Properties

Label 33.5.c.a.10.2
Level $33$
Weight $5$
Character 33.10
Analytic conductor $3.411$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 102 x^{6} + 2913 x^{4} + 23292 x^{2} + 41364\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.2
Root \(-5.58567i\) of defining polynomial
Character \(\chi\) \(=\) 33.10
Dual form 33.5.c.a.10.7

$q$-expansion

\(f(q)\) \(=\) \(q-5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} +29.0240i q^{6} +12.9420i q^{7} -4.47031i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} +29.0240i q^{6} +12.9420i q^{7} -4.47031i q^{8} +27.0000 q^{9} +166.166i q^{10} +(-100.434 - 67.4829i) q^{11} +78.9799 q^{12} +36.6685i q^{13} +72.2898 q^{14} +154.579 q^{15} -268.165 q^{16} -464.257i q^{17} -150.813i q^{18} -327.633i q^{19} +452.171 q^{20} -67.2487i q^{21} +(-376.937 + 560.993i) q^{22} +396.812 q^{23} +23.2284i q^{24} +259.987 q^{25} +204.818 q^{26} -140.296 q^{27} -196.715i q^{28} +1152.21i q^{29} -863.426i q^{30} +437.378 q^{31} +1426.35i q^{32} +(521.872 + 350.651i) q^{33} -2593.18 q^{34} -385.009i q^{35} -410.391 q^{36} +276.604 q^{37} -1830.05 q^{38} -190.535i q^{39} +132.986i q^{40} -2782.30i q^{41} -375.629 q^{42} +1663.84i q^{43} +(1526.57 + 1025.72i) q^{44} -803.216 q^{45} -2216.46i q^{46} -1855.68 q^{47} +1393.42 q^{48} +2233.50 q^{49} -1452.20i q^{50} +2412.35i q^{51} -557.350i q^{52} +3745.57 q^{53} +783.647i q^{54} +(2987.79 + 2007.53i) q^{55} +57.8549 q^{56} +1702.43i q^{57} +6435.88 q^{58} -6573.17 q^{59} -2349.55 q^{60} -5140.56i q^{61} -2443.05i q^{62} +349.435i q^{63} +3676.50 q^{64} -1090.84i q^{65} +(1958.62 - 2915.00i) q^{66} -3464.58 q^{67} +7056.56i q^{68} -2061.90 q^{69} -2150.53 q^{70} -6031.86 q^{71} -120.698i q^{72} -3580.96i q^{73} -1545.02i q^{74} -1350.93 q^{75} +4979.92i q^{76} +(873.365 - 1299.82i) q^{77} -1064.27 q^{78} -9711.53i q^{79} +7977.55 q^{80} +729.000 q^{81} -15541.0 q^{82} +11837.3i q^{83} +1022.16i q^{84} +13811.1i q^{85} +9293.66 q^{86} -5987.07i q^{87} +(-301.670 + 448.973i) q^{88} +2584.72 q^{89} +4486.50i q^{90} -474.565 q^{91} -6031.42 q^{92} -2272.69 q^{93} +10365.2i q^{94} +9746.67i q^{95} -7411.55i q^{96} +1551.68 q^{97} -12475.6i q^{98} +(-2711.73 - 1822.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10}) \) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.58567i 1.39642i −0.715895 0.698208i \(-0.753981\pi\)
0.715895 0.698208i \(-0.246019\pi\)
\(3\) −5.19615 −0.577350
\(4\) −15.1997 −0.949980
\(5\) −29.7487 −1.18995 −0.594974 0.803745i \(-0.702838\pi\)
−0.594974 + 0.803745i \(0.702838\pi\)
\(6\) 29.0240i 0.806222i
\(7\) 12.9420i 0.264123i 0.991242 + 0.132061i \(0.0421596\pi\)
−0.991242 + 0.132061i \(0.957840\pi\)
\(8\) 4.47031i 0.0698486i
\(9\) 27.0000 0.333333
\(10\) 166.166i 1.66166i
\(11\) −100.434 67.4829i −0.830036 0.557710i
\(12\) 78.9799 0.548471
\(13\) 36.6685i 0.216973i 0.994098 + 0.108487i \(0.0346005\pi\)
−0.994098 + 0.108487i \(0.965399\pi\)
\(14\) 72.2898 0.368826
\(15\) 154.579 0.687017
\(16\) −268.165 −1.04752
\(17\) 464.257i 1.60643i −0.595692 0.803213i \(-0.703122\pi\)
0.595692 0.803213i \(-0.296878\pi\)
\(18\) 150.813i 0.465472i
\(19\) 327.633i 0.907571i −0.891111 0.453786i \(-0.850073\pi\)
0.891111 0.453786i \(-0.149927\pi\)
\(20\) 452.171 1.13043
\(21\) 67.2487i 0.152491i
\(22\) −376.937 + 560.993i −0.778796 + 1.15908i
\(23\) 396.812 0.750118 0.375059 0.927001i \(-0.377622\pi\)
0.375059 + 0.927001i \(0.377622\pi\)
\(24\) 23.2284i 0.0403271i
\(25\) 259.987 0.415979
\(26\) 204.818 0.302985
\(27\) −140.296 −0.192450
\(28\) 196.715i 0.250911i
\(29\) 1152.21i 1.37005i 0.728519 + 0.685025i \(0.240209\pi\)
−0.728519 + 0.685025i \(0.759791\pi\)
\(30\) 863.426i 0.959363i
\(31\) 437.378 0.455128 0.227564 0.973763i \(-0.426924\pi\)
0.227564 + 0.973763i \(0.426924\pi\)
\(32\) 1426.35i 1.39292i
\(33\) 521.872 + 350.651i 0.479221 + 0.321994i
\(34\) −2593.18 −2.24324
\(35\) 385.009i 0.314293i
\(36\) −410.391 −0.316660
\(37\) 276.604 0.202049 0.101024 0.994884i \(-0.467788\pi\)
0.101024 + 0.994884i \(0.467788\pi\)
\(38\) −1830.05 −1.26735
\(39\) 190.535i 0.125270i
\(40\) 132.986i 0.0831163i
\(41\) 2782.30i 1.65515i −0.561358 0.827573i \(-0.689721\pi\)
0.561358 0.827573i \(-0.310279\pi\)
\(42\) −375.629 −0.212942
\(43\) 1663.84i 0.899860i 0.893064 + 0.449930i \(0.148551\pi\)
−0.893064 + 0.449930i \(0.851449\pi\)
