Properties

Label 177.5.c.a.58.11
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.11
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.30

$q$-expansion

\(f(q)\) \(=\) \(q-4.10319i q^{2} -5.19615 q^{3} -0.836195 q^{4} -39.6276 q^{5} +21.3208i q^{6} -85.8400 q^{7} -62.2200i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-4.10319i q^{2} -5.19615 q^{3} -0.836195 q^{4} -39.6276 q^{5} +21.3208i q^{6} -85.8400 q^{7} -62.2200i q^{8} +27.0000 q^{9} +162.600i q^{10} +68.0678i q^{11} +4.34500 q^{12} -254.341i q^{13} +352.218i q^{14} +205.911 q^{15} -268.680 q^{16} +229.593 q^{17} -110.786i q^{18} +425.861 q^{19} +33.1364 q^{20} +446.038 q^{21} +279.295 q^{22} +954.505i q^{23} +323.305i q^{24} +945.343 q^{25} -1043.61 q^{26} -140.296 q^{27} +71.7790 q^{28} -396.928 q^{29} -844.892i q^{30} +1421.82i q^{31} +106.925i q^{32} -353.691i q^{33} -942.065i q^{34} +3401.63 q^{35} -22.5773 q^{36} -996.969i q^{37} -1747.39i q^{38} +1321.60i q^{39} +2465.63i q^{40} -1020.06 q^{41} -1830.18i q^{42} -2587.59i q^{43} -56.9180i q^{44} -1069.94 q^{45} +3916.52 q^{46} +1477.61i q^{47} +1396.10 q^{48} +4967.50 q^{49} -3878.93i q^{50} -1193.00 q^{51} +212.679i q^{52} -3156.03 q^{53} +575.662i q^{54} -2697.36i q^{55} +5340.97i q^{56} -2212.84 q^{57} +1628.67i q^{58} +(3480.96 - 16.5981i) q^{59} -172.182 q^{60} -2170.20i q^{61} +5834.00 q^{62} -2317.68 q^{63} -3860.14 q^{64} +10078.9i q^{65} -1451.26 q^{66} -667.653i q^{67} -191.985 q^{68} -4959.75i q^{69} -13957.5i q^{70} -2586.30 q^{71} -1679.94i q^{72} -1200.66i q^{73} -4090.76 q^{74} -4912.15 q^{75} -356.103 q^{76} -5842.94i q^{77} +5422.76 q^{78} -1243.99 q^{79} +10647.1 q^{80} +729.000 q^{81} +4185.50i q^{82} +6111.54i q^{83} -372.975 q^{84} -9098.21 q^{85} -10617.4 q^{86} +2062.50 q^{87} +4235.18 q^{88} +12034.3i q^{89} +4390.19i q^{90} +21832.7i q^{91} -798.152i q^{92} -7387.98i q^{93} +6062.92 q^{94} -16875.8 q^{95} -555.600i q^{96} +16943.5i q^{97} -20382.6i q^{98} +1837.83i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.10319i 1.02580i −0.858449 0.512899i \(-0.828571\pi\)
0.858449 0.512899i \(-0.171429\pi\)
\(3\) −5.19615 −0.577350
\(4\) −0.836195 −0.0522622
\(5\) −39.6276 −1.58510 −0.792551 0.609805i \(-0.791248\pi\)
−0.792551 + 0.609805i \(0.791248\pi\)
\(6\) 21.3208i 0.592245i
\(7\) −85.8400 −1.75184 −0.875918 0.482459i \(-0.839744\pi\)
−0.875918 + 0.482459i \(0.839744\pi\)
\(8\) 62.2200i 0.972188i
\(9\) 27.0000 0.333333
\(10\) 162.600i 1.62600i
\(11\) 68.0678i 0.562544i 0.959628 + 0.281272i \(0.0907563\pi\)
−0.959628 + 0.281272i \(0.909244\pi\)
\(12\) 4.34500 0.0301736
\(13\) 254.341i 1.50498i −0.658605 0.752489i \(-0.728853\pi\)
0.658605 0.752489i \(-0.271147\pi\)
\(14\) 352.218i 1.79703i
\(15\) 205.911 0.915159
\(16\) −268.680 −1.04953
\(17\) 229.593 0.794440 0.397220 0.917724i \(-0.369975\pi\)
0.397220 + 0.917724i \(0.369975\pi\)
\(18\) 110.786i 0.341933i
\(19\) 425.861 1.17967 0.589836 0.807523i \(-0.299193\pi\)
0.589836 + 0.807523i \(0.299193\pi\)
\(20\) 33.1364 0.0828409
\(21\) 446.038 1.01142
\(22\) 279.295 0.577056
\(23\) 954.505i 1.80436i 0.431363 + 0.902178i \(0.358033\pi\)
−0.431363 + 0.902178i \(0.641967\pi\)
\(24\) 323.305i 0.561293i
\(25\) 945.343 1.51255
\(26\) −1043.61 −1.54380
\(27\) −140.296 −0.192450
\(28\) 71.7790 0.0915548
\(29\) −396.928 −0.471971 −0.235986 0.971757i \(-0.575832\pi\)
−0.235986 + 0.971757i \(0.575832\pi\)
\(30\) 844.892i 0.938769i
\(31\) 1421.82i 1.47952i 0.672871 + 0.739760i \(0.265061\pi\)
−0.672871 + 0.739760i \(0.734939\pi\)
\(32\) 106.925i 0.104419i
\(33\) 353.691i 0.324785i
\(34\) 942.065i 0.814935i
\(35\) 3401.63 2.77684
\(36\) −22.5773 −0.0174207
\(37\) 996.969i 0.728246i −0.931351 0.364123i \(-0.881369\pi\)
0.931351 0.364123i \(-0.118631\pi\)
\(38\) 1747.39i 1.21010i
\(39\) 1321.60i 0.868899i
\(40\) 2465.63i 1.54102i
\(41\) −1020.06 −0.606817 −0.303408 0.952861i \(-0.598125\pi\)
−0.303408 + 0.952861i \(0.598125\pi\)
\(42\) 1830.18i 1.03752i
\(43\) 2587.59i 1.39945i −0.714410 0.699727i \(-0.753305\pi\)
0.714410 0.699727i \(-0.246695\pi\)
\(44\) 56.9180i 0.0293998i
\(45\) −1069.94 −0.528367
\(46\) 3916.52 1.85091
\(47\) 1477.61i 0.668905i 0.942413 + 0.334452i \(0.108551\pi\)
