Properties

Label 432.2.be.b.239.1
Level $432$
Weight $2$
Character 432.239
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 239.1
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.b.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.65284 + 0.517813i) q^{3} +(-2.52917 - 0.445961i) q^{5} +(-1.40789 - 1.67786i) q^{7} +(2.46374 - 1.71172i) q^{9} +O(q^{10})\) \(q+(-1.65284 + 0.517813i) q^{3} +(-2.52917 - 0.445961i) q^{5} +(-1.40789 - 1.67786i) q^{7} +(2.46374 - 1.71172i) q^{9} +(0.751810 + 4.26373i) q^{11} +(5.33154 - 1.94052i) q^{13} +(4.41123 - 0.572537i) q^{15} +(5.53709 + 3.19684i) q^{17} +(-2.85493 + 1.64830i) q^{19} +(3.19584 + 2.04421i) q^{21} +(3.31503 + 2.78164i) q^{23} +(1.49936 + 0.545724i) q^{25} +(-3.18581 + 4.10495i) q^{27} +(0.131941 - 0.362506i) q^{29} +(4.37197 - 5.21032i) q^{31} +(-3.45043 - 6.65795i) q^{33} +(2.81254 + 4.87147i) q^{35} +(-3.81950 + 6.61557i) q^{37} +(-7.80734 + 5.96811i) q^{39} +(-0.138464 - 0.380428i) q^{41} +(9.35445 - 1.64944i) q^{43} +(-6.99458 + 3.23050i) q^{45} +(6.74409 - 5.65897i) q^{47} +(0.382480 - 2.16915i) q^{49} +(-10.8073 - 2.41668i) q^{51} +7.00741i q^{53} -11.1190i q^{55} +(3.86523 - 4.20269i) q^{57} +(0.296830 - 1.68341i) q^{59} +(8.66165 - 7.26798i) q^{61} +(-6.34071 - 1.72389i) q^{63} +(-14.3498 + 2.53025i) q^{65} +(-0.683922 - 1.87906i) q^{67} +(-6.91957 - 2.88103i) q^{69} +(-1.85419 + 3.21154i) q^{71} +(5.37828 + 9.31546i) q^{73} +(-2.76079 - 0.125602i) q^{75} +(6.09548 - 7.26431i) q^{77} +(-2.34025 + 6.42979i) q^{79} +(3.14002 - 8.43447i) q^{81} +(1.31616 + 0.479045i) q^{83} +(-12.5786 - 10.5547i) q^{85} +(-0.0303672 + 0.667485i) q^{87} +(-6.85289 + 3.95652i) q^{89} +(-10.7622 - 6.21354i) q^{91} +(-4.52819 + 10.8757i) q^{93} +(7.95569 - 2.89564i) q^{95} +(2.09088 + 11.8580i) q^{97} +(9.15058 + 9.21782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.65284 + 0.517813i −0.954266 + 0.298960i
\(4\) 0 0
\(5\) −2.52917 0.445961i −1.13108 0.199440i −0.423379 0.905952i \(-0.639156\pi\)
−0.707700 + 0.706513i \(0.750267\pi\)
\(6\) 0 0
\(7\) −1.40789 1.67786i −0.532134 0.634172i 0.431271 0.902222i \(-0.358065\pi\)
−0.963405 + 0.268050i \(0.913621\pi\)
\(8\) 0 0
\(9\) 2.46374 1.71172i 0.821246 0.570574i
\(10\) 0 0
\(11\) 0.751810 + 4.26373i 0.226679 + 1.28556i 0.859449 + 0.511222i \(0.170807\pi\)
−0.632769 + 0.774340i \(0.718082\pi\)
\(12\) 0 0
\(13\) 5.33154 1.94052i 1.47870 0.538204i 0.528255 0.849086i \(-0.322846\pi\)
0.950449 + 0.310882i \(0.100624\pi\)
\(14\) 0 0
\(15\) 4.41123 0.572537i 1.13898 0.147828i
\(16\) 0 0
\(17\) 5.53709 + 3.19684i 1.34294 + 0.775347i 0.987238 0.159252i \(-0.0509081\pi\)
0.355703 + 0.934599i \(0.384241\pi\)
\(18\) 0 0
\(19\) −2.85493 + 1.64830i −0.654967 + 0.378145i −0.790357 0.612647i \(-0.790105\pi\)
0.135390 + 0.990792i \(0.456771\pi\)
\(20\) 0 0
\(21\) 3.19584 + 2.04421i 0.697389 + 0.446082i
\(22\) 0 0
\(23\) 3.31503 + 2.78164i 0.691232 + 0.580012i 0.919264 0.393641i \(-0.128785\pi\)
−0.228033 + 0.973654i \(0.573229\pi\)
\(24\) 0 0
\(25\) 1.49936 + 0.545724i 0.299873 + 0.109145i
\(26\) 0 0
\(27\) −3.18581 + 4.10495i −0.613109 + 0.789998i
\(28\) 0 0
\(29\) 0.131941 0.362506i 0.0245009 0.0673157i −0.926839 0.375459i \(-0.877485\pi\)
0.951340 + 0.308143i \(0.0997075\pi\)
\(30\) 0 0
\(31\) 4.37197 5.21032i 0.785230 0.935800i −0.213927 0.976850i \(-0.568626\pi\)
0.999157 + 0.0410491i \(0.0130700\pi\)
\(32\) 0 0
\(33\) −3.45043 6.65795i −0.600644 1.15900i
\(34\) 0 0
\(35\) 2.81254 + 4.87147i 0.475407 + 0.823428i
\(36\) 0 0
\(37\) −3.81950 + 6.61557i −0.627922 + 1.08759i 0.360046 + 0.932934i \(0.382761\pi\)
−0.987968 + 0.154658i \(0.950572\pi\)
\(38\) 0 0
\(39\) −7.80734 + 5.96811i −1.25018 + 0.955662i
\(40\) 0 0
\(41\) −0.138464 0.380428i −0.0216245 0.0594128i 0.928411 0.371556i \(-0.121175\pi\)
−0.950035 + 0.312143i \(0.898953\pi\)
\(42\) 0 0
\(43\) 9.35445 1.64944i 1.42654 0.251538i 0.593538 0.804806i \(-0.297731\pi\)
0.833003 + 0.553269i \(0.186620\pi\)
\(44\) 0 0
\(45\) −6.99458 + 3.23050i −1.04269 + 0.481575i
\(46\) 0 0
\(47\) 6.74409 5.65897i 0.983727 0.825445i −0.000920318 1.00000i \(-0.500293\pi\)
0.984648 + 0.174554i \(0.0558485\pi\)
\(48\) 0 0
\(49\) 0.382480 2.16915i 0.0546400 0.309879i
\(50\) 0 0
\(51\) −10.8073 2.41668i −1.51332 0.338402i
\(52\) 0 0
\(53\) 7.00741i 0.962542i 0.876572 + 0.481271i \(0.159825\pi\)
−0.876572 + 0.481271i \(0.840175\pi\)
\(54\) 0 0
