Properties

Label 49.4.c.c.18.1
Level $49$
Weight $4$
Character 49.18
Analytic conductor $2.891$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.89109359028\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 18.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.4.c.c.30.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(-8.00000 - 13.8564i) q^{5} +2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(-8.00000 - 13.8564i) q^{5} +2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(8.00000 - 13.8564i) q^{10} +(4.00000 - 6.92820i) q^{11} +(-7.00000 - 12.1244i) q^{12} +28.0000 q^{13} -32.0000 q^{15} +(-20.5000 - 35.5070i) q^{16} +(-27.0000 + 46.7654i) q^{17} +(-11.5000 + 19.9186i) q^{18} +(55.0000 + 95.2628i) q^{19} -112.000 q^{20} +8.00000 q^{22} +(-24.0000 - 41.5692i) q^{23} +(15.0000 - 25.9808i) q^{24} +(-65.5000 + 113.449i) q^{25} +(14.0000 + 24.2487i) q^{26} +100.000 q^{27} -110.000 q^{29} +(-16.0000 - 27.7128i) q^{30} +(-6.00000 + 10.3923i) q^{31} +(80.5000 - 139.430i) q^{32} +(-8.00000 - 13.8564i) q^{33} -54.0000 q^{34} +161.000 q^{36} +(123.000 + 213.042i) q^{37} +(-55.0000 + 95.2628i) q^{38} +(28.0000 - 48.4974i) q^{39} +(-120.000 - 207.846i) q^{40} +182.000 q^{41} +128.000 q^{43} +(-28.0000 - 48.4974i) q^{44} +(184.000 - 318.697i) q^{45} +(24.0000 - 41.5692i) q^{46} +(-162.000 - 280.592i) q^{47} -82.0000 q^{48} -131.000 q^{50} +(54.0000 + 93.5307i) q^{51} +(98.0000 - 169.741i) q^{52} +(81.0000 - 140.296i) q^{53} +(50.0000 + 86.6025i) q^{54} -128.000 q^{55} +220.000 q^{57} +(-55.0000 - 95.2628i) q^{58} +(-405.000 + 701.481i) q^{59} +(-112.000 + 193.990i) q^{60} +(244.000 + 422.620i) q^{61} -12.0000 q^{62} -167.000 q^{64} +(-224.000 - 387.979i) q^{65} +(8.00000 - 13.8564i) q^{66} +(-122.000 + 211.310i) q^{67} +(189.000 + 327.358i) q^{68} -96.0000 q^{69} -768.000 q^{71} +(172.500 + 298.779i) q^{72} +(351.000 - 607.950i) q^{73} +(-123.000 + 213.042i) q^{74} +(131.000 + 226.899i) q^{75} +770.000 q^{76} +56.0000 q^{78} +(-220.000 - 381.051i) q^{79} +(-328.000 + 568.113i) q^{80} +(-210.500 + 364.597i) q^{81} +(91.0000 + 157.617i) q^{82} -1302.00 q^{83} +864.000 q^{85} +(64.0000 + 110.851i) q^{86} +(-110.000 + 190.526i) q^{87} +(60.0000 - 103.923i) q^{88} +(-365.000 - 632.199i) q^{89} +368.000 q^{90} -336.000 q^{92} +(12.0000 + 20.7846i) q^{93} +(162.000 - 280.592i) q^{94} +(880.000 - 1524.20i) q^{95} +(-161.000 - 278.860i) q^{96} +294.000 q^{97} +184.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 2q^{3} + 7q^{4} - 16q^{5} + 4q^{6} + 30q^{8} + 23q^{9} + O(q^{10}) \) \( 2q + q^{2} + 2q^{3} + 7q^{4} - 16q^{5} + 4q^{6} + 30q^{8} + 23q^{9} + 16q^{10} + 8q^{11} - 14q^{12} + 56q^{13} - 64q^{15} - 41q^{16} - 54q^{17} - 23q^{18} + 110q^{19} - 224q^{20} + 16q^{22} - 48q^{23} + 30q^{24} - 131q^{25} + 28q^{26} + 200q^{27} - 220q^{29} - 32q^{30} - 12q^{31} + 161q^{32} - 16q^{33} - 108q^{34} + 322q^{36} + 246q^{37} - 110q^{38} + 56q^{39} - 240q^{40} + 364q^{41} + 256q^{43} - 56q^{44} + 368q^{45} + 48q^{46} - 324q^{47} - 164q^{48} - 262q^{50} + 108q^{51} + 196q^{52} + 162q^{53} + 100q^{54} - 256q^{55} + 440q^{57} - 110q^{58} - 810q^{59} - 224q^{60} + 488q^{61} - 24q^{62} - 334q^{64} - 448q^{65} + 16q^{66} - 244q^{67} + 378q^{68} - 192q^{69} - 1536q^{71} + 345q^{72} + 702q^{73} - 246q^{74} + 262q^{75} + 1540q^{76} + 112q^{78} - 440q^{79} - 656q^{80} - 421q^{81} + 182q^{82} - 2604q^{83} + 1728q^{85} + 128q^{86} - 220q^{87} + 120q^{88} - 730q^{89} + 736q^{90} - 672q^{92} + 24q^{93} + 324q^{94} + 1760q^{95} - 322q^{96} + 588q^{97} + 368q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.176777 + 0.306186i 0.940775 0.339032i \(-0.110100\pi\)
−0.763998 + 0.645219i \(0.776766\pi\)
\(3\) 1.00000 1.73205i 0.192450 0.333333i −0.753612 0.657320i \(-0.771690\pi\)
0.946062 + 0.323987i \(0.105023\pi\)
\(4\) 3.50000 6.06218i 0.437500 0.757772i
\(5\) −8.00000 13.8564i −0.715542 1.23935i −0.962750 0.270392i \(-0.912847\pi\)
0.247208 0.968962i \(-0.420487\pi\)
\(6\) 2.00000 0.136083
\(7\) 0 0
\(8\) 15.0000 0.662913
\(9\) 11.5000 + 19.9186i 0.425926 + 0.737725i
\(10\) 8.00000 13.8564i 0.252982 0.438178i
\(11\) 4.00000 6.92820i 0.109640 0.189903i −0.805984 0.591937i \(-0.798363\pi\)
0.915625 + 0.402034i \(0.131697\pi\)
\(12\) −7.00000 12.1244i −0.168394 0.291667i
\(13\) 28.0000 0.597369 0.298685 0.954352i \(-0.403452\pi\)
0.298685 + 0.954352i \(0.403452\pi\)
\(14\) 0 0
\(15\) −32.0000 −0.550824
\(16\) −20.5000 35.5070i −0.320312 0.554798i
\(17\) −27.0000 + 46.7654i −0.385204 + 0.667192i −0.991797 0.127820i \(-0.959202\pi\)
0.606594 + 0.795012i \(0.292535\pi\)
\(18\) −11.5000 + 19.9186i −0.150588 + 0.260825i
\(19\) 55.0000 + 95.2628i 0.664098 + 1.15025i 0.979529 + 0.201303i \(0.0645177\pi\)
−0.315431 + 0.948949i \(0.602149\pi\)
\(20\) −112.000 −1.25220
\(21\) 0 0
\(22\) 8.00000 0.0775275
\(23\) −24.0000 41.5692i −0.217580 0.376860i 0.736487 0.676451i \(-0.236483\pi\)
−0.954068 + 0.299591i \(0.903150\pi\)
\(24\) 15.0000 25.9808i 0.127578 0.220971i
\(25\) −65.5000 + 113.449i −0.524000 + 0.907595i
\(26\) 14.0000 + 24.2487i 0.105601 + 0.182906i
\(27\) 100.000 0.712778
\(28\) 0 0
\(29\) −110.000 −0.704362 −0.352181 0.935932i \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(30\) −16.0000 27.7128i −0.0973729 0.168655i
