Properties

Label 60.2.e.a.11.1
Level $60$
Weight $2$
Character 60.11
Analytic conductor $0.479$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.479102412128\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.1
Root \(-1.17915 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 60.11
Dual form 60.2.e.a.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17915 - 0.780776i) q^{2} +(1.51022 + 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(-1.11862 - 2.17915i) q^{6} -3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})\) \(q+(-1.17915 - 0.780776i) q^{2} +(1.51022 + 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(-1.11862 - 2.17915i) q^{6} -3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +(0.780776 - 1.17915i) q^{10} -1.32431 q^{11} +(-0.382406 + 3.44293i) q^{12} -5.12311 q^{13} +(-2.35829 + 3.56155i) q^{14} +(-0.848071 + 1.51022i) q^{15} +(-2.78078 + 2.87529i) q^{16} -2.00000i q^{17} +(0.158699 - 4.23967i) q^{18} +1.32431i q^{19} +(-1.84130 + 0.780776i) q^{20} +(2.56155 - 4.56155i) q^{21} +(1.56155 + 1.03399i) q^{22} -0.371834 q^{23} +(3.13907 - 3.76115i) q^{24} -1.00000 q^{25} +(6.04090 + 4.00000i) q^{26} +(0.185917 + 5.19283i) q^{27} +(5.56155 - 2.35829i) q^{28} -3.12311i q^{29} +(2.17915 - 1.11862i) q^{30} -4.71659i q^{31} +(5.52390 - 1.21922i) q^{32} +(-2.00000 - 1.12311i) q^{33} +(-1.56155 + 2.35829i) q^{34} +3.02045 q^{35} +(-3.49737 + 4.87529i) q^{36} +5.12311 q^{37} +(1.03399 - 1.56155i) q^{38} +(-7.73704 - 4.34475i) q^{39} +(2.78078 + 0.516994i) q^{40} +1.12311i q^{41} +(-6.58200 + 3.37874i) q^{42} +7.73704i q^{43} +(-1.03399 - 2.43845i) q^{44} +(-2.56155 + 1.56155i) q^{45} +(0.438447 + 0.290319i) q^{46} -3.02045 q^{47} +(-6.63804 + 1.98403i) q^{48} -2.12311 q^{49} +(1.17915 + 0.780776i) q^{50} +(1.69614 - 3.02045i) q^{51} +(-4.00000 - 9.43318i) q^{52} +12.2462i q^{53} +(3.83521 - 6.26827i) q^{54} -1.32431i q^{55} +(-8.39919 - 1.56155i) q^{56} +(-1.12311 + 2.00000i) q^{57} +(-2.43845 + 3.68260i) q^{58} +14.1498 q^{59} +(-3.44293 - 0.382406i) q^{60} +3.12311 q^{61} +(-3.68260 + 5.56155i) q^{62} +(7.73704 - 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} -5.12311i q^{65} +(1.48140 + 2.88586i) q^{66} -4.34475i q^{67} +(3.68260 - 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} +(-3.56155 - 2.35829i) q^{70} -3.39228 q^{71} +(7.93042 - 3.01802i) q^{72} +8.24621 q^{73} +(-6.04090 - 4.00000i) q^{74} +(-1.51022 - 0.848071i) q^{75} +(-2.43845 + 1.03399i) q^{76} +4.00000i q^{77} +(5.73082 + 11.1640i) q^{78} +8.10887i q^{79} +(-2.87529 - 2.78078i) q^{80} +(-4.12311 + 8.00000i) q^{81} +(0.876894 - 1.32431i) q^{82} -15.1022 q^{83} +(10.3992 + 1.15504i) q^{84} +2.00000 q^{85} +(6.04090 - 9.12311i) q^{86} +(2.64861 - 4.71659i) q^{87} +(-0.684658 + 3.68260i) q^{88} -10.2462i q^{89} +(4.23967 + 0.158699i) q^{90} +15.4741i q^{91} +(-0.290319 - 0.684658i) q^{92} +(4.00000 - 7.12311i) q^{93} +(3.56155 + 2.35829i) q^{94} -1.32431 q^{95} +(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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{4} - 6q^{6} - 4q^{9} - 2q^{10} + 4q^{12} - 8q^{13} - 14q^{16} + 16q^{18} + 4q^{21} - 4q^{22} - 2q^{24} - 8q^{25} + 28q^{28} + 8q^{30} - 16q^{33} + 4q^{34} + 18q^{36} + 8q^{37} + 14q^{40} - 12q^{42} - 4q^{45} + 20q^{46} - 36q^{48} + 16q^{49} - 32q^{52} - 10q^{54} + 24q^{57} - 36q^{58} - 14q^{60} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 12q^{70} + 24q^{72} - 36q^{76} + 40q^{78} + 40q^{82} + 16q^{84} + 16q^{85} + 44q^{88} + 18q^{90} + 32q^{93} + 12q^{94} + 42q^{96} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(5\) 1.00000i 0.447214i
