Properties

Label 210.3.o.a.61.1
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 61.1
Root \(1.01575 + 1.40294i\) of \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.a.31.1

$q$-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} +(9.03504 + 15.6491i) q^{11} +(-3.00000 - 1.73205i) q^{12} +18.6604i q^{13} +(-2.26139 - 9.63774i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.33462 - 0.770543i) q^{17} +(2.12132 + 3.67423i) q^{18} +(29.4836 + 17.0224i) q^{19} +4.47214i q^{20} +(-3.50333 + 11.6072i) q^{21} -25.5549 q^{22} +(13.4938 - 23.3720i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-22.8542 - 13.1949i) q^{26} -5.19615i q^{27} +(13.4028 + 4.04529i) q^{28} -16.4662 q^{29} +(2.73861 - 4.74342i) q^{30} +(-24.1988 + 13.9712i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(27.1051 + 15.6491i) q^{33} +2.17942i q^{34} +(15.2386 - 3.57557i) q^{35} -6.00000 q^{36} +(-25.8353 + 44.7480i) q^{37} +(-41.6961 + 24.0733i) q^{38} +(16.1604 + 27.9906i) q^{39} +(-5.47723 - 3.16228i) q^{40} -37.4818i q^{41} +(-11.7386 - 12.4982i) q^{42} -63.6947 q^{43} +(18.0701 - 31.2983i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(19.0831 + 33.0529i) q^{46} +(-24.4572 - 14.1204i) q^{47} +6.92820i q^{48} +(3.06832 - 48.9038i) q^{49} -7.07107 q^{50} +(1.33462 - 2.31163i) q^{51} +(32.3208 - 18.6604i) q^{52} +(-0.221841 - 0.384239i) q^{53} +(6.36396 + 3.67423i) q^{54} -40.4059i q^{55} +(-14.4317 + 13.5546i) q^{56} +58.9672 q^{57} +(11.6434 - 20.1669i) q^{58} +(64.2260 - 37.0809i) q^{59} +(3.87298 + 6.70820i) q^{60} +(91.0443 + 52.5645i) q^{61} -39.5164i q^{62} +(4.79713 + 20.4447i) q^{63} +8.00000 q^{64} +(20.8630 - 36.1357i) q^{65} +(-38.3324 + 22.1312i) q^{66} +(6.35442 + 11.0062i) q^{67} +(-2.66924 - 1.54109i) q^{68} -46.7439i q^{69} +(-6.39617 + 21.1917i) q^{70} -45.7647 q^{71} +(4.24264 - 7.34847i) q^{72} +(31.5463 - 18.2133i) q^{73} +(-36.5366 - 63.2833i) q^{74} +(7.50000 + 4.33013i) q^{75} -68.0895i q^{76} +(-121.095 - 36.5494i) q^{77} -45.7085 q^{78} +(66.5990 - 115.353i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(45.9057 + 26.5037i) q^{82} +49.9265i q^{83} +(23.6076 - 5.53924i) q^{84} -3.44597 q^{85} +(45.0389 - 78.0097i) q^{86} +(-24.6994 + 14.2602i) q^{87} +(25.5549 + 44.2625i) q^{88} +(85.9133 + 49.6020i) q^{89} -9.48683i q^{90} +(-89.4257 - 95.2123i) q^{91} -53.9752 q^{92} +(-24.1988 + 41.9135i) q^{93} +(34.5878 - 19.9693i) q^{94} +(-38.0632 - 65.9274i) q^{95} +(-8.48528 - 4.89898i) q^{96} +150.376i q^{97} +(57.7251 + 38.3381i) q^{98} +54.2102 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
\(11\) 9.03504 + 15.6491i 0.821367 + 1.42265i 0.904664 + 0.426125i \(0.140122\pi\)
−0.0832974 + 0.996525i \(0.526545\pi\)
\(12\) −3.00000 1.73205i −0.250000 0.144338i
\(13\) 18.6604i 1.43542i 0.696344 + 0.717708i \(0.254809\pi\)
−0.696344 + 0.717708i \(0.745191\pi\)
\(14\) −2.26139 9.63774i −0.161528 0.688410i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 1.33462 0.770543i 0.0785070 0.0453261i −0.460233 0.887798i \(-0.652234\pi\)
0.538740 + 0.842472i \(0.318901\pi\)
\(18\) 2.12132 + 3.67423i 0.117851 + 0.204124i
\(19\) 29.4836 + 17.0224i 1.55177 + 0.895914i 0.997998 + 0.0632454i \(0.0201451\pi\)
0.553771 + 0.832669i \(0.313188\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −3.50333 + 11.6072i −0.166825 + 0.552723i
\(22\) −25.5549 −1.16159
\(23\) 13.4938 23.3720i 0.586687 1.01617i −0.407975 0.912993i \(-0.633765\pi\)
0.994663 0.103179i \(-0.0329015\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −22.8542 13.1949i −0.879009 0.507496i
\(27\) 5.19615i 0.192450i
\(28\) 13.4028 + 4.04529i 0.478672 + 0.144475i
\(29\) −16.4662 −0.567802 −0.283901 0.958854i \(-0.591629\pi\)
−0.283901 + 0.958854i \(0.591629\pi\)
\(30\) 2.73861 4.74342i 0.0912871 0.158114i
\(31\) −24.1988 + 13.9712i −0.780605 + 0.450683i −0.836645 0.547746i \(-0.815486\pi\)
0.0560395 + 0.998429i \(0.482153\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) 27.1051 + 15.6491i 0.821367 + 0.474216i
\(34\) 2.17942i 0.0641007i
\(35\) 15.2386 3.57557i 0.435389 0.102159i
\(36\) −6.00000 −0.166667
\(37\) −25.8353 + 44.7480i −0.698251 + 1.20941i 0.270821 + 0.962630i \(0.412705\pi\)
−0.969072 + 0.246777i \(0.920629\pi\)
\(38\) −41.6961 + 24.0733i −1.09727 + 0.633507i
\(39\) 16.1604 + 27.9906i 0.414369 + 0.717708i
\(40\) −5.47723 3.16228i −0.136931 0.0790569i
\(41\) 37.4818i 0.914191i −0.889418 0.457095i \(-0.848890\pi\)
0.889418 0.457095i \(-0.151110\pi\)
\(42\) −11.7386 12.4982i −0.279491 0.297576i
\(43\) −63.6947 −1.48127 −0.740636 0.671907i \(-0.765476\pi\)
−0.740636 + 0.671907i \(0.765476\pi\)
\(44\) 18.0701 31.2983i 0.410684 0.711325i
\(45\) −5.80948 + 3.35410i −0.129099 + 0.0745356i
\(46\) 19.0831 + 33.0529i 0.414851 + 0.718542i
\(47\) −24.4572 14.1204i −0.520367 0.300434i 0.216718 0.976234i \(-0.430465\pi\)
−0.737085 + 0.675800i \(0.763798\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 3.06832 48.9038i 0.0626188 0.998038i
\(50\) −7.07107 −0.141421
\(51\) 1.33462 2.31163i 0.0261690 0.0453261i
\(52\) 32.3208 18.6604i 0.621553 0.358854i
\(53\) −0.221841 0.384239i −0.00418567 0.00724980i 0.863925 0.503621i \(-0.167999\pi\)
−0.868111 + 0.496371i \(0.834666\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 40.4059i 0.734653i
\(56\) −14.4317 + 13.5546i −0.257709 + 0.242046i
\(57\) 58.9672 1.03451
\(58\) 11.6434 20.1669i 0.200748 0.347706i
\(59\) 64.2260 37.0809i 1.08858 0.628490i 0.155379 0.987855i \(-0.450340\pi\)
0.933197 + 0.359365i \(0.117007\pi\)
\(60\) 3.87298 + 6.70820i 0.0645497 + 0.111803i