\(31\) −6.00000 + 10.3923i −0.0347623 + 0.0602101i −0.882883 0.469593i \(-0.844401\pi\)
0.848121 + 0.529803i \(0.177734\pi\)
\(32\) 80.5000 139.430i 0.444704 0.770250i
\(33\) −8.00000 13.8564i −0.0422006 0.0730937i
\(34\) −54.0000 −0.272380
\(35\) 0 0
\(36\) 161.000 0.745370
\(37\) 123.000 + 213.042i 0.546516 + 0.946593i 0.998510 + 0.0545719i \(0.0173794\pi\)
−0.451994 + 0.892021i \(0.649287\pi\)
\(38\) −55.0000 + 95.2628i −0.234794 + 0.406675i
\(39\) 28.0000 48.4974i 0.114964 0.199123i
\(40\) −120.000 207.846i −0.474342 0.821584i
\(41\) 182.000 0.693259 0.346630 0.938002i \(-0.387326\pi\)
0.346630 + 0.938002i \(0.387326\pi\)
\(42\) 0 0
\(43\) 128.000 0.453949 0.226975 0.973901i \(-0.427117\pi\)
0.226975 + 0.973901i \(0.427117\pi\)
\(44\) −28.0000 48.4974i −0.0959354 0.166165i
\(45\) 184.000 318.697i 0.609536 1.05575i
\(46\) 24.0000 41.5692i 0.0769262 0.133240i
\(47\) −162.000 280.592i −0.502769 0.870821i −0.999995 0.00319997i \(-0.998981\pi\)
0.497226 0.867621i \(-0.334352\pi\)
\(48\) −82.0000 −0.246577
\(49\) 0 0
\(50\) −131.000 −0.370524
\(51\) 54.0000 + 93.5307i 0.148265 + 0.256802i
\(52\) 98.0000 169.741i 0.261349 0.452670i
\(53\) 81.0000 140.296i 0.209928 0.363607i −0.741763 0.670662i \(-0.766010\pi\)
0.951692 + 0.307055i \(0.0993436\pi\)
\(54\) 50.0000 + 86.6025i 0.126003 + 0.218243i
\(55\) −128.000 −0.313809
\(56\) 0 0
\(57\) 220.000 0.511223
\(58\) −55.0000 95.2628i −0.124515 0.215666i
\(59\) −405.000 + 701.481i −0.893670 + 1.54788i −0.0582271 + 0.998303i \(0.518545\pi\)
−0.835442 + 0.549578i \(0.814789\pi\)
\(60\) −112.000 + 193.990i −0.240986 + 0.417399i
\(61\) 244.000 + 422.620i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) −12.0000 −0.0245807
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) −224.000 387.979i −0.427443 0.740353i
\(66\) 8.00000 13.8564i 0.0149202 0.0258425i
\(67\) −122.000 + 211.310i −0.222458 + 0.385308i −0.955554 0.294817i \(-0.904741\pi\)
0.733096 + 0.680125i \(0.238075\pi\)
\(68\) 189.000 + 327.358i 0.337053 + 0.583793i
\(69\) −96.0000 −0.167493
\(70\) 0 0
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) 172.500 + 298.779i 0.282352 + 0.489047i
\(73\) 351.000 607.950i 0.562759 0.974728i −0.434495 0.900674i \(-0.643073\pi\)
0.997254 0.0740537i \(-0.0235936\pi\)
\(74\) −123.000 + 213.042i −0.193222 + 0.334671i
\(75\) 131.000 + 226.899i 0.201688 + 0.349333i
\(76\) 770.000 1.16217
\(77\) 0 0
\(78\) 56.0000 0.0812917
\(79\) −220.000 381.051i −0.313316 0.542679i 0.665762 0.746164i \(-0.268106\pi\)
−0.979078 + 0.203485i \(0.934773\pi\)
\(80\) −328.000 + 568.113i −0.458394 + 0.793962i
\(81\) −210.500 + 364.597i −0.288752 + 0.500133i
\(82\) 91.0000 + 157.617i 0.122552 + 0.212266i
\(83\) −1302.00 −1.72184 −0.860922 0.508737i \(-0.830113\pi\)
−0.860922 + 0.508737i \(0.830113\pi\)
\(84\) 0 0
\(85\) 864.000 1.10252
\(86\) 64.0000 + 110.851i 0.0802476 + 0.138993i
\(87\) −110.000 + 190.526i −0.135554 + 0.234787i
\(88\) 60.0000 103.923i 0.0726821 0.125889i
\(89\) −365.000 632.199i −0.434718 0.752954i 0.562554 0.826760i \(-0.309819\pi\)
−0.997273 + 0.0738062i \(0.976485\pi\)
\(90\) 368.000 0.431007
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) 12.0000 + 20.7846i 0.0133800 + 0.0231749i
\(94\) 162.000 280.592i 0.177756 0.307882i
\(95\) 880.000 1524.20i 0.950380 1.64611i
\(96\) −161.000 278.860i −0.171167 0.296469i
\(97\) 294.000 0.307744 0.153872 0.988091i \(-0.450826\pi\)
0.153872 + 0.988091i \(0.450826\pi\)
\(98\) 0 0
\(99\) 184.000 0.186795
\(100\) 458.500 + 794.145i 0.458500 + 0.794145i
\(101\) 344.000 595.825i 0.338904 0.586999i −0.645323 0.763910i \(-0.723277\pi\)
0.984227 + 0.176911i \(0.0566106\pi\)
\(102\) −54.0000 + 93.5307i −0.0524196 + 0.0907934i
\(103\) −694.000 1202.04i −0.663901 1.14991i −0.979582 0.201046i \(-0.935566\pi\)
0.315680 0.948866i \(-0.397767\pi\)
\(104\) 420.000 0.396004
\(105\) 0 0
\(106\) 162.000 0.148442
\(107\) −122.000 211.310i −0.110226 0.190917i 0.805635 0.592412i \(-0.201824\pi\)
−0.915861 + 0.401495i \(0.868491\pi\)
\(108\) 350.000 606.218i 0.311840 0.540123i
\(109\) −45.0000 + 77.9423i −0.0395433 + 0.0684910i −0.885120 0.465363i \(-0.845924\pi\)
0.845576 + 0.533854i \(0.179257\pi\)
\(110\) −64.0000 110.851i −0.0554742 0.0960841i
\(111\) 492.000 0.420708
\(112\) 0 0
\(113\) 1318.00 1.09723 0.548615 0.836075i \(-0.315155\pi\)
0.548615 + 0.836075i \(0.315155\pi\)
\(114\) 110.000 + 190.526i 0.0903723 + 0.156529i
\(115\) −384.000 + 665.108i −0.311376 + 0.539318i
\(116\) −385.000 + 666.840i −0.308158 + 0.533746i
\(117\) 322.000 + 557.720i 0.254435 + 0.440695i
\(118\) −810.000 −0.631920
\(119\) 0 0
\(120\) −480.000 −0.365148
\(121\) 633.500 + 1097.25i 0.475958 + 0.824383i
\(122\) −244.000 + 422.620i −0.181071 + 0.313625i
\(123\) 182.000 315.233i 0.133418 0.231086i
\(124\) 42.0000 + 72.7461i 0.0304170 + 0.0526838i
\(125\) 96.0000 0.0686920
\(126\) 0 0
\(127\) −1776.00 −1.24090 −0.620451 0.784245i \(-0.713050\pi\)
−0.620451 + 0.784245i \(0.713050\pi\)
\(128\) −727.500 1260.07i −0.502363 0.870119i
\(129\) 128.000 221.703i 0.0873626 0.151316i
\(130\) 224.000 387.979i 0.151124 0.261754i
\(131\) 559.000 + 968.216i 0.372825 + 0.645752i 0.989999 0.141075i \(-0.0450559\pi\)
−0.617174 + 0.786827i \(0.711723\pi\)
\(132\) −112.000 −0.0738511