−0.942413 + 0.334452i \(0.891449\pi\)
\(48\) 1396.10 0.605947
\(49\) 4967.50 2.06893
\(50\) 3878.93i 1.55157i
\(51\) −1193.00 −0.458670
\(52\) 212.679i 0.0786535i
\(53\) −3156.03 −1.12354 −0.561770 0.827293i \(-0.689880\pi\)
−0.561770 + 0.827293i \(0.689880\pi\)
\(54\) 575.662i 0.197415i
\(55\) 2697.36i 0.891689i
\(56\) 5340.97i 1.70311i
\(57\) −2212.84 −0.681083
\(58\) 1628.67i 0.484147i
\(59\) 3480.96 16.5981i 0.999989 0.00476820i
\(60\) −172.182 −0.0478282
\(61\) 2170.20i 0.583230i −0.956536 0.291615i \(-0.905807\pi\)
0.956536 0.291615i \(-0.0941927\pi\)
\(62\) 5834.00 1.51769
\(63\) −2317.68 −0.583946
\(64\) −3860.14 −0.942418
\(65\) 10078.9i 2.38554i
\(66\) −1451.26 −0.333164
\(67\) 667.653i 0.148731i −0.997231 0.0743655i \(-0.976307\pi\)
0.997231 0.0743655i \(-0.0236931\pi\)
\(68\) −191.985 −0.0415192
\(69\) 4959.75i 1.04175i
\(70\) 13957.5i 2.84848i
\(71\) −2586.30 −0.513054 −0.256527 0.966537i \(-0.582578\pi\)
−0.256527 + 0.966537i \(0.582578\pi\)
\(72\) 1679.94i 0.324063i
\(73\) 1200.66i 0.225306i −0.993634 0.112653i \(-0.964065\pi\)
0.993634 0.112653i \(-0.0359349\pi\)
\(74\) −4090.76 −0.747034
\(75\) −4912.15 −0.873271
\(76\) −356.103 −0.0616522
\(77\) 5842.94i 0.985485i
\(78\) 5422.76 0.891316
\(79\) −1243.99 −0.199325 −0.0996626 0.995021i \(-0.531776\pi\)
−0.0996626 + 0.995021i \(0.531776\pi\)
\(80\) 10647.1 1.66361
\(81\) 729.000 0.111111
\(82\) 4185.50i 0.622471i
\(83\) 6111.54i 0.887145i 0.896239 + 0.443572i \(0.146289\pi\)
−0.896239 + 0.443572i \(0.853711\pi\)
\(84\) −372.975 −0.0528592
\(85\) −9098.21 −1.25927
\(86\) −10617.4 −1.43556
\(87\) 2062.50 0.272493
\(88\) 4235.18 0.546898
\(89\) 12034.3i 1.51929i 0.650340 + 0.759643i \(0.274626\pi\)
−0.650340 + 0.759643i \(0.725374\pi\)
\(90\) 4390.19i 0.541998i
\(91\) 21832.7i 2.63648i
\(92\) 798.152i 0.0942997i
\(93\) 7387.98i 0.854201i
\(94\) 6062.92 0.686161
\(95\) −16875.8 −1.86990
\(96\) 555.600i 0.0602864i
\(97\) 16943.5i 1.80078i 0.435085 + 0.900389i \(0.356718\pi\)
−0.435085 + 0.900389i \(0.643282\pi\)
\(98\) 20382.6i 2.12231i
\(99\) 1837.83i 0.187515i
\(100\) −790.492 −0.0790492
\(101\) 8659.11i 0.848849i 0.905463 + 0.424424i \(0.139524\pi\)
−0.905463 + 0.424424i \(0.860476\pi\)
\(102\) 4895.11i 0.470503i
\(103\) 1183.70i 0.111575i −0.998443 0.0557873i \(-0.982233\pi\)
0.998443 0.0557873i \(-0.0177669\pi\)
\(104\) −15825.1 −1.46312
\(105\) −17675.4 −1.60321
\(106\) 12949.8i 1.15253i
\(107\) 11910.3 1.04029 0.520145 0.854078i \(-0.325878\pi\)
0.520145 + 0.854078i \(0.325878\pi\)
\(108\) 117.315 0.0100579
\(109\) 5882.90i 0.495152i 0.968868 + 0.247576i \(0.0796340\pi\)
−0.968868 + 0.247576i \(0.920366\pi\)
\(110\) −11067.8 −0.914693
\(111\) 5180.40i 0.420453i
\(112\) 23063.5 1.83861
\(113\) 21194.2i 1.65982i −0.557900 0.829908i \(-0.688393\pi\)
0.557900 0.829908i \(-0.311607\pi\)
\(114\) 9079.71i 0.698654i
\(115\) 37824.7i 2.86009i
\(116\) 331.909 0.0246663
\(117\) 6867.21i 0.501659i
\(118\) −68.1052 14283.1i −0.00489121 1.02579i
\(119\) −19708.3 −1.39173
\(120\) 12811.8i 0.889707i
\(121\) 10007.8 0.683545
\(122\) −8904.75 −0.598277
\(123\) 5300.38 0.350346
\(124\) 1188.92i 0.0773230i
\(125\) −12694.4 −0.812443
\(126\) 9509.89i 0.599010i
\(127\) 26800.6 1.66164 0.830820 0.556541i \(-0.187872\pi\)
0.830820 + 0.556541i \(0.187872\pi\)
\(128\) 17549.7i 1.07115i
\(129\) 13445.5i 0.807976i
\(130\) 41355.8 2.44709
\(131\) 1959.64i 0.114192i 0.998369 + 0.0570958i \(0.0181840\pi\)
−0.998369 + 0.0570958i \(0.981816\pi\)
\(132\) 295.754i 0.0169740i
\(133\) −36555.9 −2.06659
\(134\) −2739.51 −0.152568
\(135\) 5559.59 0.305053
\(136\) 14285.3i 0.772345i
\(137\) −3510.97 −0.187062 −0.0935310 0.995616i \(-0.529815\pi\)
−0.0935310 + 0.995616i \(0.529815\pi\)
\(138\) −20350.8 −1.06862
\(139\) −8435.85 −0.436616 −0.218308 0.975880i \(-0.570054\pi\)
−0.218308 + 0.975880i \(0.570054\pi\)
\(140\) −2844.43 −0.145124
\(141\) 7677.89i 0.386192i
\(142\) 10612.1i 0.526290i
\(143\) 17312.4 0.846616
\(144\) −7254.36 −0.349844
\(145\) 15729.3 0.748123
\(146\) −4926.52 −0.231119
\(147\) −25811.9 −1.19450
\(148\) 833.661i 0.0380597i
\(149\) 25735.7i 1.15921i 0.814896 + 0.579607i \(0.196794\pi\)
−0.814896 + 0.579607i \(0.803206\pi\)
