Properties

Label 177.5.b.a.119.15
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 119.15
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.64

$q$-expansion

\(f(q)\) \(=\) \(q-5.52059i q^{2} +(4.22607 + 7.94609i) q^{3} -14.4769 q^{4} +14.8774i q^{5} +(43.8671 - 23.3304i) q^{6} +83.7732 q^{7} -8.40835i q^{8} +(-45.2807 + 67.1614i) q^{9} +O(q^{10})\) \(q-5.52059i q^{2} +(4.22607 + 7.94609i) q^{3} -14.4769 q^{4} +14.8774i q^{5} +(43.8671 - 23.3304i) q^{6} +83.7732 q^{7} -8.40835i q^{8} +(-45.2807 + 67.1614i) q^{9} +82.1318 q^{10} +224.925i q^{11} +(-61.1804 - 115.035i) q^{12} -309.676 q^{13} -462.478i q^{14} +(-118.217 + 62.8727i) q^{15} -278.050 q^{16} +375.087i q^{17} +(370.771 + 249.976i) q^{18} -139.347 q^{19} -215.378i q^{20} +(354.031 + 665.670i) q^{21} +1241.72 q^{22} -571.445i q^{23} +(66.8136 - 35.5343i) q^{24} +403.664 q^{25} +1709.59i q^{26} +(-725.030 - 75.9765i) q^{27} -1212.78 q^{28} +607.695i q^{29} +(347.095 + 652.627i) q^{30} +1380.31 q^{31} +1400.46i q^{32} +(-1787.28 + 950.549i) q^{33} +2070.70 q^{34} +1246.33i q^{35} +(655.525 - 972.290i) q^{36} +595.193 q^{37} +769.279i q^{38} +(-1308.71 - 2460.71i) q^{39} +125.094 q^{40} -742.104i q^{41} +(3674.89 - 1954.46i) q^{42} +292.877 q^{43} -3256.22i q^{44} +(-999.185 - 673.658i) q^{45} -3154.71 q^{46} +534.415i q^{47} +(-1175.06 - 2209.41i) q^{48} +4616.95 q^{49} -2228.46i q^{50} +(-2980.48 + 1585.14i) q^{51} +4483.15 q^{52} +3096.79i q^{53} +(-419.435 + 4002.59i) q^{54} -3346.30 q^{55} -704.395i q^{56} +(-588.891 - 1107.27i) q^{57} +3354.84 q^{58} -453.188i q^{59} +(1711.42 - 910.203i) q^{60} -42.3089 q^{61} -7620.15i q^{62} +(-3793.31 + 5626.33i) q^{63} +3282.59 q^{64} -4607.16i q^{65} +(5247.59 + 9866.83i) q^{66} +1858.73 q^{67} -5430.11i q^{68} +(4540.75 - 2414.96i) q^{69} +6880.45 q^{70} -3827.45i q^{71} +(564.717 + 380.737i) q^{72} +8263.85 q^{73} -3285.82i q^{74} +(1705.91 + 3207.55i) q^{75} +2017.32 q^{76} +18842.7i q^{77} +(-13584.6 + 7224.86i) q^{78} -4676.83 q^{79} -4136.65i q^{80} +(-2460.31 - 6082.24i) q^{81} -4096.85 q^{82} -3665.27i q^{83} +(-5125.28 - 9636.84i) q^{84} -5580.31 q^{85} -1616.86i q^{86} +(-4828.80 + 2568.16i) q^{87} +1891.25 q^{88} -2164.68i q^{89} +(-3718.99 + 5516.09i) q^{90} -25942.6 q^{91} +8272.75i q^{92} +(5833.30 + 10968.1i) q^{93} +2950.29 q^{94} -2073.12i q^{95} +(-11128.2 + 5918.45i) q^{96} +5523.27 q^{97} -25488.3i q^{98} +(-15106.3 - 10184.8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.52059i 1.38015i −0.723739 0.690074i \(-0.757578\pi\)
0.723739 0.690074i \(-0.242422\pi\)
\(3\) 4.22607 + 7.94609i 0.469563 + 0.882899i
\(4\) −14.4769 −0.904807
\(5\) 14.8774i 0.595095i 0.954707 + 0.297547i \(0.0961686\pi\)
−0.954707 + 0.297547i \(0.903831\pi\)
\(6\) 43.8671 23.3304i 1.21853 0.648066i
\(7\) 83.7732 1.70966 0.854829 0.518910i \(-0.173662\pi\)
0.854829 + 0.518910i \(0.173662\pi\)
\(8\) 8.40835i 0.131381i
\(9\) −45.2807 + 67.1614i −0.559022 + 0.829153i
\(10\) 82.1318 0.821318
\(11\) 224.925i 1.85889i 0.368964 + 0.929444i \(0.379713\pi\)
−0.368964 + 0.929444i \(0.620287\pi\)
\(12\) −61.1804 115.035i −0.424864 0.798853i
\(13\) −309.676 −1.83240 −0.916201 0.400719i \(-0.868761\pi\)
−0.916201 + 0.400719i \(0.868761\pi\)
\(14\) 462.478i 2.35958i
\(15\) −118.217 + 62.8727i −0.525409 + 0.279434i
\(16\) −278.050 −1.08613
\(17\) 375.087i 1.29788i 0.760840 + 0.648940i \(0.224787\pi\)
−0.760840 + 0.648940i \(0.775213\pi\)
\(18\) 370.771 + 249.976i 1.14435 + 0.771532i
\(19\) −139.347 −0.386003 −0.193002 0.981198i \(-0.561822\pi\)
−0.193002 + 0.981198i \(0.561822\pi\)
\(20\) 215.378i 0.538446i
\(21\) 354.031 + 665.670i 0.802792 + 1.50946i
\(22\) 1241.72 2.56554
\(23\) 571.445i 1.08024i −0.841589 0.540118i \(-0.818380\pi\)
0.841589 0.540118i \(-0.181620\pi\)
\(24\) 66.8136 35.5343i 0.115996 0.0616914i
\(25\) 403.664 0.645862
\(26\) 1709.59i 2.52899i
\(27\) −725.030 75.9765i −0.994554 0.104220i
\(28\) −1212.78 −1.54691
\(29\) 607.695i 0.722586i 0.932452 + 0.361293i \(0.117665\pi\)
−0.932452 + 0.361293i \(0.882335\pi\)
\(30\) 347.095 + 652.627i 0.385661 + 0.725141i
\(31\) 1380.31 1.43633 0.718166 0.695872i \(-0.244982\pi\)
0.718166 + 0.695872i \(0.244982\pi\)
\(32\) 1400.46i 1.36764i
\(33\) −1787.28 + 950.549i −1.64121 + 0.872864i
\(34\) 2070.70 1.79127
\(35\) 1246.33i 1.01741i
\(36\) 655.525 972.290i 0.505807 0.750223i
\(37\) 595.193 0.434765 0.217382 0.976087i \(-0.430248\pi\)
0.217382 + 0.976087i \(0.430248\pi\)
\(38\) 769.279i 0.532742i
\(39\) −1308.71 2460.71i −0.860428 1.61783i
\(40\) 125.094 0.0781839
\(41\) 742.104i 0.441466i −0.975334 0.220733i \(-0.929155\pi\)
0.975334 0.220733i \(-0.0708449\pi\)
\(42\) 3674.89 1954.46i 2.08327 1.10797i
\(43\) 292.877 0.158398 0.0791988 0.996859i \(-0.474764\pi\)
0.0791988 + 0.996859i \(0.474764\pi\)
\(44\) 3256.22i 1.68193i
