Properties

Label 210.3.o.a.61.4
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.4
Root \(1.72286 + 0.178197i\) of \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.a.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(0.919414 + 1.59247i) q^{11} +(-3.00000 - 1.73205i) q^{12} -5.40765i q^{13} +(-2.26139 - 9.63774i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(8.71093 - 5.02926i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-7.96084 - 4.59619i) q^{19} -4.47214i q^{20} +(3.50333 - 11.6072i) q^{21} +2.60049 q^{22} +(0.460644 - 0.797858i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-6.62299 - 3.82378i) q^{26} -5.19615i q^{27} +(-13.4028 - 4.04529i) q^{28} +12.5573 q^{29} +(2.73861 - 4.74342i) q^{30} +(-36.1874 + 20.8928i) q^{31} +(2.82843 + 4.89898i) q^{32} +(2.75824 + 1.59247i) q^{33} -14.2249i q^{34} +(15.2386 - 3.57557i) q^{35} -6.00000 q^{36} +(-3.64194 + 6.30803i) q^{37} +(-11.2583 + 6.50000i) q^{38} +(-4.68316 - 8.11147i) q^{39} +(-5.47723 - 3.16228i) q^{40} +52.3877i q^{41} +(-11.7386 - 12.4982i) q^{42} -8.12312 q^{43} +(1.83883 - 3.18494i) q^{44} +(5.80948 - 3.35410i) q^{45} +(-0.651449 - 1.12834i) q^{46} +(29.4117 + 16.9809i) q^{47} +6.92820i q^{48} +(3.06832 - 48.9038i) q^{49} +7.07107 q^{50} +(8.71093 - 15.0878i) q^{51} +(-9.36632 + 5.40765i) q^{52} +(52.0396 + 90.1353i) q^{53} +(-6.36396 - 3.67423i) q^{54} +4.11174i q^{55} +(-14.4317 + 13.5546i) q^{56} -15.9217 q^{57} +(8.87938 - 15.3795i) q^{58} +(12.5918 - 7.26989i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(20.5913 + 11.8884i) q^{61} +59.0937i q^{62} +(-4.79713 - 20.4447i) q^{63} +8.00000 q^{64} +(6.04593 - 10.4719i) q^{65} +(3.90074 - 2.25209i) q^{66} +(7.46339 + 12.9270i) q^{67} +(-17.4219 - 10.0585i) q^{68} -1.59572i q^{69} +(6.39617 - 21.1917i) q^{70} -17.9620 q^{71} +(-4.24264 + 7.34847i) q^{72} +(-107.705 + 62.1833i) q^{73} +(5.15048 + 8.92090i) q^{74} +(7.50000 + 4.33013i) q^{75} +18.3848i q^{76} +(12.3227 + 3.71930i) q^{77} -13.2460 q^{78} +(40.4683 - 70.0931i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(64.1616 + 37.0437i) q^{82} +154.716i q^{83} +(-23.6076 + 5.53924i) q^{84} +22.4915 q^{85} +(-5.74391 + 9.94875i) q^{86} +(18.8360 - 10.8750i) q^{87} +(-2.60049 - 4.50419i) q^{88} +(58.9956 + 34.0611i) q^{89} -9.48683i q^{90} +(-25.9149 - 27.5918i) q^{91} -1.84258 q^{92} +(-36.1874 + 62.6784i) q^{93} +(41.5944 - 24.0146i) q^{94} +(-10.2774 - 17.8010i) q^{95} +(8.48528 + 4.89898i) q^{96} +88.1736i q^{97} +(-57.7251 - 38.3381i) q^{98} +5.51648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} - 4q^{11} - 24q^{12} - 40q^{14} - 16q^{16} + 84q^{17} + 108q^{19} - 48q^{22} + 12q^{23} + 20q^{25} - 96q^{26} + 72q^{29} - 132q^{31} - 12q^{33} + 100q^{35} - 48q^{36} - 96q^{37} - 168q^{38} + 24q^{39} - 72q^{42} - 112q^{43} - 8q^{44} + 8q^{46} - 24q^{47} + 156q^{49} + 84q^{51} + 48q^{52} + 32q^{53} + 16q^{56} + 216q^{57} + 104q^{58} + 132q^{59} + 96q^{61} + 64q^{64} + 20q^{65} - 72q^{66} - 120q^{67} - 168q^{68} + 8q^{71} + 24q^{73} - 16q^{74} + 60q^{75} - 216q^{77} - 192q^{78} + 12q^{79} - 36q^{81} + 24q^{82} + 120q^{85} - 40q^{86} + 108q^{87} + 48q^{88} + 492q^{89} - 308q^{91} - 48q^{92} - 132q^{93} + 480q^{94} - 40q^{95} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) 5.10237 4.79227i 0.728910 0.684610i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 2.73861 1.58114i 0.273861 0.158114i
\(11\) 0.919414 + 1.59247i 0.0835831 + 0.144770i 0.904787 0.425865i \(-0.140030\pi\)
−0.821203 + 0.570635i \(0.806697\pi\)
\(12\) −3.00000 1.73205i −0.250000 0.144338i
\(13\) 5.40765i 0.415973i −0.978132 0.207986i \(-0.933309\pi\)
0.978132 0.207986i \(-0.0666910\pi\)
\(14\) −2.26139 9.63774i −0.161528 0.688410i
\(15\) 3.87298 0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 8.71093 5.02926i 0.512408 0.295839i −0.221415 0.975180i \(-0.571068\pi\)
0.733823 + 0.679341i \(0.237734\pi\)
\(18\) −2.12132 3.67423i −0.117851 0.204124i
\(19\) −7.96084 4.59619i −0.418992 0.241905i 0.275654 0.961257i \(-0.411106\pi\)
−0.694646 + 0.719352i \(0.744439\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 3.50333 11.6072i 0.166825 0.552723i
\(22\) 2.60049 0.118204
\(23\) 0.460644 0.797858i 0.0200280 0.0346895i −0.855838 0.517244i \(-0.826958\pi\)
0.875866 + 0.482555i \(0.160291\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −6.62299 3.82378i −0.254730 0.147069i
\(27\) 5.19615i 0.192450i
\(28\) −13.4028 4.04529i −0.478672 0.144475i
\(29\) 12.5573 0.433012 0.216506 0.976281i \(-0.430534\pi\)
0.216506 + 0.976281i \(0.430534\pi\)
\(30\) 2.73861 4.74342i 0.0912871 0.158114i
\(31\) −36.1874 + 20.8928i −1.16733 + 0.673961i −0.953051 0.302811i \(-0.902075\pi\)
−0.214284 + 0.976771i \(0.568742\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 2.75824 + 1.59247i 0.0835831 + 0.0482567i
\(34\) 14.2249i 0.418379i
\(35\) 15.2386 3.57557i 0.435389 0.102159i
\(36\) −6.00000 −0.166667
\(37\) −3.64194 + 6.30803i −0.0984308 + 0.170487i −0.911035 0.412328i \(-0.864716\pi\)
0.812604 + 0.582816i \(0.198049\pi\)
\(38\) −11.2583 + 6.50000i −0.296272 + 0.171053i
\(39\) −4.68316 8.11147i −0.120081 0.207986i
\(40\) −5.47723 3.16228i −0.136931 0.0790569i
\(41\) 52.3877i 1.27775i 0.769311 + 0.638875i \(0.220600\pi\)
−0.769311 + 0.638875i \(0.779400\pi\)
\(42\) −11.7386 12.4982i −0.279491 0.297576i
\(43\) −8.12312 −0.188910 −0.0944549 0.995529i \(-0.530111\pi\)
−0.0944549 + 0.995529i \(0.530111\pi\)
\(44\) 1.83883 3.18494i 0.0417915 0.0723850i
\(45\) 5.80948 3.35410i 0.129099 0.0745356i
\(46\) −0.651449 1.12834i −0.0141619 0.0245292i
\(47\) 29.4117 + 16.9809i 0.625781 + 0.361295i 0.779116 0.626879i \(-0.215668\pi\)
