Properties

Label 177.3.b.a.119.19
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.19
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.20

$q$-expansion

\(f(q)\) \(=\) \(q-0.00789729i q^{2} +(2.45651 + 1.72208i) q^{3} +3.99994 q^{4} +4.78355i q^{5} +(0.0135997 - 0.0193998i) q^{6} +0.326558 q^{7} -0.0631778i q^{8} +(3.06891 + 8.46060i) q^{9} +O(q^{10})\) \(q-0.00789729i q^{2} +(2.45651 + 1.72208i) q^{3} +3.99994 q^{4} +4.78355i q^{5} +(0.0135997 - 0.0193998i) q^{6} +0.326558 q^{7} -0.0631778i q^{8} +(3.06891 + 8.46060i) q^{9} +0.0377771 q^{10} -7.17249i q^{11} +(9.82590 + 6.88819i) q^{12} -19.3728 q^{13} -0.00257892i q^{14} +(-8.23763 + 11.7509i) q^{15} +15.9993 q^{16} -10.2788i q^{17} +(0.0668158 - 0.0242361i) q^{18} -1.08623 q^{19} +19.1339i q^{20} +(0.802193 + 0.562357i) q^{21} -0.0566432 q^{22} -32.0040i q^{23} +(0.108797 - 0.155197i) q^{24} +2.11765 q^{25} +0.152993i q^{26} +(-7.03097 + 26.0685i) q^{27} +1.30621 q^{28} +29.7395i q^{29} +(0.0927999 + 0.0650550i) q^{30} +41.9784 q^{31} -0.379062i q^{32} +(12.3516 - 17.6193i) q^{33} -0.0811747 q^{34} +1.56211i q^{35} +(12.2755 + 33.8419i) q^{36} +15.1073 q^{37} +0.00857827i q^{38} +(-47.5895 - 33.3614i) q^{39} +0.302214 q^{40} +12.5253i q^{41} +(0.00444110 - 0.00633515i) q^{42} +1.19642 q^{43} -28.6895i q^{44} +(-40.4717 + 14.6803i) q^{45} -0.252745 q^{46} -75.4877i q^{47} +(39.3024 + 27.5519i) q^{48} -48.8934 q^{49} -0.0167237i q^{50} +(17.7009 - 25.2500i) q^{51} -77.4899 q^{52} -69.0255i q^{53} +(0.205870 + 0.0555256i) q^{54} +34.3100 q^{55} -0.0206312i q^{56} +(-2.66834 - 1.87057i) q^{57} +0.234861 q^{58} +7.68115i q^{59} +(-32.9500 + 47.0027i) q^{60} -87.2267 q^{61} -0.331516i q^{62} +(1.00218 + 2.76287i) q^{63} +63.9940 q^{64} -92.6707i q^{65} +(-0.139145 - 0.0975439i) q^{66} -37.6499 q^{67} -41.1146i q^{68} +(55.1133 - 78.6182i) q^{69} +0.0123364 q^{70} -36.3578i q^{71} +(0.534522 - 0.193887i) q^{72} +25.2915 q^{73} -0.119307i q^{74} +(5.20203 + 3.64675i) q^{75} -4.34485 q^{76} -2.34223i q^{77} +(-0.263465 + 0.375828i) q^{78} -103.938 q^{79} +76.5332i q^{80} +(-62.1635 + 51.9297i) q^{81} +0.0989162 q^{82} +72.1954i q^{83} +(3.20872 + 2.24939i) q^{84} +49.1692 q^{85} -0.00944845i q^{86} +(-51.2136 + 73.0554i) q^{87} -0.453142 q^{88} +143.843i q^{89} +(0.115935 + 0.319617i) q^{90} -6.32633 q^{91} -128.014i q^{92} +(103.120 + 72.2900i) q^{93} -0.596149 q^{94} -5.19603i q^{95} +(0.652773 - 0.931171i) q^{96} +57.9703 q^{97} +0.386125i q^{98} +(60.6836 - 22.0117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.00789729i 0.00394865i −0.999998 0.00197432i \(-0.999372\pi\)
0.999998 0.00197432i \(-0.000628447\pi\)
\(3\) 2.45651 + 1.72208i 0.818838 + 0.574025i
\(4\) 3.99994 0.999984
\(5\) 4.78355i 0.956710i 0.878167 + 0.478355i \(0.158767\pi\)
−0.878167 + 0.478355i \(0.841233\pi\)
\(6\) 0.0135997 0.0193998i 0.00226662 0.00323330i
\(7\) 0.326558 0.0466511 0.0233255 0.999728i \(-0.492575\pi\)
0.0233255 + 0.999728i \(0.492575\pi\)
\(8\) 0.0631778i 0.00789723i
\(9\) 3.06891 + 8.46060i 0.340990 + 0.940067i
\(10\) 0.0377771 0.00377771
\(11\) 7.17249i 0.652044i −0.945362 0.326022i \(-0.894292\pi\)
0.945362 0.326022i \(-0.105708\pi\)
\(12\) 9.82590 + 6.88819i 0.818825 + 0.574016i
\(13\) −19.3728 −1.49021 −0.745107 0.666945i \(-0.767602\pi\)
−0.745107 + 0.666945i \(0.767602\pi\)
\(14\) 0.00257892i 0.000184209i
\(15\) −8.23763 + 11.7509i −0.549176 + 0.783390i
\(16\) 15.9993 0.999953
\(17\) 10.2788i 0.604635i −0.953207 0.302318i \(-0.902240\pi\)
0.953207 0.302318i \(-0.0977603\pi\)
\(18\) 0.0668158 0.0242361i 0.00371199 0.00134645i
\(19\) −1.08623 −0.0571700 −0.0285850 0.999591i \(-0.509100\pi\)
−0.0285850 + 0.999591i \(0.509100\pi\)
\(20\) 19.1339i 0.956695i
\(21\) 0.802193 + 0.562357i 0.0381997 + 0.0267789i
\(22\) −0.0566432 −0.00257469
\(23\) 32.0040i 1.39148i −0.718295 0.695739i \(-0.755077\pi\)
0.718295 0.695739i \(-0.244923\pi\)
\(24\) 0.108797 0.155197i 0.00453321 0.00646655i
\(25\) 2.11765 0.0847058
\(26\) 0.152993i 0.00588433i
\(27\) −7.03097 + 26.0685i −0.260406 + 0.965499i
\(28\) 1.30621 0.0466504
\(29\) 29.7395i 1.02550i 0.858538 + 0.512750i \(0.171373\pi\)
−0.858538 + 0.512750i \(0.828627\pi\)
\(30\) 0.0927999 + 0.0650550i 0.00309333 + 0.00216850i
\(31\) 41.9784 1.35414 0.677071 0.735918i \(-0.263249\pi\)
0.677071 + 0.735918i \(0.263249\pi\)
\(32\) 0.379062i 0.0118457i
\(33\) 12.3516 17.6193i 0.374290 0.533918i
\(34\) −0.0811747 −0.00238749
\(35\) 1.56211i 0.0446316i
\(36\) 12.2755 + 33.8419i 0.340985 + 0.940052i
\(37\) 15.1073 0.408305 0.204153 0.978939i \(-0.434556\pi\)
0.204153 + 0.978939i \(0.434556\pi\)
\(38\) 0.00857827i 0.000225744i
\(39\) −47.5895 33.3614i −1.22024 0.855420i
\(40\) 0.302214 0.00755536
\(41\) 12.5253i 0.305496i 0.988265 + 0.152748i \(0.0488123\pi\)
−0.988265 + 0.152748i \(0.951188\pi\)
\(42\) 0.00444110 0.00633515i 0.000105740 0.000150837i
\(43\) 1.19642 0.0278236 0.0139118 0.999903i \(-0.495572\pi\)
0.0139118 + 0.999903i \(0.495572\pi\)
\(44\) 28.6895i 0.652034i
