Properties

Label 2646.2.h.c.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.c.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} -1.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-1.00000 + 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} -4.00000 q^{23} -1.00000 q^{25} +(-3.00000 + 5.19615i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{34} +(-1.00000 + 1.73205i) q^{37} +7.00000 q^{38} +2.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{44} +(2.00000 + 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{52} +(6.00000 + 10.3923i) q^{53} -2.00000 q^{55} +4.00000 q^{58} +(3.50000 - 6.06218i) q^{59} +(-6.00000 - 10.3923i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-6.50000 + 11.2583i) q^{67} -5.00000 q^{68} +8.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +2.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(3.00000 + 5.19615i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(-8.00000 + 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} -1.00000 q^{86} -1.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(2.00000 - 3.46410i) q^{92} +(-7.00000 + 12.1244i) q^{95} +(-2.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 4q^{5} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 4q^{5} + 2q^{8} - 2q^{10} - 2q^{11} - 6q^{13} - q^{16} + 5q^{17} - 7q^{19} - 2q^{20} + q^{22} - 8q^{23} - 2q^{25} - 6q^{26} - 4q^{29} - 6q^{31} - q^{32} + 5q^{34} - 2q^{37} + 14q^{38} + 4q^{40} - 3q^{41} + q^{43} + q^{44} + 4q^{46} + q^{50} + 12q^{52} + 12q^{53} - 4q^{55} + 8q^{58} + 7q^{59} - 12q^{61} + 12q^{62} + 2q^{64} - 12q^{65} - 13q^{67} - 10q^{68} + 16q^{71} + q^{73} + 4q^{74} - 7q^{76} + 6q^{79} - 2q^{80} - 3q^{82} - 16q^{83} + 10q^{85} - 2q^{86} - 2q^{88} + 6q^{89} + 4q^{92} - 14q^{95} - 5q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i \(0.0406959\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 2.50000 4.33013i 0.428746 0.742611i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 7.00000 1.13555
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 6.00000 0.832050
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) 3.50000 6.06218i 0.455661 0.789228i −0.543065 0.839691i \(-0.682736\pi\)
0.998726 + 0.0504625i \(0.0160695\pi\)
\(60\) 0 0
\(61\) −6.00000 10.3923i −0.768221 1.33060i −0.938527 0.345207i \(-0.887809\pi\)
0.170305 0.985391i \(-0.445525\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 10.3923i −0.744208 1.28901i
\(66\) 0 0
\(67\) −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i \(0.458725\pi\)
−0.923408 + 0.383819i \(0.874609\pi\)
\(68\) −5.00000 −0.606339
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) 0 0
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) −8.00000 + 13.8564i −0.878114 + 1.52094i −0.0247060 + 0.999695i \(0.507865\pi\)
−0.853408 + 0.521243i \(0.825468\pi\)
\(84\) 0 0
\(85\) 5.00000 + 8.66025i 0.542326 + 0.939336i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.00000 3.46410i 0.208514 0.361158i
\(93\) 0 0
\(94\) 0 0
\(95\) −7.00000 + 12.1244i −0.718185 + 1.24393i
\(96\) 0 0
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 0 0
\(112\) 0 0
\(113\) −5.00000 8.66025i −0.470360 0.814688i 0.529065 0.848581i \(-0.322543\pi\)
−0.999425 + 0.0338931i \(0.989209\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) −7.00000 −0.644402
\(119\) 0 0
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −6.00000 + 10.3923i −0.543214 + 0.940875i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −6.00000 + 10.3923i −0.526235 + 0.911465i
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) 2.50000 + 4.33013i 0.214373 + 0.371305i
\(137\) 19.0000 1.62328 0.811640 0.584158i \(-0.198575\pi\)
0.811640 + 0.584158i \(0.198575\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 6.92820i −0.335673 0.581402i
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 0.500000 0.866025i 0.0413803 0.0716728i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 24.0000 1.96616 0.983078 0.183186i \(-0.0586410\pi\)
0.983078 + 0.183186i \(0.0586410\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 + 10.3923i −0.481932 + 0.834730i
\(156\) 0 0
\(157\) 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 3.00000 5.19615i 0.238667 0.413384i
\(159\) 0 0
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) 16.0000 1.24184
\(167\) −10.0000 17.3205i −0.773823 1.34030i −0.935454 0.353450i \(-0.885009\pi\)
