Properties

Label 1078.2.i.d.901.9
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
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 901.9
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.d.1011.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(-1.23576 - 2.14039i) q^{10} +(-1.30225 + 3.05027i) q^{11} +(-1.60021 - 0.923880i) q^{12} +1.96452 q^{13} +4.56676 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.82487 - 4.89282i) q^{17} +(0.358719 - 0.207107i) q^{18} +(-0.453489 + 0.785466i) q^{19} -2.47151i q^{20} +(-2.65291 + 1.99049i) q^{22} +(0.468406 - 0.811303i) q^{23} +(-0.923880 - 1.60021i) q^{24} +(0.554192 + 0.959889i) q^{25} +(1.70132 + 0.982258i) q^{26} -4.77791i q^{27} -7.50358i q^{29} +(3.95493 + 2.28338i) q^{30} +(-4.08699 + 2.35963i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.734219 - 6.08418i) q^{33} -5.64974i q^{34} +0.414214 q^{36} +(4.81498 - 8.33978i) q^{37} +(-0.785466 + 0.453489i) q^{38} +(-3.14363 + 1.81498i) q^{39} +(1.23576 - 2.14039i) q^{40} +6.93240 q^{41} -6.80940i q^{43} +(-3.29274 + 0.397356i) q^{44} +(-0.886580 + 0.511867i) q^{45} +(0.811303 - 0.468406i) q^{46} +(-3.46605 - 2.00112i) q^{47} -1.84776i q^{48} +1.10838i q^{50} +(9.04075 + 5.21968i) q^{51} +(0.982258 + 1.70132i) q^{52} +(-3.28338 - 5.68698i) q^{53} +(2.38896 - 4.13779i) q^{54} +(6.55672 - 4.91952i) q^{55} -1.67588i q^{57} +(3.75179 - 6.49829i) q^{58} +(0.836265 - 0.482818i) q^{59} +(2.28338 + 3.95493i) q^{60} +(-5.95014 + 10.3059i) q^{61} -4.71925 q^{62} -1.00000 q^{64} +(-4.20484 - 2.42766i) q^{65} +(2.40624 - 5.63617i) q^{66} +(-3.36002 - 5.81973i) q^{67} +(2.82487 - 4.89282i) q^{68} +1.73100i q^{69} -11.5485 q^{71} +(0.358719 + 0.207107i) q^{72} +(5.43072 + 9.40628i) q^{73} +(8.33978 - 4.81498i) q^{74} +(-1.77364 - 1.02401i) q^{75} -0.906978 q^{76} -3.62995 q^{78} +(7.34847 + 4.24264i) q^{79} +(2.14039 - 1.23576i) q^{80} +(5.03553 + 8.72180i) q^{81} +(6.00363 + 3.46620i) q^{82} +4.83601 q^{83} +13.9634i q^{85} +(3.40470 - 5.89712i) q^{86} +(6.93240 + 12.0073i) q^{87} +(-3.05027 - 1.30225i) q^{88} +(-11.0280 - 6.36702i) q^{89} -1.02373 q^{90} +0.936812 q^{92} +(4.36002 - 7.55178i) q^{93} +(-2.00112 - 3.46605i) q^{94} +(1.94129 - 1.12080i) q^{95} +(0.923880 - 1.60021i) q^{96} -3.82683i q^{97} +(0.824487 + 1.09887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9} + O(q^{10}) \) \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −1.60021 + 0.923880i −0.923880 + 0.533402i −0.884871 0.465837i \(-0.845753\pi\)
−0.0390089 + 0.999239i \(0.512420\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.14039 1.23576i −0.957214 0.552647i −0.0618992 0.998082i \(-0.519716\pi\)
−0.895314 + 0.445435i \(0.853049\pi\)
\(6\) −1.84776 −0.754344
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.207107 0.358719i 0.0690356 0.119573i
\(10\) −1.23576 2.14039i −0.390781 0.676852i
\(11\) −1.30225 + 3.05027i −0.392642 + 0.919691i
\(12\) −1.60021 0.923880i −0.461940 0.266701i
\(13\) 1.96452 0.544859 0.272429 0.962176i \(-0.412173\pi\)
0.272429 + 0.962176i \(0.412173\pi\)
\(14\) 0 0
\(15\) 4.56676 1.17913
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.82487 4.89282i −0.685131 1.18668i −0.973395 0.229132i \(-0.926411\pi\)
0.288264 0.957551i \(-0.406922\pi\)
\(18\) 0.358719 0.207107i 0.0845510 0.0488155i
\(19\) −0.453489 + 0.785466i −0.104038 + 0.180198i −0.913345 0.407188i \(-0.866510\pi\)
0.809307 + 0.587386i \(0.199843\pi\)
\(20\) 2.47151i 0.552647i
\(21\) 0 0
\(22\) −2.65291 + 1.99049i −0.565603 + 0.424374i
\(23\) 0.468406 0.811303i 0.0976694 0.169168i −0.813050 0.582194i \(-0.802195\pi\)
0.910720 + 0.413025i \(0.135528\pi\)
\(24\) −0.923880 1.60021i −0.188586 0.326641i
\(25\) 0.554192 + 0.959889i 0.110838 + 0.191978i
\(26\) 1.70132 + 0.982258i 0.333656 + 0.192637i
\(27\) 4.77791i 0.919509i
\(28\) 0 0
\(29\) 7.50358i 1.39338i −0.717373 0.696689i \(-0.754656\pi\)
0.717373 0.696689i \(-0.245344\pi\)
\(30\) 3.95493 + 2.28338i 0.722069 + 0.416887i
\(31\) −4.08699 + 2.35963i −0.734046 + 0.423801i −0.819900 0.572506i \(-0.805971\pi\)
0.0858548 + 0.996308i \(0.472638\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −0.734219 6.08418i −0.127811 1.05912i
\(34\) 5.64974i 0.968922i
\(35\) 0 0
\(36\) 0.414214 0.0690356
\(37\) 4.81498 8.33978i 0.791577 1.37105i −0.133413 0.991061i \(-0.542594\pi\)
0.924990 0.379991i \(-0.124073\pi\)
\(38\) −0.785466 + 0.453489i −0.127419 + 0.0735656i
\(39\) −3.14363 + 1.81498i −0.503384 + 0.290629i
\(40\) 1.23576 2.14039i 0.195390 0.338426i
\(41\) 6.93240 1.08266 0.541329 0.840811i \(-0.317921\pi\)
0.541329 + 0.840811i \(0.317921\pi\)
\(42\) 0 0
\(43\) 6.80940i 1.03842i −0.854645 0.519212i \(-0.826225\pi\)
0.854645 0.519212i \(-0.173775\pi\)
\(44\) −3.29274 + 0.397356i −0.496399 + 0.0599037i
\(45\) −0.886580 + 0.511867i −0.132164 + 0.0763047i
\(46\) 0.811303 0.468406i 0.119620 0.0690627i
\(47\) −3.46605 2.00112i −0.505575 0.291894i 0.225438 0.974258i \(-0.427619\pi\)
−0.731013 + 0.682364i \(0.760952\pi\)
\(48\) 1.84776i 0.266701i
\(49\) 0 0
\(50\) 1.10838i 0.156749i
\(51\) 9.04075 + 5.21968i 1.26596 + 0.730901i
\(52\) 0.982258 + 1.70132i 0.136215 + 0.235931i
\(53\) −3.28338 5.68698i −0.451007 0.781167i 0.547442 0.836844i \(-0.315602\pi\)
