Properties

Label 177.5.c.a.58.3
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 58.3
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.38

$q$-expansion

\(f(q)\) \(=\) \(q-7.65331i q^{2} -5.19615 q^{3} -42.5731 q^{4} -38.1687 q^{5} +39.7678i q^{6} -35.1454 q^{7} +203.372i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-7.65331i q^{2} -5.19615 q^{3} -42.5731 q^{4} -38.1687 q^{5} +39.7678i q^{6} -35.1454 q^{7} +203.372i q^{8} +27.0000 q^{9} +292.117i q^{10} -147.824i q^{11} +221.217 q^{12} -17.0918i q^{13} +268.979i q^{14} +198.331 q^{15} +875.302 q^{16} -354.287 q^{17} -206.639i q^{18} -647.468 q^{19} +1624.96 q^{20} +182.621 q^{21} -1131.34 q^{22} -862.278i q^{23} -1056.75i q^{24} +831.852 q^{25} -130.809 q^{26} -140.296 q^{27} +1496.25 q^{28} +440.875 q^{29} -1517.88i q^{30} +347.019i q^{31} -3445.00i q^{32} +768.116i q^{33} +2711.47i q^{34} +1341.45 q^{35} -1149.47 q^{36} +972.830i q^{37} +4955.27i q^{38} +88.8114i q^{39} -7762.47i q^{40} +2783.36 q^{41} -1397.65i q^{42} -2837.80i q^{43} +6293.33i q^{44} -1030.56 q^{45} -6599.28 q^{46} +1287.07i q^{47} -4548.20 q^{48} -1165.80 q^{49} -6366.42i q^{50} +1840.93 q^{51} +727.650i q^{52} -1103.72 q^{53} +1073.73i q^{54} +5642.25i q^{55} -7147.61i q^{56} +3364.34 q^{57} -3374.15i q^{58} +(1692.03 + 3042.10i) q^{59} -8443.55 q^{60} -5980.77i q^{61} +2655.84 q^{62} -948.926 q^{63} -12360.8 q^{64} +652.371i q^{65} +5878.63 q^{66} +3352.44i q^{67} +15083.1 q^{68} +4480.53i q^{69} -10266.6i q^{70} -1396.21 q^{71} +5491.06i q^{72} -1649.77i q^{73} +7445.37 q^{74} -4322.43 q^{75} +27564.7 q^{76} +5195.33i q^{77} +679.701 q^{78} -8357.83 q^{79} -33409.2 q^{80} +729.000 q^{81} -21301.9i q^{82} -5025.77i q^{83} -7774.74 q^{84} +13522.7 q^{85} -21718.6 q^{86} -2290.85 q^{87} +30063.3 q^{88} +5292.92i q^{89} +7887.16i q^{90} +600.697i q^{91} +36709.9i q^{92} -1803.16i q^{93} +9850.36 q^{94} +24713.0 q^{95} +17900.7i q^{96} +14051.7i q^{97} +8922.24i q^{98} -3991.25i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.65331i 1.91333i −0.291195 0.956664i \(-0.594053\pi\)
0.291195 0.956664i \(-0.405947\pi\)
\(3\) −5.19615 −0.577350
\(4\) −42.5731 −2.66082
\(5\) −38.1687 −1.52675 −0.763375 0.645956i \(-0.776459\pi\)
−0.763375 + 0.645956i \(0.776459\pi\)
\(6\) 39.7678i 1.10466i
\(7\) −35.1454 −0.717253 −0.358626 0.933481i \(-0.616755\pi\)
−0.358626 + 0.933481i \(0.616755\pi\)
\(8\) 203.372i 3.17769i
\(9\) 27.0000 0.333333
\(10\) 292.117i 2.92117i
\(11\) 147.824i 1.22169i −0.791752 0.610843i \(-0.790831\pi\)
0.791752 0.610843i \(-0.209169\pi\)
\(12\) 221.217 1.53623
\(13\) 17.0918i 0.101135i −0.998721 0.0505674i \(-0.983897\pi\)
0.998721 0.0505674i \(-0.0161030\pi\)
\(14\) 268.979i 1.37234i
\(15\) 198.331 0.881469
\(16\) 875.302 3.41915
\(17\) −354.287 −1.22591 −0.612953 0.790119i \(-0.710019\pi\)
−0.612953 + 0.790119i \(0.710019\pi\)
\(18\) 206.639i 0.637776i
\(19\) −647.468 −1.79354 −0.896770 0.442498i \(-0.854092\pi\)
−0.896770 + 0.442498i \(0.854092\pi\)
\(20\) 1624.96 4.06241
\(21\) 182.621 0.414106
\(22\) −1131.34 −2.33748
\(23\) 862.278i 1.63001i −0.579451 0.815007i \(-0.696733\pi\)
0.579451 0.815007i \(-0.303267\pi\)
\(24\) 1056.75i 1.83464i
\(25\) 831.852 1.33096
\(26\) −130.809 −0.193504
\(27\) −140.296 −0.192450
\(28\) 1496.25 1.90848
\(29\) 440.875 0.524227 0.262113 0.965037i \(-0.415581\pi\)
0.262113 + 0.965037i \(0.415581\pi\)
\(30\) 1517.88i 1.68654i
\(31\) 347.019i 0.361101i 0.983566 + 0.180551i \(0.0577880\pi\)
−0.983566 + 0.180551i \(0.942212\pi\)
\(32\) 3445.00i 3.36426i
\(33\) 768.116i 0.705341i
\(34\) 2711.47i 2.34556i
\(35\) 1341.45 1.09507
\(36\) −1149.47 −0.886940
\(37\) 972.830i 0.710613i 0.934750 + 0.355307i \(0.115624\pi\)
−0.934750 + 0.355307i \(0.884376\pi\)
\(38\) 4955.27i 3.43163i
\(39\) 88.8114i 0.0583902i
\(40\) 7762.47i 4.85154i
\(41\) 2783.36 1.65578 0.827889 0.560892i \(-0.189542\pi\)
0.827889 + 0.560892i \(0.189542\pi\)
\(42\) 1397.65i 0.792321i
\(43\) 2837.80i 1.53478i −0.641183 0.767388i \(-0.721556\pi\)
0.641183 0.767388i \(-0.278444\pi\)
\(44\) 6293.33i 3.25069i
\(45\) −1030.56 −0.508916
\(46\) −6599.28 −3.11875
\(47\) 1287.07i 0.582649i 0.956624 + 0.291324i \(0.0940959\pi\)
