Properties

Label 177.5.c.a.58.8
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 58.8
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.33

$q$-expansion

\(f(q)\) \(=\) \(q-4.96663i q^{2} +5.19615 q^{3} -8.66741 q^{4} +41.3974 q^{5} -25.8074i q^{6} +1.08721 q^{7} -36.4182i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-4.96663i q^{2} +5.19615 q^{3} -8.66741 q^{4} +41.3974 q^{5} -25.8074i q^{6} +1.08721 q^{7} -36.4182i q^{8} +27.0000 q^{9} -205.606i q^{10} +142.708i q^{11} -45.0372 q^{12} -35.2627i q^{13} -5.39978i q^{14} +215.107 q^{15} -319.555 q^{16} +527.661 q^{17} -134.099i q^{18} +76.0375 q^{19} -358.808 q^{20} +5.64932 q^{21} +708.780 q^{22} -138.991i q^{23} -189.235i q^{24} +1088.75 q^{25} -175.137 q^{26} +140.296 q^{27} -9.42332 q^{28} -1044.28 q^{29} -1068.36i q^{30} -1364.14i q^{31} +1004.42i q^{32} +741.534i q^{33} -2620.69i q^{34} +45.0078 q^{35} -234.020 q^{36} +2076.33i q^{37} -377.650i q^{38} -183.230i q^{39} -1507.62i q^{40} -1604.49 q^{41} -28.0581i q^{42} -746.077i q^{43} -1236.91i q^{44} +1117.73 q^{45} -690.318 q^{46} +613.862i q^{47} -1660.45 q^{48} -2399.82 q^{49} -5407.39i q^{50} +2741.80 q^{51} +305.636i q^{52} -3306.58 q^{53} -696.799i q^{54} +5907.75i q^{55} -39.5944i q^{56} +395.102 q^{57} +5186.56i q^{58} +(330.884 - 3465.24i) q^{59} -1864.42 q^{60} +3021.56i q^{61} -6775.17 q^{62} +29.3547 q^{63} -124.304 q^{64} -1459.78i q^{65} +3682.93 q^{66} -3679.74i q^{67} -4573.45 q^{68} -722.220i q^{69} -223.537i q^{70} +1827.67 q^{71} -983.293i q^{72} -2692.51i q^{73} +10312.4 q^{74} +5657.29 q^{75} -659.048 q^{76} +155.154i q^{77} -910.037 q^{78} +3087.31 q^{79} -13228.7 q^{80} +729.000 q^{81} +7968.90i q^{82} -7955.09i q^{83} -48.9650 q^{84} +21843.8 q^{85} -3705.49 q^{86} -5426.25 q^{87} +5197.19 q^{88} +5141.10i q^{89} -5551.35i q^{90} -38.3380i q^{91} +1204.70i q^{92} -7088.27i q^{93} +3048.82 q^{94} +3147.75 q^{95} +5219.11i q^{96} +13063.6i q^{97} +11919.0i q^{98} +3853.13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.96663i 1.24166i −0.783946 0.620829i \(-0.786796\pi\)
0.783946 0.620829i \(-0.213204\pi\)
\(3\) 5.19615 0.577350
\(4\) −8.66741 −0.541713
\(5\) 41.3974 1.65590 0.827948 0.560805i \(-0.189508\pi\)
0.827948 + 0.560805i \(0.189508\pi\)
\(6\) 25.8074i 0.716871i
\(7\) 1.08721 0.0221880 0.0110940 0.999938i \(-0.496469\pi\)
0.0110940 + 0.999938i \(0.496469\pi\)
\(8\) 36.4182i 0.569035i
\(9\) 27.0000 0.333333
\(10\) 205.606i 2.05606i
\(11\) 142.708i 1.17941i 0.807620 + 0.589704i \(0.200756\pi\)
−0.807620 + 0.589704i \(0.799244\pi\)
\(12\) −45.0372 −0.312758
\(13\) 35.2627i 0.208655i −0.994543 0.104327i \(-0.966731\pi\)
0.994543 0.104327i \(-0.0332690\pi\)
\(14\) 5.39978i 0.0275499i
\(15\) 215.107 0.956032
\(16\) −319.555 −1.24826
\(17\) 527.661 1.82581 0.912907 0.408167i \(-0.133832\pi\)
0.912907 + 0.408167i \(0.133832\pi\)
\(18\) 134.099i 0.413886i
\(19\) 76.0375 0.210630 0.105315 0.994439i \(-0.466415\pi\)
0.105315 + 0.994439i \(0.466415\pi\)
\(20\) −358.808 −0.897021
\(21\) 5.64932 0.0128103
\(22\) 708.780 1.46442
\(23\) 138.991i 0.262744i −0.991333 0.131372i \(-0.958062\pi\)
0.991333 0.131372i \(-0.0419382\pi\)
\(24\) 189.235i 0.328533i
\(25\) 1088.75 1.74199
\(26\) −175.137 −0.259078
\(27\) 140.296 0.192450
\(28\) −9.42332 −0.0120195
\(29\) −1044.28 −1.24171 −0.620857 0.783924i \(-0.713215\pi\)
−0.620857 + 0.783924i \(0.713215\pi\)
\(30\) 1068.36i 1.18706i
\(31\) 1364.14i 1.41950i −0.704454 0.709749i \(-0.748808\pi\)
0.704454 0.709749i \(-0.251192\pi\)
\(32\) 1004.42i 0.980876i
\(33\) 741.534i 0.680931i
\(34\) 2620.69i 2.26704i
\(35\) 45.0078 0.0367410
\(36\) −234.020 −0.180571
\(37\) 2076.33i 1.51668i 0.651860 + 0.758339i \(0.273989\pi\)
−0.651860 + 0.758339i \(0.726011\pi\)
\(38\) 377.650i 0.261530i
\(39\) 183.230i 0.120467i
\(40\) 1507.62i 0.942263i
\(41\) −1604.49 −0.954485 −0.477242 0.878772i \(-0.658364\pi\)
−0.477242 + 0.878772i \(0.658364\pi\)
\(42\) 28.0581i 0.0159059i
\(43\) 746.077i 0.403503i −0.979437 0.201751i \(-0.935337\pi\)
0.979437 0.201751i \(-0.0646633\pi\)
\(44\) 1236.91i 0.638901i
\(45\) 1117.73 0.551965
\(46\) −690.318 −0.326237
\(47\) 613.862i 0.277891i 0.990300 + 0.138946i \(0.0443713\pi\)