\(55\) 11.1190i 1.49928i
\(56\) 0 0
\(57\) 3.86523 4.20269i 0.511962 0.556660i
\(58\) 0 0
\(59\) 0.296830 1.68341i 0.0386440 0.219161i −0.959370 0.282150i \(-0.908952\pi\)
0.998014 + 0.0629893i \(0.0200634\pi\)
\(60\) 0 0
\(61\) 8.66165 7.26798i 1.10901 0.930570i 0.111012 0.993819i \(-0.464591\pi\)
0.997998 + 0.0632489i \(0.0201462\pi\)
\(62\) 0 0
\(63\) −6.34071 1.72389i −0.798855 0.217190i
\(64\) 0 0
\(65\) −14.3498 + 2.53025i −1.77987 + 0.313839i
\(66\) 0 0
\(67\) −0.683922 1.87906i −0.0835543 0.229564i 0.890879 0.454241i \(-0.150089\pi\)
−0.974433 + 0.224677i \(0.927867\pi\)
\(68\) 0 0
\(69\) −6.91957 2.88103i −0.833019 0.346835i
\(70\) 0 0
\(71\) −1.85419 + 3.21154i −0.220051 + 0.381140i −0.954823 0.297174i \(-0.903956\pi\)
0.734772 + 0.678314i \(0.237289\pi\)
\(72\) 0 0
\(73\) 5.37828 + 9.31546i 0.629481 + 1.09029i 0.987656 + 0.156638i \(0.0500656\pi\)
−0.358176 + 0.933654i \(0.616601\pi\)
\(74\) 0 0
\(75\) −2.76079 0.125602i −0.318788 0.0145033i
\(76\) 0 0
\(77\) 6.09548 7.26431i 0.694644 0.827845i
\(78\) 0 0
\(79\) −2.34025 + 6.42979i −0.263299 + 0.723408i 0.735641 + 0.677372i \(0.236881\pi\)
−0.998940 + 0.0460362i \(0.985341\pi\)
\(80\) 0 0
\(81\) 3.14002 8.43447i 0.348891 0.937163i
\(82\) 0 0
\(83\) 1.31616 + 0.479045i 0.144468 + 0.0525820i 0.413242 0.910621i \(-0.364396\pi\)
−0.268774 + 0.963203i \(0.586619\pi\)
\(84\) 0 0
\(85\) −12.5786 10.5547i −1.36434 1.14482i
\(86\) 0 0
\(87\) −0.0303672 + 0.667485i −0.00325571 + 0.0715619i
\(88\) 0 0
\(89\) −6.85289 + 3.95652i −0.726404 + 0.419390i −0.817105 0.576488i \(-0.804423\pi\)
0.0907009 + 0.995878i \(0.471089\pi\)
\(90\) 0 0
\(91\) −10.7622 6.21354i −1.12818 0.651356i
\(92\) 0 0
\(93\) −4.52819 + 10.8757i −0.469551 + 1.12775i
\(94\) 0 0
\(95\) 7.95569 2.89564i 0.816237 0.297086i
\(96\) 0 0
\(97\) 2.09088 + 11.8580i 0.212297 + 1.20399i 0.885536 + 0.464570i \(0.153791\pi\)
−0.673239 + 0.739424i \(0.735098\pi\)
\(98\) 0 0
\(99\) 9.15058 + 9.21782i 0.919668 + 0.926426i
\(100\) 0 0
\(101\) −1.06468 1.26884i −0.105940 0.126254i 0.710469 0.703728i \(-0.248483\pi\)
−0.816409 + 0.577474i \(0.804038\pi\)
\(102\) 0 0
\(103\) 2.83638 + 0.500131i 0.279477 + 0.0492793i 0.311630 0.950204i \(-0.399125\pi\)
−0.0321527 + 0.999483i \(0.510236\pi\)
\(104\) 0 0
\(105\) −7.17118 6.59537i −0.699836 0.643642i
\(106\) 0 0
\(107\) −12.6955 −1.22732 −0.613659 0.789571i \(-0.710303\pi\)
−0.613659 + 0.789571i \(0.710303\pi\)
\(108\) 0 0
\(109\) −6.54537 −0.626933 −0.313466 0.949599i \(-0.601490\pi\)
−0.313466 + 0.949599i \(0.601490\pi\)
\(110\) 0 0
\(111\) 2.88738 12.9122i 0.274058 1.22558i
\(112\) 0 0
\(113\) −10.2726 1.81134i −0.966367 0.170397i −0.331873 0.943324i \(-0.607680\pi\)
−0.634494 + 0.772928i \(0.718791\pi\)
\(114\) 0 0
\(115\) −7.14378 8.51362i −0.666160 0.793899i
\(116\) 0 0
\(117\) 9.81389 13.9071i 0.907295 1.28571i
\(118\) 0 0
\(119\) −2.43177 13.7913i −0.222920 1.26424i
\(120\) 0 0
\(121\) −7.27754 + 2.64881i −0.661595 + 0.240801i
\(122\) 0 0
\(123\) 0.425850 + 0.557086i 0.0383976 + 0.0502308i
\(124\) 0 0
\(125\) 7.57180 + 4.37158i 0.677243 + 0.391006i
\(126\) 0 0
\(127\) 12.0771 6.97273i 1.07167 0.618730i 0.143034 0.989718i \(-0.454314\pi\)
0.928638 + 0.370988i \(0.120981\pi\)
\(128\) 0 0
\(129\) −14.6073 + 7.57012i −1.28610 + 0.666512i
\(130\) 0 0
\(131\) 12.8891 + 10.8153i 1.12613 + 0.944933i 0.998898 0.0469403i \(-0.0149471\pi\)
0.127230 + 0.991873i \(0.459392\pi\)
\(132\) 0 0
\(133\) 6.78506 + 2.46956i 0.588339 + 0.214138i
\(134\) 0 0
\(135\) 9.88810 8.96138i 0.851032 0.771273i
\(136\) 0 0
\(137\) −7.20373 + 19.7921i −0.615456 + 1.69095i 0.102384 + 0.994745i \(0.467353\pi\)
−0.717841 + 0.696207i \(0.754869\pi\)
\(138\) 0 0
\(139\) 5.34649 6.37169i 0.453483 0.540440i −0.490061 0.871688i \(-0.663025\pi\)
0.943544 + 0.331248i \(0.107470\pi\)
\(140\) 0 0
\(141\) −8.21660 + 12.8455i −0.691962 + 1.08179i
\(142\) 0 0
\(143\) 12.2822 + 21.2733i 1.02709 + 1.77897i
\(144\) 0 0
\(145\) −0.495366 + 0.858000i −0.0411379 + 0.0712530i
\(146\) 0 0
\(147\) 0.491038 + 3.78331i 0.0405002 + 0.312042i
\(148\) 0 0
\(149\) −2.34190 6.43432i −0.191856 0.527120i 0.806047 0.591852i \(-0.201603\pi\)
−0.997903 + 0.0647320i \(0.979381\pi\)
\(150\) 0 0
\(151\) −9.29194 + 1.63842i −0.756167 + 0.133333i −0.538425 0.842674i \(-0.680980\pi\)
−0.217742 + 0.976006i \(0.569869\pi\)
\(152\) 0 0
\(153\) 19.1140 1.60177i 1.54528 0.129496i