0.161630 0.986851i \(-0.448325\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 5.00000 8.66025i 0.383482 0.664211i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) −1.00000 1.73205i −0.0760286 0.131685i 0.825505 0.564396i \(-0.190891\pi\)
−0.901533 + 0.432710i \(0.857557\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 12.0000 + 20.7846i 0.896922 + 1.55351i 0.831408 + 0.555663i \(0.187536\pi\)
0.0655145 + 0.997852i \(0.479131\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) −2.50000 4.33013i −0.182818 0.316650i
\(188\) 0 0
\(189\) 0 0
\(190\) 14.0000 1.01567
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) −8.50000 + 14.7224i −0.611843 + 1.05974i 0.379086 + 0.925361i \(0.376238\pi\)
−0.990930 + 0.134382i \(0.957095\pi\)
\(194\) 5.00000 0.358979
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 2.00000 + 3.46410i 0.140720 + 0.243733i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) −3.00000 + 5.19615i −0.208013 + 0.360288i
\(209\) 3.50000 6.06218i 0.242100 0.419330i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) −3.00000 −0.205076
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) 0 0
\(217\) 0 0
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −5.00000 + 8.66025i −0.332595 + 0.576072i
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) 4.00000 + 6.92820i 0.263752 + 0.456832i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) −14.5000 + 25.1147i −0.949927 + 1.64532i −0.204354 + 0.978897i \(0.565509\pi\)
−0.745573 + 0.666424i \(0.767824\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.50000 + 6.06218i 0.227831 + 0.394614i
\(237\) 0 0
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) −23.0000 −1.48156 −0.740780 0.671748i \(-0.765544\pi\)
−0.740780 + 0.671748i \(0.765544\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) 0 0
\(244\) 12.0000 0.768221
\(245\) 0 0
\(246\) 0 0
\(247\) 42.0000 2.67240
\(248\) −3.00000 + 5.19615i −0.190500 + 0.329956i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −15.0000 −0.935674 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) 2.00000 + 3.46410i 0.123560 + 0.214013i
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 12.0000 + 20.7846i 0.737154 + 1.27679i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.50000 11.2583i −0.397051 0.687712i
\(269\) −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i \(-0.957952\pi\)
0.381577 0.924337i \(-0.375381\pi\)
\(270\) 0 0
\(271\) −3.00000 + 5.19615i −0.182237 + 0.315644i −0.942642 0.333805i \(-0.891667\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(272\) 2.50000 4.33013i 0.151585 0.262553i
\(273\) 0 0
\(274\) −9.50000 16.4545i −0.573916 0.994052i
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −2.50000 + 4.33013i −0.149940 + 0.259704i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0000 19.0526i 0.656205 1.13658i −0.325385 0.945582i \(-0.605494\pi\)
0.981590 0.190999i \(-0.0611727\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −4.00000 + 6.92820i −0.237356 + 0.411113i
\(285\) 0 0
\(286\) 3.00000 5.19615i 0.177394 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 8.00000 0.469776
\(291\) 0 0
\(292\) −1.00000 −0.0585206
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 0 0
\(298\) −12.0000 20.7846i −0.695141 1.20402i
\(299\) 12.0000 + 20.7846i 0.693978 + 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) −12.0000 20.7846i −0.687118 1.19012i
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 12.0000 0.681554
\(311\) −1.00000 + 1.73205i −0.0567048 + 0.0982156i −0.892984 0.450088i \(-0.851393\pi\)
0.836280 + 0.548303i \(0.184726\pi\)
\(312\) 0 0
\(313\) −8.50000 14.7224i −0.480448 0.832161i 0.519300 0.854592i \(-0.326193\pi\)
−0.999748 + 0.0224310i \(0.992859\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) 2.00000 0.111803
\(321\) 0 0
\(322\) 0 0
\(323\) −35.0000 −1.94745
\(324\) 0 0
\(325\) 3.00000 + 5.19615i 0.166410 + 0.288231i
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) 0 0
\(334\) −10.0000 + 17.3205i −0.547176 + 0.947736i
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 0 0
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 23.0000 1.25104
\(339\) 0 0
\(340\) −10.0000 −0.542326
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) −1.00000 + 1.73205i −0.0537603 + 0.0931156i
\(347\) −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 0 0
