Properties

Label 108.6.h.a.71.17
Level 108
Weight 6
Character 108.71
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.17
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.78216 + 5.36879i) q^{2} +(-25.6478 + 19.1360i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(-15.2989 + 8.83282i) q^{7} +(-148.446 - 103.595i) q^{8} +O(q^{10})\) \(q+(1.78216 + 5.36879i) q^{2} +(-25.6478 + 19.1360i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(-15.2989 + 8.83282i) q^{7} +(-148.446 - 103.595i) q^{8} +(16.9473 - 82.2944i) q^{10} +(-143.245 - 248.107i) q^{11} +(42.2460 - 73.1722i) q^{13} +(-74.6866 - 66.3951i) q^{14} +(291.624 - 981.596i) q^{16} -1609.65i q^{17} +1669.01i q^{19} +(472.025 - 55.6747i) q^{20} +(1076.75 - 1211.22i) q^{22} +(2324.29 - 4025.79i) q^{23} +(-1452.19 - 2515.27i) q^{25} +(468.135 + 96.4056i) q^{26} +(223.358 - 519.303i) q^{28} +(-2414.87 + 1394.23i) q^{29} +(2781.39 + 1605.84i) q^{31} +(5789.71 - 183.691i) q^{32} +(8641.85 - 2868.64i) q^{34} +262.388 q^{35} -4624.19 q^{37} +(-8960.54 + 2974.43i) q^{38} +(1140.13 + 2434.98i) q^{40} +(-9810.20 - 5663.92i) q^{41} +(12396.0 - 7156.83i) q^{43} +(8421.70 + 3622.27i) q^{44} +(25755.9 + 5304.05i) q^{46} +(1695.63 + 2936.92i) q^{47} +(-8247.46 + 14285.0i) q^{49} +(10915.9 - 12279.1i) q^{50} +(316.708 + 2685.13i) q^{52} -31068.4i q^{53} +4255.23i q^{55} +(3186.09 + 273.686i) q^{56} +(-11789.0 - 10480.2i) q^{58} +(-10900.3 + 18879.9i) q^{59} +(-17894.5 - 30994.2i) q^{61} +(-3664.53 + 17794.5i) q^{62} +(11304.4 + 30756.4i) q^{64} +(-1086.83 + 627.480i) q^{65} +(-18015.5 - 10401.2i) q^{67} +(30802.3 + 41283.9i) q^{68} +(467.617 + 1408.71i) q^{70} -42271.8 q^{71} -72975.6 q^{73} +(-8241.02 - 24826.3i) q^{74} +(-31938.2 - 42806.4i) q^{76} +(4382.97 + 2530.51i) q^{77} +(-76047.9 + 43906.3i) q^{79} +(-11041.0 + 10460.6i) q^{80} +(12925.1 - 62762.9i) q^{82} +(12234.8 + 21191.3i) q^{83} +(-11954.1 + 20705.0i) q^{85} +(60515.1 + 53796.9i) q^{86} +(-4438.45 + 51669.8i) q^{88} -119158. i q^{89} +1492.60i q^{91} +(17424.6 + 147731. i) q^{92} +(-12745.9 + 14337.6i) q^{94} +(12394.9 - 21468.6i) q^{95} +(39575.0 + 68545.9i) q^{97} +(-91391.6 - 18820.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78216 + 5.36879i 0.315044 + 0.949077i
\(3\) 0 0
\(4\) −25.6478 + 19.1360i −0.801495 + 0.598001i
\(5\) −12.8631 7.42651i −0.230102 0.132849i 0.380517 0.924774i \(-0.375746\pi\)
−0.610619 + 0.791924i \(0.709079\pi\)
\(6\) 0 0
\(7\) −15.2989 + 8.83282i −0.118009 + 0.0681325i −0.557843 0.829947i \(-0.688371\pi\)
0.439834 + 0.898079i \(0.355037\pi\)
\(8\) −148.446 103.595i −0.820055 0.572284i
\(9\) 0 0
\(10\) 16.9473 82.2944i 0.0535922 0.260238i
\(11\) −143.245 248.107i −0.356941 0.618240i 0.630507 0.776184i \(-0.282847\pi\)
−0.987448 + 0.157943i \(0.949514\pi\)
\(12\) 0 0
\(13\) 42.2460 73.1722i 0.0693309 0.120085i −0.829276 0.558839i \(-0.811247\pi\)
0.898607 + 0.438755i \(0.144580\pi\)
\(14\) −74.6866 66.3951i −0.101841 0.0905349i
\(15\) 0 0
\(16\) 291.624 981.596i 0.284789 0.958590i
\(17\) 1609.65i 1.35085i −0.737427 0.675427i \(-0.763960\pi\)
0.737427 0.675427i \(-0.236040\pi\)
\(18\) 0 0
\(19\) 1669.01i 1.06065i 0.847793 + 0.530327i \(0.177931\pi\)
−0.847793 + 0.530327i \(0.822069\pi\)
\(20\) 472.025 55.6747i 0.263870 0.0311231i
\(21\) 0 0
\(22\) 1076.75 1211.22i 0.474306 0.533537i
\(23\) 2324.29 4025.79i 0.916159 1.58683i 0.110963 0.993825i \(-0.464606\pi\)
0.805196 0.593009i \(-0.202060\pi\)
\(24\) 0 0
\(25\) −1452.19 2515.27i −0.464702 0.804888i
\(26\) 468.135 + 96.4056i 0.135812 + 0.0279685i
\(27\) 0 0
\(28\) 223.358 519.303i 0.0538403 0.125177i
\(29\) −2414.87 + 1394.23i −0.533211 + 0.307850i −0.742323 0.670042i \(-0.766276\pi\)
0.209112 + 0.977892i \(0.432943\pi\)
\(30\) 0 0
\(31\) 2781.39 + 1605.84i 0.519825 + 0.300121i 0.736863 0.676042i \(-0.236306\pi\)
−0.217038 + 0.976163i \(0.569640\pi\)
\(32\) 5789.71 183.691i 0.999497 0.0317113i
\(33\) 0 0
\(34\) 8641.85 2868.64i 1.28206 0.425578i
\(35\) 262.388 0.0362055
\(36\) 0 0
\(37\) −4624.19 −0.555304 −0.277652 0.960682i \(-0.589556\pi\)
−0.277652 + 0.960682i \(0.589556\pi\)
\(38\) −8960.54 + 2974.43i −1.00664 + 0.334152i
\(39\) 0 0
\(40\) 1140.13 + 2434.98i 0.112669 + 0.240628i
\(41\) −9810.20 5663.92i −0.911420 0.526208i −0.0305320 0.999534i \(-0.509720\pi\)
−0.880888 + 0.473325i \(0.843053\pi\)
\(42\) 0 0
\(43\) 12396.0 7156.83i 1.02237 0.590268i 0.107584 0.994196i \(-0.465689\pi\)
0.914791 + 0.403928i \(0.132355\pi\)
\(44\) 8421.70 + 3622.27i 0.655795 + 0.282065i
\(45\) 0 0
\(46\) 25755.9 + 5304.05i 1.79466 + 0.369584i
\(47\) 1695.63 + 2936.92i 0.111966 + 0.193931i 0.916563 0.399890i \(-0.130952\pi\)
−0.804597 + 0.593822i \(0.797618\pi\)
\(48\) 0 0
\(49\) −8247.46 + 14285.0i −0.490716 + 0.849945i
\(50\) 10915.9 12279.1i 0.617499 0.694613i
\(51\) 0 0
\(52\) 316.708 + 2685.13i 0.0162424 + 0.137707i
