Properties

Label 177.7.c.a.58.16
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.16
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.45

$q$-expansion

\(f(q)\) \(=\) \(q-8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} -138.972i q^{6} -256.162 q^{7} -432.577i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} -138.972i q^{6} -256.162 q^{7} -432.577i q^{8} +243.000 q^{9} -1565.81i q^{10} -678.296i q^{11} -241.276 q^{12} -219.397i q^{13} +2283.69i q^{14} +2737.91 q^{15} -4847.02 q^{16} +1384.65 q^{17} -2166.35i q^{18} -9224.48 q^{19} -2718.49 q^{20} -3993.17 q^{21} -6047.03 q^{22} -14351.5i q^{23} -6743.20i q^{24} +15223.4 q^{25} -1955.93 q^{26} +3788.00 q^{27} +3964.84 q^{28} +34382.4 q^{29} -24408.6i q^{30} -22681.2i q^{31} +15526.5i q^{32} -10573.6i q^{33} -12344.2i q^{34} -44991.6 q^{35} -3761.12 q^{36} -50818.4i q^{37} +82236.5i q^{38} -3420.06i q^{39} -75976.5i q^{40} +111962. q^{41} +35599.2i q^{42} -5490.26i q^{43} +10498.6i q^{44} +42679.8 q^{45} -127944. q^{46} -114737. i q^{47} -75557.6 q^{48} -52030.1 q^{49} -135717. i q^{50} +21584.5 q^{51} +3395.80i q^{52} +74936.6 q^{53} -33770.1i q^{54} -119134. i q^{55} +110810. i q^{56} -143795. q^{57} -306521. i q^{58} +(-175598. + 106518. i) q^{59} -42377.1 q^{60} -190413. i q^{61} -202203. q^{62} -62247.3 q^{63} -171790. q^{64} -38534.3i q^{65} -94263.9 q^{66} +421892. i q^{67} -21431.4 q^{68} -223717. i q^{69} +401101. i q^{70} -35267.8 q^{71} -105116. i q^{72} +698205. i q^{73} -453048. q^{74} +237310. q^{75} +142775. q^{76} +173754. i q^{77} -30490.0 q^{78} +263165. q^{79} -851317. q^{80} +59049.0 q^{81} -998142. i q^{82} +251366. i q^{83} +61805.7 q^{84} +243196. q^{85} -48945.9 q^{86} +535969. q^{87} -293415. q^{88} +429340. i q^{89} -380492. i q^{90} +56201.1i q^{91} +222130. i q^{92} -353565. i q^{93} -1.02288e6 q^{94} -1.62016e6 q^{95} +242033. i q^{96} +198287. i q^{97} +463850. i q^{98} -164826. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.91504i 1.11438i −0.830385 0.557190i \(-0.811880\pi\)
0.830385 0.557190i \(-0.188120\pi\)
\(3\) 15.5885 0.577350
\(4\) −15.4779 −0.241842
\(5\) 175.637 1.40510 0.702549 0.711635i \(-0.252045\pi\)
0.702549 + 0.711635i \(0.252045\pi\)
\(6\) 138.972i 0.643387i
\(7\) −256.162 −0.746827 −0.373414 0.927665i \(-0.621813\pi\)
−0.373414 + 0.927665i \(0.621813\pi\)
\(8\) 432.577i 0.844876i
\(9\) 243.000 0.333333
\(10\) 1565.81i 1.56581i
\(11\) 678.296i 0.509614i −0.966992 0.254807i \(-0.917988\pi\)
0.966992 0.254807i \(-0.0820119\pi\)
\(12\) −241.276 −0.139627
\(13\) 219.397i 0.0998621i −0.998753 0.0499310i \(-0.984100\pi\)
0.998753 0.0499310i \(-0.0159002\pi\)
\(14\) 2283.69i 0.832249i
\(15\) 2737.91 0.811234
\(16\) −4847.02 −1.18335
\(17\) 1384.65 0.281833 0.140917 0.990021i \(-0.454995\pi\)
0.140917 + 0.990021i \(0.454995\pi\)
\(18\) 2166.35i 0.371460i
\(19\) −9224.48 −1.34487 −0.672436 0.740155i \(-0.734752\pi\)
−0.672436 + 0.740155i \(0.734752\pi\)
\(20\) −2718.49 −0.339811
\(21\) −3993.17 −0.431181
\(22\) −6047.03 −0.567903
\(23\) 14351.5i 1.17954i −0.807571 0.589770i \(-0.799218\pi\)
0.807571 0.589770i \(-0.200782\pi\)
\(24\) 6743.20i 0.487789i
\(25\) 15223.4 0.974300
\(26\) −1955.93 −0.111284
\(27\) 3788.00 0.192450
\(28\) 3964.84 0.180614
\(29\) 34382.4 1.40975 0.704876 0.709331i \(-0.251003\pi\)
0.704876 + 0.709331i \(0.251003\pi\)
\(30\) 24408.6i 0.904022i
\(31\) 22681.2i 0.761343i −0.924710 0.380672i \(-0.875693\pi\)
0.924710 0.380672i \(-0.124307\pi\)
\(32\) 15526.5i 0.473830i
\(33\) 10573.6i 0.294226i
\(34\) 12344.2i 0.314069i
\(35\) −44991.6 −1.04937
\(36\) −3761.12 −0.0806139
\(37\) 50818.4i 1.00326i −0.865081 0.501632i \(-0.832733\pi\)
0.865081 0.501632i \(-0.167267\pi\)
\(38\) 82236.5i 1.49870i
\(39\) 3420.06i 0.0576554i
\(40\) 75976.5i 1.18713i
\(41\) 111962. 1.62449 0.812246 0.583315i \(-0.198245\pi\)
0.812246 + 0.583315i \(0.198245\pi\)
\(42\) 35599.2i 0.480499i
\(43\) 5490.26i 0.0690538i −0.999404 0.0345269i \(-0.989008\pi\)
0.999404 0.0345269i \(-0.0109924\pi\)
\(44\) 10498.6i 0.123246i
\(45\) 42679.8 0.468366
\(46\) −127944. −1.31445
\(47\) 114737.i 1.10512i −0.833473 0.552561i \(-0.813651\pi\)
0.833473 0.552561i \(-0.186349\pi\)
\(48\) −75557.6 −0.683210
\(49\) −52030.1 −0.442249
\(50\) 135717.i 1.08574i
\(51\) 21584.5 0.162717
\(52\) 3395.80i 0.0241508i
