Properties

Label 2646.2.h.t.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.t.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +(-1.93185 - 3.34607i) q^{10} +3.73205 q^{11} +(-3.34607 - 5.79555i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.70831 + 4.69093i) q^{17} +(1.48356 - 2.56961i) q^{19} +(1.93185 - 3.34607i) q^{20} +(1.86603 + 3.23205i) q^{22} +1.46410 q^{23} +9.92820 q^{25} +(3.34607 - 5.79555i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(-0.896575 + 1.55291i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.70831 + 4.69093i) q^{34} +(-0.267949 + 0.464102i) q^{37} +2.96713 q^{38} +3.86370 q^{40} +(-0.637756 - 1.10463i) q^{41} +(-1.86603 + 3.23205i) q^{43} +(-1.86603 + 3.23205i) q^{44} +(0.732051 + 1.26795i) q^{46} +(5.27792 + 9.14162i) q^{47} +(4.96410 + 8.59808i) q^{50} +6.69213 q^{52} +(-1.46410 - 2.53590i) q^{53} -14.4195 q^{55} -4.00000 q^{58} +(-4.31199 + 7.46859i) q^{59} +(-3.48477 - 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(12.9282 + 22.3923i) q^{65} +(-2.76795 + 4.79423i) q^{67} -5.41662 q^{68} -2.53590 q^{71} +(3.41542 + 5.91567i) q^{73} -0.535898 q^{74} +(1.48356 + 2.56961i) q^{76} +(2.46410 + 4.26795i) q^{79} +(1.93185 + 3.34607i) q^{80} +(0.637756 - 1.10463i) q^{82} +(-8.95215 + 15.5056i) q^{83} +(-10.4641 - 18.1244i) q^{85} -3.73205 q^{86} -3.73205 q^{88} +(3.53553 - 6.12372i) q^{89} +(-0.732051 + 1.26795i) q^{92} +(-5.27792 + 9.14162i) q^{94} +(-5.73205 + 9.92820i) q^{95} +(2.94855 - 5.10703i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + O(q^{10}) \) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} - 16 q^{23} + 24 q^{25} - 16 q^{29} + 4 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} - 32 q^{58} + 8 q^{64} + 48 q^{65} - 36 q^{67} - 48 q^{71} - 32 q^{74} - 8 q^{79} - 56 q^{85} - 16 q^{86} - 16 q^{88} + 8 q^{92} - 32 q^{95} + O(q^{100}) \)

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
\(5\) −3.86370 −1.72790 −0.863950 0.503577i \(-0.832017\pi\)
−0.863950 + 0.503577i \(0.832017\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.93185 3.34607i −0.610905 1.05812i
\(11\) 3.73205 1.12526 0.562628 0.826710i \(-0.309790\pi\)
0.562628 + 0.826710i \(0.309790\pi\)
\(12\) 0 0
\(13\) −3.34607 5.79555i −0.928032 1.60740i −0.786612 0.617448i \(-0.788167\pi\)
−0.141420 0.989950i \(-0.545167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.70831 + 4.69093i 0.656861 + 1.13772i 0.981424 + 0.191853i \(0.0614497\pi\)
−0.324562 + 0.945864i \(0.605217\pi\)
\(18\) 0 0
\(19\) 1.48356 2.56961i 0.340353 0.589509i −0.644145 0.764903i \(-0.722787\pi\)
0.984498 + 0.175395i \(0.0561201\pi\)
\(20\) 1.93185 3.34607i 0.431975 0.748203i
\(21\) 0 0
\(22\) 1.86603 + 3.23205i 0.397838 + 0.689076i
\(23\) 1.46410 0.305286 0.152643 0.988281i \(-0.451221\pi\)
0.152643 + 0.988281i \(0.451221\pi\)
\(24\) 0 0
\(25\) 9.92820 1.98564
\(26\) 3.34607 5.79555i 0.656217 1.13660i
\(27\) 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
\(31\) −0.896575 + 1.55291i −0.161030 + 0.278912i −0.935238 0.354019i \(-0.884815\pi\)
0.774209 + 0.632931i \(0.218148\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −2.70831 + 4.69093i −0.464471 + 0.804488i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.267949 + 0.464102i −0.0440506 + 0.0762978i −0.887210 0.461366i \(-0.847360\pi\)
0.843159 + 0.537664i \(0.180693\pi\)
\(38\) 2.96713 0.481332
\(39\) 0 0
\(40\) 3.86370 0.610905
\(41\) −0.637756 1.10463i −0.0996008 0.172514i 0.811919 0.583771i \(-0.198423\pi\)
−0.911519 + 0.411257i \(0.865090\pi\)
\(42\) 0 0
\(43\) −1.86603 + 3.23205i −0.284566 + 0.492883i −0.972504 0.232887i \(-0.925183\pi\)
0.687938 + 0.725770i \(0.258516\pi\)
\(44\) −1.86603 + 3.23205i −0.281314 + 0.487250i
\(45\) 0 0
\(46\) 0.732051 + 1.26795i 0.107935 + 0.186949i
\(47\) 5.27792 + 9.14162i 0.769863 + 1.33344i 0.937637 + 0.347617i \(0.113009\pi\)
−0.167773 + 0.985826i \(0.553658\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.96410 + 8.59808i 0.702030 + 1.21595i
\(51\) 0 0
\(52\) 6.69213 0.928032
\(53\) −1.46410 2.53590i −0.201110 0.348332i 0.747776 0.663951i \(-0.231121\pi\)
−0.948886 + 0.315618i \(0.897788\pi\)
\(54\) 0 0
\(55\) −14.4195 −1.94433
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) −4.31199 + 7.46859i −0.561373 + 0.972327i 0.436004 + 0.899945i \(0.356394\pi\)
