Properties

Label 108.6.b.c.107.3
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{40} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.3
Root \(5.24560 - 3.02855i\) of \(x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} - 32033996800 x^{2} + 41943040000\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.c.107.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.45658 - 3.48409i) q^{2} +(7.72226 + 31.0543i) q^{4} +40.4806i q^{5} -148.504i q^{7} +(73.7809 - 165.301i) q^{8} +O(q^{10})\) \(q+(-4.45658 - 3.48409i) q^{2} +(7.72226 + 31.0543i) q^{4} +40.4806i q^{5} -148.504i q^{7} +(73.7809 - 165.301i) q^{8} +(141.038 - 180.405i) q^{10} -608.102 q^{11} +883.839 q^{13} +(-517.402 + 661.822i) q^{14} +(-904.733 + 479.618i) q^{16} +1133.69i q^{17} +1111.90i q^{19} +(-1257.09 + 312.602i) q^{20} +(2710.06 + 2118.68i) q^{22} +1347.14 q^{23} +1486.32 q^{25} +(-3938.90 - 3079.37i) q^{26} +(4611.69 - 1146.79i) q^{28} -1856.29i q^{29} -606.496i q^{31} +(5703.05 + 1014.71i) q^{32} +(3949.86 - 5052.36i) q^{34} +6011.54 q^{35} +13662.1 q^{37} +(3873.96 - 4955.28i) q^{38} +(6691.48 + 2986.69i) q^{40} +21260.5i q^{41} +12478.1i q^{43} +(-4695.92 - 18884.1i) q^{44} +(-6003.66 - 4693.57i) q^{46} +16295.9 q^{47} -5246.55 q^{49} +(-6623.92 - 5178.48i) q^{50} +(6825.24 + 27447.0i) q^{52} +1343.79i q^{53} -24616.3i q^{55} +(-24547.9 - 10956.8i) q^{56} +(-6467.48 + 8272.72i) q^{58} +31250.9 q^{59} +6502.94 q^{61} +(-2113.09 + 2702.90i) q^{62} +(-21880.8 - 24392.1i) q^{64} +35778.3i q^{65} +2355.02i q^{67} +(-35205.7 + 8754.61i) q^{68} +(-26790.9 - 20944.7i) q^{70} -26941.5 q^{71} -52309.9 q^{73} +(-60886.2 - 47599.9i) q^{74} +(-34529.3 + 8586.40i) q^{76} +90305.8i q^{77} +35732.6i q^{79} +(-19415.2 - 36624.1i) q^{80} +(74073.6 - 94749.4i) q^{82} +62926.7 q^{83} -45892.2 q^{85} +(43474.7 - 55609.6i) q^{86} +(-44866.3 + 100520. i) q^{88} +54560.1i q^{89} -131254. i q^{91} +(10403.0 + 41834.5i) q^{92} +(-72624.2 - 56776.5i) q^{94} -45010.4 q^{95} -142704. q^{97} +(23381.7 + 18279.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 20q^{4} + O(q^{10}) \) \( 20q + 20q^{4} + 184q^{10} - 116q^{13} - 4168q^{16} + 696q^{22} - 15228q^{25} - 4764q^{28} - 16520q^{34} - 6452q^{37} + 1504q^{40} - 9336q^{46} - 44464q^{49} + 8236q^{52} - 58736q^{58} + 84604q^{61} - 6496q^{64} + 138696q^{70} + 85420q^{73} + 89172q^{76} + 221200q^{82} + 180320q^{85} - 85824q^{88} - 60936q^{94} - 219908q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45658 3.48409i −0.787820 0.615906i
\(3\) 0 0
\(4\) 7.72226 + 31.0543i 0.241321 + 0.970445i
\(5\) 40.4806i 0.724139i 0.932151 + 0.362069i \(0.117930\pi\)
−0.932151 + 0.362069i \(0.882070\pi\)
\(6\) 0 0
\(7\) 148.504i 1.14550i −0.819731 0.572749i \(-0.805877\pi\)
0.819731 0.572749i \(-0.194123\pi\)
\(8\) 73.7809 165.301i 0.407586 0.913167i
\(9\) 0 0
\(10\) 141.038 180.405i 0.446001 0.570491i
\(11\) −608.102 −1.51529 −0.757643 0.652670i \(-0.773649\pi\)
−0.757643 + 0.652670i \(0.773649\pi\)
\(12\) 0 0
\(13\) 883.839 1.45049 0.725245 0.688490i \(-0.241726\pi\)
0.725245 + 0.688490i \(0.241726\pi\)
\(14\) −517.402 + 661.822i −0.705518 + 0.902446i
\(15\) 0 0
\(16\) −904.733 + 479.618i −0.883529 + 0.468377i
\(17\) 1133.69i 0.951415i 0.879603 + 0.475708i \(0.157808\pi\)
−0.879603 + 0.475708i \(0.842192\pi\)
\(18\) 0 0
\(19\) 1111.90i 0.706614i 0.935507 + 0.353307i \(0.114943\pi\)
−0.935507 + 0.353307i \(0.885057\pi\)
\(20\) −1257.09 + 312.602i −0.702737 + 0.174750i
\(21\) 0 0
\(22\) 2710.06 + 2118.68i 1.19377 + 0.933273i
\(23\) 1347.14 0.531000 0.265500 0.964111i \(-0.414463\pi\)
0.265500 + 0.964111i \(0.414463\pi\)
\(24\) 0 0
\(25\) 1486.32 0.475623
\(26\) −3938.90 3079.37i −1.14273 0.893365i
\(27\) 0 0
\(28\) 4611.69 1146.79i 1.11164 0.276432i
\(29\) 1856.29i 0.409875i −0.978775 0.204937i \(-0.934301\pi\)
0.978775 0.204937i \(-0.0656991\pi\)
\(30\) 0 0
\(31\) 606.496i 0.113351i −0.998393 0.0566753i \(-0.981950\pi\)
0.998393 0.0566753i \(-0.0180500\pi\)
\(32\) 5703.05 + 1014.71i 0.984538 + 0.175174i
\(33\) 0 0
\(34\) 3949.86 5052.36i 0.585982 0.749544i
\(35\) 6011.54 0.829499
\(36\) 0 0
\(37\) 13662.1 1.64064 0.820319 0.571906i \(-0.193796\pi\)
0.820319 + 0.571906i \(0.193796\pi\)
\(38\) 3873.96 4955.28i 0.435208 0.556685i
\(39\) 0 0
\(40\) 6691.48 + 2986.69i 0.661260 + 0.295148i
\(41\) 21260.5i 1.97522i 0.156939 + 0.987608i \(0.449837\pi\)
−0.156939 + 0.987608i \(0.550163\pi\)
\(42\) 0 0
\(43\) 12478.1i 1.02914i 0.857447 + 0.514572i \(0.172049\pi\)