\(133\) 0 0
\(134\) −244.000 −0.157301
\(135\) −800.000 1385.64i −0.510022 0.883385i
\(136\) −405.000 + 701.481i −0.255356 + 0.442290i
\(137\) −1137.00 + 1969.34i −0.709054 + 1.22812i 0.256154 + 0.966636i \(0.417545\pi\)
−0.965208 + 0.261482i \(0.915789\pi\)
\(138\) −48.0000 83.1384i −0.0296089 0.0512842i
\(139\) −210.000 −0.128144 −0.0640718 0.997945i \(-0.520409\pi\)
−0.0640718 + 0.997945i \(0.520409\pi\)
\(140\) 0 0
\(141\) −648.000 −0.387032
\(142\) −384.000 665.108i −0.226934 0.393060i
\(143\) 112.000 193.990i 0.0654959 0.113442i
\(144\) 471.500 816.662i 0.272859 0.472605i
\(145\) 880.000 + 1524.20i 0.504000 + 0.872954i
\(146\) 702.000 0.397931
\(147\) 0 0
\(148\) 1722.00 0.956402
\(149\) 1005.00 + 1740.71i 0.552569 + 0.957078i 0.998088 + 0.0618054i \(0.0196858\pi\)
−0.445519 + 0.895272i \(0.646981\pi\)
\(150\) −131.000 + 226.899i −0.0713074 + 0.123508i
\(151\) −556.000 + 963.020i −0.299647 + 0.519003i −0.976055 0.217524i \(-0.930202\pi\)
0.676408 + 0.736527i \(0.263535\pi\)
\(152\) 825.000 + 1428.94i 0.440239 + 0.762516i
\(153\) −1242.00 −0.656273
\(154\) 0 0
\(155\) 192.000 0.0994956
\(156\) −196.000 339.482i −0.100593 0.174233i
\(157\) −62.0000 + 107.387i −0.0315168 + 0.0545887i −0.881354 0.472457i \(-0.843367\pi\)
0.849837 + 0.527046i \(0.176700\pi\)
\(158\) 220.000 381.051i 0.110774 0.191866i
\(159\) −162.000 280.592i −0.0808015 0.139952i
\(160\) −2576.00 −1.27282
\(161\) 0 0
\(162\) −421.000 −0.204178
\(163\) −1004.00 1738.98i −0.482450 0.835628i 0.517347 0.855776i \(-0.326920\pi\)
−0.999797 + 0.0201478i \(0.993586\pi\)
\(164\) 637.000 1103.32i 0.303301 0.525333i
\(165\) −128.000 + 221.703i −0.0603926 + 0.104603i
\(166\) −651.000 1127.57i −0.304382 0.527205i
\(167\) 2884.00 1.33635 0.668176 0.744004i \(-0.267076\pi\)
0.668176 + 0.744004i \(0.267076\pi\)
\(168\) 0 0
\(169\) −1413.00 −0.643150
\(170\) 432.000 + 748.246i 0.194899 + 0.337576i
\(171\) −1265.00 + 2191.04i −0.565713 + 0.979844i
\(172\) 448.000 775.959i 0.198603 0.343990i
\(173\) −1114.00 1929.50i −0.489571 0.847963i 0.510357 0.859963i \(-0.329513\pi\)
−0.999928 + 0.0120003i \(0.996180\pi\)
\(174\) −220.000 −0.0958515
\(175\) 0 0
\(176\) −328.000 −0.140477
\(177\) 810.000 + 1402.96i 0.343974 + 0.595780i
\(178\) 365.000 632.199i 0.153696 0.266209i
\(179\) 410.000 710.141i 0.171200 0.296527i −0.767640 0.640882i \(-0.778569\pi\)
0.938840 + 0.344354i \(0.111902\pi\)
\(180\) −1288.00 2230.88i −0.533344 0.923778i
\(181\) 3892.00 1.59829 0.799144 0.601140i \(-0.205287\pi\)
0.799144 + 0.601140i \(0.205287\pi\)
\(182\) 0 0
\(183\) 976.000 0.394251
\(184\) −360.000 623.538i −0.144237 0.249825i
\(185\) 1968.00 3408.68i 0.782109 1.35465i
\(186\) −12.0000 + 20.7846i −0.00473055 + 0.00819356i
\(187\) 216.000 + 374.123i 0.0844678 + 0.146303i
\(188\) −2268.00 −0.879845
\(189\) 0 0
\(190\) 1760.00 0.672020
\(191\) 2524.00 + 4371.70i 0.956179 + 1.65615i 0.731646 + 0.681684i \(0.238752\pi\)
0.224533 + 0.974466i \(0.427914\pi\)
\(192\) −167.000 + 289.252i −0.0627718 + 0.108724i
\(193\) 1481.00 2565.17i 0.552356 0.956709i −0.445748 0.895159i \(-0.647062\pi\)
0.998104 0.0615502i \(-0.0196044\pi\)
\(194\) 147.000 + 254.611i 0.0544020 + 0.0942270i
\(195\) −896.000 −0.329046
\(196\) 0 0
\(197\) 3334.00 1.20577 0.602887 0.797826i \(-0.294017\pi\)
0.602887 + 0.797826i \(0.294017\pi\)
\(198\) 92.0000 + 159.349i 0.0330210 + 0.0571940i
\(199\) −930.000 + 1610.81i −0.331286 + 0.573805i −0.982764 0.184863i \(-0.940816\pi\)
0.651478 + 0.758667i \(0.274149\pi\)
\(200\) −982.500 + 1701.74i −0.347366 + 0.601656i
\(201\) 244.000 + 422.620i 0.0856240 + 0.148305i
\(202\) 688.000 0.239641
\(203\) 0 0
\(204\) 756.000 0.259464
\(205\) −1456.00 2521.87i −0.496056 0.859194i
\(206\) 694.000 1202.04i 0.234725 0.406555i
\(207\) 552.000 956.092i 0.185346 0.321029i
\(208\) −574.000 994.197i −0.191345 0.331419i
\(209\) 880.000 0.291248
\(210\) 0 0
\(211\) −4268.00 −1.39252 −0.696259 0.717791i \(-0.745153\pi\)
−0.696259 + 0.717791i \(0.745153\pi\)
\(212\) −567.000 982.073i −0.183687 0.318156i
\(213\) −768.000 + 1330.22i −0.247054 + 0.427910i
\(214\) 122.000 211.310i 0.0389708 0.0674994i
\(215\) −1024.00 1773.62i −0.324820 0.562604i
\(216\) 1500.00 0.472510
\(217\) 0 0
\(218\) −90.0000 −0.0279613
\(219\) −702.000 1215.90i −0.216606 0.375173i
\(220\) −448.000 + 775.959i −0.137292 + 0.237796i
\(221\) −756.000 + 1309.43i −0.230109 + 0.398560i
\(222\) 246.000 + 426.084i 0.0743713 + 0.128815i
\(223\) −5432.00 −1.63118 −0.815591 0.578629i \(-0.803588\pi\)
−0.815591 + 0.578629i \(0.803588\pi\)
\(224\) 0 0
\(225\) −3013.00 −0.892741
\(226\) 659.000 + 1141.42i 0.193965 + 0.335957i
\(227\) 1023.00 1771.89i 0.299114 0.518081i −0.676819 0.736149i \(-0.736642\pi\)
0.975934 + 0.218068i \(0.0699756\pi\)
\(228\) 770.000 1333.68i 0.223660 0.387391i
\(229\) 1490.00 + 2580.76i 0.429965 + 0.744721i 0.996870 0.0790622i \(-0.0251926\pi\)
−0.566905 + 0.823783i \(0.691859\pi\)
\(230\) −768.000 −0.220176
\(231\) 0 0
\(232\) −1650.00 −0.466930
\(233\) −2229.00 3860.74i −0.626724 1.08552i −0.988205 0.153138i \(-0.951062\pi\)
0.361481 0.932379i \(-0.382271\pi\)
\(234\) −322.000 + 557.720i −0.0899564 + 0.155809i
\(235\) −2592.00 + 4489.48i −0.719504 + 1.24622i
\(236\) 2835.00 + 4910.36i 0.781961 + 1.35440i