\(53\) 31068.4i 1.51925i −0.650360 0.759626i \(-0.725382\pi\)
0.650360 0.759626i \(-0.274618\pi\)
\(54\) 0 0
\(55\) 4255.23i 0.189678i
\(56\) 3186.09 + 273.686i 0.135765 + 0.0116622i
\(57\) 0 0
\(58\) −11789.0 10480.2i −0.460158 0.409072i
\(59\) −10900.3 + 18879.9i −0.407671 + 0.706107i −0.994628 0.103511i \(-0.966992\pi\)
0.586957 + 0.809618i \(0.300326\pi\)
\(60\) 0 0
\(61\) −17894.5 30994.2i −0.615736 1.06649i −0.990255 0.139267i \(-0.955525\pi\)
0.374519 0.927219i \(-0.377808\pi\)
\(62\) −3664.53 + 17794.5i −0.121071 + 0.587906i
\(63\) 0 0
\(64\) 11304.4 + 30756.4i 0.344982 + 0.938609i
\(65\) −1086.83 + 627.480i −0.0319064 + 0.0184211i
\(66\) 0 0
\(67\) −18015.5 10401.2i −0.490296 0.283072i 0.234401 0.972140i \(-0.424687\pi\)
−0.724697 + 0.689068i \(0.758020\pi\)
\(68\) 30802.3 + 41283.9i 0.807812 + 1.08270i
\(69\) 0 0
\(70\) 467.617 + 1408.71i 0.0114063 + 0.0343618i
\(71\) −42271.8 −0.995187 −0.497593 0.867410i \(-0.665783\pi\)
−0.497593 + 0.867410i \(0.665783\pi\)
\(72\) 0 0
\(73\) −72975.6 −1.60277 −0.801384 0.598150i \(-0.795903\pi\)
−0.801384 + 0.598150i \(0.795903\pi\)
\(74\) −8241.02 24826.3i −0.174945 0.527027i
\(75\) 0 0
\(76\) −31938.2 42806.4i −0.634273 0.850109i
\(77\) 4382.97 + 2530.51i 0.0842445 + 0.0486386i
\(78\) 0 0
\(79\) −76047.9 + 43906.3i −1.37094 + 0.791514i −0.991047 0.133515i \(-0.957374\pi\)
−0.379896 + 0.925029i \(0.624040\pi\)
\(80\) −11041.0 + 10460.6i −0.192879 + 0.182739i
\(81\) 0 0
\(82\) 12925.1 62762.9i 0.212275 1.03079i
\(83\) 12234.8 + 21191.3i 0.194940 + 0.337646i 0.946881 0.321585i \(-0.104215\pi\)
−0.751941 + 0.659231i \(0.770882\pi\)
\(84\) 0 0
\(85\) −11954.1 + 20705.0i −0.179460 + 0.310834i
\(86\) 60515.1 + 53796.9i 0.882302 + 0.784352i
\(87\) 0 0
\(88\) −4438.45 + 51669.8i −0.0610976 + 0.711263i
\(89\) 119158.i 1.59459i −0.603588 0.797296i \(-0.706263\pi\)
0.603588 0.797296i \(-0.293737\pi\)
\(90\) 0 0
\(91\) 1492.60i 0.0188948i
\(92\) 17424.6 + 147731.i 0.214632 + 1.81970i
\(93\) 0 0
\(94\) −12745.9 + 14337.6i −0.148782 + 0.167362i
\(95\) 12394.9 21468.6i 0.140907 0.244059i
\(96\) 0 0
\(97\) 39575.0 + 68545.9i 0.427062 + 0.739694i 0.996611 0.0822641i \(-0.0262151\pi\)
−0.569548 + 0.821958i \(0.692882\pi\)
\(98\) −91391.6 18820.8i −0.961260 0.197958i
\(99\) 0 0
\(100\) 85378.0 + 36722.1i 0.853780 + 0.367221i
\(101\) −116647. + 67346.1i −1.13781 + 0.656915i −0.945887 0.324495i \(-0.894806\pi\)
−0.191923 + 0.981410i \(0.561472\pi\)
\(102\) 0 0
\(103\) 87239.5 + 50367.8i 0.810252 + 0.467799i 0.847044 0.531524i \(-0.178380\pi\)
−0.0367911 + 0.999323i \(0.511714\pi\)
\(104\) −13851.5 + 6485.66i −0.125578 + 0.0587991i
\(105\) 0 0
\(106\) 166800. 55368.8i 1.44189 0.478631i
\(107\) 14924.9 0.126024 0.0630118 0.998013i \(-0.479929\pi\)
0.0630118 + 0.998013i \(0.479929\pi\)
\(108\) 0 0
\(109\) 34005.6 0.274148 0.137074 0.990561i \(-0.456230\pi\)
0.137074 + 0.990561i \(0.456230\pi\)
\(110\) −22845.4 + 7583.48i −0.180019 + 0.0597568i
\(111\) 0 0
\(112\) 4208.75 + 17593.2i 0.0317035 + 0.132526i
\(113\) 89706.6 + 51792.2i 0.660889 + 0.381564i 0.792616 0.609722i \(-0.208719\pi\)
−0.131727 + 0.991286i \(0.542052\pi\)
\(114\) 0 0
\(115\) −59795.1 + 34522.7i −0.421620 + 0.243422i
\(116\) 35256.3 81970.0i 0.243272 0.565601i
\(117\) 0 0
\(118\) −120789. 24874.6i −0.798584 0.164457i
\(119\) 14217.7 + 24625.8i 0.0920370 + 0.159413i
\(120\) 0 0
\(121\) 39487.4 68394.3i 0.245186 0.424674i
\(122\) 134510. 151308.i 0.818194 0.920371i
\(123\) 0 0
\(124\) −102066. + 12038.6i −0.596110 + 0.0703105i
\(125\) 89554.6i 0.512640i
\(126\) 0 0
\(127\) 323553.i 1.78007i −0.455894 0.890034i \(-0.650680\pi\)
0.455894 0.890034i \(-0.349320\pi\)
\(128\) −144978. + 115503.i −0.782129 + 0.623117i
\(129\) 0 0
\(130\) −5305.71 4716.68i −0.0275350 0.0244781i
\(131\) 70996.7 122970.i 0.361460 0.626066i −0.626742 0.779227i \(-0.715612\pi\)
0.988201 + 0.153161i \(0.0489452\pi\)
\(132\) 0 0
\(133\) −14742.0 25534.0i −0.0722650 0.125167i
\(134\) 23735.7 115258.i 0.114193 0.554509i
\(135\) 0 0
\(136\) −166750. + 238945.i −0.773072 + 1.10777i
\(137\) 51712.9 29856.5i 0.235395 0.135906i −0.377663 0.925943i \(-0.623272\pi\)
0.613059 + 0.790037i \(0.289939\pi\)
\(138\) 0 0
\(139\) 310879. + 179486.i 1.36475 + 0.787941i 0.990252 0.139286i \(-0.0444807\pi\)
0.374501 + 0.927227i \(0.377814\pi\)
\(140\) −6729.69 + 5021.07i −0.0290185 + 0.0216509i
\(141\) 0 0
\(142\) −75334.9 226948.i −0.313527 0.944509i
\(143\) −24206.0 −0.0989882
\(144\) 0 0
\(145\) 41417.0 0.163591
\(146\) −130054. 391791.i −0.504942 1.52115i
\(147\) 0 0
\(148\) 118600. 88488.6i 0.445074 0.332073i
\(149\) 175221. + 101164.i 0.646576 + 0.373301i 0.787143 0.616770i \(-0.211559\pi\)
−0.140567 + 0.990071i \(0.544893\pi\)
\(150\) 0 0
\(151\) −15615.5 + 9015.60i −0.0557331 + 0.0321775i −0.527608 0.849488i \(-0.676911\pi\)
0.471875 + 0.881666i \(0.343578\pi\)
\(152\) 172900. 247757.i 0.606996 0.869795i
\(153\) 0 0
