Properties

Label 1323.2.g.g.667.6
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.6
Root \(-1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.g.361.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +O(q^{10})\) \(q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +(4.50036 + 7.79485i) q^{10} -0.406421 q^{11} +(0.243398 + 0.421578i) q^{13} +(-2.16372 - 3.74766i) q^{16} +(2.42792 + 4.20528i) q^{17} +(0.986757 - 1.70911i) q^{19} +(-7.41507 + 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} -4.64766 q^{23} +8.38151 q^{25} +(-0.598883 + 1.03729i) q^{26} +(3.82383 - 6.62307i) q^{29} +(-3.51360 + 6.08573i) q^{31} +(0.269748 - 0.467216i) q^{32} +(-5.97391 + 10.3471i) q^{34} +(-1.16372 + 2.01561i) q^{37} +4.85584 q^{38} -18.4882 q^{40} +(3.75700 + 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +(0.823832 - 1.42692i) q^{44} +(-5.71780 - 9.90352i) q^{46} +(-3.15811 - 5.47002i) q^{47} +(10.3114 + 17.8598i) q^{50} -1.97351 q^{52} +(-1.78434 - 3.09056i) q^{53} -1.48672 q^{55} +18.8171 q^{58} +(3.05919 - 5.29868i) q^{59} +(4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 + 1.54216i) q^{65} +(-1.80039 + 3.11836i) q^{67} -19.6860 q^{68} -8.46050 q^{71} +(-0.986757 - 1.70911i) q^{73} -5.72665 q^{74} +(4.00040 + 6.92889i) q^{76} +(-4.08113 - 7.06872i) q^{79} +(-7.91503 - 13.7092i) q^{80} +(-9.24411 + 16.0113i) q^{82} +(6.08600 - 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +5.72665 q^{86} +2.05408 q^{88} +(7.41507 - 12.8433i) q^{89} +(9.42101 - 16.3177i) q^{92} +(7.77056 - 13.4590i) q^{94} +(3.60963 - 6.25206i) q^{95} +(4.74375 - 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} + O(q^{10}) \) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} - 16q^{11} - 6q^{16} - 6q^{22} - 8q^{23} + 24q^{25} + 22q^{29} + 16q^{32} + 6q^{37} - 6q^{43} - 14q^{44} - 12q^{46} + 56q^{50} + 28q^{53} + 36q^{58} - 48q^{64} - 6q^{65} - 76q^{71} - 72q^{74} + 6q^{79} + 30q^{85} + 72q^{86} - 12q^{88} + 62q^{92} + 60q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23025 + 2.13086i 0.869920 + 1.50675i 0.862078 + 0.506776i \(0.169163\pi\)
0.00784213 + 0.999969i \(0.497504\pi\)
\(3\) 0 0
\(4\) −2.02704 + 3.51094i −1.01352 + 1.75547i
\(5\) 3.65808 1.63594 0.817970 0.575260i \(-0.195099\pi\)
0.817970 + 0.575260i \(0.195099\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −5.05408 −1.78689
\(9\) 0 0
\(10\) 4.50036 + 7.79485i 1.42314 + 2.46495i
\(11\) −0.406421 −0.122540 −0.0612702 0.998121i \(-0.519515\pi\)
−0.0612702 + 0.998121i \(0.519515\pi\)
\(12\) 0 0
\(13\) 0.243398 + 0.421578i 0.0675065 + 0.116925i 0.897803 0.440397i \(-0.145162\pi\)
−0.830297 + 0.557322i \(0.811829\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.16372 3.74766i −0.540929 0.936916i
\(17\) 2.42792 + 4.20528i 0.588857 + 1.01993i 0.994382 + 0.105847i \(0.0337553\pi\)
−0.405525 + 0.914084i \(0.632911\pi\)
\(18\) 0 0
\(19\) 0.986757 1.70911i 0.226378 0.392097i −0.730354 0.683069i \(-0.760645\pi\)
0.956732 + 0.290971i \(0.0939784\pi\)
\(20\) −7.41507 + 12.8433i −1.65806 + 2.87185i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −4.64766 −0.969105 −0.484552 0.874762i \(-0.661018\pi\)
−0.484552 + 0.874762i \(0.661018\pi\)
\(24\) 0 0
\(25\) 8.38151 1.67630
\(26\) −0.598883 + 1.03729i −0.117451 + 0.203430i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.82383 6.62307i 0.710068 1.22987i −0.254764 0.967003i \(-0.581998\pi\)
0.964831 0.262870i \(-0.0846690\pi\)
\(30\) 0 0
\(31\) −3.51360 + 6.08573i −0.631061 + 1.09303i 0.356274 + 0.934381i \(0.384047\pi\)
−0.987335 + 0.158648i \(0.949286\pi\)
\(32\) 0.269748 0.467216i 0.0476851 0.0825930i
\(33\) 0 0
\(34\) −5.97391 + 10.3471i −1.02452 + 1.77452i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.16372 + 2.01561i −0.191314 + 0.331365i −0.945686 0.325082i \(-0.894608\pi\)
0.754372 + 0.656447i \(0.227941\pi\)
\(38\) 4.85584 0.787721
\(39\) 0 0
\(40\) −18.4882 −2.92324
\(41\) 3.75700 + 6.50731i 0.586744 + 1.01627i 0.994655 + 0.103249i \(0.0329240\pi\)
−0.407911 + 0.913022i \(0.633743\pi\)
\(42\) 0 0
\(43\) 1.16372 2.01561i 0.177465 0.307378i −0.763547 0.645753i \(-0.776544\pi\)
0.941012 + 0.338374i \(0.109877\pi\)
\(44\) 0.823832 1.42692i 0.124197 0.215116i
\(45\) 0 0
\(46\) −5.71780 9.90352i −0.843044 1.46019i
\(47\) −3.15811 5.47002i −0.460658 0.797884i 0.538335 0.842731i \(-0.319053\pi\)
