Properties

Label 108.6.h.a.35.17
Level 108
Weight 6
Character 108.35
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 35.17
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.17

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

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

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 −0.610619 0.791924i \(-0.709079\pi\)
0.380517 + 0.924774i \(0.375746\pi\)
\(6\) 0 0
\(7\) −15.2989 8.83282i −0.118009 0.0681325i 0.439834 0.898079i \(-0.355037\pi\)
−0.557843 + 0.829947i \(0.688371\pi\)
\(8\) −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 −0.987448 0.157943i \(-0.949514\pi\)
0.630507 + 0.776184i \(0.282847\pi\)
\(12\) 0 0
\(13\) 42.2460 + 73.1722i 0.0693309 + 0.120085i 0.898607 0.438755i \(-0.144580\pi\)
−0.829276 + 0.558839i \(0.811247\pi\)
\(14\) −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 \(0.236040\pi\)
−0.737427 + 0.675427i \(0.763960\pi\)
\(18\) 0 0
\(19\) 1669.01i 1.06065i −0.847793 0.530327i \(-0.822069\pi\)
0.847793 0.530327i \(-0.177931\pi\)
\(20\) 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 0.805196 + 0.593009i \(0.202060\pi\)
0.110963 + 0.993825i \(0.464606\pi\)
\(24\) 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 0.209112 0.977892i \(-0.432943\pi\)
−0.742323 + 0.670042i \(0.766276\pi\)
\(30\) 0 0
\(31\) 2781.39 1605.84i 0.519825 0.300121i −0.217038 0.976163i \(-0.569640\pi\)
0.736863 + 0.676042i \(0.236306\pi\)
\(32\) 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 −0.880888 0.473325i \(-0.843053\pi\)
−0.0305320 + 0.999534i \(0.509720\pi\)
\(42\) 0 0
\(43\) 12396.0 + 7156.83i 1.02237 + 0.590268i 0.914791 0.403928i \(-0.132355\pi\)
0.107584 + 0.994196i \(0.465689\pi\)
\(44\) 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 −0.804597 0.593822i \(-0.797618\pi\)
0.916563 + 0.399890i \(0.130952\pi\)
\(48\) 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 \(0.274618\pi\)
−0.650360 + 0.759626i \(0.725382\pi\)
\(54\) 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 0.586957 0.809618i \(-0.300326\pi\)
−0.994628 + 0.103511i \(0.966992\pi\)
\(60\) 0 0
\(61\) −17894.5 + 30994.2i −0.615736 + 1.06649i 0.374519 + 0.927219i \(0.377808\pi\)
−0.990255 + 0.139267i \(0.955525\pi\)
\(62\) −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 −0.724697 0.689068i \(-0.758020\pi\)
0.234401 + 0.972140i \(0.424687\pi\)
\(68\) 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 −0.379896 0.925029i \(-0.624040\pi\)
−0.991047 + 0.133515i \(0.957374\pi\)
\(80\) −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 −0.751941 0.659231i \(-0.770882\pi\)
0.946881 + 0.321585i \(0.104215\pi\)
\(84\) 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 \(0.293737\pi\)
−0.603588 + 0.797296i \(0.706263\pi\)
\(90\) 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 −0.569548 0.821958i \(-0.692882\pi\)
0.996611 + 0.0822641i \(0.0262151\pi\)
\(98\) −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 −0.191923 0.981410i \(-0.561472\pi\)
−0.945887 + 0.324495i \(0.894806\pi\)
\(102\) 0 0
\(103\) 87239.5 50367.8i 0.810252 0.467799i −0.0367911 0.999323i \(-0.511714\pi\)
0.847044 + 0.531524i \(0.178380\pi\)
\(104\) −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 −0.131727 0.991286i \(-0.542052\pi\)
0.792616 + 0.609722i \(0.208719\pi\)
\(114\) 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 \(0.349320\pi\)
−0.455894 + 0.890034i \(0.650680\pi\)
\(128\) −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 0.988201 0.153161i \(-0.0489452\pi\)
−0.626742 + 0.779227i \(0.715612\pi\)
\(132\) 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 0.613059 0.790037i \(-0.289939\pi\)
−0.377663 + 0.925943i \(0.623272\pi\)
\(138\) 0 0
\(139\) 310879. 179486.i 1.36475 0.787941i 0.374501 0.927227i \(-0.377814\pi\)
0.990252 + 0.139286i \(0.0444807\pi\)
