Properties

Label 1323.2.o.e.440.16
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.16
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} +O(q^{10})\) \(q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} -1.84662i q^{10} +(-3.54040 - 2.04405i) q^{11} +(-3.51415 + 2.02890i) q^{13} +(0.426498 - 0.738716i) q^{16} +1.62145 q^{17} +8.12588i q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(-3.73318 + 2.15535i) q^{23} +(0.730548 - 1.26535i) q^{25} -3.98322 q^{26} +(0.542317 + 0.313107i) q^{29} +(-3.69833 + 2.13523i) q^{31} +(-4.43744 + 2.56195i) q^{32} +(1.37841 + 0.795827i) q^{34} +7.94153 q^{37} +(-3.98827 + 6.90789i) q^{38} +(-4.85591 + 2.80356i) q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +4.23698i q^{44} -4.23148 q^{46} +(-3.96868 + 6.87396i) q^{47} +(1.24209 - 0.717122i) q^{50} +(3.64214 + 2.10279i) q^{52} -8.37133i q^{53} +7.69052i q^{55} +(0.307352 + 0.532350i) q^{58} +(-4.08715 - 7.07915i) q^{59} +(-3.24253 - 1.87208i) q^{61} -4.19198 q^{62} -6.73573 q^{64} +(6.61081 + 3.81676i) q^{65} +(-6.26559 - 10.8523i) q^{67} +(-0.840253 - 1.45536i) q^{68} -14.4969i q^{71} +3.78935i q^{73} +(6.75117 + 3.89779i) q^{74} +(7.29351 - 4.21091i) q^{76} +(-4.18066 + 7.24112i) q^{79} -1.60465 q^{80} +1.79052i q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(-6.01221 + 3.47115i) q^{86} +(-6.09252 + 10.5526i) q^{88} -9.80759 q^{89} +(3.86914 + 2.23385i) q^{92} +(-6.74762 + 3.89574i) q^{94} +(13.2384 - 7.64320i) q^{95} +(-11.4579 - 6.61525i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.850109 + 0.490811i 0.601118 + 0.347056i 0.769481 0.638669i \(-0.220515\pi\)
−0.168363 + 0.985725i \(0.553848\pi\)
\(3\) 0 0
\(4\) −0.518210 0.897565i −0.259105 0.448783i
\(5\) −0.940599 1.62916i −0.420648 0.728585i 0.575355 0.817904i \(-0.304864\pi\)
−0.996003 + 0.0893196i \(0.971531\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.98061i 1.05381i
\(9\) 0 0
\(10\) 1.84662i 0.583954i
\(11\) −3.54040 2.04405i −1.06747 0.616304i −0.139980 0.990154i \(-0.544704\pi\)
−0.927489 + 0.373850i \(0.878037\pi\)
\(12\) 0 0
\(13\) −3.51415 + 2.02890i −0.974651 + 0.562715i −0.900651 0.434544i \(-0.856910\pi\)
−0.0739997 + 0.997258i \(0.523576\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.426498 0.738716i 0.106625 0.184679i
\(17\) 1.62145 0.393260 0.196630 0.980478i \(-0.437000\pi\)
0.196630 + 0.980478i \(0.437000\pi\)
\(18\) 0 0
\(19\) 8.12588i 1.86421i 0.362194 + 0.932103i \(0.382028\pi\)
−0.362194 + 0.932103i \(0.617972\pi\)
\(20\) −0.974855 + 1.68850i −0.217984 + 0.377560i
\(21\) 0 0
\(22\) −2.00648 3.47533i −0.427783 0.740943i
\(23\) −3.73318 + 2.15535i −0.778423 + 0.449423i −0.835871 0.548926i \(-0.815037\pi\)
0.0574484 + 0.998348i \(0.481704\pi\)
\(24\) 0 0
\(25\) 0.730548 1.26535i 0.146110 0.253069i
\(26\) −3.98322 −0.781173
\(27\) 0 0
\(28\) 0 0
\(29\) 0.542317 + 0.313107i 0.100706 + 0.0581425i 0.549507 0.835489i \(-0.314816\pi\)
−0.448801 + 0.893632i \(0.648149\pi\)
\(30\) 0 0
\(31\) −3.69833 + 2.13523i −0.664240 + 0.383499i −0.793891 0.608060i \(-0.791948\pi\)
0.129650 + 0.991560i \(0.458615\pi\)
\(32\) −4.43744 + 2.56195i −0.784435 + 0.452894i
\(33\) 0 0
\(34\) 1.37841 + 0.795827i 0.236396 + 0.136483i
\(35\) 0 0
\(36\) 0 0
\(37\) 7.94153 1.30558 0.652790 0.757539i \(-0.273599\pi\)
0.652790 + 0.757539i \(0.273599\pi\)
\(38\) −3.98827 + 6.90789i −0.646983 + 1.12061i
\(39\) 0 0
\(40\) −4.85591 + 2.80356i −0.767787 + 0.443282i
\(41\) 0.912023 + 1.57967i 0.142434 + 0.246703i 0.928413 0.371551i \(-0.121174\pi\)
−0.785979 + 0.618254i \(0.787840\pi\)
\(42\) 0 0
\(43\) −3.53614 + 6.12477i −0.539256 + 0.934019i 0.459688 + 0.888080i \(0.347961\pi\)
−0.998944 + 0.0459387i \(0.985372\pi\)
\(44\) 4.23698i 0.638749i
\(45\) 0 0
\(46\) −4.23148 −0.623898
\(47\) −3.96868 + 6.87396i −0.578891 + 1.00267i 0.416715 + 0.909037i \(0.363181\pi\)
−0.995607 + 0.0936324i \(0.970152\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.24209 0.717122i 0.175658 0.101416i
\(51\) 0 0
\(52\) 3.64214 + 2.10279i 0.505073 + 0.291604i
\(53\) 8.37133i 1.14989i −0.818192 0.574945i \(-0.805023\pi\)
0.818192 0.574945i \(-0.194977\pi\)
\(54\) 0 0
\(55\) 7.69052i 1.03699i
\(56\) 0 0
\(57\) 0 0
\(58\) 0.307352 + 0.532350i 0.0403573 + 0.0699009i
\(59\) −4.08715 7.07915i −0.532101 0.921627i −0.999298 0.0374731i \(-0.988069\pi\)
0.467196 0.884154i \(-0.345264\pi\)
\(60\) 0 0
