Properties

Label 1386.2.ba.a.1187.10
Level $1386$
Weight $2$
Character 1386.1187
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1187.10
Character \(\chi\) \(=\) 1386.1187
Dual form 1386.2.ba.a.989.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.03699 - 0.598709i) q^{5} +(2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.03699 - 0.598709i) q^{5} +(2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +(-1.03699 - 0.598709i) q^{10} +(-2.65352 + 1.98969i) q^{11} +3.26196i q^{13} +(-0.586237 - 2.57999i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.21006 - 3.82794i) q^{17} +(6.73468 - 3.88827i) q^{19} +1.19742i q^{20} +(3.04988 + 1.30317i) q^{22} +(-5.94749 + 3.43378i) q^{23} +(-1.78309 + 3.08841i) q^{25} +(2.82494 - 1.63098i) q^{26} +(-1.94121 + 1.79769i) q^{28} +7.85827 q^{29} +(-0.103382 + 0.179063i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.42012 q^{34} +(3.08932 - 0.701970i) q^{35} +(3.83230 + 6.63773i) q^{37} +(-6.73468 - 3.88827i) q^{38} +(1.03699 - 0.598709i) q^{40} +3.15304 q^{41} +8.00258i q^{43} +(-0.396361 - 3.29286i) q^{44} +(5.94749 + 3.43378i) q^{46} +(0.355926 - 0.205494i) q^{47} +(5.77602 + 3.95444i) q^{49} +3.56619 q^{50} +(-2.82494 - 1.63098i) q^{52} +(-5.02547 - 2.90146i) q^{53} +(-1.56044 + 3.65198i) q^{55} +(2.52745 + 0.782297i) q^{56} +(-3.92914 - 6.80547i) q^{58} +(-3.66888 - 2.11823i) q^{59} +(-9.94695 + 5.74287i) q^{61} +0.206764 q^{62} +1.00000 q^{64} +(1.95297 + 3.38264i) q^{65} +(5.61793 - 9.73055i) q^{67} +(2.21006 + 3.82794i) q^{68} +(-2.15258 - 2.32445i) q^{70} -3.80688i q^{71} +(0.195764 + 0.113024i) q^{73} +(3.83230 - 6.63773i) q^{74} +7.77654i q^{76} +(-8.26316 + 2.95300i) q^{77} +(2.00851 - 1.15961i) q^{79} +(-1.03699 - 0.598709i) q^{80} +(-1.57652 - 2.73061i) q^{82} +10.8698 q^{83} -5.29274i q^{85} +(6.93044 - 4.00129i) q^{86} +(-2.65352 + 1.98969i) q^{88} +(11.4053 - 6.58488i) q^{89} +(-2.55183 + 8.24446i) q^{91} -6.86757i q^{92} +(-0.355926 - 0.205494i) q^{94} +(4.65588 - 8.06422i) q^{95} +13.1097 q^{97} +(0.536631 - 6.97940i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.03699 0.598709i 0.463758 0.267751i −0.249865 0.968281i \(-0.580386\pi\)
0.713623 + 0.700530i \(0.247053\pi\)
\(6\) 0 0
\(7\) 2.52745 + 0.782297i 0.955287 + 0.295681i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.03699 0.598709i −0.327926 0.189328i
\(11\) −2.65352 + 1.98969i −0.800065 + 0.599913i
\(12\) 0 0
\(13\) 3.26196i 0.904706i 0.891839 + 0.452353i \(0.149415\pi\)
−0.891839 + 0.452353i \(0.850585\pi\)
\(14\) −0.586237 2.57999i −0.156678 0.689530i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.21006 3.82794i 0.536019 0.928412i −0.463095 0.886309i \(-0.653261\pi\)
0.999113 0.0421028i \(-0.0134057\pi\)
\(18\) 0 0
\(19\) 6.73468 3.88827i 1.54504 0.892030i 0.546532 0.837438i \(-0.315948\pi\)
0.998509 0.0545917i \(-0.0173857\pi\)
\(20\) 1.19742i 0.267751i
\(21\) 0 0
\(22\) 3.04988 + 1.30317i 0.650236 + 0.277836i
\(23\) −5.94749 + 3.43378i −1.24014 + 0.715993i −0.969122 0.246582i \(-0.920693\pi\)
−0.271015 + 0.962575i \(0.587359\pi\)
\(24\) 0 0
\(25\) −1.78309 + 3.08841i −0.356619 + 0.617682i
\(26\) 2.82494 1.63098i 0.554017 0.319862i
\(27\) 0 0
\(28\) −1.94121 + 1.79769i −0.366855 + 0.339731i
\(29\) 7.85827 1.45924 0.729622 0.683850i \(-0.239696\pi\)
0.729622 + 0.683850i \(0.239696\pi\)
\(30\) 0 0
\(31\) −0.103382 + 0.179063i −0.0185680 + 0.0321607i −0.875160 0.483833i \(-0.839244\pi\)
0.856592 + 0.515994i \(0.172577\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.42012 −0.758045
\(35\) 3.08932 0.701970i 0.522191 0.118655i
\(36\) 0 0
\(37\) 3.83230 + 6.63773i 0.630026 + 1.09124i 0.987546 + 0.157331i \(0.0502891\pi\)
−0.357520 + 0.933905i \(0.616378\pi\)
\(38\) −6.73468 3.88827i −1.09251 0.630760i
\(39\) 0 0
\(40\) 1.03699 0.598709i 0.163963 0.0946642i
\(41\) 3.15304 0.492422 0.246211 0.969216i \(-0.420814\pi\)
0.246211 + 0.969216i \(0.420814\pi\)
\(42\) 0 0
\(43\) 8.00258i 1.22038i 0.792254 + 0.610191i \(0.208907\pi\)
−0.792254 + 0.610191i \(0.791093\pi\)
\(44\) −0.396361 3.29286i −0.0597537 0.496417i
\(45\) 0 0
\(46\) 5.94749 + 3.43378i 0.876909 + 0.506284i
\(47\) 0.355926 0.205494i 0.0519172 0.0299744i −0.473817 0.880623i \(-0.657124\pi\)
0.525734 + 0.850649i \(0.323791\pi\)
\(48\) 0 0
\(49\) 5.77602 + 3.95444i 0.825146 + 0.564919i
\(50\) 3.56619 0.504335
\(51\) 0 0
\(52\) −2.82494 1.63098i −0.391749 0.226177i
\(53\) −5.02547 2.90146i −0.690302 0.398546i 0.113423 0.993547i \(-0.463818\pi\)
−0.803725 + 0.595001i \(0.797152\pi\)
\(54\) 0 0
\(55\) −1.56044 + 3.65198i −0.210409 + 0.492433i
\(56\) 2.52745 + 0.782297i 0.337745 + 0.104539i
\(57\) 0 0
\(58\) −3.92914 6.80547i −0.515921 0.893601i
