Properties

Label 177.6.d.b.176.14
Level $177$
Weight $6$
Character 177.176
Analytic conductor $28.388$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.14
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.13

$q$-expansion

\(f(q)\) \(=\) \(q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} +O(q^{10})\) \(q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} -831.703i q^{10} -217.796 q^{11} +(65.6618 + 686.534i) q^{12} +156.380i q^{13} -1260.94 q^{14} +(-1478.07 + 141.367i) q^{15} -482.379 q^{16} -457.850i q^{17} +(2083.33 - 402.189i) q^{18} +309.656 q^{19} +4214.12i q^{20} +(214.325 + 2240.90i) q^{21} +1901.72 q^{22} -1509.65 q^{23} +(-158.647 - 1658.76i) q^{24} -5947.79 q^{25} -1365.46i q^{26} +(-1068.87 - 3634.07i) q^{27} +6389.00 q^{28} +3620.57i q^{29} +(12906.1 - 1234.37i) q^{30} +6831.48i q^{31} +7632.61 q^{32} +(-323.241 - 3379.68i) q^{33} +3997.80i q^{34} +13755.2i q^{35} +(-10555.9 + 2037.83i) q^{36} +1687.78i q^{37} -2703.81 q^{38} +(-2426.64 + 232.090i) q^{39} -10181.9i q^{40} +7535.31i q^{41} +(-1871.42 - 19566.8i) q^{42} -17278.5i q^{43} -9635.76 q^{44} +(-4387.35 - 22726.4i) q^{45} +13181.8 q^{46} -28422.4 q^{47} +(-715.921 - 7485.39i) q^{48} +4047.18 q^{49} +51934.2 q^{50} +(7104.76 - 679.517i) q^{51} +6918.57i q^{52} -6020.14i q^{53} +(9332.99 + 31731.5i) q^{54} -20745.3i q^{55} -15436.6 q^{56} +(459.574 + 4805.13i) q^{57} -31613.6i q^{58} +(-23993.5 - 11799.8i) q^{59} +(-65393.2 + 6254.37i) q^{60} -40967.9i q^{61} -59650.3i q^{62} +(-34455.4 + 6651.64i) q^{63} -51209.4 q^{64} -14895.3 q^{65} +(2822.43 + 29510.3i) q^{66} +25548.9i q^{67} -20256.3i q^{68} +(-2240.54 - 23426.3i) q^{69} -120106. i q^{70} -28527.7i q^{71} +(25504.5 - 4923.67i) q^{72} +45267.9i q^{73} -14737.2i q^{74} +(-8827.38 - 92295.7i) q^{75} +13699.8 q^{76} -31451.8 q^{77} +(21188.7 - 2026.54i) q^{78} +83601.3 q^{79} -45947.2i q^{80} +(54805.8 - 21979.8i) q^{81} -65795.9i q^{82} -31065.0 q^{83} +(9482.21 + 99142.3i) q^{84} +43610.8 q^{85} +150870. i q^{86} +(-56182.7 + 5373.45i) q^{87} +23281.2 q^{88} -11986.6 q^{89} +(38309.0 + 198440. i) q^{90} +22582.7i q^{91} -66790.3 q^{92} +(-106009. + 10138.9i) q^{93} +248175. q^{94} +29495.1i q^{95} +(11327.9 + 118440. i) q^{96} -85247.4i q^{97} -35338.6 q^{98} +(51964.9 - 10031.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.73168 −1.54356 −0.771778 0.635891i \(-0.780633\pi\)
−0.771778 + 0.635891i \(0.780633\pi\)
\(3\) 1.48415 + 15.5176i 0.0952080 + 0.995457i
\(4\) 44.2422 1.38257
\(5\) 95.2512i 1.70390i 0.523619 + 0.851952i \(0.324582\pi\)
−0.523619 + 0.851952i \(0.675418\pi\)
\(6\) −12.9591 135.495i −0.146959 1.53655i
\(7\) 144.410 1.11391 0.556957 0.830542i \(-0.311969\pi\)
0.556957 + 0.830542i \(0.311969\pi\)
\(8\) −106.895 −0.590516
\(9\) −238.595 + 46.0609i −0.981871 + 0.189551i
\(10\) 831.703i 2.63007i
\(11\) −217.796 −0.542710 −0.271355 0.962479i \(-0.587472\pi\)
−0.271355 + 0.962479i \(0.587472\pi\)
\(12\) 65.6618 + 686.534i 0.131632 + 1.37629i
\(13\) 156.380i 0.256638i 0.991733 + 0.128319i \(0.0409582\pi\)
−0.991733 + 0.128319i \(0.959042\pi\)
\(14\) −1260.94 −1.71939
\(15\) −1478.07 + 141.367i −1.69616 + 0.162225i
\(16\) −482.379 −0.471073
\(17\) 457.850i 0.384239i −0.981372 0.192119i \(-0.938464\pi\)
0.981372 0.192119i \(-0.0615361\pi\)
\(18\) 2083.33 402.189i 1.51557 0.292583i
\(19\) 309.656 0.196786 0.0983932 0.995148i \(-0.468630\pi\)
0.0983932 + 0.995148i \(0.468630\pi\)
\(20\) 4214.12i 2.35576i
\(21\) 214.325 + 2240.90i 0.106053 + 1.10885i
\(22\) 1901.72 0.837704
\(23\) −1509.65 −0.595055 −0.297528 0.954713i \(-0.596162\pi\)
−0.297528 + 0.954713i \(0.596162\pi\)
\(24\) −158.647 1658.76i −0.0562218 0.587833i
\(25\) −5947.79 −1.90329
\(26\) 1365.46i 0.396136i
\(27\) −1068.87 3634.07i −0.282172 0.959364i
\(28\) 6389.00 1.54006
\(29\) 3620.57i 0.799432i 0.916639 + 0.399716i \(0.130891\pi\)
−0.916639 + 0.399716i \(0.869109\pi\)
\(30\) 12906.1 1234.37i 2.61813 0.250404i
\(31\) 6831.48i 1.27676i 0.769719 + 0.638382i \(0.220396\pi\)
−0.769719 + 0.638382i \(0.779604\pi\)
\(32\) 7632.61 1.31764
\(33\) −323.241 3379.68i −0.0516703 0.540245i
\(34\) 3997.80i 0.593095i
\(35\) 13755.2i 1.89800i
\(36\) −10555.9 + 2037.83i −1.35750 + 0.262067i
\(37\) 1687.78i 0.202681i 0.994852 + 0.101340i \(0.0323131\pi\)
−0.994852 + 0.101340i \(0.967687\pi\)
\(38\) −2703.81 −0.303751
\(39\) −2426.64 + 232.090i −0.255473 + 0.0244340i
\(40\) 10181.9i 1.00618i
\(41\) 7535.31i 0.700070i 0.936737 + 0.350035i \(0.113830\pi\)
−0.936737 + 0.350035i \(0.886170\pi\)
\(42\) −1871.42 19566.8i −0.163700 1.71158i
\(43\) 17278.5i 1.42506i −0.701640 0.712532i \(-0.747548\pi\)
0.701640 0.712532i \(-0.252452\pi\)
\(44\) −9635.76 −0.750334
\(45\) −4387.35 22726.4i −0.322977 1.67301i
\(46\) 13181.8 0.918502
\(47\) −28422.4 −1.87679 −0.938395 0.345565i \(-0.887687\pi\)
−0.938395 + 0.345565i \(0.887687\pi\)
\(48\) −715.921 7485.39i −0.0448499 0.468934i
\(49\) 4047.18 0.240803
\(50\) 51934.2 2.93784
