Properties

Label 69.7.d.a.22.22
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.22
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.21

$q$-expansion

\(f(q)\) \(=\) \(q+13.3624 q^{2} -15.5885 q^{3} +114.554 q^{4} +40.7784i q^{5} -208.299 q^{6} +469.379i q^{7} +675.521 q^{8} +243.000 q^{9} +O(q^{10})\) \(q+13.3624 q^{2} -15.5885 q^{3} +114.554 q^{4} +40.7784i q^{5} -208.299 q^{6} +469.379i q^{7} +675.521 q^{8} +243.000 q^{9} +544.897i q^{10} +1567.76i q^{11} -1785.72 q^{12} +3791.51 q^{13} +6272.03i q^{14} -635.672i q^{15} +1695.14 q^{16} -9021.27i q^{17} +3247.06 q^{18} +7102.08i q^{19} +4671.32i q^{20} -7316.90i q^{21} +20949.1i q^{22} +(-6001.12 + 10584.1i) q^{23} -10530.3 q^{24} +13962.1 q^{25} +50663.7 q^{26} -3788.00 q^{27} +53769.2i q^{28} -3651.94 q^{29} -8494.11i q^{30} -27537.6 q^{31} -20582.2 q^{32} -24439.0i q^{33} -120546. i q^{34} -19140.5 q^{35} +27836.6 q^{36} -75148.6i q^{37} +94900.8i q^{38} -59103.9 q^{39} +27546.7i q^{40} -1160.82 q^{41} -97771.3i q^{42} -77082.8i q^{43} +179593. i q^{44} +9909.15i q^{45} +(-80189.3 + 141429. i) q^{46} +128089. q^{47} -26424.6 q^{48} -102668. q^{49} +186568. q^{50} +140628. i q^{51} +434333. q^{52} -149342. i q^{53} -50616.7 q^{54} -63930.8 q^{55} +317076. i q^{56} -110710. i q^{57} -48798.7 q^{58} -55950.5 q^{59} -72818.7i q^{60} +167059. i q^{61} -367968. q^{62} +114059. i q^{63} -383517. q^{64} +154612. i q^{65} -326564. i q^{66} -199627. i q^{67} -1.03342e6i q^{68} +(93548.1 - 164989. i) q^{69} -255763. q^{70} +120126. q^{71} +164152. q^{72} +659602. q^{73} -1.00417e6i q^{74} -217648. q^{75} +813570. i q^{76} -735875. q^{77} -789770. q^{78} -458548. i q^{79} +69125.1i q^{80} +59049.0 q^{81} -15511.3 q^{82} -293064. i q^{83} -838179. i q^{84} +367873. q^{85} -1.03001e6i q^{86} +56928.1 q^{87} +1.05906e6i q^{88} +43046.0i q^{89} +132410. i q^{90} +1.77966e6i q^{91} +(-687451. + 1.21245e6i) q^{92} +429269. q^{93} +1.71158e6 q^{94} -289611. q^{95} +320845. q^{96} +856674. i q^{97} -1.37189e6 q^{98} +380966. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{2} + 816 q^{4} - 324 q^{6} - 940 q^{8} + 5832 q^{9} + O(q^{10}) \) \( 24 q - 20 q^{2} + 816 q^{4} - 324 q^{6} - 940 q^{8} + 5832 q^{9} + 384 q^{13} + 29544 q^{16} - 4860 q^{18} + 29336 q^{23} - 39204 q^{24} - 61272 q^{25} + 10088 q^{26} + 64672 q^{29} + 9696 q^{31} - 319620 q^{32} - 225744 q^{35} + 198288 q^{36} - 11664 q^{39} + 135280 q^{41} + 233232 q^{46} - 74336 q^{47} + 552096 q^{48} - 722136 q^{49} + 619324 q^{50} + 1059720 q^{52} - 78732 q^{54} - 1019328 q^{55} - 694344 q^{58} + 1057648 q^{59} - 488776 q^{62} - 273888 q^{64} - 23328 q^{69} + 2785512 q^{70} - 255392 q^{71} - 228420 q^{72} - 322560 q^{73} - 365472 q^{75} - 1002960 q^{77} - 171072 q^{78} + 1417176 q^{81} - 5732712 q^{82} - 2704704 q^{85} + 611712 q^{87} - 1611444 q^{92} + 2484432 q^{93} - 147720 q^{94} - 1672656 q^{95} - 1818612 q^{96} + 9104212 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.3624 1.67030 0.835150 0.550022i \(-0.185381\pi\)
0.835150 + 0.550022i \(0.185381\pi\)
\(3\) −15.5885 −0.577350
\(4\) 114.554 1.78990
\(5\) 40.7784i 0.326227i 0.986607 + 0.163114i \(0.0521537\pi\)
−0.986607 + 0.163114i \(0.947846\pi\)
\(6\) −208.299 −0.964348
\(7\) 469.379i 1.36845i 0.729270 + 0.684226i \(0.239860\pi\)
−0.729270 + 0.684226i \(0.760140\pi\)
\(8\) 675.521 1.31938
\(9\) 243.000 0.333333
\(10\) 544.897i 0.544897i
\(11\) 1567.76i 1.17788i 0.808176 + 0.588941i \(0.200455\pi\)
−0.808176 + 0.588941i \(0.799545\pi\)
\(12\) −1785.72 −1.03340
\(13\) 3791.51 1.72577 0.862884 0.505401i \(-0.168656\pi\)
0.862884 + 0.505401i \(0.168656\pi\)
\(14\) 6272.03i 2.28573i
\(15\) 635.672i 0.188347i
\(16\) 1695.14 0.413852
\(17\) 9021.27i 1.83620i −0.396343 0.918102i \(-0.629721\pi\)
0.396343 0.918102i \(-0.370279\pi\)
\(18\) 3247.06 0.556767
\(19\) 7102.08i 1.03544i 0.855550 + 0.517720i \(0.173219\pi\)
−0.855550 + 0.517720i \(0.826781\pi\)
\(20\) 4671.32i 0.583915i
\(21\) 7316.90i 0.790076i
\(22\) 20949.1i 1.96742i
\(23\) −6001.12 + 10584.1i −0.493229 + 0.869900i
\(24\) −10530.3 −0.761743
\(25\) 13962.1 0.893576
\(26\) 50663.7 2.88255
\(27\) −3788.00 −0.192450
\(28\) 53769.2i 2.44940i
\(29\) −3651.94 −0.149737 −0.0748685 0.997193i \(-0.523854\pi\)
−0.0748685 + 0.997193i \(0.523854\pi\)
\(30\) 8494.11i 0.314597i
\(31\) −27537.6 −0.924359 −0.462180 0.886786i \(-0.652932\pi\)
−0.462180 + 0.886786i \(0.652932\pi\)
\(32\) −20582.2 −0.628119
\(33\) 24439.0i 0.680051i
\(34\) 120546.i 3.06701i
