Properties

Label 177.7.c.a.58.6
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 58.6
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.55

$q$-expansion

\(f(q)\) \(=\) \(q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} -1073.05i q^{10} -259.004i q^{11} +1933.59 q^{12} +652.587i q^{13} -6204.49i q^{14} -1219.83 q^{15} +3351.31 q^{16} -3110.24 q^{17} -3332.20i q^{18} -10605.2 q^{19} -9706.35 q^{20} -7053.17 q^{21} -3551.66 q^{22} -1836.91i q^{23} -12834.1i q^{24} -9501.63 q^{25} +8948.77 q^{26} -3788.00 q^{27} -56123.1 q^{28} -3215.28 q^{29} +16727.2i q^{30} -49794.1i q^{31} +6736.18i q^{32} +4037.48i q^{33} +42650.0i q^{34} +35406.0 q^{35} -30141.6 q^{36} +3989.90i q^{37} +145427. i q^{38} -10172.8i q^{39} +64425.6i q^{40} -48864.4 q^{41} +96718.4i q^{42} +40700.9i q^{43} +32126.8i q^{44} +19015.2 q^{45} -25189.1 q^{46} -14800.9i q^{47} -52241.7 q^{48} +87071.9 q^{49} +130293. i q^{50} +48483.9 q^{51} -80946.7i q^{52} -246352. q^{53} +51943.9i q^{54} -20267.6i q^{55} +372515. i q^{56} +165319. q^{57} +44090.3i q^{58} +(-47272.8 + 199865. i) q^{59} +151307. q^{60} -253372. i q^{61} -682814. q^{62} +109948. q^{63} +306855. q^{64} +51066.3i q^{65} +55365.0 q^{66} -475304. i q^{67} +385793. q^{68} +28634.6i q^{69} -485513. i q^{70} +75588.7 q^{71} +200064. i q^{72} +284785. i q^{73} +54712.6 q^{74} +148116. q^{75} +1.31547e6 q^{76} -117189. i q^{77} -139498. q^{78} -530314. q^{79} +262246. q^{80} +59049.0 q^{81} +670065. i q^{82} +947140. i q^{83} +874873. q^{84} -243383. q^{85} +558121. q^{86} +50121.2 q^{87} +213241. q^{88} -985993. i q^{89} -260751. i q^{90} +295270. i q^{91} +227850. i q^{92} +776213. i q^{93} -202961. q^{94} -829879. q^{95} -105007. i q^{96} +310962. i q^{97} -1.19400e6i q^{98} -62938.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.7128i 1.71409i −0.515238 0.857047i \(-0.672296\pi\)
0.515238 0.857047i \(-0.327704\pi\)
\(3\) −15.5885 −0.577350
\(4\) −124.040 −1.93812
\(5\) 78.2520 0.626016 0.313008 0.949751i \(-0.398663\pi\)
0.313008 + 0.949751i \(0.398663\pi\)
\(6\) 213.761i 0.989633i
\(7\) 452.461 1.31913 0.659564 0.751648i \(-0.270741\pi\)
0.659564 + 0.751648i \(0.270741\pi\)
\(8\) 823.310i 1.60803i
\(9\) 243.000 0.333333
\(10\) 1073.05i 1.07305i
\(11\) 259.004i 0.194594i −0.995255 0.0972969i \(-0.968980\pi\)
0.995255 0.0972969i \(-0.0310196\pi\)
\(12\) 1933.59 1.11897
\(13\) 652.587i 0.297036i 0.988910 + 0.148518i \(0.0474502\pi\)
−0.988910 + 0.148518i \(0.952550\pi\)
\(14\) 6204.49i 2.26111i
\(15\) −1219.83 −0.361430
\(16\) 3351.31 0.818190
\(17\) −3110.24 −0.633064 −0.316532 0.948582i \(-0.602518\pi\)
−0.316532 + 0.948582i \(0.602518\pi\)
\(18\) 3332.20i 0.571365i
\(19\) −10605.2 −1.54618 −0.773088 0.634299i \(-0.781289\pi\)
−0.773088 + 0.634299i \(0.781289\pi\)
\(20\) −9706.35 −1.21329
\(21\) −7053.17 −0.761599
\(22\) −3551.66 −0.333552
\(23\) 1836.91i 0.150975i −0.997147 0.0754875i \(-0.975949\pi\)
0.997147 0.0754875i \(-0.0240513\pi\)
\(24\) 12834.1i 0.928395i
\(25\) −9501.63 −0.608104
\(26\) 8948.77 0.509147
\(27\) −3788.00 −0.192450
\(28\) −56123.1 −2.55663
\(29\) −3215.28 −0.131833 −0.0659165 0.997825i \(-0.520997\pi\)
−0.0659165 + 0.997825i \(0.520997\pi\)
\(30\) 16727.2i 0.619526i
\(31\) 49794.1i 1.67145i −0.549151 0.835723i \(-0.685049\pi\)
0.549151 0.835723i \(-0.314951\pi\)
\(32\) 6736.18i 0.205572i
\(33\) 4037.48i 0.112349i
\(34\) 42650.0i 1.08513i
\(35\) 35406.0 0.825795
\(36\) −30141.6 −0.646040
\(37\) 3989.90i 0.0787693i 0.999224 + 0.0393847i \(0.0125398\pi\)
−0.999224 + 0.0393847i \(0.987460\pi\)
\(38\) 145427.i 2.65029i
\(39\) 10172.8i 0.171494i
\(40\) 64425.6i 1.00665i
\(41\) −48864.4 −0.708991 −0.354495 0.935058i \(-0.615347\pi\)
−0.354495 + 0.935058i \(0.615347\pi\)
\(42\) 96718.4i 1.30545i
\(43\) 40700.9i 0.511916i 0.966688 + 0.255958i \(0.0823909\pi\)
−0.966688 + 0.255958i \(0.917609\pi\)
\(44\) 32126.8i 0.377146i
\(45\) 19015.2 0.208672
\(46\) −25189.1 −0.258785
\(47\) 14800.9i 0.142559i −0.997456 0.0712794i \(-0.977292\pi\)
0.997456 0.0712794i \(-0.0227082\pi\)
\(48\) −52241.7 −0.472382
\(49\) 87071.9 0.740099
\(50\) 130293.i 1.04235i
\(51\) 48483.9 0.365499
\(52\) 80946.7i 0.575691i
\(53\) −246352. −1.65474 −0.827368 0.561660i \(-0.810163\pi\)
−0.827368 + 0.561660i \(0.810163\pi\)
\(54\) 51943.9i 0.329878i
