Properties

Label 177.5.c.a.58.12
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 58.12
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.29

$q$-expansion

\(f(q)\) \(=\) \(q-4.05068i q^{2} -5.19615 q^{3} -0.408022 q^{4} -16.4107 q^{5} +21.0480i q^{6} +47.3137 q^{7} -63.1581i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-4.05068i q^{2} -5.19615 q^{3} -0.408022 q^{4} -16.4107 q^{5} +21.0480i q^{6} +47.3137 q^{7} -63.1581i q^{8} +27.0000 q^{9} +66.4744i q^{10} -25.6339i q^{11} +2.12014 q^{12} -105.588i q^{13} -191.653i q^{14} +85.2723 q^{15} -262.362 q^{16} +441.346 q^{17} -109.368i q^{18} -560.726 q^{19} +6.69591 q^{20} -245.849 q^{21} -103.835 q^{22} -764.114i q^{23} +328.179i q^{24} -355.690 q^{25} -427.703 q^{26} -140.296 q^{27} -19.3050 q^{28} -1381.28 q^{29} -345.411i q^{30} +950.873i q^{31} +52.2142i q^{32} +133.198i q^{33} -1787.75i q^{34} -776.449 q^{35} -11.0166 q^{36} -632.407i q^{37} +2271.32i q^{38} +548.650i q^{39} +1036.47i q^{40} +1029.59 q^{41} +995.857i q^{42} +2959.97i q^{43} +10.4592i q^{44} -443.088 q^{45} -3095.18 q^{46} -4322.20i q^{47} +1363.27 q^{48} -162.413 q^{49} +1440.79i q^{50} -2293.30 q^{51} +43.0822i q^{52} -2110.03 q^{53} +568.295i q^{54} +420.669i q^{55} -2988.25i q^{56} +2913.62 q^{57} +5595.14i q^{58} +(-3445.38 - 496.740i) q^{59} -34.7930 q^{60} -4274.01i q^{61} +3851.68 q^{62} +1277.47 q^{63} -3986.29 q^{64} +1732.77i q^{65} +539.541 q^{66} +867.430i q^{67} -180.079 q^{68} +3970.45i q^{69} +3145.15i q^{70} -236.548 q^{71} -1705.27i q^{72} +6211.26i q^{73} -2561.68 q^{74} +1848.22 q^{75} +228.788 q^{76} -1212.84i q^{77} +2222.41 q^{78} +8916.22 q^{79} +4305.53 q^{80} +729.000 q^{81} -4170.56i q^{82} -10864.4i q^{83} +100.312 q^{84} -7242.78 q^{85} +11989.9 q^{86} +7177.37 q^{87} -1618.99 q^{88} -6262.72i q^{89} +1794.81i q^{90} -4995.75i q^{91} +311.775i q^{92} -4940.88i q^{93} -17507.9 q^{94} +9201.88 q^{95} -271.313i q^{96} -7894.97i q^{97} +657.884i q^{98} -692.115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.05068i 1.01267i −0.862337 0.506335i \(-0.831000\pi\)
0.862337 0.506335i \(-0.169000\pi\)
\(3\) −5.19615 −0.577350
\(4\) −0.408022 −0.0255014
\(5\) −16.4107 −0.656426 −0.328213 0.944604i \(-0.606446\pi\)
−0.328213 + 0.944604i \(0.606446\pi\)
\(6\) 21.0480i 0.584666i
\(7\) 47.3137 0.965586 0.482793 0.875735i \(-0.339622\pi\)
0.482793 + 0.875735i \(0.339622\pi\)
\(8\) 63.1581i 0.986846i
\(9\) 27.0000 0.333333
\(10\) 66.4744i 0.664744i
\(11\) 25.6339i 0.211850i −0.994374 0.105925i \(-0.966220\pi\)
0.994374 0.105925i \(-0.0337804\pi\)
\(12\) 2.12014 0.0147232
\(13\) 105.588i 0.624780i −0.949954 0.312390i \(-0.898870\pi\)
0.949954 0.312390i \(-0.101130\pi\)
\(14\) 191.653i 0.977820i
\(15\) 85.2723 0.378988
\(16\) −262.362 −1.02485
\(17\) 441.346 1.52715 0.763575 0.645719i \(-0.223442\pi\)
0.763575 + 0.645719i \(0.223442\pi\)
\(18\) 109.368i 0.337557i
\(19\) −560.726 −1.55326 −0.776629 0.629959i \(-0.783072\pi\)
−0.776629 + 0.629959i \(0.783072\pi\)
\(20\) 6.69591 0.0167398
\(21\) −245.849 −0.557481
\(22\) −103.835 −0.214535
\(23\) 764.114i 1.44445i −0.691658 0.722225i \(-0.743120\pi\)
0.691658 0.722225i \(-0.256880\pi\)
\(24\) 328.179i 0.569756i
\(25\) −355.690 −0.569104
\(26\) −427.703 −0.632696
\(27\) −140.296 −0.192450
\(28\) −19.3050 −0.0246238
\(29\) −1381.28 −1.64243 −0.821216 0.570618i \(-0.806704\pi\)
−0.821216 + 0.570618i \(0.806704\pi\)
\(30\) 345.411i 0.383790i
\(31\) 950.873i 0.989462i 0.869046 + 0.494731i \(0.164733\pi\)
−0.869046 + 0.494731i \(0.835267\pi\)
\(32\) 52.2142i 0.0509904i
\(33\) 133.198i 0.122312i
\(34\) 1787.75i 1.54650i
\(35\) −776.449 −0.633836
\(36\) −11.0166 −0.00850046
\(37\) 632.407i 0.461948i −0.972960 0.230974i \(-0.925809\pi\)
0.972960 0.230974i \(-0.0741913\pi\)
\(38\) 2271.32i 1.57294i
\(39\) 548.650i 0.360717i
\(40\) 1036.47i 0.647792i
\(41\) 1029.59 0.612489 0.306245 0.951953i \(-0.400927\pi\)
0.306245 + 0.951953i \(0.400927\pi\)
\(42\) 995.857i 0.564545i
\(43\) 2959.97i 1.60085i 0.599434 + 0.800424i \(0.295392\pi\)
−0.599434 + 0.800424i \(0.704608\pi\)
\(44\) 10.4592i 0.00540248i
\(45\) −443.088 −0.218809
\(46\) −3095.18 −1.46275
\(47\) 4322.20i 1.95663i −0.207119 0.978316i \(-0.566409\pi\)
