.227429 + 0.393919i
\(175\) 0 0
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) −6.00000 10.3923i −0.450988 0.781133i
\(178\) 4.00000 0.299813
\(179\) 5.50000 9.52628i 0.411089 0.712028i −0.583920 0.811811i \(-0.698482\pi\)
0.995009 + 0.0997838i \(0.0318151\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −10.0000 17.3205i −0.743294 1.28742i −0.950988 0.309229i \(-0.899929\pi\)
0.207693 0.978194i \(-0.433404\pi\)
\(182\) 0 0
\(183\) 7.00000 12.1244i 0.517455 0.896258i
\(184\) 7.00000 0.516047
\(185\) 7.00000 0.514650
\(186\) 3.50000 + 4.33013i 0.256632 + 0.317500i
\(187\) 1.00000 0.0731272
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i \(-0.950525\pi\)
0.628037 + 0.778183i \(0.283859\pi\)
\(194\) −6.00000 −0.430775
\(195\) 3.00000 + 5.19615i 0.214834 + 0.372104i
\(196\) 3.50000 + 6.06218i 0.250000 + 0.433013i
\(197\) −4.00000 6.92820i −0.284988 0.493614i 0.687618 0.726073i \(-0.258656\pi\)
−0.972606 + 0.232458i \(0.925323\pi\)
\(198\) 0.500000 0.866025i 0.0355335 0.0615457i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 5.00000 0.352673
\(202\) 15.0000 1.05540
\(203\) 0 0
\(204\) 0.500000 + 0.866025i 0.0350070 + 0.0606339i
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) 1.00000 + 1.73205i 0.0696733 + 0.120678i
\(207\) −3.50000 6.06218i −0.243267 0.421350i
\(208\) 3.00000 + 5.19615i 0.208013 + 0.360288i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) 2.00000 + 3.46410i 0.137361 + 0.237915i
\(213\) 6.00000 0.411113
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) −7.00000 −0.477396
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −12.0000 −0.812743
\(219\) 2.00000 0.135147
\(220\) 0.500000 0.866025i 0.0337100 0.0583874i
\(221\) 6.00000 0.403604
\(222\) −3.50000 6.06218i −0.234905 0.406867i
\(223\) −7.00000 + 12.1244i −0.468755 + 0.811907i −0.999362 0.0357107i \(-0.988630\pi\)
0.530607 + 0.847618i \(0.321964\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −9.50000 16.4545i −0.631931 1.09454i
\(227\) 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i \(-0.0811332\pi\)
−0.702202 + 0.711977i \(0.747800\pi\)
\(228\) −2.00000 3.46410i −0.132453 0.229416i
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) −3.50000 6.06218i −0.230783 0.399728i
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 25.0000 1.63780 0.818902 0.573933i \(-0.194583\pi\)
0.818902 + 0.573933i \(0.194583\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) −1.50000 2.59808i −0.0978492 0.169480i
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) −1.50000 2.59808i −0.0974355 0.168763i
\(238\) 0 0
\(239\) −9.00000 15.5885i −0.582162 1.00833i −0.995223 0.0976302i \(-0.968874\pi\)
0.413061 0.910703i \(-0.364460\pi\)
\(240\) 1.00000 0.0645497
\(241\) −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) 5.00000 8.66025i 0.321412 0.556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −14.0000 −0.896258
\(245\) 3.50000 6.06218i 0.223607 0.387298i
\(246\) −2.00000 −0.127515
\(247\) −24.0000 −1.52708
\(248\) 2.00000 5.19615i 0.127000 0.329956i
\(249\) 16.0000 1.01396
\(250\) 1.00000 0.0632456
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) 0 0