\(150\) 20155.5i 0.895800i
\(151\) 13763.3i 0.603628i 0.953367 + 0.301814i \(0.0975921\pi\)
−0.953367 + 0.301814i \(0.902408\pi\)
\(152\) 26497.1i 1.14686i
\(153\) 6199.01 0.264813
\(154\) −23974.7 −1.01091
\(155\) 56343.2i 2.34519i
\(156\) 1105.11i 0.0454106i
\(157\) 5484.96i 0.222523i 0.993791 + 0.111261i \(0.0354891\pi\)
−0.993791 + 0.111261i \(0.964511\pi\)
\(158\) 5104.33i 0.204467i
\(159\) 16399.2 0.648676
\(160\) 4237.19i 0.165515i
\(161\) 81934.7i 3.16094i
\(162\) 2991.23i 0.113978i
\(163\) 137.440 0.00517295 0.00258648 0.999997i \(-0.499177\pi\)
0.00258648 + 0.999997i \(0.499177\pi\)
\(164\) 852.968 0.0317136
\(165\) 14015.9i 0.514817i
\(166\) 25076.8 0.910032
\(167\) −4707.17 −0.168782 −0.0843911 0.996433i \(-0.526895\pi\)
−0.0843911 + 0.996433i \(0.526895\pi\)
\(168\) 27752.5i 0.983293i
\(169\) −36128.5 −1.26496
\(170\) 37331.7i 1.29176i
\(171\) 11498.3 0.393224
\(172\) 2163.73i 0.0731386i
\(173\) 25132.5i 0.839737i 0.907585 + 0.419869i \(0.137924\pi\)
−0.907585 + 0.419869i \(0.862076\pi\)
\(174\) 8462.83i 0.279523i
\(175\) −81148.3 −2.64974
\(176\) 18288.4i 0.590407i
\(177\) −18087.6 + 86.2463i −0.577344 + 0.00275292i
\(178\) 49378.9 1.55848
\(179\) 16585.2i 0.517623i 0.965928 + 0.258811i \(0.0833308\pi\)
−0.965928 + 0.258811i \(0.916669\pi\)
\(180\) 894.682 0.0276136
\(181\) 51985.4 1.58681 0.793404 0.608695i \(-0.208307\pi\)
0.793404 + 0.608695i \(0.208307\pi\)
\(182\) 89583.6 2.70449
\(183\) 11276.7i 0.336728i
\(184\) 59389.3 1.75417
\(185\) 39507.4i 1.15434i
\(186\) −30314.3 −0.876238
\(187\) 15627.9i 0.446907i
\(188\) 1235.57i 0.0349584i
\(189\) 12043.0 0.337141
\(190\) 69244.8i 1.91814i
\(191\) 39194.8i 1.07439i −0.843458 0.537195i \(-0.819484\pi\)
0.843458 0.537195i \(-0.180516\pi\)
\(192\) 20057.9 0.544105
\(193\) 36220.3 0.972384 0.486192 0.873852i \(-0.338386\pi\)
0.486192 + 0.873852i \(0.338386\pi\)
\(194\) 69522.6 1.84724
\(195\) 52371.6i 1.37729i
\(196\) −4153.80 −0.108127
\(197\) 37466.1 0.965396 0.482698 0.875787i \(-0.339657\pi\)
0.482698 + 0.875787i \(0.339657\pi\)
\(198\) 7540.97 0.192352
\(199\) −76403.0 −1.92932 −0.964660 0.263497i \(-0.915124\pi\)
−0.964660 + 0.263497i \(0.915124\pi\)
\(200\) 58819.3i 1.47048i
\(201\) 3469.23i 0.0858698i
\(202\) 35530.0 0.870748
\(203\) 34072.3 0.826817
\(204\) 997.581 0.0239711
\(205\) 40422.4 0.961866
\(206\) −4856.93 −0.114453
\(207\) 25771.6i 0.601452i
\(208\) 68336.4i 1.57952i
\(209\) 28987.4i 0.663616i
\(210\) 72525.5i 1.64457i
\(211\) 24399.1i 0.548036i −0.961725 0.274018i \(-0.911647\pi\)
0.961725 0.274018i \(-0.0883527\pi\)
\(212\) 2639.05 0.0587187
\(213\) 13438.8 0.296212
\(214\) 48870.2i 1.06713i
\(215\) 102540.i 2.21828i
\(216\) 8729.23i 0.187098i
\(217\) 122049.i 2.59188i
\(218\) 24138.7 0.507926
\(219\) 6238.79i 0.130081i
\(220\) 2255.52i 0.0466016i
\(221\) 58395.0i 1.19561i
\(222\) 21256.2 0.431300
\(223\) −26520.0 −0.533290 −0.266645 0.963795i \(-0.585915\pi\)
−0.266645 + 0.963795i \(0.585915\pi\)
\(224\) 9178.46i 0.182925i
\(225\) 25524.3 0.504183
\(226\) −86963.9 −1.70264
\(227\) 71618.1i 1.38986i 0.719077 + 0.694930i \(0.244565\pi\)
−0.719077 + 0.694930i \(0.755435\pi\)
\(228\) 1850.37 0.0355949
\(229\) 42669.2i 0.813660i 0.913504 + 0.406830i \(0.133366\pi\)
−0.913504 + 0.406830i \(0.866634\pi\)
\(230\) −155202. −2.93388
\(231\) 30360.8i 0.568970i
\(232\) 24696.9i 0.458845i
\(233\) 68586.1i 1.26335i 0.775233 + 0.631676i \(0.217633\pi\)
−0.775233 + 0.631676i \(0.782367\pi\)
\(234\) −28177.5 −0.514601
\(235\) 58554.1i 1.06028i
\(236\) −2910.76 + 13.8793i −0.0522616 + 0.000249197i
\(237\) 6463.95 0.115080
\(238\) 80866.8i 1.42763i
\(239\) 963.908 0.0168749 0.00843743 0.999964i \(-0.497314\pi\)
0.00843743 + 0.999964i \(0.497314\pi\)
\(240\) −55324.1 −0.960488
\(241\) 16329.4 0.281149 0.140574 0.990070i \(-0.455105\pi\)
0.140574 + 0.990070i \(0.455105\pi\)
\(242\) 41063.8i 0.701179i
\(243\) −3788.00 −0.0641500
\(244\) 1814.71i 0.0304809i
\(245\) −196850. −3.27947
\(246\) 21748.5i 0.359384i
\(247\) 108314.i 1.77538i
\(248\) 88465.6 1.43837
\(249\) 31756.5i 0.512193i
\(250\) 52087.7i 0.833403i
\(251\) 57856.7 0.918346 0.459173 0.888347i \(-0.348146\pi\)
0.459173 + 0.888347i \(0.348146\pi\)