−0.990300 + 0.138946i \(0.955629\pi\)
\(48\) −1660.45 −0.720683
\(49\) −2399.82 −0.999508
\(50\) 5407.39i 2.16296i
\(51\) 2741.80 1.05413
\(52\) 305.636i 0.113031i
\(53\) −3306.58 −1.17714 −0.588569 0.808447i \(-0.700308\pi\)
−0.588569 + 0.808447i \(0.700308\pi\)
\(54\) 696.799i 0.238957i
\(55\) 5907.75i 1.95298i
\(56\) 39.5944i 0.0126258i
\(57\) 395.102 0.121607
\(58\) 5186.56i 1.54178i
\(59\) 330.884 3465.24i 0.0950543 0.995472i
\(60\) −1864.42 −0.517895
\(61\) 3021.56i 0.812028i 0.913867 + 0.406014i \(0.133082\pi\)
−0.913867 + 0.406014i \(0.866918\pi\)
\(62\) −6775.17 −1.76253
\(63\) 29.3547 0.00739600
\(64\) −124.304 −0.0303476
\(65\) 1459.78i 0.345511i
\(66\) 3682.93 0.845484
\(67\) 3679.74i 0.819724i −0.912148 0.409862i \(-0.865577\pi\)
0.912148 0.409862i \(-0.134423\pi\)
\(68\) −4573.45 −0.989068
\(69\) 722.220i 0.151695i
\(70\) 223.537i 0.0456198i
\(71\) 1827.67 0.362560 0.181280 0.983431i \(-0.441976\pi\)
0.181280 + 0.983431i \(0.441976\pi\)
\(72\) 983.293i 0.189678i
\(73\) 2692.51i 0.505256i −0.967563 0.252628i \(-0.918705\pi\)
0.967563 0.252628i \(-0.0812949\pi\)
\(74\) 10312.4 1.88320
\(75\) 5657.29 1.00574
\(76\) −659.048 −0.114101
\(77\) 155.154i 0.0261687i
\(78\) −910.037 −0.149579
\(79\) 3087.31 0.494682 0.247341 0.968928i \(-0.420443\pi\)
0.247341 + 0.968928i \(0.420443\pi\)
\(80\) −13228.7 −2.06699
\(81\) 729.000 0.111111
\(82\) 7968.90i 1.18514i
\(83\) 7955.09i 1.15475i −0.816478 0.577377i \(-0.804076\pi\)
0.816478 0.577377i \(-0.195924\pi\)
\(84\) −48.9650 −0.00693949
\(85\) 21843.8 3.02336
\(86\) −3705.49 −0.501012
\(87\) −5426.25 −0.716904
\(88\) 5197.19 0.671124
\(89\) 5141.10i 0.649047i 0.945878 + 0.324524i \(0.105204\pi\)
−0.945878 + 0.324524i \(0.894796\pi\)
\(90\) 5551.35i 0.685352i
\(91\) 38.3380i 0.00462964i
\(92\) 1204.70i 0.142332i
\(93\) 7088.27i 0.819548i
\(94\) 3048.82 0.345046
\(95\) 3147.75 0.348782
\(96\) 5219.11i 0.566309i
\(97\) 13063.6i 1.38842i 0.719772 + 0.694210i \(0.244246\pi\)
−0.719772 + 0.694210i \(0.755754\pi\)
\(98\) 11919.0i 1.24105i
\(99\) 3853.13i 0.393136i
\(100\) −9436.60 −0.943660
\(101\) 6212.97i 0.609055i −0.952504 0.304527i \(-0.901502\pi\)
0.952504 0.304527i \(-0.0984985\pi\)
\(102\) 13617.5i 1.30887i
\(103\) 12027.0i 1.13366i 0.823834 + 0.566831i \(0.191831\pi\)
−0.823834 + 0.566831i \(0.808169\pi\)
\(104\) −1284.21 −0.118732
\(105\) 233.867 0.0212125
\(106\) 16422.6i 1.46160i
\(107\) −5915.89 −0.516717 −0.258359 0.966049i \(-0.583182\pi\)
−0.258359 + 0.966049i \(0.583182\pi\)
\(108\) −1216.00 −0.104253
\(109\) 17887.0i 1.50552i 0.658298 + 0.752758i \(0.271277\pi\)
−0.658298 + 0.752758i \(0.728723\pi\)
\(110\) 29341.6 2.42493
\(111\) 10788.9i 0.875655i
\(112\) −347.424 −0.0276964
\(113\) 24933.1i 1.95262i 0.216368 + 0.976312i \(0.430579\pi\)
−0.216368 + 0.976312i \(0.569421\pi\)
\(114\) 1962.33i 0.150995i
\(115\) 5753.88i 0.435076i
\(116\) 9051.23 0.672653
\(117\) 952.093i 0.0695517i
\(118\) −17210.6 1643.38i −1.23604 0.118025i
\(119\) 573.679 0.0405112
\(120\) 7833.83i 0.544016i
\(121\) −5724.67 −0.391003
\(122\) 15007.0 1.00826
\(123\) −8337.17 −0.551072
\(124\) 11823.6i 0.768962i
\(125\) 19197.8 1.22866
\(126\) 145.794i 0.00918330i
\(127\) 22413.1 1.38961 0.694806 0.719197i \(-0.255490\pi\)
0.694806 + 0.719197i \(0.255490\pi\)
\(128\) 16688.0i 1.01856i
\(129\) 3876.73i 0.232963i
\(130\) −7250.21 −0.429006
\(131\) 17802.3i 1.03737i −0.854965 0.518685i \(-0.826422\pi\)
0.854965 0.518685i \(-0.173578\pi\)
\(132\) 6427.18i 0.368870i
\(133\) 82.6689 0.00467346
\(134\) −18275.9 −1.01782
\(135\) 5807.89 0.318677
\(136\) 19216.5i 1.03895i
\(137\) −11891.9 −0.633595 −0.316797 0.948493i \(-0.602607\pi\)
−0.316797 + 0.948493i \(0.602607\pi\)
\(138\) −3587.00 −0.188353
\(139\) −24841.5 −1.28572 −0.642862 0.765982i \(-0.722253\pi\)
−0.642862 + 0.765982i \(0.722253\pi\)
\(140\) −390.101 −0.0199031
\(141\) 3189.72i 0.160441i
\(142\) 9077.34i 0.450176i
\(143\) 5032.28 0.246089
\(144\) −8627.97 −0.416087
\(145\) −43230.6 −2.05615
\(146\) −13372.7 −0.627355
\(147\) −12469.8 −0.577066
\(148\) 17996.4i 0.821605i
\(149\) 26032.6i 1.17259i 0.810099 + 0.586293i \(0.199413\pi\)
−0.810099 + 0.586293i \(0.800587\pi\)