−0.153335 + 0.988174i \(0.549001\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 3.06832 48.9038i 0.0626188 0.998038i
\(50\) 7.07107 0.141421
\(51\) 8.71093 15.0878i 0.170803 0.295839i
\(52\) −9.36632 + 5.40765i −0.180122 + 0.103993i
\(53\) 52.0396 + 90.1353i 0.981880 + 1.70067i 0.655055 + 0.755582i \(0.272646\pi\)
0.326825 + 0.945085i \(0.394021\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 4.11174i 0.0747590i
\(56\) −14.4317 + 13.5546i −0.257709 + 0.242046i
\(57\) −15.9217 −0.279328
\(58\) 8.87938 15.3795i 0.153093 0.265164i
\(59\) 12.5918 7.26989i 0.213421 0.123218i −0.389479 0.921035i \(-0.627345\pi\)
0.602900 + 0.797817i \(0.294012\pi\)
\(60\) −3.87298 6.70820i −0.0645497 0.111803i
\(61\) 20.5913 + 11.8884i 0.337562 + 0.194892i 0.659194 0.751973i \(-0.270898\pi\)
−0.321631 + 0.946865i \(0.604231\pi\)
\(62\) 59.0937i 0.953125i
\(63\) −4.79713 20.4447i −0.0761449 0.324520i
\(64\) 8.00000 0.125000
\(65\) 6.04593 10.4719i 0.0930144 0.161106i
\(66\) 3.90074 2.25209i 0.0591021 0.0341226i
\(67\) 7.46339 + 12.9270i 0.111394 + 0.192940i 0.916332 0.400418i \(-0.131135\pi\)
−0.804939 + 0.593358i \(0.797802\pi\)
\(68\) −17.4219 10.0585i −0.256204 0.147919i
\(69\) 1.59572i 0.0231263i
\(70\) 6.39617 21.1917i 0.0913738 0.302739i
\(71\) −17.9620 −0.252987 −0.126493 0.991967i \(-0.540372\pi\)
−0.126493 + 0.991967i \(0.540372\pi\)
\(72\) −4.24264 + 7.34847i −0.0589256 + 0.102062i
\(73\) −107.705 + 62.1833i −1.47541 + 0.851826i −0.999615 0.0277318i \(-0.991172\pi\)
−0.475791 + 0.879558i \(0.657838\pi\)
\(74\) 5.15048 + 8.92090i 0.0696011 + 0.120553i
\(75\) 7.50000 + 4.33013i 0.100000 + 0.0577350i
\(76\) 18.3848i 0.241905i
\(77\) 12.3227 + 3.71930i 0.160036 + 0.0483026i
\(78\) −13.2460 −0.169820
\(79\) 40.4683 70.0931i 0.512257 0.887254i −0.487642 0.873043i \(-0.662143\pi\)
0.999899 0.0142110i \(-0.00452366\pi\)
\(80\) −7.74597 + 4.47214i −0.0968246 + 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 64.1616 + 37.0437i 0.782459 + 0.451753i
\(83\) 154.716i 1.86405i 0.362395 + 0.932025i \(0.381959\pi\)
−0.362395 + 0.932025i \(0.618041\pi\)
\(84\) −23.6076 + 5.53924i −0.281042 + 0.0659434i
\(85\) 22.4915 0.264606
\(86\) −5.74391 + 9.94875i −0.0667897 + 0.115683i
\(87\) 18.8360 10.8750i 0.216506 0.125000i
\(88\) −2.60049 4.50419i −0.0295511 0.0511840i
\(89\) 58.9956 + 34.0611i 0.662872 + 0.382709i 0.793371 0.608739i \(-0.208324\pi\)
−0.130498 + 0.991449i \(0.541658\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −25.9149 27.5918i −0.284779 0.303207i
\(92\) −1.84258 −0.0200280
\(93\) −36.1874 + 62.6784i −0.389111 + 0.673961i
\(94\) 41.5944 24.0146i 0.442494 0.255474i
\(95\) −10.2774 17.8010i −0.108183 0.187379i
\(96\) 8.48528 + 4.89898i 0.0883883 + 0.0510310i
\(97\) 88.1736i 0.909006i 0.890745 + 0.454503i \(0.150183\pi\)
−0.890745 + 0.454503i \(0.849817\pi\)
\(98\) −57.7251 38.3381i −0.589032 0.391206i
\(99\) 5.51648 0.0557220
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) −96.4537 + 55.6876i −0.954987 + 0.551362i −0.894627 0.446814i \(-0.852558\pi\)
−0.0603607 + 0.998177i \(0.519225\pi\)
\(102\) −12.3191 21.3373i −0.120776 0.209190i
\(103\) −40.6847 23.4893i −0.394997 0.228051i 0.289326 0.957231i \(-0.406569\pi\)
−0.684323 + 0.729179i \(0.739902\pi\)
\(104\) 15.2951i 0.147069i
\(105\) 19.7614 18.5604i 0.188204 0.176765i
\(106\) 147.190 1.38859
\(107\) 92.8409 160.805i 0.867672 1.50285i 0.00330196 0.999995i \(-0.498949\pi\)
0.864370 0.502857i \(-0.167718\pi\)
\(108\) −9.00000 + 5.19615i −0.0833333 + 0.0481125i
\(109\) −43.1448 74.7290i −0.395824 0.685587i 0.597382 0.801957i \(-0.296208\pi\)
−0.993206 + 0.116369i \(0.962874\pi\)
\(110\) 5.03584 + 2.90744i 0.0457803 + 0.0264313i
\(111\) 12.6161i 0.113658i
\(112\) 6.39617 + 27.2597i 0.0571087 + 0.243390i
\(113\) −85.8206 −0.759474 −0.379737 0.925094i \(-0.623986\pi\)
−0.379737 + 0.925094i \(0.623986\pi\)
\(114\) −11.2583 + 19.5000i −0.0987572 + 0.171053i
\(115\) 1.78407 1.03003i 0.0155136 0.00895679i
\(116\) −12.5573 21.7500i −0.108253 0.187500i
\(117\) −14.0495 8.11147i −0.120081 0.0693288i
\(118\) 20.5624i 0.174257i
\(119\) 20.3448 67.4062i 0.170965 0.566439i
\(120\) −10.9545 −0.0912871
\(121\) 58.8094 101.861i 0.486028 0.841825i
\(122\) 29.1205 16.8127i 0.238693 0.137809i
\(123\) 45.3691 + 78.5816i 0.368855 + 0.638875i
\(124\) 72.3747 + 41.7856i 0.583667 + 0.336980i
\(125\) 11.1803i 0.0894427i
\(126\) −28.4317 8.58136i −0.225648 0.0681060i
\(127\) −131.740 −1.03733 −0.518663 0.854979i \(-0.673570\pi\)
−0.518663 + 0.854979i \(0.673570\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) −12.1847 + 7.03483i −0.0944549 + 0.0545336i
\(130\) −8.55024 14.8095i −0.0657711 0.113919i
\(131\) −102.856 59.3839i −0.785160 0.453312i 0.0530960 0.998589i \(-0.483091\pi\)
−0.838256 + 0.545277i \(0.816424\pi\)
\(132\) 6.36988i 0.0482567i
\(133\) −62.6453 + 14.6990i −0.471017 + 0.110519i
\(134\) 21.1096 0.157535
\(135\) 5.80948 10.0623i 0.0430331 0.0745356i
\(136\) −24.6382 + 14.2249i −0.181163 + 0.104595i
\(137\) −40.5765 70.2805i −0.296179 0.512997i 0.679080 0.734065i \(-0.262379\pi\)
−0.975258 + 0.221068i \(0.929046\pi\)
\(138\) −1.95435 1.12834i −0.0141619 0.00817639i
\(139\) 248.311i 1.78641i −0.449646 0.893207i \(-0.648450\pi\)
0.449646 0.893207i \(-0.351550\pi\)
\(140\) −21.4317 22.8185i −0.153083 0.162989i
\(141\) 58.8234 0.417187
\(142\) −12.7011 + 21.9989i −0.0894442 + 0.154922i
\(143\) 8.61152 4.97186i 0.0602204 0.0347683i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) 24.3172 + 14.0395i 0.167705 + 0.0968244i
\(146\) 175.881i 1.20466i
\(147\) −37.7495 76.0130i −0.256799 0.517095i
\(148\) 14.5678 0.0984308
\(149\) 75.0048 129.912i 0.503388 0.871894i −0.496604 0.867977i \(-0.665420\pi\)
0.999992 0.00391672i \(-0.00124673\pi\)