\(44\) 1526.57 + 1025.72i 0.788518 + 0.529813i
\(45\) −803.216 −0.396650
\(46\) 2216.46i 1.04748i
\(47\) −1855.68 −0.840053 −0.420026 0.907512i \(-0.637979\pi\)
−0.420026 + 0.907512i \(0.637979\pi\)
\(48\) 1393.42 0.604785
\(49\) 2233.50 0.930239
\(50\) 1452.20i 0.580880i
\(51\) 2412.35i 0.927470i
\(52\) 557.350i 0.206120i
\(53\) 3745.57 1.33342 0.666709 0.745318i \(-0.267702\pi\)
0.666709 + 0.745318i \(0.267702\pi\)
\(54\) 783.647i 0.268741i
\(55\) 2987.79 + 2007.53i 0.987700 + 0.663646i
\(56\) 57.8549 0.0184486
\(57\) 1702.43i 0.523986i
\(58\) 6435.88 1.91316
\(59\) −6573.17 −1.88830 −0.944150 0.329516i \(-0.893114\pi\)
−0.944150 + 0.329516i \(0.893114\pi\)
\(60\) −2349.55 −0.652653
\(61\) 5140.56i 1.38150i −0.723094 0.690750i \(-0.757281\pi\)
0.723094 0.690750i \(-0.242719\pi\)
\(62\) 2443.05i 0.635549i
\(63\) 349.435i 0.0880410i
\(64\) 3676.50 0.897583
\(65\) 1090.84i 0.258187i
\(66\) 1958.62 2915.00i 0.449638 0.669193i
\(67\) −3464.58 −0.771793 −0.385897 0.922542i \(-0.626108\pi\)
−0.385897 + 0.922542i \(0.626108\pi\)
\(68\) 7056.56i 1.52607i
\(69\) −2061.90 −0.433081
\(70\) −2150.53 −0.438884
\(71\) −6031.86 −1.19656 −0.598280 0.801287i \(-0.704149\pi\)
−0.598280 + 0.801287i \(0.704149\pi\)
\(72\) 120.698i 0.0232829i
\(73\) 3580.96i 0.671976i −0.941866 0.335988i \(-0.890930\pi\)
0.941866 0.335988i \(-0.109070\pi\)
\(74\) 1545.02i 0.282144i
\(75\) −1350.93 −0.240165
\(76\) 4979.92i 0.862174i
\(77\) 873.365 1299.82i 0.147304 0.219231i
\(78\) −1064.27 −0.174929
\(79\) 9711.53i 1.55609i −0.628211 0.778043i \(-0.716213\pi\)
0.628211 0.778043i \(-0.283787\pi\)
\(80\) 7977.55 1.24649
\(81\) 729.000 0.111111
\(82\) −15541.0 −2.31127
\(83\) 11837.3i 1.71829i 0.511729 + 0.859147i \(0.329005\pi\)
−0.511729 + 0.859147i \(0.670995\pi\)
\(84\) 1022.16i 0.144864i
\(85\) 13811.1i 1.91156i
\(86\) 9293.66 1.25658
\(87\) 5987.07i 0.790999i
\(88\) −301.670 + 448.973i −0.0389553 + 0.0579769i
\(89\) 2584.72 0.326312 0.163156 0.986600i \(-0.447833\pi\)
0.163156 + 0.986600i \(0.447833\pi\)
\(90\) 4486.50i 0.553888i
\(91\) −474.565 −0.0573077
\(92\) −6031.42 −0.712597
\(93\) −2272.69 −0.262769
\(94\) 10365.2i 1.17306i
\(95\) 9746.67i 1.07996i
\(96\) 7411.55i 0.804205i
\(97\) 1551.68 0.164915 0.0824574 0.996595i \(-0.473723\pi\)
0.0824574 + 0.996595i \(0.473723\pi\)
\(98\) 12475.6i 1.29900i
\(99\) −2711.73 1822.04i −0.276679 0.185903i
\(100\) −3951.71 −0.395171
\(101\) 3939.16i 0.386154i −0.981184 0.193077i \(-0.938153\pi\)
0.981184 0.193077i \(-0.0618468\pi\)
\(102\) 13474.6 1.29513
\(103\) 12210.1 1.15092 0.575459 0.817830i \(-0.304823\pi\)
0.575459 + 0.817830i \(0.304823\pi\)
\(104\) 163.920 0.0151553
\(105\) 2000.56i 0.181457i
\(106\) 20921.5i 1.86201i
\(107\) 3756.40i 0.328099i 0.986452 + 0.164049i \(0.0524556\pi\)
−0.986452 + 0.164049i \(0.947544\pi\)
\(108\) 2132.46 0.182824
\(109\) 15338.3i 1.29099i −0.763764 0.645495i \(-0.776651\pi\)
0.763764 0.645495i \(-0.223349\pi\)
\(110\) 11213.4 16688.8i 0.926727 1.37924i
\(111\) −1437.28 −0.116653
\(112\) 3470.59i 0.276673i
\(113\) −7205.76 −0.564316 −0.282158 0.959368i \(-0.591050\pi\)
−0.282158 + 0.959368i \(0.591050\pi\)
\(114\) 9509.22 0.731703
\(115\) −11804.7 −0.892602
\(116\) 17513.3i 1.30152i
\(117\) 990.050i 0.0723245i
\(118\) 36715.6i 2.63685i
\(119\) 6008.42 0.424294
\(120\) 691.016i 0.0479872i
\(121\) 5533.12 + 13555.2i 0.377919 + 0.925839i
\(122\) −28713.5 −1.92915
\(123\) 14457.3i 0.955599i
\(124\) −6648.01 −0.432363
\(125\) 10858.7 0.694956
\(126\) 1951.83 0.122942
\(127\) 10757.4i 0.666960i 0.942757 + 0.333480i \(0.108223\pi\)
−0.942757 + 0.333480i \(0.891777\pi\)
\(128\) 2285.94i 0.139523i
\(129\) 8645.57i 0.519534i
\(130\) −6093.08 −0.360537
\(131\) 14623.4i 0.852131i −0.904692 0.426066i \(-0.859899\pi\)
0.904692 0.426066i \(-0.140101\pi\)
\(132\) −7932.29 5329.79i −0.455251 0.305888i
\(133\) 4240.24 0.239710
\(134\) 19352.0i 1.07775i
\(135\) 4173.63 0.229006
\(136\) −2075.37 −0.112207
\(137\) 25143.7 1.33964 0.669821 0.742523i \(-0.266371\pi\)
0.669821 + 0.742523i \(0.266371\pi\)
\(138\) 11517.1i 0.604761i
\(139\) 4454.38i 0.230546i −0.993334 0.115273i \(-0.963226\pi\)
0.993334 0.115273i \(-0.0367743\pi\)
\(140\) 5852.01i 0.298572i
\(141\) 9642.38 0.485005
\(142\) 33692.0i 1.67090i
\(143\) 2474.50 3682.78i 0.121008 0.180096i
\(144\) −7240.44 −0.349173
\(145\) 34276.9i 1.63029i
