Properties

Label 108.5.f.a.19.3
Level 108
Weight 5
Character 108.19
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 19.3
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +O(q^{10})\) \(q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +(6.48981 + 4.88624i) q^{10} +(-4.32958 - 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(-91.8536 - 11.2399i) q^{14} +(-9.35520 - 255.829i) q^{16} +266.009 q^{17} +367.194i q^{19} +(-31.5357 - 7.83518i) q^{20} +(19.8494 + 2.42891i) q^{22} +(544.473 - 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 + 663.194i) q^{26} +(355.732 - 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(1191.19 - 687.735i) q^{31} +(434.669 + 927.167i) q^{32} +(-979.280 + 416.155i) q^{34} -46.9843i q^{35} +1466.19 q^{37} +(-574.453 - 1351.78i) q^{38} +(128.352 - 20.4914i) q^{40} +(-593.019 - 1027.14i) q^{41} +(1430.33 + 825.804i) q^{43} +(-76.8730 + 22.1114i) q^{44} +(-1512.63 + 2009.04i) q^{46} +(-307.864 - 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(-301.649 + 2465.11i) q^{50} +(-4280.24 - 1063.44i) q^{52} -5297.49 q^{53} +10.1532i q^{55} +(-1149.51 + 933.203i) q^{56} +(-310.436 + 2536.92i) q^{58} +(5223.32 - 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 + 4395.36i) q^{62} +(-3050.68 - 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(-1908.36 + 1101.79i) q^{67} +(2954.05 - 3064.05i) q^{68} +(73.5040 + 172.967i) q^{70} +524.299i q^{71} -1492.29 q^{73} +(-5397.59 + 2293.76i) q^{74} +(4229.55 + 4077.71i) q^{76} +(-57.8293 - 100.163i) q^{77} +(4448.35 + 2568.25i) q^{79} +(-440.456 + 276.236i) q^{80} +(3790.02 + 2853.54i) q^{82} +(-6918.39 - 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(-6557.52 - 802.424i) q^{86} +(248.406 - 201.664i) q^{88} +8860.17 q^{89} -6377.03i q^{91} +(2425.53 - 9762.46i) q^{92} +(1411.44 + 172.713i) q^{94} +(645.826 - 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 + 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.68138 + 1.56444i −0.920344 + 0.391110i
\(3\) 0 0
\(4\) 11.1051 11.5186i 0.694066 0.719911i
\(5\) −1.01545 1.75881i −0.0406181 0.0703525i 0.845002 0.534764i \(-0.179599\pi\)
−0.885620 + 0.464411i \(0.846266\pi\)
\(6\) 0 0
\(7\) 20.0352 + 11.5673i 0.408882 + 0.236068i 0.690309 0.723514i \(-0.257474\pi\)
−0.281427 + 0.959583i \(0.590808\pi\)
\(8\) −22.8618 + 59.7774i −0.357216 + 0.934022i
\(9\) 0 0
\(10\) 6.48981 + 4.88624i 0.0648981 + 0.0488624i
\(11\) −4.32958 2.49968i −0.0357816 0.0206585i 0.482002 0.876170i \(-0.339910\pi\)
−0.517784 + 0.855511i \(0.673243\pi\)
\(12\) 0 0
\(13\) −137.824 238.718i −0.815527 1.41253i −0.908949 0.416908i \(-0.863114\pi\)
0.0934218 0.995627i \(-0.470219\pi\)
\(14\) −91.8536 11.2399i −0.468641 0.0573462i
\(15\) 0 0
\(16\) −9.35520 255.829i −0.0365438 0.999332i
\(17\) 266.009 0.920447 0.460224 0.887803i \(-0.347769\pi\)
0.460224 + 0.887803i \(0.347769\pi\)
\(18\) 0 0
\(19\) 367.194i 1.01716i 0.861015 + 0.508579i \(0.169829\pi\)
−0.861015 + 0.508579i \(0.830171\pi\)
\(20\) −31.5357 7.83518i −0.0788392 0.0195879i
\(21\) 0 0
\(22\) 19.8494 + 2.42891i 0.0410111 + 0.00501841i
\(23\) 544.473 314.352i 1.02925 0.594238i 0.112481 0.993654i \(-0.464120\pi\)
0.916770 + 0.399416i \(0.130787\pi\)
\(24\) 0 0
\(25\) 310.438 537.694i 0.496700 0.860310i
\(26\) 880.842 + 663.194i 1.30302 + 0.981057i
\(27\) 0 0
\(28\) 355.732 102.321i 0.453739 0.130512i
\(29\) 319.481 553.357i 0.379882 0.657975i −0.611163 0.791505i \(-0.709298\pi\)
0.991045 + 0.133530i \(0.0426312\pi\)
\(30\) 0 0
\(31\) 1191.19 687.735i 1.23953 0.715645i 0.270535 0.962710i \(-0.412799\pi\)
0.968999 + 0.247065i \(0.0794660\pi\)
\(32\) 434.669 + 927.167i 0.424481 + 0.905437i
\(33\) 0 0
\(34\) −979.280 + 416.155i −0.847128 + 0.359996i
\(35\) 46.9843i 0.0383545i
\(36\) 0 0
\(37\) 1466.19 1.07099 0.535496 0.844538i \(-0.320125\pi\)
0.535496 + 0.844538i \(0.320125\pi\)
\(38\) −574.453 1351.78i −0.397820 0.936135i
\(39\) 0 0
\(40\) 128.352 20.4914i 0.0802202 0.0128071i
\(41\) −593.019 1027.14i −0.352777 0.611028i 0.633958 0.773368i \(-0.281429\pi\)
−0.986735 + 0.162339i \(0.948096\pi\)
\(42\) 0 0
\(43\) 1430.33 + 825.804i 0.773572 + 0.446622i 0.834147 0.551542i \(-0.185960\pi\)
−0.0605755 + 0.998164i \(0.519294\pi\)
\(44\) −76.8730 + 22.1114i −0.0397071 + 0.0114212i
\(45\) 0 0
\(46\) −1512.63 + 2009.04i −0.714852 + 0.949453i
\(47\) −307.864 177.745i −0.139368 0.0804642i 0.428695 0.903449i \(-0.358974\pi\)
−0.568063 + 0.822985i \(0.692307\pi\)
\(48\) 0 0
\(49\) −932.893 1615.82i −0.388544 0.672977i
\(50\) −301.649 + 2465.11i −0.120660 + 0.986046i
\(51\) 0 0
\(52\) −4280.24 1063.44i −1.58293 0.393286i
\(53\) −5297.49 −1.88590 −0.942950 0.332934i \(-0.891961\pi\)
−0.942950 + 0.332934i \(0.891961\pi\)
\(54\) 0 0
\(55\) 10.1532i 0.00335644i