\(35\) −19140.5 −0.446426
\(36\) 27836.6 0.596635
\(37\) 75148.6i 1.48360i −0.670623 0.741799i \(-0.733973\pi\)
0.670623 0.741799i \(-0.266027\pi\)
\(38\) 94900.8i 1.72949i
\(39\) −59103.9 −0.996373
\(40\) 27546.7i 0.430417i
\(41\) −1160.82 −0.0168427 −0.00842136 0.999965i \(-0.502681\pi\)
−0.00842136 + 0.999965i \(0.502681\pi\)
\(42\) 97771.3i 1.31966i
\(43\) 77082.8i 0.969510i −0.874650 0.484755i \(-0.838909\pi\)
0.874650 0.484755i \(-0.161091\pi\)
\(44\) 179593.i 2.10830i
\(45\) 9909.15i 0.108742i
\(46\) −80189.3 + 141429.i −0.823840 + 1.45299i
\(47\) 128089. 1.23372 0.616862 0.787071i \(-0.288404\pi\)
0.616862 + 0.787071i \(0.288404\pi\)
\(48\) −26424.6 −0.238938
\(49\) −102668. −0.872662
\(50\) 186568. 1.49254
\(51\) 140628.i 1.06013i
\(52\) 434333. 3.08896
\(53\) 149342.i 1.00312i −0.865123 0.501560i \(-0.832760\pi\)
0.865123 0.501560i \(-0.167240\pi\)
\(54\) −50616.7 −0.321449
\(55\) −63930.8 −0.384257
\(56\) 317076.i 1.80550i
\(57\) 110710.i 0.597811i
\(58\) −48798.7 −0.250106
\(59\) −55950.5 −0.272425 −0.136213 0.990680i \(-0.543493\pi\)
−0.136213 + 0.990680i \(0.543493\pi\)
\(60\) 72818.7i 0.337124i
\(61\) 167059.i 0.736003i 0.929825 + 0.368002i \(0.119958\pi\)
−0.929825 + 0.368002i \(0.880042\pi\)
\(62\) −367968. −1.54396
\(63\) 114059.i 0.456151i
\(64\) −383517. −1.46300
\(65\) 154612.i 0.562993i
\(66\) 326564.i 1.13589i
\(67\) 199627.i 0.663735i −0.943326 0.331868i \(-0.892321\pi\)
0.943326 0.331868i \(-0.107679\pi\)
\(68\) 1.03342e6i 3.28663i
\(69\) 93548.1 164989.i 0.284766 0.502237i
\(70\) −255763. −0.745666
\(71\) 120126. 0.335631 0.167816 0.985818i \(-0.446329\pi\)
0.167816 + 0.985818i \(0.446329\pi\)
\(72\) 164152. 0.439792
\(73\) 659602. 1.69556 0.847781 0.530347i \(-0.177938\pi\)
0.847781 + 0.530347i \(0.177938\pi\)
\(74\) 1.00417e6i 2.47805i
\(75\) −217648. −0.515906
\(76\) 813570.i 1.85334i
\(77\) −735875. −1.61188
\(78\) −789770. −1.66424
\(79\) 458548.i 0.930045i −0.885299 0.465022i \(-0.846046\pi\)
0.885299 0.465022i \(-0.153954\pi\)
\(80\) 69125.1i 0.135010i
\(81\) 59049.0 0.111111
\(82\) −15511.3 −0.0281324
\(83\) 293064.i 0.512541i −0.966605 0.256270i \(-0.917506\pi\)
0.966605 0.256270i \(-0.0824938\pi\)
\(84\) 838179.i 1.41416i
\(85\) 367873. 0.599020
\(86\) 1.03001e6i 1.61937i
\(87\) 56928.1 0.0864507
\(88\) 1.05906e6i 1.55407i
\(89\) 43046.0i 0.0610608i 0.999534 + 0.0305304i \(0.00971964\pi\)
−0.999534 + 0.0305304i \(0.990280\pi\)
\(90\) 132410.i 0.181632i
\(91\) 1.77966e6i 2.36163i
\(92\) −687451. + 1.21245e6i −0.882832 + 1.55704i
\(93\) 429269. 0.533679
\(94\) 1.71158e6 2.06069
\(95\) −289611. −0.337788
\(96\) 320845. 0.362645
\(97\) 856674.i 0.938643i 0.883027 + 0.469321i \(0.155501\pi\)
−0.883027 + 0.469321i \(0.844499\pi\)
\(98\) −1.37189e6 −1.45761
\(99\) 380966.i 0.392628i
\(100\) 1.59942e6 1.59942
\(101\) −292195. −0.283602 −0.141801 0.989895i \(-0.545289\pi\)
−0.141801 + 0.989895i \(0.545289\pi\)
\(102\) 1.87912e6i 1.77074i
\(103\) 712314.i 0.651869i 0.945392 + 0.325934i \(0.105679\pi\)
−0.945392 + 0.325934i \(0.894321\pi\)
\(104\) 2.56125e6 2.27694
\(105\) 298371. 0.257744
\(106\) 1.99556e6i 1.67551i
\(107\) 562846.i 0.459450i −0.973256 0.229725i \(-0.926217\pi\)
0.973256 0.229725i \(-0.0737827\pi\)
\(108\) −433929. −0.344467
\(109\) 2.02076e6i 1.56040i 0.625529 + 0.780201i \(0.284883\pi\)
−0.625529 + 0.780201i \(0.715117\pi\)
\(110\) −854269. −0.641825
\(111\) 1.17145e6i 0.856555i
\(112\) 795663.i 0.566337i
\(113\) 1.65496e6i 1.14697i −0.819217 0.573484i \(-0.805591\pi\)
0.819217 0.573484i \(-0.194409\pi\)
\(114\) 1.47936e6i 0.998524i
\(115\) −431601. 244716.i −0.283785 0.160905i
\(116\) −418343. −0.268015
\(117\) 921338. 0.575256
\(118\) −747633. −0.455032
\(119\) 4.23440e6 2.51276
\(120\) 429410.i 0.248501i
\(121\) −686316. −0.387407
\(122\) 2.23231e6i 1.22935i
\(123\) 18095.4 0.00972415
\(124\) −3.15454e6 −1.65451
\(125\) 1.20652e6i 0.617736i
\(126\) 1.52410e6i 0.761909i
\(127\) 3.69029e6 1.80156 0.900781 0.434274i \(-0.142995\pi\)
0.900781 + 0.434274i \(0.142995\pi\)
\(128\) −3.80744e6 −1.81553
\(129\) 1.20160e6i 0.559747i
\(130\) 2.06599e6i 0.940367i
\(131\) −337756. −0.150241 −0.0751207 0.997174i \(-0.523934\pi\)
−0.0751207 + 0.997174i \(0.523934\pi\)
\(132\) 2.79958e6i 1.21723i
\(133\) −3.33357e6 −1.41695
\(134\) 2.66750e6i 1.10864i
\(135\) 154468.i 0.0627824i
\(136\) 6.09406e6i 2.42265i
\(137\) 737585.i 0.286847i 0.989661 + 0.143424i \(0.0458111\pi\)
−0.989661 + 0.143424i \(0.954189\pi\)
