Properties

Label 300.2.h.a.299.5
Level $300$
Weight $2$
Character 300.299
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
Defining polynomial: \(x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.5
Root \(-1.17915 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.a.299.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +O(q^{10})\) \(q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +1.32431 q^{11} +(-2.11862 + 2.74070i) q^{12} -5.12311i q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000 q^{17} +(1.80122 + 3.84130i) q^{18} -1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(1.03399 - 1.56155i) q^{22} +0.371834i q^{23} +(1.57752 + 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(5.19283 + 0.185917i) q^{27} +(2.35829 + 5.56155i) q^{28} -3.12311i q^{29} -4.71659i q^{31} +(1.21922 + 5.52390i) q^{32} +(-1.12311 - 2.00000i) q^{33} +(1.56155 - 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311i q^{37} +(-1.56155 - 1.03399i) q^{38} +(-7.73704 + 4.34475i) q^{39} -1.12311i q^{41} +(7.37874 + 0.541105i) q^{42} -7.73704 q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045i q^{47} +(6.70062 + 1.76115i) q^{48} +2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(-9.43318 + 4.00000i) q^{52} +12.2462 q^{53} +(4.27366 - 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(-2.00000 + 1.12311i) q^{57} +(-3.68260 - 2.43845i) q^{58} +14.1498 q^{59} +3.12311 q^{61} +(-5.56155 - 3.68260i) q^{62} +(4.71659 - 7.73704i) q^{63} +(7.46543 + 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} -4.34475 q^{67} +(-1.56155 - 3.68260i) q^{68} +(0.561553 - 0.315342i) q^{69} +3.39228 q^{71} +(5.66664 - 6.31579i) q^{72} +8.24621i q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000 q^{77} +(-0.917790 + 12.5154i) q^{78} -8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-1.32431 - 0.876894i) q^{82} +15.1022i q^{83} +(6.39919 - 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(-4.71659 + 2.64861i) q^{87} +(-3.68260 - 0.684658i) q^{88} -10.2462i q^{89} +15.4741i q^{91} +(0.684658 - 0.290319i) q^{92} +(-7.12311 + 4.00000i) q^{93} +(-3.56155 - 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000i q^{97} +(1.65767 - 2.50345i) q^{98} +(-2.06798 + 3.39228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} + 2q^{4} - 6q^{6} - 14q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 2q^{2} + 2q^{4} - 6q^{6} - 14q^{8} + 4q^{9} - 14q^{12} - 14q^{16} + 16q^{17} - 18q^{18} + 4q^{21} + 2q^{24} + 18q^{32} + 24q^{33} - 4q^{34} + 18q^{36} + 4q^{38} + 16q^{42} + 20q^{46} + 10q^{48} - 16q^{49} + 32q^{53} + 10q^{54} - 16q^{57} - 8q^{61} - 28q^{62} + 2q^{64} - 40q^{66} + 4q^{68} - 12q^{69} + 10q^{72} - 36q^{76} - 32q^{77} + 8q^{78} - 16q^{84} - 44q^{92} - 24q^{93} - 12q^{94} + 42q^{96} + 38q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.780776 1.17915i 0.552092 0.833783i
\(3\) −0.848071 1.51022i −0.489634 0.871928i
\(4\) −0.780776 1.84130i −0.390388 0.920650i
\(5\) 0 0
\(6\) −2.44293 0.179147i −0.997322 0.0731366i
\(7\) −3.02045 −1.14162 −0.570811 0.821081i \(-0.693371\pi\)
−0.570811 + 0.821081i \(0.693371\pi\)
\(8\) −2.78078 0.516994i −0.983153 0.182785i
\(9\) −1.56155 + 2.56155i −0.520518 + 0.853851i
\(10\) 0 0
\(11\) 1.32431 0.399294 0.199647 0.979868i \(-0.436021\pi\)
0.199647 + 0.979868i \(0.436021\pi\)
\(12\) −2.11862 + 2.74070i −0.611594 + 0.791172i
\(13\) 5.12311i 1.42089i −0.703751 0.710447i \(-0.748493\pi\)
0.703751 0.710447i \(-0.251507\pi\)
\(14\) −2.35829 + 3.56155i −0.630281 + 0.951865i
\(15\) 0 0
\(16\) −2.78078 + 2.87529i −0.695194 + 0.718822i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.80122 + 3.84130i 0.424553 + 0.905403i
\(19\) 1.32431i 0.303817i −0.988395 0.151908i \(-0.951458\pi\)
0.988395 0.151908i \(-0.0485419\pi\)
\(20\) 0 0
\(21\) 2.56155 + 4.56155i 0.558977 + 0.995412i
\(22\) 1.03399 1.56155i 0.220447 0.332924i
\(23\) 0.371834i 0.0775328i 0.999248 + 0.0387664i \(0.0123428\pi\)
−0.999248 + 0.0387664i \(0.987657\pi\)
\(24\) 1.57752 + 4.63804i 0.322010 + 0.946736i
\(25\) 0 0
\(26\) −6.04090 4.00000i −1.18472 0.784465i
\(27\) 5.19283 + 0.185917i 0.999360 + 0.0357798i
\(28\) 2.35829 + 5.56155i 0.445676 + 1.05103i
\(29\) 3.12311i 0.579946i −0.957035 0.289973i \(-0.906354\pi\)
0.957035 0.289973i \(-0.0936464\pi\)
\(30\) 0 0
\(31\) 4.71659i 0.847124i −0.905867 0.423562i \(-0.860780\pi\)
0.905867 0.423562i \(-0.139220\pi\)
\(32\) 1.21922 + 5.52390i 0.215530 + 0.976497i
\(33\) −1.12311 2.00000i −0.195508 0.348155i
\(34\) 1.56155 2.35829i 0.267804 0.404444i
\(35\) 0 0
\(36\) 5.93581 + 0.875288i 0.989302 + 0.145881i
\(37\) 5.12311i 0.842233i −0.907006 0.421117i \(-0.861638\pi\)
0.907006 0.421117i \(-0.138362\pi\)
\(38\) −1.56155 1.03399i −0.253317 0.167735i
\(39\) −7.73704 + 4.34475i −1.23892 + 0.695718i
\(40\) 0 0
\(41\) 1.12311i 0.175400i −0.996147 0.0876998i \(-0.972048\pi\)
0.996147 0.0876998i \(-0.0279516\pi\)
\(42\) 7.37874 + 0.541105i 1.13856 + 0.0834943i