\(56\) −1149.51 + 933.203i −0.366552 + 0.297578i
\(57\) 0 0
\(58\) −310.436 + 2536.92i −0.0922818 + 0.754139i
\(59\) 5223.32 3015.68i 1.50052 0.866327i 0.500522 0.865724i \(-0.333141\pi\)
1.00000 0.000603027i \(-0.000191950\pi\)
\(60\) 0 0
\(61\) −833.364 + 1443.43i −0.223962 + 0.387914i −0.956008 0.293342i \(-0.905233\pi\)
0.732045 + 0.681256i \(0.238566\pi\)
\(62\) −3309.31 + 4395.36i −0.860902 + 1.14343i
\(63\) 0 0
\(64\) −3050.68 2733.24i −0.744794 0.667295i
\(65\) −279.907 + 484.814i −0.0662502 + 0.114749i
\(66\) 0 0
\(67\) −1908.36 + 1101.79i −0.425119 + 0.245443i −0.697265 0.716813i \(-0.745600\pi\)
0.272146 + 0.962256i \(0.412267\pi\)
\(68\) 2954.05 3064.05i 0.638852 0.662640i
\(69\) 0 0
\(70\) 73.5040 + 172.967i 0.0150008 + 0.0352993i
\(71\) 524.299i 0.104007i 0.998647 + 0.0520035i \(0.0165607\pi\)
−0.998647 + 0.0520035i \(0.983439\pi\)
\(72\) 0 0
\(73\) −1492.29 −0.280032 −0.140016 0.990149i \(-0.544715\pi\)
−0.140016 + 0.990149i \(0.544715\pi\)
\(74\) −5397.59 + 2293.76i −0.985680 + 0.418875i
\(75\) 0 0
\(76\) 4229.55 + 4077.71i 0.732263 + 0.705975i
\(77\) −57.8293 100.163i −0.00975364 0.0168938i
\(78\) 0 0
\(79\) 4448.35 + 2568.25i 0.712762 + 0.411513i 0.812083 0.583542i \(-0.198334\pi\)
−0.0993209 + 0.995055i \(0.531667\pi\)
\(80\) −440.456 + 276.236i −0.0688212 + 0.0431619i
\(81\) 0 0
\(82\) 3790.02 + 2853.54i 0.563656 + 0.424382i
\(83\) −6918.39 3994.33i −1.00427 0.579813i −0.0947580 0.995500i \(-0.530208\pi\)
−0.909508 + 0.415687i \(0.863541\pi\)
\(84\) 0 0
\(85\) −270.120 467.861i −0.0373868 0.0647558i
\(86\) −6557.52 802.424i −0.886630 0.108494i
\(87\) 0 0
\(88\) 248.406 201.664i 0.0320773 0.0260413i
\(89\) 8860.17 1.11857 0.559283 0.828977i \(-0.311076\pi\)
0.559283 + 0.828977i \(0.311076\pi\)
\(90\) 0 0
\(91\) 6377.03i 0.770080i
\(92\) 2425.53 9762.46i 0.286570 1.15341i
\(93\) 0 0
\(94\) 1411.44 + 172.713i 0.159737 + 0.0195465i
\(95\) 645.826 372.868i 0.0715596 0.0413150i
\(96\) 0 0
\(97\) −3409.33 + 5905.14i −0.362348 + 0.627606i −0.988347 0.152219i \(-0.951358\pi\)
0.625999 + 0.779824i \(0.284692\pi\)
\(98\) 5962.18 + 4488.98i 0.620802 + 0.467408i
\(99\) 0 0
\(100\) −2746.04 9546.92i −0.274604 0.954692i
\(101\) 1545.53 2676.93i 0.151507 0.262418i −0.780274 0.625437i \(-0.784921\pi\)
0.931782 + 0.363019i \(0.118254\pi\)
\(102\) 0 0
\(103\) −9409.35 + 5432.49i −0.886922 + 0.512065i −0.872934 0.487838i \(-0.837786\pi\)
−0.0139875 + 0.999902i \(0.504453\pi\)
\(104\) 17420.9 2781.23i 1.61066 0.257141i
\(105\) 0 0
\(106\) 19502.1 8287.61i 1.73568 0.737594i
\(107\) 14106.5i 1.23212i 0.787699 + 0.616060i \(0.211272\pi\)
−0.787699 + 0.616060i \(0.788728\pi\)
\(108\) 0 0
\(109\) 16328.3 1.37432 0.687160 0.726506i \(-0.258857\pi\)
0.687160 + 0.726506i \(0.258857\pi\)
\(110\) −15.8841 37.3778i −0.00131273 0.00308908i
\(111\) 0 0
\(112\) 2771.83 5233.81i 0.220968 0.417236i
\(113\) 5911.44 + 10238.9i 0.462952 + 0.801857i 0.999107 0.0422631i \(-0.0134568\pi\)
−0.536154 + 0.844120i \(0.680123\pi\)
\(114\) 0 0
\(115\) −1105.77 638.418i −0.0836123 0.0482736i
\(116\) −2826.03 9825.03i −0.210020 0.730160i
\(117\) 0 0
\(118\) −14511.1 + 19273.4i −1.04217 + 1.38419i
\(119\) 5329.56 + 3077.02i 0.376354 + 0.217288i
\(120\) 0 0
\(121\) −7308.00 12657.8i −0.499146 0.864547i
\(122\) 809.770 6617.55i 0.0544054 0.444608i
\(123\) 0 0
\(124\) 5306.53 21358.2i 0.345118 1.38906i
\(125\) −2530.25 −0.161936
\(126\) 0 0
\(127\) 20979.9i 1.30076i −0.759609 0.650379i \(-0.774610\pi\)
0.759609 0.650379i \(-0.225390\pi\)
\(128\) 15506.7 + 5289.48i 0.946452 + 0.322844i
\(129\) 0 0
\(130\) 271.983 2222.68i 0.0160936 0.131519i
\(131\) −24723.9 + 14274.3i −1.44070 + 0.831789i −0.997896 0.0648298i \(-0.979350\pi\)
−0.442804 + 0.896618i \(0.646016\pi\)
\(132\) 0 0
\(133\) −4247.46 + 7356.81i −0.240119 + 0.415898i
\(134\) 5301.70 7041.62i 0.295261 0.392160i
\(135\) 0 0
\(136\) −6081.45 + 15901.3i −0.328798 + 0.859718i
\(137\) −309.436 + 535.959i −0.0164866 + 0.0285556i −0.874151 0.485654i \(-0.838581\pi\)
0.857664 + 0.514210i \(0.171915\pi\)
\(138\) 0 0
\(139\) −16819.9 + 9710.99i −0.870552 + 0.502613i −0.867532 0.497382i \(-0.834295\pi\)
−0.00302027 + 0.999995i \(0.500961\pi\)
\(140\) −541.192 521.763i −0.0276118 0.0266206i
\(141\) 0 0
\(142\) −820.234 1930.14i −0.0406781 0.0957222i
\(143\) 1378.07i 0.0673903i
\(144\) 0 0
\(145\) −1297.67 −0.0617203
\(146\) 5493.69 2334.60i 0.257726 0.109523i
\(147\) 0 0
\(148\) 16282.1 16888.4i 0.743339 0.771018i
\(149\) 309.641 + 536.313i 0.0139471 + 0.0241572i 0.872915 0.487873i \(-0.162227\pi\)
−0.858968 + 0.512030i \(0.828894\pi\)
\(150\) 0 0
\(151\) −3758.08 2169.73i −0.164821 0.0951593i 0.415321 0.909675i \(-0.363669\pi\)
−0.580141 + 0.814516i \(0.697003\pi\)
\(152\) −21949.9 8394.72i −0.950048 0.363345i
\(153\) 0 0