0.207119 0.978316i \(-0.433591\pi\)
\(48\) 1363.27 0.591698
\(49\) −162.413 −0.0676439
\(50\) 1440.79i 0.576315i
\(51\) −2293.30 −0.881700
\(52\) 43.0822i 0.0159327i
\(53\) −2110.03 −0.751168 −0.375584 0.926788i \(-0.622558\pi\)
−0.375584 + 0.926788i \(0.622558\pi\)
\(54\) 568.295i 0.194889i
\(55\) 420.669i 0.139064i
\(56\) 2988.25i 0.952884i
\(57\) 2913.62 0.896773
\(58\) 5595.14i 1.66324i
\(59\) −3445.38 496.740i −0.989766 0.142700i
\(60\) −34.7930 −0.00966471
\(61\) 4274.01i 1.14862i −0.818638 0.574309i \(-0.805271\pi\)
0.818638 0.574309i \(-0.194729\pi\)
\(62\) 3851.68 1.00200
\(63\) 1277.47 0.321862
\(64\) −3986.29 −0.973215
\(65\) 1732.77i 0.410122i
\(66\) 539.541 0.123862
\(67\) 867.430i 0.193234i 0.995322 + 0.0966172i \(0.0308023\pi\)
−0.995322 + 0.0966172i \(0.969198\pi\)
\(68\) −180.079 −0.0389444
\(69\) 3970.45i 0.833953i
\(70\) 3145.15i 0.641867i
\(71\) −236.548 −0.0469249 −0.0234624 0.999725i \(-0.507469\pi\)
−0.0234624 + 0.999725i \(0.507469\pi\)
\(72\) 1705.27i 0.328949i
\(73\) 6211.26i 1.16556i 0.812631 + 0.582779i \(0.198035\pi\)
−0.812631 + 0.582779i \(0.801965\pi\)
\(74\) −2561.68 −0.467801
\(75\) 1848.22 0.328573
\(76\) 228.788 0.0396102
\(77\) 1212.84i 0.204560i
\(78\) 2222.41 0.365287
\(79\) 8916.22 1.42865 0.714326 0.699813i \(-0.246733\pi\)
0.714326 + 0.699813i \(0.246733\pi\)
\(80\) 4305.53 0.672739
\(81\) 729.000 0.111111
\(82\) 4170.56i 0.620250i
\(83\) 10864.4i 1.57706i −0.614994 0.788532i \(-0.710842\pi\)
0.614994 0.788532i \(-0.289158\pi\)
\(84\) 100.312 0.0142165
\(85\) −7242.78 −1.00246
\(86\) 11989.9 1.62113
\(87\) 7177.37 0.948258
\(88\) −1618.99 −0.209064
\(89\) 6262.72i 0.790647i −0.918542 0.395324i \(-0.870632\pi\)
0.918542 0.395324i \(-0.129368\pi\)
\(90\) 1794.81i 0.221581i
\(91\) 4995.75i 0.603279i
\(92\) 311.775i 0.0368355i
\(93\) 4940.88i 0.571266i
\(94\) −17507.9 −1.98142
\(95\) 9201.88 1.01960
\(96\) 271.313i 0.0294393i
\(97\) 7894.97i 0.839087i −0.907735 0.419543i \(-0.862190\pi\)
0.907735 0.419543i \(-0.137810\pi\)
\(98\) 657.884i 0.0685010i
\(99\) 692.115i 0.0706168i
\(100\) 145.129 0.0145129
\(101\) 6756.86i 0.662372i −0.943566 0.331186i \(-0.892551\pi\)
0.943566 0.331186i \(-0.107449\pi\)
\(102\) 9289.44i 0.892872i
\(103\) 19989.4i 1.88420i −0.335338 0.942098i \(-0.608851\pi\)
0.335338 0.942098i \(-0.391149\pi\)
\(104\) −6668.73 −0.616562
\(105\) 4034.55 0.365945
\(106\) 8547.07i 0.760686i
\(107\) 14259.8 1.24550 0.622751 0.782420i \(-0.286015\pi\)
0.622751 + 0.782420i \(0.286015\pi\)
\(108\) 57.2439 0.00490774
\(109\) 219.395i 0.0184660i −0.999957 0.00923302i \(-0.997061\pi\)
0.999957 0.00923302i \(-0.00293900\pi\)
\(110\) 1704.00 0.140826
\(111\) 3286.08i 0.266706i
\(112\) −12413.3 −0.989582
\(113\) 12616.9i 0.988089i 0.869437 + 0.494044i \(0.164482\pi\)
−0.869437 + 0.494044i \(0.835518\pi\)
\(114\) 11802.1i 0.908136i
\(115\) 12539.6i 0.948175i
\(116\) 563.595 0.0418843
\(117\) 2850.87i 0.208260i
\(118\) −2012.14 + 13956.1i −0.144508 + 1.00231i
\(119\) 20881.7 1.47459
\(120\) 5385.64i 0.374003i
\(121\) 13983.9 0.955119
\(122\) −17312.7 −1.16317
\(123\) −5349.93 −0.353621
\(124\) 387.977i 0.0252326i
\(125\) 16093.8 1.03000
\(126\) 5174.62i 0.325940i
\(127\) 3740.54 0.231914 0.115957 0.993254i \(-0.463007\pi\)
0.115957 + 0.993254i \(0.463007\pi\)
\(128\) 16982.6i 1.03654i
\(129\) 15380.4i 0.924250i
\(130\) 7018.88 0.415318
\(131\) 21977.1i 1.28064i 0.768108 + 0.640320i \(0.221198\pi\)
−0.768108 + 0.640320i \(0.778802\pi\)
\(132\) 54.3476i 0.00311912i
\(133\) −26530.0 −1.49980
\(134\) 3513.68 0.195683
\(135\) 2302.35 0.126329
\(136\) 27874.6i 1.50706i
\(137\) −8143.37 −0.433873 −0.216937 0.976186i \(-0.569606\pi\)
−0.216937 + 0.976186i \(0.569606\pi\)
\(138\) 16083.0 0.844520
\(139\) 13508.7 0.699172 0.349586 0.936904i \(-0.386322\pi\)
0.349586 + 0.936904i \(0.386322\pi\)
\(140\) 316.808 0.0161637
\(141\) 22458.8i 1.12966i
\(142\) 958.182i 0.0475194i
\(143\) −2706.63 −0.132360
\(144\) −7083.77 −0.341617
\(145\) 22667.8 1.07814
\(146\) 25159.8 1.18033
\(147\) 843.923 0.0390542
\(148\) 258.036i 0.0117803i
\(149\) 5748.17i 0.258915i −0.991585 0.129457i \(-0.958676\pi\)
0.991585 0.129457i \(-0.0413235\pi\)
\(150\) 7486.55i 0.332736i