\(59\) −3.66888 2.11823i −0.477647 0.275770i 0.241788 0.970329i \(-0.422266\pi\)
−0.719436 + 0.694559i \(0.755599\pi\)
\(60\) 0 0
\(61\) −9.94695 + 5.74287i −1.27358 + 0.735300i −0.975659 0.219292i \(-0.929625\pi\)
−0.297917 + 0.954592i \(0.596292\pi\)
\(62\) 0.206764 0.0262591
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.95297 + 3.38264i 0.242236 + 0.419565i
\(66\) 0 0
\(67\) 5.61793 9.73055i 0.686340 1.18878i −0.286674 0.958028i \(-0.592550\pi\)
0.973014 0.230747i \(-0.0741170\pi\)
\(68\) 2.21006 + 3.82794i 0.268009 + 0.464206i
\(69\) 0 0
\(70\) −2.15258 2.32445i −0.257283 0.277824i
\(71\) 3.80688i 0.451793i −0.974151 0.225897i \(-0.927469\pi\)
0.974151 0.225897i \(-0.0725312\pi\)
\(72\) 0 0
\(73\) 0.195764 + 0.113024i 0.0229124 + 0.0132285i 0.511412 0.859335i \(-0.329122\pi\)
−0.488500 + 0.872564i \(0.662456\pi\)
\(74\) 3.83230 6.63773i 0.445496 0.771621i
\(75\) 0 0
\(76\) 7.77654i 0.892030i
\(77\) −8.26316 + 2.95300i −0.941674 + 0.336525i
\(78\) 0 0
\(79\) 2.00851 1.15961i 0.225975 0.130466i −0.382739 0.923856i \(-0.625019\pi\)
0.608714 + 0.793390i \(0.291686\pi\)
\(80\) −1.03699 0.598709i −0.115940 0.0669377i
\(81\) 0 0
\(82\) −1.57652 2.73061i −0.174098 0.301546i
\(83\) 10.8698 1.19311 0.596557 0.802571i \(-0.296535\pi\)
0.596557 + 0.802571i \(0.296535\pi\)
\(84\) 0 0
\(85\) 5.29274i 0.574078i
\(86\) 6.93044 4.00129i 0.747329 0.431470i
\(87\) 0 0
\(88\) −2.65352 + 1.98969i −0.282866 + 0.212101i
\(89\) 11.4053 6.58488i 1.20896 0.697996i 0.246431 0.969160i \(-0.420742\pi\)
0.962533 + 0.271165i \(0.0874087\pi\)
\(90\) 0 0
\(91\) −2.55183 + 8.24446i −0.267504 + 0.864254i
\(92\) 6.86757i 0.715993i
\(93\) 0 0
\(94\) −0.355926 0.205494i −0.0367110 0.0211951i
\(95\) 4.65588 8.06422i 0.477683 0.827372i
\(96\) 0 0
\(97\) 13.1097 1.33109 0.665545 0.746357i \(-0.268199\pi\)
0.665545 + 0.746357i \(0.268199\pi\)
\(98\) 0.536631 6.97940i 0.0542079 0.705026i
\(99\) 0 0
\(100\) −1.78309 3.08841i −0.178309 0.308841i
\(101\) 4.82575 8.35845i 0.480181 0.831697i −0.519561 0.854433i \(-0.673904\pi\)
0.999741 + 0.0227363i \(0.00723780\pi\)
\(102\) 0 0
\(103\) 4.95521 + 8.58267i 0.488251 + 0.845676i 0.999909 0.0135137i \(-0.00430167\pi\)
−0.511658 + 0.859189i \(0.670968\pi\)
\(104\) 3.26196i 0.319862i
\(105\) 0 0
\(106\) 5.80291i 0.563629i
\(107\) 4.82669 + 8.36007i 0.466614 + 0.808199i 0.999273 0.0381312i \(-0.0121405\pi\)
−0.532659 + 0.846330i \(0.678807\pi\)
\(108\) 0 0
\(109\) 6.34796 + 3.66500i 0.608024 + 0.351043i 0.772192 0.635390i \(-0.219160\pi\)
−0.164168 + 0.986432i \(0.552494\pi\)
\(110\) 3.94292 0.474610i 0.375943 0.0452523i
\(111\) 0 0
\(112\) −0.586237 2.57999i −0.0553941 0.243786i
\(113\) 12.0213i 1.13087i 0.824792 + 0.565436i \(0.191292\pi\)
−0.824792 + 0.565436i \(0.808708\pi\)
\(114\) 0 0
\(115\) −4.11168 + 7.12163i −0.383416 + 0.664095i
\(116\) −3.92914 + 6.80547i −0.364811 + 0.631872i
\(117\) 0 0
\(118\) 4.23646i 0.389997i
\(119\) 8.58041 7.94601i 0.786565 0.728409i
\(120\) 0 0
\(121\) 3.08229 10.5593i 0.280208 0.959939i
\(122\) 9.94695 + 5.74287i 0.900555 + 0.519935i
\(123\) 0 0
\(124\) −0.103382 0.179063i −0.00928400 0.0160804i
\(125\) 10.2573i 0.917442i
\(126\) 0 0
\(127\) 18.1862i 1.61376i −0.590715 0.806880i \(-0.701154\pi\)
0.590715 0.806880i \(-0.298846\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 1.95297 3.38264i 0.171287 0.296677i
\(131\) −0.397483 0.688460i −0.0347282 0.0601511i 0.848139 0.529774i \(-0.177723\pi\)
−0.882867 + 0.469623i \(0.844390\pi\)
\(132\) 0 0
\(133\) 20.0634 4.55889i 1.73971 0.395306i
\(134\) −11.2359 −0.970631
\(135\) 0 0
\(136\) 2.21006 3.82794i 0.189511 0.328243i
\(137\) −5.20922 3.00754i −0.445053 0.256952i 0.260685 0.965424i \(-0.416051\pi\)
−0.705739 + 0.708472i \(0.749385\pi\)
\(138\) 0 0
\(139\) 11.8585i 1.00583i 0.864337 + 0.502913i \(0.167738\pi\)
−0.864337 + 0.502913i \(0.832262\pi\)
\(140\) −0.936737 + 3.02642i −0.0791687 + 0.255779i
\(141\) 0 0
\(142\) −3.29685 + 1.90344i −0.276666 + 0.159733i
\(143\) −6.49029 8.65567i −0.542745 0.723824i
\(144\) 0 0
\(145\) 8.14899 4.70482i 0.676737 0.390714i
\(146\) 0.226048i 0.0187079i
\(147\) 0 0
\(148\) −7.66460 −0.630026
\(149\) 9.00137 + 15.5908i 0.737421 + 1.27725i 0.953653 + 0.300908i \(0.0972898\pi\)
−0.216232 + 0.976342i \(0.569377\pi\)
\(150\) 0 0
\(151\) −4.49066 2.59269i −0.365445 0.210990i 0.306022 0.952025i \(-0.401002\pi\)
−0.671467 + 0.741035i \(0.734335\pi\)
\(152\) 6.73468 3.88827i 0.546254 0.315380i
\(153\) 0 0
\(154\) 6.68895 + 5.67961i 0.539011 + 0.457676i
\(155\) 0.247583i 0.0198864i
\(156\) 0 0
\(157\) 9.83949 17.0425i 0.785277 1.36014i −0.143557 0.989642i \(-0.545854\pi\)
0.928834 0.370497i \(-0.120813\pi\)
