Properties

Label 432.2.be.c.239.6
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 239.6
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.c.47.6

$q$-expansion

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

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 0.963405 0.268050i \(-0.0863792\pi\)
−0.431271 + 0.902222i \(0.641935\pi\)
\(8\) 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 \(-0.829193\pi\)
0.632769 0.774340i \(-0.281918\pi\)
\(12\) 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 −0.135390 0.990792i \(-0.543229\pi\)
0.790357 + 0.612647i \(0.209895\pi\)
\(20\) 0 0
\(21\) 3.19584 + 2.04421i 0.697389 + 0.446082i
\(22\) 0 0
\(23\) −3.31503 2.78164i −0.691232 0.580012i 0.228033 0.973654i \(-0.426771\pi\)
−0.919264 + 0.393641i \(0.871215\pi\)
\(24\) 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 −0.999157 0.0410491i \(-0.986930\pi\)
0.213927 + 0.976850i \(0.431374\pi\)
\(32\) 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 −0.833003 0.553269i \(-0.813380\pi\)
−0.593538 + 0.804806i \(0.702269\pi\)
\(44\) 0 0
\(45\) −6.99458 + 3.23050i −1.04269 + 0.481575i
\(46\) 0 0
\(47\) −6.74409 + 5.65897i −0.983727 + 0.825445i −0.984648 0.174554i \(-0.944151\pi\)
0.000920318 1.00000i \(0.499707\pi\)
\(48\) 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 −0.998014 0.0629893i \(-0.979937\pi\)
0.959370 + 0.282150i \(0.0910477\pi\)
\(60\) 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 0.974433 0.224677i \(-0.0721328\pi\)
−0.890879 + 0.454241i \(0.849911\pi\)
\(68\) 0 0
\(69\) −6.91957 2.88103i −0.833019 0.346835i
\(70\) 0 0
\(71\) 1.85419 3.21154i 0.220051 0.381140i −0.734772 0.678314i \(-0.762711\pi\)
0.954823 + 0.297174i \(0.0960442\pi\)
\(72\) 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 \(-0.763119\pi\)
0.998940 0.0460362i \(-0.0146590\pi\)
\(80\) 0 0
\(81\) 3.14002 8.43447i 0.348891 0.937163i
\(82\) 0 0
\(83\) −1.31616 0.479045i −0.144468 0.0525820i 0.268774 0.963203i \(-0.413381\pi\)
−0.413242 + 0.910621i \(0.635604\pi\)
\(84\) 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 0.0321527 0.999483i \(-0.489764\pi\)
−0.311630 + 0.950204i \(0.600875\pi\)
\(104\) 0 0
\(105\) −7.17118 6.59537i −0.699836 0.643642i
\(106\) 0 0
\(107\) 12.6955 1.22732 0.613659 0.789571i \(-0.289697\pi\)
0.613659 + 0.789571i \(0.289697\pi\)
\(108\) 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 −0.928638 0.370988i \(-0.879019\pi\)
−0.143034 + 0.989718i \(0.545686\pi\)
\(128\) 0 0
\(129\) −14.6073 + 7.57012i −1.28610 + 0.666512i
\(130\) 0 0
\(131\) −12.8891 10.8153i −1.12613 0.944933i −0.127230 0.991873i \(-0.540608\pi\)
−0.998898 + 0.0469403i \(0.985053\pi\)
\(132\) 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 −0.943544 0.331248i \(-0.892530\pi\)
0.490061 + 0.871688i \(0.336975\pi\)
\(140\) 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 0.217742 0.976006i \(-0.430131\pi\)
0.538425 + 0.842674i \(0.319020\pi\)
\(152\) 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 \(-0.819236\pi\)
0.843039 0.537852i \(-0.180764\pi\)
\(164\) 0 0
\(165\) 5.75755 + 18.3779i 0.448225 + 1.43071i
\(166\) 0 0
\(167\) 0.294930 1.67263i 0.0228223 0.129432i −0.971268 0.237989i \(-0.923512\pi\)
0.994090 + 0.108557i \(0.0346230\pi\)
\(168\) 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 \(0.488394\pi\)
−0.883677 + 0.468097i \(0.844940\pi\)
\(180\) 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 0.898953 0.438044i \(-0.144329\pi\)
0.407069 + 0.913397i \(0.366551\pi\)
\(192\) 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 0.448813 0.893626i \(-0.351847\pi\)
−0.549496 + 0.835496i \(0.685180\pi\)
\(200\) 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 −0.350864 0.936427i \(-0.614112\pi\)
−0.649981 + 0.759951i \(0.725223\pi\)
\(212\) 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 \(-0.971427\pi\)
0.0846660 0.996409i \(-0.473018\pi\)
\(224\) 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 \(0.190707\pi\)
−0.583155 + 0.812361i \(0.698182\pi\)
\(228\) 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 0.869498 0.493937i \(-0.164443\pi\)
−0.335446 + 0.942059i \(0.608887\pi\)
\(240\) 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 0.999558 0.0297426i \(-0.00946877\pi\)
−0.525537 + 0.850771i \(0.676135\pi\)
\(252\) 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 −0.756214 0.654324i \(-0.772953\pi\)
0.513068 + 0.858348i \(0.328509\pi\)
\(264\) 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 \(-0.957337\pi\)
0.991031 0.133630i \(-0.0426634\pi\)
\(272\) 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 0.964161 0.265318i \(-0.0854770\pi\)
−0.909133 + 0.416505i \(0.863255\pi\)
\(284\) 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 0.431896 0.901923i \(-0.357845\pi\)
−0.565140 + 0.824995i \(0.691178\pi\)
\(308\) 0 0
\(309\) −4.94705 + 0.642082i −0.281428 + 0.0365267i
\(310\) 0 0
\(311\) 0.211163 0.0768571i 0.0119740 0.00435817i −0.336026 0.941853i \(-0.609083\pi\)
0.348000 + 0.937494i \(0.386861\pi\)
