Properties

Label 177.6.d.b.176.16
Level $177$
Weight $6$
Character 177.176
Analytic conductor $28.388$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 176.16
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.15

$q$-expansion

\(f(q)\) \(=\) \(q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +O(q^{10})\) \(q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +134.964i q^{10} +350.338 q^{11} +(-193.691 - 631.305i) q^{12} -274.449i q^{13} +829.473 q^{14} +(-233.245 + 71.5620i) q^{15} -585.071 q^{16} -852.484i q^{17} +(1734.90 - 1175.20i) q^{18} +764.487 q^{19} -663.003i q^{20} +(439.811 + 1433.50i) q^{21} -3021.07 q^{22} +4626.49 q^{23} +(408.540 + 1331.57i) q^{24} +2880.04 q^{25} +2366.66i q^{26} +(2950.87 + 2375.14i) q^{27} -4074.74 q^{28} +4306.70i q^{29} +(2011.35 - 617.101i) q^{30} +2771.04i q^{31} +7904.47 q^{32} +(-1601.86 - 5221.02i) q^{33} +7351.23i q^{34} +1505.47i q^{35} +(-8522.61 + 5773.08i) q^{36} +7396.72i q^{37} -6592.41 q^{38} +(-4090.07 + 1254.87i) q^{39} +1398.43i q^{40} -20713.2i q^{41} +(-3792.63 - 12361.5i) q^{42} -14509.4i q^{43} +14840.8 q^{44} +(2132.95 + 3148.80i) q^{45} -39895.7 q^{46} +9944.21 q^{47} +(2675.14 + 8719.21i) q^{48} -7554.55 q^{49} -24835.5 q^{50} +(-12704.4 + 3897.84i) q^{51} -11626.1i q^{52} -18864.2i q^{53} +(-25446.3 - 20481.5i) q^{54} -5483.17i q^{55} +8594.58 q^{56} +(-3495.49 - 11393.0i) q^{57} -37138.0i q^{58} +(15029.3 + 22114.4i) q^{59} +(-9880.62 + 3031.47i) q^{60} -2330.64i q^{61} -23895.6i q^{62} +(19352.2 - 13108.8i) q^{63} -49440.4 q^{64} -4295.43 q^{65} +(13813.4 + 45022.5i) q^{66} +4248.82i q^{67} -36112.5i q^{68} +(-21153.9 - 68947.7i) q^{69} -12982.2i q^{70} -69744.9i q^{71} +(17976.2 - 12176.8i) q^{72} +44809.4i q^{73} -63784.2i q^{74} +(-13168.5 - 42920.7i) q^{75} +32384.8 q^{76} -33698.9 q^{77} +(35269.9 - 10821.2i) q^{78} -43275.7 q^{79} +9157.00i q^{80} +(21903.9 - 54836.2i) q^{81} +178616. i q^{82} -109985. q^{83} +(18631.1 + 60725.0i) q^{84} -13342.3 q^{85} +125119. i q^{86} +(64181.9 - 19691.7i) q^{87} -31302.8 q^{88} -83865.6 q^{89} +(-18393.1 - 27153.1i) q^{90} +26399.2i q^{91} +195985. q^{92} +(41296.3 - 12670.1i) q^{93} -85752.0 q^{94} -11965.0i q^{95} +(-36141.8 - 117799. i) q^{96} +27574.0i q^{97} +65145.3 q^{98} +(-70483.6 + 47744.5i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.62331 −1.52440 −0.762200 0.647341i \(-0.775881\pi\)
−0.762200 + 0.647341i \(0.775881\pi\)
\(3\) −4.57233 14.9028i −0.293315 0.956016i
\(4\) 42.3615 1.32380
\(5\) 15.6511i 0.279975i −0.990153 0.139988i \(-0.955294\pi\)
0.990153 0.139988i \(-0.0447063\pi\)
\(6\) 39.4286 + 128.512i 0.447130 + 1.45735i
\(7\) −96.1896 −0.741965 −0.370982 0.928640i \(-0.620979\pi\)
−0.370982 + 0.928640i \(0.620979\pi\)
\(8\) −89.3504 −0.493596
\(9\) −201.188 + 136.281i −0.827932 + 0.560828i
\(10\) 134.964i 0.426794i
\(11\) 350.338 0.872982 0.436491 0.899709i \(-0.356221\pi\)
0.436491 + 0.899709i \(0.356221\pi\)
\(12\) −193.691 631.305i −0.388290 1.26557i
\(13\) 274.449i 0.450406i −0.974312 0.225203i \(-0.927696\pi\)
0.974312 0.225203i \(-0.0723045\pi\)
\(14\) 829.473 1.13105
\(15\) −233.245 + 71.5620i −0.267661 + 0.0821210i
\(16\) −585.071 −0.571359
\(17\) 852.484i 0.715424i −0.933832 0.357712i \(-0.883557\pi\)
0.933832 0.357712i \(-0.116443\pi\)
\(18\) 1734.90 1175.20i 1.26210 0.854926i
\(19\) 764.487 0.485832 0.242916 0.970047i \(-0.421896\pi\)
0.242916 + 0.970047i \(0.421896\pi\)
\(20\) 663.003i 0.370630i
\(21\) 439.811 + 1433.50i 0.217630 + 0.709330i
\(22\) −3021.07 −1.33077
\(23\) 4626.49 1.82361 0.911805 0.410623i \(-0.134689\pi\)
0.911805 + 0.410623i \(0.134689\pi\)
\(24\) 408.540 + 1331.57i 0.144779 + 0.471886i
\(25\) 2880.04 0.921614
\(26\) 2366.66i 0.686599i
\(27\) 2950.87 + 2375.14i 0.779006 + 0.627017i
\(28\) −4074.74 −0.982210
\(29\) 4306.70i 0.950932i 0.879734 + 0.475466i \(0.157720\pi\)
−0.879734 + 0.475466i \(0.842280\pi\)
\(30\) 2011.35 617.101i 0.408022 0.125185i
\(31\) 2771.04i 0.517892i 0.965892 + 0.258946i \(0.0833751\pi\)
−0.965892 + 0.258946i \(0.916625\pi\)
\(32\) 7904.47 1.36458
\(33\) −1601.86 5221.02i −0.256059 0.834585i
\(34\) 7351.23i 1.09059i
\(35\) 1505.47i 0.207732i
\(36\) −8522.61 + 5773.08i −1.09601 + 0.742422i
\(37\) 7396.72i 0.888249i 0.895965 + 0.444124i \(0.146485\pi\)
−0.895965 + 0.444124i \(0.853515\pi\)
\(38\) −6592.41 −0.740602
\(39\) −4090.07 + 1254.87i −0.430595 + 0.132111i
\(40\) 1398.43i 0.138195i
\(41\) 20713.2i 1.92436i −0.272410 0.962181i \(-0.587821\pi\)
0.272410 0.962181i \(-0.412179\pi\)
\(42\) −3792.63 12361.5i −0.331755 1.08130i
\(43\) 14509.4i 1.19668i −0.801241 0.598342i \(-0.795826\pi\)
0.801241 0.598342i \(-0.204174\pi\)
\(44\) 14840.8 1.15565
\(45\) 2132.95 + 3148.80i 0.157018 + 0.231800i
\(46\) −39895.7 −2.77991
\(47\) 9944.21 0.656637 0.328319 0.944567i \(-0.393518\pi\)
0.328319 + 0.944567i \(0.393518\pi\)
\(48\) 2675.14 + 8719.21i 0.167588 + 0.546228i
\(49\) −7554.55 −0.449489
\(50\) −24835.5 −1.40491