\(150\) 28097.6i 1.24878i
\(151\) 12278.3i 0.538497i 0.963071 + 0.269249i \(0.0867753\pi\)
−0.963071 + 0.269249i \(0.913225\pi\)
\(152\) 2769.15i 0.119856i
\(153\) 14246.8 0.608605
\(154\) 770.594 0.0324926
\(155\) 56471.8i 2.35054i
\(156\) 1588.13i 0.0652586i
\(157\) 21189.6i 0.859655i −0.902911 0.429827i \(-0.858574\pi\)
0.902911 0.429827i \(-0.141426\pi\)
\(158\) 15333.5i 0.614226i
\(159\) −17181.5 −0.679621
\(160\) 41580.3i 1.62423i
\(161\) 151.113i 0.00582976i
\(162\) 3620.67i 0.137962i
\(163\) 22822.0 0.858970 0.429485 0.903074i \(-0.358695\pi\)
0.429485 + 0.903074i \(0.358695\pi\)
\(164\) 13906.8 0.517057
\(165\) 30697.6i 1.12755i
\(166\) −39510.0 −1.43381
\(167\) −28368.2 −1.01718 −0.508592 0.861008i \(-0.669834\pi\)
−0.508592 + 0.861008i \(0.669834\pi\)
\(168\) 205.738i 0.00728948i
\(169\) 27317.5 0.956463
\(170\) 108490.i 3.75398i
\(171\) 2053.01 0.0702100
\(172\) 6466.56i 0.218583i
\(173\) 7580.94i 0.253297i −0.991948 0.126649i \(-0.959578\pi\)
0.991948 0.126649i \(-0.0404221\pi\)
\(174\) 26950.2i 0.890150i
\(175\) 1183.70 0.0386513
\(176\) 45603.1i 1.47221i
\(177\) 1719.32 18005.9i 0.0548796 0.574736i
\(178\) 25533.9 0.805894
\(179\) 34939.2i 1.09045i 0.838289 + 0.545226i \(0.183556\pi\)
−0.838289 + 0.545226i \(0.816444\pi\)
\(180\) −9687.83 −0.299007
\(181\) 37840.7 1.15505 0.577527 0.816372i \(-0.304018\pi\)
0.577527 + 0.816372i \(0.304018\pi\)
\(182\) −190.411 −0.00574843
\(183\) 15700.5i 0.468825i
\(184\) −5061.82 −0.149510
\(185\) 85954.8i 2.51146i
\(186\) −35204.8 −1.01760
\(187\) 75301.6i 2.15338i
\(188\) 5320.59i 0.150537i
\(189\) 152.532 0.00427008
\(190\) 15633.7i 0.433067i
\(191\) 3569.74i 0.0978521i 0.998802 + 0.0489261i \(0.0155799\pi\)
−0.998802 + 0.0489261i \(0.984420\pi\)
\(192\) −645.901 −0.0175212
\(193\) 24451.4 0.656430 0.328215 0.944603i \(-0.393553\pi\)
0.328215 + 0.944603i \(0.393553\pi\)
\(194\) 64882.3 1.72394
\(195\) 7585.26i 0.199481i
\(196\) 20800.2 0.541447
\(197\) −29706.3 −0.765449 −0.382724 0.923863i \(-0.625014\pi\)
−0.382724 + 0.923863i \(0.625014\pi\)
\(198\) 19137.0 0.488140
\(199\) −22181.5 −0.560125 −0.280062 0.959982i \(-0.590355\pi\)
−0.280062 + 0.959982i \(0.590355\pi\)
\(200\) 39650.2i 0.991255i
\(201\) 19120.5i 0.473268i
\(202\) −30857.5 −0.756237
\(203\) −1135.36 −0.0275512
\(204\) −23764.4 −0.571039
\(205\) −66421.7 −1.58053
\(206\) 59733.8 1.40762
\(207\) 3752.77i 0.0875812i
\(208\) 11268.4i 0.260456i
\(209\) 10851.2i 0.248419i
\(210\) 1161.53i 0.0263386i
\(211\) 81724.8i 1.83565i −0.396989 0.917824i \(-0.629945\pi\)
0.396989 0.917824i \(-0.370055\pi\)
\(212\) 28659.5 0.637671
\(213\) 9496.83 0.209324
\(214\) 29382.1i 0.641586i
\(215\) 30885.6i 0.668159i
\(216\) 5109.34i 0.109511i
\(217\) 1483.11i 0.0314959i
\(218\) 88838.3 1.86933
\(219\) 13990.7i 0.291710i
\(220\) 51205.0i 1.05795i
\(221\) 18606.7i 0.380965i
\(222\) 53584.7 1.08726
\(223\) −54373.6 −1.09340 −0.546699 0.837329i \(-0.684116\pi\)
−0.546699 + 0.837329i \(0.684116\pi\)
\(224\) 1092.02i 0.0217637i
\(225\) 29396.1 0.580664
\(226\) 123833. 2.42449
\(227\) 55801.8i 1.08292i 0.840726 + 0.541460i \(0.182128\pi\)
−0.840726 + 0.541460i \(0.817872\pi\)
\(228\) −3424.51 −0.0658763
\(229\) 102771.i 1.95975i −0.199624 0.979873i \(-0.563972\pi\)
0.199624 0.979873i \(-0.436028\pi\)
\(230\) −28577.4 −0.540215
\(231\) 806.205i 0.0151085i
\(232\) 38030.9i 0.706579i
\(233\) 60636.1i 1.11691i −0.829534 0.558457i \(-0.811394\pi\)
0.829534 0.558457i \(-0.188606\pi\)
\(234\) −4728.69 −0.0863593
\(235\) 25412.3i 0.460159i
\(236\) −2867.91 + 30034.7i −0.0514922 + 0.539261i
\(237\) 16042.1 0.285605
\(238\) 2849.25i 0.0503010i
\(239\) 12138.8 0.212510 0.106255 0.994339i \(-0.466114\pi\)
0.106255 + 0.994339i \(0.466114\pi\)
\(240\) −68738.5 −1.19338
\(241\) −13471.2 −0.231938 −0.115969 0.993253i \(-0.536997\pi\)
−0.115969 + 0.993253i \(0.536997\pi\)
\(242\) 28432.3i 0.485491i
\(243\) 3788.00 0.0641500
\(244\) 26189.1i 0.439886i
\(245\) −99346.2 −1.65508
\(246\) 41407.6i 0.684243i
\(247\) 2681.29i 0.0439490i
\(248\) −49679.5 −0.807745
\(249\) 41335.9i 0.666697i
\(250\) 95348.6i 1.52558i
\(251\) −20999.2 −0.333315 −0.166657 0.986015i \(-0.553297\pi\)