\(53\) 74936.6 0.503346 0.251673 0.967812i \(-0.419019\pi\)
0.251673 + 0.967812i \(0.419019\pi\)
\(54\) 33770.1i 0.214462i
\(55\) 119134.i 0.716057i
\(56\) 110810.i 0.630977i
\(57\) −143795. −0.776462
\(58\) 306521.i 1.57100i
\(59\) −175598. + 106518.i −0.854993 + 0.518639i
\(60\) −42377.1 −0.196190
\(61\) 190413.i 0.838896i −0.907779 0.419448i \(-0.862224\pi\)
0.907779 0.419448i \(-0.137776\pi\)
\(62\) −202203. −0.848425
\(63\) −62247.3 −0.248942
\(64\) −171790. −0.655328
\(65\) 38534.3i 0.140316i
\(66\) −94263.9 −0.327879
\(67\) 421892.i 1.40274i 0.712798 + 0.701370i \(0.247428\pi\)
−0.712798 + 0.701370i \(0.752572\pi\)
\(68\) −21431.4 −0.0681591
\(69\) 223717.i 0.681007i
\(70\) 401101.i 1.16939i
\(71\) −35267.8 −0.0985379 −0.0492689 0.998786i \(-0.515689\pi\)
−0.0492689 + 0.998786i \(0.515689\pi\)
\(72\) 105116.i 0.281625i
\(73\) 698205.i 1.79479i 0.441226 + 0.897396i \(0.354544\pi\)
−0.441226 + 0.897396i \(0.645456\pi\)
\(74\) −453048. −1.11802
\(75\) 237310. 0.562512
\(76\) 142775. 0.325246
\(77\) 173754.i 0.380594i
\(78\) −30490.0 −0.0642500
\(79\) 263165. 0.533762 0.266881 0.963730i \(-0.414007\pi\)
0.266881 + 0.963730i \(0.414007\pi\)
\(80\) −851317. −1.66273
\(81\) 59049.0 0.111111
\(82\) 998142.i 1.81030i
\(83\) 251366.i 0.439615i 0.975543 + 0.219807i \(0.0705429\pi\)
−0.975543 + 0.219807i \(0.929457\pi\)
\(84\) 61805.7 0.104278
\(85\) 243196. 0.396004
\(86\) −48945.9 −0.0769521
\(87\) 535969. 0.813921
\(88\) −293415. −0.430560
\(89\) 429340.i 0.609019i 0.952509 + 0.304510i \(0.0984926\pi\)
−0.952509 + 0.304510i \(0.901507\pi\)
\(90\) 380492.i 0.521937i
\(91\) 56201.1i 0.0745798i
\(92\) 222130.i 0.285262i
\(93\) 353565.i 0.439562i
\(94\) −1.02288e6 −1.23152
\(95\) −1.62016e6 −1.88968
\(96\) 242033.i 0.273566i
\(97\) 198287.i 0.217260i 0.994082 + 0.108630i \(0.0346464\pi\)
−0.994082 + 0.108630i \(0.965354\pi\)
\(98\) 463850.i 0.492833i
\(99\) 164826.i 0.169871i
\(100\) −235626. −0.235626
\(101\) 1.38896e6i 1.34811i −0.738680 0.674056i \(-0.764551\pi\)
0.738680 0.674056i \(-0.235449\pi\)
\(102\) 192427.i 0.181328i
\(103\) 213622.i 0.195495i 0.995211 + 0.0977473i \(0.0311637\pi\)
−0.995211 + 0.0977473i \(0.968836\pi\)
\(104\) −94906.0 −0.0843711
\(105\) −701349. −0.605852
\(106\) 668063.i 0.560918i
\(107\) −1.16918e6 −0.954402 −0.477201 0.878794i \(-0.658349\pi\)
−0.477201 + 0.878794i \(0.658349\pi\)
\(108\) −58630.1 −0.0465425
\(109\) 622536.i 0.480712i −0.970685 0.240356i \(-0.922736\pi\)
0.970685 0.240356i \(-0.0772642\pi\)
\(110\) −1.06208e6 −0.797959
\(111\) 792180.i 0.579235i
\(112\) 1.24162e6 0.883762
\(113\) 882546.i 0.611649i 0.952088 + 0.305824i \(0.0989320\pi\)
−0.952088 + 0.305824i \(0.901068\pi\)
\(114\) 1.28194e6i 0.865274i
\(115\) 2.52065e6i 1.65737i
\(116\) −532167. −0.340937
\(117\) 53313.5i 0.0332874i
\(118\) 949608. + 1.56546e6i 0.577961 + 0.952787i
\(119\) −354694. −0.210481
\(120\) 1.18436e6i 0.685392i
\(121\) 1.31148e6 0.740294
\(122\) −1.69754e6 −0.934848
\(123\) 1.74531e6 0.937901
\(124\) 351056.i 0.184125i
\(125\) −70530.1 −0.0361114
\(126\) 554937.i 0.277416i
\(127\) 2.98914e6 1.45927 0.729634 0.683838i \(-0.239691\pi\)
0.729634 + 0.683838i \(0.239691\pi\)
\(128\) 2.52521e6i 1.20411i
\(129\) 85584.7i 0.0398682i
\(130\) −343535. −0.156365
\(131\) 1.34600e6i 0.598732i −0.954138 0.299366i \(-0.903225\pi\)
0.954138 0.299366i \(-0.0967752\pi\)
\(132\) 163657.i 0.0711560i
\(133\) 2.36296e6 1.00439
\(134\) 3.76118e6 1.56318
\(135\) 665313. 0.270411
\(136\) 598966.i 0.238114i
\(137\) 1.88396e6 0.732673 0.366336 0.930483i \(-0.380612\pi\)
0.366336 + 0.930483i \(0.380612\pi\)
\(138\) −1.99445e6 −0.758901
\(139\) −860345. −0.320353 −0.160176 0.987088i \(-0.551206\pi\)
−0.160176 + 0.987088i \(0.551206\pi\)
\(140\) 696373. 0.253780
\(141\) 1.78857e6i 0.638042i
\(142\) 314414.i 0.109809i
\(143\) −148816. −0.0508911
\(144\) −1.17783e6 −0.394451
\(145\) 6.03884e6 1.98084
\(146\) 6.22452e6 2.00008
\(147\) −811069. −0.255332
\(148\) 786560.i 0.242631i
\(149\) 2.72310e6i 0.823199i 0.911365 + 0.411599i \(0.135030\pi\)
−0.911365 + 0.411599i \(0.864970\pi\)
\(150\) 2.11563e6i 0.626852i
\(151\) 825040.i 0.239632i −0.992796 0.119816i \(-0.961770\pi\)
0.992796 0.119816i \(-0.0382304\pi\)
\(152\) 3.99029e6i 1.13625i
\(153\) 336469. 0.0939445
\(154\) 1.54902e6 0.424126
\(155\) 3.98366e6i 1.06976i