\(154\) 369.591 + 278.268i 0.0155840 + 0.0117334i
\(155\) −2419.20 1396.72i −0.100695 0.0581362i
\(156\) 0 0
\(157\) 3103.88 + 5376.08i 0.125923 + 0.218105i 0.922093 0.386967i \(-0.126477\pi\)
−0.796170 + 0.605073i \(0.793144\pi\)
\(158\) −20393.9 2495.54i −0.816933 0.0999657i
\(159\) 0 0
\(160\) 1189.33 1705.99i 0.0464582 0.0666404i
\(161\) 14544.9 0.561123
\(162\) 0 0
\(163\) 15857.0i 0.596824i 0.954437 + 0.298412i \(0.0964569\pi\)
−0.954437 + 0.298412i \(0.903543\pi\)
\(164\) −18416.7 4575.71i −0.684737 0.170126i
\(165\) 0 0
\(166\) 31718.1 + 3881.25i 1.15104 + 0.140849i
\(167\) 362.861 209.498i 0.0130109 0.00751186i −0.493480 0.869757i \(-0.664276\pi\)
0.506491 + 0.862245i \(0.330942\pi\)
\(168\) 0 0
\(169\) −23710.4 + 41067.7i −0.830169 + 1.43789i
\(170\) 1726.35 + 1299.79i 0.0597353 + 0.0449753i
\(171\) 0 0
\(172\) 25396.0 7304.81i 0.858438 0.246918i
\(173\) −9600.40 + 16628.4i −0.320772 + 0.555594i −0.980648 0.195781i \(-0.937276\pi\)
0.659875 + 0.751375i \(0.270609\pi\)
\(174\) 0 0
\(175\) 12439.4 7181.88i 0.406184 0.234510i
\(176\) −598.987 + 1131.02i −0.0193371 + 0.0365127i
\(177\) 0 0
\(178\) −32617.6 + 13861.2i −1.02947 + 0.437482i
\(179\) 49821.7i 1.55494i −0.628922 0.777468i \(-0.716504\pi\)
0.628922 0.777468i \(-0.283496\pi\)
\(180\) 0 0
\(181\) 13970.7 0.426443 0.213222 0.977004i \(-0.431604\pi\)
0.213222 + 0.977004i \(0.431604\pi\)
\(182\) 9976.48 + 23476.3i 0.301186 + 0.708738i
\(183\) 0 0
\(184\) 6343.50 + 39733.9i 0.187367 + 1.17361i
\(185\) −1488.84 2578.75i −0.0435016 0.0753469i
\(186\) 0 0
\(187\) −1151.71 664.939i −0.0329351 0.0190151i
\(188\) −5466.22 + 1572.28i −0.154658 + 0.0444851i
\(189\) 0 0
\(190\) −1794.20 + 2383.02i −0.0497008 + 0.0660117i
\(191\) 26994.8 + 15585.5i 0.739969 + 0.427221i 0.822058 0.569404i \(-0.192826\pi\)
−0.0820893 + 0.996625i \(0.526159\pi\)
\(192\) 0 0
\(193\) −13498.2 23379.5i −0.362377 0.627655i 0.625975 0.779843i \(-0.284701\pi\)
−0.988351 + 0.152189i \(0.951368\pi\)
\(194\) 3312.81 27072.7i 0.0880224 0.719331i
\(195\) 0 0
\(196\) −28971.8 7198.16i −0.754159 0.187374i
\(197\) −10416.4 −0.268402 −0.134201 0.990954i \(-0.542847\pi\)
−0.134201 + 0.990954i \(0.542847\pi\)
\(198\) 0 0
\(199\) 8438.68i 0.213093i −0.994308 0.106546i \(-0.966021\pi\)
0.994308 0.106546i \(-0.0339793\pi\)
\(200\) 25044.8 + 30849.8i 0.626119 + 0.771245i
\(201\) 0 0
\(202\) −1501.77 + 12272.7i −0.0368045 + 0.300771i
\(203\) 12801.7 7391.09i 0.310654 0.179356i
\(204\) 0 0
\(205\) −1204.36 + 2086.02i −0.0286583 + 0.0496376i
\(206\) 26140.6 34719.4i 0.616000 0.818159i
\(207\) 0 0
\(208\) −59781.7 + 37492.7i −1.38179 + 0.866602i
\(209\) 917.868 1589.79i 0.0210130 0.0363956i
\(210\) 0 0
\(211\) −19871.6 + 11472.8i −0.446341 + 0.257695i −0.706284 0.707929i \(-0.749630\pi\)
0.259943 + 0.965624i \(0.416296\pi\)
\(212\) −58829.0 + 61019.6i −1.30894 + 1.35768i
\(213\) 0 0
\(214\) −22068.8 51931.5i −0.481894 1.13397i
\(215\) 3354.25i 0.0725637i
\(216\) 0 0
\(217\) 31821.1 0.675764
\(218\) −60110.6 + 25544.6i −1.26485 + 0.537510i
\(219\) 0 0
\(220\) 116.951 + 112.752i 0.00241634 + 0.00232959i
\(221\) −36662.5 63501.3i −0.750650 1.30016i
\(222\) 0 0
\(223\) 55651.0 + 32130.1i 1.11909 + 0.646105i 0.941167 0.337941i \(-0.109730\pi\)
0.177919 + 0.984045i \(0.443064\pi\)
\(224\) −2016.17 + 23604.0i −0.0401820 + 0.470423i
\(225\) 0 0
\(226\) −37780.4 28445.2i −0.739690 0.556919i
\(227\) −5807.02 3352.69i −0.112694 0.0650641i 0.442593 0.896722i \(-0.354059\pi\)
−0.555288 + 0.831658i \(0.687392\pi\)
\(228\) 0 0
\(229\) −17775.1 30787.4i −0.338955 0.587087i 0.645281 0.763945i \(-0.276740\pi\)
−0.984236 + 0.176858i \(0.943407\pi\)
\(230\) 5069.53 + 620.344i 0.0958323 + 0.0117267i
\(231\) 0 0
\(232\) 25774.4 + 31748.5i 0.478864 + 0.589857i
\(233\) −62439.9 −1.15014 −0.575070 0.818105i \(-0.695025\pi\)
−0.575070 + 0.818105i \(0.695025\pi\)
\(234\) 0 0
\(235\) 721.967i 0.0130732i
\(236\) 23268.9 93654.5i 0.417784 1.68153i
\(237\) 0 0
\(238\) −24433.9 2989.91i −0.431359 0.0527841i
\(239\) 3250.59 1876.73i 0.0569070 0.0328553i −0.471277 0.881985i \(-0.656207\pi\)
0.528184 + 0.849130i \(0.322873\pi\)
\(240\) 0 0
\(241\) 44832.6 77652.3i 0.771898 1.33697i −0.164624 0.986356i \(-0.552641\pi\)
0.936522 0.350610i \(-0.114026\pi\)
\(242\) 46705.9 + 35165.3i 0.797519 + 0.600460i
\(243\) 0 0
\(244\) 7371.68 + 25628.5i 0.123819 + 0.430471i
\(245\) −1894.62 + 3281.57i −0.0315638 + 0.0546701i
\(246\) 0 0
\(247\) 87655.9 50608.2i 1.43677 0.829520i
\(248\) 13878.2 + 86929.3i 0.225647 + 1.41339i
\(249\) 0 0
\(250\) 9314.81 3958.42i 0.149037 0.0633348i
\(251\) 9246.49i 0.146767i −0.997304 0.0733836i \(-0.976620\pi\)
0.997304 0.0733836i \(-0.0233798\pi\)
\(252\) 0 0
\(253\) −3143.12 −0.0491043
\(254\) 32821.8 + 77235.1i 0.508739 + 1.19715i