\(55\) 20267.6i 0.121819i
\(56\) 372515.i 2.12119i
\(57\) 165319. 0.892685
\(58\) 44090.3i 0.225974i
\(59\) −47272.8 + 199865.i −0.230173 + 0.973150i
\(60\) 151307. 0.700496
\(61\) 253372.i 1.11627i −0.829751 0.558134i \(-0.811517\pi\)
0.829751 0.558134i \(-0.188483\pi\)
\(62\) −682814. −2.86502
\(63\) 109948. 0.439709
\(64\) 306855. 1.17056
\(65\) 51066.3i 0.185949i
\(66\) 55365.0 0.192576
\(67\) 475304.i 1.58033i −0.612895 0.790164i \(-0.709995\pi\)
0.612895 0.790164i \(-0.290005\pi\)
\(68\) 385793. 1.22695
\(69\) 28634.6i 0.0871654i
\(70\) 485513.i 1.41549i
\(71\) 75588.7 0.211194 0.105597 0.994409i \(-0.466325\pi\)
0.105597 + 0.994409i \(0.466325\pi\)
\(72\) 200064.i 0.536009i
\(73\) 284785.i 0.732064i 0.930602 + 0.366032i \(0.119284\pi\)
−0.930602 + 0.366032i \(0.880716\pi\)
\(74\) 54712.6 0.135018
\(75\) 148116. 0.351089
\(76\) 1.31547e6 2.99667
\(77\) 117189.i 0.256694i
\(78\) −139498. −0.293956
\(79\) −530314. −1.07560 −0.537801 0.843072i \(-0.680745\pi\)
−0.537801 + 0.843072i \(0.680745\pi\)
\(80\) 262246. 0.512200
\(81\) 59049.0 0.111111
\(82\) 670065.i 1.21528i
\(83\) 947140.i 1.65646i 0.560391 + 0.828228i \(0.310651\pi\)
−0.560391 + 0.828228i \(0.689349\pi\)
\(84\) 874873. 1.47607
\(85\) −243383. −0.396308
\(86\) 558121. 0.877472
\(87\) 50121.2 0.0761138
\(88\) 213241. 0.312912
\(89\) 985993.i 1.39863i −0.714812 0.699317i \(-0.753488\pi\)
0.714812 0.699317i \(-0.246512\pi\)
\(90\) 260751.i 0.357684i
\(91\) 295270.i 0.391828i
\(92\) 227850.i 0.292608i
\(93\) 776213.i 0.965010i
\(94\) −202961. −0.244359
\(95\) −829879. −0.967930
\(96\) 105007.i 0.118687i
\(97\) 310962.i 0.340716i 0.985382 + 0.170358i \(0.0544924\pi\)
−0.985382 + 0.170358i \(0.945508\pi\)
\(98\) 1.19400e6i 1.26860i
\(99\) 62938.1i 0.0648646i
\(100\) 1.17858e6 1.17858
\(101\) 526681.i 0.511191i 0.966784 + 0.255596i \(0.0822716\pi\)
−0.966784 + 0.255596i \(0.917728\pi\)
\(102\) 664847.i 0.626501i
\(103\) 362144.i 0.331413i 0.986175 + 0.165706i \(0.0529904\pi\)
−0.986175 + 0.165706i \(0.947010\pi\)
\(104\) −537282. −0.477641
\(105\) −551924. −0.476773
\(106\) 3.37817e6i 2.83638i
\(107\) 81885.6 0.0668431 0.0334215 0.999441i \(-0.489360\pi\)
0.0334215 + 0.999441i \(0.489360\pi\)
\(108\) 469862. 0.372991
\(109\) 659312.i 0.509110i 0.967058 + 0.254555i \(0.0819290\pi\)
−0.967058 + 0.254555i \(0.918071\pi\)
\(110\) −277925. −0.208809
\(111\) 62196.4i 0.0454775i
\(112\) 1.51633e6 1.07930
\(113\) 760603.i 0.527136i 0.964641 + 0.263568i \(0.0848993\pi\)
−0.964641 + 0.263568i \(0.915101\pi\)
\(114\) 2.26698e6i 1.53015i
\(115\) 143742.i 0.0945127i
\(116\) 398822. 0.255508
\(117\) 158579.i 0.0990119i
\(118\) 2.74069e6 + 648240.i 1.66807 + 0.394539i
\(119\) −1.40726e6 −0.835092
\(120\) 1.00430e6i 0.581190i
\(121\) 1.70448e6 0.962133
\(122\) −3.47442e6 −1.91339
\(123\) 761720. 0.409336
\(124\) 6.17644e6i 3.23946i
\(125\) −1.96621e6 −1.00670
\(126\) 1.50769e6i 0.753703i
\(127\) 609001. 0.297308 0.148654 0.988889i \(-0.452506\pi\)
0.148654 + 0.988889i \(0.452506\pi\)
\(128\) 3.77672e6i 1.80088i
\(129\) 634464.i 0.295555i
\(130\) 700259. 0.318734
\(131\) 354986.i 0.157905i −0.996878 0.0789527i \(-0.974842\pi\)
0.996878 0.0789527i \(-0.0251576\pi\)
\(132\) 500808.i 0.217745i
\(133\) −4.79845e6 −2.03960
\(134\) −6.51773e6 −2.70883
\(135\) −296418. −0.120477
\(136\) 2.56069e6i 1.01798i
\(137\) −3.51364e6 −1.36646 −0.683229 0.730205i \(-0.739425\pi\)
−0.683229 + 0.730205i \(0.739425\pi\)
\(138\) 392660. 0.149410
\(139\) −3.04917e6 −1.13537 −0.567685 0.823246i \(-0.692161\pi\)
−0.567685 + 0.823246i \(0.692161\pi\)
\(140\) −4.39175e6 −1.60049
\(141\) 230723.i 0.0823064i
\(142\) 1.03653e6i 0.362006i
\(143\) 169023. 0.0578013
\(144\) 814367. 0.272730
\(145\) −251602. −0.0825296
\(146\) 3.90519e6 1.25483
\(147\) −1.35732e6 −0.427296
\(148\) 494906.i 0.152664i
\(149\) 1.71211e6i 0.517574i 0.965934 + 0.258787i \(0.0833227\pi\)
−0.965934 + 0.258787i \(0.916677\pi\)
\(150\) 2.03107e6i 0.601800i
\(151\) 2.86817e6i 0.833057i −0.909123 0.416528i \(-0.863247\pi\)
0.909123 0.416528i \(-0.136753\pi\)
\(152\) 8.73138e6i 2.48629i
\(153\) −755789. −0.211021
\(154\) −1.60699e6 −0.439998
\(155\) 3.89648e6i 1.04635i
\(156\) 1.26183e6i 0.332375i
\(157\) 22056.5i 0.00569952i −0.999996 0.00284976i \(-0.999093\pi\)
