Properties

Label 1323.2.h.g.226.2
Level $1323$
Weight $2$
Character 1323.226
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.h (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: \(\Z[a_1, \ldots, a_{11}]\)
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 226.2
Root \(-1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.g.802.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.46050 q^{2} +4.05408 q^{4} +(1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})\) \(q-2.46050 q^{2} +4.05408 q^{4} +(1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +(-4.50036 - 7.79485i) q^{10} +(0.203210 - 0.351971i) q^{11} +(-0.243398 + 0.421578i) q^{13} +4.32743 q^{16} +(-2.42792 - 4.20528i) q^{17} +(-0.986757 + 1.70911i) q^{19} +(7.41507 + 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.32383 + 4.02499i) q^{23} +(-4.19076 + 7.25860i) q^{25} +(0.598883 - 1.03729i) q^{26} +(3.82383 + 6.62307i) q^{29} -7.02720 q^{31} -0.539495 q^{32} +(5.97391 + 10.3471i) q^{34} +(-1.16372 + 2.01561i) q^{37} +(2.42792 - 4.20528i) q^{38} +(-9.24411 - 16.0113i) q^{40} +(-3.75700 + 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(0.823832 - 1.42692i) q^{44} +(-5.71780 - 9.90352i) q^{46} -6.31623 q^{47} +(10.3114 - 17.8598i) q^{50} +(-0.986757 + 1.70911i) q^{52} +(-1.78434 - 3.09056i) q^{53} +1.48672 q^{55} +(-9.40856 - 16.2961i) q^{58} +6.11839 q^{59} +8.02712 q^{61} +17.2905 q^{62} -7.32743 q^{64} -1.78074 q^{65} +3.60078 q^{67} +(-9.84299 - 17.0486i) q^{68} -8.46050 q^{71} +(0.986757 + 1.70911i) q^{73} +(2.86333 - 4.95943i) q^{74} +(-4.00040 + 6.92889i) q^{76} +8.16225 q^{79} +(7.91503 + 13.7092i) q^{80} +(9.24411 - 16.0113i) q^{82} +(-6.08600 - 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +(-2.86333 - 4.95943i) q^{86} +(-1.02704 + 1.77889i) q^{88} +(-7.41507 + 12.8433i) q^{89} +(9.42101 + 16.3177i) q^{92} +15.5411 q^{94} -7.21926 q^{95} +(-4.74375 - 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 12q^{4} - 24q^{8} + O(q^{10}) \) \( 12q - 4q^{2} + 12q^{4} - 24q^{8} + 8q^{11} + 12q^{16} - 6q^{22} + 4q^{23} - 12q^{25} + 22q^{29} - 32q^{32} + 6q^{37} - 6q^{43} - 14q^{44} - 12q^{46} + 56q^{50} + 28q^{53} - 18q^{58} - 48q^{64} + 12q^{65} - 76q^{71} + 36q^{74} - 12q^{79} + 30q^{85} - 36q^{86} + 6q^{88} + 62q^{92} - 120q^{95} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46050 −1.73984 −0.869920 0.493193i \(-0.835830\pi\)
−0.869920 + 0.493193i \(0.835830\pi\)
\(3\) 0 0
\(4\) 4.05408 2.02704
\(5\) 1.82904 + 3.16799i 0.817970 + 1.41677i 0.907175 + 0.420753i \(0.138234\pi\)
−0.0892047 + 0.996013i \(0.528433\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −5.05408 −1.78689
\(9\) 0 0
\(10\) −4.50036 7.79485i −1.42314 2.46495i
\(11\) 0.203210 0.351971i 0.0612702 0.106123i −0.833763 0.552122i \(-0.813818\pi\)
0.895033 + 0.445999i \(0.147152\pi\)
\(12\) 0 0
\(13\) −0.243398 + 0.421578i −0.0675065 + 0.116925i −0.897803 0.440397i \(-0.854838\pi\)
0.830297 + 0.557322i \(0.188171\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.32743 1.08186
\(17\) −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
\(23\) 2.32383 + 4.02499i 0.484552 + 0.839269i 0.999843 0.0177464i \(-0.00564915\pi\)