\(51\) 7104.76 679.517i 0.382493 0.0365826i
\(52\) 6918.57i 0.354820i
\(53\) 6020.14i 0.294386i −0.989108 0.147193i \(-0.952976\pi\)
0.989108 0.147193i \(-0.0470238\pi\)
\(54\) 9332.99 + 31731.5i 0.435548 + 1.48083i
\(55\) 20745.3i 0.924726i
\(56\) −15436.6 −0.657783
\(57\) 459.574 + 4805.13i 0.0187356 + 0.195892i
\(58\) 31613.6i 1.23397i
\(59\) −23993.5 11799.8i −0.897354 0.441312i
\(60\) −65393.2 + 6254.37i −2.34506 + 0.224288i
\(61\) 40967.9i 1.40968i −0.709369 0.704838i \(-0.751020\pi\)
0.709369 0.704838i \(-0.248980\pi\)
\(62\) 59650.3i 1.97076i
\(63\) −34455.4 + 6651.64i −1.09372 + 0.211143i
\(64\) −51209.4 −1.56279
\(65\) −14895.3 −0.437288
\(66\) 2822.43 + 29510.3i 0.0797561 + 0.833899i
\(67\) 25548.9i 0.695322i 0.937620 + 0.347661i \(0.113024\pi\)
−0.937620 + 0.347661i \(0.886976\pi\)
\(68\) 20256.3i 0.531236i
\(69\) −2240.54 23426.3i −0.0566540 0.592352i
\(70\) 120106.i 2.92968i
\(71\) 28527.7i 0.671616i −0.941930 0.335808i \(-0.890991\pi\)
0.941930 0.335808i \(-0.109009\pi\)
\(72\) 25504.5 4923.67i 0.579810 0.111933i
\(73\) 45267.9i 0.994221i 0.867687 + 0.497110i \(0.165606\pi\)
−0.867687 + 0.497110i \(0.834394\pi\)
\(74\) 14737.2i 0.312849i
\(75\) −8827.38 92295.7i −0.181209 1.89465i
\(76\) 13699.8 0.272071
\(77\) −31451.8 −0.604532
\(78\) 21188.7 2026.54i 0.394337 0.0377153i
\(79\) 83601.3 1.50711 0.753556 0.657384i \(-0.228337\pi\)
0.753556 + 0.657384i \(0.228337\pi\)
\(80\) 45947.2i 0.802664i
\(81\) 54805.8 21979.8i 0.928141 0.372229i
\(82\) 65795.9i 1.08060i
\(83\) −31065.0 −0.494966 −0.247483 0.968892i \(-0.579603\pi\)
−0.247483 + 0.968892i \(0.579603\pi\)
\(84\) 9482.21 + 99142.3i 0.146626 + 1.53307i
\(85\) 43610.8 0.654707
\(86\) 150870.i 2.19967i
\(87\) −56182.7 + 5373.45i −0.795800 + 0.0761123i
\(88\) 23281.2 0.320479
\(89\) −11986.6 −0.160406 −0.0802028 0.996779i \(-0.525557\pi\)
−0.0802028 + 0.996779i \(0.525557\pi\)
\(90\) 38309.0 + 198440.i 0.498533 + 2.58239i
\(91\) 22582.7i 0.285873i
\(92\) −66790.3 −0.822705
\(93\) −106009. + 10138.9i −1.27096 + 0.121558i
\(94\) 248175. 2.89693
\(95\) 29495.1i 0.335305i
\(96\) 11327.9 + 118440.i 0.125450 + 1.31166i
\(97\) 85247.4i 0.919923i −0.887939 0.459962i \(-0.847863\pi\)
0.887939 0.459962i \(-0.152137\pi\)
\(98\) −35338.6 −0.371693
\(99\) 51964.9 10031.9i 0.532871 0.102871i
\(100\) −263143. −2.63143
\(101\) 118099. 1.15197 0.575986 0.817459i \(-0.304618\pi\)
0.575986 + 0.817459i \(0.304618\pi\)
\(102\) −62036.5 + 5933.32i −0.590400 + 0.0564673i
\(103\) 173141.i 1.60808i 0.594577 + 0.804038i \(0.297319\pi\)
−0.594577 + 0.804038i \(0.702681\pi\)
\(104\) 16716.2i 0.151549i
\(105\) −213448. + 20414.7i −1.88938 + 0.180705i
\(106\) 52565.9i 0.454402i
\(107\) 110167.i 0.930230i 0.885250 + 0.465115i \(0.153987\pi\)
−0.885250 + 0.465115i \(0.846013\pi\)
\(108\) −47288.9 160779.i −0.390122 1.32639i
\(109\) 94217.1i 0.759562i −0.925076 0.379781i \(-0.875999\pi\)
0.925076 0.379781i \(-0.124001\pi\)
\(110\) 181141.i 1.42737i
\(111\) −26190.4 + 2504.92i −0.201760 + 0.0192968i
\(112\) −69660.3 −0.524735
\(113\) 176217. 1.29823 0.649116 0.760690i \(-0.275139\pi\)
0.649116 + 0.760690i \(0.275139\pi\)
\(114\) −4012.85 41956.8i −0.0289195 0.302371i
\(115\) 143796.i 1.01392i
\(116\) 160182.i 1.10527i
\(117\) −7202.98 37311.3i −0.0486461 0.251986i
\(118\) 209504. + 103032.i 1.38512 + 0.681190i
\(119\) 66118.1i 0.428009i
\(120\) 157998. 15111.4i 1.00161 0.0957966i
\(121\) −113616. −0.705466
\(122\) 357718.i 2.17591i
\(123\) −116930. + 11183.5i −0.696890 + 0.0666523i
\(124\) 302240.i 1.76521i
\(125\) 268874.i 1.53912i
\(126\) 300853. 58080.0i 1.68822 0.325912i
\(127\) 353974. 1.94743 0.973714 0.227774i \(-0.0731446\pi\)
0.973714 + 0.227774i \(0.0731446\pi\)
\(128\) 202900. 1.09460
\(129\) 268121. 25643.8i 1.41859 0.135677i
\(130\) 130061. 0.674978
\(131\) −191902. −0.977014 −0.488507 0.872560i \(-0.662458\pi\)
−0.488507 + 0.872560i \(0.662458\pi\)
\(132\) −14300.9 149524.i −0.0714378 0.746925i
\(133\) 44717.3 0.219203
\(134\) 223085.i 1.07327i
\(135\) 346149. 101811.i 1.63466 0.480794i
\(136\) 48941.8i 0.226899i
\(137\) 382198.i 1.73975i −0.493273 0.869875i \(-0.664200\pi\)
0.493273 0.869875i \(-0.335800\pi\)
\(138\) 19563.7 + 204550.i 0.0874487 + 0.914330i
\(139\) −37587.9 −0.165011 −0.0825053 0.996591i \(-0.526292\pi\)
−0.0825053 + 0.996591i \(0.526292\pi\)
\(140\) 608560.i 2.62412i
\(141\) −42182.9 441048.i −0.178685 1.86826i
\(142\) 249095.i 1.03668i
\(143\) 34058.8i 0.139280i
\(144\) 115093. 22218.8i 0.462533 0.0892924i
\(145\) −344863. −1.36216
\(146\) 395264.i 1.53464i
\(147\) 6006.60 + 62802.7i 0.0229264 + 0.239709i
\(148\) 74671.3i 0.280220i
\(149\) −43754.1 −0.161455 −0.0807277 0.996736i \(-0.525724\pi\)
−0.0807277 + 0.996736i \(0.525724\pi\)
\(150\) 77077.8 + 805896.i 0.279706 + 2.92449i
\(151\) 478677.i 1.70844i 0.519911 + 0.854221i \(0.325965\pi\)
−0.519911 + 0.854221i \(0.674035\pi\)
\(152\) −33100.6 −0.116205
\(153\) 21089.0 + 109241.i 0.0728329 + 0.377273i