\(146\) −20002.0 −0.938358
\(147\) −11605.6 −0.537074
\(148\) −4204.30 −0.191942
\(149\) 21755.9i 0.979950i 0.871737 + 0.489975i \(0.162994\pi\)
−0.871737 + 0.489975i \(0.837006\pi\)
\(150\) 7545.85i 0.335371i
\(151\) 20736.4i 0.909450i −0.890632 0.454725i \(-0.849738\pi\)
0.890632 0.454725i \(-0.150262\pi\)
\(152\) −1464.62 −0.0633926
\(153\) 12534.9i 0.535475i
\(154\) −7260.38 4878.33i −0.306139 0.205698i
\(155\) −13011.5 −0.541580
\(156\) 2896.07i 0.119004i
\(157\) −16991.5 −0.689340 −0.344670 0.938724i \(-0.612009\pi\)
−0.344670 + 0.938724i \(0.612009\pi\)
\(158\) −54245.4 −2.17294
\(159\) −19462.6 −0.769850
\(160\) 42432.2i 1.65751i
\(161\) 5135.55i 0.198123i
\(162\) 4071.95i 0.155157i
\(163\) 15654.2 0.589192 0.294596 0.955622i \(-0.404815\pi\)
0.294596 + 0.955622i \(0.404815\pi\)
\(164\) 42290.1i 1.57236i
\(165\) −15525.0 10431.4i −0.570249 0.383156i
\(166\) 66119.4 2.39945
\(167\) 13741.9i 0.492734i 0.969177 + 0.246367i \(0.0792369\pi\)
−0.969177 + 0.246367i \(0.920763\pi\)
\(168\) −300.623 −0.0106513
\(169\) 27216.4 0.952923
\(170\) 77143.9 2.66934
\(171\) 8846.10i 0.302524i
\(172\) 25289.9i 0.854849i
\(173\) 41623.1i 1.39073i −0.718657 0.695365i \(-0.755243\pi\)
0.718657 0.695365i \(-0.244757\pi\)
\(174\) −33441.8 −1.10456
\(175\) 3364.75i 0.109869i
\(176\) 26932.9 + 18096.5i 0.869478 + 0.584211i
\(177\) 34155.2 1.09021
\(178\) 14437.4i 0.455668i
\(179\) −17574.8 −0.548510 −0.274255 0.961657i \(-0.588431\pi\)
−0.274255 + 0.961657i \(0.588431\pi\)
\(180\) 12208.6 0.376809
\(181\) 10371.8 0.316588 0.158294 0.987392i \(-0.449401\pi\)
0.158294 + 0.987392i \(0.449401\pi\)
\(182\) 2650.76i 0.0800254i
\(183\) 26711.1i 0.797609i
\(184\) 1773.88i 0.0523947i
\(185\) −8228.63 −0.240427
\(186\) 12694.5i 0.366934i
\(187\) −31329.4 + 46627.3i −0.895919 + 1.33339i
\(188\) 28205.7 0.798034
\(189\) 1815.72i 0.0508305i
\(190\) 54441.7 1.50808
\(191\) −2219.45 −0.0608386 −0.0304193 0.999537i \(-0.509684\pi\)
−0.0304193 + 0.999537i \(0.509684\pi\)
\(192\) −19103.7 −0.518220
\(193\) 18368.1i 0.493117i −0.969128 0.246559i \(-0.920700\pi\)
0.969128 0.246559i \(-0.0792998\pi\)
\(194\) 8667.19i 0.230290i
\(195\) 5668.18i 0.149065i
\(196\) −33948.6 −0.883709
\(197\) 23671.0i 0.609936i −0.952363 0.304968i \(-0.901354\pi\)
0.952363 0.304968i \(-0.0986458\pi\)
\(198\) −10177.3 + 15146.8i −0.259599 + 0.386359i
\(199\) −27214.8 −0.687226 −0.343613 0.939111i \(-0.611651\pi\)
−0.343613 + 0.939111i \(0.611651\pi\)
\(200\) 1162.22i 0.0290555i
\(201\) 18002.5 0.445595
\(202\) −22002.8 −0.539232
\(203\) −14912.0 −0.361862
\(204\) 36666.9i 0.881078i
\(205\) 82769.9i 1.96954i
\(206\) 68201.5i 1.60716i
\(207\) 10713.9 0.250039
\(208\) 9833.20i 0.227284i
\(209\) −22109.6 + 32905.6i −0.506161 + 0.753317i
\(210\) 11174.5 0.253390
\(211\) 7465.71i 0.167690i −0.996479 0.0838449i \(-0.973280\pi\)
0.996479 0.0838449i \(-0.0267200\pi\)
\(212\) −56931.5 −1.26672
\(213\) 31342.5 0.690834
\(214\) 20982.0 0.458162
\(215\) 49497.1i 1.07079i
\(216\) 627.167i 0.0134424i
\(217\) 5660.56i 0.120210i
\(218\) −85674.4 −1.80276
\(219\) 18607.2i 0.387965i
\(220\) −45413.5 30513.8i −0.938296 0.630451i
\(221\) 17023.6 0.348552
\(222\) 8028.16i 0.162896i
\(223\) 13654.6 0.274581 0.137291 0.990531i \(-0.456161\pi\)
0.137291 + 0.990531i \(0.456161\pi\)
\(224\) −18459.9 −0.367903
\(225\) 7019.64 0.138660
\(226\) 40249.0i 0.788021i
\(227\) 15860.1i 0.307790i 0.988087 + 0.153895i \(0.0491817\pi\)
−0.988087 + 0.153895i \(0.950818\pi\)
\(228\) 25876.4i 0.497777i
\(229\) −99238.3 −1.89238 −0.946190 0.323612i \(-0.895103\pi\)
−0.946190 + 0.323612i \(0.895103\pi\)
\(230\) 65936.9i 1.24644i
\(231\) −4538.14 + 6754.08i −0.0850460 + 0.126573i
\(232\) 5150.75 0.0956962
\(233\) 44066.2i 0.811697i −0.913940 0.405849i \(-0.866976\pi\)
0.913940 0.405849i \(-0.133024\pi\)
\(234\) 5530.09 0.100995
\(235\) 55204.0 0.999620
\(236\) 99910.1 1.79385
\(237\) 50462.6i 0.898407i
\(238\) 33561.1i 0.592491i
\(239\) 57559.5i 1.00768i 0.863798 + 0.503838i \(0.168079\pi\)
−0.863798 + 0.503838i \(0.831921\pi\)
\(240\) −41452.6 −0.719663
\(241\) 86315.0i 1.48611i 0.669228 + 0.743057i \(0.266625\pi\)
−0.669228 + 0.743057i \(0.733375\pi\)
\(242\) 75714.9 30906.2i 1.29286 0.527733i
\(243\) −3788.00 −0.0641500
\(244\) 78134.9i 1.31240i
\(245\) −66443.9 −1.10694
\(246\) 80753.4 1.33441
\(247\) 12013.8 0.196919