\(45\) −40.4717 + 14.6803i −0.899371 + 0.326229i
\(46\) −0.252745 −0.00549445
\(47\) 75.4877i 1.60612i −0.595897 0.803061i \(-0.703203\pi\)
0.595897 0.803061i \(-0.296797\pi\)
\(48\) 39.3024 + 27.5519i 0.818799 + 0.573998i
\(49\) −48.8934 −0.997824
\(50\) 0.0167237i 0.000334473i
\(51\) 17.7009 25.2500i 0.347076 0.495098i
\(52\) −77.4899 −1.49019
\(53\) 69.0255i 1.30237i −0.758920 0.651184i \(-0.774273\pi\)
0.758920 0.651184i \(-0.225727\pi\)
\(54\) 0.205870 + 0.0555256i 0.00381241 + 0.00102825i
\(55\) 34.3100 0.623817
\(56\) 0.0206312i 0.000368414i
\(57\) −2.66834 1.87057i −0.0468129 0.0328170i
\(58\) 0.234861 0.00404933
\(59\) 7.68115i 0.130189i
\(60\) −32.9500 + 47.0027i −0.549167 + 0.783378i
\(61\) −87.2267 −1.42995 −0.714973 0.699152i \(-0.753561\pi\)
−0.714973 + 0.699152i \(0.753561\pi\)
\(62\) 0.331516i 0.00534703i
\(63\) 1.00218 + 2.76287i 0.0159076 + 0.0438551i
\(64\) 63.9940 0.999906
\(65\) 92.6707i 1.42570i
\(66\) −0.139145 0.0975439i −0.00210825 0.00147794i
\(67\) −37.6499 −0.561938 −0.280969 0.959717i \(-0.590656\pi\)
−0.280969 + 0.959717i \(0.590656\pi\)
\(68\) 41.1146i 0.604626i
\(69\) 55.1133 78.6182i 0.798743 1.13939i
\(70\) 0.0123364 0.000176234
\(71\) 36.3578i 0.512081i −0.966666 0.256041i \(-0.917582\pi\)
0.966666 0.256041i \(-0.0824181\pi\)
\(72\) 0.534522 0.193887i 0.00742392 0.00269288i
\(73\) 25.2915 0.346459 0.173230 0.984881i \(-0.444580\pi\)
0.173230 + 0.984881i \(0.444580\pi\)
\(74\) 0.119307i 0.00161225i
\(75\) 5.20203 + 3.64675i 0.0693603 + 0.0486233i
\(76\) −4.34485 −0.0571691
\(77\) 2.34223i 0.0304186i
\(78\) −0.263465 + 0.375828i −0.00337775 + 0.00481831i
\(79\) −103.938 −1.31567 −0.657836 0.753161i \(-0.728528\pi\)
−0.657836 + 0.753161i \(0.728528\pi\)
\(80\) 76.5332i 0.956665i
\(81\) −62.1635 + 51.9297i −0.767451 + 0.641107i
\(82\) 0.0989162 0.00120630
\(83\) 72.1954i 0.869824i 0.900473 + 0.434912i \(0.143220\pi\)
−0.900473 + 0.434912i \(0.856780\pi\)
\(84\) 3.20872 + 2.24939i 0.0381991 + 0.0267785i
\(85\) 49.1692 0.578461
\(86\) 0.00944845i 0.000109866i
\(87\) −51.2136 + 73.0554i −0.588662 + 0.839718i
\(88\) −0.453142 −0.00514934
\(89\) 143.843i 1.61622i 0.589034 + 0.808108i \(0.299509\pi\)
−0.589034 + 0.808108i \(0.700491\pi\)
\(90\) 0.115935 + 0.319617i 0.00128816 + 0.00355130i
\(91\) −6.32633 −0.0695201
\(92\) 128.014i 1.39146i
\(93\) 103.120 + 72.2900i 1.10882 + 0.777311i
\(94\) −0.596149 −0.00634201
\(95\) 5.19603i 0.0546951i
\(96\) 0.652773 0.931171i 0.00679972 0.00969970i
\(97\) 57.9703 0.597632 0.298816 0.954311i \(-0.403408\pi\)
0.298816 + 0.954311i \(0.403408\pi\)
\(98\) 0.386125i 0.00394005i
\(99\) 60.6836 22.0117i 0.612965 0.222341i
\(100\) 8.47045 0.0847045
\(101\) 139.103i 1.37726i −0.725113 0.688629i \(-0.758213\pi\)
0.725113 0.688629i \(-0.241787\pi\)
\(102\) −0.199407 0.139789i −0.00195497 0.00137048i
\(103\) 24.0668 0.233658 0.116829 0.993152i \(-0.462727\pi\)
0.116829 + 0.993152i \(0.462727\pi\)
\(104\) 1.22393i 0.0117686i
\(105\) −2.69006 + 3.83733i −0.0256196 + 0.0365460i
\(106\) −0.545114 −0.00514259
\(107\) 17.8500i 0.166822i 0.996515 + 0.0834111i \(0.0265815\pi\)
−0.996515 + 0.0834111i \(0.973419\pi\)
\(108\) −28.1234 + 104.272i −0.260402 + 0.965484i
\(109\) 27.7625 0.254702 0.127351 0.991858i \(-0.459353\pi\)
0.127351 + 0.991858i \(0.459353\pi\)
\(110\) 0.270956i 0.00246323i
\(111\) 37.1112 + 26.0159i 0.334336 + 0.234377i
\(112\) 5.22468 0.0466489
\(113\) 5.59084i 0.0494764i −0.999694 0.0247382i \(-0.992125\pi\)
0.999694 0.0247382i \(-0.00787522\pi\)
\(114\) −0.0147724 + 0.0210726i −0.000129583 + 0.000184848i
\(115\) 153.093 1.33124
\(116\) 118.956i 1.02548i
\(117\) −59.4534 163.905i −0.508149 1.40090i
\(118\) 0.0606602 0.000514070
\(119\) 3.35662i 0.0282069i
\(120\) 0.742393 + 0.520436i 0.00618661 + 0.00433697i
\(121\) 69.5554 0.574838
\(122\) 0.688855i 0.00564635i
\(123\) −21.5696 + 30.7687i −0.175362 + 0.250152i
\(124\) 167.911 1.35412
\(125\) 129.719i 1.03775i
\(126\) 0.0218192 0.00791448i 0.000173168 6.28134e-5i
\(127\) −21.7333 −0.171128 −0.0855641 0.996333i \(-0.527269\pi\)
−0.0855641 + 0.996333i \(0.527269\pi\)
\(128\) 2.02163i 0.0157940i
\(129\) 2.93901 + 2.06032i 0.0227831 + 0.0159715i
\(130\) −0.731847 −0.00562960
\(131\) 234.990i 1.79382i 0.442216 + 0.896909i \(0.354192\pi\)
−0.442216 + 0.896909i \(0.645808\pi\)
\(132\) 49.4055 70.4761i 0.374284 0.533910i
\(133\) −0.354717 −0.00266704
\(134\) 0.297332i 0.00221889i
\(135\) −124.700 33.6330i −0.923703 0.249133i
\(136\) −0.649392 −0.00477494
\(137\) 21.1075i 0.154069i −0.997028 0.0770346i \(-0.975455\pi\)
0.997028 0.0770346i \(-0.0245452\pi\)
\(138\) −0.620871 0.435246i −0.00449906 0.00315395i
\(139\) −166.049 −1.19459 −0.597297 0.802020i \(-0.703759\pi\)
−0.597297 + 0.802020i \(0.703759\pi\)
\(140\) 6.24832i 0.0446309i
\(141\) 129.996 185.437i 0.921954 1.31515i
\(142\) −0.287128 −0.00202203
\(143\) 138.951i 0.971686i
\(144\) 49.1003 + 135.363i 0.340974 + 0.940023i
\(145\) −142.260 −0.981106
\(146\) 0.199735i 0.00136804i
\(147\) −120.107 84.1981i −0.817056 0.572776i
