Properties

Label 1950.2.bc.k.751.1
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + 115386 x^{4} - 135130 x^{3} + 113253 x^{2} - 54888 x + 14089\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.1
Root \(0.500000 - 4.99624i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.k.901.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.83209 + 2.78981i) q^{11} +1.00000 q^{12} +(3.19076 - 1.67900i) q^{13} +5.13022 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.641326 + 1.11081i) q^{17} -1.00000i q^{18} +(5.75861 + 3.32474i) q^{19} -5.13022i q^{21} +(2.78981 - 4.83209i) q^{22} +(-3.43113 - 5.94290i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.92378 + 3.04944i) q^{26} -1.00000 q^{27} +(-4.44290 + 2.56511i) q^{28} +(-1.75214 - 3.03479i) q^{29} +6.30618i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.83209 - 2.78981i) q^{33} -1.28265i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.25861 - 4.19076i) q^{37} -6.64947 q^{38} +(3.04944 + 1.92378i) q^{39} +(1.11081 - 0.641326i) q^{41} +(2.56511 + 4.44290i) q^{42} +(2.17900 - 3.77414i) q^{43} +5.57962i q^{44} +(5.94290 + 3.43113i) q^{46} +5.02353i q^{47} +(0.500000 - 0.866025i) q^{48} +(9.65957 + 16.7309i) q^{49} -1.28265 q^{51} +(0.141326 - 3.60278i) q^{52} +6.30618 q^{53} +(0.866025 - 0.500000i) q^{54} +(2.56511 - 4.44290i) q^{56} +6.64947i q^{57} +(3.03479 + 1.75214i) q^{58} +(1.31571 + 0.759628i) q^{59} +(5.19076 - 8.99066i) q^{61} +(-3.15309 - 5.46131i) q^{62} +(4.44290 - 2.56511i) q^{63} -1.00000 q^{64} +5.57962 q^{66} +(2.48644 - 1.43555i) q^{67} +(0.641326 + 1.11081i) q^{68} +(3.43113 - 5.94290i) q^{69} +(9.44775 + 5.45466i) q^{71} +(-0.866025 - 0.500000i) q^{72} -4.94644i q^{73} +(-4.19076 + 7.25861i) q^{74} +(5.75861 - 3.32474i) q^{76} +28.6246 q^{77} +(-3.60278 - 0.141326i) q^{78} +10.1485 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.641326 + 1.11081i) q^{82} +17.3887i q^{83} +(-4.44290 - 2.56511i) q^{84} +4.35800i q^{86} +(1.75214 - 3.03479i) q^{87} +(-2.78981 - 4.83209i) q^{88} +(5.57884 - 3.22094i) q^{89} +(-18.4830 - 0.725036i) q^{91} -6.86227 q^{92} +(-5.46131 + 3.15309i) q^{93} +(-2.51176 - 4.35050i) q^{94} +1.00000i q^{96} +(-6.20806 - 3.58423i) q^{97} +(-16.7309 - 9.65957i) q^{98} -5.57962i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} + 6q^{4} + 6q^{7} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{3} + 6q^{4} + 6q^{7} - 6q^{9} - 12q^{11} + 12q^{12} + 8q^{14} - 6q^{16} - 6q^{19} + 4q^{22} - 4q^{23} - 4q^{26} - 12q^{27} + 6q^{28} - 12q^{33} + 6q^{36} + 12q^{37} - 24q^{38} + 6q^{39} + 4q^{42} + 10q^{43} + 12q^{46} + 6q^{48} + 32q^{49} - 6q^{52} + 16q^{53} + 4q^{56} + 24q^{61} - 8q^{62} - 6q^{63} - 12q^{64} + 8q^{66} - 6q^{67} + 4q^{69} + 12q^{71} - 12q^{74} - 6q^{76} + 48q^{77} - 8q^{78} + 52q^{79} - 6q^{81} + 6q^{84} - 4q^{88} + 24q^{89} - 54q^{91} - 8q^{92} - 8q^{94} - 12q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −4.44290 2.56511i −1.67926 0.969520i −0.962135 0.272574i \(-0.912125\pi\)
−0.717123 0.696947i \(-0.754541\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −4.83209 + 2.78981i −1.45693 + 0.841159i −0.998859 0.0477570i \(-0.984793\pi\)
−0.458071 + 0.888916i \(0.651459\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.19076 1.67900i 0.884958 0.465670i
\(14\) 5.13022 1.37111
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.641326 + 1.11081i −0.155545 + 0.269411i −0.933257 0.359209i \(-0.883047\pi\)
0.777713 + 0.628620i \(0.216380\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.75861 + 3.32474i 1.32112 + 0.762747i 0.983907 0.178682i \(-0.0571835\pi\)
0.337210 + 0.941430i \(0.390517\pi\)
\(20\) 0 0
\(21\) 5.13022i 1.11951i
\(22\) 2.78981 4.83209i 0.594789 1.03020i
\(23\) −3.43113 5.94290i −0.715441 1.23918i −0.962789 0.270253i \(-0.912892\pi\)
0.247348 0.968927i \(-0.420441\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −1.92378 + 3.04944i −0.377285 + 0.598044i
\(27\) −1.00000 −0.192450
\(28\) −4.44290 + 2.56511i −0.839629 + 0.484760i
\(29\) −1.75214 3.03479i −0.325364 0.563546i 0.656222 0.754568i \(-0.272153\pi\)
−0.981586 + 0.191021i \(0.938820\pi\)
\(30\) 0 0
\(31\) 6.30618i 1.13262i 0.824191 + 0.566312i \(0.191630\pi\)
−0.824191 + 0.566312i \(0.808370\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −4.83209 2.78981i −0.841159 0.485643i
\(34\) 1.28265i 0.219973i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 7.25861 4.19076i 1.19331 0.688957i 0.234253 0.972176i \(-0.424735\pi\)
0.959055 + 0.283218i \(0.0914021\pi\)
\(38\) −6.64947 −1.07869
\(39\) 3.04944 + 1.92378i 0.488301 + 0.308052i
\(40\) 0 0
\(41\) 1.11081 0.641326i 0.173479 0.100158i −0.410746 0.911750i \(-0.634732\pi\)
0.584225 + 0.811591i \(0.301398\pi\)
\(42\) 2.56511 + 4.44290i 0.395805 + 0.685554i
\(43\) 2.17900 3.77414i 0.332294 0.575550i −0.650667 0.759363i \(-0.725511\pi\)
0.982961 + 0.183813i \(0.0588440\pi\)
\(44\) 5.57962i 0.841159i
\(45\) 0 0
\(46\) 5.94290 + 3.43113i 0.876233 + 0.505893i
\(47\) 5.02353i 0.732757i 0.930466 + 0.366379i \(0.119402\pi\)