−0.997377 + 0.0723823i \(0.976940\pi\)
\(60\) 0 0
\(61\) −3.48477 6.03579i −0.446179 0.772804i 0.551955 0.833874i \(-0.313882\pi\)
−0.998133 + 0.0610700i \(0.980549\pi\)
\(62\) −1.79315 −0.227730
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 12.9282 + 22.3923i 1.60355 + 2.77742i
\(66\) 0 0
\(67\) −2.76795 + 4.79423i −0.338159 + 0.585708i −0.984086 0.177690i \(-0.943137\pi\)
0.645928 + 0.763399i \(0.276471\pi\)
\(68\) −5.41662 −0.656861
\(69\) 0 0
\(70\) 0 0
\(71\) −2.53590 −0.300956 −0.150478 0.988613i \(-0.548081\pi\)
−0.150478 + 0.988613i \(0.548081\pi\)
\(72\) 0 0
\(73\) 3.41542 + 5.91567i 0.399744 + 0.692377i 0.993694 0.112125i \(-0.0357656\pi\)
−0.593950 + 0.804502i \(0.702432\pi\)
\(74\) −0.535898 −0.0622969
\(75\) 0 0
\(76\) 1.48356 + 2.56961i 0.170176 + 0.294754i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.46410 + 4.26795i 0.277233 + 0.480182i 0.970696 0.240310i \(-0.0772492\pi\)
−0.693463 + 0.720492i \(0.743916\pi\)
\(80\) 1.93185 + 3.34607i 0.215988 + 0.374101i
\(81\) 0 0
\(82\) 0.637756 1.10463i 0.0704284 0.121986i
\(83\) −8.95215 + 15.5056i −0.982626 + 1.70196i −0.330583 + 0.943777i \(0.607245\pi\)
−0.652043 + 0.758182i \(0.726088\pi\)
\(84\) 0 0
\(85\) −10.4641 18.1244i −1.13499 1.96586i
\(86\) −3.73205 −0.402437
\(87\) 0 0
\(88\) −3.73205 −0.397838
\(89\) 3.53553 6.12372i 0.374766 0.649113i −0.615526 0.788116i \(-0.711056\pi\)
0.990292 + 0.139003i \(0.0443898\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.732051 + 1.26795i −0.0763216 + 0.132193i
\(93\) 0 0
\(94\) −5.27792 + 9.14162i −0.544376 + 0.942886i
\(95\) −5.73205 + 9.92820i −0.588096 + 1.01861i
\(96\) 0 0
\(97\) 2.94855 5.10703i 0.299379 0.518540i −0.676615 0.736337i \(-0.736554\pi\)
0.975994 + 0.217797i \(0.0698870\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −4.96410 + 8.59808i −0.496410 + 0.859808i
\(101\) −4.89898 −0.487467 −0.243733 0.969842i \(-0.578372\pi\)
−0.243733 + 0.969842i \(0.578372\pi\)
\(102\) 0 0
\(103\) 7.45001 0.734071 0.367035 0.930207i \(-0.380373\pi\)
0.367035 + 0.930207i \(0.380373\pi\)
\(104\) 3.34607 + 5.79555i 0.328109 + 0.568301i
\(105\) 0 0
\(106\) 1.46410 2.53590i 0.142206 0.246308i
\(107\) 1.69615 2.93782i 0.163973 0.284010i −0.772317 0.635237i \(-0.780902\pi\)
0.936290 + 0.351227i \(0.114236\pi\)
\(108\) 0 0
\(109\) 4.46410 + 7.73205i 0.427583 + 0.740596i 0.996658 0.0816899i \(-0.0260317\pi\)
−0.569074 + 0.822286i \(0.692698\pi\)
\(110\) −7.20977 12.4877i −0.687424 1.19065i
\(111\) 0 0
\(112\) 0 0
\(113\) 3.46410 + 6.00000i 0.325875 + 0.564433i 0.981689 0.190490i \(-0.0610077\pi\)
−0.655814 + 0.754923i \(0.727674\pi\)
\(114\) 0 0
\(115\) −5.65685 −0.527504
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) −8.62398 −0.793902
\(119\) 0 0
\(120\) 0 0
\(121\) 2.92820 0.266200
\(122\) 3.48477 6.03579i 0.315496 0.546455i
\(123\) 0 0
\(124\) −0.896575 1.55291i −0.0805149 0.139456i
\(125\) −19.0411 −1.70309
\(126\) 0 0
\(127\) 6.53590 0.579967 0.289984 0.957032i \(-0.406350\pi\)
0.289984 + 0.957032i \(0.406350\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −12.9282 + 22.3923i −1.13388 + 1.96394i
\(131\) −6.03579 −0.527350 −0.263675 0.964612i \(-0.584935\pi\)
−0.263675 + 0.964612i \(0.584935\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.53590 −0.478229
\(135\) 0 0
\(136\) −2.70831 4.69093i −0.232236 0.402244i
\(137\) 8.66025 0.739895 0.369948 0.929053i \(-0.379376\pi\)
0.369948 + 0.929053i \(0.379376\pi\)
\(138\) 0 0
\(139\) 8.17569 + 14.1607i 0.693453 + 1.20110i 0.970699 + 0.240297i \(0.0772450\pi\)
−0.277246 + 0.960799i \(0.589422\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.26795 2.19615i −0.106404 0.184297i
\(143\) −12.4877 21.6293i −1.04427 1.80873i
\(144\) 0 0
\(145\) 7.72741 13.3843i 0.641726 1.11150i
\(146\) −3.41542 + 5.91567i −0.282662 + 0.489585i
\(147\) 0 0
\(148\) −0.267949 0.464102i −0.0220253 0.0381489i
\(149\) −9.07180 −0.743191 −0.371595 0.928395i \(-0.621189\pi\)
−0.371595 + 0.928395i \(0.621189\pi\)
\(150\) 0 0
\(151\) −2.39230 −0.194683 −0.0973415 0.995251i \(-0.531034\pi\)
−0.0973415 + 0.995251i \(0.531034\pi\)
\(152\) −1.48356 + 2.56961i −0.120333 + 0.208423i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.46410 6.00000i 0.278243 0.481932i
\(156\) 0 0
\(157\) −2.31079 + 4.00240i −0.184421 + 0.319427i −0.943381 0.331710i \(-0.892374\pi\)
