Properties

Label 69.6.c.b.68.6
Level $69$
Weight $6$
Character 69.68
Analytic conductor $11.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 68.6
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.28

$q$-expansion

\(f(q)\) \(=\) \(q-8.75944i q^{2} +(10.6432 + 11.3896i) q^{3} -44.7279 q^{4} +43.1688 q^{5} +(99.7663 - 93.2285i) q^{6} +151.444i q^{7} +111.489i q^{8} +(-16.4449 + 242.443i) q^{9} +O(q^{10})\) \(q-8.75944i q^{2} +(10.6432 + 11.3896i) q^{3} -44.7279 q^{4} +43.1688 q^{5} +(99.7663 - 93.2285i) q^{6} +151.444i q^{7} +111.489i q^{8} +(-16.4449 + 242.443i) q^{9} -378.135i q^{10} +610.914 q^{11} +(-476.047 - 509.431i) q^{12} +132.232 q^{13} +1326.57 q^{14} +(459.454 + 491.674i) q^{15} -454.710 q^{16} +1720.33 q^{17} +(2123.67 + 144.048i) q^{18} -554.256i q^{19} -1930.85 q^{20} +(-1724.89 + 1611.85i) q^{21} -5351.26i q^{22} +(-2536.22 - 62.8693i) q^{23} +(-1269.81 + 1186.60i) q^{24} -1261.46 q^{25} -1158.28i q^{26} +(-2936.35 + 2393.07i) q^{27} -6773.79i q^{28} -7005.84i q^{29} +(4306.79 - 4024.56i) q^{30} +4819.56 q^{31} +7550.66i q^{32} +(6502.07 + 6958.05i) q^{33} -15069.2i q^{34} +6537.67i q^{35} +(735.543 - 10844.0i) q^{36} +1324.61i q^{37} -4854.97 q^{38} +(1407.37 + 1506.07i) q^{39} +4812.84i q^{40} +231.107i q^{41} +(14118.9 + 15109.1i) q^{42} +18413.9i q^{43} -27324.9 q^{44} +(-709.905 + 10466.0i) q^{45} +(-550.700 + 22215.8i) q^{46} -11782.0i q^{47} +(-4839.57 - 5178.96i) q^{48} -6128.42 q^{49} +11049.7i q^{50} +(18309.8 + 19593.9i) q^{51} -5914.46 q^{52} -1891.55 q^{53} +(20961.9 + 25720.8i) q^{54} +26372.4 q^{55} -16884.4 q^{56} +(6312.74 - 5899.05i) q^{57} -61367.2 q^{58} +7712.06i q^{59} +(-20550.4 - 21991.5i) q^{60} +1208.84i q^{61} -42216.7i q^{62} +(-36716.6 - 2490.48i) q^{63} +51588.8 q^{64} +5708.30 q^{65} +(60948.6 - 56954.5i) q^{66} -41089.5i q^{67} -76946.8 q^{68} +(-26277.4 - 29555.6i) q^{69} +57266.4 q^{70} -8193.96i q^{71} +(-27029.7 - 1833.42i) q^{72} -78243.7 q^{73} +11602.9 q^{74} +(-13425.9 - 14367.5i) q^{75} +24790.7i q^{76} +92519.5i q^{77} +(13192.3 - 12327.8i) q^{78} +77477.3i q^{79} -19629.3 q^{80} +(-58508.1 - 7973.88i) q^{81} +2024.37 q^{82} -17093.4 q^{83} +(77150.5 - 72094.7i) q^{84} +74264.7 q^{85} +161296. q^{86} +(79793.5 - 74564.5i) q^{87} +68110.1i q^{88} -135956. q^{89} +(91676.0 + 6218.37i) q^{90} +20025.8i q^{91} +(113439. + 2812.01i) q^{92} +(51295.5 + 54892.7i) q^{93} -103204. q^{94} -23926.5i q^{95} +(-85998.8 + 80363.1i) q^{96} -75181.6i q^{97} +53681.6i q^{98} +(-10046.4 + 148112. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 408q^{4} - 528q^{6} - 444q^{9} + O(q^{10}) \) \( 32q - 408q^{4} - 528q^{6} - 444q^{9} - 2484q^{12} + 520q^{13} + 4936q^{16} + 7188q^{18} + 18660q^{24} + 36032q^{25} - 22032q^{27} + 6544q^{31} - 33912q^{36} - 63912q^{39} + 54328q^{46} + 88284q^{48} - 207664q^{49} + 46296q^{52} - 38628q^{54} - 139296q^{55} - 184144q^{58} + 486584q^{64} - 113580q^{69} + 37176q^{70} - 15504q^{72} - 93896q^{73} + 249840q^{75} + 368028q^{78} - 339372q^{81} - 23512q^{82} + 259584q^{85} + 509928q^{87} + 82740q^{93} - 562000q^{94} + 1404q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.75944i 1.54847i −0.632901 0.774233i \(-0.718136\pi\)
0.632901 0.774233i \(-0.281864\pi\)
\(3\) 10.6432 + 11.3896i 0.682761 + 0.730642i
\(4\) −44.7279 −1.39775
\(5\) 43.1688 0.772227 0.386113 0.922451i \(-0.373817\pi\)
0.386113 + 0.922451i \(0.373817\pi\)
\(6\) 99.7663 93.2285i 1.13137 1.05723i
\(7\) 151.444i 1.16818i 0.811690 + 0.584088i \(0.198548\pi\)
−0.811690 + 0.584088i \(0.801452\pi\)
\(8\) 111.489i 0.615895i
\(9\) −16.4449 + 242.443i −0.0676743 + 0.997707i
\(10\) 378.135i 1.19577i
\(11\) 610.914 1.52229 0.761146 0.648580i \(-0.224637\pi\)
0.761146 + 0.648580i \(0.224637\pi\)
\(12\) −476.047 509.431i −0.954326 1.02125i
\(13\) 132.232 0.217009 0.108505 0.994096i \(-0.465394\pi\)
0.108505 + 0.994096i \(0.465394\pi\)
\(14\) 1326.57 1.80888
\(15\) 459.454 + 491.674i 0.527246 + 0.564221i
\(16\) −454.710 −0.444053
\(17\) 1720.33 1.44374 0.721872 0.692026i \(-0.243282\pi\)
0.721872 + 0.692026i \(0.243282\pi\)
\(18\) 2123.67 + 144.048i 1.54492 + 0.104791i
\(19\) 554.256i 0.352230i −0.984370 0.176115i \(-0.943647\pi\)
0.984370 0.176115i \(-0.0563530\pi\)
\(20\) −1930.85 −1.07938
\(21\) −1724.89 + 1611.85i −0.853518 + 0.797585i
\(22\) 5351.26i 2.35722i
\(23\) −2536.22 62.8693i −0.999693 0.0247810i
\(24\) −1269.81 + 1186.60i −0.449999 + 0.420509i
\(25\) −1261.46 −0.403666
\(26\) 1158.28i 0.336031i
\(27\) −2936.35 + 2393.07i −0.775172 + 0.631750i
\(28\) 6773.79i 1.63281i
\(29\) 7005.84i 1.54691i −0.633851 0.773455i \(-0.718527\pi\)
0.633851 0.773455i \(-0.281473\pi\)
\(30\) 4306.79 4024.56i 0.873677 0.816423i
\(31\) 4819.56 0.900748 0.450374 0.892840i \(-0.351291\pi\)
0.450374 + 0.892840i \(0.351291\pi\)
\(32\) 7550.66i 1.30350i
\(33\) 6502.07 + 6958.05i 1.03936 + 1.11225i
\(34\) 15069.2i 2.23559i
\(35\) 6537.67i 0.902097i
\(36\) 735.543 10844.0i 0.0945915 1.39454i
\(37\) 1324.61i 0.159069i 0.996832 + 0.0795343i \(0.0253433\pi\)
−0.996832 + 0.0795343i \(0.974657\pi\)
\(38\) −4854.97 −0.545416
