Properties

Label 108.6.e.a.73.5
Level 108
Weight 6
Character 108.73
Analytic conductor 17.321
Analytic rank 0
Dimension 10
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{16} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 73.5
Root \(1.11227i\) of \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Character \(\chi\) \(=\) 108.73
Dual form 108.6.e.a.37.5

$q$-expansion

\(f(q)\) \(=\) \(q+(55.1996 + 95.6086i) q^{5} +(-50.8724 + 88.1135i) q^{7} +O(q^{10})\) \(q+(55.1996 + 95.6086i) q^{5} +(-50.8724 + 88.1135i) q^{7} +(-75.1560 + 130.174i) q^{11} +(-317.712 - 550.293i) q^{13} -1498.54 q^{17} +1437.69 q^{19} +(-632.053 - 1094.75i) q^{23} +(-4531.50 + 7848.79i) q^{25} +(-1388.75 + 2405.38i) q^{29} +(3484.34 + 6035.05i) q^{31} -11232.5 q^{35} -7950.71 q^{37} +(-1013.77 - 1755.90i) q^{41} +(6261.65 - 10845.5i) q^{43} +(-3241.17 + 5613.87i) q^{47} +(3227.51 + 5590.21i) q^{49} -9827.54 q^{53} -16594.3 q^{55} +(23544.0 + 40779.3i) q^{59} +(-4168.92 + 7220.78i) q^{61} +(35075.2 - 60752.0i) q^{65} +(3630.45 + 6288.12i) q^{67} -3582.33 q^{71} +58077.5 q^{73} +(-7646.73 - 13244.5i) q^{77} +(31871.4 - 55202.9i) q^{79} +(41423.3 - 71747.2i) q^{83} +(-82718.9 - 143273. i) q^{85} +3861.51 q^{89} +64651.0 q^{91} +(79359.8 + 137455. i) q^{95} +(-34638.6 + 59995.8i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} + 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 55.1996 + 95.6086i 0.987441 + 1.71030i 0.630542 + 0.776155i \(0.282833\pi\)
0.356899 + 0.934143i \(0.383834\pi\)
\(6\) 0 0
\(7\) −50.8724 + 88.1135i −0.392407 + 0.679669i −0.992766 0.120061i \(-0.961691\pi\)
0.600359 + 0.799730i \(0.295024\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −75.1560 + 130.174i −0.187276 + 0.324371i −0.944341 0.328968i \(-0.893299\pi\)
0.757065 + 0.653339i \(0.226633\pi\)
\(12\) 0 0
\(13\) −317.712 550.293i −0.521405 0.903100i −0.999690 0.0248953i \(-0.992075\pi\)
0.478285 0.878205i \(-0.341259\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1498.54 −1.25761 −0.628806 0.777562i \(-0.716456\pi\)
−0.628806 + 0.777562i \(0.716456\pi\)
\(18\) 0 0
\(19\) 1437.69 0.913651 0.456825 0.889556i \(-0.348986\pi\)
0.456825 + 0.889556i \(0.348986\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −632.053 1094.75i −0.249134 0.431513i 0.714151 0.699991i \(-0.246813\pi\)
−0.963286 + 0.268478i \(0.913479\pi\)
\(24\) 0 0
\(25\) −4531.50 + 7848.79i −1.45008 + 2.51161i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1388.75 + 2405.38i −0.306640 + 0.531116i −0.977625 0.210355i \(-0.932538\pi\)
0.670985 + 0.741471i \(0.265871\pi\)
\(30\) 0 0
\(31\) 3484.34 + 6035.05i 0.651203 + 1.12792i 0.982831 + 0.184506i \(0.0590686\pi\)
−0.331628 + 0.943410i \(0.607598\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11232.5 −1.54992
\(36\) 0 0
\(37\) −7950.71 −0.954776 −0.477388 0.878693i \(-0.658416\pi\)
−0.477388 + 0.878693i \(0.658416\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1013.77 1755.90i −0.0941843 0.163132i 0.815084 0.579343i \(-0.196691\pi\)
−0.909268 + 0.416211i \(0.863358\pi\)
\(42\) 0 0
\(43\) 6261.65 10845.5i 0.516438 0.894496i −0.483380 0.875410i \(-0.660591\pi\)
0.999818 0.0190856i \(-0.00607551\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3241.17 + 5613.87i −0.214021 + 0.370696i −0.952969 0.303066i \(-0.901990\pi\)
0.738948 + 0.673763i \(0.235323\pi\)
\(48\) 0 0
\(49\) 3227.51 + 5590.21i 0.192034 + 0.332612i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9827.54 −0.480568 −0.240284 0.970703i \(-0.577241\pi\)
−0.240284 + 0.970703i \(0.577241\pi\)
\(54\) 0 0
\(55\) −16594.3 −0.739696
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 23544.0 + 40779.3i 0.880541 + 1.52514i 0.850741 + 0.525586i \(0.176154\pi\)