\(148\) 60.4282 0.408299
\(149\) 131.101i 0.879874i 0.898029 + 0.439937i \(0.144999\pi\)
−0.898029 + 0.439937i \(0.855001\pi\)
\(150\) 0.0287994 0.0410819i 0.000191996 0.000273879i
\(151\) −143.720 −0.951790 −0.475895 0.879502i \(-0.657876\pi\)
−0.475895 + 0.879502i \(0.657876\pi\)
\(152\) 0.0686256i 0.000451484i
\(153\) 86.9648 31.5447i 0.568398 0.206175i
\(154\) −0.0184973 −0.000120112
\(155\) 200.806i 1.29552i
\(156\) −190.355 133.444i −1.22022 0.855407i
\(157\) −116.809 −0.744006 −0.372003 0.928231i \(-0.621329\pi\)
−0.372003 + 0.928231i \(0.621329\pi\)
\(158\) 0.820829i 0.00519512i
\(159\) 118.867 169.562i 0.747592 1.06643i
\(160\) 1.81326 0.0113329
\(161\) 10.4511i 0.0649140i
\(162\) 0.410104 + 0.490924i 0.00253151 + 0.00303039i
\(163\) 240.382 1.47474 0.737369 0.675491i \(-0.236068\pi\)
0.737369 + 0.675491i \(0.236068\pi\)
\(164\) 50.1006i 0.305491i
\(165\) 84.2828 + 59.0843i 0.510805 + 0.358087i
\(166\) 0.570148 0.00343463
\(167\) 153.282i 0.917859i 0.888473 + 0.458929i \(0.151767\pi\)
−0.888473 + 0.458929i \(0.848233\pi\)
\(168\) 0.0355285 0.0506808i 0.000211479 0.000301672i
\(169\) 206.305 1.22074
\(170\) 0.388303i 0.00228414i
\(171\) −3.33354 9.19015i −0.0194944 0.0537436i
\(172\) 4.78559 0.0278232
\(173\) 198.430i 1.14699i −0.819208 0.573497i \(-0.805586\pi\)
0.819208 0.573497i \(-0.194414\pi\)
\(174\) 0.576940 + 0.404449i 0.00331575 + 0.00232442i
\(175\) 0.691534 0.00395162
\(176\) 114.754i 0.652014i
\(177\) −13.2275 + 18.8688i −0.0747317 + 0.106604i
\(178\) 1.13597 0.00638187
\(179\) 84.3641i 0.471308i −0.971837 0.235654i \(-0.924277\pi\)
0.971837 0.235654i \(-0.0757232\pi\)
\(180\) −161.884 + 58.7203i −0.899357 + 0.326224i
\(181\) −300.804 −1.66190 −0.830950 0.556348i \(-0.812202\pi\)
−0.830950 + 0.556348i \(0.812202\pi\)
\(182\) 0.0499609i 0.000274510i
\(183\) −214.274 150.211i −1.17089 0.820825i
\(184\) −2.02194 −0.0109888
\(185\) 72.2665i 0.390630i
\(186\) 0.570895 0.814372i 0.00306933 0.00437835i
\(187\) −73.7246 −0.394249
\(188\) 301.946i 1.60610i
\(189\) −2.29602 + 8.51286i −0.0121482 + 0.0450416i
\(190\) −0.0410346 −0.000215971
\(191\) 62.9427i 0.329543i 0.986332 + 0.164771i \(0.0526886\pi\)
−0.986332 + 0.164771i \(0.947311\pi\)
\(192\) 157.202 + 110.203i 0.818761 + 0.573971i
\(193\) −52.7589 −0.273362 −0.136681 0.990615i \(-0.543644\pi\)
−0.136681 + 0.990615i \(0.543644\pi\)
\(194\) 0.457808i 0.00235984i
\(195\) 159.586 227.647i 0.818389 1.16742i
\(196\) −195.570 −0.997808
\(197\) 43.3687i 0.220146i −0.993924 0.110073i \(-0.964892\pi\)
0.993924 0.110073i \(-0.0351084\pi\)
\(198\) −0.173833 0.479236i −0.000877945 0.00242038i
\(199\) 316.929 1.59261 0.796304 0.604896i \(-0.206785\pi\)
0.796304 + 0.604896i \(0.206785\pi\)
\(200\) 0.133788i 0.000668941i
\(201\) −92.4874 64.8359i −0.460136 0.322567i
\(202\) −1.09854 −0.00543831
\(203\) 9.71166i 0.0478407i
\(204\) 70.8024 100.998i 0.347070 0.495090i
\(205\) −59.9156 −0.292271
\(206\) 0.190062i 0.000922633i
\(207\) 270.773 98.2175i 1.30808 0.474481i
\(208\) −309.950 −1.49014
\(209\) 7.79097i 0.0372773i
\(210\) 0.0303045 + 0.0212442i 0.000144307 + 0.000101163i
\(211\) −6.60578 −0.0313070 −0.0156535 0.999877i \(-0.504983\pi\)
−0.0156535 + 0.999877i \(0.504983\pi\)
\(212\) 276.098i 1.30235i
\(213\) 62.6108 89.3134i 0.293948 0.419312i
\(214\) 0.140967 0.000658722
\(215\) 5.72312i 0.0266192i
\(216\) 1.64695 + 0.444201i 0.00762477 + 0.00205649i
\(217\) 13.7084 0.0631722
\(218\) 0.219249i 0.00100573i
\(219\) 62.1290 + 43.5539i 0.283694 + 0.198876i
\(220\) 137.238 0.623808
\(221\) 199.129i 0.901036i
\(222\) 0.205455 0.293078i 0.000925473 0.00132017i
\(223\) 136.161 0.610587 0.305294 0.952258i \(-0.401245\pi\)
0.305294 + 0.952258i \(0.401245\pi\)
\(224\) 0.123786i 0.000552614i
\(225\) 6.49887 + 17.9166i 0.0288839 + 0.0796292i
\(226\) −0.0441525 −0.000195365
\(227\) 405.806i 1.78769i 0.448376 + 0.893845i \(0.352003\pi\)
−0.448376 + 0.893845i \(0.647997\pi\)
\(228\) −10.6732 7.48216i −0.0468122 0.0328165i
\(229\) −347.346 −1.51680 −0.758398 0.651791i \(-0.774018\pi\)
−0.758398 + 0.651791i \(0.774018\pi\)
\(230\) 1.20902i 0.00525660i
\(231\) 4.03350 5.75372i 0.0174610 0.0249079i
\(232\) 1.87888 0.00809860
\(233\) 461.344i 1.98002i −0.141009 0.990008i \(-0.545035\pi\)
0.141009 0.990008i \(-0.454965\pi\)
\(234\) −1.29441 + 0.469521i −0.00553166 + 0.00200650i
\(235\) 361.099 1.53659
\(236\) 30.7241i 0.130187i
\(237\) −255.325 178.989i −1.07732 0.755229i
\(238\) −0.0265082 −0.000111379
\(239\) 438.371i 1.83419i 0.398670 + 0.917094i \(0.369472\pi\)
−0.398670 + 0.917094i \(0.630528\pi\)
\(240\) −131.796 + 188.005i −0.549150 + 0.783354i
\(241\) −136.775 −0.567530 −0.283765 0.958894i \(-0.591584\pi\)
−0.283765 + 0.958894i \(0.591584\pi\)
\(242\) 0.549299i 0.00226983i
\(243\) −242.132 + 20.5157i −0.996430 + 0.0844266i
\(244\) −348.901 −1.42992
\(245\) 233.884i 0.954628i
\(246\) 0.242989 + 0.170341i 0.000987760 + 0.000692444i
\(247\) 21.0433 0.0851955
\(248\) 2.65210i 0.0106940i
\(249\) −124.326 + 177.349i −0.499301 + 0.712245i