\(255\) 0 0
\(256\) −65361.0 + 4786.66i −0.997329 + 0.0730387i
\(257\) 7624.85 + 13206.6i 0.115442 + 0.199952i 0.917956 0.396681i \(-0.129838\pi\)
−0.802514 + 0.596633i \(0.796505\pi\)
\(258\) 0 0
\(259\) 29375.4 + 16959.9i 0.437909 + 0.252827i
\(260\) 2475.97 + 8608.02i 0.0366268 + 0.127338i
\(261\) 0 0
\(262\) 68686.5 91228.1i 1.00062 1.32900i
\(263\) 89478.0 + 51660.2i 1.29361 + 0.746869i 0.979293 0.202448i \(-0.0648896\pi\)
0.314322 + 0.949317i \(0.398223\pi\)
\(264\) 0 0
\(265\) 5379.35 + 9317.30i 0.0766016 + 0.132678i
\(266\) 4127.21 33728.1i 0.0583301 0.476682i
\(267\) 0 0
\(268\) −8501.38 + 34217.1i −0.118364 + 0.476402i
\(269\) 86017.8 1.18873 0.594366 0.804195i \(-0.297403\pi\)
0.594366 + 0.804195i \(0.297403\pi\)
\(270\) 0 0
\(271\) 15629.0i 0.212810i −0.994323 0.106405i \(-0.966066\pi\)
0.994323 0.106405i \(-0.0339340\pi\)
\(272\) −2488.57 68052.9i −0.0336366 0.919833i
\(273\) 0 0
\(274\) 300.676 2457.16i 0.00400495 0.0327290i
\(275\) −2688.13 + 1551.99i −0.0355455 + 0.0205222i
\(276\) 0 0
\(277\) 28307.3 49029.7i 0.368926 0.638998i −0.620472 0.784228i \(-0.713059\pi\)
0.989398 + 0.145231i \(0.0463924\pi\)
\(278\) 46728.2 62063.6i 0.604630 0.803059i
\(279\) 0 0
\(280\) 2808.60 + 1074.15i 0.0358240 + 0.0137008i
\(281\) 55533.5 96186.8i 0.703303 1.21816i −0.263998 0.964523i \(-0.585041\pi\)
0.967301 0.253633i \(-0.0816255\pi\)
\(282\) 0 0
\(283\) −78979.6 + 45598.9i −0.986148 + 0.569353i −0.904121 0.427278i \(-0.859473\pi\)
−0.0820271 + 0.996630i \(0.526139\pi\)
\(284\) 6039.18 + 5822.37i 0.0748758 + 0.0721877i
\(285\) 0 0
\(286\) −2155.90 5073.18i −0.0263570 0.0620223i
\(287\) 27438.6i 0.333118i
\(288\) 0 0
\(289\) −12760.0 −0.152776
\(290\) 4777.21 2030.12i 0.0568039 0.0241394i
\(291\) 0 0
\(292\) −16572.0 + 17189.1i −0.194361 + 0.201598i
\(293\) 41507.5 + 71893.1i 0.483494 + 0.837436i 0.999820 0.0189556i \(-0.00603412\pi\)
−0.516326 + 0.856392i \(0.672701\pi\)
\(294\) 0 0
\(295\) −10608.0 6124.56i −0.121897 0.0703770i
\(296\) −33519.7 + 87644.8i −0.382575 + 1.00033i
\(297\) 0 0
\(298\) −1978.93 1489.96i −0.0222843 0.0167780i
\(299\) −150083. 86650.5i −1.67876 0.969234i
\(300\) 0 0
\(301\) 19104.7 + 33090.3i 0.210866 + 0.365231i
\(302\) 17229.3 + 2108.30i 0.188910 + 0.0231163i
\(303\) 0 0
\(304\) 93938.9 3435.17i 1.01648 0.0371708i
\(305\) 3384.96 0.0363876
\(306\) 0 0
\(307\) 65201.8i 0.691803i 0.938271 + 0.345902i \(0.112427\pi\)
−0.938271 + 0.345902i \(0.887573\pi\)
\(308\) −1795.94 446.209i −0.0189317 0.00470367i
\(309\) 0 0
\(310\) 11091.1 + 1357.18i 0.115412 + 0.0141226i
\(311\) 115786. 66849.3i 1.19712 0.691156i 0.237206 0.971459i \(-0.423768\pi\)
0.959911 + 0.280303i \(0.0904350\pi\)
\(312\) 0 0
\(313\) −5620.04 + 9734.19i −0.0573655 + 0.0993599i −0.893282 0.449497i \(-0.851603\pi\)
0.835917 + 0.548857i \(0.184937\pi\)
\(314\) −19837.1 14935.5i −0.201196 0.151482i
\(315\) 0 0
\(316\) 78981.8 22718.0i 0.790957 0.227508i
\(317\) −19603.1 + 33953.5i −0.195077 + 0.337883i −0.946926 0.321452i \(-0.895829\pi\)
0.751849 + 0.659336i \(0.229162\pi\)
\(318\) 0 0
\(319\) −2766.43 + 1597.20i −0.0271856 + 0.0156956i
\(320\) −1709.44 + 8141.04i −0.0166938 + 0.0795023i
\(321\) 0 0
\(322\) −53545.1 + 22754.5i −0.516426 + 0.219461i
\(323\) 97677.0i 0.936240i
\(324\) 0 0
\(325\) −171143. −1.62029
\(326\) −24807.3 58375.6i −0.233424 0.549283i
\(327\) 0 0
\(328\) 74957.2 11966.9i 0.696732 0.111233i
\(329\) −4112.08 7122.34i −0.0379901 0.0658007i
\(330\) 0 0
\(331\) −64736.6 37375.7i −0.590873 0.341141i 0.174570 0.984645i \(-0.444147\pi\)
−0.765443 + 0.643504i \(0.777480\pi\)
\(332\) −122838. + 35332.7i −1.11444 + 0.320553i
\(333\) 0 0
\(334\) −1008.08 + 1338.92i −0.00903656 + 0.0120022i
\(335\) 3875.69 + 2237.63i 0.0345350 + 0.0199388i
\(336\) 0 0
\(337\) 70909.1 + 122818.i 0.624370 + 1.08144i 0.988662 + 0.150156i \(0.0479775\pi\)
−0.364293 + 0.931285i \(0.618689\pi\)
\(338\) 23039.2 188279.i 0.201666 1.64804i
\(339\) 0 0
\(340\) −8388.78 2084.23i −0.0725673 0.0180297i
\(341\) −6876.48 −0.0591367
\(342\) 0 0
\(343\) 98710.7i 0.839027i
\(344\) −82064.4 + 66622.3i −0.693487 + 0.562993i
\(345\) 0 0
\(346\) 9328.60 76234.5i 0.0779227 0.636795i
\(347\) −158508. + 91514.6i −1.31641 + 0.760032i −0.983150 0.182802i \(-0.941483\pi\)
−0.333264 + 0.942834i \(0.608150\pi\)
\(348\) 0 0
\(349\) −67279.0 + 116531.i −0.552368 + 0.956729i 0.445735 + 0.895165i \(0.352942\pi\)
−0.998103 + 0.0615644i \(0.980391\pi\)
\(350\) −34558.4 + 45899.8i −0.282110 + 0.374693i
\(351\) 0 0
\(352\) 435.691 5100.77i 0.00351636 0.0411671i
\(353\) −100139. + 173446.i −0.803626 + 1.39192i 0.113589 + 0.993528i \(0.463765\pi\)
−0.917215 + 0.398393i \(0.869568\pi\)
\(354\) 0 0
\(355\) 922.144 532.400i 0.00731715 0.00422456i
\(356\) 98392.7 102056.i 0.776359 0.805268i