−0.956624 + 0.291324i \(0.905904\pi\)
\(48\) −4548.20 −1.97405
\(49\) −1165.80 −0.485548
\(50\) 6366.42i 2.54657i
\(51\) 1840.93 0.707777
\(52\) 727.650i 0.269101i
\(53\) −1103.72 −0.392923 −0.196462 0.980511i \(-0.562945\pi\)
−0.196462 + 0.980511i \(0.562945\pi\)
\(54\) 1073.73i 0.368220i
\(55\) 5642.25i 1.86521i
\(56\) 7147.61i 2.27921i
\(57\) 3364.34 1.03550
\(58\) 3374.15i 1.00302i
\(59\) 1692.03 + 3042.10i 0.486076 + 0.873917i
\(60\) −8443.55 −2.34543
\(61\) 5980.77i 1.60730i −0.595100 0.803651i \(-0.702888\pi\)
0.595100 0.803651i \(-0.297112\pi\)
\(62\) 2655.84 0.690905
\(63\) −948.926 −0.239084
\(64\) −12360.8 −3.01777
\(65\) 652.371i 0.154407i
\(66\) 5878.63 1.34955
\(67\) 3352.44i 0.746812i 0.927668 + 0.373406i \(0.121810\pi\)
−0.927668 + 0.373406i \(0.878190\pi\)
\(68\) 15083.1 3.26192
\(69\) 4480.53i 0.941089i
\(70\) 10266.6i 2.09522i
\(71\) −1396.21 −0.276971 −0.138486 0.990364i \(-0.544223\pi\)
−0.138486 + 0.990364i \(0.544223\pi\)
\(72\) 5491.06i 1.05923i
\(73\) 1649.77i 0.309584i −0.987947 0.154792i \(-0.950529\pi\)
0.987947 0.154792i \(-0.0494707\pi\)
\(74\) 7445.37 1.35964
\(75\) −4322.43 −0.768432
\(76\) 27564.7 4.77229
\(77\) 5195.33i 0.876258i
\(78\) 679.701 0.111719
\(79\) −8357.83 −1.33918 −0.669591 0.742730i \(-0.733530\pi\)
−0.669591 + 0.742730i \(0.733530\pi\)
\(80\) −33409.2 −5.22018
\(81\) 729.000 0.111111
\(82\) 21301.9i 3.16805i
\(83\) 5025.77i 0.729536i −0.931098 0.364768i \(-0.881148\pi\)
0.931098 0.364768i \(-0.118852\pi\)
\(84\) −7774.74 −1.10186
\(85\) 13522.7 1.87165
\(86\) −21718.6 −2.93653
\(87\) −2290.85 −0.302662
\(88\) 30063.3 3.88214
\(89\) 5292.92i 0.668213i 0.942535 + 0.334107i \(0.108435\pi\)
−0.942535 + 0.334107i \(0.891565\pi\)
\(90\) 7887.16i 0.973724i
\(91\) 600.697i 0.0725392i
\(92\) 36709.9i 4.33718i
\(93\) 1803.16i 0.208482i
\(94\) 9850.36 1.11480
\(95\) 24713.0 2.73828
\(96\) 17900.7i 1.94235i
\(97\) 14051.7i 1.49343i 0.665142 + 0.746716i \(0.268371\pi\)
−0.665142 + 0.746716i \(0.731629\pi\)
\(98\) 8922.24i 0.929013i
\(99\) 3991.25i 0.407229i
\(100\) −35414.5 −3.54145
\(101\) 623.626i 0.0611338i 0.999533 + 0.0305669i \(0.00973126\pi\)
−0.999533 + 0.0305669i \(0.990269\pi\)
\(102\) 14089.2i 1.35421i
\(103\) 8032.20i 0.757112i 0.925578 + 0.378556i \(0.123579\pi\)
−0.925578 + 0.378556i \(0.876421\pi\)
\(104\) 3475.99 0.321375
\(105\) −6970.40 −0.632236
\(106\) 8447.13i 0.751791i
\(107\) 11098.7 0.969402 0.484701 0.874680i \(-0.338928\pi\)
0.484701 + 0.874680i \(0.338928\pi\)
\(108\) 5972.85 0.512075
\(109\) 7809.17i 0.657283i −0.944455 0.328641i \(-0.893409\pi\)
0.944455 0.328641i \(-0.106591\pi\)
\(110\) 43181.9 3.56875
\(111\) 5054.97i 0.410273i
\(112\) −30762.8 −2.45239
\(113\) 3130.68i 0.245178i 0.992457 + 0.122589i \(0.0391198\pi\)
−0.992457 + 0.122589i \(0.960880\pi\)
\(114\) 25748.3i 1.98125i
\(115\) 32912.0i 2.48862i
\(116\) −18769.4 −1.39487
\(117\) 461.478i 0.0337116i
\(118\) 23282.2 12949.6i 1.67209 0.930022i
\(119\) 12451.6 0.879285
\(120\) 40335.0i 2.80104i
\(121\) −7210.93 −0.492516
\(122\) −45772.7 −3.07530
\(123\) −14462.8 −0.955964
\(124\) 14773.7i 0.960827i
\(125\) −7895.26 −0.505297
\(126\) 7262.42i 0.457447i
\(127\) −18711.5 −1.16011 −0.580056 0.814576i \(-0.696969\pi\)
−0.580056 + 0.814576i \(0.696969\pi\)
\(128\) 39481.1i 2.40973i
\(129\) 14745.6i 0.886103i
\(130\) 4992.80 0.295432
\(131\) 12408.9i 0.723089i −0.932355 0.361545i \(-0.882249\pi\)
0.932355 0.361545i \(-0.117751\pi\)
\(132\) 32701.1i 1.87679i
\(133\) 22755.5 1.28642
\(134\) 25657.2 1.42889
\(135\) 5354.92 0.293823
\(136\) 72052.2i 3.89556i
\(137\) −24025.7 −1.28007 −0.640037 0.768344i \(-0.721081\pi\)
−0.640037 + 0.768344i \(0.721081\pi\)
\(138\) 34290.9 1.80061
\(139\) −3014.36 −0.156014 −0.0780072 0.996953i \(-0.524856\pi\)
−0.0780072 + 0.996953i \(0.524856\pi\)
\(140\) −57109.9 −2.91377
\(141\) 6687.82i 0.336393i
\(142\) 10685.6i 0.529937i
\(143\) −2526.57 −0.123555
\(144\) 23633.2 1.13972
\(145\) −16827.6 −0.800362
\(146\) −12626.2 −0.592335
\(147\) 6057.68 0.280331
\(148\) 41416.4i 1.89082i
\(149\) 10398.6i 0.468383i −0.972190 0.234192i \(-0.924756\pi\)
