Properties

Label 177.6.d.b.176.5
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 176.5
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.6

$q$-expansion

\(f(q)\) \(=\) \(q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +O(q^{10})\) \(q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +97.0958i q^{10} -337.866 q^{11} +(-955.042 - 695.428i) q^{12} +682.151i q^{13} -697.388 q^{14} +(-85.8167 + 117.853i) q^{15} +2294.52 q^{16} -513.997i q^{17} +(-774.509 - 2401.01i) q^{18} +189.135 q^{19} -708.783i q^{20} +(-846.479 - 616.376i) q^{21} +3507.74 q^{22} +784.190 q^{23} +(5728.72 + 4171.45i) q^{24} +3037.54 q^{25} -7082.14i q^{26} +(1182.01 - 3598.85i) q^{27} +5090.81 q^{28} -4832.42i q^{29} +(890.955 - 1223.56i) q^{30} +4999.87i q^{31} -9274.61 q^{32} +(4257.65 + 3100.27i) q^{33} +5336.35i q^{34} -628.213i q^{35} +(5653.78 + 17527.0i) q^{36} -9261.10i q^{37} -1963.61 q^{38} +(6259.44 - 8596.19i) q^{39} +4251.56i q^{40} +4658.46i q^{41} +(8788.20 + 6399.26i) q^{42} -5287.94i q^{43} -25605.9 q^{44} +(2162.85 - 697.684i) q^{45} -8141.51 q^{46} -5081.19 q^{47} +(-28914.7 - 21054.6i) q^{48} -12294.9 q^{49} -31535.9 q^{50} +(-4716.46 + 6477.18i) q^{51} +51698.4i q^{52} -8728.92i q^{53} +(-12271.8 + 37363.5i) q^{54} +3159.81i q^{55} -30536.7 q^{56} +(-2383.41 - 1735.51i) q^{57} +50170.6i q^{58} +(-25651.4 + 7545.23i) q^{59} +(-6503.82 + 8931.79i) q^{60} -26624.9i q^{61} -51909.0i q^{62} +(5011.10 + 15534.6i) q^{63} +22864.9 q^{64} +6379.65 q^{65} +(-44203.2 - 32187.2i) q^{66} -36459.7i q^{67} -38954.4i q^{68} +(-9882.04 - 7195.75i) q^{69} +6522.15i q^{70} +83513.0i q^{71} +(-33913.7 - 105134. i) q^{72} +15824.8i q^{73} +96149.4i q^{74} +(-38277.8 - 27872.5i) q^{75} +14334.1 q^{76} -22695.2 q^{77} +(-64986.0 + 89246.3i) q^{78} -20068.7 q^{79} -21459.0i q^{80} +(-47918.5 + 34505.1i) q^{81} -48364.4i q^{82} +69484.9 q^{83} +(-64152.4 - 46713.5i) q^{84} -4807.03 q^{85} +54899.7i q^{86} +(-44342.5 + 60896.3i) q^{87} +153595. q^{88} -21384.8 q^{89} +(-22454.9 + 7243.40i) q^{90} +45821.7i q^{91} +59431.6 q^{92} +(45879.0 - 63006.4i) q^{93} +52753.3 q^{94} -1768.84i q^{95} +(116875. + 85104.2i) q^{96} -151770. i q^{97} +127646. q^{98} +(-25205.0 - 78136.7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.3821 −1.83531 −0.917654 0.397381i \(-0.869919\pi\)
−0.917654 + 0.397381i \(0.869919\pi\)
\(3\) −12.6016 9.17604i −0.808393 0.588643i
\(4\) 75.7873 2.36835
\(5\) 9.35226i 0.167298i −0.996495 0.0836491i \(-0.973343\pi\)
0.996495 0.0836491i \(-0.0266575\pi\)
\(6\) 130.831 + 95.2663i 1.48365 + 1.08034i
\(7\) 67.1723 0.518138 0.259069 0.965859i \(-0.416584\pi\)
0.259069 + 0.965859i \(0.416584\pi\)
\(8\) −454.603 −2.51135
\(9\) 74.6006 + 231.266i 0.306998 + 0.951710i
\(10\) 97.0958i 0.307044i
\(11\) −337.866 −0.841903 −0.420952 0.907083i \(-0.638304\pi\)
−0.420952 + 0.907083i \(0.638304\pi\)
\(12\) −955.042 695.428i −1.91456 1.39412i
\(13\) 682.151i 1.11949i 0.828663 + 0.559747i \(0.189102\pi\)
−0.828663 + 0.559747i \(0.810898\pi\)
\(14\) −697.388 −0.950942
\(15\) −85.8167 + 117.853i −0.0984790 + 0.135243i
\(16\) 2294.52 2.24075
\(17\) 513.997i 0.431358i −0.976464 0.215679i \(-0.930803\pi\)
0.976464 0.215679i \(-0.0691965\pi\)
\(18\) −774.509 2401.01i −0.563436 1.74668i
\(19\) 189.135 0.120196 0.0600978 0.998192i \(-0.480859\pi\)
0.0600978 + 0.998192i \(0.480859\pi\)
\(20\) 708.783i 0.396221i
\(21\) −846.479 616.376i −0.418859 0.304998i
\(22\) 3507.74 1.54515
\(23\) 784.190 0.309102 0.154551 0.987985i \(-0.450607\pi\)
0.154551 + 0.987985i \(0.450607\pi\)
\(24\) 5728.72 + 4171.45i 2.03016 + 1.47829i
\(25\) 3037.54 0.972011
\(26\) 7082.14i 2.05462i
\(27\) 1182.01 3598.85i 0.312042 0.950068i
\(28\) 5090.81 1.22713
\(29\) 4832.42i 1.06701i −0.845796 0.533507i \(-0.820874\pi\)
0.845796 0.533507i \(-0.179126\pi\)
\(30\) 890.955 1223.56i 0.180739 0.248212i
\(31\) 4999.87i 0.934447i 0.884139 + 0.467223i \(0.154746\pi\)
−0.884139 + 0.467223i \(0.845254\pi\)
\(32\) −9274.61 −1.60111
\(33\) 4257.65 + 3100.27i 0.680589 + 0.495581i
\(34\) 5336.35i 0.791675i
\(35\) 628.213i 0.0866835i
\(36\) 5653.78 + 17527.0i 0.727081 + 2.25399i
\(37\) 9261.10i 1.11214i −0.831137 0.556068i \(-0.812309\pi\)
0.831137 0.556068i \(-0.187691\pi\)
\(38\) −1963.61 −0.220596
\(39\) 6259.44 8596.19i 0.658983 0.904992i
\(40\) 4251.56i 0.420145i
\(41\) 4658.46i 0.432795i 0.976305 + 0.216398i \(0.0694307\pi\)
−0.976305 + 0.216398i \(0.930569\pi\)
\(42\) 8788.20 + 6399.26i 0.768735 + 0.559766i
\(43\) 5287.94i 0.436129i −0.975934 0.218065i \(-0.930026\pi\)
0.975934 0.218065i \(-0.0699744\pi\)
\(44\) −25605.9 −1.99392
\(45\) 2162.85 697.684i 0.159219 0.0513603i
\(46\) −8141.51 −0.567297
\(47\) −5081.19 −0.335522 −0.167761 0.985828i \(-0.553654\pi\)
−0.167761 + 0.985828i \(0.553654\pi\)
\(48\) −28914.7 21054.6i −1.81140 1.31900i
\(49\) −12294.9 −0.731533
\(50\) −31535.9 −1.78394
\(51\) −4716.46 + 6477.18i −0.253916 + 0.348707i
\(52\) 51698.4i 2.65136i
