Properties

Label 49.4.c.b.30.1
Level $49$
Weight $4$
Character 49.30
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 30.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 49.30
Dual form 49.4.c.b.18.1

$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.176777 0.306186i −0.763998 0.645219i \(-0.776766\pi\)
0.940775 + 0.339032i \(0.110100\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) 3.50000 + 6.06218i 0.437500 + 0.757772i
\(5\) 8.00000 13.8564i 0.715542 1.23935i −0.247208 0.968962i \(-0.579513\pi\)
0.962750 0.270392i \(-0.0871534\pi\)
\(6\) −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 0.915625 0.402034i \(-0.131697\pi\)
−0.805984 + 0.591937i \(0.798363\pi\)
\(12\) 7.00000 12.1244i 0.168394 0.291667i
\(13\) −28.0000 −0.597369 −0.298685 0.954352i \(-0.596548\pi\)
−0.298685 + 0.954352i \(0.596548\pi\)
\(14\) 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 \(-0.0407979\pi\)
−0.606594 + 0.795012i \(0.707465\pi\)
\(18\) −11.5000 19.9186i −0.150588 0.260825i
\(19\) −55.0000 + 95.2628i −0.664098 + 1.15025i 0.315431 + 0.948949i \(0.397851\pi\)
−0.979529 + 0.201303i \(0.935482\pi\)
\(20\) 112.000 1.25220
\(21\) 0 0
\(22\) 8.00000 0.0775275
\(23\) −24.0000 + 41.5692i −0.217580 + 0.376860i −0.954068 0.299591i \(-0.903150\pi\)
0.736487 + 0.676451i \(0.236483\pi\)
\(24\) −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 \(-0.155599\pi\)
−0.848121 + 0.529803i \(0.822266\pi\)
\(32\) 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 −0.451994 0.892021i \(-0.649287\pi\)
0.998510 0.0545719i \(-0.0173794\pi\)
\(38\) 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 \(-0.612674\pi\)
−0.346630 + 0.938002i \(0.612674\pi\)
\(42\) 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 −0.497226 0.867621i \(-0.665648\pi\)
0.999995 0.00319997i \(-0.00101858\pi\)
\(48\) 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 0.951692 0.307055i \(-0.0993436\pi\)
−0.741763 + 0.670662i \(0.766010\pi\)
\(54\) −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 0.835442 + 0.549578i \(0.185211\pi\)
0.0582271 + 0.998303i \(0.481455\pi\)
\(60\) −112.000 193.990i −0.240986 0.417399i
\(61\) −244.000 + 422.620i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 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 0.733096 0.680125i \(-0.238075\pi\)
−0.955554 + 0.294817i \(0.904741\pi\)
\(68\) −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 −0.997254 0.0740537i \(-0.976406\pi\)
0.434495 0.900674i \(-0.356927\pi\)
\(74\) −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 −0.979078 0.203485i \(-0.934773\pi\)
0.665762 + 0.746164i \(0.268106\pi\)
\(80\) 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 \(-0.169887\pi\)
0.860922 + 0.508737i \(0.169887\pi\)
\(84\) 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 \(-0.690181\pi\)
0.997273 + 0.0738062i \(0.0235146\pi\)
\(90\) −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 \(-0.549174\pi\)
−0.153872 + 0.988091i \(0.549174\pi\)
\(98\) 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 \(-0.276723\pi\)
−0.984227 + 0.176911i \(0.943389\pi\)
\(102\) −54.0000 93.5307i −0.0524196 0.0907934i
\(103\) 694.000 1202.04i 0.663901 1.14991i −0.315680 0.948866i \(-0.602233\pi\)
0.979582 0.201046i \(-0.0644339\pi\)
\(104\) −420.000 −0.396004
\(105\) 0 0
\(106\) 162.000 0.148442
\(107\) −122.000 + 211.310i −0.110226 + 0.190917i −0.915861 0.401495i \(-0.868491\pi\)
0.805635 + 0.592412i \(0.201824\pi\)
\(108\) −350.000 606.218i −0.311840 0.540123i
\(109\) −45.0000 77.9423i −0.0395433 0.0684910i 0.845576 0.533854i \(-0.179257\pi\)
−0.885120 + 0.465363i \(0.845924\pi\)
\(110\) 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 \(-0.954944\pi\)
0.617174 + 0.786827i \(0.288277\pi\)
\(132\) 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 −0.965208 0.261482i \(-0.915789\pi\)
0.256154 0.966636i \(-0.417545\pi\)
\(138\) 48.0000 83.1384i 0.0296089 0.0512842i
