Properties

Label 7.4.c.a.4.1
Level 7
Weight 4
Character 7.4
Analytic conductor 0.413
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 7.c (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.41301337004\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 7.4
Dual form 7.4.c.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +14.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -24.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +14.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -24.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(-7.00000 + 12.1244i) q^{10} +(2.50000 - 4.33013i) q^{11} +(14.0000 + 24.2487i) q^{12} -14.0000 q^{13} +(7.00000 - 36.3731i) q^{14} +49.0000 q^{15} +(8.00000 + 13.8564i) q^{16} +(10.5000 - 18.1865i) q^{17} +(-22.0000 + 38.1051i) q^{18} +(-24.5000 - 42.4352i) q^{19} -28.0000 q^{20} +(-122.500 + 42.4352i) q^{21} -10.0000 q^{22} +(79.5000 + 137.698i) q^{23} +(84.0000 - 145.492i) q^{24} +(38.0000 - 65.8179i) q^{25} +(14.0000 + 24.2487i) q^{26} -35.0000 q^{27} +(70.0000 - 24.2487i) q^{28} +58.0000 q^{29} +(-49.0000 - 84.8705i) q^{30} +(-73.5000 + 127.306i) q^{31} +(-80.0000 + 138.564i) q^{32} +(17.5000 + 30.3109i) q^{33} -42.0000 q^{34} +(24.5000 - 127.306i) q^{35} -88.0000 q^{36} +(-109.500 - 189.660i) q^{37} +(-49.0000 + 84.8705i) q^{38} +(49.0000 - 84.8705i) q^{39} +(84.0000 + 145.492i) q^{40} +350.000 q^{41} +(196.000 + 169.741i) q^{42} -124.000 q^{43} +(-10.0000 - 17.3205i) q^{44} +(-77.0000 + 133.368i) q^{45} +(159.000 - 275.396i) q^{46} +(-262.500 - 454.663i) q^{47} -112.000 q^{48} +(49.0000 + 339.482i) q^{49} -152.000 q^{50} +(73.5000 + 127.306i) q^{51} +(-28.0000 + 48.4974i) q^{52} +(-151.500 + 262.406i) q^{53} +(35.0000 + 60.6218i) q^{54} -35.0000 q^{55} +(-336.000 - 290.985i) q^{56} +343.000 q^{57} +(-58.0000 - 100.459i) q^{58} +(52.5000 - 90.9327i) q^{59} +(98.0000 - 169.741i) q^{60} +(206.500 + 357.668i) q^{61} +294.000 q^{62} +(77.0000 - 400.104i) q^{63} +448.000 q^{64} +(49.0000 + 84.8705i) q^{65} +(35.0000 - 60.6218i) q^{66} +(-207.500 + 359.401i) q^{67} +(-42.0000 - 72.7461i) q^{68} -1113.00 q^{69} +(-245.000 + 84.8705i) q^{70} -432.000 q^{71} +(264.000 + 457.261i) q^{72} +(556.500 - 963.886i) q^{73} +(-219.000 + 379.319i) q^{74} +(266.000 + 460.726i) q^{75} -196.000 q^{76} +(87.5000 - 30.3109i) q^{77} -196.000 q^{78} +(51.5000 + 89.2006i) q^{79} +(56.0000 - 96.9948i) q^{80} +(419.500 - 726.595i) q^{81} +(-350.000 - 606.218i) q^{82} +1092.00 q^{83} +(-98.0000 + 509.223i) q^{84} -147.000 q^{85} +(124.000 + 214.774i) q^{86} +(-203.000 + 351.606i) q^{87} +(-60.0000 + 103.923i) q^{88} +(164.500 + 284.922i) q^{89} +308.000 q^{90} +(-196.000 - 169.741i) q^{91} +636.000 q^{92} +(-514.500 - 891.140i) q^{93} +(-525.000 + 909.327i) q^{94} +(-171.500 + 297.047i) q^{95} +(-560.000 - 969.948i) q^{96} -882.000 q^{97} +(539.000 - 424.352i) q^{98} -110.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 7q^{3} + 4q^{4} - 7q^{5} + 28q^{6} + 28q^{7} - 48q^{8} - 22q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 7q^{3} + 4q^{4} - 7q^{5} + 28q^{6} + 28q^{7} - 48q^{8} - 22q^{9} - 14q^{10} + 5q^{11} + 28q^{12} - 28q^{13} + 14q^{14} + 98q^{15} + 16q^{16} + 21q^{17} - 44q^{18} - 49q^{19} - 56q^{20} - 245q^{21} - 20q^{22} + 159q^{23} + 168q^{24} + 76q^{25} + 28q^{26} - 70q^{27} + 140q^{28} + 116q^{29} - 98q^{30} - 147q^{31} - 160q^{32} + 35q^{33} - 84q^{34} + 49q^{35} - 176q^{36} - 219q^{37} - 98q^{38} + 98q^{39} + 168q^{40} + 700q^{41} + 392q^{42} - 248q^{43} - 20q^{44} - 154q^{45} + 318q^{46} - 525q^{47} - 224q^{48} + 98q^{49} - 304q^{50} + 147q^{51} - 56q^{52} - 303q^{53} + 70q^{54} - 70q^{55} - 672q^{56} + 686q^{57} - 116q^{58} + 105q^{59} + 196q^{60} + 413q^{61} + 588q^{62} + 154q^{63} + 896q^{64} + 98q^{65} + 70q^{66} - 415q^{67} - 84q^{68} - 2226q^{69} - 490q^{70} - 864q^{71} + 528q^{72} + 1113q^{73} - 438q^{74} + 532q^{75} - 392q^{76} + 175q^{77} - 392q^{78} + 103q^{79} + 112q^{80} + 839q^{81} - 700q^{82} + 2184q^{83} - 196q^{84} - 294q^{85} + 248q^{86} - 406q^{87} - 120q^{88} + 329q^{89} + 616q^{90} - 392q^{91} + 1272q^{92} - 1029q^{93} - 1050q^{94} - 343q^{95} - 1120q^{96} - 1764q^{97} + 1078q^{98} - 220q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −3.50000 + 6.06218i −0.673575 + 1.16667i 0.303308 + 0.952893i \(0.401909\pi\)
−0.976883 + 0.213774i \(0.931424\pi\)
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) −3.50000 6.06218i −0.313050 0.542218i 0.665971 0.745977i \(-0.268017\pi\)
−0.979021 + 0.203760i \(0.934684\pi\)
\(6\) 14.0000 0.952579
\(7\) 14.0000 + 12.1244i 0.755929 + 0.654654i
\(8\) −24.0000 −1.06066
\(9\) −11.0000 19.0526i −0.407407 0.705650i
\(10\) −7.00000 + 12.1244i −0.221359 + 0.383406i
\(11\) 2.50000 4.33013i 0.0685253 0.118689i −0.829727 0.558169i \(-0.811504\pi\)
0.898252 + 0.439480i \(0.144837\pi\)
\(12\) 14.0000 + 24.2487i 0.336788 + 0.583333i
\(13\) −14.0000 −0.298685 −0.149342 0.988786i \(-0.547716\pi\)
−0.149342 + 0.988786i \(0.547716\pi\)
\(14\) 7.00000 36.3731i 0.133631 0.694365i
\(15\) 49.0000 0.843450
\(16\) 8.00000 + 13.8564i 0.125000 + 0.216506i
\(17\) 10.5000 18.1865i 0.149801 0.259464i −0.781353 0.624090i \(-0.785470\pi\)
0.931154 + 0.364626i \(0.118803\pi\)
\(18\) −22.0000 + 38.1051i −0.288081 + 0.498970i
\(19\) −24.5000 42.4352i −0.295826 0.512385i 0.679351 0.733813i \(-0.262261\pi\)
−0.975177 + 0.221429i \(0.928928\pi\)
\(20\) −28.0000 −0.313050
\(21\) −122.500 + 42.4352i −1.27294 + 0.440959i
\(22\) −10.0000 −0.0969094
\(23\) 79.5000 + 137.698i 0.720735 + 1.24835i 0.960706 + 0.277569i \(0.0895287\pi\)
−0.239971 + 0.970780i \(0.577138\pi\)
\(24\) 84.0000 145.492i 0.714435 1.23744i
\(25\) 38.0000 65.8179i 0.304000 0.526543i
\(26\) 14.0000 + 24.2487i 0.105601 + 0.182906i
\(27\) −35.0000 −0.249472
\(28\) 70.0000 24.2487i 0.472456 0.163663i