\(61\) 91.0443 + 52.5645i 1.49253 + 0.861712i 0.999963 0.00856246i \(-0.00272555\pi\)
0.492566 + 0.870275i \(0.336059\pi\)
\(62\) 39.5164i 0.637361i
\(63\) 4.79713 + 20.4447i 0.0761449 + 0.324520i
\(64\) 8.00000 0.125000
\(65\) 20.8630 36.1357i 0.320969 0.555934i
\(66\) −38.3324 + 22.1312i −0.580794 + 0.335322i
\(67\) 6.35442 + 11.0062i 0.0948420 + 0.164271i 0.909543 0.415611i \(-0.136432\pi\)
−0.814701 + 0.579882i \(0.803099\pi\)
\(68\) −2.66924 1.54109i −0.0392535 0.0226630i
\(69\) 46.7439i 0.677448i
\(70\) −6.39617 + 21.1917i −0.0913738 + 0.302739i
\(71\) −45.7647 −0.644573 −0.322286 0.946642i \(-0.604451\pi\)
−0.322286 + 0.946642i \(0.604451\pi\)
\(72\) 4.24264 7.34847i 0.0589256 0.102062i
\(73\) 31.5463 18.2133i 0.432141 0.249497i −0.268117 0.963386i \(-0.586401\pi\)
0.700258 + 0.713889i \(0.253068\pi\)
\(74\) −36.5366 63.2833i −0.493738 0.855179i
\(75\) 7.50000 + 4.33013i 0.100000 + 0.0577350i
\(76\) 68.0895i 0.895914i
\(77\) −121.095 36.5494i −1.57266 0.474667i
\(78\) −45.7085 −0.586006
\(79\) 66.5990 115.353i 0.843025 1.46016i −0.0442994 0.999018i \(-0.514106\pi\)
0.887325 0.461145i \(-0.152561\pi\)
\(80\) 7.74597 4.47214i 0.0968246 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 45.9057 + 26.5037i 0.559825 + 0.323215i
\(83\) 49.9265i 0.601524i 0.953699 + 0.300762i \(0.0972409\pi\)
−0.953699 + 0.300762i \(0.902759\pi\)
\(84\) 23.6076 5.53924i 0.281042 0.0659434i
\(85\) −3.44597 −0.0405409
\(86\) 45.0389 78.0097i 0.523709 0.907090i
\(87\) −24.6994 + 14.2602i −0.283901 + 0.163910i
\(88\) 25.5549 + 44.2625i 0.290397 + 0.502983i
\(89\) 85.9133 + 49.6020i 0.965318 + 0.557326i 0.897806 0.440392i \(-0.145161\pi\)
0.0675121 + 0.997718i \(0.478494\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −89.4257 95.2123i −0.982700 1.04629i
\(92\) −53.9752 −0.586687
\(93\) −24.1988 + 41.9135i −0.260202 + 0.450683i
\(94\) 34.5878 19.9693i 0.367955 0.212439i
\(95\) −38.0632 65.9274i −0.400665 0.693972i
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 150.376i 1.55027i 0.631796 + 0.775134i \(0.282318\pi\)
−0.631796 + 0.775134i \(0.717682\pi\)
\(98\) 57.7251 + 38.3381i 0.589032 + 0.391206i
\(99\) 54.2102 0.547578
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 40.7726 23.5401i 0.403689 0.233070i −0.284386 0.958710i \(-0.591790\pi\)
0.688074 + 0.725640i \(0.258456\pi\)
\(102\) 1.88744 + 3.26914i 0.0185043 + 0.0320504i
\(103\) −65.7708 37.9728i −0.638552 0.368668i 0.145505 0.989358i \(-0.453519\pi\)
−0.784056 + 0.620690i \(0.786853\pi\)
\(104\) 52.7796i 0.507496i
\(105\) 19.7614 18.5604i 0.188204 0.176765i
\(106\) 0.627460 0.00591944
\(107\) 53.6125 92.8597i 0.501052 0.867847i −0.498947 0.866632i \(-0.666280\pi\)
0.999999 0.00121497i \(-0.000386738\pi\)
\(108\) −9.00000 + 5.19615i −0.0833333 + 0.0481125i
\(109\) −40.4452 70.0532i −0.371057 0.642690i 0.618671 0.785650i \(-0.287671\pi\)
−0.989728 + 0.142960i \(0.954338\pi\)
\(110\) 49.4869 + 28.5713i 0.449881 + 0.259739i
\(111\) 89.4961i 0.806271i
\(112\) −6.39617 27.2597i −0.0571087 0.243390i
\(113\) −79.9061 −0.707134 −0.353567 0.935409i \(-0.615031\pi\)
−0.353567 + 0.935409i \(0.615031\pi\)
\(114\) −41.6961 + 72.2198i −0.365755 + 0.633507i
\(115\) −52.2613 + 30.1731i −0.454446 + 0.262375i
\(116\) 16.4662 + 28.5204i 0.141950 + 0.245865i
\(117\) 48.4812 + 27.9906i 0.414369 + 0.239236i
\(118\) 104.881i 0.888819i
\(119\) −3.11707 + 10.3275i −0.0261939 + 0.0867853i
\(120\) −10.9545 −0.0912871
\(121\) −102.764 + 177.992i −0.849288 + 1.47101i
\(122\) −128.756 + 74.3374i −1.05538 + 0.609323i
\(123\) −32.4602 56.2227i −0.263904 0.457095i
\(124\) 48.3975 + 27.9423i 0.390303 + 0.225341i
\(125\) 11.1803i 0.0894427i
\(126\) −28.4317 8.58136i −0.225648 0.0681060i
\(127\) 99.1937 0.781053 0.390526 0.920592i \(-0.372293\pi\)
0.390526 + 0.920592i \(0.372293\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) −95.5420 + 55.1612i −0.740636 + 0.427606i
\(130\) 29.5047 + 51.1036i 0.226959 + 0.393105i
\(131\) 144.309 + 83.3170i 1.10160 + 0.636008i 0.936640 0.350293i \(-0.113918\pi\)
0.164958 + 0.986301i \(0.447251\pi\)
\(132\) 62.5966i 0.474216i
\(133\) −232.012 + 54.4390i −1.74445 + 0.409316i
\(134\) −17.9730 −0.134127
\(135\) −5.80948 + 10.0623i −0.0430331 + 0.0745356i
\(136\) 3.77487 2.17942i 0.0277564 0.0160252i
\(137\) 75.7587 + 131.218i 0.552983 + 0.957795i 0.998057 + 0.0623012i \(0.0198439\pi\)
−0.445074 + 0.895494i \(0.646823\pi\)
\(138\) 57.2494 + 33.0529i 0.414851 + 0.239514i
\(139\) 151.816i 1.09220i −0.837719 0.546101i \(-0.816111\pi\)
0.837719 0.546101i \(-0.183889\pi\)
\(140\) −21.4317 22.8185i −0.153083 0.162989i
\(141\) −48.9145 −0.346911
\(142\) 32.3605 56.0500i 0.227891 0.394719i
\(143\) −292.019 + 168.597i −2.04209 + 1.17900i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) 31.8867 + 18.4098i 0.219909 + 0.126964i
\(146\) 51.5149i 0.352842i
\(147\) −37.7495 76.0130i −0.256799 0.517095i
\(148\) 103.341 0.698251
\(149\) −16.5970 + 28.7468i −0.111389 + 0.192931i −0.916331 0.400423i \(-0.868863\pi\)
0.804941 + 0.593354i \(0.202197\pi\)
\(150\) −10.6066 + 6.12372i −0.0707107 + 0.0408248i
\(151\) 4.65158 + 8.05678i 0.0308052 + 0.0533562i 0.881017 0.473085i \(-0.156860\pi\)
−0.850212 + 0.526441i \(0.823526\pi\)
\(152\) 83.3923 + 48.1465i 0.548633 + 0.316754i
\(153\) 4.62326i 0.0302174i
\(154\) 130.391 122.466i 0.846693 0.795235i
\(155\) 62.4809 0.403103
\(156\) 32.3208 55.9812i 0.207184 0.358854i
\(157\) −20.7746 + 11.9942i −0.132322 + 0.0763963i −0.564700 0.825296i \(-0.691008\pi\)
0.432378 + 0.901693i \(0.357675\pi\)
\(158\) 94.1852 + 163.134i 0.596109 + 1.03249i
