Properties

Label 300.2.e.c.251.2
Level $300$
Weight $2$
Character 300.251
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.e (of order \(2\), degree \(1\), 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(-1.17915 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.c.251.1

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17915 + 0.780776i −0.833783 + 0.552092i
\(3\) 1.51022 + 0.848071i 0.871928 + 0.489634i
\(4\) 0.780776 1.84130i 0.390388 0.920650i
\(5\) 0 0
\(6\) −2.44293 + 0.179147i −0.997322 + 0.0731366i
\(7\) 3.02045i 1.14162i −0.821081 0.570811i \(-0.806629\pi\)
0.821081 0.570811i \(-0.193371\pi\)
\(8\) 0.516994 + 2.78078i 0.182785 + 0.983153i
\(9\) 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 \(0.436021\pi\)
\(12\) 2.74070 2.11862i 0.791172 0.611594i
\(13\) 5.12311 1.42089 0.710447 0.703751i \(-0.248493\pi\)
0.710447 + 0.703751i \(0.248493\pi\)
\(14\) 2.35829 + 3.56155i 0.630281 + 0.951865i
\(15\) 0 0
\(16\) −2.78078 2.87529i −0.695194 0.718822i
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) −3.84130 1.80122i −0.905403 0.424553i
\(19\) 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
\(22\) −1.56155 + 1.03399i −0.332924 + 0.220447i
\(23\) −0.371834 −0.0775328 −0.0387664 0.999248i \(-0.512343\pi\)
−0.0387664 + 0.999248i \(0.512343\pi\)
\(24\) −1.57752 + 4.63804i −0.322010 + 0.946736i
\(25\) 0 0
\(26\) −6.04090 + 4.00000i −1.18472 + 0.784465i
\(27\) 0.185917 + 5.19283i 0.0357798 + 0.999360i
\(28\) −5.56155 2.35829i −1.05103 0.445676i
\(29\) 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 \(0.139220\pi\)
−0.905867 + 0.423562i \(0.860780\pi\)
\(32\) 5.52390 + 1.21922i 0.976497 + 0.215530i
\(33\) 2.00000 + 1.12311i 0.348155 + 0.195508i
\(34\) −1.56155 2.35829i −0.267804 0.404444i
\(35\) 0 0
\(36\) 5.93581 0.875288i 0.989302 0.145881i
\(37\) −5.12311 −0.842233 −0.421117 0.907006i \(-0.638362\pi\)
−0.421117 + 0.907006i \(0.638362\pi\)
\(38\) 1.03399 + 1.56155i 0.167735 + 0.253317i
\(39\) 7.73704 + 4.34475i 1.23892 + 0.695718i
\(40\) 0 0
\(41\) 1.12311i 0.175400i 0.996147 + 0.0876998i \(0.0279516\pi\)
−0.996147 + 0.0876998i \(0.972048\pi\)
\(42\) 0.541105 + 7.37874i 0.0834943 + 1.13856i
\(43\) 7.73704i 1.17989i 0.807445 + 0.589944i \(0.200850\pi\)
−0.807445 + 0.589944i \(0.799150\pi\)
\(44\) 1.03399 2.43845i 0.155879 0.367610i
\(45\) 0 0
\(46\) 0.438447 0.290319i 0.0646455 0.0428052i
\(47\) −3.02045 −0.440578 −0.220289 0.975435i \(-0.570700\pi\)
−0.220289 + 0.975435i \(0.570700\pi\)
\(48\) −1.76115 6.70062i −0.254200 0.967152i
\(49\) −2.12311 −0.303301
\(50\) 0 0
\(51\) −1.69614 + 3.02045i −0.237507 + 0.422947i
\(52\) 4.00000 9.43318i 0.554700 1.30815i
\(53\) 12.2462i 1.68215i −0.540921 0.841073i \(-0.681924\pi\)
0.540921 0.841073i \(-0.318076\pi\)
\(54\) −4.27366 5.97795i −0.581571 0.813495i
\(55\) 0 0
\(56\) 8.39919 1.56155i 1.12239 0.208671i
\(57\) 1.12311 2.00000i 0.148759 0.264906i
\(58\) 2.43845 + 3.68260i 0.320184 + 0.483549i
\(59\) −14.1498 −1.84214 −0.921071 0.389394i \(-0.872685\pi\)
−0.921071 + 0.389394i \(0.872685\pi\)
\(60\) 0 0
\(61\) 3.12311 0.399873 0.199936 0.979809i \(-0.435926\pi\)
0.199936 + 0.979809i \(0.435926\pi\)
\(62\) −3.68260 5.56155i −0.467691 0.706318i
\(63\) 7.73704 4.71659i 0.974775 0.594234i
\(64\) −7.46543 + 2.87529i −0.933179 + 0.359411i
\(65\) 0 0
\(66\) −3.23519 + 0.237246i −0.398224 + 0.0292030i
\(67\) 4.34475i 0.530796i −0.964139 0.265398i \(-0.914497\pi\)
0.964139 0.265398i \(-0.0855034\pi\)
\(68\) 3.68260 + 1.56155i 0.446581 + 0.189366i
\(69\) −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 \(0.435485\pi\)
\(72\) −6.31579 + 5.66664i −0.744323 + 0.667819i
\(73\) −8.24621 −0.965146 −0.482573 0.875856i \(-0.660298\pi\)
−0.482573 + 0.875856i \(0.660298\pi\)
\(74\) 6.04090 4.00000i 0.702240 0.464991i
\(75\) 0 0
\(76\) −2.43845 1.03399i −0.279709 0.118607i
\(77\) 4.00000i 0.455842i
\(78\) −12.5154 + 0.917790i −1.41709 + 0.103919i
\(79\) 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
\(82\) −0.876894 1.32431i −0.0968368 0.146245i
\(83\) −15.1022 −1.65769 −0.828843 0.559481i \(-0.811000\pi\)
−0.828843 + 0.559481i \(0.811000\pi\)
\(84\) −6.39919 8.27814i −0.698209 0.903219i
\(85\) 0 0
\(86\) −6.04090 9.12311i −0.651407 0.983770i
\(87\) 2.64861 4.71659i 0.283961 0.505671i
\(88\) 0.684658 + 3.68260i 0.0729848 + 0.392567i
\(89\) 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