\(45\) −999.185 673.658i −0.493425 0.332671i
\(46\) −3154.71 −1.49088
\(47\) 534.415i 0.241926i 0.992657 + 0.120963i \(0.0385983\pi\)
−0.992657 + 0.120963i \(0.961402\pi\)
\(48\) −1175.06 2209.41i −0.510007 0.958944i
\(49\) 4616.95 1.92293
\(50\) 2228.46i 0.891385i
\(51\) −2980.48 + 1585.14i −1.14590 + 0.609436i
\(52\) 4483.15 1.65797
\(53\) 3096.79i 1.10245i 0.834356 + 0.551226i \(0.185840\pi\)
−0.834356 + 0.551226i \(0.814160\pi\)
\(54\) −419.435 + 4002.59i −0.143839 + 1.37263i
\(55\) −3346.30 −1.10621
\(56\) 704.395i 0.224616i
\(57\) −588.891 1107.27i −0.181253 0.340802i
\(58\) 3354.84 0.997276
\(59\) 453.188i 0.130189i
\(60\) 1711.42 910.203i 0.475393 0.252834i
\(61\) −42.3089 −0.0113703 −0.00568515 0.999984i \(-0.501810\pi\)
−0.00568515 + 0.999984i \(0.501810\pi\)
\(62\) 7620.15i 1.98235i
\(63\) −3793.31 + 5626.33i −0.955736 + 1.41757i
\(64\) 3282.59 0.801415
\(65\) 4607.16i 1.09045i
\(66\) 5247.59 + 9866.83i 1.20468 + 2.26511i
\(67\) 1858.73 0.414063 0.207032 0.978334i \(-0.433620\pi\)
0.207032 + 0.978334i \(0.433620\pi\)
\(68\) 5430.11i 1.17433i
\(69\) 4540.75 2414.96i 0.953739 0.507239i
\(70\) 6880.45 1.40417
\(71\) 3827.45i 0.759264i −0.925138 0.379632i \(-0.876051\pi\)
0.925138 0.379632i \(-0.123949\pi\)
\(72\) 564.717 + 380.737i 0.108935 + 0.0734446i
\(73\) 8263.85 1.55073 0.775366 0.631512i \(-0.217565\pi\)
0.775366 + 0.631512i \(0.217565\pi\)
\(74\) 3285.82i 0.600040i
\(75\) 1705.91 + 3207.55i 0.303273 + 0.570231i
\(76\) 2017.32 0.349259
\(77\) 18842.7i 3.17806i
\(78\) −13584.6 + 7224.86i −2.23284 + 1.18752i
\(79\) −4676.83 −0.749371 −0.374686 0.927152i \(-0.622249\pi\)
−0.374686 + 0.927152i \(0.622249\pi\)
\(80\) 4136.65i 0.646351i
\(81\) −2460.31 6082.24i −0.374990 0.927029i
\(82\) −4096.85 −0.609288
\(83\) 3665.27i 0.532047i −0.963967 0.266024i \(-0.914290\pi\)
0.963967 0.266024i \(-0.0857099\pi\)
\(84\) −5125.28 9636.84i −0.726371 1.36577i
\(85\) −5580.31 −0.772362
\(86\) 1616.86i 0.218612i
\(87\) −4828.80 + 2568.16i −0.637971 + 0.339300i
\(88\) 1891.25 0.244222
\(89\) 2164.68i 0.273283i −0.990621 0.136642i \(-0.956369\pi\)
0.990621 0.136642i \(-0.0436309\pi\)
\(90\) −3718.99 + 5516.09i −0.459135 + 0.680999i
\(91\) −25942.6 −3.13278
\(92\) 8272.75i 0.977405i
\(93\) 5833.30 + 10968.1i 0.674448 + 1.26814i
\(94\) 2950.29 0.333894
\(95\) 2073.12i 0.229709i
\(96\) −11128.2 + 5918.45i −1.20749 + 0.642193i
\(97\) 5523.27 0.587020 0.293510 0.955956i \(-0.405177\pi\)
0.293510 + 0.955956i \(0.405177\pi\)
\(98\) 25488.3i 2.65393i
\(99\) −15106.3 10184.8i −1.54130 1.03916i
\(100\) −5843.81 −0.584381
\(101\) 2906.57i 0.284930i −0.989800 0.142465i \(-0.954497\pi\)
0.989800 0.142465i \(-0.0455028\pi\)
\(102\) 8750.93 + 16454.0i 0.841112 + 1.58151i
\(103\) −10723.3 −1.01077 −0.505387 0.862893i \(-0.668650\pi\)
−0.505387 + 0.862893i \(0.668650\pi\)
\(104\) 2603.87i 0.240742i
\(105\) −9903.41 + 5267.05i −0.898269 + 0.477737i
\(106\) 17096.1 1.52155
\(107\) 10516.9i 0.918585i −0.888285 0.459293i \(-0.848103\pi\)
0.888285 0.459293i \(-0.151897\pi\)
\(108\) 10496.2 + 1099.91i 0.899880 + 0.0942991i
\(109\) −2290.88 −0.192819 −0.0964094 0.995342i \(-0.530736\pi\)
−0.0964094 + 0.995342i \(0.530736\pi\)
\(110\) 18473.5i 1.52674i
\(111\) 2515.32 + 4729.46i 0.204149 + 0.383853i
\(112\) −23293.1 −1.85691
\(113\) 9161.51i 0.717481i −0.933437 0.358740i \(-0.883206\pi\)
0.933437 0.358740i \(-0.116794\pi\)
\(114\) −6112.76 + 3251.02i −0.470357 + 0.250156i
\(115\) 8501.59 0.642843
\(116\) 8797.55i 0.653801i
\(117\) 14022.4 20798.3i 1.02435 1.51934i
\(118\) −2501.86 −0.179680
\(119\) 31422.3i 2.21893i
\(120\) 528.656 + 994.010i 0.0367122 + 0.0690285i
\(121\) −35950.4 −2.45546
\(122\) 233.570i 0.0156927i
\(123\) 5896.83 3136.18i 0.389770 0.207296i
\(124\) −19982.7 −1.29960
\(125\) 15303.8i 0.979444i
\(126\) 31060.6 + 20941.3i 1.95645 + 1.31906i
\(127\) 15749.1 0.976447 0.488223 0.872719i \(-0.337645\pi\)
0.488223 + 0.872719i \(0.337645\pi\)
\(128\) 4285.57i 0.261571i
\(129\) 1237.72 + 2327.23i 0.0743777 + 0.139849i
\(130\) −25434.3 −1.50499
\(131\) 17476.7i 1.01839i −0.860650 0.509197i \(-0.829942\pi\)
0.860650 0.509197i \(-0.170058\pi\)
\(132\) 25874.3 13761.0i 1.48498 0.789774i
\(133\) −11673.6 −0.659934
\(134\) 10261.3i 0.571468i
\(135\) 1130.33 10786.5i 0.0620209 0.591854i
\(136\) 3153.87 0.170516
\(137\) 6131.87i 0.326702i 0.986568 + 0.163351i \(0.0522303\pi\)
−0.986568 + 0.163351i \(0.947770\pi\)
\(138\) −13332.0 25067.6i −0.700064 1.31630i
\(139\) 32312.4 1.67240 0.836198 0.548427i \(-0.184773\pi\)
0.836198 + 0.548427i \(0.184773\pi\)
\(140\) 18042.9i 0.920558i
\(141\) −4246.51 + 2258.47i −0.213596 + 0.113600i
\(142\) −21129.8 −1.04790
\(143\) 69654.0i 3.40623i
\(144\) 12590.3 18674.2i 0.607171 0.900569i
\(145\) −9040.91 −0.430007
\(146\) 45621.3i 2.14024i
\(147\) 19511.5 + 36686.7i 0.902936 + 1.69775i
