Properties

Label 177.3.b.a.119.8
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.8
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.31

$q$-expansion

\(f(q)\) \(=\) \(q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} +O(q^{10})\) \(q-2.79604i q^{2} +(0.651071 - 2.92850i) q^{3} -3.81783 q^{4} -4.04341i q^{5} +(-8.18820 - 1.82042i) q^{6} +6.95609 q^{7} -0.509352i q^{8} +(-8.15221 - 3.81332i) q^{9} -11.3055 q^{10} +3.60723i q^{11} +(-2.48568 + 11.1805i) q^{12} +6.03188 q^{13} -19.4495i q^{14} +(-11.8411 - 2.63255i) q^{15} -16.6955 q^{16} +27.5797i q^{17} +(-10.6622 + 22.7939i) q^{18} +11.5320 q^{19} +15.4371i q^{20} +(4.52891 - 20.3709i) q^{21} +10.0859 q^{22} -6.63792i q^{23} +(-1.49164 - 0.331625i) q^{24} +8.65080 q^{25} -16.8654i q^{26} +(-16.4750 + 21.3910i) q^{27} -26.5572 q^{28} +7.59974i q^{29} +(-7.36072 + 33.1083i) q^{30} +40.0199 q^{31} +44.6438i q^{32} +(10.5638 + 2.34856i) q^{33} +77.1139 q^{34} -28.1264i q^{35} +(31.1238 + 14.5586i) q^{36} -53.5956 q^{37} -32.2439i q^{38} +(3.92718 - 17.6643i) q^{39} -2.05952 q^{40} -33.0823i q^{41} +(-56.9578 - 12.6630i) q^{42} -19.3543 q^{43} -13.7718i q^{44} +(-15.4188 + 32.9628i) q^{45} -18.5599 q^{46} -51.4877i q^{47} +(-10.8700 + 48.8927i) q^{48} -0.612818 q^{49} -24.1880i q^{50} +(80.7671 + 17.9564i) q^{51} -23.0287 q^{52} -40.9324i q^{53} +(59.8101 + 46.0647i) q^{54} +14.5855 q^{55} -3.54310i q^{56} +(7.50816 - 33.7715i) q^{57} +21.2492 q^{58} +7.68115i q^{59} +(45.2075 + 10.0506i) q^{60} +48.9309 q^{61} -111.897i q^{62} +(-56.7075 - 26.5258i) q^{63} +58.0439 q^{64} -24.3894i q^{65} +(6.56667 - 29.5367i) q^{66} +85.3697 q^{67} -105.295i q^{68} +(-19.4391 - 4.32176i) q^{69} -78.6424 q^{70} -32.2458i q^{71} +(-1.94232 + 4.15235i) q^{72} +71.6167 q^{73} +149.855i q^{74} +(5.63229 - 25.3339i) q^{75} -44.0272 q^{76} +25.0922i q^{77} +(-49.3902 - 10.9806i) q^{78} -85.8602 q^{79} +67.5068i q^{80} +(51.9171 + 62.1741i) q^{81} -92.4993 q^{82} +131.770i q^{83} +(-17.2906 + 77.7727i) q^{84} +111.516 q^{85} +54.1152i q^{86} +(22.2558 + 4.94797i) q^{87} +1.83735 q^{88} -96.1523i q^{89} +(92.1652 + 43.1117i) q^{90} +41.9583 q^{91} +25.3425i q^{92} +(26.0558 - 117.198i) q^{93} -143.962 q^{94} -46.6287i q^{95} +(130.739 + 29.0663i) q^{96} -80.8331 q^{97} +1.71346i q^{98} +(13.7555 - 29.4069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.79604i 1.39802i −0.715112 0.699010i \(-0.753624\pi\)
0.715112 0.699010i \(-0.246376\pi\)
\(3\) 0.651071 2.92850i 0.217024 0.976166i
\(4\) −3.81783 −0.954458
\(5\) 4.04341i 0.808683i −0.914608 0.404341i \(-0.867501\pi\)
0.914608 0.404341i \(-0.132499\pi\)
\(6\) −8.18820 1.82042i −1.36470 0.303403i
\(7\) 6.95609 0.993727 0.496864 0.867829i \(-0.334485\pi\)
0.496864 + 0.867829i \(0.334485\pi\)
\(8\) 0.509352i 0.0636690i
\(9\) −8.15221 3.81332i −0.905801 0.423703i
\(10\) −11.3055 −1.13055
\(11\) 3.60723i 0.327930i 0.986466 + 0.163965i \(0.0524284\pi\)
−0.986466 + 0.163965i \(0.947572\pi\)
\(12\) −2.48568 + 11.1805i −0.207140 + 0.931709i
\(13\) 6.03188 0.463990 0.231995 0.972717i \(-0.425475\pi\)
0.231995 + 0.972717i \(0.425475\pi\)
\(14\) 19.4495i 1.38925i
\(15\) −11.8411 2.63255i −0.789409 0.175503i
\(16\) −16.6955 −1.04347
\(17\) 27.5797i 1.62234i 0.584813 + 0.811168i \(0.301168\pi\)
−0.584813 + 0.811168i \(0.698832\pi\)
\(18\) −10.6622 + 22.7939i −0.592344 + 1.26633i
\(19\) 11.5320 0.606948 0.303474 0.952840i \(-0.401854\pi\)
0.303474 + 0.952840i \(0.401854\pi\)
\(20\) 15.4371i 0.771854i
\(21\) 4.52891 20.3709i 0.215662 0.970043i
\(22\) 10.0859 0.458452
\(23\) 6.63792i 0.288605i −0.989534 0.144303i \(-0.953906\pi\)
0.989534 0.144303i \(-0.0460939\pi\)
\(24\) −1.49164 0.331625i −0.0621515 0.0138177i
\(25\) 8.65080 0.346032
\(26\) 16.8654i 0.648667i
\(27\) −16.4750 + 21.3910i −0.610185 + 0.792259i
\(28\) −26.5572 −0.948470
\(29\) 7.59974i 0.262060i 0.991378 + 0.131030i \(0.0418284\pi\)
−0.991378 + 0.131030i \(0.958172\pi\)
\(30\) −7.36072 + 33.1083i −0.245357 + 1.10361i
\(31\) 40.0199 1.29096 0.645482 0.763776i \(-0.276657\pi\)
0.645482 + 0.763776i \(0.276657\pi\)
\(32\) 44.6438i 1.39512i
\(33\) 10.5638 + 2.34856i 0.320114 + 0.0711685i
\(34\) 77.1139 2.26806
\(35\) 28.1264i 0.803610i
\(36\) 31.1238 + 14.5586i 0.864549 + 0.404406i
\(37\) −53.5956 −1.44853 −0.724264 0.689522i \(-0.757820\pi\)
−0.724264 + 0.689522i \(0.757820\pi\)
\(38\) 32.2439i 0.848524i
\(39\) 3.92718 17.6643i 0.100697 0.452932i
\(40\) −2.05952 −0.0514880
\(41\) 33.0823i 0.806885i −0.915005 0.403442i \(-0.867814\pi\)
0.915005 0.403442i \(-0.132186\pi\)
\(42\) −56.9578 12.6630i −1.35614 0.301500i
\(43\) −19.3543 −0.450099 −0.225049 0.974347i \(-0.572254\pi\)
−0.225049 + 0.974347i \(0.572254\pi\)
\(44\) 13.7718i 0.312995i
\(45\) −15.4188 + 32.9628i −0.342641 + 0.732506i
\(46\) −18.5599 −0.403476
\(47\) 51.4877i 1.09548i −0.836647 0.547742i \(-0.815488\pi\)
