Properties

Label 7.4.c.a.2.1
Level 7
Weight 4
Character 7.2
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 2.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 7.2
Dual form 7.4.c.a.4.1

$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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 −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −3.50000 6.06218i −0.673575 1.16667i −0.976883 0.213774i \(-0.931424\pi\)
0.303308 0.952893i \(-0.401909\pi\)
\(4\) 2.00000 + 3.46410i 0.250000 + 0.433013i
\(5\) −3.50000 + 6.06218i −0.313050 + 0.542218i −0.979021 0.203760i \(-0.934684\pi\)
0.665971 + 0.745977i \(0.268017\pi\)
\(6\) 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 0.898252 0.439480i \(-0.144837\pi\)
−0.829727 + 0.558169i \(0.811504\pi\)
\(12\) 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 0.931154 0.364626i \(-0.118803\pi\)
−0.781353 + 0.624090i \(0.785470\pi\)
\(18\) −22.0000 38.1051i −0.288081 0.498970i
\(19\) −24.5000 + 42.4352i −0.295826 + 0.512385i −0.975177 0.221429i \(-0.928928\pi\)
0.679351 + 0.733813i \(0.262261\pi\)
\(20\) −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 −0.239971 0.970780i \(-0.577138\pi\)
0.960706 0.277569i \(-0.0895287\pi\)
\(24\) 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 0.570660 0.821186i \(-0.306687\pi\)
−0.996498 + 0.0836128i \(0.973354\pi\)
\(32\) −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 −0.999880 0.0154821i \(-0.995072\pi\)
0.513348 + 0.858181i \(0.328405\pi\)
\(38\) −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 0.0948921 + 0.995488i \(0.469749\pi\)
−0.909564 + 0.415565i \(0.863584\pi\)
\(48\) −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 0.600153 0.799885i \(-0.295106\pi\)
−0.992797 + 0.119806i \(0.961773\pi\)
\(54\) 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 0.918118 0.396308i \(-0.129709\pi\)
−0.802272 + 0.596959i \(0.796375\pi\)
\(60\) 98.0000 + 169.741i 0.210862 + 0.365224i
\(61\) 206.500 357.668i 0.433436 0.750734i −0.563730 0.825959i \(-0.690634\pi\)
0.997167 + 0.0752252i \(0.0239676\pi\)
\(62\) 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 0.612463 0.790499i \(-0.290179\pi\)
−0.990824 + 0.135159i \(0.956845\pi\)
\(68\) −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 0.837186 + 0.546919i \(0.184199\pi\)
0.0550526 + 0.998483i \(0.482467\pi\)
\(74\) −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 −0.827021 0.562171i \(-0.809966\pi\)
0.900365 + 0.435135i \(0.143299\pi\)
\(80\) 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 −0.751281 0.659982i \(-0.770564\pi\)
0.947202 + 0.320637i \(0.103897\pi\)
\(90\) 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 −0.975196 0.221341i \(-0.928957\pi\)
0.295911 0.955215i \(-0.404377\pi\)
\(102\) 147.000 + 254.611i 0.142698 + 0.247160i
\(103\) 339.500 588.031i 0.324776 0.562529i −0.656691 0.754160i \(-0.728044\pi\)
0.981467 + 0.191631i \(0.0613777\pi\)
\(104\) 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 −0.950593 0.310440i \(-0.899524\pi\)
0.744145 + 0.668018i \(0.232857\pi\)
\(108\) −70.0000 121.244i −0.0623681 0.108025i
\(109\) 562.500 + 974.279i 0.494291 + 0.856137i 0.999978 0.00657959i \(-0.00209436\pi\)
−0.505687 + 0.862717i \(0.668761\pi\)
\(110\) 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 0.245687 + 0.969349i \(0.420986\pi\)
−0.962325 + 0.271903i \(0.912347\pi\)
\(132\) 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 0.986387 0.164439i \(-0.0525813\pi\)
−0.635602 + 0.772017i \(0.719248\pi\)
\(138\) 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 −0.837074 0.547090i \(-0.815736\pi\)
0.892331 + 0.451382i \(0.149069\pi\)
\(150\) 532.000 + 921.451i 0.289584 + 0.501574i
\(151\) −809.500 1402.10i −0.436266 0.755635i 0.561132 0.827726i \(-0.310366\pi\)
−0.997398 + 0.0720914i \(0.977033\pi\)
\(152\) 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 0.766741 0.641956i \(-0.221877\pi\)
−0.939321 + 0.343039i \(0.888544\pi\)
\(158\) 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 −0.804455 0.594014i \(-0.797543\pi\)
0.916658 + 0.399672i \(0.130876\pi\)
\(164\) 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 −0.369633 0.929178i \(-0.620517\pi\)
0.989508 0.144477i \(-0.0461499\pi\)
\(174\) 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 0.975233 + 0.221180i \(0.0709907\pi\)
−0.296069 + 0.955166i \(0.595676\pi\)
\(180\) 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 −0.999838 0.0179887i \(-0.994274\pi\)