\(148\) −8616.56 −0.393378
\(149\) 36060.2i 1.62426i 0.583476 + 0.812131i \(0.301692\pi\)
−0.583476 + 0.812131i \(0.698308\pi\)
\(150\) 17707.6 9417.63i 0.787003 0.418561i
\(151\) 9345.67 0.409880 0.204940 0.978775i \(-0.434300\pi\)
0.204940 + 0.978775i \(0.434300\pi\)
\(152\) 1171.68i 0.0507133i
\(153\) −25191.4 16984.2i −1.07614 0.725543i
\(154\) 104023. 4.38619
\(155\) 20535.4i 0.854753i
\(156\) 18946.1 + 35623.5i 0.778521 + 1.46382i
\(157\) 27677.2 1.12285 0.561426 0.827527i \(-0.310253\pi\)
0.561426 + 0.827527i \(0.310253\pi\)
\(158\) 25818.8i 1.03424i
\(159\) −24607.4 + 13087.2i −0.973354 + 0.517670i
\(160\) −20835.2 −0.813876
\(161\) 47871.8i 1.84683i
\(162\) −33577.5 + 13582.4i −1.27944 + 0.517541i
\(163\) 22755.5 0.856469 0.428235 0.903668i \(-0.359136\pi\)
0.428235 + 0.903668i \(0.359136\pi\)
\(164\) 10743.4i 0.399441i
\(165\) −14141.7 26590.0i −0.519437 0.976675i
\(166\) −20234.5 −0.734304
\(167\) 12179.6i 0.436716i −0.975869 0.218358i \(-0.929930\pi\)
0.975869 0.218358i \(-0.0700701\pi\)
\(168\) 5597.19 2976.82i 0.198313 0.105471i
\(169\) 67338.2 2.35770
\(170\) 30806.6i 1.06597i
\(171\) 6309.75 9358.76i 0.215784 0.320056i
\(172\) −4239.96 −0.143319
\(173\) 8146.41i 0.272191i −0.990696 0.136096i \(-0.956545\pi\)
0.990696 0.136096i \(-0.0434554\pi\)
\(174\) 14177.8 + 26657.8i 0.468284 + 0.880494i
\(175\) 33816.2 1.10420
\(176\) 62540.4i 2.01900i
\(177\) 3601.07 1915.20i 0.114944 0.0611319i
\(178\) −11950.3 −0.377171
\(179\) 16581.8i 0.517517i −0.965942 0.258759i \(-0.916687\pi\)
0.965942 0.258759i \(-0.0833134\pi\)
\(180\) 14465.1 + 9752.49i 0.446454 + 0.301003i
\(181\) −27569.2 −0.841526 −0.420763 0.907171i \(-0.638238\pi\)
−0.420763 + 0.907171i \(0.638238\pi\)
\(182\) 143218.i 4.32370i
\(183\) −178.800 336.190i −0.00533907 0.0100388i
\(184\) −4804.91 −0.141922
\(185\) 8854.91i 0.258726i
\(186\) 60550.4 32203.2i 1.75021 0.930837i
\(187\) −84366.7 −2.41261
\(188\) 7736.68i 0.218896i
\(189\) −60738.1 6364.80i −1.70035 0.178181i
\(190\) −11444.8 −0.317032
\(191\) 15213.9i 0.417037i −0.978018 0.208518i \(-0.933136\pi\)
0.978018 0.208518i \(-0.0668641\pi\)
\(192\) 13872.5 + 26083.8i 0.376314 + 0.707568i
\(193\) −23560.4 −0.632510 −0.316255 0.948674i \(-0.602426\pi\)
−0.316255 + 0.948674i \(0.602426\pi\)
\(194\) 30491.7i 0.810174i
\(195\) 36608.9 19470.2i 0.962760 0.512036i
\(196\) −66839.2 −1.73988
\(197\) 39153.3i 1.00887i 0.863449 + 0.504436i \(0.168300\pi\)
−0.863449 + 0.504436i \(0.831700\pi\)
\(198\) −56226.0 + 83395.7i −1.43419 + 2.12722i
\(199\) −71055.1 −1.79428 −0.897138 0.441751i \(-0.854357\pi\)
−0.897138 + 0.441751i \(0.854357\pi\)
\(200\) 3394.15i 0.0848537i
\(201\) 7855.12 + 14769.6i 0.194429 + 0.365576i
\(202\) −16046.0 −0.393245
\(203\) 50908.6i 1.23538i
\(204\) 43148.1 22948.0i 1.03682 0.551422i
\(205\) 11040.6 0.262714
\(206\) 59198.9i 1.39502i
\(207\) 38379.0 + 25875.4i 0.895681 + 0.603875i
\(208\) 86105.3 1.99023
\(209\) 31342.7i 0.717537i
\(210\) 29077.2 + 54672.7i 0.659348 + 1.23974i
\(211\) 484.586 0.0108844 0.00544222 0.999985i \(-0.498268\pi\)
0.00544222 + 0.999985i \(0.498268\pi\)
\(212\) 44831.9i 0.997506i
\(213\) 30413.3 16175.0i 0.670353 0.356522i
\(214\) −58059.4 −1.26778
\(215\) 4357.24i 0.0942616i
\(216\) −638.837 + 6096.31i −0.0136925 + 0.130665i
\(217\) 115633. 2.45563
\(218\) 12647.0i 0.266118i
\(219\) 34923.6 + 65665.3i 0.728166 + 1.36914i
\(220\) 48444.0 1.00091
\(221\) 116156.i 2.37824i
\(222\) 26109.4 13886.1i 0.529774 0.281756i
\(223\) −58515.5 −1.17669 −0.588343 0.808611i \(-0.700220\pi\)
−0.588343 + 0.808611i \(0.700220\pi\)
\(224\) 117321.i 2.33820i
\(225\) −18278.2 + 27110.6i −0.361051 + 0.535519i
\(226\) −50577.0 −0.990229
\(227\) 44301.3i 0.859734i −0.902892 0.429867i \(-0.858560\pi\)
0.902892 0.429867i \(-0.141440\pi\)
\(228\) 8525.32 + 16029.8i 0.163999 + 0.308360i
\(229\) −29044.0 −0.553841 −0.276921 0.960893i \(-0.589314\pi\)
−0.276921 + 0.960893i \(0.589314\pi\)
\(230\) 46933.8i 0.887218i
\(231\) −149726. + 79630.6i −2.80591 + 1.49230i
\(232\) 5109.72 0.0949338
\(233\) 56988.7i 1.04973i −0.851186 0.524864i \(-0.824116\pi\)
0.851186 0.524864i \(-0.175884\pi\)
\(234\) −114819. 77411.7i −2.09692 1.41376i
\(235\) −7950.69 −0.143969
\(236\) 6560.76i 0.117796i
\(237\) −19764.6 37162.5i −0.351877 0.661619i
\(238\) 173470. 3.06245
\(239\) 37945.5i 0.664301i 0.943226 + 0.332150i \(0.107774\pi\)
−0.943226 + 0.332150i \(0.892226\pi\)
\(240\) 32870.2 17481.7i 0.570663 0.303502i
\(241\) −65516.7 −1.12802 −0.564011 0.825767i \(-0.690742\pi\)
−0.564011 + 0.825767i \(0.690742\pi\)
\(242\) 198468.i 3.38890i
\(243\) 37932.6 45253.8i 0.642392 0.766376i
\(244\) 612.502 0.0102879
\(245\) 68688.1i 1.14433i
\(246\) −17313.6 32554.0i −0.286099 0.537940i
\(247\) 43152.5 0.707314
\(248\) 11606.2i 0.188706i
\(249\) 29124.6 15489.7i 0.469744 0.249830i
\(250\) 84486.1 1.35178