\(252\) 1938.03 0.0305183
\(253\) −64971.0 −1.01503
\(254\) 109968.i 1.70451i
\(255\) 47275.7 0.727039
\(256\) 10247.6 0.156366
\(257\) −94257.4 −1.42708 −0.713542 0.700613i \(-0.752910\pi\)
−0.713542 + 0.700613i \(0.752910\pi\)
\(258\) 55169.6 0.828820
\(259\) 85579.8i 1.27577i
\(260\) 8427.95i 0.124674i
\(261\) −10717.1 −0.157324
\(262\) 8040.79 0.117137
\(263\) 6388.77 0.0923646 0.0461823 0.998933i \(-0.485294\pi\)
0.0461823 + 0.998933i \(0.485294\pi\)
\(264\) −22006.6 −0.315752
\(265\) 125066. 1.78093
\(266\) 149996.i 2.11991i
\(267\) 62531.9i 0.877160i
\(268\) 558.288i 0.00777301i
\(269\) 50975.4i 0.704460i −0.935914 0.352230i \(-0.885424\pi\)
0.935914 0.352230i \(-0.114576\pi\)
\(270\) 22812.1i 0.312923i
\(271\) 103419. 1.40820 0.704098 0.710103i \(-0.251352\pi\)
0.704098 + 0.710103i \(0.251352\pi\)
\(272\) −61687.0 −0.833789
\(273\) 113446.i 1.52217i
\(274\) 14406.2i 0.191888i
\(275\) 64347.4i 0.850875i
\(276\) 4147.32i 0.0544439i
\(277\) −118682. −1.54676 −0.773381 0.633941i \(-0.781436\pi\)
−0.773381 + 0.633941i \(0.781436\pi\)
\(278\) 34613.9i 0.447879i
\(279\) 38389.1i 0.493173i
\(280\) 211649.i 2.69961i
\(281\) −63690.0 −0.806600 −0.403300 0.915068i \(-0.632137\pi\)
−0.403300 + 0.915068i \(0.632137\pi\)
\(282\) −31503.9 −0.396155
\(283\) 7522.96i 0.0939325i 0.998896 + 0.0469662i \(0.0149553\pi\)
−0.998896 + 0.0469662i \(0.985045\pi\)
\(284\) 2162.66 0.0268133
\(285\) 87689.4 1.07959
\(286\) 71036.3i 0.868457i
\(287\) 87561.8 1.06304
\(288\) 2886.98i 0.0348064i
\(289\) −30808.0 −0.368866
\(290\) 64540.3i 0.767423i
\(291\) 88041.1i 1.03968i
\(292\) 1003.98i 0.0117750i
\(293\) −32964.4 −0.383981 −0.191990 0.981397i \(-0.561494\pi\)
−0.191990 + 0.981397i \(0.561494\pi\)
\(294\) 105911.i 1.22531i
\(295\) −137942. + 657.742i −1.58508 + 0.00755809i
\(296\) −62031.4 −0.707992
\(297\) 9549.65i 0.108262i
\(298\) 105599. 1.18912
\(299\) 242770. 2.71552
\(300\) 4107.52 0.0456391
\(301\) 222119.i 2.45162i
\(302\) 56473.5 0.619200
\(303\) 44994.0i 0.490083i
\(304\) −114420. −1.23810
\(305\) 85999.7i 0.924480i
\(306\) 25435.7i 0.271645i
\(307\) −85864.5 −0.911039 −0.455520 0.890226i \(-0.650547\pi\)
−0.455520 + 0.890226i \(0.650547\pi\)
\(308\) 4885.84i 0.0515036i
\(309\) 6150.66i 0.0644177i
\(310\) −231187. −2.40569
\(311\) −20927.4 −0.216368 −0.108184 0.994131i \(-0.534504\pi\)
−0.108184 + 0.994131i \(0.534504\pi\)
\(312\) 82229.7 0.844733
\(313\) 132516.i 1.35264i −0.736610 0.676318i \(-0.763575\pi\)
0.736610 0.676318i \(-0.236425\pi\)
\(314\) 22505.9 0.228263
\(315\) 91844.0 0.925613
\(316\) 1040.22 0.0104172
\(317\) −108659. −1.08130 −0.540649 0.841248i \(-0.681821\pi\)
−0.540649 + 0.841248i \(0.681821\pi\)
\(318\) 67289.0i 0.665411i
\(319\) 27018.0i 0.265504i
\(320\) 152968. 1.49383
\(321\) −61887.6 −0.600611
\(322\) −336194. −3.24249
\(323\) 97774.8 0.937177
\(324\) −609.586 −0.00580691
\(325\) 240440.i 2.27635i
\(326\) 563.944i 0.00530641i
\(327\) 30568.5i 0.285876i
\(328\) 63468.1i 0.589940i
\(329\) 126838.i 1.17181i
\(330\) 57509.9 0.528098
\(331\) −101850. −0.929619 −0.464809 0.885411i \(-0.653877\pi\)
−0.464809 + 0.885411i \(0.653877\pi\)
\(332\) 5110.44i 0.0463641i
\(333\) 26918.2i 0.242749i
\(334\) 19314.4i 0.173137i
\(335\) 26457.5i 0.235754i
\(336\) −119841. −1.06152
\(337\) 74871.2i 0.659258i −0.944111 0.329629i \(-0.893076\pi\)
0.944111 0.329629i \(-0.106924\pi\)
\(338\) 148242.i 1.29759i
\(339\) 110128.i 0.958295i
\(340\) 7607.88 0.0658121
\(341\) −96780.0 −0.832294
\(342\) 47179.6i 0.403368i
\(343\) −220309. −1.87259
\(344\) −161000. −1.36053
\(345\) 196543.i 1.65127i
\(346\) 103123. 0.861401
\(347\) 90583.5i 0.752298i −0.926559 0.376149i \(-0.877248\pi\)
0.926559 0.376149i \(-0.122752\pi\)
\(348\) −1724.65 −0.0142411
\(349\) 134492.i 1.10420i 0.833779 + 0.552098i \(0.186172\pi\)
−0.833779 + 0.552098i \(0.813828\pi\)
\(350\) 332967.i 2.71810i
\(351\) 35683.1i 0.289633i
\(352\) −7278.16 −0.0587403
\(353\) 81414.3i 0.653358i 0.945135 + 0.326679i \(0.105930\pi\)
−0.945135 + 0.326679i \(0.894070\pi\)
\(354\) 353.885 + 74216.9i 0.00282394 + 0.592238i
\(355\) 102489. 0.813243
\(356\) 10063.0i 0.0794013i
\(357\) 102407. 0.803515
\(358\) 68052.1 0.530977
