Properties

Label 1323.2.g.g.361.6
Level $1323$
Weight $2$
Character 1323.361
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 361.6
Root \(-1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.g.667.6

$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23025 2.13086i 0.869920 1.50675i 0.00784213 0.999969i \(-0.497504\pi\)
0.862078 0.506776i \(-0.169163\pi\)
\(3\) 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 −0.830297 0.557322i \(-0.811829\pi\)
0.897803 + 0.440397i \(0.145162\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.16372 + 3.74766i −0.540929 + 0.936916i
\(17\) 2.42792 4.20528i 0.588857 1.01993i −0.405525 0.914084i \(-0.632911\pi\)
0.994382 0.105847i \(-0.0337553\pi\)
\(18\) 0 0
\(19\) 0.986757 + 1.70911i 0.226378 + 0.392097i 0.956732 0.290971i \(-0.0939784\pi\)
−0.730354 + 0.683069i \(0.760645\pi\)
\(20\) −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 0.964831 + 0.262870i \(0.0846690\pi\)
−0.254764 + 0.967003i \(0.581998\pi\)
\(30\) 0 0
\(31\) −3.51360 6.08573i −0.631061 1.09303i −0.987335 0.158648i \(-0.949286\pi\)
0.356274 0.934381i \(-0.384047\pi\)
\(32\) 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 0.754372 0.656447i \(-0.227941\pi\)
−0.945686 + 0.325082i \(0.894608\pi\)
\(38\) 4.85584 0.787721
\(39\) 0 0
\(40\) −18.4882 −2.92324
\(41\) 3.75700 6.50731i 0.586744 1.01627i −0.407911 0.913022i \(-0.633743\pi\)
0.994655 0.103249i \(-0.0329240\pi\)
\(42\) 0 0
\(43\) 1.16372 + 2.01561i 0.177465 + 0.307378i 0.941012 0.338374i \(-0.109877\pi\)
−0.763547 + 0.645753i \(0.776544\pi\)
\(44\) 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 −0.998994 0.0448469i \(-0.985720\pi\)
0.538335 + 0.842731i \(0.319053\pi\)
\(48\) 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 −0.962159 0.272489i \(-0.912153\pi\)
0.717062 + 0.697010i \(0.245487\pi\)
\(54\) 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 0.993513 0.113719i \(-0.0362763\pi\)
−0.595240 + 0.803548i \(0.702943\pi\)
\(60\) 0 0
\(61\) 4.01356 6.95169i 0.513884 0.890073i −0.485987 0.873966i \(-0.661540\pi\)
0.999870 0.0161063i \(-0.00512703\pi\)
\(62\) −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 0.734841 0.678240i \(-0.237257\pi\)
−0.954793 + 0.297271i \(0.903924\pi\)
\(68\) −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 −0.917976 0.396636i \(-0.870178\pi\)
0.802485 + 0.596673i \(0.203511\pi\)
\(74\) −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 −0.998917 0.0465297i \(-0.985184\pi\)
0.539754 + 0.841823i \(0.318517\pi\)
\(80\) −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 0.978456 + 0.206457i \(0.0661933\pi\)
−0.310431 + 0.950596i \(0.600473\pi\)
\(84\) 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 0.928402 + 0.371577i \(0.121183\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(90\) 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 0.999778 0.0210547i \(-0.00670241\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(98\) 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 0.989348 + 0.145571i \(0.0465021\pi\)
−0.368605 + 0.929586i \(0.620165\pi\)
\(108\) 0 0
\(109\) −1.30039 + 2.25234i −0.124555 + 0.215735i −0.921559 0.388239i \(-0.873084\pi\)
0.797004 + 0.603974i \(0.206417\pi\)
\(110\) −1.82904 + 3.16799i −0.174392 + 0.302056i
\(111\) 0 0
\(112\) 0 0
\(113\) −6.97509 + 12.0812i −0.656162 + 1.13651i 0.325440 + 0.945563i \(0.394488\pi\)
−0.981601 + 0.190942i \(0.938846\pi\)