\(140\) −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 −0.140567 0.990071i \(-0.544893\pi\)
0.787143 + 0.616770i \(0.211559\pi\)
\(150\) 0 0
\(151\) −15615.5 9015.60i −0.0557331 0.0321775i 0.471875 0.881666i \(-0.343578\pi\)
−0.527608 + 0.849488i \(0.676911\pi\)
\(152\) 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 0.936865 + 0.349692i \(0.113714\pi\)
−0.165590 + 0.986195i \(0.552953\pi\)
\(158\) −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 \(0.116896\pi\)
−0.933322 + 0.359040i \(0.883104\pi\)
\(164\) 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 0.835288 0.549813i \(-0.185301\pi\)
−0.893796 + 0.448474i \(0.851968\pi\)
\(168\) 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 0.374653 0.927165i \(-0.377762\pi\)
−0.615622 + 0.788042i \(0.711095\pi\)
\(174\) 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 −0.913215 0.407477i \(-0.866409\pi\)
0.809493 + 0.587129i \(0.199742\pi\)
\(192\) 0 0
\(193\) −271784. 470744.i −0.525207 0.909685i −0.999569 0.0293554i \(-0.990655\pi\)
0.474362 0.880330i \(-0.342679\pi\)
\(194\) −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 \(-0.678755\pi\)
0.532519 0.846418i \(-0.321245\pi\)
\(198\) 0 0
\(199\) 93172.6i 0.166784i 0.996517 + 0.0833922i \(0.0265754\pi\)
−0.996517 + 0.0833922i \(0.973425\pi\)
\(200\) −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 −0.496410 0.868088i \(-0.665349\pi\)
0.503581 + 0.863948i \(0.332015\pi\)
\(212\) 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 −0.0653606 0.997862i \(-0.520820\pi\)
−0.896854 + 0.442327i \(0.854153\pi\)
\(224\) −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 −0.686084 0.727522i \(-0.740672\pi\)
0.973095 + 0.230405i \(0.0740051\pi\)
\(228\) 0 0
\(229\) 121497. + 210439.i 0.153101 + 0.265178i 0.932366 0.361516i \(-0.117741\pi\)
−0.779265 + 0.626694i \(0.784407\pi\)
\(230\) −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 \(0.0943091\pi\)
−0.956429 + 0.291965i \(0.905691\pi\)
\(234\) 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 0.571806 0.820389i \(-0.306243\pi\)
−0.996381 + 0.0850045i \(0.972910\pi\)
\(240\) 0 0
\(241\) −214184. + 370977.i −0.237544 + 0.411438i −0.960009 0.279969i \(-0.909676\pi\)
0.722465 + 0.691408i \(0.243009\pi\)
\(242\) 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 −0.948306 0.317357i \(-0.897205\pi\)
−0.199314 + 0.979936i \(0.563871\pi\)
\(258\) 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 −0.995403 0.0957708i \(-0.969468\pi\)
0.580642 + 0.814159i \(0.302802\pi\)
\(264\) 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 \(0.142478\pi\)
−0.901485 + 0.432810i \(0.857522\pi\)
\(270\) 0 0
\(271\) 1.66981e6i 1.38116i 0.723255 + 0.690581i \(0.242645\pi\)
−0.723255 + 0.690581i \(0.757355\pi\)
\(272\) −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 −0.995533 0.0944109i \(-0.969903\pi\)
0.579529 + 0.814952i \(0.303237\pi\)
\(278\) −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 0.749390 0.662128i \(-0.230347\pi\)
−0.198725 + 0.980055i \(0.563680\pi\)
\(282\) 0 0
\(283\) 1.59876e6 923047.i 1.18664 0.685106i 0.229097 0.973404i \(-0.426423\pi\)
0.957541 + 0.288298i \(0.0930893\pi\)
\(284\) 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 −0.894953 0.446161i \(-0.852791\pi\)
−0.0610899 + 0.998132i \(0.519458\pi\)
\(294\) 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 \(-0.883412\pi\)
0.933669 0.358137i \(-0.116588\pi\)
\(308\) −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 0.993926 0.110048i \(-0.0351005\pi\)
−0.592268 + 0.805741i \(0.701767\pi\)
\(312\) 0 0
\(313\) 130578. 226168.i 0.0753372 0.130488i −0.825896 0.563823i \(-0.809330\pi\)
0.901233 + 0.433335i \(0.142663\pi\)
\(314\) 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 0.344618 0.938743i \(-0.388009\pi\)
−0.640667 + 0.767819i \(0.721342\pi\)
\(318\) 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 0.270470 0.962728i \(-0.412821\pi\)