0.758960 + 0.651137i \(0.225708\pi\)
\(158\) −2.46410 + 4.26795i −0.196033 + 0.339540i
\(159\) 0 0
\(160\) −1.93185 + 3.34607i −0.152726 + 0.264530i
\(161\) 0 0
\(162\) 0 0
\(163\) −10.6603 + 18.4641i −0.834976 + 1.44622i 0.0590748 + 0.998254i \(0.481185\pi\)
−0.894050 + 0.447966i \(0.852148\pi\)
\(164\) 1.27551 0.0996008
\(165\) 0 0
\(166\) −17.9043 −1.38964
\(167\) 10.5558 + 18.2832i 0.816835 + 1.41480i 0.908003 + 0.418964i \(0.137607\pi\)
−0.0911679 + 0.995836i \(0.529060\pi\)
\(168\) 0 0
\(169\) −15.8923 + 27.5263i −1.22248 + 2.11741i
\(170\) 10.4641 18.1244i 0.802560 1.39007i
\(171\) 0 0
\(172\) −1.86603 3.23205i −0.142283 0.246442i
\(173\) 0.896575 + 1.55291i 0.0681654 + 0.118066i 0.898094 0.439804i \(-0.144952\pi\)
−0.829928 + 0.557870i \(0.811619\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.86603 3.23205i −0.140657 0.243625i
\(177\) 0 0
\(178\) 7.07107 0.529999
\(179\) 9.46410 + 16.3923i 0.707380 + 1.22522i 0.965826 + 0.259193i \(0.0834564\pi\)
−0.258446 + 0.966026i \(0.583210\pi\)
\(180\) 0 0
\(181\) −16.9706 −1.26141 −0.630706 0.776022i \(-0.717235\pi\)
−0.630706 + 0.776022i \(0.717235\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.46410 −0.107935
\(185\) 1.03528 1.79315i 0.0761150 0.131835i
\(186\) 0 0
\(187\) 10.1075 + 17.5068i 0.739137 + 1.28022i
\(188\) −10.5558 −0.769863
\(189\) 0 0
\(190\) −11.4641 −0.831693
\(191\) 0.535898 + 0.928203i 0.0387762 + 0.0671624i 0.884762 0.466043i \(-0.154321\pi\)
−0.845986 + 0.533205i \(0.820987\pi\)
\(192\) 0 0
\(193\) 11.5263 19.9641i 0.829680 1.43705i −0.0686098 0.997644i \(-0.521856\pi\)
0.898290 0.439404i \(-0.144810\pi\)
\(194\) 5.89709 0.423386
\(195\) 0 0
\(196\) 0 0
\(197\) 3.07180 0.218856 0.109428 0.993995i \(-0.465098\pi\)
0.109428 + 0.993995i \(0.465098\pi\)
\(198\) 0 0
\(199\) 8.90138 + 15.4176i 0.631002 + 1.09293i 0.987347 + 0.158574i \(0.0506895\pi\)
−0.356345 + 0.934355i \(0.615977\pi\)
\(200\) −9.92820 −0.702030
\(201\) 0 0
\(202\) −2.44949 4.24264i −0.172345 0.298511i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.46410 + 4.26795i 0.172100 + 0.298087i
\(206\) 3.72500 + 6.45189i 0.259533 + 0.449525i
\(207\) 0 0
\(208\) −3.34607 + 5.79555i −0.232008 + 0.401849i
\(209\) 5.53674 9.58991i 0.382984 0.663348i
\(210\) 0 0
\(211\) −2.53590 4.39230i −0.174578 0.302379i 0.765437 0.643511i \(-0.222523\pi\)
−0.940015 + 0.341132i \(0.889190\pi\)
\(212\) 2.92820 0.201110
\(213\) 0 0
\(214\) 3.39230 0.231893
\(215\) 7.20977 12.4877i 0.491702 0.851653i
\(216\) 0 0
\(217\) 0 0
\(218\) −4.46410 + 7.73205i −0.302347 + 0.523681i
\(219\) 0 0
\(220\) 7.20977 12.4877i 0.486082 0.841920i
\(221\) 18.1244 31.3923i 1.21918 2.11167i
\(222\) 0 0
\(223\) 13.3843 23.1822i 0.896276 1.55240i 0.0640595 0.997946i \(-0.479595\pi\)
0.832217 0.554450i \(-0.187071\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.46410 + 6.00000i −0.230429 + 0.399114i
\(227\) 10.5187 0.698149 0.349074 0.937095i \(-0.386496\pi\)
0.349074 + 0.937095i \(0.386496\pi\)
\(228\) 0 0
\(229\) 24.9754 1.65042 0.825209 0.564827i \(-0.191057\pi\)
0.825209 + 0.564827i \(0.191057\pi\)
\(230\) −2.82843 4.89898i −0.186501 0.323029i
\(231\) 0 0
\(232\) 2.00000 3.46410i 0.131306 0.227429i
\(233\) −12.0622 + 20.8923i −0.790220 + 1.36870i 0.135611 + 0.990762i \(0.456700\pi\)
−0.925831 + 0.377938i \(0.876633\pi\)
\(234\) 0 0
\(235\) −20.3923 35.3205i −1.33025 2.30406i
\(236\) −4.31199 7.46859i −0.280687 0.486164i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.46410 11.1962i −0.418128 0.724219i 0.577623 0.816304i \(-0.303980\pi\)
−0.995751 + 0.0920846i \(0.970647\pi\)
\(240\) 0 0
\(241\) 23.4225 1.50877 0.754387 0.656430i \(-0.227934\pi\)
0.754387 + 0.656430i \(0.227934\pi\)
\(242\) 1.46410 + 2.53590i 0.0941160 + 0.163014i
\(243\) 0 0
\(244\) 6.96953 0.446179
\(245\) 0 0
\(246\) 0 0
\(247\) −19.8564 −1.26343
\(248\) 0.896575 1.55291i 0.0569326 0.0986102i
\(249\) 0 0
\(250\) −9.52056 16.4901i −0.602133 1.04292i
\(251\) 16.3514 1.03209 0.516045 0.856561i \(-0.327404\pi\)
0.516045 + 0.856561i \(0.327404\pi\)
\(252\) 0 0
\(253\) 5.46410 0.343525
\(254\) 3.26795 + 5.66025i 0.205049 + 0.355156i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.68973 −0.167781 −0.0838903 0.996475i \(-0.526735\pi\)
−0.0838903 + 0.996475i \(0.526735\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −25.8564 −1.60355
