Properties

Label 108.6.e.a.37.5
Level 108
Weight 6
Character 108.37
Analytic conductor 17.321
Analytic rank 0
Dimension 10
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 37.5
Root \(-1.11227i\) of \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Character \(\chi\) \(=\) 108.37
Dual form 108.6.e.a.73.5

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 0.356899 0.934143i \(-0.383834\pi\)
0.630542 0.776155i \(-0.282833\pi\)
\(6\) 0 0
\(7\) −50.8724 88.1135i −0.392407 0.679669i 0.600359 0.799730i \(-0.295024\pi\)
−0.992766 + 0.120061i \(0.961691\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −75.1560 130.174i −0.187276 0.324371i 0.757065 0.653339i \(-0.226633\pi\)
−0.944341 + 0.328968i \(0.893299\pi\)
\(12\) 0 0
\(13\) −317.712 + 550.293i −0.521405 + 0.903100i 0.478285 + 0.878205i \(0.341259\pi\)
−0.999690 + 0.0248953i \(0.992075\pi\)
\(14\) 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 −0.963286 0.268478i \(-0.913479\pi\)
0.714151 + 0.699991i \(0.246813\pi\)
\(24\) 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 0.670985 0.741471i \(-0.265871\pi\)
−0.977625 + 0.210355i \(0.932538\pi\)
\(30\) 0 0
\(31\) 3484.34 6035.05i 0.651203 1.12792i −0.331628 0.943410i \(-0.607598\pi\)
0.982831 0.184506i \(-0.0590686\pi\)
\(32\) 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 −0.909268 0.416211i \(-0.863358\pi\)
0.815084 + 0.579343i \(0.196691\pi\)
\(42\) 0 0
\(43\) 6261.65 + 10845.5i 0.516438 + 0.894496i 0.999818 + 0.0190856i \(0.00607551\pi\)
−0.483380 + 0.875410i \(0.660591\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3241.17 5613.87i −0.214021 0.370696i 0.738948 0.673763i \(-0.235323\pi\)
−0.952969 + 0.303066i \(0.901990\pi\)
\(48\) 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 0.0298005 0.999556i \(-0.490513\pi\)
0.850741 0.525586i \(-0.176154\pi\)
\(60\) 0 0
\(61\) −4168.92 7220.78i −0.143450 0.248462i 0.785344 0.619060i \(-0.212486\pi\)
−0.928793 + 0.370598i \(0.879153\pi\)
\(62\) 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 −0.812386 0.583120i \(-0.801832\pi\)
0.911190 + 0.411987i \(0.135165\pi\)
\(68\) 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 0.996090 + 0.0883495i \(0.0281592\pi\)
−0.421532 + 0.906814i \(0.638507\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 41423.3 + 71747.2i 0.660008 + 1.14317i 0.980613 + 0.195954i \(0.0627804\pi\)
−0.320605 + 0.947213i \(0.603886\pi\)
\(84\) 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 0.616353 0.787470i \(-0.288610\pi\)
−0.990146 + 0.140042i \(0.955276\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12722.8 22036.6i −0.124103 0.214952i 0.797279 0.603611i \(-0.206272\pi\)
−0.921382 + 0.388659i \(0.872939\pi\)
\(102\) 0 0
\(103\) 31693.9 54895.4i 0.294363 0.509851i −0.680474 0.732772i \(-0.738226\pi\)
0.974836 + 0.222922i \(0.0715594\pi\)
\(104\) 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 −0.564503 0.825431i \(-0.690932\pi\)
0.997096 + 0.0761589i \(0.0242656\pi\)
\(114\) 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 −0.997535 0.0701777i \(-0.977643\pi\)
0.559543 + 0.828801i \(0.310977\pi\)
\(132\) 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 0.997152 0.0754216i \(-0.0240303\pi\)
−0.563893 + 0.825848i \(0.690697\pi\)
\(138\) 0 0
\(139\) 168532. 291905.i 0.739852 1.28146i −0.212710 0.977115i \(-0.568229\pi\)
