Properties

Label 108.5.f.a.19.12
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 19.12
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +O(q^{10})\) \(q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +(6.48981 - 4.88624i) q^{10} +(4.32958 + 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(36.1928 - 85.1675i) q^{14} +(226.232 - 119.813i) q^{16} +266.009 q^{17} -367.194i q^{19} +(22.5533 + 23.3931i) q^{20} +(-7.82120 + 18.4045i) q^{22} +(-544.473 + 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 - 663.194i) q^{26} +(355.732 + 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(-1191.19 + 687.735i) q^{31} +(585.616 + 840.018i) q^{32} +(129.239 + 1056.16i) q^{34} +46.9843i q^{35} +1466.19 q^{37} +(1457.90 - 178.399i) q^{38} +(-81.9222 + 100.911i) q^{40} +(-593.019 - 1027.14i) q^{41} +(-1430.33 - 825.804i) q^{43} +(-76.8730 - 22.1114i) q^{44} +(-1512.63 - 2009.04i) q^{46} +(307.864 + 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(2285.68 + 971.322i) q^{50} +(3061.09 + 3175.07i) q^{52} -5297.49 q^{53} -10.1532i q^{55} +(-233.424 + 1462.10i) q^{56} +(2352.26 + 999.617i) q^{58} +(-5223.32 + 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 - 4395.36i) q^{62} +(-3050.68 + 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(1908.36 - 1101.79i) q^{67} +(-4130.57 + 1026.26i) q^{68} +(-186.546 + 22.8270i) q^{70} -524.299i q^{71} -1492.29 q^{73} +(712.338 + 5821.33i) q^{74} +(1416.63 + 5701.76i) q^{76} +(-57.8293 - 100.163i) q^{77} +(-4448.35 - 2568.25i) q^{79} +(-440.456 - 276.236i) q^{80} +(3790.02 - 2853.54i) q^{82} +(6918.39 + 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(2583.84 - 6080.19i) q^{86} +(50.4426 - 315.958i) q^{88} +8860.17 q^{89} +6377.03i q^{91} +(7241.77 - 6981.79i) q^{92} +(-556.144 + 1308.70i) q^{94} +(-645.826 + 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 - 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.485844 + 3.97038i 0.121461 + 0.992596i
\(3\) 0 0
\(4\) −15.5279 + 3.85798i −0.970494 + 0.241124i
\(5\) −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 0.281427 0.959583i \(-0.409192\pi\)
−0.690309 + 0.723514i \(0.742526\pi\)
\(8\) −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 \(-0.326757\pi\)
−0.482002 + 0.876170i \(0.660090\pi\)
\(12\) 0 0
\(13\) −137.824 238.718i −0.815527 1.41253i −0.908949 0.416908i \(-0.863114\pi\)
0.0934218 0.995627i \(-0.470219\pi\)
\(14\) 36.1928 85.1675i 0.184657 0.434528i
\(15\) 0 0
\(16\) 226.232 119.813i 0.883719 0.468018i
\(17\) 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 \(-0.169829\pi\)
\(20\) 22.5533 + 23.3931i 0.0563832 + 0.0584828i
\(21\) 0 0
\(22\) −7.82120 + 18.4045i −0.0161595 + 0.0380259i
\(23\) −544.473 + 314.352i −1.02925 + 0.594238i −0.916770 0.399416i \(-0.869213\pi\)
−0.112481 + 0.993654i \(0.535880\pi\)
\(24\) 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 −0.968999 0.247065i \(-0.920534\pi\)
−0.270535 + 0.962710i \(0.587201\pi\)