\(154\) −5774.64 + 28041.0i −0.0196211 + 0.0952779i
\(155\) −23851.5 41312.0i −0.0797419 0.138117i
\(156\) 0 0
\(157\) 238209. 412590.i 0.771274 1.33589i −0.165590 0.986195i \(-0.552953\pi\)
0.936865 0.349692i \(-0.113714\pi\)
\(158\) −371253. 330037.i −1.18312 1.05177i
\(159\) 0 0
\(160\) −75837.7 40634.5i −0.234199 0.125486i
\(161\) 82120.2i 0.249681i
\(162\) 0 0
\(163\) 243580.i 0.718080i −0.933322 0.359040i \(-0.883104\pi\)
0.933322 0.359040i \(-0.116896\pi\)
\(164\) 359996. 42461.1i 1.04517 0.123277i
\(165\) 0 0
\(166\) −91967.2 + 103452.i −0.259037 + 0.291386i
\(167\) −21086.7 + 36523.3i −0.0585083 + 0.101339i −0.893796 0.448474i \(-0.851968\pi\)
0.835288 + 0.549813i \(0.185301\pi\)
\(168\) 0 0
\(169\) 182077. + 315367.i 0.490386 + 0.849374i
\(170\) −132465. 27279.2i −0.351543 0.0723952i
\(171\) 0 0
\(172\) −180977. + 420767.i −0.466447 + 1.08448i
\(173\) −94858.3 + 54766.5i −0.240968 + 0.139123i −0.615622 0.788042i \(-0.711095\pi\)
0.374653 + 0.927165i \(0.377762\pi\)
\(174\) 0 0
\(175\) 44433.9 + 25653.9i 0.109678 + 0.0633226i
\(176\) −285314. + 68254.6i −0.694292 + 0.166093i
\(177\) 0 0
\(178\) 639737. 212359.i 1.51339 0.502366i
\(179\) 264309. 0.616566 0.308283 0.951295i \(-0.400246\pi\)
0.308283 + 0.951295i \(0.400246\pi\)
\(180\) 0 0
\(181\) 508179. 1.15298 0.576488 0.817105i \(-0.304423\pi\)
0.576488 + 0.817105i \(0.304423\pi\)
\(182\) −8013.48 + 2660.05i −0.0179326 + 0.00595267i
\(183\) 0 0
\(184\) −762081. + 356828.i −1.65942 + 0.776988i
\(185\) 59481.3 + 34341.6i 0.127777 + 0.0737718i
\(186\) 0 0
\(187\) −399364. + 230573.i −0.835152 + 0.482175i
\(188\) −99690.5 42878.0i −0.205712 0.0884790i
\(189\) 0 0
\(190\) 137350. + 28285.2i 0.276022 + 0.0568428i
\(191\) −52294.2 90576.3i −0.103722 0.179652i 0.809493 0.587129i \(-0.199742\pi\)
−0.913215 + 0.407477i \(0.866409\pi\)
\(192\) 0 0
\(193\) −271784. + 470744.i −0.525207 + 0.909685i 0.474362 + 0.880330i \(0.342679\pi\)
−0.999569 + 0.0293554i \(0.990655\pi\)
\(194\) −297480. + 334629.i −0.567483 + 0.638351i
\(195\) 0 0
\(196\) −61829.2 524204.i −0.114962 0.974675i
\(197\) 922105.i 1.69284i 0.532519 + 0.846418i \(0.321245\pi\)
−0.532519 + 0.846418i \(0.678755\pi\)
\(198\) 0 0
\(199\) 93172.6i 0.166784i −0.996517 0.0833922i \(-0.973425\pi\)
0.996517 0.0833922i \(-0.0265754\pi\)
\(200\) −44996.3 + 523821.i −0.0795430 + 0.925994i
\(201\) 0 0
\(202\) −569450. 506232.i −0.981923 0.872913i
\(203\) 24629.9 42660.3i 0.0419491 0.0726580i
\(204\) 0 0
\(205\) 84126.4 + 145711.i 0.139813 + 0.242163i
\(206\) −114940. + 558134.i −0.188713 + 0.916369i
\(207\) 0 0
\(208\) −59505.6 62807.2i −0.0953673 0.100659i
\(209\) 414092. 239076.i 0.655739 0.378591i
\(210\) 0 0
\(211\) 4637.49 + 2677.46i 0.00717096 + 0.00414015i 0.503581 0.863948i \(-0.332015\pi\)
−0.496410 + 0.868088i \(0.665349\pi\)
\(212\) 594527. + 796839.i 0.908515 + 1.21767i
\(213\) 0 0
\(214\) 26598.5 + 80128.7i 0.0397029 + 0.119606i
\(215\) −212601. −0.313667
\(216\) 0 0
\(217\) −56736.2 −0.0817921
\(218\) 60603.4 + 182569.i 0.0863685 + 0.260187i
\(219\) 0 0
\(220\) −81428.3 109137.i −0.113428 0.152026i
\(221\) −117781. 68001.1i −0.162217 0.0936559i
\(222\) 0 0
\(223\) −714552. + 412547.i −0.962214 + 0.555535i −0.896854 0.442327i \(-0.854153\pi\)
−0.0653606 + 0.997862i \(0.520820\pi\)
\(224\) −86953.6 + 53949.7i −0.115789 + 0.0718405i
\(225\) 0 0
\(226\) −118190. + 573918.i −0.153925 + 0.747444i
\(227\) 222824. + 385943.i 0.287011 + 0.497117i 0.973095 0.230405i \(-0.0740051\pi\)
−0.686084 + 0.727522i \(0.740672\pi\)
\(228\) 0 0
\(229\) 121497. 210439.i 0.153101 0.265178i −0.779265 0.626694i \(-0.784407\pi\)
0.932366 + 0.361516i \(0.117741\pi\)
\(230\) −291910. 259503.i −0.363855 0.323461i
\(231\) 0 0
\(232\) 502912. + 43200.2i 0.613440 + 0.0526946i
\(233\) 483894.i 0.583930i −0.956429 0.291965i \(-0.905691\pi\)
0.956429 0.291965i \(-0.0943091\pi\)
\(234\) 0 0
\(235\) 50370.6i 0.0594987i
\(236\) −81717.2 692819.i −0.0955066 0.809729i
\(237\) 0 0
\(238\) −106873. + 120219.i −0.122299 + 0.137572i
\(239\) −374928. + 649395.i −0.424574 + 0.735384i −0.996381 0.0850045i \(-0.972910\pi\)
0.571806 + 0.820389i \(0.306243\pi\)
\(240\) 0 0
\(241\) −214184. 370977.i −0.237544 0.411438i 0.722465 0.691408i \(-0.243009\pi\)
−0.960009 + 0.279969i \(0.909676\pi\)
\(242\) 437567. + 90110.6i 0.480293 + 0.0989094i
\(243\) 0 0
\(244\) 1.05206e6 + 452504.i 1.13127 + 0.486572i
\(245\) 212176. 122500.i 0.225829 0.130383i
\(246\) 0 0
\(247\) 122125. + 70508.8i 0.127368 + 0.0735361i
\(248\) −246530. 526516.i −0.254531 0.543604i
\(249\) 0 0
\(250\) −480800. + 159600.i −0.486535 + 0.161504i
\(251\) −168039. −0.168355 −0.0841773 0.996451i \(-0.526826\pi\)
−0.0841773 + 0.996451i \(0.526826\pi\)
\(252\) 0 0
\(253\) −1.33177e6 −1.30806
\(254\) 1.73709e6 576623.i 1.68942 0.560799i
\(255\) 0 0
\(256\) −878487. 572513.i −0.837791 0.545991i
