Properties

Label 177.3.c.a.58.1
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.1
Root \(-3.65759i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.20

$q$-expansion

\(f(q)\) \(=\) \(q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-3.65759i q^{2} -1.73205 q^{3} -9.37798 q^{4} +0.395869 q^{5} +6.33514i q^{6} -6.20847 q^{7} +19.6705i q^{8} +3.00000 q^{9} -1.44793i q^{10} +8.54756i q^{11} +16.2431 q^{12} +0.0887419i q^{13} +22.7081i q^{14} -0.685665 q^{15} +34.4346 q^{16} -8.10940 q^{17} -10.9728i q^{18} +10.5067 q^{19} -3.71245 q^{20} +10.7534 q^{21} +31.2635 q^{22} +14.0307i q^{23} -34.0702i q^{24} -24.8433 q^{25} +0.324582 q^{26} -5.19615 q^{27} +58.2229 q^{28} -56.9344 q^{29} +2.50788i q^{30} -0.471045i q^{31} -47.2659i q^{32} -14.8048i q^{33} +29.6609i q^{34} -2.45774 q^{35} -28.1339 q^{36} -43.8322i q^{37} -38.4292i q^{38} -0.153705i q^{39} +7.78692i q^{40} +13.8735 q^{41} -39.3315i q^{42} +53.7675i q^{43} -80.1588i q^{44} +1.18761 q^{45} +51.3187 q^{46} +34.1786i q^{47} -59.6425 q^{48} -10.4549 q^{49} +90.8666i q^{50} +14.0459 q^{51} -0.832220i q^{52} -79.3757 q^{53} +19.0054i q^{54} +3.38371i q^{55} -122.123i q^{56} -18.1981 q^{57} +208.243i q^{58} +(-41.5316 + 41.9061i) q^{59} +6.43015 q^{60} +45.7782i q^{61} -1.72289 q^{62} -18.6254 q^{63} -35.1409 q^{64} +0.0351301i q^{65} -54.1499 q^{66} -104.453i q^{67} +76.0498 q^{68} -24.3019i q^{69} +8.98940i q^{70} +74.0325 q^{71} +59.0114i q^{72} -109.458i q^{73} -160.320 q^{74} +43.0298 q^{75} -98.5316 q^{76} -53.0673i q^{77} -0.562192 q^{78} -74.2528 q^{79} +13.6316 q^{80} +9.00000 q^{81} -50.7436i q^{82} -88.8936i q^{83} -100.845 q^{84} -3.21026 q^{85} +196.660 q^{86} +98.6133 q^{87} -168.134 q^{88} +142.879i q^{89} -4.34378i q^{90} -0.550951i q^{91} -131.580i q^{92} +0.815874i q^{93} +125.012 q^{94} +4.15927 q^{95} +81.8669i q^{96} -81.4737i q^{97} +38.2398i q^{98} +25.6427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.65759i 1.82880i −0.404816 0.914398i \(-0.632665\pi\)
0.404816 0.914398i \(-0.367335\pi\)
\(3\) −1.73205 −0.577350
\(4\) −9.37798 −2.34450
\(5\) 0.395869 0.0791737 0.0395869 0.999216i \(-0.487396\pi\)
0.0395869 + 0.999216i \(0.487396\pi\)
\(6\) 6.33514i 1.05586i
\(7\) −6.20847 −0.886924 −0.443462 0.896293i \(-0.646250\pi\)
−0.443462 + 0.896293i \(0.646250\pi\)
\(8\) 19.6705i 2.45881i
\(9\) 3.00000 0.333333
\(10\) 1.44793i 0.144793i
\(11\) 8.54756i 0.777051i 0.921438 + 0.388525i \(0.127015\pi\)
−0.921438 + 0.388525i \(0.872985\pi\)
\(12\) 16.2431 1.35359
\(13\) 0.0887419i 0.00682630i 0.999994 + 0.00341315i \(0.00108644\pi\)
−0.999994 + 0.00341315i \(0.998914\pi\)
\(14\) 22.7081i 1.62200i
\(15\) −0.685665 −0.0457110
\(16\) 34.4346 2.15216
\(17\) −8.10940 −0.477023 −0.238512 0.971140i \(-0.576660\pi\)
−0.238512 + 0.971140i \(0.576660\pi\)
\(18\) 10.9728i 0.609599i
\(19\) 10.5067 0.552984 0.276492 0.961016i \(-0.410828\pi\)
0.276492 + 0.961016i \(0.410828\pi\)
\(20\) −3.71245 −0.185622
\(21\) 10.7534 0.512066
\(22\) 31.2635 1.42107
\(23\) 14.0307i 0.610032i 0.952347 + 0.305016i \(0.0986618\pi\)
−0.952347 + 0.305016i \(0.901338\pi\)
\(24\) 34.0702i 1.41959i
\(25\) −24.8433 −0.993732
\(26\) 0.324582 0.0124839
\(27\) −5.19615 −0.192450
\(28\) 58.2229 2.07939
\(29\) −56.9344 −1.96325 −0.981627 0.190808i \(-0.938889\pi\)
−0.981627 + 0.190808i \(0.938889\pi\)
\(30\) 2.50788i 0.0835960i
\(31\) 0.471045i 0.0151950i −0.999971 0.00759751i \(-0.997582\pi\)
0.999971 0.00759751i \(-0.00241838\pi\)
\(32\) 47.2659i 1.47706i
\(33\) 14.8048i 0.448631i
\(34\) 29.6609i 0.872378i
\(35\) −2.45774 −0.0702211
\(36\) −28.1339 −0.781498
\(37\) 43.8322i 1.18465i −0.805698 0.592327i \(-0.798209\pi\)
0.805698 0.592327i \(-0.201791\pi\)
\(38\) 38.4292i 1.01129i
\(39\) 0.153705i 0.00394117i
\(40\) 7.78692i 0.194673i
\(41\) 13.8735 0.338378 0.169189 0.985584i \(-0.445885\pi\)
0.169189 + 0.985584i \(0.445885\pi\)
\(42\) 39.3315i 0.936464i
\(43\) 53.7675i 1.25041i 0.780462 + 0.625204i \(0.214984\pi\)
−0.780462 + 0.625204i \(0.785016\pi\)
\(44\) 80.1588i 1.82179i
\(45\) 1.18761 0.0263912
\(46\) 51.3187 1.11562
\(47\) 34.1786i 0.727205i 0.931554 + 0.363602i \(0.118453\pi\)
−0.931554 + 0.363602i \(0.881547\pi\)
