Properties

Label 300.2.e.c.251.8
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 251.8
Root \(1.17915 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.c.251.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})\) \(q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} -1.32431 q^{11} +(0.382406 - 3.44293i) q^{12} +5.12311 q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000i q^{17} +(-0.158699 + 4.23967i) q^{18} +1.32431i q^{19} +(2.56155 - 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} +0.371834 q^{23} +(3.13907 - 3.76115i) 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} +(-3.49737 + 4.87529i) q^{36} -5.12311 q^{37} +(-1.03399 + 1.56155i) q^{38} +(-7.73704 - 4.34475i) q^{39} +1.12311i q^{41} +(6.58200 - 3.37874i) q^{42} -7.73704i q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} +3.02045 q^{47} +(6.63804 - 1.98403i) q^{48} -2.12311 q^{49} +(1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} -12.2462i q^{53} +(3.83521 - 6.26827i) 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} +(1.48140 + 2.88586i) q^{66} +4.34475i q^{67} +(-3.68260 + 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} -3.39228 q^{71} +(-7.93042 + 3.01802i) q^{72} -8.24621 q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000i q^{77} +(-5.73082 - 11.1640i) q^{78} +8.10887i q^{79} +(-4.12311 + 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} +15.1022 q^{83} +(10.3992 + 1.15504i) 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} +(9.37632 + 2.84336i) 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
\(6\) −1.11862 2.17915i −0.456676 0.889633i
\(7\) 3.02045i 1.14162i 0.821081 + 0.570811i \(0.193371\pi\)
−0.821081 + 0.570811i \(0.806629\pi\)
\(8\) −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 \(-0.563979\pi\)
−0.199647 + 0.979868i \(0.563979\pi\)
\(12\) 0.382406 3.44293i 0.110391 0.993888i
\(13\) 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 \(0.922021\pi\)
\(18\) −0.158699 + 4.23967i −0.0374058 + 0.999300i
\(19\) 1.32431i 0.303817i 0.988395 + 0.151908i \(0.0485419\pi\)
−0.988395 + 0.151908i \(0.951458\pi\)
\(20\) 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 \(-0.487657\pi\)
0.0387664 + 0.999248i \(0.487657\pi\)
\(24\) 3.13907 3.76115i 0.640760 0.767741i
\(25\) 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 \(-0.860780\pi\)
0.905867 0.423562i \(-0.139220\pi\)
\(32\) −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
\(36\) −3.49737 + 4.87529i −0.582894 + 0.812548i
\(37\) −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 \(0.972048\pi\)
\(42\) 6.58200 3.37874i 1.01562 0.521351i
\(43\) 7.73704i 1.17989i −0.807445 0.589944i \(-0.799150\pi\)
0.807445 0.589944i \(-0.200850\pi\)
\(44\) −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 \(-0.429300\pi\)
0.220289 + 0.975435i \(0.429300\pi\)
\(48\) 6.63804 1.98403i 0.958119 0.286371i
\(49\) −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 \(-0.318076\pi\)
\(54\) 3.83521 6.26827i 0.521906 0.853003i
\(55\) 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 \(-0.127315\pi\)
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 \(0.435926\pi\)
\(62\) 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
\(66\) 1.48140 + 2.88586i 0.182348 + 0.355225i
\(67\) 4.34475i 0.530796i 0.964139 + 0.265398i \(0.0855034\pi\)
−0.964139 + 0.265398i \(0.914497\pi\)
\(68\) −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 \(-0.564515\pi\)
−0.201295 + 0.979531i \(0.564515\pi\)
\(72\) −7.93042 + 3.01802i −0.934609 + 0.355677i
\(73\) −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
\(78\) −5.73082 11.1640i −0.648888 1.26407i
\(79\) 8.10887i 0.912319i 0.889898 + 0.456160i \(0.150775\pi\)
−0.889898 + 0.456160i \(0.849225\pi\)
\(80\) 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 \(-0.189000\pi\)
0.828843 + 0.559481i \(0.189000\pi\)
\(84\) 10.3992 + 1.15504i 1.13464 + 0.126025i
\(85\) 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