−0.930466 + 0.366379i \(0.880598\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 9.65957 + 16.7309i 1.37994 + 2.39012i
\(50\) 0 0
\(51\) −1.28265 −0.179607
\(52\) 0.141326 3.60278i 0.0195985 0.499616i
\(53\) 6.30618 0.866221 0.433110 0.901341i \(-0.357416\pi\)
0.433110 + 0.901341i \(0.357416\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 2.56511 4.44290i 0.342777 0.593707i
\(57\) 6.64947i 0.880744i
\(58\) 3.03479 + 1.75214i 0.398487 + 0.230067i
\(59\) 1.31571 + 0.759628i 0.171291 + 0.0988952i 0.583195 0.812332i \(-0.301802\pi\)
−0.411903 + 0.911228i \(0.635136\pi\)
\(60\) 0 0
\(61\) 5.19076 8.99066i 0.664609 1.15114i −0.314782 0.949164i \(-0.601931\pi\)
0.979391 0.201973i \(-0.0647352\pi\)
\(62\) −3.15309 5.46131i −0.400443 0.693588i
\(63\) 4.44290 2.56511i 0.559753 0.323173i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 5.57962 0.686803
\(67\) 2.48644 1.43555i 0.303767 0.175380i −0.340367 0.940293i \(-0.610551\pi\)
0.644134 + 0.764913i \(0.277218\pi\)
\(68\) 0.641326 + 1.11081i 0.0777723 + 0.134706i
\(69\) 3.43113 5.94290i 0.413060 0.715441i
\(70\) 0 0
\(71\) 9.44775 + 5.45466i 1.12124 + 0.647350i 0.941718 0.336404i \(-0.109211\pi\)
0.179524 + 0.983754i \(0.442544\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 4.94644i 0.578937i −0.957188 0.289468i \(-0.906522\pi\)
0.957188 0.289468i \(-0.0934785\pi\)
\(74\) −4.19076 + 7.25861i −0.487166 + 0.843797i
\(75\) 0 0
\(76\) 5.75861 3.32474i 0.660558 0.381374i
\(77\) 28.6246 3.26208
\(78\) −3.60278 0.141326i −0.407935 0.0160021i
\(79\) 10.1485 1.14179 0.570895 0.821023i \(-0.306596\pi\)
0.570895 + 0.821023i \(0.306596\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.641326 + 1.11081i −0.0708227 + 0.122668i
\(83\) 17.3887i 1.90866i 0.298755 + 0.954330i \(0.403429\pi\)
−0.298755 + 0.954330i \(0.596571\pi\)
\(84\) −4.44290 2.56511i −0.484760 0.279876i
\(85\) 0 0
\(86\) 4.35800i 0.469935i
\(87\) 1.75214 3.03479i 0.187849 0.325364i
\(88\) −2.78981 4.83209i −0.297395 0.515102i
\(89\) 5.57884 3.22094i 0.591355 0.341419i −0.174278 0.984697i \(-0.555759\pi\)
0.765633 + 0.643277i \(0.222426\pi\)
\(90\) 0 0
\(91\) −18.4830 0.725036i −1.93755 0.0760044i
\(92\) −6.86227 −0.715441
\(93\) −5.46131 + 3.15309i −0.566312 + 0.326960i
\(94\) −2.51176 4.35050i −0.259069 0.448720i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −6.20806 3.58423i −0.630333 0.363923i 0.150548 0.988603i \(-0.451896\pi\)
−0.780881 + 0.624680i \(0.785230\pi\)
\(98\) −16.7309 9.65957i −1.69007 0.975764i
\(99\) 5.57962i 0.560772i
\(100\) 0 0
\(101\) −7.33175 12.6990i −0.729537 1.26359i −0.957079 0.289826i \(-0.906402\pi\)
0.227543 0.973768i \(-0.426931\pi\)
\(102\) 1.11081 0.641326i 0.109987 0.0635008i
\(103\) 4.04929 0.398989 0.199494 0.979899i \(-0.436070\pi\)
0.199494 + 0.979899i \(0.436070\pi\)
\(104\) 1.67900 + 3.19076i 0.164639 + 0.312880i
\(105\) 0 0
\(106\) −5.46131 + 3.15309i −0.530450 + 0.306255i
\(107\) −3.88044 6.72112i −0.375136 0.649755i 0.615211 0.788362i \(-0.289071\pi\)
−0.990347 + 0.138608i \(0.955737\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 0.792690i 0.0759259i 0.999279 + 0.0379630i \(0.0120869\pi\)
−0.999279 + 0.0379630i \(0.987913\pi\)
\(110\) 0 0
\(111\) 7.25861 + 4.19076i 0.688957 + 0.397770i
\(112\) 5.13022i 0.484760i
\(113\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) −3.32474 5.75861i −0.311390 0.539344i
\(115\) 0 0
\(116\) −3.50427 −0.325364
\(117\) −0.141326 + 3.60278i −0.0130656 + 0.333077i
\(118\) −1.51926 −0.139859
\(119\) 5.69870 3.29014i 0.522399 0.301607i
\(120\) 0 0
\(121\) 10.0661 17.4349i 0.915096 1.58499i
\(122\) 10.3815i 0.939899i
\(123\) 1.11081 + 0.641326i 0.100158 + 0.0578265i
\(124\) 5.46131 + 3.15309i 0.490440 + 0.283156i
\(125\) 0 0
\(126\) −2.56511 + 4.44290i −0.228518 + 0.395805i
\(127\) 8.12651 + 14.0755i 0.721111 + 1.24900i 0.960555 + 0.278090i \(0.0897015\pi\)
−0.239444 + 0.970910i \(0.576965\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 4.35800 0.383700
\(130\) 0 0
\(131\) 7.04605 0.615616 0.307808 0.951448i \(-0.400405\pi\)
0.307808 + 0.951448i \(0.400405\pi\)
\(132\) −4.83209 + 2.78981i −0.420579 + 0.242822i
\(133\) −17.0566 29.5429i −1.47900 2.56170i
\(134\) −1.43555 + 2.48644i −0.124012 + 0.214796i
\(135\) 0 0
\(136\) −1.11081 0.641326i −0.0952512 0.0549933i
\(137\) 0.769058 + 0.444016i 0.0657051 + 0.0379348i 0.532493 0.846435i \(-0.321255\pi\)
−0.466788 + 0.884369i \(0.654589\pi\)
\(138\) 6.86227i 0.584155i
\(139\) −0.266279 + 0.461208i −0.0225854 + 0.0391191i −0.877097 0.480313i \(-0.840523\pi\)
0.854512 + 0.519432i \(0.173856\pi\)
\(140\) 0 0
\(141\) −4.35050 + 2.51176i −0.366379 + 0.211529i
\(142\) −10.9093 −0.915490
\(143\) −10.7340 + 17.0147i −0.897619 + 1.42284i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.47322 + 4.28374i 0.204685 + 0.354525i
\(147\) −9.65957 + 16.7309i −0.796708 + 1.37994i
\(148\) 8.38153i 0.688957i
\(149\) 18.0113 + 10.3988i 1.47554 + 0.851905i 0.999620 0.0275822i \(-0.00878080\pi\)
0.475923 + 0.879487i \(0.342114\pi\)