\(159\) −0.665522 0.384239i −0.00418567 0.00241660i
\(160\) 12.6491i 0.0790569i
\(161\) 43.1543 + 183.918i 0.268039 + 1.14235i
\(162\) 12.7279 0.0785674
\(163\) 126.564 219.215i 0.776464 1.34488i −0.157504 0.987518i \(-0.550345\pi\)
0.933968 0.357357i \(-0.116322\pi\)
\(164\) −64.9204 + 37.4818i −0.395856 + 0.228548i
\(165\) −34.9926 60.6089i −0.212076 0.367327i
\(166\) −61.1472 35.3033i −0.368357 0.212671i
\(167\) 85.7259i 0.513329i 0.966501 + 0.256664i \(0.0826235\pi\)
−0.966501 + 0.256664i \(0.917376\pi\)
\(168\) −9.90890 + 32.8301i −0.0589816 + 0.195417i
\(169\) −179.211 −1.06042
\(170\) 2.43667 4.22044i 0.0143334 0.0248261i
\(171\) 88.4508 51.0671i 0.517256 0.298638i
\(172\) 63.6947 + 110.322i 0.370318 + 0.641409i
\(173\) −16.8672 9.73826i −0.0974980 0.0562905i 0.450458 0.892798i \(-0.351261\pi\)
−0.547956 + 0.836507i \(0.684594\pi\)
\(174\) 40.3339i 0.231804i
\(175\) −33.5071 10.1132i −0.191469 0.0577899i
\(176\) −72.2803 −0.410684
\(177\) 64.2260 111.243i 0.362859 0.628490i
\(178\) −121.500 + 70.1479i −0.682583 + 0.394089i
\(179\) −126.417 218.961i −0.706241 1.22324i −0.966242 0.257637i \(-0.917056\pi\)
0.260001 0.965608i \(-0.416277\pi\)
\(180\) 11.6190 + 6.70820i 0.0645497 + 0.0372678i
\(181\) 144.224i 0.796820i 0.917207 + 0.398410i \(0.130438\pi\)
−0.917207 + 0.398410i \(0.869562\pi\)
\(182\) 179.844 42.1984i 0.988155 0.231859i
\(183\) 182.089 0.995020
\(184\) 38.1663 66.1059i 0.207425 0.359271i
\(185\) 100.060 57.7695i 0.540863 0.312267i
\(186\) −34.2222 59.2746i −0.183990 0.318681i
\(187\) 24.1167 + 13.9238i 0.128966 + 0.0744587i
\(188\) 56.4816i 0.300434i
\(189\) 24.9014 + 26.5127i 0.131753 + 0.140279i
\(190\) 107.659 0.566626
\(191\) 157.049 272.017i 0.822246 1.42417i −0.0817601 0.996652i \(-0.526054\pi\)
0.904006 0.427520i \(-0.140613\pi\)
\(192\) 12.0000 6.92820i 0.0625000 0.0360844i
\(193\) −26.4142 45.7507i −0.136861 0.237050i 0.789446 0.613820i \(-0.210368\pi\)
−0.926307 + 0.376770i \(0.877035\pi\)
\(194\) −184.172 106.332i −0.949342 0.548103i
\(195\) 72.2714i 0.370623i
\(196\) −87.7723 + 43.5893i −0.447818 + 0.222395i
\(197\) 54.2005 0.275129 0.137565 0.990493i \(-0.456073\pi\)
0.137565 + 0.990493i \(0.456073\pi\)
\(198\) −38.3324 + 66.3937i −0.193598 + 0.335322i
\(199\) 19.8934 11.4855i 0.0999670 0.0577160i −0.449183 0.893440i \(-0.648285\pi\)
0.549150 + 0.835724i \(0.314952\pi\)
\(200\) 7.07107 + 12.2474i 0.0353553 + 0.0612372i
\(201\) 19.0632 + 11.0062i 0.0948420 + 0.0547571i
\(202\) 66.5813i 0.329611i
\(203\) 84.0168 78.9107i 0.413876 0.388722i
\(204\) −5.33848 −0.0261690
\(205\) −41.9060 + 72.5832i −0.204419 + 0.354065i
\(206\) 93.0140 53.7017i 0.451524 0.260688i
\(207\) −40.4814 70.1159i −0.195562 0.338724i
\(208\) −64.6415 37.3208i −0.310777 0.179427i
\(209\) 615.191i 2.94350i
\(210\) 8.75832 + 37.3268i 0.0417063 + 0.177747i
\(211\) −292.203 −1.38485 −0.692425 0.721490i \(-0.743457\pi\)
−0.692425 + 0.721490i \(0.743457\pi\)
\(212\) −0.443681 + 0.768479i −0.00209284 + 0.00362490i
\(213\) −68.6470 + 39.6334i −0.322286 + 0.186072i
\(214\) 75.8196 + 131.323i 0.354297 + 0.613661i
\(215\) 123.344 + 71.2128i 0.573694 + 0.331222i
\(216\) 14.6969i 0.0680414i
\(217\) 56.5174 187.253i 0.260449 0.862917i
\(218\) 114.396 0.524754
\(219\) 31.5463 54.6398i 0.144047 0.249497i
\(220\) −69.9851 + 40.4059i −0.318114 + 0.183663i
\(221\) 14.3786 + 24.9045i 0.0650617 + 0.112690i
\(222\) −109.610 63.2833i −0.493738 0.285060i
\(223\) 271.305i 1.21661i −0.793702 0.608306i \(-0.791849\pi\)
0.793702 0.608306i \(-0.208151\pi\)
\(224\) 37.9089 + 11.4418i 0.169236 + 0.0510795i
\(225\) 15.0000 0.0666667
\(226\) 56.5021 97.8646i 0.250009 0.433029i
\(227\) 128.699 74.3044i 0.566956 0.327332i −0.188977 0.981982i \(-0.560517\pi\)
0.755933 + 0.654649i \(0.227184\pi\)
\(228\) −58.9672 102.134i −0.258628 0.447957i
\(229\) 21.9394 + 12.6667i 0.0958053 + 0.0553132i 0.547137 0.837043i \(-0.315718\pi\)
−0.451332 + 0.892356i \(0.649051\pi\)
\(230\) 85.3423i 0.371054i
\(231\) −213.295 + 50.0473i −0.923356 + 0.216655i
\(232\) −46.5736 −0.200748
\(233\) 204.443 354.106i 0.877438 1.51977i 0.0232943 0.999729i \(-0.492585\pi\)
0.854143 0.520038i \(-0.174082\pi\)
\(234\) −68.5627 + 39.5847i −0.293003 + 0.169165i
\(235\) 31.5742 + 54.6881i 0.134358 + 0.232715i
\(236\) −128.452 74.1618i −0.544288 0.314245i
\(237\) 230.706i 0.973442i
\(238\) −10.4444 11.1202i −0.0438840 0.0467236i
\(239\) 67.0352 0.280482 0.140241 0.990117i \(-0.455212\pi\)
0.140241 + 0.990117i \(0.455212\pi\)
\(240\) 7.74597 13.4164i 0.0322749 0.0559017i
\(241\) 205.143 118.440i 0.851217 0.491451i −0.00984406 0.999952i \(-0.503134\pi\)
0.861061 + 0.508501i \(0.169800\pi\)
\(242\) −145.330 251.719i −0.600537 1.04016i
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 210.258i 0.861712i
\(245\) −60.6179 + 91.2714i −0.247420 + 0.372536i
\(246\) 91.8113 0.373217
\(247\) −317.644 + 550.176i −1.28601 + 2.22743i
\(248\) −68.4444 + 39.5164i −0.275986 + 0.159340i
\(249\) 43.2376 + 74.8897i 0.173645 + 0.300762i
\(250\) 13.6931 + 7.90569i 0.0547723 + 0.0316228i
\(251\) 483.382i 1.92582i 0.269815 + 0.962912i \(0.413037\pi\)
−0.269815 + 0.962912i \(0.586963\pi\)
\(252\) 30.6142 28.7536i 0.121485 0.114102i
\(253\) 487.668 1.92754
\(254\) −70.1406 + 121.487i −0.276144 + 0.478295i
\(255\) −5.16896 + 2.98430i −0.0202704 + 0.0117031i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −281.097 162.291i −1.09376 0.631484i −0.159187 0.987248i \(-0.550887\pi\)
−0.934576 + 0.355764i \(0.884221\pi\)
\(258\) 156.019i 0.604727i
\(259\) −82.6234 352.131i −0.319009 1.35958i
\(260\) −83.4519 −0.320969