\(48\) −59.6425 −1.24255
\(49\) −10.4549 −0.213365
\(50\) 90.8666i 1.81733i
\(51\) 14.0459 0.275410
\(52\) 0.832220i 0.0160042i
\(53\) −79.3757 −1.49765 −0.748827 0.662765i \(-0.769383\pi\)
−0.748827 + 0.662765i \(0.769383\pi\)
\(54\) 19.0054i 0.351952i
\(55\) 3.38371i 0.0615220i
\(56\) 122.123i 2.18078i
\(57\) −18.1981 −0.319265
\(58\) 208.243i 3.59039i
\(59\) −41.5316 + 41.9061i −0.703926 + 0.710273i
\(60\) 6.43015 0.107169
\(61\) 45.7782i 0.750462i 0.926931 + 0.375231i \(0.122437\pi\)
−0.926931 + 0.375231i \(0.877563\pi\)
\(62\) −1.72289 −0.0277886
\(63\) −18.6254 −0.295641
\(64\) −35.1409 −0.549077
\(65\) 0.0351301i 0.000540463i
\(66\) −54.1499 −0.820454
\(67\) 104.453i 1.55900i −0.626403 0.779499i \(-0.715474\pi\)
0.626403 0.779499i \(-0.284526\pi\)
\(68\) 76.0498 1.11838
\(69\) 24.3019i 0.352202i
\(70\) 8.98940i 0.128420i
\(71\) 74.0325 1.04271 0.521356 0.853340i \(-0.325427\pi\)
0.521356 + 0.853340i \(0.325427\pi\)
\(72\) 59.0114i 0.819602i
\(73\) 109.458i 1.49943i −0.661761 0.749715i \(-0.730190\pi\)
0.661761 0.749715i \(-0.269810\pi\)
\(74\) −160.320 −2.16649
\(75\) 43.0298 0.573731
\(76\) −98.5316 −1.29647
\(77\) 53.0673i 0.689185i
\(78\) −0.562192 −0.00720759
\(79\) −74.2528 −0.939909 −0.469954 0.882691i \(-0.655730\pi\)
−0.469954 + 0.882691i \(0.655730\pi\)
\(80\) 13.6316 0.170395
\(81\) 9.00000 0.111111
\(82\) 50.7436i 0.618825i
\(83\) 88.8936i 1.07101i −0.844533 0.535503i \(-0.820122\pi\)
0.844533 0.535503i \(-0.179878\pi\)
\(84\) −100.845 −1.20054
\(85\) −3.21026 −0.0377677
\(86\) 196.660 2.28674
\(87\) 98.6133 1.13349
\(88\) −168.134 −1.91062
\(89\) 142.879i 1.60538i 0.596394 + 0.802692i \(0.296600\pi\)
−0.596394 + 0.802692i \(0.703400\pi\)
\(90\) 4.34378i 0.0482642i
\(91\) 0.550951i 0.00605441i
\(92\) 131.580i 1.43022i
\(93\) 0.815874i 0.00877284i
\(94\) 125.012 1.32991
\(95\) 4.15927 0.0437818
\(96\) 81.8669i 0.852780i
\(97\) 81.4737i 0.839935i −0.907539 0.419968i \(-0.862041\pi\)
0.907539 0.419968i \(-0.137959\pi\)
\(98\) 38.2398i 0.390202i
\(99\) 25.6427i 0.259017i
\(100\) 232.980 2.32980
\(101\) 92.0885i 0.911768i −0.890039 0.455884i \(-0.849323\pi\)
0.890039 0.455884i \(-0.150677\pi\)
\(102\) 51.3741i 0.503668i
\(103\) 147.520i 1.43223i −0.697982 0.716115i \(-0.745918\pi\)
0.697982 0.716115i \(-0.254082\pi\)
\(104\) −1.74559 −0.0167846
\(105\) 4.25693 0.0405422
\(106\) 290.324i 2.73891i
\(107\) 68.9648 0.644530 0.322265 0.946649i \(-0.395556\pi\)
0.322265 + 0.946649i \(0.395556\pi\)
\(108\) 48.7294 0.451198
\(109\) 57.3299i 0.525963i −0.964801 0.262981i \(-0.915294\pi\)
0.964801 0.262981i \(-0.0847058\pi\)
\(110\) 12.3762 0.112511
\(111\) 75.9196i 0.683961i
\(112\) −213.786 −1.90881
\(113\) 19.6848i 0.174201i −0.996200 0.0871007i \(-0.972240\pi\)
0.996200 0.0871007i \(-0.0277602\pi\)
\(114\) 66.5613i 0.583871i
\(115\) 5.55433i 0.0482985i
\(116\) 533.930 4.60284
\(117\) 0.266226i 0.00227543i
\(118\) 153.276 + 151.906i 1.29894 + 1.28734i
\(119\) 50.3469 0.423084
\(120\) 13.4873i 0.112394i
\(121\) 47.9392 0.396192
\(122\) 167.438 1.37244
\(123\) −24.0296 −0.195363
\(124\) 4.41745i 0.0356246i
\(125\) −19.7314 −0.157851
\(126\) 68.1242i 0.540668i
\(127\) 5.95404 0.0468822 0.0234411 0.999725i \(-0.492538\pi\)
0.0234411 + 0.999725i \(0.492538\pi\)
\(128\) 60.5324i 0.472909i
\(129\) 93.1281i 0.721923i
\(130\) 0.128492 0.000988397
\(131\) 207.532i 1.58421i 0.610384 + 0.792106i \(0.291015\pi\)
−0.610384 + 0.792106i \(0.708985\pi\)
\(132\) 138.839i 1.05181i
\(133\) −65.2305 −0.490455
\(134\) −382.046 −2.85109
\(135\) −2.05699 −0.0152370
\(136\) 159.516i 1.17291i
\(137\) −62.5295 −0.456419 −0.228210 0.973612i \(-0.573287\pi\)
−0.228210 + 0.973612i \(0.573287\pi\)
\(138\) −88.8866 −0.644106
\(139\) −101.500 −0.730217 −0.365108 0.930965i \(-0.618968\pi\)
−0.365108 + 0.930965i \(0.618968\pi\)
\(140\) 23.0486 0.164633
\(141\) 59.1991i 0.419852i
\(142\) 270.781i 1.90691i
\(143\) −0.758526 −0.00530438
\(144\) 103.304 0.717387
\(145\) −22.5385 −0.155438
\(146\) −400.354 −2.74215
\(147\) 18.1084 0.123187
\(148\) 411.058i 2.77742i
\(149\) 15.5533i 0.104385i −0.998637 0.0521924i \(-0.983379\pi\)
0.998637 0.0521924i \(-0.0166209\pi\)
\(150\) 157.386i 1.04924i