\(150\) 10.6066 6.12372i 0.0707107 0.0408248i
\(151\) −91.5149 158.509i −0.606059 1.04973i −0.991883 0.127153i \(-0.959416\pi\)
0.385824 0.922572i \(-0.373917\pi\)
\(152\) 22.5167 + 13.0000i 0.148136 + 0.0855263i
\(153\) 30.1755i 0.197226i
\(154\) 13.2687 12.4623i 0.0861603 0.0809238i
\(155\) −93.4354 −0.602809
\(156\) −9.36632 + 16.2229i −0.0600405 + 0.103993i
\(157\) −255.724 + 147.643i −1.62882 + 0.940398i −0.644371 + 0.764713i \(0.722881\pi\)
−0.984446 + 0.175685i \(0.943786\pi\)
\(158\) −57.2308 99.1266i −0.362220 0.627384i
\(159\) 156.119 + 90.1353i 0.981880 + 0.566889i
\(160\) 12.6491i 0.0790569i
\(161\) −1.47318 6.27850i −0.00915017 0.0389969i
\(162\) −12.7279 −0.0785674
\(163\) 59.1631 102.473i 0.362964 0.628671i −0.625484 0.780237i \(-0.715098\pi\)
0.988447 + 0.151566i \(0.0484316\pi\)
\(164\) 90.7382 52.3877i 0.553282 0.319437i
\(165\) 3.56087 + 6.16761i 0.0215811 + 0.0373795i
\(166\) 189.488 + 109.401i 1.14149 + 0.659041i
\(167\) 205.186i 1.22866i −0.789050 0.614329i \(-0.789427\pi\)
0.789050 0.614329i \(-0.210573\pi\)
\(168\) −9.90890 + 32.8301i −0.0589816 + 0.195417i
\(169\) 139.757 0.826967
\(170\) 15.9039 27.5464i 0.0935524 0.162038i
\(171\) −23.8825 + 13.7886i −0.139664 + 0.0806350i
\(172\) 8.12312 + 14.0697i 0.0472274 + 0.0818003i
\(173\) 97.4572 + 56.2670i 0.563337 + 0.325242i 0.754484 0.656319i \(-0.227887\pi\)
−0.191147 + 0.981561i \(0.561221\pi\)
\(174\) 30.7591i 0.176776i
\(175\) 33.5071 + 10.1132i 0.191469 + 0.0577899i
\(176\) −7.35531 −0.0417915
\(177\) 12.5918 21.8097i 0.0711402 0.123218i
\(178\) 83.4324 48.1697i 0.468721 0.270616i
\(179\) 22.2349 + 38.5120i 0.124217 + 0.215151i 0.921427 0.388552i \(-0.127025\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(180\) −11.6190 6.70820i −0.0645497 0.0372678i
\(181\) 9.24555i 0.0510804i 0.999674 + 0.0255402i \(0.00813058\pi\)
−0.999674 + 0.0255402i \(0.991869\pi\)
\(182\) −52.1175 + 12.2288i −0.286360 + 0.0671911i
\(183\) 41.1826 0.225041
\(184\) −1.30290 + 2.25668i −0.00708096 + 0.0122646i
\(185\) −14.1052 + 8.14363i −0.0762442 + 0.0440196i
\(186\) 51.1767 + 88.6406i 0.275143 + 0.476562i
\(187\) 16.0179 + 9.24793i 0.0856572 + 0.0494542i
\(188\) 67.9234i 0.361295i
\(189\) −24.9014 26.5127i −0.131753 0.140279i
\(190\) −29.0689 −0.152994
\(191\) 68.4044 118.480i 0.358138 0.620314i −0.629511 0.776991i \(-0.716745\pi\)
0.987650 + 0.156677i \(0.0500783\pi\)
\(192\) 12.0000 6.92820i 0.0625000 0.0360844i
\(193\) 182.937 + 316.856i 0.947860 + 1.64174i 0.749921 + 0.661527i \(0.230091\pi\)
0.197939 + 0.980214i \(0.436575\pi\)
\(194\) 107.990 + 62.3481i 0.556650 + 0.321382i
\(195\) 20.9437i 0.107404i
\(196\) −87.7723 + 43.5893i −0.447818 + 0.222395i
\(197\) −194.925 −0.989468 −0.494734 0.869045i \(-0.664734\pi\)
−0.494734 + 0.869045i \(0.664734\pi\)
\(198\) 3.90074 6.75628i 0.0197007 0.0341226i
\(199\) −210.301 + 121.418i −1.05679 + 0.610138i −0.924543 0.381078i \(-0.875553\pi\)
−0.132248 + 0.991217i \(0.542219\pi\)
\(200\) −7.07107 12.2474i −0.0353553 0.0612372i
\(201\) 22.3902 + 12.9270i 0.111394 + 0.0643133i
\(202\) 157.508i 0.779744i
\(203\) 64.0722 60.1782i 0.315627 0.296444i
\(204\) −34.8437 −0.170803
\(205\) −58.5713 + 101.448i −0.285714 + 0.494870i
\(206\) −57.5368 + 33.2189i −0.279305 + 0.161257i
\(207\) −1.38193 2.39358i −0.00667600 0.0115632i
\(208\) 18.7326 + 10.8153i 0.0900608 + 0.0519966i
\(209\) 16.9032i 0.0808766i
\(210\) −8.75832 37.3268i −0.0417063 0.177747i
\(211\) 185.930 0.881184 0.440592 0.897707i \(-0.354769\pi\)
0.440592 + 0.897707i \(0.354769\pi\)
\(212\) 104.079 180.271i 0.490940 0.850333i
\(213\) −26.9431 + 15.5556i −0.126493 + 0.0730309i
\(214\) −131.297 227.413i −0.613537 1.06268i
\(215\) −15.7304 9.08192i −0.0731644 0.0422415i
\(216\) 14.6969i 0.0680414i
\(217\) −84.5174 + 280.022i −0.389481 + 1.29043i
\(218\) −122.032 −0.559780
\(219\) −107.705 + 186.550i −0.491802 + 0.851826i
\(220\) 7.12175 4.11174i 0.0323716 0.0186897i
\(221\) −27.1965 47.1056i −0.123061 0.213148i
\(222\) 15.4514 + 8.92090i 0.0696011 + 0.0401842i
\(223\) 53.6348i 0.240515i −0.992743 0.120257i \(-0.961628\pi\)
0.992743 0.120257i \(-0.0383720\pi\)
\(224\) 37.9089 + 11.4418i 0.169236 + 0.0510795i
\(225\) 15.0000 0.0666667
\(226\) −60.6843 + 105.108i −0.268515 + 0.465081i
\(227\) 146.392 84.5195i 0.644899 0.372333i −0.141600 0.989924i \(-0.545225\pi\)
0.786499 + 0.617591i \(0.211891\pi\)
\(228\) 15.9217 + 27.5772i 0.0698319 + 0.120952i
\(229\) 247.698 + 143.009i 1.08165 + 0.624492i 0.931342 0.364147i \(-0.118639\pi\)
0.150310 + 0.988639i \(0.451973\pi\)
\(230\) 2.91337i 0.0126668i
\(231\) 21.7051 5.09286i 0.0939615 0.0220470i
\(232\) −35.5175 −0.153093
\(233\) 90.9194 157.477i 0.390212 0.675867i −0.602265 0.798296i \(-0.705735\pi\)
0.992477 + 0.122429i \(0.0390684\pi\)
\(234\) −19.8690 + 11.4714i −0.0849101 + 0.0490229i
\(235\) 37.9703 + 65.7666i 0.161576 + 0.279858i
\(236\) −25.1836 14.5398i −0.106710 0.0616092i
\(237\) 140.186i 0.591503i
\(238\) −68.1695 72.5806i −0.286426 0.304961i
\(239\) −382.489 −1.60037 −0.800185 0.599753i \(-0.795266\pi\)
−0.800185 + 0.599753i \(0.795266\pi\)
\(240\) −7.74597 + 13.4164i −0.0322749 + 0.0559017i
\(241\) −180.324 + 104.110i −0.748230 + 0.431991i −0.825054 0.565054i \(-0.808855\pi\)
0.0768238 + 0.997045i \(0.475522\pi\)
\(242\) −83.1690 144.053i −0.343674 0.595260i
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 47.5536i 0.194892i
\(245\) 60.6179 91.2714i 0.247420 0.372536i
\(246\) 128.323 0.521639
\(247\) −24.8546 + 43.0494i −0.100626 + 0.174289i
\(248\) 102.353 59.0937i 0.412715 0.238281i
\(249\) 133.988 + 232.074i 0.538105 + 0.932025i
\(250\) 13.6931 + 7.90569i 0.0547723 + 0.0316228i