\(29\) 58.0000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −49.0000 84.8705i −0.298205 0.516505i
\(31\) −73.5000 + 127.306i −0.425838 + 0.737574i −0.996498 0.0836128i \(-0.973354\pi\)
0.570660 + 0.821186i \(0.306687\pi\)
\(32\) −80.0000 + 138.564i −0.441942 + 0.765466i
\(33\) 17.5000 + 30.3109i 0.0923139 + 0.159892i
\(34\) −42.0000 −0.211851
\(35\) 24.5000 127.306i 0.118322 0.614817i
\(36\) −88.0000 −0.407407
\(37\) −109.500 189.660i −0.486532 0.842698i 0.513348 0.858181i \(-0.328405\pi\)
−0.999880 + 0.0154821i \(0.995072\pi\)
\(38\) −49.0000 + 84.8705i −0.209180 + 0.362311i
\(39\) 49.0000 84.8705i 0.201187 0.348466i
\(40\) 84.0000 + 145.492i 0.332039 + 0.575109i
\(41\) 350.000 1.33319 0.666595 0.745420i \(-0.267751\pi\)
0.666595 + 0.745420i \(0.267751\pi\)
\(42\) 196.000 + 169.741i 0.720082 + 0.623610i
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) −10.0000 17.3205i −0.0342627 0.0593447i
\(45\) −77.0000 + 133.368i −0.255077 + 0.441807i
\(46\) 159.000 275.396i 0.509636 0.882716i
\(47\) −262.500 454.663i −0.814671 1.41105i −0.909564 0.415565i \(-0.863584\pi\)
0.0948921 0.995488i \(-0.469749\pi\)
\(48\) −112.000 −0.336788
\(49\) 49.0000 + 339.482i 0.142857 + 0.989743i
\(50\) −152.000 −0.429921
\(51\) 73.5000 + 127.306i 0.201805 + 0.349537i
\(52\) −28.0000 + 48.4974i −0.0746712 + 0.129334i
\(53\) −151.500 + 262.406i −0.392644 + 0.680079i −0.992797 0.119806i \(-0.961773\pi\)
0.600153 + 0.799885i \(0.295106\pi\)
\(54\) 35.0000 + 60.6218i 0.0882018 + 0.152770i
\(55\) −35.0000 −0.0858073
\(56\) −336.000 290.985i −0.801784 0.694365i
\(57\) 343.000 0.797043
\(58\) −58.0000 100.459i −0.131306 0.227429i
\(59\) 52.5000 90.9327i 0.115846 0.200651i −0.802272 0.596959i \(-0.796375\pi\)
0.918118 + 0.396308i \(0.129709\pi\)
\(60\) 98.0000 169.741i 0.210862 0.365224i
\(61\) 206.500 + 357.668i 0.433436 + 0.750734i 0.997167 0.0752252i \(-0.0239676\pi\)
−0.563730 + 0.825959i \(0.690634\pi\)
\(62\) 294.000 0.602226
\(63\) 77.0000 400.104i 0.153986 0.800132i
\(64\) 448.000 0.875000
\(65\) 49.0000 + 84.8705i 0.0935031 + 0.161952i
\(66\) 35.0000 60.6218i 0.0652758 0.113061i
\(67\) −207.500 + 359.401i −0.378361 + 0.655340i −0.990824 0.135159i \(-0.956845\pi\)
0.612463 + 0.790499i \(0.290179\pi\)
\(68\) −42.0000 72.7461i −0.0749007 0.129732i
\(69\) −1113.00 −1.94188
\(70\) −245.000 + 84.8705i −0.418330 + 0.144914i
\(71\) −432.000 −0.722098 −0.361049 0.932547i \(-0.617581\pi\)
−0.361049 + 0.932547i \(0.617581\pi\)
\(72\) 264.000 + 457.261i 0.432121 + 0.748455i
\(73\) 556.500 963.886i 0.892238 1.54540i 0.0550526 0.998483i \(-0.482467\pi\)
0.837186 0.546919i \(-0.184199\pi\)
\(74\) −219.000 + 379.319i −0.344030 + 0.595878i
\(75\) 266.000 + 460.726i 0.409534 + 0.709333i
\(76\) −196.000 −0.295826
\(77\) 87.5000 30.3109i 0.129501 0.0448603i
\(78\) −196.000 −0.284521
\(79\) 51.5000 + 89.2006i 0.0733443 + 0.127036i 0.900365 0.435135i \(-0.143299\pi\)
−0.827021 + 0.562171i \(0.809966\pi\)
\(80\) 56.0000 96.9948i 0.0782624 0.135554i
\(81\) 419.500 726.595i 0.575446 0.996701i
\(82\) −350.000 606.218i −0.471354 0.816409i
\(83\) 1092.00 1.44413 0.722064 0.691827i \(-0.243194\pi\)
0.722064 + 0.691827i \(0.243194\pi\)
\(84\) −98.0000 + 509.223i −0.127294 + 0.661438i
\(85\) −147.000 −0.187581
\(86\) 124.000 + 214.774i 0.155480 + 0.269299i
\(87\) −203.000 + 351.606i −0.250160 + 0.433289i
\(88\) −60.0000 + 103.923i −0.0726821 + 0.125889i
\(89\) 164.500 + 284.922i 0.195921 + 0.339345i 0.947202 0.320637i \(-0.103897\pi\)
−0.751281 + 0.659982i \(0.770564\pi\)
\(90\) 308.000 0.360734
\(91\) −196.000 169.741i −0.225784 0.195535i
\(92\) 636.000 0.720735
\(93\) −514.500 891.140i −0.573668 0.993623i
\(94\) −525.000 + 909.327i −0.576060 + 0.997765i
\(95\) −171.500 + 297.047i −0.185216 + 0.320804i
\(96\) −560.000 969.948i −0.595362 1.03120i
\(97\) −882.000 −0.923232 −0.461616 0.887080i \(-0.652730\pi\)
−0.461616 + 0.887080i \(0.652730\pi\)
\(98\) 539.000 424.352i 0.555584 0.437409i
\(99\) −110.000 −0.111671
\(100\) −152.000 263.272i −0.152000 0.263272i
\(101\) −689.500 + 1194.25i −0.679285 + 1.17656i 0.295911 + 0.955215i \(0.404377\pi\)
−0.975196 + 0.221341i \(0.928957\pi\)
\(102\) 147.000 254.611i 0.142698 0.247160i
\(103\) 339.500 + 588.031i 0.324776 + 0.562529i 0.981467 0.191631i \(-0.0613777\pi\)
−0.656691 + 0.754160i \(0.728044\pi\)
\(104\) 336.000 0.316803
\(105\) 686.000 + 594.093i 0.637588 + 0.552167i
\(106\) 606.000 0.555282
\(107\) −228.500 395.774i −0.206448 0.357578i 0.744145 0.668018i \(-0.232857\pi\)
−0.950593 + 0.310440i \(0.899524\pi\)
\(108\) −70.0000 + 121.244i −0.0623681 + 0.108025i
\(109\) 562.500 974.279i 0.494291 0.856137i −0.505687 0.862717i \(-0.668761\pi\)
0.999978 + 0.00657959i \(0.00209436\pi\)
\(110\) 35.0000 + 60.6218i 0.0303374 + 0.0525460i
\(111\) 1533.00 1.31086
\(112\) −56.0000 + 290.985i −0.0472456 + 0.245495i
\(113\) −1538.00 −1.28038 −0.640190 0.768217i \(-0.721144\pi\)
−0.640190 + 0.768217i \(0.721144\pi\)
\(114\) −343.000 594.093i −0.281797 0.488087i
\(115\) 556.500 963.886i 0.451251 0.781590i
\(116\) 116.000 200.918i 0.0928477 0.160817i
\(117\) 154.000 + 266.736i 0.121686 + 0.210767i
\(118\) −210.000 −0.163831
\(119\) 367.500 127.306i 0.283098 0.0980680i
\(120\) −1176.00 −0.894614
\(121\) 653.000 + 1131.03i 0.490609 + 0.849759i
\(122\) 413.000 715.337i 0.306486 0.530849i
\(123\) −1225.00 + 2121.76i −0.898004 + 1.55539i
\(124\) 294.000 + 509.223i 0.212919 + 0.368787i
\(125\) −1407.00 −1.00677
\(126\) −770.000 + 266.736i −0.544421 + 0.188593i
\(127\) 72.0000 0.0503068 0.0251534 0.999684i \(-0.491993\pi\)
0.0251534 + 0.999684i \(0.491993\pi\)
\(128\) 192.000 + 332.554i 0.132583 + 0.229640i
\(129\) 434.000 751.710i 0.296214 0.513057i
\(130\) 98.0000 169.741i 0.0661167 0.114517i
\(131\) −1074.50 1861.09i −0.716637 1.24125i −0.962325 0.271903i \(-0.912347\pi\)
0.245687 0.969349i \(-0.420986\pi\)
\(132\) 140.000 0.0923139