\(6\) −1.11862 2.17915i −0.456676 0.889633i
\(7\) 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
\(10\) 0.780776 1.17915i 0.246903 0.372879i
\(11\) −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 \(-0.751507\pi\)
−0.710447 + 0.703751i \(0.751507\pi\)
\(14\) −2.35829 + 3.56155i −0.630281 + 0.951865i
\(15\) −0.848071 + 1.51022i −0.218971 + 0.389938i
\(16\) −2.78078 + 2.87529i −0.695194 + 0.718822i
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 0.158699 4.23967i 0.0374058 0.999300i
\(19\) 1.32431i 0.303817i 0.988395 + 0.151908i \(0.0485419\pi\)
−0.988395 + 0.151908i \(0.951458\pi\)
\(20\) −1.84130 + 0.780776i −0.411727 + 0.174587i
\(21\) 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 \(0.512343\pi\)
\(24\) 3.13907 3.76115i 0.640760 0.767741i
\(25\) −1.00000 −0.200000
\(26\) 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 \(-0.0936464\pi\)
\(30\) 2.17915 1.11862i 0.397856 0.204232i
\(31\) 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
\(35\) 3.02045 0.510549
\(36\) −3.49737 + 4.87529i −0.582894 + 0.812548i
\(37\) 5.12311 0.842233 0.421117 0.907006i \(-0.361638\pi\)
0.421117 + 0.907006i \(0.361638\pi\)
\(38\) 1.03399 1.56155i 0.167735 0.253317i
\(39\) −7.73704 4.34475i −1.23892 0.695718i
\(40\) 2.78078 + 0.516994i 0.439679 + 0.0817439i
\(41\) 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 \(0.200850\pi\)
−0.807445 + 0.589944i \(0.799150\pi\)
\(44\) −1.03399 2.43845i −0.155879 0.367610i
\(45\) −2.56155 + 1.56155i −0.381854 + 0.232783i
\(46\) 0.438447 + 0.290319i 0.0646455 + 0.0428052i
\(47\) −3.02045 −0.440578 −0.220289 0.975435i \(-0.570700\pi\)
−0.220289 + 0.975435i \(0.570700\pi\)
\(48\) −6.63804 + 1.98403i −0.958119 + 0.286371i
\(49\) −2.12311 −0.303301
\(50\) 1.17915 + 0.780776i 0.166757 + 0.110418i
\(51\) 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 \(0.318076\pi\)
−0.540921 + 0.841073i \(0.681924\pi\)
\(54\) 3.83521 6.26827i 0.521906 0.853003i
\(55\) 1.32431i 0.178570i
\(56\) −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 \(0.127315\pi\)
\(60\) −3.44293 0.382406i −0.444480 0.0493683i
\(61\) 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
\(65\) 5.12311i 0.635443i
\(66\) 1.48140 + 2.88586i 0.182348 + 0.355225i
\(67\) 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
\(70\) −3.56155 2.35829i −0.425687 0.281870i
\(71\) −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 \(-0.339702\pi\)
0.482573 + 0.875856i \(0.339702\pi\)
\(74\) −6.04090 4.00000i −0.702240 0.464991i
\(75\) −1.51022 0.848071i −0.174386 0.0979267i
\(76\) −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 \(0.849225\pi\)
\(80\) −2.87529 2.78078i −0.321467 0.310900i
\(81\) −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 \(0.811000\pi\)
\(84\) 10.3992 + 1.15504i 1.13464 + 0.126025i
\(85\) 2.00000 0.216930
\(86\) 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 \(-0.182730\pi\)
\(90\) 4.23967 + 0.158699i 0.446901 + 0.0167284i
\(91\) 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
\(95\) −1.32431 −0.135871
\(96\) 9.37632 + 2.84336i 0.956966 + 0.290199i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 2.50345 + 1.65767i 0.252887 + 0.167450i
\(99\) −2.06798 3.39228i −0.207839 0.340937i
\(100\) −0.780776 1.84130i −0.0780776 0.184130i
\(101\) 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 \(-0.839526\pi\)
0.875588 0.483058i \(-0.160474\pi\)
\(104\) −2.64861 + 14.2462i −0.259718 + 1.39696i
\(105\) 4.56155 + 2.56155i 0.445162 + 0.249982i