\(253\) 3.50000 + 6.06218i 0.220043 + 0.381126i
\(254\) 9.00000 15.5885i 0.564710 0.978107i
\(255\) 0.500000 0.866025i 0.0313112 0.0542326i
\(256\) 1.00000 0.0625000
\(257\) −11.5000 19.9186i −0.717350 1.24249i −0.962046 0.272887i \(-0.912021\pi\)
0.244696 0.969600i \(-0.421312\pi\)
\(258\) 3.50000 + 6.06218i 0.217900 + 0.377415i
\(259\) 0 0
\(260\) 3.00000 5.19615i 0.186052 0.322252i
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0.500000 0.866025i 0.0308901 0.0535032i
\(263\) −11.0000 −0.678289 −0.339145 0.940734i \(-0.610138\pi\)
−0.339145 + 0.940734i \(0.610138\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 2.00000 3.46410i 0.122859 0.212798i
\(266\) 0 0
\(267\) −2.00000 + 3.46410i −0.122398 + 0.212000i
\(268\) −2.50000 4.33013i −0.152712 0.264505i
\(269\) 12.5000 + 21.6506i 0.762138 + 1.32006i 0.941746 + 0.336324i \(0.109184\pi\)
−0.179608 + 0.983738i \(0.557483\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0.500000 0.866025i 0.0303170 0.0525105i
\(273\) 0 0
\(274\) 3.50000 + 6.06218i 0.211443 + 0.366230i
\(275\) −1.00000 −0.0603023
\(276\) −3.50000 + 6.06218i −0.210675 + 0.364900i
\(277\) 13.0000 0.781094 0.390547 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) −10.0000 −0.599760
\(279\) −5.50000 + 0.866025i −0.329276 + 0.0518476i
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) −19.0000 −1.12943 −0.564716 0.825285i \(-0.691014\pi\)
−0.564716 + 0.825285i \(0.691014\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) −2.00000 + 3.46410i −0.118470 + 0.205196i
\(286\) −3.00000 + 5.19615i −0.177394 + 0.307255i
\(287\) 0 0
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 3.00000 5.19615i 0.175863 0.304604i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −8.00000 + 13.8564i −0.467365 + 0.809500i −0.999305 0.0372823i \(-0.988130\pi\)
0.531940 + 0.846782i \(0.321463\pi\)
\(294\) −7.00000 −0.408248
\(295\) 12.0000 0.698667
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 0.500000 + 0.866025i 0.0290129 + 0.0502519i
\(298\) −7.00000 + 12.1244i −0.405499 + 0.702345i
\(299\) 21.0000 + 36.3731i 1.21446 + 2.10351i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 0 0
\(302\) −7.00000 −0.402805
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 7.00000 + 12.1244i 0.400819 + 0.694239i
\(306\) −1.00000 −0.0571662
\(307\) −8.00000 + 13.8564i −0.456584 + 0.790827i −0.998778 0.0494267i \(-0.984261\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 0 0
\(309\) −2.00000 −0.113776
\(310\) −5.50000 + 0.866025i −0.312379 + 0.0491869i
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) −6.00000 −0.339683
\(313\) −3.00000 + 5.19615i −0.169570 + 0.293704i −0.938269 0.345907i \(-0.887571\pi\)
0.768699 + 0.639611i \(0.220905\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −1.50000 + 2.59808i −0.0843816 + 0.146153i
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) −4.00000 −0.224309
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 2.00000 + 3.46410i 0.111629 + 0.193347i
\(322\) 0 0
\(323\) 2.00000 + 3.46410i 0.111283 + 0.192748i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −6.00000 −0.332820