0.0298005 + 0.999556i \(0.490513\pi\)
\(60\) 0 0
\(61\) −4168.92 + 7220.78i −0.143450 + 0.248462i −0.928793 0.370598i \(-0.879153\pi\)
0.785344 + 0.619060i \(0.212486\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 35075.2 60752.0i 1.02971 1.78352i
\(66\) 0 0
\(67\) 3630.45 + 6288.12i 0.0988036 + 0.171133i 0.911190 0.411987i \(-0.135165\pi\)
−0.812386 + 0.583120i \(0.801832\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3582.33 −0.0843372 −0.0421686 0.999111i \(-0.513427\pi\)
−0.0421686 + 0.999111i \(0.513427\pi\)
\(72\) 0 0
\(73\) 58077.5 1.27556 0.637780 0.770218i \(-0.279853\pi\)
0.637780 + 0.770218i \(0.279853\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7646.73 13244.5i −0.146977 0.254571i
\(78\) 0 0
\(79\) 31871.4 55202.9i 0.574558 0.995163i −0.421532 0.906814i \(-0.638507\pi\)
0.996090 0.0883495i \(-0.0281592\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 41423.3 71747.2i 0.660008 1.14317i −0.320605 0.947213i \(-0.603886\pi\)
0.980613 0.195954i \(-0.0627804\pi\)
\(84\) 0 0
\(85\) −82718.9 143273.i −1.24182 2.15089i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3861.51 0.0516752 0.0258376 0.999666i \(-0.491775\pi\)
0.0258376 + 0.999666i \(0.491775\pi\)
\(90\) 0 0
\(91\) 64651.0 0.818412
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 79359.8 + 137455.i 0.902176 + 1.56262i
\(96\) 0 0
\(97\) −34638.6 + 59995.8i −0.373793 + 0.647428i −0.990146 0.140042i \(-0.955276\pi\)
0.616353 + 0.787470i \(0.288610\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12722.8 + 22036.6i −0.124103 + 0.214952i −0.921382 0.388659i \(-0.872939\pi\)
0.797279 + 0.603611i \(0.206272\pi\)
\(102\) 0 0
\(103\) 31693.9 + 54895.4i 0.294363 + 0.509851i 0.974836 0.222922i \(-0.0715594\pi\)
−0.680474 + 0.732772i \(0.738226\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 61158.9 0.516417 0.258208 0.966089i \(-0.416868\pi\)
0.258208 + 0.966089i \(0.416868\pi\)
\(108\) 0 0
\(109\) −124036. −0.999957 −0.499979 0.866038i \(-0.666659\pi\)
−0.499979 + 0.866038i \(0.666659\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 58718.5 + 101703.i 0.432592 + 0.749272i 0.997096 0.0761589i \(-0.0242656\pi\)
−0.564503 + 0.825431i \(0.690932\pi\)
\(114\) 0 0
\(115\) 69778.2 120859.i 0.492011 0.852188i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 76234.3 132042.i 0.493495 0.854759i
\(120\) 0 0
\(121\) 69228.6 + 119908.i 0.429855 + 0.744531i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −655551. −3.75259
\(126\) 0 0
\(127\) −29838.6 −0.164161 −0.0820803 0.996626i \(-0.526156\pi\)
−0.0820803 + 0.996626i \(0.526156\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −86028.8 149006.i −0.437992 0.758624i 0.559543 0.828801i \(-0.310977\pi\)
−0.997535 + 0.0701777i \(0.977643\pi\)
\(132\) 0 0
\(133\) −73138.5 + 126680.i −0.358523 + 0.620980i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 95180.7 164858.i 0.433259 0.750426i −0.563893 0.825848i \(-0.690697\pi\)
0.997152 + 0.0754216i \(0.0240303\pi\)
\(138\) 0 0
\(139\) 168532. + 291905.i 0.739852 + 1.28146i 0.952562 + 0.304345i \(0.0984376\pi\)
−0.212710 + 0.977115i \(0.568229\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 95511.9 0.390586
\(144\) 0 0
\(145\) −306634. −1.21115
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −27549.4 47716.9i −0.101659 0.176079i 0.810709 0.585449i \(-0.199082\pi\)
−0.912368 + 0.409370i \(0.865748\pi\)
\(150\) 0 0
\(151\) −167032. + 289308.i −0.596152 + 1.03257i 0.397231 + 0.917719i \(0.369971\pi\)
−0.993383 + 0.114847i \(0.963362\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −384669. + 666266.i −1.28605 + 2.22750i
\(156\) 0 0
\(157\) 60053.4 + 104015.i 0.194441 + 0.336782i 0.946717 0.322066i \(-0.104377\pi\)