\(359\) 64385.0 0.499570 0.249785 0.968301i \(-0.419640\pi\)
0.249785 + 0.968301i \(0.419640\pi\)
\(360\) 66571.9i 0.513672i
\(361\) 51036.8 0.391624
\(362\) 213306.i 1.62775i
\(363\) −52001.9 −0.394645
\(364\) 18256.4i 0.137788i
\(365\) 47579.1i 0.357133i
\(366\) 46270.4 0.345415
\(367\) 129178.i 0.959083i 0.877519 + 0.479541i \(0.159197\pi\)
−0.877519 + 0.479541i \(0.840803\pi\)
\(368\) 256456.i 1.89373i
\(369\) −27541.6 −0.202272
\(370\) 162107. 1.18412
\(371\) 270913. 1.96826
\(372\) 6177.80i 0.0446424i
\(373\) −71866.8 −0.516548 −0.258274 0.966072i \(-0.583154\pi\)
−0.258274 + 0.966072i \(0.583154\pi\)
\(374\) 64124.3 0.458436
\(375\) 65962.2 0.469064
\(376\) 91936.9 0.650301
\(377\) 100955.i 0.710306i
\(378\) 49414.8i 0.345839i
\(379\) 85467.7 0.595009 0.297504 0.954720i \(-0.403846\pi\)
0.297504 + 0.954720i \(0.403846\pi\)
\(380\) 14111.5 0.0977251
\(381\) −139260. −0.959349
\(382\) −160824. −1.10211
\(383\) 278371. 1.89769 0.948846 0.315739i \(-0.102253\pi\)
0.948846 + 0.315739i \(0.102253\pi\)
\(384\) 91191.0i 0.618429i
\(385\) 231541.i 1.56209i
\(386\) 148619.i 0.997470i
\(387\) 69865.0i 0.466485i
\(388\) 14168.1i 0.0941127i
\(389\) −21226.2 −0.140273 −0.0701364 0.997537i \(-0.522343\pi\)
−0.0701364 + 0.997537i \(0.522343\pi\)
\(390\) −214891. −1.41283
\(391\) 219148.i 1.43345i
\(392\) 309078.i 2.01139i
\(393\) 10182.6i 0.0659285i
\(394\) 153731.i 0.990302i
\(395\) 49296.2 0.315951
\(396\) 1536.78i 0.00979992i
\(397\) 45611.1i 0.289394i 0.989476 + 0.144697i \(0.0462208\pi\)
−0.989476 + 0.144697i \(0.953779\pi\)
\(398\) 313496.i 1.97909i
\(399\) 189950. 1.19315
\(400\) −253995. −1.58747
\(401\) 56817.4i 0.353340i 0.984270 + 0.176670i \(0.0565325\pi\)
−0.984270 + 0.176670i \(0.943468\pi\)
\(402\) 14234.9 0.0880851
\(403\) 361627. 2.22664
\(404\) 7240.70i 0.0443627i
\(405\) −28888.5 −0.176122
\(406\) 139805.i 0.848147i
\(407\) 67861.5 0.409670
\(408\) 74228.5i 0.445913i
\(409\) 152246.i 0.910123i 0.890460 + 0.455061i \(0.150383\pi\)
−0.890460 + 0.455061i \(0.849617\pi\)
\(410\) 165861.i 0.986681i
\(411\) 18243.5 0.108000
\(412\) 989.801i 0.00583114i
\(413\) −298806. + 1424.78i −1.75182 + 0.00835311i
\(414\) 105746. 0.616969
\(415\) 242185.i 1.40622i
\(416\) 27195.5 0.157149
\(417\) 43834.0 0.252080
\(418\) 118941. 0.680737
\(419\) 14956.8i 0.0851945i 0.999092 + 0.0425972i \(0.0135632\pi\)
−0.999092 + 0.0425972i \(0.986437\pi\)
\(420\) 14780.1 0.0837873
\(421\) 192146.i 1.08410i 0.840347 + 0.542048i \(0.182351\pi\)
−0.840347 + 0.542048i \(0.817649\pi\)
\(422\) −100114. −0.562174
\(423\) 39895.5i 0.222968i
\(424\) 196368.i 1.09229i
\(425\) 217044. 1.20163
\(426\) 55142.1i 0.303854i
\(427\) 186290.i 1.02172i
\(428\) −9959.31 −0.0543678
\(429\) −89958.1 −0.488794
\(430\) 420741. 2.27551
\(431\) 134989.i 0.726679i 0.931657 + 0.363340i \(0.118364\pi\)
−0.931657 + 0.363340i \(0.881636\pi\)
\(432\) 37694.7 0.201982
\(433\) −27732.6 −0.147916 −0.0739580 0.997261i \(-0.523563\pi\)
−0.0739580 + 0.997261i \(0.523563\pi\)
\(434\) −500790. −2.65874
\(435\) −81731.7 −0.431929
\(436\) 4919.25i 0.0258777i
\(437\) 406487.i 2.12855i
\(438\) 25599.0 0.133436
\(439\) −256732. −1.33215 −0.666073 0.745887i \(-0.732026\pi\)
−0.666073 + 0.745887i \(0.732026\pi\)
\(440\) −167830. −0.866889
\(441\) 134123. 0.689644
\(442\) −239606. −1.22646
\(443\) 104213.i 0.531022i 0.964108 + 0.265511i \(0.0855407\pi\)
−0.964108 + 0.265511i \(0.914459\pi\)
\(444\) 4331.83i 0.0219738i
\(445\) 476889.i 2.40822i
\(446\) 108817.i 0.547048i
\(447\) 133727.i 0.669272i
\(448\) 331355. 1.65096
\(449\) 15237.3 0.0755814 0.0377907 0.999286i \(-0.487968\pi\)
0.0377907 + 0.999286i \(0.487968\pi\)
\(450\) 104731.i 0.517190i
\(451\) 69433.1i 0.341361i
\(452\) 17722.5i 0.0867457i
\(453\) 71516.3i 0.348505i
\(454\) 293863. 1.42572
\(455\) 865175.i 4.17908i
\(456\) 137683.i 0.662141i
\(457\) 351744.i 1.68420i −0.539318 0.842102i \(-0.681318\pi\)
0.539318 0.842102i \(-0.318682\pi\)
\(458\) 175080. 0.834651
\(459\) −32211.0 −0.152890
\(460\) 31628.8i 0.149475i
\(461\) −91900.9 −0.432432 −0.216216 0.976346i \(-0.569372\pi\)
−0.216216 + 0.976346i \(0.569372\pi\)
\(462\) 124576. 0.583648