\(154\) 0 0
\(155\) −13.3811 + 11.2281i −1.07479 + 0.901859i
\(156\) 0 0
\(157\) 1.84720 10.4760i 0.147422 0.836074i −0.817968 0.575264i \(-0.804899\pi\)
0.965390 0.260810i \(-0.0839897\pi\)
\(158\) 0 0
\(159\) −3.62853 11.5821i −0.287761 0.918521i
\(160\) 0 0
\(161\) 9.47842i 0.747004i
\(162\) 0 0
\(163\) 13.7337i 1.07570i 0.843039 + 0.537852i \(0.180764\pi\)
−0.843039 + 0.537852i \(0.819236\pi\)
\(164\) 0 0
\(165\) 5.75755 + 18.3779i 0.448225 + 1.43071i
\(166\) 0 0
\(167\) −0.294930 + 1.67263i −0.0228223 + 0.129432i −0.994090 0.108557i \(-0.965377\pi\)
0.971268 + 0.237989i \(0.0764881\pi\)
\(168\) 0 0
\(169\) 14.7011 12.3357i 1.13086 0.948901i
\(170\) 0 0
\(171\) −4.21239 + 8.94782i −0.322129 + 0.684257i
\(172\) 0 0
\(173\) 0.171533 0.0302458i 0.0130414 0.00229955i −0.167124 0.985936i \(-0.553448\pi\)
0.180165 + 0.983636i \(0.442337\pi\)
\(174\) 0 0
\(175\) −1.19530 3.28405i −0.0903558 0.248251i
\(176\) 0 0
\(177\) 0.381079 + 2.93610i 0.0286436 + 0.220691i
\(178\) 0 0
\(179\) 11.3351 19.6329i 0.847223 1.46743i −0.0364543 0.999335i \(-0.511606\pi\)
0.883677 0.468097i \(-0.155060\pi\)
\(180\) 0 0
\(181\) −5.78896 10.0268i −0.430290 0.745284i 0.566608 0.823987i \(-0.308255\pi\)
−0.996898 + 0.0787036i \(0.974922\pi\)
\(182\) 0 0
\(183\) −10.5528 + 16.4979i −0.780088 + 1.21956i
\(184\) 0 0
\(185\) 12.6105 15.0286i 0.927139 1.10492i
\(186\) 0 0
\(187\) −9.46761 + 26.0121i −0.692340 + 1.90219i
\(188\) 0 0
\(189\) 11.3728 0.433992i 0.827251 0.0315682i
\(190\) 0 0
\(191\) −18.0496 6.56951i −1.30602 0.475353i −0.407069 0.913397i \(-0.633449\pi\)
−0.898953 + 0.438044i \(0.855671\pi\)
\(192\) 0 0
\(193\) 6.28804 + 5.27629i 0.452623 + 0.379796i 0.840408 0.541954i \(-0.182315\pi\)
−0.387785 + 0.921750i \(0.626760\pi\)
\(194\) 0 0
\(195\) 22.4076 11.6126i 1.60465 0.831596i
\(196\) 0 0
\(197\) 13.9850 8.07425i 0.996391 0.575266i 0.0892122 0.996013i \(-0.471565\pi\)
0.907178 + 0.420746i \(0.138232\pi\)
\(198\) 0 0
\(199\) 1.42031 + 0.820018i 0.100683 + 0.0581295i 0.549496 0.835496i \(-0.314820\pi\)
−0.448813 + 0.893626i \(0.648153\pi\)
\(200\) 0 0
\(201\) 2.10341 + 2.75163i 0.148363 + 0.194085i
\(202\) 0 0
\(203\) −0.793995 + 0.288991i −0.0557275 + 0.0202832i
\(204\) 0 0
\(205\) 0.180544 + 1.02392i 0.0126098 + 0.0715135i
\(206\) 0 0
\(207\) 12.9288 + 1.17883i 0.898611 + 0.0819343i
\(208\) 0 0
\(209\) −9.17426 10.9335i −0.634597 0.756283i
\(210\) 0 0
\(211\) 14.5381 + 2.56346i 1.00084 + 0.176476i 0.649981 0.759951i \(-0.274777\pi\)
0.350864 + 0.936427i \(0.385888\pi\)
\(212\) 0 0
\(213\) 1.40169 6.26828i 0.0960420 0.429495i
\(214\) 0 0
\(215\) −24.3946 −1.66370
\(216\) 0 0
\(217\) −14.8975 −1.01131
\(218\) 0 0
\(219\) −13.7131 12.6120i −0.926645 0.852239i
\(220\) 0 0
\(221\) 35.7248 + 6.29924i 2.40311 + 0.423733i
\(222\) 0 0
\(223\) 13.6087 + 16.2182i 0.911308 + 1.08605i 0.995974 + 0.0896449i \(0.0285732\pi\)
−0.0846660 + 0.996409i \(0.526982\pi\)
\(224\) 0 0
\(225\) 4.62817 1.22197i 0.308545 0.0814648i
\(226\) 0 0
\(227\) −3.65627 20.7357i −0.242675 1.37628i −0.825830 0.563919i \(-0.809293\pi\)
0.583155 0.812361i \(-0.301818\pi\)
\(228\) 0 0
\(229\) −21.1473 + 7.69700i −1.39746 + 0.508632i −0.927422 0.374017i \(-0.877980\pi\)
−0.470033 + 0.882649i \(0.655758\pi\)
\(230\) 0 0
\(231\) −6.31328 + 15.1630i −0.415383 + 0.997655i
\(232\) 0 0
\(233\) 22.3267 + 12.8903i 1.46267 + 0.844472i 0.999134 0.0416070i \(-0.0132478\pi\)
0.463534 + 0.886079i \(0.346581\pi\)
\(234\) 0 0
\(235\) −19.5806 + 11.3049i −1.27730 + 0.737450i
\(236\) 0 0
\(237\) 0.538625 11.8392i 0.0349875 0.769039i
\(238\) 0 0
\(239\) −8.25623 6.92780i −0.534051 0.448122i 0.335446 0.942059i \(-0.391113\pi\)
−0.869498 + 0.493937i \(0.835557\pi\)
\(240\) 0 0
\(241\) 23.7530 + 8.64537i 1.53006 + 0.556897i 0.963637 0.267215i \(-0.0861034\pi\)
0.566426 + 0.824112i \(0.308326\pi\)
\(242\) 0 0
\(243\) −0.822462 + 15.5667i −0.0527609 + 0.998607i
\(244\) 0 0
\(245\) −1.93471 + 5.31558i −0.123604 + 0.339600i
\(246\) 0 0
\(247\) −12.0226 + 14.3280i −0.764982 + 0.911671i
\(248\) 0 0
\(249\) −2.42346 0.110255i −0.153581 0.00698715i
\(250\) 0 0
\(251\) −7.50990 13.0075i −0.474021 0.821028i 0.525537 0.850771i \(-0.323865\pi\)
−0.999558 + 0.0297426i \(0.990531\pi\)
\(252\) 0 0
\(253\) −9.36788 + 16.2257i −0.588954 + 1.02010i
\(254\) 0 0
\(255\) 26.2557 + 10.9318i 1.64420 + 0.684577i
\(256\) 0 0