\(61\) −3.24253 1.87208i −0.415164 0.239695i 0.277842 0.960627i \(-0.410381\pi\)
−0.693006 + 0.720932i \(0.743714\pi\)
\(62\) −4.19198 −0.532382
\(63\) 0 0
\(64\) −6.73573 −0.841966
\(65\) 6.61081 + 3.81676i 0.819971 + 0.473410i
\(66\) 0 0
\(67\) −6.26559 10.8523i −0.765464 1.32582i −0.940001 0.341171i \(-0.889176\pi\)
0.174537 0.984651i \(-0.444157\pi\)
\(68\) −0.840253 1.45536i −0.101896 0.176489i
\(69\) 0 0
\(70\) 0 0
\(71\) 14.4969i 1.72047i −0.509898 0.860235i \(-0.670317\pi\)
0.509898 0.860235i \(-0.329683\pi\)
\(72\) 0 0
\(73\) 3.78935i 0.443510i 0.975102 + 0.221755i \(0.0711785\pi\)
−0.975102 + 0.221755i \(0.928821\pi\)
\(74\) 6.75117 + 3.89779i 0.784807 + 0.453109i
\(75\) 0 0
\(76\) 7.29351 4.21091i 0.836623 0.483025i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.18066 + 7.24112i −0.470361 + 0.814690i −0.999426 0.0338919i \(-0.989210\pi\)
0.529064 + 0.848582i \(0.322543\pi\)
\(80\) −1.60465 −0.179406
\(81\) 0 0
\(82\) 1.79052i 0.197730i
\(83\) 4.38300 7.59159i 0.481097 0.833285i −0.518668 0.854976i \(-0.673572\pi\)
0.999765 + 0.0216912i \(0.00690508\pi\)
\(84\) 0 0
\(85\) −1.52514 2.64162i −0.165424 0.286524i
\(86\) −6.01221 + 3.47115i −0.648313 + 0.374304i
\(87\) 0 0
\(88\) −6.09252 + 10.5526i −0.649465 + 1.12491i
\(89\) −9.80759 −1.03960 −0.519801 0.854287i \(-0.673994\pi\)
−0.519801 + 0.854287i \(0.673994\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.86914 + 2.23385i 0.403386 + 0.232895i
\(93\) 0 0
\(94\) −6.74762 + 3.89574i −0.695964 + 0.401815i
\(95\) 13.2384 7.64320i 1.35823 0.784175i
\(96\) 0 0
\(97\) −11.4579 6.61525i −1.16338 0.671677i −0.211267 0.977428i \(-0.567759\pi\)
−0.952111 + 0.305752i \(0.901092\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.51431 −0.151431
\(101\) −0.524900 + 0.909154i −0.0522295 + 0.0904642i −0.890958 0.454085i \(-0.849966\pi\)
0.838729 + 0.544550i \(0.183299\pi\)
\(102\) 0 0
\(103\) 1.41937 0.819472i 0.139854 0.0807449i −0.428440 0.903570i \(-0.640937\pi\)
0.568295 + 0.822825i \(0.307603\pi\)
\(104\) 6.04736 + 10.4743i 0.592992 + 1.02709i
\(105\) 0 0
\(106\) 4.10874 7.11654i 0.399076 0.691220i
\(107\) 3.43549i 0.332122i −0.986116 0.166061i \(-0.946895\pi\)
0.986116 0.166061i \(-0.0531048\pi\)
\(108\) 0 0
\(109\) 3.69058 0.353494 0.176747 0.984256i \(-0.443443\pi\)
0.176747 + 0.984256i \(0.443443\pi\)
\(110\) −3.77459 + 6.53778i −0.359893 + 0.623353i
\(111\) 0 0
\(112\) 0 0
\(113\) −15.0858 + 8.70977i −1.41915 + 0.819346i −0.996224 0.0868183i \(-0.972330\pi\)
−0.422925 + 0.906165i \(0.638997\pi\)
\(114\) 0 0
\(115\) 7.02285 + 4.05465i 0.654885 + 0.378098i
\(116\) 0.649020i 0.0602600i
\(117\) 0 0
\(118\) 8.02407i 0.738675i
\(119\) 0 0
\(120\) 0 0
\(121\) 2.85627 + 4.94720i 0.259661 + 0.449746i
\(122\) −1.83767 3.18294i −0.166375 0.288170i
\(123\) 0 0
\(124\) 3.83303 + 2.21300i 0.344216 + 0.198733i
\(125\) −12.1546 −1.08714
\(126\) 0 0
\(127\) −10.1288 −0.898783 −0.449391 0.893335i \(-0.648359\pi\)
−0.449391 + 0.893335i \(0.648359\pi\)
\(128\) 3.14876 + 1.81794i 0.278314 + 0.160685i
\(129\) 0 0
\(130\) 3.74661 + 6.48932i 0.328599 + 0.569151i
\(131\) −2.48851 4.31022i −0.217422 0.376586i 0.736597 0.676332i \(-0.236431\pi\)
−0.954019 + 0.299746i \(0.903098\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.3009i 1.06263i
\(135\) 0 0
\(136\) 4.83293i 0.414420i
\(137\) −0.728035 0.420331i −0.0622003 0.0359113i 0.468577 0.883422i \(-0.344767\pi\)
−0.530778 + 0.847511i \(0.678100\pi\)
\(138\) 0 0
\(139\) 5.74392 3.31626i 0.487193 0.281281i −0.236216 0.971701i \(-0.575907\pi\)
0.723409 + 0.690419i \(0.242574\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.11525 12.3240i 0.597098 1.03420i
\(143\) 16.5887 1.38721
\(144\) 0 0
\(145\) 1.17803i 0.0978301i
\(146\) −1.85985 + 3.22136i −0.153923 + 0.266602i
\(147\) 0 0
\(148\) −4.11538 7.12804i −0.338282 0.585921i
\(149\) 14.7023 8.48838i 1.20446 0.695395i 0.242916 0.970047i \(-0.421896\pi\)
0.961544 + 0.274652i \(0.0885627\pi\)
\(150\) 0 0
\(151\) −0.975709 + 1.68998i −0.0794021 + 0.137528i −0.902992 0.429657i \(-0.858634\pi\)
0.823590 + 0.567186i \(0.191968\pi\)
\(152\) 24.2201 1.96451
\(153\) 0 0
\(154\) 0 0
\(155\) 6.95730 + 4.01680i 0.558823 + 0.322637i
\(156\) 0 0
\(157\) 8.24558 4.76059i 0.658069 0.379936i −0.133472 0.991053i \(-0.542613\pi\)
0.791541 + 0.611116i \(0.209279\pi\)
\(158\) −7.10804 + 4.10383i −0.565485 + 0.326483i