\(151\) 39105.9i 1.71510i 0.514404 + 0.857548i \(0.328013\pi\)
−0.514404 + 0.857548i \(0.671987\pi\)
\(152\) 35414.4i 1.53283i
\(153\) 11916.3 0.509050
\(154\) −4912.81 −0.207152
\(155\) 15604.5i 0.649509i
\(156\) 223.861i 0.00919878i
\(157\) 995.408i 0.0403833i −0.999796 0.0201917i \(-0.993572\pi\)
0.999796 0.0201917i \(-0.00642764\pi\)
\(158\) 36116.8i 1.44675i
\(159\) 10964.0 0.433687
\(160\) 856.869i 0.0334715i
\(161\) 36153.1i 1.39474i
\(162\) 2952.95i 0.112519i
\(163\) −51373.5 −1.93359 −0.966794 0.255559i \(-0.917741\pi\)
−0.966794 + 0.255559i \(0.917741\pi\)
\(164\) −420.097 −0.0156193
\(165\) 2185.86i 0.0802888i
\(166\) −44008.2 −1.59705
\(167\) −17563.4 −0.629760 −0.314880 0.949132i \(-0.601964\pi\)
−0.314880 + 0.949132i \(0.601964\pi\)
\(168\) 15527.4i 0.550148i
\(169\) 17412.2 0.609650
\(170\) 29338.2i 1.01516i
\(171\) −15139.6 −0.517752
\(172\) 1207.73i 0.0408238i
\(173\) 59732.1i 1.99579i 0.0648356 + 0.997896i \(0.479348\pi\)
−0.0648356 + 0.997896i \(0.520652\pi\)
\(174\) 29073.2i 0.960273i
\(175\) −16829.0 −0.549519
\(176\) 6725.36i 0.217115i
\(177\) 17902.7 + 2581.14i 0.571442 + 0.0823881i
\(178\) −25368.3 −0.800665
\(179\) 52499.1i 1.63850i 0.573439 + 0.819248i \(0.305609\pi\)
−0.573439 + 0.819248i \(0.694391\pi\)
\(180\) 180.790 0.00557993
\(181\) −1001.39 −0.0305665 −0.0152832 0.999883i \(-0.504865\pi\)
−0.0152832 + 0.999883i \(0.504865\pi\)
\(182\) −20236.2 −0.610923
\(183\) 22208.4i 0.663155i
\(184\) −48260.0 −1.42545
\(185\) 10378.2i 0.303235i
\(186\) −20013.9 −0.578504
\(187\) 11313.4i 0.323527i
\(188\) 1763.55i 0.0498968i
\(189\) −6637.93 −0.185827
\(190\) 37273.9i 1.03252i
\(191\) 65871.0i 1.80563i −0.430034 0.902813i \(-0.641498\pi\)
0.430034 0.902813i \(-0.358502\pi\)
\(192\) 20713.4 0.561886
\(193\) 46752.7 1.25514 0.627570 0.778560i \(-0.284050\pi\)
0.627570 + 0.778560i \(0.284050\pi\)
\(194\) −31980.0 −0.849718
\(195\) 9003.72i 0.236784i
\(196\) 66.2681 0.00172501
\(197\) 56429.6 1.45403 0.727017 0.686619i \(-0.240906\pi\)
0.727017 + 0.686619i \(0.240906\pi\)
\(198\) −2803.54 −0.0715116
\(199\) 4451.64 0.112412 0.0562061 0.998419i \(-0.482100\pi\)
0.0562061 + 0.998419i \(0.482100\pi\)
\(200\) 22464.7i 0.561618i
\(201\) 4507.30i 0.111564i
\(202\) −27369.9 −0.670764
\(203\) −65353.7 −1.58591
\(204\) 935.718 0.0224846
\(205\) −16896.3 −0.402054
\(206\) −80970.8 −1.90807
\(207\) 20631.1i 0.481483i
\(208\) 27702.2i 0.640306i
\(209\) 14373.6i 0.329058i
\(210\) 16342.7i 0.370582i
\(211\) 42832.4i 0.962071i −0.876701 0.481036i \(-0.840261\pi\)
0.876701 0.481036i \(-0.159739\pi\)
\(212\) 860.939 0.0191558
\(213\) 1229.14 0.0270921
\(214\) 57761.7i 1.26128i
\(215\) 48575.0i 1.05084i
\(216\) 8860.84i 0.189919i
\(217\) 44989.3i 0.955411i
\(218\) −888.699 −0.0187000
\(219\) 32274.6i 0.672935i
\(220\) 171.642i 0.00354633i
\(221\) 46600.8i 0.954132i
\(222\) 13310.9 0.270085
\(223\) −14776.1 −0.297132 −0.148566 0.988902i \(-0.547466\pi\)
−0.148566 + 0.988902i \(0.547466\pi\)
\(224\) 2470.45i 0.0492356i
\(225\) −9603.64 −0.189701
\(226\) 51107.1 1.00061
\(227\) 37257.5i 0.723040i 0.932364 + 0.361520i \(0.117742\pi\)
−0.932364 + 0.361520i \(0.882258\pi\)
\(228\) −1188.82 −0.0228690
\(229\) 36389.1i 0.693906i −0.937883 0.346953i \(-0.887216\pi\)
0.937883 0.346953i \(-0.112784\pi\)
\(230\) 50794.0 0.960189
\(231\) 6302.08i 0.118103i
\(232\) 87239.4i 1.62083i
\(233\) 20634.6i 0.380088i −0.981776 0.190044i \(-0.939137\pi\)
0.981776 0.190044i \(-0.0608630\pi\)
\(234\) −11548.0 −0.210899
\(235\) 70930.1i 1.28438i
\(236\) 1405.79 + 202.681i 0.0252404 + 0.00363906i
\(237\) −46330.0 −0.824833
\(238\) 84585.2i 1.49328i
\(239\) −18302.2 −0.320411 −0.160205 0.987084i \(-0.551216\pi\)
−0.160205 + 0.987084i \(0.551216\pi\)
\(240\) −22372.2 −0.388406
\(241\) 73211.9 1.26051 0.630257 0.776386i \(-0.282949\pi\)
0.630257 + 0.776386i \(0.282949\pi\)
\(242\) 56644.3i 0.967221i
\(243\) −3788.00 −0.0641500
\(244\) 1743.89i 0.0292914i
\(245\) 2665.31 0.0444033
\(246\) 21670.9i 0.358101i
\(247\) 59205.8i 0.970444i
\(248\) 60055.4 0.976447
\(249\) 56453.0i 0.910518i
\(250\) 65190.8i 1.04305i
\(251\) 66492.8 1.05542 0.527712 0.849423i \(-0.323050\pi\)
0.527712 + 0.849423i \(0.323050\pi\)