\(150\) 0 0
\(151\) 2.15400i 0.175290i 0.996152 + 0.0876448i \(0.0279341\pi\)
−0.996152 + 0.0876448i \(0.972066\pi\)
\(152\) −3.32474 + 5.75861i −0.269672 + 0.467085i
\(153\) −0.641326 1.11081i −0.0518482 0.0898037i
\(154\) −24.7897 + 14.3123i −1.99761 + 1.15332i
\(155\) 0 0
\(156\) 3.19076 1.67900i 0.255465 0.134427i
\(157\) −7.70236 −0.614716 −0.307358 0.951594i \(-0.599445\pi\)
−0.307358 + 0.951594i \(0.599445\pi\)
\(158\) −8.78882 + 5.07423i −0.699201 + 0.403684i
\(159\) 3.15309 + 5.46131i 0.250056 + 0.433110i
\(160\) 0 0
\(161\) 35.2049i 2.77454i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 0.382683 + 0.220942i 0.0299741 + 0.0173055i 0.514912 0.857243i \(-0.327825\pi\)
−0.484938 + 0.874548i \(0.661158\pi\)
\(164\) 1.28265i 0.100158i
\(165\) 0 0
\(166\) −8.69436 15.0591i −0.674813 1.16881i
\(167\) 5.94290 3.43113i 0.459875 0.265509i −0.252116 0.967697i \(-0.581127\pi\)
0.711992 + 0.702188i \(0.247793\pi\)
\(168\) 5.13022 0.395805
\(169\) 7.36193 10.7146i 0.566302 0.824197i
\(170\) 0 0
\(171\) −5.75861 + 3.32474i −0.440372 + 0.254249i
\(172\) −2.17900 3.77414i −0.166147 0.287775i
\(173\) 11.1449 19.3036i 0.847333 1.46762i −0.0362472 0.999343i \(-0.511540\pi\)
0.883580 0.468280i \(-0.155126\pi\)
\(174\) 3.50427i 0.265658i
\(175\) 0 0
\(176\) 4.83209 + 2.78981i 0.364232 + 0.210290i
\(177\) 1.51926i 0.114194i
\(178\) −3.22094 + 5.57884i −0.241420 + 0.418151i
\(179\) 0.784447 + 1.35870i 0.0586324 + 0.101554i 0.893852 0.448363i \(-0.147993\pi\)
−0.835219 + 0.549917i \(0.814659\pi\)
\(180\) 0 0
\(181\) 11.4419 0.850469 0.425234 0.905083i \(-0.360192\pi\)
0.425234 + 0.905083i \(0.360192\pi\)
\(182\) 16.3693 8.61363i 1.21337 0.638484i
\(183\) 10.3815 0.767424
\(184\) 5.94290 3.43113i 0.438116 0.252947i
\(185\) 0 0
\(186\) 3.15309 5.46131i 0.231196 0.400443i
\(187\) 7.15671i 0.523351i
\(188\) 4.35050 + 2.51176i 0.317293 + 0.183189i
\(189\) 4.44290 + 2.56511i 0.323173 + 0.186584i
\(190\) 0 0
\(191\) −4.41092 + 7.63995i −0.319163 + 0.552807i −0.980314 0.197446i \(-0.936735\pi\)
0.661150 + 0.750253i \(0.270069\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −9.68914 + 5.59403i −0.697440 + 0.402667i −0.806393 0.591380i \(-0.798583\pi\)
0.108953 + 0.994047i \(0.465250\pi\)
\(194\) 7.16845 0.514665
\(195\) 0 0
\(196\) 19.3191 1.37994
\(197\) −19.8624 + 11.4675i −1.41514 + 0.817029i −0.995866 0.0908332i \(-0.971047\pi\)
−0.419269 + 0.907862i \(0.637714\pi\)
\(198\) 2.78981 + 4.83209i 0.198263 + 0.343402i
\(199\) 5.52892 9.57637i 0.391935 0.678851i −0.600770 0.799422i \(-0.705139\pi\)
0.992705 + 0.120571i \(0.0384726\pi\)
\(200\) 0 0
\(201\) 2.48644 + 1.43555i 0.175380 + 0.101256i
\(202\) 12.6990 + 7.33175i 0.893496 + 0.515860i
\(203\) 17.9777i 1.26179i
\(204\) −0.641326 + 1.11081i −0.0449018 + 0.0777723i
\(205\) 0 0
\(206\) −3.50679 + 2.02465i −0.244330 + 0.141064i
\(207\) 6.86227 0.476961
\(208\) −3.04944 1.92378i −0.211440 0.133390i
\(209\) −37.1015 −2.56637
\(210\) 0 0
\(211\) −13.4171 23.2391i −0.923671 1.59984i −0.793685 0.608329i \(-0.791840\pi\)
−0.129986 0.991516i \(-0.541493\pi\)
\(212\) 3.15309 5.46131i 0.216555 0.375085i
\(213\) 10.9093i 0.747495i
\(214\) 6.72112 + 3.88044i 0.459446 + 0.265261i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 16.1760 28.0177i 1.09810 1.90197i
\(218\) −0.396345 0.686490i −0.0268439 0.0464949i
\(219\) 4.28374 2.47322i 0.289468 0.167125i
\(220\) 0 0
\(221\) −0.181273 + 4.62112i −0.0121937 + 0.310850i
\(222\) −8.38153 −0.562531
\(223\) 0.0599161 0.0345926i 0.00401228 0.00231649i −0.497993 0.867181i \(-0.665929\pi\)
0.502005 + 0.864865i \(0.332596\pi\)
\(224\) −2.56511 4.44290i −0.171389 0.296854i
\(225\) 0 0
\(226\) 0 0
\(227\) −5.36241 3.09599i −0.355916 0.205488i 0.311372 0.950288i \(-0.399212\pi\)
−0.667288 + 0.744800i \(0.732545\pi\)
\(228\) 5.75861 + 3.32474i 0.381374 + 0.220186i
\(229\) 17.3857i 1.14888i 0.818548 + 0.574438i \(0.194779\pi\)
−0.818548 + 0.574438i \(0.805221\pi\)
\(230\) 0 0
\(231\) 14.3123 + 24.7897i 0.941682 + 1.63104i
\(232\) 3.03479 1.75214i 0.199244 0.115033i
\(233\) 17.7716 1.16426 0.582128 0.813097i \(-0.302220\pi\)
0.582128 + 0.813097i \(0.302220\pi\)
\(234\) −1.67900 3.19076i −0.109760 0.208587i
\(235\) 0 0
\(236\) 1.31571 0.759628i 0.0856457 0.0494476i
\(237\) 5.07423 + 8.78882i 0.329606 + 0.570895i
\(238\) −3.29014 + 5.69870i −0.213268 + 0.369392i
\(239\) 17.1487i 1.10925i −0.832099 0.554627i \(-0.812861\pi\)
0.832099 0.554627i \(-0.187139\pi\)
\(240\) 0 0
\(241\) −15.1831 8.76597i −0.978029 0.564665i −0.0763547 0.997081i \(-0.524328\pi\)
−0.901675 + 0.432415i \(0.857661\pi\)
\(242\) 20.1321i 1.29414i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.19076 8.99066i −0.332305 0.575568i
\(245\) 0 0
\(246\) −1.28265 −0.0817790
\(247\) 23.9566 + 0.939747i 1.52432 + 0.0597947i
\(248\) −6.30618 −0.400443
\(249\) −15.0591 + 8.69436i −0.954330 + 0.550983i
\(250\) 0 0
\(251\) −9.10358 + 15.7679i −0.574613 + 0.995259i 0.421470 + 0.906842i \(0.361514\pi\)
−0.996084 + 0.0884170i \(0.971819\pi\)
