Properties

Label 177.3.b.a.119.4
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 119.4
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.35

$q$-expansion

\(f(q)\) \(=\) \(q-3.49731i q^{2} +(-2.91161 - 0.722867i) q^{3} -8.23119 q^{4} -8.21287i q^{5} +(-2.52809 + 10.1828i) q^{6} -3.56525 q^{7} +14.7978i q^{8} +(7.95493 + 4.20941i) q^{9} +O(q^{10})\) \(q-3.49731i q^{2} +(-2.91161 - 0.722867i) q^{3} -8.23119 q^{4} -8.21287i q^{5} +(-2.52809 + 10.1828i) q^{6} -3.56525 q^{7} +14.7978i q^{8} +(7.95493 + 4.20941i) q^{9} -28.7230 q^{10} -6.15586i q^{11} +(23.9660 + 5.95006i) q^{12} +2.36040 q^{13} +12.4688i q^{14} +(-5.93681 + 23.9127i) q^{15} +18.8277 q^{16} +0.880690i q^{17} +(14.7216 - 27.8209i) q^{18} +32.8857 q^{19} +67.6017i q^{20} +(10.3806 + 2.57720i) q^{21} -21.5290 q^{22} +20.2343i q^{23} +(10.6968 - 43.0854i) q^{24} -42.4512 q^{25} -8.25505i q^{26} +(-20.1188 - 18.0065i) q^{27} +29.3462 q^{28} -46.3821i q^{29} +(83.6300 + 20.7629i) q^{30} -55.1410 q^{31} -6.65529i q^{32} +(-4.44987 + 17.9235i) q^{33} +3.08005 q^{34} +29.2809i q^{35} +(-65.4785 - 34.6485i) q^{36} -10.4535 q^{37} -115.012i q^{38} +(-6.87256 - 1.70626i) q^{39} +121.532 q^{40} -5.03972i q^{41} +(9.01328 - 36.3042i) q^{42} +14.2432 q^{43} +50.6701i q^{44} +(34.5713 - 65.3327i) q^{45} +70.7656 q^{46} +75.4957i q^{47} +(-54.8190 - 13.6100i) q^{48} -36.2890 q^{49} +148.465i q^{50} +(0.636622 - 2.56423i) q^{51} -19.4289 q^{52} -72.2215i q^{53} +(-62.9744 + 70.3617i) q^{54} -50.5573 q^{55} -52.7578i q^{56} +(-95.7504 - 23.7720i) q^{57} -162.213 q^{58} -7.68115i q^{59} +(48.8670 - 196.830i) q^{60} -8.24650 q^{61} +192.845i q^{62} +(-28.3613 - 15.0076i) q^{63} +52.0353 q^{64} -19.3856i q^{65} +(62.6840 + 15.5626i) q^{66} -101.205 q^{67} -7.24913i q^{68} +(14.6267 - 58.9143i) q^{69} +102.404 q^{70} -97.6488i q^{71} +(-62.2900 + 117.715i) q^{72} +28.7308 q^{73} +36.5592i q^{74} +(123.601 + 30.6866i) q^{75} -270.689 q^{76} +21.9472i q^{77} +(-5.96731 + 24.0355i) q^{78} +149.129 q^{79} -154.630i q^{80} +(45.5617 + 66.9711i) q^{81} -17.6255 q^{82} +85.1008i q^{83} +(-85.4447 - 21.2134i) q^{84} +7.23299 q^{85} -49.8130i q^{86} +(-33.5281 + 135.047i) q^{87} +91.0932 q^{88} -98.6034i q^{89} +(-228.489 - 120.907i) q^{90} -8.41541 q^{91} -166.552i q^{92} +(160.549 + 39.8596i) q^{93} +264.032 q^{94} -270.086i q^{95} +(-4.81090 + 19.3776i) q^{96} +93.2794 q^{97} +126.914i q^{98} +(25.9126 - 48.9694i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.49731i 1.74866i −0.485336 0.874328i \(-0.661303\pi\)
0.485336 0.874328i \(-0.338697\pi\)
\(3\) −2.91161 0.722867i −0.970536 0.240956i
\(4\) −8.23119 −2.05780
\(5\) 8.21287i 1.64257i −0.570516 0.821287i \(-0.693257\pi\)
0.570516 0.821287i \(-0.306743\pi\)
\(6\) −2.52809 + 10.1828i −0.421349 + 1.69713i
\(7\) −3.56525 −0.509321 −0.254661 0.967031i \(-0.581964\pi\)
−0.254661 + 0.967031i \(0.581964\pi\)
\(8\) 14.7978i 1.84972i
\(9\) 7.95493 + 4.20941i 0.883881 + 0.467713i
\(10\) −28.7230 −2.87230
\(11\) 6.15586i 0.559624i −0.960055 0.279812i \(-0.909728\pi\)
0.960055 0.279812i \(-0.0902721\pi\)
\(12\) 23.9660 + 5.95006i 1.99717 + 0.495838i
\(13\) 2.36040 0.181569 0.0907846 0.995871i \(-0.471063\pi\)
0.0907846 + 0.995871i \(0.471063\pi\)
\(14\) 12.4688i 0.890627i
\(15\) −5.93681 + 23.9127i −0.395788 + 1.59418i
\(16\) 18.8277 1.17673
\(17\) 0.880690i 0.0518053i 0.999664 + 0.0259027i \(0.00824600\pi\)
−0.999664 + 0.0259027i \(0.991754\pi\)
\(18\) 14.7216 27.8209i 0.817868 1.54560i
\(19\) 32.8857 1.73083 0.865414 0.501057i \(-0.167055\pi\)
0.865414 + 0.501057i \(0.167055\pi\)
\(20\) 67.6017i 3.38008i
\(21\) 10.3806 + 2.57720i 0.494314 + 0.122724i
\(22\) −21.5290 −0.978590
\(23\) 20.2343i 0.879752i 0.898059 + 0.439876i \(0.144978\pi\)
−0.898059 + 0.439876i \(0.855022\pi\)
\(24\) 10.6968 43.0854i 0.445702 1.79522i
\(25\) −42.4512 −1.69805
\(26\) 8.25505i 0.317502i
\(27\) −20.1188 18.0065i −0.745140 0.666908i
\(28\) 29.3462 1.04808
\(29\) 46.3821i 1.59938i −0.600411 0.799691i \(-0.704996\pi\)
0.600411 0.799691i \(-0.295004\pi\)
\(30\) 83.6300 + 20.7629i 2.78767 + 0.692096i
\(31\) −55.1410 −1.77874 −0.889371 0.457186i \(-0.848857\pi\)
−0.889371 + 0.457186i \(0.848857\pi\)
\(32\) 6.65529i 0.207978i
\(33\) −4.44987 + 17.9235i −0.134845 + 0.543135i
\(34\) 3.08005 0.0905897
\(35\) 29.2809i 0.836597i
\(36\) −65.4785 34.6485i −1.81885 0.962458i
\(37\) −10.4535 −0.282527 −0.141264 0.989972i \(-0.545117\pi\)
−0.141264 + 0.989972i \(0.545117\pi\)
\(38\) 115.012i 3.02662i
\(39\) −6.87256 1.70626i −0.176219 0.0437501i
\(40\) 121.532 3.03831
\(41\) 5.03972i 0.122920i −0.998110 0.0614599i \(-0.980424\pi\)
0.998110 0.0614599i \(-0.0195756\pi\)
\(42\) 9.01328 36.3042i 0.214602 0.864386i
\(43\) 14.2432 0.331238 0.165619 0.986190i \(-0.447038\pi\)
0.165619 + 0.986190i \(0.447038\pi\)
\(44\) 50.6701i 1.15159i
\(45\) 34.5713 65.3327i 0.768252 1.45184i
