Properties

Label 124.6.f.a.33.1
Level $124$
Weight $6$
Character 124.33
Analytic conductor $19.888$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 124.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8875936568\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 33.1
Character \(\chi\) \(=\) 124.33
Dual form 124.6.f.a.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.7500 + 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 - 142.432i) q^{7} +(148.259 - 456.295i) q^{9} +O(q^{10})\) \(q+(-21.7500 + 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 - 142.432i) q^{7} +(148.259 - 456.295i) q^{9} +(53.6179 + 165.019i) q^{11} +(684.216 - 497.112i) q^{13} +(580.483 - 421.746i) q^{15} +(-444.272 + 1367.33i) q^{17} +(-2426.00 - 1762.59i) q^{19} +(3257.34 + 2366.59i) q^{21} +(-706.831 + 2175.40i) q^{23} -2412.71 q^{25} +(1967.09 + 6054.09i) q^{27} +(3738.58 + 2716.23i) q^{29} +(3838.05 + 3728.08i) q^{31} +(-3773.87 - 2741.88i) q^{33} +(1235.14 + 3801.36i) q^{35} +4924.45 q^{37} +(-7026.19 + 21624.4i) q^{39} +(9302.94 + 6758.98i) q^{41} +(-1497.30 - 1087.85i) q^{43} +(-3956.87 + 12178.0i) q^{45} +(12861.5 - 9344.46i) q^{47} +(-4548.09 + 3304.38i) q^{49} +(-11944.0 - 36759.9i) q^{51} +(5993.12 - 18444.9i) q^{53} +(-1431.00 - 4404.16i) q^{55} +80618.6 q^{57} +(-29277.0 + 21271.0i) q^{59} +35110.8 q^{61} -71852.6 q^{63} +(-18260.9 + 13267.3i) q^{65} -8530.75 q^{67} +(-19002.8 - 58484.6i) q^{69} +(-14105.9 + 43413.4i) q^{71} +(7533.30 + 23185.1i) q^{73} +(52476.4 - 38126.4i) q^{75} +(21022.6 - 15273.8i) q^{77} +(-14199.4 + 43701.3i) q^{79} +(-44133.0 - 32064.5i) q^{81} +(57767.9 + 41970.8i) q^{83} +(11857.1 - 36492.4i) q^{85} -124237. q^{87} +(10240.9 + 31518.4i) q^{89} +(-102470. - 74448.6i) q^{91} +(-142390. - 20435.8i) q^{93} +(64747.1 + 47041.5i) q^{95} +(33219.9 + 102240. i) q^{97} +83246.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) −21.7500 + 15.8023i −1.39527 + 1.01372i −0.400001 + 0.916515i \(0.630990\pi\)
−0.995264 + 0.0972047i \(0.969010\pi\)
\(4\) 0 0
\(5\) −26.6888 −0.477424 −0.238712 0.971090i \(-0.576725\pi\)
−0.238712 + 0.971090i \(0.576725\pi\)
\(6\) 0 0
\(7\) −46.2791 142.432i −0.356977 1.09866i −0.954854 0.297074i \(-0.903989\pi\)
0.597878 0.801587i \(-0.296011\pi\)
\(8\) 0 0
\(9\) 148.259 456.295i 0.610121 1.87776i
\(10\) 0 0
\(11\) 53.6179 + 165.019i 0.133607 + 0.411199i 0.995371 0.0961105i \(-0.0306402\pi\)
−0.861764 + 0.507309i \(0.830640\pi\)
\(12\) 0 0
\(13\) 684.216 497.112i 1.12288 0.815822i 0.138240 0.990399i \(-0.455856\pi\)
0.984644 + 0.174576i \(0.0558556\pi\)
\(14\) 0 0
\(15\) 580.483 421.746i 0.666134 0.483974i
\(16\) 0 0
\(17\) −444.272 + 1367.33i −0.372843 + 1.14749i 0.572079 + 0.820198i \(0.306137\pi\)
−0.944922 + 0.327295i \(0.893863\pi\)
\(18\) 0 0
\(19\) −2426.00 1762.59i −1.54172 1.12013i −0.949243 0.314543i \(-0.898149\pi\)
−0.592480 0.805585i \(-0.701851\pi\)
\(20\) 0 0
\(21\) 3257.34 + 2366.59i 1.61181 + 1.17105i
\(22\) 0 0
\(23\) −706.831 + 2175.40i −0.278610 + 0.857472i 0.709632 + 0.704572i \(0.248861\pi\)
−0.988242 + 0.152900i \(0.951139\pi\)
\(24\) 0 0
\(25\) −2412.71 −0.772066
\(26\) 0 0
\(27\) 1967.09 + 6054.09i 0.519296 + 1.59823i
\(28\) 0 0
\(29\) 3738.58 + 2716.23i 0.825489 + 0.599753i 0.918279 0.395933i \(-0.129579\pi\)
−0.0927907 + 0.995686i \(0.529579\pi\)
\(30\) 0 0
\(31\) 3838.05 + 3728.08i 0.717308 + 0.696756i
\(32\) 0 0
\(33\) −3773.87 2741.88i −0.603257 0.438292i
\(34\) 0 0
\(35\) 1235.14 + 3801.36i 0.170429 + 0.524528i
\(36\) 0 0
\(37\) 4924.45 0.591362 0.295681 0.955287i \(-0.404453\pi\)
0.295681 + 0.955287i \(0.404453\pi\)
\(38\) 0 0
\(39\) −7026.19 + 21624.4i −0.739705 + 2.27658i
\(40\) 0 0
\(41\) 9302.94 + 6758.98i 0.864292 + 0.627945i 0.929049 0.369956i \(-0.120627\pi\)
−0.0647572 + 0.997901i \(0.520627\pi\)
\(42\) 0 0
\(43\) −1497.30 1087.85i −0.123492 0.0897218i 0.524325 0.851518i \(-0.324318\pi\)
−0.647817 + 0.761796i \(0.724318\pi\)
\(44\) 0 0
\(45\) −3956.87 + 12178.0i −0.291287 + 0.896488i
\(46\) 0 0
\(47\) 12861.5 9344.46i 0.849275 0.617035i −0.0756709 0.997133i \(-0.524110\pi\)
0.924946 + 0.380098i \(0.124110\pi\)
\(48\) 0 0
\(49\) −4548.09 + 3304.38i −0.270607 + 0.196608i
\(50\) 0 0
\(51\) −11944.0 36759.9i −0.643021 1.97902i
\(52\) 0 0
\(53\) 5993.12 18444.9i 0.293065 0.901960i −0.690800 0.723046i \(-0.742741\pi\)