\(92\) −0.290319 + 0.684658i −0.0302679 + 0.0713806i
\(93\) −4.00000 + 7.12311i −0.414781 + 0.738632i
\(94\) 3.56155 2.35829i 0.367346 0.243240i
\(95\) 0 0
\(96\) 7.30834 + 6.52596i 0.745904 + 0.666053i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 2.50345 1.65767i 0.252887 0.167450i
\(99\) 2.06798 + 3.39228i 0.207839 + 0.340937i
\(100\) 0 0
\(101\) 0.876894i 0.0872543i 0.999048 + 0.0436271i \(0.0138914\pi\)
−0.999048 + 0.0436271i \(0.986109\pi\)
\(102\) −0.358294 4.88586i −0.0354764 0.483772i
\(103\) 9.80501i 0.966117i −0.875588 0.483058i \(-0.839526\pi\)
0.875588 0.483058i \(-0.160474\pi\)
\(104\) 2.64861 + 14.2462i 0.259718 + 1.39696i
\(105\) 0 0
\(106\) 9.56155 + 14.4401i 0.928700 + 1.40255i
\(107\) 3.02045 0.291998 0.145999 0.989285i \(-0.453360\pi\)
0.145999 + 0.989285i \(0.453360\pi\)
\(108\) 9.70671 + 3.71211i 0.934029 + 0.357198i
\(109\) −0.876894 −0.0839912 −0.0419956 0.999118i \(-0.513372\pi\)
−0.0419956 + 0.999118i \(0.513372\pi\)
\(110\) 0 0
\(111\) −7.73704 4.34475i −0.734367 0.412386i
\(112\) −8.68466 + 8.39919i −0.820623 + 0.793649i
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0.237246 + 3.23519i 0.0222201 + 0.303003i
\(115\) 0 0
\(116\) −5.75058 2.43845i −0.533928 0.226404i
\(117\) 8.00000 + 13.1231i 0.739600 + 1.21323i
\(118\) 16.6847 11.0478i 1.53595 1.01703i
\(119\) 6.04090 0.553768
\(120\) 0 0
\(121\) −9.24621 −0.840565
\(122\) −3.68260 + 2.43845i −0.333407 + 0.220767i
\(123\) −0.952473 + 1.69614i −0.0858816 + 0.152936i
\(124\) 8.68466 + 3.68260i 0.779905 + 0.330707i
\(125\) 0 0
\(126\) −5.44050 + 11.6024i −0.484679 + 1.03363i
\(127\) 15.1022i 1.34011i 0.742313 + 0.670054i \(0.233729\pi\)
−0.742313 + 0.670054i \(0.766271\pi\)
\(128\) 6.55789 9.21922i 0.579641 0.814872i
\(129\) −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 \(0.423334\pi\)
\(132\) 3.62953 2.80571i 0.315910 0.244205i
\(133\) −4.00000 −0.346844
\(134\) 3.39228 + 5.12311i 0.293049 + 0.442569i
\(135\) 0 0
\(136\) −5.56155 + 1.03399i −0.476899 + 0.0886637i
\(137\) 8.24621i 0.704521i −0.935902 0.352261i \(-0.885413\pi\)
0.935902 0.352261i \(-0.114587\pi\)
\(138\) 0.908365 0.0666131i 0.0773251 0.00567048i
\(139\) 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
\(142\) −4.00000 + 2.64861i −0.335673 + 0.222267i
\(143\) 6.78456 0.567354
\(144\) 3.02287 11.6130i 0.251906 0.967752i
\(145\) 0 0
\(146\) 9.72350 6.43845i 0.804722 0.532850i
\(147\) −3.20636 1.80054i −0.264457 0.148506i
\(148\) −4.00000 + 9.43318i −0.328798 + 0.775402i
\(149\) 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 \(0.0968819\pi\)
−0.954038 + 0.299686i \(0.903118\pi\)
\(152\) 3.68260 0.684658i 0.298698 0.0555331i
\(153\) −5.12311 + 3.12311i −0.414179 + 0.252488i
\(154\) 3.12311 + 4.71659i 0.251667 + 0.380074i
\(155\) 0 0
\(156\) 14.0409 10.8539i 1.12417 0.869010i
\(157\) 3.36932 0.268901 0.134450 0.990920i \(-0.457073\pi\)
0.134450 + 0.990920i \(0.457073\pi\)
\(158\) 6.33122 + 9.56155i 0.503684 + 0.760676i
\(159\) 10.3857 18.4945i 0.823636 1.46671i
\(160\) 0 0
\(161\) 1.12311i 0.0885131i
\(162\) −1.38446 12.6524i −0.108774 0.994067i
\(163\) 15.6829i 1.22838i −0.789159 0.614189i \(-0.789483\pi\)
0.789159 0.614189i \(-0.210517\pi\)
\(164\) 2.06798 + 0.876894i 0.161482 + 0.0684739i
\(165\) 0 0
\(166\) 17.8078 11.7915i 1.38215 0.915196i
\(167\) 9.06134 0.701188 0.350594 0.936528i \(-0.385980\pi\)
0.350594 + 0.936528i \(0.385980\pi\)
\(168\) 14.0090 + 4.76481i 1.08082 + 0.367613i
\(169\) 13.2462 1.01894
\(170\) 0 0
\(171\) 3.39228 2.06798i 0.259414 0.158142i
\(172\) 14.2462 + 6.04090i 1.08626 + 0.460614i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 0.559496 + 7.62953i 0.0424153 + 0.578393i
\(175\) 0 0
\(176\) −3.68260 3.80776i −0.277587 0.287021i
\(177\) −21.3693 12.0000i −1.60622 0.901975i
\(178\) 8.00000 + 12.0818i 0.599625 + 0.905569i
\(179\) −10.0138 −0.748468 −0.374234 0.927334i \(-0.622094\pi\)
−0.374234 + 0.927334i \(0.622094\pi\)
\(180\) 0 0
\(181\) −12.2462 −0.910254 −0.455127 0.890427i \(-0.650406\pi\)
−0.455127 + 0.890427i \(0.650406\pi\)
\(182\) 12.0818 + 18.2462i 0.895562 + 1.35250i
\(183\) 4.71659 + 2.64861i 0.348660 + 0.195791i
\(184\) −0.192236 1.03399i −0.0141718 0.0762266i
\(185\) 0 0
\(186\) −0.844964 11.5223i −0.0619558 0.844856i
\(187\) 2.64861i 0.193686i
\(188\) −2.35829 + 5.56155i −0.171996 + 0.405618i
\(189\) 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 \(0.857248\pi\)