\(114\) 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 −0.109888 0.993944i \(-0.535049\pi\)
0.915725 0.401806i \(-0.131617\pi\)
\(140\) 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 −0.893265 0.449531i \(-0.851591\pi\)
0.0573276 0.998355i \(-0.481742\pi\)
\(158\) 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 0.997468 0.0711140i \(-0.0226554\pi\)
−0.560321 + 0.828276i \(0.689322\pi\)
\(164\) −30.4624 −2.37871
\(165\) 0 0
\(166\) 29.9492 2.32451
\(167\) 1.73012 2.99665i 0.133880 0.231888i −0.791289 0.611443i \(-0.790590\pi\)
0.925169 + 0.379555i \(0.123923\pi\)
\(168\) 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 −0.957844 0.287288i \(-0.907246\pi\)
0.727721 + 0.685874i \(0.240580\pi\)
\(174\) 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 −0.643359 0.765565i \(-0.722460\pi\)
0.984678 + 0.174383i \(0.0557930\pi\)
\(180\) 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 −0.651963 0.758251i \(-0.726054\pi\)
0.982646 + 0.185491i \(0.0593874\pi\)
\(192\) 0 0
\(193\) −8.47150 14.6731i −0.609792 1.05619i −0.991274 0.131814i \(-0.957920\pi\)
0.381483 0.924376i \(-0.375414\pi\)
\(194\) 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 −0.986865 0.161546i \(-0.948352\pi\)
0.633335 + 0.773877i \(0.281685\pi\)
\(200\) −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 −0.937852 0.347036i \(-0.887188\pi\)
0.769468 + 0.638685i \(0.220521\pi\)
\(212\) 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 0.929722 + 0.368263i \(0.120047\pi\)
−0.145936 + 0.989294i \(0.546619\pi\)
\(224\) 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 0.563244 0.826291i \(-0.309553\pi\)
−0.997211 + 0.0746378i \(0.976220\pi\)
\(234\) 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 −0.361060 0.932543i \(-0.617585\pi\)
0.988136 0.153584i \(-0.0490817\pi\)
\(240\) 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 0.354423 + 0.935085i \(0.384677\pi\)
−0.987019 + 0.160603i \(0.948656\pi\)
\(270\) 0 0
\(271\) −14.2444 24.6721i −0.865287 1.49872i −0.866762 0.498723i \(-0.833803\pi\)
0.00147433 0.999999i \(-0.499531\pi\)
\(272\) 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 0.971793 0.235837i \(-0.0757833\pi\)
−0.690138 + 0.723678i \(0.742450\pi\)
\(282\) 0 0
\(283\) 8.43422 + 14.6085i 0.501362 + 0.868385i 0.999999 + 0.00157378i \(0.000500949\pi\)
−0.498636 + 0.866811i \(0.666166\pi\)
\(284\) 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 −0.806517 0.591211i \(-0.798650\pi\)
0.915262 + 0.402858i \(0.131983\pi\)
\(294\) 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 0.975182 0.221403i \(-0.0710635\pi\)
−0.679332 + 0.733831i \(0.737730\pi\)
\(312\) 0 0
\(313\) −0.309930 + 0.536815i −0.0175183 + 0.0303426i −0.874652 0.484752i \(-0.838910\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(314\) −51.5440 −2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) 5.12422 8.87541i 0.287805 0.498493i −0.685481 0.728091i \(-0.740408\pi\)
0.973285 + 0.229598i \(0.0737412\pi\)
\(318\) 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 −0.437878 0.899035i \(-0.644270\pi\)
0.997526 0.0703042i \(-0.0223970\pi\)
\(332\) 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 −0.777695 0.628642i \(-0.783611\pi\)
0.933267 + 0.359182i \(0.116944\pi\)
\(338\) 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 0.960252 0.279136i \(-0.0900480\pi\)
−0.721865 + 0.692034i \(0.756715\pi\)
\(348\) 0 0