\(39\) 1407.37 + 1506.07i 0.148166 + 0.158556i
\(40\) 4812.84i 0.475611i
\(41\) 231.107i 0.0214710i 0.999942 + 0.0107355i \(0.00341729\pi\)
−0.999942 + 0.0107355i \(0.996583\pi\)
\(42\) 14118.9 + 15109.1i 1.23503 + 1.32164i
\(43\) 18413.9i 1.51871i 0.650675 + 0.759357i \(0.274486\pi\)
−0.650675 + 0.759357i \(0.725514\pi\)
\(44\) −27324.9 −2.12778
\(45\) −709.905 + 10466.0i −0.0522599 + 0.770456i
\(46\) −550.700 + 22215.8i −0.0383726 + 1.54799i
\(47\) 11782.0i 0.777990i −0.921240 0.388995i \(-0.872822\pi\)
0.921240 0.388995i \(-0.127178\pi\)
\(48\) −4839.57 5178.96i −0.303182 0.324444i
\(49\) −6128.42 −0.364635
\(50\) 11049.7i 0.625063i
\(51\) 18309.8 + 19593.9i 0.985733 + 1.05486i
\(52\) −5914.46 −0.303324
\(53\) −1891.55 −0.0924973 −0.0462487 0.998930i \(-0.514727\pi\)
−0.0462487 + 0.998930i \(0.514727\pi\)
\(54\) 20961.9 + 25720.8i 0.978244 + 1.20033i
\(55\) 26372.4 1.17556
\(56\) −16884.4 −0.719474
\(57\) 6312.74 5899.05i 0.257354 0.240489i
\(58\) −61367.2 −2.39534
\(59\) 7712.06i 0.288430i 0.989546 + 0.144215i \(0.0460657\pi\)
−0.989546 + 0.144215i \(0.953934\pi\)
\(60\) −20550.4 21991.5i −0.736956 0.788637i
\(61\) 1208.84i 0.0415953i 0.999784 + 0.0207977i \(0.00662058\pi\)
−0.999784 + 0.0207977i \(0.993379\pi\)
\(62\) 42216.7i 1.39478i
\(63\) −36716.6 2490.48i −1.16550 0.0790555i
\(64\) 51588.8 1.57437
\(65\) 5708.30 0.167580
\(66\) 60948.6 56954.5i 1.72228 1.60942i
\(67\) 41089.5i 1.11826i −0.829080 0.559131i \(-0.811135\pi\)
0.829080 0.559131i \(-0.188865\pi\)
\(68\) −76946.8 −2.01799
\(69\) −26277.4 29555.6i −0.664445 0.747337i
\(70\) 57266.4 1.39687
\(71\) 8193.96i 0.192907i −0.995337 0.0964535i \(-0.969250\pi\)
0.995337 0.0964535i \(-0.0307499\pi\)
\(72\) −27029.7 1833.42i −0.614483 0.0416803i
\(73\) −78243.7 −1.71847 −0.859235 0.511581i \(-0.829060\pi\)
−0.859235 + 0.511581i \(0.829060\pi\)
\(74\) 11602.9 0.246312
\(75\) −13425.9 14367.5i −0.275607 0.294935i
\(76\) 24790.7i 0.492328i
\(77\) 92519.5i 1.77831i
\(78\) 13192.3 12327.8i 0.245519 0.229429i
\(79\) 77477.3i 1.39671i 0.715751 + 0.698356i \(0.246085\pi\)
−0.715751 + 0.698356i \(0.753915\pi\)
\(80\) −19629.3 −0.342910
\(81\) −58508.1 7973.88i −0.990840 0.135038i
\(82\) 2024.37 0.0332472
\(83\) −17093.4 −0.272354 −0.136177 0.990685i \(-0.543482\pi\)
−0.136177 + 0.990685i \(0.543482\pi\)
\(84\) 77150.5 72094.7i 1.19300 1.11482i
\(85\) 74264.7 1.11490
\(86\) 161296. 2.35168
\(87\) 79793.5 74564.5i 1.13024 1.05617i
\(88\) 68110.1i 0.937573i
\(89\) −135956. −1.81938 −0.909691 0.415286i \(-0.863681\pi\)
−0.909691 + 0.415286i \(0.863681\pi\)
\(90\) 91676.0 + 6218.37i 1.19303 + 0.0809227i
\(91\) 20025.8i 0.253505i
\(92\) 113439. + 2812.01i 1.39732 + 0.0346376i
\(93\) 51295.5 + 54892.7i 0.614996 + 0.658124i
\(94\) −103204. −1.20469
\(95\) 23926.5i 0.272001i
\(96\) −85998.8 + 80363.1i −0.952388 + 0.889976i
\(97\) 75181.6i 0.811302i −0.914028 0.405651i \(-0.867045\pi\)
0.914028 0.405651i \(-0.132955\pi\)
\(98\) 53681.6i 0.564625i
\(99\) −10046.4 + 148112.i −0.103020 + 1.51880i
\(100\) 56422.2 0.564222
\(101\) 182646.i 1.78159i −0.454410 0.890793i \(-0.650150\pi\)
0.454410 0.890793i \(-0.349850\pi\)
\(102\) 171631. 160384.i 1.63341 1.52637i
\(103\) 60433.1i 0.561283i −0.959813 0.280642i \(-0.909453\pi\)
0.959813 0.280642i \(-0.0905472\pi\)
\(104\) 14742.4i 0.133655i
\(105\) −74461.3 + 69581.7i −0.659109 + 0.615917i
\(106\) 16569.0i 0.143229i
\(107\) 19007.4 0.160495 0.0802477 0.996775i \(-0.474429\pi\)
0.0802477 + 0.996775i \(0.474429\pi\)
\(108\) 131337. 107037.i 1.08349 0.883026i
\(109\) 95078.3i 0.766505i −0.923644 0.383253i \(-0.874804\pi\)
0.923644 0.383253i \(-0.125196\pi\)
\(110\) 231008.i 1.82031i
\(111\) −15086.8 + 14098.1i −0.116222 + 0.108606i
\(112\) 68863.3i 0.518732i
\(113\) −68259.2 −0.502881 −0.251440 0.967873i \(-0.580904\pi\)
−0.251440 + 0.967873i \(0.580904\pi\)
\(114\) −51672.4 55296.1i −0.372389 0.398503i
\(115\) −109485. 2713.99i −0.771989 0.0191366i
\(116\) 313356.i 2.16219i
\(117\) −2174.54 + 32058.7i −0.0146860 + 0.216512i
\(118\) 67553.3 0.446624
\(119\) 260535.i 1.68655i
\(120\) −54816.2 + 51224.0i −0.347501 + 0.324729i
\(121\) 212165. 1.31738
\(122\) 10588.8 0.0644089
\(123\) −2632.21 + 2459.71i −0.0156876 + 0.0146596i
\(124\) −215569. −1.25902
\(125\) −189358. −1.08395
\(126\) −21815.2 + 321617.i −0.122415 + 1.80473i
\(127\) −162337. −0.893116 −0.446558 0.894755i \(-0.647350\pi\)
−0.446558 + 0.894755i \(0.647350\pi\)
\(128\) 210268.i 1.13435i
\(129\) −209727. + 195983.i −1.10964 + 1.03692i
\(130\) 50001.5i 0.259492i
\(131\) 120535.i 0.613669i −0.951763 0.306835i \(-0.900730\pi\)
0.951763 0.306835i \(-0.0992699\pi\)
\(132\) −290824. 311219.i −1.45276 1.55464i
\(133\) 83939.0 0.411466
\(134\) −359921. −1.73159
\(135\) −126759. + 103306.i −0.598608 + 0.487854i
\(136\) 191798.i 0.889195i
\(137\) 324305. 1.47623 0.738113 0.674677i \(-0.235717\pi\)
0.738113 + 0.674677i \(0.235717\pi\)
\(138\) −258890. + 230175.i −1.15723 + 1.02887i
\(139\) 168785. 0.740964 0.370482 0.928840i \(-0.379193\pi\)
0.370482 + 0.928840i \(0.379193\pi\)
\(140\) 292416.i 1.26090i