−0.998449 + 0.0556765i \(0.982268\pi\)
\(54\) 2.38896 4.13779i 0.325096 0.563082i
\(55\) 6.55672 4.91952i 0.884108 0.663348i
\(56\) 0 0
\(57\) 1.67588i 0.221975i
\(58\) 3.75179 6.49829i 0.492634 0.853267i
\(59\) 0.836265 0.482818i 0.108872 0.0628575i −0.444575 0.895742i \(-0.646645\pi\)
0.553447 + 0.832884i \(0.313312\pi\)
\(60\) 2.28338 + 3.95493i 0.294783 + 0.510580i
\(61\) −5.95014 + 10.3059i −0.761838 + 1.31954i 0.180065 + 0.983655i \(0.442369\pi\)
−0.941902 + 0.335887i \(0.890964\pi\)
\(62\) −4.71925 −0.599346
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.20484 2.42766i −0.521546 0.301115i
\(66\) 2.40624 5.63617i 0.296188 0.693764i
\(67\) −3.36002 5.81973i −0.410492 0.710993i 0.584452 0.811429i \(-0.301310\pi\)
−0.994944 + 0.100436i \(0.967976\pi\)
\(68\) 2.82487 4.89282i 0.342566 0.593341i
\(69\) 1.73100i 0.208388i
\(70\) 0 0
\(71\) −11.5485 −1.37055 −0.685276 0.728284i \(-0.740318\pi\)
−0.685276 + 0.728284i \(0.740318\pi\)
\(72\) 0.358719 + 0.207107i 0.0422755 + 0.0244078i
\(73\) 5.43072 + 9.40628i 0.635617 + 1.10092i 0.986384 + 0.164458i \(0.0525876\pi\)
−0.350767 + 0.936463i \(0.614079\pi\)
\(74\) 8.33978 4.81498i 0.969480 0.559730i
\(75\) −1.77364 1.02401i −0.204803 0.118243i
\(76\) −0.906978 −0.104038
\(77\) 0 0
\(78\) −3.62995 −0.411011
\(79\) 7.34847 + 4.24264i 0.826767 + 0.477334i 0.852745 0.522328i \(-0.174936\pi\)
−0.0259772 + 0.999663i \(0.508270\pi\)
\(80\) 2.14039 1.23576i 0.239303 0.138162i
\(81\) 5.03553 + 8.72180i 0.559504 + 0.969089i
\(82\) 6.00363 + 3.46620i 0.662990 + 0.382778i
\(83\) 4.83601 0.530821 0.265411 0.964135i \(-0.414493\pi\)
0.265411 + 0.964135i \(0.414493\pi\)
\(84\) 0 0
\(85\) 13.9634i 1.51454i
\(86\) 3.40470 5.89712i 0.367138 0.635902i
\(87\) 6.93240 + 12.0073i 0.743231 + 1.28731i
\(88\) −3.05027 1.30225i −0.325160 0.138820i
\(89\) −11.0280 6.36702i −1.16897 0.674903i −0.215530 0.976497i \(-0.569148\pi\)
−0.953436 + 0.301594i \(0.902481\pi\)
\(90\) −1.02373 −0.107911
\(91\) 0 0
\(92\) 0.936812 0.0976694
\(93\) 4.36002 7.55178i 0.452113 0.783083i
\(94\) −2.00112 3.46605i −0.206400 0.357496i
\(95\) 1.94129 1.12080i 0.199172 0.114992i
\(96\) 0.923880 1.60021i 0.0942931 0.163320i
\(97\) 3.82683i 0.388556i −0.980946 0.194278i \(-0.937764\pi\)
0.980946 0.194278i \(-0.0622364\pi\)
\(98\) 0 0
\(99\) 0.824487 + 1.09887i 0.0828641 + 0.110441i
\(100\) −0.554192 + 0.959889i −0.0554192 + 0.0959889i
\(101\) −7.91466 13.7086i −0.787538 1.36406i −0.927471 0.373895i \(-0.878022\pi\)
0.139933 0.990161i \(-0.455311\pi\)
\(102\) 5.21968 + 9.04075i 0.516825 + 0.895167i
\(103\) 0.684352 + 0.395111i 0.0674312 + 0.0389314i 0.533337 0.845903i \(-0.320938\pi\)
−0.465905 + 0.884835i \(0.654271\pi\)
\(104\) 1.96452i 0.192637i
\(105\) 0 0
\(106\) 6.56676i 0.637820i
\(107\) 14.3861 + 8.30583i 1.39076 + 0.802955i 0.993399 0.114708i \(-0.0365933\pi\)
0.397359 + 0.917663i \(0.369927\pi\)
\(108\) 4.13779 2.38896i 0.398159 0.229877i
\(109\) −5.19615 + 3.00000i −0.497701 + 0.287348i −0.727764 0.685828i \(-0.759440\pi\)
0.230063 + 0.973176i \(0.426107\pi\)
\(110\) 8.13804 0.982072i 0.775932 0.0936369i
\(111\) 17.7938i 1.68892i
\(112\) 0 0
\(113\) −5.76421 −0.542251 −0.271126 0.962544i \(-0.587396\pi\)
−0.271126 + 0.962544i \(0.587396\pi\)
\(114\) 0.837939 1.45135i 0.0784801 0.135932i
\(115\) −2.00515 + 1.15767i −0.186981 + 0.107953i
\(116\) 6.49829 3.75179i 0.603351 0.348345i
\(117\) 0.406865 0.704710i 0.0376146 0.0651505i
\(118\) 0.965635 0.0888940
\(119\) 0 0
\(120\) 4.56676i 0.416887i
\(121\) −7.60831 7.94441i −0.691664 0.722219i
\(122\) −10.3059 + 5.95014i −0.933057 + 0.538701i
\(123\) −11.0933 + 6.40470i −1.00025 + 0.577493i
\(124\) −4.08699 2.35963i −0.367023 0.211901i
\(125\) 9.61818i 0.860277i
\(126\) 0 0
\(127\) 18.6371i 1.65378i 0.562367 + 0.826888i \(0.309891\pi\)
−0.562367 + 0.826888i \(0.690109\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 6.29107 + 10.8965i 0.553898 + 0.959379i
\(130\) −2.42766 4.20484i −0.212920 0.368789i
\(131\) 9.99173 17.3062i 0.872982 1.51205i 0.0140849 0.999901i \(-0.495516\pi\)
0.858897 0.512148i \(-0.171150\pi\)
\(132\) 4.90195 3.67794i 0.426660 0.320124i
\(133\) 0 0
\(134\) 6.72004i 0.580523i
\(135\) −5.90434 + 10.2266i −0.508164 + 0.880167i
\(136\) 4.89282 2.82487i 0.419556 0.242231i
\(137\) −8.21968 14.2369i −0.702254 1.21634i −0.967673 0.252207i \(-0.918844\pi\)
0.265419 0.964133i \(-0.414490\pi\)
\(138\) −0.865501 + 1.49909i −0.0736764 + 0.127611i
\(139\) −10.7109 −0.908484 −0.454242 0.890878i \(-0.650090\pi\)
−0.454242 + 0.890878i \(0.650090\pi\)
\(140\) 0 0
\(141\) 7.39519 0.622787
\(142\) −10.0013 5.77423i −0.839288 0.484563i
\(143\) −2.55828 + 5.99231i −0.213935 + 0.501102i
\(144\) 0.207107 + 0.358719i 0.0172589 + 0.0298933i
\(145\) −9.27260 + 16.0606i −0.770047 + 1.33376i
\(146\) 10.8614i 0.898898i
\(147\) 0 0
\(148\) 9.62995 0.791577
\(149\) −12.7855 7.38174i −1.04743 0.604736i −0.125503 0.992093i \(-0.540055\pi\)
−0.921930 + 0.387358i \(0.873388\pi\)
\(150\) −1.02401 1.77364i −0.0836104 0.144817i
\(151\) 9.09017 5.24821i 0.739748 0.427093i −0.0822300 0.996613i \(-0.526204\pi\)
0.821978 + 0.569520i \(0.192871\pi\)
\(152\) −0.785466 0.453489i −0.0637097 0.0367828i