\(139\) 210.000 0.128144 0.0640718 0.997945i \(-0.479591\pi\)
0.0640718 + 0.997945i \(0.479591\pi\)
\(140\) 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 −0.445519 0.895272i \(-0.646981\pi\)
0.998088 0.0618054i \(-0.0196858\pi\)
\(150\) 131.000 + 226.899i 0.0713074 + 0.123508i
\(151\) −556.000 963.020i −0.299647 0.519003i 0.676408 0.736527i \(-0.263535\pi\)
−0.976055 + 0.217524i \(0.930202\pi\)
\(152\) −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 \(-0.156633\pi\)
−0.849837 + 0.527046i \(0.823300\pi\)
\(158\) 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 −0.999797 0.0201478i \(-0.993586\pi\)
0.517347 + 0.855776i \(0.326920\pi\)
\(164\) −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 \(-0.732924\pi\)
−0.668176 + 0.744004i \(0.732924\pi\)
\(168\) 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 \(-0.670487\pi\)
0.999928 + 0.0120003i \(0.00381992\pi\)
\(174\) 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 0.938840 0.344354i \(-0.111902\pi\)
−0.767640 + 0.640882i \(0.778569\pi\)
\(180\) 1288.00 2230.88i 0.533344 0.923778i
\(181\) −3892.00 −1.59829 −0.799144 0.601140i \(-0.794713\pi\)
−0.799144 + 0.601140i \(0.794713\pi\)
\(182\) 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 0.224533 0.974466i \(-0.427914\pi\)
0.731646 0.681684i \(-0.238752\pi\)
\(192\) 167.000 + 289.252i 0.0627718 + 0.108724i
\(193\) 1481.00 + 2565.17i 0.552356 + 0.956709i 0.998104 + 0.0615502i \(0.0196044\pi\)
−0.445748 + 0.895159i \(0.647062\pi\)
\(194\) −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 \(-0.0591841\pi\)
−0.651478 + 0.758667i \(0.725851\pi\)
\(200\) −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 \(-0.196412\pi\)
0.815591 + 0.578629i \(0.196412\pi\)
\(224\) 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 \(-0.263358\pi\)
−0.975934 + 0.218068i \(0.930024\pi\)
\(228\) 770.000 + 1333.68i 0.223660 + 0.387391i
\(229\) −1490.00 + 2580.76i −0.429965 + 0.744721i −0.996870 0.0790622i \(-0.974807\pi\)
0.566905 + 0.823783i \(0.308141\pi\)
\(230\) 768.000 0.220176
\(231\) 0 0
\(232\) −1650.00 −0.466930
\(233\) −2229.00 + 3860.74i −0.626724 + 1.08552i 0.361481 + 0.932379i \(0.382271\pi\)
−0.988205 + 0.153138i \(0.951062\pi\)
\(234\) 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 \(-0.0211886\pi\)
−0.556498 + 0.830849i \(0.687855\pi\)
\(242\) −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 \(-0.563742\pi\)
−0.198914 + 0.980017i \(0.563742\pi\)
\(252\) 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 \(-0.741115\pi\)
0.972773 + 0.231758i \(0.0744479\pi\)
\(258\) −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 0.998625 0.0524239i \(-0.0166947\pi\)
−0.544713 + 0.838623i \(0.683361\pi\)
\(264\) 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 \(-0.160173\pi\)
−0.855646 + 0.517562i \(0.826840\pi\)
\(270\) 800.000 + 1385.64i 0.180320 + 0.312324i
\(271\) 1016.00 1759.76i 0.227740 0.394458i −0.729398 0.684090i \(-0.760200\pi\)
0.957138 + 0.289632i \(0.0935330\pi\)
\(272\) −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 0.994432 + 0.105380i \(0.0336059\pi\)
−0.405954 + 0.913893i \(0.633061\pi\)
\(278\) 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 \(-0.296686\pi\)
−0.993380 + 0.114878i \(0.963352\pi\)
\(284\) −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 \(-0.358556\pi\)
0.429880 + 0.902886i \(0.358556\pi\)
\(294\) 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 \(-0.579956\pi\)
−0.248556 + 0.968618i \(0.579956\pi\)
\(308\) 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 \(-0.278283\pi\)
−0.985082 + 0.172085i \(0.944950\pi\)
\(312\) 420.000 + 727.461i 0.0762110 + 0.132001i
\(313\) 1219.00 2111.37i 0.220134 0.381283i −0.734714 0.678376i \(-0.762684\pi\)
0.954849 + 0.297093i \(0.0960172\pi\)
\(314\) 124.000 0.0222857
\(315\) 0 0
\(316\) −3080.00 −0.548302