\(158\) −2.00851 1.15961i −0.159788 0.0922537i
\(159\) 0 0
\(160\) 1.19742i 0.0946642i
\(161\) −17.7182 + 4.02602i −1.39639 + 0.317295i
\(162\) 0 0
\(163\) −12.0169 20.8138i −0.941234 1.63026i −0.763122 0.646254i \(-0.776335\pi\)
−0.178111 0.984010i \(-0.556999\pi\)
\(164\) −1.57652 + 2.73061i −0.123106 + 0.213225i
\(165\) 0 0
\(166\) −5.43489 9.41350i −0.421829 0.730630i
\(167\) −13.3713 −1.03471 −0.517353 0.855772i \(-0.673082\pi\)
−0.517353 + 0.855772i \(0.673082\pi\)
\(168\) 0 0
\(169\) 2.35959 0.181507
\(170\) −4.58364 + 2.64637i −0.351549 + 0.202967i
\(171\) 0 0
\(172\) −6.93044 4.00129i −0.528441 0.305096i
\(173\) −11.9348 20.6717i −0.907385 1.57164i −0.817684 0.575668i \(-0.804742\pi\)
−0.0897011 0.995969i \(-0.528591\pi\)
\(174\) 0 0
\(175\) −6.92274 + 6.41090i −0.523310 + 0.484618i
\(176\) 3.04988 + 1.30317i 0.229893 + 0.0982300i
\(177\) 0 0
\(178\) −11.4053 6.58488i −0.854867 0.493558i
\(179\) −17.6015 10.1622i −1.31560 0.759560i −0.332580 0.943075i \(-0.607919\pi\)
−0.983017 + 0.183515i \(0.941252\pi\)
\(180\) 0 0
\(181\) −19.4560 −1.44616 −0.723078 0.690766i \(-0.757273\pi\)
−0.723078 + 0.690766i \(0.757273\pi\)
\(182\) 8.41582 1.91228i 0.623822 0.141748i
\(183\) 0 0
\(184\) −5.94749 + 3.43378i −0.438455 + 0.253142i
\(185\) 7.94814 + 4.58886i 0.584359 + 0.337380i
\(186\) 0 0
\(187\) 1.75197 + 14.5548i 0.128116 + 1.06435i
\(188\) 0.410988i 0.0299744i
\(189\) 0 0
\(190\) −9.31176 −0.675546
\(191\) −8.14743 + 4.70392i −0.589527 + 0.340364i −0.764911 0.644136i \(-0.777217\pi\)
0.175383 + 0.984500i \(0.443884\pi\)
\(192\) 0 0
\(193\) 2.92081 + 1.68633i 0.210245 + 0.121385i 0.601425 0.798929i \(-0.294600\pi\)
−0.391180 + 0.920314i \(0.627933\pi\)
\(194\) −6.55486 11.3534i −0.470612 0.815123i
\(195\) 0 0
\(196\) −6.31265 + 3.02496i −0.450904 + 0.216069i
\(197\) 6.33128 0.451085 0.225543 0.974233i \(-0.427585\pi\)
0.225543 + 0.974233i \(0.427585\pi\)
\(198\) 0 0
\(199\) 0.331375 0.573958i 0.0234905 0.0406868i −0.854041 0.520205i \(-0.825855\pi\)
0.877532 + 0.479519i \(0.159189\pi\)
\(200\) −1.78309 + 3.08841i −0.126084 + 0.218384i
\(201\) 0 0
\(202\) −9.65151 −0.679078
\(203\) 19.8614 + 6.14751i 1.39400 + 0.431470i
\(204\) 0 0
\(205\) 3.26969 1.88775i 0.228365 0.131846i
\(206\) 4.95521 8.58267i 0.345246 0.597983i
\(207\) 0 0
\(208\) 2.82494 1.63098i 0.195875 0.113088i
\(209\) −10.1341 + 23.7175i −0.700993 + 1.64057i
\(210\) 0 0
\(211\) 14.9427i 1.02870i −0.857580 0.514350i \(-0.828033\pi\)
0.857580 0.514350i \(-0.171967\pi\)
\(212\) 5.02547 2.90146i 0.345151 0.199273i
\(213\) 0 0
\(214\) 4.82669 8.36007i 0.329946 0.571483i
\(215\) 4.79122 + 8.29864i 0.326758 + 0.565962i
\(216\) 0 0
\(217\) −0.401374 + 0.371698i −0.0272471 + 0.0252325i
\(218\) 7.32999i 0.496450i
\(219\) 0 0
\(220\) −2.38249 3.17737i −0.160627 0.214218i
\(221\) 12.4866 + 7.20914i 0.839940 + 0.484939i
\(222\) 0 0
\(223\) −17.0313 −1.14050 −0.570250 0.821471i \(-0.693154\pi\)
−0.570250 + 0.821471i \(0.693154\pi\)
\(224\) −1.94121 + 1.79769i −0.129703 + 0.120113i
\(225\) 0 0
\(226\) 10.4108 6.01066i 0.692514 0.399823i
\(227\) −9.58521 + 16.6021i −0.636193 + 1.10192i 0.350068 + 0.936724i \(0.386158\pi\)
−0.986261 + 0.165194i \(0.947175\pi\)
\(228\) 0 0
\(229\) 6.51023 + 11.2760i 0.430208 + 0.745142i 0.996891 0.0787938i \(-0.0251069\pi\)
−0.566683 + 0.823936i \(0.691774\pi\)
\(230\) 8.22335 0.542232
\(231\) 0 0
\(232\) 7.85827 0.515921
\(233\) 2.04857 + 3.54823i 0.134206 + 0.232452i 0.925294 0.379251i \(-0.123818\pi\)
−0.791088 + 0.611703i \(0.790485\pi\)
\(234\) 0 0
\(235\) 0.246063 0.426193i 0.0160513 0.0278018i
\(236\) 3.66888 2.11823i 0.238824 0.137885i
\(237\) 0 0
\(238\) −11.1716 3.45785i −0.724150 0.224139i
\(239\) −4.68979 −0.303357 −0.151679 0.988430i \(-0.548468\pi\)
−0.151679 + 0.988430i \(0.548468\pi\)
\(240\) 0 0
\(241\) −11.0323 6.36950i −0.710652 0.410295i 0.100650 0.994922i \(-0.467908\pi\)
−0.811303 + 0.584627i \(0.801241\pi\)
\(242\) −10.6858 + 2.61032i −0.686909 + 0.167798i
\(243\) 0 0
\(244\) 11.4857i 0.735300i
\(245\) 8.35726 + 0.642572i 0.533926 + 0.0410524i
\(246\) 0 0
\(247\) 12.6834 + 21.9683i 0.807025 + 1.39781i
\(248\) −0.103382 + 0.179063i −0.00656478 + 0.0113705i
\(249\) 0 0
\(250\) 8.88309 5.12866i 0.561816 0.324365i
\(251\) 25.6272i 1.61758i 0.588100 + 0.808788i \(0.299876\pi\)
−0.588100 + 0.808788i \(0.700124\pi\)
\(252\) 0 0
\(253\) 8.94960 20.9452i 0.562657 1.31682i
\(254\) −15.7497 + 9.09308i −0.988222 + 0.570550i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.92122 + 2.84127i −0.306978 + 0.177234i −0.645573 0.763698i \(-0.723381\pi\)
0.338596 + 0.940932i \(0.390048\pi\)
\(258\) 0 0
\(259\) 4.49327 + 19.7745i 0.279198 + 1.22873i
\(260\) −3.90594 −0.242236