\(257\) −1.21515e6 701569.i −1.14762 0.662579i −0.199314 0.979936i \(-0.563871\pi\)
−0.948306 + 0.317357i \(0.897205\pi\)
\(258\) 0 0
\(259\) 70744.9 40844.6i 0.0655309 0.0378343i
\(260\) 15867.3 36891.1i 0.0145569 0.0338445i
\(261\) 0 0
\(262\) 786727. + 162015.i 0.708061 + 0.145815i
\(263\) −465252. 805840.i −0.414762 0.718388i 0.580642 0.814159i \(-0.302802\pi\)
−0.995403 + 0.0957708i \(0.969468\pi\)
\(264\) 0 0
\(265\) −230730. + 399636.i −0.201832 + 0.349583i
\(266\) 110814. 124652.i 0.0960263 0.108018i
\(267\) 0 0
\(268\) 661096. 77975.5i 0.562247 0.0663164i
\(269\) 1.02733e6i 0.865621i −0.901485 0.432810i \(-0.857522\pi\)
0.901485 0.432810i \(-0.142478\pi\)
\(270\) 0 0
\(271\) 1.66981e6i 1.38116i −0.723255 0.690581i \(-0.757355\pi\)
0.723255 0.690581i \(-0.242645\pi\)
\(272\) −1.58002e6 469411.i −1.29491 0.384708i
\(273\) 0 0
\(274\) 252454. + 224427.i 0.203145 + 0.180592i
\(275\) −416038. + 720599.i −0.331743 + 0.574595i
\(276\) 0 0
\(277\) −531248. 920149.i −0.416004 0.720541i 0.579529 0.814952i \(-0.303237\pi\)
−0.995533 + 0.0944109i \(0.969903\pi\)
\(278\) −409588. + 1.98892e6i −0.317860 + 1.54349i
\(279\) 0 0
\(280\) −38950.4 27182.0i −0.0296905 0.0207198i
\(281\) 728876. 420817.i 0.550666 0.317927i −0.198725 0.980055i \(-0.563680\pi\)
0.749390 + 0.662128i \(0.230347\pi\)
\(282\) 0 0
\(283\) 1.59876e6 + 923047.i 1.18664 + 0.685106i 0.957541 0.288298i \(-0.0930893\pi\)
0.229097 + 0.973404i \(0.426423\pi\)
\(284\) 1.08418e6 808914.i 0.797637 0.595123i
\(285\) 0 0
\(286\) −43138.9 129957.i −0.0311856 0.0939475i
\(287\) 200114. 0.143408
\(288\) 0 0
\(289\) −1.17110e6 −0.824804
\(290\) 73811.5 + 222359.i 0.0515381 + 0.155260i
\(291\) 0 0
\(292\) 1.87167e6 1.39647e6i 1.28461 0.958458i
\(293\) −1.40490e6 811121.i −0.956043 0.551972i −0.0610899 0.998132i \(-0.519458\pi\)
−0.894953 + 0.446161i \(0.852791\pi\)
\(294\) 0 0
\(295\) 280424. 161903.i 0.187612 0.108318i
\(296\) 686441. + 479040.i 0.455380 + 0.317792i
\(297\) 0 0
\(298\) −230856. + 1.12101e6i −0.150592 + 0.731256i
\(299\) −196384. 340147.i −0.127036 0.220033i
\(300\) 0 0
\(301\) −126430. + 218983.i −0.0804329 + 0.139314i
\(302\) −76232.1 67769.1i −0.0480973 0.0427577i
\(303\) 0 0
\(304\) 1.63829e6 + 486722.i 1.01673 + 0.302062i
\(305\) 531574.i 0.327201i
\(306\) 0 0
\(307\) 1.18284e6i 0.716275i 0.933669 + 0.358137i \(0.116588\pi\)
−0.933669 + 0.358137i \(0.883412\pi\)
\(308\) −160838. + 18970.6i −0.0966075 + 0.0113947i
\(309\) 0 0
\(310\) 179288. 201678.i 0.105962 0.119194i
\(311\) 685107. 1.18664e6i 0.401659 0.695693i −0.592268 0.805741i \(-0.701767\pi\)
0.993926 + 0.110048i \(0.0351005\pi\)
\(312\) 0 0
\(313\) 130578. + 226168.i 0.0753372 + 0.130488i 0.901233 0.433335i \(-0.142663\pi\)
−0.825896 + 0.563823i \(0.809330\pi\)
\(314\) 2.63963e6 + 543594.i 1.51084 + 0.311136i
\(315\) 0 0
\(316\) 1.11027e6 2.58136e6i 0.625478 1.45422i
\(317\) −529678. + 305810.i −0.296049 + 0.170924i −0.640667 0.767819i \(-0.721342\pi\)
0.344618 + 0.938743i \(0.388009\pi\)
\(318\) 0 0
\(319\) 691835. + 399431.i 0.380650 + 0.219768i
\(320\) 83003.4 479574.i 0.0453128 0.261806i
\(321\) 0 0
\(322\) −440886. + 146351.i −0.236966 + 0.0786603i
\(323\) 2.68651e6 1.43279
\(324\) 0 0
\(325\) −245397. −0.128873
\(326\) 1.30773e6 434098.i 0.681513 0.226226i
\(327\) 0 0
\(328\) 869533. + 1.85707e6i 0.446274 + 0.953111i
\(329\) −51882.7 29954.5i −0.0264261 0.0152571i
\(330\) 0 0
\(331\) −853212. + 492602.i −0.428043 + 0.247131i −0.698512 0.715598i \(-0.746154\pi\)
0.270470 + 0.962728i \(0.412821\pi\)
\(332\) −719312. 309385.i −0.358156 0.154047i
\(333\) 0 0
\(334\) −233666. 48120.0i −0.114612 0.0236026i
\(335\) 154490. + 267584.i 0.0752120 + 0.130271i
\(336\) 0 0
\(337\) 1.10946e6 1.92164e6i 0.532153 0.921716i −0.467142 0.884182i \(-0.654716\pi\)
0.999295 0.0375341i \(-0.0119503\pi\)
\(338\) −1.36865e6 + 1.53957e6i −0.651629 + 0.733005i
\(339\) 0 0
\(340\) −89616.6 759792.i −0.0420428 0.356449i
\(341\) 920109.i 0.428503i
\(342\) 0 0
\(343\) 588300.i 0.270000i
\(344\) −2.58154e6 221755.i −1.17620 0.101036i
\(345\) 0 0
\(346\) −463082. 411672.i −0.207954 0.184868i
\(347\) 1.28567e6 2.22684e6i 0.573199 0.992810i −0.423036 0.906113i \(-0.639036\pi\)
0.996235 0.0866969i \(-0.0276312\pi\)
\(348\) 0 0
\(349\) 935689. + 1.62066e6i 0.411214 + 0.712243i 0.995023 0.0996478i \(-0.0317716\pi\)
−0.583809 + 0.811891i \(0.698438\pi\)
\(350\) −58542.5 + 284276.i −0.0255447 + 0.124042i
\(351\) 0 0
\(352\) −874919. 1.41015e6i −0.376367 0.606610i
\(353\) −1.19697e6 + 691073.i −0.511267 + 0.295180i −0.733354 0.679847i \(-0.762046\pi\)
0.222087 + 0.975027i \(0.428713\pi\)
\(354\) 0 0
\(355\) 543746. + 313932.i 0.228994 + 0.132210i
\(356\) 2.28022e6 + 3.05616e6i 0.953569 + 1.27806i
\(357\) 0 0
\(358\) 471040. + 1.41902e6i 0.194245 + 0.585169i
\(359\) −4.58930e6 −1.87936 −0.939680 0.342054i \(-0.888877\pi\)
−0.939680 + 0.342054i \(0.888877\pi\)
