Properties

Label 128.3.h.a.111.5
Level $128$
Weight $3$
Character 128.111
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 111.5
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37292 + 0.568682i) q^{3} +(2.28872 - 0.948019i) q^{5} +(6.37744 + 6.37744i) q^{7} +(-4.80245 - 4.80245i) q^{9} +O(q^{10})\) \(q+(1.37292 + 0.568682i) q^{3} +(2.28872 - 0.948019i) q^{5} +(6.37744 + 6.37744i) q^{7} +(-4.80245 - 4.80245i) q^{9} +(1.79646 - 0.744117i) q^{11} +(16.7036 + 6.91888i) q^{13} +3.68135 q^{15} +6.19811i q^{17} +(8.50083 - 20.5228i) q^{19} +(5.12898 + 12.3825i) q^{21} +(-23.6476 + 23.6476i) q^{23} +(-13.3382 + 13.3382i) q^{25} +(-8.98045 - 21.6807i) q^{27} +(14.5725 - 35.1811i) q^{29} -14.1609i q^{31} +2.88956 q^{33} +(20.6421 + 8.55025i) q^{35} +(-30.0695 + 12.4552i) q^{37} +(18.9981 + 18.9981i) q^{39} +(-56.9700 - 56.9700i) q^{41} +(-54.5034 + 22.5760i) q^{43} +(-15.5443 - 6.43866i) q^{45} -34.8047 q^{47} +32.3435i q^{49} +(-3.52475 + 8.50951i) q^{51} +(3.92967 + 9.48706i) q^{53} +(3.40615 - 3.40615i) q^{55} +(23.3419 - 23.3419i) q^{57} +(-9.41777 - 22.7365i) q^{59} +(3.00467 - 7.25391i) q^{61} -61.2547i q^{63} +44.7892 q^{65} +(55.9040 + 23.1562i) q^{67} +(-45.9141 + 19.0183i) q^{69} +(-6.27499 - 6.27499i) q^{71} +(66.4597 + 66.4597i) q^{73} +(-25.8974 + 10.7271i) q^{75} +(16.2024 + 6.71124i) q^{77} +75.8508 q^{79} +26.2523i q^{81} +(1.23390 - 2.97891i) q^{83} +(5.87593 + 14.1857i) q^{85} +(40.0138 - 40.0138i) q^{87} +(36.7030 - 36.7030i) q^{89} +(62.4018 + 150.651i) q^{91} +(8.05304 - 19.4417i) q^{93} -55.0300i q^{95} +90.0528 q^{97} +(-12.2010 - 5.05381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

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 0
\(3\) 1.37292 + 0.568682i 0.457640 + 0.189561i 0.599580 0.800315i \(-0.295334\pi\)
−0.141940 + 0.989875i \(0.545334\pi\)
\(4\) 0 0
\(5\) 2.28872 0.948019i 0.457744 0.189604i −0.141883 0.989883i \(-0.545316\pi\)
0.599627 + 0.800280i \(0.295316\pi\)
\(6\) 0 0
\(7\) 6.37744 + 6.37744i 0.911063 + 0.911063i 0.996356 0.0852929i \(-0.0271826\pi\)
−0.0852929 + 0.996356i \(0.527183\pi\)
\(8\) 0 0
\(9\) −4.80245 4.80245i −0.533606 0.533606i
\(10\) 0 0
\(11\) 1.79646 0.744117i 0.163314 0.0676470i −0.299529 0.954087i \(-0.596829\pi\)
0.462843 + 0.886440i \(0.346829\pi\)
\(12\) 0 0
\(13\) 16.7036 + 6.91888i 1.28490 + 0.532221i 0.917460 0.397827i \(-0.130236\pi\)
0.367436 + 0.930049i \(0.380236\pi\)
\(14\) 0 0
\(15\) 3.68135 0.245423
\(16\) 0 0
\(17\) 6.19811i 0.364595i 0.983243 + 0.182297i \(0.0583533\pi\)
−0.983243 + 0.182297i \(0.941647\pi\)
\(18\) 0 0
\(19\) 8.50083 20.5228i 0.447412 1.08015i −0.525876 0.850561i \(-0.676262\pi\)
0.973288 0.229587i \(-0.0737375\pi\)
\(20\) 0 0
\(21\) 5.12898 + 12.3825i 0.244237 + 0.589641i
\(22\) 0 0
\(23\) −23.6476 + 23.6476i −1.02815 + 1.02815i −0.0285625 + 0.999592i \(0.509093\pi\)
−0.999592 + 0.0285625i \(0.990907\pi\)
\(24\) 0 0
\(25\) −13.3382 + 13.3382i −0.533527 + 0.533527i
\(26\) 0 0
\(27\) −8.98045 21.6807i −0.332609 0.802990i
\(28\) 0 0
\(29\) 14.5725 35.1811i 0.502500 1.21314i −0.445618 0.895223i \(-0.647016\pi\)
0.948118 0.317919i \(-0.102984\pi\)
\(30\) 0 0
\(31\) 14.1609i 0.456803i −0.973567 0.228401i \(-0.926650\pi\)
0.973567 0.228401i \(-0.0733498\pi\)
\(32\) 0 0
\(33\) 2.88956 0.0875623
\(34\) 0 0
\(35\) 20.6421 + 8.55025i 0.589775 + 0.244293i
\(36\) 0 0
\(37\) −30.0695 + 12.4552i −0.812689 + 0.336627i −0.750027 0.661408i \(-0.769959\pi\)
−0.0626629 + 0.998035i \(0.519959\pi\)
\(38\) 0 0
\(39\) 18.9981 + 18.9981i 0.487131 + 0.487131i
\(40\) 0 0
\(41\) −56.9700 56.9700i −1.38951 1.38951i −0.826341 0.563170i \(-0.809582\pi\)
−0.563170 0.826341i \(-0.690418\pi\)
\(42\) 0 0
\(43\) −54.5034 + 22.5760i −1.26752 + 0.525024i −0.912209 0.409724i \(-0.865625\pi\)
−0.355310 + 0.934748i \(0.615625\pi\)
\(44\) 0 0
\(45\) −15.5443 6.43866i −0.345429 0.143081i
\(46\) 0 0
\(47\) −34.8047 −0.740525 −0.370263 0.928927i \(-0.620732\pi\)
−0.370263 + 0.928927i \(0.620732\pi\)
\(48\) 0 0
\(49\) 32.3435i 0.660072i
\(50\) 0 0
\(51\) −3.52475 + 8.50951i −0.0691128 + 0.166853i
\(52\) 0 0
\(53\) 3.92967 + 9.48706i 0.0741447 + 0.179001i 0.956606 0.291383i \(-0.0941154\pi\)
−0.882462 + 0.470384i \(0.844115\pi\)