\(141\) 134192. 125398.i 0.568432 0.531182i
\(142\) −71774.5 −0.298710
\(143\) 80782.4 0.330352
\(144\) 7477.65 110241.i 0.0300510 0.443035i
\(145\) 302433.i 1.19456i
\(146\) 685371.i 2.66099i
\(147\) −65226.0 69800.1i −0.248959 0.266417i
\(148\) 59247.1i 0.222338i
\(149\) 346489. 1.27857 0.639283 0.768971i \(-0.279231\pi\)
0.639283 + 0.768971i \(0.279231\pi\)
\(150\) −125851. + 117604.i −0.456697 + 0.426769i
\(151\) −484291. −1.72848 −0.864239 0.503082i \(-0.832199\pi\)
−0.864239 + 0.503082i \(0.832199\pi\)
\(152\) 61793.4 0.216937
\(153\) −28290.6 + 417083.i −0.0977044 + 1.44043i
\(154\) 810419. 2.75365
\(155\) 208055. 0.695581
\(156\) −62948.7 67363.1i −0.207098 0.221621i
\(157\) 129167.i 0.418218i −0.977892 0.209109i \(-0.932944\pi\)
0.977892 0.209109i \(-0.0670564\pi\)
\(158\) 678658. 2.16276
\(159\) −20132.2 21544.0i −0.0631536 0.0675824i
\(160\) 325953.i 1.00659i
\(161\) 9521.21 384096.i 0.0289486 1.16782i
\(162\) −69846.7 + 512499.i −0.209102 + 1.53428i
\(163\) −54105.7 −0.159505 −0.0797525 0.996815i \(-0.525413\pi\)
−0.0797525 + 0.996815i \(0.525413\pi\)
\(164\) 10336.9i 0.0300110i
\(165\) 280687. + 300370.i 0.802623 + 0.858909i
\(166\) 149729.i 0.421730i
\(167\) 46358.5i 0.128629i −0.997930 0.0643144i \(-0.979514\pi\)
0.997930 0.0643144i \(-0.0204861\pi\)
\(168\) −179704. 192306.i −0.491229 0.525678i
\(169\) −353808. −0.952907
\(170\) 650517.i 1.72638i
\(171\) 134375. + 9114.66i 0.351422 + 0.0238369i
\(172\) 823617.i 2.12277i
\(173\) 371854.i 0.944620i 0.881433 + 0.472310i \(0.156580\pi\)
−0.881433 + 0.472310i \(0.843420\pi\)
\(174\) −653143. 698947.i −1.63544 1.75013i
\(175\) 191041.i 0.471553i
\(176\) −277789. −0.675979
\(177\) −87837.0 + 82080.9i −0.210739 + 0.196929i
\(178\) 1.19090e6i 2.81725i
\(179\) 320039.i 0.746570i 0.927717 + 0.373285i \(0.121769\pi\)
−0.927717 + 0.373285i \(0.878231\pi\)
\(180\) 31752.5 468120.i 0.0730461 1.07690i
\(181\) 512556.i 1.16291i 0.813580 + 0.581453i \(0.197516\pi\)
−0.813580 + 0.581453i \(0.802484\pi\)
\(182\) 175415. 0.392544
\(183\) −13768.2 + 12865.9i −0.0303913 + 0.0283997i
\(184\) 7009.23 282760.i 0.0152625 0.615706i
\(185\) 57181.9i 0.122837i
\(186\) 480830. 449320.i 1.01908 0.952299i
\(187\) 1.05098e6 2.19780
\(188\) 526983.i 1.08743i
\(189\) −362417. 444694.i −0.737995 0.905537i
\(190\) −209583. −0.421185
\(191\) 269982. 0.535489 0.267745 0.963490i \(-0.413722\pi\)
0.267745 + 0.963490i \(0.413722\pi\)
\(192\) 549070. + 587575.i 1.07492 + 1.15030i
\(193\) −624538. −1.20688 −0.603442 0.797407i \(-0.706205\pi\)
−0.603442 + 0.797407i \(0.706205\pi\)
\(194\) −658549. −1.25627
\(195\) 60754.5 + 65015.1i 0.114417 + 0.122441i
\(196\) 274111. 0.509667
\(197\) 733978.i 1.34747i −0.738975 0.673733i \(-0.764690\pi\)
0.738975 0.673733i \(-0.235310\pi\)
\(198\) 1.29738e6 + 88000.8i 2.35181 + 0.159523i
\(199\) 896250.i 1.60434i −0.597095 0.802170i \(-0.703679\pi\)
0.597095 0.802170i \(-0.296321\pi\)
\(200\) 140638.i 0.248616i
\(201\) 467991. 437323.i 0.817048 0.763505i
\(202\) −1.59988e6 −2.75872
\(203\) 1.06099e6 1.80706
\(204\) −818960. 876392.i −1.37780 1.47443i
\(205\) 9976.60i 0.0165805i
\(206\) −529360. −0.869127
\(207\) 56949.9 613854.i 0.0923777 0.995724i
\(208\) −60127.3 −0.0963636
\(209\) 338602.i 0.536197i
\(210\) 609497. + 652240.i 0.953726 + 1.02061i
\(211\) 1.08224e6 1.67347 0.836737 0.547605i \(-0.184460\pi\)
0.836737 + 0.547605i \(0.184460\pi\)
\(212\) 84605.2 0.129288
\(213\) 93325.7 87209.9i 0.140946 0.131709i
\(214\) 166494.i 0.248522i
\(215\) 794908.i 1.17279i
\(216\) −266801. 327370.i −0.389092 0.477425i
\(217\) 729896.i 1.05223i
\(218\) −832833. −1.18691
\(219\) −832763. 891162.i −1.17330 1.25559i
\(220\) −1.17958e6 −1.64313
\(221\) 227483. 0.313306
\(222\) 123492. + 132152.i 0.168173 + 0.179966i
\(223\) 472939. 0.636859 0.318430 0.947947i \(-0.396845\pi\)
0.318430 + 0.947947i \(0.396845\pi\)
\(224\) −1.14350e6 −1.52271
\(225\) 20744.5 305831.i 0.0273178 0.402741i
\(226\) 597913.i 0.778694i
\(227\) 410057. 0.528177 0.264089 0.964498i \(-0.414929\pi\)
0.264089 + 0.964498i \(0.414929\pi\)
\(228\) −282355. + 263852.i −0.359715 + 0.336142i
\(229\) 395268.i 0.498085i −0.968493 0.249042i \(-0.919884\pi\)
0.968493 0.249042i \(-0.0801158\pi\)
\(230\) −23773.1 + 959031.i −0.0296323 + 1.19540i
\(231\) −1.05376e6 + 984703.i −1.29930 + 1.21416i
\(232\) 781073. 0.952734
\(233\) 1.00983e6i 1.21859i 0.792944 + 0.609294i \(0.208547\pi\)
−0.792944 + 0.609294i \(0.791453\pi\)
\(234\) 280817. + 19047.7i 0.335261 + 0.0227407i
\(235\) 508614.i 0.600785i
\(236\) 344944.i 0.403151i
\(237\) −882434. + 824606.i −1.02050 + 0.953621i
\(238\) 2.28214e6 2.61156
\(239\) 1.07223e6i 1.21421i −0.794623 0.607103i \(-0.792332\pi\)
0.794623 0.607103i \(-0.207668\pi\)
\(240\) −208918. 223569.i −0.234125 0.250544i
\(241\) 1.41714e6i 1.57170i 0.618415 + 0.785851i \(0.287775\pi\)
−0.618415 + 0.785851i \(0.712225\pi\)
\(242\) 1.85844e6i 2.03991i
\(243\) −531894. 751250.i −0.577843 0.816148i
\(244\) 54068.8i 0.0581397i
\(245\) −264556. −0.281581
\(246\) 21545.7 + 23056.7i 0.0226999 + 0.0242918i
\(247\) 73290.4i 0.0764372i