\(251\) 83957.4i 1.33264i −0.745668 0.666318i \(-0.767869\pi\)
0.745668 0.666318i \(-0.232131\pi\)
\(252\) 54915.5 81451.8i 0.864756 1.28263i
\(253\) 128532. 2.00804
\(254\) 86944.4i 1.34764i
\(255\) −23582.8 44341.7i −0.362672 0.681917i
\(256\) 76180.4 1.16242
\(257\) 12693.2i 0.192178i 0.995373 + 0.0960890i \(0.0306333\pi\)
−0.995373 + 0.0960890i \(0.969367\pi\)
\(258\) 12847.7 6832.94i 0.193012 0.102652i
\(259\) 49861.2 0.743299
\(260\) 66697.5i 0.986649i
\(261\) −40813.7 27516.9i −0.599135 0.403941i
\(262\) −96481.5 −1.40553
\(263\) 48754.8i 0.704866i 0.935837 + 0.352433i \(0.114645\pi\)
−0.935837 + 0.352433i \(0.885355\pi\)
\(264\) 7992.56 + 15028.1i 0.114677 + 0.215623i
\(265\) −46072.0 −0.656063
\(266\) 64445.0i 0.910806i
\(267\) 17200.7 9148.07i 0.241282 0.128324i
\(268\) −26908.7 −0.374647
\(269\) 67655.3i 0.934970i −0.884001 0.467485i \(-0.845160\pi\)
0.884001 0.467485i \(-0.154840\pi\)
\(270\) −59548.1 6240.09i −0.816846 0.0855979i
\(271\) 76385.1 1.04009 0.520044 0.854140i \(-0.325916\pi\)
0.520044 + 0.854140i \(0.325916\pi\)
\(272\) 104293.i 1.40967i
\(273\) −109635. 206142.i −1.47104 2.76593i
\(274\) 33851.5 0.450897
\(275\) 90794.3i 1.20059i
\(276\) −65736.1 + 34961.2i −0.862950 + 0.458953i
\(277\) 22731.1 0.296252 0.148126 0.988969i \(-0.452676\pi\)
0.148126 + 0.988969i \(0.452676\pi\)
\(278\) 178383.i 2.30815i
\(279\) −62501.7 + 92703.8i −0.802940 + 1.19094i
\(280\) 10479.5 0.133668
\(281\) 6215.48i 0.0787158i 0.999225 + 0.0393579i \(0.0125312\pi\)
−0.999225 + 0.0393579i \(0.987469\pi\)
\(282\) 12468.1 + 23443.2i 0.156784 + 0.294794i
\(283\) −5364.36 −0.0669800 −0.0334900 0.999439i \(-0.510662\pi\)
−0.0334900 + 0.999439i \(0.510662\pi\)
\(284\) 55409.6i 0.686987i
\(285\) 16473.2 8761.14i 0.202810 0.107863i
\(286\) −384531. −4.70110
\(287\) 62168.5i 0.754756i
\(288\) −94057.1 63414.1i −1.13398 0.764541i
\(289\) −57169.5 −0.684493
\(290\) 49911.1i 0.593474i
\(291\) 23341.7 + 43888.4i 0.275643 + 0.518279i
\(292\) −119635. −1.40311
\(293\) 159220.i 1.85465i 0.374258 + 0.927324i \(0.377897\pi\)
−0.374258 + 0.927324i \(0.622103\pi\)
\(294\) 202532. 107715.i 2.34315 1.24618i
\(295\) 6742.24 0.0774747
\(296\) 5004.59i 0.0571196i
\(297\) 17089.0 163078.i 0.193734 1.84876i
\(298\) 199074. 2.24172
\(299\) 176963.i 1.97943i
\(300\) −24696.3 46435.4i −0.274403 0.515949i
\(301\) 24535.3 0.270806
\(302\) 51593.6i 0.565695i
\(303\) 23095.9 12283.4i 0.251564 0.133793i
\(304\) 38745.5 0.419250
\(305\) 629.445i 0.00676640i
\(306\) −93763.0 + 139071.i −1.00136 + 1.48523i
\(307\) −20540.8 −0.217942 −0.108971 0.994045i \(-0.534756\pi\)
−0.108971 + 0.994045i \(0.534756\pi\)
\(308\) 272784.i 2.87553i
\(309\) −45317.4 85208.3i −0.474622 0.892411i
\(310\) 113368. 1.17969
\(311\) 123879.i 1.28079i 0.768047 + 0.640393i \(0.221229\pi\)
−0.768047 + 0.640393i \(0.778771\pi\)
\(312\) −20690.6 + 11004.1i −0.212551 + 0.113043i
\(313\) 21875.0 0.223285 0.111643 0.993748i \(-0.464389\pi\)
0.111643 + 0.993748i \(0.464389\pi\)
\(314\) 152794.i 1.54970i
\(315\) −83704.9 56434.5i −0.843587 0.568753i
\(316\) 67706.0 0.678036
\(317\) 74997.6i 0.746326i 0.927766 + 0.373163i \(0.121727\pi\)
−0.927766 + 0.373163i \(0.878273\pi\)
\(318\) 72249.2 + 135847.i 0.714461 + 1.34337i
\(319\) −136686. −1.34321
\(320\) 48836.4i 0.476918i
\(321\) 83568.1 44445.0i 0.811018 0.431333i
\(322\) −264280. −2.54890
\(323\) 52267.4i 0.500986i
\(324\) 35617.7 + 88052.0i 0.339293 + 0.838782i
\(325\) −125005. −1.18348
\(326\) 125624.i 1.18205i
\(327\) −9681.41 18203.5i −0.0905405 0.170240i
\(328\) −6239.88 −0.0580000
\(329\) 44769.7i 0.413611i
\(330\) −146792. + 78070.4i −1.34796 + 0.716900i
\(331\) 99534.5 0.908484 0.454242 0.890878i \(-0.349910\pi\)
0.454242 + 0.890878i \(0.349910\pi\)
\(332\) 53061.8i 0.481400i
\(333\) −26950.8 + 39974.0i −0.243043 + 0.360487i
\(334\) −67238.5 −0.602733
\(335\) 27653.0i 0.246407i
\(336\) −98438.2 185089.i −0.871937 1.63947i
\(337\) 98533.0 0.867605 0.433802 0.901008i \(-0.357172\pi\)
0.433802 + 0.901008i \(0.357172\pi\)
\(338\) 371747.i 3.25397i
\(339\) 72798.2 38717.1i 0.633463 0.336902i
\(340\) 80785.7 0.698838
\(341\) 310468.i 2.66998i
\(342\) −51665.9 34833.5i −0.441724 0.297814i
\(343\) 185638. 1.57789
\(344\) 2462.62i 0.0208104i
\(345\) 35928.3 + 67554.4i 0.301855 + 0.567565i
\(346\) −44973.0 −0.375664
\(347\) 142395.i 1.18260i 0.806453 + 0.591299i \(0.201385\pi\)
−0.806453 + 0.591299i \(0.798615\pi\)
\(348\) 69906.1 37179.0i 0.577240 0.307001i
\(349\) 102446. 0.841092 0.420546 0.907271i \(-0.361838\pi\)
0.420546 + 0.907271i \(0.361838\pi\)
\(350\) 186686.i 1.52396i
\(351\) 224524. + 23528.1i 1.82242 + 0.190973i
\(352\) −315000. −2.54229
\(353\) 51077.6i 0.409903i −0.978772 0.204952i \(-0.934296\pi\)
0.978772 0.204952i \(-0.0657037\pi\)
\(354\) −10573.0 19880.0i −0.0843710 0.158639i