\(250\) 1.02443 0.00409770
\(251\) 106.863i 0.425749i −0.977080 0.212875i \(-0.931717\pi\)
0.977080 0.212875i \(-0.0682826\pi\)
\(252\) 4.00865 + 11.0513i 0.0159073 + 0.0438545i
\(253\) −229.548 −0.907305
\(254\) 0.171634i 0.000675724i
\(255\) 120.785 + 84.6730i 0.473665 + 0.332051i
\(256\) 255.960 0.999844
\(257\) 113.716i 0.442474i 0.975220 + 0.221237i \(0.0710094\pi\)
−0.975220 + 0.221237i \(0.928991\pi\)
\(258\) 0.0162709 0.0232102i 6.30657e−5 8.99622e-5i
\(259\) 4.93340 0.0190479
\(260\) 370.677i 1.42568i
\(261\) −251.614 + 91.2679i −0.964038 + 0.349685i
\(262\) 1.85578 0.00708315
\(263\) 75.6208i 0.287532i −0.989612 0.143766i \(-0.954079\pi\)
0.989612 0.143766i \(-0.0459212\pi\)
\(264\) −1.11315 0.780345i −0.00421648 0.00295585i
\(265\) 330.187 1.24599
\(266\) 0.00280130i 1.05312e-5i
\(267\) −247.709 + 353.353i −0.927749 + 1.32342i
\(268\) −150.597 −0.561929
\(269\) 154.580i 0.574648i 0.957833 + 0.287324i \(0.0927657\pi\)
−0.957833 + 0.287324i \(0.907234\pi\)
\(270\) −0.265609 + 0.984791i −0.000983739 + 0.00364737i
\(271\) 355.108 1.31036 0.655181 0.755472i \(-0.272592\pi\)
0.655181 + 0.755472i \(0.272592\pi\)
\(272\) 164.453i 0.604607i
\(273\) −15.5407 10.8944i −0.0569257 0.0399063i
\(274\) −0.166692 −0.000608365
\(275\) 15.1888i 0.0552320i
\(276\) 220.450 314.468i 0.798731 1.13938i
\(277\) 226.249 0.816783 0.408391 0.912807i \(-0.366090\pi\)
0.408391 + 0.912807i \(0.366090\pi\)
\(278\) 1.31133i 0.00471703i
\(279\) 128.828 + 355.162i 0.461749 + 1.27298i
\(280\) 0.0986904 0.000352466
\(281\) 516.299i 1.83736i −0.394999 0.918681i \(-0.629255\pi\)
0.394999 0.918681i \(-0.370745\pi\)
\(282\) −1.46445 1.02661i −0.00519307 0.00364047i
\(283\) −127.805 −0.451609 −0.225805 0.974173i \(-0.572501\pi\)
−0.225805 + 0.974173i \(0.572501\pi\)
\(284\) 145.429i 0.512073i
\(285\) 8.94796 12.7641i 0.0313963 0.0447864i
\(286\) 1.09734 0.00383684
\(287\) 4.09025i 0.0142517i
\(288\) 3.20709 1.16331i 0.0111357 0.00403927i
\(289\) 183.346 0.634416
\(290\) 1.12347i 0.00387404i
\(291\) 142.405 + 99.8292i 0.489363 + 0.343056i
\(292\) 101.165 0.346454
\(293\) 469.558i 1.60259i 0.598272 + 0.801293i \(0.295854\pi\)
−0.598272 + 0.801293i \(0.704146\pi\)
\(294\) −0.664936 + 0.948521i −0.00226169 + 0.00322626i
\(295\) −36.7431 −0.124553
\(296\) 0.954446i 0.00322448i
\(297\) 186.976 + 50.4295i 0.629548 + 0.169796i
\(298\) 1.03534 0.00347431
\(299\) 620.007i 2.07360i
\(300\) 20.8078 + 14.5868i 0.0693593 + 0.0486225i
\(301\) 0.390699 0.00129800
\(302\) 1.13500i 0.00375828i
\(303\) 239.546 341.709i 0.790581 1.12775i
\(304\) −17.3789 −0.0571673
\(305\) 417.253i 1.36804i
\(306\) −0.249118 0.686787i −0.000814111 0.00224440i
\(307\) −199.843 −0.650953 −0.325477 0.945550i \(-0.605525\pi\)
−0.325477 + 0.945550i \(0.605525\pi\)
\(308\) 9.36878i 0.0304181i
\(309\) 59.1204 + 41.4448i 0.191328 + 0.134126i
\(310\) 1.58582 0.00511555
\(311\) 281.008i 0.903563i 0.892129 + 0.451782i \(0.149211\pi\)
−0.892129 + 0.451782i \(0.850789\pi\)
\(312\) −2.10770 + 3.00660i −0.00675545 + 0.00963654i
\(313\) 35.5922 0.113713 0.0568566 0.998382i \(-0.481892\pi\)
0.0568566 + 0.998382i \(0.481892\pi\)
\(314\) 0.922475i 0.00293782i
\(315\) −13.2163 + 4.79396i −0.0419567 + 0.0152189i
\(316\) −415.746 −1.31565
\(317\) 31.7840i 0.100265i 0.998743 + 0.0501324i \(0.0159643\pi\)
−0.998743 + 0.0501324i \(0.984036\pi\)
\(318\) −1.33908 0.938728i −0.00421095 0.00295198i
\(319\) 213.306 0.668671
\(320\) 306.119i 0.956621i
\(321\) −30.7390 + 43.8487i −0.0957602 + 0.136600i
\(322\) −0.0825358 −0.000256322
\(323\) 11.1651i 0.0345670i
\(324\) −248.650 + 207.716i −0.767439 + 0.641097i
\(325\) −41.0247 −0.126230
\(326\) 1.89837i 0.00582321i
\(327\) 68.1990 + 47.8091i 0.208560 + 0.146205i
\(328\) 0.791324 0.00241257
\(329\) 24.6511i 0.0749273i
\(330\) 0.466606 0.665606i 0.00141396 0.00201699i
\(331\) 383.342 1.15813 0.579066 0.815281i \(-0.303417\pi\)
0.579066 + 0.815281i \(0.303417\pi\)
\(332\) 288.777i 0.869810i
\(333\) 46.3630 + 127.817i 0.139228 + 0.383834i
\(334\) 1.21052 0.00362430
\(335\) 180.100i 0.537612i
\(336\) 12.8345 + 8.99729i 0.0381979 + 0.0267776i
\(337\) 294.098 0.872693 0.436346 0.899779i \(-0.356272\pi\)
0.436346 + 0.899779i \(0.356272\pi\)
\(338\) 1.62925i 0.00482026i
\(339\) 9.62784 13.7340i 0.0284007 0.0405132i
\(340\) 196.674 0.578452
\(341\) 301.089i 0.882960i
\(342\) −0.0725773 + 0.0263260i −0.000212214 + 7.69765e-5i
\(343\) −31.9678 −0.0932007
\(344\) 0.0755870i 0.000219730i
\(345\) 376.074 + 263.637i 1.09007 + 0.764166i
\(346\) −1.56706 −0.00452907
\(347\) 260.831i 0.751674i 0.926686 + 0.375837i \(0.122645\pi\)
−0.926686 + 0.375837i \(0.877355\pi\)
\(348\) −204.851 + 292.217i −0.588653 + 0.839704i
\(349\) 65.8252 0.188611 0.0943054 0.995543i \(-0.469937\pi\)
0.0943054 + 0.995543i \(0.469937\pi\)
\(350\) 0.00546124i 1.56035e-5i
\(351\) 136.209 505.019i 0.388061 1.43880i
\(352\) −2.71882 −0.00772391
\(353\) 204.142i 0.578306i 0.957283 + 0.289153i \(0.0933736\pi\)
−0.957283 + 0.289153i \(0.906626\pi\)
