Properties

Label 108.5.k.a.5.2
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.09115 - 3.94122i) q^{3} +(14.0198 + 38.5191i) q^{5} +(-13.2730 - 75.2747i) q^{7} +(49.9335 + 63.7781i) q^{9} +O(q^{10})\) \(q+(-8.09115 - 3.94122i) q^{3} +(14.0198 + 38.5191i) q^{5} +(-13.2730 - 75.2747i) q^{7} +(49.9335 + 63.7781i) q^{9} +(-14.4803 + 39.7844i) q^{11} +(-99.4208 - 83.4239i) q^{13} +(38.3759 - 366.919i) q^{15} +(25.0688 + 14.4735i) q^{17} +(-340.107 - 589.082i) q^{19} +(-189.281 + 661.371i) q^{21} +(-925.342 - 163.163i) q^{23} +(-808.388 + 678.318i) q^{25} +(-152.656 - 712.837i) q^{27} +(-743.151 - 885.653i) q^{29} +(-216.511 + 1227.89i) q^{31} +(273.962 - 264.832i) q^{33} +(2713.43 - 1566.60i) q^{35} +(951.756 - 1648.49i) q^{37} +(475.637 + 1066.84i) q^{39} +(663.134 - 790.292i) q^{41} +(989.699 + 360.221i) q^{43} +(-1756.61 + 2817.55i) q^{45} +(747.698 - 131.839i) q^{47} +(-3233.91 + 1177.05i) q^{49} +(-145.793 - 215.909i) q^{51} -202.878i q^{53} -1735.47 q^{55} +(430.153 + 6106.79i) q^{57} +(1284.25 + 3528.44i) q^{59} +(-211.588 - 1199.97i) q^{61} +(4138.11 - 4605.26i) q^{63} +(1819.55 - 4999.18i) q^{65} +(-2491.41 - 2090.54i) q^{67} +(6844.03 + 4967.15i) q^{69} +(2946.68 + 1701.27i) q^{71} +(-1292.56 - 2238.78i) q^{73} +(9214.19 - 2302.34i) q^{75} +(3186.96 + 561.947i) q^{77} +(-5812.54 + 4877.30i) q^{79} +(-1574.28 + 6369.33i) q^{81} +(-5284.48 - 6297.80i) q^{83} +(-206.046 + 1168.54i) q^{85} +(2522.40 + 10094.9i) q^{87} +(-11385.8 + 6573.58i) q^{89} +(-4960.10 + 8591.15i) q^{91} +(6591.22 - 9081.76i) q^{93} +(17922.7 - 21359.4i) q^{95} +(-3367.63 - 1225.72i) q^{97} +(-3260.43 + 1063.05i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −8.09115 3.94122i −0.899017 0.437914i
\(4\) 0 0
\(5\) 14.0198 + 38.5191i 0.560792 + 1.54076i 0.818480 + 0.574535i \(0.194817\pi\)
−0.257688 + 0.966228i \(0.582961\pi\)
\(6\) 0 0
\(7\) −13.2730 75.2747i −0.270877 1.53622i −0.751762 0.659435i \(-0.770796\pi\)
0.480885 0.876784i \(-0.340315\pi\)
\(8\) 0 0
\(9\) 49.9335 + 63.7781i 0.616463 + 0.787384i
\(10\) 0 0
\(11\) −14.4803 + 39.7844i −0.119672 + 0.328797i −0.985036 0.172347i \(-0.944865\pi\)
0.865364 + 0.501144i \(0.167087\pi\)
\(12\) 0 0
\(13\) −99.4208 83.4239i −0.588289 0.493633i 0.299369 0.954138i \(-0.403224\pi\)
−0.887657 + 0.460505i \(0.847668\pi\)
\(14\) 0 0
\(15\) 38.3759 366.919i 0.170560 1.63075i
\(16\) 0 0
\(17\) 25.0688 + 14.4735i 0.0867434 + 0.0500813i 0.542744 0.839898i \(-0.317385\pi\)
−0.456001 + 0.889979i \(0.650719\pi\)
\(18\) 0 0
\(19\) −340.107 589.082i −0.942124 1.63181i −0.761409 0.648271i \(-0.775492\pi\)
−0.180715 0.983536i \(-0.557841\pi\)
\(20\) 0 0
\(21\) −189.281 + 661.371i −0.429208 + 1.49971i
\(22\) 0 0
\(23\) −925.342 163.163i −1.74923 0.308436i −0.794800 0.606872i \(-0.792424\pi\)
−0.954430 + 0.298436i \(0.903535\pi\)
\(24\) 0 0
\(25\) −808.388 + 678.318i −1.29342 + 1.08531i
\(26\) 0 0
\(27\) −152.656 712.837i −0.209405 0.977829i
\(28\) 0 0
\(29\) −743.151 885.653i −0.883652 1.05310i −0.998218 0.0596798i \(-0.980992\pi\)
0.114566 0.993416i \(-0.463452\pi\)
\(30\) 0 0
\(31\) −216.511 + 1227.89i −0.225297 + 1.27773i 0.636818 + 0.771014i \(0.280250\pi\)
−0.862116 + 0.506711i \(0.830861\pi\)
\(32\) 0 0
\(33\) 273.962 264.832i 0.251572 0.243188i
\(34\) 0 0
\(35\) 2713.43 1566.60i 2.21504 1.27886i
\(36\) 0 0
\(37\) 951.756 1648.49i 0.695220 1.20416i −0.274886 0.961477i \(-0.588640\pi\)
0.970106 0.242680i \(-0.0780265\pi\)
\(38\) 0 0
\(39\) 475.637 + 1066.84i 0.312713 + 0.701404i
\(40\) 0 0
\(41\) 663.134 790.292i 0.394488 0.470132i −0.531843 0.846843i \(-0.678500\pi\)
0.926331 + 0.376711i \(0.122945\pi\)
\(42\) 0 0
\(43\) 989.699 + 360.221i 0.535262 + 0.194819i 0.595486 0.803365i \(-0.296959\pi\)
−0.0602245 + 0.998185i \(0.519182\pi\)
\(44\) 0 0
\(45\) −1756.61 + 2817.55i −0.867464 + 1.39138i
\(46\) 0 0
\(47\) 747.698 131.839i 0.338478 0.0596828i −0.00182574 0.999998i \(-0.500581\pi\)
0.340304 + 0.940315i \(0.389470\pi\)
\(48\) 0 0
\(49\) −3233.91 + 1177.05i −1.34690 + 0.490232i
\(50\) 0 0
\(51\) −145.793 215.909i −0.0560525 0.0830100i
\(52\) 0 0
\(53\) 202.878i 0.0722244i −0.999348 0.0361122i \(-0.988503\pi\)
0.999348 0.0361122i \(-0.0114974\pi\)
\(54\) 0 0
\(55\) −1735.47 −0.573709
\(56\) 0 0
\(57\) 430.153 + 6106.79i 0.132395 + 1.87959i