\(257\) −6.91255 18.9921i −0.431193 1.18469i −0.945081 0.326836i \(-0.894018\pi\)
0.513888 0.857857i \(-0.328205\pi\)
\(258\) 0 0
\(259\) 16.4775 2.90542i 1.02386 0.180534i
\(260\) 0 0
\(261\) −0.295440 1.11897i −0.0182873 0.0692624i
\(262\) 0 0
\(263\) 3.94316 3.30870i 0.243146 0.204023i −0.513068 0.858348i \(-0.671491\pi\)
0.756214 + 0.654324i \(0.227047\pi\)
\(264\) 0 0
\(265\) 3.12503 17.7229i 0.191969 1.08871i
\(266\) 0 0
\(267\) 9.27797 10.0880i 0.567802 0.617375i
\(268\) 0 0
\(269\) 5.82144i 0.354939i −0.984126 0.177470i \(-0.943209\pi\)
0.984126 0.177470i \(-0.0567912\pi\)
\(270\) 0 0
\(271\) 4.39965i 0.267260i 0.991031 + 0.133630i \(0.0426634\pi\)
−0.991031 + 0.133630i \(0.957337\pi\)
\(272\) 0 0
\(273\) 21.0056 + 4.69718i 1.27131 + 0.284286i
\(274\) 0 0
\(275\) −1.19958 + 6.80316i −0.0723374 + 0.410246i
\(276\) 0 0
\(277\) −7.99331 + 6.70718i −0.480271 + 0.402995i −0.850525 0.525935i \(-0.823715\pi\)
0.370253 + 0.928931i \(0.379271\pi\)
\(278\) 0 0
\(279\) 1.85279 20.3205i 0.110924 1.21655i
\(280\) 0 0
\(281\) −4.88693 + 0.861697i −0.291530 + 0.0514045i −0.317500 0.948258i \(-0.602843\pi\)
0.0259707 + 0.999663i \(0.491732\pi\)
\(282\) 0 0
\(283\) −0.925706 2.54336i −0.0550275 0.151187i 0.909133 0.416505i \(-0.136745\pi\)
−0.964161 + 0.265318i \(0.914523\pi\)
\(284\) 0 0
\(285\) −11.6501 + 8.90558i −0.690090 + 0.527521i
\(286\) 0 0
\(287\) −0.443362 + 0.767926i −0.0261709 + 0.0453292i
\(288\) 0 0
\(289\) 11.9396 + 20.6799i 0.702327 + 1.21647i
\(290\) 0 0
\(291\) −9.59610 18.5166i −0.562533 1.08546i
\(292\) 0 0
\(293\) 1.38940 1.65583i 0.0811699 0.0967345i −0.723931 0.689872i \(-0.757667\pi\)
0.805101 + 0.593138i \(0.202111\pi\)
\(294\) 0 0
\(295\) −1.50147 + 4.12525i −0.0874189 + 0.240182i
\(296\) 0 0
\(297\) −19.8975 10.4973i −1.15457 0.609113i
\(298\) 0 0
\(299\) 23.0721 + 8.39754i 1.33429 + 0.485642i
\(300\) 0 0
\(301\) −15.9376 13.3732i −0.918629 0.770821i
\(302\) 0 0
\(303\) 2.41677 + 1.54588i 0.138840 + 0.0888083i
\(304\) 0 0
\(305\) −25.1480 + 14.5192i −1.43997 + 0.831368i
\(306\) 0 0
\(307\) 2.33463 + 1.34790i 0.133244 + 0.0769287i 0.565140 0.824995i \(-0.308822\pi\)
−0.431896 + 0.901923i \(0.642155\pi\)
\(308\) 0 0
\(309\) −4.94705 + 0.642082i −0.281428 + 0.0365267i
\(310\) 0 0
\(311\) −0.211163 + 0.0768571i −0.0119740 + 0.00435817i −0.348000 0.937494i \(-0.613139\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(312\) 0 0
\(313\) −1.54162 8.74295i −0.0871374 0.494181i −0.996875 0.0789969i \(-0.974828\pi\)
0.909737 0.415184i \(-0.136283\pi\)
\(314\) 0 0
\(315\) 15.2680 + 7.18773i 0.860252 + 0.404983i
\(316\) 0 0
\(317\) 2.12018 + 2.52673i 0.119081 + 0.141915i 0.822292 0.569066i \(-0.192695\pi\)
−0.703210 + 0.710982i \(0.748251\pi\)
\(318\) 0 0
\(319\) 1.64482 + 0.290027i 0.0920924 + 0.0162384i
\(320\) 0 0
\(321\) 20.9836 6.57389i 1.17119 0.366919i
\(322\) 0 0
\(323\) −21.0774 −1.17278
\(324\) 0 0
\(325\) 9.05291 0.502165
\(326\) 0 0
\(327\) 10.8184 3.38928i 0.598261 0.187428i
\(328\) 0 0
\(329\) −18.9899 3.34844i −1.04695 0.184605i
\(330\) 0 0
\(331\) 14.8545 + 17.7029i 0.816478 + 0.973041i 0.999950 0.00998434i \(-0.00317817\pi\)
−0.183472 + 0.983025i \(0.558734\pi\)
\(332\) 0 0
\(333\) 1.91376 + 22.8370i 0.104873 + 1.25146i
\(334\) 0 0
\(335\) 0.891768 + 5.05746i 0.0487225 + 0.276319i
\(336\) 0 0
\(337\) 9.67555 3.52161i 0.527061 0.191834i −0.0647647 0.997901i \(-0.520630\pi\)
0.591826 + 0.806066i \(0.298407\pi\)
\(338\) 0 0
\(339\) 17.9169 2.32545i 0.973112 0.126301i
\(340\) 0 0
\(341\) 25.5023 + 14.7237i 1.38103 + 0.797335i
\(342\) 0 0
\(343\) −17.4560 + 10.0782i −0.942534 + 0.544172i
\(344\) 0 0
\(345\) 16.2160 + 10.3725i 0.873038 + 0.558436i
\(346\) 0 0
\(347\) −27.5760 23.1390i −1.48036 1.24217i −0.905799 0.423707i \(-0.860729\pi\)
−0.574560 0.818462i \(-0.694827\pi\)
\(348\) 0 0
\(349\) −21.1590 7.70125i −1.13262 0.412238i −0.293374 0.955998i \(-0.594778\pi\)
−0.839241 + 0.543759i \(0.817000\pi\)
\(350\) 0 0
\(351\) −9.01951 + 28.0679i −0.481426 + 1.49815i
\(352\) 0 0
\(353\) 9.62764 26.4517i 0.512428 1.40788i −0.366272 0.930508i \(-0.619366\pi\)
0.878700 0.477375i \(-0.158412\pi\)
\(354\) 0 0
\(355\) 6.12178 7.29565i 0.324910 0.387213i
\(356\) 0 0
\(357\) 11.1606 + 21.5355i 0.590683 + 1.13978i
\(358\) 0 0
\(359\) 13.4479 + 23.2924i 0.709753 + 1.22933i 0.964949 + 0.262439i \(0.0845268\pi\)
−0.255196 + 0.966889i \(0.582140\pi\)
\(360\) 0 0
