Properties

Label 108.5.f.a.91.3
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 91.3
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.3

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.885620 0.464411i \(-0.846266\pi\)
0.845002 + 0.534764i \(0.179599\pi\)
\(6\) 0 0
\(7\) 20.0352 11.5673i 0.408882 0.236068i −0.281427 0.959583i \(-0.590808\pi\)
0.690309 + 0.723514i \(0.257474\pi\)
\(8\) −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 −0.517784 0.855511i \(-0.673243\pi\)
0.482002 + 0.876170i \(0.339910\pi\)
\(12\) 0 0
\(13\) −137.824 + 238.718i −0.815527 + 1.41253i 0.0934218 + 0.995627i \(0.470219\pi\)
−0.908949 + 0.416908i \(0.863114\pi\)
\(14\) −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 \(-0.830171\pi\)
0.861015 0.508579i \(-0.169829\pi\)
\(20\) −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 0.916770 0.399416i \(-0.130787\pi\)
0.112481 + 0.993654i \(0.464120\pi\)
\(24\) 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 0.991045 0.133530i \(-0.0426312\pi\)
−0.611163 + 0.791505i \(0.709298\pi\)
\(30\) 0 0
\(31\) 1191.19 + 687.735i 1.23953 + 0.715645i 0.968999 0.247065i \(-0.0794660\pi\)
0.270535 + 0.962710i \(0.412799\pi\)
\(32\) 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 −0.986735 0.162339i \(-0.948096\pi\)
0.633958 + 0.773368i \(0.281429\pi\)
\(42\) 0 0
\(43\) 1430.33 825.804i 0.773572 0.446622i −0.0605755 0.998164i \(-0.519294\pi\)
0.834147 + 0.551542i \(0.185960\pi\)
\(44\) −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 −0.568063 0.822985i \(-0.692307\pi\)
0.428695 + 0.903449i \(0.358974\pi\)
\(48\) 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 1.00000 0.000603027i \(0.000191950\pi\)
0.500522 + 0.865724i \(0.333141\pi\)
\(60\) 0 0
\(61\) −833.364 1443.43i −0.223962 0.387914i 0.732045 0.681256i \(-0.238566\pi\)
−0.956008 + 0.293342i \(0.905233\pi\)
\(62\) −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 0.272146 0.962256i \(-0.412267\pi\)
−0.697265 + 0.716813i \(0.745600\pi\)
\(68\) 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 \(-0.983439\pi\)
0.998647 0.0520035i \(-0.0165607\pi\)
\(72\) 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 −0.0993209 0.995055i \(-0.531667\pi\)
0.812083 + 0.583542i \(0.198334\pi\)
\(80\) −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 −0.909508 0.415687i \(-0.863541\pi\)
−0.0947580 + 0.995500i \(0.530208\pi\)
\(84\) 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 0.625999 0.779824i \(-0.284692\pi\)
−0.988347 + 0.152219i \(0.951358\pi\)
\(98\) 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 0.931782 0.363019i \(-0.118254\pi\)
−0.780274 + 0.625437i \(0.784921\pi\)
\(102\) 0 0
\(103\) −9409.35 5432.49i −0.886922 0.512065i −0.0139875 0.999902i \(-0.504453\pi\)
−0.872934 + 0.487838i \(0.837786\pi\)
\(104\) 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 \(-0.788728\pi\)
0.787699 0.616060i \(-0.211272\pi\)
\(108\) 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 −0.536154 0.844120i \(-0.680123\pi\)
0.999107 + 0.0422631i \(0.0134568\pi\)
\(114\) 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 \(0.225390\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(128\) 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 −0.442804 0.896618i \(-0.646016\pi\)
−0.997896 + 0.0648298i \(0.979350\pi\)
\(132\) 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 0.857664 0.514210i \(-0.171915\pi\)
−0.874151 + 0.485654i \(0.838581\pi\)
\(138\) 0 0
\(139\) −16819.9 9710.99i −0.870552 0.502613i −0.00302027 0.999995i \(-0.500961\pi\)
−0.867532 + 0.497382i \(0.834295\pi\)
\(140\) −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 −0.858968 0.512030i \(-0.828894\pi\)
0.872915 + 0.487873i \(0.162227\pi\)
\(150\) 0 0
\(151\) −3758.08 + 2169.73i −0.164821 + 0.0951593i −0.580141 0.814516i \(-0.697003\pi\)
