Properties

Label 128.3.h.a.111.4
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 111.4
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.374985 + 0.155324i) q^{3} +(-7.60625 + 3.15061i) q^{5} +(-6.84161 - 6.84161i) q^{7} +(-6.24747 - 6.24747i) q^{9} +O(q^{10})\) \(q+(0.374985 + 0.155324i) q^{3} +(-7.60625 + 3.15061i) q^{5} +(-6.84161 - 6.84161i) q^{7} +(-6.24747 - 6.24747i) q^{9} +(2.23818 - 0.927086i) q^{11} +(1.40964 + 0.583890i) q^{13} -3.34159 q^{15} +2.67812i q^{17} +(-5.38908 + 13.0104i) q^{19} +(-1.50283 - 3.62816i) q^{21} +(-18.8388 + 18.8388i) q^{23} +(30.2510 - 30.2510i) q^{25} +(-2.77024 - 6.68795i) q^{27} +(-10.0298 + 24.2140i) q^{29} -47.5858i q^{31} +0.983283 q^{33} +(73.5942 + 30.4837i) q^{35} +(-28.2682 + 11.7091i) q^{37} +(0.437900 + 0.437900i) q^{39} +(6.93962 + 6.93962i) q^{41} +(-8.48982 + 3.51660i) q^{43} +(67.2032 + 27.8365i) q^{45} +67.0112 q^{47} +44.6152i q^{49} +(-0.415976 + 1.00426i) q^{51} +(-10.5006 - 25.3507i) q^{53} +(-14.1033 + 14.1033i) q^{55} +(-4.04165 + 4.04165i) q^{57} +(-27.9364 - 67.4445i) q^{59} +(31.5752 - 76.2294i) q^{61} +85.4855i q^{63} -12.5616 q^{65} +(-90.1903 - 37.3580i) q^{67} +(-9.99035 + 4.13814i) q^{69} +(-1.98379 - 1.98379i) q^{71} +(-55.5273 - 55.5273i) q^{73} +(16.0424 - 6.64496i) q^{75} +(-21.6555 - 8.97002i) q^{77} -10.9856 q^{79} +76.5792i q^{81} +(-34.1779 + 82.5128i) q^{83} +(-8.43772 - 20.3705i) q^{85} +(-7.52203 + 7.52203i) q^{87} +(-16.1705 + 16.1705i) q^{89} +(-5.64942 - 13.6389i) q^{91} +(7.39121 - 17.8440i) q^{93} -115.939i q^{95} -62.6434 q^{97} +(-19.7749 - 8.19105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

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
\(3\) 0.374985 + 0.155324i 0.124995 + 0.0517746i 0.444304 0.895876i \(-0.353451\pi\)
−0.319309 + 0.947651i \(0.603451\pi\)
\(4\) 0 0
\(5\) −7.60625 + 3.15061i −1.52125 + 0.630122i −0.977842 0.209346i \(-0.932866\pi\)
−0.543408 + 0.839469i \(0.682866\pi\)
\(6\) 0 0
\(7\) −6.84161 6.84161i −0.977372 0.977372i 0.0223772 0.999750i \(-0.492877\pi\)
−0.999750 + 0.0223772i \(0.992877\pi\)
\(8\) 0 0
\(9\) −6.24747 6.24747i −0.694164 0.694164i
\(10\) 0 0
\(11\) 2.23818 0.927086i 0.203471 0.0842806i −0.278621 0.960401i \(-0.589877\pi\)
0.482092 + 0.876121i \(0.339877\pi\)
\(12\) 0 0
\(13\) 1.40964 + 0.583890i 0.108433 + 0.0449146i 0.436241 0.899830i \(-0.356310\pi\)
−0.327807 + 0.944745i \(0.606310\pi\)
\(14\) 0 0
\(15\) −3.34159 −0.222773
\(16\) 0 0
\(17\) 2.67812i 0.157537i 0.996893 + 0.0787683i \(0.0250987\pi\)
−0.996893 + 0.0787683i \(0.974901\pi\)
\(18\) 0 0
\(19\) −5.38908 + 13.0104i −0.283636 + 0.684757i −0.999915 0.0130566i \(-0.995844\pi\)
0.716279 + 0.697814i \(0.245844\pi\)
\(20\) 0 0
\(21\) −1.50283 3.62816i −0.0715635 0.172770i
\(22\) 0 0
\(23\) −18.8388 + 18.8388i −0.819076 + 0.819076i −0.985974 0.166898i \(-0.946625\pi\)
0.166898 + 0.985974i \(0.446625\pi\)
\(24\) 0 0
\(25\) 30.2510 30.2510i 1.21004 1.21004i
\(26\) 0 0
\(27\) −2.77024 6.68795i −0.102601 0.247702i
\(28\) 0 0
\(29\) −10.0298 + 24.2140i −0.345855 + 0.834967i 0.651245 + 0.758867i \(0.274247\pi\)
−0.997100 + 0.0761000i \(0.975753\pi\)
\(30\) 0 0
\(31\) 47.5858i 1.53503i −0.641033 0.767513i \(-0.721494\pi\)
0.641033 0.767513i \(-0.278506\pi\)
\(32\) 0 0
\(33\) 0.983283 0.0297965
\(34\) 0 0
\(35\) 73.5942 + 30.4837i 2.10269 + 0.870963i
\(36\) 0 0
\(37\) −28.2682 + 11.7091i −0.764006 + 0.316462i −0.730442 0.682975i \(-0.760686\pi\)
−0.0335642 + 0.999437i \(0.510686\pi\)
\(38\) 0 0
\(39\) 0.437900 + 0.437900i 0.0112282 + 0.0112282i
\(40\) 0 0
\(41\) 6.93962 + 6.93962i 0.169259 + 0.169259i 0.786654 0.617395i \(-0.211812\pi\)
−0.617395 + 0.786654i \(0.711812\pi\)
\(42\) 0 0
\(43\) −8.48982 + 3.51660i −0.197438 + 0.0817814i −0.479211 0.877700i \(-0.659077\pi\)
0.281774 + 0.959481i \(0.409077\pi\)
\(44\) 0 0
\(45\) 67.2032 + 27.8365i 1.49340 + 0.618588i
\(46\) 0 0
\(47\) 67.0112 1.42577 0.712885 0.701281i \(-0.247388\pi\)
0.712885 + 0.701281i \(0.247388\pi\)
\(48\) 0 0
\(49\) 44.6152i 0.910513i
\(50\) 0 0
\(51\) −0.415976 + 1.00426i −0.00815639 + 0.0196913i
\(52\) 0 0
\(53\) −10.5006 25.3507i −0.198124 0.478315i 0.793326 0.608797i \(-0.208347\pi\)
−0.991451 + 0.130482i \(0.958347\pi\)
\(54\) 0 0
