Properties

Label 108.6.h.a.35.8
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 35.8
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.75843 + 4.22779i) q^{2} +(-3.74838 - 31.7797i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(15.2989 + 8.83282i) q^{7} +(148.446 + 103.595i) q^{8} +O(q^{10})\) \(q+(-3.75843 + 4.22779i) q^{2} +(-3.74838 - 31.7797i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(15.2989 + 8.83282i) q^{7} +(148.446 + 103.595i) q^{8} +(16.9473 - 82.2944i) q^{10} +(143.245 - 248.107i) q^{11} +(42.2460 + 73.1722i) q^{13} +(-94.8432 + 31.4829i) q^{14} +(-995.899 + 238.245i) q^{16} +1609.65i q^{17} +1669.01i q^{19} +(284.228 + 380.948i) q^{20} +(510.569 + 1538.10i) q^{22} +(-2324.29 - 4025.79i) q^{23} +(-1452.19 + 2515.27i) q^{25} +(-468.135 - 96.4056i) q^{26} +(223.358 - 519.303i) q^{28} +(-2414.87 - 1394.23i) q^{29} +(-2781.39 + 1605.84i) q^{31} +(2735.77 - 5105.88i) q^{32} +(-6805.24 - 6049.75i) q^{34} -262.388 q^{35} -4624.19 q^{37} +(-7056.20 - 6272.84i) q^{38} +(-2678.82 - 230.111i) q^{40} +(-9810.20 + 5663.92i) q^{41} +(-12396.0 - 7156.83i) q^{43} +(-8421.70 - 3622.27i) q^{44} +(25755.9 + 5304.05i) q^{46} +(-1695.63 + 2936.92i) q^{47} +(-8247.46 - 14285.0i) q^{49} +(-5176.07 - 15593.1i) q^{50} +(2167.04 - 1616.84i) q^{52} +31068.4i q^{53} +4255.23i q^{55} +(1356.03 + 2896.08i) q^{56} +(14970.6 - 4969.46i) q^{58} +(10900.3 + 18879.9i) q^{59} +(-17894.5 + 30994.2i) q^{61} +(3664.53 - 17794.5i) q^{62} +(11304.4 + 30756.4i) q^{64} +(-1086.83 - 627.480i) q^{65} +(18015.5 - 10401.2i) q^{67} +(51154.1 - 6033.56i) q^{68} +(986.168 - 1109.32i) q^{70} +42271.8 q^{71} -72975.6 q^{73} +(17379.7 - 19550.1i) q^{74} +(53040.5 - 6256.07i) q^{76} +(4382.97 - 2530.51i) q^{77} +(76047.9 + 43906.3i) q^{79} +(11041.0 - 10460.6i) q^{80} +(12925.1 - 62762.9i) q^{82} +(-12234.8 + 21191.3i) q^{83} +(-11954.1 - 20705.0i) q^{85} +(76847.0 - 25509.2i) q^{86} +(46966.6 - 21991.1i) q^{88} +119158. i q^{89} +1492.60i q^{91} +(-119226. + 88955.4i) q^{92} +(-6043.77 - 18207.0i) q^{94} +(-12394.9 - 21468.6i) q^{95} +(39575.0 - 68545.9i) q^{97} +(91391.6 + 18820.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.75843 + 4.22779i −0.664403 + 0.747374i
\(3\) 0 0
\(4\) −3.74838 31.7797i −0.117137 0.993116i
\(5\) −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 0.557843 0.829947i \(-0.311629\pi\)
−0.439834 + 0.898079i \(0.644963\pi\)
\(8\) 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 \(-0.717153\pi\)
0.987448 + 0.157943i \(0.0504863\pi\)
\(12\) 0 0
\(13\) 42.2460 + 73.1722i 0.0693309 + 0.120085i 0.898607 0.438755i \(-0.144580\pi\)
−0.829276 + 0.558839i \(0.811247\pi\)
\(14\) −94.8432 + 31.4829i −0.129326 + 0.0429294i
\(15\) 0 0
\(16\) −995.899 + 238.245i −0.972558 + 0.232661i
\(17\) 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 \(0.177931\pi\)
−0.847793 + 0.530327i \(0.822069\pi\)
\(20\) 284.228 + 380.948i 0.158888 + 0.212956i
\(21\) 0 0
\(22\) 510.569 + 1538.10i 0.224904 + 0.677530i
\(23\) −2324.29 4025.79i −0.916159 1.58683i −0.805196 0.593009i \(-0.797940\pi\)
−0.110963 0.993825i \(1.46461\pi\)
\(24\) 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 −0.736863 0.676042i \(-0.763694\pi\)