\(138\) 1.25003e6 2.20465e6i 0.475645 0.838886i
\(139\) 495563. 0.184525 0.0922624 0.995735i \(-0.470590\pi\)
0.0922624 + 0.995735i \(0.470590\pi\)
\(140\) −2.19262e6 −0.799060
\(141\) −1.99671e6 −0.712291
\(142\) 1.60517e6 0.560605
\(143\) 5.94419e6i 2.03275i
\(144\) 411919. 0.137951
\(145\) 148920.i 0.0488483i
\(146\) 8.81387e6 2.83210
\(147\) 1.60043e6 0.503831
\(148\) 8.60857e6i 2.65550i
\(149\) 3.68998e6i 1.11549i −0.830013 0.557744i \(-0.811667\pi\)
0.830013 0.557744i \(-0.188333\pi\)
\(150\) −2.90830e6 −0.861719
\(151\) 2.42810e6 0.705239 0.352619 0.935767i \(-0.385291\pi\)
0.352619 + 0.935767i \(0.385291\pi\)
\(152\) 4.79760e6i 1.36613i
\(153\) 2.19217e6i 0.612068i
\(154\) −9.83305e6 −2.69232
\(155\) 1.12294e6i 0.301551i
\(156\) −6.77057e6 −1.78341
\(157\) 3.65883e6i 0.945461i 0.881207 + 0.472730i \(0.156732\pi\)
−0.881207 + 0.472730i \(0.843268\pi\)
\(158\) 6.12731e6i 1.55345i
\(159\) 2.32800e6i 0.579152i
\(160\) 839309.i 0.204909i
\(161\) −4.96794e6 2.81680e6i −1.19042 0.674960i
\(162\) 789037. 0.185589
\(163\) −2.54229e6 −0.587032 −0.293516 0.955954i \(-0.594825\pi\)
−0.293516 + 0.955954i \(0.594825\pi\)
\(164\) −132976. −0.0301469
\(165\) 996582. 0.221851
\(166\) 3.91604e6i 0.856097i
\(167\) −5.08973e6 −1.09281 −0.546406 0.837520i \(-0.684005\pi\)
−0.546406 + 0.837520i \(0.684005\pi\)
\(168\) 4.94272e6i 1.04241i
\(169\) 9.54877e6 1.97828
\(170\) 4.91567e6 1.00054
\(171\) 1.72580e6i 0.345146i
\(172\) 8.83014e6i 1.73533i
\(173\) 214344. 0.0413975 0.0206987 0.999786i \(-0.493411\pi\)
0.0206987 + 0.999786i \(0.493411\pi\)
\(174\) 760696. 0.144399
\(175\) 6.55353e6i 1.22282i
\(176\) 2.65758e6i 0.487470i
\(177\) 872182. 0.157285
\(178\) 575198.i 0.101990i
\(179\) −9.94625e6 −1.73420 −0.867102 0.498131i \(-0.834020\pi\)
−0.867102 + 0.498131i \(0.834020\pi\)
\(180\) 1.13513e6i 0.194638i
\(181\) 504979.i 0.0851604i −0.999093 0.0425802i \(-0.986442\pi\)
0.999093 0.0425802i \(-0.0135578\pi\)
\(182\) 2.37805e7i 3.94464i
\(183\) 2.60419e6i 0.424932i
\(184\) −4.05388e6 + 7.14976e6i −0.650755 + 1.14773i
\(185\) 3.06444e6 0.483990
\(186\) 5.73606e6 0.891405
\(187\) 1.41432e7 2.16283
\(188\) 1.46731e7 2.20825
\(189\) 1.77801e6i 0.263359i
\(190\) −3.86990e6 −0.564208
\(191\) 7.85205e6i 1.12689i −0.826152 0.563447i \(-0.809475\pi\)
0.826152 0.563447i \(-0.190525\pi\)
\(192\) 5.97843e6 0.844664
\(193\) −1.28145e7 −1.78250 −0.891248 0.453516i \(-0.850169\pi\)
−0.891248 + 0.453516i \(0.850169\pi\)
\(194\) 1.14472e7i 1.56782i
\(195\) 2.41016e6i 0.325044i
\(196\) −1.17610e7 −1.56198
\(197\) 1.12045e7 1.46552 0.732762 0.680485i \(-0.238231\pi\)
0.732762 + 0.680485i \(0.238231\pi\)
\(198\) 5.09062e6i 0.655806i
\(199\) 8.48481e6i 1.07667i −0.842731 0.538335i \(-0.819053\pi\)
0.842731 0.538335i \(-0.180947\pi\)
\(200\) 9.43171e6 1.17896
\(201\) 3.11188e6i 0.383208i
\(202\) −3.90443e6 −0.473700
\(203\) 1.71414e6i 0.204908i
\(204\) 1.61095e7i 1.89754i
\(205\) 47336.3i 0.00549455i
\(206\) 9.51823e6i 1.08882i
\(207\) −1.45827e6 + 2.57193e6i −0.164410 + 0.289967i
\(208\) 6.42715e6 0.714214
\(209\) −1.11344e7 −1.21963
\(210\) 3.98696e6 0.430510
\(211\) −2.24487e6 −0.238971 −0.119485 0.992836i \(-0.538124\pi\)
−0.119485 + 0.992836i \(0.538124\pi\)
\(212\) 1.71077e7i 1.79549i
\(213\) −1.87258e6 −0.193777
\(214\) 7.52098e6i 0.767420i
\(215\) 3.14331e6 0.316280
\(216\) −2.55887e6 −0.253914
\(217\) 1.29256e7i 1.26494i
\(218\) 2.70023e7i 2.60634i
\(219\) −1.02822e7 −0.978933
\(220\) −7.32352e6 −0.687784
\(221\) 3.42043e7i 3.16886i
\(222\) 1.56534e7i 1.43070i
\(223\) −7.16592e6 −0.646185 −0.323093 0.946367i \(-0.604723\pi\)
−0.323093 + 0.946367i \(0.604723\pi\)
\(224\) 9.66086e6i 0.859551i
\(225\) 3.39280e6 0.297859
\(226\) 2.21142e7i 1.91578i
\(227\) 6.95534e6i 0.594622i 0.954781 + 0.297311i \(0.0960898\pi\)
−0.954781 + 0.297311i \(0.903910\pi\)
\(228\) 1.26823e7i 1.07002i
\(229\) 2.26736e6i 0.188805i 0.995534 + 0.0944026i \(0.0300941\pi\)
−0.995534 + 0.0944026i \(0.969906\pi\)
\(230\) −5.76723e6 3.26999e6i −0.474006 0.268759i
\(231\) 1.14712e7 0.930617
\(232\) −2.46696e6 −0.197560
\(233\) −8.37836e6 −0.662356 −0.331178 0.943568i \(-0.607446\pi\)
−0.331178 + 0.943568i \(0.607446\pi\)
\(234\) 1.23113e7 0.960851
\(235\) 5.22326e6i 0.402474i
\(236\) −6.40934e6 −0.487615
\(237\) 7.14806e6i 0.536961i
\(238\) 5.65817e7 4.19706
\(239\) −1.84843e7 −1.35397 −0.676986 0.735996i \(-0.736714\pi\)
−0.676986 + 0.735996i \(0.736714\pi\)
\(240\) 1.07755e6i 0.0779480i
\(241\) 1.13802e7i 0.813018i 0.913647 + 0.406509i \(0.133254\pi\)
