Properties

Label 177.5.b.a.119.6
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.6
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.73

$q$-expansion

\(f(q)\) \(=\) \(q-7.08630i q^{2} +(-1.58963 - 8.85850i) q^{3} -34.2156 q^{4} -8.65783i q^{5} +(-62.7740 + 11.2646i) q^{6} -70.0243 q^{7} +129.081i q^{8} +(-75.9462 + 28.1634i) q^{9} +O(q^{10})\) \(q-7.08630i q^{2} +(-1.58963 - 8.85850i) q^{3} -34.2156 q^{4} -8.65783i q^{5} +(-62.7740 + 11.2646i) q^{6} -70.0243 q^{7} +129.081i q^{8} +(-75.9462 + 28.1634i) q^{9} -61.3520 q^{10} -225.973i q^{11} +(54.3901 + 303.099i) q^{12} +156.064 q^{13} +496.213i q^{14} +(-76.6954 + 13.7627i) q^{15} +367.259 q^{16} +15.4786i q^{17} +(199.575 + 538.177i) q^{18} +179.462 q^{19} +296.233i q^{20} +(111.313 + 620.310i) q^{21} -1601.31 q^{22} -621.607i q^{23} +(1143.47 - 205.191i) q^{24} +550.042 q^{25} -1105.91i q^{26} +(370.212 + 628.000i) q^{27} +2395.92 q^{28} +442.113i q^{29} +(97.5268 + 543.487i) q^{30} -258.752 q^{31} -537.204i q^{32} +(-2001.78 + 359.212i) q^{33} +109.686 q^{34} +606.259i q^{35} +(2598.55 - 963.629i) q^{36} -2503.21 q^{37} -1271.72i q^{38} +(-248.083 - 1382.49i) q^{39} +1117.56 q^{40} +241.937i q^{41} +(4395.70 - 788.794i) q^{42} +2192.78 q^{43} +7731.79i q^{44} +(243.834 + 657.529i) q^{45} -4404.89 q^{46} -2940.86i q^{47} +(-583.804 - 3253.36i) q^{48} +2502.40 q^{49} -3897.76i q^{50} +(137.117 - 24.6052i) q^{51} -5339.82 q^{52} +289.041i q^{53} +(4450.20 - 2623.43i) q^{54} -1956.43 q^{55} -9038.83i q^{56} +(-285.278 - 1589.77i) q^{57} +3132.94 q^{58} +453.188i q^{59} +(2624.18 - 470.900i) q^{60} -4432.23 q^{61} +1833.59i q^{62} +(5318.08 - 1972.12i) q^{63} +2069.35 q^{64} -1351.17i q^{65} +(2545.48 + 14185.2i) q^{66} -1621.56 q^{67} -529.609i q^{68} +(-5506.51 + 988.123i) q^{69} +4296.13 q^{70} +7336.07i q^{71} +(-3635.37 - 9803.23i) q^{72} -1743.91 q^{73} +17738.5i q^{74} +(-874.362 - 4872.55i) q^{75} -6140.41 q^{76} +15823.6i q^{77} +(-9796.75 + 1757.99i) q^{78} +2560.10 q^{79} -3179.66i q^{80} +(4974.64 - 4277.81i) q^{81} +1714.44 q^{82} +4640.76i q^{83} +(-3808.63 - 21224.3i) q^{84} +134.011 q^{85} -15538.7i q^{86} +(3916.46 - 702.795i) q^{87} +29168.8 q^{88} +8720.43i q^{89} +(4659.45 - 1727.88i) q^{90} -10928.3 q^{91} +21268.7i q^{92} +(411.319 + 2292.15i) q^{93} -20839.8 q^{94} -1553.75i q^{95} +(-4758.82 + 853.953i) q^{96} +12826.5 q^{97} -17732.8i q^{98} +(6364.16 + 17161.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.08630i 1.77157i −0.464092 0.885787i \(-0.653619\pi\)
0.464092 0.885787i \(-0.346381\pi\)
\(3\) −1.58963 8.85850i −0.176625 0.984278i
\(4\) −34.2156 −2.13848
\(5\) 8.65783i 0.346313i −0.984894 0.173157i \(-0.944603\pi\)
0.984894 0.173157i \(-0.0553967\pi\)
\(6\) −62.7740 + 11.2646i −1.74372 + 0.312905i
\(7\) −70.0243 −1.42907 −0.714534 0.699601i \(-0.753361\pi\)
−0.714534 + 0.699601i \(0.753361\pi\)
\(8\) 129.081i 2.01690i
\(9\) −75.9462 + 28.1634i −0.937607 + 0.347697i
\(10\) −61.3520 −0.613520
\(11\) 225.973i 1.86754i −0.357871 0.933771i \(-0.616497\pi\)
0.357871 0.933771i \(-0.383503\pi\)
\(12\) 54.3901 + 303.099i 0.377709 + 2.10486i
\(13\) 156.064 0.923455 0.461727 0.887022i \(-0.347230\pi\)
0.461727 + 0.887022i \(0.347230\pi\)
\(14\) 496.213i 2.53170i
\(15\) −76.6954 + 13.7627i −0.340869 + 0.0611677i
\(16\) 367.259 1.43460
\(17\) 15.4786i 0.0535591i 0.999641 + 0.0267795i \(0.00852521\pi\)
−0.999641 + 0.0267795i \(0.991475\pi\)
\(18\) 199.575 + 538.177i 0.615971 + 1.66104i
\(19\) 179.462 0.497125 0.248563 0.968616i \(-0.420042\pi\)
0.248563 + 0.968616i \(0.420042\pi\)
\(20\) 296.233i 0.740583i
\(21\) 111.313 + 620.310i 0.252409 + 1.40660i
\(22\) −1601.31 −3.30849
\(23\) 621.607i 1.17506i −0.809202 0.587530i \(-0.800100\pi\)
0.809202 0.587530i \(-0.199900\pi\)
\(24\) 1143.47 205.191i 1.98519 0.356235i
\(25\) 550.042 0.880067
\(26\) 1105.91i 1.63597i
\(27\) 370.212 + 628.000i 0.507835 + 0.861454i
\(28\) 2395.92 3.05603
\(29\) 442.113i 0.525699i 0.964837 + 0.262850i \(0.0846623\pi\)
−0.964837 + 0.262850i \(0.915338\pi\)
\(30\) 97.5268 + 543.487i 0.108363 + 0.603874i
\(31\) −258.752 −0.269252 −0.134626 0.990896i \(-0.542983\pi\)
−0.134626 + 0.990896i \(0.542983\pi\)
\(32\) 537.204i 0.524613i
\(33\) −2001.78 + 359.212i −1.83818 + 0.329855i
\(34\) 109.686 0.0948838
\(35\) 606.259i 0.494905i
\(36\) 2598.55 963.629i 2.00505 0.743541i
\(37\) −2503.21 −1.82850 −0.914248 0.405154i \(-0.867218\pi\)
−0.914248 + 0.405154i \(0.867218\pi\)
\(38\) 1271.72i 0.880694i
\(39\) −248.083 1382.49i −0.163105 0.908936i
\(40\) 1117.56 0.698478
\(41\) 241.937i 0.143925i 0.997407 + 0.0719623i \(0.0229261\pi\)
−0.997407 + 0.0719623i \(0.977074\pi\)
\(42\) 4395.70 788.794i 2.49190 0.447162i
\(43\) 2192.78 1.18593 0.592964 0.805229i \(-0.297958\pi\)
0.592964 + 0.805229i \(0.297958\pi\)
\(44\) 7731.79i 3.99369i