0.217038 + 0.976163i \(0.430360\pi\)
\(32\) 2735.77 5105.88i 0.472286 0.881445i
\(33\) 0 0
\(34\) −6805.24 6049.75i −1.00959 0.897511i
\(35\) −262.388 −0.0362055
\(36\) 0 0
\(37\) −4624.19 −0.555304 −0.277652 0.960682i \(-0.589556\pi\)
−0.277652 + 0.960682i \(0.589556\pi\)
\(38\) −7056.20 6272.84i −0.792706 0.704702i
\(39\) 0 0
\(40\) −2678.82 230.111i −0.264724 0.0227398i
\(41\) −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 −0.107584 0.994196i \(-0.534311\pi\)
−0.914791 + 0.403928i \(0.867645\pi\)
\(44\) −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 \(-0.869048\pi\)
0.804597 + 0.593822i \(0.202382\pi\)
\(48\) 0 0
\(49\) −8247.46 14285.0i −0.490716 0.849945i
\(50\) −5176.07 15593.1i −0.292803 0.882076i
\(51\) 0 0
\(52\) 2167.04 1616.84i 0.111137 0.0829200i
\(53\) 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
\(56\) 1356.03 + 2896.08i 0.0577827 + 0.123407i
\(57\) 0 0
\(58\) 14970.6 4969.46i 0.584346 0.193972i
\(59\) 10900.3 + 18879.9i 0.407671 + 0.706107i 0.994628 0.103511i \(-0.0330077\pi\)
−0.586957 + 0.809618i \(0.699674\pi\)
\(60\) 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 −0.234401 0.972140i \(-0.575313\pi\)
0.724697 + 0.689068i \(0.241980\pi\)
\(68\) 51154.1 6033.56i 1.34155 0.158235i
\(69\) 0 0
\(70\) 986.168 1109.32i 0.0240550 0.0270590i
\(71\) 42271.8 0.995187 0.497593 0.867410i \(-0.334217\pi\)
0.497593 + 0.867410i \(0.334217\pi\)
\(72\) 0 0
\(73\) −72975.6 −1.60277 −0.801384 0.598150i \(-0.795903\pi\)
−0.801384 + 0.598150i \(0.795903\pi\)
\(74\) 17379.7 19550.1i 0.368946 0.415020i
\(75\) 0 0
\(76\) 53040.5 6256.07i 1.05335 0.124242i
\(77\) 4382.97 2530.51i 0.0842445 0.0486386i
\(78\) 0 0
\(79\) 76047.9 + 43906.3i 1.37094 + 0.791514i 0.991047 0.133515i \(-0.0426263\pi\)
0.379896 + 0.925029i \(0.375960\pi\)
\(80\) 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 \(-0.895785\pi\)
0.751941 + 0.659231i \(0.229118\pi\)
\(84\) 0 0
\(85\) −11954.1 20705.0i −0.179460 0.310834i
\(86\) 76847.0 25509.2i 1.12042 0.371920i
\(87\) 0 0
\(88\) 46966.6 21991.1i 0.646521 0.302719i
\(89\) 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
\(92\) −119226. + 88955.4i −1.46859 + 1.09573i
\(93\) 0 0
\(94\) −6043.77 18207.0i −0.0705486 0.212529i
\(95\) −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 −0.847044 0.531524i \(-0.821620\pi\)
0.0367911 + 0.999323i \(0.488286\pi\)
\(104\) −1308.99 + 15238.6i −0.0118674 + 0.138153i
\(105\) 0 0
\(106\) −131351. 116769.i −1.13545 1.00940i
\(107\) −14924.9 −0.126024 −0.0630118 0.998013i \(-0.520071\pi\)
−0.0630118 + 0.998013i \(0.520071\pi\)
\(108\) 0 0
\(109\) 34005.6 0.274148 0.137074 0.990561i \(-0.456230\pi\)
0.137074 + 0.990561i \(0.456230\pi\)
\(110\) −17990.2 15993.0i −0.141760 0.126022i
\(111\) 0 0
\(112\) −17340.5 5151.72i −0.130622 0.0388067i
\(113\) 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
\(122\) −63781.5 192143.i −0.387967 1.16876i
\(123\) 0 0
\(124\) 61458.7 + 82372.4i 0.358946 + 0.481091i
\(125\) 89554.6i 0.512640i
\(126\) 0 0
\(127\) 323553.i 1.78007i −0.455894 0.890034i \(-0.650680\pi\)
0.455894 0.890034i \(-0.349320\pi\)
\(128\) −172518. 67803.2i −0.930700 0.365785i
\(129\) 0 0