\(159\) 0 0
\(160\) 8.34769 + 4.81954i 0.659943 + 0.381018i
\(161\) 0 0
\(162\) 0 0
\(163\) 1.11021 0.0869585 0.0434793 0.999054i \(-0.486156\pi\)
0.0434793 + 0.999054i \(0.486156\pi\)
\(164\) 0.945238 1.63720i 0.0738107 0.127844i
\(165\) 0 0
\(166\) 7.45206 4.30245i 0.578392 0.333935i
\(167\) −7.00830 12.1387i −0.542319 0.939324i −0.998770 0.0495754i \(-0.984213\pi\)
0.456452 0.889748i \(-0.349120\pi\)
\(168\) 0 0
\(169\) 1.73285 3.00138i 0.133296 0.230875i
\(170\) 2.99422i 0.229646i
\(171\) 0 0
\(172\) 7.32985 0.558896
\(173\) 3.55884 6.16410i 0.270574 0.468647i −0.698435 0.715673i \(-0.746120\pi\)
0.969009 + 0.247026i \(0.0794533\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.01994 + 1.74357i −0.227637 + 0.131426i
\(177\) 0 0
\(178\) −8.33752 4.81367i −0.624924 0.360800i
\(179\) 6.00265i 0.448659i 0.974513 + 0.224330i \(0.0720192\pi\)
−0.974513 + 0.224330i \(0.927981\pi\)
\(180\) 0 0
\(181\) 1.30283i 0.0968385i 0.998827 + 0.0484192i \(0.0154184\pi\)
−0.998827 + 0.0484192i \(0.984582\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 6.42428 + 11.1272i 0.473604 + 0.820307i
\(185\) −7.46979 12.9381i −0.549190 0.951225i
\(186\) 0 0
\(187\) −5.74059 3.31433i −0.419794 0.242368i
\(188\) 8.22643 0.599974
\(189\) 0 0
\(190\) 15.0054 1.08861
\(191\) −4.96482 2.86644i −0.359242 0.207408i 0.309506 0.950897i \(-0.399836\pi\)
−0.668748 + 0.743489i \(0.733170\pi\)
\(192\) 0 0
\(193\) −0.779518 1.35016i −0.0561109 0.0971869i 0.836606 0.547806i \(-0.184537\pi\)
−0.892716 + 0.450619i \(0.851203\pi\)
\(194\) −6.49367 11.2474i −0.466218 0.807514i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.5504i 1.39291i 0.717602 + 0.696454i \(0.245240\pi\)
−0.717602 + 0.696454i \(0.754760\pi\)
\(198\) 0 0
\(199\) 0.976403i 0.0692154i −0.999401 0.0346077i \(-0.988982\pi\)
0.999401 0.0346077i \(-0.0110182\pi\)
\(200\) −3.77151 2.17748i −0.266686 0.153971i
\(201\) 0 0
\(202\) −0.892445 + 0.515253i −0.0627922 + 0.0362531i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.71570 2.97167i 0.119829 0.207551i
\(206\) 1.60882 0.112092
\(207\) 0 0
\(208\) 3.46128i 0.239997i
\(209\) 16.6097 28.7688i 1.14892 1.98998i
\(210\) 0 0
\(211\) 11.9752 + 20.7417i 0.824408 + 1.42792i 0.902371 + 0.430961i \(0.141825\pi\)
−0.0779625 + 0.996956i \(0.524841\pi\)
\(212\) −7.51382 + 4.33810i −0.516051 + 0.297942i
\(213\) 0 0
\(214\) 1.68618 2.92054i 0.115265 0.199644i
\(215\) 13.3044 0.907349
\(216\) 0 0
\(217\) 0 0
\(218\) 3.13740 + 1.81138i 0.212491 + 0.122682i
\(219\) 0 0
\(220\) 6.90274 3.98530i 0.465383 0.268689i
\(221\) −5.69804 + 3.28976i −0.383292 + 0.221293i
\(222\) 0 0
\(223\) 2.68394 + 1.54957i 0.179730 + 0.103767i 0.587166 0.809467i \(-0.300244\pi\)
−0.407436 + 0.913234i \(0.633577\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −17.0994 −1.13743
\(227\) −10.8991 + 18.8779i −0.723401 + 1.25297i 0.236228 + 0.971698i \(0.424089\pi\)
−0.959629 + 0.281269i \(0.909245\pi\)
\(228\) 0 0
\(229\) 11.1810 6.45536i 0.738862 0.426582i −0.0827937 0.996567i \(-0.526384\pi\)
0.821655 + 0.569985i \(0.193051\pi\)
\(230\) 3.98013 + 6.89378i 0.262442 + 0.454563i
\(231\) 0 0
\(232\) 0.933250 1.61644i 0.0612709 0.106124i
\(233\) 0.808011i 0.0529345i 0.999650 + 0.0264673i \(0.00842578\pi\)
−0.999650 + 0.0264673i \(0.991574\pi\)
\(234\) 0 0
\(235\) 14.9317 0.974039
\(236\) −4.23600 + 7.33697i −0.275740 + 0.477596i
\(237\) 0 0
\(238\) 0 0
\(239\) −12.2032 + 7.04552i −0.789360 + 0.455737i −0.839737 0.542993i \(-0.817291\pi\)
0.0503775 + 0.998730i \(0.483958\pi\)
\(240\) 0 0
\(241\) −16.0205 9.24943i −1.03197 0.595808i −0.114422 0.993432i \(-0.536502\pi\)
−0.917549 + 0.397624i \(0.869835\pi\)
\(242\) 5.60755i 0.360467i
\(243\) 0 0
\(244\) 3.88051i 0.248424i
\(245\) 0 0
\(246\) 0 0
\(247\) −16.4866 28.5556i −1.04902 1.81695i
\(248\) 6.36431 + 11.0233i 0.404134 + 0.699981i
\(249\) 0 0
\(250\) −10.3327 5.96561i −0.653499 0.377298i
\(251\) −22.1733 −1.39957 −0.699783 0.714355i \(-0.746720\pi\)
−0.699783 + 0.714355i \(0.746720\pi\)
\(252\) 0 0
\(253\) 17.6226 1.10792
\(254\) −8.61056 4.97131i −0.540274 0.311928i
\(255\) 0 0
\(256\) 8.52026 + 14.7575i 0.532516 + 0.922345i
\(257\) −2.02896 3.51427i −0.126563 0.219214i 0.795780 0.605586i \(-0.207061\pi\)
−0.922343 + 0.386372i \(0.873728\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.91152i 0.490652i
\(261\) 0 0
\(262\) 4.88554i 0.301830i