\(317\) 1593.00 2759.16i 0.282245 0.488863i −0.689692 0.724103i \(-0.742254\pi\)
0.971937 + 0.235239i \(0.0755874\pi\)
\(318\) −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 0.240965 + 0.970534i \(0.422536\pi\)
−0.960989 + 0.276585i \(0.910797\pi\)
\(332\) 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 −0.959880 0.280413i \(-0.909529\pi\)
0.237095 0.971486i \(-0.423805\pi\)
\(348\) −770.000 + 1333.68i −0.118610 + 0.205439i
\(349\) 5180.00 0.794496 0.397248 0.917711i \(-0.369965\pi\)
0.397248 + 0.917711i \(0.369965\pi\)
\(350\) 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 0.802317 + 0.596898i \(0.203600\pi\)
0.115770 + 0.993276i \(0.463067\pi\)
\(354\) −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 −0.881744 0.471729i \(-0.843630\pi\)
0.849401 + 0.527748i \(0.176964\pi\)
\(360\) −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 −0.969131 0.246546i \(-0.920704\pi\)
0.271051 0.962565i \(-0.412629\pi\)
\(368\) −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 −0.850279 0.526333i \(-0.823567\pi\)
0.880957 + 0.473197i \(0.156900\pi\)
\(374\) 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 \(-0.685658\pi\)
0.998221 + 0.0596280i \(0.0189914\pi\)
\(384\) 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 0.861980 + 0.506943i \(0.169225\pi\)
0.00803563 + 0.999968i \(0.497442\pi\)
\(390\) 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 \(-0.860650\pi\)
0.819982 + 0.572389i \(0.193983\pi\)
\(398\) 1860.00 0.234255
\(399\) 0 0
\(400\) 5371.00 0.671375
\(401\) −3111.00 + 5388.41i −0.387421 + 0.671033i −0.992102 0.125435i \(-0.959967\pi\)
0.604681 + 0.796468i \(0.293301\pi\)
\(402\) 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 \(-0.0658991\pi\)
−0.667337 + 0.744756i \(0.732566\pi\)
\(410\) 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 \(-0.542996\pi\)
−0.134667 + 0.990891i \(0.542996\pi\)
\(420\) 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 0.963743 0.266832i \(-0.0859769\pi\)
−0.712955 + 0.701210i \(0.752644\pi\)
\(432\) 2050.00 3550.70i 0.228312 0.395448i
\(433\) −17038.0 −1.89098 −0.945490 0.325652i \(-0.894416\pi\)
−0.945490 + 0.325652i \(0.894416\pi\)
\(434\) 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 0.0299658 0.999551i \(-0.490460\pi\)
0.850654 0.525727i \(-0.176206\pi\)
\(440\) 1920.00 0.208028
\(441\) 0 0
\(442\) −1512.00 −0.162712
\(443\) 4386.00 7596.77i 0.470395 0.814749i −0.529031 0.848602i \(-0.677445\pi\)
0.999427 + 0.0338535i \(0.0107780\pi\)
\(444\) −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 0.459827 + 0.888009i \(0.347911\pi\)
−0.998951 + 0.0457824i \(0.985422\pi\)
\(458\) 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 \(-0.344913\pi\)
0.468171 + 0.883638i \(0.344913\pi\)
\(462\) 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 0.463768 + 0.885957i \(0.346497\pi\)
−0.999145 + 0.0413434i \(0.986836\pi\)
\(468\) −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 \(-0.0909579\pi\)
−0.723840 + 0.689968i \(0.757625\pi\)
\(480\) −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 0.961474 0.274897i \(-0.0886438\pi\)
−0.718805 + 0.695212i \(0.755310\pi\)
\(488\) −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 0.0217362 + 0.999764i \(0.493081\pi\)
−0.876689 + 0.481058i \(0.840253\pi\)
\(500\) −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 \(-0.691472\pi\)
−0.565902 + 0.824473i \(0.691472\pi\)
\(504\) 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 \(-0.910308\pi\)
0.721090 + 0.692841i \(0.243641\pi\)
\(510\) −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 \(-0.266502\pi\)
−0.978040 + 0.208417i \(0.933169\pi\)
\(522\) 1265.00 + 2191.04i 0.106068 + 0.183715i
\(523\) −8791.00 + 15226.5i −0.734997 + 1.27305i 0.219727 + 0.975561i \(0.429483\pi\)
−0.954725 + 0.297491i \(0.903850\pi\)
\(524\) −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 −0.832088 0.554644i \(-0.812855\pi\)
0.896379 + 0.443288i \(0.146188\pi\)