−0.857447 + 0.514572i \(0.827951\pi\)
\(44\) −4695.92 18884.1i −0.365670 1.47050i
\(45\) 0 0
\(46\) −6003.66 4693.57i −0.418332 0.327046i
\(47\) 16295.9 1.07606 0.538028 0.842927i \(-0.319170\pi\)
0.538028 + 0.842927i \(0.319170\pi\)
\(48\) 0 0
\(49\) −5246.55 −0.312165
\(50\) −6623.92 5178.48i −0.374705 0.292939i
\(51\) 0 0
\(52\) 6825.24 + 27447.0i 0.350033 + 1.40762i
\(53\) 1343.79i 0.0657115i 0.999460 + 0.0328558i \(0.0104602\pi\)
−0.999460 + 0.0328558i \(0.989540\pi\)
\(54\) 0 0
\(55\) 24616.3i 1.09728i
\(56\) −24547.9 10956.8i −1.04603 0.466888i
\(57\) 0 0
\(58\) −6467.48 + 8272.72i −0.252444 + 0.322907i
\(59\) 31250.9 1.16878 0.584389 0.811474i \(-0.301334\pi\)
0.584389 + 0.811474i \(0.301334\pi\)
\(60\) 0 0
\(61\) 6502.94 0.223761 0.111881 0.993722i \(-0.464313\pi\)
0.111881 + 0.993722i \(0.464313\pi\)
\(62\) −2113.09 + 2702.90i −0.0698133 + 0.0892999i
\(63\) 0 0
\(64\) −21880.8 24392.1i −0.667748 0.744387i
\(65\) 35778.3i 1.05036i
\(66\) 0 0
\(67\) 2355.02i 0.0640924i 0.999486 + 0.0320462i \(0.0102024\pi\)
−0.999486 + 0.0320462i \(0.989798\pi\)
\(68\) −35205.7 + 8754.61i −0.923297 + 0.229596i
\(69\) 0 0
\(70\) −26790.9 20944.7i −0.653496 0.510893i
\(71\) −26941.5 −0.634273 −0.317137 0.948380i \(-0.602721\pi\)
−0.317137 + 0.948380i \(0.602721\pi\)
\(72\) 0 0
\(73\) −52309.9 −1.14889 −0.574443 0.818545i \(-0.694781\pi\)
−0.574443 + 0.818545i \(0.694781\pi\)
\(74\) −60886.2 47599.9i −1.29253 1.01048i
\(75\) 0 0
\(76\) −34529.3 + 8586.40i −0.685731 + 0.170521i
\(77\) 90305.8i 1.73576i
\(78\) 0 0
\(79\) 35732.6i 0.644165i 0.946712 + 0.322082i \(0.104383\pi\)
−0.946712 + 0.322082i \(0.895617\pi\)
\(80\) −19415.2 36624.1i −0.339170 0.639797i
\(81\) 0 0
\(82\) 74073.6 94749.4i 1.21655 1.55612i
\(83\) 62926.7 1.00263 0.501314 0.865266i \(-0.332850\pi\)
0.501314 + 0.865266i \(0.332850\pi\)
\(84\) 0 0
\(85\) −45892.2 −0.688957
\(86\) 43474.7 55609.6i 0.633856 0.810781i
\(87\) 0 0
\(88\) −44866.3 + 100520.i −0.617608 + 1.38371i
\(89\) 54560.1i 0.730130i 0.930982 + 0.365065i \(0.118953\pi\)
−0.930982 + 0.365065i \(0.881047\pi\)
\(90\) 0 0
\(91\) 131254.i 1.66153i
\(92\) 10403.0 + 41834.5i 0.128141 + 0.515306i
\(93\) 0 0
\(94\) −72624.2 56776.5i −0.847738 0.662749i
\(95\) −45010.4 −0.511687
\(96\) 0 0
\(97\) −142704. −1.53995 −0.769973 0.638076i \(-0.779730\pi\)
−0.769973 + 0.638076i \(0.779730\pi\)
\(98\) 23381.7 + 18279.4i 0.245930 + 0.192264i
\(99\) 0 0
\(100\) 11477.8 + 46156.6i 0.114778 + 0.461566i
\(101\) 81531.3i 0.795282i −0.917541 0.397641i \(-0.869829\pi\)
0.917541 0.397641i \(-0.130171\pi\)
\(102\) 0 0
\(103\) 154038.i 1.43065i 0.698790 + 0.715327i \(0.253722\pi\)
−0.698790 + 0.715327i \(0.746278\pi\)
\(104\) 65210.4 146099.i 0.591199 1.32454i
\(105\) 0 0
\(106\) 4681.88 5988.71i 0.0404721 0.0517688i
\(107\) 164110. 1.38572 0.692859 0.721073i \(-0.256351\pi\)
0.692859 + 0.721073i \(0.256351\pi\)
\(108\) 0 0
\(109\) 136782. 1.10271 0.551355 0.834271i \(-0.314111\pi\)
0.551355 + 0.834271i \(0.314111\pi\)
\(110\) −85765.4 + 109705.i −0.675819 + 0.864456i
\(111\) 0 0
\(112\) 71225.4 + 134357.i 0.536525 + 1.01208i
\(113\) 172572.i 1.27138i −0.771946 0.635688i \(-0.780716\pi\)
0.771946 0.635688i \(-0.219284\pi\)
\(114\) 0 0
\(115\) 54533.2i 0.384517i
\(116\) 57645.7 14334.8i 0.397761 0.0989112i
\(117\) 0 0
\(118\) −139272. 108881.i −0.920786 0.719857i
\(119\) 168357. 1.08984
\(120\) 0 0
\(121\) 208737. 1.29609
\(122\) −28980.9 22656.8i −0.176284 0.137816i
\(123\) 0 0
\(124\) 18834.3 4683.52i 0.110001 0.0273538i
\(125\) 186669.i 1.06856i
\(126\) 0 0
\(127\) 247316.i 1.36064i −0.732916 0.680319i \(-0.761841\pi\)
0.732916 0.680319i \(-0.238159\pi\)
\(128\) 12529.3 + 184940.i 0.0675929 + 0.997713i
\(129\) 0 0
\(130\) 124655. 159449.i 0.646920 0.827492i
\(131\) −356981. −1.81747 −0.908733 0.417377i \(-0.862949\pi\)
−0.908733 + 0.417377i \(0.862949\pi\)
\(132\) 0 0
\(133\) 165122. 0.809425
\(134\) 8205.08 10495.3i 0.0394749 0.0504933i
\(135\) 0 0
\(136\) 187399. + 83644.3i 0.868801 + 0.387783i
\(137\) 256006.i 1.16533i −0.812713 0.582664i \(-0.802010\pi\)
0.812713 0.582664i \(-0.197990\pi\)
\(138\) 0 0
\(139\) 69026.5i 0.303025i −0.988455 0.151513i \(-0.951586\pi\)
0.988455 0.151513i \(-0.0484144\pi\)
\(140\) 46422.7 + 186684.i 0.200175 + 0.804984i
\(141\) 0 0
\(142\) 120067. + 93866.7i 0.499693 + 0.390653i
\(143\) −537464. −2.19791
\(144\) 0 0
\(145\) 75143.7 0.296806
\(146\) 233123. + 182252.i 0.905115 + 0.707605i
\(147\) 0 0
\(148\) 105502. + 424266.i 0.395920 + 1.59215i