\(153\) −2.34020 −0.189194
\(154\) 0 0
\(155\) 11.6637 0.936851
\(156\) −3.14363 1.81498i −0.251692 0.145314i
\(157\) −3.99732 + 2.30785i −0.319021 + 0.184187i −0.650956 0.759115i \(-0.725632\pi\)
0.331935 + 0.943302i \(0.392298\pi\)
\(158\) 4.24264 + 7.34847i 0.337526 + 0.584613i
\(159\) 10.5082 + 6.06690i 0.833353 + 0.481136i
\(160\) 2.47151 0.195390
\(161\) 0 0
\(162\) 10.0711i 0.791258i
\(163\) −7.28732 + 12.6220i −0.570787 + 0.988632i 0.425698 + 0.904865i \(0.360028\pi\)
−0.996485 + 0.0837671i \(0.973305\pi\)
\(164\) 3.46620 + 6.00363i 0.270665 + 0.468805i
\(165\) −5.94705 + 13.9299i −0.462978 + 1.08444i
\(166\) 4.18811 + 2.41800i 0.325060 + 0.187674i
\(167\) −7.37045 −0.570342 −0.285171 0.958477i \(-0.592050\pi\)
−0.285171 + 0.958477i \(0.592050\pi\)
\(168\) 0 0
\(169\) −9.14068 −0.703129
\(170\) −6.98171 + 12.0927i −0.535472 + 0.927465i
\(171\) 0.187841 + 0.325351i 0.0143646 + 0.0248802i
\(172\) 5.89712 3.40470i 0.449651 0.259606i
\(173\) −5.57446 + 9.65525i −0.423818 + 0.734075i −0.996309 0.0858362i \(-0.972644\pi\)
0.572491 + 0.819911i \(0.305977\pi\)
\(174\) 13.8648i 1.05109i
\(175\) 0 0
\(176\) −1.99049 2.65291i −0.150039 0.199971i
\(177\) −0.892131 + 1.54522i −0.0670567 + 0.116146i
\(178\) −6.36702 11.0280i −0.477229 0.826584i
\(179\) −7.90434 13.6907i −0.590798 1.02329i −0.994125 0.108236i \(-0.965480\pi\)
0.403327 0.915056i \(-0.367854\pi\)
\(180\) −0.886580 0.511867i −0.0660818 0.0381523i
\(181\) 16.6528i 1.23779i −0.785473 0.618896i \(-0.787580\pi\)
0.785473 0.618896i \(-0.212420\pi\)
\(182\) 0 0
\(183\) 21.9889i 1.62546i
\(184\) 0.811303 + 0.468406i 0.0598100 + 0.0345313i
\(185\) −20.6119 + 11.9003i −1.51542 + 0.874926i
\(186\) 7.55178 4.36002i 0.553723 0.319692i
\(187\) 18.6031 2.24496i 1.36039 0.164168i
\(188\) 4.00225i 0.291894i
\(189\) 0 0
\(190\) 2.24161 0.162623
\(191\) −13.1784 + 22.8257i −0.953557 + 1.65161i −0.215921 + 0.976411i \(0.569275\pi\)
−0.737636 + 0.675199i \(0.764058\pi\)
\(192\) 1.60021 0.923880i 0.115485 0.0666753i
\(193\) 0.601170 0.347086i 0.0432731 0.0249838i −0.478207 0.878247i \(-0.658713\pi\)
0.521481 + 0.853263i \(0.325380\pi\)
\(194\) 1.91342 3.31414i 0.137375 0.237941i
\(195\) 8.97148 0.642461
\(196\) 0 0
\(197\) 9.74519i 0.694316i 0.937807 + 0.347158i \(0.112853\pi\)
−0.937807 + 0.347158i \(0.887147\pi\)
\(198\) 0.164590 + 1.36390i 0.0116969 + 0.0969279i
\(199\) 6.09214 3.51730i 0.431860 0.249335i −0.268279 0.963341i \(-0.586455\pi\)
0.700139 + 0.714007i \(0.253121\pi\)
\(200\) −0.959889 + 0.554192i −0.0678744 + 0.0391873i
\(201\) 10.7535 + 6.20851i 0.758490 + 0.437915i
\(202\) 15.8293i 1.11375i
\(203\) 0 0
\(204\) 10.4394i 0.730901i
\(205\) −14.8381 8.56676i −1.03634 0.598329i
\(206\) 0.395111 + 0.684352i 0.0275287 + 0.0476811i
\(207\) −0.194020 0.336053i −0.0134853 0.0233573i
\(208\) −0.982258 + 1.70132i −0.0681073 + 0.117965i
\(209\) −1.80533 2.40614i −0.124877 0.166436i
\(210\) 0 0
\(211\) 24.1152i 1.66016i −0.557643 0.830081i \(-0.688294\pi\)
0.557643 0.830081i \(-0.311706\pi\)
\(212\) 3.28338 5.68698i 0.225504 0.390584i
\(213\) 18.4799 10.6694i 1.26622 0.731055i
\(214\) 8.30583 + 14.3861i 0.567775 + 0.983415i
\(215\) −8.41477 + 14.5748i −0.573883 + 0.993994i
\(216\) 4.77791 0.325096
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) −17.3805 10.0347i −1.17447 0.678079i
\(220\) 7.53879 + 3.21852i 0.508265 + 0.216993i
\(221\) −5.54950 9.61202i −0.373300 0.646574i
\(222\) −8.89692 + 15.4099i −0.597122 + 1.03425i
\(223\) 2.90530i 0.194553i −0.995257 0.0972765i \(-0.968987\pi\)
0.995257 0.0972765i \(-0.0310131\pi\)
\(224\) 0 0
\(225\) 0.459108 0.0306072
\(226\) −4.99195 2.88210i −0.332060 0.191715i
\(227\) −7.21349 12.4941i −0.478776 0.829265i 0.520928 0.853601i \(-0.325586\pi\)
−0.999704 + 0.0243362i \(0.992253\pi\)
\(228\) 1.45135 0.837939i 0.0961181 0.0554938i
\(229\) −6.14615 3.54848i −0.406149 0.234490i 0.282985 0.959124i \(-0.408675\pi\)
−0.689134 + 0.724634i \(0.742009\pi\)
\(230\) −2.31534 −0.152669
\(231\) 0 0
\(232\) 7.50358 0.492634
\(233\) 3.60367 + 2.08058i 0.236084 + 0.136303i 0.613376 0.789791i \(-0.289811\pi\)
−0.377291 + 0.926095i \(0.623145\pi\)
\(234\) 0.704710 0.406865i 0.0460683 0.0265976i
\(235\) 4.94581 + 8.56639i 0.322629 + 0.558810i
\(236\) 0.836265 + 0.482818i 0.0544362 + 0.0314288i
\(237\) −15.6788 −1.01844
\(238\) 0 0
\(239\) 19.8625i 1.28480i 0.766371 + 0.642399i \(0.222061\pi\)
−0.766371 + 0.642399i \(0.777939\pi\)
\(240\) −2.28338 + 3.95493i −0.147392 + 0.255290i
\(241\) 7.24467 + 12.5481i 0.466670 + 0.808297i 0.999275 0.0380673i \(-0.0121201\pi\)
−0.532605 + 0.846364i \(0.678787\pi\)
\(242\) −2.61678 10.6842i −0.168213 0.686807i
\(243\) −3.70241 2.13759i −0.237510 0.137126i
\(244\) −11.9003 −0.761838
\(245\) 0 0
\(246\) −12.8094 −0.816698
\(247\) −0.890886 + 1.54306i −0.0566857 + 0.0981826i
\(248\) −2.35963 4.08699i −0.149836 0.259524i
\(249\) −7.73861 + 4.46789i −0.490415 + 0.283141i
\(250\) −4.80909 + 8.32959i −0.304154 + 0.526810i
\(251\) 14.6156i 0.922529i 0.887263 + 0.461264i \(0.152604\pi\)
−0.887263 + 0.461264i \(0.847396\pi\)
\(252\) 0 0
\(253\) 1.86471 + 2.48528i 0.117234 + 0.156248i
\(254\) −9.31855 + 16.1402i −0.584698 + 1.01273i