\(106\) 9.56155 14.4401i 0.928700 1.40255i
\(107\) 3.02045 0.291998 0.145999 0.989285i \(-0.453360\pi\)
0.145999 + 0.989285i \(0.453360\pi\)
\(108\) −9.41639 + 4.39676i −0.906093 + 0.423079i
\(109\) −0.876894 −0.0839912 −0.0419956 0.999118i \(-0.513372\pi\)
−0.0419956 + 0.999118i \(0.513372\pi\)
\(110\) −1.03399 + 1.56155i −0.0985868 + 0.148888i
\(111\) 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 \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 2.88586 1.48140i 0.270286 0.138746i
\(115\) 0.371834i 0.0346737i
\(116\) 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
\(120\) 3.76115 + 3.13907i 0.343344 + 0.286557i
\(121\) −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
\(125\) 1.00000i 0.0894427i
\(126\) −12.8057 0.479343i −1.14082 0.0427033i
\(127\) 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
\(130\) −4.00000 + 6.04090i −0.350823 + 0.529822i
\(131\) −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
\(135\) −5.19283 + 0.185917i −0.446927 + 0.0160012i
\(136\) −5.56155 1.03399i −0.476899 0.0886637i
\(137\) 8.24621i 0.704521i 0.935902 + 0.352261i \(0.114587\pi\)
−0.935902 + 0.352261i \(0.885413\pi\)
\(138\) 0.415942 + 0.810281i 0.0354074 + 0.0689757i
\(139\) 17.5420i 1.48790i −0.668237 0.743949i \(-0.732951\pi\)
0.668237 0.743949i \(-0.267049\pi\)
\(140\) 2.35829 + 5.56155i 0.199312 + 0.470037i
\(141\) −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
\(145\) 3.12311 0.259360
\(146\) −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 \(0.805600\pi\)
\(150\) 1.11862 + 2.17915i 0.0913352 + 0.177927i
\(151\) 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
\(155\) 4.71659 0.378846
\(156\) 1.95910 17.6385i 0.156854 1.41221i
\(157\) −3.36932 −0.268901 −0.134450 0.990920i \(-0.542927\pi\)
−0.134450 + 0.990920i \(0.542927\pi\)
\(158\) 6.33122 9.56155i 0.503684 0.760676i
\(159\) −10.3857 + 18.4945i −0.823636 + 1.46671i
\(160\) 1.21922 + 5.52390i 0.0963881 + 0.436703i
\(161\) 1.12311i 0.0885131i
\(162\) 11.1080 6.21395i 0.872724 0.488214i
\(163\) 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
\(165\) 1.12311 2.00000i 0.0874337 0.155700i
\(166\) 17.8078 + 11.7915i 1.38215 + 0.915196i
\(167\) 9.06134 0.701188 0.350594 0.936528i \(-0.385980\pi\)
0.350594 + 0.936528i \(0.385980\pi\)
\(168\) −11.3604 9.48140i −0.876470 0.731506i
\(169\) 13.2462 1.01894
\(170\) −2.35829 1.56155i −0.180873 0.119766i
\(171\) −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 \(-0.975776\pi\)
0.997106 0.0760286i \(-0.0242240\pi\)
\(174\) −6.80571 + 3.49358i −0.515939 + 0.264847i
\(175\) 3.02045i 0.228324i
\(176\) 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 \(0.377906\pi\)
\(180\) −4.87529 3.49737i −0.363383 0.260678i
\(181\) −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
\(185\) 5.12311i 0.376658i
\(186\) −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
\(190\) 1.56155 + 1.03399i 0.113287 + 0.0750133i
\(191\) 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 \(-0.502821\pi\)
−0.00886134 + 0.999961i \(0.502821\pi\)
\(194\) 7.07488 + 4.68466i 0.507947 + 0.336339i
\(195\) 4.34475 7.73704i 0.311134 0.554061i
\(196\) −1.65767 3.90928i −0.118405 0.279234i
\(197\) 4.24621i 0.302530i −0.988493 0.151265i \(-0.951665\pi\)
0.988493 0.151265i \(-0.0483347\pi\)
\(198\) −0.210167 + 5.61463i −0.0149359 + 0.399014i
\(199\) 5.46026i 0.387067i 0.981094 + 0.193534i \(0.0619949\pi\)
−0.981094 + 0.193534i \(0.938005\pi\)
\(200\) −0.516994 + 2.78078i −0.0365570 + 0.196631i
\(201\) 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