\(45\) 243.834 + 657.529i 0.120412 + 0.324706i
\(46\) −4404.89 −2.08171
\(47\) 2940.86i 1.33131i −0.746261 0.665654i \(-0.768153\pi\)
0.746261 0.665654i \(-0.231847\pi\)
\(48\) −583.804 3253.36i −0.253387 1.41205i
\(49\) 2502.40 1.04223
\(50\) 3897.76i 1.55910i
\(51\) 137.117 24.6052i 0.0527170 0.00945988i
\(52\) −5339.82 −1.97479
\(53\) 289.041i 0.102898i 0.998676 + 0.0514491i \(0.0163840\pi\)
−0.998676 + 0.0514491i \(0.983616\pi\)
\(54\) 4450.20 2623.43i 1.52613 0.899668i
\(55\) −1956.43 −0.646755
\(56\) 9038.83i 2.88228i
\(57\) −285.278 1589.77i −0.0878049 0.489310i
\(58\) 3132.94 0.931315
\(59\) 453.188i 0.130189i
\(60\) 2624.18 470.900i 0.728939 0.130806i
\(61\) −4432.23 −1.19114 −0.595570 0.803304i \(-0.703074\pi\)
−0.595570 + 0.803304i \(0.703074\pi\)
\(62\) 1833.59i 0.477001i
\(63\) 5318.08 1972.12i 1.33990 0.496882i
\(64\) 2069.35 0.505213
\(65\) 1351.17i 0.319805i
\(66\) 2545.48 + 14185.2i 0.584363 + 3.25647i
\(67\) −1621.56 −0.361229 −0.180615 0.983554i \(-0.557809\pi\)
−0.180615 + 0.983554i \(0.557809\pi\)
\(68\) 529.609i 0.114535i
\(69\) −5506.51 + 988.123i −1.15659 + 0.207545i
\(70\) 4296.13 0.876761
\(71\) 7336.07i 1.45528i 0.685958 + 0.727641i \(0.259383\pi\)
−0.685958 + 0.727641i \(0.740617\pi\)
\(72\) −3635.37 9803.23i −0.701268 1.89106i
\(73\) −1743.91 −0.327250 −0.163625 0.986523i \(-0.552319\pi\)
−0.163625 + 0.986523i \(0.552319\pi\)
\(74\) 17738.5i 3.23932i
\(75\) −874.362 4872.55i −0.155442 0.866231i
\(76\) −6140.41 −1.06309
\(77\) 15823.6i 2.66884i
\(78\) −9796.75 + 1757.99i −1.61025 + 0.288953i
\(79\) 2560.10 0.410206 0.205103 0.978740i \(-0.434247\pi\)
0.205103 + 0.978740i \(0.434247\pi\)
\(80\) 3179.66i 0.496823i
\(81\) 4974.64 4277.81i 0.758214 0.652006i
\(82\) 1714.44 0.254973
\(83\) 4640.76i 0.673648i 0.941568 + 0.336824i \(0.109353\pi\)
−0.941568 + 0.336824i \(0.890647\pi\)
\(84\) −3808.63 21224.3i −0.539771 3.00798i
\(85\) 134.011 0.0185482
\(86\) 15538.7i 2.10096i
\(87\) 3916.46 702.795i 0.517434 0.0928518i
\(88\) 29168.8 3.76664
\(89\) 8720.43i 1.10093i 0.834860 + 0.550463i \(0.185549\pi\)
−0.834860 + 0.550463i \(0.814451\pi\)
\(90\) 4659.45 1727.88i 0.575241 0.213319i
\(91\) −10928.3 −1.31968
\(92\) 21268.7i 2.51284i
\(93\) 411.319 + 2292.15i 0.0475568 + 0.265019i
\(94\) −20839.8 −2.35851
\(95\) 1553.75i 0.172161i
\(96\) −4758.82 + 853.953i −0.516365 + 0.0926599i
\(97\) 12826.5 1.36322 0.681610 0.731715i \(-0.261280\pi\)
0.681610 + 0.731715i \(0.261280\pi\)
\(98\) 17732.8i 1.84639i
\(99\) 6364.16 + 17161.8i 0.649338 + 1.75102i
\(100\) −18820.0 −1.88200
\(101\) 9691.64i 0.950067i −0.879968 0.475034i \(-0.842436\pi\)
0.879968 0.475034i \(-0.157564\pi\)
\(102\) −174.359 971.651i −0.0167589 0.0933921i
\(103\) −19054.9 −1.79610 −0.898052 0.439889i \(-0.855018\pi\)
−0.898052 + 0.439889i \(0.855018\pi\)
\(104\) 20144.9i 1.86251i
\(105\) 5370.54 963.725i 0.487124 0.0874127i
\(106\) 2048.23 0.182292
\(107\) 13776.4i 1.20329i −0.798764 0.601644i \(-0.794513\pi\)
0.798764 0.601644i \(-0.205487\pi\)
\(108\) −12667.0 21487.4i −1.08599 1.84220i
\(109\) −5789.04 −0.487252 −0.243626 0.969869i \(-0.578337\pi\)
−0.243626 + 0.969869i \(0.578337\pi\)
\(110\) 13863.9i 1.14577i
\(111\) 3979.17 + 22174.7i 0.322959 + 1.79975i
\(112\) −25717.0 −2.05015
\(113\) 16701.6i 1.30798i 0.756502 + 0.653992i \(0.226907\pi\)
−0.756502 + 0.653992i \(0.773093\pi\)
\(114\) −11265.6 + 2021.57i −0.866848 + 0.155553i
\(115\) −5381.77 −0.406939
\(116\) 15127.2i 1.12420i
\(117\) −11852.5 + 4395.29i −0.865838 + 0.321082i
\(118\) 3211.42 0.230639
\(119\) 1083.88i 0.0765395i
\(120\) −1776.51 9899.95i −0.123369 0.687496i
\(121\) −36422.6 −2.48771
\(122\) 31408.1i 2.11019i
\(123\) 2143.20 384.590i 0.141662 0.0254207i
\(124\) 8853.35 0.575790
\(125\) 10173.3i 0.651092i
\(126\) −13975.1 37685.5i −0.880264 2.37374i
\(127\) 30521.6 1.89234 0.946170 0.323670i \(-0.104917\pi\)
0.946170 + 0.323670i \(0.104917\pi\)
\(128\) 23259.3i 1.41964i
\(129\) −3485.70 19424.8i −0.209465 1.16728i
\(130\) −9574.83 −0.566558
\(131\) 9964.10i 0.580625i 0.956932 + 0.290312i \(0.0937592\pi\)
−0.956932 + 0.290312i \(0.906241\pi\)
\(132\) 68492.1 12290.7i 3.93091 0.705387i
\(133\) −12566.7 −0.710425
\(134\) 11490.9i 0.639945i
\(135\) 5437.12 3205.23i 0.298333 0.175870i
\(136\) −1997.99 −0.108023
\(137\) 8591.87i 0.457769i 0.973454 + 0.228885i \(0.0735079\pi\)
−0.973454 + 0.228885i \(0.926492\pi\)
\(138\) 7002.14 + 39020.8i 0.367682 + 2.04898i
\(139\) −33423.9 −1.72992 −0.864962 0.501837i \(-0.832658\pi\)
−0.864962 + 0.501837i \(0.832658\pi\)
\(140\) 20743.5i 1.05834i
\(141\) −26051.6 + 4674.87i −1.31038 + 0.235142i
\(142\) 51985.6 2.57814
\(143\) 35266.2i 1.72459i
\(144\) −27891.9 + 10343.3i −1.34510 + 0.498807i
\(145\) 3827.74 0.182057
\(146\) 12357.9i 0.579747i
\(147\) −3977.89 22167.5i −0.184085 1.02585i
\(148\) 85648.9 3.91020