0.983865 0.178914i \(-0.0572585\pi\)
\(54\) 0 0
\(55\) −1431.00 4404.16i −0.0637870 0.196316i
\(56\) 0 0
\(57\) 80618.6 3.28661
\(58\) 0 0
\(59\) −29277.0 + 21271.0i −1.09496 + 0.795533i −0.980230 0.197864i \(-0.936600\pi\)
−0.114728 + 0.993397i \(0.536600\pi\)
\(60\) 0 0
\(61\) 35110.8 1.20814 0.604069 0.796932i \(-0.293545\pi\)
0.604069 + 0.796932i \(0.293545\pi\)
\(62\) 0 0
\(63\) −71852.6 −2.28082
\(64\) 0 0
\(65\) −18260.9 + 13267.3i −0.536092 + 0.389494i
\(66\) 0 0
\(67\) −8530.75 −0.232167 −0.116083 0.993239i \(-0.537034\pi\)
−0.116083 + 0.993239i \(0.537034\pi\)
\(68\) 0 0
\(69\) −19002.8 58484.6i −0.480502 1.47883i
\(70\) 0 0
\(71\) −14105.9 + 43413.4i −0.332089 + 1.02206i 0.636050 + 0.771648i \(0.280567\pi\)
−0.968138 + 0.250416i \(0.919433\pi\)
\(72\) 0 0
\(73\) 7533.30 + 23185.1i 0.165454 + 0.509216i 0.999069 0.0431296i \(-0.0137328\pi\)
−0.833615 + 0.552346i \(0.813733\pi\)
\(74\) 0 0
\(75\) 52476.4 38126.4i 1.07724 0.782658i
\(76\) 0 0
\(77\) 21022.6 15273.8i 0.404074 0.293577i
\(78\) 0 0
\(79\) −14199.4 + 43701.3i −0.255978 + 0.787819i 0.737658 + 0.675175i \(0.235932\pi\)
−0.993635 + 0.112644i \(0.964068\pi\)
\(80\) 0 0
\(81\) −44133.0 32064.5i −0.747396 0.543015i
\(82\) 0 0
\(83\) 57767.9 + 41970.8i 0.920431 + 0.668732i 0.943631 0.330999i \(-0.107386\pi\)
−0.0232004 + 0.999731i \(0.507386\pi\)
\(84\) 0 0
\(85\) 11857.1 36492.4i 0.178004 0.547841i
\(86\) 0 0
\(87\) −124237. −1.75976
\(88\) 0 0
\(89\) 10240.9 + 31518.4i 0.137046 + 0.421783i 0.995903 0.0904326i \(-0.0288250\pi\)
−0.858857 + 0.512215i \(0.828825\pi\)
\(90\) 0 0
\(91\) −102470. 74448.6i −1.29716 0.942439i
\(92\) 0 0
\(93\) −142390. 20435.8i −1.70715 0.245010i
\(94\) 0 0
\(95\) 64747.1 + 47041.5i 0.736057 + 0.534776i
\(96\) 0 0
\(97\) 33219.9 + 102240.i 0.358484 + 1.10330i 0.953962 + 0.299928i \(0.0969627\pi\)
−0.595478 + 0.803372i \(0.703037\pi\)
\(98\) 0 0
\(99\) 83246.7 0.853648
\(100\) 0 0
\(101\) 53189.2 163699.i 0.518824 1.59678i −0.257391 0.966307i \(-0.582863\pi\)
0.776215 0.630468i \(-0.217137\pi\)
\(102\) 0 0
\(103\) 52378.7 + 38055.3i 0.486476 + 0.353446i 0.803828 0.594862i \(-0.202793\pi\)
−0.317351 + 0.948308i \(0.602793\pi\)
\(104\) 0 0
\(105\) −86934.5 63161.6i −0.769518 0.559088i
\(106\) 0 0
\(107\) 58011.3 178540.i 0.489839 1.50757i −0.335010 0.942215i \(-0.608740\pi\)
0.824848 0.565354i \(-0.191260\pi\)
\(108\) 0 0
\(109\) 27059.5 19659.9i 0.218149 0.158495i −0.473344 0.880878i \(-0.656953\pi\)
0.691493 + 0.722383i \(0.256953\pi\)
\(110\) 0 0
\(111\) −107107. + 77817.8i −0.825107 + 0.599476i
\(112\) 0 0
\(113\) −39256.4 120819.i −0.289211 0.890099i −0.985105 0.171955i \(-0.944992\pi\)
0.695894 0.718144i \(-0.255008\pi\)
\(114\) 0 0
\(115\) 18864.5 58059.0i 0.133015 0.409378i
\(116\) 0 0
\(117\) −125388. 385906.i −0.846823 2.60625i
\(118\) 0 0
\(119\) 215312. 1.39380
\(120\) 0 0
\(121\) 105937. 76967.5i 0.657783 0.477908i
\(122\) 0 0
\(123\) −309147. −1.84248
\(124\) 0 0
\(125\) 147795. 0.846028
\(126\) 0 0
\(127\) 129424. 94031.7i 0.712039 0.517327i −0.171792 0.985133i \(-0.554956\pi\)
0.883831 + 0.467807i \(0.154956\pi\)
\(128\) 0 0
\(129\) 49756.8 0.263256
\(130\) 0 0
\(131\) 96356.9 + 296556.i 0.490574 + 1.50983i 0.823742 + 0.566965i \(0.191882\pi\)
−0.333168 + 0.942868i \(0.608118\pi\)
\(132\) 0 0
\(133\) −138777. + 427112.i −0.680282 + 2.09369i
\(134\) 0 0
\(135\) −52499.4 161577.i −0.247925 0.763034i
\(136\) 0 0
\(137\) −151756. + 110257.i −0.690786 + 0.501886i −0.876919 0.480639i \(-0.840405\pi\)
0.186132 + 0.982525i \(0.440405\pi\)
\(138\) 0 0
\(139\) −122791. + 89213.2i −0.539052 + 0.391644i −0.823733 0.566978i \(-0.808112\pi\)
0.284681 + 0.958622i \(0.408112\pi\)
\(140\) 0 0
\(141\) −132075. + 406485.i −0.559464 + 1.72185i
\(142\) 0 0
\(143\) 118719. + 86254.4i 0.485490 + 0.352729i
\(144\) 0 0
\(145\) −99778.2 72493.1i −0.394109 0.286337i
\(146\) 0 0
\(147\) 46704.3 143741.i 0.178264 0.548640i
\(148\) 0 0
\(149\) −117531. −0.433697 −0.216848 0.976205i \(-0.569578\pi\)
−0.216848 + 0.976205i \(0.569578\pi\)
\(150\) 0 0
\(151\) 149025. + 458651.i 0.531883 + 1.63697i 0.750290 + 0.661109i \(0.229914\pi\)
−0.218408 + 0.975858i \(0.570086\pi\)
\(152\) 0 0
\(153\) 558038. + 405438.i 1.92724 + 1.40022i
\(154\) 0 0
\(155\) −102433. 99498.0i −0.342461 0.332648i
\(156\) 0 0