−0.913647 + 0.406509i \(0.866746\pi\)
\(242\) −9.17083e6 −0.647087
\(243\) −920483. −0.0641500
\(244\) 1.91372e7i 1.31738i
\(245\) 4.18663e6i 0.284686i
\(246\) 241797. 0.0162423
\(247\) 2.69276e7i 1.78693i
\(248\) −1.86022e7 −1.21958
\(249\) 4.56842e6i 0.295916i
\(250\) 1.61219e7i 1.03180i
\(251\) 1.24948e7i 0.790149i −0.918649 0.395074i \(-0.870719\pi\)
0.918649 0.395074i \(-0.129281\pi\)
\(252\) 1.30659e7i 0.816466i
\(253\) −1.65933e7 9.40832e6i −1.02464 0.580966i
\(254\) 4.93111e7 3.00915
\(255\) −5.73457e6 −0.345844
\(256\) −2.63315e7 −1.56948
\(257\) −2.74092e6 −0.161472 −0.0807360 0.996736i \(-0.525727\pi\)
−0.0807360 + 0.996736i \(0.525727\pi\)
\(258\) 1.60563e7i 0.934945i
\(259\) 3.52732e7 2.03023
\(260\) 1.77114e7i 1.00770i
\(261\) −887421. −0.0499124
\(262\) −4.51323e6 −0.250948
\(263\) 3.24876e7i 1.78587i −0.450181 0.892937i \(-0.648641\pi\)
0.450181 0.892937i \(-0.351359\pi\)
\(264\) 1.65091e7i 0.897244i
\(265\) 6.08991e6 0.327245
\(266\) −4.45445e7 −2.36673
\(267\) 671020.i 0.0352535i
\(268\) 2.28680e7i 1.18802i
\(269\) 3.23907e7 1.66404 0.832020 0.554746i \(-0.187185\pi\)
0.832020 + 0.554746i \(0.187185\pi\)
\(270\) 2.06407e6i 0.104866i
\(271\) 4.38123e6 0.220135 0.110067 0.993924i \(-0.464893\pi\)
0.110067 + 0.993924i \(0.464893\pi\)
\(272\) 1.52923e7i 0.759918i
\(273\) 2.77421e7i 1.36349i
\(274\) 9.85592e6i 0.479121i
\(275\) 2.18893e7i 1.05253i
\(276\) 1.07163e7 1.89002e7i 0.509703 0.898956i
\(277\) −1.89203e7 −0.890203 −0.445102 0.895480i \(-0.646832\pi\)
−0.445102 + 0.895480i \(0.646832\pi\)
\(278\) 6.62192e6 0.308212
\(279\) −6.69163e6 −0.308120
\(280\) −1.29298e7 −0.589005
\(281\) 1.82191e7i 0.821124i −0.911833 0.410562i \(-0.865333\pi\)
0.911833 0.410562i \(-0.134667\pi\)
\(282\) −2.66808e7 −1.18974
\(283\) 1.04736e7i 0.462100i 0.972942 + 0.231050i \(0.0742162\pi\)
−0.972942 + 0.231050i \(0.925784\pi\)
\(284\) 1.37609e7 0.600748
\(285\) 4.51459e6 0.195022
\(286\) 7.94287e7i 3.39531i
\(287\) 544863.i 0.0230485i
\(288\) −5.00148e6 −0.209373
\(289\) −5.72458e7 −2.37165
\(290\) 1.98993e6i 0.0815913i
\(291\) 1.33542e7i 0.541926i
\(292\) 7.55600e7 3.03489
\(293\) 6.92202e6i 0.275188i 0.990489 + 0.137594i \(0.0439370\pi\)
−0.990489 + 0.137594i \(0.956063\pi\)
\(294\) 2.13856e7 0.841550
\(295\) 2.28157e6i 0.0888726i
\(296\) 5.07645e7i 1.95742i
\(297\) 5.93867e6i 0.226684i
\(298\) 4.93070e7i 1.86320i
\(299\) −2.27533e7 + 4.01296e7i −0.851199 + 1.50125i
\(300\) −2.49324e7 −0.923423
\(301\) 3.61811e7 1.32673
\(302\) 3.24453e7 1.17796
\(303\) 4.55487e6 0.163738
\(304\) 1.20390e7i 0.428519i
\(305\) −6.81239e6 −0.240104
\(306\) 2.92927e7i 1.02234i
\(307\) −4.92649e6 −0.170264 −0.0851319 0.996370i \(-0.527131\pi\)
−0.0851319 + 0.996370i \(0.527131\pi\)
\(308\) −8.42973e7 −2.88510
\(309\) 1.11039e7i 0.376356i
\(310\) 1.50052e7i 0.503681i
\(311\) −2.07147e7 −0.688647 −0.344323 0.938851i \(-0.611892\pi\)
−0.344323 + 0.938851i \(0.611892\pi\)
\(312\) −3.99259e7 −1.31459
\(313\) 2.78344e6i 0.0907712i 0.998970 + 0.0453856i \(0.0144517\pi\)
−0.998970 + 0.0453856i \(0.985548\pi\)
\(314\) 4.88908e7i 1.57920i
\(315\) −4.65115e6 −0.148809
\(316\) 5.25285e7i 1.66469i
\(317\) 1.45950e7 0.458171 0.229085 0.973406i \(-0.426426\pi\)
0.229085 + 0.973406i \(0.426426\pi\)
\(318\) 3.11077e7i 0.967358i
\(319\) 5.72537e6i 0.176373i
\(320\) 1.56392e7i 0.477270i
\(321\) 8.77390e6i 0.265264i
\(322\) −6.63836e7 3.76392e7i −1.98835 1.12739i
\(323\) 6.40698e7 1.90128
\(324\) 6.76429e6 0.198878
\(325\) 5.29376e7 1.54211
\(326\) −3.39711e7 −0.980521
\(327\) 3.15006e7i 0.900898i
\(328\) −784157. −0.0222219
\(329\) 6.01223e7i 1.68829i
\(330\) 1.33167e7 0.370558
\(331\) 2.33621e6 0.0644211 0.0322105 0.999481i \(-0.489745\pi\)
0.0322105 + 0.999481i \(0.489745\pi\)
\(332\) 3.35716e7i 0.917399i
\(333\) 1.82611e7i 0.494532i
\(334\) −6.80111e7 −1.82533
\(335\) 8.14047e6 0.216528
\(336\) 1.24032e7i 0.326975i
\(337\) 1.06893e7i 0.279293i 0.990201 + 0.139647i \(0.0445967\pi\)
−0.990201 + 0.139647i \(0.955403\pi\)
\(338\) 1.27595e8 3.30432
\(339\) 2.57982e7i 0.662203i
\(340\) 4.21413e7 1.07219
\(341\) 4.31724e7i 1.08879i
\(342\) 2.30609e7i 0.576498i
\(343\) 7.03188e6i 0.174257i
\(344\) 5.20711e7i 1.27915i
\(345\) 6.72800e6 + 3.81474e6i 0.163843 + 0.0928983i
\(346\) 2.86416e6 0.0691462
\(347\) −2.24727e7 −0.537857 −0.268929 0.963160i \(-0.586670\pi\)
−0.268929 + 0.963160i \(0.586670\pi\)
\(348\) 6.52133e6 0.154739
\(349\) 4.55946e7 1.07260 0.536299 0.844028i \(-0.319822\pi\)