\(154\) 274627. 0.933130
\(155\) −650707. −2.17549
\(156\) −107360. + 10268.2i −0.353208 + 0.0337817i
\(157\) 167723.i 0.543053i −0.962431 0.271527i \(-0.912472\pi\)
0.962431 0.271527i \(-0.0875285\pi\)
\(158\) −729980. −2.32631
\(159\) 93418.5 8934.77i 0.293049 0.0280279i
\(160\) 727015.i 2.24514i
\(161\) −218009. −0.662840
\(162\) −478546. + 191920.i −1.43264 + 0.574557i
\(163\) −381537. −1.12478 −0.562390 0.826872i \(-0.690118\pi\)
−0.562390 + 0.826872i \(0.690118\pi\)
\(164\) 333379.i 0.967895i
\(165\) 321918. 30789.1i 0.920526 0.0880413i
\(166\) 271249. 0.764009
\(167\) 130083.i 0.360936i −0.983581 0.180468i \(-0.942239\pi\)
0.983581 0.180468i \(-0.0577612\pi\)
\(168\) −22910.2 239540.i −0.0626262 0.654795i
\(169\) 346838. 0.934137
\(170\) −380795. −1.01058
\(171\) −73882.2 + 14263.0i −0.193219 + 0.0373010i
\(172\) 764437.i 1.97025i
\(173\) 555383. 1.41084 0.705419 0.708791i \(-0.250759\pi\)
0.705419 + 0.708791i \(0.250759\pi\)
\(174\) 490569. 46919.2i 1.22836 0.117484i
\(175\) −858919. −2.12010
\(176\) 105060. 0.255656
\(177\) 147496. 389835.i 0.353872 0.935294i
\(178\) 104663. 0.247595
\(179\) −391499. −0.913269 −0.456634 0.889654i \(-0.650945\pi\)
−0.456634 + 0.889654i \(0.650945\pi\)
\(180\) −194106. 1.00547e6i −0.446537 2.31306i
\(181\) −460900. −1.04571 −0.522854 0.852422i \(-0.675133\pi\)
−0.522854 + 0.852422i \(0.675133\pi\)
\(182\) 197185.i 0.441261i
\(183\) 635725. 60802.3i 1.40327 0.134212i
\(184\) 161374. 0.351390
\(185\) −160763. −0.345349
\(186\) 925632. 88529.7i 1.96181 0.187632i
\(187\) 99717.9i 0.208530i
\(188\) −1.25747e6 −2.59479
\(189\) −154355. 524795.i −0.314315 1.06865i
\(190\) 257541.i 0.517563i
\(191\) −588891. −1.16802 −0.584012 0.811745i \(-0.698518\pi\)
−0.584012 + 0.811745i \(0.698518\pi\)
\(192\) −76002.1 794649.i −0.148790 1.55569i
\(193\) −13813.2 −0.0266931 −0.0133466 0.999911i \(-0.504248\pi\)
−0.0133466 + 0.999911i \(0.504248\pi\)
\(194\) 744352.i 1.41995i
\(195\) −22106.9 231141.i −0.0416333 0.435301i
\(196\) 179056. 0.332927
\(197\) 499597.i 0.917179i 0.888648 + 0.458590i \(0.151645\pi\)
−0.888648 + 0.458590i \(0.848355\pi\)
\(198\) −453741. + 87595.0i −0.822517 + 0.158788i
\(199\) 712826. 1.27600 0.638000 0.770036i \(-0.279762\pi\)
0.638000 + 0.770036i \(0.279762\pi\)
\(200\) 635787. 1.12392
\(201\) −396460. + 37918.4i −0.692164 + 0.0662002i
\(202\) −1.03120e6 −1.77814
\(203\) 522845.i 0.890498i
\(204\) 314330. 30063.3i 0.528823 0.0505779i
\(205\) −717747. −1.19285
\(206\) 1.51181e6i 2.48216i
\(207\) 360195. 69535.9i 0.584268 0.112793i
\(208\) 75434.3i 0.120896i
\(209\) −67441.7 −0.106798
\(210\) 1.86376e6 178255.i 2.91637 0.278928i
\(211\) 736655.i 1.13909i −0.821960 0.569545i \(-0.807119\pi\)
0.821960 0.569545i \(-0.192881\pi\)
\(212\) 266344.i 0.407009i
\(213\) 442683. 42339.3i 0.668566 0.0639432i
\(214\) 961938.i 1.43586i
\(215\) 1.64580e6 2.42817
\(216\) 114256. + 388463.i 0.166627 + 0.566520i
\(217\) 986533.i 1.42221i
\(218\) 822673.i 1.17243i
\(219\) −702451. + 67184.1i −0.989704 + 0.0946577i
\(220\) 917818.i 1.27850i
\(221\) 71598.5 0.0986105
\(222\) 228686. 21872.1i 0.311428 0.0297858i
\(223\) −1.08470e6 −1.46065 −0.730327 0.683098i \(-0.760632\pi\)
−0.730327 + 0.683098i \(0.760632\pi\)
\(224\) 1.10222e6 1.46774
\(225\) 1.41911e6 273960.i 1.86879 0.360771i
\(226\) −1.53867e6 −2.00389
\(227\) 1.18705e6 1.52899 0.764493 0.644632i \(-0.222989\pi\)
0.764493 + 0.644632i \(0.222989\pi\)
\(228\) 20332.6 + 212589.i 0.0259033 + 0.270835i
\(229\) 1.02701e6i 1.29415i 0.762426 + 0.647076i \(0.224008\pi\)
−0.762426 + 0.647076i \(0.775992\pi\)
\(230\) 1.25558e6i 1.56504i
\(231\) −46679.1 488059.i −0.0575563 0.601786i
\(232\) 387020.i 0.472077i
\(233\) −730905. −0.882005 −0.441002 0.897506i \(-0.645377\pi\)
−0.441002 + 0.897506i \(0.645377\pi\)
\(234\) 62894.1 + 325790.i 0.0750880 + 0.388954i
\(235\) 2.70726e6i 3.19787i
\(236\) −1.06152e6 522050.i −1.24065 0.610144i
\(237\) 124077. + 1.29730e6i 0.143489 + 1.50027i
\(238\) 577322.i 0.660656i
\(239\) 138876.i 0.157265i −0.996904 0.0786324i \(-0.974945\pi\)
0.996904 0.0786324i \(-0.0250553\pi\)
\(240\) 712992. 68192.3i 0.799018 0.0764200i
\(241\) −438905. −0.486775 −0.243387 0.969929i \(-0.578259\pi\)
−0.243387 + 0.969929i \(0.578259\pi\)
\(242\) 992058. 1.08893
\(243\) 422414. + 817836.i 0.458905 + 0.888486i
\(244\) 1.81251e6i 1.94897i
\(245\) 385498.i 0.410306i
\(246\) 1.02100e6 97650.7i 1.07569 0.102882i
\(247\) 48423.8i 0.0505029i
\(248\) 730250.i 0.753950i
\(249\) −46104.9 482055.i −0.0471247 0.492718i
\(250\) 2.34772e6i 2.37573i
\(251\) 303320.i 0.303891i 0.988389 + 0.151945i \(0.0485538\pi\)
−0.988389 + 0.151945i \(0.951446\pi\)
\(252\) −1.52438e6 + 294283.i −1.51214 + 0.291920i
\(253\) 328796. 0.322943
\(254\) −3.09078e6 −3.00597
\(255\) 64724.8 + 676737.i 0.0623333 + 0.651733i
\(256\) −132958. −0.126799
\(257\) 845091.i 0.798125i 0.916924 + 0.399062i \(0.130664\pi\)
−0.916924 + 0.399062i \(0.869336\pi\)