\(192\) −13.7129 1.98889i −0.989645 0.143535i
\(193\) 0.246211 0.0177227 0.00886134 0.999961i \(-0.497179\pi\)
0.00886134 + 0.999961i \(0.497179\pi\)
\(194\) −7.07488 + 4.68466i −0.507947 + 0.336339i
\(195\) 0 0
\(196\) −1.65767 + 3.90928i −0.118405 + 0.279234i
\(197\) 4.24621i 0.302530i 0.988493 + 0.151265i \(0.0483347\pi\)
−0.988493 + 0.151265i \(0.951665\pi\)
\(198\) −5.08706 2.38537i −0.361522 0.169521i
\(199\) 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
\(202\) −0.684658 1.03399i −0.0481724 0.0727511i
\(203\) −9.43318 −0.662079
\(204\) 4.23725 + 5.48140i 0.296667 + 0.383775i
\(205\) 0 0
\(206\) 7.65552 + 11.5616i 0.533385 + 0.805532i
\(207\) −0.580639 0.952473i −0.0403572 0.0662014i
\(208\) −14.2462 14.7304i −0.987797 1.02137i
\(209\) 1.75379i 0.121312i
\(210\) 0 0
\(211\) 16.7984i 1.15645i 0.815878 + 0.578224i \(0.196254\pi\)
−0.815878 + 0.578224i \(0.803746\pi\)
\(212\) −22.5490 9.56155i −1.54867 0.656690i
\(213\) 5.12311 + 2.87689i 0.351029 + 0.197122i
\(214\) −3.56155 + 2.35829i −0.243463 + 0.161210i
\(215\) 0 0
\(216\) −14.3440 + 3.20165i −0.975983 + 0.217845i
\(217\) 14.2462 0.967096
\(218\) 1.03399 0.684658i 0.0700305 0.0463709i
\(219\) −12.4536 6.99337i −0.841538 0.472568i
\(220\) 0 0
\(221\) 10.2462i 0.689235i
\(222\) 12.5154 0.917790i 0.839978 0.0615980i
\(223\) 8.31768i 0.556993i 0.960437 + 0.278496i \(0.0898360\pi\)
−0.960437 + 0.278496i \(0.910164\pi\)
\(224\) 3.68260 16.6847i 0.246054 1.11479i
\(225\) 0 0
\(226\) −10.9309 16.5081i −0.727111 1.09810i
\(227\) −21.8868 −1.45268 −0.726339 0.687337i \(-0.758780\pi\)
−0.726339 + 0.687337i \(0.758780\pi\)
\(228\) −2.80571 3.62953i −0.185812 0.240371i
\(229\) −16.2462 −1.07358 −0.536790 0.843716i \(-0.680363\pi\)
−0.536790 + 0.843716i \(0.680363\pi\)
\(230\) 0 0
\(231\) 3.39228 6.04090i 0.223196 0.397462i
\(232\) 8.68466 1.61463i 0.570176 0.106005i
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) −19.6794 9.22786i −1.28648 0.603244i
\(235\) 0 0
\(236\) −11.0478 + 26.0540i −0.719151 + 1.69597i
\(237\) 6.87689 12.2462i 0.446702 0.795477i
\(238\) −7.12311 + 4.71659i −0.461722 + 0.305731i
\(239\) 17.3790 1.12416 0.562078 0.827084i \(-0.310002\pi\)
0.562078 + 0.827084i \(0.310002\pi\)
\(240\) 0 0
\(241\) 13.3693 0.861193 0.430597 0.902544i \(-0.358303\pi\)
0.430597 + 0.902544i \(0.358303\pi\)
\(242\) 10.9026 7.21922i 0.700849 0.464069i
\(243\) −13.0114 + 8.58511i −0.834680 + 0.550735i
\(244\) 2.43845 5.75058i 0.156106 0.368143i
\(245\) 0 0
\(246\) −0.201201 2.74367i −0.0128281 0.174930i
\(247\) 6.78456i 0.431691i
\(248\) −13.1158 + 2.43845i −0.832853 + 0.154842i
\(249\) −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 \(0.299021\pi\)
\(252\) −2.64376 17.9288i −0.166541 1.12941i
\(253\) −0.492423 −0.0309583
\(254\) −11.7915 17.8078i −0.739863 1.11736i
\(255\) 0 0
\(256\) −0.534565 + 15.9911i −0.0334103 + 0.999442i
\(257\) 30.4924i 1.90207i 0.309091 + 0.951033i \(0.399975\pi\)
−0.309091 + 0.951033i \(0.600025\pi\)
\(258\) −1.38607 18.9010i −0.0862929 1.17673i
\(259\) 15.4741i 0.961512i
\(260\) 0 0
\(261\) 8.00000 4.87689i 0.495188 0.301872i
\(262\) −6.43845 + 4.26324i −0.397769 + 0.263384i
\(263\) 23.7917 1.46706 0.733531 0.679656i \(-0.237871\pi\)
0.733531 + 0.679656i \(0.237871\pi\)
\(264\) −2.08912 + 6.14219i −0.128576 + 0.378026i
\(265\) 0 0
\(266\) 4.71659 3.12311i 0.289193 0.191490i
\(267\) 8.68951 15.4741i 0.531789 0.946998i
\(268\) −8.00000 3.39228i −0.488678 0.207217i
\(269\) 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 \(-0.846040\pi\)
0.885290 0.465040i \(-0.153960\pi\)
\(272\) 5.75058 5.56155i 0.348680 0.337219i
\(273\) 13.1231 23.3693i 0.794246 1.41438i
\(274\) 6.43845 + 9.72350i 0.388961 + 0.587418i
\(275\) 0 0
\(276\) −1.01909 + 0.787776i −0.0613418 + 0.0474186i
\(277\) −23.3693 −1.40413 −0.702063 0.712115i \(-0.747738\pi\)
−0.702063 + 0.712115i \(0.747738\pi\)
\(278\) −13.6964 20.6847i −0.821457 1.24058i
\(279\) −12.0818 + 7.36520i −0.723318 + 0.440943i
\(280\) 0 0
\(281\) 13.6155i 0.812234i −0.913821 0.406117i \(-0.866882\pi\)
0.913821 0.406117i \(-0.133118\pi\)
\(282\) 7.37874 0.541105i 0.439398 0.0322223i
\(283\) 23.2111i 1.37976i 0.723925 + 0.689879i \(0.242336\pi\)
−0.723925 + 0.689879i \(0.757664\pi\)
\(284\) 2.64861 6.24621i 0.157166 0.370644i
\(285\) 0 0
\(286\) −8.00000 + 5.29723i −0.473050 + 0.313232i
\(287\) 3.39228 0.200240