\(326\) 5.00000 0.276924
\(327\) 6.00000 10.3923i 0.331801 0.574696i
\(328\) 1.00000 + 1.73205i 0.0552158 + 0.0956365i
\(329\) 0 0
\(330\) 0.500000 + 0.866025i 0.0275241 + 0.0476731i
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) 7.00000 0.383598
\(334\) 12.0000 20.7846i 0.656611 1.13728i
\(335\) −2.50000 + 4.33013i −0.136590 + 0.236580i
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −11.5000 + 19.9186i −0.625518 + 1.08343i
\(339\) 19.0000 1.03194
\(340\) −1.00000 −0.0542326
\(341\) 5.50000 0.866025i 0.297842 0.0468979i
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 3.50000 6.06218i 0.188707 0.326851i
\(345\) 7.00000 0.376867
\(346\) −1.00000 1.73205i −0.0537603 0.0931156i
\(347\) 7.00000 12.1244i 0.375780 0.650870i −0.614664 0.788789i \(-0.710708\pi\)
0.990443 + 0.137920i \(0.0440416\pi\)
\(348\) −3.00000 + 5.19615i −0.160817 + 0.278543i
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) 3.00000 + 5.19615i 0.160128 + 0.277350i
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i \(-0.738768\pi\)
0.974456 + 0.224580i \(0.0721011\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 4.00000 0.212000
\(357\) 0 0
\(358\) 5.50000 9.52628i 0.290684 0.503480i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −10.0000 17.3205i −0.525588 0.910346i
\(363\) 5.00000 + 8.66025i 0.262432 + 0.454545i
\(364\) 0 0
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) 7.00000 12.1244i 0.365896 0.633750i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 7.00000 0.364900
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 7.00000 0.363913
\(371\) 0 0
\(372\) 3.50000 + 4.33013i 0.181467 + 0.224507i
\(373\) −19.0000 −0.983783 −0.491891 0.870657i \(-0.663694\pi\)
−0.491891 + 0.870657i \(0.663694\pi\)
\(374\) 1.00000 0.0517088
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 3.00000 0.154713
\(377\) 18.0000 + 31.1769i 0.927047 + 1.60569i
\(378\) 0 0
\(379\) −3.00000 + 5.19615i −0.154100 + 0.266908i −0.932731 0.360573i \(-0.882581\pi\)
0.778631 + 0.627482i \(0.215914\pi\)
\(380\) 4.00000 0.205196
\(381\) 9.00000 + 15.5885i 0.461084 + 0.798621i
\(382\) 3.00000 + 5.19615i 0.153493 + 0.265858i
\(383\) −9.50000 16.4545i −0.485427 0.840785i 0.514432 0.857531i \(-0.328003\pi\)
−0.999860 + 0.0167461i \(0.994669\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −5.00000 + 8.66025i −0.254493 + 0.440795i
\(387\) −7.00000 −0.355830
\(388\) −6.00000 −0.304604
\(389\) −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i \(-0.906604\pi\)
0.729103 + 0.684403i \(0.239937\pi\)
\(390\) 3.00000 + 5.19615i 0.151911 + 0.263117i
\(391\) 3.50000 6.06218i 0.177003 0.306578i
\(392\) 3.50000 + 6.06218i 0.176777 + 0.306186i
\(393\) 0.500000 + 0.866025i 0.0252217 + 0.0436852i
\(394\) −4.00000 6.92820i −0.201517 0.349038i
\(395\) 3.00000 0.150946
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 10.5000 18.1865i 0.526980 0.912756i −0.472526 0.881317i \(-0.656658\pi\)
0.999506 0.0314391i \(-0.0100090\pi\)
\(398\) −8.00000 13.8564i −0.401004 0.694559i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 5.00000 0.249377
\(403\) 33.0000 5.19615i 1.64385 0.258839i