\(258\) −2.34115e6 + 223913.i −2.18967 + 0.209426i
\(259\) 243733.i 0.225769i
\(260\) −659002. −0.604580
\(261\) −166766. 863848.i −0.151533 0.784939i
\(262\) 1.67562e6 1.50808
\(263\) 1.21321e6i 1.08155i −0.841168 0.540774i \(-0.818132\pi\)
0.841168 0.540774i \(-0.181868\pi\)
\(264\) 34552.7 + 361270.i 0.0305121 + 0.319023i
\(265\) 573426. 0.501606
\(266\) −390457. −0.338352
\(267\) −17789.8 186003.i −0.0152719 0.159677i
\(268\) 1.13034e6i 0.961330i
\(269\) 834151. 0.702853 0.351426 0.936216i \(-0.385697\pi\)
0.351426 + 0.936216i \(0.385697\pi\)
\(270\) −3.02246e6 + 888978.i −2.52320 + 0.742133i
\(271\) −1.22568e6 −1.01380 −0.506901 0.862004i \(-0.669209\pi\)
−0.506901 + 0.862004i \(0.669209\pi\)
\(272\) 220858.i 0.181005i
\(273\) −350431. + 33516.1i −0.284574 + 0.0272174i
\(274\) 3.33723e6i 2.68540i
\(275\) 1.29540e6 1.03294
\(276\) −99126.6 1.03643e6i −0.0783280 0.818968i
\(277\) −995993. −0.779932 −0.389966 0.920829i \(-0.627513\pi\)
−0.389966 + 0.920829i \(0.627513\pi\)
\(278\) 328206. 0.254703
\(279\) −314664. 1.62996e6i −0.242012 1.25362i
\(280\) 1.47036e6i 1.12080i
\(281\) 1.11245e6i 0.840453i 0.907419 + 0.420226i \(0.138049\pi\)
−0.907419 + 0.420226i \(0.861951\pi\)
\(282\) 368328. + 3.85109e6i 0.275811 + 2.88377i
\(283\) 82590.3i 0.0613003i 0.999530 + 0.0306502i \(0.00975778\pi\)
−0.999530 + 0.0306502i \(0.990242\pi\)
\(284\) 1.26213e6i 0.928556i
\(285\) −457694. + 43775.0i −0.333782 + 0.0319237i
\(286\) 297391.i 0.214987i
\(287\) 1.08817e6i 0.779818i
\(288\) −1.82110e6 + 351565.i −1.29376 + 0.249761i
\(289\) 1.21023e6 0.852360
\(290\) 3.01123e6 2.10257
\(291\) 1.32284e6 126519.i 0.915744 0.0875840i
\(292\) 2.00275e6i 1.37458i
\(293\) 691968.i 0.470887i 0.971888 + 0.235444i \(0.0756543\pi\)
−0.971888 + 0.235444i \(0.924346\pi\)
\(294\) −52447.7 548373.i −0.0353882 0.370005i
\(295\) 1.12395e6 2.28541e6i 0.751954 1.52901i
\(296\) 180415.i 0.119686i
\(297\) 232794. + 791484.i 0.153138 + 0.520656i
\(298\) 382046. 0.249216
\(299\) 236079.i 0.152714i
\(300\) −390543. 4.08336e6i −0.250533 2.61948i
\(301\) 2.49518e6i 1.58740i
\(302\) 4.17965e6i 2.63708i
\(303\) 175276. + 1.83262e6i 0.109677 + 1.14674i
\(304\) −149371. −0.0927008
\(305\) 3.90224e6 2.40195
\(306\) −184142. 953854.i −0.112422 0.582342i
\(307\) −1.88853e6 −1.14361 −0.571804 0.820391i \(-0.693756\pi\)
−0.571804 + 0.820391i \(0.693756\pi\)
\(308\) −1.39150e6 −0.835807
\(309\) −2.68674e6 + 256966.i −1.60077 + 0.153102i
\(310\) 5.68176e6 3.35799
\(311\) 1.74107e6i 1.02074i 0.859955 + 0.510369i \(0.170491\pi\)
−0.859955 + 0.510369i \(0.829509\pi\)
\(312\) 259395. 24809.2i 0.150861 0.0144287i
\(313\) 630418.i 0.363721i 0.983324 + 0.181860i \(0.0582119\pi\)
−0.983324 + 0.181860i \(0.941788\pi\)
\(314\) 1.46450e6i 0.838233i
\(315\) −633577. 3.28192e6i −0.359768 1.86359i
\(316\) 3.69871e6 2.08368
\(317\) 1.54644e6i 0.864339i 0.901792 + 0.432169i \(0.142252\pi\)
−0.901792 + 0.432169i \(0.857748\pi\)
\(318\) −815700. + 78015.5i −0.452337 + 0.0432627i
\(319\) 788544.i 0.433860i
\(320\) 4.87775e6i 2.66284i
\(321\) −1.70952e6 + 163503.i −0.926004 + 0.0885653i
\(322\) 1.90358e6 1.02313
\(323\) 141776.i 0.0756130i
\(324\) 2.42473e6 972432.i 1.28322 0.514632i
\(325\) 930113.i 0.488458i
\(326\) 3.33146e6 1.73616
\(327\) 1.46203e6 139832.i 0.756112 0.0723164i
\(328\) 805485.i 0.413402i
\(329\) −4.10447e6 −2.09058
\(330\) −2.81089e6 + 268840.i −1.42088 + 0.135897i
\(331\) −3.13699e6 −1.57378 −0.786888 0.617096i \(-0.788309\pi\)
−0.786888 + 0.617096i \(0.788309\pi\)
\(332\) −1.37438e6 −0.684325
\(333\) −77740.8 402696.i −0.0384183 0.199006i
\(334\) 1.13584e6i 0.557125i
\(335\) −2.43357e6 −1.18476
\(336\) −103386. 1.08096e6i −0.0499590 0.522351i
\(337\) 2.22407e6i 1.06678i 0.845871 + 0.533388i \(0.179081\pi\)
−0.845871 + 0.533388i \(0.820919\pi\)
\(338\) −3.02848e6 −1.44189
\(339\) 261532. + 2.73448e6i 0.123602 + 1.29233i
\(340\) 1.92944e6 0.905176
\(341\) 1.48787e6i 0.692913i
\(342\) 645115. 124540.i 0.298244 0.0575763i
\(343\) −1.84264e6 −0.845680
\(344\) 1.84698e6i 0.841523i
\(345\) 2.23138e6 213414.i 1.00931 0.0965331i
\(346\) −4.84942e6 −2.17771
\(347\) −1.28027e6 −0.570794 −0.285397 0.958409i \(-0.592125\pi\)
−0.285397 + 0.958409i \(0.592125\pi\)
\(348\) −2.48564e6 + 237733.i −1.10025 + 0.105230i
\(349\) 2.22537e6i 0.977999i 0.872284 + 0.488999i \(0.162638\pi\)
−0.872284 + 0.488999i \(0.837362\pi\)
\(350\) 7.49980e6 3.27250
\(351\) 568294. 167149.i 0.246210 0.0724161i
\(352\) −1.66235e6 −0.715099
\(353\) −3.33127e6 −1.42290 −0.711449 0.702738i \(-0.751961\pi\)
−0.711449 + 0.702738i \(0.751961\pi\)
\(354\) −1.28789e6 + 3.40392e6i −0.546222 + 1.44368i
\(355\) 2.71730e6 1.14437
\(356\) −530312. −0.221772
\(357\) 1.02600e6 98128.8i 0.426065 0.0407499i
\(358\) 3.41845e6 1.40968
\(359\) 3.86339e6i 1.58209i −0.611756 0.791046i \(-0.709537\pi\)
0.611756 0.791046i \(-0.290463\pi\)
\(360\) 468985. + 2.42934e6i 0.190723 + 0.987942i
\(361\) −2.38021e6 −0.961275
\(362\) 4.02443e6 1.61411