\(96\) 9.37632 + 2.84336i 0.956966 + 0.290199i
\(97\) 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 \(0.986109\pi\)
\(102\) 4.35829 2.23725i 0.431535 0.221520i
\(103\) 9.80501i 0.966117i 0.875588 + 0.483058i \(0.160474\pi\)
−0.875588 + 0.483058i \(0.839526\pi\)
\(104\) −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 \(-0.546640\pi\)
−0.145999 + 0.989285i \(0.546640\pi\)
\(108\) 9.41639 4.39676i 0.906093 0.423079i
\(109\) −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 \(0.771189\pi\)
\(114\) 2.88586 1.48140i 0.270286 0.138746i
\(115\) 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
\(126\) −12.8057 0.479343i −1.14082 0.0427033i
\(127\) 15.1022i 1.34011i −0.742313 0.670054i \(-0.766271\pi\)
0.742313 0.670054i \(-0.233729\pi\)
\(128\) −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 \(-0.576666\pi\)
−0.238532 + 0.971135i \(0.576666\pi\)
\(132\) −0.506422 + 4.55950i −0.0440784 + 0.396853i
\(133\) −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 \(-0.114587\pi\)
\(138\) −0.415942 0.810281i −0.0354074 0.0689757i
\(139\) 17.5420i 1.48790i −0.668237 0.743949i \(-0.732951\pi\)
0.668237 0.743949i \(-0.267049\pi\)
\(140\) 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
\(144\) −11.7075 2.63319i −0.975628 0.219433i
\(145\) 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 \(-0.903118\pi\)
0.954038 0.299686i \(-0.0968819\pi\)
\(152\) −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
\(156\) 1.95910 17.6385i 0.156854 1.41221i
\(157\) 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
\(162\) −11.1080 + 6.21395i −0.872724 + 0.488214i
\(163\) 15.6829i 1.22838i 0.789159 + 0.614189i \(0.210517\pi\)
−0.789159 + 0.614189i \(0.789483\pi\)
\(164\) −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 \(-0.614020\pi\)
−0.350594 + 0.936528i \(0.614020\pi\)
\(168\) 11.3604 + 9.48140i 0.876470 + 0.731506i
\(169\) 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 \(0.975776\pi\)
\(174\) −6.80571 + 3.49358i −0.515939 + 0.264847i
\(175\) 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 \(-0.377906\pi\)
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 \(0.650406\pi\)
\(182\) −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
\(186\) −10.2781 + 5.27608i −0.753630 + 0.386861i
\(187\) 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 \(-0.142752\pi\)
0.901113 + 0.433585i \(0.142752\pi\)
\(192\) 8.83603 + 10.6735i 0.637686 + 0.770297i
\(193\) 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 \(0.951665\pi\)
\(198\) 0.210167 5.61463i 0.0149359 0.399014i
\(199\) 5.46026i 0.387067i 0.981094 + 0.193534i \(0.0619949\pi\)
−0.981094 + 0.193534i \(0.938005\pi\)
\(200\) 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
\(204\) 6.88586 + 0.764811i 0.482107 + 0.0535475i
\(205\) 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 \(-0.803746\pi\)
0.815878 0.578224i \(-0.196254\pi\)
\(212\) 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
\(216\) 14.5362 + 2.16766i 0.989063 + 0.147491i
\(217\) 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
\(222\) 5.73082 + 11.1640i 0.384628 + 0.749279i
\(223\) 8.31768i 0.556993i −0.960437 0.278496i \(-0.910164\pi\)
0.960437 0.278496i \(-0.0898360\pi\)
\(224\) −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 \(-0.241220\pi\)
0.726339 + 0.687337i \(0.241220\pi\)
\(228\) 4.55950 + 0.506422i 0.301960 + 0.0335386i
\(229\) −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 \(-0.106227\pi\)
\(234\) −0.813033 + 21.7203i −0.0531497 + 1.41990i
\(235\) 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 \(-0.689998\pi\)
−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 \(0.358303\pi\)
\(242\) −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
\(246\) 2.44741 1.25633i 0.156041 0.0801008i
\(247\) 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 \(-0.700979\pi\)
−0.590272 + 0.807205i \(0.700979\pi\)
\(252\) −14.7256 10.5636i −0.927623 0.665445i