\(43\) −7.73704 −1.17989 −0.589944 0.807445i \(-0.700850\pi\)
−0.589944 + 0.807445i \(0.700850\pi\)
\(44\) −1.03399 2.43845i −0.155879 0.367610i
\(45\) 0 0
\(46\) 0.438447 + 0.290319i 0.0646455 + 0.0428052i
\(47\) 3.02045i 0.440578i −0.975435 0.220289i \(-0.929300\pi\)
0.975435 0.220289i \(-0.0707000\pi\)
\(48\) 6.70062 + 1.76115i 0.967152 + 0.254200i
\(49\) 2.12311 0.303301
\(50\) 0 0
\(51\) −1.69614 3.02045i −0.237507 0.422947i
\(52\) −9.43318 + 4.00000i −1.30815 + 0.554700i
\(53\) 12.2462 1.68215 0.841073 0.540921i \(-0.181924\pi\)
0.841073 + 0.540921i \(0.181924\pi\)
\(54\) 4.27366 5.97795i 0.581571 0.813495i
\(55\) 0 0
\(56\) 8.39919 + 1.56155i 1.12239 + 0.208671i
\(57\) −2.00000 + 1.12311i −0.264906 + 0.148759i
\(58\) −3.68260 2.43845i −0.483549 0.320184i
\(59\) 14.1498 1.84214 0.921071 0.389394i \(-0.127315\pi\)
0.921071 + 0.389394i \(0.127315\pi\)
\(60\) 0 0
\(61\) 3.12311 0.399873 0.199936 0.979809i \(-0.435926\pi\)
0.199936 + 0.979809i \(0.435926\pi\)
\(62\) −5.56155 3.68260i −0.706318 0.467691i
\(63\) 4.71659 7.73704i 0.594234 0.974775i
\(64\) 7.46543 + 2.87529i 0.933179 + 0.359411i
\(65\) 0 0
\(66\) −3.23519 0.237246i −0.398224 0.0292030i
\(67\) −4.34475 −0.530796 −0.265398 0.964139i \(-0.585503\pi\)
−0.265398 + 0.964139i \(0.585503\pi\)
\(68\) −1.56155 3.68260i −0.189366 0.446581i
\(69\) 0.561553 0.315342i 0.0676030 0.0379627i
\(70\) 0 0
\(71\) 3.39228 0.402590 0.201295 0.979531i \(-0.435485\pi\)
0.201295 + 0.979531i \(0.435485\pi\)
\(72\) 5.66664 6.31579i 0.667819 0.744323i
\(73\) 8.24621i 0.965146i 0.875856 + 0.482573i \(0.160298\pi\)
−0.875856 + 0.482573i \(0.839702\pi\)
\(74\) −6.04090 4.00000i −0.702240 0.464991i
\(75\) 0 0
\(76\) −2.43845 + 1.03399i −0.279709 + 0.118607i
\(77\) −4.00000 −0.455842
\(78\) −0.917790 + 12.5154i −0.103919 + 1.41709i
\(79\) 8.10887i 0.912319i −0.889898 0.456160i \(-0.849225\pi\)
0.889898 0.456160i \(-0.150775\pi\)
\(80\) 0 0
\(81\) −4.12311 8.00000i −0.458123 0.888889i
\(82\) −1.32431 0.876894i −0.146245 0.0968368i
\(83\) 15.1022i 1.65769i 0.559481 + 0.828843i \(0.311000\pi\)
−0.559481 + 0.828843i \(0.689000\pi\)
\(84\) 6.39919 8.27814i 0.698209 0.903219i
\(85\) 0 0
\(86\) −6.04090 + 9.12311i −0.651407 + 0.983770i
\(87\) −4.71659 + 2.64861i −0.505671 + 0.283961i
\(88\) −3.68260 0.684658i −0.392567 0.0729848i
\(89\) 10.2462i 1.08610i −0.839702 0.543048i \(-0.817270\pi\)
0.839702 0.543048i \(-0.182730\pi\)
\(90\) 0 0
\(91\) 15.4741i 1.62212i
\(92\) 0.684658 0.290319i 0.0713806 0.0302679i
\(93\) −7.12311 + 4.00000i −0.738632 + 0.414781i
\(94\) −3.56155 2.35829i −0.367346 0.243240i
\(95\) 0 0
\(96\) 7.30834 6.52596i 0.745904 0.666053i
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 1.65767 2.50345i 0.167450 0.252887i
\(99\) −2.06798 + 3.39228i −0.207839 + 0.340937i
\(100\) 0 0
\(101\) 0.876894i 0.0872543i −0.999048 0.0436271i \(-0.986109\pi\)
0.999048 0.0436271i \(-0.0138914\pi\)
\(102\) −4.88586 0.358294i −0.483772 0.0354764i
\(103\) 9.80501 0.966117 0.483058 0.875588i \(-0.339526\pi\)
0.483058 + 0.875588i \(0.339526\pi\)
\(104\) −2.64861 + 14.2462i −0.259718 + 1.39696i
\(105\) 0 0
\(106\) 9.56155 14.4401i 0.928700 1.40255i
\(107\) 3.02045i 0.291998i 0.989285 + 0.145999i \(0.0466396\pi\)
−0.989285 + 0.145999i \(0.953360\pi\)
\(108\) −3.71211 9.70671i −0.357198 0.934029i
\(109\) 0.876894 0.0839912 0.0419956 0.999118i \(-0.486628\pi\)
0.0419956 + 0.999118i \(0.486628\pi\)
\(110\) 0 0
\(111\) −7.73704 + 4.34475i −0.734367 + 0.412386i
\(112\) 8.39919 8.68466i 0.793649 0.820623i
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −0.237246 + 3.23519i −0.0222201 + 0.303003i
\(115\) 0 0
\(116\) −5.75058 + 2.43845i −0.533928 + 0.226404i
\(117\) 13.1231 + 8.00000i 1.21323 + 0.739600i
\(118\) 11.0478 16.6847i 1.01703 1.53595i
\(119\) −6.04090 −0.553768
\(120\) 0 0
\(121\) −9.24621 −0.840565
\(122\) 2.43845 3.68260i 0.220767 0.333407i
\(123\) −1.69614 + 0.952473i −0.152936 + 0.0858816i
\(124\) −8.68466 + 3.68260i −0.779905 + 0.330707i
\(125\) 0 0
\(126\) −5.44050 11.6024i −0.484679 1.03363i
\(127\) 15.1022 1.34011 0.670054 0.742313i \(-0.266271\pi\)
0.670054 + 0.742313i \(0.266271\pi\)
\(128\) 9.21922 6.55789i 0.814872 0.579641i
\(129\) 6.56155 + 11.6847i 0.577713 + 1.02878i
\(130\) 0 0
\(131\) 5.46026 0.477065 0.238532 0.971135i \(-0.423334\pi\)
0.238532 + 0.971135i \(0.423334\pi\)
\(132\) −2.80571 + 3.62953i −0.244205 + 0.315910i
\(133\) 4.00000i 0.346844i
\(134\) −3.39228 + 5.12311i −0.293049 + 0.442569i
\(135\) 0 0
\(136\) −5.56155 1.03399i −0.476899 0.0886637i
\(137\) −8.24621 −0.704521 −0.352261 0.935902i \(-0.614587\pi\)
−0.352261 + 0.935902i \(0.614587\pi\)
\(138\) 0.0666131 0.908365i 0.00567048 0.0773251i
\(139\) 17.5420i 1.48790i 0.668237 + 0.743949i \(0.267049\pi\)
−0.668237 + 0.743949i \(0.732951\pi\)
\(140\) 0 0
\(141\) −4.56155 + 2.56155i −0.384152 + 0.215722i
\(142\) 2.64861 4.00000i 0.222267 0.335673i
\(143\) 6.78456i 0.567354i
\(144\) −3.02287 11.6130i −0.251906 0.967752i