\(354\) 0.149013 + 0.104461i 0.000420940 + 0.000295089i
\(355\) 173.919 0.489913
\(356\) 575.364i 1.61619i
\(357\) 5.78035 8.24558i 0.0161915 0.0230969i
\(358\) −0.666248 −0.00186103
\(359\) 347.563i 0.968142i 0.875029 + 0.484071i \(0.160842\pi\)
−0.875029 + 0.484071i \(0.839158\pi\)
\(360\) 0.927469 + 2.55691i 0.00257630 + 0.00710254i
\(361\) −359.820 −0.996732
\(362\) 2.37553i 0.00656225i
\(363\) 170.864 + 119.780i 0.470699 + 0.329972i
\(364\) −25.3049 −0.0695190
\(365\) 120.983i 0.331461i
\(366\) −1.18626 + 1.69218i −0.00324115 + 0.00462344i
\(367\) −147.776 −0.402659 −0.201329 0.979524i \(-0.564526\pi\)
−0.201329 + 0.979524i \(0.564526\pi\)
\(368\) 512.040i 1.39141i
\(369\) −105.972 + 38.4392i −0.287187 + 0.104171i
\(370\) 0.570709 0.00154246
\(371\) 22.5408i 0.0607569i
\(372\) 412.475 + 289.155i 1.10881 + 0.777299i
\(373\) −384.525 −1.03090 −0.515450 0.856920i \(-0.672375\pi\)
−0.515450 + 0.856920i \(0.672375\pi\)
\(374\) 0.582224i 0.00155675i
\(375\) −223.385 + 318.655i −0.595694 + 0.849748i
\(376\) −4.76915 −0.0126839
\(377\) 576.137i 1.52821i
\(378\) 0.0672285 + 0.0181323i 0.000177853 + 4.79691e-5i
\(379\) 341.583 0.901276 0.450638 0.892707i \(-0.351197\pi\)
0.450638 + 0.892707i \(0.351197\pi\)
\(380\) 20.7838i 0.0546942i
\(381\) −53.3881 37.4263i −0.140126 0.0982319i
\(382\) 0.497077 0.00130125
\(383\) 537.530i 1.40347i −0.712437 0.701736i \(-0.752409\pi\)
0.712437 0.701736i \(-0.247591\pi\)
\(384\) 3.48139 4.96615i 0.00906613 0.0129327i
\(385\) 11.2042 0.0291018
\(386\) 0.416652i 0.00107941i
\(387\) 3.67170 + 10.1224i 0.00948759 + 0.0261561i
\(388\) 231.877 0.597622
\(389\) 551.322i 1.41728i −0.705570 0.708641i \(-0.749309\pi\)
0.705570 0.708641i \(-0.250691\pi\)
\(390\) −1.79779 1.26030i −0.00460972 0.00323153i
\(391\) −328.963 −0.841337
\(392\) 3.08898i 0.00788004i
\(393\) −404.671 + 577.256i −1.02970 + 1.46885i
\(394\) −0.342495 −0.000869277
\(395\) 497.193i 1.25872i
\(396\) 242.730 88.0456i 0.612956 0.222337i
\(397\) −535.112 −1.34789 −0.673945 0.738781i \(-0.735402\pi\)
−0.673945 + 0.738781i \(0.735402\pi\)
\(398\) 2.50288i 0.00628865i
\(399\) −0.871366 0.610849i −0.00218387 0.00153095i
\(400\) 33.8808 0.0847019
\(401\) 270.808i 0.675331i −0.941266 0.337666i \(-0.890363\pi\)
0.941266 0.337666i \(-0.109637\pi\)
\(402\) −0.512028 + 0.730400i −0.00127370 + 0.00181691i
\(403\) −813.238 −2.01796
\(404\) 556.404i 1.37724i
\(405\) −248.408 297.362i −0.613354 0.734228i
\(406\) 0.0766958 0.000188906
\(407\) 108.357i 0.266233i
\(408\) −1.59524 1.11830i −0.00390990 0.00274094i
\(409\) 714.539 1.74704 0.873520 0.486789i \(-0.161832\pi\)
0.873520 + 0.486789i \(0.161832\pi\)
\(410\) 0.473171i 0.00115408i
\(411\) 36.3487 51.8508i 0.0884396 0.126158i
\(412\) 96.2657 0.233655
\(413\) 2.50834i 0.00607346i
\(414\) −0.775652 2.13837i −0.00187356 0.00516515i
\(415\) −345.350 −0.832169
\(416\) 7.34349i 0.0176526i
\(417\) −407.900 285.948i −0.978178 0.685727i
\(418\) 0.0615275 0.000147195
\(419\) 136.316i 0.325337i 0.986681 + 0.162668i \(0.0520100\pi\)
−0.986681 + 0.162668i \(0.947990\pi\)
\(420\) −10.7601 + 15.3491i −0.0256192 + 0.0365454i
\(421\) −153.259 −0.364035 −0.182017 0.983295i \(-0.558263\pi\)
−0.182017 + 0.983295i \(0.558263\pi\)
\(422\) 0.0521678i 0.000123620i
\(423\) 638.672 231.665i 1.50986 0.547672i
\(424\) −4.36088 −0.0102851
\(425\) 21.7669i 0.0512161i
\(426\) −0.705334 0.494456i −0.00165571 0.00116069i
\(427\) −28.4846 −0.0667086
\(428\) 71.3988i 0.166820i
\(429\) −239.284 + 341.335i −0.557772 + 0.795653i
\(430\) 0.0451971 0.000105110
\(431\) 324.323i 0.752488i −0.926521 0.376244i \(-0.877215\pi\)
0.926521 0.376244i \(-0.122785\pi\)
\(432\) −112.490 + 417.076i −0.260394 + 0.965454i
\(433\) −443.293 −1.02377 −0.511885 0.859054i \(-0.671053\pi\)
−0.511885 + 0.859054i \(0.671053\pi\)
\(434\) 0.108259i 0.000249445i
\(435\) −349.464 244.983i −0.803366 0.563179i
\(436\) 111.048 0.254698
\(437\) 34.7637i 0.0795507i
\(438\) 0.343958 0.490650i 0.000785292 0.00112021i
\(439\) 678.276 1.54505 0.772524 0.634986i \(-0.218994\pi\)
0.772524 + 0.634986i \(0.218994\pi\)
\(440\) 2.16763i 0.00492643i
\(441\) −150.049 413.667i −0.340248 0.938021i
\(442\) 1.57258 0.00355787
\(443\) 353.521i 0.798015i −0.916948 0.399008i \(-0.869355\pi\)
0.916948 0.399008i \(-0.130645\pi\)
\(444\) 148.443 + 104.062i 0.334330 + 0.234374i
\(445\) −688.082 −1.54625
\(446\) 1.07530i 0.00241099i
\(447\) −225.766 + 322.052i −0.505070 + 0.720474i
\(448\) 20.8977 0.0466467
\(449\) 648.304i 1.44388i 0.691954 + 0.721942i \(0.256750\pi\)
−0.691954 + 0.721942i \(0.743250\pi\)
\(450\) 0.141492 0.0513235i 0.000314427 0.000114052i
\(451\) 89.8378 0.199197
\(452\) 22.3630i 0.0494756i
\(453\) −353.051 247.497i −0.779362 0.546352i
\(454\) 3.20477 0.00705895
\(455\) 30.2623i 0.0665106i
\(456\) −0.118178 + 0.168580i −0.000259163 + 0.000369692i
\(457\) 419.983 0.918999 0.459499 0.888178i \(-0.348029\pi\)
0.459499 + 0.888178i \(0.348029\pi\)
\(458\) 2.74310i 0.00598929i
\(459\) 267.953 + 72.2699i 0.583775 + 0.157451i
