Properties

Label 177.4.d.c.176.11
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.11
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.12

$q$-expansion

\(f(q)\) \(=\) \(q-3.85434 q^{2} +(-4.18856 - 3.07505i) q^{3} +6.85594 q^{4} -0.146910i q^{5} +(16.1441 + 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 + 25.7601i) q^{9} +O(q^{10})\) \(q-3.85434 q^{2} +(-4.18856 - 3.07505i) q^{3} +6.85594 q^{4} -0.146910i q^{5} +(16.1441 + 11.8523i) q^{6} -24.4419 q^{7} +4.40959 q^{8} +(8.08809 + 25.7601i) q^{9} +0.566243i q^{10} +16.8186 q^{11} +(-28.7165 - 21.0824i) q^{12} +51.2069i q^{13} +94.2076 q^{14} +(-0.451757 + 0.615343i) q^{15} -71.8436 q^{16} +61.9717i q^{17} +(-31.1743 - 99.2882i) q^{18} -98.2877 q^{19} -1.00721i q^{20} +(102.377 + 75.1603i) q^{21} -64.8246 q^{22} +40.4578 q^{23} +(-18.4699 - 13.5597i) q^{24} +124.978 q^{25} -197.369i q^{26} +(45.3362 - 132.769i) q^{27} -167.572 q^{28} -235.127i q^{29} +(1.74123 - 2.37174i) q^{30} -306.017i q^{31} +241.633 q^{32} +(-70.4458 - 51.7181i) q^{33} -238.860i q^{34} +3.59077i q^{35} +(55.4515 + 176.610i) q^{36} +353.773i q^{37} +378.834 q^{38} +(157.464 - 214.483i) q^{39} -0.647815i q^{40} -259.306i q^{41} +(-394.594 - 289.693i) q^{42} -58.9877i q^{43} +115.307 q^{44} +(3.78443 - 1.18822i) q^{45} -155.938 q^{46} +36.9696 q^{47} +(300.921 + 220.923i) q^{48} +254.408 q^{49} -481.709 q^{50} +(190.566 - 259.572i) q^{51} +351.072i q^{52} -105.746i q^{53} +(-174.741 + 511.737i) q^{54} -2.47083i q^{55} -107.779 q^{56} +(411.684 + 302.240i) q^{57} +906.258i q^{58} +(-384.876 - 239.268i) q^{59} +(-3.09722 + 4.21876i) q^{60} -270.462i q^{61} +1179.49i q^{62} +(-197.689 - 629.627i) q^{63} -356.587 q^{64} +7.52283 q^{65} +(271.522 + 199.339i) q^{66} +201.641i q^{67} +424.874i q^{68} +(-169.460 - 124.410i) q^{69} -13.8401i q^{70} +659.691i q^{71} +(35.6652 + 113.592i) q^{72} -604.150i q^{73} -1363.56i q^{74} +(-523.480 - 384.315i) q^{75} -673.855 q^{76} -411.079 q^{77} +(-606.920 + 826.692i) q^{78} +496.729 q^{79} +10.5546i q^{80} +(-598.166 + 416.700i) q^{81} +999.455i q^{82} +1456.75 q^{83} +(701.888 + 515.294i) q^{84} +9.10429 q^{85} +227.359i q^{86} +(-723.027 + 984.843i) q^{87} +74.1632 q^{88} +145.988 q^{89} +(-14.5865 + 4.57982i) q^{90} -1251.60i q^{91} +277.377 q^{92} +(-941.017 + 1281.77i) q^{93} -142.493 q^{94} +14.4395i q^{95} +(-1012.09 - 743.034i) q^{96} +1332.12i q^{97} -980.577 q^{98} +(136.030 + 433.249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.85434 −1.36272 −0.681358 0.731951i \(-0.738610\pi\)
−0.681358 + 0.731951i \(0.738610\pi\)
\(3\) −4.18856 3.07505i −0.806089 0.591794i
\(4\) 6.85594 0.856993
\(5\) 0.146910i 0.0131401i −0.999978 0.00657003i \(-0.997909\pi\)
0.999978 0.00657003i \(-0.00209132\pi\)
\(6\) 16.1441 + 11.8523i 1.09847 + 0.806447i
\(7\) −24.4419 −1.31974 −0.659870 0.751379i \(-0.729389\pi\)
−0.659870 + 0.751379i \(0.729389\pi\)
\(8\) 4.40959 0.194878
\(9\) 8.08809 + 25.7601i 0.299559 + 0.954078i
\(10\) 0.566243i 0.0179062i
\(11\) 16.8186 0.461000 0.230500 0.973072i \(-0.425964\pi\)
0.230500 + 0.973072i \(0.425964\pi\)
\(12\) −28.7165 21.0824i −0.690812 0.507163i
\(13\) 51.2069i 1.09248i 0.837628 + 0.546240i \(0.183942\pi\)
−0.837628 + 0.546240i \(0.816058\pi\)
\(14\) 94.2076 1.79843
\(15\) −0.451757 + 0.615343i −0.00777622 + 0.0105921i
\(16\) −71.8436 −1.12256
\(17\) 61.9717i 0.884138i 0.896981 + 0.442069i \(0.145755\pi\)
−0.896981 + 0.442069i \(0.854245\pi\)
\(18\) −31.1743 99.2882i −0.408213 1.30014i
\(19\) −98.2877 −1.18678 −0.593388 0.804916i \(-0.702210\pi\)
−0.593388 + 0.804916i \(0.702210\pi\)
\(20\) 1.00721i 0.0112609i
\(21\) 102.377 + 75.1603i 1.06383 + 0.781015i
\(22\) −64.8246 −0.628212
\(23\) 40.4578 0.366785 0.183392 0.983040i \(-0.441292\pi\)
0.183392 + 0.983040i \(0.441292\pi\)
\(24\) −18.4699 13.5597i −0.157089 0.115328i
\(25\) 124.978 0.999827
\(26\) 197.369i 1.48874i
\(27\) 45.3362 132.769i 0.323147 0.946349i
\(28\) −167.572 −1.13101
\(29\) 235.127i 1.50558i −0.658259 0.752792i \(-0.728707\pi\)
0.658259 0.752792i \(-0.271293\pi\)
\(30\) 1.74123 2.37174i 0.0105968 0.0144340i
\(31\) 306.017i 1.77297i −0.462753 0.886487i \(-0.653138\pi\)
0.462753 0.886487i \(-0.346862\pi\)
\(32\) 241.633 1.33485
\(33\) −70.4458 51.7181i −0.371607 0.272817i
\(34\) 238.860i 1.20483i
\(35\) 3.59077i 0.0173415i
\(36\) 55.4515 + 176.610i 0.256720 + 0.817638i
\(37\) 353.773i 1.57189i 0.618298 + 0.785944i \(0.287823\pi\)
−0.618298 + 0.785944i \(0.712177\pi\)
\(38\) 378.834 1.61724
\(39\) 157.464 214.483i 0.646524 0.880637i
\(40\) 0.647815i 0.00256071i
\(41\) 259.306i 0.987728i −0.869539 0.493864i \(-0.835584\pi\)
0.869539 0.493864i \(-0.164416\pi\)
\(42\) −394.594 289.693i −1.44970 1.06430i
\(43\) 58.9877i 0.209199i −0.994514 0.104599i \(-0.966644\pi\)
0.994514 0.104599i \(-0.0333560\pi\)
\(44\) 115.307 0.395074
\(45\) 3.78443 1.18822i 0.0125366 0.00393622i