\(263\) 8.62617 + 4.98032i 0.531913 + 0.307100i 0.741795 0.670627i \(-0.233975\pi\)
−0.209882 + 0.977727i \(0.567308\pi\)
\(264\) 0 0
\(265\) −13.6383 + 7.87406i −0.837793 + 0.483700i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.49378 + 11.2476i −0.396671 + 0.687054i
\(269\) 9.96799 0.607759 0.303880 0.952710i \(-0.401718\pi\)
0.303880 + 0.952710i \(0.401718\pi\)
\(270\) 0 0
\(271\) 19.0320i 1.15611i −0.815997 0.578057i \(-0.803811\pi\)
0.815997 0.578057i \(-0.196189\pi\)
\(272\) 0.691547 1.19780i 0.0419312 0.0726270i
\(273\) 0 0
\(274\) −0.412606 0.714655i −0.0249265 0.0431739i
\(275\) −5.17286 + 2.98655i −0.311935 + 0.180096i
\(276\) 0 0
\(277\) 7.81184 13.5305i 0.469368 0.812969i −0.530019 0.847986i \(-0.677815\pi\)
0.999387 + 0.0350166i \(0.0111484\pi\)
\(278\) 6.51062 0.390481
\(279\) 0 0
\(280\) 0 0
\(281\) 20.8780 + 12.0539i 1.24547 + 0.719075i 0.970203 0.242292i \(-0.0778991\pi\)
0.275271 + 0.961367i \(0.411232\pi\)
\(282\) 0 0
\(283\) 2.61349 1.50890i 0.155356 0.0896946i −0.420307 0.907382i \(-0.638078\pi\)
0.575662 + 0.817687i \(0.304744\pi\)
\(284\) −13.0119 + 7.51245i −0.772117 + 0.445782i
\(285\) 0 0
\(286\) 14.1022 + 8.14189i 0.833879 + 0.481440i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.3709 −0.845346
\(290\) 0.578190 1.00145i 0.0339525 0.0588074i
\(291\) 0 0
\(292\) 3.40119 1.96368i 0.199040 0.114916i
\(293\) 14.9237 + 25.8485i 0.871849 + 1.51009i 0.860082 + 0.510156i \(0.170412\pi\)
0.0117671 + 0.999931i \(0.496254\pi\)
\(294\) 0 0
\(295\) −7.68873 + 13.3173i −0.447655 + 0.775362i
\(296\) 23.6706i 1.37583i
\(297\) 0 0
\(298\) 16.6648 0.965363
\(299\) 8.74598 15.1485i 0.505793 0.876060i
\(300\) 0 0
\(301\) 0 0
\(302\) −1.65892 + 0.957777i −0.0954600 + 0.0551139i
\(303\) 0 0
\(304\) 6.00272 + 3.46567i 0.344280 + 0.198770i
\(305\) 7.04349i 0.403309i
\(306\) 0 0
\(307\) 2.68853i 0.153442i −0.997053 0.0767212i \(-0.975555\pi\)
0.997053 0.0767212i \(-0.0244451\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.94297 + 6.82943i 0.223946 + 0.387886i
\(311\) 5.53763 + 9.59145i 0.314010 + 0.543881i 0.979227 0.202769i \(-0.0649941\pi\)
−0.665217 + 0.746650i \(0.731661\pi\)
\(312\) 0 0
\(313\) 14.4970 + 8.36987i 0.819421 + 0.473093i 0.850217 0.526433i \(-0.176471\pi\)
−0.0307957 + 0.999526i \(0.509804\pi\)
\(314\) 9.34619 0.527436
\(315\) 0 0
\(316\) 8.66584 0.487492
\(317\) 2.54774 + 1.47094i 0.143095 + 0.0826160i 0.569838 0.821757i \(-0.307006\pi\)
−0.426743 + 0.904373i \(0.640339\pi\)
\(318\) 0 0
\(319\) −1.28001 2.21704i −0.0716668 0.124131i
\(320\) 6.33562 + 10.9736i 0.354172 + 0.613444i
\(321\) 0 0
\(322\) 0 0
\(323\) 13.1758i 0.733118i
\(324\) 0 0
\(325\) 5.92883i 0.328872i
\(326\) 0.943801 + 0.544904i 0.0522723 + 0.0301794i
\(327\) 0 0
\(328\) 4.70839 2.71839i 0.259977 0.150098i
\(329\) 0 0
\(330\) 0 0
\(331\) −2.44077 + 4.22753i −0.134157 + 0.232366i −0.925275 0.379297i \(-0.876166\pi\)
0.791118 + 0.611663i \(0.209499\pi\)
\(332\) −9.08526 −0.498618
\(333\) 0 0
\(334\) 13.7590i 0.752859i
\(335\) −11.7868 + 20.4154i −0.643982 + 1.11541i
\(336\) 0 0
\(337\) 6.51421 + 11.2830i 0.354852 + 0.614621i 0.987093 0.160151i \(-0.0511980\pi\)
−0.632241 + 0.774772i \(0.717865\pi\)
\(338\) 2.94622 1.70100i 0.160253 0.0925221i
\(339\) 0 0
\(340\) −1.58068 + 2.73782i −0.0857245 + 0.148479i
\(341\) 17.4581 0.945409
\(342\) 0 0
\(343\) 0 0
\(344\) 18.2556 + 10.5399i 0.984275 + 0.568272i
\(345\) 0 0
\(346\) 6.05081 3.49344i 0.325293 0.187808i
\(347\) 1.86351 1.07590i 0.100039 0.0577573i −0.449146 0.893458i \(-0.648272\pi\)
0.549185 + 0.835701i \(0.314938\pi\)
\(348\) 0 0
\(349\) −25.2919 14.6023i −1.35384 0.781642i −0.365058 0.930985i \(-0.618951\pi\)
−0.988785 + 0.149343i \(0.952284\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.9470 1.11648
\(353\) 5.41764 9.38362i 0.288352 0.499440i −0.685065 0.728482i \(-0.740226\pi\)
0.973416 + 0.229042i \(0.0735595\pi\)
\(354\) 0 0
\(355\) −23.6179 + 13.6358i −1.25351 + 0.723713i
\(356\) 5.08239 + 8.80295i 0.269366 + 0.466556i
\(357\) 0 0
\(358\) −2.94617 + 5.10291i −0.155710 + 0.269697i
\(359\) 20.9492i 1.10566i −0.833295 0.552829i \(-0.813548\pi\)
0.833295 0.552829i \(-0.186452\pi\)
\(360\) 0 0
\(361\) −47.0300 −2.47526
\(362\) −0.639442 + 1.10755i −0.0336083 + 0.0582113i
\(363\) 0 0
\(364\) 0 0
\(365\) 6.17348 3.56426i 0.323135 0.186562i
\(366\) 0 0