\(205\) −1.12311 −0.0784411
\(206\) −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
\(210\) −3.37874 6.58200i −0.233155 0.454201i
\(211\) 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
\(215\) −7.73704 −0.527662
\(216\) 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
\(220\) 2.43845 1.03399i 0.164400 0.0697114i
\(221\) 10.2462i 0.689235i
\(222\) −5.73082 11.1640i −0.384628 0.749279i
\(223\) 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
\(225\) −1.56155 2.56155i −0.104104 0.170770i
\(226\) −10.9309 + 16.5081i −0.727111 + 1.09810i
\(227\) −21.8868 −1.45268 −0.726339 0.687337i \(-0.758780\pi\)
−0.726339 + 0.687337i \(0.758780\pi\)
\(228\) −4.55950 0.506422i −0.301960 0.0335386i
\(229\) −16.2462 −1.07358 −0.536790 0.843716i \(-0.680363\pi\)
−0.536790 + 0.843716i \(0.680363\pi\)
\(230\) −0.290319 + 0.438447i −0.0191431 + 0.0289104i
\(231\) −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 \(0.106227\pi\)
−0.944830 + 0.327561i \(0.893773\pi\)
\(234\) −0.813033 + 21.7203i −0.0531497 + 1.41990i
\(235\) 3.02045i 0.197032i
\(236\) 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 \(0.689998\pi\)
\(240\) −1.98403 6.63804i −0.128069 0.428484i
\(241\) 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
\(245\) 2.12311i 0.135640i
\(246\) 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
\(250\) −0.780776 + 1.17915i −0.0493806 + 0.0745758i
\(251\) −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
\(255\) 3.02045 + 1.69614i 0.189148 + 0.106216i
\(256\) −0.534565 15.9911i −0.0334103 0.999442i
\(257\) 30.4924i 1.90207i −0.309091 0.951033i \(-0.600025\pi\)
0.309091 0.951033i \(-0.399975\pi\)
\(258\) 16.8601 8.65483i 1.04967 0.538826i
\(259\) 15.4741i 0.961512i
\(260\) 9.43318 4.00000i 0.585021 0.248069i
\(261\) 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 \(0.237871\pi\)
\(264\) −4.15709 + 4.98091i −0.255851 + 0.306554i
\(265\) −12.2462 −0.752279
\(266\) −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 \(-0.140358\pi\)
\(270\) 6.26827 + 3.83521i 0.381474 + 0.233404i
\(271\) 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
\(275\) 1.32431 0.0798587
\(276\) 0.142191 1.28020i 0.00855892 0.0770589i
\(277\) 23.3693 1.40413 0.702063 0.712115i \(-0.252262\pi\)
0.702063 + 0.712115i \(0.252262\pi\)
\(278\) −13.6964 + 20.6847i −0.821457 + 1.24058i
\(279\) 12.0818 7.36520i 0.723318 0.440943i
\(280\) 1.56155 8.39919i 0.0933206 0.501948i
\(281\) 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 \(0.242336\pi\)
−0.723925 + 0.689879i \(0.757664\pi\)
\(284\) −2.64861 6.24621i −0.157166 0.370644i
\(285\) −2.00000 1.12311i −0.118470 0.0665270i
\(286\) −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
\(290\) −3.68260 2.43845i −0.216250 0.143191i
\(291\) −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 \(-0.976805\pi\)
0.997346 0.0728044i \(-0.0231949\pi\)
\(294\) 2.37495 + 4.62656i 0.138510 + 0.269826i
\(295\) 14.1498i 0.823831i
\(296\) 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
\(300\) 0.382406 3.44293i 0.0220782 0.198778i
\(301\) 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
\(305\) 3.12311i 0.178829i
\(306\) −8.47934 0.317399i −0.484732 0.0181445i
\(307\) 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
\(310\) −5.56155 3.68260i −0.315875 0.209158i
\(311\) −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 \(-0.719278\pi\)
−0.635673 + 0.771958i \(0.719278\pi\)
\(314\) 3.97292 + 2.63068i 0.224205 + 0.148458i
\(315\) 4.71659 + 7.73704i 0.265750 + 0.435933i
\(316\) −14.9309 + 6.33122i −0.839927 + 0.356159i