−0.515290 + 0.857016i \(0.672316\pi\)
\(24\) 0 0
\(25\) −4.19076 + 7.25860i −0.838151 + 1.45172i
\(26\) 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
\(31\) −7.02720 −1.26212 −0.631061 0.775733i \(-0.717380\pi\)
−0.631061 + 0.775733i \(0.717380\pi\)
\(32\) −0.539495 −0.0953702
\(33\) 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 \(0.227941\pi\)
\(38\) 2.42792 4.20528i 0.393861 0.682187i
\(39\) 0 0
\(40\) −9.24411 16.0113i −1.46162 2.53160i
\(41\) −3.75700 + 6.50731i −0.586744 + 1.01627i 0.407911 + 0.913022i \(0.366257\pi\)
−0.994655 + 0.103249i \(0.967076\pi\)
\(42\) 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
\(47\) −6.31623 −0.921317 −0.460658 0.887578i \(-0.652387\pi\)
−0.460658 + 0.887578i \(0.652387\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 10.3114 17.8598i 1.45825 2.52576i
\(51\) 0 0
\(52\) −0.986757 + 1.70911i −0.136839 + 0.237011i
\(53\) −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
\(58\) −9.40856 16.2961i −1.23540 2.13978i
\(59\) 6.11839 0.796546 0.398273 0.917267i \(-0.369610\pi\)
0.398273 + 0.917267i \(0.369610\pi\)
\(60\) 0 0
\(61\) 8.02712 1.02777 0.513884 0.857860i \(-0.328206\pi\)
0.513884 + 0.857860i \(0.328206\pi\)
\(62\) 17.2905 2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −1.78074 −0.220873
\(66\) 0 0
\(67\) 3.60078 0.439905 0.219952 0.975511i \(-0.429410\pi\)
0.219952 + 0.975511i \(0.429410\pi\)
\(68\) −9.84299 17.0486i −1.19364 2.06744i
\(69\) 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 \(0.796489\pi\)
\(74\) 2.86333 4.95943i 0.332855 0.576522i
\(75\) 0 0
\(76\) −4.00040 + 6.92889i −0.458877 + 0.794798i
\(77\) 0 0
\(78\) 0 0
\(79\) 8.16225 0.918325 0.459163 0.888352i \(-0.348150\pi\)
0.459163 + 0.888352i \(0.348150\pi\)
\(80\) 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 \(-0.933807\pi\)
0.310431 0.950596i \(-0.399527\pi\)
\(84\) 0 0
\(85\) 8.88151 15.3832i 0.963336 1.66855i
\(86\) −2.86333 4.95943i −0.308760 0.534789i
\(87\) 0 0
\(88\) −1.02704 + 1.77889i −0.109483 + 0.189630i
\(89\) −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
\(94\) 15.5411 1.60294
\(95\) −7.21926 −0.740681
\(96\) 0 0
\(97\) −4.74375 8.21642i −0.481655 0.834251i 0.518123 0.855306i \(-0.326631\pi\)
−0.999778 + 0.0210547i \(0.993298\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −16.9897 + 29.4270i −1.69897 + 2.94270i
\(101\) −4.35588 + 7.54461i −0.433426 + 0.750716i −0.997166 0.0752364i \(-0.976029\pi\)
0.563739 + 0.825953i \(0.309362\pi\)
\(102\) 0 0
\(103\) 4.01356 + 6.95169i 0.395468 + 0.684970i 0.993161 0.116755i \(-0.0372492\pi\)
−0.597693 + 0.801725i \(0.703916\pi\)
\(104\) 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 \(0.873084\pi\)
\(110\) −3.65808 −0.348784
\(111\) 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
\(115\) −8.50075 + 14.7237i −0.792699 + 1.37300i
\(116\) 15.5021 + 26.8505i 1.43934 + 2.49301i
\(117\) 0 0
\(118\) −15.0543 −1.38586
\(119\) 0 0
\(120\) 0 0
\(121\) 5.41741 + 9.38323i 0.492492 + 0.853021i
\(122\) −19.7508 −1.78815
\(123\) 0 0
\(124\) −28.4889 −2.55837
\(125\) −12.3698 −1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) 19.1082 1.68894
\(129\) 0 0
\(130\) 4.38151 0.384284