\(255\) −12.9005 22.3443i −0.807861 1.39926i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 20.0209 + 11.5591i 1.24887 + 0.721035i 0.970884 0.239550i \(-0.0769998\pi\)
0.277986 + 0.960585i \(0.410333\pi\)
\(258\) 12.5821i 0.783330i
\(259\) 0 0
\(260\) 4.85533i 0.301115i
\(261\) −2.69168 1.55404i −0.166611 0.0961927i
\(262\) 17.3062 9.99173i 1.06918 0.617291i
\(263\) −7.34847 + 4.24264i −0.453126 + 0.261612i −0.709150 0.705058i \(-0.750921\pi\)
0.256023 + 0.966671i \(0.417588\pi\)
\(264\) 6.08418 0.734219i 0.374456 0.0451881i
\(265\) 16.2299i 0.996992i
\(266\) 0 0
\(267\) 23.5294 1.43998
\(268\) 3.36002 5.81973i 0.205246 0.355496i
\(269\) 26.5008 15.3003i 1.61578 0.932874i 0.627791 0.778382i \(-0.283959\pi\)
0.987994 0.154492i \(-0.0493739\pi\)
\(270\) −10.2266 + 5.90434i −0.622372 + 0.359327i
\(271\) −6.60081 + 11.4329i −0.400971 + 0.694502i −0.993843 0.110794i \(-0.964661\pi\)
0.592872 + 0.805296i \(0.297994\pi\)
\(272\) 5.64974 0.342566
\(273\) 0 0
\(274\) 16.4394i 0.993138i
\(275\) −3.64962 + 0.440424i −0.220080 + 0.0265586i
\(276\) −1.49909 + 0.865501i −0.0902347 + 0.0520970i
\(277\) 3.45445 1.99443i 0.207558 0.119834i −0.392618 0.919702i \(-0.628431\pi\)
0.600176 + 0.799868i \(0.295097\pi\)
\(278\) −9.27589 5.35544i −0.556331 0.321198i
\(279\) 1.95478i 0.117030i
\(280\) 0 0
\(281\) 5.94293i 0.354526i −0.984164 0.177263i \(-0.943276\pi\)
0.984164 0.177263i \(-0.0567243\pi\)
\(282\) 6.40442 + 3.69760i 0.381378 + 0.220189i
\(283\) 10.6331 + 18.4170i 0.632070 + 1.09478i 0.987128 + 0.159933i \(0.0511279\pi\)
−0.355058 + 0.934844i \(0.615539\pi\)
\(284\) −5.77423 10.0013i −0.342638 0.593466i
\(285\) −2.07098 + 3.58704i −0.122674 + 0.212478i
\(286\) −5.21169 + 3.91035i −0.308174 + 0.231224i
\(287\) 0 0
\(288\) 0.414214i 0.0244078i
\(289\) −7.45977 + 12.9207i −0.438810 + 0.760042i
\(290\) −16.0606 + 9.27260i −0.943112 + 0.544506i
\(291\) 3.53553 + 6.12372i 0.207257 + 0.358979i
\(292\) −5.43072 + 9.40628i −0.317809 + 0.550461i
\(293\) −27.7920 −1.62362 −0.811812 0.583919i \(-0.801519\pi\)
−0.811812 + 0.583919i \(0.801519\pi\)
\(294\) 0 0
\(295\) −2.38658 −0.138952
\(296\) 8.33978 + 4.81498i 0.484740 + 0.279865i
\(297\) 14.5739 + 6.22202i 0.845665 + 0.361038i
\(298\) −7.38174 12.7855i −0.427613 0.740647i
\(299\) 0.920191 1.59382i 0.0532160 0.0921728i
\(300\) 2.04803i 0.118243i
\(301\) 0 0
\(302\) 10.4964 0.604001
\(303\) 25.3302 + 14.6244i 1.45518 + 0.840149i
\(304\) −0.453489 0.785466i −0.0260094 0.0450496i
\(305\) 25.4713 14.7059i 1.45848 0.842055i
\(306\) −2.02667 1.17010i −0.115857 0.0668901i
\(307\) 16.2674 0.928427 0.464214 0.885723i \(-0.346337\pi\)
0.464214 + 0.885723i \(0.346337\pi\)
\(308\) 0 0
\(309\) −1.46014 −0.0830644
\(310\) 10.1011 + 5.83185i 0.573702 + 0.331227i
\(311\) 9.34656 5.39624i 0.529995 0.305993i −0.211020 0.977482i \(-0.567678\pi\)
0.741014 + 0.671489i \(0.234345\pi\)
\(312\) −1.81498 3.14363i −0.102753 0.177973i
\(313\) −15.8579 9.15556i −0.896341 0.517503i −0.0203300 0.999793i \(-0.506472\pi\)
−0.876011 + 0.482290i \(0.839805\pi\)
\(314\) −4.61571 −0.260480
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) 0.179452 0.310821i 0.0100791 0.0174574i −0.860942 0.508703i \(-0.830125\pi\)
0.871021 + 0.491246i \(0.163458\pi\)
\(318\) 6.06690 + 10.5082i 0.340215 + 0.589269i
\(319\) 22.8879 + 9.77151i 1.28148 + 0.547099i
\(320\) 2.14039 + 1.23576i 0.119652 + 0.0690809i
\(321\) −30.6943 −1.71319
\(322\) 0 0
\(323\) 5.12419 0.285118
\(324\) −5.03553 + 8.72180i −0.279752 + 0.484544i
\(325\) 1.08872 + 1.88572i 0.0603913 + 0.104601i
\(326\) −12.6220 + 7.28732i −0.699069 + 0.403607i
\(327\) 5.54328 9.60124i 0.306544 0.530950i
\(328\) 6.93240i 0.382778i
\(329\) 0 0
\(330\) −12.1152 + 9.09009i −0.666922 + 0.500393i
\(331\) 14.4567 25.0398i 0.794615 1.37631i −0.128469 0.991714i \(-0.541006\pi\)
0.923084 0.384599i \(-0.125660\pi\)
\(332\) 2.41800 + 4.18811i 0.132705 + 0.229852i
\(333\) −1.99443 3.45445i −0.109294 0.189303i
\(334\) −6.38299 3.68522i −0.349262 0.201646i
\(335\) 16.6087i 0.907429i
\(336\) 0 0
\(337\) 7.96341i 0.433795i −0.976194 0.216897i \(-0.930406\pi\)
0.976194 0.216897i \(-0.0695937\pi\)
\(338\) −7.91606 4.57034i −0.430577 0.248594i
\(339\) 9.22392 5.32543i 0.500975 0.289238i
\(340\) −12.0927 + 6.98171i −0.655817 + 0.378636i
\(341\) −1.87523 15.5393i −0.101549 0.841498i
\(342\) 0.375683i 0.0203146i
\(343\) 0 0
\(344\) 6.80940 0.367138
\(345\) 2.13910 3.70503i 0.115165 0.199472i
\(346\) −9.65525 + 5.57446i −0.519069 + 0.299685i
\(347\) 21.3743 12.3405i 1.14743 0.662472i 0.199174 0.979964i \(-0.436174\pi\)
0.948261 + 0.317492i \(0.102841\pi\)
\(348\) −6.93240 + 12.0073i −0.371616 + 0.643657i
\(349\) 11.1489 0.596788 0.298394 0.954443i \(-0.403549\pi\)
0.298394 + 0.954443i \(0.403549\pi\)
\(350\) 0 0
\(351\) 9.38628i 0.501003i
\(352\) −0.397356 3.29274i −0.0211792 0.175503i
\(353\) −18.5202 + 10.6926i −0.985729 + 0.569111i −0.903995 0.427543i \(-0.859379\pi\)
−0.0817341 + 0.996654i \(0.526046\pi\)
\(354\) −1.54522 + 0.892131i −0.0821273 + 0.0474162i
\(355\) 24.7183 + 14.2711i 1.31191 + 0.757432i
\(356\) 12.7340i 0.674903i
\(357\) 0 0
\(358\) 15.8087i 0.835514i
\(359\) 5.40718 + 3.12184i 0.285380 + 0.164764i 0.635856 0.771807i \(-0.280647\pi\)