\(53\) 8728.92i 0.426846i −0.976960 0.213423i \(-0.931539\pi\)
0.976960 0.213423i \(-0.0684612\pi\)
\(54\) −12271.8 + 37363.5i −0.572694 + 1.74367i
\(55\) 3159.81i 0.140849i
\(56\) −30536.7 −1.30123
\(57\) −2383.41 1735.51i −0.0971652 0.0707523i
\(58\) 50170.6i 1.95830i
\(59\) −25651.4 + 7545.23i −0.959358 + 0.282191i
\(60\) −6503.82 + 8931.79i −0.233233 + 0.320303i
\(61\) 26624.9i 0.916143i −0.888915 0.458071i \(-0.848540\pi\)
0.888915 0.458071i \(-0.151460\pi\)
\(62\) 51909.0i 1.71500i
\(63\) 5011.10 + 15534.6i 0.159067 + 0.493117i
\(64\) 22864.9 0.697781
\(65\) 6379.65 0.187290
\(66\) −44203.2 32187.2i −1.24909 0.909543i
\(67\) 36459.7i 0.992262i −0.868248 0.496131i \(-0.834754\pi\)
0.868248 0.496131i \(-0.165246\pi\)
\(68\) 38954.4i 1.02161i
\(69\) −9882.04 7195.75i −0.249876 0.181951i
\(70\) 6522.15i 0.159091i
\(71\) 83513.0i 1.96611i 0.183305 + 0.983056i \(0.441320\pi\)
−0.183305 + 0.983056i \(0.558680\pi\)
\(72\) −33913.7 105134.i −0.770981 2.39008i
\(73\) 15824.8i 0.347561i 0.984784 + 0.173780i \(0.0555983\pi\)
−0.984784 + 0.173780i \(0.944402\pi\)
\(74\) 96149.4i 2.04111i
\(75\) −38277.8 27872.5i −0.785767 0.572168i
\(76\) 14334.1 0.284666
\(77\) −22695.2 −0.436222
\(78\) −64986.0 + 89246.3i −1.20944 + 1.66094i
\(79\) −20068.7 −0.361786 −0.180893 0.983503i \(-0.557899\pi\)
−0.180893 + 0.983503i \(0.557899\pi\)
\(80\) 21459.0i 0.374873i
\(81\) −47918.5 + 34505.1i −0.811504 + 0.584347i
\(82\) 48364.4i 0.794312i
\(83\) 69484.9 1.10712 0.553561 0.832809i \(-0.313269\pi\)
0.553561 + 0.832809i \(0.313269\pi\)
\(84\) −64152.4 46713.5i −0.992006 0.722344i
\(85\) −4807.03 −0.0721655
\(86\) 54899.7i 0.800431i
\(87\) −44342.5 + 60896.3i −0.628090 + 0.862566i
\(88\) 153595. 2.11431
\(89\) −21384.8 −0.286174 −0.143087 0.989710i \(-0.545703\pi\)
−0.143087 + 0.989710i \(0.545703\pi\)
\(90\) −22454.9 + 7243.40i −0.292217 + 0.0942619i
\(91\) 45821.7i 0.580053i
\(92\) 59431.6 0.732062
\(93\) 45879.0 63006.4i 0.550056 0.755400i
\(94\) 52753.3 0.615786
\(95\) 1768.84i 0.0201085i
\(96\) 116875. + 85104.2i 1.29433 + 0.942482i
\(97\) 151770.i 1.63779i −0.573944 0.818894i \(-0.694587\pi\)
0.573944 0.818894i \(-0.305413\pi\)
\(98\) 127646. 1.34259
\(99\) −25205.0 78136.7i −0.258463 0.801248i
\(100\) 230207. 2.30207
\(101\) 22547.4 0.219934 0.109967 0.993935i \(-0.464925\pi\)
0.109967 + 0.993935i \(0.464925\pi\)
\(102\) 48966.6 67246.5i 0.466014 0.639985i
\(103\) 91170.0i 0.846757i 0.905953 + 0.423379i \(0.139156\pi\)
−0.905953 + 0.423379i \(0.860844\pi\)
\(104\) 310108.i 2.81144i
\(105\) −5764.51 + 7916.49i −0.0510257 + 0.0700744i
\(106\) 90624.2i 0.783393i
\(107\) 112334.i 0.948529i 0.880383 + 0.474264i \(0.157286\pi\)
−0.880383 + 0.474264i \(0.842714\pi\)
\(108\) 89581.7 272748.i 0.739027 2.25010i
\(109\) 102382.i 0.825383i 0.910871 + 0.412692i \(0.135411\pi\)
−0.910871 + 0.412692i \(0.864589\pi\)
\(110\) 32805.3i 0.258501i
\(111\) −84980.2 + 116705.i −0.654652 + 0.899044i
\(112\) 154129. 1.16102
\(113\) −84179.3 −0.620168 −0.310084 0.950709i \(-0.600357\pi\)
−0.310084 + 0.950709i \(0.600357\pi\)
\(114\) 24744.7 + 18018.2i 0.178328 + 0.129852i
\(115\) 7333.94i 0.0517122i
\(116\) 366237.i 2.52707i
\(117\) −157758. + 50888.9i −1.06543 + 0.343683i
\(118\) 266314. 78335.1i 1.76072 0.517907i
\(119\) 34526.4i 0.223503i
\(120\) 39012.5 53576.5i 0.247315 0.339642i
\(121\) −46897.9 −0.291199
\(122\) 276421.i 1.68140i
\(123\) 42746.2 58704.0i 0.254762 0.349869i
\(124\) 378927.i 2.21310i
\(125\) 57633.6i 0.329914i
\(126\) −52025.5 161282.i −0.291938 0.905021i
\(127\) −293804. −1.61640 −0.808200 0.588909i \(-0.799558\pi\)
−0.808200 + 0.588909i \(0.799558\pi\)
\(128\) 59402.9 0.320467
\(129\) −48522.3 + 66636.5i −0.256725 + 0.352564i
\(130\) −66234.0 −0.343734
\(131\) −142504. −0.725517 −0.362758 0.931883i \(-0.618165\pi\)
−0.362758 + 0.931883i \(0.618165\pi\)
\(132\) 322676. + 234961.i 1.61187 + 1.17371i
\(133\) 12704.7 0.0622779
\(134\) 378527.i 1.82111i
\(135\) −33657.4 11054.5i −0.158945 0.0522041i
\(136\) 233665.i 1.08329i
\(137\) 240224.i 1.09349i 0.837299 + 0.546746i \(0.184134\pi\)
−0.837299 + 0.546746i \(0.815866\pi\)
\(138\) 102596. + 74706.8i 0.458599 + 0.333935i
\(139\) −433932. −1.90495 −0.952477 0.304610i \(-0.901474\pi\)
−0.952477 + 0.304610i \(0.901474\pi\)
\(140\) 47610.6i 0.205297i
\(141\) 64031.1 + 46625.2i 0.271234 + 0.197503i
\(142\) 867038.i 3.60842i
\(143\) 230475.i 0.942506i
\(144\) 171173. + 530644.i 0.687906 + 2.13254i
\(145\) −45194.1 −0.178510
\(146\) 164294.i 0.637881i
\(147\) 154935. + 112818.i 0.591366 + 0.430612i
\(148\) 701874.i 2.63393i
\(149\) −194855. −0.719027 −0.359513 0.933140i \(-0.617057\pi\)
−0.359513 + 0.933140i \(0.617057\pi\)
\(150\) 397403. + 289375.i 1.44212 + 1.05010i
\(151\) 257172.i 0.917870i 0.888470 + 0.458935i \(0.151769\pi\)
−0.888470 + 0.458935i \(0.848231\pi\)
\(152\) −85981.4 −0.301853
\(153\) 118870. 38344.5i 0.410528 0.132426i
\(154\) 235623. 0.800601
\(155\) 46760.1 0.156331