\(349\) −10.4874 18.1648i −0.561379 0.972337i −0.997376 0.0723893i \(-0.976938\pi\)
0.435997 0.899948i \(-0.356396\pi\)
\(350\) 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 0.945356 0.326040i \(-0.105714\pi\)
−0.755037 + 0.655682i \(0.772381\pi\)
\(360\) 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 0.976095 0.217344i \(-0.0697394\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(398\) 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 0.530250 0.847841i \(-0.322098\pi\)
−0.999377 + 0.0352893i \(0.988765\pi\)
\(410\) −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 −0.996169 0.0874539i \(-0.972127\pi\)
0.573822 + 0.818980i \(0.305460\pi\)
\(420\) 0 0
\(421\) −9.30039 16.1087i −0.453273 0.785092i 0.545314 0.838232i \(-0.316410\pi\)
−0.998587 + 0.0531397i \(0.983077\pi\)
\(422\) 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 −0.991407 0.130811i \(-0.958242\pi\)
0.608990 + 0.793178i \(0.291575\pi\)
\(432\) 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 −0.975532 0.219857i \(-0.929441\pi\)
0.678168 + 0.734907i \(0.262774\pi\)
\(440\) 7.51399 0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) −4.11537 + 7.12802i −0.195527 + 0.338663i −0.947073 0.321018i \(-0.895975\pi\)
0.751546 + 0.659680i \(0.229308\pi\)
\(444\) 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 −0.919196 0.393801i \(-0.871160\pi\)
0.800640 + 0.599146i \(0.204493\pi\)
\(458\) 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 0.761158 0.648567i \(-0.224631\pi\)
−0.942254 + 0.334898i \(0.891298\pi\)
\(462\) 0 0
\(463\) 4.58998 7.95008i 0.213314 0.369472i −0.739435 0.673228i \(-0.764907\pi\)
0.952750 + 0.303756i \(0.0982408\pi\)
\(464\) −33.0947 −1.53638
\(465\) 0 0
\(466\) −32.5979 −1.51007
\(467\) −6.88272 11.9212i −0.318494 0.551648i 0.661680 0.749787i \(-0.269844\pi\)
−0.980174 + 0.198138i \(0.936511\pi\)
\(468\) 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 −0.586086 0.810249i \(-0.699332\pi\)
0.994739 + 0.102441i \(0.0326653\pi\)
\(488\) −20.2849 + 35.1344i −0.918253 + 1.59046i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.02344 1.77266i 0.0461874 0.0799989i −0.842007 0.539466i \(-0.818626\pi\)
0.888195 + 0.459467i \(0.151960\pi\)
\(492\) 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 −0.854128 0.520062i \(-0.825909\pi\)
0.877451 + 0.479666i \(0.159242\pi\)
\(522\) 0 0
\(523\) −6.69094 11.5890i −0.292574 0.506754i 0.681843 0.731498i \(-0.261179\pi\)
−0.974418 + 0.224745i \(0.927845\pi\)
\(524\) −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 0.955695 + 0.294358i \(0.0951056\pi\)
−0.222927 + 0.974835i \(0.571561\pi\)
\(542\) −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 0.922533 0.385918i \(-0.126115\pi\)
−0.795481 + 0.605978i \(0.792782\pi\)
\(548\) 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 0.348756 + 0.937213i \(0.386604\pi\)
−0.986029 + 0.166575i \(0.946729\pi\)
\(558\) 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 0.995266 0.0971860i \(-0.0309842\pi\)
−0.581799 + 0.813333i \(0.697651\pi\)
\(564\) 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 −0.880070 0.474845i \(-0.842504\pi\)
0.851262 + 0.524740i \(0.175838\pi\)
\(570\) 0 0
\(571\) −8.69076 15.0528i −0.363697 0.629941i 0.624869 0.780729i \(-0.285152\pi\)
−0.988566 + 0.150788i \(0.951819\pi\)
\(572\) 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 0.434066 + 0.900881i \(0.357078\pi\)