\(288\) 5.50276 + 16.0536i 0.324253 + 0.945970i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 9.06134 + 5.08842i 0.531185 + 0.298289i
\(292\) −6.43845 + 15.1838i −0.376782 + 0.888562i
\(293\) 2.49242i 0.145609i 0.997346 + 0.0728044i \(0.0231949\pi\)
−0.997346 + 0.0728044i \(0.976805\pi\)
\(294\) 5.18660 0.380349i 0.302489 0.0221824i
\(295\) 0 0
\(296\) −2.64861 14.2462i −0.153948 0.828044i
\(297\) 0.246211 + 6.87689i 0.0142866 + 0.399038i
\(298\) −10.9309 16.5081i −0.633208 0.956286i
\(299\) −1.90495 −0.110166
\(300\) 0 0
\(301\) 23.3693 1.34699
\(302\) −5.75058 8.68466i −0.330908 0.499746i
\(303\) −0.743668 + 1.32431i −0.0427226 + 0.0760794i
\(304\) −3.80776 + 3.68260i −0.218390 + 0.211212i
\(305\) 0 0
\(306\) 3.60245 7.68260i 0.205938 0.439185i
\(307\) 11.1293i 0.635184i 0.948227 + 0.317592i \(0.102874\pi\)
−0.948227 + 0.317592i \(0.897126\pi\)
\(308\) −7.36520 3.12311i −0.419671 0.177955i
\(309\) 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 \(0.299555\pi\)
\(312\) −8.08179 + 23.7612i −0.457541 + 1.34521i
\(313\) 22.4924 1.27135 0.635673 0.771958i \(-0.280722\pi\)
0.635673 + 0.771958i \(0.280722\pi\)
\(314\) −3.97292 + 2.63068i −0.224205 + 0.148458i
\(315\) 0 0
\(316\) −14.9309 6.33122i −0.839927 0.356159i
\(317\) 16.7386i 0.940135i −0.882630 0.470068i \(-0.844230\pi\)
0.882630 0.470068i \(-0.155770\pi\)
\(318\) 2.19387 + 29.9166i 0.123026 + 1.67764i
\(319\) 4.13595i 0.231569i
\(320\) 0 0
\(321\) 4.56155 + 2.56155i 0.254601 + 0.142972i
\(322\) −0.876894 1.32431i −0.0488674 0.0738007i
\(323\) 2.64861 0.147373
\(324\) 11.5112 + 13.8381i 0.639510 + 0.768783i
\(325\) 0 0
\(326\) 12.2448 + 18.4924i 0.678178 + 1.02420i
\(327\) −1.32431 0.743668i −0.0732343 0.0411249i
\(328\) −3.12311 + 0.580639i −0.172445 + 0.0320604i
\(329\) 9.12311i 0.502973i
\(330\) 0 0
\(331\) 3.22925i 0.177496i 0.996054 + 0.0887479i \(0.0282865\pi\)
−0.996054 + 0.0887479i \(0.971713\pi\)
\(332\) −11.7915 + 27.8078i −0.647141 + 1.52615i
\(333\) −8.00000 13.1231i −0.438397 0.719142i
\(334\) −10.6847 + 7.07488i −0.584638 + 0.387120i
\(335\) 0 0
\(336\) −20.2389 + 5.31946i −1.10412 + 0.290200i
\(337\) 1.50758 0.0821230 0.0410615 0.999157i \(-0.486926\pi\)
0.0410615 + 0.999157i \(0.486926\pi\)
\(338\) −15.6192 + 10.3423i −0.849574 + 0.562549i
\(339\) −11.8730 + 21.1431i −0.644852 + 1.14834i
\(340\) 0 0
\(341\) 6.24621i 0.338251i
\(342\) −2.38537 + 5.08706i −0.128986 + 0.275077i
\(343\) 14.7304i 0.795367i
\(344\) −21.5150 + 4.00000i −1.16001 + 0.215666i
\(345\) 0 0
\(346\) −1.56155 2.35829i −0.0839496 0.126783i
\(347\) 22.6305 1.21487 0.607434 0.794370i \(-0.292199\pi\)
0.607434 + 0.794370i \(0.292199\pi\)
\(348\) −6.61668 8.55950i −0.354691 0.458837i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0.952473 + 26.6034i 0.0508392 + 1.41998i
\(352\) 7.31534 + 1.61463i 0.389909 + 0.0860599i
\(353\) 20.2462i 1.07760i −0.842435 0.538799i \(-0.818878\pi\)
0.842435 0.538799i \(-0.181122\pi\)
\(354\) 34.5669 2.53489i 1.83721 0.134728i
\(355\) 0 0
\(356\) −18.8664 8.00000i −0.999915 0.423999i
\(357\) 9.12311 + 5.12311i 0.482846 + 0.271144i
\(358\) 11.8078 7.81855i 0.624060 0.413223i
\(359\) 21.5150 1.13552 0.567758 0.823195i \(-0.307811\pi\)
0.567758 + 0.823195i \(0.307811\pi\)
\(360\) 0 0
\(361\) 17.2462 0.907695
\(362\) 14.4401 9.56155i 0.758954 0.502544i
\(363\) −13.9638 7.84144i −0.732912 0.411569i
\(364\) −28.4924 12.0818i −1.49341 0.633258i
\(365\) 0 0
\(366\) −7.62953 + 0.559496i −0.398802 + 0.0292453i
\(367\) 10.9663i 0.572436i −0.958165 0.286218i \(-0.907602\pi\)
0.958165 0.286218i \(-0.0923981\pi\)
\(368\) 1.03399 + 1.06913i 0.0539003 + 0.0557323i
\(369\) −2.87689 + 1.75379i −0.149765 + 0.0912986i
\(370\) 0 0
\(371\) −36.9890 −1.92038
\(372\) 9.99267 + 12.9268i 0.518096 + 0.670221i
\(373\) 9.12311 0.472377 0.236188 0.971707i \(-0.424102\pi\)
0.236188 + 0.971707i \(0.424102\pi\)
\(374\) −2.06798 3.12311i −0.106932 0.161492i
\(375\) 0 0
\(376\) −1.56155 8.39919i −0.0805309 0.433155i
\(377\) 16.0000i 0.824042i
\(378\) −18.0561 + 12.9084i −0.928704 + 0.663935i
\(379\) 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
\(382\) 29.3693 19.4470i 1.50266 0.994995i
\(383\) 15.1022 0.771688 0.385844 0.922564i \(-0.373910\pi\)
0.385844 + 0.922564i \(0.373910\pi\)
\(384\) 17.7224 8.36154i 0.904394 0.426698i
\(385\) 0 0
\(386\) −0.290319 + 0.192236i −0.0147769 + 0.00978455i
\(387\) −19.8188 + 12.0818i −1.00745 + 0.614152i