\(156\) 52935.3i 0.0139435i
\(157\) 5.37648e6i 1.38931i 0.719343 + 0.694655i \(0.244443\pi\)
−0.719343 + 0.694655i \(0.755557\pi\)
\(158\) 2.34613e6i 0.594813i
\(159\) 1.16815e6 0.290607
\(160\) 2.72702e6i 0.665777i
\(161\) 3.67630e6i 0.880913i
\(162\) 526424.i 0.123820i
\(163\) 5193.54 0.00119923 0.000599613 1.00000i \(-0.499809\pi\)
0.000599613 1.00000i \(0.499809\pi\)
\(164\) −1.73293e6 −0.392870
\(165\) 1.85712e6i 0.413416i
\(166\) 2.24094e6 0.489898
\(167\) −2.00433e6 −0.430347 −0.215174 0.976576i \(-0.569032\pi\)
−0.215174 + 0.976576i \(0.569032\pi\)
\(168\) 1.72735e6i 0.364295i
\(169\) 4.77867e6 0.990028
\(170\) 2.16810e6i 0.441298i
\(171\) −2.24155e6 −0.448291
\(172\) 84977.5i 0.0167001i
\(173\) 8.23796e6i 1.59104i −0.605926 0.795521i \(-0.707197\pi\)
0.605926 0.795521i \(-0.292803\pi\)
\(174\) 4.77818e6i 0.907016i
\(175\) −3.89966e6 −0.727634
\(176\) 3.28771e6i 0.603054i
\(177\) −2.73730e6 + 1.66044e6i −0.493631 + 0.299436i
\(178\) 3.82758e6 0.678679
\(179\) 1.00882e7i 1.75896i 0.475935 + 0.879481i \(0.342110\pi\)
−0.475935 + 0.879481i \(0.657890\pi\)
\(180\) −660593. −0.113270
\(181\) −1.21608e6 −0.205081 −0.102540 0.994729i \(-0.532697\pi\)
−0.102540 + 0.994729i \(0.532697\pi\)
\(182\) 501035. 0.0831102
\(183\) 2.96825e6i 0.484337i
\(184\) −6.20810e6 −0.996565
\(185\) 8.92560e6i 1.40969i
\(186\) −3.15204e6 −0.489839
\(187\) 939201.i 0.143626i
\(188\) 1.77588e6i 0.267264i
\(189\) −970340. −0.143727
\(190\) 1.44438e7i 2.10582i
\(191\) 5.16473e6i 0.741221i 0.928788 + 0.370610i \(0.120851\pi\)
−0.928788 + 0.370610i \(0.879149\pi\)
\(192\) −2.67795e6 −0.378354
\(193\) 6.15505e6 0.856169 0.428085 0.903739i \(-0.359189\pi\)
0.428085 + 0.903739i \(0.359189\pi\)
\(194\) 1.76774e6 0.242110
\(195\) 600690.i 0.0810115i
\(196\) 805315. 0.106954
\(197\) 1.40188e6 0.183363 0.0916815 0.995788i \(-0.470776\pi\)
0.0916815 + 0.995788i \(0.470776\pi\)
\(198\) −1.46943e6 −0.189301
\(199\) −3.86038e6 −0.489858 −0.244929 0.969541i \(-0.578765\pi\)
−0.244929 + 0.969541i \(0.578765\pi\)
\(200\) 6.58530e6i 0.823163i
\(201\) 6.57665e6i 0.809872i
\(202\) −1.23826e7 −1.50231
\(203\) −8.80747e6 −1.05284
\(204\) −334082. −0.0393517
\(205\) 1.96646e7 2.28257
\(206\) 1.90445e6 0.217855
\(207\) 3.48740e6i 0.393180i
\(208\) 1.06342e6i 0.118172i
\(209\) 6.25693e6i 0.685365i
\(210\) 6.25255e6i 0.675149i
\(211\) 1.32505e6i 0.141054i −0.997510 0.0705269i \(-0.977532\pi\)
0.997510 0.0705269i \(-0.0224680\pi\)
\(212\) −1.15986e6 −0.121730
\(213\) −549770. −0.0568909
\(214\) 1.04233e7i 1.06357i
\(215\) 964294.i 0.0970273i
\(216\) 1.63860e6i 0.162596i
\(217\) 5.81005e6i 0.568592i
\(218\) −5.54993e6 −0.535696
\(219\) 1.08839e7i 1.03622i
\(220\) 1.84394e6i 0.173173i
\(221\) 303788.i 0.0281445i
\(222\) −7.06231e6 −0.645488
\(223\) 1.32277e7 1.19281 0.596403 0.802685i \(-0.296596\pi\)
0.596403 + 0.802685i \(0.296596\pi\)
\(224\) 3.97728e6i 0.353869i
\(225\) 3.69929e6 0.324767
\(226\) 7.86793e6 0.681609
\(227\) 2.00790e7i 1.71659i −0.513160 0.858293i \(-0.671525\pi\)
0.513160 0.858293i \(-0.328475\pi\)
\(228\) 2.22565e6 0.187781
\(229\) 2.04020e7i 1.69889i 0.527675 + 0.849446i \(0.323064\pi\)
−0.527675 + 0.849446i \(0.676936\pi\)
\(230\) −2.24717e7 −1.84694
\(231\) 2.70855e6i 0.219736i
\(232\) 1.48730e7i 1.19107i
\(233\) 1.71127e7i 1.35285i 0.736511 + 0.676426i \(0.236472\pi\)
−0.736511 + 0.676426i \(0.763528\pi\)
\(234\) −475292. −0.0370948
\(235\) 2.01521e7i 1.55280i
\(236\) 2.71788e6 1.64866e6i 0.206773 0.125429i
\(237\) 4.10234e6 0.308167
\(238\) 3.16211e6i 0.234556i
\(239\) 1.54360e7 1.13068 0.565341 0.824858i \(-0.308745\pi\)
0.565341 + 0.824858i \(0.308745\pi\)
\(240\) −1.32707e7 −0.959977
\(241\) 9.78176e6 0.698821 0.349410 0.936970i \(-0.386382\pi\)
0.349410 + 0.936970i \(0.386382\pi\)
\(242\) 1.16919e7i 0.824968i
\(243\) 920483. 0.0641500
\(244\) 2.94719e6i 0.202880i
\(245\) −9.13843e6 −0.621403
\(246\) 1.55595e7i 1.04518i
\(247\) 2.02382e6i 0.134302i
\(248\) −9.81134e6 −0.643241
\(249\) 3.91841e6i 0.253812i
\(250\) 628778.i 0.0402418i
\(251\) 880652. 0.0556908 0.0278454 0.999612i \(-0.491135\pi\)
0.0278454 + 0.999612i \(0.491135\pi\)
\(252\) 963456. 0.0602047
\(253\) −9.73454e6 −0.601110
\(254\) 2.66483e7i 1.62618i
\(255\) 3.79105e6 0.228633
\(256\) 1.15178e7 0.686512
\(257\) 2.44085e7 1.43794 0.718971 0.695040i \(-0.244614\pi\)
