Properties

Label 108.5.f.a.19.14
Level 108
Weight 5
Character 108.19
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.14
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +O(q^{10})\) \(q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +(118.977 - 4.89106i) q^{10} +(-195.278 - 112.744i) q^{11} +(-85.8824 - 148.753i) q^{13} +(-202.400 + 128.219i) q^{14} +(-90.0035 + 239.657i) q^{16} +99.0725 q^{17} +169.267i q^{19} +(203.494 - 430.653i) q^{20} +(-761.929 + 482.678i) q^{22} +(-310.777 + 179.427i) q^{23} +(-130.609 + 226.221i) q^{25} +(-686.480 + 28.2206i) q^{26} +(78.6636 + 955.147i) q^{28} +(-9.01635 + 15.6168i) q^{29} +(671.898 - 387.920i) q^{31} +(682.133 + 763.721i) q^{32} +(183.881 - 351.046i) q^{34} -1783.15i q^{35} +609.762 q^{37} +(599.768 + 314.164i) q^{38} +(-1148.25 - 1520.35i) q^{40} +(-206.545 - 357.747i) q^{41} +(265.498 + 153.286i) q^{43} +(296.127 + 3595.63i) q^{44} +(58.9591 + 1434.21i) q^{46} +(-2270.59 - 1310.93i) q^{47} +(593.432 + 1027.85i) q^{49} +(559.161 + 882.661i) q^{50} +(-1174.13 + 2484.80i) q^{52} -2034.30 q^{53} -6712.63i q^{55} +(3530.40 + 1494.05i) q^{56} +(38.6008 + 60.9330i) q^{58} +(2250.48 - 1299.32i) q^{59} +(708.681 - 1227.47i) q^{61} +(-127.469 - 3100.74i) q^{62} +(3972.17 - 999.536i) q^{64} +(2556.67 - 4428.28i) q^{65} +(5191.93 - 2997.56i) q^{67} +(-902.584 - 1303.10i) q^{68} +(-6318.29 - 3309.57i) q^{70} -1239.44i q^{71} -5060.60 q^{73} +(1131.73 - 2160.59i) q^{74} +(2226.37 - 1542.08i) q^{76} +(6753.22 + 11696.9i) q^{77} +(1635.99 + 944.538i) q^{79} +(-7518.28 + 1246.83i) q^{80} +(-1650.97 + 67.8700i) q^{82} +(5831.54 + 3366.84i) q^{83} +(1474.66 + 2554.19i) q^{85} +(1035.91 - 656.246i) q^{86} +(13290.1 + 5624.30i) q^{88} -9436.67 q^{89} +10288.5i q^{91} +(5191.29 + 2453.01i) q^{92} +(-8859.31 + 5612.33i) q^{94} +(-4363.88 + 2519.49i) q^{95} +(7297.91 - 12640.4i) q^{97} +(4743.45 - 195.000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85603 3.54333i 0.464006 0.885832i
\(3\) 0 0
\(4\) −9.11034 13.1530i −0.569396 0.822063i
\(5\) 14.8847 + 25.7811i 0.595388 + 1.03124i 0.993492 + 0.113902i \(0.0363350\pi\)
−0.398104 + 0.917340i \(0.630332\pi\)
\(6\) 0 0
\(7\) −51.8739 29.9494i −1.05865 0.611212i −0.133592 0.991036i \(-0.542651\pi\)
−0.925059 + 0.379824i \(0.875984\pi\)
\(8\) −63.5145 + 7.86857i −0.992413 + 0.122946i
\(9\) 0 0
\(10\) 118.977 4.89106i 1.18977 0.0489106i
\(11\) −195.278 112.744i −1.61387 0.931767i −0.988462 0.151467i \(-0.951600\pi\)
−0.625406 0.780300i \(1.28493\pi\)
\(12\) 0 0
\(13\) −85.8824 148.753i −0.508180 0.880194i −0.999955 0.00947137i \(-0.996985\pi\)
0.491775 0.870722i \(-0.336348\pi\)
\(14\) −202.400 + 128.219i −1.03265 + 0.654180i
\(15\) 0 0
\(16\) −90.0035 + 239.657i −0.351576 + 0.936159i
\(17\) 99.0725 0.342812 0.171406 0.985201i \(-0.445169\pi\)
0.171406 + 0.985201i \(0.445169\pi\)
\(18\) 0 0
\(19\) 169.267i 0.468884i 0.972130 + 0.234442i \(0.0753262\pi\)
−0.972130 + 0.234442i \(0.924674\pi\)
\(20\) 203.494 430.653i 0.508735 1.07663i
\(21\) 0 0
\(22\) −761.929 + 482.678i −1.57423 + 0.997270i
\(23\) −310.777 + 179.427i −0.587480 + 0.339182i −0.764101 0.645097i \(-0.776817\pi\)
0.176620 + 0.984279i \(0.443484\pi\)
\(24\) 0 0
\(25\) −130.609 + 226.221i −0.208974 + 0.361953i
\(26\) −686.480 + 28.2206i −1.01550 + 0.0417465i
\(27\) 0 0
\(28\) 78.6636 + 955.147i 0.100336 + 1.21830i
\(29\) −9.01635 + 15.6168i −0.0107210 + 0.0185693i −0.871336 0.490687i \(-0.836746\pi\)
0.860615 + 0.509256i \(0.170079\pi\)
\(30\) 0 0
\(31\) 671.898 387.920i 0.699165 0.403663i −0.107871 0.994165i \(-0.534403\pi\)
0.807036 + 0.590502i \(0.201070\pi\)
\(32\) 682.133 + 763.721i 0.666146 + 0.745821i
\(33\) 0 0
\(34\) 183.881 351.046i 0.159067 0.303673i
\(35\) 1783.15i 1.45563i
\(36\) 0 0
\(37\) 609.762 0.445407 0.222703 0.974886i \(-0.428512\pi\)
0.222703 + 0.974886i \(0.428512\pi\)
\(38\) 599.768 + 314.164i 0.415352 + 0.217565i
\(39\) 0 0
\(40\) −1148.25 1520.35i −0.717659 0.950218i
\(41\) −206.545 357.747i −0.122871 0.212818i 0.798028 0.602620i \(-0.205877\pi\)
−0.920899 + 0.389802i \(0.872543\pi\)
\(42\) 0 0
\(43\) 265.498 + 153.286i 0.143590 + 0.0829019i 0.570074 0.821593i \(-0.306915\pi\)
−0.426484 + 0.904495i \(0.640248\pi\)
\(44\) 296.127 + 3595.63i 0.152958 + 1.85725i
\(45\) 0 0
\(46\) 58.9591 + 1434.21i 0.0278635 + 0.677791i
\(47\) −2270.59 1310.93i −1.02788 0.593447i −0.111504 0.993764i \(-0.535567\pi\)
−0.916377 + 0.400317i \(0.868900\pi\)
\(48\) 0 0
\(49\) 593.432 + 1027.85i 0.247160 + 0.428094i
\(50\) 559.161 + 882.661i 0.223665 + 0.353064i
\(51\) 0 0
\(52\) −1174.13 + 2484.80i −0.434219 + 0.918935i
\(53\) −2034.30 −0.724209 −0.362104 0.932138i \(-0.617942\pi\)
−0.362104 + 0.932138i \(0.617942\pi\)
\(54\) 0 0
\(55\) 6712.63i 2.21905i