\(51\) −12704.4 + 3897.84i −0.683957 + 0.209845i
\(52\) 11626.1i 0.596246i
\(53\) 18864.2i 0.922461i −0.887280 0.461231i \(-0.847408\pi\)
0.887280 0.461231i \(-0.152592\pi\)
\(54\) −25446.3 20481.5i −1.18752 0.955825i
\(55\) 5483.17i 0.244413i
\(56\) 8594.58 0.366231
\(57\) −3495.49 11393.0i −0.142502 0.464463i
\(58\) 37138.0i 1.44960i
\(59\) 15029.3 + 22114.4i 0.562092 + 0.827074i
\(60\) −9880.62 + 3031.47i −0.354328 + 0.108711i
\(61\) 2330.64i 0.0801957i −0.999196 0.0400978i \(-0.987233\pi\)
0.999196 0.0400978i \(-0.0127670\pi\)
\(62\) 23895.6i 0.789475i
\(63\) 19352.2 13108.8i 0.614296 0.416115i
\(64\) −49440.4 −1.50880
\(65\) −4295.43 −0.126102
\(66\) 13813.4 + 45022.5i 0.390337 + 1.27224i
\(67\) 4248.82i 0.115633i 0.998327 + 0.0578165i \(0.0184138\pi\)
−0.998327 + 0.0578165i \(0.981586\pi\)
\(68\) 36112.5i 0.947076i
\(69\) −21153.9 68947.7i −0.534893 1.74340i
\(70\) 12982.2i 0.316666i
\(71\) 69744.9i 1.64197i −0.570947 0.820987i \(-0.693424\pi\)
0.570947 0.820987i \(-0.306576\pi\)
\(72\) 17976.2 12176.8i 0.408664 0.276822i
\(73\) 44809.4i 0.984150i 0.870553 + 0.492075i \(0.163762\pi\)
−0.870553 + 0.492075i \(0.836238\pi\)
\(74\) 63784.2i 1.35405i
\(75\) −13168.5 42920.7i −0.270323 0.881077i
\(76\) 32384.8 0.643142
\(77\) −33698.9 −0.647722
\(78\) 35269.9 10821.2i 0.656399 0.201390i
\(79\) −43275.7 −0.780147 −0.390073 0.920784i \(-0.627550\pi\)
−0.390073 + 0.920784i \(0.627550\pi\)
\(80\) 9157.00i 0.159966i
\(81\) 21903.9 54836.2i 0.370944 0.928655i
\(82\) 178616.i 2.93350i
\(83\) −109985. −1.75242 −0.876211 0.481927i \(-0.839937\pi\)
−0.876211 + 0.481927i \(0.839937\pi\)
\(84\) 18631.1 + 60725.0i 0.288097 + 0.939009i
\(85\) −13342.3 −0.200301
\(86\) 125119.i 1.82423i
\(87\) 64181.9 19691.7i 0.909106 0.278923i
\(88\) −31302.8 −0.430901
\(89\) −83865.6 −1.12230 −0.561150 0.827714i \(-0.689641\pi\)
−0.561150 + 0.827714i \(0.689641\pi\)
\(90\) −18393.1 27153.1i −0.239358 0.353357i
\(91\) 26399.2i 0.334185i
\(92\) 195985. 2.41409
\(93\) 41296.3 12670.1i 0.495113 0.151906i
\(94\) −85752.0 −1.00098
\(95\) 11965.0i 0.136021i
\(96\) −36141.8 117799.i −0.400251 1.30456i
\(97\) 27574.0i 0.297557i 0.988871 + 0.148778i \(0.0475341\pi\)
−0.988871 + 0.148778i \(0.952466\pi\)
\(98\) 65145.3 0.685201
\(99\) −70483.6 + 47744.5i −0.722770 + 0.489593i
\(100\) 122003. 1.22003
\(101\) 18455.7 0.180022 0.0900111 0.995941i \(-0.471310\pi\)
0.0900111 + 0.995941i \(0.471310\pi\)
\(102\) 109554. 33612.3i 1.04262 0.319888i
\(103\) 65878.4i 0.611857i −0.952055 0.305928i \(-0.901033\pi\)
0.952055 0.305928i \(-0.0989668\pi\)
\(104\) 24522.2i 0.222318i
\(105\) 22435.8 6883.52i 0.198595 0.0609309i
\(106\) 162672.i 1.40620i
\(107\) 82467.5i 0.696344i 0.937431 + 0.348172i \(0.113197\pi\)
−0.937431 + 0.348172i \(0.886803\pi\)
\(108\) 125003. + 100614.i 1.03125 + 0.830043i
\(109\) 21260.6i 0.171400i 0.996321 + 0.0856998i \(0.0273126\pi\)
−0.996321 + 0.0856998i \(0.972687\pi\)
\(110\) 47283.1i 0.372584i
\(111\) 110232. 33820.2i 0.849180 0.260537i
\(112\) 56277.8 0.423928
\(113\) 136138. 1.00296 0.501481 0.865168i \(-0.332789\pi\)
0.501481 + 0.865168i \(0.332789\pi\)
\(114\) 30142.7 + 98245.4i 0.217230 + 0.708027i
\(115\) 72409.6i 0.510566i
\(116\) 182438.i 1.25884i
\(117\) 37402.3 + 55215.8i 0.252600 + 0.372905i
\(118\) −129602. 190699.i −0.856854 1.26079i
\(119\) 82000.1i 0.530820i
\(120\) 20840.6 6394.09i 0.132116 0.0405346i
\(121\) −38314.3 −0.237902
\(122\) 20097.9i 0.122250i
\(123\) −308684. + 94707.5i −1.83972 + 0.564445i
\(124\) 117386.i 0.685584i
\(125\) 93985.5i 0.538004i
\(126\) −166880. + 113042.i −0.936434 + 0.634325i
\(127\) 116559. 0.641265 0.320632 0.947204i \(-0.396105\pi\)
0.320632 + 0.947204i \(0.396105\pi\)
\(128\) 173397. 0.935441
\(129\) −216231. + 66342.0i −1.14405 + 0.351006i
\(130\) 37040.8 0.192231
\(131\) −145699. −0.741783 −0.370892 0.928676i \(-0.620948\pi\)
−0.370892 + 0.928676i \(0.620948\pi\)
\(132\) −67857.3 221170.i −0.338970 1.10482i
\(133\) −73535.7 −0.360470
\(134\) 36638.9i 0.176271i
\(135\) 37173.5 46184.3i 0.175549 0.218102i
\(136\) 76169.8i 0.353131i
\(137\) 241219.i 1.09802i −0.835816 0.549009i \(-0.815005\pi\)
0.835816 0.549009i \(-0.184995\pi\)
\(138\) 182416. + 594558.i 0.815391 + 2.65764i
\(139\) 122912. 0.539580 0.269790 0.962919i \(-0.413046\pi\)
0.269790 + 0.962919i \(0.413046\pi\)
\(140\) 63774.1i 0.274994i
\(141\) −45468.2 148197.i −0.192602 0.627756i
\(142\) 601432.i 2.50303i
\(143\) 96150.0i 0.393196i
\(144\) 117709. 79734.2i 0.473046 0.320434i
\(145\) 67404.5 0.266237
\(146\) 386405.i 1.50024i
\(147\) 34541.9 + 112584.i 0.131842 + 0.429718i
\(148\) 313336.i 1.17586i
\(149\) 243124. 0.897144 0.448572 0.893747i \(-0.351933\pi\)
0.448572 + 0.893747i \(0.351933\pi\)
\(150\) 113556. + 370119.i 0.412081 + 1.34311i
\(151\) 332950.i 1.18833i −0.804343 0.594165i \(-0.797483\pi\)
0.804343 0.594165i \(-0.202517\pi\)
\(152\) −68307.2 −0.239805
\(153\) 116177. + 171509.i 0.401230 + 0.592323i
\(154\) 290596. 0.987388