−0.997219 + 0.0745283i \(0.976255\pi\)
\(578\) −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 0.778016 0.628245i \(-0.216226\pi\)
−0.933084 + 0.359659i \(0.882893\pi\)
\(588\) 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 −0.956642 0.291266i \(-0.905924\pi\)
0.226077 0.974109i \(-0.427410\pi\)
\(594\) 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 0.724576 0.689195i \(-0.242036\pi\)
−0.959148 + 0.282903i \(0.908702\pi\)
\(600\) 0 0
\(601\) −0.190030 0.329142i −0.00775150 0.0134260i 0.862124 0.506698i \(-0.169134\pi\)
−0.869875 + 0.493272i \(0.835801\pi\)
\(602\) 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 −0.930457 0.366400i \(-0.880590\pi\)
0.782540 + 0.622600i \(0.213924\pi\)
\(614\) −37.6077 + 65.1385i −1.51772 + 2.62877i
\(615\) 0 0
\(616\) 0 0
\(617\) −12.7427 + 22.0710i −0.513002 + 0.888546i 0.486884 + 0.873466i \(0.338133\pi\)
−0.999886 + 0.0150791i \(0.995200\pi\)
\(618\) 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 −0.984939 0.172903i \(-0.944685\pi\)
0.642208 + 0.766531i \(0.278019\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.7896 20.4202i 0.463855 0.803421i
\(647\) −12.6720 + 21.9485i −0.498186 + 0.862883i −0.999998 0.00209358i \(-0.999334\pi\)
0.501812 + 0.864977i \(0.332667\pi\)
\(648\) 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 0.950910 + 0.309467i \(0.100151\pi\)
−0.207449 + 0.978246i \(0.566516\pi\)
\(660\) 0 0
\(661\) −0.176866 0.306341i −0.00687930 0.0119153i 0.862565 0.505946i \(-0.168856\pi\)
−0.869445 + 0.494031i \(0.835523\pi\)
\(662\) −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 0.994539 0.104365i \(-0.0332811\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(674\) −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 −0.994479 0.104938i \(-0.966536\pi\)
0.588118 + 0.808775i \(0.299869\pi\)
\(678\) 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 −0.313969 0.949433i \(-0.601659\pi\)
0.979218 0.202811i \(-0.0650078\pi\)
\(684\) 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 −0.321801 0.946807i \(-0.604288\pi\)
0.980860 0.194716i \(-0.0623785\pi\)
\(692\) 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 −0.902016 0.431702i \(-0.857913\pi\)
0.824873 + 0.565318i \(0.191246\pi\)
\(710\) −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 −0.827106 0.562047i \(-0.810014\pi\)
−0.0731939 0.997318i \(-0.523319\pi\)
\(720\) 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 −0.942406 0.334470i \(-0.891443\pi\)
0.181543 0.983383i \(-0.441891\pi\)
\(728\) 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 −0.997544 0.0700384i \(-0.977688\pi\)
0.559427 + 0.828880i \(0.311021\pi\)
\(740\) −17.2581 + 29.8918i −0.634419 + 1.09885i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.26089 9.11213i 0.193003 0.334292i −0.753241 0.657745i \(-0.771510\pi\)
0.946244 + 0.323453i \(0.104844\pi\)
\(744\) 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 0.379324 + 0.925264i \(0.376157\pi\)
−0.990964 + 0.134128i \(0.957177\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −34.3442 + 59.4858i −1.23607 + 2.14094i
\(773\) 14.2978 24.7645i 0.514256 0.890717i −0.485607 0.874177i \(-0.661401\pi\)
0.999863 0.0165403i \(-0.00526518\pi\)
\(774\) 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 0.905738 + 0.423838i \(0.139317\pi\)
−0.0858145 + 0.996311i \(0.527349\pi\)
\(788\) −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
\(795\) 0 0