\(149\) 38544.7i 1.73617i −0.496418 0.868084i \(-0.665352\pi\)
0.496418 0.868084i \(-0.334648\pi\)
\(150\) −34528.3 + 6195.99i −1.53459 + 0.275377i
\(151\) 13143.4 0.576441 0.288221 0.957564i \(-0.406936\pi\)
0.288221 + 0.957564i \(0.406936\pi\)
\(152\) 23165.2i 1.00265i
\(153\) −435.930 1175.54i −0.0186223 0.0502173i
\(154\) 112131. 4.72805
\(155\) 2240.23i 0.0932457i
\(156\) 8488.33 + 47302.8i 0.348797 + 1.94374i
\(157\) 1902.76 0.0771942 0.0385971 0.999255i \(-0.487711\pi\)
0.0385971 + 0.999255i \(0.487711\pi\)
\(158\) 18141.6i 0.726711i
\(159\) 2560.47 459.467i 0.101280 0.0181744i
\(160\) −4651.02 −0.181680
\(161\) 43527.6i 1.67924i
\(162\) −30313.8 35251.8i −1.15508 1.34323i
\(163\) 16415.8 0.617854 0.308927 0.951086i \(-0.400030\pi\)
0.308927 + 0.951086i \(0.400030\pi\)
\(164\) 8278.04i 0.307779i
\(165\) 3110.00 + 17331.1i 0.114233 + 0.636586i
\(166\) 32885.8 1.19342
\(167\) 25416.2i 0.911333i −0.890151 0.455667i \(-0.849401\pi\)
0.890151 0.455667i \(-0.150599\pi\)
\(168\) −80070.5 + 14368.4i −2.83696 + 0.509083i
\(169\) −4205.07 −0.147231
\(170\) 949.641i 0.0328595i
\(171\) −13629.5 + 5054.27i −0.466108 + 0.172849i
\(172\) −75027.4 −2.53608
\(173\) 23861.0i 0.797252i −0.917114 0.398626i \(-0.869487\pi\)
0.917114 0.398626i \(-0.130513\pi\)
\(174\) −4980.21 27753.2i −0.164494 0.916673i
\(175\) −38516.3 −1.25767
\(176\) 82990.4i 2.67918i
\(177\) 4014.56 720.399i 0.128142 0.0229946i
\(178\) 61795.6 1.95037
\(179\) 21390.9i 0.667610i 0.942642 + 0.333805i \(0.108333\pi\)
−0.942642 + 0.333805i \(0.891667\pi\)
\(180\) −8342.94 22497.8i −0.257498 0.694376i
\(181\) 36138.0 1.10308 0.551540 0.834148i \(-0.314040\pi\)
0.551540 + 0.834148i \(0.314040\pi\)
\(182\) 77440.9i 2.33791i
\(183\) 7045.59 + 39262.9i 0.210385 + 1.17241i
\(184\) 80237.8 2.36997
\(185\) 21672.4i 0.633233i
\(186\) 16242.9 2914.73i 0.469501 0.0842504i
\(187\) 3497.73 0.100024
\(188\) 100623.i 2.84697i
\(189\) −25923.8 43975.3i −0.725731 1.23108i
\(190\) −11010.4 −0.304996
\(191\) 38862.2i 1.06527i −0.846344 0.532636i \(-0.821201\pi\)
0.846344 0.532636i \(-0.178799\pi\)
\(192\) −3289.50 18331.4i −0.0892335 0.497271i
\(193\) −32884.5 −0.882830 −0.441415 0.897303i \(-0.645523\pi\)
−0.441415 + 0.897303i \(0.645523\pi\)
\(194\) 90892.7i 2.41505i
\(195\) −11969.4 + 2147.86i −0.314777 + 0.0564856i
\(196\) −85621.2 −2.22879
\(197\) 40794.8i 1.05117i −0.850742 0.525584i \(-0.823847\pi\)
0.850742 0.525584i \(-0.176153\pi\)
\(198\) 121613. 45098.4i 3.10206 1.15035i
\(199\) −22665.5 −0.572346 −0.286173 0.958178i \(-0.592383\pi\)
−0.286173 + 0.958178i \(0.592383\pi\)
\(200\) 71000.1i 1.77500i
\(201\) 2577.67 + 14364.6i 0.0638023 + 0.355550i
\(202\) −68677.8 −1.68312
\(203\) 30958.7i 0.751260i
\(204\) −4691.54 + 841.880i −0.112734 + 0.0202297i
\(205\) 2094.65 0.0498430
\(206\) 135028.i 3.18193i
\(207\) 17506.6 + 47208.7i 0.408565 + 1.10174i
\(208\) 57315.8 1.32479
\(209\) 40553.5i 0.928402i
\(210\) −6829.24 38057.3i −0.154858 0.862977i
\(211\) −29824.6 −0.669899 −0.334949 0.942236i \(-0.608719\pi\)
−0.334949 + 0.942236i \(0.608719\pi\)
\(212\) 9889.71i 0.220045i
\(213\) 64986.6 11661.6i 1.43240 0.257039i
\(214\) −97624.0 −2.13171
\(215\) 18984.7i 0.410703i
\(216\) −81063.1 + 47787.5i −1.73746 + 1.02425i
\(217\) 18118.9 0.384780
\(218\) 41022.9i 0.863203i
\(219\) 2772.17 + 15448.5i 0.0578006 + 0.322105i
\(220\) 66940.6 1.38307
\(221\) 2415.64i 0.0494594i
\(222\) 157137. 28197.6i 3.18839 0.572145i
\(223\) 15909.7 0.319927 0.159964 0.987123i \(-0.448862\pi\)
0.159964 + 0.987123i \(0.448862\pi\)
\(224\) 37617.3i 0.749707i
\(225\) −41773.6 + 15491.1i −0.825157 + 0.305996i
\(226\) 118353. 2.31719
\(227\) 26000.0i 0.504570i −0.967653 0.252285i \(-0.918818\pi\)
0.967653 0.252285i \(-0.0811820\pi\)
\(228\) 9760.97 + 54394.9i 0.187769 + 1.04638i
\(229\) −27370.1 −0.521922 −0.260961 0.965349i \(-0.584039\pi\)
−0.260961 + 0.965349i \(0.584039\pi\)
\(230\) 38136.8i 0.720923i
\(231\) 140173. 25153.6i 2.62688 0.471385i
\(232\) −57068.5 −1.06028
\(233\) 87779.4i 1.61689i 0.588571 + 0.808446i \(0.299691\pi\)
−0.588571 + 0.808446i \(0.700309\pi\)
\(234\) 31146.4 + 83990.0i 0.568821 + 1.53390i
\(235\) −25461.5 −0.461049
\(236\) 15506.1i 0.278406i
\(237\) −4069.60 22678.6i −0.0724528 0.403757i
\(238\) −7680.67 −0.135595
\(239\) 27127.4i 0.474911i 0.971398 + 0.237455i \(0.0763134\pi\)
−0.971398 + 0.237455i \(0.923687\pi\)
\(240\) −28167.1 + 5054.48i −0.489012 + 0.0877514i
\(241\) 13743.6 0.236628 0.118314 0.992976i \(-0.462251\pi\)
0.118314 + 0.992976i \(0.462251\pi\)
\(242\) 258101.i 4.40717i
\(243\) −45802.8 37267.8i −0.775675 0.631133i
\(244\) 151652. 2.54722
\(245\) 21665.4i 0.360939i
\(246\) −2725.32 15187.4i −0.0450347 0.250965i
\(247\) 28007.6 0.459073
\(248\) 33400.0i 0.543054i
\(249\) 41110.2 7377.08i 0.663057 0.118983i
\(250\) −72091.2 −1.15346
\(251\) 78056.8i 1.23898i −0.785006 0.619488i \(-0.787340\pi\)