\(145\) 0 0
\(146\) 9.72350 + 6.43845i 0.804722 + 0.532850i
\(147\) −1.80054 3.20636i −0.148506 0.264457i
\(148\) −9.43318 + 4.00000i −0.775402 + 0.328798i
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 7.36520i 0.599372i −0.954038 0.299686i \(-0.903118\pi\)
0.954038 0.299686i \(-0.0968819\pi\)
\(152\) −0.684658 + 3.68260i −0.0555331 + 0.298698i
\(153\) −3.12311 + 5.12311i −0.252488 + 0.414179i
\(154\) −3.12311 + 4.71659i −0.251667 + 0.380074i
\(155\) 0 0
\(156\) 14.0409 + 10.8539i 1.12417 + 0.869010i
\(157\) 3.36932i 0.268901i 0.990920 + 0.134450i \(0.0429269\pi\)
−0.990920 + 0.134450i \(0.957073\pi\)
\(158\) −9.56155 6.33122i −0.760676 0.503684i
\(159\) −10.3857 18.4945i −0.823636 1.46671i
\(160\) 0 0
\(161\) 1.12311i 0.0885131i
\(162\) −12.6524 1.38446i −0.994067 0.108774i
\(163\) 15.6829 1.22838 0.614189 0.789159i \(-0.289483\pi\)
0.614189 + 0.789159i \(0.289483\pi\)
\(164\) −2.06798 + 0.876894i −0.161482 + 0.0684739i
\(165\) 0 0
\(166\) 17.8078 + 11.7915i 1.38215 + 0.915196i
\(167\) 9.06134i 0.701188i 0.936528 + 0.350594i \(0.114020\pi\)
−0.936528 + 0.350594i \(0.885980\pi\)
\(168\) −4.76481 14.0090i −0.367613 1.08082i
\(169\) −13.2462 −1.01894
\(170\) 0 0
\(171\) 3.39228 + 2.06798i 0.259414 + 0.158142i
\(172\) 6.04090 + 14.2462i 0.460614 + 1.08626i
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) −0.559496 + 7.62953i −0.0424153 + 0.578393i
\(175\) 0 0
\(176\) −3.68260 + 3.80776i −0.277587 + 0.287021i
\(177\) −12.0000 21.3693i −0.901975 1.60622i
\(178\) −12.0818 8.00000i −0.905569 0.599625i
\(179\) 10.0138 0.748468 0.374234 0.927334i \(-0.377906\pi\)
0.374234 + 0.927334i \(0.377906\pi\)
\(180\) 0 0
\(181\) −12.2462 −0.910254 −0.455127 0.890427i \(-0.650406\pi\)
−0.455127 + 0.890427i \(0.650406\pi\)
\(182\) 18.2462 + 12.0818i 1.35250 + 0.895562i
\(183\) −2.64861 4.71659i −0.195791 0.348660i
\(184\) 0.192236 1.03399i 0.0141718 0.0762266i
\(185\) 0 0
\(186\) −0.844964 + 11.5223i −0.0619558 + 0.844856i
\(187\) 2.64861 0.193686
\(188\) −5.56155 + 2.35829i −0.405618 + 0.171996i
\(189\) −15.6847 0.561553i −1.14089 0.0408470i
\(190\) 0 0
\(191\) −24.9073 −1.80223 −0.901113 0.433585i \(-0.857248\pi\)
−0.901113 + 0.433585i \(0.857248\pi\)
\(192\) −1.98889 13.7129i −0.143535 0.989645i
\(193\) 0.246211i 0.0177227i −0.999961 0.00886134i \(-0.997179\pi\)
0.999961 0.00886134i \(-0.00282069\pi\)
\(194\) 7.07488 + 4.68466i 0.507947 + 0.336339i
\(195\) 0 0
\(196\) −1.65767 3.90928i −0.118405 0.279234i
\(197\) 4.24621 0.302530 0.151265 0.988493i \(-0.451665\pi\)
0.151265 + 0.988493i \(0.451665\pi\)
\(198\) 2.38537 + 5.08706i 0.169521 + 0.361522i
\(199\) 5.46026i 0.387067i −0.981094 0.193534i \(-0.938005\pi\)
0.981094 0.193534i \(-0.0619949\pi\)
\(200\) 0 0
\(201\) 3.68466 + 6.56155i 0.259896 + 0.462816i
\(202\) −1.03399 0.684658i −0.0727511 0.0481724i
\(203\) 9.43318i 0.662079i
\(204\) −4.23725 + 5.48140i −0.296667 + 0.383775i
\(205\) 0 0
\(206\) 7.65552 11.5616i 0.533385 0.805532i
\(207\) −0.952473 0.580639i −0.0662014 0.0403572i
\(208\) 14.7304 + 14.2462i 1.02137 + 0.987797i
\(209\) 1.75379i 0.121312i
\(210\) 0 0
\(211\) 16.7984i 1.15645i −0.815878 0.578224i \(-0.803746\pi\)
0.815878 0.578224i \(-0.196254\pi\)
\(212\) −9.56155 22.5490i −0.656690 1.54867i
\(213\) −2.87689 5.12311i −0.197122 0.351029i
\(214\) 3.56155 + 2.35829i 0.243463 + 0.161210i
\(215\) 0 0
\(216\) −14.3440 3.20165i −0.975983 0.217845i
\(217\) 14.2462i 0.967096i
\(218\) 0.684658 1.03399i 0.0463709 0.0700305i
\(219\) 12.4536 6.99337i 0.841538 0.472568i
\(220\) 0 0
\(221\) 10.2462i 0.689235i
\(222\) −0.917790 + 12.5154i −0.0615980 + 0.839978i
\(223\) −8.31768 −0.556993 −0.278496 0.960437i \(-0.589836\pi\)
−0.278496 + 0.960437i \(0.589836\pi\)
\(224\) −3.68260 16.6847i −0.246054 1.11479i
\(225\) 0 0
\(226\) −10.9309 + 16.5081i −0.727111 + 1.09810i
\(227\) 21.8868i 1.45268i −0.687337 0.726339i \(-0.741220\pi\)
0.687337 0.726339i \(-0.258780\pi\)
\(228\) 3.62953 + 2.80571i 0.240371 + 0.185812i
\(229\) 16.2462 1.07358 0.536790 0.843716i \(-0.319637\pi\)
0.536790 + 0.843716i \(0.319637\pi\)
\(230\) 0 0
\(231\) 3.39228 + 6.04090i 0.223196 + 0.397462i
\(232\) −1.61463 + 8.68466i −0.106005 + 0.570176i
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 19.6794 9.22786i 1.28648 0.603244i
\(235\) 0 0
\(236\) −11.0478 26.0540i −0.719151 1.69597i
\(237\) −12.2462 + 6.87689i −0.795477 + 0.446702i
\(238\) −4.71659 + 7.12311i −0.305731 + 0.461722i
\(239\) −17.3790 −1.12416 −0.562078 0.827084i \(-0.689998\pi\)
−0.562078 + 0.827084i \(0.689998\pi\)
\(240\) 0 0
\(241\) 13.3693 0.861193 0.430597 0.902544i \(-0.358303\pi\)
0.430597 + 0.902544i \(0.358303\pi\)
\(242\) −7.21922 + 10.9026i −0.464069 + 0.700849i
\(243\) −8.58511 + 13.0114i −0.550735 + 0.834680i
\(244\) −2.43845 5.75058i −0.156106 0.368143i
\(245\) 0 0
\(246\) −0.201201 + 2.74367i −0.0128281 + 0.174930i
\(247\) −6.78456 −0.431691
\(248\) −2.43845 + 13.1158i −0.154842 + 0.832853i
\(249\) 22.8078 12.8078i 1.44538 0.811659i