\(32\) 585.616 + 840.018i 0.571891 + 0.820330i
\(33\) 0 0
\(34\) 129.239 + 1056.16i 0.111799 + 0.913633i
\(35\) 46.9843i 0.0383545i
\(36\) 0 0
\(37\) 1466.19 1.07099 0.535496 0.844538i \(-0.320125\pi\)
0.535496 + 0.844538i \(0.320125\pi\)
\(38\) 1457.90 178.399i 1.00963 0.123545i
\(39\) 0 0
\(40\) −81.9222 + 100.911i −0.0512014 + 0.0630692i
\(41\) −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 0.0605755 0.998164i \(-0.480706\pi\)
−0.834147 + 0.551542i \(0.814040\pi\)
\(44\) −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 \(-0.307693\pi\)
−0.428695 + 0.903449i \(0.641026\pi\)
\(48\) 0 0
\(49\) −932.893 1615.82i −0.388544 0.672977i
\(50\) 2285.68 + 971.322i 0.914270 + 0.388529i
\(51\) 0 0
\(52\) 3061.09 + 3175.07i 1.13206 + 1.17421i
\(53\) −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
\(56\) −233.424 + 1462.10i −0.0744338 + 0.466232i
\(57\) 0 0
\(58\) 2352.26 + 999.617i 0.699245 + 0.297151i
\(59\) −5223.32 + 3015.68i −1.50052 + 0.866327i −0.500522 + 0.865724i \(0.666859\pi\)
−1.00000 0.000603027i \(0.999808\pi\)
\(60\) 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 −0.272146 0.962256i \(-0.587733\pi\)
0.697265 + 0.716813i \(0.254400\pi\)
\(68\) −4130.57 + 1026.26i −0.893289 + 0.221942i
\(69\) 0 0
\(70\) −186.546 + 22.8270i −0.0380705 + 0.00465858i
\(71\) 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 \(0.544715\pi\)
\(74\) 712.338 + 5821.33i 0.130084 + 1.06306i
\(75\) 0 0
\(76\) 1416.63 + 5701.76i 0.245261 + 0.987146i
\(77\) −57.8293 100.163i −0.00975364 0.0168938i
\(78\) 0 0
\(79\) −4448.35 2568.25i −0.712762 0.411513i 0.0993209 0.995055i \(-0.468333\pi\)
−0.812083 + 0.583542i \(0.801666\pi\)
\(80\) −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 \(-0.136459\pi\)
0.0947580 + 0.995500i \(0.469792\pi\)
\(84\) 0 0
\(85\) −270.120 467.861i −0.0373868 0.0647558i
\(86\) 2583.84 6080.19i 0.349356 0.822092i
\(87\) 0 0
\(88\) 50.4426 315.958i 0.00651376 0.0408004i
\(89\) 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
\(92\) 7241.77 6981.79i 0.855597 0.824881i
\(93\) 0 0
\(94\) −556.144 + 1308.70i −0.0629407 + 0.148110i
\(95\) −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 0.0139875 0.999902i \(-0.495547\pi\)
0.872934 + 0.487838i \(0.162214\pi\)
\(104\) −11119.1 + 13696.3i −1.02802 + 1.26630i
\(105\) 0 0
\(106\) −2573.76 21033.1i −0.229063 1.87194i
\(107\) 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 \(0.258857\pi\)
\(110\) 40.3122 4.93288i 0.00333159 0.000407676i
\(111\) 0 0
\(112\) −5918.52 216.430i −0.471821 0.0172536i
\(113\) 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
\(122\) −6135.85 2607.49i −0.412245 0.175188i
\(123\) 0 0
\(124\) 15843.5 15274.7i 1.03040 0.993411i
\(125\) −2530.25 −0.161936
\(126\) 0 0
\(127\) 20979.9i 1.30076i 0.759609 + 0.650379i \(0.225390\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(128\) −12334.2 10784.4i −0.752817 0.658229i
\(129\) 0 0
\(130\) −2060.89 875.796i −0.121946 0.0518222i
