Properties

Label 210.3.o.a.31.4
Level 210
Weight 3
Character 210.31
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
Defining polynomial: \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
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 31.4
Root \(1.72286 - 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 210.31
Dual form 210.3.o.a.61.4

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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 −0.821203 0.570635i \(-0.806697\pi\)
0.904787 + 0.425865i \(0.140030\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 5.40765i 0.415973i 0.978132 + 0.207986i \(0.0666910\pi\)
−0.978132 + 0.207986i \(0.933309\pi\)
\(14\) −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 0.733823 0.679341i \(-0.237734\pi\)
−0.221415 + 0.975180i \(0.571068\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) −7.96084 + 4.59619i −0.418992 + 0.241905i −0.694646 0.719352i \(-0.744439\pi\)
0.275654 + 0.961257i \(0.411106\pi\)
\(20\) 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 0.875866 0.482555i \(-0.160291\pi\)
−0.855838 + 0.517244i \(0.826958\pi\)
\(24\) −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 −0.214284 0.976771i \(-0.568742\pi\)
−0.953051 + 0.302811i \(0.902075\pi\)
\(32\) 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 0.812604 0.582816i \(-0.198049\pi\)
−0.911035 + 0.412328i \(0.864716\pi\)
\(38\) −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 \(-0.779400\pi\)
0.769311 0.638875i \(-0.220600\pi\)
\(42\) −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 −0.153335 0.988174i \(-0.549001\pi\)
0.779116 + 0.626879i \(0.215668\pi\)
\(48\) 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 0.326825 0.945085i \(-0.394021\pi\)
0.655055 0.755582i \(-0.272646\pi\)
\(54\) −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 0.602900 0.797817i \(-0.294012\pi\)
−0.389479 + 0.921035i \(0.627345\pi\)
\(60\) −3.87298 + 6.70820i −0.0645497 + 0.111803i
\(61\) 20.5913 11.8884i 0.337562 0.194892i −0.321631 0.946865i \(-0.604231\pi\)
0.659194 + 0.751973i \(0.270898\pi\)
\(62\) 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 −0.804939 0.593358i \(-0.797802\pi\)
0.916332 + 0.400418i \(0.131135\pi\)
\(68\) −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 −0.475791 0.879558i \(-0.657838\pi\)
−0.999615 + 0.0277318i \(0.991172\pi\)
\(74\) 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 0.999899 + 0.0142110i \(0.00452366\pi\)
−0.487642 + 0.873043i \(0.662143\pi\)
\(80\) −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 \(-0.618041\pi\)
0.362395 0.932025i \(-0.381959\pi\)
\(84\) −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 −0.130498 0.991449i \(-0.541658\pi\)
0.793371 + 0.608739i \(0.208324\pi\)
\(90\) 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 \(-0.849817\pi\)
0.890745 0.454503i \(-0.150183\pi\)
\(98\) −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 −0.0603607 0.998177i \(-0.519225\pi\)
−0.894627 + 0.446814i \(0.852558\pi\)
\(102\) −12.3191 + 21.3373i −0.120776 + 0.209190i
\(103\) −40.6847 + 23.4893i −0.394997 + 0.228051i −0.684323 0.729179i \(-0.739902\pi\)
0.289326 + 0.957231i \(0.406569\pi\)
\(104\) 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 0.864370 + 0.502857i \(0.167718\pi\)
0.00330196 + 0.999995i \(0.498949\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) −43.1448 + 74.7290i −0.395824 + 0.685587i −0.993206 0.116369i \(-0.962874\pi\)
0.597382 + 0.801957i \(0.296208\pi\)
\(110\) 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 −0.838256 0.545277i \(-0.816424\pi\)
0.0530960 + 0.998589i \(0.483091\pi\)
\(132\) 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 −0.975258 0.221068i \(-0.929046\pi\)
0.679080 + 0.734065i \(0.262379\pi\)
\(138\) −1.95435 + 1.12834i −0.0141619 + 0.00817639i
\(139\) 248.311i 1.78641i 0.449646 + 0.893207i \(0.351550\pi\)
−0.449646 + 0.893207i \(0.648450\pi\)