\(157\) 296642. + 215523.i 0.960469 + 0.697822i 0.953260 0.302152i \(-0.0977051\pi\)
0.00720949 + 0.999974i \(0.497705\pi\)
\(158\) 0 0
\(159\) 161122. + 495883.i 0.505432 + 1.55556i
\(160\) 0 0
\(161\) 342559. 1.04153
\(162\) 0 0
\(163\) 198060. 609567.i 0.583887 1.79702i −0.0198100 0.999804i \(-0.506306\pi\)
0.603697 0.797214i \(-0.293694\pi\)
\(164\) 0 0
\(165\) 100720. + 73177.5i 0.288010 + 0.209251i
\(166\) 0 0
\(167\) 68541.4 + 49798.2i 0.190179 + 0.138173i 0.678800 0.734323i \(-0.262500\pi\)
−0.488622 + 0.872496i \(0.662500\pi\)
\(168\) 0 0
\(169\) 106295. 327143.i 0.286283 0.881090i
\(170\) 0 0
\(171\) −1.16394e6 + 845651.i −3.04397 + 2.21157i
\(172\) 0 0
\(173\) −182473. + 132575.i −0.463536 + 0.336779i −0.794917 0.606718i \(-0.792486\pi\)
0.331381 + 0.943497i \(0.392486\pi\)
\(174\) 0 0
\(175\) 111658. + 343648.i 0.275610 + 0.848239i
\(176\) 0 0
\(177\) 300645. 925291.i 0.721309 2.21996i
\(178\) 0 0
\(179\) 8146.05 + 25071.0i 0.0190027 + 0.0584842i 0.960108 0.279629i \(-0.0902114\pi\)
−0.941106 + 0.338113i \(0.890211\pi\)
\(180\) 0 0
\(181\) −72253.0 −0.163930 −0.0819652 0.996635i \(-0.526120\pi\)
−0.0819652 + 0.996635i \(0.526120\pi\)
\(182\) 0 0
\(183\) −763661. + 554832.i −1.68567 + 1.22471i
\(184\) 0 0
\(185\) −131428. −0.282331
\(186\) 0 0
\(187\) −249456. −0.521662
\(188\) 0 0
\(189\) 771263. 560355.i 1.57054 1.14106i
\(190\) 0 0
\(191\) 146192. 0.289961 0.144980 0.989435i \(-0.453688\pi\)
0.144980 + 0.989435i \(0.453688\pi\)
\(192\) 0 0
\(193\) −89454.4 275312.i −0.172866 0.532026i 0.826664 0.562696i \(-0.190236\pi\)
−0.999530 + 0.0306703i \(0.990236\pi\)
\(194\) 0 0
\(195\) 187521. 577130.i 0.353153 1.08689i
\(196\) 0 0
\(197\) 119110. + 366583.i 0.218667 + 0.672987i 0.998873 + 0.0474643i \(0.0151140\pi\)
−0.780206 + 0.625522i \(0.784886\pi\)
\(198\) 0 0
\(199\) −9347.05 + 6791.03i −0.0167318 + 0.0121563i −0.596120 0.802896i \(-0.703292\pi\)
0.579388 + 0.815052i \(0.303292\pi\)
\(200\) 0 0
\(201\) 185544. 134806.i 0.323934 0.235352i
\(202\) 0 0
\(203\) 213862. 658199.i 0.364245 1.12103i
\(204\) 0 0
\(205\) −248285. 180389.i −0.412634 0.299796i
\(206\) 0 0
\(207\) 887832. + 645047.i 1.44014 + 1.04632i
\(208\) 0 0
\(209\) 160784. 494842.i 0.254611 0.783611i
\(210\) 0 0
\(211\) −61040.0 −0.0943861 −0.0471931 0.998886i \(-0.515028\pi\)
−0.0471931 + 0.998886i \(0.515028\pi\)
\(212\) 0 0
\(213\) −379230. 1.16715e6i −0.572734 1.76269i
\(214\) 0 0
\(215\) 39961.1 + 29033.5i 0.0589579 + 0.0428354i
\(216\) 0 0
\(217\) 353378. 719194.i 0.509436 1.03680i
\(218\) 0 0
\(219\) −530228. 385233.i −0.747055 0.542767i
\(220\) 0 0
\(221\) 375737. + 1.15640e6i 0.517491 + 1.59267i
\(222\) 0 0
\(223\) −1.07543e6 −1.44817 −0.724083 0.689713i \(-0.757737\pi\)
−0.724083 + 0.689713i \(0.757737\pi\)
\(224\) 0 0
\(225\) −357706. + 1.10091e6i −0.471053 + 1.44975i
\(226\) 0 0
\(227\) 244158. + 177391.i 0.314489 + 0.228490i 0.733820 0.679344i \(-0.237735\pi\)
−0.419331 + 0.907833i \(0.637735\pi\)
\(228\) 0 0
\(229\) 82310.7 + 59802.3i 0.103721 + 0.0753579i 0.638437 0.769674i \(-0.279581\pi\)
−0.534716 + 0.845032i \(0.679581\pi\)
\(230\) 0 0
\(231\) −215881. + 664413.i −0.266186 + 0.819235i
\(232\) 0 0
\(233\) 682802. 496085.i 0.823958 0.598640i −0.0938856 0.995583i \(-0.529929\pi\)
0.917843 + 0.396943i \(0.129929\pi\)
\(234\) 0 0
\(235\) −343260. + 249393.i −0.405465 + 0.294587i
\(236\) 0 0
\(237\) −381744. 1.17489e6i −0.441470 1.35871i
\(238\) 0 0
\(239\) 482533. 1.48508e6i 0.546427 1.68173i −0.171145 0.985246i \(-0.554747\pi\)
0.717572 0.696484i \(-0.245253\pi\)
\(240\) 0 0
\(241\) 341482. + 1.05097e6i 0.378726 + 1.16560i 0.940931 + 0.338600i \(0.109953\pi\)
−0.562205 + 0.826998i \(0.690047\pi\)
\(242\) 0 0
\(243\) −80263.7 −0.0871974
\(244\) 0 0
\(245\) 121383. 88190.2i 0.129194 0.0938653i
\(246\) 0 0
\(247\) −2.53611e6 −2.64500
\(248\) 0 0
\(249\) −1.91969e6 −1.96215
\(250\) 0 0
\(251\) −1.05809e6 + 768751.i −1.06008 + 0.770196i −0.974104 0.226101i \(-0.927402\pi\)
−0.0859802 + 0.996297i \(0.527402\pi\)
\(252\) 0 0
\(253\) −396881. −0.389816
\(254\) 0 0
\(255\) 318772. + 981080.i 0.306994 + 0.944831i
\(256\) 0 0
\(257\) −505145. + 1.55468e6i −0.477071 + 1.46827i 0.366073 + 0.930586i \(0.380702\pi\)
−0.843144 + 0.537687i \(0.819298\pi\)
\(258\) 0 0
\(259\) −227899. 701402.i −0.211103 0.649707i
\(260\) 0 0