\(131\) 24723.9 14274.3i 1.44070 0.831789i 0.442804 0.896618i \(-0.353984\pi\)
0.997896 + 0.0648298i \(0.0206504\pi\)
\(132\) 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 0.00302027 0.999995i \(-0.499039\pi\)
0.867532 + 0.497382i \(0.165705\pi\)
\(140\) −181.264 729.568i −0.00924818 0.0372228i
\(141\) 0 0
\(142\) 2081.67 254.728i 0.103237 0.0126328i
\(143\) 1378.07i 0.0673903i
\(144\) 0 0
\(145\) −1297.67 −0.0617203
\(146\) −725.022 5924.98i −0.0340130 0.277959i
\(147\) 0 0
\(148\) −22766.8 + 5656.52i −1.03939 + 0.258241i
\(149\) 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 0.580141 0.814516i \(-0.302997\pi\)
−0.415321 + 0.909675i \(0.636331\pi\)
\(152\) −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 \(0.793144\pi\)
\(158\) 8035.75 18909.4i 0.321894 0.757468i
\(159\) 0 0
\(160\) 882.770 1882.99i 0.0344832 0.0735541i
\(161\) 14544.9 0.561123
\(162\) 0 0
\(163\) 15857.0i 0.596824i −0.954437 0.298412i \(-0.903543\pi\)
0.954437 0.298412i \(-0.0964569\pi\)
\(164\) 13171.0 + 13661.5i 0.489702 + 0.507937i
\(165\) 0 0
\(166\) −12497.8 + 29409.3i −0.453541 + 1.06725i
\(167\) −362.861 + 209.498i −0.0130109 + 0.00751186i −0.506491 0.862245i \(-0.669058\pi\)
0.493480 + 0.869757i \(0.335724\pi\)
\(168\) 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
\(176\) 1278.98 + 46.7701i 0.0412895 + 0.00150988i
\(177\) 0 0
\(178\) 4304.66 + 35178.3i 0.135862 + 1.11028i
\(179\) 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 \(0.431604\pi\)
\(182\) −25319.3 + 3098.24i −0.764378 + 0.0935347i
\(183\) 0 0
\(184\) 31238.8 + 25360.6i 0.922696 + 0.749071i
\(185\) −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 \(-0.473841\pi\)
−0.822058 + 0.569404i \(0.807174\pi\)
\(192\) 0 0
\(193\) −13498.2 23379.5i −0.362377 0.627655i 0.625975 0.779843i \(-0.284701\pi\)
−0.988351 + 0.152189i \(0.951368\pi\)
\(194\) −25102.1 10667.4i −0.666970 0.283436i
\(195\) 0 0
\(196\) 20719.7 + 21491.2i 0.539350 + 0.559434i
\(197\) −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 \(0.966021\pi\)
\(200\) −39239.1 6264.51i −0.980978 0.156613i
\(201\) 0 0
\(202\) 11379.3 + 4835.76i 0.278878 + 0.118512i
\(203\) −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 \(-0.583704\pi\)
0.706284 + 0.707929i \(0.250370\pi\)
\(212\) 82259.0 20437.6i 1.83026 0.454735i
\(213\) 0 0
\(214\) 56008.4 6853.58i 1.22300 0.149655i
\(215\) 3354.25i 0.0725637i
\(216\) 0 0
\(217\) 31821.1 0.675764
\(218\) 7933.01 + 64829.6i 0.166926 + 1.36414i
\(219\) 0 0
\(220\) 39.1709 + 157.658i 0.000809316 + 0.00325740i
\(221\) −36662.5 63501.3i −0.750650 1.30016i
\(222\) 0 0
\(223\) −55651.0 32130.1i −1.11909 0.646105i −0.177919 0.984045i \(-0.556936\pi\)
−0.941167 + 0.337941i \(0.890270\pi\)
\(224\) −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 \(-0.312608\pi\)
−0.442593 + 0.896722i \(0.645941\pi\)
\(228\) 0 0
\(229\) −17775.1 30787.4i −0.338955 0.587087i 0.645281 0.763945i \(-0.276740\pi\)
−0.984236 + 0.176858i \(0.943407\pi\)