\(404\) 15.0000 0.746278
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −7.00000 −0.346977
\(408\) 0.500000 + 0.866025i 0.0247537 + 0.0428746i
\(409\) −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i \(-0.988987\pi\)
0.529657 + 0.848212i \(0.322321\pi\)
\(410\) 1.00000 1.73205i 0.0493865 0.0855399i
\(411\) −7.00000 −0.345285
\(412\) 1.00000 + 1.73205i 0.0492665 + 0.0853320i
\(413\) 0 0
\(414\) −3.50000 6.06218i −0.172016 0.297940i
\(415\) −8.00000 + 13.8564i −0.392705 + 0.680184i
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) 5.00000 8.66025i 0.244851 0.424094i
\(418\) −4.00000 −0.195646
\(419\) 7.00000 0.341972 0.170986 0.985273i \(-0.445305\pi\)
0.170986 + 0.985273i \(0.445305\pi\)
\(420\) 0 0
\(421\) −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i \(-0.948251\pi\)
0.353233 0.935536i \(-0.385082\pi\)
\(422\) 4.00000 6.92820i 0.194717 0.337260i
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) 2.00000 + 3.46410i 0.0971286 + 0.168232i
\(425\) 0.500000 + 0.866025i 0.0242536 + 0.0420084i
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) 2.00000 3.46410i 0.0966736 0.167444i
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) −7.00000 −0.337570
\(431\) −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 1.00000 0.0481125
\(433\) 8.00000 0.384455 0.192228 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) −12.0000 −0.574696
\(437\) −14.0000 + 24.2487i −0.669711 + 1.15997i
\(438\) 2.00000 0.0955637
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0.500000 0.866025i 0.0238366 0.0412861i
\(441\) 3.50000 6.06218i 0.166667 0.288675i
\(442\) 6.00000 0.285391
\(443\) −17.0000 29.4449i −0.807694 1.39897i −0.914457 0.404683i \(-0.867382\pi\)
0.106763 0.994285i \(-0.465952\pi\)
\(444\) −3.50000 6.06218i −0.166103 0.287698i
\(445\) −2.00000 3.46410i −0.0948091 0.164214i
\(446\) −7.00000 + 12.1244i −0.331460 + 0.574105i
\(447\) −7.00000 12.1244i −0.331089 0.573462i
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 1.00000 0.0471405
\(451\) −1.00000 + 1.73205i −0.0470882 + 0.0815591i
\(452\) −9.50000 16.4545i −0.446842 0.773954i
\(453\) 3.50000 6.06218i 0.164444 0.284826i
\(454\) 4.00000 + 6.92820i 0.187729 + 0.325157i
\(455\) 0 0
\(456\) −2.00000 3.46410i −0.0936586 0.162221i
\(457\) 32.0000 1.49690 0.748448 0.663193i \(-0.230799\pi\)
0.748448 + 0.663193i \(0.230799\pi\)
\(458\) −10.0000 + 17.3205i −0.467269 + 0.809334i
\(459\) 0.500000 0.866025i 0.0233380 0.0404226i
\(460\) −3.50000 6.06218i −0.163188 0.282650i
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 6.00000 0.278543
\(465\) 2.00000 5.19615i 0.0927478 0.240966i
\(466\) 25.0000 1.15810
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 3.00000 5.19615i 0.138675 0.240192i
\(469\) 0 0
\(470\) −1.50000 2.59808i −0.0691898 0.119840i
\(471\) −7.00000 + 12.1244i −0.322543 + 0.558661i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) 7.00000 0.321860
\(474\) −1.50000 2.59808i −0.0688973 0.119334i
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) 0 0
\(477\) 2.00000 3.46410i 0.0915737 0.158610i
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 1.00000 0.0456435