\(55\) −14.1033 + 14.1033i −0.256424 + 0.256424i
\(56\) 0 0
\(57\) −4.04165 + 4.04165i −0.0709061 + 0.0709061i
\(58\) 0 0
\(59\) −27.9364 67.4445i −0.473499 1.14313i −0.962606 0.270904i \(-0.912677\pi\)
0.489107 0.872224i \(-0.337323\pi\)
\(60\) 0 0
\(61\) 31.5752 76.2294i 0.517627 1.24966i −0.421730 0.906721i \(-0.638577\pi\)
0.939357 0.342941i \(-0.111423\pi\)
\(62\) 0 0
\(63\) 85.4855i 1.35691i
\(64\) 0 0
\(65\) −12.5616 −0.193256
\(66\) 0 0
\(67\) −90.1903 37.3580i −1.34612 0.557583i −0.410913 0.911674i \(-0.634790\pi\)
−0.935211 + 0.354092i \(0.884790\pi\)
\(68\) 0 0
\(69\) −9.99035 + 4.13814i −0.144788 + 0.0599730i
\(70\) 0 0
\(71\) −1.98379 1.98379i −0.0279407 0.0279407i 0.692998 0.720939i \(-0.256289\pi\)
−0.720939 + 0.692998i \(0.756289\pi\)
\(72\) 0 0
\(73\) −55.5273 55.5273i −0.760648 0.760648i 0.215792 0.976439i \(-0.430767\pi\)
−0.976439 + 0.215792i \(0.930767\pi\)
\(74\) 0 0
\(75\) 16.0424 6.64496i 0.213898 0.0885995i
\(76\) 0 0
\(77\) −21.6555 8.97002i −0.281241 0.116494i
\(78\) 0 0
\(79\) −10.9856 −0.139058 −0.0695292 0.997580i \(-0.522150\pi\)
−0.0695292 + 0.997580i \(0.522150\pi\)
\(80\) 0 0
\(81\) 76.5792i 0.945422i
\(82\) 0 0
\(83\) −34.1779 + 82.5128i −0.411782 + 0.994130i 0.572877 + 0.819641i \(0.305827\pi\)
−0.984659 + 0.174489i \(0.944173\pi\)
\(84\) 0 0
\(85\) −8.43772 20.3705i −0.0992674 0.239653i
\(86\) 0 0
\(87\) −7.52203 + 7.52203i −0.0864602 + 0.0864602i
\(88\) 0 0
\(89\) −16.1705 + 16.1705i −0.181691 + 0.181691i −0.792093 0.610401i \(-0.791008\pi\)
0.610401 + 0.792093i \(0.291008\pi\)
\(90\) 0 0
\(91\) −5.64942 13.6389i −0.0620816 0.149878i
\(92\) 0 0
\(93\) 7.39121 17.8440i 0.0794754 0.191870i
\(94\) 0 0
\(95\) 115.939i 1.22041i
\(96\) 0 0
\(97\) −62.6434 −0.645808 −0.322904 0.946432i \(-0.604659\pi\)
−0.322904 + 0.946432i \(0.604659\pi\)
\(98\) 0 0
\(99\) −19.7749 8.19105i −0.199747 0.0827379i
\(100\) 0 0
\(101\) 39.7340 16.4584i 0.393406 0.162954i −0.177206 0.984174i \(-0.556706\pi\)
0.570612 + 0.821220i \(0.306706\pi\)
\(102\) 0 0
\(103\) 36.3254 + 36.3254i 0.352674 + 0.352674i 0.861104 0.508430i \(-0.169774\pi\)
−0.508430 + 0.861104i \(0.669774\pi\)
\(104\) 0 0
\(105\) 22.8619 + 22.8619i 0.217732 + 0.217732i
\(106\) 0 0
\(107\) −111.798 + 46.3084i −1.04484 + 0.432789i −0.838049 0.545596i \(-0.816304\pi\)
−0.206796 + 0.978384i \(0.566304\pi\)
\(108\) 0 0
\(109\) −55.7631 23.0978i −0.511588 0.211907i 0.111929 0.993716i \(-0.464297\pi\)
−0.623517 + 0.781809i \(0.714297\pi\)
\(110\) 0 0
\(111\) −12.4189 −0.111882
\(112\) 0 0
\(113\) 80.7753i 0.714825i −0.933947 0.357413i \(-0.883659\pi\)
0.933947 0.357413i \(-0.116341\pi\)
\(114\) 0 0
\(115\) 83.9387 202.646i 0.729901 1.76214i
\(116\) 0 0
\(117\) −5.15882 12.4545i −0.0440925 0.106449i
\(118\) 0 0
\(119\) 18.3227 18.3227i 0.153972 0.153972i
\(120\) 0 0
\(121\) −81.4099 + 81.4099i −0.672809 + 0.672809i
\(122\) 0 0
\(123\) 1.52436 + 3.68014i 0.0123932 + 0.0299198i
\(124\) 0 0
\(125\) −56.0222 + 135.250i −0.448178 + 1.08200i
\(126\) 0 0
\(127\) 143.036i 1.12627i 0.826365 + 0.563135i \(0.190405\pi\)
−0.826365 + 0.563135i \(0.809595\pi\)
\(128\) 0 0
\(129\) −3.72976 −0.0289129
\(130\) 0 0
\(131\) 56.1430 + 23.2552i 0.428573 + 0.177521i 0.586534 0.809925i \(-0.300492\pi\)
−0.157961 + 0.987445i \(0.550492\pi\)
\(132\) 0 0
\(133\) 125.882 52.1420i 0.946481 0.392045i
\(134\) 0 0
\(135\) 42.1423 + 42.1423i 0.312165 + 0.312165i
\(136\) 0 0
\(137\) 168.165 + 168.165i 1.22748 + 1.22748i 0.964915 + 0.262563i \(0.0845679\pi\)
0.262563 + 0.964915i \(0.415432\pi\)
\(138\) 0 0
\(139\) 97.5768 40.4176i 0.701991 0.290774i −0.00299484 0.999996i \(-0.500953\pi\)
0.704986 + 0.709221i \(0.250953\pi\)
\(140\) 0 0
\(141\) 25.1282 + 10.4084i 0.178214 + 0.0738187i
\(142\) 0 0
\(143\) 3.69634 0.0258485
\(144\) 0 0
\(145\) 215.778i 1.48812i
\(146\) 0 0
\(147\) −6.92979 + 16.7300i −0.0471415 + 0.113810i
\(148\) 0 0
\(149\) 44.3735 + 107.127i 0.297809 + 0.718974i 0.999976 + 0.00696156i \(0.00221595\pi\)
−0.702167 + 0.712012i \(0.747784\pi\)
\(150\) 0 0
\(151\) 128.078 128.078i 0.848200 0.848200i −0.141708 0.989908i \(-0.545259\pi\)
0.989908 + 0.141708i \(0.0452594\pi\)
\(152\) 0 0
\(153\) 16.7315 16.7315i 0.109356 0.109356i
\(154\) 0 0