0.999996 0.00284976i \(-0.000907108\pi\)
\(158\) 7.27206e6i 1.84368i
\(159\) 3.84025e6 0.955363
\(160\) 527120.i 0.128691i
\(161\) 831131.i 0.199155i
\(162\) 809725.i 0.190455i
\(163\) −3.33224e6 −0.769438 −0.384719 0.923034i \(-0.625702\pi\)
−0.384719 + 0.923034i \(0.625702\pi\)
\(164\) 6.06112e6 1.37411
\(165\) 315941.i 0.0703321i
\(166\) 1.29879e7 2.83932
\(167\) −1.78430e6 −0.383106 −0.191553 0.981482i \(-0.561352\pi\)
−0.191553 + 0.981482i \(0.561352\pi\)
\(168\) 5.80694e6i 1.22467i
\(169\) 4.40094e6 0.911770
\(170\) 3.33745e6i 0.679309i
\(171\) −2.57707e6 −0.515392
\(172\) 5.04853e6i 0.992155i
\(173\) 3.85930e6i 0.745367i −0.927959 0.372684i \(-0.878438\pi\)
0.927959 0.372684i \(-0.121562\pi\)
\(174\) 687300.i 0.130466i
\(175\) −4.29911e6 −0.802167
\(176\) 868003.i 0.159215i
\(177\) 736910. 3.11558e6i 0.132891 0.561848i
\(178\) −1.35207e7 −2.39739
\(179\) 686308.i 0.119663i −0.998208 0.0598315i \(-0.980944\pi\)
0.998208 0.0598315i \(-0.0190563\pi\)
\(180\) −2.35864e6 −0.404431
\(181\) 3.82235e6 0.644606 0.322303 0.946637i \(-0.395543\pi\)
0.322303 + 0.946637i \(0.395543\pi\)
\(182\) 4.04897e6 0.671630
\(183\) 3.94967e6i 0.644478i
\(184\) 1.51235e6 0.242772
\(185\) 312218.i 0.0493109i
\(186\) 1.06440e7 1.65412
\(187\) 805566.i 0.123190i
\(188\) 1.83590e6i 0.276296i
\(189\) −1.71392e6 −0.253866
\(190\) 1.13799e7i 1.65912i
\(191\) 1.30564e6i 0.187380i 0.995601 + 0.0936899i \(0.0298662\pi\)
−0.995601 + 0.0936899i \(0.970134\pi\)
\(192\) −4.78340e6 −0.675823
\(193\) 2.12355e6 0.295386 0.147693 0.989033i \(-0.452815\pi\)
0.147693 + 0.989033i \(0.452815\pi\)
\(194\) 4.26415e6 0.584019
\(195\) 796044.i 0.107358i
\(196\) −1.08004e7 −1.43440
\(197\) −1.97152e6 −0.257872 −0.128936 0.991653i \(-0.541156\pi\)
−0.128936 + 0.991653i \(0.541156\pi\)
\(198\) −863054. −0.111184
\(199\) 1.10320e7 1.39990 0.699949 0.714193i \(-0.253206\pi\)
0.699949 + 0.714193i \(0.253206\pi\)
\(200\) 7.82278e6i 0.977848i
\(201\) 7.40926e6i 0.912403i
\(202\) 7.22225e6 0.876231
\(203\) −1.45479e6 −0.173905
\(204\) −6.01392e6 −0.708382
\(205\) −3.82373e6 −0.443840
\(206\) 4.96599e6 0.568073
\(207\) 446370.i 0.0503250i
\(208\) 2.18702e6i 0.243032i
\(209\) 2.74680e6i 0.300876i
\(210\) 7.56840e6i 0.817234i
\(211\) 1.15651e7i 1.23112i −0.788089 0.615561i \(-0.788929\pi\)
0.788089 0.615561i \(-0.211071\pi\)
\(212\) 3.05575e7 3.20708
\(213\) −1.17831e6 −0.121933
\(214\) 1.12288e6i 0.114575i
\(215\) 3.18493e6i 0.320467i
\(216\) 3.11869e6i 0.309465i
\(217\) 2.25299e7i 2.20485i
\(218\) 9.04098e6 0.872662
\(219\) 4.43937e6i 0.422658i
\(220\) 2.51399e6i 0.236100i
\(221\) 2.02970e6i 0.188042i
\(222\) −852885. −0.0779527
\(223\) −966458. −0.0871502 −0.0435751 0.999050i \(-0.513875\pi\)
−0.0435751 + 0.999050i \(0.513875\pi\)
\(224\) 3.04786e6i 0.271176i
\(225\) −2.30890e6 −0.202701
\(226\) 1.04300e7 0.903561
\(227\) 1.11687e6i 0.0954824i −0.998860 0.0477412i \(-0.984798\pi\)
0.998860 0.0477412i \(-0.0152023\pi\)
\(228\) −2.05061e7 −1.73013
\(229\) 8.34569e6i 0.694953i 0.937689 + 0.347477i \(0.112961\pi\)
−0.937689 + 0.347477i \(0.887039\pi\)
\(230\) −1.97110e6 −0.162004
\(231\) 1.82680e6i 0.148202i
\(232\) 2.64717e6i 0.211991i
\(233\) 1.74749e7i 1.38148i −0.723101 0.690742i \(-0.757284\pi\)
0.723101 0.690742i \(-0.242716\pi\)
\(234\) 2.17455e6 0.169716
\(235\) 1.15820e6i 0.0892441i
\(236\) 5.86370e6 2.47911e7i 0.446104 1.88608i
\(237\) 8.26677e6 0.620999
\(238\) 1.92974e7i 1.43143i
\(239\) −1.75221e7 −1.28349 −0.641744 0.766919i \(-0.721789\pi\)
−0.641744 + 0.766919i \(0.721789\pi\)
\(240\) −4.08802e6 −0.295719
\(241\) −424356. −0.0303165 −0.0151583 0.999885i \(-0.504825\pi\)
−0.0151583 + 0.999885i \(0.504825\pi\)
\(242\) 2.33731e7i 1.64919i
\(243\) −920483. −0.0641500
\(244\) 3.14281e7i 2.16346i
\(245\) 6.81355e6 0.463313
\(246\) 1.04453e7i 0.701641i
\(247\) 6.92083e6i 0.459269i
\(248\) 4.09959e7 2.68773
\(249\) 1.47645e7i 0.956355i
\(250\) 2.69621e7i 1.72558i
\(251\) −1.87344e6 −0.118473 −0.0592364 0.998244i \(-0.518867\pi\)
−0.0592364 + 0.998244i \(0.518867\pi\)
\(252\) −1.36379e7 −0.852210
\(253\) −475768. −0.0293788
\(254\) 8.35108e6i 0.509614i
\(255\) 3.79396e6 0.228808
\(256\) −3.21504e7 −1.91632
\(257\) 3.56173e6 0.209827 0.104914 0.994481i \(-0.466543\pi\)
0.104914 + 0.994481i \(0.466543\pi\)
\(258\) −8.70025e6 −0.506609