\(46\) 70.7656 1.53838
\(47\) 75.4957i 1.60629i 0.595783 + 0.803146i \(0.296842\pi\)
−0.595783 + 0.803146i \(0.703158\pi\)
\(48\) −54.8190 13.6100i −1.14206 0.283541i
\(49\) −36.2890 −0.740592
\(50\) 148.465i 2.96930i
\(51\) 0.636622 2.56423i 0.0124828 0.0502789i
\(52\) −19.4289 −0.373633
\(53\) 72.2215i 1.36267i −0.731972 0.681335i \(-0.761400\pi\)
0.731972 0.681335i \(-0.238600\pi\)
\(54\) −62.9744 + 70.3617i −1.16619 + 1.30299i
\(55\) −50.5573 −0.919224
\(56\) 52.7578i 0.942103i
\(57\) −95.7504 23.7720i −1.67983 0.417053i
\(58\) −162.213 −2.79677
\(59\) 7.68115i 0.130189i
\(60\) 48.8670 196.830i 0.814451 3.28049i
\(61\) −8.24650 −0.135188 −0.0675942 0.997713i \(-0.521532\pi\)
−0.0675942 + 0.997713i \(0.521532\pi\)
\(62\) 192.845i 3.11041i
\(63\) −28.3613 15.0076i −0.450179 0.238216i
\(64\) 52.0353 0.813052
\(65\) 19.3856i 0.298241i
\(66\) 62.6840 + 15.5626i 0.949757 + 0.235797i
\(67\) −101.205 −1.51052 −0.755259 0.655427i \(-0.772489\pi\)
−0.755259 + 0.655427i \(0.772489\pi\)
\(68\) 7.24913i 0.106605i
\(69\) 14.6267 58.9143i 0.211981 0.853831i
\(70\) 102.404 1.46292
\(71\) 97.6488i 1.37533i −0.726026 0.687667i \(-0.758635\pi\)
0.726026 0.687667i \(-0.241365\pi\)
\(72\) −62.2900 + 117.715i −0.865139 + 1.63494i
\(73\) 28.7308 0.393573 0.196786 0.980446i \(-0.436949\pi\)
0.196786 + 0.980446i \(0.436949\pi\)
\(74\) 36.5592i 0.494043i
\(75\) 123.601 + 30.6866i 1.64802 + 0.409154i
\(76\) −270.689 −3.56169
\(77\) 21.9472i 0.285028i
\(78\) −5.96731 + 24.0355i −0.0765040 + 0.308147i
\(79\) 149.129 1.88771 0.943855 0.330359i \(-0.107170\pi\)
0.943855 + 0.330359i \(0.107170\pi\)
\(80\) 154.630i 1.93287i
\(81\) 45.5617 + 66.9711i 0.562490 + 0.826804i
\(82\) −17.6255 −0.214945
\(83\) 85.1008i 1.02531i 0.858595 + 0.512655i \(0.171338\pi\)
−0.858595 + 0.512655i \(0.828662\pi\)
\(84\) −85.4447 21.2134i −1.01720 0.252541i
\(85\) 7.23299 0.0850940
\(86\) 49.8130i 0.579221i
\(87\) −33.5281 + 135.047i −0.385380 + 1.55226i
\(88\) 91.0932 1.03515
\(89\) 98.6034i 1.10790i −0.832549 0.553952i \(-0.813119\pi\)
0.832549 0.553952i \(-0.186881\pi\)
\(90\) −228.489 120.907i −2.53877 1.34341i
\(91\) −8.41541 −0.0924770
\(92\) 166.552i 1.81035i
\(93\) 160.549 + 39.8596i 1.72633 + 0.428598i
\(94\) 264.032 2.80885
\(95\) 270.086i 2.84301i
\(96\) −4.81090 + 19.3776i −0.0501135 + 0.201850i
\(97\) 93.2794 0.961644 0.480822 0.876818i \(-0.340338\pi\)
0.480822 + 0.876818i \(0.340338\pi\)
\(98\) 126.914i 1.29504i
\(99\) 25.9126 48.9694i 0.261743 0.494641i
\(100\) 349.424 3.49424
\(101\) 40.3505i 0.399510i −0.979846 0.199755i \(-0.935985\pi\)
0.979846 0.199755i \(-0.0640146\pi\)
\(102\) −8.96790 2.22647i −0.0879206 0.0218281i
\(103\) −119.073 −1.15605 −0.578023 0.816021i \(-0.696175\pi\)
−0.578023 + 0.816021i \(0.696175\pi\)
\(104\) 34.9287i 0.335853i
\(105\) 21.1662 85.2545i 0.201583 0.811948i
\(106\) −252.581 −2.38284
\(107\) 99.0486i 0.925688i 0.886440 + 0.462844i \(0.153171\pi\)
−0.886440 + 0.462844i \(0.846829\pi\)
\(108\) 165.602 + 148.215i 1.53335 + 1.37236i
\(109\) 20.2659 0.185926 0.0929630 0.995670i \(-0.470366\pi\)
0.0929630 + 0.995670i \(0.470366\pi\)
\(110\) 176.815i 1.60741i
\(111\) 30.4365 + 7.55650i 0.274203 + 0.0680766i
\(112\) −67.1255 −0.599335
\(113\) 68.4754i 0.605977i −0.952994 0.302988i \(-0.902016\pi\)
0.952994 0.302988i \(-0.0979843\pi\)
\(114\) −83.1382 + 334.869i −0.729282 + 2.93745i
\(115\) 166.182 1.44506
\(116\) 381.780i 3.29121i
\(117\) 18.7768 + 9.93590i 0.160485 + 0.0849222i
\(118\) −26.8634 −0.227656
\(119\) 3.13988i 0.0263855i
\(120\) −353.854 87.8517i −2.94879 0.732098i
\(121\) 83.1053 0.686821
\(122\) 28.8406i 0.236398i
\(123\) −3.64305 + 14.6737i −0.0296183 + 0.119298i
\(124\) 453.876 3.66029
\(125\) 143.324i 1.14659i
\(126\) −52.4863 + 99.1882i −0.416558 + 0.787208i
\(127\) 76.7243 0.604128 0.302064 0.953288i \(-0.402324\pi\)
0.302064 + 0.953288i \(0.402324\pi\)
\(128\) 208.605i 1.62973i
\(129\) −41.4707 10.2960i −0.321478 0.0798136i
\(130\) −67.7977 −0.521520
\(131\) 218.508i 1.66800i −0.551766 0.833999i \(-0.686046\pi\)
0.551766 0.833999i \(-0.313954\pi\)
\(132\) 36.6278 147.531i 0.277483 1.11766i
\(133\) −117.246 −0.881547
\(134\) 353.944i 2.64138i
\(135\) −147.885 + 165.233i −1.09545 + 1.22395i
\(136\) −13.0323 −0.0958256
\(137\) 56.4715i 0.412201i −0.978531 0.206101i \(-0.933923\pi\)
0.978531 0.206101i \(-0.0660774\pi\)
\(138\) −206.042 51.1542i −1.49306 0.370682i
\(139\) 62.0097 0.446113 0.223056 0.974806i \(-0.428397\pi\)
0.223056 + 0.974806i \(0.428397\pi\)
\(140\) 241.017i 1.72155i
\(141\) 54.5734 219.814i 0.387045 1.55896i
\(142\) −341.508 −2.40499
\(143\) 14.5303i 0.101610i
\(144\) 149.773 + 79.2537i 1.04009 + 0.550373i
\(145\) −380.930 −2.62710
\(146\) 100.481i 0.688223i
\(147\) 105.659 + 26.2321i 0.718771 + 0.178450i
\(148\) 86.0448 0.581384