\(360\) 0 0
\(361\) −309482. −0.124988
\(362\) 905655. + 2.72831e6i 0.363238 + 1.09426i
\(363\) 0 0
\(364\) −28562.6 38282.1i −0.0112991 0.0151441i
\(365\) 938692. + 541954.i 0.368800 + 0.212927i
\(366\) 0 0
\(367\) −318059. + 183631.i −0.123266 + 0.0711675i −0.560365 0.828246i \(-0.689339\pi\)
0.437099 + 0.899413i \(0.356006\pi\)
\(368\) −3.27388e6 3.45553e6i −1.26021 1.33013i
\(369\) 0 0
\(370\) −78367.7 + 380545.i −0.0297600 + 0.144511i
\(371\) 274422. + 475313.i 0.103510 + 0.179285i
\(372\) 0 0
\(373\) −1.45750e6 + 2.52447e6i −0.542421 + 0.939501i 0.456343 + 0.889804i \(0.349159\pi\)
−0.998764 + 0.0496972i \(0.984174\pi\)
\(374\) −1.94963e6 1.73319e6i −0.720731 0.640717i
\(375\) 0 0
\(376\) 52539.3 611633.i 0.0191653 0.223111i
\(377\) 235602.i 0.0853740i
\(378\) 0 0
\(379\) 1.95071e6i 0.697579i 0.937201 + 0.348790i \(0.113407\pi\)
−0.937201 + 0.348790i \(0.886593\pi\)
\(380\) 92921.5 + 787812.i 0.0330109 + 0.279875i
\(381\) 0 0
\(382\) 393089. 442178.i 0.137826 0.155038i
\(383\) −1.91266e6 + 3.31282e6i −0.666254 + 1.15399i 0.312690 + 0.949855i \(0.398770\pi\)
−0.978944 + 0.204130i \(0.934563\pi\)
\(384\) 0 0
\(385\) −37585.7 65100.3i −0.0129232 0.0223837i
\(386\) −3.01169e6 620213.i −1.02882 0.211872i
\(387\) 0 0
\(388\) −2.32671e6 1.00075e6i −0.784626 0.337477i
\(389\) 1.38080e6 797204.i 0.462654 0.267113i −0.250506 0.968115i \(-0.580597\pi\)
0.713159 + 0.701002i \(0.247264\pi\)
\(390\) 0 0
\(391\) −6.48010e6 3.74128e6i −2.14358 1.23760i
\(392\) 2.70415e6 1.26616e6i 0.888824 0.416173i
\(393\) 0 0
\(394\) −4.95059e6 + 1.64333e6i −1.60663 + 0.533317i
\(395\) 1.30428e6 0.420609
\(396\) 0 0
\(397\) 4.04020e6 1.28655 0.643275 0.765635i \(-0.277575\pi\)
0.643275 + 0.765635i \(0.277575\pi\)
\(398\) 500224. 166048.i 0.158291 0.0525444i
\(399\) 0 0
\(400\) −2.89248e6 + 691955.i −0.903899 + 0.216236i
\(401\) 4.84780e6 + 2.79888e6i 1.50551 + 0.869207i 0.999980 + 0.00639934i \(0.00203699\pi\)
0.505532 + 0.862808i \(0.331296\pi\)
\(402\) 0 0
\(403\) 235005. 135680.i 0.0720799 0.0416154i
\(404\) 1.70300e6 3.95944e6i 0.519113 1.20693i
\(405\) 0 0
\(406\) 272928. + 56205.7i 0.0821739 + 0.0169225i
\(407\) 662390. + 1.14729e6i 0.198211 + 0.343311i
\(408\) 0 0
\(409\) 1.24641e6 2.15885e6i 0.368429 0.638138i −0.620891 0.783897i \(-0.713229\pi\)
0.989320 + 0.145759i \(0.0465625\pi\)
\(410\) −632366. + 711337.i −0.185784 + 0.208985i
\(411\) 0 0
\(412\) −3.20135e6 + 377595.i −0.929158 + 0.109593i
\(413\) 385123.i 0.111103i
\(414\) 0 0
\(415\) 363447.i 0.103591i
\(416\) 231151. 431406.i 0.0654880 0.122223i
\(417\) 0 0
\(418\) 2.02153e6 + 1.79710e6i 0.565899 + 0.503074i
\(419\) 476950. 826102.i 0.132720 0.229879i −0.792004 0.610516i \(-0.790962\pi\)
0.924724 + 0.380637i \(0.124295\pi\)
\(420\) 0 0
\(421\) −1.44880e6 2.50940e6i −0.398386 0.690025i 0.595141 0.803621i \(-0.297096\pi\)
−0.993527 + 0.113597i \(0.963763\pi\)
\(422\) −6109.98 + 29669.4i −0.00167016 + 0.00811012i
\(423\) 0 0
\(424\) −3.21852e6 + 4.61198e6i −0.869444 + 1.24587i
\(425\) −4.04870e6 + 2.33752e6i −1.08728 + 0.627744i
\(426\) 0 0
\(427\) 547532. + 316118.i 0.145325 + 0.0839033i
\(428\) −382791. + 285604.i −0.101007 + 0.0753623i
\(429\) 0 0
\(430\) −378888. 1.14141e6i −0.0988188 0.297694i
\(431\) −3.72242e6 −0.965234 −0.482617 0.875831i \(-0.660314\pi\)
−0.482617 + 0.875831i \(0.660314\pi\)
\(432\) 0 0
\(433\) 4.74890e6 1.21723 0.608616 0.793465i \(-0.291725\pi\)
0.608616 + 0.793465i \(0.291725\pi\)
\(434\) −101113. 304605.i −0.0257681 0.0776270i
\(435\) 0 0
\(436\) −872172. + 650734.i −0.219728 + 0.163941i
\(437\) 6.71907e6 + 3.87925e6i 1.68308 + 0.971728i
\(438\) 0 0
\(439\) 6.29205e6 3.63272e6i 1.55823 0.899644i 0.560802 0.827950i \(-0.310493\pi\)
0.997427 0.0716934i \(-0.0228403\pi\)
\(440\) 440819. 631671.i 0.108550 0.155546i
\(441\) 0 0
\(442\) 155179. 753532.i 0.0377813 0.183462i
\(443\) 2.83250e6 + 4.90603e6i 0.685741 + 1.18774i 0.973203 + 0.229946i \(0.0738549\pi\)
−0.287463 + 0.957792i \(0.592812\pi\)
\(444\) 0 0
\(445\) −884931. + 1.53275e6i −0.211841 + 0.366919i
\(446\) −3.48832e6 3.10106e6i −0.830385 0.738198i
\(447\) 0 0
\(448\) −444610. 370689.i −0.104661 0.0872599i
\(449\) 4.08820e6i 0.957011i 0.878085 + 0.478505i \(0.158821\pi\)
−0.878085 + 0.478505i \(0.841179\pi\)
\(450\) 0 0
\(451\) 3.24531e6i 0.751302i
\(452\) −3.29188e6 + 388273.i −0.757875 + 0.0893905i
\(453\) 0 0
\(454\) −1.67494e6 + 1.88411e6i −0.381382 + 0.429009i
\(455\) 11084.8 19199.5i 0.00251016 0.00434772i
\(456\) 0 0
\(457\) 2.07648e6 + 3.59658e6i 0.465091 + 0.805562i 0.999206 0.0398504i \(-0.0126881\pi\)
−0.534114 + 0.845412i \(0.679355\pi\)
\(458\) 1.34633e6 + 277257.i 0.299908 + 0.0617617i
\(459\) 0 0
\(460\) 872987. 2.02968e6i 0.192359 0.447231i
\(461\) −293141. + 169245.i −0.0642427 + 0.0370905i −0.531777 0.846884i \(-0.678476\pi\)
0.467535 + 0.883975i \(0.345142\pi\)
\(462\) 0 0