−0.998994 + 0.0448469i \(0.985720\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 10.3114 + 17.8598i 1.45825 + 2.52576i
\(51\) 0 0
\(52\) −1.97351 −0.273677
\(53\) −1.78434 3.09056i −0.245097 0.424521i 0.717062 0.697010i \(-0.245487\pi\)
−0.962159 + 0.272489i \(0.912153\pi\)
\(54\) 0 0
\(55\) −1.48672 −0.200469
\(56\) 0 0
\(57\) 0 0
\(58\) 18.8171 2.47081
\(59\) 3.05919 5.29868i 0.398273 0.689829i −0.595240 0.803548i \(-0.702943\pi\)
0.993513 + 0.113719i \(0.0362763\pi\)
\(60\) 0 0
\(61\) 4.01356 + 6.95169i 0.513884 + 0.890073i 0.999870 + 0.0161063i \(0.00512703\pi\)
−0.485987 + 0.873966i \(0.661540\pi\)
\(62\) −17.2905 −2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 0.890369 + 1.54216i 0.110437 + 0.191282i
\(66\) 0 0
\(67\) −1.80039 + 3.11836i −0.219952 + 0.380969i −0.954793 0.297271i \(-0.903924\pi\)
0.734841 + 0.678240i \(0.237257\pi\)
\(68\) −19.6860 −2.38728
\(69\) 0 0
\(70\) 0 0
\(71\) −8.46050 −1.00408 −0.502039 0.864845i \(-0.667416\pi\)
−0.502039 + 0.864845i \(0.667416\pi\)
\(72\) 0 0
\(73\) −0.986757 1.70911i −0.115491 0.200037i 0.802485 0.596673i \(-0.203511\pi\)
−0.917976 + 0.396636i \(0.870178\pi\)
\(74\) −5.72665 −0.665710
\(75\) 0 0
\(76\) 4.00040 + 6.92889i 0.458877 + 0.794798i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.08113 7.06872i −0.459163 0.795293i 0.539754 0.841823i \(-0.318517\pi\)
−0.998917 + 0.0465297i \(0.985184\pi\)
\(80\) −7.91503 13.7092i −0.884928 1.53274i
\(81\) 0 0
\(82\) −9.24411 + 16.0113i −1.02084 + 1.76815i
\(83\) 6.08600 10.5413i 0.668025 1.15705i −0.310431 0.950596i \(-0.600473\pi\)
0.978456 0.206457i \(-0.0661933\pi\)
\(84\) 0 0
\(85\) 8.88151 + 15.3832i 0.963336 + 1.66855i
\(86\) 5.72665 0.617521
\(87\) 0 0
\(88\) 2.05408 0.218966
\(89\) 7.41507 12.8433i 0.785996 1.36139i −0.142406 0.989808i \(-0.545484\pi\)
0.928402 0.371577i \(-0.121183\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 9.42101 16.3177i 0.982208 1.70123i
\(93\) 0 0
\(94\) 7.77056 13.4590i 0.801472 1.38819i
\(95\) 3.60963 6.25206i 0.370340 0.641448i
\(96\) 0 0
\(97\) 4.74375 8.21642i 0.481655 0.834251i −0.518123 0.855306i \(-0.673369\pi\)
0.999778 + 0.0210547i \(0.00670241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −16.9897 + 29.4270i −1.69897 + 2.94270i
\(101\) −8.71176 −0.866852 −0.433426 0.901189i \(-0.642696\pi\)
−0.433426 + 0.901189i \(0.642696\pi\)
\(102\) 0 0
\(103\) 8.02712 0.790936 0.395468 0.918480i \(-0.370582\pi\)
0.395468 + 0.918480i \(0.370582\pi\)
\(104\) −1.23016 2.13069i −0.120627 0.208931i
\(105\) 0 0
\(106\) 4.39037 7.60434i 0.426430 0.738599i
\(107\) 6.42101 11.1215i 0.620742 1.07516i −0.368605 0.929586i \(-0.620165\pi\)
0.989348 0.145571i \(-0.0465021\pi\)
\(108\) 0 0
\(109\) −1.30039 2.25234i −0.124555 0.215735i 0.797004 0.603974i \(-0.206417\pi\)
−0.921559 + 0.388239i \(0.873084\pi\)
\(110\) −1.82904 3.16799i −0.174392 0.302056i
\(111\) 0 0
\(112\) 0 0
\(113\) −6.97509 12.0812i −0.656162 1.13651i −0.981601 0.190942i \(-0.938846\pi\)
0.325440 0.945563i \(-0.394488\pi\)
\(114\) 0 0
\(115\) −17.0015 −1.58540
\(116\) 15.5021 + 26.8505i 1.43934 + 2.49301i
\(117\) 0 0
\(118\) 15.0543 1.38586
\(119\) 0 0
\(120\) 0 0
\(121\) −10.8348 −0.984984
\(122\) −9.87538 + 17.1047i −0.894075 + 1.54858i
\(123\) 0 0
\(124\) −14.2444 24.6721i −1.27919 2.21562i
\(125\) 12.3698 1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) −9.55408 16.5482i −0.844470 1.46266i
\(129\) 0 0
\(130\) −2.19076 + 3.79450i −0.192142 + 0.332800i
\(131\) 8.51392 0.743864 0.371932 0.928260i \(-0.378695\pi\)
0.371932 + 0.928260i \(0.378695\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.85973 −0.765364
\(135\) 0 0
\(136\) −12.2709 21.2538i −1.05222 1.82250i
\(137\) −0.377242 −0.0322300 −0.0161150 0.999870i \(-0.505130\pi\)
−0.0161150 + 0.999870i \(0.505130\pi\)
\(138\) 0 0
\(139\) 9.50067 + 16.4556i 0.805837 + 1.39575i 0.915725 + 0.401806i \(0.131617\pi\)
−0.109888 + 0.993944i \(0.535049\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.4086 18.0281i −0.873467 1.51289i
\(143\) −0.0989221 0.171338i −0.00827228 0.0143280i
\(144\) 0 0
\(145\) 13.9879 24.2277i 1.16163 2.01200i
\(146\) 2.42792 4.20528i 0.200936 0.348032i
\(147\) 0 0
\(148\) −4.71780 8.17147i −0.387801 0.671691i
\(149\) 9.70175 0.794798 0.397399 0.917646i \(-0.369913\pi\)
0.397399 + 0.917646i \(0.369913\pi\)
\(150\) 0 0
