Properties

Label 38.5.b.a.37.5
Level $38$
Weight $5$
Character 38.37
Analytic conductor $3.928$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 38.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92805859719\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 450 x^{6} + 68229 x^{4} + 4001228 x^{2} + 77475204\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.5
Root \(-12.2418i\) of defining polynomial
Character \(\chi\) \(=\) 38.37
Dual form 38.5.b.a.37.4

$q$-expansion

\(f(q)\) \(=\) \(q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} +O(q^{10})\) \(q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} -74.1886i q^{10} +114.743 q^{11} +86.6206i q^{12} -231.848i q^{13} -243.502i q^{14} +284.003i q^{15} +64.0000 q^{16} -244.466 q^{17} -102.492i q^{18} +(253.655 + 256.866i) q^{19} +209.837 q^{20} +932.157i q^{21} +324.543i q^{22} -269.052 q^{23} -245.000 q^{24} +62.9931 q^{25} +655.766 q^{26} -484.681i q^{27} +688.728 q^{28} -1131.05i q^{29} -803.282 q^{30} +1037.59i q^{31} +181.019i q^{32} -1242.39i q^{33} -691.455i q^{34} +2258.14 q^{35} +289.891 q^{36} +302.815i q^{37} +(-726.527 + 717.444i) q^{38} -2510.36 q^{39} +593.509i q^{40} -1769.82i q^{41} -2636.54 q^{42} -2316.56 q^{43} -917.946 q^{44} +950.467 q^{45} -760.993i q^{46} -835.757 q^{47} -692.965i q^{48} +5010.66 q^{49} +178.171i q^{50} +2646.98i q^{51} +1854.79i q^{52} -656.208i q^{53} +1370.89 q^{54} -3009.67 q^{55} +1948.02i q^{56} +(2781.24 - 2746.47i) q^{57} +3199.09 q^{58} -4923.33i q^{59} -2272.03i q^{60} -1576.71 q^{61} -2934.75 q^{62} +3119.63 q^{63} -512.000 q^{64} +6081.30i q^{65} +3514.01 q^{66} +7000.44i q^{67} +1955.73 q^{68} +2913.18i q^{69} +6386.97i q^{70} -4101.26i q^{71} +819.936i q^{72} +7018.02 q^{73} -856.490 q^{74} -682.062i q^{75} +(-2029.24 - 2054.93i) q^{76} -9878.36 q^{77} -7100.36i q^{78} +1264.00i q^{79} -1678.70 q^{80} -8183.07 q^{81} +5005.79 q^{82} +1020.09 q^{83} -7457.26i q^{84} +6412.25 q^{85} -6552.21i q^{86} -12246.5 q^{87} -2596.34i q^{88} -3746.30i q^{89} +2688.33i q^{90} +19960.1i q^{91} +2152.41 q^{92} +11234.6 q^{93} -2363.88i q^{94} +(-6653.27 - 6737.50i) q^{95} +1960.00 q^{96} -13041.0i q^{97} +14172.3i q^{98} -4157.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} + O(q^{10}) \) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} - 6q^{11} + 512q^{16} + 510q^{17} - 12q^{19} - 144q^{20} - 396q^{23} + 256q^{24} + 3458q^{25} - 192q^{26} + 1296q^{28} - 2752q^{30} + 1002q^{35} + 2144q^{36} - 3216q^{38} - 6588q^{39} + 1376q^{42} - 8654q^{43} + 48q^{44} - 10334q^{45} + 3210q^{47} + 9222q^{49} + 9088q^{54} + 17146q^{55} - 14076q^{57} - 960q^{58} + 1314q^{61} - 15168q^{62} + 29938q^{63} - 4096q^{64} + 4928q^{66} - 4080q^{68} + 23398q^{73} + 13152q^{74} + 96q^{76} - 44622q^{77} + 1152q^{80} - 20368q^{81} + 16512q^{82} - 10440q^{83} + 21274q^{85} - 14316q^{87} + 3168q^{92} + 19416q^{93} - 34686q^{95} - 2048q^{96} - 56798q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82843i 0.707107i
\(3\) 10.8276i 1.20306i −0.798849 0.601532i \(-0.794557\pi\)
0.798849 0.601532i \(-0.205443\pi\)
\(4\) −8.00000 −0.500000
\(5\) −26.2296 −1.04918 −0.524592 0.851353i \(-0.675782\pi\)
−0.524592 + 0.851353i \(0.675782\pi\)
\(6\) 30.6250 0.850695
\(7\) −86.0910 −1.75696 −0.878480 0.477779i \(-0.841442\pi\)
−0.878480 + 0.477779i \(0.841442\pi\)
\(8\) 22.6274i 0.353553i
\(9\) −36.2364 −0.447363
\(10\) 74.1886i 0.741886i
\(11\) 114.743 0.948291 0.474145 0.880447i \(-0.342757\pi\)
0.474145 + 0.880447i \(0.342757\pi\)
\(12\) 86.6206i 0.601532i
\(13\) 231.848i 1.37188i −0.727656 0.685942i \(-0.759390\pi\)
0.727656 0.685942i \(-0.240610\pi\)
\(14\) 243.502i 1.24236i
\(15\) 284.003i 1.26224i
\(16\) 64.0000 0.250000
\(17\) −244.466 −0.845903 −0.422952 0.906152i \(-0.639006\pi\)
−0.422952 + 0.906152i \(0.639006\pi\)
\(18\) 102.492i 0.316333i
\(19\) 253.655 + 256.866i 0.702645 + 0.711540i
\(20\) 209.837 0.524592
\(21\) 932.157i 2.11373i
\(22\) 324.543i 0.670543i
\(23\) −269.052 −0.508604 −0.254302 0.967125i \(-0.581846\pi\)
−0.254302 + 0.967125i \(0.581846\pi\)
\(24\) −245.000 −0.425347
\(25\) 62.9931 0.100789
\(26\) 655.766 0.970069
\(27\) 484.681i 0.664858i
\(28\) 688.728 0.878480
\(29\) 1131.05i 1.34489i −0.740148 0.672443i \(-0.765245\pi\)
0.740148 0.672443i \(-0.234755\pi\)
\(30\) −803.282 −0.892536