\(250\) 0 0
\(251\) 18.7033 1.18054 0.590272 0.807205i \(-0.299021\pi\)
0.590272 + 0.807205i \(0.299021\pi\)
\(252\) −17.9288 2.64376i −1.12941 0.166541i
\(253\) 0.492423i 0.0309583i
\(254\) 11.7915 17.8078i 0.739863 1.11736i
\(255\) 0 0
\(256\) −0.534565 15.9911i −0.0334103 0.999442i
\(257\) 30.4924 1.90207 0.951033 0.309091i \(-0.100025\pi\)
0.951033 + 0.309091i \(0.100025\pi\)
\(258\) 18.9010 + 1.38607i 1.17673 + 0.0862929i
\(259\) 15.4741i 0.961512i
\(260\) 0 0
\(261\) 8.00000 + 4.87689i 0.495188 + 0.301872i
\(262\) 4.26324 6.43845i 0.263384 0.397769i
\(263\) 23.7917i 1.46706i −0.679656 0.733531i \(-0.737871\pi\)
0.679656 0.733531i \(-0.262129\pi\)
\(264\) 2.08912 + 6.14219i 0.128576 + 0.378026i
\(265\) 0 0
\(266\) 4.71659 + 3.12311i 0.289193 + 0.191490i
\(267\) −15.4741 + 8.68951i −0.946998 + 0.531789i
\(268\) 3.39228 + 8.00000i 0.207217 + 0.488678i
\(269\) 14.0000i 0.853595i −0.904347 0.426798i \(-0.859642\pi\)
0.904347 0.426798i \(-0.140358\pi\)
\(270\) 0 0
\(271\) 15.3110i 0.930080i 0.885290 + 0.465040i \(0.153960\pi\)
−0.885290 + 0.465040i \(0.846040\pi\)
\(272\) −5.56155 + 5.75058i −0.337219 + 0.348680i
\(273\) 23.3693 13.1231i 1.41438 0.794246i
\(274\) −6.43845 + 9.72350i −0.388961 + 0.587418i
\(275\) 0 0
\(276\) −1.01909 0.787776i −0.0613418 0.0474186i
\(277\) 23.3693i 1.40413i −0.712115 0.702063i \(-0.752262\pi\)
0.712115 0.702063i \(-0.247738\pi\)
\(278\) 20.6847 + 13.6964i 1.24058 + 0.821457i
\(279\) 12.0818 + 7.36520i 0.723318 + 0.440943i
\(280\) 0 0
\(281\) 13.6155i 0.812234i 0.913821 + 0.406117i \(0.133118\pi\)
−0.913821 + 0.406117i \(0.866882\pi\)
\(282\) −0.541105 + 7.37874i −0.0322223 + 0.439398i
\(283\) −23.2111 −1.37976 −0.689879 0.723925i \(-0.742336\pi\)
−0.689879 + 0.723925i \(0.742336\pi\)
\(284\) −2.64861 6.24621i −0.157166 0.370644i
\(285\) 0 0
\(286\) −8.00000 5.29723i −0.473050 0.313232i
\(287\) 3.39228i 0.200240i
\(288\) −16.0536 5.50276i −0.945970 0.324253i
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 9.06134 5.08842i 0.531185 0.298289i
\(292\) 15.1838 6.43845i 0.888562 0.376782i
\(293\) −2.49242 −0.145609 −0.0728044 0.997346i \(-0.523195\pi\)
−0.0728044 + 0.997346i \(0.523195\pi\)
\(294\) −5.18660 0.380349i −0.302489 0.0221824i
\(295\) 0 0
\(296\) −2.64861 + 14.2462i −0.153948 + 0.828044i
\(297\) 6.87689 + 0.246211i 0.399038 + 0.0142866i
\(298\) 16.5081 + 10.9309i 0.956286 + 0.633208i
\(299\) 1.90495 0.110166
\(300\) 0 0
\(301\) 23.3693 1.34699
\(302\) −8.68466 5.75058i −0.499746 0.330908i
\(303\) −1.32431 + 0.743668i −0.0760794 + 0.0427226i
\(304\) 3.80776 + 3.68260i 0.218390 + 0.211212i
\(305\) 0 0
\(306\) 3.60245 + 7.68260i 0.205938 + 0.439185i
\(307\) 11.1293 0.635184 0.317592 0.948227i \(-0.397126\pi\)
0.317592 + 0.948227i \(0.397126\pi\)
\(308\) 3.12311 + 7.36520i 0.177955 + 0.419671i
\(309\) −8.31534 14.8078i −0.473043 0.842384i
\(310\) 0 0
\(311\) 20.7713 1.17783 0.588916 0.808194i \(-0.299555\pi\)
0.588916 + 0.808194i \(0.299555\pi\)
\(312\) 23.7612 8.08179i 1.34521 0.457541i
\(313\) 22.4924i 1.27135i −0.771958 0.635673i \(-0.780722\pi\)
0.771958 0.635673i \(-0.219278\pi\)
\(314\) 3.97292 + 2.63068i 0.224205 + 0.148458i
\(315\) 0 0
\(316\) −14.9309 + 6.33122i −0.839927 + 0.356159i
\(317\) −16.7386 −0.940135 −0.470068 0.882630i \(-0.655770\pi\)
−0.470068 + 0.882630i \(0.655770\pi\)
\(318\) −29.9166 2.19387i −1.67764 0.123026i
\(319\) 4.13595i 0.231569i
\(320\) 0 0
\(321\) 4.56155 2.56155i 0.254601 0.142972i
\(322\) −1.32431 0.876894i −0.0738007 0.0488674i
\(323\) 2.64861i 0.147373i
\(324\) −11.5112 + 13.8381i −0.639510 + 0.768783i
\(325\) 0 0
\(326\) 12.2448 18.4924i 0.678178 1.02420i
\(327\) −0.743668 1.32431i −0.0411249 0.0732343i
\(328\) −0.580639 + 3.12311i −0.0320604 + 0.172445i
\(329\) 9.12311i 0.502973i
\(330\) 0 0
\(331\) 3.22925i 0.177496i −0.996054 0.0887479i \(-0.971713\pi\)
0.996054 0.0887479i \(-0.0282865\pi\)
\(332\) 27.8078 11.7915i 1.52615 0.647141i
\(333\) 13.1231 + 8.00000i 0.719142 + 0.438397i
\(334\) 10.6847 + 7.07488i 0.584638 + 0.387120i
\(335\) 0 0
\(336\) −20.2389 5.31946i −1.10412 0.290200i
\(337\) 1.50758i 0.0821230i 0.999157 + 0.0410615i \(0.0130740\pi\)
−0.999157 + 0.0410615i \(0.986926\pi\)
\(338\) −10.3423 + 15.6192i −0.562549 + 0.849574i
\(339\) 11.8730 + 21.1431i 0.644852 + 1.14834i
\(340\) 0 0
\(341\) 6.24621i 0.338251i
\(342\) 5.08706 2.38537i 0.275077 0.128986i
\(343\) 14.7304 0.795367
\(344\) 21.5150 + 4.00000i 1.16001 + 0.215666i
\(345\) 0 0
\(346\) −1.56155 + 2.35829i −0.0839496 + 0.126783i
\(347\) 22.6305i 1.21487i 0.794370 + 0.607434i \(0.207801\pi\)
−0.794370 + 0.607434i \(0.792199\pi\)
\(348\) 8.55950 + 6.61668i 0.458837 + 0.354691i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0.952473 26.6034i 0.0508392 1.41998i
\(352\) 1.61463 + 7.31534i 0.0860599 + 0.389909i
\(353\) 20.2462 1.07760 0.538799 0.842435i \(-0.318878\pi\)
0.538799 + 0.842435i \(0.318878\pi\)
\(354\) −34.5669 2.53489i −1.83721 0.134728i
