Properties

Label 80.6.n.d.63.10
Level $80$
Weight $6$
Character 80.63
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 63.10
Root \(11.4741 - 7.80740i\) of defining polynomial
Character \(\chi\) \(=\) 80.63
Dual form 80.6.n.d.47.10

$q$-expansion

\(f(q)\) \(=\) \(q+(20.3843 - 20.3843i) q^{3} +(-46.4503 - 31.1026i) q^{5} +(76.9082 + 76.9082i) q^{7} -588.037i q^{9} +O(q^{10})\) \(q+(20.3843 - 20.3843i) q^{3} +(-46.4503 - 31.1026i) q^{5} +(76.9082 + 76.9082i) q^{7} -588.037i q^{9} -556.846i q^{11} +(141.317 + 141.317i) q^{13} +(-1580.86 + 312.851i) q^{15} +(-477.013 + 477.013i) q^{17} -1608.20 q^{19} +3135.44 q^{21} +(346.617 - 346.617i) q^{23} +(1190.25 + 2889.45i) q^{25} +(-7033.34 - 7033.34i) q^{27} -7486.67i q^{29} +7927.33i q^{31} +(-11350.9 - 11350.9i) q^{33} +(-1180.36 - 5964.46i) q^{35} +(3329.26 - 3329.26i) q^{37} +5761.27 q^{39} +18717.9 q^{41} +(8253.12 - 8253.12i) q^{43} +(-18289.5 + 27314.5i) q^{45} +(5098.15 + 5098.15i) q^{47} -4977.25i q^{49} +19447.1i q^{51} +(19488.7 + 19488.7i) q^{53} +(-17319.4 + 25865.6i) q^{55} +(-32782.1 + 32782.1i) q^{57} -108.893 q^{59} +14287.1 q^{61} +(45224.9 - 45224.9i) q^{63} +(-2168.88 - 10959.5i) q^{65} +(28986.5 + 28986.5i) q^{67} -14131.1i q^{69} -982.591i q^{71} +(-21571.6 - 21571.6i) q^{73} +(83161.8 + 34636.9i) q^{75} +(42826.0 - 42826.0i) q^{77} +9383.55 q^{79} -143846. q^{81} +(-9451.97 + 9451.97i) q^{83} +(36993.7 - 7321.02i) q^{85} +(-152610. - 152610. i) q^{87} +8489.66i q^{89} +21736.8i q^{91} +(161593. + 161593. i) q^{93} +(74701.5 + 50019.3i) q^{95} +(122282. - 122282. i) q^{97} -327446. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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
\(3\) 20.3843 20.3843i 1.30765 1.30765i 0.384546 0.923106i \(-0.374358\pi\)
0.923106 0.384546i \(-0.125642\pi\)
\(4\) 0 0
\(5\) −46.4503 31.1026i −0.830928 0.556381i
\(6\) 0 0
\(7\) 76.9082 + 76.9082i 0.593236 + 0.593236i 0.938504 0.345268i \(-0.112212\pi\)
−0.345268 + 0.938504i \(0.612212\pi\)
\(8\) 0 0
\(9\) 588.037i 2.41991i
\(10\) 0 0
\(11\) 556.846i 1.38756i −0.720185 0.693782i \(-0.755943\pi\)
0.720185 0.693782i \(-0.244057\pi\)
\(12\) 0 0
\(13\) 141.317 + 141.317i 0.231918 + 0.231918i 0.813493 0.581575i \(-0.197563\pi\)
−0.581575 + 0.813493i \(0.697563\pi\)
\(14\) 0 0
\(15\) −1580.86 + 312.851i −1.81412 + 0.359012i
\(16\) 0 0
\(17\) −477.013 + 477.013i −0.400320 + 0.400320i −0.878346 0.478026i \(-0.841353\pi\)
0.478026 + 0.878346i \(0.341353\pi\)
\(18\) 0 0
\(19\) −1608.20 −1.02201 −0.511007 0.859577i \(-0.670727\pi\)
−0.511007 + 0.859577i \(0.670727\pi\)
\(20\) 0 0
\(21\) 3135.44 1.55149
\(22\) 0 0
\(23\) 346.617 346.617i 0.136625 0.136625i −0.635487 0.772112i \(-0.719201\pi\)
0.772112 + 0.635487i \(0.219201\pi\)
\(24\) 0 0
\(25\) 1190.25 + 2889.45i 0.380881 + 0.924624i
\(26\) 0 0
\(27\) −7033.34 7033.34i −1.85674 1.85674i
\(28\) 0 0
\(29\) 7486.67i 1.65308i −0.562879 0.826539i \(-0.690306\pi\)
0.562879 0.826539i \(-0.309694\pi\)
\(30\) 0 0
\(31\) 7927.33i 1.48157i 0.671742 + 0.740786i \(0.265547\pi\)
−0.671742 + 0.740786i \(0.734453\pi\)
\(32\) 0 0
\(33\) −11350.9 11350.9i −1.81445 1.81445i
\(34\) 0 0
\(35\) −1180.36 5964.46i −0.162871 0.823002i
\(36\) 0 0
\(37\) 3329.26 3329.26i 0.399801 0.399801i −0.478362 0.878163i \(-0.658769\pi\)
0.878163 + 0.478362i \(0.158769\pi\)
\(38\) 0 0
\(39\) 5761.27 0.606536
\(40\) 0 0
\(41\) 18717.9 1.73899 0.869497 0.493938i \(-0.164443\pi\)
0.869497 + 0.493938i \(0.164443\pi\)
\(42\) 0 0
\(43\) 8253.12 8253.12i 0.680686 0.680686i −0.279468 0.960155i \(-0.590158\pi\)
0.960155 + 0.279468i \(0.0901582\pi\)
\(44\) 0 0
\(45\) −18289.5 + 27314.5i −1.34639 + 2.01077i
\(46\) 0 0
\(47\) 5098.15 + 5098.15i 0.336642 + 0.336642i 0.855102 0.518460i \(-0.173494\pi\)
−0.518460 + 0.855102i \(0.673494\pi\)
\(48\) 0 0
\(49\) 4977.25i 0.296141i
\(50\) 0 0
\(51\) 19447.1i 1.04696i
\(52\) 0 0
\(53\) 19488.7 + 19488.7i 0.953001 + 0.953001i 0.998944 0.0459428i \(-0.0146292\pi\)
−0.0459428 + 0.998944i \(0.514629\pi\)
\(54\) 0 0
\(55\) −17319.4 + 25865.6i −0.772014 + 1.15297i
\(56\) 0 0