0.836647 0.547742i \(-0.184512\pi\)
\(48\) −10.8700 + 48.8927i −0.226457 + 1.01860i
\(49\) −0.612818 −0.0125065
\(50\) 24.1880i 0.483759i
\(51\) 80.7671 + 17.9564i 1.58367 + 0.352085i
\(52\) −23.0287 −0.442859
\(53\) 40.9324i 0.772309i −0.922434 0.386155i \(-0.873803\pi\)
0.922434 0.386155i \(-0.126197\pi\)
\(54\) 59.8101 + 46.0647i 1.10759 + 0.853050i
\(55\) 14.5855 0.265191
\(56\) 3.54310i 0.0632696i
\(57\) 7.50816 33.7715i 0.131722 0.592482i
\(58\) 21.2492 0.366365
\(59\) 7.68115i 0.130189i
\(60\) 45.2075 + 10.0506i 0.753458 + 0.167511i
\(61\) 48.9309 0.802146 0.401073 0.916046i \(-0.368637\pi\)
0.401073 + 0.916046i \(0.368637\pi\)
\(62\) 111.897i 1.80479i
\(63\) −56.7075 26.5258i −0.900119 0.421045i
\(64\) 58.0439 0.906936
\(65\) 24.3894i 0.375221i
\(66\) 6.56667 29.5367i 0.0994950 0.447525i
\(67\) 85.3697 1.27417 0.637087 0.770792i \(-0.280139\pi\)
0.637087 + 0.770792i \(0.280139\pi\)
\(68\) 105.295i 1.54845i
\(69\) −19.4391 4.32176i −0.281727 0.0626342i
\(70\) −78.6424 −1.12346
\(71\) 32.2458i 0.454166i −0.973875 0.227083i \(-0.927081\pi\)
0.973875 0.227083i \(-0.0729188\pi\)
\(72\) −1.94232 + 4.15235i −0.0269767 + 0.0576715i
\(73\) 71.6167 0.981050 0.490525 0.871427i \(-0.336805\pi\)
0.490525 + 0.871427i \(0.336805\pi\)
\(74\) 149.855i 2.02507i
\(75\) 5.63229 25.3339i 0.0750972 0.337785i
\(76\) −44.0272 −0.579306
\(77\) 25.0922i 0.325873i
\(78\) −49.3902 10.9806i −0.633207 0.140776i
\(79\) −85.8602 −1.08684 −0.543419 0.839462i \(-0.682871\pi\)
−0.543419 + 0.839462i \(0.682871\pi\)
\(80\) 67.5068i 0.843835i
\(81\) 51.9171 + 62.1741i 0.640952 + 0.767581i
\(82\) −92.4993 −1.12804
\(83\) 131.770i 1.58759i 0.608185 + 0.793795i \(0.291898\pi\)
−0.608185 + 0.793795i \(0.708102\pi\)
\(84\) −17.2906 + 77.7727i −0.205841 + 0.925865i
\(85\) 111.516 1.31196
\(86\) 54.1152i 0.629247i
\(87\) 22.2558 + 4.94797i 0.255814 + 0.0568732i
\(88\) 1.83735 0.0208790
\(89\) 96.1523i 1.08036i −0.841549 0.540182i \(-0.818356\pi\)
0.841549 0.540182i \(-0.181644\pi\)
\(90\) 92.1652 + 43.1117i 1.02406 + 0.479019i
\(91\) 41.9583 0.461080
\(92\) 25.3425i 0.275462i
\(93\) 26.0558 117.198i 0.280170 1.26019i
\(94\) −143.962 −1.53151
\(95\) 46.6287i 0.490828i
\(96\) 130.739 + 29.0663i 1.36187 + 0.302774i
\(97\) −80.8331 −0.833331 −0.416665 0.909060i \(-0.636801\pi\)
−0.416665 + 0.909060i \(0.636801\pi\)
\(98\) 1.71346i 0.0174843i
\(99\) 13.7555 29.4069i 0.138945 0.297039i
\(100\) −33.0273 −0.330273
\(101\) 106.431i 1.05378i 0.849935 + 0.526888i \(0.176641\pi\)
−0.849935 + 0.526888i \(0.823359\pi\)
\(102\) 50.2067 225.828i 0.492222 2.21400i
\(103\) −98.8938 −0.960134 −0.480067 0.877232i \(-0.659388\pi\)
−0.480067 + 0.877232i \(0.659388\pi\)
\(104\) 3.07235i 0.0295418i
\(105\) −82.3680 18.3123i −0.784457 0.174403i
\(106\) −114.449 −1.07970
\(107\) 170.612i 1.59451i 0.603645 + 0.797253i \(0.293714\pi\)
−0.603645 + 0.797253i \(0.706286\pi\)
\(108\) 62.8987 81.6672i 0.582396 0.756178i
\(109\) 158.872 1.45754 0.728769 0.684760i \(-0.240093\pi\)
0.728769 + 0.684760i \(0.240093\pi\)
\(110\) 40.7817i 0.370742i
\(111\) −34.8945 + 156.955i −0.314365 + 1.41400i
\(112\) −116.135 −1.03692
\(113\) 122.753i 1.08631i 0.839632 + 0.543156i \(0.182771\pi\)
−0.839632 + 0.543156i \(0.817229\pi\)
\(114\) −94.4263 20.9931i −0.828301 0.184150i
\(115\) −26.8399 −0.233390
\(116\) 29.0145i 0.250125i
\(117\) −49.1731 23.0015i −0.420283 0.196594i
\(118\) 21.4768 0.182007
\(119\) 191.847i 1.61216i
\(120\) −1.34090 + 6.03131i −0.0111741 + 0.0502609i
\(121\) 107.988 0.892462
\(122\) 136.813i 1.12142i
\(123\) −96.8814 21.5389i −0.787654 0.175113i
\(124\) −152.789 −1.23217
\(125\) 136.064i 1.08851i
\(126\) −74.1672 + 158.556i −0.588629 + 1.25838i
\(127\) −158.076 −1.24469 −0.622347 0.782742i \(-0.713821\pi\)
−0.622347 + 0.782742i \(0.713821\pi\)
\(128\) 16.2824i 0.127206i
\(129\) −12.6010 + 56.6789i −0.0976822 + 0.439371i
\(130\) −68.1936 −0.524566
\(131\) 164.456i 1.25539i 0.778459 + 0.627696i \(0.216002\pi\)
−0.778459 + 0.627696i \(0.783998\pi\)
\(132\) −40.3306 8.96641i −0.305535 0.0679274i
\(133\) 80.2176 0.603140
\(134\) 238.697i 1.78132i
\(135\) 86.4927 + 66.6152i 0.640686 + 0.493446i
\(136\) 14.0478 0.103292
\(137\) 215.202i 1.57082i −0.618977 0.785409i \(-0.712453\pi\)
0.618977 0.785409i \(-0.287547\pi\)
\(138\) −12.0838 + 54.3526i −0.0875638 + 0.393859i
\(139\) −74.2004 −0.533816 −0.266908 0.963722i \(-0.586002\pi\)
−0.266908 + 0.963722i \(0.586002\pi\)
\(140\) 107.382i 0.767012i
\(141\) −150.782 33.5222i −1.06937 0.237746i
\(142\) −90.1604 −0.634932
\(143\) 21.7583i 0.152156i
\(144\) 136.105 + 63.6653i 0.945175 + 0.442120i
\(145\) 30.7289 0.211923
\(146\) 200.243i 1.37153i
\(147\) −0.398988 + 1.79464i −0.00271420 + 0.0122084i
\(148\) 204.619 1.38256
\(149\) 241.103i 1.61814i 0.587711 + 0.809071i \(0.300029\pi\)
−0.587711 + 0.809071i \(0.699971\pi\)