\(248\) 1955.22i 0.0317901i
\(249\) 61508.6i 0.992057i
\(250\) 60653.0i 0.970448i
\(251\) 93826.2 1.48928 0.744641 0.667465i \(-0.232621\pi\)
0.744641 + 0.667465i \(0.232621\pi\)
\(252\) 5311.29i 0.0836372i
\(253\) −39853.6 26778.1i −0.622625 0.418348i
\(254\) 60087.2 0.931354
\(255\) 71764.3i 1.10364i
\(256\) 71592.5 1.09241
\(257\) −24489.3 −0.370775 −0.185387 0.982666i \(-0.559354\pi\)
−0.185387 + 0.982666i \(0.559354\pi\)
\(258\) −48291.3 −0.725487
\(259\) 3579.82i 0.0533656i
\(260\) 16580.4i 0.245273i
\(261\) 31109.7i 0.456684i
\(262\) −81681.6 −1.18993
\(263\) 74432.3i 1.07609i −0.842915 0.538047i \(-0.819162\pi\)
0.842915 0.538047i \(-0.180838\pi\)
\(264\) 1567.52 2332.93i 0.0224908 0.0334730i
\(265\) −111426. −1.58670
\(266\) 23684.5i 0.334736i
\(267\) −13430.6 −0.188397
\(268\) 52660.5 0.733188
\(269\) 114719. 1.58537 0.792684 0.609633i \(-0.208683\pi\)
0.792684 + 0.609633i \(0.208683\pi\)
\(270\) 23312.5i 0.319788i
\(271\) 18016.5i 0.245319i −0.992449 0.122660i \(-0.960858\pi\)
0.992449 0.122660i \(-0.0391423\pi\)
\(272\) 124497.i 1.68276i
\(273\) 2465.91 0.0330866
\(274\) 140445.i 1.87070i
\(275\) −26111.6 17544.7i −0.345277 0.231995i
\(276\) 31340.2 0.411418
\(277\) 82563.5i 1.07604i 0.842932 + 0.538020i \(0.180828\pi\)
−0.842932 + 0.538020i \(0.819172\pi\)
\(278\) −24880.7 −0.321938
\(279\) 11809.2 0.151709
\(280\) −1721.11 −0.0219529
\(281\) 7495.15i 0.0949222i −0.998873 0.0474611i \(-0.984887\pi\)
0.998873 0.0474611i \(-0.0151130\pi\)
\(282\) 53859.1i 0.677269i
\(283\) 104220.i 1.30130i −0.759376 0.650652i \(-0.774495\pi\)
0.759376 0.650652i \(-0.225505\pi\)
\(284\) 91682.3 1.13671
\(285\) 50645.2i 0.623517i
\(286\) −20570.8 13821.7i −0.251489 0.168978i
\(287\) 36008.6 0.437162
\(288\) 38511.5i 0.464308i
\(289\) −132014. −1.58060
\(290\) −191459. −2.27656
\(291\) −8062.78 −0.0952136
\(292\) 54429.4i 0.638363i
\(293\) 54033.8i 0.629405i −0.949190 0.314703i \(-0.898095\pi\)
0.949190 0.314703i \(-0.101905\pi\)
\(294\) 64825.2i 0.749979i
\(295\) 195543. 2.24698
\(296\) 1236.51i 0.0141128i
\(297\) 14090.5 + 9467.59i 0.159740 + 0.107331i
\(298\) 121521. 1.36842
\(299\) 14550.5i 0.162756i
\(300\) 20533.7 0.228152
\(301\) −21533.5 −0.237674
\(302\) −115826. −1.26997
\(303\) 20468.5i 0.222946i
\(304\) 87859.6i 0.950697i
\(305\) 152925.i 1.64391i
\(306\) −70016.0 −0.747747
\(307\) 69862.2i 0.741251i −0.928782 0.370625i \(-0.879143\pi\)
0.928782 0.370625i \(-0.120857\pi\)
\(308\) −13274.9 + 19756.9i −0.139936 + 0.208266i
\(309\) −63445.5 −0.664483
\(310\) 72677.6i 0.756271i
\(311\) −34406.8 −0.355732 −0.177866 0.984055i \(-0.556919\pi\)
−0.177866 + 0.984055i \(0.556919\pi\)
\(312\) −851.752 −0.00874992
\(313\) 34145.2 0.348531 0.174266 0.984699i \(-0.444245\pi\)
0.174266 + 0.984699i \(0.444245\pi\)
\(314\) 94909.0i 0.962605i
\(315\) 10395.2i 0.104764i
\(316\) 147612.i 1.47825i
\(317\) 67080.7 0.667543 0.333771 0.942654i \(-0.391679\pi\)
0.333771 + 0.942654i \(0.391679\pi\)
\(318\) 108711.i 1.07503i
\(319\) 77754.6 115722.i 0.764091 1.13719i
\(320\) −109371. −1.06808
\(321\) 19518.8i 0.189428i
\(322\) 28685.5 0.276663
\(323\) −152106. −1.45795
\(324\) −11080.6 −0.105553
\(325\) 9533.32i 0.0902563i
\(326\) 87439.4i 0.822757i
\(327\) 79699.9i 0.745354i
\(328\) −12437.8 −0.115610
\(329\) 24016.2i 0.221877i
\(330\) −58266.5 + 86717.7i −0.535046 + 0.796305i
\(331\) −22562.2 −0.205933 −0.102967 0.994685i \(-0.532833\pi\)
−0.102967 + 0.994685i \(0.532833\pi\)
\(332\) 179924.i 1.63235i
\(333\) 7468.32 0.0673495
\(334\) 76757.5 0.688062
\(335\) 103067. 0.918395
\(336\) 18033.7i 0.159737i
\(337\) 54658.6i 0.481281i 0.970614 + 0.240641i \(0.0773575\pi\)
−0.970614 + 0.240641i \(0.922642\pi\)
\(338\) 152022.i 1.33068i
\(339\) 37442.2 0.325808
\(340\) 209924.i 1.81595i
\(341\) −43927.8 29515.6i −0.377773 0.253830i
\(342\) −49411.3 −0.422449
\(343\) 59979.9i 0.509820i
\(344\) 7437.89 0.0628540
\(345\) 61338.8 0.515344
\(346\) −232493. −1.94204
\(347\) 116149.i 0.964618i 0.876001 + 0.482309i \(0.160202\pi\)
−0.876001 + 0.482309i \(0.839798\pi\)
\(348\) 91001.6i 0.751433i
\(349\) 131862.i 1.08260i −0.840829 0.541301i \(-0.817932\pi\)
0.840829 0.541301i \(-0.182068\pi\)
\(350\) 18794.4 0.153424
\(351\) 5144.45i 0.0417566i
\(352\) 96254.4 143255.i 0.776847 1.15618i
\(353\) 27814.5 0.223215 0.111607 0.993752i \(-0.464400\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(354\) 190780.i 1.52239i