\(54\) 0 0
\(55\) 3.40615 3.40615i 0.0619300 0.0619300i
\(56\) 0 0
\(57\) 23.3419 23.3419i 0.409507 0.409507i
\(58\) 0 0
\(59\) −9.41777 22.7365i −0.159623 0.385365i 0.823752 0.566951i \(-0.191877\pi\)
−0.983375 + 0.181586i \(0.941877\pi\)
\(60\) 0 0
\(61\) 3.00467 7.25391i 0.0492568 0.118916i −0.897336 0.441348i \(-0.854500\pi\)
0.946593 + 0.322432i \(0.104500\pi\)
\(62\) 0 0
\(63\) 61.2547i 0.972297i
\(64\) 0 0
\(65\) 44.7892 0.689065
\(66\) 0 0
\(67\) 55.9040 + 23.1562i 0.834388 + 0.345615i 0.758638 0.651512i \(-0.225865\pi\)
0.0757497 + 0.997127i \(0.475865\pi\)
\(68\) 0 0
\(69\) −45.9141 + 19.0183i −0.665422 + 0.275627i
\(70\) 0 0
\(71\) −6.27499 6.27499i −0.0883801 0.0883801i 0.661535 0.749915i \(-0.269905\pi\)
−0.749915 + 0.661535i \(0.769905\pi\)
\(72\) 0 0
\(73\) 66.4597 + 66.4597i 0.910406 + 0.910406i 0.996304 0.0858977i \(-0.0273758\pi\)
−0.0858977 + 0.996304i \(0.527376\pi\)
\(74\) 0 0
\(75\) −25.8974 + 10.7271i −0.345299 + 0.143027i
\(76\) 0 0
\(77\) 16.2024 + 6.71124i 0.210420 + 0.0871589i
\(78\) 0 0
\(79\) 75.8508 0.960136 0.480068 0.877231i \(-0.340612\pi\)
0.480068 + 0.877231i \(0.340612\pi\)
\(80\) 0 0
\(81\) 26.2523i 0.324103i
\(82\) 0 0
\(83\) 1.23390 2.97891i 0.0148663 0.0358905i −0.916272 0.400556i \(-0.868817\pi\)
0.931138 + 0.364666i \(0.118817\pi\)
\(84\) 0 0
\(85\) 5.87593 + 14.1857i 0.0691286 + 0.166891i
\(86\) 0 0
\(87\) 40.0138 40.0138i 0.459928 0.459928i
\(88\) 0 0
\(89\) 36.7030 36.7030i 0.412393 0.412393i −0.470178 0.882572i \(-0.655810\pi\)
0.882572 + 0.470178i \(0.155810\pi\)
\(90\) 0 0
\(91\) 62.4018 + 150.651i 0.685734 + 1.65551i
\(92\) 0 0
\(93\) 8.05304 19.4417i 0.0865918 0.209051i
\(94\) 0 0
\(95\) 55.0300i 0.579263i
\(96\) 0 0
\(97\) 90.0528 0.928379 0.464189 0.885736i \(-0.346346\pi\)
0.464189 + 0.885736i \(0.346346\pi\)
\(98\) 0 0
\(99\) −12.2010 5.05381i −0.123242 0.0510486i
\(100\) 0 0
\(101\) −20.0870 + 8.32031i −0.198881 + 0.0823793i −0.479901 0.877323i \(-0.659327\pi\)
0.281020 + 0.959702i \(0.409327\pi\)
\(102\) 0 0
\(103\) −4.88882 4.88882i −0.0474642 0.0474642i 0.682976 0.730441i \(-0.260685\pi\)
−0.730441 + 0.682976i \(0.760685\pi\)
\(104\) 0 0
\(105\) 23.4776 + 23.4776i 0.223596 + 0.223596i
\(106\) 0 0
\(107\) 51.9710 21.5271i 0.485710 0.201188i −0.126371 0.991983i \(-0.540333\pi\)
0.612080 + 0.790795i \(0.290333\pi\)
\(108\) 0 0
\(109\) −49.8054 20.6301i −0.456931 0.189267i 0.142333 0.989819i \(-0.454540\pi\)
−0.599263 + 0.800552i \(0.704540\pi\)
\(110\) 0 0
\(111\) −48.3661 −0.435730
\(112\) 0 0
\(113\) 62.0870i 0.549442i −0.961524 0.274721i \(-0.911414\pi\)
0.961524 0.274721i \(-0.0885855\pi\)
\(114\) 0 0
\(115\) −31.7043 + 76.5410i −0.275690 + 0.665574i
\(116\) 0 0
\(117\) −46.9909 113.446i −0.401632 0.969624i
\(118\) 0 0
\(119\) −39.5281 + 39.5281i −0.332169 + 0.332169i
\(120\) 0 0
\(121\) −82.8864 + 82.8864i −0.685011 + 0.685011i
\(122\) 0 0
\(123\) −45.8174 110.613i −0.372499 0.899292i
\(124\) 0 0
\(125\) −41.5830 + 100.390i −0.332664 + 0.803122i
\(126\) 0 0
\(127\) 177.045i 1.39406i 0.717043 + 0.697029i \(0.245495\pi\)
−0.717043 + 0.697029i \(0.754505\pi\)
\(128\) 0 0
\(129\) −87.6673 −0.679592
\(130\) 0 0
\(131\) −88.7654 36.7678i −0.677598 0.280670i 0.0172241 0.999852i \(-0.494517\pi\)
−0.694823 + 0.719181i \(0.744517\pi\)
\(132\) 0 0
\(133\) 185.097 76.6695i 1.39170 0.576462i
\(134\) 0 0
\(135\) −41.1075 41.1075i −0.304500 0.304500i
\(136\) 0 0
\(137\) −58.5583 58.5583i −0.427433 0.427433i 0.460320 0.887753i \(-0.347735\pi\)
−0.887753 + 0.460320i \(0.847735\pi\)
\(138\) 0 0
\(139\) 166.832 69.1039i 1.20023 0.497151i 0.309155 0.951012i \(-0.399954\pi\)
0.891072 + 0.453861i \(0.149954\pi\)
\(140\) 0 0
\(141\) −47.7840 19.7928i −0.338894 0.140374i
\(142\) 0 0
\(143\) 35.1558 0.245845
\(144\) 0 0
\(145\) 94.3348i 0.650585i
\(146\) 0 0
\(147\) −18.3932 + 44.4050i −0.125124 + 0.302075i
\(148\) 0 0
\(149\) 18.0040 + 43.4655i 0.120832 + 0.291715i 0.972709 0.232027i \(-0.0745357\pi\)
−0.851877 + 0.523742i \(0.824536\pi\)
\(150\) 0 0
\(151\) 68.3596 68.3596i 0.452713 0.452713i −0.443541 0.896254i \(-0.646278\pi\)
0.896254 + 0.443541i \(0.146278\pi\)
\(152\) 0 0
\(153\) 29.7661 29.7661i 0.194550 0.194550i
\(154\) 0 0