\(31\) 1037.59i 1.07970i 0.841762 + 0.539850i \(0.181519\pi\)
−0.841762 + 0.539850i \(0.818481\pi\)
\(32\) 181.019i 0.176777i
\(33\) 1242.39i 1.14085i
\(34\) 691.455i 0.598144i
\(35\) 2258.14 1.84338
\(36\) 289.891 0.223681
\(37\) 302.815i 0.221194i 0.993865 + 0.110597i \(0.0352763\pi\)
−0.993865 + 0.110597i \(0.964724\pi\)
\(38\) −726.527 + 717.444i −0.503135 + 0.496845i
\(39\) −2510.36 −1.65046
\(40\) 593.509i 0.370943i
\(41\) 1769.82i 1.05283i −0.850226 0.526417i \(-0.823535\pi\)
0.850226 0.526417i \(-0.176465\pi\)
\(42\) −2636.54 −1.49464
\(43\) −2316.56 −1.25287 −0.626435 0.779474i \(-0.715487\pi\)
−0.626435 + 0.779474i \(0.715487\pi\)
\(44\) −917.946 −0.474145
\(45\) 950.467 0.469366
\(46\) 760.993i 0.359638i
\(47\) −835.757 −0.378342 −0.189171 0.981944i \(-0.560580\pi\)
−0.189171 + 0.981944i \(0.560580\pi\)
\(48\) 692.965i 0.300766i
\(49\) 5010.66 2.08691
\(50\) 178.171i 0.0712685i
\(51\) 2646.98i 1.01768i
\(52\) 1854.79i 0.685942i
\(53\) 656.208i 0.233609i −0.993155 0.116805i \(-0.962735\pi\)
0.993155 0.116805i \(-0.0372651\pi\)
\(54\) 1370.89 0.470125
\(55\) −3009.67 −0.994932
\(56\) 1948.02i 0.621179i
\(57\) 2781.24 2746.47i 0.856029 0.845327i
\(58\) 3199.09 0.950979
\(59\) 4923.33i 1.41434i −0.707042 0.707171i \(-0.749971\pi\)
0.707042 0.707171i \(-0.250029\pi\)
\(60\) 2272.03i 0.631118i
\(61\) −1576.71 −0.423733 −0.211866 0.977299i \(-0.567954\pi\)
−0.211866 + 0.977299i \(0.567954\pi\)
\(62\) −2934.75 −0.763463
\(63\) 3119.63 0.785999
\(64\) −512.000 −0.125000
\(65\) 6081.30i 1.43936i
\(66\) 3514.01 0.806706
\(67\) 7000.44i 1.55946i 0.626113 + 0.779732i \(0.284645\pi\)
−0.626113 + 0.779732i \(0.715355\pi\)
\(68\) 1955.73 0.422952
\(69\) 2913.18i 0.611884i
\(70\) 6386.97i 1.30346i
\(71\) 4101.26i 0.813581i −0.913521 0.406790i \(-0.866648\pi\)
0.913521 0.406790i \(-0.133352\pi\)
\(72\) 819.936i 0.158167i
\(73\) 7018.02 1.31695 0.658474 0.752603i \(-0.271202\pi\)
0.658474 + 0.752603i \(0.271202\pi\)
\(74\) −856.490 −0.156408
\(75\) 682.062i 0.121256i
\(76\) −2029.24 2054.93i −0.351323 0.355770i
\(77\) −9878.36 −1.66611
\(78\) 7100.36i 1.16705i
\(79\) 1264.00i 0.202532i 0.994859 + 0.101266i \(0.0322893\pi\)
−0.994859 + 0.101266i \(0.967711\pi\)
\(80\) −1678.70 −0.262296
\(81\) −8183.07 −1.24723
\(82\) 5005.79 0.744467
\(83\) 1020.09 0.148075 0.0740377 0.997255i \(-0.476411\pi\)
0.0740377 + 0.997255i \(0.476411\pi\)
\(84\) 7457.26i 1.05687i
\(85\) 6412.25 0.887509
\(86\) 6552.21i 0.885913i
\(87\) −12246.5 −1.61799
\(88\) 2596.34i 0.335271i
\(89\) 3746.30i 0.472958i −0.971637 0.236479i \(-0.924007\pi\)
0.971637 0.236479i \(-0.0759934\pi\)
\(90\) 2688.33i 0.331892i
\(91\) 19960.1i 2.41034i
\(92\) 2152.41 0.254302
\(93\) 11234.6 1.29895
\(94\) 2363.88i 0.267528i
\(95\) −6653.27 6737.50i −0.737205 0.746537i
\(96\) 1960.00 0.212674
\(97\) 13041.0i 1.38601i −0.720933 0.693005i \(-0.756287\pi\)
0.720933 0.693005i \(-0.243713\pi\)
\(98\) 14172.3i 1.47567i
\(99\) −4157.88 −0.424230
\(100\) −503.945 −0.0503945
\(101\) −4755.84 −0.466213 −0.233106 0.972451i \(-0.574889\pi\)
−0.233106 + 0.972451i \(0.574889\pi\)
\(102\) −7486.78 −0.719606
\(103\) 8727.79i 0.822678i −0.911483 0.411339i \(-0.865061\pi\)
0.911483 0.411339i \(-0.134939\pi\)
\(104\) −5246.13 −0.485034
\(105\) 24450.1i 2.21770i
\(106\) 1856.04 0.165187
\(107\) 16884.9i 1.47479i 0.675462 + 0.737395i \(0.263944\pi\)
−0.675462 + 0.737395i \(0.736056\pi\)
\(108\) 3877.45i 0.332429i
\(109\) 205.403i 0.0172883i 0.999963 + 0.00864416i \(0.00275156\pi\)
−0.999963 + 0.00864416i \(0.997248\pi\)
\(110\) 8512.63i 0.703524i
\(111\) 3278.75 0.266111
\(112\) −5509.83 −0.439240
\(113\) 4276.02i 0.334875i 0.985883 + 0.167438i \(0.0535492\pi\)
−0.985883 + 0.167438i \(0.946451\pi\)
\(114\) 7768.18 + 7866.53i 0.597737 + 0.605304i
\(115\) 7057.13 0.533620
\(116\) 9048.40i 0.672443i
\(117\) 8401.35i 0.613730i
\(118\) 13925.3 1.00009
\(119\) 21046.3 1.48622
\(120\) 6426.26 0.446268
\(121\) −1475.00 −0.100744
\(122\) 4459.61i 0.299624i
\(123\) −19162.8 −1.26663
\(124\) 8300.73i 0.539850i
\(125\) 14741.2 0.943439
\(126\) 8823.64i 0.555785i
\(127\) 4501.00i 0.279063i 0.990218 + 0.139531i \(0.0445596\pi\)
−0.990218 + 0.139531i \(0.955440\pi\)
\(128\) 1448.15i 0.0883883i
\(129\) 25082.7i 1.50728i
\(130\) −17200.5 −1.01778
\(131\) 27606.3 1.60866 0.804332 0.594180i \(-0.202523\pi\)
0.804332 + 0.594180i \(0.202523\pi\)