\(58\) 0 0
\(59\) 1284.25 + 3528.44i 0.368931 + 1.01363i 0.975769 + 0.218804i \(0.0702154\pi\)
−0.606838 + 0.794825i \(0.707562\pi\)
\(60\) 0 0
\(61\) −211.588 1199.97i −0.0568631 0.322487i 0.943086 0.332548i \(-0.107908\pi\)
−0.999949 + 0.0100614i \(0.996797\pi\)
\(62\) 0 0
\(63\) 4138.11 4605.26i 1.04261 1.16031i
\(64\) 0 0
\(65\) 1819.55 4999.18i 0.430664 1.18324i
\(66\) 0 0
\(67\) −2491.41 2090.54i −0.555003 0.465702i 0.321628 0.946866i \(-0.395770\pi\)
−0.876631 + 0.481164i \(0.840214\pi\)
\(68\) 0 0
\(69\) 6844.03 + 4967.15i 1.43752 + 1.04330i
\(70\) 0 0
\(71\) 2946.68 + 1701.27i 0.584543 + 0.337486i 0.762937 0.646473i \(-0.223757\pi\)
−0.178394 + 0.983959i \(0.557090\pi\)
\(72\) 0 0
\(73\) −1292.56 2238.78i −0.242552 0.420112i 0.718889 0.695125i \(-0.244651\pi\)
−0.961440 + 0.275013i \(0.911318\pi\)
\(74\) 0 0
\(75\) 9214.19 2302.34i 1.63808 0.409305i
\(76\) 0 0
\(77\) 3186.96 + 561.947i 0.537520 + 0.0947793i
\(78\) 0 0
\(79\) −5812.54 + 4877.30i −0.931347 + 0.781493i −0.976059 0.217507i \(-0.930207\pi\)
0.0447118 + 0.999000i \(0.485763\pi\)
\(80\) 0 0
\(81\) −1574.28 + 6369.33i −0.239946 + 0.970786i
\(82\) 0 0
\(83\) −5284.48 6297.80i −0.767090 0.914182i 0.231184 0.972910i \(-0.425740\pi\)
−0.998274 + 0.0587278i \(0.981296\pi\)
\(84\) 0 0
\(85\) −206.046 + 1168.54i −0.0285185 + 0.161736i
\(86\) 0 0
\(87\) 2522.40 + 10094.9i 0.333254 + 1.33371i
\(88\) 0 0
\(89\) −11385.8 + 6573.58i −1.43742 + 0.829892i −0.997670 0.0682303i \(-0.978265\pi\)
−0.439746 + 0.898122i \(0.644931\pi\)
\(90\) 0 0
\(91\) −4960.10 + 8591.15i −0.598974 + 1.03745i
\(92\) 0 0
\(93\) 6591.22 9081.76i 0.762079 1.05004i
\(94\) 0 0
\(95\) 17922.7 21359.4i 1.98589 2.36669i
\(96\) 0 0
\(97\) −3367.63 1225.72i −0.357916 0.130271i 0.156803 0.987630i \(-0.449881\pi\)
−0.514718 + 0.857359i \(0.672104\pi\)
\(98\) 0 0
\(99\) −3260.43 + 1063.05i −0.332663 + 0.108463i
\(100\) 0 0
\(101\) 4409.08 777.440i 0.432221 0.0762122i 0.0466949 0.998909i \(-0.485131\pi\)
0.385526 + 0.922697i \(0.374020\pi\)
\(102\) 0 0
\(103\) 5907.83 2150.28i 0.556870 0.202684i −0.0482263 0.998836i \(-0.515357\pi\)
0.605096 + 0.796152i \(0.293135\pi\)
\(104\) 0 0
\(105\) −28129.1 + 1981.37i −2.55139 + 0.179716i
\(106\) 0 0
\(107\) 1788.65i 0.156228i −0.996944 0.0781138i \(-0.975110\pi\)
0.996944 0.0781138i \(-0.0248898\pi\)
\(108\) 0 0
\(109\) 1062.30 0.0894121 0.0447060 0.999000i \(-0.485765\pi\)
0.0447060 + 0.999000i \(0.485765\pi\)
\(110\) 0 0
\(111\) −14197.9 + 9587.11i −1.15233 + 0.778111i
\(112\) 0 0
\(113\) 1289.08 + 3541.72i 0.100954 + 0.277369i 0.979879 0.199590i \(-0.0639611\pi\)
−0.878925 + 0.476959i \(0.841739\pi\)
\(114\) 0 0
\(115\) −6688.23 37930.9i −0.505726 2.86812i
\(116\) 0 0
\(117\) 356.186 10506.5i 0.0260198 0.767515i
\(118\) 0 0
\(119\) 756.751 2079.16i 0.0534391 0.146823i
\(120\) 0 0
\(121\) 9842.54 + 8258.87i 0.672259 + 0.564092i
\(122\) 0 0
\(123\) −8480.24 + 3780.82i −0.560529 + 0.249905i
\(124\) 0 0
\(125\) −15274.5 8818.74i −0.977568 0.564399i
\(126\) 0 0
\(127\) 3488.64 + 6042.49i 0.216296 + 0.374635i 0.953673 0.300846i \(-0.0972691\pi\)
−0.737377 + 0.675482i \(0.763936\pi\)
\(128\) 0 0
\(129\) −6588.10 6815.23i −0.395895 0.409544i
\(130\) 0 0
\(131\) −16625.3 2931.49i −0.968785 0.170823i −0.333202 0.942856i \(-0.608129\pi\)
−0.635583 + 0.772033i \(0.719240\pi\)
\(132\) 0 0
\(133\) −39828.8 + 33420.3i −2.25161 + 1.88933i
\(134\) 0 0
\(135\) 25317.6 15874.0i 1.38917 0.871003i
\(136\) 0 0
\(137\) 11323.7 + 13495.0i 0.603317 + 0.719006i 0.978107 0.208104i \(-0.0667294\pi\)
−0.374789 + 0.927110i \(0.622285\pi\)
\(138\) 0 0
\(139\) −2285.93 + 12964.2i −0.118313 + 0.670989i 0.866743 + 0.498755i \(0.166209\pi\)
−0.985056 + 0.172233i \(0.944902\pi\)
\(140\) 0 0
\(141\) −6569.35 1880.11i −0.330434 0.0945683i
\(142\) 0 0
\(143\) 4758.62 2747.39i 0.232707 0.134353i
\(144\) 0 0
\(145\) 23695.7 41042.2i 1.12703 1.95207i
\(146\) 0 0
\(147\) 30805.1 + 3221.89i 1.42557 + 0.149099i
\(148\) 0 0
\(149\) 8675.93 10339.6i 0.390790 0.465726i −0.534399 0.845232i \(-0.679462\pi\)
0.925189 + 0.379507i \(0.123906\pi\)
\(150\) 0 0
\(151\) 5618.82 + 2045.08i 0.246429 + 0.0896926i 0.462281 0.886733i \(-0.347031\pi\)
−0.215853 + 0.976426i \(0.569253\pi\)
\(152\) 0 0
\(153\) 328.684 + 2321.55i 0.0140409 + 0.0991736i
\(154\) 0 0