\(56\) 3530.40 + 1494.05i 1.12577 + 0.476418i
\(57\) 0 0
\(58\) 38.6008 + 60.9330i 0.0114747 + 0.0181133i
\(59\) 2250.48 1299.32i 0.646505 0.373260i −0.140611 0.990065i \(-0.544907\pi\)
0.787116 + 0.616805i \(0.211573\pi\)
\(60\) 0 0
\(61\) 708.681 1227.47i 0.190455 0.329877i −0.754946 0.655786i \(-0.772337\pi\)
0.945401 + 0.325910i \(0.105670\pi\)
\(62\) −127.469 3100.74i −0.0331606 0.806645i
\(63\) 0 0
\(64\) 3972.17 999.536i 0.969768 0.244027i
\(65\) 2556.67 4428.28i 0.605129 1.04811i
\(66\) 0 0
\(67\) 5191.93 2997.56i 1.15659 0.667758i 0.206106 0.978530i \(-0.433921\pi\)
0.950485 + 0.310772i \(0.100588\pi\)
\(68\) −902.584 1303.10i −0.195196 0.281813i
\(69\) 0 0
\(70\) −6318.29 3309.57i −1.28945 0.675423i
\(71\) 1239.44i 0.245872i −0.992415 0.122936i \(-0.960769\pi\)
0.992415 0.122936i \(-0.0392310\pi\)
\(72\) 0 0
\(73\) −5060.60 −0.949633 −0.474817 0.880085i \(-0.657486\pi\)
−0.474817 + 0.880085i \(0.657486\pi\)
\(74\) 1131.73 2160.59i 0.206672 0.394555i
\(75\) 0 0
\(76\) 2226.37 1542.08i 0.385452 0.266980i
\(77\) 6753.22 + 11696.9i 1.13901 + 1.97283i
\(78\) 0 0
\(79\) 1635.99 + 944.538i 0.262135 + 0.151344i 0.625308 0.780378i \(-0.284973\pi\)
−0.363173 + 0.931722i \(0.618307\pi\)
\(80\) −7518.28 + 1246.83i −1.17473 + 0.194818i
\(81\) 0 0
\(82\) −1650.97 + 67.8700i −0.245534 + 0.0100937i
\(83\) 5831.54 + 3366.84i 0.846500 + 0.488727i 0.859469 0.511189i \(-0.170795\pi\)
−0.0129681 + 0.999916i \(0.504128\pi\)
\(84\) 0 0
\(85\) 1474.66 + 2554.19i 0.204106 + 0.353522i
\(86\) 1035.91 656.246i 0.140064 0.0887298i
\(87\) 0 0
\(88\) 13290.1 + 5624.30i 1.71618 + 0.726279i
\(89\) −9436.67 −1.19135 −0.595674 0.803226i \(-0.703115\pi\)
−0.595674 + 0.803226i \(0.703115\pi\)
\(90\) 0 0
\(91\) 10288.5i 1.24242i
\(92\) 5191.29 + 2453.01i 0.613338 + 0.289817i
\(93\) 0 0
\(94\) −8859.31 + 5612.33i −1.00264 + 0.635166i
\(95\) −4363.88 + 2519.49i −0.483533 + 0.279168i
\(96\) 0 0
\(97\) 7297.91 12640.4i 0.775631 1.34343i −0.158808 0.987309i \(-0.550765\pi\)
0.934439 0.356123i \(-0.115902\pi\)
\(98\) 4743.45 195.000i 0.493904 0.0203040i
\(99\) 0 0
\(100\) 4165.37 343.050i 0.416537 0.0343050i
\(101\) 3230.71 5595.76i 0.316705 0.548550i −0.663093 0.748537i \(-0.730757\pi\)
0.979799 + 0.199987i \(0.0640900\pi\)
\(102\) 0 0
\(103\) −13991.6 + 8078.04i −1.31884 + 0.761432i −0.983542 0.180680i \(-0.942170\pi\)
−0.335298 + 0.942112i \(0.608837\pi\)
\(104\) 6625.25 + 8772.18i 0.612541 + 0.811037i
\(105\) 0 0
\(106\) −3775.72 + 7208.20i −0.336037 + 0.641527i
\(107\) 3065.27i 0.267732i 0.990999 + 0.133866i \(0.0427392\pi\)
−0.990999 + 0.133866i \(0.957261\pi\)
\(108\) 0 0
\(109\) −17728.8 −1.49220 −0.746098 0.665836i \(-0.768075\pi\)
−0.746098 + 0.665836i \(0.768075\pi\)
\(110\) −23785.1 12458.8i −1.96571 1.02965i
\(111\) 0 0
\(112\) 11846.4 9736.37i 0.944388 0.776178i
\(113\) −7396.56 12811.2i −0.579259 1.00331i −0.995565 0.0940814i \(-0.970009\pi\)
0.416305 0.909225i \(-0.363325\pi\)
\(114\) 0 0
\(115\) −9251.65 5341.44i −0.699558 0.403890i
\(116\) 287.550 23.6819i 0.0213696 0.00175995i
\(117\) 0 0
\(118\) −426.951 10385.8i −0.0306629 0.745890i
\(119\) −5139.28 2967.16i −0.362918 0.209531i
\(120\) 0 0
\(121\) 18101.8 + 31353.3i 1.23638 + 2.14147i
\(122\) −3034.00 4789.31i −0.203843 0.321776i
\(123\) 0 0
\(124\) −11223.5 5303.40i −0.729939 0.344914i
\(125\) 10829.6 0.693094
\(126\) 0 0
\(127\) 18478.7i 1.14568i 0.819667 + 0.572841i \(0.194159\pi\)
−0.819667 + 0.572841i \(0.805841\pi\)
\(128\) 3830.77 15929.9i 0.233812 0.972282i
\(129\) 0 0
\(130\) −10945.6 17278.1i −0.647669 1.02237i
\(131\) −7205.95 + 4160.35i −0.419902 + 0.242431i −0.695036 0.718975i \(-0.744611\pi\)
0.275133 + 0.961406i \(0.411278\pi\)
\(132\) 0 0
\(133\) 5069.44 8780.53i 0.286587 0.496384i
\(134\) −984.989 23960.3i −0.0548557 1.33439i
\(135\) 0 0
\(136\) −6292.54 + 779.559i −0.340211 + 0.0421474i
\(137\) −10703.4 + 18538.7i −0.570268 + 0.987732i 0.426271 + 0.904596i \(0.359827\pi\)
−0.996538 + 0.0831367i \(0.973506\pi\)
\(138\) 0 0
\(139\) −15783.6 + 9112.67i −0.816915 + 0.471646i −0.849351 0.527828i \(-0.823007\pi\)
0.0324367 + 0.999474i \(0.489673\pi\)
\(140\) −23453.8 + 16245.1i −1.19662 + 0.828832i
\(141\) 0 0
\(142\) −4391.75 2300.44i −0.217802 0.114086i
\(143\) 38730.8i 1.89402i
\(144\) 0 0
\(145\) −536.823 −0.0255326
\(146\) −9392.60 + 17931.3i −0.440636 + 0.841215i
\(147\) 0 0
\(148\) −5555.13 8020.20i −0.253613 0.366152i
\(149\) −8119.72 14063.8i −0.365736 0.633474i 0.623158 0.782096i \(-0.285850\pi\)
−0.988894 + 0.148622i \(0.952516\pi\)
\(150\) 0 0
\(151\) 21240.4 + 12263.2i 0.931557 + 0.537835i 0.887304 0.461186i \(-0.152576\pi\)
0.0442533 + 0.999020i \(0.485909\pi\)
\(152\) −1331.89 10750.9i −0.0576476 0.465326i
\(153\) 0 0