\(149\) 26.8893i 0.180465i −0.995921 0.0902324i \(-0.971239\pi\)
0.995921 0.0902324i \(-0.0287610\pi\)
\(150\) 107.321 432.272i 0.715470 2.88181i
\(151\) −124.391 −0.823785 −0.411892 0.911233i \(-0.635132\pi\)
−0.411892 + 0.911233i \(0.635132\pi\)
\(152\) 486.636i 3.20155i
\(153\) −3.70719 + 7.00583i −0.0242300 + 0.0457897i
\(154\) 76.7561 0.498416
\(155\) 452.866i 2.92171i
\(156\) 56.5693 + 14.0445i 0.362624 + 0.0900289i
\(157\) −223.209 −1.42172 −0.710858 0.703336i \(-0.751693\pi\)
−0.710858 + 0.703336i \(0.751693\pi\)
\(158\) 521.551i 3.30096i
\(159\) −52.2066 + 210.281i −0.328343 + 1.32252i
\(160\) −54.6591 −0.341619
\(161\) 72.1403i 0.448076i
\(162\) 234.219 159.343i 1.44580 0.983601i
\(163\) 61.7561 0.378872 0.189436 0.981893i \(-0.439334\pi\)
0.189436 + 0.981893i \(0.439334\pi\)
\(164\) 41.4829i 0.252944i
\(165\) 147.203 + 36.5462i 0.892140 + 0.221492i
\(166\) 297.624 1.79291
\(167\) 60.8323i 0.364265i −0.983274 0.182133i \(-0.941700\pi\)
0.983274 0.182133i \(-0.0583000\pi\)
\(168\) −38.1369 + 153.610i −0.227005 + 0.914345i
\(169\) −163.429 −0.967033
\(170\) 25.2960i 0.148800i
\(171\) 261.604 + 138.430i 1.52985 + 0.809530i
\(172\) −117.239 −0.681620
\(173\) 110.975i 0.641477i 0.947168 + 0.320738i \(0.103931\pi\)
−0.947168 + 0.320738i \(0.896069\pi\)
\(174\) 472.300 + 117.258i 2.71437 + 0.673898i
\(175\) 151.349 0.864851
\(176\) 115.901i 0.658528i
\(177\) −5.55245 + 22.3645i −0.0313698 + 0.126353i
\(178\) −344.847 −1.93734
\(179\) 54.6001i 0.305029i 0.988301 + 0.152514i \(0.0487370\pi\)
−0.988301 + 0.152514i \(0.951263\pi\)
\(180\) −284.563 + 537.766i −1.58091 + 2.98759i
\(181\) −124.891 −0.690008 −0.345004 0.938601i \(-0.612122\pi\)
−0.345004 + 0.938601i \(0.612122\pi\)
\(182\) 29.4313i 0.161710i
\(183\) 24.0106 + 5.96112i 0.131205 + 0.0325744i
\(184\) −299.423 −1.62730
\(185\) 85.8533i 0.464072i
\(186\) 139.402 561.490i 0.749471 3.01876i
\(187\) 5.42141 0.0289915
\(188\) 621.419i 3.30542i
\(189\) 71.7284 + 64.1977i 0.379516 + 0.339670i
\(190\) −944.576 −4.97145
\(191\) 96.6411i 0.505974i −0.967470 0.252987i \(-0.918587\pi\)
0.967470 0.252987i \(-0.0814130\pi\)
\(192\) −151.506 37.6146i −0.789096 0.195909i
\(193\) −6.90714 −0.0357883 −0.0178941 0.999840i \(-0.505696\pi\)
−0.0178941 + 0.999840i \(0.505696\pi\)
\(194\) 326.227i 1.68158i
\(195\) −14.0133 + 56.4434i −0.0718628 + 0.289453i
\(196\) 298.702 1.52399
\(197\) 24.7912i 0.125844i 0.998018 + 0.0629218i \(0.0200419\pi\)
−0.998018 + 0.0629218i \(0.979958\pi\)
\(198\) −171.261 90.6244i −0.864957 0.457699i
\(199\) −20.1503 −0.101258 −0.0506289 0.998718i \(-0.516123\pi\)
−0.0506289 + 0.998718i \(0.516123\pi\)
\(200\) 628.184i 3.14092i
\(201\) 294.668 + 73.1576i 1.46601 + 0.363968i
\(202\) −141.118 −0.698605
\(203\) 165.364i 0.814599i
\(204\) −5.24016 + 21.1066i −0.0256871 + 0.103464i
\(205\) −41.3905 −0.201905
\(206\) 416.434i 2.02153i
\(207\) −85.1745 + 160.962i −0.411471 + 0.777596i
\(208\) 44.4410 0.213659
\(209\) 202.440i 0.968613i
\(210\) −298.162 74.0248i −1.41982 0.352499i
\(211\) 325.183 1.54115 0.770575 0.637349i \(-0.219969\pi\)
0.770575 + 0.637349i \(0.219969\pi\)
\(212\) 594.469i 2.80410i
\(213\) −70.5871 + 284.315i −0.331395 + 1.33481i
\(214\) 346.404 1.61871
\(215\) 116.978i 0.544082i
\(216\) 266.457 297.714i 1.23360 1.37830i
\(217\) 196.591 0.905951
\(218\) 70.8763i 0.325121i
\(219\) −83.6528 20.7686i −0.381976 0.0948336i
\(220\) 416.147 1.89158
\(221\) 2.07878i 0.00940625i
\(222\) 26.4274 106.446i 0.119042 0.479486i
\(223\) −146.044 −0.654908 −0.327454 0.944867i \(-0.606191\pi\)
−0.327454 + 0.944867i \(0.606191\pi\)
\(224\) 23.7278i 0.105928i
\(225\) −337.696 178.695i −1.50087 0.794198i
\(226\) −239.480 −1.05964
\(227\) 115.837i 0.510296i −0.966902 0.255148i \(-0.917876\pi\)
0.966902 0.255148i \(-0.0821242\pi\)
\(228\) 788.140 + 195.672i 3.45675 + 0.858211i
\(229\) −425.811 −1.85944 −0.929719 0.368271i \(-0.879950\pi\)
−0.929719 + 0.368271i \(0.879950\pi\)
\(230\) 581.189i 2.52691i
\(231\) 15.8649 63.9016i 0.0686792 0.276630i
\(232\) 686.353 2.95842
\(233\) 160.262i 0.687820i −0.939003 0.343910i \(-0.888248\pi\)
0.939003 0.343910i \(-0.111752\pi\)
\(234\) 34.7489 65.6683i 0.148500 0.280634i
\(235\) 620.036 2.63845
\(236\) 63.2250i 0.267902i
\(237\) −434.206 107.801i −1.83209 0.454855i
\(238\) −10.9811 −0.0461392
\(239\) 215.732i 0.902644i 0.892361 + 0.451322i \(0.149047\pi\)
−0.892361 + 0.451322i \(0.850953\pi\)
\(240\) −111.777 + 450.221i −0.465736 + 1.87592i
\(241\) 308.468 1.27995 0.639975 0.768396i \(-0.278945\pi\)
0.639975 + 0.768396i \(0.278945\pi\)
\(242\) 290.645i 1.20101i
\(243\) −84.2465 227.929i −0.346694 0.937978i
\(244\) 67.8785 0.278191
\(245\) 298.037i 1.21648i
\(246\) 51.3184 + 12.7409i 0.208612 + 0.0517921i
\(247\) 77.6235 0.314265
\(248\) 815.965i 3.29018i
\(249\) 61.5166 247.780i 0.247054 0.995101i
\(250\) 501.250 2.00500