\(155\) 43369.8 0.144997
\(156\) −173261. + 53158.3i −0.570020 + 0.174888i
\(157\) 255785.i 0.828182i −0.910236 0.414091i \(-0.864100\pi\)
0.910236 0.414091i \(-0.135900\pi\)
\(158\) 373180. 1.18926
\(159\) −281129. + 86253.3i −0.881887 + 0.270572i
\(160\) 123713.i 0.382047i
\(161\) −445021. −1.35305
\(162\) −188884. + 472869.i −0.565467 + 1.41564i
\(163\) −46565.4 −0.137276 −0.0686380 0.997642i \(-0.521865\pi\)
−0.0686380 + 0.997642i \(0.521865\pi\)
\(164\) 877441.i 2.54746i
\(165\) −81714.7 + 25070.9i −0.233663 + 0.0716902i
\(166\) 948436. 2.67139
\(167\) 325845.i 0.904106i −0.891991 0.452053i \(-0.850692\pi\)
0.891991 0.452053i \(-0.149308\pi\)
\(168\) −39297.3 128083.i −0.107421 0.350122i
\(169\) 295971. 0.797135
\(170\) 115055. 0.305339
\(171\) −153805. + 104185.i −0.402236 + 0.272468i
\(172\) 614642.i 1.58417i
\(173\) 244902. 0.622125 0.311063 0.950389i \(-0.399315\pi\)
0.311063 + 0.950389i \(0.399315\pi\)
\(174\) −553461. + 169807.i −1.38584 + 0.425190i
\(175\) −277030. −0.683805
\(176\) −204973. −0.498786
\(177\) 260848. 325093.i 0.625826 0.779963i
\(178\) 723199. 1.71083
\(179\) −514091. −1.19924 −0.599622 0.800283i \(-0.704682\pi\)
−0.599622 + 0.800283i \(0.704682\pi\)
\(180\) 90354.9 + 133388.i 0.207860 + 0.306857i
\(181\) −38977.1 −0.0884327 −0.0442163 0.999022i \(-0.514079\pi\)
−0.0442163 + 0.999022i \(0.514079\pi\)
\(182\) 227648.i 0.509432i
\(183\) −34733.1 + 10656.5i −0.0766683 + 0.0235226i
\(184\) −413379. −0.900127
\(185\) 115767. 0.248688
\(186\) −356111. + 109258.i −0.754750 + 0.231565i
\(187\) 298657.i 0.624553i
\(188\) 421252. 0.869254
\(189\) −283843. 228464.i −0.577995 0.465224i
\(190\) 103178.i 0.207350i
\(191\) 411306. 0.815796 0.407898 0.913028i \(-0.366262\pi\)
0.407898 + 0.913028i \(0.366262\pi\)
\(192\) 226058. + 736801.i 0.442554 + 1.44244i
\(193\) 162426. 0.313879 0.156940 0.987608i \(-0.449837\pi\)
0.156940 + 0.987608i \(0.449837\pi\)
\(194\) 237779.i 0.453596i
\(195\) 19640.1 + 64014.0i 0.0369878 + 0.120556i
\(196\) −320022. −0.595031
\(197\) 13331.7i 0.0244749i 0.999925 + 0.0122375i \(0.00389540\pi\)
−0.999925 + 0.0122375i \(0.996105\pi\)
\(198\) 607802. 411716.i 1.10179 0.746336i
\(199\) −997443. −1.78548 −0.892741 0.450570i \(-0.851221\pi\)
−0.892741 + 0.450570i \(0.851221\pi\)
\(200\) −257333. −0.454905
\(201\) 63319.4 19427.0i 0.110547 0.0339169i
\(202\) −159149. −0.274426
\(203\) 414260.i 0.705558i
\(204\) −538177. + 165118.i −0.905420 + 0.277792i
\(205\) −324184. −0.538774
\(206\) 568090.i 0.932715i
\(207\) −930792. + 630504.i −1.50983 + 1.02273i
\(208\) 160573.i 0.257343i
\(209\) 267829. 0.424123
\(210\) −193471. + 59358.7i −0.302738 + 0.0928830i
\(211\) 1.26844e6i 1.96138i −0.195565 0.980691i \(-0.562654\pi\)
0.195565 0.980691i \(-0.437346\pi\)
\(212\) 799115.i 1.22115i
\(213\) −1.03939e6 + 318897.i −1.56975 + 0.481616i
\(214\) 711143.i 1.06151i
\(215\) −227088. −0.335042
\(216\) −263661. 212220.i −0.384514 0.309493i
\(217\) 266546.i 0.384257i
\(218\) 183337.i 0.261282i
\(219\) 667785. 204883.i 0.940863 0.288666i
\(220\) 232275.i 0.323554i
\(221\) −233964. −0.322231
\(222\) −950564. + 291643.i −1.29449 + 0.397163i
\(223\) −38038.8 −0.0512230 −0.0256115 0.999672i \(-0.508153\pi\)
−0.0256115 + 0.999672i \(0.508153\pi\)
\(224\) −760328. −1.01247
\(225\) −579429. + 392496.i −0.763034 + 0.516867i
\(226\) −1.17396e6 −1.52892
\(227\) 774403. 0.997475 0.498738 0.866753i \(-0.333797\pi\)
0.498738 + 0.866753i \(0.333797\pi\)
\(228\) −148074. 482624.i −0.188643 0.614854i
\(229\) 444152.i 0.559684i 0.960046 + 0.279842i \(0.0902820\pi\)
−0.960046 + 0.279842i \(0.909718\pi\)
\(230\) 624411.i 0.778307i
\(231\) 154082. + 502208.i 0.189987 + 0.619233i
\(232\) 384805.i 0.469376i
\(233\) 1.08612e6 1.31066 0.655328 0.755345i \(-0.272530\pi\)
0.655328 + 0.755345i \(0.272530\pi\)
\(234\) −322532. 476143.i −0.385064 0.568457i
\(235\) 155638.i 0.183842i
\(236\) 636662. + 936798.i 0.744096 + 1.09488i
\(237\) 197871. + 644929.i 0.228829 + 0.745833i
\(238\) 707112.i 0.809182i
\(239\) 96829.0i 0.109651i 0.998496 + 0.0548253i \(0.0174602\pi\)
−0.998496 + 0.0548253i \(0.982540\pi\)
\(240\) 136465. 41868.9i 0.152930 0.0469205i
\(241\) −574811. −0.637504 −0.318752 0.947838i \(-0.603264\pi\)
−0.318752 + 0.947838i \(0.603264\pi\)
\(242\) 330396. 0.362657
\(243\) −917365. 75700.0i −0.996613 0.0822395i
\(244\) 98729.5i 0.106163i
\(245\) 118237.i 0.125846i
\(246\) 2.66188e6 816692.i 2.80447 0.860440i
\(247\) 209813.i 0.218821i
\(248\) 247594.i 0.255629i
\(249\) 502889. + 1.63909e6i 0.514012 + 1.67534i
\(250\) 810466.i 0.820134i
\(251\) 594217.i 0.595334i 0.954670 + 0.297667i \(0.0962085\pi\)
−0.954670 + 0.297667i \(0.903792\pi\)
\(252\) 819786. 555310.i 0.813204 0.550851i
\(253\) 1.62084e6 1.59198
\(254\) −1.00513e6 −0.977544
\(255\) 61005.4 + 198838.i 0.0587513 + 0.191491i
\(256\) 86836.7 0.0828139
\(257\) 1.81712e6i 1.71614i 0.513535 + 0.858069i \(0.328336\pi\)
−0.513535 + 0.858069i \(0.671664\pi\)
\(258\) 1.86463e6 572088.i 1.74399 0.535073i