\(481\) −42.0000 −1.91504
\(482\) −9.00000 + 15.5885i −0.409939 + 0.710035i
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) 3.00000 + 5.19615i 0.136223 + 0.235945i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i \(-0.908493\pi\)
0.233933 0.972253i \(-0.424840\pi\)
\(488\) −14.0000 −0.633750
\(489\) −2.50000 + 4.33013i −0.113054 + 0.195815i
\(490\) 3.50000 6.06218i 0.158114 0.273861i
\(491\) 14.5000 + 25.1147i 0.654376 + 1.13341i 0.982050 + 0.188621i \(0.0604019\pi\)
−0.327674 + 0.944791i \(0.606265\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 3.00000 5.19615i 0.135113 0.234023i
\(494\) −24.0000 −1.07981
\(495\) −1.00000 −0.0449467
\(496\) 2.00000 5.19615i 0.0898027 0.233314i
\(497\) 0 0
\(498\) 16.0000 0.716977
\(499\) 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) 1.00000 0.0447214
\(501\) 12.0000 + 20.7846i 0.536120 + 0.928588i
\(502\) −1.50000 + 2.59808i −0.0669483 + 0.115958i
\(503\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(504\) 0 0
\(505\) −7.50000 12.9904i −0.333746 0.578064i
\(506\) 3.50000 + 6.06218i 0.155594 + 0.269497i
\(507\) −11.5000 19.9186i −0.510733 0.884615i
\(508\) 9.00000 15.5885i 0.399310 0.691626i
\(509\) −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i \(-0.944480\pi\)
0.342126 0.939654i \(-0.388853\pi\)
\(510\) 0.500000 0.866025i 0.0221404 0.0383482i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −2.00000 + 3.46410i −0.0883022 + 0.152944i
\(514\) −11.5000 19.9186i −0.507243 0.878571i
\(515\) 1.00000 1.73205i 0.0440653 0.0763233i
\(516\) 3.50000 + 6.06218i 0.154079 + 0.266872i
\(517\) 1.50000 + 2.59808i 0.0659699 + 0.114263i
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 0.500000 0.866025i 0.0218426 0.0378325i
\(525\) 0 0
\(526\) −11.0000 −0.479623
\(527\) −3.50000 4.33013i −0.152462 0.188623i
\(528\) −1.00000 −0.0435194
\(529\) 26.0000 1.13043
\(530\) 2.00000 3.46410i 0.0868744 0.150471i
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −6.00000 + 10.3923i −0.259889 + 0.450141i
\(534\) −2.00000 + 3.46410i −0.0865485 + 0.149906i
\(535\) −4.00000 −0.172935
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) 5.50000 + 9.52628i 0.237343 + 0.411089i
\(538\) 12.5000 + 21.6506i 0.538913 + 0.933425i
\(539\) −3.50000 + 6.06218i −0.150756 + 0.261116i
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) −28.0000 −1.20270
\(543\) 20.0000 0.858282
\(544\) 0.500000 0.866025i 0.0214373 0.0371305i
\(545\) 6.00000 + 10.3923i 0.257012 + 0.445157i
\(546\) 0 0
\(547\) 8.50000 + 14.7224i 0.363434 + 0.629486i 0.988524 0.151067i \(-0.0482710\pi\)
−0.625090 + 0.780553i \(0.714938\pi\)
\(548\) 3.50000 + 6.06218i 0.149513 + 0.258963i
\(549\) 7.00000 + 12.1244i 0.298753 + 0.517455i
\(550\) −1.00000 −0.0426401
\(551\) −12.0000 + 20.7846i −0.511217 + 0.885454i
\(552\) −3.50000 + 6.06218i −0.148970 + 0.258023i
\(553\) 0 0
\(554\) 13.0000 0.552317
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) −10.0000 −0.424094
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) −5.50000 + 0.866025i −0.232834 + 0.0366618i
\(559\) 42.0000 1.77641
\(560\) 0 0
\(561\) −0.500000 + 0.866025i −0.0211100 + 0.0365636i