\(151\) 48.2391i 0.319464i −0.987160 0.159732i \(-0.948937\pi\)
0.987160 0.159732i \(-0.0510631\pi\)
\(152\) 206.671i 1.35968i
\(153\) −24.3282 −0.159008
\(154\) −194.098 −1.26038
\(155\) 0.186472i 0.00120305i
\(156\) 1.44145i 0.00924004i
\(157\) 218.253i 1.39014i 0.718940 + 0.695072i \(0.244628\pi\)
−0.718940 + 0.695072i \(0.755372\pi\)
\(158\) 271.586i 1.71890i
\(159\) 137.483 0.864671
\(160\) 18.7111i 0.116944i
\(161\) 87.1094i 0.541052i
\(162\) 32.9183i 0.203200i
\(163\) 300.810 1.84546 0.922729 0.385449i \(-0.125953\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(164\) −130.106 −0.793326
\(165\) 5.86076i 0.0355197i
\(166\) −325.136 −1.95865
\(167\) −285.372 −1.70881 −0.854407 0.519605i \(-0.826079\pi\)
−0.854407 + 0.519605i \(0.826079\pi\)
\(168\) 211.524i 1.25907i
\(169\) 168.992 0.999953
\(170\) 11.7418i 0.0690694i
\(171\) 31.5201 0.184328
\(172\) 504.231i 2.93157i
\(173\) 115.450i 0.667344i 0.942689 + 0.333672i \(0.108288\pi\)
−0.942689 + 0.333672i \(0.891712\pi\)
\(174\) 360.687i 2.07291i
\(175\) 154.239 0.881365
\(176\) 294.332i 1.67234i
\(177\) 71.9349 72.5835i 0.406412 0.410076i
\(178\) 522.594 2.93592
\(179\) 145.888i 0.815016i 0.913202 + 0.407508i \(0.133602\pi\)
−0.913202 + 0.407508i \(0.866398\pi\)
\(180\) −11.1373 −0.0618741
\(181\) −40.9343 −0.226157 −0.113078 0.993586i \(-0.536071\pi\)
−0.113078 + 0.993586i \(0.536071\pi\)
\(182\) −2.01516 −0.0110723
\(183\) 79.2901i 0.433280i
\(184\) −275.991 −1.49995
\(185\) 17.3518i 0.0937935i
\(186\) 2.98414 0.0160437
\(187\) 69.3155i 0.370671i
\(188\) 320.527i 1.70493i
\(189\) 32.2602 0.170689
\(190\) 15.2129i 0.0800680i
\(191\) 281.121i 1.47184i 0.677070 + 0.735919i \(0.263249\pi\)
−0.677070 + 0.735919i \(0.736751\pi\)
\(192\) 60.8658 0.317010
\(193\) 46.9362 0.243193 0.121596 0.992580i \(-0.461199\pi\)
0.121596 + 0.992580i \(0.461199\pi\)
\(194\) −297.998 −1.53607
\(195\) 0.0608472i 0.000312037i
\(196\) 98.0459 0.500234
\(197\) 20.8170 0.105670 0.0528350 0.998603i \(-0.483174\pi\)
0.0528350 + 0.998603i \(0.483174\pi\)
\(198\) 93.7905 0.473689
\(199\) −206.378 −1.03707 −0.518537 0.855055i \(-0.673523\pi\)
−0.518537 + 0.855055i \(0.673523\pi\)
\(200\) 488.679i 2.44339i
\(201\) 180.918i 0.900088i
\(202\) −336.822 −1.66744
\(203\) 353.475 1.74126
\(204\) −131.722 −0.645696
\(205\) 5.49209 0.0267907
\(206\) −539.567 −2.61926
\(207\) 42.0922i 0.203344i
\(208\) 3.05579i 0.0146913i
\(209\) 89.8066i 0.429697i
\(210\) 15.5701i 0.0741434i
\(211\) 200.660i 0.950993i 0.879718 + 0.475497i \(0.157732\pi\)
−0.879718 + 0.475497i \(0.842268\pi\)
\(212\) 744.384 3.51124
\(213\) −128.228 −0.602010
\(214\) 252.245i 1.17871i
\(215\) 21.2849i 0.0989994i
\(216\) 102.211i 0.473198i
\(217\) 2.92447i 0.0134768i
\(218\) −209.690 −0.961879
\(219\) 189.588i 0.865697i
\(220\) 31.7324i 0.144238i
\(221\) 0.719643i 0.00325630i
\(222\) 277.683 1.25082
\(223\) −271.603 −1.21795 −0.608976 0.793189i \(-0.708419\pi\)
−0.608976 + 0.793189i \(0.708419\pi\)
\(224\) 293.449i 1.31004i
\(225\) −74.5299 −0.331244
\(226\) −71.9989 −0.318579
\(227\) 124.072i 0.546571i 0.961933 + 0.273286i \(0.0881104\pi\)
−0.961933 + 0.273286i \(0.911890\pi\)
\(228\) 170.662 0.748516
\(229\) 269.653i 1.17752i −0.808307 0.588762i \(-0.799616\pi\)
0.808307 0.588762i \(-0.200384\pi\)
\(230\) 20.3155 0.0883281
\(231\) 91.9152i 0.397901i
\(232\) 1119.93i 4.82727i
\(233\) 432.383i 1.85572i −0.372928 0.927860i \(-0.621646\pi\)
0.372928 0.927860i \(-0.378354\pi\)
\(234\) 0.973745 0.00416130
\(235\) 13.5302i 0.0575755i
\(236\) 389.483 392.995i 1.65035 1.66523i
\(237\) 128.610 0.542657
\(238\) 184.149i 0.773733i
\(239\) 345.014 1.44357 0.721787 0.692115i \(-0.243321\pi\)
0.721787 + 0.692115i \(0.243321\pi\)
\(240\) −23.6106 −0.0983774
\(241\) −395.883 −1.64267 −0.821334 0.570447i \(-0.806770\pi\)
−0.821334 + 0.570447i \(0.806770\pi\)
\(242\) 175.342i 0.724554i
\(243\) −15.5885 −0.0641500
\(244\) 429.307i 1.75945i
\(245\) −4.13877 −0.0168929
\(246\) 87.8906i 0.357279i
\(247\) 0.932384i 0.00377483i
\(248\) 9.26568 0.0373616
\(249\) 153.968i 0.618346i
\(250\) 72.1694i 0.288678i
\(251\) 98.2846 0.391572 0.195786 0.980647i \(-0.437274\pi\)
0.195786 + 0.980647i \(0.437274\pi\)
\(252\) 174.669 0.693130