\(46\) −155.938 −0.499823
\(47\) 36.9696 0.114736 0.0573678 0.998353i \(-0.481729\pi\)
0.0573678 + 0.998353i \(0.481729\pi\)
\(48\) 300.921 + 220.923i 0.904880 + 0.664322i
\(49\) 254.408 0.741715
\(50\) −481.709 −1.36248
\(51\) 190.566 259.572i 0.523228 0.712694i
\(52\) 351.072i 0.936248i
\(53\) 105.746i 0.274064i −0.990567 0.137032i \(-0.956244\pi\)
0.990567 0.137032i \(-0.0437563\pi\)
\(54\) −174.741 + 511.737i −0.440357 + 1.28960i
\(55\) 2.47083i 0.00605757i
\(56\) −107.779 −0.257189
\(57\) 411.684 + 302.240i 0.956647 + 0.702328i
\(58\) 906.258i 2.05168i
\(59\) −384.876 239.268i −0.849265 0.527967i
\(60\) −3.09722 + 4.21876i −0.00666416 + 0.00907732i
\(61\) 270.462i 0.567690i −0.958870 0.283845i \(-0.908390\pi\)
0.958870 0.283845i \(-0.0916101\pi\)
\(62\) 1179.49i 2.41606i
\(63\) −197.689 629.627i −0.395340 1.25914i
\(64\) −356.587 −0.696459
\(65\) 7.52283 0.0143553
\(66\) 271.522 + 199.339i 0.506395 + 0.371772i
\(67\) 201.641i 0.367678i 0.982956 + 0.183839i \(0.0588525\pi\)
−0.982956 + 0.183839i \(0.941147\pi\)
\(68\) 424.874i 0.757700i
\(69\) −169.460 124.410i −0.295661 0.217061i
\(70\) 13.8401i 0.0236315i
\(71\) 659.691i 1.10269i 0.834278 + 0.551345i \(0.185885\pi\)
−0.834278 + 0.551345i \(0.814115\pi\)
\(72\) 35.6652 + 113.592i 0.0583776 + 0.185929i
\(73\) 604.150i 0.968636i −0.874892 0.484318i \(-0.839068\pi\)
0.874892 0.484318i \(-0.160932\pi\)
\(74\) 1363.56i 2.14204i
\(75\) −523.480 384.315i −0.805950 0.591692i
\(76\) −673.855 −1.01706
\(77\) −411.079 −0.608401
\(78\) −606.920 + 826.692i −0.881028 + 1.20006i
\(79\) 496.729 0.707422 0.353711 0.935355i \(-0.384920\pi\)
0.353711 + 0.935355i \(0.384920\pi\)
\(80\) 10.5546i 0.0147505i
\(81\) −598.166 + 416.700i −0.820529 + 0.571605i
\(82\) 999.455i 1.34599i
\(83\) 1456.75 1.92649 0.963246 0.268620i \(-0.0865675\pi\)
0.963246 + 0.268620i \(0.0865675\pi\)
\(84\) 701.888 + 515.294i 0.911693 + 0.669324i
\(85\) 9.10429 0.0116176
\(86\) 227.359i 0.285078i
\(87\) −723.027 + 984.843i −0.890996 + 1.21363i
\(88\) 74.1632 0.0898389
\(89\) 145.988 0.173874 0.0869368 0.996214i \(-0.472292\pi\)
0.0869368 + 0.996214i \(0.472292\pi\)
\(90\) −14.5865 + 4.57982i −0.0170839 + 0.00536395i
\(91\) 1251.60i 1.44179i
\(92\) 277.377 0.314332
\(93\) −941.017 + 1281.77i −1.04924 + 1.42918i
\(94\) −142.493 −0.156352
\(95\) 14.4395i 0.0155943i
\(96\) −1012.09 743.034i −1.07600 0.789954i
\(97\) 1332.12i 1.39440i 0.716878 + 0.697198i \(0.245570\pi\)
−0.716878 + 0.697198i \(0.754430\pi\)
\(98\) −980.577 −1.01075
\(99\) 136.030 + 433.249i 0.138097 + 0.439830i
\(100\) 856.845 0.856845
\(101\) 1810.79 1.78397 0.891984 0.452067i \(-0.149313\pi\)
0.891984 + 0.452067i \(0.149313\pi\)
\(102\) −734.507 + 1000.48i −0.713010 + 0.971199i
\(103\) 1377.13i 1.31740i −0.752405 0.658701i \(-0.771106\pi\)
0.752405 0.658701i \(-0.228894\pi\)
\(104\) 225.802i 0.212901i
\(105\) 11.0418 15.0402i 0.0102626 0.0139788i
\(106\) 407.582i 0.373471i
\(107\) 1084.01i 0.979390i −0.871894 0.489695i \(-0.837108\pi\)
0.871894 0.489695i \(-0.162892\pi\)
\(108\) 310.823 910.257i 0.276934 0.811014i
\(109\) 455.929i 0.400643i −0.979730 0.200322i \(-0.935801\pi\)
0.979730 0.200322i \(-0.0641987\pi\)
\(110\) 9.52341i 0.00825474i
\(111\) 1087.87 1481.80i 0.930235 1.26708i
\(112\) 1756.00 1.48148
\(113\) −356.645 −0.296905 −0.148453 0.988920i \(-0.547429\pi\)
−0.148453 + 0.988920i \(0.547429\pi\)
\(114\) −1586.77 1164.94i −1.30364 0.957073i
\(115\) 5.94368i 0.00481957i
\(116\) 1612.01i 1.29027i
\(117\) −1319.10 + 414.166i −1.04231 + 0.327262i
\(118\) 1483.44 + 922.220i 1.15731 + 0.719468i
\(119\) 1514.71i 1.16683i
\(120\) −1.99207 + 2.71341i −0.00151542 + 0.00206416i
\(121\) −1048.13 −0.787479
\(122\) 1042.45i 0.773600i
\(123\) −797.381 + 1086.12i −0.584532 + 0.796197i
\(124\) 2098.03i 1.51943i
\(125\) 36.7244i 0.0262779i
\(126\) 761.959 + 2426.80i 0.538736 + 1.71584i
\(127\) −467.771 −0.326834 −0.163417 0.986557i \(-0.552252\pi\)
−0.163417 + 0.986557i \(0.552252\pi\)
\(128\) −558.657 −0.385771
\(129\) −181.390 + 247.074i −0.123803 + 0.168633i
\(130\) −28.9956 −0.0195621
\(131\) 2005.53 1.33759 0.668795 0.743447i \(-0.266811\pi\)
0.668795 + 0.743447i \(0.266811\pi\)
\(132\) −482.972 354.576i −0.318464 0.233802i
\(133\) 2402.34 1.56624
\(134\) 777.195i 0.501040i
\(135\) −19.5052 6.66036i −0.0124351 0.00424617i
\(136\) 273.270i 0.172299i
\(137\) 1176.51i 0.733695i −0.930281 0.366848i \(-0.880437\pi\)
0.930281 0.366848i \(-0.119563\pi\)
\(138\) 653.157 + 479.519i 0.402902 + 0.295792i
\(139\) 1219.44 0.744111 0.372055 0.928210i \(-0.378653\pi\)
0.372055 + 0.928210i \(0.378653\pi\)
\(140\) 24.6181i 0.0148615i
\(141\) −154.849 113.684i −0.0924871 0.0678999i
\(142\) 2542.67i 1.50265i
\(143\) 861.229i 0.503634i
\(144\) −581.078 1850.70i −0.336272 1.07101i
\(145\) −34.5426 −0.0197835
\(146\) 2328.60i 1.31998i
\(147\) −1065.61 782.319i −0.597889 0.438943i
\(148\) 2425.44i 1.34710i