\(355\) 179440. 1.42385
\(356\) −39286.9 −0.309990
\(357\) −31220.7 −0.244966
\(358\) 98167.0i 0.765948i
\(359\) 75277.7i 0.584087i −0.956405 0.292044i \(-0.905665\pi\)
0.956405 0.292044i \(-0.0943352\pi\)
\(360\) 3590.62i 0.0277054i
\(361\) 22977.5 0.176315
\(362\) 57933.2i 0.442089i
\(363\) −28750.9 70434.9i −0.218192 0.534533i
\(364\) 7213.23 0.0544411
\(365\) 106529.i 0.799617i
\(366\) 149199. 1.11379
\(367\) 133254. 0.989346 0.494673 0.869079i \(-0.335288\pi\)
0.494673 + 0.869079i \(0.335288\pi\)
\(368\) −106411. −0.785762
\(369\) 75122.1i 0.551715i
\(370\) 45962.4i 0.335737i
\(371\) 48475.3i 0.352186i
\(372\) 34544.1 0.249625
\(373\) 125160.i 0.899600i 0.893129 + 0.449800i \(0.148505\pi\)
−0.893129 + 0.449800i \(0.851495\pi\)
\(374\) 260445. + 174996.i 1.86197 + 1.25108i
\(375\) −56423.4 −0.401233
\(376\) 8295.46i 0.0586766i
\(377\) −42249.9 −0.297265
\(378\) −10142.0 −0.0709805
\(379\) −138734. −0.965841 −0.482920 0.875664i \(-0.660424\pi\)
−0.482920 + 0.875664i \(0.660424\pi\)
\(380\) 148146.i 1.02594i
\(381\) 55897.1i 0.385069i
\(382\) 12397.1i 0.0849561i
\(383\) 121841. 0.830611 0.415305 0.909682i \(-0.363675\pi\)
0.415305 + 0.909682i \(0.363675\pi\)
\(384\) 11878.1i 0.0805534i
\(385\) −25981.5 + 38668.1i −0.175284 + 0.260874i
\(386\) −102598. −0.688597
\(387\) 44923.7i 0.299953i
\(388\) −23585.1 −0.156666
\(389\) 275759. 1.82234 0.911172 0.412026i \(-0.135179\pi\)
0.911172 + 0.412026i \(0.135179\pi\)
\(390\) 31660.6 0.208156
\(391\) 184223.i 1.20501i
\(392\) 9984.46i 0.0649759i
\(393\) 75985.6i 0.491978i
\(394\) −132218. −0.851725
\(395\) 288906.i 1.85166i
\(396\) 41217.4 + 27694.4i 0.262839 + 0.176604i
\(397\) −1004.21 −0.00637151 −0.00318576 0.999995i \(-0.501014\pi\)
−0.00318576 + 0.999995i \(0.501014\pi\)
\(398\) 152013.i 0.959654i
\(399\) −22032.9 −0.138397
\(400\) −69719.2 −0.435745
\(401\) −127748. −0.794447 −0.397224 0.917722i \(-0.630026\pi\)
−0.397224 + 0.917722i \(0.630026\pi\)
\(402\) 100556.i 0.622237i
\(403\) 16038.0i 0.0987508i
\(404\) 59874.0i 0.366839i
\(405\) −21686.8 −0.132217
\(406\) 83293.2i 0.505310i
\(407\) −27780.6 18666.1i −0.167708 0.112684i
\(408\) 10784.0 0.0647825
\(409\) 147696.i 0.882920i 0.897281 + 0.441460i \(0.145539\pi\)
−0.897281 + 0.441460i \(0.854461\pi\)
\(410\) 462325. 2.75030
\(411\) −130651. −0.773443
\(412\) −185590. −1.09335
\(413\) 85070.1i 0.498743i
\(414\) 59844.5i 0.349159i
\(415\) 352145.i 2.04468i
\(416\) −52302.3 −0.302227
\(417\) 23145.6i 0.133106i
\(418\) 183800. + 123497.i 1.05194 + 0.706812i
\(419\) −319997. −1.82271 −0.911355 0.411621i \(-0.864963\pi\)
−0.911355 + 0.411621i \(0.864963\pi\)
\(420\) 30407.9i 0.172381i
\(421\) −244090. −1.37716 −0.688582 0.725159i \(-0.741766\pi\)
−0.688582 + 0.725159i \(0.741766\pi\)
\(422\) −41701.0 −0.234165
\(423\) −50103.3 −0.280018
\(424\) 16743.9i 0.0931375i
\(425\) 120701.i 0.668239i
\(426\) 175069.i 0.964693i
\(427\) 66529.2 0.364886
\(428\) 57096.1i 0.311687i
\(429\) −12857.9 + 19136.3i −0.0698642 + 0.103978i
\(430\) −276475. −1.49527
\(431\) 144764.i 0.779303i −0.920962 0.389651i \(-0.872596\pi\)
0.920962 0.389651i \(-0.127404\pi\)
\(432\) 37622.4 0.201595
\(433\) −98589.6 −0.525842 −0.262921 0.964817i \(-0.584686\pi\)
−0.262921 + 0.964817i \(0.584686\pi\)
\(434\) 31618.0 0.167863
\(435\) 178108.i 0.941249i
\(436\) 233137.i 1.22642i
\(437\) 130009.i 0.680785i
\(438\) 103934. 0.541761
\(439\) 241475.i 1.25298i 0.779430 + 0.626490i \(0.215509\pi\)
−0.779430 + 0.626490i \(0.784491\pi\)
\(440\) 8974.29 13356.4i 0.0463548 0.0689895i
\(441\) 60304.6 0.310080
\(442\) 95088.3i 0.486724i
\(443\) −106301. −0.541666 −0.270833 0.962626i \(-0.587299\pi\)
−0.270833 + 0.962626i \(0.587299\pi\)
\(444\) 21846.2 0.110818
\(445\) −76892.1 −0.388295
\(446\) 76270.3i 0.383430i
\(447\) 113047.i 0.565774i
\(448\) 47581.4i 0.237072i
\(449\) −265627. −1.31759 −0.658794 0.752323i \(-0.728933\pi\)
−0.658794 + 0.752323i \(0.728933\pi\)
\(450\) 39209.4i 0.193627i
\(451\) −187758. + 279439.i −0.923091 + 1.37383i
\(452\) 109525. 0.536089
\(453\) 107749.i 0.525071i
\(454\) 88589.2 0.429803
\(455\) 14117.7 0.0681932
\(456\) 7610.40 0.0365997
\(457\) 116157.i 0.556177i −0.960556 0.278088i \(-0.910299\pi\)
0.960556 0.278088i \(-0.0897008\pi\)
\(458\) 554312.i 2.64255i
\(459\) 65133.4i 0.309157i