\(149\) 52137.4i 0.192390i −0.995362 0.0961952i \(-0.969333\pi\)
0.995362 0.0961952i \(-0.0306673\pi\)
\(150\) 0 0
\(151\) 328419.i 1.17216i 0.810254 + 0.586078i \(0.199329\pi\)
−0.810254 + 0.586078i \(0.800671\pi\)
\(152\) 183798. + 82037.1i 0.645257 + 0.288006i
\(153\) 0 0
\(154\) 314633. 402455.i 1.06906 1.36746i
\(155\) 24551.3 0.0820816
\(156\) 0 0
\(157\) −312765. −1.01267 −0.506336 0.862336i \(-0.669001\pi\)
−0.506336 + 0.862336i \(0.669001\pi\)
\(158\) 124496. 159245.i 0.396745 0.507486i
\(159\) 0 0
\(160\) −41076.2 + 230863.i −0.126850 + 0.712942i
\(161\) 200057.i 0.608259i
\(162\) 0 0
\(163\) 517503.i 1.52561i 0.646628 + 0.762806i \(0.276179\pi\)
−0.646628 + 0.762806i \(0.723821\pi\)
\(164\) −660230. + 164179.i −1.91684 + 0.476661i
\(165\) 0 0
\(166\) −280438. 219242.i −0.789890 0.617524i
\(167\) −315354. −0.875000 −0.437500 0.899219i \(-0.644136\pi\)
−0.437500 + 0.899219i \(0.644136\pi\)
\(168\) 0 0
\(169\) 409879. 1.10392
\(170\) 204523. + 159893.i 0.542774 + 0.424332i
\(171\) 0 0
\(172\) −387497. + 96359.0i −0.998729 + 0.248354i
\(173\) 624427.i 1.58623i −0.609072 0.793115i \(-0.708458\pi\)
0.609072 0.793115i \(-0.291542\pi\)
\(174\) 0 0
\(175\) 220725.i 0.544825i
\(176\) 550170. 291656.i 1.33880 0.709725i
\(177\) 0 0
\(178\) 190092. 243152.i 0.449691 0.575211i
\(179\) −69186.2 −0.161394 −0.0806969 0.996739i \(-0.525715\pi\)
−0.0806969 + 0.996739i \(0.525715\pi\)
\(180\) 0 0
\(181\) −193421. −0.438840 −0.219420 0.975630i \(-0.570417\pi\)
−0.219420 + 0.975630i \(0.570417\pi\)
\(182\) −457301. + 584944.i −1.02335 + 1.30899i
\(183\) 0 0
\(184\) 99393.4 222684.i 0.216428 0.484891i
\(185\) 553049.i 1.18805i
\(186\) 0 0
\(187\) 689396.i 1.44167i
\(188\) 125841. + 506058.i 0.259674 + 1.04425i
\(189\) 0 0
\(190\) 200593. + 156820.i 0.403117 + 0.315151i
\(191\) 790470. 1.56784 0.783920 0.620861i \(-0.213217\pi\)
0.783920 + 0.620861i \(0.213217\pi\)
\(192\) 0 0
\(193\) −62439.3 −0.120660 −0.0603302 0.998178i \(-0.519215\pi\)
−0.0603302 + 0.998178i \(0.519215\pi\)
\(194\) 635970. + 497192.i 1.21320 + 0.948461i
\(195\) 0 0
\(196\) −40515.2 162928.i −0.0753318 0.302939i
\(197\) 965729.i 1.77292i −0.462803 0.886461i \(-0.653156\pi\)
0.462803 0.886461i \(-0.346844\pi\)
\(198\) 0 0
\(199\) 63953.7i 0.114481i −0.998360 0.0572405i \(-0.981770\pi\)
0.998360 0.0572405i \(-0.0182302\pi\)
\(200\) 109662. 245690.i 0.193857 0.434323i
\(201\) 0 0
\(202\) −284062. + 363351.i −0.489818 + 0.626539i
\(203\) −275667. −0.469510
\(204\) 0 0
\(205\) −860639. −1.43033
\(206\) 536682. 686483.i 0.881148 1.12710i
\(207\) 0 0
\(208\) −799639. + 423905.i −1.28155 + 0.679377i
\(209\) 676149.i 1.07072i
\(210\) 0 0
\(211\) 351620.i 0.543710i −0.962338 0.271855i \(-0.912363\pi\)
0.962338 0.271855i \(-0.0876371\pi\)
\(212\) −41730.4 + 10377.1i −0.0637694 + 0.0158575i
\(213\) 0 0
\(214\) −731369. 571773.i −1.09170 0.853472i
\(215\) −505120. −0.745244
\(216\) 0 0
\(217\) −90067.4 −0.129843
\(218\) −609578. 476559.i −0.868737 0.679165i
\(219\) 0 0
\(220\) 764441. 190094.i 1.06485 0.264795i
\(221\) 1.00200e6i 1.38002i
\(222\) 0 0
\(223\) 146682.i 0.197521i 0.995111 + 0.0987605i \(0.0314878\pi\)
−0.995111 + 0.0987605i \(0.968512\pi\)
\(224\) 150689. 846928.i 0.200661 1.12779i
\(225\) 0 0
\(226\) −601256. + 769082.i −0.783048 + 1.00162i
\(227\) 647121. 0.833529 0.416764 0.909015i \(-0.363164\pi\)
0.416764 + 0.909015i \(0.363164\pi\)
\(228\) 0 0
\(229\) 290803. 0.366446 0.183223 0.983071i \(-0.441347\pi\)
0.183223 + 0.983071i \(0.441347\pi\)
\(230\) 189998. 243032.i 0.236826 0.302931i
\(231\) 0 0
\(232\) −306847. 136959.i −0.374284 0.167059i
\(233\) 1.59729e6i 1.92750i 0.266808 + 0.963750i \(0.414031\pi\)
−0.266808 + 0.963750i \(0.585969\pi\)
\(234\) 0 0
\(235\) 659669.i 0.779213i
\(236\) 241327. + 970472.i 0.282050 + 1.13423i
\(237\) 0 0
\(238\) −750298. 586571.i −0.858601 0.671241i
\(239\) 129472. 0.146616 0.0733082 0.997309i \(-0.476644\pi\)
0.0733082 + 0.997309i \(0.476644\pi\)
\(240\) 0 0
\(241\) −609709. −0.676208 −0.338104 0.941109i \(-0.609786\pi\)
−0.338104 + 0.941109i \(0.609786\pi\)
\(242\) −930252. 727256.i −1.02109 0.798269i
\(243\) 0 0
\(244\) 50217.4 + 201944.i 0.0539982 + 0.217148i
\(245\) 212383.i 0.226050i
\(246\) 0 0
\(247\) 982743.i 1.02494i
\(248\) −100254. 44747.8i −0.103508 0.0462001i
\(249\) 0 0
\(250\) 650371. 831906.i 0.658129 0.841830i
\(251\) −529459. −0.530454 −0.265227 0.964186i \(-0.585447\pi\)
−0.265227 + 0.964186i \(0.585447\pi\)
\(252\) 0 0
\(253\) −819200. −0.804616