\(317\) 16.7386i 0.940135i 0.882630 + 0.470068i \(0.155770\pi\)
−0.882630 + 0.470068i \(0.844230\pi\)
\(318\) 26.6863 13.6989i 1.49649 0.768196i
\(319\) 4.13595i 0.231569i
\(320\) 2.87529 7.46543i 0.160734 0.417330i
\(321\) 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
\(325\) 5.12311 0.284179
\(326\) −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
\(330\) −2.88586 + 1.48140i −0.158861 + 0.0815484i
\(331\) 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
\(335\) 4.34475 0.237379
\(336\) 5.99267 + 20.0499i 0.326927 + 1.09381i
\(337\) −1.50758 −0.0821230 −0.0410615 0.999157i \(-0.513074\pi\)
−0.0410615 + 0.999157i \(0.513074\pi\)
\(338\) −15.6192 10.3423i −0.849574 0.562549i
\(339\) 11.8730 21.1431i 0.644852 1.14834i
\(340\) 1.56155 + 3.68260i 0.0846871 + 0.199717i
\(341\) 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
\(345\) 0.315342 0.561553i 0.0169774 0.0302330i
\(346\) −1.56155 + 2.35829i −0.0839496 + 0.126783i
\(347\) 22.6305 1.21487 0.607434 0.794370i \(-0.292199\pi\)
0.607434 + 0.794370i \(0.292199\pi\)
\(348\) 10.7526 + 1.19429i 0.576402 + 0.0640208i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 2.35829 3.56155i 0.126056 0.190373i
\(351\) −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 \(0.181122\pi\)
−0.842435 + 0.538799i \(0.818878\pi\)
\(354\) −15.8283 30.8344i −0.841262 1.63883i
\(355\) 3.39228i 0.180044i
\(356\) 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 \(0.692189\pi\)
\(360\) 3.01802 + 7.93042i 0.159064 + 0.417970i
\(361\) 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
\(365\) 8.24621i 0.431626i
\(366\) −3.49358 6.80571i −0.182612 0.355740i
\(367\) 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
\(370\) 4.00000 6.04090i 0.207950 0.314051i
\(371\) 36.9890 1.92038
\(372\) 16.2389 + 1.80365i 0.841947 + 0.0935149i
\(373\) −9.12311 −0.472377 −0.236188 0.971707i \(-0.575898\pi\)
−0.236188 + 0.971707i \(0.575898\pi\)
\(374\) 2.06798 3.12311i 0.106932 0.161492i
\(375\) 0.848071 1.51022i 0.0437942 0.0779876i
\(376\) −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 \(0.840505\pi\)
\(380\) −1.03399 2.43845i −0.0530424 0.125090i
\(381\) −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 \(0.373910\pi\)
\(384\) 2.08533 + 19.4846i 0.106417 + 0.994322i
\(385\) −4.00000 −0.203859
\(386\) 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 \(0.823787\pi\)
\(390\) −11.1640 + 5.73082i −0.565311 + 0.290192i
\(391\) 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
\(395\) −8.10887 −0.408002
\(396\) 4.63159 6.45638i 0.232746 0.324445i
\(397\) 14.8769 0.746650 0.373325 0.927701i \(-0.378218\pi\)
0.373325 + 0.927701i \(0.378218\pi\)
\(398\) 4.26324 6.43845i 0.213697 0.322730i
\(399\) 6.04090 + 3.39228i 0.302423 + 0.169827i
\(400\) 2.78078 2.87529i 0.139039 0.143764i
\(401\) 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
\(405\) −8.00000 4.12311i −0.397523 0.204879i
\(406\) 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 \(0.284194\pi\)
\(410\) 1.32431 + 0.876894i 0.0654029 + 0.0433067i
\(411\) −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
\(415\) 15.1022i 0.741340i
\(416\) −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 \(0.557580\pi\)
\(420\) −1.15504 + 10.3992i −0.0563600 + 0.507429i
\(421\) −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
\(425\) 2.00000i 0.0970143i
\(426\) 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
\(430\) 9.12311 + 6.04090i 0.439955 + 0.291318i