\(251\) 43.4959i 0.173291i −0.996239 0.0866453i \(-0.972385\pi\)
0.996239 0.0866453i \(-0.0276147\pi\)
\(252\) −30.6142 + 28.7536i −0.121485 + 0.114102i
\(253\) 1.69409 0.00669600
\(254\) −93.1545 + 161.348i −0.366750 + 0.635229i
\(255\) 33.7373 19.4782i 0.132303 0.0763852i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 3.68915 + 2.12993i 0.0143547 + 0.00828766i 0.507160 0.861852i \(-0.330695\pi\)
−0.492806 + 0.870139i \(0.664029\pi\)
\(258\) 19.8975i 0.0771221i
\(259\) 11.6472 + 49.6390i 0.0449700 + 0.191656i
\(260\) −24.1837 −0.0930144
\(261\) 18.8360 32.6249i 0.0721686 0.125000i
\(262\) −145.460 + 83.9815i −0.555192 + 0.320540i
\(263\) 209.187 + 362.323i 0.795388 + 1.37765i 0.922592 + 0.385776i \(0.126066\pi\)
−0.127204 + 0.991877i \(0.540600\pi\)
\(264\) −7.80148 4.50419i −0.0295511 0.0170613i
\(265\) 232.728i 0.878220i
\(266\) −26.2944 + 87.1183i −0.0988511 + 0.327512i
\(267\) 117.991 0.441915
\(268\) 14.9268 25.8539i 0.0556969 0.0964699i
\(269\) −319.086 + 184.224i −1.18619 + 0.684848i −0.957439 0.288636i \(-0.906798\pi\)
−0.228753 + 0.973484i \(0.573465\pi\)
\(270\) −8.21584 14.2302i −0.0304290 0.0527046i
\(271\) −191.411 110.511i −0.706312 0.407790i 0.103382 0.994642i \(-0.467034\pi\)
−0.809694 + 0.586852i \(0.800367\pi\)
\(272\) 40.2341i 0.147919i
\(273\) −62.7676 18.9448i −0.229918 0.0693947i
\(274\) −114.768 −0.418860
\(275\) −4.59707 + 7.96235i −0.0167166 + 0.0289540i
\(276\) −2.76386 + 1.59572i −0.0100140 + 0.00578158i
\(277\) 198.427 + 343.686i 0.716343 + 1.24074i 0.962439 + 0.271497i \(0.0875187\pi\)
−0.246096 + 0.969245i \(0.579148\pi\)
\(278\) −304.118 175.583i −1.09395 0.631593i
\(279\) 125.357i 0.449307i
\(280\) −43.1013 + 10.1132i −0.153933 + 0.0361187i
\(281\) −114.244 −0.406562 −0.203281 0.979120i \(-0.565161\pi\)
−0.203281 + 0.979120i \(0.565161\pi\)
\(282\) 41.5944 72.0437i 0.147498 0.255474i
\(283\) 391.819 226.217i 1.38452 0.799353i 0.391829 0.920038i \(-0.371843\pi\)
0.992691 + 0.120685i \(0.0385092\pi\)
\(284\) 17.9620 + 31.1112i 0.0632466 + 0.109546i
\(285\) −30.8322 17.8010i −0.108183 0.0624596i
\(286\) 14.0626i 0.0491698i
\(287\) 251.056 + 267.302i 0.874760 + 0.931364i
\(288\) 16.9706 0.0589256
\(289\) −93.9131 + 162.662i −0.324959 + 0.562845i
\(290\) 34.3897 19.8549i 0.118585 0.0684652i
\(291\) 76.3606 + 132.260i 0.262407 + 0.454503i
\(292\) 215.409 + 124.367i 0.737703 + 0.425913i
\(293\) 119.134i 0.406600i 0.979116 + 0.203300i \(0.0651667\pi\)
−0.979116 + 0.203300i \(0.934833\pi\)
\(294\) −119.789 7.51583i −0.407447 0.0255640i
\(295\) 32.5119 0.110210
\(296\) 10.3010 17.8418i 0.0348006 0.0602763i
\(297\) 8.27472 4.77741i 0.0278610 0.0160856i
\(298\) −106.073 183.724i −0.355949 0.616522i
\(299\) −4.31454 2.49100i −0.0144299 0.00833110i
\(300\) 17.3205i 0.0577350i
\(301\) −41.4471 + 38.9282i −0.137698 + 0.129329i
\(302\) −258.843 −0.857097
\(303\) −96.4537 + 167.063i −0.318329 + 0.551362i
\(304\) 31.8434 18.3848i 0.104748 0.0604762i
\(305\) 26.5833 + 46.0435i 0.0871582 + 0.150962i
\(306\) −36.9573 21.3373i −0.120776 0.0697298i
\(307\) 272.643i 0.888087i −0.896005 0.444043i \(-0.853544\pi\)
0.896005 0.444043i \(-0.146456\pi\)
\(308\) −5.88072 25.0629i −0.0190933 0.0813731i
\(309\) −81.3693 −0.263331
\(310\) −66.0688 + 114.435i −0.213125 + 0.369144i
\(311\) 65.4476 37.7862i 0.210443 0.121499i −0.391074 0.920359i \(-0.627897\pi\)
0.601517 + 0.798860i \(0.294563\pi\)
\(312\) 13.2460 + 22.9427i 0.0424551 + 0.0735343i
\(313\) −55.1057 31.8153i −0.176057 0.101646i 0.409382 0.912363i \(-0.365744\pi\)
−0.585439 + 0.810717i \(0.699078\pi\)
\(314\) 417.596i 1.32992i
\(315\) 13.5683 44.9544i 0.0430740 0.142712i
\(316\) −161.873 −0.512257
\(317\) −7.72605 + 13.3819i −0.0243724 + 0.0422142i −0.877954 0.478744i \(-0.841092\pi\)
0.853582 + 0.520959i \(0.174425\pi\)
\(318\) 220.786 127.471i 0.694294 0.400851i
\(319\) 11.5454 + 19.9972i 0.0361924 + 0.0626872i
\(320\) 15.4919 + 8.94427i 0.0484123 + 0.0279508i
\(321\) 321.610i 1.00190i
\(322\) −8.73125 2.63530i −0.0271157 0.00818416i
\(323\) −92.4617 −0.286259
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) 23.4158 13.5191i 0.0720486 0.0415973i
\(326\) −83.6692 144.919i −0.256654 0.444538i
\(327\) −129.434 74.7290i −0.395824 0.228529i
\(328\) 148.175i 0.451753i
\(329\) 231.446 54.3062i 0.703484 0.165064i
\(330\) 10.0717 0.0305202
\(331\) 186.540 323.096i 0.563564 0.976121i −0.433618 0.901097i \(-0.642763\pi\)
0.997182 0.0750241i \(-0.0239034\pi\)
\(332\) 267.976 154.716i 0.807157 0.466012i
\(333\) 10.9258 + 18.9241i 0.0328103 + 0.0568291i
\(334\) −251.301 145.088i −0.752397 0.434397i
\(335\) 33.3773i 0.0996337i
\(336\) 33.2018 + 35.3502i 0.0988149 + 0.105209i
\(337\) 642.919 1.90777 0.953885 0.300171i \(-0.0970437\pi\)
0.953885 + 0.300171i \(0.0970437\pi\)
\(338\) 98.8234 171.167i 0.292377 0.506412i
\(339\) −128.731 + 74.3228i −0.379737 + 0.219241i
\(340\) −22.4915 38.9565i −0.0661515 0.114578i
\(341\) −66.5423 38.4182i −0.195139 0.112663i
\(342\) 39.0000i 0.114035i
\(343\) −218.705 264.230i −0.637623 0.770349i
\(344\) 22.9757 0.0667897
\(345\) 1.78407 3.09009i 0.00517120 0.00895679i
\(346\) 137.825 79.5735i 0.398339 0.229981i
\(347\) −72.0043 124.715i −0.207505 0.359409i 0.743423 0.668822i \(-0.233201\pi\)
−0.950928 + 0.309412i \(0.899868\pi\)
\(348\) −37.6720 21.7500i −0.108253 0.0624999i
\(349\) 566.507i 1.62323i −0.584194 0.811614i \(-0.698589\pi\)
0.584194 0.811614i \(-0.301411\pi\)
\(350\) 36.0792 33.8865i 0.103083 0.0968184i
\(351\) −28.0990 −0.0800540
\(352\) −5.20099 + 9.00838i −0.0147755 + 0.0255920i
\(353\) 441.814 255.082i 1.25160 0.722611i 0.280172 0.959950i \(-0.409609\pi\)
0.971427 + 0.237339i \(0.0762753\pi\)
\(354\) −17.8075 30.8435i −0.0503037 0.0871286i