\(253\) −119.929 −0.474026
\(254\) 21.7774i 0.0857379i
\(255\) 5.56033 0.0218052
\(256\) −361.966 −1.41393
\(257\) −248.162 −0.965609 −0.482805 0.875728i \(-0.660382\pi\)
−0.482805 + 0.875728i \(0.660382\pi\)
\(258\) −340.625 −1.32025
\(259\) 272.131i 1.05070i
\(260\) 0.329450i 0.00126711i
\(261\) −170.803 −0.654418
\(262\) 759.066 2.89720
\(263\) 194.073 0.737919 0.368959 0.929446i \(-0.379714\pi\)
0.368959 + 0.929446i \(0.379714\pi\)
\(264\) 291.217 1.10310
\(265\) −31.4224 −0.118575
\(266\) 238.587i 0.896942i
\(267\) 247.474i 0.926869i
\(268\) 979.557i 3.65506i
\(269\) 213.661i 0.794278i 0.917758 + 0.397139i \(0.129997\pi\)
−0.917758 + 0.397139i \(0.870003\pi\)
\(270\) 7.52364i 0.0278653i
\(271\) −56.3572 −0.207960 −0.103980 0.994579i \(-0.533158\pi\)
−0.103980 + 0.994579i \(0.533158\pi\)
\(272\) −279.244 −1.02663
\(273\) 0.954276i 0.00349552i
\(274\) 228.707i 0.834698i
\(275\) 212.349i 0.772180i
\(276\) 227.903i 0.825736i
\(277\) 170.342 0.614953 0.307476 0.951556i \(-0.400515\pi\)
0.307476 + 0.951556i \(0.400515\pi\)
\(278\) 371.246i 1.33542i
\(279\) 1.41314i 0.00506500i
\(280\) 48.3448i 0.172660i
\(281\) −39.9961 −0.142335 −0.0711674 0.997464i \(-0.522672\pi\)
−0.0711674 + 0.997464i \(0.522672\pi\)
\(282\) −216.526 −0.767824
\(283\) 357.475i 1.26316i 0.775309 + 0.631581i \(0.217594\pi\)
−0.775309 + 0.631581i \(0.782406\pi\)
\(284\) −694.275 −2.44463
\(285\) −7.20407 −0.0252774
\(286\) 2.77438i 0.00970063i
\(287\) −86.1333 −0.300116
\(288\) 141.798i 0.492353i
\(289\) −223.238 −0.772449
\(290\) 82.4368i 0.284265i
\(291\) 141.117i 0.484937i
\(292\) 1026.50i 3.51541i
\(293\) 67.1472 0.229171 0.114586 0.993413i \(-0.463446\pi\)
0.114586 + 0.993413i \(0.463446\pi\)
\(294\) 66.2332i 0.225283i
\(295\) −16.4411 + 16.5893i −0.0557324 + 0.0562350i
\(296\) 862.200 2.91284
\(297\) 44.4144i 0.149544i
\(298\) −56.8878 −0.190899
\(299\) −1.24511 −0.00416426
\(300\) −403.533 −1.34511
\(301\) 333.814i 1.10902i
\(302\) −176.439 −0.584235
\(303\) 159.502i 0.526409i
\(304\) 361.794 1.19011
\(305\) 18.1221i 0.0594169i
\(306\) 88.9826i 0.290793i
\(307\) 123.299 0.401626 0.200813 0.979630i \(-0.435642\pi\)
0.200813 + 0.979630i \(0.435642\pi\)
\(308\) 497.664i 1.61579i
\(309\) 255.512i 0.826899i
\(310\) −0.682039 −0.00220013
\(311\) −246.230 −0.791737 −0.395868 0.918307i \(-0.629556\pi\)
−0.395868 + 0.918307i \(0.629556\pi\)
\(312\) 3.02346 0.00969057
\(313\) 489.577i 1.56414i 0.623189 + 0.782071i \(0.285837\pi\)
−0.623189 + 0.782071i \(0.714163\pi\)
\(314\) 798.280 2.54229
\(315\) −7.37322 −0.0234070
\(316\) 696.341 2.20361
\(317\) 319.318 1.00731 0.503656 0.863904i \(-0.331988\pi\)
0.503656 + 0.863904i \(0.331988\pi\)
\(318\) 502.856i 1.58131i
\(319\) 486.650i 1.52555i
\(320\) −13.9112 −0.0434725
\(321\) −119.450 −0.372120
\(322\) −318.611 −0.989474
\(323\) −85.2029 −0.263786
\(324\) −84.4018 −0.260499
\(325\) 2.20464i 0.00678351i
\(326\) 1100.24i 3.37497i
\(327\) 99.2984i 0.303665i
\(328\) 272.898i 0.832007i
\(329\) 212.197i 0.644976i
\(330\) −21.4363 −0.0649584
\(331\) −222.382 −0.671850 −0.335925 0.941889i \(-0.609049\pi\)
−0.335925 + 0.941889i \(0.609049\pi\)
\(332\) 833.642i 2.51097i
\(333\) 131.497i 0.394885i
\(334\) 1043.77i 3.12507i
\(335\) 41.3496i 0.123432i
\(336\) 370.288 1.10205
\(337\) 285.028i 0.845781i 0.906181 + 0.422890i \(0.138984\pi\)
−0.906181 + 0.422890i \(0.861016\pi\)
\(338\) 618.104i 1.82871i
\(339\) 34.0950i 0.100575i
\(340\) 30.1057 0.0885462
\(341\) 4.02629 0.0118073
\(342\) 115.288i 0.337098i
\(343\) 369.124 1.07616
\(344\) −1057.63 −3.07451
\(345\) 9.62037i 0.0278851i
\(346\) 422.271 1.22044
\(347\) 62.2130i 0.179288i −0.995974 0.0896441i \(-0.971427\pi\)
0.995974 0.0896441i \(-0.0285730\pi\)
\(348\) −924.793 −2.65745
\(349\) 291.454i 0.835112i 0.908651 + 0.417556i \(0.137113\pi\)
−0.908651 + 0.417556i \(0.862887\pi\)
\(350\) 564.143i 1.61184i
\(351\) 0.461116i 0.00131372i
\(352\) 404.008 1.14775
\(353\) 306.106i 0.867156i −0.901116 0.433578i \(-0.857251\pi\)
0.901116 0.433578i \(-0.142749\pi\)
\(354\) −265.481 263.109i −0.749946 0.743245i
\(355\) 29.3071 0.0825553
\(356\) 1339.92i 3.76382i
\(357\) −87.2035 −0.244267
\(358\) 533.598 1.49050