\(140\) −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 0.999992 + 0.00391672i \(0.00124673\pi\)
−0.496604 + 0.867977i \(0.665420\pi\)
\(150\) 10.6066 + 6.12372i 0.0707107 + 0.0408248i
\(151\) −91.5149 + 158.509i −0.606059 + 1.04973i 0.385824 + 0.922572i \(0.373917\pi\)
−0.991883 + 0.127153i \(0.959416\pi\)
\(152\) 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 −0.984446 0.175685i \(-0.943786\pi\)
−0.644371 0.764713i \(-0.722881\pi\)
\(158\) −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 0.988447 0.151566i \(-0.0484316\pi\)
−0.625484 + 0.780237i \(0.715098\pi\)
\(164\) 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 \(0.210573\pi\)
−0.789050 + 0.614329i \(0.789427\pi\)
\(168\) −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 −0.191147 0.981561i \(-0.561221\pi\)
0.754484 + 0.656319i \(0.227887\pi\)
\(174\) 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 −0.797209 0.603703i \(-0.793691\pi\)
0.921427 + 0.388552i \(0.127025\pi\)
\(180\) −11.6190 + 6.70820i −0.0645497 + 0.0372678i
\(181\) 9.24555i 0.0510804i −0.999674 0.0255402i \(-0.991869\pi\)
0.999674 0.0255402i \(-0.00813058\pi\)
\(182\) −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 0.987650 0.156677i \(-0.0500783\pi\)
−0.629511 + 0.776991i \(0.716745\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) 182.937 316.856i 0.947860 1.64174i 0.197939 0.980214i \(-0.436575\pi\)
0.749921 0.661527i \(-0.230091\pi\)
\(194\) 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 −0.132248 0.991217i \(-0.542219\pi\)
−0.924543 + 0.381078i \(0.875553\pi\)
\(200\) −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 \(0.0383720\pi\)
−0.992743 + 0.120257i \(0.961628\pi\)
\(224\) 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 0.786499 0.617591i \(-0.211891\pi\)
−0.141600 + 0.989924i \(0.545225\pi\)
\(228\) 15.9217 27.5772i 0.0698319 0.120952i
\(229\) 247.698 143.009i 1.08165 0.624492i 0.150310 0.988639i \(-0.451973\pi\)
0.931342 + 0.364147i \(0.118639\pi\)
\(230\) 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 0.992477 0.122429i \(-0.0390684\pi\)
−0.602265 + 0.798296i \(0.705735\pi\)
\(234\) −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 0.0768238 0.997045i \(-0.475522\pi\)
−0.825054 + 0.565054i \(0.808855\pi\)
\(242\) −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 \(0.0276147\pi\)
−0.996239 + 0.0866453i \(0.972385\pi\)
\(252\) −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 −0.492806 0.870139i \(-0.664029\pi\)
0.507160 + 0.861852i \(0.330695\pi\)
\(258\) 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 −0.127204 0.991877i \(-0.540600\pi\)
0.922592 0.385776i \(-0.126066\pi\)
\(264\) −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 −0.228753 0.973484i \(-0.573465\pi\)
−0.957439 + 0.288636i \(0.906798\pi\)
\(270\) −8.21584 + 14.2302i −0.0304290 + 0.0527046i
\(271\) −191.411 + 110.511i −0.706312 + 0.407790i −0.809694 0.586852i \(-0.800367\pi\)
0.103382 + 0.994642i \(0.467034\pi\)
\(272\) 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 −0.246096 0.969245i \(-0.579148\pi\)
0.962439 0.271497i \(-0.0875187\pi\)
\(278\) −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 0.992691 0.120685i \(-0.0385092\pi\)
0.391829 + 0.920038i \(0.371843\pi\)
\(284\) 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 \(-0.934833\pi\)
0.979116 0.203300i \(-0.0651667\pi\)
\(294\) −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 \(0.146456\pi\)
−0.896005 + 0.444043i \(0.853544\pi\)
\(308\) −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 0.601517 0.798860i \(-0.294563\pi\)
−0.391074 + 0.920359i \(0.627897\pi\)
\(312\) 13.2460 22.9427i 0.0424551 0.0735343i
\(313\) −55.1057 + 31.8153i −0.176057 + 0.101646i −0.585439 0.810717i \(-0.699078\pi\)
0.409382 + 0.912363i \(0.365744\pi\)
\(314\) 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 0.853582 0.520959i \(-0.174425\pi\)
−0.877954 + 0.478744i \(0.841092\pi\)
\(318\) 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 0.997182 + 0.0750241i \(0.0239034\pi\)