\(254\) −861670. + 1.10218e6i −0.838025 + 1.07194i
\(255\) 0 0
\(256\) 588509. 867853.i 0.561246 0.827649i
\(257\) 82551.1i 0.0779633i −0.999240 0.0389817i \(-0.987589\pi\)
0.999240 0.0389817i \(-0.0124114\pi\)
\(258\) 0 0
\(259\) 2.02888e6i 1.87935i
\(260\) −1.11107e6 + 276290.i −1.01931 + 0.253473i
\(261\) 0 0
\(262\) 1.59091e6 + 1.24375e6i 1.43184 + 1.11939i
\(263\) 866335. 0.772318 0.386159 0.922432i \(-0.373802\pi\)
0.386159 + 0.922432i \(0.373802\pi\)
\(264\) 0 0
\(265\) −54397.4 −0.0475842
\(266\) −735881. 575301.i −0.637681 0.498529i
\(267\) 0 0
\(268\) −73133.3 + 18186.0i −0.0621982 + 0.0154668i
\(269\) 1.20342e6i 1.01400i 0.861946 + 0.507000i \(0.169245\pi\)
−0.861946 + 0.507000i \(0.830755\pi\)
\(270\) 0 0
\(271\) 1.46736e6i 1.21371i 0.794814 + 0.606853i \(0.207568\pi\)
−0.794814 + 0.606853i \(0.792432\pi\)
\(272\) −543736. 1.02568e6i −0.445621 0.840603i
\(273\) 0 0
\(274\) −891946. + 1.14091e6i −0.717732 + 0.918068i
\(275\) −903835. −0.720705
\(276\) 0 0
\(277\) 2.23950e6 1.75368 0.876841 0.480781i \(-0.159647\pi\)
0.876841 + 0.480781i \(0.159647\pi\)
\(278\) −240494. + 307622.i −0.186635 + 0.238729i
\(279\) 0 0
\(280\) 443537. 993714.i 0.338092 0.757471i
\(281\) 153902.i 0.116273i 0.998309 + 0.0581364i \(0.0185158\pi\)
−0.998309 + 0.0581364i \(0.981484\pi\)
\(282\) 0 0
\(283\) 1.61247e6i 1.19681i −0.801194 0.598405i \(-0.795801\pi\)
0.801194 0.598405i \(-0.204199\pi\)
\(284\) −208050. 836649.i −0.153063 0.615528i
\(285\) 0 0
\(286\) 2.39525e6 + 1.87257e6i 1.73156 + 1.35370i
\(287\) 3.15728e6 2.26261
\(288\) 0 0
\(289\) 134615. 0.0948090
\(290\) −334884. 261807.i −0.233830 0.182805i
\(291\) 0 0
\(292\) −403951. 1.62445e6i −0.277250 1.11493i
\(293\) 1.89615e6i 1.29034i 0.764041 + 0.645168i \(0.223213\pi\)
−0.764041 + 0.645168i \(0.776787\pi\)
\(294\) 0 0
\(295\) 1.26505e6i 0.846357i
\(296\) 1.00800e6 2.25835e6i 0.668700 1.49818i
\(297\) 0 0
\(298\) −181651. + 232355.i −0.118494 + 0.151569i
\(299\) 1.19066e6 0.770210
\(300\) 0 0
\(301\) 1.85305e6 1.17888
\(302\) 1.14424e6 1.46363e6i 0.721938 0.923449i
\(303\) 0 0
\(304\) −533288. 1.00597e6i −0.330962 0.624314i
\(305\) 263243.i 0.162034i
\(306\) 0 0
\(307\) 92336.2i 0.0559147i 0.999609 + 0.0279573i \(0.00890026\pi\)
−0.999609 + 0.0279573i \(0.991100\pi\)
\(308\) −2.80438e6 + 697364.i −1.68446 + 0.418874i
\(309\) 0 0
\(310\) −109415. 85539.0i −0.0646655 0.0505545i
\(311\) −30371.7 −0.0178060 −0.00890302 0.999960i \(-0.502834\pi\)
−0.00890302 + 0.999960i \(0.502834\pi\)
\(312\) 0 0
\(313\) 1.36319e6 0.786494 0.393247 0.919433i \(-0.371352\pi\)
0.393247 + 0.919433i \(0.371352\pi\)
\(314\) 1.39386e6 + 1.08970e6i 0.797804 + 0.623711i
\(315\) 0 0
\(316\) −1.10965e6 + 275937.i −0.625127 + 0.155450i
\(317\) 1.16441e6i 0.650818i 0.945573 + 0.325409i \(0.105502\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(318\) 0 0
\(319\) 1.12881e6i 0.621077i
\(320\) 987406. 885746.i 0.539040 0.483542i
\(321\) 0 0
\(322\) −697015. + 891569.i −0.374630 + 0.479199i
\(323\) −1.26055e6 −0.672284
\(324\) 0 0
\(325\) 1.31367e6 0.689887
\(326\) 1.80303e6 2.30629e6i 0.939632 1.20191i
\(327\) 0 0
\(328\) 3.51439e6 + 1.56862e6i 1.80370 + 0.805070i
\(329\) 2.42002e6i 1.23262i
\(330\) 0 0
\(331\) 451430.i 0.226475i 0.993568 + 0.113237i \(0.0361221\pi\)
−0.993568 + 0.113237i \(0.963878\pi\)
\(332\) 485936. + 1.95414e6i 0.241955 + 0.972995i
\(333\) 0 0
\(334\) 1.40540e6 + 1.09872e6i 0.689342 + 0.538917i
\(335\) −95332.4 −0.0464118
\(336\) 0 0
\(337\) −2.16248e6 −1.03723 −0.518617 0.855007i \(-0.673553\pi\)
−0.518617 + 0.855007i \(0.673553\pi\)
\(338\) −1.82666e6 1.42805e6i −0.869693 0.679913i
\(339\) 0 0
\(340\) −354392. 1.42515e6i −0.166259 0.668595i
\(341\) 368811.i 0.171759i
\(342\) 0 0
\(343\) 1.71678e6i 0.787914i
\(344\) 2.06264e6 + 920643.i 0.939781 + 0.419465i
\(345\) 0 0
\(346\) −2.17556e6 + 2.78281e6i −0.976968 + 1.24966i
\(347\) 3.10525e6 1.38444 0.692219 0.721688i \(-0.256633\pi\)
0.692219 + 0.721688i \(0.256633\pi\)
\(348\) 0 0
\(349\) −2.35425e6 −1.03464 −0.517320 0.855792i \(-0.673070\pi\)
−0.517320 + 0.855792i \(0.673070\pi\)
\(350\) −769027. + 983681.i −0.335561 + 0.429224i
\(351\) 0 0
\(352\) −3.46803e6 617049.i −1.49186 0.265438i
\(353\) 1.94097e6i 0.829052i 0.910037 + 0.414526i \(0.136053\pi\)
−0.910037 + 0.414526i \(0.863947\pi\)
\(354\) 0 0
\(355\) 1.09061e6i 0.459302i
\(356\) −1.69432e6 + 421327.i −0.708552 + 0.176195i
\(357\) 0 0
\(358\) 308334. + 241051.i 0.127149 + 0.0994034i