\(230\) −1997.53 + 4700.51i −0.0377605 + 0.0888566i
\(231\) 0 0
\(232\) −40382.2 6447.00i −0.750263 0.119779i
\(233\) −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
\(236\) 69472.8 66978.7i 1.24736 1.20258i
\(237\) 0 0
\(238\) 9627.62 22655.3i 0.169967 0.399960i
\(239\) −3250.59 + 1876.73i −0.0569070 + 0.0328553i −0.528184 0.849130i \(-0.677127\pi\)
0.471277 + 0.881985i \(0.343793\pi\)
\(240\) 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
\(248\) 68343.8 + 55483.5i 1.11121 + 0.902112i
\(249\) 0 0
\(250\) −1229.31 10046.1i −0.0196689 0.160737i
\(251\) 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
\(254\) −83298.4 + 10193.0i −1.29113 + 0.157992i
\(255\) 0 0
\(256\) 36825.9 54210.9i 0.561918 0.827193i
\(257\) 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 −0.314322 0.949317i \(-0.601777\pi\)
−0.979293 + 0.202448i \(0.935110\pi\)
\(264\) 0 0
\(265\) 5379.35 + 9317.30i 0.0766016 + 0.132678i
\(266\) −31273.0 13289.8i −0.441983 0.187825i
\(267\) 0 0
\(268\) −25382.2 + 24470.9i −0.353394 + 0.340707i
\(269\) 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 \(0.966066\pi\)
\(272\) 60179.8 31871.3i 0.813417 0.430786i
\(273\) 0 0
\(274\) −2278.30 968.188i −0.0303466 0.0128961i
\(275\) 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 0.0820271 0.996630i \(-0.473861\pi\)
0.904121 + 0.427278i \(0.140527\pi\)
\(284\) 2022.73 + 8141.27i 0.0250785 + 0.100938i
\(285\) 0 0
\(286\) 5471.45 669.525i 0.0668914 0.00818530i
\(287\) 27438.6i 0.333118i
\(288\) 0 0
\(289\) −12760.0 −0.152776
\(290\) −630.465 5152.25i −0.00749661 0.0612633i
\(291\) 0 0
\(292\) 23172.2 5757.23i 0.271770 0.0675224i
\(293\) 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
\(302\) −6788.81 + 15975.2i −0.0744355 + 0.175159i
\(303\) 0 0
\(304\) −43994.5 83071.0i −0.476048 0.898882i
\(305\) 3384.96 0.0363876
\(306\) 0 0
\(307\) 65201.8i 0.691803i −0.938271 0.345902i \(-0.887573\pi\)
0.938271 0.345902i \(-0.112427\pi\)
\(308\) 1284.40 + 1332.22i 0.0135393 + 0.0140435i
\(309\) 0 0
\(310\) −4370.18 + 10283.7i −0.0454753 + 0.107011i
\(311\) −115786. + 66849.3i −1.19712 + 0.691156i −0.959911 0.280303i \(-0.909565\pi\)
−0.237206 + 0.971459i \(0.576232\pi\)
\(312\) 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
\(320\) 7905.07 + 2590.10i 0.0771979 + 0.0252939i
\(321\) 0 0
\(322\) 7066.54 + 57748.7i 0.0681546 + 0.556968i
\(323\) 97677.0i 0.936240i
\(324\) 0 0
\(325\) −171143. −1.62029
\(326\) 62958.4 7704.04i 0.592405 0.0724908i
\(327\) 0 0
\(328\) −47842.2 + 58931.4i −0.444696 + 0.547771i
\(329\) −4112.08 7122.34i −0.0379901 0.0658007i
\(330\) 0 0
\(331\) 64736.6 + 37375.7i 0.590873 + 0.341141i 0.765443 0.643504i \(-0.222520\pi\)
−0.174570 + 0.984645i \(0.555853\pi\)
\(332\) −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 \(0.618689\pi\)
\(338\) −174574. 74187.1i −1.52808 0.649374i
\(339\) 0 0
\(340\) 5999.39 + 6222.78i 0.0518978 + 0.0538303i
\(341\) −6876.48 −0.0591367
\(342\) 0 0