\(155\) −50332.8 + 8875.03i −2.09502 + 0.369408i
\(156\) 0 0
\(157\) 7950.66 2893.80i 0.322555 0.117400i −0.175668 0.984450i \(-0.556208\pi\)
0.498223 + 0.867049i \(0.333986\pi\)
\(158\) 0 0
\(159\) −799.589 + 1641.52i −0.0316280 + 0.0649310i
\(160\) 0 0
\(161\) 71820.5i 2.77075i
\(162\) 0 0
\(163\) 27677.0 1.04170 0.520852 0.853647i \(-0.325614\pi\)
0.520852 + 0.853647i \(0.325614\pi\)
\(164\) 0 0
\(165\) 14042.0 + 6839.88i 0.515775 + 0.251235i
\(166\) 0 0
\(167\) 3153.79 + 8664.97i 0.113084 + 0.310695i 0.983305 0.181967i \(-0.0582463\pi\)
−0.870221 + 0.492661i \(0.836024\pi\)
\(168\) 0 0
\(169\) −2034.63 11539.0i −0.0712380 0.404011i
\(170\) 0 0
\(171\) 20587.8 51106.3i 0.704073 1.74776i
\(172\) 0 0
\(173\) −3872.82 + 10640.5i −0.129400 + 0.355524i −0.987426 0.158083i \(-0.949469\pi\)
0.858026 + 0.513607i \(0.171691\pi\)
\(174\) 0 0
\(175\) 61789.9 + 51847.9i 2.01763 + 1.69299i
\(176\) 0 0
\(177\) 3515.33 33610.7i 0.112207 1.07283i
\(178\) 0 0
\(179\) 17264.7 + 9967.80i 0.538833 + 0.311095i 0.744606 0.667505i \(-0.232638\pi\)
−0.205773 + 0.978600i \(0.565971\pi\)
\(180\) 0 0
\(181\) −18973.5 32863.1i −0.579150 1.00312i −0.995577 0.0939484i \(-0.970051\pi\)
0.416427 0.909169i \(-0.363282\pi\)
\(182\) 0 0
\(183\) −3017.37 + 10543.1i −0.0901004 + 0.314822i
\(184\) 0 0
\(185\) 76841.8 + 13549.3i 2.24519 + 0.395888i
\(186\) 0 0
\(187\) −938.825 + 787.768i −0.0268473 + 0.0225276i
\(188\) 0 0
\(189\) −51632.4 + 20952.6i −1.44544 + 0.586564i
\(190\) 0 0
\(191\) −43742.9 52130.7i −1.19906 1.42898i −0.875802 0.482671i \(-0.839667\pi\)
−0.323257 0.946311i \(-0.604778\pi\)
\(192\) 0 0
\(193\) −4087.08 + 23179.0i −0.109723 + 0.622272i 0.879505 + 0.475890i \(0.157874\pi\)
−0.989228 + 0.146382i \(0.953237\pi\)
\(194\) 0 0
\(195\) −34425.2 + 33277.9i −0.905330 + 0.875159i
\(196\) 0 0
\(197\) −9679.76 + 5588.61i −0.249420 + 0.144003i −0.619499 0.784998i \(-0.712664\pi\)
0.370078 + 0.929001i \(0.379331\pi\)
\(198\) 0 0
\(199\) 18006.3 31187.8i 0.454693 0.787551i −0.543978 0.839100i \(-0.683082\pi\)
0.998670 + 0.0515490i \(0.0164158\pi\)
\(200\) 0 0
\(201\) 11919.1 + 26734.1i 0.295019 + 0.661718i
\(202\) 0 0
\(203\) −56803.5 + 67695.7i −1.37842 + 1.64274i
\(204\) 0 0
\(205\) 39738.4 + 14463.6i 0.945588 + 0.344166i
\(206\) 0 0
\(207\) −35799.4 67163.8i −0.835478 1.56745i
\(208\) 0 0
\(209\) 28361.2 5000.84i 0.649279 0.114485i
\(210\) 0 0
\(211\) −15217.5 + 5538.72i −0.341805 + 0.124407i −0.507219 0.861817i \(-0.669326\pi\)
0.165413 + 0.986224i \(0.447104\pi\)
\(212\) 0 0
\(213\) −17137.0 25378.7i −0.377725 0.559385i
\(214\) 0 0
\(215\) 43172.5i 0.933965i
\(216\) 0 0
\(217\) 95303.1 2.02389
\(218\) 0 0
\(219\) 1634.77 + 23208.5i 0.0340855 + 0.483904i
\(220\) 0 0
\(221\) −1284.93 3530.31i −0.0263084 0.0722816i
\(222\) 0 0
\(223\) 11489.0 + 65157.3i 0.231032 + 1.31025i 0.850811 + 0.525472i \(0.176111\pi\)
−0.619779 + 0.784776i \(0.712778\pi\)
\(224\) 0 0
\(225\) −83627.4 17686.6i −1.65190 0.349365i
\(226\) 0 0
\(227\) 21727.7 59696.4i 0.421660 1.15850i −0.529097 0.848562i \(-0.677469\pi\)
0.950756 0.309939i \(-0.100309\pi\)
\(228\) 0 0
\(229\) −44843.4 37628.1i −0.855121 0.717532i 0.105790 0.994389i \(-0.466263\pi\)
−0.960911 + 0.276856i \(0.910707\pi\)
\(230\) 0 0
\(231\) −23571.4 17107.3i −0.441735 0.320596i
\(232\) 0 0
\(233\) 5317.36 + 3069.98i 0.0979454 + 0.0565488i 0.548173 0.836365i \(-0.315324\pi\)
−0.450227 + 0.892914i \(0.648657\pi\)
\(234\) 0 0
\(235\) 15560.9 + 26952.3i 0.281773 + 0.488045i
\(236\) 0 0
\(237\) 66252.6 16554.5i 1.17952 0.294726i
\(238\) 0 0
\(239\) 68273.2 + 12038.4i 1.19524 + 0.210753i 0.735639 0.677374i \(-0.236882\pi\)
0.459599 + 0.888126i \(0.347993\pi\)
\(240\) 0 0
\(241\) 61153.9 51314.3i 1.05291 0.883495i 0.0595115 0.998228i \(-0.481046\pi\)
0.993396 + 0.114733i \(0.0366012\pi\)
\(242\) 0 0
\(243\) 37840.7 45330.6i 0.640836 0.767678i
\(244\) 0 0
\(245\) −90677.5 108065.i −1.51066 1.80034i
\(246\) 0 0
\(247\) −15329.9 + 86940.1i −0.251272 + 1.42504i
\(248\) 0 0
\(249\) 17936.5 + 71783.8i 0.289294 + 1.15778i
\(250\) 0 0
\(251\) −61753.5 + 35653.4i −0.980199 + 0.565918i −0.902330 0.431046i \(-0.858145\pi\)
−0.0778687 + 0.996964i \(0.524812\pi\)
\(252\) 0 0
\(253\) 19890.6 34451.5i 0.310747 0.538230i
\(254\) 0 0
\(255\) 6272.64 8642.80i 0.0964651 0.132915i