0.718971 + 0.695040i \(0.244614\pi\)
\(258\) −762990. −0.0444283
\(259\) 1.30177e7i 0.749266i
\(260\) 596429.i 0.0339343i
\(261\) 8.35493e6 0.469917
\(262\) −1.19997e7 −0.667215
\(263\) −3.37403e6 −0.185474 −0.0927368 0.995691i \(-0.529562\pi\)
−0.0927368 + 0.995691i \(0.529562\pi\)
\(264\) −4.57389e6 −0.248584
\(265\) 1.31617e7 0.707250
\(266\) 2.10659e7i 1.11927i
\(267\) 6.69274e6i 0.351617i
\(268\) 6.52999e6i 0.339241i
\(269\) 2.59519e7i 1.33325i −0.745392 0.666626i \(-0.767738\pi\)
0.745392 0.666626i \(-0.232262\pi\)
\(270\) 5.93129e6i 0.301341i
\(271\) −6.90104e6 −0.346742 −0.173371 0.984857i \(-0.555466\pi\)
−0.173371 + 0.984857i \(0.555466\pi\)
\(272\) −6.71142e6 −0.333509
\(273\) 876089.i 0.0430586i
\(274\) 1.67956e7i 0.816475i
\(275\) 1.03260e7i 0.496517i
\(276\) 3.46266e6i 0.164696i
\(277\) −2.79897e7 −1.31692 −0.658459 0.752617i \(-0.728791\pi\)
−0.658459 + 0.752617i \(0.728791\pi\)
\(278\) 7.67001e6i 0.356994i
\(279\) 5.51153e6i 0.253781i
\(280\) 1.94623e7i 0.886584i
\(281\) −2.13816e7 −0.963654 −0.481827 0.876266i \(-0.660027\pi\)
−0.481827 + 0.876266i \(0.660027\pi\)
\(282\) −1.59452e7 −0.711021
\(283\) 1.30117e7i 0.574082i 0.957918 + 0.287041i \(0.0926715\pi\)
−0.957918 + 0.287041i \(0.907328\pi\)
\(284\) 545870. 0.0238306
\(285\) −2.52558e7 −1.09101
\(286\) 1.32670e6i 0.0567120i
\(287\) −2.86803e7 −1.21322
\(288\) 3.77293e6i 0.157943i
\(289\) −2.22203e7 −0.920570
\(290\) 5.38364e7i 2.20741i
\(291\) 3.09100e6i 0.125435i
\(292\) 1.08067e7i 0.434056i
\(293\) 594514. 0.0236352 0.0118176 0.999930i \(-0.496238\pi\)
0.0118176 + 0.999930i \(0.496238\pi\)
\(294\) 7.23071e6i 0.284537i
\(295\) −3.08415e7 + 1.87084e7i −1.20135 + 0.728738i
\(296\) −2.19828e7 −0.847634
\(297\) 2.56938e6i 0.0980752i
\(298\) 2.42765e7 0.917356
\(299\) −3.14867e6 −0.117791
\(300\) −3.67305e6 −0.136039
\(301\) 1.40639e6i 0.0515713i
\(302\) −7.35526e6 −0.267040
\(303\) 2.16518e7i 0.778333i
\(304\) 4.47112e7 1.59146
\(305\) 3.34437e7i 1.17873i
\(306\) 2.99964e6i 0.104690i
\(307\) 3.44659e7 1.19117 0.595585 0.803292i \(-0.296920\pi\)
0.595585 + 0.803292i \(0.296920\pi\)
\(308\) 2.68933e6i 0.0920434i
\(309\) 3.33004e6i 0.112869i
\(310\) −3.55145e7 −1.19212
\(311\) 3.44883e7 1.14654 0.573272 0.819365i \(-0.305674\pi\)
0.573272 + 0.819365i \(0.305674\pi\)
\(312\) −1.47944e6 −0.0487117
\(313\) 2.97001e7i 0.968558i 0.874914 + 0.484279i \(0.160918\pi\)
−0.874914 + 0.484279i \(0.839082\pi\)
\(314\) 4.79315e7 1.54822
\(315\) −1.09329e7 −0.349789
\(316\) −4.07324e6 −0.129086
\(317\) 4.48502e7 1.40795 0.703973 0.710226i \(-0.251407\pi\)
0.703973 + 0.710226i \(0.251407\pi\)
\(318\) 1.04141e7i 0.323846i
\(319\) 2.33215e7i 0.718429i
\(320\) −3.01728e7 −0.920800
\(321\) −1.82258e7 −0.551024
\(322\) 3.27743e7 0.981671
\(323\) −1.27727e7 −0.379030
\(324\) −913953. −0.0268713
\(325\) 3.33998e6i 0.0972956i
\(326\) 46300.6i 0.00133639i
\(327\) 9.70438e6i 0.277539i
\(328\) 4.84320e7i 1.37249i
\(329\) 2.93912e7i 0.825335i
\(330\) −1.65563e7 −0.460702
\(331\) −2.90849e6 −0.0802018 −0.0401009 0.999196i \(-0.512768\pi\)
−0.0401009 + 0.999196i \(0.512768\pi\)
\(332\) 3.89061e6i 0.106317i
\(333\) 1.23489e7i 0.334422i
\(334\) 1.78686e7i 0.479570i
\(335\) 7.40999e7i 1.97099i
\(336\) 1.93550e7 0.510240
\(337\) 4.52124e7i 1.18132i −0.806921 0.590660i \(-0.798868\pi\)
0.806921 0.590660i \(-0.201132\pi\)
\(338\) 4.26021e7i 1.10327i
\(339\) 1.37575e7i 0.353135i
\(340\) −3.76415e6 −0.0957702
\(341\) −1.53845e7 −0.387991
\(342\) 1.99835e7i 0.499566i
\(343\) 4.34653e7 1.07711
\(344\) −2.37496e6 −0.0583419
\(345\) 3.92930e7i 0.956882i
\(346\) −7.34417e7 −1.77302
\(347\) 4.88593e7i 1.16939i 0.811253 + 0.584695i \(0.198786\pi\)
−0.811253 + 0.584695i \(0.801214\pi\)
\(348\) −8.29566e6 −0.196840
\(349\) 693047.i 0.0163037i −0.999967 0.00815185i \(-0.997405\pi\)
0.999967 0.00815185i \(-0.00259484\pi\)
\(350\) 3.47656e7i 0.810860i
\(351\) 831075.i 0.0192185i
\(352\) 1.05315e7 0.241470
\(353\) 8.18650e7i 1.86112i 0.366140 + 0.930560i \(0.380679\pi\)
−0.366140 + 0.930560i \(0.619321\pi\)
\(354\) 1.48029e7 + 2.44031e7i 0.333686 + 0.550092i
\(355\) −6.19434e6 −0.138455
\(356\) 6.64527e6i 0.147286i
\(357\) −5.52913e6 −0.121521
\(358\) 8.99370e7 1.96015
\(359\) 5.78879e6 0.125114 0.0625568 0.998041i \(-0.480075\pi\)
0.0625568 + 0.998041i \(0.480075\pi\)