\(460\) 612.361 1.33122
\(461\) 831.173i 1.80298i −0.432802 0.901489i \(-0.642475\pi\)
0.432802 0.901489i \(-0.357525\pi\)
\(462\) −0.0454388 0.0318537i −9.83524e−5 6.89474e-5i
\(463\) −323.289 −0.698248 −0.349124 0.937076i \(-0.613521\pi\)
−0.349124 + 0.937076i \(0.613521\pi\)
\(464\) 475.809i 1.02545i
\(465\) −345.803 + 493.282i −0.743662 + 1.06082i
\(466\) −3.64337 −0.00781838
\(467\) 467.788i 1.00169i −0.865538 0.500844i \(-0.833023\pi\)
0.865538 0.500844i \(-0.166977\pi\)
\(468\) −237.810 655.611i −0.508141 1.40088i
\(469\) −12.2949 −0.0262150
\(470\) 2.85171i 0.00606746i
\(471\) −286.943 201.154i −0.609220 0.427078i
\(472\) 0.485278 0.00102813
\(473\) 8.58128i 0.0181422i
\(474\) −1.41353 + 2.01638i −0.00298213 + 0.00425396i
\(475\) −2.30025 −0.00484263
\(476\) 13.4263i 0.0282065i
\(477\) 583.997 211.833i 1.22431 0.444095i
\(478\) 3.46194 0.00724256
\(479\) 24.1346i 0.0503853i 0.999683 + 0.0251927i \(0.00801992\pi\)
−0.999683 + 0.0251927i \(0.991980\pi\)
\(480\) 4.45430 + 3.12257i 0.00927980 + 0.00650536i
\(481\) −292.670 −0.608462
\(482\) 1.08015i 0.00224098i
\(483\) 17.9977 25.6734i 0.0372622 0.0531540i
\(484\) 278.217 0.574829
\(485\) 277.304i 0.571760i
\(486\) 0.162018 + 1.91219i 0.000333371 + 0.00393455i
\(487\) −800.518 −1.64377 −0.821887 0.569650i \(-0.807079\pi\)
−0.821887 + 0.569650i \(0.807079\pi\)
\(488\) 5.51080i 0.0112926i
\(489\) 590.502 + 413.956i 1.20757 + 0.846536i
\(490\) −1.84705 −0.00376949
\(491\) 119.978i 0.244355i 0.992508 + 0.122177i \(0.0389877\pi\)
−0.992508 + 0.122177i \(0.961012\pi\)
\(492\) −86.2770 + 123.073i −0.175360 + 0.250148i
\(493\) 305.686 0.620053
\(494\) 0.166185i 0.000336407i
\(495\) 105.294 + 290.283i 0.212716 + 0.586430i
\(496\) 671.623 1.35408
\(497\) 11.8729i 0.0238892i
\(498\) 1.40058 + 0.981838i 0.00281240 + 0.00197156i
\(499\) 231.859 0.464647 0.232323 0.972639i \(-0.425367\pi\)
0.232323 + 0.972639i \(0.425367\pi\)
\(500\) 518.866i 1.03773i
\(501\) −263.964 + 376.540i −0.526874 + 0.751577i
\(502\) −0.843928 −0.00168113
\(503\) 688.560i 1.36891i −0.729056 0.684454i \(-0.760041\pi\)
0.729056 0.684454i \(-0.239959\pi\)
\(504\) 0.174552 0.0633154i 0.000346334 0.000125626i
\(505\) 665.407 1.31764
\(506\) 1.81281i 0.00358263i
\(507\) 506.791 + 355.272i 0.999587 + 0.700735i
\(508\) −86.9317 −0.171125
\(509\) 142.587i 0.280131i −0.990142 0.140065i \(-0.955269\pi\)
0.990142 0.140065i \(-0.0447313\pi\)
\(510\) 0.668687 0.953872i 0.00131115 0.00187034i
\(511\) 8.25914 0.0161627
\(512\) 10.1079i 0.0197420i
\(513\) 7.63724 28.3163i 0.0148874 0.0551975i
\(514\) 0.898047 0.00174717
\(515\) 115.125i 0.223543i
\(516\) 11.7559 + 8.24115i 0.0227827 + 0.0159712i
\(517\) −541.435 −1.04726
\(518\) 0.0389605i 7.52133e-5i
\(519\) 341.711 487.446i 0.658403 0.939202i
\(520\) −5.85473 −0.0112591
\(521\) 617.668i 1.18554i 0.805370 + 0.592772i \(0.201966\pi\)
−0.805370 + 0.592772i \(0.798034\pi\)
\(522\) 0.720769 + 1.98707i 0.00138078 + 0.00380664i
\(523\) 118.969 0.227473 0.113737 0.993511i \(-0.463718\pi\)
0.113737 + 0.993511i \(0.463718\pi\)
\(524\) 939.945i 1.79379i
\(525\) 1.69876 + 1.19087i 0.00323574 + 0.00226833i
\(526\) −0.597200 −0.00113536
\(527\) 431.488i 0.818762i
\(528\) 197.616 281.896i 0.374272 0.533893i
\(529\) −495.256 −0.936211
\(530\) 2.60758i 0.00491997i
\(531\) −64.9871 + 23.5728i −0.122386 + 0.0443932i
\(532\) −1.41884 −0.00266700
\(533\) 242.651i 0.455255i
\(534\) 2.79053 + 1.95623i 0.00522571 + 0.00366335i
\(535\) −85.3863 −0.159601
\(536\) 2.37864i 0.00443775i
\(537\) 145.281 207.242i 0.270543 0.385925i
\(538\) 1.22077 0.00226908
\(539\) 350.687i 0.650625i
\(540\) −498.792 134.530i −0.923688 0.249129i
\(541\) 773.951 1.43059 0.715296 0.698821i \(-0.246292\pi\)
0.715296 + 0.698821i \(0.246292\pi\)
\(542\) 2.80439i 0.00517416i
\(543\) −738.928 518.007i −1.36083 0.953972i
\(544\) −3.89630 −0.00716232
\(545\) 132.803i 0.243676i
\(546\) −0.0860364 + 0.122730i −0.000157576 + 0.000224779i
\(547\) −119.657 −0.218751 −0.109375 0.994001i \(-0.534885\pi\)
−0.109375 + 0.994001i \(0.534885\pi\)
\(548\) 84.4286i 0.154067i
\(549\) −267.691 737.991i −0.487598 1.34425i
\(550\) −0.119950 −0.000218091
\(551\) 32.3039i 0.0586278i
\(552\) −4.96693 3.48194i −0.00899806 0.00630786i
\(553\) −33.9418 −0.0613775
\(554\) 1.78675i 0.00322518i
\(555\) −124.448 + 177.524i −0.224231 + 0.319862i
\(556\) −664.184 −1.19457
\(557\) 885.523i 1.58981i −0.606735 0.794904i \(-0.707521\pi\)
0.606735 0.794904i \(-0.292479\pi\)
\(558\) 2.80482 1.01739i 0.00502656 0.00182328i
\(559\) −23.1779 −0.0414632
\(560\) 24.9925i 0.0446295i
\(561\) −181.105 126.959i −0.322826 0.226309i
\(562\) −4.07736 −0.00725509
\(563\) 849.508i 1.50889i 0.656361 + 0.754447i \(0.272095\pi\)
−0.656361 + 0.754447i \(0.727905\pi\)
\(564\) 519.974 741.735i 0.921940 1.31513i
\(565\) 26.7440 0.0473346
\(566\) 1.00932i 0.00178325i
\(567\) −20.3000 + 16.9580i −0.0358024 + 0.0299084i
\(568\) −2.29701 −0.00404402
\(569\) 659.670i 1.15935i 0.814848 + 0.579675i \(0.196820\pi\)