\(256\) 0 0
\(257\) 25901.3 30867.9i 0.392152 0.467349i −0.533458 0.845826i \(-0.679108\pi\)
0.925610 + 0.378478i \(0.123552\pi\)
\(258\) 0 0
\(259\) −136722. 49762.8i −2.03817 0.741832i
\(260\) 0 0
\(261\) 19377.1 91620.6i 0.284451 1.34497i
\(262\) 0 0
\(263\) −102694. + 18107.8i −1.48469 + 0.261790i −0.856449 0.516232i \(-0.827334\pi\)
−0.628237 + 0.778022i \(0.716223\pi\)
\(264\) 0 0
\(265\) 7814.69 2844.31i 0.111281 0.0405029i
\(266\) 0 0
\(267\) 118032. 8313.98i 1.65568 0.116624i
\(268\) 0 0
\(269\) 79054.1i 1.09250i 0.837624 + 0.546248i \(0.183944\pi\)
−0.837624 + 0.546248i \(0.816056\pi\)
\(270\) 0 0
\(271\) −138085. −1.88021 −0.940107 0.340878i \(-0.889276\pi\)
−0.940107 + 0.340878i \(0.889276\pi\)
\(272\) 0 0
\(273\) 73992.6 49963.5i 0.992803 0.670390i
\(274\) 0 0
\(275\) −15280.7 41983.5i −0.202059 0.555154i
\(276\) 0 0
\(277\) −15081.1 85529.3i −0.196550 1.11469i −0.910193 0.414183i \(-0.864067\pi\)
0.713643 0.700510i \(-0.247044\pi\)
\(278\) 0 0
\(279\) −89123.8 + 47504.4i −1.14495 + 0.610275i
\(280\) 0 0
\(281\) −23913.1 + 65700.6i −0.302847 + 0.832064i 0.691156 + 0.722706i \(0.257102\pi\)
−0.994002 + 0.109358i \(0.965120\pi\)
\(282\) 0 0
\(283\) 31541.7 + 26466.6i 0.393833 + 0.330465i 0.818104 0.575070i \(-0.195025\pi\)
−0.424271 + 0.905535i \(0.639470\pi\)
\(284\) 0 0
\(285\) −229197. + 102185.i −2.82176 + 1.25805i
\(286\) 0 0
\(287\) −68290.8 39427.7i −0.829084 0.478672i
\(288\) 0 0
\(289\) −41341.5 71605.6i −0.494984 0.857337i
\(290\) 0 0
\(291\) 22417.2 + 23190.0i 0.264725 + 0.273852i
\(292\) 0 0
\(293\) 46384.3 + 8178.80i 0.540300 + 0.0952695i 0.437137 0.899395i \(-0.355992\pi\)
0.103163 + 0.994664i \(0.467104\pi\)
\(294\) 0 0
\(295\) −117908. + 98936.1i −1.35487 + 1.13687i
\(296\) 0 0
\(297\) 30570.3 + 4248.78i 0.346567 + 0.0481672i
\(298\) 0 0
\(299\) 78386.6 + 93417.5i 0.876797 + 1.04493i
\(300\) 0 0
\(301\) 13979.3 79280.5i 0.154295 0.875051i
\(302\) 0 0
\(303\) −38738.6 11086.8i −0.421948 0.120759i
\(304\) 0 0
\(305\) 43255.5 24973.6i 0.464988 0.268461i
\(306\) 0 0
\(307\) 38793.6 67192.5i 0.411608 0.712925i −0.583458 0.812143i \(-0.698301\pi\)
0.995066 + 0.0992180i \(0.0316341\pi\)
\(308\) 0 0
\(309\) −56275.9 5885.87i −0.589394 0.0616444i
\(310\) 0 0
\(311\) 83544.6 99564.5i 0.863769 1.02940i −0.135485 0.990779i \(-0.543259\pi\)
0.999254 0.0386201i \(-0.0122962\pi\)
\(312\) 0 0
\(313\) −135922. 49471.7i −1.38740 0.504973i −0.462989 0.886364i \(-0.653223\pi\)
−0.924414 + 0.381391i \(0.875445\pi\)
\(314\) 0 0
\(315\) 235406. + 94831.4i 2.37244 + 0.955721i
\(316\) 0 0
\(317\) 127720. 22520.6i 1.27099 0.224110i 0.502839 0.864380i \(-0.332289\pi\)
0.768150 + 0.640270i \(0.221178\pi\)
\(318\) 0 0
\(319\) 45996.3 16741.3i 0.452003 0.164516i
\(320\) 0 0
\(321\) −7049.47 + 14472.2i −0.0684142 + 0.140451i
\(322\) 0 0
\(323\) 19690.1i 0.188731i
\(324\) 0 0
\(325\) 136958. 1.29665
\(326\) 0 0
\(327\) −8595.27 4186.78i −0.0803830 0.0391548i
\(328\) 0 0
\(329\) −19848.3 54532.9i −0.183372 0.503810i
\(330\) 0 0
\(331\) 16860.1 + 95618.2i 0.153887 + 0.872739i 0.959796 + 0.280699i \(0.0905663\pi\)
−0.805908 + 0.592040i \(0.798323\pi\)
\(332\) 0 0
\(333\) 152662. 21613.8i 1.37671 0.194914i
\(334\) 0 0
\(335\) 45596.6 125276.i 0.406296 1.11629i
\(336\) 0 0
\(337\) 104364. + 87572.1i 0.918951 + 0.771091i 0.973801 0.227403i \(-0.0730236\pi\)
−0.0548500 + 0.998495i \(0.517468\pi\)
\(338\) 0 0
\(339\) 3528.56 33737.2i 0.0307042 0.293569i
\(340\) 0 0
\(341\) −45715.9 26394.1i −0.393150 0.226985i
\(342\) 0 0
\(343\) 39764.0 + 68873.4i 0.337989 + 0.585414i
\(344\) 0 0
\(345\) −95378.4 + 333264.i −0.801331 + 2.79995i
\(346\) 0 0
\(347\) 25871.4 + 4561.82i 0.214863 + 0.0378861i 0.280043 0.959987i \(-0.409651\pi\)
−0.0651805 + 0.997873i \(0.520762\pi\)
\(348\) 0 0
\(349\) 69050.2 57940.0i 0.566910 0.475694i −0.313709 0.949519i \(-0.601572\pi\)
0.880619 + 0.473825i \(0.157127\pi\)
\(350\) 0 0
\(351\) −44290.5 + 83606.0i −0.359498 + 0.678615i
\(352\) 0 0
\(353\) 35190.7 + 41938.7i 0.282409 + 0.336562i 0.888537 0.458805i \(-0.151722\pi\)
−0.606128 + 0.795367i \(0.707278\pi\)
\(354\) 0 0
\(355\) −24219.4 + 137355.i −0.192179 + 1.08990i
\(356\) 0 0
\(357\) −14317.4 + 13840.2i −0.112338 + 0.108594i
\(358\) 0 0
\(359\) 209960. 121221.i 1.62910 0.940562i 0.644739 0.764403i \(-0.276966\pi\)
