Properties

Label 177.4.d.c.176.4
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 176.4
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.3

$q$-expansion

\(f(q)\) \(=\) \(q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +O(q^{10})\) \(q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +79.3161i q^{10} -36.5750 q^{11} +(75.0198 + 48.9172i) q^{12} +4.20455i q^{13} +95.2574 q^{14} +(44.8112 - 68.7228i) q^{15} +95.1835 q^{16} +97.3906i q^{17} +(-54.7061 - 124.113i) q^{18} -44.1528 q^{19} -272.134i q^{20} +(-82.5351 - 53.8175i) q^{21} +183.735 q^{22} +190.656 q^{23} +(-201.941 - 131.677i) q^{24} -124.291 q^{25} -21.1216i q^{26} +(-22.7204 + 138.444i) q^{27} -326.828 q^{28} +131.011i q^{29} +(-225.110 + 345.230i) q^{30} +206.913i q^{31} -106.991 q^{32} +(-159.196 - 103.805i) q^{33} -489.243i q^{34} +299.395i q^{35} +(187.697 + 425.832i) q^{36} +106.024i q^{37} +221.802 q^{38} +(-11.9331 + 18.3006i) q^{39} +732.539i q^{40} +214.440i q^{41} +(414.616 + 270.353i) q^{42} +213.227i q^{43} -630.396 q^{44} +(390.089 - 171.942i) q^{45} -957.762 q^{46} -444.240 q^{47} +(414.294 + 270.143i) q^{48} +16.5690 q^{49} +624.380 q^{50} +(-276.407 + 423.901i) q^{51} +72.4682i q^{52} -624.911i q^{53} +(114.136 - 695.476i) q^{54} +577.482i q^{55} +879.768 q^{56} +(-192.179 - 125.312i) q^{57} -658.135i q^{58} +(-389.685 - 231.353i) q^{59} +(772.352 - 1184.49i) q^{60} +437.873i q^{61} -1039.43i q^{62} +(-206.500 - 468.491i) q^{63} -223.999 q^{64} +66.3854 q^{65} +(799.723 + 521.465i) q^{66} -648.388i q^{67} +1678.59i q^{68} +(829.846 + 541.106i) q^{69} -1504.02i q^{70} +809.977i q^{71} +(-505.248 - 1146.27i) q^{72} -39.3227i q^{73} -532.613i q^{74} +(-540.989 - 352.756i) q^{75} -761.005 q^{76} +693.547 q^{77} +(59.9459 - 91.9335i) q^{78} +595.268 q^{79} -1502.85i q^{80} +(-491.816 + 538.106i) q^{81} -1077.24i q^{82} -642.266 q^{83} +(-1422.55 - 927.582i) q^{84} +1537.70 q^{85} -1071.15i q^{86} +(-371.826 + 570.236i) q^{87} +1696.92 q^{88} -258.723 q^{89} +(-1959.62 + 863.753i) q^{90} -79.7279i q^{91} +3286.08 q^{92} +(-587.246 + 900.605i) q^{93} +2231.65 q^{94} +697.128i q^{95} +(-465.685 - 303.653i) q^{96} +1812.27i q^{97} -83.2344 q^{98} +(-398.302 - 903.639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.02351 −1.77608 −0.888040 0.459766i \(-0.847933\pi\)
−0.888040 + 0.459766i \(0.847933\pi\)
\(3\) 4.35259 + 2.83813i 0.837656 + 0.546199i
\(4\) 17.2357 2.15446
\(5\) 15.7890i 1.41221i −0.708108 0.706104i \(-0.750451\pi\)
0.708108 0.706104i \(-0.249549\pi\)
\(6\) −21.8653 14.2574i −1.48774 0.970093i
\(7\) −18.9623 −1.02387 −0.511934 0.859025i \(-0.671071\pi\)
−0.511934 + 0.859025i \(0.671071\pi\)
\(8\) −46.3956 −2.05042
\(9\) 10.8900 + 24.7064i 0.403334 + 0.915053i