0.972190 0.234192i \(-0.0752443\pi\)
\(150\) 33080.9i 1.47026i
\(151\) 35440.0i 1.55432i −0.629305 0.777159i \(-0.716660\pi\)
0.629305 0.777159i \(-0.283340\pi\)
\(152\) 131677.i 5.69932i
\(153\) −9565.75 −0.408635
\(154\) 39761.5 1.67657
\(155\) 13245.3i 0.551311i
\(156\) 3780.98i 0.155366i
\(157\) 23302.5i 0.945373i 0.881231 + 0.472686i \(0.156716\pi\)
−0.881231 + 0.472686i \(0.843284\pi\)
\(158\) 63965.0i 2.56229i
\(159\) 5735.11 0.226854
\(160\) 131491.i 5.13637i
\(161\) 30305.1i 1.16913i
\(162\) 5579.26i 0.212592i
\(163\) −8996.62 −0.338613 −0.169307 0.985563i \(-0.554153\pi\)
−0.169307 + 0.985563i \(0.554153\pi\)
\(164\) −118497. −4.40573
\(165\) 29318.0i 1.07688i
\(166\) −38463.8 −1.39584
\(167\) −441.902 −0.0158450 −0.00792252 0.999969i \(-0.502522\pi\)
−0.00792252 + 0.999969i \(0.502522\pi\)
\(168\) 37140.0i 1.31590i
\(169\) 28268.9 0.989772
\(170\) 103493.i 3.58108i
\(171\) −17481.6 −0.597846
\(172\) 120814.i 4.08376i
\(173\) 2947.42i 0.0984803i −0.998787 0.0492402i \(-0.984320\pi\)
0.998787 0.0492402i \(-0.0156800\pi\)
\(174\) 17532.6i 0.579092i
\(175\) −29235.8 −0.954637
\(176\) 129391.i 4.17713i
\(177\) −8792.04 15807.2i −0.280636 0.504556i
\(178\) 40508.3 1.27851
\(179\) 17326.2i 0.540750i 0.962755 + 0.270375i \(0.0871477\pi\)
−0.962755 + 0.270375i \(0.912852\pi\)
\(180\) 43874.0 1.35414
\(181\) −9276.44 −0.283155 −0.141578 0.989927i \(-0.545217\pi\)
−0.141578 + 0.989927i \(0.545217\pi\)
\(182\) 4597.32 0.138791
\(183\) 31077.0i 0.927977i
\(184\) 175364. 5.17969
\(185\) 37131.7i 1.08493i
\(186\) −13800.2 −0.398894
\(187\) 52372.1i 1.49767i
\(188\) 54794.7i 1.55032i
\(189\) 4930.76 0.138035
\(190\) 189136.i 5.23923i
\(191\) 14709.0i 0.403195i 0.979468 + 0.201598i \(0.0646134\pi\)
−0.979468 + 0.201598i \(0.935387\pi\)
\(192\) 64228.6 1.74231
\(193\) −34249.4 −0.919472 −0.459736 0.888056i \(-0.652056\pi\)
−0.459736 + 0.888056i \(0.652056\pi\)
\(194\) 107542. 2.85743
\(195\) 3389.82i 0.0891471i
\(196\) 49631.8 1.29196
\(197\) 7911.51 0.203858 0.101929 0.994792i \(-0.467499\pi\)
0.101929 + 0.994792i \(0.467499\pi\)
\(198\) −30546.3 −0.779162
\(199\) −57454.5 −1.45084 −0.725418 0.688309i \(-0.758353\pi\)
−0.725418 + 0.688309i \(0.758353\pi\)
\(200\) 169176.i 4.22939i
\(201\) 17419.8i 0.431172i
\(202\) 4772.80 0.116969
\(203\) −15494.7 −0.376003
\(204\) −78374.1 −1.88327
\(205\) −106237. −2.52796
\(206\) 61472.9 1.44860
\(207\) 23281.5i 0.543338i
\(208\) 14960.5i 0.345795i
\(209\) 95711.3i 2.19114i
\(210\) 53346.7i 1.20967i
\(211\) 49004.2i 1.10070i 0.834935 + 0.550349i \(0.185505\pi\)
−0.834935 + 0.550349i \(0.814495\pi\)
\(212\) 46988.9 1.04550
\(213\) 7254.93 0.159909
\(214\) 84941.6i 1.85478i
\(215\) 108315.i 2.34322i
\(216\) 28532.4i 0.611548i
\(217\) 12196.1i 0.259001i
\(218\) −59766.0 −1.25760
\(219\) 8572.47i 0.178738i
\(220\) 240208.i 4.96298i
\(221\) 6055.39i 0.123982i
\(222\) −38687.3 −0.784986
\(223\) 94322.8 1.89674 0.948368 0.317171i \(-0.102733\pi\)
0.948368 + 0.317171i \(0.102733\pi\)
\(224\) 121076.i 2.41302i
\(225\) 22460.0 0.443654
\(226\) 23960.1 0.469107
\(227\) 73496.8i 1.42632i −0.701002 0.713159i \(-0.747264\pi\)
0.701002 0.713159i \(-0.252736\pi\)
\(228\) −143231. −2.75528
\(229\) 71268.4i 1.35902i −0.733666 0.679510i \(-0.762192\pi\)
0.733666 0.679510i \(-0.237808\pi\)
\(230\) 251886. 4.76155
\(231\) 26995.7i 0.505908i
\(232\) 89661.7i 1.66583i
\(233\) 21675.4i 0.399259i −0.979871 0.199630i \(-0.936026\pi\)
0.979871 0.199630i \(-0.0639739\pi\)
\(234\) −3531.83 −0.0645013
\(235\) 49125.9i 0.889559i
\(236\) −72035.0 129512.i −1.29336 2.32534i
\(237\) 43428.6 0.773177
\(238\) 95295.6i 1.68236i
\(239\) −556.432 −0.00974129 −0.00487065 0.999988i \(-0.501550\pi\)
−0.00487065 + 0.999988i \(0.501550\pi\)
\(240\) 173599. 3.01387
\(241\) 34167.1 0.588266 0.294133 0.955764i \(-0.404969\pi\)
0.294133 + 0.955764i \(0.404969\pi\)
\(242\) 55187.5i 0.942345i
\(243\) −3788.00 −0.0641500
\(244\) 254620.i 4.27675i
\(245\) 44497.2 0.741310
\(246\) 110688.i 1.82907i
\(247\) 11066.4i 0.181389i
\(248\) −70574.0 −1.14747
\(249\) 26114.7i 0.421198i
\(250\) 60424.9i 0.966798i
\(251\) 57018.6 0.905043 0.452522 0.891753i \(-0.350525\pi\)