\(261\) 0 0
\(262\) −0.397483 + 0.688460i −0.0245566 + 0.0425332i
\(263\) −14.4242 + 24.9835i −0.889436 + 1.54055i −0.0488920 + 0.998804i \(0.515569\pi\)
−0.840544 + 0.541744i \(0.817764\pi\)
\(264\) 0 0
\(265\) −6.94852 −0.426844
\(266\) −13.9798 15.0959i −0.857156 0.925591i
\(267\) 0 0
\(268\) 5.61793 + 9.73055i 0.343170 + 0.594388i
\(269\) −15.8208 9.13413i −0.964610 0.556918i −0.0670210 0.997752i \(-0.521349\pi\)
−0.897589 + 0.440834i \(0.854683\pi\)
\(270\) 0 0
\(271\) 5.05904 2.92084i 0.307315 0.177428i −0.338410 0.940999i \(-0.609889\pi\)
0.645724 + 0.763571i \(0.276556\pi\)
\(272\) −4.42012 −0.268009
\(273\) 0 0
\(274\) 6.01509i 0.363385i
\(275\) −1.41350 11.7429i −0.0852373 0.708126i
\(276\) 0 0
\(277\) −13.0938 7.55973i −0.786732 0.454220i 0.0520786 0.998643i \(-0.483415\pi\)
−0.838811 + 0.544423i \(0.816749\pi\)
\(278\) 10.2698 5.92926i 0.615940 0.355613i
\(279\) 0 0
\(280\) 3.08932 0.701970i 0.184622 0.0419507i
\(281\) −7.22799 −0.431186 −0.215593 0.976483i \(-0.569168\pi\)
−0.215593 + 0.976483i \(0.569168\pi\)
\(282\) 0 0
\(283\) 0.0575633 + 0.0332342i 0.00342179 + 0.00197557i 0.501710 0.865036i \(-0.332704\pi\)
−0.498288 + 0.867011i \(0.666038\pi\)
\(284\) 3.29685 + 1.90344i 0.195632 + 0.112948i
\(285\) 0 0
\(286\) −4.25089 + 9.94859i −0.251360 + 0.588272i
\(287\) 7.96916 + 2.46662i 0.470405 + 0.145600i
\(288\) 0 0
\(289\) −1.26875 2.19753i −0.0746322 0.129267i
\(290\) −8.14899 4.70482i −0.478525 0.276277i
\(291\) 0 0
\(292\) −0.195764 + 0.113024i −0.0114562 + 0.00661424i
\(293\) 22.1095 1.29165 0.645824 0.763486i \(-0.276514\pi\)
0.645824 + 0.763486i \(0.276514\pi\)
\(294\) 0 0
\(295\) −5.07281 −0.295350
\(296\) 3.83230 + 6.63773i 0.222748 + 0.385810i
\(297\) 0 0
\(298\) 9.00137 15.5908i 0.521435 0.903152i
\(299\) −11.2009 19.4005i −0.647764 1.12196i
\(300\) 0 0
\(301\) −6.26040 + 20.2261i −0.360843 + 1.16582i
\(302\) 5.18537i 0.298385i
\(303\) 0 0
\(304\) −6.73468 3.88827i −0.386260 0.223007i
\(305\) −6.87662 + 11.9107i −0.393754 + 0.682002i
\(306\) 0 0
\(307\) 20.0987i 1.14710i −0.819172 0.573548i \(-0.805567\pi\)
0.819172 0.573548i \(-0.194433\pi\)
\(308\) 1.57421 8.63261i 0.0896988 0.491888i
\(309\) 0 0
\(310\) 0.214414 0.123792i 0.0121779 0.00703090i
\(311\) −13.7708 7.95055i −0.780868 0.450834i 0.0558698 0.998438i \(-0.482207\pi\)
−0.836738 + 0.547604i \(0.815540\pi\)
\(312\) 0 0
\(313\) 8.27538 + 14.3334i 0.467752 + 0.810170i 0.999321 0.0368447i \(-0.0117307\pi\)
−0.531569 + 0.847015i \(0.678397\pi\)
\(314\) −19.6790 −1.11055
\(315\) 0 0
\(316\) 2.31922i 0.130466i
\(317\) 8.65990 4.99980i 0.486389 0.280817i −0.236686 0.971586i \(-0.576061\pi\)
0.723075 + 0.690770i \(0.242728\pi\)
\(318\) 0 0
\(319\) −20.8521 + 15.6355i −1.16749 + 0.875420i
\(320\) 1.03699 0.598709i 0.0579698 0.0334689i
\(321\) 0 0
\(322\) 12.3457 + 13.3314i 0.688002 + 0.742931i
\(323\) 34.3733i 1.91258i
\(324\) 0 0
\(325\) −10.0743 5.81639i −0.558821 0.322635i
\(326\) −12.0169 + 20.8138i −0.665553 + 1.15277i
\(327\) 0 0
\(328\) 3.15304 0.174098
\(329\) 1.06034 0.240936i 0.0584587 0.0132833i
\(330\) 0 0
\(331\) −16.5068 28.5906i −0.907294 1.57148i −0.817808 0.575491i \(-0.804811\pi\)
−0.0894857 0.995988i \(-0.528522\pi\)
\(332\) −5.43489 + 9.41350i −0.298278 + 0.516633i
\(333\) 0 0
\(334\) 6.68567 + 11.5799i 0.365824 + 0.633625i
\(335\) 13.4540i 0.735072i
\(336\) 0 0
\(337\) 0.870822i 0.0474367i 0.999719 + 0.0237184i \(0.00755050\pi\)
−0.999719 + 0.0237184i \(0.992450\pi\)
\(338\) −1.17979 2.04346i −0.0641724 0.111150i
\(339\) 0 0
\(340\) 4.58364 + 2.64637i 0.248583 + 0.143519i
\(341\) −0.0819535 0.680845i −0.00443803 0.0368698i
\(342\) 0 0
\(343\) 11.5051 + 14.5132i 0.621215 + 0.783640i
\(344\) 8.00258i 0.431470i
\(345\) 0 0
\(346\) −11.9348 + 20.6717i −0.641618 + 1.11131i
\(347\) −3.92630 + 6.80054i −0.210775 + 0.365072i −0.951957 0.306231i \(-0.900932\pi\)
0.741183 + 0.671304i \(0.234265\pi\)
\(348\) 0 0
\(349\) 20.6953i 1.10779i −0.832586 0.553896i \(-0.813140\pi\)
0.832586 0.553896i \(-0.186860\pi\)
\(350\) 9.01337 + 2.78982i 0.481785 + 0.149122i
\(351\) 0 0
\(352\) −0.396361 3.29286i −0.0211261 0.175510i
\(353\) 23.0277 + 13.2951i 1.22564 + 0.707625i 0.966115 0.258111i \(-0.0831001\pi\)
0.259527 + 0.965736i \(0.416433\pi\)
\(354\) 0 0
\(355\) −2.27921 3.94771i −0.120968 0.209523i
\(356\) 13.1698i 0.697996i
\(357\) 0 0
\(358\) 20.3244i 1.07418i
\(359\) 0.0346521 + 0.0600191i 0.00182887 + 0.00316769i 0.866938 0.498415i \(-0.166085\pi\)
−0.865110 + 0.501583i \(0.832751\pi\)
\(360\) 0 0
\(361\) 20.7373 35.9180i 1.09143 1.89042i
\(362\) 9.72802 + 16.8494i 0.511293 + 0.885586i
\(363\) 0 0
\(364\) −5.86400 6.33217i −0.307357 0.331896i
\(365\) 0.270674 0.0141677