\(149\) 2092.78 1.15065 0.575327 0.817924i \(-0.304875\pi\)
0.575327 + 0.817924i \(0.304875\pi\)
\(150\) 2017.67 + 1481.28i 1.09828 + 0.806308i
\(151\) 1352.06i 0.728668i −0.931268 0.364334i \(-0.881297\pi\)
0.931268 0.364334i \(-0.118703\pi\)
\(152\) −433.409 −0.231277
\(153\) −1596.40 + 501.233i −0.843536 + 0.264851i
\(154\) 1584.44 0.829077
\(155\) −44.9570 −0.0232970
\(156\) 1079.56 1470.49i 0.554066 0.754699i
\(157\) 2269.35i 1.15359i −0.816888 0.576797i \(-0.804302\pi\)
0.816888 0.576797i \(-0.195698\pi\)
\(158\) −1914.56 −0.964015
\(159\) −325.176 + 442.925i −0.162189 + 0.220920i
\(160\) 35.4984i 0.0175400i
\(161\) −988.868 −0.484060
\(162\) 2305.53 1606.10i 1.11815 0.778935i
\(163\) −253.195 −0.121667 −0.0608336 0.998148i \(-0.519376\pi\)
−0.0608336 + 0.998148i \(0.519376\pi\)
\(164\) 1777.79i 0.846476i
\(165\) −7.59793 + 10.3492i −0.00358484 + 0.00488294i
\(166\) −5614.80 −2.62526
\(167\) 1565.36i 0.725335i −0.931919 0.362668i \(-0.881866\pi\)
0.931919 0.362668i \(-0.118134\pi\)
\(168\) 451.439 + 331.426i 0.207317 + 0.152203i
\(169\) −425.151 −0.193514
\(170\) −35.0910 −0.0158315
\(171\) −794.960 2531.90i −0.355509 1.13228i
\(172\) 404.416i 0.179282i
\(173\) 2408.08 1.05828 0.529142 0.848534i \(-0.322514\pi\)
0.529142 + 0.848534i \(0.322514\pi\)
\(174\) 2786.79 3795.92i 1.21417 1.65384i
\(175\) −3054.71 −1.31951
\(176\) −1208.31 −0.517499
\(177\) 876.317 + 2185.70i 0.372136 + 0.928178i
\(178\) −562.689 −0.236940
\(179\) −254.566 −0.106297 −0.0531484 0.998587i \(-0.516926\pi\)
−0.0531484 + 0.998587i \(0.516926\pi\)
\(180\) 25.9458 8.14640i 0.0107438 0.00337331i
\(181\) −2916.59 −1.19773 −0.598864 0.800851i \(-0.704381\pi\)
−0.598864 + 0.800851i \(0.704381\pi\)
\(182\) 4824.08i 1.96475i
\(183\) −831.685 + 1132.85i −0.335956 + 0.457609i
\(184\) 178.403 0.0714784
\(185\) 51.9729 0.0206547
\(186\) 3627.00 4940.38i 1.42981 1.94756i
\(187\) 1042.28i 0.407588i
\(188\) 253.461 0.0983275
\(189\) −1108.11 + 3245.13i −0.426470 + 1.24894i
\(190\) 55.6547i 0.0212506i
\(191\) 821.031 0.311035 0.155518 0.987833i \(-0.450295\pi\)
0.155518 + 0.987833i \(0.450295\pi\)
\(192\) 1493.59 + 1096.52i 0.561408 + 0.412160i
\(193\) 4097.34 1.52815 0.764074 0.645128i \(-0.223196\pi\)
0.764074 + 0.645128i \(0.223196\pi\)
\(194\) 5134.45i 1.90017i
\(195\) −31.5098 23.1331i −0.0115716 0.00849537i
\(196\) 1744.21 0.635645
\(197\) 770.845i 0.278784i 0.990237 + 0.139392i \(0.0445148\pi\)
−0.990237 + 0.139392i \(0.955485\pi\)
\(198\) −524.307 1669.89i −0.188186 0.599363i
\(199\) −732.811 −0.261043 −0.130522 0.991445i \(-0.541665\pi\)
−0.130522 + 0.991445i \(0.541665\pi\)
\(200\) 551.104 0.194845
\(201\) 620.058 844.588i 0.217590 0.296381i
\(202\) −6979.42 −2.43104
\(203\) 5746.95i 1.98698i
\(204\) 1306.51 1779.61i 0.448402 0.610773i
\(205\) −38.0948 −0.0129788
\(206\) 5307.92i 1.79524i
\(207\) 327.227 + 1042.20i 0.109874 + 0.349941i
\(208\) 3678.89i 1.22637i
\(209\) −1653.06 −0.547104
\(210\) −42.5590 + 57.9700i −0.0139850 + 0.0190491i
\(211\) 3592.04i 1.17197i 0.810321 + 0.585986i \(0.199293\pi\)
−0.810321 + 0.585986i \(0.800707\pi\)
\(212\) 724.990i 0.234870i
\(213\) 2028.59 2763.16i 0.652565 0.888865i
\(214\) 4178.12i 1.33463i
\(215\) −8.66591 −0.00274888
\(216\) 199.914 585.458i 0.0629743 0.184423i
\(217\) 7479.64i 2.33987i
\(218\) 1757.31i 0.545963i
\(219\) −1857.79 + 2530.52i −0.573233 + 0.780807i
\(220\) 16.9398i 0.00519129i
\(221\) −3173.38 −0.965904
\(222\) −4193.02 + 5711.36i −1.26764 + 1.72667i
\(223\) 3666.01 1.10087 0.550435 0.834878i \(-0.314462\pi\)
0.550435 + 0.834878i \(0.314462\pi\)
\(224\) −5905.98 −1.76165
\(225\) 1010.84 + 3219.46i 0.299507 + 0.953913i
\(226\) 1374.63 0.404597
\(227\) −3118.42 −0.911792 −0.455896 0.890033i \(-0.650681\pi\)
−0.455896 + 0.890033i \(0.650681\pi\)
\(228\) 2822.48 + 2072.14i 0.819840 + 0.601890i
\(229\) 2426.36i 0.700169i 0.936718 + 0.350084i \(0.113847\pi\)
−0.936718 + 0.350084i \(0.886153\pi\)
\(230\) 22.9090i 0.00656770i
\(231\) 1721.83 + 1264.09i 0.490425 + 0.360048i
\(232\) 1036.81i 0.293406i
\(233\) −2575.90 −0.724262 −0.362131 0.932127i \(-0.617951\pi\)
−0.362131 + 0.932127i \(0.617951\pi\)
\(234\) 5084.25 1596.34i 1.42037 0.445965i
\(235\) 5.43122i 0.00150763i
\(236\) −2638.69 1640.41i −0.727814 0.452463i
\(237\) −2080.58 1527.47i −0.570245 0.418648i
\(238\) 5838.20i 1.59006i
\(239\) 4360.94i 1.18028i 0.807303 + 0.590138i \(0.200927\pi\)
−0.807303 + 0.590138i \(0.799073\pi\)
\(240\) 32.4559 44.2085i 0.00872924 0.0118902i
\(241\) 3041.06 0.812829 0.406415 0.913689i \(-0.366779\pi\)
0.406415 + 0.913689i \(0.366779\pi\)
\(242\) 4039.87 1.07311
\(243\) 3786.83 + 94.0177i 0.999692 + 0.0248199i
\(244\) 1854.27i 0.486506i
\(245\) 37.3752i 0.00974619i
\(246\) 3073.38 4186.28i 0.796550 1.08499i
\(247\) 5033.01i 1.29653i
\(248\) 1349.41i 0.345514i
\(249\) −6101.68 4479.58i −1.55292 1.14009i
\(250\) 141.548i 0.0358092i