\(252\) 5.13022i 0.323173i
\(253\) 33.1591 + 19.1444i 2.08469 + 1.20360i
\(254\) −14.0755 8.12651i −0.883177 0.509902i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.80056 + 15.2430i 0.548964 + 0.950833i 0.998346 + 0.0574935i \(0.0183108\pi\)
−0.449382 + 0.893340i \(0.648356\pi\)
\(258\) −3.77414 + 2.17900i −0.234967 + 0.135658i
\(259\) −42.9991 −2.67183
\(260\) 0 0
\(261\) 3.50427 0.216909
\(262\) −6.10206 + 3.52302i −0.376986 + 0.217653i
\(263\) 5.88051 + 10.1853i 0.362608 + 0.628055i 0.988389 0.151943i \(-0.0485531\pi\)
−0.625781 + 0.779999i \(0.715220\pi\)
\(264\) 2.78981 4.83209i 0.171701 0.297395i
\(265\) 0 0
\(266\) 29.5429 + 17.0566i 1.81139 + 1.04581i
\(267\) 5.57884 + 3.22094i 0.341419 + 0.197118i
\(268\) 2.87109i 0.175380i
\(269\) 3.20490 5.55106i 0.195406 0.338454i −0.751627 0.659588i \(-0.770731\pi\)
0.947034 + 0.321134i \(0.104064\pi\)
\(270\) 0 0
\(271\) 13.6919 7.90503i 0.831725 0.480196i −0.0227182 0.999742i \(-0.507232\pi\)
0.854443 + 0.519545i \(0.173899\pi\)
\(272\) 1.28265 0.0777723
\(273\) −8.61363 16.3693i −0.521320 0.990716i
\(274\) −0.888032 −0.0536480
\(275\) 0 0
\(276\) −3.43113 5.94290i −0.206530 0.357720i
\(277\) −2.49319 + 4.31832i −0.149801 + 0.259463i −0.931154 0.364627i \(-0.881197\pi\)
0.781353 + 0.624090i \(0.214530\pi\)
\(278\) 0.532557i 0.0319406i
\(279\) −5.46131 3.15309i −0.326960 0.188771i
\(280\) 0 0
\(281\) 0.515726i 0.0307656i 0.999882 + 0.0153828i \(0.00489670\pi\)
−0.999882 + 0.0153828i \(0.995103\pi\)
\(282\) 2.51176 4.35050i 0.149573 0.259069i
\(283\) 8.97308 + 15.5418i 0.533394 + 0.923866i 0.999239 + 0.0389995i \(0.0124171\pi\)
−0.465845 + 0.884866i \(0.654250\pi\)
\(284\) 9.44775 5.45466i 0.560621 0.323675i
\(285\) 0 0
\(286\) 0.788547 20.1021i 0.0466278 1.18866i
\(287\) −6.58029 −0.388422
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 7.67740 + 13.2976i 0.451612 + 0.782215i
\(290\) 0 0
\(291\) 7.16845i 0.420222i
\(292\) −4.28374 2.47322i −0.250687 0.144734i
\(293\) 14.9572 + 8.63553i 0.873808 + 0.504493i 0.868612 0.495493i \(-0.165013\pi\)
0.00519587 + 0.999987i \(0.498346\pi\)
\(294\) 19.3191i 1.12671i
\(295\) 0 0
\(296\) 4.19076 + 7.25861i 0.243583 + 0.421898i
\(297\) 4.83209 2.78981i 0.280386 0.161881i
\(298\) −20.7976 −1.20478
\(299\) −20.9261 13.2015i −1.21018 0.763463i
\(300\) 0 0
\(301\) −19.3621 + 11.1787i −1.11601 + 0.644332i
\(302\) −1.07700 1.86541i −0.0619742 0.107343i
\(303\) 7.33175 12.6990i 0.421198 0.729537i
\(304\) 6.64947i 0.381374i
\(305\) 0 0
\(306\) 1.11081 + 0.641326i 0.0635008 + 0.0366622i
\(307\) 14.2673i 0.814279i −0.913366 0.407140i \(-0.866526\pi\)
0.913366 0.407140i \(-0.133474\pi\)
\(308\) 14.3123 24.7897i 0.815520 1.41252i
\(309\) 2.02465 + 3.50679i 0.115178 + 0.199494i
\(310\) 0 0
\(311\) −23.1487 −1.31264 −0.656320 0.754483i \(-0.727888\pi\)
−0.656320 + 0.754483i \(0.727888\pi\)
\(312\) −1.92378 + 3.04944i −0.108913 + 0.172640i
\(313\) 14.1122 0.797667 0.398834 0.917023i \(-0.369415\pi\)
0.398834 + 0.917023i \(0.369415\pi\)
\(314\) 6.67044 3.85118i 0.376435 0.217335i
\(315\) 0 0
\(316\) 5.07423 8.78882i 0.285448 0.494410i
\(317\) 12.1814i 0.684176i −0.939668 0.342088i \(-0.888866\pi\)
0.939668 0.342088i \(-0.111134\pi\)
\(318\) −5.46131 3.15309i −0.306255 0.176817i
\(319\) 16.9330 + 9.77625i 0.948064 + 0.547365i
\(320\) 0 0
\(321\) 3.88044 6.72112i 0.216585 0.375136i
\(322\) −17.6025 30.4884i −0.980947 1.69905i
\(323\) −7.38630 + 4.26448i −0.410985 + 0.237282i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −0.441885 −0.0244737
\(327\) −0.686490 + 0.396345i −0.0379630 + 0.0219179i
\(328\) 0.641326 + 1.11081i 0.0354113 + 0.0613342i
\(329\) 12.8859 22.3190i 0.710423 1.23049i
\(330\) 0 0
\(331\) 3.86463 + 2.23125i 0.212419 + 0.122640i 0.602435 0.798168i \(-0.294197\pi\)
−0.390016 + 0.920808i \(0.627530\pi\)
\(332\) 15.0591 + 8.69436i 0.826474 + 0.477165i
\(333\) 8.38153i 0.459305i
\(334\) −3.43113 + 5.94290i −0.187743 + 0.325181i
\(335\) 0 0
\(336\) −4.44290 + 2.56511i −0.242380 + 0.139938i
\(337\) 6.04773 0.329441 0.164720 0.986340i \(-0.447328\pi\)
0.164720 + 0.986340i \(0.447328\pi\)
\(338\) −1.01834 + 12.9601i −0.0553902 + 0.704934i
\(339\) 0 0
\(340\) 0 0
\(341\) −17.5930 30.4720i −0.952716 1.65015i
\(342\) 3.32474 5.75861i 0.179781 0.311390i
\(343\) 63.1999i 3.41247i
\(344\) 3.77414 + 2.17900i 0.203488 + 0.117484i
\(345\) 0 0
\(346\) 22.2898i 1.19831i
\(347\) −3.17327 + 5.49627i −0.170350 + 0.295055i −0.938542 0.345164i \(-0.887823\pi\)
0.768192 + 0.640219i \(0.221157\pi\)
\(348\) −1.75214 3.03479i −0.0939244 0.162682i
\(349\) −24.4438 + 14.1126i −1.30844 + 0.755431i −0.981836 0.189729i \(-0.939239\pi\)
−0.326608 + 0.945160i \(0.605906\pi\)
\(350\) 0 0
\(351\) −3.19076 + 1.67900i −0.170310 + 0.0896183i
\(352\) −5.57962 −0.297395
\(353\) 13.9378 8.04696i 0.741832 0.428297i −0.0809033 0.996722i \(-0.525780\pi\)
0.822735 + 0.568425i \(0.192447\pi\)
\(354\) −0.759628 1.31571i −0.0403738 0.0699294i
\(355\) 0 0
\(356\) 6.44188i 0.341419i
\(357\) 5.69870 + 3.29014i 0.301607 + 0.174133i