\(156\) 474387. 651482.i 1.56071 2.14334i
\(157\) 294763.i 0.954384i −0.878799 0.477192i \(-0.841655\pi\)
0.878799 0.477192i \(-0.158345\pi\)
\(158\) 208355. 0.663988
\(159\) −80096.9 + 109998.i −0.251260 + 0.345059i
\(160\) 86738.6i 0.267863i
\(161\) 52675.8 0.160157
\(162\) 497493. 358234.i 1.48936 1.07246i
\(163\) 466677. 1.37578 0.687888 0.725817i \(-0.258538\pi\)
0.687888 + 0.725817i \(0.258538\pi\)
\(164\) 353052.i 1.02501i
\(165\) 28994.5 39818.6i 0.0829098 0.113861i
\(166\) −721397. −2.03191
\(167\) 483482.i 1.34150i −0.741686 0.670748i \(-0.765973\pi\)
0.741686 0.670748i \(-0.234027\pi\)
\(168\) 384812. + 280206.i 1.05190 + 0.765958i
\(169\) −94036.9 −0.253269
\(170\) 49906.9 0.132446
\(171\) 14109.6 + 43740.5i 0.0368998 + 0.114391i
\(172\) 400759.i 1.03291i
\(173\) −422426. −1.07309 −0.536545 0.843872i \(-0.680271\pi\)
−0.536545 + 0.843872i \(0.680271\pi\)
\(174\) 460367. 632229.i 1.15274 1.58307i
\(175\) 204038. 0.503636
\(176\) −775241. −1.88649
\(177\) 392484. + 140296.i 0.941648 + 0.336599i
\(178\) 222018. 0.525217
\(179\) 183578. 0.428242 0.214121 0.976807i \(-0.431311\pi\)
0.214121 + 0.976807i \(0.431311\pi\)
\(180\) 163917. 52875.6i 0.377088 0.121639i
\(181\) −452441. −1.02652 −0.513258 0.858234i \(-0.671562\pi\)
−0.513258 + 0.858234i \(0.671562\pi\)
\(182\) 475724.i 1.06458i
\(183\) −244311. + 335516.i −0.539281 + 0.740603i
\(184\) −356495. −0.776263
\(185\) −86612.2 −0.186059
\(186\) −476319. + 654136.i −1.00952 + 1.38639i
\(187\) 173662.i 0.363162i
\(188\) −385090. −0.794635
\(189\) 79398.7 241743.i 0.161681 0.492266i
\(190\) 18364.2i 0.0369053i
\(191\) −612167. −1.21419 −0.607095 0.794629i \(-0.707665\pi\)
−0.607095 + 0.794629i \(0.707665\pi\)
\(192\) −288134. 209809.i −0.564081 0.410744i
\(193\) −545872. −1.05487 −0.527433 0.849596i \(-0.676846\pi\)
−0.527433 + 0.849596i \(0.676846\pi\)
\(194\) 1.57569e6i 3.00585i
\(195\) −80393.8 58539.9i −0.151404 0.110247i
\(196\) −931796. −1.73253
\(197\) 788573.i 1.44769i 0.689962 + 0.723846i \(0.257627\pi\)
−0.689962 + 0.723846i \(0.742373\pi\)
\(198\) 261680. + 811220.i 0.474359 + 1.47054i
\(199\) −305544. −0.546942 −0.273471 0.961880i \(-0.588172\pi\)
−0.273471 + 0.961880i \(0.588172\pi\)
\(200\) −1.38087e6 −2.44106
\(201\) −334556. + 459451.i −0.584088 + 0.802137i
\(202\) −234088. −0.403647
\(203\) 324605.i 0.552860i
\(204\) −357448. + 490888.i −0.601363 + 0.825862i
\(205\) 43567.1 0.0724059
\(206\) 946533.i 1.55406i
\(207\) 58501.0 + 181356.i 0.0948937 + 0.294175i
\(208\) 1.56521e6i 2.50850i
\(209\) −63902.3 −0.101193
\(210\) 59847.5 82189.5i 0.0936478 0.128608i
\(211\) 406972.i 0.629301i 0.949208 + 0.314651i \(0.101887\pi\)
−0.949208 + 0.314651i \(0.898113\pi\)
\(212\) 661541.i 1.01092i
\(213\) 766319. 1.05240e6i 1.15734 1.58939i
\(214\) 1.16626e6i 1.74084i
\(215\) −49454.2 −0.0729637
\(216\) −537347. + 1.63605e6i −0.783648 + 2.38595i
\(217\) 335853.i 0.484172i
\(218\) 1.06293e6i 1.51483i
\(219\) 145209. 199418.i 0.204589 0.280966i
\(220\) 239473.i 0.333580i
\(221\) 350623. 0.482903
\(222\) 882270. 1.21164e6i 1.20149 1.65002i
\(223\) −234388. −0.315627 −0.157813 0.987469i \(-0.550444\pi\)
−0.157813 + 0.987469i \(0.550444\pi\)
\(224\) −622997. −0.829595
\(225\) 226602. + 702477.i 0.298406 + 0.925073i
\(226\) 873956. 1.13820
\(227\) −1.11450e6 −1.43554 −0.717768 0.696283i \(-0.754836\pi\)
−0.717768 + 0.696283i \(0.754836\pi\)
\(228\) −180632. 131530.i −0.230122 0.167566i
\(229\) 255462.i 0.321912i 0.986962 + 0.160956i \(0.0514578\pi\)
−0.986962 + 0.160956i \(0.948542\pi\)
\(230\) 76141.5i 0.0949078i
\(231\) 285996. + 208252.i 0.352639 + 0.256779i
\(232\) 2.19683e6i 2.67965i
\(233\) 783301. 0.945233 0.472617 0.881268i \(-0.343310\pi\)
0.472617 + 0.881268i \(0.343310\pi\)
\(234\) 1.63785e6 528332.i 1.95540 0.630764i
\(235\) 47520.6i 0.0561322i
\(236\) −1.94405e6 + 571833.i −2.27210 + 0.668327i
\(237\) 252898. + 184151.i 0.292465 + 0.212963i
\(238\) 358455.i 0.410197i
\(239\) 1.01079e6i 1.14463i −0.820032 0.572317i \(-0.806044\pi\)
0.820032 0.572317i \(-0.193956\pi\)
\(240\) −196908. + 270417.i −0.220666 + 0.303045i
\(241\) −354547. −0.393216 −0.196608 0.980482i \(-0.562993\pi\)
−0.196608 + 0.980482i \(0.562993\pi\)
\(242\) 486897. 0.534440
\(243\) 920470. + 4882.62i 0.999986 + 0.00530442i
\(244\) 2.01783e6i 2.16975i
\(245\) 114985.i 0.122384i
\(246\) −443794. + 609469.i −0.467567 + 0.642116i
\(247\) 129019.i 0.134558i
\(248\) 2.27296e6i 2.34672i
\(249\) −875621. 637597.i −0.894990 0.651700i
\(250\) 598356.i 0.605494i
\(251\) 1.03607e6i 1.03802i 0.854768 + 0.519010i \(0.173699\pi\)
−0.854768 + 0.519010i \(0.826301\pi\)
\(252\) 379778. + 1.17733e6i 0.376728 + 1.16788i
\(253\) −264951. −0.260234
\(254\) 3.05029e6 2.96659
\(255\) 60576.3 + 44109.5i 0.0583381 + 0.0424797i
\(256\) −1.34840e6 −1.28594
\(257\) 303483.i 0.286617i 0.989678 + 0.143308i \(0.0457741\pi\)
−0.989678 + 0.143308i \(0.954226\pi\)
\(258\) 503762. 691824.i 0.471168 0.647063i