\(154\) 53980.1 2219.08i 2.27611 0.0935690i
\(155\) 20002.0 + 11548.2i 0.832549 + 0.480672i
\(156\) 0 0
\(157\) −19827.0 34341.4i −0.804375 1.39322i −0.916712 0.399548i \(-0.869167\pi\)
0.112337 0.993670i \(-0.464166\pi\)
\(158\) 6383.24 4043.75i 0.255698 0.161983i
\(159\) 0 0
\(160\) −9536.19 + 28953.9i −0.372507 + 1.13101i
\(161\) 21494.9 0.829248
\(162\) 0 0
\(163\) 25324.6i 0.953162i −0.879130 0.476581i \(-0.841876\pi\)
0.879130 0.476581i \(-0.158124\pi\)
\(164\) −2823.75 + 5975.89i −0.104988 + 0.222185i
\(165\) 0 0
\(166\) 22753.3 14414.1i 0.825712 0.523084i
\(167\) 24109.7 13919.8i 0.864490 0.499113i −0.00102363 0.999999i \(-0.500326\pi\)
0.865513 + 0.500886i \(0.166992\pi\)
\(168\) 0 0
\(169\) −471.081 + 815.937i −0.0164939 + 0.0285682i
\(170\) 11787.4 484.569i 0.407867 0.0167671i
\(171\) 0 0
\(172\) −402.612 4888.59i −0.0136091 0.165244i
\(173\) −11027.3 + 19099.8i −0.368448 + 0.638170i −0.989323 0.145739i \(-0.953444\pi\)
0.620875 + 0.783909i \(0.286777\pi\)
\(174\) 0 0
\(175\) 13550.4 7823.30i 0.442461 0.255455i
\(176\) 44595.5 36652.4i 1.43968 1.18325i
\(177\) 0 0
\(178\) −17514.7 + 33437.2i −0.552794 + 1.05533i
\(179\) 52513.4i 1.63895i −0.573118 0.819473i \(-0.694266\pi\)
0.573118 0.819473i \(-0.305734\pi\)
\(180\) 0 0
\(181\) −7223.25 −0.220483 −0.110242 0.993905i \(-0.535162\pi\)
−0.110242 + 0.993905i \(0.535162\pi\)
\(182\) 36455.5 + 19095.7i 1.10058 + 0.576492i
\(183\) 0 0
\(184\) 18327.0 13841.6i 0.541322 0.408837i
\(185\) 9076.12 + 15720.3i 0.265190 + 0.459322i
\(186\) 0 0
\(187\) −19346.7 11169.8i −0.553252 0.319420i
\(188\) 3443.21 + 41808.1i 0.0974200 + 1.18289i
\(189\) 0 0
\(190\) 827.894 + 20138.9i 0.0229334 + 0.557864i
\(191\) 9164.94 + 5291.38i 0.251225 + 0.145045i 0.620325 0.784345i \(-0.287001\pi\)
−0.369100 + 0.929390i \(0.620334\pi\)
\(192\) 0 0
\(193\) 19543.2 + 33849.9i 0.524665 + 0.908746i 0.999588 + 0.0287188i \(0.00914273\pi\)
−0.474923 + 0.880028i \(0.657524\pi\)
\(194\) −31243.8 49319.7i −0.830157 1.31044i
\(195\) 0 0
\(196\) 8113.02 17169.5i 0.211189 0.446937i
\(197\) 10820.0 0.278802 0.139401 0.990236i \(-0.455482\pi\)
0.139401 + 0.990236i \(0.455482\pi\)
\(198\) 0 0
\(199\) 807.389i 0.0203881i 0.999948 + 0.0101940i \(0.00324492\pi\)
−0.999948 + 0.0101940i \(0.996755\pi\)
\(200\) 6515.50 15396.0i 0.162888 0.384900i
\(201\) 0 0
\(202\) −13831.3 21833.3i −0.338970 0.535078i
\(203\) 935.426 540.068i 0.0226996 0.0131056i
\(204\) 0 0
\(205\) 6148.73 10649.9i 0.146311 0.253419i
\(206\) 2654.41 + 64569.8i 0.0625510 + 1.52158i
\(207\) 0 0
\(208\) 43379.3 7194.03i 1.00267 0.166282i
\(209\) 19083.8 33054.1i 0.436890 0.756716i
\(210\) 0 0
\(211\) 52683.9 30417.0i 1.18335 0.683207i 0.226562 0.973997i \(-0.427251\pi\)
0.956787 + 0.290790i \(0.0939181\pi\)
\(212\) 18533.2 + 26757.2i 0.412361 + 0.595345i
\(213\) 0 0
\(214\) 10861.2 + 5689.21i 0.237166 + 0.124229i
\(215\) 9126.44i 0.197435i
\(216\) 0 0
\(217\) −46471.9 −0.986895
\(218\) −32905.1 + 62818.9i −0.692389 + 1.32184i
\(219\) 0 0
\(220\) −88291.3 + 61154.3i −1.82420 + 1.26352i
\(221\) −8508.59 14737.3i −0.174210 0.301741i
\(222\) 0 0
\(223\) 9292.11 + 5364.80i 0.186855 + 0.107881i 0.590509 0.807031i \(-0.298927\pi\)
−0.403654 + 0.914912i \(0.632260\pi\)
\(224\) −12511.9 60046.6i −0.249361 1.19672i
\(225\) 0 0
\(226\) −59122.5 + 2430.48i −1.15754 + 0.0475856i
\(227\) −65585.2 37865.7i −1.27278 0.734842i −0.297272 0.954793i \(-0.596077\pi\)
−0.975511 + 0.219951i \(0.929410\pi\)
\(228\) 0 0
\(229\) 26683.3 + 46216.8i 0.508825 + 0.881311i 0.999948 + 0.0102204i \(0.00325330\pi\)
−0.491123 + 0.871090i \(0.663413\pi\)
\(230\) −36097.8 + 22867.8i −0.682378 + 0.432283i
\(231\) 0 0
\(232\) 449.787 1062.84i 0.00835662 0.0197465i
\(233\) −56485.5 −1.04046 −0.520230 0.854026i \(-0.674154\pi\)
−0.520230 + 0.854026i \(0.674154\pi\)
\(234\) 0 0
\(235\) 78050.9i 1.41333i
\(236\) −37592.6 17763.4i −0.674961 0.318935i
\(237\) 0 0
\(238\) −20052.3 + 12703.0i −0.354005 + 0.224260i
\(239\) −41561.8 + 23995.7i −0.727610 + 0.420086i −0.817547 0.575862i \(-0.804667\pi\)
0.0899375 + 0.995947i \(0.471333\pi\)
\(240\) 0 0
\(241\) 32075.1 55555.6i 0.552247 0.956520i −0.445865 0.895100i \(-0.647104\pi\)
0.998112 0.0614196i \(-0.0195628\pi\)
\(242\) 144692. 5948.19i 2.47067 0.101567i
\(243\) 0 0
\(244\) −22601.3 + 1861.39i −0.379624 + 0.0312649i
\(245\) −17666.1 + 30598.6i −0.294313 + 0.509764i
\(246\) 0 0
\(247\) 25178.9 14537.1i 0.412708 0.238277i
\(248\) −39622.8 + 29925.4i −0.644232 + 0.486561i
\(249\) 0 0
\(250\) 20100.0 38372.8i 0.321600 0.613965i
\(251\) 65230.8i 1.03539i −0.855564 0.517696i \(-0.826790\pi\)
0.855564 0.517696i \(-0.173210\pi\)
\(252\) 0 0
\(253\) 80917.3 1.26415
\(254\) 65476.1 + 34296.9i 1.01488 + 0.531604i
\(255\) 0 0