\(361\) −4.06623 + 7.04293i −0.214012 + 0.370680i
\(362\) 0 0
\(363\) 10.6570 8.14645i 0.559347 0.427578i
\(364\) 0 0
\(365\) −9.44827 25.9589i −0.494545 1.35875i
\(366\) 0 0
\(367\) −27.9737 + 4.93252i −1.46022 + 0.257475i −0.846642 0.532162i \(-0.821380\pi\)
−0.613574 + 0.789638i \(0.710269\pi\)
\(368\) 0 0
\(369\) −0.992327 0.700262i −0.0516585 0.0364542i
\(370\) 0 0
\(371\) 11.7575 9.86569i 0.610418 0.512201i
\(372\) 0 0
\(373\) 2.05586 11.6594i 0.106448 0.603699i −0.884183 0.467140i \(-0.845284\pi\)
0.990632 0.136559i \(-0.0436045\pi\)
\(374\) 0 0
\(375\) −14.7786 3.30473i −0.763165 0.170656i
\(376\) 0 0
\(377\) 2.18875i 0.112726i
\(378\) 0 0
\(379\) 21.1690i 1.08738i −0.839286 0.543690i \(-0.817027\pi\)
0.839286 0.543690i \(-0.182973\pi\)
\(380\) 0 0
\(381\) −16.3509 + 17.7785i −0.837684 + 0.910819i
\(382\) 0 0
\(383\) 3.40920 19.3346i 0.174202 0.987950i −0.764859 0.644198i \(-0.777191\pi\)
0.939061 0.343751i \(-0.111698\pi\)
\(384\) 0 0
\(385\) −18.6561 + 15.6543i −0.950804 + 0.797819i
\(386\) 0 0
\(387\) 20.2235 20.0760i 1.02802 1.02052i
\(388\) 0 0
\(389\) −8.24025 + 1.45298i −0.417798 + 0.0736690i −0.378595 0.925562i \(-0.623593\pi\)
−0.0392022 + 0.999231i \(0.512482\pi\)
\(390\) 0 0
\(391\) 9.46316 + 25.9998i 0.478572 + 1.31487i
\(392\) 0 0
\(393\) −26.9039 11.2017i −1.35712 0.565051i
\(394\) 0 0
\(395\) 8.78634 15.2184i 0.442089 0.765720i
\(396\) 0 0
\(397\) −13.4307 23.2627i −0.674068 1.16752i −0.976740 0.214426i \(-0.931212\pi\)
0.302672 0.953095i \(-0.402121\pi\)
\(398\) 0 0
\(399\) −12.4934 0.568386i −0.625451 0.0284549i
\(400\) 0 0
\(401\) −12.5634 + 14.9724i −0.627385 + 0.747688i −0.982321 0.187203i \(-0.940058\pi\)
0.354937 + 0.934890i \(0.384502\pi\)
\(402\) 0 0
\(403\) 13.1986 36.2629i 0.657471 1.80639i
\(404\) 0 0
\(405\) −11.7031 + 19.9319i −0.581531 + 0.990424i
\(406\) 0 0
\(407\) −31.0785 11.3117i −1.54051 0.560698i
\(408\) 0 0
\(409\) −2.96469 2.48767i −0.146594 0.123007i 0.566541 0.824033i \(-0.308281\pi\)
−0.713136 + 0.701026i \(0.752726\pi\)
\(410\) 0 0
\(411\) 1.65799 36.4433i 0.0817825 1.79761i
\(412\) 0 0
\(413\) −3.24243 + 1.87202i −0.159550 + 0.0921161i
\(414\) 0 0
\(415\) −3.11517 1.79854i −0.152918 0.0882871i
\(416\) 0 0
\(417\) −5.53752 + 13.2999i −0.271174 + 0.651297i
\(418\) 0 0
\(419\) −5.55790 + 2.02291i −0.271521 + 0.0988256i −0.474192 0.880421i \(-0.657260\pi\)
0.202671 + 0.979247i \(0.435038\pi\)
\(420\) 0 0
\(421\) −2.43514 13.8103i −0.118681 0.673075i −0.984862 0.173343i \(-0.944543\pi\)
0.866180 0.499732i \(-0.166568\pi\)
\(422\) 0 0
\(423\) 6.92911 25.4862i 0.336905 1.23918i
\(424\) 0 0
\(425\) 6.55752 + 7.81495i 0.318086 + 0.379081i
\(426\) 0 0
\(427\) −24.3894 4.30050i −1.18028 0.208116i
\(428\) 0 0
\(429\) −31.3160 28.8015i −1.51195 1.39055i
\(430\) 0 0
\(431\) −34.8272 −1.67757 −0.838784 0.544465i \(-0.816733\pi\)
−0.838784 + 0.544465i \(0.816733\pi\)
\(432\) 0 0
\(433\) −13.7584 −0.661187 −0.330593 0.943773i \(-0.607249\pi\)
−0.330593 + 0.943773i \(0.607249\pi\)
\(434\) 0 0
\(435\) 0.374476 1.67464i 0.0179548 0.0802929i
\(436\) 0 0
\(437\) −14.0492 2.47725i −0.672062 0.118503i
\(438\) 0 0
\(439\) −14.8296 17.6732i −0.707779 0.843498i 0.285604 0.958348i \(-0.407806\pi\)
−0.993383 + 0.114850i \(0.963361\pi\)
\(440\) 0 0
\(441\) −2.77065 5.99892i −0.131936 0.285663i
\(442\) 0 0
\(443\) 4.37334 + 24.8025i 0.207784 + 1.17840i 0.892999 + 0.450059i \(0.148597\pi\)
−0.685215 + 0.728341i \(0.740292\pi\)
\(444\) 0 0
\(445\) 19.0966 6.95058i 0.905264 0.329489i
\(446\) 0 0
\(447\) 7.20256 + 9.42221i 0.340669 + 0.445655i
\(448\) 0 0
\(449\) −11.0355 6.37137i −0.520799 0.300683i 0.216463 0.976291i \(-0.430548\pi\)
−0.737261 + 0.675608i \(0.763881\pi\)
\(450\) 0 0
\(451\) 1.51794 0.876384i 0.0714771 0.0412673i
\(452\) 0 0
\(453\) 14.5097 7.51953i 0.681723 0.353298i
\(454\) 0 0
\(455\) 24.4484 + 20.5146i 1.14616 + 0.961741i
\(456\) 0 0
\(457\) −17.7529 6.46151i −0.830444 0.302257i −0.108403 0.994107i \(-0.534574\pi\)
−0.722041 + 0.691850i \(0.756796\pi\)
\(458\) 0 0
\(459\) −30.7630 + 12.5450i −1.43589 + 0.585549i
\(460\) 0 0
\(461\) 2.34645 6.44682i 0.109285 0.300258i −0.872980 0.487756i \(-0.837816\pi\)
0.982265 + 0.187498i \(0.0600378\pi\)
\(462\) 0 0
\(463\) −4.22001 + 5.02921i −0.196120 + 0.233727i −0.855138 0.518400i \(-0.826528\pi\)
0.659018 + 0.752127i \(0.270972\pi\)
\(464\) 0 0
\(465\) 16.3027 25.4870i 0.756019 1.18193i
\(466\) 0 0
