Properties

Label 108.5.f.a.91.14
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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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 91.14
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.14

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 −0.398104 0.917340i \(-0.630332\pi\)
0.993492 0.113902i \(-0.0363350\pi\)
\(6\) 0 0
\(7\) −51.8739 + 29.9494i −1.05865 + 0.611212i −0.925059 0.379824i \(-0.875984\pi\)
−0.133592 + 0.991036i \(0.542651\pi\)
\(8\) −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 −0.625406 + 0.780300i \(0.715066\pi\)
−0.988462 + 0.151467i \(0.951600\pi\)
\(12\) 0 0
\(13\) −85.8824 + 148.753i −0.508180 + 0.880194i 0.491775 + 0.870722i \(0.336348\pi\)
−0.999955 + 0.00947137i \(0.996985\pi\)
\(14\) −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 \(-0.924674\pi\)
0.972130 0.234442i \(-0.0753262\pi\)
\(20\) 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 0.176620 0.984279i \(-0.443484\pi\)
−0.764101 + 0.645097i \(0.776817\pi\)
\(24\) 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 0.860615 0.509256i \(-0.170079\pi\)
−0.871336 + 0.490687i \(0.836746\pi\)
\(30\) 0 0
\(31\) 671.898 + 387.920i 0.699165 + 0.403663i 0.807036 0.590502i \(-0.201070\pi\)
−0.107871 + 0.994165i \(0.534403\pi\)
\(32\) 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 −0.920899 0.389802i \(-0.872543\pi\)
0.798028 + 0.602620i \(0.205877\pi\)
\(42\) 0 0
\(43\) 265.498 153.286i 0.143590 0.0829019i −0.426484 0.904495i \(-0.640248\pi\)
0.570074 + 0.821593i \(0.306915\pi\)
\(44\) 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 −0.916377 0.400317i \(-0.868900\pi\)
−0.111504 + 0.993764i \(0.535567\pi\)
\(48\) 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 0.787116 0.616805i \(-0.211573\pi\)
−0.140611 + 0.990065i \(0.544907\pi\)
\(60\) 0 0
\(61\) 708.681 + 1227.47i 0.190455 + 0.329877i 0.945401 0.325910i \(-0.105670\pi\)
−0.754946 + 0.655786i \(0.772337\pi\)
\(62\) −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 0.950485 0.310772i \(-0.100588\pi\)
0.206106 + 0.978530i \(0.433921\pi\)
\(68\) −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 \(0.0392310\pi\)
−0.992415 + 0.122936i \(0.960769\pi\)
\(72\) 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 −0.363173 0.931722i \(-0.618307\pi\)
0.625308 + 0.780378i \(0.284973\pi\)
\(80\) −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 −0.0129681 0.999916i \(-0.504128\pi\)
0.859469 + 0.511189i \(0.170795\pi\)
\(84\) 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 0.934439 + 0.356123i \(0.115902\pi\)
−0.158808 + 0.987309i \(0.550765\pi\)
\(98\) 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 0.979799 0.199987i \(-0.0640900\pi\)
−0.663093 + 0.748537i \(0.730757\pi\)
\(102\) 0 0
\(103\) −13991.6 8078.04i −1.31884 0.761432i −0.335298 0.942112i \(-0.608837\pi\)
−0.983542 + 0.180680i \(0.942170\pi\)
\(104\) 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 \(-0.957261\pi\)
0.990999 0.133866i \(-0.0427392\pi\)
\(108\) 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 0.416305 + 0.909225i \(0.363325\pi\)
−0.995565 + 0.0940814i \(0.970009\pi\)
\(114\) 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 \(-0.805841\pi\)
0.819667 0.572841i \(-0.194159\pi\)
\(128\) 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 0.275133 0.961406i \(-0.411278\pi\)
−0.695036 + 0.718975i \(0.744611\pi\)
\(132\) 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 −0.996538 0.0831367i \(-0.973506\pi\)
0.426271 0.904596i \(-0.359827\pi\)
\(138\) 0 0
\(139\) −15783.6 9112.67i −0.816915 0.471646i 0.0324367 0.999474i \(-0.489673\pi\)
−0.849351 + 0.527828i \(0.823007\pi\)
\(140\) −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 −0.988894 0.148622i \(-0.952516\pi\)
0.623158 + 0.782096i \(0.285850\pi\)