\(256\) −49334.7 43139.9i −0.752788 0.658263i
\(257\) −21657.9 37512.6i −0.327907 0.567951i 0.654190 0.756331i \(-0.273010\pi\)
−0.982096 + 0.188380i \(0.939676\pi\)
\(258\) 0 0
\(259\) −31630.7 18262.0i −0.471530 0.272238i
\(260\) −81537.3 + 6715.22i −1.20617 + 0.0993376i
\(261\) 0 0
\(262\) 1367.08 + 33254.7i 0.0199155 + 0.484452i
\(263\) −73443.4 42402.6i −1.06180 0.613029i −0.135868 0.990727i \(-0.543382\pi\)
−0.925929 + 0.377698i \(0.876716\pi\)
\(264\) 0 0
\(265\) −30280.0 52446.5i −0.431185 0.746835i
\(266\) −21703.3 34259.6i −0.306734 0.484193i
\(267\) 0 0
\(268\) −86727.3 40980.8i −1.20750 0.570572i
\(269\) 66685.5 0.921567 0.460784 0.887513i \(-0.347568\pi\)
0.460784 + 0.887513i \(0.347568\pi\)
\(270\) 0 0
\(271\) 122426.i 1.66700i 0.552516 + 0.833502i \(0.313668\pi\)
−0.552516 + 0.833502i \(0.686332\pi\)
\(272\) −8916.88 + 23743.4i −0.120524 + 0.320926i
\(273\) 0 0
\(274\) 45823.2 + 72333.9i 0.610357 + 0.963475i
\(275\) 51010.0 29450.6i 0.674512 0.389430i
\(276\) 0 0
\(277\) −68726.1 + 119037.i −0.895699 + 1.55140i −0.0627613 + 0.998029i \(0.519991\pi\)
−0.832937 + 0.553367i \(0.813343\pi\)
\(278\) 2994.39 + 72839.8i 0.0387453 + 0.942496i
\(279\) 0 0
\(280\) 14030.8 + 113256.i 0.178965 + 1.44459i
\(281\) 7001.61 12127.2i 0.0886718 0.153584i −0.818278 0.574822i \(-0.805071\pi\)
0.906950 + 0.421238i \(0.138404\pi\)
\(282\) 0 0
\(283\) −99634.2 + 57523.8i −1.24404 + 0.718249i −0.969915 0.243444i \(-0.921723\pi\)
−0.274129 + 0.961693i \(0.588389\pi\)
\(284\) −16302.4 + 11291.7i −0.202123 + 0.139999i
\(285\) 0 0
\(286\) 137236. + 71885.5i 1.67778 + 0.878838i
\(287\) 24743.6i 0.300400i
\(288\) 0 0
\(289\) −73705.6 −0.882480
\(290\) −996.357 + 1902.14i −0.0118473 + 0.0226176i
\(291\) 0 0
\(292\) 46103.7 + 66562.1i 0.540717 + 0.780659i
\(293\) 14259.3 + 24697.8i 0.166097 + 0.287689i 0.937044 0.349210i \(-0.113550\pi\)
−0.770947 + 0.636899i \(0.780217\pi\)
\(294\) 0 0
\(295\) 66995.6 + 38679.9i 0.769843 + 0.444469i
\(296\) −38728.7 + 4797.95i −0.442027 + 0.0547611i
\(297\) 0 0
\(298\) −64902.9 + 2668.11i −0.730856 + 0.0300449i
\(299\) 53380.6 + 30819.3i 0.597092 + 0.344731i
\(300\) 0 0
\(301\) −9181.62 15903.0i −0.101341 0.175528i
\(302\) 82875.2 52501.0i 0.908679 0.575644i
\(303\) 0 0
\(304\) −40566.0 15234.6i −0.438950 0.164848i
\(305\) 42194.0 0.453577
\(306\) 0 0
\(307\) 115338.i 1.22376i −0.790952 0.611879i \(-0.790414\pi\)
0.790952 0.611879i \(-0.209586\pi\)
\(308\) 92325.6 195388.i 0.973242 2.05966i
\(309\) 0 0
\(310\) 78043.1 49439.9i 0.812103 0.514463i
\(311\) −85566.6 + 49401.9i −0.884674 + 0.510767i −0.872197 0.489155i \(-0.837305\pi\)
−0.0124776 + 0.999922i \(0.503972\pi\)
\(312\) 0 0
\(313\) 37066.1 64200.3i 0.378345 0.655313i −0.612477 0.790489i \(-0.709827\pi\)
0.990822 + 0.135176i \(0.0431600\pi\)
\(314\) −158482. + 6515.09i −1.60739 + 0.0660786i
\(315\) 0 0
\(316\) −2480.88 30123.2i −0.0248445 0.301667i
\(317\) −1057.30 + 1831.29i −0.0105215 + 0.0182238i −0.871238 0.490860i \(-0.836682\pi\)
0.860717 + 0.509084i \(0.170016\pi\)
\(318\) 0 0
\(319\) 3521.39 2033.08i 0.0346045 0.0199789i
\(320\) 84893.7 + 87529.0i 0.829040 + 0.854775i
\(321\) 0 0
\(322\) 39895.2 76163.6i 0.384777 0.734575i
\(323\) 16769.7i 0.160739i
\(324\) 0 0
\(325\) 44868.0 0.424785
\(326\) −89733.2 47003.1i −0.844342 0.442273i
\(327\) 0 0
\(328\) 15933.6 + 21096.9i 0.148104 + 0.196097i
\(329\) 78522.8 + 136006.i 0.725444 + 1.25651i
\(330\) 0 0
\(331\) 12334.0 + 7121.02i 0.112576 + 0.0649960i 0.555231 0.831696i \(-0.312630\pi\)
−0.442655 + 0.896692i \(0.645963\pi\)
\(332\) −8843.19 107375.i −0.0802292 0.974156i
\(333\) 0 0
\(334\) −4573.98 111264.i −0.0410017 0.997384i
\(335\) 154561. + 89235.7i 1.37724 + 0.795150i
\(336\) 0 0
\(337\) −37711.8 65318.7i −0.332061 0.575146i 0.650855 0.759202i \(-0.274411\pi\)
−0.982916 + 0.184056i \(0.941077\pi\)
\(338\) 2016.79 + 3183.59i 0.0176534 + 0.0278666i
\(339\) 0 0
\(340\) 20160.7 42665.9i 0.174400 0.369082i
\(341\) −174942. −1.50448
\(342\) 0 0
\(343\) 72725.3i 0.618155i
\(344\) −18069.1 7646.75i −0.152693 0.0646190i
\(345\) 0 0
\(346\) 47209.9 + 74522.9i 0.394349 + 0.622498i
\(347\) 128553. 74220.2i 1.06764 0.616401i 0.140103 0.990137i \(-0.455257\pi\)
0.927535 + 0.373736i \(0.121923\pi\)
\(348\) 0 0
\(349\) 11665.4 20205.1i 0.0957745 0.165886i −0.814157 0.580645i \(-0.802801\pi\)
0.909932 + 0.414758i \(0.136134\pi\)
\(350\) −2570.71 62533.6i −0.0209854 0.510478i
\(351\) 0 0
\(352\) −47100.8 226044.i −0.380140 1.82435i
\(353\) 9687.21 16778.7i 0.0777409 0.134651i −0.824534 0.565812i \(-0.808563\pi\)
0.902275 + 0.431161i \(0.141896\pi\)
\(354\) 0 0
\(355\) 31954.1 18448.7i 0.253554 0.146389i
\(356\) 85971.3 + 124121.i 0.678349 + 0.979364i
\(357\) 0 0
\(358\) −186072. 97466.3i −1.45183 0.760481i