−0.433618 + 0.901097i \(0.642763\pi\)
\(332\) 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 −0.950928 0.309412i \(-0.899868\pi\)
0.743423 + 0.668822i \(0.233201\pi\)
\(348\) −37.6720 + 21.7500i −0.108253 + 0.0624999i
\(349\) 566.507i 1.62323i 0.584194 + 0.811614i \(0.301411\pi\)
−0.584194 + 0.811614i \(0.698589\pi\)
\(350\) 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 0.971427 0.237339i \(-0.0762753\pi\)
0.280172 + 0.959950i \(0.409609\pi\)
\(354\) −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 −0.783026 0.621989i \(-0.786325\pi\)
−0.147145 0.989115i \(-0.547008\pi\)
\(360\) −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 0.458261 0.888818i \(-0.348473\pi\)
−0.540608 + 0.841274i \(0.681806\pi\)
\(368\) 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 0.998481 + 0.0550895i \(0.0175444\pi\)
−0.451532 + 0.892255i \(0.649122\pi\)
\(374\) 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 −0.737481 0.675367i \(-0.763985\pi\)
0.216145 + 0.976361i \(0.430652\pi\)
\(384\) 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 −0.00632331 + 0.999980i \(0.502013\pi\)
−0.862846 + 0.505466i \(0.831321\pi\)
\(390\) −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 −0.667666 0.744461i \(-0.732707\pi\)
0.310889 + 0.950446i \(0.399373\pi\)
\(398\) 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 0.990045 0.140753i \(-0.0449524\pi\)
−0.616918 + 0.787027i \(0.711619\pi\)
\(402\) 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 0.904069 0.427387i \(-0.140566\pi\)
0.0819067 + 0.996640i \(0.473899\pi\)
\(410\) 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 \(-0.758835\pi\)
0.726458 0.687211i \(-0.241165\pi\)
\(420\) −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 −0.849854 0.527018i \(-0.823310\pi\)
0.881338 + 0.472486i \(0.156643\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 363.408i 0.839279i 0.907691 + 0.419640i \(0.137844\pi\)
−0.907691 + 0.419640i \(0.862156\pi\)
\(434\) 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 −0.883036 0.469305i \(-0.844505\pi\)
−0.0350882 + 0.999384i \(0.511171\pi\)
\(440\) 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 −0.998223 0.0595896i \(-0.981021\pi\)
0.447505 0.894281i \(-0.352313\pi\)
\(444\) 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 0.536041 0.844192i \(-0.319919\pi\)
−0.999112 + 0.0421292i \(0.986586\pi\)
\(458\) 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 \(-0.829032\pi\)
0.859190 0.511657i \(-0.170968\pi\)
\(462\) 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 −0.510466 0.859898i \(-0.670527\pi\)
0.489461 + 0.872025i \(0.337194\pi\)
\(468\) 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 −0.196512 0.980501i \(-0.562962\pi\)
−0.947395 + 0.320066i \(0.896295\pi\)
\(480\) 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 −0.831859 0.554986i \(-0.812723\pi\)
0.896562 + 0.442918i \(0.146057\pi\)
\(488\) −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 0.557834 0.829952i \(-0.311632\pi\)
−0.997677 + 0.0681226i \(0.978299\pi\)
\(500\) 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 \(-0.753992\pi\)
0.715919 0.698183i \(-0.246008\pi\)
\(504\) 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 −0.597927 0.801551i \(-0.704009\pi\)
0.395200 + 0.918595i \(0.370675\pi\)
\(510\) 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 0.0748694 0.997193i \(-0.476146\pi\)
−0.826160 + 0.563435i \(0.809479\pi\)
\(522\) −26.6381 + 46.1386i −0.0510309 + 0.0883882i
\(523\) −775.007 + 447.451i −1.48185 + 0.855546i −0.999788 0.0205911i \(-0.993445\pi\)
−0.482062 + 0.876137i \(0.660112\pi\)
\(524\) 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 0.974409 0.224783i \(-0.0721672\pi\)
−0.681872 + 0.731472i \(0.738834\pi\)
\(542\) −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 −0.971392 0.237484i \(-0.923677\pi\)
0.691363 + 0.722508i \(0.257011\pi\)
\(558\) 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 0.892805 0.450443i \(-0.148734\pi\)