\(261\) −24.6994 + 42.7806i −0.0946336 + 0.163910i
\(262\) −204.084 + 117.828i −0.778948 + 0.449726i
\(263\) −153.686 266.192i −0.584358 1.01214i −0.994955 0.100320i \(-0.968013\pi\)
0.410598 0.911817i \(-0.365320\pi\)
\(264\) 76.6648 + 44.2625i 0.290397 + 0.167661i
\(265\) 0.992102i 0.00374378i
\(266\) 97.3834 322.650i 0.366103 1.21297i
\(267\) 171.827 0.643545
\(268\) 12.7088 22.0123i 0.0474210 0.0821356i
\(269\) −65.6866 + 37.9242i −0.244188 + 0.140982i −0.617100 0.786885i \(-0.711693\pi\)
0.372912 + 0.927867i \(0.378359\pi\)
\(270\) −8.21584 14.2302i −0.0304290 0.0527046i
\(271\) −18.8151 10.8629i −0.0694283 0.0400844i 0.464884 0.885372i \(-0.346096\pi\)
−0.534312 + 0.845287i \(0.679429\pi\)
\(272\) 6.16434i 0.0226630i
\(273\) −216.595 65.3735i −0.793387 0.239463i
\(274\) −214.278 −0.782036
\(275\) −45.1752 + 78.2457i −0.164273 + 0.284530i
\(276\) −80.9628 + 46.7439i −0.293344 + 0.169362i
\(277\) 55.8659 + 96.7627i 0.201682 + 0.349324i 0.949071 0.315064i \(-0.102026\pi\)
−0.747388 + 0.664387i \(0.768693\pi\)
\(278\) 185.936 + 107.350i 0.668835 + 0.386152i
\(279\) 83.8270i 0.300455i
\(280\) 43.1013 10.1132i 0.153933 0.0361187i
\(281\) −188.298 −0.670101 −0.335051 0.942200i \(-0.608753\pi\)
−0.335051 + 0.942200i \(0.608753\pi\)
\(282\) 34.5878 59.9078i 0.122652 0.212439i
\(283\) 187.769 108.408i 0.663495 0.383069i −0.130113 0.991499i \(-0.541534\pi\)
0.793607 + 0.608430i \(0.208201\pi\)
\(284\) 45.7647 + 79.2667i 0.161143 + 0.279108i
\(285\) −114.190 65.9274i −0.400665 0.231324i
\(286\) 476.866i 1.66736i
\(287\) 179.623 + 191.246i 0.625864 + 0.666363i
\(288\) −16.9706 −0.0589256
\(289\) −143.313 + 248.225i −0.495891 + 0.858909i
\(290\) −45.0947 + 26.0354i −0.155499 + 0.0897773i
\(291\) 130.230 + 225.564i 0.447524 + 0.775134i
\(292\) −63.0926 36.4265i −0.216071 0.124748i
\(293\) 57.3776i 0.195828i 0.995195 + 0.0979140i \(0.0312170\pi\)
−0.995195 + 0.0979140i \(0.968783\pi\)
\(294\) 119.789 + 7.51583i 0.407447 + 0.0255640i
\(295\) −165.831 −0.562138
\(296\) −73.0732 + 126.567i −0.246869 + 0.427590i
\(297\) 81.3153 46.9474i 0.273789 0.158072i
\(298\) −23.4717 40.6541i −0.0787640 0.136423i
\(299\) 436.130 + 251.800i 1.45863 + 0.842140i
\(300\) 17.3205i 0.0577350i
\(301\) 324.994 305.242i 1.07971 1.01409i
\(302\) −13.1567 −0.0435651
\(303\) 40.7726 70.6202i 0.134563 0.233070i
\(304\) −117.934 + 68.0895i −0.387942 + 0.223979i
\(305\) −117.538 203.581i −0.385370 0.667480i
\(306\) 5.66231 + 3.26914i 0.0185043 + 0.0106835i
\(307\) 291.273i 0.948773i 0.880317 + 0.474386i \(0.157330\pi\)
−0.880317 + 0.474386i \(0.842670\pi\)
\(308\) 57.7896 + 246.292i 0.187629 + 0.799650i
\(309\) −131.542 −0.425701
\(310\) −44.1807 + 76.5232i −0.142518 + 0.246849i
\(311\) 216.368 124.920i 0.695717 0.401673i −0.110033 0.993928i \(-0.535096\pi\)
0.805750 + 0.592255i \(0.201762\pi\)
\(312\) 45.7085 + 79.1694i 0.146502 + 0.253748i
\(313\) −3.27832 1.89274i −0.0104739 0.00604709i 0.494754 0.869033i \(-0.335258\pi\)
−0.505228 + 0.862986i \(0.668592\pi\)
\(314\) 33.9248i 0.108041i
\(315\) 13.5683 44.9544i 0.0430740 0.142712i
\(316\) −266.396 −0.843025
\(317\) 35.6805 61.8004i 0.112557 0.194954i −0.804244 0.594300i \(-0.797429\pi\)
0.916800 + 0.399346i \(0.130763\pi\)
\(318\) 0.941190 0.543397i 0.00295972 0.00170879i
\(319\) −148.773 257.683i −0.466373 0.807783i
\(320\) −15.4919 8.94427i −0.0484123 0.0279508i
\(321\) 185.719i 0.578565i
\(322\) −255.768 77.1968i −0.794310 0.239742i
\(323\) 52.4659 0.162433
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) −80.8019 + 46.6510i −0.248621 + 0.143542i
\(326\) 178.988 + 310.016i 0.549043 + 0.950970i
\(327\) −121.336 70.0532i −0.371057 0.214230i
\(328\) 106.015i 0.323215i
\(329\) 192.459 45.1582i 0.584981 0.137259i
\(330\) 98.9739 0.299921
\(331\) 170.983 296.152i 0.516566 0.894718i −0.483249 0.875483i \(-0.660544\pi\)
0.999815 0.0192351i \(-0.00612311\pi\)
\(332\) 86.4752 49.9265i 0.260467 0.150381i
\(333\) 77.5059 + 134.244i 0.232750 + 0.403135i
\(334\) −104.992 60.6174i −0.314349 0.181489i
\(335\) 28.4178i 0.0848293i
\(336\) −33.2018 35.3502i −0.0988149 0.105209i
\(337\) 246.396 0.731145 0.365573 0.930783i \(-0.380873\pi\)
0.365573 + 0.930783i \(0.380873\pi\)
\(338\) 126.721 219.487i 0.374915 0.649371i
\(339\) −119.859 + 69.2007i −0.353567 + 0.204132i
\(340\) 3.44597 + 5.96860i 0.0101352 + 0.0175547i
\(341\) −437.273 252.460i −1.28233 0.740352i
\(342\) 144.440i 0.422338i
\(343\) 218.705 + 264.230i 0.637623 + 0.770349i
\(344\) −180.156 −0.523709
\(345\) −52.2613 + 90.5192i −0.151482 + 0.262375i
\(346\) 23.8538 13.7720i 0.0689415 0.0398034i
\(347\) −69.1758 119.816i −0.199354 0.345291i 0.748965 0.662609i \(-0.230551\pi\)
−0.948319 + 0.317318i \(0.897218\pi\)
\(348\) 49.3987 + 28.5204i 0.141950 + 0.0819551i
\(349\) 115.858i 0.331971i 0.986128 + 0.165986i \(0.0530805\pi\)
−0.986128 + 0.165986i \(0.946919\pi\)
\(350\) 36.0792 33.8865i 0.103083 0.0968184i
\(351\) 96.9623 0.276246
\(352\) 51.1099 88.5249i 0.145199 0.251491i
\(353\) 162.136 93.6093i 0.459309 0.265182i −0.252445 0.967611i \(-0.581235\pi\)
0.711754 + 0.702429i \(0.247901\pi\)
\(354\) 90.8293 + 157.321i 0.256580 + 0.444409i
\(355\) 88.6229 + 51.1664i 0.249642 + 0.144131i
\(356\) 198.408i 0.557326i
\(357\) 4.26823 + 18.1906i 0.0119558 + 0.0509542i
\(358\) 357.562 0.998775
\(359\) −318.748 + 552.087i −0.887876 + 1.53785i −0.0454957 + 0.998965i \(0.514487\pi\)
−0.842381 + 0.538883i \(0.818847\pi\)
\(360\) −16.4317 + 9.48683i −0.0456435 + 0.0263523i
\(361\) 399.022 + 691.127i 1.10532 + 1.91448i
\(362\) −176.638 101.982i −0.487951 0.281718i