\(359\) 461.119 1.28445 0.642226 0.766515i \(-0.278011\pi\)
0.642226 + 0.766515i \(0.278011\pi\)
\(360\) 23.3608i 0.0648910i
\(361\) −250.609 −0.694209
\(362\) 149.721i 0.413594i
\(363\) −83.0332 −0.228742
\(364\) 5.16681i 0.0141945i
\(365\) 43.3312i 0.118715i
\(366\) −290.011 −0.792380
\(367\) 232.591i 0.633763i −0.948465 0.316881i \(-0.897364\pi\)
0.948465 0.316881i \(-0.102636\pi\)
\(368\) 483.143i 1.31289i
\(369\) 41.6205 0.112793
\(370\) −63.4658 −0.171529
\(371\) 492.802 1.32831
\(372\) 7.65125i 0.0205679i
\(373\) −36.2600 −0.0972117 −0.0486058 0.998818i \(-0.515478\pi\)
−0.0486058 + 0.998818i \(0.515478\pi\)
\(374\) −253.528 −0.677882
\(375\) 34.1758 0.0911354
\(376\) −672.309 −1.78806
\(377\) 5.05246i 0.0134018i
\(378\) 117.994i 0.312155i
\(379\) −37.4494 −0.0988110 −0.0494055 0.998779i \(-0.515733\pi\)
−0.0494055 + 0.998779i \(0.515733\pi\)
\(380\) −39.0056 −0.102646
\(381\) −10.3127 −0.0270674
\(382\) 1028.23 2.69169
\(383\) −487.151 −1.27193 −0.635967 0.771716i \(-0.719399\pi\)
−0.635967 + 0.771716i \(0.719399\pi\)
\(384\) 104.845i 0.273034i
\(385\) 21.0077i 0.0545654i
\(386\) 171.673i 0.444750i
\(387\) 161.303i 0.416802i
\(388\) 764.059i 1.96922i
\(389\) 377.266 0.969834 0.484917 0.874560i \(-0.338850\pi\)
0.484917 + 0.874560i \(0.338850\pi\)
\(390\) −0.222554 −0.000570652
\(391\) 113.781i 0.290999i
\(392\) 205.653i 0.524624i
\(393\) 359.455i 0.914645i
\(394\) 76.1400i 0.193249i
\(395\) −29.3944 −0.0744161
\(396\) 240.477i 0.607264i
\(397\) 457.106i 1.15140i −0.817661 0.575700i \(-0.804730\pi\)
0.817661 0.575700i \(-0.195270\pi\)
\(398\) 754.845i 1.89660i
\(399\) 112.983 0.283164
\(400\) −855.469 −2.13867
\(401\) 242.627i 0.605056i −0.953141 0.302528i \(-0.902169\pi\)
0.953141 0.302528i \(-0.0978305\pi\)
\(402\) 661.723 1.64608
\(403\) 0.0418014 0.000103726
\(404\) 863.605i 2.13764i
\(405\) 3.56282 0.00879708
\(406\) 1292.87i 3.18441i
\(407\) 374.658 0.920537
\(408\) 276.289i 0.677179i
\(409\) 362.561i 0.886458i −0.896408 0.443229i \(-0.853833\pi\)
0.896408 0.443229i \(-0.146167\pi\)
\(410\) 20.0878i 0.0489947i
\(411\) 108.304 0.263514
\(412\) 1383.44i 3.35786i
\(413\) 257.848 260.173i 0.624329 0.629959i
\(414\) 153.956 0.371875
\(415\) 35.1902i 0.0847956i
\(416\) 4.19446 0.0100828
\(417\) 175.803 0.421591
\(418\) 328.476 0.785827
\(419\) 818.928i 1.95448i −0.212133 0.977241i \(-0.568041\pi\)
0.212133 0.977241i \(-0.431959\pi\)
\(420\) −39.9214 −0.0950509
\(421\) 329.980i 0.783801i −0.920008 0.391901i \(-0.871818\pi\)
0.920008 0.391901i \(-0.128182\pi\)
\(422\) 733.931 1.73917
\(423\) 102.536i 0.242402i
\(424\) 1561.36i 3.68244i
\(425\) 201.464 0.474033
\(426\) 469.006i 1.10095i
\(427\) 284.213i 0.665603i
\(428\) −646.750 −1.51110
\(429\) 1.31381 0.00306249
\(430\) 77.8514 0.181050
\(431\) 713.566i 1.65561i 0.561019 + 0.827803i \(0.310410\pi\)
−0.561019 + 0.827803i \(0.689590\pi\)
\(432\) −178.927 −0.414184
\(433\) 625.618 1.44485 0.722423 0.691452i \(-0.243029\pi\)
0.722423 + 0.691452i \(0.243029\pi\)
\(434\) 10.6965 0.0246464
\(435\) 39.0379 0.0897423
\(436\) 537.639i 1.23312i
\(437\) 147.417i 0.337338i
\(438\) 693.434 1.58318
\(439\) −461.737 −1.05179 −0.525897 0.850548i \(-0.676270\pi\)
−0.525897 + 0.850548i \(0.676270\pi\)
\(440\) −66.5591 −0.151271
\(441\) −31.3647 −0.0711218
\(442\) −2.63216 −0.00595511
\(443\) 255.246i 0.576175i 0.957604 + 0.288088i \(0.0930195\pi\)
−0.957604 + 0.288088i \(0.906981\pi\)
\(444\) 711.973i 1.60354i
\(445\) 56.5614i 0.127104i
\(446\) 993.413i 2.22738i
\(447\) 26.9392i 0.0602666i
\(448\) 218.171 0.486989
\(449\) −224.485 −0.499966 −0.249983 0.968250i \(-0.580425\pi\)
−0.249983 + 0.968250i \(0.580425\pi\)
\(450\) 272.600i 0.605777i
\(451\) 118.585i 0.262937i
\(452\) 184.603i 0.408415i
\(453\) 83.5526i 0.184443i
\(454\) 453.804 0.999568
\(455\) 0.218104i 0.000479350i
\(456\) 357.966i 0.785012i
\(457\) 64.2869i 0.140671i −0.997523 0.0703357i \(-0.977593\pi\)
0.997523 0.0703357i \(-0.0224071\pi\)
\(458\) −986.281 −2.15345
\(459\) 42.1377 0.0918032
\(460\) 52.0884i 0.113236i
\(461\) −212.758 −0.461513 −0.230757 0.973012i \(-0.574120\pi\)
−0.230757 + 0.973012i \(0.574120\pi\)
\(462\) 336.188 0.727680
\(463\) 291.329i 0.629221i −0.949221 0.314610i \(-0.898126\pi\)