\(237\) −880.000 −0.241190
\(238\) 0 0
\(239\) 4440.00 1.20167 0.600836 0.799372i \(-0.294834\pi\)
0.600836 + 0.799372i \(0.294834\pi\)
\(240\) 656.000 + 1136.23i 0.176436 + 0.305596i
\(241\) −1651.00 + 2859.62i −0.441287 + 0.764332i −0.997785 0.0665168i \(-0.978811\pi\)
0.556498 + 0.830849i \(0.312145\pi\)
\(242\) −633.500 + 1097.25i −0.168277 + 0.291464i
\(243\) 1771.00 + 3067.46i 0.467530 + 0.809785i
\(244\) 3416.00 0.896258
\(245\) 0 0
\(246\) 364.000 0.0943406
\(247\) 1540.00 + 2667.36i 0.396712 + 0.687125i
\(248\) −90.0000 + 155.885i −0.0230444 + 0.0399140i
\(249\) −1302.00 + 2255.13i −0.331369 + 0.573948i
\(250\) 48.0000 + 83.1384i 0.0121431 + 0.0210325i
\(251\) 1582.00 0.397829 0.198914 0.980017i \(-0.436258\pi\)
0.198914 + 0.980017i \(0.436258\pi\)
\(252\) 0 0
\(253\) −384.000 −0.0954224
\(254\) −888.000 1538.06i −0.219363 0.379947i
\(255\) 864.000 1496.49i 0.212180 0.367506i
\(256\) 59.5000 103.057i 0.0145264 0.0251604i
\(257\) −1177.00 2038.62i −0.285678 0.494809i 0.687095 0.726567i \(-0.258885\pi\)
−0.972773 + 0.231758i \(0.925552\pi\)
\(258\) 256.000 0.0617747
\(259\) 0 0
\(260\) −3136.00 −0.748025
\(261\) −1265.00 2191.04i −0.300006 0.519625i
\(262\) −559.000 + 968.216i −0.131813 + 0.228308i
\(263\) 1936.00 3353.25i 0.453912 0.786199i −0.544713 0.838623i \(-0.683361\pi\)
0.998625 + 0.0524239i \(0.0166947\pi\)
\(264\) −120.000 207.846i −0.0279753 0.0484547i
\(265\) −2592.00 −0.600850
\(266\) 0 0
\(267\) −1460.00 −0.334646
\(268\) 854.000 + 1479.17i 0.194651 + 0.337145i
\(269\) −90.0000 + 155.885i −0.0203992 + 0.0353325i −0.876045 0.482230i \(-0.839827\pi\)
0.855646 + 0.517562i \(0.173160\pi\)
\(270\) 800.000 1385.64i 0.180320 0.312324i
\(271\) −1016.00 1759.76i −0.227740 0.394458i 0.729398 0.684090i \(-0.239800\pi\)
−0.957138 + 0.289632i \(0.906467\pi\)
\(272\) 2214.00 0.493542
\(273\) 0 0
\(274\) −2274.00 −0.501377
\(275\) 524.000 + 907.595i 0.114903 + 0.199018i
\(276\) −336.000 + 581.969i −0.0732783 + 0.126922i
\(277\) 2713.00 4699.05i 0.588478 1.01927i −0.405954 0.913893i \(-0.633061\pi\)
0.994432 0.105380i \(-0.0336059\pi\)
\(278\) −105.000 181.865i −0.0226528 0.0392358i
\(279\) −276.000 −0.0592247
\(280\) 0 0
\(281\) 842.000 0.178753 0.0893764 0.995998i \(-0.471513\pi\)
0.0893764 + 0.995998i \(0.471513\pi\)
\(282\) −324.000 561.184i −0.0684182 0.118504i
\(283\) 1891.00 3275.31i 0.397202 0.687975i −0.596177 0.802853i \(-0.703314\pi\)
0.993380 + 0.114878i \(0.0366478\pi\)
\(284\) −2688.00 + 4655.75i −0.561632 + 0.972775i
\(285\) −1760.00 3048.41i −0.365801 0.633587i
\(286\) 224.000 0.0463126
\(287\) 0 0
\(288\) 3703.00 0.757644
\(289\) 998.500 + 1729.45i 0.203236 + 0.352016i
\(290\) −880.000 + 1524.20i −0.178191 + 0.308636i
\(291\) 294.000 509.223i 0.0592254 0.102581i
\(292\) −2457.00 4255.65i −0.492415 0.852887i
\(293\) −4312.00 −0.859760 −0.429880 0.902886i \(-0.641444\pi\)
−0.429880 + 0.902886i \(0.641444\pi\)
\(294\) 0 0
\(295\) 12960.0 2.55783
\(296\) 1845.00 + 3195.63i 0.362292 + 0.627508i
\(297\) 400.000 692.820i 0.0781493 0.135359i
\(298\) −1005.00 + 1740.71i −0.195363 + 0.338378i
\(299\) −672.000 1163.94i −0.129976 0.225125i
\(300\) 1834.00 0.352953
\(301\) 0 0
\(302\) −1112.00 −0.211882
\(303\) −688.000 1191.65i −0.130444 0.225936i
\(304\) 2255.00 3905.77i 0.425438 0.736880i
\(305\) 3904.00 6761.93i 0.732926 1.26946i
\(306\) −621.000 1075.60i −0.116014 0.200942i
\(307\) 2674.00 0.497112 0.248556 0.968618i \(-0.420044\pi\)
0.248556 + 0.968618i \(0.420044\pi\)
\(308\) 0 0
\(309\) −2776.00 −0.511072
\(310\) 96.0000 + 166.277i 0.0175885 + 0.0304642i
\(311\) 1884.00 3263.18i 0.343511 0.594978i −0.641571 0.767063i \(-0.721717\pi\)
0.985082 + 0.172085i \(0.0550505\pi\)
\(312\) 420.000 727.461i 0.0762110 0.132001i
\(313\) −1219.00 2111.37i −0.220134 0.381283i 0.734714 0.678376i \(-0.237316\pi\)
−0.954849 + 0.297093i \(0.903983\pi\)
\(314\) −124.000 −0.0222857
\(315\) 0 0
\(316\) −3080.00 −0.548302
\(317\) 1593.00 + 2759.16i 0.282245 + 0.488863i 0.971937 0.235239i \(-0.0755874\pi\)
−0.689692 + 0.724103i \(0.742254\pi\)
\(318\) 162.000 280.592i 0.0285676 0.0494806i
\(319\) −440.000 + 762.102i −0.0772266 + 0.133760i
\(320\) 1336.00 + 2314.02i 0.233390 + 0.404243i
\(321\) −488.000 −0.0848520
\(322\) 0 0
\(323\) −5940.00 −1.02325
\(324\) 1473.50 + 2552.18i 0.252658 + 0.437616i
\(325\) −1834.00 + 3176.58i −0.313022 + 0.542169i
\(326\) 1004.00 1738.98i 0.170572 0.295439i
\(327\) 90.0000 + 155.885i 0.0152202 + 0.0263622i
\(328\) 2730.00 0.459570
\(329\) 0 0
\(330\) −256.000 −0.0427040
\(331\) −4336.00 7510.17i −0.720025 1.24712i −0.960989 0.276585i \(-0.910797\pi\)
0.240965 0.970534i \(-0.422536\pi\)
\(332\) −4557.00 + 7892.96i −0.753307 + 1.30477i
\(333\) −2829.00 + 4899.97i −0.465550 + 0.806357i
\(334\) 1442.00 + 2497.62i 0.236236 + 0.409172i
\(335\) 3904.00 0.636711
\(336\) 0 0
\(337\) 814.000 0.131577 0.0657884 0.997834i \(-0.479044\pi\)
0.0657884 + 0.997834i \(0.479044\pi\)
\(338\) −706.500 1223.69i −0.113694 0.196924i
\(339\) 1318.00 2282.84i 0.211162 0.365743i
\(340\) 3024.00 5237.72i 0.482351 0.835457i
\(341\) 48.0000 + 83.1384i 0.00762271 + 0.0132029i
\(342\) −2530.00 −0.400020
\(343\) 0 0
\(344\) 1920.00 0.300929
\(345\) 768.000 + 1330.22i 0.119848 + 0.207584i