\(358\) −1.35870 0.784447i −0.0718097 0.0414593i
\(359\) 8.79689i 0.464282i −0.972682 0.232141i \(-0.925427\pi\)
0.972682 0.232141i \(-0.0745731\pi\)
\(360\) 0 0
\(361\) 12.6078 + 21.8373i 0.663566 + 1.14933i
\(362\) −9.90896 + 5.72094i −0.520804 + 0.300686i
\(363\) 20.1321 1.05666
\(364\) −9.86942 + 15.6443i −0.517298 + 0.819983i
\(365\) 0 0
\(366\) −8.99066 + 5.19076i −0.469950 + 0.271326i
\(367\) −19.0032 32.9145i −0.991958 1.71812i −0.605588 0.795779i \(-0.707062\pi\)
−0.386371 0.922344i \(-0.626271\pi\)
\(368\) −3.43113 + 5.94290i −0.178860 + 0.309795i
\(369\) 1.28265i 0.0667722i
\(370\) 0 0
\(371\) −28.0177 16.1760i −1.45461 0.839818i
\(372\) 6.30618i 0.326960i
\(373\) −8.50787 + 14.7361i −0.440521 + 0.763004i −0.997728 0.0673691i \(-0.978540\pi\)
0.557207 + 0.830373i \(0.311873\pi\)
\(374\) 3.57836 + 6.19789i 0.185032 + 0.320485i
\(375\) 0 0
\(376\) −5.02353 −0.259069
\(377\) −10.6861 6.74146i −0.550360 0.347203i
\(378\) −5.13022 −0.263870
\(379\) 11.0257 6.36569i 0.566352 0.326983i −0.189339 0.981912i \(-0.560635\pi\)
0.755691 + 0.654928i \(0.227301\pi\)
\(380\) 0 0
\(381\) −8.12651 + 14.0755i −0.416334 + 0.721111i
\(382\) 8.82185i 0.451365i
\(383\) −19.5478 11.2859i −0.998845 0.576683i −0.0909383 0.995857i \(-0.528987\pi\)
−0.907906 + 0.419173i \(0.862320\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 5.59403 9.68914i 0.284729 0.493164i
\(387\) 2.17900 + 3.77414i 0.110765 + 0.191850i
\(388\) −6.20806 + 3.58423i −0.315167 + 0.181961i
\(389\) 3.50427 0.177674 0.0888368 0.996046i \(-0.471685\pi\)
0.0888368 + 0.996046i \(0.471685\pi\)
\(390\) 0 0
\(391\) 8.80191 0.445132
\(392\) −16.7309 + 9.65957i −0.845036 + 0.487882i
\(393\) 3.52302 + 6.10206i 0.177713 + 0.307808i
\(394\) 11.4675 19.8624i 0.577727 1.00065i
\(395\) 0 0
\(396\) −4.83209 2.78981i −0.242822 0.140193i
\(397\) −25.8640 14.9326i −1.29808 0.749445i −0.318005 0.948089i \(-0.603013\pi\)
−0.980072 + 0.198644i \(0.936346\pi\)
\(398\) 11.0578i 0.554279i
\(399\) 17.0566 29.5429i 0.853899 1.47900i
\(400\) 0 0
\(401\) −21.7592 + 12.5627i −1.08660 + 0.627351i −0.932670 0.360730i \(-0.882528\pi\)
−0.153934 + 0.988081i \(0.549194\pi\)
\(402\) −2.87109 −0.143197
\(403\) 10.5881 + 20.1215i 0.527429 + 1.00232i
\(404\) −14.6635 −0.729537
\(405\) 0 0
\(406\) −8.98884 15.5691i −0.446109 0.772683i
\(407\) −23.3828 + 40.5003i −1.15904 + 2.00752i
\(408\) 1.28265i 0.0635008i
\(409\) 4.54462 + 2.62384i 0.224717 + 0.129740i 0.608132 0.793836i \(-0.291919\pi\)
−0.383416 + 0.923576i \(0.625252\pi\)
\(410\) 0 0
\(411\) 0.888032i 0.0438034i
\(412\) 2.02465 3.50679i 0.0997472 0.172767i
\(413\) −3.89706 6.74990i −0.191762 0.332141i
\(414\) −5.94290 + 3.43113i −0.292078 + 0.168631i
\(415\) 0 0
\(416\) 3.60278 + 0.141326i 0.176641 + 0.00692910i
\(417\) −0.532557 −0.0260794
\(418\) 32.1309 18.5508i 1.57157 0.907347i
\(419\) 9.01326 + 15.6114i 0.440326 + 0.762668i 0.997714 0.0675850i \(-0.0215294\pi\)
−0.557387 + 0.830253i \(0.688196\pi\)
\(420\) 0 0
\(421\) 7.92370i 0.386178i 0.981181 + 0.193089i \(0.0618506\pi\)
−0.981181 + 0.193089i \(0.938149\pi\)
\(422\) 23.2391 + 13.4171i 1.13126 + 0.653134i
\(423\) −4.35050 2.51176i −0.211529 0.122126i
\(424\) 6.30618i 0.306255i
\(425\) 0 0
\(426\) −5.45466 9.44775i −0.264279 0.457745i
\(427\) −46.1241 + 26.6297i −2.23210 + 1.28870i
\(428\) −7.76088 −0.375136
\(429\) −20.1021 0.788547i −0.970540 0.0380714i
\(430\) 0 0
\(431\) 33.1752 19.1537i 1.59800 0.922603i 0.606122 0.795372i \(-0.292724\pi\)
0.991873 0.127231i \(-0.0406090\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −10.0026 + 17.3250i −0.480693 + 0.832585i −0.999755 0.0221517i \(-0.992948\pi\)
0.519061 + 0.854737i \(0.326282\pi\)
\(434\) 32.3521i 1.55295i
\(435\) 0 0
\(436\) 0.686490 + 0.396345i 0.0328769 + 0.0189815i
\(437\) 45.6305i 2.18280i
\(438\) −2.47322 + 4.28374i −0.118175 + 0.204685i
\(439\) 5.96660 + 10.3345i 0.284770 + 0.493237i 0.972553 0.232680i \(-0.0747493\pi\)
−0.687783 + 0.725916i \(0.741416\pi\)
\(440\) 0 0
\(441\) −19.3191 −0.919959
\(442\) −2.15357 4.09264i −0.102435 0.194667i
\(443\) 26.0565 1.23798 0.618990 0.785399i \(-0.287542\pi\)
0.618990 + 0.785399i \(0.287542\pi\)
\(444\) 7.25861 4.19076i 0.344479 0.198885i
\(445\) 0 0
\(446\) −0.0345926 + 0.0599161i −0.00163801 + 0.00283711i
\(447\) 20.7976i 0.983695i
\(448\) 4.44290 + 2.56511i 0.209907 + 0.121190i
\(449\) −14.4966 8.36959i −0.684135 0.394985i 0.117276 0.993099i \(-0.462584\pi\)
−0.801411 + 0.598114i \(0.795917\pi\)
\(450\) 0 0
\(451\) −3.57836 + 6.19789i −0.168498 + 0.291847i
\(452\) 0 0
\(453\) −1.86541 + 1.07700i −0.0876448 + 0.0506018i
\(454\) 6.19198 0.290604
\(455\) 0 0
\(456\) −6.64947 −0.311390
\(457\) 6.15626 3.55432i 0.287977 0.166264i −0.349052 0.937103i \(-0.613496\pi\)
0.637029 + 0.770840i \(0.280163\pi\)
\(458\) −8.69283 15.0564i −0.406189 0.703540i
\(459\) 0.641326 1.11081i 0.0299346 0.0518482i
\(460\) 0 0
\(461\) −4.77730 2.75817i −0.222501 0.128461i 0.384607 0.923081i \(-0.374337\pi\)
−0.607108 + 0.794620i \(0.707670\pi\)