\(131\) 4.25696 + 7.37327i 0.371932 + 0.644205i 0.989863 0.142027i \(-0.0453621\pi\)
−0.617931 + 0.786233i \(0.712029\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.85973 −0.765364
\(135\) 0 0
\(136\) 12.2709 + 21.2538i 1.05222 + 1.82250i
\(137\) 0.188621 0.326702i 0.0161150 0.0279120i −0.857855 0.513891i \(-0.828204\pi\)
0.873970 + 0.485979i \(0.161537\pi\)
\(138\) 0 0
\(139\) −9.50067 + 16.4556i −0.805837 + 1.39575i 0.109888 + 0.993944i \(0.464951\pi\)
−0.915725 + 0.401806i \(0.868383\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 20.8171 1.74693
\(143\) 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
\(149\) −4.85087 8.40196i −0.397399 0.688315i 0.596005 0.802981i \(-0.296754\pi\)
−0.993404 + 0.114665i \(0.963420\pi\)
\(150\) 0 0
\(151\) 6.41741 11.1153i 0.522242 0.904549i −0.477424 0.878673i \(-0.658429\pi\)
0.999665 0.0258756i \(-0.00823738\pi\)
\(152\) 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
\(157\) −20.9485 −1.67187 −0.835937 0.548825i \(-0.815075\pi\)
−0.835937 + 0.548825i \(0.815075\pi\)
\(158\) −20.0833 −1.59774
\(159\) 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 \(0.0226554\pi\)
\(164\) −15.2312 + 26.3812i −1.18936 + 2.06002i
\(165\) 0 0
\(166\) 14.9746 + 25.9368i 1.16226 + 2.01309i
\(167\) −1.73012 + 2.99665i −0.133880 + 0.231888i −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(168\) 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
\(173\) −6.05361 −0.460247 −0.230124 0.973161i \(-0.573913\pi\)
−0.230124 + 0.973161i \(0.573913\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.879379 1.52313i 0.0662857 0.114810i
\(177\) 0 0
\(178\) 18.2448 31.6010i 1.36751 2.36859i
\(179\) 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
\(184\) −11.7448 20.3427i −0.865841 1.49968i
\(185\) −8.51392 −0.625956
\(186\) 0 0
\(187\) −1.97351 −0.144318
\(188\) −25.6065 −1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) −9.14027 −0.661367 −0.330683 0.943742i \(-0.607279\pi\)
−0.330683 + 0.943742i \(0.607279\pi\)
\(192\) 0 0
\(193\) 16.9430 1.21958 0.609792 0.792562i \(-0.291253\pi\)
0.609792 + 0.792562i \(0.291253\pi\)
\(194\) 11.6720 + 20.2165i 0.838003 + 1.45146i
\(195\) 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 \(0.718315\pi\)
\(200\) 21.1804 36.6856i 1.49768 2.59406i
\(201\) 0 0
\(202\) 10.7177 18.5635i 0.754092 1.30613i
\(203\) 0 0
\(204\) 0 0
\(205\) −27.4868 −1.91976
\(206\) −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 \(0.220521\pi\)
\(212\) −7.23385 12.5294i −0.496823 0.860523i
\(213\) 0 0
\(214\) −15.7989 + 27.3645i −1.07999 + 1.87060i
\(215\) −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
\(220\) 6.02728 0.406359
\(221\) 2.36381 0.159007
\(222\) 0 0
\(223\) −11.7044 20.2727i −0.783786 1.35756i −0.929722 0.368263i \(-0.879953\pi\)
0.145936 0.989294i \(-0.453381\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 17.1623 29.7259i 1.14162 1.97734i
\(227\) 3.05919 5.29868i 0.203046 0.351686i −0.746463 0.665427i \(-0.768249\pi\)
0.949508 + 0.313742i \(0.101583\pi\)
\(228\) 0 0
\(229\) 0.730195 + 1.26473i 0.0482526 + 0.0835760i 0.889143 0.457630i \(-0.151301\pi\)
−0.840890 + 0.541206i \(0.817968\pi\)