\(363\) 355.984i 0.980673i
\(364\) −75.4868 + 250.102i −0.207381 + 0.687094i
\(365\) −81.4522 −0.223157
\(366\) −128.756 + 223.012i −0.351793 + 0.609323i
\(367\) 47.6750 27.5252i 0.129905 0.0750005i −0.433639 0.901087i \(-0.642771\pi\)
0.563544 + 0.826086i \(0.309437\pi\)
\(368\) 53.9752 + 93.4878i 0.146672 + 0.254043i
\(369\) −97.3806 56.2227i −0.263904 0.152365i
\(370\) 163.397i 0.441613i
\(371\) 2.97329 + 0.897411i 0.00801426 + 0.00241890i
\(372\) 96.7950 0.260202
\(373\) −134.578 + 233.097i −0.360800 + 0.624924i −0.988093 0.153859i \(-0.950830\pi\)
0.627293 + 0.778784i \(0.284163\pi\)
\(374\) −34.1061 + 19.6912i −0.0911929 + 0.0526502i
\(375\) −9.68246 16.7705i −0.0258199 0.0447214i
\(376\) −69.1755 39.9385i −0.183978 0.106219i
\(377\) 307.267i 0.815031i
\(378\) −50.0792 + 11.7505i −0.132485 + 0.0310860i
\(379\) 469.785 1.23954 0.619769 0.784784i \(-0.287226\pi\)
0.619769 + 0.784784i \(0.287226\pi\)
\(380\) −76.1264 + 131.855i −0.200333 + 0.346986i
\(381\) 148.791 85.9043i 0.390526 0.225471i
\(382\) 222.101 + 384.690i 0.581416 + 1.00704i
\(383\) −348.324 201.105i −0.909462 0.525078i −0.0292039 0.999573i \(-0.509297\pi\)
−0.880258 + 0.474495i \(0.842631\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 193.636 + 206.166i 0.502951 + 0.535496i
\(386\) 74.7107 0.193551
\(387\) −95.5420 + 165.484i −0.246879 + 0.427606i
\(388\) 260.459 150.376i 0.671286 0.387567i
\(389\) 55.3803 + 95.9215i 0.142366 + 0.246585i 0.928387 0.371615i \(-0.121196\pi\)
−0.786021 + 0.618200i \(0.787862\pi\)
\(390\) 88.5141 + 51.1036i 0.226959 + 0.131035i
\(391\) 41.5902i 0.106369i
\(392\) 8.67853 138.321i 0.0221391 0.352860i
\(393\) 288.619 0.734399
\(394\) −38.3255 + 66.3817i −0.0972729 + 0.168482i
\(395\) −257.937 + 148.920i −0.653005 + 0.377012i
\(396\) −54.2102 93.8949i −0.136895 0.237108i
\(397\) 363.569 + 209.907i 0.915792 + 0.528733i 0.882290 0.470706i \(-0.156001\pi\)
0.0335018 + 0.999439i \(0.489334\pi\)
\(398\) 32.4858i 0.0816227i
\(399\) −300.873 + 282.587i −0.754066 + 0.708238i
\(400\) −20.0000 −0.0500000
\(401\) −157.034 + 271.990i −0.391605 + 0.678280i −0.992661 0.120927i \(-0.961413\pi\)
0.601056 + 0.799207i \(0.294747\pi\)
\(402\) −26.9595 + 15.5651i −0.0670634 + 0.0387191i
\(403\) −260.708 451.559i −0.646917 1.12049i
\(404\) −81.5451 47.0801i −0.201844 0.116535i
\(405\) 20.1246i 0.0496904i
\(406\) 37.2366 + 158.697i 0.0917156 + 0.390880i
\(407\) −933.691 −2.29408
\(408\) 3.77487 6.53827i 0.00925214 0.0160252i
\(409\) 105.506 60.9140i 0.257961 0.148934i −0.365443 0.930834i \(-0.619082\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(410\) −59.2640 102.648i −0.144546 0.250361i
\(411\) 227.276 + 131.218i 0.552983 + 0.319265i
\(412\) 151.891i 0.368668i
\(413\) −150.003 + 496.989i −0.363203 + 1.20336i
\(414\) 114.499 0.276567
\(415\) 55.8195 96.6822i 0.134505 0.232969i
\(416\) 91.4169 52.7796i 0.219752 0.126874i
\(417\) −131.477 227.724i −0.315292 0.546101i
\(418\) −753.452 435.006i −1.80252 1.04068i
\(419\) 43.0872i 0.102833i 0.998677 + 0.0514167i \(0.0163737\pi\)
−0.998677 + 0.0514167i \(0.983626\pi\)
\(420\) −51.9089 15.6674i −0.123593 0.0373032i
\(421\) 135.571 0.322022 0.161011 0.986953i \(-0.448525\pi\)
0.161011 + 0.986953i \(0.448525\pi\)
\(422\) 206.619 357.874i 0.489618 0.848043i
\(423\) −73.3717 + 42.3612i −0.173456 + 0.100145i
\(424\) −0.627460 1.08679i −0.00147986 0.00256319i
\(425\) 6.67310 + 3.85272i 0.0157014 + 0.00906521i
\(426\) 112.100i 0.263146i
\(427\) −716.445 + 168.106i −1.67786 + 0.393690i
\(428\) −214.450 −0.501052
\(429\) −292.019 + 505.792i −0.680698 + 1.17900i
\(430\) −174.435 + 100.710i −0.405663 + 0.234210i
\(431\) −95.6132 165.607i −0.221840 0.384239i 0.733527 0.679661i \(-0.237873\pi\)
−0.955367 + 0.295422i \(0.904540\pi\)
\(432\) 18.0000 + 10.3923i 0.0416667 + 0.0240563i
\(433\) 339.825i 0.784815i −0.919791 0.392408i \(-0.871642\pi\)
0.919791 0.392408i \(-0.128358\pi\)
\(434\) 189.373 + 201.627i 0.436344 + 0.464579i
\(435\) 63.7735 0.146606
\(436\) −80.8905 + 140.106i −0.185529 + 0.321345i
\(437\) 795.692 459.393i 1.82081 1.05124i
\(438\) 44.6132 + 77.2723i 0.101857 + 0.176421i
\(439\) 286.015 + 165.131i 0.651515 + 0.376153i 0.789037 0.614346i \(-0.210580\pi\)
−0.137521 + 0.990499i \(0.543914\pi\)
\(440\) 114.285i 0.259739i
\(441\) −122.453 81.3275i −0.277672 0.184416i
\(442\) −40.6690 −0.0920112
\(443\) 280.831 486.414i 0.633931 1.09800i −0.352810 0.935695i \(-0.614774\pi\)
0.986741 0.162305i \(-0.0518928\pi\)
\(444\) 155.012 89.4961i 0.349125 0.201568i
\(445\) −110.914 192.108i −0.249244 0.431703i
\(446\) 332.279 + 191.841i 0.745020 + 0.430138i
\(447\) 57.4936i 0.128621i
\(448\) −40.8189 + 38.3381i −0.0911137 + 0.0855762i
\(449\) −386.250 −0.860244 −0.430122 0.902771i \(-0.641529\pi\)
−0.430122 + 0.902771i \(0.641529\pi\)
\(450\) −10.6066 + 18.3712i −0.0235702 + 0.0408248i
\(451\) 586.558 338.650i 1.30057 0.750886i
\(452\) 79.9061 + 138.401i 0.176783 + 0.306198i
\(453\) 13.9548 + 8.05678i 0.0308052 + 0.0177854i
\(454\) 210.165i 0.462918i
\(455\) 66.7215 + 284.359i 0.146641 + 0.624964i
\(456\) 166.785 0.365755
\(457\) −249.533 + 432.203i −0.546024 + 0.945741i 0.452518 + 0.891755i \(0.350526\pi\)
−0.998542 + 0.0539854i \(0.982808\pi\)
\(458\) −31.0270 + 17.9135i −0.0677446 + 0.0391124i
\(459\) −4.00386 6.93489i −0.00872300 0.0151087i
\(460\) 104.523 + 60.3461i 0.227223 + 0.131187i
\(461\) 618.290i 1.34119i −0.741823 0.670596i \(-0.766038\pi\)
0.741823 0.670596i \(-0.233962\pi\)
\(462\) 89.5273 296.621i 0.193782 0.642037i
\(463\) −194.433 −0.419941 −0.209971 0.977708i \(-0.567337\pi\)