\(251\) 136.796i 0.545004i −0.962155 0.272502i \(-0.912149\pi\)
0.962155 0.272502i \(-0.0878512\pi\)
\(252\) 233.447 + 123.530i 0.926377 + 0.490200i
\(253\) 124.560 0.492330
\(254\) 268.329i 1.05641i
\(255\) −21.0596 5.22849i −0.0825868 0.0205039i
\(256\) −521.415 −2.03678
\(257\) 14.0185i 0.0545468i 0.999628 + 0.0272734i \(0.00868247\pi\)
−0.999628 + 0.0272734i \(0.991318\pi\)
\(258\) −36.0082 + 145.036i −0.139567 + 0.562155i
\(259\) 37.2693 0.143897
\(260\) 159.567i 0.613719i
\(261\) 195.241 368.966i 0.748051 1.41366i
\(262\) −764.190 −2.91675
\(263\) 157.760i 0.599847i −0.953963 0.299924i \(-0.903039\pi\)
0.953963 0.299924i \(-0.0969612\pi\)
\(264\) −265.228 65.8483i −1.00465 0.249425i
\(265\) −593.146 −2.23828
\(266\) 410.045i 1.54152i
\(267\) −71.2772 + 287.094i −0.266956 + 1.07526i
\(268\) 833.035 3.10834
\(269\) 4.90919i 0.0182498i 0.999958 + 0.00912488i \(0.00290458\pi\)
−0.999958 + 0.00912488i \(0.997095\pi\)
\(270\) 577.871 + 517.200i 2.14026 + 1.91556i
\(271\) −169.663 −0.626061 −0.313031 0.949743i \(-0.601344\pi\)
−0.313031 + 0.949743i \(0.601344\pi\)
\(272\) 16.5814i 0.0609611i
\(273\) 24.5024 + 6.08322i 0.0897523 + 0.0222829i
\(274\) −197.499 −0.720798
\(275\) 261.324i 0.950268i
\(276\) −120.395 + 484.935i −0.436215 + 1.75701i
\(277\) 247.335 0.892907 0.446453 0.894807i \(-0.352687\pi\)
0.446453 + 0.894807i \(0.352687\pi\)
\(278\) 216.867i 0.780098i
\(279\) −438.643 232.111i −1.57220 0.831940i
\(280\) −433.293 −1.54747
\(281\) 36.5748i 0.130159i 0.997880 + 0.0650797i \(0.0207302\pi\)
−0.997880 + 0.0650797i \(0.979270\pi\)
\(282\) −768.758 190.860i −2.72609 0.676809i
\(283\) −298.925 −1.05627 −0.528135 0.849160i \(-0.677109\pi\)
−0.528135 + 0.849160i \(0.677109\pi\)
\(284\) 803.766i 2.83016i
\(285\) −195.236 + 786.385i −0.685040 + 2.75925i
\(286\) −50.8170 −0.177682
\(287\) 17.9678i 0.0626057i
\(288\) 28.0149 52.9424i 0.0972739 0.183828i
\(289\) 288.224 0.997316
\(290\) 1332.23i 4.59390i
\(291\) −271.593 67.4287i −0.933310 0.231714i
\(292\) −236.489 −0.809893
\(293\) 168.158i 0.573918i −0.957943 0.286959i \(-0.907356\pi\)
0.957943 0.286959i \(-0.0926444\pi\)
\(294\) 91.7420 369.524i 0.312048 1.25688i
\(295\) −63.0842 −0.213845
\(296\) 154.689i 0.522597i
\(297\) −110.846 + 123.848i −0.373218 + 0.416998i
\(298\) −94.0401 −0.315571
\(299\) 47.7610i 0.159736i
\(300\) −1017.39 252.587i −3.39128 0.841957i
\(301\) −50.7806 −0.168706
\(302\) 435.036i 1.44052i
\(303\) −29.1681 + 117.485i −0.0962642 + 0.387739i
\(304\) 619.164 2.03672
\(305\) 67.7274i 0.222057i
\(306\) 24.5016 + 12.9652i 0.0800705 + 0.0423699i
\(307\) 159.132 0.518345 0.259172 0.965831i \(-0.416550\pi\)
0.259172 + 0.965831i \(0.416550\pi\)
\(308\) 180.651i 0.586531i
\(309\) 346.693 + 86.0737i 1.12198 + 0.278556i
\(310\) 1583.81 5.10907
\(311\) 371.820i 1.19556i 0.801659 + 0.597782i \(0.203951\pi\)
−0.801659 + 0.597782i \(0.796049\pi\)
\(312\) 25.2488 101.699i 0.0809257 0.325957i
\(313\) −1.08898 −0.00347918 −0.00173959 0.999998i \(-0.500554\pi\)
−0.00173959 + 0.999998i \(0.500554\pi\)
\(314\) 780.633i 2.48609i
\(315\) −123.255 + 232.927i −0.391287 + 0.739452i
\(316\) −1227.51 −3.88453
\(317\) 333.579i 1.05230i −0.850392 0.526150i \(-0.823635\pi\)
0.850392 0.526150i \(-0.176365\pi\)
\(318\) 735.417 + 182.583i 2.31263 + 0.574159i
\(319\) −285.522 −0.895053
\(320\) 427.359i 1.33550i
\(321\) 71.5990 288.391i 0.223050 0.898413i
\(322\) −252.297 −0.783531
\(323\) 28.9622i 0.0896661i
\(324\) −375.027 551.252i −1.15749 1.70140i
\(325\) −100.202 −0.308313
\(326\) 215.980i 0.662516i
\(327\) −59.0065 14.6496i −0.180448 0.0448000i
\(328\) 74.5767 0.227368
\(329\) 269.161i 0.818118i
\(330\) 127.814 514.815i 0.387314 1.56005i
\(331\) 333.908 1.00878 0.504392 0.863475i \(-0.331717\pi\)
0.504392 + 0.863475i \(0.331717\pi\)
\(332\) 700.481i 2.10988i
\(333\) −83.1569 44.0031i −0.249720 0.132142i
\(334\) −212.749 −0.636974
\(335\) 831.181i 2.48114i
\(336\) 195.443 + 48.5229i 0.581676 + 0.144413i
\(337\) 368.536 1.09358 0.546789 0.837271i \(-0.315850\pi\)
0.546789 + 0.837271i \(0.315850\pi\)
\(338\) 571.560i 1.69101i
\(339\) −49.4986 + 199.373i −0.146014 + 0.588122i
\(340\) −59.5362 −0.175106
\(341\) 339.441i 0.995427i
\(342\) 484.132 914.909i 1.41559 2.67517i
\(343\) 304.076 0.886520
\(344\) 210.768i 0.612698i
\(345\) −483.856 120.127i −1.40248 0.348195i
\(346\) 388.116 1.12172
\(347\) 454.904i 1.31096i −0.755211 0.655482i \(-0.772466\pi\)
0.755211 0.655482i \(-0.227534\pi\)
\(348\) 275.976 1111.59i 0.793035 3.19423i
\(349\) 483.918 1.38658 0.693292 0.720657i \(-0.256160\pi\)
0.693292 + 0.720657i \(0.256160\pi\)
\(350\) 529.315i 1.51233i
\(351\) −47.4884 42.5026i −0.135294 0.121090i
\(352\) −40.9691 −0.116389
\(353\) 294.298i 0.833705i −0.908974 0.416853i \(-0.863133\pi\)
0.908974 0.416853i \(-0.136867\pi\)
\(354\) 78.2156 + 19.4186i 0.220948 + 0.0548549i
\(355\) −801.976 −2.25909