\(155\) −13.4248 32.4103i −0.0866115 0.209099i
\(156\) 0 0
\(157\) −74.5650 + 180.016i −0.474936 + 1.14660i 0.487020 + 0.873391i \(0.338084\pi\)
−0.961956 + 0.273206i \(0.911916\pi\)
\(158\) 0 0
\(159\) 15.2597i 0.0959730i
\(160\) 0 0
\(161\) −301.622 −1.87343
\(162\) 0 0
\(163\) −267.123 110.646i −1.63879 0.678811i −0.642619 0.766186i \(-0.722152\pi\)
−0.996175 + 0.0873756i \(0.972152\pi\)
\(164\) 0 0
\(165\) 6.61339 2.73936i 0.0400812 0.0166022i
\(166\) 0 0
\(167\) −99.3059 99.3059i −0.594646 0.594646i 0.344237 0.938883i \(-0.388138\pi\)
−0.938883 + 0.344237i \(0.888138\pi\)
\(168\) 0 0
\(169\) 111.640 + 111.640i 0.660592 + 0.660592i
\(170\) 0 0
\(171\) −139.385 + 57.7350i −0.815115 + 0.337632i
\(172\) 0 0
\(173\) 187.259 + 77.5652i 1.08242 + 0.448354i 0.851358 0.524585i \(-0.175780\pi\)
0.231063 + 0.972939i \(0.425780\pi\)
\(174\) 0 0
\(175\) −170.127 −0.972153
\(176\) 0 0
\(177\) 36.5711i 0.206617i
\(178\) 0 0
\(179\) 101.230 244.390i 0.565528 1.36531i −0.339761 0.940512i \(-0.610346\pi\)
0.905290 0.424795i \(-0.139654\pi\)
\(180\) 0 0
\(181\) 6.07796 + 14.6735i 0.0335799 + 0.0810690i 0.939780 0.341780i \(-0.111030\pi\)
−0.906200 + 0.422849i \(0.861030\pi\)
\(182\) 0 0
\(183\) 8.25033 8.25033i 0.0450838 0.0450838i
\(184\) 0 0
\(185\) −57.0130 + 57.0130i −0.308178 + 0.308178i
\(186\) 0 0
\(187\) 4.61212 + 11.1346i 0.0246637 + 0.0595435i
\(188\) 0 0
\(189\) 80.9953 195.540i 0.428546 1.03460i
\(190\) 0 0
\(191\) 370.577i 1.94019i 0.242716 + 0.970097i \(0.421962\pi\)
−0.242716 + 0.970097i \(0.578038\pi\)
\(192\) 0 0
\(193\) −132.679 −0.687456 −0.343728 0.939069i \(-0.611690\pi\)
−0.343728 + 0.939069i \(0.611690\pi\)
\(194\) 0 0
\(195\) 61.4920 + 25.4708i 0.315344 + 0.130620i
\(196\) 0 0
\(197\) 116.390 48.2104i 0.590814 0.244723i −0.0671870 0.997740i \(-0.521402\pi\)
0.658001 + 0.753017i \(0.271402\pi\)
\(198\) 0 0
\(199\) 89.9950 + 89.9950i 0.452236 + 0.452236i 0.896096 0.443860i \(-0.146391\pi\)
−0.443860 + 0.896096i \(0.646391\pi\)
\(200\) 0 0
\(201\) 63.5832 + 63.5832i 0.316334 + 0.316334i
\(202\) 0 0
\(203\) 317.301 131.430i 1.56306 0.647440i
\(204\) 0 0
\(205\) −184.397 76.3797i −0.899498 0.372584i
\(206\) 0 0
\(207\) 227.132 1.09726
\(208\) 0 0
\(209\) 43.1940i 0.206670i
\(210\) 0 0
\(211\) −20.9287 + 50.5264i −0.0991883 + 0.239462i −0.965683 0.259725i \(-0.916368\pi\)
0.866494 + 0.499187i \(0.166368\pi\)
\(212\) 0 0
\(213\) −5.04658 12.1835i −0.0236929 0.0571996i
\(214\) 0 0
\(215\) −103.340 + 103.340i −0.480653 + 0.480653i
\(216\) 0 0
\(217\) 90.3102 90.3102i 0.416176 0.416176i
\(218\) 0 0
\(219\) 53.4494 + 129.038i 0.244061 + 0.589215i
\(220\) 0 0
\(221\) −42.8840 + 103.531i −0.194045 + 0.468466i
\(222\) 0 0
\(223\) 52.7540i 0.236565i −0.992980 0.118283i \(-0.962261\pi\)
0.992980 0.118283i \(-0.0377388\pi\)
\(224\) 0 0
\(225\) 128.112 0.569386
\(226\) 0 0
\(227\) 327.101 + 135.490i 1.44097 + 0.596871i 0.960034 0.279883i \(-0.0902957\pi\)
0.480939 + 0.876754i \(0.340296\pi\)
\(228\) 0 0
\(229\) 245.430 101.660i 1.07175 0.443932i 0.224139 0.974557i \(-0.428043\pi\)
0.847606 + 0.530625i \(0.178043\pi\)
\(230\) 0 0
\(231\) 18.4280 + 18.4280i 0.0797748 + 0.0797748i
\(232\) 0 0
\(233\) −31.8772 31.8772i −0.136812 0.136812i 0.635384 0.772196i \(-0.280842\pi\)
−0.772196 + 0.635384i \(0.780842\pi\)
\(234\) 0 0
\(235\) −79.6582 + 32.9955i −0.338971 + 0.140406i
\(236\) 0 0
\(237\) 104.137 + 43.1350i 0.439397 + 0.182004i
\(238\) 0 0
\(239\) −90.0511 −0.376783 −0.188391 0.982094i \(-0.560327\pi\)
−0.188391 + 0.982094i \(0.560327\pi\)
\(240\) 0 0
\(241\) 20.9972i 0.0871252i 0.999051 + 0.0435626i \(0.0138708\pi\)
−0.999051 + 0.0435626i \(0.986129\pi\)
\(242\) 0 0
\(243\) −95.7533 + 231.169i −0.394046 + 0.951312i
\(244\) 0 0
\(245\) 30.6623 + 74.0253i 0.125152 + 0.302144i
\(246\) 0 0
\(247\) 283.990 283.990i 1.14976 1.14976i
\(248\) 0 0
\(249\) 3.38810 3.38810i 0.0136068 0.0136068i
\(250\) 0 0
\(251\) −105.207 253.991i −0.419150 1.01192i −0.982594 0.185764i \(-0.940524\pi\)
0.563444 0.826154i \(-0.309476\pi\)
\(252\) 0 0
\(253\) −24.8853 + 60.0783i −0.0983607 + 0.237464i
\(254\) 0 0
\(255\) 22.8174i 0.0894801i
\(256\) 0 0
\(257\) 236.584 0.920561 0.460281 0.887773i \(-0.347749\pi\)
0.460281 + 0.887773i \(0.347749\pi\)