−0.166657 + 0.986015i \(0.553297\pi\)
\(252\) −254.430 −0.00400651
\(253\) 19835.2 0.309882
\(254\) 111317.i 1.72542i
\(255\) 113504. 1.74554
\(256\) 80894.5 1.23435
\(257\) −39315.0 −0.595240 −0.297620 0.954684i \(-0.596193\pi\)
−0.297620 + 0.954684i \(0.596193\pi\)
\(258\) −19254.3 −0.289260
\(259\) 2257.42i 0.0336521i
\(260\) 12652.5i 0.187168i
\(261\) −28195.6 −0.413905
\(262\) −88417.5 −1.28806
\(263\) 37861.6 0.547378 0.273689 0.961818i \(-0.411756\pi\)
0.273689 + 0.961818i \(0.411756\pi\)
\(264\) 27005.4 0.387474
\(265\) −136884. −1.94922
\(266\) 410.586i 0.00580284i
\(267\) 26713.9i 0.374727i
\(268\) 31893.8i 0.444055i
\(269\) 123756.i 1.71026i 0.518413 + 0.855130i \(0.326523\pi\)
−0.518413 + 0.855130i \(0.673477\pi\)
\(270\) 28845.7i 0.395688i
\(271\) 4855.26 0.0661110 0.0330555 0.999454i \(-0.489476\pi\)
0.0330555 + 0.999454i \(0.489476\pi\)
\(272\) −168616. −2.27909
\(273\) 199.210i 0.00267292i
\(274\) 59062.9i 0.786707i
\(275\) 155373.i 2.05452i
\(276\) 6259.78i 0.0821752i
\(277\) 97089.7 1.26536 0.632680 0.774414i \(-0.281955\pi\)
0.632680 + 0.774414i \(0.281955\pi\)
\(278\) 123378.i 1.59643i
\(279\) 36831.7i 0.473166i
\(280\) 1639.10i 0.0209069i
\(281\) −108342. −1.37209 −0.686045 0.727559i \(-0.740655\pi\)
−0.686045 + 0.727559i \(0.740655\pi\)
\(282\) 15842.2 0.199212
\(283\) 67893.8i 0.847729i 0.905726 + 0.423864i \(0.139327\pi\)
−0.905726 + 0.423864i \(0.860673\pi\)
\(284\) −15841.1 −0.196404
\(285\) 16356.2 0.201369
\(286\) 24993.5i 0.305559i
\(287\) −1744.42 −0.0211781
\(288\) 27119.3i 0.326959i
\(289\) 194905. 2.33360
\(290\) 214710.i 2.55304i
\(291\) 67880.7i 0.801605i
\(292\) 23337.1i 0.273704i
\(293\) 51965.3 0.605311 0.302655 0.953100i \(-0.402127\pi\)
0.302655 + 0.953100i \(0.402127\pi\)
\(294\) 61933.0i 0.716518i
\(295\) 13697.7 143452.i 0.157400 1.64840i
\(296\) 75616.4 0.863043
\(297\) 20021.4i 0.226977i
\(298\) 129294. 1.45595
\(299\) −4901.21 −0.0548227
\(300\) −49034.0 −0.544823
\(301\) 811.144i 0.00895293i
\(302\) 60981.7 0.668629
\(303\) 32283.5i 0.351638i
\(304\) −24298.1 −0.262921
\(305\) 125085.i 1.34463i
\(306\) 70758.8i 0.755679i
\(307\) 122608. 1.30089 0.650445 0.759553i \(-0.274582\pi\)
0.650445 + 0.759553i \(0.274582\pi\)
\(308\) 1344.79i 0.0141759i
\(309\) 62494.2i 0.654520i
\(310\) −280475. −2.91857
\(311\) −159419. −1.64823 −0.824117 0.566420i \(-0.808328\pi\)
−0.824117 + 0.566420i \(0.808328\pi\)
\(312\) −6672.93 −0.0685499
\(313\) 17723.3i 0.180907i 0.995901 + 0.0904534i \(0.0288316\pi\)
−0.995901 + 0.0904534i \(0.971168\pi\)
\(314\) −105241. −1.06740
\(315\) 1215.21 0.0122470
\(316\) −26759.0 −0.267976
\(317\) −112577. −1.12029 −0.560145 0.828394i \(-0.689255\pi\)
−0.560145 + 0.828394i \(0.689255\pi\)
\(318\) 85334.1i 0.843856i
\(319\) 149028.i 1.46449i
\(320\) −5145.85 −0.0502524
\(321\) −30739.9 −0.298327
\(322\) −750.523 −0.00723856
\(323\) 40122.0 0.384572
\(324\) −6318.54 −0.0601904
\(325\) 38392.1i 0.363475i
\(326\) 113348.i 1.06655i
\(327\) 92943.7i 0.869210i
\(328\) 58432.7i 0.543135i
\(329\) 667.398i 0.00616585i
\(330\) 152464. 1.40003
\(331\) −126890. −1.15817 −0.579083 0.815268i \(-0.696589\pi\)
−0.579083 + 0.815268i \(0.696589\pi\)
\(332\) 68950.1i 0.625545i
\(333\) 56061.0i 0.505560i
\(334\) 140895.i 1.26299i
\(335\) 152332.i 1.35738i
\(336\) −1805.27 −0.0159905
\(337\) 145883.i 1.28454i −0.766480 0.642268i \(-0.777994\pi\)
0.766480 0.642268i \(-0.222006\pi\)
\(338\) 135676.i 1.18760i
\(339\) 129556.i 1.12735i
\(340\) −189329. −1.63779
\(341\) 194674. 1.67417
\(342\) 10196.5i 0.0871768i
\(343\) −5219.51 −0.0443651
\(344\) −27170.8 −0.229607
\(345\) 29898.0i 0.251191i
\(346\) −37651.7 −0.314509
\(347\) 118230.i 0.981905i 0.871186 + 0.490953i \(0.163351\pi\)
−0.871186 + 0.490953i \(0.836649\pi\)
\(348\) 47031.5 0.388357
\(349\) 24509.0i 0.201222i −0.994926 0.100611i \(-0.967920\pi\)
0.994926 0.100611i \(-0.0320797\pi\)
\(350\) 5878.99i 0.0479917i
\(351\) 4947.22i 0.0401557i
\(352\) −143339. −1.15685
\(353\) 38007.7i 0.305015i −0.988302 0.152508i \(-0.951265\pi\)
0.988302 0.152508i \(-0.0487349\pi\)
\(354\) −89428.7 8539.24i −0.713625 0.0681417i
\(355\) 75660.7 0.600362
\(356\) 44560.1i 0.351597i
\(357\) 2980.92 0.0233892