\(355\) 0 0
\(356\) −18.8664 + 8.00000i −0.999915 + 0.423999i
\(357\) 5.12311 + 9.12311i 0.271144 + 0.482846i
\(358\) 7.81855 11.8078i 0.413223 0.624060i
\(359\) −21.5150 −1.13552 −0.567758 0.823195i \(-0.692189\pi\)
−0.567758 + 0.823195i \(0.692189\pi\)
\(360\) 0 0
\(361\) 17.2462 0.907695
\(362\) −9.56155 + 14.4401i −0.502544 + 0.758954i
\(363\) 7.84144 + 13.9638i 0.411569 + 0.732912i
\(364\) 28.4924 12.0818i 1.49341 0.633258i
\(365\) 0 0
\(366\) −7.62953 0.559496i −0.398802 0.0292453i
\(367\) −10.9663 −0.572436 −0.286218 0.958165i \(-0.592398\pi\)
−0.286218 + 0.958165i \(0.592398\pi\)
\(368\) −1.06913 1.03399i −0.0557323 0.0539003i
\(369\) 2.87689 + 1.75379i 0.149765 + 0.0912986i
\(370\) 0 0
\(371\) −36.9890 −1.92038
\(372\) 12.9268 + 9.99267i 0.670221 + 0.518096i
\(373\) 9.12311i 0.472377i −0.971707 0.236188i \(-0.924102\pi\)
0.971707 0.236188i \(-0.0758982\pi\)
\(374\) 2.06798 3.12311i 0.106932 0.161492i
\(375\) 0 0
\(376\) −1.56155 + 8.39919i −0.0805309 + 0.433155i
\(377\) −16.0000 −0.824042
\(378\) −12.9084 + 18.0561i −0.663935 + 0.928704i
\(379\) 18.7033i 0.960725i −0.877070 0.480363i \(-0.840505\pi\)
0.877070 0.480363i \(-0.159495\pi\)
\(380\) 0 0
\(381\) −12.8078 22.8078i −0.656162 1.16848i
\(382\) −19.4470 + 29.3693i −0.994995 + 1.50266i
\(383\) 15.1022i 0.771688i −0.922564 0.385844i \(-0.873910\pi\)
0.922564 0.385844i \(-0.126090\pi\)
\(384\) −17.7224 8.36154i −0.904394 0.426698i
\(385\) 0 0
\(386\) −0.290319 0.192236i −0.0147769 0.00978455i
\(387\) 12.0818 19.8188i 0.614152 1.00745i
\(388\) 11.0478 4.68466i 0.560867 0.237827i
\(389\) 20.7386i 1.05149i 0.850642 + 0.525745i \(0.176213\pi\)
−0.850642 + 0.525745i \(0.823787\pi\)
\(390\) 0 0
\(391\) 0.743668i 0.0376089i
\(392\) −5.90388 1.09763i −0.298191 0.0554388i
\(393\) −4.63068 8.24621i −0.233587 0.415966i
\(394\) 3.31534 5.00691i 0.167024 0.252244i
\(395\) 0 0
\(396\) 7.86084 + 1.15915i 0.395022 + 0.0582495i
\(397\) 14.8769i 0.746650i −0.927701 0.373325i \(-0.878218\pi\)
0.927701 0.373325i \(-0.121782\pi\)
\(398\) −6.43845 4.26324i −0.322730 0.213697i
\(399\) 6.04090 3.39228i 0.302423 0.169827i
\(400\) 0 0
\(401\) 24.0000i 1.19850i 0.800561 + 0.599251i \(0.204535\pi\)
−0.800561 + 0.599251i \(0.795465\pi\)
\(402\) 10.6139 + 0.778351i 0.529375 + 0.0388206i
\(403\) −24.1636 −1.20367
\(404\) −1.61463 + 0.684658i −0.0803307 + 0.0340630i
\(405\) 0 0
\(406\) 11.1231 + 7.36520i 0.552030 + 0.365529i
\(407\) 6.78456i 0.336298i
\(408\) 3.15504 + 9.27608i 0.156198 + 0.459235i
\(409\) −25.3693 −1.25443 −0.627216 0.778845i \(-0.715806\pi\)
−0.627216 + 0.778845i \(0.715806\pi\)
\(410\) 0 0
\(411\) 6.99337 + 12.4536i 0.344957 + 0.614292i
\(412\) −7.65552 18.0540i −0.377161 0.889456i
\(413\) −42.7386 −2.10303
\(414\) −1.42833 + 0.669757i −0.0701984 + 0.0329167i
\(415\) 0 0
\(416\) 28.2995 6.24621i 1.38750 0.306246i
\(417\) 26.4924 14.8769i 1.29734 0.728525i
\(418\) −2.06798 1.36932i −0.101148 0.0669755i
\(419\) −7.36520 −0.359814 −0.179907 0.983684i \(-0.557580\pi\)
−0.179907 + 0.983684i \(0.557580\pi\)
\(420\) 0 0
\(421\) −25.3693 −1.23642 −0.618212 0.786011i \(-0.712143\pi\)
−0.618212 + 0.786011i \(0.712143\pi\)
\(422\) −19.8078 13.1158i −0.964227 0.638466i
\(423\) 7.73704 + 4.71659i 0.376188 + 0.229328i
\(424\) −34.0540 6.33122i −1.65381 0.307471i
\(425\) 0 0
\(426\) −8.28711 0.607718i −0.401512 0.0294440i
\(427\) −9.43318 −0.456503
\(428\) 5.56155 2.35829i 0.268828 0.113992i
\(429\) −10.2462 + 5.75379i −0.494692 + 0.277796i
\(430\) 0 0
\(431\) −16.6354 −0.801297 −0.400648 0.916232i \(-0.631215\pi\)
−0.400648 + 0.916232i \(0.631215\pi\)
\(432\) −14.9747 + 14.4139i −0.720468 + 0.693488i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) 16.7984 + 11.1231i 0.806348 + 0.533926i
\(435\) 0 0
\(436\) −0.684658 1.61463i −0.0327892 0.0773266i
\(437\) 0.492423 0.0235558
\(438\) 1.47729 20.1449i 0.0705875 0.962561i
\(439\) 9.27015i 0.442440i −0.975224 0.221220i \(-0.928996\pi\)
0.975224 0.221220i \(-0.0710039\pi\)
\(440\) 0 0
\(441\) −3.31534 + 5.43845i −0.157873 + 0.258974i
\(442\) −12.0818 8.00000i −0.574672 0.380521i
\(443\) 16.5896i 0.788195i −0.919069 0.394097i \(-0.871057\pi\)
0.919069 0.394097i \(-0.128943\pi\)
\(444\) 14.0409 + 10.8539i 0.666351 + 0.515105i
\(445\) 0 0
\(446\) −6.49424 + 9.80776i −0.307511 + 0.464411i
\(447\) 21.1431 11.8730i 1.00004 0.561573i
\(448\) −22.5490 8.68466i −1.06534 0.410312i
\(449\) 27.3693i 1.29164i 0.763491 + 0.645819i \(0.223484\pi\)
−0.763491 + 0.645819i \(0.776516\pi\)
\(450\) 0 0
\(451\) 1.48734i 0.0700359i
\(452\) 10.9309 + 25.7782i 0.514145 + 1.21250i
\(453\) −11.1231 + 6.24621i −0.522609 + 0.293473i
\(454\) −25.8078 17.0887i −1.21122 0.802012i
\(455\) 0 0
\(456\) 6.14219 2.08912i 0.287634 0.0978319i
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) 12.6847 19.1567i 0.592715 0.895133i
\(459\) 10.3857 + 0.371834i 0.484761 + 0.0173557i
\(460\) 0 0
\(461\) 41.8617i 1.94970i 0.222872 + 0.974848i \(0.428457\pi\)
−0.222872 + 0.974848i \(0.571543\pi\)