\(460\) 179427. 0.847954
\(461\) 121516.i 0.571784i 0.958262 + 0.285892i \(0.0922899\pi\)
−0.958262 + 0.285892i \(0.907710\pi\)
\(462\) 37726.1 + 25348.5i 0.176749 + 0.118760i
\(463\) 370675. 1.72914 0.864572 0.502509i \(-0.167590\pi\)
0.864572 + 0.502509i \(0.167590\pi\)
\(464\) 308983.i 1.43515i
\(465\) 67609.5 0.312681
\(466\) −246139. −1.13347
\(467\) 17468.5 0.0800980 0.0400490 0.999198i \(-0.487249\pi\)
0.0400490 + 0.999198i \(0.487249\pi\)
\(468\) 15048.4i 0.0687068i
\(469\) 44838.7i 0.203848i
\(470\) 308351.i 1.39589i
\(471\) 88290.6 0.397990
\(472\) 29384.1i 0.131895i
\(473\) 112281. 167107.i 0.501861 0.746916i
\(474\) 281867. 1.25455
\(475\) 85180.2i 0.377530i
\(476\) −91326.1 −0.403071
\(477\) 101130. 0.444473
\(478\) 321508. 1.40714
\(479\) 37311.4i 0.162619i −0.996689 0.0813094i \(-0.974090\pi\)
0.996689 0.0813094i \(-0.0259102\pi\)
\(480\) 220484.i 0.956962i
\(481\) 10142.7i 0.0438392i
\(482\) 482127. 2.07523
\(483\) 26685.1i 0.114387i
\(484\) −84101.6 206035.i −0.359016 0.879528i
\(485\) −46160.6 −0.196240
\(486\) 21158.5i 0.0895802i
\(487\) 177099. 0.746721 0.373360 0.927686i \(-0.378205\pi\)
0.373360 + 0.927686i \(0.378205\pi\)
\(488\) −22979.9 −0.0964958
\(489\) −81341.8 −0.340170
\(490\) 371134.i 1.54575i
\(491\) 127053.i 0.527013i −0.964658 0.263507i \(-0.915121\pi\)
0.964658 0.263507i \(-0.0848791\pi\)
\(492\) 219746.i 0.907800i
\(493\) 534923. 2.20088
\(494\) 67105.2i 0.274981i
\(495\) 80670.4 + 54203.3i 0.329233 + 0.221215i
\(496\) −117289. −0.476755
\(497\) 78064.5i 0.316039i
\(498\) −343566. −1.38533
\(499\) −166524. −0.668767 −0.334383 0.942437i \(-0.608528\pi\)
−0.334383 + 0.942437i \(0.608528\pi\)
\(500\) −165049. −0.660194
\(501\) 71404.8i 0.284480i
\(502\) 524082.i 2.07966i
\(503\) 163251.i 0.645236i 0.946529 + 0.322618i \(0.104563\pi\)
−0.946529 + 0.322618i \(0.895437\pi\)
\(504\) 1562.08 0.00614954
\(505\) 117185.i 0.459504i
\(506\) −149573. + 222609.i −0.584189 + 0.869444i
\(507\) −141421. −0.550170
\(508\) 163509.i 0.633599i
\(509\) −206271. −0.796164 −0.398082 0.917350i \(-0.630324\pi\)
−0.398082 + 0.917350i \(0.630324\pi\)
\(510\) −400852. −1.54114
\(511\) 46344.8 0.177484
\(512\) 363317.i 1.38594i
\(513\) 45965.7i 0.174662i
\(514\) 136789.i 0.517756i
\(515\) −363235. −1.36953
\(516\) 131410.i 0.493547i
\(517\) 186374. + 125226.i 0.697274 + 0.468506i
\(518\) 19995.7 0.0745207
\(519\) 216280.i 0.802938i
\(520\) −4876.40 −0.0180340
\(521\) 442001. 1.62835 0.814174 0.580620i \(-0.197190\pi\)
0.814174 + 0.580620i \(0.197190\pi\)
\(522\) 173769. 0.637721
\(523\) 373577.i 1.36577i −0.730527 0.682884i \(-0.760726\pi\)
0.730527 0.682884i \(-0.239274\pi\)
\(524\) 222271.i 0.809508i
\(525\) 17483.8i 0.0634332i
\(526\) −415754. −1.50268
\(527\) 203056.i 0.731130i
\(528\) −139948. 94032.3i −0.501993 0.337294i
\(529\) −122381. −0.437323
\(530\) 622389.i 2.21569i
\(531\) −177476. −0.629433
\(532\) −64450.2 −0.227720
\(533\) 102023. 0.359123
\(534\) 75018.9i 0.263080i
\(535\) 111748.i 0.390421i
\(536\) 15487.8i 0.0539087i
\(537\) 91321.4 0.316682
\(538\) 640781.i 2.21383i
\(539\) −224321. 150723.i −0.772132 0.518804i
\(540\) −63437.9 −0.217551
\(541\) 339954.i 1.16152i −0.814075 0.580759i \(-0.802756\pi\)
0.814075 0.580759i \(-0.197244\pi\)
\(542\) −100634. −0.342568
\(543\) −53893.2 −0.182782
\(544\) 662194. 2.23763
\(545\) 456294.i 1.53621i
\(546\) 13773.8i 0.0462027i
\(547\) 568245.i 1.89916i 0.313531 + 0.949578i \(0.398488\pi\)
−0.313531 + 0.949578i \(0.601512\pi\)
\(548\) −382177. −1.27263
\(549\) 138795.i 0.460500i
\(550\) −97998.6 + 145851.i −0.323962 + 0.482151i
\(551\) 377503. 1.24342
\(552\) 9217.33i 0.0302501i
\(553\) 125687. 0.410998
\(554\) 461172. 1.50260
\(555\) 42757.2 0.138811
\(556\) 67705.2i 0.219014i
\(557\) 211216.i 0.680795i 0.940282 + 0.340398i \(0.110562\pi\)
−0.940282 + 0.340398i \(0.889438\pi\)
\(558\) 65962.4i 0.211850i
\(559\) −61010.6 −0.195246
\(560\) 103246.i 0.329227i
\(561\) 162792. 242283.i 0.517259 0.769834i
\(562\) −41865.4 −0.132551
\(563\) 595910.i 1.88003i 0.341140 + 0.940013i \(0.389187\pi\)
−0.341140 + 0.940013i \(0.610813\pi\)
\(564\) −146561. −0.460745
\(565\) 214362. 0.671508
\(566\) −582139. −1.81716
\(567\) 9434.73i 0.0293470i
\(568\) 26964.3i 0.0835781i
\(569\) 15875.4i 0.0490342i −0.999699 0.0245171i \(-0.992195\pi\)
0.999699 0.0245171i \(-0.00780482\pi\)