\(258\) 0 0
\(259\) −271.199 112.334i −1.04710 0.433723i
\(260\) 0 0
\(261\) −238.939 + 98.9720i −0.915477 + 0.379203i
\(262\) 0 0
\(263\) −32.0070 32.0070i −0.121700 0.121700i 0.643634 0.765334i \(-0.277426\pi\)
−0.765334 + 0.643634i \(0.777426\pi\)
\(264\) 0 0
\(265\) 17.9878 + 17.9878i 0.0678786 + 0.0678786i
\(266\) 0 0
\(267\) 71.2626 29.5179i 0.266901 0.110554i
\(268\) 0 0
\(269\) 115.344 + 47.7769i 0.428787 + 0.177609i 0.586630 0.809855i \(-0.300454\pi\)
−0.157844 + 0.987464i \(0.550454\pi\)
\(270\) 0 0
\(271\) 55.4325 0.204548 0.102274 0.994756i \(-0.467388\pi\)
0.102274 + 0.994756i \(0.467388\pi\)
\(272\) 0 0
\(273\) 242.319i 0.887615i
\(274\) 0 0
\(275\) −14.0363 + 33.8866i −0.0510410 + 0.123224i
\(276\) 0 0
\(277\) −35.7881 86.4001i −0.129199 0.311914i 0.846022 0.533148i \(-0.178991\pi\)
−0.975221 + 0.221235i \(0.928991\pi\)
\(278\) 0 0
\(279\) −68.0069 + 68.0069i −0.243752 + 0.243752i
\(280\) 0 0
\(281\) 13.8509 13.8509i 0.0492914 0.0492914i −0.682031 0.731323i \(-0.738903\pi\)
0.731323 + 0.682031i \(0.238903\pi\)
\(282\) 0 0
\(283\) 135.615 + 327.403i 0.479205 + 1.15690i 0.959982 + 0.280060i \(0.0903544\pi\)
−0.480778 + 0.876843i \(0.659646\pi\)
\(284\) 0 0
\(285\) 31.2945 75.5517i 0.109805 0.265094i
\(286\) 0 0
\(287\) 726.645i 2.53186i
\(288\) 0 0
\(289\) 250.583 0.867071
\(290\) 0 0
\(291\) 123.635 + 51.2114i 0.424863 + 0.175984i
\(292\) 0 0
\(293\) −412.791 + 170.984i −1.40884 + 0.583562i −0.952031 0.306002i \(-0.901009\pi\)
−0.456811 + 0.889564i \(0.651009\pi\)
\(294\) 0 0
\(295\) −43.1093 43.1093i −0.146133 0.146133i
\(296\) 0 0
\(297\) −32.2660 32.2660i −0.108640 0.108640i
\(298\) 0 0
\(299\) −558.615 + 231.386i −1.86828 + 0.773866i
\(300\) 0 0
\(301\) −491.569 203.615i −1.63312 0.676461i
\(302\) 0 0
\(303\) −32.3094 −0.106632
\(304\) 0 0
\(305\) 19.4507i 0.0637726i
\(306\) 0 0
\(307\) 42.3557 102.256i 0.137967 0.333081i −0.839762 0.542955i \(-0.817305\pi\)
0.977728 + 0.209874i \(0.0673054\pi\)
\(308\) 0 0
\(309\) −3.93177 9.49213i −0.0127242 0.0307189i
\(310\) 0 0
\(311\) −337.326 + 337.326i −1.08465 + 1.08465i −0.0885790 + 0.996069i \(0.528233\pi\)
−0.996069 + 0.0885790i \(0.971767\pi\)
\(312\) 0 0
\(313\) −70.0735 + 70.0735i −0.223877 + 0.223877i −0.810129 0.586252i \(-0.800603\pi\)
0.586252 + 0.810129i \(0.300603\pi\)
\(314\) 0 0
\(315\) −58.0707 140.195i −0.184351 0.445063i
\(316\) 0 0
\(317\) 32.8632 79.3388i 0.103669 0.250280i −0.863530 0.504297i \(-0.831752\pi\)
0.967200 + 0.254017i \(0.0817518\pi\)
\(318\) 0 0
\(319\) 74.0450i 0.232116i
\(320\) 0 0
\(321\) 83.5940 0.260417
\(322\) 0 0
\(323\) 127.203 + 52.6891i 0.393816 + 0.163124i
\(324\) 0 0
\(325\) −315.081 + 130.511i −0.969480 + 0.401572i
\(326\) 0 0
\(327\) −56.6469 56.6469i −0.173232 0.173232i
\(328\) 0 0
\(329\) −221.965 221.965i −0.674665 0.674665i
\(330\) 0 0
\(331\) −124.865 + 51.7206i −0.377234 + 0.156256i −0.563240 0.826293i \(-0.690446\pi\)
0.186006 + 0.982549i \(0.440446\pi\)
\(332\) 0 0
\(333\) 204.223 + 84.5919i 0.613282 + 0.254030i
\(334\) 0 0
\(335\) 149.901 0.447466
\(336\) 0 0
\(337\) 323.529i 0.960027i −0.877261 0.480014i \(-0.840632\pi\)
0.877261 0.480014i \(-0.159368\pi\)
\(338\) 0 0
\(339\) 35.3077 85.2404i 0.104153 0.251447i
\(340\) 0 0
\(341\) −10.5373 25.4394i −0.0309013 0.0746024i
\(342\) 0 0
\(343\) 106.226 106.226i 0.309696 0.309696i
\(344\) 0 0
\(345\) −87.0550 + 87.0550i −0.252333 + 0.252333i
\(346\) 0 0
\(347\) 135.065 + 326.076i 0.389236 + 0.939700i 0.990102 + 0.140350i \(0.0448226\pi\)
−0.600866 + 0.799350i \(0.705177\pi\)
\(348\) 0 0
\(349\) 187.869 453.555i 0.538305 1.29958i −0.387600 0.921828i \(-0.626696\pi\)
0.925905 0.377756i \(-0.123304\pi\)
\(350\) 0 0
\(351\) 424.282i 1.20878i
\(352\) 0 0
\(353\) −70.5556 −0.199874 −0.0999372 0.994994i \(-0.531864\pi\)
−0.0999372 + 0.994994i \(0.531864\pi\)
\(354\) 0 0
\(355\) −20.3105 8.41289i −0.0572127 0.0236983i
\(356\) 0 0
\(357\) −76.7478 + 31.7900i −0.214980 + 0.0890475i
\(358\) 0 0
\(359\) 409.567 + 409.567i 1.14086 + 1.14086i 0.988294 + 0.152561i \(0.0487522\pi\)
0.152561 + 0.988294i \(0.451248\pi\)
\(360\) 0 0
\(361\) −93.6563 93.6563i −0.259436 0.259436i
\(362\) 0 0
\(363\) −160.932 + 66.6604i −0.443340 + 0.183637i