\(150\) −70.8344 15.7481i −0.472230 0.104987i
\(151\) 30.4950 0.201954 0.100977 0.994889i \(-0.467803\pi\)
0.100977 + 0.994889i \(0.467803\pi\)
\(152\) 5.87385i 0.0386437i
\(153\) 105.170 224.836i 0.687388 1.46951i
\(154\) 70.1587 0.455576
\(155\) 161.817i 1.04398i
\(156\) −14.9933 + 67.4395i −0.0961110 + 0.432304i
\(157\) 65.8024 0.419124 0.209562 0.977795i \(-0.432796\pi\)
0.209562 + 0.977795i \(0.432796\pi\)
\(158\) 240.068i 1.51942i
\(159\) −119.870 26.6499i −0.753902 0.167609i
\(160\) 180.513 1.12821
\(161\) 46.1740i 0.286795i
\(162\) 173.841 145.162i 1.07309 0.896063i
\(163\) −71.4607 −0.438409 −0.219205 0.975679i \(-0.570346\pi\)
−0.219205 + 0.975679i \(0.570346\pi\)
\(164\) 126.303i 0.770137i
\(165\) 9.49621 42.7137i 0.0575528 0.258871i
\(166\) 368.434 2.21948
\(167\) 94.7545i 0.567392i 0.958914 + 0.283696i \(0.0915607\pi\)
−0.958914 + 0.283696i \(0.908439\pi\)
\(168\) −10.3760 2.30681i −0.0617617 0.0137310i
\(169\) −132.616 −0.784713
\(170\) 311.804i 1.83414i
\(171\) −94.0113 43.9753i −0.549774 0.257165i
\(172\) 73.8913 0.429600
\(173\) 92.2355i 0.533153i 0.963814 + 0.266576i \(0.0858925\pi\)
−0.963814 + 0.266576i \(0.914108\pi\)
\(174\) 13.8347 62.2281i 0.0795099 0.357633i
\(175\) 60.1757 0.343861
\(176\) 60.2244i 0.342184i
\(177\) 22.4942 + 5.00097i 0.127086 + 0.0282541i
\(178\) −268.846 −1.51037
\(179\) 48.5009i 0.270955i −0.990780 0.135477i \(-0.956743\pi\)
0.990780 0.135477i \(-0.0432568\pi\)
\(180\) 58.8666 125.846i 0.327036 0.699146i
\(181\) 177.194 0.978975 0.489487 0.872010i \(-0.337184\pi\)
0.489487 + 0.872010i \(0.337184\pi\)
\(182\) 117.317i 0.644598i
\(183\) 31.8575 143.294i 0.174085 0.783028i
\(184\) −3.38104 −0.0183752
\(185\) 216.709i 1.17140i
\(186\) −327.690 72.8530i −1.76178 0.391683i
\(187\) −99.4863 −0.532012
\(188\) 196.572i 1.04559i
\(189\) −114.601 + 148.798i −0.606357 + 0.787289i
\(190\) −130.376 −0.686187
\(191\) 137.245i 0.718559i −0.933230 0.359279i \(-0.883023\pi\)
0.933230 0.359279i \(-0.116977\pi\)
\(192\) 37.7907 169.981i 0.196827 0.885320i
\(193\) 363.765 1.88479 0.942396 0.334499i \(-0.108567\pi\)
0.942396 + 0.334499i \(0.108567\pi\)
\(194\) 226.012i 1.16501i
\(195\) −71.4242 15.8792i −0.366278 0.0814319i
\(196\) 2.33963 0.0119369
\(197\) 117.106i 0.594445i −0.954808 0.297223i \(-0.903940\pi\)
0.954808 0.297223i \(-0.0960603\pi\)
\(198\) −82.2228 38.4610i −0.415266 0.194247i
\(199\) −176.062 −0.884732 −0.442366 0.896835i \(-0.645861\pi\)
−0.442366 + 0.896835i \(0.645861\pi\)
\(200\) 4.40630i 0.0220315i
\(201\) 55.5818 250.005i 0.276526 1.24381i
\(202\) 297.586 1.47320
\(203\) 52.8645i 0.260416i
\(204\) −308.355 68.5543i −1.51155 0.336051i
\(205\) −133.765 −0.652514
\(206\) 276.511i 1.34229i
\(207\) −25.3125 + 54.1137i −0.122283 + 0.261419i
\(208\) −100.705 −0.484159
\(209\) 41.5985i 0.199036i
\(210\) −51.2018 + 230.304i −0.243818 + 1.09669i
\(211\) 9.09339 0.0430966 0.0215483 0.999768i \(-0.493140\pi\)
0.0215483 + 0.999768i \(0.493140\pi\)
\(212\) 156.273i 0.737136i
\(213\) −94.4317 20.9943i −0.443341 0.0985648i
\(214\) 477.038 2.22915
\(215\) 78.2573i 0.363987i
\(216\) 10.8955 + 8.39157i 0.0504423 + 0.0388498i
\(217\) 278.382 1.28287
\(218\) 444.211i 2.03767i
\(219\) 46.6276 209.729i 0.212911 0.957668i
\(220\) −55.6850 −0.253114
\(221\) 166.357i 0.752748i
\(222\) 438.851 + 97.5665i 1.97681 + 0.439489i
\(223\) 244.350 1.09574 0.547869 0.836564i \(-0.315439\pi\)
0.547869 + 0.836564i \(0.315439\pi\)
\(224\) 310.546i 1.38637i
\(225\) −70.5232 32.9883i −0.313436 0.146615i
\(226\) 343.223 1.51868
\(227\) 46.8646i 0.206452i 0.994658 + 0.103226i \(0.0329165\pi\)
−0.994658 + 0.103226i \(0.967084\pi\)
\(228\) −28.6649 + 128.934i −0.125723 + 0.565499i
\(229\) −142.421 −0.621925 −0.310963 0.950422i \(-0.600651\pi\)
−0.310963 + 0.950422i \(0.600651\pi\)
\(230\) 75.0453i 0.326284i
\(231\) 73.4825 + 16.3368i 0.318106 + 0.0707221i
\(232\) 3.87094 0.0166851
\(233\) 226.548i 0.972308i −0.873873 0.486154i \(-0.838399\pi\)
0.873873 0.486154i \(-0.161601\pi\)
\(234\) −64.3131 + 137.490i −0.274842 + 0.587564i
\(235\) −208.186 −0.885899
\(236\) 29.3253i 0.124260i
\(237\) −55.9011 + 251.442i −0.235870 + 1.06093i
\(238\) 536.411 2.25383
\(239\) 50.3598i 0.210711i 0.994435 + 0.105355i \(0.0335980\pi\)
−0.994435 + 0.105355i \(0.966402\pi\)
\(240\) 197.694 + 43.9517i 0.823723 + 0.183132i
\(241\) −252.513 −1.04777 −0.523887 0.851788i \(-0.675519\pi\)
−0.523887 + 0.851788i \(0.675519\pi\)
\(242\) 301.938i 1.24768i
\(243\) 215.878 111.559i 0.888388 0.459093i
\(244\) −186.810 −0.765614
\(245\) 2.47788i 0.0101138i
\(246\) −60.2237 + 270.884i −0.244812 + 1.10116i
\(247\) 69.5596 0.281618
\(248\) 20.3842i 0.0821943i
\(249\) 385.888 + 85.7917i 1.54975 + 0.344545i
\(250\) −380.441 −1.52176
\(251\) 115.362i 0.459610i −0.973237 0.229805i \(-0.926191\pi\)
0.973237 0.229805i \(-0.0738088\pi\)