\(57\) −32782.1 + 32782.1i −1.33644 + 1.33644i
\(58\) 0 0
\(59\) −108.893 −0.00407257 −0.00203628 0.999998i \(-0.500648\pi\)
−0.00203628 + 0.999998i \(0.500648\pi\)
\(60\) 0 0
\(61\) 14287.1 0.491608 0.245804 0.969320i \(-0.420948\pi\)
0.245804 + 0.969320i \(0.420948\pi\)
\(62\) 0 0
\(63\) 45224.9 45224.9i 1.43558 1.43558i
\(64\) 0 0
\(65\) −2168.88 10959.5i −0.0636724 0.321742i
\(66\) 0 0
\(67\) 28986.5 + 28986.5i 0.788875 + 0.788875i 0.981310 0.192435i \(-0.0616384\pi\)
−0.192435 + 0.981310i \(0.561638\pi\)
\(68\) 0 0
\(69\) 14131.1i 0.357316i
\(70\) 0 0
\(71\) 982.591i 0.0231327i −0.999933 0.0115664i \(-0.996318\pi\)
0.999933 0.0115664i \(-0.00368177\pi\)
\(72\) 0 0
\(73\) −21571.6 21571.6i −0.473778 0.473778i 0.429357 0.903135i \(-0.358740\pi\)
−0.903135 + 0.429357i \(0.858740\pi\)
\(74\) 0 0
\(75\) 83161.8 + 34636.9i 1.70715 + 0.711026i
\(76\) 0 0
\(77\) 42826.0 42826.0i 0.823154 0.823154i
\(78\) 0 0
\(79\) 9383.55 0.169161 0.0845803 0.996417i \(-0.473045\pi\)
0.0845803 + 0.996417i \(0.473045\pi\)
\(80\) 0 0
\(81\) −143846. −2.43604
\(82\) 0 0
\(83\) −9451.97 + 9451.97i −0.150601 + 0.150601i −0.778386 0.627786i \(-0.783961\pi\)
0.627786 + 0.778386i \(0.283961\pi\)
\(84\) 0 0
\(85\) 36993.7 7321.02i 0.555367 0.109907i
\(86\) 0 0
\(87\) −152610. 152610.i −2.16165 2.16165i
\(88\) 0 0
\(89\) 8489.66i 0.113610i 0.998385 + 0.0568049i \(0.0180913\pi\)
−0.998385 + 0.0568049i \(0.981909\pi\)
\(90\) 0 0
\(91\) 21736.8i 0.275165i
\(92\) 0 0
\(93\) 161593. + 161593.i 1.93738 + 1.93738i
\(94\) 0 0
\(95\) 74701.5 + 50019.3i 0.849220 + 0.568629i
\(96\) 0 0
\(97\) 122282. 122282.i 1.31957 1.31957i 0.405453 0.914116i \(-0.367114\pi\)
0.914116 0.405453i \(-0.132886\pi\)
\(98\) 0 0
\(99\) −327446. −3.35778
\(100\) 0 0
\(101\) −49322.0 −0.481102 −0.240551 0.970636i \(-0.577328\pi\)
−0.240551 + 0.970636i \(0.577328\pi\)
\(102\) 0 0
\(103\) −63162.5 + 63162.5i −0.586633 + 0.586633i −0.936718 0.350085i \(-0.886153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(104\) 0 0
\(105\) −145642. 97520.3i −1.28918 0.863221i
\(106\) 0 0
\(107\) 25175.2 + 25175.2i 0.212575 + 0.212575i 0.805361 0.592785i \(-0.201972\pi\)
−0.592785 + 0.805361i \(0.701972\pi\)
\(108\) 0 0
\(109\) 79771.5i 0.643104i 0.946892 + 0.321552i \(0.104205\pi\)
−0.946892 + 0.321552i \(0.895795\pi\)
\(110\) 0 0
\(111\) 135729.i 1.04560i
\(112\) 0 0
\(113\) 93876.0 + 93876.0i 0.691606 + 0.691606i 0.962585 0.270980i \(-0.0873476\pi\)
−0.270980 + 0.962585i \(0.587348\pi\)
\(114\) 0 0
\(115\) −26881.2 + 5319.76i −0.189541 + 0.0375100i
\(116\) 0 0
\(117\) 83099.4 83099.4i 0.561220 0.561220i
\(118\) 0 0
\(119\) −73372.4 −0.474969
\(120\) 0 0
\(121\) −149026. −0.925336
\(122\) 0 0
\(123\) 381551. 381551.i 2.27400 2.27400i
\(124\) 0 0
\(125\) 34581.8 171236.i 0.197958 0.980210i
\(126\) 0 0
\(127\) 5616.82 + 5616.82i 0.0309016 + 0.0309016i 0.722389 0.691487i \(-0.243044\pi\)
−0.691487 + 0.722389i \(0.743044\pi\)
\(128\) 0 0
\(129\) 336468.i 1.78020i
\(130\) 0 0
\(131\) 56715.0i 0.288749i 0.989523 + 0.144374i \(0.0461169\pi\)
−0.989523 + 0.144374i \(0.953883\pi\)
\(132\) 0 0
\(133\) −123684. 123684.i −0.606296 0.606296i
\(134\) 0 0
\(135\) 107945. + 545456.i 0.509764 + 2.57588i
\(136\) 0 0
\(137\) −95096.7 + 95096.7i −0.432877 + 0.432877i −0.889606 0.456729i \(-0.849021\pi\)
0.456729 + 0.889606i \(0.349021\pi\)
\(138\) 0 0
\(139\) −276110. −1.21212 −0.606059 0.795420i \(-0.707251\pi\)
−0.606059 + 0.795420i \(0.707251\pi\)
\(140\) 0 0
\(141\) 207844. 0.880421
\(142\) 0 0
\(143\) 78691.5 78691.5i 0.321801 0.321801i
\(144\) 0 0
\(145\) −232855. + 347758.i −0.919741 + 1.37359i
\(146\) 0 0
\(147\) −101458. 101458.i −0.387250 0.387250i
\(148\) 0 0
\(149\) 258844.i 0.955153i 0.878590 + 0.477577i \(0.158485\pi\)
−0.878590 + 0.477577i \(0.841515\pi\)
\(150\) 0 0
\(151\) 399655.i 1.42640i 0.700958 + 0.713202i \(0.252756\pi\)
−0.700958 + 0.713202i \(0.747244\pi\)
\(152\) 0 0
\(153\) 280501. + 280501.i 0.968738 + 0.968738i
\(154\) 0 0
\(155\) 246561. 368226.i 0.824317 1.23108i
\(156\) 0 0
\(157\) −174590. + 174590.i −0.565289 + 0.565289i −0.930805 0.365516i \(-0.880893\pi\)