0.949221 0.314610i \(-0.101874\pi\)
\(464\) −1960.51 −4.22524
\(465\) 0.322979i 0.000694579i
\(466\) −1581.48 −3.39373
\(467\) 31.5294i 0.0675148i 0.999430 + 0.0337574i \(0.0107474\pi\)
−0.999430 + 0.0337574i \(0.989253\pi\)
\(468\) 2.49666i 0.00533474i
\(469\) 648.493i 1.38271i
\(470\) 49.4881 0.105294
\(471\) 378.025i 0.802600i
\(472\) −824.313 816.946i −1.74643 1.73082i
\(473\) −459.581 −0.971630
\(474\) 470.402i 0.992408i
\(475\) −261.021 −0.549518
\(476\) −472.153 −0.991917
\(477\) −238.127 −0.499218
\(478\) 1261.92i 2.64000i
\(479\) −172.294 −0.359695 −0.179848 0.983694i \(-0.557560\pi\)
−0.179848 + 0.983694i \(0.557560\pi\)
\(480\) 32.4085i 0.0675178i
\(481\) 3.88975 0.00808680
\(482\) 1447.98i 3.00411i
\(483\) 150.878i 0.312376i
\(484\) −449.573 −0.928870
\(485\) 32.2529i 0.0665008i
\(486\) 57.0162i 0.117317i
\(487\) −403.087 −0.827694 −0.413847 0.910347i \(-0.635815\pi\)
−0.413847 + 0.910347i \(0.635815\pi\)
\(488\) −900.478 −1.84524
\(489\) −521.018 −1.06548
\(490\) 15.1379i 0.0308937i
\(491\) 294.608 0.600017 0.300008 0.953937i \(-0.403011\pi\)
0.300008 + 0.953937i \(0.403011\pi\)
\(492\) 225.349 0.458027
\(493\) 461.703 0.936518
\(494\) 3.41028 0.00690340
\(495\) 10.1511i 0.0205073i
\(496\) 16.2203i 0.0327021i
\(497\) −459.628 −0.924806
\(498\) 563.153 1.13083
\(499\) 515.505 1.03308 0.516538 0.856264i \(-0.327220\pi\)
0.516538 + 0.856264i \(0.327220\pi\)
\(500\) 185.041 0.370081
\(501\) 494.279 0.986584
\(502\) 359.485i 0.716105i
\(503\) 618.687i 1.22999i −0.788529 0.614997i \(-0.789157\pi\)
0.788529 0.614997i \(-0.210843\pi\)
\(504\) 366.370i 0.726925i
\(505\) 36.4550i 0.0721881i
\(506\) 438.650i 0.866896i
\(507\) −292.703 −0.577323
\(508\) −55.8368 −0.109915
\(509\) 597.596i 1.17406i −0.809566 0.587029i \(-0.800297\pi\)
0.809566 0.587029i \(-0.199703\pi\)
\(510\) 20.3374i 0.0398773i
\(511\) 679.569i 1.32988i
\(512\) 1081.80i 2.11288i
\(513\) −54.5944 −0.106422
\(514\) 907.674i 1.76590i
\(515\) 58.3984i 0.113395i
\(516\) 873.353i 1.69255i
\(517\) −292.144 −0.565075
\(518\) 995.344 1.92151
\(519\) 199.966i 0.385291i
\(520\) −0.691026 −0.00132890
\(521\) −190.298 −0.365256 −0.182628 0.983182i \(-0.558460\pi\)
−0.182628 + 0.983182i \(0.558460\pi\)
\(522\) 624.728i 1.19680i
\(523\) −579.438 −1.10791 −0.553956 0.832546i \(-0.686882\pi\)
−0.553956 + 0.832546i \(0.686882\pi\)
\(524\) 1946.23i 3.71418i
\(525\) −267.149 −0.508856
\(526\) 709.838i 1.34950i
\(527\) 3.81989i 0.00724837i
\(528\) 509.798i 0.965526i
\(529\) 332.139 0.627861
\(530\) 114.930i 0.216849i
\(531\) −124.595 + 125.718i −0.234642 + 0.236758i
\(532\) 611.730 1.14987
\(533\) 1.23116i 0.00230987i
\(534\) −905.159 −1.69505
\(535\) 27.3010 0.0510299
\(536\) 2054.64 3.83328
\(537\) 252.685i 0.470550i
\(538\) 781.484 1.45257
\(539\) 89.3639i 0.165796i
\(540\) 19.2904 0.0357230
\(541\) 808.858i 1.49512i 0.664196 + 0.747558i \(0.268774\pi\)
−0.664196 + 0.747558i \(0.731226\pi\)
\(542\) 206.132i 0.380317i
\(543\) 70.9004 0.130572
\(544\) 383.298i 0.704591i
\(545\) 22.6951i 0.0416424i
\(546\) 3.49035 0.00639258
\(547\) 270.832 0.495122 0.247561 0.968872i \(-0.420371\pi\)
0.247561 + 0.968872i \(0.420371\pi\)
\(548\) 586.400 1.07007
\(549\) 137.335i 0.250154i
\(550\) −776.688 −1.41216
\(551\) −598.192 −1.08565
\(552\) 478.030 0.865997
\(553\) 460.996 0.833628
\(554\) 623.041i 1.12462i
\(555\) 30.0542i 0.0541517i
\(556\) 951.866 1.71199
\(557\) −519.832 −0.933270 −0.466635 0.884450i \(-0.654534\pi\)
−0.466635 + 0.884450i \(0.654534\pi\)
\(558\) −5.16868 −0.00926286
\(559\) −4.77143 −0.00853565
\(560\) −84.6312 −0.151127
\(561\) 120.058i 0.214007i
\(562\) 146.289i 0.260301i
\(563\) 417.978i 0.742411i 0.928551 + 0.371206i \(0.121056\pi\)
−0.928551 + 0.371206i \(0.878944\pi\)
\(564\) 555.168i 0.984341i
\(565\) 7.79258i 0.0137922i
\(566\) 1307.50 2.31007
\(567\) −55.8762 −0.0985471
\(568\) 1456.25i 2.56383i
\(569\) 285.720i 0.502144i −0.967968 0.251072i \(-0.919217\pi\)
0.967968 0.251072i \(-0.0807831\pi\)
\(570\) 26.3495i 0.0462273i
\(571\) 69.7739i 0.122196i −0.998132 0.0610980i \(-0.980540\pi\)
0.998132 0.0610980i \(-0.0194602\pi\)
\(572\) 7.11345 0.0124361
\(573\) 486.916i 0.849766i
\(574\) 315.040i 0.548851i