\(346\) 1114.00 1929.50i 0.173090 0.299800i
\(347\) −4672.00 + 8092.14i −0.722784 + 1.25190i 0.237095 + 0.971486i \(0.423805\pi\)
−0.959880 + 0.280413i \(0.909529\pi\)
\(348\) 770.000 + 1333.68i 0.118610 + 0.205439i
\(349\) −5180.00 −0.794496 −0.397248 0.917711i \(-0.630035\pi\)
−0.397248 + 0.917711i \(0.630035\pi\)
\(350\) 0 0
\(351\) 2800.00 0.425792
\(352\) −644.000 1115.44i −0.0975151 0.168901i
\(353\) −6089.00 + 10546.5i −0.918087 + 1.59017i −0.115770 + 0.993276i \(0.536933\pi\)
−0.802317 + 0.596898i \(0.796400\pi\)
\(354\) −810.000 + 1402.96i −0.121613 + 0.210640i
\(355\) 6144.00 + 10641.7i 0.918562 + 1.59100i
\(356\) −5110.00 −0.760757
\(357\) 0 0
\(358\) 820.000 0.121057
\(359\) −220.000 381.051i −0.0323431 0.0560198i 0.849401 0.527748i \(-0.176964\pi\)
−0.881744 + 0.471729i \(0.843630\pi\)
\(360\) 2760.00 4780.46i 0.404069 0.699868i
\(361\) −2620.50 + 4538.84i −0.382053 + 0.661735i
\(362\) 1946.00 + 3370.57i 0.282540 + 0.489374i
\(363\) 2534.00 0.366393
\(364\) 0 0
\(365\) −11232.0 −1.61071
\(366\) 488.000 + 845.241i 0.0696944 + 0.120714i
\(367\) 4908.00 8500.91i 0.698080 1.20911i −0.271051 0.962565i \(-0.587371\pi\)
0.969131 0.246546i \(-0.0792955\pi\)
\(368\) −984.000 + 1704.34i −0.139387 + 0.241426i
\(369\) 2093.00 + 3625.18i 0.295277 + 0.511435i
\(370\) 3936.00 0.553035
\(371\) 0 0
\(372\) 168.000 0.0234150
\(373\) 221.000 + 382.783i 0.0306781 + 0.0531361i 0.880957 0.473197i \(-0.156900\pi\)
−0.850279 + 0.526333i \(0.823567\pi\)
\(374\) −216.000 + 374.123i −0.0298639 + 0.0517258i
\(375\) 96.0000 166.277i 0.0132198 0.0228973i
\(376\) −2430.00 4208.88i −0.333292 0.577278i
\(377\) −3080.00 −0.420764
\(378\) 0 0
\(379\) −3960.00 −0.536706 −0.268353 0.963321i \(-0.586479\pi\)
−0.268353 + 0.963321i \(0.586479\pi\)
\(380\) −6160.00 10669.4i −0.831582 1.44034i
\(381\) −1776.00 + 3076.12i −0.238812 + 0.413634i
\(382\) −2524.00 + 4371.70i −0.338060 + 0.585538i
\(383\) −3354.00 5809.30i −0.447471 0.775043i 0.550750 0.834670i \(-0.314342\pi\)
−0.998221 + 0.0596280i \(0.981009\pi\)
\(384\) −2910.00 −0.386720
\(385\) 0 0
\(386\) 2962.00 0.390575
\(387\) 1472.00 + 2549.58i 0.193349 + 0.334890i
\(388\) 1029.00 1782.28i 0.134638 0.233200i
\(389\) 6675.00 11561.4i 0.870015 1.50691i 0.00803563 0.999968i \(-0.497442\pi\)
0.861980 0.506943i \(-0.169225\pi\)
\(390\) −448.000 775.959i −0.0581676 0.100749i
\(391\) 2592.00 0.335251
\(392\) 0 0
\(393\) 2236.00 0.287001
\(394\) 1667.00 + 2887.33i 0.213153 + 0.369192i
\(395\) −3520.00 + 6096.82i −0.448381 + 0.776618i
\(396\) 644.000 1115.44i 0.0817228 0.141548i
\(397\) 678.000 + 1174.33i 0.0857125 + 0.148458i 0.905695 0.423931i \(-0.139350\pi\)
−0.819982 + 0.572389i \(0.806017\pi\)
\(398\) −1860.00 −0.234255
\(399\) 0 0
\(400\) 5371.00 0.671375
\(401\) −3111.00 5388.41i −0.387421 0.671033i 0.604681 0.796468i \(-0.293301\pi\)
−0.992102 + 0.125435i \(0.959967\pi\)
\(402\) −244.000 + 422.620i −0.0302727 + 0.0524338i
\(403\) −168.000 + 290.985i −0.0207659 + 0.0359677i
\(404\) −2408.00 4170.78i −0.296541 0.513624i
\(405\) 6736.00 0.826456
\(406\) 0 0
\(407\) 1968.00 0.239681
\(408\) 810.000 + 1402.96i 0.0982867 + 0.170238i
\(409\) −2575.00 + 4460.03i −0.311309 + 0.539204i −0.978646 0.205552i \(-0.934101\pi\)
0.667337 + 0.744756i \(0.267434\pi\)
\(410\) 1456.00 2521.87i 0.175382 0.303771i
\(411\) 2274.00 + 3938.68i 0.272915 + 0.472703i
\(412\) −9716.00 −1.16183
\(413\) 0 0
\(414\) 1104.00 0.131060
\(415\) 10416.0 + 18041.0i 1.23205 + 2.13398i
\(416\) 2254.00 3904.04i 0.265653 0.460124i
\(417\) −210.000 + 363.731i −0.0246613 + 0.0427146i
\(418\) 440.000 + 762.102i 0.0514859 + 0.0891762i
\(419\) 2310.00 0.269334 0.134667 0.990891i \(-0.457004\pi\)
0.134667 + 0.990891i \(0.457004\pi\)
\(420\) 0 0
\(421\) 1262.00 0.146095 0.0730476 0.997328i \(-0.476727\pi\)
0.0730476 + 0.997328i \(0.476727\pi\)
\(422\) −2134.00 3696.20i −0.246165 0.426370i
\(423\) 3726.00 6453.62i 0.428284 0.741810i
\(424\) 1215.00 2104.44i 0.139164 0.241039i
\(425\) −3537.00 6126.26i −0.403693 0.699218i
\(426\) −1536.00 −0.174694
\(427\) 0 0
\(428\) −1708.00 −0.192896
\(429\) −224.000 387.979i −0.0252094 0.0436639i
\(430\) 1024.00 1773.62i 0.114841 0.198911i
\(431\) 2244.00 3886.72i 0.250788 0.434378i −0.712955 0.701210i \(-0.752644\pi\)
0.963743 + 0.266832i \(0.0859769\pi\)
\(432\) −2050.00 3550.70i −0.228312 0.395448i
\(433\) 17038.0 1.89098 0.945490 0.325652i \(-0.105584\pi\)
0.945490 + 0.325652i \(0.105584\pi\)
\(434\) 0 0
\(435\) 3520.00 0.387979
\(436\) 315.000 + 545.596i 0.0346004 + 0.0599296i
\(437\) 2640.00 4572.61i 0.288989 0.500544i
\(438\) 702.000 1215.90i 0.0765819 0.132644i
\(439\) −8100.00 14029.6i −0.880619 1.52528i −0.850654 0.525727i \(-0.823794\pi\)
−0.0299658 0.999551i \(-0.509540\pi\)
\(440\) −1920.00 −0.208028
\(441\) 0 0
\(442\) −1512.00 −0.162712
\(443\) 4386.00 + 7596.77i 0.470395 + 0.814749i 0.999427 0.0338535i \(-0.0107780\pi\)
−0.529031 + 0.848602i \(0.677445\pi\)
\(444\) 1722.00 2982.59i 0.184060 0.318801i
\(445\) −5840.00 + 10115.2i −0.622118 + 1.07754i
\(446\) −2716.00 4704.25i −0.288355 0.499446i
\(447\) 4020.00 0.425368
\(448\) 0 0
\(449\) 2130.00 0.223877 0.111939 0.993715i \(-0.464294\pi\)
0.111939 + 0.993715i \(0.464294\pi\)
\(450\) −1506.50 2609.33i −0.157816 0.273345i