\(570\) −282887. −0.870690
\(571\) 413970.i 1.26969i 0.772641 + 0.634843i \(0.218935\pi\)
−0.772641 + 0.634843i \(0.781065\pi\)
\(572\) −37611.6 + 55977.1i −0.114955 + 0.171087i
\(573\) 11532.6 0.0351252
\(574\) 201132.i 0.610460i
\(575\) 103166. 0.312033
\(576\) 99265.5 0.299194
\(577\) −102654. −0.308337 −0.154169 0.988045i \(-0.549270\pi\)
−0.154169 + 0.988045i \(0.549270\pi\)
\(578\) 737384.i 2.20718i
\(579\) 95443.6i 0.284701i
\(580\) 520997.i 1.54874i
\(581\) −153199. −0.453841
\(582\) 45036.0i 0.132958i
\(583\) −376184. 252762.i −1.10679 0.743661i
\(584\) −16008.0 −0.0469366
\(585\) 29452.7i 0.0860625i
\(586\) −301815. −0.878912
\(587\) 127414. 0.369779 0.184889 0.982759i \(-0.440807\pi\)
0.184889 + 0.982759i \(0.440807\pi\)
\(588\) 176402. 0.510209
\(589\) 143300.i 0.413061i
\(590\) 1.09224e6i 3.13772i
\(591\) 122998.i 0.352147i
\(592\) −74175.5 −0.211649
\(593\) 477628.i 1.35825i −0.734022 0.679126i \(-0.762359\pi\)
0.734022 0.679126i \(-0.237641\pi\)
\(594\) 52882.8 78705.1i 0.149879 0.223064i
\(595\) −178743. −0.504888
\(596\) 330682.i 0.930933i
\(597\) 141412. 0.396770
\(598\) 81274.4 0.227275
\(599\) 301738. 0.840961 0.420480 0.907302i \(-0.361862\pi\)
0.420480 + 0.907302i \(0.361862\pi\)
\(600\) 6039.08i 0.0167752i
\(601\) 294665.i 0.815793i −0.913028 0.407896i \(-0.866262\pi\)
0.913028 0.407896i \(-0.133738\pi\)
\(602\) 120279.i 0.331891i
\(603\) −93543.7 −0.257264
\(604\) 315186.i 0.863959i
\(605\) −164603. 403250.i −0.449705 1.10170i
\(606\) 114330. 0.311326
\(607\) 308433.i 0.837113i −0.908191 0.418556i \(-0.862536\pi\)
0.908191 0.418556i \(-0.137464\pi\)
\(608\) 467321. 1.26418
\(609\) 77484.8 0.208921
\(610\) 854189. 2.29559
\(611\) 68044.9i 0.182269i
\(612\) 190527.i 0.508691i
\(613\) 222563.i 0.592287i −0.955143 0.296144i \(-0.904299\pi\)
0.955143 0.296144i \(-0.0957007\pi\)
\(614\) −390227. −1.03510
\(615\) 430085.i 1.13711i
\(616\) −5810.62 3904.22i −0.0153130 0.0102890i
\(617\) 478612. 1.25723 0.628613 0.777718i \(-0.283623\pi\)
0.628613 + 0.777718i \(0.283623\pi\)
\(618\) 354386.i 0.927896i
\(619\) −110719. −0.288963 −0.144482 0.989507i \(-0.546151\pi\)
−0.144482 + 0.989507i \(0.546151\pi\)
\(620\) 197770. 0.514490
\(621\) −55671.2 −0.144360
\(622\) 192185.i 0.496750i
\(623\) 33451.5i 0.0861866i
\(624\) 51094.8i 0.131222i
\(625\) −485524. −1.24294
\(626\) 190724.i 0.486695i
\(627\) 114885. 170983.i 0.292232 0.434928i
\(628\) 258266. 0.654859
\(629\) 128416.i 0.324576i
\(630\) −58064.3 −0.146295
\(631\) −77313.0 −0.194175 −0.0970876 0.995276i \(-0.530953\pi\)
−0.0970876 + 0.995276i \(0.530953\pi\)
\(632\) −43413.6 −0.108690
\(633\) 38793.0i 0.0968157i
\(634\) 374690.i 0.932168i
\(635\) 320019.i 0.793648i
\(636\) 295825. 0.731342
\(637\) 81899.3i 0.201837i
\(638\) −646383. 434312.i −1.58799 1.06699i
\(639\) −162860. −0.398853
\(640\) 68003.7i 0.166025i
\(641\) 382285. 0.930404 0.465202 0.885205i \(-0.345982\pi\)
0.465202 + 0.885205i \(0.345982\pi\)
\(642\) −109026. −0.264520
\(643\) −216575. −0.523825 −0.261912 0.965092i \(-0.584353\pi\)
−0.261912 + 0.965092i \(0.584353\pi\)
\(644\) 78058.8i 0.188213i
\(645\) 257195.i 0.618219i
\(646\) 849613.i 2.03590i
\(647\) −151109. −0.360979 −0.180489 0.983577i \(-0.557768\pi\)
−0.180489 + 0.983577i \(0.557768\pi\)
\(648\) 3258.86i 0.00776096i
\(649\) 660172. + 443577.i 1.56736 + 1.05312i
\(650\) 53250.0 0.126035
\(651\) 29413.1i 0.0694032i
\(652\) −237939. −0.559721
\(653\) −191077. −0.448107 −0.224053 0.974577i \(-0.571929\pi\)
−0.224053 + 0.974577i \(0.571929\pi\)
\(654\) 445177. 1.04082
\(655\) 435028.i 1.01399i
\(656\) 746114.i 1.73380i
\(657\) 96685.9i 0.223992i
\(658\) −134147. −0.309833
\(659\) 452930.i 1.04294i −0.853269 0.521471i \(-0.825384\pi\)
0.853269 0.521471i \(-0.174616\pi\)
\(660\) 235976. + 158554.i 0.541725 + 0.363991i
\(661\) 307053. 0.702767 0.351383 0.936232i \(-0.385711\pi\)
0.351383 + 0.936232i \(0.385711\pi\)
\(662\) 126025.i 0.287568i
\(663\) −88457.3 −0.201236
\(664\) 52916.6 0.120020
\(665\) −126142. −0.285243
\(666\) 41715.6i 0.0940480i
\(667\) 457212.i 1.02770i
\(668\) 208872.i 0.468088i
\(669\) −70951.6 −0.158529
\(670\) 575697.i 1.28246i
\(671\) −346900. + 516289.i −0.770476 + 1.14669i
\(672\) 95920.4 0.212409
\(673\) 216281.i 0.477517i 0.971079 + 0.238758i \(0.0767404\pi\)
−0.971079 + 0.238758i \(0.923260\pi\)