\(367\) 4.97835 + 2.87425i 0.259868 + 0.150035i 0.624274 0.781205i \(-0.285395\pi\)
−0.364407 + 0.931240i \(0.618728\pi\)
\(368\) 3.67702i 0.191678i
\(369\) 0 0
\(370\) 14.6650i 0.762398i
\(371\) 0 0
\(372\) 0 0
\(373\) −14.4467 25.0224i −0.748023 1.29561i −0.948769 0.315970i \(-0.897670\pi\)
0.200747 0.979643i \(-0.435663\pi\)
\(374\) −3.25342 5.63509i −0.168230 0.291383i
\(375\) 0 0
\(376\) 20.4886 + 11.8291i 1.05662 + 0.610039i
\(377\) −2.54104 −0.130870
\(378\) 0 0
\(379\) −0.411434 −0.0211339 −0.0105670 0.999944i \(-0.503364\pi\)
−0.0105670 + 0.999944i \(0.503364\pi\)
\(380\) −13.7205 7.92156i −0.703849 0.406367i
\(381\) 0 0
\(382\) −2.81376 4.87358i −0.143965 0.249354i
\(383\) 12.4007 + 21.4787i 0.633648 + 1.09751i 0.986800 + 0.161944i \(0.0517765\pi\)
−0.353152 + 0.935566i \(0.614890\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.53038i 0.0778944i
\(387\) 0 0
\(388\) 13.7123i 0.696139i
\(389\) −3.82694 2.20948i −0.194033 0.112025i 0.399836 0.916587i \(-0.369067\pi\)
−0.593869 + 0.804561i \(0.702400\pi\)
\(390\) 0 0
\(391\) −6.05319 + 3.49481i −0.306123 + 0.176740i
\(392\) 0 0
\(393\) 0 0
\(394\) −9.59554 + 16.6200i −0.483416 + 0.837302i
\(395\) 15.7293 0.791427
\(396\) 0 0
\(397\) 22.2603i 1.11721i −0.829434 0.558605i \(-0.811337\pi\)
0.829434 0.558605i \(-0.188663\pi\)
\(398\) 0.479229 0.830049i 0.0240216 0.0416066i
\(399\) 0 0
\(400\) −0.623155 1.07934i −0.0311578 0.0539668i
\(401\) 5.31899 3.07092i 0.265617 0.153354i −0.361277 0.932459i \(-0.617659\pi\)
0.626894 + 0.779104i \(0.284326\pi\)
\(402\) 0 0
\(403\) 8.66434 15.0071i 0.431602 0.747556i
\(404\) 1.08803 0.0541317
\(405\) 0 0
\(406\) 0 0
\(407\) −28.1162 16.2329i −1.39367 0.804633i
\(408\) 0 0
\(409\) −0.765886 + 0.442185i −0.0378706 + 0.0218646i −0.518816 0.854886i \(-0.673627\pi\)
0.480945 + 0.876751i \(0.340294\pi\)
\(410\) 2.91706 1.68416i 0.144063 0.0831749i
\(411\) 0 0
\(412\) −1.47106 0.849316i −0.0724739 0.0418428i
\(413\) 0 0
\(414\) 0 0
\(415\) −16.4906 −0.809491
\(416\) 10.3959 18.0062i 0.509700 0.882827i
\(417\) 0 0
\(418\) 28.2401 16.3044i 1.38127 0.797476i
\(419\) −7.59365 13.1526i −0.370974 0.642546i 0.618742 0.785595i \(-0.287643\pi\)
−0.989716 + 0.143049i \(0.954309\pi\)
\(420\) 0 0
\(421\) 13.3318 23.0914i 0.649753 1.12541i −0.333428 0.942775i \(-0.608206\pi\)
0.983182 0.182630i \(-0.0584611\pi\)
\(422\) 23.5103i 1.14446i
\(423\) 0 0
\(424\) −24.9517 −1.21176
\(425\) 1.18455 2.05170i 0.0574592 0.0995222i
\(426\) 0 0
\(427\) 0 0
\(428\) −3.08358 + 1.78031i −0.149050 + 0.0860543i
\(429\) 0 0
\(430\) 11.3102 + 6.52992i 0.545424 + 0.314901i
\(431\) 4.69715i 0.226254i 0.993581 + 0.113127i \(0.0360866\pi\)
−0.993581 + 0.113127i \(0.963913\pi\)
\(432\) 0 0
\(433\) 8.97714i 0.431414i 0.976458 + 0.215707i \(0.0692056\pi\)
−0.976458 + 0.215707i \(0.930794\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.91250 3.31254i −0.0915919 0.158642i
\(437\) −17.5142 30.3354i −0.837816 1.45114i
\(438\) 0 0
\(439\) −14.3012 8.25679i −0.682558 0.394075i 0.118260 0.992983i \(-0.462268\pi\)
−0.800818 + 0.598907i \(0.795602\pi\)
\(440\) 22.9225 1.09279
\(441\) 0 0
\(442\) −6.45861 −0.307205
\(443\) −0.921171 0.531838i −0.0437661 0.0252684i 0.477957 0.878383i \(-0.341377\pi\)
−0.521723 + 0.853115i \(0.674711\pi\)
\(444\) 0 0
\(445\) 9.22500 + 15.9782i 0.437307 + 0.757438i
\(446\) 1.52110 + 2.63461i 0.0720260 + 0.124753i
\(447\) 0 0
\(448\) 0 0
\(449\) 15.9081i 0.750749i −0.926873 0.375374i \(-0.877514\pi\)
0.926873 0.375374i \(-0.122486\pi\)
\(450\) 0 0
\(451\) 7.45688i 0.351131i
\(452\) 15.6352 + 9.02697i 0.735417 + 0.424593i
\(453\) 0 0
\(454\) −18.5309 + 10.6988i −0.869698 + 0.502121i
\(455\) 0 0
\(456\) 0 0
\(457\) 16.3963 28.3992i 0.766985 1.32846i −0.172206 0.985061i \(-0.555090\pi\)
0.939191 0.343395i \(-0.111577\pi\)
\(458\) 12.6734 0.592191
\(459\) 0 0
\(460\) 8.40463i 0.391868i
\(461\) −9.23690 + 15.9988i −0.430205 + 0.745138i −0.996891 0.0787967i \(-0.974892\pi\)
0.566685 + 0.823934i \(0.308226\pi\)
\(462\) 0 0
\(463\) −0.201921 0.349738i −0.00938408 0.0162537i 0.861295 0.508105i \(-0.169654\pi\)
−0.870679 + 0.491851i \(0.836320\pi\)
\(464\) 0.462594 0.267079i 0.0214754 0.0123988i
\(465\) 0 0
\(466\) −0.396580 + 0.686897i −0.0183712 + 0.0318199i
\(467\) −15.0257 −0.695304 −0.347652 0.937624i \(-0.613021\pi\)
−0.347652 + 0.937624i \(0.613021\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 12.6936 + 7.32866i 0.585512 + 0.338046i