\(132\) 9939.13i 0.570427i
\(133\) −21837.4 22113.9i −1.23452 1.25015i
\(134\) −19800.2 −1.10271
\(135\) 12713.0i 0.697559i
\(136\) 5531.64i 0.299072i
\(137\) 8250.29 0.439570 0.219785 0.975548i \(-0.429464\pi\)
0.219785 + 0.975548i \(0.429464\pi\)
\(138\) −8239.71 −0.432667
\(139\) 27435.0 1.41996 0.709978 0.704224i \(-0.248705\pi\)
0.709978 + 0.704224i \(0.248705\pi\)
\(140\) −18065.1 −0.921688
\(141\) 9049.22i 0.455169i
\(142\) 11600.1 0.575289
\(143\) 26603.0i 1.30095i
\(144\) −2319.13 −0.111841
\(145\) 29667.0i 1.41104i
\(146\) 19850.0i 0.931223i
\(147\) 54253.3i 2.51068i
\(148\) 2422.52i 0.110597i
\(149\) −40247.3 −1.81286 −0.906430 0.422355i \(-0.861204\pi\)
−0.906430 + 0.422355i \(0.861204\pi\)
\(150\) 1929.16 0.0857406
\(151\) 16932.1i 0.742605i 0.928512 + 0.371303i \(0.121089\pi\)
−0.928512 + 0.371303i \(0.878911\pi\)
\(152\) 5812.22 5739.56i 0.251568 0.248423i
\(153\) 8858.57 0.378426
\(154\) 27940.2i 1.17812i
\(155\) 27215.6i 1.13280i
\(156\) 20082.8 0.825232
\(157\) 5684.97 0.230637 0.115319 0.993329i \(-0.463211\pi\)
0.115319 + 0.993329i \(0.463211\pi\)
\(158\) −3575.14 −0.143212
\(159\) −7105.14 −0.281047
\(160\) 4748.07i 0.185471i
\(161\) 23162.9 0.893597
\(162\) 23145.2i 0.881924i
\(163\) −30550.6 −1.14986 −0.574929 0.818203i \(-0.694970\pi\)
−0.574929 + 0.818203i \(0.694970\pi\)
\(164\) 14158.5i 0.526417i
\(165\) 32587.4i 1.19697i
\(166\) 2885.26i 0.104705i
\(167\) 28241.5i 1.01264i −0.862345 0.506320i \(-0.831005\pi\)
0.862345 0.506320i \(-0.168995\pi\)
\(168\) 21092.3 0.747318
\(169\) −25192.7 −0.882066
\(170\) 18136.6i 0.627564i
\(171\) −9191.54 9307.90i −0.314337 0.318317i
\(172\) 18532.4 0.626435
\(173\) 35673.0i 1.19192i −0.803013 0.595961i \(-0.796771\pi\)
0.803013 0.595961i \(-0.203229\pi\)
\(174\) 34638.4i 1.14409i
\(175\) −5423.14 −0.177082
\(176\) 7343.56 0.237073
\(177\) −53307.7 −1.70154
\(178\) 10596.1 0.334432
\(179\) 34371.5i 1.07273i 0.843985 + 0.536367i \(0.180204\pi\)
−0.843985 + 0.536367i \(0.819796\pi\)
\(180\) −7603.74 −0.234683
\(181\) 29195.1i 0.891153i 0.895244 + 0.445577i \(0.147001\pi\)
−0.895244 + 0.445577i \(0.852999\pi\)
\(182\) −56455.6 −1.70437
\(183\) 17071.9i 0.509777i
\(184\) 6087.95i 0.179819i
\(185\) 7942.72i 0.232074i
\(186\) 31776.2i 0.918494i
\(187\) −28050.8 −0.802163
\(188\) 6686.05 0.189171
\(189\) 41726.7i 1.16813i
\(190\) 19056.5 18818.3i 0.527882 0.521282i
\(191\) 13498.2 0.370008 0.185004 0.982738i \(-0.440770\pi\)
0.185004 + 0.982738i \(0.440770\pi\)
\(192\) 5543.72i 0.150383i
\(193\) 20819.7i 0.558933i −0.960155 0.279467i \(-0.909842\pi\)
0.960155 0.279467i \(-0.0901577\pi\)
\(194\) 36885.4 0.980056
\(195\) 65845.7 1.73164
\(196\) −40085.3 −1.04345
\(197\) 34233.5 0.882101 0.441051 0.897482i \(-0.354606\pi\)
0.441051 + 0.897482i \(0.354606\pi\)
\(198\) 11760.3i 0.299976i
\(199\) −55504.1 −1.40158 −0.700792 0.713366i \(-0.747170\pi\)
−0.700792 + 0.713366i \(0.747170\pi\)
\(200\) 1425.37i 0.0356343i
\(201\) 75797.8 1.87614
\(202\) 13451.5i 0.329662i
\(203\) 97373.2i 2.36291i
\(204\) 21175.8i 0.508838i
\(205\) 46421.6i 1.10462i
\(206\) 24685.9 0.581721
\(207\) 9749.46 0.227531
\(208\) 14838.3i 0.342971i
\(209\) 29105.2 + 29473.6i 0.666312 + 0.674747i
\(210\) 69155.4 1.56815
\(211\) 77552.5i 1.74193i −0.491345 0.870965i \(-0.663495\pi\)
0.491345 0.870965i \(-0.336505\pi\)
\(212\) 5249.66i 0.116805i
\(213\) −44406.7 −0.978790
\(214\) −47757.6 −1.04283
\(215\) 60762.4 1.31449
\(216\) −10967.1 −0.235063
\(217\) 89327.3i 1.89699i
\(218\) −580.966 −0.0122247
\(219\) 75988.1i 1.58437i
\(220\) 24077.4 0.497466
\(221\) 56679.1i 1.16048i
\(222\) 9273.71i 0.188169i
\(223\) 30754.3i 0.618438i 0.950991 + 0.309219i \(0.100068\pi\)
−0.950991 + 0.309219i \(0.899932\pi\)
\(224\) 15584.1i 0.310590i
\(225\) −2282.64 −0.0450892
\(226\) −12094.4 −0.236792
\(227\) 81299.3i 1.57774i −0.614561 0.788869i \(-0.710667\pi\)
0.614561 0.788869i \(-0.289333\pi\)
\(228\) −22249.9 + 21971.7i −0.428014 + 0.422664i
\(229\) −93187.0 −1.77699 −0.888494 0.458889i \(-0.848248\pi\)
−0.888494 + 0.458889i \(0.848248\pi\)
\(230\) 19960.6i 0.377326i
\(231\) 106959.i 2.00444i
\(232\) −25592.7 −0.475489
\(233\) −3379.09 −0.0622426 −0.0311213 0.999516i \(-0.509908\pi\)
−0.0311213 + 0.999516i \(0.509908\pi\)
\(234\) −23762.6 −0.433973
\(235\) 21921.6 0.396950
\(236\) 39386.6i 0.707171i
\(237\) 13686.1 0.243659