\(259\) 1.80528e6i 0.103907i
\(260\) 6.33424e6i 0.360392i
\(261\) −781312. −0.0439443
\(262\) −4.86783e6 −0.270665
\(263\) −1.09649e6 −0.0602748 −0.0301374 0.999546i \(-0.509594\pi\)
−0.0301374 + 0.999546i \(0.509594\pi\)
\(264\) −3.32410e6 −0.180660
\(265\) −1.92776e7 −1.03589
\(266\) 6.57999e7i 3.49607i
\(267\) 1.53701e7i 0.807501i
\(268\) 5.89566e7i 3.06287i
\(269\) 1.29997e7i 0.667848i −0.942600 0.333924i \(-0.891627\pi\)
0.942600 0.333924i \(-0.108373\pi\)
\(270\) 4.06471e6i 0.206509i
\(271\) 4.49647e6 0.225925 0.112962 0.993599i \(-0.463966\pi\)
0.112962 + 0.993599i \(0.463966\pi\)
\(272\) −1.04234e7 −0.517966
\(273\) 4.60281e6i 0.226222i
\(274\) 4.81817e7i 2.34224i
\(275\) 2.46096e6i 0.118333i
\(276\) 3.55183e6i 0.168937i
\(277\) 9.37091e6 0.440902 0.220451 0.975398i \(-0.429247\pi\)
0.220451 + 0.975398i \(0.429247\pi\)
\(278\) 4.18126e7i 1.94613i
\(279\) 1.21000e7i 0.557149i
\(280\) 2.91501e7i 1.32790i
\(281\) −2.71429e7 −1.22331 −0.611657 0.791123i \(-0.709497\pi\)
−0.611657 + 0.791123i \(0.709497\pi\)
\(282\) 3.16385e6 0.141081
\(283\) 2.60309e7i 1.14850i 0.818681 + 0.574249i \(0.194706\pi\)
−0.818681 + 0.574249i \(0.805294\pi\)
\(284\) −9.37599e6 −0.409319
\(285\) 1.29365e7 0.558835
\(286\) 2.31777e6i 0.0990769i
\(287\) −2.21092e7 −0.935250
\(288\) 1.63689e6i 0.0685240i
\(289\) −1.44640e7 −0.599231
\(290\) 3.45015e6i 0.141464i
\(291\) 4.84742e6i 0.196712i
\(292\) 3.53247e7i 1.41883i
\(293\) −2.55220e7 −1.01464 −0.507319 0.861758i \(-0.669363\pi\)
−0.507319 + 0.861758i \(0.669363\pi\)
\(294\) 1.86125e7i 0.732426i
\(295\) −3.69919e6 + 1.56398e7i −0.144092 + 0.609207i
\(296\) −3.28493e6 −0.126663
\(297\) 981107.i 0.0374496i
\(298\) 2.34777e7 0.887170
\(299\) 1.19875e6 0.0448449
\(300\) −1.83722e7 −0.680453
\(301\) 1.84156e7i 0.675283i
\(302\) −3.93306e7 −1.42794
\(303\) 8.21015e6i 0.295137i
\(304\) −3.55413e7 −1.26506
\(305\) 1.98268e7i 0.698802i
\(306\) 1.03639e7i 0.361710i
\(307\) 4.11042e7 1.42060 0.710299 0.703900i \(-0.248560\pi\)
0.710299 + 0.703900i \(0.248560\pi\)
\(308\) 1.45361e7i 0.497504i
\(309\) 5.64526e6i 0.191341i
\(310\) −5.34315e7 −1.79355
\(311\) 4.47374e7 1.48727 0.743634 0.668587i \(-0.233101\pi\)
0.743634 + 0.668587i \(0.233101\pi\)
\(312\) 8.37539e6 0.275766
\(313\) 3.06210e7i 0.998589i −0.866432 0.499295i \(-0.833593\pi\)
0.866432 0.499295i \(-0.166407\pi\)
\(314\) −302456. −0.00976952
\(315\) 8.60365e6 0.275265
\(316\) 6.57800e7 2.08465
\(317\) 5.80961e7 1.82377 0.911883 0.410450i \(-0.134629\pi\)
0.911883 + 0.410450i \(0.134629\pi\)
\(318\) 5.26604e7i 1.63758i
\(319\) 832770.i 0.0256539i
\(320\) 2.40120e7 0.732789
\(321\) −1.27647e6 −0.0385919
\(322\) −1.13971e7 −0.341371
\(323\) 3.29848e7 0.978827
\(324\) −7.32442e6 −0.215347
\(325\) 6.20064e6i 0.180629i
\(326\) 4.56942e7i 1.31889i
\(327\) 1.02777e7i 0.293935i
\(328\) 4.02305e7i 1.14008i
\(329\) 6.69682e6i 0.188053i
\(330\) 4.33242e6 0.120556
\(331\) 3.32831e7 0.917783 0.458891 0.888492i \(-0.348247\pi\)
0.458891 + 0.888492i \(0.348247\pi\)
\(332\) 1.17483e8i 3.21041i
\(333\) 969547.i 0.0262564i
\(334\) 2.44677e7i 0.656680i
\(335\) 3.71935e7i 0.989310i
\(336\) −2.36373e7 −0.623133
\(337\) 1.87279e7i 0.489326i −0.969608 0.244663i \(-0.921323\pi\)
0.969608 0.244663i \(-0.0786773\pi\)
\(338\) 6.03490e7i 1.56286i
\(339\) 1.18566e7i 0.304342i
\(340\) 3.01891e7 0.768092
\(341\) −1.28969e7 −0.325253
\(342\) 3.53387e7i 0.883430i
\(343\) −1.38350e7 −0.342843
\(344\) −3.35094e7 −0.823174
\(345\) 2.24072e6i 0.0545669i
\(346\) −5.29216e7 −1.27763
\(347\) 2.98270e7i 0.713874i 0.934128 + 0.356937i \(0.116179\pi\)
−0.934128 + 0.356937i \(0.883821\pi\)
\(348\) −6.21702e6 −0.147518
\(349\) 7.76118e7i 1.82579i −0.408190 0.912897i \(-0.633840\pi\)
0.408190 0.912897i \(-0.366160\pi\)
\(350\) 5.89527e7i 1.37499i
\(351\) 2.47200e6i 0.0571645i
\(352\) 1.74470e6 0.0400030
\(353\) 6.61940e7i 1.50485i −0.658676 0.752427i \(-0.728883\pi\)
0.658676 0.752427i \(-0.271117\pi\)
\(354\) −4.27232e7 1.01051e7i −0.963061 0.227787i
\(355\) 5.91496e6 0.132211
\(356\) 1.22302e8i 2.71072i
\(357\) 2.19371e7 0.482140
\(358\) −9.41118e6 −0.205114
\(359\) 5.98796e7 1.29418 0.647091 0.762413i \(-0.275985\pi\)
0.647091 + 0.762413i \(0.275985\pi\)
\(360\) 1.56554e7i 0.335550i
\(361\) 6.54247e7 1.39066
\(362\) 5.24149e7i 1.10492i