\(471\) 0 0
\(472\) −21.1002 + 12.1822i −0.971216 + 0.560732i
\(473\) 25.0387 14.4561i 1.15128 0.664691i
\(474\) 0 0
\(475\) 10.2821 + 5.93635i 0.471773 + 0.272379i
\(476\) 0 0
\(477\) 0 0
\(478\) −13.8321 −0.632664
\(479\) −15.5400 + 26.9161i −0.710041 + 1.22983i 0.254800 + 0.966994i \(0.417990\pi\)
−0.964841 + 0.262833i \(0.915343\pi\)
\(480\) 0 0
\(481\) −27.9077 + 16.1125i −1.27248 + 0.734669i
\(482\) −9.07944 15.7261i −0.413557 0.716302i
\(483\) 0 0
\(484\) 2.96029 5.12738i 0.134559 0.233063i
\(485\) 24.8892i 1.13016i
\(486\) 0 0
\(487\) 13.4956 0.611546 0.305773 0.952104i \(-0.401085\pi\)
0.305773 + 0.952104i \(0.401085\pi\)
\(488\) −5.57994 + 9.66474i −0.252592 + 0.437502i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.07098 4.08243i 0.319109 0.184238i −0.331886 0.943319i \(-0.607685\pi\)
0.650995 + 0.759082i \(0.274352\pi\)
\(492\) 0 0
\(493\) 0.879342 + 0.507688i 0.0396036 + 0.0228651i
\(494\) 32.3672i 1.45627i
\(495\) 0 0
\(496\) 3.64269i 0.163562i
\(497\) 0 0
\(498\) 0 0
\(499\) 14.0097 + 24.2655i 0.627159 + 1.08627i 0.988119 + 0.153690i \(0.0491158\pi\)
−0.360960 + 0.932581i \(0.617551\pi\)
\(500\) 6.29863 + 10.9095i 0.281683 + 0.487890i
\(501\) 0 0
\(502\) −18.8497 10.8829i −0.841305 0.485727i
\(503\) −5.89656 −0.262915 −0.131457 0.991322i \(-0.541966\pi\)
−0.131457 + 0.991322i \(0.541966\pi\)
\(504\) 0 0
\(505\) 1.97488 0.0878811
\(506\) 14.9811 + 8.64936i 0.665992 + 0.384511i
\(507\) 0 0
\(508\) 5.24883 + 9.09123i 0.232879 + 0.403358i
\(509\) −7.01957 12.1582i −0.311137 0.538905i 0.667472 0.744635i \(-0.267376\pi\)
−0.978609 + 0.205730i \(0.934043\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 9.45558i 0.417882i
\(513\) 0 0
\(514\) 3.98335i 0.175698i
\(515\) −2.67011 1.54159i −0.117659 0.0679305i
\(516\) 0 0
\(517\) 28.1014 16.2243i 1.23590 0.713546i
\(518\) 0 0
\(519\) 0 0
\(520\) 11.3763 19.7043i 0.498883 0.864090i
\(521\) −38.4458 −1.68434 −0.842170 0.539213i \(-0.818722\pi\)
−0.842170 + 0.539213i \(0.818722\pi\)
\(522\) 0 0
\(523\) 10.4932i 0.458834i 0.973328 + 0.229417i \(0.0736819\pi\)
−0.973328 + 0.229417i \(0.926318\pi\)
\(524\) −2.57914 + 4.46720i −0.112670 + 0.195150i
\(525\) 0 0
\(526\) 4.88879 + 8.46764i 0.213161 + 0.369207i
\(527\) −5.99668 + 3.46219i −0.261220 + 0.150815i
\(528\) 0 0
\(529\) −2.20889 + 3.82591i −0.0960388 + 0.166344i
\(530\) −15.4587 −0.671483
\(531\) 0 0
\(532\) 0 0
\(533\) −6.40998 3.70080i −0.277647 0.160300i
\(534\) 0 0
\(535\) −5.59698 + 3.23142i −0.241979 + 0.139706i
\(536\) −32.3466 + 18.6753i −1.39716 + 0.806650i
\(537\) 0 0
\(538\) 8.47388 + 4.89240i 0.365335 + 0.210926i
\(539\) 0 0
\(540\) 0 0
\(541\) 45.1565 1.94143 0.970715 0.240232i \(-0.0772235\pi\)
0.970715 + 0.240232i \(0.0772235\pi\)
\(542\) 9.34112 16.1793i 0.401236 0.694960i
\(543\) 0 0
\(544\) −7.19510 + 4.15409i −0.308487 + 0.178105i
\(545\) −3.47136 6.01257i −0.148697 0.257550i
\(546\) 0 0
\(547\) −4.05733 + 7.02751i −0.173479 + 0.300475i −0.939634 0.342181i \(-0.888834\pi\)
0.766155 + 0.642656i \(0.222168\pi\)
\(548\) 0.871279i 0.0372192i
\(549\) 0 0
\(550\) −5.86333 −0.250013
\(551\) −2.54427 + 4.40680i −0.108389 + 0.187736i
\(552\) 0 0
\(553\) 0 0
\(554\) 13.2818 7.66827i 0.564291 0.325794i
\(555\) 0 0
\(556\) −5.95311 3.43703i −0.252468 0.145763i
\(557\) 16.2727i 0.689494i 0.938696 + 0.344747i \(0.112035\pi\)
−0.938696 + 0.344747i \(0.887965\pi\)
\(558\) 0 0
\(559\) 28.6978i 1.21379i
\(560\) 0 0
\(561\) 0 0
\(562\) 11.8324 + 20.4942i 0.499118 + 0.864498i
\(563\) 5.13594 + 8.89572i 0.216454 + 0.374910i 0.953721 0.300692i \(-0.0972175\pi\)
−0.737267 + 0.675601i \(0.763884\pi\)
\(564\) 0 0
\(565\) 28.3793 + 16.3848i 1.19393 + 0.689314i
\(566\) 2.96233 0.124516
\(567\) 0 0
\(568\) −43.2098 −1.81304
\(569\) 17.8537 + 10.3079i 0.748468 + 0.432128i 0.825140 0.564928i \(-0.191096\pi\)
−0.0766722 + 0.997056i \(0.524429\pi\)
\(570\) 0 0
\(571\) −2.12828 3.68628i −0.0890656 0.154266i 0.818051 0.575146i \(-0.195055\pi\)
−0.907116 + 0.420880i \(0.861721\pi\)
\(572\) −8.59640 14.8894i −0.359434 0.622557i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.29836i 0.262660i
\(576\) 0 0
\(577\) 16.9289i 0.704760i −0.935857 0.352380i \(-0.885372\pi\)
0.935857 0.352380i \(-0.114628\pi\)
\(578\) −12.2168 7.05338i −0.508153 0.293382i
\(579\) 0 0
\(580\) −1.05736 + 0.610467i −0.0439045 + 0.0253483i