\(463\) −6.16958e6 3.56201e6i −1.33753 0.772223i −0.351089 0.936342i \(-0.614189\pi\)
−0.986441 + 0.164119i \(0.947522\pi\)
\(464\) 664335. + 2.77702e6i 0.143249 + 0.598803i
\(465\) 0 0
\(466\) 2.59793e6 862375.i 0.554195 0.183963i
\(467\) 3.96727e6 0.841782 0.420891 0.907111i \(-0.361717\pi\)
0.420891 + 0.907111i \(0.361717\pi\)
\(468\) 0 0
\(469\) 367489. 0.0771457
\(470\) 270429. 89768.2i 0.0564688 0.0187447i
\(471\) 0 0
\(472\) 3.57397e6 1.67343e6i 0.738407 0.345743i
\(473\) −3.55132e6 2.05035e6i −0.729855 0.421382i
\(474\) 0 0
\(475\) 4.19801e6 2.42372e6i 0.853707 0.492888i
\(476\) −835894. 359528.i −0.169096 0.0727303i
\(477\) 0 0
\(478\) −4.15465e6 855589.i −0.831696 0.171276i
\(479\) −3.84509e6 6.65989e6i −0.765716 1.32626i −0.939867 0.341540i \(-0.889052\pi\)
0.174151 0.984719i \(1.55572\pi\)
\(480\) 0 0
\(481\) −195353. + 338362.i −0.0384997 + 0.0666835i
\(482\) 1.60999e6 1.81105e6i 0.315650 0.355069i
\(483\) 0 0
\(484\) 296028. + 2.50980e6i 0.0574406 + 0.486996i
\(485\) 1.17562e6i 0.226940i
\(486\) 0 0
\(487\) 1.17689e6i 0.224860i 0.993660 + 0.112430i \(0.0358634\pi\)
−0.993660 + 0.112430i \(0.964137\pi\)
\(488\) −554462. + 6.45472e6i −0.105395 + 1.22695i
\(489\) 0 0
\(490\) 1.03581e6 + 920814.i 0.194889 + 0.173253i
\(491\) 730305. 1.26493e6i 0.136710 0.236789i −0.789539 0.613700i \(-0.789680\pi\)
0.926249 + 0.376911i \(0.123014\pi\)
\(492\) 0 0
\(493\) 2.24421e6 + 3.88709e6i 0.415859 + 0.720290i
\(494\) −160902. + 781320.i −0.0296649 + 0.144049i
\(495\) 0 0
\(496\) 2.38740e6 2.26190e6i 0.435734 0.412828i
\(497\) 646711. 373379.i 0.117441 0.0678046i
\(498\) 0 0
\(499\) 3.61275e6 + 2.08582e6i 0.649510 + 0.374995i 0.788269 0.615331i \(-0.210978\pi\)
−0.138758 + 0.990326i \(0.544311\pi\)
\(500\) −1.71372e6 2.29688e6i −0.306560 0.410879i
\(501\) 0 0
\(502\) −299471. 902165.i −0.0530390 0.159782i
\(503\) 3.55656e6 0.626773 0.313387 0.949626i \(-0.398536\pi\)
0.313387 + 0.949626i \(0.398536\pi\)
\(504\) 0 0
\(505\) 2.00059e6 0.349083
\(506\) −2.37342e6 7.14999e6i −0.412096 1.24145i
\(507\) 0 0
\(508\) 6.19153e6 + 8.29845e6i 1.06448 + 1.42672i
\(509\) −5.64282e6 3.25788e6i −0.965388 0.557367i −0.0675606 0.997715i \(-0.521522\pi\)
−0.897827 + 0.440348i \(0.854855\pi\)
\(510\) 0 0
\(511\) 1.11645e6 644581.i 0.189141 0.109201i
\(512\) 1.50810e6 5.73672e6i 0.254247 0.967139i
\(513\) 0 0
\(514\) 1.60099e6 7.77421e6i 0.267288 1.29792i
\(515\) −748113. 1.29577e6i −0.124294 0.215283i
\(516\) 0 0
\(517\) 485781. 841397.i 0.0799308 0.138444i
\(518\) 345365. + 307023.i 0.0565527 + 0.0502744i
\(519\) 0 0
\(520\) 226339. + 19442.5i 0.0367071 + 0.00315315i
\(521\) 551264.i 0.0889744i 0.999010 + 0.0444872i \(0.0141654\pi\)
−0.999010 + 0.0444872i \(0.985835\pi\)
\(522\) 0 0
\(523\) 1.10624e7i 1.76846i 0.467053 + 0.884230i \(0.345316\pi\)
−0.467053 + 0.884230i \(0.654684\pi\)
\(524\) 532245. + 4.51251e6i 0.0846805 + 0.717942i
\(525\) 0 0
\(526\) 3.49723e6 3.93397e6i 0.551138 0.619965i
\(527\) 2.58483e6 4.47705e6i 0.405420 0.702208i
\(528\) 0 0
\(529\) −7.58648e6 1.31402e7i −1.17869 2.04156i
\(530\) −2.55676e6 526528.i −0.395367 0.0814201i
\(531\) 0 0
\(532\) 866720. + 372787.i 0.132770 + 0.0571059i
\(533\) −828883. + 478556.i −0.126379 + 0.0729650i
\(534\) 0 0
\(535\) −191980. 110840.i −0.0289983 0.0167422i
\(536\) 1.59681e6 + 3.41032e6i 0.240072 + 0.512724i
\(537\) 0 0
\(538\) 5.51550e6 1.83086e6i 0.821541 0.272708i
\(539\) 4.72562e6 0.700627
\(540\) 0 0
\(541\) −3.00701e6 −0.441715 −0.220858 0.975306i \(-0.570886\pi\)
−0.220858 + 0.975306i \(0.570886\pi\)
\(542\) 8.96488e6 2.97587e6i 1.31083 0.435126i
\(543\) 0 0
\(544\) −295678. 9.31938e6i −0.0428373 1.35017i
\(545\) −437418. 252543.i −0.0630820 0.0364204i
\(546\) 0 0
\(547\) 1.52151e6 878446.i 0.217424 0.125530i −0.387333 0.921940i \(-0.626604\pi\)
0.604757 + 0.796410i \(0.293270\pi\)
\(548\) −754990. + 1.75533e6i −0.107396 + 0.249694i
\(549\) 0 0
\(550\) −4.61019e6 949402.i −0.649849 0.133827i
\(551\) −2.32697e6 4.03044e6i −0.326522 0.565553i
\(552\) 0 0
\(553\) 775633. 1.34344e6i 0.107856 0.186812i
\(554\) 3.99332e6 4.49201e6i 0.552789 0.621822i
\(555\) 0 0
\(556\) −1.14080e7 + 1.34556e6i −1.56503 + 0.184594i
\(557\) 1.04568e7i 1.42811i −0.700090 0.714055i \(-0.746857\pi\)
0.700090 0.714055i \(-0.253143\pi\)
\(558\) 0 0
\(559\) 1.20939e6i 0.163695i
\(560\) 76518.6 257559.i 0.0103109 0.0347062i
\(561\) 0 0
\(562\) 3.55825e6 + 3.16322e6i 0.475221 + 0.422463i
\(563\) 2.79625e6 4.84324e6i 0.371796 0.643969i −0.618046 0.786142i \(-0.712075\pi\)
0.989842 + 0.142173i \(0.0454088\pi\)
\(564\) 0 0
\(565\) −769270. 1.33241e6i −0.101381 0.175597i
\(566\) −2.10640e6 + 1.02284e7i −0.276376 + 1.34205i
\(567\) 0 0
\(568\) 6.27507e6 + 4.37912e6i 0.816108 + 0.569530i
\(569\) 5.00540e6 2.88987e6i 0.648124 0.374195i −0.139613 0.990206i \(-0.544586\pi\)
0.787737 + 0.616012i \(0.211253\pi\)
\(570\) 0 0