\(261\) 1.79368e6 1.30319e6i 1.62984 1.18415i
\(262\) 0 0
\(263\) 1.13975e6 828078.i 1.01606 0.738214i 0.0505915 0.998719i \(-0.483889\pi\)
0.965472 + 0.260506i \(0.0838893\pi\)
\(264\) 0 0
\(265\) −159949. + 492274.i −0.139916 + 0.430618i
\(266\) 0 0
\(267\) −720804. 523695.i −0.618784 0.449573i
\(268\) 0 0
\(269\) 421106. + 305951.i 0.354822 + 0.257793i 0.750889 0.660428i \(-0.229625\pi\)
−0.396067 + 0.918222i \(0.629625\pi\)
\(270\) 0 0
\(271\) 154785. 476378.i 0.128028 0.394030i −0.866413 0.499329i \(-0.833580\pi\)
0.994441 + 0.105299i \(0.0335800\pi\)
\(272\) 0 0
\(273\) 3.40518e6 2.76524
\(274\) 0 0
\(275\) −129364. 398142.i −0.103153 0.317473i
\(276\) 0 0
\(277\) 20780.8 + 15098.1i 0.0162728 + 0.0118229i 0.595892 0.803065i \(-0.296799\pi\)
−0.579619 + 0.814888i \(0.696799\pi\)
\(278\) 0 0
\(279\) 2.27013e6 1.19856e6i 1.74598 0.921827i
\(280\) 0 0
\(281\) −475825. 345707.i −0.359486 0.261182i 0.393352 0.919388i \(-0.371315\pi\)
−0.752837 + 0.658206i \(0.771315\pi\)
\(282\) 0 0
\(283\) −295083. 908173.i −0.219017 0.674066i −0.998844 0.0480704i \(-0.984693\pi\)
0.779827 0.625996i \(-0.215307\pi\)
\(284\) 0 0
\(285\) −2.15162e6 −1.56911
\(286\) 0 0
\(287\) 532166. 1.63784e6i 0.381367 1.17373i
\(288\) 0 0
\(289\) −523518. 380358.i −0.368712 0.267885i
\(290\) 0 0
\(291\) −2.33817e6 1.69878e6i −1.61862 1.17599i
\(292\) 0 0
\(293\) 393034. 1.20963e6i 0.267461 0.823161i −0.723655 0.690162i \(-0.757539\pi\)
0.991116 0.132999i \(-0.0424608\pi\)
\(294\) 0 0
\(295\) 781370. 567699.i 0.522759 0.379807i
\(296\) 0 0
\(297\) −893567. + 649214.i −0.587809 + 0.427068i
\(298\) 0 0
\(299\) 597793. + 1.83982e6i 0.386699 + 1.19014i
\(300\) 0 0
\(301\) −85651.6 + 263609.i −0.0544903 + 0.167704i
\(302\) 0 0
\(303\) 1.42997e6 + 4.40098e6i 0.894786 + 2.75387i
\(304\) 0 0
\(305\) −937067. −0.576794
\(306\) 0 0
\(307\) 1.22837e6 892465.i 0.743848 0.540437i −0.150066 0.988676i \(-0.547949\pi\)
0.893914 + 0.448239i \(0.147949\pi\)
\(308\) 0 0
\(309\) −1.74060e6 −1.03706
\(310\) 0 0
\(311\) 838425. 0.491545 0.245773 0.969328i \(-0.420958\pi\)
0.245773 + 0.969328i \(0.420958\pi\)
\(312\) 0 0
\(313\) −2.19212e6 + 1.59267e6i −1.26474 + 0.918891i −0.998980 0.0451474i \(-0.985624\pi\)
−0.265764 + 0.964038i \(0.585624\pi\)
\(314\) 0 0
\(315\) 1.91766e6 1.08892
\(316\) 0 0
\(317\) −664445. 2.04495e6i −0.371373 1.14297i −0.945893 0.324479i \(-0.894811\pi\)
0.574519 0.818491i \(-0.305189\pi\)
\(318\) 0 0
\(319\) −247775. + 762574.i −0.136327 + 0.419571i
\(320\) 0 0
\(321\) 1.55961e6 + 4.79997e6i 0.844797 + 2.60002i
\(322\) 0 0
\(323\) 3.48784e6 2.53406e6i 1.86016 1.35149i
\(324\) 0 0
\(325\) −1.65081e6 + 1.19938e6i −0.866940 + 0.629869i
\(326\) 0 0
\(327\) −277874. + 855207.i −0.143707 + 0.442285i
\(328\) 0 0
\(329\) −1.92617e6 1.39945e6i −0.981083 0.712799i
\(330\) 0 0
\(331\) −825552. 599799.i −0.414166 0.300909i 0.361120 0.932519i \(-0.382394\pi\)
−0.775286 + 0.631610i \(0.782394\pi\)
\(332\) 0 0
\(333\) 730096. 2.24701e6i 0.360802 1.11044i
\(334\) 0 0
\(335\) 227676. 0.110842
\(336\) 0 0
\(337\) −1.08433e6 3.33724e6i −0.520102 1.60071i −0.773803 0.633426i \(-0.781648\pi\)
0.253702 0.967282i \(-0.418352\pi\)
\(338\) 0 0
\(339\) 2.76305e6 + 2.00747e6i 1.30584 + 0.948746i
\(340\) 0 0
\(341\) −409415. + 833241.i −0.190668 + 0.388047i
\(342\) 0 0
\(343\) −1.35521e6 984616.i −0.621971 0.451889i
\(344\) 0 0
\(345\) 507163. + 1.56089e6i 0.229403 + 0.706031i
\(346\) 0 0
\(347\) 4.38790e6 1.95629 0.978145 0.207923i \(-0.0666704\pi\)
0.978145 + 0.207923i \(0.0666704\pi\)
\(348\) 0 0
\(349\) −962993. + 2.96379e6i −0.423214 + 1.30252i 0.481481 + 0.876457i \(0.340099\pi\)
−0.904694 + 0.426061i \(0.859901\pi\)
\(350\) 0 0
\(351\) 4.35547e6 + 3.16444e6i 1.88698 + 1.37097i
\(352\) 0 0
\(353\) 1.15223e6 + 837143.i 0.492155 + 0.357571i 0.806012 0.591899i \(-0.201621\pi\)
−0.313858 + 0.949470i \(0.601621\pi\)
\(354\) 0 0
\(355\) 376469. 1.15865e6i 0.158547 0.487958i
\(356\) 0 0
\(357\) −4.68305e6 + 3.40243e6i −1.94472 + 1.41292i
\(358\) 0 0
\(359\) −121674. + 88401.4i −0.0498267 + 0.0362012i −0.612420 0.790533i \(-0.709804\pi\)
0.562593 + 0.826734i \(0.309804\pi\)
\(360\) 0 0
\(361\) 2.01358e6 + 6.19718e6i 0.813209 + 2.50280i
\(362\) 0 0
\(363\) −1.08786e6 + 3.34809e6i −0.433318 + 1.33362i
\(364\) 0 0
\(365\) −201055. 618784.i −0.0789919 0.243112i
\(366\) 0 0