\(261\) 0 0
\(262\) −3.01790 5.22715i −0.186446 0.322934i
\(263\) 15.4641 0.953557 0.476779 0.879023i \(-0.341804\pi\)
0.476779 + 0.879023i \(0.341804\pi\)
\(264\) 0 0
\(265\) 5.65685 + 9.79796i 0.347498 + 0.601884i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.76795 4.79423i −0.169079 0.292854i
\(269\) −2.82843 4.89898i −0.172452 0.298696i 0.766824 0.641857i \(-0.221836\pi\)
−0.939277 + 0.343161i \(0.888502\pi\)
\(270\) 0 0
\(271\) −9.00292 + 15.5935i −0.546888 + 0.947239i 0.451597 + 0.892222i \(0.350854\pi\)
−0.998485 + 0.0550165i \(0.982479\pi\)
\(272\) 2.70831 4.69093i 0.164215 0.284429i
\(273\) 0 0
\(274\) 4.33013 + 7.50000i 0.261593 + 0.453092i
\(275\) 37.0526 2.23435
\(276\) 0 0
\(277\) 24.5359 1.47422 0.737110 0.675773i \(-0.236190\pi\)
0.737110 + 0.675773i \(0.236190\pi\)
\(278\) −8.17569 + 14.1607i −0.490346 + 0.849303i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.92820 + 8.53590i −0.293992 + 0.509209i −0.974750 0.223299i \(-0.928317\pi\)
0.680758 + 0.732508i \(0.261651\pi\)
\(282\) 0 0
\(283\) −4.70951 + 8.15711i −0.279951 + 0.484890i −0.971372 0.237562i \(-0.923652\pi\)
0.691421 + 0.722452i \(0.256985\pi\)
\(284\) 1.26795 2.19615i 0.0752389 0.130318i
\(285\) 0 0
\(286\) 12.4877 21.6293i 0.738412 1.27897i
\(287\) 0 0
\(288\) 0 0
\(289\) −6.16987 + 10.6865i −0.362934 + 0.628620i
\(290\) 15.4548 0.907538
\(291\) 0 0
\(292\) −6.83083 −0.399744
\(293\) −9.52056 16.4901i −0.556197 0.963361i −0.997809 0.0661554i \(-0.978927\pi\)
0.441612 0.897206i \(-0.354407\pi\)
\(294\) 0 0
\(295\) 16.6603 28.8564i 0.969997 1.68008i
\(296\) 0.267949 0.464102i 0.0155742 0.0269754i
\(297\) 0 0
\(298\) −4.53590 7.85641i −0.262758 0.455109i
\(299\) −4.89898 8.48528i −0.283315 0.490716i
\(300\) 0 0
\(301\) 0 0
\(302\) −1.19615 2.07180i −0.0688308 0.119219i
\(303\) 0 0
\(304\) −2.96713 −0.170176
\(305\) 13.4641 + 23.3205i 0.770952 + 1.33533i
\(306\) 0 0
\(307\) −11.0735 −0.631996 −0.315998 0.948760i \(-0.602339\pi\)
−0.315998 + 0.948760i \(0.602339\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.92820 0.393496
\(311\) −6.17449 + 10.6945i −0.350123 + 0.606431i −0.986271 0.165136i \(-0.947194\pi\)
0.636147 + 0.771568i \(0.280527\pi\)
\(312\) 0 0
\(313\) −11.7112 20.2844i −0.661958 1.14654i −0.980101 0.198502i \(-0.936392\pi\)
0.318143 0.948043i \(-0.396941\pi\)
\(314\) −4.62158 −0.260811
\(315\) 0 0
\(316\) −4.92820 −0.277233
\(317\) −13.0000 22.5167i −0.730153 1.26466i −0.956818 0.290689i \(-0.906116\pi\)
0.226665 0.973973i \(-0.427218\pi\)
\(318\) 0 0
\(319\) −7.46410 + 12.9282i −0.417909 + 0.723840i
\(320\) −3.86370 −0.215988
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0718 0.894259
\(324\) 0 0
\(325\) −33.2204 57.5394i −1.84274 3.19171i
\(326\) −21.3205 −1.18083
\(327\) 0 0
\(328\) 0.637756 + 1.10463i 0.0352142 + 0.0609928i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.26795 + 3.92820i 0.124658 + 0.215914i 0.921599 0.388143i \(-0.126883\pi\)
−0.796941 + 0.604057i \(0.793550\pi\)
\(332\) −8.95215 15.5056i −0.491313 0.850979i
\(333\) 0 0
\(334\) −10.5558 + 18.2832i −0.577590 + 1.00041i
\(335\) 10.6945 18.5235i 0.584305 1.01205i
\(336\) 0 0
\(337\) 3.50000 + 6.06218i 0.190657 + 0.330228i 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) −31.7846 −1.72885
\(339\) 0 0
\(340\) 20.9282 1.13499
\(341\) −3.34607 + 5.79555i −0.181200 + 0.313847i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.86603 3.23205i 0.100609 0.174261i
\(345\) 0 0
\(346\) −0.896575 + 1.55291i −0.0482002 + 0.0834852i
\(347\) 10.7942 18.6962i 0.579465 1.00366i −0.416076 0.909330i \(-0.636595\pi\)
0.995541 0.0943323i \(-0.0300716\pi\)
\(348\) 0 0
\(349\) −8.24504 + 14.2808i −0.441347 + 0.764436i −0.997790 0.0664504i \(-0.978833\pi\)
0.556443 + 0.830886i \(0.312166\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.86603 3.23205i 0.0994595 0.172269i
\(353\) 26.4267 1.40655 0.703277 0.710916i \(-0.251719\pi\)
0.703277 + 0.710916i \(0.251719\pi\)
\(354\) 0 0
\(355\) 9.79796 0.520022
\(356\) 3.53553 + 6.12372i 0.187383 + 0.324557i
\(357\) 0 0
\(358\) −9.46410 + 16.3923i −0.500193 + 0.866360i
\(359\) 0.267949 0.464102i 0.0141418 0.0244943i −0.858868 0.512197i \(-0.828832\pi\)
0.873010 + 0.487703i \(0.162165\pi\)
\(360\) 0 0
\(361\) 5.09808 + 8.83013i 0.268320 + 0.464744i