\(248\) 537328.i 0.554766i
\(249\) −181928. 194687.i −0.185952 0.198993i
\(250\) 1.65867e6i 1.67846i
\(251\) 387993. 0.388722 0.194361 0.980930i \(-0.437737\pi\)
0.194361 + 0.980930i \(0.437737\pi\)
\(252\) 1.64226e6 + 111394.i 1.62907 + 0.110499i
\(253\) −1.54941e6 38407.7i −1.52183 0.0377240i
\(254\) 1.42198e6i 1.38296i
\(255\) 790414. + 845843.i 0.761209 + 0.814591i
\(256\) −190992. −0.182144
\(257\) 972339.i 0.918301i −0.888359 0.459150i \(-0.848154\pi\)
0.888359 0.459150i \(-0.151846\pi\)
\(258\) 1.71670e6 + 1.83709e6i 1.60563 + 1.71823i
\(259\) −200605. −0.185820
\(260\) −255320. −0.234235
\(261\) 1.69852e6 + 115210.i 1.54336 + 0.104686i
\(262\) −1.05582e6 −0.950246
\(263\) 1.47839e6 1.31795 0.658977 0.752163i \(-0.270989\pi\)
0.658977 + 0.752163i \(0.270989\pi\)
\(264\) −775746. + 724909.i −0.685030 + 0.640138i
\(265\) −81656.1 −0.0714289
\(266\) 735259.i 0.637142i
\(267\) −1.44701e6 1.54848e6i −1.24220 1.32932i
\(268\) 1.83784e6i 1.56304i
\(269\) 1.39260e6i 1.17340i 0.809805 + 0.586699i \(0.199573\pi\)
−0.809805 + 0.586699i \(0.800427\pi\)
\(270\) 904901. + 1.11033e6i 0.755426 + 0.926925i
\(271\) −1.26005e6 −1.04223 −0.521115 0.853486i \(-0.674484\pi\)
−0.521115 + 0.853486i \(0.674484\pi\)
\(272\) −782253. −0.641099
\(273\) −228085. + 213139.i −0.185221 + 0.173083i
\(274\) 2.84073e6i 2.28588i
\(275\) −770641. −0.614498
\(276\) 1.17533e6 + 1.32196e6i 0.928726 + 1.04459i
\(277\) 1.23028e6 0.963397 0.481699 0.876337i \(-0.340020\pi\)
0.481699 + 0.876337i \(0.340020\pi\)
\(278\) 1.47846e6i 1.14736i
\(279\) −79257.0 + 1.16847e6i −0.0609575 + 0.898683i
\(280\) −728878. −0.555597
\(281\) −2.37975e6 −1.79790 −0.898951 0.438050i \(-0.855669\pi\)
−0.898951 + 0.438050i \(0.855669\pi\)
\(282\) −1.09842e6 1.17545e6i −0.822516 0.880198i
\(283\) 1.01299e6i 0.751863i −0.926647 0.375932i \(-0.877323\pi\)
0.926647 0.375932i \(-0.122677\pi\)
\(284\) 366498.i 0.269635i
\(285\) 272513. 254655.i 0.198735 0.185712i
\(286\) 707609.i 0.511538i
\(287\) −34999.8 −0.0250819
\(288\) −1.83060e6 124169.i −1.30051 0.0882132i
\(289\) 1.53969e6 1.08440
\(290\) −2.64915e6 −1.84974
\(291\) 856287. 800173.i 0.592771 0.553925i
\(292\) 3.49967e6 2.40198
\(293\) −1.28525e6 −0.874618 −0.437309 0.899311i \(-0.644068\pi\)
−0.437309 + 0.899311i \(0.644068\pi\)
\(294\) −611410. + 571343.i −0.412538 + 0.385504i
\(295\) 332920.i 0.222733i
\(296\) −147680. −0.0979696
\(297\) −1.79386e6 + 1.46196e6i −1.18004 + 0.961709i
\(298\) 3.03505e6i 1.97982i
\(299\) −335369. 8313.34i −0.216943 0.00537771i
\(300\) 600513. + 642625.i 0.385229 + 0.412244i
\(301\) −2.78869e6 −1.77412
\(302\) 4.24212e6i 2.67649i
\(303\) 2.08026e6 1.94394e6i 1.30170 1.21640i
\(304\) 252026.i 0.156409i
\(305\) 52184.2i 0.0321210i
\(306\) 3.65341e6 + 247810.i 2.23046 + 0.151292i
\(307\) 440102. 0.266507 0.133253 0.991082i \(-0.457458\pi\)
0.133253 + 0.991082i \(0.457458\pi\)
\(308\) 4.13820e6i 2.48562i
\(309\) 688308. 643201.i 0.410097 0.383222i
\(310\) 1.82244e6i 1.07708i
\(311\) 459889.i 0.269620i −0.990871 0.134810i \(-0.956958\pi\)
0.990871 0.134810i \(-0.0430424\pi\)
\(312\) −167910. + 156906.i −0.0976539 + 0.0912544i
\(313\) 2.79451e6i 1.61230i 0.591712 + 0.806149i \(0.298452\pi\)
−0.591712 + 0.806149i \(0.701548\pi\)
\(314\) −1.13143e6 −0.647597
\(315\) −1.58501e6 107511.i −0.900028 0.0610488i
\(316\) 3.46539e6i 1.95225i
\(317\) 2.26703e6i 1.26709i 0.773704 + 0.633547i \(0.218402\pi\)
−0.773704 + 0.633547i \(0.781598\pi\)
\(318\) −188713. + 176347.i −0.104649 + 0.0977911i
\(319\) 4.27996e6i 2.35485i
\(320\) 2.22703e6 1.21577
\(321\) 202299. + 216486.i 0.109580 + 0.117265i
\(322\) −3.36447e6 83400.5i −1.80832 0.0448259i
\(323\) 953505.i 0.508530i
\(324\) 2.61694e6 + 356655.i 1.38494 + 0.188749i
\(325\) −166805. −0.0875993
\(326\) 473936.i 0.246988i
\(327\) 1.08290e6 1.01194e6i 0.560041 0.523340i
\(328\) −25765.8 −0.0132239
\(329\) 1.78432e6 0.908830
\(330\) 2.63108e6 2.45866e6i 1.32999 1.24283i
\(331\) 85093.5 0.0426900 0.0213450 0.999772i \(-0.493205\pi\)
0.0213450 + 0.999772i \(0.493205\pi\)
\(332\) 764551. 0.380681
\(333\) −321143. 21783.1i −0.158704 0.0107649i
\(334\) −406075. −0.199177
\(335\) 1.77378e6i 0.863551i
\(336\) 784324. 732926.i 0.379007 0.354170i
\(337\) 2.25704e6i 1.08259i 0.840832 + 0.541297i \(0.182066\pi\)
−0.840832 + 0.541297i \(0.817934\pi\)
\(338\) 3.09916e6i 1.47554i
\(339\) −726496. 777443.i −0.343347 0.367426i
\(340\) −3.32170e6 −1.55834
\(341\) 2.94434e6 1.37120
\(342\) 79839.3 1.17705e6i 0.0369106 0.544165i
\(343\) 1.61721e6i 0.742218i
\(344\) −2.05295e6 −0.935368
\(345\) −1.13436e6 1.27588e6i −0.513102 0.577113i
\(346\) 3.25723e6 1.46271
\(347\) 895437.i 0.399219i −0.979876 0.199610i \(-0.936033\pi\)
0.979876 0.199610i \(-0.0639674\pi\)
\(348\) −3.56899e6 + 3.33511e6i −1.57978 + 1.47626i
\(349\) 1.69659e6 0.745614 0.372807 0.927909i \(-0.378395\pi\)
0.372807 + 0.927909i \(0.378395\pi\)
\(350\) −1.67341e6 −0.730183
\(351\) −388279. + 316440.i −0.168220 + 0.137096i
\(352\) 4.61280e6i 1.98430i
\(353\) 603075.i 0.257593i −0.991671 0.128797i \(-0.958889\pi\)
0.991671 0.128797i \(-0.0411114\pi\)