\(133\) 171.500 891.140i 0.111812 0.580990i
\(134\) 830.000 0.535083
\(135\) 122.500 + 212.176i 0.0780972 + 0.135268i
\(136\) −252.000 + 436.477i −0.158888 + 0.275203i
\(137\) 562.500 974.279i 0.350786 0.607578i −0.635602 0.772017i \(-0.719248\pi\)
0.986387 + 0.164439i \(0.0525813\pi\)
\(138\) 1113.00 + 1927.77i 0.686557 + 1.18915i
\(139\) 252.000 0.153772 0.0768862 0.997040i \(-0.475502\pi\)
0.0768862 + 0.997040i \(0.475502\pi\)
\(140\) −392.000 339.482i −0.236643 0.204939i
\(141\) 3675.00 2.19497
\(142\) 432.000 + 748.246i 0.255300 + 0.442193i
\(143\) −35.0000 + 60.6218i −0.0204675 + 0.0354507i
\(144\) 176.000 304.841i 0.101852 0.176413i
\(145\) −203.000 351.606i −0.116264 0.201375i
\(146\) −2226.00 −1.26182
\(147\) −2229.50 891.140i −1.25093 0.500000i
\(148\) −876.000 −0.486532
\(149\) 100.500 + 174.071i 0.0552569 + 0.0957078i 0.892331 0.451382i \(-0.149069\pi\)
−0.837074 + 0.547090i \(0.815736\pi\)
\(150\) 532.000 921.451i 0.289584 0.501574i
\(151\) −809.500 + 1402.10i −0.436266 + 0.755635i −0.997398 0.0720914i \(-0.977033\pi\)
0.561132 + 0.827726i \(0.310366\pi\)
\(152\) 588.000 + 1018.45i 0.313770 + 0.543466i
\(153\) −462.000 −0.244121
\(154\) −140.000 121.244i −0.0732566 0.0634421i
\(155\) 1029.00 0.533234
\(156\) −196.000 339.482i −0.100593 0.174233i
\(157\) −339.500 + 588.031i −0.172580 + 0.298917i −0.939321 0.343039i \(-0.888544\pi\)
0.766741 + 0.641956i \(0.221877\pi\)
\(158\) 103.000 178.401i 0.0518623 0.0898281i
\(159\) −1060.50 1836.84i −0.528950 0.916169i
\(160\) 1120.00 0.553399
\(161\) −556.500 + 2891.66i −0.272412 + 1.41549i
\(162\) −1678.00 −0.813803
\(163\) 233.500 + 404.434i 0.112203 + 0.194342i 0.916658 0.399672i \(-0.130876\pi\)
−0.804455 + 0.594014i \(0.797543\pi\)
\(164\) 700.000 1212.44i 0.333298 0.577288i
\(165\) 122.500 212.176i 0.0577976 0.100108i
\(166\) −1092.00 1891.40i −0.510576 0.884344i
\(167\) 1204.00 0.557894 0.278947 0.960306i \(-0.410015\pi\)
0.278947 + 0.960306i \(0.410015\pi\)
\(168\) 2940.00 1018.45i 1.35015 0.467707i
\(169\) −2001.00 −0.910787
\(170\) 147.000 + 254.611i 0.0663199 + 0.114869i
\(171\) −539.000 + 933.575i −0.241043 + 0.417499i
\(172\) −248.000 + 429.549i −0.109941 + 0.190423i
\(173\) 1410.50 + 2443.06i 0.619875 + 1.07365i 0.989508 + 0.144477i \(0.0461499\pi\)
−0.369633 + 0.929178i \(0.620517\pi\)
\(174\) 812.000 0.353779
\(175\) 1330.00 460.726i 0.574506 0.199015i
\(176\) 80.0000 0.0342627
\(177\) 367.500 + 636.529i 0.156062 + 0.270307i
\(178\) 329.000 569.845i 0.138537 0.239953i
\(179\) 1626.50 2817.18i 0.679164 1.17635i −0.296069 0.955166i \(-0.595676\pi\)
0.975233 0.221180i \(-0.0709907\pi\)
\(180\) 308.000 + 533.472i 0.127539 + 0.220903i
\(181\) 1582.00 0.649664 0.324832 0.945772i \(-0.394692\pi\)
0.324832 + 0.945772i \(0.394692\pi\)
\(182\) −98.0000 + 509.223i −0.0399134 + 0.207396i
\(183\) −2891.00 −1.16781
\(184\) −1908.00 3304.75i −0.764454 1.32407i
\(185\) −766.500 + 1327.62i −0.304617 + 0.527613i
\(186\) −1029.00 + 1782.28i −0.405645 + 0.702597i
\(187\) −52.5000 90.9327i −0.0205304 0.0355597i
\(188\) −2100.00 −0.814671
\(189\) −490.000 424.352i −0.188583 0.163318i
\(190\) 686.000 0.261935
\(191\) −1278.50 2214.43i −0.484340 0.838902i 0.515498 0.856891i \(-0.327607\pi\)
−0.999838 + 0.0179887i \(0.994274\pi\)
\(192\) −1568.00 + 2715.86i −0.589378 + 1.02083i
\(193\) 198.500 343.812i 0.0740329 0.128229i −0.826632 0.562742i \(-0.809746\pi\)
0.900665 + 0.434514i \(0.143080\pi\)
\(194\) 882.000 + 1527.67i 0.326412 + 0.565362i
\(195\) −686.000 −0.251926
\(196\) 1274.00 + 509.223i 0.464286 + 0.185577i
\(197\) 2914.00 1.05388 0.526939 0.849903i \(-0.323340\pi\)
0.526939 + 0.849903i \(0.323340\pi\)
\(198\) 110.000 + 190.526i 0.0394816 + 0.0683842i
\(199\) −1669.50 + 2891.66i −0.594712 + 1.03007i 0.398875 + 0.917005i \(0.369401\pi\)
−0.993587 + 0.113066i \(0.963933\pi\)
\(200\) −912.000 + 1579.63i −0.322441 + 0.558484i
\(201\) −1452.50 2515.80i −0.509709 0.882841i
\(202\) 2758.00 0.960654
\(203\) 812.000 + 703.213i 0.280745 + 0.243132i
\(204\) 588.000 0.201805
\(205\) −1225.00 2121.76i −0.417355 0.722880i
\(206\) 679.000 1176.06i 0.229651 0.397768i
\(207\) 1749.00 3029.36i 0.587265 1.01717i
\(208\) −112.000 193.990i −0.0373356 0.0646671i
\(209\) −245.000 −0.0810861
\(210\) 343.000 1782.28i 0.112711 0.585662i
\(211\) 1780.00 0.580759 0.290380 0.956911i \(-0.406218\pi\)
0.290380 + 0.956911i \(0.406218\pi\)
\(212\) 606.000 + 1049.62i 0.196322 + 0.340040i
\(213\) 1512.00 2618.86i 0.486387 0.842448i
\(214\) −457.000 + 791.547i −0.145981 + 0.252846i
\(215\) 434.000 + 751.710i 0.137668 + 0.238447i
\(216\) 840.000 0.264605
\(217\) −2572.50 + 891.140i −0.804759 + 0.278777i
\(218\) −2250.00 −0.699033
\(219\) 3895.50 + 6747.20i 1.20198 + 2.08189i
\(220\) −70.0000 + 121.244i −0.0214518 + 0.0371556i
\(221\) −147.000 + 254.611i −0.0447434 + 0.0774978i
\(222\) −1533.00 2655.23i −0.463460 0.802737i
\(223\) −1400.00 −0.420408 −0.210204 0.977658i \(-0.567413\pi\)
−0.210204 + 0.977658i \(0.567413\pi\)
\(224\) −2800.00 + 969.948i −0.835191 + 0.289319i
\(225\) −1672.00 −0.495407
\(226\) 1538.00 + 2663.89i 0.452682 + 0.784069i
\(227\) 1102.50 1909.59i 0.322359 0.558342i −0.658615 0.752480i \(-0.728858\pi\)
0.980974 + 0.194138i \(0.0621908\pi\)
\(228\) 686.000 1188.19i 0.199261 0.345130i
\(229\) −143.500 248.549i −0.0414094 0.0717231i 0.844578 0.535433i \(-0.179851\pi\)
−0.885987 + 0.463710i \(0.846518\pi\)
\(230\) −2226.00 −0.638166
\(231\) −122.500 + 636.529i −0.0348914 + 0.181301i
\(232\) −1392.00 −0.393919
\(233\) −2293.50 3972.46i −0.644859 1.11693i −0.984334 0.176314i \(-0.943583\pi\)
0.339475 0.940615i \(-0.389751\pi\)
\(234\) 308.000 533.472i 0.0860453 0.149035i
\(235\) −1837.50 + 3182.64i −0.510065 + 0.883459i
\(236\) −210.000 363.731i −0.0579230 0.100326i
\(237\) −721.000 −0.197612
\(238\) −588.000 509.223i −0.160144 0.138689i