\(259\) 622090.i 0.576240i
\(260\) 483497. 0.443568
\(261\) 1.11757e6 360502.i 1.01549 0.327572i
\(262\) 1.47948e6 1.33155
\(263\) 531107.i 0.473470i −0.971574 0.236735i \(-0.923923\pi\)
0.971574 0.236735i \(-0.0760773\pi\)
\(264\) −1.93554e6 1.40939e6i −1.70920 1.24458i
\(265\) −81635.1 −0.0714105
\(266\) −131901. −0.114299
\(267\) 269482. + 196228.i 0.231341 + 0.168454i
\(268\) 2.76318e6i 2.35003i
\(269\) 1.65340e6 1.39315 0.696576 0.717483i \(-0.254706\pi\)
0.696576 + 0.717483i \(0.254706\pi\)
\(270\) 349433. + 114769.i 0.291713 + 0.0958106i
\(271\) 436144. 0.360751 0.180375 0.983598i \(-0.442269\pi\)
0.180375 + 0.983598i \(0.442269\pi\)
\(272\) 1.17938e6i 0.966565i
\(273\) 420461. 577426.i 0.341444 0.468910i
\(274\) 2.49402e6i 2.00689i
\(275\) −1.02628e6 −0.818339
\(276\) −748934. 545347.i −0.591794 0.430924i
\(277\) 546800. 0.428182 0.214091 0.976814i \(-0.431321\pi\)
0.214091 + 0.976814i \(0.431321\pi\)
\(278\) 4.50511e6 3.49618
\(279\) −1.15630e6 + 372993.i −0.889322 + 0.286874i
\(280\) 285587.i 0.217693i
\(281\) 1.70601e6i 1.28889i −0.764652 0.644443i \(-0.777089\pi\)
0.764652 0.644443i \(-0.222911\pi\)
\(282\) −664776. 484066.i −0.497797 0.362478i
\(283\) 1.13239e6i 0.840482i 0.907412 + 0.420241i \(0.138055\pi\)
−0.907412 + 0.420241i \(0.861945\pi\)
\(284\) 6.32923e6i 4.65645i
\(285\) −16231.0 + 22290.2i −0.0118367 + 0.0162556i
\(286\) 2.39281e6i 1.72979i
\(287\) 312919.i 0.224248i
\(288\) −691892. 2.14490e6i −0.491538 1.52379i
\(289\) 1.15566e6 0.813930
\(290\) 469208. 0.327620
\(291\) −1.39265e6 + 1.91255e6i −0.964073 + 1.32398i
\(292\) 1.19932e6i 0.823147i
\(293\) 745834.i 0.507543i −0.967264 0.253772i \(-0.918329\pi\)
0.967264 0.253772i \(-0.0816712\pi\)
\(294\) −1.60855e6 1.17129e6i −1.08534 0.790306i
\(295\) 70565.0 + 239898.i 0.0472100 + 0.160499i
\(296\) 4.21012e6i 2.79297i
\(297\) −399362. + 1.21593e6i −0.262709 + 0.799866i
\(298\) 2.02299e6 1.31964
\(299\) 534936.i 0.346038i
\(300\) −2.90097e6 2.11239e6i −1.86097 1.35510i
\(301\) 355203.i 0.225975i
\(302\) 2.66998e6i 1.68457i
\(303\) −284133. 206896.i −0.177793 0.129463i
\(304\) 433975. 0.269328
\(305\) −249003. −0.153269
\(306\) −1.23411e6 + 398095.i −0.753445 + 0.243043i
\(307\) 1.41643e6 0.857726 0.428863 0.903369i \(-0.358914\pi\)
0.428863 + 0.903369i \(0.358914\pi\)
\(308\) −1.72001e6 −1.03313
\(309\) 836580. 1.14889e6i 0.498438 0.684513i
\(310\) −485466. −0.286916
\(311\) 2.54619e6i 1.49276i −0.665521 0.746379i \(-0.731791\pi\)
0.665521 0.746379i \(-0.268209\pi\)
\(312\) −2.84556e6 + 3.90786e6i −1.65494 + 2.27275i
\(313\) 3.07369e6i 1.77337i −0.462375 0.886684i \(-0.653003\pi\)
0.462375 0.886684i \(-0.346997\pi\)
\(314\) 3.06025e6i 1.75159i
\(315\) 145284. 46865.1i 0.0824976 0.0266117i
\(316\) −1.52095e6 −0.856837
\(317\) 175287.i 0.0979719i 0.998799 + 0.0489860i \(0.0155990\pi\)
−0.998799 + 0.0489860i \(0.984401\pi\)
\(318\) 831572. 1.14201e6i 0.461139 0.633289i
\(319\) 1.63271e6i 0.898322i
\(320\) 213838.i 0.116737i
\(321\) 1.03078e6 1.41558e6i 0.558345 0.766784i
\(322\) −546884. −0.293938
\(323\) 97214.9i 0.0518474i
\(324\) −3.63162e6 + 2.61505e6i −1.92193 + 1.38394i
\(325\) 2.07206e6i 1.08816i
\(326\) −4.84507e6 −2.52497
\(327\) 939457. 1.29017e6i 0.485856 0.667234i
\(328\) 2.11775e6i 1.08690i
\(329\) −341315. −0.173847
\(330\) −301023. + 413399.i −0.152165 + 0.208971i
\(331\) −1.28354e6 −0.643929 −0.321965 0.946752i \(-0.604343\pi\)
−0.321965 + 0.946752i \(0.604343\pi\)
\(332\) 5.26608e6 2.62206
\(333\) 2.14177e6 690884.i 1.05843 0.341424i
\(334\) 5.01954e6i 2.46206i
\(335\) −340981. −0.166004
\(336\) −1.94227e6 1.41429e6i −0.938557 0.683424i
\(337\) 3.76381e6i 1.80532i −0.430358 0.902659i \(-0.641613\pi\)
0.430358 0.902659i \(-0.358387\pi\)
\(338\) 976298. 0.464826
\(339\) 1.06079e6 + 772433.i 0.501340 + 0.365058i
\(340\) −364312. −0.170913
\(341\) 1.68928e6i 0.786714i
\(342\) −146487. 454116.i −0.0677226 0.209943i
\(343\) −1.95484e6 −0.897173
\(344\) 2.40391e6i 1.09527i
\(345\) −67296.5 + 92419.4i −0.0304400 + 0.0418038i
\(346\) 4.38566e6 1.96945
\(347\) −3.62674e6 −1.61694 −0.808469 0.588539i \(-0.799703\pi\)
−0.808469 + 0.588539i \(0.799703\pi\)
\(348\) −3.36060e6 + 4.61517e6i −1.48754 + 2.04286i
\(349\) 1.91448e6i 0.841370i −0.907207 0.420685i \(-0.861790\pi\)
0.907207 0.420685i \(-0.138210\pi\)
\(350\) −2.11834e6 −0.924327
\(351\) 2.45496e6 + 806313.i 1.06360 + 0.349330i
\(352\) 3.13357e6 1.34798
\(353\) −1.73817e6 −0.742428 −0.371214 0.928547i \(-0.621058\pi\)
−0.371214 + 0.928547i \(0.621058\pi\)
\(354\) −4.07479e6 1.45656e6i −1.72821 0.617762i
\(355\) 781035. 0.328927
\(356\) −1.62069e6 −0.677760
\(357\) −316815. + 435087.i −0.131564 + 0.180678i
\(358\) −1.90592e6 −0.785955
\(359\) 2.34856e6i 0.961759i −0.876787 0.480880i \(-0.840317\pi\)
0.876787 0.480880i \(-0.159683\pi\)
\(360\) −983240. + 317169.i −0.399856 + 0.128984i
\(361\) −2.44033e6 −0.985553
\(362\) 4.69728e6 1.88397
\(363\) 590988. + 430337.i 0.235403 + 0.171412i