\(462\) −24.7897 14.3123i −1.15332 0.665870i
\(463\) 4.98759i 0.231793i −0.993261 0.115896i \(-0.963026\pi\)
0.993261 0.115896i \(-0.0369741\pi\)
\(464\) −1.75214 + 3.03479i −0.0813409 + 0.140887i
\(465\) 0 0
\(466\) −15.3907 + 8.88580i −0.712958 + 0.411627i
\(467\) −19.7410 −0.913506 −0.456753 0.889594i \(-0.650988\pi\)
−0.456753 + 0.889594i \(0.650988\pi\)
\(468\) 3.04944 + 1.92378i 0.140960 + 0.0889269i
\(469\) −14.7293 −0.680138
\(470\) 0 0
\(471\) −3.85118 6.67044i −0.177453 0.307358i
\(472\) −0.759628 + 1.31571i −0.0349647 + 0.0605607i
\(473\) 24.3159i 1.11805i
\(474\) −8.78882 5.07423i −0.403684 0.233067i
\(475\) 0 0
\(476\) 6.58029i 0.301607i
\(477\) −3.15309 + 5.46131i −0.144370 + 0.250056i
\(478\) 8.57433 + 14.8512i 0.392181 + 0.679277i
\(479\) −7.46188 + 4.30812i −0.340942 + 0.196843i −0.660689 0.750660i \(-0.729736\pi\)
0.319746 + 0.947503i \(0.396402\pi\)
\(480\) 0 0
\(481\) 16.1242 25.5589i 0.735202 1.16539i
\(482\) 17.5319 0.798558
\(483\) −30.4884 + 17.6025i −1.38727 + 0.800940i
\(484\) −10.0661 17.4349i −0.457548 0.792496i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 16.9919 + 9.81026i 0.769975 + 0.444545i 0.832866 0.553475i \(-0.186699\pi\)
−0.0628907 + 0.998020i \(0.520032\pi\)
\(488\) 8.99066 + 5.19076i 0.406988 + 0.234975i
\(489\) 0.441885i 0.0199827i
\(490\) 0 0
\(491\) −19.8921 34.4541i −0.897718 1.55489i −0.830404 0.557161i \(-0.811890\pi\)
−0.0673138 0.997732i \(-0.521443\pi\)
\(492\) 1.11081 0.641326i 0.0500792 0.0289132i
\(493\) 4.49477 0.202434
\(494\) −21.2169 + 11.1645i −0.954593 + 0.502313i
\(495\) 0 0
\(496\) 5.46131 3.15309i 0.245220 0.141578i
\(497\) −27.9836 48.4690i −1.25524 2.17413i
\(498\) 8.69436 15.0591i 0.389603 0.674813i
\(499\) 7.84082i 0.351004i −0.984479 0.175502i \(-0.943845\pi\)
0.984479 0.175502i \(-0.0561548\pi\)
\(500\) 0 0
\(501\) 5.94290 + 3.43113i 0.265509 + 0.153292i
\(502\) 18.2072i 0.812626i
\(503\) 3.55194 6.15215i 0.158373 0.274311i −0.775909 0.630845i \(-0.782708\pi\)
0.934282 + 0.356534i \(0.116042\pi\)
\(504\) 2.56511 + 4.44290i 0.114259 + 0.197902i
\(505\) 0 0
\(506\) −38.2888 −1.70215
\(507\) 12.9601 + 1.01834i 0.575576 + 0.0452259i
\(508\) 16.2530 0.721111
\(509\) 34.0477 19.6575i 1.50914 0.871302i 0.509196 0.860651i \(-0.329943\pi\)
0.999943 0.0106512i \(-0.00339045\pi\)
\(510\) 0 0
\(511\) −12.6882 + 21.9765i −0.561291 + 0.972184i
\(512\) 1.00000i 0.0441942i
\(513\) −5.75861 3.32474i −0.254249 0.146791i
\(514\) −15.2430 8.80056i −0.672341 0.388176i
\(515\) 0 0
\(516\) 2.17900 3.77414i 0.0959250 0.166147i
\(517\) −14.0147 24.2741i −0.616365 1.06758i
\(518\) 37.2383 21.4995i 1.63616 0.944635i
\(519\) 22.2898 0.978416
\(520\) 0 0
\(521\) 39.1840 1.71668 0.858341 0.513080i \(-0.171496\pi\)
0.858341 + 0.513080i \(0.171496\pi\)
\(522\) −3.03479 + 1.75214i −0.132829 + 0.0766889i
\(523\) 4.23654 + 7.33790i 0.185251 + 0.320864i 0.943661 0.330914i \(-0.107357\pi\)
−0.758410 + 0.651778i \(0.774024\pi\)
\(524\) 3.52302 6.10206i 0.153904 0.266570i
\(525\) 0 0
\(526\) −10.1853 5.88051i −0.444102 0.256402i
\(527\) −7.00497 4.04432i −0.305141 0.176173i
\(528\) 5.57962i 0.242822i
\(529\) −12.0454 + 20.8632i −0.523712 + 0.907095i
\(530\) 0 0
\(531\) −1.31571 + 0.759628i −0.0570972 + 0.0329651i
\(532\) −34.1133 −1.47900
\(533\) 2.46755 3.91137i 0.106881 0.169420i
\(534\) −6.44188 −0.278768
\(535\) 0 0
\(536\) 1.43555 + 2.48644i 0.0620062 + 0.107398i
\(537\) −0.784447 + 1.35870i −0.0338514 + 0.0586324i
\(538\) 6.40981i 0.276346i
\(539\) −93.3518 53.8967i −4.02095 2.32149i
\(540\) 0 0
\(541\) 14.5899i 0.627269i 0.949544 + 0.313634i \(0.101547\pi\)
−0.949544 + 0.313634i \(0.898453\pi\)
\(542\) −7.90503 + 13.6919i −0.339550 + 0.588118i
\(543\) 5.72094 + 9.90896i 0.245509 + 0.425234i
\(544\) −1.11081 + 0.641326i −0.0476256 + 0.0274966i
\(545\) 0 0
\(546\) 15.6443 + 9.86942i 0.669513 + 0.422372i
\(547\) 14.2246 0.608200 0.304100 0.952640i \(-0.401644\pi\)
0.304100 + 0.952640i \(0.401644\pi\)
\(548\) 0.769058 0.444016i 0.0328525 0.0189674i
\(549\) 5.19076 + 8.99066i 0.221536 + 0.383712i
\(550\) 0 0
\(551\) 23.3016i 0.992680i
\(552\) 5.94290 + 3.43113i 0.252947 + 0.146039i
\(553\) −45.0885 26.0319i −1.91736 1.10699i
\(554\) 4.98637i 0.211851i
\(555\) 0 0
\(556\) 0.266279 + 0.461208i 0.0112927 + 0.0195596i
\(557\) 30.2289 17.4527i 1.28084 0.739493i 0.303838 0.952724i \(-0.401732\pi\)
0.977002 + 0.213231i \(0.0683986\pi\)
\(558\) 6.30618 0.266962
\(559\) 0.615900 15.7009i 0.0260498 0.664077i
\(560\) 0 0
\(561\) 6.19789 3.57836i 0.261675 0.151078i
\(562\) −0.257863 0.446632i −0.0108773 0.0188400i
\(563\) 7.90879 13.6984i 0.333316 0.577320i −0.649844 0.760067i \(-0.725166\pi\)
0.983160 + 0.182748i \(0.0584992\pi\)
\(564\) 5.02353i 0.211529i
\(565\) 0 0
\(566\) −15.5418 8.97308i −0.653272 0.377167i
\(567\) 5.13022i 0.215449i
\(568\) −5.45466 + 9.44775i −0.228873 + 0.396419i
\(569\) −0.234472 0.406118i −0.00982959 0.0170253i 0.861069 0.508489i \(-0.169796\pi\)
−0.870898 + 0.491463i \(0.836462\pi\)
\(570\) 0 0