\(362\) −8.48528 14.6969i −0.445976 0.772454i
\(363\) 0 0
\(364\) 0 0
\(365\) −13.1962 22.8564i −0.690718 1.19636i
\(366\) 0 0
\(367\) −15.7322 −0.821215 −0.410607 0.911812i \(-0.634683\pi\)
−0.410607 + 0.911812i \(0.634683\pi\)
\(368\) −0.732051 1.26795i −0.0381608 0.0660964i
\(369\) 0 0
\(370\) 2.07055 0.107643
\(371\) 0 0
\(372\) 0 0
\(373\) 30.7846 1.59397 0.796983 0.604001i \(-0.206428\pi\)
0.796983 + 0.604001i \(0.206428\pi\)
\(374\) −10.1075 + 17.5068i −0.522649 + 0.905254i
\(375\) 0 0
\(376\) −5.27792 9.14162i −0.272188 0.471443i
\(377\) 26.7685 1.37865
\(378\) 0 0
\(379\) −17.5885 −0.903458 −0.451729 0.892155i \(-0.649193\pi\)
−0.451729 + 0.892155i \(0.649193\pi\)
\(380\) −5.73205 9.92820i −0.294048 0.509306i
\(381\) 0 0
\(382\) −0.535898 + 0.928203i −0.0274189 + 0.0474910i
\(383\) 21.6665 1.10710 0.553552 0.832814i \(-0.313272\pi\)
0.553552 + 0.832814i \(0.313272\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 23.0526 1.17334
\(387\) 0 0
\(388\) 2.94855 + 5.10703i 0.149690 + 0.259270i
\(389\) −8.00000 −0.405616 −0.202808 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) 3.96524 + 6.86800i 0.200531 + 0.347329i
\(392\) 0 0
\(393\) 0 0
\(394\) 1.53590 + 2.66025i 0.0773774 + 0.134022i
\(395\) −9.52056 16.4901i −0.479031 0.829706i
\(396\) 0 0
\(397\) −9.00292 + 15.5935i −0.451844 + 0.782616i −0.998501 0.0547406i \(-0.982567\pi\)
0.546657 + 0.837357i \(0.315900\pi\)
\(398\) −8.90138 + 15.4176i −0.446186 + 0.772817i
\(399\) 0 0
\(400\) −4.96410 8.59808i −0.248205 0.429904i
\(401\) −17.7846 −0.888121 −0.444061 0.895997i \(-0.646462\pi\)
−0.444061 + 0.895997i \(0.646462\pi\)
\(402\) 0 0
\(403\) 12.0000 0.597763
\(404\) 2.44949 4.24264i 0.121867 0.211079i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.00000 + 1.73205i −0.0495682 + 0.0858546i
\(408\) 0 0
\(409\) −8.36516 + 14.4889i −0.413631 + 0.716429i −0.995284 0.0970077i \(-0.969073\pi\)
0.581653 + 0.813437i \(0.302406\pi\)
\(410\) −2.46410 + 4.26795i −0.121693 + 0.210779i
\(411\) 0 0
\(412\) −3.72500 + 6.45189i −0.183518 + 0.317862i
\(413\) 0 0
\(414\) 0 0
\(415\) 34.5885 59.9090i 1.69788 2.94082i
\(416\) −6.69213 −0.328109
\(417\) 0 0
\(418\) 11.0735 0.541621
\(419\) −3.95164 6.84443i −0.193050 0.334373i 0.753209 0.657781i \(-0.228505\pi\)
−0.946260 + 0.323408i \(0.895171\pi\)
\(420\) 0 0
\(421\) −14.1962 + 24.5885i −0.691878 + 1.19837i 0.279344 + 0.960191i \(0.409883\pi\)
−0.971222 + 0.238177i \(0.923450\pi\)
\(422\) 2.53590 4.39230i 0.123446 0.213814i
\(423\) 0 0
\(424\) 1.46410 + 2.53590i 0.0711031 + 0.123154i
\(425\) 26.8886 + 46.5725i 1.30429 + 2.25910i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.69615 + 2.93782i 0.0819866 + 0.142005i
\(429\) 0 0
\(430\) 14.4195 0.695372
\(431\) −18.9282 32.7846i −0.911739 1.57918i −0.811606 0.584205i \(-0.801406\pi\)
−0.100133 0.994974i \(-0.531927\pi\)
\(432\) 0 0
\(433\) 7.10823 0.341600 0.170800 0.985306i \(-0.445365\pi\)
0.170800 + 0.985306i \(0.445365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −8.92820 −0.427583
\(437\) 2.17209 3.76217i 0.103905 0.179969i
\(438\) 0 0
\(439\) 9.79796 + 16.9706i 0.467631 + 0.809961i 0.999316 0.0369815i \(-0.0117743\pi\)
−0.531685 + 0.846942i \(0.678441\pi\)
\(440\) 14.4195 0.687424
\(441\) 0 0
\(442\) 36.2487 1.72418
\(443\) −9.16025 15.8660i −0.435217 0.753818i 0.562097 0.827072i \(-0.309995\pi\)
−0.997313 + 0.0732540i \(0.976662\pi\)
\(444\) 0 0
\(445\) −13.6603 + 23.6603i −0.647558 + 1.12160i
\(446\) 26.7685 1.26753
\(447\) 0 0
\(448\) 0 0
\(449\) 17.7846 0.839308 0.419654 0.907684i \(-0.362151\pi\)
0.419654 + 0.907684i \(0.362151\pi\)
\(450\) 0 0
\(451\) −2.38014 4.12252i −0.112076 0.194122i
\(452\) −6.92820 −0.325875
\(453\) 0 0
\(454\) 5.25933 + 9.10943i 0.246833 + 0.427527i
\(455\) 0 0
\(456\) 0 0
\(457\) −3.52628 6.10770i −0.164952 0.285706i 0.771686 0.636004i \(-0.219414\pi\)
−0.936638 + 0.350298i \(0.886080\pi\)
\(458\) 12.4877 + 21.6293i 0.583511 + 1.01067i
\(459\) 0 0
\(460\) 2.82843 4.89898i 0.131876 0.228416i
\(461\) −12.8666 + 22.2856i −0.599258 + 1.03795i 0.393672 + 0.919251i \(0.371204\pi\)
−0.992931 + 0.118695i \(0.962129\pi\)
\(462\) 0 0
\(463\) −19.3205 33.4641i −0.897900 1.55521i −0.830174 0.557505i \(-0.811759\pi\)
−0.0677264 0.997704i \(-0.521575\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) −24.1244 −1.11754
