Properties

Label 128.3.h.a.15.5
Level $128$
Weight $3$
Character 128.15
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 15.5
Character \(\chi\) \(=\) 128.15
Dual form 128.3.h.a.111.5

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 −0.141940 0.989875i \(-0.545334\pi\)
0.599580 + 0.800315i \(0.295334\pi\)
\(4\) 0 0
\(5\) 2.28872 + 0.948019i 0.457744 + 0.189604i 0.599627 0.800280i \(-0.295316\pi\)
−0.141883 + 0.989883i \(0.545316\pi\)
\(6\) 0 0
\(7\) 6.37744 6.37744i 0.911063 0.911063i −0.0852929 0.996356i \(-0.527183\pi\)
0.996356 + 0.0852929i \(0.0271826\pi\)
\(8\) 0 0
\(9\) −4.80245 + 4.80245i −0.533606 + 0.533606i
\(10\) 0 0
\(11\) 1.79646 + 0.744117i 0.163314 + 0.0676470i 0.462843 0.886440i \(-0.346829\pi\)
−0.299529 + 0.954087i \(0.596829\pi\)
\(12\) 0 0
\(13\) 16.7036 6.91888i 1.28490 0.532221i 0.367436 0.930049i \(-0.380236\pi\)
0.917460 + 0.397827i \(0.130236\pi\)
\(14\) 0 0
\(15\) 3.68135 0.245423
\(16\) 0 0
\(17\) 6.19811i 0.364595i −0.983243 0.182297i \(-0.941647\pi\)
0.983243 0.182297i \(-0.0583533\pi\)
\(18\) 0 0
\(19\) 8.50083 + 20.5228i 0.447412 + 1.08015i 0.973288 + 0.229587i \(0.0737375\pi\)
−0.525876 + 0.850561i \(0.676262\pi\)
\(20\) 0 0
\(21\) 5.12898 12.3825i 0.244237 0.589641i
\(22\) 0 0
\(23\) −23.6476 23.6476i −1.02815 1.02815i −0.999592 0.0285625i \(-0.990907\pi\)
−0.0285625 0.999592i \(-0.509093\pi\)
\(24\) 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 0.948118 + 0.317919i \(0.102984\pi\)
−0.445618 + 0.895223i \(0.647016\pi\)
\(30\) 0 0
\(31\) 14.1609i 0.456803i 0.973567 + 0.228401i \(0.0733498\pi\)
−0.973567 + 0.228401i \(0.926650\pi\)
\(32\) 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 −0.0626629 0.998035i \(-0.519959\pi\)
−0.750027 + 0.661408i \(0.769959\pi\)
\(38\) 0 0
\(39\) 18.9981 18.9981i 0.487131 0.487131i
\(40\) 0 0
\(41\) −56.9700 + 56.9700i −1.38951 + 1.38951i −0.563170 + 0.826341i \(0.690418\pi\)
−0.826341 + 0.563170i \(0.809582\pi\)
\(42\) 0 0
\(43\) −54.5034 22.5760i −1.26752 0.525024i −0.355310 0.934748i \(-0.615625\pi\)
−0.912209 + 0.409724i \(0.865625\pi\)
\(44\) 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 −0.882462 0.470384i \(-0.844115\pi\)
0.956606 + 0.291383i \(0.0941154\pi\)
\(54\) 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 −0.983375 0.181586i \(-0.941877\pi\)
0.823752 + 0.566951i \(0.191877\pi\)
\(60\) 0 0
\(61\) 3.00467 + 7.25391i 0.0492568 + 0.118916i 0.946593 0.322432i \(-0.104500\pi\)
−0.897336 + 0.441348i \(0.854500\pi\)
\(62\) 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 0.0757497 0.997127i \(-0.475865\pi\)
0.758638 + 0.651512i \(0.225865\pi\)
\(68\) 0 0
\(69\) −45.9141 19.0183i −0.665422 0.275627i
\(70\) 0 0
\(71\) −6.27499 + 6.27499i −0.0883801 + 0.0883801i −0.749915 0.661535i \(-0.769905\pi\)
0.661535 + 0.749915i \(0.269905\pi\)
\(72\) 0 0
\(73\) 66.4597 66.4597i 0.910406 0.910406i −0.0858977 0.996304i \(-0.527376\pi\)
0.996304 + 0.0858977i \(0.0273758\pi\)
\(74\) 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 0.931138 0.364666i \(-0.118817\pi\)
−0.916272 + 0.400556i \(0.868817\pi\)
\(84\) 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 0.882572 0.470178i \(-0.155810\pi\)
−0.470178 + 0.882572i \(0.655810\pi\)
\(90\) 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 0.281020 0.959702i \(-0.409327\pi\)
−0.479901 + 0.877323i \(0.659327\pi\)
\(102\) 0 0
\(103\) −4.88882 + 4.88882i −0.0474642 + 0.0474642i −0.730441 0.682976i \(-0.760685\pi\)
0.682976 + 0.730441i \(0.260685\pi\)