\(367\) 102384. 0.0396794 0.0198397 0.999803i \(-0.493684\pi\)
0.0198397 + 0.999803i \(0.493684\pi\)
\(368\) 0 0
\(369\) 4.46334e6 3.24281e6i 1.70645 1.23981i
\(370\) 0 0
\(371\) −2.90451e6 −1.09557
\(372\) 0 0
\(373\) −4.23392e6 −1.57569 −0.787844 0.615875i \(-0.788803\pi\)
−0.787844 + 0.615875i \(0.788803\pi\)
\(374\) 0 0
\(375\) −3.21454e6 + 2.33550e6i −1.18043 + 0.857635i
\(376\) 0 0
\(377\) 3.90826e6 1.41622
\(378\) 0 0
\(379\) 757954. + 2.33274e6i 0.271047 + 0.834197i 0.990238 + 0.139385i \(0.0445125\pi\)
−0.719191 + 0.694812i \(0.755487\pi\)
\(380\) 0 0
\(381\) −1.32905e6 + 4.09038e6i −0.469059 + 1.44362i
\(382\) 0 0
\(383\) 513463. + 1.58028e6i 0.178859 + 0.550473i 0.999789 0.0205572i \(-0.00654402\pi\)
−0.820929 + 0.571030i \(0.806544\pi\)
\(384\) 0 0
\(385\) −561070. + 407641.i −0.192915 + 0.140161i
\(386\) 0 0
\(387\) −718370. + 521926.i −0.243821 + 0.177146i
\(388\) 0 0
\(389\) 436955. 1.34481e6i 0.146407 0.450595i −0.850782 0.525519i \(-0.823871\pi\)
0.997189 + 0.0749237i \(0.0238713\pi\)
\(390\) 0 0
\(391\) −2.66046e6 1.93294e6i −0.880066 0.639405i
\(392\) 0 0
\(393\) −6.78204e6 4.92744e6i −2.21503 1.60931i
\(394\) 0 0
\(395\) 378966. 1.16634e6i 0.122210 0.376124i
\(396\) 0 0
\(397\) 5.73602e6 1.82656 0.913281 0.407330i \(-0.133540\pi\)
0.913281 + 0.407330i \(0.133540\pi\)
\(398\) 0 0
\(399\) −3.73096e6 1.14827e7i −1.17324 3.61087i
\(400\) 0 0
\(401\) 4.29975e6 + 3.12395e6i 1.33531 + 0.970159i 0.999603 + 0.0281924i \(0.00897512\pi\)
0.335707 + 0.941967i \(0.391025\pi\)
\(402\) 0 0
\(403\) 4.47932e6 + 642871.i 1.37388 + 0.197179i
\(404\) 0 0
\(405\) 1.17786e6 + 855764.i 0.356825 + 0.259249i
\(406\) 0 0
\(407\) 264039. + 812627.i 0.0790099 + 0.243167i
\(408\) 0 0
\(409\) −1.97200e6 −0.582906 −0.291453 0.956585i \(-0.594139\pi\)
−0.291453 + 0.956585i \(0.594139\pi\)
\(410\) 0 0
\(411\) 1.55838e6 4.79619e6i 0.455059 1.40053i
\(412\) 0 0
\(413\) 4.38460e6 + 3.18560e6i 1.26490 + 0.919001i
\(414\) 0 0
\(415\) −1.54176e6 1.12015e6i −0.439436 0.319269i
\(416\) 0 0
\(417\) 1.26094e6 3.88078e6i 0.355103 1.09290i
\(418\) 0 0
\(419\) −1.98969e6 + 1.44560e6i −0.553670 + 0.402265i −0.829137 0.559046i \(-0.811168\pi\)
0.275467 + 0.961311i \(0.411168\pi\)
\(420\) 0 0
\(421\) 355801. 258504.i 0.0978366 0.0710824i −0.537791 0.843078i \(-0.680741\pi\)
0.635628 + 0.771995i \(0.280741\pi\)
\(422\) 0 0
\(423\) −2.35699e6 7.25407e6i −0.640481 1.97120i
\(424\) 0 0
\(425\) 1.07190e6 3.29896e6i 0.287859 0.885940i
\(426\) 0 0
\(427\) −1.62490e6 5.00092e6i −0.431277 1.32733i
\(428\) 0 0
\(429\) −3.94516e6 −1.03496
\(430\) 0 0
\(431\) −4.78481e6 + 3.47637e6i −1.24071 + 0.901430i −0.997646 0.0685791i \(-0.978153\pi\)
−0.243067 + 0.970010i \(0.578153\pi\)
\(432\) 0 0
\(433\) −3.30384e6 −0.846837 −0.423418 0.905934i \(-0.639170\pi\)
−0.423418 + 0.905934i \(0.639170\pi\)
\(434\) 0 0
\(435\) 3.31574e6 0.840151
\(436\) 0 0
\(437\) 5.54912e6 4.03167e6i 1.39002 1.00991i
\(438\) 0 0
\(439\) 6.25526e6 1.54912 0.774558 0.632503i \(-0.217972\pi\)
0.774558 + 0.632503i \(0.217972\pi\)
\(440\) 0 0
\(441\) 833478. + 2.56518e6i 0.204079 + 0.628089i
\(442\) 0 0
\(443\) 514049. 1.58208e6i 0.124450 0.383018i −0.869350 0.494196i \(-0.835462\pi\)
0.993801 + 0.111178i \(0.0354624\pi\)
\(444\) 0 0
\(445\) −273319. 841189.i −0.0654289 0.201369i
\(446\) 0 0
\(447\) 2.55630e6 1.85726e6i 0.605122 0.439647i
\(448\) 0 0
\(449\) −5.81564e6 + 4.22531e6i −1.36139 + 0.989106i −0.363032 + 0.931777i \(0.618258\pi\)
−0.998355 + 0.0573292i \(0.981742\pi\)
\(450\) 0 0
\(451\) −616555. + 1.89756e6i −0.142735 + 0.439293i
\(452\) 0 0
\(453\) −1.04890e7 7.62073e6i −2.40154 1.74482i
\(454\) 0 0
\(455\) 2.73480e6 + 1.98695e6i 0.619294 + 0.449943i
\(456\) 0 0
\(457\) 2.15900e6 6.64473e6i 0.483574 1.48829i −0.350463 0.936577i \(-0.613976\pi\)
0.834036 0.551710i \(-0.186024\pi\)
\(458\) 0 0
\(459\) −9.15184e6 −2.02757
\(460\) 0 0
\(461\) 1.96508e6 + 6.04790e6i 0.430654 + 1.32542i 0.897476 + 0.441064i \(0.145399\pi\)
−0.466822 + 0.884351i \(0.654601\pi\)
\(462\) 0 0
\(463\) −615022. 446840.i −0.133333 0.0968722i 0.519120 0.854702i \(-0.326260\pi\)
−0.652453 + 0.757829i \(0.726260\pi\)
\(464\) 0 0
\(465\) 3.80022e6 + 545407.i 0.815035 + 0.116974i
\(466\) 0 0
\(467\) 1.07875e6 + 783755.i 0.228890 + 0.166298i 0.696319 0.717732i \(-0.254820\pi\)