\(581\) 0 0
\(582\) 0 0
\(583\) −17.1114 + 29.6378i −0.708682 + 1.22747i
\(584\) 11.2946 0.467374
\(585\) 0 0
\(586\) 29.2988i 1.21032i
\(587\) 12.0558 20.8812i 0.497594 0.861858i −0.502402 0.864634i \(-0.667550\pi\)
0.999996 + 0.00277589i \(0.000883594\pi\)
\(588\) 0 0
\(589\) −17.3507 30.0522i −0.714922 1.23828i
\(590\) −13.0725 + 7.54743i −0.538187 + 0.310723i
\(591\) 0 0
\(592\) 3.38705 5.86654i 0.139207 0.241113i
\(593\) −38.5816 −1.58436 −0.792178 0.610290i \(-0.791053\pi\)
−0.792178 + 0.610290i \(0.791053\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −15.2378 8.79752i −0.624163 0.360360i
\(597\) 0 0
\(598\) 14.8701 8.58525i 0.608083 0.351077i
\(599\) 29.2921 16.9118i 1.19684 0.690997i 0.236992 0.971511i \(-0.423838\pi\)
0.959850 + 0.280514i \(0.0905050\pi\)
\(600\) 0 0
\(601\) 27.4855 + 15.8688i 1.12116 + 0.647300i 0.941696 0.336465i \(-0.109231\pi\)
0.179461 + 0.983765i \(0.442565\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.02249 0.0822939
\(605\) 5.37320 9.30666i 0.218452 0.378370i
\(606\) 0 0
\(607\) 0.169355 0.0977772i 0.00687391 0.00396865i −0.496559 0.868003i \(-0.665403\pi\)
0.503433 + 0.864034i \(0.332070\pi\)
\(608\) −20.8181 36.0581i −0.844287 1.46235i
\(609\) 0 0
\(610\) −3.45702 + 5.98774i −0.139971 + 0.242436i
\(611\) 32.2082i 1.30300i
\(612\) 0 0
\(613\) 2.93328 0.118474 0.0592370 0.998244i \(-0.481133\pi\)
0.0592370 + 0.998244i \(0.481133\pi\)
\(614\) 1.31956 2.28554i 0.0532530 0.0922370i
\(615\) 0 0
\(616\) 0 0
\(617\) 7.86982 4.54365i 0.316827 0.182920i −0.333150 0.942874i \(-0.608112\pi\)
0.649977 + 0.759953i \(0.274778\pi\)
\(618\) 0 0
\(619\) −24.8586 14.3521i −0.999152 0.576861i −0.0911550 0.995837i \(-0.529056\pi\)
−0.907997 + 0.418976i \(0.862389\pi\)
\(620\) 8.32617i 0.334387i
\(621\) 0 0
\(622\) 10.8717i 0.435916i
\(623\) 0 0
\(624\) 0 0
\(625\) 7.77986 + 13.4751i 0.311194 + 0.539004i
\(626\) 8.21604 + 14.2306i 0.328379 + 0.568769i
\(627\) 0 0
\(628\) −8.54588 4.93397i −0.341018 0.196887i
\(629\) 12.8768 0.513433
\(630\) 0 0
\(631\) −20.7691 −0.826805 −0.413403 0.910548i \(-0.635660\pi\)
−0.413403 + 0.910548i \(0.635660\pi\)
\(632\) 21.5830 + 12.4609i 0.858525 + 0.495670i
\(633\) 0 0
\(634\) 1.44390 + 2.50091i 0.0573447 + 0.0993240i
\(635\) 9.52711 + 16.5014i 0.378072 + 0.654839i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.51297i 0.0994895i
\(639\) 0 0
\(640\) 6.83981i 0.270367i
\(641\) −39.7733 22.9632i −1.57095 0.906990i −0.996052 0.0887664i \(-0.971708\pi\)
−0.574900 0.818224i \(-0.694959\pi\)
\(642\) 0 0
\(643\) −9.15428 + 5.28523i −0.361010 + 0.208429i −0.669524 0.742791i \(-0.733502\pi\)
0.308514 + 0.951220i \(0.400168\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.46680 + 11.2008i −0.254433 + 0.440691i
\(647\) −38.5123 −1.51408 −0.757038 0.653371i \(-0.773354\pi\)
−0.757038 + 0.653371i \(0.773354\pi\)
\(648\) 0 0
\(649\) 33.4173i 1.31174i
\(650\) −2.90993 + 5.04015i −0.114137 + 0.197691i
\(651\) 0 0
\(652\) −0.575323 0.996488i −0.0225314 0.0390255i
\(653\) 11.0867 6.40089i 0.433855 0.250486i −0.267133 0.963660i \(-0.586076\pi\)
0.700988 + 0.713173i \(0.252743\pi\)
\(654\) 0 0
\(655\) −4.68137 + 8.10837i −0.182916 + 0.316820i
\(656\) 1.55590 0.0607479
\(657\) 0 0
\(658\) 0 0
\(659\) −41.5777 24.0049i −1.61964 0.935097i −0.987014 0.160636i \(-0.948645\pi\)
−0.632622 0.774461i \(-0.718021\pi\)
\(660\) 0 0
\(661\) 9.38011 5.41561i 0.364844 0.210643i −0.306360 0.951916i \(-0.599111\pi\)
0.671204 + 0.741273i \(0.265778\pi\)
\(662\) −4.14983 + 2.39591i −0.161288 + 0.0931196i
\(663\) 0 0
\(664\) −22.6276 13.0640i −0.878121 0.506983i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.69942 −0.104522
\(668\) −7.26354 + 12.5808i −0.281035 + 0.486767i
\(669\) 0 0
\(670\) −20.0402 + 11.5702i −0.774219 + 0.446995i
\(671\) 7.65323 + 13.2558i 0.295450 + 0.511734i
\(672\) 0 0
\(673\) −6.19553 + 10.7310i −0.238820 + 0.413649i −0.960376 0.278707i \(-0.910094\pi\)
0.721556 + 0.692356i \(0.243427\pi\)
\(674\) 12.7890i 0.492613i
\(675\) 0 0
\(676\) −3.59191 −0.138150
\(677\) 14.4947 25.1056i 0.557078 0.964888i −0.440660 0.897674i \(-0.645256\pi\)
0.997739 0.0672139i \(-0.0214110\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −7.87364 + 4.54585i −0.301940 + 0.174325i
\(681\) 0 0
\(682\) 14.8413 + 8.56862i 0.568302 + 0.328109i
\(683\) 0.152476i 0.00583433i −0.999996 0.00291717i \(-0.999071\pi\)