\(150\) 0 0
\(151\) 21240.4 12263.2i 0.931557 0.537835i 0.0442533 0.999020i \(-0.485909\pi\)
0.887304 + 0.461186i \(0.152576\pi\)
\(152\) −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 0.112337 + 0.993670i \(0.464166\pi\)
−0.916712 + 0.399548i \(0.869167\pi\)
\(158\) 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 \(0.158124\pi\)
−0.879130 + 0.476581i \(0.841876\pi\)
\(164\) −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 0.865513 0.500886i \(-0.166992\pi\)
−0.00102363 + 0.999999i \(0.500326\pi\)
\(168\) 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 0.620875 0.783909i \(-0.286777\pi\)
−0.989323 + 0.145739i \(0.953444\pi\)
\(174\) 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 \(0.305734\pi\)
−0.573118 + 0.819473i \(0.694266\pi\)
\(180\) 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 −0.369100 0.929390i \(-0.620334\pi\)
0.620325 + 0.784345i \(0.287001\pi\)
\(192\) 0 0
\(193\) 19543.2 33849.9i 0.524665 0.908746i −0.474923 0.880028i \(-0.657524\pi\)
0.999588 0.0287188i \(-0.00914273\pi\)
\(194\) −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 \(-0.996755\pi\)
0.999948 0.0101940i \(-0.00324492\pi\)
\(200\) 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 0.956787 0.290790i \(-0.0939181\pi\)
0.226562 + 0.973997i \(0.427251\pi\)
\(212\) 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 −0.403654 0.914912i \(-0.632260\pi\)
0.590509 + 0.807031i \(0.298927\pi\)
\(224\) −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 −0.975511 0.219951i \(-0.929410\pi\)
−0.297272 + 0.954793i \(0.596077\pi\)
\(228\) 0 0
\(229\) 26683.3 46216.8i 0.508825 0.881311i −0.491123 0.871090i \(-0.663413\pi\)
0.999948 0.0102204i \(-0.00325330\pi\)
\(230\) −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 0.0899375 0.995947i \(-0.471333\pi\)
−0.817547 + 0.575862i \(0.804667\pi\)
\(240\) 0 0
\(241\) 32075.1 + 55555.6i 0.552247 + 0.956520i 0.998112 + 0.0614196i \(0.0195628\pi\)
−0.445865 + 0.895100i \(0.647104\pi\)
\(242\) 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 \(0.173210\pi\)
−0.855564 + 0.517696i \(0.826790\pi\)
\(252\) 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 −0.982096 0.188380i \(-0.939676\pi\)
0.654190 + 0.756331i \(0.273010\pi\)
\(258\) 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 −0.925929 0.377698i \(-0.876716\pi\)
−0.135868 + 0.990727i \(0.543382\pi\)
\(264\) 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 \(-0.686332\pi\)
0.552516 0.833502i \(-0.313668\pi\)
\(272\) −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 −0.832937 0.553367i \(-0.813343\pi\)
−0.0627613 0.998029i \(-0.519991\pi\)
\(278\) 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 0.906950 0.421238i \(-0.138404\pi\)
−0.818278 + 0.574822i \(0.805071\pi\)
\(282\) 0 0
\(283\) −99634.2 57523.8i −1.24404 0.718249i −0.274129 0.961693i \(-0.588389\pi\)
−0.969915 + 0.243444i \(0.921723\pi\)
\(284\) −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 −0.770947 0.636899i \(-0.780217\pi\)
0.937044 + 0.349210i \(0.113550\pi\)
\(294\) 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 \(0.209586\pi\)
−0.790952 + 0.611879i \(0.790414\pi\)
\(308\) 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 −0.0124776 0.999922i \(-0.503972\pi\)
−0.872197 + 0.489155i \(0.837305\pi\)
\(312\) 0 0
\(313\) 37066.1 + 64200.3i 0.378345 + 0.655313i 0.990822 0.135176i \(-0.0431600\pi\)
−0.612477 + 0.790489i \(0.709827\pi\)
\(314\) −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 0.860717 0.509084i \(-0.170016\pi\)
−0.871238 + 0.490860i \(0.836682\pi\)
\(318\) 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 −0.442655 0.896692i \(-0.645963\pi\)
0.555231 + 0.831696i \(0.312630\pi\)
\(332\) −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 −0.982916 0.184056i \(-0.941077\pi\)
0.650855 + 0.759202i \(0.274411\pi\)