\(358\) 173530. 1.35397
\(359\) 192503. 1.49365 0.746826 0.665020i \(-0.231577\pi\)
0.746826 + 0.665020i \(0.231577\pi\)
\(360\) 40705.8i 0.314088i
\(361\) −124539. −0.955635
\(362\) 187941.i 1.43418i
\(363\) −29746.3 −0.225745
\(364\) 332.292i 0.00250794i
\(365\) 111463.i 0.836652i
\(366\) 77978.4 0.582120
\(367\) 18295.0i 0.135831i −0.997691 0.0679157i \(-0.978365\pi\)
0.997691 0.0679157i \(-0.0216349\pi\)
\(368\) 44415.3i 0.327972i
\(369\) −43321.2 −0.318162
\(370\) 426906. 3.11838
\(371\) −3594.96 −0.0261183
\(372\) 61437.0i 0.443960i
\(373\) 57630.7 0.414225 0.207112 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 373995. 2.67376
\(375\) 99754.9 0.709368
\(376\) 22355.8 0.158130
\(377\) 36824.2i 0.259090i
\(378\) 757.569i 0.00530198i
\(379\) 170818. 1.18920 0.594599 0.804023i \(-0.297311\pi\)
0.594599 + 0.804023i \(0.297311\pi\)
\(380\) −27282.9 −0.188940
\(381\) 116462. 0.802293
\(382\) 17729.6 0.121499
\(383\) −221122. −1.50742 −0.753709 0.657208i \(-0.771737\pi\)
−0.753709 + 0.657208i \(0.771737\pi\)
\(384\) 86713.6i 0.588065i
\(385\) 6422.99i 0.0433327i
\(386\) 121441.i 0.815061i
\(387\) 20144.1i 0.134501i
\(388\) 113228.i 0.752126i
\(389\) 87151.4 0.575937 0.287969 0.957640i \(-0.407020\pi\)
0.287969 + 0.957640i \(0.407020\pi\)
\(390\) −37673.2 −0.247687
\(391\) 73340.2i 0.479721i
\(392\) 87397.2i 0.568755i
\(393\) 92503.6i 0.598926i
\(394\) 147540.i 0.950425i
\(395\) 127807. 0.819143
\(396\) 33396.6i 0.212967i
\(397\) 126155.i 0.800431i −0.916421 0.400216i \(-0.868935\pi\)
0.916421 0.400216i \(-0.131065\pi\)
\(398\) 110167.i 0.695483i
\(399\) 429.560 0.00269823
\(400\) −347913. −2.17446
\(401\) 27343.9i 0.170048i 0.996379 + 0.0850242i \(0.0270967\pi\)
−0.996379 + 0.0850242i \(0.972903\pi\)
\(402\) −94964.4 −0.587637
\(403\) −48103.2 −0.296185
\(404\) 53850.4i 0.329933i
\(405\) 30178.7 0.183988
\(406\) 5638.90i 0.0342091i
\(407\) −296310. −1.78878
\(408\) 99851.7i 0.599840i
\(409\) 104932.i 0.627282i 0.949542 + 0.313641i \(0.101549\pi\)
−0.949542 + 0.313641i \(0.898451\pi\)
\(410\) 329892.i 1.96247i
\(411\) −61792.3 −0.365806
\(412\) 104243.i 0.614120i
\(413\) 359.741 3767.45i 0.00210907 0.0220875i
\(414\) −18638.6 −0.108746
\(415\) 329320.i 1.91215i
\(416\) 35418.5 0.204665
\(417\) −129080. −0.742313
\(418\) 53893.8 0.308451
\(419\) 203320.i 1.15812i −0.815286 0.579058i \(-0.803420\pi\)
0.815286 0.579058i \(-0.196580\pi\)
\(420\) −2027.02 −0.0114911
\(421\) 7915.89i 0.0446617i 0.999751 + 0.0223309i \(0.00710872\pi\)
−0.999751 + 0.0223309i \(0.992891\pi\)
\(422\) −405897. −2.27924
\(423\) 16574.3i 0.0926304i
\(424\) 120420.i 0.669833i
\(425\) 574488. 3.18056
\(426\) 47167.3i 0.259909i
\(427\) 3285.07i 0.0180173i
\(428\) 51275.5 0.279913
\(429\) 26148.5 0.142080
\(430\) −153398. −0.829625
\(431\) 166950.i 0.898734i −0.893347 0.449367i \(-0.851650\pi\)
0.893347 0.449367i \(-0.148350\pi\)
\(432\) −44832.3 −0.240228
\(433\) −47184.7 −0.251666 −0.125833 0.992051i \(-0.540160\pi\)
−0.125833 + 0.992051i \(0.540160\pi\)
\(434\) −7366.05 −0.0391071
\(435\) −224633. −1.18712
\(436\) 155034.i 0.815558i
\(437\) 10568.5i 0.0553417i
\(438\) −69486.6 −0.362204
\(439\) 168825. 0.876010 0.438005 0.898973i \(-0.355685\pi\)
0.438005 + 0.898973i \(0.355685\pi\)
\(440\) 215150. 1.11131
\(441\) −64795.1 −0.333169
\(442\) −92412.7 −0.473028
\(443\) 307500.i 1.56689i −0.621462 0.783444i \(-0.713461\pi\)
0.621462 0.783444i \(-0.286539\pi\)
\(444\) 93512.2i 0.474354i
\(445\) 212828.i 1.07475i
\(446\) 270053.i 1.35763i
\(447\) 135269.i 0.676993i
\(448\) −135.145 −0.000673352
\(449\) −243616. −1.20841 −0.604203 0.796830i \(-0.706509\pi\)
−0.604203 + 0.796830i \(0.706509\pi\)
\(450\) 146000.i 0.720986i
\(451\) 228974.i 1.12573i
\(452\) 216105.i 1.05776i
\(453\) 63799.8i 0.310902i
\(454\) 277147. 1.34462
\(455\) 1587.10i 0.00766620i
\(456\) 14388.9i 0.0691988i
\(457\) 240817.i 1.15307i −0.817073 0.576535i \(-0.804405\pi\)
0.817073 0.576535i \(-0.195595\pi\)
\(458\) −510426. −2.43333
\(459\) 74028.7 0.351378
\(460\) 49871.3i 0.235686i
\(461\) 105419. 0.496043 0.248021 0.968755i \(-0.420220\pi\)
0.248021 + 0.968755i \(0.420220\pi\)
\(462\) 4004.12 0.0187596
