Properties

Label 240.6.f.a.49.2
Level $240$
Weight $6$
Character 240.49
Analytic conductor $38.492$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 240.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.4921167551\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 240.49
Dual form 240.6.f.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.00000i q^{3} +(-55.0000 - 10.0000i) q^{5} -4.00000i q^{7} -81.0000 q^{9} +O(q^{10})\) \(q+9.00000i q^{3} +(-55.0000 - 10.0000i) q^{5} -4.00000i q^{7} -81.0000 q^{9} +500.000 q^{11} -288.000i q^{13} +(90.0000 - 495.000i) q^{15} -1516.00i q^{17} -1344.00 q^{19} +36.0000 q^{21} +4100.00i q^{23} +(2925.00 + 1100.00i) q^{25} -729.000i q^{27} +2646.00 q^{29} +5612.00 q^{31} +4500.00i q^{33} +(-40.0000 + 220.000i) q^{35} +7288.00i q^{37} +2592.00 q^{39} -18986.0 q^{41} +2404.00i q^{43} +(4455.00 + 810.000i) q^{45} +8900.00i q^{47} +16791.0 q^{49} +13644.0 q^{51} +39804.0i q^{53} +(-27500.0 - 5000.00i) q^{55} -12096.0i q^{57} -28300.0 q^{59} +18290.0 q^{61} +324.000i q^{63} +(-2880.00 + 15840.0i) q^{65} +65956.0i q^{67} -36900.0 q^{69} +28800.0 q^{71} -30808.0i q^{73} +(-9900.00 + 26325.0i) q^{75} -2000.00i q^{77} +60228.0 q^{79} +6561.00 q^{81} +2468.00i q^{83} +(-15160.0 + 83380.0i) q^{85} +23814.0i q^{87} -22678.0 q^{89} -1152.00 q^{91} +50508.0i q^{93} +(73920.0 + 13440.0i) q^{95} +36968.0i q^{97} -40500.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 110q^{5} - 162q^{9} + O(q^{10}) \) \( 2q - 110q^{5} - 162q^{9} + 1000q^{11} + 180q^{15} - 2688q^{19} + 72q^{21} + 5850q^{25} + 5292q^{29} + 11224q^{31} - 80q^{35} + 5184q^{39} - 37972q^{41} + 8910q^{45} + 33582q^{49} + 27288q^{51} - 55000q^{55} - 56600q^{59} + 36580q^{61} - 5760q^{65} - 73800q^{69} + 57600q^{71} - 19800q^{75} + 120456q^{79} + 13122q^{81} - 30320q^{85} - 45356q^{89} - 2304q^{91} + 147840q^{95} - 81000q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 9.00000i 0.577350i
\(4\) 0 0
\(5\) −55.0000 10.0000i −0.983870 0.178885i
\(6\) 0 0
\(7\) 4.00000i 0.0308542i −0.999881 0.0154271i \(-0.995089\pi\)
0.999881 0.0154271i \(-0.00491080\pi\)
\(8\) 0 0
\(9\) −81.0000 −0.333333
\(10\) 0 0
\(11\) 500.000 1.24591 0.622957 0.782256i \(-0.285931\pi\)
0.622957 + 0.782256i \(0.285931\pi\)
\(12\) 0 0
\(13\) 288.000i 0.472644i −0.971675 0.236322i \(-0.924058\pi\)
0.971675 0.236322i \(-0.0759420\pi\)
\(14\) 0 0
\(15\) 90.0000 495.000i 0.103280 0.568038i
\(16\) 0 0
\(17\) 1516.00i 1.27226i −0.771581 0.636132i \(-0.780534\pi\)
0.771581 0.636132i \(-0.219466\pi\)
\(18\) 0 0
\(19\) −1344.00 −0.854113 −0.427056 0.904225i \(-0.640449\pi\)
−0.427056 + 0.904225i \(0.640449\pi\)
\(20\) 0 0
\(21\) 36.0000 0.0178137
\(22\) 0 0
\(23\) 4100.00i 1.61609i 0.589124 + 0.808043i \(0.299473\pi\)
−0.589124 + 0.808043i \(0.700527\pi\)
\(24\) 0 0
\(25\) 2925.00 + 1100.00i 0.936000 + 0.352000i
\(26\) 0 0
\(27\) 729.000i 0.192450i
\(28\) 0 0
\(29\) 2646.00 0.584245 0.292122 0.956381i \(-0.405639\pi\)
0.292122 + 0.956381i \(0.405639\pi\)
\(30\) 0 0
\(31\) 5612.00 1.04885 0.524425 0.851457i \(-0.324280\pi\)
0.524425 + 0.851457i \(0.324280\pi\)
\(32\) 0 0
\(33\) 4500.00i 0.719329i
\(34\) 0 0
\(35\) −40.0000 + 220.000i −0.00551937 + 0.0303566i
\(36\) 0 0
\(37\) 7288.00i 0.875193i 0.899171 + 0.437597i \(0.144170\pi\)
−0.899171 + 0.437597i \(0.855830\pi\)
\(38\) 0 0
\(39\) 2592.00 0.272881
\(40\) 0 0
\(41\) −18986.0 −1.76390 −0.881950 0.471343i \(-0.843769\pi\)
−0.881950 + 0.471343i \(0.843769\pi\)
\(42\) 0 0
\(43\) 2404.00i 0.198273i 0.995074 + 0.0991364i \(0.0316080\pi\)
−0.995074 + 0.0991364i \(0.968392\pi\)
\(44\) 0 0
\(45\) 4455.00 + 810.000i 0.327957 + 0.0596285i
\(46\) 0 0