\(130\) 6737.62 2236.53i 0.0349662 0.0116069i
\(131\) −70996.7 122970.i −0.361460 0.626066i 0.626742 0.779227i \(-0.284388\pi\)
−0.988201 + 0.153161i \(0.951055\pi\)
\(132\) 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 −0.990252 0.139286i \(-0.955519\pi\)
−0.374501 + 0.927227i \(0.622186\pi\)
\(140\) 983.530 + 8338.62i 0.00424099 + 0.0359562i
\(141\) 0 0
\(142\) −158876. + 178716.i −0.661205 + 0.743777i
\(143\) 24206.0 0.0989882
\(144\) 0 0
\(145\) 41417.0 0.163591
\(146\) 274274. 308526.i 1.06488 1.19787i
\(147\) 0 0
\(148\) 17333.2 + 146955.i 0.0650466 + 0.551481i
\(149\) 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 0.527608 0.849488i \(-0.323089\pi\)
−0.471875 + 0.881666i \(0.656422\pi\)
\(152\) −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 \(0.552953\pi\)
\(158\) −471447. + 156496.i −1.50242 + 0.498723i
\(159\) 0 0
\(160\) 2728.37 + 85994.6i 0.00842565 + 0.265565i
\(161\) 82120.2i 0.249681i
\(162\) 0 0
\(163\) 243580.i 0.718080i −0.933322 0.359040i \(-0.883104\pi\)
0.933322 0.359040i \(-0.116896\pi\)
\(164\) 216770. + 290535.i 0.629347 + 0.843507i
\(165\) 0 0
\(166\) −43608.6 131372.i −0.122829 0.370026i
\(167\) 21086.7 + 36523.3i 0.0585083 + 0.101339i 0.893796 0.448474i \(-0.148032\pi\)
−0.835288 + 0.549813i \(0.814699\pi\)
\(168\) 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
\(176\) −83547.0 + 281217.i −0.203306 + 0.684321i
\(177\) 0 0
\(178\) −503777. 447849.i −1.19176 1.05945i
\(179\) −264309. −0.616566 −0.308283 0.951295i \(-0.599754\pi\)
−0.308283 + 0.951295i \(0.599754\pi\)
\(180\) 0 0
\(181\) 508179. 1.15298 0.576488 0.817105i \(-0.304423\pi\)
0.576488 + 0.817105i \(0.304423\pi\)
\(182\) −6310.42 5609.85i −0.0141215 0.0125537i
\(183\) 0 0
\(184\) 72018.3 838395.i 0.156819 1.82559i
\(185\) 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 \(-0.800258\pi\)
0.913215 + 0.407477i \(0.133591\pi\)
\(192\) 0 0
\(193\) −271784. 470744.i −0.525207 0.909685i −0.999569 0.0293554i \(-0.990655\pi\)
0.474362 0.880330i \(-0.342679\pi\)
\(194\) 141058. + 424940.i 0.269087 + 0.810631i
\(195\) 0 0
\(196\) −423059. + 315648.i −0.786613 + 0.586898i
\(197\) 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 \(-0.973425\pi\)
0.996517 0.0833922i \(-0.0265754\pi\)
\(200\) −476141. + 222943.i −0.841706 + 0.394111i
\(201\) 0 0
\(202\) 723135. 240043.i 1.24693 0.413914i
\(203\) −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 \(-0.667985\pi\)
0.496410 + 0.868088i \(0.334651\pi\)
\(212\) 987346. 116456.i 1.50879 0.177960i
\(213\) 0 0
\(214\) 56094.2 63099.3i 0.0837305 0.0941868i
\(215\) 212601. 0.313667
\(216\) 0 0
\(217\) −56736.2 −0.0817921
\(218\) −127808. + 143769.i −0.182145 + 0.204891i
\(219\) 0 0
\(220\) 135230. 15950.2i 0.188372 0.0222183i
\(221\) −117781. + 68001.1i −0.162217 + 0.0936559i
\(222\) 0 0
\(223\) 714552. + 412547.i 0.962214 + 0.555535i 0.896854 0.442327i \(-0.145847\pi\)
0.0653606 + 0.997862i \(0.479180\pi\)
\(224\) 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 \(-0.925995\pi\)
0.686084 + 0.727522i \(0.259328\pi\)
\(228\) 0 0
\(229\) 121497. + 210439.i 0.153101 + 0.265178i 0.932366 0.361516i \(-0.117741\pi\)
−0.779265 + 0.626694i \(0.784407\pi\)
\(230\) −370691. + 123050.i −0.462053 + 0.153377i