−0.752276 + 0.658848i \(0.771044\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 128616. 0.391048
\(162\) 0 0
\(163\) 367083. 1.08217 0.541085 0.840968i \(-0.318014\pi\)
0.541085 + 0.840968i \(0.318014\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 294724. + 510477.i 0.817758 + 1.41640i 0.907331 + 0.420418i \(0.138116\pi\)
−0.0895730 + 0.995980i \(0.528550\pi\)
\(168\) 0 0
\(169\) −16235.3 + 28120.4i −0.0437264 + 0.0757363i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 218229. 377983.i 0.554366 0.960190i −0.443587 0.896231i \(-0.646294\pi\)
0.997953 0.0639583i \(-0.0203725\pi\)
\(174\) 0 0
\(175\) −461056. 798572.i −1.13804 1.97115i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −241064. −0.562341 −0.281171 0.959658i \(-0.590723\pi\)
−0.281171 + 0.959658i \(0.590723\pi\)
\(180\) 0 0
\(181\) 27128.8 0.0615510 0.0307755 0.999526i \(-0.490202\pi\)
0.0307755 + 0.999526i \(0.490202\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −438876. 760156.i −0.942785 1.63295i
\(186\) 0 0
\(187\) 112624. 195071.i 0.235520 0.407933i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −28036.3 + 48560.2i −0.0556079 + 0.0963157i −0.892489 0.451068i \(-0.851043\pi\)
0.836881 + 0.547384i \(0.184376\pi\)
\(192\) 0 0
\(193\) −177242. 306992.i −0.342510 0.593244i 0.642388 0.766379i \(-0.277944\pi\)
−0.984898 + 0.173135i \(0.944610\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 816895. 1.49969 0.749844 0.661615i \(-0.230129\pi\)
0.749844 + 0.661615i \(0.230129\pi\)
\(198\) 0 0
\(199\) 860396. 1.54016 0.770079 0.637948i \(-0.220217\pi\)
0.770079 + 0.637948i \(0.220217\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −141298. 244735.i −0.240655 0.416827i
\(204\) 0 0
\(205\) 111919. 193850.i 0.186003 0.322166i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −108051. + 187149.i −0.171105 + 0.296362i
\(210\) 0 0
\(211\) 193586. + 335300.i 0.299341 + 0.518475i 0.975985 0.217836i \(-0.0698997\pi\)
−0.676644 + 0.736310i \(0.736566\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.38256e6 2.03981
\(216\) 0 0
\(217\) −709026. −1.02215
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 476105. + 824637.i 0.655725 + 1.13575i
\(222\) 0 0
\(223\) 147497. 255472.i 0.198619 0.344018i −0.749462 0.662047i \(-0.769688\pi\)
0.948081 + 0.318029i \(0.103021\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 343990. 595808.i 0.443079 0.767435i −0.554837 0.831959i \(-0.687220\pi\)
0.997916 + 0.0645238i \(0.0205529\pi\)
\(228\) 0 0
\(229\) 543233. + 940908.i 0.684538 + 1.18565i 0.973582 + 0.228339i \(0.0733294\pi\)
−0.289044 + 0.957316i \(0.593337\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −168058. −0.202801 −0.101400 0.994846i \(-0.532332\pi\)
−0.101400 + 0.994846i \(0.532332\pi\)
\(234\) 0 0
\(235\) −715646. −0.845334
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −773138. 1.33911e6i −0.875512 1.51643i −0.856217 0.516617i \(-0.827191\pi\)
−0.0192952 0.999814i \(-0.506142\pi\)
\(240\) 0 0
\(241\) 576865. 999160.i 0.639782 1.10813i −0.345699 0.938346i \(-0.612358\pi\)
0.985480 0.169789i \(-0.0543086\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −356314. + 617155.i −0.379244 + 0.656869i
\(246\) 0 0
\(247\) −456770. 791149.i −0.476382 0.825118i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 586711. 0.587814 0.293907 0.955834i \(-0.405044\pi\)
0.293907 + 0.955834i \(0.405044\pi\)
\(252\) 0 0
\(253\) 190010. 0.186628
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 54171.0 + 93826.9i 0.0511604 + 0.0886124i 0.890471 0.455039i \(-0.150375\pi\)
−0.839311 + 0.543651i \(0.817041\pi\)
\(258\) 0 0
\(259\) 404471. 700565.i 0.374661 0.648931i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −868353. + 1.50403e6i −0.774117 + 1.34081i 0.161172 + 0.986926i \(0.448473\pi\)