\(252\) −521.236 −0.00820792
\(253\) −19587.2 −0.306007
\(254\) 15151.7i 0.234852i
\(255\) 37634.6 0.578771
\(256\) 5010.54 0.0764548
\(257\) −48002.7 −0.726774 −0.363387 0.931638i \(-0.618380\pi\)
−0.363387 + 0.931638i \(0.618380\pi\)
\(258\) −62301.3 −0.935961
\(259\) 29921.5i 0.446051i
\(260\) 707.007i 0.0104587i
\(261\) −37294.7 −0.547477
\(262\) 89022.1 1.29687
\(263\) 23476.9 0.339413 0.169707 0.985495i \(-0.445718\pi\)
0.169707 + 0.985495i \(0.445718\pi\)
\(264\) 8412.52 0.120703
\(265\) 34627.0 0.493087
\(266\) 107465.i 1.51881i
\(267\) 32542.0i 0.456480i
\(268\) 353.930i 0.00492775i
\(269\) 86186.2i 1.19106i −0.803334 0.595529i \(-0.796942\pi\)
0.803334 0.595529i \(-0.203058\pi\)
\(270\) 9326.09i 0.127930i
\(271\) −18673.8 −0.254270 −0.127135 0.991885i \(-0.540578\pi\)
−0.127135 + 0.991885i \(0.540578\pi\)
\(272\) −115792. −1.56510
\(273\) 25958.7i 0.348303i
\(274\) 32986.2i 0.439371i
\(275\) 9117.73i 0.120565i
\(276\) 1620.03i 0.0212670i
\(277\) 132710. 1.72959 0.864797 0.502122i \(-0.167447\pi\)
0.864797 + 0.502122i \(0.167447\pi\)
\(278\) 54719.4i 0.708030i
\(279\) 25673.6i 0.329821i
\(280\) 49039.1i 0.625499i
\(281\) 42447.9 0.537581 0.268790 0.963199i \(-0.413376\pi\)
0.268790 + 0.963199i \(0.413376\pi\)
\(282\) 90973.5 1.14398
\(283\) 1417.90i 0.0177041i 0.999961 + 0.00885205i \(0.00281773\pi\)
−0.999961 + 0.00885205i \(0.997182\pi\)
\(284\) 96.5169 0.00119665
\(285\) −47814.4 −0.588666
\(286\) 10963.7i 0.134037i
\(287\) 48713.9 0.591411
\(288\) 1409.78i 0.0169968i
\(289\) 111265. 1.33219
\(290\) 91820.0i 1.09180i
\(291\) 41023.5i 0.484447i
\(292\) 2534.33i 0.0297233i
\(293\) 44835.8 0.522264 0.261132 0.965303i \(-0.415904\pi\)
0.261132 + 0.965303i \(0.415904\pi\)
\(294\) 3418.46i 0.0395491i
\(295\) 56540.9 + 8151.83i 0.649708 + 0.0936723i
\(296\) −39941.7 −0.455872
\(297\) 3596.34i 0.0407706i
\(298\) −23284.0 −0.262195
\(299\) −80681.1 −0.902463
\(300\) −754.115 −0.00837905
\(301\) 140047.i 1.54576i
\(302\) 158406. 1.73683
\(303\) 35109.7i 0.382421i
\(304\) 147113. 1.59186
\(305\) 70139.3i 0.753984i
\(306\) 48269.3i 0.515500i
\(307\) −15561.6 −0.165112 −0.0825559 0.996586i \(-0.526308\pi\)
−0.0825559 + 0.996586i \(0.526308\pi\)
\(308\) 494.863i 0.00521656i
\(309\) 103868.i 1.08784i
\(310\) −63208.7 −0.657739
\(311\) −160952. −1.66409 −0.832043 0.554711i \(-0.812829\pi\)
−0.832043 + 0.554711i \(0.812829\pi\)
\(312\) 34651.7 0.355972
\(313\) 79828.7i 0.814836i −0.913242 0.407418i \(-0.866429\pi\)
0.913242 0.407418i \(-0.133571\pi\)
\(314\) −4032.08 −0.0408950
\(315\) −20964.1 −0.211279
\(316\) −3638.01 −0.0364326
\(317\) 108281. 1.07754 0.538770 0.842453i \(-0.318889\pi\)
0.538770 + 0.842453i \(0.318889\pi\)
\(318\) 44411.9i 0.439182i
\(319\) 35407.7i 0.347950i
\(320\) 65417.6 0.638844
\(321\) −74095.9 −0.719091
\(322\) −146445. −1.41241
\(323\) −247474. −2.37206
\(324\) −297.448 −0.00283349
\(325\) 37556.6i 0.355565i
\(326\) 208098.i 1.95809i
\(327\) 1140.01i 0.0106614i
\(328\) 65027.2i 0.604432i
\(329\) 204499.i 1.88930i
\(330\) −8854.23 −0.0813061
\(331\) 124431. 1.13573 0.567864 0.823123i \(-0.307770\pi\)
0.567864 + 0.823123i \(0.307770\pi\)
\(332\) 4432.91i 0.0402173i
\(333\) 17075.0i 0.153983i
\(334\) 71143.6i 0.637739i
\(335\) 14235.1i 0.126844i
\(336\) 64501.5 0.571335
\(337\) 88676.9i 0.780820i −0.920641 0.390410i \(-0.872333\pi\)
0.920641 0.390410i \(-0.127667\pi\)
\(338\) 70531.3i 0.617374i
\(339\) 65559.4i 0.570473i
\(340\) 2955.21 0.0255641
\(341\) 24374.6 0.209618
\(342\) 61325.7i 0.524313i
\(343\) −121285. −1.03090
\(344\) 186946. 1.57979
\(345\) 65157.7i 0.547429i
\(346\) 241956. 2.02108
\(347\) 55831.8i 0.463685i −0.972753 0.231842i \(-0.925525\pi\)
0.972753 0.231842i \(-0.0744754\pi\)
\(348\) −2928.52 −0.0241819
\(349\) 66212.9i 0.543616i −0.962352 0.271808i \(-0.912378\pi\)
0.962352 0.271808i \(-0.0876215\pi\)
\(350\) 68169.0i 0.556482i
\(351\) 14813.6i 0.120239i
\(352\) 1338.45 0.0108023
\(353\) 119306.i 0.957439i −0.877968 0.478719i \(-0.841101\pi\)
0.877968 0.478719i \(-0.158899\pi\)
\(354\) 10455.4 72518.1i 0.0834320 0.578682i
\(355\) 3881.91 0.0308027
\(356\) 2555.33i 0.0201626i
\(357\) −108505. −0.851357
\(358\) 212657. 1.65926