\(259\) 711488.i 0.659049i
\(260\) −181961. −0.166934
\(261\) −586922. 866454.i −0.533309 0.787307i
\(262\) 1.25640e6 1.13077
\(263\) 166247.i 0.148205i −0.997251 0.0741026i \(-0.976391\pi\)
0.997251 0.0741026i \(-0.0236092\pi\)
\(264\) 143127. + 466500.i 0.126390 + 0.411948i
\(265\) −295245. −0.258266
\(266\) 634121. 0.549501
\(267\) 383461. + 1.24983e6i 0.329188 + 1.07294i
\(268\) 179986.i 0.153075i
\(269\) 1.12035e6 0.944003 0.472001 0.881598i \(-0.343532\pi\)
0.472001 + 0.881598i \(0.343532\pi\)
\(270\) −320558. + 398262.i −0.267607 + 0.332475i
\(271\) −434153. −0.359103 −0.179552 0.983749i \(-0.557465\pi\)
−0.179552 + 0.983749i \(0.557465\pi\)
\(272\) 498764.i 0.408764i
\(273\) 393422. 120706.i 0.319486 0.0980216i
\(274\) 2.08010e6i 1.67382i
\(275\) 1.00899e6 0.804553
\(276\) −896109. 2.92073e6i −0.708089 2.30791i
\(277\) 234261. 0.183442 0.0917212 0.995785i \(-0.470763\pi\)
0.0917212 + 0.995785i \(0.470763\pi\)
\(278\) −1.05990e6 −0.822536
\(279\) −377641. 557499.i −0.290448 0.428779i
\(280\) 134515.i 0.102536i
\(281\) 1.68698e6i 1.27451i −0.770653 0.637256i \(-0.780070\pi\)
0.770653 0.637256i \(-0.219930\pi\)
\(282\) 392087. + 1.27795e6i 0.293602 + 0.956951i
\(283\) 932461.i 0.692093i −0.938217 0.346047i \(-0.887524\pi\)
0.938217 0.346047i \(-0.112476\pi\)
\(284\) 2.95450e6i 2.17364i
\(285\) −178313. + 54708.2i −0.130038 + 0.0398970i
\(286\) 829132.i 0.599389i
\(287\) 1.99239e6i 1.42781i
\(288\) −1.59028e6 + 1.07723e6i −1.12978 + 0.765292i
\(289\) 693129. 0.488168
\(290\) −581250. −0.405852
\(291\) 410930. 126077.i 0.284469 0.0872780i
\(292\) 1.89819e6i 1.30282i
\(293\) 2.30802e6i 1.57062i −0.619103 0.785310i \(-0.712504\pi\)
0.619103 0.785310i \(-0.287496\pi\)
\(294\) −297866. 970848.i −0.200980 0.655063i
\(295\) 346114. 235224.i 0.231560 0.157372i
\(296\) 660900.i 0.438436i
\(297\) 1.03380e6 + 832101.i 0.680058 + 0.547375i
\(298\) −2.09653e6 −1.36761
\(299\) 1.26974e6i 0.821365i
\(300\) −557838. 1.81819e6i −0.357853 1.16637i
\(301\) 1.39566e6i 0.887897i
\(302\) 2.87113e6i 1.81149i
\(303\) −84385.4 275041.i −0.0528032 0.172104i
\(304\) −447279. −0.277584
\(305\) −36477.1 −0.0224528
\(306\) −1.00183e6 1.47898e6i −0.611635 0.902937i
\(307\) −1.65134e6 −0.999978 −0.499989 0.866032i \(-0.666663\pi\)
−0.499989 + 0.866032i \(0.666663\pi\)
\(308\) −1.42754e6 −0.857452
\(309\) −981773. + 301218.i −0.584945 + 0.179467i
\(310\) −373992. −0.221033
\(311\) 1.37371e6i 0.805365i 0.915340 + 0.402682i \(0.131922\pi\)
−0.915340 + 0.402682i \(0.868078\pi\)
\(312\) 365449. 112123.i 0.212540 0.0652094i
\(313\) 2.41493e6i 1.39330i −0.717413 0.696648i \(-0.754674\pi\)
0.717413 0.696648i \(-0.245326\pi\)
\(314\) 2.20571e6i 1.26248i
\(315\) −205168. 302882.i −0.116502 0.171988i
\(316\) −1.83322e6 −1.03276
\(317\) 2.08853e6i 1.16733i −0.811995 0.583664i \(-0.801619\pi\)
0.811995 0.583664i \(-0.198381\pi\)
\(318\) 2.42426e6 743789.i 1.34435 0.412460i
\(319\) 1.50880e6i 0.830147i
\(320\) 773796.i 0.422427i
\(321\) 1.22900e6 377069.i 0.665716 0.204248i
\(322\) 3.83755e6 2.06260
\(323\) 651712.i 0.347576i
\(324\) 927881. 2.32294e6i 0.491054 1.22935i
\(325\) 790426.i 0.415100i
\(326\) 401548. 0.209264
\(327\) 316843. 97210.7i 0.163861 0.0502741i
\(328\) 1.85073e6i 0.949857i
\(329\) −956530. −0.487202
\(330\) 704651. 216194.i 0.356196 0.109285i
\(331\) −599565. −0.300792 −0.150396 0.988626i \(-0.548055\pi\)
−0.150396 + 0.988626i \(0.548055\pi\)
\(332\) −4.65914e6 −2.31985
\(333\) −1.00803e6 1.48813e6i −0.498155 0.735410i
\(334\) 2.80986e6i 1.37822i
\(335\) 66498.7 0.0323743
\(336\) −257321. 838698.i −0.124345 0.405282i
\(337\) 389127.i 0.186645i 0.995636 + 0.0933227i \(0.0297488\pi\)
−0.995636 + 0.0933227i \(0.970251\pi\)
\(338\) −2.55225e6 −1.21515
\(339\) −622470. 2.02885e6i −0.294184 0.958848i
\(340\) −565200. −0.265158
\(341\) 970802.i 0.452111i
\(342\) 1.32631e6 898421.i 0.613168 0.415350i
\(343\) 2.34333e6 1.07547
\(344\) 1.29642e6i 0.590678i
\(345\) −1.07911e6 + 331081.i −0.488109 + 0.149757i
\(346\) −2.11187e6 −0.948368
\(347\) −1.15354e6 −0.514289 −0.257144 0.966373i \(-0.582782\pi\)
−0.257144 + 0.966373i \(0.582782\pi\)
\(348\) 2.71884e6 834168.i 1.20347 0.369237i
\(349\) 2.19216e6i 0.963405i −0.876335 0.481703i \(-0.840019\pi\)
0.876335 0.481703i \(-0.159981\pi\)
\(350\) 2.38892e6 1.04239
\(351\) 651855. 809864.i 0.282412 0.350869i
\(352\) 2.76923e6 1.19125
\(353\) 1.67958e6 0.717405 0.358702 0.933452i \(-0.383219\pi\)
0.358702 + 0.933452i \(0.383219\pi\)
\(354\) −2.24937e6 + 2.80337e6i −0.954009 + 1.18898i
\(355\) −1.09158e6 −0.459712
\(356\) −3.55267e6 −1.48570
\(357\) 1.22203e6 374932.i 0.507472 0.155697i
\(358\) 4.43317e6 1.82813
\(359\) 1.36229e6i 0.557872i 0.960310 + 0.278936i \(0.0899818\pi\)
−0.960310 + 0.278936i \(0.910018\pi\)
\(360\) −190580. 281347.i −0.0775034 0.114416i
\(361\) −1.89166e6 −0.763968
\(362\) 336111. 0.134807
\(363\) 175186. + 570991.i 0.0697802 + 0.227438i
\(364\) 1.11831e6i 0.442393i