\(463\) 284633.i 1.32777i 0.747835 + 0.663885i \(0.231093\pi\)
−0.747835 + 0.663885i \(0.768907\pi\)
\(464\) 106647. 0.495348
\(465\) 292768.i 1.35400i
\(466\) 281422. 1.29594
\(467\) 304437.i 1.39593i −0.716132 0.697965i \(-0.754089\pi\)
0.716132 0.697965i \(-0.245911\pi\)
\(468\) 5742.33i 0.0262178i
\(469\) 57311.3i 0.260552i
\(470\) −240259. −1.08764
\(471\) 28500.7i 0.128474i
\(472\) −1032.73 216585.i −0.00463559 0.972177i
\(473\) 176132. 0.787254
\(474\) 26522.9i 0.118049i
\(475\) 402585. 1.78431
\(476\) 16480.0 0.0727348
\(477\) −85212.7 −0.374514
\(478\) 3955.10i 0.0173102i
\(479\) 397464. 1.73231 0.866157 0.499772i \(-0.166583\pi\)
0.866157 + 0.499772i \(0.166583\pi\)
\(480\) 22017.1i 0.0955602i
\(481\) −253570. −1.09599
\(482\) 67002.7i 0.288402i
\(483\) 425745.i 1.82497i
\(484\) −8368.46 −0.0357235
\(485\) 671431.i 2.85442i
\(486\) 15542.9i 0.0658050i
\(487\) −157762. −0.665187 −0.332593 0.943070i \(-0.607924\pi\)
−0.332593 + 0.943070i \(0.607924\pi\)
\(488\) −135030. −0.567010
\(489\) −714.160 −0.00298660
\(490\) 807714.i 3.36407i
\(491\) 76943.9 0.319162 0.159581 0.987185i \(-0.448986\pi\)
0.159581 + 0.987185i \(0.448986\pi\)
\(492\) −4432.15 −0.0183098
\(493\) −91131.9 −0.374953
\(494\) −444434. −1.82118
\(495\) 72828.7i 0.297230i
\(496\) 382014.i 1.55280i
\(497\) 222008. 0.898787
\(498\) −130303. −0.525407
\(499\) 1118.26 0.00449100 0.00224550 0.999997i \(-0.499285\pi\)
0.00224550 + 0.999997i \(0.499285\pi\)
\(500\) 10615.0 0.0424601
\(501\) 24459.2 0.0974465
\(502\) 237397.i 0.942038i
\(503\) 143292.i 0.566351i −0.959068 0.283176i \(-0.908612\pi\)
0.959068 0.283176i \(-0.0913879\pi\)
\(504\) 144206.i 0.567705i
\(505\) 343139.i 1.34551i
\(506\) 266589.i 1.04122i
\(507\) 187729. 0.730324
\(508\) −22410.5 −0.0868410
\(509\) 39802.5i 0.153630i 0.997045 + 0.0768148i \(0.0244750\pi\)
−0.997045 + 0.0768148i \(0.975525\pi\)
\(510\) 193981.i 0.745795i
\(511\) 103064.i 0.394699i
\(512\) 238748.i 0.910750i
\(513\) −59746.7 −0.227028
\(514\) 386756.i 1.46390i
\(515\) 46907.0i 0.176857i
\(516\) 11243.1i 0.0422266i
\(517\) −100578. −0.376288
\(518\) 351150. 1.30868
\(519\) 130592.i 0.484823i
\(520\) 627111. 2.31920
\(521\) −228531. −0.841917 −0.420958 0.907080i \(-0.638306\pi\)
−0.420958 + 0.907080i \(0.638306\pi\)
\(522\) 43974.1i 0.161382i
\(523\) 508793. 1.86011 0.930054 0.367423i \(-0.119760\pi\)
0.930054 + 0.367423i \(0.119760\pi\)
\(524\) 1638.64i 0.00596790i
\(525\) 421659. 1.52983
\(526\) 26214.4i 0.0947475i
\(527\) 326440.i 1.17539i
\(528\) 95029.5i 0.340872i
\(529\) −631238. −2.25570
\(530\) 513168.i 1.82687i
\(531\) 93985.9 448.149i 0.333330 0.00158940i
\(532\) 30567.9 0.108005
\(533\) 259443.i 0.913246i
\(534\) −256580. −0.899790
\(535\) −471975. −1.64897
\(536\) −41541.4 −0.144594
\(537\) 86179.0i 0.298850i
\(538\) −209162. −0.722634
\(539\) 338127.i 1.16386i
\(540\) −4648.90 −0.0159427
\(541\) 560174.i 1.91394i −0.290187 0.956970i \(-0.593718\pi\)
0.290187 0.956970i \(-0.406282\pi\)
\(542\) 424349.i 1.44452i
\(543\) −270124. −0.916144
\(544\) 24549.3i 0.0829547i
\(545\) 233125.i 0.784867i
\(546\) −465490. −1.56144
\(547\) −273979. −0.915679 −0.457839 0.889035i \(-0.651377\pi\)
−0.457839 + 0.889035i \(0.651377\pi\)
\(548\) 2935.85 0.00977627
\(549\) 58595.4i 0.194410i
\(550\) 264030. 0.872826
\(551\) −169036. −0.556771
\(552\) −308596. −1.01277
\(553\) 106784. 0.349185
\(554\) 486973.i 1.58667i
\(555\) 205287.i 0.666461i
\(556\) 7054.02 0.0228185
\(557\) 339532. 1.09439 0.547193 0.837006i \(-0.315696\pi\)
0.547193 + 0.837006i \(0.315696\pi\)
\(558\) 157518. 0.505896
\(559\) −658131. −2.10615
\(560\) −913949. −2.91438
\(561\) 81204.9i 0.258022i
\(562\) 261332.i 0.827409i
\(563\) 92097.7i 0.290558i 0.989391 + 0.145279i \(0.0464079\pi\)
−0.989391 + 0.145279i \(0.953592\pi\)
\(564\) 6420.21i 0.0201833i
\(565\) 839874.i 2.63098i
\(566\) 30868.1 0.0963558
\(567\) −62577.4 −0.194649
\(568\) 160920.i 0.498785i
\(569\) 443913.i 1.37111i −0.728019 0.685557i \(-0.759559\pi\)
0.728019 0.685557i \(-0.240441\pi\)
\(570\) 359807.i 1.10744i
\(571\) 254417.i 0.780321i −0.920747 0.390161i \(-0.872419\pi\)
0.920747 0.390161i \(-0.127581\pi\)
\(572\) −14476.6 −0.0442460
\(573\) 203662.i 0.620299i