\(467\) 19.4184 + 33.6337i 0.898578 + 1.55638i 0.829313 + 0.558784i \(0.188732\pi\)
0.0692651 + 0.997598i \(0.477935\pi\)
\(468\) 0 0
\(469\) −2.18991 + 3.79304i −0.101121 + 0.175146i
\(470\) 0 0
\(471\) 2.37148 + 18.2716i 0.109272 + 0.841911i
\(472\) 0 0
\(473\) 14.0655 + 38.6448i 0.646735 + 1.77689i
\(474\) 0 0
\(475\) −5.18010 + 0.913391i −0.237679 + 0.0419093i
\(476\) 0 0
\(477\) 11.9947 + 17.2644i 0.549201 + 0.790484i
\(478\) 0 0
\(479\) −1.85078 + 1.55299i −0.0845645 + 0.0709580i −0.684090 0.729398i \(-0.739800\pi\)
0.599525 + 0.800356i \(0.295356\pi\)
\(480\) 0 0
\(481\) −7.52616 + 42.6830i −0.343164 + 1.94618i
\(482\) 0 0
\(483\) 4.90805 + 15.6663i 0.223324 + 0.712840i
\(484\) 0 0
\(485\) 30.9233i 1.40415i
\(486\) 0 0
\(487\) 1.69185i 0.0766648i −0.999265 0.0383324i \(-0.987795\pi\)
0.999265 0.0383324i \(-0.0122046\pi\)
\(488\) 0 0
\(489\) −7.11147 22.6995i −0.321592 1.02651i
\(490\) 0 0
\(491\) −1.07391 + 6.09047i −0.0484650 + 0.274859i −0.999404 0.0345196i \(-0.989010\pi\)
0.950939 + 0.309378i \(0.100121\pi\)
\(492\) 0 0
\(493\) 1.88945 1.58543i 0.0850964 0.0714043i
\(494\) 0 0
\(495\) −19.0326 27.3943i −0.855451 1.23128i
\(496\) 0 0
\(497\) 7.99902 1.41044i 0.358805 0.0632670i
\(498\) 0 0
\(499\) −7.06711 19.4167i −0.316367 0.869213i −0.991334 0.131364i \(-0.958064\pi\)
0.674967 0.737848i \(-0.264158\pi\)
\(500\) 0 0
\(501\) −0.378639 2.91730i −0.0169163 0.130335i
\(502\) 0 0
\(503\) 15.4292 26.7241i 0.687954 1.19157i −0.284545 0.958663i \(-0.591843\pi\)
0.972499 0.232908i \(-0.0748241\pi\)
\(504\) 0 0
\(505\) 2.12691 + 3.68392i 0.0946463 + 0.163932i
\(506\) 0 0
\(507\) −17.9110 + 28.0014i −0.795455 + 1.24358i
\(508\) 0 0
\(509\) −25.1823 + 30.0112i −1.11619 + 1.33022i −0.178026 + 0.984026i \(0.556971\pi\)
−0.938162 + 0.346195i \(0.887473\pi\)
\(510\) 0 0
\(511\) 8.05801 22.1392i 0.356465 0.979380i
\(512\) 0 0
\(513\) 2.32909 16.9705i 0.102832 0.749267i
\(514\) 0 0
\(515\) −6.95066 2.52983i −0.306283 0.111478i
\(516\) 0 0
\(517\) 29.1986 + 24.5005i 1.28415 + 1.07753i
\(518\) 0 0
\(519\) −0.267854 + 0.138813i −0.0117575 + 0.00609322i
\(520\) 0 0
\(521\) −0.354649 + 0.204757i −0.0155375 + 0.00897056i −0.507749 0.861505i \(-0.669522\pi\)
0.492211 + 0.870476i \(0.336189\pi\)
\(522\) 0 0
\(523\) 11.5381 + 6.66155i 0.504528 + 0.291289i 0.730581 0.682826i \(-0.239249\pi\)
−0.226054 + 0.974115i \(0.572582\pi\)
\(524\) 0 0
\(525\) 3.67615 + 4.80905i 0.160440 + 0.209884i
\(526\) 0 0
\(527\) 40.8646 14.8735i 1.78009 0.647899i
\(528\) 0 0
\(529\) −0.742008 4.20814i −0.0322612 0.182962i
\(530\) 0 0
\(531\) −2.15021 4.65557i −0.0933113 0.202035i
\(532\) 0 0
\(533\) −1.47646 1.75957i −0.0639525 0.0762156i
\(534\) 0 0
\(535\) 32.1090 + 5.66169i 1.38820 + 0.244776i
\(536\) 0 0
\(537\) −8.56884 + 38.3194i −0.369773 + 1.65361i
\(538\) 0 0
\(539\) 9.53622 0.410754
\(540\) 0 0
\(541\) 27.7454 1.19287 0.596434 0.802662i \(-0.296584\pi\)
0.596434 + 0.802662i \(0.296584\pi\)
\(542\) 0 0
\(543\) 14.7602 + 13.5750i 0.633420 + 0.582559i
\(544\) 0 0
\(545\) 16.5544 + 2.91898i 0.709111 + 0.125035i
\(546\) 0 0
\(547\) 22.7506 + 27.1131i 0.972744 + 1.15927i 0.987218 + 0.159375i \(0.0509480\pi\)
−0.0144745 + 0.999895i \(0.504608\pi\)
\(548\) 0 0
\(549\) 8.89927 32.7327i 0.379812 1.39700i
\(550\) 0 0
\(551\) 0.220834 + 1.25241i 0.00940783 + 0.0533545i
\(552\) 0 0
\(553\) 14.0831 5.12584i 0.598876 0.217973i
\(554\) 0 0
\(555\) −13.0610 + 31.3696i −0.554410 + 1.33157i
\(556\) 0 0
\(557\) 4.22184 + 2.43748i 0.178885 + 0.103279i 0.586769 0.809755i \(-0.300400\pi\)
−0.407884 + 0.913034i \(0.633733\pi\)
\(558\) 0 0
\(559\) 46.6729 26.9466i 1.97405 1.13972i
\(560\) 0 0
\(561\) 2.17904 47.8961i 0.0919990 2.02218i
\(562\) 0 0
\(563\) −17.8937 15.0146i −0.754131 0.632791i 0.182461 0.983213i \(-0.441594\pi\)
−0.936592 + 0.350422i \(0.886038\pi\)
\(564\) 0 0
\(565\) 25.1734 + 9.16238i 1.05905 + 0.385464i
\(566\) 0 0
\(567\) −18.5727 + 6.60631i −0.779980 + 0.277439i
\(568\) 0 0
\(569\) −1.89142 + 5.19662i −0.0792923 + 0.217854i −0.973004 0.230788i \(-0.925870\pi\)
0.893712 + 0.448641i \(0.148092\pi\)
\(570\) 0 0
\(571\) 5.47700 6.52724i 0.229205 0.273156i −0.639168 0.769067i \(-0.720721\pi\)
0.868374 + 0.495911i \(0.165166\pi\)
\(572\) 0 0
\(573\) 33.2348 + 1.51202i 1.38840 + 0.0631655i
\(574\) 0 0
\(575\) 3.45243 + 5.97978i 0.143976 + 0.249374i
\(576\) 0 0