\(359\) −164492. −1.27631 −0.638155 0.769908i \(-0.720302\pi\)
−0.638155 + 0.769908i \(0.720302\pi\)
\(360\) 27984.6i 0.215931i
\(361\) 184092. 1.41261
\(362\) 4056.30i 0.0309538i
\(363\) −72662.5 −0.551438
\(364\) 2038.38i 0.0153844i
\(365\) 101931.i 0.765103i
\(366\) 89959.2 0.671558
\(367\) 10621.8i 0.0788613i 0.999222 + 0.0394307i \(0.0125544\pi\)
−0.999222 + 0.0394307i \(0.987446\pi\)
\(368\) 200474.i 1.48035i
\(369\) 27799.0 0.204163
\(370\) 42038.9 0.307077
\(371\) −99833.4 −0.725318
\(372\) 2015.99i 0.0145681i
\(373\) 49988.6 0.359297 0.179648 0.983731i \(-0.442504\pi\)
0.179648 + 0.983731i \(0.442504\pi\)
\(374\) −45827.1 −0.327627
\(375\) −83625.7 −0.594672
\(376\) −272982. −1.93089
\(377\) 145847.i 1.02616i
\(378\) 26888.1i 0.188182i
\(379\) −23033.2 −0.160352 −0.0801762 0.996781i \(-0.525548\pi\)
−0.0801762 + 0.996781i \(0.525548\pi\)
\(380\) −3754.57 −0.0260012
\(381\) −19436.4 −0.133895
\(382\) −266823. −1.82850
\(383\) −35518.2 −0.242133 −0.121067 0.992644i \(-0.538631\pi\)
−0.121067 + 0.992644i \(0.538631\pi\)
\(384\) 88244.2i 0.598444i
\(385\) 19903.4i 0.134278i
\(386\) 189380.i 1.27104i
\(387\) 79919.1i 0.533616i
\(388\) 3221.32i 0.0213979i
\(389\) 157436. 1.04041 0.520206 0.854041i \(-0.325855\pi\)
0.520206 + 0.854041i \(0.325855\pi\)
\(390\) −36471.2 −0.239784
\(391\) 337239.i 2.20589i
\(392\) 10257.7i 0.0667541i
\(393\) 114196.i 0.739378i
\(394\) 228578.i 1.47246i
\(395\) −146321. −0.937805
\(396\) 282.398i 0.00180083i
\(397\) 163490.i 1.03731i 0.854983 + 0.518656i \(0.173568\pi\)
−0.854983 + 0.518656i \(0.826432\pi\)
\(398\) 18032.2i 0.113837i
\(399\) 137854. 0.865912
\(400\) 93319.6 0.583247
\(401\) 74973.1i 0.466248i 0.972447 + 0.233124i \(0.0748948\pi\)
−0.972447 + 0.233124i \(0.925105\pi\)
\(402\) −18257.6 −0.112978
\(403\) 100401. 0.618196
\(404\) 2756.95i 0.0168914i
\(405\) −11963.4 −0.0729363
\(406\) 264727.i 1.60600i
\(407\) −16211.1 −0.0978640
\(408\) 144841.i 0.870102i
\(409\) 216548.i 1.29452i −0.762271 0.647258i \(-0.775916\pi\)
0.762271 0.647258i \(-0.224084\pi\)
\(410\) 68441.6i 0.407148i
\(411\) 42314.2 0.250497
\(412\) 8156.13i 0.0480496i
\(413\) −163013. 23502.6i −0.955704 0.137789i
\(414\) −83569.9 −0.487584
\(415\) 178292.i 1.03523i
\(416\) 5513.18 0.0318578
\(417\) −70193.2 −0.403667
\(418\) 58222.8 0.333228
\(419\) 221474.i 1.26152i 0.775977 + 0.630761i \(0.217257\pi\)
−0.775977 + 0.630761i \(0.782743\pi\)
\(420\) −1646.18 −0.00933211
\(421\) 315604.i 1.78065i −0.455329 0.890323i \(-0.650478\pi\)
0.455329 0.890323i \(-0.349522\pi\)
\(422\) −173500. −0.974261
\(423\) 116699.i 0.652211i
\(424\) 133266.i 0.741287i
\(425\) −156983. −0.869107
\(426\) 4978.86i 0.0274353i
\(427\) 202219.i 1.10909i
\(428\) −5818.29 −0.0317620
\(429\) 14064.1 0.0764180
\(430\) −196762. −1.06415
\(431\) 37329.5i 0.200954i −0.994939 0.100477i \(-0.967963\pi\)
0.994939 0.100477i \(-0.0320369\pi\)
\(432\) 36808.4 0.197233
\(433\) 60211.0 0.321144 0.160572 0.987024i \(-0.448666\pi\)
0.160572 + 0.987024i \(0.448666\pi\)
\(434\) 182237. 0.967516
\(435\) −117785. −0.622462
\(436\) 89.5180i 0.000470909i
\(437\) 428458.i 2.24360i
\(438\) −130734. −0.681461
\(439\) −185108. −0.960495 −0.480248 0.877133i \(-0.659453\pi\)
−0.480248 + 0.877133i \(0.659453\pi\)
\(440\) 26568.7 0.137235
\(441\) −4385.15 −0.0225480
\(442\) −188765. −0.966222
\(443\) 234937.i 1.19714i −0.801071 0.598569i \(-0.795736\pi\)
0.801071 0.598569i \(-0.204264\pi\)
\(444\) 1340.79i 0.00680137i
\(445\) 102775.i 0.519002i
\(446\) 59853.3i 0.300897i
\(447\) 29868.3i 0.149484i
\(448\) −188606. −0.939722
\(449\) −69120.8 −0.342859 −0.171430 0.985196i \(-0.554839\pi\)
−0.171430 + 0.985196i \(0.554839\pi\)
\(450\) 38901.3i 0.192105i
\(451\) 26392.5i 0.129756i
\(452\) 5147.98i 0.0251976i
\(453\) 203200.i 0.990211i
\(454\) 150918. 0.732201
\(455\) 81983.6i 0.396008i
\(456\) 184019.i 0.884977i
\(457\) 307630.i 1.47298i 0.676449 + 0.736489i \(0.263518\pi\)
−0.676449 + 0.736489i \(0.736482\pi\)
\(458\) −147401. −0.702698
\(459\) −61919.2 −0.293900
\(460\) 5116.44i 0.0241798i
\(461\) 20386.5 0.0959272 0.0479636 0.998849i \(-0.484727\pi\)
0.0479636 + 0.998849i \(0.484727\pi\)
\(462\) 25527.7 0.119599