\(365\) 701315. 0.275538
\(366\) 299515. 91894.1i 0.116873 0.0358579i
\(367\) 2.94384e6i 1.14091i 0.821330 + 0.570453i \(0.193232\pi\)
−0.821330 + 0.570453i \(0.806768\pi\)
\(368\) −2.70683e6 −1.04194
\(369\) 2.82282e6 + 4.16723e6i 1.07924 + 1.59324i
\(370\) −998292. −0.379100
\(371\) 1.81454e6i 0.684434i
\(372\) 1.74937e6 536726.i 0.655429 0.201092i
\(373\) 4.37376e6 1.62773 0.813866 0.581052i \(-0.197359\pi\)
0.813866 + 0.581052i \(0.197359\pi\)
\(374\) 2.57542e6i 0.952069i
\(375\) −1.40065e6 + 429733.i −0.514340 + 0.157805i
\(376\) −888519. −0.324114
\(377\) 1.18197e6 0.428305
\(378\) 2.44767e6 + 1.97011e6i 0.881095 + 0.709188i
\(379\) 1.01380e6 0.362537 0.181269 0.983434i \(-0.441980\pi\)
0.181269 + 0.983434i \(0.441980\pi\)
\(380\) 506857.i 0.180064i
\(381\) −532947. 1.73706e6i −0.188093 0.613059i
\(382\) −3.54682e6 −1.24360
\(383\) 230361.i 0.0802439i −0.999195 0.0401220i \(-0.987225\pi\)
0.999195 0.0401220i \(-0.0127746\pi\)
\(384\) −792828. 2.58410e6i −0.274379 0.894297i
\(385\) 527424.i 0.181346i
\(386\) −1.40065e6 −0.478477
\(387\) 1.97736e6 + 2.91912e6i 0.671134 + 0.990773i
\(388\) 1.16807e6i 0.393905i
\(389\) 5.12823e6i 1.71828i −0.511743 0.859138i \(-0.671000\pi\)
0.511743 0.859138i \(-0.329000\pi\)
\(390\) −169363. 552013.i −0.0563842 0.183775i
\(391\) 3.94401e6i 1.30466i
\(392\) 675003. 0.221866
\(393\) 666182. + 2.17132e6i 0.217576 + 0.709156i
\(394\) 114964.i 0.0373096i
\(395\) 677312.i 0.218422i
\(396\) −2.98579e6 + 2.02253e6i −0.956801 + 0.648122i
\(397\) 4.84182e6i 1.54182i 0.636946 + 0.770908i \(0.280197\pi\)
−0.636946 + 0.770908i \(0.719803\pi\)
\(398\) 8.60126e6 2.72179
\(399\) 336230. + 1.09589e6i 0.105731 + 0.344615i
\(400\) −1.68503e6 −0.526572
\(401\) 433851. 0.134735 0.0673674 0.997728i \(-0.478540\pi\)
0.0673674 + 0.997728i \(0.478540\pi\)
\(402\) −546023. + 167525.i −0.168518 + 0.0517029i
\(403\) 760511. 0.233261
\(404\) 781809. 0.238313
\(405\) −858246. 342819.i −0.260000 0.103855i
\(406\) 3.57229e6i 1.07555i
\(407\) 2.59135e6i 0.775426i
\(408\) 1.13514e6 348273.i 0.337598 0.103579i
\(409\) 5.76995e6i 1.70555i 0.522280 + 0.852774i \(0.325081\pi\)
−0.522280 + 0.852774i \(0.674919\pi\)
\(410\) 2.79554e6 0.821307
\(411\) −3.59484e6 + 1.10293e6i −1.04972 + 0.322065i
\(412\) 2.79071e6i 0.809974i
\(413\) −1.44566e6 2.12717e6i −0.417053 0.613660i
\(414\) 8.02651e6 5.43703e6i 2.30158 1.55905i
\(415\) 1.72139e6i 0.490635i
\(416\) 2.16938e6i 0.614613i
\(417\) −561992. 1.83173e6i −0.158267 0.515847i
\(418\) −2.30957e6 −0.646533
\(419\) −3.15128e6 −0.876904 −0.438452 0.898755i \(-0.644473\pi\)
−0.438452 + 0.898755i \(0.644473\pi\)
\(420\) 950413. 291596.i 0.262899 0.0806601i
\(421\) 6.24640e6i 1.71761i −0.512302 0.858806i \(-0.671207\pi\)
0.512302 0.858806i \(-0.328793\pi\)
\(422\) 1.09381e7i 2.98993i
\(423\) −2.00065e6 + 1.35521e6i −0.543651 + 0.368261i
\(424\) 1.68552e6i 0.455323i
\(425\) 2.45519e6i 0.659345i
\(426\) 8.96302e6 2.74995e6i 2.39293 0.734176i
\(427\) 224184.i 0.0595024i
\(428\) 3.49345e6i 0.921818i
\(429\) −1.43291e6 + 439630.i −0.375902 + 0.115330i
\(430\) 1.95825e6 0.510738
\(431\) −4.95326e6 −1.28439 −0.642196 0.766540i \(-0.721977\pi\)
−0.642196 + 0.766540i \(0.721977\pi\)
\(432\) −1.72647e6 1.38963e6i −0.445092 0.358252i
\(433\) −3.42411e6 −0.877663 −0.438832 0.898569i \(-0.644608\pi\)
−0.438832 + 0.898569i \(0.644608\pi\)
\(434\) 2.29851e6i 0.585762i
\(435\) −308196. 1.00452e6i −0.0780915 0.254527i
\(436\) 900632.i 0.226898i
\(437\) 3.53689e6 0.885968
\(438\) −5.75852e6 + 1.76677e6i −1.43425 + 0.440043i
\(439\) 957857. 0.237213 0.118607 0.992941i \(-0.462157\pi\)
0.118607 + 0.992941i \(0.462157\pi\)
\(440\) 489924.i 0.120641i
\(441\) 1.51988e6 1.02954e6i 0.372146 0.252086i
\(442\) 2.01754e6 0.491209
\(443\) −3.67193e6 −0.888967 −0.444484 0.895787i \(-0.646613\pi\)
−0.444484 + 0.895787i \(0.646613\pi\)
\(444\) 4.66959e6 1.43268e6i 1.12414 0.344898i
\(445\) 1.31259e6i 0.314216i
\(446\) 328021. 0.0780843
\(447\) −1.11164e6 3.62323e6i −0.263146 0.857684i
\(448\) 4.75565e6 1.11948
\(449\) 3.99551e6i 0.935312i 0.883911 + 0.467656i \(0.154901\pi\)
−0.883911 + 0.467656i \(0.845099\pi\)
\(450\) 4.99660e6 3.38461e6i 1.16317 0.787912i
\(451\) 7.25661e6i 1.67993i
\(452\) 5.76703e6 1.32772
\(453\) −4.96190e6 + 1.52236e6i −1.13606 + 0.348555i
\(454\) −6.67792e6 −1.52055
\(455\) 413176. 0.0935635
\(456\) 312323. + 1.01797e6i 0.0703383 + 0.229257i
\(457\) 2.61120e6i 0.584858i −0.956287 0.292429i \(-0.905536\pi\)
0.956287 0.292429i \(-0.0944635\pi\)
\(458\) 3.83006e6i 0.853182i
\(459\) 2.02477e6 2.51557e6i 0.448583 0.557320i
\(460\) 3.06738e6i 0.675885i
\(461\) 1.79955e6i 0.394378i 0.980366 + 0.197189i \(0.0631812\pi\)
−0.980366 + 0.197189i \(0.936819\pi\)
\(462\) −1.32870e6 4.33070e6i −0.289616 0.943958i
\(463\) 182590.i 0.0395844i 0.999804 + 0.0197922i \(0.00630047\pi\)
−0.999804 + 0.0197922i \(0.993700\pi\)
\(464\) 2.51973e6i 0.543323i
\(465\) −198301. 646333.i −0.0425298 0.138619i
\(466\) −9.36596e6 −1.99796