\(388\) 4.68466 11.0478i 0.237827 0.560867i
\(389\) 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
\(392\) −1.09763 5.90388i −0.0554388 0.298191i
\(393\) 8.24621 + 4.63068i 0.415966 + 0.233587i
\(394\) −3.31534 5.00691i −0.167024 0.252244i
\(395\) 0 0
\(396\) 7.86084 1.15915i 0.395022 0.0582495i
\(397\) −14.8769 −0.746650 −0.373325 0.927701i \(-0.621782\pi\)
−0.373325 + 0.927701i \(0.621782\pi\)
\(398\) 4.26324 + 6.43845i 0.213697 + 0.322730i
\(399\) −6.04090 3.39228i −0.302423 0.169827i
\(400\) 0 0
\(401\) 24.0000i 1.19850i −0.800561 0.599251i \(-0.795465\pi\)
0.800561 0.599251i \(-0.204535\pi\)
\(402\) 0.778351 + 10.6139i 0.0388206 + 0.529375i
\(403\) 24.1636i 1.20367i
\(404\) 1.61463 + 0.684658i 0.0803307 + 0.0340630i
\(405\) 0 0
\(406\) 11.1231 7.36520i 0.552030 0.365529i
\(407\) −6.78456 −0.336298
\(408\) −9.27608 3.15504i −0.459235 0.156198i
\(409\) 25.3693 1.25443 0.627216 0.778845i \(-0.284194\pi\)
0.627216 + 0.778845i \(0.284194\pi\)
\(410\) 0 0
\(411\) 6.99337 12.4536i 0.344957 0.614292i
\(412\) −18.0540 7.65552i −0.889456 0.377161i
\(413\) 42.7386i 2.10303i
\(414\) 1.42833 + 0.669757i 0.0701984 + 0.0329167i
\(415\) 0 0
\(416\) 28.2995 + 6.24621i 1.38750 + 0.306246i
\(417\) −14.8769 + 26.4924i −0.728525 + 1.29734i
\(418\) 1.36932 + 2.06798i 0.0669755 + 0.101148i
\(419\) 7.36520 0.359814 0.179907 0.983684i \(-0.442420\pi\)
0.179907 + 0.983684i \(0.442420\pi\)
\(420\) 0 0
\(421\) −25.3693 −1.23642 −0.618212 0.786011i \(-0.712143\pi\)
−0.618212 + 0.786011i \(0.712143\pi\)
\(422\) −13.1158 19.8078i −0.638466 0.964227i
\(423\) −4.71659 7.73704i −0.229328 0.376188i
\(424\) 34.0540 6.33122i 1.65381 0.307471i
\(425\) 0 0
\(426\) −8.28711 + 0.607718i −0.401512 + 0.0294440i
\(427\) 9.43318i 0.456503i
\(428\) 2.35829 5.56155i 0.113992 0.268828i
\(429\) 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 \(0.631215\pi\)
\(432\) 14.4139 14.9747i 0.693488 0.720468i
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) −16.7984 + 11.1231i −0.806348 + 0.533926i
\(435\) 0 0
\(436\) −0.684658 + 1.61463i −0.0327892 + 0.0773266i
\(437\) 0.492423i 0.0235558i
\(438\) 20.1449 1.47729i 0.962561 0.0705875i
\(439\) 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
\(442\) −8.00000 12.0818i −0.380521 0.574672i
\(443\) 16.5896 0.788195 0.394097 0.919069i \(-0.371057\pi\)
0.394097 + 0.919069i \(0.371057\pi\)
\(444\) −14.0409 + 10.8539i −0.666351 + 0.515105i
\(445\) 0 0
\(446\) −6.49424 9.80776i −0.307511 0.464411i
\(447\) −11.8730 + 21.1431i −0.561573 + 1.00004i
\(448\) 8.68466 + 22.5490i 0.410312 + 1.06534i
\(449\) 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
\(452\) 25.7782 + 10.9309i 1.21250 + 0.514145i
\(453\) −6.24621 + 11.1231i −0.293473 + 0.522609i
\(454\) 25.8078 17.0887i 1.21122 0.802012i
\(455\) 0 0
\(456\) 6.14219 + 2.08912i 0.287634 + 0.0978319i
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 19.1567 12.6847i 0.895133 0.592715i
\(459\) −10.3857 + 0.371834i −0.484761 + 0.0173557i
\(460\) 0 0
\(461\) 41.8617i 1.94970i −0.222872 0.974848i \(-0.571543\pi\)
0.222872 0.974848i \(-0.428457\pi\)
\(462\) 0.716589 + 9.77172i 0.0333387 + 0.454622i
\(463\) 3.02045i 0.140372i 0.997534 + 0.0701861i \(0.0223593\pi\)
−0.997534 + 0.0701861i \(0.977641\pi\)
\(464\) −8.97983 + 8.68466i −0.416878 + 0.403175i
\(465\) 0 0
\(466\) 7.80776 + 11.7915i 0.361688 + 0.546229i
\(467\) −2.27678 −0.105357 −0.0526784 0.998612i \(-0.516776\pi\)
−0.0526784 + 0.998612i \(0.516776\pi\)
\(468\) 30.4098 4.48419i 1.40569 0.207282i
\(469\) −13.1231 −0.605969
\(470\) 0 0
\(471\) 5.08842 + 2.85742i 0.234462 + 0.131663i
\(472\) −7.31534 39.3473i −0.336716 1.81111i
\(473\) 10.2462i 0.471121i
\(474\) 1.45268 + 19.8094i 0.0667239 + 0.909876i
\(475\) 0 0
\(476\) 4.71659 11.1231i 0.216184 0.509827i
\(477\) 31.3693 19.1231i 1.43630 0.875587i
\(478\) −20.4924 + 13.5691i −0.937302 + 0.620637i
\(479\) 25.6509 1.17202 0.586010 0.810304i \(-0.300698\pi\)
0.586010 + 0.810304i \(0.300698\pi\)
\(480\) 0 0
\(481\) −26.2462 −1.19672
\(482\) −15.7644 + 10.4384i −0.718048 + 0.475458i
\(483\) −0.952473 + 1.69614i −0.0433390 + 0.0771771i
\(484\) −7.21922 + 17.0251i −0.328147 + 0.773866i
\(485\) 0 0
\(486\) 8.63928 20.2821i 0.391886 0.920014i
\(487\) 25.2791i 1.14550i −0.819728 0.572752i \(-0.805876\pi\)
0.819728 0.572752i \(-0.194124\pi\)
\(488\) 1.61463 + 8.68466i 0.0730907 + 0.393136i