\(462\) 9.77172 + 0.716589i 0.454622 + 0.0333387i
\(463\) −3.02045 −0.140372 −0.0701861 0.997534i \(-0.522359\pi\)
−0.0701861 + 0.997534i \(0.522359\pi\)
\(464\) 8.97983 + 8.68466i 0.416878 + 0.403175i
\(465\) 0 0
\(466\) 7.80776 11.7915i 0.361688 0.546229i
\(467\) 2.27678i 0.105357i −0.998612 0.0526784i \(-0.983224\pi\)
0.998612 0.0526784i \(-0.0167758\pi\)
\(468\) 4.48419 30.4098i 0.207282 1.40569i
\(469\) 13.1231 0.605969
\(470\) 0 0
\(471\) 5.08842 2.85742i 0.234462 0.131663i
\(472\) −39.3473 7.31534i −1.81111 0.336716i
\(473\) −10.2462 −0.471121
\(474\) −1.45268 + 19.8094i −0.0667239 + 0.909876i
\(475\) 0 0
\(476\) 4.71659 + 11.1231i 0.216184 + 0.509827i
\(477\) −19.1231 + 31.3693i −0.875587 + 1.43630i
\(478\) −13.5691 + 20.4924i −0.620637 + 0.937302i
\(479\) −25.6509 −1.17202 −0.586010 0.810304i \(-0.699302\pi\)
−0.586010 + 0.810304i \(0.699302\pi\)
\(480\) 0 0
\(481\) −26.2462 −1.19672
\(482\) 10.4384 15.7644i 0.475458 0.718048i
\(483\) −1.69614 + 0.952473i −0.0771771 + 0.0433390i
\(484\) 7.21922 + 17.0251i 0.328147 + 0.773866i
\(485\) 0 0
\(486\) 8.63928 + 20.2821i 0.391886 + 0.920014i
\(487\) −25.2791 −1.14550 −0.572752 0.819728i \(-0.694124\pi\)
−0.572752 + 0.819728i \(0.694124\pi\)
\(488\) −8.68466 1.61463i −0.393136 0.0730907i
\(489\) −13.3002 23.6847i −0.601455 1.07106i
\(490\) 0 0
\(491\) 26.9752 1.21737 0.608687 0.793410i \(-0.291696\pi\)
0.608687 + 0.793410i \(0.291696\pi\)
\(492\) 3.07810 + 2.37944i 0.138771 + 0.107273i
\(493\) 6.24621i 0.281315i
\(494\) −5.29723 + 8.00000i −0.238334 + 0.359937i
\(495\) 0 0
\(496\) 13.5616 + 13.1158i 0.608932 + 0.588916i
\(497\) −10.2462 −0.459605
\(498\) 2.70552 36.8937i 0.121237 1.65325i
\(499\) 32.2725i 1.44471i −0.691521 0.722357i \(-0.743059\pi\)
0.691521 0.722357i \(-0.256941\pi\)
\(500\) 0 0
\(501\) 13.6847 7.68466i 0.611385 0.343325i
\(502\) 14.6031 22.0540i 0.651769 0.984317i
\(503\) 14.3586i 0.640217i 0.947381 + 0.320109i \(0.103719\pi\)
−0.947381 + 0.320109i \(0.896281\pi\)
\(504\) −17.1158 + 19.0765i −0.762397 + 0.849736i
\(505\) 0 0
\(506\) 0.580639 + 0.384472i 0.0258125 + 0.0170919i
\(507\) 11.2337 + 20.0047i 0.498907 + 0.888442i
\(508\) −11.7915 27.8078i −0.523162 1.23377i
\(509\) 11.1231i 0.493023i −0.969140 0.246511i \(-0.920716\pi\)
0.969140 0.246511i \(-0.0792843\pi\)
\(510\) 0 0
\(511\) 24.9073i 1.10183i
\(512\) −19.2732 11.8551i −0.851763 0.523927i
\(513\) 0.246211 6.87689i 0.0108705 0.303622i
\(514\) 23.8078 35.9551i 1.05012 1.58591i
\(515\) 0 0
\(516\) 16.3919 21.2049i 0.721612 0.933494i
\(517\) 4.00000i 0.175920i
\(518\) 18.2462 + 12.0818i 0.801692 + 0.530843i
\(519\) 1.69614 + 3.02045i 0.0744523 + 0.132583i
\(520\) 0 0
\(521\) 38.2462i 1.67560i −0.545980 0.837798i \(-0.683842\pi\)
0.545980 0.837798i \(-0.316158\pi\)
\(522\) 11.9968 5.62541i 0.525085 0.246218i
\(523\) 35.2929 1.54325 0.771625 0.636077i \(-0.219444\pi\)
0.771625 + 0.636077i \(0.219444\pi\)
\(524\) −4.26324 10.0540i −0.186241 0.439210i
\(525\) 0 0
\(526\) −28.0540 18.5760i −1.22321 0.809954i
\(527\) 9.43318i 0.410916i
\(528\) 8.87368 + 2.33230i 0.386177 + 0.101500i
\(529\) 22.8617 0.993989
\(530\) 0 0
\(531\) −22.0956 + 36.2454i −0.958868 + 1.57292i
\(532\) 7.36520 3.12311i 0.319322 0.135404i
\(533\) −5.75379 −0.249224
\(534\) −1.83558 + 25.0308i −0.0794333 + 1.08319i
\(535\) 0 0
\(536\) 12.0818 + 2.24621i 0.521854 + 0.0970215i
\(537\) −8.49242 15.1231i −0.366475 0.652610i
\(538\) −16.5081 10.9309i −0.711713 0.471263i
\(539\) 2.81164 0.121106
\(540\) 0 0
\(541\) −26.9848 −1.16017 −0.580085 0.814556i \(-0.696980\pi\)
−0.580085 + 0.814556i \(0.696980\pi\)
\(542\) 18.0540 + 11.9545i 0.775485 + 0.513490i
\(543\) 10.3857 + 18.4945i 0.445691 + 0.793676i
\(544\) 2.43845 + 11.0478i 0.104548 + 0.473671i
\(545\) 0 0
\(546\) 2.77214 37.8021i 0.118637 1.61778i
\(547\) 5.83209 0.249362 0.124681 0.992197i \(-0.460209\pi\)
0.124681 + 0.992197i \(0.460209\pi\)
\(548\) 6.43845 + 15.1838i 0.275037 + 0.648618i
\(549\) −4.87689 + 8.00000i −0.208141 + 0.341432i
\(550\) 0 0
\(551\) −4.13595 −0.176197
\(552\) −1.72458 + 0.586575i −0.0734031 + 0.0249663i
\(553\) 24.4924i 1.04152i
\(554\) −27.5559 18.2462i −1.17074 0.775207i
\(555\) 0 0
\(556\) 32.3002 13.6964i 1.36983 0.580858i
\(557\) 36.2462 1.53580 0.767901 0.640569i \(-0.221301\pi\)
0.767901 + 0.640569i \(0.221301\pi\)
\(558\) 18.1178 8.49563i 0.766989 0.359649i
\(559\) 39.6377i 1.67649i
\(560\) 0 0
\(561\) −2.24621 4.00000i −0.0948351 0.168880i
\(562\) 16.0547 + 10.6307i 0.677227 + 0.448428i
\(563\) 7.90007i 0.332948i −0.986046 0.166474i \(-0.946762\pi\)
0.986046 0.166474i \(-0.0532382\pi\)
\(564\) 8.27814 + 6.39919i 0.348573 + 0.269455i
\(565\) 0 0
\(566\) −18.1227 + 27.3693i −0.761753 + 1.15042i
\(567\) 12.4536 + 24.1636i 0.523003 + 1.01478i
\(568\) −9.43318 1.75379i −0.395807 0.0735873i
\(569\) 13.1231i 0.550149i 0.961423 + 0.275075i \(0.0887026\pi\)
−0.961423 + 0.275075i \(0.911297\pi\)
\(570\) 0 0