\(542\) −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 0.763841 0.645405i \(-0.223311\pi\)
−0.940857 + 0.338803i \(0.889978\pi\)
\(558\) 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 \(-0.0435506\pi\)
−0.613446 + 0.789736i \(0.710217\pi\)
\(564\) −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 −0.735883 0.677109i \(-0.763233\pi\)
0.954335 + 0.298739i \(0.0965659\pi\)
\(570\) −1760.00 3048.41i −0.129330 0.224007i
\(571\) 9524.00 + 16496.1i 0.698016 + 1.20900i 0.969153 + 0.246458i \(0.0792668\pi\)
−0.271138 + 0.962541i \(0.587400\pi\)
\(572\) 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 −0.999775 0.0212070i \(-0.993249\pi\)
0.481522 0.876434i \(-0.340084\pi\)
\(578\) −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 \(-0.459311\pi\)
0.127480 + 0.991841i \(0.459311\pi\)
\(588\) 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 \(-0.845041\pi\)
0.847054 + 0.531507i \(0.178374\pi\)
\(594\) −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 0.985873 0.167496i \(-0.0535682\pi\)
−0.637992 + 0.770043i \(0.720235\pi\)
\(600\) −1965.00 + 3403.48i −0.133701 + 0.231577i
\(601\) 25158.0 1.70751 0.853757 0.520671i \(-0.174318\pi\)
0.853757 + 0.520671i \(0.174318\pi\)
\(602\) 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 −0.0157413 0.999876i \(-0.505011\pi\)
0.873789 0.486306i \(-0.161656\pi\)
\(608\) −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 −0.988242 0.152896i \(-0.951140\pi\)
0.361709 0.932291i \(-0.382193\pi\)
\(614\) −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 0.991554 + 0.129694i \(0.0413996\pi\)
−0.383459 + 0.923558i \(0.625267\pi\)
\(620\) 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 −0.999997 0.00260525i \(-0.999171\pi\)
0.497742 0.867325i \(-0.334163\pi\)
\(642\) 244.000 422.620i 0.0149999 0.0259805i
\(643\) −4718.00 −0.289362 −0.144681 0.989478i \(-0.546216\pi\)
−0.144681 + 0.989478i \(0.546216\pi\)
\(644\) 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 −0.982816 0.184586i \(-0.940906\pi\)
0.331552 0.943437i \(-0.392428\pi\)
\(648\) −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 −0.925054 0.379836i \(-0.875981\pi\)
0.791474 + 0.611202i \(0.209314\pi\)
\(654\) 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 \(-0.0964974\pi\)
−0.735737 + 0.677267i \(0.763164\pi\)
\(662\) 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 0.380389 + 0.924827i \(0.375790\pi\)
−0.991118 + 0.132987i \(0.957543\pi\)
\(678\) −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 −0.999965 0.00837480i \(-0.997334\pi\)
0.492730 0.870182i \(-0.335999\pi\)
\(684\) −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 \(-0.922810\pi\)
0.693328 + 0.720622i \(0.256144\pi\)
\(692\) 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 −0.942004 0.335601i \(-0.891061\pi\)
0.761641 + 0.647999i \(0.224394\pi\)
\(710\) 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 \(-0.793106\pi\)
0.922140 + 0.386858i \(0.126439\pi\)
\(720\) 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 \(-0.386922\pi\)
0.347821 + 0.937561i \(0.386922\pi\)
\(728\) 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 \(-0.816580\pi\)
0.891130 + 0.453749i \(0.149914\pi\)
\(734\) −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 0.923067 0.384639i \(-0.125674\pi\)
−0.794641 + 0.607080i \(0.792341\pi\)
\(740\) 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 −0.586360 0.810050i \(-0.699440\pi\)
0.994704 + 0.102778i \(0.0327731\pi\)
\(752\) 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 \(-0.776768\pi\)
0.940773 + 0.339037i \(0.110101\pi\)
\(762\) 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 \(-0.604802\pi\)
−0.323329 + 0.946287i \(0.604802\pi\)
\(770\) 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 \(-0.212981\pi\)
−0.929368 + 0.369155i \(0.879647\pi\)
\(774\) −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