\(104\) 0 0
\(105\) 23.4776 23.4776i 0.223596 0.223596i
\(106\) 0 0
\(107\) 51.9710 + 21.5271i 0.485710 + 0.201188i 0.612080 0.790795i \(-0.290333\pi\)
−0.126371 + 0.991983i \(0.540333\pi\)
\(108\) 0 0
\(109\) −49.8054 + 20.6301i −0.456931 + 0.189267i −0.599263 0.800552i \(-0.704540\pi\)
0.142333 + 0.989819i \(0.454540\pi\)
\(110\) 0 0
\(111\) −48.3661 −0.435730
\(112\) 0 0
\(113\) 62.0870i 0.549442i 0.961524 + 0.274721i \(0.0885855\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(114\) 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 \(-0.754505\pi\)
0.717043 0.697029i \(-0.245495\pi\)
\(128\) 0 0
\(129\) −87.6673 −0.679592
\(130\) 0 0
\(131\) −88.7654 + 36.7678i −0.677598 + 0.280670i −0.694823 0.719181i \(-0.744517\pi\)
0.0172241 + 0.999852i \(0.494517\pi\)
\(132\) 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 −0.887753 0.460320i \(-0.847735\pi\)
0.460320 + 0.887753i \(0.347735\pi\)
\(138\) 0 0
\(139\) 166.832 + 69.1039i 1.20023 + 0.497151i 0.891072 0.453861i \(-0.149954\pi\)
0.309155 + 0.951012i \(0.399954\pi\)
\(140\) 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 −0.851877 0.523742i \(-0.824536\pi\)
0.972709 + 0.232027i \(0.0745357\pi\)
\(150\) 0 0
\(151\) 68.3596 + 68.3596i 0.452713 + 0.452713i 0.896254 0.443541i \(-0.146278\pi\)
−0.443541 + 0.896254i \(0.646278\pi\)
\(152\) 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 −0.961956 0.273206i \(-0.911916\pi\)
0.487020 0.873391i \(-0.338084\pi\)
\(158\) 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 −0.996175 0.0873756i \(-0.972152\pi\)
−0.642619 + 0.766186i \(0.722152\pi\)
\(164\) 0 0
\(165\) 6.61339 + 2.73936i 0.0400812 + 0.0166022i
\(166\) 0 0
\(167\) −99.3059 + 99.3059i −0.594646 + 0.594646i −0.938883 0.344237i \(-0.888138\pi\)
0.344237 + 0.938883i \(0.388138\pi\)
\(168\) 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 0.231063 0.972939i \(-0.425780\pi\)
0.851358 + 0.524585i \(0.175780\pi\)
\(174\) 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 0.905290 + 0.424795i \(0.139654\pi\)
−0.339761 + 0.940512i \(0.610346\pi\)
\(180\) 0 0
\(181\) 6.07796 14.6735i 0.0335799 0.0810690i −0.906200 0.422849i \(-0.861030\pi\)
0.939780 + 0.341780i \(0.111030\pi\)
\(182\) 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 \(-0.578038\pi\)
0.242716 0.970097i \(-0.421962\pi\)
\(192\) 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 0.658001 0.753017i \(-0.271402\pi\)
−0.0671870 + 0.997740i \(0.521402\pi\)
\(198\) 0 0
\(199\) 89.9950 89.9950i 0.452236 0.452236i −0.443860 0.896096i \(-0.646391\pi\)
0.896096 + 0.443860i \(0.146391\pi\)
\(200\) 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 0.866494 0.499187i \(-0.166368\pi\)
−0.965683 + 0.259725i \(0.916368\pi\)
\(212\) 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 \(0.0377388\pi\)
−0.992980 + 0.118283i \(0.962261\pi\)
\(224\) 0 0
\(225\) 128.112 0.569386
\(226\) 0 0
\(227\) 327.101 135.490i 1.44097 0.596871i 0.480939 0.876754i \(-0.340296\pi\)
0.960034 + 0.279883i \(0.0902957\pi\)
\(228\) 0 0
\(229\) 245.430 + 101.660i 1.07175 + 0.443932i 0.847606 0.530625i \(-0.178043\pi\)
0.224139 + 0.974557i \(0.428043\pi\)
\(230\) 0 0
\(231\) 18.4280 18.4280i 0.0797748 0.0797748i
\(232\) 0 0
\(233\) −31.8772 + 31.8772i −0.136812 + 0.136812i −0.772196 0.635384i \(-0.780842\pi\)
0.635384 + 0.772196i \(0.280842\pi\)
\(234\) 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 \(-0.986129\pi\)
0.999051 0.0435626i \(-0.0138708\pi\)