−0.814848 + 0.579675i \(0.803180\pi\)
\(570\) −0.100802 0.0706646i −0.000176846 0.000123973i
\(571\) 528.453 0.925487 0.462744 0.886492i \(-0.346865\pi\)
0.462744 + 0.886492i \(0.346865\pi\)
\(572\) 555.796i 0.971671i
\(573\) −108.392 + 154.619i −0.189166 + 0.269842i
\(574\) 0.0323019 5.62750e−5
\(575\) 67.7731i 0.117866i
\(576\) 196.392 + 541.428i 0.340958 + 0.939979i
\(577\) 133.967 0.232178 0.116089 0.993239i \(-0.462964\pi\)
0.116089 + 0.993239i \(0.462964\pi\)
\(578\) 1.44794i 0.00250508i
\(579\) −129.603 90.8548i −0.223839 0.156917i
\(580\) −569.032 −0.981090
\(581\) 23.5760i 0.0405782i
\(582\) 0.788380 1.12461i 0.00135460 0.00193232i
\(583\) −495.084 −0.849202
\(584\) 1.59786i 0.00273607i
\(585\) 784.050 284.398i 1.34026 0.486151i
\(586\) 3.70823 0.00632804
\(587\) 771.291i 1.31395i 0.753911 + 0.656977i \(0.228165\pi\)
−0.753911 + 0.656977i \(0.771835\pi\)
\(588\) −480.421 336.787i −0.817043 0.572767i
\(589\) −45.5982 −0.0774162
\(590\) 0.290171i 0.000491816i
\(591\) 74.6842 106.536i 0.126369 0.180264i
\(592\) 241.705 0.408286
\(593\) 590.309i 0.995461i −0.867332 0.497731i \(-0.834167\pi\)
0.867332 0.497731i \(-0.165833\pi\)
\(594\) 0.398257 1.47660i 0.000670466 0.00248586i
\(595\) 16.0566 0.0269858
\(596\) 524.397i 0.879860i
\(597\) 778.541 + 545.776i 1.30409 + 0.914197i
\(598\) 4.89637 0.00818791
\(599\) 859.176i 1.43435i 0.696893 + 0.717175i \(0.254565\pi\)
−0.696893 + 0.717175i \(0.745435\pi\)
\(600\) 0.230394 0.328653i 0.000383989 0.000547754i
\(601\) −704.324 −1.17192 −0.585960 0.810340i \(-0.699283\pi\)
−0.585960 + 0.810340i \(0.699283\pi\)
\(602\) 0.00308546i 5.12536e-6i
\(603\) −115.544 318.540i −0.191615 0.528259i
\(604\) −574.872 −0.951776
\(605\) 332.722i 0.549954i
\(606\) −2.69857 1.89176i −0.00445309 0.00312172i
\(607\) 904.339 1.48985 0.744925 0.667148i \(-0.232485\pi\)
0.744925 + 0.667148i \(0.232485\pi\)
\(608\) 0.411748i 0.000677218i
\(609\) −16.7242 + 23.8568i −0.0274617 + 0.0391737i
\(610\) −3.29517 −0.00540192
\(611\) 1462.41i 2.39347i
\(612\) 347.854 126.177i 0.568389 0.206172i
\(613\) 612.747 0.999588 0.499794 0.866144i \(-0.333409\pi\)
0.499794 + 0.866144i \(0.333409\pi\)
\(614\) 1.57821i 0.00257038i
\(615\) −147.183 103.179i −0.239323 0.167771i
\(616\) −0.147977 −0.000240222
\(617\) 101.948i 0.165232i −0.996581 0.0826159i \(-0.973673\pi\)
0.996581 0.0826159i \(-0.0263275\pi\)
\(618\) 0.327302 0.466891i 0.000529615 0.000755487i
\(619\) 511.560 0.826430 0.413215 0.910633i \(-0.364406\pi\)
0.413215 + 0.910633i \(0.364406\pi\)
\(620\) 803.211i 1.29550i
\(621\) 834.295 + 225.019i 1.34347 + 0.362350i
\(622\) 2.21920 0.00356785
\(623\) 46.9731i 0.0753983i
\(624\) −761.396 533.757i −1.22019 0.855380i
\(625\) −567.574 −0.908119
\(626\) 0.281082i 0.000449013i
\(627\) −13.4166 + 19.1386i −0.0213981 + 0.0305241i
\(628\) −467.229 −0.743995
\(629\) 155.285i 0.246876i
\(630\) 0.0378593 + 0.104373i 6.00942e−5 + 0.000165672i
\(631\) −705.626 −1.11827 −0.559133 0.829078i \(-0.688866\pi\)
−0.559133 + 0.829078i \(0.688866\pi\)
\(632\) 6.56658i 0.0103902i
\(633\) −16.2272 11.3757i −0.0256354 0.0179710i
\(634\) 0.251007 0.000395910
\(635\) 103.962i 0.163720i
\(636\) 475.461 678.238i 0.747580 1.06641i
\(637\) 947.201 1.48697
\(638\) 1.68454i 0.00264034i
\(639\) 307.609 111.579i 0.481391 0.174615i
\(640\) 9.67056 0.0151102
\(641\) 589.256i 0.919277i −0.888106 0.459638i \(-0.847979\pi\)
0.888106 0.459638i \(-0.152021\pi\)
\(642\) 0.346286 + 0.242755i 0.000539386 + 0.000378123i
\(643\) −518.072 −0.805711 −0.402856 0.915264i \(-0.631982\pi\)
−0.402856 + 0.915264i \(0.631982\pi\)
\(644\) 41.8039i 0.0649130i
\(645\) −9.85564 + 14.0589i −0.0152801 + 0.0217968i
\(646\) 0.0881743 0.000136493
\(647\) 696.737i 1.07687i −0.842666 0.538437i \(-0.819015\pi\)
0.842666 0.538437i \(-0.180985\pi\)
\(648\) 3.28081 + 3.92736i 0.00506297 + 0.00606074i
\(649\) 55.0929 0.0848889
\(650\) 0.323984i 0.000498437i
\(651\) 33.6748 + 23.6068i 0.0517278 + 0.0362624i
\(652\) 961.514 1.47471
\(653\) 628.404i 0.962334i 0.876629 + 0.481167i \(0.159787\pi\)
−0.876629 + 0.481167i \(0.840213\pi\)
\(654\) 0.377563 0.538587i 0.000577313 0.000823528i
\(655\) −1124.09 −1.71616
\(656\) 200.396i 0.305482i
\(657\) 77.6175 + 213.982i 0.118139 + 0.325695i
\(658\) −0.194677 −0.000295861
\(659\) 89.8096i 0.136282i −0.997676 0.0681409i \(-0.978293\pi\)
0.997676 0.0681409i \(-0.0217067\pi\)
\(660\) 337.126 + 236.334i 0.510797 + 0.358081i
\(661\) 1209.31 1.82952 0.914761 0.403996i \(-0.132379\pi\)
0.914761 + 0.403996i \(0.132379\pi\)
\(662\) 3.02736i 0.00457305i
\(663\) −342.915 + 489.163i −0.517217 + 0.737802i
\(664\) 4.56115 0.00686920
\(665\) 1.69680i 0.00255159i
\(666\) 1.00941 0.366142i 0.00151562 0.000549762i
\(667\) 951.782 1.42696
\(668\) 613.120i 0.917844i
\(669\) 334.481 + 234.479i 0.499972 + 0.350492i
\(670\) −1.42230 −0.00212284
\(671\) 625.633i 0.932388i
\(672\) 0.213168 0.304081i 0.000317215 0.000452501i
\(673\) 1060.34 1.57554 0.787771 0.615968i \(-0.211235\pi\)
0.787771 + 0.615968i \(0.211235\pi\)