\(155\) 149.924 + 361.950i 0.967254 + 2.33516i
\(156\) 0 0
\(157\) 20.1590 48.6682i 0.128401 0.309988i −0.846585 0.532254i \(-0.821345\pi\)
0.974986 + 0.222265i \(0.0713452\pi\)
\(158\) 0 0
\(159\) 11.1371i 0.0700447i
\(160\) 0 0
\(161\) 257.775 1.60109
\(162\) 0 0
\(163\) −68.6749 28.4461i −0.421319 0.174516i 0.161943 0.986800i \(-0.448224\pi\)
−0.583262 + 0.812284i \(0.698224\pi\)
\(164\) 0 0
\(165\) −7.47910 + 3.09794i −0.0453279 + 0.0187754i
\(166\) 0 0
\(167\) −131.350 131.350i −0.786527 0.786527i 0.194396 0.980923i \(-0.437725\pi\)
−0.980923 + 0.194396i \(0.937725\pi\)
\(168\) 0 0
\(169\) −117.855 117.855i −0.697366 0.697366i
\(170\) 0 0
\(171\) 114.950 47.6139i 0.672223 0.278444i
\(172\) 0 0
\(173\) −206.045 85.3465i −1.19101 0.493333i −0.302926 0.953014i \(-0.597964\pi\)
−0.888084 + 0.459681i \(0.847964\pi\)
\(174\) 0 0
\(175\) −413.931 −2.36532
\(176\) 0 0
\(177\) 29.6299i 0.167400i
\(178\) 0 0
\(179\) −80.2014 + 193.623i −0.448053 + 1.08169i 0.524998 + 0.851104i \(0.324066\pi\)
−0.973051 + 0.230591i \(0.925934\pi\)
\(180\) 0 0
\(181\) 93.4345 + 225.571i 0.516213 + 1.24625i 0.940213 + 0.340586i \(0.110626\pi\)
−0.424000 + 0.905662i \(0.639374\pi\)
\(182\) 0 0
\(183\) 23.6805 23.6805i 0.129401 0.129401i
\(184\) 0 0
\(185\) 178.124 178.124i 0.962835 0.962835i
\(186\) 0 0
\(187\) 2.48285 + 5.99413i 0.0132773 + 0.0320542i
\(188\) 0 0
\(189\) −26.8034 + 64.7092i −0.141817 + 0.342377i
\(190\) 0 0
\(191\) 20.1639i 0.105570i 0.998606 + 0.0527851i \(0.0168098\pi\)
−0.998606 + 0.0527851i \(0.983190\pi\)
\(192\) 0 0
\(193\) 115.896 0.600497 0.300248 0.953861i \(-0.402930\pi\)
0.300248 + 0.953861i \(0.402930\pi\)
\(194\) 0 0
\(195\) −4.71043 1.95112i −0.0241560 0.0100058i
\(196\) 0 0
\(197\) −177.705 + 73.6077i −0.902055 + 0.373643i −0.785010 0.619483i \(-0.787342\pi\)
−0.117045 + 0.993127i \(0.537342\pi\)
\(198\) 0 0
\(199\) 22.1763 + 22.1763i 0.111439 + 0.111439i 0.760627 0.649189i \(-0.224891\pi\)
−0.649189 + 0.760627i \(0.724891\pi\)
\(200\) 0 0
\(201\) −28.0174 28.0174i −0.139390 0.139390i
\(202\) 0 0
\(203\) 234.283 97.0431i 1.15410 0.478045i
\(204\) 0 0
\(205\) −74.6485 30.9204i −0.364139 0.150831i
\(206\) 0 0
\(207\) 235.389 1.13715
\(208\) 0 0
\(209\) 34.1158i 0.163233i
\(210\) 0 0
\(211\) 116.936 282.308i 0.554197 1.33795i −0.360103 0.932913i \(-0.617258\pi\)
0.914300 0.405038i \(-0.132742\pi\)
\(212\) 0 0
\(213\) −0.435761 1.05202i −0.00204583 0.00493906i
\(214\) 0 0
\(215\) 53.4962 53.4962i 0.248820 0.248820i
\(216\) 0 0
\(217\) −325.563 + 325.563i −1.50029 + 1.50029i
\(218\) 0 0
\(219\) −12.1972 29.4466i −0.0556949 0.134459i
\(220\) 0 0
\(221\) −1.56373 + 3.77518i −0.00707570 + 0.0170822i
\(222\) 0 0
\(223\) 12.1409i 0.0544434i −0.999629 0.0272217i \(-0.991334\pi\)
0.999629 0.0272217i \(-0.00866601\pi\)
\(224\) 0 0
\(225\) −377.985 −1.67993
\(226\) 0 0
\(227\) −215.118 89.1048i −0.947656 0.392532i −0.145307 0.989387i \(-0.546417\pi\)
−0.802350 + 0.596854i \(0.796417\pi\)
\(228\) 0 0
\(229\) 85.4872 35.4100i 0.373307 0.154629i −0.188139 0.982142i \(-0.560245\pi\)
0.561445 + 0.827514i \(0.310245\pi\)
\(230\) 0 0
\(231\) −6.72724 6.72724i −0.0291222 0.0291222i
\(232\) 0 0
\(233\) 33.1162 + 33.1162i 0.142129 + 0.142129i 0.774591 0.632462i \(-0.217956\pi\)
−0.632462 + 0.774591i \(0.717956\pi\)
\(234\) 0 0
\(235\) −509.704 + 211.126i −2.16895 + 0.898410i
\(236\) 0 0
\(237\) −4.11944 1.70633i −0.0173816 0.00719970i
\(238\) 0 0
\(239\) −332.992 −1.39327 −0.696636 0.717425i \(-0.745321\pi\)
−0.696636 + 0.717425i \(0.745321\pi\)
\(240\) 0 0
\(241\) 218.867i 0.908160i −0.890961 0.454080i \(-0.849968\pi\)
0.890961 0.454080i \(-0.150032\pi\)
\(242\) 0 0
\(243\) −36.8267 + 88.9076i −0.151550 + 0.365875i
\(244\) 0 0
\(245\) −140.565 339.354i −0.573735 1.38512i
\(246\) 0 0
\(247\) −15.1933 + 15.1933i −0.0615112 + 0.0615112i
\(248\) 0 0
\(249\) −25.6324 + 25.6324i −0.102941 + 0.102941i
\(250\) 0 0
\(251\) −92.6681 223.721i −0.369196 0.891318i −0.993883 0.110442i \(-0.964773\pi\)
0.624687 0.780875i \(-0.285227\pi\)
\(252\) 0 0
\(253\) −24.6995 + 59.6298i −0.0976263 + 0.235691i
\(254\) 0 0
\(255\) 8.94919i 0.0350949i
\(256\) 0 0
\(257\) −138.514 −0.538966 −0.269483 0.963005i \(-0.586853\pi\)