\(357\) 0 0
\(358\) 77943.1 + 183413.i 0.608151 + 1.43108i
\(359\) 161179.i 1.25060i 0.780385 + 0.625300i \(0.215023\pi\)
−0.780385 + 0.625300i \(0.784977\pi\)
\(360\) 0 0
\(361\) −4510.46 −0.0346104
\(362\) −51431.4 + 21856.3i −0.392474 + 0.166786i
\(363\) 0 0
\(364\) −73454.3 70817.3i −0.554389 0.534487i
\(365\) 1515.35 + 2624.66i 0.0113744 + 0.0197010i
\(366\) 0 0
\(367\) −172828. 99782.5i −1.28317 0.740836i −0.305740 0.952115i \(-0.598904\pi\)
−0.977426 + 0.211279i \(0.932237\pi\)
\(368\) −85514.0 136351.i −0.631454 1.00685i
\(369\) 0 0
\(370\) 9515.28 + 7164.14i 0.0695053 + 0.0523312i
\(371\) −106136. 61277.9i −0.771111 0.445201i
\(372\) 0 0
\(373\) 2894.35 + 5013.15i 0.0208033 + 0.0360324i 0.876240 0.481876i \(-0.160044\pi\)
−0.855436 + 0.517908i \(0.826711\pi\)
\(374\) 5280.12 + 646.113i 0.0377486 + 0.00461919i
\(375\) 0 0
\(376\) 17663.5 14339.7i 0.124940 0.101430i
\(377\) −176129. −1.23922
\(378\) 0 0
\(379\) 217930.i 1.51719i 0.651565 + 0.758593i \(0.274113\pi\)
−0.651565 + 0.758593i \(0.725887\pi\)
\(380\) 2877.03 11579.7i 0.0199240 0.0801919i
\(381\) 0 0
\(382\) −123760. 15144.2i −0.848116 0.103781i
\(383\) 60187.2 34749.1i 0.410305 0.236890i −0.280616 0.959820i \(-0.590539\pi\)
0.690921 + 0.722930i \(0.257205\pi\)
\(384\) 0 0
\(385\) −117.446 + 203.422i −0.000792348 + 0.00137239i
\(386\) 86267.6 + 64951.7i 0.578993 + 0.435929i
\(387\) 0 0
\(388\) 30157.9 + 104848.i 0.200326 + 0.696458i
\(389\) 28733.0 49767.0i 0.189881 0.328884i −0.755329 0.655345i \(-0.772523\pi\)
0.945210 + 0.326462i \(0.105856\pi\)
\(390\) 0 0
\(391\) 144835. 83620.5i 0.947371 0.546965i
\(392\) 117917. 18825.4i 0.767369 0.122510i
\(393\) 0 0
\(394\) 38346.8 16295.9i 0.247023 0.104975i
\(395\) 10431.7i 0.0668595i
\(396\) 0 0
\(397\) 13255.8 0.0841056 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(398\) 13201.8 + 31066.0i 0.0833426 + 0.196119i
\(399\) 0 0
\(400\) −140462. 74388.7i −0.877887 0.464930i
\(401\) −2687.66 4655.16i −0.0167142 0.0289498i 0.857547 0.514405i \(-0.171987\pi\)
−0.874262 + 0.485455i \(0.838654\pi\)
\(402\) 0 0
\(403\) −328350. 189573.i −2.02175 1.16726i
\(404\) −13671.3 47529.7i −0.0837618 0.291208i
\(405\) 0 0
\(406\) −35565.1 + 47236.9i −0.215761 + 0.286569i
\(407\) −6347.97 3665.00i −0.0383218 0.0221251i
\(408\) 0 0
\(409\) 120347. + 208446.i 0.719427 + 1.24608i 0.961227 + 0.275758i \(0.0889289\pi\)
−0.241800 + 0.970326i \(0.577738\pi\)
\(410\) 1170.27 9563.57i 0.00696173 0.0568922i
\(411\) 0 0
\(412\) −41916.9 + 168711.i −0.246942 + 0.993912i
\(413\) 139534. 0.818049
\(414\) 0 0
\(415\) 16224.2i 0.0942035i
\(416\) 161424. 231549.i 0.932784 1.33800i
\(417\) 0 0
\(418\) −891.882 + 7288.58i −0.00510452 + 0.0417148i
\(419\) −30669.6 + 17707.1i −0.174695 + 0.100860i −0.584798 0.811179i \(-0.698826\pi\)
0.410103 + 0.912039i \(0.365493\pi\)
\(420\) 0 0
\(421\) 82548.0 142977.i 0.465739 0.806683i −0.533496 0.845803i \(-0.679122\pi\)
0.999235 + 0.0391198i \(0.0124554\pi\)
\(422\) 55206.1 73323.7i 0.310000 0.411737i
\(423\) 0 0
\(424\) 121110. 316670.i 0.673673 1.76147i
\(425\) 82579.3 143032.i 0.457187 0.791870i
\(426\) 0 0
\(427\) −33393.2 + 19279.6i −0.183148 + 0.105741i
\(428\) 162487. + 156654.i 0.887017 + 0.855173i
\(429\) 0 0
\(430\) 5247.53 + 12348.3i 0.0283803 + 0.0667835i
\(431\) 161673.i 0.870327i 0.900351 + 0.435163i \(0.143309\pi\)
−0.900351 + 0.435163i \(0.856691\pi\)
\(432\) 0 0
\(433\) −61835.3 −0.329808 −0.164904 0.986310i \(-0.552731\pi\)
−0.164904 + 0.986310i \(0.552731\pi\)
\(434\) −117145. + 49782.1i −0.621936 + 0.264298i
\(435\) 0 0
\(436\) 181327. 188079.i 0.953869 0.989388i
\(437\) 115428. + 199927.i 0.604434 + 1.04691i
\(438\) 0 0
\(439\) 268021. + 154742.i 1.39072 + 0.802933i 0.993395 0.114744i \(-0.0366049\pi\)
0.397326 + 0.917677i \(0.369938\pi\)
\(440\) −606.933 232.121i −0.00313499 0.00119897i
\(441\) 0 0
\(442\) 234312. + 176416.i 1.19936 + 0.903011i
\(443\) 40615.5 + 23449.4i 0.206959 + 0.119488i 0.599897 0.800077i \(-0.295208\pi\)
−0.392938 + 0.919565i \(0.628541\pi\)
\(444\) 0 0
\(445\) −8997.07 15583.4i −0.0454340 0.0786940i
\(446\) −255138. 31220.5i −1.28264 0.156953i
\(447\) 0 0
\(448\) −29504.7 90049.2i −0.147006 0.448667i
\(449\) 124857. 0.619328 0.309664 0.950846i \(-0.399783\pi\)
0.309664 + 0.950846i \(0.399783\pi\)
\(450\) 0 0
\(451\) 5929.43i 0.0291514i
\(452\) 183585. + 45612.4i 0.898585 + 0.223257i
\(453\) 0 0
\(454\) 26622.9 + 3257.77i 0.129165 + 0.0158055i
\(455\) −11216.0 + 6475.56i −0.0541771 + 0.0312791i
\(456\) 0 0
\(457\) 62748.5 108684.i 0.300449 0.520393i −0.675789 0.737095i \(-0.736197\pi\)
0.976238 + 0.216703i \(0.0695302\pi\)
\(458\) 113602. + 85532.1i 0.541571 + 0.407754i
\(459\) 0 0
\(460\) −19633.3 + 5647.25i −0.0927852 + 0.0266883i