0.536299 + 0.844028i \(0.319822\pi\)
\(350\) 8.75709e7i 2.04247i
\(351\) −1.43622e7 −0.332124
\(352\) 3.22680e7i 0.739851i
\(353\) −6.29900e7 −1.43201 −0.716007 0.698093i \(-0.754032\pi\)
−0.716007 + 0.698093i \(0.754032\pi\)
\(354\) 1.16544e7 0.262713
\(355\) 4.89855e6i 0.109492i
\(356\) 4.93108e6i 0.109293i
\(357\) −6.60077e7 −1.45074
\(358\) −1.32906e8 −2.89664
\(359\) 6.83335e7i 1.47690i 0.674309 + 0.738449i \(0.264441\pi\)
−0.674309 + 0.738449i \(0.735559\pi\)
\(360\) 6.69384e6i 0.143472i
\(361\) −3.39362e6 −0.0721342
\(362\) 6.74774e6i 0.142244i
\(363\) 1.06986e7 0.223670
\(364\) 2.03867e8i 4.22709i
\(365\) 2.68975e7i 0.553138i
\(366\) 3.47982e7i 0.709764i
\(367\) 7.33714e7i 1.48432i −0.670221 0.742162i \(-0.733801\pi\)
0.670221 0.742162i \(-0.266199\pi\)
\(368\) −1.01727e7 + 1.79415e7i −0.204124 + 0.360010i
\(369\) −282079. −0.00561424
\(370\) 4.09483e7 0.808408
\(371\) 7.00978e7 1.37272
\(372\) 4.91744e7 0.955234
\(373\) 8.30679e7i 1.60069i 0.599541 + 0.800344i \(0.295350\pi\)
−0.599541 + 0.800344i \(0.704650\pi\)
\(374\) 1.88987e8 3.61258
\(375\) 1.88077e7i 0.356650i
\(376\) 8.65268e7 1.62775
\(377\) −1.38464e7 −0.258412
\(378\) 2.37584e7i 0.439888i
\(379\) 6.89177e7i 1.26594i 0.774176 + 0.632970i \(0.218164\pi\)
−0.774176 + 0.632970i \(0.781836\pi\)
\(380\) −3.31761e7 −0.604609
\(381\) −5.75259e7 −1.04013
\(382\) 1.04922e8i 1.88225i
\(383\) 7.07466e7i 1.25924i 0.776902 + 0.629621i \(0.216790\pi\)
−0.776902 + 0.629621i \(0.783210\pi\)
\(384\) 5.93522e7 1.04820
\(385\) 3.00078e7i 0.525838i
\(386\) −1.71232e8 −2.97730
\(387\) 1.87311e7i 0.323170i
\(388\) 9.81353e7i 1.68008i
\(389\) 1.19445e7i 0.202917i −0.994840 0.101458i \(-0.967649\pi\)
0.994840 0.101458i \(-0.0323509\pi\)
\(390\) 3.22055e7i 0.542921i
\(391\) 9.54818e7 + 5.41377e7i 1.59731 + 0.905669i
\(392\) −6.93542e7 −1.15137
\(393\) 5.26510e6 0.0867419
\(394\) 1.49719e8 2.44787
\(395\) 1.86989e7 0.303406
\(396\) 4.36411e7i 0.702766i
\(397\) −1.35684e7 −0.216849 −0.108425 0.994105i \(-0.534581\pi\)
−0.108425 + 0.994105i \(0.534581\pi\)
\(398\) 1.13377e8i 1.79836i
\(399\) 5.19652e7 0.818076
\(400\) 2.36677e7 0.369809
\(401\) 6.30703e7i 0.978119i 0.872250 + 0.489059i \(0.162660\pi\)
−0.872250 + 0.489059i \(0.837340\pi\)
\(402\) 4.15822e7i 0.640072i
\(403\) −1.04409e8 −1.59523
\(404\) −3.34721e7 −0.507620
\(405\) 2.40792e6i 0.0362475i
\(406\) 2.29051e7i 0.342258i
\(407\) 1.17815e8 1.74750
\(408\) 9.49970e7i 1.39872i
\(409\) 6.92270e6 0.101183 0.0505913 0.998719i \(-0.483889\pi\)
0.0505913 + 0.998719i \(0.483889\pi\)
\(410\) 632526.i 0.00917756i
\(411\) 1.14978e7i 0.165611i
\(412\) 8.15984e7i 1.16678i
\(413\) 2.62620e7i 0.372801i
\(414\) −1.94860e7 + 3.43672e7i −0.274613 + 0.484331i
\(415\) 1.19507e7 0.167205
\(416\) −7.80377e7 −1.08399
\(417\) −7.72507e6 −0.106535
\(418\) −1.48782e8 −2.03714
\(419\) 3.86181e7i 0.524987i −0.964934 0.262494i \(-0.915455\pi\)
0.964934 0.262494i \(-0.0845449\pi\)
\(420\) 3.41796e7 0.461338
\(421\) 5.59677e7i 0.750052i 0.927014 + 0.375026i \(0.122366\pi\)
−0.927014 + 0.375026i \(0.877634\pi\)
\(422\) −2.99969e7 −0.399153
\(423\) 3.11256e7 0.411241
\(424\) 1.00883e8i 1.32349i
\(425\) 1.25956e8i 1.64079i
\(426\) −2.50222e7 −0.323666
\(427\) −7.84139e7 −1.00719
\(428\) 6.44762e7i 0.822372i
\(429\) 9.26608e7i 1.17361i
\(430\) 4.20022e7 0.528283
\(431\) 9.77946e7i 1.22147i −0.791835 0.610735i \(-0.790874\pi\)
0.791835 0.610735i \(-0.209126\pi\)
\(432\) −6.42118e6 −0.0796459
\(433\) 1.55568e8i 1.91627i −0.286315 0.958136i \(-0.592430\pi\)
0.286315 0.958136i \(-0.407570\pi\)
\(434\) 1.72717e8i 2.11283i
\(435\) 2.32143e6i 0.0282026i
\(436\) 2.31486e8i 2.79297i
\(437\) −7.51689e7 4.26204e7i −0.900728 0.510708i
\(438\) −1.37395e8 −1.63511
\(439\) 1.32635e7 0.156770 0.0783851 0.996923i \(-0.475024\pi\)
0.0783851 + 0.996923i \(0.475024\pi\)
\(440\) −4.31866e7 −0.506980
\(441\) −2.49483e7 −0.290887
\(442\) 4.57052e8i 5.29296i
\(443\) −1.32324e6 −0.0152205 −0.00761023 0.999971i \(-0.502422\pi\)
−0.00761023 + 0.999971i \(0.502422\pi\)
\(444\) 1.34194e8i 1.53315i
\(445\) −1.75535e6 −0.0199197
\(446\) −9.57539e7 −1.07932
\(447\) 5.75211e7i 0.644027i
\(448\) 1.80015e8i 2.00205i
\(449\) −8.63709e7 −0.954176 −0.477088 0.878855i \(-0.658308\pi\)
−0.477088 + 0.878855i \(0.658308\pi\)
\(450\) 4.53359e7 0.497513
\(451\) 1.81989e6i 0.0198388i
\(452\) 1.89582e8i 2.05296i
\(453\) −3.78504e7 −0.407170
\(454\) 9.29401e7i 0.993197i
\(455\) −7.25716e7 −0.770428
\(456\) 7.47872e7i 0.788738i