\(359\) −1.33715e6 −0.547574 −0.273787 0.961790i \(-0.588276\pi\)
−0.273787 + 0.961790i \(0.588276\pi\)
\(360\) 0 0
\(361\) 1.23977e6 0.500696
\(362\) 861995. + 673895.i 0.345727 + 0.270284i
\(363\) 0 0
\(364\) 4.07600e6 1.01358e6i 1.61243 0.400962i
\(365\) 2.11754e6i 0.831953i
\(366\) 0 0
\(367\) 1.64386e6i 0.637087i 0.947908 + 0.318544i \(0.103194\pi\)
−0.947908 + 0.318544i \(0.896806\pi\)
\(368\) −1.21881e6 + 646114.i −0.469154 + 0.248708i
\(369\) 0 0
\(370\) 1.92687e6 2.46471e6i 0.731726 0.935969i
\(371\) 199559. 0.0752724
\(372\) 0 0
\(373\) −393084. −0.146290 −0.0731448 0.997321i \(-0.523304\pi\)
−0.0731448 + 0.997321i \(0.523304\pi\)
\(374\) −2.40192e6 + 3.07235e6i −0.887930 + 1.13577i
\(375\) 0 0
\(376\) 1.20233e6 2.69373e6i 0.438585 0.982618i
\(377\) 1.64066e6i 0.594519i
\(378\) 0 0
\(379\) 2.30537e6i 0.824410i −0.911091 0.412205i \(-0.864759\pi\)
0.911091 0.412205i \(-0.135241\pi\)
\(380\) −347582. 1.39777e6i −0.123481 0.496564i
\(381\) 0 0
\(382\) −3.52279e6 2.75407e6i −1.23518 0.965642i
\(383\) −2.70064e6 −0.940741 −0.470370 0.882469i \(-0.655880\pi\)
−0.470370 + 0.882469i \(0.655880\pi\)
\(384\) 0 0
\(385\) −3.65563e6 −1.25693
\(386\) 278266. + 217544.i 0.0950587 + 0.0743154i
\(387\) 0 0
\(388\) −1.10199e6 4.43155e6i −0.371621 1.49443i
\(389\) 1.65579e6i 0.554793i −0.960755 0.277397i \(-0.910528\pi\)
0.960755 0.277397i \(-0.0894716\pi\)
\(390\) 0 0
\(391\) 1.52724e6i 0.505201i
\(392\) −387095. + 867260.i −0.127234 + 0.285058i
\(393\) 0 0
\(394\) −3.36469e6 + 4.30385e6i −1.09195 + 1.39674i
\(395\) −1.44648e6 −0.466465
\(396\) 0 0
\(397\) −1.69988e6 −0.541306 −0.270653 0.962677i \(-0.587240\pi\)
−0.270653 + 0.962677i \(0.587240\pi\)
\(398\) −222820. + 285015.i −0.0705095 + 0.0901904i
\(399\) 0 0
\(400\) −1.34473e6 + 712867.i −0.420227 + 0.222771i
\(401\) 535612.i 0.166337i −0.996535 0.0831687i \(-0.973496\pi\)
0.996535 0.0831687i \(-0.0265040\pi\)
\(402\) 0 0
\(403\) 536045.i 0.164414i
\(404\) 2.53189e6 629606.i 0.771778 0.191918i
\(405\) 0 0
\(406\) 1.22853e6 + 960449.i 0.369890 + 0.289174i
\(407\) −8.30794e6 −2.48603
\(408\) 0 0
\(409\) −1.71273e6 −0.506268 −0.253134 0.967431i \(-0.581461\pi\)
−0.253134 + 0.967431i \(0.581461\pi\)
\(410\) 3.83551e6 + 2.99854e6i 1.12684 + 0.880949i
\(411\) 0 0
\(412\) −4.78353e6 + 1.18952e6i −1.38837 + 0.345246i
\(413\) 4.64089e6i 1.33883i
\(414\) 0 0
\(415\) 2.54731e6i 0.726041i
\(416\) 5.04058e6 + 896844.i 1.42806 + 0.254088i
\(417\) 0 0
\(418\) −2.35576e6 + 3.01332e6i −0.659464 + 0.843537i
\(419\) −1.98989e6 −0.553725 −0.276863 0.960909i \(-0.589295\pi\)
−0.276863 + 0.960909i \(0.589295\pi\)
\(420\) 0 0
\(421\) 849032. 0.233463 0.116732 0.993163i \(-0.462758\pi\)
0.116732 + 0.993163i \(0.462758\pi\)
\(422\) −1.22507e6 + 1.56702e6i −0.334874 + 0.428346i
\(423\) 0 0
\(424\) 222130. + 99145.9i 0.0600056 + 0.0267831i
\(425\) 1.68502e6i 0.452515i
\(426\) 0 0
\(427\) 965714.i 0.256318i
\(428\) 1.26730e6 + 5.09631e6i 0.334403 + 1.34476i
\(429\) 0 0
\(430\) 2.25111e6 + 1.75988e6i 0.587118 + 0.459000i
\(431\) 3.02456e6 0.784277 0.392139 0.919906i \(-0.371735\pi\)
0.392139 + 0.919906i \(0.371735\pi\)
\(432\) 0 0
\(433\) −1.32400e6 −0.339365 −0.169683 0.985499i \(-0.554274\pi\)
−0.169683 + 0.985499i \(0.554274\pi\)
\(434\) 401393. + 313803.i 0.102293 + 0.0799709i
\(435\) 0 0
\(436\) 1.05626e6 + 4.24765e6i 0.266107 + 1.07012i
\(437\) 1.49789e6i 0.375212i
\(438\) 0 0
\(439\) 1.74480e6i 0.432100i 0.976382 + 0.216050i \(0.0693175\pi\)
−0.976382 + 0.216050i \(0.930683\pi\)
\(440\) −4.06910e6 1.81621e6i −1.00200 0.447234i
\(441\) 0 0
\(442\) 3.49104e6 4.46548e6i 0.849961 1.08721i
\(443\) −4.60857e6 −1.11572 −0.557862 0.829934i \(-0.688378\pi\)
−0.557862 + 0.829934i \(0.688378\pi\)
\(444\) 0 0
\(445\) −2.20863e6 −0.528715
\(446\) 511051. 653698.i 0.121654 0.155611i
\(447\) 0 0
\(448\) −3.62233e6 + 3.24939e6i −0.852694 + 0.764904i
\(449\) 363410.i 0.0850709i 0.999095 + 0.0425355i \(0.0135435\pi\)
−0.999095 + 0.0425355i \(0.986456\pi\)
\(450\) 0 0
\(451\) 1.29286e7i 2.99302i
\(452\) 5.35910e6 1.33265e6i 1.23380 0.306809i
\(453\) 0 0
\(454\) −2.88395e6 2.25463e6i −0.656671 0.513375i
\(455\) 5.31324e6 1.20318
\(456\) 0 0
\(457\) 2.52447e6 0.565431 0.282716 0.959204i \(-0.408765\pi\)
0.282716 + 0.959204i \(0.408765\pi\)
\(458\) −1.29599e6 1.01318e6i −0.288693 0.225696i
\(459\) 0 0
\(460\) −1.69349e6 + 421119.i −0.373153 + 0.0927920i
\(461\) 6.13081e6i 1.34359i −0.740739 0.671793i \(-0.765524\pi\)
0.740739 0.671793i \(-0.234476\pi\)
\(462\) 0 0