0.984362 0.176159i \(-0.0563673\pi\)
\(360\) 0 0
\(361\) −166185. + 287840.i −1.27520 + 2.20870i
\(362\) 0 0
\(363\) −47087.4 105615.i −0.357348 0.801519i
\(364\) 0 0
\(365\) 68114.2 81175.3i 0.511272 0.609310i
\(366\) 0 0
\(367\) −229564. 83554.5i −1.70440 0.620351i −0.708086 0.706126i \(-0.750441\pi\)
−0.996315 + 0.0857748i \(0.972663\pi\)
\(368\) 0 0
\(369\) 83516.0 + 2831.31i 0.613362 + 0.0207938i
\(370\) 0 0
\(371\) −15271.6 + 2692.80i −0.110952 + 0.0195639i
\(372\) 0 0
\(373\) −23536.5 + 8566.57i −0.169170 + 0.0615729i −0.425217 0.905092i \(-0.639802\pi\)
0.256047 + 0.966664i \(0.417580\pi\)
\(374\) 0 0
\(375\) 88831.7 + 131554.i 0.631692 + 0.935495i
\(376\) 0 0
\(377\) 150049.i 1.05572i
\(378\) 0 0
\(379\) −55835.8 −0.388717 −0.194359 0.980931i \(-0.562263\pi\)
−0.194359 + 0.980931i \(0.562263\pi\)
\(380\) 0 0
\(381\) −4412.28 62640.2i −0.0303958 0.431522i
\(382\) 0 0
\(383\) −74077.0 203525.i −0.504993 1.38746i −0.886344 0.463027i \(-0.846763\pi\)
0.381351 0.924430i \(-0.375459\pi\)
\(384\) 0 0
\(385\) 23034.8 + 130637.i 0.155405 + 0.881343i
\(386\) 0 0
\(387\) 26445.0 + 81108.2i 0.176572 + 0.541555i
\(388\) 0 0
\(389\) −21052.0 + 57839.9i −0.139121 + 0.382233i −0.989613 0.143755i \(-0.954082\pi\)
0.850492 + 0.525988i \(0.176304\pi\)
\(390\) 0 0
\(391\) −20835.7 17483.2i −0.136287 0.114358i
\(392\) 0 0
\(393\) 122964. + 89243.2i 0.796148 + 0.577817i
\(394\) 0 0
\(395\) −269360. 155515.i −1.72639 0.996730i
\(396\) 0 0
\(397\) −45460.4 78739.7i −0.288438 0.499589i 0.684999 0.728544i \(-0.259803\pi\)
−0.973437 + 0.228955i \(0.926469\pi\)
\(398\) 0 0
\(399\) 453978. 113435.i 2.85160 0.712526i
\(400\) 0 0
\(401\) −45351.9 7996.77i −0.282038 0.0497308i 0.0308399 0.999524i \(-0.490182\pi\)
−0.312877 + 0.949794i \(0.601293\pi\)
\(402\) 0 0
\(403\) 123961. 104016.i 0.763267 0.640457i
\(404\) 0 0
\(405\) −267412. + 28656.8i −1.63031 + 0.174710i
\(406\) 0 0
\(407\) 51802.5 + 61735.8i 0.312724 + 0.372690i
\(408\) 0 0
\(409\) 20626.2 116977.i 0.123303 0.699284i −0.858999 0.511977i \(-0.828913\pi\)
0.982302 0.187306i \(-0.0599757\pi\)
\(410\) 0 0
\(411\) −38434.6 153819.i −0.227530 0.910599i
\(412\) 0 0
\(413\) 248557. 143504.i 1.45722 0.841327i
\(414\) 0 0
\(415\) 168498. 291847.i 0.978361 1.69457i
\(416\) 0 0
\(417\) 69590.5 95885.7i 0.400201 0.551419i
\(418\) 0 0
\(419\) −52759.1 + 62875.9i −0.300517 + 0.358143i −0.895079 0.445907i \(-0.852881\pi\)
0.594562 + 0.804050i \(0.297326\pi\)
\(420\) 0 0
\(421\) −87248.8 31756.0i −0.492261 0.179168i 0.0839492 0.996470i \(-0.473247\pi\)
−0.576210 + 0.817302i \(0.695469\pi\)
\(422\) 0 0
\(423\) 45743.7 + 41103.5i 0.255653 + 0.229720i
\(424\) 0 0
\(425\) −30083.0 + 5304.44i −0.166549 + 0.0293671i
\(426\) 0 0
\(427\) −87519.3 + 31854.4i −0.480007 + 0.174708i
\(428\) 0 0
\(429\) −49330.8 + 3474.78i −0.268042 + 0.0188805i
\(430\) 0 0
\(431\) 220842.i 1.18885i 0.804151 + 0.594425i \(0.202620\pi\)
−0.804151 + 0.594425i \(0.797380\pi\)
\(432\) 0 0
\(433\) −289818. −1.54579 −0.772894 0.634535i \(-0.781191\pi\)
−0.772894 + 0.634535i \(0.781191\pi\)
\(434\) 0 0
\(435\) −353482. + 238689.i −1.86805 + 1.26140i
\(436\) 0 0
\(437\) 218599. + 600596.i 1.14468 + 3.14499i
\(438\) 0 0
\(439\) 26622.1 + 150981.i 0.138138 + 0.783419i 0.972623 + 0.232389i \(0.0746542\pi\)
−0.834485 + 0.551031i \(0.814235\pi\)
\(440\) 0 0
\(441\) −236550. 147478.i −1.21632 0.758318i
\(442\) 0 0
\(443\) 13976.1 38399.0i 0.0712161 0.195665i −0.898978 0.437994i \(-0.855689\pi\)
0.970194 + 0.242329i \(0.0779114\pi\)
\(444\) 0 0
\(445\) −412834. 346409.i −2.08476 1.74932i
\(446\) 0 0
\(447\) −110949. + 49465.3i −0.555274 + 0.247563i
\(448\) 0 0
\(449\) 22218.8 + 12828.0i 0.110212 + 0.0636307i 0.554093 0.832455i \(-0.313065\pi\)
−0.443881 + 0.896086i \(0.646399\pi\)
\(450\) 0 0
\(451\) 21838.9 + 37826.1i 0.107369 + 0.185968i
\(452\) 0 0
\(453\) −37402.6 38692.1i −0.182266 0.188550i
\(454\) 0 0
\(455\) −400463. 70612.4i −1.93437 0.341082i
\(456\) 0 0
\(457\) 266155. 223330.i 1.27439 1.06934i 0.280397 0.959884i \(-0.409534\pi\)
0.993992 0.109455i \(-0.0349106\pi\)
\(458\) 0 0
\(459\) 6490.33 20079.5i 0.0308064 0.0953075i
\(460\) 0 0
\(461\) −229113. 273047.i −1.07807 1.28480i −0.956347 0.292235i \(-0.905601\pi\)
−0.121727 0.992564i \(-0.538843\pi\)