\(577\) 11.9313 20.6656i 0.496706 0.860319i −0.503287 0.864119i \(-0.667876\pi\)
0.999993 + 0.00379980i \(0.00120952\pi\)
\(578\) 0 0
\(579\) −13.1252 5.46482i −0.545466 0.227110i
\(580\) 0 0
\(581\) −1.04925 2.88279i −0.0435302 0.119598i
\(582\) 0 0
\(583\) −29.8777 + 5.26824i −1.23741 + 0.218188i
\(584\) 0 0
\(585\) −31.0230 + 30.7967i −1.28264 + 1.27329i
\(586\) 0 0
\(587\) 15.5765 13.0702i 0.642910 0.539466i −0.262000 0.965068i \(-0.584382\pi\)
0.904910 + 0.425602i \(0.139938\pi\)
\(588\) 0 0
\(589\) −3.89355 + 22.0814i −0.160431 + 0.909849i
\(590\) 0 0
\(591\) −18.9340 + 20.5870i −0.778840 + 0.846838i
\(592\) 0 0
\(593\) 4.06230i 0.166819i 0.996515 + 0.0834094i \(0.0265809\pi\)
−0.996515 + 0.0834094i \(0.973419\pi\)
\(594\) 0 0
\(595\) 35.9650i 1.47442i
\(596\) 0 0
\(597\) −2.77216 0.619899i −0.113457 0.0253708i
\(598\) 0 0
\(599\) −4.78180 + 27.1190i −0.195379 + 1.10805i 0.716499 + 0.697589i \(0.245744\pi\)
−0.911878 + 0.410462i \(0.865367\pi\)
\(600\) 0 0
\(601\) 5.76201 4.83490i 0.235037 0.197220i −0.517660 0.855586i \(-0.673197\pi\)
0.752697 + 0.658367i \(0.228752\pi\)
\(602\) 0 0
\(603\) −4.90143 3.45883i −0.199602 0.140854i
\(604\) 0 0
\(605\) 19.5874 3.45379i 0.796341 0.140416i
\(606\) 0 0
\(607\) 12.5106 + 34.3727i 0.507791 + 1.39514i 0.883511 + 0.468411i \(0.155173\pi\)
−0.375719 + 0.926733i \(0.622604\pi\)
\(608\) 0 0
\(609\) 1.16270 0.888795i 0.0471150 0.0360158i
\(610\) 0 0
\(611\) 24.9751 43.2581i 1.01038 1.75003i
\(612\) 0 0
\(613\) 13.0121 + 22.5376i 0.525552 + 0.910283i 0.999557 + 0.0297610i \(0.00947463\pi\)
−0.474005 + 0.880522i \(0.657192\pi\)
\(614\) 0 0
\(615\) −0.828608 1.59888i −0.0334127 0.0644730i
\(616\) 0 0
\(617\) 9.69439 11.5533i 0.390281 0.465119i −0.534750 0.845010i \(-0.679594\pi\)
0.925031 + 0.379891i \(0.124039\pi\)
\(618\) 0 0
\(619\) 5.42776 14.9126i 0.218160 0.599390i −0.781541 0.623854i \(-0.785566\pi\)
0.999701 + 0.0244646i \(0.00778810\pi\)
\(620\) 0 0
\(621\) −21.9795 + 4.74627i −0.882009 + 0.190461i
\(622\) 0 0
\(623\) 16.2866 + 5.92785i 0.652510 + 0.237494i
\(624\) 0 0
\(625\) −23.3123 19.5613i −0.932492 0.782454i
\(626\) 0 0
\(627\) 20.8250 + 13.3207i 0.831672 + 0.531976i
\(628\) 0 0
\(629\) −42.2978 + 24.4207i −1.68652 + 0.973715i
\(630\) 0 0
\(631\) −6.79006 3.92024i −0.270308 0.156062i 0.358720 0.933445i \(-0.383213\pi\)
−0.629028 + 0.777383i \(0.716547\pi\)
\(632\) 0 0
\(633\) −25.3565 + 3.29104i −1.00783 + 0.130807i
\(634\) 0 0
\(635\) −33.6547 + 12.2493i −1.33555 + 0.486099i
\(636\) 0 0
\(637\) −2.17008 12.3071i −0.0859817 0.487626i
\(638\) 0 0
\(639\) 0.929038 + 11.0863i 0.0367522 + 0.438565i
\(640\) 0 0
\(641\) 2.91672 + 3.47601i 0.115204 + 0.137294i 0.820564 0.571554i \(-0.193659\pi\)
−0.705361 + 0.708849i \(0.749215\pi\)
\(642\) 0 0
\(643\) −34.2656 6.04196i −1.35131 0.238272i −0.549318 0.835613i \(-0.685113\pi\)
−0.801987 + 0.597342i \(0.796224\pi\)
\(644\) 0 0
\(645\) 40.3203 12.6318i 1.58761 0.497378i
\(646\) 0 0
\(647\) −14.0701 −0.553153 −0.276576 0.960992i \(-0.589200\pi\)
−0.276576 + 0.960992i \(0.589200\pi\)
\(648\) 0 0
\(649\) 7.40076 0.290505
\(650\) 0 0
\(651\) 24.6231 7.71411i 0.965055 0.302340i
\(652\) 0 0
\(653\) 20.1254 + 3.54865i 0.787567 + 0.138869i 0.552945 0.833217i \(-0.313504\pi\)
0.234622 + 0.972087i \(0.424615\pi\)
\(654\) 0 0
\(655\) −27.7756 33.1017i −1.08528 1.29339i
\(656\) 0 0
\(657\) 29.1962 + 13.7447i 1.13905 + 0.536233i
\(658\) 0 0
\(659\) 6.56089 + 37.2087i 0.255576 + 1.44944i 0.794590 + 0.607147i \(0.207686\pi\)
−0.539014 + 0.842297i \(0.681203\pi\)
\(660\) 0 0
\(661\) −7.02492 + 2.55686i −0.273238 + 0.0994505i −0.475005 0.879983i \(-0.657554\pi\)
0.201767 + 0.979434i \(0.435332\pi\)
\(662\) 0 0
\(663\) −62.3090 + 8.08714i −2.41988 + 0.314078i
\(664\) 0 0
\(665\) −16.0592 9.27181i −0.622751 0.359545i
\(666\) 0 0
\(667\) 1.44575 0.834705i 0.0559797 0.0323199i
\(668\) 0 0
\(669\) −30.8910 19.7593i −1.19432 0.763940i
\(670\) 0 0
\(671\) 37.5006 + 31.4668i 1.44770 + 1.21476i
\(672\) 0 0
\(673\) 17.8914 + 6.51195i 0.689664 + 0.251017i 0.662991 0.748627i \(-0.269287\pi\)
0.0266725 + 0.999644i \(0.491509\pi\)
\(674\) 0 0
\(675\) −7.01685 + 4.41625i −0.270079 + 0.169981i
\(676\) 0 0
\(677\) 4.20531 11.5540i 0.161623 0.444056i −0.832274 0.554364i \(-0.812961\pi\)
0.993897 + 0.110308i \(0.0351837\pi\)
\(678\) 0 0
\(679\) 16.9523 20.2030i 0.650570 0.775319i
\(680\) 0 0
\(681\) 16.7805 + 32.3795i 0.643028 + 1.24079i