\(574\) 359283.i 1.09047i
\(575\) 902335.i 2.72918i
\(576\) −104224. −0.314139
\(577\) 311437. 0.935445 0.467723 0.883875i \(-0.345075\pi\)
0.467723 + 0.883875i \(0.345075\pi\)
\(578\) 126411.i 0.378382i
\(579\) −188206. −0.561406
\(580\) −13152.8 −0.0390985
\(581\) 524615.i 1.55413i
\(582\) −361250. −1.06650
\(583\) 214824.i 0.632041i
\(584\) −74704.8 −0.219040
\(585\) 272131.i 0.795181i
\(586\) 135259.i 0.393887i
\(587\) 581088.i 1.68642i 0.537584 + 0.843210i \(0.319337\pi\)
−0.537584 + 0.843210i \(0.680663\pi\)
\(588\) 21583.8 0.0624271
\(589\) 605497.i 1.74535i
\(590\) 2698.84 + 566003.i 0.00775307 + 1.62598i
\(591\) −194679. −0.557372
\(592\) 267866.i 0.764317i
\(593\) −218284. −0.620743 −0.310371 0.950615i \(-0.600453\pi\)
−0.310371 + 0.950615i \(0.600453\pi\)
\(594\) −39184.0 −0.111055
\(595\) 780990. 2.20603
\(596\) 21520.1i 0.0605830i
\(597\) 397002. 1.11389
\(598\) 996132.i 2.78557i
\(599\) −549532. −1.53158 −0.765789 0.643091i \(-0.777651\pi\)
−0.765789 + 0.643091i \(0.777651\pi\)
\(600\) 305634.i 0.848983i
\(601\) 611697.i 1.69351i 0.531984 + 0.846755i \(0.321447\pi\)
−0.531984 + 0.846755i \(0.678553\pi\)
\(602\) 911397. 2.51486
\(603\) 18026.6i 0.0495770i
\(604\) 11508.8i 0.0315469i
\(605\) −396584. −1.08349
\(606\) −184619. −0.502726
\(607\) 1086.59 0.00294908 0.00147454 0.999999i \(-0.499531\pi\)
0.00147454 + 0.999999i \(0.499531\pi\)
\(608\) 45535.3i 0.123180i
\(609\) −177045. −0.477363
\(610\) 352874. 0.948330
\(611\) 375817. 1.00669
\(612\) −5183.58 −0.0138397
\(613\) 331052.i 0.880999i 0.897753 + 0.440500i \(0.145199\pi\)
−0.897753 + 0.440500i \(0.854801\pi\)
\(614\) 352319.i 0.934543i
\(615\) −210041. −0.555334
\(616\) −363548. −0.958076
\(617\) −247255. −0.649492 −0.324746 0.945801i \(-0.605279\pi\)
−0.324746 + 0.945801i \(0.605279\pi\)
\(618\) 25237.4 0.0660795
\(619\) 307344. 0.802127 0.401064 0.916050i \(-0.368641\pi\)
0.401064 + 0.916050i \(0.368641\pi\)
\(620\) 47113.9i 0.122565i
\(621\) 133913.i 0.347249i
\(622\) 85869.1i 0.221950i
\(623\) 1.03302e6i 2.66154i
\(624\) 355086.i 0.911937i
\(625\) −87790.4 −0.224744
\(626\) −543740. −1.38753
\(627\) 150623.i 0.383139i
\(628\) 4586.50i 0.0116295i
\(629\) 228897.i 0.578548i
\(630\) 376854.i 0.949493i
\(631\) 469556. 1.17931 0.589657 0.807654i \(-0.299263\pi\)
0.589657 + 0.807654i \(0.299263\pi\)
\(632\) 77401.0i 0.193782i
\(633\) 126781.i 0.316409i
\(634\) 445847.i 1.10919i
\(635\) −1.06204e6 −2.63387
\(636\) −13712.9 −0.0339013
\(637\) 1.26344e6i 3.11370i
\(638\) −110860. −0.272354
\(639\) −69830.2 −0.171018
\(640\) 695453.i 1.69788i
\(641\) 244837. 0.595882 0.297941 0.954584i \(-0.403700\pi\)
0.297941 + 0.954584i \(0.403700\pi\)
\(642\) 253937.i 0.616106i
\(643\) −199751. −0.483133 −0.241567 0.970384i \(-0.577661\pi\)
−0.241567 + 0.970384i \(0.577661\pi\)
\(644\) 68513.4i 0.165198i
\(645\) 532813.i 1.28072i
\(646\) 401189.i 0.961355i
\(647\) 406276. 0.970538 0.485269 0.874365i \(-0.338722\pi\)
0.485269 + 0.874365i \(0.338722\pi\)
\(648\) 45358.4i 0.108021i
\(649\) 1129.80 + 236941.i 0.00268232 + 0.562537i
\(650\) −986571. −2.33508
\(651\) 634185.i 1.49642i
\(652\) −114.927 −0.000270350
\(653\) 334544. 0.784562 0.392281 0.919845i \(-0.371686\pi\)
0.392281 + 0.919845i \(0.371686\pi\)
\(654\) −125428. −0.293251
\(655\) 77655.8i 0.181005i
\(656\) 274069. 0.636873
\(657\) 32417.7i 0.0751020i
\(658\) −520441. −1.20204
\(659\) 286185.i 0.658986i 0.944158 + 0.329493i \(0.106878\pi\)
−0.944158 + 0.329493i \(0.893122\pi\)
\(660\) 11720.0i 0.0269055i
\(661\) 759053. 1.73728 0.868639 0.495446i \(-0.164995\pi\)
0.868639 + 0.495446i \(0.164995\pi\)
\(662\) 417910.i 0.953601i
\(663\) 303429.i 0.690288i
\(664\) 380260. 0.862471
\(665\) 1.44862e6 3.27576
\(666\) −110450. −0.249011
\(667\) 378870.i 0.851605i
\(668\) 3936.11 0.00882093
\(669\) 137802. 0.307895
\(670\) 108560. 0.241836
\(671\) 147721. 0.328093
\(672\) 47692.7i 0.105612i
\(673\) 664503.i 1.46712i 0.679622 + 0.733562i \(0.262144\pi\)
−0.679622 + 0.733562i \(0.737856\pi\)
\(674\) −307211. −0.676265
\(675\) −132628. −0.291090
\(676\) 30210.5 0.0661095
\(677\) −252653. −0.551249 −0.275624 0.961265i \(-0.588885\pi\)
−0.275624 + 0.961265i \(0.588885\pi\)