\(462\) 0 0
\(463\) 31344.4 177763.i 0.146217 0.829239i −0.820165 0.572128i \(-0.806118\pi\)
0.966382 0.257111i \(-0.0827708\pi\)
\(464\) 0 0
\(465\) 442229. + 126563.i 2.04523 + 0.585332i
\(466\) 0 0
\(467\) 36379.9 21003.9i 0.166812 0.0963090i −0.414270 0.910154i \(-0.635963\pi\)
0.581082 + 0.813845i \(0.302630\pi\)
\(468\) 0 0
\(469\) −124296. + 215288.i −0.565083 + 0.978753i
\(470\) 0 0
\(471\) −75735.1 7921.11i −0.341394 0.0357062i
\(472\) 0 0
\(473\) −28662.4 + 34158.5i −0.128112 + 0.152678i
\(474\) 0 0
\(475\) 674523. + 245506.i 2.98958 + 1.08812i
\(476\) 0 0
\(477\) 12939.2 10130.4i 0.0568683 0.0445237i
\(478\) 0 0
\(479\) 70992.0 12517.8i 0.309413 0.0545578i −0.0167857 0.999859i \(-0.505343\pi\)
0.326199 + 0.945301i \(0.394232\pi\)
\(480\) 0 0
\(481\) −232148. + 84494.9i −1.00340 + 0.365208i
\(482\) 0 0
\(483\) 283061. 581111.i 1.21335 2.49095i
\(484\) 0 0
\(485\) 146902.i 0.624518i
\(486\) 0 0
\(487\) 109686. 0.462480 0.231240 0.972897i \(-0.425722\pi\)
0.231240 + 0.972897i \(0.425722\pi\)
\(488\) 0 0
\(489\) −223939. 109081.i −0.936509 0.456176i
\(490\) 0 0
\(491\) 38757.8 + 106486.i 0.160767 + 0.441703i 0.993755 0.111588i \(-0.0355938\pi\)
−0.832988 + 0.553292i \(0.813372\pi\)
\(492\) 0 0
\(493\) −5811.44 32958.3i −0.0239106 0.135603i
\(494\) 0 0
\(495\) −86658.2 110685.i −0.353671 0.451729i
\(496\) 0 0
\(497\) 88951.2 244391.i 0.360113 0.989403i
\(498\) 0 0
\(499\) 7589.09 + 6368.00i 0.0304781 + 0.0255742i 0.657899 0.753106i \(-0.271445\pi\)
−0.627421 + 0.778680i \(0.715890\pi\)
\(500\) 0 0
\(501\) 8632.76 82539.4i 0.0343933 0.328841i
\(502\) 0 0
\(503\) −137742. 79525.2i −0.544414 0.314318i 0.202452 0.979292i \(-0.435109\pi\)
−0.746866 + 0.664975i \(0.768442\pi\)
\(504\) 0 0
\(505\) 91760.8 + 158934.i 0.359811 + 0.623211i
\(506\) 0 0
\(507\) −29015.1 + 101382.i −0.112878 + 0.394409i
\(508\) 0 0
\(509\) −283839. 50048.5i −1.09556 0.193177i −0.403475 0.914991i \(-0.632198\pi\)
−0.692088 + 0.721814i \(0.743309\pi\)
\(510\) 0 0
\(511\) −151367. + 127012.i −0.579682 + 0.486411i
\(512\) 0 0
\(513\) −368000. + 332368.i −1.39834 + 1.26295i
\(514\) 0 0
\(515\) 165653. + 197418.i 0.624576 + 0.744341i
\(516\) 0 0
\(517\) −5581.78 + 31655.8i −0.0208829 + 0.118433i
\(518\) 0 0
\(519\) 73272.0 70830.1i 0.272022 0.262956i
\(520\) 0 0
\(521\) −23240.6 + 13418.0i −0.0856195 + 0.0494324i −0.542198 0.840250i \(-0.682408\pi\)
0.456579 + 0.889683i \(0.349075\pi\)
\(522\) 0 0
\(523\) −15425.6 + 26717.8i −0.0563946 + 0.0976783i −0.892844 0.450365i \(-0.851294\pi\)
0.836450 + 0.548043i \(0.184627\pi\)
\(524\) 0 0
\(525\) −295607. 663037.i −1.07250 2.40557i
\(526\) 0 0
\(527\) −23199.6 + 27648.2i −0.0835332 + 0.0995510i
\(528\) 0 0
\(529\) 566672. + 206252.i 2.02498 + 0.737032i
\(530\) 0 0
\(531\) −160910. + 258095.i −0.570682 + 0.915355i
\(532\) 0 0
\(533\) −131859. + 23250.2i −0.464145 + 0.0818414i
\(534\) 0 0
\(535\) 68897.2 25076.5i 0.240710 0.0876112i
\(536\) 0 0
\(537\) −100406. 148695.i −0.348187 0.515642i
\(538\) 0 0
\(539\) 145703.i 0.501524i
\(540\) 0 0
\(541\) 179058. 0.611786 0.305893 0.952066i \(-0.401045\pi\)
0.305893 + 0.952066i \(0.401045\pi\)
\(542\) 0 0
\(543\) 23996.9 + 340680.i 0.0813872 + 1.15544i
\(544\) 0 0
\(545\) 14893.3 + 40919.0i 0.0501416 + 0.137763i
\(546\) 0 0
\(547\) −13041.3 73961.0i −0.0435860 0.247188i 0.955228 0.295869i \(-0.0956093\pi\)
−0.998814 + 0.0486811i \(0.984498\pi\)
\(548\) 0 0
\(549\) 65966.7 73413.6i 0.218867 0.243574i
\(550\) 0 0
\(551\) −268972. + 738994.i −0.885939 + 2.43410i
\(552\) 0 0
\(553\) 444287. + 372801.i 1.45282 + 1.21906i
\(554\) 0 0
\(555\) −568338. 412480.i −1.84510 1.33911i
\(556\) 0 0
\(557\) −142602. 82331.2i −0.459637 0.265371i 0.252255 0.967661i \(-0.418828\pi\)
−0.711891 + 0.702290i \(0.752161\pi\)
\(558\) 0 0
\(559\) −68345.6 118378.i −0.218719 0.378833i
\(560\) 0 0
\(561\) 10700.9 2673.83i 0.0340014 0.00849588i
\(562\) 0 0
\(563\) −187372. 33038.7i −0.591136 0.104233i −0.129925 0.991524i \(-0.541474\pi\)
−0.461211 + 0.887291i \(0.652585\pi\)
\(564\) 0 0
\(565\) −118351. + 99308.5i −0.370746 + 0.311093i
\(566\) 0 0
\(567\) 500345. + 33963.8i 1.55634 + 0.105645i
\(568\) 0 0
\(569\) 277003. + 330120.i 0.855579 + 1.01964i 0.999548 + 0.0300575i \(0.00956905\pi\)
−0.143969 + 0.989582i \(0.545987\pi\)