\(349\) −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i \(-0.955588\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −15.0000 −0.798369 −0.399185 0.916871i \(-0.630707\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(354\) 0 0
\(355\) 16.0000 0.849192
\(356\) 3.00000 + 5.19615i 0.159000 + 0.275396i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 0 0
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −2.50000 + 4.33013i −0.129272 + 0.223906i
\(375\) 0 0
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) −7.00000 12.1244i −0.359092 0.621966i
\(381\) 0 0
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) 4.00000 0.204390 0.102195 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.0000 0.865277
\(387\) 0 0
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) −8.00000 −0.405616 −0.202808 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) −10.0000 17.3205i −0.505722 0.875936i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) 6.00000 + 10.3923i 0.301893 + 0.522894i
\(396\) 0 0
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) 7.00000 12.1244i 0.350878 0.607739i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −9.00000 −0.449439 −0.224719 0.974424i \(-0.572147\pi\)
−0.224719 + 0.974424i \(0.572147\pi\)
\(402\) 0 0
\(403\) 36.0000 1.79329
\(404\) 2.00000 3.46410i 0.0995037 0.172345i
\(405\) 0 0
\(406\) 0 0
\(407\) 1.00000 1.73205i 0.0495682 0.0858546i
\(408\) 0 0
\(409\) 5.50000 9.52628i 0.271957 0.471044i −0.697406 0.716677i \(-0.745662\pi\)
0.969363 + 0.245633i \(0.0789957\pi\)
\(410\) −3.00000 + 5.19615i −0.148159 + 0.256620i
\(411\) 0 0
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) −16.0000 + 27.7128i −0.785409 + 1.36037i
\(416\) 6.00000 0.294174
\(417\) 0 0
\(418\) −7.00000 −0.342381
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) 6.00000 10.3923i 0.292422 0.506490i −0.681960 0.731390i \(-0.738872\pi\)
0.974382 + 0.224900i \(0.0722054\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) 0 0
\(424\) 6.00000 + 10.3923i 0.291386 + 0.504695i
\(425\) −2.50000 4.33013i −0.121268 0.210042i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) 0 0
\(430\) −2.00000 −0.0964486
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) 25.0000 1.20142 0.600712 0.799466i \(-0.294884\pi\)
0.600712 + 0.799466i \(0.294884\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) 14.0000 24.2487i 0.669711 1.15997i
\(438\) 0 0
\(439\) −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) 3.50000 + 6.06218i 0.166290 + 0.288023i 0.937113 0.349027i \(-0.113488\pi\)
−0.770823 + 0.637050i \(0.780155\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) 4.00000 0.189405
\(447\) 0 0
\(448\) 0 0
\(449\) −17.0000 −0.802280 −0.401140 0.916017i \(-0.631386\pi\)
−0.401140 + 0.916017i \(0.631386\pi\)
\(450\) 0 0
\(451\) 1.50000 + 2.59808i 0.0706322 + 0.122339i
\(452\) 10.0000 0.470360
\(453\) 0 0
\(454\) −1.50000 2.59808i −0.0703985 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 0.866025i −0.0233890 0.0405110i 0.854094 0.520119i \(-0.174112\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(458\) −13.0000 22.5167i −0.607450 1.05213i
\(459\) 0 0
\(460\) 4.00000 6.92820i 0.186501 0.323029i
\(461\) −7.00000 + 12.1244i −0.326023 + 0.564688i −0.981719 0.190337i \(-0.939042\pi\)
0.655696 + 0.755025i \(0.272375\pi\)
\(462\) 0 0
\(463\) 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i \(-0.107148\pi\)
−0.757982 + 0.652275i \(0.773815\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) 29.0000 1.34340
\(467\) 6.50000 11.2583i 0.300784 0.520973i −0.675530 0.737333i \(-0.736085\pi\)
0.976314 + 0.216359i \(0.0694183\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 3.50000 6.06218i 0.161101 0.279034i
\(473\) −0.500000 + 0.866025i −0.0229900 + 0.0398199i
\(474\) 0 0
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 11.5000 + 19.9186i 0.523811 + 0.907267i
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 0 0
\(487\) 5.00000 + 8.66025i 0.226572 + 0.392434i 0.956790 0.290780i \(-0.0939149\pi\)
−0.730218 + 0.683214i \(0.760582\pi\)
\(488\) −6.00000 10.3923i −0.271607 0.470438i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.5000 + 28.5788i 0.744635 + 1.28974i 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) 0 0
\(493\) −20.0000 −0.900755
\(494\) −21.0000 36.3731i −0.944835 1.63650i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 0 0