−0.935289 + 0.353884i \(0.884861\pi\)
\(264\) 0 0
\(265\) −542476. 939597.i −0.474533 0.821915i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18297.3 −0.0154172 −0.00770860 0.999970i \(-0.502454\pi\)
−0.00770860 + 0.999970i \(0.502454\pi\)
\(270\) 0 0
\(271\) 7105.09 0.00587688 0.00293844 0.999996i \(-0.499065\pi\)
0.00293844 + 0.999996i \(0.499065\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −681139. 1.17977e6i −0.543130 0.940729i
\(276\) 0 0
\(277\) −355202. + 615227.i −0.278148 + 0.481766i −0.970924 0.239386i \(-0.923054\pi\)
0.692777 + 0.721152i \(0.256387\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −514224. + 890661.i −0.388496 + 0.672894i −0.992247 0.124278i \(-0.960338\pi\)
0.603752 + 0.797172i \(0.293672\pi\)
\(282\) 0 0
\(283\) 922317. + 1.59750e6i 0.684564 + 1.18570i 0.973574 + 0.228374i \(0.0733407\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 206291. 0.147834
\(288\) 0 0
\(289\) 825769. 0.581586
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 470486. + 814906.i 0.320168 + 0.554547i 0.980522 0.196407i \(-0.0629274\pi\)
−0.660355 + 0.750954i \(0.729594\pi\)
\(294\) 0 0
\(295\) −2.59924e6 + 4.50201e6i −1.73896 + 3.01198i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −401621. + 695629.i −0.259800 + 0.449987i
\(300\) 0 0
\(301\) 637090. + 1.10347e6i 0.405307 + 0.702013i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −920492. −0.566592
\(306\) 0 0
\(307\) −2.93094e6 −1.77485 −0.887425 0.460952i \(-0.847508\pi\)
−0.887425 + 0.460952i \(0.847508\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.14126e6 1.97671e6i −0.669086 1.15889i −0.978160 0.207853i \(-0.933352\pi\)
0.309074 0.951038i \(-0.399981\pi\)
\(312\) 0 0
\(313\) −401324. + 695114.i −0.231544 + 0.401047i −0.958263 0.285889i \(-0.907711\pi\)
0.726718 + 0.686936i \(0.241045\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 555982. 962990.i 0.310751 0.538237i −0.667774 0.744364i \(-0.732753\pi\)
0.978525 + 0.206127i \(0.0660861\pi\)
\(318\) 0 0
\(319\) −208746. 361558.i −0.114853 0.198930i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.15443e6 −1.14902
\(324\) 0 0
\(325\) 5.75885e6 3.02432
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −329772. 571182.i −0.167967 0.290927i
\(330\) 0 0
\(331\) 613290. 1.06225e6i 0.307678 0.532913i −0.670176 0.742202i \(-0.733782\pi\)
0.977854 + 0.209289i \(0.0671149\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −400799. + 694203.i −0.195126 + 0.337967i
\(336\) 0 0
\(337\) −1.15064e6 1.99297e6i −0.551907 0.955930i −0.998137 0.0610122i \(-0.980567\pi\)
0.446230 0.894918i \(-0.352766\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.04748e6 −0.487818
\(342\) 0 0
\(343\) −2.36679e6 −1.08624
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 809651. + 1.40236e6i 0.360973 + 0.625223i 0.988121 0.153677i \(-0.0491115\pi\)
−0.627149 + 0.778900i \(0.715778\pi\)
\(348\) 0 0
\(349\) 139307. 241287.i 0.0612223 0.106040i −0.833790 0.552082i \(-0.813833\pi\)
0.895012 + 0.446042i \(0.147167\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.68496e6 2.91844e6i 0.719704 1.24656i −0.241413 0.970422i \(-0.577611\pi\)
0.961117 0.276142i \(-0.0890559\pi\)
\(354\) 0 0
\(355\) −197743. 342501.i −0.0832781 0.144242i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −272571. −0.111621 −0.0558103 0.998441i \(-0.517774\pi\)
−0.0558103 + 0.998441i \(0.517774\pi\)
\(360\) 0 0
\(361\) −409156. −0.165242
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.20586e6 + 5.55271e6i 1.25954 + 2.18159i
\(366\) 0 0
\(367\) 1.97882e6 3.42743e6i 0.766906 1.32832i −0.172327 0.985040i \(-0.555129\pi\)
0.939233 0.343281i \(-0.111538\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 499950. 865939.i 0.188578 0.326627i