\(678\) 451878. 0.983018
\(679\) 1.45443e6i 3.15467i
\(680\) 566091.i 1.22425i
\(681\) 372139.i 0.802436i
\(682\) 397107.i 0.853766i
\(683\) 506823.i 1.08646i −0.839583 0.543232i \(-0.817200\pi\)
0.839583 0.543232i \(-0.182800\pi\)
\(684\) −9614.79 −0.0205507
\(685\) 139131. 0.296512
\(686\) 903969.i 1.92090i
\(687\) 221715.i 0.469767i
\(688\) 695234.i 1.46877i
\(689\) 802708.i 1.69090i
\(690\) 806453. 1.69387
\(691\) 789140.i 1.65271i 0.563146 + 0.826357i \(0.309591\pi\)
−0.563146 + 0.826357i \(0.690409\pi\)
\(692\) 21015.7i 0.0438865i
\(693\) 157759.i 0.328495i
\(694\) −371682. −0.771706
\(695\) 334292. 0.692080
\(696\) 128329.i 0.264914i
\(697\) −234198. −0.482079
\(698\) 551847. 1.13268
\(699\) 356384.i 0.729396i
\(700\) 67855.8 0.138481
\(701\) 259759.i 0.528608i −0.964439 0.264304i \(-0.914858\pi\)
0.964439 0.264304i \(-0.0851423\pi\)
\(702\) 146415. 0.297105
\(703\) 424570.i 0.859091i
\(704\) 262751.i 0.530151i
\(705\) 304256.i 0.612154i
\(706\) 334059. 0.670213
\(707\) 743298.i 1.48704i
\(708\) 15124.8 72.1187i 0.0301733 0.000143874i
\(709\) 171973. 0.342112 0.171056 0.985261i \(-0.445282\pi\)
0.171056 + 0.985261i \(0.445282\pi\)
\(710\) 420532.i 0.834223i
\(711\) −33587.7 −0.0664417
\(712\) 748772. 1.47703
\(713\) −1.35713e6 −2.66958
\(714\) 420196.i 0.824244i
\(715\) −686050. −1.34197
\(716\) 13868.4i 0.0270521i
\(717\) −5008.62 −0.00974270
\(718\) 264184.i 0.512458i
\(719\) 823365.i 1.59270i 0.604835 + 0.796351i \(0.293239\pi\)
−0.604835 + 0.796351i \(0.706761\pi\)
\(720\) 287472. 0.554538
\(721\) 101608.i 0.195461i
\(722\) 209414.i 0.401727i
\(723\) −84850.0 −0.162321
\(724\) −43470.0 −0.0829301
\(725\) −375233. −0.713880
\(726\) 213374.i 0.404826i
\(727\) −403704. −0.763825 −0.381912 0.924198i \(-0.624734\pi\)
−0.381912 + 0.924198i \(0.624734\pi\)
\(728\) 1.35843e6 2.56315
\(729\) 19683.0 0.0370370
\(730\) 195226. 0.366347
\(731\) 594093.i 1.11178i
\(732\) 9429.52i 0.0175982i
\(733\) −472977. −0.880302 −0.440151 0.897924i \(-0.645075\pi\)
−0.440151 + 0.897924i \(0.645075\pi\)
\(734\) 530042. 0.983825
\(735\) 1.02286e6 1.89340
\(736\) −102061. −0.188409
\(737\) 45445.7 0.0836676
\(738\) 113008.i 0.207490i
\(739\) 107013.i 0.195951i −0.995189 0.0979757i \(-0.968763\pi\)
0.995189 0.0979757i \(-0.0312368\pi\)
\(740\) 33035.9i 0.0603286i
\(741\) 562817.i 1.02502i
\(742\) 1.11161e6i 2.01904i
\(743\) −915468. −1.65831 −0.829155 0.559019i \(-0.811178\pi\)
−0.829155 + 0.559019i \(0.811178\pi\)
\(744\) −459681. −0.830444
\(745\) 1.01984e6i 1.83747i
\(746\) 294883.i 0.529874i
\(747\) 165012.i 0.295715i
\(748\) 13068.0i 0.0233563i
\(749\) −1.02238e6 −1.82242
\(750\) 270656.i 0.481165i
\(751\) 832564.i 1.47617i 0.674705 + 0.738087i \(0.264271\pi\)
−0.674705 + 0.738087i \(0.735729\pi\)
\(752\) 397004.i 0.702036i
\(753\) −300632. −0.530208
\(754\) 414238. 0.728631
\(755\) 545406.i 0.956811i
\(756\) −10070.3 −0.0176197
\(757\) 247540. 0.431970 0.215985 0.976397i \(-0.430704\pi\)
0.215985 + 0.976397i \(0.430704\pi\)
\(758\) 350690.i 0.610359i
\(759\) 337599. 0.586028
\(760\) 1.05002e6i 1.81789i
\(761\) −539545. −0.931662 −0.465831 0.884874i \(-0.654244\pi\)
−0.465831 + 0.884874i \(0.654244\pi\)
\(762\) 571411.i 0.984098i
\(763\) 504988.i 0.867425i
\(764\) 32774.5i 0.0561500i
\(765\) −245652. −0.419756
\(766\) 1.14221e6i 1.94665i
\(767\) −4221.58 885352.i −0.00717604 1.50496i
\(768\) −53248.0 −0.0902779
\(769\) 97270.6i 0.164486i −0.996612 0.0822430i \(-0.973792\pi\)
0.996612 0.0822430i \(-0.0262084\pi\)
\(770\) 950059. 1.60239
\(771\) 489776. 0.823927
\(772\) −30287.3 −0.0508189
\(773\) 234313.i 0.392136i 0.980590 + 0.196068i \(0.0628173\pi\)
−0.980590 + 0.196068i \(0.937183\pi\)
\(774\) −286670. −0.478520
\(775\) 1.34411e6i 2.23785i
\(776\) 1.05423e6 1.75069
\(777\) 444686.i 0.736565i
\(778\) 87095.3i 0.143892i
\(779\) −434403. −0.715844
\(780\) 43792.9i 0.0719804i
\(781\) 176044.i 0.288615i
\(782\) 899205. 1.47043
\(783\) 55687.4 0.0908309
\(784\) −1.33467e6 −2.17141
\(785\) 217356.i 0.352721i
\(786\) −41781.1 −0.0676294
\(787\) 773520. 1.24888 0.624442 0.781071i \(-0.285327\pi\)
0.624442 + 0.781071i \(0.285327\pi\)
\(788\) −31328.9 −0.0504537
\(789\) −33197.0 −0.0533267