\(251\) 6103.22i 1.53479i −0.641176 0.767394i \(-0.721553\pi\)
0.641176 0.767394i \(-0.278447\pi\)
\(252\) −1355.34 4316.68i −0.338803 1.07907i
\(253\) 680.445 0.169088
\(254\) 1802.95 0.445382
\(255\) −38.1339 27.9962i −0.00936484 0.00687525i
\(256\) 5005.95 1.22216
\(257\) 1101.84i 0.267435i 0.991019 + 0.133717i \(0.0426915\pi\)
−0.991019 + 0.133717i \(0.957309\pi\)
\(258\) 699.140 952.306i 0.168708 0.229798i
\(259\) 8646.89i 2.07448i
\(260\) 51.5761 0.0123024
\(261\) 6056.89 1901.73i 1.43644 0.451011i
\(262\) −7730.00 −1.82275
\(263\) 6790.33i 1.59205i −0.605262 0.796026i \(-0.706932\pi\)
0.605262 0.796026i \(-0.293068\pi\)
\(264\) −310.637 228.056i −0.0724182 0.0531662i
\(265\) −15.5352 −0.00360121
\(266\) −9259.45 −2.13434
\(267\) −611.482 448.922i −0.140158 0.102897i
\(268\) 1382.44i 0.315097i
\(269\) 2014.39 0.456579 0.228290 0.973593i \(-0.426687\pi\)
0.228290 + 0.973593i \(0.426687\pi\)
\(270\) 75.1795 + 25.6713i 0.0169455 + 0.00578632i
\(271\) −2969.59 −0.665646 −0.332823 0.942989i \(-0.608001\pi\)
−0.332823 + 0.942989i \(0.608001\pi\)
\(272\) 4452.27i 0.992494i
\(273\) −3848.73 + 5242.39i −0.853244 + 1.16221i
\(274\) 4534.68i 0.999818i
\(275\) 2101.96 0.460920
\(276\) −1161.81 852.948i −0.253379 0.186020i
\(277\) 3663.21 0.794589 0.397294 0.917691i \(-0.369949\pi\)
0.397294 + 0.917691i \(0.369949\pi\)
\(278\) −4700.13 −1.01401
\(279\) 7883.02 2475.09i 1.69156 0.531110i
\(280\) 15.8339i 0.00337948i
\(281\) 4303.92i 0.913703i 0.889543 + 0.456851i \(0.151023\pi\)
−0.889543 + 0.456851i \(0.848977\pi\)
\(282\) 596.843 + 438.175i 0.126034 + 0.0925282i
\(283\) 5311.32i 1.11564i 0.829963 + 0.557819i \(0.188362\pi\)
−0.829963 + 0.557819i \(0.811638\pi\)
\(284\) 4522.80i 0.944996i
\(285\) 44.4022 60.4807i 0.00922863 0.0125704i
\(286\) 3319.47i 0.686309i
\(287\) 6337.95i 1.30354i
\(288\) 1954.35 + 6224.49i 0.399865 + 1.27355i
\(289\) 1072.51 0.218300
\(290\) 133.139 0.0269592
\(291\) 4096.35 5579.67i 0.825196 1.12401i
\(292\) 4142.02i 0.830114i
\(293\) 1647.73i 0.328538i −0.986416 0.164269i \(-0.947473\pi\)
0.986416 0.164269i \(-0.0525265\pi\)
\(294\) 4107.21 + 3015.33i 0.814752 + 0.598154i
\(295\) −35.1509 + 56.5423i −0.00693752 + 0.0111594i
\(296\) 1559.99i 0.306327i
\(297\) 762.492 2232.99i 0.148971 0.436267i
\(298\) −8066.29 −1.56801
\(299\) 2071.72i 0.400705i
\(300\) −3588.95 2634.84i −0.690693 0.507076i
\(301\) 1441.77i 0.276088i
\(302\) 5211.29i 0.992967i
\(303\) −7584.62 5568.29i −1.43804 1.05574i
\(304\) 7061.35 1.33222
\(305\) −39.7337 −0.00745948
\(306\) 6153.06 1931.92i 1.14950 0.360917i
\(307\) −9335.42 −1.73551 −0.867753 0.496995i \(-0.834437\pi\)
−0.867753 + 0.496995i \(0.834437\pi\)
\(308\) −2818.34 −0.521395
\(309\) −4234.74 + 5768.18i −0.779631 + 1.06194i
\(310\) 173.280 0.0317472
\(311\) 2094.69i 0.381925i −0.981597 0.190963i \(-0.938839\pi\)
0.981597 0.190963i \(-0.0611610\pi\)
\(312\) 694.353 945.785i 0.125994 0.171617i
\(313\) 2126.17i 0.383956i −0.981399 0.191978i \(-0.938510\pi\)
0.981399 0.191978i \(-0.0614903\pi\)
\(314\) 8746.86i 1.57202i
\(315\) −92.4987 + 29.0425i −0.0165451 + 0.00519479i
\(316\) 3405.54 0.606255
\(317\) 310.556i 0.0550239i 0.999621 + 0.0275119i \(0.00875842\pi\)
−0.999621 + 0.0275119i \(0.991242\pi\)
\(318\) 1253.34 1707.18i 0.221018 0.301051i
\(319\) 3954.50i 0.694074i
\(320\) 52.3863i 0.00915151i
\(321\) −3333.37 + 4540.42i −0.579597 + 0.789476i
\(322\) 3811.43 0.659637
\(323\) 6091.06i 1.04927i
\(324\) −4100.99 + 2856.87i −0.703187 + 0.489861i
\(325\) 6399.76i 1.09229i
\(326\) 975.900 0.165798
\(327\) −1402.01 + 1909.69i −0.237098 + 0.322954i
\(328\) 1143.44i 0.192487i
\(329\) −903.609 −0.151421
\(330\) 29.2850 39.8894i 0.00488511 0.00665406i
\(331\) 3520.17 0.584550 0.292275 0.956334i \(-0.405588\pi\)
0.292275 + 0.956334i \(0.405588\pi\)
\(332\) 9987.38 1.65099
\(333\) −9113.22 + 2861.35i −1.49970 + 0.470873i
\(334\) 6033.42i 0.988425i
\(335\) 29.6232 0.00483131
\(336\) −7355.10 5399.79i −1.19421 0.876733i
\(337\) 5562.60i 0.899152i 0.893242 + 0.449576i \(0.148425\pi\)
−0.893242 + 0.449576i \(0.851575\pi\)
\(338\) 1638.68 0.263705
\(339\) 1493.83 + 1096.70i 0.239332 + 0.175707i
\(340\) 62.4184 0.00995622
\(341\) 5146.77i 0.817341i
\(342\) 3064.05 + 9758.81i 0.484458 + 1.54297i
\(343\) 2165.35 0.340869
\(344\) 260.112i 0.0407683i
\(345\) −18.2771 + 24.8955i −0.00285220 + 0.00388500i
\(346\) −9281.56 −1.44214
\(347\) −679.142 −0.105067 −0.0525335 0.998619i \(-0.516730\pi\)
−0.0525335 + 0.998619i \(0.516730\pi\)
\(348\) −4957.03 + 6752.02i −0.763577 + 1.04008i
\(349\) 11855.2i 1.81832i −0.416452 0.909158i \(-0.636727\pi\)
0.416452 0.909158i \(-0.363273\pi\)
\(350\) 11773.9 1.79812
\(351\) 6798.70 + 2321.53i 1.03387 + 0.353032i
\(352\) 4063.93 0.615364
\(353\) −8993.79 −1.35607 −0.678033 0.735032i \(-0.737167\pi\)
−0.678033 + 0.735032i \(0.737167\pi\)
\(354\) −3377.62 8424.45i −0.507115 1.26484i