\(372\) 0 0
\(373\) 961939. + 1.66613e6i 0.357994 + 0.620063i 0.987626 0.156830i \(-0.0501276\pi\)
−0.629632 + 0.776894i \(0.716794\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.76489e6 0.639534
\(378\) 0 0
\(379\) −3.11015e6 −1.11220 −0.556101 0.831115i \(-0.687703\pi\)
−0.556101 + 0.831115i \(0.687703\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.41711e6 2.45450e6i −0.493634 0.855000i 0.506339 0.862335i \(-0.330999\pi\)
−0.999973 + 0.00733479i \(0.997665\pi\)
\(384\) 0 0
\(385\) 844193. 1.46218e6i 0.290262 0.502748i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.02692e6 + 1.77867e6i −0.344081 + 0.595966i −0.985186 0.171487i \(-0.945143\pi\)
0.641105 + 0.767453i \(0.278476\pi\)
\(390\) 0 0
\(391\) 947157. + 1.64052e6i 0.313314 + 0.542676i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.03716e6 2.26937
\(396\) 0 0
\(397\) −3.82167e6 −1.21696 −0.608480 0.793569i \(-0.708220\pi\)
−0.608480 + 0.793569i \(0.708220\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.65864e6 + 4.60491e6i 0.825656 + 1.43008i 0.901417 + 0.432953i \(0.142528\pi\)
−0.0757604 + 0.997126i \(0.524138\pi\)
\(402\) 0 0
\(403\) 2.21403e6 3.83482e6i 0.679081 1.17620i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 597543. 1.03498e6i 0.178807 0.309702i
\(408\) 0 0
\(409\) −1.57922e6 2.73528e6i −0.466803 0.808526i 0.532478 0.846444i \(-0.321261\pi\)
−0.999281 + 0.0379179i \(0.987927\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.79095e6 −1.38212
\(414\) 0 0
\(415\) 9.14620e6 2.60688
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.80782e6 3.13124e6i −0.503060 0.871326i −0.999994 0.00353739i \(-0.998874\pi\)
0.496933 0.867789i \(-0.334459\pi\)
\(420\) 0 0
\(421\) −514445. + 891044.i −0.141460 + 0.245016i −0.928047 0.372464i \(-0.878513\pi\)
0.786587 + 0.617480i \(0.211846\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.79064e6 1.17617e7i 1.82364 3.15863i
\(426\) 0 0
\(427\) −424166. 734677.i −0.112581 0.194996i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.21668e6 −1.61200 −0.806001 0.591914i \(-0.798372\pi\)
−0.806001 + 0.591914i \(0.798372\pi\)
\(432\) 0 0
\(433\) −598070. −0.153297 −0.0766483 0.997058i \(-0.524422\pi\)
−0.0766483 + 0.997058i \(0.524422\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −908694. 1.57390e6i −0.227622 0.394253i
\(438\) 0 0
\(439\) 246548. 427034.i 0.0610577 0.105755i −0.833881 0.551945i \(-0.813886\pi\)
0.894938 + 0.446190i \(0.147219\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −97755.8 + 169318.i −0.0236665 + 0.0409915i −0.877616 0.479364i \(-0.840867\pi\)
0.853950 + 0.520356i \(0.174201\pi\)
\(444\) 0 0
\(445\) 213154. + 369194.i 0.0510263 + 0.0883801i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.51225e6 0.354004 0.177002 0.984210i \(-0.443360\pi\)
0.177002 + 0.984210i \(0.443360\pi\)
\(450\) 0 0
\(451\) 304763. 0.0705538
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.56871e6 + 6.18119e6i 0.808133 + 1.39973i
\(456\) 0 0
\(457\) −1.28236e6 + 2.22111e6i −0.287223 + 0.497484i −0.973146 0.230190i \(-0.926065\pi\)
0.685923 + 0.727674i \(0.259399\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.68336e6 + 4.64772e6i −0.588067 + 1.01856i 0.406418 + 0.913687i \(0.366778\pi\)
−0.994485 + 0.104875i \(0.966556\pi\)
\(462\) 0 0
\(463\) −2.75107e6 4.76500e6i −0.596417 1.03302i −0.993345 0.115175i \(-0.963257\pi\)
0.396928 0.917850i \(-0.370076\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −964114. −0.204567 −0.102284 0.994755i \(-0.532615\pi\)
−0.102284 + 0.994755i \(0.532615\pi\)
\(468\) 0 0
\(469\) −738757. −0.155085
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 941202. + 1.63021e6i 0.193433 + 0.335035i
\(474\) 0 0
