Properties

Label 1323.2.g.g.667.5
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 667.5
Root \(1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.g.361.5

$q$-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 \(-0.804901\pi\)
−0.817970 + 0.575260i \(0.804901\pi\)
\(6\) 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 \(-0.188171\pi\)
−0.897803 + 0.440397i \(0.854838\pi\)
\(14\) 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 \(-0.966245\pi\)
0.405525 0.914084i \(-0.367089\pi\)
\(18\) 0 0
\(19\) −0.986757 + 1.70911i −0.226378 + 0.392097i −0.956732 0.290971i \(-0.906022\pi\)
0.730354 + 0.683069i \(0.239355\pi\)
\(20\) 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 \(-0.615953\pi\)
0.987335 0.158648i \(-0.0507136\pi\)
\(32\) 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 \(-0.967076\pi\)
0.407911 0.913022i \(-0.366257\pi\)
\(42\) 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 0.998994 0.0448469i \(-0.0142800\pi\)
−0.538335 + 0.842731i \(0.680947\pi\)
\(48\) 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 −0.993513 0.113719i \(-0.963724\pi\)
0.595240 + 0.803548i \(0.297057\pi\)
\(60\) 0 0
\(61\) −4.01356 6.95169i −0.513884 0.890073i −0.999870 0.0161063i \(-0.994873\pi\)
0.485987 0.873966i \(-0.338460\pi\)
\(62\) 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 0.917976 0.396636i \(-0.129822\pi\)
−0.802485 + 0.596673i \(0.796489\pi\)
\(74\) −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 \(0.399527\pi\)
−0.978456 + 0.206457i \(0.933807\pi\)
\(84\) 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 \(0.454516\pi\)
−0.928402 + 0.371577i \(0.878817\pi\)
\(90\) 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 \(-0.993298\pi\)
0.518123 + 0.855306i \(0.326631\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −16.9897 + 29.4270i −1.69897 + 2.94270i
\(101\) 8.71176 0.866852 0.433426 0.901189i \(-0.357304\pi\)
0.433426 + 0.901189i \(0.357304\pi\)
\(102\) 0 0
\(103\) −8.02712 −0.790936 −0.395468 0.918480i \(-0.629418\pi\)
−0.395468 + 0.918480i \(0.629418\pi\)
\(104\) 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 \(-0.621305\pi\)
−0.371932 + 0.928260i \(0.621305\pi\)
\(132\) 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 \(-0.868383\pi\)
0.109888 0.993944i \(-0.464951\pi\)
\(140\) 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 \(-0.518258\pi\)
0.893265 0.449531i \(-0.148409\pi\)
\(158\) 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 0.791289 0.611443i \(-0.209410\pi\)
−0.925169 + 0.379555i \(0.876077\pi\)
\(168\) 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 \(-0.0927536\pi\)
−0.727721 + 0.685874i \(0.759420\pi\)
\(174\) 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 \(-0.646454\pi\)
−0.444037 + 0.896008i \(0.646454\pi\)
\(182\) 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 0.986865 0.161546i \(-0.0516479\pi\)
−0.633335 + 0.773877i \(0.718315\pi\)
\(200\) −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 \(0.453381\pi\)
−0.929722 + 0.368263i \(0.879953\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 17.1623 29.7259i 1.14162 1.97734i
\(227\) −6.11839 −0.406092 −0.203046 0.979169i \(-0.565084\pi\)
−0.203046 + 0.979169i \(0.565084\pi\)
\(228\) 0 0
\(229\) −1.46039 −0.0965052 −0.0482526 0.998835i \(-0.515365\pi\)
−0.0482526 + 0.998835i \(0.515365\pi\)
\(230\) 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 \(-0.447958\pi\)
0.162768 + 0.986664i \(0.447958\pi\)
\(242\) −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 \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(252\) 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 \(-0.577320\pi\)
−0.240526 + 0.970643i \(0.577320\pi\)
\(258\) 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 \(0.0513439\pi\)
−0.354423 + 0.935085i \(0.615323\pi\)
\(270\) 0 0
\(271\) 14.2444 24.6721i 0.865287 1.49872i −0.00147433 0.999999i \(-0.500469\pi\)
0.866762 0.498723i \(-0.166197\pi\)
\(272\) −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 \(0.333834\pi\)
−0.999999 + 0.00157378i \(0.999499\pi\)
\(284\) 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 \(-0.201350\pi\)
−0.915262 + 0.402858i \(0.868017\pi\)
\(294\) 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 \(-0.162605\pi\)
0.872335 + 0.488908i \(0.162605\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −63.2498 −3.59235
\(311\) −5.21739 + 9.03678i −0.295851 + 0.512429i −0.975182 0.221403i \(-0.928936\pi\)
0.679332 + 0.733831i \(0.262270\pi\)
\(312\) 0 0