\(252\) 216.500 + 101.271i 0.859126 + 0.401869i
\(253\) 23.9445 0.0946422
\(254\) 441.987i 1.74011i
\(255\) 72.6050 326.575i 0.284726 1.28069i
\(256\) 277.702 1.08477
\(257\) 67.7037i 0.263439i 0.991287 + 0.131719i \(0.0420498\pi\)
−0.991287 + 0.131719i \(0.957950\pi\)
\(258\) 158.476 + 35.2329i 0.614250 + 0.136562i
\(259\) −372.816 −1.43944
\(260\) 93.1145i 0.358133i
\(261\) 28.9803 61.9547i 0.111035 0.237374i
\(262\) 459.826 1.75506
\(263\) 295.997i 1.12546i 0.826639 + 0.562732i \(0.190250\pi\)
−0.826639 + 0.562732i \(0.809750\pi\)
\(264\) 1.19624 5.38067i 0.00453123 0.0203813i
\(265\) −165.507 −0.624553
\(266\) 224.292i 0.843202i
\(267\) −281.582 62.6020i −1.05461 0.234465i
\(268\) −325.927 −1.21615
\(269\) 446.809i 1.66100i 0.557019 + 0.830500i \(0.311945\pi\)
−0.557019 + 0.830500i \(0.688055\pi\)
\(270\) 186.259 241.837i 0.689847 0.895692i
\(271\) 111.864 0.412781 0.206391 0.978470i \(-0.433828\pi\)
0.206391 + 0.978470i \(0.433828\pi\)
\(272\) 460.457i 1.69286i
\(273\) 27.3178 122.875i 0.100065 0.450091i
\(274\) −601.713 −2.19603
\(275\) 31.2054i 0.113474i
\(276\) 74.2154 + 16.4998i 0.268896 + 0.0597817i
\(277\) −245.137 −0.884970 −0.442485 0.896776i \(-0.645903\pi\)
−0.442485 + 0.896776i \(0.645903\pi\)
\(278\) 207.467i 0.746285i
\(279\) −326.250 152.609i −1.16936 0.546985i
\(280\) −14.3262 −0.0511650
\(281\) 197.586i 0.703153i −0.936159 0.351576i \(-0.885646\pi\)
0.936159 0.351576i \(-0.114354\pi\)
\(282\) −93.7294 + 421.592i −0.332374 + 1.49501i
\(283\) −355.505 −1.25620 −0.628101 0.778132i \(-0.716168\pi\)
−0.628101 + 0.778132i \(0.716168\pi\)
\(284\) 123.109i 0.433482i
\(285\) −136.552 30.3586i −0.479130 0.106521i
\(286\) 60.8372 0.212717
\(287\) 230.123i 0.801823i
\(288\) 170.241 363.946i 0.591116 1.26370i
\(289\) −471.640 −1.63197
\(290\) 85.9192i 0.296273i
\(291\) −52.6281 + 236.720i −0.180853 + 0.813469i
\(292\) −273.420 −0.936371
\(293\) 438.814i 1.49766i −0.662762 0.748830i \(-0.730616\pi\)
0.662762 0.748830i \(-0.269384\pi\)
\(294\) 5.01787 + 1.11559i 0.0170676 + 0.00379451i
\(295\) 31.0581 0.105282
\(296\) 27.2990i 0.0922264i
\(297\) −77.1622 59.4290i −0.259805 0.200098i
\(298\) 674.134 2.26219
\(299\) 40.0391i 0.133910i
\(300\) −21.5031 + 96.7204i −0.0716771 + 0.322401i
\(301\) −134.630 −0.447276
\(302\) 85.2652i 0.282335i
\(303\) 311.684 + 69.2944i 1.02866 + 0.228694i
\(304\) −192.532 −0.633330
\(305\) 197.848i 0.648682i
\(306\) −628.649 294.060i −2.05441 0.960982i
\(307\) −519.064 −1.69076 −0.845381 0.534163i \(-0.820627\pi\)
−0.845381 + 0.534163i \(0.820627\pi\)
\(308\) 95.7977i 0.311032i
\(309\) −64.3869 + 289.610i −0.208372 + 0.937250i
\(310\) −452.446 −1.45950
\(311\) 327.149i 1.05193i −0.850507 0.525963i \(-0.823705\pi\)
0.850507 0.525963i \(-0.176295\pi\)
\(312\) −8.99737 2.00032i −0.0288377 0.00641127i
\(313\) −309.990 −0.990383 −0.495191 0.868784i \(-0.664902\pi\)
−0.495191 + 0.868784i \(0.664902\pi\)
\(314\) 183.986i 0.585943i
\(315\) −107.255 + 229.292i −0.340492 + 0.727911i
\(316\) 327.800 1.03734
\(317\) 335.223i 1.05749i −0.848782 0.528743i \(-0.822664\pi\)
0.848782 0.528743i \(-0.177336\pi\)
\(318\) −74.5142 + 335.162i −0.234321 + 1.05397i
\(319\) −27.4140 −0.0859372
\(320\) 234.696i 0.733423i
\(321\) 499.637 + 111.081i 1.55650 + 0.346046i
\(322\) −129.104 −0.400945
\(323\) 318.049i 0.984673i
\(324\) −198.211 237.370i −0.611762 0.732623i
\(325\) 52.1805 0.160556
\(326\) 199.807i 0.612904i
\(327\) 103.437 465.255i 0.316320 1.42280i
\(328\) −16.8505 −0.0513735
\(329\) 358.153i 1.08861i
\(330\) −119.429 26.5518i −0.361906 0.0804599i
\(331\) 379.087 1.14528 0.572639 0.819808i \(-0.305920\pi\)
0.572639 + 0.819808i \(0.305920\pi\)
\(332\) 503.076i 1.51529i
\(333\) 436.922 + 204.377i 1.31208 + 0.613745i
\(334\) 264.937 0.793225
\(335\) 345.185i 1.03040i
\(336\) −75.6124 + 340.102i −0.225037 + 1.01221i
\(337\) 308.875 0.916542 0.458271 0.888813i \(-0.348469\pi\)
0.458271 + 0.888813i \(0.348469\pi\)
\(338\) 370.801i 1.09704i
\(339\) 359.483 + 79.9211i 1.06042 + 0.235756i
\(340\) −425.750 −1.25221
\(341\) 144.361i 0.423345i
\(342\) −122.957 + 262.859i −0.359522 + 0.768594i
\(343\) −345.111 −1.00616
\(344\) 9.85813i 0.0286573i
\(345\) −17.4747 + 78.6005i −0.0506512 + 0.227828i
\(346\) 257.894 0.745358
\(347\) 515.591i 1.48585i 0.669373 + 0.742926i \(0.266563\pi\)
−0.669373 + 0.742926i \(0.733437\pi\)
\(348\) −84.9690 18.8905i −0.244164 0.0542831i
\(349\) 540.605 1.54901 0.774506 0.632567i \(-0.217999\pi\)
0.774506 + 0.632567i \(0.217999\pi\)
\(350\) 168.254i 0.480725i
\(351\) −99.3751 + 129.028i −0.283120 + 0.367601i
\(352\) −161.040 −0.457501
\(353\) 34.9577i 0.0990304i −0.998773 0.0495152i \(-0.984232\pi\)
0.998773 0.0495152i \(-0.0157676\pi\)
\(354\) 13.9829 62.8947i 0.0394998 0.177669i
\(355\) −130.383 −0.367276
\(356\) 367.093i 1.03116i
\(357\) 561.823 + 124.906i 1.57374 + 0.349877i