\(151\) −12.8348 −1.04448 −0.522242 0.852798i \(-0.674904\pi\)
−0.522242 + 0.852798i \(0.674904\pi\)
\(152\) −4.98715 + 8.63800i −0.404511 + 0.700634i
\(153\) 0 0
\(154\) 0 0
\(155\) −12.8530 + 22.2621i −1.03238 + 1.78813i
\(156\) 0 0
\(157\) −10.4743 + 18.1420i −0.835937 + 1.44789i 0.0573276 + 0.998355i \(0.481742\pi\)
−0.893265 + 0.449531i \(0.851591\pi\)
\(158\) 10.0416 17.3926i 0.798869 1.38368i
\(159\) 0 0
\(160\) 0.986757 1.70911i 0.0780100 0.135117i
\(161\) 0 0
\(162\) 0 0
\(163\) 5.58113 9.66679i 0.437148 0.757162i −0.560321 0.828276i \(-0.689322\pi\)
0.997468 + 0.0711140i \(0.0226554\pi\)
\(164\) −30.4624 −2.37871
\(165\) 0 0
\(166\) 29.9492 2.32451
\(167\) 1.73012 + 2.99665i 0.133880 + 0.231888i 0.925169 0.379555i \(-0.123923\pi\)
−0.791289 + 0.611443i \(0.790590\pi\)
\(168\) 0 0
\(169\) 6.38151 11.0531i 0.490886 0.850239i
\(170\) −21.8530 + 37.8505i −1.67605 + 2.90300i
\(171\) 0 0
\(172\) 4.71780 + 8.17147i 0.359729 + 0.623069i
\(173\) −3.02680 5.24258i −0.230124 0.398586i 0.727721 0.685874i \(-0.240580\pi\)
−0.957844 + 0.287288i \(0.907246\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.879379 + 1.52313i 0.0662857 + 0.114810i
\(177\) 0 0
\(178\) 36.4896 2.73501
\(179\) 4.56654 + 7.90947i 0.341319 + 0.591182i 0.984678 0.174383i \(-0.0557930\pi\)
−0.643359 + 0.765565i \(0.722460\pi\)
\(180\) 0 0
\(181\) 11.9478 0.888074 0.444037 0.896008i \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 23.4897 1.73168
\(185\) −4.25696 + 7.37327i −0.312978 + 0.542093i
\(186\) 0 0
\(187\) −0.986757 1.70911i −0.0721588 0.124983i
\(188\) 25.6065 1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) 4.57014 + 7.91571i 0.330683 + 0.572760i 0.982646 0.185491i \(-0.0593874\pi\)
−0.651963 + 0.758251i \(0.726054\pi\)
\(192\) 0 0
\(193\) −8.47150 + 14.6731i −0.609792 + 1.05619i 0.381483 + 0.924376i \(0.375414\pi\)
−0.991274 + 0.131814i \(0.957920\pi\)
\(194\) 23.3441 1.67601
\(195\) 0 0
\(196\) 0 0
\(197\) 21.3173 1.51880 0.759398 0.650627i \(-0.225494\pi\)
0.759398 + 0.650627i \(0.225494\pi\)
\(198\) 0 0
\(199\) −4.98715 8.63800i −0.353530 0.612332i 0.633335 0.773877i \(-0.281685\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(200\) −42.3609 −2.99537
\(201\) 0 0
\(202\) −10.7177 18.5635i −0.754092 1.30613i
\(203\) 0 0
\(204\) 0 0
\(205\) 13.7434 + 23.8042i 0.959879 + 1.66256i
\(206\) 9.87538 + 17.1047i 0.688051 + 1.19174i
\(207\) 0 0
\(208\) 1.05329 1.82435i 0.0730324 0.126496i
\(209\) −0.401038 + 0.694619i −0.0277404 + 0.0480478i
\(210\) 0 0
\(211\) −2.44592 4.23645i −0.168384 0.291649i 0.769468 0.638685i \(-0.220521\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(212\) 14.4677 0.993646
\(213\) 0 0
\(214\) 31.5979 2.15998
\(215\) 4.25696 7.37327i 0.290322 0.502853i
\(216\) 0 0
\(217\) 0 0
\(218\) 3.19961 5.54189i 0.216705 0.375344i
\(219\) 0 0
\(220\) 3.01364 5.21978i 0.203179 0.351917i
\(221\) −1.18190 + 2.04712i −0.0795034 + 0.137704i
\(222\) 0 0
\(223\) 11.7044 20.2727i 0.783786 1.35756i −0.145936 0.989294i \(-0.546619\pi\)
0.929722 0.368263i \(-0.120047\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 17.1623 29.7259i 1.14162 1.97734i
\(227\) 6.11839 0.406092 0.203046 0.979169i \(-0.434916\pi\)
0.203046 + 0.979169i \(0.434916\pi\)
\(228\) 0 0
\(229\) 1.46039 0.0965052 0.0482526 0.998835i \(-0.484635\pi\)
0.0482526 + 0.998835i \(0.484635\pi\)
\(230\) −20.9161 36.2278i −1.37917 2.38879i
\(231\) 0 0
\(232\) −19.3260 + 33.4736i −1.26881 + 2.19765i
\(233\) −6.62422 + 11.4735i −0.433967 + 0.751653i −0.997211 0.0746378i \(-0.976220\pi\)
0.563244 + 0.826291i \(0.309553\pi\)
\(234\) 0 0
\(235\) −11.5526 20.0097i −0.753610 1.30529i
\(236\) 12.4022 + 21.4813i 0.807316 + 1.39831i
\(237\) 0 0
\(238\) 0 0
\(239\) 9.69436 + 16.7911i 0.627076 + 1.08613i 0.988136 + 0.153584i \(0.0490817\pi\)
−0.361060 + 0.932543i \(0.617585\pi\)
\(240\) 0 0
\(241\) −5.05368 −0.325536 −0.162768 0.986664i \(-0.552042\pi\)
−0.162768 + 0.986664i \(0.552042\pi\)
\(242\) −13.3296 23.0875i −0.856857 1.48412i
\(243\) 0 0
\(244\) −32.5426 −2.08333
\(245\) 0 0
\(246\) 0 0
\(247\) 0.960699 0.0611278
\(248\) 17.7580 30.7578i 1.12764 1.95312i
\(249\) 0 0
\(250\) 15.2180 + 26.3584i 0.962472 + 1.66705i
\(251\) 15.0928 0.952647 0.476324 0.879270i \(-0.341969\pi\)
0.476324 + 0.879270i \(0.341969\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) −19.1228 33.1216i −1.19987 2.07823i