−0.350477 + 0.936572i \(0.613980\pi\)
\(360\) −0.511867 0.886580i −0.0269778 0.0467269i
\(361\) 9.08870 + 15.7421i 0.478352 + 0.828531i
\(362\) 8.32639 14.4217i 0.437625 0.757989i
\(363\) 19.5145 + 5.68354i 1.02425 + 0.298309i
\(364\) 0 0
\(365\) 26.8442i 1.40509i
\(366\) 10.9944 19.0429i 0.574688 0.995389i
\(367\) 24.9011 14.3767i 1.29983 0.750456i 0.319454 0.947602i \(-0.396501\pi\)
0.980374 + 0.197146i \(0.0631673\pi\)
\(368\) 0.468406 + 0.811303i 0.0244173 + 0.0422921i
\(369\) 1.43575 2.48679i 0.0747420 0.129457i
\(370\) −23.8006 −1.23733
\(371\) 0 0
\(372\) 8.72004 0.452113
\(373\) −10.7031 6.17945i −0.554187 0.319960i 0.196622 0.980479i \(-0.437003\pi\)
−0.750809 + 0.660519i \(0.770336\pi\)
\(374\) 17.2332 + 7.35736i 0.891109 + 0.380440i
\(375\) −8.88604 15.3911i −0.458873 0.794792i
\(376\) 2.00112 3.46605i 0.103200 0.178748i
\(377\) 14.7409i 0.759195i
\(378\) 0 0
\(379\) −23.7822 −1.22161 −0.610805 0.791781i \(-0.709154\pi\)
−0.610805 + 0.791781i \(0.709154\pi\)
\(380\) 1.94129 + 1.12080i 0.0995861 + 0.0574961i
\(381\) −17.2184 29.8232i −0.882127 1.52789i
\(382\) −22.8257 + 13.1784i −1.16786 + 0.674267i
\(383\) −27.5955 15.9323i −1.41006 0.814100i −0.414669 0.909972i \(-0.636103\pi\)
−0.995394 + 0.0958720i \(0.969436\pi\)
\(384\) 1.84776 0.0942931
\(385\) 0 0
\(386\) 0.694171 0.0353324
\(387\) −2.44267 1.41027i −0.124168 0.0716882i
\(388\) 3.31414 1.91342i 0.168250 0.0971390i
\(389\) −10.5077 18.1999i −0.532763 0.922773i −0.999268 0.0382540i \(-0.987820\pi\)
0.466505 0.884519i \(-0.345513\pi\)
\(390\) 7.76953 + 4.48574i 0.393425 + 0.227144i
\(391\) −5.29274 −0.267665
\(392\) 0 0
\(393\) 36.9246i 1.86260i
\(394\) −4.87259 + 8.43958i −0.245478 + 0.425180i
\(395\) −10.4857 18.1618i −0.527595 0.913822i
\(396\) −0.539408 + 1.26346i −0.0271063 + 0.0634914i
\(397\) −7.20364 4.15902i −0.361540 0.208735i 0.308216 0.951316i \(-0.400268\pi\)
−0.669756 + 0.742581i \(0.733601\pi\)
\(398\) 7.03460 0.352612
\(399\) 0 0
\(400\) −1.10838 −0.0554192
\(401\) 15.3410 26.5714i 0.766093 1.32691i −0.173574 0.984821i \(-0.555532\pi\)
0.939667 0.342091i \(-0.111135\pi\)
\(402\) 6.20851 + 10.7535i 0.309652 + 0.536334i
\(403\) −8.02896 + 4.63552i −0.399951 + 0.230912i
\(404\) 7.91466 13.7086i 0.393769 0.682028i
\(405\) 24.8908i 1.23683i
\(406\) 0 0
\(407\) 19.1683 + 25.5474i 0.950138 + 1.26634i
\(408\) −5.21968 + 9.04075i −0.258413 + 0.447584i
\(409\) 4.78939 + 8.29546i 0.236820 + 0.410184i 0.959800 0.280685i \(-0.0905615\pi\)
−0.722980 + 0.690869i \(0.757228\pi\)
\(410\) −8.56676 14.8381i −0.423082 0.732800i
\(411\) 26.3064 + 15.1880i 1.29760 + 0.749168i
\(412\) 0.790221i 0.0389314i
\(413\) 0 0
\(414\) 0.388040i 0.0190711i
\(415\) −10.3510 5.97613i −0.508109 0.293357i
\(416\) −1.70132 + 0.982258i −0.0834141 + 0.0481592i
\(417\) 17.1396 9.89556i 0.839330 0.484587i
\(418\) −0.360394 2.98644i −0.0176274 0.146072i
\(419\) 10.3074i 0.503550i 0.967786 + 0.251775i \(0.0810143\pi\)
−0.967786 + 0.251775i \(0.918986\pi\)
\(420\) 0 0
\(421\) −25.8805 −1.26134 −0.630669 0.776052i \(-0.717219\pi\)
−0.630669 + 0.776052i \(0.717219\pi\)
\(422\) 12.0576 20.8844i 0.586956 1.01664i
\(423\) −1.43568 + 0.828893i −0.0698054 + 0.0403021i
\(424\) 5.68698 3.28338i 0.276184 0.159455i
\(425\) 3.13104 5.42312i 0.151878 0.263060i
\(426\) 21.3388 1.03387
\(427\) 0 0
\(428\) 16.6117i 0.802955i
\(429\) −1.44238 11.9525i −0.0696390 0.577071i
\(430\) −14.5748 + 8.41477i −0.702860 + 0.405796i
\(431\) 14.7967 8.54290i 0.712734 0.411497i −0.0993388 0.995054i \(-0.531673\pi\)
0.812072 + 0.583557i \(0.198339\pi\)
\(432\) 4.13779 + 2.38896i 0.199080 + 0.114939i
\(433\) 1.92881i 0.0926926i 0.998925 + 0.0463463i \(0.0147578\pi\)
−0.998925 + 0.0463463i \(0.985242\pi\)
\(434\) 0 0
\(435\) 34.2671i 1.64298i
\(436\) −5.19615 3.00000i −0.248851 0.143674i
\(437\) 0.424834 + 0.735834i 0.0203226 + 0.0351997i
\(438\) −10.0347 17.3805i −0.479474 0.830474i
\(439\) 5.21169 9.02692i 0.248741 0.430831i −0.714436 0.699701i \(-0.753317\pi\)
0.963177 + 0.268869i \(0.0866500\pi\)
\(440\) 4.91952 + 6.55672i 0.234529 + 0.312579i
\(441\) 0 0
\(442\) 11.0990i 0.527926i
\(443\) −7.96268 + 13.7918i −0.378318 + 0.655267i −0.990818 0.135204i \(-0.956831\pi\)
0.612499 + 0.790471i \(0.290164\pi\)
\(444\) −15.4099 + 8.89692i −0.731322 + 0.422229i
\(445\) 15.7362 + 27.2559i 0.745967 + 1.29205i
\(446\) 1.45265 2.51606i 0.0687849 0.119139i
\(447\) 27.2794 1.29027
\(448\) 0 0
\(449\) 10.4404 0.492712 0.246356 0.969179i \(-0.420767\pi\)
0.246356 + 0.969179i \(0.420767\pi\)
\(450\) 0.397599 + 0.229554i 0.0187430 + 0.0108213i
\(451\) −9.02770 + 21.1457i −0.425098 + 0.995712i
\(452\) −2.88210 4.99195i −0.135563 0.234802i
\(453\) −9.69743 + 16.7964i −0.455625 + 0.789166i
\(454\) 14.4270i 0.677092i
\(455\) 0 0
\(456\) 1.67588 0.0784801
\(457\) 15.6388 + 9.02908i 0.731554 + 0.422363i 0.818990 0.573807i \(-0.194534\pi\)
−0.0874367 + 0.996170i \(0.527868\pi\)
\(458\) −3.54848 6.14615i −0.165810 0.287191i
\(459\) −23.3774 + 13.4970i −1.09117 + 0.629985i
\(460\) −2.00515 1.15767i −0.0934904 0.0539767i
\(461\) −11.4500 −0.533281 −0.266641 0.963796i \(-0.585914\pi\)
−0.266641 + 0.963796i \(0.585914\pi\)
\(462\) 0 0