\(363\) −168623. 1.76305e6i −0.0671660 0.702261i
\(364\) 999110.i 0.395239i
\(365\) −4.31182e6 −1.69406
\(366\) −5.55095e6 + 530906.i −2.16603 + 0.207164i
\(367\) 3.94334e6i 1.52827i 0.645058 + 0.764134i \(0.276833\pi\)
−0.645058 + 0.764134i \(0.723167\pi\)
\(368\) 728225. 0.280315
\(369\) −347083. 1.79788e6i −0.132699 0.687378i
\(370\) 1.40373e6 0.533066
\(371\) 869367.i 0.327921i
\(372\) −4.69005e6 + 448568.i −1.75720 + 0.168062i
\(373\) 2.27599e6 0.847031 0.423515 0.905889i \(-0.360796\pi\)
0.423515 + 0.905889i \(0.360796\pi\)
\(374\) 870705.i 0.321878i
\(375\) 4.17229e6 399048.i 1.53213 0.146537i
\(376\) 3.03820e6 1.10827
\(377\) −566183. −0.205165
\(378\) 1.34777e6 + 4.58234e6i 0.485163 + 1.64952i
\(379\) 386178. 0.138099 0.0690493 0.997613i \(-0.478003\pi\)
0.0690493 + 0.997613i \(0.478003\pi\)
\(380\) 1.30493e6i 0.463582i
\(381\) 525348. + 5.49284e6i 0.185411 + 1.93858i
\(382\) 5.14201e6 1.80291
\(383\) 1.51157e6i 0.526539i −0.964722 0.263269i \(-0.915199\pi\)
0.964722 0.263269i \(-0.0848008\pi\)
\(384\) 301133. + 3.14853e6i 0.104215 + 1.08963i
\(385\) 2.99583e6i 1.03007i
\(386\) 120612. 0.0412024
\(387\) 795862. + 4.12255e6i 0.270122 + 1.39923i
\(388\) 3.77153e6i 1.27186i
\(389\) 1.73742e6i 0.582146i −0.956701 0.291073i \(-0.905988\pi\)
0.956701 0.291073i \(-0.0940123\pi\)
\(390\) 193030. + 2.01825e6i 0.0642633 + 0.671912i
\(391\) 691195.i 0.228643i
\(392\) −432622. −0.142198
\(393\) −284810. 2.97786e6i −0.0930195 0.972576i
\(394\) 4.36232e6i 1.41572i
\(395\) 7.96313e6i 2.56798i
\(396\) 2.29904e6 443832.i 0.736731 0.142226i
\(397\) 5.64435e6i 1.79737i 0.438593 + 0.898686i \(0.355477\pi\)
−0.438593 + 0.898686i \(0.644523\pi\)
\(398\) −6.22417e6 −1.96958
\(399\) 66367.0 + 693907.i 0.0208699 + 0.218207i
\(400\) 2.86909e6 0.896590
\(401\) 417749. 0.129734 0.0648671 0.997894i \(-0.479338\pi\)
0.0648671 + 0.997894i \(0.479338\pi\)
\(402\) 3.46176e6 331091.i 1.06839 0.102184i
\(403\) −1.06830e6 −0.327667
\(404\) 5.22495e6 1.59268
\(405\) 2.09360e6 + 5.22032e6i 0.634243 + 1.58146i
\(406\) 4.56531e6i 1.37453i
\(407\) 367592.i 0.109997i
\(408\) −759462. + 72636.8i −0.225868 + 0.0216026i
\(409\) 2.39087e6i 0.706720i −0.935487 0.353360i \(-0.885039\pi\)
0.935487 0.353360i \(-0.114961\pi\)
\(410\) 6.26714e6 1.84124
\(411\) 5.93081e6 567237.i 1.73185 0.165638i
\(412\) 7.66013e6i 2.22328i
\(413\) −3.46490e6 1.70401e6i −0.999574 0.491584i
\(414\) −3.14511e6 + 607165.i −0.901850 + 0.174103i
\(415\) 2.95897e6i 0.843376i
\(416\) 1.19358e6i 0.338158i
\(417\) −55786.0 583276.i −0.0157103 0.164261i
\(418\) 588879. 0.164849
\(419\) 5.64700e6 1.57138 0.785692 0.618618i \(-0.212307\pi\)
0.785692 + 0.618618i \(0.212307\pi\)
\(420\) −9.44342e6 + 903192.i −2.61220 + 0.249837i
\(421\) 2.96945e6i 0.816528i 0.912864 + 0.408264i \(0.133866\pi\)
−0.912864 + 0.408264i \(0.866134\pi\)
\(422\) 6.43223e6i 1.75825i
\(423\) 6.78142e6 1.30916e6i 1.84276 0.355747i
\(424\) 643522.i 0.173840i
\(425\) 2.72320e6i 0.731319i
\(426\) −3.86537e6 + 369693.i −1.03197 + 0.0987000i
\(427\) 5.91616e6i 1.57026i
\(428\) 4.87401e6i 1.28611i
\(429\) 528513. 50548.3i 0.138648 0.0132606i
\(430\) −1.43706e7 −3.74802
\(431\) 998455. 0.258902 0.129451 0.991586i \(-0.458679\pi\)
0.129451 + 0.991586i \(0.458679\pi\)
\(432\) 515598. + 1.75300e6i 0.132924 + 0.451931i
\(433\) −930962. −0.238623 −0.119312 0.992857i \(-0.538069\pi\)
−0.119312 + 0.992857i \(0.538069\pi\)
\(434\) 8.61409e6i 2.19526i
\(435\) −511827. 5.35147e6i −0.129688 1.35597i
\(436\) 4.16837e6i 1.05015i
\(437\) −467472. −0.117099
\(438\) 6.13357e6 586630.i 1.52767 0.146110i
\(439\) 2.37455e6 0.588057 0.294028 0.955797i \(-0.405004\pi\)
0.294028 + 0.955797i \(0.405004\pi\)
\(440\) 2.21757e6i 0.546066i
\(441\) −965635. + 186417.i −0.236438 + 0.0456445i
\(442\) −625175. −0.152211
\(443\) −1.46413e6 −0.354464 −0.177232 0.984169i \(-0.556714\pi\)
−0.177232 + 0.984169i \(0.556714\pi\)
\(444\) −1.15872e6 + 110823.i −0.278947 + 0.0266792i
\(445\) 1.14173e6i 0.273316i
\(446\) 9.47124e6 2.25460
\(447\) −64937.4 678960.i −0.0153718 0.160722i
\(448\) −7.39513e6 −1.74081
\(449\) 6.38769e6i 1.49530i −0.664094 0.747649i \(-0.731182\pi\)
0.664094 0.747649i \(-0.268818\pi\)
\(450\) −1.23912e7 + 2.39213e6i −2.88458 + 0.556870i
\(451\) 1.64116e6i 0.379935i
\(452\) 7.79623e6 1.79489
\(453\) −7.42794e6 + 710426.i −1.70068 + 0.162657i
\(454\) −1.03649e7 −2.36008
\(455\) −2.15103e6 −0.487100
\(456\) −49126.1 513643.i −0.0110637 0.115678i
\(457\) 3.94017e6i 0.882520i 0.897379 + 0.441260i \(0.145468\pi\)
−0.897379 + 0.441260i \(0.854532\pi\)
\(458\) 8.96750e6i 1.99760i
\(459\) −1.66386e6 + 489381.i −0.368625 + 0.108421i
\(460\) 6.36186e6i 1.40181i
\(461\) 1.83132e6i 0.401340i 0.979659 + 0.200670i \(0.0643118\pi\)
−0.979659 + 0.200670i \(0.935688\pi\)
\(462\) 407587. + 4.26157e6i 0.0888414 + 0.928891i
\(463\) 34543.7i 0.00748888i −0.999993 0.00374444i \(-0.998808\pi\)
0.999993 0.00374444i \(-0.00119189\pi\)
\(464\) 1.74649e6i 0.376591i