\(571\) 21.6325 0.905292 0.452646 0.891690i \(-0.350480\pi\)
0.452646 + 0.891690i \(0.350480\pi\)
\(572\) 9.36816 + 17.8032i 0.391703 + 0.744390i
\(573\) −8.82185 −0.368538
\(574\) 5.69870 3.29014i 0.237859 0.137328i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 21.2140i 0.883149i −0.897225 0.441574i \(-0.854420\pi\)
0.897225 0.441574i \(-0.145580\pi\)
\(578\) −13.2976 7.67740i −0.553109 0.319338i
\(579\) −9.68914 5.59403i −0.402667 0.232480i
\(580\) 0 0
\(581\) 44.6040 77.2563i 1.85048 3.20513i
\(582\) 3.58423 + 6.20806i 0.148571 + 0.257332i
\(583\) −30.4720 + 17.5930i −1.26202 + 0.728629i
\(584\) 4.94644 0.204685
\(585\) 0 0
\(586\) −17.2711 −0.713461
\(587\) −2.05536 + 1.18666i −0.0848338 + 0.0489788i −0.541817 0.840497i \(-0.682263\pi\)
0.456983 + 0.889475i \(0.348930\pi\)
\(588\) 9.65957 + 16.7309i 0.398354 + 0.689969i
\(589\) −20.9664 + 36.3149i −0.863905 + 1.49633i
\(590\) 0 0
\(591\) −19.8624 11.4675i −0.817029 0.471712i
\(592\) −7.25861 4.19076i −0.298327 0.172239i
\(593\) 2.26258i 0.0929130i 0.998920 + 0.0464565i \(0.0147929\pi\)
−0.998920 + 0.0464565i \(0.985207\pi\)
\(594\) −2.78981 + 4.83209i −0.114467 + 0.198263i
\(595\) 0 0
\(596\) 18.0113 10.3988i 0.737771 0.425952i
\(597\) 11.0578 0.452567
\(598\) 24.7232 + 0.969820i 1.01101 + 0.0396589i
\(599\) −8.04828 −0.328844 −0.164422 0.986390i \(-0.552576\pi\)
−0.164422 + 0.986390i \(0.552576\pi\)
\(600\) 0 0
\(601\) −1.32625 2.29713i −0.0540988 0.0937019i 0.837708 0.546119i \(-0.183895\pi\)
−0.891807 + 0.452417i \(0.850562\pi\)
\(602\) 11.1787 19.3621i 0.455611 0.789142i
\(603\) 2.87109i 0.116920i
\(604\) 1.86541 + 1.07700i 0.0759026 + 0.0438224i
\(605\) 0 0
\(606\) 14.6635i 0.595664i
\(607\) 1.09680 1.89971i 0.0445177 0.0771070i −0.842908 0.538058i \(-0.819158\pi\)
0.887426 + 0.460951i \(0.152492\pi\)
\(608\) 3.32474 + 5.75861i 0.134836 + 0.233543i
\(609\) −15.5691 + 8.98884i −0.630893 + 0.364246i
\(610\) 0 0
\(611\) 8.43450 + 16.0289i 0.341223 + 0.648459i
\(612\) −1.28265 −0.0518482
\(613\) 0.0840326 0.0485163i 0.00339405 0.00195955i −0.498302 0.867004i \(-0.666043\pi\)
0.501696 + 0.865044i \(0.332710\pi\)
\(614\) 7.13366 + 12.3559i 0.287891 + 0.498642i
\(615\) 0 0
\(616\) 28.6246i 1.15332i
\(617\) 5.74580 + 3.31734i 0.231317 + 0.133551i 0.611180 0.791492i \(-0.290695\pi\)
−0.379862 + 0.925043i \(0.624029\pi\)
\(618\) −3.50679 2.02465i −0.141064 0.0814432i
\(619\) 14.0315i 0.563973i −0.959418 0.281987i \(-0.909007\pi\)
0.959418 0.281987i \(-0.0909934\pi\)
\(620\) 0 0
\(621\) 3.43113 + 5.94290i 0.137687 + 0.238480i
\(622\) 20.0473 11.5743i 0.803824 0.464088i
\(623\) −33.0483 −1.32405
\(624\) 0.141326 3.60278i 0.00565759 0.144227i
\(625\) 0 0
\(626\) −12.2215 + 7.05609i −0.488469 + 0.282018i
\(627\) −18.5508 32.1309i −0.740846 1.28318i
\(628\) −3.85118 + 6.67044i −0.153679 + 0.266180i
\(629\) 10.7506i 0.428654i
\(630\) 0 0
\(631\) −36.1445 20.8680i −1.43889 0.830743i −0.441116 0.897450i \(-0.645417\pi\)
−0.997773 + 0.0667070i \(0.978751\pi\)
\(632\) 10.1485i 0.403684i
\(633\) 13.4171 23.2391i 0.533282 0.923671i
\(634\) 6.09070 + 10.5494i 0.241893 + 0.418970i
\(635\) 0 0
\(636\) 6.30618 0.250056
\(637\) 58.9125 + 37.1658i 2.33420 + 1.47256i
\(638\) −19.5525 −0.774091
\(639\) −9.44775 + 5.45466i −0.373747 + 0.215783i
\(640\) 0 0
\(641\) −18.4382 + 31.9358i −0.728264 + 1.26139i 0.229353 + 0.973343i \(0.426339\pi\)
−0.957617 + 0.288046i \(0.906994\pi\)
\(642\) 7.76088i 0.306297i
\(643\) −18.9996 10.9694i −0.749271 0.432592i 0.0761597 0.997096i \(-0.475734\pi\)
−0.825430 + 0.564504i \(0.809067\pi\)
\(644\) 30.4884 + 17.6025i 1.20141 + 0.693634i
\(645\) 0 0
\(646\) 4.26448 7.38630i 0.167784 0.290610i
\(647\) −0.971183 1.68214i −0.0381811 0.0661317i 0.846303 0.532701i \(-0.178823\pi\)
−0.884485 + 0.466570i \(0.845490\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −8.47687 −0.332746
\(650\) 0 0
\(651\) 32.3521 1.26798
\(652\) 0.382683 0.220942i 0.0149870 0.00865277i
\(653\) 5.27812 + 9.14197i 0.206549 + 0.357753i 0.950625 0.310342i \(-0.100443\pi\)
−0.744076 + 0.668095i \(0.767110\pi\)
\(654\) 0.396345 0.686490i 0.0154983 0.0268439i
\(655\) 0 0
\(656\) −1.11081 0.641326i −0.0433698 0.0250396i
\(657\) 4.28374 + 2.47322i 0.167125 + 0.0964895i
\(658\) 25.7718i 1.00469i
\(659\) 0.191440 0.331584i 0.00745746 0.0129167i −0.862273 0.506444i \(-0.830960\pi\)
0.869730 + 0.493528i \(0.164293\pi\)
\(660\) 0 0
\(661\) 22.5877 13.0410i 0.878560 0.507237i 0.00837690 0.999965i \(-0.497334\pi\)
0.870183 + 0.492728i \(0.164000\pi\)
\(662\) −4.46249 −0.173440
\(663\) −4.09264 + 2.15357i −0.158945 + 0.0836378i
\(664\) −17.3887 −0.674813
\(665\) 0 0
\(666\) −4.19076 7.25861i −0.162389 0.281266i
\(667\) −12.0236 + 20.8255i −0.465557 + 0.806368i
\(668\) 6.86227i 0.265509i
\(669\) 0.0599161 + 0.0345926i 0.00231649 + 0.00133743i
\(670\) 0 0
\(671\) 57.9249i 2.23617i
\(672\) 2.56511 4.44290i 0.0989512 0.171389i
\(673\) 6.41571 + 11.1123i 0.247307 + 0.428349i 0.962778 0.270294i \(-0.0871209\pi\)
−0.715470 + 0.698643i \(0.753788\pi\)