\(364\) 3.47270e6i 1.37377i
\(365\) 147997. 0.0581463
\(366\) 2.53645e6 3.48335e6i 0.989747 1.35923i
\(367\) 4.90872e6i 1.90240i 0.308567 + 0.951202i \(0.400150\pi\)
−0.308567 + 0.951202i \(0.599850\pi\)
\(368\) 1.79934e6 0.692619
\(369\) −1.07734e6 + 347524.i −0.411896 + 0.132867i
\(370\) 899213. 0.341475
\(371\) 586342.i 0.221165i
\(372\) 3.47705e6 4.77508e6i 1.30273 1.78906i
\(373\) 1.54029e6 0.573232 0.286616 0.958045i \(-0.407470\pi\)
0.286616 + 0.958045i \(0.407470\pi\)
\(374\) 1.80297e6i 0.666514i
\(375\) −528848. + 726276.i −0.194202 + 0.266700i
\(376\) 2.30992e6 0.842613
\(377\) 3.29644e6 1.19452
\(378\) −824322. + 2.50980e6i −0.296734 + 0.903460i
\(379\) −3.31374e6 −1.18501 −0.592503 0.805568i \(-0.701860\pi\)
−0.592503 + 0.805568i \(0.701860\pi\)
\(380\) 134056.i 0.0476241i
\(381\) 3.70240e6 + 2.69596e6i 1.30669 + 0.951482i
\(382\) 6.35556e6 2.22841
\(383\) 4.60560e6i 1.60431i 0.597113 + 0.802157i \(0.296314\pi\)
−0.597113 + 0.802157i \(0.703686\pi\)
\(384\) −748572. 545084.i −0.259063 0.188641i
\(385\) 212251.i 0.0729792i
\(386\) 5.66728e6 1.93600
\(387\) 1.22292e6 394483.i 0.415069 0.133891i
\(388\) 1.15023e7i 3.87886i
\(389\) 1.85129e6i 0.620298i 0.950688 + 0.310149i \(0.100379\pi\)
−0.950688 + 0.310149i \(0.899621\pi\)
\(390\) 834654. + 607765.i 0.277872 + 0.202337i
\(391\) 403071.i 0.133334i
\(392\) 5.58929e6 1.83714
\(393\) 1.79577e6 + 1.30762e6i 0.586503 + 0.427071i
\(394\) 8.18701e6i 2.65696i
\(395\) 187688.i 0.0605261i
\(396\) −1.91022e6 5.92177e6i −0.612132 1.89764i
\(397\) 4.77548e6i 1.52069i −0.649520 0.760345i \(-0.725030\pi\)
0.649520 0.760345i \(-0.274970\pi\)
\(398\) 3.17218e6 1.00381
\(399\) −160099. 116578.i −0.0503450 0.0366594i
\(400\) 6.96970e6 2.17803
\(401\) −2.40174e6 −0.745872 −0.372936 0.927857i \(-0.621649\pi\)
−0.372936 + 0.927857i \(0.621649\pi\)
\(402\) 3.47338e6 4.77005e6i 1.07198 1.47217i
\(403\) −3.41067e6 −1.04611
\(404\) 1.70881e6 0.520882
\(405\) 322701. + 448146.i 0.0977602 + 0.135763i
\(406\) 3.37007e6i 1.01467i
\(407\) 3.12901e6i 0.936312i
\(408\) 2.14411e6 2.94455e6i 0.637672 0.875726i
\(409\) 4.44463e6i 1.31379i 0.753980 + 0.656897i \(0.228131\pi\)
−0.753980 + 0.656897i \(0.771869\pi\)
\(410\) −452316. −0.132887
\(411\) 2.20431e6 3.02721e6i 0.643676 0.883971i
\(412\) 6.90953e6i 2.00542i
\(413\) −1.72306e6 + 506831.i −0.497080 + 0.146214i
\(414\) −607361. 1.88285e6i −0.174159 0.539902i
\(415\) 649841.i 0.185220i
\(416\) 6.32669e6i 1.79243i
\(417\) 5.46824e6 + 3.98178e6i 1.53995 + 1.12134i
\(418\) 663438. 0.185720
\(419\) −4.40819e6 −1.22666 −0.613331 0.789826i \(-0.710171\pi\)
−0.613331 + 0.789826i \(0.710171\pi\)
\(420\) −436876. + 599969.i −0.120847 + 0.165961i
\(421\) 1.52637e6i 0.419715i −0.977732 0.209857i \(-0.932700\pi\)
0.977732 0.209857i \(-0.0673000\pi\)
\(422\) 4.22521e6i 1.15496i
\(423\) −379060. 1.17510e6i −0.103005 0.319320i
\(424\) 3.96819e6i 1.07196i
\(425\) 1.56128e6i 0.419285i
\(426\) −7.95597e6 + 1.09261e7i −2.12407 + 2.91702i
\(427\) 1.78846e6i 0.474688i
\(428\) 8.51347e6i 2.24645i
\(429\) −2.11485e6 + 2.90436e6i −0.554800 + 0.761916i
\(430\) 513436. 0.133911
\(431\) −311908. −0.0808785 −0.0404393 0.999182i \(-0.512876\pi\)
−0.0404393 + 0.999182i \(0.512876\pi\)
\(432\) 2.71216e6 8.25766e6i 0.699208 2.12886i
\(433\) −6.61265e6 −1.69494 −0.847472 0.530840i \(-0.821877\pi\)
−0.847472 + 0.530840i \(0.821877\pi\)
\(434\) 3.48685e6i 0.888605i
\(435\) 569518. + 414703.i 0.144306 + 0.105078i
\(436\) 7.75923e6i 1.95480i
\(437\) 148318. 0.0371527
\(438\) −1.50757e6 + 2.07037e6i −0.375484 + 0.515658i
\(439\) −3.66105e6 −0.906659 −0.453329 0.891343i \(-0.649764\pi\)
−0.453329 + 0.891343i \(0.649764\pi\)
\(440\) 1.43646e6i 0.353721i
\(441\) −917205. 2.84338e6i −0.224580 0.696208i
\(442\) −3.64020e6 −0.886276
\(443\) −1.92663e6 −0.466433 −0.233217 0.972425i \(-0.574925\pi\)
−0.233217 + 0.972425i \(0.574925\pi\)
\(444\) −6.44042e6 + 8.84473e6i −1.55045 + 2.12925i
\(445\) 199996.i 0.0478763i
\(446\) 2.43344e6 0.579272
\(447\) 2.45548e6 + 1.78799e6i 0.581256 + 0.423250i
\(448\) 1.53589e6 0.361547
\(449\) 6.86780e6i 1.60769i 0.594841 + 0.803844i \(0.297215\pi\)
−0.594841 + 0.803844i \(0.702785\pi\)
\(450\) −2.35260e6 7.29317e6i −0.547667 1.69779i
\(451\) 1.57393e6i 0.364372i
\(452\) −6.37973e6 −1.46878
\(453\) 2.35982e6 3.24078e6i 0.540298 0.742000i
\(454\) 1.15708e7 2.63465
\(455\) 428536. 0.0970418
\(456\) 1.08350e6 + 788969.i 0.244016 + 0.177684i
\(457\) 925489.i 0.207291i −0.994614 0.103646i \(-0.966949\pi\)
0.994614 0.103646i \(-0.0330508\pi\)
\(458\) 2.65222e6i 0.590808i
\(459\) −1.84980e6 607552.i −0.409820 0.134602i
\(460\) 555820.i 0.122473i
\(461\) 6.86778e6i 1.50510i −0.658537 0.752548i \(-0.728825\pi\)
0.658537 0.752548i \(-0.271175\pi\)
\(462\) −2.96923e6 2.16209e6i −0.647201 0.471269i
\(463\) 2.05018e6i 0.444467i 0.974993 + 0.222233i \(0.0713347\pi\)
−0.974993 + 0.222233i \(0.928665\pi\)
\(464\) 1.10881e7i 2.39091i