\(242\) 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 0.563444 + 0.826154i \(0.309476\pi\)
−0.982594 + 0.185764i \(0.940524\pi\)
\(252\) 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 −0.765334 0.643634i \(-0.777426\pi\)
0.643634 + 0.765334i \(0.277426\pi\)
\(264\) 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 −0.157844 0.987464i \(-0.550454\pi\)
0.586630 + 0.809855i \(0.300454\pi\)
\(270\) 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 −0.975221 0.221235i \(-0.928991\pi\)
0.846022 + 0.533148i \(0.178991\pi\)
\(278\) 0 0
\(279\) −68.0069 68.0069i −0.243752 0.243752i
\(280\) 0 0
\(281\) 13.8509 + 13.8509i 0.0492914 + 0.0492914i 0.731323 0.682031i \(-0.238903\pi\)
−0.682031 + 0.731323i \(0.738903\pi\)
\(282\) 0 0
\(283\) 135.615 327.403i 0.479205 1.15690i −0.480778 0.876843i \(-0.659646\pi\)
0.959982 0.280060i \(-0.0903544\pi\)
\(284\) 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 −0.456811 0.889564i \(-0.651009\pi\)
−0.952031 + 0.306002i \(0.901009\pi\)
\(294\) 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 0.977728 0.209874i \(-0.0673054\pi\)
−0.839762 + 0.542955i \(0.817305\pi\)
\(308\) 0 0
\(309\) −3.93177 + 9.49213i −0.0127242 + 0.0307189i
\(310\) 0 0
\(311\) −337.326 337.326i −1.08465 1.08465i −0.996069 0.0885790i \(-0.971767\pi\)
−0.0885790 0.996069i \(-0.528233\pi\)
\(312\) 0 0
\(313\) −70.0735 70.0735i −0.223877 0.223877i 0.586252 0.810129i \(-0.300603\pi\)
−0.810129 + 0.586252i \(0.800603\pi\)
\(314\) 0 0
\(315\) −58.0707 + 140.195i −0.184351 + 0.445063i
\(316\) 0 0
\(317\) 32.8632 + 79.3388i 0.103669 + 0.250280i 0.967200 0.254017i \(-0.0817518\pi\)
−0.863530 + 0.504297i \(0.831752\pi\)
\(318\) 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 0.186006 0.982549i \(-0.440446\pi\)
−0.563240 + 0.826293i \(0.690446\pi\)
\(332\) 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 \(0.159368\pi\)
−0.877261 + 0.480014i \(0.840632\pi\)
\(338\) 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 −0.600866 0.799350i \(-0.705177\pi\)
0.990102 0.140350i \(-0.0448226\pi\)
\(348\) 0 0
\(349\) 187.869 + 453.555i 0.538305 + 1.29958i 0.925905 + 0.377756i \(0.123304\pi\)
−0.387600 + 0.921828i \(0.626696\pi\)
\(350\) 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 0.152561 0.988294i \(-0.451248\pi\)
0.988294 0.152561i \(-0.0487522\pi\)
\(360\) 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 −0.973887 0.227032i \(-0.927098\pi\)
0.849178 + 0.528106i \(0.177098\pi\)
\(374\) 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 0.516699 + 0.856167i \(0.327160\pi\)
−0.970763 + 0.240040i \(0.922840\pi\)
\(380\) 0 0
\(381\) −100.683 243.069i −0.264259 0.637977i
\(382\) 0 0
\(383\) 430.627i 1.12435i −0.827017 0.562177i \(-0.809964\pi\)
0.827017 0.562177i \(-0.190036\pi\)
\(384\) 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 0.453327 0.891344i \(-0.350237\pi\)
−0.309725 + 0.950826i \(0.600237\pi\)
\(390\) 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 −0.466271 0.884642i \(-0.654403\pi\)
0.295833 + 0.955240i \(0.404403\pi\)
\(398\) 0 0
\(399\) 297.723 0.746174
\(400\) 0 0
\(401\) 536.024i 1.33672i −0.743839 0.668359i \(-0.766997\pi\)
0.743839 0.668359i \(-0.233003\pi\)
\(402\) 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 −0.912790 0.408430i \(-0.866077\pi\)
−0.408430 0.912790i \(-0.633923\pi\)
\(410\) 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 0.0636205 0.997974i \(-0.479735\pi\)
0.750661 + 0.660688i \(0.229735\pi\)