\(231\) 0 0
\(232\) −214044. 457135.i −0.261085 0.557602i
\(233\) 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
\(236\) 559140. 417179.i 0.653493 0.487576i
\(237\) 0 0
\(238\) −50676.4 152664.i −0.0579913 0.174700i
\(239\) 374928. + 649395.i 0.424574 + 0.735384i 0.996381 0.0850045i \(-0.0270905\pi\)
−0.571806 + 0.820389i \(0.693757\pi\)
\(240\) 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
\(248\) −579241. 49756.9i −0.598040 0.0513717i
\(249\) 0 0
\(250\) 378618. + 336585.i 0.383134 + 0.340600i
\(251\) 168039. 0.168355 0.0841773 0.996451i \(-0.473174\pi\)
0.0841773 + 0.996451i \(0.473174\pi\)
\(252\) 0 0
\(253\) −1.33177e6 −1.30806
\(254\) 1.36792e6 + 1.21605e6i 1.33038 + 1.18268i
\(255\) 0 0
\(256\) 935055. 474536.i 0.891738 0.452552i
\(257\) −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 −0.580642 0.814159i \(-0.697198\pi\)
0.995403 + 0.0957708i \(0.0305316\pi\)
\(264\) 0 0
\(265\) −230730. 399636.i −0.201832 0.349583i
\(266\) −52545.2 158294.i −0.0455333 0.137170i
\(267\) 0 0
\(268\) −398077. 533538.i −0.338555 0.453762i
\(269\) 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 \(-0.757355\pi\)
0.723255 0.690581i \(-0.242645\pi\)
\(272\) −383490. 1.60305e6i −0.314291 1.31378i
\(273\) 0 0
\(274\) −320586. + 106418.i −0.257970 + 0.0856323i
\(275\) 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 −0.957541 0.288298i \(-0.906911\pi\)
−0.229097 + 0.973404i \(0.573577\pi\)
\(284\) −158451. 1.34338e6i −0.116573 0.988336i
\(285\) 0 0
\(286\) −90976.8 + 102338.i −0.0657681 + 0.0739813i
\(287\) −200114. −0.143408
\(288\) 0 0
\(289\) −1.17110e6 −0.824804
\(290\) −155663. + 175102.i −0.108690 + 0.122263i
\(291\) 0 0
\(292\) 273540. + 2.31914e6i 0.187743 + 1.59173i
\(293\) −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
\(302\) −96805.8 + 32134.4i −0.0610779 + 0.0202746i
\(303\) 0 0
\(304\) −397632. 1.66216e6i −0.246773 1.03155i
\(305\) 531574.i 0.327201i
\(306\) 0 0
\(307\) 1.18284e6i 0.716275i 0.933669 + 0.358137i \(0.116588\pi\)
−0.933669 + 0.358137i \(0.883412\pi\)
\(308\) −96847.9 129804.i −0.0581719 0.0779672i
\(309\) 0 0
\(310\) 85014.2 + 256107.i 0.0502443 + 0.151362i
\(311\) −685107. 1.18664e6i −0.401659 0.695693i 0.592268 0.805741i \(-0.298233\pi\)
−0.993926 + 0.110048i \(0.964900\pi\)
\(312\) 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
\(320\) −373821. 311670.i −0.204075 0.170145i
\(321\) 0 0
\(322\) 347187. + 308643.i 0.186605 + 0.165889i
\(323\) −2.68651e6 −1.43279
\(324\) 0 0
\(325\) −245397. −0.128873
\(326\) 1.02980e6 + 915479.i 0.536674 + 0.477094i
\(327\) 0 0
\(328\) −2.04304e6 175497.i −1.04856 0.0900711i
\(329\) −51882.7 + 29954.5i −0.0264261 + 0.0152571i
\(330\) 0 0
\(331\) 853212. + 492602.i 0.428043 + 0.247131i 0.698512 0.715598i \(-0.253846\pi\)
−0.270470 + 0.962728i \(0.587179\pi\)
\(332\) 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 \(0.654716\pi\)
\(338\) 648979. + 1.95507e6i 0.308986 + 0.930829i
\(339\) 0 0
\(340\) −613191. + 457507.i −0.287673 + 0.214635i
\(341\) 920109.i 0.428503i
\(342\) 0 0
\(343\) 588300.i 0.270000i
\(344\) −1.09873e6 2.34656e6i −0.500602 1.06914i
\(345\) 0 0
\(346\) 588059. 195205.i 0.264077 0.0876597i