\(570\) 0 0
\(571\) 69768.2 395675.i 0.213986 1.21357i −0.668671 0.743558i \(-0.733137\pi\)
0.882657 0.470017i \(-0.155752\pi\)
\(572\) 0 0
\(573\) 148472. + 594198.i 0.452203 + 1.80976i
\(574\) 0 0
\(575\) 858711. 495777.i 2.59724 1.49952i
\(576\) 0 0
\(577\) −194165. + 336303.i −0.583202 + 1.01014i 0.411895 + 0.911231i \(0.364867\pi\)
−0.995097 + 0.0989042i \(0.968466\pi\)
\(578\) 0 0
\(579\) 124423. 171437.i 0.371144 0.511384i
\(580\) 0 0
\(581\) −403924. + 481378.i −1.19660 + 1.42605i
\(582\) 0 0
\(583\) 8071.40 + 2937.75i 0.0237472 + 0.00864326i
\(584\) 0 0
\(585\) 409695. 133579.i 1.19715 0.390326i
\(586\) 0 0
\(587\) 306677. 54075.5i 0.890032 0.156937i 0.290108 0.956994i \(-0.406309\pi\)
0.599924 + 0.800057i \(0.295198\pi\)
\(588\) 0 0
\(589\) 796967. 290072.i 2.29726 0.836134i
\(590\) 0 0
\(591\) 100346. 7068.24i 0.287294 0.0202365i
\(592\) 0 0
\(593\) 665766.i 1.89327i 0.322311 + 0.946634i \(0.395540\pi\)
−0.322311 + 0.946634i \(0.604460\pi\)
\(594\) 0 0
\(595\) 90696.7 0.256187
\(596\) 0 0
\(597\) −268610. + 181378.i −0.753655 + 0.508905i
\(598\) 0 0
\(599\) −157004. 431365.i −0.437580 1.20224i −0.941062 0.338235i \(-0.890170\pi\)
0.503482 0.864006i \(-0.332052\pi\)
\(600\) 0 0
\(601\) −77878.2 441669.i −0.215609 1.22278i −0.879846 0.475258i \(-0.842355\pi\)
0.664237 0.747522i \(-0.268756\pi\)
\(602\) 0 0
\(603\) 8925.73 263285.i 0.0245476 0.724088i
\(604\) 0 0
\(605\) −180134. + 494913.i −0.492135 + 1.35213i
\(606\) 0 0
\(607\) −223553. 187584.i −0.606742 0.509117i 0.286863 0.957972i \(-0.407388\pi\)
−0.893605 + 0.448855i \(0.851832\pi\)
\(608\) 0 0
\(609\) 726410. 323862.i 1.95861 0.873222i
\(610\) 0 0
\(611\) −85335.3 49268.4i −0.228584 0.131973i
\(612\) 0 0
\(613\) 47539.3 + 82340.6i 0.126512 + 0.219125i 0.922323 0.386420i \(-0.126288\pi\)
−0.795811 + 0.605545i \(0.792955\pi\)
\(614\) 0 0
\(615\) −264525. 273645.i −0.699385 0.723497i
\(616\) 0 0
\(617\) 42137.2 + 7429.92i 0.110687 + 0.0195170i 0.228717 0.973493i \(-0.426547\pi\)
−0.118030 + 0.993010i \(0.537658\pi\)
\(618\) 0 0
\(619\) −103830. + 87124.1i −0.270984 + 0.227382i −0.768145 0.640276i \(-0.778820\pi\)
0.497161 + 0.867658i \(0.334376\pi\)
\(620\) 0 0
\(621\) 24951.0 + 684526.i 0.0647000 + 1.77504i
\(622\) 0 0
\(623\) 645947. + 769809.i 1.66426 + 1.98339i
\(624\) 0 0
\(625\) 11015.1 62469.8i 0.0281987 0.159923i
\(626\) 0 0
\(627\) −249184. 71315.1i −0.633848 0.181404i
\(628\) 0 0
\(629\) 47718.8 27550.5i 0.120611 0.0696351i
\(630\) 0 0
\(631\) 101308. 175471.i 0.254441 0.440705i −0.710303 0.703896i \(-0.751442\pi\)
0.964744 + 0.263192i \(0.0847752\pi\)
\(632\) 0 0
\(633\) 144957. + 15160.9i 0.361768 + 0.0378372i
\(634\) 0 0
\(635\) −183841. + 219094.i −0.455928 + 0.543353i
\(636\) 0 0
\(637\) 419712. + 152763.i 1.03436 + 0.376477i
\(638\) 0 0
\(639\) 38634.7 + 272884.i 0.0946185 + 0.668307i
\(640\) 0 0
\(641\) 584996. 103151.i 1.42376 0.251047i 0.591891 0.806018i \(-0.298382\pi\)
0.831870 + 0.554971i \(0.187270\pi\)
\(642\) 0 0
\(643\) −239103. + 87026.4i −0.578313 + 0.210489i −0.614582 0.788853i \(-0.710675\pi\)
0.0362682 + 0.999342i \(0.488453\pi\)
\(644\) 0 0
\(645\) 170153. 349316.i 0.408996 0.839651i
\(646\) 0 0
\(647\) 582535.i 1.39160i 0.718237 + 0.695798i \(0.244949\pi\)
−0.718237 + 0.695798i \(0.755051\pi\)
\(648\) 0 0
\(649\) −158973. −0.377429
\(650\) 0 0
\(651\) −771112. 375611.i −1.81951 0.886290i
\(652\) 0 0
\(653\) −193842. 532577.i −0.454592 1.24898i −0.929460 0.368924i \(-0.879726\pi\)
0.474868 0.880057i \(-0.342496\pi\)
\(654\) 0 0
\(655\) −120165. 681491.i −0.280089 1.58846i
\(656\) 0 0
\(657\) 78242.8 194227.i 0.181265 0.449965i
\(658\) 0 0
\(659\) −88685.0 + 243660.i −0.204211 + 0.561065i −0.998946 0.0458907i \(-0.985387\pi\)
0.794735 + 0.606956i \(0.207610\pi\)
\(660\) 0 0
\(661\) −515464. 432525.i −1.17976 0.989939i −0.999981 0.00623300i \(-0.998016\pi\)
−0.179783 0.983706i \(-0.557540\pi\)
\(662\) 0 0
\(663\) −3517.18 + 33628.4i −0.00800144 + 0.0765032i
\(664\) 0 0
\(665\) −1.84571e6 1.06562e6i −4.17369 2.40968i
\(666\) 0 0
\(667\) 543164. + 940787.i 1.22090 + 2.11466i
\(668\) 0 0
\(669\) 163840. 572479.i 0.366073 1.27911i
\(670\) 0 0
\(671\) 50804.1 + 8958.14i 0.112838 + 0.0198963i
\(672\) 0 0
\(673\) −94255.5 + 79089.7i −0.208102 + 0.174618i −0.740881 0.671636i \(-0.765592\pi\)