\(461\) 51647.4 89455.9i 0.243022 0.420927i −0.718551 0.695474i \(-0.755194\pi\)
0.961574 + 0.274547i \(0.0885278\pi\)
\(462\) 0 0
\(463\) 277564. 160252.i 1.29480 0.747552i 0.315297 0.948993i \(-0.397896\pi\)
0.979501 + 0.201442i \(0.0645626\pi\)
\(464\) −144554. 76555.7i −0.671418 0.355584i
\(465\) 0 0
\(466\) 229865. 97683.4i 1.05852 0.449831i
\(467\) 427381.i 1.95967i −0.199820 0.979833i \(-0.564036\pi\)
0.199820 0.979833i \(-0.435964\pi\)
\(468\) 0 0
\(469\) −50979.2 −0.231765
\(470\) −1129.47 2657.83i −0.00511305 0.0120318i
\(471\) 0 0
\(472\) 60855.3 + 381180.i 0.273158 + 1.71099i
\(473\) −4128.49 7150.76i −0.0184531 0.0319617i
\(474\) 0 0
\(475\) 197438. + 113991.i 0.875071 + 0.505223i
\(476\) 94627.9 27218.4i 0.417643 0.120129i
\(477\) 0 0
\(478\) −9030.61 + 11994.3i −0.0395240 + 0.0524951i
\(479\) 166330. + 96030.5i 0.724935 + 0.418541i 0.816566 0.577252i \(-0.195875\pi\)
−0.0916316 + 0.995793i \(0.529208\pi\)
\(480\) 0 0
\(481\) −202076. 350006.i −0.873422 1.51281i
\(482\) −43563.3 + 356005.i −0.187511 + 1.53237i
\(483\) 0 0
\(484\) −226956. 56388.2i −0.968838 0.240712i
\(485\) 13848.1 0.0588715
\(486\) 0 0
\(487\) 52885.1i 0.222985i 0.993765 + 0.111492i \(0.0355631\pi\)
−0.993765 + 0.111492i \(0.964437\pi\)
\(488\) −67232.2 82815.7i −0.282317 0.347755i
\(489\) 0 0
\(490\) 1840.98 15044.7i 0.00766754 0.0626602i
\(491\) −6368.89 + 3677.08i −0.0264180 + 0.0152525i −0.513151 0.858298i \(-0.671522\pi\)
0.486733 + 0.873551i \(0.338189\pi\)
\(492\) 0 0
\(493\) 84984.9 147198.i 0.349662 0.605632i
\(494\) −243521. + 323440.i −0.997890 + 1.32538i
\(495\) 0 0
\(496\) −187086. 298308.i −0.760465 1.21255i
\(497\) −6064.75 + 10504.4i −0.0245527 + 0.0425266i
\(498\) 0 0
\(499\) −359442. + 207524.i −1.44354 + 0.833426i −0.998084 0.0618804i \(-0.980290\pi\)
−0.445452 + 0.895306i \(0.646957\pi\)
\(500\) −28098.6 + 29144.9i −0.112394 + 0.116580i
\(501\) 0 0
\(502\) 14465.6 + 34039.8i 0.0574021 + 0.135076i
\(503\) 53242.3i 0.210436i −0.994449 0.105218i \(-0.966446\pi\)
0.994449 0.105218i \(-0.0335541\pi\)
\(504\) 0 0
\(505\) −6277.63 −0.0246157
\(506\) 11571.0 4917.22i 0.0451929 0.0192052i
\(507\) 0 0
\(508\) −241659. 232984.i −0.936431 0.902813i
\(509\) −248630. 430640.i −0.959662 1.66218i −0.723319 0.690515i \(-0.757384\pi\)
−0.236344 0.971669i \(-0.575949\pi\)
\(510\) 0 0
\(511\) −29898.4 17261.9i −0.114500 0.0661068i
\(512\) 233130. 119875.i 0.889320 0.457286i
\(513\) 0 0
\(514\) −48730.9 36689.9i −0.184450 0.138874i
\(515\) 19109.5 + 11032.9i 0.0720501 + 0.0415981i
\(516\) 0 0
\(517\) 888.614 + 1539.12i 0.00332454 + 0.00575828i
\(518\) −134675. 16479.7i −0.501910 0.0614173i
\(519\) 0 0
\(520\) −22581.7 27815.8i −0.0835123 0.102869i
\(521\) 58965.8 0.217233 0.108616 0.994084i \(-0.465358\pi\)
0.108616 + 0.994084i \(0.465358\pi\)
\(522\) 0 0
\(523\) 117488.i 0.429527i 0.976666 + 0.214763i \(0.0688980\pi\)
−0.976666 + 0.214763i \(0.931102\pi\)
\(524\) −110140. + 443301.i −0.401128 + 1.61449i
\(525\) 0 0
\(526\) −410222. 50197.6i −1.48268 0.181431i
\(527\) 316868. 182944.i 1.14093 0.658714i
\(528\) 0 0
\(529\) 57713.8 99963.2i 0.206238 0.357214i
\(530\) −34379.8 25884.8i −0.122391 0.0921497i
\(531\) 0 0
\(532\) 37571.7 + 130623.i 0.132751 + 0.461525i
\(533\) −163465. + 283129.i −0.575399 + 0.996620i
\(534\) 0 0
\(535\) 24810.8 14324.5i 0.0866828 0.0500463i
\(536\) −22233.7 139266.i −0.0773896 0.484747i
\(537\) 0 0
\(538\) −316664. + 134570.i −1.09404 + 0.464925i
\(539\) 9327.75i 0.0321070i
\(540\) 0 0
\(541\) −16461.8 −0.0562448 −0.0281224 0.999604i \(-0.508953\pi\)
−0.0281224 + 0.999604i \(0.508953\pi\)
\(542\) 24450.6 + 57536.2i 0.0832322 + 0.195859i
\(543\) 0 0
\(544\) 115626. + 246635.i 0.390713 + 0.833407i
\(545\) −16580.6 28718.4i −0.0558222 0.0966869i
\(546\) 0 0
\(547\) 337391. + 194793.i 1.12761 + 0.651026i 0.943333 0.331848i \(-0.107672\pi\)
0.184277 + 0.982874i \(0.441006\pi\)
\(548\) 2737.18 + 9516.13i 0.00911470 + 0.0316883i
\(549\) 0 0
\(550\) 7468.01 9918.87i 0.0246876 0.0327897i
\(551\) 203189. + 117312.i 0.669265 + 0.386400i
\(552\) 0 0
\(553\) 59415.7 + 102911.i 0.194290 + 0.336521i
\(554\) −27505.9 + 224782.i −0.0896202 + 0.732388i
\(555\) 0 0
\(556\) −74929.6 + 301583.i −0.242384 + 0.975567i
\(557\) −434133. −1.39931 −0.699653 0.714483i \(-0.746662\pi\)
−0.699653 + 0.714483i \(0.746662\pi\)
\(558\) 0 0
\(559\) 455263.i 1.45693i
\(560\) −12019.9 + 439.547i −0.0383289 + 0.00140162i
\(561\) 0 0
\(562\) −53961.3 + 440979.i −0.170848 + 1.39619i
\(563\) −192477. + 111127.i −0.607244 + 0.350592i −0.771886 0.635761i \(-0.780686\pi\)
0.164642 + 0.986353i \(0.447353\pi\)
\(564\) 0 0
\(565\) 12005.6 20794.2i 0.0376084 0.0651397i
\(566\) 219417. 291425.i 0.684916 0.909692i
\(567\) 0 0
\(568\) −31341.2 11986.4i −0.0971448 0.0371529i