\(239\) 1668.00 0.451439 0.225720 0.974192i \(-0.427527\pi\)
0.225720 + 0.974192i \(0.427527\pi\)
\(240\) 392.000 + 678.964i 0.105431 + 0.182612i
\(241\) 1704.50 2952.28i 0.455587 0.789100i −0.543135 0.839646i \(-0.682763\pi\)
0.998722 + 0.0505456i \(0.0160960\pi\)
\(242\) 1306.00 2262.06i 0.346913 0.600870i
\(243\) 2464.00 + 4267.77i 0.650476 + 1.12666i
\(244\) 1652.00 0.433436
\(245\) 1886.50 1485.23i 0.491935 0.387298i
\(246\) 4900.00 1.26997
\(247\) 343.000 + 594.093i 0.0883586 + 0.153042i
\(248\) 1764.00 3055.34i 0.451670 0.782315i
\(249\) −3822.00 + 6619.90i −0.972729 + 1.68482i
\(250\) 1407.00 + 2437.00i 0.355946 + 0.616517i
\(251\) −4760.00 −1.19701 −0.598503 0.801121i \(-0.704238\pi\)
−0.598503 + 0.801121i \(0.704238\pi\)
\(252\) −1232.00 1066.94i −0.307971 0.266711i
\(253\) 795.000 0.197554
\(254\) −72.0000 124.708i −0.0177861 0.0308065i
\(255\) 514.500 891.140i 0.126350 0.218845i
\(256\) 2176.00 3768.94i 0.531250 0.920152i
\(257\) 402.500 + 697.150i 0.0976936 + 0.169210i 0.910730 0.413003i \(-0.135520\pi\)
−0.813036 + 0.582213i \(0.802187\pi\)
\(258\) −1736.00 −0.418909
\(259\) 766.500 3982.85i 0.183892 0.955530i
\(260\) 392.000 0.0935031
\(261\) −638.000 1105.05i −0.151307 0.262072i
\(262\) −2149.00 + 3722.18i −0.506739 + 0.877698i
\(263\) 128.500 222.569i 0.0301279 0.0521831i −0.850568 0.525865i \(-0.823742\pi\)
0.880696 + 0.473681i \(0.157075\pi\)
\(264\) −420.000 727.461i −0.0979137 0.169591i
\(265\) 2121.00 0.491668
\(266\) −1715.00 + 594.093i −0.395314 + 0.136941i
\(267\) −2303.00 −0.527870
\(268\) 830.000 + 1437.60i 0.189180 + 0.327670i
\(269\) −1795.50 + 3109.90i −0.406965 + 0.704884i −0.994548 0.104280i \(-0.966746\pi\)
0.587583 + 0.809164i \(0.300080\pi\)
\(270\) 245.000 424.352i 0.0552231 0.0956491i
\(271\) −696.500 1206.37i −0.156123 0.270413i 0.777344 0.629075i \(-0.216566\pi\)
−0.933467 + 0.358662i \(0.883233\pi\)
\(272\) 336.000 0.0749007
\(273\) 1715.00 594.093i 0.380207 0.131708i
\(274\) −2250.00 −0.496086
\(275\) −190.000 329.090i −0.0416634 0.0721631i
\(276\) −2226.00 + 3855.55i −0.485469 + 0.840857i
\(277\) −207.500 + 359.401i −0.0450089 + 0.0779577i −0.887652 0.460514i \(-0.847665\pi\)
0.842643 + 0.538472i \(0.180998\pi\)
\(278\) −252.000 436.477i −0.0543667 0.0941660i
\(279\) 3234.00 0.693959
\(280\) −588.000 + 3055.34i −0.125499 + 0.652112i
\(281\) −4954.00 −1.05171 −0.525856 0.850574i \(-0.676255\pi\)
−0.525856 + 0.850574i \(0.676255\pi\)
\(282\) −3675.00 6365.29i −0.776039 1.34414i
\(283\) 2138.50 3703.99i 0.449190 0.778019i −0.549144 0.835728i \(-0.685046\pi\)
0.998333 + 0.0577087i \(0.0183795\pi\)
\(284\) −864.000 + 1496.49i −0.180525 + 0.312678i
\(285\) −1200.50 2079.33i −0.249514 0.432171i
\(286\) 140.000 0.0289454
\(287\) 4900.00 + 4243.52i 1.00780 + 0.872778i
\(288\) 3520.00 0.720201
\(289\) 2236.00 + 3872.87i 0.455119 + 0.788289i
\(290\) −406.000 + 703.213i −0.0822108 + 0.142393i
\(291\) 3087.00 5346.84i 0.621866 1.07710i
\(292\) −2226.00 3855.55i −0.446119 0.772701i
\(293\) 7742.00 1.54366 0.771830 0.635829i \(-0.219342\pi\)
0.771830 + 0.635829i \(0.219342\pi\)
\(294\) 686.000 + 4752.75i 0.136083 + 0.942809i
\(295\) −735.000 −0.145062
\(296\) 2628.00 + 4551.83i 0.516045 + 0.893817i
\(297\) −87.5000 + 151.554i −0.0170952 + 0.0296097i
\(298\) 201.000 348.142i 0.0390725 0.0676756i
\(299\) −1113.00 1927.77i −0.215272 0.372863i
\(300\) 2128.00 0.409534
\(301\) −1736.00 1503.42i −0.332430 0.287893i
\(302\) 3238.00 0.616973
\(303\) −4826.50 8359.74i −0.915100 1.58500i
\(304\) 392.000 678.964i 0.0739564 0.128096i
\(305\) 1445.50 2503.68i 0.271374 0.470034i
\(306\) 462.000 + 800.207i 0.0863097 + 0.149493i
\(307\) −7364.00 −1.36901 −0.684504 0.729009i \(-0.739981\pi\)
−0.684504 + 0.729009i \(0.739981\pi\)
\(308\) 70.0000 363.731i 0.0129501 0.0672905i
\(309\) −4753.00 −0.875044
\(310\) −1029.00 1782.28i −0.188527 0.326538i
\(311\) −4987.50 + 8638.60i −0.909374 + 1.57508i −0.0944372 + 0.995531i \(0.530105\pi\)
−0.814936 + 0.579550i \(0.803228\pi\)
\(312\) −1176.00 + 2036.89i −0.213391 + 0.369603i
\(313\) 2376.50 + 4116.22i 0.429162 + 0.743330i 0.996799 0.0799485i \(-0.0254756\pi\)
−0.567637 + 0.823279i \(0.692142\pi\)
\(314\) 1358.00 0.244065
\(315\) −2695.00 + 933.575i −0.482051 + 0.166987i
\(316\) 412.000 0.0733443
\(317\) 1738.50 + 3011.17i 0.308025 + 0.533515i 0.977930 0.208932i \(-0.0669987\pi\)
−0.669905 + 0.742447i \(0.733665\pi\)
\(318\) −2121.00 + 3673.68i −0.374024 + 0.647829i
\(319\) 145.000 251.147i 0.0254497 0.0440801i
\(320\) −1568.00 2715.86i −0.273918 0.474440i
\(321\) 3199.00 0.556233
\(322\) 5565.00 1927.77i 0.963122 0.333635i
\(323\) −1029.00 −0.177260
\(324\) −1678.00 2906.38i −0.287723 0.498351i
\(325\) −532.000 + 921.451i −0.0908002 + 0.157270i
\(326\) 467.000 808.868i 0.0793397 0.137420i
\(327\) 3937.50 + 6819.95i 0.665885 + 1.15335i
\(328\) −8400.00 −1.41406
\(329\) 1837.50 9547.93i 0.307917 1.59998i
\(330\) −490.000 −0.0817382
\(331\) −1670.50 2893.39i −0.277399 0.480469i 0.693339 0.720612i \(-0.256139\pi\)
−0.970738 + 0.240143i \(0.922806\pi\)
\(332\) 2184.00 3782.80i 0.361032 0.625325i
\(333\) −2409.00 + 4172.51i −0.396434 + 0.686643i
\(334\) −1204.00 2085.39i −0.197245 0.341639i
\(335\) 2905.00 0.473782
\(336\) −1568.00 1357.93i −0.254588 0.220479i
\(337\) 7366.00 1.19066 0.595329 0.803482i \(-0.297022\pi\)
0.595329 + 0.803482i \(0.297022\pi\)
\(338\) 2001.00 + 3465.83i 0.322012 + 0.557741i
\(339\) 5383.00 9323.63i 0.862432 1.49378i
\(340\) −294.000 + 509.223i −0.0468953 + 0.0812250i
\(341\) 367.500 + 636.529i 0.0583614 + 0.101085i
\(342\) 2156.00 0.340886
\(343\) −3430.00 + 5346.84i −0.539949 + 0.841698i
\(344\) 2976.00 0.466439
\(345\) 3895.50 + 6747.20i 0.607903 + 1.05292i
\(346\) 2821.00 4886.12i 0.438318 0.759188i
\(347\) −3707.50 + 6421.58i −0.573571 + 0.993454i 0.422625 + 0.906305i \(0.361109\pi\)
−0.996195 + 0.0871487i \(0.972224\pi\)