\(364\) 0 0
\(365\) 215.113 + 89.1026i 0.589350 + 0.244117i
\(366\) 0 0
\(367\) −513.680 −1.39967 −0.699837 0.714303i \(-0.746744\pi\)
−0.699837 + 0.714303i \(0.746744\pi\)
\(368\) 0 0
\(369\) 547.191i 1.48290i
\(370\) 0 0
\(371\) −35.4419 + 85.5644i −0.0955308 + 0.230632i
\(372\) 0 0
\(373\) −46.5164 112.301i −0.124709 0.301074i 0.849178 0.528106i \(-0.177098\pi\)
−0.973887 + 0.227032i \(0.927098\pi\)
\(374\) 0 0
\(375\) −114.180 + 114.180i −0.304481 + 0.304481i
\(376\) 0 0
\(377\) 486.828 486.828i 1.29132 1.29132i
\(378\) 0 0
\(379\) −172.090 415.462i −0.454064 1.09621i −0.970763 0.240040i \(-0.922840\pi\)
0.516699 0.856167i \(-0.327160\pi\)
\(380\) 0 0
\(381\) −100.683 + 243.069i −0.264259 + 0.637977i
\(382\) 0 0
\(383\) 430.627i 1.12435i 0.827017 + 0.562177i \(0.190036\pi\)
−0.827017 + 0.562177i \(0.809964\pi\)
\(384\) 0 0
\(385\) 43.4451 0.112844
\(386\) 0 0
\(387\) 370.170 + 153.329i 0.956512 + 0.396200i
\(388\) 0 0
\(389\) 55.8615 23.1386i 0.143603 0.0594823i −0.309725 0.950826i \(-0.600237\pi\)
0.453327 + 0.891344i \(0.350237\pi\)
\(390\) 0 0
\(391\) −146.570 146.570i −0.374860 0.374860i
\(392\) 0 0
\(393\) −100.959 100.959i −0.256892 0.256892i
\(394\) 0 0
\(395\) 173.601 71.9080i 0.439497 0.182046i
\(396\) 0 0
\(397\) −67.6641 28.0274i −0.170439 0.0705979i 0.295833 0.955240i \(-0.404403\pi\)
−0.466271 + 0.884642i \(0.654403\pi\)
\(398\) 0 0
\(399\) 297.723 0.746174
\(400\) 0 0
\(401\) 536.024i 1.33672i 0.743839 + 0.668359i \(0.233003\pi\)
−0.743839 + 0.668359i \(0.766997\pi\)
\(402\) 0 0
\(403\) 97.9774 236.538i 0.243120 0.586944i
\(404\) 0 0
\(405\) 24.8877 + 60.0842i 0.0614511 + 0.148356i
\(406\) 0 0
\(407\) −44.7505 + 44.7505i −0.109952 + 0.109952i
\(408\) 0 0
\(409\) −540.379 + 540.379i −1.32122 + 1.32122i −0.408430 + 0.912790i \(0.633923\pi\)
−0.912790 + 0.408430i \(0.866077\pi\)
\(410\) 0 0
\(411\) −47.0948 113.697i −0.114586 0.276635i
\(412\) 0 0
\(413\) 84.9395 205.062i 0.205665 0.496518i
\(414\) 0 0
\(415\) 7.98765i 0.0192474i
\(416\) 0 0
\(417\) 268.345 0.643512
\(418\) 0 0
\(419\) 341.184 + 141.323i 0.814281 + 0.337286i 0.750661 0.660688i \(-0.229735\pi\)
0.0636205 + 0.997974i \(0.479735\pi\)
\(420\) 0 0
\(421\) 339.196 140.500i 0.805692 0.333728i 0.0584581 0.998290i \(-0.481382\pi\)
0.747234 + 0.664561i \(0.231382\pi\)
\(422\) 0 0
\(423\) 167.148 + 167.148i 0.395149 + 0.395149i
\(424\) 0 0
\(425\) −82.6714 82.6714i −0.194521 0.194521i
\(426\) 0 0
\(427\) 65.4234 27.0993i 0.153216 0.0634643i
\(428\) 0 0
\(429\) 48.2661 + 19.9925i 0.112508 + 0.0466025i
\(430\) 0 0
\(431\) −154.504 −0.358478 −0.179239 0.983806i \(-0.557363\pi\)
−0.179239 + 0.983806i \(0.557363\pi\)
\(432\) 0 0
\(433\) 506.808i 1.17046i −0.810868 0.585228i \(-0.801005\pi\)
0.810868 0.585228i \(-0.198995\pi\)
\(434\) 0 0
\(435\) 53.6465 129.514i 0.123325 0.297734i
\(436\) 0 0
\(437\) 284.291 + 686.338i 0.650550 + 1.57057i
\(438\) 0 0
\(439\) 144.746 144.746i 0.329718 0.329718i −0.522761 0.852479i \(-0.675098\pi\)
0.852479 + 0.522761i \(0.175098\pi\)
\(440\) 0 0
\(441\) 155.328 155.328i 0.352218 0.352218i
\(442\) 0 0
\(443\) −230.959 557.584i −0.521351 1.25865i −0.937064 0.349158i \(-0.886468\pi\)
0.415713 0.909496i \(-0.363532\pi\)
\(444\) 0 0
\(445\) 49.2078 118.798i 0.110579 0.266962i
\(446\) 0 0
\(447\) 69.9132i 0.156405i
\(448\) 0 0
\(449\) −0.201052 −0.000447778 −0.000223889 1.00000i \(-0.500071\pi\)
−0.000223889 1.00000i \(0.500071\pi\)
\(450\) 0 0
\(451\) −144.736 59.9518i −0.320923 0.132931i
\(452\) 0 0
\(453\) 132.727 54.9774i 0.292996 0.121363i
\(454\) 0 0
\(455\) 285.641 + 285.641i 0.627782 + 0.627782i
\(456\) 0 0
\(457\) 226.835 + 226.835i 0.496358 + 0.496358i 0.910302 0.413944i \(-0.135849\pi\)
−0.413944 + 0.910302i \(0.635849\pi\)
\(458\) 0 0
\(459\) 134.379 55.6618i 0.292766 0.121268i
\(460\) 0 0
\(461\) 496.600 + 205.699i 1.07722 + 0.446201i 0.849535 0.527533i \(-0.176883\pi\)
0.227690 + 0.973734i \(0.426883\pi\)
\(462\) 0 0
\(463\) 520.019 1.12315 0.561576 0.827425i \(-0.310195\pi\)
0.561576 + 0.827425i \(0.310195\pi\)
\(464\) 0 0
\(465\) 52.1312i 0.112110i
\(466\) 0 0
\(467\) −35.4966 + 85.6964i −0.0760099 + 0.183504i −0.957317 0.289040i \(-0.906664\pi\)
0.881307 + 0.472544i \(0.156664\pi\)