\(571\) −2.38689e6 1.37807e6i −0.306367 0.176881i 0.338933 0.940811i \(-0.389934\pi\)
−0.645300 + 0.763930i \(0.723267\pi\)
\(572\) 620833. 463208.i 0.0793386 0.0591951i
\(573\) 0 0
\(574\) 356634. + 1.07437e6i 0.0451796 + 0.136105i
\(575\) −1.35013e7 −1.70296
\(576\) 0 0
\(577\) −9.66103e6 −1.20805 −0.604024 0.796966i \(-0.706437\pi\)
−0.604024 + 0.796966i \(0.706437\pi\)
\(578\) −2.08709e6 6.28741e6i −0.259849 0.782803i
\(579\) 0 0
\(580\) −1.06226e6 + 792557.i −0.131117 + 0.0978274i
\(581\) −374357. 216135.i −0.0460093 0.0265635i
\(582\) 0 0
\(583\) −7.70830e6 + 4.45039e6i −0.939263 + 0.542284i
\(584\) 1.08329e7 + 7.55987e6i 1.31436 + 0.917239i
\(585\) 0 0
\(586\) 1.85098e6 8.98818e6i 0.222668 1.08125i
\(587\) 4.72166e6 + 8.17816e6i 0.565587 + 0.979626i 0.996995 + 0.0774689i \(0.0246838\pi\)
−0.431407 + 0.902157i \(0.641983\pi\)
\(588\) 0 0
\(589\) −2.68015e6 + 4.64215e6i −0.318325 + 0.551355i
\(590\) 1.36898e6 + 1.21700e6i 0.161908 + 0.143933i
\(591\) 0 0
\(592\) −1.34852e6 + 4.53908e6i −0.158144 + 0.532309i
\(593\) 1.32881e6i 0.155177i −0.996985 0.0775883i \(-0.975278\pi\)
0.996985 0.0775883i \(-0.0247220\pi\)
\(594\) 0 0
\(595\) 422352.i 0.0489083i
\(596\) −6.42990e6 + 758399.i −0.741462 + 0.0874545i
\(597\) 0 0
\(598\) 1.47619e6 1.66054e6i 0.168807 0.189887i
\(599\) −8.44536e6 + 1.46278e7i −0.961726 + 1.66576i −0.243560 + 0.969886i \(0.578315\pi\)
−0.718166 + 0.695872i \(0.755018\pi\)
\(600\) 0 0
\(601\) 3.86305e6 + 6.69101e6i 0.436259 + 0.755623i 0.997397 0.0720990i \(-0.0229698\pi\)
−0.561138 + 0.827722i \(0.689636\pi\)
\(602\) −1.40099e6 288514.i −0.157559 0.0324471i
\(603\) 0 0
\(604\) 227980. 530049.i 0.0254276 0.0591186i
\(605\) −1.01586e6 + 586508.i −0.112836 + 0.0651456i
\(606\) 0 0
\(607\) −1.99470e6 1.15164e6i −0.219739 0.126866i 0.386091 0.922461i \(-0.373825\pi\)
−0.605829 + 0.795595i \(0.707159\pi\)
\(608\) 306582. + 9.66305e6i 0.0336347 + 1.06012i
\(609\) 0 0
\(610\) −2.85391e6 + 947348.i −0.310539 + 0.103082i
\(611\) 286535. 0.0310509
\(612\) 0 0
\(613\) −1.18649e7 −1.27531 −0.637653 0.770324i \(-0.720095\pi\)
−0.637653 + 0.770324i \(0.720095\pi\)
\(614\) −6.35042e6 + 2.10800e6i −0.679800 + 0.225658i
\(615\) 0 0
\(616\) −388487. 829695.i −0.0412501 0.0880982i
\(617\) −1.03585e7 5.98047e6i −1.09543 0.632445i −0.160410 0.987050i \(-0.551282\pi\)
−0.935016 + 0.354606i \(0.884615\pi\)
\(618\) 0 0
\(619\) 6.60708e6 3.81460e6i 0.693079 0.400149i −0.111685 0.993744i \(-0.535625\pi\)
0.804764 + 0.593594i \(0.202292\pi\)
\(620\) 1.40229e6 + 603141.i 0.146507 + 0.0630143i
\(621\) 0 0
\(622\) 7.59179e6 + 1.56342e6i 0.786807 + 0.162031i
\(623\) 1.05251e6 + 1.82299e6i 0.108644 + 0.188176i
\(624\) 0 0
\(625\) −3.87303e6 + 6.70828e6i −0.396598 + 0.686928i
\(626\) −981538. + 1.10411e6i −0.100109 + 0.112610i
\(627\) 0 0
\(628\) 1.78579e6 + 1.51404e7i 0.180689 + 1.53193i
\(629\) 7.44330e6i 0.750134i
\(630\) 0 0
\(631\) 1.69017e7i 1.68988i −0.534861 0.844940i \(-0.679636\pi\)
0.534861 0.844940i \(-0.320364\pi\)
\(632\) 1.58374e7 + 1.36044e6i 1.57722 + 0.135483i
\(633\) 0 0
\(634\) −2.58580e6 2.29873e6i −0.255488 0.227125i
\(635\) −2.40287e6 + 4.16190e6i −0.236481 + 0.409597i
\(636\) 0 0
\(637\) 696844. + 1.20697e6i 0.0680436 + 0.117855i
\(638\) −911505. + 4.42617e6i −0.0886558 + 0.430503i
\(639\) 0 0
\(640\) 2.72266e6 409047.i 0.262750 0.0394751i
\(641\) 6.42076e6 3.70703e6i 0.617222 0.356353i −0.158565 0.987349i \(-0.550687\pi\)
0.775787 + 0.630995i \(0.217353\pi\)
\(642\) 0 0
\(643\) 3.01403e6 + 1.74015e6i 0.287488 + 0.165981i 0.636809 0.771022i \(-0.280254\pi\)
−0.349320 + 0.937003i \(0.613587\pi\)
\(644\) −1.57146e6 2.10621e6i −0.149309 0.200118i
\(645\) 0 0
\(646\) 4.78778e6 + 1.44233e7i 0.451391 + 1.35983i
\(647\) −2.88799e6 −0.271229 −0.135614 0.990762i \(-0.543301\pi\)
−0.135614 + 0.990762i \(0.543301\pi\)
\(648\) 0 0
\(649\) 6.24566e6 0.582058
\(650\) −437336. 1.31749e6i −0.0406006 0.122310i
\(651\) 0 0
\(652\) 4.66116e6 + 6.24730e6i 0.429413 + 0.575537i
\(653\) −4.44008e6 2.56348e6i −0.407482 0.235260i 0.282225 0.959348i \(-0.408927\pi\)
−0.689707 + 0.724088i \(0.742261\pi\)
\(654\) 0 0
\(655\) −1.82647e6 + 1.05451e6i −0.166345 + 0.0960394i
\(656\) −8.42058e6 + 7.97793e6i −0.763980 + 0.723820i
\(657\) 0 0
\(658\) 68356.3 331931.i 0.00615480 0.0298870i
\(659\) 1.30044e6 + 2.25243e6i 0.116648 + 0.202041i 0.918437 0.395566i \(-0.129452\pi\)
−0.801789 + 0.597607i \(0.796118\pi\)
\(660\) 0 0
\(661\) 6.08660e6 1.05423e7i 0.541840 0.938494i −0.456959 0.889488i \(-0.651061\pi\)
0.998798 0.0490059i \(-0.0156053\pi\)
\(662\) −4.16524e6 3.70283e6i −0.369398 0.328389i
\(663\) 0 0
\(664\) 379095. 4.41321e6i 0.0333679 0.388449i
\(665\) 437927.i 0.0384015i
\(666\) 0 0
\(667\) 1.29624e7i 1.12816i
\(668\) −158082. 1.34026e6i −0.0137070 0.116211i
\(669\) 0 0
\(670\) −1.16128e6 + 1.30630e6i −0.0999422 + 0.112423i
\(671\) −5.12658e6 + 8.87949e6i −0.439563 + 0.761346i