\(255\) 0 0
\(256\) 16.1804 28.0253i 1.01128 1.75158i
\(257\) 7.71184 0.481051 0.240526 0.970643i \(-0.422680\pi\)
0.240526 + 0.970643i \(0.422680\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7.21926 −0.447720
\(261\) 0 0
\(262\) 10.4743 + 18.1420i 0.647102 + 1.12081i
\(263\) −4.21206 −0.259727 −0.129864 0.991532i \(-0.541454\pi\)
−0.129864 + 0.991532i \(0.541454\pi\)
\(264\) 0 0
\(265\) −6.52724 11.3055i −0.400965 0.694492i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.29893 12.6421i −0.445853 0.772240i
\(269\) −10.3753 17.9706i −0.632596 1.09569i −0.987019 0.160603i \(-0.948656\pi\)
0.354423 0.935085i \(-0.384677\pi\)
\(270\) 0 0
\(271\) −14.2444 + 24.6721i −0.865287 + 1.49872i 0.00147433 + 0.999999i \(0.499531\pi\)
−0.866762 + 0.498723i \(0.833803\pi\)
\(272\) 10.5067 18.1981i 0.637060 1.10342i
\(273\) 0 0
\(274\) −0.464103 0.803851i −0.0280375 0.0485624i
\(275\) −3.40642 −0.205415
\(276\) 0 0
\(277\) 17.1623 1.03118 0.515590 0.856835i \(-0.327573\pi\)
0.515590 + 0.856835i \(0.327573\pi\)
\(278\) −23.3765 + 40.4892i −1.40203 + 2.42838i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.72140 8.17770i 0.281655 0.487841i −0.690138 0.723678i \(-0.742450\pi\)
0.971793 + 0.235837i \(0.0757833\pi\)
\(282\) 0 0
\(283\) 8.43422 14.6085i 0.501362 0.868385i −0.498636 0.866811i \(-0.666166\pi\)
0.999999 0.00157378i \(-0.000500949\pi\)
\(284\) 17.1498 29.7043i 1.01765 1.76263i
\(285\) 0 0
\(286\) 0.243398 0.421578i 0.0143924 0.0249284i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.28959 + 5.69774i −0.193505 + 0.335161i
\(290\) 68.8344 4.04210
\(291\) 0 0
\(292\) 8.00079 0.468211
\(293\) 1.86143 + 3.22409i 0.108746 + 0.188353i 0.915262 0.402858i \(-0.131983\pi\)
−0.806517 + 0.591211i \(0.798650\pi\)
\(294\) 0 0
\(295\) 11.1908 19.3830i 0.651551 1.12852i
\(296\) 5.88151 10.1871i 0.341856 0.592112i
\(297\) 0 0
\(298\) 11.9356 + 20.6731i 0.691411 + 1.19756i
\(299\) −1.13123 1.95935i −0.0654209 0.113312i
\(300\) 0 0
\(301\) 0 0
\(302\) −15.7901 27.3492i −0.908617 1.57377i
\(303\) 0 0
\(304\) −8.54024 −0.489817
\(305\) 14.6819 + 25.4298i 0.840683 + 1.45611i
\(306\) 0 0
\(307\) −30.5691 −1.74467 −0.872335 0.488908i \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −63.2498 −3.59235
\(311\) 5.21739 9.03678i 0.295851 0.512429i −0.679332 0.733831i \(-0.737730\pi\)
0.975182 + 0.221403i \(0.0710635\pi\)
\(312\) 0 0
\(313\) −0.309930 0.536815i −0.0175183 0.0303426i 0.857133 0.515095i \(-0.172243\pi\)
−0.874652 + 0.484752i \(0.838910\pi\)
\(314\) −51.5440 −2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) 5.12422 + 8.87541i 0.287805 + 0.498493i 0.973285 0.229598i \(-0.0737412\pi\)
−0.685481 + 0.728091i \(0.740408\pi\)
\(318\) 0 0
\(319\) −1.55408 + 2.69175i −0.0870120 + 0.150709i
\(320\) −26.8043 −1.49841
\(321\) 0 0
\(322\) 0 0
\(323\) 9.58307 0.533216
\(324\) 0 0
\(325\) 2.04005 + 3.53346i 0.113161 + 0.196001i
\(326\) 27.4648 1.52113
\(327\) 0 0
\(328\) −18.9882 32.8885i −1.04845 1.81596i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.1819 + 17.6356i 0.559648 + 0.969339i 0.997526 + 0.0703042i \(0.0223970\pi\)
−0.437878 + 0.899035i \(0.644270\pi\)
\(332\) 24.6731 + 42.7351i 1.35411 + 2.34539i
\(333\) 0 0
\(334\) −4.25696 + 7.37327i −0.232930 + 0.403447i
\(335\) −6.58596 + 11.4072i −0.359829 + 0.623242i
\(336\) 0 0
\(337\) 2.85594 + 4.94662i 0.155573 + 0.269460i 0.933267 0.359182i \(-0.116944\pi\)
−0.777695 + 0.628642i \(0.783611\pi\)
\(338\) 31.4035 1.70812
\(339\) 0 0
\(340\) −72.0128 −3.90544
\(341\) 1.42800 2.47337i 0.0773305 0.133940i
\(342\) 0 0
\(343\) 0 0
\(344\) −5.88151 + 10.1871i −0.317110 + 0.549251i
\(345\) 0 0
\(346\) 7.44746 12.8994i 0.400378 0.693475i
\(347\) 4.44066 7.69145i 0.238387 0.412899i −0.721865 0.692034i \(-0.756715\pi\)
0.960252 + 0.279136i \(0.0900480\pi\)
\(348\) 0 0
\(349\) −10.4874 + 18.1648i −0.561379 + 0.972337i 0.435997 + 0.899948i \(0.356396\pi\)
−0.997376 + 0.0723893i \(0.976938\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.109631 + 0.189886i −0.00584335 + 0.0101210i
\(353\) 14.7654 0.785881 0.392941 0.919564i \(-0.371458\pi\)
0.392941 + 0.919564i \(0.371458\pi\)
\(354\) 0 0
\(355\) −30.9492 −1.64261
\(356\) 30.0613 + 52.0677i 1.59325 + 2.75959i
\(357\) 0 0
\(358\) −11.2360 + 19.4613i −0.593840 + 1.02856i