\(354\) 718983. + 769404.i 0.304937 + 0.326322i
\(355\) 353723.i 0.148968i
\(356\) 6.08103e6 2.54303
\(357\) −2.96738e6 + 2.77292e6i −1.23226 + 1.15151i
\(358\) 2.80337e6 1.15604
\(359\) 3.74407e6 1.53323 0.766617 0.642105i \(-0.221939\pi\)
0.766617 + 0.642105i \(0.221939\pi\)
\(360\) −1.16684e6 79146.5i −0.474520 0.0321866i
\(361\) 2.16890e6 0.875934
\(362\) 4.48970e6 1.80072
\(363\) 2.25811e6 + 2.41647e6i 0.899453 + 0.962529i
\(364\) 895712.i 0.354336i
\(365\) −3.37768e6 −1.32705
\(366\) 112698. + 120602.i 0.0439759 + 0.0470598i
\(367\) 4.16068e6i 1.61250i 0.591577 + 0.806249i \(0.298506\pi\)
−0.591577 + 0.806249i \(0.701494\pi\)
\(368\) 1.15324e6 + 28587.3i 0.443917 + 0.0110041i
\(369\) −56030.2 3800.52i −0.0214218 0.00145304i
\(370\) 500882. 0.190209
\(371\) 286465.i 0.108053i
\(372\) −2.29434e6 2.45523e6i −0.859607 0.919890i
\(373\) 3.99193e6i 1.48563i 0.669496 + 0.742816i \(0.266510\pi\)
−0.669496 + 0.742816i \(0.733490\pi\)
\(374\) 9.20596e6i 3.40322i
\(375\) −2.01537e6 2.15671e6i −0.740078 0.791978i
\(376\) 1.31356e6 0.479161
\(377\) 926396.i 0.335694i
\(378\) −3.89527e6 + 3.17457e6i −1.40219 + 1.14276i
\(379\) 98283.1i 0.0351464i 0.999846 + 0.0175732i \(0.00559401\pi\)
−0.999846 + 0.0175732i \(0.994406\pi\)
\(380\) 1.07018e6i 0.380189i
\(381\) −1.72778e6 1.84895e6i −0.609785 0.652547i
\(382\) 2.36489e6i 0.829186i
\(383\) 2.81372e6 0.980130 0.490065 0.871686i \(-0.336973\pi\)
0.490065 + 0.871686i \(0.336973\pi\)
\(384\) 2.39487e6 2.23793e6i 0.828807 0.774494i
\(385\) 3.99395e6i 1.37326i
\(386\) 5.47061e6i 1.86882i
\(387\) −4.46433e6 302815.i −1.51523 0.102778i
\(388\) 3.36271e6i 1.13399i
\(389\) −2.68573e6 −0.899889 −0.449944 0.893057i \(-0.648556\pi\)
−0.449944 + 0.893057i \(0.648556\pi\)
\(390\) 569496. 532176.i 0.189596 0.177171i
\(391\) −4.36314e6 108156.i −1.44330 0.0357775i
\(392\) 683251.i 0.224577i
\(393\) 1.37284e6 1.28288e6i 0.448372 0.418990i
\(394\) −6.42924e6 −2.08650
\(395\) 3.34460e6i 1.07858i
\(396\) 449354. 6.62472e6i 0.143996 2.12290i
\(397\) 3.49044e6 1.11149 0.555743 0.831354i \(-0.312434\pi\)
0.555743 + 0.831354i \(0.312434\pi\)
\(398\) −7.85065e6 −2.48427
\(399\) 893379. + 956029.i 0.280933 + 0.300635i
\(400\) 573597. 0.179249
\(401\) −1.45743e6 −0.452613 −0.226307 0.974056i \(-0.572665\pi\)
−0.226307 + 0.974056i \(0.572665\pi\)
\(402\) −3.83071e6 4.09934e6i −1.18226 1.26517i
\(403\) 637300. 0.195471
\(404\) 8.16936e6i 2.49020i
\(405\) −2.52572e6 344223.i −0.765153 0.104280i
\(406\) 9.29372e6i 2.79817i
\(407\) 809224.i 0.242149i
\(408\) −2.18450e6 + 2.04134e6i −0.649683 + 0.607108i
\(409\) −397052. −0.117365 −0.0586825 0.998277i \(-0.518690\pi\)
−0.0586825 + 0.998277i \(0.518690\pi\)
\(410\) 87389.4 0.0256743
\(411\) 3.45164e6 + 3.69370e6i 1.00791 + 1.07859i
\(412\) 2.70304e6i 0.784531i
\(413\) −1.16795e6 −0.336937
\(414\) −5.37702e6 498850.i −1.54184 0.143044i
\(415\) −737901. −0.210319
\(416\) 998439.i 0.282871i
\(417\) 1.79641e6 + 1.92239e6i 0.505901 + 0.541379i
\(418\) −2.96597e6 −0.830283
\(419\) 4.90111e6 1.36383 0.681913 0.731433i \(-0.261148\pi\)
0.681913 + 0.731433i \(0.261148\pi\)
\(420\) 3.33049e6 3.11224e6i 0.921267 0.860895i
\(421\) 4.82268e6i 1.32612i −0.748566 0.663061i \(-0.769257\pi\)
0.748566 0.663061i \(-0.230743\pi\)
\(422\) 9.47985e6i 2.59132i
\(423\) 2.85646e6 + 193753.i 0.776207 + 0.0526500i
\(424\) 210887.i 0.0569687i
\(425\) −2.17013e6 −0.582791
\(426\) −763910. 817481.i −0.203947 0.218250i
\(427\) −183072. −0.0485906
\(428\) −850159. −0.224332
\(429\) 859783. + 920077.i 0.225551 + 0.241369i
\(430\) 6.96295e6 1.81603
\(431\) −3.02169e6 −0.783533 −0.391767 0.920065i \(-0.628136\pi\)
−0.391767 + 0.920065i \(0.628136\pi\)
\(432\) 1.33519e6 1.08815e6i 0.344217 0.280531i
\(433\) 3.30312e6i 0.846650i 0.905978 + 0.423325i \(0.139137\pi\)
−0.905978 + 0.423325i \(0.860863\pi\)
\(434\) 6.39348e6 1.62934
\(435\) 3.44459e6 3.21886e6i 0.872799 0.815602i
\(436\) 4.25265e6i 1.07138i
\(437\) −34845.7 + 1.40571e6i −0.00872862 + 0.352122i
\(438\) −7.80609e6 + 7.29454e6i −1.94423 + 1.81682i
\(439\) −3.90756e6 −0.967708 −0.483854 0.875149i \(-0.660763\pi\)
−0.483854 + 0.875149i \(0.660763\pi\)
\(440\) 2.94023e6i 0.724019i
\(441\) 100781. 1.48579e6i 0.0246764 0.363799i
\(442\) 1.99263e6i 0.485143i
\(443\) 2.12284e6i 0.513934i −0.966420 0.256967i \(-0.917277\pi\)
0.966420 0.256967i \(-0.0827231\pi\)
\(444\) 674799. 630578.i 0.162449 0.151803i
\(445\) −5.86906e6 −1.40497
\(446\) 4.14269e6i 0.986154i
\(447\) 3.68775e6 + 3.94636e6i 0.872956 + 0.934174i
\(448\) 7.81284e6i 1.83914i
\(449\) 551494.i 0.129100i −0.997914 0.0645499i \(-0.979439\pi\)
0.997914 0.0645499i \(-0.0205612\pi\)
\(450\) −2.67891e6 181710.i −0.623630 0.0423007i
\(451\) 141186.i 0.0326852i
\(452\) 3.05309e6 0.702899
\(453\) −5.15440e6 5.51586e6i −1.18014 1.26290i
\(454\) 3.59187e6i 0.817864i
\(455\) 864490.i 0.195763i
\(456\) 657679. + 703800.i 0.148116 + 0.158503i
\(457\) 146258.i 0.0327590i −0.999866 0.0163795i \(-0.994786\pi\)
0.999866 0.0163795i \(-0.00521398\pi\)
\(458\) −3.46233e6 −0.771267
\(459\) −5.05150e6 + 4.11687e6i −1.11915 + 0.912086i