0.452522 + 0.891753i \(0.350525\pi\)
\(252\) 40398.7 0.636161
\(253\) −127465. −1.99137
\(254\) 143205.i 2.21967i
\(255\) −70265.9 −1.08060
\(256\) 104388. 1.59283
\(257\) −3529.50 −0.0534375 −0.0267188 0.999643i \(-0.508506\pi\)
−0.0267188 + 0.999643i \(0.508506\pi\)
\(258\) 112853. 1.69540
\(259\) 34190.5i 0.509689i
\(260\) 27773.5i 0.410850i
\(261\) 11903.6 0.174742
\(262\) −94969.4 −1.38351
\(263\) 39797.7 0.575369 0.287684 0.957725i \(-0.407115\pi\)
0.287684 + 0.957725i \(0.407115\pi\)
\(264\) −156214. −2.24136
\(265\) 42127.7 0.599896
\(266\) 174155.i 2.46134i
\(267\) 27502.8i 0.385793i
\(268\) 142724.i 1.98713i
\(269\) 99994.5i 1.38188i 0.722910 + 0.690942i \(0.242804\pi\)
−0.722910 + 0.690942i \(0.757196\pi\)
\(270\) 40982.9i 0.562180i
\(271\) −70921.8 −0.965698 −0.482849 0.875704i \(-0.660398\pi\)
−0.482849 + 0.875704i \(0.660398\pi\)
\(272\) −310108. −4.19156
\(273\) 3121.31i 0.0418805i
\(274\) 183876.i 2.44920i
\(275\) 122968.i 1.62602i
\(276\) 190750.i 2.50407i
\(277\) −27566.1 −0.359265 −0.179633 0.983734i \(-0.557491\pi\)
−0.179633 + 0.983734i \(0.557491\pi\)
\(278\) 23069.8i 0.298507i
\(279\) 9369.50i 0.120367i
\(280\) 272815.i 3.47978i
\(281\) 116989. 1.48160 0.740802 0.671723i \(-0.234446\pi\)
0.740802 + 0.671723i \(0.234446\pi\)
\(282\) −51183.9 −0.643629
\(283\) 124680.i 1.55676i −0.627791 0.778382i \(-0.716041\pi\)
0.627791 0.778382i \(-0.283959\pi\)
\(284\) 59441.1 0.736971
\(285\) −128413. −1.58095
\(286\) 19336.6i 0.236401i
\(287\) −97822.4 −1.18761
\(288\) 93014.9i 1.12142i
\(289\) 41998.2 0.502846
\(290\) 128787.i 1.53136i
\(291\) 73014.8i 0.862234i
\(292\) 70236.0i 0.823747i
\(293\) −117066. −1.36362 −0.681812 0.731528i \(-0.738808\pi\)
−0.681812 + 0.731528i \(0.738808\pi\)
\(294\) 46361.3i 0.536366i
\(295\) −64582.6 116113.i −0.742116 1.33425i
\(296\) −197847. −2.25811
\(297\) 20739.1i 0.235114i
\(298\) −79583.5 −0.896170
\(299\) −14737.8 −0.164851
\(300\) 184019. 2.04466
\(301\) 99735.6i 1.10082i
\(302\) −271233. −2.97392
\(303\) 3240.45i 0.0352956i
\(304\) −566730. −6.13238
\(305\) 228278.i 2.45395i
\(306\) 73209.6i 0.781853i
\(307\) −74586.4 −0.791376 −0.395688 0.918385i \(-0.629494\pi\)
−0.395688 + 0.918385i \(0.629494\pi\)
\(308\) 221182.i 2.33157i
\(309\) 41736.5i 0.437119i
\(310\) −101370. −1.05484
\(311\) 164539. 1.70117 0.850587 0.525834i \(-0.176247\pi\)
0.850587 + 0.525834i \(0.176247\pi\)
\(312\) −18061.8 −0.185546
\(313\) 135789.i 1.38604i 0.720919 + 0.693019i \(0.243720\pi\)
−0.720919 + 0.693019i \(0.756280\pi\)
\(314\) 178341. 1.80881
\(315\) 36219.3 0.365022
\(316\) 355819. 3.56332
\(317\) −92280.2 −0.918311 −0.459156 0.888356i \(-0.651848\pi\)
−0.459156 + 0.888356i \(0.651848\pi\)
\(318\) 43892.6i 0.434047i
\(319\) 65171.8i 0.640440i
\(320\) 471796. 4.60738
\(321\) −57670.4 −0.559684
\(322\) 231934. 2.23693
\(323\) 229389. 2.19871
\(324\) −31035.8 −0.295647
\(325\) 14217.8i 0.134607i
\(326\) 68853.9i 0.647878i
\(327\) 40577.7i 0.379482i
\(328\) 566059.i 5.26156i
\(329\) 45234.6i 0.417907i
\(330\) −224380. −2.06042
\(331\) 10830.5 0.0988536 0.0494268 0.998778i \(-0.484261\pi\)
0.0494268 + 0.998778i \(0.484261\pi\)
\(332\) 213963.i 1.94116i
\(333\) 26266.4i 0.236871i
\(334\) 3382.02i 0.0303167i
\(335\) 127958.i 1.14019i
\(336\) 159848. 1.41589
\(337\) 124414.i 1.09549i −0.836645 0.547746i \(-0.815486\pi\)
0.836645 0.547746i \(-0.184514\pi\)
\(338\) 216350.i 1.89376i
\(339\) 16267.5i 0.141554i
\(340\) −575703. −4.98013
\(341\) 51297.7 0.441153
\(342\) 133792.i 1.14388i
\(343\) 125357. 1.06551
\(344\) 577130. 4.87705
\(345\) 171016.i 1.43681i
\(346\) −22557.5 −0.188425
\(347\) 226048.i 1.87733i −0.344829 0.938665i \(-0.612063\pi\)
0.344829 0.938665i \(-0.387937\pi\)
\(348\) 97528.7 0.805330
\(349\) 223773.i 1.83720i 0.395185 + 0.918602i \(0.370681\pi\)
−0.395185 + 0.918602i \(0.629319\pi\)
\(350\) 223750.i 1.82653i
\(351\) 2397.91i 0.0194634i
\(352\) −509253. −4.11006
\(353\) 132923.i 1.06672i 0.845889 + 0.533358i \(0.179070\pi\)
−0.845889 + 0.533358i \(0.820930\pi\)
\(354\) −120978. + 67288.2i −0.965381 + 0.536948i
\(355\) 53291.6 0.422866
\(356\) 225336.i 1.77800i
\(357\) −64700.2 −0.507655