\(360\) 1.84623e7i 0.395711i
\(361\) 3.80451e7 0.808680
\(362\) 1.08414e7i 0.228538i
\(363\) 2.04439e7 0.427409
\(364\) 869874.i 0.0180365i
\(365\) 1.22631e8i 2.52186i
\(366\) −2.64621e7 −0.539735
\(367\) 5.60143e7i 1.13319i 0.823998 + 0.566593i \(0.191739\pi\)
−0.823998 + 0.566593i \(0.808261\pi\)
\(368\) 6.95618e7i 1.39581i
\(369\) 2.72067e7 0.541497
\(370\) −7.95720e7 −1.57092
\(371\) −1.91959e7 −0.375913
\(372\) 5.47243e6i 0.106304i
\(373\) −6.78694e7 −1.30782 −0.653909 0.756573i \(-0.726872\pi\)
−0.653909 + 0.756573i \(0.726872\pi\)
\(374\) −8.37301e6 −0.160054
\(375\) −1.09946e6 −0.0208489
\(376\) −4.96325e7 −0.933691
\(377\) 7.54340e6i 0.140781i
\(378\) 8.65061e6i 0.160166i
\(379\) 3.93573e7 0.722948 0.361474 0.932382i \(-0.382274\pi\)
0.361474 + 0.932382i \(0.382274\pi\)
\(380\) 2.50766e7 0.457003
\(381\) 4.65961e7 0.842508
\(382\) 4.60438e7 0.826001
\(383\) 1.72548e7 0.307123 0.153562 0.988139i \(-0.450926\pi\)
0.153562 + 0.988139i \(0.450926\pi\)
\(384\) 3.93641e7i 0.695196i
\(385\) 3.05176e7i 0.534771i
\(386\) 5.48725e7i 0.954097i
\(387\) 1.33413e6i 0.0230179i
\(388\) 3.06907e6i 0.0525426i
\(389\) −3.77016e7 −0.640488 −0.320244 0.947335i \(-0.603765\pi\)
−0.320244 + 0.947335i \(0.603765\pi\)
\(390\) −5.35517e6 −0.0902775
\(391\) 1.98717e7i 0.332434i
\(392\) 2.25070e7i 0.373645i
\(393\) 2.09821e7i 0.345678i
\(394\) 1.24978e7i 0.204336i
\(395\) 4.62216e7 0.749987
\(396\) 2.55115e6i 0.0410820i
\(397\) 4.78319e6i 0.0764445i 0.999269 + 0.0382222i \(0.0121695\pi\)
−0.999269 + 0.0382222i \(0.987831\pi\)
\(398\) 3.44154e7i 0.545888i
\(399\) 3.68349e7 0.579883
\(400\) −7.37883e7 −1.15294
\(401\) 3.14396e7i 0.487577i −0.969828 0.243789i \(-0.921610\pi\)
0.969828 0.243789i \(-0.0783903\pi\)
\(402\) 5.86310e7 0.902505
\(403\) −4.97618e6 −0.0760293
\(404\) 2.14982e7i 0.326030i
\(405\) 1.03712e7 0.156122
\(406\) 7.85189e7i 1.17326i
\(407\) −3.44699e7 −0.511278
\(408\) 9.33696e6i 0.137475i
\(409\) 1.12711e8i 1.64739i −0.567033 0.823695i \(-0.691909\pi\)
0.567033 0.823695i \(-0.308091\pi\)
\(410\) 1.75311e8i 2.54365i
\(411\) 2.93680e7 0.423009
\(412\) 3.30642e6i 0.0472788i
\(413\) 4.49814e7 2.72857e7i 0.638533 0.387334i
\(414\) −3.10903e7 −0.438152
\(415\) 4.41492e7i 0.617702i
\(416\) 3.40646e6 0.0473176
\(417\) −1.34115e7 −0.184956
\(418\) 5.57807e7 0.763757
\(419\) 3.52543e7i 0.479259i 0.970864 + 0.239630i \(0.0770260\pi\)
−0.970864 + 0.239630i \(0.922974\pi\)
\(420\) 1.08554e7 0.146520
\(421\) 8.97239e7i 1.20244i −0.799085 0.601218i \(-0.794682\pi\)
0.799085 0.601218i \(-0.205318\pi\)
\(422\) −1.18129e7 −0.157187
\(423\) 2.78811e7i 0.368374i
\(424\) 3.24158e7i 0.425265i
\(425\) 2.10791e7 0.274590
\(426\) 4.90122e6i 0.0633980i
\(427\) 4.87766e7i 0.626510i
\(428\) 1.80965e7 0.230814
\(429\) −2.31981e6 −0.0293820
\(430\) −8.59671e6 −0.108125
\(431\) 9.58317e7i 1.19695i 0.801140 + 0.598477i \(0.204227\pi\)
−0.801140 + 0.598477i \(0.795773\pi\)
\(432\) −1.83605e7 −0.227737
\(433\) −2.93429e7 −0.361443 −0.180721 0.983534i \(-0.557843\pi\)
−0.180721 + 0.983534i \(0.557843\pi\)
\(434\) 5.17968e7 0.633627
\(435\) 9.41361e7 1.14364
\(436\) 9.63553e6i 0.116256i
\(437\) 1.32385e8i 1.58633i
\(438\) 9.70307e7 1.15475
\(439\) 1.15409e8 1.36410 0.682050 0.731305i \(-0.261089\pi\)
0.682050 + 0.731305i \(0.261089\pi\)
\(440\) −5.15346e7 −0.604980
\(441\) −1.26433e7 −0.147416
\(442\) −2.70828e6 −0.0313636
\(443\) 6.74042e7i 0.775311i 0.921804 + 0.387656i \(0.126715\pi\)
−0.921804 + 0.387656i \(0.873285\pi\)
\(444\) 1.22613e7i 0.140083i
\(445\) 7.54080e7i 0.855732i
\(446\) 1.17925e8i 1.32924i
\(447\) 4.24489e7i 0.475274i
\(448\) 4.40061e7 0.489417
\(449\) 1.13935e8 1.25869 0.629346 0.777125i \(-0.283323\pi\)
0.629346 + 0.777125i \(0.283323\pi\)
\(450\) 3.29793e7i 0.361913i
\(451\) 7.59431e7i 0.827864i
\(452\) 1.36599e7i 0.147922i
\(453\) 1.28611e7i 0.138351i
\(454\) −1.79005e8 −1.91293
\(455\) 9.87101e6i 0.104792i
\(456\) 6.22025e7i 0.656014i
\(457\) 4.52840e7i 0.474456i 0.971454 + 0.237228i \(0.0762388\pi\)
−0.971454 + 0.237228i \(0.923761\pi\)
\(458\) 1.81884e8 1.89321
\(459\) 5.24504e6 0.0542389
\(460\) 3.90143e7i 0.400821i
\(461\) 2.51264e7 0.256465 0.128232 0.991744i \(-0.459070\pi\)
0.128232 + 0.991744i \(0.459070\pi\)
\(462\) 2.41468e7 0.244869
\(463\) 1.56900e8i 1.58081i −0.612584 0.790405i \(-0.709870\pi\)