\(355\) −34.7833 20.0822i −0.0979813 0.0565695i
\(356\) 136.245i 0.382709i
\(357\) −27.8583 118.728i −0.0780344 0.332573i
\(358\) 62.8898 0.175670
\(359\) −333.931 + 578.386i −0.930171 + 1.61110i −0.147145 + 0.989115i \(0.547008\pi\)
−0.783026 + 0.621989i \(0.786325\pi\)
\(360\) −16.4317 + 9.48683i −0.0456435 + 0.0263523i
\(361\) −138.250 239.456i −0.382964 0.663313i
\(362\) 11.3234 + 6.53759i 0.0312802 + 0.0180596i
\(363\) 203.722i 0.561217i
\(364\) −21.8755 + 72.4777i −0.0600976 + 0.199115i
\(365\) −278.092 −0.761897
\(366\) 29.1205 50.4382i 0.0795642 0.137809i
\(367\) −30.2216 + 17.4485i −0.0823478 + 0.0475435i −0.540608 0.841274i \(-0.681806\pi\)
0.458261 + 0.888818i \(0.348473\pi\)
\(368\) 1.84258 + 3.19143i 0.00500700 + 0.00867237i
\(369\) 136.107 + 78.5816i 0.368855 + 0.212958i
\(370\) 23.0337i 0.0622531i
\(371\) 697.478 + 210.516i 1.87999 + 0.567427i
\(372\) 144.749 0.389111
\(373\) 204.012 353.360i 0.546950 0.947345i −0.451532 0.892255i \(-0.649122\pi\)
0.998481 0.0550895i \(-0.0175444\pi\)
\(374\) 22.6527 13.0786i 0.0605688 0.0349694i
\(375\) 9.68246 + 16.7705i 0.0258199 + 0.0447214i
\(376\) −83.1888 48.0291i −0.221247 0.127737i
\(377\) 67.9057i 0.180121i
\(378\) −50.0792 + 11.7505i −0.132485 + 0.0310860i
\(379\) −10.4706 −0.0276268 −0.0138134 0.999905i \(-0.504397\pi\)
−0.0138134 + 0.999905i \(0.504397\pi\)
\(380\) −20.5548 + 35.6020i −0.0540916 + 0.0936893i
\(381\) −197.610 + 114.090i −0.518663 + 0.299450i
\(382\) −96.7385 167.556i −0.253242 0.438628i
\(383\) −199.672 115.281i −0.521337 0.300994i 0.216145 0.976361i \(-0.430652\pi\)
−0.737481 + 0.675367i \(0.763985\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 19.7046 + 20.9796i 0.0511807 + 0.0544925i
\(386\) 517.424 1.34048
\(387\) −12.1847 + 21.1045i −0.0314850 + 0.0545336i
\(388\) 152.721 88.1736i 0.393611 0.227251i
\(389\) −338.107 585.619i −0.869170 1.50545i −0.862846 0.505466i \(-0.831321\pi\)
−0.00632331 0.999980i \(-0.502013\pi\)
\(390\) −25.6507 14.8095i −0.0657711 0.0379730i
\(391\) 9.26678i 0.0237002i
\(392\) −8.67853 + 138.321i −0.0221391 + 0.352860i
\(393\) −205.712 −0.523440
\(394\) −137.833 + 238.734i −0.349830 + 0.605923i
\(395\) 156.733 90.4898i 0.396792 0.229088i
\(396\) −5.51648 9.55483i −0.0139305 0.0241283i
\(397\) −141.641 81.7764i −0.356778 0.205986i 0.310889 0.950446i \(-0.399373\pi\)
−0.667666 + 0.744461i \(0.732707\pi\)
\(398\) 343.421i 0.862866i
\(399\) −81.2383 + 76.3010i −0.203605 + 0.191230i
\(400\) −20.0000 −0.0500000
\(401\) 149.624 259.156i 0.373127 0.646274i −0.616918 0.787027i \(-0.711619\pi\)
0.990045 + 0.140753i \(0.0449524\pi\)
\(402\) 31.6645 18.2815i 0.0787674 0.0454764i
\(403\) 112.981 + 195.689i 0.280349 + 0.485579i
\(404\) 192.907 + 111.375i 0.477494 + 0.275681i
\(405\) 20.1246i 0.0496904i
\(406\) −28.3970 121.024i −0.0699434 0.298090i
\(407\) −13.3938 −0.0329086
\(408\) −24.6382 + 42.6747i −0.0603878 + 0.104595i
\(409\) 403.264 232.825i 0.985976 0.569253i 0.0819067 0.996640i \(-0.473899\pi\)
0.904069 + 0.427387i \(0.140566\pi\)
\(410\) 82.8323 + 143.470i 0.202030 + 0.349926i
\(411\) −121.729 70.2805i −0.296179 0.170999i
\(412\) 93.9572i 0.228051i
\(413\) 29.4088 97.4370i 0.0712078 0.235925i
\(414\) −3.90869 −0.00944129
\(415\) −172.978 + 299.606i −0.416814 + 0.721943i
\(416\) 26.4920 15.2951i 0.0636826 0.0367672i
\(417\) −215.044 372.467i −0.515693 0.893207i
\(418\) −20.7021 11.9524i −0.0495266 0.0285942i
\(419\) 575.882i 1.37442i 0.726458 + 0.687211i \(0.241165\pi\)
−0.726458 + 0.687211i \(0.758835\pi\)
\(420\) −51.9089 15.6674i −0.123593 0.0373032i
\(421\) 571.149 1.35665 0.678324 0.734763i \(-0.262706\pi\)
0.678324 + 0.734763i \(0.262706\pi\)
\(422\) 131.472 227.717i 0.311546 0.539613i
\(423\) 88.2351 50.9426i 0.208594 0.120432i
\(424\) −147.190 254.941i −0.347147 0.601276i
\(425\) 43.5546 + 25.1463i 0.102482 + 0.0591677i
\(426\) 43.9978i 0.103281i
\(427\) 162.037 38.0201i 0.379477 0.0890400i
\(428\) −371.363 −0.867672
\(429\) 8.61152 14.9156i 0.0200735 0.0347683i
\(430\) −22.2461 + 12.8438i −0.0517351 + 0.0298693i
\(431\) 13.5697 + 23.5034i 0.0314842 + 0.0545322i 0.881338 0.472486i \(-0.156643\pi\)
−0.849854 + 0.527018i \(0.823310\pi\)
\(432\) 18.0000 + 10.3923i 0.0416667 + 0.0240563i
\(433\) 363.408i 0.839279i −0.907691 0.419640i \(-0.862156\pi\)
0.907691 0.419640i \(-0.137844\pi\)
\(434\) 283.193 + 301.518i 0.652518 + 0.694742i
\(435\) 48.6344 0.111803
\(436\) −86.2897 + 149.458i −0.197912 + 0.342794i
\(437\) −7.33422 + 4.23441i −0.0167831 + 0.00968974i
\(438\) 152.317 + 263.822i 0.347757 + 0.602332i
\(439\) −403.057 232.705i −0.918124 0.530079i −0.0350882 0.999384i \(-0.511171\pi\)
−0.883036 + 0.469305i \(0.844505\pi\)
\(440\) 11.6298i 0.0264313i
\(441\) −122.453 81.3275i −0.277672 0.184416i
\(442\) −76.9232 −0.174034
\(443\) −243.968 + 422.565i −0.550718 + 0.953871i 0.447505 + 0.894281i \(0.352313\pi\)
−0.998223 + 0.0595896i \(0.981021\pi\)
\(444\) 21.8516 12.6161i 0.0492154 0.0284145i
\(445\) 76.1630 + 131.918i 0.171153 + 0.296445i
\(446\) −65.6889 37.9255i −0.147285 0.0850348i
\(447\) 259.824i 0.581263i
\(448\) 40.8189 38.3381i 0.0911137 0.0855762i
\(449\) −285.837 −0.636609 −0.318304 0.947989i \(-0.603113\pi\)
−0.318304 + 0.947989i \(0.603113\pi\)
\(450\) 10.6066 18.3712i 0.0235702 0.0408248i
\(451\) −83.4260 + 48.1660i −0.184980 + 0.106798i
\(452\) 85.8206 + 148.646i 0.189869 + 0.328862i
\(453\) −274.545 158.509i −0.606059 0.349908i
\(454\) 239.057i 0.526558i
\(455\) −19.3354 82.4050i −0.0424954 0.181110i
\(456\) 45.0333 0.0987572
\(457\) −211.624 + 366.543i −0.463071 + 0.802063i −0.999112 0.0421292i \(-0.986586\pi\)
0.536041 + 0.844192i \(0.319919\pi\)
\(458\) 350.298 202.245i 0.764843 0.441583i