\(420\) 0 0
\(421\) 339.196 + 140.500i 0.805692 + 0.333728i 0.747234 0.664561i \(-0.231382\pi\)
0.0584581 + 0.998290i \(0.481382\pi\)
\(422\) 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 \(0.198995\pi\)
−0.810868 + 0.585228i \(0.801005\pi\)
\(434\) 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 0.852479 0.522761i \(-0.175098\pi\)
−0.522761 + 0.852479i \(0.675098\pi\)
\(440\) 0 0
\(441\) 155.328 + 155.328i 0.352218 + 0.352218i
\(442\) 0 0
\(443\) −230.959 + 557.584i −0.521351 + 1.25865i 0.415713 + 0.909496i \(0.363532\pi\)
−0.937064 + 0.349158i \(0.886468\pi\)
\(444\) 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 −0.413944 0.910302i \(-0.635849\pi\)
0.910302 + 0.413944i \(0.135849\pi\)
\(458\) 0 0
\(459\) 134.379 + 55.6618i 0.292766 + 0.121268i
\(460\) 0 0
\(461\) 496.600 205.699i 1.07722 0.446201i 0.227690 0.973734i \(-0.426883\pi\)
0.849535 + 0.527533i \(0.176883\pi\)
\(462\) 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 0.881307 0.472544i \(-0.156664\pi\)
−0.957317 + 0.289040i \(0.906664\pi\)
\(468\) 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 \(-0.945537\pi\)
0.985398 0.170268i \(-0.0544632\pi\)
\(480\) 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 −0.976916 0.213622i \(-0.931474\pi\)
0.213622 + 0.976916i \(0.431474\pi\)
\(488\) 0 0
\(489\) −303.817 + 303.817i −0.621302 + 0.621302i
\(490\) 0 0
\(491\) −281.201 116.477i −0.572710 0.237224i 0.0774824 0.996994i \(-0.475312\pi\)
−0.650193 + 0.759769i \(0.725312\pi\)
\(492\) 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 0.962741 + 0.270424i \(0.0871639\pi\)
−0.489542 + 0.871980i \(0.662836\pi\)
\(500\) 0 0
\(501\) −79.8656 + 192.813i −0.159412 + 0.384855i
\(502\) 0 0
\(503\) −12.8902 12.8902i −0.0256266 0.0256266i 0.694177 0.719804i \(-0.255768\pi\)
−0.719804 + 0.694177i \(0.755768\pi\)
\(504\) 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 0.971258 0.238028i \(-0.0765011\pi\)
−0.855095 + 0.518472i \(0.826501\pi\)
\(510\) 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 −0.582684 0.812699i \(-0.697997\pi\)
0.812699 + 0.582684i \(0.197997\pi\)
\(522\) 0 0
\(523\) 689.004 + 285.395i 1.31741 + 0.545688i 0.927037 0.374970i \(-0.122347\pi\)
0.390370 + 0.920658i \(0.372347\pi\)
\(524\) 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 −0.921204 0.389081i \(-0.872793\pi\)
0.376267 0.926511i \(-0.377207\pi\)
\(542\) 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 −0.802736 0.596335i \(-0.796623\pi\)
−0.145948 + 0.989292i \(0.546623\pi\)
\(548\) 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 −0.989380 0.145355i \(-0.953568\pi\)
−0.596816 + 0.802378i \(0.703568\pi\)
\(558\) 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 −0.756656 0.653813i \(-0.773168\pi\)
0.0727214 0.997352i \(-0.476832\pi\)
\(564\) 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 0.109886 0.993944i \(-0.464951\pi\)
−0.993944 + 0.109886i \(0.964951\pi\)
\(570\) 0 0
\(571\) 48.1525 116.250i 0.0843301 0.203591i −0.876089 0.482149i \(-0.839856\pi\)
0.960419 + 0.278558i \(0.0898564\pi\)
\(572\) 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 0.763236 0.646120i \(-0.223610\pi\)
0.0828132 + 0.996565i \(0.473610\pi\)
\(588\) 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 \(-0.887507\pi\)
0.938199 0.346097i \(-0.112493\pi\)
\(594\) 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 0.998541 0.0540033i \(-0.0171982\pi\)
−0.0540033 + 0.998541i \(0.517198\pi\)
\(600\) 0 0