\(463\) −26.6805 −1.23995 −0.619975 0.784622i \(-0.712857\pi\)
−0.619975 + 0.784622i \(0.712857\pi\)
\(464\) 6.49829 + 3.75179i 0.301675 + 0.174172i
\(465\) −18.6643 + 10.7759i −0.865538 + 0.499718i
\(466\) 2.08058 + 3.60367i 0.0963810 + 0.166937i
\(467\) −8.41452 4.85813i −0.389378 0.224807i 0.292513 0.956262i \(-0.405509\pi\)
−0.681890 + 0.731454i \(0.738842\pi\)
\(468\) 0.813729 0.0376146
\(469\) 0 0
\(470\) 9.89162i 0.456266i
\(471\) 4.26436 7.38609i 0.196491 0.340333i
\(472\) 0.482818 + 0.836265i 0.0222235 + 0.0384922i
\(473\) 20.7705 + 8.86753i 0.955030 + 0.407729i
\(474\) −13.5782 7.83938i −0.623667 0.360075i
\(475\) −1.00528 −0.0461254
\(476\) 0 0
\(477\) −2.72004 −0.124542
\(478\) −9.93124 + 17.2014i −0.454244 + 0.786774i
\(479\) −9.60418 16.6349i −0.438826 0.760069i 0.558773 0.829321i \(-0.311272\pi\)
−0.997599 + 0.0692512i \(0.977939\pi\)
\(480\) −3.95493 + 2.28338i −0.180517 + 0.104222i
\(481\) 9.45910 16.3836i 0.431298 0.747029i
\(482\) 14.4893i 0.659972i
\(483\) 0 0
\(484\) 3.07591 10.5612i 0.139814 0.480054i
\(485\) −4.72904 + 8.19093i −0.214735 + 0.371931i
\(486\) −2.13759 3.70241i −0.0969630 0.167945i
\(487\) −0.181298 0.314017i −0.00821539 0.0142295i 0.861888 0.507098i \(-0.169282\pi\)
−0.870104 + 0.492868i \(0.835948\pi\)
\(488\) −10.3059 5.95014i −0.466528 0.269350i
\(489\) 26.9304i 1.21784i
\(490\) 0 0
\(491\) 1.04374i 0.0471033i 0.999723 + 0.0235516i \(0.00749741\pi\)
−0.999723 + 0.0235516i \(0.992503\pi\)
\(492\) −11.0933 6.40470i −0.500123 0.288746i
\(493\) −36.7136 + 21.1966i −1.65350 + 0.954648i
\(494\) −1.54306 + 0.890886i −0.0694256 + 0.0400829i
\(495\) −0.406788 3.37089i −0.0182837 0.151510i
\(496\) 4.71925i 0.211901i
\(497\) 0 0
\(498\) −8.93578 −0.400422
\(499\) −9.80041 + 16.9748i −0.438727 + 0.759897i −0.997592 0.0693620i \(-0.977904\pi\)
0.558865 + 0.829259i \(0.311237\pi\)
\(500\) −8.32959 + 4.80909i −0.372511 + 0.215069i
\(501\) 11.7942 6.80940i 0.526928 0.304222i
\(502\) −7.30780 + 12.6575i −0.326163 + 0.564931i
\(503\) 36.6503 1.63415 0.817077 0.576529i \(-0.195593\pi\)
0.817077 + 0.576529i \(0.195593\pi\)
\(504\) 0 0
\(505\) 39.1224i 1.74092i
\(506\) 0.372248 + 3.08467i 0.0165484 + 0.137130i
\(507\) 14.6270 8.44489i 0.649607 0.375051i
\(508\) −16.1402 + 9.31855i −0.716106 + 0.413444i
\(509\) −32.1251 18.5474i −1.42392 0.822101i −0.427290 0.904115i \(-0.640531\pi\)
−0.996631 + 0.0820139i \(0.973865\pi\)
\(510\) 25.8010i 1.14249i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 3.75289 + 2.16673i 0.165694 + 0.0956635i
\(514\) 11.5591 + 20.0209i 0.509849 + 0.883084i
\(515\) −0.976522 1.69139i −0.0430307 0.0745314i
\(516\) −6.29107 + 10.8965i −0.276949 + 0.479690i
\(517\) 10.6176 7.96643i 0.466963 0.350363i
\(518\) 0 0
\(519\) 20.6005i 0.904262i
\(520\) 2.42766 4.20484i 0.106460 0.184394i
\(521\) −16.8745 + 9.74250i −0.739285 + 0.426827i −0.821809 0.569762i \(-0.807035\pi\)
0.0825240 + 0.996589i \(0.473702\pi\)
\(522\) −1.55404 2.69168i −0.0680185 0.117812i
\(523\) 21.5163 37.2674i 0.940844 1.62959i 0.176977 0.984215i \(-0.443368\pi\)
0.763867 0.645374i \(-0.223298\pi\)
\(524\) 19.9835 0.872982
\(525\) 0 0
\(526\) −8.48528 −0.369976
\(527\) 23.0904 + 13.3313i 1.00584 + 0.580719i
\(528\) 5.63617 + 2.40624i 0.245283 + 0.104718i
\(529\) 11.0612 + 19.1585i 0.480921 + 0.832980i
\(530\) −8.11493 + 14.0555i −0.352490 + 0.610530i
\(531\) 0.399979i 0.0173576i
\(532\) 0 0
\(533\) 13.6188 0.589896
\(534\) 20.3771 + 11.7647i 0.881803 + 0.509109i
\(535\) −20.5280 35.5555i −0.887502 1.53720i
\(536\) 5.81973 3.36002i 0.251374 0.145131i
\(537\) 25.2971 + 14.6053i 1.09165 + 0.630266i
\(538\) 30.6005 1.31928
\(539\) 0 0
\(540\) −11.8087 −0.508164
\(541\) 16.9904 + 9.80940i 0.730474 + 0.421739i 0.818595 0.574370i \(-0.194753\pi\)
−0.0881217 + 0.996110i \(0.528086\pi\)
\(542\) −11.4329 + 6.60081i −0.491087 + 0.283529i
\(543\) 15.3852 + 26.6479i 0.660241 + 1.14357i
\(544\) 4.89282 + 2.82487i 0.209778 + 0.121115i
\(545\) 14.8291 0.635208
\(546\) 0 0
\(547\) 42.5800i 1.82059i 0.413959 + 0.910295i \(0.364146\pi\)
−0.413959 + 0.910295i \(0.635854\pi\)
\(548\) 8.21968 14.2369i 0.351127 0.608170i
\(549\) 2.46463 + 4.26886i 0.105188 + 0.182191i
\(550\) −3.38087 1.44339i −0.144161 0.0615464i
\(551\) 5.89380 + 3.40279i 0.251085 + 0.144964i
\(552\) −1.73100 −0.0736764
\(553\) 0 0
\(554\) 3.98886 0.169470
\(555\) 21.9889 38.0858i 0.933375 1.61665i
\(556\) −5.35544 9.27589i −0.227121 0.393385i
\(557\) −7.67681 + 4.43221i −0.325277 + 0.187799i −0.653742 0.756717i \(-0.726802\pi\)
0.328465 + 0.944516i \(0.393469\pi\)
\(558\) −0.977389 + 1.69289i −0.0413762 + 0.0716657i
\(559\) 13.3772i 0.565795i
\(560\) 0 0
\(561\) −27.6947 + 20.7794i −1.16927 + 0.877308i
\(562\) 2.97147 5.14673i 0.125344 0.217102i
\(563\) −8.13368 14.0879i −0.342794 0.593736i 0.642157 0.766573i \(-0.278040\pi\)
−0.984950 + 0.172837i \(0.944707\pi\)
\(564\) 3.69760 + 6.40442i 0.155697 + 0.269675i
\(565\) 12.3377 + 7.12316i 0.519050 + 0.299674i
\(566\) 21.2661i 0.893882i
\(567\) 0 0
\(568\) 11.5485i 0.484563i
\(569\) −37.3354 21.5556i −1.56518 0.903659i −0.996718 0.0809508i \(-0.974204\pi\)
−0.568465 0.822708i \(-0.692462\pi\)
\(570\) −3.58704 + 2.07098i −0.150244 + 0.0867437i