\(674\) −5.23749 + 3.02387i −0.201741 + 0.116475i
\(675\) 0 0
\(676\) −5.59812 11.7329i −0.215312 0.451266i
\(677\) −22.3408 −0.858626 −0.429313 0.903156i \(-0.641244\pi\)
−0.429313 + 0.903156i \(0.641244\pi\)
\(678\) 0 0
\(679\) 18.3879 + 31.8487i 0.705661 + 1.22224i
\(680\) 0 0
\(681\) 6.19198i 0.237277i
\(682\) 30.4720 + 17.5930i 1.16683 + 0.673672i
\(683\) −17.5060 10.1071i −0.669850 0.386738i 0.126170 0.992009i \(-0.459732\pi\)
−0.796020 + 0.605271i \(0.793065\pi\)
\(684\) 6.64947i 0.254249i
\(685\) 0 0
\(686\) 31.5999 + 54.7327i 1.20649 + 2.08970i
\(687\) −15.0564 + 8.69283i −0.574438 + 0.331652i
\(688\) −4.35800 −0.166147
\(689\) 20.1215 10.5881i 0.766569 0.403373i
\(690\) 0 0
\(691\) 21.3351 12.3178i 0.811625 0.468592i −0.0358950 0.999356i \(-0.511428\pi\)
0.847520 + 0.530764i \(0.178095\pi\)
\(692\) −11.1449 19.3036i −0.423666 0.733812i
\(693\) −14.3123 + 24.7897i −0.543680 + 0.941682i
\(694\) 6.34654i 0.240911i
\(695\) 0 0
\(696\) 3.03479 + 1.75214i 0.115033 + 0.0664146i
\(697\) 1.64520i 0.0623163i
\(698\) 14.1126 24.4438i 0.534170 0.925210i
\(699\) 8.88580 + 15.3907i 0.336092 + 0.582128i
\(700\) 0 0
\(701\) 43.4688 1.64179 0.820897 0.571076i \(-0.193474\pi\)
0.820897 + 0.571076i \(0.193474\pi\)
\(702\) 1.92378 3.04944i 0.0726085 0.115094i
\(703\) 55.7327 2.10200
\(704\) 4.83209 2.78981i 0.182116 0.105145i
\(705\) 0 0
\(706\) −8.04696 + 13.9378i −0.302851 + 0.524554i
\(707\) 75.2270i 2.82920i
\(708\) 1.31571 + 0.759628i 0.0494476 + 0.0285486i
\(709\) 4.05937 + 2.34368i 0.152453 + 0.0880187i 0.574286 0.818655i \(-0.305280\pi\)
−0.421833 + 0.906674i \(0.638613\pi\)
\(710\) 0 0
\(711\) −5.07423 + 8.78882i −0.190298 + 0.329606i
\(712\) 3.22094 + 5.57884i 0.120710 + 0.209076i
\(713\) 37.4770 21.6374i 1.40352 0.810325i
\(714\) −6.58029 −0.246261
\(715\) 0 0
\(716\) 1.56889 0.0586324
\(717\) 14.8512 8.57433i 0.554627 0.320214i
\(718\) 4.39845 + 7.61833i 0.164149 + 0.284314i
\(719\) 13.6893 23.7106i 0.510526 0.884257i −0.489400 0.872060i \(-0.662784\pi\)
0.999926 0.0121971i \(-0.00388256\pi\)
\(720\) 0 0
\(721\) −17.9906 10.3869i −0.670005 0.386827i
\(722\) −21.8373 12.6078i −0.812699 0.469212i
\(723\) 17.5319i 0.652020i
\(724\) 5.72094 9.90896i 0.212617 0.368264i
\(725\) 0 0
\(726\) −17.4349 + 10.0661i −0.647071 + 0.373586i
\(727\) −12.4066 −0.460136 −0.230068 0.973175i \(-0.573895\pi\)
−0.230068 + 0.973175i \(0.573895\pi\)
\(728\) 0.725036 18.4830i 0.0268716 0.685027i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.79490 + 4.84091i 0.103373 + 0.179047i
\(732\) 5.19076 8.99066i 0.191856 0.332305i
\(733\) 18.7638i 0.693056i −0.938040 0.346528i \(-0.887361\pi\)
0.938040 0.346528i \(-0.112639\pi\)
\(734\) 32.9145 + 19.0032i 1.21490 + 0.701420i
\(735\) 0 0
\(736\) 6.86227i 0.252947i
\(737\) −8.00980 + 13.8734i −0.295045 + 0.511033i
\(738\) −0.641326 1.11081i −0.0236076 0.0408895i
\(739\) 44.5751 25.7355i 1.63972 0.946694i 0.658794 0.752324i \(-0.271067\pi\)
0.980928 0.194370i \(-0.0622663\pi\)
\(740\) 0 0
\(741\) 11.1645 + 21.2169i 0.410136 + 0.779422i
\(742\) 32.3521 1.18768
\(743\) −42.9547 + 24.7999i −1.57585 + 0.909819i −0.580424 + 0.814314i \(0.697113\pi\)
−0.995429 + 0.0955053i \(0.969553\pi\)
\(744\) −3.15309 5.46131i −0.115598 0.200221i
\(745\) 0 0
\(746\) 17.0157i 0.622990i
\(747\) −15.0591 8.69436i −0.550983 0.318110i
\(748\) −6.19789 3.57836i −0.226617 0.130838i
\(749\) 39.8150i 1.45481i
\(750\) 0 0
\(751\) 5.15058 + 8.92107i 0.187947 + 0.325535i 0.944566 0.328322i \(-0.106483\pi\)
−0.756618 + 0.653857i \(0.773150\pi\)
\(752\) 4.35050 2.51176i 0.158647 0.0915946i
\(753\) −18.2072 −0.663506
\(754\) 12.6251 + 0.495247i 0.459780 + 0.0180358i
\(755\) 0 0
\(756\) 4.44290 2.56511i 0.161587 0.0932921i
\(757\) −2.21571 3.83773i −0.0805314 0.139485i 0.822947 0.568118i \(-0.192328\pi\)
−0.903478 + 0.428634i \(0.858995\pi\)
\(758\) −6.36569 + 11.0257i −0.231212 + 0.400471i
\(759\) 38.2888i 1.38980i
\(760\) 0 0
\(761\) 9.89888 + 5.71512i 0.358834 + 0.207173i 0.668569 0.743650i \(-0.266907\pi\)
−0.309735 + 0.950823i \(0.600240\pi\)
\(762\) 16.2530i 0.588785i
\(763\) 2.03334 3.52184i 0.0736117 0.127499i
\(764\) 4.41092 + 7.63995i 0.159582 + 0.276404i
\(765\) 0 0
\(766\) 22.5718 0.815553
\(767\) 5.47355 + 0.214711i 0.197638 + 0.00775277i
\(768\) −1.00000 −0.0360844
\(769\) 8.46766 4.88880i 0.305352 0.176295i −0.339493 0.940609i \(-0.610255\pi\)
0.644844 + 0.764314i \(0.276922\pi\)
\(770\) 0 0
\(771\) −8.80056 + 15.2430i −0.316944 + 0.548964i
\(772\) 11.1881i 0.402667i
\(773\) −5.88192 3.39593i −0.211558 0.122143i 0.390477 0.920613i \(-0.372310\pi\)
−0.602035 + 0.798470i \(0.705643\pi\)
\(774\) −3.77414 2.17900i −0.135658 0.0783225i
\(775\) 0 0
\(776\) 3.58423 6.20806i 0.128666 0.222856i
\(777\) −21.4995 37.2383i −0.771291 1.33592i
\(778\) −3.03479 + 1.75214i −0.108802 + 0.0628171i
\(779\) 8.52897 0.305582
\(780\) 0 0
\(781\) −60.8699 −2.17809
\(782\) −7.62268 + 4.40095i −0.272586 + 0.157378i
\(783\) 1.75214 + 3.03479i 0.0626163 + 0.108455i
\(784\) 9.65957 16.7309i 0.344985 0.597531i
\(785\) 0