\(358\) 132603. 1.03463
\(359\) 52427.0 0.406786 0.203393 0.979097i \(-0.434803\pi\)
0.203393 + 0.979097i \(0.434803\pi\)
\(360\) 209587.i 1.61718i
\(361\) 288893. 2.21678
\(362\) 70995.5i 0.541768i
\(363\) 37469.1 0.284354
\(364\) 25573.6i 0.193014i
\(365\) 62969.7i 0.472657i
\(366\) 237842. 1.77552
\(367\) 30282.9i 0.224835i 0.993661 + 0.112418i \(0.0358595\pi\)
−0.993661 + 0.112418i \(0.964141\pi\)
\(368\) 754753.i 5.57326i
\(369\) 75150.8 0.551926
\(370\) −284180. −2.07582
\(371\) 38790.7 0.281826
\(372\) 76766.2i 0.554733i
\(373\) 47523.7 0.341580 0.170790 0.985307i \(-0.445368\pi\)
0.170790 + 0.985307i \(0.445368\pi\)
\(374\) 400820. 2.86554
\(375\) 41025.0 0.291733
\(376\) −261755. −1.85148
\(377\) 7535.33i 0.0530175i
\(378\) 37736.6i 0.264107i
\(379\) 185993. 1.29485 0.647425 0.762130i \(-0.275846\pi\)
0.647425 + 0.762130i \(0.275846\pi\)
\(380\) −1.05211e6 −7.28609
\(381\) 97227.6 0.669791
\(382\) 112572. 0.771445
\(383\) −141142. −0.962188 −0.481094 0.876669i \(-0.659760\pi\)
−0.481094 + 0.876669i \(0.659760\pi\)
\(384\) 205150.i 1.39126i
\(385\) 198299.i 1.33783i
\(386\) 262121.i 1.75925i
\(387\) 76620.6i 0.511592i
\(388\) 598225.i 3.97376i
\(389\) 58679.8 0.387784 0.193892 0.981023i \(-0.437889\pi\)
0.193892 + 0.981023i \(0.437889\pi\)
\(390\) −25943.3 −0.170568
\(391\) 305494.i 1.99825i
\(392\) 237092.i 1.54292i
\(393\) 64478.7i 0.417476i
\(394\) 60549.3i 0.390046i
\(395\) 319008. 2.04459
\(396\) 169920.i 1.08356i
\(397\) 277665.i 1.76173i 0.473365 + 0.880866i \(0.343039\pi\)
−0.473365 + 0.880866i \(0.656961\pi\)
\(398\) 439717.i 2.77592i
\(399\) −118241. −0.742716
\(400\) 728121. 4.55076
\(401\) 59794.3i 0.371853i −0.982564 0.185927i \(-0.940471\pi\)
0.982564 0.185927i \(-0.0595286\pi\)
\(402\) −133319. −0.824973
\(403\) 5931.16 0.0365199
\(404\) 26549.7i 0.162666i
\(405\) −27825.0 −0.169639
\(406\) 118586.i 0.719417i
\(407\) 143808. 0.868146
\(408\) 374394.i 2.24910i
\(409\) 92288.3i 0.551696i −0.961201 0.275848i \(-0.911041\pi\)
0.961201 0.275848i \(-0.0889587\pi\)
\(410\) 813068.i 4.83681i
\(411\) 124841. 0.739051
\(412\) 341956.i 2.01454i
\(413\) −59467.0 106916.i −0.348639 0.626819i
\(414\) −178180. −1.03958
\(415\) 191827.i 1.11382i
\(416\) −58881.1 −0.340243
\(417\) 15663.1 0.0900750
\(418\) 732508. 4.19237
\(419\) 100145.i 0.570429i −0.958464 0.285214i \(-0.907935\pi\)
0.958464 0.285214i \(-0.0920648\pi\)
\(420\) 296752. 1.68227
\(421\) 102049.i 0.575762i 0.957666 + 0.287881i \(0.0929507\pi\)
−0.957666 + 0.287881i \(0.907049\pi\)
\(422\) 375044. 2.10600
\(423\) 34750.9i 0.194216i
\(424\) 224467.i 1.24859i
\(425\) −294714. −1.63164
\(426\) 55524.2i 0.305959i
\(427\) 210197.i 1.15284i
\(428\) −472506. −2.57941
\(429\) 13128.5 0.0713344
\(430\) 828970. 4.48334
\(431\) 259464.i 1.39676i −0.715725 0.698382i \(-0.753904\pi\)
0.715725 0.698382i \(-0.246096\pi\)
\(432\) −122801. −0.658015
\(433\) −332067. −1.77113 −0.885565 0.464516i \(-0.846228\pi\)
−0.885565 + 0.464516i \(0.846228\pi\)
\(434\) −93340.5 −0.495554
\(435\) 87438.9 0.462089
\(436\) 332461.i 1.74891i
\(437\) 558297.i 2.92350i
\(438\) 65607.8 0.341985
\(439\) 70862.7 0.367696 0.183848 0.982955i \(-0.441145\pi\)
0.183848 + 0.982955i \(0.441145\pi\)
\(440\) −1.14748e6 −5.92706
\(441\) −31476.6 −0.161849
\(442\) 46343.8 0.237218
\(443\) 85593.5i 0.436147i −0.975932 0.218074i \(-0.930023\pi\)
0.975932 0.218074i \(-0.0699773\pi\)
\(444\) 215206.i 1.09166i
\(445\) 202024.i 1.02019i
\(446\) 721882.i 3.62908i
\(447\) 54032.6i 0.270421i
\(448\) 434425. 2.16451
\(449\) 70020.7 0.347323 0.173662 0.984805i \(-0.444440\pi\)
0.173662 + 0.984805i \(0.444440\pi\)
\(450\) 171893.i 0.848856i
\(451\) 411448.i 2.02284i
\(452\) 133283.i 0.652376i
\(453\) 184152.i 0.897386i
\(454\) −562494. −2.72901
\(455\) 22927.8i 0.110749i
\(456\) 684214.i 3.29050i
\(457\) 97704.0i 0.467821i −0.972258 0.233911i \(-0.924848\pi\)
0.972258 0.233911i \(-0.0751523\pi\)
\(458\) −545439. −2.60025
\(459\) 49705.1 0.235926
\(460\) 1.40117e6i 6.62178i
\(461\) 149231. 0.702194 0.351097 0.936339i \(-0.385809\pi\)
0.351097 + 0.936339i \(0.385809\pi\)
\(462\) −206607. −0.967967
\(463\) 350096.i 1.63315i 0.577242 + 0.816573i \(0.304129\pi\)