\(431\) 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 \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 16.7984 + 11.1231i 0.806348 + 0.533926i
\(435\) 4.71659 + 2.64861i 0.226143 + 0.126991i
\(436\) −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 \(0.928996\pi\)
\(440\) −3.68260 0.684658i −0.175561 0.0326398i
\(441\) −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 \(0.371057\pi\)
\(444\) −1.95910 + 17.6385i −0.0929750 + 0.837086i
\(445\) 10.2462 0.485717
\(446\) 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 \(0.776516\pi\)
\(450\) −0.158699 + 4.23967i −0.00748116 + 0.199860i
\(451\) 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
\(455\) −15.4741 −0.725436
\(456\) 4.98091 + 4.15709i 0.233253 + 0.194674i
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 19.1567 + 12.6847i 0.895133 + 0.592715i
\(459\) 10.3857 0.371834i 0.484761 0.0173557i
\(460\) 0.684658 0.290319i 0.0319224 0.0135362i
\(461\) 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 \(0.0223593\pi\)
−0.997534 + 0.0701861i \(0.977641\pi\)
\(464\) 8.97983 + 8.68466i 0.416878 + 0.403175i
\(465\) 7.12311 + 4.00000i 0.330326 + 0.185496i
\(466\) 7.80776 11.7915i 0.361688 0.546229i
\(467\) −2.27678 −0.105357 −0.0526784 0.998612i \(-0.516776\pi\)
−0.0526784 + 0.998612i \(0.516776\pi\)
\(468\) 17.9174 24.9766i 0.828231 1.15454i
\(469\) −13.1231 −0.605969
\(470\) −2.35829 + 3.56155i −0.108780 + 0.164282i
\(471\) −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
\(475\) 1.32431i 0.0607634i
\(476\) −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 \(0.699302\pi\)
\(480\) −2.84336 + 9.37632i −0.129781 + 0.427968i
\(481\) −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
\(485\) 6.00000i 0.272446i
\(486\) 22.0454 + 0.0358705i 0.999999 + 0.00162712i
\(487\) 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
\(490\) −1.65767 + 2.50345i −0.0748859 + 0.113095i
\(491\) −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
\(495\) 3.39228 2.06798i 0.152472 0.0929486i
\(496\) 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 \(0.743059\pi\)
\(500\) 1.84130 0.780776i 0.0823455 0.0349174i
\(501\) 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 \(0.603719\pi\)
\(504\) −9.11578 23.9534i −0.406049 1.06697i
\(505\) −0.876894 −0.0390213
\(506\) −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 \(-0.0792843\pi\)
\(510\) −2.23725 4.35829i −0.0990669 0.192989i
\(511\) 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
\(515\) 9.80501 0.432060
\(516\) −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
\(520\) −14.2462 2.64861i −0.624738 0.116149i
\(521\) 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 \(-0.719444\pi\)
0.636077 0.771625i \(-0.280556\pi\)
\(524\) −4.26324 10.0540i −0.186241 0.439210i
\(525\) −2.56155 + 4.56155i −0.111795 + 0.199082i
\(526\) −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
\(530\) 14.4401 + 9.56155i 0.627237 + 0.415327i
\(531\) 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
\(535\) 3.02045i 0.130585i
\(536\) −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
\(540\) −4.39676 9.41639i −0.189207 0.405217i
\(541\) −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
\(545\) 0.876894i 0.0375620i
\(546\) 33.7203 17.3097i 1.44309 0.740785i
\(547\) 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
\(550\) −1.56155 1.03399i −0.0665848 0.0440894i
\(551\) 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
\(555\) −4.34475 + 7.73704i −0.184425 + 0.328419i
\(556\) 32.3002 13.6964i 1.36983 0.580858i
\(557\) 36.2462i 1.53580i −0.640569 0.767901i \(-0.721301\pi\)