−0.467429 + 0.884031i \(0.654820\pi\)
\(468\) 0 0
\(469\) 394796. + 1.21506e6i 0.0828782 + 0.255073i
\(470\) 0 0
\(471\) −9.85774e6 −2.04750
\(472\) 0 0
\(473\) 99233.9 305411.i 0.0203942 0.0627670i
\(474\) 0 0
\(475\) 5.85322e6 + 4.25261e6i 1.19031 + 0.864812i
\(476\) 0 0
\(477\) −7.52780e6 5.46927e6i −1.51486 1.10061i
\(478\) 0 0
\(479\) 2.25445e6 6.93847e6i 0.448953 1.38174i −0.429137 0.903240i \(-0.641182\pi\)
0.878090 0.478496i \(-0.158818\pi\)
\(480\) 0 0
\(481\) 3.36939e6 2.44800e6i 0.664031 0.482447i
\(482\) 0 0
\(483\) −7.45068e6 + 5.41323e6i −1.45321 + 1.05582i
\(484\) 0 0
\(485\) −886602. 2.72868e6i −0.171149 0.526742i
\(486\) 0 0
\(487\) 2.02370e6 6.22832e6i 0.386656 1.19000i −0.548616 0.836074i \(-0.684845\pi\)
0.935272 0.353930i \(-0.115155\pi\)
\(488\) 0 0
\(489\) 5.32476e6 + 1.63879e7i 1.00700 + 3.09921i
\(490\) 0 0
\(491\) 5.94893e6 1.11362 0.556808 0.830642i \(-0.312026\pi\)
0.556808 + 0.830642i \(0.312026\pi\)
\(492\) 0 0
\(493\) −5.37492e6 + 3.90511e6i −0.995990 + 0.723629i
\(494\) 0 0
\(495\) −2.22176e6 −0.407552
\(496\) 0 0
\(497\) 6.83628e6 1.24145
\(498\) 0 0
\(499\) −6.42970e6 + 4.67145e6i −1.15595 + 0.839847i −0.989261 0.146163i \(-0.953308\pi\)
−0.166689 + 0.986009i \(0.553308\pi\)
\(500\) 0 0
\(501\) −2.27770e6 −0.405418
\(502\) 0 0
\(503\) 1.71561e6 + 5.28009e6i 0.302341 + 0.930511i 0.980656 + 0.195739i \(0.0627106\pi\)
−0.678315 + 0.734771i \(0.737289\pi\)
\(504\) 0 0
\(505\) −1.41956e6 + 4.36895e6i −0.247699 + 0.762340i
\(506\) 0 0
\(507\) 2.85769e6 + 8.79507e6i 0.493737 + 1.51957i
\(508\) 0 0
\(509\) −462236. + 335834.i −0.0790804 + 0.0574553i −0.626623 0.779323i \(-0.715563\pi\)
0.547543 + 0.836778i \(0.315563\pi\)
\(510\) 0 0
\(511\) 2.95368e6 2.14597e6i 0.500393 0.363557i
\(512\) 0 0
\(513\) 5.89872e6 1.81544e7i 0.989610 3.04571i
\(514\) 0 0
\(515\) −1.39793e6 1.01565e6i −0.232256 0.168744i
\(516\) 0 0
\(517\) 2.23162e6 + 1.62137e6i 0.367193 + 0.266781i
\(518\) 0 0
\(519\) 1.87381e6 5.76700e6i 0.305357 0.939792i
\(520\) 0 0
\(521\) −2.71739e6 −0.438590 −0.219295 0.975659i \(-0.570376\pi\)
−0.219295 + 0.975659i \(0.570376\pi\)
\(522\) 0 0
\(523\) −1.29608e6 3.98892e6i −0.207194 0.637678i −0.999616 0.0277047i \(-0.991180\pi\)
0.792422 0.609973i \(-0.208820\pi\)
\(524\) 0 0
\(525\) −7.85899e6 5.70989e6i −1.24442 0.904127i
\(526\) 0 0
\(527\) −6.80264e6 + 3.59159e6i −1.06697 + 0.563326i
\(528\) 0 0
\(529\) 974346. + 707904.i 0.151382 + 0.109985i
\(530\) 0 0
\(531\) 5.36527e6 + 1.65126e7i 0.825763 + 2.54144i
\(532\) 0 0
\(533\) 9.72518e6 1.48279
\(534\) 0 0
\(535\) −1.54825e6 + 4.76504e6i −0.233861 + 0.719750i
\(536\) 0 0
\(537\) −573357. 416568.i −0.0858003 0.0623376i
\(538\) 0 0
\(539\) −789145. 573347.i −0.117000 0.0850053i
\(540\) 0 0
\(541\) −3.24332e6 + 9.98190e6i −0.476427 + 1.46629i 0.367597 + 0.929985i \(0.380181\pi\)
−0.844024 + 0.536306i \(0.819819\pi\)
\(542\) 0 0
\(543\) 1.57150e6 1.14176e6i 0.228726 0.166179i
\(544\) 0 0
\(545\) −722188. + 524700.i −0.104150 + 0.0756693i
\(546\) 0 0
\(547\) −1.14384e6 3.52039e6i −0.163455 0.503063i 0.835464 0.549545i \(-0.185199\pi\)
−0.998919 + 0.0464820i \(0.985199\pi\)
\(548\) 0 0
\(549\) 5.20551e6 1.60209e7i 0.737110 2.26859i
\(550\) 0 0
\(551\) −4.28217e6 1.31792e7i −0.600876 1.84931i
\(552\) 0 0
\(553\) 6.88162e6 0.956924
\(554\) 0 0
\(555\) 2.85856e6 2.07687e6i 0.393926 0.286204i
\(556\) 0 0
\(557\) −1.01944e7 −1.39226 −0.696132 0.717913i \(-0.745097\pi\)
−0.696132 + 0.717913i \(0.745097\pi\)
\(558\) 0 0
\(559\) −1.56526e6 −0.211864
\(560\) 0 0
\(561\) 5.42567e6 3.94198e6i 0.727857 0.528819i
\(562\) 0 0
\(563\) 3.31607e6 0.440913 0.220457 0.975397i \(-0.429245\pi\)
0.220457 + 0.975397i \(0.429245\pi\)
\(564\) 0 0
\(565\) 1.04771e6 + 3.22451e6i 0.138076 + 0.424955i
\(566\) 0 0
\(567\) −2.52459e6 + 7.76989e6i −0.329787 + 1.01498i
\(568\) 0 0
\(569\) 1.69736e6 + 5.22394e6i 0.219783 + 0.676422i 0.998779 + 0.0493936i \(0.0157289\pi\)
−0.778997 + 0.627028i \(0.784271\pi\)
\(570\) 0 0
\(571\) 161411. 117272.i 0.0207178 0.0150523i −0.577378 0.816477i \(-0.695924\pi\)
0.598096 + 0.801424i \(0.295924\pi\)
\(572\) 0 0
\(573\) −3.17968e6 + 2.31017e6i −0.404572 + 0.293939i
\(574\) 0 0
\(575\) 1.70538e6 5.24861e6i 0.215105 0.662025i
\(576\) 0 0
\(577\) 6.93626e6 + 5.03949e6i 0.867333 + 0.630154i 0.929870 0.367888i \(-0.119919\pi\)