\(672\) 0 0
\(673\) 1.21145e6 + 2.09828e6i 0.103102 + 0.178577i 0.912961 0.408047i \(-0.133790\pi\)
−0.809859 + 0.586624i \(0.800457\pi\)
\(674\) 1.22941e7 + 2.53179e6i 1.04243 + 0.214674i
\(675\) 0 0
\(676\) −1.07048e7 4.60424e6i −0.900969 0.387517i
\(677\) −2.75301e6 + 1.58945e6i −0.230854 + 0.133283i −0.610966 0.791657i \(-0.709219\pi\)
0.380112 + 0.924940i \(0.375885\pi\)
\(678\) 0 0
\(679\) −1.21091e6 699118.i −0.100794 0.0581937i
\(680\) 3.91946e6 1.83520e6i 0.325053 0.152199i
\(681\) 0 0
\(682\) 4.93987e6 1.63978e6i 0.406682 0.134997i
\(683\) 1.16442e7 0.955123 0.477562 0.878598i \(-0.341521\pi\)
0.477562 + 0.878598i \(0.341521\pi\)
\(684\) 0 0
\(685\) −886917. −0.0722199
\(686\) 3.15846e6 1.04844e6i 0.256251 0.0850617i
\(687\) 0 0
\(688\) −3.41015e6 1.42550e7i −0.274665 1.14814i
\(689\) −2.27335e6 1.31252e6i −0.182439 0.105331i
\(690\) 0 0
\(691\) −1.57763e7 + 9.10845e6i −1.25693 + 0.725687i −0.972476 0.233004i \(-0.925145\pi\)
−0.284451 + 0.958691i \(0.591811\pi\)
\(692\) 1.38490e6 3.21985e6i 0.109939 0.255606i
\(693\) 0 0
\(694\) 1.42467e7 + 2.93391e6i 1.12284 + 0.231232i
\(695\) −2.66591e6 4.61749e6i −0.209355 0.362613i
\(696\) 0 0
\(697\) −9.11691e6 + 1.57910e7i −0.710830 + 1.23119i
\(698\) −7.03344e6 + 7.91179e6i −0.546424 + 0.614661i
\(699\) 0 0
\(700\) −1.63055e6 + 192321.i −0.125773 + 0.0148348i
\(701\) 8.51403e6i 0.654395i 0.944956 + 0.327197i \(0.106104\pi\)
−0.944956 + 0.327197i \(0.893896\pi\)
\(702\) 0 0
\(703\) 7.71779e6i 0.588986i
\(704\) 6.01158e6 7.21037e6i 0.457148 0.548310i
\(705\) 0 0
\(706\) −5.84342e6 5.19470e6i −0.441220 0.392237i
\(707\) 1.18971e6 2.06064e6i 0.0895145 0.155044i
\(708\) 0 0
\(709\) −5.32118e6 9.21656e6i −0.397551 0.688578i 0.595872 0.803079i \(-0.296806\pi\)
−0.993423 + 0.114501i \(0.963473\pi\)
\(710\) −716394. + 3.47873e6i −0.0533343 + 0.258985i
\(711\) 0 0
\(712\) −1.23442e7 + 1.76886e7i −0.912560 + 1.30765i
\(713\) 1.29295e7 7.46485e6i 0.952485 0.549918i
\(714\) 0 0
\(715\) 311364. + 179766.i 0.0227774 + 0.0131505i
\(716\) −6.77896e6 + 5.05783e6i −0.494175 + 0.368707i
\(717\) 0 0
\(718\) −8.17884e6 2.46390e7i −0.592081 1.78366i
\(719\) 3.66390e6 0.264315 0.132157 0.991229i \(-0.457810\pi\)
0.132157 + 0.991229i \(0.457810\pi\)
\(720\) 0 0
\(721\) −1.77956e6 −0.127489
\(722\) −551544. 1.66154e6i −0.0393765 0.118623i
\(723\) 0 0
\(724\) −1.30337e7 + 9.72454e6i −0.924105 + 0.689482i
\(725\) 7.01372e6 + 4.04938e6i 0.495568 + 0.286117i
\(726\) 0 0
\(727\) 5.20680e6 3.00615e6i 0.365372 0.210948i −0.306063 0.952011i \(-0.599012\pi\)
0.671435 + 0.741064i \(0.265678\pi\)
\(728\) 154626. 221571.i 0.0108132 0.0154947i
\(729\) 0 0
\(730\) −1.23674e6 + 6.00549e6i −0.0858959 + 0.417101i
\(731\) −1.15200e7 1.99532e7i −0.797365 1.38108i
\(732\) 0 0
\(733\) 5.88479e6 1.01927e7i 0.404549 0.700699i −0.589720 0.807608i \(-0.700762\pi\)
0.994269 + 0.106909i \(0.0340953\pi\)
\(734\) −1.55271e6 1.38033e6i −0.106378 0.0945679i
\(735\) 0 0
\(736\) 1.27175e7 2.37351e7i 0.865378 1.61509i
\(737\) 5.95968e6i 0.404161i
\(738\) 0 0
\(739\) 1.44915e7i 0.976118i 0.872811 + 0.488059i \(0.162295\pi\)
−0.872811 + 0.488059i \(0.837705\pi\)
\(740\) −2.18273e6 + 257450.i −0.146528 + 0.0172828i
\(741\) 0 0
\(742\) −2.06279e6 + 2.32040e6i −0.137545 + 0.154722i
\(743\) 1.03693e7 1.79602e7i 0.689094 1.19355i −0.283038 0.959109i \(-0.591342\pi\)
0.972131 0.234436i \(-0.0753245\pi\)
\(744\) 0 0
\(745\) −1.50259e6 2.60255e6i −0.0991856 0.171794i
\(746\) −1.61508e7 3.32603e6i −1.06255 0.218816i
\(747\) 0 0
\(748\) 5.83058e6 1.35560e7i 0.381029 0.885883i
\(749\) −228335. + 131829.i −0.0148719 + 0.00858631i
\(750\) 0 0
\(751\) 126982. + 73312.8i 0.00821563 + 0.00474329i 0.504102 0.863644i \(-0.331823\pi\)
−0.495887 + 0.868387i \(0.665157\pi\)
\(752\) 3.37736e6 807952.i 0.217788 0.0521004i
\(753\) 0 0
\(754\) −1.26490e6 + 419879.i −0.0810265 + 0.0268965i
\(755\) 267818. 0.0170991
\(756\) 0 0
\(757\) 2.59573e7 1.64634 0.823170 0.567795i \(-0.192203\pi\)
0.823170 + 0.567795i \(0.192203\pi\)
\(758\) −1.04729e7 + 3.47646e6i −0.662057 + 0.219768i
\(759\) 0 0
\(760\) −4.06400e6 + 1.90288e6i −0.255223 + 0.119503i
\(761\) −3.55514e6 2.05256e6i −0.222534 0.128480i 0.384589 0.923088i \(-0.374343\pi\)
−0.607123 + 0.794608i \(0.707676\pi\)
\(762\) 0 0
\(763\) −520249. + 300366.i −0.0323519 + 0.0186784i
\(764\) 3.07451e6 + 1.32238e6i 0.190564 + 0.0819640i
\(765\) 0 0
\(766\) −2.11945e7 4.36469e6i −1.30512 0.268771i
\(767\) 920991. + 1.59520e6i 0.0565284 + 0.0979101i
\(768\) 0 0
\(769\) 1.04927e7 1.81739e7i 0.639839 1.10823i −0.345629 0.938371i \(-0.612334\pi\)
0.985468 0.169862i \(-0.0543323\pi\)
\(770\) 282527. 317809.i 0.0171725 0.0193170i
\(771\) 0 0
\(772\) −2.03750e6 1.72744e7i −0.123042 1.04318i
\(773\) 4.46768e6i 0.268926i 0.990919 + 0.134463i \(0.0429310\pi\)
−0.990919 + 0.134463i \(0.957069\pi\)
\(774\) 0 0
\(775\) 9.32794e6i 0.557868i