\(363\) −2.65702e7 −0.555488
\(364\) 3.66252e7i 0.759410i
\(365\) 2.22850e7i 0.458284i
\(366\) 5.41609e7 1.10470
\(367\) 6.54533e7i 1.32414i 0.749443 + 0.662069i \(0.230322\pi\)
−0.749443 + 0.662069i \(0.769678\pi\)
\(368\) 6.15605e6i 0.123526i
\(369\) −1.18740e7 −0.236330
\(370\) 4.28137e6 0.0845235
\(371\) −1.11465e8 −2.18281
\(372\) 9.62812e7i 1.87031i
\(373\) 6.29630e7 1.21327 0.606637 0.794979i \(-0.292518\pi\)
0.606637 + 0.794979i \(0.292518\pi\)
\(374\) 1.10465e7 0.211160
\(375\) 3.06502e7 0.581218
\(376\) 1.21857e7 0.229238
\(377\) 2.09825e6i 0.0391591i
\(378\) 2.35026e7i 0.435151i
\(379\) −2.82722e7 −0.519328 −0.259664 0.965699i \(-0.583612\pi\)
−0.259664 + 0.965699i \(0.583612\pi\)
\(380\) 1.02938e8 1.87597
\(381\) −9.49338e6 −0.171651
\(382\) 1.79039e7 0.321187
\(383\) −1.86237e7 −0.331489 −0.165744 0.986169i \(-0.553003\pi\)
−0.165744 + 0.986169i \(0.553003\pi\)
\(384\) 5.88732e7i 1.03974i
\(385\) 9.17030e6i 0.160695i
\(386\) 2.91197e7i 0.506320i
\(387\) 9.89032e6i 0.170639i
\(388\) 3.85716e7i 0.660348i
\(389\) −4.03075e7 −0.684758 −0.342379 0.939562i \(-0.611233\pi\)
−0.342379 + 0.939562i \(0.611233\pi\)
\(390\) −1.09160e7 −0.184021
\(391\) 5.71324e6i 0.0955767i
\(392\) 7.16871e7i 1.19010i
\(393\) 5.53368e6i 0.0911667i
\(394\) 2.70350e7i 0.442016i
\(395\) −4.14981e7 −0.673344
\(396\) 7.80682e6i 0.125715i
\(397\) 6.55839e7i 1.04816i −0.851671 0.524078i \(-0.824410\pi\)
0.851671 0.524078i \(-0.175590\pi\)
\(398\) 1.51280e8i 2.39956i
\(399\) 7.48004e7 1.17757
\(400\) −3.18429e7 −0.497545
\(401\) 1.24598e8i 1.93232i 0.257950 + 0.966158i \(0.416953\pi\)
−0.257950 + 0.966158i \(0.583047\pi\)
\(402\) 1.01601e8 1.56394
\(403\) 3.24950e7 0.496479
\(404\) 6.53294e7i 0.990751i
\(405\) 4.62070e6 0.0695573
\(406\) 1.99491e7i 0.298089i
\(407\) 1.03340e6 0.0153280
\(408\) 3.99172e7i 0.587733i
\(409\) 1.03807e8i 1.51725i −0.651526 0.758626i \(-0.725871\pi\)
0.651526 0.758626i \(-0.274129\pi\)
\(410\) 5.24339e7i 0.760783i
\(411\) 5.47723e7 0.788924
\(412\) 4.49202e7i 0.642318i
\(413\) −2.13891e7 + 9.04309e7i −0.303628 + 1.28371i
\(414\) −6.12096e6 −0.0862618
\(415\) 7.41156e7i 1.03697i
\(416\) −4.39595e6 −0.0610622
\(417\) 4.75319e7 0.655507
\(418\) 3.76662e7 0.515730
\(419\) 9.05965e7i 1.23160i 0.787903 + 0.615799i \(0.211167\pi\)
−0.787903 + 0.615799i \(0.788833\pi\)
\(420\) 6.84605e7 0.924043
\(421\) 2.63419e7i 0.353022i 0.984299 + 0.176511i \(0.0564811\pi\)
−0.984299 + 0.176511i \(0.943519\pi\)
\(422\) −1.58589e8 −2.11026
\(423\) 3.59662e6i 0.0475196i
\(424\) 2.02824e8i 2.66086i
\(425\) 2.95523e7 0.384968
\(426\) 1.61579e7i 0.209005i
\(427\) 1.14641e8i 1.47250i
\(428\) −1.01571e7 −0.129550
\(429\) −2.63481e6 −0.0333716
\(430\) 4.36741e7 0.549312
\(431\) 4.56261e7i 0.569877i −0.958546 0.284939i \(-0.908027\pi\)
0.958546 0.284939i \(-0.0919732\pi\)
\(432\) −1.26947e7 −0.157461
\(433\) −1.22197e8 −1.50521 −0.752604 0.658473i \(-0.771202\pi\)
−0.752604 + 0.658473i \(0.771202\pi\)
\(434\) −3.08947e8 −3.77932
\(435\) 3.92208e6 0.0476485
\(436\) 8.17808e7i 0.986716i
\(437\) 1.94808e7i 0.233434i
\(438\) −6.08760e7 −0.724475
\(439\) 5.78606e7 0.683895 0.341947 0.939719i \(-0.388914\pi\)
0.341947 + 0.939719i \(0.388914\pi\)
\(440\) 1.66865e7 0.195888
\(441\) 2.11585e7 0.246700
\(442\) −2.78328e7 −0.322323
\(443\) 1.17033e8i 1.34616i 0.739570 + 0.673079i \(0.235029\pi\)
−0.739570 + 0.673079i \(0.764971\pi\)
\(444\) 7.71483e6i 0.0881409i
\(445\) 7.71559e7i 0.875567i
\(446\) 1.32528e7i 0.149384i
\(447\) 2.66891e7i 0.298821i
\(448\) 1.38840e8 1.54412
\(449\) −1.21901e8 −1.34669 −0.673344 0.739329i \(-0.735143\pi\)
−0.673344 + 0.739329i \(0.735143\pi\)
\(450\) 3.16613e7i 0.347449i
\(451\) 1.26561e7i 0.137965i
\(452\) 9.43450e7i 1.02165i
\(453\) 4.47104e7i 0.480966i
\(454\) −1.53153e7 −0.163666
\(455\) 2.31055e7i 0.245291i
\(456\) 1.36109e8i 1.43546i
\(457\) 1.76454e8i 1.84877i −0.381462 0.924385i \(-0.624579\pi\)
0.381462 0.924385i \(-0.375421\pi\)
\(458\) 1.14442e8 1.19122
\(459\) 1.17816e7 0.121833
\(460\) 1.78297e7i 0.183177i
\(461\) −1.42578e8 −1.45530 −0.727648 0.685951i \(-0.759386\pi\)
−0.727648 + 0.685951i \(0.759386\pi\)
\(462\) 2.50505e7 0.254033
\(463\) 1.45074e8i 1.46166i 0.682558 + 0.730832i \(0.260868\pi\)
−0.682558 + 0.730832i \(0.739132\pi\)
\(464\) −1.07754e7 −0.107864