\(47\) 8900.00i 0.587686i 0.955854 + 0.293843i \(0.0949343\pi\)
−0.955854 + 0.293843i \(0.905066\pi\)
\(48\) 0 0
\(49\) 16791.0 0.999048
\(50\) 0 0
\(51\) 13644.0 0.734541
\(52\) 0 0
\(53\) 39804.0i 1.94642i 0.229913 + 0.973211i \(0.426156\pi\)
−0.229913 + 0.973211i \(0.573844\pi\)
\(54\) 0 0
\(55\) −27500.0 5000.00i −1.22582 0.222876i
\(56\) 0 0
\(57\) 12096.0i 0.493122i
\(58\) 0 0
\(59\) −28300.0 −1.05842 −0.529208 0.848492i \(-0.677511\pi\)
−0.529208 + 0.848492i \(0.677511\pi\)
\(60\) 0 0
\(61\) 18290.0 0.629345 0.314673 0.949200i \(-0.398105\pi\)
0.314673 + 0.949200i \(0.398105\pi\)
\(62\) 0 0
\(63\) 324.000i 0.0102847i
\(64\) 0 0
\(65\) −2880.00 + 15840.0i −0.0845491 + 0.465020i
\(66\) 0 0
\(67\) 65956.0i 1.79501i 0.441002 + 0.897506i \(0.354623\pi\)
−0.441002 + 0.897506i \(0.645377\pi\)
\(68\) 0 0
\(69\) −36900.0 −0.933047
\(70\) 0 0
\(71\) 28800.0 0.678026 0.339013 0.940782i \(-0.389907\pi\)
0.339013 + 0.940782i \(0.389907\pi\)
\(72\) 0 0
\(73\) 30808.0i 0.676638i −0.941031 0.338319i \(-0.890142\pi\)
0.941031 0.338319i \(-0.109858\pi\)
\(74\) 0 0
\(75\) −9900.00 + 26325.0i −0.203227 + 0.540400i
\(76\) 0 0
\(77\) 2000.00i 0.0384418i
\(78\) 0 0
\(79\) 60228.0 1.08575 0.542876 0.839813i \(-0.317335\pi\)
0.542876 + 0.839813i \(0.317335\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) 2468.00i 0.0393233i 0.999807 + 0.0196616i \(0.00625890\pi\)
−0.999807 + 0.0196616i \(0.993741\pi\)
\(84\) 0 0
\(85\) −15160.0 + 83380.0i −0.227589 + 1.25174i
\(86\) 0 0
\(87\) 23814.0i 0.337314i
\(88\) 0 0
\(89\) −22678.0 −0.303480 −0.151740 0.988420i \(-0.548488\pi\)
−0.151740 + 0.988420i \(0.548488\pi\)
\(90\) 0 0
\(91\) −1152.00 −0.0145831
\(92\) 0 0
\(93\) 50508.0i 0.605554i
\(94\) 0 0
\(95\) 73920.0 + 13440.0i 0.840336 + 0.152788i
\(96\) 0 0
\(97\) 36968.0i 0.398930i 0.979905 + 0.199465i \(0.0639204\pi\)
−0.979905 + 0.199465i \(0.936080\pi\)
\(98\) 0 0
\(99\) −40500.0 −0.415305
\(100\) 0 0
\(101\) 167918. 1.63792 0.818962 0.573848i \(-0.194550\pi\)
0.818962 + 0.573848i \(0.194550\pi\)
\(102\) 0 0
\(103\) 154364.i 1.43368i 0.697236 + 0.716841i \(0.254413\pi\)
−0.697236 + 0.716841i \(0.745587\pi\)
\(104\) 0 0
\(105\) −1980.00 360.000i −0.0175264 0.00318661i
\(106\) 0 0
\(107\) 136788.i 1.15502i 0.816385 + 0.577509i \(0.195975\pi\)
−0.816385 + 0.577509i \(0.804025\pi\)
\(108\) 0 0
\(109\) 53810.0 0.433807 0.216904 0.976193i \(-0.430404\pi\)
0.216904 + 0.976193i \(0.430404\pi\)
\(110\) 0 0
\(111\) −65592.0 −0.505293
\(112\) 0 0
\(113\) 82692.0i 0.609211i 0.952479 + 0.304605i \(0.0985245\pi\)
−0.952479 + 0.304605i \(0.901475\pi\)
\(114\) 0 0
\(115\) 41000.0 225500.i 0.289094 1.59002i
\(116\) 0 0
\(117\) 23328.0i 0.157548i
\(118\) 0 0
\(119\) −6064.00 −0.0392547
\(120\) 0 0
\(121\) 88949.0 0.552303
\(122\) 0 0
\(123\) 170874.i 1.01839i
\(124\) 0 0
\(125\) −149875. 89750.0i −0.857935 0.513759i
\(126\) 0 0
\(127\) 211780.i 1.16513i −0.812783 0.582567i \(-0.802048\pi\)
0.812783 0.582567i \(-0.197952\pi\)
\(128\) 0 0
\(129\) −21636.0 −0.114473
\(130\) 0 0
\(131\) −169500. −0.862962 −0.431481 0.902122i \(-0.642009\pi\)
−0.431481 + 0.902122i \(0.642009\pi\)
\(132\) 0 0
\(133\) 5376.00i 0.0263530i
\(134\) 0 0
\(135\) −7290.00 + 40095.0i −0.0344265 + 0.189346i
\(136\) 0 0
\(137\) 252036.i 1.14726i −0.819115 0.573629i \(-0.805535\pi\)
0.819115 0.573629i \(-0.194465\pi\)
\(138\) 0 0
\(139\) 192016. 0.842947 0.421474 0.906841i \(-0.361513\pi\)
0.421474 + 0.906841i \(0.361513\pi\)
\(140\) 0 0
\(141\) −80100.0 −0.339301
\(142\) 0 0
\(143\) 144000.i 0.588874i
\(144\) 0 0
\(145\) −145530. 26460.0i −0.574821 0.104513i
\(146\) 0 0
\(147\) 151119.i 0.576801i
\(148\) 0 0
\(149\) −235694. −0.869727 −0.434863 0.900496i \(-0.643203\pi\)