\(356\) 811.623i 2.27984i
\(357\) −2.26972 + 9.14210i −0.00635775 + 0.0256081i
\(358\) 190.954 0.533390
\(359\) 152.605i 0.425083i 0.977152 + 0.212541i \(0.0681740\pi\)
−0.977152 + 0.212541i \(0.931826\pi\)
\(360\) 966.781 + 511.580i 2.68550 + 1.42105i
\(361\) 720.472 1.99577
\(362\) 436.784i 1.20659i
\(363\) −241.970 60.0741i −0.666584 0.165493i
\(364\) 69.2688 0.190299
\(365\) 235.962i 0.646472i
\(366\) 20.8479 83.9725i 0.0569615 0.229433i
\(367\) −252.819 −0.688881 −0.344441 0.938808i \(-0.611931\pi\)
−0.344441 + 0.938808i \(0.611931\pi\)
\(368\) 380.966i 1.03523i
\(369\) 21.2142 40.0906i 0.0574912 0.108647i
\(370\) 300.256 0.811502
\(371\) 257.487i 0.694036i
\(372\) −1321.51 328.092i −3.55245 0.881968i
\(373\) 630.560 1.69051 0.845255 0.534363i \(-0.179449\pi\)
0.845255 + 0.534363i \(0.179449\pi\)
\(374\) 18.9604i 0.0506962i
\(375\) 103.604 417.304i 0.276279 1.11281i
\(376\) −1117.17 −2.97120
\(377\) 109.480i 0.290399i
\(378\) 224.519 250.857i 0.593967 0.663642i
\(379\) 14.5692 0.0384412 0.0192206 0.999815i \(-0.493882\pi\)
0.0192206 + 0.999815i \(0.493882\pi\)
\(380\) 2223.13i 5.85034i
\(381\) −223.391 55.4615i −0.586328 0.145568i
\(382\) −337.984 −0.884775
\(383\) 594.960i 1.55342i −0.629858 0.776710i \(-0.716887\pi\)
0.629858 0.776710i \(-0.283113\pi\)
\(384\) −150.794 + 607.376i −0.392692 + 1.58171i
\(385\) 180.249 0.468180
\(386\) 24.1564i 0.0625814i
\(387\) 113.304 + 59.9556i 0.292775 + 0.154924i
\(388\) −767.801 −1.97887
\(389\) 405.842i 1.04330i −0.853161 0.521648i \(-0.825318\pi\)
0.853161 0.521648i \(-0.174682\pi\)
\(390\) 197.400 + 49.0087i 0.506154 + 0.125663i
\(391\) −17.8202 −0.0455758
\(392\) 536.997i 1.36989i
\(393\) −157.952 + 636.209i −0.401914 + 1.61885i
\(394\) 86.7025 0.220057
\(395\) 1224.78i 3.10070i
\(396\) −213.291 + 403.077i −0.538615 + 1.01787i
\(397\) 203.579 0.512793 0.256396 0.966572i \(-0.417465\pi\)
0.256396 + 0.966572i \(0.417465\pi\)
\(398\) 70.4720i 0.177065i
\(399\) 341.374 + 84.7531i 0.855573 + 0.212414i
\(400\) −799.260 −1.99815
\(401\) 266.091i 0.663568i 0.943355 + 0.331784i \(0.107651\pi\)
−0.943355 + 0.331784i \(0.892349\pi\)
\(402\) 255.855 1030.55i 0.636455 2.56355i
\(403\) −130.155 −0.322965
\(404\) 332.133i 0.822111i
\(405\) 550.025 374.192i 1.35809 0.923931i
\(406\) 578.328 1.42445
\(407\) 64.3504i 0.158109i
\(408\) 37.9449 + 9.42061i 0.0930022 + 0.0230897i
\(409\) −50.9470 −0.124565 −0.0622824 0.998059i \(-0.519838\pi\)
−0.0622824 + 0.998059i \(0.519838\pi\)
\(410\) 144.756i 0.353062i
\(411\) −40.8214 + 164.423i −0.0993222 + 0.400056i
\(412\) 980.110 2.37891
\(413\) 27.3852i 0.0663080i
\(414\) 562.935 + 297.882i 1.35975 + 0.719521i
\(415\) 698.921 1.68415
\(416\) 15.7092i 0.0377624i
\(417\) −180.548 44.8248i −0.432969 0.107493i
\(418\) −707.996 −1.69377
\(419\) 159.456i 0.380564i −0.981730 0.190282i \(-0.939060\pi\)
0.981730 0.190282i \(-0.0609402\pi\)
\(420\) −174.223 + 701.746i −0.414817 + 1.67082i
\(421\) 413.018 0.981041 0.490520 0.871430i \(-0.336807\pi\)
0.490520 + 0.871430i \(0.336807\pi\)
\(422\) 1137.27i 2.69494i
\(423\) −317.793 + 600.563i −0.751283 + 1.41977i
\(424\) 1068.72 2.52056
\(425\) 37.3864i 0.0879679i
\(426\) 994.338 + 246.865i 2.33413 + 0.579496i
\(427\) 29.4008 0.0688543
\(428\) 815.288i 1.90488i
\(429\) −10.5035 + 42.3065i −0.0244836 + 0.0986166i
\(430\) −409.107 −0.951413
\(431\) 797.605i 1.85059i −0.379246 0.925296i \(-0.623816\pi\)
0.379246 0.925296i \(-0.376184\pi\)
\(432\) −378.791 339.022i −0.876831 0.784773i
\(433\) 139.027 0.321079 0.160539 0.987029i \(-0.448677\pi\)
0.160539 + 0.987029i \(0.448677\pi\)
\(434\) 687.541i 1.58420i
\(435\) 1109.12 + 275.362i 2.54970 + 0.633016i
\(436\) −166.813 −0.382598
\(437\) 665.420i 1.52270i
\(438\) −72.6341 + 292.560i −0.165831 + 0.667945i
\(439\) −179.734 −0.409417 −0.204708 0.978823i \(-0.565625\pi\)
−0.204708 + 0.978823i \(0.565625\pi\)
\(440\) 748.136i 1.70031i
\(441\) −288.676 152.755i −0.654595 0.346384i
\(442\) 7.27015 0.0164483
\(443\) 1.01657i 0.00229473i −0.999999 0.00114737i \(-0.999635\pi\)
0.999999 0.00114737i \(-0.000365218\pi\)
\(444\) −250.529 62.1990i −0.564254 0.140088i
\(445\) −809.816 −1.81981
\(446\) 510.763i 1.14521i
\(447\) −19.4374 + 78.2910i −0.0434840 + 0.175148i
\(448\) −185.519 −0.414104
\(449\) 486.766i 1.08411i 0.840343 + 0.542055i \(0.182354\pi\)
−0.840343 + 0.542055i \(0.817646\pi\)
\(450\) −624.951 + 1181.03i −1.38878 + 2.62451i
\(451\) −31.0238 −0.0687889
\(452\) 563.634i 1.24698i
\(453\) 362.179 + 89.9185i 0.799513 + 0.198496i
\(454\) −405.119 −0.892332
\(455\) 69.1146i 0.151900i
\(456\) 351.773 1416.89i 0.771433 3.10722i
\(457\) −333.251 −0.729214 −0.364607 0.931161i \(-0.618797\pi\)
−0.364607 + 0.931161i \(0.618797\pi\)
\(458\) 1489.19i 3.25152i
\(459\) 15.8582 17.7184i 0.0345494 0.0386022i
\(460\) −1367.87 −2.97364
\(461\) 459.339i 0.996398i 0.867063 + 0.498199i \(0.166005\pi\)