−0.209971 + 0.977708i \(0.567337\pi\)
\(464\) 32.9325 57.0407i 0.0709752 0.122933i
\(465\) 93.7214 54.1101i 0.201551 0.116366i
\(466\) 289.126 + 500.781i 0.620442 + 1.07464i
\(467\) 131.449 + 75.8923i 0.281476 + 0.162510i 0.634091 0.773258i \(-0.281374\pi\)
−0.352615 + 0.935768i \(0.614708\pi\)
\(468\) 111.962i 0.239236i
\(469\) −85.1671 25.7055i −0.181593 0.0548091i
\(470\) −89.3052 −0.190011
\(471\) −20.7746 + 35.9827i −0.0441074 + 0.0763963i
\(472\) 181.659 104.881i 0.384870 0.222205i
\(473\) −575.484 996.767i −1.21667 2.10733i
\(474\) 282.556 + 163.134i 0.596109 + 0.344164i
\(475\) 170.224i 0.358366i
\(476\) 21.0047 4.92852i 0.0441276 0.0103540i
\(477\) −1.33104 −0.00279045
\(478\) −47.4010 + 82.1010i −0.0991653 + 0.171759i
\(479\) 194.656 112.385i 0.406381 0.234624i −0.282853 0.959163i \(-0.591281\pi\)
0.689233 + 0.724539i \(0.257947\pi\)
\(480\) 10.9545 + 18.9737i 0.0228218 + 0.0395285i
\(481\) −835.016 482.097i −1.73600 1.00228i
\(482\) 334.998i 0.695016i
\(483\) 224.009 + 238.505i 0.463788 + 0.493799i
\(484\) 411.055 0.849288
\(485\) 168.126 291.202i 0.346651 0.600417i
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) −34.7814 60.2432i −0.0714198 0.123703i 0.828104 0.560575i \(-0.189420\pi\)
−0.899524 + 0.436872i \(0.856086\pi\)
\(488\) 257.512 + 148.675i 0.527689 + 0.304661i
\(489\) 438.429i 0.896584i
\(490\) −68.9208 138.780i −0.140655 0.283225i
\(491\) −750.454 −1.52842 −0.764210 0.644967i \(-0.776871\pi\)
−0.764210 + 0.644967i \(0.776871\pi\)
\(492\) −64.9204 + 112.445i −0.131952 + 0.228548i
\(493\) −21.9762 + 12.6880i −0.0445764 + 0.0257362i
\(494\) −449.217 778.067i −0.909346 1.57503i
\(495\) −104.978 60.6089i −0.212076 0.122442i
\(496\) 111.769i 0.225341i
\(497\) 233.508 219.317i 0.469835 0.441281i
\(498\) −122.294 −0.245571
\(499\) −80.0848 + 138.711i −0.160491 + 0.277978i −0.935045 0.354530i \(-0.884641\pi\)
0.774554 + 0.632508i \(0.217974\pi\)
\(500\) −19.3649 + 11.1803i −0.0387298 + 0.0223607i
\(501\) 74.2408 + 128.589i 0.148185 + 0.256664i
\(502\) −592.019 341.803i −1.17932 0.680882i
\(503\) 724.412i 1.44018i 0.693879 + 0.720092i \(0.255900\pi\)
−0.693879 + 0.720092i \(0.744100\pi\)
\(504\) 13.5683 + 57.8265i 0.0269213 + 0.114735i
\(505\) −105.274 −0.208464
\(506\) −344.834 + 597.269i −0.681489 + 1.18037i
\(507\) −268.816 + 155.201i −0.530209 + 0.306117i
\(508\) −99.1937 171.809i −0.195263 0.338206i
\(509\) −711.944 411.041i −1.39871 0.807547i −0.404454 0.914558i \(-0.632538\pi\)
−0.994258 + 0.107012i \(0.965872\pi\)
\(510\) 8.44088i 0.0165507i
\(511\) −73.6780 + 244.109i −0.144184 + 0.477709i
\(512\) 22.6274 0.0441942
\(513\) 88.4508 153.201i 0.172419 0.298638i
\(514\) 397.531 229.515i 0.773407 0.446527i
\(515\) 84.9098 + 147.068i 0.164873 + 0.285569i
\(516\) 191.084 + 110.322i 0.370318 + 0.213803i
\(517\) 510.313i 0.987066i
\(518\) 489.694 + 147.801i 0.945355 + 0.285331i
\(519\) −33.7343 −0.0649987
\(520\) 59.0094 102.207i 0.113480 0.196552i
\(521\) 392.147 226.406i 0.752681 0.434561i −0.0739805 0.997260i \(-0.523570\pi\)
0.826662 + 0.562699i \(0.190237\pi\)
\(522\) −34.9302 60.5008i −0.0669161 0.115902i
\(523\) 843.597 + 487.051i 1.61300 + 0.931264i 0.988671 + 0.150100i \(0.0479597\pi\)
0.624326 + 0.781164i \(0.285374\pi\)
\(524\) 333.268i 0.636008i
\(525\) −59.0189 + 13.8481i −0.112417 + 0.0263774i
\(526\) 434.690 0.826406
\(527\) −21.5308 + 37.2924i −0.0408553 + 0.0707635i
\(528\) −108.420 + 62.5966i −0.205342 + 0.118554i
\(529\) −99.6657 172.626i −0.188404 0.326325i
\(530\) −1.21507 0.701522i −0.00229259 0.00132363i
\(531\) 222.485i 0.418993i
\(532\) 326.303 + 347.418i 0.613352 + 0.653041i
\(533\) 699.426 1.31224
\(534\) −121.500 + 210.444i −0.227528 + 0.394089i
\(535\) −207.640 + 119.881i −0.388113 + 0.224077i
\(536\) 17.9730 + 31.1302i 0.0335317 + 0.0580786i
\(537\) −379.251 218.961i −0.706241 0.407748i
\(538\) 107.266i 0.199379i
\(539\) 793.026 393.831i 1.47129 0.730670i
\(540\) 23.2379 0.0430331
\(541\) −138.078 + 239.158i −0.255228 + 0.442067i −0.964957 0.262407i \(-0.915484\pi\)
0.709730 + 0.704474i \(0.248817\pi\)
\(542\) 26.6085 15.3624i 0.0490932 0.0283440i
\(543\) 124.902 + 216.337i 0.230022 + 0.398410i
\(544\) −7.54975 4.35885i −0.0138782 0.00801259i
\(545\) 180.877i 0.331884i
\(546\) 233.221 219.047i 0.427146 0.401186i
\(547\) 426.436 0.779591 0.389795 0.920901i \(-0.372546\pi\)
0.389795 + 0.920901i \(0.372546\pi\)
\(548\) 151.517 262.436i 0.276492 0.478897i
\(549\) 273.133 157.693i 0.497510 0.287237i
\(550\) −63.8874 110.656i −0.116159 0.201193i
\(551\) −485.484 280.295i −0.881097 0.508702i
\(552\) 132.212i 0.239514i
\(553\) 212.989 + 907.733i 0.385152 + 1.64147i
\(554\) −158.013 −0.285222
\(555\) 100.060 173.308i 0.180288 0.312267i
\(556\) −262.953 + 151.816i −0.472938 + 0.273051i
\(557\) 60.9782 + 105.617i 0.109476 + 0.189618i 0.915558 0.402186i \(-0.131749\pi\)
−0.806082 + 0.591804i \(0.798416\pi\)
\(558\) −102.667 59.2746i −0.183990 0.106227i
\(559\) 1188.57i 2.12624i
\(560\) −18.0911 + 59.9392i −0.0323055 + 0.107034i
\(561\) 48.2334 0.0859775
\(562\) 133.147 230.618i 0.236917 0.410351i
\(563\) −376.532 + 217.391i −0.668796 + 0.386130i −0.795620 0.605796i \(-0.792855\pi\)
0.126824 + 0.991925i \(0.459522\pi\)
\(564\) 48.9145 + 84.7224i 0.0867278 + 0.150217i
\(565\) 154.737 + 89.3377i 0.273872 + 0.158120i
\(566\) 306.625i 0.541741i
\(567\) 60.3127 + 18.2038i 0.106372 + 0.0321055i
\(568\) −129.442 −0.227891
\(569\) 148.138 256.583i 0.260349 0.450937i −0.705986 0.708226i \(-0.749496\pi\)
0.966335 + 0.257289i \(0.0828291\pi\)
\(570\) 161.488 93.2354i 0.283313 0.163571i