\(601\) 224.391 + 224.391i 0.373362 + 0.373362i 0.868700 0.495338i \(-0.164956\pi\)
−0.495338 + 0.868700i \(0.664956\pi\)
\(602\) 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 \(-0.994791\pi\)
0.999866 0.0163636i \(-0.00520892\pi\)
\(608\) 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 0.968464 0.249152i \(-0.0801518\pi\)
0.508631 + 0.860985i \(0.330152\pi\)
\(614\) 0 0
\(615\) −209.726 + 209.726i −0.341019 + 0.341019i
\(616\) 0 0
\(617\) 673.907 673.907i 1.09223 1.09223i 0.0969409 0.995290i \(-0.469094\pi\)
0.995290 0.0969409i \(-0.0309058\pi\)
\(618\) 0 0
\(619\) −354.963 147.030i −0.573446 0.237529i 0.0770649 0.997026i \(-0.475445\pi\)
−0.650511 + 0.759497i \(0.725445\pi\)
\(620\) 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 0.980502 0.196511i \(-0.0629611\pi\)
−0.196511 + 0.980502i \(0.562961\pi\)
\(632\) 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 −0.212479 0.977166i \(-0.568154\pi\)
0.540715 + 0.841206i \(0.318154\pi\)
\(644\) 0 0
\(645\) −200.646 83.1103i −0.311079 0.128853i
\(646\) 0 0
\(647\) −515.935 + 515.935i −0.797426 + 0.797426i −0.982689 0.185263i \(-0.940686\pi\)
0.185263 + 0.982689i \(0.440686\pi\)
\(648\) 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 −0.799082 0.601222i \(-0.794681\pi\)
−0.139909 + 0.990164i \(0.544681\pi\)
\(654\) 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 0.937962 0.346738i \(-0.112711\pi\)
−0.908420 + 0.418058i \(0.862711\pi\)
\(660\) 0 0
\(661\) 46.1458 111.406i 0.0698122 0.168541i −0.885122 0.465359i \(-0.845925\pi\)
0.954934 + 0.296817i \(0.0959253\pi\)
\(662\) 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 −0.998742 0.0501357i \(-0.984035\pi\)
−0.741669 0.670766i \(-0.765965\pi\)
\(678\) 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 0.664861 0.746967i \(-0.268491\pi\)
−0.0580582 + 0.998313i \(0.518491\pi\)
\(684\) 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 −0.990181 0.139794i \(-0.955356\pi\)
0.601314 0.799012i \(-0.294644\pi\)
\(692\) 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 0.793941 + 0.607995i \(0.208026\pi\)
−0.131484 + 0.991318i \(0.541974\pi\)
\(702\) 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 0.758863 0.651250i \(-0.225755\pi\)
0.0760937 + 0.997101i \(0.475755\pi\)
\(710\) 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 0.453766 0.891121i \(-0.350080\pi\)
−0.891121 + 0.453766i \(0.850080\pi\)
\(728\) 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 0.776811 0.629734i \(-0.216836\pi\)
−0.994577 + 0.103999i \(0.966836\pi\)
\(734\) 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 −0.110073 0.993924i \(-0.535108\pi\)
0.624977 + 0.780643i \(0.285108\pi\)
\(740\) 0 0
\(741\) 551.395 + 228.395i 0.744123 + 0.308226i
\(742\) 0 0
\(743\) −5.76228 + 5.76228i −0.00775542 + 0.00775542i −0.710974 0.703218i \(-0.751746\pi\)
0.703218 + 0.710974i \(0.251746\pi\)
\(744\) 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 −0.929914 0.367778i \(-0.880119\pi\)
0.917607 + 0.397490i \(0.130119\pi\)
\(758\) 0 0
\(759\) −68.3309 68.3309i −0.0900276 0.0900276i
\(760\) 0 0
\(761\) −163.034 163.034i −0.214236 0.214236i 0.591828 0.806064i \(-0.298406\pi\)
−0.806064 + 0.591828i \(0.798406\pi\)
\(762\) 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 0.506284 0.862367i \(-0.331019\pi\)
−0.251789 + 0.967782i \(0.581019\pi\)
\(774\) 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 0.864293 0.502990i \(-0.167767\pi\)
−0.966814 + 0.255480i \(0.917767\pi\)
\(788\) 0 0