−0.867063 + 0.498199i \(0.833995\pi\)
\(462\) −223.484 55.4845i −0.483731 0.120096i
\(463\) 493.142 1.06510 0.532551 0.846398i \(-0.321233\pi\)
0.532551 + 0.846398i \(0.321233\pi\)
\(464\) 873.270i 1.88205i
\(465\) 327.362 1318.57i 0.704004 2.83563i
\(466\) −560.487 −1.20276
\(467\) 531.264i 1.13761i 0.822473 + 0.568805i \(0.192594\pi\)
−0.822473 + 0.568805i \(0.807406\pi\)
\(468\) −154.555 81.7843i −0.330247 0.174753i
\(469\) 360.820 0.769338
\(470\) 2168.46i 4.61374i
\(471\) 649.898 + 161.351i 1.37983 + 0.342571i
\(472\) 113.664 0.240814
\(473\) 87.6794i 0.185369i
\(474\) −377.012 + 1518.55i −0.795385 + 3.20370i
\(475\) −1396.04 −2.93903
\(476\) 25.8449i 0.0542961i
\(477\) 304.010 574.517i 0.637338 1.20444i
\(478\) 754.482 1.57841
\(479\) 601.359i 1.25545i −0.778437 0.627723i \(-0.783987\pi\)
0.778437 0.627723i \(-0.216013\pi\)
\(480\) 159.146 + 39.5112i 0.331554 + 0.0823151i
\(481\) −24.6744 −0.0512982
\(482\) 1078.81i 2.23819i
\(483\) −52.1478 + 210.044i −0.107967 + 0.434874i
\(484\) −684.056 −1.41334
\(485\) 766.092i 1.57957i
\(486\) −797.138 + 294.636i −1.64020 + 0.606248i
\(487\) −555.132 −1.13990 −0.569951 0.821679i \(-0.693038\pi\)
−0.569951 + 0.821679i \(0.693038\pi\)
\(488\) 122.030i 0.250061i
\(489\) −179.809 44.6414i −0.367709 0.0912913i
\(490\) 1042.33 2.12720
\(491\) 10.0690i 0.0205071i −0.999947 0.0102535i \(-0.996736\pi\)
0.999947 0.0102535i \(-0.00326386\pi\)
\(492\) 29.9866 120.782i 0.0609484 0.245492i
\(493\) 40.8483 0.0828565
\(494\) 271.473i 0.549541i
\(495\) −402.180 212.817i −0.812484 0.429932i
\(496\) −1038.18 −2.09311
\(497\) 348.142i 0.700487i
\(498\) −866.564 215.143i −1.74009 0.432013i
\(499\) 409.942 0.821526 0.410763 0.911742i \(-0.365262\pi\)
0.410763 + 0.911742i \(0.365262\pi\)
\(500\) 1179.73i 2.35946i
\(501\) −43.9737 + 177.120i −0.0877718 + 0.353532i
\(502\) −478.419 −0.953025
\(503\) 50.1524i 0.0997065i −0.998757 0.0498532i \(-0.984125\pi\)
0.998757 0.0498532i \(-0.0158754\pi\)
\(504\) 222.079 419.684i 0.440634 0.832707i
\(505\) −331.393 −0.656224
\(506\) 435.624i 0.860916i
\(507\) 475.840 + 118.137i 0.938540 + 0.233012i
\(508\) −631.532 −1.24317
\(509\) 615.820i 1.20986i 0.796278 + 0.604931i \(0.206799\pi\)
−0.796278 + 0.604931i \(0.793201\pi\)
\(510\) −18.2857 + 73.6521i −0.0358543 + 0.144416i
\(511\) −102.432 −0.200455
\(512\) 989.132i 1.93190i
\(513\) −661.621 592.158i −1.28971 1.15430i
\(514\) 49.0272 0.0953836
\(515\) 977.928i 1.89889i
\(516\) 341.353 + 84.7480i 0.661537 + 0.164240i
\(517\) 464.741 0.898919
\(518\) 130.342i 0.251626i
\(519\) 80.2206 323.117i 0.154568 0.622576i
\(520\) 286.865 0.551663
\(521\) 428.898i 0.823220i 0.911360 + 0.411610i \(0.135033\pi\)
−0.911360 + 0.411610i \(0.864967\pi\)
\(522\) −1290.39 682.820i −2.47201 1.30808i
\(523\) −636.438 −1.21690 −0.608450 0.793592i \(-0.708208\pi\)
−0.608450 + 0.793592i \(0.708208\pi\)
\(524\) 1798.58i 3.43240i
\(525\) −440.669 109.405i −0.839369 0.208391i
\(526\) −551.735 −1.04893
\(527\) 48.5622i 0.0921483i
\(528\) −83.7810 + 337.458i −0.158676 + 0.639126i
\(529\) 119.573 0.226036
\(530\) 2074.41i 3.91399i
\(531\) 32.3331 61.1029i 0.0608910 0.115071i
\(532\) 965.072 1.81405
\(533\) 11.8957i 0.0223185i
\(534\) 1004.06 + 249.278i 1.88026 + 0.466814i
\(535\) 813.473 1.52051
\(536\) 1497.61i 2.79404i
\(537\) 39.4687 158.974i 0.0734984 0.296041i
\(538\) 17.1690 0.0319126
\(539\) 223.390i 0.414453i
\(540\) 1217.27 1360.06i 2.25421 2.51864i
\(541\) −724.827 −1.33979 −0.669896 0.742455i \(-0.733661\pi\)
−0.669896 + 0.742455i \(0.733661\pi\)
\(542\) 593.363i 1.09477i
\(543\) 363.635 + 90.2799i 0.669677 + 0.166261i
\(544\) 5.86125 0.0107744
\(545\) 166.442i 0.305397i
\(546\) 21.2749 85.6924i 0.0389651 0.156946i
\(547\) 869.429 1.58945 0.794725 0.606970i \(-0.207615\pi\)
0.794725 + 0.606970i \(0.207615\pi\)
\(548\) 464.828i 0.848226i
\(549\) −65.6003 34.7129i −0.119490 0.0632294i
\(550\) 913.931 1.66169
\(551\) 1525.31i 2.76826i
\(552\) 871.802 + 216.443i 1.57935 + 0.392107i
\(553\) −531.682 −0.961451
\(554\) 865.008i 1.56139i
\(555\) 62.0605 249.971i 0.111821 0.450398i
\(556\) −510.414 −0.918010
\(557\) 382.734i 0.687135i 0.939128 + 0.343568i \(0.111635\pi\)
−0.939128 + 0.343568i \(0.888365\pi\)
\(558\) −811.766 + 1534.07i −1.45478 + 2.74923i
\(559\) 33.6197 0.0601426
\(560\) 551.293i 0.984452i
\(561\) −15.7850 3.91896i −0.0281373 0.00698567i
\(562\) 127.913 0.227604
\(563\) 870.684i 1.54651i 0.634096 + 0.773254i \(0.281372\pi\)
−0.634096 + 0.773254i \(0.718628\pi\)
\(564\) −449.204 + 1809.33i −0.796461 + 3.20803i
\(565\) −562.379 −0.995361
\(566\) 1045.43i 1.84705i
\(567\) −162.439 238.769i −0.286488 0.421109i
\(568\) 1444.99 2.54399
\(569\) 678.235i 1.19198i 0.802993 + 0.595989i \(0.203240\pi\)
−0.802993 + 0.595989i \(0.796760\pi\)
\(570\) 2750.23 + 682.803i 4.82497 + 1.19790i