\(359\) 3.60603 6.24583i 0.190319 0.329642i −0.755037 0.655682i \(-0.772381\pi\)
0.945356 + 0.326040i \(0.105714\pi\)
\(360\) 0 0
\(361\) 7.55262 + 13.0815i 0.397506 + 0.688501i
\(362\) 14.6988 + 25.4591i 0.772554 + 1.33810i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.60963 6.25206i −0.188937 0.327248i
\(366\) 0 0
\(367\) −10.9742 −0.572850 −0.286425 0.958103i \(-0.592467\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(368\) 10.0562 + 17.4179i 0.524217 + 0.907970i
\(369\) 0 0
\(370\) −20.9485 −1.08906
\(371\) 0 0
\(372\) 0 0
\(373\) −0.543767 −0.0281552 −0.0140776 0.999901i \(-0.504481\pi\)
−0.0140776 + 0.999901i \(0.504481\pi\)
\(374\) 2.42792 4.20528i 0.125545 0.217450i
\(375\) 0 0
\(376\) 15.9614 + 27.6459i 0.823145 + 1.42573i
\(377\) 3.72286 0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) 14.6337 + 25.3464i 0.750695 + 1.30024i
\(381\) 0 0
\(382\) −11.2448 + 19.4766i −0.575336 + 0.996511i
\(383\) −35.7139 −1.82489 −0.912447 0.409194i \(-0.865810\pi\)
−0.912447 + 0.409194i \(0.865810\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −41.6883 −2.12188
\(387\) 0 0
\(388\) 19.2316 + 33.3101i 0.976336 + 1.69106i
\(389\) −38.6591 −1.96010 −0.980048 0.198761i \(-0.936308\pi\)
−0.980048 + 0.198761i \(0.936308\pi\)
\(390\) 0 0
\(391\) −11.2842 19.5447i −0.570664 0.988420i
\(392\) 0 0
\(393\) 0 0
\(394\) 26.2257 + 45.4242i 1.32123 + 2.28844i
\(395\) −14.9291 25.8579i −0.751163 1.30105i
\(396\) 0 0
\(397\) 5.97391 10.3471i 0.299822 0.519307i −0.676273 0.736651i \(-0.736406\pi\)
0.976095 + 0.217344i \(0.0697394\pi\)
\(398\) 12.2709 21.2538i 0.615085 1.06536i
\(399\) 0 0
\(400\) −18.1352 31.4111i −0.906761 1.57056i
\(401\) −32.3566 −1.61581 −0.807906 0.589311i \(-0.799399\pi\)
−0.807906 + 0.589311i \(0.799399\pi\)
\(402\) 0 0
\(403\) −3.42082 −0.170403
\(404\) 17.6591 30.5865i 0.878573 1.52173i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.472958 0.819187i 0.0234437 0.0406056i
\(408\) 0 0
\(409\) −9.48751 + 16.4328i −0.469127 + 0.812552i −0.999377 0.0352893i \(-0.988765\pi\)
0.530250 + 0.847841i \(0.322098\pi\)
\(410\) −33.8157 + 58.5704i −1.67004 + 2.89259i
\(411\) 0 0
\(412\) −16.2713 + 28.1827i −0.801630 + 1.38846i
\(413\) 0 0
\(414\) 0 0
\(415\) 22.2630 38.5607i 1.09285 1.89287i
\(416\) 0.262624 0.0128762
\(417\) 0 0
\(418\) −1.97351 −0.0965277
\(419\) −8.64523 14.9740i −0.422347 0.731526i 0.573822 0.818980i \(-0.305460\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(420\) 0 0
\(421\) −9.30039 + 16.1087i −0.453273 + 0.785092i −0.998587 0.0531397i \(-0.983077\pi\)
0.545314 + 0.838232i \(0.316410\pi\)
\(422\) 6.01819 10.4238i 0.292961 0.507423i
\(423\) 0 0
\(424\) 9.01819 + 15.6200i 0.437962 + 0.758572i
\(425\) 20.3496 + 35.2466i 0.987103 + 1.70971i
\(426\) 0 0
\(427\) 0 0
\(428\) 26.0313 + 45.0876i 1.25827 + 2.17939i
\(429\) 0 0
\(430\) 20.9485 1.01023
\(431\) −7.93920 13.7511i −0.382418 0.662367i 0.608990 0.793178i \(-0.291575\pi\)
−0.991407 + 0.130811i \(0.958242\pi\)
\(432\) 0 0
\(433\) 40.4367 1.94326 0.971631 0.236501i \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10.5438 0.504955
\(437\) −4.58611 + 7.94338i −0.219384 + 0.379984i
\(438\) 0 0
\(439\) −6.23047 10.7915i −0.297364 0.515050i 0.678168 0.734907i \(-0.262774\pi\)
−0.975532 + 0.219857i \(0.929441\pi\)
\(440\) 7.51399 0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) −4.11537 7.12802i −0.195527 0.338663i 0.751546 0.659680i \(-0.229308\pi\)
−0.947073 + 0.321018i \(0.895975\pi\)
\(444\) 0 0
\(445\) 27.1249 46.9817i 1.28584 2.22715i
\(446\) 57.5976 2.72732
\(447\) 0 0
\(448\) 0 0
\(449\) −5.64474 −0.266392 −0.133196 0.991090i \(-0.542524\pi\)
−0.133196 + 0.991090i \(0.542524\pi\)
\(450\) 0 0
\(451\) −1.52692 2.64471i −0.0718999 0.124534i
\(452\) 56.5552 2.66013
\(453\) 0 0
\(454\) 7.52716 + 13.0374i 0.353267 + 0.611876i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.53443 4.38977i −0.118556 0.205345i 0.800640 0.599146i \(-0.204493\pi\)
−0.919196 + 0.393801i \(0.871160\pi\)
\(458\) 1.79665 + 3.11188i 0.0839518 + 0.145409i
\(459\) 0 0
\(460\) 34.4628 59.6913i 1.60683 2.78312i
\(461\) −3.88831 + 6.73475i −0.181097 + 0.313669i −0.942254 0.334898i \(-0.891298\pi\)
0.761158 + 0.648567i \(0.224631\pi\)
\(462\) 0 0
\(463\) 4.58998 + 7.95008i 0.213314 + 0.369472i 0.952750 0.303756i \(-0.0982408\pi\)
−0.739435 + 0.673228i \(0.764907\pi\)