\(463\) 177261.i 0.826895i 0.910528 + 0.413447i \(0.135675\pi\)
−0.910528 + 0.413447i \(0.864325\pi\)
\(464\) 333705. 1.54998
\(465\) 293436.i 1.35709i
\(466\) −301157. −1.38682
\(467\) 387563.i 1.77709i −0.458792 0.888544i \(-0.651718\pi\)
0.458792 0.888544i \(-0.348282\pi\)
\(468\) 8252.18i 0.0376771i
\(469\) 4000.66i 0.0181880i
\(470\) 126213. 0.571360
\(471\) 110105.i 0.496322i
\(472\) −126198. 12050.2i −0.566459 0.0540892i
\(473\) 106471. 0.475894
\(474\) 79675.4i 0.354624i
\(475\) 82785.4 0.366916
\(476\) −4972.31 −0.0219455
\(477\) −89277.7 −0.392379
\(478\) 60288.8i 0.263865i
\(479\) 346182. 1.50881 0.754404 0.656411i \(-0.227926\pi\)
0.754404 + 0.656411i \(0.227926\pi\)
\(480\) 216057.i 0.937749i
\(481\) 73217.1 0.316463
\(482\) 66906.3i 0.287987i
\(483\) 785.207i 0.00336581i
\(484\) 49618.1 0.211811
\(485\) 540801.i 2.29908i
\(486\) 18813.6i 0.0796524i
\(487\) −204643. −0.862855 −0.431428 0.902148i \(-0.641990\pi\)
−0.431428 + 0.902148i \(0.641990\pi\)
\(488\) 110040. 0.462072
\(489\) 118586. 0.495927
\(490\) 493416.i 2.05504i
\(491\) −124429. −0.516128 −0.258064 0.966128i \(-0.583085\pi\)
−0.258064 + 0.966128i \(0.583085\pi\)
\(492\) 72261.7 0.298523
\(493\) −551026. −2.26714
\(494\) −13317.0 −0.0545696
\(495\) 159509.i 0.650992i
\(496\) 435917.i 1.77190i
\(497\) 1987.06 0.00804449
\(498\) −205300. −0.827809
\(499\) −410778. −1.64970 −0.824851 0.565350i \(-0.808741\pi\)
−0.824851 + 0.565350i \(0.808741\pi\)
\(500\) −166396. −0.665583
\(501\) −147406. −0.587271
\(502\) 104295.i 0.413863i
\(503\) 245979.i 0.972213i −0.873899 0.486107i \(-0.838417\pi\)
0.873899 0.486107i \(-0.161583\pi\)
\(504\) 1069.05i 0.00420859i
\(505\) 257201.i 1.00853i
\(506\) 98514.2i 0.384767i
\(507\) 141946. 0.552214
\(508\) −194263. −0.752771
\(509\) 32679.0i 0.126134i −0.998009 0.0630672i \(-0.979912\pi\)
0.998009 0.0630672i \(-0.0200882\pi\)
\(510\) 563730.i 2.16736i
\(511\) 2927.33i 0.0112106i
\(512\) 134764.i 0.514085i
\(513\) 10667.8 0.0405358
\(514\) 195263.i 0.739084i
\(515\) 497887.i 1.87723i
\(516\) 33601.2i 0.126199i
\(517\) −87603.2 −0.327747
\(518\) 11211.7 0.0417844
\(519\) 39391.7i 0.146241i
\(520\) −53162.8 −0.196608
\(521\) −113050. −0.416479 −0.208240 0.978078i \(-0.566773\pi\)
−0.208240 + 0.978078i \(0.566773\pi\)
\(522\) 140037.i 0.513928i
\(523\) 237542. 0.868435 0.434218 0.900808i \(-0.357025\pi\)
0.434218 + 0.900808i \(0.357025\pi\)
\(524\) 154300.i 0.561957i
\(525\) 6150.67 0.0223154
\(526\) 188044.i 0.679656i
\(527\) 719802.i 2.59174i
\(528\) 236961.i 0.849979i
\(529\) 260522. 0.930966
\(530\) 679851.i 2.42026i
\(531\) 8933.87 93561.4i 0.0316848 0.331824i
\(532\) −716.525 −0.00253168
\(533\) 56578.6i 0.199158i
\(534\) 132678. 0.465283
\(535\) −244903. −0.855630
\(536\) −134010. −0.466452
\(537\) 181549.i 0.629573i
\(538\) 614651. 2.12356
\(539\) 342474.i 1.17883i
\(540\) −50339.4 −0.172632
\(541\) 203519.i 0.695360i −0.937613 0.347680i \(-0.886970\pi\)
0.937613 0.347680i \(-0.113030\pi\)
\(542\) 24114.3i 0.0820873i
\(543\) 196626. 0.666871
\(544\) 529991.i 1.79090i
\(545\) 740477.i 2.49298i
\(546\) −989.404 −0.00331886
\(547\) −388812. −1.29947 −0.649733 0.760163i \(-0.725119\pi\)
−0.649733 + 0.760163i \(0.725119\pi\)
\(548\) 103072. 0.343227
\(549\) 81582.0i 0.270676i
\(550\) 771680. 2.55101
\(551\) −79404.6 −0.261543
\(552\) −26302.0 −0.0863198
\(553\) 3356.57 0.0109760
\(554\) 482209.i 1.57114i
\(555\) 446634.i 1.44999i
\(556\) 215311. 0.696493
\(557\) 307150. 0.990011 0.495006 0.868890i \(-0.335166\pi\)
0.495006 + 0.868890i \(0.335166\pi\)
\(558\) −182930. −0.587511
\(559\) −26308.7 −0.0841929
\(560\) −14382.4 −0.0458624
\(561\) 391278.i 1.24325i
\(562\) 538093.i 1.70367i
\(563\) 224936.i 0.709647i −0.934933 0.354824i \(-0.884541\pi\)
0.934933 0.354824i \(-0.115459\pi\)
\(564\) 27646.6i 0.0869128i
\(565\) 1.03216e6i 3.23334i
\(566\) 337203. 1.05259
\(567\) 792.578 0.00246533
\(568\) 66560.4i 0.206310i
\(569\) 48390.1i 0.149463i 0.997204 + 0.0747313i \(0.0238099\pi\)
−0.997204 + 0.0747313i \(0.976190\pi\)
\(570\) 81235.2i 0.250032i
\(571\) 344185.i 1.05565i 0.849353 + 0.527825i \(0.176992\pi\)
−0.849353 + 0.527825i \(0.823008\pi\)
\(572\) −43616.8 −0.133310
\(573\) 18548.9i 0.0564949i