\(230\) 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
\(236\) 24.8045 1.61463
\(237\) 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
\(241\) −2.52684 + 4.37662i −0.162768 + 0.281923i −0.935860 0.352371i \(-0.885376\pi\)
0.773092 + 0.634294i \(0.218709\pi\)
\(242\) −13.3296 23.0875i −0.856857 1.48412i
\(243\) 0 0
\(244\) 32.5426 2.08333
\(245\) 0 0
\(246\) 0 0
\(247\) −0.480350 0.831990i −0.0305639 0.0529383i
\(248\) 35.5161 2.25527
\(249\) 0 0
\(250\) 30.4360 1.92494
\(251\) −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
\(254\) 38.2455 2.39974
\(255\) 0 0
\(256\) −32.3609 −2.02256
\(257\) 3.85592 + 6.67865i 0.240526 + 0.416603i 0.960864 0.277020i \(-0.0893469\pi\)
−0.720338 + 0.693623i \(0.756014\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7.21926 −0.447720
\(261\) 0 0
\(262\) −10.4743 18.1420i −0.647102 1.12081i
\(263\) 2.10603 3.64776i 0.129864 0.224930i −0.793760 0.608231i \(-0.791879\pi\)
0.923624 + 0.383301i \(0.125213\pi\)
\(264\) 0 0
\(265\) 6.52724 11.3055i 0.400965 0.694492i
\(266\) 0 0
\(267\) 0 0
\(268\) 14.5979 0.891706
\(269\) 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
\(275\) 1.70321 + 2.95005i 0.102707 + 0.177895i
\(276\) 0 0
\(277\) −8.58113 + 14.8629i −0.515590 + 0.893028i 0.484246 + 0.874932i \(0.339094\pi\)
−0.999836 + 0.0180962i \(0.994239\pi\)
\(278\) 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
\(283\) 16.8684 1.00272 0.501362 0.865237i \(-0.332832\pi\)
0.501362 + 0.865237i \(0.332832\pi\)
\(284\) −34.2996 −2.03531
\(285\) 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
\(290\) 34.4172 59.6124i 2.02105 3.50056i
\(291\) 0 0
\(292\) 4.00040 + 6.92889i 0.234105 + 0.405483i
\(293\) −1.86143 + 3.22409i −0.108746 + 0.188353i −0.915262 0.402858i \(-0.868017\pi\)
0.806517 + 0.591211i \(0.201350\pi\)
\(294\) 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
\(299\) −2.26247 −0.130842
\(300\) 0 0
\(301\) 0 0
\(302\) −15.7901 + 27.3492i −0.908617 + 1.57377i
\(303\) 0 0
\(304\) −4.27012 + 7.39607i −0.244908 + 0.424194i
\(305\) 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
\(310\) 31.6249 + 54.7759i 1.79617 + 3.11106i
\(311\) 10.4348 0.591702 0.295851 0.955234i \(-0.404397\pi\)
0.295851 + 0.955234i \(0.404397\pi\)
\(312\) 0 0
\(313\) −0.619860 −0.0350366 −0.0175183 0.999847i \(-0.505577\pi\)
−0.0175183 + 0.999847i \(0.505577\pi\)
\(314\) 51.5440 2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) −10.2484 −0.575610 −0.287805 0.957689i \(-0.592925\pi\)
−0.287805 + 0.957689i \(0.592925\pi\)
\(318\) 0 0
\(319\) 3.10817 0.174024
\(320\) −13.4021 23.2132i −0.749203 1.29766i
\(321\) 0 0
\(322\) 0 0
\(323\) 9.58307 0.533216
\(324\) 0 0
\(325\) −2.04005 3.53346i −0.113161 0.196001i
\(326\) −13.7324 + 23.7852i −0.760567 + 1.31734i
\(327\) 0 0
\(328\) 18.9882 32.8885i 1.04845 1.81596i
\(329\) 0 0
\(330\) 0 0
\(331\) −20.3638 −1.11930 −0.559648 0.828730i \(-0.689064\pi\)
−0.559648 + 0.828730i \(0.689064\pi\)
\(332\) −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 \(0.116944\pi\)
\(338\) −15.7017 27.1962i −0.854062 1.47928i
\(339\) 0 0
\(340\) 36.0064 62.3649i 1.95272 3.38221i
\(341\) −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