\(468\) 0 0
\(469\) 208.847 + 504.202i 0.445303 + 1.07506i
\(470\) 0 0
\(471\) −204.743 + 204.743i −0.434699 + 0.434699i
\(472\) 0 0
\(473\) −81.1137 + 81.1137i −0.171488 + 0.171488i
\(474\) 0 0
\(475\) 160.351 + 387.122i 0.337582 + 0.814994i
\(476\) 0 0
\(477\) 26.6891 64.4332i 0.0559520 0.135080i
\(478\) 0 0
\(479\) 163.116i 0.340535i 0.985398 + 0.170268i \(0.0544632\pi\)
−0.985398 + 0.170268i \(0.945537\pi\)
\(480\) 0 0
\(481\) −588.447 −1.22338
\(482\) 0 0
\(483\) −414.102 171.527i −0.857355 0.355128i
\(484\) 0 0
\(485\) 206.106 85.3718i 0.424960 0.176024i
\(486\) 0 0
\(487\) −371.724 371.724i −0.763294 0.763294i 0.213622 0.976916i \(-0.431474\pi\)
−0.976916 + 0.213622i \(0.931474\pi\)
\(488\) 0 0
\(489\) −303.817 303.817i −0.621302 0.621302i
\(490\) 0 0
\(491\) −281.201 + 116.477i −0.572710 + 0.237224i −0.650193 0.759769i \(-0.725312\pi\)
0.0774824 + 0.996994i \(0.475312\pi\)
\(492\) 0 0
\(493\) 218.056 + 90.3220i 0.442305 + 0.183209i
\(494\) 0 0
\(495\) −32.7158 −0.0660924
\(496\) 0 0
\(497\) 80.0367i 0.161040i
\(498\) 0 0
\(499\) 236.126 570.059i 0.473199 1.14240i −0.489542 0.871980i \(-0.662836\pi\)
0.962741 0.270424i \(-0.0871639\pi\)
\(500\) 0 0
\(501\) −79.8656 192.813i −0.159412 0.384855i
\(502\) 0 0
\(503\) −12.8902 + 12.8902i −0.0256266 + 0.0256266i −0.719804 0.694177i \(-0.755768\pi\)
0.694177 + 0.719804i \(0.255768\pi\)
\(504\) 0 0
\(505\) −38.0857 + 38.0857i −0.0754173 + 0.0754173i
\(506\) 0 0
\(507\) 89.7851 + 216.760i 0.177091 + 0.427535i
\(508\) 0 0
\(509\) 59.1272 142.746i 0.116163 0.280443i −0.855095 0.518472i \(-0.826501\pi\)
0.971258 + 0.238028i \(0.0765011\pi\)
\(510\) 0 0
\(511\) 847.685i 1.65888i
\(512\) 0 0
\(513\) −521.291 −1.01616
\(514\) 0 0
\(515\) −15.8238 6.55444i −0.0307259 0.0127271i
\(516\) 0 0
\(517\) −62.5251 + 25.8988i −0.120938 + 0.0500943i
\(518\) 0 0
\(519\) 212.982 + 212.982i 0.410369 + 0.410369i
\(520\) 0 0
\(521\) 119.838 + 119.838i 0.230015 + 0.230015i 0.812699 0.582684i \(-0.197997\pi\)
−0.582684 + 0.812699i \(0.697997\pi\)
\(522\) 0 0
\(523\) 689.004 285.395i 1.31741 0.545688i 0.390370 0.920658i \(-0.372347\pi\)
0.927037 + 0.374970i \(0.122347\pi\)
\(524\) 0 0
\(525\) −233.570 96.7480i −0.444896 0.184282i
\(526\) 0 0
\(527\) 87.7707 0.166548
\(528\) 0 0
\(529\) 589.413i 1.11420i
\(530\) 0 0
\(531\) −63.9626 + 154.419i −0.120457 + 0.290809i
\(532\) 0 0
\(533\) −557.438 1345.77i −1.04585 2.52490i
\(534\) 0 0
\(535\) 98.5390 98.5390i 0.184185 0.184185i
\(536\) 0 0
\(537\) 277.960 277.960i 0.517617 0.517617i
\(538\) 0 0
\(539\) 24.0673 + 58.1037i 0.0446519 + 0.107799i
\(540\) 0 0
\(541\) −294.810 + 711.735i −0.544936 + 1.31559i 0.376267 + 0.926511i \(0.377207\pi\)
−0.921204 + 0.389081i \(0.872793\pi\)
\(542\) 0 0
\(543\) 23.6020i 0.0434658i
\(544\) 0 0
\(545\) −133.549 −0.245043
\(546\) 0 0
\(547\) −518.930 214.948i −0.948683 0.392957i −0.145948 0.989292i \(-0.546623\pi\)
−0.802736 + 0.596335i \(0.796623\pi\)
\(548\) 0 0
\(549\) −49.2663 + 20.4068i −0.0897382 + 0.0371708i
\(550\) 0 0
\(551\) −598.138 598.138i −1.08555 1.08555i
\(552\) 0 0
\(553\) 483.734 + 483.734i 0.874745 + 0.874745i
\(554\) 0 0
\(555\) −110.696 + 45.8520i −0.199453 + 0.0826162i
\(556\) 0 0
\(557\) −883.511 365.962i −1.58620 0.657024i −0.596816 0.802378i \(-0.703568\pi\)
−0.989380 + 0.145355i \(0.953568\pi\)
\(558\) 0 0
\(559\) −1066.61 −1.90806
\(560\) 0 0
\(561\) 17.9098i 0.0319248i
\(562\) 0 0
\(563\) −385.055 + 929.606i −0.683935 + 1.65117i 0.0727214 + 0.997352i \(0.476832\pi\)
−0.756656 + 0.653813i \(0.773168\pi\)
\(564\) 0 0
\(565\) −58.8596 142.100i −0.104176 0.251504i
\(566\) 0 0
\(567\) −167.423 + 167.423i −0.295278 + 0.295278i
\(568\) 0 0
\(569\) −503.029 + 503.029i −0.884058 + 0.884058i −0.993944 0.109886i \(-0.964951\pi\)
0.109886 + 0.993944i \(0.464951\pi\)
\(570\) 0 0
\(571\) 48.1525 + 116.250i 0.0843301 + 0.203591i 0.960419 0.278558i \(-0.0898564\pi\)
−0.876089 + 0.482149i \(0.839856\pi\)
\(572\) 0 0
\(573\) −210.741 + 508.773i −0.367785 + 0.887910i
\(574\) 0 0
\(575\) 630.830i 1.09710i
\(576\) 0 0
\(577\) −11.8629 −0.0205595 −0.0102798 0.999947i \(-0.503272\pi\)
−0.0102798 + 0.999947i \(0.503272\pi\)
\(578\) 0 0
\(579\) −182.158 75.4522i −0.314607 0.130315i