\(463\) 4.72811e6i 1.02503i 0.858679 + 0.512513i \(0.171285\pi\)
−0.858679 + 0.512513i \(0.828715\pi\)
\(464\) 890311. + 1.67945e6i 0.191976 + 0.362136i
\(465\) 0 0
\(466\) 5.56510e6 7.11846e6i 1.18716 1.51852i
\(467\) 3.47705e6 0.737767 0.368884 0.929476i \(-0.379740\pi\)
0.368884 + 0.929476i \(0.379740\pi\)
\(468\) 0 0
\(469\) 349730. 0.0734177
\(470\) 2.29834e6 2.93987e6i 0.479922 0.613880i
\(471\) 0 0
\(472\) 2.30572e6 5.16579e6i 0.476377 1.06729i
\(473\) 7.58794e6i 1.55945i
\(474\) 0 0
\(475\) 1.65265e6i 0.336082i
\(476\) 1.30010e6 + 5.22821e6i 0.263002 + 1.05763i
\(477\) 0 0
\(478\) −577004. 451093.i −0.115507 0.0903018i
\(479\) −2.90668e6 −0.578841 −0.289420 0.957202i \(-0.593463\pi\)
−0.289420 + 0.957202i \(0.593463\pi\)
\(480\) 0 0
\(481\) 1.20751e7 2.37973
\(482\) 2.71722e6 + 2.12428e6i 0.532730 + 0.416480i
\(483\) 0 0
\(484\) 1.61192e6 + 6.48216e6i 0.312773 + 1.25778i
\(485\) 5.77672e6i 1.11513i
\(486\) 0 0
\(487\) 5.40021e6i 1.03178i 0.856654 + 0.515892i \(0.172539\pi\)
−0.856654 + 0.515892i \(0.827461\pi\)
\(488\) 479792. 1.07494e6i 0.0912019 0.204331i
\(489\) 0 0
\(490\) −739963. + 946504.i −0.139226 + 0.178087i
\(491\) 9.72452e6 1.82039 0.910195 0.414181i \(-0.135932\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(492\) 0 0
\(493\) 2.10445e6 0.389961
\(494\) 3.42396e6 4.37967e6i 0.631265 0.807466i
\(495\) 0 0
\(496\) 290887. + 548717.i 0.0530908 + 0.100149i
\(497\) 4.00094e6i 0.726559i
\(498\) 0 0
\(499\) 1.47884e6i 0.265870i −0.991125 0.132935i \(-0.957560\pi\)
0.991125 0.132935i \(-0.0424402\pi\)
\(500\) −5.79687e6 + 1.44151e6i −1.03698 + 0.257865i
\(501\) 0 0
\(502\) 2.35958e6 + 1.84468e6i 0.417902 + 0.326710i
\(503\) −6.19630e6 −1.09198 −0.545988 0.837793i \(-0.683845\pi\)
−0.545988 + 0.837793i \(0.683845\pi\)
\(504\) 0 0
\(505\) 3.30043e6 0.575894
\(506\) 3.65083e6 + 2.85417e6i 0.633893 + 0.495568i
\(507\) 0 0
\(508\) 7.68021e6 1.90984e6i 1.32042 0.328350i
\(509\) 400657.i 0.0685454i 0.999413 + 0.0342727i \(0.0109115\pi\)
−0.999413 + 0.0342727i \(0.989089\pi\)
\(510\) 0 0
\(511\) 7.76825e6i 1.31605i
\(512\) −5.64642e6 + 1.81724e6i −0.951914 + 0.306364i
\(513\) 0 0
\(514\) −287615. + 367896.i −0.0480180 + 0.0614210i
\(515\) −6.23554e6 −1.03599
\(516\) 0 0
\(517\) −9.90958e6 −1.63053
\(518\) −7.06880e6 + 9.04187e6i −1.15750 + 1.48059i
\(519\) 0 0
\(520\) 5.91419e6 + 2.63976e6i 0.959151 + 0.428110i
\(521\) 210060.i 0.0339039i −0.999856 0.0169520i \(-0.994604\pi\)
0.999856 0.0169520i \(-0.00539624\pi\)
\(522\) 0 0
\(523\) 5.32849e6i 0.851824i −0.904765 0.425912i \(-0.859953\pi\)
0.904765 0.425912i \(-0.140047\pi\)
\(524\) −2.75670e6 1.10858e7i −0.438592 1.76375i
\(525\) 0 0
\(526\) −3.86089e6 3.01839e6i −0.608448 0.475675i
\(527\) 687576. 0.107844
\(528\) 0 0
\(529\) −4.62155e6 −0.718039
\(530\) 242426. + 189525.i 0.0374878 + 0.0293074i
\(531\) 0 0
\(532\) 1.27512e6 + 5.12775e6i 0.195331 + 0.785503i
\(533\) 1.87909e7i 2.86503i
\(534\) 0 0
\(535\) 6.64326e6i 1.00345i
\(536\) 389286. + 173755.i 0.0585271 + 0.0261232i
\(537\) 0 0
\(538\) 4.19283e6 5.36315e6i 0.624528 0.798849i
\(539\) 3.19044e6 0.473019
\(540\) 0 0
\(541\) 4.80721e6 0.706155 0.353077 0.935594i \(-0.385135\pi\)
0.353077 + 0.935594i \(0.385135\pi\)
\(542\) 5.11241e6 6.53941e6i 0.747529 0.956182i
\(543\) 0 0
\(544\) −1.15037e6 + 6.46546e6i −0.166663 + 0.936704i
\(545\) 5.53700e6i 0.798515i
\(546\) 0 0
\(547\) 1.22838e7i 1.75535i −0.479254 0.877676i \(-0.659093\pi\)
0.479254 0.877676i \(-0.340907\pi\)
\(548\) 7.95006e6 1.97694e6i 1.13089 0.281218i
\(549\) 0 0
\(550\) 4.02802e6 + 3.14904e6i 0.567786 + 0.443886i
\(551\) 2.06401e6 0.289623
\(552\) 0 0
\(553\) 5.30645e6 0.737889
\(554\) −9.98050e6 7.80260e6i −1.38159 1.08010i
\(555\) 0 0
\(556\) 2.14357e6 533041.i 0.294070 0.0731263i
\(557\) 6.64124e6i 0.907008i 0.891254 + 0.453504i \(0.149826\pi\)
−0.891254 + 0.453504i \(0.850174\pi\)
\(558\) 0 0
\(559\) 1.10286e7i 1.49277i
\(560\) −5.43884e6 + 2.88324e6i −0.732886 + 0.388518i
\(561\) 0 0
\(562\) 536207. 685876.i 0.0716130 0.0916020i
\(563\) −9.15547e6 −1.21733 −0.608667 0.793426i \(-0.708295\pi\)
−0.608667 + 0.793426i \(0.708295\pi\)
\(564\) 0 0
\(565\) 6.98582e6 0.920653
\(566\) −5.61798e6 + 7.18610e6i −0.737122 + 0.942871i
\(567\) 0 0
\(568\) −1.98777e6 + 4.45346e6i −0.258521 + 0.579198i
\(569\) 538876.i 0.0697763i 0.999391 + 0.0348882i \(0.0111075\pi\)
−0.999391 + 0.0348882i \(0.988893\pi\)
\(570\) 0 0
\(571\) 4.75530e6i 0.610362i −0.952294 0.305181i \(-0.901283\pi\)
0.952294 0.305181i \(-0.0987170\pi\)