\(355\) 56942.3 0.451834
\(356\) 31337.9i 0.247269i
\(357\) −249684. + 132793.i −1.95909 + 1.04193i
\(358\) −91541.2 −0.714250
\(359\) 204305.i 1.58522i −0.609726 0.792612i \(-0.708721\pi\)
0.609726 0.792612i \(-0.291279\pi\)
\(360\) −5664.36 + 8401.50i −0.0437065 + 0.0648264i
\(361\) −110903. −0.851001
\(362\) 152198.i 1.16143i
\(363\) −151929. 285665.i −1.15299 2.16793i
\(364\) 375568. 2.83456
\(365\) 122944.i 0.922833i
\(366\) −1855.97 + 987.082i −0.0138551 + 0.00736870i
\(367\) 161415. 1.19843 0.599215 0.800589i \(-0.295480\pi\)
0.599215 + 0.800589i \(0.295480\pi\)
\(368\) 158890.i 1.17328i
\(369\) 49840.8 + 33603.0i 0.366043 + 0.246789i
\(370\) 48884.3 0.357080
\(371\) 259428.i 1.88482i
\(372\) −84448.1 158784.i −0.610245 1.14742i
\(373\) 183154. 1.31643 0.658216 0.752829i \(-0.271311\pi\)
0.658216 + 0.752829i \(0.271311\pi\)
\(374\) 465754.i 3.32976i
\(375\) −121605. + 64674.9i −0.864750 + 0.459910i
\(376\) 4493.55 0.0317844
\(377\) 188189.i 1.32407i
\(378\) −35137.4 + 335310.i −0.245916 + 2.34673i
\(379\) 122913. 0.855694 0.427847 0.903851i \(-0.359272\pi\)
0.427847 + 0.903851i \(0.359272\pi\)
\(380\) 30012.4i 0.207842i
\(381\) 66556.8 + 125144.i 0.458503 + 0.862104i
\(382\) −83989.8 −0.575572
\(383\) 207603.i 1.41526i 0.706583 + 0.707631i \(0.250236\pi\)
−0.706583 + 0.707631i \(0.749764\pi\)
\(384\) −34053.5 + 18111.1i −0.230940 + 0.122824i
\(385\) −280330. −1.89125
\(386\) 130067.i 0.872957i
\(387\) −13261.7 + 19670.1i −0.0885477 + 0.131336i
\(388\) −79959.9 −0.531139
\(389\) 155335.i 1.02652i −0.858232 0.513262i \(-0.828437\pi\)
0.858232 0.513262i \(-0.171563\pi\)
\(390\) −107487. 202103.i −0.706685 1.32875i
\(391\) 214342. 1.40202
\(392\) 38821.0i 0.252635i
\(393\) 138871. 73857.5i 0.899140 0.478200i
\(394\) 216150. 1.39239
\(395\) 69578.9i 0.445947i
\(396\) 218693. + 147444.i 1.39458 + 0.940237i
\(397\) −51240.7 −0.325113 −0.162557 0.986699i \(-0.551974\pi\)
−0.162557 + 0.986699i \(0.551974\pi\)
\(398\) 392266.i 2.47636i
\(399\) −49333.3 92759.2i −0.309880 0.582655i
\(400\) −112239. −0.701491
\(401\) 38985.7i 0.242447i −0.992625 0.121224i \(-0.961318\pi\)
0.992625 0.121224i \(-0.0386818\pi\)
\(402\) 81537.1 43364.9i 0.504549 0.268340i
\(403\) −427450. −2.63194
\(404\) 42078.2i 0.257807i
\(405\) 90487.7 36602.9i 0.551670 0.223154i
\(406\) 281045. 1.70500
\(407\) 133874.i 0.808179i
\(408\) 13328.4 + 25060.9i 0.0800681 + 0.150549i
\(409\) −135878. −0.812273 −0.406137 0.913812i \(-0.633124\pi\)
−0.406137 + 0.913812i \(0.633124\pi\)
\(410\) 60950.4i 0.362584i
\(411\) −48724.4 + 25913.7i −0.288445 + 0.153407i
\(412\) 155240. 0.914555
\(413\) 37965.0i 0.222578i
\(414\) 142848. 211875.i 0.833437 1.23617i
\(415\) 54529.6 0.316618
\(416\) 433690.i 2.50607i
\(417\) 136554. + 256757.i 0.785295 + 1.47656i
\(418\) −173030. −0.990307
\(419\) 145521.i 0.828893i −0.910074 0.414446i \(-0.863975\pi\)
0.910074 0.414446i \(-0.136025\pi\)
\(420\) 143371. 76250.6i 0.812760 0.432260i
\(421\) −231179. −1.30432 −0.652161 0.758081i \(-0.726137\pi\)
−0.652161 + 0.758081i \(0.726137\pi\)
\(422\) 2675.20i 0.0150221i
\(423\) −35892.1 24198.7i −0.200594 0.135242i
\(424\) 26038.9 0.144841
\(425\) 151409.i 0.838252i
\(426\) −89295.8 167899.i −0.492053 0.925186i
\(427\) −3544.35 −0.0194393
\(428\) 152252.i 0.831142i
\(429\) 553477. 294362.i 3.00736 1.59944i
\(430\) 24054.6 0.130095
\(431\) 48295.7i 0.259988i 0.991515 + 0.129994i \(0.0414958\pi\)
−0.991515 + 0.129994i \(0.958504\pi\)
\(432\) 201594. + 21125.2i 1.08022 + 0.113197i
\(433\) −246945. −1.31712 −0.658558 0.752530i \(-0.728833\pi\)
−0.658558 + 0.752530i \(0.728833\pi\)
\(434\) 638364.i 3.38914i
\(435\) −38207.5 71839.9i −0.201915 0.379653i
\(436\) 33164.9 0.174464
\(437\) 79629.3i 0.416975i
\(438\) 362511. 192799.i 1.88962 1.00498i
\(439\) 285588. 1.48187 0.740937 0.671575i \(-0.234382\pi\)
0.740937 + 0.671575i \(0.234382\pi\)
\(440\) 28136.9i 0.145335i
\(441\) −209059. + 310081.i −1.07496 + 1.59440i
\(442\) −641247. −3.28232
\(443\) 47873.0i 0.243940i 0.992534 + 0.121970i \(0.0389212\pi\)
−0.992534 + 0.121970i \(0.961079\pi\)
\(444\) −36414.1 68467.9i −0.184716 0.347313i
\(445\) 32204.7 0.162630
\(446\) 323040.i 1.62400i
\(447\) −286538. + 152393.i −1.43406 + 0.762693i
\(448\) 274994. 1.37014
\(449\) 356568.i 1.76868i −0.466841 0.884341i \(-0.654608\pi\)
0.466841 0.884341i \(-0.345392\pi\)
\(450\) 149667. + 100906.i 0.739095 + 0.498304i
\(451\) 166918. 0.820636
\(452\) 132630.i 0.649182i
\(453\) 39495.4 + 74261.6i 0.192464 + 0.361883i
\(454\) −244569. −1.18656
\(455\) 385957.i 1.86430i
\(456\) −9310.29 + 4951.60i −0.0447748 + 0.0238131i
\(457\) 83662.8 0.400590 0.200295 0.979736i \(-0.435810\pi\)
0.200295 + 0.979736i \(0.435810\pi\)
\(458\) 160340.i 0.764383i
\(459\) 28497.8 271950.i 0.135265 1.29081i
\(460\) −123077. −0.581648