\(451\) 728.000 1260.93i 0.0760093 0.131652i
\(452\) 4613.00 7989.95i 0.480038 0.831451i
\(453\) 1112.00 + 1926.04i 0.115334 + 0.199764i
\(454\) 2046.00 0.211506
\(455\) 0 0
\(456\) 3300.00 0.338896
\(457\) −5267.00 9122.71i −0.539124 0.933791i −0.998951 0.0457824i \(-0.985422\pi\)
0.459827 0.888009i \(-0.347911\pi\)
\(458\) −1490.00 + 2580.76i −0.152016 + 0.263299i
\(459\) −2700.00 + 4676.54i −0.274565 + 0.475560i
\(460\) 2688.00 + 4655.75i 0.272454 + 0.471903i
\(461\) −9268.00 −0.936342 −0.468171 0.883638i \(-0.655087\pi\)
−0.468171 + 0.883638i \(0.655087\pi\)
\(462\) 0 0
\(463\) −9392.00 −0.942728 −0.471364 0.881939i \(-0.656238\pi\)
−0.471364 + 0.881939i \(0.656238\pi\)
\(464\) 2255.00 + 3905.77i 0.225616 + 0.390778i
\(465\) 192.000 332.554i 0.0191479 0.0331652i
\(466\) 2229.00 3860.74i 0.221580 0.383788i
\(467\) 5403.00 + 9358.27i 0.535377 + 0.927300i 0.999145 + 0.0413434i \(0.0131638\pi\)
−0.463768 + 0.885957i \(0.653503\pi\)
\(468\) 4508.00 0.445261
\(469\) 0 0
\(470\) −5184.00 −0.508766
\(471\) 124.000 + 214.774i 0.0121308 + 0.0210112i
\(472\) −6075.00 + 10522.2i −0.592425 + 1.02611i
\(473\) 512.000 886.810i 0.0497712 0.0862063i
\(474\) −440.000 762.102i −0.0426369 0.0738492i
\(475\) −14410.0 −1.39195
\(476\) 0 0
\(477\) 3726.00 0.357656
\(478\) 2220.00 + 3845.15i 0.212428 + 0.367936i
\(479\) −2470.00 + 4278.17i −0.235610 + 0.408088i −0.959450 0.281880i \(-0.909042\pi\)
0.723840 + 0.689968i \(0.242375\pi\)
\(480\) −2576.00 + 4461.76i −0.244954 + 0.424272i
\(481\) 3444.00 + 5965.18i 0.326472 + 0.565466i
\(482\) −3302.00 −0.312037
\(483\) 0 0
\(484\) 8869.00 0.832926
\(485\) −2352.00 4073.78i −0.220204 0.381404i
\(486\) −1771.00 + 3067.46i −0.165297 + 0.286302i
\(487\) 2608.00 4517.19i 0.242669 0.420315i −0.718805 0.695212i \(-0.755310\pi\)
0.961474 + 0.274897i \(0.0886438\pi\)
\(488\) 3660.00 + 6339.31i 0.339509 + 0.588047i
\(489\) −4016.00 −0.371390
\(490\) 0 0
\(491\) 4412.00 0.405521 0.202760 0.979228i \(-0.435009\pi\)
0.202760 + 0.979228i \(0.435009\pi\)
\(492\) −1274.00 2206.63i −0.116741 0.202201i
\(493\) 2970.00 5144.19i 0.271323 0.469945i
\(494\) −1540.00 + 2667.36i −0.140259 + 0.242935i
\(495\) −1472.00 2549.58i −0.133660 0.231505i
\(496\) 492.000 0.0445392
\(497\) 0 0
\(498\) −2604.00 −0.234313
\(499\) −9530.00 16506.4i −0.854953 1.48082i −0.876689 0.481058i \(-0.840253\pi\)
0.0217362 0.999764i \(-0.493081\pi\)
\(500\) 336.000 581.969i 0.0300528 0.0520529i
\(501\) 2884.00 4995.23i 0.257181 0.445450i
\(502\) 791.000 + 1370.05i 0.0703268 + 0.121810i
\(503\) 12768.0 1.13180 0.565902 0.824473i \(-0.308528\pi\)
0.565902 + 0.824473i \(0.308528\pi\)
\(504\) 0 0
\(505\) −11008.0 −0.969999
\(506\) −192.000 332.554i −0.0168685 0.0292170i
\(507\) −1413.00 + 2447.39i −0.123774 + 0.214383i
\(508\) −6216.00 + 10766.4i −0.542894 + 0.940321i
\(509\) 2750.00 + 4763.14i 0.239473 + 0.414779i 0.960563 0.278062i \(-0.0896921\pi\)
−0.721090 + 0.692841i \(0.756359\pi\)
\(510\) 1728.00 0.150034
\(511\) 0 0
\(512\) −11521.0 −0.994455
\(513\) 5500.00 + 9526.28i 0.473355 + 0.819874i
\(514\) 1177.00 2038.62i 0.101002 0.174941i
\(515\) −11104.0 + 19232.7i −0.950098 + 1.64562i
\(516\) −896.000 1551.92i −0.0764422 0.132402i
\(517\) −2592.00 −0.220495
\(518\) 0 0
\(519\) −4456.00 −0.376872
\(520\) −3360.00 5819.69i −0.283357 0.490789i
\(521\) 3669.00 6354.89i 0.308526 0.534382i −0.669514 0.742799i \(-0.733498\pi\)
0.978040 + 0.208417i \(0.0668311\pi\)
\(522\) 1265.00 2191.04i 0.106068 0.183715i
\(523\) 8791.00 + 15226.5i 0.734997 + 1.27305i 0.954725 + 0.297491i \(0.0961499\pi\)
−0.219727 + 0.975561i \(0.570517\pi\)
\(524\) 7826.00 0.652444
\(525\) 0 0
\(526\) 3872.00 0.320964
\(527\) −324.000 561.184i −0.0267811 0.0463863i
\(528\) −328.000 + 568.113i −0.0270348 + 0.0468256i
\(529\) 4931.50 8541.61i 0.405318 0.702031i
\(530\) −1296.00 2244.74i −0.106216 0.183972i
\(531\) −18630.0 −1.52255
\(532\) 0 0
\(533\) 5096.00 0.414132
\(534\) −730.000 1264.40i −0.0591577 0.102464i
\(535\) −1952.00 + 3380.96i −0.157743 + 0.273218i
\(536\) −1830.00 + 3169.65i −0.147470 + 0.255426i
\(537\) −820.000 1420.28i −0.0658950 0.114133i
\(538\) −180.000 −0.0144244
\(539\) 0 0
\(540\) −11200.0 −0.892539
\(541\) 809.000 + 1401.23i 0.0642914 + 0.111356i 0.896379 0.443288i \(-0.146188\pi\)
−0.832088 + 0.554644i \(0.812855\pi\)
\(542\) 1016.00 1759.76i 0.0805183 0.139462i
\(543\) 3892.00 6741.14i 0.307591 0.532763i
\(544\) 4347.00 + 7529.22i 0.342603 + 0.593406i
\(545\) 1440.00 0.113179
\(546\) 0 0
\(547\) 16144.0 1.26192 0.630958 0.775817i \(-0.282662\pi\)
0.630958 + 0.775817i \(0.282662\pi\)
\(548\) 7959.00 + 13785.4i 0.620423 + 1.07460i
\(549\) −5612.00 + 9720.27i −0.436274 + 0.755648i
\(550\) −524.000 + 907.595i −0.0406244 + 0.0703636i
\(551\) −6050.00 10478.9i −0.467765 0.810193i
\(552\) −1440.00 −0.111033
\(553\) 0 0
\(554\) 5426.00 0.416117
\(555\) −3936.00 6817.35i −0.301034 0.521406i
\(556\) −735.000 + 1273.06i −0.0560628 + 0.0971037i
\(557\) −2327.00 + 4030.48i −0.177016 + 0.306601i −0.940857 0.338803i \(-0.889978\pi\)
0.763841 + 0.645405i \(0.223311\pi\)
\(558\) −138.000 239.023i −0.0104695 0.0181338i
\(559\) 3584.00 0.271175
\(560\) 0 0
\(561\) 864.000 0.0650234
\(562\) 421.000 + 729.193i 0.0315993 + 0.0547316i