\(346\) 14.8949 0.800756
\(347\) −8.88132 −0.476774 −0.238387 0.971170i \(-0.576619\pi\)
−0.238387 + 0.971170i \(0.576619\pi\)
\(348\) 0 0
\(349\) 10.4874 + 18.1648i 0.561379 + 0.972337i 0.997376 + 0.0723893i \(0.0230624\pi\)
−0.435997 + 0.899948i \(0.643604\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.109631 + 0.189886i −0.00584335 + 0.0101210i
\(353\) 7.38268 12.7872i 0.392941 0.680593i −0.599895 0.800078i \(-0.704791\pi\)
0.992836 + 0.119485i \(0.0381245\pi\)
\(354\) 0 0
\(355\) −15.4746 26.8028i −0.821306 1.42254i
\(356\) −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
\(362\) 29.3977 1.54511
\(363\) 0 0
\(364\) 0 0
\(365\) −3.60963 + 6.25206i −0.188937 + 0.327248i
\(366\) 0 0
\(367\) −5.48711 + 9.50396i −0.286425 + 0.496103i −0.972954 0.231000i \(-0.925800\pi\)
0.686529 + 0.727103i \(0.259134\pi\)
\(368\) 10.0562 + 17.4179i 0.524217 + 0.907970i
\(369\) 0 0
\(370\) 20.9485 1.08906
\(371\) 0 0
\(372\) 0 0
\(373\) 0.271884 + 0.470916i 0.0140776 + 0.0243831i 0.872978 0.487759i \(-0.162185\pi\)
−0.858901 + 0.512142i \(0.828852\pi\)
\(374\) 4.85584 0.251090
\(375\) 0 0
\(376\) 31.9228 1.64629
\(377\) −3.72286 −0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) −29.2675 −1.50139
\(381\) 0 0
\(382\) 22.4897 1.15067
\(383\) −17.8569 30.9291i −0.912447 1.58041i −0.810596 0.585606i \(-0.800857\pi\)
−0.101851 0.994800i \(-0.532477\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −41.6883 −2.12188
\(387\) 0 0
\(388\) −19.2316 33.3101i −0.976336 1.69106i
\(389\) 19.3296 33.4798i 0.980048 1.69749i 0.317892 0.948127i \(-0.397025\pi\)
0.662156 0.749366i \(-0.269641\pi\)
\(390\) 0 0
\(391\) 11.2842 19.5447i 0.570664 0.988420i
\(392\) 0 0
\(393\) 0 0
\(394\) −52.4513 −2.64246
\(395\) 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
\(401\) 16.1783 + 28.0216i 0.807906 + 1.39933i 0.914312 + 0.405011i \(0.132732\pi\)
−0.106406 + 0.994323i \(0.533934\pi\)
\(402\) 0 0
\(403\) 1.71041 2.96251i 0.0852015 0.147573i
\(404\) −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
\(409\) −18.9750 −0.938254 −0.469127 0.883131i \(-0.655431\pi\)
−0.469127 + 0.883131i \(0.655431\pi\)
\(410\) 67.6313 3.34007
\(411\) 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
\(416\) 0.131312 0.227439i 0.00643811 0.0111511i
\(417\) 0 0
\(418\) −0.986757 1.70911i −0.0482639 0.0835955i
\(419\) 8.64523 14.9740i 0.422347 0.731526i −0.573822 0.818980i \(-0.694540\pi\)
0.996169 + 0.0874539i \(0.0278730\pi\)
\(420\) 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
\(425\) 40.6993 1.97421
\(426\) 0 0
\(427\) 0 0
\(428\) 26.0313 45.0876i 1.25827 2.17939i
\(429\) 0 0
\(430\) 10.4743 18.1420i 0.505114 0.874883i
\(431\) −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
\(436\) −5.27188 9.13117i −0.252477 0.437304i
\(437\) −9.17223 −0.438767
\(438\) 0 0
\(439\) −12.4609 −0.594728 −0.297364 0.954764i \(-0.596108\pi\)
−0.297364 + 0.954764i \(0.596108\pi\)
\(440\) −7.51399 −0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) 8.23073 0.391054 0.195527 0.980698i \(-0.437358\pi\)
0.195527 + 0.980698i \(0.437358\pi\)
\(444\) 0 0
\(445\) −54.2498 −2.57169
\(446\) 28.7988 + 49.8810i 1.36366 + 2.36193i