\(359\) 139927.i 1.08571i 0.839827 + 0.542854i \(0.182656\pi\)
−0.839827 + 0.542854i \(0.817344\pi\)
\(360\) 0 0
\(361\) 101670. 0.780148
\(362\) −13406.5 + 25594.4i −0.102306 + 0.195311i
\(363\) 0 0
\(364\) 135325. 93731.7i 1.02135 0.707431i
\(365\) −75325.5 130468.i −0.565400 0.979302i
\(366\) 0 0
\(367\) −79304.5 45786.5i −0.588797 0.339942i 0.175825 0.984421i \(-0.443741\pi\)
−0.764622 + 0.644479i \(0.777074\pi\)
\(368\) −15029.9 90628.9i −0.110984 0.669224i
\(369\) 0 0
\(370\) 72547.7 2982.38i 0.529932 0.0217851i
\(371\) 105527. + 60926.1i 0.766684 + 0.442645i
\(372\) 0 0
\(373\) −42790.4 74115.1i −0.307559 0.532708i 0.670269 0.742118i \(-0.266179\pi\)
−0.977828 + 0.209411i \(0.932845\pi\)
\(374\) −75486.3 + 47820.2i −0.539666 + 0.341875i
\(375\) 0 0
\(376\) 154530. + 65396.4i 1.09304 + 0.462571i
\(377\) 3097.38 0.0217928
\(378\) 0 0
\(379\) 39838.1i 0.277345i 0.990338 + 0.138672i \(0.0442835\pi\)
−0.990338 + 0.138672i \(0.955716\pi\)
\(380\) 72895.3 + 34444.8i 0.504815 + 0.238537i
\(381\) 0 0
\(382\) 35759.4 22653.4i 0.245055 0.155241i
\(383\) −147816. + 85341.8i −1.00769 + 0.581787i −0.910513 0.413480i \(-0.864313\pi\)
−0.0971722 + 0.995268i \(0.530980\pi\)
\(384\) 0 0
\(385\) −201039. + 348210.i −1.35631 + 2.34920i
\(386\) 156214. 6421.84i 1.04844 0.0431007i
\(387\) 0 0
\(388\) −232745. + 19168.3i −1.54603 + 0.127327i
\(389\) 107907. 186901.i 0.713103 1.23513i −0.250583 0.968095i \(-0.580622\pi\)
0.963687 0.267036i \(-0.0860443\pi\)
\(390\) 0 0
\(391\) −30789.5 + 17776.3i −0.201395 + 0.116275i
\(392\) −45779.3 60614.2i −0.297918 0.394459i
\(393\) 0 0
\(394\) 20082.3 38338.9i 0.129366 0.246972i
\(395\) 56236.6i 0.360434i
\(396\) 0 0
\(397\) 292553. 1.85620 0.928098 0.372336i \(-0.121443\pi\)
0.928098 + 0.372336i \(0.121443\pi\)
\(398\) 2860.84 + 1498.53i 0.0180604 + 0.00946021i
\(399\) 0 0
\(400\) −42460.1 51661.9i −0.265376 0.322887i
\(401\) 102157. + 176941.i 0.635300 + 1.10037i 0.986452 + 0.164053i \(0.0524567\pi\)
−0.351152 + 0.936318i \(0.614210\pi\)
\(402\) 0 0
\(403\) −115408. 66631.1i −0.710604 0.410267i
\(404\) −103034. + 8485.63i −0.631274 + 0.0519902i
\(405\) 0 0
\(406\) −177.464 4316.90i −0.00107661 0.0261891i
\(407\) −119073. 68746.9i −0.718827 0.415015i
\(408\) 0 0
\(409\) −17364.4 30076.0i −0.103804 0.179793i 0.809445 0.587196i \(-0.199768\pi\)
−0.913249 + 0.407402i \(0.866435\pi\)
\(410\) −26323.9 41553.5i −0.156597 0.247195i
\(411\) 0 0
\(412\) 233718. + 110438.i 1.37689 + 0.650613i
\(413\) −155655. −0.912564
\(414\) 0 0
\(415\) 200458.i 1.16393i
\(416\) 55022.3 167059.i 0.317945 0.965349i
\(417\) 0 0
\(418\) −81701.5 128969.i −0.467603 0.738132i
\(419\) 277682. 160320.i 1.58169 0.913187i 0.587073 0.809534i \(-0.300280\pi\)
0.994614 0.103653i \(-0.0330530\pi\)
\(420\) 0 0
\(421\) −67885.7 + 117582.i −0.383014 + 0.663399i −0.991491 0.130172i \(-0.958447\pi\)
0.608478 + 0.793571i \(0.291780\pi\)
\(422\) −9994.93 243131.i −0.0561248 1.36526i
\(423\) 0 0
\(424\) 129208. 16007.0i 0.718714 0.0890388i
\(425\) −12939.7 + 22412.3i −0.0716386 + 0.124082i
\(426\) 0 0
\(427\) −73524.1 + 42449.2i −0.403250 + 0.232816i
\(428\) 40317.5 27925.6i 0.220093 0.152446i
\(429\) 0 0
\(430\) 32338.0 + 16938.9i 0.174894 + 0.0916112i
\(431\) 31343.0i 0.168728i 0.996435 + 0.0843638i \(0.0268858\pi\)
−0.996435 + 0.0843638i \(0.973114\pi\)
\(432\) 0 0
\(433\) 101022. 0.538815 0.269407 0.963026i \(-0.413172\pi\)
0.269407 + 0.963026i \(0.413172\pi\)
\(434\) −86253.1 + 164665.i −0.457926 + 0.874223i
\(435\) 0 0
\(436\) 161515. + 233187.i 0.849651 + 1.22668i
\(437\) −30371.1 52604.3i −0.159037 0.275460i
\(438\) 0 0
\(439\) 157593. + 90986.2i 0.817724 + 0.472113i 0.849631 0.527378i \(-0.176825\pi\)
−0.0319068 + 0.999491i \(0.510158\pi\)
\(440\) 52818.8 + 426349.i 0.272824 + 2.20222i
\(441\) 0 0
\(442\) −68011.3 + 2795.89i −0.348126 + 0.0143112i
\(443\) −32206.4 18594.4i −0.164110 0.0947490i 0.415696 0.909504i \(-0.363538\pi\)
−0.579806 + 0.814755i \(0.696872\pi\)
\(444\) 0 0
\(445\) −140462. 243287.i −0.709315 1.22857i
\(446\) 36255.7 22967.8i 0.182266 0.115465i
\(447\) 0 0
\(448\) −235987. 67114.3i −1.17580 0.334395i
\(449\) 20385.0 0.101115 0.0505577 0.998721i \(-0.483900\pi\)
0.0505577 + 0.998721i \(0.483900\pi\)
\(450\) 0 0
\(451\) 93146.9i 0.457947i
\(452\) −101121. + 214002.i −0.494953 + 1.04747i
\(453\) 0 0
\(454\) −255898. + 162110.i −1.24153 + 0.786501i
\(455\) −265249. + 153141.i −1.28124 + 0.739724i
\(456\) 0 0
\(457\) 139829. 242191.i 0.669521 1.15964i −0.308517 0.951219i \(-0.599833\pi\)
0.978038 0.208426i \(-0.0668340\pi\)
\(458\) 213286. 8768.03i 1.01679 0.0417995i
\(459\) 0 0
\(460\) 14029.6 + 170349.i 0.0663023 + 0.805054i
\(461\) −80298.4 + 139081.i −0.377838 + 0.654434i −0.990747 0.135719i \(-0.956666\pi\)