\(348\) 812.000 + 1406.43i 0.125080 + 0.216645i
\(349\) −3878.00 −0.594798 −0.297399 0.954753i \(-0.596119\pi\)
−0.297399 + 0.954753i \(0.596119\pi\)
\(350\) −2128.00 1842.90i −0.324990 0.281449i
\(351\) 490.000 0.0745136
\(352\) 400.000 + 692.820i 0.0605684 + 0.104908i
\(353\) −633.500 + 1097.25i −0.0955179 + 0.165442i −0.909825 0.414993i \(-0.863784\pi\)
0.814307 + 0.580435i \(0.197117\pi\)
\(354\) 735.000 1273.06i 0.110353 0.191136i
\(355\) 1512.00 + 2618.86i 0.226052 + 0.391534i
\(356\) 1316.00 0.195921
\(357\) −514.500 + 2673.42i −0.0762751 + 0.396337i
\(358\) −6506.00 −0.960483
\(359\) −2342.50 4057.33i −0.344380 0.596484i 0.640861 0.767657i \(-0.278578\pi\)
−0.985241 + 0.171173i \(0.945244\pi\)
\(360\) 1848.00 3200.83i 0.270550 0.468607i
\(361\) 2229.00 3860.74i 0.324974 0.562872i
\(362\) −1582.00 2740.10i −0.229691 0.397836i
\(363\) −9142.00 −1.32185
\(364\) −980.000 + 339.482i −0.141115 + 0.0488838i
\(365\) −7791.00 −1.11726
\(366\) 2891.00 + 5007.36i 0.412882 + 0.715133i
\(367\) 2320.50 4019.22i 0.330052 0.571667i −0.652470 0.757815i \(-0.726267\pi\)
0.982522 + 0.186148i \(0.0596004\pi\)
\(368\) −1272.00 + 2203.17i −0.180184 + 0.312087i
\(369\) −3850.00 6668.40i −0.543152 0.940766i
\(370\) 3066.00 0.430794
\(371\) −5302.50 + 1836.84i −0.742027 + 0.257046i
\(372\) −4116.00 −0.573668
\(373\) 4398.50 + 7618.43i 0.610578 + 1.05755i 0.991143 + 0.132798i \(0.0423963\pi\)
−0.380565 + 0.924754i \(0.624270\pi\)
\(374\) −105.000 + 181.865i −0.0145172 + 0.0251445i
\(375\) 4924.50 8529.48i 0.678134 1.17456i
\(376\) 6300.00 + 10911.9i 0.864090 + 1.49665i
\(377\) −812.000 −0.110929
\(378\) −245.000 + 1273.06i −0.0333371 + 0.173225i
\(379\) 13680.0 1.85407 0.927037 0.374969i \(-0.122347\pi\)
0.927037 + 0.374969i \(0.122347\pi\)
\(380\) 686.000 + 1188.19i 0.0926080 + 0.160402i
\(381\) −252.000 + 436.477i −0.0338854 + 0.0586913i
\(382\) −2557.00 + 4428.85i −0.342480 + 0.593193i
\(383\) −4882.50 8456.74i −0.651395 1.12825i −0.982785 0.184755i \(-0.940851\pi\)
0.331390 0.943494i \(-0.392482\pi\)
\(384\) −2688.00 −0.357217
\(385\) −490.000 424.352i −0.0648642 0.0561740i
\(386\) −794.000 −0.104698
\(387\) 1364.00 + 2362.52i 0.179163 + 0.310319i
\(388\) −1764.00 + 3055.34i −0.230808 + 0.399771i
\(389\) −865.500 + 1499.09i −0.112809 + 0.195390i −0.916902 0.399113i \(-0.869318\pi\)
0.804093 + 0.594504i \(0.202651\pi\)
\(390\) 686.000 + 1188.19i 0.0890691 + 0.154272i
\(391\) 3339.00 0.431868
\(392\) −1176.00 8147.57i −0.151523 1.04978i
\(393\) 15043.0 1.93084
\(394\) −2914.00 5047.20i −0.372602 0.645366i
\(395\) 360.500 624.404i 0.0459208 0.0795372i
\(396\) −220.000 + 381.051i −0.0279177 + 0.0483549i
\(397\) −5491.50 9511.56i −0.694233 1.20245i −0.970439 0.241348i \(-0.922410\pi\)
0.276206 0.961099i \(-0.410923\pi\)
\(398\) 6678.00 0.841050
\(399\) 4802.00 + 4158.65i 0.602508 + 0.521787i
\(400\) 1216.00 0.152000
\(401\) −3301.50 5718.37i −0.411145 0.712124i 0.583870 0.811847i \(-0.301538\pi\)
−0.995015 + 0.0997232i \(0.968204\pi\)
\(402\) −2905.00 + 5031.61i −0.360418 + 0.624263i
\(403\) 1029.00 1782.28i 0.127191 0.220302i
\(404\) 2758.00 + 4777.00i 0.339643 + 0.588278i
\(405\) −5873.00 −0.720572
\(406\) 406.000 2109.64i 0.0496292 0.257881i
\(407\) −1095.00 −0.133359
\(408\) −1764.00 3055.34i −0.214047 0.370740i
\(409\) −5477.50 + 9487.31i −0.662213 + 1.14699i 0.317820 + 0.948151i \(0.397049\pi\)
−0.980033 + 0.198835i \(0.936284\pi\)
\(410\) −2450.00 + 4243.52i −0.295114 + 0.511153i
\(411\) 3937.50 + 6819.95i 0.472561 + 0.818500i
\(412\) 2716.00 0.324776
\(413\) 1837.50 636.529i 0.218928 0.0758391i
\(414\) −6996.00 −0.830518
\(415\) −3822.00 6619.90i −0.452083 0.783031i
\(416\) 1120.00 1939.90i 0.132001 0.228633i
\(417\) −882.000 + 1527.67i −0.103577 + 0.179401i
\(418\) 245.000 + 424.352i 0.0286683 + 0.0496549i
\(419\) 6636.00 0.773723 0.386861 0.922138i \(-0.373559\pi\)
0.386861 + 0.922138i \(0.373559\pi\)
\(420\) 3430.00 1188.19i 0.398493 0.138042i
\(421\) −16630.0 −1.92517 −0.962585 0.270980i \(-0.912652\pi\)
−0.962585 + 0.270980i \(0.912652\pi\)
\(422\) −1780.00 3083.05i −0.205329 0.355641i
\(423\) −5775.00 + 10002.6i −0.663806 + 1.14975i
\(424\) 3636.00 6297.74i 0.416462 0.721333i
\(425\) −798.000 1382.18i −0.0910793 0.157754i
\(426\) −6048.00 −0.687856
\(427\) −1445.50 + 7511.04i −0.163824 + 0.851252i
\(428\) −1828.00 −0.206448
\(429\) −245.000 424.352i −0.0275728 0.0477574i
\(430\) 868.000 1503.42i 0.0973458 0.168608i
\(431\) −2461.50 + 4263.44i −0.275096 + 0.476480i −0.970159 0.242468i \(-0.922043\pi\)
0.695064 + 0.718948i \(0.255376\pi\)
\(432\) −280.000 484.974i −0.0311840 0.0540123i
\(433\) 8974.00 0.995988 0.497994 0.867180i \(-0.334070\pi\)
0.497994 + 0.867180i \(0.334070\pi\)
\(434\) 4116.00 + 3564.56i 0.455240 + 0.394250i
\(435\) 2842.00 0.313249
\(436\) −2250.00 3897.11i −0.247146 0.428069i
\(437\) 3895.50 6747.20i 0.426423 0.738587i
\(438\) 7791.00 13494.4i 0.849928 1.47212i
\(439\) 2089.50 + 3619.12i 0.227167 + 0.393465i 0.956967 0.290195i \(-0.0937203\pi\)
−0.729800 + 0.683660i \(0.760387\pi\)
\(440\) 840.000 0.0910123
\(441\) 5929.00 4667.88i 0.640212 0.504036i
\(442\) 588.000 0.0632767
\(443\) 6463.50 + 11195.1i 0.693206 + 1.20067i 0.970782 + 0.239964i \(0.0771356\pi\)
−0.277576 + 0.960704i \(0.589531\pi\)
\(444\) 3066.00 5310.47i 0.327716 0.567621i
\(445\) 1151.50 1994.46i 0.122666 0.212464i
\(446\) 1400.00 + 2424.87i 0.148637 + 0.257446i
\(447\) −1407.00 −0.148879
\(448\) 6272.00 + 5431.71i 0.661438 + 0.572822i
\(449\) −2826.00 −0.297032 −0.148516 0.988910i \(-0.547450\pi\)
−0.148516 + 0.988910i \(0.547450\pi\)
\(450\) 1672.00 + 2895.99i 0.175153 + 0.303374i
\(451\) 875.000 1515.54i 0.0913573 0.158235i
\(452\) −3076.00 + 5327.79i −0.320095 + 0.554421i
\(453\) −5666.50 9814.67i −0.587716 1.01795i
\(454\) −4410.00 −0.455884
\(455\) −343.000 + 1782.28i −0.0353409 + 0.183636i