\(569\) 1962.56 3399.25i 0.00606175 0.0104993i −0.862979 0.505240i \(-0.831404\pi\)
0.869040 + 0.494741i \(0.164737\pi\)
\(570\) 0 0
\(571\) 331554. 191423.i 1.01691 0.587112i 0.103702 0.994608i \(-0.466931\pi\)
0.913207 + 0.407496i \(0.133598\pi\)
\(572\) 15873.3 + 15303.5i 0.0485151 + 0.0467734i
\(573\) 0 0
\(574\) 42926.0 + 101012.i 0.130286 + 0.306583i
\(575\) 390347.i 1.18063i
\(576\) 0 0
\(577\) 18219.2 0.0547239 0.0273620 0.999626i \(-0.491289\pi\)
0.0273620 + 0.999626i \(0.491289\pi\)
\(578\) 46974.5 19962.3i 0.140607 0.0597524i
\(579\) 0 0
\(580\) −14410.7 + 14947.3i −0.0428380 + 0.0444331i
\(581\) −92407.6 160055.i −0.273751 0.474150i
\(582\) 0 0
\(583\) 22935.9 + 13242.0i 0.0674806 + 0.0389599i
\(584\) 34116.5 89205.4i 0.100032 0.261556i
\(585\) 0 0
\(586\) −265277. 199730.i −0.772510 0.581630i
\(587\) −45835.0 26462.8i −0.133021 0.0767998i 0.432013 0.901868i \(-0.357804\pi\)
−0.565034 + 0.825068i \(0.691137\pi\)
\(588\) 0 0
\(589\) 252532. + 437399.i 0.727924 + 1.26080i
\(590\) 48633.7 + 5951.16i 0.139712 + 0.0170961i
\(591\) 0 0
\(592\) −13716.5 375093.i −0.0391380 1.07028i
\(593\) −216280. −0.615046 −0.307523 0.951541i \(-0.599500\pi\)
−0.307523 + 0.951541i \(0.599500\pi\)
\(594\) 0 0
\(595\) 12498.3i 0.0353033i
\(596\) 9616.14 + 2389.17i 0.0270713 + 0.00672597i
\(597\) 0 0
\(598\) 688072. + 84197.3i 1.92412 + 0.235448i
\(599\) −260151. + 150198.i −0.725057 + 0.418612i −0.816611 0.577188i \(-0.804150\pi\)
0.0915543 + 0.995800i \(0.470816\pi\)
\(600\) 0 0
\(601\) −255485. + 442514.i −0.707322 + 1.22512i 0.258525 + 0.966005i \(0.416764\pi\)
−0.965847 + 0.259113i \(0.916570\pi\)
\(602\) −122099. 91929.8i −0.336915 0.253667i
\(603\) 0 0
\(604\) −66725.9 + 19192.8i −0.182903 + 0.0526094i
\(605\) −14841.8 + 25706.8i −0.0405487 + 0.0702324i
\(606\) 0 0
\(607\) −154217. + 89037.5i −0.418558 + 0.241655i −0.694460 0.719531i \(-0.744357\pi\)
0.275902 + 0.961186i \(0.411024\pi\)
\(608\) −340450. + 159608.i −0.920972 + 0.431765i
\(609\) 0 0
\(610\) −12461.3 + 5295.56i −0.0334892 + 0.0142316i
\(611\) 97990.4i 0.262483i
\(612\) 0 0
\(613\) 570495. 1.51821 0.759103 0.650970i \(-0.225638\pi\)
0.759103 + 0.650970i \(0.225638\pi\)
\(614\) −102004. 240032.i −0.270571 0.636697i
\(615\) 0 0
\(616\) 7309.59 1166.97i 0.0192633 0.00307538i
\(617\) 107951. + 186976.i 0.283567 + 0.491153i 0.972261 0.233900i \(-0.0751488\pi\)
−0.688694 + 0.725052i \(0.741815\pi\)
\(618\) 0 0
\(619\) −158318. 91404.9i −0.413189 0.238555i 0.278970 0.960300i \(-0.410007\pi\)
−0.692159 + 0.721745i \(0.743340\pi\)
\(620\) −42953.6 + 12355.0i −0.111742 + 0.0321410i
\(621\) 0 0
\(622\) −321672. + 427238.i −0.831442 + 1.10431i
\(623\) 177515. + 102489.i 0.457362 + 0.264058i
\(624\) 0 0
\(625\) −191454. 331608.i −0.490123 0.848918i
\(626\) 5460.93 44627.4i 0.0139353 0.113881i
\(627\) 0 0
\(628\) 96393.6 + 23949.4i 0.244415 + 0.0607261i
\(629\) 390019. 0.985791
\(630\) 0 0
\(631\) 153307.i 0.385037i 0.981293 + 0.192518i \(0.0616655\pi\)
−0.981293 + 0.192518i \(0.938335\pi\)
\(632\) −255221. + 207196.i −0.638972 + 0.518736i
\(633\) 0 0
\(634\) 19048.1 155664.i 0.0473885 0.387265i
\(635\) −36899.8 + 21304.1i −0.0915117 + 0.0528343i
\(636\) 0 0
\(637\) −257150. + 445397.i −0.633736 + 1.09766i
\(638\) 7685.56 10207.8i 0.0188814 0.0250779i
\(639\) 0 0
\(640\) −6443.06 32644.5i −0.0157301 0.0796986i
\(641\) 196626. 340566.i 0.478547 0.828869i −0.521150 0.853465i \(-0.674497\pi\)
0.999697 + 0.0245966i \(0.00783012\pi\)
\(642\) 0 0
\(643\) −384971. + 222263.i −0.931120 + 0.537583i −0.887166 0.461451i \(-0.847329\pi\)
−0.0439545 + 0.999034i \(0.513996\pi\)
\(644\) 161522. 167536.i 0.389456 0.403958i
\(645\) 0 0
\(646\) −152810. 359586.i −0.366173 0.861663i
\(647\) 152505.i 0.364314i −0.983269 0.182157i \(-0.941692\pi\)
0.983269 0.182157i \(-0.0583079\pi\)
\(648\) 0 0
\(649\) −30153.0 −0.0715881
\(650\) 630042. 267743.i 1.49122 0.633711i
\(651\) 0 0
\(652\) 182650. + 176093.i 0.429660 + 0.414235i
\(653\) −149617. 259144.i −0.350876 0.607736i 0.635527 0.772079i \(-0.280783\pi\)
−0.986403 + 0.164343i \(0.947450\pi\)
\(654\) 0 0
\(655\) 50211.7 + 28989.8i 0.117037 + 0.0675713i
\(656\) −257224. + 161321.i −0.597728 + 0.374871i
\(657\) 0 0
\(658\) 26280.6 + 19786.9i 0.0606992 + 0.0457010i
\(659\) −361192. 208535.i −0.831702 0.480183i 0.0227330 0.999742i \(-0.492763\pi\)
−0.854435 + 0.519558i \(0.826097\pi\)
\(660\) 0 0
\(661\) −379775. 657790.i −0.869208 1.50551i −0.862808 0.505532i \(-0.831296\pi\)
−0.00639999 0.999980i \(-0.502037\pi\)
\(662\) 296792. + 36317.5i 0.677230 + 0.0828706i
\(663\) 0 0
\(664\) 396938. 322246.i 0.900298 0.730888i
\(665\) 17252.3 0.0390126
\(666\) 0 0
\(667\) 401718.i 0.902962i
\(668\) 1616.48 6506.14i 0.00362257 0.0145804i
\(669\) 0 0
\(670\) −17768.5 2174.28i −0.0395824 0.00484358i