0.365516 + 0.930805i \(0.380893\pi\)
\(158\) 0 0
\(159\) 794527. 2.49239
\(160\) 0 0
\(161\) 53315.4 0.162102
\(162\) 0 0
\(163\) 1364.52 1364.52i 0.00402264 0.00402264i −0.705093 0.709115i \(-0.749095\pi\)
0.709115 + 0.705093i \(0.249095\pi\)
\(164\) 0 0
\(165\) 174210. + 880295.i 0.498152 + 2.51720i
\(166\) 0 0
\(167\) −323133. 323133.i −0.896581 0.896581i 0.0985507 0.995132i \(-0.468579\pi\)
−0.995132 + 0.0985507i \(0.968579\pi\)
\(168\) 0 0
\(169\) 331352.i 0.892428i
\(170\) 0 0
\(171\) 945684.i 2.47318i
\(172\) 0 0
\(173\) −173917. 173917.i −0.441800 0.441800i 0.450816 0.892617i \(-0.351133\pi\)
−0.892617 + 0.450816i \(0.851133\pi\)
\(174\) 0 0
\(175\) −130682. + 313763.i −0.322568 + 0.774473i
\(176\) 0 0
\(177\) −2219.70 + 2219.70i −0.00532550 + 0.00532550i
\(178\) 0 0
\(179\) 60036.1 0.140049 0.0700245 0.997545i \(-0.477692\pi\)
0.0700245 + 0.997545i \(0.477692\pi\)
\(180\) 0 0
\(181\) −71086.8 −0.161285 −0.0806423 0.996743i \(-0.525697\pi\)
−0.0806423 + 0.996743i \(0.525697\pi\)
\(182\) 0 0
\(183\) 291232. 291232.i 0.642852 0.642852i
\(184\) 0 0
\(185\) −258194. + 51096.3i −0.554647 + 0.109764i
\(186\) 0 0
\(187\) 265622. + 265622.i 0.555470 + 0.555470i
\(188\) 0 0
\(189\) 1.08184e6i 2.20298i
\(190\) 0 0
\(191\) 898374.i 1.78186i −0.454139 0.890931i \(-0.650053\pi\)
0.454139 0.890931i \(-0.349947\pi\)
\(192\) 0 0
\(193\) −514879. 514879.i −0.994974 0.994974i 0.00501311 0.999987i \(-0.498404\pi\)
−0.999987 + 0.00501311i \(0.998404\pi\)
\(194\) 0 0
\(195\) −267613. 179191.i −0.503988 0.337465i
\(196\) 0 0
\(197\) 320182. 320182.i 0.587802 0.587802i −0.349234 0.937036i \(-0.613558\pi\)
0.937036 + 0.349234i \(0.113558\pi\)
\(198\) 0 0
\(199\) −458886. −0.821433 −0.410717 0.911763i \(-0.634721\pi\)
−0.410717 + 0.911763i \(0.634721\pi\)
\(200\) 0 0
\(201\) 1.18174e6 2.06315
\(202\) 0 0
\(203\) 575786. 575786.i 0.980666 0.980666i
\(204\) 0 0
\(205\) −869453. 582177.i −1.44498 0.967542i
\(206\) 0 0
\(207\) −203824. 203824.i −0.330620 0.330620i
\(208\) 0 0
\(209\) 895521.i 1.41811i
\(210\) 0 0
\(211\) 561846.i 0.868783i 0.900724 + 0.434391i \(0.143037\pi\)
−0.900724 + 0.434391i \(0.856963\pi\)
\(212\) 0 0
\(213\) −20029.4 20029.4i −0.0302495 0.0302495i
\(214\) 0 0
\(215\) −640053. + 126666.i −0.944322 + 0.186880i
\(216\) 0 0
\(217\) −609677. + 609677.i −0.878922 + 0.878922i
\(218\) 0 0
\(219\) −879443. −1.23907
\(220\) 0 0
\(221\) −134820. −0.185683
\(222\) 0 0
\(223\) −821427. + 821427.i −1.10613 + 1.10613i −0.112478 + 0.993654i \(0.535879\pi\)
−0.993654 + 0.112478i \(0.964121\pi\)
\(224\) 0 0
\(225\) 1.69910e6 699914.i 2.23750 0.921697i
\(226\) 0 0
\(227\) 276085. + 276085.i 0.355613 + 0.355613i 0.862193 0.506580i \(-0.169090\pi\)
−0.506580 + 0.862193i \(0.669090\pi\)
\(228\) 0 0
\(229\) 503195.i 0.634085i 0.948411 + 0.317043i \(0.102690\pi\)
−0.948411 + 0.317043i \(0.897310\pi\)
\(230\) 0 0
\(231\) 1.74596e6i 2.15280i
\(232\) 0 0
\(233\) 594823. + 594823.i 0.717790 + 0.717790i 0.968152 0.250362i \(-0.0805496\pi\)
−0.250362 + 0.968152i \(0.580550\pi\)
\(234\) 0 0
\(235\) −78244.7 395377.i −0.0924241 0.467026i
\(236\) 0 0
\(237\) 191277. 191277.i 0.221203 0.221203i
\(238\) 0 0
\(239\) −348307. −0.394428 −0.197214 0.980360i \(-0.563189\pi\)
−0.197214 + 0.980360i \(0.563189\pi\)
\(240\) 0 0
\(241\) 252895. 0.280477 0.140239 0.990118i \(-0.455213\pi\)
0.140239 + 0.990118i \(0.455213\pi\)
\(242\) 0 0
\(243\) −1.22309e6 + 1.22309e6i −1.32875 + 1.32875i
\(244\) 0 0
\(245\) −154805. + 231194.i −0.164767 + 0.246072i
\(246\) 0 0
\(247\) −227266. 227266.i −0.237024 0.237024i
\(248\) 0 0
\(249\) 385343.i 0.393867i
\(250\) 0 0
\(251\) 493537.i 0.494465i −0.968956 0.247232i \(-0.920479\pi\)
0.968956 0.247232i \(-0.0795211\pi\)
\(252\) 0 0
\(253\) −193012. 193012.i −0.189576 0.189576i
\(254\) 0 0
\(255\) 604856. 903323.i 0.582508 0.869947i
\(256\) 0 0
\(257\) 1.28934e6 1.28934e6i 1.21768 1.21768i 0.249242 0.968441i \(-0.419819\pi\)
0.968441 0.249242i \(-0.0801814\pi\)
\(258\) 0 0
\(259\) 512095. 0.474352
\(260\) 0 0
\(261\) −4.40244e6 −4.00030
\(262\) 0 0