\(355\) 96.9155 0.0144894
\(356\) 1000.89 0.149008
\(357\) −4657.81 + 6344.45i −0.690525 + 0.940571i
\(358\) 981.183 0.144852
\(359\) 10648.2i 1.56543i −0.622383 0.782713i \(-0.713835\pi\)
0.622383 0.782713i \(-0.286165\pi\)
\(360\) 16.6878 5.23959i 0.00244312 0.000767085i
\(361\) 2801.48 0.408439
\(362\) 11241.5 1.63216
\(363\) 4390.18 + 3223.07i 0.634778 + 0.466026i
\(364\) 8580.88i 1.23560i
\(365\) −88.7559 −0.0127279
\(366\) 3205.60 4366.37i 0.457812 0.623590i
\(367\) 2110.22i 0.300144i −0.988675 0.150072i \(-0.952049\pi\)
0.988675 0.150072i \(-0.0479505\pi\)
\(368\) −2906.64 −0.411736
\(369\) 6679.76 2097.29i 0.942369 0.295883i
\(370\) −200.321 −0.0281465
\(371\) 2584.64i 0.361693i
\(372\) −6451.56 + 8787.73i −0.899188 + 1.22479i
\(373\) −5335.64 −0.740668 −0.370334 0.928899i \(-0.620757\pi\)
−0.370334 + 0.928899i \(0.620757\pi\)
\(374\) 4017.29i 0.555426i
\(375\) −112.930 + 153.823i −0.0155511 + 0.0211823i
\(376\) 163.021 0.0223595
\(377\) 12040.1 1.64482
\(378\) 4271.02 12507.8i 0.581157 1.70194i
\(379\) 4285.73 0.580853 0.290426 0.956897i \(-0.406203\pi\)
0.290426 + 0.956897i \(0.406203\pi\)
\(380\) 98.9963i 0.0133642i
\(381\) 1959.29 + 1438.42i 0.263458 + 0.193419i
\(382\) −3164.53 −0.423853
\(383\) 5665.62i 0.755873i −0.925831 0.377937i \(-0.876634\pi\)
0.925831 0.377937i \(-0.123366\pi\)
\(384\) 2339.97 + 1717.90i 0.310966 + 0.228297i
\(385\) 60.3918i 0.00799442i
\(386\) −15792.5 −2.08243
\(387\) 1519.53 477.098i 0.199592 0.0626673i
\(388\) 9132.95i 1.19499i
\(389\) 522.623i 0.0681183i −0.999420 0.0340592i \(-0.989157\pi\)
0.999420 0.0340592i \(-0.0108435\pi\)
\(390\) 121.450 + 89.1629i 0.0157688 + 0.0115768i
\(391\) 2507.24i 0.324288i
\(392\) 1121.84 0.144544
\(393\) −8400.30 6167.12i −1.07822 0.791578i
\(394\) 2971.10i 0.379903i
\(395\) 72.9746i 0.00929557i
\(396\) 932.616 + 2970.33i 0.118348 + 0.376931i
\(397\) 7111.99i 0.899094i 0.893257 + 0.449547i \(0.148415\pi\)
−0.893257 + 0.449547i \(0.851585\pi\)
\(398\) 2824.50 0.355727
\(399\) −10062.4 7387.33i −1.26253 0.926890i
\(400\) −8978.90 −1.12236
\(401\) −6816.87 −0.848923 −0.424461 0.905446i \(-0.639537\pi\)
−0.424461 + 0.905446i \(0.639537\pi\)
\(402\) −2389.92 + 3255.33i −0.296513 + 0.403883i
\(403\) 15670.2 1.93694
\(404\) 12414.7 1.52885
\(405\) 61.2176 + 87.8767i 0.00751093 + 0.0107818i
\(406\) 22150.7i 2.70769i
\(407\) 5949.96i 0.724641i
\(408\) 840.320 1144.61i 0.101966 0.138889i
\(409\) 15723.8i 1.90096i −0.310787 0.950480i \(-0.600593\pi\)
0.310787 0.950480i \(-0.399407\pi\)
\(410\) 146.830 0.0176864
\(411\) −3617.84 + 4927.90i −0.434197 + 0.591424i
\(412\) 9441.50i 1.12900i
\(413\) 9407.13 + 5848.17i 1.12081 + 0.696779i
\(414\) −1261.24 4016.99i −0.149726 0.476870i
\(415\) 214.011i 0.0253142i
\(416\) 12373.3i 1.45829i
\(417\) −5107.69 3749.84i −0.599820 0.440361i
\(418\) 6371.47 0.745547
\(419\) 9134.66 1.06505 0.532526 0.846413i \(-0.321243\pi\)
0.532526 + 0.846413i \(0.321243\pi\)
\(420\) 75.7021 103.115i 0.00879496 0.0119797i
\(421\) 8009.90i 0.927265i 0.886027 + 0.463633i \(0.153454\pi\)
−0.886027 + 0.463633i \(0.846546\pi\)
\(422\) 13844.9i 1.59706i
\(423\) 299.013 + 952.341i 0.0343701 + 0.109467i
\(424\) 466.298i 0.0534091i
\(425\) 7745.12i 0.883985i
\(426\) −7818.86 + 10650.1i −0.889260 + 1.21127i
\(427\) 6610.61i 0.749204i
\(428\) 7431.87i 0.839330i
\(429\) 2648.33 3607.31i 0.298048 0.405974i
\(430\) 33.4014 0.00374595
\(431\) 11276.8 1.26028 0.630142 0.776480i \(-0.282997\pi\)
0.630142 + 0.776480i \(0.282997\pi\)
\(432\) −3257.12 + 9538.61i −0.362750 + 1.06233i
\(433\) −733.247 −0.0813801 −0.0406901 0.999172i \(-0.512956\pi\)
−0.0406901 + 0.999172i \(0.512956\pi\)
\(434\) 28829.1i 3.18857i
\(435\) 144.684 + 106.220i 0.0159472 + 0.0117077i
\(436\) 3125.83i 0.343348i
\(437\) −3976.51 −0.435291
\(438\) 7160.57 9753.49i 0.781154 1.06402i
\(439\) −3985.01 −0.433244 −0.216622 0.976256i \(-0.569504\pi\)
−0.216622 + 0.976256i \(0.569504\pi\)
\(440\) 10.8953i 0.00118049i
\(441\) 2057.68 + 6553.59i 0.222187 + 0.707654i
\(442\) 12231.3 1.31625
\(443\) −14314.5 −1.53522 −0.767609 0.640918i \(-0.778554\pi\)
−0.767609 + 0.640918i \(0.778554\pi\)
\(444\) 7458.37 10159.1i 0.797204 1.08588i
\(445\) 21.4472i 0.00228471i
\(446\) −14130.0 −1.50017
\(447\) −8765.74 6435.42i −0.927529 0.680950i
\(448\) 8715.67 0.919145
\(449\) 3845.79i 0.404219i −0.979363 0.202109i \(-0.935220\pi\)
0.979363 0.202109i \(-0.0647796\pi\)
\(450\) −3896.11 12408.9i −0.408143 1.29991i
\(451\) 4361.17i 0.455343i
\(452\) −2445.13 −0.254446
\(453\) −4157.65 + 5663.17i −0.431222 + 0.587371i
\(454\) 12019.5 1.24251
\(455\) −183.873 −0.0189452
\(456\) 1815.36 + 1332.76i 0.186430 + 0.136868i
\(457\) 1970.01i 0.201648i −0.994904 0.100824i \(-0.967852\pi\)
0.994904 0.100824i \(-0.0321479\pi\)
\(458\) 9352.03i 0.954130i
\(459\) 8227.92 + 2809.56i 0.836703 + 0.285706i
\(460\) 40.7495i 0.00413034i