−0.269483 + 0.963005i \(0.586853\pi\)
\(258\) 0 0
\(259\) 273.509 + 113.291i 1.05602 + 0.437418i
\(260\) 0 0
\(261\) 213.937 88.6158i 0.819684 0.339524i
\(262\) 0 0
\(263\) −91.6940 91.6940i −0.348647 0.348647i 0.510959 0.859605i \(-0.329290\pi\)
−0.859605 + 0.510959i \(0.829290\pi\)
\(264\) 0 0
\(265\) 159.740 + 159.740i 0.602793 + 0.602793i
\(266\) 0 0
\(267\) −8.57537 + 3.55204i −0.0321175 + 0.0133035i
\(268\) 0 0
\(269\) 179.504 + 74.3530i 0.667301 + 0.276405i 0.690507 0.723325i \(-0.257387\pi\)
−0.0232059 + 0.999731i \(0.507387\pi\)
\(270\) 0 0
\(271\) 454.375 1.67666 0.838331 0.545161i \(-0.183532\pi\)
0.838331 + 0.545161i \(0.183532\pi\)
\(272\) 0 0
\(273\) 5.99188i 0.0219483i
\(274\) 0 0
\(275\) 39.6620 95.7526i 0.144226 0.348191i
\(276\) 0 0
\(277\) −12.5345 30.2610i −0.0452510 0.109246i 0.899638 0.436637i \(-0.143830\pi\)
−0.944889 + 0.327391i \(0.893830\pi\)
\(278\) 0 0
\(279\) −297.291 + 297.291i −1.06556 + 1.06556i
\(280\) 0 0
\(281\) 312.777 312.777i 1.11308 1.11308i 0.120353 0.992731i \(-0.461597\pi\)
0.992731 0.120353i \(-0.0384027\pi\)
\(282\) 0 0
\(283\) 74.2838 + 179.337i 0.262487 + 0.633700i 0.999091 0.0426244i \(-0.0135719\pi\)
−0.736604 + 0.676324i \(0.763572\pi\)
\(284\) 0 0
\(285\) 18.0081 43.4754i 0.0631864 0.152545i
\(286\) 0 0
\(287\) 94.9562i 0.330858i
\(288\) 0 0
\(289\) 281.828 0.975182
\(290\) 0 0
\(291\) −23.4903 9.73000i −0.0807227 0.0334364i
\(292\) 0 0
\(293\) −156.211 + 64.7046i −0.533143 + 0.220835i −0.632979 0.774169i \(-0.718168\pi\)
0.0998364 + 0.995004i \(0.468168\pi\)
\(294\) 0 0
\(295\) 424.983 + 424.983i 1.44062 + 1.44062i
\(296\) 0 0
\(297\) −12.4006 12.4006i −0.0417529 0.0417529i
\(298\) 0 0
\(299\) −37.5555 + 15.5560i −0.125604 + 0.0520268i
\(300\) 0 0
\(301\) 82.1432 + 34.0248i 0.272901 + 0.113039i
\(302\) 0 0
\(303\) 17.4560 0.0576106
\(304\) 0 0
\(305\) 679.301i 2.22722i
\(306\) 0 0
\(307\) −111.488 + 269.157i −0.363155 + 0.876733i 0.631681 + 0.775229i \(0.282365\pi\)
−0.994835 + 0.101504i \(0.967635\pi\)
\(308\) 0 0
\(309\) 7.97928 + 19.2637i 0.0258229 + 0.0623420i
\(310\) 0 0
\(311\) 74.0508 74.0508i 0.238105 0.238105i −0.577960 0.816065i \(-0.696151\pi\)
0.816065 + 0.577960i \(0.196151\pi\)
\(312\) 0 0
\(313\) −119.709 + 119.709i −0.382458 + 0.382458i −0.871987 0.489529i \(-0.837169\pi\)
0.489529 + 0.871987i \(0.337169\pi\)
\(314\) 0 0
\(315\) −269.332 650.224i −0.855021 2.06420i
\(316\) 0 0
\(317\) 154.558 373.135i 0.487563 1.17708i −0.468379 0.883528i \(-0.655162\pi\)
0.955942 0.293554i \(-0.0948382\pi\)
\(318\) 0 0
\(319\) 63.4940i 0.199041i
\(320\) 0 0
\(321\) −49.1155 −0.153008
\(322\) 0 0
\(323\) −34.8434 14.4326i −0.107874 0.0446830i
\(324\) 0 0
\(325\) 60.3061 24.9796i 0.185557 0.0768604i
\(326\) 0 0
\(327\) −17.3227 17.3227i −0.0529745 0.0529745i
\(328\) 0 0
\(329\) −458.464 458.464i −1.39351 1.39351i
\(330\) 0 0
\(331\) 376.019 155.752i 1.13601 0.470551i 0.266190 0.963921i \(-0.414235\pi\)
0.869820 + 0.493370i \(0.164235\pi\)
\(332\) 0 0
\(333\) 249.757 + 103.453i 0.750021 + 0.310669i
\(334\) 0 0
\(335\) 803.711 2.39914
\(336\) 0 0
\(337\) 584.284i 1.73378i 0.498499 + 0.866890i \(0.333885\pi\)
−0.498499 + 0.866890i \(0.666115\pi\)
\(338\) 0 0
\(339\) 12.5463 30.2895i 0.0370098 0.0893495i
\(340\) 0 0
\(341\) −44.1162 106.506i −0.129373 0.312334i
\(342\) 0 0
\(343\) −29.9994 + 29.9994i −0.0874617 + 0.0874617i
\(344\) 0 0
\(345\) 62.9514 62.9514i 0.182468 0.182468i
\(346\) 0 0
\(347\) 15.0226 + 36.2679i 0.0432929 + 0.104518i 0.944047 0.329812i \(-0.106985\pi\)
−0.900754 + 0.434330i \(0.856985\pi\)
\(348\) 0 0
\(349\) 82.9090 200.160i 0.237562 0.573525i −0.759468 0.650545i \(-0.774541\pi\)
0.997030 + 0.0770202i \(0.0245406\pi\)
\(350\) 0 0
\(351\) 11.0451i 0.0314675i
\(352\) 0 0
\(353\) −213.926 −0.606022 −0.303011 0.952987i \(-0.597992\pi\)
−0.303011 + 0.952987i \(0.597992\pi\)
\(354\) 0 0
\(355\) 21.3394 + 8.83905i 0.0601109 + 0.0248987i
\(356\) 0 0
\(357\) 9.71666 4.02477i 0.0272175 0.0112739i
\(358\) 0 0
\(359\) −235.583 235.583i −0.656219 0.656219i 0.298264 0.954483i \(-0.403592\pi\)
−0.954483 + 0.298264i \(0.903592\pi\)
\(360\) 0 0
\(361\) 115.037 + 115.037i 0.318663 + 0.318663i
\(362\) 0 0
\(363\) −43.1724 + 17.8826i −0.118932 + 0.0492633i