\(571\) 33.0161i 1.38168i 0.723007 + 0.690841i \(0.242759\pi\)
−0.723007 + 0.690841i \(0.757241\pi\)
\(572\) −12.4924 + 5.29723i −0.522334 + 0.221488i
\(573\) 21.1231 + 37.6155i 0.882430 + 1.57141i
\(574\) 4.00000 + 2.64861i 0.166957 + 0.110551i
\(575\) 0 0
\(576\) −19.0229 + 14.6332i −0.792620 + 0.609716i
\(577\) 32.2462i 1.34243i 0.741264 + 0.671214i \(0.234227\pi\)
−0.741264 + 0.671214i \(0.765773\pi\)
\(578\) −10.1501 + 15.3289i −0.422188 + 0.637599i
\(579\) −0.371834 + 0.208805i −0.0154529 + 0.00867762i
\(580\) 0 0
\(581\) 45.6155i 1.89245i
\(582\) 1.07488 14.6576i 0.0445554 0.607576i
\(583\) 16.2177 0.671670
\(584\) 4.26324 22.9309i 0.176414 0.948886i
\(585\) 0 0
\(586\) −1.94602 + 2.93893i −0.0803895 + 0.121406i
\(587\) 1.85917i 0.0767362i −0.999264 0.0383681i \(-0.987784\pi\)
0.999264 0.0383681i \(-0.0122159\pi\)
\(588\) −4.49806 + 5.81880i −0.185497 + 0.239963i
\(589\) −6.24621 −0.257371
\(590\) 0 0
\(591\) −3.60109 6.41273i −0.148129 0.263784i
\(592\) 14.7304 + 14.2462i 0.605416 + 0.585516i
\(593\) −8.24621 −0.338631 −0.169316 0.985562i \(-0.554156\pi\)
−0.169316 + 0.985562i \(0.554156\pi\)
\(594\) 5.65964 7.91664i 0.232218 0.324823i
\(595\) 0 0
\(596\) 25.7782 10.9309i 1.05592 0.447746i
\(597\) −8.24621 + 4.63068i −0.337495 + 0.189521i
\(598\) 1.48734 2.24621i 0.0608217 0.0918544i
\(599\) 44.1912 1.80560 0.902802 0.430056i \(-0.141506\pi\)
0.902802 + 0.430056i \(0.141506\pi\)
\(600\) 0 0
\(601\) 23.1231 0.943211 0.471606 0.881810i \(-0.343675\pi\)
0.471606 + 0.881810i \(0.343675\pi\)
\(602\) 18.2462 27.5559i 0.743660 1.12309i
\(603\) 6.78456 11.1293i 0.276289 0.453221i
\(604\) −13.5616 + 5.75058i −0.551812 + 0.233988i
\(605\) 0 0
\(606\) −0.157093 + 2.14219i −0.00638148 + 0.0870206i
\(607\) 4.50778 0.182965 0.0914827 0.995807i \(-0.470839\pi\)
0.0914827 + 0.995807i \(0.470839\pi\)
\(608\) 7.31534 1.61463i 0.296676 0.0654817i
\(609\) 14.2462 8.00000i 0.577286 0.324176i
\(610\) 0 0
\(611\) −15.4741 −0.626014
\(612\) 11.8716 + 1.75058i 0.479882 + 0.0707629i
\(613\) 9.12311i 0.368479i 0.982881 + 0.184239i \(0.0589822\pi\)
−0.982881 + 0.184239i \(0.941018\pi\)
\(614\) 8.68951 13.1231i 0.350680 0.529605i
\(615\) 0 0
\(616\) 11.1231 + 2.06798i 0.448163 + 0.0833211i
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) −23.9530 1.75654i −0.963529 0.0706584i
\(619\) 28.1365i 1.13090i 0.824782 + 0.565451i \(0.191298\pi\)
−0.824782 + 0.565451i \(0.808702\pi\)
\(620\) 0 0
\(621\) −0.0691303 + 1.93087i −0.00277410 + 0.0774831i
\(622\) 16.2177 24.4924i 0.650272 0.982057i
\(623\) 30.9481i 1.23991i
\(624\) 9.02255 34.3280i 0.361191 1.37422i
\(625\) 0 0
\(626\) −26.5219 17.5616i −1.06003 0.701901i
\(627\) −2.64861 + 1.48734i −0.105775 + 0.0593985i
\(628\) 6.20393 2.63068i 0.247564 0.104976i
\(629\) 10.2462i 0.408543i
\(630\) 0 0
\(631\) 39.8007i 1.58444i 0.610235 + 0.792220i \(0.291075\pi\)
−0.610235 + 0.792220i \(0.708925\pi\)
\(632\) −4.19224 + 22.5490i −0.166758 + 0.896949i
\(633\) −25.3693 + 14.2462i −1.00834 + 0.566236i
\(634\) −13.0691 + 19.7373i −0.519041 + 0.783869i
\(635\) 0 0
\(636\) −25.9451 + 33.5632i −1.02879 + 1.33087i
\(637\) 10.8769i 0.430958i
\(638\) −4.87689 3.22925i −0.193078 0.127847i
\(639\) −5.29723 + 8.68951i −0.209555 + 0.343752i
\(640\) 0 0
\(641\) 6.38447i 0.252171i −0.992019 0.126086i \(-0.959759\pi\)
0.992019 0.126086i \(-0.0402414\pi\)
\(642\) 0.541105 7.37874i 0.0213557 0.291216i
\(643\) −3.60109 −0.142013 −0.0710065 0.997476i \(-0.522621\pi\)
−0.0710065 + 0.997476i \(0.522621\pi\)
\(644\) −2.06798 + 0.876894i −0.0814896 + 0.0345545i
\(645\) 0 0
\(646\) −3.12311 2.06798i −0.122877 0.0813634i
\(647\) 36.6172i 1.43957i 0.694197 + 0.719786i \(0.255760\pi\)
−0.694197 + 0.719786i \(0.744240\pi\)
\(648\) 7.32948 + 24.3778i 0.287929 + 0.957652i
\(649\) 18.7386 0.735556
\(650\) 0 0
\(651\) 21.5150 12.0818i 0.843238 0.473523i
\(652\) −12.2448 28.8769i −0.479544 1.13091i
\(653\) 38.9848 1.52559 0.762797 0.646638i \(-0.223825\pi\)
0.762797 + 0.646638i \(0.223825\pi\)
\(654\) −2.14219 0.157093i −0.0837663 0.00614283i
\(655\) 0 0
\(656\) 3.22925 + 3.12311i 0.126081 + 0.121937i
\(657\) −21.1231 12.8769i −0.824091 0.502375i
\(658\) 10.7575 + 7.12311i 0.419370 + 0.277688i
\(659\) −24.7442 −0.963898 −0.481949 0.876199i \(-0.660071\pi\)
−0.481949 + 0.876199i \(0.660071\pi\)
\(660\) 0 0
\(661\) 28.1080 1.09327 0.546636 0.837370i \(-0.315908\pi\)
0.546636 + 0.837370i \(0.315908\pi\)
\(662\) −3.80776 2.52132i −0.147993 0.0979940i
\(663\) −15.4741 + 8.68951i −0.600963 + 0.337473i
\(664\) 7.80776 41.9960i 0.303000 1.62976i
\(665\) 0 0
\(666\) 19.6794 9.22786i 0.762561 0.357572i
\(667\) 1.16128 0.0449648
\(668\) 16.6847 7.07488i 0.645549 0.273735i
\(669\) 7.05398 + 12.5616i 0.272722 + 0.485658i
\(670\) 0 0
\(671\) 4.13595 0.159667
\(672\) −22.0745 + 19.7113i −0.851541 + 0.760381i
\(673\) 22.4924i 0.867019i 0.901149 + 0.433510i \(0.142725\pi\)
−0.901149 + 0.433510i \(0.857275\pi\)
\(674\) 1.77766 + 1.17708i 0.0684727 + 0.0453395i
\(675\) 0 0