0.515498 + 0.856891i \(0.327607\pi\)
\(192\) −1568.00 2715.86i −0.589378 1.02083i
\(193\) 198.500 + 343.812i 0.0740329 + 0.128229i 0.900665 0.434514i \(-0.143080\pi\)
−0.826632 + 0.562742i \(0.809746\pi\)
\(194\) 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 −0.993587 0.113066i \(-0.963933\pi\)
0.398875 0.917005i \(-0.369401\pi\)
\(200\) −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 0.980974 0.194138i \(-0.0621908\pi\)
−0.658615 + 0.752480i \(0.728858\pi\)
\(228\) 686.000 + 1188.19i 0.199261 + 0.345130i
\(229\) −143.500 + 248.549i −0.0414094 + 0.0717231i −0.885987 0.463710i \(-0.846518\pi\)
0.844578 + 0.535433i \(0.179851\pi\)
\(230\) −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 0.339475 + 0.940615i \(0.389751\pi\)
−0.984334 + 0.176314i \(0.943583\pi\)
\(234\) 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 0.998722 0.0505456i \(-0.0160960\pi\)
−0.543135 + 0.839646i \(0.682763\pi\)
\(242\) 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 −0.813036 0.582213i \(-0.802187\pi\)
0.910730 + 0.413003i \(0.135520\pi\)
\(258\) −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 0.880696 0.473681i \(-0.157075\pi\)
−0.850568 + 0.525865i \(0.823742\pi\)
\(264\) −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 0.587583 0.809164i \(-0.300080\pi\)
−0.994548 + 0.104280i \(0.966746\pi\)
\(270\) 245.000 + 424.352i 0.0552231 + 0.0956491i
\(271\) −696.500 + 1206.37i −0.156123 + 0.270413i −0.933467 0.358662i \(-0.883233\pi\)
0.777344 + 0.629075i \(0.216566\pi\)
\(272\) 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 0.842643 0.538472i \(-0.180998\pi\)
−0.887652 + 0.460514i \(0.847665\pi\)
\(278\) −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 0.998333 0.0577087i \(-0.0183795\pi\)
−0.549144 + 0.835728i \(0.685046\pi\)
\(284\) −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 −0.814936 0.579550i \(-0.803228\pi\)
−0.0944372 0.995531i \(-0.530105\pi\)
\(312\) −1176.00 2036.89i −0.213391 0.369603i
\(313\) 2376.50 4116.22i 0.429162 0.743330i −0.567637 0.823279i \(-0.692142\pi\)
0.996799 + 0.0799485i \(0.0254756\pi\)
\(314\) 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 −0.669905 0.742447i \(-0.733665\pi\)
0.977930 + 0.208932i \(0.0669987\pi\)
\(318\) −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 −0.970738 0.240143i \(-0.922806\pi\)
0.693339 + 0.720612i \(0.256139\pi\)
\(332\) 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 −0.996195 0.0871487i \(-0.972224\pi\)
0.422625 0.906305i \(-0.361109\pi\)
\(348\) 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 0.814307 0.580435i \(-0.197117\pi\)
−0.909825 + 0.414993i \(0.863784\pi\)
\(354\) 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 −0.985241 0.171173i \(-0.945244\pi\)
0.640861 + 0.767657i \(0.278578\pi\)
\(360\) 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 0.982522 0.186148i \(-0.0596004\pi\)
−0.652470 + 0.757815i \(0.726267\pi\)
\(368\) −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 −0.380565 0.924754i \(-0.624270\pi\)
0.991143 0.132798i \(-0.0423963\pi\)
\(374\) −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 0.331390 + 0.943494i \(0.392482\pi\)
−0.982785 + 0.184755i \(0.940851\pi\)
\(384\) −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 0.804093 0.594504i \(-0.202651\pi\)
−0.916902 + 0.399113i \(0.869318\pi\)
\(390\) 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 0.276206 + 0.961099i \(0.410923\pi\)
−0.970439 + 0.241348i \(0.922410\pi\)
\(398\) 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 −0.995015 0.0997232i \(-0.968204\pi\)
0.583870 + 0.811847i \(0.301538\pi\)
\(402\) −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 −0.980033 0.198835i \(-0.936284\pi\)
0.317820 0.948151i \(-0.397049\pi\)
\(410\) −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 0.695064 0.718948i \(-0.255376\pi\)
−0.970159 + 0.242468i \(0.922043\pi\)
\(432\) −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 −0.729800 0.683660i \(-0.760387\pi\)
0.956967 + 0.290195i \(0.0937203\pi\)
\(440\) 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 −0.277576 0.960704i \(-0.589531\pi\)
0.970782 0.239964i \(-0.0771356\pi\)
\(444\) 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 −0.997209 0.0746560i \(-0.976214\pi\)
0.563259 + 0.826281i \(0.309547\pi\)
\(458\) −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 −0.683595 0.729861i \(-0.739585\pi\)