\(465\) −589252. 429072.i −0.126377 0.0920234i
\(466\) −8.13228e6 −1.73479
\(467\) 7.22686e6 1.53341 0.766704 0.642001i \(-0.221896\pi\)
0.766704 + 0.642001i \(0.221896\pi\)
\(468\) −1.19561e7 + 3.85673e6i −2.52333 + 0.813963i
\(469\) 2.44908e6i 0.514128i
\(470\) 493362.i 0.103020i
\(471\) −2.70475e6 + 3.71448e6i −0.561792 + 0.771517i
\(472\) 1.16612e7 3.43009e6i 2.40929 0.708680i
\(473\) 1.78661e6i 0.367179i
\(474\) −2.62560e6 1.91187e6i −0.536763 0.390852i
\(475\) 574505. 0.116831
\(476\) 2.61666e6i 0.529334i
\(477\) 2.01870e6 651183.i 0.406233 0.131041i
\(478\) 1.04941e7i 2.10076i
\(479\) 2.56610e6i 0.511017i 0.966807 + 0.255508i \(0.0822429\pi\)
−0.966807 + 0.255508i \(0.917757\pi\)
\(480\) 795916. 1.09304e6i 0.157676 0.216538i
\(481\) 6.31747e6 1.24503
\(482\) 3.68093e6 0.721672
\(483\) −663800. 483356.i −0.129470 0.0942755i
\(484\) −3.55426e6 −0.689662
\(485\) −1.41940e6 −0.273999
\(486\) −9.55638e6 50691.7i −1.83528 0.00973524i
\(487\) −7.24144e6 −1.38357 −0.691787 0.722101i \(-0.743177\pi\)
−0.691787 + 0.722101i \(0.743177\pi\)
\(488\) 1.21038e7i 2.30076i
\(489\) −5.88088e6 4.28225e6i −1.11217 0.809841i
\(490\) 1.19378e6i 0.224613i
\(491\) 3.59515e6i 0.672997i −0.941684 0.336498i \(-0.890757\pi\)
0.941684 0.336498i \(-0.109243\pi\)
\(492\) 3.23962e6 4.44902e6i 0.603366 0.828613i
\(493\) −2.48385e6 −0.460265
\(494\) 1.33948e6i 0.246956i
\(495\) −730754. + 235723.i −0.134047 + 0.0432404i
\(496\) 1.14723e7i 2.09386i
\(497\) 5.60976e6i 1.01872i
\(498\) 9.09076e6 + 6.61957e6i 1.64258 + 1.19607i
\(499\) 2.28721e6 0.411202 0.205601 0.978636i \(-0.434085\pi\)
0.205601 + 0.978636i \(0.434085\pi\)
\(500\) 4.36790e6i 0.781353i
\(501\) −4.43645e6 + 6.09265e6i −0.789662 + 1.08446i
\(502\) 1.07566e7i 1.90509i
\(503\) −7.76929e6 −1.36918 −0.684591 0.728927i \(-0.740019\pi\)
−0.684591 + 0.728927i \(0.740019\pi\)
\(504\) −2.27806e6 7.06210e6i −0.399474 1.23839i
\(505\) 210869.i 0.0367946i
\(506\) 2.75074e6 0.477609
\(507\) 1.18502e6 + 862887.i 0.204741 + 0.149085i
\(508\) −2.22666e7 −3.82821
\(509\) 1.00260e7 1.71527 0.857635 0.514259i \(-0.171933\pi\)
0.857635 + 0.514259i \(0.171933\pi\)
\(510\) −628907. 457948.i −0.107068 0.0779634i
\(511\) 1.06299e6i 0.180084i
\(512\) 1.20983e7 2.03962
\(513\) 223561. 680670.i 0.0375061 0.114194i
\(514\) 3.15078e6i 0.526030i
\(515\) 852645. 0.141661
\(516\) −3.67738e6 + 5.05020e6i −0.608015 + 0.834996i
\(517\) 1.71676e6 0.282477
\(518\) 6.45858e6i 1.05758i
\(519\) 5.32325e6 + 3.87620e6i 0.867478 + 0.631667i
\(520\) −2.90021e6 −0.470350
\(521\) 9.90696e6i 1.59899i 0.600672 + 0.799496i \(0.294900\pi\)
−0.600672 + 0.799496i \(0.705100\pi\)
\(522\) −1.16027e7 + 3.74275e6i −1.86373 + 0.601194i
\(523\) −418873. −0.0669619 −0.0334810 0.999439i \(-0.510659\pi\)
−0.0334810 + 0.999439i \(0.510659\pi\)
\(524\) −1.08000e7 −1.71828
\(525\) −2.57121e6 1.87226e6i −0.407136 0.296462i
\(526\) 5.51399e6i 0.868963i
\(527\) 2.56992e6 0.403081
\(528\) 9.76927e6 + 7.11364e6i 1.52503 + 1.11047i
\(529\) −5.82139e6 −0.904456
\(530\) 847541. 0.131060
\(531\) −3.65856e6 5.36940e6i −0.563085 0.826399i
\(532\) 962852. 0.147496
\(533\) −3.17777e6 −0.484512
\(534\) −2.79778e6 2.03725e6i −0.424581 0.309165i
\(535\) 1.05057e6 0.158687
\(536\) 1.65747e7i 2.49192i
\(537\) −2.31338e6 1.68452e6i −0.346187 0.252081i
\(538\) −1.71658e7 −2.55686
\(539\) 4.15402e6 0.615880
\(540\) −2.55080e6 837791.i −0.376437 0.123638i
\(541\) 1.21275e7i 1.78147i −0.454518 0.890737i \(-0.650189\pi\)
0.454518 0.890737i \(-0.349811\pi\)
\(542\) −4.52808e6 −0.662088
\(543\) 5.70148e6 + 4.15162e6i 0.829829 + 0.604252i
\(544\) 4.76712e6i 0.690652i
\(545\) 957499. 0.138085
\(546\) −4.36526e6 + 5.99488e6i −0.626655 + 0.860595i
\(547\) −2.13534e6 −0.305139 −0.152570 0.988293i \(-0.548755\pi\)
−0.152570 + 0.988293i \(0.548755\pi\)
\(548\) 1.82059e7i 2.58977i
\(549\) 6.15742e6 1.98623e6i 0.871902 0.281254i
\(550\) 1.06549e7 1.50190
\(551\) 913982.i 0.128250i
\(552\) 4.49241e6 + 3.27121e6i 0.627525 + 0.456942i
\(553\) −1.34806e6 −0.187455
\(554\) −5.67691e6 −0.785846
\(555\) 1.09145e6 + 794757.i 0.150408 + 0.109522i
\(556\) −3.28865e7 −4.51161
\(557\) 2.87203e6i 0.392240i −0.980580 0.196120i \(-0.937166\pi\)
0.980580 0.196120i \(-0.0628342\pi\)
\(558\) 1.20048e7 3.87244e6i 1.63218 0.526501i
\(559\) 3.60717e6 0.488244
\(560\) 1.44145e6i 0.194236i
\(561\) 1.59353e6 2.18842e6i 0.213773 0.293578i
\(562\) 1.77119e7i 2.36550i
\(563\) −8.75269e6 −1.16378 −0.581890 0.813268i \(-0.697686\pi\)
−0.581890 + 0.813268i \(0.697686\pi\)
\(564\) 4.85275e6 + 3.53360e6i 0.642377 + 0.467756i
\(565\) 787267.i 0.103753i
\(566\) 1.17565e7i 1.54254i
\(567\) −3.21880e6 + 2.31779e6i −0.420471 + 0.302772i
\(568\) 3.79653e7i 4.93760i
\(569\) 3.22905e6 0.418114 0.209057 0.977904i \(-0.432961\pi\)
0.209057 + 0.977904i \(0.432961\pi\)
\(570\) 168511. 231419.i 0.0217241 0.0298340i
\(571\) 9.79432e6i 1.25714i −0.777752 0.628571i \(-0.783640\pi\)
0.777752 0.628571i \(-0.216360\pi\)