−0.698512 + 0.715598i \(0.746154\pi\)
\(332\) −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 0.999295 + 0.0375341i \(0.0119503\pi\)
−0.467142 + 0.884182i \(0.654716\pi\)
\(338\) −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 0.996235 + 0.0866969i \(0.0276312\pi\)
−0.423036 + 0.906113i \(0.639036\pi\)
\(348\) 0 0
\(349\) 935689. 1.62066e6i 0.411214 0.712243i −0.583809 0.811891i \(-0.698438\pi\)
0.995023 + 0.0996478i \(0.0317716\pi\)
\(350\) −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 0.222087 0.975027i \(-0.428713\pi\)
−0.733354 + 0.679847i \(0.762046\pi\)
\(354\) 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 0.437099 0.899413i \(-0.356006\pi\)
−0.560365 + 0.828246i \(0.689339\pi\)
\(368\) −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 −0.998764 0.0496972i \(-0.984174\pi\)
0.456343 0.889804i \(-0.349159\pi\)
\(374\) −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 \(-0.886593\pi\)
0.937201 0.348790i \(-0.113407\pi\)
\(380\) 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 −0.978944 0.204130i \(-0.934563\pi\)
0.312690 0.949855i \(1.60123\pi\)
\(384\) 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 0.713159 0.701002i \(-0.247264\pi\)
−0.250506 + 0.968115i \(0.580597\pi\)
\(390\) 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 0.505532 0.862808i \(-0.331296\pi\)
0.999980 0.00639934i \(-0.00203699\pi\)
\(402\) 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 0.989320 0.145759i \(-0.0465625\pi\)
−0.620891 + 0.783897i \(0.713229\pi\)
\(410\) −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 0.924724 0.380637i \(-0.124295\pi\)
−0.792004 + 0.610516i \(0.790962\pi\)
\(420\) 0 0
\(421\) −1.44880e6 + 2.50940e6i −0.398386 + 0.690025i −0.993527 0.113597i \(-0.963763\pi\)
0.595141 + 0.803621i \(0.297096\pi\)
\(422\) −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 0.997427 + 0.0716934i \(0.0228403\pi\)
0.560802 + 0.827950i \(0.310493\pi\)
\(440\) 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 −0.287463 0.957792i \(-0.592812\pi\)
0.973203 0.229946i \(-0.0738549\pi\)
\(444\) 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 \(-0.841179\pi\)
0.878085 0.478505i \(-0.158821\pi\)
\(450\) 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 −0.534114 0.845412i \(-0.679355\pi\)
0.999206 + 0.0398504i \(0.0126881\pi\)
\(458\) 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 0.467535 0.883975i \(-0.345142\pi\)
−0.531777 + 0.846884i \(0.678476\pi\)
\(462\) 0 0
\(463\) −6.16958e6 + 3.56201e6i −1.33753 + 0.772223i −0.986441 0.164119i \(-0.947522\pi\)
−0.351089 + 0.936342i \(0.614189\pi\)
\(464\) 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 0.174151 + 0.984719i \(0.444282\pi\)
−0.939867 + 0.341540i \(0.889052\pi\)
\(480\) 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 \(-0.964137\pi\)
0.993660 0.112430i \(-0.0358634\pi\)
\(488\) −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 0.926249 0.376911i \(-0.123014\pi\)
−0.789539 + 0.613700i \(0.789680\pi\)
\(492\) 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 −0.138758 0.990326i \(-0.544311\pi\)
0.788269 + 0.615331i \(0.210978\pi\)
\(500\) −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 −0.897827 0.440348i \(-0.854855\pi\)
−0.0675606 + 0.997715i \(0.521522\pi\)
\(510\) 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 \(-0.985835\pi\)
0.999010 0.0444872i \(-0.0141654\pi\)
\(522\) 0 0
\(523\) 1.10624e7i 1.76846i −0.467053 0.884230i \(-0.654684\pi\)
0.467053 0.884230i \(-0.345316\pi\)
\(524\) 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 0.604757 0.796410i \(-0.293270\pi\)
−0.387333 + 0.921940i \(0.626604\pi\)
\(548\) −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 \(0.253143\pi\)
−0.700090 + 0.714055i \(0.746857\pi\)