\(467\) −13.7818 + 23.8707i −0.637745 + 1.10461i 0.348182 + 0.937427i \(0.386799\pi\)
−0.985927 + 0.167179i \(0.946534\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 20.3923 35.3205i 0.940627 1.62921i
\(471\) 0 0
\(472\) 4.31199 7.46859i 0.198475 0.343770i
\(473\) −6.96410 + 12.0622i −0.320210 + 0.554620i
\(474\) 0 0
\(475\) 14.7291 25.5116i 0.675819 1.17055i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.46410 11.1962i 0.295661 0.512100i
\(479\) −15.4548 −0.706148 −0.353074 0.935595i \(-0.614864\pi\)
−0.353074 + 0.935595i \(0.614864\pi\)
\(480\) 0 0
\(481\) 3.58630 0.163521
\(482\) 11.7112 + 20.2844i 0.533432 + 0.923931i
\(483\) 0 0
\(484\) −1.46410 + 2.53590i −0.0665501 + 0.115268i
\(485\) −11.3923 + 19.7321i −0.517298 + 0.895986i
\(486\) 0 0
\(487\) −19.3923 33.5885i −0.878749 1.52204i −0.852714 0.522377i \(-0.825045\pi\)
−0.0260347 0.999661i \(-0.508288\pi\)
\(488\) 3.48477 + 6.03579i 0.157748 + 0.273227i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.696152 1.20577i −0.0314169 0.0544157i 0.849889 0.526961i \(-0.176669\pi\)
−0.881306 + 0.472545i \(0.843335\pi\)
\(492\) 0 0
\(493\) −21.6665 −0.975809
\(494\) −9.92820 17.1962i −0.446691 0.773691i
\(495\) 0 0
\(496\) 1.79315 0.0805149
\(497\) 0 0
\(498\) 0 0
\(499\) 12.6077 0.564398 0.282199 0.959356i \(-0.408936\pi\)
0.282199 + 0.959356i \(0.408936\pi\)
\(500\) 9.52056 16.4901i 0.425772 0.737459i
\(501\) 0 0
\(502\) 8.17569 + 14.1607i 0.364899 + 0.632024i
\(503\) 7.45001 0.332179 0.166090 0.986111i \(-0.446886\pi\)
0.166090 + 0.986111i \(0.446886\pi\)
\(504\) 0 0
\(505\) 18.9282 0.842294
\(506\) 2.73205 + 4.73205i 0.121454 + 0.210365i
\(507\) 0 0
\(508\) −3.26795 + 5.66025i −0.144992 + 0.251133i
\(509\) −26.4911 −1.17420 −0.587099 0.809515i \(-0.699730\pi\)
−0.587099 + 0.809515i \(0.699730\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −1.34486 2.32937i −0.0593194 0.102744i
\(515\) −28.7846 −1.26840
\(516\) 0 0
\(517\) 19.6975 + 34.1170i 0.866293 + 1.50046i
\(518\) 0 0
\(519\) 0 0
\(520\) −12.9282 22.3923i −0.566939 0.981968i
\(521\) 16.1805 + 28.0255i 0.708881 + 1.22782i 0.965273 + 0.261244i \(0.0841329\pi\)
−0.256392 + 0.966573i \(0.582534\pi\)
\(522\) 0 0
\(523\) 1.88108 3.25813i 0.0822540 0.142468i −0.821964 0.569540i \(-0.807121\pi\)
0.904218 + 0.427072i \(0.140455\pi\)
\(524\) 3.01790 5.22715i 0.131837 0.228349i
\(525\) 0 0
\(526\) 7.73205 + 13.3923i 0.337133 + 0.583932i
\(527\) −9.71281 −0.423097
\(528\) 0 0
\(529\) −20.8564 −0.906800
\(530\) −5.65685 + 9.79796i −0.245718 + 0.425596i
\(531\) 0 0
\(532\) 0 0
\(533\) −4.26795 + 7.39230i −0.184865 + 0.320196i
\(534\) 0 0
\(535\) −6.55343 + 11.3509i −0.283329 + 0.490741i
\(536\) 2.76795 4.79423i 0.119557 0.207079i
\(537\) 0 0
\(538\) 2.82843 4.89898i 0.121942 0.211210i
\(539\) 0 0
\(540\) 0 0
\(541\) 9.66025 16.7321i 0.415327 0.719367i −0.580136 0.814520i \(-0.697001\pi\)
0.995463 + 0.0951526i \(0.0303339\pi\)
\(542\) −18.0058 −0.773417
\(543\) 0 0
\(544\) 5.41662 0.232236
\(545\) −17.2480 29.8744i −0.738822 1.27968i
\(546\) 0 0
\(547\) 19.1865 33.2321i 0.820357 1.42090i −0.0850597 0.996376i \(-0.527108\pi\)
0.905417 0.424524i \(-0.139559\pi\)
\(548\) −4.33013 + 7.50000i −0.184974 + 0.320384i
\(549\) 0 0
\(550\) 18.5263 + 32.0885i 0.789963 + 1.36826i
\(551\) 5.93426 + 10.2784i 0.252808 + 0.437876i
\(552\) 0 0
\(553\) 0 0
\(554\) 12.2679 + 21.2487i 0.521215 + 0.902771i
\(555\) 0 0
\(556\) −16.3514 −0.693453
\(557\) 3.46410 + 6.00000i 0.146779 + 0.254228i 0.930035 0.367471i \(-0.119776\pi\)
−0.783256 + 0.621699i \(0.786443\pi\)
\(558\) 0 0
\(559\) 24.9754 1.05635
\(560\) 0 0
\(561\) 0 0
\(562\) −9.85641 −0.415767
\(563\) −12.7973 + 22.1655i −0.539341 + 0.934166i 0.459599 + 0.888127i \(0.347993\pi\)
−0.998940 + 0.0460390i \(0.985340\pi\)
\(564\) 0 0
\(565\) −13.3843 23.1822i −0.563080 0.975283i
\(566\) −9.41902 −0.395911
\(567\) 0 0
\(568\) 2.53590 0.106404
\(569\) 7.89230 + 13.6699i 0.330863 + 0.573071i 0.982681 0.185304i \(-0.0593270\pi\)
−0.651819 + 0.758375i \(0.725994\pi\)
\(570\) 0 0
\(571\) −2.52628 + 4.37564i −0.105722 + 0.183115i −0.914033 0.405640i \(-0.867049\pi\)
0.808311 + 0.588755i \(0.200382\pi\)
\(572\) 24.9754 1.04427
\(573\) 0 0
\(574\) 0 0
\(575\) 14.5359 0.606189
\(576\) 0 0
\(577\) 22.3178 + 38.6556i 0.929103 + 1.60925i 0.784825 + 0.619717i \(0.212753\pi\)