\(364\) 0 0
\(365\) 597.299 + 247.410i 1.63644 + 0.677834i
\(366\) 0 0
\(367\) −266.252 −0.725482 −0.362741 0.931890i \(-0.618159\pi\)
−0.362741 + 0.931890i \(0.618159\pi\)
\(368\) 0 0
\(369\) 86.7101i 0.234987i
\(370\) 0 0
\(371\) −101.598 + 245.280i −0.273850 + 0.661133i
\(372\) 0 0
\(373\) 133.648 + 322.655i 0.358306 + 0.865028i 0.995539 + 0.0943560i \(0.0300792\pi\)
−0.637232 + 0.770672i \(0.719921\pi\)
\(374\) 0 0
\(375\) −42.0150 + 42.0150i −0.112040 + 0.112040i
\(376\) 0 0
\(377\) −28.2767 + 28.2767i −0.0750045 + 0.0750045i
\(378\) 0 0
\(379\) −1.26349 3.05034i −0.00333376 0.00804840i 0.922204 0.386704i \(-0.126386\pi\)
−0.925538 + 0.378656i \(0.876386\pi\)
\(380\) 0 0
\(381\) −22.2169 + 53.6364i −0.0583122 + 0.140778i
\(382\) 0 0
\(383\) 310.584i 0.810923i 0.914112 + 0.405462i \(0.132889\pi\)
−0.914112 + 0.405462i \(0.867111\pi\)
\(384\) 0 0
\(385\) 192.978 0.501243
\(386\) 0 0
\(387\) 75.0098 + 31.0701i 0.193824 + 0.0802844i
\(388\) 0 0
\(389\) −677.246 + 280.524i −1.74099 + 0.721142i −0.742296 + 0.670072i \(0.766263\pi\)
−0.998695 + 0.0510705i \(0.983737\pi\)
\(390\) 0 0
\(391\) −50.4525 50.4525i −0.129035 0.129035i
\(392\) 0 0
\(393\) 17.4407 + 17.4407i 0.0443783 + 0.0443783i
\(394\) 0 0
\(395\) 83.5594 34.6114i 0.211543 0.0876239i
\(396\) 0 0
\(397\) −467.679 193.719i −1.17803 0.487957i −0.294192 0.955746i \(-0.595051\pi\)
−0.883840 + 0.467789i \(0.845051\pi\)
\(398\) 0 0
\(399\) 55.3027 0.138603
\(400\) 0 0
\(401\) 447.783i 1.11667i −0.829617 0.558333i \(-0.811441\pi\)
0.829617 0.558333i \(-0.188559\pi\)
\(402\) 0 0
\(403\) 27.7849 67.0786i 0.0689451 0.166448i
\(404\) 0 0
\(405\) −241.271 582.480i −0.595732 1.43822i
\(406\) 0 0
\(407\) −52.4142 + 52.4142i −0.128782 + 0.128782i
\(408\) 0 0
\(409\) 266.640 266.640i 0.651931 0.651931i −0.301527 0.953458i \(-0.597496\pi\)
0.953458 + 0.301527i \(0.0974962\pi\)
\(410\) 0 0
\(411\) 36.9392 + 89.1791i 0.0898763 + 0.216981i
\(412\) 0 0
\(413\) −270.299 + 652.559i −0.654477 + 1.58005i
\(414\) 0 0
\(415\) 735.294i 1.77179i
\(416\) 0 0
\(417\) 42.8676 0.102800
\(418\) 0 0
\(419\) 565.518 + 234.245i 1.34969 + 0.559058i 0.936205 0.351455i \(-0.114313\pi\)
0.413481 + 0.910513i \(0.364313\pi\)
\(420\) 0 0
\(421\) −184.538 + 76.4382i −0.438333 + 0.181564i −0.590926 0.806726i \(-0.701238\pi\)
0.152593 + 0.988289i \(0.451238\pi\)
\(422\) 0 0
\(423\) −418.651 418.651i −0.989718 0.989718i
\(424\) 0 0
\(425\) 81.0159 + 81.0159i 0.190626 + 0.190626i
\(426\) 0 0
\(427\) −737.557 + 305.506i −1.72730 + 0.715471i
\(428\) 0 0
\(429\) 1.38607 + 0.574129i 0.00323093 + 0.00133830i
\(430\) 0 0
\(431\) −329.019 −0.763385 −0.381692 0.924289i \(-0.624659\pi\)
−0.381692 + 0.924289i \(0.624659\pi\)
\(432\) 0 0
\(433\) 403.449i 0.931753i −0.884850 0.465877i \(-0.845739\pi\)
0.884850 0.465877i \(-0.154261\pi\)
\(434\) 0 0
\(435\) 33.5155 80.9135i 0.0770470 0.186008i
\(436\) 0 0
\(437\) −143.576 346.623i −0.328549 0.793188i
\(438\) 0 0
\(439\) −432.214 + 432.214i −0.984542 + 0.984542i −0.999882 0.0153402i \(-0.995117\pi\)
0.0153402 + 0.999882i \(0.495117\pi\)
\(440\) 0 0
\(441\) 278.732 278.732i 0.632045 0.632045i
\(442\) 0 0
\(443\) −138.144 333.509i −0.311838 0.752843i −0.999637 0.0269419i \(-0.991423\pi\)
0.687799 0.725901i \(-0.258577\pi\)
\(444\) 0 0
\(445\) 72.0501 173.944i 0.161910 0.390886i
\(446\) 0 0
\(447\) 47.0633i 0.105287i
\(448\) 0 0
\(449\) −320.009 −0.712715 −0.356358 0.934350i \(-0.615981\pi\)
−0.356358 + 0.934350i \(0.615981\pi\)
\(450\) 0 0
\(451\) 21.9658 + 9.09852i 0.0487046 + 0.0201741i
\(452\) 0 0
\(453\) 67.9210 28.1338i 0.149936 0.0621055i
\(454\) 0 0
\(455\) 85.9419 + 85.9419i 0.188883 + 0.188883i
\(456\) 0 0
\(457\) −148.390 148.390i −0.324705 0.324705i 0.525864 0.850569i \(-0.323742\pi\)
−0.850569 + 0.525864i \(0.823742\pi\)
\(458\) 0 0
\(459\) 17.9112 7.41904i 0.0390221 0.0161635i
\(460\) 0 0
\(461\) −224.303 92.9092i −0.486557 0.201538i 0.125899 0.992043i \(-0.459818\pi\)
−0.612456 + 0.790505i \(0.709818\pi\)
\(462\) 0 0
\(463\) −675.592 −1.45916 −0.729581 0.683894i \(-0.760285\pi\)
−0.729581 + 0.683894i \(0.760285\pi\)
\(464\) 0 0
\(465\) 159.012i 0.341962i
\(466\) 0 0
\(467\) −190.920 + 460.923i −0.408823 + 0.986987i 0.576625 + 0.817009i \(0.304369\pi\)