−0.577242 + 0.816573i \(0.695871\pi\)
\(464\) 385898. 1.79241
\(465\) 68824.4i 0.318300i
\(466\) −165888. −0.763914
\(467\) 370985.i 1.70107i −0.525917 0.850536i \(-0.676278\pi\)
0.525917 0.850536i \(-0.323722\pi\)
\(468\) 19646.6i 0.0897005i
\(469\) 117823.i 0.535653i
\(470\) −375976. −1.70202
\(471\) 121083.i 0.545811i
\(472\) −618680. + 344112.i −2.77704 + 1.54460i
\(473\) −419495. −1.87501
\(474\) 332372.i 1.47934i
\(475\) −538597. −2.38713
\(476\) −530102. −2.33962
\(477\) −29800.5 −0.130974
\(478\) 4258.55i 0.0186383i
\(479\) −64617.2 −0.281629 −0.140814 0.990036i \(-0.544972\pi\)
−0.140814 + 0.990036i \(0.544972\pi\)
\(480\) 683248.i 2.96549i
\(481\) 16627.4 0.0718677
\(482\) 261491.i 1.12555i
\(483\) 157470.i 0.674999i
\(484\) 306992. 1.31050
\(485\) 536336.i 2.28010i
\(486\) 28990.7i 0.122740i
\(487\) 177831. 0.749808 0.374904 0.927064i \(-0.377676\pi\)
0.374904 + 0.927064i \(0.377676\pi\)
\(488\) 1.21632e6 5.10752
\(489\) 46747.8 0.195499
\(490\) 340550.i 1.41837i
\(491\) −146359. −0.607094 −0.303547 0.952817i \(-0.598171\pi\)
−0.303547 + 0.952817i \(0.598171\pi\)
\(492\) 615726. 2.54365
\(493\) −156196. −0.642653
\(494\) 84694.3 0.347057
\(495\) 152341.i 0.621736i
\(496\) 303746.i 1.23466i
\(497\) 49070.4 0.198658
\(498\) 199864. 0.805889
\(499\) 297990. 1.19674 0.598372 0.801218i \(-0.295815\pi\)
0.598372 + 0.801218i \(0.295815\pi\)
\(500\) 336126. 1.34450
\(501\) 2296.19 0.00914814
\(502\) 436381.i 1.73164i
\(503\) 379938.i 1.50168i 0.660486 + 0.750839i \(0.270350\pi\)
−0.660486 + 0.750839i \(0.729650\pi\)
\(504\) 192985.i 0.759737i
\(505\) 23803.0i 0.0933359i
\(506\) 975532.i 3.81013i
\(507\) −146889. −0.571445
\(508\) 796605. 3.08685
\(509\) 68834.8i 0.265688i −0.991137 0.132844i \(-0.957589\pi\)
0.991137 0.132844i \(-0.0424110\pi\)
\(510\) 537767.i 2.06754i
\(511\) 57981.9i 0.222050i
\(512\) 167216.i 0.637880i
\(513\) 90837.2 0.345167
\(514\) 27012.3i 0.102243i
\(515\) 306579.i 1.15592i
\(516\) 627768.i 2.35776i
\(517\) 190260. 0.711814
\(518\) −261670. −0.975203
\(519\) 15315.2i 0.0568576i
\(520\) −132674. −0.490659
\(521\) 450862. 1.66099 0.830497 0.557023i \(-0.188057\pi\)
0.830497 + 0.557023i \(0.188057\pi\)
\(522\) 91102.0i 0.334339i
\(523\) −157180. −0.574639 −0.287319 0.957835i \(-0.592764\pi\)
−0.287319 + 0.957835i \(0.592764\pi\)
\(524\) 528287.i 1.92401i
\(525\) 151913. 0.551160
\(526\) 304584.i 1.10087i
\(527\) 122944.i 0.442677i
\(528\) 672334.i 2.41166i
\(529\) −463682. −1.65695
\(530\) 322416.i 1.14780i
\(531\) 45684.8 + 82136.8i 0.162025 + 0.291306i
\(532\) −968773. −3.42294
\(533\) 47572.6i 0.167457i
\(534\) −210487. −0.738149
\(535\) −423623. −1.48003
\(536\) −681793. −2.37314
\(537\) 90029.5i 0.312202i
\(538\) 765289. 2.64400
\(539\) 172333.i 0.593187i
\(540\) −227976. −0.781810
\(541\) 272034.i 0.929455i 0.885454 + 0.464727i \(0.153848\pi\)
−0.885454 + 0.464727i \(0.846152\pi\)
\(542\) 542787.i 1.84770i
\(543\) 48201.8 0.163480
\(544\) 1.22052e6i 4.12426i
\(545\) 298066.i 1.00351i
\(546\) −23888.4 −0.0801311
\(547\) 351369. 1.17433 0.587163 0.809469i \(-0.300245\pi\)
0.587163 + 0.809469i \(0.300245\pi\)
\(548\) 1.02285e6 3.40605
\(549\) 161481.i 0.535768i
\(550\) −941109. −3.11110
\(551\) −285452. −0.940221
\(552\) −911216. −2.99049
\(553\) 293739. 0.960532
\(554\) 210972.i 0.687392i
\(555\) 192942.i 0.626384i
\(556\) 128331. 0.415127
\(557\) 88233.8 0.284397 0.142198 0.989838i \(-0.454583\pi\)
0.142198 + 0.989838i \(0.454583\pi\)
\(558\) 71707.7 0.230302
\(559\) −48503.0 −0.155219
\(560\) 1.17418e6 3.74419
\(561\) 272133.i 0.864682i
\(562\) 895352.i 2.83479i
\(563\) 203437.i 0.641819i −0.947110 0.320910i \(-0.896011\pi\)
0.947110 0.320910i \(-0.103989\pi\)
\(564\) 284721.i 0.895080i
\(565\) 119494.i 0.374326i
\(566\) −954212. −2.97860
\(567\) −25621.0 −0.0796948
\(568\) 283951.i 0.880130i
\(569\) 20875.8i 0.0644791i −0.999480 0.0322395i \(-0.989736\pi\)
0.999480 0.0322395i \(-0.0102639\pi\)
\(570\) 982781.i 3.02487i
\(571\) 308480.i 0.946139i 0.881025 + 0.473069i \(0.156854\pi\)
−0.881025 + 0.473069i \(0.843146\pi\)
\(572\) 107564. 0.328757
\(573\) 76430.1i 0.232785i