\(465\) 6.07402e7i 0.604112i
\(466\) −2.39628e8 −2.36799
\(467\) 1.48028e8i 1.45342i −0.686942 0.726712i \(-0.741048\pi\)
0.686942 0.726712i \(-0.258952\pi\)
\(468\) 1.96701e7i 0.191897i
\(469\) 2.15057e8i 2.08465i
\(470\) −1.58821e7 −0.152973
\(471\) 343827.i 0.00329062i
\(472\) −1.64550e8 3.89201e7i −1.56485 0.370125i
\(473\) 1.05417e7 0.0996157
\(474\) 1.13360e8i 1.06445i
\(475\) 1.00767e8 0.940235
\(476\) 1.74556e8 1.61851
\(477\) −5.98636e7 −0.551579
\(478\) 2.40276e8i 2.20002i
\(479\) −1.49506e8 −1.36036 −0.680178 0.733047i \(-0.738098\pi\)
−0.680178 + 0.733047i \(0.738098\pi\)
\(480\) 8.21698e6i 0.0743000i
\(481\) −2.60376e6 −0.0233973
\(482\) 5.81910e6i 0.0519654i
\(483\) 1.29560e7i 0.114982i
\(484\) −2.11423e8 −1.86473
\(485\) 2.43334e7i 0.213293i
\(486\) 1.26224e7i 0.109959i
\(487\) −1.09033e8 −0.943996 −0.471998 0.881600i \(-0.656467\pi\)
−0.471998 + 0.881600i \(0.656467\pi\)
\(488\) 2.08603e8 1.79499
\(489\) 5.19445e7 0.444235
\(490\) 9.34325e7i 0.794163i
\(491\) −1.57201e8 −1.32804 −0.664019 0.747715i \(-0.731151\pi\)
−0.664019 + 0.747715i \(0.731151\pi\)
\(492\) −9.44835e7 −0.793343
\(493\) 1.00003e7 0.0834587
\(494\) −9.49037e7 −0.787231
\(495\) 4.92503e6i 0.0406063i
\(496\) 1.66875e8i 1.36756i
\(497\) 3.42009e7 0.278592
\(498\) −2.02461e8 −1.63928
\(499\) 6.89738e7 0.555114 0.277557 0.960709i \(-0.410475\pi\)
0.277557 + 0.960709i \(0.410475\pi\)
\(500\) 2.43888e8 1.95110
\(501\) 2.78145e7 0.221186
\(502\) 2.56900e7i 0.203073i
\(503\) 1.36368e8i 1.07154i −0.844363 0.535771i \(-0.820021\pi\)
0.844363 0.535771i \(-0.179979\pi\)
\(504\) 9.05213e7i 0.707064i
\(505\) 4.12138e7i 0.320014i
\(506\) 6.52409e6i 0.0503580i
\(507\) −6.86038e7 −0.526411
\(508\) −7.55402e7 −0.576219
\(509\) 2.13696e7i 0.162047i 0.996712 + 0.0810237i \(0.0258190\pi\)
−0.996712 + 0.0810237i \(0.974181\pi\)
\(510\) 5.20256e7i 0.392199i
\(511\) 1.28854e8i 0.965687i
\(512\) 1.99161e8i 1.48387i
\(513\) 4.01725e7 0.297562
\(514\) 4.88412e7i 0.359664i
\(515\) 2.83385e7i 0.207470i
\(516\) 7.86987e7i 0.572821i
\(517\) −3.83349e6 −0.0277411
\(518\) 2.47553e7 0.178106
\(519\) 6.01605e7i 0.430338i
\(520\) −4.20434e7 −0.299011
\(521\) −2.25805e8 −1.59669 −0.798345 0.602200i \(-0.794291\pi\)
−0.798345 + 0.602200i \(0.794291\pi\)
\(522\) 1.07139e7i 0.0753248i
\(523\) 3.75262e7 0.262319 0.131160 0.991361i \(-0.458130\pi\)
0.131160 + 0.991361i \(0.458130\pi\)
\(524\) 4.40323e7i 0.306040i
\(525\) 6.70166e7 0.463131
\(526\) 1.50358e7i 0.103317i
\(527\) 1.54872e8i 1.05813i
\(528\) 1.35308e7i 0.0919227i
\(529\) 1.44662e8 0.977207
\(530\) 2.64348e8i 1.77562i
\(531\) −1.14873e7 + 4.85671e7i −0.0767244 + 0.324383i
\(532\) 5.95198e8 3.95300
\(533\) 3.18883e7i 0.210596i
\(534\) 2.10767e8 1.38413
\(535\) 6.40771e6 0.0418448
\(536\) 3.91323e8 2.54121
\(537\) 1.06985e7i 0.0690875i
\(538\) −1.78262e8 −1.14476
\(539\) 2.25520e7i 0.144019i
\(540\) 3.67676e7 0.233499
\(541\) 1.13661e8i 0.717825i −0.933371 0.358913i \(-0.883148\pi\)
0.933371 0.358913i \(-0.116852\pi\)
\(542\) 6.16590e7i 0.387257i
\(543\) −5.95845e7 −0.372163
\(544\) 2.09511e7i 0.130140i
\(545\) 5.15925e7i 0.318711i
\(546\) −6.31172e7 −0.387766
\(547\) −1.35059e8 −0.825203 −0.412601 0.910912i \(-0.635380\pi\)
−0.412601 + 0.910912i \(0.635380\pi\)
\(548\) 4.35831e8 2.64836
\(549\) 6.15693e7i 0.372089i
\(550\) 3.37466e7 0.202834
\(551\) 3.40987e7 0.203837
\(552\) −2.35752e7 −0.140164
\(553\) −2.39946e8 −1.41886
\(554\) 1.28501e8i 0.755748i
\(555\) 4.86700e6i 0.0284696i
\(556\) 3.78218e8 2.20048
\(557\) 8.63421e7 0.499640 0.249820 0.968292i \(-0.419629\pi\)
0.249820 + 0.968292i \(0.419629\pi\)
\(558\) −1.65924e8 −0.955006
\(559\) −2.65609e7 −0.152057
\(560\) 1.18656e8 0.675657
\(561\) 1.25575e7i 0.0711239i
\(562\) 3.72204e8i 2.09687i
\(563\) 1.55337e8i 0.870461i 0.900319 + 0.435231i \(0.143333\pi\)
−0.900319 + 0.435231i \(0.856667\pi\)
\(564\) 2.86188e7i 0.159520i
\(565\) 5.95187e7i 0.329996i
\(566\) 3.56956e8 1.96864
\(567\) 2.67174e7 0.146570
\(568\) 6.22329e7i 0.339606i
\(569\) 3.58071e7i 0.194371i −0.995266 0.0971856i \(-0.969016\pi\)
0.995266 0.0971856i \(-0.0309840\pi\)
\(570\) 1.77396e8i 0.957896i
\(571\) 4.23278e7i 0.227362i −0.993517 0.113681i \(-0.963736\pi\)
0.993517 0.113681i \(-0.0362642\pi\)
\(572\) −2.09656e7 −0.112026
\(573\) 2.03529e7i 0.108184i