\(461\) 18528.1i 1.87188i 0.352157 + 0.935941i \(0.385448\pi\)
−0.352157 + 0.935941i \(0.614552\pi\)
\(462\) −6636.52 4872.24i −0.668310 0.490643i
\(463\) 16647.8i 1.67103i 0.549465 + 0.835517i \(0.314832\pi\)
−0.549465 + 0.835517i \(0.685168\pi\)
\(464\) 16892.3i 1.69010i
\(465\) 188.305 + 138.245i 0.0187795 + 0.0137870i
\(466\) 9928.41 0.986963
\(467\) 9292.78 0.920811 0.460405 0.887709i \(-0.347704\pi\)
0.460405 + 0.887709i \(0.347704\pi\)
\(468\) −9043.64 + 2839.50i −0.893253 + 0.280461i
\(469\) 4928.51i 0.485240i
\(470\) 20.9338i 0.00205447i
\(471\) −6978.38 + 9505.33i −0.682690 + 0.929899i
\(472\) −1697.15 1055.07i −0.165503 0.102889i
\(473\) 992.091i 0.0964406i
\(474\) 8019.26 + 5887.38i 0.777082 + 0.570498i
\(475\) −12283.8 −1.18657
\(476\) 10384.8i 0.999967i
\(477\) 2724.04 855.286i 0.261478 0.0820982i
\(478\) 16808.5i 1.60838i
\(479\) 19464.5i 1.85670i −0.371712 0.928348i \(-0.621229\pi\)
0.371712 0.928348i \(-0.378771\pi\)
\(480\) −109.159 + 148.687i −0.0103801 + 0.0141388i
\(481\) −18115.6 −1.71726
\(482\) −11721.3 −1.10765
\(483\) 4141.93 + 3040.82i 0.390196 + 0.286464i
\(484\) −7185.95 −0.674864
\(485\) 195.703 0.0183225
\(486\) −14595.7 362.376i −1.36230 0.0338225i
\(487\) −3403.75 −0.316712 −0.158356 0.987382i \(-0.550619\pi\)
−0.158356 + 0.987382i \(0.550619\pi\)
\(488\) 1192.63i 0.110631i
\(489\) 1060.52 + 778.588i 0.0980746 + 0.0720020i
\(490\) 144.057i 0.0132813i
\(491\) 10503.8i 0.965436i 0.875776 + 0.482718i \(0.160350\pi\)
−0.875776 + 0.482718i \(0.839650\pi\)
\(492\) −5466.80 + 7446.38i −0.500939 + 0.682335i
\(493\) 14571.2 1.33114
\(494\) 19399.0i 1.76680i
\(495\) 63.6488 19.9843i 0.00577939 0.00181460i
\(496\) 21985.3i 1.99026i
\(497\) 16124.1i 1.45526i
\(498\) 23517.9 + 17265.8i 2.11619 + 1.55361i
\(499\) −5259.11 −0.471804 −0.235902 0.971777i \(-0.575804\pi\)
−0.235902 + 0.971777i \(0.575804\pi\)
\(500\) 251.780i 0.0225199i
\(501\) −4813.56 + 6556.59i −0.429249 + 0.584685i
\(502\) 23523.9i 2.09148i
\(503\) 18638.3 1.65217 0.826086 0.563544i \(-0.190562\pi\)
0.826086 + 0.563544i \(0.190562\pi\)
\(504\) −871.727 2776.40i −0.0770432 0.245378i
\(505\) 266.024i 0.0234415i
\(506\) −2622.66 −0.230418
\(507\) 1780.77 + 1307.36i 0.155990 + 0.114521i
\(508\) −3207.01 −0.280095
\(509\) −11732.0 −1.02163 −0.510817 0.859689i \(-0.670657\pi\)
−0.510817 + 0.859689i \(0.670657\pi\)
\(510\) 146.981 + 107.907i 0.0127616 + 0.00936900i
\(511\) 14766.6i 1.27835i
\(512\) −14825.4 −1.27968
\(513\) −4456.00 + 13049.6i −0.383503 + 1.12310i
\(514\) 4246.86i 0.364438i
\(515\) −202.314 −0.0173107
\(516\) −1243.60 + 1693.92i −0.106098 + 0.144517i
\(517\) 621.777 0.0528931
\(518\) 33328.1i 2.82693i
\(519\) −10086.4 7404.98i −0.853070 0.626286i
\(520\) 33.1726 0.00279753
\(521\) 13671.5i 1.14964i −0.818281 0.574818i \(-0.805073\pi\)
0.818281 0.574818i \(-0.194927\pi\)
\(522\) −23345.3 + 7329.90i −1.95746 + 0.614600i
\(523\) −19787.6 −1.65440 −0.827198 0.561910i \(-0.810067\pi\)
−0.827198 + 0.561910i \(0.810067\pi\)
\(524\) 13749.8 1.14630
\(525\) 12794.9 + 9393.41i 1.06364 + 0.780880i
\(526\) 26172.2i 2.16951i
\(527\) 18964.4 1.56755
\(528\) 5061.08 + 3715.62i 0.417150 + 0.306253i
\(529\) −10530.2 −0.865469
\(530\) 59.8781 0.00490743
\(531\) 3050.65 11849.7i 0.249316 0.968422i
\(532\) 16470.3 1.34225
\(533\) 13278.3 1.07907
\(534\) 2356.86 + 1730.30i 0.190995 + 0.140220i
\(535\) −159.252 −0.0128692
\(536\) 889.157i 0.0716525i
\(537\) 1066.26 + 782.803i 0.0856847 + 0.0629058i
\(538\) −7764.16 −0.622187
\(539\) 4278.79 0.341931
\(540\) −133.726 45.6631i −0.0106568 0.00363894i
\(541\) 12188.6i 0.968630i 0.874894 + 0.484315i \(0.160931\pi\)
−0.874894 + 0.484315i \(0.839069\pi\)
\(542\) 11445.8 0.907086
\(543\) 12216.3 + 8968.68i 0.965475 + 0.708808i
\(544\) 14974.4i 1.18019i
\(545\) −66.9808 −0.00526448
\(546\) 14834.3 20206.0i 1.16273 1.58376i
\(547\) −10285.8 −0.804003 −0.402001 0.915639i \(-0.631685\pi\)
−0.402001 + 0.915639i \(0.631685\pi\)
\(548\) 8066.10i 0.628771i
\(549\) 6967.12 2187.52i 0.541620 0.170057i
\(550\) −8101.68 −0.628103
\(551\) 23110.1i 1.78679i
\(552\) −747.251 548.598i −0.0576179 0.0423005i
\(553\) −12141.0 −0.933614
\(554\) −14119.3 −1.08280
\(555\) −217.692 159.819i −0.0166495 0.0122233i
\(556\) 8360.40 0.637698
\(557\) 2994.00i 0.227756i 0.993495 + 0.113878i \(0.0363272\pi\)
−0.993495 + 0.113878i \(0.963673\pi\)
\(558\) −30383.8 + 9539.84i −2.30511 + 0.723752i
\(559\) 3020.58 0.228546
\(560\) 257.974i 0.0194668i
\(561\) 3205.06 4365.64i 0.241208 0.328552i
\(562\) 16588.8i 1.24512i
\(563\) 3200.12 0.239554 0.119777 0.992801i \(-0.461782\pi\)
0.119777 + 0.992801i \(0.461782\pi\)
\(564\) −1061.64 779.407i −0.0792607 0.0581897i
\(565\) 52.3948i 0.00390135i
\(566\) 20471.6i 1.52030i
\(567\) 14620.3 10185.0i 1.08289 0.754370i
\(568\) 2908.97i 0.214890i
\(569\) 25341.0 1.86705 0.933524 0.358515i \(-0.116717\pi\)
0.933524 + 0.358515i \(0.116717\pi\)