\(682\) 0 0
\(683\) 14.1366 + 24.4853i 0.540921 + 0.936903i 0.998851 + 0.0479145i \(0.0152575\pi\)
−0.457931 + 0.888988i \(0.651409\pi\)
\(684\) 0 0
\(685\) 27.0460 46.8450i 1.03337 1.78986i
\(686\) 0 0
\(687\) 30.9675 23.6723i 1.18148 0.903153i
\(688\) 0 0
\(689\) 13.5980 + 37.3603i 0.518044 + 1.42331i
\(690\) 0 0
\(691\) 9.74960 1.71912i 0.370892 0.0653983i 0.0149045 0.999889i \(-0.495256\pi\)
0.355988 + 0.934491i \(0.384144\pi\)
\(692\) 0 0
\(693\) 2.58320 28.3311i 0.0981275 1.07621i
\(694\) 0 0
\(695\) −16.3637 + 13.7308i −0.620711 + 0.520838i
\(696\) 0 0
\(697\) 0.449477 2.54911i 0.0170252 0.0965545i
\(698\) 0 0
\(699\) −43.5771 9.74453i −1.64824 0.368572i
\(700\) 0 0
\(701\) 9.95360i 0.375942i −0.982175 0.187971i \(-0.939809\pi\)
0.982175 0.187971i \(-0.0601911\pi\)
\(702\) 0 0
\(703\) 25.1827i 0.949783i
\(704\) 0 0
\(705\) 26.5098 28.8243i 0.998417 1.08558i
\(706\) 0 0
\(707\) −0.629978 + 3.57278i −0.0236927 + 0.134368i
\(708\) 0 0
\(709\) −17.3138 + 14.5280i −0.650232 + 0.545610i −0.907141 0.420826i \(-0.861740\pi\)
0.256909 + 0.966436i \(0.417296\pi\)
\(710\) 0 0
\(711\) 5.24024 + 19.8472i 0.196524 + 0.744328i
\(712\) 0 0
\(713\) 28.9865 5.11109i 1.08555 0.191412i
\(714\) 0 0
\(715\) −21.5766 59.2813i −0.806920 2.21699i
\(716\) 0 0
\(717\) 17.2335 + 7.17534i 0.643597 + 0.267968i
\(718\) 0 0
\(719\) −16.3460 + 28.3121i −0.609602 + 1.05586i 0.381704 + 0.924285i \(0.375337\pi\)
−0.991306 + 0.131577i \(0.957996\pi\)
\(720\) 0 0
\(721\) −3.15417 5.46319i −0.117468 0.203460i
\(722\) 0 0
\(723\) −43.7365 1.98979i −1.62658 0.0740011i
\(724\) 0 0
\(725\) 0.395657 0.471525i 0.0146943 0.0175120i
\(726\) 0 0
\(727\) 3.76774 10.3518i 0.139738 0.383926i −0.850007 0.526771i \(-0.823403\pi\)
0.989745 + 0.142844i \(0.0456248\pi\)
\(728\) 0 0
\(729\) −6.70127 26.1552i −0.248195 0.968710i
\(730\) 0 0
\(731\) 57.0694 + 20.7716i 2.11079 + 0.768264i
\(732\) 0 0
\(733\) 24.1879 + 20.2961i 0.893402 + 0.749653i 0.968890 0.247493i \(-0.0796068\pi\)
−0.0754875 + 0.997147i \(0.524051\pi\)
\(734\) 0 0
\(735\) 0.445288 9.78761i 0.0164247 0.361022i
\(736\) 0 0
\(737\) 7.49762 4.32875i 0.276178 0.159452i
\(738\) 0 0
\(739\) −6.54458 3.77851i −0.240746 0.138995i 0.374773 0.927116i \(-0.377720\pi\)
−0.615520 + 0.788122i \(0.711054\pi\)
\(740\) 0 0
\(741\) 12.4522 29.9074i 0.457444 1.09867i
\(742\) 0 0
\(743\) −27.9075 + 10.1575i −1.02383 + 0.372643i −0.798728 0.601692i \(-0.794493\pi\)
−0.225101 + 0.974336i \(0.572271\pi\)
\(744\) 0 0
\(745\) 3.05361 + 17.3179i 0.111876 + 0.634479i
\(746\) 0 0
\(747\) 4.06268 1.07267i 0.148646 0.0392468i
\(748\) 0 0
\(749\) 17.8739 + 21.3013i 0.653098 + 0.778331i
\(750\) 0 0
\(751\) −35.8098 6.31424i −1.30672 0.230410i −0.523430 0.852068i \(-0.675348\pi\)
−0.783288 + 0.621659i \(0.786459\pi\)
\(752\) 0 0
\(753\) 19.1481 + 17.6106i 0.697796 + 0.641766i
\(754\) 0 0
\(755\) 24.2316 0.881877
\(756\) 0 0
\(757\) 20.1447 0.732170 0.366085 0.930581i \(-0.380698\pi\)
0.366085 + 0.930581i \(0.380698\pi\)
\(758\) 0 0
\(759\) 7.08173 31.6692i 0.257050 1.14952i
\(760\) 0 0
\(761\) −17.1911 3.03125i −0.623175 0.109883i −0.146860 0.989157i \(-0.546917\pi\)
−0.476315 + 0.879275i \(0.658028\pi\)
\(762\) 0 0
\(763\) 9.21519 + 10.9822i 0.333612 + 0.397584i
\(764\) 0 0
\(765\) −49.0570 4.47296i −1.77366 0.161720i
\(766\) 0 0
\(767\) −1.68413 9.55117i −0.0608104 0.344873i
\(768\) 0 0
\(769\) 11.4962 4.18429i 0.414565 0.150889i −0.126313 0.991990i \(-0.540314\pi\)
0.540878 + 0.841101i \(0.318092\pi\)
\(770\) 0 0
\(771\) 21.2597 + 27.8114i 0.765648 + 1.00160i
\(772\) 0 0
\(773\) −28.3344 16.3589i −1.01912 0.588389i −0.105270 0.994444i \(-0.533571\pi\)
−0.913849 + 0.406055i \(0.866904\pi\)
\(774\) 0 0
\(775\) 9.39857 5.42627i 0.337607 0.194917i
\(776\) 0 0
\(777\) −25.7301 + 13.3344i −0.923062 + 0.478370i
\(778\) 0 0
\(779\) 1.02236 + 0.857866i 0.0366300 + 0.0307362i
\(780\) 0 0
\(781\) −15.0871 5.49127i −0.539860 0.196493i
\(782\) 0 0
\(783\) 1.06773 + 1.69649i 0.0381576 + 0.0606275i
\(784\) 0 0
\(785\) −9.34376 + 25.6718i −0.333493 + 0.916265i
\(786\) 0 0
\(787\) −12.3621 + 14.7326i −0.440662 + 0.525161i −0.939967 0.341266i \(-0.889144\pi\)
0.499305 + 0.866427i \(0.333589\pi\)
\(788\) 0 0
\(789\) −4.80411 + 7.51057i −0.171031 + 0.267383i
\(790\) 0 0
\(791\) 11.4236 + 19.7862i 0.406176 + 0.703517i
\(792\) 0 0
\(793\) 32.0762 55.5577i 1.13906 1.97291i
\(794\) 0 0