0.785006 0.619488i \(-0.212660\pi\)
\(252\) −181961. + 67477.5i −2.86535 + 1.06257i
\(253\) −140466. −2.19447
\(254\) 216285.i 3.35242i
\(255\) −213.027 1187.14i −0.00327608 0.0182566i
\(256\) −131713. −2.00978
\(257\) 78115.9i 1.18270i 0.806416 + 0.591348i \(0.201404\pi\)
−0.806416 + 0.591348i \(0.798596\pi\)
\(258\) −137650. + 24700.7i −2.06793 + 0.371083i
\(259\) 175286. 2.61304
\(260\) 46231.3i 0.683895i
\(261\) −12451.4 33576.8i −0.182784 0.492899i
\(262\) 70608.6 1.02862
\(263\) 17157.0i 0.248045i 0.992279 + 0.124022i \(0.0395795\pi\)
−0.992279 + 0.124022i \(0.960421\pi\)
\(264\) −46367.6 258392.i −0.665283 3.70742i
\(265\) 2502.47 0.0356350
\(266\) 89051.5i 1.25857i
\(267\) 77249.9 13862.2i 1.08362 0.194451i
\(268\) 55482.7 0.772481
\(269\) 111286.i 1.53792i −0.639295 0.768961i \(-0.720774\pi\)
0.639295 0.768961i \(-0.279226\pi\)
\(270\) −22713.2 38529.0i −0.311567 0.528519i
\(271\) −86909.3 −1.18339 −0.591695 0.806162i \(-0.701541\pi\)
−0.591695 + 0.806162i \(0.701541\pi\)
\(272\) 5684.64i 0.0768360i
\(273\) 17371.9 + 96808.0i 0.233089 + 1.29893i
\(274\) 60884.6 0.810972
\(275\) 124294.i 1.64356i
\(276\) 188409. 33809.3i 2.47333 0.443831i
\(277\) −96252.5 −1.25445 −0.627224 0.778839i \(-0.715809\pi\)
−0.627224 + 0.778839i \(0.715809\pi\)
\(278\) 236851.i 3.06469i
\(279\) 19651.2 7287.34i 0.252453 0.0936182i
\(280\) −78256.7 −0.998172
\(281\) 39522.8i 0.500535i −0.968177 0.250268i \(-0.919481\pi\)
0.968177 0.250268i \(-0.0805186\pi\)
\(282\) 33127.5 + 184609.i 0.416572 + 2.32143i
\(283\) −100369. −1.25322 −0.626611 0.779333i \(-0.715558\pi\)
−0.626611 + 0.779333i \(0.715558\pi\)
\(284\) 251008.i 3.11208i
\(285\) −13763.9 + 2469.89i −0.169454 + 0.0304080i
\(286\) −249906. −3.05524
\(287\) 16941.5i 0.205678i
\(288\) 15129.5 + 40798.6i 0.182406 + 0.491881i
\(289\) 83281.4 0.997131
\(290\) 27124.5i 0.322527i
\(291\) −20389.4 113624.i −0.240779 1.34179i
\(292\) 59669.1 0.699816
\(293\) 44745.7i 0.521214i 0.965445 + 0.260607i \(0.0839227\pi\)
−0.965445 + 0.260607i \(0.916077\pi\)
\(294\) −157086. + 28188.5i −1.81736 + 0.326120i
\(295\) 3923.62 0.0450862
\(296\) 323118.i 3.68789i
\(297\) 141911. 83657.8i 1.60880 0.948404i
\(298\) −273139. −3.07575
\(299\) 97010.4i 1.08512i
\(300\) 29916.8 + 166717.i 0.332409 + 1.85241i
\(301\) −153548. −1.69477
\(302\) 93138.3i 1.02121i
\(303\) −85853.4 + 15406.1i −0.935131 + 0.167806i
\(304\) 65909.1 0.713178
\(305\) 38373.5i 0.412507i
\(306\) −8330.21 + 3089.13i −0.0889638 + 0.0329908i
\(307\) −125274. −1.32918 −0.664589 0.747209i \(-0.731393\pi\)
−0.664589 + 0.747209i \(0.731393\pi\)
\(308\) 541413.i 5.70726i
\(309\) 30290.1 + 168798.i 0.317237 + 1.76787i
\(310\) 15874.9 0.165192
\(311\) 23197.4i 0.239839i −0.992784 0.119919i \(-0.961736\pi\)
0.992784 0.119919i \(-0.0382636\pi\)
\(312\) 178454. 32022.9i 1.83323 0.328967i
\(313\) −43815.3 −0.447236 −0.223618 0.974677i \(-0.571787\pi\)
−0.223618 + 0.974677i \(0.571787\pi\)
\(314\) 13483.5i 0.136755i
\(315\) −17074.3 46043.0i −0.172077 0.464026i
\(316\) −87595.3 −0.877216
\(317\) 49751.8i 0.495096i 0.968876 + 0.247548i \(0.0796249\pi\)
−0.968876 + 0.247548i \(0.920375\pi\)
\(318\) −3255.92 18144.2i −0.0321973 0.179426i
\(319\) 99905.4 0.981765
\(320\) 17916.1i 0.174962i
\(321\) −122039. + 21899.4i −1.18437 + 0.212531i
\(322\) 308449. 2.97490
\(323\) 2777.82i 0.0266256i
\(324\) −170210. + 146368.i −1.62142 + 1.39430i
\(325\) 85841.7 0.812702
\(326\) 116327.i 1.09457i
\(327\) 9202.42 + 51282.2i 0.0860610 + 0.479591i
\(328\) −31229.6 −0.290281
\(329\) 205931.i 1.90253i
\(330\) 122813. 22038.4i 1.12776 0.202373i
\(331\) −61831.6 −0.564358 −0.282179 0.959362i \(-0.591057\pi\)
−0.282179 + 0.959362i \(0.591057\pi\)
\(332\) 158787.i 1.44058i
\(333\) 190109. 70499.1i 1.71441 0.635762i
\(334\) −180107. −1.61449
\(335\) 14039.2i 0.125099i
\(336\) 40880.5 + 227814.i 0.362108 + 2.01791i
\(337\) −59090.1 −0.520302 −0.260151 0.965568i \(-0.583772\pi\)
−0.260151 + 0.965568i \(0.583772\pi\)
\(338\) 29798.4i 0.260831i
\(339\) 147952. 26549.4i 1.28742 0.231023i
\(340\) −4585.26 −0.0396649
\(341\) 58470.8i 0.502840i
\(342\) 35816.1 + 96582.5i 0.306215 + 0.825745i
\(343\) −7100.56 −0.0603538
\(344\) 283047.i 2.39189i
\(345\) 8555.01 + 47674.4i 0.0718757 + 0.400541i
\(346\) −169086. −1.41239
\(347\) 98499.7i 0.818043i 0.912525 + 0.409021i \(0.134130\pi\)
−0.912525 + 0.409021i \(0.865870\pi\)
\(348\) −134004. + 24046.6i −1.10652 + 0.198561i
\(349\) −47248.8 −0.387918 −0.193959 0.981010i \(-0.562133\pi\)
−0.193959 + 0.981010i \(0.562133\pi\)
\(350\) 272938.i 2.22806i
\(351\) 57776.7 + 98008.1i 0.468963 + 0.795514i
\(352\) −121393. −0.979737
\(353\) 115826.i 0.929513i 0.885438 + 0.464757i \(0.153858\pi\)
−0.885438 + 0.464757i \(0.846142\pi\)
\(354\) −5104.96 28448.4i −0.0407367 0.227013i
\(355\) 63514.5 0.503983