\(676\) 10.3423 + 24.3903i 0.397782 + 0.938087i
\(677\) 1.50758 0.0579409 0.0289705 0.999580i \(-0.490777\pi\)
0.0289705 + 0.999580i \(0.490777\pi\)
\(678\) 34.2010 + 2.50806i 1.31348 + 0.0963215i
\(679\) 18.1227i 0.695485i
\(680\) 0 0
\(681\) −33.0540 + 18.5616i −1.26663 + 0.711280i
\(682\) −7.36520 4.87689i −0.282028 0.186746i
\(683\) 7.90007i 0.302288i 0.988512 + 0.151144i \(0.0482957\pi\)
−0.988512 + 0.151144i \(0.951704\pi\)
\(684\) 1.15915 7.86084i 0.0443212 0.300567i
\(685\) 0 0
\(686\) 11.5012 17.3693i 0.439116 0.663164i
\(687\) −13.7779 24.5354i −0.525661 0.936085i
\(688\) 21.5150 22.2462i 0.820251 0.848129i
\(689\) 62.7386i 2.39015i
\(690\) 0 0
\(691\) 18.2857i 0.695621i −0.937565 0.347811i \(-0.886925\pi\)
0.937565 0.347811i \(-0.113075\pi\)
\(692\) 1.56155 + 3.68260i 0.0593613 + 0.139991i
\(693\) 6.24621 10.2462i 0.237274 0.389221i
\(694\) 26.6847 + 17.6693i 1.01294 + 0.670719i
\(695\) 0 0
\(696\) 14.4851 4.92676i 0.549056 0.186748i
\(697\) 2.24621i 0.0850813i
\(698\) 10.9309 16.5081i 0.413740 0.624839i
\(699\) −8.48071 15.1022i −0.320770 0.571219i
\(700\) 0 0
\(701\) 17.5076i 0.661252i 0.943762 + 0.330626i \(0.107260\pi\)
−0.943762 + 0.330626i \(0.892740\pi\)
\(702\) −30.6256 21.8944i −1.15589 0.826351i
\(703\) −6.78456 −0.255885
\(704\) 9.88653 + 3.80776i 0.372612 + 0.143511i
\(705\) 0 0
\(706\) 15.8078 23.8733i 0.594933 0.898482i
\(707\) 2.64861i 0.0996114i
\(708\) −29.9780 + 38.7803i −1.12664 + 1.45745i
\(709\) −6.49242 −0.243828 −0.121914 0.992541i \(-0.538903\pi\)
−0.121914 + 0.992541i \(0.538903\pi\)
\(710\) 0 0
\(711\) 20.7713 + 12.6624i 0.778985 + 0.474878i
\(712\) −5.29723 + 28.4924i −0.198522 + 1.06780i
\(713\) 1.75379 0.0656799
\(714\) 14.7575 + 1.08221i 0.552285 + 0.0405007i
\(715\) 0 0
\(716\) −7.81855 18.4384i −0.292193 0.689077i
\(717\) 14.7386 + 26.2462i 0.550424 + 0.980183i
\(718\) −16.7984 + 25.3693i −0.626910 + 0.946774i
\(719\) 30.9481 1.15417 0.577086 0.816684i \(-0.304190\pi\)
0.577086 + 0.816684i \(0.304190\pi\)
\(720\) 0 0
\(721\) −29.6155 −1.10294
\(722\) 13.4654 20.3358i 0.501132 0.756821i
\(723\) −11.3381 20.1907i −0.421669 0.750899i
\(724\) 9.56155 + 22.5490i 0.355352 + 0.838025i
\(725\) 0 0
\(726\) 22.5878 + 1.65643i 0.838314 + 0.0614760i
\(727\) 10.9663 0.406717 0.203359 0.979104i \(-0.434814\pi\)
0.203359 + 0.979104i \(0.434814\pi\)
\(728\) 8.00000 43.0299i 0.296500 1.59480i
\(729\) 26.9309 + 1.93087i 0.997440 + 0.0715137i
\(730\) 0 0
\(731\) −15.4741 −0.572329
\(732\) −6.61668 + 8.55950i −0.244560 + 0.316368i
\(733\) 26.8769i 0.992721i −0.868117 0.496360i \(-0.834669\pi\)
0.868117 0.496360i \(-0.165331\pi\)
\(734\) −8.56222 + 12.9309i −0.316037 + 0.477287i
\(735\) 0 0
\(736\) −2.05398 + 0.453349i −0.0757105 + 0.0167107i
\(737\) −5.75379 −0.211944
\(738\) 4.31419 2.02297i 0.158807 0.0744664i
\(739\) 26.9752i 0.992300i −0.868237 0.496150i \(-0.834747\pi\)
0.868237 0.496150i \(-0.165253\pi\)
\(740\) 0 0
\(741\) 5.75379 + 10.2462i 0.211371 + 0.376404i
\(742\) −28.8802 + 43.6155i −1.06022 + 1.60118i
\(743\) 9.80501i 0.359711i −0.983693 0.179856i \(-0.942437\pi\)
0.983693 0.179856i \(-0.0575630\pi\)
\(744\) 21.8757 7.44050i 0.802004 0.272782i
\(745\) 0 0
\(746\) −10.7575 7.12311i −0.393860 0.260795i
\(747\) −38.6852 23.5829i −1.41542 0.862855i
\(748\) −2.06798 4.87689i −0.0756127 0.178317i
\(749\) 9.12311i 0.333351i
\(750\) 0 0
\(751\) 11.5012i 0.419683i −0.977735 0.209842i \(-0.932705\pi\)
0.977735 0.209842i \(-0.0672948\pi\)
\(752\) 8.68466 + 8.39919i 0.316697 + 0.306287i
\(753\) −15.8617 28.2462i −0.578034 1.02935i
\(754\) −12.4924 + 18.8664i −0.454947 + 0.687072i
\(755\) 0 0
\(756\) 11.2122 + 29.3186i 0.407785 + 1.06631i
\(757\) 10.8769i 0.395327i −0.980270 0.197664i \(-0.936665\pi\)
0.980270 0.197664i \(-0.0633354\pi\)
\(758\) −22.0540 14.6031i −0.801036 0.530409i
\(759\) 0.743668 0.417609i 0.0269934 0.0151582i
\(760\) 0 0
\(761\) 31.2311i 1.13212i −0.824362 0.566062i \(-0.808466\pi\)
0.824362 0.566062i \(-0.191534\pi\)
\(762\) −36.8937 2.70552i −1.33652 0.0980108i
\(763\) −2.64861 −0.0958863
\(764\) 19.4470 + 45.8617i 0.703568 + 1.65922i
\(765\) 0 0
\(766\) −17.8078 11.7915i −0.643421 0.426043i
\(767\) 72.4908i 2.61749i
\(768\) −23.6967 + 14.3689i −0.855083 + 0.518492i
\(769\) −38.9848 −1.40583 −0.702915 0.711274i \(-0.748118\pi\)
−0.702915 + 0.711274i \(0.748118\pi\)
\(770\) 0 0
\(771\) −25.8597 46.0504i −0.931315 1.65846i
\(772\) −0.453349 + 0.192236i −0.0163164 + 0.00691872i
\(773\) 0.246211 0.00885560 0.00442780 0.999990i \(-0.498591\pi\)
0.00442780 + 0.999990i \(0.498591\pi\)
\(774\) −13.9361 29.7203i −0.500924 1.06827i
\(775\) 0 0
\(776\) 3.10196 16.6847i 0.111354 0.598944i
\(777\) 23.3693 13.1231i 0.838370 0.470789i
\(778\) 24.4539 + 16.1922i 0.876715 + 0.580520i
\(779\) −1.48734 −0.0532894
\(780\) 0 0
\(781\) 4.49242 0.160752
\(782\) 0.876894 + 0.580639i 0.0313577 + 0.0207636i
\(783\) 0.580639 16.2177i 0.0207503 0.579575i
\(784\) −5.90388 + 6.10454i −0.210853 + 0.218019i