\(343\) 98710.7i 0.839027i
\(344\) −16664.4 + 104381.i −0.140823 + 0.882073i
\(345\) 0 0
\(346\) −70685.3 30038.5i −0.590442 0.250914i
\(347\) 158508. 91514.6i 1.31641 0.760032i 0.333264 0.942834i \(-0.391850\pi\)
0.983150 + 0.182802i \(0.0585168\pi\)
\(348\) 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
\(356\) −137580. + 34182.3i −1.08556 + 0.269713i
\(357\) 0 0
\(358\) −197811. + 24205.6i −1.54342 + 0.188864i
\(359\) 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
\(362\) 6787.59 + 55469.1i 0.0517962 + 0.423286i
\(363\) 0 0
\(364\) −24602.4 99022.0i −0.185684 0.747358i
\(365\) 1515.35 + 2624.66i 0.0113744 + 0.0197010i
\(366\) 0 0
\(367\) 172828. + 99782.5i 1.28317 + 0.740836i 0.977426 0.211279i \(-0.0677627\pi\)
0.305740 + 0.952115i \(0.401096\pi\)
\(368\) −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 \(0.826711\pi\)
\(374\) −2080.51 + 4895.78i −0.0148740 + 0.0350008i
\(375\) 0 0
\(376\) 3586.83 22466.9i 0.0253709 0.158916i
\(377\) −176129. −1.23922
\(378\) 0 0
\(379\) 217930.i 1.51719i −0.651565 0.758593i \(-0.725887\pi\)
0.651565 0.758593i \(-0.274113\pi\)
\(380\) 8589.81 8281.44i 0.0594862 0.0573507i
\(381\) 0 0
\(382\) 48765.0 114752.i 0.334181 0.786381i
\(383\) −60187.2 + 34749.1i −0.410305 + 0.236890i −0.690921 0.722930i \(-0.742795\pi\)
0.280616 + 0.959820i \(0.409461\pi\)
\(384\) 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
\(392\) −75261.8 + 92706.5i −0.489782 + 0.603306i
\(393\) 0 0
\(394\) −5060.76 41357.2i −0.0326004 0.266415i
\(395\) 10431.7i 0.0668595i
\(396\) 0 0
\(397\) 13255.8 0.0841056 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(398\) −33504.8 + 4099.89i −0.211515 + 0.0258825i
\(399\) 0 0
\(400\) 5808.42 158838.i 0.0363026 0.992737i
\(401\) −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 \(0.577738\pi\)
\(410\) −8867.43 3768.31i −0.0527509 0.0224170i
\(411\) 0 0
\(412\) −125149. + 120656.i −0.737282 + 0.710814i
\(413\) 139534. 0.818049
\(414\) 0 0
\(415\) 16224.2i 0.0942035i
\(416\) 119816. 255572.i 0.692352 1.47682i
\(417\) 0 0
\(418\) 6758.04 + 2871.90i 0.0386784 + 0.0164368i
\(419\) 30669.6 17707.1i 0.174695 0.100860i −0.410103 0.912039i \(-0.634507\pi\)
0.584798 + 0.811179i \(0.301174\pi\)
\(420\) 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
\(428\) 54422.7 + 219045.i 0.297093 + 1.19577i
\(429\) 0 0
\(430\) −13317.7 + 1629.65i −0.0720264 + 0.00881366i
\(431\) 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 \(0.552731\pi\)
\(434\) 15460.1 + 126342.i 0.0820791 + 0.670761i
\(435\) 0 0
\(436\) −253544. + 62994.2i −1.33377 + 0.331381i
\(437\) 115428. + 199927.i 0.604434 + 1.04691i
\(438\) 0 0
\(439\) −268021. 154742.i −1.39072 0.802933i −0.397326 0.917677i \(-0.630062\pi\)
−0.993395 + 0.114744i \(0.963395\pi\)
\(440\) −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 \(-0.371459\pi\)
−0.599897 + 0.800077i \(0.704792\pi\)
\(444\) 0 0
\(445\) −8997.07 15583.4i −0.0454340 0.0786940i
\(446\) 100531. 236566.i 0.505396 1.18928i