\(253\) −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 \(0.600025\pi\)
\(258\) −16.8601 + 8.65483i −1.04967 + 0.538826i
\(259\) 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 \(-0.762129\pi\)
−0.733531 + 0.679656i \(0.762129\pi\)
\(264\) −4.15709 + 4.98091i −0.255851 + 0.306554i
\(265\) 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 \(0.153960\pi\)
−0.885290 + 0.465040i \(0.846040\pi\)
\(272\) −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
\(276\) 0.142191 1.28020i 0.00855892 0.0770589i
\(277\) −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 \(-0.133118\pi\)
\(282\) −3.37874 6.58200i −0.201201 0.391952i
\(283\) 23.2111i 1.37976i −0.723925 0.689879i \(-0.757664\pi\)
0.723925 0.689879i \(-0.242336\pi\)
\(284\) −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
\(288\) −11.7490 12.2459i −0.692315 0.721596i
\(289\) 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 \(0.976805\pi\)
\(294\) 2.37495 + 4.62656i 0.138510 + 0.269826i
\(295\) 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
\(306\) −8.47934 0.317399i −0.484732 0.0181445i
\(307\) 11.1293i 0.635184i −0.948227 0.317592i \(-0.897126\pi\)
0.948227 0.317592i \(-0.102874\pi\)
\(308\) 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 \(-0.700445\pi\)
−0.588916 + 0.808194i \(0.700445\pi\)
\(312\) 16.0818 19.2688i 0.910452 1.09088i
\(313\) 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 \(-0.155770\pi\)
\(318\) −26.6863 + 13.6989i −1.49649 + 0.768196i
\(319\) 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
\(324\) −17.9496 1.34567i −0.997202 0.0747592i
\(325\) 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 \(-0.971713\pi\)
0.996054 0.0887479i \(-0.0282865\pi\)
\(332\) 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
\(336\) 5.99267 + 20.0499i 0.326927 + 1.09381i
\(337\) 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
\(342\) −5.61463 0.210167i −0.303604 0.0113645i
\(343\) 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 \(-0.707801\pi\)
−0.607434 + 0.794370i \(0.707801\pi\)
\(348\) −10.7526 1.19429i −0.576402 0.0640208i
\(349\) −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 \(-0.181122\pi\)
\(354\) −15.8283 30.8344i −0.841262 1.63883i
\(355\) 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 \(-0.692189\pi\)
−0.567758 + 0.823195i \(0.692189\pi\)
\(360\) 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
\(366\) −3.49358 6.80571i −0.182612 0.355740i
\(367\) 10.9663i 0.572436i 0.958165 + 0.286218i \(0.0923981\pi\)
−0.958165 + 0.286218i \(0.907602\pi\)
\(368\) −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
\(372\) −16.2389 1.80365i −0.841947 0.0935149i
\(373\) 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
\(378\) 18.9330 + 11.5841i 0.973807 + 0.595820i
\(379\) 18.7033i 0.960725i 0.877070 + 0.480363i \(0.159495\pi\)
−0.877070 + 0.480363i \(0.840505\pi\)
\(380\) 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 \(-0.626090\pi\)
−0.385844 + 0.922564i \(0.626090\pi\)
\(384\) 2.08533 + 19.4846i 0.106417 + 0.994322i
\(385\) 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
\(396\) 4.63159 6.45638i 0.232746 0.324445i
\(397\) −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 \(-0.204535\pi\)
\(402\) 9.46786 4.86014i 0.472214 0.242402i
\(403\) 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
\(408\) 7.52230 + 6.27814i 0.372409 + 0.310814i
\(409\) 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
\(414\) −0.0590098 + 1.57645i −0.00290017 + 0.0774785i
\(415\) 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 \(-0.557580\pi\)
−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 \(0.712143\pi\)
\(422\) 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
\(426\) 3.79468 + 7.39228i 0.183853 + 0.358157i
\(427\) 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 \(-0.368785\pi\)
0.400648 + 0.916232i \(0.368785\pi\)
\(432\) 15.4479 + 13.9055i 0.743236 + 0.669030i
\(433\) −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