\(499\) −29.0000 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) −1.50000 2.59808i −0.0669483 0.115958i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) −2.00000 3.46410i −0.0889108 0.153998i
\(507\) 0 0
\(508\) 6.00000 10.3923i 0.266207 0.461084i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 7.50000 + 12.9904i 0.330811 + 0.572981i
\(515\) −28.0000 −1.23383
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −6.00000 10.3923i −0.263117 0.455733i
\(521\) 4.50000 + 7.79423i 0.197149 + 0.341471i 0.947603 0.319451i \(-0.103499\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(522\) 0 0
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) 2.00000 3.46410i 0.0873704 0.151330i
\(525\) 0 0
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −30.0000 −1.30682
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 12.0000 20.7846i 0.521247 0.902826i
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 + 15.5885i −0.389833 + 0.675211i
\(534\) 0 0
\(535\) 3.00000 5.19615i 0.129701 0.224649i
\(536\) −6.50000 + 11.2583i −0.280757 + 0.486286i
\(537\) 0 0
\(538\) −10.0000 + 17.3205i −0.431131 + 0.746740i
\(539\) 0 0
\(540\) 0 0
\(541\) 12.0000 20.7846i 0.515920 0.893600i −0.483909 0.875118i \(-0.660783\pi\)
0.999829 0.0184818i \(-0.00588327\pi\)
\(542\) 6.00000 0.257722
\(543\) 0 0
\(544\) −5.00000 −0.214373
\(545\) 2.00000 + 3.46410i 0.0856706 + 0.148386i
\(546\) 0 0
\(547\) 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i \(-0.685132\pi\)
0.998318 + 0.0579790i \(0.0184657\pi\)
\(548\) −9.50000 + 16.4545i −0.405820 + 0.702901i
\(549\) 0 0
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) −14.0000 24.2487i −0.596420 1.03303i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 1.73205i −0.0424859 0.0735878i
\(555\) 0 0
\(556\) 5.00000 0.212047
\(557\) −14.0000 24.2487i −0.593199 1.02745i −0.993798 0.111198i \(-0.964531\pi\)
0.400599 0.916253i \(-0.368802\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 0 0
\(562\) −22.0000 −0.928014
\(563\) −15.5000 + 26.8468i −0.653247 + 1.13146i 0.329083 + 0.944301i \(0.393260\pi\)
−0.982330 + 0.187156i \(0.940073\pi\)
\(564\) 0 0
\(565\) −10.0000 17.3205i −0.420703 0.728679i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) 16.5000 28.5788i 0.690504 1.19599i −0.281170 0.959658i \(-0.590722\pi\)
0.971673 0.236329i \(-0.0759443\pi\)
\(572\) −6.00000 −0.250873
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) −17.5000 30.3109i −0.728535 1.26186i −0.957503 0.288425i \(-0.906868\pi\)
0.228968 0.973434i \(-0.426465\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) −4.00000 6.92820i −0.166091 0.287678i
\(581\) 0 0
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) 0.500000 + 0.866025i 0.0206901 + 0.0358364i
\(585\) 0 0
\(586\) 0 0
\(587\) 23.5000 40.7032i 0.969949 1.68000i 0.274263 0.961655i \(-0.411566\pi\)
0.695686 0.718346i \(-0.255100\pi\)
\(588\) 0 0
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) −14.0000 −0.576371
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 + 20.7846i −0.491539 + 0.851371i
\(597\) 0 0
\(598\) 12.0000 20.7846i 0.490716 0.849946i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i \(-0.959999\pi\)
0.604601 + 0.796528i \(0.293332\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.00000 + 8.66025i −0.203447 + 0.352381i
\(605\) −20.0000 −0.813116
\(606\) 0 0
\(607\) 24.0000 0.974130 0.487065 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) 0 0
\(612\) 0 0
\(613\) −21.0000 36.3731i −0.848182 1.46909i −0.882829 0.469695i \(-0.844364\pi\)
0.0346469 0.999400i \(-0.488969\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 0 0
\(617\) −8.50000 14.7224i −0.342197 0.592703i 0.642643 0.766165i \(-0.277838\pi\)
−0.984840 + 0.173463i \(0.944504\pi\)
\(618\) 0 0
\(619\) −37.0000 −1.48716 −0.743578 0.668649i \(-0.766873\pi\)
−0.743578 + 0.668649i \(0.766873\pi\)
\(620\) −6.00000 10.3923i −0.240966 0.417365i
\(621\) 0 0
\(622\) 2.00000 0.0801927
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −8.50000 + 14.7224i −0.339728 + 0.588427i
\(627\) 0 0
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 3.00000 + 5.19615i 0.119334 + 0.206692i
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) −24.0000 −0.952411
\(636\) 0 0
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) −1.00000 −0.0394976 −0.0197488 0.999805i \(-0.506287\pi\)
−0.0197488 + 0.999805i \(0.506287\pi\)
\(642\) 0 0