\(447\) 0 0
\(448\) 92737.3 19472.8i 0.462060 0.0970226i
\(449\) 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
\(452\) −131294. 136183.i −0.642639 0.666569i
\(453\) 0 0
\(454\) −10490.1 + 24685.0i −0.0508944 + 0.119763i
\(455\) 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 −0.979501 0.201442i \(-0.935437\pi\)
−0.315297 + 0.948993i \(0.602104\pi\)
\(464\) 5977.62 163465.i 0.0277646 0.759257i
\(465\) 0 0
\(466\) −30336.1 247910.i −0.139697 1.14162i
\(467\) 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
\(470\) 2866.49 350.764i 0.0129764 0.00158788i
\(471\) 0 0
\(472\) 299684. + 243292.i 1.34518 + 1.09205i
\(473\) −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 \(-0.470792\pi\)
−0.816566 + 0.577252i \(0.804125\pi\)
\(480\) 0 0
\(481\) −202076. 350006.i −0.873422 1.51281i
\(482\) 330091. + 140276.i 1.42082 + 0.603793i
\(483\) 0 0
\(484\) 162312. + 168356.i 0.692882 + 0.718682i
\(485\) 13848.1 0.0588715
\(486\) 0 0
\(487\) 52885.1i 0.222985i −0.993765 0.111492i \(-0.964437\pi\)
0.993765 0.111492i \(-0.0355631\pi\)
\(488\) 105337. + 16816.9i 0.442323 + 0.0706167i
\(489\) 0 0
\(490\) −13949.6 5928.02i −0.0580991 0.0246898i
\(491\) 6368.89 3677.08i 0.0264180 0.0152525i −0.486733 0.873551i \(-0.661811\pi\)
0.513151 + 0.858298i \(0.328478\pi\)
\(492\) 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 \(-0.353043\pi\)
0.998084 + 0.0618804i \(0.0197097\pi\)
\(500\) 39289.5 9761.65i 0.157158 0.0390466i
\(501\) 0 0
\(502\) −36712.1 + 4492.35i −0.145681 + 0.0178265i
\(503\) 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
\(506\) −1527.07 12479.4i −0.00596426 0.0487408i
\(507\) 0 0
\(508\) −80940.1 325775.i −0.313644 1.26238i
\(509\) −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
\(518\) 53065.4 124871.i 0.197766 0.465375i
\(519\) 0 0
\(520\) 35380.1 + 5648.42i 0.130843 + 0.0208891i
\(521\) 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 \(-0.0688980\pi\)
\(524\) −328840. + 317035.i −1.19763 + 1.15463i
\(525\) 0 0
\(526\) 161638. 380361.i 0.584215 1.37475i
\(527\) −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
\(536\) −109491. 88887.9i −0.381108 0.309395i
\(537\) 0 0
\(538\) 41791.3 + 341524.i 0.144385 + 1.17993i
\(539\) 9327.75i 0.0321070i
\(540\) 0 0
\(541\) −16461.8 −0.0562448 −0.0281224 0.999604i \(-0.508953\pi\)
−0.0281224 + 0.999604i \(0.508953\pi\)
\(542\) −62053.1 + 7593.26i −0.211235 + 0.0258482i
\(543\) 0 0
\(544\) 155779. + 223453.i 0.526395 + 0.755071i
\(545\) −16580.6 28718.4i −0.0558222 0.0966869i
\(546\) 0 0
\(547\) −337391. 194793.i −1.12761 0.651026i −0.184277 0.982874i \(-0.558994\pi\)
−0.943333 + 0.331848i \(0.892328\pi\)
\(548\) 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
\(554\) 208420. + 88570.1i 0.679077 + 0.288581i
\(555\) 0 0
\(556\) −223714. + 215682.i −0.723674 + 0.697694i
\(557\) −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
\(560\) 5629.31 + 10629.3i 0.0179506 + 0.0338946i
\(561\) 0 0