\(238\) 59528.0i 1.05091i
\(239\) 35917.8 0.628802 0.314401 0.949290i \(-0.398196\pi\)
0.314401 + 0.949290i \(0.398196\pi\)
\(240\) 18176.2i 0.315559i
\(241\) 57352.1i 0.987451i −0.869618 0.493726i \(-0.835635\pi\)
0.869618 0.493726i \(-0.164365\pi\)
\(242\) 4171.92i 0.0712370i
\(243\) 49343.6i 0.835639i
\(244\) 12613.7 0.211866
\(245\) −131428. −2.18955
\(246\) 54200.6i 0.895641i
\(247\) 59554.0 58809.5i 0.976151 0.963948i
\(248\) 23478.0 0.381731
\(249\) 11045.1i 0.178144i
\(250\) 41694.5i 0.667112i
\(251\) −52486.8 −0.833110 −0.416555 0.909110i \(-0.636763\pi\)
−0.416555 + 0.909110i \(0.636763\pi\)
\(252\) −24957.0 −0.392999
\(253\) −30871.9 −0.482305
\(254\) −12730.8 −0.197327
\(255\) 69429.2i 1.06773i
\(256\) 4096.00 0.0625000
\(257\) 85222.5i 1.29029i −0.764059 0.645146i \(-0.776796\pi\)
0.764059 0.645146i \(-0.223204\pi\)
\(258\) −70944.5 −1.06581
\(259\) 26069.6i 0.388629i
\(260\) 48650.4i 0.719680i
\(261\) 40985.2i 0.601653i
\(262\) 78082.4i 1.13750i
\(263\) −27539.5 −0.398149 −0.199074 0.979984i \(-0.563794\pi\)
−0.199074 + 0.979984i \(0.563794\pi\)
\(264\) −28112.1 −0.403353
\(265\) 17212.1i 0.245099i
\(266\) 62547.5 61765.5i 0.883988 0.872937i
\(267\) −40563.3 −0.568999
\(268\) 56003.5i 0.779732i
\(269\) 58880.0i 0.813697i −0.913496 0.406849i \(-0.866628\pi\)
0.913496 0.406849i \(-0.133372\pi\)
\(270\) −35957.8 −0.493249
\(271\) 99955.1 1.36103 0.680513 0.732736i \(-0.261757\pi\)
0.680513 + 0.732736i \(0.261757\pi\)
\(272\) −15645.8 −0.211476
\(273\) 216119. 2.89980
\(274\) 23335.4i 0.310823i
\(275\) 7228.03 0.0955772
\(276\) 23305.4i 0.305942i
\(277\) 66298.2 0.864056 0.432028 0.901860i \(-0.357798\pi\)
0.432028 + 0.901860i \(0.357798\pi\)
\(278\) 77597.8i 1.00406i
\(279\) 37598.6i 0.483017i
\(280\) 51095.8i 0.651732i
\(281\) 55021.9i 0.696824i −0.937341 0.348412i \(-0.886721\pi\)
0.937341 0.348412i \(-0.113279\pi\)
\(282\) −25595.1 −0.321853
\(283\) 10575.2 0.132044 0.0660219 0.997818i \(-0.478969\pi\)
0.0660219 + 0.997818i \(0.478969\pi\)
\(284\) 32810.1i 0.406790i
\(285\) −72950.8 + 72038.8i −0.898132 + 0.886904i
\(286\) 75244.7 0.919907
\(287\) 152365.i 1.84979i
\(288\) 6559.49i 0.0790833i
\(289\) −23757.3 −0.284447
\(290\) −83911.0 −0.997752
\(291\) −141202. −1.66746
\(292\) −56144.2 −0.658474
\(293\) 9449.70i 0.110074i 0.998484 + 0.0550368i \(0.0175276\pi\)
−0.998484 + 0.0550368i \(0.982472\pi\)
\(294\) 153452. 1.77532
\(295\) 129137.i 1.48391i
\(296\) 6851.92 0.0782040
\(297\) 55613.9i 0.630479i
\(298\) 113837.i 1.28189i
\(299\) 62379.2i 0.697746i
\(300\) 5456.50i 0.0606278i
\(301\) 199435. 2.20124
\(302\) −47891.3 −0.525101
\(303\) 51494.2i 0.560884i
\(304\) 16233.9 + 16439.4i 0.175661 + 0.177885i
\(305\) 41356.5 0.444574
\(306\) 25055.8i 0.267587i
\(307\) 112622.i 1.19494i 0.801890 + 0.597472i \(0.203828\pi\)
−0.801890 + 0.597472i \(0.796172\pi\)
\(308\) 79026.9 0.833054
\(309\) −94500.8 −0.989734
\(310\) 76977.4 0.801013
\(311\) −75878.9 −0.784513 −0.392257 0.919856i \(-0.628305\pi\)
−0.392257 + 0.919856i \(0.628305\pi\)
\(312\) 56802.9i 0.583527i
\(313\) −110960. −1.13260 −0.566301 0.824199i \(-0.691626\pi\)
−0.566301 + 0.824199i \(0.691626\pi\)
\(314\) 16079.5i 0.163085i
\(315\) −81826.7 −0.824658
\(316\) 10112.0i 0.101266i
\(317\) 63970.1i 0.636589i 0.947992 + 0.318294i \(0.103110\pi\)
−0.947992 + 0.318294i \(0.896890\pi\)
\(318\) 20096.4i 0.198730i
\(319\) 129780.i 1.27534i
\(320\) 13429.6 0.131148
\(321\) 182822. 1.77427
\(322\) 65514.7i 0.631869i
\(323\) −62010.0 62795.0i −0.594370 0.601894i
\(324\) 65464.6 0.623615
\(325\) 14604.8i 0.138271i
\(326\) 86410.0i 0.813072i
\(327\) 2224.01 0.0207990
\(328\) −40046.4 −0.372233
\(329\) 71951.1 0.664731
\(330\) −92171.2 −0.846384
\(331\) 79462.6i 0.725282i 0.931929 + 0.362641i \(0.118125\pi\)
−0.931929 + 0.362641i \(0.881875\pi\)
\(332\) −8160.74 −0.0740377
\(333\) 10972.9i 0.0989541i
\(334\) 79879.1 0.716045
\(335\) 183619.i 1.63617i
\(336\) 59658.1i 0.528434i
\(337\) 2779.80i 0.0244767i 0.999925 + 0.0122384i \(0.00389569\pi\)
−0.999925 + 0.0122384i \(0.996104\pi\)
\(338\) 71255.7i 0.623715i
\(339\) 46298.9 0.402876
\(340\) −51298.0 −0.443755
\(341\) 119057.i 1.02387i
\(342\) 26326.7 25997.6i 0.225084 0.222270i
\(343\) −224669. −1.90965
\(344\) 52417.7i 0.442956i
\(345\) 76411.6i 0.641979i
\(346\) 100899. 0.842816
\(347\) −15728.1 −0.130622 −0.0653110 0.997865i \(-0.520804\pi\)