\(465\) −965744. 1.00974e7i −0.207124 2.16560i
\(466\) 6.38202e6 1.36142
\(467\) −1.09698e6 −0.232759 −0.116379 0.993205i \(-0.537129\pi\)
−0.116379 + 0.993205i \(0.537129\pi\)
\(468\) −318676. 1.65073e6i −0.0672565 0.348388i
\(469\) 3.68952e6i 0.774529i
\(470\) 2.36390e7i 4.93610i
\(471\) 2.60266e6 248925.i 0.540586 0.0517030i
\(472\) 2.56478e6 + 1.26134e6i 0.529901 + 0.260602i
\(473\) 3.76318e6i 0.773397i
\(474\) −1.08340e6 1.13276e7i −0.221484 2.31575i
\(475\) −1.84177e6 −0.374542
\(476\) 2.92521e6i 0.591751i
\(477\) 277293. + 1.43637e6i 0.0558012 + 0.289049i
\(478\) 1.21262e6i 0.242747i
\(479\) 6.36093e6i 1.26672i −0.773856 0.633361i \(-0.781675\pi\)
0.773856 0.633361i \(-0.218325\pi\)
\(480\) −1.12816e7 + 1.07900e6i −2.23494 + 0.213755i
\(481\) −263935. −0.0520157
\(482\) 3.83238e6 0.751365
\(483\) −323556. 3.38298e6i −0.0631077 0.659829i
\(484\) −5.02662e6 −0.975354
\(485\) 8.11991e6 1.56746
\(486\) −3.68838e6 7.14108e6i −0.708345 1.37143i
\(487\) 728855. 0.139258 0.0696288 0.997573i \(-0.477819\pi\)
0.0696288 + 0.997573i \(0.477819\pi\)
\(488\) 4.37925e6i 0.832435i
\(489\) −566256. 5.92055e6i −0.107088 1.11967i
\(490\) 3.36605e6i 0.633330i
\(491\) 8.18233e6i 1.53170i −0.643020 0.765849i \(-0.722319\pi\)
0.643020 0.765849i \(-0.277681\pi\)
\(492\) −5.17325e6 + 494782.i −0.963498 + 0.0921513i
\(493\) 1.65768e6 0.307173
\(494\) 422821.i 0.0779542i
\(495\) 955547. + 4.94972e6i 0.175283 + 0.907962i
\(496\) 3.29537e6i 0.601450i
\(497\) 4.11968e6i 0.748123i
\(498\) 402573. + 4.20915e6i 0.0727397 + 0.760538i
\(499\) 2.98295e6 0.536284 0.268142 0.963379i \(-0.413590\pi\)
0.268142 + 0.963379i \(0.413590\pi\)
\(500\) 1.18956e7i 2.12794i
\(501\) 2.01859e6 193062.i 0.359296 0.0343640i
\(502\) 2.64850e6i 0.469072i
\(503\) 9.05383e6 1.59556 0.797779 0.602950i \(-0.206008\pi\)
0.797779 + 0.602950i \(0.206008\pi\)
\(504\) 3.68310e6 711026.i 0.645858 0.124683i
\(505\) 1.12491e7i 1.96285i
\(506\) −2.87094e6 −0.498480
\(507\) 514759. + 5.38212e6i 0.0889373 + 0.929893i
\(508\) 1.56606e7 2.69245
\(509\) −2.07161e6 −0.354416 −0.177208 0.984173i \(-0.556707\pi\)
−0.177208 + 0.984173i \(0.556707\pi\)
\(510\) −565156. 5.90905e6i −0.0962150 1.00599i
\(511\) 6.53712e6i 1.10748i
\(512\) −5.33186e6 −0.898884
\(513\) −330980. 1.12531e6i −0.0555276 0.188790i
\(514\) 7.37906e6i 1.23195i
\(515\) −1.64919e7 −2.74001
\(516\) 1.18623e7 1.13454e6i 1.96130 0.187583i
\(517\) 6.19027e6 1.01855
\(518\) 2.12819e6i 0.348487i
\(519\) 824269. + 8.61823e6i 0.134323 + 1.40443i
\(520\) 1.59223e6 0.258225
\(521\) 7.18160e6i 1.15912i −0.814931 0.579558i \(-0.803225\pi\)
0.814931 0.579558i \(-0.196775\pi\)
\(522\) 1.45615e6 + 7.54284e6i 0.233900 + 1.21160i
\(523\) −7.71703e6 −1.23366 −0.616830 0.787096i \(-0.711584\pi\)
−0.616830 + 0.787096i \(0.711584\pi\)
\(524\) −8.49015e6 −1.35079
\(525\) −1.27476e6 1.33284e7i −0.201851 2.11047i
\(526\) 1.05933e7i 1.66943i
\(527\) 3.12780e6 0.490583
\(528\) 155925. + 1.63029e6i 0.0243405 + 0.254495i
\(529\) −4.15729e6 −0.645909
\(530\) −5.00697e6 −0.774257
\(531\) 6.26823e6 + 1.71022e6i 0.964737 + 0.263217i
\(532\) 1.97839e6 0.303063
\(533\) −1.17837e6 −0.179665
\(534\) 155335. + 1.62412e6i 0.0235730 + 0.246471i
\(535\) −1.04935e7 −1.58502
\(536\) 2.73105e6i 0.410599i
\(537\) −581042. 6.07515e6i −0.0869505 0.909120i
\(538\) −7.28354e6 −1.08489
\(539\) −881459. −0.130686
\(540\) 1.53144e7 4.50433e6i 2.26004 0.664730i
\(541\) 502453.i 0.0738078i 0.999319 + 0.0369039i \(0.0117495\pi\)
−0.999319 + 0.0369039i \(0.988250\pi\)
\(542\) 1.07022e7 1.56486
\(543\) −684043. 7.15208e6i −0.0995597 1.04096i
\(544\) 3.49459e6i 0.506290i
\(545\) 8.97429e6 1.29422
\(546\) 3.05985e6 292651.i 0.439257 0.0420116i
\(547\) −6.67433e6 −0.953761 −0.476880 0.878968i \(-0.658232\pi\)
−0.476880 + 0.878968i \(0.658232\pi\)
\(548\) 1.69093e7i 2.40532i
\(549\) 1.88702e6 + 9.77472e6i 0.267205 + 1.38412i
\(550\) −1.13110e7 −1.59440
\(551\) 1.12113e6i 0.157317i
\(552\) 239502. + 2.50414e6i 0.0334551 + 0.349793i
\(553\) 1.20728e7 1.67879
\(554\) 8.69669e6 1.20387
\(555\) −238596. 2.49467e6i −0.0328800 0.343780i
\(556\) −1.66297e6 −0.228138
\(557\) 7.25630e6i 0.991008i 0.868606 + 0.495504i \(0.165017\pi\)
−0.868606 + 0.495504i \(0.834983\pi\)
\(558\) 2.74755e6 + 1.42322e7i 0.373559 + 1.93503i
\(559\) 2.70200e6 0.365726
\(560\) 6.63522e6i 0.894099i
\(561\) −1.54739e6 + 147996.i −0.207583 + 0.0198538i
\(562\) 9.71352e6i 1.29729i
\(563\) −3.31267e6 −0.440461 −0.220230 0.975448i \(-0.570681\pi\)
−0.220230 + 0.975448i \(0.570681\pi\)
\(564\) −1.86626e6 1.95129e7i −0.247045 2.58300i
\(565\) 1.67849e7i 2.21206i
\(566\) 721152.i 0.0946206i
\(567\) 7.91449e6 3.17409e6i 1.03387 0.414631i
\(568\) 3.04947e6i 0.396600i
\(569\) −1.16764e7 −1.51192 −0.755958 0.654620i \(-0.772828\pi\)
−0.755958 + 0.654620i \(0.772828\pi\)
\(570\) 3.99644e6 382229.i 0.515212 0.0492761i
\(571\) 7.84759e6i 1.00727i −0.863916 0.503635i \(-0.831996\pi\)
0.863916 0.503635i \(-0.168004\pi\)
\(572\) 1.50684e6i 0.192564i