\(464\) −33.0947 −1.53638
\(465\) 0 0
\(466\) −32.5979 −1.51007
\(467\) −6.88272 + 11.9212i −0.318494 + 0.551648i −0.980174 0.198138i \(-0.936511\pi\)
0.661680 + 0.749787i \(0.269844\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 28.4253 49.2340i 1.31116 2.27100i
\(471\) 0 0
\(472\) −15.4614 + 26.7800i −0.711669 + 1.23265i
\(473\) −0.472958 + 0.819187i −0.0217466 + 0.0376663i
\(474\) 0 0
\(475\) 8.27052 14.3250i 0.379477 0.657274i
\(476\) 0 0
\(477\) 0 0
\(478\) −23.8530 + 41.3146i −1.09101 + 1.88969i
\(479\) −8.71176 −0.398050 −0.199025 0.979994i \(-0.563778\pi\)
−0.199025 + 0.979994i \(0.563778\pi\)
\(480\) 0 0
\(481\) −1.13298 −0.0516597
\(482\) −6.21731 10.7687i −0.283191 0.490501i
\(483\) 0 0
\(484\) 21.9626 38.0404i 0.998302 1.72911i
\(485\) 17.3530 30.0563i 0.787960 1.36479i
\(486\) 0 0
\(487\) 9.01819 + 15.6200i 0.408653 + 0.707808i 0.994739 0.102441i \(-0.0326653\pi\)
−0.586086 + 0.810249i \(0.699332\pi\)
\(488\) −20.2849 35.1344i −0.918253 1.59046i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.02344 + 1.77266i 0.0461874 + 0.0799989i 0.888195 0.459467i \(-0.151960\pi\)
−0.842007 + 0.539466i \(0.818626\pi\)
\(492\) 0 0
\(493\) 37.1358 1.67251
\(494\) 1.18190 + 2.04712i 0.0531763 + 0.0921041i
\(495\) 0 0
\(496\) 30.4097 1.36544
\(497\) 0 0
\(498\) 0 0
\(499\) −39.0875 −1.74980 −0.874899 0.484305i \(-0.839072\pi\)
−0.874899 + 0.484305i \(0.839072\pi\)
\(500\) −25.0742 + 43.4297i −1.12135 + 1.94224i
\(501\) 0 0
\(502\) 18.5679 + 32.1606i 0.828727 + 1.43540i
\(503\) −5.11846 −0.228221 −0.114111 0.993468i \(-0.536402\pi\)
−0.114111 + 0.993468i \(0.536402\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) 2.32383 + 4.02499i 0.103307 + 0.178933i
\(507\) 0 0
\(508\) 31.5079 54.5732i 1.39794 2.42130i
\(509\) 29.5272 1.30877 0.654386 0.756161i \(-0.272927\pi\)
0.654386 + 0.756161i \(0.272927\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 41.4078 1.82998
\(513\) 0 0
\(514\) 9.48751 + 16.4328i 0.418476 + 0.724822i
\(515\) 29.3638 1.29392
\(516\) 0 0
\(517\) 1.28352 + 2.22313i 0.0564493 + 0.0977730i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) 0.532351 + 0.922058i 0.0233227 + 0.0403961i 0.877451 0.479666i \(-0.159242\pi\)
−0.854128 + 0.520062i \(0.825909\pi\)
\(522\) 0 0
\(523\) −6.69094 + 11.5890i −0.292574 + 0.506754i −0.974418 0.224745i \(-0.927845\pi\)
0.681843 + 0.731498i \(0.261179\pi\)
\(524\) −17.2581 + 29.8918i −0.753922 + 1.30583i
\(525\) 0 0
\(526\) −5.18190 8.97532i −0.225942 0.391343i
\(527\) −34.1230 −1.48642
\(528\) 0 0
\(529\) −1.39922 −0.0608358
\(530\) 16.0603 27.8173i 0.697615 1.20830i
\(531\) 0 0
\(532\) 0 0
\(533\) −1.82889 + 3.16774i −0.0792181 + 0.137210i
\(534\) 0 0
\(535\) 23.4885 40.6833i 1.01550 1.75889i
\(536\) 9.09931 15.7605i 0.393031 0.680749i
\(537\) 0 0
\(538\) 25.5286 44.2168i 1.10062 1.90632i
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0438 29.5207i 0.732769 1.26919i −0.222927 0.974835i \(-0.571561\pi\)
0.955695 0.294358i \(-0.0951056\pi\)
\(542\) −70.0970 −3.01092
\(543\) 0 0
\(544\) 2.61970 0.112319
\(545\) −4.75692 8.23922i −0.203764 0.352930i
\(546\) 0 0
\(547\) 2.97150 5.14678i 0.127052 0.220060i −0.795481 0.605978i \(-0.792782\pi\)
0.922533 + 0.385918i \(0.126115\pi\)
\(548\) 0.764686 1.32448i 0.0326658 0.0565788i
\(549\) 0 0
\(550\) −4.19076 7.25860i −0.178694 0.309508i
\(551\) −7.54638 13.0707i −0.321487 0.556831i
\(552\) 0 0
\(553\) 0 0
\(554\) 21.1139 + 36.5704i 0.897044 + 1.55373i
\(555\) 0 0
\(556\) −77.0331 −3.26693
\(557\) −15.0402 26.0503i −0.637272 1.10379i −0.986029 0.166575i \(-0.946729\pi\)
0.348756 0.937213i \(-0.386604\pi\)
\(558\) 0 0
\(559\) 1.13298 0.0479202
\(560\) 0 0
\(561\) 0 0
\(562\) 23.2340 0.980069
\(563\) 9.81060 16.9925i 0.413468 0.716147i −0.581799 0.813333i \(-0.697651\pi\)
0.995266 + 0.0971860i \(0.0309842\pi\)
\(564\) 0 0
\(565\) −25.5154 44.1940i −1.07344 1.85926i
\(566\) 41.5049 1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) −0.687159 1.19019i −0.0288072 0.0498955i 0.851262 0.524740i \(-0.175838\pi\)
−0.880070 + 0.474845i \(0.842504\pi\)
\(570\) 0 0
\(571\) −8.69076 + 15.0528i −0.363697 + 0.629941i −0.988566 0.150788i \(-0.951819\pi\)
0.624869 + 0.780729i \(0.285152\pi\)
\(572\) 0.802077 0.0335365
\(573\) 0 0
\(574\) 0 0
\(575\) −38.9545 −1.62451
\(576\) 0 0