−0.0653110 + 0.997865i \(0.520804\pi\)
\(348\) 97972.2 0.808993
\(349\) −41782.5 −0.343039 −0.171519 0.985181i \(-0.554868\pi\)
−0.171519 + 0.985181i \(0.554868\pi\)
\(350\) 15339.0i 0.125216i
\(351\) −112373. −0.912108
\(352\) 20770.7i 0.167636i
\(353\) 39292.1 0.315323 0.157661 0.987493i \(-0.449605\pi\)
0.157661 + 0.987493i \(0.449605\pi\)
\(354\) 150777.i 1.20317i
\(355\) 107575.i 0.853597i
\(356\) 29970.4i 0.236479i
\(357\) 227881.i 1.78802i
\(358\) −97217.2 −0.758537
\(359\) 160964. 1.24894 0.624468 0.781050i \(-0.285316\pi\)
0.624468 + 0.781050i \(0.285316\pi\)
\(360\) 21506.6i 0.165946i
\(361\) −1639.37 + 130311.i −0.0125794 + 0.999921i
\(362\) −82576.1 −0.630141
\(363\) 15970.7i 0.121202i
\(364\) 159681.i 1.20517i
\(365\) −184080. −1.38172
\(366\) −48286.7 −0.360467
\(367\) 19835.4 0.147268 0.0736340 0.997285i \(-0.476540\pi\)
0.0736340 + 0.997285i \(0.476540\pi\)
\(368\) −17219.3 −0.127151
\(369\) 64131.7i 0.470999i
\(370\) 22465.4 0.164101
\(371\) 56493.6i 0.410442i
\(372\) −89876.8 −0.649474
\(373\) 14463.5i 0.103958i −0.998648 0.0519788i \(-0.983447\pi\)
0.998648 0.0519788i \(-0.0165528\pi\)
\(374\) 79339.7i 0.567215i
\(375\) 159612.i 1.13502i
\(376\) 18911.0i 0.133764i
\(377\) −262232. −1.84503
\(378\) −118021. −0.825991
\(379\) 25932.7i 0.180539i −0.995917 0.0902693i \(-0.971227\pi\)
0.995917 0.0902693i \(-0.0287728\pi\)
\(380\) 53226.2 + 53900.0i 0.368602 + 0.373269i
\(381\) 48734.9 0.335730
\(382\) 38178.8i 0.261635i
\(383\) 9634.98i 0.0656831i −0.999461 0.0328415i \(-0.989544\pi\)
0.999461 0.0328415i \(-0.0104557\pi\)
\(384\) −15680.0 −0.106337
\(385\) 259106. 1.74806
\(386\) 58887.0 0.395226
\(387\) 83943.6 0.560487
\(388\) 104328.i 0.693005i
\(389\) 101890. 0.673335 0.336668 0.941624i \(-0.390700\pi\)
0.336668 + 0.941624i \(0.390700\pi\)
\(390\) 186240.i 1.22446i
\(391\) 65774.0 0.430230
\(392\) 113378.i 0.737833i
\(393\) 298909.i 1.93533i
\(394\) 96826.9i 0.623740i
\(395\) 33154.3i 0.212494i
\(396\) 33263.0 0.212115
\(397\) 100161. 0.635503 0.317752 0.948174i \(-0.397072\pi\)
0.317752 + 0.948174i \(0.397072\pi\)
\(398\) 156989.i 0.991069i
\(399\) −239440. + 236446.i −1.50401 + 1.48521i
\(400\) 4031.56 0.0251972
\(401\) 16696.5i 0.103833i 0.998651 + 0.0519165i \(0.0165330\pi\)
−0.998651 + 0.0519165i \(0.983467\pi\)
\(402\) 214388.i 1.32663i
\(403\) 240564. 1.48122
\(404\) 38046.7 0.233106
\(405\) 214639. 1.30857
\(406\) −275413. −1.67083
\(407\) 34745.9i 0.209756i
\(408\) 59894.2 0.359803
\(409\) 1173.94i 0.00701780i 0.999994 + 0.00350890i \(0.00111692\pi\)
−0.999994 + 0.00350890i \(0.998883\pi\)
\(410\) −131300. −0.781083
\(411\) 89330.7i 0.528831i
\(412\) 69822.3i 0.411339i
\(413\) 423854.i 2.48494i
\(414\) 27575.7i 0.160889i
\(415\) −26756.6 −0.155359
\(416\) 41969.0 0.242517
\(417\) 297054.i 1.70830i
\(418\) −83364.0 + 82321.9i −0.477118 + 0.471154i
\(419\) −209961. −1.19595 −0.597973 0.801517i \(-0.704027\pi\)
−0.597973 + 0.801517i \(0.704027\pi\)
\(420\) 195601.i 1.10885i
\(421\) 249117.i 1.40552i −0.711425 0.702762i \(-0.751950\pi\)
0.711425 0.702762i \(-0.248050\pi\)
\(422\) 219351. 1.23173
\(423\) 30284.8 0.169256
\(424\) −14848.3 −0.0825933
\(425\) −15399.7 −0.0852577
\(426\) 125601.i 0.692109i
\(427\) 135741. 0.744481
\(428\) 135079.i 0.737395i
\(429\) −288046. −1.56512
\(430\) 171862.i 0.929486i
\(431\) 126947.i 0.683387i −0.939811 0.341694i \(-0.888999\pi\)
0.939811 0.341694i \(-0.111001\pi\)
\(432\) 31019.6i 0.166214i
\(433\) 327343.i 1.74593i 0.487783 + 0.872965i \(0.337806\pi\)
−0.487783 + 0.872965i \(0.662194\pi\)
\(434\) 252656. 1.34137
\(435\) 321222. 1.69757
\(436\) 1643.22i 0.00864416i
\(437\) −68246.3 69110.3i −0.357368 0.361893i
\(438\) 214927. 1.12032
\(439\) 323562.i 1.67891i 0.543425 + 0.839457i \(0.317127\pi\)
−0.543425 + 0.839457i \(0.682873\pi\)
\(440\) 68101.1i 0.351762i
\(441\) −181568. −0.933605
\(442\) −160313. −0.820584
\(443\) 188338. 0.959689 0.479845 0.877354i \(-0.340693\pi\)
0.479845 + 0.877354i \(0.340693\pi\)
\(444\) −26230.0 −0.133055
\(445\) 98264.0i 0.496220i
\(446\) −86986.3 −0.437302
\(447\) 435781.i 2.18099i
\(448\) 44078.6 0.219620
\(449\) 31205.6i 0.154789i −0.997001 0.0773945i \(-0.975340\pi\)
0.997001 0.0773945i \(-0.0246601\pi\)
\(450\) 6456.29i 0.0318829i
\(451\) 203074.i 0.998394i
\(452\) 34208.2i 0.167438i
\(453\) 183334. 0.893402