\(571\) −615.610 −1.07813 −0.539063 0.842266i \(-0.681221\pi\)
−0.539063 + 0.842266i \(0.681221\pi\)
\(572\) 119.602i 0.209094i
\(573\) −69.8587 + 281.381i −0.121917 + 0.491066i
\(574\) 62.8391 0.109476
\(575\) 858.970i 1.49386i
\(576\) 413.937 + 219.038i 0.718641 + 0.380274i
\(577\) 755.566 1.30947 0.654737 0.755857i \(-0.272780\pi\)
0.654737 + 0.755857i \(0.272780\pi\)
\(578\) 1008.01i 1.74396i
\(579\) 20.1109 + 4.99294i 0.0347338 + 0.00862339i
\(580\) 3135.51 5.40605
\(581\) 303.405i 0.522212i
\(582\) −235.819 + 949.846i −0.405187 + 1.63204i
\(583\) −444.586 −0.762583
\(584\) 425.152i 0.728001i
\(585\) 81.6022 154.211i 0.139491 0.263609i
\(586\) −588.101 −1.00359
\(587\) 464.614i 0.791505i 0.918357 + 0.395753i \(0.129516\pi\)
−0.918357 + 0.395753i \(0.870484\pi\)
\(588\) −869.703 215.922i −1.47909 0.367214i
\(589\) −1813.35 −3.07870
\(590\) 220.625i 0.373941i
\(591\) 17.9207 72.1822i 0.0303227 0.122136i
\(592\) −196.816 −0.332459
\(593\) 401.514i 0.677090i −0.940950 0.338545i \(-0.890065\pi\)
0.940950 0.338545i \(-0.109935\pi\)
\(594\) 433.137 + 387.662i 0.729187 + 0.652630i
\(595\) −25.7874 −0.0433402
\(596\) 221.331i 0.371360i
\(597\) 58.6698 + 14.5660i 0.0982744 + 0.0243987i
\(598\) 167.035 0.279323
\(599\) 488.252i 0.815111i 0.913180 + 0.407556i \(0.133619\pi\)
−0.913180 + 0.407556i \(0.866381\pi\)
\(600\) −454.094 + 1829.03i −0.756823 + 3.04838i
\(601\) 353.891 0.588836 0.294418 0.955677i \(-0.404874\pi\)
0.294418 + 0.955677i \(0.404874\pi\)
\(602\) 177.596i 0.295009i
\(603\) −805.076 426.012i −1.33512 0.706488i
\(604\) 1023.89 1.69518
\(605\) 682.533i 1.12815i
\(606\) 410.881 + 102.010i 0.678022 + 0.168333i
\(607\) 571.185 0.940996 0.470498 0.882401i \(-0.344074\pi\)
0.470498 + 0.882401i \(0.344074\pi\)
\(608\) 218.864i 0.359974i
\(609\) 119.536 481.474i 0.196282 0.790598i
\(610\) 236.864 0.388301
\(611\) 178.200i 0.291653i
\(612\) 30.5146 57.6663i 0.0498604 0.0942260i
\(613\) 48.0285 0.0783499 0.0391750 0.999232i \(-0.487527\pi\)
0.0391750 + 0.999232i \(0.487527\pi\)
\(614\) 556.534i 0.906407i
\(615\) 120.513 + 29.9199i 0.195956 + 0.0486502i
\(616\) −324.770 −0.527224
\(617\) 529.530i 0.858233i −0.903249 0.429116i \(-0.858825\pi\)
0.903249 0.429116i \(-0.141175\pi\)
\(618\) 301.027 1212.49i 0.487098 1.96196i
\(619\) −35.3405 −0.0570929 −0.0285465 0.999592i \(-0.509088\pi\)
−0.0285465 + 0.999592i \(0.509088\pi\)
\(620\) 3727.62i 6.01230i
\(621\) 364.349 407.089i 0.586714 0.655538i
\(622\) 1300.37 2.09063
\(623\) 351.545i 0.564278i
\(624\) −129.395 32.1249i −0.207363 0.0514823i
\(625\) 115.824 0.185318
\(626\) 3.80852i 0.00608390i
\(627\) −146.337 + 589.426i −0.233393 + 0.940074i
\(628\) 1837.28 2.92560
\(629\) 9.20630i 0.0146364i
\(630\) 814.620 + 431.063i 1.29305 + 0.684226i
\(631\) −33.5343 −0.0531447 −0.0265724 0.999647i \(-0.508459\pi\)
−0.0265724 + 0.999647i \(0.508459\pi\)
\(632\) 2206.78i 3.49174i
\(633\) −946.805 235.064i −1.49574 0.371349i
\(634\) −1166.63 −1.84011
\(635\) 630.127i 0.992325i
\(636\) 429.722 1730.86i 0.675664 2.72148i
\(637\) −85.6566 −0.134469
\(638\) 998.559i 1.56514i
\(639\) 411.044 776.789i 0.643261 1.21563i
\(640\) −1713.24 −2.67694
\(641\) 177.729i 0.277268i 0.990344 + 0.138634i \(0.0442712\pi\)
−0.990344 + 0.138634i \(0.955729\pi\)
\(642\) −1008.59 250.404i −1.57102 0.390037i
\(643\) −182.397 −0.283666 −0.141833 0.989891i \(-0.545300\pi\)
−0.141833 + 0.989891i \(0.545300\pi\)
\(644\) 593.800i 0.922050i
\(645\) −84.5594 + 340.593i −0.131100 + 0.528052i
\(646\) 101.290 0.156795
\(647\) 713.043i 1.10208i 0.834480 + 0.551038i \(0.185768\pi\)
−0.834480 + 0.551038i \(0.814232\pi\)
\(648\) −991.025 + 674.212i −1.52936 + 1.04045i
\(649\) −47.2841 −0.0728568
\(650\) 350.437i 0.539134i
\(651\) −572.397 142.109i −0.879258 0.218294i
\(652\) −508.326 −0.779641
\(653\) 173.772i 0.266114i −0.991108 0.133057i \(-0.957521\pi\)
0.991108 0.133057i \(-0.0424793\pi\)
\(654\) −51.2342 + 206.364i −0.0783397 + 0.315541i
\(655\) −1794.57 −2.73981
\(656\) 94.8864i 0.144644i
\(657\) 228.551 + 120.940i 0.347871 + 0.184079i
\(658\) −941.339 −1.43061
\(659\) 741.153i 1.12466i −0.826912 0.562332i \(-0.809904\pi\)
0.826912 0.562332i \(-0.190096\pi\)
\(660\) −1211.66 300.819i −1.83584 0.455786i
\(661\) 583.315 0.882474 0.441237 0.897391i \(-0.354540\pi\)
0.441237 + 0.897391i \(0.354540\pi\)
\(662\) 1167.78i 1.76402i
\(663\) 1.50268 6.05260i 0.00226649 0.00912911i
\(664\) −1259.30 −1.89654
\(665\) 962.924i 1.44801i
\(666\) −153.893 + 290.825i −0.231070 + 0.436675i
\(667\) 938.509 1.40706
\(668\) 500.722i 0.749584i
\(669\) 425.224 + 105.571i 0.635612 + 0.157804i
\(670\) 2906.90 4.33865
\(671\) 50.7643i 0.0756547i
\(672\) 17.1520 69.0860i 0.0255239 0.102807i
\(673\) −879.243 −1.30645 −0.653226 0.757163i \(-0.726585\pi\)
−0.653226 + 0.757163i \(0.726585\pi\)
\(674\) 1288.88i 1.91229i