0.612584 0.790405i \(-0.290130\pi\)
\(464\) −1.66652e8 −1.66824
\(465\) 6.20991e7i 0.617627i
\(466\) 1.52560e8 1.50759
\(467\) 1.05635e8i 1.03719i −0.855021 0.518593i \(-0.826456\pi\)
0.855021 0.518593i \(-0.173544\pi\)
\(468\) 825179.i 0.00805027i
\(469\) 1.08073e8i 1.04760i
\(470\) −1.79657e8 −1.73041
\(471\) 8.38110e7i 0.802118i
\(472\) 4.60770e7 + 7.59594e7i 0.438186 + 0.722363i
\(473\) −3.72402e6 −0.0351908
\(474\) 3.65725e7i 0.343416i
\(475\) −1.40428e8 −1.31031
\(476\) 5.48991e6 0.0509031
\(477\) 1.82096e7 0.167782
\(478\) 1.37612e8i 1.26001i
\(479\) 2.49010e7 0.226574 0.113287 0.993562i \(-0.463862\pi\)
0.113287 + 0.993562i \(0.463862\pi\)
\(480\) 4.25101e7i 0.384387i
\(481\) −1.11494e7 −0.100188
\(482\) 8.72048e7i 0.778752i
\(483\) 5.73078e7i 0.508595i
\(484\) −2.02988e7 −0.179034
\(485\) 3.48267e7i 0.305272i
\(486\) 8.20614e6i 0.0714875i
\(487\) 2.58850e7 0.224110 0.112055 0.993702i \(-0.464257\pi\)
0.112055 + 0.993702i \(0.464257\pi\)
\(488\) −8.23684e7 −0.708763
\(489\) 80959.3 0.000692373
\(490\) 8.14694e7i 0.692478i
\(491\) 2.98001e7 0.251753 0.125876 0.992046i \(-0.459826\pi\)
0.125876 + 0.992046i \(0.459826\pi\)
\(492\) −2.70137e7 −0.226824
\(493\) 4.76076e7 0.397315
\(494\) 1.80425e7 0.149663
\(495\) 2.89496e7i 0.238686i
\(496\) 1.09936e8i 0.900939i
\(497\) 9.03426e6 0.0735908
\(498\) 3.49327e7 0.282842
\(499\) −7.82912e7 −0.630103 −0.315051 0.949075i \(-0.602022\pi\)
−0.315051 + 0.949075i \(0.602022\pi\)
\(500\) 1.09166e6 0.00873325
\(501\) −3.12443e7 −0.248461
\(502\) 7.85105e6i 0.0620607i
\(503\) 2.05439e7i 0.161428i −0.996737 0.0807140i \(-0.974280\pi\)
0.996737 0.0807140i \(-0.0257200\pi\)
\(504\) 2.69267e7i 0.210326i
\(505\) 2.43953e8i 1.89423i
\(506\) 8.67837e7i 0.669864i
\(507\) 7.44922e7 0.571593
\(508\) −4.62655e7 −0.352912
\(509\) 1.35190e8i 1.02516i 0.858639 + 0.512581i \(0.171311\pi\)
−0.858639 + 0.512581i \(0.828689\pi\)
\(510\) 3.37973e7i 0.254784i
\(511\) 1.78853e8i 1.34040i
\(512\) 5.89322e7i 0.439079i
\(513\) −3.49423e7 −0.258821
\(514\) 2.17602e8i 1.60241i
\(515\) 3.75200e7i 0.274689i
\(516\) 1.32467e6i 0.00964180i
\(517\) −7.78257e7 −0.563185
\(518\) 1.16054e8 0.834966
\(519\) 1.28417e8i 0.918588i
\(520\) −1.66690e7 −0.118550
\(521\) −2.04501e8 −1.44604 −0.723022 0.690825i \(-0.757248\pi\)
−0.723022 + 0.690825i \(0.757248\pi\)
\(522\) 7.44845e7i 0.523666i
\(523\) 1.61277e8 1.12737 0.563686 0.825989i \(-0.309383\pi\)
0.563686 + 0.825989i \(0.309383\pi\)
\(524\) 2.08333e7i 0.144798i
\(525\) −6.07897e7 −0.420100
\(526\) 3.00796e7i 0.206688i
\(527\) 3.14054e7i 0.214572i
\(528\) 5.12504e7i 0.348173i
\(529\) −5.79285e7 −0.391314
\(530\) 1.17337e8i 0.788145i
\(531\) −4.26702e7 + 2.58838e7i −0.284998 + 0.172880i
\(532\) −3.65736e7 −0.242903
\(533\) 2.45640e7i 0.162225i
\(534\) 5.96661e7 0.391835
\(535\) −2.05352e8 −1.34103
\(536\) 1.82501e8 1.18514
\(537\) 1.57260e8i 1.01554i
\(538\) −2.31362e8 −1.48575
\(539\) 3.52918e7i 0.225376i
\(540\) −1.02976e7 −0.0653967
\(541\) 1.33762e8i 0.844772i −0.906416 0.422386i \(-0.861193\pi\)
0.906416 0.422386i \(-0.138807\pi\)
\(542\) 6.15230e7i 0.386402i
\(543\) −1.89567e7 −0.118403
\(544\) 2.14987e7i 0.133541i
\(545\) 1.09340e8i 0.675447i
\(546\) 7.81037e6 0.0479837
\(547\) −2.40525e8 −1.46959 −0.734797 0.678287i \(-0.762723\pi\)
−0.734797 + 0.678287i \(0.762723\pi\)
\(548\) −2.91597e7 −0.177191
\(549\) 4.62705e7i 0.279632i
\(550\) −9.20566e7 −0.553308
\(551\) −3.17160e8 −1.89594
\(552\) −9.67748e7 −0.575367
\(553\) −6.74129e7 −0.398628
\(554\) 2.49529e8i 1.46755i
\(555\) 1.39136e8i 0.813882i
\(556\) 1.33163e7 0.0774746
\(557\) 5.88909e7 0.340787 0.170393 0.985376i \(-0.445496\pi\)
0.170393 + 0.985376i \(0.445496\pi\)
\(558\) −4.91354e7 −0.282808
\(559\) −1.20455e6 −0.00689585
\(560\) 2.18075e8 1.24177
\(561\) 1.46407e7i 0.0829226i
\(562\) 1.90618e8i 1.07388i
\(563\) 8.90157e7i 0.498817i −0.968398 0.249409i \(-0.919764\pi\)
0.968398 0.249409i \(-0.0802363\pi\)
\(564\) 2.76833e7i 0.154305i
\(565\) 1.55008e8i 0.859426i
\(566\) 1.15999e8 0.639745
\(567\) −1.51261e7 −0.0829808
\(568\) 1.52560e7i 0.0832523i
\(569\) 3.46633e8i 1.88162i −0.338929 0.940812i \(-0.610065\pi\)
0.338929 0.940812i \(-0.389935\pi\)
\(570\) 2.25157e8i 1.21579i
\(571\) 3.04837e7i 0.163741i 0.996643 + 0.0818707i \(0.0260895\pi\)
−0.996643 + 0.0818707i \(0.973911\pi\)