\(457\) 5.19478e7i 0.544275i 0.962258 + 0.272138i \(0.0877306\pi\)
−0.962258 + 0.272138i \(0.912269\pi\)
\(458\) 3.02974e7i 0.315362i
\(459\) 3.41725e7i 0.353378i
\(460\) −4.94416e7 2.80331e7i −0.507948 0.288004i
\(461\) −4.67094e7 −0.476762 −0.238381 0.971172i \(-0.576617\pi\)
−0.238381 + 0.971172i \(0.576617\pi\)
\(462\) 1.53282e8 1.55441
\(463\) 5.63404e7 0.567646 0.283823 0.958877i \(-0.408397\pi\)
0.283823 + 0.958877i \(0.408397\pi\)
\(464\) −6.19054e6 −0.0619690
\(465\) 1.75049e7i 0.174101i
\(466\) −1.11955e8 −1.10633
\(467\) 1.36113e8i 1.33643i 0.743966 + 0.668217i \(0.232942\pi\)
−0.743966 + 0.668217i \(0.767058\pi\)
\(468\) 1.05543e8 1.02965
\(469\) 9.37008e7 0.908290
\(470\) 6.97953e7i 0.672253i
\(471\) 5.70356e7i 0.545862i
\(472\) −3.77957e7 −0.359432
\(473\) 1.20848e8 1.14197
\(474\) 9.55153e7i 0.896887i
\(475\) 9.91601e7i 0.925243i
\(476\) 4.85067e8 4.49760
\(477\) 3.62900e7i 0.334373i
\(478\) −2.46995e8 −2.26154
\(479\) 5.92042e7i 0.538699i 0.963043 + 0.269349i \(0.0868086\pi\)
−0.963043 + 0.269349i \(0.913191\pi\)
\(480\) 1.30835e7i 0.118305i
\(481\) 2.84927e8i 2.56035i
\(482\) 1.52067e8i 1.35798i
\(483\) 7.74425e7 + 4.39095e7i 0.687287 + 0.389688i
\(484\) −7.86201e7 −0.693422
\(485\) −3.49338e7 −0.306211
\(486\) −1.22999e7 −0.107150
\(487\) −1.88221e7 −0.162960 −0.0814798 0.996675i \(-0.525965\pi\)
−0.0814798 + 0.996675i \(0.525965\pi\)
\(488\) 1.12852e8i 0.971066i
\(489\) 3.96304e7 0.338923
\(490\) 5.59434e7i 0.475511i
\(491\) 5.97827e7 0.505046 0.252523 0.967591i \(-0.418740\pi\)
0.252523 + 0.967591i \(0.418740\pi\)
\(492\) 2.07289e6 0.0174053
\(493\) 3.29451e7i 0.274948i
\(494\) 3.59818e8i 2.98471i
\(495\) −1.55352e7 −0.128086
\(496\) −4.66801e7 −0.382548
\(497\) 5.63847e7i 0.459296i
\(498\) 6.10451e7i 0.494268i
\(499\) −7.60944e7 −0.612423 −0.306211 0.951964i \(-0.599061\pi\)
−0.306211 + 0.951964i \(0.599061\pi\)
\(500\) 1.38211e8i 1.10569i
\(501\) 7.93411e7 0.630936
\(502\) 1.66961e8i 1.31979i
\(503\) 1.17172e8i 0.920703i 0.887737 + 0.460352i \(0.152277\pi\)
−0.887737 + 0.460352i \(0.847723\pi\)
\(504\) 7.70493e7i 0.601835i
\(505\) 1.19152e7i 0.0925186i
\(506\) −2.21726e8 1.25718e8i −1.71146 0.970387i
\(507\) −1.48851e8 −1.14216
\(508\) 4.22737e8 3.22462
\(509\) 1.36371e8 1.03412 0.517059 0.855950i \(-0.327027\pi\)
0.517059 + 0.855950i \(0.327027\pi\)
\(510\) −7.66277e7 −0.577664
\(511\) 3.09604e8i 2.32030i
\(512\) −1.08176e8 −0.805976
\(513\) 2.69026e7i 0.199270i
\(514\) −3.66253e7 −0.269707
\(515\) −2.90470e7 −0.212657
\(516\) 1.37648e8i 1.00189i
\(517\) 2.00813e8i 1.45318i
\(518\) 4.71335e8 3.39110
\(519\) −3.34130e6 −0.0239008
\(520\) 1.04444e8i 0.742799i
\(521\) 1.08762e8i 0.769068i −0.923111 0.384534i \(-0.874362\pi\)
0.923111 0.384534i \(-0.125638\pi\)
\(522\) −1.18581e7 −0.0833686
\(523\) 1.00555e7i 0.0702908i 0.999382 + 0.0351454i \(0.0111894\pi\)
−0.999382 + 0.0351454i \(0.988811\pi\)
\(524\) −3.86913e7 −0.268918
\(525\) 1.02159e8i 0.705993i
\(526\) 4.34113e8i 2.98295i
\(527\) 2.48424e8i 1.69731i
\(528\) 4.14275e7i 0.281441i
\(529\) −7.60091e7 1.27032e8i −0.513451 0.858119i
\(530\) 8.13758e7 0.546598
\(531\) −1.35960e7 −0.0908085
\(532\) −3.81873e8 −2.53620
\(533\) −4.40126e6 −0.0290666
\(534\) 8.96644e6i 0.0588839i
\(535\) 2.29520e7 0.149885
\(536\) 1.34852e8i 0.875717i
\(537\) 1.55047e8 1.00124
\(538\) 4.32818e8 2.77945
\(539\) 1.60959e8i 1.02789i
\(540\) 1.76949e7i 0.112375i
\(541\) −1.74284e8 −1.10069 −0.550347 0.834936i \(-0.685505\pi\)
−0.550347 + 0.834936i \(0.685505\pi\)
\(542\) 5.85438e7 0.367691
\(543\) 7.87185e6i 0.0491674i
\(544\) 1.85678e8i 1.15336i
\(545\) −8.24035e7 −0.509045
\(546\) 3.70701e8i 2.27744i
\(547\) −1.67420e8 −1.02293 −0.511465 0.859304i \(-0.670897\pi\)
−0.511465 + 0.859304i \(0.670897\pi\)
\(548\) 8.44933e7i 0.513429i
\(549\) 4.05953e7i 0.245334i
\(550\) 2.92493e8i 1.75804i
\(551\) 2.59363e7i 0.155044i
\(552\) 6.31937e7 1.11454e8i 0.375714 0.662640i
\(553\) 2.15233e8 1.27272
\(554\) −2.52821e8 −1.48691
\(555\) −4.77699e7 −0.279432
\(556\) 5.67687e7 0.330282
\(557\) 1.38029e8i 0.798736i −0.916791 0.399368i \(-0.869230\pi\)
0.916791 0.399368i \(-0.130770\pi\)
\(558\) −8.94163e7 −0.514653
\(559\) 2.92261e8i 1.67315i
\(560\) −3.24459e7 −0.184755
\(561\) −2.20471e8 −1.24871
\(562\) 2.43451e8i 1.37152i
\(563\) 3.21701e8i 1.80271i −0.433077 0.901357i \(-0.642572\pi\)
0.433077 0.901357i \(-0.357428\pi\)
\(564\) −2.28731e8 −1.27493
\(565\) 6.74865e7 0.374172
\(566\) 1.39952e8i 0.771847i