0.999996 0.00291717i \(-0.000928564\pi\)
\(684\) 0 0
\(685\) 1.58145i 0.0604242i
\(686\) 0 0
\(687\) 0 0
\(688\) 3.01631 + 5.22441i 0.114996 + 0.199179i
\(689\) 16.9846 + 29.4181i 0.647060 + 1.12074i
\(690\) 0 0
\(691\) 37.4428 + 21.6176i 1.42439 + 0.822373i 0.996670 0.0815369i \(-0.0259828\pi\)
0.427722 + 0.903910i \(0.359316\pi\)
\(692\) −7.37691 −0.280428
\(693\) 0 0
\(694\) 2.11225 0.0801799
\(695\) −10.8055 6.23853i −0.409874 0.236641i
\(696\) 0 0
\(697\) 1.47880 + 2.56136i 0.0560137 + 0.0970186i
\(698\) −14.3339 24.8271i −0.542546 0.939718i
\(699\) 0 0
\(700\) 0 0
\(701\) 11.5821i 0.437451i 0.975786 + 0.218726i \(0.0701900\pi\)
−0.975786 + 0.218726i \(0.929810\pi\)
\(702\) 0 0
\(703\) 64.5319i 2.43387i
\(704\) 23.8472 + 13.7682i 0.898774 + 0.518907i
\(705\) 0 0
\(706\) 9.21116 5.31807i 0.346667 0.200148i
\(707\) 0 0
\(708\) 0 0
\(709\) 18.9474 32.8178i 0.711584 1.23250i −0.252678 0.967550i \(-0.581311\pi\)
0.964262 0.264949i \(-0.0853552\pi\)
\(710\) −26.7704 −1.00467
\(711\) 0 0
\(712\) 29.2326i 1.09554i
\(713\) 9.20437 15.9424i 0.344707 0.597049i
\(714\) 0 0
\(715\) −15.6033 27.0256i −0.583529 1.01070i
\(716\) 5.38777 3.11063i 0.201351 0.116250i
\(717\) 0 0
\(718\) 10.2821 17.8091i 0.383724 0.664630i
\(719\) −46.6317 −1.73907 −0.869534 0.493873i \(-0.835581\pi\)
−0.869534 + 0.493873i \(0.835581\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −39.9806 23.0828i −1.48792 0.859054i
\(723\) 0 0
\(724\) 1.16937 0.675138i 0.0434594 0.0250913i
\(725\) 0.792377 0.457479i 0.0294282 0.0169904i
\(726\) 0 0
\(727\) 3.72659 + 2.15155i 0.138212 + 0.0797965i 0.567511 0.823366i \(-0.307906\pi\)
−0.429300 + 0.903162i \(0.641240\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 6.99751 0.258989
\(731\) −5.73369 + 9.93104i −0.212068 + 0.367313i
\(732\) 0 0
\(733\) −12.1337 + 7.00539i −0.448168 + 0.258750i −0.707056 0.707157i \(-0.749977\pi\)
0.258888 + 0.965907i \(0.416644\pi\)
\(734\) 2.82143 + 4.88685i 0.104141 + 0.180377i
\(735\) 0 0
\(736\) 11.0438 19.1285i 0.407081 0.705086i
\(737\) 51.2287i 1.88703i
\(738\) 0 0
\(739\) 37.8627 1.39280 0.696401 0.717653i \(-0.254784\pi\)
0.696401 + 0.717653i \(0.254784\pi\)
\(740\) −7.74184 + 13.4093i −0.284596 + 0.492934i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0489 13.8847i 0.882269 0.509378i 0.0108634 0.999941i \(-0.496542\pi\)
0.871406 + 0.490563i \(0.163209\pi\)
\(744\) 0 0
\(745\) −27.6579 15.9683i −1.01331 0.585034i
\(746\) 28.3624i 1.03842i
\(747\) 0 0
\(748\) 6.87007i 0.251195i
\(749\) 0 0
\(750\) 0 0
\(751\) 8.67540 + 15.0262i 0.316570 + 0.548315i 0.979770 0.200127i \(-0.0641355\pi\)
−0.663200 + 0.748442i \(0.730802\pi\)
\(752\) 3.38527 + 5.86346i 0.123448 + 0.213818i
\(753\) 0 0
\(754\) −2.16017 1.24717i −0.0786686 0.0454193i
\(755\) 3.67100 0.133601
\(756\) 0 0
\(757\) 18.8111 0.683701 0.341850 0.939754i \(-0.388946\pi\)
0.341850 + 0.939754i \(0.388946\pi\)
\(758\) −0.349764 0.201936i −0.0127040 0.00733465i
\(759\) 0 0
\(760\) −22.7814 39.4586i −0.826369 1.43131i
\(761\) 4.22520 + 7.31825i 0.153163 + 0.265286i 0.932389 0.361457i \(-0.117721\pi\)
−0.779225 + 0.626744i \(0.784387\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5.94167i 0.214962i
\(765\) 0 0
\(766\) 24.3457i 0.879644i
\(767\) 28.7257 + 16.5848i 1.03723 + 0.598843i
\(768\) 0 0
\(769\) −19.8100 + 11.4373i −0.714366 + 0.412440i −0.812676 0.582716i \(-0.801990\pi\)
0.0983092 + 0.995156i \(0.468657\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.807907 + 1.39934i −0.0290772 + 0.0503632i
\(773\) 37.6747 1.35507 0.677533 0.735492i \(-0.263049\pi\)
0.677533 + 0.735492i \(0.263049\pi\)
\(774\) 0 0
\(775\) 6.23957i 0.224132i
\(776\) −19.7175 + 34.1517i −0.707817 + 1.22598i
\(777\) 0 0
\(778\) −2.16888 3.75660i −0.0777579 0.134681i
\(779\) −12.8362 + 7.41099i −0.459905 + 0.265526i
\(780\) 0 0
\(781\) −29.6324 + 51.3249i −1.06033 + 1.83655i
\(782\) −6.86116 −0.245355
\(783\) 0 0
\(784\) 0 0
\(785\) −15.5116 8.95561i −0.553632 0.319639i
\(786\) 0 0
\(787\) 20.3222 11.7330i 0.724408 0.418237i −0.0919648 0.995762i \(-0.529315\pi\)
0.816373 + 0.577525i \(0.195981\pi\)
\(788\) 17.5478 10.1312i 0.625113 0.360909i
\(789\) 0 0
\(790\) 13.3716 + 7.72011i 0.475741 + 0.274669i
\(791\) 0 0
\(792\) 0 0
\(793\) 15.1930 0.539519
\(794\) 10.9256 18.9237i 0.387734 0.671575i
\(795\) 0 0
\(796\) −0.876386 + 0.505981i −0.0310627 + 0.0179340i