\(347\) −1.28567e6 2.22684e6i −0.573199 0.992810i −0.996235 0.0866969i \(-0.972369\pi\)
0.423036 0.906113i \(1.63904\pi\)
\(348\) 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
\(356\) 3.78682e6 446651.i 1.58362 0.186786i
\(357\) 0 0
\(358\) 993388. 1.11744e6i 0.409648 0.460806i
\(359\) 4.58930e6 1.87936 0.939680 0.342054i \(-0.111123\pi\)
0.939680 + 0.342054i \(0.111123\pi\)
\(360\) 0 0
\(361\) −309482. −0.124988
\(362\) −1.90996e6 + 2.14847e6i −0.766041 + 0.861705i
\(363\) 0 0
\(364\) 47434.5 5594.85i 0.0187647 0.00221327i
\(365\) 938692. 541954.i 0.368800 0.212927i
\(366\) 0 0
\(367\) 318059. + 183631.i 0.123266 + 0.0711675i 0.560365 0.828246i \(-0.310661\pi\)
−0.437099 + 0.899413i \(0.643994\pi\)
\(368\) 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 \(-0.349159\pi\)
\(374\) −2.47580e6 + 821835.i −0.915243 + 0.303812i
\(375\) 0 0
\(376\) −555959. + 260316.i −0.202802 + 0.0949579i
\(377\) 235602.i 0.0853740i
\(378\) 0 0
\(379\) 1.95071e6i 0.697579i 0.937201 + 0.348790i \(0.113407\pi\)
−0.937201 + 0.348790i \(0.886593\pi\)
\(380\) −635804. + 474378.i −0.225873 + 0.168526i
\(381\) 0 0
\(382\) 186393. + 561514.i 0.0653538 + 0.196880i
\(383\) 1.91266e6 + 3.31282e6i 0.666254 + 1.15399i 0.978944 + 0.204130i \(0.0654367\pi\)
−0.312690 + 0.949855i \(0.601230\pi\)
\(384\) 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
\(392\) 255548. 2.97494e6i 0.0839958 0.977831i
\(393\) 0 0
\(394\) 3.89846e6 + 3.46567e6i 1.26518 + 1.12473i
\(395\) −1.30428e6 −0.420609
\(396\) 0 0
\(397\) 4.04020e6 1.28655 0.643275 0.765635i \(-0.277575\pi\)
0.643275 + 0.765635i \(0.277575\pi\)
\(398\) 393914. + 350183.i 0.124650 + 0.110812i
\(399\) 0 0
\(400\) 846988. 2.85094e6i 0.264684 0.890918i
\(401\) 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 \(0.713229\pi\)
\(410\) 299853. + 903314.i 0.0880944 + 0.265387i
\(411\) 0 0
\(412\) 1.92768e6 + 2.58365e6i 0.559489 + 0.749878i
\(413\) 385123.i 0.111103i
\(414\) 0 0
\(415\) 363447.i 0.103591i
\(416\) 489183. 15520.4i 0.138592 0.00439714i
\(417\) 0 0
\(418\) −2.56710e6 + 852142.i −0.718625 + 0.238545i
\(419\) −476950. 826102.i −0.132720 0.229879i 0.792004 0.610516i \(-0.209038\pi\)
−0.924724 + 0.380637i \(0.875705\pi\)
\(420\) 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
\(428\) 55944.2 + 474309.i 0.0147620 + 0.125156i
\(429\) 0 0
\(430\) −799046. + 898832.i −0.208401 + 0.234427i
\(431\) 3.72242e6 0.965234 0.482617 0.875831i \(-0.339686\pi\)
0.482617 + 0.875831i \(0.339686\pi\)
\(432\) 0 0
\(433\) 4.74890e6 1.21723 0.608616 0.793465i \(-0.291725\pi\)
0.608616 + 0.793465i \(0.291725\pi\)
\(434\) 213239. 239869.i 0.0543429 0.0611293i
\(435\) 0 0
\(436\) −127466. 1.08069e6i −0.0321128 0.272261i
\(437\) 6.71907e6 3.87925e6i 1.68308 0.971728i
\(438\) 0 0
\(439\) −6.29205e6 3.63272e6i −1.55823 0.899644i −0.997427 0.0716934i \(-0.977160\pi\)
−0.560802 0.827950i \(1.31049\pi\)
\(440\) −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 \(0.407188\pi\)
−0.973203 + 0.229946i \(0.926145\pi\)
\(444\) 0 0
\(445\) −884931. 1.53275e6i −0.211841 0.366919i
\(446\) −4.42976e6 + 1.47045e6i −1.05449 + 0.350035i
\(447\) 0 0
\(448\) −98721.2 + 570388.i −0.0232389 + 0.134269i