\(671\) 7216.22 4166.29i 0.0160275 0.00925346i
\(672\) 0 0
\(673\) 18836.0 32624.9i 0.0415871 0.0720309i −0.844483 0.535583i \(-0.820092\pi\)
0.886070 + 0.463552i \(0.153425\pi\)
\(674\) −453184. 341207.i −0.997597 0.751100i
\(675\) 0 0
\(676\) 209735. + 729170.i 0.458964 + 1.59564i
\(677\) −347010. + 601039.i −0.757120 + 1.31137i 0.187193 + 0.982323i \(0.440061\pi\)
−0.944313 + 0.329047i \(0.893272\pi\)
\(678\) 0 0
\(679\) −136614. + 78873.9i −0.296315 + 0.171078i
\(680\) 34142.9 5450.90i 0.0738385 0.0117883i
\(681\) 0 0
\(682\) 25314.9 10757.8i 0.0544261 0.0231289i
\(683\) 357197.i 0.765714i 0.923808 + 0.382857i \(0.125060\pi\)
−0.923808 + 0.382857i \(0.874940\pi\)
\(684\) 0 0
\(685\) 1256.87 0.00267861
\(686\) 154427. + 363391.i 0.328152 + 0.772194i
\(687\) 0 0
\(688\) 197884. 373647.i 0.418054 0.789376i
\(689\) 730122. + 1.26461e6i 1.53800 + 2.66390i
\(690\) 0 0
\(691\) −384473. 221976.i −0.805212 0.464889i 0.0400786 0.999197i \(-0.487239\pi\)
−0.845290 + 0.534307i \(0.820573\pi\)
\(692\) 84922.2 + 295242.i 0.177341 + 0.616547i
\(693\) 0 0
\(694\) 440359. 584876.i 0.914297 1.21435i
\(695\) 34159.6 + 19722.1i 0.0707202 + 0.0408304i
\(696\) 0 0
\(697\) −157749. 273228.i −0.324713 0.562420i
\(698\) 65374.2 534247.i 0.134182 1.09656i
\(699\) 0 0
\(700\) 55415.0 223039.i 0.113092 0.455182i
\(701\) 483771. 0.984474 0.492237 0.870461i \(-0.336179\pi\)
0.492237 + 0.870461i \(0.336179\pi\)
\(702\) 0 0
\(703\) 538375.i 1.08937i
\(704\) 6375.91 + 19459.5i 0.0128646 + 0.0392632i
\(705\) 0 0
\(706\) 97304.0 795181.i 0.195219 1.59535i
\(707\) 61929.9 35755.3i 0.123897 0.0715321i
\(708\) 0 0
\(709\) −79169.5 + 137126.i −0.157494 + 0.272788i −0.933965 0.357366i \(-0.883675\pi\)
0.776470 + 0.630154i \(0.217008\pi\)
\(710\) −2561.85 + 3402.60i −0.00508203 + 0.00674986i
\(711\) 0 0
\(712\) −202559. + 529638.i −0.399569 + 1.04477i
\(713\) 432382. 748907.i 0.850527 1.47316i
\(714\) 0 0
\(715\) 2423.76 1399.36i 0.00474108 0.00273726i
\(716\) −573875. 553273.i −1.11942 1.07923i
\(717\) 0 0
\(718\) −252154. 593359.i −0.489122 1.15098i
\(719\) 781622.i 1.51196i 0.654597 + 0.755978i \(0.272838\pi\)
−0.654597 + 0.755978i \(0.727162\pi\)
\(720\) 0 0
\(721\) −251358. −0.483529
\(722\) 16604.7 7056.34i 0.0318535 0.0135365i
\(723\) 0 0
\(724\) 155146. 160923.i 0.295980 0.307001i
\(725\) −198358. 343566.i −0.377375 0.653633i
\(726\) 0 0
\(727\) −51590.1 29785.6i −0.0976107 0.0563556i 0.450400 0.892827i \(-0.351281\pi\)
−0.548011 + 0.836471i \(0.684615\pi\)
\(728\) 381202. + 145790.i 0.719271 + 0.275085i
\(729\) 0 0
\(730\) −9684.71 7291.71i −0.0181736 0.0136831i
\(731\) 380482. + 219672.i 0.712032 + 0.411092i
\(732\) 0 0
\(733\) 106923. + 185196.i 0.199004 + 0.344685i 0.948206 0.317657i \(-0.102896\pi\)
−0.749202 + 0.662342i \(0.769563\pi\)
\(734\) 792350. + 96957.5i 1.47070 + 0.179966i
\(735\) 0 0
\(736\) 528122. + 368179.i 0.974943 + 0.679678i
\(737\) 11016.5 0.0202819
\(738\) 0 0
\(739\) 218903.i 0.400832i −0.979711 0.200416i \(-0.935771\pi\)
0.979711 0.200416i \(-0.0642294\pi\)
\(740\) −46237.2 11487.8i −0.0844361 0.0209785i
\(741\) 0 0
\(742\) 486594. + 59543.1i 0.883810 + 0.108149i
\(743\) −431487. + 249119.i −0.781610 + 0.451263i −0.837001 0.547202i \(-0.815693\pi\)
0.0553907 + 0.998465i \(0.482360\pi\)
\(744\) 0 0
\(745\) 628.850 1089.20i 0.00113301 0.00196243i
\(746\) −18497.9 13927.3i −0.0332388 0.0250258i
\(747\) 0 0
\(748\) −20448.9 + 5881.85i −0.0365483 + 0.0105126i
\(749\) −163175. + 282628.i −0.290864 + 0.503792i
\(750\) 0 0
\(751\) −534346. + 308505.i −0.947421 + 0.546994i −0.892279 0.451485i \(-0.850894\pi\)
−0.0551419 + 0.998479i \(0.517561\pi\)
\(752\) −42592.3 + 80423.4i −0.0753174 + 0.142215i
\(753\) 0 0
\(754\) 648396. 275543.i 1.14051 0.484670i
\(755\) 8813.01i 0.0154607i
\(756\) 0 0
\(757\) 483106. 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(758\) −340938. 802283.i −0.593386 1.39633i
\(759\) 0 0
\(760\) 7524.32 + 47130.2i 0.0130269 + 0.0815966i
\(761\) −68847.3 119247.i −0.118882 0.205910i 0.800443 0.599409i \(-0.204598\pi\)
−0.919325 + 0.393499i \(0.871264\pi\)
\(762\) 0 0
\(763\) 327141. + 188875.i 0.561935 + 0.324433i
\(764\) 479301. 137864.i 0.821148 0.236192i
\(765\) 0 0
\(766\) −167209. + 222084.i −0.284972 + 0.378494i
\(767\) −1.43980e6 831268.i −2.44743 1.41303i
\(768\) 0 0
\(769\) 173385. + 300311.i 0.293196 + 0.507830i 0.974564 0.224111i \(-0.0719478\pi\)
−0.681368 + 0.731941i \(0.738614\pi\)
\(770\) 114.121 932.610i 0.000192479 0.00157296i
\(771\) 0 0
\(772\) −419197. 104151.i −0.703369 0.174755i
\(773\) 456941. 0.764717 0.382358 0.924014i \(-0.375112\pi\)
0.382358 + 0.924014i \(0.375112\pi\)
\(774\) 0 0
\(775\) 853996.i 1.42185i
\(776\) −275050. 338803.i −0.456761 0.562632i
\(777\) 0 0