\(675\) 854.066 + 764.398i 1.26528 + 1.13244i
\(676\) 1345.21 1.98996
\(677\) 916.427i 1.35366i 0.736140 + 0.676830i \(0.236647\pi\)
−0.736140 + 0.676830i \(0.763353\pi\)
\(678\) 697.271 + 173.112i 1.02842 + 0.255328i
\(679\) −332.564 −0.489785
\(680\) 107.032i 0.157401i
\(681\) −83.7349 + 337.272i −0.122959 + 0.495261i
\(682\) 1187.13 1.74066
\(683\) 744.048i 1.08938i 0.838637 + 0.544691i \(0.183353\pi\)
−0.838637 + 0.544691i \(0.816647\pi\)
\(684\) −2153.31 1139.44i −3.14811 1.66585i
\(685\) −463.793 −0.677070
\(686\) 1063.45i 1.55022i
\(687\) 1239.80 + 307.805i 1.80465 + 0.448042i
\(688\) 268.168 0.389779
\(689\) 170.472i 0.247419i
\(690\) −420.122 + 1692.19i −0.608873 + 2.45246i
\(691\) 252.740 0.365760 0.182880 0.983135i \(-0.441458\pi\)
0.182880 + 0.983135i \(0.441458\pi\)
\(692\) 913.460i 1.32003i
\(693\) −92.3847 + 174.588i −0.133311 + 0.251931i
\(694\) −1590.94 −2.29242
\(695\) 509.277i 0.732773i
\(696\) −1998.39 496.142i −2.87125 0.712848i
\(697\) 4.43843 0.00636790
\(698\) 1692.41i 2.42466i
\(699\) −115.848 + 466.620i −0.165734 + 0.667554i
\(700\) −1245.78 −1.77969
\(701\) 590.422i 0.842256i −0.907001 0.421128i \(-0.861634\pi\)
0.907001 0.421128i \(-0.138366\pi\)
\(702\) −148.645 + 166.082i −0.211745 + 0.236583i
\(703\) −343.771 −0.489006
\(704\) 320.322i 0.455003i
\(705\) −1805.30 448.204i −2.56071 0.635750i
\(706\) −1029.25 −1.45786
\(707\) 143.860i 0.203479i
\(708\) 45.7033 184.086i 0.0645526 0.260009i
\(709\) 648.001 0.913964 0.456982 0.889476i \(-0.348930\pi\)
0.456982 + 0.889476i \(0.348930\pi\)
\(710\) 2804.76i 3.95037i
\(711\) 1186.31 + 627.746i 1.66851 + 0.882906i
\(712\) 1459.11 2.04932
\(713\) 1115.74i 1.56485i
\(714\) 31.9728 + 7.93791i 0.0447798 + 0.0111175i
\(715\) −119.335 −0.166903
\(716\) 449.424i 0.627687i
\(717\) 155.946 628.127i 0.217497 0.876049i
\(718\) 533.706 0.743323
\(719\) 532.079i 0.740027i −0.929026 0.370014i \(-0.879353\pi\)
0.929026 0.370014i \(-0.120647\pi\)
\(720\) 650.900 1230.07i 0.904028 1.70843i
\(721\) 424.524 0.588798
\(722\) 2519.71i 3.48991i
\(723\) −898.138 222.981i −1.24224 0.308411i
\(724\) 1028.00 1.41990
\(725\) 1968.98i 2.71583i
\(726\) −210.098 + 846.245i −0.289391 + 1.16563i
\(727\) −1288.32 −1.77210 −0.886049 0.463592i \(-0.846560\pi\)
−0.886049 + 0.463592i \(0.846560\pi\)
\(728\) 124.529i 0.171057i
\(729\) 80.5307 + 724.538i 0.110467 + 0.993880i
\(730\) −825.234 −1.13046
\(731\) 12.5439i 0.0171599i
\(732\) −197.636 49.0671i −0.269994 0.0670316i
\(733\) 394.335 0.537974 0.268987 0.963144i \(-0.413311\pi\)
0.268987 + 0.963144i \(0.413311\pi\)
\(734\) 884.188i 1.20462i
\(735\) 215.441 867.766i 0.293117 1.18063i
\(736\) 134.665 0.182969
\(737\) 623.002i 0.845322i
\(738\) −140.209 74.1928i −0.189985 0.100532i
\(739\) −199.786 −0.270347 −0.135173 0.990822i \(-0.543159\pi\)
−0.135173 + 0.990822i \(0.543159\pi\)
\(740\) 706.675i 0.954966i
\(741\) −226.009 56.1115i −0.305006 0.0757240i
\(742\) 900.514 1.21363
\(743\) 112.421i 0.151306i 0.997134 + 0.0756531i \(0.0241042\pi\)
−0.997134 + 0.0756531i \(0.975896\pi\)
\(744\) −589.835 + 2375.77i −0.792789 + 3.19324i
\(745\) −220.838 −0.296427
\(746\) 2205.27i 2.95612i
\(747\) −358.224 + 676.970i −0.479551 + 0.906252i
\(748\) −44.6247 −0.0596587
\(749\) 353.133i 0.471472i
\(750\) −1459.44 362.337i −1.94592 0.483116i
\(751\) 785.625 1.04611 0.523053 0.852300i \(-0.324793\pi\)
0.523053 + 0.852300i \(0.324793\pi\)
\(752\) 1421.41i 1.89018i
\(753\) −98.8854 + 398.297i −0.131322 + 0.528947i
\(754\) −382.887 −0.507807
\(755\) 1021.61i 1.35313i
\(756\) −590.410 528.423i −0.780966 0.698973i
\(757\) 1361.82 1.79897 0.899486 0.436950i \(-0.143941\pi\)
0.899486 + 0.436950i \(0.143941\pi\)
\(758\) 50.9531i 0.0672205i
\(759\) −362.669 90.0401i −0.477824 0.118630i
\(760\) 3996.68 5.25879
\(761\) 1092.13i 1.43512i −0.696494 0.717562i \(-0.745258\pi\)
0.696494 0.717562i \(-0.254742\pi\)
\(762\) −193.966 + 781.269i −0.254549 + 1.02529i
\(763\) −72.2531 −0.0946961
\(764\) 795.471i 1.04119i
\(765\) 57.5379 + 30.4467i 0.0752130 + 0.0397996i
\(766\) −2080.76 −2.71640
\(767\) 18.1306i 0.0236383i
\(768\) 1518.16 + 376.914i 1.97677 + 0.490773i
\(769\) 428.468 0.557176 0.278588 0.960411i \(-0.410134\pi\)
0.278588 + 0.960411i \(0.410134\pi\)
\(770\) 630.388i 0.818686i
\(771\) 10.1335 40.8165i 0.0131434 0.0529396i
\(772\) 56.8540 0.0736450
\(773\) 493.717i 0.638702i −0.947637 0.319351i \(-0.896535\pi\)
0.947637 0.319351i \(-0.103465\pi\)
\(774\) 209.683 396.259i 0.270909 0.511962i
\(775\) 2340.80 3.02039
\(776\) 1380.33i 1.77878i
\(777\) −108.514 26.9408i −0.139657 0.0346728i
\(778\) −1419.36 −1.82436
\(779\) 165.735i 0.212753i
\(780\) 115.346 464.596i 0.147879 0.595637i
\(781\) −601.113 −0.769670
\(782\) 62.3226i 0.0796965i
\(783\) −835.180 + 933.151i −1.06664 + 1.19176i
\(784\) −683.240 −0.871480
\(785\) 1833.19i 2.33527i
\(786\) 2225.02 + 552.408i 2.83082 +