\(459\) −26.1328 45.2633i −0.0569342 0.0986129i
\(460\) −3.56813 2.06006i −0.00775681 0.00447839i
\(461\) 471.748i 1.02331i 0.859190 + 0.511657i \(0.170968\pi\)
−0.859190 + 0.511657i \(0.829032\pi\)
\(462\) 9.11038 30.1844i 0.0197194 0.0653342i
\(463\) −194.019 −0.419046 −0.209523 0.977804i \(-0.567191\pi\)
−0.209523 + 0.977804i \(0.567191\pi\)
\(464\) −25.1147 + 43.4999i −0.0541265 + 0.0937498i
\(465\) −140.153 + 80.9174i −0.301404 + 0.174016i
\(466\) −128.579 222.706i −0.275921 0.477910i
\(467\) −9.80955 5.66354i −0.0210055 0.0121275i 0.489461 0.872025i \(-0.337194\pi\)
−0.510466 + 0.859898i \(0.670527\pi\)
\(468\) 32.4459i 0.0693288i
\(469\) 100.030 + 30.1916i 0.213285 + 0.0643744i
\(470\) 107.396 0.228503
\(471\) −255.724 + 442.928i −0.542939 + 0.940398i
\(472\) −35.6150 + 20.5624i −0.0754556 + 0.0435643i
\(473\) −7.46851 12.9358i −0.0157897 0.0273485i
\(474\) −171.692 99.1266i −0.362220 0.209128i
\(475\) 45.9619i 0.0967619i
\(476\) −137.096 + 32.1680i −0.288016 + 0.0675798i
\(477\) 312.238 0.654587
\(478\) −270.460 + 468.451i −0.565816 + 0.980023i
\(479\) −547.932 + 316.349i −1.14391 + 0.660435i −0.947395 0.320066i \(-0.896295\pi\)
−0.196512 + 0.980501i \(0.562962\pi\)
\(480\) 10.9545 + 18.9737i 0.0228218 + 0.0395285i
\(481\) 34.1116 + 19.6943i 0.0709181 + 0.0409446i
\(482\) 294.467i 0.610927i
\(483\) −7.64710 8.14193i −0.0158325 0.0168570i
\(484\) −235.237 −0.486028
\(485\) −98.5811 + 170.747i −0.203260 + 0.352056i
\(486\) −19.0919 + 11.0227i −0.0392837 + 0.0226805i
\(487\) 31.5102 + 54.5773i 0.0647027 + 0.112068i 0.896562 0.442918i \(-0.146057\pi\)
−0.831859 + 0.554986i \(0.812723\pi\)
\(488\) −58.2410 33.6254i −0.119346 0.0689046i
\(489\) 204.947i 0.419114i
\(490\) −68.9208 138.780i −0.140655 0.283225i
\(491\) 261.092 0.531756 0.265878 0.964007i \(-0.414338\pi\)
0.265878 + 0.964007i \(0.414338\pi\)
\(492\) 90.7382 157.163i 0.184427 0.319437i
\(493\) 109.386 63.1541i 0.221879 0.128102i
\(494\) 35.1497 + 60.8811i 0.0711532 + 0.123241i
\(495\) 10.6826 + 6.16761i 0.0215811 + 0.0124598i
\(496\) 167.142i 0.336980i
\(497\) −91.6490 + 86.0789i −0.184404 + 0.173197i
\(498\) 378.976 0.760995
\(499\) −219.481 + 380.153i −0.439843 + 0.761830i −0.997677 0.0681226i \(-0.978299\pi\)
0.557834 + 0.829952i \(0.311632\pi\)
\(500\) 19.3649 11.1803i 0.0387298 0.0223607i
\(501\) −177.696 307.779i −0.354683 0.614329i
\(502\) −53.2714 30.7563i −0.106118 0.0612675i
\(503\) 702.372i 1.39637i 0.715919 + 0.698183i \(0.246008\pi\)
−0.715919 + 0.698183i \(0.753992\pi\)
\(504\) 13.5683 + 57.8265i 0.0269213 + 0.114735i
\(505\) −249.042 −0.493153
\(506\) 1.19790 2.07483i 0.00236739 0.00410045i
\(507\) 209.636 121.033i 0.413483 0.238725i
\(508\) 131.740 + 228.181i 0.259331 + 0.449175i
\(509\) −103.188 59.5758i −0.202727 0.117045i 0.395200 0.918595i \(-0.370675\pi\)
−0.597927 + 0.801551i \(0.704009\pi\)
\(510\) 55.0928i 0.108025i
\(511\) −251.550 + 833.432i −0.492270 + 1.63098i
\(512\) −22.6274 −0.0441942
\(513\) −23.8825 + 41.3657i −0.0465546 + 0.0806350i
\(514\) 5.21724 3.01217i 0.0101503 0.00586026i
\(515\) −52.5237 90.9736i −0.101988 0.176648i
\(516\) 24.3694 + 14.0697i 0.0472274 + 0.0272668i
\(517\) 62.4497i 0.120792i
\(518\) 69.0310 + 20.8352i 0.133264 + 0.0402224i
\(519\) 194.914 0.375558
\(520\) −17.1005 + 29.6189i −0.0328855 + 0.0569594i
\(521\) −391.422 + 225.988i −0.751291 + 0.433758i −0.826160 0.563435i \(-0.809479\pi\)
0.0748694 + 0.997193i \(0.476146\pi\)
\(522\) −26.6381 46.1386i −0.0510309 0.0883882i
\(523\) −775.007 447.451i −1.48185 0.855546i −0.482062 0.876137i \(-0.660112\pi\)
−0.999788 + 0.0205911i \(0.993445\pi\)
\(524\) 237.536i 0.453312i
\(525\) 59.0189 13.8481i 0.112417 0.0263774i
\(526\) 591.670 1.12485
\(527\) −210.150 + 363.991i −0.398767 + 0.690685i
\(528\) −11.0330 + 6.36988i −0.0208958 + 0.0120642i
\(529\) 264.076 + 457.392i 0.499198 + 0.864636i
\(530\) 285.033 + 164.564i 0.537798 + 0.310498i
\(531\) 43.6193i 0.0821457i
\(532\) 88.1048 + 93.8059i 0.165610 + 0.176327i
\(533\) 283.294 0.531509
\(534\) 83.4324 144.509i 0.156240 0.270616i
\(535\) 359.571 207.598i 0.672096 0.388035i
\(536\) −21.1096 36.5630i −0.0393837 0.0682145i
\(537\) 66.7047 + 38.5120i 0.124217 + 0.0717169i
\(538\) 521.065i 0.968522i
\(539\) 80.6990 40.0766i 0.149720 0.0743537i
\(540\) −23.2379 −0.0430331
\(541\) 158.262 274.119i 0.292537 0.506689i −0.681872 0.731472i \(-0.738834\pi\)
0.974409 + 0.224783i \(0.0721672\pi\)
\(542\) −270.695 + 156.286i −0.499438 + 0.288351i
\(543\) 8.00688 + 13.8683i 0.0147456 + 0.0255402i
\(544\) 49.2765 + 28.4498i 0.0905817 + 0.0522974i
\(545\) 192.950i 0.354036i
\(546\) −67.5859 + 63.4783i −0.123784 + 0.116261i
\(547\) 796.193 1.45556 0.727782 0.685809i \(-0.240551\pi\)
0.727782 + 0.685809i \(0.240551\pi\)
\(548\) −81.1530 + 140.561i −0.148089 + 0.256498i
\(549\) 61.7739 35.6652i 0.112521 0.0649639i
\(550\) 6.50124 + 11.2605i 0.0118204 + 0.0204736i
\(551\) −99.9670 57.7160i −0.181428 0.104748i
\(552\) 4.51337i 0.00817639i
\(553\) −129.421 551.576i −0.234034 0.997424i
\(554\) 561.236 1.01306
\(555\) −14.1052 + 24.4309i −0.0254147 + 0.0440196i
\(556\) −430.088 + 248.311i −0.773540 + 0.446603i
\(557\) −155.976 270.159i −0.280029 0.485025i 0.691363 0.722508i \(-0.257011\pi\)
−0.971392 + 0.237484i \(0.923677\pi\)
\(558\) 153.530 + 88.6406i 0.275143 + 0.158854i
\(559\) 43.9270i 0.0785813i
\(560\) −18.0911 + 59.9392i −0.0323055 + 0.107034i
\(561\) 32.0358 0.0571048
\(562\) −80.7827 + 139.920i −0.143741 + 0.248968i
\(563\) 534.350 308.507i 0.949112 0.547970i 0.0563071 0.998413i \(-0.482067\pi\)
0.892805 + 0.450443i \(0.148734\pi\)
\(564\) −58.8234 101.885i −0.104297 0.180647i
\(565\) −166.191 95.9504i −0.294143 0.169824i
\(566\) 639.838i 1.13046i