\(572\) 2.30336e6 0.0123076
\(573\) 8.05102e7i 0.427944i
\(574\) 2.55686e8i 1.35198i
\(575\) 2.18478e8i 1.14923i
\(576\) −4.17451e7 −0.218443
\(577\) −4.21117e7 −0.219217 −0.109609 0.993975i \(-0.534960\pi\)
−0.109609 + 0.993975i \(0.534960\pi\)
\(578\) 1.98095e8i 1.02586i
\(579\) 9.59477e7 0.494309
\(580\) −9.34683e7 −0.479050
\(581\) 6.43904e7i 0.328316i
\(582\) 2.75563e7 0.139782
\(583\) 5.08292e7i 0.256512i
\(584\) 3.02027e8 1.51638
\(585\) 9.36383e6i 0.0467720i
\(586\) 5.30011e6i 0.0263386i
\(587\) 1.34414e8i 0.664554i 0.943182 + 0.332277i \(0.107817\pi\)
−0.943182 + 0.332277i \(0.892183\pi\)
\(588\) 1.25536e7 0.0617500
\(589\) 2.09222e8i 1.02391i
\(590\) 1.66786e8 + 2.74953e8i 0.812091 + 1.33876i
\(591\) 2.18531e7 0.105865
\(592\) 2.46318e8i 1.18722i
\(593\) −6.13574e7 −0.294241 −0.147120 0.989119i \(-0.547000\pi\)
−0.147120 + 0.989119i \(0.547000\pi\)
\(594\) −2.29061e7 −0.109293
\(595\) −6.22975e7 −0.295746
\(596\) 4.21478e7i 0.199084i
\(597\) −6.01773e7 −0.282820
\(598\) 2.80705e7i 0.131264i
\(599\) 8.23867e6 0.0383333 0.0191667 0.999816i \(-0.493899\pi\)
0.0191667 + 0.999816i \(0.493899\pi\)
\(600\) 1.02655e8i 0.475253i
\(601\) 4.33229e7i 0.199569i 0.995009 + 0.0997847i \(0.0318154\pi\)
−0.995009 + 0.0997847i \(0.968185\pi\)
\(602\) 1.25381e7 0.0574700
\(603\) 1.02520e8i 0.467580i
\(604\) 1.27699e7i 0.0579529i
\(605\) 2.30344e8 1.04019
\(606\) −1.93026e8 −0.867358
\(607\) −1.49938e8 −0.670417 −0.335209 0.942144i \(-0.608807\pi\)
−0.335209 + 0.942144i \(0.608807\pi\)
\(608\) 1.43223e8i 0.637240i
\(609\) −1.37295e8 −0.607858
\(610\) −2.98152e8 −1.31355
\(611\) −2.51730e7 −0.110360
\(612\) −5.20783e6 −0.0227197
\(613\) 2.33739e8i 1.01473i −0.861732 0.507363i \(-0.830620\pi\)
0.861732 0.507363i \(-0.169380\pi\)
\(614\) 3.07264e8i 1.32742i
\(615\) 3.06541e8 1.31784
\(616\) 7.51617e7 0.321554
\(617\) −3.31897e8 −1.41302 −0.706510 0.707703i \(-0.749731\pi\)
−0.706510 + 0.707703i \(0.749731\pi\)
\(618\) 2.96874e7 0.125779
\(619\) 4.22537e8 1.78153 0.890765 0.454464i \(-0.150169\pi\)
0.890765 + 0.454464i \(0.150169\pi\)
\(620\) 6.16586e7i 0.258713i
\(621\) 5.43633e7i 0.227002i
\(622\) 3.07465e8i 1.27769i
\(623\) 1.09980e8i 0.454832i
\(624\) 1.65771e7i 0.0682268i
\(625\) −2.50254e8 −1.02504
\(626\) 2.64778e8 1.07934
\(627\) 9.75358e7i 0.395696i
\(628\) 8.32164e7i 0.335993i
\(629\) 7.03656e7i 0.282754i
\(630\) 9.74676e7i 0.389797i
\(631\) −3.42333e8 −1.36257 −0.681287 0.732016i \(-0.738580\pi\)
−0.681287 + 0.732016i \(0.738580\pi\)
\(632\) 1.13839e8i 0.450962i
\(633\) 2.06555e7i 0.0814374i
\(634\) 3.99841e8i 1.56899i
\(635\) 5.25004e8 2.05041
\(636\) −1.80804e7 −0.0702809
\(637\) 1.14153e7i 0.0441639i
\(638\) −2.07912e8 −0.800603
\(639\) −8.57007e6 −0.0328460
\(640\) 4.43521e8i 1.69190i
\(641\) −3.46348e8 −1.31504 −0.657519 0.753438i \(-0.728394\pi\)
−0.657519 + 0.753438i \(0.728394\pi\)
\(642\) 1.62483e8i 0.614050i
\(643\) −2.34493e8 −0.882058 −0.441029 0.897493i \(-0.645386\pi\)
−0.441029 + 0.897493i \(0.645386\pi\)
\(644\) 5.69012e7i 0.213041i
\(645\) 1.50319e7i 0.0560187i
\(646\) 1.13869e8i 0.422383i
\(647\) −3.76403e8 −1.38976 −0.694881 0.719125i \(-0.744543\pi\)
−0.694881 + 0.719125i \(0.744543\pi\)
\(648\) 2.55432e7i 0.0938751i
\(649\) 7.22504e7 + 1.19107e8i 0.264306 + 0.435716i
\(650\) −2.97760e7 −0.108424
\(651\) 9.05697e7i 0.328277i
\(652\) −80385.0 −0.000290023
\(653\) 1.07408e8 0.385742 0.192871 0.981224i \(-0.438220\pi\)
0.192871 + 0.981224i \(0.438220\pi\)
\(654\) −8.65149e7 −0.309284
\(655\) 2.36408e8i 0.841277i
\(656\) −5.42680e8 −1.92235
\(657\) 1.69664e8i 0.598264i
\(658\) 2.62024e8 0.919737
\(659\) 2.76117e8i 0.964801i −0.875951 0.482400i \(-0.839765\pi\)
0.875951 0.482400i \(-0.160235\pi\)
\(660\) 2.87442e7i 0.0999812i
\(661\) −4.07007e8 −1.40928 −0.704641 0.709564i \(-0.748892\pi\)
−0.704641 + 0.709564i \(0.748892\pi\)
\(662\) 2.59293e7i 0.0893753i
\(663\) 4.73558e6i 0.0162492i
\(664\) 1.08735e8 0.371420
\(665\) 4.15023e8 1.41126
\(666\) −1.10091e8 −0.372673
\(667\) 4.93438e8i 1.66286i
\(668\) 3.10227e7 0.104076
\(669\) 2.06199e8 0.688667
\(670\) 6.60604e8 2.19643
\(671\) −1.29157e8 −0.427513
\(672\) 6.19997e7i 0.204306i
\(673\) 1.63452e7i 0.0536223i −0.999641 0.0268112i \(-0.991465\pi\)
0.999641 0.0268112i \(-0.00853528\pi\)
\(674\) −4.03070e8 −1.31644
\(675\) 5.76663e7 0.187504