\(674\) 305305. 0.672069
\(675\) −36475.1 −0.0800551
\(676\) −413681. −0.905257
\(677\) 23957.4i 0.0522712i −0.999658 0.0261356i \(-0.991680\pi\)
0.999658 0.0261356i \(-0.00832017\pi\)
\(678\) 209140.i 0.454964i
\(679\) 20081.9i 0.0435578i
\(680\) 61739.7 0.133520
\(681\) 82411.5i 0.177702i
\(682\) −164864. + 245366.i −0.354452 + 0.527529i
\(683\) 547099. 1.17280 0.586401 0.810021i \(-0.300544\pi\)
0.586401 + 0.810021i \(0.300544\pi\)
\(684\) 134458.i 0.287391i
\(685\) −747994. −1.59411
\(686\) 335028. 0.711922
\(687\) 515657. 1.09257
\(688\) 446183.i 0.942619i
\(689\) 137345.i 0.289316i
\(690\) 342618.i 0.719635i
\(691\) −299138. −0.626493 −0.313246 0.949672i \(-0.601417\pi\)
−0.313246 + 0.949672i \(0.601417\pi\)
\(692\) 632658.i 1.32117i
\(693\) 23580.9 35095.2i 0.0491013 0.0730772i
\(694\) 648768. 1.34701
\(695\) 132512.i 0.274338i
\(696\) −26764.1 −0.0552502
\(697\) −1.29170e6 −2.65887
\(698\) −736538. −1.51176
\(699\) 228975.i 0.468633i
\(700\) 51143.2i 0.104374i
\(701\) 876409.i 1.78349i 0.452538 + 0.891745i \(0.350519\pi\)
−0.452538 + 0.891745i \(0.649481\pi\)
\(702\) −28735.2 −0.0583096
\(703\) 90624.8i 0.183373i
\(704\) −369247. 248101.i −0.745026 0.500591i
\(705\) −286849. −0.577131
\(706\) 155363.i 0.311701i
\(707\) 50980.7 0.101992
\(708\) −519148. −1.03568
\(709\) 266386. 0.529931 0.264965 0.964258i \(-0.414639\pi\)
0.264965 + 0.964258i \(0.414639\pi\)
\(710\) 1.00229e6i 1.98828i
\(711\) 262211.i 0.518695i
\(712\) 11554.5i 0.0227925i
\(713\) 173557. 0.341400
\(714\) 174388.i 0.342075i
\(715\) −73613.2 + 109558.i −0.143994 + 0.214305i
\(716\) 267131. 0.521073
\(717\) 299088.i 0.581782i
\(718\) −420476. −0.815629
\(719\) −747175. −1.44532 −0.722661 0.691203i \(-0.757081\pi\)
−0.722661 + 0.691203i \(0.757081\pi\)
\(720\) 215394. 0.415498
\(721\) 158023.i 0.303984i
\(722\) 128345.i 0.246209i
\(723\) 448506.i 0.858008i
\(724\) −157647. −0.300753
\(725\) 299560.i 0.569912i
\(726\) −393426. + 160593.i −0.746431 + 0.304687i
\(727\) −685597. −1.29718 −0.648590 0.761138i \(-0.724641\pi\)
−0.648590 + 0.761138i \(0.724641\pi\)
\(728\) 2121.45i 0.00400286i
\(729\) 19683.0 0.0370370
\(730\) 595035. 1.11660
\(731\) 772450. 1.44556
\(732\) 406001.i 0.757713i
\(733\) 64133.6i 0.119365i −0.998217 0.0596826i \(-0.980991\pi\)
0.998217 0.0596826i \(-0.0190089\pi\)
\(734\) 744313.i 1.38154i
\(735\) 345253. 0.639090
\(736\) 565995.i 1.04486i
\(737\) 347963. + 233800.i 0.640616 + 0.430437i
\(738\) −419607. −0.770425
\(739\) 350880.i 0.642495i −0.946995 0.321248i \(-0.895898\pi\)
0.946995 0.321248i \(-0.104102\pi\)
\(740\) 125073. 0.228401
\(741\) −62425.7 −0.113691
\(742\) 270767. 0.491799
\(743\) 214737.i 0.388981i 0.980904 + 0.194491i \(0.0623054\pi\)
−0.980904 + 0.194491i \(0.937695\pi\)
\(744\) 10159.6i 0.0183540i
\(745\) 647209.i 1.16609i
\(746\) 699105. 1.25622
\(747\) 319608.i 0.572765i
\(748\) 476197. 708721.i 0.851106 1.26669i
\(749\) −48615.4 −0.0866583
\(750\) 315162.i 0.560288i
\(751\) 656340. 1.16372 0.581861 0.813288i \(-0.302325\pi\)
0.581861 + 0.813288i \(0.302325\pi\)
\(752\) 497627. 0.879970
\(753\) −487535. −0.859837
\(754\) 235994.i 0.415105i
\(755\) 616880.i 1.08220i
\(756\) 27598.3i 0.0482879i
\(757\) 667153. 1.16422 0.582108 0.813111i \(-0.302228\pi\)
0.582108 + 0.813111i \(0.302228\pi\)
\(758\) 774924.i 1.34872i
\(759\) 207085. + 139143.i 0.359473 + 0.241533i
\(760\) 43570.7 0.0754340
\(761\) 125398.i 0.216532i −0.994122 0.108266i \(-0.965470\pi\)
0.994122 0.108266i \(-0.0345298\pi\)
\(762\) −312222. −0.537717
\(763\) 198508. 0.340980
\(764\) 33735.0 0.0577955
\(765\) 372898.i 0.637188i
\(766\) 680566.i 1.15988i
\(767\) 241028.i 0.409711i
\(768\) −372006. −0.630706
\(769\) 232947.i 0.393916i 0.980412 + 0.196958i \(0.0631063\pi\)
−0.980412 + 0.196958i \(0.936894\pi\)
\(770\) 215987. + 145124.i 0.364289 + 0.244770i
\(771\) 127250. 0.214067
\(772\) 279190.i 0.468452i
\(773\) −283047. −0.473697 −0.236848 0.971547i \(-0.576114\pi\)
−0.236848 + 0.971547i \(0.576114\pi\)
\(774\) 250929. 0.418860
\(775\) 113713. 0.189324
\(776\) 6936.51i 0.0115191i
\(777\) 18601.3i 0.0308107i
\(778\) 1.54030e6i 2.54475i
\(779\) −911574. −1.50216
\(780\) 86154.5i 0.141608i
\(781\) 605806. + 407047.i 0.993188 + 0.667333i
\(782\) −1.02901e6 −1.68269
\(783\) 161651.i 0.263666i
\(784\) −598947. −0.974442
\(785\) 505476. 0.820279
\(786\)