\(475\) −6.51488e6 + 1.12841e7i −1.32487 + 2.29474i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −281267. + 487168.i −0.0560118 + 0.0970153i −0.892672 0.450707i \(-0.851172\pi\)
0.836660 + 0.547723i \(0.184505\pi\)
\(480\) 0 0
\(481\) 2.52603e6 + 4.37522e6i 0.497825 + 0.862258i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.64815e6 −1.47639
\(486\) 0 0
\(487\) 3.14185e6 0.600292 0.300146 0.953893i \(-0.402965\pi\)
0.300146 + 0.953893i \(0.402965\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.86681e6 + 4.96545e6i 0.536654 + 0.929512i 0.999081 + 0.0428549i \(0.0136453\pi\)
−0.462427 + 0.886657i \(0.653021\pi\)
\(492\) 0 0
\(493\) 2.08110e6 3.60457e6i 0.385634 0.667937i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 182241. 315651.i 0.0330945 0.0573214i
\(498\) 0 0
\(499\) −857810. 1.48577e6i −0.154220 0.267116i 0.778555 0.627576i \(-0.215953\pi\)
−0.932775 + 0.360460i \(0.882620\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.15229e6 0.907989 0.453995 0.891004i \(-0.349999\pi\)
0.453995 + 0.891004i \(0.349999\pi\)
\(504\) 0 0
\(505\) −2.80919e6 −0.490176
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −521280. 902884.i −0.0891819 0.154468i 0.817984 0.575242i \(-0.195092\pi\)
−0.907166 + 0.420774i \(0.861759\pi\)
\(510\) 0 0
\(511\) −2.95454e6 + 5.11742e6i −0.500539 + 0.866959i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.49898e6 + 6.06041e6i −0.581331 + 1.00690i
\(516\) 0 0
\(517\) −487187. 843833.i −0.0801621 0.138845i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.52239e6 −1.53692 −0.768461 0.639897i \(-0.778977\pi\)
−0.768461 + 0.639897i \(0.778977\pi\)
\(522\) 0 0
\(523\) −2.97573e6 −0.475706 −0.237853 0.971301i \(-0.576444\pi\)
−0.237853 + 0.971301i \(0.576444\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.22143e6 9.04378e6i −0.818960 1.41848i
\(528\) 0 0
\(529\) 2.41919e6 4.19016e6i 0.375864 0.651016i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −644172. + 1.11574e6i −0.0982163 + 0.170116i
\(534\) 0 0
\(535\) 3.37595e6 + 5.84731e6i 0.509931 + 0.883226i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −970266. −0.143853
\(540\) 0 0
\(541\) 1.80579e6 0.265261 0.132631 0.991166i \(-0.457658\pi\)
0.132631 + 0.991166i \(0.457658\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.84674e6 1.18589e7i −0.987399 1.71023i
\(546\) 0 0
\(547\) 4.68486e6 8.11442e6i 0.669466 1.15955i −0.308587 0.951196i \(-0.599856\pi\)
0.978054 0.208353i \(-0.0668104\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.99658e6 + 3.45819e6i −0.280162 + 0.485254i
\(552\) 0 0
\(553\) 3.24275e6 + 5.61660e6i 0.450921 + 0.781018i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.53733e6 −0.483101 −0.241550 0.970388i \(-0.577656\pi\)
−0.241550 + 0.970388i \(0.577656\pi\)
\(558\) 0 0
\(559\) −7.95761e6 −1.07709
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.39030e6 + 2.40807e6i 0.184858 + 0.320183i 0.943529 0.331291i \(-0.107484\pi\)
−0.758671 + 0.651474i \(0.774151\pi\)
\(564\) 0 0
\(565\) −6.48248e6 + 1.12280e7i −0.854319 + 1.47972i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.67647e6 6.36782e6i 0.476047 0.824537i −0.523576 0.851979i \(-0.675403\pi\)
0.999623 + 0.0274412i \(0.00873590\pi\)
\(570\) 0 0
\(571\) 2.87585e6 + 4.98112e6i 0.369128 + 0.639348i 0.989429 0.145016i \(-0.0463232\pi\)
−0.620302 + 0.784363i \(0.712990\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.14566e7 1.44506
\(576\) 0 0
\(577\) −1.30488e7 −1.63167 −0.815835 0.578285i \(-0.803722\pi\)
−0.815835 + 0.578285i \(0.803722\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.21460e6 + 7.29990e6i 0.517983 + 0.897173i
\(582\) 0 0
\(583\) 738598. 1.27929e6i 0.0899989 0.155883i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 623618. 1.08014e6i 0.0747005 0.129385i −0.826255 0.563296i \(-0.809533\pi\)