\(438\) 9.22440 + 17.9697i 0.440759 + 0.858626i
\(439\) 9.27015i 0.442440i 0.975224 + 0.221220i \(0.0710039\pi\)
−0.975224 + 0.221220i \(0.928996\pi\)
\(440\) 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 \(-0.628943\pi\)
−0.394097 + 0.919069i \(0.628943\pi\)
\(444\) −1.95910 + 17.6385i −0.0929750 + 0.837086i
\(445\) 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
\(456\) 4.98091 + 4.15709i 0.233253 + 0.194674i
\(457\) 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 \(-0.428457\pi\)
\(462\) −8.71659 + 4.47449i −0.405532 + 0.208172i
\(463\) 3.02045i 0.140372i −0.997534 0.0701861i \(-0.977641\pi\)
0.997534 0.0701861i \(-0.0223593\pi\)
\(464\) 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 \(-0.483224\pi\)
0.0526784 + 0.998612i \(0.483224\pi\)
\(468\) −17.9174 + 24.9766i −0.828231 + 1.15454i
\(469\) −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
\(474\) 17.6704 9.07077i 0.811629 0.416634i
\(475\) 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 \(-0.699302\pi\)
−0.586010 + 0.810304i \(0.699302\pi\)
\(480\) 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
\(486\) 22.0454 + 0.0358705i 0.999999 + 0.00162712i
\(487\) 25.2791i 1.14550i 0.819728 + 0.572752i \(0.194124\pi\)
−0.819728 + 0.572752i \(0.805876\pi\)
\(488\) −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 \(-0.708304\pi\)
−0.608687 + 0.793410i \(0.708304\pi\)
\(492\) 3.86677 + 0.429482i 0.174328 + 0.0193625i
\(493\) 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
\(498\) −16.8937 32.9100i −0.757025 1.47473i
\(499\) 32.2725i 1.44471i 0.691521 + 0.722357i \(0.256941\pi\)
−0.691521 + 0.722357i \(0.743059\pi\)
\(500\) 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 \(-0.396281\pi\)
0.320109 + 0.947381i \(0.396281\pi\)
\(504\) −9.11578 23.9534i −0.406049 1.06697i
\(505\) 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
\(516\) −26.6381 2.95869i −1.17268 0.130249i
\(517\) −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 \(0.683842\pi\)
\(522\) 13.2409 + 0.495635i 0.579540 + 0.0216933i
\(523\) 35.2929i 1.54325i 0.636077 + 0.771625i \(0.280556\pi\)
−0.636077 + 0.771625i \(0.719444\pi\)
\(524\) −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
\(528\) −8.79081 + 2.62747i −0.382571 + 0.114346i
\(529\) −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
\(534\) −22.3280 + 11.4616i −0.966227 + 0.495994i
\(535\) 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
\(546\) 33.7203 17.3097i 1.44309 0.740785i
\(547\) 5.83209i 0.249362i −0.992197 0.124681i \(-0.960209\pi\)
0.992197 0.124681i \(-0.0397908\pi\)
\(548\) 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
\(552\) 1.16721 1.39852i 0.0496799 0.0595251i
\(553\) −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 \(0.721301\pi\)
\(558\) 19.9968 + 0.748519i 0.846532 + 0.0316874i
\(559\) 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 \(-0.553238\pi\)
−0.166474 + 0.986046i \(0.553238\pi\)
\(564\) 1.15504 10.3992i 0.0486358 0.437885i
\(565\) 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 \(0.242759\pi\)
−0.723007 + 0.690841i \(0.757241\pi\)
\(572\) −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
\(576\) −4.29247 23.6130i −0.178853 0.983876i
\(577\) 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
\(582\) −6.71174 13.0749i −0.278210 0.541971i
\(583\) 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 \(-0.487784\pi\)
0.0383681 + 0.999264i \(0.487784\pi\)
\(588\) −0.811887 + 7.30970i −0.0334817 + 0.301447i
\(589\) 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 \(0.945844\pi\)
\(594\) −5.07900 + 8.30111i −0.208394 + 0.340599i
\(595\) 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 \(-0.141506\pi\)
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 \(0.343675\pi\)
\(602\) 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
\(606\) 1.91088 0.980914i 0.0776243 0.0398469i
\(607\) 4.50778i 0.182965i −0.995807 0.0914827i \(-0.970839\pi\)