\(572\) 1.74671e7i 2.23219i
\(573\) 7.71428e6 + 5.61727e6i 0.981542 + 0.714724i
\(574\) 3.24875e6i 0.411563i
\(575\) 2.38200e6 0.300450
\(576\) 1.70573e6 + 5.28786e6i 0.214218 + 0.664085i
\(577\) 2.28516e6 0.285744 0.142872 0.989741i \(-0.454366\pi\)
0.142872 + 0.989741i \(0.454366\pi\)
\(578\) −1.19982e7 −1.49381
\(579\) 6.87886e6 + 5.00894e6i 0.852747 + 0.620940i
\(580\) −3.42514e6 −0.422774
\(581\) 4.66747e6 0.573642
\(582\) 1.44586e7 1.98562e7i 1.76937 2.42990i
\(583\) 2.94920e6i 0.359363i
\(584\) 7.19400e6i 0.872847i
\(585\) 475926. + 1.47539e6i 0.0574976 + 0.178245i
\(586\) 7.74330e6i 0.931498i
\(587\) −5.57604e6 −0.667929 −0.333965 0.942586i \(-0.608387\pi\)
−0.333965 + 0.942586i \(0.608387\pi\)
\(588\) 1.17421e7 + 8.55020e6i 1.40056 + 1.01984i
\(589\) 945652.i 0.112316i
\(590\) −732610. 2.49064e6i −0.0866449 0.294565i
\(591\) 7.23597e6 9.93728e6i 0.852174 1.17030i
\(592\) 2.12498e7i 2.49202i
\(593\) 1.15688e7i 1.35099i −0.737363 0.675496i \(-0.763929\pi\)
0.737363 0.675496i \(-0.236071\pi\)
\(594\) 4.14620e6 1.26239e7i 0.482153 1.46800i
\(595\) −322899. −0.0373917
\(596\) −1.47675e7 −1.70291
\(597\) 3.85035e6 + 2.80369e6i 0.442144 + 0.321954i
\(598\) 5.55374e6i 0.635086i
\(599\) 8.72307e6i 0.993350i −0.867937 0.496675i \(-0.834554\pi\)
0.867937 0.496675i \(-0.165446\pi\)
\(600\) 1.74012e7 + 1.26709e7i 1.97334 + 1.43691i
\(601\) 1.67437e7i 1.89089i 0.325788 + 0.945443i \(0.394370\pi\)
−0.325788 + 0.945443i \(0.605630\pi\)
\(602\) 3.68774e6i 0.414734i
\(603\) 8.43188e6 2.71992e6i 0.944345 0.304623i
\(604\) 1.94904e7i 2.17384i
\(605\) 438601.i 0.0487171i
\(606\) 2.94989e6 + 2.14800e6i 0.326305 + 0.237604i
\(607\) 4.23190e6 0.466191 0.233096 0.972454i \(-0.425114\pi\)
0.233096 + 0.972454i \(0.425114\pi\)
\(608\) −1.75416e6 −0.192446
\(609\) −2.97859e6 + 4.09054e6i −0.325437 + 0.446928i
\(610\) 2.58516e6 0.281296
\(611\) 3.46614e6i 0.375615i
\(612\) 9.00882e6 2.90603e6i 0.972276 0.313632i
\(613\) 7.26766e6i 0.781166i 0.920568 + 0.390583i \(0.127727\pi\)
−0.920568 + 0.390583i \(0.872273\pi\)
\(614\) −1.47055e7 −1.57419
\(615\) −549015. 399773.i −0.0585324 0.0426212i
\(616\) 1.03173e7 1.09551
\(617\) 1.38840e7i 1.46826i −0.679009 0.734130i \(-0.737590\pi\)
0.679009 0.734130i \(-0.262410\pi\)
\(618\) −8.68543e6 + 1.19278e7i −0.914787 + 1.25629i
\(619\) −5.18447e6 −0.543849 −0.271924 0.962319i \(-0.587660\pi\)
−0.271924 + 0.962319i \(0.587660\pi\)
\(620\) 3.54382e6 0.370248
\(621\) 926924. 2.82218e6i 0.0964528 0.293668i
\(622\) 2.64347e7i 2.73967i
\(623\) −1.43646e6 −0.148277
\(624\) 1.43624e7 1.97242e7i 1.47661 2.02786i
\(625\) 8.95329e6 0.916817
\(626\) 3.19112e7i 3.25468i
\(627\) 805271. + 586370.i 0.0818037 + 0.0595666i
\(628\) 2.23393e7i 2.26032i
\(629\) −4.76018e6 −0.479729
\(630\) −1.50835e6 + 486556.i −0.151408 + 0.0488407i
\(631\) 1.48363e7 1.48338 0.741689 0.670744i \(-0.234025\pi\)
0.741689 + 0.670744i \(0.234025\pi\)
\(632\) 9.12329e6 0.908571
\(633\) 3.73439e6 5.12850e6i 0.370434 0.508723i
\(634\) 1.81984e6i 0.179809i
\(635\) 2.74773e6i 0.270421i
\(636\) −6.07033e6 + 8.33648e6i −0.595072 + 0.817222i
\(637\) 8.38696e6i 0.818948i
\(638\) 1.69509e7i 1.64870i
\(639\) −1.93137e7 + 6.23012e6i −1.87117 + 0.603593i
\(640\) 555552.i 0.0536135i
\(641\) 6.98516e6i 0.671478i −0.941955 0.335739i \(-0.891014\pi\)
0.941955 0.335739i \(-0.108986\pi\)
\(642\) −1.07016e7 + 1.46967e7i −1.02473 + 1.40728i
\(643\) 9.85148e6 0.939667 0.469834 0.882755i \(-0.344314\pi\)
0.469834 + 0.882755i \(0.344314\pi\)
\(644\) 3.99216e6 0.379309
\(645\) 623201. + 453793.i 0.0589833 + 0.0429496i
\(646\) 1.00929e6i 0.0951558i
\(647\) 782301.i 0.0734705i 0.999325 + 0.0367353i \(0.0116958\pi\)
−0.999325 + 0.0367353i \(0.988304\pi\)
\(648\) 2.17839e7 1.56861e7i 2.03797 1.46750i
\(649\) 8.66672e6 2.54927e6i 0.807687 0.237577i
\(650\) 2.15122e7i 1.99711i
\(651\) 3.08180e6 4.23228e6i 0.285005 0.391401i
\(652\) 3.53682e7 3.25832
\(653\) 1.18437e6i 0.108694i −0.998522 0.0543468i \(-0.982692\pi\)
0.998522 0.0543468i \(-0.0173077\pi\)
\(654\) −9.75351e6 + 1.33946e7i −0.891695 + 1.22458i
\(655\) 1.33273e6i 0.121378i
\(656\) 1.06889e7i 0.969784i
\(657\) −3.65973e6 + 1.18054e6i −0.330777 + 0.106701i
\(658\) 3.54356e6 0.319062
\(659\) −5.36643e6 −0.481362 −0.240681 0.970604i \(-0.577371\pi\)
−0.240681 + 0.970604i \(0.577371\pi\)
\(660\) 2.19742e6 3.01775e6i 0.196360 0.269664i
\(661\) 1.31364e6 0.116943 0.0584715 0.998289i \(-0.481377\pi\)
0.0584715 + 0.998289i \(0.481377\pi\)
\(662\) 1.33258e7 1.18181
\(663\) −4.41842e6 3.21733e6i −0.390376 0.284258i
\(664\) −3.15881e7 −2.78037
\(665\) 118817.i 0.0104190i
\(666\) −2.22360e7 + 7.17280e6i −1.94255 + 0.626618i
\(667\) 3.78954e6i 0.329816i
\(668\) 3.66418e7i 3.17714i
\(669\) 2.95367e6 + 2.15076e6i 0.255151 + 0.185792i
\(670\) 3.54008e6 0.304668
\(671\) 8.99563e6i 0.771303i
\(672\) 7.85076e6 + 5.71665e6i 0.670639 + 0.488335i
\(673\) 997261.i 0.0848733i −0.999099 0.0424367i \(-0.986488\pi\)
0.999099 0.0424367i \(-0.0135121\pi\)