0.415321 + 0.909675i \(0.363669\pi\)
\(152\) −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 −0.796170 0.605073i \(-0.793144\pi\)
0.922093 + 0.386967i \(0.126477\pi\)
\(158\) −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 \(-0.903543\pi\)
0.954437 0.298412i \(-0.0964569\pi\)
\(164\) −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 0.506491 0.862245i \(-0.330942\pi\)
−0.493480 + 0.869757i \(0.664276\pi\)
\(168\) 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 0.659875 0.751375i \(-0.270609\pi\)
−0.980648 + 0.195781i \(0.937276\pi\)
\(174\) 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 \(0.283496\pi\)
−0.628922 + 0.777468i \(0.716504\pi\)
\(180\) 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 −0.0820893 0.996625i \(-0.526159\pi\)
0.822058 + 0.569404i \(0.192826\pi\)
\(192\) 0 0
\(193\) −13498.2 + 23379.5i −0.362377 + 0.627655i −0.988351 0.152189i \(-0.951368\pi\)
0.625975 + 0.779843i \(0.284701\pi\)
\(194\) 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 \(0.0339793\pi\)
−0.994308 + 0.106546i \(0.966021\pi\)
\(200\) 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 0.259943 0.965624i \(-0.416296\pi\)
−0.706284 + 0.707929i \(0.749630\pi\)
\(212\) −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 0.177919 0.984045i \(-0.443064\pi\)
0.941167 + 0.337941i \(0.109730\pi\)
\(224\) −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 −0.555288 0.831658i \(-0.687392\pi\)
0.442593 + 0.896722i \(0.354059\pi\)
\(228\) 0 0
\(229\) −17775.1 + 30787.4i −0.338955 + 0.587087i −0.984236 0.176858i \(-0.943407\pi\)
0.645281 + 0.763945i \(0.276740\pi\)
\(230\) 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 0.528184 0.849130i \(-0.322873\pi\)
−0.471277 + 0.881985i \(0.656207\pi\)
\(240\) 0 0
\(241\) 44832.6 + 77652.3i 0.771898 + 1.33697i 0.936522 + 0.350610i \(0.114026\pi\)
−0.164624 + 0.986356i \(0.552641\pi\)
\(242\) 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 \(0.0233798\pi\)
−0.997304 + 0.0733836i \(0.976620\pi\)
\(252\) 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 −0.802514 0.596633i \(-0.796505\pi\)
0.917956 + 0.396681i \(0.129838\pi\)
\(258\) 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 0.314322 0.949317i \(-0.398223\pi\)
0.979293 + 0.202448i \(0.0648896\pi\)
\(264\) 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 \(0.0339340\pi\)
−0.994323 + 0.106405i \(0.966066\pi\)
\(272\) −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 0.989398 0.145231i \(-0.0463924\pi\)
−0.620472 + 0.784228i \(0.713059\pi\)
\(278\) 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 0.967301 + 0.253633i \(0.0816255\pi\)
−0.263998 + 0.964523i \(0.585041\pi\)
\(282\) 0 0
\(283\) −78979.6 45598.9i −0.986148 0.569353i −0.0820271 0.996630i \(-0.526139\pi\)
−0.904121 + 0.427278i \(0.859473\pi\)
\(284\) 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 −0.516326 0.856392i \(-0.672701\pi\)
0.999820 + 0.0189556i \(0.00603412\pi\)
\(294\) 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 \(-0.887573\pi\)
0.938271 0.345902i \(-0.112427\pi\)
\(308\) −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 0.959911 0.280303i \(-0.0904350\pi\)
0.237206 + 0.971459i \(0.423768\pi\)
\(312\) 0 0
\(313\) −5620.04 9734.19i −0.0573655 0.0993599i 0.835917 0.548857i \(-0.184937\pi\)
−0.893282 + 0.449497i \(0.851603\pi\)
\(314\) −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 0.751849 0.659336i \(-0.229162\pi\)
−0.946926 + 0.321452i \(0.895829\pi\)
\(318\) 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 −0.765443 0.643504i \(-0.777480\pi\)
0.174570 + 0.984645i \(0.444147\pi\)
\(332\) −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 −0.364293 0.931285i \(-0.618689\pi\)
0.988662 0.150156i \(-0.0479775\pi\)