\(563\) −5039.00 + 8727.80i −0.377209 + 0.653345i −0.990655 0.136392i \(-0.956449\pi\)
0.613446 + 0.789736i \(0.289783\pi\)
\(564\) −2268.00 + 3928.29i −0.169326 + 0.293282i
\(565\) −10544.0 18262.7i −0.785114 1.35986i
\(566\) 3782.00 0.280865
\(567\) 0 0
\(568\) −11520.0 −0.851001
\(569\) 2965.00 + 5135.53i 0.218452 + 0.378370i 0.954335 0.298739i \(-0.0965659\pi\)
−0.735883 + 0.677109i \(0.763233\pi\)
\(570\) 1760.00 3048.41i 0.129330 0.224007i
\(571\) 9524.00 16496.1i 0.698016 1.20900i −0.271138 0.962541i \(-0.587400\pi\)
0.969153 0.246458i \(-0.0792668\pi\)
\(572\) −784.000 1357.93i −0.0573089 0.0992619i
\(573\) 10096.0 0.736067
\(574\) 0 0
\(575\) 6288.00 0.456048
\(576\) −1920.50 3326.40i −0.138925 0.240625i
\(577\) 7183.00 12441.3i 0.518253 0.897641i −0.481522 0.876434i \(-0.659916\pi\)
0.999775 0.0212070i \(-0.00675092\pi\)
\(578\) −998.500 + 1729.45i −0.0718549 + 0.124456i
\(579\) −2962.00 5130.33i −0.212602 0.368237i
\(580\) 12320.0 0.882000
\(581\) 0 0
\(582\) 588.000 0.0418787
\(583\) −648.000 1122.37i −0.0460333 0.0797320i
\(584\) 5265.00 9119.25i 0.373060 0.646159i
\(585\) 5152.00 8923.53i 0.364118 0.630671i
\(586\) −2156.00 3734.30i −0.151986 0.263247i
\(587\) −3626.00 −0.254959 −0.127480 0.991841i \(-0.540689\pi\)
−0.127480 + 0.991841i \(0.540689\pi\)
\(588\) 0 0
\(589\) −1320.00 −0.0923424
\(590\) 6480.00 + 11223.7i 0.452165 + 0.783173i
\(591\) 3334.00 5774.66i 0.232051 0.401925i
\(592\) 5043.00 8734.73i 0.350112 0.606411i
\(593\) 531.000 + 919.719i 0.0367716 + 0.0636903i 0.883826 0.467817i \(-0.154959\pi\)
−0.847054 + 0.531507i \(0.821626\pi\)
\(594\) 800.000 0.0552599
\(595\) 0 0
\(596\) 14070.0 0.966996
\(597\) 1860.00 + 3221.61i 0.127512 + 0.220857i
\(598\) 672.000 1163.94i 0.0459534 0.0795936i
\(599\) 5100.00 8833.46i 0.347880 0.602547i −0.637992 0.770043i \(-0.720235\pi\)
0.985873 + 0.167496i \(0.0535682\pi\)
\(600\) 1965.00 + 3403.48i 0.133701 + 0.231577i
\(601\) −25158.0 −1.70751 −0.853757 0.520671i \(-0.825682\pi\)
−0.853757 + 0.520671i \(0.825682\pi\)
\(602\) 0 0
\(603\) −5612.00 −0.379002
\(604\) 3892.00 + 6741.14i 0.262191 + 0.454128i
\(605\) 10136.0 17556.1i 0.681136 1.17976i
\(606\) 688.000 1191.65i 0.0461190 0.0798804i
\(607\) −12832.0 22225.7i −0.858047 1.48618i −0.873789 0.486306i \(-0.838344\pi\)
0.0157413 0.999876i \(-0.494989\pi\)
\(608\) 17710.0 1.18131
\(609\) 0 0
\(610\) 7808.00 0.518257
\(611\) −4536.00 7856.58i −0.300339 0.520202i
\(612\) −4347.00 + 7529.22i −0.287119 + 0.497305i
\(613\) −9509.00 + 16470.1i −0.626533 + 1.08519i 0.361709 + 0.932291i \(0.382193\pi\)
−0.988242 + 0.152896i \(0.951140\pi\)
\(614\) 1337.00 + 2315.75i 0.0878777 + 0.152209i
\(615\) −5824.00 −0.381864
\(616\) 0 0
\(617\) 17334.0 1.13102 0.565511 0.824741i \(-0.308679\pi\)
0.565511 + 0.824741i \(0.308679\pi\)
\(618\) −1388.00 2404.09i −0.0903455 0.156483i
\(619\) −9365.00 + 16220.7i −0.608096 + 1.05325i 0.383459 + 0.923558i \(0.374733\pi\)
−0.991554 + 0.129694i \(0.958600\pi\)
\(620\) 672.000 1163.94i 0.0435293 0.0753950i
\(621\) −2400.00 4156.92i −0.155086 0.268618i
\(622\) 3768.00 0.242899
\(623\) 0 0
\(624\) −2296.00 −0.147297
\(625\) 7419.50 + 12851.0i 0.474848 + 0.822461i
\(626\) 1219.00 2111.37i 0.0778291 0.134804i
\(627\) 880.000 1524.20i 0.0560507 0.0970827i
\(628\) 434.000 + 751.710i 0.0275772 + 0.0477651i
\(629\) −13284.0 −0.842079
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) −3300.00 5715.77i −0.207701 0.359748i
\(633\) −4268.00 + 7392.39i −0.267990 + 0.464173i
\(634\) −1593.00 + 2759.16i −0.0997888 + 0.172839i
\(635\) 14208.0 + 24609.0i 0.887917 + 1.53792i
\(636\) −2268.00 −0.141403
\(637\) 0 0
\(638\) −880.000 −0.0546074
\(639\) −8832.00 15297.5i −0.546774 0.947040i
\(640\) −11640.0 + 20161.1i −0.718924 + 1.24521i
\(641\) −8151.00 + 14117.9i −0.502255 + 0.869930i 0.497742 + 0.867325i \(0.334163\pi\)
−0.999997 + 0.00260525i \(0.999171\pi\)
\(642\) −244.000 422.620i −0.0149999 0.0259805i
\(643\) 4718.00 0.289362 0.144681 0.989478i \(-0.453784\pi\)
0.144681 + 0.989478i \(0.453784\pi\)
\(644\) 0 0
\(645\) −4096.00 −0.250046
\(646\) −2970.00 5144.19i −0.180887 0.313306i
\(647\) 10718.0 18564.1i 0.651264 1.12802i −0.331552 0.943437i \(-0.607572\pi\)
0.982816 0.184586i \(-0.0590944\pi\)
\(648\) −3157.50 + 5468.95i −0.191417 + 0.331544i
\(649\) 3240.00 + 5611.84i 0.195965 + 0.339421i
\(650\) −3668.00 −0.221340
\(651\) 0 0
\(652\) −14056.0 −0.844287
\(653\) −2229.00 3860.74i −0.133580 0.231367i 0.791474 0.611202i \(-0.209314\pi\)
−0.925054 + 0.379836i \(0.875981\pi\)
\(654\) −90.0000 + 155.885i −0.00538116 + 0.00932044i
\(655\) 8944.00 15491.5i 0.533544 0.924124i
\(656\) −3731.00 6462.28i −0.222060 0.384618i
\(657\) 16146.0 0.958775
\(658\) 0 0
\(659\) −26640.0 −1.57473 −0.787365 0.616487i \(-0.788555\pi\)
−0.787365 + 0.616487i \(0.788555\pi\)
\(660\) 896.000 + 1551.92i 0.0528436 + 0.0915277i
\(661\) −3716.00 + 6436.30i −0.218662 + 0.378734i −0.954399 0.298533i \(-0.903503\pi\)
0.735737 + 0.677267i \(0.236836\pi\)
\(662\) 4336.00 7510.17i 0.254567 0.440923i
\(663\) 1512.00 + 2618.86i 0.0885690 + 0.153406i
\(664\) −19530.0 −1.14143
\(665\) 0 0
\(666\) −5658.00 −0.329194
\(667\) 2640.00 + 4572.61i 0.153255 + 0.265446i
\(668\) 10094.0 17483.3i 0.584654 1.01265i
\(669\) −5432.00 + 9408.50i −0.313921 + 0.543727i