0.952562 0.304345i \(-0.0984376\pi\)
\(140\) 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 −0.912368 0.409370i \(-0.865748\pi\)
0.810709 + 0.585449i \(0.199082\pi\)
\(150\) 0 0
\(151\) −167032. 289308.i −0.596152 1.03257i −0.993383 0.114847i \(-0.963362\pi\)
0.397231 0.917719i \(-0.369971\pi\)
\(152\) 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 −0.752276 0.658848i \(-0.771044\pi\)
0.946717 + 0.322066i \(0.104377\pi\)
\(158\) 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 −0.0895730 0.995980i \(-0.528550\pi\)
0.907331 0.420418i \(-0.138116\pi\)
\(168\) 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 0.997953 + 0.0639583i \(0.0203725\pi\)
−0.443587 + 0.896231i \(0.646294\pi\)
\(174\) 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 0.836881 0.547384i \(-0.184376\pi\)
−0.892489 + 0.451068i \(0.851043\pi\)
\(192\) 0 0
\(193\) −177242. + 306992.i −0.342510 + 0.593244i −0.984898 0.173135i \(-0.944610\pi\)
0.642388 + 0.766379i \(0.277944\pi\)
\(194\) 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 −0.676644 0.736310i \(-0.736566\pi\)
0.975985 + 0.217836i \(0.0698997\pi\)
\(212\) 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 0.948081 0.318029i \(-0.103021\pi\)
−0.749462 + 0.662047i \(0.769688\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 343990. + 595808.i 0.443079 + 0.767435i 0.997916 0.0645238i \(-0.0205529\pi\)
−0.554837 + 0.831959i \(0.687220\pi\)
\(228\) 0 0
\(229\) 543233. 940908.i 0.684538 1.18565i −0.289044 0.957316i \(-0.593337\pi\)
0.973582 0.228339i \(-0.0733294\pi\)
\(230\) 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 −0.0192952 + 0.999814i \(0.506142\pi\)
−0.856217 + 0.516617i \(0.827191\pi\)
\(240\) 0 0
\(241\) 576865. + 999160.i 0.639782 + 1.10813i 0.985480 + 0.169789i \(0.0543086\pi\)
−0.345699 + 0.938346i \(0.612358\pi\)
\(242\) 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 −0.839311 0.543651i \(-0.817041\pi\)
0.890471 + 0.455039i \(0.150375\pi\)
\(258\) 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 −0.935289 0.353884i \(-0.884861\pi\)
0.161172 0.986926i \(-0.448473\pi\)
\(264\) 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 0.692777 0.721152i \(-0.256387\pi\)
−0.970924 + 0.239386i \(0.923054\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −514224. 890661.i −0.388496 0.672894i 0.603752 0.797172i \(-0.293672\pi\)
−0.992247 + 0.124278i \(0.960338\pi\)
\(282\) 0 0
\(283\) 922317. 1.59750e6i 0.684564 1.18570i −0.289010 0.957326i \(-0.593326\pi\)
0.973574 0.228374i \(-0.0733407\pi\)
\(284\) 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 −0.660355 0.750954i \(-0.729594\pi\)
0.980522 + 0.196407i \(0.0629274\pi\)
\(294\) 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 0.309074 + 0.951038i \(0.399981\pi\)
−0.978160 + 0.207853i \(0.933352\pi\)
\(312\) 0 0
\(313\) −401324. 695114.i −0.231544 0.401047i 0.726718 0.686936i \(-0.241045\pi\)
−0.958263 + 0.285889i \(0.907711\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 555982. + 962990.i 0.310751 + 0.538237i 0.978525 0.206127i \(-0.0660861\pi\)
−0.667774 + 0.744364i \(0.732753\pi\)
\(318\) 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 0.977854 0.209289i \(-0.0671149\pi\)
−0.670176 + 0.742202i \(0.733782\pi\)
\(332\) 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 0.446230 + 0.894918i \(0.352766\pi\)