\(358\) −135.610 −0.378800
\(359\) 474.613i 1.32204i 0.750368 + 0.661021i \(0.229876\pi\)
−0.750368 + 0.661021i \(0.770124\pi\)
\(360\) 16.7897 + 7.85362i 0.0466379 + 0.0218156i
\(361\) −228.013 −0.631615
\(362\) 495.442i 1.36863i
\(363\) 70.3078 316.242i 0.193686 0.871191i
\(364\) −160.190 −0.440081
\(365\) 289.576i 0.793359i
\(366\) −400.656 89.0748i −1.09469 0.243374i
\(367\) −573.939 −1.56387 −0.781934 0.623362i \(-0.785767\pi\)
−0.781934 + 0.623362i \(0.785767\pi\)
\(368\) 110.823i 0.301150i
\(369\) −126.153 + 269.694i −0.341879 + 0.730877i
\(370\) 605.927 1.63764
\(371\) 284.729i 0.767465i
\(372\) −99.4766 + 447.443i −0.267410 + 1.20280i
\(373\) 485.686 1.30211 0.651053 0.759032i \(-0.274327\pi\)
0.651053 + 0.759032i \(0.274327\pi\)
\(374\) 278.167i 0.743763i
\(375\) −398.464 88.5875i −1.06257 0.236233i
\(376\) −26.2254 −0.0697484
\(377\) 45.8407i 0.121593i
\(378\) 416.044 + 320.430i 1.10065 + 0.847699i
\(379\) −599.727 −1.58239 −0.791196 0.611562i \(-0.790541\pi\)
−0.791196 + 0.611562i \(0.790541\pi\)
\(380\) 178.020i 0.468475i
\(381\) −102.919 + 462.926i −0.270128 + 1.21503i
\(382\) −383.742 −1.00456
\(383\) 51.7725i 0.135176i −0.997713 0.0675881i \(-0.978470\pi\)
0.997713 0.0675881i \(-0.0215304\pi\)
\(384\) 47.6829 + 10.6010i 0.124174 + 0.0276067i
\(385\) 101.458 0.263528
\(386\) 1017.10i 2.63498i
\(387\) 157.780 + 73.8040i 0.407700 + 0.190708i
\(388\) 308.607 0.795379
\(389\) 505.152i 1.29859i 0.760536 + 0.649296i \(0.224936\pi\)
−0.760536 + 0.649296i \(0.775064\pi\)
\(390\) −44.3989 + 199.705i −0.113843 + 0.512064i
\(391\) 183.072 0.468215
\(392\) 0.312140i 0.000796275i
\(393\) 481.610 + 107.073i 1.22547 + 0.272450i
\(394\) −327.432 −0.831046
\(395\) 347.168i 0.878908i
\(396\) −52.5163 + 112.270i −0.132617 + 0.283511i
\(397\) 372.570 0.938465 0.469232 0.883075i \(-0.344531\pi\)
0.469232 + 0.883075i \(0.344531\pi\)
\(398\) 492.275i 1.23687i
\(399\) 52.2274 234.917i 0.130896 0.588765i
\(400\) −144.429 −0.361073
\(401\) 420.779i 1.04933i 0.851310 + 0.524663i \(0.175809\pi\)
−0.851310 + 0.524663i \(0.824191\pi\)
\(402\) −699.024 155.409i −1.73887 0.386589i
\(403\) 241.395 0.598995
\(404\) 406.337i 1.00578i
\(405\) 251.395 209.922i 0.620730 0.518327i
\(406\) 147.811 0.364067
\(407\) 193.331i 0.475016i
\(408\) 9.14611 41.1389i 0.0224169 0.100831i
\(409\) 392.844 0.960500 0.480250 0.877132i \(-0.340546\pi\)
0.480250 + 0.877132i \(0.340546\pi\)
\(410\) 374.013i 0.912227i
\(411\) −630.219 140.112i −1.53338 0.340905i
\(412\) 377.560 0.916407
\(413\) 53.4307i 0.129372i
\(414\) 151.304 + 70.7748i 0.365469 + 0.170954i
\(415\) 532.801 1.28386
\(416\) 269.286i 0.647322i
\(417\) −48.3098 + 217.296i −0.115851 + 0.521093i
\(418\) 116.311 0.278256
\(419\) 286.270i 0.683223i 0.939841 + 0.341612i \(0.110973\pi\)
−0.939841 + 0.341612i \(0.889027\pi\)
\(420\) 314.467 + 69.9131i 0.748731 + 0.166460i
\(421\) 629.689 1.49570 0.747849 0.663869i \(-0.231087\pi\)
0.747849 + 0.663869i \(0.231087\pi\)
\(422\) 25.4255i 0.0602499i
\(423\) −196.339 + 419.739i −0.464159 + 0.992291i
\(424\) −20.8490 −0.0491721
\(425\) 238.587i 0.561380i
\(426\) −58.7009 + 264.035i −0.137795 + 0.619800i
\(427\) 340.368 0.797114
\(428\) 651.368i 1.52189i
\(429\) 63.7193 + 14.1662i 0.148530 + 0.0330215i
\(430\) 218.810 0.508861
\(431\) 125.145i 0.290359i −0.989405 0.145179i \(-0.953624\pi\)
0.989405 0.145179i \(-0.0463759\pi\)
\(432\) 275.058 357.133i 0.636708 0.826697i
\(433\) −336.848 −0.777941 −0.388970 0.921250i \(-0.627169\pi\)
−0.388970 + 0.921250i \(0.627169\pi\)
\(434\) 778.366i 1.79347i
\(435\) 20.0067 89.9895i 0.0459924 0.206872i
\(436\) −606.545 −1.39116
\(437\) 76.5485i 0.175168i
\(438\) −586.411 130.372i −1.33884 0.297654i
\(439\) 204.185 0.465115 0.232557 0.972583i \(-0.425291\pi\)
0.232557 + 0.972583i \(0.425291\pi\)
\(440\) 7.42916i 0.0168845i
\(441\) 4.99582 + 2.33687i 0.0113284 + 0.00529903i
\(442\) 465.142 1.05236
\(443\) 367.998i 0.830695i 0.909663 + 0.415348i \(0.136340\pi\)
−0.909663 + 0.415348i \(0.863660\pi\)
\(444\) 133.221 599.226i 0.300048 1.34961i
\(445\) −388.784 −0.873671
\(446\) 683.211i 1.53186i
\(447\) 706.070 + 156.975i 1.57958 + 0.351175i
\(448\) 403.758 0.901247
\(449\) 42.2232i 0.0940384i 0.998894 + 0.0470192i \(0.0149722\pi\)
−0.998894 + 0.0470192i \(0.985028\pi\)
\(450\) −92.2366 + 197.185i −0.204970 + 0.438190i
\(451\) 119.335 0.264601
\(452\) 468.651i 1.03684i
\(453\) 19.8544 89.3046i 0.0438288 0.197140i
\(454\) 131.035 0.288624
\(455\) 169.655i 0.372867i
\(456\) −17.2016 3.82429i −0.0377227 0.00838661i
\(457\) −454.706 −0.994981 −0.497491 0.867469i \(-0.665745\pi\)
−0.497491 + 0.867469i \(0.665745\pi\)
\(458\) 398.214i 0.869464i
\(459\) −589.957 454.375i −1.28531 0.989925i
\(460\) 102.470 0.222761
\(461\) 101.873i 0.220984i 0.993877 + 0.110492i \(0.0352426\pi\)
−0.993877 + 0.110492i \(0.964757\pi\)