\(573\) −874000. 9.13821e6i −0.111205 1.16272i
\(574\) 9.50157e6i 1.20369i
\(575\) 8.97909e6 1.13256
\(576\) 1.22183e7 2.35875e6i 1.53445 0.296228i
\(577\) −3.59585e6 −0.449638 −0.224819 0.974401i \(-0.572179\pi\)
−0.224819 + 0.974401i \(0.572179\pi\)
\(578\) −1.05673e7 −1.31567
\(579\) −20500.7 214348.i −0.00254140 0.0265719i
\(580\) −1.52575e7 −1.88327
\(581\) −4.48608e6 −0.551350
\(582\) −1.15506e7 + 1.10473e6i −1.41350 + 0.135191i
\(583\) 1.31116e6i 0.159766i
\(584\) 4.83890e6i 0.587103i
\(585\) 3.55395e6 686093.i 0.429360 0.0828883i
\(586\) 6.04204e6i 0.726841i
\(587\) −3.72961e6 −0.446754 −0.223377 0.974732i \(-0.571708\pi\)
−0.223377 + 0.974732i \(0.571708\pi\)
\(588\) 265745. + 2.77853e6i 0.0316973 + 0.331414i
\(589\) 2.11541e6i 0.251250i
\(590\) −9.81395e6 + 1.99555e7i −1.16068 + 2.36011i
\(591\) −7.75257e6 + 741475.i −0.913013 + 0.0873228i
\(592\) 814152.i 0.0954775i
\(593\) 8.48469e6i 0.990830i 0.868657 + 0.495415i \(0.164984\pi\)
−0.868657 + 0.495415i \(0.835016\pi\)
\(594\) −2.03269e6 6.91099e6i −0.236376 0.803663i
\(595\) 6.29782e6 0.729286
\(596\) −1.93577e6 −0.223223
\(597\) 1.05794e6 + 1.10614e7i 0.121485 + 1.27020i
\(598\) 2.06136e6i 0.235723i
\(599\) 6.34558e6i 0.722610i 0.932448 + 0.361305i \(0.117669\pi\)
−0.932448 + 0.361305i \(0.882331\pi\)
\(600\) 943601. + 9.86592e6i 0.107007 + 1.11882i
\(601\) 419675.i 0.0473944i 0.999719 + 0.0236972i \(0.00754376\pi\)
−0.999719 + 0.0236972i \(0.992456\pi\)
\(602\) 2.17871e7i 2.45024i
\(603\) −1.17681e6 6.09584e6i −0.131799 0.682717i
\(604\) 2.11777e7i 2.36204i
\(605\) 1.08221e7i 1.20205i
\(606\) −1.53045e6 1.60018e7i −0.169293 1.77006i
\(607\) 1.49015e7 1.64157 0.820784 0.571239i \(-0.193537\pi\)
0.820784 + 0.571239i \(0.193537\pi\)
\(608\) 2.36348e6 0.259294
\(609\) −8.11332e6 + 775978.i −0.886453 + 0.0847825i
\(610\) −3.40731e7 −3.70755
\(611\) 4.44468e6i 0.481656i
\(612\) 933023. + 4.83304e6i 0.100696 + 0.521606i
\(613\) 1.24526e7i 1.33847i 0.743050 + 0.669236i \(0.233379\pi\)
−0.743050 + 0.669236i \(0.766621\pi\)
\(614\) 1.64900e7 1.76522
\(615\) −1.06524e6 1.11377e7i −0.113569 1.18743i
\(616\) 3.36204e6 0.356986
\(617\) 1.53268e7i 1.62084i 0.585851 + 0.810419i \(0.300760\pi\)
−0.585851 + 0.810419i \(0.699240\pi\)
\(618\) 2.34597e7 2.24375e6i 2.47088 0.236321i
\(619\) 1.81170e6 0.190047 0.0950233 0.995475i \(-0.469707\pi\)
0.0950233 + 0.995475i \(0.469707\pi\)
\(620\) −2.87887e7 −3.00776
\(621\) 1.61362e6 + 5.48618e6i 0.167908 + 0.570875i
\(622\) 1.52024e7i 1.57557i
\(623\) −1.73098e6 −0.178678
\(624\) 1.17056e6 111955.i 0.120346 0.0115102i
\(625\) 7.02372e6 0.719229
\(626\) 5.50461e6i 0.561424i
\(627\) −100093. 1.04654e6i −0.0101680 0.106313i
\(628\) 7.42041e6i 0.750808i
\(629\) 772753. 0.0778778
\(630\) 5.53219e6 + 2.86566e7i 0.555323 + 2.87656i
\(631\) 1.30180e6 0.130158 0.0650790 0.997880i \(-0.479270\pi\)
0.0650790 + 0.997880i \(0.479270\pi\)
\(632\) −8.93655e6 −0.889973
\(633\) 1.14312e7 1.09330e6i 1.13392 0.108450i
\(634\) 1.35030e7i 1.33416i
\(635\) 3.37164e7i 3.31823i
\(636\) 4.13304e6 395294.i 0.405160 0.0387505i
\(637\) 632896.i 0.0617993i
\(638\) 6.88531e6i 0.669687i
\(639\) 1.31401e6 + 6.80656e6i 0.127306 + 0.659441i
\(640\) 1.93265e7i 1.86510i
\(641\) 6.75437e6i 0.649292i 0.945836 + 0.324646i \(0.105245\pi\)
−0.945836 + 0.324646i \(0.894755\pi\)
\(642\) 1.49270e7 1.42766e6i 1.42934 0.136706i
\(643\) −1.60869e7 −1.53442 −0.767211 0.641395i \(-0.778356\pi\)
−0.767211 + 0.641395i \(0.778356\pi\)
\(644\) −9.64517e6 −0.916422
\(645\) 2.44260e6 + 2.55389e7i 0.231181 + 2.41714i
\(646\) 1.23794e6i 0.116713i
\(647\) 1.76697e6i 0.165947i 0.996552 + 0.0829733i \(0.0264416\pi\)
−0.996552 + 0.0829733i \(0.973558\pi\)
\(648\) −5.85845e6 + 2.34952e6i −0.548082 + 0.219807i
\(649\) 5.22569e6 + 2.56996e6i 0.487003 + 0.239505i
\(650\) 8.12144e6i 0.753963i
\(651\) −1.53087e7 + 1.46416e6i −1.41574 + 0.135405i
\(652\) −1.68800e7 −1.55508
\(653\) 1.06273e7i 0.975305i 0.873038 + 0.487652i \(0.162147\pi\)
−0.873038 + 0.487652i \(0.837853\pi\)
\(654\) −1.27660e7 + 1.22097e6i −1.16710 + 0.111624i
\(655\) 1.82789e7i 1.66474i
\(656\) 3.63488e6i 0.329784i
\(657\) −2.08508e6 1.08007e7i −0.188455 0.976196i
\(658\) 3.58389e7 3.22693
\(659\) −1.82151e7 −1.63387 −0.816937 0.576727i \(-0.804330\pi\)
−0.816937 + 0.576727i \(0.804330\pi\)
\(660\) 1.42424e7 1.36218e6i 1.27269 0.121723i
\(661\) 9.70544e6 0.863996 0.431998 0.901875i \(-0.357809\pi\)
0.431998 + 0.901875i \(0.357809\pi\)
\(662\) 2.73912e7 2.42921
\(663\) 106263. + 1.11104e6i 0.00938850 + 0.0981625i
\(664\) 3.32068e6 0.292285
\(665\) 4.25937e6i 0.373501i
\(666\) 678808. + 3.51621e6i 0.0593009 + 0.307178i
\(667\) 5.46580e6i 0.475706i
\(668\) 5.75517e6i 0.499019i
\(669\) −1.60985e6 1.68320e7i −0.139066 1.45402i
\(670\) 2.12491e7 1.82875
\(671\) 8.92264e6i 0.765045i
\(672\) 1.63586e6 + 1.71039e7i 0.139741 + 1.46107i
\(673\) 1.50186e7i 1.27818i −0.769131 0.639092i \(-0.779310\pi\)
0.769131 0.639092i \(-0.220690\pi\)