0.900956 + 0.433910i \(0.142867\pi\)
\(588\) 0 0
\(589\) 5.00939e6 + 8.67652e6i 0.594972 + 1.03052i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.32769e7 1.55045 0.775226 0.631684i \(-0.217636\pi\)
0.775226 + 0.631684i \(0.217636\pi\)
\(594\) 0 0
\(595\) 1.68324e7 1.94919
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.02457e6 + 3.50666e6i 0.230551 + 0.399325i 0.957970 0.286868i \(-0.0926140\pi\)
−0.727420 + 0.686193i \(0.759281\pi\)
\(600\) 0 0
\(601\) 3.41857e6 5.92113e6i 0.386063 0.668681i −0.605853 0.795577i \(-0.707168\pi\)
0.991916 + 0.126896i \(0.0405014\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.64279e6 + 1.32377e7i −0.848914 + 1.47036i
\(606\) 0 0
\(607\) −348100. 602927.i −0.0383471 0.0664191i 0.846215 0.532842i \(-0.178876\pi\)
−0.884562 + 0.466423i \(0.845543\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.11904e6 0.446367
\(612\) 0 0
\(613\) −1.42785e6 −0.153473 −0.0767363 0.997051i \(-0.524450\pi\)
−0.0767363 + 0.997051i \(0.524450\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.51675e6 1.30194e7i −0.794908 1.37682i −0.922897 0.385046i \(-0.874186\pi\)
0.127989 0.991776i \(-0.459148\pi\)
\(618\) 0 0
\(619\) 3.58151e6 6.20336e6i 0.375699 0.650730i −0.614732 0.788736i \(-0.710736\pi\)
0.990431 + 0.138006i \(0.0440693\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −196444. + 340251.i −0.0202777 + 0.0351221i
\(624\) 0 0
\(625\) −2.20252e7 3.81488e7i −2.25538 3.90644i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.19145e7 1.20074
\(630\) 0 0
\(631\) 1.38021e7 1.37998 0.689989 0.723820i \(-0.257615\pi\)
0.689989 + 0.723820i \(0.257615\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.64708e6 2.85283e6i −0.162099 0.280764i
\(636\) 0 0
\(637\) 2.05084e6 3.55215e6i 0.200254 0.346851i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.02329e6 + 3.50445e6i −0.194497 + 0.336879i −0.946736 0.322012i \(-0.895641\pi\)
0.752238 + 0.658891i \(0.228974\pi\)
\(642\) 0 0
\(643\) −5.44381e6 9.42896e6i −0.519249 0.899366i −0.999750 0.0223713i \(-0.992878\pi\)
0.480501 0.876994i \(-0.340455\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.45797e6 0.794339 0.397169 0.917745i \(-0.369993\pi\)
0.397169 + 0.917745i \(0.369993\pi\)
\(648\) 0 0
\(649\) −7.07788e6 −0.659617
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.47774e6 + 4.29157e6i 0.227391 + 0.393853i 0.957034 0.289975i \(-0.0936472\pi\)
−0.729643 + 0.683828i \(0.760314\pi\)
\(654\) 0 0
\(655\) 9.49752e6 1.64502e7i 0.864982 1.49819i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.37152e6 1.44999e7i 0.750915 1.30062i −0.196464 0.980511i \(-0.562946\pi\)
0.947380 0.320113i \(-0.103721\pi\)
\(660\) 0 0
\(661\) 7.53992e6 + 1.30595e7i 0.671217 + 1.16258i 0.977559 + 0.210661i \(0.0675617\pi\)
−0.306342 + 0.951922i \(0.599105\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.61489e7 −1.41608
\(666\) 0 0
\(667\) 3.51105e6 0.305578
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −626639. 1.08537e6i −0.0537293 0.0930619i
\(672\) 0 0
\(673\) −7.07096e6 + 1.22473e7i −0.601784 + 1.04232i 0.390767 + 0.920490i \(0.372210\pi\)
−0.992551 + 0.121831i \(0.961123\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.29397e6 1.26335e7i 0.611635 1.05938i −0.379330 0.925262i \(-0.623845\pi\)
0.990965 0.134122i \(-0.0428213\pi\)
\(678\) 0 0
\(679\) −3.52429e6 6.10425e6i −0.293358 0.508110i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.10096e7 0.903065 0.451532 0.892255i \(-0.350878\pi\)
0.451532 + 0.892255i \(0.350878\pi\)
\(684\) 0 0
\(685\) 2.10158e7 1.71127
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.12233e6 + 5.40803e6i 0.250571 + 0.434001i