\(313\) 0.309930 + 0.536815i 0.0175183 + 0.0303426i 0.874652 0.484752i \(-0.161090\pi\)
−0.857133 + 0.515095i \(0.827757\pi\)
\(314\) 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 \(-0.643604\pi\)
0.997376 0.0723893i \(-0.0230624\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.109631 + 0.189886i −0.00584335 + 0.0101210i
\(353\) −14.7654 −0.785881 −0.392941 0.919564i \(-0.628542\pi\)
−0.392941 + 0.919564i \(0.628542\pi\)
\(354\) 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 \(-0.407533\pi\)
0.286425 + 0.958103i \(0.407533\pi\)
\(368\) 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 \(-0.134190\pi\)
0.912447 + 0.409194i \(0.134190\pi\)
\(384\) 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 \(-0.930261\pi\)
0.676273 + 0.736651i \(0.263594\pi\)
\(398\) −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 \(-0.677902\pi\)
0.999377 + 0.0352893i \(0.0112353\pi\)
\(410\) −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 \(-0.0278730\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(420\) 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 \(-0.923999\pi\)
−0.971631 + 0.236501i \(0.923999\pi\)
\(434\) 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 \(-0.0705591\pi\)
−0.678168 + 0.734907i \(0.737226\pi\)
\(440\) −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 −0.761158 0.648567i \(-0.775369\pi\)
0.942254 + 0.334898i \(0.108702\pi\)
\(462\) 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 −0.661680 0.749787i \(-0.730156\pi\)
0.980174 + 0.198138i \(0.0634895\pi\)
\(468\) 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 \(-0.436222\pi\)
0.199025 + 0.979994i \(0.436222\pi\)
\(480\) 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 \(-0.463598\pi\)
0.114111 + 0.993468i \(0.463598\pi\)
\(504\) 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 \(-0.727073\pi\)
−0.654386 + 0.756161i \(0.727073\pi\)
\(510\) 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 \(-0.174091\pi\)
−0.877451 + 0.479666i \(0.840758\pi\)
\(522\) 0 0
\(523\) 6.69094 11.5890i 0.292574 0.506754i −0.681843 0.731498i \(-0.738821\pi\)
0.974418 + 0.224745i \(0.0721548\pi\)
\(524\) 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 −0.995266 0.0971860i \(-0.969016\pi\)
0.581799 + 0.813333i \(0.302349\pi\)
\(564\) 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 \(0.0237451\pi\)
−0.434066 + 0.900881i \(0.642922\pi\)
\(578\) −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 \(-0.783774\pi\)
0.933084 + 0.359659i \(0.117107\pi\)
\(588\) 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 \(-0.572590\pi\)
0.956642 0.291266i \(-0.0940765\pi\)
\(594\) 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 −0.862124 0.506698i \(-0.830866\pi\)
0.869875 + 0.493272i \(0.164199\pi\)
\(602\) 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 \(-0.622795\pi\)
−0.376275 + 0.926508i \(0.622795\pi\)
\(608\) 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 \(-0.270087\pi\)
0.661108 + 0.750291i \(0.270087\pi\)
\(620\) −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 \(-0.0553147\pi\)
−0.642208 + 0.766531i \(0.721981\pi\)
\(644\) 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 \(-0.000666408\pi\)
−0.501812 + 0.864977i \(0.667333\pi\)
\(648\) 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 −0.862565 0.505946i \(-0.831144\pi\)
0.869445 + 0.494031i \(0.164477\pi\)
\(662\) −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 0.994479 0.104938i \(-0.0334643\pi\)
−0.588118 + 0.808775i \(0.700131\pi\)
\(678\) 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 \(-0.937622\pi\)
0.321801 0.946807i \(-0.395712\pi\)
\(692\) −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 \(-0.476681\pi\)
0.827106 0.562047i \(-0.189986\pi\)
\(720\) 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 \(-0.558109\pi\)
0.942406 0.334470i \(-0.108557\pi\)
\(728\) 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 \(-0.309238\pi\)
0.564062 + 0.825733i \(0.309238\pi\)
\(734\) 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 \(-0.667161\pi\)
−0.501345 + 0.865247i \(0.667161\pi\)
\(762\) 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 \(0.0428233\pi\)
−0.379324 + 0.925264i \(0.623843\pi\)
\(770\) 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 \(-0.994735\pi\)
0.485607 0.874177i \(-0.338599\pi\)
\(774\) 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 \(0.472651\pi\)
−0.905738 + 0.423838i \(0.860683\pi\)
\(788\) −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