\(572\) −4.15044e6 1.66905e7i −0.530400 2.13295i
\(573\) 0 0
\(574\) −1.40707e7 1.10003e7i −1.78253 1.39355i
\(575\) 2.00229e6 0.252556
\(576\) 0 0
\(577\) −573068. −0.0716583 −0.0358291 0.999358i \(-0.511407\pi\)
−0.0358291 + 0.999358i \(0.511407\pi\)
\(578\) −599924. 469011.i −0.0746924 0.0583934i
\(579\) 0 0
\(580\) 580280. + 2.33353e6i 0.0716254 + 0.288034i
\(581\) 9.34489e6i 1.14851i
\(582\) 0 0
\(583\) 817160.i 0.0995717i
\(584\) −3.85947e6 + 8.64688e6i −0.468269 + 1.04912i
\(585\) 0 0
\(586\) 6.60634e6 8.45033e6i 0.794725 1.01655i
\(587\) 3.58562e6 0.429505 0.214753 0.976668i \(-0.431105\pi\)
0.214753 + 0.976668i \(0.431105\pi\)
\(588\) 0 0
\(589\) 674364. 0.0800952
\(590\) 4.40756e6 5.63781e6i 0.521276 0.666777i
\(591\) 0 0
\(592\) −1.23605e7 + 6.55258e6i −1.44955 + 0.768437i
\(593\) 3.03733e6i 0.354695i −0.984148 0.177348i \(-0.943248\pi\)
0.984148 0.177348i \(-0.0567517\pi\)
\(594\) 0 0
\(595\) 6.81520e6i 0.789198i
\(596\) 1.61909e6 402618.i 0.186704 0.0464278i
\(597\) 0 0
\(598\) −5.30627e6 4.14836e6i −0.606787 0.474377i
\(599\) 8.69696e6 0.990377 0.495188 0.868786i \(-0.335099\pi\)
0.495188 + 0.868786i \(0.335099\pi\)
\(600\) 0 0
\(601\) −2.30820e6 −0.260668 −0.130334 0.991470i \(-0.541605\pi\)
−0.130334 + 0.991470i \(0.541605\pi\)
\(602\) −8.25827e6 6.45619e6i −0.928748 0.726081i
\(603\) 0 0
\(604\) −1.01988e7 + 2.53614e6i −1.13751 + 0.282866i
\(605\) 8.44978e6i 0.938549i
\(606\) 0 0
\(607\) 1.78272e7i 1.96387i −0.189229 0.981933i \(-0.560599\pi\)
0.189229 0.981933i \(-0.439401\pi\)
\(608\) −1.12826e6 + 6.34123e6i −0.123780 + 0.695688i
\(609\) 0 0
\(610\) 917160. 1.17316e6i 0.0997978 0.127654i
\(611\) 1.44030e7 1.56081
\(612\) 0 0
\(613\) −8.66354e6 −0.931202 −0.465601 0.884995i \(-0.654162\pi\)
−0.465601 + 0.884995i \(0.654162\pi\)
\(614\) 321707. 411504.i 0.0344382 0.0440507i
\(615\) 0 0
\(616\) 1.49276e7 + 6.66284e6i 1.58503 + 0.707469i
\(617\) 4.06215e6i 0.429579i 0.976660 + 0.214789i \(0.0689065\pi\)
−0.976660 + 0.214789i \(0.931093\pi\)
\(618\) 0 0
\(619\) 4.23718e6i 0.444478i −0.974992 0.222239i \(-0.928664\pi\)
0.974992 0.222239i \(-0.0713365\pi\)
\(620\) 189592. + 762423.i 0.0198080 + 0.0796557i
\(621\) 0 0
\(622\) 135354. + 105818.i 0.0140280 + 0.0109668i
\(623\) 8.10242e6 0.836362
\(624\) 0 0
\(625\) −2.91171e6 −0.298159
\(626\) −6.07517e6 4.74947e6i −0.619616 0.484406i
\(627\) 0 0
\(628\) −2.41525e6 9.71269e6i −0.244379 0.982744i
\(629\) 1.54885e7i 1.56093i
\(630\) 0 0
\(631\) 1.26919e7i 1.26898i 0.772932 + 0.634489i \(0.218789\pi\)
−0.772932 + 0.634489i \(0.781211\pi\)
\(632\) 5.90663e6 + 2.63638e6i 0.588230 + 0.262552i
\(633\) 0 0
\(634\) 4.05692e6 5.18931e6i 0.400842 0.512727i
\(635\) 1.00115e7 0.985291
\(636\) 0 0
\(637\) −4.63711e6 −0.452792
\(638\) 3.93289e6 5.03065e6i 0.382525 0.489297i
\(639\) 0 0
\(640\) −7.48647e6 + 507192.i −0.722483 + 0.0489466i
\(641\) 5.25962e6i 0.505603i −0.967518 0.252801i \(-0.918648\pi\)
0.967518 0.252801i \(-0.0813519\pi\)
\(642\) 0 0
\(643\) 2.43696e6i 0.232446i −0.993223 0.116223i \(-0.962921\pi\)
0.993223 0.116223i \(-0.0370787\pi\)
\(644\) 6.21261e6 1.54489e6i 0.590282 0.146785i
\(645\) 0 0
\(646\) 5.61773e6 + 4.39186e6i 0.529639 + 0.414063i
\(647\) 3.95714e6 0.371639 0.185819 0.982584i \(-0.440506\pi\)
0.185819 + 0.982584i \(0.440506\pi\)
\(648\) 0 0
\(649\) −1.90037e7 −1.77103
\(650\) −5.85448e6 4.57694e6i −0.543507 0.424905i
\(651\) 0 0
\(652\) −1.60707e7 + 3.99629e6i −1.48052 + 0.368161i
\(653\) 1.87789e6i 0.172340i −0.996280 0.0861702i \(-0.972537\pi\)
0.996280 0.0861702i \(-0.0274629\pi\)
\(654\) 0 0
\(655\) 1.44508e7i 1.31610i
\(656\) −1.01969e7 1.92351e7i −0.925146 1.74516i
\(657\) 0 0
\(658\) −8.43155e6 + 1.07850e7i −0.759177 + 0.971082i
\(659\) −6.18082e6 −0.554412 −0.277206 0.960810i \(-0.589408\pi\)
−0.277206 + 0.960810i \(0.589408\pi\)
\(660\) 0 0
\(661\) −468167. −0.0416771 −0.0208385 0.999783i \(-0.506634\pi\)
−0.0208385 + 0.999783i \(0.506634\pi\)
\(662\) 1.57282e6 2.01183e6i 0.139487 0.178421i
\(663\) 0 0
\(664\) 4.64278e6 1.04018e7i 0.408656 0.915566i
\(665\) 6.68425e6i 0.586136i
\(666\) 0 0
\(667\) 2.50069e6i 0.217643i
\(668\) −2.43525e6 9.79310e6i −0.211155 0.849139i
\(669\) 0 0
\(670\) 424857. + 332147.i 0.0365642 + 0.0285853i
\(671\) −3.95445e6 −0.339062
\(672\) 0 0
\(673\) −7.27492e6 −0.619142 −0.309571 0.950876i \(-0.600186\pi\)
−0.309571 + 0.950876i \(0.600186\pi\)
\(674\) 9.63726e6 + 7.53426e6i 0.817154 + 0.638838i
\(675\) 0 0
\(676\) 3.16519e6 + 1.27285e7i 0.266399 + 1.07130i