\(454\) 229949. 1.11563
\(455\) 523545.i 2.52890i
\(456\) −62145.5 62932.2i −0.298868 0.302652i
\(457\) 89688.2 0.429440 0.214720 0.976676i \(-0.431116\pi\)
0.214720 + 0.976676i \(0.431116\pi\)
\(458\) 263573.i 1.25652i
\(459\) 118488.i 0.562405i
\(460\) −56457.0 −0.266810
\(461\) −71209.7 −0.335071 −0.167536 0.985866i \(-0.553581\pi\)
−0.167536 + 0.985866i \(0.553581\pi\)
\(462\) −302525. −1.41735
\(463\) −96472.6 −0.450030 −0.225015 0.974355i \(-0.572243\pi\)
−0.225015 + 0.974355i \(0.572243\pi\)
\(464\) 72387.2i 0.336222i
\(465\) −294679. −1.36284
\(466\) 9557.51i 0.0440122i
\(467\) 337202. 1.54617 0.773084 0.634304i \(-0.218713\pi\)
0.773084 + 0.634304i \(0.218713\pi\)
\(468\) 67210.8i 0.306865i
\(469\) 602675.i 2.73992i
\(470\) 62003.6i 0.280686i
\(471\) 61554.5i 0.277471i
\(472\) −111402. −0.500046
\(473\) −265809. −1.18808
\(474\) 38710.1i 0.172293i
\(475\) 15978.5 + 16180.8i 0.0708189 + 0.0717154i
\(476\) −168371. −0.743109
\(477\) 23778.6i 0.104508i
\(478\) 101591.i 0.444630i
\(479\) 126684. 0.552143 0.276071 0.961137i \(-0.410967\pi\)
0.276071 + 0.961137i \(0.410967\pi\)
\(480\) −51410.1 −0.223134
\(481\) 70207.1 0.303453
\(482\) 162216. 0.698233
\(483\) 250798.i 1.07505i
\(484\) 11800.0 0.0503722
\(485\) 342059.i 1.45418i
\(486\) −139565. −0.590886
\(487\) 233861.i 0.986053i −0.870014 0.493027i \(-0.835891\pi\)
0.870014 0.493027i \(-0.164109\pi\)
\(488\) 35676.9i 0.149812i
\(489\) 330789.i 1.38335i
\(490\) 371734.i 1.54825i
\(491\) −423929. −1.75845 −0.879226 0.476406i \(-0.841939\pi\)
−0.879226 + 0.476406i \(0.841939\pi\)
\(492\) 153302. 0.633314
\(493\) 276503.i 1.13764i
\(494\) 166338. + 168444.i 0.681614 + 0.690243i
\(495\) 109060. 0.445096
\(496\) 66405.8i 0.269925i
\(497\) 353082.i 1.42943i
\(498\) 31240.3 0.125967
\(499\) −175944. −0.706600 −0.353300 0.935510i \(-0.614941\pi\)
−0.353300 + 0.935510i \(0.614941\pi\)
\(500\) −117930. −0.471719
\(501\) −305787. −1.21827
\(502\) 148455.i 0.589098i
\(503\) 108798. 0.430017 0.215009 0.976612i \(-0.431022\pi\)
0.215009 + 0.976612i \(0.431022\pi\)
\(504\) 70589.1i 0.277892i
\(505\) 124744. 0.489143
\(506\) 87318.8i 0.341041i
\(507\) 272776.i 1.06118i
\(508\) 36008.0i 0.139531i
\(509\) 72826.1i 0.281094i −0.990074 0.140547i \(-0.955114\pi\)
0.990074 0.140547i \(-0.0448861\pi\)
\(510\) 196375. 0.754999
\(511\) −604188. −2.31383
\(512\) 11585.2i 0.0441942i
\(513\) 124498. 122942.i 0.473073 0.467159i
\(514\) 241046. 0.912375
\(515\) 228927.i 0.863141i
\(516\) 200661.i 0.753641i
\(517\) −95897.4 −0.358778
\(518\) 73736.1 0.274802
\(519\) −386253. −1.43396
\(520\) 137604. 0.508891
\(521\) 93748.1i 0.345372i −0.984977 0.172686i \(-0.944755\pi\)
0.984977 0.172686i \(-0.0552446\pi\)
\(522\) −115924. −0.425433
\(523\) 87245.8i 0.318964i −0.987201 0.159482i \(-0.949018\pi\)
0.987201 0.159482i \(-0.0509823\pi\)
\(524\) −220850. −0.804332
\(525\) 58719.4i 0.213041i
\(526\) 77893.6i 0.281534i
\(527\) 253656.i 0.913321i
\(528\) 79513.0i 0.285214i
\(529\) −207452. −0.741322
\(530\) −48683.1 −0.173311
\(531\) 178404.i 0.632724i
\(532\) 174699. + 176911.i 0.617260 + 0.625074i
\(533\) −410329. −1.44437
\(534\) 114730.i 0.402343i
\(535\) 442884.i 1.54733i
\(536\) 158402. 0.551354
\(537\) 372160. 1.29057
\(538\) 166538. 0.575371
\(539\) 574940. 1.97900
\(540\) 101704.i 0.348779i
\(541\) 374060. 1.27805 0.639024 0.769187i \(-0.279338\pi\)
0.639024 + 0.769187i \(0.279338\pi\)
\(542\) 282716.i 0.962391i
\(543\) 316112. 1.07211
\(544\) 44253.1i 0.149536i
\(545\) 5387.63i 0.0181386i
\(546\) 611277.i 2.05047i
\(547\) 160411.i 0.536118i −0.963402 0.268059i \(-0.913618\pi\)
0.963402 0.268059i \(-0.0863823\pi\)
\(548\) −66002.3 −0.219785
\(549\) 57134.3 0.189562
\(550\) 20443.9i 0.0675833i
\(551\) 290528. 286896.i 0.956941 0.944978i
\(552\) 65917.7 0.216334
\(553\) 108819.i 0.355841i
\(554\) 187520.i 0.610980i
\(555\) −86000.4 −0.279199
\(556\) −219480. −0.709978
\(557\) 460605. 1.48463 0.742314 0.670052i \(-0.233728\pi\)
0.742314 + 0.670052i \(0.233728\pi\)
\(558\) 106345. 0.341545
\(559\) 537090.i 1.71879i
\(560\) 144521. 0.460844
\(561\) 303722.i 0.965053i
\(562\) 155626. 0.492729
\(563\) 73084.0i 0.230571i 0.993332 + 0.115286i \(0.0367783\pi\)
−0.993332 + 0.115286i \(0.963222\pi\)
\(564\) 72393.7i 0.227585i
\(565\) 112158.i 0.351346i
\(566\) 29911.3i 0.0933690i
\(567\) 704489. 2.19133