\(449\) 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
\(452\) −1.98219e6 2.65671e6i −0.456352 0.611644i
\(453\) 0 0
\(454\) −794216. 2.39260e6i −0.180842 0.544791i
\(455\) −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 0.351089 0.936342i \(-0.385811\pi\)
0.986441 + 0.164119i \(0.0524781\pi\)
\(464\) 2.73714e6 + 813179.i 0.590203 + 0.175344i
\(465\) 0 0
\(466\) −2.04580e6 1.81868e6i −0.436414 0.387965i
\(467\) −3.96727e6 −0.841782 −0.420891 0.907111i \(-0.638283\pi\)
−0.420891 + 0.907111i \(0.638283\pi\)
\(468\) 0 0
\(469\) 367489. 0.0771457
\(470\) 212956. + 189314.i 0.0444678 + 0.0395311i
\(471\) 0 0
\(472\) −337748. + 3.93186e6i −0.0697810 + 0.812351i
\(473\) −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 \(-0.555718\pi\)
0.939867 0.341540i \(-0.110948\pi\)
\(480\) 0 0
\(481\) −195353. 338362.i −0.0384997 0.0666835i
\(482\) −763418. 2.29982e6i −0.149673 0.450895i
\(483\) 0 0
\(484\) 2.02554e6 1.51127e6i 0.393031 0.293243i
\(485\) 1.17562e6i 0.226940i
\(486\) 0 0
\(487\) 1.17689e6i 0.224860i 0.993660 + 0.112430i \(0.0358634\pi\)
−0.993660 + 0.112430i \(0.964137\pi\)
\(488\) −5.86719e6 + 2.74718e6i −1.11527 + 0.522202i
\(489\) 0 0
\(490\) −1.31535e6 + 436627.i −0.247486 + 0.0821524i
\(491\) −730305. 1.26493e6i −0.136710 0.236789i 0.789539 0.613700i \(-0.210320\pi\)
−0.926249 + 0.376911i \(0.876986\pi\)
\(492\) 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 \(-0.789022\pi\)
0.138758 + 0.990326i \(0.455689\pi\)
\(500\) −2.84602e6 + 335685.i −0.509111 + 0.0600491i
\(501\) 0 0
\(502\) −631562. + 710432.i −0.111855 + 0.125824i
\(503\) −3.55656e6 −0.626773 −0.313387 0.949626i \(-0.601464\pi\)
−0.313387 + 0.949626i \(0.601464\pi\)
\(504\) 0 0
\(505\) 2.00059e6 0.349083
\(506\) 5.00536e6 5.63043e6i 0.869079 0.977610i
\(507\) 0 0
\(508\) −1.02824e7 + 1.21280e6i −1.76781 + 0.208512i
\(509\) −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
\(518\) 438572. 145583.i 0.0718153 0.0238389i
\(519\) 0 0
\(520\) −96331.6 205736.i −0.0156229 0.0333659i
\(521\) 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 \(0.345316\pi\)
−0.467053 + 0.884230i \(0.654684\pi\)
\(524\) −3.64182e6 + 2.71719e6i −0.579416 + 0.432307i
\(525\) 0 0
\(526\) 1.65830e6 + 4.99568e6i 0.261336 + 0.787282i
\(527\) −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
\(536\) 3.75183e6 + 322283.i 0.564068 + 0.0484535i
\(537\) 0 0
\(538\) −4.34332e6 3.86114e6i −0.646943 0.575121i
\(539\) −4.72562e6 −0.700627
\(540\) 0 0
\(541\) −3.00701e6 −0.441715 −0.220858 0.975306i \(-0.570886\pi\)
−0.220858 + 0.975306i \(0.570886\pi\)
\(542\) 7.05962e6 + 6.27588e6i 1.03225 + 0.917649i
\(543\) 0 0
\(544\) 8.21866e6 + 4.40362e6i 1.19070 + 0.637989i
\(545\) −437418. + 252543.i −0.0630820 + 0.0364204i
\(546\) 0 0
\(547\) −1.52151e6 878446.i −0.217424 0.125530i 0.387333 0.921940i \(-0.373396\pi\)
−0.604757 + 0.796410i \(0.706730\pi\)
\(548\) 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
\(554\) −1.89353e6 5.70432e6i −0.262119 0.789641i
\(555\) 0 0
\(556\) 6.86930e6 + 9.20686e6i 0.942379 + 1.26306i
\(557\) 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
\(560\) 261312. 62512.6i 0.0352119 0.00842360i
\(561\) 0 0