\(356\) 298375.i 2.35430i
\(357\) −9601.52 + 1722.96i −0.0753361 + 0.0135188i
\(358\) 151582. 1.18272
\(359\) 66309.4i 0.514501i −0.966345 0.257250i \(-0.917184\pi\)
0.966345 0.257250i \(-0.0828165\pi\)
\(360\) −84874.7 + 31474.5i −0.654898 + 0.242858i
\(361\) −98114.3 −0.752866
\(362\) 256085.i 1.95419i
\(363\) 57898.4 + 322650.i 0.439393 + 2.44860i
\(364\) 373917. 2.82210
\(365\) 15098.5i 0.113331i
\(366\) 278229. 49927.2i 2.07702 0.372713i
\(367\) 227240. 1.68714 0.843572 0.537016i \(-0.180449\pi\)
0.843572 + 0.537016i \(0.180449\pi\)
\(368\) 228291.i 1.68575i
\(369\) −6813.79 18374.2i −0.0500421 0.134945i
\(370\) 153577. 1.12182
\(371\) 20239.9i 0.147048i
\(372\) −14073.5 78427.4i −0.101699 0.566738i
\(373\) 252202. 1.81272 0.906361 0.422504i \(-0.138849\pi\)
0.906361 + 0.422504i \(0.138849\pi\)
\(374\) 24786.0i 0.177200i
\(375\) −90120.4 + 16171.8i −0.640856 + 0.114999i
\(376\) 379610. 2.68511
\(377\) 68997.9i 0.485459i
\(378\) −311622. + 183704.i −2.18094 + 1.28569i
\(379\) −20628.3 −0.143610 −0.0718049 0.997419i \(-0.522876\pi\)
−0.0718049 + 0.997419i \(0.522876\pi\)
\(380\) 53162.7i 0.368162i
\(381\) −48517.9 270375.i −0.334235 1.86259i
\(382\) −275389. −1.88721
\(383\) 269587.i 1.83781i −0.394474 0.918907i \(-0.629073\pi\)
0.394474 0.918907i \(-0.370927\pi\)
\(384\) −206043. + 36973.6i −1.39732 + 0.250744i
\(385\) 136998. 0.924256
\(386\) 233030.i 1.56400i
\(387\) −166533. + 61756.3i −1.11193 + 0.412343i
\(388\) −438868. −2.91522
\(389\) 151849.i 1.00349i 0.865015 + 0.501746i \(0.167309\pi\)
−0.865015 + 0.501746i \(0.832691\pi\)
\(390\) 15220.4 + 84818.6i 0.100068 + 0.557650i
\(391\) 9621.58 0.0629351
\(392\) 323013.i 2.10207i
\(393\) 88267.0 15839.2i 0.571496 0.102553i
\(394\) −289084. −1.86222
\(395\) 22164.9i 0.142060i
\(396\) −217754. 587200.i −1.38859 3.74452i
\(397\) −116775. −0.740919 −0.370459 0.928849i \(-0.620800\pi\)
−0.370459 + 0.928849i \(0.620800\pi\)
\(398\) 160614.i 1.01395i
\(399\) 19976.4 + 111322.i 0.125479 + 0.699256i
\(400\) 202008. 1.26255
\(401\) 131648.i 0.818700i −0.912377 0.409350i \(-0.865755\pi\)
0.912377 0.409350i \(-0.134245\pi\)
\(402\) 101792. 18266.2i 0.629884 0.113030i
\(403\) −40381.8 −0.248642
\(404\) 331605.i 2.03170i
\(405\) −37036.6 43069.6i −0.225798 0.262580i
\(406\) −219382. −1.33091
\(407\) 565657.i 3.41479i
\(408\) 3176.06 + 17699.2i 0.0190796 + 0.106325i
\(409\) −130585. −0.780630 −0.390315 0.920681i \(-0.627634\pi\)
−0.390315 + 0.920681i \(0.627634\pi\)
\(410\) 14843.3i 0.0883006i
\(411\) 76111.1 13657.9i 0.450572 0.0808536i
\(412\) 651974. 3.84093
\(413\) 31734.1i 0.186049i
\(414\) 334535. 124057.i 1.95182 0.723803i
\(415\) 40178.9 0.233293
\(416\) 83838.1i 0.484456i
\(417\) 53131.5 + 296085.i 0.305548 + 1.70273i
\(418\) −287374. −1.64473
\(419\) 21577.2i 0.122904i 0.998110 + 0.0614522i \(0.0195732\pi\)
−0.998110 + 0.0614522i \(0.980427\pi\)
\(420\) −183756. + 32974.5i −1.04170 + 0.186930i
\(421\) −115411. −0.651152 −0.325576 0.945516i \(-0.605558\pi\)
−0.325576 + 0.945516i \(0.605558\pi\)
\(422\) 211346.i 1.18678i
\(423\) 82824.7 + 223347.i 0.462891 + 1.24824i
\(424\) −37309.8 −0.207535
\(425\) 8513.86i 0.0471356i
\(426\) −82637.7 460515.i −0.455365 2.53761i
\(427\) 310364. 1.70222
\(428\) 471369.i 2.57320i
\(429\) −312405. + 56060.0i −1.69748 + 0.304606i
\(430\) −134531. −0.727590
\(431\) 17024.2i 0.0916459i 0.998950 + 0.0458229i \(0.0145910\pi\)
−0.998950 + 0.0458229i \(0.985409\pi\)
\(432\) 135964. + 230638.i 0.728543 + 1.23585i
\(433\) 125401. 0.668844 0.334422 0.942423i \(-0.391459\pi\)
0.334422 + 0.942423i \(0.391459\pi\)
\(434\) 128396.i 0.681666i
\(435\) −6084.68 33908.1i −0.0321558 0.179194i
\(436\) 198076. 1.04198
\(437\) 111555.i 0.584152i
\(438\) 109472. 19644.4i 0.570633 0.102398i
\(439\) 277022. 1.43743 0.718713 0.695307i \(-0.244732\pi\)
0.718713 + 0.695307i \(0.244732\pi\)
\(440\) 252539.i 1.30444i
\(441\) −190048. + 70476.2i −0.977205 + 0.362381i
\(442\) 17118.0 0.0876209
\(443\) 241189.i 1.22900i 0.788918 + 0.614499i \(0.210642\pi\)
−0.788918 + 0.614499i \(0.789358\pi\)
\(444\) −136150. 758722.i −0.690639 3.84872i
\(445\) 75500.0 0.381265
\(446\) 112741.i 0.566775i
\(447\) −341448. + 61271.6i −1.70887 + 0.306651i
\(448\) −144905. −0.721984
\(449\) 58868.2i 0.292004i −0.989284 0.146002i \(-0.953359\pi\)
0.989284 0.146002i \(-0.0466405\pi\)
\(450\) 109774. + 296020.i 0.542096 + 1.46183i
\(451\) 54671.2 0.268785
\(452\) 571457.i 2.79709i
\(453\) −20893.2 116431.i −0.101814 0.567378i
\(454\) −184244. −0.893883
\(455\) 94615.1i 0.457022i
\(456\) 205209. 36824.1i 0.986886 0.177093i
\(457\) 198349. 0.949726 0.474863 0.880060i \(-0.342498\pi\)
0.474863 + 0.880060i \(0.342498\pi\)
\(458\) 193953.i 0.924624i
\(459\) −9720.54 + 5730.35i −0.0461387 + 0.0271992i
\(460\) 184141. 0.870230
\(461\) 368156.i 1.73233i −0.499761 0.866163i \(-0.666579\pi\)