\(574\) 8663.89i 0.0262960i
\(575\) 151326.i 0.457697i
\(576\) −3356.20 −0.0101159
\(577\) 68280.6 0.205091 0.102545 0.994728i \(-0.467301\pi\)
0.102545 + 0.994728i \(0.467301\pi\)
\(578\) 968019.i 2.89753i
\(579\) 127053. 0.378990
\(580\) 374697. 1.11384
\(581\) 8648.88i 0.0256217i
\(582\) 337138. 0.995319
\(583\) 471876.i 1.38833i
\(584\) −98056.5 −0.287509
\(585\) 39414.2i 0.115170i
\(586\) 258093.i 0.751589i
\(587\) 275118.i 0.798441i 0.916855 + 0.399220i \(0.130719\pi\)
−0.916855 + 0.399220i \(0.869281\pi\)
\(588\) 108081. 0.312604
\(589\) 103726.i 0.298989i
\(590\) −712472. 68031.6i −2.04675 0.195437i
\(591\) −154359. −0.441932
\(592\) 663502.i 1.89321i
\(593\) 84870.1 0.241349 0.120674 0.992692i \(-0.461494\pi\)
0.120674 + 0.992692i \(0.461494\pi\)
\(594\) 99439.0 0.281828
\(595\) 23748.8 0.0670823
\(596\) 225635.i 0.635206i
\(597\) −115258. −0.323388
\(598\) 24342.5i 0.0680711i
\(599\) −75105.1 −0.209322 −0.104661 0.994508i \(-0.533376\pi\)
−0.104661 + 0.994508i \(0.533376\pi\)
\(600\) 206028.i 0.572301i
\(601\) 94230.3i 0.260880i 0.991456 + 0.130440i \(0.0416391\pi\)
−0.991456 + 0.130440i \(0.958361\pi\)
\(602\) −4028.65 −0.0111165
\(603\) 99353.0i 0.273241i
\(604\) 106421.i 0.291711i
\(605\) −236986. −0.647460
\(606\) −160340. −0.436614
\(607\) 247136. 0.670747 0.335374 0.942085i \(-0.391137\pi\)
0.335374 + 0.942085i \(0.391137\pi\)
\(608\) 76373.4i 0.206602i
\(609\) −5899.49 −0.0159067
\(610\) 621249. 1.66957
\(611\) 21646.4 0.0579834
\(612\) −123483. −0.329689
\(613\) 349727.i 0.930696i 0.885128 + 0.465348i \(0.154071\pi\)
−0.885128 + 0.465348i \(0.845929\pi\)
\(614\) 608947.i 1.61526i
\(615\) −345137. −0.912518
\(616\) 5650.45 0.0148909
\(617\) −645133. −1.69465 −0.847323 0.531078i \(-0.821787\pi\)
−0.847323 + 0.531078i \(0.821787\pi\)
\(618\) 310386. 0.812690
\(619\) −473269. −1.23517 −0.617585 0.786504i \(-0.711889\pi\)
−0.617585 + 0.786504i \(0.711889\pi\)
\(620\) 489464.i 1.27332i
\(621\) 19499.9i 0.0505650i
\(622\) 791774.i 2.04654i
\(623\) 5589.47i 0.0144011i
\(624\) 58552.1i 0.150374i
\(625\) 114275. 0.292544
\(626\) 88024.9 0.224624
\(627\) 56384.4i 0.143425i
\(628\) 183659.i 0.465687i
\(629\) 1.09560e6i 2.76917i
\(630\) 6035.50i 0.0152066i
\(631\) 775739. 1.94831 0.974153 0.225891i \(-0.0725294\pi\)
0.974153 + 0.225891i \(0.0725294\pi\)
\(632\) 112435.i 0.281492i
\(633\) 424655.i 1.05981i
\(634\) 559128.i 1.39102i
\(635\) 927842. 2.30105
\(636\) 148919. 0.368160
\(637\) 84624.0i 0.208552i
\(638\) −740166. −1.81839
\(639\) 49347.0 0.120853
\(640\) 690842.i 1.68663i
\(641\) 368716. 0.897380 0.448690 0.893688i \(-0.351891\pi\)
0.448690 + 0.893688i \(0.351891\pi\)
\(642\) 152674.i 0.370420i
\(643\) −81254.3 −0.196528 −0.0982640 0.995160i \(-0.531329\pi\)
−0.0982640 + 0.995160i \(0.531329\pi\)
\(644\) 1309.76i 0.00315806i
\(645\) 160487.i 0.385762i
\(646\) 199271.i 0.477506i
\(647\) −176909. −0.422612 −0.211306 0.977420i \(-0.567772\pi\)
−0.211306 + 0.977420i \(0.567772\pi\)
\(648\) 26548.9i 0.0632261i
\(649\) 494518. + 47219.9i 1.17407 + 0.112108i
\(650\) −190679. −0.451312
\(651\) 7706.46i 0.0181841i
\(652\) −197807. −0.465316
\(653\) 467222. 1.09571 0.547857 0.836572i \(-0.315444\pi\)
0.547857 + 0.836572i \(0.315444\pi\)
\(654\) 461617. 1.07926
\(655\) 736970.i 1.71778i
\(656\) 512722. 1.19145
\(657\) 72697.8i 0.168419i
\(658\) 3314.72 0.00765588
\(659\) 41300.9i 0.0951018i 0.998869 + 0.0475509i \(0.0151416\pi\)
−0.998869 + 0.0475509i \(0.984858\pi\)
\(660\) 266069.i 0.610810i
\(661\) −298921. −0.684153 −0.342077 0.939672i \(-0.611130\pi\)
−0.342077 + 0.939672i \(0.611130\pi\)
\(662\) 630215.i 1.43805i
\(663\) 96683.4i 0.219950i
\(664\) −289711. −0.657095
\(665\) 3422.28 0.00773877
\(666\) 278434. 0.627732
\(667\) 145146.i 0.326253i
\(668\) 245879. 0.551022
\(669\) −282533. −0.631274
\(670\) −756575. −1.68540
\(671\) −431201. −0.957712
\(672\) 5674.28i 0.0125653i
\(673\) 814423.i 1.79812i 0.437821 + 0.899062i \(0.355751\pi\)
−0.437821 + 0.899062i \(0.644249\pi\)
\(674\) −724549. −1.59495
\(675\) 152747. 0.335247
\(676\) −236772. −0.518129
\(677\) −345729. −0.754324 −0.377162 0.926147i \(-0.623100\pi\)
−0.377162 + 0.926147i \(0.623100\pi\)