\(571\) −4.15542 + 2.39913i −0.173899 + 0.100400i −0.584423 0.811449i \(-0.698679\pi\)
0.410524 + 0.911850i \(0.365346\pi\)
\(572\) −6.46863 + 0.780613i −0.270467 + 0.0326391i
\(573\) 48.7011i 2.03452i
\(574\) 0 0
\(575\) 1.03835 0.0433021
\(576\) −0.207107 + 0.358719i −0.00862945 + 0.0149466i
\(577\) 1.65586 0.956014i 0.0689345 0.0397994i −0.465137 0.885239i \(-0.653995\pi\)
0.534071 + 0.845440i \(0.320661\pi\)
\(578\) −12.9207 + 7.45977i −0.537431 + 0.310286i
\(579\) −0.641330 + 1.11082i −0.0266528 + 0.0461640i
\(580\) −18.5452 −0.770047
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) 21.6226 2.60935i 0.895517 0.108068i
\(584\) −9.40628 + 5.43072i −0.389234 + 0.224725i
\(585\) −1.74170 + 1.00557i −0.0720105 + 0.0415753i
\(586\) −24.0685 13.8960i −0.994262 0.574038i
\(587\) 1.71510i 0.0707896i −0.999373 0.0353948i \(-0.988731\pi\)
0.999373 0.0353948i \(-0.0112689\pi\)
\(588\) 0 0
\(589\) 4.28026i 0.176365i
\(590\) −2.06684 1.19329i −0.0850905 0.0491270i
\(591\) −9.00338 15.5943i −0.370349 0.641464i
\(592\) 4.81498 + 8.33978i 0.197894 + 0.342763i
\(593\) 7.01955 12.1582i 0.288258 0.499278i −0.685136 0.728415i \(-0.740257\pi\)
0.973394 + 0.229137i \(0.0735905\pi\)
\(594\) 9.51038 + 12.6754i 0.390215 + 0.520077i
\(595\) 0 0
\(596\) 14.7635i 0.604736i
\(597\) −6.49912 + 11.2568i −0.265991 + 0.460710i
\(598\) 1.59382 0.920191i 0.0651760 0.0376294i
\(599\) −3.03517 5.25707i −0.124014 0.214798i 0.797333 0.603539i \(-0.206243\pi\)
−0.921347 + 0.388741i \(0.872910\pi\)
\(600\) 1.02401 1.77364i 0.0418052 0.0724087i
\(601\) −18.3373 −0.747995 −0.373998 0.927430i \(-0.622013\pi\)
−0.373998 + 0.927430i \(0.622013\pi\)
\(602\) 0 0
\(603\) −2.78353 −0.113354
\(604\) 9.09017 + 5.24821i 0.369874 + 0.213547i
\(605\) 6.46741 + 26.4062i 0.262938 + 1.07356i
\(606\) 14.6244 + 25.3302i 0.594075 + 1.02897i
\(607\) 0.106462 0.184397i 0.00432114 0.00748444i −0.863857 0.503738i \(-0.831958\pi\)
0.868178 + 0.496253i \(0.165291\pi\)
\(608\) 0.906978i 0.0367828i
\(609\) 0 0
\(610\) 29.4117 1.19085
\(611\) −6.80911 3.93124i −0.275467 0.159041i
\(612\) −1.17010 2.02667i −0.0472985 0.0819233i
\(613\) −14.6270 + 8.44493i −0.590781 + 0.341087i −0.765406 0.643548i \(-0.777462\pi\)
0.174625 + 0.984635i \(0.444129\pi\)
\(614\) 14.0879 + 8.13368i 0.568543 + 0.328249i
\(615\) 31.6586 1.27660
\(616\) 0 0
\(617\) 33.0864 1.33201 0.666004 0.745948i \(-0.268003\pi\)
0.666004 + 0.745948i \(0.268003\pi\)
\(618\) −1.26452 0.730069i −0.0508663 0.0293677i
\(619\) 12.3404 7.12472i 0.496001 0.286366i −0.231059 0.972940i \(-0.574219\pi\)
0.727061 + 0.686573i \(0.240886\pi\)
\(620\) 5.83185 + 10.1011i 0.234213 + 0.405668i
\(621\) −3.87633 2.23800i −0.155552 0.0898079i
\(622\) 10.7925 0.432739
\(623\) 0 0
\(624\) 3.62995i 0.145314i
\(625\) 14.6567 25.3862i 0.586268 1.01545i
\(626\) −9.15556 15.8579i −0.365930 0.633809i
\(627\) 5.11188 + 2.18241i 0.204149 + 0.0871569i
\(628\) −3.99732 2.30785i −0.159510 0.0920934i
\(629\) −54.4067 −2.16934
\(630\) 0 0
\(631\) −19.3751 −0.771312 −0.385656 0.922643i \(-0.626025\pi\)
−0.385656 + 0.922643i \(0.626025\pi\)
\(632\) −4.24264 + 7.34847i −0.168763 + 0.292306i
\(633\) 22.2796 + 38.5893i 0.885533 + 1.53379i
\(634\) 0.310821 0.179452i 0.0123443 0.00712697i
\(635\) 23.0309 39.8908i 0.913955 1.58302i
\(636\) 12.1338i 0.481136i
\(637\) 0 0
\(638\) 14.9358 + 19.9063i 0.591313 + 0.788100i
\(639\) −2.39177 + 4.14266i −0.0946168 + 0.163881i
\(640\) 1.23576 + 2.14039i 0.0488476 + 0.0846065i
\(641\) 18.2543 + 31.6174i 0.721003 + 1.24881i 0.960598 + 0.277941i \(0.0896518\pi\)
−0.239595 + 0.970873i \(0.577015\pi\)
\(642\) −26.5821 15.3472i −1.04911 0.605705i
\(643\) 2.49558i 0.0984161i 0.998789 + 0.0492080i \(0.0156697\pi\)
−0.998789 + 0.0492080i \(0.984330\pi\)
\(644\) 0 0
\(645\) 31.0969i 1.22444i
\(646\) 4.43768 + 2.56209i 0.174598 + 0.100804i
\(647\) 3.65045 2.10759i 0.143514 0.0828577i −0.426524 0.904476i \(-0.640262\pi\)
0.570038 + 0.821619i \(0.306929\pi\)
\(648\) −8.72180 + 5.03553i −0.342625 + 0.197814i
\(649\) 0.383701 + 3.17958i 0.0150616 + 0.124810i
\(650\) 2.17744i 0.0854062i
\(651\) 0 0
\(652\) −14.5746 −0.570787
\(653\) 5.39862 9.35068i 0.211264 0.365920i −0.740846 0.671675i \(-0.765575\pi\)
0.952110 + 0.305754i \(0.0989086\pi\)
\(654\) 9.60124 5.54328i 0.375438 0.216759i
\(655\) −42.7725 + 24.6947i −1.67126 + 0.964903i
\(656\) −3.46620 + 6.00363i −0.135332 + 0.234403i
\(657\) 4.49895 0.175521
\(658\) 0 0
\(659\) 42.1591i 1.64229i 0.570723 + 0.821143i \(0.306663\pi\)
−0.570723 + 0.821143i \(0.693337\pi\)
\(660\) −15.0371 + 1.81463i −0.585320 + 0.0706345i
\(661\) 7.77796 4.49061i 0.302528 0.174664i −0.341050 0.940045i \(-0.610783\pi\)
0.643578 + 0.765381i \(0.277449\pi\)
\(662\) 25.0398 14.4567i 0.973200 0.561877i
\(663\) 17.7607 + 10.2541i 0.689768 + 0.398238i
\(664\) 4.83601i 0.187674i
\(665\) 0 0
\(666\) 3.98886i 0.154565i
\(667\) −6.08767 3.51472i −0.235716 0.136090i
\(668\) −3.68522 6.38299i −0.142586 0.246965i
\(669\) 2.68414 + 4.64907i 0.103775 + 0.179744i
\(670\) −8.30434 + 14.3835i −0.320825 + 0.555685i
\(671\) −23.6874 31.5704i −0.914441 1.21876i
\(672\) 0 0
\(673\) 26.4282i 1.01873i −0.860550 0.509366i \(-0.829880\pi\)
0.860550 0.509366i \(-0.170120\pi\)