\(674\) 3.90762e7i 3.31331i
\(675\) 3.59041e6 1.09316e7i 0.303309 0.923477i
\(676\) −7.12681e6 −0.599830
\(677\) 1.00182e7i 0.840071i 0.907508 + 0.420036i \(0.137982\pi\)
−0.907508 + 0.420036i \(0.862018\pi\)
\(678\) −1.10132e7 8.01945e6i −0.920112 0.669993i
\(679\) 1.01948e7i 0.848600i
\(680\) 2.18529e6 0.181233
\(681\) 1.40444e7 + 1.02267e7i 1.16048 + 0.845018i
\(682\) 1.75383e7i 1.44386i
\(683\) −1.44372e6 −0.118421 −0.0592107 0.998246i \(-0.518858\pi\)
−0.0592107 + 0.998246i \(0.518858\pi\)
\(684\) 1.06933e6 + 3.31497e6i 0.0873919 + 0.270919i
\(685\) 2.24664e6 0.182939
\(686\) 2.02953e7 1.64659
\(687\) 2.34413e6 3.21923e6i 0.189492 0.260232i
\(688\) 1.21333e7i 0.977255i
\(689\) 5.95444e6 0.477851
\(690\) 698677. 959504.i 0.0558668 0.0767228i
\(691\) 8.99999e6i 0.717046i −0.933521 0.358523i \(-0.883280\pi\)
0.933521 0.358523i \(-0.116720\pi\)
\(692\) −3.20146e7 −2.54146
\(693\) −1.69308e6 5.24862e6i −0.133919 0.415157i
\(694\) 3.76531e7 2.96758
\(695\) 4.05824e6i 0.318696i
\(696\) 2.01582e7 2.76836e7i 1.57736 2.16621i
\(697\) 2.39443e6 0.186690
\(698\) 1.98762e7i 1.54417i
\(699\) −9.87085e6 7.18760e6i −0.764120 0.556405i
\(700\) 1.54635e7 1.19279
\(701\) 1.53156e7 1.17717 0.588584 0.808436i \(-0.299686\pi\)
0.588584 + 0.808436i \(0.299686\pi\)
\(702\) −2.54876e7 8.37119e6i −1.95203 0.641128i
\(703\) 1.75160e6i 0.133674i
\(704\) −7.72525e6 −0.587464
\(705\) 436051. 598836.i 0.0330419 0.0453769i
\(706\) 1.80458e7 1.36258
\(707\) 1.51456e6 0.113956
\(708\) 2.97453e7 + 1.06327e7i 2.23016 + 0.797185i
\(709\) 2.03520e7 1.52051 0.760257 0.649622i \(-0.225073\pi\)
0.760257 + 0.649622i \(0.225073\pi\)
\(710\) −8.10876e6 −0.603682
\(711\) −1.49714e6 4.64120e6i −0.111068 0.344315i
\(712\) 9.72158e6 0.718682
\(713\) 3.92085e6i 0.288839i
\(714\) 3.28920e6 4.51711e6i 0.241460 0.331600i
\(715\) −2.15546e6 −0.157680
\(716\) 1.39129e7 1.01423
\(717\) −9.27507e6 + 1.27376e7i −0.673782 + 0.925315i
\(718\) 2.43830e7i 1.76512i
\(719\) −1.83467e7 −1.32353 −0.661767 0.749710i \(-0.730193\pi\)
−0.661767 + 0.749710i \(0.730193\pi\)
\(720\) 4.96272e6 1.60085e6i 0.356770 0.115085i
\(721\) 6.12410e6i 0.438737i
\(722\) 2.53356e7 1.80879
\(723\) 4.46786e6 + 3.25333e6i 0.317873 + 0.231464i
\(724\) −3.42893e7 −2.43115
\(725\) 1.46787e7i 1.03715i
\(726\) −6.13568e6 4.46778e6i −0.432037 0.314594i
\(727\) 2.11091e7 1.48127 0.740636 0.671907i \(-0.234524\pi\)
0.740636 + 0.671907i \(0.234524\pi\)
\(728\) 2.08307e7i 1.45672i
\(729\) −1.15546e7 8.50780e6i −0.805259 0.592923i
\(730\) −1.53652e6 −0.106716
\(731\) −2.71798e6 −0.188128
\(732\) −1.85157e7 + 2.54279e7i −1.27721 + 1.75401i
\(733\) −1.29047e7 −0.887132 −0.443566 0.896242i \(-0.646287\pi\)
−0.443566 + 0.896242i \(0.646287\pi\)
\(734\) 5.09626e7i 3.49150i
\(735\) 1.05511e6 1.44899e6i 0.0720406 0.0989345i
\(736\) −7.27305e6 −0.494906
\(737\) 1.23185e7i 0.835388i
\(738\) 1.11850e7 3.60801e6i 0.755955 0.243853i
\(739\) 6.93935e6i 0.467420i 0.972306 + 0.233710i \(0.0750867\pi\)
−0.972306 + 0.233710i \(0.924913\pi\)
\(740\) −6.56411e6 −0.440653
\(741\) 1.18388e6 1.62584e6i 0.0792068 0.108776i
\(742\) 6.08744e6i 0.405906i
\(743\) 4.29355e6i 0.285328i 0.989771 + 0.142664i \(0.0455668\pi\)
−0.989771 + 0.142664i \(0.954433\pi\)
\(744\) −2.08567e7 + 2.86429e7i −1.38138 + 1.89707i
\(745\) 1.82233e6i 0.120292i
\(746\) −1.59914e7 −1.05206
\(747\) 5.18362e6 + 1.60695e7i 0.339885 + 1.05366i
\(748\) 1.31614e7i 0.860096i
\(749\) 7.54571e6i 0.491468i
\(750\) 5.49054e6 7.54024e6i 0.356420 0.489477i
\(751\) 1.38957e6i 0.0899045i −0.998989 0.0449522i \(-0.985686\pi\)
0.998989 0.0449522i \(-0.0143136\pi\)
\(752\) −1.16589e7 −0.751820
\(753\) 9.50705e6 1.30562e7i 0.611024 0.839129i
\(754\) −3.42239e7 −2.19231
\(755\) 2.40514e6 0.153558
\(756\) 6.01741e6 1.83211e7i 0.382918 1.16586i
\(757\) 3.31380e6 0.210178 0.105089 0.994463i \(-0.466487\pi\)
0.105089 + 0.994463i \(0.466487\pi\)
\(758\) 3.44035e7 2.17485
\(759\) 3.33880e6 + 2.43120e6i 0.210371 + 0.153185i
\(760\) 804120.i 0.0504995i
\(761\) 2.79825e6i 0.175156i 0.996158 + 0.0875779i \(0.0279127\pi\)
−0.996158 + 0.0875779i \(0.972087\pi\)
\(762\) −3.84386e7 2.79896e7i −2.39817 1.74626i
\(763\) 6.87721e6i 0.427662i
\(764\) −4.63945e7 −2.87563
\(765\) −358607. 1.11170e6i −0.0221547 0.0686806i
\(766\) 4.78157e7i 2.94441i
\(767\) −5.14699e6 1.74981e7i −0.315911 1.07400i
\(768\) 1.69920e7 + 1.23730e7i 1.03954 + 0.756957i
\(769\) 1.98174e7i 1.20846i 0.796811 + 0.604229i \(0.206519\pi\)
−0.796811 + 0.604229i \(0.793481\pi\)
\(770\) 2.20361e6i 0.133939i
\(771\) 2.78477e6 3.82437e6i 0.168715 0.231699i
\(772\) −4.13702e7 −2.49830
\(773\) −1.17719e7 −0.708594 −0.354297 0.935133i \(-0.615280\pi\)
−0.354297 + 0.935133i \(0.615280\pi\)
\(774\) −1.26964e7 + 4.09555e6i −0.761779 + 0.245731i
\(775\) 1.51873e7i 0.908293i
\(776\) 6.89953e7i 4.11306i
\(777\) −5.70832e6 + 7.83932e6i −0.339200 + 0.465828i
\(778\) 1.92202e7i 1.13844i
\(779\) 881078.i 0.0520201i