\(575\) 348.569i 0.606208i
\(576\) −105.423 −0.183026
\(577\) 114.805 0.198968 0.0994840 0.995039i \(-0.468281\pi\)
0.0994840 + 0.995039i \(0.468281\pi\)
\(578\) 816.512i 1.41265i
\(579\) −81.2959 −0.140407
\(580\) 211.366 0.364424
\(581\) 551.893i 0.949902i
\(582\) 516.147 0.886850
\(583\) 678.469i 1.16375i
\(584\) 2153.10 3.68681
\(585\) 0.105390i 0.000180154i
\(586\) 245.597i 0.419108i
\(587\) 861.663i 1.46791i 0.679199 + 0.733954i \(0.262327\pi\)
−0.679199 + 0.733954i \(0.737673\pi\)
\(588\) −169.820 −0.288810
\(589\) 4.94913i 0.00840260i
\(590\) 60.6770 + 60.1347i 0.102842 + 0.101923i
\(591\) −36.0561 −0.0610085
\(592\) 1509.34i 2.54957i
\(593\) 903.733 1.52400 0.762001 0.647576i \(-0.224217\pi\)
0.762001 + 0.647576i \(0.224217\pi\)
\(594\) −162.450 −0.273485
\(595\) 19.9308 0.0334971
\(596\) 145.859i 0.244730i
\(597\) 357.457 0.598755
\(598\) 4.55412i 0.00761558i
\(599\) 236.884 0.395466 0.197733 0.980256i \(-0.436642\pi\)
0.197733 + 0.980256i \(0.436642\pi\)
\(600\) 846.417i 1.41069i
\(601\) 681.352i 1.13370i 0.823822 + 0.566848i \(0.191837\pi\)
−0.823822 + 0.566848i \(0.808163\pi\)
\(602\) −1220.96 −2.02817
\(603\) 313.359i 0.519666i
\(604\) 452.386i 0.748983i
\(605\) 18.9776 0.0313680
\(606\) 583.393 0.962695
\(607\) −855.559 −1.40949 −0.704744 0.709462i \(-0.748938\pi\)
−0.704744 + 0.709462i \(0.748938\pi\)
\(608\) 496.608i 0.816790i
\(609\) −612.237 −1.00532
\(610\) 66.2834 0.108661
\(611\) −3.03308 −0.00496412
\(612\) 228.149 0.372793
\(613\) 629.123i 1.02630i 0.858299 + 0.513151i \(0.171522\pi\)
−0.858299 + 0.513151i \(0.828478\pi\)
\(614\) 450.978i 0.734492i
\(615\) −9.51257 −0.0154676
\(616\) 1043.86 1.69457
\(617\) −909.047 −1.47333 −0.736667 0.676256i \(-0.763602\pi\)
−0.736667 + 0.676256i \(0.763602\pi\)
\(618\) 934.558 1.51223
\(619\) 437.303 0.706466 0.353233 0.935535i \(-0.385082\pi\)
0.353233 + 0.935535i \(0.385082\pi\)
\(620\) 1.74873i 0.00282053i
\(621\) 72.9058i 0.117401i
\(622\) 900.609i 1.44792i
\(623\) 887.061i 1.42385i
\(624\) 5.29279i 0.00848203i
\(625\) 613.271 0.981234
\(626\) 1790.67 2.86050
\(627\) 155.550i 0.248085i
\(628\) 2046.77i 3.25919i
\(629\) 355.453i 0.565108i
\(630\) 26.9682i 0.0428067i
\(631\) −548.459 −0.869190 −0.434595 0.900626i \(-0.643108\pi\)
−0.434595 + 0.900626i \(0.643108\pi\)
\(632\) 1460.59i 2.31106i
\(633\) 347.553i 0.549056i
\(634\) 1167.93i 1.84217i
\(635\) 2.35702 0.00371184
\(636\) −1289.31 −2.02722
\(637\) 0.927788i 0.00145650i
\(638\) −1779.97 −2.78992
\(639\) 222.097 0.347570
\(640\) 23.9629i 0.0374420i
\(641\) −1064.88 −1.66128 −0.830640 0.556810i \(-0.812025\pi\)
−0.830640 + 0.556810i \(0.812025\pi\)
\(642\) 436.901i 0.680531i
\(643\) 1042.17 1.62079 0.810395 0.585884i \(-0.199252\pi\)
0.810395 + 0.585884i \(0.199252\pi\)
\(644\) 816.910i 1.26849i
\(645\) 36.8665i 0.0571573i
\(646\) 311.638i 0.482411i
\(647\) −144.371 −0.223138 −0.111569 0.993757i \(-0.535588\pi\)
−0.111569 + 0.993757i \(0.535588\pi\)
\(648\) 177.034i 0.273201i
\(649\) −358.195 354.994i −0.551918 0.546986i
\(650\) −8.06367 −0.0124057
\(651\) 5.06533i 0.00778085i
\(652\) −2820.99 −4.32667
\(653\) −816.374 −1.25019 −0.625095 0.780549i \(-0.714940\pi\)
−0.625095 + 0.780549i \(0.714940\pi\)
\(654\) 363.193 0.555341
\(655\) 82.1553i 0.125428i
\(656\) 477.729 0.728245
\(657\) 328.375i 0.499810i
\(658\) −776.130 −1.17953
\(659\) 317.201i 0.481337i 0.970607 + 0.240669i \(0.0773667\pi\)
−0.970607 + 0.240669i \(0.922633\pi\)
\(660\) 54.9621i 0.0832759i
\(661\) 307.730 0.465552 0.232776 0.972530i \(-0.425219\pi\)
0.232776 + 0.972530i \(0.425219\pi\)
\(662\) 813.384i 1.22868i
\(663\) 1.24646i 0.00188003i
\(664\) 1748.58 2.63340
\(665\) −25.8227 −0.0388311
\(666\) −480.961 −0.722164
\(667\) 798.831i 1.19765i
\(668\) 2676.21 4.00631
\(669\) 470.430 0.703184
\(670\) −151.240 −0.225731
\(671\) −391.292 −0.583147
\(672\) 508.268i 0.756351i
\(673\) 1083.95i 1.61062i −0.592853 0.805311i \(-0.701998\pi\)
0.592853 0.805311i \(-0.298002\pi\)
\(674\) 1042.52 1.54676
\(675\) 129.090 0.191244
\(676\) −1584.80 −2.34439
\(677\) −815.853 −1.20510 −0.602550 0.798081i \(-0.705849\pi\)
−0.602550 + 0.798081i \(0.705849\pi\)
\(678\) 124.706 0.183932
\(679\) 505.827i 0.744959i