\(338\) 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 0.927535 0.373736i \(-0.121923\pi\)
0.140103 + 0.990137i \(0.455257\pi\)
\(348\) 0 0
\(349\) 11665.4 + 20205.1i 0.0957745 + 0.165886i 0.909932 0.414758i \(-0.136134\pi\)
−0.814157 + 0.580645i \(0.802801\pi\)
\(350\) −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 0.902275 0.431161i \(-0.141896\pi\)
−0.824534 + 0.565812i \(0.808563\pi\)
\(354\) 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 \(-0.817344\pi\)
0.839827 0.542854i \(-0.182656\pi\)
\(360\) 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 −0.764622 0.644479i \(-0.777074\pi\)
0.175825 + 0.984421i \(0.443741\pi\)
\(368\) −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 −0.977828 0.209411i \(-0.932845\pi\)
0.670269 + 0.742118i \(0.266179\pi\)
\(374\) −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 \(-0.955716\pi\)
0.990338 0.138672i \(-0.0442835\pi\)
\(380\) 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 −0.0971722 0.995268i \(-0.530980\pi\)
−0.910513 + 0.413480i \(0.864313\pi\)
\(384\) 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 0.963687 + 0.267036i \(0.0860443\pi\)
−0.250583 + 0.968095i \(0.580622\pi\)
\(390\) 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 −0.351152 0.936318i \(-0.614210\pi\)
0.986452 0.164053i \(-0.0524567\pi\)
\(402\) 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 −0.913249 0.407402i \(-0.866435\pi\)
0.809445 + 0.587196i \(0.199768\pi\)
\(410\) −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 0.994614 + 0.103653i \(0.0330530\pi\)
0.587073 + 0.809534i \(0.300280\pi\)
\(420\) 0 0
\(421\) −67885.7 117582.i −0.383014 0.663399i 0.608478 0.793571i \(-0.291780\pi\)
−0.991491 + 0.130172i \(0.958447\pi\)
\(422\) −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 \(-0.973114\pi\)
0.996435 0.0843638i \(-0.0268858\pi\)
\(432\) 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 −0.0319068 0.999491i \(-0.510158\pi\)
0.849631 + 0.527378i \(0.176825\pi\)
\(440\) 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 −0.579806 0.814755i \(-0.696872\pi\)
0.415696 + 0.909504i \(0.363538\pi\)
\(444\) 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 0.978038 + 0.208426i \(0.0668340\pi\)
−0.308517 + 0.951219i \(0.599833\pi\)
\(458\) 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 0.612910 0.790153i \(-0.289999\pi\)
−0.990747 + 0.135719i \(0.956666\pi\)
\(462\) 0 0
\(463\) −85869.5 49576.8i −0.400569 0.231268i 0.286161 0.958182i \(-0.407621\pi\)
−0.686729 + 0.726913i \(0.740954\pi\)
\(464\) −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 \(0.220721\pi\)
−0.769068 + 0.639167i \(0.779279\pi\)
\(468\) 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 −0.438407 0.898776i \(-0.644457\pi\)
0.559160 + 0.829060i \(0.311124\pi\)
\(480\) 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 \(0.261027\pi\)
−0.682192 + 0.731173i \(0.738973\pi\)
\(488\) −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 0.00263098 0.999997i \(-0.499163\pi\)
−0.864707 + 0.502277i \(0.832496\pi\)
\(492\) 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 0.957431 0.288663i \(-0.0932107\pi\)
0.228726 + 0.973491i \(0.426544\pi\)
\(500\) −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 \(-0.997555\pi\)
0.999971 0.00768001i \(-0.00244465\pi\)
\(504\) 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 −0.610327 0.792150i \(-0.708962\pi\)
0.991185 + 0.132484i \(0.0422952\pi\)
\(510\) 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 \(0.218467\pi\)
−0.773575 + 0.633705i \(0.781533\pi\)
\(524\) 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 −0.641054 + 0.767496i \(0.721502\pi\)
−0.985198 + 0.171421i \(0.945164\pi\)
\(548\) 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 0.999715 + 0.0238561i \(0.00759436\pi\)
0.520518 + 0.853851i \(0.325739\pi\)