\(366\) 0 0
\(367\) −18.5149 + 32.0687i −0.966469 + 1.67397i −0.260854 + 0.965378i \(0.584004\pi\)
−0.705615 + 0.708595i \(0.749329\pi\)
\(368\) 5.94749 + 3.43378i 0.310034 + 0.178998i
\(369\) 0 0
\(370\) 9.17773i 0.477127i
\(371\) −10.4318 11.2647i −0.541594 0.584834i
\(372\) 0 0
\(373\) 10.9206 6.30501i 0.565447 0.326461i −0.189882 0.981807i \(-0.560810\pi\)
0.755329 + 0.655346i \(0.227477\pi\)
\(374\) 11.7289 8.79466i 0.606485 0.454761i
\(375\) 0 0
\(376\) 0.355926 0.205494i 0.0183555 0.0105976i
\(377\) 25.6334i 1.32019i
\(378\) 0 0
\(379\) −4.45725 −0.228954 −0.114477 0.993426i \(-0.536519\pi\)
−0.114477 + 0.993426i \(0.536519\pi\)
\(380\) 4.65588 + 8.06422i 0.238842 + 0.413686i
\(381\) 0 0
\(382\) 8.14743 + 4.70392i 0.416859 + 0.240674i
\(383\) −11.0167 + 6.36051i −0.562928 + 0.325007i −0.754320 0.656507i \(-0.772033\pi\)
0.191392 + 0.981514i \(0.438700\pi\)
\(384\) 0 0
\(385\) −6.80086 + 8.00947i −0.346604 + 0.408200i
\(386\) 3.37267i 0.171664i
\(387\) 0 0
\(388\) −6.55486 + 11.3534i −0.332773 + 0.576379i
\(389\) −18.7691 10.8364i −0.951633 0.549426i −0.0580454 0.998314i \(-0.518487\pi\)
−0.893588 + 0.448888i \(0.851820\pi\)
\(390\) 0 0
\(391\) 30.3555i 1.53514i
\(392\) 5.77602 + 3.95444i 0.291733 + 0.199729i
\(393\) 0 0
\(394\) −3.16564 5.48305i −0.159483 0.276232i
\(395\) 1.38854 2.40502i 0.0698650 0.121010i
\(396\) 0 0
\(397\) −6.77259 11.7305i −0.339907 0.588736i 0.644508 0.764597i \(-0.277062\pi\)
−0.984415 + 0.175862i \(0.943729\pi\)
\(398\) −0.662749 −0.0332206
\(399\) 0 0
\(400\) 3.56619 0.178309
\(401\) −23.0277 + 13.2951i −1.14995 + 0.663924i −0.948875 0.315652i \(-0.897777\pi\)
−0.201075 + 0.979576i \(0.564443\pi\)
\(402\) 0 0
\(403\) −0.584098 0.337229i −0.0290960 0.0167986i
\(404\) 4.82575 + 8.35845i 0.240090 + 0.415849i
\(405\) 0 0
\(406\) −4.60681 20.2742i −0.228632 1.00619i
\(407\) −23.3761 9.98826i −1.15871 0.495100i
\(408\) 0 0
\(409\) 5.51290 + 3.18288i 0.272596 + 0.157383i 0.630067 0.776541i \(-0.283028\pi\)
−0.357471 + 0.933924i \(0.616361\pi\)
\(410\) −3.26969 1.88775i −0.161478 0.0932296i
\(411\) 0 0
\(412\) −9.91042 −0.488251
\(413\) −7.61583 8.22387i −0.374751 0.404670i
\(414\) 0 0
\(415\) 11.2719 6.50783i 0.553316 0.319457i
\(416\) −2.82494 1.63098i −0.138504 0.0799655i
\(417\) 0 0
\(418\) 25.6070 3.08232i 1.25248 0.150761i
\(419\) 21.1161i 1.03159i 0.856713 + 0.515794i \(0.172503\pi\)
−0.856713 + 0.515794i \(0.827497\pi\)
\(420\) 0 0
\(421\) −8.94131 −0.435773 −0.217886 0.975974i \(-0.569916\pi\)
−0.217886 + 0.975974i \(0.569916\pi\)
\(422\) −12.9408 + 7.47137i −0.629948 + 0.363701i
\(423\) 0 0
\(424\) −5.02547 2.90146i −0.244058 0.140907i
\(425\) 7.88150 + 13.6512i 0.382309 + 0.662178i
\(426\) 0 0
\(427\) −29.6331 + 6.73337i −1.43404 + 0.325850i
\(428\) −9.65338 −0.466614
\(429\) 0 0
\(430\) 4.79122 8.29864i 0.231053 0.400196i
\(431\) 4.16534 7.21459i 0.200638 0.347514i −0.748096 0.663590i \(-0.769032\pi\)
0.948734 + 0.316076i \(0.102365\pi\)
\(432\) 0 0
\(433\) 0.288704 0.0138742 0.00693711 0.999976i \(-0.497792\pi\)
0.00693711 + 0.999976i \(0.497792\pi\)
\(434\) 0.522587 + 0.161751i 0.0250850 + 0.00776431i
\(435\) 0 0
\(436\) −6.34796 + 3.66500i −0.304012 + 0.175521i
\(437\) −26.7029 + 46.2509i −1.27738 + 2.21248i
\(438\) 0 0
\(439\) −10.0491 + 5.80186i −0.479618 + 0.276908i −0.720257 0.693707i \(-0.755976\pi\)
0.240639 + 0.970615i \(0.422643\pi\)
\(440\) −1.56044 + 3.65198i −0.0743910 + 0.174101i
\(441\) 0 0
\(442\) 14.4183i 0.685808i
\(443\) 4.34544 2.50884i 0.206458 0.119199i −0.393206 0.919450i \(-0.628634\pi\)
0.599664 + 0.800252i \(0.295301\pi\)
\(444\) 0 0
\(445\) 7.88485 13.6570i 0.373778 0.647402i
\(446\) 8.51565 + 14.7495i 0.403228 + 0.698411i
\(447\) 0 0
\(448\) 2.52745 + 0.782297i 0.119411 + 0.0369601i
\(449\) 14.7868i 0.697835i −0.937154 0.348917i \(-0.886549\pi\)
0.937154 0.348917i \(-0.113451\pi\)
\(450\) 0 0
\(451\) −8.36665 + 6.27357i −0.393970 + 0.295411i
\(452\) −10.4108 6.01066i −0.489682 0.282718i
\(453\) 0 0
\(454\) 19.1704 0.899712
\(455\) 2.28980 + 10.0773i 0.107348 + 0.472429i
\(456\) 0 0
\(457\) −29.4805 + 17.0205i −1.37904 + 0.796188i −0.992044 0.125895i \(-0.959820\pi\)
−0.386994 + 0.922082i \(0.626487\pi\)
\(458\) 6.51023 11.2760i 0.304203 0.526895i
\(459\) 0 0
\(460\) −4.11168 7.12163i −0.191708 0.332048i
\(461\) 31.2127 1.45372 0.726861 0.686785i \(-0.240979\pi\)
0.726861 + 0.686785i \(0.240979\pi\)
\(462\) 0 0
\(463\) 6.66544 0.309769 0.154885 0.987933i \(-0.450499\pi\)
0.154885 + 0.987933i \(0.450499\pi\)
\(464\) −3.92914 6.80547i −0.182406 0.315936i
\(465\) 0 0
\(466\) 2.04857 3.54823i 0.0948983 0.164369i
\(467\) −6.58720 + 3.80312i −0.304819 + 0.175987i −0.644606 0.764515i \(-0.722978\pi\)