−0.0625371 + 0.998043i \(0.519919\pi\)
\(578\) 0 0
\(579\) 6.29621e6 + 4.57447e6i 0.780518 + 0.567080i
\(580\) 0 0
\(581\) 3.30456e6 1.01704e7i 0.406138 1.24996i
\(582\) 0 0
\(583\) 3.36510e6 0.410040
\(584\) 0 0
\(585\) 3.34647e6 + 1.02994e7i 0.404294 + 1.24429i
\(586\) 0 0
\(587\) −1.99734e6 1.45115e6i −0.239252 0.173827i 0.461698 0.887037i \(-0.347240\pi\)
−0.700950 + 0.713210i \(0.747240\pi\)
\(588\) 0 0
\(589\) −2.74002e6 1.58092e7i −0.325436 1.87768i
\(590\) 0 0
\(591\) −8.38350e6 6.09097e6i −0.987317 0.717328i
\(592\) 0 0
\(593\) 1.67007e6 + 5.13993e6i 0.195028 + 0.600234i 0.999976 + 0.00688944i \(0.00219299\pi\)
−0.804948 + 0.593345i \(0.797807\pi\)
\(594\) 0 0
\(595\) −5.74643e6 −0.665435
\(596\) 0 0
\(597\) 95984.6 295410.i 0.0110221 0.0339227i
\(598\) 0 0
\(599\) 1.08924e7 + 7.91381e6i 1.24039 + 0.901195i 0.997624 0.0688909i \(-0.0219460\pi\)
0.242764 + 0.970085i \(0.421946\pi\)
\(600\) 0 0
\(601\) 6.80663e6 + 4.94531e6i 0.768681 + 0.558479i 0.901561 0.432653i \(-0.142422\pi\)
−0.132880 + 0.991132i \(0.542422\pi\)
\(602\) 0 0
\(603\) −1.26476e6 + 3.89254e6i −0.141650 + 0.435953i
\(604\) 0 0
\(605\) −2.82733e6 + 2.05417e6i −0.314042 + 0.228165i
\(606\) 0 0
\(607\) −1.09299e7 + 7.94102e6i −1.20405 + 0.874792i −0.994677 0.103045i \(-0.967142\pi\)
−0.209371 + 0.977836i \(0.567142\pi\)
\(608\) 0 0
\(609\) 5.74957e6 + 1.76954e7i 0.628192 + 1.93338i
\(610\) 0 0
\(611\) 4.15483e6 1.27872e7i 0.450246 1.38572i
\(612\) 0 0
\(613\) −313982. 966338.i −0.0337484 0.103867i 0.932763 0.360489i \(-0.117390\pi\)
−0.966512 + 0.256622i \(0.917390\pi\)
\(614\) 0 0
\(615\) 8.25077e6 0.879643
\(616\) 0 0
\(617\) −1.14704e7 + 8.33372e6i −1.21301 + 0.881305i −0.995501 0.0947527i \(-0.969794\pi\)
−0.217511 + 0.976058i \(0.569794\pi\)
\(618\) 0 0
\(619\) 5.12797e6 0.537922 0.268961 0.963151i \(-0.413320\pi\)
0.268961 + 0.963151i \(0.413320\pi\)
\(620\) 0 0
\(621\) −1.45605e7 −1.51512
\(622\) 0 0
\(623\) 4.01530e6 2.91728e6i 0.414474 0.301133i
\(624\) 0 0
\(625\) 3.59523e6 0.368152
\(626\) 0 0
\(627\) 4.32260e6 + 1.33036e7i 0.439113 + 1.35145i
\(628\) 0 0
\(629\) −2.18779e6 + 6.73334e6i −0.220485 + 0.678584i
\(630\) 0 0
\(631\) 935703. + 2.87980e6i 0.0935544 + 0.287931i 0.986874 0.161491i \(-0.0516301\pi\)
−0.893320 + 0.449422i \(0.851630\pi\)
\(632\) 0 0
\(633\) 1.32762e6 964574.i 0.131694 0.0956811i
\(634\) 0 0
\(635\) −3.45416e6 + 2.50960e6i −0.339945 + 0.246984i
\(636\) 0 0
\(637\) −1.46923e6 + 4.52182e6i −0.143463 + 0.441535i
\(638\) 0 0
\(639\) 1.77180e7 + 1.28729e7i 1.71657 + 1.24716i
\(640\) 0 0
\(641\) 1.79066e6 + 1.30099e6i 0.172134 + 0.125063i 0.670517 0.741894i \(-0.266072\pi\)
−0.498382 + 0.866957i \(0.666072\pi\)
\(642\) 0 0
\(643\) −2.13532e6 + 6.57183e6i −0.203674 + 0.626843i 0.796092 + 0.605176i \(0.206897\pi\)
−0.999765 + 0.0216669i \(0.993103\pi\)
\(644\) 0 0
\(645\) −1.32795e6 −0.125685
\(646\) 0 0
\(647\) 4.52020e6 + 1.39117e7i 0.424519 + 1.30653i 0.903454 + 0.428684i \(0.141023\pi\)
−0.478936 + 0.877850i \(0.658977\pi\)
\(648\) 0 0
\(649\) −5.07989e6 3.69076e6i −0.473416 0.343957i
\(650\) 0 0
\(651\) 3.67896e6 + 2.12267e7i 0.340230 + 1.96304i
\(652\) 0 0
\(653\) −1.47422e7 1.07108e7i −1.35294 0.982968i −0.998859 0.0477522i \(-0.984794\pi\)
−0.354080 0.935215i \(-0.615206\pi\)
\(654\) 0 0
\(655\) −2.57165e6 7.91474e6i −0.234212 0.720831i
\(656\) 0 0
\(657\) 1.16961e7 1.05713
\(658\) 0 0
\(659\) −2.18466e6 + 6.72370e6i −0.195962 + 0.603108i 0.804002 + 0.594626i \(0.202700\pi\)
−0.999964 + 0.00848169i \(0.997300\pi\)
\(660\) 0 0
\(661\) −5.58119e6 4.05497e6i −0.496848 0.360981i 0.310964 0.950422i \(-0.399348\pi\)
−0.807812 + 0.589441i \(0.799348\pi\)
\(662\) 0 0
\(663\) −2.64461e7 1.92142e7i −2.33656 1.69761i
\(664\) 0 0
\(665\) 3.70380e6 1.13991e7i 0.324783 0.999580i
\(666\) 0 0
\(667\) −8.55144e6 + 6.21299e6i −0.744260 + 0.540737i
\(668\) 0 0
\(669\) 2.33906e7 1.69942e7i 2.02058 1.46803i
\(670\) 0 0
\(671\) 1.88257e6 + 5.79394e6i 0.161415 + 0.496784i
\(672\) 0 0
\(673\) −3.56696e6 + 1.09780e7i −0.303571 + 0.934295i 0.676636 + 0.736318i \(0.263437\pi\)
−0.980207 + 0.197977i \(0.936563\pi\)
\(674\) 0 0
\(675\) −4.74602e6 1.46067e7i −0.400931 1.23394i
\(676\) 0 0
\(677\) 5.20391e6 0.436373 0.218187 0.975907i \(-0.429986\pi\)
0.218187 + 0.975907i \(0.429986\pi\)
\(678\) 0 0
\(679\) 1.30250e7 9.46320e6i 1.08418 0.787705i