−0.434863 + 0.900496i \(0.643203\pi\)
\(150\) 0 0
\(151\) 371492. 1.32589 0.662944 0.748669i \(-0.269307\pi\)
0.662944 + 0.748669i \(0.269307\pi\)
\(152\) 0 0
\(153\) 122796.i 0.424088i
\(154\) 0 0
\(155\) −308660. 56120.0i −1.03193 0.187624i
\(156\) 0 0
\(157\) 264952.i 0.857863i −0.903337 0.428932i \(-0.858890\pi\)
0.903337 0.428932i \(-0.141110\pi\)
\(158\) 0 0
\(159\) −358236. −1.12377
\(160\) 0 0
\(161\) 16400.0 0.0498631
\(162\) 0 0
\(163\) 403124.i 1.18842i 0.804310 + 0.594210i \(0.202535\pi\)
−0.804310 + 0.594210i \(0.797465\pi\)
\(164\) 0 0
\(165\) 45000.0 247500.i 0.128678 0.707726i
\(166\) 0 0
\(167\) 261900.i 0.726682i −0.931656 0.363341i \(-0.881636\pi\)
0.931656 0.363341i \(-0.118364\pi\)
\(168\) 0 0
\(169\) 288349. 0.776608
\(170\) 0 0
\(171\) 108864. 0.284704
\(172\) 0 0
\(173\) 326228.i 0.828716i 0.910114 + 0.414358i \(0.135994\pi\)
−0.910114 + 0.414358i \(0.864006\pi\)
\(174\) 0 0
\(175\) 4400.00 11700.0i 0.0108607 0.0288796i
\(176\) 0 0
\(177\) 254700.i 0.611077i
\(178\) 0 0
\(179\) −109516. −0.255473 −0.127736 0.991808i \(-0.540771\pi\)
−0.127736 + 0.991808i \(0.540771\pi\)
\(180\) 0 0
\(181\) −53146.0 −0.120580 −0.0602898 0.998181i \(-0.519202\pi\)
−0.0602898 + 0.998181i \(0.519202\pi\)
\(182\) 0 0
\(183\) 164610.i 0.363353i
\(184\) 0 0
\(185\) 72880.0 400840.i 0.156559 0.861076i
\(186\) 0 0
\(187\) 758000.i 1.58513i
\(188\) 0 0
\(189\) −2916.00 −0.00593790
\(190\) 0 0
\(191\) −232056. −0.460267 −0.230133 0.973159i \(-0.573916\pi\)
−0.230133 + 0.973159i \(0.573916\pi\)
\(192\) 0 0
\(193\) 1.03067e6i 1.99172i −0.0909274 0.995858i \(-0.528983\pi\)
0.0909274 0.995858i \(-0.471017\pi\)
\(194\) 0 0
\(195\) −142560. 25920.0i −0.268480 0.0488145i
\(196\) 0 0
\(197\) 522796.i 0.959769i 0.877332 + 0.479884i \(0.159321\pi\)
−0.877332 + 0.479884i \(0.840679\pi\)
\(198\) 0 0
\(199\) −215292. −0.385385 −0.192693 0.981259i \(-0.561722\pi\)
−0.192693 + 0.981259i \(0.561722\pi\)
\(200\) 0 0
\(201\) −593604. −1.03635
\(202\) 0 0
\(203\) 10584.0i 0.0180264i
\(204\) 0 0
\(205\) 1.04423e6 + 189860.i 1.73545 + 0.315536i
\(206\) 0 0
\(207\) 332100.i 0.538695i
\(208\) 0 0
\(209\) −672000. −1.06415
\(210\) 0 0
\(211\) 1.03008e6 1.59281 0.796407 0.604762i \(-0.206732\pi\)
0.796407 + 0.604762i \(0.206732\pi\)
\(212\) 0 0
\(213\) 259200.i 0.391459i
\(214\) 0 0
\(215\) 24040.0 132220.i 0.0354681 0.195075i
\(216\) 0 0
\(217\) 22448.0i 0.0323615i
\(218\) 0 0
\(219\) 277272. 0.390657
\(220\) 0 0
\(221\) −436608. −0.601327
\(222\) 0 0
\(223\) 456020.i 0.614075i −0.951697 0.307038i \(-0.900662\pi\)
0.951697 0.307038i \(-0.0993378\pi\)
\(224\) 0 0
\(225\) −236925. 89100.0i −0.312000 0.117333i
\(226\) 0 0
\(227\) 434252.i 0.559342i −0.960096 0.279671i \(-0.909775\pi\)
0.960096 0.279671i \(-0.0902253\pi\)
\(228\) 0 0
\(229\) 722710. 0.910700 0.455350 0.890313i \(-0.349514\pi\)
0.455350 + 0.890313i \(0.349514\pi\)
\(230\) 0 0
\(231\) 18000.0 0.0221944
\(232\) 0 0
\(233\) 565348.i 0.682223i −0.940023 0.341111i \(-0.889197\pi\)
0.940023 0.341111i \(-0.110803\pi\)
\(234\) 0 0
\(235\) 89000.0 489500.i 0.105128 0.578207i
\(236\) 0 0
\(237\) 542052.i 0.626859i
\(238\) 0 0
\(239\) 324904. 0.367926 0.183963 0.982933i \(-0.441107\pi\)
0.183963 + 0.982933i \(0.441107\pi\)
\(240\) 0 0
\(241\) 915262. 1.01509 0.507543 0.861626i \(-0.330554\pi\)
0.507543 + 0.861626i \(0.330554\pi\)
\(242\) 0 0
\(243\) 59049.0i 0.0641500i
\(244\) 0 0
\(245\) −923505. 167910.i −0.982933 0.178715i
\(246\) 0 0
\(247\) 387072.i 0.403691i
\(248\) 0 0
\(249\) −22212.0 −0.0227033
\(250\) 0 0
\(251\) −1.36708e6 −1.36965 −0.684823 0.728709i \(-0.740121\pi\)
−0.684823 + 0.728709i \(0.740121\pi\)
\(252\) 0 0
\(253\) 2.05000e6i 2.01350i