−0.985448 + 0.169977i \(0.945631\pi\)
\(468\) 0 0
\(469\) 361.458 + 872.636i 0.770698 + 1.86063i
\(470\) 0 0
\(471\) 15.1187 15.1187i 0.0320991 0.0320991i
\(472\) 0 0
\(473\) −15.7416 + 15.7416i −0.0332803 + 0.0332803i
\(474\) 0 0
\(475\) 230.552 + 556.603i 0.485373 + 1.17179i
\(476\) 0 0
\(477\) −92.7755 + 223.980i −0.194498 + 0.469559i
\(478\) 0 0
\(479\) 775.709i 1.61943i −0.586821 0.809717i \(-0.699621\pi\)
0.586821 0.809717i \(-0.300379\pi\)
\(480\) 0 0
\(481\) −46.6847 −0.0970576
\(482\) 0 0
\(483\) 96.6616 + 40.0385i 0.200127 + 0.0828955i
\(484\) 0 0
\(485\) 476.481 197.365i 0.982435 0.406938i
\(486\) 0 0
\(487\) 422.101 + 422.101i 0.866738 + 0.866738i 0.992110 0.125372i \(-0.0400125\pi\)
−0.125372 + 0.992110i \(0.540012\pi\)
\(488\) 0 0
\(489\) −21.3337 21.3337i −0.0436272 0.0436272i
\(490\) 0 0
\(491\) 277.565 114.971i 0.565306 0.234157i −0.0816809 0.996659i \(-0.526029\pi\)
0.646987 + 0.762501i \(0.276029\pi\)
\(492\) 0 0
\(493\) −64.8482 26.8610i −0.131538 0.0544848i
\(494\) 0 0
\(495\) 176.220 0.356000
\(496\) 0 0
\(497\) 27.1446i 0.0546170i
\(498\) 0 0
\(499\) 328.498 793.063i 0.658312 1.58930i −0.142099 0.989852i \(-0.545385\pi\)
0.800410 0.599452i \(-0.204615\pi\)
\(500\) 0 0
\(501\) −28.8525 69.6560i −0.0575897 0.139034i
\(502\) 0 0
\(503\) 115.459 115.459i 0.229540 0.229540i −0.582960 0.812501i \(-0.698106\pi\)
0.812501 + 0.582960i \(0.198106\pi\)
\(504\) 0 0
\(505\) −250.373 + 250.373i −0.495788 + 0.495788i
\(506\) 0 0
\(507\) −25.8881 62.4995i −0.0510614 0.123273i
\(508\) 0 0
\(509\) −97.7110 + 235.895i −0.191967 + 0.463449i −0.990331 0.138727i \(-0.955699\pi\)
0.798364 + 0.602175i \(0.205699\pi\)
\(510\) 0 0
\(511\) 759.792i 1.48687i
\(512\) 0 0
\(513\) 101.942 0.198717
\(514\) 0 0
\(515\) −390.747 161.853i −0.758733 0.314277i
\(516\) 0 0
\(517\) 149.983 62.1252i 0.290103 0.120165i
\(518\) 0 0
\(519\) −64.0073 64.0073i −0.123328 0.123328i
\(520\) 0 0
\(521\) 229.899 + 229.899i 0.441264 + 0.441264i 0.892437 0.451173i \(-0.148994\pi\)
−0.451173 + 0.892437i \(0.648994\pi\)
\(522\) 0 0
\(523\) 900.921 373.174i 1.72260 0.713525i 0.722856 0.690999i \(-0.242829\pi\)
0.999746 0.0225265i \(-0.00717100\pi\)
\(524\) 0 0
\(525\) −155.218 64.2933i −0.295653 0.122463i
\(526\) 0 0
\(527\) 127.441 0.241823
\(528\) 0 0
\(529\) 180.797i 0.341772i
\(530\) 0 0
\(531\) −246.826 + 595.890i −0.464832 + 1.12220i
\(532\) 0 0
\(533\) 5.73035 + 13.8343i 0.0107511 + 0.0259555i
\(534\) 0 0
\(535\) 704.466 704.466i 1.31676 1.31676i
\(536\) 0 0
\(537\) −60.1486 + 60.1486i −0.112009 + 0.112009i
\(538\) 0 0
\(539\) 41.3621 + 99.8569i 0.0767386 + 0.185263i
\(540\) 0 0
\(541\) 86.3781 208.535i 0.159664 0.385462i −0.823721 0.566995i \(-0.808106\pi\)
0.983385 + 0.181533i \(0.0581058\pi\)
\(542\) 0 0
\(543\) 99.0983i 0.182501i
\(544\) 0 0
\(545\) 496.920 0.911780
\(546\) 0 0
\(547\) −497.491 206.067i −0.909489 0.376723i −0.121628 0.992576i \(-0.538812\pi\)
−0.787861 + 0.615853i \(0.788812\pi\)
\(548\) 0 0
\(549\) −673.507 + 278.976i −1.22679 + 0.508152i
\(550\) 0 0
\(551\) −260.983 260.983i −0.473653 0.473653i
\(552\) 0 0
\(553\) 75.1593 + 75.1593i 0.135912 + 0.135912i
\(554\) 0 0
\(555\) 94.4609 39.1270i 0.170200 0.0704991i
\(556\) 0 0
\(557\) −527.914 218.669i −0.947782 0.392584i −0.145385 0.989375i \(-0.546442\pi\)
−0.802397 + 0.596791i \(0.796442\pi\)
\(558\) 0 0
\(559\) −14.0209 −0.0250820
\(560\) 0 0
\(561\) 2.63335i 0.00469404i
\(562\) 0 0
\(563\) 303.900 733.680i 0.539788 1.30316i −0.385084 0.922882i \(-0.625827\pi\)
0.924871 0.380281i \(-0.124173\pi\)
\(564\) 0 0
\(565\) 254.491 + 614.397i 0.450427 + 1.08743i
\(566\) 0 0
\(567\) 523.925 523.925i 0.924029 0.924029i
\(568\) 0 0
\(569\) −143.631 + 143.631i −0.252426 + 0.252426i −0.821965 0.569538i \(-0.807122\pi\)
0.569538 + 0.821965i \(0.307122\pi\)
\(570\) 0 0
\(571\) 371.018 + 895.717i 0.649769 + 1.56868i 0.813109 + 0.582112i \(0.197773\pi\)
−0.163339 + 0.986570i \(0.552227\pi\)
\(572\) 0 0
\(573\) −3.13194 + 7.56116i −0.00546586 + 0.0131957i
\(574\) 0 0
\(575\) 1139.78i 1.98223i
\(576\) 0 0
\(577\) 706.702 1.22479 0.612393 0.790553i \(-0.290207\pi\)
0.612393 + 0.790553i \(0.290207\pi\)
\(578\) 0 0
\(579\) 43.4592 + 18.0014i 0.0750590 + 0.0310905i