0.612910 + 0.790153i \(0.289999\pi\)
\(462\) 0 0
\(463\) −85869.5 + 49576.8i −0.400569 + 0.231268i −0.686729 0.726913i \(-0.740954\pi\)
0.286161 + 0.958182i \(0.407621\pi\)
\(464\) −2931.16 3566.39i −0.0136146 0.0165651i
\(465\) 0 0
\(466\) −104839. + 200147.i −0.482780 + 0.921673i
\(467\) 278790.i 1.27833i −0.769068 0.639167i \(-0.779279\pi\)
0.769068 0.639167i \(-0.220721\pi\)
\(468\) 0 0
\(469\) −359101. −1.63257
\(470\) −276560. 144865.i −1.25197 0.655792i
\(471\) 0 0
\(472\) −132714. + 100234.i −0.595709 + 0.449913i
\(473\) −34564.0 59866.6i −0.154490 0.267585i
\(474\) 0 0
\(475\) −38291.7 22107.7i −0.169714 0.0979844i
\(476\) 7793.40 + 94628.8i 0.0343964 + 0.417647i
\(477\) 0 0
\(478\) 7884.90 + 191804.i 0.0345096 + 0.839462i
\(479\) 27705.5 + 15995.8i 0.120752 + 0.0697163i 0.559160 0.829060i \(-0.311124\pi\)
−0.438407 + 0.898776i \(0.644457\pi\)
\(480\) 0 0
\(481\) −52367.8 90703.7i −0.226347 0.392044i
\(482\) −137320. 216765.i −0.591070 0.933029i
\(483\) 0 0
\(484\) 247477. 523733.i 1.05644 2.23573i
\(485\) 434509. 1.84721
\(486\) 0 0
\(487\) 346823.i 1.46235i −0.682192 0.731173i \(-0.738973\pi\)
0.682192 0.731173i \(-0.261027\pi\)
\(488\) −35353.1 + 83538.5i −0.148452 + 0.350790i
\(489\) 0 0
\(490\) 75632.1 + 119389.i 0.315003 + 0.497246i
\(491\) −207830. + 119991.i −0.862076 + 0.497720i −0.864707 0.502277i \(-0.832496\pi\)
0.00263098 + 0.999997i \(0.499163\pi\)
\(492\) 0 0
\(493\) −893.273 + 1547.19i −0.00367528 + 0.00636577i
\(494\) −4776.82 116198.i −0.0195743 0.476152i
\(495\) 0 0
\(496\) 32494.6 + 195939.i 0.132083 + 0.796448i
\(497\) −37120.5 + 64294.7i −0.150280 + 0.260293i
\(498\) 0 0
\(499\) 295354. 170523.i 1.18616 0.684828i 0.228726 0.973491i \(-0.426544\pi\)
0.957431 + 0.288663i \(0.0932107\pi\)
\(500\) −98661.2 142442.i −0.394645 0.569767i
\(501\) 0 0
\(502\) −231134. 121070.i −0.917184 0.480429i
\(503\) 3886.22i 0.0153600i 0.999971 + 0.00768001i \(0.00244465\pi\)
−0.999971 + 0.00768001i \(0.997555\pi\)
\(504\) 0 0
\(505\) 192353. 0.754250
\(506\) 150185. 286716.i 0.586576 1.11983i
\(507\) 0 0
\(508\) 243051. 168347.i 0.941823 0.652347i
\(509\) 98673.1 + 170907.i 0.380858 + 0.659666i 0.991185 0.132484i \(-0.0422952\pi\)
−0.610327 + 0.792150i \(0.708962\pi\)
\(510\) 0 0
\(511\) 262513. + 151562.i 1.00533 + 0.580427i
\(512\) −244425. + 94740.3i −0.932409 + 0.361405i
\(513\) 0 0
\(514\) −173117. + 7116.71i −0.655260 + 0.0269372i
\(515\) −416521. 240478.i −1.57044 0.906696i
\(516\) 0 0
\(517\) 295597. + 511990.i 1.10591 + 1.91549i
\(518\) −123416. + 78183.2i −0.459950 + 0.291376i
\(519\) 0 0
\(520\) −127541. + 301377.i −0.471676 + 1.11456i
\(521\) −229165. −0.844255 −0.422127 0.906536i \(-0.638717\pi\)
−0.422127 + 0.906536i \(0.638717\pi\)
\(522\) 0 0
\(523\) 346673.i 1.26741i −0.773575 0.633705i \(-0.781533\pi\)
0.773575 0.633705i \(-0.218467\pi\)
\(524\) 120370. + 56877.7i 0.438384 + 0.207147i
\(525\) 0 0
\(526\) −286559. + 181534.i −1.03572 + 0.656124i
\(527\) 66566.6 38432.2i 0.239682 0.138380i
\(528\) 0 0
\(529\) −75532.2 + 130826.i −0.269911 + 0.467500i
\(530\) −242035. + 9949.89i −0.861642 + 0.0354215i
\(531\) 0 0
\(532\) −161675. + 13315.2i −0.571241 + 0.0470460i
\(533\) −35477.2 + 61448.4i −0.124881 + 0.216300i
\(534\) 0 0
\(535\) −79025.8 + 45625.6i −0.276097 + 0.159405i
\(536\) −306176. + 231242.i −1.06572 + 0.804890i
\(537\) 0 0
\(538\) 123770. 236289.i 0.427613 0.816353i
\(539\) 267623.i 0.921184i
\(540\) 0 0
\(541\) −287354. −0.981799 −0.490900 0.871216i \(-0.663332\pi\)
−0.490900 + 0.871216i \(0.663332\pi\)
\(542\) 433797. + 227227.i 1.47669 + 0.773501i
\(543\) 0 0
\(544\) 67580.7 + 75663.8i 0.228362 + 0.255676i
\(545\) −263888. 457067.i −0.888436 1.53882i
\(546\) 0 0
\(547\) −486589. 280932.i −1.62625 0.938917i −0.985198 0.171421i \(-0.945164\pi\)
−0.641054 0.767496i \(1.27850\pi\)
\(548\) 341352. 28112.9i 1.13669 0.0936148i
\(549\) 0 0
\(550\) −9677.37 235406.i −0.0319913 0.778203i
\(551\) −2643.40 1526.17i −0.00870684 0.00502689i
\(552\) 0 0
\(553\) −56576.7 97993.6i −0.185006 0.320441i
\(554\) 294230. + 464455.i 0.958666 + 1.51330i
\(555\) 0 0
\(556\) 263653. + 124583.i 0.852871 + 0.403002i
\(557\) 393303. 1.26770 0.633850 0.773456i \(-0.281474\pi\)
0.633850 + 0.773456i \(0.281474\pi\)
\(558\) 0 0
\(559\) 52658.1i 0.168516i
\(560\) 427344. + 160490.i 1.36270 + 0.511766i
\(561\) 0 0
\(562\) −29975.3 47317.3i −0.0949054 0.149812i
\(563\) 481867. 278206.i 1.52023 0.877707i 0.520518 0.853851i \(-0.325739\pi\)
0.999715 0.0238561i \(-0.00759436\pi\)
\(564\) 0 0
\(565\) 220191. 381382.i 0.689768 1.19471i
\(566\) 18902.1 + 459802.i 0.0590035 + 1.43529i
\(567\) 0 0
\(568\) 9752.64 + 78722.5i 0.0302291 + 0.244007i