\(461\) 105132.i 0.494692i 0.968927 + 0.247346i \(0.0795584\pi\)
−0.968927 + 0.247346i \(0.920442\pi\)
\(462\) 439608. + 826576.i 2.05959 + 3.87257i
\(463\) 244357. 1.13989 0.569946 0.821682i \(-0.306964\pi\)
0.569946 + 0.821682i \(0.306964\pi\)
\(464\) 168969.i 0.784824i
\(465\) −163177. + 86784.1i −0.754661 + 0.401360i
\(466\) −314611. −1.44878
\(467\) 291275.i 1.33558i 0.744351 + 0.667789i \(0.232759\pi\)
−0.744351 + 0.667789i \(0.767241\pi\)
\(468\) −203000. + 301095.i −0.926841 + 1.37471i
\(469\) 155712. 0.707907
\(470\) 43892.5i 0.198698i
\(471\) 116966. + 219925.i 0.527250 + 0.991365i
\(472\) −3810.56 −0.0171043
\(473\) 65875.5i 0.294443i
\(474\) −205159. + 109112.i −0.913132 + 0.485642i
\(475\) −56249.5 −0.249305
\(476\) 454897.i 2.00770i
\(477\) −207985. 140225.i −0.914101 0.616294i
\(478\) 209482. 0.916833
\(479\) 126030.i 0.549290i −0.961546 0.274645i \(-0.911440\pi\)
0.961546 0.274645i \(-0.0885603\pi\)
\(480\) −88051.0 165559.i −0.382166 0.718570i
\(481\) −184317. −0.796664
\(482\) 361691.i 1.55684i
\(483\) 380393. 202309.i 1.63057 0.867204i
\(484\) 520451. 2.22172
\(485\) 82171.7i 0.349332i
\(486\) −249827. 209410.i −1.05771 0.886595i
\(487\) 129502. 0.546031 0.273016 0.962010i \(-0.411979\pi\)
0.273016 + 0.962010i \(0.411979\pi\)
\(488\) 355.748i 0.00149384i
\(489\) 96166.4 + 180818.i 0.402166 + 0.756176i
\(490\) 379199. 1.57934
\(491\) 49733.7i 0.206295i 0.994666 + 0.103147i \(0.0328913\pi\)
−0.994666 + 0.103147i \(0.967109\pi\)
\(492\) −85367.9 + 45402.2i −0.352667 + 0.187563i
\(493\) −227939. −0.937831
\(494\) 238227.i 0.976197i
\(495\) 151523. 224742.i 0.618397 0.917221i
\(496\) −383796. −1.56004
\(497\) 320638.i 1.29808i
\(498\) −85512.2 160785.i −0.344802 0.648316i
\(499\) 76821.6 0.308519 0.154260 0.988030i \(-0.450701\pi\)
0.154260 + 0.988030i \(0.450701\pi\)
\(500\) 221552.i 0.886208i
\(501\) 96780.1 51471.7i 0.385577 0.205066i
\(502\) −463494. −1.83923
\(503\) 226728.i 0.896128i −0.894002 0.448064i \(-0.852114\pi\)
0.894002 0.448064i \(-0.147886\pi\)
\(504\) 47308.2 + 31895.5i 0.186241 + 0.125565i
\(505\) 43242.1 0.169560
\(506\) 709575.i 2.77139i
\(507\) 284576. + 535076.i 1.10709 + 2.08161i
\(508\) −227998. −0.883496
\(509\) 285677.i 1.10266i 0.834288 + 0.551329i \(0.185879\pi\)
−0.834288 + 0.551329i \(0.814121\pi\)
\(510\) −244792. + 130191.i −0.941146 + 0.500541i
\(511\) 692290. 2.65122
\(512\) 351992.i 1.34274i
\(513\) 101031. + 10587.1i 0.383901 + 0.0402293i
\(514\) 70073.8 0.265234
\(515\) 159535.i 0.601506i
\(516\) −17918.3 33691.1i −0.0672974 0.126537i
\(517\) −120203. −0.449713
\(518\) 275263.i 1.02586i
\(519\) 64732.1 34427.2i 0.240317 0.127811i
\(520\) −38738.7 −0.143264
\(521\) 422420.i 1.55621i −0.628132 0.778107i \(-0.716180\pi\)
0.628132 0.778107i \(-0.283820\pi\)
\(522\) −151909. + 225315.i −0.557499 + 0.826894i
\(523\) −293362. −1.07251 −0.536254 0.844056i \(-0.680161\pi\)
−0.536254 + 0.844056i \(0.680161\pi\)
\(524\) 253008.i 0.921450i
\(525\) 142910. + 268707.i 0.518493 + 0.974900i
\(526\) 269156. 0.972818
\(527\) 517738.i 1.86419i
\(528\) 496952. 264300.i 1.78257 0.948045i
\(529\) −46708.1 −0.166909
\(530\) 254345.i 0.905464i
\(531\) 30436.7 + 20520.7i 0.107947 + 0.0727784i
\(532\) 168997. 0.597113
\(533\) 229812.i 0.808943i
\(534\) −50502.8 94958.2i −0.177106 0.333004i
\(535\) 156463. 0.546645
\(536\) 15628.9i 0.0543999i
\(537\) 131760. 70075.7i 0.456916 0.243007i
\(538\) −373497. −1.29040
\(539\) 1.03847e6i 3.57451i
\(540\) −16363.7 + 156156.i −0.0561169 + 0.535514i
\(541\) 298138. 1.01865 0.509323 0.860576i \(-0.329896\pi\)
0.509323 + 0.860576i \(0.329896\pi\)
\(542\) 421691.i 1.43547i
\(543\) −116509. 219068.i −0.395149 0.742983i
\(544\) −525296. −1.77503
\(545\) 34082.3i 0.114745i
\(546\) −1.13803e6 + 605250.i −3.81739 + 2.03025i
\(547\) −174085. −0.581817 −0.290908 0.956751i \(-0.593957\pi\)
−0.290908 + 0.956751i \(0.593957\pi\)
\(548\) 88770.6i 0.295602i
\(549\) 1915.78 2841.52i 0.00635624 0.00942772i
\(550\) 501238. 1.65698
\(551\) 84680.7i 0.278921i
\(552\) −20305.9 38180.3i −0.0666413 0.125303i
\(553\) −391793. −1.28117
\(554\) 125489.i 0.408871i
\(555\) −70361.9 + 37421.4i −0.228429 + 0.121488i
\(556\) −467783. −1.51320
\(557\) 42791.2i 0.137925i −0.997619 0.0689626i \(-0.978031\pi\)
0.997619 0.0689626i \(-0.0219689\pi\)
\(558\) 511780. + 345046.i 1.64367 + 1.10818i
\(559\) −90697.1 −0.290248
\(560\) 346540.i 1.10504i
\(561\) −356539. 670385.i −1.13287 2.13009i
\(562\) 34313.1 0.108639
\(563\) 335794.i 1.05939i −0.848188 0.529695i \(-0.822306\pi\)
0.848188 0.529695i \(-0.177694\pi\)
\(564\) 61476.3 32695.7i 0.193263 0.102786i
\(565\) 136299. 0.426969
\(566\) 29614.5i 0.0924423i
\(567\) −206108. 509529.i −0.641104 1.58490i
\(568\) −32182.5 −0.0997525
\(569\) 395920.i 1.22288i 0.791292 + 0.611438i \(0.209409\pi\)
−0.791292 + 0.611438i \(0.790591\pi\)