−0.998137 + 0.0610122i \(0.980567\pi\)
\(338\) 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 −0.627149 0.778900i \(-0.715778\pi\)
0.988121 + 0.153677i \(0.0491115\pi\)
\(348\) 0 0
\(349\) 139307. + 241287.i 0.0612223 + 0.106040i 0.895012 0.446042i \(-0.147167\pi\)
−0.833790 + 0.552082i \(0.813833\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.68496e6 + 2.91844e6i 0.719704 + 1.24656i 0.961117 + 0.276142i \(0.0890559\pi\)
−0.241413 + 0.970422i \(0.577611\pi\)
\(354\) 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 0.939233 + 0.343281i \(0.111538\pi\)
−0.172327 + 0.985040i \(0.555129\pi\)
\(368\) 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 −0.629632 0.776894i \(-0.716794\pi\)
0.987626 + 0.156830i \(0.0501276\pi\)
\(374\) 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 −0.999973 0.00733479i \(-0.997665\pi\)
0.506339 + 0.862335i \(0.330999\pi\)
\(384\) 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 0.641105 0.767453i \(-0.278476\pi\)
−0.985186 + 0.171487i \(0.945143\pi\)
\(390\) 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 −0.0757604 0.997126i \(-0.524138\pi\)
0.901417 0.432953i \(-0.142528\pi\)
\(402\) 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 −0.999281 0.0379179i \(-0.987927\pi\)
0.532478 + 0.846444i \(0.321261\pi\)
\(410\) 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 0.496933 + 0.867789i \(0.334459\pi\)
−0.999994 + 0.00353739i \(0.998874\pi\)
\(420\) 0 0
\(421\) −514445. 891044.i −0.141460 0.245016i 0.786587 0.617480i \(-0.211846\pi\)
−0.928047 + 0.372464i \(0.878513\pi\)
\(422\) 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 0.894938 0.446190i \(-0.147219\pi\)
−0.833881 + 0.551945i \(0.813886\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −97755.8 169318.i −0.0236665 0.0409915i 0.853950 0.520356i \(-0.174201\pi\)
−0.877616 + 0.479364i \(0.840867\pi\)
\(444\) 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 0.685923 0.727674i \(-0.259399\pi\)
−0.973146 + 0.230190i \(0.926065\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.68336e6 4.64772e6i −0.588067 1.01856i −0.994485 0.104875i \(-0.966556\pi\)
0.406418 0.913687i \(-0.366778\pi\)
\(462\) 0 0
\(463\) −2.75107e6 + 4.76500e6i −0.596417 + 1.03302i 0.396928 + 0.917850i \(0.370076\pi\)
−0.993345 + 0.115175i \(0.963257\pi\)
\(464\) 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 0.836660 0.547723i \(-0.184505\pi\)
−0.892672 + 0.450707i \(0.851172\pi\)
\(480\) 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 −0.462427 0.886657i \(-0.653021\pi\)
0.999081 0.0428549i \(-0.0136453\pi\)
\(492\) 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 −0.932775 0.360460i \(-0.882620\pi\)
0.778555 + 0.627576i \(0.215953\pi\)
\(500\) 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 −0.907166 0.420774i \(-0.861759\pi\)
0.817984 + 0.575242i \(0.195092\pi\)
\(510\) 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 0.978054 + 0.208353i \(0.0668104\pi\)
−0.308587 + 0.951196i \(0.599856\pi\)
\(548\) 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 −0.758671 0.651474i \(-0.774151\pi\)
0.943529 + 0.331291i \(0.107484\pi\)
\(564\) 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 0.999623 0.0274412i \(-0.00873590\pi\)
−0.523576 + 0.851979i \(0.675403\pi\)
\(570\) 0 0
\(571\) 2.87585e6 4.98112e6i 0.369128 0.639348i −0.620302 0.784363i \(-0.712990\pi\)