\(574\) 3.03178e8i 1.60311i
\(575\) 1.74537e7i 0.0918085i
\(576\) 7.45658e7 0.390187
\(577\) −1.16324e8 −0.605541 −0.302770 0.953064i \(-0.597912\pi\)
−0.302770 + 0.953064i \(0.597912\pi\)
\(578\) 1.98341e8i 1.02714i
\(579\) −3.31029e7 −0.170541
\(580\) 3.12086e7 0.159952
\(581\) 4.28544e8i 2.18508i
\(582\) −6.64715e7 −0.337183
\(583\) 6.38063e7i 0.322002i
\(584\) −2.34467e8 −1.17718
\(585\) 1.24091e7i 0.0619830i
\(586\) 3.49977e8i 1.73919i
\(587\) 2.56920e8i 1.27024i −0.772415 0.635118i \(-0.780951\pi\)
0.772415 0.635118i \(-0.219049\pi\)
\(588\) 1.68361e8 0.828151
\(589\) 5.28077e8i 2.58435i
\(590\) 2.14465e8 + 5.07261e7i 1.04424 + 0.246988i
\(591\) 3.07330e7 0.148882
\(592\) 1.33714e7i 0.0644483i
\(593\) 2.20865e7 0.105916 0.0529581 0.998597i \(-0.483135\pi\)
0.0529581 + 0.998597i \(0.483135\pi\)
\(594\) 1.34537e7 0.0641922
\(595\) −1.10121e8 −0.522781
\(596\) 2.12369e8i 1.00312i
\(597\) −1.71972e8 −0.808231
\(598\) 1.64381e7i 0.0768685i
\(599\) −3.37760e8 −1.57155 −0.785773 0.618515i \(-0.787735\pi\)
−0.785773 + 0.618515i \(0.787735\pi\)
\(600\) 1.21945e8i 0.564561i
\(601\) 1.94838e8i 0.897533i −0.893649 0.448766i \(-0.851864\pi\)
0.893649 0.448766i \(-0.148136\pi\)
\(602\) 2.52528e8 1.15750
\(603\) 1.15499e8i 0.526776i
\(604\) 3.55767e8i 1.61456i
\(605\) 1.33379e8 0.602311
\(606\) −1.12584e8 −0.505892
\(607\) 1.31760e7 0.0589138 0.0294569 0.999566i \(-0.490622\pi\)
0.0294569 + 0.999566i \(0.490622\pi\)
\(608\) 7.14387e7i 0.317850i
\(609\) 2.26779e7 0.100404
\(610\) −2.71881e8 −1.19781
\(611\) 9.65887e6 0.0423451
\(612\) 9.37478e7 0.408984
\(613\) 9.33914e7i 0.405439i 0.979237 + 0.202719i \(0.0649779\pi\)
−0.979237 + 0.202719i \(0.935022\pi\)
\(614\) 5.63652e8i 2.43504i
\(615\) 5.96061e7 0.256251
\(616\) 9.64831e7 0.412771
\(617\) 2.34906e8 1.00009 0.500045 0.866000i \(-0.333317\pi\)
0.500045 + 0.866000i \(0.333317\pi\)
\(618\) −7.74121e7 −0.327977
\(619\) 3.69057e8 1.55604 0.778020 0.628239i \(-0.216224\pi\)
0.778020 + 0.628239i \(0.216224\pi\)
\(620\) 4.83319e8i 2.02796i
\(621\) 6.95821e6i 0.0290551i
\(622\) 6.13472e8i 2.54932i
\(623\) 4.46123e8i 1.84498i
\(624\) 3.40923e7i 0.140314i
\(625\) −5.39683e6 −0.0221054
\(626\) −4.19899e8 −1.71168
\(627\) 4.28183e7i 0.173711i
\(628\) 2.73589e6i 0.0110464i
\(629\) 1.24096e7i 0.0498660i
\(630\) 1.17980e8i 0.471830i
\(631\) −2.90620e7 −0.115675 −0.0578373 0.998326i \(-0.518420\pi\)
−0.0578373 + 0.998326i \(0.518420\pi\)
\(632\) 4.36613e8i 1.72960i
\(633\) 1.80282e8i 0.710789i
\(634\) 7.96657e8i 3.12611i
\(635\) 4.76555e7 0.186120
\(636\) −4.76344e8 −1.85161
\(637\) 5.68220e7i 0.219836i
\(638\) 1.14196e7 0.0439732
\(639\) 1.83680e7 0.0703980
\(640\) 2.95535e8i 1.12738i
\(641\) 5.18494e8 1.96865 0.984327 0.176353i \(-0.0564301\pi\)
0.984327 + 0.176353i \(0.0564301\pi\)
\(642\) 1.75039e7i 0.0661501i
\(643\) −1.94176e8 −0.730403 −0.365202 0.930928i \(-0.619000\pi\)
−0.365202 + 0.930928i \(0.619000\pi\)
\(644\) 1.03093e8i 0.385987i
\(645\) 4.96481e7i 0.185022i
\(646\) 4.52312e8i 1.67780i
\(647\) 5.09645e8 1.88172 0.940859 0.338798i \(-0.110020\pi\)
0.940859 + 0.338798i \(0.110020\pi\)
\(648\) 4.86156e7i 0.178670i
\(649\) 5.17658e7 + 1.22439e7i 0.189369 + 0.0447903i
\(650\) −8.50279e7 −0.309614
\(651\) 3.51206e8i 1.27297i
\(652\) 4.13330e8 1.49126
\(653\) 1.15463e8 0.414672 0.207336 0.978270i \(-0.433521\pi\)
0.207336 + 0.978270i \(0.433521\pi\)
\(654\) −1.40935e8 −0.503832
\(655\) 2.77783e7i 0.0988513i
\(656\) −1.63759e8 −0.580089
\(657\) 6.92029e7i 0.244021i
\(658\) −9.18319e7 −0.322341
\(659\) 2.63375e8i 0.920277i 0.887847 + 0.460139i \(0.152200\pi\)
−0.887847 + 0.460139i \(0.847800\pi\)
\(660\) 3.91892e7i 0.136312i
\(661\) −3.64442e7 −0.126190 −0.0630948 0.998008i \(-0.520097\pi\)
−0.0630948 + 0.998008i \(0.520097\pi\)
\(662\) 4.56403e8i 1.57317i
\(663\) 3.16400e7i 0.108566i
\(664\) −7.79790e8 −2.66363
\(665\) −3.75488e8 −1.27682
\(666\) 1.32952e7 0.0450060
\(667\) 5.90618e6i 0.0199035i
\(668\) 2.21324e8 0.742505
\(669\) 1.50656e7 0.0503162
\(670\) −5.10025e8 −1.69577
\(671\) −6.56244e7 −0.217219
\(672\) 4.75114e7i 0.156563i
\(673\) 3.87285e8i 1.27053i −0.772293 0.635266i \(-0.780890\pi\)
0.772293 0.635266i \(-0.219110\pi\)
\(674\) −2.56811e8 −0.838751
\(675\) 3.59921e7 0.117030
\(676\) −5.45891e8 −1.76712