\(462\) 45.6783 205.460i 0.0988709 0.444718i
\(463\) 835.368 1.80425 0.902125 0.431475i \(-0.142007\pi\)
0.902125 + 0.431475i \(0.142007\pi\)
\(464\) 126.881i 0.273451i
\(465\) −473.881 105.354i −1.01910 0.226568i
\(466\) −633.436 −1.35931
\(467\) 5.68550i 0.0121745i 0.999981 + 0.00608726i \(0.00193765\pi\)
−0.999981 + 0.00608726i \(0.998062\pi\)
\(468\) 187.735 + 87.8158i 0.401142 + 0.187641i
\(469\) 593.839 1.26618
\(470\) 582.097i 1.23850i
\(471\) 42.8421 192.702i 0.0909598 0.409134i
\(472\) 3.91241 0.00828900
\(473\) 69.8152i 0.147601i
\(474\) 703.040 + 156.302i 1.48321 + 0.329751i
\(475\) 99.7610 0.210023
\(476\) 732.439i 1.53874i
\(477\) −156.088 + 333.689i −0.327229 + 0.699559i
\(478\) 140.808 0.294577
\(479\) 565.886i 1.18139i −0.806895 0.590695i \(-0.798853\pi\)
0.806895 0.590695i \(-0.201147\pi\)
\(480\) 117.527 528.634i 0.244848 1.10132i
\(481\) −323.282 −0.672103
\(482\) 706.037i 1.46481i
\(483\) −135.220 30.0626i −0.279959 0.0622413i
\(484\) −412.280 −0.851817
\(485\) 326.842i 0.673900i
\(486\) −311.925 603.604i −0.641820 1.24198i
\(487\) −576.100 −1.18296 −0.591478 0.806321i \(-0.701455\pi\)
−0.591478 + 0.806321i \(0.701455\pi\)
\(488\) 24.9230i 0.0510718i
\(489\) −46.5260 + 209.273i −0.0951452 + 0.427960i
\(490\) 6.92824 0.0141393
\(491\) 475.446i 0.968321i 0.874979 + 0.484161i \(0.160875\pi\)
−0.874979 + 0.484161i \(0.839125\pi\)
\(492\) 369.877 + 82.2320i 0.751782 + 0.167138i
\(493\) −209.599 −0.425149
\(494\) 194.491i 0.393707i
\(495\) −118.904 55.6193i −0.240210 0.112362i
\(496\) −668.151 −1.34708
\(497\) 224.304i 0.451317i
\(498\) 239.877 1078.96i 0.481681 2.16658i
\(499\) 61.4468 0.123140 0.0615699 0.998103i \(-0.480389\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(500\) 519.470i 1.03894i
\(501\) 277.488 + 61.6919i 0.553869 + 0.123138i
\(502\) −322.557 −0.642543
\(503\) 838.880i 1.66775i −0.551951 0.833876i \(-0.686117\pi\)
0.551951 0.833876i \(-0.313883\pi\)
\(504\) −13.5110 + 28.8841i −0.0268075 + 0.0573097i
\(505\) 430.346 0.852171
\(506\) 66.9497i 0.132312i
\(507\) −86.3428 + 388.367i −0.170301 + 0.766010i
\(508\) 603.508 1.18801
\(509\) 877.915i 1.72478i −0.506242 0.862391i \(-0.668966\pi\)
0.506242 0.862391i \(-0.331034\pi\)
\(510\) −913.116 203.006i −1.79042 0.398052i
\(511\) 498.172 0.974896
\(512\) 711.335i 1.38933i
\(513\) −189.990 + 246.681i −0.370350 + 0.480860i
\(514\) 189.302 0.368292
\(515\) 399.869i 0.776444i
\(516\) 48.1085 216.391i 0.0932335 0.419361i
\(517\) 185.728 0.359242
\(518\) 1042.41i 2.01237i
\(519\) 270.111 + 60.0519i 0.520446 + 0.115707i
\(520\) −12.4228 −0.0238899
\(521\) 868.672i 1.66732i −0.552281 0.833658i \(-0.686242\pi\)
0.552281 0.833658i \(-0.313758\pi\)
\(522\) −173.228 81.0299i −0.331854 0.155230i
\(523\) −971.738 −1.85801 −0.929004 0.370070i \(-0.879334\pi\)
−0.929004 + 0.370070i \(0.879334\pi\)
\(524\) 627.866i 1.19822i
\(525\) 39.1787 176.225i 0.0746261 0.335666i
\(526\) 827.619 1.57342
\(527\) 1103.74i 2.09438i
\(528\) −176.367 39.2104i −0.334029 0.0742621i
\(529\) 484.938 0.916707
\(530\) 462.763i 0.873137i
\(531\) 29.2907 62.6183i 0.0551614 0.117925i
\(532\) −306.257 −0.575672
\(533\) 199.548i 0.374387i
\(534\) −175.038 + 787.314i −0.327786 + 1.47437i
\(535\) 689.856 1.28945
\(536\) 43.4832i 0.0811254i
\(537\) −142.035 31.5775i −0.264497 0.0588036i
\(538\) 1249.29 2.32211
\(539\) 2.21057i 0.00410125i
\(540\) −330.214 254.326i −0.611508 0.470973i
\(541\) 349.329 0.645710 0.322855 0.946448i \(-0.395357\pi\)
0.322855 + 0.946448i \(0.395357\pi\)
\(542\) 312.775i 0.577076i
\(543\) 115.366 518.914i 0.212461 0.955642i
\(544\) −1231.26 −2.26335
\(545\) 642.384i 1.17869i
\(546\) −343.562 76.3817i −0.629235 0.139893i
\(547\) −97.0056 −0.177341 −0.0886706 0.996061i \(-0.528262\pi\)
−0.0886706 + 0.996061i \(0.528262\pi\)
\(548\) 821.605i 1.49928i
\(549\) −398.895 186.589i −0.726585 0.339871i
\(550\) 87.2515 0.158639
\(551\) 87.6402i 0.159057i
\(552\) −2.20130 + 9.90137i −0.00398786 + 0.0179373i
\(553\) −597.251 −1.08002
\(554\) 685.412i 1.23721i
\(555\) 634.632 + 141.093i 1.14348 + 0.254222i
\(556\) 283.285 0.509505
\(557\) 670.323i 1.20345i 0.798703 + 0.601726i \(0.205520\pi\)
−0.798703 + 0.601726i \(0.794480\pi\)
\(558\) −426.700 + 912.209i −0.764695 + 1.63478i
\(559\) −116.742 −0.208842
\(560\) 469.583i 0.838542i
\(561\) −64.7727 + 291.345i −0.115459 + 0.519332i
\(562\) −552.458 −0.983021
\(563\) 354.081i 0.628919i −0.949271 0.314459i \(-0.898177\pi\)
0.949271 0.314459i \(-0.101823\pi\)
\(564\) 575.659 + 127.982i 1.02067 + 0.226919i
\(565\) 496.342 0.878482
\(566\) 994.006i 1.75620i
\(567\) 361.140 + 432.488i 0.636931 + 0.762766i
\(568\) −16.4244 −0.0289163
\(569\) 923.710i 1.62339i −0.584080 0.811696i \(-0.698545\pi\)
0.584080 0.811696i \(-0.301455\pi\)
\(570\) −84.8838 + 381.805i −0.148919 + 0.669833i