\(680\) 63.1472i 0.0928635i
\(681\) 214.899i 0.315563i
\(682\) 14.7265i 0.0215931i
\(683\) 1151.50i 1.68594i 0.537957 + 0.842972i \(0.319196\pi\)
−0.537957 + 0.842972i \(0.680804\pi\)
\(684\) −295.595 −0.432156
\(685\) −24.7534 −0.0361364
\(686\) 1350.10i 1.96808i
\(687\) 467.053i 0.679844i
\(688\) 1851.46i 2.69108i
\(689\) 7.04395i 0.0102234i
\(690\) −35.1874 −0.0509962
\(691\) 939.727i 1.35995i 0.733234 + 0.679976i \(0.238010\pi\)
−0.733234 + 0.679976i \(0.761990\pi\)
\(692\) 1082.69i 1.56458i
\(693\) 159.202i 0.229728i
\(694\) −227.550 −0.327882
\(695\) −40.1807 −0.0578140
\(696\) 1939.77i 2.78702i
\(697\) −112.506 −0.161414
\(698\) 1066.02 1.52725
\(699\) 748.909i 1.07140i
\(700\) −1446.45 −2.06636
\(701\) 782.026i 1.11559i 0.829980 + 0.557793i \(0.188352\pi\)
−0.829980 + 0.557793i \(0.811648\pi\)
\(702\) −1.68658 −0.00240253
\(703\) 460.532i 0.655095i
\(704\) 300.369i 0.426661i
\(705\) 23.4351i 0.0332412i
\(706\) −1119.61 −1.58585
\(707\) 571.729i 0.808669i
\(708\) −674.604 + 680.687i −0.952831 + 0.961422i
\(709\) −461.863 −0.651429 −0.325715 0.945468i \(-0.605605\pi\)
−0.325715 + 0.945468i \(0.605605\pi\)
\(710\) 107.194i 0.150977i
\(711\) −222.758 −0.313303
\(712\) −2810.50 −3.94733
\(713\) 6.60911 0.00926944
\(714\) 318.955i 0.446715i
\(715\) −0.300277 −0.000419968
\(716\) 1368.13i 1.91080i
\(717\) −597.582 −0.833448
\(718\) 1686.58i 2.34900i
\(719\) 398.240i 0.553881i −0.960887 0.276940i \(-0.910680\pi\)
0.960887 0.276940i \(-0.0893205\pi\)
\(720\) 40.8947 0.0567982
\(721\) 915.872i 1.27028i
\(722\) 916.627i 1.26957i
\(723\) 685.690 0.948395
\(724\) 383.881 0.530223
\(725\) 1414.44 1.95095
\(726\) 303.701i 0.418322i
\(727\) −402.797 −0.554053 −0.277027 0.960862i \(-0.589349\pi\)
−0.277027 + 0.960862i \(0.589349\pi\)
\(728\) 10.8375 0.0148866
\(729\) 27.0000 0.0370370
\(730\) −158.488 −0.217106
\(731\) 436.022i 0.596473i
\(732\) 743.581i 1.01582i
\(733\) 701.565 0.957114 0.478557 0.878056i \(-0.341160\pi\)
0.478557 + 0.878056i \(0.341160\pi\)
\(734\) −850.723 −1.15902
\(735\) 7.16856 0.00975314
\(736\) 663.175 0.901053
\(737\) 892.817 1.21142
\(738\) 152.231i 0.206275i
\(739\) 952.579i 1.28901i 0.764599 + 0.644506i \(0.222937\pi\)
−0.764599 + 0.644506i \(0.777063\pi\)
\(740\) 162.725i 0.219898i
\(741\) 1.61494i 0.00217940i
\(742\) 1802.47i 2.42920i
\(743\) −681.496 −0.917222 −0.458611 0.888637i \(-0.651653\pi\)
−0.458611 + 0.888637i \(0.651653\pi\)
\(744\) −16.0486 −0.0215707
\(745\) 6.15708i 0.00826454i
\(746\) 132.624i 0.177780i
\(747\) 266.681i 0.357002i
\(748\) 650.040i 0.869037i
\(749\) −428.166 −0.571650
\(750\) 125.001i 0.166668i
\(751\) 1302.06i 1.73376i −0.498514 0.866882i \(-0.666121\pi\)
0.498514 0.866882i \(-0.333879\pi\)
\(752\) 1176.93i 1.56506i
\(753\) −170.234 −0.226074
\(754\) −18.4799 −0.0245091
\(755\) 19.0964i 0.0252932i
\(756\) −302.535 −0.400179
\(757\) 653.976 0.863904 0.431952 0.901896i \(-0.357825\pi\)
0.431952 + 0.901896i \(0.357825\pi\)
\(758\) 136.975i 0.180705i
\(759\) 207.722 0.273679
\(760\) 81.8148i 0.107651i
\(761\) 638.164 0.838586 0.419293 0.907851i \(-0.362278\pi\)
0.419293 + 0.907851i \(0.362278\pi\)
\(762\) 37.7196i 0.0495008i
\(763\) 355.931i 0.466489i
\(764\) 2636.35i 3.45072i
\(765\) −9.63077 −0.0125892
\(766\) 1781.80i 2.32611i
\(767\) −3.71883 3.68560i −0.00484854 0.00480521i
\(768\) 626.944 0.816334
\(769\) 1305.23i 1.69730i 0.528951 + 0.848652i \(0.322586\pi\)
−0.528951 + 0.848652i \(0.677414\pi\)
\(770\) −76.8375 −0.0997889
\(771\) 429.829 0.557495
\(772\) −440.167 −0.570164
\(773\) 155.891i 0.201671i 0.994903 + 0.100835i \(0.0321515\pi\)
−0.994903 + 0.100835i \(0.967848\pi\)
\(774\) 589.979 0.762247
\(775\) 11.7023i 0.0150998i
\(776\) 1602.63 2.06524
\(777\) 471.345i 0.606621i
\(778\) 1379.88i 1.77363i
\(779\) 145.765 0.187118
\(780\) 0.570623i 0.000731569i
\(781\) 632.797i 0.810240i
\(782\) −416.164 −0.532178
\(783\) 295.840 0.377829
\(784\) −360.010 −0.459197
\(785\) 86.3994i 0.110063i
\(786\) −1314.74 −1.67270
\(787\) 389.653 0.495111 0.247556 0.968874i \(-0.420373\pi\)
0.247556 + 0.968874i \(0.420373\pi\)
\(788\) −195.221 −0.247743
\(789\) −336.144 −0.426037
\(790\) 107.513i 0.136092i
\(791\) 122.212i 0.154504i