0.989429 + 0.145016i \(0.0463232\pi\)
\(572\) 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 0.900956 0.433910i \(-0.142867\pi\)
−0.826255 + 0.563296i \(0.809533\pi\)
\(588\) 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 −0.727420 0.686193i \(-0.759281\pi\)
0.957970 + 0.286868i \(0.0926140\pi\)
\(600\) 0 0
\(601\) 3.41857e6 + 5.92113e6i 0.386063 + 0.668681i 0.991916 0.126896i \(-0.0405014\pi\)
−0.605853 + 0.795577i \(0.707168\pi\)
\(602\) 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 −0.884562 0.466423i \(-0.845543\pi\)
0.846215 + 0.532842i \(0.178876\pi\)
\(608\) 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 0.127989 + 0.991776i \(0.459148\pi\)
−0.922897 + 0.385046i \(0.874186\pi\)
\(618\) 0 0
\(619\) 3.58151e6 + 6.20336e6i 0.375699 + 0.650730i 0.990431 0.138006i \(-0.0440693\pi\)
−0.614732 + 0.788736i \(0.710736\pi\)
\(620\) 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 0.752238 0.658891i \(-0.228974\pi\)
−0.946736 + 0.322012i \(0.895641\pi\)
\(642\) 0 0
\(643\) −5.44381e6 + 9.42896e6i −0.519249 + 0.899366i 0.480501 + 0.876994i \(0.340455\pi\)
−0.999750 + 0.0223713i \(0.992878\pi\)
\(644\) 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 −0.729643 0.683828i \(-0.760314\pi\)
0.957034 + 0.289975i \(0.0936472\pi\)
\(654\) 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 0.947380 + 0.320113i \(0.103721\pi\)
−0.196464 + 0.980511i \(0.562946\pi\)
\(660\) 0 0
\(661\) 7.53992e6 1.30595e7i 0.671217 1.16258i −0.306342 0.951922i \(-0.599105\pi\)
0.977559 0.210661i \(-0.0675617\pi\)
\(662\) 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 −0.992551 0.121831i \(-0.961123\pi\)
0.390767 0.920490i \(-0.372210\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.29397e6 + 1.26335e7i 0.611635 + 1.05938i 0.990965 + 0.134122i \(0.0428213\pi\)
−0.379330 + 0.925262i \(0.623845\pi\)
\(678\) 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 0.558037 0.829816i \(-0.311555\pi\)
−0.997660 + 0.0683661i \(0.978221\pi\)
\(692\) 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 0.531266 0.847205i \(-0.321717\pi\)
−0.999334 + 0.0364869i \(0.988383\pi\)
\(710\) 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 0.716989 0.697084i \(-0.245520\pi\)
−0.962187 + 0.272389i \(0.912186\pi\)
\(728\) 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 −0.746022 0.665922i \(-0.768039\pi\)
0.949716 + 0.313113i \(0.101372\pi\)
\(734\) 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 0.375779 + 0.926709i \(0.377375\pi\)
−0.990443 + 0.137920i \(0.955958\pi\)
\(744\) 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 −0.0403845 0.999184i \(-0.512858\pi\)
0.885511 0.464618i \(-0.153808\pi\)
\(752\) 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 −0.634679 0.772776i \(-0.718868\pi\)
0.986583 + 0.163260i \(0.0522010\pi\)
\(762\) 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 −0.967429 0.253142i \(-0.918536\pi\)
0.702942 + 0.711247i \(0.251869\pi\)
\(770\) 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 −0.956710 0.291043i \(-0.905998\pi\)
0.730406 + 0.683014i \(0.239331\pi\)
\(788\) 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 −0.470747 0.882268i \(-0.656016\pi\)
0.999440 0.0334547i \(-0.0106509\pi\)
\(798\) 0 0
\(799\) 4.85703e6 + 8.41262e6i 0.269156 + 0.466192i
\(800\) 0 0
\(801\) 0 0