0.973876 + 0.227080i \(0.0729180\pi\)
\(468\) 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 0.668240 0.743946i \(-0.267048\pi\)
−0.978396 + 0.206740i \(0.933715\pi\)
\(480\) −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 0.949414 + 0.314028i \(0.101678\pi\)
−0.202751 + 0.979230i \(0.564988\pi\)
\(488\) −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 −0.540833 0.841130i \(-0.681891\pi\)
0.998856 + 0.0478104i \(0.0152243\pi\)
\(500\) −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 −0.583320 0.812242i \(-0.698247\pi\)
0.995083 + 0.0990489i \(0.0315800\pi\)
\(510\) −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 0.942740 + 0.333528i \(0.108239\pi\)
−0.182526 + 0.983201i \(0.558427\pi\)
\(522\) −1276.00 2210.10i −0.106990 0.185313i
\(523\) −10188.5 + 17647.0i −0.851839 + 1.47543i 0.0277071 + 0.999616i \(0.491179\pi\)
−0.879546 + 0.475813i \(0.842154\pi\)
\(524\) −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 −0.716355 0.697736i \(-0.754191\pi\)
0.962435 + 0.271514i \(0.0875243\pi\)
\(542\) −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 0.987631 0.156796i \(-0.0501164\pi\)
−0.629604 + 0.776916i \(0.716783\pi\)
\(558\) −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 0.799928 0.600097i \(-0.204871\pi\)
−0.919663 + 0.392709i \(0.871538\pi\)
\(564\) 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 0.127701 + 0.991813i \(0.459240\pi\)
−0.922785 + 0.385314i \(0.874093\pi\)
\(570\) −2401.00 4158.65i −0.176433 0.305591i
\(571\) −10133.5 17551.7i −0.742686 1.28637i −0.951268 0.308365i \(-0.900218\pi\)
0.208582 0.978005i \(-0.433115\pi\)
\(572\) 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 −0.999993 0.00379418i \(-0.998792\pi\)
0.496711 0.867916i \(-0.334541\pi\)
\(578\) 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 −0.862735 0.505657i \(-0.831250\pi\)
0.869279 + 0.494322i \(0.164584\pi\)
\(594\) 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 0.986362 0.164589i \(-0.0526297\pi\)
−0.635719 + 0.771920i \(0.719296\pi\)
\(600\) −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 −0.936820 0.349812i \(-0.886246\pi\)
0.771356 + 0.636404i \(0.219579\pi\)
\(608\) 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 0.999718 + 0.0237416i \(0.00755791\pi\)
−0.479298 + 0.877652i \(0.659109\pi\)
\(614\) 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 0.925562 + 0.378595i \(0.123593\pi\)
−0.134908 + 0.990858i \(0.543074\pi\)
\(620\) 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 0.881616 0.471967i \(-0.156456\pi\)
−0.849544 + 0.527518i \(0.823123\pi\)
\(642\) −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 0.911050 0.412295i \(-0.135273\pi\)
−0.812583 + 0.582845i \(0.801939\pi\)
\(648\) −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 −0.702363 0.711819i \(-0.747872\pi\)
0.967635 + 0.252355i \(0.0812051\pi\)
\(654\) 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 0.987234 0.159277i \(-0.0509163\pi\)
−0.631555 + 0.775331i \(0.717583\pi\)
\(662\) −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 0.000164659 1.00000i \(-0.499948\pi\)
0.865943 0.500143i \(-0.166719\pi\)
\(678\) −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 0.659350 0.751836i \(-0.270831\pi\)
−0.980784 + 0.195096i \(0.937498\pi\)
\(684\) 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 −0.152862 0.988248i \(-0.548849\pi\)
0.932279 0.361741i \(-0.117818\pi\)
\(692\) 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 −0.969570 0.244814i \(-0.921273\pi\)
0.696801 + 0.717265i \(0.254606\pi\)
\(710\) 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 0.0431924 + 0.999067i \(0.486247\pi\)
−0.886813 + 0.462128i \(0.847086\pi\)
\(720\) −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 0.265616 + 0.964079i \(0.414425\pi\)
−0.967725 + 0.252009i \(0.918909\pi\)
\(734\) −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 0.513574 0.858045i \(-0.328321\pi\)
−0.999876 + 0.0157460i \(0.994988\pi\)
\(740\) 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 0.291704 + 0.956509i \(0.405778\pi\)
−0.974213 + 0.225631i \(0.927556\pi\)
\(752\) 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 −0.855590 0.517654i \(-0.826805\pi\)
0.876097 + 0.482136i \(0.160139\pi\)
\(762\) 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 0.607761 0.794120i \(-0.292068\pi\)
−0.991609 + 0.129277i \(0.958734\pi\)
\(774\) 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