\(571\) −29.9578 51.8885i −0.0524655 0.0908730i 0.838600 0.544748i \(-0.183375\pi\)
−0.891065 + 0.453875i \(0.850041\pi\)
\(572\) 584.039 + 337.195i 1.02105 + 0.589502i
\(573\) 544.034i 0.949448i
\(574\) −361.240 + 84.7609i −0.629338 + 0.147667i
\(575\) 134.938 0.234675
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 288.128 166.351i 0.499355 0.288303i −0.229092 0.973405i \(-0.573576\pi\)
0.728447 + 0.685102i \(0.240242\pi\)
\(578\) −202.675 351.043i −0.350648 0.607340i
\(579\) −79.2426 45.7507i −0.136861 0.0790168i
\(580\) 73.6393i 0.126964i
\(581\) −239.261 254.743i −0.411809 0.438456i
\(582\) −368.345 −0.632895
\(583\) 4.00868 6.94323i 0.00687595 0.0119095i
\(584\) 89.2264 51.5149i 0.152785 0.0882104i
\(585\) −62.5889 108.407i −0.106990 0.185311i
\(586\) −70.2729 40.5721i −0.119920 0.0692356i
\(587\) 656.221i 1.11792i −0.829194 0.558961i \(-0.811200\pi\)
0.829194 0.558961i \(-0.188800\pi\)
\(588\) −93.9089 + 141.397i −0.159709 + 0.240471i
\(589\) −951.289 −1.61509
\(590\) 117.260 203.100i 0.198746 0.344238i
\(591\) 81.3007 46.9390i 0.137565 0.0794230i
\(592\) −103.341 178.992i −0.174563 0.302352i
\(593\) −353.808 204.271i −0.596640 0.344471i 0.171078 0.985257i \(-0.445275\pi\)
−0.767719 + 0.640787i \(0.778608\pi\)
\(594\) 132.787i 0.223548i
\(595\) 17.5826 16.5140i 0.0295506 0.0277547i
\(596\) 66.3879 0.111389
\(597\) 19.8934 34.4564i 0.0333223 0.0577160i
\(598\) −616.781 + 356.099i −1.03141 + 0.595483i
\(599\) 588.643 + 1019.56i 0.982709 + 1.70210i 0.651705 + 0.758472i \(0.274054\pi\)
0.331003 + 0.943630i \(0.392613\pi\)
\(600\) 21.2132 + 12.2474i 0.0353553 + 0.0204124i
\(601\) 162.592i 0.270536i 0.990809 + 0.135268i \(0.0431896\pi\)
−0.990809 + 0.135268i \(0.956810\pi\)
\(602\) 144.038 + 613.873i 0.239266 + 1.01972i
\(603\) 38.1265 0.0632280
\(604\) 9.30317 16.1136i 0.0154026 0.0266781i
\(605\) 398.003 229.787i 0.657855 0.379813i
\(606\) 57.6611 + 99.8720i 0.0951504 + 0.164805i
\(607\) −318.116 183.664i −0.524079 0.302577i 0.214523 0.976719i \(-0.431180\pi\)
−0.738602 + 0.674142i \(0.764514\pi\)
\(608\) 192.586i 0.316754i
\(609\) 57.6866 191.127i 0.0947235 0.313837i
\(610\) 332.447 0.544995
\(611\) 263.492 456.382i 0.431248 0.746943i
\(612\) −8.00772 + 4.62326i −0.0130845 + 0.00755434i
\(613\) −182.636 316.335i −0.297938 0.516044i 0.677726 0.735315i \(-0.262966\pi\)
−0.975664 + 0.219270i \(0.929632\pi\)
\(614\) −356.735 205.961i −0.581002 0.335442i
\(615\) 145.166i 0.236043i
\(616\) −342.508 103.377i −0.556020 0.167820i
\(617\) −64.2245 −0.104092 −0.0520458 0.998645i \(-0.516574\pi\)
−0.0520458 + 0.998645i \(0.516574\pi\)
\(618\) 93.0140 161.105i 0.150508 0.260688i
\(619\) −990.646 + 571.949i −1.60040 + 0.923989i −0.608989 + 0.793178i \(0.708425\pi\)
−0.991407 + 0.130811i \(0.958242\pi\)
\(620\) −62.4809 108.220i −0.100776 0.174549i
\(621\) −121.444 70.1159i −0.195562 0.112908i
\(622\) 353.328i 0.568051i
\(623\) −676.067 + 158.632i −1.08518 + 0.254625i
\(624\) −129.283 −0.207184
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 4.63624 2.67674i 0.00740614 0.00427594i
\(627\) 532.771 + 922.787i 0.849715 + 1.47175i
\(628\) 41.5492 + 23.9884i 0.0661611 + 0.0381982i
\(629\) 79.6288i 0.126596i
\(630\) 45.4635 + 48.4053i 0.0721642 + 0.0768338i
\(631\) 257.367 0.407872 0.203936 0.978984i \(-0.434627\pi\)
0.203936 + 0.978984i \(0.434627\pi\)
\(632\) 188.370 326.267i 0.298055 0.516246i
\(633\) −438.305 + 253.055i −0.692425 + 0.399771i
\(634\) 50.4598 + 87.3990i 0.0795897 + 0.137853i
\(635\) −192.088 110.902i −0.302501 0.174649i
\(636\) 1.53696i 0.00241660i
\(637\) 912.565 + 57.2562i 1.43260 + 0.0898841i
\(638\) 420.794 0.659552
\(639\) −68.6470 + 118.900i −0.107429 + 0.186072i
\(640\) 21.9089 12.6491i 0.0342327 0.0197642i
\(641\) −99.4860 172.315i −0.155204 0.268822i 0.777929 0.628352i \(-0.216270\pi\)
−0.933133 + 0.359530i \(0.882937\pi\)
\(642\) 227.459 + 131.323i 0.354297 + 0.204554i
\(643\) 708.223i 1.10144i −0.834692 0.550718i \(-0.814354\pi\)
0.834692 0.550718i \(-0.185646\pi\)
\(644\) 275.401 258.664i 0.427642 0.401652i
\(645\) 246.688 0.382463
\(646\) −37.0990 + 64.2573i −0.0574288 + 0.0994695i
\(647\) −140.794 + 81.2876i −0.217611 + 0.125638i −0.604844 0.796344i \(-0.706764\pi\)
0.387233 + 0.921982i \(0.373431\pi\)
\(648\) −12.7279 22.0454i −0.0196419 0.0340207i
\(649\) 1160.57 + 670.054i 1.78824 + 1.03244i
\(650\) 131.949i 0.202998i
\(651\) −77.3897 329.825i −0.118878 0.506644i
\(652\) −506.255 −0.776464
\(653\) −497.880 + 862.354i −0.762450 + 1.32060i 0.179134 + 0.983825i \(0.442671\pi\)
−0.941584 + 0.336778i \(0.890663\pi\)
\(654\) 171.595 99.0702i 0.262377 0.151483i
\(655\) −186.303 322.686i −0.284431 0.492650i
\(656\) 129.841 + 74.9636i 0.197928 + 0.114274i
\(657\) 109.280i 0.166331i
\(658\) −80.7815 + 267.644i −0.122768 + 0.406754i
\(659\) 897.542 1.36198 0.680988 0.732295i \(-0.261551\pi\)
0.680988 + 0.732295i \(0.261551\pi\)
\(660\) −69.9851 + 121.218i −0.106038 + 0.183663i
\(661\) −74.7048 + 43.1308i −0.113018 + 0.0652508i −0.555443 0.831554i \(-0.687451\pi\)
0.442426 + 0.896805i \(0.354118\pi\)
\(662\) 241.807 + 418.822i 0.365267 + 0.632661i
\(663\) 43.1359 + 24.9045i 0.0650617 + 0.0375634i
\(664\) 141.213i 0.212671i
\(665\) 510.154 + 153.977i 0.767149 + 0.231544i
\(666\) −219.220 −0.329159
\(667\) −222.192 + 384.848i −0.333122 + 0.576984i
\(668\) 148.482 85.7259i 0.222278 0.128332i
\(669\) −234.957 406.957i −0.351206 0.608306i
\(670\) 34.8046 + 20.0944i 0.0519471 + 0.0299917i
\(671\) 1899.69i 2.83113i
\(672\) 66.7723 15.6674i 0.0993635 0.0233145i
\(673\) 486.598 0.723028 0.361514 0.932367i \(-0.382260\pi\)