\(569\) 91030.8 157670.i 0.281167 0.486995i −0.690506 0.723327i \(-0.742612\pi\)
0.971672 + 0.236332i \(0.0759453\pi\)
\(570\) 0 0
\(571\) 190279. 109858.i 0.583604 0.336944i −0.178960 0.983856i \(-0.557273\pi\)
0.762565 + 0.646912i \(0.223940\pi\)
\(572\) 509427. 352851.i 1.55701 1.07845i
\(573\) 0 0
\(574\) 87674.8 + 45924.8i 0.266104 + 0.139387i
\(575\) 93739.0i 0.283521i
\(576\) 0 0
\(577\) 9527.81 0.0286181 0.0143091 0.999898i \(-0.495445\pi\)
0.0143091 + 0.999898i \(0.495445\pi\)
\(578\) −136800. + 261163.i −0.409477 + 0.781729i
\(579\) 0 0
\(580\) 4890.64 + 7060.84i 0.0145382 + 0.0209894i
\(581\) −201670. 349302.i −0.597432 1.03478i
\(582\) 0 0
\(583\) 397254. + 229355.i 1.16878 + 0.674794i
\(584\) 321421. 39819.7i 0.942429 0.116754i
\(585\) 0 0
\(586\) 113978. 4685.55i 0.331914 0.0136447i
\(587\) −8948.63 5166.49i −0.0259705 0.0149941i 0.486959 0.873425i \(-0.338106\pi\)
−0.512929 + 0.858431i \(0.671440\pi\)
\(588\) 0 0
\(589\) 65662.1 + 113730.i 0.189271 + 0.327827i
\(590\) 261401. 165596.i 0.750937 0.475715i
\(591\) 0 0
\(592\) −54880.7 + 146134.i −0.156594 + 0.416972i
\(593\) −143639. −0.408473 −0.204236 0.978922i \(-0.565471\pi\)
−0.204236 + 0.978922i \(0.565471\pi\)
\(594\) 0 0
\(595\) 176661.i 0.499008i
\(596\) −111007. + 234924.i −0.312507 + 0.661356i
\(597\) 0 0
\(598\) 208279. 131943.i 0.582428 0.368965i
\(599\) 305650. 176467.i 0.851865 0.491824i −0.00941494 0.999956i \(-0.502997\pi\)
0.861280 + 0.508131i \(0.169664\pi\)
\(600\) 0 0
\(601\) −17733.8 + 30715.9i −0.0490969 + 0.0850382i −0.889529 0.456878i \(-0.848968\pi\)
0.840433 + 0.541916i \(0.182301\pi\)
\(602\) −73390.9 + 3017.04i −0.202511 + 0.00832509i
\(603\) 0 0
\(604\) −32209.8 391097.i −0.0882907 1.07204i
\(605\) −538881. + 933369.i −1.47225 + 2.55001i
\(606\) 0 0
\(607\) 424309. 244975.i 1.15161 0.664881i 0.202330 0.979317i \(-0.435149\pi\)
0.949279 + 0.314436i \(0.101815\pi\)
\(608\) −129273. + 115463.i −0.349703 + 0.312345i
\(609\) 0 0
\(610\) 78313.2 149507.i 0.210463 0.401793i
\(611\) 450342.i 1.20631i
\(612\) 0 0
\(613\) 284390. 0.756821 0.378410 0.925638i \(-0.376471\pi\)
0.378410 + 0.925638i \(0.376471\pi\)
\(614\) −408680. 214070.i −1.08404 0.567831i
\(615\) 0 0
\(616\) −520965. 689785.i −1.37293 1.81783i
\(617\) 98237.4 + 170152.i 0.258052 + 0.446958i 0.965720 0.259586i \(-0.0835862\pi\)
−0.707668 + 0.706545i \(0.750253\pi\)
\(618\) 0 0
\(619\) −58731.2 33908.5i −0.153281 0.0884967i 0.421398 0.906876i \(-0.361540\pi\)
−0.574679 + 0.818379i \(0.694873\pi\)
\(620\) −30331.8 368294.i −0.0789069 0.958101i
\(621\) 0 0
\(622\) 16233.3 + 394882.i 0.0419590 + 1.02067i
\(623\) 489517. + 282623.i 1.26122 + 0.728167i
\(624\) 0 0
\(625\) 242826. + 420586.i 0.621634 + 1.07670i
\(626\) −158687. 250495.i −0.404942 0.639219i
\(627\) 0 0
\(628\) −271062. + 573647.i −0.687306 + 1.45454i
\(629\) 60410.6 0.152691
\(630\) 0 0
\(631\) 716972.i 1.80071i 0.435158 + 0.900354i \(0.356692\pi\)
−0.435158 + 0.900354i \(0.643308\pi\)
\(632\) −111341. 47118.9i −0.278754 0.117967i
\(633\) 0 0
\(634\) 4526.49 + 7145.27i 0.0112612 + 0.0177762i
\(635\) −476401. + 275050.i −1.18148 + 0.682125i
\(636\) 0 0
\(637\) 101931. 176549.i 0.251204 0.435098i
\(638\) −668.061 16250.9i −0.00164125 0.0399241i
\(639\) 0 0
\(640\) 467709. 138350.i 1.14187 0.337769i
\(641\) 321445. 556760.i 0.782332 1.35504i −0.148248 0.988950i \(-0.547363\pi\)
0.930580 0.366089i \(-0.119303\pi\)
\(642\) 0 0
\(643\) 1326.59 765.910i 0.00320861 0.00185249i −0.498395 0.866950i \(-0.666077\pi\)
0.501603 + 0.865098i \(0.332744\pi\)
\(644\) −195826. 282723.i −0.472171 0.681695i
\(645\) 0 0
\(646\) 59420.6 + 31125.0i 0.142387 + 0.0745838i
\(647\) 106720.i 0.254938i 0.991843 + 0.127469i \(0.0406854\pi\)
−0.991843 + 0.127469i \(0.959315\pi\)
\(648\) 0 0
\(649\) −585960. −1.39116
\(650\) 83276.1 158982.i 0.197103 0.376288i
\(651\) 0 0
\(652\) −333094. + 230715.i −0.783560 + 0.542727i
\(653\) 114833. + 198896.i 0.269301 + 0.466444i 0.968682 0.248306i \(-0.0798739\pi\)
−0.699380 + 0.714750i \(0.746541\pi\)
\(654\) 0 0
\(655\) −214517. 123851.i −0.500010 0.288681i
\(656\) 104326. 17301.5i 0.242430 0.0402046i
\(657\) 0 0
\(658\) 627652. 25802.3i 1.44966 0.0595946i
\(659\) 337909. + 195092.i 0.778089 + 0.449230i 0.835753 0.549106i \(-0.185032\pi\)
−0.0576633 + 0.998336i \(0.518365\pi\)
\(660\) 0 0
\(661\) −223443. 387014.i −0.511403 0.885776i −0.999913 0.0132177i \(-0.995793\pi\)
0.488509 0.872559i \(-0.337541\pi\)
\(662\) 48124.3 30486.5i 0.109812 0.0695651i
\(663\) 0 0
\(664\) −396879. 167957.i −0.900166 0.380945i
\(665\) 301829. 0.682523
\(666\) 0 0
\(667\) 6471.12i 0.0145455i
\(668\) −402735. 190302.i −0.902540 0.426472i
\(669\) 0 0
\(670\) 603060. 382036.i 1.34342 0.851048i
\(671\) −276780. + 159799.i −0.614737 + 0.354919i