\(489\) 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 \(0.291696\pi\)
\(492\) 2.37944 + 3.07810i 0.107273 + 0.138771i
\(493\) 6.24621 0.281315
\(494\) 5.29723 + 8.00000i 0.238334 + 0.359937i
\(495\) 0 0
\(496\) 13.5616 13.1158i 0.608932 0.588916i
\(497\) 10.2462i 0.459605i
\(498\) 36.8937 2.70552i 1.65325 0.121237i
\(499\) 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
\(502\) −22.0540 + 14.6031i −0.984317 + 0.651769i
\(503\) −14.3586 −0.640217 −0.320109 0.947381i \(-0.603719\pi\)
−0.320109 + 0.947381i \(0.603719\pi\)
\(504\) 17.1158 + 19.0765i 0.762397 + 0.849736i
\(505\) 0 0
\(506\) 0.580639 0.384472i 0.0258125 0.0170919i
\(507\) 20.0047 + 11.2337i 0.888442 + 0.498907i
\(508\) 27.8078 + 11.7915i 1.23377 + 0.523162i
\(509\) 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
\(512\) −11.8551 19.2732i −0.523927 0.851763i
\(513\) 6.87689 0.246211i 0.303622 0.0108705i
\(514\) −23.8078 35.9551i −1.05012 1.58591i
\(515\) 0 0
\(516\) 16.3919 + 21.2049i 0.721612 + 0.933494i
\(517\) −4.00000 −0.175920
\(518\) −12.0818 18.2462i −0.530843 0.801692i
\(519\) −1.69614 + 3.02045i −0.0744523 + 0.132583i
\(520\) 0 0
\(521\) 38.2462i 1.67560i 0.545980 + 0.837798i \(0.316158\pi\)
−0.545980 + 0.837798i \(0.683842\pi\)
\(522\) −5.62541 + 11.9968i −0.246218 + 0.525085i
\(523\) 35.2929i 1.54325i −0.636077 0.771625i \(-0.719444\pi\)
0.636077 0.771625i \(-0.280556\pi\)
\(524\) 4.26324 10.0540i 0.186241 0.439210i
\(525\) 0 0
\(526\) −28.0540 + 18.5760i −1.22321 + 0.809954i
\(527\) −9.43318 −0.410916
\(528\) −2.33230 8.87368i −0.101500 0.386177i
\(529\) −22.8617 −0.993989
\(530\) 0 0
\(531\) −22.0956 36.2454i −0.958868 1.57292i
\(532\) −3.12311 + 7.36520i −0.135404 + 0.319322i
\(533\) 5.75379i 0.249224i
\(534\) 1.83558 + 25.0308i 0.0794333 + 1.08319i
\(535\) 0 0
\(536\) 12.0818 2.24621i 0.521854 0.0970215i
\(537\) −15.1231 8.49242i −0.652610 0.366475i
\(538\) 10.9309 + 16.5081i 0.471263 + 0.711713i
\(539\) −2.81164 −0.121106
\(540\) 0 0
\(541\) −26.9848 −1.16017 −0.580085 0.814556i \(-0.696980\pi\)
−0.580085 + 0.814556i \(0.696980\pi\)
\(542\) 11.9545 + 18.0540i 0.513490 + 0.775485i
\(543\) −18.4945 10.3857i −0.793676 0.445691i
\(544\) −2.43845 + 11.0478i −0.104548 + 0.473671i
\(545\) 0 0
\(546\) 2.77214 + 37.8021i 0.118637 + 1.61778i
\(547\) 5.83209i 0.249362i 0.992197 + 0.124681i \(0.0397908\pi\)
−0.992197 + 0.124681i \(0.960209\pi\)
\(548\) −15.1838 6.43845i −0.648618 0.275037i
\(549\) 4.87689 + 8.00000i 0.208141 + 0.341432i
\(550\) 0 0
\(551\) −4.13595 −0.176197
\(552\) 0.586575 1.72458i 0.0249663 0.0734031i
\(553\) −24.4924 −1.04152
\(554\) 27.5559 18.2462i 1.17074 0.775207i
\(555\) 0 0
\(556\) 32.3002 + 13.6964i 1.36983 + 0.580858i
\(557\) 36.2462i 1.53580i 0.640569 + 0.767901i \(0.278699\pi\)
−0.640569 + 0.767901i \(0.721301\pi\)
\(558\) 8.49563 18.1178i 0.359649 0.766989i
\(559\) 39.6377i 1.67649i
\(560\) 0 0
\(561\) −2.24621 + 4.00000i −0.0948351 + 0.168880i
\(562\) 10.6307 + 16.0547i 0.448428 + 0.677227i
\(563\) 7.90007 0.332948 0.166474 0.986046i \(-0.446762\pi\)
0.166474 + 0.986046i \(0.446762\pi\)
\(564\) −8.27814 + 6.39919i −0.348573 + 0.269455i
\(565\) 0 0
\(566\) −18.1227 27.3693i −0.761753 1.15042i
\(567\) 24.1636 + 12.4536i 1.01478 + 0.523003i
\(568\) 1.75379 + 9.43318i 0.0735873 + 0.395807i
\(569\) 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 \(-0.757241\pi\)
0.723007 0.690841i \(-0.242759\pi\)
\(572\) 5.29723 12.4924i 0.221488 0.522334i
\(573\) −37.6155 21.1231i −1.57141 0.882430i
\(574\) −4.00000 + 2.64861i −0.166957 + 0.110551i
\(575\) 0 0
\(576\) −19.0229 14.6332i −0.792620 0.609716i
\(577\) 32.2462 1.34243 0.671214 0.741264i \(-0.265773\pi\)
0.671214 + 0.741264i \(0.265773\pi\)
\(578\) −15.3289 + 10.1501i −0.637599 + 0.422188i
\(579\) 0.371834 + 0.208805i 0.0154529 + 0.00867762i
\(580\) 0 0
\(581\) 45.6155i 1.89245i
\(582\) −14.6576 + 1.07488i −0.607576 + 0.0445554i
\(583\) 16.2177i 0.671670i
\(584\) −4.26324 22.9309i −0.176414 0.948886i
\(585\) 0 0
\(586\) −1.94602 2.93893i −0.0803895 0.121406i
\(587\) −1.85917 −0.0767362 −0.0383681 0.999264i \(-0.512216\pi\)
−0.0383681 + 0.999264i \(0.512216\pi\)
\(588\) −5.81880 + 4.49806i −0.239963 + 0.185497i
\(589\) 6.24621 0.257371
\(590\) 0 0
\(591\) −3.60109 + 6.41273i −0.148129 + 0.263784i
\(592\) 14.2462 + 14.7304i 0.585516 + 0.605416i
\(593\) 8.24621i 0.338631i 0.985562 + 0.169316i \(0.0541557\pi\)