\(570\) −171.141 + 233.113i −0.0125760 + 0.0171299i
\(571\) 2220.28i 0.162724i −0.996685 0.0813622i \(-0.974073\pi\)
0.996685 0.0813622i \(-0.0259271\pi\)
\(572\) 5904.54i 0.431610i
\(573\) −3438.94 2524.72i −0.250722 0.184069i
\(574\) 24428.6i 1.77636i
\(575\) 5056.36 0.366721
\(576\) −2884.11 9185.71i −0.208630 0.664476i
\(577\) −8017.59 −0.578469 −0.289234 0.957258i \(-0.593401\pi\)
−0.289234 + 0.957258i \(0.593401\pi\)
\(578\) −4133.82 −0.297481
\(579\) −17161.9 12599.5i −1.23182 0.904350i
\(580\) −236.822 −0.0169543
\(581\) −35605.7 −2.54247
\(582\) −15788.7 + 21506.0i −1.12451 + 1.53170i
\(583\) 1778.51i 0.126343i
\(584\) 2664.06i 0.188766i
\(585\) 60.8453 + 193.789i 0.00430025 + 0.0136960i
\(586\) 6350.93i 0.447704i
\(587\) −18610.1 −1.30856 −0.654278 0.756254i \(-0.727027\pi\)
−0.654278 + 0.756254i \(0.727027\pi\)
\(588\) −7305.73 5363.54i −0.512386 0.376171i
\(589\) 30077.7i 2.10412i
\(590\) 135.484 217.933i 0.00945386 0.0152071i
\(591\) 2370.39 3228.73i 0.164983 0.224725i
\(592\) 25416.3i 1.76453i
\(593\) 9313.64i 0.644967i −0.946575 0.322484i \(-0.895482\pi\)
0.946575 0.322484i \(-0.104518\pi\)
\(594\) −2938.90 + 8606.71i −0.203005 + 0.594507i
\(595\) −222.526 −0.0153323
\(596\) 14348.0 0.986101
\(597\) 3069.42 + 2253.43i 0.210424 + 0.154484i
\(598\) 7985.12i 0.546047i
\(599\) 17777.5i 1.21263i −0.795223 0.606317i \(-0.792646\pi\)
0.795223 0.606317i \(-0.207354\pi\)
\(600\) −2308.33 1694.67i −0.157062 0.115308i
\(601\) 17209.0i 1.16800i −0.811753 0.584001i \(-0.801486\pi\)
0.811753 0.584001i \(-0.198514\pi\)
\(602\) 5557.09i 0.376229i
\(603\) −5194.31 + 1630.89i −0.350793 + 0.110141i
\(604\) 9269.62i 0.624463i
\(605\) 153.982i 0.0103475i
\(606\) 29233.7 + 21462.1i 1.95963 + 1.43868i
\(607\) 7356.60 0.491920 0.245960 0.969280i \(-0.420897\pi\)
0.245960 + 0.969280i \(0.420897\pi\)
\(608\) −23749.6 −1.58416
\(609\) 17672.2 24071.5i 1.17588 1.60168i
\(610\) 153.147 0.0101652
\(611\) 1893.10i 0.125346i
\(612\) −10944.8 + 3436.42i −0.722904 + 0.226976i
\(613\) 3287.75i 0.216625i 0.994117 + 0.108312i \(0.0345447\pi\)
−0.994117 + 0.108312i \(0.965455\pi\)
\(614\) 35981.9 2.36500
\(615\) 159.562 + 117.144i 0.0104621 + 0.00768079i
\(616\) −1812.69 −0.118564
\(617\) 17552.0i 1.14524i 0.819820 + 0.572622i \(0.194074\pi\)
−0.819820 + 0.572622i \(0.805926\pi\)
\(618\) 16322.1 22232.5i 1.06241 1.44713i
\(619\) 24087.0 1.56404 0.782019 0.623254i \(-0.214190\pi\)
0.782019 + 0.623254i \(0.214190\pi\)
\(620\) −308.223 −0.0199654
\(621\) 1834.21 5371.55i 0.118525 0.347106i
\(622\) 8073.64i 0.520456i
\(623\) −3568.24 −0.229468
\(624\) −11312.8 + 15409.3i −0.725760 + 0.988564i
\(625\) 15616.9 0.999482
\(626\) 8194.99i 0.523223i
\(627\) 6923.95 + 5083.26i 0.441015 + 0.323773i
\(628\) 15558.6i 0.988621i
\(629\) −21923.9 −1.38977
\(630\) 356.522 111.940i 0.0225463 0.00707902i
\(631\) −12126.1 −0.765026 −0.382513 0.923950i \(-0.624941\pi\)
−0.382513 + 0.923950i \(0.624941\pi\)
\(632\) 2190.37 0.137861
\(633\) 11045.7 15045.5i 0.693567 0.944714i
\(634\) 1196.99i 0.0749818i
\(635\) 68.7204i 0.00429462i
\(636\) −2229.38 + 3036.67i −0.138995 + 0.189326i
\(637\) 13027.5i 0.810310i
\(638\) 15242.0i 0.945825i
\(639\) −16993.7 + 5335.64i −1.05205 + 0.330320i
\(640\) 82.0724i 0.00506906i
\(641\) 15578.1i 0.959905i −0.877294 0.479952i \(-0.840654\pi\)
0.877294 0.479952i \(-0.159346\pi\)
\(642\) 12848.0 17500.3i 0.789826 1.07583i
\(643\) −12027.9 −0.737692 −0.368846 0.929491i \(-0.620247\pi\)
−0.368846 + 0.929491i \(0.620247\pi\)
\(644\) −6779.62 −0.414836
\(645\) 36.2977 + 26.6481i 0.00221584 + 0.00162677i
\(646\) 23477.0i 1.42986i
\(647\) 11285.9i 0.685775i 0.939376 + 0.342888i \(0.111405\pi\)
−0.939376 + 0.342888i \(0.888595\pi\)
\(648\) −2637.67 + 1837.48i −0.159903 + 0.111393i
\(649\) −6473.08 4024.15i −0.391511 0.243393i
\(650\) 24666.9i 1.48848i
\(651\) 23000.3 31328.9i 1.38472 1.88614i
\(652\) −1735.89 −0.104268
\(653\) 9149.02i 0.548283i −0.961689 0.274141i \(-0.911606\pi\)
0.961689 0.274141i \(-0.0883936\pi\)
\(654\) 5403.81 7360.59i 0.323098 0.440095i
\(655\) 294.634i 0.0175760i
\(656\) 18629.5i 1.10878i
\(657\) 15563.0 4886.42i 0.924154 0.290164i
\(658\) 3482.82 0.206344
\(659\) −4684.57 −0.276912 −0.138456 0.990369i \(-0.544214\pi\)
−0.138456 + 0.990369i \(0.544214\pi\)
\(660\) −52.0909 + 70.9536i −0.00307218 + 0.00418464i
\(661\) −23736.6 −1.39675 −0.698373 0.715734i \(-0.746092\pi\)
−0.698373 + 0.715734i \(0.746092\pi\)
\(662\) −13567.9 −0.796575
\(663\) 13291.9 + 9758.32i 0.778604 + 0.571616i
\(664\) 6423.67 0.375432
\(665\) 352.929i 0.0205805i
\(666\) 35125.4 11028.6i 2.04367 0.641666i
\(667\) 9512.72i 0.552225i
\(668\) 10732.0i 0.621607i
\(669\) −15355.3 11273.2i −0.887399 0.651489i
\(670\) −114.178 −0.00658370
\(671\) 4548.79i 0.261705i
\(672\) 24737.6 + 18161.2i 1.42005 + 1.04253i
\(673\) 27614.0i 1.58164i −0.612052 0.790818i \(-0.709656\pi\)