\(263\) −562452. + 562452.i −0.501414 + 0.501414i −0.911877 0.410463i \(-0.865367\pi\)
0.410463 + 0.911877i \(0.365367\pi\)
\(264\) 0 0
\(265\) −299106. 1.51141e6i −0.261644 1.32211i
\(266\) 0 0
\(267\) 173056. + 173056.i 0.148562 + 0.148562i
\(268\) 0 0
\(269\) 305884.i 0.257737i 0.991662 + 0.128868i \(0.0411345\pi\)
−0.991662 + 0.128868i \(0.958866\pi\)
\(270\) 0 0
\(271\) 1.98399e6i 1.64103i 0.571626 + 0.820514i \(0.306313\pi\)
−0.571626 + 0.820514i \(0.693687\pi\)
\(272\) 0 0
\(273\) 443089. + 443089.i 0.359819 + 0.359819i
\(274\) 0 0
\(275\) 1.60898e6 662788.i 1.28298 0.528497i
\(276\) 0 0
\(277\) 669845. 669845.i 0.524536 0.524536i −0.394402 0.918938i \(-0.629048\pi\)
0.918938 + 0.394402i \(0.129048\pi\)
\(278\) 0 0
\(279\) 4.66157e6 3.58526
\(280\) 0 0
\(281\) 374638. 0.283039 0.141520 0.989935i \(-0.454801\pi\)
0.141520 + 0.989935i \(0.454801\pi\)
\(282\) 0 0
\(283\) −894492. + 894492.i −0.663912 + 0.663912i −0.956300 0.292388i \(-0.905550\pi\)
0.292388 + 0.956300i \(0.405550\pi\)
\(284\) 0 0
\(285\) 2.54234e6 503127.i 1.85405 0.366915i
\(286\) 0 0
\(287\) 1.43956e6 + 1.43956e6i 1.03163 + 1.03163i
\(288\) 0 0
\(289\) 964775.i 0.679488i
\(290\) 0 0
\(291\) 4.98525e6i 3.45107i
\(292\) 0 0
\(293\) −788207. 788207.i −0.536379 0.536379i 0.386085 0.922463i \(-0.373827\pi\)
−0.922463 + 0.386085i \(0.873827\pi\)
\(294\) 0 0
\(295\) 5058.09 + 3386.85i 0.00338401 + 0.00226590i
\(296\) 0 0
\(297\) −3.91649e6 + 3.91649e6i −2.57635 + 2.57635i
\(298\) 0 0
\(299\) 97965.5 0.0633717
\(300\) 0 0
\(301\) 1.26947e6 0.807616
\(302\) 0 0
\(303\) −1.00539e6 + 1.00539e6i −0.629114 + 0.629114i
\(304\) 0 0
\(305\) −663638. 444365.i −0.408490 0.273521i
\(306\) 0 0
\(307\) 2.03742e6 + 2.03742e6i 1.23377 + 1.23377i 0.962505 + 0.271264i \(0.0874415\pi\)
0.271264 + 0.962505i \(0.412558\pi\)
\(308\) 0 0
\(309\) 2.57504e6i 1.53422i
\(310\) 0 0
\(311\) 2.55652e6i 1.49881i 0.662109 + 0.749407i \(0.269661\pi\)
−0.662109 + 0.749407i \(0.730339\pi\)
\(312\) 0 0
\(313\) 985823. + 985823.i 0.568772 + 0.568772i 0.931784 0.363012i \(-0.118252\pi\)
−0.363012 + 0.931784i \(0.618252\pi\)
\(314\) 0 0
\(315\) −3.50732e6 + 694096.i −1.99159 + 0.394133i
\(316\) 0 0
\(317\) −113582. + 113582.i −0.0634836 + 0.0634836i −0.738136 0.674652i \(-0.764294\pi\)
0.674652 + 0.738136i \(0.264294\pi\)
\(318\) 0 0
\(319\) −4.16892e6 −2.29375
\(320\) 0 0
\(321\) 1.02636e6 0.555949
\(322\) 0 0
\(323\) 767133. 767133.i 0.409133 0.409133i
\(324\) 0 0
\(325\) −240125. + 576530.i −0.126104 + 0.302770i
\(326\) 0 0
\(327\) 1.62608e6 + 1.62608e6i 0.840956 + 0.840956i
\(328\) 0 0
\(329\) 784180.i 0.399417i
\(330\) 0 0
\(331\) 327502.i 0.164303i 0.996620 + 0.0821513i \(0.0261791\pi\)
−0.996620 + 0.0821513i \(0.973821\pi\)
\(332\) 0 0
\(333\) −1.95773e6 1.95773e6i −0.967480 0.967480i
\(334\) 0 0
\(335\) −444874. 2.24798e6i −0.216583 1.09441i
\(336\) 0 0
\(337\) 1.20574e6 1.20574e6i 0.578335 0.578335i −0.356110 0.934444i \(-0.615897\pi\)
0.934444 + 0.356110i \(0.115897\pi\)
\(338\) 0 0
\(339\) 3.82719e6 1.80876
\(340\) 0 0
\(341\) 4.41430e6 2.05578
\(342\) 0 0
\(343\) 1.67539e6 1.67539e6i 0.768918 0.768918i
\(344\) 0 0
\(345\) −439514. + 656392.i −0.198804 + 0.296904i
\(346\) 0 0
\(347\) −1.84834e6 1.84834e6i −0.824058 0.824058i 0.162629 0.986687i \(-0.448002\pi\)
−0.986687 + 0.162629i \(0.948002\pi\)
\(348\) 0 0
\(349\) 28570.5i 0.0125561i −0.999980 0.00627804i \(-0.998002\pi\)
0.999980 0.00627804i \(-0.00199838\pi\)
\(350\) 0 0
\(351\) 1.98785e6i 0.861225i
\(352\) 0 0
\(353\) −1.77770e6 1.77770e6i −0.759316 0.759316i 0.216882 0.976198i \(-0.430411\pi\)
−0.976198 + 0.216882i \(0.930411\pi\)
\(354\) 0 0
\(355\) −30561.1 + 45641.6i −0.0128706 + 0.0192216i
\(356\) 0 0
\(357\) −1.49564e6 + 1.49564e6i −0.621094 + 0.621094i
\(358\) 0 0
\(359\) 736136. 0.301454 0.150727 0.988575i \(-0.451838\pi\)
0.150727 + 0.988575i \(0.451838\pi\)
\(360\) 0 0
\(361\) 110218. 0.0445130
\(362\) 0 0
\(363\) −3.03779e6 + 3.03779e6i −1.21002 + 1.21002i
\(364\) 0 0
\(365\) 331073. + 1.67294e6i 0.130074 + 0.657276i
\(366\) 0 0