0.499761 0.866163i \(-0.333421\pi\)
\(462\) −178246. 993309.i −0.835094 4.65372i
\(463\) 258187. 1.20441 0.602203 0.798343i \(-0.294290\pi\)
0.602203 + 0.798343i \(0.294290\pi\)
\(464\) 162370.i 0.754170i
\(465\) 19845.1 3561.13i 0.0917797 0.0164695i
\(466\) 622031. 2.86444
\(467\) 78827.9i 0.361448i 0.983534 + 0.180724i \(0.0578441\pi\)
−0.983534 + 0.180724i \(0.942156\pi\)
\(468\) 405539. 150388.i 1.85157 0.686627i
\(469\) 113549. 0.516221
\(470\) 180427.i 0.816783i
\(471\) −3024.68 16855.6i −0.0136344 0.0759806i
\(472\) −58498.0 −0.262577
\(473\) 495508.i 2.21477i
\(474\) −160708. + 28838.4i −0.715286 + 0.128355i
\(475\) 98711.7 0.437504
\(476\) 37085.5i 0.163678i
\(477\) −8140.38 21951.5i −0.0357773 0.0964780i
\(478\) 192233. 0.841340
\(479\) 240842.i 1.04969i −0.851197 0.524846i \(-0.824123\pi\)
0.851197 0.524846i \(-0.175877\pi\)
\(480\) 7393.39 + 41201.1i 0.0320894 + 0.178824i
\(481\) −390661. −1.68853
\(482\) 97391.2i 0.419204i
\(483\) 385589. 69192.6i 1.65284 0.296596i
\(484\) 1.24622e6 5.31991
\(485\) 111050.i 0.472102i
\(486\) −264090. + 324572.i −1.11810 + 1.37417i
\(487\) −132259. −0.557656 −0.278828 0.960341i \(-0.589946\pi\)
−0.278828 + 0.960341i \(0.589946\pi\)
\(488\) 572118.i 2.40240i
\(489\) −26094.9 145419.i −0.109129 0.608140i
\(490\) −153527. −0.639431
\(491\) 159708.i 0.662467i 0.943549 + 0.331233i \(0.107465\pi\)
−0.943549 + 0.331233i \(0.892535\pi\)
\(492\) −73331.0 + 13159.0i −0.302941 + 0.0543616i
\(493\) −6843.28 −0.0281560
\(494\) 198470.i 0.813281i
\(495\) 148584. 55099.9i 0.606402 0.224874i
\(496\) −95028.8 −0.386271
\(497\) 513703.i 2.07970i
\(498\) −52276.2 291319.i −0.210788 1.17466i
\(499\) 438821. 1.76233 0.881163 0.472813i \(-0.156761\pi\)
0.881163 + 0.472813i \(0.156761\pi\)
\(500\) 348086.i 1.39235i
\(501\) −225149. + 40402.2i −0.897005 + 0.160964i
\(502\) −553134. −2.19494
\(503\) 231337.i 0.914343i 0.889379 + 0.457171i \(0.151137\pi\)
−0.889379 + 0.457171i \(0.848863\pi\)
\(504\) 254564. + 686464.i 1.00216 + 2.70245i
\(505\) −83908.6 −0.329021
\(506\) 995385.i 3.88768i
\(507\) 6684.50 + 37250.7i 0.0260048 + 0.144917i
\(508\) −1.04431e6 −4.04672
\(509\) 317545.i 1.22566i 0.790215 + 0.612830i \(0.209969\pi\)
−0.790215 + 0.612830i \(0.790031\pi\)
\(510\) −8412.40 + 1509.57i −0.0323429 + 0.00580382i
\(511\) 122116. 0.467662
\(512\) 561207.i 2.14083i
\(513\) 66439.1 + 112702.i 0.252458 + 0.428251i
\(514\) 553553. 2.09523
\(515\) 164974.i 0.622015i
\(516\) 119266. + 664630.i 0.447936 + 2.49621i
\(517\) −664553. −2.48627
\(518\) 1.24213e6i 4.62920i
\(519\) −211372. + 37930.0i −0.784718 + 0.140815i
\(520\) 174411. 0.645013
\(521\) 203095.i 0.748210i −0.927386 0.374105i \(-0.877950\pi\)
0.927386 0.374105i \(-0.122050\pi\)
\(522\) −237935. + 88234.5i −0.873208 + 0.323815i
\(523\) 188696. 0.689858 0.344929 0.938629i \(-0.387903\pi\)
0.344929 + 0.938629i \(0.387903\pi\)
\(524\) 340928.i 1.24165i
\(525\) 61226.6 + 341197.i 0.222137 + 1.23790i
\(526\) 121580. 0.439430
\(527\) 4005.10i 0.0144209i
\(528\) −735171. + 131924.i −2.63706 + 0.473211i
\(529\) −106554. −0.380767
\(530\) 17733.2i 0.0631300i
\(531\) −12763.3 34417.9i −0.0452663 0.122066i
\(532\) 429978. 1.51923
\(533\) 37757.7i 0.132908i
\(534\) −98231.9 547416.i −0.344485 1.91971i
\(535\) −119274. −0.416715
\(536\) 209313.i 0.728562i
\(537\) 189491. 34003.6i 0.657114 0.117917i
\(538\) −788603. −2.72454
\(539\) 565474.i 1.94641i
\(540\) −186034. + 109669.i −0.637978 + 0.376094i
\(541\) −424126. −1.44911 −0.724553 0.689219i \(-0.757954\pi\)
−0.724553 + 0.689219i \(0.757954\pi\)
\(542\) 615865.i 2.09646i
\(543\) −57446.0 320129.i −0.194832 1.08574i
\(544\) 8315.14 0.0280978
\(545\) 50120.5i 0.168742i
\(546\) 686011. 123102.i 2.30115 0.412934i
\(547\) −133095. −0.444823 −0.222412 0.974953i \(-0.571393\pi\)
−0.222412 + 0.974953i \(0.571393\pi\)
\(548\) 293976.i 0.978929i
\(549\) 336611. 124827.i 1.11682 0.414155i
\(550\) −880787. −2.91169
\(551\) 79342.6i 0.261338i
\(552\) −127548. 710787.i −0.418597 2.33271i
\(553\) −179269. −0.586212
\(554\) 682074.i 2.22235i
\(555\) 191985. 34451.0i 0.623277 0.111845i
\(556\) 1.14362e6 3.69940
\(557\) 23822.6i 0.0767854i 0.999263 + 0.0383927i \(0.0122238\pi\)
−0.999263 + 0.0383927i \(0.987776\pi\)
\(558\) −51640.2 139254.i −0.165852 0.447239i
\(559\) 342214. 1.09515
\(560\) 222654.i 0.709993i
\(561\) −5560.09 30984.7i −0.0176667 0.0984512i
\(562\) −280070. −0.886736
\(563\) 225139.i 0.710286i 0.934812 + 0.355143i \(0.115568\pi\)
−0.934812 + 0.355143i \(0.884432\pi\)
\(564\) 891372. 159953.i 2.80221 0.502847i
\(565\) 144600. 0.452972
\(566\) 711246.i 2.22017i
\(567\) −348346. + 299551.i −1.08354 + 0.931760i
\(568\) −946950. −2.93515
\(569\) 356315.i 1.10055i −0.834983 0.550275i \(-0.814523\pi\)
0.834983 0.550275i \(-0.185477\pi\)
\(570\) 17502.4 + 97535.3i 0.0538700 + 0.300201i