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 17.5000 + 30.3109i 0.688528 + 1.19257i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 0 0
\(649\) −3.50000 + 6.06218i −0.137387 + 0.237961i
\(650\) 3.00000 5.19615i 0.117670 0.203810i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) −8.00000 −0.312586
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 0 0
\(659\) 8.00000 13.8564i 0.311636 0.539769i −0.667081 0.744985i \(-0.732456\pi\)
0.978717 + 0.205216i \(0.0657898\pi\)
\(660\) 0 0
\(661\) 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i \(-0.650039\pi\)
0.998636 0.0522143i \(-0.0166279\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 0 0
\(664\) −8.00000 + 13.8564i −0.310460 + 0.537733i
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 20.0000 0.773823
\(669\) 0 0
\(670\) 26.0000 1.00447
\(671\) 6.00000 + 10.3923i 0.231627 + 0.401190i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 4.50000 7.79423i 0.173334 0.300222i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) −15.0000 25.9808i −0.576497 0.998522i −0.995877 0.0907112i \(-0.971086\pi\)
0.419380 0.907811i \(-0.362247\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 5.00000 + 8.66025i 0.191741 + 0.332106i
\(681\) 0 0
\(682\) −6.00000 −0.229752
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) 38.0000 1.45191
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 36.0000 62.3538i 1.37149 2.37549i
\(690\) 0 0
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) −5.00000 8.66025i −0.189661 0.328502i
\(696\) 0 0
\(697\) 7.50000 12.9904i 0.284083 0.492046i
\(698\) 14.0000 0.529908
\(699\) 0 0
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 0 0
\(703\) −7.00000 12.1244i −0.264010 0.457279i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 7.50000 + 12.9904i 0.282266 + 0.488899i
\(707\) 0 0
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) −8.00000 13.8564i −0.300235 0.520022i
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −24.0000 −0.896922
\(717\) 0 0
\(718\) −2.00000 −0.0746393
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) 0 0
\(725\) 2.00000 3.46410i 0.0742781 0.128654i
\(726\) 0 0
\(727\) −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.00000 1.73205i 0.0370117 0.0641061i
\(731\) 5.00000 0.184932
\(732\) 0 0
\(733\) 18.0000 0.664845 0.332423 0.943131i \(-0.392134\pi\)
0.332423 + 0.943131i \(0.392134\pi\)
\(734\) −11.0000 19.0526i −0.406017 0.703243i
\(735\) 0 0
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) 6.50000 11.2583i 0.239431 0.414706i
\(738\) 0 0
\(739\) 16.5000 + 28.5788i 0.606962 + 1.05129i 0.991738 + 0.128279i \(0.0409454\pi\)
−0.384776 + 0.923010i \(0.625721\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) 0 0
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 0 0
\(745\) 48.0000 1.75858
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) 0 0
\(748\) 5.00000 0.182818
\(749\) 0 0
\(750\) 0 0
\(751\) −18.0000 −0.656829 −0.328415 0.944534i \(-0.606514\pi\)
−0.328415 + 0.944534i \(0.606514\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −12.0000 20.7846i −0.437014 0.756931i
\(755\) 20.0000 0.727875
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 8.50000 + 14.7224i 0.308734 + 0.534743i
\(759\) 0 0
\(760\) −7.00000 + 12.1244i −0.253917 + 0.439797i
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −2.00000 3.46410i −0.0722629 0.125163i
\(767\) −42.0000 −1.51653
\(768\) 0 0
\(769\) 11.0000 + 19.0526i 0.396670 + 0.687053i 0.993313 0.115454i \(-0.0368323\pi\)
−0.596643 + 0.802507i \(0.703499\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.50000 14.7224i −0.305922 0.529872i
\(773\) 26.0000 + 45.0333i 0.935155 + 1.61974i 0.774357 + 0.632749i \(0.218073\pi\)
0.160798 + 0.986987i \(0.448593\pi\)
\(774\) 0 0
\(775\) 3.00000 5.19615i 0.107763 0.186651i
\(776\) −2.50000 + 4.33013i −0.0897448 + 0.155443i
\(777\) 0 0
\(778\) 4.00000 + 6.92820i 0.143407 + 0.248388i
\(779\) 21.0000 0.752403
\(780\) 0 0
\(781\) −8.00000 −0.286263
\(782\) −10.0000 + 17.3205i −0.357599 + 0.619380i
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00000 3.46410i 0.0713831 0.123639i
\(786\) 0 0
\(787\) −6.00000 + 10.3923i −0.213877 + 0.370446i −0.952925 0.303207i \(-0.901942\pi\)
0.739048 + 0.673653i \(0.235276\pi\)
\(788\) 5.00000 8.66025i 0.178118 0.308509i
\(789\) 0 0
\(790\) 6.00000 10.3923i 0.213470 0.369742i
\(791\) 0 0
\(792\) 0 0
\(793\) −36.0000 + 62.3538i −1.27840 + 2.21425i
\(794\) −18.0000 −0.638796
\(795\) 0 0