\(562\) 408879. + 173758.i 1.29456 + 0.550137i
\(563\) 192477. 111127.i 0.607244 0.350592i −0.164642 0.986353i \(-0.552647\pi\)
0.771886 + 0.635761i \(0.219314\pi\)
\(564\) 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 −0.913207 0.407496i \(-0.866402\pi\)
−0.103702 + 0.994608i \(0.533069\pi\)
\(572\) 5316.54 + 21398.5i 0.0162494 + 0.0654020i
\(573\) 0 0
\(574\) −108942. + 13330.9i −0.330652 + 0.0404609i
\(575\) 390347.i 1.18063i
\(576\) 0 0
\(577\) 18219.2 0.0547239 0.0273620 0.999626i \(-0.491289\pi\)
0.0273620 + 0.999626i \(0.491289\pi\)
\(578\) −6199.39 50662.3i −0.0185564 0.151645i
\(579\) 0 0
\(580\) 20150.1 5006.38i 0.0598992 0.0148822i
\(581\) −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 \(-0.308863\pi\)
−0.432013 + 0.901868i \(0.642196\pi\)
\(588\) 0 0
\(589\) 252532. + 437399.i 0.727924 + 1.26080i
\(590\) −19163.0 + 45093.6i −0.0550503 + 0.129542i
\(591\) 0 0
\(592\) 331698. 175668.i 0.946455 0.501243i
\(593\) −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
\(596\) −6877.16 7133.24i −0.0193605 0.0200814i
\(597\) 0 0
\(598\) −271119. + 637986.i −0.758154 + 1.78406i
\(599\) 260151. 150198.i 0.725057 0.418612i −0.0915543 0.995800i \(-0.529184\pi\)
0.816611 + 0.577188i \(0.195850\pi\)
\(600\) 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 −0.275902 0.961186i \(-0.588976\pi\)
0.694460 + 0.719531i \(0.255643\pi\)
\(608\) 308450. 215035.i 0.834405 0.581703i
\(609\) 0 0
\(610\) 1644.56 + 13439.6i 0.00441968 + 0.0361182i
\(611\) 97990.4i 0.262483i
\(612\) 0 0
\(613\) 570495. 1.51821 0.759103 0.650970i \(-0.225638\pi\)
0.759103 + 0.650970i \(0.225638\pi\)
\(614\) 258876. 31677.9i 0.686681 0.0840272i
\(615\) 0 0
\(616\) −4665.42 + 5746.80i −0.0122950 + 0.0151448i
\(617\) 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 0.692159 0.721745i \(-0.256660\pi\)
−0.278970 + 0.960300i \(0.589993\pi\)
\(620\) −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
\(626\) −41378.9 17584.4i −0.105592 0.0448724i
\(627\) 0 0
\(628\) −68937.6 71504.6i −0.174798 0.181307i
\(629\) 390019. 0.985791
\(630\) 0 0
\(631\) 153307.i 0.385037i −0.981293 0.192518i \(-0.938335\pi\)
0.981293 0.192518i \(-0.0616655\pi\)
\(632\) −51826.4 + 324626.i −0.129753 + 0.812734i
\(633\) 0 0
\(634\) −144333. 61335.7i −0.359076 0.152593i
\(635\) 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 0.0439545 0.999034i \(-0.486004\pi\)
0.887166 + 0.461451i \(0.152671\pi\)
\(644\) −225851. + 56113.7i −0.544566 + 0.135300i
\(645\) 0 0
\(646\) 387815. 47455.8i 0.929309 0.113717i
\(647\) 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
\(650\) −83148.9 679504.i −0.196802 1.60829i
\(651\) 0 0
\(652\) 61176.0 + 246226.i 0.143908 + 0.579214i
\(653\) −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 0.854435 0.519558i \(-0.173903\pi\)
−0.0227330 + 0.999742i \(0.507237\pi\)
\(660\) 0 0
\(661\) −379775. 657790.i −0.869208 1.50551i −0.862808 0.505532i \(-0.831296\pi\)
−0.00639999 0.999980i \(-0.502037\pi\)