\(567\) 2.77164e7i 0.152050i
\(568\) 8.11478e7 0.442824
\(569\) 7.25247e7i 0.393685i 0.980435 + 0.196843i \(0.0630688\pi\)
−0.980435 + 0.196843i \(0.936931\pi\)
\(570\) 6.03258e7 0.325746
\(571\) 3.26457e8i 1.75355i 0.480903 + 0.876774i \(0.340309\pi\)
−0.480903 + 0.876774i \(0.659691\pi\)
\(572\) 6.80930e8i 3.63843i
\(573\) 1.22401e8i 0.650612i
\(574\) 7.28069e6i 0.0384979i
\(575\) −8.37883e7 + 1.47776e8i −0.440737 + 0.777321i
\(576\) −9.31946e7 −0.487667
\(577\) 2.03247e8 1.05803 0.529014 0.848613i \(-0.322562\pi\)
0.529014 + 0.848613i \(0.322562\pi\)
\(578\) −7.64942e8 −3.96136
\(579\) 1.99758e8 1.02912
\(580\) 1.70594e7i 0.0874337i
\(581\) 1.37558e8 0.701388
\(582\) 1.78445e8i 0.905179i
\(583\) 2.34132e8 1.18156
\(584\) 4.45575e8 2.23709
\(585\) 3.75707e7i 0.187664i
\(586\) 9.24948e7i 0.459647i
\(587\) 3.41225e8 1.68704 0.843522 0.537094i \(-0.180478\pi\)
0.843522 + 0.537094i \(0.180478\pi\)
\(588\) 1.83336e8 0.901810
\(589\) 1.95574e8i 0.957118i
\(590\) 3.04873e7i 0.148444i
\(591\) −1.74661e8 −0.846121
\(592\) 1.27387e8i 0.613990i
\(593\) −4.85029e7 −0.232597 −0.116298 0.993214i \(-0.537103\pi\)
−0.116298 + 0.993214i \(0.537103\pi\)
\(594\) 7.93550e7i 0.378630i
\(595\) 1.72672e8i 0.819730i
\(596\) 4.22701e8i 1.99662i
\(597\) 1.32265e8i 0.621616i
\(598\) −3.04039e8 + 5.36229e8i −1.42176 + 2.50753i
\(599\) −2.09120e8 −0.973005 −0.486502 0.873679i \(-0.661728\pi\)
−0.486502 + 0.873679i \(0.661728\pi\)
\(600\) −1.47026e8 −0.680675
\(601\) −4.08234e8 −1.88056 −0.940278 0.340409i \(-0.889435\pi\)
−0.940278 + 0.340409i \(0.889435\pi\)
\(602\) 4.83466e8 2.21603
\(603\) 4.85094e7i 0.221245i
\(604\) 2.78149e8 1.26231
\(605\) 2.79869e7i 0.126383i
\(606\) 6.08641e7 0.273491
\(607\) 3.04590e8 1.36191 0.680957 0.732323i \(-0.261564\pi\)
0.680957 + 0.732323i \(0.261564\pi\)
\(608\) 1.46176e8i 0.650379i
\(609\) 2.67208e7i 0.118304i
\(610\) −9.10299e7 −0.401046
\(611\) 4.85651e8 2.12912
\(612\) 2.51121e8i 1.09554i
\(613\) 5.70085e7i 0.247491i −0.992314 0.123745i \(-0.960509\pi\)
0.992314 0.123745i \(-0.0394906\pi\)
\(614\) −6.58298e7 −0.284392
\(615\) 737899.i 0.00317228i
\(616\) −4.97099e8 −2.12667
\(617\) 3.77637e7i 0.160775i 0.996764 + 0.0803877i \(0.0256158\pi\)
−0.996764 + 0.0803877i \(0.974384\pi\)
\(618\) 1.48375e8i 0.628628i
\(619\) 3.40594e7i 0.143604i −0.997419 0.0718018i \(-0.977125\pi\)
0.997419 0.0718018i \(-0.0228749\pi\)
\(620\) 1.28637e8i 0.539747i
\(621\) 2.27322e7 4.00924e7i 0.0949219 0.167412i
\(622\) −2.76798e8 −1.15025
\(623\) −2.02049e7 −0.0835588
\(624\) −1.00189e8 −0.412351
\(625\) 1.68958e8 0.692054
\(626\) 3.71934e7i 0.151615i
\(627\) 1.73568e8 0.704151
\(628\) 4.19133e8i 1.69228i
\(629\) −6.77937e8 −2.72419
\(630\) −6.21505e7 −0.248555
\(631\) 2.37604e8i 0.945725i −0.881136 0.472863i \(-0.843221\pi\)
0.881136 0.472863i \(-0.156779\pi\)
\(632\) 3.09759e8i 1.22708i
\(633\) 3.49941e7 0.137970
\(634\) 1.95025e8 0.765283
\(635\) 1.50484e8i 0.587718i
\(636\) 2.66682e8i 1.03663i
\(637\) −3.89266e8 −1.50601
\(638\) 7.65047e7i 0.294595i
\(639\) 2.91907e7 0.111877
\(640\) 1.55261e8i 0.592275i
\(641\) 4.50113e8i 1.70902i −0.519433 0.854511i \(-0.673857\pi\)
0.519433 0.854511i \(-0.326143\pi\)
\(642\) 1.17240e8i 0.443070i
\(643\) 1.93945e8i 0.729533i −0.931099 0.364767i \(-0.881149\pi\)
0.931099 0.364767i \(-0.118851\pi\)
\(644\) −5.69097e8 3.22675e8i −2.13073 1.20811i
\(645\) −4.89994e7 −0.182605
\(646\) 8.56126e8 3.17571
\(647\) −2.17106e8 −0.801601 −0.400800 0.916165i \(-0.631268\pi\)
−0.400800 + 0.916165i \(0.631268\pi\)
\(648\) 3.98888e7 0.146597
\(649\) 8.77170e7i 0.320885i
\(650\) 7.07373e8 2.57578
\(651\) 2.01490e8i 0.730314i
\(652\) −2.91229e8 −1.05073
\(653\) −4.36163e8 −1.56642 −0.783212 0.621755i \(-0.786420\pi\)
−0.783212 + 0.621755i \(0.786420\pi\)
\(654\) 4.20924e8i 1.50477i
\(655\) 1.37732e7i 0.0490128i
\(656\) −1.96775e6 −0.00697040
\(657\) 1.60283e8 0.565187
\(658\) 8.03378e8i 2.81996i
\(659\) 1.46383e8i 0.511486i −0.966745 0.255743i \(-0.917680\pi\)
0.966745 0.255743i \(-0.0823200\pi\)
\(660\) 1.14162e8 0.397092
\(661\) 3.35799e8i 1.16272i 0.813647 + 0.581359i \(0.197479\pi\)
−0.813647 + 0.581359i \(0.802521\pi\)
\(662\) 3.12174e7 0.107603
\(663\) 5.33192e8i 1.82954i
\(664\) 1.97971e8i 0.676235i
\(665\) 1.35937e8i 0.462247i
\(666\) 2.44012e8i 0.826018i
\(667\) 2.19157e7 3.86523e7i 0.0738546 0.130256i
\(668\) −5.83049e8 −1.95603
\(669\) 1.11706e8 0.373075
\(670\) 1.08776e8 0.361668
\(671\) −2.61908e8 −0.866925
\(672\) 1.50598e8i 0.496262i