0.361514 + 0.932367i \(0.382260\pi\)
\(674\) −174.228 + 301.772i −0.258499 + 0.447733i
\(675\) 22.5000 12.9904i 0.0333333 0.0192450i
\(676\) 179.211 + 310.402i 0.265105 + 0.459175i
\(677\) 47.5668 + 27.4627i 0.0702612 + 0.0405653i 0.534719 0.845030i \(-0.320417\pi\)
−0.464458 + 0.885595i \(0.653751\pi\)
\(678\) 195.729i 0.288686i
\(679\) −720.643 767.274i −1.06133 1.13001i
\(680\) −9.74668 −0.0143334
\(681\) 128.699 222.913i 0.188985 0.327332i
\(682\) 618.398 357.032i 0.906742 0.523508i
\(683\) 477.185 + 826.509i 0.698661 + 1.21012i 0.968931 + 0.247331i \(0.0795535\pi\)
−0.270270 + 0.962784i \(0.587113\pi\)
\(684\) −176.902 102.134i −0.258628 0.149319i
\(685\) 338.803i 0.494603i
\(686\) −478.261 + 81.0188i −0.697174 + 0.118103i
\(687\) 43.8788 0.0638702
\(688\) 127.389 220.645i 0.185159 0.320705i
\(689\) 7.17006 4.13964i 0.0104065 0.00600818i
\(690\) −73.9086 128.013i −0.107114 0.185527i
\(691\) −22.3860 12.9246i −0.0323966 0.0187042i 0.483714 0.875226i \(-0.339287\pi\)
−0.516111 + 0.856522i \(0.672621\pi\)
\(692\) 38.9530i 0.0562905i
\(693\) −276.601 + 259.790i −0.399135 + 0.374877i
\(694\) 195.659 0.281929
\(695\) −169.736 + 293.991i −0.244224 + 0.423008i
\(696\) −69.8604 + 40.3339i −0.100374 + 0.0579510i
\(697\) −28.8814 50.0240i −0.0414367 0.0717704i
\(698\) −141.896 81.9239i −0.203290 0.117370i
\(699\) 708.211i 1.01318i
\(700\) 15.9904 + 68.1491i 0.0228435 + 0.0973559i
\(701\) −942.060 −1.34388 −0.671940 0.740606i \(-0.734539\pi\)
−0.671940 + 0.740606i \(0.734539\pi\)
\(702\) −68.5627 + 118.754i −0.0976677 + 0.169165i
\(703\) −1523.44 + 879.556i −2.16705 + 1.25115i
\(704\) 72.2803 + 125.193i 0.102671 + 0.177831i
\(705\) 94.7225 + 54.6881i 0.134358 + 0.0775717i
\(706\) 264.767i 0.375024i
\(707\) −95.2264 + 315.503i −0.134691 + 0.446256i
\(708\) −256.904 −0.362859
\(709\) 168.282 291.473i 0.237351 0.411105i −0.722602 0.691264i \(-0.757054\pi\)
0.959953 + 0.280160i \(0.0903874\pi\)
\(710\) −125.332 + 72.3603i −0.176524 + 0.101916i
\(711\) −199.797 346.059i −0.281008 0.486721i
\(712\) 242.999 + 140.296i 0.341291 + 0.197045i
\(713\) 754.097i 1.05764i
\(714\) −25.2970 7.63524i −0.0354300 0.0106936i
\(715\) 753.991 1.05453
\(716\) −252.834 + 437.922i −0.353120 + 0.611622i
\(717\) 100.553 58.0542i 0.140241 0.0809681i
\(718\) −450.777 780.769i −0.627823 1.08742i
\(719\) −111.447 64.3438i −0.155002 0.0894907i 0.420493 0.907296i \(-0.361857\pi\)
−0.575495 + 0.817805i \(0.695191\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 517.563 121.440i 0.717840 0.168433i
\(722\) −1128.61 −1.56317
\(723\) 205.143 355.319i 0.283739 0.491451i
\(724\) 249.804 144.224i 0.345033 0.199205i
\(725\) −41.1656 71.3009i −0.0567802 0.0983461i
\(726\) −435.990 251.719i −0.600537 0.346720i
\(727\) 684.683i 0.941792i 0.882189 + 0.470896i \(0.156069\pi\)
−0.882189 + 0.470896i \(0.843931\pi\)
\(728\) −252.934 269.301i −0.347437 0.369919i
\(729\) −27.0000 −0.0370370
\(730\) 57.5954 99.7582i 0.0788978 0.136655i
\(731\) −85.0082 + 49.0795i −0.116290 + 0.0671402i
\(732\) −182.089 315.387i −0.248755 0.430856i
\(733\) 512.533 + 295.911i 0.699227 + 0.403699i 0.807059 0.590470i \(-0.201058\pi\)
−0.107832 + 0.994169i \(0.534391\pi\)
\(734\) 77.8530i 0.106067i
\(735\) −11.8836 + 189.404i −0.0161681 + 0.257692i
\(736\) −152.665 −0.207425
\(737\) −114.825 + 198.882i −0.155800 + 0.269854i
\(738\) 137.717 79.5110i 0.186608 0.107738i
\(739\) −252.105 436.659i −0.341144 0.590878i 0.643502 0.765445i \(-0.277481\pi\)
−0.984645 + 0.174567i \(0.944148\pi\)
\(740\) −200.119 115.539i −0.270431 0.156134i
\(741\) 1100.35i 1.48496i
\(742\) −3.20153 + 3.00696i −0.00431473 + 0.00405250i
\(743\) 983.540 1.32374 0.661871 0.749618i \(-0.269763\pi\)
0.661871 + 0.749618i \(0.269763\pi\)
\(744\) −68.4444 + 118.549i −0.0919952 + 0.159340i
\(745\) 64.2798 37.1120i 0.0862816 0.0498147i
\(746\) −190.323 329.649i −0.255124 0.441888i
\(747\) 129.713 + 74.8897i 0.173645 + 0.100254i
\(748\) 55.6951i 0.0744587i
\(749\) 171.457 + 730.730i 0.228915 + 0.975607i
\(750\) 27.3861 0.0365148
\(751\) −458.462 + 794.080i −0.610469 + 1.05736i 0.380692 + 0.924702i \(0.375686\pi\)
−0.991161 + 0.132662i \(0.957648\pi\)
\(752\) 97.8290 56.4816i 0.130092 0.0751085i
\(753\) 418.621 + 725.073i 0.555938 + 0.962912i
\(754\) 376.323 + 217.270i 0.499103 + 0.288157i
\(755\) 20.8025i 0.0275530i
\(756\) 21.0200 69.6431i 0.0278042 0.0921205i
\(757\) 82.2419 0.108642 0.0543209 0.998524i \(-0.482701\pi\)
0.0543209 + 0.998524i \(0.482701\pi\)
\(758\) −332.188 + 575.367i −0.438243 + 0.759059i
\(759\) 731.502 422.333i 0.963771 0.556434i
\(760\) −107.659 186.471i −0.141656 0.245356i
\(761\) 303.297 + 175.108i 0.398550 + 0.230103i 0.685858 0.727735i \(-0.259427\pi\)
−0.287308 + 0.957838i \(0.592760\pi\)
\(762\) 242.974i 0.318864i
\(763\) 542.080 + 163.613i 0.710459 + 0.214434i
\(764\) −628.196 −0.822246
\(765\) −5.16896 + 8.95290i −0.00675681 + 0.0117031i
\(766\) 492.604 284.405i 0.643087 0.371286i
\(767\) 691.944 + 1198.48i 0.902144 + 1.56256i
\(768\) −24.0000 13.8564i −0.0312500 0.0180422i
\(769\) 319.560i 0.415553i 0.978176 + 0.207777i \(0.0666227\pi\)
−0.978176 + 0.207777i \(0.933377\pi\)
\(770\) −389.422 + 91.3734i −0.505743 + 0.118667i
\(771\) −562.194 −0.729175
\(772\) −52.8284 + 91.5015i −0.0684306 + 0.118525i
\(773\) −866.904 + 500.507i −1.12148 + 0.647487i −0.941778 0.336235i \(-0.890847\pi\)
−0.179702 + 0.983721i \(0.557513\pi\)
\(774\) −135.117 234.029i −0.174570 0.302363i
\(775\) −120.994 69.8558i −0.156121 0.0901365i
\(776\) 425.328i 0.548103i
\(777\) −428.889 456.642i