\(367\) −477935. 477935.i −0.185227 0.185227i 0.608402 0.793629i \(-0.291811\pi\)
−0.793629 + 0.608402i \(0.791811\pi\)
\(368\) 0 0
\(369\) 1.10068e7i 4.20820i
\(370\) 0 0
\(371\) 2.99769e6i 1.13071i
\(372\) 0 0
\(373\) −3.22422e6 3.22422e6i −1.19992 1.19992i −0.974189 0.225732i \(-0.927523\pi\)
−0.225732 0.974189i \(-0.572477\pi\)
\(374\) 0 0
\(375\) −2.78559e6 4.19544e6i −1.02291 1.54063i
\(376\) 0 0
\(377\) 1.05799e6 1.05799e6i 0.383379 0.383379i
\(378\) 0 0
\(379\) 4.24297e6 1.51730 0.758652 0.651496i \(-0.225858\pi\)
0.758652 + 0.651496i \(0.225858\pi\)
\(380\) 0 0
\(381\) 228990. 0.0808171
\(382\) 0 0
\(383\) −654083. + 654083.i −0.227843 + 0.227843i −0.811791 0.583948i \(-0.801507\pi\)
0.583948 + 0.811791i \(0.301507\pi\)
\(384\) 0 0
\(385\) −3.32128e6 + 657279.i −1.14197 + 0.225994i
\(386\) 0 0
\(387\) −4.85314e6 4.85314e6i −1.64720 1.64720i
\(388\) 0 0
\(389\) 2.46468e6i 0.825823i 0.910771 + 0.412911i \(0.135488\pi\)
−0.910771 + 0.412911i \(0.864512\pi\)
\(390\) 0 0
\(391\) 330681.i 0.109388i
\(392\) 0 0
\(393\) 1.15609e6 + 1.15609e6i 0.377583 + 0.377583i
\(394\) 0 0
\(395\) −435868. 291853.i −0.140560 0.0941177i
\(396\) 0 0
\(397\) 4.06922e6 4.06922e6i 1.29579 1.29579i 0.364645 0.931147i \(-0.381190\pi\)
0.931147 0.364645i \(-0.118810\pi\)
\(398\) 0 0
\(399\) −5.04242e6 −1.58565
\(400\) 0 0
\(401\) 3.14549e6 0.976849 0.488424 0.872606i \(-0.337572\pi\)
0.488424 + 0.872606i \(0.337572\pi\)
\(402\) 0 0
\(403\) −1.12026e6 + 1.12026e6i −0.343603 + 0.343603i
\(404\) 0 0
\(405\) 6.68168e6 + 4.47399e6i 2.02418 + 1.35537i
\(406\) 0 0
\(407\) −1.85388e6 1.85388e6i −0.554749 0.554749i
\(408\) 0 0
\(409\) 4.42634e6i 1.30839i 0.756327 + 0.654194i \(0.226992\pi\)
−0.756327 + 0.654194i \(0.773008\pi\)
\(410\) 0 0
\(411\) 3.87696e6i 1.13210i
\(412\) 0 0
\(413\) −8374.74 8374.74i −0.00241600 0.00241600i
\(414\) 0 0
\(415\) 733028. 145066.i 0.208930 0.0413470i
\(416\) 0 0
\(417\) −5.62830e6 + 5.62830e6i −1.58503 + 1.58503i
\(418\) 0 0
\(419\) −2.19963e6 −0.612090 −0.306045 0.952017i \(-0.599006\pi\)
−0.306045 + 0.952017i \(0.599006\pi\)
\(420\) 0 0
\(421\) 1240.34 0.000341063 0.000170532 1.00000i \(-0.499946\pi\)
0.000170532 1.00000i \(0.499946\pi\)
\(422\) 0 0
\(423\) 2.99791e6 2.99791e6i 0.814642 0.814642i
\(424\) 0 0
\(425\) −1.94607e6 810538.i −0.522620 0.217671i
\(426\) 0 0
\(427\) 1.09879e6 + 1.09879e6i 0.291640 + 0.291640i
\(428\) 0 0
\(429\) 3.20814e6i 0.841609i
\(430\) 0 0
\(431\) 1.29826e6i 0.336642i −0.985732 0.168321i \(-0.946166\pi\)
0.985732 0.168321i \(-0.0538344\pi\)
\(432\) 0 0
\(433\) 665935. + 665935.i 0.170691 + 0.170691i 0.787283 0.616592i \(-0.211487\pi\)
−0.616592 + 0.787283i \(0.711487\pi\)
\(434\) 0 0
\(435\) 2.34221e6 + 1.18354e7i 0.593475 + 2.99888i
\(436\) 0 0
\(437\) −557431. + 557431.i −0.139633 + 0.139633i
\(438\) 0 0
\(439\) −3.73469e6 −0.924898 −0.462449 0.886646i \(-0.653029\pi\)
−0.462449 + 0.886646i \(0.653029\pi\)
\(440\) 0 0
\(441\) −2.92681e6 −0.716634
\(442\) 0 0
\(443\) 2.91756e6 2.91756e6i 0.706336 0.706336i −0.259427 0.965763i \(-0.583534\pi\)
0.965763 + 0.259427i \(0.0835337\pi\)
\(444\) 0 0
\(445\) 264051. 394347.i 0.0632102 0.0944014i
\(446\) 0 0
\(447\) 5.27635e6 + 5.27635e6i 1.24901 + 1.24901i
\(448\) 0 0
\(449\) 992830.i 0.232412i −0.993225 0.116206i \(-0.962927\pi\)
0.993225 0.116206i \(-0.0370733\pi\)
\(450\) 0 0
\(451\) 1.04230e7i 2.41297i
\(452\) 0 0
\(453\) 8.14667e6 + 8.14667e6i 1.86524 + 1.86524i
\(454\) 0 0
\(455\) 676072. 1.00968e6i 0.153096 0.228642i
\(456\) 0 0
\(457\) −4.19086e6 + 4.19086e6i −0.938670 + 0.938670i −0.998225 0.0595554i \(-0.981032\pi\)
0.0595554 + 0.998225i \(0.481032\pi\)
\(458\) 0 0
\(459\) 6.70998e6 1.48658
\(460\) 0 0
\(461\) −5.83166e6 −1.27803 −0.639013 0.769196i \(-0.720657\pi\)
−0.639013 + 0.769196i \(0.720657\pi\)
\(462\) 0 0
\(463\) 4.17783e6 4.17783e6i 0.905728 0.905728i −0.0901957 0.995924i \(-0.528749\pi\)
0.995924 + 0.0901957i \(0.0287492\pi\)
\(464\) 0 0
\(465\) −2.48007e6 1.25320e7i −0.531902 2.68774i
\(466\) 0 0
\(467\) 2.18280e6 + 2.18280e6i 0.463150 + 0.463150i 0.899686 0.436537i \(-0.143795\pi\)