\(463\) 50749.8i 0.236740i 0.992970 + 0.118370i \(0.0377669\pi\)
−0.992970 + 0.118370i \(0.962233\pi\)
\(464\) 362396. 1.68325
\(465\) 81083.1i 0.374994i
\(466\) −83584.1 −0.384904
\(467\) 9160.46i 0.0420033i −0.999779 0.0210017i \(-0.993314\pi\)
0.999779 0.0210017i \(-0.00668553\pi\)
\(468\) 1163.22i 0.00531092i
\(469\) 41041.3i 0.186584i
\(470\) 287315. 1.30066
\(471\) 5172.29i 0.0233153i
\(472\) −31373.2 + 217603.i −0.140823 + 0.976746i
\(473\) 75875.5 0.339140
\(474\) 187668.i 0.835284i
\(475\) 199445. 0.883965
\(476\) −8520.20 −0.0376042
\(477\) −56970.9 −0.250389
\(478\) 74136.3i 0.324471i
\(479\) 281255. 1.22583 0.612913 0.790150i \(-0.289997\pi\)
0.612913 + 0.790150i \(0.289997\pi\)
\(480\) 4452.42i 0.0193248i
\(481\) −66774.5 −0.288616
\(482\) 296558.i 1.27649i
\(483\) 187857.i 0.805254i
\(484\) −5705.74 −0.0243569
\(485\) 129562.i 0.550799i
\(486\) 15344.0i 0.0649628i
\(487\) −12464.0 −0.0525534 −0.0262767 0.999655i \(-0.508365\pi\)
−0.0262767 + 0.999655i \(0.508365\pi\)
\(488\) −269939. −1.13351
\(489\) 266944. 1.11636
\(490\) 10796.3i 0.0449659i
\(491\) −267488. −1.10954 −0.554768 0.832005i \(-0.687193\pi\)
−0.554768 + 0.832005i \(0.687193\pi\)
\(492\) 2182.89 0.00901781
\(493\) −609625. −2.50824
\(494\) 239824. 0.982740
\(495\) 11358.1i 0.0463547i
\(496\) 249473.i 1.01405i
\(497\) −11192.0 −0.0453100
\(498\) 228673. 0.922054
\(499\) −211721. −0.850283 −0.425142 0.905127i \(-0.639776\pi\)
−0.425142 + 0.905127i \(0.639776\pi\)
\(500\) −6566.61 −0.0262665
\(501\) 91261.9 0.363592
\(502\) 269341.i 1.06880i
\(503\) 46231.2i 0.182725i −0.995818 0.0913627i \(-0.970878\pi\)
0.995818 0.0913627i \(-0.0291223\pi\)
\(504\) 80682.6i 0.317628i
\(505\) 110884.i 0.434798i
\(506\) 79341.6i 0.309885i
\(507\) −90476.5 −0.351982
\(508\) −1526.22 −0.00591412
\(509\) 118612.i 0.457819i 0.973448 + 0.228909i \(0.0735159\pi\)
−0.973448 + 0.228909i \(0.926484\pi\)
\(510\) 152446.i 0.586105i
\(511\) 293878.i 1.12545i
\(512\) 251426.i 0.959113i
\(513\) 78667.7 0.298924
\(514\) 194444.i 0.735982i
\(515\) 328040.i 1.23684i
\(516\) 6275.56i 0.0235696i
\(517\) −110795. −0.414513
\(518\) −121203. −0.451702
\(519\) 310377.i 1.15227i
\(520\) 109438. 0.404727
\(521\) −20361.9 −0.0750140 −0.0375070 0.999296i \(-0.511942\pi\)
−0.0375070 + 0.999296i \(0.511942\pi\)
\(522\) 151069.i 0.554414i
\(523\) 36769.4 0.134426 0.0672130 0.997739i \(-0.478589\pi\)
0.0672130 + 0.997739i \(0.478589\pi\)
\(524\) 8967.13i 0.0326581i
\(525\) 87446.2 0.317265
\(526\) 95097.4i 0.343714i
\(527\) 419664.i 1.51106i
\(528\) 34946.0i 0.125351i
\(529\) −304029. −1.08643
\(530\) 140263.i 0.499334i
\(531\) −93025.1 13412.0i −0.329922 0.0475668i
\(532\) 10824.8 0.0382470
\(533\) 108713.i 0.382671i
\(534\) 131817. 0.462264
\(535\) −234012. −0.817581
\(536\) 54785.2 0.190693
\(537\) 272793.i 0.945986i
\(538\) −349113. −1.20615
\(539\) 4163.28i 0.0143304i
\(540\) −939.410 −0.00322157
\(541\) 136111.i 0.465049i −0.972590 0.232525i \(-0.925301\pi\)
0.972590 0.232525i \(-0.0746986\pi\)
\(542\) 75641.7i 0.257491i
\(543\) 5203.37 0.0176476
\(544\) 23044.5i 0.0778700i
\(545\) 3600.42i 0.0121216i
\(546\) 105150. 0.352716
\(547\) 532541. 1.77983 0.889915 0.456125i \(-0.150763\pi\)
0.889915 + 0.456125i \(0.150763\pi\)
\(548\) 3322.67 0.0110644
\(549\) 115398.i 0.382873i
\(550\) 36933.0 0.122093
\(551\) 774522. 2.55112
\(552\) 250766. 0.822983
\(553\) 421859. 1.37949
\(554\) 537566.i 1.75151i
\(555\) 53926.8i 0.175073i
\(556\) −5511.84 −0.0178298
\(557\) −166657. −0.537172 −0.268586 0.963256i \(-0.586556\pi\)
−0.268586 + 0.963256i \(0.586556\pi\)
\(558\) 103995. 0.334000
\(559\) 312537. 1.00018
\(560\) 203711. 0.649588
\(561\) 58786.3i 0.186789i
\(562\) 171943.i 0.544392i
\(563\) 111610.i 0.352116i −0.984380 0.176058i \(-0.943665\pi\)
0.984380 0.176058i \(-0.0563347\pi\)
\(564\) 9163.69i 0.0288079i
\(565\) 207052.i 0.648608i
\(566\) 5743.47 0.0179284
\(567\) 34491.7 0.107287
\(568\) 14939.9i 0.0463076i
\(569\) 112850.i 0.348560i 0.984696 + 0.174280i \(0.0557598\pi\)
−0.984696 + 0.174280i \(0.944240\pi\)
\(570\) 193681.i 0.596124i
\(571\) 441479.i 1.35406i −0.735956 0.677029i \(-0.763267\pi\)
0.735956 0.677029i \(-0.236733\pi\)
\(572\) 1104.36 0.00337536
\(573\) 342276.i 1.04248i