0.640569 0.767901i \(-0.278699\pi\)
\(558\) −19.9968 0.748519i −0.846532 0.0316874i
\(559\) 39.6377i 1.67649i
\(560\) −8.39919 + 8.68466i −0.354931 + 0.366994i
\(561\) −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 \(0.446762\pi\)
\(564\) 1.15504 10.3992i 0.0486358 0.437885i
\(565\) 14.0000 0.588984
\(566\) 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 \(0.911297\pi\)
\(570\) 1.48140 + 2.88586i 0.0620490 + 0.120875i
\(571\) 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
\(575\) 0.371834 0.0155066
\(576\) −4.29247 23.6130i −0.178853 0.983876i
\(577\) −32.2462 −1.34243 −0.671214 0.741264i \(-0.734227\pi\)
−0.671214 + 0.741264i \(0.734227\pi\)
\(578\) −15.3289 10.1501i −0.637599 0.422188i
\(579\) −0.371834 0.208805i −0.0154529 0.00867762i
\(580\) 2.43845 + 5.75058i 0.101251 + 0.238780i
\(581\) 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
\(585\) 13.1231 8.00000i 0.542574 0.330759i
\(586\) −1.94602 + 2.93893i −0.0803895 + 0.121406i
\(587\) −1.85917 −0.0767362 −0.0383681 0.999264i \(-0.512216\pi\)
−0.0383681 + 0.999264i \(0.512216\pi\)
\(588\) 0.811887 7.30970i 0.0334817 0.301447i
\(589\) 6.24621 0.257371
\(590\) 11.0478 16.6847i 0.454831 0.686897i
\(591\) 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 \(-0.945844\pi\)
0.985562 0.169316i \(-0.0541557\pi\)
\(594\) −5.07900 + 8.30111i −0.208394 + 0.340599i
\(595\) 6.04090i 0.247653i
\(596\) −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 \(0.141506\pi\)
\(600\) −3.13907 + 3.76115i −0.128152 + 0.153548i
\(601\) 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
\(605\) 9.24621i 0.375912i
\(606\) 1.91088 0.980914i 0.0776243 0.0398469i
\(607\) 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
\(610\) 2.43845 3.68260i 0.0987298 0.149104i
\(611\) 15.4741 0.626014
\(612\) 9.75058 + 6.99473i 0.394144 + 0.282745i
\(613\) 9.12311 0.368479 0.184239 0.982881i \(-0.441018\pi\)
0.184239 + 0.982881i \(0.441018\pi\)
\(614\) 8.68951 13.1231i 0.350680 0.529605i
\(615\) −1.69614 0.952473i −0.0683950 0.0384074i
\(616\) 11.1231 + 2.06798i 0.448163 + 0.0833211i
\(617\) 14.0000i 0.563619i 0.959470 + 0.281809i \(0.0909346\pi\)
−0.959470 + 0.281809i \(0.909065\pi\)
\(618\) −21.3666 + 10.9681i −0.859489 + 0.441202i
\(619\) 28.1365i 1.13090i −0.824782 0.565451i \(-0.808702\pi\)
0.824782 0.565451i \(-0.191298\pi\)
\(620\) 3.68260 + 8.68466i 0.147897 + 0.348784i
\(621\) −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
\(625\) 1.00000 0.0400000
\(626\) 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
\(630\) 0.479343 12.8057i 0.0190975 0.510192i
\(631\) 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
\(635\) −15.1022 −0.599314
\(636\) −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
\(640\) −9.21922 + 6.55789i −0.364422 + 0.259223i
\(641\) 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 \(0.0226211\pi\)
−0.997476 + 0.0710065i \(0.977379\pi\)
\(644\) −2.06798 + 0.876894i −0.0814896 + 0.0345545i
\(645\) −11.6847 6.56155i −0.460083 0.258361i
\(646\) −3.12311 2.06798i −0.122877 0.0813634i
\(647\) 36.6172 1.43957 0.719786 0.694197i \(-0.244240\pi\)
0.719786 + 0.694197i \(0.244240\pi\)
\(648\) 20.1146 + 15.6014i 0.790176 + 0.612880i
\(649\) −18.7386 −0.735556
\(650\) −6.04090 4.00000i −0.236943 0.156893i
\(651\) −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 \(0.276175\pi\)
−0.646638 + 0.762797i \(0.723825\pi\)
\(654\) 0.980914 + 1.91088i 0.0383568 + 0.0747214i
\(655\) 5.46026i 0.213350i
\(656\) −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 \(0.660071\pi\)