−0.436537 + 0.899686i \(0.643795\pi\)
\(468\) 0 0
\(469\) 4.45859e6i 0.935978i
\(470\) 0 0
\(471\) 7.11779e6i 1.47840i
\(472\) 0 0
\(473\) −4.59572e6 4.59572e6i −0.944497 0.944497i
\(474\) 0 0
\(475\) −1.91417e6 4.64682e6i −0.389266 0.944979i
\(476\) 0 0
\(477\) 1.14601e7 1.14601e7i 2.30617 2.30617i
\(478\) 0 0
\(479\) −1.70781e6 −0.340095 −0.170047 0.985436i \(-0.554392\pi\)
−0.170047 + 0.985436i \(0.554392\pi\)
\(480\) 0 0
\(481\) 940959. 0.185442
\(482\) 0 0
\(483\) 1.08680e6 1.08680e6i 0.211973 0.211973i
\(484\) 0 0
\(485\) −9.48330e6 + 1.87674e6i −1.83065 + 0.362284i
\(486\) 0 0
\(487\) 3.89197e6 + 3.89197e6i 0.743613 + 0.743613i 0.973271 0.229658i \(-0.0737608\pi\)
−0.229658 + 0.973271i \(0.573761\pi\)
\(488\) 0 0
\(489\) 55629.6i 0.0105204i
\(490\) 0 0
\(491\) 3.79408e6i 0.710236i 0.934821 + 0.355118i \(0.115559\pi\)
−0.934821 + 0.355118i \(0.884441\pi\)
\(492\) 0 0
\(493\) 3.57123e6 + 3.57123e6i 0.661761 + 0.661761i
\(494\) 0 0
\(495\) 1.52100e7 + 1.01844e7i 2.79007 + 1.86820i
\(496\) 0 0
\(497\) 75569.3 75569.3i 0.0137232 0.0137232i
\(498\) 0 0
\(499\) −5.45318e6 −0.980388 −0.490194 0.871613i \(-0.663074\pi\)
−0.490194 + 0.871613i \(0.663074\pi\)
\(500\) 0 0
\(501\) −1.31737e7 −2.34483
\(502\) 0 0
\(503\) −5.05453e6 + 5.05453e6i −0.890760 + 0.890760i −0.994595 0.103834i \(-0.966889\pi\)
0.103834 + 0.994595i \(0.466889\pi\)
\(504\) 0 0
\(505\) 2.29102e6 + 1.53404e6i 0.399761 + 0.267676i
\(506\) 0 0
\(507\) −6.75438e6 6.75438e6i −1.16699 1.16699i
\(508\) 0 0
\(509\) 5.72886e6i 0.980108i 0.871692 + 0.490054i \(0.163023\pi\)
−0.871692 + 0.490054i \(0.836977\pi\)
\(510\) 0 0
\(511\) 3.31807e6i 0.562125i
\(512\) 0 0
\(513\) 1.13110e7 + 1.13110e7i 1.89762 + 1.89762i
\(514\) 0 0
\(515\) 4.89844e6 969396.i 0.813841 0.161058i
\(516\) 0 0
\(517\) 2.83889e6 2.83889e6i 0.467113 0.467113i
\(518\) 0 0
\(519\) −7.09033e6 −1.15544
\(520\) 0 0
\(521\) −6.55438e6 −1.05788 −0.528941 0.848659i \(-0.677411\pi\)
−0.528941 + 0.848659i \(0.677411\pi\)
\(522\) 0 0
\(523\) 7.16908e6 7.16908e6i 1.14606 1.14606i 0.158745 0.987320i \(-0.449255\pi\)
0.987320 0.158745i \(-0.0507447\pi\)
\(524\) 0 0
\(525\) 3.73197e6 + 9.05969e6i 0.590935 + 1.43455i
\(526\) 0 0
\(527\) −3.78143e6 3.78143e6i −0.593103 0.593103i
\(528\) 0 0
\(529\) 6.19606e6i 0.962667i
\(530\) 0 0
\(531\) 64033.0i 0.00985524i
\(532\) 0 0
\(533\) 2.64515e6 + 2.64515e6i 0.403304 + 0.403304i
\(534\) 0 0
\(535\) −386380. 1.95241e6i −0.0583619 0.294908i
\(536\) 0 0
\(537\) 1.22379e6 1.22379e6i 0.183135 0.183135i
\(538\) 0 0
\(539\) −2.77156e6 −0.410915
\(540\) 0 0
\(541\) 47552.7 0.00698526 0.00349263 0.999994i \(-0.498888\pi\)
0.00349263 + 0.999994i \(0.498888\pi\)
\(542\) 0 0
\(543\) −1.44905e6 + 1.44905e6i −0.210904 + 0.210904i
\(544\) 0 0
\(545\) 2.48110e6 3.70541e6i 0.357811 0.534373i
\(546\) 0 0
\(547\) −4.55854e6 4.55854e6i −0.651415 0.651415i 0.301919 0.953334i \(-0.402373\pi\)
−0.953334 + 0.301919i \(0.902373\pi\)
\(548\) 0 0
\(549\) 8.40134e6i 1.18965i
\(550\) 0 0
\(551\) 1.20401e7i 1.68947i
\(552\) 0 0
\(553\) 721672. + 721672.i 0.100352 + 0.100352i
\(554\) 0 0
\(555\) −4.22153e6 + 6.30465e6i −0.581751 + 0.868818i
\(556\) 0 0
\(557\) 3.11785e6 3.11785e6i 0.425811 0.425811i −0.461388 0.887199i \(-0.652648\pi\)
0.887199 + 0.461388i \(0.152648\pi\)
\(558\) 0 0
\(559\) 2.33261e6 0.315727
\(560\) 0 0
\(561\) 1.08290e7 1.45272
\(562\) 0 0
\(563\) −8.10403e6 + 8.10403e6i −1.07753 + 1.07753i −0.0808018 + 0.996730i \(0.525748\pi\)
−0.996730 + 0.0808018i \(0.974252\pi\)
\(564\) 0 0
\(565\) −1.44078e6 7.28035e6i −0.189878 0.959470i
\(566\) 0 0
\(567\) −1.10629e7 1.10629e7i −1.44515 1.44515i
\(568\) 0 0
\(569\) 3.79477e6i 0.491366i −0.969350 0.245683i \(-0.920988\pi\)
0.969350 0.245683i \(-0.0790122\pi\)
\(570\) 0 0
\(571\) 3.17124e6i 0.407042i −0.979071 0.203521i \(-0.934761\pi\)
0.979071 0.203521i \(-0.0652385\pi\)
\(572\) 0 0
\(573\) −1.83127e7 1.83127e7i −2.33005 2.33005i
\(574\) 0 0
\(575\) 1.41410e6 + 588970.i 0.178365 + 0.0742889i
\(576\) 0 0
\(577\) −407507. + 407507.i −0.0509560 + 0.0509560i −0.732126 0.681170i \(-0.761472\pi\)