\(568\) −92801.0 −0.287644
\(569\) 609592.i 1.88285i 0.337227 + 0.941424i \(0.390511\pi\)
−0.337227 + 0.941424i \(0.609489\pi\)
\(570\) −203757. 206336.i −0.627136 0.635075i
\(571\) −11273.0 −0.0345755 −0.0172877 0.999851i \(-0.505503\pi\)
−0.0172877 + 0.999851i \(0.505503\pi\)
\(572\) 212824.i 0.650473i
\(573\) 146153.i 0.445143i
\(574\) −430954. −1.30800
\(575\) −16948.4 −0.0512617
\(576\) 18553.0 0.0559204
\(577\) −186962. −0.561567 −0.280783 0.959771i \(-0.590594\pi\)
−0.280783 + 0.959771i \(0.590594\pi\)
\(578\) 67195.9i 0.201135i
\(579\) −225427. −0.672433
\(580\) 237336.i 0.705518i
\(581\) −87820.8 −0.260163
\(582\) 399379.i 1.17907i
\(583\) 75295.4i 0.221529i
\(584\) 158800.i 0.465612i
\(585\) 220364.i 0.643916i
\(586\) −26727.8 −0.0778337
\(587\) −258778. −0.751020 −0.375510 0.926818i \(-0.622532\pi\)
−0.375510 + 0.926818i \(0.622532\pi\)
\(588\) 434027.i 1.25534i
\(589\) −266522. + 263190.i −0.768250 + 0.758645i
\(590\) −365255. −1.04928
\(591\) 370665.i 1.06122i
\(592\) 19380.2i 0.0552986i
\(593\) −603214. −1.71539 −0.857693 0.514162i \(-0.828103\pi\)
−0.857693 + 0.514162i \(0.828103\pi\)
\(594\) 157300. 0.445816
\(595\) −552037. −1.55932
\(596\) 321979. 0.906430
\(597\) 600975.i 1.68619i
\(598\) −176435. −0.493381
\(599\) 32971.2i 0.0918927i −0.998944 0.0459464i \(-0.985370\pi\)
0.998944 0.0459464i \(-0.0146303\pi\)
\(600\) −15433.3 −0.0428703
\(601\) 61000.3i 0.168882i −0.996428 0.0844410i \(-0.973090\pi\)
0.996428 0.0844410i \(-0.0269104\pi\)
\(602\) 564086.i 1.55651i
\(603\) 253671.i 0.697647i
\(604\) 135457.i 0.371303i
\(605\) 38688.6 0.105699
\(606\) −145648. −0.396605
\(607\) 252238.i 0.684594i −0.939592 0.342297i \(-0.888795\pi\)
0.939592 0.342297i \(-0.111205\pi\)
\(608\) −46497.7 + 45916.4i −0.125784 + 0.124211i
\(609\) 1.05432e6 2.84273
\(610\) 116974.i 0.314361i
\(611\) 193769.i 0.519041i
\(612\) −70868.6 −0.189213
\(613\) 384604. 1.02351 0.511757 0.859131i \(-0.328995\pi\)
0.511757 + 0.859131i \(0.328995\pi\)
\(614\) −318544. −0.844953
\(615\) 502633. 1.32893
\(616\) 223522.i 0.589058i
\(617\) 89917.4 0.236197 0.118098 0.993002i \(-0.462320\pi\)
0.118098 + 0.993002i \(0.462320\pi\)
\(618\) 267289.i 0.699847i
\(619\) −133253. −0.347772 −0.173886 0.984766i \(-0.555632\pi\)
−0.173886 + 0.984766i \(0.555632\pi\)
\(620\) 217725.i 0.566402i
\(621\) 130404.i 0.338150i
\(622\) 214618.i 0.554735i
\(623\) 322523.i 0.830968i
\(624\) −160663. −0.412616
\(625\) −426028. −1.09063
\(626\) 313842.i 0.800870i
\(627\) 319128. 315139.i 0.811764 0.801616i
\(628\) −45479.8 −0.115319
\(629\) 74028.0i 0.187109i
\(630\) 231441.i 0.583121i
\(631\) 250184. 0.628348 0.314174 0.949365i \(-0.398273\pi\)
0.314174 + 0.949365i \(0.398273\pi\)
\(632\) 28601.1 0.0716059
\(633\) −839705. −2.09565
\(634\) −180935. −0.450136
\(635\) 118060.i 0.292788i
\(636\) 56841.1 0.140523
\(637\) 1.16171e6i 2.86299i
\(638\) 367074. 0.901804
\(639\) 148615.i 0.363966i
\(640\) 37984.6i 0.0927357i
\(641\) 601164.i 1.46311i −0.681782 0.731555i \(-0.738795\pi\)
0.681782 0.731555i \(-0.261205\pi\)
\(642\) 517099.i 1.25460i
\(643\) 379057. 0.916816 0.458408 0.888742i \(-0.348420\pi\)
0.458408 + 0.888742i \(0.348420\pi\)
\(644\) −185304. −0.446799
\(645\) 657909.i 1.58142i
\(646\) 177611. 175391.i 0.425604 0.420283i
\(647\) 245678. 0.586892 0.293446 0.955976i \(-0.405198\pi\)
0.293446 + 0.955976i \(0.405198\pi\)
\(648\) 185162.i 0.440962i
\(649\) 564918.i 1.34121i
\(650\) 41308.7 0.0977722
\(651\) −967198. −2.28220
\(652\) 244405. 0.574929
\(653\) −15905.7 −0.0373016 −0.0186508 0.999826i \(-0.505937\pi\)
−0.0186508 + 0.999826i \(0.505937\pi\)
\(654\) 6290.45i 0.0147071i
\(655\) −724102. −1.68779
\(656\) 113268.i 0.263209i
\(657\) −254308. −0.589154
\(658\) 203509.i 0.470036i
\(659\) 481053.i 1.10770i −0.832617 0.553850i \(-0.813158\pi\)
0.832617 0.553850i \(-0.186842\pi\)
\(660\) 260700.i 0.598484i
\(661\) 468775.i 1.07290i 0.843931 + 0.536452i \(0.180236\pi\)
−0.843931 + 0.536452i \(0.819764\pi\)
\(662\) −224754. −0.512852
\(663\) 613697. 1.39613
\(664\) 23082.0i 0.0523526i
\(665\) 572787. + 580038.i 1.29524 + 1.31164i
\(666\) 31036.1 0.0699711
\(667\) 304311.i 0.684015i
\(668\) 225932.i 0.506320i
\(669\) 332994. 0.744020
\(670\) 519352. 1.15694
\(671\) −180917. −0.401822
\(672\) −168738. −0.373659
\(673\) 229158.i 0.505947i −0.967473 0.252973i \(-0.918592\pi\)