\(673\) −1.42716e8 −0.468196 −0.234098 0.972213i \(-0.575214\pi\)
−0.234098 + 0.972213i \(0.575214\pi\)
\(674\) 1.42835e8i 0.466504i
\(675\) −5.28885e7 −0.171969
\(676\) 1.09385e9 3.54093
\(677\) 4.50766e8i 1.45273i 0.687308 + 0.726366i \(0.258792\pi\)
−0.687308 + 0.726366i \(0.741208\pi\)
\(678\) 3.44726e8i 1.10608i
\(679\) −4.02105e8 −1.28449
\(680\) 2.48506e8 0.790333
\(681\) 1.08423e8i 0.343305i
\(682\) 5.76887e8i 1.81860i
\(683\) 2.27098e8 0.712773 0.356387 0.934339i \(-0.384009\pi\)
0.356387 + 0.934339i \(0.384009\pi\)
\(684\) 1.97698e8i 0.617779i
\(685\) −3.00775e7 −0.0935773
\(686\) 9.39628e7i 0.291061i
\(687\) 3.53447e7i 0.109007i
\(688\) 1.30666e8i 0.401234i
\(689\) 5.66231e8i 1.73115i
\(690\) 8.99022e7 + 5.09741e7i 0.273667 + 0.155168i
\(691\) 5.21427e8 1.58037 0.790186 0.612867i \(-0.209984\pi\)
0.790186 + 0.612867i \(0.209984\pi\)
\(692\) 2.45540e7 0.0740975
\(693\) −1.78818e8 −0.537292
\(694\) −3.00289e8 −0.898383
\(695\) 2.02083e7i 0.0601970i
\(696\) 3.84561e7 0.114061
\(697\) 1.04721e7i 0.0309267i
\(698\) 6.09254e8 1.79156
\(699\) 1.30606e8 0.382411
\(700\) 7.50732e8i 2.18872i
\(701\) 5.08788e7i 0.147701i −0.997269 0.0738503i \(-0.976471\pi\)
0.997269 0.0738503i \(-0.0235287\pi\)
\(702\) −1.91914e8 −0.554748
\(703\) 5.33711e8 1.53617
\(704\) 6.01263e8i 1.72324i
\(705\) 8.14226e7i 0.232369i
\(706\) −8.41697e8 −2.39189
\(707\) 1.37150e8i 0.388096i
\(708\) 9.99118e7 0.281525
\(709\) 4.19730e8i 1.17769i −0.808245 0.588846i \(-0.799583\pi\)
0.808245 0.588846i \(-0.200417\pi\)
\(710\) 6.54564e7i 0.182885i
\(711\) 1.11427e8i 0.310015i
\(712\) 2.90785e7i 0.0805622i
\(713\) 1.65256e8 2.91460e8i 0.455921 0.804100i
\(714\) −8.82022e8 −2.42317
\(715\) −2.42394e8 −0.663139
\(716\) −1.13938e9 −3.10406
\(717\) 2.88142e8 0.781716
\(718\) 9.13100e8i 2.46686i
\(719\) −2.31060e8 −0.621639 −0.310820 0.950469i \(-0.600604\pi\)
−0.310820 + 0.950469i \(0.600604\pi\)
\(720\) 1.67974e7i 0.0450033i
\(721\) −3.34346e8 −0.892051
\(722\) −4.53469e7 −0.120486
\(723\) 1.77400e8i 0.469396i
\(724\) 5.78473e7i 0.152429i
\(725\) −5.09888e7 −0.133801
\(726\) 1.42959e8 0.373596
\(727\) 6.06964e8i 1.57965i −0.613335 0.789823i \(-0.710172\pi\)
0.613335 0.789823i \(-0.289828\pi\)
\(728\) 1.20220e9i 3.11588i
\(729\) 1.43489e7 0.0370370
\(730\) 3.59415e8i 0.923907i
\(731\) −6.95385e8 −1.78022
\(732\) 2.98320e8i 0.760587i
\(733\) 9.92159e7i 0.251924i 0.992035 + 0.125962i \(0.0402017\pi\)
−0.992035 + 0.125962i \(0.959798\pi\)
\(734\) 9.80418e8i 2.47927i
\(735\) 6.52630e7i 0.164363i
\(736\) 1.23516e8 2.17844e8i 0.309807 0.546401i
\(737\) 3.12968e8 0.781802
\(738\) −3.76925e6 −0.00937747
\(739\) −9.18743e7 −0.227646 −0.113823 0.993501i \(-0.536310\pi\)
−0.113823 + 0.993501i \(0.536310\pi\)
\(740\) 3.51043e8 0.866295
\(741\) 4.19760e8i 1.03168i
\(742\) 9.36675e8 2.29286
\(743\) 6.62329e8i 1.61476i −0.590034 0.807379i \(-0.700886\pi\)
0.590034 0.807379i \(-0.299114\pi\)
\(744\) 2.89980e8 0.704124
\(745\) 1.50471e8 0.363902
\(746\) 1.10999e9i 2.67363i
\(747\) 7.12146e7i 0.170847i
\(748\) 1.62016e9 3.87126
\(749\) 2.64188e8 0.628736
\(750\) 2.51316e8i 0.595713i
\(751\) 3.19510e8i 0.754335i −0.926145 0.377167i \(-0.876898\pi\)
0.926145 0.377167i \(-0.123102\pi\)
\(752\) 2.17129e8 0.510580
\(753\) 1.94775e8i 0.456193i
\(754\) −1.85021e8 −0.431625
\(755\) 9.90141e7i 0.230068i
\(756\) 2.03677e8i 0.471387i
\(757\) 5.19511e8i 1.19759i 0.800903 + 0.598794i \(0.204353\pi\)
−0.800903 + 0.598794i \(0.795647\pi\)
\(758\) 9.20906e8i 2.11450i
\(759\) 2.58664e8 + 1.46661e8i 0.591576 + 0.335421i
\(760\) −1.95638e8 −0.445670
\(761\) 3.04486e8 0.690896 0.345448 0.938438i \(-0.387727\pi\)
0.345448 + 0.938438i \(0.387727\pi\)
\(762\) −7.68684e8 −1.73733
\(763\) −9.48505e8 −2.13533
\(764\) 8.99482e8i 2.01703i
\(765\) 8.93931e7 0.199673
\(766\) 9.45345e8i 2.10331i
\(767\) −2.12137e8 −0.470143
\(768\) 4.10468e8 0.906141
\(769\) 1.99259e8i 0.438167i 0.975706 + 0.219083i \(0.0703067\pi\)
−0.975706 + 0.219083i \(0.929693\pi\)
\(770\) 4.00976e8i 0.878307i
\(771\) 4.27268e7 0.0932260
\(772\) −1.46795e9 −3.19050
\(773\) 3.83867e7i 0.0831079i −0.999136 0.0415539i \(-0.986769\pi\)
0.999136 0.0415539i \(-0.0132308\pi\)
\(774\) 2.50293e8i 0.539791i
\(775\) −3.84483e8 −0.825985
\(776\) 5.78701e8i 1.23842i
\(777\) −5.49855e8 −1.17215
\(778\) 1.59607e8i 0.338932i
\(779\) 8.24421e6i 0.0174396i
\(780\) 2.76093e8i 0.581797i
\(781\) 1.88329e8i 0.395334i
\(782\) 1.27587e9 + 7.23410e8i 2.66799 + 1.51274i
\(783\) 1.38335e7 0.0288169