\(254\) 0 0
\(255\) −750420. 136440.i −0.722693 0.131399i
\(256\) 0 0
\(257\) 892932.i 0.843307i −0.906757 0.421653i \(-0.861450\pi\)
0.906757 0.421653i \(-0.138550\pi\)
\(258\) 0 0
\(259\) 29152.0 0.0270034
\(260\) 0 0
\(261\) −214326. −0.194748
\(262\) 0 0
\(263\) 1.86650e6i 1.66394i 0.554818 + 0.831972i \(0.312788\pi\)
−0.554818 + 0.831972i \(0.687212\pi\)
\(264\) 0 0
\(265\) 398040. 2.18922e6i 0.348187 1.91503i
\(266\) 0 0
\(267\) 204102.i 0.175214i
\(268\) 0 0
\(269\) 1.37227e6 1.15627 0.578133 0.815943i \(-0.303782\pi\)
0.578133 + 0.815943i \(0.303782\pi\)
\(270\) 0 0
\(271\) −458644. −0.379361 −0.189680 0.981846i \(-0.560745\pi\)
−0.189680 + 0.981846i \(0.560745\pi\)
\(272\) 0 0
\(273\) 10368.0i 0.00841954i
\(274\) 0 0
\(275\) 1.46250e6 + 550000.i 1.16618 + 0.438562i
\(276\) 0 0
\(277\) 985408.i 0.771643i 0.922573 + 0.385822i \(0.126082\pi\)
−0.922573 + 0.385822i \(0.873918\pi\)
\(278\) 0 0
\(279\) −454572. −0.349617
\(280\) 0 0
\(281\) 165798. 0.125260 0.0626302 0.998037i \(-0.480051\pi\)
0.0626302 + 0.998037i \(0.480051\pi\)
\(282\) 0 0
\(283\) 1.66471e6i 1.23558i 0.786342 + 0.617792i \(0.211972\pi\)
−0.786342 + 0.617792i \(0.788028\pi\)
\(284\) 0 0
\(285\) −120960. + 665280.i −0.0882124 + 0.485168i
\(286\) 0 0
\(287\) 75944.0i 0.0544238i
\(288\) 0 0
\(289\) −878399. −0.618653
\(290\) 0 0
\(291\) −332712. −0.230322
\(292\) 0 0
\(293\) 2.55104e6i 1.73600i 0.496567 + 0.867998i \(0.334594\pi\)
−0.496567 + 0.867998i \(0.665406\pi\)
\(294\) 0 0
\(295\) 1.55650e6 + 283000.i 1.04134 + 0.189335i
\(296\) 0 0
\(297\) 364500.i 0.239776i
\(298\) 0 0
\(299\) 1.18080e6 0.763833
\(300\) 0 0
\(301\) 9616.00 0.00611756
\(302\) 0 0
\(303\) 1.51126e6i 0.945656i
\(304\) 0 0
\(305\) −1.00595e6 182900.i −0.619194 0.112581i
\(306\) 0 0
\(307\) 736020.i 0.445701i 0.974853 + 0.222851i \(0.0715362\pi\)
−0.974853 + 0.222851i \(0.928464\pi\)
\(308\) 0 0
\(309\) −1.38928e6 −0.827737
\(310\) 0 0
\(311\) −1.71660e6 −1.00639 −0.503197 0.864172i \(-0.667843\pi\)
−0.503197 + 0.864172i \(0.667843\pi\)
\(312\) 0 0
\(313\) 2.83851e6i 1.63768i 0.574020 + 0.818842i \(0.305383\pi\)
−0.574020 + 0.818842i \(0.694617\pi\)
\(314\) 0 0
\(315\) 3240.00 17820.0i 0.00183979 0.0101189i
\(316\) 0 0
\(317\) 1.27605e6i 0.713215i 0.934254 + 0.356607i \(0.116067\pi\)
−0.934254 + 0.356607i \(0.883933\pi\)
\(318\) 0 0
\(319\) 1.32300e6 0.727919
\(320\) 0 0
\(321\) −1.23109e6 −0.666850
\(322\) 0 0
\(323\) 2.03750e6i 1.08666i
\(324\) 0 0
\(325\) 316800. 842400.i 0.166371 0.442395i
\(326\) 0 0
\(327\) 484290.i 0.250459i
\(328\) 0 0
\(329\) 35600.0 0.0181326
\(330\) 0 0
\(331\) −443992. −0.222744 −0.111372 0.993779i \(-0.535524\pi\)
−0.111372 + 0.993779i \(0.535524\pi\)
\(332\) 0 0
\(333\) 590328.i 0.291731i
\(334\) 0 0
\(335\) 659560. 3.62758e6i 0.321101 1.76606i
\(336\) 0 0
\(337\) 2.71326e6i 1.30142i −0.759328 0.650708i \(-0.774472\pi\)
0.759328 0.650708i \(-0.225528\pi\)
\(338\) 0 0
\(339\) −744228. −0.351728
\(340\) 0 0
\(341\) 2.80600e6 1.30678
\(342\) 0 0
\(343\) 134392.i 0.0616791i
\(344\) 0 0
\(345\) 2.02950e6 + 369000.i 0.917997 + 0.166909i
\(346\) 0 0
\(347\) 1.31051e6i 0.584273i −0.956377 0.292137i \(-0.905634\pi\)
0.956377 0.292137i \(-0.0943662\pi\)
\(348\) 0 0
\(349\) 298910. 0.131364 0.0656821 0.997841i \(-0.479078\pi\)
0.0656821 + 0.997841i \(0.479078\pi\)
\(350\) 0 0
\(351\) −209952. −0.0909604
\(352\) 0 0
\(353\) 737996.i 0.315223i 0.987501 + 0.157611i \(0.0503793\pi\)
−0.987501 + 0.157611i \(0.949621\pi\)
\(354\) 0 0
\(355\) −1.58400e6 288000.i −0.667090 0.121289i
\(356\) 0 0
\(357\) 54576.0i 0.0226637i
\(358\) 0 0
\(359\) −2.34074e6 −0.958557 −0.479278 0.877663i \(-0.659102\pi\)
−0.479278 + 0.877663i \(0.659102\pi\)