0.967473 0.252973i \(-0.0814085\pi\)
\(674\) −7862.46 −0.0173077
\(675\) 30531.6i 0.0670103i
\(676\) 201541. 0.441033
\(677\) 38248.1i 0.0834512i 0.999129 + 0.0417256i \(0.0132855\pi\)
−0.999129 + 0.0417256i \(0.986714\pi\)
\(678\) 130953.i 0.284876i
\(679\) 1.12271e6i 2.43516i
\(680\) 145093.i 0.313782i
\(681\) −880274. −1.89812
\(682\) −336743. −0.723985
\(683\) 31694.5i 0.0679426i −0.999423 0.0339713i \(-0.989185\pi\)
0.999423 0.0339713i \(-0.0108155\pi\)
\(684\) 73532.3 + 74463.2i 0.157169 + 0.159158i
\(685\) −216402. −0.461190
\(686\) 635459.i 1.35033i
\(687\) 1.00899e6i 2.13783i
\(688\) −148260. −0.313217
\(689\) −152141. −0.320484
\(690\) 216125. 0.453948
\(691\) 140291. 0.293815 0.146907 0.989150i \(-0.453068\pi\)
0.146907 + 0.989150i \(0.453068\pi\)
\(692\) 285384.i 0.595961i
\(693\) 357956. 0.745355
\(694\) 44485.7i 0.0923637i
\(695\) −719609. −1.48980
\(696\) 277107.i 0.572044i
\(697\) 432660.i 0.890597i
\(698\) 118179.i 0.242565i
\(699\) 36587.3i 0.0748818i
\(700\) 43385.1 0.0885410
\(701\) 550797. 1.12087 0.560436 0.828198i \(-0.310634\pi\)
0.560436 + 0.828198i \(0.310634\pi\)
\(702\) 317838.i 0.644958i
\(703\) −77782.9 + 76810.5i −0.157389 + 0.155421i
\(704\) −58748.5 −0.118536
\(705\) 237358.i 0.477557i
\(706\) 111135.i 0.222967i
\(707\) 409435. 0.819117
\(708\) 426461. 0.850772
\(709\) 725719. 1.44370 0.721848 0.692051i \(-0.243293\pi\)
0.721848 + 0.692051i \(0.243293\pi\)
\(710\) −304267. −0.603584
\(711\) 45802.9i 0.0906053i
\(712\) −84769.1 −0.167216
\(713\) 279166.i 0.549140i
\(714\) 644544. 1.26432
\(715\) 697787.i 1.36493i
\(716\) 274972.i 0.536367i
\(717\) 388903.i 0.756489i
\(718\) 455275.i 0.883131i
\(719\) 184282. 0.356472 0.178236 0.983988i \(-0.442961\pi\)
0.178236 + 0.983988i \(0.442961\pi\)
\(720\) 60829.9 0.117342
\(721\) 751384.i 1.44541i
\(722\) −368574. 4636.83i −0.707051 0.00889501i
\(723\) −620985. −1.18797
\(724\) 233561.i 0.445577i
\(725\) 71248.3i 0.135550i
\(726\) −45171.8 −0.0857027
\(727\) −30302.5 −0.0573336 −0.0286668 0.999589i \(-0.509126\pi\)
−0.0286668 + 0.999589i \(0.509126\pi\)
\(728\) 451645. 0.852186
\(729\) −128557. −0.241902
\(730\) 520657.i 0.977025i
\(731\) 566319. 1.05981
\(732\) 136575.i 0.254889i
\(733\) 210592. 0.391954 0.195977 0.980609i \(-0.437212\pi\)
0.195977 + 0.980609i \(0.437212\pi\)
\(734\) 56102.9i 0.104134i
\(735\) 1.42304e6i 2.63417i
\(736\) 48703.6i 0.0899094i
\(737\) 803252.i 1.47883i
\(738\) −181392. −0.333047
\(739\) −257029. −0.470645 −0.235323 0.971917i \(-0.575615\pi\)
−0.235323 + 0.971917i \(0.575615\pi\)
\(740\) 63541.8i 0.116037i
\(741\) −636764. 644825.i −1.15969 1.17437i
\(742\) −159788. −0.290226
\(743\) 459249.i 0.831899i −0.909388 0.415949i \(-0.863449\pi\)
0.909388 0.415949i \(-0.136551\pi\)
\(744\) 254210.i 0.459247i
\(745\) 1.05567e6 1.90203
\(746\) 40909.0 0.0735091
\(747\) −36964.5 −0.0662435
\(748\) 224407. 0.401081
\(749\) 1.45364e6i 2.59115i
\(750\) 451450. 0.802578
\(751\) 705805.i 1.25142i −0.780054 0.625712i \(-0.784808\pi\)
0.780054 0.625712i \(-0.215192\pi\)
\(752\) −53488.4 −0.0945854
\(753\) 568305.i 1.00228i
\(754\) 741704.i 1.30463i
\(755\) 444124.i 0.779130i
\(756\) 333814.i 0.584064i
\(757\) 128249. 0.223801 0.111901 0.993719i \(-0.464306\pi\)
0.111901 + 0.993719i \(0.464306\pi\)
\(758\) 73348.8 0.127660
\(759\) 334267.i 0.580244i
\(760\) −152452. + 150546.i −0.263941 + 0.260641i
\(761\) 779962. 1.34680 0.673402 0.739277i \(-0.264833\pi\)
0.673402 + 0.739277i \(0.264833\pi\)
\(762\) 137843.i 0.237397i
\(763\) 17683.3i 0.0303749i
\(764\) −107986. −0.185004
\(765\) −232357. −0.397039
\(766\) 27251.8 0.0464449
\(767\) −1.14147e6 −1.94031
\(768\) 44349.7i 0.0751915i
\(769\) −50722.8 −0.0857730 −0.0428865 0.999080i \(-0.513655\pi\)
−0.0428865 + 0.999080i \(0.513655\pi\)
\(770\) 732861.i 1.23606i
\(771\) −922754. −1.55230
\(772\) 166558.i 0.279467i
\(773\) 942086.i 1.57664i 0.615267 + 0.788318i \(0.289048\pi\)
−0.615267 + 0.788318i \(0.710952\pi\)
\(774\) 237428.i 0.396324i
\(775\) 65361.0i 0.108822i
\(776\) −295083. −0.490028
\(777\) −282271. −0.467546
\(778\) 288188.i 0.476120i
\(779\) 454606. 448922.i 0.749135 0.739769i
\(780\) −526766. −0.865821
\(781\) 470592.i 0.771511i
\(782\) 186037.i 0.304219i
\(783\) −548199. −0.894159
\(784\) 320683. 0.521727
\(785\) −149115. −0.241981
\(786\) 845443. 1.36848
\(787\) 764737.i