\(670\) 1952.00 + 3380.96i 0.112556 + 0.194952i
\(671\) 3904.00 0.224608
\(672\) 0 0
\(673\) 58.0000 0.00332204 0.00166102 0.999999i \(-0.499471\pi\)
0.00166102 + 0.999999i \(0.499471\pi\)
\(674\) 407.000 + 704.945i 0.0232597 + 0.0402870i
\(675\) −6550.00 + 11344.9i −0.373496 + 0.646914i
\(676\) −4945.50 + 8565.86i −0.281378 + 0.487361i
\(677\) 10758.0 + 18633.4i 0.610729 + 1.05781i 0.991118 + 0.132987i \(0.0424568\pi\)
−0.380389 + 0.924827i \(0.624210\pi\)
\(678\) 2636.00 0.149314
\(679\) 0 0
\(680\) 12960.0 0.730873
\(681\) −2046.00 3543.78i −0.115129 0.199409i
\(682\) −48.0000 + 83.1384i −0.00269504 + 0.00466794i
\(683\) −9054.00 + 15682.0i −0.507235 + 0.878557i 0.492730 + 0.870182i \(0.335999\pi\)
−0.999965 + 0.00837480i \(0.997334\pi\)
\(684\) 8855.00 + 15337.3i 0.494999 + 0.857364i
\(685\) 36384.0 2.02943
\(686\) 0 0
\(687\) 5960.00 0.330987
\(688\) −2624.00 4544.90i −0.145406 0.251850i
\(689\) 2268.00 3928.29i 0.125405 0.217208i
\(690\) −768.000 + 1330.22i −0.0423728 + 0.0733919i
\(691\) 5039.00 + 8727.80i 0.277413 + 0.480494i 0.970741 0.240128i \(-0.0771895\pi\)
−0.693328 + 0.720622i \(0.743856\pi\)
\(692\) −15596.0 −0.856750
\(693\) 0 0
\(694\) −9344.00 −0.511086
\(695\) 1680.00 + 2909.85i 0.0916921 + 0.158815i
\(696\) −1650.00 + 2857.88i −0.0898608 + 0.155643i
\(697\) −4914.00 + 8511.30i −0.267046 + 0.462537i
\(698\) −2590.00 4486.01i −0.140448 0.243264i
\(699\) −8916.00 −0.482452
\(700\) 0 0
\(701\) 18762.0 1.01089 0.505443 0.862860i \(-0.331329\pi\)
0.505443 + 0.862860i \(0.331329\pi\)
\(702\) 1400.00 + 2424.87i 0.0752701 + 0.130372i
\(703\) −13530.0 + 23434.6i −0.725880 + 1.25726i
\(704\) −668.000 + 1157.01i −0.0357616 + 0.0619410i
\(705\) 5184.00 + 8978.95i 0.276937 + 0.479669i
\(706\) −12178.0 −0.649186
\(707\) 0 0
\(708\) 11340.0 0.601954
\(709\) −3405.00 5897.63i −0.180363 0.312398i 0.761641 0.647999i \(-0.224394\pi\)
−0.942004 + 0.335601i \(0.891061\pi\)
\(710\) −6144.00 + 10641.7i −0.324761 + 0.562502i
\(711\) 5060.00 8764.18i 0.266898 0.462282i
\(712\) −5475.00 9482.98i −0.288180 0.499143i
\(713\) 576.000 0.0302544
\(714\) 0 0
\(715\) −3584.00 −0.187460
\(716\) −2870.00 4970.99i −0.149800 0.259462i
\(717\) 4440.00 7690.31i 0.231262 0.400557i
\(718\) 220.000 381.051i 0.0114350 0.0198060i
\(719\) −2430.00 4208.88i −0.126041 0.218310i 0.796098 0.605167i \(-0.206894\pi\)
−0.922140 + 0.386858i \(0.873561\pi\)
\(720\) −15088.0 −0.780967
\(721\) 0 0
\(722\) −5241.00 −0.270152
\(723\) 3302.00 + 5719.23i 0.169852 + 0.294192i
\(724\) 13622.0 23594.0i 0.699251 1.21114i
\(725\) 7205.00 12479.4i 0.369085 0.639275i
\(726\) 1267.00 + 2194.51i 0.0647697 + 0.112184i
\(727\) −13636.0 −0.695641 −0.347821 0.937561i \(-0.613078\pi\)
−0.347821 + 0.937561i \(0.613078\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) −5616.00 9727.20i −0.284736 0.493178i
\(731\) −3456.00 + 5985.97i −0.174863 + 0.302871i
\(732\) 3416.00 5916.69i 0.172485 0.298753i
\(733\) −1044.00 1808.26i −0.0526071 0.0911182i 0.838523 0.544867i \(-0.183420\pi\)
−0.891130 + 0.453749i \(0.850086\pi\)
\(734\) 9816.00 0.493617
\(735\) 0 0
\(736\) −7728.00 −0.387035
\(737\) 976.000 + 1690.48i 0.0487808 + 0.0844908i
\(738\) −2093.00 + 3625.18i −0.104396 + 0.180820i
\(739\) 2580.00 4468.69i 0.128426 0.222440i −0.794641 0.607080i \(-0.792341\pi\)
0.923067 + 0.384639i \(0.125674\pi\)
\(740\) −13776.0 23860.7i −0.684346 1.18532i
\(741\) 6160.00 0.305389
\(742\) 0 0
\(743\) −28152.0 −1.39004 −0.695018 0.718992i \(-0.744604\pi\)
−0.695018 + 0.718992i \(0.744604\pi\)
\(744\) 180.000 + 311.769i 0.00886979 + 0.0153629i
\(745\) 16080.0 27851.4i 0.790773 1.36966i
\(746\) −221.000 + 382.783i −0.0108464 + 0.0187864i
\(747\) −14973.0 25934.0i −0.733378 1.27025i
\(748\) 3024.00 0.147819
\(749\) 0 0
\(750\) 192.000 0.00934780
\(751\) 8404.00 + 14556.2i 0.408344 + 0.707272i 0.994704 0.102778i \(-0.0327731\pi\)
−0.586360 + 0.810050i \(0.699440\pi\)
\(752\) −6642.00 + 11504.3i −0.322086 + 0.557870i
\(753\) 1582.00 2740.10i 0.0765621 0.132610i
\(754\) −1540.00 2667.36i −0.0743813 0.128832i
\(755\) 17792.0 0.857639
\(756\) 0 0
\(757\) 21674.0 1.04063 0.520314 0.853975i \(-0.325815\pi\)
0.520314 + 0.853975i \(0.325815\pi\)
\(758\) −1980.00 3429.46i −0.0948771 0.164332i
\(759\) −384.000 + 665.108i −0.0183641 + 0.0318075i
\(760\) 13200.0 22863.1i 0.630019 1.09122i
\(761\) −3711.00 6427.64i −0.176772 0.306178i 0.764001 0.645215i \(-0.223232\pi\)
−0.940773 + 0.339037i \(0.889899\pi\)
\(762\) −3552.00 −0.168865
\(763\) 0 0
\(764\) 35336.0 1.67331
\(765\) 9936.00 + 17209.7i 0.469591 + 0.813355i
\(766\) 3354.00 5809.30i 0.158205 0.274019i
\(767\) −11340.0 + 19641.5i −0.533851 + 0.924657i
\(768\) −119.000 206.114i −0.00559120 0.00968424i
\(769\) 13790.0 0.646658 0.323329 0.946287i \(-0.395198\pi\)
0.323329 + 0.946287i \(0.395198\pi\)
\(770\) 0 0
\(771\) −4708.00 −0.219915
\(772\) −10367.0 17956.2i −0.483312 0.837120i
\(773\) 3116.00 5397.07i 0.144987 0.251124i −0.784381 0.620279i \(-0.787019\pi\)
0.929368 + 0.369155i \(0.120353\pi\)
\(774\) −1472.00 + 2549.58i −0.0683591 + 0.118401i
\(775\) −786.000 1361.39i −0.0364309 0.0631002i
\(776\) 4410.00 0.204007
\(777\) 0 0
\(778\) 13350.0 0.615194
\(779\) 10010.0 + 17337.8i 0.460392 + 0.797423i
\(780\) −3136.00 + 5431.71