\(456\) −8232.00 −0.845392
\(457\) −4239.50 7343.03i −0.433951 0.751625i 0.563259 0.826281i \(-0.309547\pi\)
−0.997209 + 0.0746560i \(0.976214\pi\)
\(458\) −287.000 + 497.099i −0.0292808 + 0.0507159i
\(459\) −367.500 + 636.529i −0.0373713 + 0.0647290i
\(460\) −2226.00 3855.55i −0.225626 0.390795i
\(461\) 9338.00 0.943414 0.471707 0.881755i \(-0.343638\pi\)
0.471707 + 0.881755i \(0.343638\pi\)
\(462\) 1225.00 424.352i 0.123360 0.0427330i
\(463\) −4016.00 −0.403109 −0.201554 0.979477i \(-0.564599\pi\)
−0.201554 + 0.979477i \(0.564599\pi\)
\(464\) 464.000 + 803.672i 0.0464238 + 0.0804084i
\(465\) −3601.50 + 6237.98i −0.359173 + 0.622106i
\(466\) −4587.00 + 7944.92i −0.455984 + 0.789788i
\(467\) 2929.50 + 5074.04i 0.290281 + 0.502781i 0.973876 0.227080i \(-0.0729180\pi\)
−0.683595 + 0.729861i \(0.739585\pi\)
\(468\) 1232.00 0.121686
\(469\) −7262.50 + 2515.80i −0.715034 + 0.247695i
\(470\) 7350.00 0.721341
\(471\) −2376.50 4116.22i −0.232491 0.402687i
\(472\) −1260.00 + 2182.38i −0.122873 + 0.212823i
\(473\) −310.000 + 536.936i −0.0301349 + 0.0521952i
\(474\) 721.000 + 1248.81i 0.0698663 + 0.121012i
\(475\) −3724.00 −0.359724
\(476\) 294.000 1527.67i 0.0283098 0.147102i
\(477\) 6666.00 0.639864
\(478\) −1668.00 2889.06i −0.159608 0.276449i
\(479\) −3251.50 + 5631.76i −0.310156 + 0.537206i −0.978396 0.206740i \(-0.933715\pi\)
0.668240 + 0.743946i \(0.267048\pi\)
\(480\) −3920.00 + 6789.64i −0.372756 + 0.645632i
\(481\) 1533.00 + 2655.23i 0.145320 + 0.251701i
\(482\) −6818.00 −0.644297
\(483\) −15582.0 13494.4i −1.46792 1.27126i
\(484\) 5224.00 0.490609
\(485\) 3087.00 + 5346.84i 0.289017 + 0.500593i
\(486\) 4928.00 8535.55i 0.459956 0.796667i
\(487\) 8024.50 13898.8i 0.746663 1.29326i −0.202751 0.979230i \(-0.564988\pi\)
0.949414 0.314028i \(-0.101678\pi\)
\(488\) −4956.00 8584.04i −0.459729 0.796273i
\(489\) −3269.00 −0.302309
\(490\) −4459.00 1782.28i −0.411096 0.164317i
\(491\) 8864.00 0.814718 0.407359 0.913268i \(-0.366450\pi\)
0.407359 + 0.913268i \(0.366450\pi\)
\(492\) 4900.00 + 8487.05i 0.449002 + 0.777695i
\(493\) 609.000 1054.82i 0.0556348 0.0963624i
\(494\) 686.000 1188.19i 0.0624789 0.108217i
\(495\) 385.000 + 666.840i 0.0349585 + 0.0605499i
\(496\) −2352.00 −0.212919
\(497\) −6048.00 5237.72i −0.545855 0.472724i
\(498\) 15288.0 1.37565
\(499\) 5105.50 + 8842.99i 0.458023 + 0.793319i 0.998856 0.0478104i \(-0.0152243\pi\)
−0.540833 + 0.841130i \(0.681891\pi\)
\(500\) −2814.00 + 4873.99i −0.251692 + 0.435943i
\(501\) −4214.00 + 7298.86i −0.375784 + 0.650876i
\(502\) 4760.00 + 8244.56i 0.423206 + 0.733014i
\(503\) −1680.00 −0.148921 −0.0744607 0.997224i \(-0.523724\pi\)
−0.0744607 + 0.997224i \(0.523724\pi\)
\(504\) −1848.00 + 9602.49i −0.163326 + 0.848668i
\(505\) 9653.00 0.850600
\(506\) −795.000 1376.98i −0.0698460 0.120977i
\(507\) 7003.50 12130.4i 0.613484 1.06259i
\(508\) 144.000 249.415i 0.0125767 0.0217835i
\(509\) 4728.50 + 8190.00i 0.411762 + 0.713193i 0.995083 0.0990489i \(-0.0315800\pi\)
−0.583320 + 0.812242i \(0.698247\pi\)
\(510\) −2058.00 −0.178686
\(511\) 19477.5 6747.20i 1.68617 0.584107i
\(512\) −5632.00 −0.486136
\(513\) 857.500 + 1485.23i 0.0738003 + 0.127826i
\(514\) 805.000 1394.30i 0.0690798 0.119650i
\(515\) 2376.50 4116.22i 0.203342 0.352199i
\(516\) −1736.00 3006.84i −0.148107 0.256529i
\(517\) −2625.00 −0.223302
\(518\) −7665.00 + 2655.23i −0.650156 + 0.225221i
\(519\) −19747.0 −1.67013
\(520\) −1176.00 2036.89i −0.0991750 0.171776i
\(521\) 9040.50 15658.6i 0.760214 1.31673i −0.182526 0.983201i \(-0.558427\pi\)
0.942740 0.333528i \(-0.108239\pi\)
\(522\) −1276.00 + 2210.10i −0.106990 + 0.185313i
\(523\) −10188.5 17647.0i −0.851839 1.47543i −0.879546 0.475813i \(-0.842154\pi\)
0.0277071 0.999616i \(-0.491179\pi\)
\(524\) −8596.00 −0.716637
\(525\) −1862.00 + 9675.24i −0.154789 + 0.804308i
\(526\) −514.000 −0.0426073
\(527\) 1543.50 + 2673.42i 0.127582 + 0.220979i
\(528\) −280.000 + 484.974i −0.0230785 + 0.0399731i
\(529\) −6557.00 + 11357.1i −0.538917 + 0.933431i
\(530\) −2121.00 3673.68i −0.173831 0.301084i
\(531\) −2310.00 −0.188786
\(532\) −2744.00 2376.37i −0.223623 0.193663i
\(533\) −4900.00 −0.398204
\(534\) 2303.00 + 3988.91i 0.186630 + 0.323253i
\(535\) −1599.50 + 2770.42i −0.129257 + 0.223879i
\(536\) 4980.00 8625.61i 0.401312 0.695093i
\(537\) 11385.5 + 19720.3i 0.914936 + 1.58472i
\(538\) 7182.00 0.575535
\(539\) 1592.50 + 636.529i 0.127261 + 0.0508668i
\(540\) 980.000 0.0780972
\(541\) 3096.50 + 5363.30i 0.246079 + 0.426222i 0.962435 0.271514i \(-0.0875243\pi\)
−0.716355 + 0.697736i \(0.754191\pi\)
\(542\) −1393.00 + 2412.75i −0.110396 + 0.191211i
\(543\) −5537.00 + 9590.37i −0.437597 + 0.757941i
\(544\) 1680.00 + 2909.85i 0.132407 + 0.229336i
\(545\) −7875.00 −0.618950
\(546\) −2744.00 2376.37i −0.215078 0.186263i
\(547\) −18464.0 −1.44326 −0.721630 0.692279i \(-0.756607\pi\)
−0.721630 + 0.692279i \(0.756607\pi\)
\(548\) −2250.00 3897.11i −0.175393 0.303789i
\(549\) 4543.00 7868.71i 0.353170 0.611709i
\(550\) −380.000 + 658.179i −0.0294605 + 0.0510270i
\(551\) −1421.00 2461.24i −0.109867 0.190295i
\(552\) 26712.0 2.05967
\(553\) −360.500 + 1873.21i −0.0277216 + 0.144045i
\(554\) 830.000 0.0636522
\(555\) −5365.50 9293.32i −0.410365 0.710774i
\(556\) 504.000 872.954i 0.0384431 0.0665854i
\(557\) 4706.50 8151.90i 0.358027 0.620120i −0.629604 0.776916i \(-0.716783\pi\)
0.987631 + 0.156796i \(0.0501164\pi\)
\(558\) −3234.00 5601.45i −0.245351 0.424961i
\(559\) 1736.00 0.131351
\(560\) 1960.00 678.964i 0.147902 0.0512348i
\(561\) 735.000 0.0553150
\(562\) 4954.00 + 8580.58i 0.371836 + 0.644039i
\(563\) −1599.50 + 2770.42i −0.119735 + 0.207387i −0.919663 0.392709i \(-0.871538\pi\)
0.799928 + 0.600097i \(0.204871\pi\)
\(564\) 7350.00 12730.6i 0.548743 0.950450i
\(565\) 5383.00 + 9323.63i 0.400822 + 0.694244i
\(566\) −8554.00 −0.635250