\(447\) 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
\(452\) −28.2776 + 48.9783i −1.33007 + 2.30374i
\(453\) 0 0
\(454\) −7.52716 + 13.0374i −0.353267 + 0.611876i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.06887 0.237112 0.118556 0.992947i \(-0.462174\pi\)
0.118556 + 0.992947i \(0.462174\pi\)
\(458\) −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 \(-0.108702\pi\)
−0.761158 + 0.648567i \(0.775369\pi\)
\(462\) 0 0
\(463\) 4.58998 7.95008i 0.213314 0.369472i −0.739435 0.673228i \(-0.764907\pi\)
0.952750 + 0.303756i \(0.0982408\pi\)
\(464\) 16.5474 + 28.6609i 0.768192 + 1.33055i
\(465\) 0 0
\(466\) 16.2989 28.2306i 0.755033 1.30776i
\(467\) 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
\(472\) −30.9228 −1.42334
\(473\) 0.945916 0.0434933
\(474\) 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
\(479\) −4.35588 + 7.54461i −0.199025 + 0.344722i −0.948213 0.317636i \(-0.897111\pi\)
0.749187 + 0.662358i \(0.230444\pi\)
\(480\) 0 0
\(481\) −0.566492 0.981194i −0.0258298 0.0447386i
\(482\) 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 \(0.699332\pi\)
\(488\) −40.5697 −1.83651
\(489\) 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
\(493\) 18.5679 32.1606i 0.836257 1.44844i
\(494\) 1.18190 + 2.04712i 0.0531763 + 0.0921041i
\(495\) 0 0
\(496\) −30.4097 −1.36544
\(497\) 0 0
\(498\) 0 0
\(499\) 19.5438 + 33.8508i 0.874899 + 1.51537i 0.856870 + 0.515532i \(0.172406\pi\)
0.0180291 + 0.999837i \(0.494261\pi\)
\(500\) −50.1484 −2.24270
\(501\) 0 0
\(502\) 37.1358 1.65745
\(503\) 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
\(506\) −4.64766 −0.206614
\(507\) 0 0
\(508\) −63.0157 −2.79587
\(509\) 14.7636 + 25.5713i 0.654386 + 1.13343i 0.982047 + 0.188634i \(0.0604060\pi\)
−0.327662 + 0.944795i \(0.606261\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 41.4078 1.82998
\(513\) 0 0
\(514\) −9.48751 16.4328i −0.418476 0.724822i
\(515\) −14.6819 + 25.4298i −0.646962 + 1.12057i
\(516\) 0 0
\(517\) −1.28352 + 2.22313i −0.0564493 + 0.0977730i
\(518\) 0 0
\(519\) 0 0
\(520\) 9.00000 0.394676
\(521\) −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
\(527\) 17.0615 + 29.5513i 0.743210 + 1.28728i
\(528\) 0 0
\(529\) 0.699612 1.21176i 0.0304179 0.0526853i
\(530\) −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
\(535\) 46.9771 2.03100
\(536\) −18.1986 −0.786061
\(537\) 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 \(-0.0951056\pi\)
\(542\) −35.0485 + 60.7058i −1.50546 + 2.60754i
\(543\) 0 0
\(544\) 1.30985 + 2.26873i 0.0561594 + 0.0972709i
\(545\) 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
\(551\) −15.0928 −0.642974
\(552\) 0 0
\(553\) 0 0
\(554\) 21.1139 36.5704i 0.897044 1.55373i
\(555\) 0 0
\(556\) −38.5165 + 66.7126i −1.63346 + 2.82924i
\(557\) −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
\(562\) −11.6170 20.1213i −0.490035 0.848765i
\(563\) 19.6212 0.826935 0.413468 0.910519i \(-0.364317\pi\)
0.413468 + 0.910519i \(0.364317\pi\)
\(564\) 0 0
\(565\) −51.0308 −2.14688
\(566\) −41.5049 −1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) 1.37432 0.0576144 0.0288072 0.999585i \(-0.490829\pi\)