\(580\) 0 0
\(581\) 798.352 330.688i 1.37410 0.569171i
\(582\) 0 0
\(583\) −47.0045 47.0045i −0.0806253 0.0806253i
\(584\) 0 0
\(585\) 78.4786 + 78.4786i 0.134151 + 0.134151i
\(586\) 0 0
\(587\) −293.599 + 121.613i −0.500169 + 0.207177i −0.618481 0.785800i \(-0.712252\pi\)
0.118312 + 0.992976i \(0.462252\pi\)
\(588\) 0 0
\(589\) 619.110 + 256.444i 1.05112 + 0.435389i
\(590\) 0 0
\(591\) −78.0696 −0.132097
\(592\) 0 0
\(593\) 674.627i 1.13765i −0.822458 0.568825i \(-0.807398\pi\)
0.822458 0.568825i \(-0.192602\pi\)
\(594\) 0 0
\(595\) −81.6391 + 197.094i −0.137209 + 0.331251i
\(596\) 0 0
\(597\) 4.87127 + 11.7603i 0.00815958 + 0.0196990i
\(598\) 0 0
\(599\) −379.725 + 379.725i −0.633932 + 0.633932i −0.949052 0.315120i \(-0.897955\pi\)
0.315120 + 0.949052i \(0.397955\pi\)
\(600\) 0 0
\(601\) −548.542 + 548.542i −0.912715 + 0.912715i −0.996485 0.0837700i \(-0.973304\pi\)
0.0837700 + 0.996485i \(0.473304\pi\)
\(602\) 0 0
\(603\) 330.068 + 796.855i 0.547377 + 1.32148i
\(604\) 0 0
\(605\) 362.733 875.715i 0.599559 1.44746i
\(606\) 0 0
\(607\) 1.05067i 0.00173092i 1.00000 0.000865460i \(0.000275484\pi\)
−1.00000 0.000865460i \(0.999725\pi\)
\(608\) 0 0
\(609\) 102.926 0.169008
\(610\) 0 0
\(611\) 94.4614 + 39.1272i 0.154601 + 0.0640379i
\(612\) 0 0
\(613\) 625.826 259.226i 1.02092 0.422881i 0.191495 0.981494i \(-0.438666\pi\)
0.829428 + 0.558613i \(0.188666\pi\)
\(614\) 0 0
\(615\) −23.1894 23.1894i −0.0377063 0.0377063i
\(616\) 0 0
\(617\) 180.644 + 180.644i 0.292779 + 0.292779i 0.838177 0.545398i \(-0.183622\pi\)
−0.545398 + 0.838177i \(0.683622\pi\)
\(618\) 0 0
\(619\) −555.651 + 230.158i −0.897658 + 0.371822i −0.783319 0.621620i \(-0.786475\pi\)
−0.114339 + 0.993442i \(0.536475\pi\)
\(620\) 0 0
\(621\) 178.181 + 73.8048i 0.286925 + 0.118848i
\(622\) 0 0
\(623\) 221.265 0.355160
\(624\) 0 0
\(625\) 135.712i 0.217139i
\(626\) 0 0
\(627\) −5.29899 + 12.7929i −0.00845135 + 0.0204034i
\(628\) 0 0
\(629\) −31.3584 75.7058i −0.0498543 0.120359i
\(630\) 0 0
\(631\) 267.583 267.583i 0.424062 0.424062i −0.462537 0.886600i \(-0.653061\pi\)
0.886600 + 0.462537i \(0.153061\pi\)
\(632\) 0 0
\(633\) 87.6981 87.6981i 0.138544 0.138544i
\(634\) 0 0
\(635\) −450.652 1087.97i −0.709688 1.71334i
\(636\) 0 0
\(637\) −26.0503 + 62.8911i −0.0408954 + 0.0987301i
\(638\) 0 0
\(639\) 24.7874i 0.0387908i
\(640\) 0 0
\(641\) −834.869 −1.30245 −0.651224 0.758886i \(-0.725744\pi\)
−0.651224 + 0.758886i \(0.725744\pi\)
\(642\) 0 0
\(643\) −1006.71 416.995i −1.56565 0.648514i −0.579592 0.814907i \(-0.696788\pi\)
−0.986060 + 0.166393i \(0.946788\pi\)
\(644\) 0 0
\(645\) 28.3695 11.7510i 0.0439837 0.0182187i
\(646\) 0 0
\(647\) 857.194 + 857.194i 1.32488 + 1.32488i 0.909776 + 0.415099i \(0.136253\pi\)
0.415099 + 0.909776i \(0.363747\pi\)
\(648\) 0 0
\(649\) −125.054 125.054i −0.192687 0.192687i
\(650\) 0 0
\(651\) −172.649 + 71.5136i −0.265206 + 0.109852i
\(652\) 0 0
\(653\) −105.248 43.5953i −0.161177 0.0667616i 0.300636 0.953739i \(-0.402801\pi\)
−0.461813 + 0.886977i \(0.652801\pi\)
\(654\) 0 0
\(655\) −500.306 −0.763826
\(656\) 0 0
\(657\) 693.811i 1.05603i
\(658\) 0 0
\(659\) 222.875 538.067i 0.338201 0.816490i −0.659687 0.751540i \(-0.729311\pi\)
0.997889 0.0649499i \(-0.0206888\pi\)
\(660\) 0 0
\(661\) −396.971 958.372i −0.600561 1.44988i −0.873005 0.487711i \(-0.837832\pi\)
0.272445 0.962171i \(-0.412168\pi\)
\(662\) 0 0
\(663\) −1.17275 + 1.17275i −0.00176885 + 0.00176885i
\(664\) 0 0
\(665\) −793.210 + 793.210i −1.19280 + 1.19280i
\(666\) 0 0
\(667\) −267.214 645.111i −0.400620 0.967183i
\(668\) 0 0
\(669\) 1.88577 4.55265i 0.00281879 0.00680515i
\(670\) 0 0
\(671\) 199.888i 0.297896i
\(672\) 0 0
\(673\) −908.805 −1.35038 −0.675190 0.737644i \(-0.735938\pi\)
−0.675190 + 0.737644i \(0.735938\pi\)
\(674\) 0 0
\(675\) −286.120 118.515i −0.423881 0.175577i
\(676\) 0 0
\(677\) 963.142 398.947i 1.42266 0.589286i 0.467134 0.884186i \(-0.345287\pi\)
0.955528 + 0.294900i \(0.0952865\pi\)
\(678\) 0 0
\(679\) 428.581 + 428.581i 0.631195 + 0.631195i
\(680\) 0 0
\(681\) −66.8259 66.8259i −0.0981290 0.0981290i
\(682\) 0 0
\(683\) −248.963 + 103.124i −0.364515 + 0.150987i −0.557420 0.830230i \(-0.688209\pi\)
0.192906 + 0.981217i \(0.438209\pi\)