\(577\) −13.5274 23.4301i −0.563153 0.975409i −0.997219 0.0745283i \(-0.976255\pi\)
0.434066 0.900881i \(-0.357078\pi\)
\(578\) −16.1881 −0.673337
\(579\) 0 0
\(580\) 56.7080 + 98.2211i 2.35467 + 4.07841i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.725191 + 1.25607i 0.0300344 + 0.0520210i
\(584\) 4.98715 + 8.63800i 0.206370 + 0.357443i
\(585\) 0 0
\(586\) −4.58005 + 7.93288i −0.189200 + 0.327704i
\(587\) −3.75700 + 6.50731i −0.155068 + 0.268585i −0.933084 0.359659i \(-0.882893\pi\)
0.778016 + 0.628245i \(0.216226\pi\)
\(588\) 0 0
\(589\) 6.93414 + 12.0103i 0.285716 + 0.494875i
\(590\) 55.0698 2.26719
\(591\) 0 0
\(592\) 10.0718 0.413948
\(593\) −17.7904 + 30.8139i −0.730565 + 1.26538i 0.226077 + 0.974109i \(0.427410\pi\)
−0.956642 + 0.291266i \(0.905924\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −19.6659 + 34.0623i −0.805545 + 1.39524i
\(597\) 0 0
\(598\) 2.78340 4.82100i 0.113822 0.197145i
\(599\) −5.74105 + 9.94379i −0.234573 + 0.406292i −0.959148 0.282903i \(-0.908702\pi\)
0.724576 + 0.689195i \(0.242036\pi\)
\(600\) 0 0
\(601\) −0.190030 + 0.329142i −0.00775150 + 0.0134260i −0.869875 0.493272i \(-0.835801\pi\)
0.862124 + 0.506698i \(0.169134\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 26.0167 45.0623i 1.05861 1.83356i
\(605\) −39.6346 −1.61138
\(606\) 0 0
\(607\) 18.5409 0.752551 0.376275 0.926508i \(-0.377205\pi\)
0.376275 + 0.926508i \(0.377205\pi\)
\(608\) −0.532351 0.922058i −0.0215897 0.0373944i
\(609\) 0 0
\(610\) −36.1249 + 62.5702i −1.46265 + 2.53339i
\(611\) 1.53736 2.66278i 0.0621949 0.107725i
\(612\) 0 0
\(613\) −3.66225 6.34321i −0.147917 0.256200i 0.782540 0.622600i \(-0.213924\pi\)
−0.930457 + 0.366400i \(0.880590\pi\)
\(614\) −37.6077 65.1385i −1.51772 2.62877i
\(615\) 0 0
\(616\) 0 0
\(617\) −12.7427 22.0710i −0.513002 0.888546i −0.999886 0.0150791i \(-0.995200\pi\)
0.486884 0.873466i \(-0.338133\pi\)
\(618\) 0 0
\(619\) −32.8963 −1.32222 −0.661108 0.750291i \(-0.729913\pi\)
−0.661108 + 0.750291i \(0.729913\pi\)
\(620\) −52.1072 90.2523i −2.09267 3.62462i
\(621\) 0 0
\(622\) 25.6748 1.02947
\(623\) 0 0
\(624\) 0 0
\(625\) 3.34221 0.133689
\(626\) 0.762585 1.32084i 0.0304790 0.0527912i
\(627\) 0 0
\(628\) −42.4636 73.5490i −1.69448 2.93493i
\(629\) −11.3016 −0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) 20.6264 + 35.7259i 0.820472 + 1.42110i
\(633\) 0 0
\(634\) −12.6082 + 21.8380i −0.500734 + 0.867297i
\(635\) −56.8603 −2.25643
\(636\) 0 0
\(637\) 0 0
\(638\) −7.64766 −0.302774
\(639\) 0 0
\(640\) −34.9496 60.5344i −1.38150 2.39283i
\(641\) −11.4605 −0.452663 −0.226331 0.974050i \(-0.572673\pi\)
−0.226331 + 0.974050i \(0.572673\pi\)
\(642\) 0 0
\(643\) −8.69078 15.0529i −0.342731 0.593627i 0.642208 0.766531i \(-0.278019\pi\)
−0.984939 + 0.172903i \(0.944685\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.7896 + 20.4202i 0.463855 + 0.803421i
\(647\) −12.6720 21.9485i −0.498186 0.862883i 0.501812 0.864977i \(-0.332667\pi\)
−0.999998 + 0.00209358i \(0.999334\pi\)
\(648\) 0 0
\(649\) −1.24332 + 2.15349i −0.0488045 + 0.0845320i
\(650\) −5.01954 + 8.69410i −0.196883 + 0.341011i
\(651\) 0 0
\(652\) 22.6264 + 39.1900i 0.886116 + 1.53480i
\(653\) −14.0833 −0.551121 −0.275560 0.961284i \(-0.588863\pi\)
−0.275560 + 0.961284i \(0.588863\pi\)
\(654\) 0 0
\(655\) 31.1445 1.21692
\(656\) 16.2581 28.1599i 0.634774 1.09946i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.0854 33.0569i 0.743462 1.28771i −0.207449 0.978246i \(-0.566516\pi\)
0.950910 0.309467i \(-0.100151\pi\)
\(660\) 0 0
\(661\) −0.176866 + 0.306341i −0.00687930 + 0.0119153i −0.869445 0.494031i \(-0.835523\pi\)
0.862565 + 0.505946i \(0.168856\pi\)
\(662\) −25.0526 + 43.3924i −0.973698 + 1.68649i
\(663\) 0 0
\(664\) −30.7591 + 53.2764i −1.19369 + 2.06752i
\(665\) 0 0
\(666\) 0 0
\(667\) −17.7719 + 30.7818i −0.688130 + 1.19188i
\(668\) −14.0281 −0.542762
\(669\) 0 0
\(670\) −32.4096 −1.25209
\(671\) −1.63119 2.82531i −0.0629715 0.109070i
\(672\) 0 0
\(673\) 10.5555 18.2827i 0.406886 0.704748i −0.587653 0.809113i \(-0.699948\pi\)
0.994539 + 0.104365i \(0.0332811\pi\)
\(674\) −7.02704 + 12.1712i −0.270672 + 0.468817i
\(675\) 0 0
\(676\) 25.8712 + 44.8102i 0.995046 + 1.72347i
\(677\) −10.5732 18.3133i −0.406361 0.703837i 0.588118 0.808775i \(-0.299869\pi\)
−0.994479 + 0.104938i \(0.966536\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −44.8879 77.7482i −1.72137 2.98151i