\(564\) 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 0.971672 0.236332i \(-0.0759453\pi\)
−0.690506 + 0.723327i \(0.742612\pi\)
\(570\) 0 0
\(571\) 190279. + 109858.i 0.583604 + 0.336944i 0.762565 0.646912i \(-0.223940\pi\)
−0.178960 + 0.983856i \(0.557273\pi\)
\(572\) 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 −0.512929 0.858431i \(-0.671440\pi\)
0.486959 + 0.873425i \(0.338106\pi\)
\(588\) 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 0.861280 0.508131i \(-0.169664\pi\)
−0.00941494 + 0.999956i \(0.502997\pi\)
\(600\) 0 0
\(601\) −17733.8 30715.9i −0.0490969 0.0850382i 0.840433 0.541916i \(-0.182301\pi\)
−0.889529 + 0.456878i \(0.848968\pi\)
\(602\) −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 0.949279 0.314436i \(-0.101815\pi\)
0.202330 + 0.979317i \(0.435149\pi\)
\(608\) −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 −0.707668 0.706545i \(-0.750253\pi\)
0.965720 + 0.259586i \(0.0835862\pi\)
\(618\) 0 0
\(619\) −58731.2 + 33908.5i −0.153281 + 0.0884967i −0.574679 0.818379i \(-0.694873\pi\)
0.421398 + 0.906876i \(0.361540\pi\)
\(620\) −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 \(-0.643308\pi\)
0.435158 0.900354i \(-0.356692\pi\)
\(632\) −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 0.930580 + 0.366089i \(0.119303\pi\)
−0.148248 + 0.988950i \(0.547363\pi\)
\(642\) 0 0
\(643\) 1326.59 + 765.910i 0.00320861 + 0.00185249i 0.501603 0.865098i \(-0.332744\pi\)
−0.498395 + 0.866950i \(0.666077\pi\)
\(644\) −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 \(-0.959315\pi\)
0.991843 0.127469i \(-0.0406854\pi\)
\(648\) 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 −0.699380 0.714750i \(-0.746541\pi\)
0.968682 + 0.248306i \(0.0798739\pi\)
\(654\) 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 −0.0576633 0.998336i \(-0.518365\pi\)
0.835753 + 0.549106i \(0.185032\pi\)
\(660\) 0 0
\(661\) −223443. + 387014.i −0.511403 + 0.885776i 0.488509 + 0.872559i \(0.337541\pi\)
−0.999913 + 0.0132177i \(0.995793\pi\)
\(662\) 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 0.615519 0.788122i \(-0.288946\pi\)
−0.990293 + 0.138994i \(0.955613\pi\)
\(674\) −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 0.995254 + 0.0973098i \(0.0310238\pi\)
−0.413354 + 0.910570i \(0.635643\pi\)
\(678\) 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 \(0.0603624\pi\)
−0.982073 + 0.188500i \(0.939638\pi\)
\(684\) 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 −0.271993 0.962299i \(-0.587683\pi\)
0.697379 + 0.716702i \(0.254349\pi\)
\(692\) 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 0.993164 + 0.116731i \(0.0372417\pi\)
−0.395489 + 0.918471i \(0.629425\pi\)
\(710\) −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 \(-0.988513\pi\)
0.999349 0.0360786i \(-0.0114867\pi\)
\(720\) 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 −0.966138 0.258027i \(-0.916928\pi\)
−0.259611 + 0.965713i \(0.583594\pi\)
\(728\) −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 −0.717034 0.697038i \(-0.754501\pi\)
0.962170 + 0.272450i \(0.0878341\pi\)
\(734\) −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 \(-0.914790\pi\)
0.964383 0.264509i \(-0.0852099\pi\)
\(740\) 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 0.725259 0.688476i \(-0.241720\pi\)
−0.233608 + 0.972331i \(0.575053\pi\)
\(744\) 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 0.670246 0.742139i \(-0.266189\pi\)
−0.307588 + 0.951520i \(0.599522\pi\)
\(752\) 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 −0.139010 0.990291i \(-0.544392\pi\)
0.927122 0.374759i \(-0.122275\pi\)
\(762\) 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 −0.764235 0.644938i \(-0.776883\pi\)
0.940650 + 0.339378i \(0.110216\pi\)
\(770\) 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
\(778\) −461973.