\(571\) 50591.2 0.155168 0.0775841 0.996986i \(-0.475279\pi\)
0.0775841 + 0.996986i \(0.475279\pi\)
\(572\) 1.20665e6i 3.68800i
\(573\) −344261. + 61776.4i −1.04852 + 0.188154i
\(574\) −120052. −0.364374
\(575\) 341910.i 1.03413i
\(576\) −157160. + 58280.1i −0.473692 + 0.175661i
\(577\) 25449.4 0.0764409 0.0382205 0.999269i \(-0.487831\pi\)
0.0382205 + 0.999269i \(0.487831\pi\)
\(578\) 590157.i 1.76649i
\(579\) 52274.2 + 291308.i 0.155930 + 0.868951i
\(580\) −130969. −0.389324
\(581\) 324966.i 0.962688i
\(582\) −805174. + 144486.i −2.37708 + 0.426558i
\(583\) 65315.3 0.192167
\(584\) 225107.i 0.660029i
\(585\) 38053.7 + 102617.i 0.111195 + 0.299851i
\(586\) 317081. 0.923370
\(587\) 479696.i 1.39216i 0.717963 + 0.696081i \(0.245075\pi\)
−0.717963 + 0.696081i \(0.754925\pi\)
\(588\) 136106. + 758476.i 0.393661 + 2.19375i
\(589\) −46436.1 −0.133852
\(590\) 27804.0i 0.0798735i
\(591\) −361381. + 64848.5i −1.03464 + 0.185663i
\(592\) −919326. −2.62317
\(593\) 84236.0i 0.239546i 0.992801 + 0.119773i \(0.0382166\pi\)
−0.992801 + 0.119773i \(0.961783\pi\)
\(594\) −592824. 1.00562e6i −1.68017 2.85011i
\(595\) −9384.01 −0.0265066
\(596\) 1.31883e6i 3.71275i
\(597\) 36029.7 + 200782.i 0.101091 + 0.563348i
\(598\) −687444. −1.92236
\(599\) 505826.i 1.40977i −0.709323 0.704883i \(-0.750999\pi\)
0.709323 0.704883i \(-0.249001\pi\)
\(600\) 628955. 112864.i 1.74710 0.313510i
\(601\) −4842.12 −0.0134056 −0.00670281 0.999978i \(-0.502134\pi\)
−0.00670281 + 0.999978i \(0.502134\pi\)
\(602\) 1.08809e6i 3.00241i
\(603\) 123151. 45668.7i 0.338691 0.125598i
\(604\) −449711. −1.23271
\(605\) 315341.i 0.861528i
\(606\) 109172. + 608383.i 0.297281 + 1.65665i
\(607\) 535910. 1.45450 0.727252 0.686371i \(-0.240797\pi\)
0.727252 + 0.686371i \(0.240797\pi\)
\(608\) 96407.8i 0.260798i
\(609\) −274247. + 49212.7i −0.739448 + 0.132691i
\(610\) 271926. 0.730788
\(611\) 458962.i 1.22940i
\(612\) 14915.6 + 40221.8i 0.0398234 + 0.107389i
\(613\) 341628. 0.909143 0.454571 0.890710i \(-0.349792\pi\)
0.454571 + 0.890710i \(0.349792\pi\)
\(614\) 887727.i 2.35474i
\(615\) −3329.72 18555.5i −0.00880354 0.0490594i
\(616\) −2.04253e6 −5.38278
\(617\) 374929.i 0.984870i −0.870349 0.492435i \(-0.836107\pi\)
0.870349 0.492435i \(-0.163893\pi\)
\(618\) 1.19615e6 214645.i 3.13191 0.562010i
\(619\) 176698. 0.461158 0.230579 0.973054i \(-0.425938\pi\)
0.230579 + 0.973054i \(0.425938\pi\)
\(620\) 76650.8i 0.199404i
\(621\) 390369. 230126.i 1.01226 0.596737i
\(622\) −164384. −0.424892
\(623\) 610642.i 1.57330i
\(624\) −91110.8 507732.i −0.233992 1.30396i
\(625\) 255697. 0.654585
\(626\) 310488.i 0.792313i
\(627\) −359244. + 64465.0i −0.913806 + 0.163979i
\(628\) −65104.1 −0.165078
\(629\) 38746.1i 0.0979325i
\(630\) −326275. + 120994.i −0.822057 + 0.304847i
\(631\) 414056. 1.03992 0.519960 0.854190i \(-0.325947\pi\)
0.519960 + 0.854190i \(0.325947\pi\)
\(632\) 330461.i 0.827343i
\(633\) 47409.9 + 264201.i 0.118321 + 0.659367i
\(634\) 352556. 0.877100
\(635\) 264251.i 0.655343i
\(636\) −87608.0 + 15721.0i −0.216586 + 0.0388655i
\(637\) 390534. 0.962455
\(638\) 707960.i 1.73927i
\(639\) −206609. 557147.i −0.505997 1.36448i
\(640\) −201375. −0.491639
\(641\) 275394.i 0.670252i −0.942173 0.335126i \(-0.891221\pi\)
0.942173 0.335126i \(-0.108779\pi\)
\(642\) 155186. + 864802.i 0.376514 + 2.09820i
\(643\) 267744. 0.647586 0.323793 0.946128i \(-0.395042\pi\)
0.323793 + 0.946128i \(0.395042\pi\)
\(644\) 1.48932e6i 3.59102i
\(645\) −168176. + 30178.6i −0.404246 + 0.0725405i
\(646\) 19684.4 0.0471692
\(647\) 680208.i 1.62493i −0.583013 0.812463i \(-0.698126\pi\)
0.583013 0.812463i \(-0.301874\pi\)
\(648\) 552185. + 642133.i 1.31503 + 1.52924i
\(649\) 102408. 0.243133
\(650\) 608300.i 1.43976i
\(651\) −28802.3 160506.i −0.0679618 0.378730i
\(652\) −561675. −1.32127
\(653\) 714728.i 1.67616i −0.545550 0.838078i \(-0.683679\pi\)
0.545550 0.838078i \(-0.316321\pi\)
\(654\) 363401. 65211.1i 0.849632 0.152463i
\(655\) 86267.5 0.201078
\(656\) 88853.6i 0.206475i
\(657\) 132444. 49114.6i 0.306832 0.113784i
\(658\) 1.45929e6 3.37047
\(659\) 257886.i 0.593824i 0.954905 + 0.296912i \(0.0959568\pi\)
−0.954905 + 0.296912i \(0.904043\pi\)
\(660\) −106411. 592993.i −0.244285 1.36133i
\(661\) −157805. −0.361174 −0.180587 0.983559i \(-0.557800\pi\)
−0.180587 + 0.983559i \(0.557800\pi\)
\(662\) 438157.i 0.999802i
\(663\) 21399.0 3839.97i 0.0486818 0.00873577i
\(664\) −599036. −1.35868
\(665\) 108801.i 0.246030i
\(666\) −499577. 1.34717e6i −1.12630 3.03721i
\(667\) 274821. 0.617728
\(668\) 869630.i 1.94886i
\(669\) −25290.4 140936.i −0.0565072 0.314897i
\(670\) 99485.9 0.221621
\(671\) 1.00156e6i 2.22450i
\(672\) 333233. 59797.5i 0.737920 0.132417i
\(673\) −160084. −0.353441 −0.176720 0.984261i \(-0.556549\pi\)
−0.176720 + 0.984261i \(0.556549\pi\)