\(360\) 0 0
\(361\) −669763. −0.270491
\(362\) 0 0
\(363\) 800541.i 0.318872i
\(364\) 0 0
\(365\) −308080. + 1.69444e6i −0.121041 + 0.665724i
\(366\) 0 0
\(367\) 127292.i 0.0493328i 0.999696 + 0.0246664i \(0.00785236\pi\)
−0.999696 + 0.0246664i \(0.992148\pi\)
\(368\) 0 0
\(369\) 1.53787e6 0.587966
\(370\) 0 0
\(371\) 159216. 0.0600554
\(372\) 0 0
\(373\) 4.03870e6i 1.50303i 0.659713 + 0.751517i \(0.270678\pi\)
−0.659713 + 0.751517i \(0.729322\pi\)
\(374\) 0 0
\(375\) 807750. 1.34888e6i 0.296619 0.495329i
\(376\) 0 0
\(377\) 762048.i 0.276140i
\(378\) 0 0
\(379\) 1.01214e6 0.361944 0.180972 0.983488i \(-0.442076\pi\)
0.180972 + 0.983488i \(0.442076\pi\)
\(380\) 0 0
\(381\) 1.90602e6 0.672690
\(382\) 0 0
\(383\) 2.37610e6i 0.827690i 0.910347 + 0.413845i \(0.135814\pi\)
−0.910347 + 0.413845i \(0.864186\pi\)
\(384\) 0 0
\(385\) −20000.0 + 110000.i −0.00687667 + 0.0378217i
\(386\) 0 0
\(387\) 194724.i 0.0660910i
\(388\) 0 0
\(389\) −1.42497e6 −0.477456 −0.238728 0.971087i \(-0.576730\pi\)
−0.238728 + 0.971087i \(0.576730\pi\)
\(390\) 0 0
\(391\) 6.21560e6 2.05609
\(392\) 0 0
\(393\) 1.52550e6i 0.498231i
\(394\) 0 0
\(395\) −3.31254e6 602280.i −1.06824 0.194225i
\(396\) 0 0
\(397\) 1.69345e6i 0.539257i −0.962964 0.269628i \(-0.913099\pi\)
0.962964 0.269628i \(-0.0869009\pi\)
\(398\) 0 0
\(399\) −48384.0 −0.0152149
\(400\) 0 0
\(401\) −2.84501e6 −0.883532 −0.441766 0.897130i \(-0.645648\pi\)
−0.441766 + 0.897130i \(0.645648\pi\)
\(402\) 0 0
\(403\) 1.61626e6i 0.495733i
\(404\) 0 0
\(405\) −360855. 65610.0i −0.109319 0.0198762i
\(406\) 0 0
\(407\) 3.64400e6i 1.09042i
\(408\) 0 0
\(409\) 1.89069e6 0.558873 0.279436 0.960164i \(-0.409852\pi\)
0.279436 + 0.960164i \(0.409852\pi\)
\(410\) 0 0
\(411\) 2.26832e6 0.662370
\(412\) 0 0
\(413\) 113200.i 0.0326566i
\(414\) 0 0
\(415\) 24680.0 135740.i 0.00703437 0.0386890i
\(416\) 0 0
\(417\) 1.72814e6i 0.486676i
\(418\) 0 0
\(419\) 4.60930e6 1.28263 0.641313 0.767280i \(-0.278390\pi\)
0.641313 + 0.767280i \(0.278390\pi\)
\(420\) 0 0
\(421\) −6.04151e6 −1.66127 −0.830635 0.556817i \(-0.812022\pi\)
−0.830635 + 0.556817i \(0.812022\pi\)
\(422\) 0 0
\(423\) 720900.i 0.195895i
\(424\) 0 0
\(425\) 1.66760e6 4.43430e6i 0.447837 1.19084i
\(426\) 0 0
\(427\) 73160.0i 0.0194180i
\(428\) 0 0
\(429\) 1.29600e6 0.339987
\(430\) 0 0
\(431\) 3800.00 0.000985350 0.000492675 1.00000i \(-0.499843\pi\)
0.000492675 1.00000i \(0.499843\pi\)
\(432\) 0 0
\(433\) 250736.i 0.0642683i 0.999484 + 0.0321342i \(0.0102304\pi\)
−0.999484 + 0.0321342i \(0.989770\pi\)
\(434\) 0 0
\(435\) 238140. 1.30977e6i 0.0603405 0.331873i
\(436\) 0 0
\(437\) 5.51040e6i 1.38032i
\(438\) 0 0
\(439\) −3.58873e6 −0.888750 −0.444375 0.895841i \(-0.646574\pi\)
−0.444375 + 0.895841i \(0.646574\pi\)
\(440\) 0 0
\(441\) −1.36007e6 −0.333016
\(442\) 0 0
\(443\) 1.41479e6i 0.342517i 0.985226 + 0.171258i \(0.0547833\pi\)
−0.985226 + 0.171258i \(0.945217\pi\)
\(444\) 0 0
\(445\) 1.24729e6 + 226780.i 0.298585 + 0.0542881i
\(446\) 0 0
\(447\) 2.12125e6i 0.502137i
\(448\) 0 0
\(449\) 829806. 0.194250 0.0971249 0.995272i \(-0.469035\pi\)
0.0971249 + 0.995272i \(0.469035\pi\)
\(450\) 0 0
\(451\) −9.49300e6 −2.19767
\(452\) 0 0
\(453\) 3.34343e6i 0.765502i
\(454\) 0 0
\(455\) 63360.0 + 11520.0i 0.0143478 + 0.00260870i
\(456\) 0 0
\(457\) 4.68198e6i 1.04867i −0.851512 0.524335i \(-0.824314\pi\)
0.851512 0.524335i \(-0.175686\pi\)
\(458\) 0 0
\(459\) −1.10516e6 −0.244847
\(460\) 0 0
\(461\) −141930. −0.0311044 −0.0155522 0.999879i \(-0.504951\pi\)
−0.0155522 + 0.999879i \(0.504951\pi\)
\(462\) 0 0
\(463\) 727476.i 0.157713i −0.996886 0.0788563i \(-0.974873\pi\)
0.996886 0.0788563i \(-0.0251268\pi\)