\(558\) 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 0.989842 0.142173i \(-0.0454088\pi\)
−0.618046 + 0.786142i \(0.712075\pi\)
\(564\) 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 0.787737 0.616012i \(-0.211253\pi\)
−0.139613 + 0.990206i \(0.544586\pi\)
\(570\) 0 0
\(571\) −2.38689e6 + 1.37807e6i −0.306367 + 0.176881i −0.645300 0.763930i \(-0.723267\pi\)
0.338933 + 0.940811i \(0.389934\pi\)
\(572\) 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 −0.431407 0.902157i \(-0.641983\pi\)
0.996995 0.0774689i \(-0.0246838\pi\)
\(588\) 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 \(0.0247220\pi\)
−0.996985 + 0.0775883i \(0.975278\pi\)
\(594\) 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 −0.718166 0.695872i \(-0.755018\pi\)
−0.243560 0.969886i \(1.42168\pi\)
\(600\) 0 0
\(601\) 3.86305e6 6.69101e6i 0.436259 0.755623i −0.561138 0.827722i \(-0.689636\pi\)
0.997397 + 0.0720990i \(0.0229698\pi\)
\(602\) −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 −0.605829 0.795595i \(-0.707159\pi\)
0.386091 + 0.922461i \(0.373825\pi\)
\(608\) 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 −0.935016 0.354606i \(-0.884615\pi\)
−0.160410 + 0.987050i \(0.551282\pi\)
\(618\) 0 0
\(619\) 6.60708e6 + 3.81460e6i 0.693079 + 0.400149i 0.804764 0.593594i \(-0.202292\pi\)
−0.111685 + 0.993744i \(0.535625\pi\)
\(620\) 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 \(0.320364\pi\)
−0.534861 + 0.844940i \(0.679636\pi\)
\(632\) 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 0.775787 0.630995i \(-0.217353\pi\)
−0.158565 + 0.987349i \(0.550687\pi\)
\(642\) 0 0
\(643\) 3.01403e6 1.74015e6i 0.287488 0.165981i −0.349320 0.937003i \(-0.613587\pi\)
0.636809 + 0.771022i \(0.280254\pi\)
\(644\) −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 −0.689707 0.724088i \(-0.742261\pi\)
0.282225 + 0.959348i \(0.408927\pi\)
\(654\) 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 −0.801789 0.597607i \(-0.796118\pi\)
0.918437 + 0.395566i \(0.129452\pi\)
\(660\) 0 0
\(661\) 6.08660e6 + 1.05423e7i 0.541840 + 0.938494i 0.998798 + 0.0490059i \(0.0156053\pi\)
−0.456959 + 0.889488i \(0.651061\pi\)
\(662\) −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 −0.809859 0.586624i \(-0.800457\pi\)
0.912961 + 0.408047i \(0.133790\pi\)
\(674\) 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 0.380112 0.924940i \(-0.375885\pi\)
−0.610966 + 0.791657i \(0.709219\pi\)
\(678\) 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 −0.284451 0.958691i \(-0.591811\pi\)
−0.972476 + 0.233004i \(0.925145\pi\)
\(692\) 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 \(-0.893896\pi\)
0.944956 0.327197i \(-0.106104\pi\)
\(702\) 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 −0.993423 0.114501i \(-0.963473\pi\)
0.595872 + 0.803079i \(0.296806\pi\)
\(710\) −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 0.671435 0.741064i \(-0.265678\pi\)
−0.306063 + 0.952011i \(0.599012\pi\)
\(728\) 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 0.994269 0.106909i \(-0.0340953\pi\)
−0.589720 + 0.807608i \(0.700762\pi\)
\(734\) −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 \(-0.837705\pi\)
0.872811 0.488059i \(-0.162295\pi\)
\(740\) −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 0.972131 + 0.234436i \(0.0753245\pi\)
−0.283038 + 0.959109i \(0.591342\pi\)
\(744\) 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 −0.495887 0.868387i \(-0.665157\pi\)
0.504102 + 0.863644i \(0.331823\pi\)
\(752\) 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 −0.607123 0.794608i \(-0.707676\pi\)
0.384589 + 0.923088i \(0.374343\pi\)
\(762\) 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 0.985468 + 0.169862i \(0.0543323\pi\)
−0.345629 + 0.938371i \(0.612334\pi\)
\(770\) 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 \(-0.957069\pi\)
0.990919 0.134463i \(-0.0429310\pi\)
\(774\) 0 0