\(562\) −4.51856e6 + 1.49992e6i −0.603474 + 0.200322i
\(563\) −2.79625e6 4.84324e6i −0.371796 0.643969i 0.618046 0.786142i \(-0.287925\pi\)
−0.989842 + 0.142173i \(0.954591\pi\)
\(564\) 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 −0.338933 0.940811i \(-0.610066\pi\)
0.645300 + 0.763930i \(0.276733\pi\)
\(572\) −90733.4 769261.i −0.0115952 0.0983068i
\(573\) 0 0
\(574\) 752114. 846038.i 0.0952805 0.107179i
\(575\) 1.35013e7 1.70296
\(576\) 0 0
\(577\) −9.66103e6 −1.20805 −0.604024 0.796966i \(-0.706437\pi\)
−0.604024 + 0.796966i \(0.706437\pi\)
\(578\) 4.40151e6 4.95118e6i 0.548002 0.616437i
\(579\) 0 0
\(580\) −155246. 1.31622e6i −0.0191625 0.162464i
\(581\) −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 \(0.358017\pi\)
−0.996995 + 0.0774689i \(0.975316\pi\)
\(588\) 0 0
\(589\) −2.68015e6 4.64215e6i −0.318325 0.551355i
\(590\) 1.73845e6 577072.i 0.205604 0.0682496i
\(591\) 0 0
\(592\) 4.60522e6 1.10169e6i 0.540065 0.129198i
\(593\) 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
\(596\) −3.87174e6 5.18926e6i −0.446469 0.598397i
\(597\) 0 0
\(598\) 699973. + 2.10869e6i 0.0800439 + 0.241134i
\(599\) 8.44536e6 + 1.46278e7i 0.961726 + 1.66576i 0.718166 + 0.695872i \(0.244982\pi\)
0.243560 + 0.969886i \(0.421685\pi\)
\(600\) 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 −0.386091 0.922461i \(-0.626175\pi\)
0.605829 + 0.795595i \(0.292841\pi\)
\(608\) 8.52174e6 + 4.56602e6i 0.934909 + 0.500932i
\(609\) 0 0
\(610\) 2.24738e6 + 1.99789e6i 0.244541 + 0.217393i
\(611\) −286535. −0.0310509
\(612\) 0 0
\(613\) −1.18649e7 −1.27531 −0.637653 0.770324i \(-0.720095\pi\)
−0.637653 + 0.770324i \(0.720095\pi\)
\(614\) −5.00079e6 4.44562e6i −0.535325 0.475895i
\(615\) 0 0
\(616\) 912781. + 78408.0i 0.0969203 + 0.00832547i
\(617\) −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 0.111685 0.993744i \(-0.464375\pi\)
−0.804764 + 0.593594i \(0.797708\pi\)
\(620\) −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
\(626\) 465421. + 1.40209e6i 0.0474690 + 0.143002i
\(627\) 0 0
\(628\) 1.22191e7 9.11675e6i 1.23635 0.922446i
\(629\) 7.44330e6i 0.750134i
\(630\) 0 0
\(631\) 1.69017e7i 1.68988i −0.534861 0.844940i \(-0.679636\pi\)
0.534861 0.844940i \(-0.320364\pi\)
\(632\) 6.74055e6 + 1.43958e7i 0.671278 + 1.43365i
\(633\) 0 0
\(634\) 3.28366e6 1.09000e6i 0.324440 0.107697i
\(635\) 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 −0.636809 0.771022i \(-0.719746\pi\)
0.349320 + 0.937003i \(0.386413\pi\)
\(644\) −2.60975e6 + 307818.i −0.247962 + 0.0292468i
\(645\) 0 0
\(646\) 1.00971e7 1.13580e7i 0.951949 1.07083i
\(647\) 2.88799e6 0.271229 0.135614 0.990762i \(-0.456699\pi\)
0.135614 + 0.990762i \(0.456699\pi\)
\(648\) 0 0
\(649\) 6.24566e6 0.582058
\(650\) 922309. 1.03749e6i 0.0856235 0.0963163i
\(651\) 0 0
\(652\) −7.74090e6 + 913030.i −0.713136 + 0.0841136i
\(653\) −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 −0.918437 0.395566i \(-0.870548\pi\)
0.801789 + 0.597607i \(0.203882\pi\)
\(660\) 0 0
\(661\) 6.08660e6 + 1.05423e7i 0.541840 + 0.938494i 0.998798 + 0.0490059i \(0.0156053\pi\)
−0.456959 + 0.889488i \(0.651061\pi\)
\(662\) −5.28936e6 + 1.75579e6i −0.469092 + 0.155714i
\(663\) 0 0