\(464\) 0 0
\(465\) 505080. 2.77794e6i 0.108325 0.595786i
\(466\) 0 0
\(467\) 4.47640e6i 0.949809i −0.880037 0.474905i \(-0.842483\pi\)
0.880037 0.474905i \(-0.157517\pi\)
\(468\) 0 0
\(469\) 263824. 0.0553837
\(470\) 0 0
\(471\) 2.38457e6 0.495288
\(472\) 0 0
\(473\) 1.20200e6i 0.247031i
\(474\) 0 0
\(475\) −3.93120e6 1.47840e6i −0.799450 0.300648i
\(476\) 0 0
\(477\) 3.22412e6i 0.648807i
\(478\) 0 0
\(479\) −1.32718e6 −0.264297 −0.132149 0.991230i \(-0.542188\pi\)
−0.132149 + 0.991230i \(0.542188\pi\)
\(480\) 0 0
\(481\) 2.09894e6 0.413655
\(482\) 0 0
\(483\) 147600.i 0.0287885i
\(484\) 0 0
\(485\) 369680. 2.03324e6i 0.0713628 0.392495i
\(486\) 0 0
\(487\) 4.11647e6i 0.786507i −0.919430 0.393253i \(-0.871350\pi\)
0.919430 0.393253i \(-0.128650\pi\)
\(488\) 0 0
\(489\) −3.62812e6 −0.686134
\(490\) 0 0
\(491\) 6.12316e6 1.14623 0.573115 0.819475i \(-0.305735\pi\)
0.573115 + 0.819475i \(0.305735\pi\)
\(492\) 0 0
\(493\) 4.01134e6i 0.743313i
\(494\) 0 0
\(495\) 2.22750e6 + 405000.i 0.408606 + 0.0742920i
\(496\) 0 0
\(497\) 115200.i 0.0209200i
\(498\) 0 0
\(499\) −7.90490e6 −1.42117 −0.710584 0.703613i \(-0.751569\pi\)
−0.710584 + 0.703613i \(0.751569\pi\)
\(500\) 0 0
\(501\) 2.35710e6 0.419550
\(502\) 0 0
\(503\) 3.97628e6i 0.700741i −0.936611 0.350370i \(-0.886056\pi\)
0.936611 0.350370i \(-0.113944\pi\)
\(504\) 0 0
\(505\) −9.23549e6 1.67918e6i −1.61150 0.293001i
\(506\) 0 0
\(507\) 2.59514e6i 0.448375i
\(508\) 0 0
\(509\) −781914. −0.133772 −0.0668859 0.997761i \(-0.521306\pi\)
−0.0668859 + 0.997761i \(0.521306\pi\)
\(510\) 0 0
\(511\) −123232. −0.0208772
\(512\) 0 0
\(513\) 979776.i 0.164374i
\(514\) 0 0
\(515\) 1.54364e6 8.49002e6i 0.256465 1.41056i
\(516\) 0 0
\(517\) 4.45000e6i 0.732207i
\(518\) 0 0
\(519\) −2.93605e6 −0.478460
\(520\) 0 0
\(521\) 5.82694e6 0.940472 0.470236 0.882541i \(-0.344169\pi\)
0.470236 + 0.882541i \(0.344169\pi\)
\(522\) 0 0
\(523\) 9.78938e6i 1.56495i 0.622681 + 0.782476i \(0.286043\pi\)
−0.622681 + 0.782476i \(0.713957\pi\)
\(524\) 0 0
\(525\) 105300. + 39600.0i 0.0166736 + 0.00627042i
\(526\) 0 0
\(527\) 8.50779e6i 1.33441i
\(528\) 0 0
\(529\) −1.03737e7 −1.61173
\(530\) 0 0
\(531\) 2.29230e6 0.352805
\(532\) 0 0
\(533\) 5.46797e6i 0.833696i
\(534\) 0 0
\(535\) 1.36788e6 7.52334e6i 0.206616 1.13639i
\(536\) 0 0
\(537\) 985644.i 0.147497i
\(538\) 0 0
\(539\) 8.39550e6 1.24473
\(540\) 0 0
\(541\) 4.76059e6 0.699307 0.349653 0.936879i \(-0.386299\pi\)
0.349653 + 0.936879i \(0.386299\pi\)
\(542\) 0 0
\(543\) 478314.i 0.0696167i
\(544\) 0 0
\(545\) −2.95955e6 538100.i −0.426810 0.0776018i
\(546\) 0 0
\(547\) 1.16595e6i 0.166614i −0.996524 0.0833069i \(-0.973452\pi\)
0.996524 0.0833069i \(-0.0265482\pi\)
\(548\) 0 0
\(549\) −1.48149e6 −0.209782
\(550\) 0 0
\(551\) −3.55622e6 −0.499011
\(552\) 0 0
\(553\) 240912.i 0.0335001i
\(554\) 0 0
\(555\) 3.60756e6 + 655920.i 0.497143 + 0.0903896i
\(556\) 0 0
\(557\) 1.61293e6i 0.220282i 0.993916 + 0.110141i \(0.0351302\pi\)
−0.993916 + 0.110141i \(0.964870\pi\)
\(558\) 0 0
\(559\) 692352. 0.0937125
\(560\) 0 0
\(561\) 6.82200e6 0.915176
\(562\) 0 0
\(563\) 3.40603e6i 0.452874i −0.974026 0.226437i \(-0.927292\pi\)
0.974026 0.226437i \(-0.0727077\pi\)
\(564\) 0 0
\(565\) 826920. 4.54806e6i 0.108979 0.599384i
\(566\) 0 0
\(567\) 26244.0i 0.00342825i
\(568\) 0 0
\(569\) 1.44009e7 1.86470 0.932350 0.361557i \(-0.117755\pi\)
0.932350 + 0.361557i \(0.117755\pi\)
\(570\) 0 0
\(571\) −4.74772e6 −0.609389 −0.304695 0.952450i \(-0.598554\pi\)
−0.304695 + 0.952450i \(0.598554\pi\)
\(572\) 0 0
\(573\) 2.08850e6i 0.265735i
\(574\) 0 0
\(575\) −4.51000e6 + 1.19925e7i −0.568862 + 1.51266i
\(576\) 0 0