\(460\) 4.89704e6 + 121391.i 1.07904 + 0.0267480i
\(461\) 5.82484e6i 1.27653i −0.769816 0.638266i \(-0.779652\pi\)
0.769816 0.638266i \(-0.220348\pi\)
\(462\) 8.62545e6 + 9.23033e6i 1.88008 + 2.01193i
\(463\) 4.42318e6 0.958920 0.479460 0.877564i \(-0.340833\pi\)
0.479460 + 0.877564i \(0.340833\pi\)
\(464\) 3.18563e6i 0.686910i
\(465\) 2.21436e6 + 2.36965e6i 0.474916 + 0.508221i
\(466\) 8.84552e6 1.88694
\(467\) 1.31195e6 0.278371 0.139185 0.990266i \(-0.455552\pi\)
0.139185 + 0.990266i \(0.455552\pi\)
\(468\) 97262.4 1.43392e6i 0.0205272 0.302628i
\(469\) 6.22277e6 1.30633
\(470\) −4.45518e6 −0.930295
\(471\) 1.47116e6 1.37475e6i 0.305568 0.285543i
\(472\) −859809. −0.177643
\(473\) 1.12493e7i 2.31193i
\(474\) 7.22309e6 + 7.72963e6i 1.47665 + 1.58020i
\(475\) 699169.i 0.142183i
\(476\) 1.16532e7i 2.35736i
\(477\) 31106.3 458594.i 0.00625969 0.0922853i
\(478\) −9.39212e6 −1.88016
\(479\) 491382. 0.0978545 0.0489273 0.998802i \(-0.484420\pi\)
0.0489273 + 0.998802i \(0.484420\pi\)
\(480\) −3.71246e6 + 3.46918e6i −0.735460 + 0.687264i
\(481\) 175156.i 0.0345194i
\(482\) 1.24134e7 2.43373
\(483\) 4.47602e6 3.97956e6i 0.873021 0.776189i
\(484\) −9.48967e6 −1.84136
\(485\) 3.24550e6i 0.626509i
\(486\) −6.58054e6 + 4.65910e6i −1.26378 + 0.894770i
\(487\) −2.13183e6 −0.407315 −0.203657 0.979042i \(-0.565283\pi\)
−0.203657 + 0.979042i \(0.565283\pi\)
\(488\) −134772. −0.0256184
\(489\) −575858. 616241.i −0.108904 0.116541i
\(490\) 2.31737e6i 0.436018i
\(491\) 4.98864e6i 0.933854i 0.884296 + 0.466927i \(0.154639\pi\)
−0.884296 + 0.466927i \(0.845361\pi\)
\(492\) 117733. 110018.i 0.0219273 0.0204904i
\(493\) 1.20524e7i 2.23334i
\(494\) −641983. −0.118360
\(495\) −433690. + 6.39380e6i −0.0795549 + 1.17286i
\(496\) −2.19150e6 −0.399980
\(497\) 1.24093e6 0.225349
\(498\) −1.70535e6 + 1.59359e6i −0.308134 + 0.287941i
\(499\) 3.54759e6 0.637797 0.318898 0.947789i \(-0.396687\pi\)
0.318898 + 0.947789i \(0.396687\pi\)
\(500\) 8.46958e6 1.51508
\(501\) 528004. 493403.i 0.0939816 0.0878228i
\(502\) 3.39860e6i 0.601923i
\(503\) 442972. 0.0780651 0.0390325 0.999238i \(-0.487572\pi\)
0.0390325 + 0.999238i \(0.487572\pi\)
\(504\) 277661. 4.09350e6i 0.0486899 0.717825i
\(505\) 7.88460e6i 1.37579i
\(506\) −336430. + 1.35720e7i −0.0584143 + 2.35649i
\(507\) −3.76564e6 4.02972e6i −0.650608 0.696233i
\(508\) 7.26098e6 1.24835
\(509\) 5.88309e6i 1.00649i −0.864143 0.503247i \(-0.832139\pi\)
0.864143 0.503247i \(-0.167861\pi\)
\(510\) 7.40912e6 6.92358e6i 1.26137 1.17871i
\(511\) 1.18496e7i 2.00748i
\(512\) 5.05561e6i 0.852311i
\(513\) 1.32637e6 + 1.62749e6i 0.222521 + 0.273039i
\(514\) −8.51715e6 −1.42196
\(515\) 2.60882e6i 0.433438i
\(516\) 9.38064e6 8.76591e6i 1.55099 1.44935i
\(517\) 7.19778e6i 1.18433i
\(518\) 1.75719e6i 0.287736i
\(519\) −4.23526e6 + 3.95771e6i −0.690179 + 0.644950i
\(520\) 636412.i 0.103212i
\(521\) −8.70774e6 −1.40544 −0.702718 0.711468i \(-0.748031\pi\)
−0.702718 + 0.711468i \(0.748031\pi\)
\(522\) 1.00918e6 1.48780e7i 0.162103 2.38984i
\(523\) 4.34219e6i 0.694153i −0.937837 0.347076i \(-0.887174\pi\)
0.937837 0.347076i \(-0.112826\pi\)
\(524\) 5.39127e6i 0.857754i
\(525\) 2.17587e6 2.03328e6i 0.344536 0.321958i
\(526\) 1.29499e7i 2.04081i
\(527\) 8.29125e6 1.30045
\(528\) −2.95656e6 3.16390e6i −0.461532 0.493898i
\(529\) 6.42844e6 + 318900.i 0.998772 + 0.0495468i
\(530\) 715262.i 0.110605i
\(531\) −1.86973e6 126824.i −0.287769 0.0195193i
\(532\) −3.75441e6 −0.575125
\(533\) 30559.7i 0.00465941i
\(534\) −1.35638e7 + 1.26750e7i −2.05840 + 1.92351i
\(535\) 820525. 0.123939
\(536\) 4.58102e6 0.688732
\(537\) −3.64511e6 + 3.40624e6i −0.545475 + 0.509729i
\(538\) 1.21984e7 1.81697
\(539\) −3.74394e6 −0.555081
\(540\) 5.66964e6 4.62065e6i 0.836702 0.681896i
\(541\) 9.64282e6 1.41648 0.708241 0.705971i \(-0.249489\pi\)
0.708241 + 0.705971i \(0.249489\pi\)
\(542\) 1.10373e7i 1.61386i
\(543\) −5.83779e6 + 5.45523e6i −0.849668 + 0.793987i
\(544\) 1.29896e7i 1.88192i
\(545\) 4.10441e6i 0.591916i
\(546\) 1.86698e6 + 1.99790e6i 0.268014 + 0.286809i
\(547\) −4.65385e6 −0.665034 −0.332517 0.943097i \(-0.607898\pi\)
−0.332517 + 0.943097i \(0.607898\pi\)
\(548\) −1.45055e7 −2.06339
\(549\) −293075. 19879.2i −0.0415000 0.00281493i
\(550\) 6.75039e6i 0.951529i
\(551\) −3.88302e6 −0.544868
\(552\) 3.29512e6 2.92964e6i 0.460281 0.409229i
\(553\) −1.17335e7 −1.63161
\(554\) 1.07766e7i 1.49179i
\(555\) −651278. + 608598.i −0.0897499 + 0.0838684i
\(556\) −7.54940e6 −1.03568
\(557\) −1.19450e7 −1.63136 −0.815680 0.578504i \(-0.803637\pi\)
−0.815680 + 0.578504i \(0.803637\pi\)
\(558\) 1.02351e7 + 694247.i 1.39158 + 0.0943906i
\(559\) 2.43491e6i 0.329575i
\(560\) 2.97275e6i 0.400579i
\(561\) 1.11857e7 + 1.19702e7i 1.50057 + 1.60581i
\(562\) 2.08453e7i 2.78399i
\(563\) −5.15603e6 −0.685558 −0.342779 0.939416i \(-0.611368\pi\)
−0.342779 + 0.939416i \(0.611368\pi\)
\(564\) −6.00212e6 + 5.60879e6i −0.794523 + 0.742457i
\(565\) −2.94667e6 −0.388338
\(566\) −8.87322e6 −1.16423
\(567\) 1.20760e6 8.86073e6i 0.157749 1.15748i
\(568\) 913536. 0.118810