\(681\) 0 0
\(682\) 7.02720 0.269085
\(683\) 17.3858 + 30.1131i 0.665249 + 1.15224i 0.979218 + 0.202811i \(0.0650078\pi\)
−0.313969 + 0.949433i \(0.601659\pi\)
\(684\) 0 0
\(685\) −1.37998 −0.0527264
\(686\) 0 0
\(687\) 0 0
\(688\) −10.0718 −0.383984
\(689\) 0.868609 1.50447i 0.0330914 0.0573159i
\(690\) 0 0
\(691\) 17.3246 + 30.0071i 0.659059 + 1.14152i 0.980860 + 0.194716i \(0.0623785\pi\)
−0.321801 + 0.946807i \(0.604288\pi\)
\(692\) 24.5418 0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) 34.7542 + 60.1960i 1.31830 + 2.28336i
\(696\) 0 0
\(697\) −18.2434 + 31.5985i −0.691017 + 1.19688i
\(698\) −51.6087 −1.95342
\(699\) 0 0
\(700\) 0 0
\(701\) 48.6050 1.83579 0.917894 0.396826i \(-0.129889\pi\)
0.917894 + 0.396826i \(0.129889\pi\)
\(702\) 0 0
\(703\) 2.29661 + 3.97784i 0.0866182 + 0.150027i
\(704\) 2.97802 0.112238
\(705\) 0 0
\(706\) 18.1651 + 31.4629i 0.683654 + 1.18412i
\(707\) 0 0
\(708\) 0 0
\(709\) −2.05408 3.55778i −0.0771428 0.133615i 0.824873 0.565318i \(-0.191246\pi\)
−0.902016 + 0.431702i \(0.857913\pi\)
\(710\) −38.0753 65.9483i −1.42894 2.47500i
\(711\) 0 0
\(712\) −37.4764 + 64.9110i −1.40449 + 2.43264i
\(713\) 16.3300 28.2844i 0.611564 1.05926i
\(714\) 0 0
\(715\) −0.361864 0.626767i −0.0135330 0.0234398i
\(716\) −37.0263 −1.38374
\(717\) 0 0
\(718\) 17.7453 0.662249
\(719\) −24.1408 + 41.8131i −0.900299 + 1.55936i −0.0731939 + 0.997318i \(0.523319\pi\)
−0.827106 + 0.562047i \(0.810014\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −18.5833 + 32.1872i −0.691597 + 1.19788i
\(723\) 0 0
\(724\) −24.2187 + 41.9481i −0.900082 + 1.55899i
\(725\) 32.0495 55.5114i 1.19029 2.06164i
\(726\) 0 0
\(727\) −20.5151 + 35.5332i −0.760863 + 1.31785i 0.181543 + 0.983383i \(0.441891\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 8.88151 15.3832i 0.328720 0.569359i
\(731\) 11.3016 0.418006
\(732\) 0 0
\(733\) −30.5428 −1.12812 −0.564062 0.825733i \(-0.690762\pi\)
−0.564062 + 0.825733i \(0.690762\pi\)
\(734\) −13.5011 23.3845i −0.498334 0.863139i
\(735\) 0 0
\(736\) −1.25370 + 2.17147i −0.0462118 + 0.0800413i
\(737\) 0.731715 1.26737i 0.0269531 0.0466841i
\(738\) 0 0
\(739\) −11.9100 20.6288i −0.438117 0.758841i 0.559427 0.828880i \(-0.311021\pi\)
−0.997544 + 0.0700384i \(0.977688\pi\)
\(740\) −17.2581 29.8918i −0.634419 1.09885i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.26089 + 9.11213i 0.193003 + 0.334292i 0.946244 0.323453i \(-0.104844\pi\)
−0.753241 + 0.657745i \(0.771510\pi\)
\(744\) 0 0
\(745\) 35.4897 1.30024
\(746\) −0.668971 1.15869i −0.0244928 0.0424227i
\(747\) 0 0
\(748\) 8.00079 0.292538
\(749\) 0 0
\(750\) 0 0
\(751\) −10.2704 −0.374773 −0.187386 0.982286i \(-0.560002\pi\)
−0.187386 + 0.982286i \(0.560002\pi\)
\(752\) −13.6665 + 23.6711i −0.498367 + 0.863197i
\(753\) 0 0
\(754\) 4.58005 + 7.93288i 0.166796 + 0.288899i
\(755\) −46.9507 −1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) −27.9159 48.3518i −1.01395 1.75622i
\(759\) 0 0
\(760\) −18.2434 + 31.5985i −0.661757 + 1.14620i
\(761\) 27.6604 1.00269 0.501345 0.865247i \(-0.332839\pi\)
0.501345 + 0.865247i \(0.332839\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −37.0554 −1.34062
\(765\) 0 0
\(766\) −43.9371 76.1013i −1.58751 2.74965i
\(767\) 2.97841 0.107544
\(768\) 0 0
\(769\) −16.9613 29.3778i −0.611640 1.05939i −0.990964 0.134128i \(-0.957177\pi\)
0.379324 0.925264i \(-0.376157\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −34.3442 59.4858i −1.23607 2.14094i
\(773\) 14.2978 + 24.7645i 0.514256 + 0.890717i 0.999863 + 0.0165403i \(0.00526518\pi\)
−0.485607 + 0.874177i \(0.661401\pi\)
\(774\) 0 0
\(775\) −29.4493 + 51.0077i −1.05785 + 1.83225i
\(776\) −23.9753 + 41.5265i −0.860664 + 1.49071i
\(777\) 0 0
\(778\) −47.5605 82.3772i −1.70513 2.95337i
\(779\) 14.8290 0.531303
\(780\) 0 0
\(781\) 3.43852 0.123040
\(782\) 27.7647 48.0899i 0.992864 1.71969i
\(783\) 0 0
\(784\) 0 0
\(785\) −38.3157 + 66.3647i −1.36754 + 2.36866i
\(786\) 0 0
\(787\) 23.0017 39.8402i 0.819923 1.42015i −0.0858145 0.996311i \(-0.527349\pi\)
0.905738 0.423838i \(-0.139317\pi\)
\(788\) −43.2111 + 74.8438i −1.53933 + 2.66620i
\(789\) 0 0
\(790\) 36.7330 63.6235i 1.30690 2.26362i
\(791\) 0 0
\(792\) 0 0
\(793\) −1.95379 + 3.38406i −0.0693810 + 0.120171i
\(794\) 29.3977 1.04328
\(795\)