\(674\) 418730.i 0.921753i
\(675\) 203632. + 345426.i 0.446929 + 0.758137i
\(676\) 143879. 0.314851
\(677\) 402856.i 0.878968i 0.898251 + 0.439484i \(0.144839\pi\)
−0.898251 + 0.439484i \(0.855161\pi\)
\(678\) −188137. 1.04843e6i −0.409274 2.28076i
\(679\) −898170. −1.94813
\(680\) 17298.3i 0.0374098i
\(681\) −230321. + 41330.3i −0.496637 + 0.0891198i
\(682\) 414341. 0.890819
\(683\) 37881.8i 0.0812061i −0.999175 0.0406031i \(-0.987072\pi\)
0.999175 0.0406031i \(-0.0129279\pi\)
\(684\) 466341. 172935.i 0.996761 0.369633i
\(685\) 74387.0 0.158532
\(686\) 50316.7i 0.106921i
\(687\) 43508.3 + 242458.i 0.0921847 + 0.513717i
\(688\) 805318. 1.70134
\(689\) 45108.8i 0.0950218i
\(690\) 337835. 60623.3i 0.709589 0.127333i
\(691\) −559150. −1.17104 −0.585521 0.810658i \(-0.699110\pi\)
−0.585521 + 0.810658i \(0.699110\pi\)
\(692\) 816418.i 1.70490i
\(693\) −445646. 1.20174e6i −0.927948 2.50233i
\(694\) 697998. 1.44922
\(695\) 289378.i 0.599096i
\(696\) 90717.7 + 505542.i 0.187272 + 1.04361i
\(697\) −3744.84 −0.00770847
\(698\) 334819.i 0.687225i
\(699\) 777594. 139537.i 1.59147 0.285584i
\(700\) 1.31786e6 2.68951
\(701\) 628916.i 1.27984i −0.768440 0.639921i \(-0.778967\pi\)
0.768440 0.639921i \(-0.221033\pi\)
\(702\) 694515. 409423.i 1.40931 0.830803i
\(703\) −449232. −0.908992
\(704\) 467617.i 0.943507i
\(705\) 40474.2 + 225550.i 0.0814330 + 0.453801i
\(706\) 820775. 1.64670
\(707\) 678650.i 1.35771i
\(708\) −137361. + 24648.9i −0.274029 + 0.0491735i
\(709\) −244960. −0.487307 −0.243653 0.969862i \(-0.578346\pi\)
−0.243653 + 0.969862i \(0.578346\pi\)
\(710\) 450083.i 0.892844i
\(711\) −194430. + 72101.1i −0.384612 + 0.142627i
\(712\) −1.12564e6 −2.22045
\(713\) 160842.i 0.316388i
\(714\) 12209.4 + 68039.2i 0.0239496 + 0.133464i
\(715\) −305328. −0.597249
\(716\) 731903.i 1.42767i
\(717\) 240308. 43122.4i 0.467445 0.0838813i
\(718\) −469888. −0.911476
\(719\) 689940.i 1.33461i 0.744785 + 0.667304i \(0.232552\pi\)
−0.744785 + 0.667304i \(0.767448\pi\)
\(720\) 89550.3 + 241483.i 0.172744 + 0.465824i
\(721\) 1.33430e6 2.56675
\(722\) 695267.i 1.33376i
\(723\) −21847.2 121748.i −0.0417945 0.232908i
\(724\) −1.23648e6 −2.35891
\(725\) 243181.i 0.462651i
\(726\) 2.28639e6 410285.i 4.33788 0.778417i
\(727\) −35938.5 −0.0679973 −0.0339986 0.999422i \(-0.510824\pi\)
−0.0339986 + 0.999422i \(0.510824\pi\)
\(728\) 1.41063e6i 2.66165i
\(729\) −257327. + 464986.i −0.484206 + 0.874954i
\(730\) 106993. 0.200774
\(731\) 33941.1i 0.0635172i
\(732\) −241069. 1.34341e6i −0.449904 2.50718i
\(733\) −165921. −0.308811 −0.154406 0.988008i \(-0.549346\pi\)
−0.154406 + 0.988008i \(0.549346\pi\)
\(734\) 1.61029e6i 2.98890i
\(735\) −191923. + 34439.9i −0.355265 + 0.0637510i
\(736\) −333929. −0.616452
\(737\) 366428.i 0.674611i
\(738\) −130205. + 48284.5i −0.239065 + 0.0886534i
\(739\) −748038. −1.36973 −0.684865 0.728670i \(-0.740139\pi\)
−0.684865 + 0.728670i \(0.740139\pi\)
\(740\) 741534.i 1.35415i
\(741\) −44521.6 248105.i −0.0810838 0.451855i
\(742\) −143426. −0.260507
\(743\) 534864.i 0.968871i −0.874827 0.484435i \(-0.839025\pi\)
0.874827 0.484435i \(-0.160975\pi\)
\(744\) −295874. + 53093.5i −0.534516 + 0.0959171i
\(745\) −333713. −0.601258
\(746\) 1.78718e6i 3.21137i
\(747\) −130700. 352448.i −0.234225 0.631617i
\(748\) −119677. −0.213898
\(749\) 964686.i 1.71958i
\(750\) 114598. + 638620.i 0.203730 + 1.13532i
\(751\) −911644. −1.61639 −0.808194 0.588917i \(-0.799555\pi\)
−0.808194 + 0.588917i \(0.799555\pi\)
\(752\) 1.08006e6i 1.90990i
\(753\) −691466. + 124081.i −1.21950 + 0.218835i
\(754\) 488939. 0.860028
\(755\) 113794.i 0.199629i
\(756\) 887000. + 1.50464e6i 1.55196 + 2.63263i
\(757\) −738108. −1.28804 −0.644019 0.765010i \(-0.722734\pi\)
−0.644019 + 0.765010i \(0.722734\pi\)
\(758\) 146178.i 0.254416i
\(759\) 223289. + 1.24432e6i 0.387600 + 2.15997i
\(760\) 200561. 0.347231
\(761\) 931700.i 1.60882i 0.594076 + 0.804409i \(0.297518\pi\)
−0.594076 + 0.804409i \(0.702482\pi\)
\(762\) −1.91596e6 + 343812.i −3.29972 + 0.592122i
\(763\) 405373. 0.696316
\(764\) 1.32969e6i 2.27806i
\(765\) −10177.6 + 3774.21i −0.0173909 + 0.00644915i
\(766\) −1.91037e6 −3.25582
\(767\) 70726.2i 0.120224i
\(768\) 209374. + 1.16678e6i 0.354977 + 1.97818i
\(769\) −1.09188e6 −1.84639 −0.923193 0.384336i \(-0.874430\pi\)
−0.923193 + 0.384336i \(0.874430\pi\)
\(770\) 970807.i 1.63739i
\(771\) 691990. 124175.i 1.16410 0.208894i
\(772\) 1.12517e6 1.88791
\(773\) 641269.i 1.07320i 0.843836 + 0.536601i \(0.180292\pi\)
−0.843836 + 0.536601i \(0.819708\pi\)
\(774\) 437623. + 1.18010e6i 0.730497 + 1.96987i
\(775\) −142324. −0.236960
\(776\) 1.65567e6i 2.74947i
\(777\) −278639. 1.55277e6i −0.461530 2.57196i
\(778\) 1.07605e6 1.77776
\(779\) 43418.6i 0.0715486i
\(780\) 409540. 73490.5i 0.673143 0.120793i
\(781\) 1.65775e6 2.71780
\(782\) 68181.4i 0.111494i