\(571\) −95.5951 −0.167417 −0.0837085 0.996490i \(-0.526676\pi\)
−0.0837085 + 0.996490i \(0.526676\pi\)
\(572\) 83.0697i 0.145227i
\(573\) −401.921 89.3561i −0.701433 0.155944i
\(574\) −643.434 −1.12096
\(575\) 57.4233i 0.0998666i
\(576\) −473.186 221.340i −0.821504 0.384271i
\(577\) −709.681 −1.22995 −0.614975 0.788546i \(-0.710834\pi\)
−0.614975 + 0.788546i \(0.710834\pi\)
\(578\) 1318.72i 2.28153i
\(579\) 236.837 1065.29i 0.409045 1.83987i
\(580\) −117.318 −0.202272
\(581\) 916.604i 1.57763i
\(582\) 661.877 + 147.150i 1.13725 + 0.252835i
\(583\) 147.652 0.253263
\(584\) 36.4781i 0.0624625i
\(585\) −93.0046 + 198.827i −0.158982 + 0.339876i
\(586\) −1226.94 −2.09376
\(587\) 305.912i 0.521144i 0.965454 + 0.260572i \(0.0839112\pi\)
−0.965454 + 0.260572i \(0.916089\pi\)
\(588\) 1.52327 6.85162i 0.00259059 0.0116524i
\(589\) 461.509 0.783547
\(590\) 86.8395i 0.147186i
\(591\) −342.944 76.2442i −0.580277 0.129009i
\(592\) 894.804 1.51149
\(593\) 485.726i 0.819100i −0.912288 0.409550i \(-0.865686\pi\)
0.912288 0.409550i \(-0.134314\pi\)
\(594\) −166.166 + 215.748i −0.279740 + 0.363213i
\(595\) 775.717 1.30373
\(596\) 920.491i 1.54445i
\(597\) −114.629 + 515.596i −0.192008 + 0.863646i
\(598\) −111.951 −0.187209
\(599\) 1115.58i 1.86240i 0.364513 + 0.931198i \(0.381235\pi\)
−0.364513 + 0.931198i \(0.618765\pi\)
\(600\) −12.9038 2.86882i −0.0215064 0.00478136i
\(601\) −447.398 −0.744423 −0.372212 0.928148i \(-0.621400\pi\)
−0.372212 + 0.928148i \(0.621400\pi\)
\(602\) 376.430i 0.625300i
\(603\) −695.952 325.542i −1.15415 0.539871i
\(604\) −116.425 −0.192756
\(605\) 436.640i 0.721719i
\(606\) 193.750 871.481i 0.319719 1.43809i
\(607\) 717.432 1.18193 0.590965 0.806697i \(-0.298747\pi\)
0.590965 + 0.806697i \(0.298747\pi\)
\(608\) 514.833i 0.846764i
\(609\) 154.814 + 34.4185i 0.254209 + 0.0565165i
\(610\) −553.190 −0.906869
\(611\) 310.568i 0.508294i
\(612\) −401.523 + 858.384i −0.656083 + 1.40259i
\(613\) −1101.82 −1.79743 −0.898715 0.438534i \(-0.855498\pi\)
−0.898715 + 0.438534i \(0.855498\pi\)
\(614\) 1451.32i 2.36372i
\(615\) −87.0908 + 391.732i −0.141611 + 0.636962i
\(616\) 12.7808 0.0207480
\(617\) 150.603i 0.244089i −0.992525 0.122044i \(-0.961055\pi\)
0.992525 0.122044i \(-0.0389450\pi\)
\(618\) 809.762 + 180.028i 1.31029 + 0.291308i
\(619\) −621.716 −1.00439 −0.502193 0.864755i \(-0.667473\pi\)
−0.502193 + 0.864755i \(0.667473\pi\)
\(620\) 617.789i 0.996435i
\(621\) 141.992 + 109.360i 0.228650 + 0.176103i
\(622\) −914.722 −1.47061
\(623\) 668.844i 1.07359i
\(624\) −65.5662 + 294.915i −0.105074 + 0.472620i
\(625\) −333.894 −0.534230
\(626\) 866.743i 1.38457i
\(627\) 121.821 + 27.0836i 0.194292 + 0.0431956i
\(628\) −251.222 −0.400036
\(629\) 1478.15i 2.35000i
\(630\) 641.109 + 299.889i 1.01763 + 0.476014i
\(631\) 310.615 0.492259 0.246129 0.969237i \(-0.420841\pi\)
0.246129 + 0.969237i \(0.420841\pi\)
\(632\) 43.7331i 0.0691979i
\(633\) 5.92044 26.6300i 0.00935299 0.0420695i
\(634\) −937.296 −1.47838
\(635\) 639.167i 1.00656i
\(636\) 457.645 + 101.745i 0.719568 + 0.159976i
\(637\) −3.69644 −0.00580289
\(638\) 76.6505i 0.120142i
\(639\) −122.964 + 262.874i −0.192431 + 0.411384i
\(640\) 65.8363 0.102869
\(641\) 184.355i 0.287606i 0.989606 + 0.143803i \(0.0459331\pi\)
−0.989606 + 0.143803i \(0.954067\pi\)
\(642\) 310.586 1397.01i 0.483779 2.17602i
\(643\) −428.215 −0.665964 −0.332982 0.942933i \(-0.608055\pi\)
−0.332982 + 0.942933i \(0.608055\pi\)
\(644\) 176.284i 0.273734i
\(645\) 229.176 + 50.9511i 0.355312 + 0.0789939i
\(646\) 889.278 1.37659
\(647\) 516.078i 0.797648i 0.917028 + 0.398824i \(0.130581\pi\)
−0.917028 + 0.398824i \(0.869419\pi\)
\(648\) 31.6685 26.4441i 0.0488711 0.0408088i
\(649\) −27.7076 −0.0426928
\(650\) 145.899i 0.224460i
\(651\) 181.246 815.241i 0.278412 1.25229i
\(652\) 272.825 0.418443
\(653\) 983.392i 1.50596i −0.658044 0.752980i \(-0.728616\pi\)
0.658044 0.752980i \(-0.271384\pi\)
\(654\) −1300.87 289.213i −1.98910 0.442222i
\(655\) 664.965 1.01521
\(656\) 552.325i 0.841959i
\(657\) −583.834 273.098i −0.888637 0.415674i
\(658\) −1001.41 −1.52190
\(659\) 152.558i 0.231499i −0.993278 0.115749i \(-0.963073\pi\)
0.993278 0.115749i \(-0.0369270\pi\)
\(660\) −36.2549 + 163.074i −0.0549317 + 0.247081i
\(661\) −585.844 −0.886300 −0.443150 0.896447i \(-0.646139\pi\)
−0.443150 + 0.896447i \(0.646139\pi\)
\(662\) 1059.94i 1.60112i
\(663\) 487.177 + 108.311i 0.734807 + 0.163364i
\(664\) 67.1173 0.101080
\(665\) 324.353i 0.487749i
\(666\) 571.447 1221.65i 0.858028 1.83431i
\(667\) 50.4465 0.0756319
\(668\) 361.757i 0.541552i
\(669\) 159.089 715.577i 0.237801 1.06962i
\(670\) −965.151 −1.44052
\(671\) 176.505i 0.263047i
\(672\) 909.435 + 202.188i 1.35333 + 0.300875i
\(673\) 742.833 1.10376 0.551882 0.833922i \(-0.313910\pi\)
0.551882 + 0.833922i \(0.313910\pi\)
\(674\) 863.625i 1.28134i