0.0288072 + 0.999585i \(0.490829\pi\)
\(570\) 0 0
\(571\) 17.3815 0.727394 0.363697 0.931517i \(-0.381514\pi\)
0.363697 + 0.931517i \(0.381514\pi\)
\(572\) 0.401038 + 0.694619i 0.0167683 + 0.0290435i
\(573\) 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 \(0.642922\pi\)
\(578\) 8.09406 14.0193i 0.336668 0.583127i
\(579\) 0 0
\(580\) −56.7080 + 98.2211i −2.35467 + 4.07841i
\(581\) 0 0
\(582\) 0 0
\(583\) −1.45038 −0.0600687
\(584\) −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 \(-0.117107\pi\)
−0.778016 + 0.628245i \(0.783774\pi\)
\(588\) 0 0
\(589\) 6.93414 12.0103i 0.285716 0.494875i
\(590\) −27.5349 47.6919i −1.13359 1.96344i
\(591\) 0 0
\(592\) −5.03590 + 8.72243i −0.206974 + 0.358490i
\(593\) 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
\(598\) 5.56681 0.227644
\(599\) 11.4821 0.469146 0.234573 0.972099i \(-0.424631\pi\)
0.234573 + 0.972099i \(0.424631\pi\)
\(600\) 0 0
\(601\) 0.190030 + 0.329142i 0.00775150 + 0.0134260i 0.869875 0.493272i \(-0.164199\pi\)
−0.862124 + 0.506698i \(0.830866\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 26.0167 45.0623i 1.05861 1.83356i
\(605\) −19.8173 + 34.3246i −0.805688 + 1.39549i
\(606\) 0 0
\(607\) 9.27044 + 16.0569i 0.376275 + 0.651728i 0.990517 0.137390i \(-0.0438713\pi\)
−0.614242 + 0.789118i \(0.710538\pi\)
\(608\) 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 \(0.880590\pi\)
\(614\) −75.2154 −3.03545
\(615\) 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
\(619\) −16.4482 + 28.4891i −0.661108 + 1.14507i 0.319217 + 0.947682i \(0.396580\pi\)
−0.980325 + 0.197391i \(0.936753\pi\)
\(620\) −52.1072 90.2523i −2.09267 3.62462i
\(621\) 0 0
\(622\) −25.6748 −1.02947
\(623\) 0 0
\(624\) 0 0
\(625\) −1.67111 2.89444i −0.0668443 0.115778i
\(626\) 1.52517 0.0609580
\(627\) 0 0
\(628\) −84.9271 −3.38896
\(629\) 11.3016 0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) −41.2527 −1.64094
\(633\) 0 0
\(634\) 25.2163 1.00147
\(635\) −28.4301 49.2424i −1.12822 1.95413i
\(636\) 0 0
\(637\) 0 0
\(638\) −7.64766 −0.302774
\(639\) 0 0
\(640\) 34.9496 + 60.5344i 1.38150 + 2.39283i
\(641\) 5.73025 9.92509i 0.226331 0.392017i −0.730387 0.683034i \(-0.760660\pi\)
0.956718 + 0.291016i \(0.0939934\pi\)
\(642\) 0 0
\(643\) 8.69078 15.0529i 0.342731 0.593627i −0.642208 0.766531i \(-0.721981\pi\)
0.984939 + 0.172903i \(0.0553147\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −23.5792 −0.927711
\(647\) 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
\(653\) 7.04163 + 12.1965i 0.275560 + 0.477284i 0.970276 0.242000i \(-0.0778033\pi\)
−0.694716 + 0.719284i \(0.744470\pi\)
\(654\) 0 0
\(655\) −15.5723 + 26.9720i −0.608459 + 1.05388i
\(656\) −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
\(661\) −0.353732 −0.0137586 −0.00687930 0.999976i \(-0.502190\pi\)
−0.00687930 + 0.999976i \(0.502190\pi\)
\(662\) 50.1052 1.94740
\(663\) 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
\(668\) −7.01403 + 12.1487i −0.271381 + 0.470046i
\(669\) 0 0
\(670\) −16.2048 28.0675i −0.626045 1.08434i
\(671\) 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
\(677\) −21.1464 −0.812721 −0.406361 0.913713i \(-0.633202\pi\)