\(570\) −48366.7 90941.8i −0.148866 0.279907i
\(571\) 452552. 1.38802 0.694011 0.719965i \(-0.255842\pi\)
0.694011 + 0.719965i \(0.255842\pi\)
\(572\) 1.00837e6i 3.08198i
\(573\) 120891. 64295.0i 0.368201 0.195825i
\(574\) −343207. −1.04167
\(575\) 230672.i 0.697684i
\(576\) −148638. + 220464.i −0.448008 + 0.664495i
\(577\) −294717. −0.885226 −0.442613 0.896713i \(-0.645948\pi\)
−0.442613 + 0.896713i \(0.645948\pi\)
\(578\) 315609.i 0.944701i
\(579\) −99567.7 187213.i −0.297003 0.558443i
\(580\) 130884. 0.389074
\(581\) 307052.i 0.909619i
\(582\) 242290. 128860.i 0.715302 0.380427i
\(583\) −696546. −2.04933
\(584\) 69485.4i 0.203736i
\(585\) 309424. + 208616.i 0.904152 + 0.609587i
\(586\) 878987. 2.55969
\(587\) 252374.i 0.732432i 0.930530 + 0.366216i \(0.119347\pi\)
−0.930530 + 0.366216i \(0.880653\pi\)
\(588\) −282467. 531111.i −0.816983 1.53614i
\(589\) −192343. −0.554429
\(590\) 37221.1i 0.106927i
\(591\) −311116. + 165465.i −0.890733 + 0.473729i
\(592\) −165493. −0.472212
\(593\) 249978.i 0.710874i 0.934700 + 0.355437i \(0.115668\pi\)
−0.934700 + 0.355437i \(0.884332\pi\)
\(594\) −900285. 94341.6i −2.55157 0.267381i
\(595\) −467481. −1.32047
\(596\) 522041.i 1.46964i
\(597\) −300283. 564610.i −0.842525 1.58416i
\(598\) 976939. 2.73190
\(599\) 527472.i 1.47010i −0.678014 0.735049i \(-0.737159\pi\)
0.678014 0.735049i \(-0.262841\pi\)
\(600\) 26970.2 14343.9i 0.0749173 0.0398442i
\(601\) 53469.5 0.148032 0.0740162 0.997257i \(-0.476418\pi\)
0.0740162 + 0.997257i \(0.476418\pi\)
\(602\) 135449.i 0.373752i
\(603\) −84164.7 + 124835.i −0.231470 + 0.343322i
\(604\) −135296. −0.370862
\(605\) 534848.i 1.46123i
\(606\) −67811.4 127503.i −0.184653 0.347196i
\(607\) −486157. −1.31947 −0.659734 0.751499i \(-0.729331\pi\)
−0.659734 + 0.751499i \(0.729331\pi\)
\(608\) 195151.i 0.527914i
\(609\) −404524. + 215143.i −1.09071 + 0.580086i
\(610\) −3474.91 −0.00933864
\(611\) 165495.i 0.443306i
\(612\) 364694. + 245879.i 0.973700 + 0.656476i
\(613\) −28121.3 −0.0748366 −0.0374183 0.999300i \(-0.511913\pi\)
−0.0374183 + 0.999300i \(0.511913\pi\)
\(614\) 113398.i 0.300792i
\(615\) 46658.1 + 87729.3i 0.123361 + 0.231950i
\(616\) 158436. 0.417535
\(617\) 81431.3i 0.213905i 0.994264 + 0.106953i \(0.0341093\pi\)
−0.994264 + 0.106953i \(0.965891\pi\)
\(618\) −470400. + 250179.i −1.23166 + 0.655048i
\(619\) 53438.8 0.139468 0.0697342 0.997566i \(-0.477785\pi\)
0.0697342 + 0.997566i \(0.477785\pi\)
\(620\) 297290.i 0.773386i
\(621\) −43416.4 + 414315.i −0.112582 + 1.07435i
\(622\) 683885. 1.76767
\(623\) 181342.i 0.467221i
\(624\) 363887. + 684201.i 0.934538 + 1.75717i
\(625\) 24609.5 0.0630004
\(626\) 120763.i 0.308167i
\(627\) 249052. 132456.i 0.633513 0.336929i
\(628\) −400680. −1.01596
\(629\) 223249.i 0.564273i
\(630\) −311552. + 462101.i −0.784963 + 1.16427i
\(631\) 707294. 1.77640 0.888201 0.459454i \(-0.151955\pi\)
0.888201 + 0.459454i \(0.151955\pi\)
\(632\) 39324.4i 0.0984528i
\(633\) 2047.89 + 3850.56i 0.00511092 + 0.00960985i
\(634\) 414031. 1.03004
\(635\) 234305.i 0.581078i
\(636\) 356238. 189463.i 0.880697 0.468392i
\(637\) −1.42976e6 −3.52358
\(638\) 754588.i 1.85382i
\(639\) 257057. + 173310.i 0.629546 + 0.424445i
\(640\) −63758.0 −0.155659
\(641\) 39907.8i 0.0971275i 0.998820 + 0.0485637i \(0.0154644\pi\)
−0.998820 + 0.0485637i \(0.984536\pi\)
\(642\) −245363. 461345.i −0.595304 1.11932i
\(643\) 154629. 0.373999 0.186999 0.982360i \(-0.440124\pi\)
0.186999 + 0.982360i \(0.440124\pi\)
\(644\) 693035.i 1.67103i
\(645\) −34623.1 + 18414.0i −0.0832235 + 0.0442618i
\(646\) −288547. −0.691435
\(647\) 658179.i 1.57230i 0.618036 + 0.786149i \(0.287928\pi\)
−0.618036 + 0.786149i \(0.712072\pi\)
\(648\) −51141.6 + 20687.1i −0.121794 + 0.0492664i
\(649\) 101933. 0.242007
\(650\) 690101.i 1.63338i
\(651\) 488674. + 918833.i 1.15307 + 2.16808i
\(652\) −329430. −0.774939
\(653\) 110641.i 0.259472i 0.991549 + 0.129736i \(0.0414129\pi\)
−0.991549 + 0.129736i \(0.958587\pi\)
\(654\) −100494. + 53447.1i −0.234956 + 0.124959i
\(655\) 260007. 0.606041
\(656\) 206342.i 0.479490i
\(657\) −374193. + 555012.i −0.866893 + 1.28579i
\(658\) 247155. 0.570844
\(659\) 240883.i 0.554672i −0.960773 0.277336i \(-0.910549\pi\)
0.960773 0.277336i \(-0.0894515\pi\)
\(660\) 204728. + 384941.i 0.469990 + 0.883703i
\(661\) −164589. −0.376701 −0.188351 0.982102i \(-0.560314\pi\)
−0.188351 + 0.982102i \(0.560314\pi\)
\(662\) 549489.i 1.25384i
\(663\) 922983. 490881.i 2.09974 1.11673i
\(664\) −30818.9 −0.0699006
\(665\) 173672.i 0.392723i
\(666\) 220680. + 148784.i 0.497525 + 0.335435i
\(667\) 347264. 0.780564
\(668\) 176323.i 0.395144i
\(669\) −247290. 464969.i −0.552528 1.03890i
\(670\) 152661. 0.340078
\(671\) 9516.34i 0.0211361i
\(672\) −932247. + 495808.i −2.06439 + 1.09793i
\(673\) 590080. 1.30281 0.651404 0.758731i \(-0.274180\pi\)