\(574\) 748665.i 2.27229i
\(575\) 717287.i 2.16949i
\(576\) −333742. −1.00592
\(577\) −332414. −0.998454 −0.499227 0.866471i \(-0.666383\pi\)
−0.499227 + 0.866471i \(0.666383\pi\)
\(578\) 321425.i 0.962110i
\(579\) 177965. 0.530857
\(580\) 716405. 2.12962
\(581\) 176633.i 0.523262i
\(582\) −558805. −1.64974
\(583\) 163157.i 0.480029i
\(584\) 335518. 0.983763
\(585\) 17614.0i 0.0514691i
\(586\) 895940.i 2.60906i
\(587\) 398675.i 1.15703i −0.815673 0.578513i \(-0.803633\pi\)
0.815673 0.578513i \(-0.196367\pi\)
\(588\) −257895. −0.745912
\(589\) 224683.i 0.647650i
\(590\) −888650. + 494271.i −2.55286 + 1.41991i
\(591\) −41109.4 −0.117697
\(592\) 851520.i 2.42969i
\(593\) 150216. 0.427177 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(594\) 158723. 0.449849
\(595\) −475260. −1.34245
\(596\) 442700.i 1.24628i
\(597\) 298543. 0.837640
\(598\) 112793.i 0.315414i
\(599\) −79272.8 −0.220938 −0.110469 0.993880i \(-0.535235\pi\)
−0.110469 + 0.993880i \(0.535235\pi\)
\(600\) 879063.i 2.44184i
\(601\) 510334.i 1.41288i 0.707772 + 0.706441i \(0.249700\pi\)
−0.707772 + 0.706441i \(0.750300\pi\)
\(602\) 763307. 2.10623
\(603\) 90515.8i 0.248937i
\(604\) 1.50879e6i 4.13576i
\(605\) 275232. 0.751949
\(606\) −24800.2 −0.0675320
\(607\) −108872. −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(608\) 2.23052e6i 6.03392i
\(609\) 80512.9 0.217085
\(610\) 1.74709e6 4.69521
\(611\) 21998.3 0.0589260
\(612\) 407244. 1.08731
\(613\) 71190.4i 0.189453i 0.995503 + 0.0947263i \(0.0301976\pi\)
−0.995503 + 0.0947263i \(0.969802\pi\)
\(614\) 570833.i 1.51416i
\(615\) 552026. 1.45952
\(616\) −1.05659e6 −2.78448
\(617\) −463811. −1.21835 −0.609173 0.793037i \(-0.708498\pi\)
−0.609173 + 0.793037i \(0.708498\pi\)
\(618\) −319423. −0.836351
\(619\) 192587. 0.502627 0.251313 0.967906i \(-0.419138\pi\)
0.251313 + 0.967906i \(0.419138\pi\)
\(620\) 563892.i 1.46694i
\(621\) 120974.i 0.313696i
\(622\) 1.25927e6i 3.25490i
\(623\) 186022.i 0.479278i
\(624\) 77736.8i 0.199645i
\(625\) −218555. −0.559501
\(626\) 1.03923e6 2.65194
\(627\) 497330.i 1.26506i
\(628\) 992060.i 2.51547i
\(629\) 344661.i 0.871145i
\(630\) 277197.i 0.698406i
\(631\) −13953.1 −0.0350438 −0.0175219 0.999846i \(-0.505578\pi\)
−0.0175219 + 0.999846i \(0.505578\pi\)
\(632\) 1.69975e6i 4.25551i
\(633\) 254633.i 0.635489i
\(634\) 706249.i 1.75703i
\(635\) 714192. 1.77120
\(636\) −244162. −0.603619
\(637\) 19925.6i 0.0491058i
\(638\) −498780. −1.22537
\(639\) −37697.7 −0.0923238
\(640\) 1.50694e6i 3.67906i
\(641\) −416645. −1.01403 −0.507014 0.861938i \(-0.669251\pi\)
−0.507014 + 0.861938i \(0.669251\pi\)
\(642\) 441370.i 1.07086i
\(643\) 79601.2 0.192530 0.0962648 0.995356i \(-0.469310\pi\)
0.0962648 + 0.995356i \(0.469310\pi\)
\(644\) 1.29018e6i 3.11085i
\(645\) 562822.i 1.35286i
\(646\) 1.75559e6i 4.20685i
\(647\) −681530. −1.62808 −0.814041 0.580807i \(-0.802737\pi\)
−0.814041 + 0.580807i \(0.802737\pi\)
\(648\) 148259.i 0.353077i
\(649\) 449696. 250123.i 1.06765 0.593832i
\(650\) −108813. −0.257546
\(651\) 63372.8i 0.149534i
\(652\) 383014. 0.900990
\(653\) −383016. −0.898237 −0.449118 0.893472i \(-0.648262\pi\)
−0.449118 + 0.893472i \(0.648262\pi\)
\(654\) 310553. 0.726074
\(655\) 473633.i 1.10398i
\(656\) 2.43628e6 5.66135
\(657\) 44543.9i 0.103195i
\(658\) −346195. −0.799592
\(659\) 527534.i 1.21473i −0.794423 0.607365i \(-0.792227\pi\)
0.794423 0.607365i \(-0.207773\pi\)
\(660\) 1.24816e6i 2.86538i
\(661\) 282774. 0.647197 0.323599 0.946194i \(-0.395107\pi\)
0.323599 + 0.946194i \(0.395107\pi\)
\(662\) 82889.2i 0.189139i
\(663\) 31464.7i 0.0715809i
\(664\) 1.02210e6 2.31824
\(665\) −868549. −1.96404
\(666\) 201025. 0.453212
\(667\) 380156.i 0.854497i
\(668\) 18813.2 0.0421608
\(669\) −490116. −1.09508
\(670\) −979304. −2.18156
\(671\) −884102. −1.96362
\(672\) 629128.i 1.39316i
\(673\) 709243.i 1.56590i 0.622083 + 0.782952i \(0.286287\pi\)
−0.622083 + 0.782952i \(0.713713\pi\)
\(674\) −952178. −2.09604
\(675\) −116706. −0.256144
\(676\) −1.20349e6 −2.63361
\(677\) −419269. −0.914777 −0.457389 0.889267i \(-0.651215\pi\)
−0.457389 + 0.889267i \(0.651215\pi\)
\(678\) −124500. −0.270839