\(677\) 5.70914e6i 0.478739i −0.970929 0.239370i \(-0.923059\pi\)
0.970929 0.239370i \(-0.0769407\pi\)
\(678\) 0 0
\(679\) 2.11921e7i 1.76400i
\(680\) −3.38597e6 + 7.58603e6i −0.280809 + 0.629132i
\(681\) 0 0
\(682\) 1.28497e6 1.64364e6i 0.105787 0.135315i
\(683\) −6.52835e6 −0.535490 −0.267745 0.963490i \(-0.586279\pi\)
−0.267745 + 0.963490i \(0.586279\pi\)
\(684\) 0 0
\(685\) 1.03633e7 0.843859
\(686\) −5.98140e6 + 7.65096e6i −0.485280 + 0.620734i
\(687\) 0 0
\(688\) −5.98471e6 1.12893e7i −0.482028 0.909279i
\(689\) 1.18769e6i 0.0953139i
\(690\) 0 0
\(691\) 1.14706e7i 0.913884i 0.889496 + 0.456942i \(0.151055\pi\)
−0.889496 + 0.456942i \(0.848945\pi\)
\(692\) 1.93911e7 4.82198e6i 1.53935 0.382790i
\(693\) 0 0
\(694\) −1.38388e7 1.08190e7i −1.09069 0.852683i
\(695\) 2.79423e6 0.219432
\(696\) 0 0
\(697\) −2.41028e7 −1.87925
\(698\) 1.04919e7 + 8.20242e6i 0.815110 + 0.637240i
\(699\) 0 0
\(700\) 6.85446e6 1.70450e6i 0.528723 0.131478i
\(701\) 1.82344e6i 0.140151i −0.997542 0.0700756i \(-0.977676\pi\)
0.997542 0.0700756i \(-0.0223240\pi\)
\(702\) 0 0
\(703\) 1.51909e7i 1.15930i
\(704\) 1.33057e7 + 1.48329e7i 1.01183 + 1.12796i
\(705\) 0 0
\(706\) 6.76251e6 8.65009e6i 0.510618 0.653144i
\(707\) −1.21078e7 −0.910993
\(708\) 0 0
\(709\) 1.40708e7 1.05124 0.525621 0.850719i \(-0.323833\pi\)
0.525621 + 0.850719i \(0.323833\pi\)
\(710\) −3.79978e6 + 4.86039e6i −0.282887 + 0.361847i
\(711\) 0 0
\(712\) 9.01884e6 + 4.02549e6i 0.666731 + 0.297591i
\(713\) 817038.i 0.0601892i
\(714\) 0 0
\(715\) 2.17569e7i 1.59159i
\(716\) −534274. 2.14853e6i −0.0389477 0.156624i
\(717\) 0 0
\(718\) 5.95910e6 + 4.65874e6i 0.431390 + 0.337254i
\(719\) −3.92597e6 −0.283220 −0.141610 0.989923i \(-0.545228\pi\)
−0.141610 + 0.989923i \(0.545228\pi\)
\(720\) 0 0
\(721\) 2.28753e7 1.63881
\(722\) −5.52515e6 4.31948e6i −0.394458 0.308381i
\(723\) 0 0
\(724\) −1.49365e6 6.00654e6i −0.105901 0.425871i
\(725\) 2.75905e6i 0.194946i
\(726\) 0 0
\(727\) 8.54731e6i 0.599782i 0.953973 + 0.299891i \(0.0969503\pi\)
−0.953973 + 0.299891i \(0.903050\pi\)
\(728\) −2.16964e7 9.68404e6i −1.51726 0.677217i
\(729\) 0 0
\(730\) −7.37768e6 + 9.43697e6i −0.512404 + 0.655429i
\(731\) −1.41462e7 −0.979144
\(732\) 0 0
\(733\) 1.32847e7 0.913256 0.456628 0.889658i \(-0.349057\pi\)
0.456628 + 0.889658i \(0.349057\pi\)
\(734\) 5.72734e6 7.32598e6i 0.392385 0.501910i
\(735\) 0 0
\(736\) 7.68283e6 + 1.36696e6i 0.522789 + 0.0930171i
\(737\) 1.43209e6i 0.0971183i
\(738\) 0 0
\(739\) 2.75514e7i 1.85581i −0.372819 0.927904i \(-0.621609\pi\)
0.372819 0.927904i \(-0.378391\pi\)
\(740\) −1.71745e7 + 4.27079e6i −1.15294 + 0.286701i
\(741\) 0 0
\(742\) −889349. 695280.i −0.0593011 0.0463607i
\(743\) −357532. −0.0237598 −0.0118799 0.999929i \(-0.503782\pi\)
−0.0118799 + 0.999929i \(0.503782\pi\)
\(744\) 0 0
\(745\) 2.11055e6 0.139317
\(746\) 1.75181e6 + 1.36954e6i 0.115250 + 0.0901006i
\(747\) 0 0
\(748\) 2.14087e7 5.32369e6i 1.39906 0.347904i
\(749\) 2.43710e7i 1.58734i
\(750\) 0 0
\(751\) 2.39756e6i 0.155121i −0.996988 0.0775603i \(-0.975287\pi\)
0.996988 0.0775603i \(-0.0247130\pi\)
\(752\) −1.47435e7 + 7.81582e6i −0.950726 + 0.504000i
\(753\) 0 0
\(754\) −5.71622e6 + 7.31175e6i −0.366168 + 0.468374i
\(755\) −1.32946e7 −0.848804
\(756\) 0 0
\(757\) −1.85832e7 −1.17864 −0.589320 0.807900i \(-0.700604\pi\)
−0.589320 + 0.807900i \(0.700604\pi\)
\(758\) −8.03213e6 + 1.02741e7i −0.507759 + 0.649487i
\(759\) 0 0
\(760\) −3.32091e6 + 7.44027e6i −0.208556 + 0.467256i
\(761\) 2.59191e7i 1.62240i 0.584769 + 0.811200i \(0.301185\pi\)
−0.584769 + 0.811200i \(0.698815\pi\)
\(762\) 0 0
\(763\) 2.03127e7i 1.26315i
\(764\) 6.10421e6 + 2.45475e7i 0.378352 + 1.52150i
\(765\) 0 0
\(766\) 1.20356e7 + 9.40927e6i 0.741134 + 0.579408i
\(767\) 2.76207e7 1.69530
\(768\) 0 0
\(769\) 2.70826e7 1.65148 0.825741 0.564050i \(-0.190757\pi\)
0.825741 + 0.564050i \(0.190757\pi\)
\(770\) 1.62916e7 + 1.27365e7i 0.990233 + 0.774149i
\(771\) 0 0
\(772\) −482173. 1.93901e6i −0.0291178 0.117094i
\(773\) 3.16270e7i 1.90375i −0.306492 0.951873i \(-0.599155\pi\)
0.306492 0.951873i \(-0.400845\pi\)
\(774\) 0 0
\(775\) 901449.i 0.0539122i
\(776\) −1.05288e7 + 2.35890e7i −0.627660 + 1.40623i
\(777\) 0 0
\(778\) −5.76892e6 + 7.37917e6i −0.341700 + 0.437077i
\(779\) −2.36396e7 −1.39572
\(780\) 0 0
\(781\) 1.63832e7 0.961105
\(782\) 5.32103e6 6.80626e6i 0.311156 0.398008i
\(783\) 0 0
\(784\) 4.74673e6 2.51634e6i 0.275806 0.146211i
\(785\) 1.26609e7i 0.733316i
\(786\) 0 0