0.651404 + 0.758731i \(0.274180\pi\)
\(674\) 543960.i 1.19742i
\(675\) −292668. 30669.0i −0.642345 0.0673119i
\(676\) −974849. −2.13326
\(677\) 605944.i 1.32207i −0.750355 0.661036i \(-0.770117\pi\)
0.750355 0.661036i \(-0.229883\pi\)
\(678\) −213741. 401889.i −0.464975 0.874273i
\(679\) 462702. 1.00360
\(680\) 46921.2i 0.101473i
\(681\) 352022. 187220.i 0.759059 0.403699i
\(682\) 1.71396e6 3.68496
\(683\) 417679.i 0.895367i −0.894192 0.447683i \(-0.852249\pi\)
0.894192 0.447683i \(-0.147751\pi\)
\(684\) −91345.6 + 135486.i −0.195243 + 0.289589i
\(685\) −91226.1 −0.194419
\(686\) 1.02483e6i 2.17773i
\(687\) −122742. 230786.i −0.260063 0.488986i
\(688\) −81434.4 −0.172041
\(689\) 959001.i 2.02014i
\(690\) 372940. 198345.i 0.783324 0.416604i
\(691\) −205400. −0.430175 −0.215087 0.976595i \(-0.569004\pi\)
−0.215087 + 0.976595i \(0.569004\pi\)
\(692\) 117935.i 0.246280i
\(693\) −1.26550e6 853213.i −2.63510 1.77660i
\(694\) 786106. 1.63216
\(695\) 480723.i 0.995234i
\(696\) 21594.0 + 40602.3i 0.0445774 + 0.0838170i
\(697\) 278354. 0.572970
\(698\) 565562.i 1.16083i
\(699\) 452837. 240838.i 0.926804 0.492913i
\(700\) −489555. −0.999091
\(701\) 152513.i 0.310364i 0.987886 + 0.155182i \(0.0495965\pi\)
−0.987886 + 0.155182i \(0.950404\pi\)
\(702\) 129889. 1.23951e6i 0.263571 2.51521i
\(703\) −82938.5 −0.167821
\(704\) 738339.i 1.48974i
\(705\) −33600.1 63176.9i −0.0676025 0.127110i
\(706\) −281979. −0.565727
\(707\) 243493.i 0.487133i
\(708\) −52132.4 + 27726.2i −0.104002 + 0.0553125i
\(709\) −444089. −0.883441 −0.441720 0.897153i \(-0.645632\pi\)
−0.441720 + 0.897153i \(0.645632\pi\)
\(710\) 314355.i 0.623597i
\(711\) 211770. 314102.i 0.418915 0.621344i
\(712\) −18201.4 −0.0359041
\(713\) 788773.i 1.55158i
\(714\) 733093. + 1.37840e6i 1.43801 + 2.70384i
\(715\) 1.03627e6 2.02703
\(716\) 240053.i 0.468253i
\(717\) −301519. + 160360.i −0.586511 + 0.311931i
\(718\) −1.12789e6 −2.18784
\(719\) 218028.i 0.421749i −0.977513 0.210875i \(-0.932369\pi\)
0.977513 0.210875i \(-0.0676312\pi\)
\(720\) 277823. + 187310.i 0.535924 + 0.361324i
\(721\) −898326. −1.72808
\(722\) 612252.i 1.17451i
\(723\) −276878. 520601.i −0.529677 0.995930i
\(724\) 399117. 0.761419
\(725\) 245305.i 0.466691i
\(726\) −1.57704e6 + 838737.i −2.99206 + 1.59130i
\(727\) 734861. 1.39039 0.695195 0.718822i \(-0.255318\pi\)
0.695195 + 0.718822i \(0.255318\pi\)
\(728\) 218134.i 0.411586i
\(729\) 519896. + 110170.i 0.978276 + 0.207305i
\(730\) 678726. 1.27365
\(731\) 109855.i 0.205581i
\(732\) 2588.47 + 4867.00i 0.00483083 + 0.00908320i
\(733\) −1.04114e6 −1.93777 −0.968885 0.247512i \(-0.920387\pi\)
−0.968885 + 0.247512i \(0.920387\pi\)
\(734\) 891107.i 1.65401i
\(735\) −545802. + 290280.i −1.01032 + 0.537332i
\(736\) 800288. 1.47737
\(737\) 418076.i 0.769697i
\(738\) 185509. 275150.i 0.340605 0.505193i
\(739\) −131269. −0.240365 −0.120183 0.992752i \(-0.538348\pi\)
−0.120183 + 0.992752i \(0.538348\pi\)
\(740\) 128192.i 0.234097i
\(741\) 182365. + 342894.i 0.332128 + 0.624487i
\(742\) 1.43219e6 2.60132
\(743\) 629101.i 1.13957i 0.821792 + 0.569787i \(0.192974\pi\)
−0.821792 + 0.569787i \(0.807026\pi\)
\(744\) 92223.7 49048.4i 0.166608 0.0886093i
\(745\) −536481. −0.966589
\(746\) 1.01112e6i 1.81687i
\(747\) 246165. + 165966.i 0.441149 + 0.297426i
\(748\) 1.22137e6 2.18295
\(749\) 881033.i 1.57047i
\(750\) 357044. + 671334.i 0.634744 + 1.19348i
\(751\) −288597. −0.511696 −0.255848 0.966717i \(-0.582355\pi\)
−0.255848 + 0.966717i \(0.582355\pi\)
\(752\) 148594.i 0.262764i
\(753\) 667133. 354810.i 1.17658 0.625756i
\(754\) −1.03891e6 −1.82741
\(755\) 139039.i 0.243917i
\(756\) 879300. + 92142.6i 1.53849 + 0.161219i
\(757\) −764156. −1.33349 −0.666746 0.745285i \(-0.732313\pi\)
−0.666746 + 0.745285i \(0.732313\pi\)
\(758\) 678550.i 1.18098i
\(759\) 543186. + 1.02133e6i 0.942899 + 1.77289i
\(760\) −17431.5 −0.0301792
\(761\) 390317.i 0.673983i −0.941508 0.336991i \(-0.890591\pi\)
0.941508 0.336991i \(-0.109409\pi\)
\(762\) 690868. 367433.i 1.18983 0.632802i
\(763\) −191914. −0.329654
\(764\) 220251.i 0.377338i
\(765\) 252681. 374782.i 0.431767 0.640406i
\(766\) 1.14609e6 1.95327
\(767\) 140341.i 0.238558i
\(768\) 321943. + 605336.i 0.545829 + 1.02630i
\(769\) 358531. 0.606282 0.303141 0.952946i \(-0.401965\pi\)
0.303141 + 0.952946i \(0.401965\pi\)
\(770\) 1.54759e6i 2.61020i
\(771\) −100861. + 53642.2i −0.169674 + 0.0902397i
\(772\) 341081. 0.572299
\(773\) 239213.i 0.400336i −0.979762 0.200168i \(-0.935851\pi\)
0.979762 0.200168i \(-0.0641489\pi\)
\(774\) 108590. + 73212.4i 0.181263 + 0.122209i
\(775\) 557183. 0.927672
\(776\) 46441.6i 0.0771230i
\(777\) 210717. + 396202.i 0.349026 + 0.656258i
\(778\) −857538. −1.41675
\(779\) 103410.i 0.170407i
\(780\) −529984. + 281868.i −0.871112 + 0.463294i
\(781\) 860890. 1.41139
\(782\) 1.18329e6i 1.93499i