\(660\) 4.55950 + 0.506422i 0.177478 + 0.0197125i
\(661\) 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
\(665\) 4.00000i 0.155113i
\(666\) 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
\(670\) −5.12311 3.39228i −0.197923 0.131055i
\(671\) −4.13595 −0.159667
\(672\) 8.58821 28.3207i 0.331298 1.09249i
\(673\) 22.4924 0.867019 0.433510 0.901149i \(-0.357275\pi\)
0.433510 + 0.901149i \(0.357275\pi\)
\(674\) 1.77766 + 1.17708i 0.0684727 + 0.0453395i
\(675\) −0.185917 5.19283i −0.00715595 0.199872i
\(676\) 10.3423 + 24.3903i 0.397782 + 0.938087i
\(677\) 1.50758i 0.0579409i −0.999580 0.0289705i \(-0.990777\pi\)
0.999580 0.0289705i \(-0.00922287\pi\)
\(678\) −30.5081 + 15.6607i −1.17166 + 0.601446i
\(679\) 18.1227i 0.695485i
\(680\) 1.03399 5.56155i 0.0396516 0.213276i
\(681\) −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 \(0.548296\pi\)
\(684\) −6.45638 4.63159i −0.246866 0.177093i
\(685\) −8.24621 −0.315072
\(686\) −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
\(690\) −0.810281 + 0.415942i −0.0308469 + 0.0158346i
\(691\) 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
\(695\) 17.5420 0.665408
\(696\) −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
\(700\) −5.56155 + 2.35829i −0.210207 + 0.0891352i
\(701\) 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
\(705\) 2.56155 4.56155i 0.0964737 0.171798i
\(706\) 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 \(0.461097\pi\)
\(710\) −2.64861 + 4.00000i −0.0994007 + 0.150117i
\(711\) −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
\(715\) 6.78456i 0.253728i
\(716\) 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 \(0.304190\pi\)
\(720\) 2.63319 11.7075i 0.0981332 0.436314i
\(721\) −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
\(725\) 3.12311i 0.115989i
\(726\) 10.3430 + 20.1489i 0.383866 + 0.747794i
\(727\) 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
\(730\) 6.43845 9.72350i 0.238298 0.359883i
\(731\) 15.4741 0.572329
\(732\) −1.19429 + 10.7526i −0.0441423 + 0.397429i
\(733\) −26.8769 −0.992721 −0.496360 0.868117i \(-0.665331\pi\)
−0.496360 + 0.868117i \(0.665331\pi\)
\(734\) −8.56222 + 12.9309i −0.316037 + 0.477287i
\(735\) 1.80054 3.20636i 0.0664140 0.118269i
\(736\) −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 \(0.834747\pi\)
\(740\) −9.43318 + 4.00000i −0.346771 + 0.147043i
\(741\) 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 \(0.442437\pi\)
\(744\) −17.7398 14.8057i −0.650372 0.542804i
\(745\) −14.0000 −0.512920
\(746\) 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
\(750\) −2.17915 + 1.11862i −0.0795712 + 0.0408463i
\(751\) 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
\(755\) 7.36520 0.268047
\(756\) 13.2802 + 28.4417i 0.482996 + 1.03442i
\(757\) 10.8769 0.395327 0.197664 0.980270i \(-0.436665\pi\)
0.197664 + 0.980270i \(0.436665\pi\)
\(758\) 14.6031 22.0540i 0.530409 0.801036i
\(759\) 0.743668 + 0.417609i 0.0269934 + 0.0151582i
\(760\) −0.684658 + 3.68260i −0.0248352 + 0.133582i
\(761\) 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
\(765\) 3.12311 + 5.12311i 0.112916 + 0.185226i
\(766\) −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 \(0.251882\pi\)
\(770\) 4.71659 + 3.12311i 0.169974 + 0.112549i
\(771\) 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 \(0.00140942\pi\)
−0.999990 + 0.00442780i \(0.998591\pi\)
\(774\) 32.8025 + 1.22786i 1.17906 + 0.0441346i
\(775\) 4.71659i 0.169425i
\(776\) −3.10196 + 16.6847i −0.111354 + 0.598944i
\(777\) 13.1231 23.3693i 0.470789 0.838370i
\(778\)