\(569\) 1.87013e6 0.242154 0.121077 0.992643i \(-0.461365\pi\)
0.121077 + 0.992643i \(0.461365\pi\)
\(570\) −2.23063e6 2.38706e6i −0.287569 0.307735i
\(571\) 7.63524e6i 0.980015i −0.871718 0.490007i \(-0.836994\pi\)
0.871718 0.490007i \(-0.163006\pi\)
\(572\) −3.61322e6 −0.461748
\(573\) 2.87347e6 + 3.07497e6i 0.365611 + 0.391251i
\(574\) 306579.i 0.0388385i
\(575\) 3.19933e6 + 79306.9i 0.403542 + 0.0100033i
\(576\) −848371. + 1.25073e7i −0.106544 + 1.57076i
\(577\) −3.94420e6 −0.493196 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(578\) 1.34868e7i 1.67915i
\(579\) −6.64708e6 7.11322e6i −0.824014 0.881800i
\(580\) 1.35272e7i 1.66970i
\(581\) 2.58870e6i 0.318157i
\(582\) −7.00907e6 7.50060e6i −0.857735 0.917885i
\(583\) −1.15558e6 −0.140808
\(584\) 8.72330e6i 1.05840i
\(585\) −93872.1 + 1.38394e6i −0.0113409 + 0.167196i
\(586\) 1.12581e7i 1.35432i
\(587\) 1.46795e7i 1.75839i 0.476464 + 0.879194i \(0.341918\pi\)
−0.476464 + 0.879194i \(0.658082\pi\)
\(588\) 2.91742e6 + 3.12201e6i 0.347981 + 0.372384i
\(589\) 2.67127e6i 0.317270i
\(590\) 2.91619e6 0.344895
\(591\) 8.35970e6 7.81187e6i 0.984514 0.919997i
\(592\) 602315.i 0.0706349i
\(593\) 9.13831e6i 1.06716i 0.845750 + 0.533580i \(0.179154\pi\)
−0.845750 + 0.533580i \(0.820846\pi\)
\(594\) 1.28059e7 + 1.57132e7i 1.48917 + 1.82725i
\(595\) 1.12470e7i 1.30240i
\(596\) −1.54977e7 −1.78711
\(597\) 1.02079e7 9.53896e6i 1.17220 1.09538i
\(598\) −72820.2 + 2.93765e6i −0.00832720 + 0.335928i
\(599\) 7.63288e6i 0.869203i −0.900623 0.434602i \(-0.856889\pi\)
0.900623 0.434602i \(-0.143111\pi\)
\(600\) 1.60181e6 1.49684e6i 0.181649 0.169745i
\(601\) −7.47363e6 −0.844006 −0.422003 0.906594i \(-0.638673\pi\)
−0.422003 + 0.906594i \(0.638673\pi\)
\(602\) 2.44274e7i 2.74717i
\(603\) 9.96185e6 + 675710.i 1.11570 + 0.0756776i
\(604\) 2.16613e7 2.41597
\(605\) 9.15889e6 1.01731
\(606\) −1.70278e7 1.82219e7i −1.88355 2.01564i
\(607\) 7.40886e6 0.816168 0.408084 0.912944i \(-0.366197\pi\)
0.408084 + 0.912944i \(0.366197\pi\)
\(608\) 4.18499e6 0.459130
\(609\) 1.12924e7 + 1.20843e7i 1.23379 + 1.32032i
\(610\) 457104. 0.0497383
\(611\) 1.55796e6i 0.168831i
\(612\) 1.26538e6 1.86552e7i 0.136566 2.01336i
\(613\) 1.25160e7i 1.34528i 0.739969 + 0.672641i \(0.234840\pi\)
−0.739969 + 0.672641i \(0.765160\pi\)
\(614\) 3.85505e6i 0.412676i
\(615\) −113629. + 106183.i −0.0121144 + 0.0113205i
\(616\) −1.03149e7 −1.09525
\(617\) 4.97604e6 0.526225 0.263112 0.964765i \(-0.415251\pi\)
0.263112 + 0.964765i \(0.415251\pi\)
\(618\) −5.63409e6 6.02919e6i −0.593406 0.635021i
\(619\) 5.54618e6i 0.581792i −0.956755 0.290896i \(-0.906047\pi\)
0.956755 0.290896i \(-0.0939534\pi\)
\(620\) −9.30583e6 −0.972246
\(621\) 7.59766e6 5.88473e6i 0.790589 0.612347i
\(622\) −4.02838e6 −0.417498
\(623\) 2.05898e7i 2.12536i
\(624\) −639946. 684824.i −0.0657933 0.0704073i
\(625\) −4.23230e6 −0.433388
\(626\) 2.44784e7 2.49659
\(627\) 3.85654e6 3.60381e6i 0.391768 0.366095i
\(628\) 5.77737e6i 0.584563i
\(629\) 2.27878e6i 0.229654i
\(630\) −941737. + 1.38838e7i −0.0945319 + 1.39366i
\(631\) 3.82572e6i 0.382507i −0.981541 0.191254i \(-0.938745\pi\)
0.981541 0.191254i \(-0.0612553\pi\)
\(632\) −8.63786e6 −0.860228
\(633\) 1.15185e7 + 1.23263e7i 1.14258 + 1.22271i
\(634\) 1.98579e7 1.96205
\(635\) −7.00788e6 −0.689688
\(636\) 900469. + 963617.i 0.0882726 + 0.0944630i
\(637\) −810374. −0.0791292
\(638\) −3.74901e7 −3.64640
\(639\) 1.98657e6 + 134748.i 0.192465 + 0.0130548i
\(640\) 9.07703e6i 0.875979i
\(641\) −4.33390e6 −0.416614 −0.208307 0.978063i \(-0.566795\pi\)
−0.208307 + 0.978063i \(0.566795\pi\)
\(642\) 1.89630e6 1.77203e6i 0.181580 0.169681i
\(643\) 1.11605e7i 1.06453i 0.846578 + 0.532265i \(0.178659\pi\)
−0.846578 + 0.532265i \(0.821341\pi\)
\(644\) −425863. + 1.71798e7i −0.0404628 + 1.63231i
\(645\) −9.05366e6 + 8.46036e6i −0.856890 + 0.800736i
\(646\) −8.35217e6 −0.787441
\(647\) 3.89565e6i 0.365863i −0.983126 0.182932i \(-0.941441\pi\)
0.983126 0.182932i \(-0.0585587\pi\)
\(648\) 888999. 6.52301e6i 0.0831695 0.610254i
\(649\) 4.71140e6i 0.439075i
\(650\) 1.46112e6i 0.135644i
\(651\) −8.31320e6 + 7.76842e6i −0.768804 + 0.718423i
\(652\) 2.42003e6 0.222947
\(653\) 1.74450e6i 0.160099i 0.996791 + 0.0800495i \(0.0255078\pi\)
−0.996791 + 0.0800495i \(0.974492\pi\)
\(654\) −8.86400e6 9.48561e6i −0.810374 0.867204i
\(655\) 5.20334e6i 0.473892i
\(656\) 105087.i 0.00953428i
\(657\) 1.28671e6 1.89696e7i 0.116296 1.71453i
\(658\) 1.56296e7i 1.40729i
\(659\) 732273. 0.0656839 0.0328420 0.999461i \(-0.489544\pi\)
0.0328420 + 0.999461i \(0.489544\pi\)
\(660\) −1.25545e7 1.34349e7i −1.12186 1.20054i
\(661\) 6.40243e6i 0.569956i 0.958534 + 0.284978i \(0.0919863\pi\)
−0.958534 + 0.284978i \(0.908014\pi\)
\(662\) 745372.i 0.0661041i
\(663\) 2.42115e6 + 2.59094e6i 0.213913 + 0.228914i
\(664\) 1.90572e6i 0.167741i
\(665\) 3.62354e6 0.317745
\(666\) −190808. + 2.81303e6i −0.0166690 + 0.245748i
\(667\) −440452. + 1.77683e7i −0.0383340 + 1.54643i
\(668\) 2.07352e6i 0.179790i
\(669\) 5.03359e6 + 5.38658e6i 0.434823 + 0.465316i
\(670\) −1.55373e7 −1.33718
\(671\) 738497.i 0.0633203i