0.995807 0.0914827i \(-0.0291606\pi\)
\(608\) −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
\(612\) −9.75058 6.99473i −0.394144 0.282745i
\(613\) −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 \(-0.0909346\pi\)
\(618\) 21.3666 10.9681i 0.859489 0.441202i
\(619\) 28.1365i 1.13090i −0.824782 0.565451i \(-0.808702\pi\)
0.824782 0.565451i \(-0.191298\pi\)
\(620\) 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
\(624\) 34.0074 10.1644i 1.36139 0.406902i
\(625\) 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 \(0.291075\pi\)
−0.610235 + 0.792220i \(0.708925\pi\)
\(632\) −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
\(636\) −42.1628 4.68302i −1.67187 0.185694i
\(637\) −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 \(0.959759\pi\)
\(642\) 3.37874 + 6.58200i 0.133348 + 0.259771i
\(643\) 3.60109i 0.142013i −0.997476 0.0710065i \(-0.977379\pi\)
0.997476 0.0710065i \(-0.0226211\pi\)
\(644\) −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 \(-0.755760\pi\)
−0.719786 + 0.694197i \(0.755760\pi\)
\(648\) −20.1146 15.6014i −0.790176 0.612880i
\(649\) −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 \(-0.276175\pi\)
\(654\) 0.980914 + 1.91088i 0.0383568 + 0.0747214i
\(655\) 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 \(-0.660071\pi\)
−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 \(0.315908\pi\)
\(662\) 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
\(666\) 0.813033 21.7203i 0.0315044 0.841644i
\(667\) 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
\(672\) −8.58821 + 28.3207i −0.331298 + 1.09249i
\(673\) −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 \(0.990777\pi\)
\(678\) 30.5081 15.6607i 1.17166 0.601446i
\(679\) 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 \(-0.451704\pi\)
0.151144 + 0.988512i \(0.451704\pi\)
\(684\) −6.45638 4.63159i −0.246866 0.177093i
\(685\) 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 \(-0.886925\pi\)
0.937565 0.347811i \(-0.113075\pi\)
\(692\) −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
\(696\) −11.7465 9.80365i −0.445249 0.371606i
\(697\) −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 \(-0.107260\pi\)
\(702\) 19.6482 32.1130i 0.741573 1.21203i
\(703\) 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
\(708\) 5.41095 48.7167i 0.203356 1.83088i
\(709\) 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
\(714\) 6.75748 + 13.1640i 0.252893 + 0.492650i
\(715\) 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 \(-0.304190\pi\)
0.577086 + 0.816684i \(0.304190\pi\)
\(720\) 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
\(726\) 10.3430 + 20.1489i 0.383866 + 0.747794i
\(727\) 10.9663i 0.406717i −0.979104 0.203359i \(-0.934814\pi\)
0.979104 0.203359i \(-0.0651857\pi\)
\(728\) −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
\(732\) 1.19429 10.7526i 0.0441423 0.397429i
\(733\) 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
\(738\) −4.76160 0.178236i −0.175277 0.00656096i
\(739\) 26.9752i 0.992300i 0.868237 + 0.496150i \(0.165253\pi\)
−0.868237 + 0.496150i \(0.834747\pi\)
\(740\) 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 \(-0.557563\pi\)
−0.179856 + 0.983693i \(0.557563\pi\)
\(744\) −17.7398 14.8057i −0.650372 0.542804i
\(745\) 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 \(-0.932705\pi\)
0.977735 0.209842i \(-0.0672948\pi\)
\(752\) −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
\(756\) 13.2802 + 28.4417i 0.482996 + 1.03442i
\(757\) −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 \(0.808466\pi\)
\(762\) −32.9100 + 16.8937i −1.19220 + 0.611995i
\(763\) 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
\(768\) −12.7542 + 24.6034i −0.460229 + 0.887800i
\(769\) 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 \(-0.00140942\pi\)
\(774\) 32.8025 + 1.22786i 1.17906 + 0.0441346i
\(775\) 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
\(786\) 6.10797 + 11.8987i