0.612052 0.790818i \(-0.290344\pi\)
\(674\) 21440.2i 1.22529i
\(675\) 5666.05 16593.3i 0.323091 0.946185i
\(676\) −2914.81 −0.165840
\(677\) 13798.0i 0.783306i 0.920113 + 0.391653i \(0.128097\pi\)
−0.920113 + 0.391653i \(0.871903\pi\)
\(678\) −5757.72 4227.06i −0.326141 0.239438i
\(679\) 32559.6i 1.84024i
\(680\) 40.1462 0.00226402
\(681\) 13061.7 + 9589.31i 0.734986 + 0.539593i
\(682\) 19837.4i 1.11380i
\(683\) −16270.4 −0.911522 −0.455761 0.890102i \(-0.650633\pi\)
−0.455761 + 0.890102i \(0.650633\pi\)
\(684\) −5450.20 17358.6i −0.304669 0.970353i
\(685\) −172.842 −0.00964080
\(686\) −8346.00 −0.464507
\(687\) 7461.20 10163.0i 0.414356 0.564398i
\(688\) 4237.89i 0.234837i
\(689\) 5414.94 0.299409
\(690\) 70.4463 95.9556i 0.00388673 0.00529415i
\(691\) 27102.8i 1.49210i −0.665891 0.746049i \(-0.731948\pi\)
0.665891 0.746049i \(-0.268052\pi\)
\(692\) 16509.7 0.906941
\(693\) −3324.85 10589.4i −0.182252 0.580461i
\(694\) 2617.64 0.143176
\(695\) 179.148i 0.00977767i
\(696\) −3188.26 + 4342.76i −0.173636 + 0.236511i
\(697\) 16069.7 0.873288
\(698\) 45693.8i 2.47785i
\(699\) 10789.3 + 7921.04i 0.583820 + 0.428614i
\(700\) −20942.9 −1.13081
\(701\) 30512.1 1.64398 0.821988 0.569505i \(-0.192865\pi\)
0.821988 + 0.569505i \(0.192865\pi\)
\(702\) −26204.5 8947.97i −1.40887 0.481082i
\(703\) 34771.5i 1.86548i
\(704\) −5997.29 −0.321067
\(705\) −16.7013 + 22.7490i −0.000892208 + 0.00121529i
\(706\) 34665.1 1.84793
\(707\) −44259.3 −2.35437
\(708\) 6007.98 + 14985.1i 0.318917 + 0.795442i
\(709\) 27019.6 1.43123 0.715615 0.698495i \(-0.246146\pi\)
0.715615 + 0.698495i \(0.246146\pi\)
\(710\) −373.545 −0.0197449
\(711\) 4017.59 + 12795.8i 0.211915 + 0.674936i
\(712\) 643.750 0.0338842
\(713\) 12380.8i 0.650300i
\(714\) 17952.8 24453.7i 0.940989 1.28173i
\(715\) 126.524 0.00661778
\(716\) −1745.29 −0.0910956
\(717\) 13410.1 18266.1i 0.698480 0.951407i
\(718\) 41041.6i 2.13323i
\(719\) 29232.7 1.51627 0.758135 0.652098i \(-0.226111\pi\)
0.758135 + 0.652098i \(0.226111\pi\)
\(720\) −271.887 + 85.3663i −0.0140731 + 0.00441863i
\(721\) 33659.7i 1.73863i
\(722\) −10797.9 −0.556585
\(723\) −12737.7 9351.42i −0.655213 0.481028i
\(724\) −19996.0 −1.02644
\(725\) 29385.8i 1.50532i
\(726\) −16921.2 12422.8i −0.865022 0.635060i
\(727\) −2919.43 −0.148935 −0.0744676 0.997223i \(-0.523726\pi\)
−0.0744676 + 0.997223i \(0.523726\pi\)
\(728\) 5519.04i 0.280974i
\(729\) −15572.3 12038.5i −0.791152 0.611619i
\(730\) 342.096 0.0173446
\(731\) 3655.57 0.184960
\(732\) −5701.98 + 7766.72i −0.287912 + 0.392167i
\(733\) 21990.4 1.10809 0.554047 0.832485i \(-0.313083\pi\)
0.554047 + 0.832485i \(0.313083\pi\)
\(734\) 8133.52i 0.409010i
\(735\) −114.931 + 156.548i −0.00576774 + 0.00785630i
\(736\) 9775.95 0.489601
\(737\) 3391.33i 0.169500i
\(738\) −25746.1 + 8083.68i −1.28418 + 0.403204i
\(739\) 1784.00i 0.0888033i 0.999014 + 0.0444017i \(0.0141381\pi\)
−0.999014 + 0.0444017i \(0.985862\pi\)
\(740\) 356.323 0.0177009
\(741\) −15476.8 + 21081.1i −0.767280 + 1.04512i
\(742\) 9962.10i 0.492884i
\(743\) 3104.70i 0.153298i 0.997058 + 0.0766491i \(0.0244221\pi\)
−0.997058 + 0.0766491i \(0.975578\pi\)
\(744\) −4149.51 + 5652.08i −0.204473 + 0.278515i
\(745\) 307.451i 0.0151197i
\(746\) 20565.4 1.00932
\(747\) 11782.3 + 37526.0i 0.577098 + 1.83802i
\(748\) 7145.79i 0.349300i
\(749\) 26495.2i 1.29254i
\(750\) 435.269 592.884i 0.0211917 0.0288654i
\(751\) 4396.17i 0.213607i −0.994280 0.106803i \(-0.965938\pi\)
0.994280 0.106803i \(-0.0340615\pi\)
\(752\) −2656.03 −0.128797
\(753\) −18767.7 + 25563.7i −0.908279 + 1.23718i
\(754\) −46406.7 −2.24142
\(755\) −198.631 −0.00957474
\(756\) −7597.10 + 22248.4i −0.365482 + 1.07033i
\(757\) 5977.58 0.287000 0.143500 0.989650i \(-0.454164\pi\)
0.143500 + 0.989650i \(0.454164\pi\)
\(758\) −16518.7 −0.791537
\(759\) −2850.08 2092.40i −0.136300 0.100065i
\(760\) 63.6723i 0.00303900i
\(761\) 20959.5i 0.998400i 0.866487 + 0.499200i \(0.166373\pi\)
−0.866487 + 0.499200i \(0.833627\pi\)
\(762\) −7551.76 5544.16i −0.359018 0.263575i
\(763\) 11143.8i 0.528745i
\(764\) 5628.94 0.266555
\(765\) 73.6363 + 234.527i 0.00348016 + 0.0110841i
\(766\) 21837.2i 1.03004i
\(767\) 12252.2 19708.3i 0.576793 0.927806i
\(768\) −20967.7 15393.6i −0.985166 0.723264i
\(769\) 37081.2i 1.73886i −0.494056 0.869430i \(-0.664486\pi\)
0.494056 0.869430i \(-0.335514\pi\)
\(770\) 232.771i 0.0108941i
\(771\) 3388.21 4615.12i 0.158266 0.215576i
\(772\) 28091.1 1.30961
\(773\) 3721.27 0.173150 0.0865749 0.996245i \(-0.472408\pi\)
0.0865749 + 0.996245i \(0.472408\pi\)
\(774\) −5856.78 + 1838.90i −0.271987 + 0.0853977i
\(775\) 38245.5i 1.77267i
\(776\) 5874.12i 0.271738i
\(777\) −26589.6 + 36218.0i −1.22767 + 1.67222i
\(778\) 2014.37i 0.0928259i
\(779\) 25486.6i 1.17221i
\(780\) −216.030 158.599i −0.00991680 0.00728047i
\(781\) 11095.1i 0.508340i
\(782\) 9663.76i 0.441912i
\(783\) −31217.6 10659.8i −1.42481