\(567\) −60.3127 18.2038i −0.106372 0.0321055i
\(568\) 50.8043 0.0894442
\(569\) 391.495 678.089i 0.688041 1.19172i −0.284430 0.958697i \(-0.591804\pi\)
0.972471 0.233025i \(-0.0748623\pi\)
\(570\) −43.6033 + 25.1744i −0.0764970 + 0.0441656i
\(571\) −1.06600 1.84636i −0.00186689 0.00323355i 0.865090 0.501616i \(-0.167261\pi\)
−0.866957 + 0.498382i \(0.833928\pi\)
\(572\) −17.2230 9.94373i −0.0301102 0.0173841i
\(573\) 236.960i 0.413543i
\(574\) 504.900 118.469i 0.879616 0.206392i
\(575\) 4.60644 0.00801120
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −828.056 + 478.079i −1.43511 + 0.828559i −0.997504 0.0706096i \(-0.977506\pi\)
−0.437602 + 0.899169i \(0.644172\pi\)
\(578\) 132.813 + 230.039i 0.229781 + 0.397992i
\(579\) 548.811 + 316.856i 0.947860 + 0.547247i
\(580\) 56.1581i 0.0968244i
\(581\) 741.441 + 789.419i 1.27615 + 1.35872i
\(582\) 215.980 0.371100
\(583\) −95.6919 + 165.743i −0.164137 + 0.284294i
\(584\) 304.635 175.881i 0.521635 0.301166i
\(585\) −18.1378 31.4156i −0.0310048 0.0537019i
\(586\) 145.909 + 84.2403i 0.248991 + 0.143755i
\(587\) 628.961i 1.07148i −0.844382 0.535742i \(-0.820032\pi\)
0.844382 0.535742i \(-0.179968\pi\)
\(588\) −93.9089 + 141.397i −0.159709 + 0.240471i
\(589\) 384.109 0.652138
\(590\) 22.9894 39.8188i 0.0389651 0.0674895i
\(591\) −292.388 + 168.810i −0.494734 + 0.285635i
\(592\) −14.5678 25.2321i −0.0246077 0.0426218i
\(593\) −417.691 241.154i −0.704370 0.406668i 0.104603 0.994514i \(-0.466643\pi\)
−0.808973 + 0.587846i \(0.799976\pi\)
\(594\) 13.5126i 0.0227484i
\(595\) 114.760 107.785i 0.192874 0.181152i
\(596\) −300.019 −0.503388
\(597\) −210.301 + 364.253i −0.352263 + 0.610138i
\(598\) −6.10168 + 3.52280i −0.0102035 + 0.00589098i
\(599\) −181.233 313.904i −0.302559 0.524047i 0.674156 0.738589i \(-0.264508\pi\)
−0.976715 + 0.214542i \(0.931174\pi\)
\(600\) −21.2132 12.2474i −0.0353553 0.0204124i
\(601\) 545.450i 0.907570i 0.891111 + 0.453785i \(0.149927\pi\)
−0.891111 + 0.453785i \(0.850073\pi\)
\(602\) 18.3695 + 78.2886i 0.0305142 + 0.130047i
\(603\) 44.7803 0.0742626
\(604\) −183.030 + 317.017i −0.303030 + 0.524863i
\(605\) 227.768 131.502i 0.376475 0.217358i
\(606\) 136.406 + 236.262i 0.225093 + 0.389872i
\(607\) −554.426 320.098i −0.913388 0.527345i −0.0318683 0.999492i \(-0.510146\pi\)
−0.881520 + 0.472147i \(0.843479\pi\)
\(608\) 52.0000i 0.0855263i
\(609\) 43.9925 145.755i 0.0722372 0.239336i
\(610\) 75.1888 0.123260
\(611\) 91.8265 159.048i 0.150289 0.260308i
\(612\) −52.2656 + 30.1755i −0.0854013 + 0.0493064i
\(613\) 198.272 + 343.417i 0.323445 + 0.560223i 0.981196 0.193012i \(-0.0618256\pi\)
−0.657751 + 0.753235i \(0.728492\pi\)
\(614\) −333.918 192.787i −0.543840 0.313986i
\(615\) 202.897i 0.329914i
\(616\) −34.8540 10.5198i −0.0565811 0.0170775i
\(617\) −421.502 −0.683148 −0.341574 0.939855i \(-0.610960\pi\)
−0.341574 + 0.939855i \(0.610960\pi\)
\(618\) −57.5368 + 99.6566i −0.0931016 + 0.161257i
\(619\) 629.261 363.304i 1.01658 0.586921i 0.103467 0.994633i \(-0.467006\pi\)
0.913111 + 0.407712i \(0.133673\pi\)
\(620\) 93.4354 + 161.835i 0.150702 + 0.261024i
\(621\) −4.14579 2.39358i −0.00667600 0.00385439i
\(622\) 106.876i 0.171826i
\(623\) 464.248 108.930i 0.745181 0.174848i
\(624\) 37.4653 0.0600405
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) −77.9313 + 44.9936i −0.124491 + 0.0718748i
\(627\) −14.6386 25.3548i −0.0233471 0.0404383i
\(628\) 511.449 + 295.285i 0.814409 + 0.470199i
\(629\) 73.2650i 0.116479i
\(630\) −45.4635 48.4053i −0.0721642 0.0768338i
\(631\) −537.550 −0.851901 −0.425950 0.904746i \(-0.640060\pi\)
−0.425950 + 0.904746i \(0.640060\pi\)
\(632\) −114.462 + 198.253i −0.181110 + 0.313692i
\(633\) 278.895 161.020i 0.440592 0.254376i
\(634\) 10.9263 + 18.9249i 0.0172339 + 0.0298500i
\(635\) −255.114 147.290i −0.401754 0.231953i
\(636\) 360.541i 0.566889i
\(637\) −264.455 16.5924i −0.415157 0.0260477i
\(638\) 32.6553 0.0511838
\(639\) −26.9431 + 46.6668i −0.0421644 + 0.0730309i
\(640\) 21.9089 12.6491i 0.0342327 0.0197642i
\(641\) −488.924 846.841i −0.762752 1.32112i −0.941427 0.337217i \(-0.890514\pi\)
0.178675 0.983908i \(-0.442819\pi\)
\(642\) −393.890 227.413i −0.613537 0.354225i
\(643\) 276.520i 0.430047i 0.976609 + 0.215023i \(0.0689828\pi\)
−0.976609 + 0.215023i \(0.931017\pi\)
\(644\) −9.40150 + 8.83011i −0.0145986 + 0.0137114i
\(645\) −31.4607 −0.0487763
\(646\) −65.3803 + 113.242i −0.101208 + 0.175297i
\(647\) −210.206 + 121.362i −0.324893 + 0.187577i −0.653571 0.756865i \(-0.726730\pi\)
0.328679 + 0.944442i \(0.393397\pi\)
\(648\) 12.7279 + 22.0454i 0.0196419 + 0.0340207i
\(649\) 23.1542 + 13.3681i 0.0356767 + 0.0205980i
\(650\) 38.2378i 0.0588275i
\(651\) 115.730 + 493.228i 0.177773 + 0.757646i
\(652\) −236.652 −0.362964
\(653\) 26.6109 46.0914i 0.0407518 0.0705841i −0.844930 0.534877i \(-0.820358\pi\)
0.885682 + 0.464293i \(0.153691\pi\)
\(654\) −183.048 + 105.683i −0.279890 + 0.161595i
\(655\) −132.786 229.993i −0.202727 0.351134i
\(656\) −181.476 104.775i −0.276641 0.159719i
\(657\) 373.100i 0.567884i
\(658\) 97.1459 321.863i 0.147638 0.489153i
\(659\) 640.732 0.972279 0.486139 0.873881i \(-0.338405\pi\)
0.486139 + 0.873881i \(0.338405\pi\)
\(660\) 7.12175 12.3352i 0.0107905 0.0186897i
\(661\) 10.4335 6.02380i 0.0157845 0.00911317i −0.492087 0.870546i \(-0.663766\pi\)
0.507871 + 0.861433i \(0.330432\pi\)
\(662\) −263.807 456.927i −0.398500 0.690222i
\(663\) −81.5894 47.1056i −0.123061 0.0710492i
\(664\) 437.603i 0.659041i
\(665\) −137.746 41.5751i −0.207137 0.0625189i
\(666\) 30.9029 0.0464007
\(667\) 5.78446 10.0190i 0.00867236 0.0150210i
\(668\) −355.393 + 205.186i −0.532025 + 0.307165i
\(669\) −46.4491 80.4522i −0.0694306 0.120257i