0.681170 + 0.732126i \(0.261472\pi\)
\(578\) 0 0
\(579\) −2.09909e7 −2.60216
\(580\) 0 0
\(581\) −1.45387e6 −0.178684
\(582\) 0 0
\(583\) 1.08522e7 1.08522e7i 1.32235 1.32235i
\(584\) 0 0
\(585\) −6.44460e6 + 1.27538e6i −0.778586 + 0.154081i
\(586\) 0 0
\(587\) 3.38451e6 + 3.38451e6i 0.405416 + 0.405416i 0.880136 0.474721i \(-0.157451\pi\)
−0.474721 + 0.880136i \(0.657451\pi\)
\(588\) 0 0
\(589\) 1.27488e7i 1.51419i
\(590\) 0 0
\(591\) 1.30533e7i 1.53728i
\(592\) 0 0
\(593\) 1.57715e6 + 1.57715e6i 0.184178 + 0.184178i 0.793174 0.608996i \(-0.208427\pi\)
−0.608996 + 0.793174i \(0.708427\pi\)
\(594\) 0 0
\(595\) 3.40817e6 + 2.28207e6i 0.394665 + 0.264264i
\(596\) 0 0
\(597\) −9.35406e6 + 9.35406e6i −1.07415 + 1.07415i
\(598\) 0 0
\(599\) 1.09992e7 1.25254 0.626272 0.779605i \(-0.284580\pi\)
0.626272 + 0.779605i \(0.284580\pi\)
\(600\) 0 0
\(601\) 1.44320e7 1.62982 0.814909 0.579589i \(-0.196787\pi\)
0.814909 + 0.579589i \(0.196787\pi\)
\(602\) 0 0
\(603\) 1.70451e7 1.70451e7i 1.90900 1.90900i
\(604\) 0 0
\(605\) 6.92231e6 + 4.63511e6i 0.768887 + 0.514839i
\(606\) 0 0
\(607\) −4.21170e6 4.21170e6i −0.463966 0.463966i 0.435987 0.899953i \(-0.356399\pi\)
−0.899953 + 0.435987i \(0.856399\pi\)
\(608\) 0 0
\(609\) 2.34740e7i 2.56474i
\(610\) 0 0
\(611\) 1.44091e6i 0.156147i
\(612\) 0 0
\(613\) 3.54916e6 + 3.54916e6i 0.381482 + 0.381482i 0.871636 0.490154i \(-0.163059\pi\)
−0.490154 + 0.871636i \(0.663059\pi\)
\(614\) 0 0
\(615\) −2.95904e7 + 5.85591e6i −3.15474 + 0.624320i
\(616\) 0 0
\(617\) 2.56234e6 2.56234e6i 0.270971 0.270971i −0.558520 0.829491i \(-0.688631\pi\)
0.829491 + 0.558520i \(0.188631\pi\)
\(618\) 0 0
\(619\) 6.34177e6 0.665248 0.332624 0.943060i \(-0.392066\pi\)
0.332624 + 0.943060i \(0.392066\pi\)
\(620\) 0 0
\(621\) −4.87575e6 −0.507356
\(622\) 0 0
\(623\) −652925. + 652925.i −0.0673974 + 0.0673974i
\(624\) 0 0
\(625\) −6.93222e6 + 6.87836e6i −0.709859 + 0.704344i
\(626\) 0 0
\(627\) 1.82546e7 + 1.82546e7i 1.85440 + 1.85440i
\(628\) 0 0
\(629\) 3.17620e6i 0.320096i
\(630\) 0 0
\(631\) 4.54433e6i 0.454356i 0.973853 + 0.227178i \(0.0729500\pi\)
−0.973853 + 0.227178i \(0.927050\pi\)
\(632\) 0 0
\(633\) 1.14528e7 + 1.14528e7i 1.13607 + 1.13607i
\(634\) 0 0
\(635\) −86205.0 435601.i −0.00848395 0.0428701i
\(636\) 0 0
\(637\) 703367. 703367.i 0.0686805 0.0686805i
\(638\) 0 0
\(639\) −577800. −0.0559790
\(640\) 0 0
\(641\) 6.59831e6 0.634290 0.317145 0.948377i \(-0.397276\pi\)
0.317145 + 0.948377i \(0.397276\pi\)
\(642\) 0 0
\(643\) −6.81404e6 + 6.81404e6i −0.649946 + 0.649946i −0.952980 0.303034i \(-0.902000\pi\)
0.303034 + 0.952980i \(0.402000\pi\)
\(644\) 0 0
\(645\) −1.04650e7 + 1.56290e7i −0.990470 + 1.47922i
\(646\) 0 0
\(647\) −1.11169e7 1.11169e7i −1.04405 1.04405i −0.998984 0.0450702i \(-0.985649\pi\)
−0.0450702 0.998984i \(1.48565\pi\)
\(648\) 0 0
\(649\) 60636.4i 0.00565095i
\(650\) 0 0
\(651\) 2.48556e7i 2.29865i
\(652\) 0 0
\(653\) −1.27508e7 1.27508e7i −1.17019 1.17019i −0.982164 0.188025i \(-0.939791\pi\)
−0.188025 0.982164i \(-0.560209\pi\)
\(654\) 0 0
\(655\) 1.76399e6 2.63443e6i 0.160654 0.239929i
\(656\) 0 0
\(657\) −1.26849e7 + 1.26849e7i −1.14650 + 1.14650i
\(658\) 0 0
\(659\) −9.10667e6 −0.816857 −0.408429 0.912790i \(-0.633923\pi\)
−0.408429 + 0.912790i \(0.633923\pi\)
\(660\) 0 0
\(661\) 1.89210e7 1.68438 0.842189 0.539182i \(-0.181266\pi\)
0.842189 + 0.539182i \(0.181266\pi\)
\(662\) 0 0
\(663\) −2.74820e6 + 2.74820e6i −0.242809 + 0.242809i
\(664\) 0 0
\(665\) 1.89826e6 + 9.59206e6i 0.166457 + 0.841119i
\(666\) 0 0
\(667\) −2.59501e6 2.59501e6i −0.225852 0.225852i
\(668\) 0 0
\(669\) 3.34884e7i 2.89287i
\(670\) 0 0
\(671\) 7.95570e6i 0.682138i
\(672\) 0 0
\(673\) 3.24765e6 + 3.24765e6i 0.276395 + 0.276395i 0.831668 0.555273i \(-0.187386\pi\)
−0.555273 + 0.831668i \(0.687386\pi\)
\(674\) 0 0
\(675\) 1.19510e7 2.86939e7i 1.00959 2.42399i
\(676\) 0 0
\(677\) 1.17838e7 1.17838e7i 0.988128 0.988128i −0.0118027 0.999930i \(-0.503757\pi\)
0.999930 + 0.0118027i \(0.00375700\pi\)
\(678\) 0 0
\(679\) 1.88089e7 1.56563
\(680\) 0 0
\(681\) 1.12556e7 0.930036