\(679\) 493853.i 1.07117i
\(680\) 2.75014e6i 5.94754i
\(681\) 381900.i 0.823486i
\(682\) 392597.i 0.844069i
\(683\) 341293.i 0.731620i 0.930690 + 0.365810i \(0.119208\pi\)
−0.930690 + 0.365810i \(0.880792\pi\)
\(684\) 744248. 1.59076
\(685\) 917030. 1.95435
\(686\) 959393.i 2.03868i
\(687\) 370322.i 0.784631i
\(688\) 2.48393e6i 5.24762i
\(689\) 18864.6i 0.0397382i
\(690\) −1.30884e6 −2.74908
\(691\) 57041.7i 0.119464i −0.998214 0.0597319i \(-0.980975\pi\)
0.998214 0.0597319i \(-0.0190246\pi\)
\(692\) 125481.i 0.262039i
\(693\) 140274.i 0.292086i
\(694\) −1.73001e6 −3.59195
\(695\) 115054. 0.238195
\(696\) 465896.i 0.961769i
\(697\) −986109. −2.02983
\(698\) 1.71261e6 3.51517
\(699\) 112629.i 0.230512i
\(700\) 1.24466e6 2.54012
\(701\) 292521.i 0.595279i 0.954678 + 0.297640i \(0.0961994\pi\)
−0.954678 + 0.297640i \(0.903801\pi\)
\(702\) 18351.9 0.0372398
\(703\) 629876.i 1.27451i
\(704\) 1.82722e6i 3.68677i
\(705\) 255266.i 0.513587i
\(706\) 1.01730e6 2.04098
\(707\) 21917.6i 0.0438484i
\(708\) 374305. + 672964.i 0.746722 + 1.34253i
\(709\) 265410. 0.527988 0.263994 0.964524i \(-0.414960\pi\)
0.263994 + 0.964524i \(0.414960\pi\)
\(710\) 407857.i 0.809080i
\(711\) −225661. −0.446394
\(712\) −1.07643e6 −2.12338
\(713\) 299226. 0.588601
\(714\) 495170.i 0.971311i
\(715\) 96436.1 0.188637
\(716\) 737630.i 1.43884i
\(717\) 2891.31 0.00562414
\(718\) 401240.i 0.778315i
\(719\) 843328.i 1.63132i 0.578532 + 0.815659i \(0.303626\pi\)
−0.578532 + 0.815659i \(0.696374\pi\)
\(720\) −902047. −1.74006
\(721\) 282295.i 0.543041i
\(722\) 2.21099e6i 4.24143i
\(723\) −177537. −0.339636
\(724\) 394927. 0.753425
\(725\) 366742. 0.697726
\(726\) 286763.i 0.544063i
\(727\) 361987. 0.684895 0.342448 0.939537i \(-0.388744\pi\)
0.342448 + 0.939537i \(0.388744\pi\)
\(728\) −122165. −0.230507
\(729\) 19683.0 0.0370370
\(730\) 481927. 0.904347
\(731\) 1.00540e6i 1.88149i
\(732\) 1.32305e6i 2.46918i
\(733\) 364992. 0.679322 0.339661 0.940548i \(-0.389688\pi\)
0.339661 + 0.940548i \(0.389688\pi\)
\(734\) 231764. 0.430184
\(735\) −231214. −0.427996
\(736\) −2.97054e6 −5.48379
\(737\) 495571. 0.912369
\(738\) 575152.i 1.05602i
\(739\) 397416.i 0.727707i −0.931456 0.363854i \(-0.881461\pi\)
0.931456 0.363854i \(-0.118539\pi\)
\(740\) 1.58081e6i 2.88680i
\(741\) 57502.5i 0.104725i
\(742\) 296878.i 0.539224i
\(743\) 208889. 0.378389 0.189195 0.981940i \(-0.439412\pi\)
0.189195 + 0.981940i \(0.439412\pi\)
\(744\) 366713. 0.662492
\(745\) 396900.i 0.715104i
\(746\) 363714.i 0.653555i
\(747\) 135696.i 0.243179i
\(748\) 2.22965e6i 3.98504i
\(749\) −390068. −0.695306
\(750\) 313977.i 0.558181i
\(751\) 1.12660e6i 1.99751i 0.0498694 + 0.998756i \(0.484120\pi\)
−0.0498694 + 0.998756i \(0.515880\pi\)
\(752\) 1.12658e6i 1.99216i
\(753\) −296277. −0.522527
\(754\) −57670.2 −0.101440
\(755\) 1.35270e6i 2.37305i
\(756\) −209918. −0.367288
\(757\) −287250. −0.501266 −0.250633 0.968082i \(-0.580639\pi\)
−0.250633 + 0.968082i \(0.580639\pi\)
\(758\) 1.42347e6i 2.47747i
\(759\) 662329. 1.14972
\(760\) 5.02595e6i 8.70143i
\(761\) −39472.2 −0.0681587 −0.0340794 0.999419i \(-0.510850\pi\)
−0.0340794 + 0.999419i \(0.510850\pi\)
\(762\) 744113.i 1.28153i
\(763\) 274456.i 0.471438i
\(764\) 626207.i 1.07283i
\(765\) 365112. 0.623884
\(766\) 1.08021e6i 1.84098i
\(767\) 51994.9 28919.8i 0.0883833 0.0491591i
\(768\) −542416. −0.919623
\(769\) 696042.i 1.17702i 0.808491 + 0.588509i \(0.200285\pi\)
−0.808491 + 0.588509i \(0.799715\pi\)
\(770\) −1.51765e6 −2.55970
\(771\) 18339.8 0.0308522
\(772\) 1.45810e6 2.44655
\(773\) 245846.i 0.411438i 0.978611 + 0.205719i \(0.0659533\pi\)
−0.978611 + 0.205719i \(0.934047\pi\)
\(774\) −586401. −0.978843
\(775\) 288668.i 0.480613i
\(776\) −2.85773e6 −4.74567
\(777\) 177659.i 0.294269i
\(778\) 449095.i 0.741957i
\(779\) −1.80214e6 −2.96970
\(780\) 144315.i 0.237205i
\(781\) 206394.i 0.338372i
\(782\) 2.33804e6 3.82330
\(783\) −61853.0 −0.100887
\(784\) −1.02043e6 −1.66016
\(785\) 889426.i 1.44335i
\(786\) 493476. 0.798768
\(787\) 437284. 0.706016 0.353008 0.935620i \(-0.385159\pi\)
0.353008 + 0.935620i \(0.385159\pi\)
\(788\) −336818. −0.542429
\(789\) −206795. −0.332189