\(678\) 643456. 1.39978
\(679\) 14203.0i 0.0308063i
\(680\) 795512.i 1.72040i
\(681\) 289955.i 0.625225i
\(682\) 966873.i 2.07874i
\(683\) 239945.i 0.514363i 0.966363 + 0.257181i \(0.0827938\pi\)
−0.966363 + 0.257181i \(0.917206\pi\)
\(684\) −17794.3 −0.0380337
\(685\) −492295. −1.04917
\(686\) 25923.4i 0.0550863i
\(687\) 534014.i 1.13146i
\(688\) 238412.i 0.503677i
\(689\) 116599.i 0.245616i
\(690\) −148492. −0.311893
\(691\) 695558.i 1.45672i −0.685193 0.728362i \(-0.740282\pi\)
0.685193 0.728362i \(-0.259718\pi\)
\(692\) 65707.1i 0.137215i
\(693\) 4189.17i 0.00872290i
\(694\) 587206. 1.21919
\(695\) −1.02837e6 −2.12902
\(696\) 197614.i 0.407944i
\(697\) −846626. −1.74271
\(698\) −121727. −0.249848
\(699\) 315075.i 0.644850i
\(700\) −10259.6 −0.0209379
\(701\) 839756.i 1.70890i 0.519533 + 0.854451i \(0.326106\pi\)
−0.519533 + 0.854451i \(0.673894\pi\)
\(702\) −24571.0 −0.0498596
\(703\) 157879.i 0.319458i
\(704\) 17739.2i 0.0357922i
\(705\) 132046.i 0.265673i
\(706\) −188770. −0.378725
\(707\) 6754.82i 0.0135137i
\(708\) −14902.1 + 156065.i −0.0297290 + 0.311342i
\(709\) 340569. 0.677505 0.338753 0.940875i \(-0.389995\pi\)
0.338753 + 0.940875i \(0.389995\pi\)
\(710\) 375778.i 0.745444i
\(711\) 83357.5 0.164894
\(712\) 187230. 0.369331
\(713\) −189603. −0.372964
\(714\) 14805.1i 0.0290413i
\(715\) 208323. 0.407498
\(716\) 302832.i 0.590712i
\(717\) 63075.0 0.122693
\(718\) 956093.i 1.85460i
\(719\) 155487.i 0.300770i 0.988627 + 0.150385i \(0.0480514\pi\)
−0.988627 + 0.150385i \(0.951949\pi\)
\(720\) −357176. −0.688996
\(721\) 13075.9i 0.0251537i
\(722\) 618541.i 1.18657i
\(723\) −69998.2 −0.133909
\(724\) −327981. −0.625708
\(725\) −1.13696e6 −2.16306
\(726\) 147739.i 0.280299i
\(727\) −61349.1 −0.116075 −0.0580376 0.998314i \(-0.518484\pi\)
−0.0580376 + 0.998314i \(0.518484\pi\)
\(728\) −1396.20 −0.00263443
\(729\) 19683.0 0.0370370
\(730\) −553595. −1.03884
\(731\) 393675.i 0.736722i
\(732\) 136082.i 0.253969i
\(733\) 39246.3 0.0730451 0.0365225 0.999333i \(-0.488372\pi\)
0.0365225 + 0.999333i \(0.488372\pi\)
\(734\) −90864.4 −0.168656
\(735\) −516218. −0.955561
\(736\) 139605. 0.257719
\(737\) 525130. 0.966789
\(738\) 215160.i 0.395048i
\(739\) 856850.i 1.56898i −0.620144 0.784488i \(-0.712926\pi\)
0.620144 0.784488i \(-0.287074\pi\)
\(740\) 745006.i 1.36049i
\(741\) 13932.4i 0.0253740i
\(742\) 17854.8i 0.0324300i
\(743\) 598825. 1.08473 0.542366 0.840143i \(-0.317529\pi\)
0.542366 + 0.840143i \(0.317529\pi\)
\(744\) −258142. −0.466352
\(745\) 1.07768e6i 1.94168i
\(746\) 286230.i 0.514325i
\(747\) 214788.i 0.384918i
\(748\) 652670.i 1.16651i
\(749\) −6431.83 −0.0114649
\(750\) 495446.i 0.880792i
\(751\) 332338.i 0.589250i −0.955613 0.294625i \(-0.904805\pi\)
0.955613 0.294625i \(-0.0951947\pi\)
\(752\) 196162.i 0.346880i
\(753\) −109115. −0.192439
\(754\) 182892. 0.321701
\(755\) 508289.i 0.891696i
\(756\) −1322.06 −0.00231316
\(757\) 824719. 1.43918 0.719588 0.694401i \(-0.244331\pi\)
0.719588 + 0.694401i \(0.244331\pi\)
\(758\) 848387.i 1.47658i
\(759\) 103067. 0.178910
\(760\) 114636.i 0.198469i
\(761\) 1.09768e6 1.89542 0.947711 0.319130i \(-0.103391\pi\)
0.947711 + 0.319130i \(0.103391\pi\)
\(762\) 578422.i 0.996173i
\(763\) 19447.0i 0.0334044i
\(764\) 30940.4i 0.0530078i
\(765\) 589782. 1.00779
\(766\) 1.09823e6i 1.87170i
\(767\) −122194. 11667.9i −0.207710 0.0198336i
\(768\) 420340. 0.712654
\(769\) 237713.i 0.401976i −0.979594 0.200988i \(-0.935585\pi\)
0.979594 0.200988i \(-0.0644153\pi\)
\(770\) 31900.6 0.0538043
\(771\) −204287. −0.343662
\(772\) −211930. −0.355597
\(773\) 998180.i 1.67051i −0.549860 0.835257i \(-0.685319\pi\)
0.549860 0.835257i \(-0.314681\pi\)
\(774\) −100048. −0.167004
\(775\) 1.48520e6i 2.47276i
\(776\) 475755. 0.790060
\(777\) 11729.9i 0.0194290i
\(778\) 432849.i 0.715117i
\(779\) −122001. −0.201043
\(780\) 65744.6i 0.108061i
\(781\) 260823.i 0.427606i
\(782\) −364254. −0.595649
\(783\) −146509. −0.238968
\(784\) 766873. 1.24765
\(785\) 877196.i 1.42350i
\(786\) −459431. −0.743661
\(787\) −292759. −0.472673 −0.236337 0.971671i \(-0.575947\pi\)
−0.236337 + 0.971671i \(0.575947\pi\)
\(788\) 257477. 0.414654
\(789\) 196734.