\(682\) 0 0
\(683\) −8.18028e6 + 8.18028e6i −0.670991 + 0.670991i −0.957944 0.286954i \(-0.907357\pi\)
0.286954 + 0.957944i \(0.407357\pi\)
\(684\) 0 0
\(685\) 7.37502e6 1.45951e6i 0.600533 0.118845i
\(686\) 0 0
\(687\) 1.02573e7 + 1.02573e7i 0.829163 + 0.829163i
\(688\) 0 0
\(689\) 5.50816e6i 0.442037i
\(690\) 0 0
\(691\) 1.23162e7i 0.981253i 0.871370 + 0.490626i \(0.163232\pi\)
−0.871370 + 0.490626i \(0.836768\pi\)
\(692\) 0 0
\(693\) −2.51833e7 2.51833e7i −1.99196 1.99196i
\(694\) 0 0
\(695\) 1.28254e7 + 8.58774e6i 1.00718 + 0.674399i
\(696\) 0 0
\(697\) −8.92868e6 + 8.92868e6i −0.696154 + 0.696154i
\(698\) 0 0
\(699\) 2.42501e7 1.87724
\(700\) 0 0
\(701\) −2.10018e7 −1.61421 −0.807107 0.590405i \(-0.798968\pi\)
−0.807107 + 0.590405i \(0.798968\pi\)
\(702\) 0 0
\(703\) −5.35413e6 + 5.35413e6i −0.408602 + 0.408602i
\(704\) 0 0
\(705\) −9.65443e6 6.46450e6i −0.731566 0.489849i
\(706\) 0 0
\(707\) −3.79327e6 3.79327e6i −0.285407 0.285407i
\(708\) 0 0
\(709\) 1.87952e7i 1.40421i −0.712074 0.702105i \(-0.752244\pi\)
0.712074 0.702105i \(-0.247756\pi\)
\(710\) 0 0
\(711\) 5.51788e6i 0.409353i
\(712\) 0 0
\(713\) 2.74775e6 + 2.74775e6i 0.202420 + 0.202420i
\(714\) 0 0
\(715\) −6.10276e6 + 1.20773e6i −0.446438 + 0.0883496i
\(716\) 0 0
\(717\) −7.09999e6 + 7.09999e6i −0.515774 + 0.515774i
\(718\) 0 0
\(719\) 2.33655e7 1.68559 0.842797 0.538232i \(-0.180908\pi\)
0.842797 + 0.538232i \(0.180908\pi\)
\(720\) 0 0
\(721\) −9.71544e6 −0.696024
\(722\) 0 0
\(723\) 5.15508e6 5.15508e6i 0.366767 0.366767i
\(724\) 0 0
\(725\) 2.16324e7 8.91104e6i 1.52848 0.629627i
\(726\) 0 0
\(727\) 1.18759e7 + 1.18759e7i 0.833355 + 0.833355i 0.987974 0.154619i \(-0.0494151\pi\)
−0.154619 + 0.987974i \(0.549415\pi\)
\(728\) 0 0
\(729\) 1.49092e7i 1.03905i
\(730\) 0 0
\(731\) 7.87368e6i 0.544985i
\(732\) 0 0
\(733\) 8.08731e6 + 8.08731e6i 0.555961 + 0.555961i 0.928155 0.372194i \(-0.121394\pi\)
−0.372194 + 0.928155i \(0.621394\pi\)
\(734\) 0 0
\(735\) 1.55713e6 + 7.86833e6i 0.106318 + 0.537235i
\(736\) 0 0
\(737\) 1.61410e7 1.61410e7i 1.09461 1.09461i
\(738\) 0 0
\(739\) −1.24230e7 −0.836786 −0.418393 0.908266i \(-0.637407\pi\)
−0.418393 + 0.908266i \(0.637407\pi\)
\(740\) 0 0
\(741\) −9.26530e6 −0.619889
\(742\) 0 0
\(743\) 9.76492e6 9.76492e6i 0.648928 0.648928i −0.303806 0.952734i \(-0.598257\pi\)
0.952734 + 0.303806i \(0.0982575\pi\)
\(744\) 0 0
\(745\) 8.05074e6 1.20234e7i 0.531429 0.793663i
\(746\) 0 0
\(747\) 5.55811e6 + 5.55811e6i 0.364440 + 0.364440i
\(748\) 0 0
\(749\) 3.87236e6i 0.252215i
\(750\) 0 0
\(751\) 2.15742e7i 1.39584i −0.716178 0.697918i \(-0.754110\pi\)
0.716178 0.697918i \(-0.245890\pi\)
\(752\) 0 0
\(753\) −1.00604e7 1.00604e7i −0.646588 0.646588i
\(754\) 0 0
\(755\) 1.24303e7 1.85641e7i 0.793624 1.18524i
\(756\) 0 0
\(757\) −1.09605e7 + 1.09605e7i −0.695169 + 0.695169i −0.963364 0.268196i \(-0.913573\pi\)
0.268196 + 0.963364i \(0.413573\pi\)
\(758\) 0 0
\(759\) −7.86883e6 −0.495799
\(760\) 0 0
\(761\) −3.94007e6 −0.246628 −0.123314 0.992368i \(-0.539352\pi\)
−0.123314 + 0.992368i \(0.539352\pi\)
\(762\) 0 0
\(763\) −6.13508e6 + 6.13508e6i −0.381513 + 0.381513i
\(764\) 0 0
\(765\) −4.30503e6 2.17537e7i −0.265964 1.34394i
\(766\) 0 0
\(767\) −15388.3 15388.3i −0.000944503 0.000944503i
\(768\) 0 0
\(769\) 1.05073e7i 0.640730i 0.947294 + 0.320365i \(0.103805\pi\)
−0.947294 + 0.320365i \(0.896195\pi\)
\(770\) 0 0
\(771\) 5.25645e7i 3.18461i
\(772\) 0 0
\(773\) 1.29271e7 + 1.29271e7i 0.778128 + 0.778128i 0.979512 0.201384i \(-0.0645439\pi\)
−0.201384 + 0.979512i \(0.564544\pi\)
\(774\) 0 0
\(775\) −2.29056e7 + 9.43553e6i −1.36990 + 0.564303i
\(776\) 0 0
\(777\) 1.04387e7 1.04387e7i 0.620288 0.620288i
\(778\) 0 0
\(779\) −3.01022e7 −1.77728
\(780\) 0 0
\(781\) −547151. −0.0320981
\(782\) 0 0
\(783\) −5.26563e7 + 5.26563e7i −3.06934 + 3.06934i
\(784\) 0 0
\(785\) 1.35400e7 2.67955e6i 0.784230 0.155198i
\(786\) 0 0
\(787\) 2.08585e7 + 2.08585e7i 1.20046 + 1.20046i 0.974028 + 0.226427i \(0.0727045\pi\)
0.226427 + 0.974028i \(0.427295\pi\)
\(788\) 0 0
\(789\) 2.29304e7i 1.31135i
\(790\) 0 0