\(567\) 14682.5 5086.17i 1.08749 0.376718i
\(568\) 10368.0 0.765901
\(569\) −10791.5 18691.4i −0.795085 1.37713i −0.922785 0.385314i \(-0.874093\pi\)
0.127701 0.991813i \(-0.459240\pi\)
\(570\) −2401.00 + 4158.65i −0.176433 + 0.305591i
\(571\) −10133.5 + 17551.7i −0.742686 + 1.28637i 0.208582 + 0.978005i \(0.433115\pi\)
−0.951268 + 0.308365i \(0.900218\pi\)
\(572\) 140.000 + 242.487i 0.0102337 + 0.0177253i
\(573\) 17899.0 1.30496
\(574\) 2450.00 12730.6i 0.178155 0.925721i
\(575\) 12084.0 0.876413
\(576\) −4928.00 8535.55i −0.356481 0.617444i
\(577\) −6975.50 + 12081.9i −0.503282 + 0.871710i 0.496711 + 0.867916i \(0.334541\pi\)
−0.999993 + 0.00379418i \(0.998792\pi\)
\(578\) 4472.00 7745.73i 0.321818 0.557405i
\(579\) 1389.50 + 2406.68i 0.0997334 + 0.172743i
\(580\) −1624.00 −0.116264
\(581\) 15288.0 + 13239.8i 1.09166 + 0.945403i
\(582\) −12348.0 −0.879452
\(583\) 757.500 + 1312.03i 0.0538121 + 0.0932053i
\(584\) −13356.0 + 23133.3i −0.946362 + 1.63915i
\(585\) 1078.00 1867.15i 0.0761877 0.131961i
\(586\) −7742.00 13409.5i −0.545766 0.945295i
\(587\) −20972.0 −1.47463 −0.737314 0.675550i \(-0.763906\pi\)
−0.737314 + 0.675550i \(0.763906\pi\)
\(588\) −7546.00 + 5940.93i −0.529238 + 0.416667i
\(589\) 7203.00 0.503895
\(590\) 735.000 + 1273.06i 0.0512872 + 0.0888321i
\(591\) −10199.0 + 17665.2i −0.709866 + 1.22952i
\(592\) 1752.00 3034.55i 0.121633 0.210675i
\(593\) 94.5000 + 163.679i 0.00654410 + 0.0113347i 0.869279 0.494322i \(-0.164584\pi\)
−0.862735 + 0.505657i \(0.831250\pi\)
\(594\) 350.000 0.0241762
\(595\) −2058.00 1782.28i −0.141798 0.122801i
\(596\) 804.000 0.0552569
\(597\) −11686.5 20241.6i −0.801167 1.38766i
\(598\) −2226.00 + 3855.55i −0.152221 + 0.263654i
\(599\) 5140.50 8903.61i 0.350643 0.607331i −0.635719 0.771920i \(-0.719296\pi\)
0.986362 + 0.164589i \(0.0526297\pi\)
\(600\) −6384.00 11057.4i −0.434376 0.752362i
\(601\) −6090.00 −0.413338 −0.206669 0.978411i \(-0.566262\pi\)
−0.206669 + 0.978411i \(0.566262\pi\)
\(602\) −868.000 + 4510.26i −0.0587658 + 0.305356i
\(603\) 9130.00 0.616588
\(604\) 3238.00 + 5608.38i 0.218133 + 0.377817i
\(605\) 4571.00 7917.20i 0.307170 0.532033i
\(606\) −9653.00 + 16719.5i −0.647073 + 1.12076i
\(607\) −2474.50 4285.96i −0.165464 0.286593i 0.771356 0.636404i \(-0.219579\pi\)
−0.936820 + 0.349812i \(0.886246\pi\)
\(608\) 7840.00 0.522951
\(609\) −7105.00 + 2461.24i −0.472757 + 0.163768i
\(610\) −5782.00 −0.383781
\(611\) 3675.00 + 6365.29i 0.243330 + 0.421460i
\(612\) −924.000 + 1600.41i −0.0610302 + 0.105707i
\(613\) 7898.50 13680.6i 0.520420 0.901394i −0.479298 0.877652i \(-0.659109\pi\)
0.999718 0.0237416i \(-0.00755791\pi\)
\(614\) 7364.00 + 12754.8i 0.484018 + 0.838343i
\(615\) 17150.0 1.12448
\(616\) −2100.00 + 727.461i −0.137356 + 0.0475816i
\(617\) −9378.00 −0.611903 −0.305951 0.952047i \(-0.598975\pi\)
−0.305951 + 0.952047i \(0.598975\pi\)
\(618\) 4753.00 + 8232.44i 0.309375 + 0.535853i
\(619\) 12176.5 21090.3i 0.790654 1.36945i −0.134908 0.990858i \(-0.543074\pi\)
0.925562 0.378595i \(-0.123593\pi\)
\(620\) 2058.00 3564.56i 0.133308 0.230897i
\(621\) −2782.50 4819.43i −0.179803 0.311429i
\(622\) 19950.0 1.28605
\(623\) −1151.50 + 5983.37i −0.0740512 + 0.384781i
\(624\) 1568.00 0.100593
\(625\) 174.500 + 302.243i 0.0111680 + 0.0193435i
\(626\) 4753.00 8232.44i 0.303463 0.525614i
\(627\) 857.500 1485.23i 0.0546176 0.0946005i
\(628\) 1358.00 + 2352.12i 0.0862900 + 0.149459i
\(629\) −4599.00 −0.291533
\(630\) 4312.00 + 3734.30i 0.272689 + 0.236156i
\(631\) −12640.0 −0.797449 −0.398725 0.917071i \(-0.630547\pi\)
−0.398725 + 0.917071i \(0.630547\pi\)
\(632\) −1236.00 2140.81i −0.0777934 0.134742i
\(633\) −6230.00 + 10790.7i −0.391185 + 0.677553i
\(634\) 3477.00 6022.34i 0.217806 0.377252i
\(635\) −252.000 436.477i −0.0157485 0.0272772i
\(636\) −8484.00 −0.528950
\(637\) −686.000 4752.75i −0.0426692 0.295621i
\(638\) −580.000 −0.0359913
\(639\) 4752.00 + 8230.71i 0.294188 + 0.509549i
\(640\) 1344.00 2327.88i 0.0830098 0.143777i
\(641\) 520.500 901.532i 0.0320726 0.0555513i −0.849544 0.527518i \(-0.823123\pi\)
0.881616 + 0.471967i \(0.156456\pi\)
\(642\) −3199.00 5540.83i −0.196658 0.340622i
\(643\) 9548.00 0.585593 0.292797 0.956175i \(-0.405414\pi\)
0.292797 + 0.956175i \(0.405414\pi\)
\(644\) 8904.00 + 7711.09i 0.544824 + 0.471832i
\(645\) −6076.00 −0.370918
\(646\) 1029.00 + 1782.28i 0.0626710 + 0.108549i
\(647\) 1620.50 2806.79i 0.0984674 0.170551i −0.812583 0.582845i \(-0.801939\pi\)
0.911050 + 0.412295i \(0.135273\pi\)
\(648\) −10068.0 + 17438.3i −0.610352 + 1.05716i
\(649\) −262.500 454.663i −0.0158768 0.0274994i
\(650\) 2128.00 0.128411
\(651\) 3601.50 18713.9i 0.216826 1.12666i
\(652\) 1868.00 0.112203
\(653\) 4426.50 + 7666.92i 0.265272 + 0.459464i 0.967635 0.252355i \(-0.0812051\pi\)
−0.702363 + 0.711819i \(0.747872\pi\)
\(654\) 7875.00 13639.9i 0.470851 0.815539i
\(655\) −7521.50 + 13027.6i −0.448686 + 0.777147i
\(656\) 2800.00 + 4849.74i 0.166649 + 0.288644i
\(657\) −24486.0 −1.45402
\(658\) −18375.0 + 6365.29i −1.08865 + 0.377120i
\(659\) 7044.00 0.416381 0.208191 0.978088i \(-0.433243\pi\)
0.208191 + 0.978088i \(0.433243\pi\)
\(660\) −490.000 848.705i −0.0288988 0.0500542i
\(661\) 6044.50 10469.4i 0.355679 0.616054i −0.631555 0.775331i \(-0.717583\pi\)
0.987234 + 0.159277i \(0.0509163\pi\)
\(662\) −3341.00 + 5786.78i −0.196151 + 0.339743i
\(663\) −1029.00 1782.28i −0.0602761 0.104401i
\(664\) −26208.0 −1.53173
\(665\) −6002.50 + 2079.33i −0.350026 + 0.121252i
\(666\) 9636.00 0.560642
\(667\) 4611.00 + 7986.49i 0.267674 + 0.463625i
\(668\) 2408.00 4170.78i 0.139474 0.241575i
\(669\) 4900.00 8487.05i 0.283176 0.490476i
\(670\) −2905.00 5031.61i −0.167507 0.290131i
\(671\) 2065.00 0.118805
\(672\) 3920.00 20368.9i 0.225026 1.16927i
\(673\) 982.000 0.0562456 0.0281228 0.999604i \(-0.491047\pi\)