\(677\) −6.45220e7 −0.207942 −0.103971 0.994580i \(-0.533155\pi\)
−0.103971 + 0.994580i \(0.533155\pi\)
\(678\) −1.62587e8 −0.521671
\(679\) 1.40698e8i 0.449448i
\(680\) 2.00379e8i 0.637274i
\(681\) 1.74102e7i 0.0551268i
\(682\) 1.76852e8i 0.557515i
\(683\) 2.66210e8i 0.835531i 0.908555 + 0.417765i \(0.137187\pi\)
−0.908555 + 0.417765i \(0.862813\pi\)
\(684\) 3.19659e8 0.998891
\(685\) −2.74950e8 −0.855424
\(686\) 1.89715e8i 0.587666i
\(687\) 1.30096e8i 0.401231i
\(688\) 1.36401e8i 0.418844i
\(689\) 1.60766e8i 0.491516i
\(690\) 3.07264e7 0.0935329
\(691\) 2.91925e6i 0.00884785i −0.999990 0.00442392i \(-0.998592\pi\)
0.999990 0.00442392i \(-0.00140818\pi\)
\(692\) 4.78706e8i 1.44461i
\(693\) 2.84770e7i 0.0855647i
\(694\) 4.09011e8 1.22365
\(695\) −2.38604e8 −0.710760
\(696\) 4.12653e7i 0.122393i
\(697\) 1.51980e8 0.448836
\(698\) −1.06427e9 −3.12958
\(699\) 2.72406e8i 0.797600i
\(700\) 5.33261e8 1.55470
\(701\) 5.60034e8i 1.62577i 0.582421 + 0.812887i \(0.302105\pi\)
−0.582421 + 0.812887i \(0.697895\pi\)
\(702\) −3.38979e7 −0.0979854
\(703\) 4.23138e7i 0.121791i
\(704\) 7.94768e7i 0.227784i
\(705\) 1.80545e7i 0.0515251i
\(706\) −9.07702e8 −2.57946
\(707\) 2.38303e8i 0.674327i
\(708\) −9.14060e7 + 3.86456e8i −0.257558 + 1.08893i
\(709\) −1.51717e7 −0.0425692 −0.0212846 0.999773i \(-0.506776\pi\)
−0.0212846 + 0.999773i \(0.506776\pi\)
\(710\) 8.11104e7i 0.226622i
\(711\) −1.28866e8 −0.358534
\(712\) 8.11778e8 2.24904
\(713\) −9.14673e7 −0.252347
\(714\) 3.00817e8i 0.826434i
\(715\) 1.32264e7 0.0361845
\(716\) 8.51294e7i 0.231921i
\(717\) 2.73142e8 0.741023
\(718\) 8.21114e8i 2.21835i
\(719\) 3.86036e8i 1.03858i 0.854597 + 0.519292i \(0.173804\pi\)
−0.854597 + 0.519292i \(0.826196\pi\)
\(720\) 6.37259e7 0.170733
\(721\) 1.63856e8i 0.437176i
\(722\) 8.97153e8i 2.38372i
\(723\) 6.61506e6 0.0175033
\(724\) −4.74123e8 −1.24932
\(725\) 3.05503e7 0.0801682
\(726\) 3.64350e8i 0.952159i
\(727\) 3.33880e8 0.868935 0.434468 0.900687i \(-0.356937\pi\)
0.434468 + 0.900687i \(0.356937\pi\)
\(728\) −2.43099e8 −0.630070
\(729\) 1.43489e7 0.0370370
\(730\) 3.05589e8 0.785542
\(731\) 1.26590e8i 0.324075i
\(732\) 4.89916e8i 1.24908i
\(733\) −7.33257e8 −1.86185 −0.930924 0.365214i \(-0.880996\pi\)
−0.930924 + 0.365214i \(0.880996\pi\)
\(734\) 8.97545e8 2.26970
\(735\) −1.06213e8 −0.267494
\(736\) 1.23738e7 0.0310362
\(737\) −1.23106e8 −0.307522
\(738\) 1.62826e8i 0.405092i
\(739\) 8.14134e7i 0.201726i −0.994900 0.100863i \(-0.967840\pi\)
0.994900 0.100863i \(-0.0321604\pi\)
\(740\) 3.87274e7i 0.0955704i
\(741\) 1.07885e8i 0.265159i
\(742\) 1.52849e9i 3.74154i
\(743\) 3.99055e8 0.972895 0.486448 0.873710i \(-0.338292\pi\)
0.486448 + 0.873710i \(0.338292\pi\)
\(744\) −6.39063e8 −1.55176
\(745\) 1.33976e8i 0.324009i
\(746\) 8.63397e8i 2.07967i
\(747\) 2.30155e8i 0.552152i
\(748\) 9.99222e7i 0.238758i
\(749\) 3.70500e7 0.0881746
\(750\) 4.20298e8i 0.996262i
\(751\) 6.73928e8i 1.59109i −0.605897 0.795543i \(-0.707186\pi\)
0.605897 0.795543i \(-0.292814\pi\)
\(752\) 4.96023e7i 0.116640i
\(753\) 2.92040e7 0.0684003
\(754\) −2.87728e7 −0.0671224
\(755\) 2.24440e8i 0.521507i
\(756\) 2.12594e8 0.492023
\(757\) 6.32443e8 1.45792 0.728960 0.684556i \(-0.240004\pi\)
0.728960 + 0.684556i \(0.240004\pi\)
\(758\) 3.87689e8i 0.890177i
\(759\) 7.41649e6 0.0169619
\(760\) 6.83248e8i 1.55646i
\(761\) −3.07136e8 −0.696909 −0.348454 0.937326i \(-0.613293\pi\)
−0.348454 + 0.937326i \(0.613293\pi\)
\(762\) 1.30180e8i 0.294226i
\(763\) 2.98313e8i 0.671581i
\(764\) 1.61951e8i 0.363164i
\(765\) −5.91420e7 −0.132103
\(766\) 2.55382e8i 0.568203i
\(767\) −1.30429e8 3.08496e7i −0.289060 0.0683697i
\(768\) 5.01176e8 1.10639
\(769\) 4.77329e8i 1.04964i −0.851214 0.524818i \(-0.824133\pi\)
0.851214 0.524818i \(-0.175867\pi\)
\(770\) −1.25750e8 −0.275446
\(771\) −5.55219e7 −0.121144
\(772\) −2.63404e8 −0.572494
\(773\) 2.57272e8i 0.556999i 0.960436 + 0.278500i \(0.0898371\pi\)
−0.960436 + 0.278500i \(0.910163\pi\)
\(774\) 1.35624e8 0.292491
\(775\) 4.73125e8i 1.01641i
\(776\) −2.56018e8 −0.547880
\(777\) 2.81415e7i 0.0599906i
\(778\) 5.52727e8i 1.17374i
\(779\) 5.18217e8 1.09622
\(780\) 9.87411e7i 0.208072i
\(781\) 1.95778e7i 0.0410970i
\(782\) 7.83443e7 0.163828
\(783\) 1.21794e7 0.0253713
\(784\) 2.91804e8 0.605541
\(785\) 1.72597e6i 0.00356799i