\(662\) −116944. + 275188.i −0.266847 + 0.627933i
\(663\) 0 0
\(664\) 80604.0 504881.i 0.182819 1.14512i
\(665\) 17252.3 0.0390126
\(666\) 0 0
\(667\) 401718.i 0.902962i
\(668\) 4826.24 4652.98i 0.0108157 0.0104275i
\(669\) 0 0
\(670\) 7001.28 16475.1i 0.0155965 0.0367011i
\(671\) −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
\(680\) −21792.1 + 26843.2i −0.0471282 + 0.0580519i
\(681\) 0 0
\(682\) −3340.90 27302.3i −0.00718281 0.0586989i
\(683\) 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
\(686\) −391920. + 47958.0i −0.832815 + 0.101909i
\(687\) 0 0
\(688\) −422529. 15451.1i −0.892647 0.0326425i
\(689\) 730122. + 1.26461e6i 1.53800 + 2.66390i
\(690\) 0 0
\(691\) 384473. + 221976.i 0.805212 + 0.464889i 0.845290 0.534307i \(-0.179427\pi\)
−0.0400786 + 0.999197i \(0.512761\pi\)
\(692\) 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
\(698\) −495358. 210508.i −1.01674 0.432073i
\(699\) 0 0
\(700\) 165450. 159510.i 0.337653 0.325531i
\(701\) 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
\(704\) −20040.4 + 4208.04i −0.0404353 + 0.00849053i
\(705\) 0 0
\(706\) −737299. 313323.i −1.47922 0.628612i
\(707\) −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
\(716\) −192211. 773627.i −0.374932 1.50906i
\(717\) 0 0
\(718\) 639941. 78307.7i 1.24134 0.151899i
\(719\) 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
\(722\) −2191.38 17908.3i −0.00420381 0.0343541i
\(723\) 0 0
\(724\) −216936. + 53898.7i −0.413861 + 0.102826i
\(725\) −198358. 343566.i −0.377375 0.653633i
\(726\) 0 0
\(727\) 51590.1 + 29785.6i 0.0976107 + 0.0563556i 0.548011 0.836471i \(-0.315385\pi\)
−0.450400 + 0.892827i \(0.648719\pi\)
\(728\) 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 \(0.769563\pi\)
\(734\) −312207. + 734674.i −0.579497 + 1.36365i
\(735\) 0 0
\(736\) −582914. 273278.i −1.07609 0.504486i
\(737\) 11016.5 0.0202819
\(738\) 0 0
\(739\) 218903.i 0.400832i 0.979711 + 0.200416i \(0.0642294\pi\)
−0.979711 + 0.200416i \(0.935771\pi\)
\(740\) 33067.3 + 34298.7i 0.0603860 + 0.0626345i
\(741\) 0 0
\(742\) −191731. + 451174.i −0.348245 + 0.819476i
\(743\) 431487. 249119.i 0.781610 0.451263i −0.0553907 0.998465i \(-0.517640\pi\)
0.837001 + 0.547202i \(0.184307\pi\)
\(744\) 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 \(-0.482439\pi\)
0.892279 + 0.451485i \(0.149106\pi\)
\(752\) 90944.9 + 3325.69i 0.160821 + 0.00588093i
\(753\) 0 0
\(754\) −85571.1 699299.i −0.150517 1.23004i
\(755\) 8813.01i 0.0154607i
\(756\) 0 0
\(757\) 483106. 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(758\) 865266. 105880.i 1.50595 0.184279i
\(759\) 0 0
\(760\) 37053.8 + 30081.4i 0.0641513 + 0.0520799i
\(761\) −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 \(0.738614\pi\)
\(770\) −864.724 367.473i −0.00145847 0.000619790i
\(771\) 0 0
\(772\) 299796. + 310959.i 0.503027 + 0.521758i
\(773\) 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
\(776\) 430938. + 68799.0i