\(577\) 1.09094e7i 1.36415i 0.731283 + 0.682074i \(0.238922\pi\)
−0.731283 + 0.682074i \(0.761078\pi\)
\(578\) 0 0
\(579\) 9.27605e6 1.14992
\(580\) 0 0
\(581\) 9872.00 0.00121329
\(582\) 0 0
\(583\) 1.99020e7i 2.42508i
\(584\) 0 0
\(585\) 233280. 1.28304e6i 0.0281830 0.155007i
\(586\) 0 0
\(587\) 8.53223e6i 1.02204i 0.859569 + 0.511019i \(0.170732\pi\)
−0.859569 + 0.511019i \(0.829268\pi\)
\(588\) 0 0
\(589\) −7.54253e6 −0.895836
\(590\) 0 0
\(591\) −4.70516e6 −0.554123
\(592\) 0 0
\(593\) 4.63182e6i 0.540897i −0.962734 0.270449i \(-0.912828\pi\)
0.962734 0.270449i \(-0.0871721\pi\)
\(594\) 0 0
\(595\) 333520. + 60640.0i 0.0386215 + 0.00702210i
\(596\) 0 0
\(597\) 1.93763e6i 0.222502i
\(598\) 0 0
\(599\) 6.27598e6 0.714684 0.357342 0.933974i \(-0.383683\pi\)
0.357342 + 0.933974i \(0.383683\pi\)
\(600\) 0 0
\(601\) 7.71988e6 0.871815 0.435907 0.899992i \(-0.356428\pi\)
0.435907 + 0.899992i \(0.356428\pi\)
\(602\) 0 0
\(603\) 5.34244e6i 0.598337i
\(604\) 0 0
\(605\) −4.89220e6 889490.i −0.543395 0.0987990i
\(606\) 0 0
\(607\) 6.06160e6i 0.667753i −0.942617 0.333876i \(-0.891643\pi\)
0.942617 0.333876i \(-0.108357\pi\)
\(608\) 0 0
\(609\) 95256.0 0.0104076
\(610\) 0 0
\(611\) 2.56320e6 0.277766
\(612\) 0 0
\(613\) 3.66489e6i 0.393921i −0.980411 0.196961i \(-0.936893\pi\)
0.980411 0.196961i \(-0.0631071\pi\)
\(614\) 0 0
\(615\) −1.70874e6 + 9.39807e6i −0.182175 + 1.00196i
\(616\) 0 0
\(617\) 9.32522e6i 0.986157i 0.869985 + 0.493079i \(0.164129\pi\)
−0.869985 + 0.493079i \(0.835871\pi\)
\(618\) 0 0
\(619\) −7.40162e6 −0.776426 −0.388213 0.921570i \(-0.626907\pi\)
−0.388213 + 0.921570i \(0.626907\pi\)
\(620\) 0 0
\(621\) 2.98890e6 0.311016
\(622\) 0 0
\(623\) 90712.0i 0.00936364i
\(624\) 0 0
\(625\) 7.34562e6 + 6.43500e6i 0.752192 + 0.658944i
\(626\) 0 0
\(627\) 6.04800e6i 0.614388i
\(628\) 0 0
\(629\) 1.10486e7 1.11348
\(630\) 0 0
\(631\) −160052. −0.0160025 −0.00800125 0.999968i \(-0.502547\pi\)
−0.00800125 + 0.999968i \(0.502547\pi\)
\(632\) 0 0
\(633\) 9.27072e6i 0.919611i
\(634\) 0 0
\(635\) −2.11780e6 + 1.16479e7i −0.208425 + 1.14634i
\(636\) 0 0
\(637\) 4.83581e6i 0.472194i
\(638\) 0 0
\(639\) −2.33280e6 −0.226009
\(640\) 0 0
\(641\) −1.69565e7 −1.63002 −0.815008 0.579450i \(-0.803268\pi\)
−0.815008 + 0.579450i \(0.803268\pi\)
\(642\) 0 0
\(643\) 1.10128e7i 1.05044i −0.850967 0.525219i \(-0.823984\pi\)
0.850967 0.525219i \(-0.176016\pi\)
\(644\) 0 0
\(645\) 1.18998e6 + 216360.i 0.112626 + 0.0204775i
\(646\) 0 0
\(647\) 3.33848e6i 0.313537i 0.987635 + 0.156768i \(0.0501076\pi\)
−0.987635 + 0.156768i \(0.949892\pi\)
\(648\) 0 0
\(649\) −1.41500e7 −1.31870
\(650\) 0 0
\(651\) 202032. 0.0186839
\(652\) 0 0
\(653\) 4.76181e6i 0.437008i −0.975836 0.218504i \(-0.929882\pi\)
0.975836 0.218504i \(-0.0701177\pi\)
\(654\) 0 0
\(655\) 9.32250e6 + 1.69500e6i 0.849042 + 0.154371i
\(656\) 0 0
\(657\) 2.49545e6i 0.225546i
\(658\) 0 0
\(659\) 798188. 0.0715965 0.0357982 0.999359i \(-0.488603\pi\)
0.0357982 + 0.999359i \(0.488603\pi\)
\(660\) 0 0
\(661\) −1.54048e7 −1.37136 −0.685682 0.727901i \(-0.740496\pi\)
−0.685682 + 0.727901i \(0.740496\pi\)
\(662\) 0 0
\(663\) 3.92947e6i 0.347177i
\(664\) 0 0
\(665\) 53760.0 295680.i 0.00471417 0.0259279i
\(666\) 0 0
\(667\) 1.08486e7i 0.944189i
\(668\) 0 0
\(669\) 4.10418e6 0.354537
\(670\) 0 0
\(671\) 9.14500e6 0.784111
\(672\) 0 0
\(673\) 976704.i 0.0831238i −0.999136 0.0415619i \(-0.986767\pi\)
0.999136 0.0415619i \(-0.0132334\pi\)
\(674\) 0 0
\(675\) 801900. 2.13232e6i 0.0677424 0.180133i
\(676\) 0 0
\(677\) 1.93885e7i 1.62582i −0.582388 0.812911i \(-0.697881\pi\)
0.582388 0.812911i \(-0.302119\pi\)
\(678\) 0 0
\(679\) 147872. 0.0123087
\(680\) 0 0
\(681\) 3.90827e6 0.322936