0.144278 + 0.989537i \(0.453914\pi\)
\(578\) −12.3397 −0.513266
\(579\) 0 0
\(580\) 7.72741 + 13.3843i 0.320863 + 0.555751i
\(581\) 0 0
\(582\) 0 0
\(583\) −5.46410 9.46410i −0.226300 0.391963i
\(584\) −3.41542 5.91567i −0.141331 0.244792i
\(585\) 0 0
\(586\) 9.52056 16.4901i 0.393291 0.681199i
\(587\) 14.5768 25.2478i 0.601650 1.04209i −0.390922 0.920424i \(-0.627844\pi\)
0.992571 0.121664i \(-0.0388230\pi\)
\(588\) 0 0
\(589\) 2.66025 + 4.60770i 0.109614 + 0.189857i
\(590\) 33.3205 1.37178
\(591\) 0 0
\(592\) 0.535898 0.0220253
\(593\) −1.36345 + 2.36156i −0.0559900 + 0.0969775i −0.892662 0.450727i \(-0.851165\pi\)
0.836672 + 0.547704i \(0.184498\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.53590 7.85641i 0.185798 0.321811i
\(597\) 0 0
\(598\) 4.89898 8.48528i 0.200334 0.346989i
\(599\) −18.3923 + 31.8564i −0.751489 + 1.30162i 0.195612 + 0.980681i \(0.437331\pi\)
−0.947101 + 0.320936i \(0.896003\pi\)
\(600\) 0 0
\(601\) 0.448288 0.776457i 0.0182860 0.0316723i −0.856738 0.515753i \(-0.827512\pi\)
0.875024 + 0.484080i \(0.160846\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.19615 2.07180i 0.0486708 0.0843002i
\(605\) −11.3137 −0.459968
\(606\) 0 0
\(607\) −31.6675 −1.28534 −0.642672 0.766141i \(-0.722174\pi\)
−0.642672 + 0.766141i \(0.722174\pi\)
\(608\) −1.48356 2.56961i −0.0601665 0.104211i
\(609\) 0 0
\(610\) −13.4641 + 23.3205i −0.545146 + 0.944220i
\(611\) 35.3205 61.1769i 1.42891 2.47495i
\(612\) 0 0
\(613\) −5.53590 9.58846i −0.223593 0.387274i 0.732304 0.680978i \(-0.238445\pi\)
−0.955896 + 0.293704i \(0.905112\pi\)
\(614\) −5.53674 9.58991i −0.223444 0.387017i
\(615\) 0 0
\(616\) 0 0
\(617\) −15.4282 26.7224i −0.621116 1.07580i −0.989278 0.146043i \(-0.953346\pi\)
0.368162 0.929762i \(-0.379987\pi\)
\(618\) 0 0
\(619\) 24.6336 0.990108 0.495054 0.868862i \(-0.335148\pi\)
0.495054 + 0.868862i \(0.335148\pi\)
\(620\) 3.46410 + 6.00000i 0.139122 + 0.240966i
\(621\) 0 0
\(622\) −12.3490 −0.495149
\(623\) 0 0
\(624\) 0 0
\(625\) 23.9282 0.957128
\(626\) 11.7112 20.2844i 0.468075 0.810729i
\(627\) 0 0
\(628\) −2.31079 4.00240i −0.0922105 0.159713i
\(629\) −2.90276 −0.115740
\(630\) 0 0
\(631\) 35.7128 1.42170 0.710852 0.703341i \(-0.248309\pi\)
0.710852 + 0.703341i \(0.248309\pi\)
\(632\) −2.46410 4.26795i −0.0980167 0.169770i
\(633\) 0 0
\(634\) 13.0000 22.5167i 0.516296 0.894251i
\(635\) −25.2528 −1.00213
\(636\) 0 0
\(637\) 0 0
\(638\) −14.9282 −0.591013
\(639\) 0 0
\(640\) −1.93185 3.34607i −0.0763631 0.132265i
\(641\) −17.9282 −0.708121 −0.354061 0.935222i \(-0.615199\pi\)
−0.354061 + 0.935222i \(0.615199\pi\)
\(642\) 0 0
\(643\) 6.53485 + 11.3187i 0.257709 + 0.446365i 0.965628 0.259929i \(-0.0836990\pi\)
−0.707919 + 0.706294i \(0.750366\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.03590 + 13.9186i 0.316168 + 0.547619i
\(647\) 6.03579 + 10.4543i 0.237291 + 0.411001i 0.959936 0.280219i \(-0.0904070\pi\)
−0.722645 + 0.691220i \(0.757074\pi\)
\(648\) 0 0
\(649\) −16.0926 + 27.8731i −0.631689 + 1.09412i
\(650\) 33.2204 57.5394i 1.30301 2.25688i
\(651\) 0 0
\(652\) −10.6603 18.4641i −0.417488 0.723110i
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) 23.3205 0.911208
\(656\) −0.637756 + 1.10463i −0.0249002 + 0.0431284i
\(657\) 0 0
\(658\) 0 0
\(659\) 0.124356 0.215390i 0.00484421 0.00839042i −0.863593 0.504189i \(-0.831791\pi\)
0.868437 + 0.495799i \(0.165125\pi\)
\(660\) 0 0
\(661\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(662\) −2.26795 + 3.92820i −0.0881463 + 0.152674i
\(663\) 0 0
\(664\) 8.95215 15.5056i 0.347411 0.601733i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.92820 + 5.07180i −0.113380 + 0.196381i
\(668\) −21.1117 −0.816835
\(669\) 0 0
\(670\) 21.3891 0.826332
\(671\) −13.0053 22.5259i −0.502065 0.869602i
\(672\) 0 0
\(673\) 20.7846 36.0000i 0.801188 1.38770i −0.117647 0.993055i \(-0.537535\pi\)
0.918835 0.394643i \(-0.129132\pi\)
\(674\) −3.50000 + 6.06218i −0.134815 + 0.233506i
\(675\) 0 0
\(676\) −15.8923 27.5263i −0.611242 1.05870i
\(677\) −10.0382 17.3867i −0.385799 0.668224i 0.606081 0.795403i \(-0.292741\pi\)
−0.991880 + 0.127179i \(0.959408\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 10.4641 + 18.1244i 0.401280 + 0.695037i
\(681\) 0 0
\(682\) −6.69213 −0.256255
\(683\) −1.83975 3.18653i −0.0703959 0.121929i 0.828679 0.559724i \(-0.189093\pi\)