\(675\) −142.522 + 185.049i −0.211143 + 0.274147i
\(676\) 506.307 0.748975
\(677\) 514.809i 0.760427i −0.924899 0.380213i \(-0.875851\pi\)
0.924899 0.380213i \(-0.124149\pi\)
\(678\) 223.463 1005.13i 0.329591 1.48249i
\(679\) −562.282 −0.828103
\(680\) 56.8010i 0.0835309i
\(681\) 137.243 + 30.5122i 0.201531 + 0.0448050i
\(682\) 403.638 0.591845
\(683\) 387.873i 0.567896i −0.958840 0.283948i \(-0.908356\pi\)
0.958840 0.283948i \(-0.0916444\pi\)
\(684\) 358.919 + 167.890i 0.524736 + 0.245453i
\(685\) −870.151 −1.27029
\(686\) 964.944i 1.40662i
\(687\) −92.7262 + 417.080i −0.134973 + 0.607103i
\(688\) 323.129 0.469664
\(689\) 246.899i 0.358344i
\(690\) 219.770 + 48.8598i 0.318507 + 0.0708114i
\(691\) 1208.04 1.74826 0.874128 0.485696i \(-0.161434\pi\)
0.874128 + 0.485696i \(0.161434\pi\)
\(692\) 352.139i 0.508872i
\(693\) 95.6847 204.557i 0.138073 0.295176i
\(694\) 1441.61 2.07725
\(695\) 300.023i 0.431688i
\(696\) 2.52026 11.3360i 0.00362106 0.0162874i
\(697\) 912.399 1.30904
\(698\) 1511.55i 2.16555i
\(699\) −663.445 147.499i −0.949134 0.211014i
\(700\) −229.741 −0.328201
\(701\) 370.498i 0.528527i 0.964451 + 0.264264i \(0.0851289\pi\)
−0.964451 + 0.264264i \(0.914871\pi\)
\(702\) 360.767 + 277.857i 0.513913 + 0.395807i
\(703\) −618.064 −0.879181
\(704\) 209.377i 0.297411i
\(705\) −135.544 + 609.673i −0.192261 + 0.864785i
\(706\) −97.7432 −0.138446
\(707\) 740.346i 1.04717i
\(708\) −85.8792 19.0929i −0.121298 0.0269673i
\(709\) −1040.67 −1.46779 −0.733897 0.679260i \(-0.762301\pi\)
−0.733897 + 0.679260i \(0.762301\pi\)
\(710\) 364.556i 0.513459i
\(711\) 699.951 + 327.413i 0.984460 + 0.460496i
\(712\) −48.9754 −0.0687856
\(713\) 265.649i 0.372579i
\(714\) 349.242 1570.88i 0.489135 2.20011i
\(715\) 87.9780 0.123046
\(716\) 185.168i 0.258615i
\(717\) 147.479 + 32.7878i 0.205689 + 0.0457292i
\(718\) 1327.04 1.84824
\(719\) 760.116i 1.05719i −0.848876 0.528593i \(-0.822720\pi\)
0.848876 0.528593i \(-0.177280\pi\)
\(720\) 257.425 550.330i 0.357535 0.764347i
\(721\) −687.914 −0.954111
\(722\) 637.533i 0.883009i
\(723\) −164.404 + 739.485i −0.227392 + 1.02280i
\(724\) −676.498 −0.934390
\(725\) 65.7438i 0.0906811i
\(726\) −884.226 196.583i −1.21794 0.270776i
\(727\) −683.054 −0.939552 −0.469776 0.882786i \(-0.655665\pi\)
−0.469776 + 0.882786i \(0.655665\pi\)
\(728\) 21.3715i 0.0293565i
\(729\) −186.150 704.833i −0.255349 0.966849i
\(730\) −809.665 −1.10913
\(731\) 533.785i 0.730212i
\(732\) −121.627 + 547.072i −0.166157 + 0.747367i
\(733\) −1050.25 −1.43282 −0.716408 0.697681i \(-0.754215\pi\)
−0.716408 + 0.697681i \(0.754215\pi\)
\(734\) 1604.76i 2.18632i
\(735\) 7.25646 + 1.61327i 0.00987273 + 0.00219493i
\(736\) 296.342 0.402639
\(737\) 307.948i 0.417840i
\(738\) 754.074 + 352.730i 1.02178 + 0.477954i
\(739\) −863.855 −1.16895 −0.584476 0.811411i \(-0.698700\pi\)
−0.584476 + 0.811411i \(0.698700\pi\)
\(740\) 827.359i 1.11805i
\(741\) 45.2883 203.705i 0.0611178 0.274906i
\(742\) −796.114 −1.07293
\(743\) 604.163i 0.813140i −0.913620 0.406570i \(-0.866725\pi\)
0.913620 0.406570i \(-0.133275\pi\)
\(744\) −59.6951 13.2716i −0.0802353 0.0178381i
\(745\) 974.880 1.30856
\(746\) 1358.00i 1.82037i
\(747\) 502.482 1074.22i 0.672667 1.43804i
\(748\) 379.822 0.507783
\(749\) 1186.79i 1.58450i
\(750\) −247.694 + 1114.12i −0.330259 + 1.48549i
\(751\) 7.84121 0.0104410 0.00522051 0.999986i \(-0.498338\pi\)
0.00522051 + 0.999986i \(0.498338\pi\)
\(752\) 859.613i 1.14310i
\(753\) −337.838 75.1089i −0.448656 0.0997463i
\(754\) 128.172 0.169990
\(755\) 123.304i 0.163317i
\(756\) 437.529 568.084i 0.578742 0.751434i
\(757\) 483.558 0.638782 0.319391 0.947623i \(-0.396522\pi\)
0.319391 + 0.947623i \(0.396522\pi\)
\(758\) 1676.86i 2.21222i
\(759\) 15.5896 70.1214i 0.0205396 0.0923866i
\(760\) −23.7504 −0.0312505
\(761\) 951.213i 1.24995i 0.780644 + 0.624976i \(0.214891\pi\)
−0.780644 + 0.624976i \(0.785109\pi\)
\(762\) 1294.36 + 287.765i 1.69863 + 0.377644i
\(763\) 1105.12 1.44839
\(764\) 523.977i 0.685834i
\(765\) −909.104 425.247i −1.18837 0.555879i
\(766\) −144.758 −0.188979
\(767\) 46.3317i 0.0604064i
\(768\) 180.804 813.249i 0.235421 1.05892i
\(769\) −650.550 −0.845969 −0.422985 0.906137i \(-0.639018\pi\)
−0.422985 + 0.906137i \(0.639018\pi\)
\(770\) 283.681i 0.368417i
\(771\) 198.270 + 44.0800i 0.257160 + 0.0571725i
\(772\) −1388.79 −1.79895
\(773\) 992.020i 1.28334i 0.766982 + 0.641669i \(0.221758\pi\)
−0.766982 + 0.641669i \(0.778242\pi\)
\(774\) 206.359 441.159i 0.266614 0.569973i
\(775\) 346.204 0.446715
\(776\) 41.1725i 0.0530573i
\(777\) −242.730 + 1091.79i −0.312393 + 1.40513i
\(778\) 1412.42 1.81546
\(779\) 381.505i 0.489737i
\(780\) 272.686 + 60.6242i 0.349597 + 0.0777233i
\(781\) 116.318 0.148934
\(782\) 511.876i 0.654573i
\(783\) −162.566 125.206i −0.207619 0.159905i
\(784\) 10.2313 0.0130501
\(785\) 266.066i 0.338938i
\(786\)