\(562\) 22.0000 0.928014
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) −1.50000 + 2.59808i −0.0631614 + 0.109399i
\(565\) −9.50000 + 16.4545i −0.399668 + 0.692245i
\(566\) −19.0000 −0.798630
\(567\) 0 0
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) −17.0000 29.4449i −0.712677 1.23439i −0.963849 0.266450i \(-0.914149\pi\)
0.251172 0.967943i \(-0.419184\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) −3.50000 + 6.06218i −0.145960 + 0.252810i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −16.0000 + 27.7128i −0.666089 + 1.15370i 0.312900 + 0.949786i \(0.398699\pi\)
−0.978989 + 0.203913i \(0.934634\pi\)
\(578\) 8.00000 + 13.8564i 0.332756 + 0.576351i
\(579\) −5.00000 8.66025i −0.207793 0.359908i
\(580\) −3.00000 5.19615i −0.124568 0.215758i
\(581\) 0 0
\(582\) 3.00000 5.19615i 0.124354 0.215387i
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) −6.00000 −0.248069
\(586\) −8.00000 + 13.8564i −0.330477 + 0.572403i
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) −7.00000 −0.288675
\(589\) 14.0000 + 17.3205i 0.576860 + 0.713679i
\(590\) 12.0000 0.494032
\(591\) 8.00000 0.329076
\(592\) −3.50000 + 6.06218i −0.143849 + 0.249154i
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0.500000 + 0.866025i 0.0205152 + 0.0355335i
\(595\) 0 0
\(596\) −7.00000 + 12.1244i −0.286731 + 0.496633i
\(597\) 16.0000 0.654836
\(598\) 21.0000 + 36.3731i 0.858754 + 1.48741i
\(599\) −17.0000 29.4449i −0.694601 1.20308i −0.970315 0.241845i \(-0.922248\pi\)
0.275714 0.961240i \(-0.411086\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 21.5000 37.2391i 0.877003 1.51901i 0.0223900 0.999749i \(-0.492872\pi\)
0.854613 0.519265i \(-0.173794\pi\)
\(602\) 0 0
\(603\) −2.50000 + 4.33013i −0.101808 + 0.176336i
\(604\) −7.00000 −0.284826
\(605\) −10.0000 −0.406558
\(606\) −7.50000 + 12.9904i −0.304667 + 0.527698i
\(607\) −10.0000 17.3205i −0.405887 0.703018i 0.588537 0.808470i \(-0.299704\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) −2.00000 + 3.46410i −0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 7.00000 + 12.1244i 0.283422 + 0.490901i
\(611\) 9.00000 + 15.5885i 0.364101 + 0.630641i
\(612\) −1.00000 −0.0404226
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) −8.00000 + 13.8564i −0.322854 + 0.559199i
\(615\) 1.00000 + 1.73205i 0.0403239 + 0.0698430i
\(616\) 0 0
\(617\) 3.50000 6.06218i 0.140905 0.244054i −0.786933 0.617039i \(-0.788332\pi\)
0.927838 + 0.372985i \(0.121666\pi\)
\(618\) −2.00000 −0.0804518
\(619\) 36.0000 1.44696 0.723481 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) −5.50000 + 0.866025i −0.220885 + 0.0347804i
\(621\) 7.00000 0.280900
\(622\) −6.00000 −0.240578
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 2.00000 3.46410i 0.0798723 0.138343i
\(628\) 14.0000 0.558661
\(629\) 3.50000 + 6.06218i 0.139554 + 0.241715i
\(630\) 0 0
\(631\) −14.5000 25.1147i −0.577236 0.999802i −0.995795 0.0916122i \(-0.970798\pi\)
0.418559 0.908190i \(-0.362535\pi\)
\(632\) −1.50000 + 2.59808i −0.0596668 + 0.103346i
\(633\) 4.00000 + 6.92820i 0.158986 + 0.275371i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) −18.0000 −0.714308