\(672\) −1.21705e7 1.30240e7i −1.03965 1.11256i
\(673\) −1.55698e7 −1.32509 −0.662546 0.749021i \(-0.730524\pi\)
−0.662546 + 0.749021i \(0.730524\pi\)
\(674\) 1.97704e7 1.67636
\(675\) 3.70407e6 3.01875e6i 0.312911 0.255016i
\(676\) 1.58251e7 1.33192
\(677\) −445662. −0.0373710 −0.0186855 0.999825i \(-0.505948\pi\)
−0.0186855 + 0.999825i \(0.505948\pi\)
\(678\) −6.80997e6 + 6.36370e6i −0.568946 + 0.531662i
\(679\) 1.13858e7 0.947743
\(680\) 8.27969e6i 0.686660i
\(681\) 4.36432e6 + 4.67038e6i 0.360619 + 0.385908i
\(682\) 2.57907e7i 2.12326i
\(683\) 5.85494e6i 0.480254i 0.970741 + 0.240127i \(0.0771891\pi\)
−0.970741 + 0.240127i \(0.922811\pi\)
\(684\) −6.01032e6 407679.i −0.491199 0.0333179i
\(685\) 1.39999e7 1.13998
\(686\) 1.41659e7 1.14930
\(687\) 4.50194e6 4.20692e6i 0.363921 0.340073i
\(688\) 8.37301e6i 0.674389i
\(689\) −250124. −0.0200728
\(690\) −1.11760e7 + 9.93638e6i −0.893640 + 0.794522i
\(691\) 801751. 0.0638770 0.0319385 0.999490i \(-0.489832\pi\)
0.0319385 + 0.999490i \(0.489832\pi\)
\(692\) 1.66322e7i 1.32034i
\(693\) −2.24307e7 1.52147e6i −1.77423 0.120346i
\(694\) −7.84353e6 −0.618177
\(695\) 7.28625e6 0.572192
\(696\) 8.31311e6 + 8.89609e6i 0.650490 + 0.696107i
\(697\) 397581.i 0.0309987i
\(698\) 1.48612e7i 1.15456i
\(699\) −1.15015e7 + 1.07478e7i −0.890351 + 0.832004i
\(700\) 8.54483e6i 0.659111i
\(701\) −2.12413e7 −1.63263 −0.816313 0.577610i \(-0.803985\pi\)
−0.816313 + 0.577610i \(0.803985\pi\)
\(702\) 2.77184e6 + 3.40111e6i 0.212288 + 0.260482i
\(703\) 734174. 0.0560287
\(704\) 3.15163e7 2.39665
\(705\) 5.79290e6 5.41328e6i 0.438958 0.410193i
\(706\) −5.28260e6 −0.398874
\(707\) 2.76607e7 2.08121
\(708\) 3.92876e6 3.67130e6i 0.294559 0.275256i
\(709\) 3.90485e6i 0.291735i −0.989304 0.145868i \(-0.953403\pi\)
0.989304 0.145868i \(-0.0465974\pi\)
\(710\) −3.09842e6 −0.230672
\(711\) −1.87838e7 1.27410e6i −1.39351 0.0945215i
\(712\) 1.51576e7i 1.12055i
\(713\) −1.22234e7 303002.i −0.900471 0.0223214i
\(714\) 2.42893e7 + 2.59926e7i 1.78307 + 1.90811i
\(715\) 3.48728e6 0.255106
\(716\) 1.43147e7i 1.04352i
\(717\) 1.22122e7 1.14119e7i 0.887149 0.829013i
\(718\) 3.27960e7i 2.37416i
\(719\) 1.90699e7i 1.37571i 0.725848 + 0.687855i \(0.241448\pi\)
−0.725848 + 0.687855i \(0.758552\pi\)
\(720\) 322801. 4.75898e6i 0.0232062 0.342123i
\(721\) 9.15226e6 0.655677
\(722\) 1.89984e7i 1.35635i
\(723\) −1.61406e7 + 1.50829e7i −1.14835 + 1.07310i
\(724\) 2.29255e7i 1.62545i
\(725\) 8.83756e6i 0.624435i
\(726\) 2.11669e7 1.97798e7i 1.49044 1.39277i
\(727\) 1.09662e7i 0.769522i −0.923016 0.384761i \(-0.874284\pi\)
0.923016 0.384761i \(-0.125716\pi\)
\(728\) −2.23266e6 −0.156133
\(729\) 2.89537e6 1.40538e7i 0.201783 0.979430i
\(730\) 2.95866e7i 2.05489i
\(731\) 3.16781e7i 2.19263i
\(732\) 615821. 575465.i 0.0424793 0.0396955i
\(733\) 945012.i 0.0649647i −0.999472 0.0324824i \(-0.989659\pi\)
0.999472 0.0324824i \(-0.0103413\pi\)
\(734\) 3.64452e7 2.49690
\(735\) −2.81573e6 3.01319e6i −0.192252 0.205735i
\(736\) 474705. 1.91501e7i 0.0323020 1.30310i
\(737\) 2.51021e7i 1.70232i
\(738\) −33290.4 + 490793.i −0.00224998 + 0.0331709i
\(739\) −2.68786e7 −1.81049 −0.905243 0.424894i \(-0.860311\pi\)
−0.905243 + 0.424894i \(0.860311\pi\)
\(740\) 2.55762e6i 0.171695i
\(741\) 834746. 780044.i 0.0558482 0.0521883i
\(742\) −2.50928e6 −0.167317
\(743\) −1.24569e7 −0.827825 −0.413912 0.910317i \(-0.635838\pi\)
−0.413912 + 0.910317i \(0.635838\pi\)
\(744\) −6.11993e6 + 5.71888e6i −0.405335 + 0.378773i
\(745\) 1.49575e7 0.987343
\(746\) 3.49671e7 2.30045
\(747\) 281098. 4.14417e6i 0.0184313 0.271729i
\(748\) −4.70079e7 −3.07197
\(749\) 2.87856e6i 0.187487i
\(750\) −1.88916e7 + 1.76536e7i −1.22635 + 1.14599i
\(751\) 5.77627e6i 0.373721i 0.982386 + 0.186861i \(0.0598313\pi\)
−0.982386 + 0.186861i \(0.940169\pi\)
\(752\) 5.35739e6i 0.345469i
\(753\) 4.12948e6 + 4.41907e6i 0.265404 + 0.284017i
\(754\) −8.11471e6 −0.519810
\(755\) −2.09062e7 −1.33478
\(756\) 1.62101e7 + 1.98902e7i 1.03153 + 1.26571i
\(757\) 8.56985e6i 0.543542i 0.962362 + 0.271771i \(0.0876094\pi\)
−0.962362 + 0.271771i \(0.912391\pi\)
\(758\) 860906. 0.0544230
\(759\) −1.60532e7 1.80559e7i −1.01148 1.13767i
\(760\) 2.66755e6 0.167524
\(761\) 1.26939e7i 0.794570i −0.917695 0.397285i \(-0.869952\pi\)
0.917695 0.397285i \(-0.130048\pi\)
\(762\) −1.61957e7 + 1.51344e7i −1.01045 + 0.944230i
\(763\) 1.43991e7 0.895413
\(764\) −1.20757e7 −0.748477
\(765\) −1.22127e6 + 1.80049e7i −0.0754500 + 1.11234i
\(766\) 2.46466e7i 1.51770i
\(767\) 1.01978e6i 0.0625919i
\(768\) −2.03276e6 2.17531e6i −0.124361 0.133082i
\(769\) 216230.i 0.0131856i 0.999978 + 0.00659281i \(0.00209857\pi\)
−0.999978 + 0.00659281i \(0.997901\pi\)
\(770\) 3.49848e7 2.12644
\(771\) 1.10745e7 1.03488e7i 0.670949 0.626980i
\(772\) 2.79343e7 1.68692
\(773\) 2.26652e7 1.36430 0.682150 0.731212i \(-0.261045\pi\)
0.682150 + 0.731212i \(0.261045\pi\)
\(774\) −2.65249e6 + 3.91051e7i −0.159148 + 2.34628i
\(775\) −6.07966e6 −0.363601
\(776\) 8.38192e6 0.499677
\(777\) −2.13508e6 2.28481e6i −0.126871 0.135768i
\(778\) 2.35255e7i 1.39345i