\(676\) −7.39637e7 −0.239430
\(677\) 4.66815e8 1.50445 0.752227 0.658904i \(-0.228980\pi\)
0.752227 + 0.658904i \(0.228980\pi\)
\(678\) 1.22649e8 0.393527
\(679\) 5.07937e7i 0.162256i
\(680\) 1.05201e8i 0.334574i
\(681\) 3.13001e8i 0.991071i
\(682\) 1.37154e8i 0.432369i
\(683\) 7.64516e7i 0.239952i −0.992777 0.119976i \(-0.961718\pi\)
0.992777 0.119976i \(-0.0382818\pi\)
\(684\) 3.46944e7 0.108415
\(685\) 3.30893e8 1.02948
\(686\) 3.87495e8i 1.20031i
\(687\) 3.18035e8i 0.980856i
\(688\) 2.66114e7i 0.0817151i
\(689\) 1.64409e7i 0.0502652i
\(690\) −3.50299e8 −1.06633
\(691\) 1.86619e8i 0.565615i 0.959177 + 0.282807i \(0.0912657\pi\)
−0.959177 + 0.282807i \(0.908734\pi\)
\(692\) 1.27506e8i 0.384780i
\(693\) 4.22221e7i 0.126865i
\(694\) 4.35583e8 1.30314
\(695\) −1.51109e8 −0.450127
\(696\) 2.31848e8i 0.687662i
\(697\) 1.55027e8 0.457836
\(698\) −6.17854e6 −0.0181685
\(699\) 2.66760e8i 0.781069i
\(700\) 6.03585e7 0.175972
\(701\) 2.64441e8i 0.767669i 0.923402 + 0.383835i \(0.125397\pi\)
−0.923402 + 0.383835i \(0.874603\pi\)
\(702\) −7.40906e6 −0.0214167
\(703\) 4.68773e8i 1.34926i
\(704\) 1.16525e8i 0.333964i
\(705\) 3.14140e8i 0.896512i
\(706\) 7.29830e8 2.07399
\(707\) 3.55799e8i 1.00681i
\(708\) 4.23675e7 2.57001e7i 0.119380 0.0724162i
\(709\) −2.07674e8 −0.582697 −0.291348 0.956617i \(-0.594104\pi\)
−0.291348 + 0.956617i \(0.594104\pi\)
\(710\) 5.52227e7i 0.154292i
\(711\) 6.39492e7 0.177921
\(712\) 1.85722e8 0.514546
\(713\) −3.25508e8 −0.898034
\(714\) 4.92924e7i 0.135421i
\(715\) −2.61376e7 −0.0715070
\(716\) 1.56144e8i 0.425390i
\(717\) 2.40623e8 0.652799
\(718\) 5.16072e7i 0.139424i
\(719\) 5.52111e8i 1.48539i −0.669631 0.742694i \(-0.733548\pi\)
0.669631 0.742694i \(-0.266452\pi\)
\(720\) −2.06870e8 −0.554243
\(721\) 5.47219e7i 0.146001i
\(722\) 3.39173e8i 0.901177i
\(723\) 1.52483e8 0.403464
\(724\) 1.88223e7 0.0495971
\(725\) 5.23419e8 1.37352
\(726\) 1.82258e8i 0.476296i
\(727\) −1.55964e8 −0.405902 −0.202951 0.979189i \(-0.565053\pi\)
−0.202951 + 0.979189i \(0.565053\pi\)
\(728\) 2.43113e7 0.0630106
\(729\) 1.43489e7 0.0370370
\(730\) 1.09326e9 2.81031
\(731\) 7.60207e6i 0.0194617i
\(732\) 4.59422e7i 0.117133i
\(733\) 7.36970e8 1.87128 0.935638 0.352962i \(-0.114825\pi\)
0.935638 + 0.352962i \(0.114825\pi\)
\(734\) 4.99370e8 1.26280
\(735\) −1.42454e8 −0.358767
\(736\) 2.22827e8 0.558901
\(737\) 2.86168e8 0.714855
\(738\) 2.42549e8i 0.603434i
\(739\) 3.38338e8i 0.838336i −0.907909 0.419168i \(-0.862322\pi\)
0.907909 0.419168i \(-0.137678\pi\)
\(740\) 1.38149e8i 0.340921i
\(741\) 3.15483e7i 0.0775391i
\(742\) 1.71132e8i 0.418909i
\(743\) −5.92755e8 −1.44514 −0.722568 0.691300i \(-0.757038\pi\)
−0.722568 + 0.691300i \(0.757038\pi\)
\(744\) −1.52944e8 −0.371375
\(745\) 4.78278e8i 1.15667i
\(746\) 6.05058e8i 1.45741i
\(747\) 6.10819e7i 0.146538i
\(748\) 1.45368e7i 0.0347348i
\(749\) 2.99500e8 0.712773
\(750\) 9.80168e6i 0.0232336i
\(751\) 5.01083e8i 1.18301i 0.806300 + 0.591507i \(0.201467\pi\)
−0.806300 + 0.591507i \(0.798533\pi\)
\(752\) 5.56133e8i 1.30775i
\(753\) 1.37280e7 0.0321531
\(754\) −6.72497e7 −0.156883
\(755\) 1.44908e8i 0.336706i
\(756\) 1.50188e7 0.0347592
\(757\) −2.69345e8 −0.620900 −0.310450 0.950590i \(-0.600480\pi\)
−0.310450 + 0.950590i \(0.600480\pi\)
\(758\) 3.50871e8i 0.805639i
\(759\) −1.51746e8 −0.347051
\(760\) 7.00844e8i 1.59654i
\(761\) 1.03962e8 0.235896 0.117948 0.993020i \(-0.462368\pi\)
0.117948 + 0.993020i \(0.462368\pi\)
\(762\) 4.15406e8i 0.938874i
\(763\) 1.59470e8i 0.359009i
\(764\) 7.99390e7i 0.179258i
\(765\) 5.90966e7 0.132001
\(766\) 1.53827e8i 0.342252i
\(767\) 2.33696e7 + 3.85256e7i 0.0517924 + 0.0853814i
\(768\) 1.79544e8 0.396358
\(769\) 6.72944e7i 0.147979i 0.997259 + 0.0739895i \(0.0235731\pi\)
−0.997259 + 0.0739895i \(0.976427\pi\)
\(770\) 2.72065e8 0.595938
\(771\) 3.80490e8 0.830196
\(772\) −9.52670e7 −0.207057
\(773\) 6.24379e8i 1.35179i 0.736997 + 0.675896i \(0.236243\pi\)
−0.736997 + 0.675896i \(0.763757\pi\)
\(774\) −1.18938e7 −0.0256507
\(775\) 3.45285e8i 0.741776i
\(776\) 8.57745e7 0.183558
\(777\) 2.02926e8i 0.432589i
\(778\) 3.36111e8i 0.713747i
\(779\) −1.03279e9 −2.18473
\(780\) 9.29740e6i 0.0195920i
\(781\) 2.39220e7i 0.0502163i
\(782\) −1.77157e8 −0.370457
\(783\) 1.30240e8 0.271307
\(784\) 2.52191e8 0.523337
\(785\) 9.44310e8i 1.95212i