\(636\) −4.00000 −0.158610
\(637\) −21.0000 + 36.3731i −0.832050 + 1.44115i
\(638\) 3.00000 + 5.19615i 0.118771 + 0.205718i
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −2.00000 3.46410i −0.0789953 0.136824i 0.823821 0.566849i \(-0.191838\pi\)
−0.902817 + 0.430026i \(0.858505\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 3.50000 6.06218i 0.137812 0.238698i
\(646\) 2.00000 + 3.46410i 0.0786889 + 0.136293i
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −12.0000 −0.471041
\(650\) −6.00000 −0.235339
\(651\) 0 0
\(652\) 5.00000 0.195815
\(653\) −12.0000 −0.469596 −0.234798 0.972044i \(-0.575443\pi\)
−0.234798 + 0.972044i \(0.575443\pi\)
\(654\) 6.00000 10.3923i 0.234619 0.406371i
\(655\) −1.00000 −0.0390732
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) −1.00000 + 1.73205i −0.0390137 + 0.0675737i
\(658\) 0 0
\(659\) −37.0000 −1.44132 −0.720658 0.693291i \(-0.756160\pi\)
−0.720658 + 0.693291i \(0.756160\pi\)
\(660\) 0.500000 + 0.866025i 0.0194625 + 0.0337100i
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) −3.00000 + 5.19615i −0.116510 + 0.201802i
\(664\) −8.00000 13.8564i −0.310460 0.537733i
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) 42.0000 1.62625
\(668\) 12.0000 20.7846i 0.464294 0.804181i
\(669\) −7.00000 12.1244i −0.270636 0.468755i
\(670\) −2.50000 + 4.33013i −0.0965834 + 0.167287i
\(671\) −7.00000 12.1244i −0.270232 0.468056i
\(672\) 0 0
\(673\) −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) 8.00000 0.308148
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 25.0000 + 43.3013i 0.960828 + 1.66420i 0.720429 + 0.693529i \(0.243945\pi\)
0.240399 + 0.970674i \(0.422722\pi\)
\(678\) 19.0000 0.729691
\(679\) 0 0
\(680\) −1.00000 −0.0383482
\(681\) −8.00000 −0.306561
\(682\) 5.50000 0.866025i 0.210606 0.0331618i
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 4.00000 0.152944
\(685\) 3.50000 6.06218i 0.133728 0.231624i
\(686\) 0 0
\(687\) −10.0000 17.3205i −0.381524 0.660819i
\(688\) 3.50000 6.06218i 0.133436 0.231118i
\(689\) −12.0000 + 20.7846i −0.457164 + 0.791831i
\(690\) 7.00000 0.266485
\(691\) 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i \(-0.0292368\pi\)
−0.577325 + 0.816514i \(0.695903\pi\)
\(692\) −1.00000 1.73205i −0.0380143 0.0658427i
\(693\) 0 0
\(694\) 7.00000 12.1244i 0.265716 0.460234i
\(695\) 5.00000 + 8.66025i 0.189661 + 0.328502i
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) 2.00000 0.0757554
\(698\) 18.0000 0.681310
\(699\) −12.5000 + 21.6506i −0.472793 + 0.818902i
\(700\) 0 0
\(701\) −12.5000 + 21.6506i −0.472118 + 0.817733i −0.999491 0.0319010i \(-0.989844\pi\)
0.527373 + 0.849634i \(0.323177\pi\)
\(702\) 3.00000 + 5.19615i 0.113228 + 0.196116i
\(703\) −14.0000 24.2487i −0.528020 0.914557i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 3.00000 0.112987
\(706\) 5.50000 9.52628i 0.206995 0.358526i
\(707\) 0 0
\(708\) −6.00000 10.3923i −0.225494 0.390567i
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) −3.00000 + 5.19615i −0.112588 + 0.195008i
\(711\) 3.00000 0.112509
\(712\) 4.00000 0.149906
\(713\) 14.0000 36.3731i 0.524304 1.36218i