\(674\) 3.98171 6.89652i 0.153370 0.265644i
\(675\) 4.58626 2.64788i 0.176525 0.101917i
\(676\) −4.57034 7.91606i −0.175782 0.304464i
\(677\) 5.85689 10.1444i 0.225099 0.389882i −0.731250 0.682109i \(-0.761063\pi\)
0.956349 + 0.292227i \(0.0943962\pi\)
\(678\) 10.6509 0.409044
\(679\) 0 0
\(680\) −13.9634 −0.535472
\(681\) 23.0861 + 13.3288i 0.884663 + 0.510760i
\(682\) 6.14563 14.3950i 0.235328 0.551213i
\(683\) −17.9934 31.1655i −0.688498 1.19251i −0.972324 0.233638i \(-0.924937\pi\)
0.283825 0.958876i \(-0.408396\pi\)
\(684\) −0.187841 + 0.325351i −0.00718229 + 0.0124401i
\(685\) 40.6301i 1.55240i
\(686\) 0 0
\(687\) 13.1135 0.500310
\(688\) 5.89712 + 3.40470i 0.224825 + 0.129803i
\(689\) −6.45026 11.1722i −0.245735 0.425626i
\(690\) 3.70503 2.13910i 0.141048 0.0814341i
\(691\) −5.11870 2.95528i −0.194725 0.112424i 0.399468 0.916747i \(-0.369195\pi\)
−0.594192 + 0.804323i \(0.702528\pi\)
\(692\) −11.1489 −0.423818
\(693\) 0 0
\(694\) 24.6810 0.936877
\(695\) 22.9255 + 13.2360i 0.869613 + 0.502072i
\(696\) −12.0073 + 6.93240i −0.455134 + 0.262772i
\(697\) −19.5831 33.9190i −0.741764 1.28477i
\(698\) 9.65525 + 5.57446i 0.365456 + 0.210996i
\(699\) −7.68882 −0.290818
\(700\) 0 0
\(701\) 39.6167i 1.49630i −0.663527 0.748152i \(-0.730941\pi\)
0.663527 0.748152i \(-0.269059\pi\)
\(702\) 4.69314 8.12876i 0.177131 0.306800i
\(703\) 4.36708 + 7.56400i 0.164707 + 0.285282i
\(704\) 1.30225 3.05027i 0.0490803 0.114961i
\(705\) −15.8286 9.13866i −0.596141 0.344182i
\(706\) −21.3852 −0.804844
\(707\) 0 0
\(708\) −1.78426 −0.0670567
\(709\) 10.2012 17.6689i 0.383113 0.663571i −0.608392 0.793636i \(-0.708185\pi\)
0.991505 + 0.130065i \(0.0415186\pi\)
\(710\) 14.2711 + 24.7183i 0.535585 + 0.927661i
\(711\) 3.04384 1.75736i 0.114153 0.0659061i
\(712\) 6.36702 11.0280i 0.238614 0.413292i
\(713\) 4.42105i 0.165570i
\(714\) 0 0
\(715\) 12.8808 9.66448i 0.481714 0.361431i
\(716\) 7.90434 13.6907i 0.295399 0.511646i
\(717\) −18.3505 31.7841i −0.685313 1.18700i
\(718\) 3.12184 + 5.40718i 0.116506 + 0.201794i
\(719\) −24.8714 14.3595i −0.927545 0.535518i −0.0415109 0.999138i \(-0.513217\pi\)
−0.886034 + 0.463620i \(0.846550\pi\)
\(720\) 1.02373i 0.0381523i
\(721\) 0 0
\(722\) 18.1774i 0.676492i
\(723\) −23.1859 13.3864i −0.862294 0.497846i
\(724\) 14.4217 8.32639i 0.535979 0.309448i
\(725\) 7.20260 4.15842i 0.267498 0.154440i
\(726\) 14.0583 + 14.6794i 0.521753 + 0.544802i
\(727\) 9.15820i 0.339659i 0.985473 + 0.169829i \(0.0543217\pi\)
−0.985473 + 0.169829i \(0.945678\pi\)
\(728\) 0 0
\(729\) −22.3137 −0.826434
\(730\) 13.4221 23.2477i 0.496774 0.860438i
\(731\) −33.3172 + 19.2357i −1.23228 + 0.711457i
\(732\) 19.0429 10.9944i 0.703846 0.406366i
\(733\) −22.3549 + 38.7197i −0.825695 + 1.43015i 0.0756916 + 0.997131i \(0.475884\pi\)
−0.901387 + 0.433015i \(0.857450\pi\)
\(734\) 28.7533 1.06130
\(735\) 0 0
\(736\) 0.936812i 0.0345313i
\(737\) 22.1273 2.67025i 0.815070 0.0983600i
\(738\) 2.48679 1.43575i 0.0915399 0.0528506i
\(739\) −18.7939 + 10.8507i −0.691345 + 0.399148i −0.804116 0.594473i \(-0.797361\pi\)
0.112771 + 0.993621i \(0.464027\pi\)
\(740\) −20.6119 11.9003i −0.757708 0.437463i
\(741\) 3.29229i 0.120945i
\(742\) 0 0
\(743\) 8.20708i 0.301089i −0.988603 0.150544i \(-0.951897\pi\)
0.988603 0.150544i \(-0.0481026\pi\)
\(744\) 7.55178 + 4.36002i 0.276862 + 0.159846i
\(745\) 18.2441 + 31.5997i 0.668411 + 1.15772i
\(746\) −6.17945 10.7031i −0.226246 0.391869i
\(747\) 1.00157 1.73477i 0.0366455 0.0634719i
\(748\) 11.2457 + 14.9883i 0.411185 + 0.548026i
\(749\) 0 0
\(750\) 17.7721i 0.648945i
\(751\) 9.71032 16.8188i 0.354335 0.613725i −0.632669 0.774422i \(-0.718041\pi\)
0.987004 + 0.160697i \(0.0513741\pi\)
\(752\) 3.46605 2.00112i 0.126394 0.0729735i
\(753\) −13.5031 23.3880i −0.492079 0.852306i
\(754\) 7.37045 12.7660i 0.268416 0.464910i
\(755\) −25.9421 −0.944128
\(756\) 0 0
\(757\) 44.7958 1.62813 0.814065 0.580774i \(-0.197250\pi\)
0.814065 + 0.580774i \(0.197250\pi\)
\(758\) −20.5960 11.8911i −0.748080 0.431904i
\(759\) −5.28003 2.25419i −0.191653 0.0818220i
\(760\) 1.12080 + 1.94129i 0.0406559 + 0.0704180i
\(761\) −1.91789 + 3.32189i −0.0695235 + 0.120418i −0.898692 0.438581i \(-0.855481\pi\)
0.829168 + 0.558999i \(0.188815\pi\)
\(762\) 34.4369i 1.24752i
\(763\) 0 0
\(764\) −26.3568 −0.953557
\(765\) 5.00895 + 2.89192i 0.181099 + 0.104557i
\(766\) −15.9323 27.5955i −0.575656 0.997065i
\(767\) 1.64286 0.948503i 0.0593201 0.0342485i
\(768\) 1.60021 + 0.923880i 0.0577425 + 0.0333376i
\(769\) 37.6267 1.35685 0.678427 0.734667i \(-0.262662\pi\)
0.678427 + 0.734667i \(0.262662\pi\)
\(770\) 0 0
\(771\) −42.7168 −1.53841
\(772\) 0.601170 + 0.347086i 0.0216366 + 0.0124919i
\(773\) 24.7455 14.2868i 0.890034 0.513861i 0.0160805 0.999871i \(-0.494881\pi\)
0.873954 + 0.486009i \(0.161548\pi\)
\(774\) −1.41027 2.44267i −0.0506912 0.0877998i
\(775\) −4.52996 2.61537i −0.162721 0.0939470i
\(776\) 3.82683 0.137375
\(777\) 0 0
\(778\) 21.0155i 0.753441i
\(779\) −3.14377 + 5.44517i −0.112637 + 0.195093i
\(780\) 4.48574 + 7.76953i 0.160615 + 0.278194i
\(781\) 15.0390 35.2260i 0.538136 1.26048i
\(782\) −4.58365 2.64637i −0.163911 0.0946340i
\(783\) −35.8514 −1.28122