\(338\) 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 −0.333264 0.942834i \(-0.608150\pi\)
−0.983150 + 0.182802i \(0.941483\pi\)
\(348\) 0 0
\(349\) −67279.0 116531.i −0.552368 0.956729i −0.998103 0.0615644i \(-0.980391\pi\)
0.445735 0.895165i \(-0.352942\pi\)
\(350\) −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 −0.917215 0.398393i \(-0.869568\pi\)
0.113589 0.993528i \(-0.463765\pi\)
\(354\) 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 \(-0.784977\pi\)
0.780385 0.625300i \(-0.215023\pi\)
\(360\) 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 −0.977426 0.211279i \(-0.932237\pi\)
−0.305740 + 0.952115i \(0.598904\pi\)
\(368\) −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 −0.855436 0.517908i \(-0.826711\pi\)
0.876240 + 0.481876i \(0.160044\pi\)
\(374\) 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 \(-0.725887\pi\)
0.651565 0.758593i \(-0.274113\pi\)
\(380\) 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 0.690921 0.722930i \(-0.257205\pi\)
−0.280616 + 0.959820i \(0.590539\pi\)
\(384\) 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 0.945210 0.326462i \(-0.105856\pi\)
−0.755329 + 0.655345i \(0.772523\pi\)
\(390\) 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 −0.874262 0.485455i \(-0.838654\pi\)
0.857547 + 0.514405i \(0.171987\pi\)
\(402\) 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 −0.241800 0.970326i \(-0.577738\pi\)
0.961227 0.275758i \(-0.0889289\pi\)
\(410\) 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 0.410103 0.912039i \(-0.365493\pi\)
−0.584798 + 0.811179i \(0.698826\pi\)
\(420\) 0 0
\(421\) 82548.0 + 142977.i 0.465739 + 0.806683i 0.999235 0.0391198i \(-0.0124554\pi\)
−0.533496 + 0.845803i \(0.679122\pi\)
\(422\) 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 \(-0.856691\pi\)
0.900351 0.435163i \(-0.143309\pi\)
\(432\) 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 0.397326 0.917677i \(-0.369938\pi\)
0.993395 + 0.114744i \(0.0366049\pi\)
\(440\) −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 −0.392938 0.919565i \(-0.628541\pi\)
0.599897 + 0.800077i \(0.295208\pi\)
\(444\) 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 0.976238 0.216703i \(-0.0695302\pi\)
−0.675789 + 0.737095i \(0.736197\pi\)
\(458\) 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 0.961574 0.274547i \(-0.0885278\pi\)
−0.718551 + 0.695474i \(0.755194\pi\)
\(462\) 0 0
\(463\) 277564. + 160252.i 1.29480 + 0.747552i 0.979501 0.201442i \(-0.0645626\pi\)
0.315297 + 0.948993i \(0.397896\pi\)
\(464\) −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 \(0.435964\pi\)
−0.199820 + 0.979833i \(0.564036\pi\)
\(468\) 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 −0.0916316 0.995793i \(-0.529208\pi\)
0.816566 + 0.577252i \(0.195875\pi\)
\(480\) 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 \(-0.964437\pi\)
0.993765 0.111492i \(-0.0355631\pi\)
\(488\) −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 0.486733 0.873551i \(-0.338189\pi\)
−0.513151 + 0.858298i \(0.671522\pi\)
\(492\) 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 −0.445452 0.895306i \(-0.646957\pi\)
−0.998084 + 0.0618804i \(0.980290\pi\)
\(500\) −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 \(0.0335541\pi\)
−0.994449 + 0.105218i \(0.966446\pi\)
\(504\) 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 −0.236344 + 0.971669i \(0.575949\pi\)
−0.723319 + 0.690515i \(0.757384\pi\)
\(510\) 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 \(-0.931102\pi\)
0.976666 0.214763i \(-0.0688980\pi\)
\(524\) −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 0.184277 0.982874i \(-0.441006\pi\)
0.943333 + 0.331848i \(0.107672\pi\)
\(548\) 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 0.164642 0.986353i \(-0.447353\pi\)
−0.771886 + 0.635761i \(0.780686\pi\)