0.0281228 + 0.999604i \(0.491047\pi\)
\(674\) −7366.00 12758.3i −0.420961 0.729126i
\(675\) −1330.00 + 2303.63i −0.0758396 + 0.131358i
\(676\) −4002.00 + 6931.67i −0.227697 + 0.394383i
\(677\) 15256.5 + 26425.0i 0.866108 + 1.50014i 0.865943 + 0.500143i \(0.166719\pi\)
0.000164659 1.00000i \(0.499948\pi\)
\(678\) −21532.0 −1.21966
\(679\) −12348.0 10693.7i −0.697898 0.604397i
\(680\) 3528.00 0.198960
\(681\) 7717.50 + 13367.1i 0.434266 + 0.752171i
\(682\) 735.000 1273.06i 0.0412677 0.0714778i
\(683\) −5737.50 + 9937.64i −0.321434 + 0.556740i −0.980784 0.195096i \(-0.937498\pi\)
0.659350 + 0.751836i \(0.270831\pi\)
\(684\) 2156.00 + 3734.30i 0.120522 + 0.208749i
\(685\) −7875.00 −0.439253
\(686\) 12691.0 + 594.093i 0.706333 + 0.0330650i
\(687\) 2009.00 0.111569
\(688\) −992.000 1718.19i −0.0549704 0.0952116i
\(689\) 2121.00 3673.68i 0.117277 0.203129i
\(690\) 7791.00 13494.4i 0.429853 0.744527i
\(691\) 14157.5 + 24521.5i 0.779416 + 1.34999i 0.932279 + 0.361741i \(0.117818\pi\)
−0.152862 + 0.988248i \(0.548849\pi\)
\(692\) 11284.0 0.619875
\(693\) −1540.00 1333.68i −0.0844152 0.0731057i
\(694\) 14830.0 0.811151
\(695\) −882.000 1527.67i −0.0481384 0.0833781i
\(696\) 4872.00 8438.55i 0.265334 0.459573i
\(697\) 3675.00 6365.29i 0.199714 0.345915i
\(698\) 3878.00 + 6716.89i 0.210293 + 0.364238i
\(699\) 32109.0 1.73744
\(700\) 1064.00 5528.71i 0.0574506 0.298522i
\(701\) 10614.0 0.571876 0.285938 0.958248i \(-0.407695\pi\)
0.285938 + 0.958248i \(0.407695\pi\)
\(702\) −490.000 848.705i −0.0263445 0.0456301i
\(703\) −5365.50 + 9293.32i −0.287857 + 0.498583i
\(704\) 1120.00 1939.90i 0.0599596 0.103853i
\(705\) −12862.5 22278.5i −0.687134 1.19015i
\(706\) 2534.00 0.135083
\(707\) −24132.5 + 8359.74i −1.28373 + 0.444697i
\(708\) 2940.00 0.156062
\(709\) −5149.50 8919.20i −0.272769 0.472451i 0.696801 0.717265i \(-0.254606\pi\)
−0.969570 + 0.244814i \(0.921273\pi\)
\(710\) 3024.00 5237.72i 0.159843 0.276857i
\(711\) 1133.00 1962.41i 0.0597621 0.103511i
\(712\) −3948.00 6838.14i −0.207806 0.359930i
\(713\) −23373.0 −1.22767
\(714\) 5145.00 1782.28i 0.269673 0.0934176i
\(715\) 490.000 0.0256293
\(716\) −6506.00 11268.7i −0.339582 0.588173i
\(717\) −5838.00 + 10111.7i −0.304078 + 0.526679i
\(718\) −4685.00 + 8114.66i −0.243513 + 0.421778i
\(719\) −16264.5 28170.9i −0.843621 1.46119i −0.886813 0.462128i \(-0.847086\pi\)
0.0431924 0.999067i \(-0.486247\pi\)
\(720\) −2464.00 −0.127539
\(721\) −2376.50 + 12348.7i −0.122754 + 0.637847i
\(722\) −8916.00 −0.459583
\(723\) 11931.5 + 20666.0i 0.613744 + 1.06304i
\(724\) 3164.00 5480.21i 0.162416 0.281313i
\(725\) 2204.00 3817.44i 0.112903 0.195553i
\(726\) 9142.00 + 15834.4i 0.467344 + 0.809463i
\(727\) 29456.0 1.50270 0.751350 0.659904i \(-0.229403\pi\)
0.751350 + 0.659904i \(0.229403\pi\)
\(728\) 4704.00 + 4073.78i 0.239481 + 0.207396i
\(729\) −11843.0 −0.601687
\(730\) 7791.00 + 13494.4i 0.395011 + 0.684179i
\(731\) −1302.00 + 2255.13i −0.0658772 + 0.114103i
\(732\) −5782.00 + 10014.7i −0.291952 + 0.505676i
\(733\) −13933.5 24133.5i −0.702109 1.21609i −0.967725 0.252009i \(-0.918909\pi\)
0.265616 0.964079i \(-0.414425\pi\)
\(734\) −9282.00 −0.466764
\(735\) 2401.00 + 16634.6i 0.120493 + 0.834799i
\(736\) −25440.0 −1.27409
\(737\) 1037.50 + 1797.00i 0.0518546 + 0.0898147i
\(738\) −7700.00 + 13336.8i −0.384066 + 0.665222i
\(739\) −9769.50 + 16921.3i −0.486302 + 0.842299i −0.999876 0.0157460i \(-0.994988\pi\)
0.513574 + 0.858045i \(0.328321\pi\)
\(740\) 3066.00 + 5310.47i 0.152309 + 0.263806i
\(741\) −4802.00 −0.238065
\(742\) 8484.00 + 7347.36i 0.419754 + 0.363518i
\(743\) 1248.00 0.0616214 0.0308107 0.999525i \(-0.490191\pi\)
0.0308107 + 0.999525i \(0.490191\pi\)
\(744\) 12348.0 + 21387.4i 0.608467 + 1.05390i
\(745\) 703.500 1218.50i 0.0345963 0.0599226i
\(746\) 8797.00 15236.9i 0.431744 0.747803i
\(747\) −12012.0 20805.4i −0.588348 1.01905i
\(748\) −420.000 −0.0205304
\(749\) 1599.50 8311.25i 0.0780300 0.405456i
\(750\) −19698.0 −0.959026
\(751\) −14046.5 24329.3i −0.682509 1.18214i −0.974213 0.225631i \(-0.927556\pi\)
0.291704 0.956509i \(-0.405778\pi\)
\(752\) 4200.00 7274.61i 0.203668 0.352763i
\(753\) 16660.0 28856.0i 0.806274 1.39651i
\(754\) 812.000 + 1406.43i 0.0392192 + 0.0679297i
\(755\) 11333.0 0.546292
\(756\) −2450.00 + 848.705i −0.117865 + 0.0408295i
\(757\) 35954.0 1.72625 0.863124 0.504991i \(-0.168504\pi\)
0.863124 + 0.504991i \(0.168504\pi\)
\(758\) −13680.0 23694.5i −0.655514 1.13538i
\(759\) −2782.50 + 4819.43i −0.133068 + 0.230480i
\(760\) 4116.00 7129.12i 0.196451 0.340264i
\(761\) 430.500 + 745.648i 0.0205067 + 0.0355187i 0.876097 0.482136i \(-0.160139\pi\)
−0.855590 + 0.517654i \(0.826805\pi\)
\(762\) 1008.00 0.0479212
\(763\) 19687.5 6819.95i 0.934122 0.323589i
\(764\) −10228.0 −0.484340
\(765\) 1617.00 + 2800.73i 0.0764219 + 0.132367i
\(766\) −9765.00 + 16913.5i −0.460605 + 0.797792i
\(767\) −735.000 + 1273.06i −0.0346014 + 0.0599315i
\(768\) 15232.0 + 26382.6i 0.715674 + 1.23958i
\(769\) 24710.0 1.15873 0.579366 0.815067i \(-0.303300\pi\)
0.579366 + 0.815067i \(0.303300\pi\)
\(770\) −245.000 + 1273.06i −0.0114665 + 0.0595816i
\(771\) −5635.00 −0.263216
\(772\) −794.000 1375.25i −0.0370164 0.0641143i
\(773\) −8249.50 + 14288.6i −0.383847 + 0.664843i −0.991609 0.129277i \(-0.958734\pi\)
0.607761 + 0.794120i \(0.292068\pi\)
\(774\) 2728.00 4725.03i 0.126687 0.219429i
\(775\) 5586.00 + 9675.24i 0.258910 + 0.448445i
\(776\) 21168.0 0.979236
\(777\) 21462.0 + 18586.6i 0.990920 + 0.858162i
\(778\) 3462.00 0.159536
\(779\) −8575.00 14852.3i −0.394392 0.683107i
\(780\) −1372.00 + 2376.37i −0.0629814 + 0.109087i
\(781\) −1080.00 + 1870.61i −0.0494820 + 0.0857053i
\(782\) −3339.00 5783.32i −0.152688 0.264464i
\(783\) −2030.00 −0.0926517
\(784\) −4312.00 + 3394.82i −0.196429 + 0.154647i
\(785\) 4753.00 0.216104
\(786\) −15043.0 26055.2i −0.682654 </