−0.406361 + 0.913713i \(0.633202\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −44.8879 + 77.7482i −1.72137 + 2.98151i
\(681\) 0 0
\(682\) 3.51360 6.08573i 0.134543 0.233035i
\(683\) 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
\(688\) 5.03590 + 8.72243i 0.191992 + 0.332539i
\(689\) 1.73722 0.0661827
\(690\) 0 0
\(691\) 34.6492 1.31812 0.659059 0.752091i \(-0.270955\pi\)
0.659059 + 0.752091i \(0.270955\pi\)
\(692\) −24.5418 −0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) −69.5083 −2.63660
\(696\) 0 0
\(697\) 36.4868 1.38203
\(698\) −25.8044 44.6945i −0.976710 1.69171i
\(699\) 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
\(704\) −1.48901 + 2.57904i −0.0561192 + 0.0972012i
\(705\) 0 0
\(706\) −18.1651 + 31.4629i −0.683654 + 1.18412i
\(707\) 0 0
\(708\) 0 0
\(709\) 4.10817 0.154286 0.0771428 0.997020i \(-0.475420\pi\)
0.0771428 + 0.997020i \(0.475420\pi\)
\(710\) 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
\(716\) 18.5131 + 32.0657i 0.691868 + 1.19835i
\(717\) 0 0
\(718\) −8.87266 + 15.3679i −0.331125 + 0.573525i
\(719\) 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
\(724\) −48.4375 −1.80016
\(725\) −64.0990 −2.38058
\(726\) 0 0
\(727\) 20.5151 + 35.5332i 0.760863 + 1.31785i 0.942406 + 0.334470i \(0.108557\pi\)
−0.181543 + 0.983383i \(0.558109\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 8.88151 15.3832i 0.328720 0.569359i
\(731\) 5.65082 9.78750i 0.209003 0.362004i
\(732\) 0 0
\(733\) −15.2714 26.4508i −0.564062 0.976983i −0.997136 0.0756253i \(-0.975905\pi\)
0.433075 0.901358i \(-0.357429\pi\)
\(734\) 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 \(0.977688\pi\)
\(740\) −34.5161 −1.26884
\(741\) 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
\(745\) 17.7449 30.7350i 0.650121 1.12604i
\(746\) −0.668971 1.15869i −0.0244928 0.0424227i
\(747\) 0 0
\(748\) −8.00079 −0.292538
\(749\) 0 0
\(750\) 0 0
\(751\) 5.13521 + 8.89445i 0.187386 + 0.324563i 0.944378 0.328862i \(-0.106665\pi\)
−0.756992 + 0.653425i \(0.773332\pi\)
\(752\) −27.3330 −0.996734
\(753\) 0 0
\(754\) 9.16010 0.333591
\(755\) 46.9507 1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) 55.8319 2.02791
\(759\) 0 0
\(760\) 36.4868 1.32351
\(761\) 13.8302 + 23.9547i 0.501345 + 0.868355i 0.999999 + 0.00155404i \(0.000494668\pi\)
−0.498654 + 0.866801i \(0.666172\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −37.0554 −1.34062
\(765\) 0 0
\(766\) 43.9371 + 76.1013i 1.58751 + 2.74965i
\(767\) −1.48920 + 2.57938i −0.0537720 + 0.0931359i
\(768\) 0 0
\(769\) 16.9613 29.3778i 0.611640 1.05939i −0.379324 0.925264i \(-0.623843\pi\)
0.990964 0.134128i \(-0.0428233\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 68.6883 2.47215
\(773\) −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
\(779\) −7.41449 12.8423i −0.265652 0.460122i
\(780\) 0 0
\(781\) −1.71926 + 2.97785i −0.0615200 + 0.106556i
\(782\) −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
\(787\) 46.0035 1.63985 0.819923 0.572473i \(-0.194016\pi\)
0.819923 + 0.572473i \(0.194016\pi\)
\(788\) 86.4222 3.07866
\(789\) 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
\(794\) 14.6988 25.4591i 0.521642 0.903511i
\(795\) 0