\(467\) 4.66007e6 0.988781 0.494390 0.869240i \(-0.335391\pi\)
0.494390 + 0.869240i \(0.335391\pi\)
\(468\) 1.58442e6 + 2.33902e6i 0.334391 + 0.493651i
\(469\) 408693.i 0.0857955i
\(470\) 1.34211e6i 0.280249i
\(471\) −3.81191e6 + 1.16953e6i −0.791755 + 0.242918i
\(472\) −1.34287e6 1.97593e6i −0.277447 0.408241i
\(473\) 5.08321e6i 1.04468i
\(474\) −1.70630e6 5.56143e6i −0.348827 1.13695i
\(475\) 2.20175e6 0.447749
\(476\) 3.47365e6i 0.702697i
\(477\) 2.57083e6 + 3.79524e6i 0.517342 + 0.763735i
\(478\) 834987.i 0.167151i
\(479\) 3.00565e6i 0.598548i −0.954167 0.299274i \(-0.903256\pi\)
0.954167 0.299274i \(-0.0967445\pi\)
\(480\) −1.84368e6 + 565659.i −0.365243 + 0.112060i
\(481\) 2.03002e6 0.400072
\(482\) 4.95678e6 0.971811
\(483\) 2.03478e6 + 6.63206e6i 0.396872 + 1.29354i
\(484\) −1.62305e6 −0.314933
\(485\) 431563. 0.0833085
\(486\) 7.91072e6 + 652785.i 1.51924 + 0.125366i
\(487\) −3.26398e6 −0.623627 −0.311813 0.950143i \(-0.600936\pi\)
−0.311813 + 0.950143i \(0.600936\pi\)
\(488\) 208244.i 0.0395843i
\(489\) 212913. + 693956.i 0.0402651 + 0.131238i
\(490\) 1.01959e6i 0.191839i
\(491\) 7.79526e6i 1.45924i −0.683852 0.729620i \(-0.739697\pi\)
0.683852 0.729620i \(-0.260303\pi\)
\(492\) −1.30763e7 + 4.01195e6i −2.43542 + 0.747210i
\(493\) 3.67139e6 0.680320
\(494\) 1.80928e6i 0.333571i
\(495\) 747253. + 1.10315e6i 0.137074 + 0.202358i
\(496\) 1.62126e6i 0.295902i
\(497\) 6.70873e6i 1.21829i
\(498\) −4.33657e6 1.41344e7i −0.783561 2.55389i
\(499\) −6.33385e6 −1.13872 −0.569359 0.822089i \(-0.692809\pi\)
−0.569359 + 0.822089i \(0.692809\pi\)
\(500\) 3.98136e6i 0.712208i
\(501\) −4.85600e6 + 1.48987e6i −0.864340 + 0.265188i
\(502\) 5.12412e6i 0.907527i
\(503\) −8.49659e6 −1.49736 −0.748678 0.662934i \(-0.769311\pi\)
−0.748678 + 0.662934i \(0.769311\pi\)
\(504\) −1.72912e6 + 1.17128e6i −0.303214 + 0.205392i
\(505\) 288851.i 0.0504017i
\(506\) −1.39770e7 −2.42682
\(507\) −1.35328e6 4.41079e6i −0.233812 0.762073i
\(508\) 4.93762e6 0.848904
\(509\) −8.30576e6 −1.42097 −0.710485 0.703713i \(-0.751524\pi\)
−0.710485 + 0.703713i \(0.751524\pi\)
\(510\) −526069. 1.71464e6i −0.0895606 0.291909i
\(511\) 4.31020e6i 0.730205i
\(512\) −6.29752e6 −1.06168
\(513\) 2.25590e6 + 1.81576e6i 0.378466 + 0.304625i
\(514\) 1.56696e7i 2.61608i
\(515\) −1.03107e6 −0.171305
\(516\) −9.15989e6 + 2.81035e6i −1.51449 + 0.464660i
\(517\) 3.48383e6 0.573233
\(518\) 6.13538e6i 1.00466i
\(519\) −1.11977e6 3.64973e6i −0.182479 0.594761i
\(520\) 383799. 0.0622436
\(521\) 8.67596e6i 1.40031i 0.713993 + 0.700153i \(0.246885\pi\)
−0.713993 + 0.700153i \(0.753115\pi\)
\(522\) 5.06121e6 + 7.47170e6i 0.812977 + 1.20017i
\(523\) 1.07225e6 0.171412 0.0857059 0.996320i \(-0.472685\pi\)
0.0857059 + 0.996320i \(0.472685\pi\)
\(524\) −6.17201e6 −0.981970
\(525\) 1.26667e6 + 4.12853e6i 0.200570 + 0.653728i
\(526\) 1.43360e6i 0.225924i
\(527\) 2.36227e6 0.370512
\(528\) 937204. + 3.05467e6i 0.146302 + 0.476848i
\(529\) 1.49681e7 2.32556
\(530\) 2.54599e6 0.393701
\(531\) −6.03747e6 2.40093e6i −0.929221 0.369524i
\(532\) −3.11508e6 −0.477189
\(533\) −5.68472e6 −0.866744
\(534\) −3.30671e6 1.07777e7i −0.501814 1.63558i
\(535\) 1.29071e6 0.194959
\(536\) 379634.i 0.0570760i
\(537\) 2.35060e6 + 7.66141e6i 0.351757 + 1.14650i
\(538\) −9.66113e6 −1.43904
\(539\) −2.64665e6 −0.392396
\(540\) 1.57472e6 1.95644e6i 0.232391 0.288723i
\(541\) 7.13930e6i 1.04873i 0.851494 + 0.524364i \(0.175697\pi\)
−0.851494 + 0.524364i \(0.824303\pi\)
\(542\) 3.74383e6 0.547417
\(543\) 178216. + 580868.i 0.0259387 + 0.0845430i
\(544\) 6.73843e6i 0.976251i
\(545\) 332752. 0.0479876
\(546\) −3.39260e6 + 1.04088e6i −0.487025 + 0.149424i
\(547\) 9.15909e6 1.30883 0.654416 0.756134i \(-0.272914\pi\)
0.654416 + 0.756134i \(0.272914\pi\)
\(548\) 1.02184e7i 1.45355i
\(549\) 317623. + 468896.i 0.0449760 + 0.0663966i
\(550\) −8.70082e6 −1.22646
\(551\) 3.29241e6i 0.461993i
\(552\) 1.89011e6 + 6.16051e6i 0.264021 + 0.860536i
\(553\) 4.16267e6 0.578841
\(554\) −2.02010e6 −0.279640
\(555\) −529324. 1.72525e6i −0.0729439 0.237749i
\(556\) 5.20672e6 0.714294
\(557\) 7.17374e6i 0.979733i −0.871797 0.489867i \(-0.837046\pi\)
0.871797 0.489867i \(-0.162954\pi\)
\(558\) 3.25652e6 + 4.80749e6i 0.442759 + 0.653632i
\(559\) −3.98211e6 −0.538993
\(560\) 880809.i 0.118689i
\(561\) −4.45083e6 + 1.36556e6i −0.597082 + 0.183191i
\(562\) 1.45473e7i 1.94287i
\(563\) 6.50423e6 0.864818 0.432409 0.901678i \(-0.357664\pi\)
0.432409 + 0.901678i \(0.357664\pi\)
\(564\) −1.92610e6 6.27783e6i −0.254966 0.831021i
\(565\) 2.13071e6i 0.280805i
\(566\) 8.04090e6i 1.05503i
\(567\) −2.10693e6 + 5.27467e6i −0.275227 + 0.689029i
\(568\) 6.23173e6i 0.810472i
\(569\) −9.92281e6 −1.28485 −0.642427 0.766347i \(-0.722073\pi\)
−0.642427 + 0.766347i \(0.722073\pi\)
\(570\) 1.53765e6 471765.i 0.198230 0.0608190i
\(571\) 8.16059e6i 1.04745i −0.851889 0.523723i \(-0.824543\pi\)
0.851889 0.523723i \(-0.175457\pi\)
\(572\) 4.07306e6i 0.520512i