\(674\) 1.94198e7i 1.64663i
\(675\) 6.35739e6 + 2.16147e7i 0.537055 + 1.82595i
\(676\) 1.53449e7 1.29151
\(677\) 1.77507e6i 0.148848i −0.997227 0.0744242i \(-0.976288\pi\)
0.997227 0.0744242i \(-0.0237119\pi\)
\(678\) −2.28361e6 2.38766e7i −0.190787 1.99479i
\(679\) 1.23105e7i 1.02471i
\(680\) −4.66177e6 −0.386615
\(681\) 1.76175e6 + 1.84202e7i 0.145572 + 1.52204i
\(682\) 1.29916e7i 1.06955i
\(683\) −1.56418e7 −1.28302 −0.641512 0.767113i \(-0.721693\pi\)
−0.641512 + 0.767113i \(0.721693\pi\)
\(684\) −3.26871e6 + 631027.i −0.267138 + 0.0515712i
\(685\) 3.64048e7 2.96437
\(686\) 1.60894e7 1.30535
\(687\) −1.59367e7 + 1.52423e6i −1.28827 + 0.123214i
\(688\) 8.33478e6i 0.671310i
\(689\) 941428. 0.0755508
\(690\) −1.94837e7 + 1.86347e6i −1.55793 + 0.149004i
\(691\) 1.77867e7i 1.41710i 0.705663 + 0.708548i \(0.250649\pi\)
−0.705663 + 0.708548i \(0.749351\pi\)
\(692\) 2.45713e7 1.95058
\(693\) 7.50424e6 1.44870e6i 0.593572 0.114590i
\(694\) 1.11789e7 0.881053
\(695\) 3.58030e6i 0.281162i
\(696\) 6.00563e6 574393.i 0.469933 0.0449455i
\(697\) 3.45005e6 0.268994
\(698\) 1.94312e7i 1.50960i
\(699\) −1.08477e6 1.13419e7i −0.0839739 0.877998i
\(700\) −3.80004e7 −2.93119
\(701\) 1.29116e7 0.992396 0.496198 0.868209i \(-0.334729\pi\)
0.496198 + 0.868209i \(0.334729\pi\)
\(702\) −4.96216e6 + 1.45949e6i −0.380039 + 0.111778i
\(703\) 522632.i 0.0398848i
\(704\) 1.11532e7 0.848140
\(705\) 4.20104e7 4.01797e6i 3.18334 0.304463i
\(706\) 2.90876e7 2.19632
\(707\) 1.70546e7 1.28320
\(708\) 6.52554e6 1.72472e7i 0.489253 1.29311i
\(709\) −2.17279e7 −1.62331 −0.811657 0.584134i \(-0.801434\pi\)
−0.811657 + 0.584134i \(0.801434\pi\)
\(710\) −2.37266e7 −1.76640
\(711\) −1.99468e7 + 3.85075e6i −1.47979 + 0.285674i
\(712\) 1.28130e6 0.0947221
\(713\) 1.03132e7i 0.759746i
\(714\) −8.95867e6 + 856829.i −0.657655 + 0.0628997i
\(715\) 3.24414e6 0.237320
\(716\) −1.73208e7 −1.26266
\(717\) 2.15502e6 206112.i 0.156550 0.0149729i
\(718\) 3.37338e7i 2.44205i
\(719\) −7.86562e6 −0.567428 −0.283714 0.958909i \(-0.591567\pi\)
−0.283714 + 0.958909i \(0.591567\pi\)
\(720\) 2.11637e6 + 1.09628e7i 0.152146 + 0.788113i
\(721\) 2.50032e7i 1.79126i
\(722\) 2.07832e7 1.48378
\(723\) −651399. 6.81078e6i −0.0463449 0.484564i
\(724\) −2.03912e7 −1.44576
\(725\) 2.15344e7i 1.52155i
\(726\) 1.47236e6 + 1.53944e7i 0.103674 + 1.08398i
\(727\) −2.35104e7 −1.64977 −0.824886 0.565300i \(-0.808761\pi\)
−0.824886 + 0.565300i \(0.808761\pi\)
\(728\) 2.41398e6i 0.168813i
\(729\) −1.20640e7 + 7.76866e6i −0.840758 + 0.541411i
\(730\) 3.76494e7 2.61487
\(731\) −7.91096e6 −0.547565
\(732\) 2.81259e7 2.69003e6i 1.94012 0.185558i
\(733\) −1.03370e7 −0.710615 −0.355308 0.934749i \(-0.615624\pi\)
−0.355308 + 0.934749i \(0.615624\pi\)
\(734\) 3.44320e7i 2.35897i
\(735\) −5.98203e6 + 572136.i −0.408442 + 0.0390644i
\(736\) −1.15226e7 −0.784072
\(737\) 5.56446e6i 0.377358i
\(738\) 3.03062e6 + 1.56985e7i 0.204828 + 1.06101i
\(739\) 1.98195e7i 1.33500i −0.744611 0.667499i \(-0.767365\pi\)
0.744611 0.667499i \(-0.232635\pi\)
\(740\) −7.11253e6 −0.477468
\(741\) −751424. + 71868.0i −0.0502735 + 0.00480828i
\(742\) 7.59104e6i 0.506164i
\(743\) 1.67323e7i 1.11195i 0.831200 + 0.555973i \(0.187654\pi\)
−0.831200 + 0.555973i \(0.812346\pi\)
\(744\) 1.13318e7 1.08380e6i 0.750525 0.0717820i
\(745\) 4.16763e6i 0.275105i
\(746\) −1.98732e7 −1.30744
\(747\) 7.41193e6 1.43088e6i 0.485993 0.0938213i
\(748\) 4.41174e6i 0.288307i
\(749\) 1.59091e7i 1.03620i
\(750\) −3.64311e7 + 3.48436e6i −2.36493 + 0.226188i
\(751\) 6.30270e6i 0.407781i 0.978994 + 0.203890i \(0.0653586\pi\)
−0.978994 + 0.203890i \(0.934641\pi\)
\(752\) 1.37104e7 0.884106
\(753\) −4.70682e6 + 450172.i −0.302510 + 0.0289328i
\(754\) 4.94372e6 0.316684
\(755\) −4.55945e7 −2.91102
\(756\) −6.82898e6 2.32181e7i −0.434562 1.47748i
\(757\) 1.17960e7 0.748161 0.374081 0.927396i \(-0.377958\pi\)
0.374081 + 0.927396i \(0.377958\pi\)
\(758\) −3.37198e6 −0.213163
\(759\) 487981. + 5.10214e6i 0.0307467 + 0.321476i
\(760\) 3.15287e6i 0.198003i
\(761\) 1.13477e7i 0.710306i −0.934808 0.355153i \(-0.884429\pi\)
0.934808 0.355153i \(-0.115571\pi\)
\(762\) −4.58717e6 4.79617e7i −0.286192 2.99231i
\(763\) 1.36059e7i 0.846087i
\(764\) −2.60538e7 −1.61487
\(765\) −1.04053e7 + 2.00875e6i −0.642837 + 0.124100i
\(766\) 1.31985e7i 0.812743i
\(767\) 1.84525e6 3.75209e6i 0.113258 0.230295i
\(768\) −197329. 2.06320e6i −0.0120722 0.126223i
\(769\) 3.63980e6i 0.221954i 0.993823 + 0.110977i \(0.0353979\pi\)
−0.993823 + 0.110977i \(0.964602\pi\)
\(770\) 2.61586e7i 1.58996i
\(771\) −1.31138e7 + 1.25424e6i −0.794499 + 0.0759878i
\(772\) −611124. −0.0369051
\(773\) −2.88048e7 −1.73387 −0.866934 0.498423i \(-0.833913\pi\)
−0.866934 + 0.498423i \(0.833913\pi\)
\(774\) −6.94921e6 3.59968e7i −0.416949 2.15979i
\(775\) 4.06322e7i 2.43006i
\(776\) 9.11250e6i 0.543229i
\(777\) −3.78215e6 + 361734.i −0.224743 + 0.0214950i
\(778\) 1.51706e7i 0.898576i
\(779\) 2.33335e6i