\(564\) 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 0.869040 0.494741i \(-0.164737\pi\)
−0.862979 + 0.505240i \(0.831404\pi\)
\(570\) 0 0
\(571\) 331554. + 191423.i 1.01691 + 0.587112i 0.913207 0.407496i \(-0.133598\pi\)
0.103702 + 0.994608i \(0.466931\pi\)
\(572\) 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 −0.565034 0.825068i \(-0.691137\pi\)
0.432013 + 0.901868i \(0.357804\pi\)
\(588\) 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 0.0915543 0.995800i \(-0.470816\pi\)
−0.816611 + 0.577188i \(0.804150\pi\)
\(600\) 0 0
\(601\) −255485. 442514.i −0.707322 1.22512i −0.965847 0.259113i \(-0.916570\pi\)
0.258525 0.966005i \(-0.416764\pi\)
\(602\) −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 0.275902 0.961186i \(-0.411024\pi\)
−0.694460 + 0.719531i \(0.744357\pi\)
\(608\) −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 −0.688694 0.725052i \(-0.741815\pi\)
0.972261 + 0.233900i \(0.0751488\pi\)
\(618\) 0 0
\(619\) −158318. + 91404.9i −0.413189 + 0.238555i −0.692159 0.721745i \(-0.743340\pi\)
0.278970 + 0.960300i \(0.410007\pi\)
\(620\) −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 \(-0.938335\pi\)
0.981293 0.192518i \(-0.0616655\pi\)
\(632\) −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 0.999697 0.0245966i \(-0.00783012\pi\)
−0.521150 + 0.853465i \(0.674497\pi\)
\(642\) 0 0
\(643\) −384971. 222263.i −0.931120 0.537583i −0.0439545 0.999034i \(-0.513996\pi\)
−0.887166 + 0.461451i \(0.847329\pi\)
\(644\) 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 \(0.0583079\pi\)
−0.983269 + 0.182157i \(0.941692\pi\)
\(648\) 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 −0.986403 0.164343i \(-0.947450\pi\)
0.635527 + 0.772079i \(0.280783\pi\)
\(654\) 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 −0.854435 0.519558i \(-0.826097\pi\)
0.0227330 + 0.999742i \(0.492763\pi\)
\(660\) 0 0
\(661\) −379775. + 657790.i −0.869208 + 1.50551i −0.00639999 + 0.999980i \(0.502037\pi\)
−0.862808 + 0.505532i \(0.831296\pi\)
\(662\) 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 0.886070 0.463552i \(-0.153425\pi\)
−0.844483 + 0.535583i \(0.820092\pi\)
\(674\) −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 −0.944313 0.329047i \(-0.893272\pi\)
0.187193 0.982323i \(-0.440061\pi\)
\(678\) 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 \(-0.874940\pi\)
0.923808 0.382857i \(-0.125060\pi\)
\(684\) 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 −0.845290 0.534307i \(-0.820573\pi\)
0.0400786 + 0.999197i \(0.487239\pi\)
\(692\) 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 0.776470 0.630154i \(-0.217008\pi\)
−0.933965 + 0.357366i \(0.883675\pi\)
\(710\) −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 \(-0.727162\pi\)
0.654597 0.755978i \(-0.272838\pi\)
\(720\) 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 −0.548011 0.836471i \(-0.684615\pi\)
0.450400 + 0.892827i \(0.351281\pi\)
\(728\) 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 −0.749202 0.662342i \(-0.769563\pi\)
0.948206 + 0.317657i \(0.102896\pi\)
\(734\) 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 \(0.0642294\pi\)
−0.979711 + 0.200416i \(0.935771\pi\)
\(740\) −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 0.0553907 0.998465i \(-0.482360\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(744\) 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 −0.0551419 0.998479i \(-0.517561\pi\)
−0.892279 + 0.451485i \(0.850894\pi\)
\(752\) −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 −0.919325 0.393499i \(-0.871264\pi\)
0.800443 + 0.599409i \(0.204598\pi\)
\(762\) 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 −0.681368 0.731941i \(-0.738614\pi\)
0.974564 + 0.224111i \(0.0719478\pi\)
\(770\) 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