\(573\) −1.88063e6 6.12961e6i −0.239285 0.779913i
\(574\) 1.71810e7i 2.17655i
\(575\) 1.33245e7 1.68067
\(576\) 9.94679e6 6.73780e6i 1.24919 0.846178i
\(577\) 5.41195e6 0.676729 0.338364 0.941015i \(-0.390126\pi\)
0.338364 + 0.941015i \(0.390126\pi\)
\(578\) −5.97707e6 −0.744164
\(579\) −742666. 2.42060e6i −0.0920655 0.300073i
\(580\) 2.85536e6 0.352444
\(581\) 1.05794e7 1.30024
\(582\) −3.54358e6 + 1.08720e6i −0.433645 + 0.133047i
\(583\) 6.60884e6i 0.805292i
\(584\) 4.00373e6i 0.485773i
\(585\) 864187. 585387.i 0.104404 0.0707218i
\(586\) 1.99028e7i 2.39425i
\(587\) 9.62890e6 1.15340 0.576702 0.816955i \(-0.304339\pi\)
0.576702 + 0.816955i \(0.304339\pi\)
\(588\) 1.46325e6 + 4.76923e6i 0.174532 + 0.568859i
\(589\) 2.11843e6i 0.251608i
\(590\) −2.98465e6 + 2.02841e6i −0.352991 + 0.239898i
\(591\) 198680. 60957.2i 0.0233984 0.00717887i
\(592\) 4.32761e6i 0.507509i
\(593\) 1.49397e7i 1.74464i −0.488937 0.872319i \(-0.662615\pi\)
0.488937 0.872319i \(-0.337385\pi\)
\(594\) −8.91479e6 7.17546e6i −1.03668 0.834418i
\(595\) 1.28339e6 0.148616
\(596\) 1.02991e7 1.18764
\(597\) 4.56064e6 + 1.48647e7i 0.523709 + 1.70695i
\(598\) 1.09493e7i 1.25209i
\(599\) 4.04336e6i 0.460442i −0.973138 0.230221i \(-0.926055\pi\)
0.973138 0.230221i \(-0.0739450\pi\)
\(600\) 1.17661e6 + 3.83499e6i 0.133431 + 0.434896i
\(601\) 6.81347e6i 0.769453i −0.923031 0.384726i \(-0.874296\pi\)
0.923031 0.384726i \(-0.125704\pi\)
\(602\) 1.20352e7i 1.35351i
\(603\) −579035. 854810.i −0.0648502 0.0957362i
\(604\) 1.41043e7i 1.57311i
\(605\) 599660.i 0.0666065i
\(606\) 727681. + 2.37177e6i 0.0804933 + 0.262355i
\(607\) −1.15741e7 −1.27501 −0.637506 0.770445i \(-0.720034\pi\)
−0.637506 + 0.770445i \(0.720034\pi\)
\(608\) 6.04286e6 0.662954
\(609\) −6.17363e6 + 1.89413e6i −0.674524 + 0.206951i
\(610\) 314553. 0.0342271
\(611\) 2.72918e6i 0.295753i
\(612\) 4.92145e6 + 7.26538e6i 0.531147 + 0.784115i
\(613\) 1.47599e7i 1.58647i 0.608916 + 0.793234i \(0.291604\pi\)
−0.608916 + 0.793234i \(0.708396\pi\)
\(614\) 1.42400e7 1.52437
\(615\) 1.48227e6 + 4.83125e6i 0.158031 + 0.515076i
\(616\) 3.01101e6 0.319713
\(617\) 1.65063e7i 1.74557i 0.488102 + 0.872786i \(0.337689\pi\)
−0.488102 + 0.872786i \(0.662311\pi\)
\(618\) 8.46613e6 2.59749e6i 0.891690 0.273579i
\(619\) −2.52855e6 −0.265244 −0.132622 0.991167i \(-0.542340\pi\)
−0.132622 + 0.991167i \(0.542340\pi\)
\(620\) 1.83721e6 0.191946
\(621\) 1.36522e7 + 1.09886e7i 1.42060 + 1.14343i
\(622\) 1.18459e7i 1.22770i
\(623\) 8.06700e6 0.832707
\(624\) 2.39298e6 734191.i 0.246024 0.0754827i
\(625\) 7.52916e6 0.770986
\(626\) 2.08247e7i 2.12394i
\(627\) −1.22460e6 3.99140e6i −0.124402 0.405468i
\(628\) 1.08354e7i 1.09634i
\(629\) 6.30558e6 0.635475
\(630\) 1.76922e6 + 2.61185e6i 0.177595 + 0.262178i
\(631\) −3.72212e6 −0.372149 −0.186074 0.982536i \(-0.559577\pi\)
−0.186074 + 0.982536i \(0.559577\pi\)
\(632\) 3.86670e6 0.385077
\(633\) −1.89032e7 + 5.79971e6i −1.87511 + 0.575303i
\(634\) 1.80101e7i 1.77948i
\(635\) 1.82428e6i 0.179538i
\(636\) −1.19091e7 + 3.65382e6i −1.16744 + 0.358182i
\(637\) 2.07334e6i 0.202452i
\(638\) 1.30109e7i 1.26548i
\(639\) 9.50491e6 + 1.40318e7i 0.920865 + 1.35944i
\(640\) 2.71385e6i 0.261900i
\(641\) 1.33112e7i 1.27959i −0.768544 0.639796i \(-0.779019\pi\)
0.768544 0.639796i \(-0.220981\pi\)
\(642\) −1.05980e7 + 3.25158e6i −1.01482 + 0.311356i
\(643\) −1.20938e7 −1.15355 −0.576774 0.816904i \(-0.695689\pi\)
−0.576774 + 0.816904i \(0.695689\pi\)
\(644\) −1.88517e7 −1.79117
\(645\) 1.03832e6 + 3.38426e6i 0.0982729 + 0.320305i
\(646\) 5.61992e6i 0.529845i
\(647\) 1.85305e7i 1.74031i −0.492783 0.870153i \(-0.664020\pi\)
0.492783 0.870153i \(-0.335980\pi\)
\(648\) −1.95712e6 + 4.89963e6i −0.183096 + 0.458381i
\(649\) 5.26532e6 + 7.74750e6i 0.490697 + 0.722021i
\(650\) 6.81609e6i 0.632779i
\(651\) −3.97228e6 + 1.21874e6i −0.367356 + 0.112709i
\(652\) −1.97258e6 −0.181726
\(653\) 3.20324e6i 0.293972i −0.989139 0.146986i \(-0.953043\pi\)
0.989139 0.146986i \(-0.0469573\pi\)
\(654\) −2.73224e6 + 838278.i −0.249789 + 0.0766379i
\(655\) 2.28034e6i 0.207681i
\(656\) 1.21187e7i 1.09950i
\(657\) −6.10667e6 9.01508e6i −0.551939 0.814810i
\(658\) 8.24845e6 0.742690
\(659\) 1.42323e7 1.27662 0.638308 0.769781i \(-0.279635\pi\)
0.638308 + 0.769781i \(0.279635\pi\)
\(660\) −3.46155e6 + 1.06204e6i −0.309322 + 0.0949032i
\(661\) 1.50721e7 1.34175 0.670873 0.741572i \(-0.265920\pi\)
0.670873 + 0.741572i \(0.265920\pi\)
\(662\) 5.17024e6 0.458528
\(663\) 1.06976e6 + 3.48672e6i 0.0945153 + 0.308058i
\(664\) 9.82722e6 0.864989
\(665\) 1.15091e6i 0.100923i
\(666\) 8.69259e6 + 1.28326e7i 0.759388 + 1.12106i
\(667\) 1.99249e7i 1.73413i
\(668\) 1.38033e7i 1.19685i
\(669\) 173926. + 566885.i 0.0150245 + 0.0489700i
\(670\) −573439. −0.0493515
\(671\) 816513.i 0.0700094i
\(672\) 3.47647e6 + 1.13310e7i 0.296972 + 0.967934i
\(673\) 1.72295e7i 1.46634i 0.680046 + 0.733169i \(0.261960\pi\)
−0.680046 + 0.733169i \(0.738040\pi\)