−0.899075 + 0.437795i \(0.855760\pi\)
\(684\) 0 0
\(685\) −33.4607 −1.27847
\(686\) 0 0
\(687\) 0 0
\(688\) 3.73205 0.142283
\(689\) −9.79796 + 16.9706i −0.373273 + 0.646527i
\(690\) 0 0
\(691\) −4.81105 8.33298i −0.183021 0.317001i 0.759887 0.650055i \(-0.225254\pi\)
−0.942908 + 0.333054i \(0.891921\pi\)
\(692\) −1.79315 −0.0681654
\(693\) 0 0
\(694\) 21.5885 0.819487
\(695\) −31.5885 54.7128i −1.19822 2.07538i
\(696\) 0 0
\(697\) 3.45448 5.98334i 0.130848 0.226635i
\(698\) −16.4901 −0.624159
\(699\) 0 0
\(700\) 0 0
\(701\) −20.7846 −0.785024 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(702\) 0 0
\(703\) 0.795040 + 1.37705i 0.0299855 + 0.0519364i
\(704\) 3.73205 0.140657
\(705\) 0 0
\(706\) 13.2134 + 22.8862i 0.497292 + 0.861335i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.19615 7.26795i −0.157590 0.272954i 0.776409 0.630229i \(-0.217039\pi\)
−0.933999 + 0.357276i \(0.883706\pi\)
\(710\) 4.89898 + 8.48528i 0.183855 + 0.318447i
\(711\) 0 0
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) −1.31268 + 2.27362i −0.0491602 + 0.0851479i
\(714\) 0 0
\(715\) 48.2487 + 83.5692i 1.80440 + 3.12531i
\(716\) −18.9282 −0.707380
\(717\) 0 0
\(718\) 0.535898 0.0199996
\(719\) −7.69024 + 13.3199i −0.286798 + 0.496748i −0.973044 0.230622i \(-0.925924\pi\)
0.686246 + 0.727370i \(0.259257\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −5.09808 + 8.83013i −0.189731 + 0.328623i
\(723\) 0 0
\(724\) 8.48528 14.6969i 0.315353 0.546207i
\(725\) −19.8564 + 34.3923i −0.737448 + 1.27730i
\(726\) 0 0
\(727\) 0.795040 1.37705i 0.0294864 0.0510719i −0.850906 0.525319i \(-0.823946\pi\)
0.880392 + 0.474247i \(0.157279\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 13.1962 22.8564i 0.488412 0.845954i
\(731\) −20.2151 −0.747682
\(732\) 0 0
\(733\) −16.4901 −0.609075 −0.304538 0.952500i \(-0.598502\pi\)
−0.304538 + 0.952500i \(0.598502\pi\)
\(734\) −7.86611 13.6245i −0.290343 0.502889i
\(735\) 0 0
\(736\) 0.732051 1.26795i 0.0269838 0.0467372i
\(737\) −10.3301 + 17.8923i −0.380515 + 0.659072i
\(738\) 0 0
\(739\) 9.06218 + 15.6962i 0.333358 + 0.577392i 0.983168 0.182704i \(-0.0584850\pi\)
−0.649810 + 0.760096i \(0.725152\pi\)
\(740\) 1.03528 + 1.79315i 0.0380575 + 0.0659175i
\(741\) 0 0
\(742\) 0 0
\(743\) 25.7846 + 44.6603i 0.945946 + 1.63843i 0.753847 + 0.657050i \(0.228196\pi\)
0.192099 + 0.981376i \(0.438471\pi\)
\(744\) 0 0
\(745\) 35.0507 1.28416
\(746\) 15.3923 + 26.6603i 0.563552 + 0.976101i
\(747\) 0 0
\(748\) −20.2151 −0.739137
\(749\) 0 0
\(750\) 0 0
\(751\) −6.78461 −0.247574 −0.123787 0.992309i \(-0.539504\pi\)
−0.123787 + 0.992309i \(0.539504\pi\)
\(752\) 5.27792 9.14162i 0.192466 0.333361i
\(753\) 0 0
\(754\) 13.3843 + 23.1822i 0.487426 + 0.844247i
\(755\) 9.24316 0.336393
\(756\) 0 0
\(757\) −15.3205 −0.556833 −0.278417 0.960460i \(-0.589810\pi\)
−0.278417 + 0.960460i \(0.589810\pi\)
\(758\) −8.79423 15.2321i −0.319421 0.553253i
\(759\) 0 0
\(760\) 5.73205 9.92820i 0.207923 0.360134i
\(761\) 30.4564 1.10404 0.552021 0.833830i \(-0.313857\pi\)
0.552021 + 0.833830i \(0.313857\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.07180 −0.0387762
\(765\) 0 0
\(766\) 10.8332 + 18.7637i 0.391421 + 0.677961i
\(767\) 57.7128 2.08389
\(768\) 0 0
\(769\) −19.0919 33.0681i −0.688471 1.19247i −0.972332 0.233601i \(-0.924949\pi\)
0.283862 0.958865i \(-0.408384\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.5263 + 19.9641i 0.414840 + 0.718524i
\(773\) 0.101536 + 0.175865i 0.00365199 + 0.00632544i 0.867846 0.496834i \(-0.165504\pi\)
−0.864194 + 0.503159i \(0.832171\pi\)
\(774\) 0 0
\(775\) −8.90138 + 15.4176i −0.319747 + 0.553818i
\(776\) −2.94855 + 5.10703i −0.105847 + 0.183332i
\(777\) 0 0
\(778\) −4.00000 6.92820i −0.143407 0.248388i
\(779\) −3.78461 −0.135598
\(780\) 0 0
\(781\) −9.46410 −0.338652
\(782\) −3.96524 + 6.86800i −0.141797 + 0.245599i
\(783\) 0 0
\(784\) 0 0
\(785\) 8.92820 15.4641i 0.318661 0.551937i
\(786\) 0 0
\(787\) 23.3717 40.4810i 0.833111 1.44299i −0.0624487 0.998048i \(-0.519891\pi\)
0.895559 0.444942i \(-0.146776\pi\)
\(788\) −1.53590 + 2.66025i −0.0547141 + 0.0947676i
\(789\) 0 0
\(790\) 9.52056 16.4901i 0.338726 0.586691i
\(791\) 0 0
\(792\) 0 0
\(793\) −23.3205 + 40.3923i −0.828136 + 1.43437i
\(794\) −18.0058 −0.639003
\(795\) 0