−0.985562 + 0.169316i \(0.945844\pi\)
\(594\) −5.65964 7.91664i −0.232218 0.324823i
\(595\) 0 0
\(596\) 25.7782 + 10.9309i 1.05592 + 0.447746i
\(597\) 4.63068 8.24621i 0.189521 0.337495i
\(598\) 2.24621 1.48734i 0.0918544 0.0608217i
\(599\) −44.1912 −1.80560 −0.902802 0.430056i \(-0.858494\pi\)
−0.902802 + 0.430056i \(0.858494\pi\)
\(600\) 0 0
\(601\) 23.1231 0.943211 0.471606 0.881810i \(-0.343675\pi\)
0.471606 + 0.881810i \(0.343675\pi\)
\(602\) −27.5559 + 18.2462i −1.12309 + 0.743660i
\(603\) 11.1293 6.78456i 0.453221 0.276289i
\(604\) 13.5616 + 5.75058i 0.551812 + 0.233988i
\(605\) 0 0
\(606\) −0.157093 2.14219i −0.00638148 0.0870206i
\(607\) 4.50778i 0.182965i 0.995807 + 0.0914827i \(0.0291606\pi\)
−0.995807 + 0.0914827i \(0.970839\pi\)
\(608\) 1.61463 7.31534i 0.0654817 0.296676i
\(609\) −14.2462 8.00000i −0.577286 0.324176i
\(610\) 0 0
\(611\) −15.4741 −0.626014
\(612\) 1.75058 + 11.8716i 0.0707629 + 0.479882i
\(613\) −9.12311 −0.368479 −0.184239 0.982881i \(-0.558982\pi\)
−0.184239 + 0.982881i \(0.558982\pi\)
\(614\) −8.68951 13.1231i −0.350680 0.529605i
\(615\) 0 0
\(616\) 11.1231 2.06798i 0.448163 0.0833211i
\(617\) 14.0000i 0.563619i −0.959470 0.281809i \(-0.909065\pi\)
0.959470 0.281809i \(-0.0909346\pi\)
\(618\) 1.75654 + 23.9530i 0.0706584 + 0.963529i
\(619\) 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
\(622\) −24.4924 + 16.2177i −0.982057 + 0.650272i
\(623\) −30.9481 −1.23991
\(624\) −9.02255 34.3280i −0.361191 1.37422i
\(625\) 0 0
\(626\) −26.5219 + 17.5616i −1.06003 + 0.701901i
\(627\) 1.48734 2.64861i 0.0593985 0.105775i
\(628\) 2.63068 6.20393i 0.104976 0.247564i
\(629\) 10.2462i 0.408543i
\(630\) 0 0
\(631\) 39.8007i 1.58444i −0.610235 0.792220i \(-0.708925\pi\)
0.610235 0.792220i \(-0.291075\pi\)
\(632\) 22.5490 4.19224i 0.896949 0.166758i
\(633\) −14.2462 + 25.3693i −0.566236 + 1.00834i
\(634\) 13.0691 + 19.7373i 0.519041 + 0.783869i
\(635\) 0 0
\(636\) −25.9451 33.5632i −1.02879 1.33087i
\(637\) −10.8769 −0.430958
\(638\) 3.22925 + 4.87689i 0.127847 + 0.193078i
\(639\) 5.29723 + 8.68951i 0.209555 + 0.343752i
\(640\) 0 0
\(641\) 6.38447i 0.252171i 0.992019 + 0.126086i \(0.0402414\pi\)
−0.992019 + 0.126086i \(0.959759\pi\)
\(642\) −7.37874 + 0.541105i −0.291216 + 0.0213557i
\(643\) 3.60109i 0.142013i 0.997476 + 0.0710065i \(0.0226211\pi\)
−0.997476 + 0.0710065i \(0.977379\pi\)
\(644\) 2.06798 + 0.876894i 0.0814896 + 0.0345545i
\(645\) 0 0
\(646\) −3.12311 + 2.06798i −0.122877 + 0.0813634i
\(647\) 36.6172 1.43957 0.719786 0.694197i \(-0.244240\pi\)
0.719786 + 0.694197i \(0.244240\pi\)
\(648\) −24.3778 7.32948i −0.957652 0.287929i
\(649\) −18.7386 −0.735556
\(650\) 0 0
\(651\) 21.5150 + 12.0818i 0.843238 + 0.473523i
\(652\) −28.8769 12.2448i −1.13091 0.479544i
\(653\) 38.9848i 1.52559i −0.646638 0.762797i \(-0.723825\pi\)
0.646638 0.762797i \(-0.276175\pi\)
\(654\) 2.14219 0.157093i 0.0837663 0.00614283i
\(655\) 0 0
\(656\) 3.22925 3.12311i 0.126081 0.121937i
\(657\) −12.8769 21.1231i −0.502375 0.824091i
\(658\) −7.12311 10.7575i −0.277688 0.419370i
\(659\) 24.7442 0.963898 0.481949 0.876199i \(-0.339929\pi\)
0.481949 + 0.876199i \(0.339929\pi\)
\(660\) 0 0
\(661\) 28.1080 1.09327 0.546636 0.837370i \(-0.315908\pi\)
0.546636 + 0.837370i \(0.315908\pi\)
\(662\) −2.52132 3.80776i −0.0979940 0.147993i
\(663\) −8.68951 + 15.4741i −0.337473 + 0.600963i
\(664\) −7.80776 41.9960i −0.303000 1.62976i
\(665\) 0 0
\(666\) 19.6794 + 9.22786i 0.762561 + 0.357572i
\(667\) 1.16128i 0.0449648i
\(668\) 7.07488 16.6847i 0.273735 0.645549i
\(669\) −7.05398 + 12.5616i −0.272722 + 0.485658i
\(670\) 0 0
\(671\) 4.13595 0.159667
\(672\) 19.7113 22.0745i 0.760381 0.851541i
\(673\) −22.4924 −0.867019 −0.433510 0.901149i \(-0.642725\pi\)
−0.433510 + 0.901149i \(0.642725\pi\)
\(674\) −1.77766 + 1.17708i −0.0684727 + 0.0453395i
\(675\) 0 0
\(676\) 10.3423 24.3903i 0.397782 0.938087i
\(677\) 1.50758i 0.0579409i 0.999580 + 0.0289705i \(0.00922287\pi\)
−0.999580 + 0.0289705i \(0.990777\pi\)
\(678\) −2.50806 34.2010i −0.0963215 1.31348i
\(679\) 18.1227i 0.695485i
\(680\) 0 0
\(681\) −33.0540 18.5616i −1.26663 0.711280i
\(682\) −4.87689 7.36520i −0.186746 0.282028i
\(683\) −7.90007 −0.302288 −0.151144 0.988512i \(-0.548296\pi\)
−0.151144 + 0.988512i \(0.548296\pi\)
\(684\) −1.15915 7.86084i −0.0443212 0.300567i
\(685\) 0 0
\(686\) 11.5012 + 17.3693i 0.439116 + 0.663164i