0.339787 + 0.940503i \(0.389645\pi\)
\(468\) 0 0
\(469\) 21.8112 20.1986i 1.00715 0.932684i
\(470\) −0.492125 −0.0227000
\(471\) 0 0
\(472\) −3.66888 2.11823i −0.168874 0.0974994i
\(473\) −15.9226 21.2350i −0.732124 0.976386i
\(474\) 0 0
\(475\) 27.7326i 1.27246i
\(476\) 2.59124 + 11.4039i 0.118769 + 0.522695i
\(477\) 0 0
\(478\) 2.34489 + 4.06147i 0.107253 + 0.185767i
\(479\) 7.64294 13.2380i 0.349215 0.604858i −0.636895 0.770950i \(-0.719782\pi\)
0.986110 + 0.166092i \(0.0531150\pi\)
\(480\) 0 0
\(481\) −21.6521 + 12.5008i −0.987249 + 0.569988i
\(482\) 12.7390i 0.580245i
\(483\) 0 0
\(484\) 7.60350 + 7.94901i 0.345614 + 0.361319i
\(485\) 13.5947 7.84891i 0.617304 0.356401i
\(486\) 0 0
\(487\) 0.790493 1.36917i 0.0358206 0.0620432i −0.847559 0.530701i \(-0.821929\pi\)
0.883380 + 0.468658i \(0.155262\pi\)
\(488\) −9.94695 + 5.74287i −0.450277 + 0.259968i
\(489\) 0 0
\(490\) −3.62215 7.55889i −0.163632 0.341476i
\(491\) 6.90788 0.311748 0.155874 0.987777i \(-0.450181\pi\)
0.155874 + 0.987777i \(0.450181\pi\)
\(492\) 0 0
\(493\) 17.3673 30.0810i 0.782183 1.35478i
\(494\) 12.6834 21.9683i 0.570653 0.988400i
\(495\) 0 0
\(496\) 0.206764 0.00928400
\(497\) 2.97811 9.62170i 0.133587 0.431592i
\(498\) 0 0
\(499\) −0.474107 0.821178i −0.0212240 0.0367610i 0.855218 0.518268i \(-0.173423\pi\)
−0.876442 + 0.481507i \(0.840090\pi\)
\(500\) −8.88309 5.12866i −0.397264 0.229360i
\(501\) 0 0
\(502\) 22.1938 12.8136i 0.990559 0.571900i
\(503\) −30.8752 −1.37666 −0.688328 0.725400i \(-0.741655\pi\)
−0.688328 + 0.725400i \(0.741655\pi\)
\(504\) 0 0
\(505\) 11.5569i 0.514275i
\(506\) −22.6139 + 2.72204i −1.00531 + 0.121009i
\(507\) 0 0
\(508\) 15.7497 + 9.09308i 0.698779 + 0.403440i
\(509\) 31.6394 18.2670i 1.40239 0.809670i 0.407752 0.913093i \(-0.366313\pi\)
0.994638 + 0.103422i \(0.0329794\pi\)
\(510\) 0 0
\(511\) 0.406364 + 0.438808i 0.0179765 + 0.0194117i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 4.92122 + 2.84127i 0.217066 + 0.125323i
\(515\) 10.2770 + 5.93346i 0.452861 + 0.261459i
\(516\) 0 0
\(517\) −0.535587 + 1.25346i −0.0235551 + 0.0551273i
\(518\) 14.8786 13.7786i 0.653729 0.605395i
\(519\) 0 0
\(520\) 1.95297 + 3.38264i 0.0856433 + 0.148339i
\(521\) 0.780812 + 0.450802i 0.0342080 + 0.0197500i 0.517006 0.855981i \(-0.327046\pi\)
−0.482798 + 0.875731i \(0.660380\pi\)
\(522\) 0 0
\(523\) 8.65582 4.99744i 0.378492 0.218523i −0.298670 0.954357i \(-0.596543\pi\)
0.677162 + 0.735834i \(0.263210\pi\)
\(524\) 0.794965 0.0347282
\(525\) 0 0
\(526\) 28.8484 1.25785
\(527\) 0.456962 + 0.791482i 0.0199056 + 0.0344775i
\(528\) 0 0
\(529\) 12.0817 20.9262i 0.525293 0.909835i
\(530\) 3.47426 + 6.01759i 0.150912 + 0.261387i
\(531\) 0 0
\(532\) −6.08356 + 19.6548i −0.263756 + 0.852144i
\(533\) 10.2851i 0.445498i
\(534\) 0 0
\(535\) 10.0105 + 5.77957i 0.432792 + 0.249872i
\(536\) 5.61793 9.73055i 0.242658 0.420296i
\(537\) 0 0
\(538\) 18.2683i 0.787601i
\(539\) −23.1949 + 0.999316i −0.999073 + 0.0430436i
\(540\) 0 0
\(541\) 30.8485 17.8104i 1.32628 0.765727i 0.341557 0.939861i \(-0.389046\pi\)
0.984722 + 0.174134i \(0.0557126\pi\)
\(542\) −5.05904 2.92084i −0.217304 0.125461i
\(543\) 0 0
\(544\) 2.21006 + 3.82794i 0.0947556 + 0.164122i
\(545\) 8.77706 0.375968
\(546\) 0 0
\(547\) 7.11968i 0.304416i 0.988349 + 0.152208i \(0.0486383\pi\)
−0.988349 + 0.152208i \(0.951362\pi\)
\(548\) 5.20922 3.00754i 0.222527 0.128476i
\(549\) 0 0
\(550\) −9.46294 + 7.09560i −0.403501 + 0.302557i
\(551\) 52.9229 30.5551i 2.25459 1.30169i
\(552\) 0 0
\(553\) 5.98356 1.35961i 0.254447 0.0578166i
\(554\) 15.1195i 0.642364i
\(555\) 0 0
\(556\) −10.2698 5.92926i −0.435535 0.251457i
\(557\) 9.08485 15.7354i 0.384938 0.666731i −0.606823 0.794837i \(-0.707556\pi\)
0.991761 + 0.128106i \(0.0408896\pi\)
\(558\) 0 0
\(559\) −26.1041 −1.10409
\(560\) −2.15258 2.32445i −0.0909633 0.0982258i
\(561\) 0 0
\(562\) 3.61399 + 6.25962i 0.152447 + 0.264046i
\(563\) 6.69275 11.5922i 0.282066 0.488552i −0.689828 0.723974i \(-0.742314\pi\)
0.971893 + 0.235422i \(0.0756471\pi\)
\(564\) 0 0
\(565\) 7.19728 + 12.4660i 0.302792 + 0.524451i
\(566\) 0.0664684i 0.00279388i
\(567\) 0 0
\(568\) 3.80688i 0.159733i
\(569\) −0.774915 1.34219i −0.0324861 0.0562676i 0.849325 0.527870i \(-0.177009\pi\)
−0.881811 + 0.471602i \(0.843676\pi\)
\(570\) 0 0
\(571\) −36.9067 21.3081i −1.54450 0.891715i −0.998547 0.0538962i \(-0.982836\pi\)
−0.545949 0.837819i \(-0.683831\pi\)
\(572\) 10.7412 1.29292i 0.449111 0.0540596i
\(573\) 0 0
\(574\) −1.84843 8.13480i −0.0771519 0.339540i
\(575\) 24.4911i 1.02135i
\(576\) 0 0
\(577\) 0.303156 0.525081i 0.0126205 0.0218594i −0.859646 0.510890i \(-0.829316\pi\)