\(580\) 0 0
\(581\) 26.8670 11.1287i 0.0462426 0.0191543i
\(582\) 0 0
\(583\) 14.1190 + 14.1190i 0.0242178 + 0.0242178i
\(584\) 0 0
\(585\) −215.098 215.098i −0.367689 0.367689i
\(586\) 0 0
\(587\) 496.631 205.711i 0.846049 0.350445i 0.0828132 0.996565i \(-0.473610\pi\)
0.763236 + 0.646120i \(0.223610\pi\)
\(588\) 0 0
\(589\) −290.621 120.379i −0.493414 0.204379i
\(590\) 0 0
\(591\) 187.211 0.316770
\(592\) 0 0
\(593\) 410.471i 0.692193i 0.938199 + 0.346097i \(0.112493\pi\)
−0.938199 + 0.346097i \(0.887507\pi\)
\(594\) 0 0
\(595\) −52.9954 + 127.942i −0.0890678 + 0.215029i
\(596\) 0 0
\(597\) 72.3774 + 174.735i 0.121235 + 0.292688i
\(598\) 0 0
\(599\) 565.778 565.778i 0.944537 0.944537i −0.0540033 0.998541i \(-0.517198\pi\)
0.998541 + 0.0540033i \(0.0171982\pi\)
\(600\) 0 0
\(601\) 224.391 224.391i 0.373362 0.373362i −0.495338 0.868700i \(-0.664956\pi\)
0.868700 + 0.495338i \(0.164956\pi\)
\(602\) 0 0
\(603\) −157.270 379.683i −0.260812 0.629656i
\(604\) 0 0
\(605\) −111.126 + 268.282i −0.183679 + 0.443441i
\(606\) 0 0
\(607\) 19.8654i 0.0327271i 0.999866 + 0.0163636i \(0.00520892\pi\)
−0.999866 + 0.0163636i \(0.994791\pi\)
\(608\) 0 0
\(609\) 510.371 0.838047
\(610\) 0 0
\(611\) −581.365 240.809i −0.951498 0.394123i
\(612\) 0 0
\(613\) 905.460 375.054i 1.47710 0.611833i 0.508631 0.860985i \(-0.330152\pi\)
0.968464 + 0.249152i \(0.0801518\pi\)
\(614\) 0 0
\(615\) −209.726 209.726i −0.341019 0.341019i
\(616\) 0 0
\(617\) 673.907 + 673.907i 1.09223 + 1.09223i 0.995290 + 0.0969409i \(0.0309058\pi\)
0.0969409 + 0.995290i \(0.469094\pi\)
\(618\) 0 0
\(619\) −354.963 + 147.030i −0.573446 + 0.237529i −0.650511 0.759497i \(-0.725445\pi\)
0.0770649 + 0.997026i \(0.475445\pi\)
\(620\) 0 0
\(621\) 725.062 + 300.330i 1.16757 + 0.483624i
\(622\) 0 0
\(623\) 468.143 0.751433
\(624\) 0 0
\(625\) 202.389i 0.323822i
\(626\) 0 0
\(627\) 24.5636 59.3018i 0.0391764 0.0945803i
\(628\) 0 0
\(629\) −77.1987 186.374i −0.122732 0.296302i
\(630\) 0 0
\(631\) 494.698 494.698i 0.783991 0.783991i −0.196511 0.980502i \(-0.562961\pi\)
0.980502 + 0.196511i \(0.0629611\pi\)
\(632\) 0 0
\(633\) −57.4669 + 57.4669i −0.0907850 + 0.0907850i
\(634\) 0 0
\(635\) 167.843 + 405.208i 0.264319 + 0.638122i
\(636\) 0 0
\(637\) −223.781 + 540.255i −0.351304 + 0.848124i
\(638\) 0 0
\(639\) 60.2706i 0.0943202i
\(640\) 0 0
\(641\) 440.457 0.687141 0.343571 0.939127i \(-0.388364\pi\)
0.343571 + 0.939127i \(0.388364\pi\)
\(642\) 0 0
\(643\) 211.055 + 87.4220i 0.328235 + 0.135960i 0.540715 0.841206i \(-0.318154\pi\)
−0.212479 + 0.977166i \(0.568154\pi\)
\(644\) 0 0
\(645\) −200.646 + 83.1103i −0.311079 + 0.128853i
\(646\) 0 0
\(647\) −515.935 515.935i −0.797426 0.797426i 0.185263 0.982689i \(-0.440686\pi\)
−0.982689 + 0.185263i \(0.940686\pi\)
\(648\) 0 0
\(649\) −33.8372 33.8372i −0.0521375 0.0521375i
\(650\) 0 0
\(651\) 175.346 72.6309i 0.269349 0.111568i
\(652\) 0 0
\(653\) −613.161 253.980i −0.938991 0.388943i −0.139909 0.990164i \(-0.544681\pi\)
−0.799082 + 0.601222i \(0.794681\pi\)
\(654\) 0 0
\(655\) −238.016 −0.363383
\(656\) 0 0
\(657\) 638.339i 0.971596i
\(658\) 0 0
\(659\) 19.4679 46.9996i 0.0295416 0.0713196i −0.908420 0.418058i \(-0.862711\pi\)
0.937962 + 0.346738i \(0.112711\pi\)
\(660\) 0 0
\(661\) 46.1458 + 111.406i 0.0698122 + 0.168541i 0.954934 0.296817i \(-0.0959253\pi\)
−0.885122 + 0.465359i \(0.845925\pi\)
\(662\) 0 0
\(663\) −117.752 + 117.752i −0.177606 + 0.177606i
\(664\) 0 0
\(665\) 350.950 350.950i 0.527745 0.527745i
\(666\) 0 0
\(667\) 487.344 + 1176.55i 0.730650 + 1.76395i
\(668\) 0 0
\(669\) 30.0002 72.4270i 0.0448434 0.108262i
\(670\) 0 0
\(671\) 15.2672i 0.0227528i
\(672\) 0 0
\(673\) −352.344 −0.523542 −0.261771 0.965130i \(-0.584306\pi\)
−0.261771 + 0.965130i \(0.584306\pi\)
\(674\) 0 0
\(675\) 408.964 + 169.398i 0.605872 + 0.250961i
\(676\) 0 0
\(677\) −1178.26 + 488.051i −1.74041 + 0.720902i −0.741669 + 0.670766i \(0.765965\pi\)
−0.998742 + 0.0501357i \(0.984035\pi\)
\(678\) 0 0
\(679\) 574.306 + 574.306i 0.845812 + 0.845812i
\(680\) 0 0
\(681\) 372.033 + 372.033i 0.546304 + 0.546304i
\(682\) 0 0
\(683\) 414.446 171.669i 0.606802 0.251346i −0.0580582 0.998313i \(-0.518491\pi\)
0.664861 + 0.746967i \(0.268491\pi\)