0.0563071 + 0.998413i \(0.482067\pi\)
\(564\) −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 0.972471 + 0.233025i \(0.0748623\pi\)
−0.284430 + 0.958697i \(0.591804\pi\)
\(570\) −43.6033 25.1744i −0.0764970 0.0441656i
\(571\) −1.06600 + 1.84636i −0.00186689 + 0.00323355i −0.866957 0.498382i \(-0.833928\pi\)
0.865090 + 0.501616i \(0.167261\pi\)
\(572\) −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 −0.437602 0.899169i \(-0.644172\pi\)
−0.997504 + 0.0706096i \(0.977506\pi\)
\(578\) 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 \(0.179968\pi\)
−0.844382 + 0.535742i \(0.820032\pi\)
\(588\) −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 −0.808973 0.587846i \(-0.799976\pi\)
0.104603 + 0.994514i \(0.466643\pi\)
\(594\) 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 −0.976715 0.214542i \(-0.931174\pi\)
0.674156 + 0.738589i \(0.264508\pi\)
\(600\) −21.2132 + 12.2474i −0.0353553 + 0.0204124i
\(601\) 545.450i 0.907570i −0.891111 0.453785i \(-0.850073\pi\)
0.891111 0.453785i \(-0.149927\pi\)
\(602\) 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 −0.881520 0.472147i \(-0.843479\pi\)
−0.0318683 + 0.999492i \(0.510146\pi\)
\(608\) 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 −0.657751 0.753235i \(-0.728492\pi\)
0.981196 + 0.193012i \(0.0618256\pi\)
\(614\) −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 0.913111 0.407712i \(-0.133673\pi\)
0.103467 + 0.994633i \(0.467006\pi\)
\(620\) 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 0.178675 + 0.983908i \(0.442819\pi\)
−0.941427 + 0.337217i \(0.890514\pi\)
\(642\) −393.890 + 227.413i −0.613537 + 0.354225i
\(643\) 276.520i 0.430047i −0.976609 0.215023i \(-0.931017\pi\)
0.976609 0.215023i \(-0.0689828\pi\)
\(644\) −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 0.328679 0.944442i \(-0.393397\pi\)
−0.653571 + 0.756865i \(0.726730\pi\)
\(648\) 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 0.885682 0.464293i \(-0.153691\pi\)
−0.844930 + 0.534877i \(0.820358\pi\)
\(654\) −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 0.507871 0.861433i \(-0.330432\pi\)
−0.492087 + 0.870546i \(0.663766\pi\)
\(662\) −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 −0.486426 0.873722i \(-0.661700\pi\)
0.513452 + 0.858118i \(0.328366\pi\)
\(678\) 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 −0.685617 0.727963i \(-0.740467\pi\)
0.973243 + 0.229780i \(0.0738007\pi\)
\(684\) 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 −0.323486 0.946233i \(-0.604855\pi\)
0.657718 + 0.753264i \(0.271522\pi\)
\(692\) 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 0.987251 + 0.159172i \(0.0508823\pi\)
−0.355779 + 0.934570i \(0.615784\pi\)
\(710\) −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 −0.710282 0.703917i \(-0.751433\pi\)
0.254469 + 0.967081i \(0.418099\pi\)
\(720\) 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 \(0.101553\pi\)
−0.949538 + 0.313653i \(0.898447\pi\)
\(728\) 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 0.0220553 0.999757i \(-0.492979\pi\)
0.876842 + 0.480778i \(0.159646\pi\)
\(734\) 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 −0.856340 0.516413i \(-0.827267\pi\)
0.875397 + 0.483405i \(0.160600\pi\)
\(740\) 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 0.799817 0.600244i \(-0.204930\pi\)
−0.919735 + 0.392540i \(0.871596\pi\)
\(752\) −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 0.464637 0.885501i \(-0.346185\pi\)
0.999185 + 0.0403636i \(0.0128516\pi\)
\(762\) 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 \(-0.923615\pi\)
0.971345 0.237674i \(-0.0763850\pi\)
\(770\) 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 0.662765 0.748827i \(-0.269383\pi\)
−0.317121 + 0.948385i \(0.602716\pi\)
\(774\) 17.2317 29.8462i 0.0222632 0.0385610i
\(775\) −180.937 + 104.464i −0.233467 + 0.134792i
\(776\) 249.393i 0.321382i
\(777\) 60.4595 64.3717i 0.0778115 0.0828465i
\(778\) −956.311 −1.22919