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) 5.50000 9.52628i 0.205545 0.356014i
\(717\) 18.0000 0.672222
\(718\) −10.0000 17.3205i −0.373197 0.646396i
\(719\) −2.00000 + 3.46410i −0.0745874 + 0.129189i −0.900907 0.434013i \(-0.857097\pi\)
0.826319 + 0.563202i \(0.190431\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 0 0
\(722\) 1.50000 + 2.59808i 0.0558242 + 0.0966904i
\(723\) −9.00000 15.5885i −0.334714 0.579741i
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 5.00000 + 8.66025i 0.185567 + 0.321412i
\(727\) −12.0000 + 20.7846i −0.445055 + 0.770859i −0.998056 0.0623223i \(-0.980149\pi\)
0.553001 + 0.833181i \(0.313483\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.00000 + 1.73205i −0.0370117 + 0.0641061i
\(731\) −3.50000 6.06218i −0.129452 0.224218i
\(732\) 7.00000 12.1244i 0.258727 0.448129i
\(733\) 17.5000 + 30.3109i 0.646377 + 1.11956i 0.983982 + 0.178270i \(0.0570501\pi\)
−0.337604 + 0.941288i \(0.609617\pi\)
\(734\) 2.00000 + 3.46410i 0.0738213 + 0.127862i
\(735\) 3.50000 + 6.06218i 0.129099 + 0.223607i
\(736\) 7.00000 0.258023
\(737\) 2.50000 4.33013i 0.0920887 0.159502i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i \(0.0796718\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(740\) 7.00000 0.257325
\(741\) 12.0000 20.7846i 0.440831 0.763542i
\(742\) 0 0
\(743\) −27.0000 −0.990534 −0.495267 0.868741i \(-0.664930\pi\)
−0.495267 + 0.868741i \(0.664930\pi\)
\(744\) 3.50000 + 4.33013i 0.128316 + 0.158750i
\(745\) 14.0000 0.512920
\(746\) −19.0000 −0.695639
\(747\) −8.00000 + 13.8564i −0.292705 + 0.506979i
\(748\) 1.00000 0.0365636
\(749\) 0 0
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 12.5000 21.6506i 0.456131 0.790043i −0.542621 0.839978i \(-0.682568\pi\)
0.998752 + 0.0499348i \(0.0159013\pi\)
\(752\) 3.00000 0.109399
\(753\) −1.50000 2.59808i −0.0546630 0.0946792i
\(754\) 18.0000 + 31.1769i 0.655521 + 1.13540i
\(755\) 3.50000 + 6.06218i 0.127378 + 0.220625i
\(756\) 0 0
\(757\) 9.50000 + 16.4545i 0.345283 + 0.598048i 0.985405 0.170225i \(-0.0544495\pi\)
−0.640122 + 0.768273i \(0.721116\pi\)
\(758\) −3.00000 + 5.19615i −0.108965 + 0.188733i
\(759\) −7.00000 −0.254084
\(760\) 4.00000 0.145095
\(761\) 8.00000 13.8564i 0.290000 0.502294i −0.683810 0.729661i \(-0.739678\pi\)
0.973809 + 0.227366i \(0.0730114\pi\)
\(762\) 9.00000 + 15.5885i 0.326036 + 0.564710i
\(763\) 0 0
\(764\) 3.00000 + 5.19615i 0.108536 + 0.187990i
\(765\) 0.500000 + 0.866025i 0.0180775 + 0.0313112i
\(766\) −9.50000 16.4545i −0.343249 0.594525i
\(767\) −72.0000 −2.59977
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 13.0000 22.5167i 0.468792 0.811972i −0.530572 0.847640i \(-0.678023\pi\)
0.999364 + 0.0356685i \(0.0113561\pi\)
\(770\) 0 0
\(771\) 23.0000 0.828325
\(772\) −5.00000 + 8.66025i −0.179954 + 0.311689i
\(773\) −30.0000 −1.07903 −0.539513 0.841978i \(-0.681391\pi\)
−0.539513 + 0.841978i \(0.681391\pi\)
\(774\) −7.00000 −0.251610
\(775\) 3.50000 + 4.33013i 0.125724 + 0.155543i
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −4.50000 + 7.79423i −0.161333 + 0.279437i
\(779\) −8.00000 −0.286630
\(780\) 3.00000 + 5.19615i 0.107417 + 0.186052i