\(690\) 0 0
\(691\) −5.51793e6 + 9.55733e6i −0.439623 + 0.761450i −0.997660 0.0683661i \(-0.978221\pi\)
0.558037 + 0.829816i \(0.311555\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.86058e7 + 3.22261e7i −1.46112 + 2.53073i
\(696\) 0 0
\(697\) 1.51917e6 + 2.63128e6i 0.118447 + 0.205157i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.51294e7 1.93146 0.965732 0.259542i \(-0.0835717\pi\)
0.965732 + 0.259542i \(0.0835717\pi\)
\(702\) 0 0
\(703\) −1.14306e7 −0.872332
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.29448e6 2.24211e6i −0.0973974 0.168697i
\(708\) 0 0
\(709\) −6.26506e6 + 1.08514e7i −0.468068 + 0.810718i −0.999334 0.0364869i \(-0.988383\pi\)
0.531266 + 0.847205i \(0.321717\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.40457e6 7.62894e6i 0.324474 0.562006i
\(714\) 0 0
\(715\) 5.27222e6 + 9.13175e6i 0.385681 + 0.668019i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.72246e6 0.124258 0.0621292 0.998068i \(-0.480211\pi\)
0.0621292 + 0.998068i \(0.480211\pi\)
\(720\) 0 0
\(721\) −6.44937e6 −0.462040
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.25862e7 2.18000e7i −0.889304 1.54032i
\(726\) 0 0
\(727\) −3.49425e6 + 6.05221e6i −0.245198 + 0.424696i −0.962187 0.272389i \(-0.912186\pi\)
0.716989 + 0.697084i \(0.245520\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −9.38335e6 + 1.62524e7i −0.649478 + 1.12493i
\(732\) 0 0
\(733\) 2.96305e6 + 5.13214e6i 0.203694 + 0.352808i 0.949716 0.313113i \(-0.101372\pi\)
−0.746022 + 0.665922i \(0.768039\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.09140e6 −0.0740142
\(738\) 0 0
\(739\) −1.06632e7 −0.718254 −0.359127 0.933289i \(-0.616925\pi\)
−0.359127 + 0.933289i \(0.616925\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.24932e6 1.60203e7i −0.614664 1.06463i −0.990443 0.137920i \(-0.955958\pi\)
0.375779 0.926709i \(-0.377375\pi\)
\(744\) 0 0
\(745\) 3.04143e6 5.26791e6i 0.200765 0.347734i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.11130e6 + 5.38892e6i −0.202645 + 0.350992i
\(750\) 0 0
\(751\) 1.30624e7 + 2.26247e7i 0.845127 + 1.46380i 0.885511 + 0.464618i \(0.153808\pi\)
−0.0403845 + 0.999184i \(0.512858\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.68804e7 −2.35466
\(756\) 0 0
\(757\) 2.49174e7 1.58039 0.790193 0.612858i \(-0.209980\pi\)
0.790193 + 0.612858i \(0.209980\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.62194e6 + 9.73748e6i 0.351904 + 0.609516i 0.986583 0.163260i \(-0.0522010\pi\)
−0.634679 + 0.772776i \(0.718868\pi\)
\(762\) 0 0
\(763\) 6.31000e6 1.09292e7i 0.392390 0.679640i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.49604e7 2.59122e7i 0.918237 1.59043i
\(768\) 0 0
\(769\) −4.33731e6 7.51244e6i −0.264487 0.458105i 0.702942 0.711247i \(-0.251869\pi\)
−0.967429 + 0.253142i \(0.918536\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.17066e7 −1.30660 −0.653300 0.757099i \(-0.726616\pi\)
−0.653300 + 0.757099i \(0.726616\pi\)
\(774\) 0 0
\(775\) −6.31571e7 −3.77718
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.45748e6 2.52443e6i −0.0860516 0.149046i
\(780\) 0 0
\(781\) 269233. 466326.i 0.0157943 0.0273566i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.62985e6 + 1.14832e7i −0.383998 + 0.665105i
\(786\) 0 0
\(787\) −3.93215e6 6.81068e6i −0.226304 0.391971i 0.730406 0.683014i \(-0.239331\pi\)
−0.956710 + 0.291043i \(0.905998\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.19486e7 −0.679009
\(792\) 0 0
\(793\) 5.29807e6 0.299181
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.48089e6 + 1.64214e7i 0.528693 + 0.915723i 0.999440 + 0.0334547i \(0.0106509\pi\)
−0.470747 + 0.882268i \(0.656016\pi\)
\(798\) 0 0
\(799\) 4.85703e6 8.41262e6i 0.269156 0.466192i
\(800\) 0 0
\(801\) 0 0