\(674\) 3.35557e6i 0.284522i
\(675\) 8.49863e6 + 6.84050e6i 0.717942 + 0.577868i
\(676\) 1.25378e7 1.05524
\(677\) 6.38671e6i 0.535557i 0.963481 + 0.267778i \(0.0862895\pi\)
−0.963481 + 0.267778i \(0.913710\pi\)
\(678\) 5.36775e6 + 1.74954e7i 0.448455 + 1.46167i
\(679\) 2.65233e6i 0.220777i
\(680\) 1.19214e6 0.0988678
\(681\) −3.54083e6 1.15408e7i −0.292575 0.953602i
\(682\) 8.37153e6i 0.689197i
\(683\) 1.27583e7 1.04650 0.523251 0.852179i \(-0.324719\pi\)
0.523251 + 0.852179i \(0.324719\pi\)
\(684\) −6.51542e6 + 4.41344e6i −0.532478 + 0.360692i
\(685\) −3.77533e6 −0.307418
\(686\) −2.02073e7 −1.63945
\(687\) 6.61911e6 2.03081e6i 0.535066 0.164164i
\(688\) 8.48906e6i 0.683736i
\(689\) −5.17726e6 −0.415482
\(690\) 9.30547e6 2.85501e6i 0.744073 0.228289i
\(691\) 1.67771e7i 1.33666i 0.743865 + 0.668330i \(0.232991\pi\)
−0.743865 + 0.668330i \(0.767009\pi\)
\(692\) 1.03744e7 0.823567
\(693\) 6.77980e6 4.59252e6i 0.536270 0.363261i
\(694\) 9.94729e6 0.783982
\(695\) 1.92370e6i 0.151069i
\(696\) −5.73468e6 + 1.75946e6i −0.448731 + 0.137675i
\(697\) −1.76576e7 −1.37674
\(698\) 1.89037e7i 1.46862i
\(699\) −4.96611e6 1.61863e7i −0.384435 1.25301i
\(700\) −1.17354e7 −0.905219
\(701\) 2.10706e7 1.61951 0.809753 0.586771i \(-0.199601\pi\)
0.809753 + 0.586771i \(0.199601\pi\)
\(702\) −5.62115e6 + 6.98371e6i −0.430509 + 0.534864i
\(703\) 5.65469e6i 0.431539i
\(704\) −1.73208e7 −1.31716
\(705\) −2.31944e6 + 711627.i −0.175756 + 0.0539237i
\(706\) −1.44836e7 −1.09361
\(707\) −1.77524e6 −0.133570
\(708\) 1.10499e7 1.37714e7i 0.828466 1.03251i
\(709\) −1.18269e6 −0.0883603 −0.0441801 0.999024i \(-0.514068\pi\)
−0.0441801 + 0.999024i \(0.514068\pi\)
\(710\) 9.41306e6 0.700785
\(711\) 8.70653e6 5.89766e6i 0.645909 0.437528i
\(712\) 7.49343e6 0.553963
\(713\) 1.28202e7i 0.944433i
\(714\) −1.05380e7 + 3.23315e6i −0.773590 + 0.237345i
\(715\) −1.50485e6 −0.110085
\(716\) −2.17777e7 −1.58756
\(717\) 1.44302e6 442734.i 0.104828 0.0321622i
\(718\) 1.17475e7i 0.850421i
\(719\) 3.67116e6 0.264839 0.132419 0.991194i \(-0.457725\pi\)
0.132419 + 0.991194i \(0.457725\pi\)
\(720\) −1.24793e6 1.84228e6i −0.0897136 0.132441i
\(721\) 6.33682e6i 0.453976i
\(722\) 1.63124e7 1.16459
\(723\) 2.62823e6 + 8.56631e6i 0.186990 + 0.609464i
\(724\) −1.65113e6 −0.117067
\(725\) 1.24035e7i 0.876392i
\(726\) −1.51068e6 4.92383e6i −0.106373 0.346706i
\(727\) −9.23008e6 −0.647693 −0.323847 0.946110i \(-0.604976\pi\)
−0.323847 + 0.946110i \(0.604976\pi\)
\(728\) 2.35878e6i 0.164952i
\(729\) 3.06635e6 + 1.40174e7i 0.213699 + 0.976899i
\(730\) −6.04766e6 −0.420030
\(731\) −1.23691e7 −0.856137
\(732\) −1.47135e6 + 451424.i −0.101493 + 0.0311392i
\(733\) 8.77331e6 0.603120 0.301560 0.953447i \(-0.402493\pi\)
0.301560 + 0.953447i \(0.402493\pi\)
\(734\) 2.53857e7i 1.73920i
\(735\) 1.76206e6 540619.i 0.120310 0.0369124i
\(736\) 3.65699e7 2.48845
\(737\) 1.48852e6i 0.100946i
\(738\) −2.43420e7 3.59353e7i −1.64519 2.42874i
\(739\) 685603.i 0.0461808i 0.999733 + 0.0230904i \(0.00735055\pi\)
−0.999733 + 0.0230904i \(0.992649\pi\)
\(740\) 4.90405e6 0.329212
\(741\) −3.12680e6 + 959334.i −0.209197 + 0.0641836i
\(742\) 1.56473e7i 1.04335i
\(743\) 2.53146e7i 1.68228i −0.540814 0.841142i \(-0.681884\pi\)
0.540814 0.841142i \(-0.318116\pi\)
\(744\) −3.68984e6 + 1.13208e6i −0.244386 + 0.0749800i
\(745\) 3.80515e6i 0.251178i
\(746\) −3.77163e7 −2.48132
\(747\) 2.21276e7 1.49889e7i 1.45089 0.982808i
\(748\) 1.26516e7i 0.826781i
\(749\) 7.93252e6i 0.516662i
\(750\) 1.20782e7 3.70572e6i 0.784061 0.240558i
\(751\) 8.32162e6i 0.538404i 0.963084 + 0.269202i \(0.0867599\pi\)
−0.963084 + 0.269202i \(0.913240\pi\)
\(752\) −5.81807e6 −0.375176
\(753\) 8.85550e6 2.71696e6i 0.569149 0.174620i
\(754\) −1.01925e7 −0.652909
\(755\) −5.21103e6 −0.332703
\(756\) −1.20240e7 9.67806e6i −0.765147 0.615863i
\(757\) −2.70456e7 −1.71537 −0.857684 0.514176i \(-0.828098\pi\)
−0.857684 + 0.514176i \(0.828098\pi\)
\(758\) −8.74228e6 −0.552652
\(759\) −7.41100e6 2.41550e7i −0.466952 1.52196i
\(760\) 1.06908e6i 0.0671393i
\(761\) 1.64090e7i 1.02712i 0.858053 + 0.513561i \(0.171674\pi\)
−0.858053 + 0.513561i \(0.828326\pi\)
\(762\) 4.59577e6 + 1.49792e7i 0.286729 + 0.934548i
\(763\) 2.04505e6i 0.127172i
\(764\) 1.74235e7 1.07995
\(765\) 2.68430e6 1.81830e6i 0.165836 0.112334i
\(766\) 1.98647e6i 0.122324i
\(767\) 6.06928e6 4.12477e6i 0.372519 0.253170i
\(768\) −397046. 1.29411e6i −0.0242906 0.0791714i
\(769\) 4.53309e6i 0.276426i 0.990403 + 0.138213i \(0.0441358\pi\)
−0.990403 + 0.138213i \(0.955864\pi\)
\(770\) 4.54814e6i 0.276444i
\(771\) 2.70803e7 8.30850e6i 1.64065 0.503369i
\(772\) 6.88061e6 0.415512
\(773\) −1.52665e7 −0.918948 −0.459474 0.888191i \(-0.651962\pi\)
−0.459474 + 0.888191i \(0.651962\pi\)
\(774\) −1.70514e7 2.51725e7i −1.02308 1.51034i
\(775\) 7.98073e6i 0.477296i
\(776\) 2.46375e6i 0.146873i
\(777\) −1.06032e7 + 3.25316e6i −0.630061 + 0.193309i
\(778\) 4.42223e7i 2.61934i
\(779\) 1.58349e7i 0.934916i