\(684\) 0 0
\(685\) −189.538 78.5093i −0.276698 0.114612i
\(686\) 0 0
\(687\) 394.768 0.574626
\(688\) 0 0
\(689\) 185.657i 0.269459i
\(690\) 0 0
\(691\) −268.707 + 648.715i −0.388866 + 0.938806i 0.601314 + 0.799012i \(0.294644\pi\)
−0.990181 + 0.139794i \(0.955356\pi\)
\(692\) 0 0
\(693\) −45.5807 110.041i −0.0657729 0.158790i
\(694\) 0 0
\(695\) 316.319 316.319i 0.455136 0.455136i
\(696\) 0 0
\(697\) 353.106 353.106i 0.506608 0.506608i
\(698\) 0 0
\(699\) −25.6368 61.8927i −0.0366764 0.0885447i
\(700\) 0 0
\(701\) 464.382 1121.12i 0.662457 1.59931i −0.131484 0.991318i \(-0.541974\pi\)
0.793941 0.607995i \(-0.208026\pi\)
\(702\) 0 0
\(703\) 722.990i 1.02844i
\(704\) 0 0
\(705\) −128.128 −0.181742
\(706\) 0 0
\(707\) −181.166 75.0414i −0.256246 0.106141i
\(708\) 0 0
\(709\) 591.984 245.208i 0.834957 0.345850i 0.0760937 0.997101i \(-0.475755\pi\)
0.758863 + 0.651250i \(0.225755\pi\)
\(710\) 0 0
\(711\) −364.270 364.270i −0.512334 0.512334i
\(712\) 0 0
\(713\) 334.870 + 334.870i 0.469664 + 0.469664i
\(714\) 0 0
\(715\) 80.4619 33.3284i 0.112534 0.0466132i
\(716\) 0 0
\(717\) −123.633 51.2104i −0.172431 0.0714232i
\(718\) 0 0
\(719\) 906.230 1.26040 0.630202 0.776432i \(-0.282972\pi\)
0.630202 + 0.776432i \(0.282972\pi\)
\(720\) 0 0
\(721\) 62.3563i 0.0864858i
\(722\) 0 0
\(723\) −11.9407 + 28.8274i −0.0165155 + 0.0398720i
\(724\) 0 0
\(725\) 274.881 + 663.622i 0.379147 + 0.915341i
\(726\) 0 0
\(727\) −317.957 + 317.957i −0.437355 + 0.437355i −0.891121 0.453766i \(-0.850080\pi\)
0.453766 + 0.891121i \(0.350080\pi\)
\(728\) 0 0
\(729\) −95.8544 + 95.8544i −0.131488 + 0.131488i
\(730\) 0 0
\(731\) −139.929 337.818i −0.191421 0.462131i
\(732\) 0 0
\(733\) −159.623 + 385.363i −0.217766 + 0.525734i −0.994577 0.103999i \(-0.966836\pi\)
0.776811 + 0.629734i \(0.216836\pi\)
\(734\) 0 0
\(735\) 119.068i 0.161997i
\(736\) 0 0
\(737\) 117.660 0.159647
\(738\) 0 0
\(739\) 380.514 + 157.614i 0.514904 + 0.213280i 0.624977 0.780643i \(-0.285108\pi\)
−0.110073 + 0.993924i \(0.535108\pi\)
\(740\) 0 0
\(741\) 551.395 228.395i 0.744123 0.308226i
\(742\) 0 0
\(743\) −5.76228 5.76228i −0.00775542 0.00775542i 0.703218 0.710974i \(-0.251746\pi\)
−0.710974 + 0.703218i \(0.751746\pi\)
\(744\) 0 0
\(745\) 82.4123 + 82.4123i 0.110620 + 0.110620i
\(746\) 0 0
\(747\) −20.2318 + 8.38030i −0.0270841 + 0.0112186i
\(748\) 0 0
\(749\) 468.729 + 194.154i 0.625807 + 0.259218i
\(750\) 0 0
\(751\) 302.377 0.402632 0.201316 0.979526i \(-0.435478\pi\)
0.201316 + 0.979526i \(0.435478\pi\)
\(752\) 0 0
\(753\) 408.539i 0.542548i
\(754\) 0 0
\(755\) 91.6499 221.262i 0.121391 0.293063i
\(756\) 0 0
\(757\) −9.31627 22.4915i −0.0123068 0.0297113i 0.917607 0.397490i \(-0.130119\pi\)
−0.929914 + 0.367778i \(0.880119\pi\)
\(758\) 0 0
\(759\) −68.3309 + 68.3309i −0.0900276 + 0.0900276i
\(760\) 0 0
\(761\) −163.034 + 163.034i −0.214236 + 0.214236i −0.806064 0.591828i \(-0.798406\pi\)
0.591828 + 0.806064i \(0.298406\pi\)
\(762\) 0 0
\(763\) −186.064 449.198i −0.243859 0.588727i
\(764\) 0 0
\(765\) 39.9075 96.3452i 0.0521667 0.125941i
\(766\) 0 0
\(767\) 444.943i 0.580109i
\(768\) 0 0
\(769\) 180.205 0.234337 0.117168 0.993112i \(-0.462618\pi\)
0.117168 + 0.993112i \(0.462618\pi\)
\(770\) 0 0
\(771\) 324.811 + 134.541i 0.421286 + 0.174502i
\(772\) 0 0
\(773\) 196.725 81.4860i 0.254495 0.105415i −0.251789 0.967782i \(-0.581019\pi\)
0.506284 + 0.862367i \(0.331019\pi\)
\(774\) 0 0
\(775\) 188.880 + 188.880i 0.243716 + 0.243716i
\(776\) 0 0
\(777\) −308.452 308.452i −0.396978 0.396978i
\(778\) 0 0
\(779\) −1653.48 + 684.892i −2.12256 + 0.879194i
\(780\) 0 0
\(781\) −15.9421 6.60342i −0.0204124 0.00845508i
\(782\) 0 0
\(783\) −893.620 −1.14128
\(784\) 0 0
\(785\) 482.695i 0.614898i
\(786\) 0 0
\(787\) −80.6847 + 194.790i −0.102522 + 0.247510i −0.966814 0.255480i \(-0.917767\pi\)
0.864293 + 0.502990i \(0.167767\pi\)
\(788\) 0 0
\(789\) −25.7412 62.1448i −0.0326251 0.0787640i
\(790\) 0 0
\(791\) 395.956 395.956i 0.500576 0.500576i
\(792\) 0 0
\(793\) 100.378 100.378i 0.126580 0.126580i
\(794\) 0 0
\(795\) 14.4665 + 34.9252i 0.0181969 + 0.0439311i
\(796\) 0 0
\(797\) −256.509 + 619.268i −0.321843 + 0.776999i 0.677304 + 0.735704i \(0.263148\pi\)
−0