0.532779 + 0.846254i \(0.321148\pi\)
\(674\) 0 0
\(675\) 606936. + 472699.i 1.33209 + 1.03747i
\(676\) 0 0
\(677\) −438550. 522644.i −0.956846 1.14033i −0.990027 0.140876i \(-0.955008\pi\)
0.0331810 0.999449i \(-0.489436\pi\)
\(678\) 0 0
\(679\) −47567.1 + 269766.i −0.103173 + 0.585124i
\(680\) 0 0
\(681\) −411079. + 397379.i −0.886403 + 0.856862i
\(682\) 0 0
\(683\) 619865. 357879.i 1.32879 0.767177i 0.343676 0.939088i \(-0.388328\pi\)
0.985112 + 0.171912i \(0.0549943\pi\)
\(684\) 0 0
\(685\) −361060. + 625375.i −0.769482 + 1.33278i
\(686\) 0 0
\(687\) 214534. + 481193.i 0.454552 + 1.01954i
\(688\) 0 0
\(689\) −16924.9 + 20170.3i −0.0356523 + 0.0424888i
\(690\) 0 0
\(691\) −347045. 126314.i −0.726824 0.264542i −0.0480040 0.998847i \(-0.515286\pi\)
−0.678820 + 0.734305i \(0.737508\pi\)
\(692\) 0 0
\(693\) 123296. + 231318.i 0.256734 + 0.481663i
\(694\) 0 0
\(695\) −531416. + 93703.1i −1.10018 + 0.193992i
\(696\) 0 0
\(697\) 28062.3 10213.8i 0.0577640 0.0210244i
\(698\) 0 0
\(699\) −30924.1 45796.6i −0.0632911 0.0937300i
\(700\) 0 0
\(701\) 641748.i 1.30596i −0.757377 0.652978i \(-0.773519\pi\)
0.757377 0.652978i \(-0.226481\pi\)
\(702\) 0 0
\(703\) −1.29480e6 −2.61993
\(704\) 0 0
\(705\) −19680.8 279404.i −0.0395972 0.562153i
\(706\) 0 0
\(707\) −117043. 321574.i −0.234157 0.643341i
\(708\) 0 0
\(709\) 136757. + 775588.i 0.272055 + 1.54290i 0.748163 + 0.663515i \(0.230936\pi\)
−0.476107 + 0.879387i \(0.657953\pi\)
\(710\) 0 0
\(711\) −601305. 127172.i −1.18948 0.251565i
\(712\) 0 0
\(713\) 400693. 1.10090e6i 0.788194 2.16554i
\(714\) 0 0
\(715\) 172542. + 144780.i 0.337507 + 0.283202i
\(716\) 0 0
\(717\) −504963. 366485.i −0.982248 0.712882i
\(718\) 0 0
\(719\) 301133. + 173859.i 0.582506 + 0.336310i 0.762128 0.647426i \(-0.224154\pi\)
−0.179623 + 0.983736i \(0.557488\pi\)
\(720\) 0 0
\(721\) −240276. 416170.i −0.462210 0.800571i
\(722\) 0 0
\(723\) −697047. + 174170.i −1.33348 + 0.333194i
\(724\) 0 0
\(725\) 1.20151e6 + 211858.i 2.28587 + 0.403060i
\(726\) 0 0
\(727\) 108810. 91302.1i 0.205872 0.172747i −0.534022 0.845471i \(-0.679320\pi\)
0.739894 + 0.672723i \(0.234876\pi\)
\(728\) 0 0
\(729\) −484833. + 217638.i −0.912299 + 0.409525i
\(730\) 0 0
\(731\) 19596.9 + 23354.7i 0.0366736 + 0.0437059i
\(732\) 0 0
\(733\) 134924. 765191.i 0.251120 1.42417i −0.554720 0.832037i \(-0.687175\pi\)
0.805840 0.592134i \(-0.201714\pi\)
\(734\) 0 0
\(735\) 307777. + 1.23175e6i 0.569719 + 2.28007i
\(736\) 0 0
\(737\) 119247. 68847.4i 0.219540 0.126751i
\(738\) 0 0
\(739\) −69727.6 + 120772.i −0.127678 + 0.221145i −0.922777 0.385335i \(-0.874086\pi\)
0.795099 + 0.606480i \(0.207419\pi\)
\(740\) 0 0
\(741\) 466686. 643027.i 0.849941 1.17110i
\(742\) 0 0
\(743\) 105774. 126057.i 0.191603 0.228344i −0.661687 0.749780i \(-0.730159\pi\)
0.853290 + 0.521436i \(0.174604\pi\)
\(744\) 0 0
\(745\) 519906. + 189230.i 0.936725 + 0.340940i
\(746\) 0 0
\(747\) 137789. 651506.i 0.246929 1.16755i
\(748\) 0 0
\(749\) −134640. + 23740.7i −0.240000 + 0.0423184i
\(750\) 0 0
\(751\) 404142. 147096.i 0.716563 0.260807i 0.0420967 0.999114i \(-0.486596\pi\)
0.674466 + 0.738306i \(0.264374\pi\)
\(752\) 0 0
\(753\) 640175. 45092.9i 1.12904 0.0795277i
\(754\) 0 0
\(755\) 245103.i 0.429987i
\(756\) 0 0
\(757\) 685545. 1.19631 0.598156 0.801380i \(-0.295900\pi\)
0.598156 + 0.801380i \(0.295900\pi\)
\(758\) 0 0
\(759\) −296719. + 200359.i −0.515065 + 0.347797i
\(760\) 0 0
\(761\) −45745.1 125684.i −0.0789906 0.217025i 0.893911 0.448245i \(-0.147951\pi\)
−0.972902 + 0.231220i \(0.925728\pi\)
\(762\) 0 0
\(763\) −14099.9 79964.7i −0.0242197 0.137357i
\(764\) 0 0
\(765\) −84816.1 + 45208.3i −0.144929 + 0.0772495i
\(766\) 0 0
\(767\) 166676. 457938.i 0.283323 0.778423i
\(768\) 0 0
\(769\) −653305. 548188.i −1.10475 0.926994i −0.107013 0.994258i \(-0.534129\pi\)
−0.997735 + 0.0672641i \(0.978573\pi\)
\(770\) 0 0
\(771\) −331228. + 147674.i −0.557210 + 0.248426i
\(772\) 0 0
\(773\) 430687. + 248657.i 0.720780 + 0.416143i 0.815040 0.579405i \(-0.196715\pi\)
−0.0942596 + 0.995548i \(0.530048\pi\)
\(774\) 0 0
\(775\) −657877. 1.13948e6i −1.09532 1.89715i
\(776\) 0 0
\(777\) 910115. + 941492.i 1.50749 + 1.55946i
\(778\) 0 0
\(779\) −691084. 121857.i −1.13882 0.200805i
\(780\) 0 0