\(670\) 40.8787 + 23.6013i 0.0610129 + 0.0352258i
\(671\) 43.7214i 0.0651586i
\(672\) 66.7723 15.6674i 0.0993635 0.0233145i
\(673\) −952.008 −1.41457 −0.707286 0.706927i \(-0.750081\pi\)
−0.707286 + 0.706927i \(0.750081\pi\)
\(674\) 454.612 787.412i 0.674499 1.16827i
\(675\) 22.5000 12.9904i 0.0333333 0.0192450i
\(676\) −139.757 242.067i −0.206742 0.358087i
\(677\) 18.2965 + 10.5635i 0.0270259 + 0.0156034i 0.513452 0.858118i \(-0.328366\pi\)
−0.486426 + 0.873722i \(0.661700\pi\)
\(678\) 210.217i 0.310054i
\(679\) 422.551 + 449.894i 0.622314 + 0.662583i
\(680\) −63.6156 −0.0935524
\(681\) 146.392 253.559i 0.214966 0.372333i
\(682\) −94.1050 + 54.3316i −0.137984 + 0.0796651i
\(683\) 196.448 + 340.259i 0.287626 + 0.498182i 0.973243 0.229780i \(-0.0738007\pi\)
−0.685617 + 0.727963i \(0.740467\pi\)
\(684\) 47.7650 + 27.5772i 0.0698319 + 0.0403175i
\(685\) 181.464i 0.264910i
\(686\) −478.261 + 81.0188i −0.697174 + 0.118103i
\(687\) 495.397 0.721101
\(688\) 16.2462 28.1393i 0.0236137 0.0409002i
\(689\) 487.420 281.412i 0.707431 0.408436i
\(690\) −2.52305 4.37005i −0.00365659 0.00633341i
\(691\) 230.954 + 133.342i 0.334232 + 0.192969i 0.657718 0.753264i \(-0.271522\pi\)
−0.323486 + 0.946233i \(0.604855\pi\)
\(692\) 225.068i 0.325242i
\(693\) 28.1471 26.4365i 0.0406163 0.0381479i
\(694\) −203.659 −0.293457
\(695\) 277.621 480.853i 0.399454 0.691875i
\(696\) −53.2763 + 30.7591i −0.0765464 + 0.0441941i
\(697\) 263.471 + 456.346i 0.378008 + 0.654729i
\(698\) −693.826 400.581i −0.994020 0.573898i
\(699\) 314.954i 0.450578i
\(700\) −15.9904 68.1491i −0.0228435 0.0973559i
\(701\) 207.973 0.296680 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(702\) −19.8690 + 34.4141i −0.0283034 + 0.0490229i
\(703\) 57.9858 33.4781i 0.0824834 0.0476218i
\(704\) 7.35531 + 12.7398i 0.0104479 + 0.0180963i
\(705\) 113.911 + 65.7666i 0.161576 + 0.0932859i
\(706\) 721.480i 1.02193i
\(707\) −225.273 + 746.371i −0.318632 + 1.05569i
\(708\) −50.3673 −0.0711402
\(709\) 447.714 775.463i 0.631472 1.09374i −0.355779 0.934570i \(-0.615784\pi\)
0.987251 0.159172i \(-0.0508823\pi\)
\(710\) −49.1911 + 28.4005i −0.0692832 + 0.0400007i
\(711\) −121.405 210.279i −0.170752 0.295751i
\(712\) −166.865 96.3395i −0.234361 0.135308i
\(713\) 38.4965i 0.0539923i
\(714\) −165.111 49.8344i −0.231248 0.0697961i
\(715\) 22.2349 0.0310977
\(716\) 44.4698 77.0240i 0.0621087 0.107575i
\(717\) −573.733 + 331.245i −0.800185 + 0.461987i
\(718\) 472.250 + 817.962i 0.657730 + 1.13922i
\(719\) −327.729 189.215i −0.455813 0.263163i 0.254469 0.967081i \(-0.418099\pi\)
−0.710282 + 0.703917i \(0.751433\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −320.155 + 75.1207i −0.444043 + 0.104190i
\(722\) −391.030 −0.541593
\(723\) −180.324 + 312.329i −0.249410 + 0.431991i
\(724\) 16.0138 9.24555i 0.0221185 0.0127701i
\(725\) 31.3934 + 54.3749i 0.0433012 + 0.0749998i
\(726\) −249.507 144.053i −0.343674 0.198420i
\(727\) 456.052i 0.627307i −0.949538 0.313653i \(-0.898447\pi\)
0.949538 0.313653i \(-0.101553\pi\)
\(728\) 73.2984 + 78.0414i 0.100685 + 0.107200i
\(729\) −27.0000 −0.0370370
\(730\) −196.641 + 340.592i −0.269371 + 0.466565i
\(731\) −70.7599 + 40.8533i −0.0967988 + 0.0558868i
\(732\) −41.1826 71.3303i −0.0562604 0.0974458i
\(733\) 658.892 + 380.412i 0.898898 + 0.518979i 0.876842 0.480778i \(-0.159646\pi\)
0.0220553 + 0.999757i \(0.492979\pi\)
\(734\) 49.3517i 0.0672367i
\(735\) 11.8836 189.404i 0.0161681 0.257692i
\(736\) 5.21159 0.00708096
\(737\) −13.7239 + 23.7705i −0.0186213 + 0.0322530i
\(738\) 192.485 111.131i 0.260820 0.150584i
\(739\) 14.0833 + 24.3930i 0.0190573 + 0.0330081i 0.875397 0.483405i \(-0.160600\pi\)
−0.856340 + 0.516413i \(0.827267\pi\)
\(740\) 28.2104 + 16.2873i 0.0381221 + 0.0220098i
\(741\) 86.0988i 0.116193i
\(742\) 751.019 705.376i 1.01216 0.950641i
\(743\) −1077.90 −1.45073 −0.725367 0.688362i \(-0.758330\pi\)
−0.725367 + 0.688362i \(0.758330\pi\)
\(744\) 102.353 177.281i 0.137572 0.238281i
\(745\) 290.492 167.716i 0.389923 0.225122i
\(746\) −288.517 499.726i −0.386752 0.669874i
\(747\) 401.964 + 232.074i 0.538105 + 0.310675i
\(748\) 36.9917i 0.0494542i
\(749\) −296.913 1265.41i −0.396412 1.68946i
\(750\) 27.3861 0.0365148
\(751\) −90.0583 + 155.986i −0.119918 + 0.207704i −0.919735 0.392540i \(-0.871596\pi\)
0.799817 + 0.600244i \(0.204930\pi\)
\(752\) −117.647 + 67.9234i −0.156445 + 0.0903237i
\(753\) −37.6686 65.2439i −0.0500247 0.0866453i
\(754\) −83.1671 48.0166i −0.110301 0.0636824i
\(755\) 409.267i 0.542076i
\(756\) −21.0200 + 69.6431i −0.0278042 + 0.0921205i
\(757\) 219.675 0.290192 0.145096 0.989418i \(-0.453651\pi\)
0.145096 + 0.989418i \(0.453651\pi\)
\(758\) −7.40380 + 12.8238i −0.00976755 + 0.0169179i
\(759\) 2.54113 1.46712i 0.00334800 0.00193297i
\(760\) 29.0689 + 50.3488i 0.0382485 + 0.0662484i
\(761\) 1113.97 + 643.150i 1.46382 + 0.845138i 0.999185 0.0403636i \(-0.0128516\pi\)
0.464637 + 0.885501i \(0.346185\pi\)
\(762\) 322.697i 0.423486i
\(763\) −578.262 174.533i −0.757880 0.228746i
\(764\) −273.618 −0.358138
\(765\) 33.7373 58.4347i 0.0441010 0.0763852i
\(766\) −282.379 + 163.031i −0.368641 + 0.212835i
\(767\) −39.3130 68.0921i −0.0512555 0.0887772i
\(768\) −24.0000 13.8564i −0.0312500 0.0180422i
\(769\) 365.543i 0.475348i 0.971345 + 0.237674i \(0.0763850\pi\)
−0.971345 + 0.237674i \(0.923615\pi\)
\(770\) 39.6279 9.29824i 0.0514648 0.0120756i
\(771\) 7.37829 0.00956977
\(772\) 365.874 633.712i 0.473930 0.820871i
\(773\) 267.183 154.258i 0.345645 0.199558i −0.317121 0.948385i \(-0.602716\pi\)
0.662765 + 0.748827i \(0.269383\pi\)
\(774\) 17.2317 + 29.8462i 0.0222632 + 0.0385610i
\(775\) −180.937 104.464i −0.233467 0.134792i
\(776\) 249.393i