\(680\) 0 0
\(681\) −8.11362e6 −0.670420
\(682\) 0 0
\(683\) 8.17958e6 0.670933 0.335467 0.942052i \(-0.391106\pi\)
0.335467 + 0.942052i \(0.391106\pi\)
\(684\) 0 0
\(685\) 4.05019e6 2.94263e6i 0.329798 0.239613i
\(686\) 0 0
\(687\) −2.73528e6 −0.221110
\(688\) 0 0
\(689\) −5.06861e6 1.55996e7i −0.406762 1.25188i
\(690\) 0 0
\(691\) 6.82672e6 2.10105e7i 0.543898 1.67395i −0.179699 0.983722i \(-0.557512\pi\)
0.723596 0.690223i \(-0.242488\pi\)
\(692\) 0 0
\(693\) −3.85258e6 1.18570e7i −0.304732 0.937870i
\(694\) 0 0
\(695\) 3.27716e6 2.38100e6i 0.257357 0.186981i
\(696\) 0 0
\(697\) −1.33748e7 + 9.71734e6i −1.04281 + 0.757644i
\(698\) 0 0
\(699\) −7.01167e6 + 2.15797e7i −0.542786 + 1.67052i
\(700\) 0 0
\(701\) 5.31409e6 + 3.86092e6i 0.408446 + 0.296753i 0.772972 0.634440i \(-0.218769\pi\)
−0.364527 + 0.931193i \(0.618769\pi\)
\(702\) 0 0
\(703\) −1.19467e7 8.67980e6i −0.911717 0.662401i
\(704\) 0 0
\(705\) 3.52492e6 1.08486e7i 0.267102 0.822055i
\(706\) 0 0
\(707\) −2.57777e7 −1.93952
\(708\) 0 0
\(709\) −5.54476e6 1.70650e7i −0.414255 1.27494i −0.912916 0.408148i \(-0.866175\pi\)
0.498661 0.866797i \(-0.333825\pi\)
\(710\) 0 0
\(711\) 1.78355e7 + 1.29582e7i 1.32316 + 0.961329i
\(712\) 0 0
\(713\) −1.08229e7 + 5.71417e6i −0.797298 + 0.420949i
\(714\) 0 0
\(715\) −3.16847e6 2.30203e6i −0.231785 0.168401i
\(716\) 0 0
\(717\) 1.29727e7 + 3.99258e7i 0.942392 + 2.90038i
\(718\) 0 0
\(719\) −1.86398e7 −1.34468 −0.672342 0.740241i \(-0.734711\pi\)
−0.672342 + 0.740241i \(0.734711\pi\)
\(720\) 0 0
\(721\) 2.99628e6 9.22159e6i 0.214656 0.660644i
\(722\) 0 0
\(723\) −2.40350e7 1.74625e7i −1.71001 1.24240i
\(724\) 0 0
\(725\) −9.02008e6 6.55347e6i −0.637332 0.463049i
\(726\) 0 0
\(727\) 3.72319e6 1.14588e7i 0.261264 0.804087i −0.731267 0.682091i \(-0.761071\pi\)
0.992531 0.121995i \(-0.0389293\pi\)
\(728\) 0 0
\(729\) 1.24701e7 9.06003e6i 0.869060 0.631409i
\(730\) 0 0
\(731\) 2.15265e6 1.56400e6i 0.148998 0.108254i
\(732\) 0 0
\(733\) −561422. 1.72788e6i −0.0385948 0.118783i 0.929903 0.367805i \(-0.119891\pi\)
−0.968498 + 0.249022i \(0.919891\pi\)
\(734\) 0 0
\(735\) −1.24648e6 + 3.83628e6i −0.0851075 + 0.261934i
\(736\) 0 0
\(737\) −457401. 1.40773e6i −0.0310190 0.0954667i
\(738\) 0 0
\(739\) 1.51132e7 1.01800 0.508998 0.860768i \(-0.330016\pi\)
0.508998 + 0.860768i \(0.330016\pi\)
\(740\) 0 0
\(741\) 5.51605e7 4.00764e7i 3.69048 2.68129i
\(742\) 0 0
\(743\) −1.42040e7 −0.943928 −0.471964 0.881618i \(-0.656455\pi\)
−0.471964 + 0.881618i \(0.656455\pi\)
\(744\) 0 0
\(745\) 3.13676e6 0.207057
\(746\) 0 0
\(747\) 2.77157e7 2.01366e7i 1.81729 1.32034i
\(748\) 0 0
\(749\) −2.81147e7 −1.83117
\(750\) 0 0
\(751\) 6.51260e6 + 2.00437e7i 0.421361 + 1.29682i 0.906436 + 0.422344i \(0.138793\pi\)
−0.485074 + 0.874473i \(0.661207\pi\)
\(752\) 0 0
\(753\) 1.08655e7 3.34407e7i 0.698336 2.14926i
\(754\) 0 0
\(755\) −3.97729e6 1.22409e7i −0.253934 0.781528i
\(756\) 0 0
\(757\) −1.21281e7 + 8.81159e6i −0.769225 + 0.558875i −0.901726 0.432308i \(-0.857699\pi\)
0.132501 + 0.991183i \(0.457699\pi\)
\(758\) 0 0
\(759\) 8.63218e6 6.27164e6i 0.543896 0.395164i
\(760\) 0 0
\(761\) −420785. + 1.29504e6i −0.0263389 + 0.0810629i −0.963362 0.268205i \(-0.913570\pi\)
0.937023 + 0.349268i \(0.113570\pi\)
\(762\) 0 0
\(763\) −4.05250e6 2.94431e6i −0.252006 0.183093i
\(764\) 0 0
\(765\) −1.48934e7 1.08207e7i −0.920110 0.668499i
\(766\) 0 0
\(767\) −9.45774e6 + 2.91079e7i −0.580496 + 1.78658i
\(768\) 0 0
\(769\) 1.74032e7 1.06124 0.530621 0.847609i \(-0.321959\pi\)
0.530621 + 0.847609i \(0.321959\pi\)
\(770\) 0 0
\(771\) −1.35806e7 4.17967e7i −0.822777 2.53225i
\(772\) 0 0
\(773\) 397342. + 288686.i 0.0239175 + 0.0173771i 0.599680 0.800240i \(-0.295295\pi\)
−0.575762 + 0.817617i \(0.695295\pi\)
\(774\) 0 0
\(775\) −9.26007e6 8.99475e6i −0.553809 0.537941i
\(776\) 0 0
\(777\) 1.60406e7 + 1.16542e7i 0.953165 + 0.692515i
\(778\) 0 0
\(779\) −1.06556e7 3.27946e7i −0.629121 1.93623i
\(780\) 0 0
\(781\) −7.92036e6 −0.464641
\(782\) 0 0
\(783\) −9.09020e6 + 2.79767e7i −0.529869 + 1.63077i
\(784\) 0 0
\(785\) −7.91703e6 5.75206e6i −0.458551 0.333157i
\(786\) 0 0
\(787\) 2.65583e7 + 1.92957e7i 1.52849 + 1.11051i 0.957070 + 0.289858i \(0.0936080\pi\)
0.571422 + 0.820656i \(0.306392\pi\)
\(788\) 0 0
\(789\) −1.17041e7 + 3.60215e7i