\(684\) 0 0
\(685\) −1808.92 749.280i −2.64076 1.09384i
\(686\) 0 0
\(687\) 37.5564 0.0546673
\(688\) 0 0
\(689\) 41.8664i 0.0607640i
\(690\) 0 0
\(691\) 222.756 537.780i 0.322367 0.778263i −0.676748 0.736214i \(-0.736612\pi\)
0.999116 0.0420488i \(-0.0133885\pi\)
\(692\) 0 0
\(693\) 79.2524 + 191.332i 0.114361 + 0.276093i
\(694\) 0 0
\(695\) −614.853 + 614.853i −0.884681 + 0.884681i
\(696\) 0 0
\(697\) −18.5851 + 18.5851i −0.0266645 + 0.0266645i
\(698\) 0 0
\(699\) 7.27433 + 17.5618i 0.0104068 + 0.0251242i
\(700\) 0 0
\(701\) −236.347 + 570.592i −0.337157 + 0.813969i 0.660829 + 0.750536i \(0.270205\pi\)
−0.997986 + 0.0634324i \(0.979795\pi\)
\(702\) 0 0
\(703\) 430.882i 0.612919i
\(704\) 0 0
\(705\) −223.924 −0.317623
\(706\) 0 0
\(707\) −384.446 159.243i −0.543771 0.225237i
\(708\) 0 0
\(709\) −599.630 + 248.375i −0.845740 + 0.350317i −0.763114 0.646264i \(-0.776331\pi\)
−0.0826257 + 0.996581i \(0.526331\pi\)
\(710\) 0 0
\(711\) 68.6324 + 68.6324i 0.0965293 + 0.0965293i
\(712\) 0 0
\(713\) 896.458 + 896.458i 1.25730 + 1.25730i
\(714\) 0 0
\(715\) −28.1153 + 11.6457i −0.0393221 + 0.0162877i
\(716\) 0 0
\(717\) −124.867 51.7216i −0.174152 0.0721361i
\(718\) 0 0
\(719\) −96.4410 −0.134132 −0.0670661 0.997749i \(-0.521364\pi\)
−0.0670661 + 0.997749i \(0.521364\pi\)
\(720\) 0 0
\(721\) 497.048i 0.689388i
\(722\) 0 0
\(723\) 33.9952 82.0716i 0.0470196 0.113515i
\(724\) 0 0
\(725\) 429.088 + 1035.91i 0.591846 + 1.42884i
\(726\) 0 0
\(727\) 708.402 708.402i 0.974418 0.974418i −0.0252626 0.999681i \(-0.508042\pi\)
0.999681 + 0.0252626i \(0.00804218\pi\)
\(728\) 0 0
\(729\) 459.728 459.728i 0.630628 0.630628i
\(730\) 0 0
\(731\) −9.41788 22.7368i −0.0128836 0.0311037i
\(732\) 0 0
\(733\) −149.531 + 361.000i −0.203999 + 0.492497i −0.992457 0.122591i \(-0.960880\pi\)
0.788458 + 0.615088i \(0.210880\pi\)
\(734\) 0 0
\(735\) 149.086i 0.202838i
\(736\) 0 0
\(737\) −236.497 −0.320891
\(738\) 0 0
\(739\) 971.442 + 402.384i 1.31454 + 0.544499i 0.926205 0.377021i \(-0.123052\pi\)
0.388331 + 0.921520i \(0.373052\pi\)
\(740\) 0 0
\(741\) −8.05712 + 3.33737i −0.0108733 + 0.00450387i
\(742\) 0 0
\(743\) −117.181 117.181i −0.157714 0.157714i 0.623839 0.781553i \(-0.285572\pi\)
−0.781553 + 0.623839i \(0.785572\pi\)
\(744\) 0 0
\(745\) −675.032 675.032i −0.906083 0.906083i
\(746\) 0 0
\(747\) 729.022 301.971i 0.975933 0.404245i
\(748\) 0 0
\(749\) 1081.70 + 448.056i 1.44420 + 0.598206i
\(750\) 0 0
\(751\) −604.910 −0.805473 −0.402736 0.915316i \(-0.631941\pi\)
−0.402736 + 0.915316i \(0.631941\pi\)
\(752\) 0 0
\(753\) 98.2854i 0.130525i
\(754\) 0 0
\(755\) −570.670 + 1377.72i −0.755855 + 1.82479i
\(756\) 0 0
\(757\) −459.899 1110.29i −0.607528 1.46670i −0.865680 0.500598i \(-0.833113\pi\)
0.258152 0.966104i \(-0.416887\pi\)
\(758\) 0 0
\(759\) −18.5238 + 18.5238i −0.0244056 + 0.0244056i
\(760\) 0 0
\(761\) 202.753 202.753i 0.266430 0.266430i −0.561230 0.827660i \(-0.689672\pi\)
0.827660 + 0.561230i \(0.189672\pi\)
\(762\) 0 0
\(763\) 223.483 + 539.535i 0.292900 + 0.707124i
\(764\) 0 0
\(765\) −74.5495 + 179.978i −0.0974503 + 0.235266i
\(766\) 0 0
\(767\) 111.384i 0.145220i
\(768\) 0 0
\(769\) 954.072 1.24067 0.620333 0.784338i \(-0.286997\pi\)
0.620333 + 0.784338i \(0.286997\pi\)
\(770\) 0 0
\(771\) −51.9407 21.5146i −0.0673680 0.0279047i
\(772\) 0 0
\(773\) 244.204 101.153i 0.315918 0.130857i −0.219090 0.975705i \(-0.570309\pi\)
0.535007 + 0.844847i \(0.320309\pi\)
\(774\) 0 0
\(775\) −1439.52 1439.52i −1.85744 1.85744i
\(776\) 0 0
\(777\) 84.9649 + 84.9649i 0.109350 + 0.109350i
\(778\) 0 0
\(779\) −127.685 + 52.8890i −0.163909 + 0.0678934i
\(780\) 0 0
\(781\) −6.27923 2.60094i −0.00803999 0.00333027i
\(782\) 0 0
\(783\) 189.727 0.242308
\(784\) 0 0
\(785\) 433.696i 0.552479i
\(786\) 0 0
\(787\) 19.8368 47.8903i 0.0252056 0.0608518i −0.910776 0.412902i \(-0.864515\pi\)
0.935981 + 0.352050i \(0.114515\pi\)
\(788\) 0 0
\(789\) −20.1416 48.6261i −0.0255280 0.0616301i
\(790\) 0 0
\(791\) −552.633 + 552.633i −0.698650 + 0.698650i
\(792\) 0 0
\(793\) 89.0192 89.0192i 0.112256 0.112256i
\(794\) 0 0
\(795\) 35.0887 + 84.7116i 0.0441367 + 0.106556i
\(796\) 0 0
\(797\) 187.462 452.574i 0.235210 0.567847i −0.761566