\(574\) 197325.i 0.598904i
\(575\) 271788.i 0.822043i
\(576\) −107630. −0.324405
\(577\) 214151. 0.643234 0.321617 0.946870i \(-0.395774\pi\)
0.321617 + 0.946870i \(0.395774\pi\)
\(578\) 450701.i 1.34906i
\(579\) −242934. −0.724655
\(580\) −9248.96 −0.0274939
\(581\) 514034.i 1.52279i
\(582\) 166173. 0.490585
\(583\) 54088.4i 0.159135i
\(584\) 392291. 1.15023
\(585\) 46784.7i 0.136707i
\(586\) 181616.i 0.528881i
\(587\) 229548.i 0.666189i −0.942893 0.333094i \(-0.891907\pi\)
0.942893 0.333094i \(-0.108093\pi\)
\(588\) −344.339 −0.000995937
\(589\) 533179.i 1.53689i
\(590\) 33020.5 229029.i 0.0948592 0.657941i
\(591\) −293217. −0.839487
\(592\) 165920.i 0.473428i
\(593\) 161537. 0.459371 0.229686 0.973265i \(-0.426230\pi\)
0.229686 + 0.973265i \(0.426230\pi\)
\(594\) 14567.6 0.0412872
\(595\) −342683. −0.967962
\(596\) 2345.38i 0.00660268i
\(597\) −23131.4 −0.0649012
\(598\) 326813.i 0.913898i
\(599\) −259778. −0.724017 −0.362008 0.932175i \(-0.617909\pi\)
−0.362008 + 0.932175i \(0.617909\pi\)
\(600\) 116730.i 0.324251i
\(601\) 609538.i 1.68753i 0.536713 + 0.843765i \(0.319666\pi\)
−0.536713 + 0.843765i \(0.680334\pi\)
\(602\) 567286. 1.56534
\(603\) 23420.6i 0.0644115i
\(604\) 15956.1i 0.0437373i
\(605\) −229485. −0.626966
\(606\) 142218. 0.387266
\(607\) 123432. 0.335005 0.167502 0.985872i \(-0.446430\pi\)
0.167502 + 0.985872i \(0.446430\pi\)
\(608\) 29277.8i 0.0792012i
\(609\) 339588. 0.915625
\(610\) 284112. 0.763537
\(611\) −456372. −1.22246
\(612\) −4862.13 −0.0129815
\(613\) 182402.i 0.485409i 0.970100 + 0.242705i \(0.0780346\pi\)
−0.970100 + 0.242705i \(0.921965\pi\)
\(614\) 63035.2i 0.167204i
\(615\) 87795.8 0.232126
\(616\) −76600.4 −0.201869
\(617\) 550891. 1.44709 0.723544 0.690278i \(-0.242512\pi\)
0.723544 + 0.690278i \(0.242512\pi\)
\(618\) 420737. 1.10162
\(619\) 172751. 0.450856 0.225428 0.974260i \(-0.427622\pi\)
0.225428 + 0.974260i \(0.427622\pi\)
\(620\) 6366.96i 0.0165634i
\(621\) 107202.i 0.277984i
\(622\) 651966.i 1.68517i
\(623\) 296312.i 0.763438i
\(624\) 143945.i 0.369681i
\(625\) −41803.1 −0.107016
\(626\) −323361. −0.825160
\(627\) 74687.4i 0.189982i
\(628\) 406.149i 0.00102983i
\(629\) 279111.i 0.705464i
\(630\) 84919.0i 0.213956i
\(631\) −6939.21 −0.0174282 −0.00871408 0.999962i \(-0.502774\pi\)
−0.00871408 + 0.999962i \(0.502774\pi\)
\(632\) 563132.i 1.40986i
\(633\) 222563.i 0.555452i
\(634\) 438611.i 1.09119i
\(635\) −61384.7 −0.152234
\(636\) −4473.57 −0.0110596
\(637\) 17148.8i 0.0422626i
\(638\) 143425. 0.352358
\(639\) −6386.80 −0.0156416
\(640\) 278696.i 0.680410i
\(641\) −213083. −0.518601 −0.259300 0.965797i \(-0.583492\pi\)
−0.259300 + 0.965797i \(0.583492\pi\)
\(642\) 300139.i 0.728202i
\(643\) −323868. −0.783333 −0.391666 0.920107i \(-0.628101\pi\)
−0.391666 + 0.920107i \(0.628101\pi\)
\(644\) 14751.2i 0.0355678i
\(645\) 252403.i 0.606702i
\(646\) 1.00244e6i 2.40211i
\(647\) −268558. −0.641548 −0.320774 0.947156i \(-0.603943\pi\)
−0.320774 + 0.947156i \(0.603943\pi\)
\(648\) 46042.3i 0.109650i
\(649\) −12733.4 + 88318.4i −0.0302311 + 0.209682i
\(650\) 152130. 0.360070
\(651\) 233771.i 0.551607i
\(652\) 20961.5 0.0493091
\(653\) −43918.8 −0.102997 −0.0514985 0.998673i \(-0.516400\pi\)
−0.0514985 + 0.998673i \(0.516400\pi\)
\(654\) 4617.82 0.0107965
\(655\) 360658.i 0.840646i
\(656\) −270126. −0.627710
\(657\) 167704.i 0.388519i
\(658\) −828361. −1.91323
\(659\) 246753.i 0.568187i 0.958797 + 0.284093i \(0.0916925\pi\)
−0.958797 + 0.284093i \(0.908307\pi\)
\(660\) 891.880i 0.00204747i
\(661\) 91190.3 0.208711 0.104356 0.994540i \(-0.466722\pi\)
0.104356 + 0.994540i \(0.466722\pi\)
\(662\) 504032.i 1.15012i
\(663\) 242145.i 0.550869i
\(664\) −686175. −1.55632
\(665\) 435375. 0.984510
\(666\) −69165.4 −0.155934
\(667\) 1.05546e6i 2.37241i
\(668\) 7166.24 0.0160597
\(669\) 76778.8 0.171549
\(670\) −57661.8 −0.128451
\(671\) −109560. −0.243335
\(672\) 12836.8i 0.0284262i
\(673\) 377278.i 0.832973i 0.909142 + 0.416486i \(0.136739\pi\)
−0.909142 + 0.416486i \(0.863261\pi\)
\(674\) −359202. −0.790713
\(675\) 49902.0 0.109524
\(676\) −7104.57 −0.0155469
\(677\) 301726. 0.658317 0.329159 0.944275i \(-0.393235\pi\)
0.329159 + 0.944275i \(0.393235\pi\)