0.872267 + 0.489030i \(0.162649\pi\)
\(578\) −1.26875 + 2.19753i −0.0527729 + 0.0914054i
\(579\) 0 0
\(580\) 9.40964i 0.390714i
\(581\) 27.4728 + 8.50340i 1.13977 + 0.352780i
\(582\) 0 0
\(583\) 19.1082 2.30005i 0.791379 0.0952584i
\(584\) 0.195764 + 0.113024i 0.00810075 + 0.00467697i
\(585\) 0 0
\(586\) −11.0547 19.1474i −0.456667 0.790970i
\(587\) 2.21478i 0.0914137i 0.998955 + 0.0457069i \(0.0145540\pi\)
−0.998955 + 0.0457069i \(0.985446\pi\)
\(588\) 0 0
\(589\) 1.60791i 0.0662528i
\(590\) 2.53641 + 4.39318i 0.104422 + 0.180864i
\(591\) 0 0
\(592\) 3.83230 6.63773i 0.157506 0.272809i
\(593\) −16.2190 28.0922i −0.666036 1.15361i −0.979003 0.203844i \(-0.934656\pi\)
0.312967 0.949764i \(-0.398677\pi\)
\(594\) 0 0
\(595\) 4.14049 13.3771i 0.169744 0.548409i
\(596\) −18.0027 −0.737421
\(597\) 0 0
\(598\) −11.2009 + 19.4005i −0.458038 + 0.793345i
\(599\) −39.3780 22.7349i −1.60894 0.928922i −0.989608 0.143794i \(-0.954070\pi\)
−0.619333 0.785128i \(-0.712597\pi\)
\(600\) 0 0
\(601\) 23.7080i 0.967069i 0.875325 + 0.483535i \(0.160647\pi\)
−0.875325 + 0.483535i \(0.839353\pi\)
\(602\) 20.6466 4.69141i 0.841491 0.191207i
\(603\) 0 0
\(604\) 4.49066 2.59269i 0.182723 0.105495i
\(605\) −3.12565 12.7954i −0.127076 0.520206i
\(606\) 0 0
\(607\) −16.5637 + 9.56306i −0.672300 + 0.388153i −0.796948 0.604049i \(-0.793553\pi\)
0.124648 + 0.992201i \(0.460220\pi\)
\(608\) 7.77654i 0.315380i
\(609\) 0 0
\(610\) 13.7532 0.556853
\(611\) 0.670315 + 1.16102i 0.0271180 + 0.0469698i
\(612\) 0 0
\(613\) −3.26599 1.88562i −0.131912 0.0761595i 0.432592 0.901590i \(-0.357599\pi\)
−0.564504 + 0.825430i \(0.690932\pi\)
\(614\) −17.4060 + 10.0494i −0.702450 + 0.405560i
\(615\) 0 0
\(616\) −8.26316 + 2.95300i −0.332932 + 0.118980i
\(617\) 13.0431i 0.525096i −0.964919 0.262548i \(-0.915437\pi\)
0.964919 0.262548i \(-0.0845628\pi\)
\(618\) 0 0
\(619\) 20.6271 35.7272i 0.829074 1.43600i −0.0696922 0.997569i \(-0.522202\pi\)
0.898766 0.438429i \(-0.144465\pi\)
\(620\) −0.214414 0.123792i −0.00861106 0.00497160i
\(621\) 0 0
\(622\) 15.9011i 0.637576i
\(623\) 33.9778 7.72059i 1.36129 0.309319i
\(624\) 0 0
\(625\) −2.77433 4.80528i −0.110973 0.192211i
\(626\) 8.27538 14.3334i 0.330751 0.572877i
\(627\) 0 0
\(628\) 9.83949 + 17.0425i 0.392638 + 0.680070i
\(629\) 33.8785 1.35082
\(630\) 0 0
\(631\) −35.4512 −1.41129 −0.705645 0.708566i \(-0.749343\pi\)
−0.705645 + 0.708566i \(0.749343\pi\)
\(632\) 2.00851 1.15961i 0.0798941 0.0461269i
\(633\) 0 0
\(634\) −8.65990 4.99980i −0.343929 0.198567i
\(635\) −10.8882 18.8589i −0.432086 0.748394i
\(636\) 0 0
\(637\) −12.8992 + 18.8412i −0.511086 + 0.746515i
\(638\) 23.9668 + 10.2407i 0.948854 + 0.405431i
\(639\) 0 0
\(640\) −1.03699 0.598709i −0.0409908 0.0236661i
\(641\) 14.8938 + 8.59891i 0.588268 + 0.339637i 0.764412 0.644728i \(-0.223029\pi\)
−0.176144 + 0.984364i \(0.556363\pi\)
\(642\) 0 0
\(643\) −14.9068 −0.587869 −0.293934 0.955826i \(-0.594965\pi\)
−0.293934 + 0.955826i \(0.594965\pi\)
\(644\) 5.37248 17.3574i 0.211705 0.683979i
\(645\) 0 0
\(646\) −29.7681 + 17.1866i −1.17121 + 0.676199i
\(647\) 8.06855 + 4.65838i 0.317208 + 0.183140i 0.650147 0.759808i \(-0.274707\pi\)
−0.332940 + 0.942948i \(0.608041\pi\)
\(648\) 0 0
\(649\) 13.9500 1.67917i 0.547587 0.0659131i
\(650\) 11.6328i 0.456275i
\(651\) 0 0
\(652\) 24.0337 0.941234
\(653\) −16.4127 + 9.47591i −0.642281 + 0.370821i −0.785492 0.618871i \(-0.787590\pi\)
0.143212 + 0.989692i \(0.454257\pi\)
\(654\) 0 0
\(655\) −0.824375 0.475953i −0.0322110 0.0185970i
\(656\) −1.57652 2.73061i −0.0615528 0.106613i
\(657\) 0 0
\(658\) −0.738829 0.797817i −0.0288026 0.0311021i
\(659\) 22.1801 0.864016 0.432008 0.901870i \(-0.357805\pi\)
0.432008 + 0.901870i \(0.357805\pi\)
\(660\) 0 0
\(661\) 17.8342 30.8897i 0.693670 1.20147i −0.276957 0.960882i \(-0.589326\pi\)
0.970627 0.240589i \(-0.0773406\pi\)
\(662\) −16.5068 + 28.5906i −0.641554 + 1.11120i
\(663\) 0 0
\(664\) 10.8698 0.421829
\(665\) 18.0761 16.7397i 0.700963 0.649136i
\(666\) 0 0
\(667\) −46.7370 + 26.9836i −1.80966 + 1.04481i
\(668\) 6.68567 11.5799i 0.258676 0.448041i
\(669\) 0 0
\(670\) −11.6515 + 6.72702i −0.450138 + 0.259887i
\(671\) 14.9679 35.0301i 0.577828 1.35232i
\(672\) 0 0
\(673\) 18.5749i 0.716010i 0.933720 + 0.358005i \(0.116543\pi\)
−0.933720 + 0.358005i \(0.883457\pi\)
\(674\) 0.754154 0.435411i 0.0290489 0.0167714i
\(675\) 0 0
\(676\) −1.17979 + 2.04346i −0.0453767 + 0.0785948i
\(677\) 0.0528202 + 0.0914873i 0.00203005 + 0.00351614i 0.867039 0.498241i \(-0.166020\pi\)
−0.865009 + 0.501757i \(0.832687\pi\)
\(678\) 0 0
\(679\) 33.1342 + 10.2557i 1.27157 + 0.393578i
\(680\) 5.29274i 0.202967i
\(681\) 0 0