\(687\) −24.5354 13.7779i −0.936085 0.525661i
\(688\) 22.2462 21.5150i 0.848129 0.820251i
\(689\) 62.7386i 2.39015i
\(690\) 0 0
\(691\) 18.2857i 0.695621i 0.937565 + 0.347811i \(0.113075\pi\)
−0.937565 + 0.347811i \(0.886925\pi\)
\(692\) 3.68260 + 1.56155i 0.139991 + 0.0593613i
\(693\) 10.2462 6.24621i 0.389221 0.237274i
\(694\) −26.6847 + 17.6693i −1.01294 + 0.670719i
\(695\) 0 0
\(696\) 14.4851 + 4.92676i 0.549056 + 0.186748i
\(697\) −2.24621 −0.0850813
\(698\) 16.5081 10.9309i 0.624839 0.413740i
\(699\) 8.48071 15.1022i 0.320770 0.571219i
\(700\) 0 0
\(701\) 17.5076i 0.661252i −0.943762 0.330626i \(-0.892740\pi\)
0.943762 0.330626i \(-0.107260\pi\)
\(702\) −21.8944 30.6256i −0.826351 1.15589i
\(703\) 6.78456i 0.255885i
\(704\) −9.88653 + 3.80776i −0.372612 + 0.143511i
\(705\) 0 0
\(706\) 15.8078 + 23.8733i 0.594933 + 0.898482i
\(707\) 2.64861 0.0996114
\(708\) −38.7803 + 29.9780i −1.45745 + 1.12664i
\(709\) 6.49242 0.243828 0.121914 0.992541i \(-0.461097\pi\)
0.121914 + 0.992541i \(0.461097\pi\)
\(710\) 0 0
\(711\) 20.7713 12.6624i 0.778985 0.474878i
\(712\) 28.4924 5.29723i 1.06780 0.198522i
\(713\) 1.75379i 0.0656799i
\(714\) −14.7575 + 1.08221i −0.552285 + 0.0405007i
\(715\) 0 0
\(716\) −7.81855 + 18.4384i −0.292193 + 0.689077i
\(717\) 26.2462 + 14.7386i 0.980183 + 0.550424i
\(718\) −25.3693 + 16.7984i −0.946774 + 0.626910i
\(719\) −30.9481 −1.15417 −0.577086 0.816684i \(-0.695810\pi\)
−0.577086 + 0.816684i \(0.695810\pi\)
\(720\) 0 0
\(721\) −29.6155 −1.10294
\(722\) −20.3358 + 13.4654i −0.756821 + 0.501132i
\(723\) 20.1907 + 11.3381i 0.750899 + 0.421669i
\(724\) −9.56155 + 22.5490i −0.355352 + 0.838025i
\(725\) 0 0
\(726\) 22.5878 1.65643i 0.838314 0.0614760i
\(727\) 10.9663i 0.406717i 0.979104 + 0.203359i \(0.0651857\pi\)
−0.979104 + 0.203359i \(0.934814\pi\)
\(728\) 43.0299 8.00000i 1.59480 0.296500i
\(729\) −26.9309 + 1.93087i −0.997440 + 0.0715137i
\(730\) 0 0
\(731\) −15.4741 −0.572329
\(732\) 8.55950 6.61668i 0.316368 0.244560i
\(733\) 26.8769 0.992721 0.496360 0.868117i \(-0.334669\pi\)
0.496360 + 0.868117i \(0.334669\pi\)
\(734\) 8.56222 + 12.9309i 0.316037 + 0.477287i
\(735\) 0 0
\(736\) −2.05398 0.453349i −0.0757105 0.0167107i
\(737\) 5.75379i 0.211944i
\(738\) 2.02297 4.31419i 0.0744664 0.158807i
\(739\) 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
\(742\) 43.6155 28.8802i 1.60118 1.06022i
\(743\) 9.80501 0.359711 0.179856 0.983693i \(-0.442437\pi\)
0.179856 + 0.983693i \(0.442437\pi\)
\(744\) −21.8757 7.44050i −0.802004 0.272782i
\(745\) 0 0
\(746\) −10.7575 + 7.12311i −0.393860 + 0.260795i
\(747\) −23.5829 38.6852i −0.862855 1.41542i
\(748\) 4.87689 + 2.06798i 0.178317 + 0.0756127i
\(749\) 9.12311i 0.333351i
\(750\) 0 0
\(751\) 11.5012i 0.419683i 0.977735 + 0.209842i \(0.0672948\pi\)
−0.977735 + 0.209842i \(0.932705\pi\)
\(752\) 8.39919 + 8.68466i 0.306287 + 0.316697i
\(753\) 28.2462 + 15.8617i 1.02935 + 0.578034i
\(754\) 12.4924 + 18.8664i 0.454947 + 0.687072i
\(755\) 0 0
\(756\) 11.2122 29.3186i 0.407785 1.06631i
\(757\) −10.8769 −0.395327 −0.197664 0.980270i \(-0.563335\pi\)
−0.197664 + 0.980270i \(0.563335\pi\)
\(758\) 14.6031 + 22.0540i 0.530409 + 0.801036i
\(759\) −0.743668 0.417609i −0.0269934 0.0151582i
\(760\) 0 0
\(761\) 31.2311i 1.13212i 0.824362 + 0.566062i \(0.191534\pi\)
−0.824362 + 0.566062i \(0.808466\pi\)
\(762\) −2.70552 36.8937i −0.0980108 1.33652i
\(763\) 2.64861i 0.0958863i
\(764\) −19.4470 + 45.8617i −0.703568 + 1.65922i
\(765\) 0 0
\(766\) −17.8078 + 11.7915i −0.643421 + 0.426043i
\(767\) −72.4908 −2.61749
\(768\) −14.3689 + 23.6967i −0.518492 + 0.855083i
\(769\) 38.9848 1.40583 0.702915 0.711274i \(-0.251882\pi\)
0.702915 + 0.711274i \(0.251882\pi\)
\(770\) 0 0
\(771\) −25.8597 + 46.0504i −0.931315 + 1.65846i
\(772\) 0.192236 0.453349i 0.00691872 0.0163164i
\(773\) 0.246211i 0.00885560i −0.999990 0.00442780i \(-0.998591\pi\)
0.999990 0.00442780i \(-0.00140942\pi\)
\(774\) 13.9361 29.7203i 0.500924 1.06827i
\(775\) 0 0
\(776\) 3.10196 + 16.6847i 0.111354 + 0.598944i
\(777\) −13.1231 + 23.3693i −0.470789 + 0.838370i
\(778\) −16.1922 24.4539i −0.580520 0.876715i
\(779\) 1.48734 0.0532894
\(780\) 0 0
\(781\) 4.49242 0.160752
\(782\) 0.580639 + 0.876894i 0.0207636 + 0.0313577i
\(783\) 16.2177 0.580639i 0.579575 0.0207503i
\(784\) 5.90388 + 6.10454i 0.210853 + 0.218019i
\(785\) 0 0
\(786\) −13.3390 + 0.978190i −0.475787 + 0.0348909i