\(678\) −265560. −0.577701
\(679\) 373540.i 0.810210i
\(680\) 457441.i 0.989275i
\(681\) 193596.i 0.417447i
\(682\) 98733.7i 0.212274i
\(683\) 44408.5i 0.0951974i −0.998867 0.0475987i \(-0.984843\pi\)
0.998867 0.0475987i \(-0.0151569\pi\)
\(684\) 6177.29 0.0132034
\(685\) 133638. 0.284806
\(686\) 491285.i 1.04396i
\(687\) 189083.i 0.400627i
\(688\) 776583.i 1.64063i
\(689\) 222794.i 0.469315i
\(690\) −263933. −0.554365
\(691\) 428913.i 0.898284i −0.893460 0.449142i \(-0.851730\pi\)
0.893460 0.449142i \(-0.148270\pi\)
\(692\) 24372.0i 0.0508954i
\(693\) 32746.5i 0.0681866i
\(694\) −226157. −0.469560
\(695\) −221687. −0.458955
\(696\) 453309.i 0.935785i
\(697\) 454407. 0.935362
\(698\) −268208. −0.550504
\(699\) 107220.i 0.219444i
\(700\) 6866.61 0.0140135
\(701\) 142828.i 0.290654i 0.989384 + 0.145327i \(0.0464234\pi\)
−0.989384 + 0.145327i \(0.953577\pi\)
\(702\) 60005.0 0.121762
\(703\) 354607.i 0.717525i
\(704\) 102184.i 0.206176i
\(705\) 368564.i 0.741540i
\(706\) −483269. −0.969570
\(707\) 319692.i 0.639577i
\(708\) −7304.69 1053.16i −0.0145725 0.00210101i
\(709\) 361262. 0.718670 0.359335 0.933209i \(-0.383004\pi\)
0.359335 + 0.933209i \(0.383004\pi\)
\(710\) 15724.4i 0.0311930i
\(711\) 240738. 0.476217
\(712\) −395542. −0.780247
\(713\) 726575. 1.42923
\(714\) 439518.i 0.862144i
\(715\) 44417.6 0.0868845
\(716\) 21420.8i 0.0417839i
\(717\) 95101.0 0.184989
\(718\) 666305.i 1.29248i
\(719\) 364020.i 0.704154i −0.935971 0.352077i \(-0.885475\pi\)
0.935971 0.352077i \(-0.114525\pi\)
\(720\) 116249. 0.224246
\(721\) 945774.i 1.81935i
\(722\) 745700.i 1.43051i
\(723\) −380420. −0.727758
\(724\) 408.588 0.000779487
\(725\) 491309. 0.934715
\(726\) 294333.i 0.558425i
\(727\) 295247. 0.558619 0.279310 0.960201i \(-0.409894\pi\)
0.279310 + 0.960201i \(0.409894\pi\)
\(728\) −315522. −0.595343
\(729\) 19683.0 0.0370370
\(730\) −412889. −0.774797
\(731\) 1.30637e6i 2.44473i
\(732\) 9061.52i 0.0169114i
\(733\) 203200. 0.378195 0.189097 0.981958i \(-0.439444\pi\)
0.189097 + 0.981958i \(0.439444\pi\)
\(734\) 43025.3 0.0798605
\(735\) −13849.3 −0.0256362
\(736\) 39897.6 0.0736531
\(737\) 22235.6 0.0409368
\(738\) 112605.i 0.206750i
\(739\) 1.00932e6i 1.84816i 0.382195 + 0.924082i \(0.375168\pi\)
−0.382195 + 0.924082i \(0.624832\pi\)
\(740\) 4234.54i 0.00773291i
\(741\) 307642.i 0.560286i
\(742\) 404393.i 0.734508i
\(743\) −535342. −0.969737 −0.484869 0.874587i \(-0.661133\pi\)
−0.484869 + 0.874587i \(0.661133\pi\)
\(744\) −312057. −0.563752
\(745\) 94331.2i 0.169958i
\(746\) 202488.i 0.363849i
\(747\) 293338.i 0.525688i
\(748\) 4616.13i 0.00825039i
\(749\) 674682. 1.20264
\(750\) 338741.i 0.602206i
\(751\) 808120.i 1.43283i 0.697672 + 0.716417i \(0.254219\pi\)
−0.697672 + 0.716417i \(0.745781\pi\)
\(752\) 1.13398e6i 2.00526i
\(753\) −345507. −0.609350
\(754\) 590779. 1.03916
\(755\) 641754.i 1.12583i
\(756\) 2708.42 0.00473885
\(757\) −597248. −1.04223 −0.521114 0.853487i \(-0.674483\pi\)
−0.521114 + 0.853487i \(0.674483\pi\)
\(758\) 93300.0i 0.162384i
\(759\) 101778. 0.176673
\(760\) 581174.i 1.00619i
\(761\) 337522. 0.582818 0.291409 0.956599i \(-0.405876\pi\)
0.291409 + 0.956599i \(0.405876\pi\)
\(762\) 78730.7i 0.135592i
\(763\) 10380.4i 0.0178305i
\(764\) 26876.8i 0.0460459i
\(765\) −195555. −0.334154
\(766\) 143873.i 0.245201i
\(767\) −52449.7 + 363790.i −0.0891564 + 0.618386i
\(768\) −26035.5 −0.0441412
\(769\) 135631.i 0.229354i 0.993403 + 0.114677i \(0.0365833\pi\)
−0.993403 + 0.114677i \(0.963417\pi\)
\(770\) 80622.4 0.135980
\(771\) 249429. 0.419603
\(772\) −19076.1 −0.0320078
\(773\) 320257.i 0.535969i 0.963423 + 0.267985i \(0.0863576\pi\)
−0.963423 + 0.267985i \(0.913642\pi\)
\(774\) 323727. 0.540377
\(775\) 338216.i 0.563107i
\(776\) −498631. −0.828049
\(777\) 155477.i 0.257528i
\(778\) 637723.i 1.05359i
\(779\) −577320. −0.951353
\(780\) 3673.71i 0.00603832i
\(781\) 6063.65i 0.00994105i
\(782\) −1.36605e6 −2.23384
\(783\) 193789. 0.316086
\(784\) 42611.0 0.0693249
\(785\) 16335.3i 0.0265087i
\(786\) −462573. −0.748746
\(787\) −584994. −0.944500 −0.472250 0.881465i \(-0.656558\pi\)
−0.472250 + 0.881465i \(0.656558\pi\)
\(788\) −23024.5 −0.0370799
\(789\) −121989. −0.195960