\(682\) −0.548653 + 0.411397i −0.0210090 + 0.0157532i
\(683\) −6.42302 3.70833i −0.245770 0.141895i 0.372056 0.928210i \(-0.378653\pi\)
−0.617826 + 0.786315i \(0.711986\pi\)
\(684\) 0 0
\(685\) −7.20257 −0.275196
\(686\) 6.81627 17.2203i 0.260247 0.657474i
\(687\) 0 0
\(688\) 6.93044 4.00129i 0.264221 0.152548i
\(689\) 9.46445 16.3929i 0.360567 0.624520i
\(690\) 0 0
\(691\) −10.5227 18.2258i −0.400302 0.693343i 0.593460 0.804863i \(-0.297761\pi\)
−0.993762 + 0.111520i \(0.964428\pi\)
\(692\) 23.8696 0.907385
\(693\) 0 0
\(694\) 7.85259 0.298080
\(695\) 7.09980 + 12.2972i 0.269311 + 0.466460i
\(696\) 0 0
\(697\) 6.96842 12.0697i 0.263948 0.457171i
\(698\) −17.9226 + 10.3476i −0.678382 + 0.391664i
\(699\) 0 0
\(700\) −2.09063 9.20072i −0.0790184 0.347755i
\(701\) −2.71470 −0.102533 −0.0512663 0.998685i \(-0.516326\pi\)
−0.0512663 + 0.998685i \(0.516326\pi\)
\(702\) 0 0
\(703\) 51.6186 + 29.8020i 1.94683 + 1.12400i
\(704\) −2.65352 + 1.98969i −0.100008 + 0.0749891i
\(705\) 0 0
\(706\) 26.5901i 1.00073i
\(707\) 18.7357 17.3504i 0.704627 0.652529i
\(708\) 0 0
\(709\) −11.7895 20.4200i −0.442763 0.766888i 0.555130 0.831763i \(-0.312668\pi\)
−0.997893 + 0.0648754i \(0.979335\pi\)
\(710\) −2.27921 + 3.94771i −0.0855373 + 0.148155i
\(711\) 0 0
\(712\) 11.4053 6.58488i 0.427433 0.246779i
\(713\) 1.41997i 0.0531783i
\(714\) 0 0
\(715\) −11.9126 5.09009i −0.445507 0.190359i
\(716\) 17.6015 10.1622i 0.657798 0.379780i
\(717\) 0 0
\(718\) 0.0346521 0.0600191i 0.00129320 0.00223989i
\(719\) −39.6365 + 22.8842i −1.47819 + 0.853435i −0.999696 0.0246536i \(-0.992152\pi\)
−0.478497 + 0.878089i \(0.658818\pi\)
\(720\) 0 0
\(721\) 5.80985 + 25.5687i 0.216370 + 0.952229i
\(722\) −41.4745 −1.54352
\(723\) 0 0
\(724\) 9.72802 16.8494i 0.361539 0.626204i
\(725\) −14.0120 + 24.2696i −0.520394 + 0.901350i
\(726\) 0 0
\(727\) −6.07152 −0.225180 −0.112590 0.993642i \(-0.535915\pi\)
−0.112590 + 0.993642i \(0.535915\pi\)
\(728\) −2.55183 + 8.24446i −0.0945769 + 0.305560i
\(729\) 0 0
\(730\) −0.135337 0.234411i −0.00500905 0.00867593i
\(731\) 30.6334 + 17.6862i 1.13302 + 0.654148i
\(732\) 0 0
\(733\) −36.1021 + 20.8436i −1.33346 + 0.769875i −0.985829 0.167755i \(-0.946348\pi\)
−0.347634 + 0.937630i \(0.613015\pi\)
\(734\) 37.0298 1.36679
\(735\) 0 0
\(736\) 6.86757i 0.253142i
\(737\) 4.45346 + 36.9981i 0.164045 + 1.36284i
\(738\) 0 0
\(739\) 7.62892 + 4.40456i 0.280635 + 0.162024i 0.633711 0.773570i \(-0.281531\pi\)
−0.353076 + 0.935595i \(0.614864\pi\)
\(740\) −7.94814 + 4.58886i −0.292180 + 0.168690i
\(741\) 0 0
\(742\) −4.53960 + 14.6666i −0.166654 + 0.538427i
\(743\) 45.0818 1.65389 0.826945 0.562283i \(-0.190077\pi\)
0.826945 + 0.562283i \(0.190077\pi\)
\(744\) 0 0
\(745\) 18.6687 + 10.7784i 0.683970 + 0.394890i
\(746\) −10.9206 6.30501i −0.399831 0.230843i
\(747\) 0 0
\(748\) −13.4808 5.76017i −0.492908 0.210613i
\(749\) 5.65916 + 24.9056i 0.206781 + 0.910030i
\(750\) 0 0
\(751\) 0.739343 + 1.28058i 0.0269790 + 0.0467290i 0.879200 0.476453i \(-0.158078\pi\)
−0.852221 + 0.523183i \(0.824745\pi\)
\(752\) −0.355926 0.205494i −0.0129793 0.00749360i
\(753\) 0 0
\(754\) 22.1992 12.8167i 0.808447 0.466757i
\(755\) −6.20906 −0.225971
\(756\) 0 0
\(757\) 19.5239 0.709608 0.354804 0.934941i \(-0.384548\pi\)
0.354804 + 0.934941i \(0.384548\pi\)
\(758\) 2.22863 + 3.86010i 0.0809474 + 0.140205i
\(759\) 0 0
\(760\) 4.65588 8.06422i 0.168887 0.292520i
\(761\) −14.9359 25.8697i −0.541426 0.937777i −0.998822 0.0485145i \(-0.984551\pi\)
0.457396 0.889263i \(-0.348782\pi\)
\(762\) 0 0
\(763\) 13.1770 + 14.2291i 0.477041 + 0.515128i
\(764\) 9.40784i 0.340364i
\(765\) 0 0
\(766\) 11.0167 + 6.36051i 0.398050 + 0.229815i
\(767\) 6.90959 11.9678i 0.249491 0.432131i
\(768\) 0 0
\(769\) 2.72669i 0.0983268i 0.998791 + 0.0491634i \(0.0156555\pi\)
−0.998791 + 0.0491634i \(0.984344\pi\)
\(770\) 10.3368 + 1.88498i 0.372514 + 0.0679301i
\(771\) 0 0
\(772\) −2.92081 + 1.68633i −0.105122 + 0.0606925i
\(773\) 9.27880 + 5.35712i 0.333735 + 0.192682i 0.657498 0.753456i \(-0.271615\pi\)
−0.323763 + 0.946138i \(0.604948\pi\)
\(774\) 0 0
\(775\) −0.368681 0.638574i −0.0132434 0.0229382i
\(776\) 13.1097 0.470612
\(777\) 0 0
\(778\) 21.6727i 0.777005i
\(779\) 21.2347 12.2599i 0.760813 0.439255i
\(780\) 0 0
\(781\) 7.57450 + 10.1016i 0.271037 + 0.361464i
\(782\) 26.2886 15.1778i 0.940080 0.542755i
\(783\) 0 0
\(784\) 0.536631 6.97940i 0.0191654 0.249264i
\(785\) 23.5640i 0.841034i
\(786\) 0 0
\(787\) −13.6208 7.86396i −0.485529 0.280320i 0.237189 0.971464i \(-0.423774\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(788\) −3.16564 + 5.48305i −0.112771 + 0.195326i
\(789\) 0 0
\(790\) −2.77708 −0.0988040
\(791\) −9.40425 +