\(664\) −4.01150e6 + 1.87830e6i −0.353091 + 0.165327i
\(665\) 437927.i 0.0384015i
\(666\) 0 0
\(667\) 1.29624e7i 1.12816i
\(668\) 1.08166e6 807033.i 0.0937883 0.0699761i
\(669\) 0 0
\(670\) −550649. 1.65884e6i −0.0473901 0.142764i
\(671\) 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
\(680\) 370397. 4.31195e6i 0.0307182 0.357603i
\(681\) 0 0
\(682\) −3.89003e6 3.45817e6i −0.320252 0.284698i
\(683\) −1.16442e7 −0.955123 −0.477562 0.878598i \(-0.658479\pi\)
−0.477562 + 0.878598i \(0.658479\pi\)
\(684\) 0 0
\(685\) −886917. −0.0722199
\(686\) 2.48721e6 + 2.21109e6i 0.201791 + 0.179389i
\(687\) 0 0
\(688\) 1.40502e7 + 4.17420e6i 1.13165 + 0.336203i
\(689\) −2.27335e6 + 1.31252e6i −0.182439 + 0.105331i
\(690\) 0 0
\(691\) 1.57763e7 + 9.10845e6i 1.25693 + 0.725687i 0.972476 0.233004i \(-0.0748555\pi\)
0.284451 + 0.958691i \(0.408189\pi\)
\(692\) −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
\(698\) 3.33509e6 + 1.00470e7i 0.259101 + 0.780547i
\(699\) 0 0
\(700\) 981830. + 1.31594e6i 0.0757341 + 0.101506i
\(701\) 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
\(704\) 9.25016e6 + 1.60099e6i 0.703424 + 0.121747i
\(705\) 0 0
\(706\) 7.42045e6 2.46320e6i 0.560297 0.185989i
\(707\) −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
\(716\) 990731. + 8.39967e6i 0.0722226 + 0.612322i
\(717\) 0 0
\(718\) −1.72486e7 + 1.94026e7i −1.24865 + 1.40459i
\(719\) −3.66390e6 −0.264315 −0.132157 0.991229i \(-0.542190\pi\)
−0.132157 + 0.991229i \(0.542190\pi\)
\(720\) 0 0
\(721\) −1.77956e6 −0.127489
\(722\) 1.16317e6 1.30842e6i 0.0830422 0.0934125i
\(723\) 0 0
\(724\) −1.90485e6 1.61498e7i −0.135056 1.14504i
\(725\) 7.01372e6 4.04938e6i 0.495568 0.286117i
\(726\) 0 0
\(727\) −5.20680e6 3.00615e6i −0.365372 0.210948i 0.306063 0.952011i \(-0.400988\pi\)
−0.671435 + 0.741064i \(0.734322\pi\)
\(728\) −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 \(0.700762\pi\)
\(734\) −1.97176e6 + 654520.i −0.135087 + 0.0448418i
\(735\) 0 0
\(736\) −2.69139e7 + 853904.i −1.83140 + 0.0581051i
\(737\) 5.95968e6i 0.404161i
\(738\) 0 0
\(739\) 1.44915e7i 0.976118i 0.872811 + 0.488059i \(0.162295\pi\)
−0.872811 + 0.488059i \(0.837705\pi\)
\(740\) −1.31432e6 1.76157e6i −0.0882313 0.118256i
\(741\) 0 0
\(742\) −978126. 2.94663e6i −0.0652206 0.196479i
\(743\) −1.03693e7 1.79602e7i −0.689094 1.19355i −0.972131 0.234436i \(-0.924676\pi\)
0.283038 0.959109i \(1.59134\pi\)
\(744\) 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 \(-0.668177\pi\)
0.495887 + 0.868387i \(0.334843\pi\)
\(752\) 988974. 3.32886e6i 0.0637735 0.214660i
\(753\) 0 0
\(754\) 996075. + 885494.i 0.0638063 + 0.0567227i
\(755\) −267818. −0.0170991
\(756\) 0 0
\(757\) 2.59573e7 1.64634 0.823170 0.567795i \(-0.192203\pi\)
0.823170 + 0.567795i \(0.192203\pi\)
\(758\) −8.24717e6 7.33159e6i −0.521353 0.463474i
\(759\) 0 0
\(760\) 384056. 4.47096e6i 0.0241191 0.280781i
\(761\) −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 \(0.612334\pi\)
\(770\) −133967. 403580.i −0.00814276 0.0245303i
\(771\) 0 0
\(772\) −1.39413e7 + 1.04017e7i −0.841902 + 0.628149i
\(773\) 4.46768e6i 0.268926i −0.990919 0.134463i \(-0.957069\pi\)
0.990919 0.134463i \(-0.0429310\pi\)
\(774\) 0 0