\(674\) 2.32257i 0.00344595i
\(675\) −14.8891 + 55.2038i −0.0220579 + 0.0817834i
\(676\) 825.206 1.22072
\(677\) 136.594i 0.201764i 0.994898 + 0.100882i \(0.0321665\pi\)
−0.994898 + 0.100882i \(0.967834\pi\)
\(678\) −0.108461 0.0760338i −0.000159972 0.000112144i
\(679\) 18.9306 0.0278802
\(680\) 3.10640i 0.00456824i
\(681\) −698.828 + 996.867i −1.02618 + 1.46383i
\(682\) −2.37779 −0.00348650
\(683\) 167.507i 0.245251i −0.992453 0.122626i \(-0.960869\pi\)
0.992453 0.122626i \(-0.0391315\pi\)
\(684\) −13.3340 36.7600i −0.0194941 0.0537427i
\(685\) 100.969 0.147400
\(686\) 0.252459i 0.000368016i
\(687\) −853.261 598.157i −1.24201 0.870679i
\(688\) 19.1418 0.0278223
\(689\) 1337.22i 1.94081i
\(690\) 2.08202 2.96997i 0.00301742 0.00430430i
\(691\) 512.344 0.741454 0.370727 0.928742i \(-0.379109\pi\)
0.370727 + 0.928742i \(0.379109\pi\)
\(692\) 793.707i 1.14698i
\(693\) 19.8167 7.18810i 0.0285955 0.0103724i
\(694\) 2.05986 0.00296809
\(695\) 794.301i 1.14288i
\(696\) 4.61548 + 3.23557i 0.00663144 + 0.00464880i
\(697\) 128.745 0.184714
\(698\) 0.519841i 0.000744757i
\(699\) 794.469 1133.30i 1.13658 1.62131i
\(700\) 2.76609 0.00395156
\(701\) 810.841i 1.15669i −0.815792 0.578346i \(-0.803698\pi\)
0.815792 0.578346i \(-0.196302\pi\)
\(702\) −3.98828 1.07569i −0.00568131 0.00153232i
\(703\) −16.4100 −0.0233428
\(704\) 458.996i 0.651983i
\(705\) 887.045 + 621.840i 1.25822 + 0.882043i
\(706\) 1.61217 0.00228352
\(707\) 45.4252i 0.0642506i
\(708\) −52.9092 + 75.4742i −0.0747305 + 0.106602i
\(709\) 466.935 0.658583 0.329291 0.944228i \(-0.393190\pi\)
0.329291 + 0.944228i \(0.393190\pi\)
\(710\) 1.37349i 0.00193449i
\(711\) −318.977 879.379i −0.448631 1.23682i
\(712\) 9.08771 0.0127636
\(713\) 1343.48i 1.88426i
\(714\) −0.0651178 0.0456491i −9.12014e−5 6.39344e-5i
\(715\) −664.679 −0.929621
\(716\) 337.451i 0.471300i
\(717\) −754.908 + 1076.86i −1.05287 + 1.50190i
\(718\) 2.74481 0.00382285
\(719\) 532.897i 0.741165i 0.928800 + 0.370582i \(0.120842\pi\)
−0.928800 + 0.370582i \(0.879158\pi\)
\(720\) −647.517 + 234.874i −0.899329 + 0.326214i
\(721\) 7.85920 0.0109004
\(722\) 2.84160i 0.00393574i
\(723\) −335.989 235.536i −0.464715 0.325777i
\(724\) −1203.20 −1.66187
\(725\) 62.9777i 0.0868658i
\(726\) 0.945935 1.34936i 0.00130294 0.00185862i
\(727\) −1402.75 −1.92950 −0.964751 0.263164i \(-0.915234\pi\)
−0.964751 + 0.263164i \(0.915234\pi\)
\(728\) 0.399684i 0.000549016i
\(729\) −630.131 366.573i −0.864377 0.502844i
\(730\) 0.955440 0.00130882
\(731\) 12.2977i 0.0168232i
\(732\) −857.081 600.835i −1.17088 0.820812i
\(733\) −323.758 −0.441688 −0.220844 0.975309i \(-0.570881\pi\)
−0.220844 + 0.975309i \(0.570881\pi\)
\(734\) 1.16703i 0.00158996i
\(735\) 402.766 574.539i 0.547980 0.781685i
\(736\) −12.1315 −0.0164830
\(737\) 270.043i 0.366409i
\(738\) 0.303565 + 0.836891i 0.000411335 + 0.00113400i
\(739\) −815.403 −1.10339 −0.551694 0.834047i \(-0.686018\pi\)
−0.551694 + 0.834047i \(0.686018\pi\)
\(740\) 289.061i 0.390623i
\(741\) 51.6931 + 36.2381i 0.0697613 + 0.0489044i
\(742\) −0.178011 −0.000239907
\(743\) 681.903i 0.917769i −0.888496 0.458885i \(-0.848249\pi\)
0.888496 0.458885i \(-0.151751\pi\)
\(744\) 4.56712 6.51493i 0.00613861 0.00875662i
\(745\) −627.129 −0.841784
\(746\) 3.03671i 0.00407065i
\(747\) −610.816 + 221.561i −0.817692 + 0.296602i
\(748\) −294.894 −0.394243
\(749\) 5.82905i 0.00778244i
\(750\) 2.51651 + 1.76414i 0.00335535 + 0.00235218i
\(751\) −761.193 −1.01357 −0.506786 0.862072i \(-0.669167\pi\)
−0.506786 + 0.862072i \(0.669167\pi\)
\(752\) 1207.75i 1.60605i
\(753\) 184.026 262.510i 0.244391 0.348619i
\(754\) −4.54992 −0.00603437
\(755\) 687.494i 0.910588i
\(756\) −9.18392 + 34.0509i −0.0121480 + 0.0450409i
\(757\) −1302.94 −1.72119 −0.860594 0.509291i \(-0.829908\pi\)
−0.860594 + 0.509291i \(0.829908\pi\)
\(758\) 2.69758i 0.00355882i
\(759\) −563.888 395.299i −0.742936 0.520816i
\(760\) −0.328274 −0.000431940
\(761\) 42.0468i 0.0552521i −0.999618 0.0276260i \(-0.991205\pi\)
0.999618 0.0276260i \(-0.00879476\pi\)
\(762\) −0.295567 + 0.421621i −0.000387883 + 0.000553309i
\(763\) 9.06606 0.0118821
\(764\) 251.767i 0.329538i
\(765\) 150.896 + 416.001i 0.197250 + 0.543792i
\(766\) −4.24503 −0.00554181
\(767\) 148.805i 0.194009i
\(768\) 628.769 + 440.783i 0.818710 + 0.573936i
\(769\) 1230.19 1.59973 0.799863 0.600183i \(-0.204905\pi\)
0.799863 + 0.600183i \(0.204905\pi\)
\(770\) 0.0884826i 0.000114913i
\(771\) −195.827 + 279.344i −0.253991 + 0.362314i
\(772\) −211.032 −0.273358
\(773\) 1097.05i 1.41921i 0.704599 + 0.709606i \(0.251127\pi\)
−0.704599 + 0.709606i \(0.748873\pi\)
\(774\) 0.0799396 0.0289965i 0.000103281 3.74631e-5i
\(775\) 88.8954 0.114704
\(776\) 3.66244i 0.00471963i
\(777\) 12.1190 + 8.49569i 0.0155971 + 0.0109340i
\(778\) −4.35395 −0.00559634
\(779\) 13.6054i 0.0174652i
\(780\) 638.334 910.573i 0.818377 1.16740i
\(781\) −260.776 −0.333900
\(782\) 2.59791i 0.00332214i
\(783\) −775.263 209.097i −0.990119 0.267046i
\(784\) −782.257 −0.997777
\(785\)