\(682\) 0 0
\(683\) 5.25573e6i 0.431103i 0.976492 + 0.215552i \(0.0691550\pi\)
−0.976492 + 0.215552i \(0.930845\pi\)
\(684\) 0 0
\(685\) −2.52036e6 + 1.38620e7i −0.205228 + 1.12875i
\(686\) 0 0
\(687\) 6.50439e6i 0.525793i
\(688\) 0 0
\(689\) 1.14636e7 0.919965
\(690\) 0 0
\(691\) 5.45034e6 0.434238 0.217119 0.976145i \(-0.430334\pi\)
0.217119 + 0.976145i \(0.430334\pi\)
\(692\) 0 0
\(693\) 162000.i 0.0128139i
\(694\) 0 0
\(695\) −1.05609e7 1.92016e6i −0.829350 0.150791i
\(696\) 0 0
\(697\) 2.87828e7i 2.24414i
\(698\) 0 0
\(699\) 5.08813e6 0.393881
\(700\) 0 0
\(701\) −4.43961e6 −0.341232 −0.170616 0.985338i \(-0.554576\pi\)
−0.170616 + 0.985338i \(0.554576\pi\)
\(702\) 0 0
\(703\) 9.79507e6i 0.747514i
\(704\) 0 0
\(705\) 4.40550e6 + 801000.i 0.333828 + 0.0606960i
\(706\) 0 0
\(707\) 671672.i 0.0505369i
\(708\) 0 0
\(709\) −4.55918e6 −0.340621 −0.170310 0.985390i \(-0.554477\pi\)
−0.170310 + 0.985390i \(0.554477\pi\)
\(710\) 0 0
\(711\) −4.87847e6 −0.361917
\(712\) 0 0
\(713\) 2.30092e7i 1.69503i
\(714\) 0 0
\(715\) −1.44000e6 + 7.92000e6i −0.105341 + 0.579375i
\(716\) 0 0
\(717\) 2.92414e6i 0.212422i
\(718\) 0 0
\(719\) −2.06630e7 −1.49063 −0.745317 0.666710i \(-0.767702\pi\)
−0.745317 + 0.666710i \(0.767702\pi\)
\(720\) 0 0
\(721\) 617456. 0.0442352
\(722\) 0 0
\(723\) 8.23736e6i 0.586060i
\(724\) 0 0
\(725\) 7.73955e6 + 2.91060e6i 0.546853 + 0.205654i
\(726\) 0 0
\(727\) 5.48161e6i 0.384656i 0.981331 + 0.192328i \(0.0616037\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(728\) 0 0
\(729\) −531441. −0.0370370
\(730\) 0 0
\(731\) 3.64446e6 0.252255
\(732\) 0 0
\(733\) 8.55579e6i 0.588166i −0.955780 0.294083i \(-0.904986\pi\)
0.955780 0.294083i \(-0.0950143\pi\)
\(734\) 0 0
\(735\) 1.51119e6 8.31154e6i 0.103181 0.567497i
\(736\) 0 0
\(737\) 3.29780e7i 2.23643i
\(738\) 0 0
\(739\) −5.29119e6 −0.356404 −0.178202 0.983994i \(-0.557028\pi\)
−0.178202 + 0.983994i \(0.557028\pi\)
\(740\) 0 0
\(741\) −3.48365e6 −0.233071
\(742\) 0 0
\(743\) 2.36432e6i 0.157121i 0.996909 + 0.0785606i \(0.0250324\pi\)
−0.996909 + 0.0785606i \(0.974968\pi\)
\(744\) 0 0
\(745\) 1.29632e7 + 2.35694e6i 0.855698 + 0.155581i
\(746\) 0 0
\(747\) 199908.i 0.0131078i
\(748\) 0 0
\(749\) 547152. 0.0356372
\(750\) 0 0
\(751\) 8.79694e6 0.569157 0.284578 0.958653i \(-0.408146\pi\)
0.284578 + 0.958653i \(0.408146\pi\)
\(752\) 0 0
\(753\) 1.23037e7i 0.790766i
\(754\) 0 0
\(755\) −2.04321e7 3.71492e6i −1.30450 0.237182i
\(756\) 0 0
\(757\) 2.95808e7i 1.87616i −0.346421 0.938079i \(-0.612603\pi\)
0.346421 0.938079i \(-0.387397\pi\)
\(758\) 0 0
\(759\) −1.84500e7 −1.16250
\(760\) 0 0
\(761\) −1.26296e7 −0.790549 −0.395274 0.918563i \(-0.629351\pi\)
−0.395274 + 0.918563i \(0.629351\pi\)
\(762\) 0 0
\(763\) 215240.i 0.0133848i
\(764\) 0 0
\(765\) 1.22796e6 6.75378e6i 0.0758631 0.417247i
\(766\) 0 0
\(767\) 8.15040e6i 0.500254i
\(768\) 0 0
\(769\) 2.32186e7 1.41586 0.707929 0.706283i \(-0.249630\pi\)
0.707929 + 0.706283i \(0.249630\pi\)
\(770\) 0 0
\(771\) 8.03639e6 0.486883
\(772\) 0 0
\(773\) 1.73201e7i 1.04256i −0.853386 0.521280i \(-0.825455\pi\)
0.853386 0.521280i \(-0.174545\pi\)
\(774\) 0 0
\(775\) 1.64151e7 + 6.17320e6i 0.981724 + 0.369195i
\(776\) 0 0
\(777\) 262368.i 0.0155904i
\(778\) 0 0
\(779\) 2.55172e7 1.50657
\(780\) 0 0
\(781\) 1.44000e7 0.844763
\(782\) 0 0
\(783\) 1.92893e6i 0.112438i
\(784\) 0 0
\(785\) −2.64952e6 + 1.45724e7i −0.153459 + 0.844026i
\(786\) 0 0
\(787\) 556676.i 0.0320380i 0.999872 + 0.0160190i \(0.00509923\pi\)
−0.999872 + 0.0160190i \(0.994901\pi\)
\(788\) 0 0
\(789\) −1.67985e7 −0.960678
\(790\) 0 0
\(791\) 330768. 0.0187967
\(792\) 0 0
\(793\) 5.26752e6i 0.297456i
\(794\)