\(312\) 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 0.183472 0.983025i \(-0.441266\pi\)
−0.999950 + 0.00998434i \(0.996822\pi\)
\(332\) 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 \(0.139271\pi\)
0.574560 + 0.818462i \(0.305173\pi\)
\(348\) 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 \(-0.915473\pi\)
0.255196 0.966889i \(-0.417860\pi\)
\(360\) 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 0.613574 0.789638i \(-0.289731\pi\)
0.846642 + 0.532162i \(0.178620\pi\)
\(368\) 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 \(0.182973\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(380\) 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 \(0.222809\pi\)
−0.939061 + 0.343751i \(0.888302\pi\)
\(384\) 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 −0.202671 0.979247i \(-0.564962\pi\)
0.474192 + 0.880421i \(0.342740\pi\)
\(420\) 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 \(-0.183267\pi\)
0.838784 + 0.544465i \(0.183267\pi\)
\(432\) 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 0.993383 0.114850i \(-0.0366387\pi\)
−0.285604 + 0.958348i \(0.592194\pi\)
\(440\) 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 \(-0.851403\pi\)
0.685215 0.728341i \(-0.259708\pi\)
\(444\) 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 −0.659018 0.752127i \(-0.729028\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(464\) 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 \(-0.811268\pi\)
−0.0692651 0.997598i \(-0.522065\pi\)
\(468\) 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 −0.599525 0.800356i \(-0.704644\pi\)
0.684090 + 0.729398i \(0.260200\pi\)
\(480\) 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 \(0.0122046\pi\)
−0.999265 + 0.0383324i \(0.987795\pi\)
\(488\) 0 0
\(489\) −7.11147 22.6995i −0.321592 1.02651i
\(490\) 0 0
\(491\) 1.07391 6.09047i 0.0484650 0.274859i −0.950939 0.309378i \(-0.899879\pi\)
0.999404 + 0.0345196i \(0.0109901\pi\)
\(492\) 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 \(0.0419358\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(500\) 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 \(0.408157\pi\)
−0.972499 + 0.232908i \(0.925176\pi\)
\(504\) 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 0.226054 0.974115i \(-0.427418\pi\)
−0.730581 + 0.682826i \(0.760751\pi\)
\(524\) 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 \(-0.949052\pi\)
0.0144745 0.999895i \(-0.495392\pi\)
\(548\) 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 0.936592 0.350422i \(-0.113962\pi\)
−0.182461 + 0.983213i \(0.558406\pi\)
\(564\) 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 −0.868374 0.495911i \(-0.834834\pi\)
0.639168 + 0.769067i \(0.279279\pi\)
\(572\) 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 −0.904910 0.425602i \(-0.860062\pi\)
0.262000 + 0.965068i \(0.415618\pi\)
\(588\) 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 \(-0.754256\pi\)
0.911878 0.410462i \(-0.134633\pi\)
\(600\) 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 \(-0.844827\pi\)
0.375719 0.926733i \(-0.377396\pi\)
\(608\) 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 −0.999701 0.0244646i \(-0.992212\pi\)
0.781541 + 0.623854i \(0.214434\pi\)
\(620\) 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 0.629028 0.777383i \(-0.283453\pi\)
−0.358720 + 0.933445i \(0.616787\pi\)
\(632\) 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 0.801987 0.597342i \(-0.203776\pi\)
0.549318 + 0.835613i \(0.314887\pi\)
\(644\) 0 0
\(645\) 40.3203 12.6318i 1.58761 0.497378i
\(646\) 0 0
\(647\) 14.0701 0.553153 0.276576 0.960992i \(-0.410800\pi\)
0.276576 + 0.960992i \(0.410800\pi\)
\(648\) 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 \(-0.792314\pi\)
0.539014 0.842297i \(-0.318797\pi\)
\(660\) 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 \(-0.984742\pi\)
0.457931 0.888988i \(-0.348591\pi\)
\(684\) 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 −0.355988 0.934491i \(-0.615856\pi\)
−0.0149045 + 0.999889i \(0.504744\pi\)
\(692\) 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 \(-0.624663\pi\)
0.991306 0.131577i \(-0.0420040\pi\)
\(720\) 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 −0.989745 0.142844i \(-0.954375\pi\)
0.850007 + 0.526771i \(0.176597\pi\)
\(728\) 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 0.615520 0.788122i \(-0.288946\pi\)
−0.374773 + 0.927116i \(0.622280\pi\)
\(740\) 0 0
\(741\) 12.4522 29.9074i 0.457444 1.09867i
\(742\) 0 0
\(743\) 27.9075 10.1575i 1.02383 0.372643i 0.225101 0.974336i \(-0.427729\pi\)
0.798728 + 0.601692i \(0.205507\pi\)
\(744\) 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 0.783288 0.621659i \(-0.213541\pi\)
0.523430 + 0.852068i \(0.324652\pi\)
\(752\) 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 −0.499305 0.866427i \(-0.666411\pi\)
0.939967 + 0.341266i \(0.110856\pi\)
\(788\) 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
\(795\) −4.01200 30.9113i −0.142291 1.09631i