\(672\) 0 0
\(673\) −169746. + 294009.i −0.374774 + 0.649128i −0.990293 0.138994i \(-0.955613\pi\)
0.615519 + 0.788122i \(0.288946\pi\)
\(674\) −301440. + 12392.0i −0.663561 + 0.0272785i
\(675\) 0 0
\(676\) 15023.7 1237.32i 0.0328764 0.00270762i
\(677\) 266702. 461941.i 0.581900 1.00788i −0.413354 0.910570i \(-0.635643\pi\)
0.995254 0.0973098i \(-0.0310238\pi\)
\(678\) 0 0
\(679\) −757142. + 437136.i −1.64224 + 0.948150i
\(680\) −113760. 150625.i −0.246022 0.325746i
\(681\) 0 0
\(682\) −324698. + 619878.i −0.698089 + 1.33272i
\(683\) 175866.i 0.376999i −0.982073 0.188500i \(-0.939638\pi\)
0.982073 0.188500i \(-0.0603624\pi\)
\(684\) 0 0
\(685\) −637265. −1.35812
\(686\) 257689. + 134980.i 0.547581 + 0.286828i
\(687\) 0 0
\(688\) −60631.7 + 49832.2i −0.128092 + 0.105277i
\(689\) 174711. + 302608.i 0.368028 + 0.637444i
\(690\) 0 0
\(691\) 203114. + 117268.i 0.425386 + 0.245597i 0.697379 0.716702i \(-0.254349\pi\)
−0.271993 + 0.962299i \(0.587683\pi\)
\(692\) 351682. 28963.7i 0.734409 0.0604842i
\(693\) 0 0
\(694\) −24388.5 593261.i −0.0506368 1.23176i
\(695\) −469869. 271279.i −0.972762 0.561625i
\(696\) 0 0
\(697\) −20463.0 35442.9i −0.0421214 0.0729565i
\(698\) −49942.0 78835.6i −0.102507 0.161812i
\(699\) 0 0
\(700\) −226348. 106955.i −0.461935 0.218276i
\(701\) −192485. −0.391707 −0.195853 0.980633i \(-0.562748\pi\)
−0.195853 + 0.980633i \(0.562748\pi\)
\(702\) 0 0
\(703\) 103213.i 0.208844i
\(704\) −888369. 252650.i −1.79245 0.509770i
\(705\) 0 0
\(706\) −41472.9 65466.7i −0.0832060 0.131344i
\(707\) −335179. + 193516.i −0.670561 + 0.387148i
\(708\) 0 0
\(709\) 300439. 520376.i 0.597674 1.03520i −0.395489 0.918471i \(-0.629425\pi\)
0.993164 0.116731i \(-0.0372417\pi\)
\(710\) −6062.18 147465.i −0.0120258 0.292532i
\(711\) 0 0
\(712\) 599365. 74253.1i 1.18231 0.146472i
\(713\) −139207. + 241114.i −0.273831 + 0.474288i
\(714\) 0 0
\(715\) −998522. + 576497.i −1.95320 + 1.12768i
\(716\) −690710. + 478415.i −1.34732 + 0.933209i
\(717\) 0 0
\(718\) 495808. + 259708.i 0.961755 + 0.503776i
\(719\) 37302.4i 0.0721571i 0.999349 + 0.0360786i \(0.0114867\pi\)
−0.999349 + 0.0360786i \(0.988513\pi\)
\(720\) 0 0
\(721\) 967729. 1.86159
\(722\) 188702. 360249.i 0.361994 0.691080i
\(723\) 0 0
\(724\) 65806.3 + 95007.6i 0.125542 + 0.181251i
\(725\) −2355.23 4079.37i −0.00448081 0.00776099i
\(726\) 0 0
\(727\) −647844. 374033.i −1.22575 0.707686i −0.259611 0.965713i \(-0.583594\pi\)
−0.966138 + 0.258027i \(0.916928\pi\)
\(728\) −80955.8 653469.i −0.152751 1.23300i
\(729\) 0 0
\(730\) −602095. + 24751.7i −1.12985 + 0.0464471i
\(731\) 26303.6 + 15186.4i 0.0492244 + 0.0284197i
\(732\) 0 0
\(733\) 131709. + 228126.i 0.245136 + 0.424588i 0.962170 0.272450i \(-0.0878341\pi\)
−0.717034 + 0.697038i \(0.754501\pi\)
\(734\) −309428. + 196021.i −0.574337 + 0.363840i
\(735\) 0 0
\(736\) −349024. 114954.i −0.644317 0.212211i
\(737\) −1.35183e6 −2.48878
\(738\) 0 0
\(739\) 288908.i 0.529018i 0.964383 + 0.264509i \(0.0852099\pi\)
−0.964383 + 0.264509i \(0.914790\pi\)
\(740\) 124083. 262596.i 0.226594 0.479539i
\(741\) 0 0
\(742\) 411742. 260837.i 0.747855 0.473763i
\(743\) 271416. 156702.i 0.491651 0.283855i −0.233608 0.972331i \(-0.575053\pi\)
0.725259 + 0.688476i \(0.241720\pi\)
\(744\) 0 0
\(745\) 241719. 418670.i 0.435510 0.754326i
\(746\) −342034. + 14060.8i −0.614599 + 0.0252657i
\(747\) 0 0
\(748\) 29338.1 + 356228.i 0.0524359 + 0.636685i
\(749\) 91802.9 159007.i 0.163641 0.283435i
\(750\) 0 0
\(751\) 204539. 118091.i 0.362658 0.209381i −0.307588 0.951520i \(-0.599522\pi\)
0.670246 + 0.742139i \(0.266189\pi\)
\(752\) 518533. 426174.i 0.916940 0.753618i
\(753\) 0 0
\(754\) 5748.83 10975.0i 0.0101120 0.0193047i
\(755\) 730134.i 1.28088i
\(756\) 0 0
\(757\) −1.00219e6 −1.74888 −0.874438 0.485137i \(-0.838770\pi\)
−0.874438 + 0.485137i \(0.838770\pi\)
\(758\) 141159. + 73940.5i 0.245681 + 0.128690i
\(759\) 0 0
\(760\) 257345. 194361.i 0.445542 0.336498i
\(761\) 456412. + 790529.i 0.788112 + 1.36505i 0.927122 + 0.374759i \(0.122275\pi\)
−0.139010 + 0.990291i \(0.544392\pi\)
\(762\) 0 0
\(763\) 919661. + 530967.i 1.57971 + 0.912049i
\(764\) −13898.1 168753.i −0.0238105 0.289111i
\(765\) 0 0
\(766\) 28043.0 + 682158.i 0.0477933 + 1.16259i
\(767\) −386554. 223177.i −0.657082 0.379366i
\(768\) 0 0
\(769\) 104325. + 180697.i 0.176416 + 0.305561i 0.940650 0.339378i \(-0.110216\pi\)
−0.764235 + 0.644938i \(0.776883\pi\)
\(770\) 860689. + 1.35863e6i 1.45166 + 2.29151i
\(771\) 0 0
\(772\) 267183. 565437.i 0.448305 0.948744i
\(773\) 661279. 1.10669 0.553345 0.832952i \(-0.313351\pi\)
0.553345 + 0.832952i \(0.313351\pi\)
\(774\) 0 0
\(775\) 202663.i 0.337420i
\(776\) −364061. + 860269.i −0.604576 + 1.42860i
\(777\) 0 0
\(778\)