\(10\) 79.3161i 2.50819i
\(11\) −36.5750 −1.00253 −0.501263 0.865295i \(-0.667131\pi\)
−0.501263 + 0.865295i \(0.667131\pi\)
\(12\) 75.0198 + 48.9172i 1.80470 + 1.17676i
\(13\) 4.20455i 0.0897024i 0.998994 + 0.0448512i \(0.0142814\pi\)
−0.998994 + 0.0448512i \(0.985719\pi\)
\(14\) 95.2574 1.81847
\(15\) 44.8112 68.7228i 0.771346 1.18294i
\(16\) 95.1835 1.48724
\(17\) 97.3906i 1.38945i 0.719274 + 0.694726i \(0.244474\pi\)
−0.719274 + 0.694726i \(0.755526\pi\)
\(18\) −54.7061 124.113i −0.716353 1.62521i
\(19\) −44.1528 −0.533124 −0.266562 0.963818i \(-0.585888\pi\)
−0.266562 + 0.963818i \(0.585888\pi\)
\(20\) 272.134i 3.04255i
\(21\) −82.5351 53.8175i −0.857649 0.559236i
\(22\) 183.735 1.78057
\(23\) 190.656 1.72846 0.864228 0.503101i \(-0.167807\pi\)
0.864228 + 0.503101i \(0.167807\pi\)
\(24\) −201.941 131.677i −1.71754 1.11993i
\(25\) −124.291 −0.994331
\(26\) 21.1216i 0.159319i
\(27\) −22.7204 + 138.444i −0.161946 + 0.986800i
\(28\) −326.828 −2.20588
\(29\) 131.011i 0.838900i 0.907778 + 0.419450i \(0.137777\pi\)
−0.907778 + 0.419450i \(0.862223\pi\)
\(30\) −225.110 + 345.230i −1.36997 + 2.10100i
\(31\) 206.913i 1.19879i 0.800452 + 0.599397i \(0.204593\pi\)
−0.800452 + 0.599397i \(0.795407\pi\)
\(32\) −106.991 −0.591045
\(33\) −159.196 103.805i −0.839772 0.547579i
\(34\) 489.243i 2.46778i
\(35\) 299.395i 1.44591i
\(36\) 187.697 + 425.832i 0.868966 + 1.97145i
\(37\) 106.024i 0.471088i 0.971864 + 0.235544i \(0.0756871\pi\)
−0.971864 + 0.235544i \(0.924313\pi\)
\(38\) 221.802 0.946871
\(39\) −11.9331 + 18.3006i −0.0489954 + 0.0751397i
\(40\) 732.539i 2.89561i
\(41\) 214.440i 0.816827i 0.912797 + 0.408413i \(0.133918\pi\)
−0.912797 + 0.408413i \(0.866082\pi\)
\(42\) 414.616 + 270.353i 1.52325 + 0.993247i
\(43\) 213.227i 0.756206i 0.925763 + 0.378103i \(0.123424\pi\)
−0.925763 + 0.378103i \(0.876576\pi\)
\(44\) −630.396 −2.15990
\(45\) 390.089 171.942i 1.29225 0.569591i
\(46\) −957.762 −3.06988
\(47\) −444.240 −1.37870 −0.689352 0.724426i \(-0.742105\pi\)
−0.689352 + 0.724426i \(0.742105\pi\)
\(48\) 414.294 + 270.143i 1.24580 + 0.812330i
\(49\) 16.5690 0.0483060
\(50\) 624.380 1.76601
\(51\) −276.407 + 423.901i −0.758917 + 1.16388i
\(52\) 72.4682i 0.193260i
\(53\) 624.911i 1.61959i −0.586714 0.809794i \(-0.699579\pi\)
0.586714 0.809794i \(-0.300421\pi\)
\(54\) 114.136 695.476i 0.287630 1.75264i
\(55\) 577.482i 1.41578i
\(56\) 879.768 2.09936
\(57\) −192.179 125.312i −0.446574 0.291192i
\(58\) 658.135i 1.48995i
\(59\) −389.685 231.353i −0.859876 0.510502i
\(60\) 772.352 1184.49i 1.66184 2.54861i
\(61\) 437.873i 0.919080i 0.888157 + 0.459540i \(0.151986\pi\)
−0.888157 + 0.459540i \(0.848014\pi\)
\(62\) 1039.43i 2.12915i
\(63\) −206.500 468.491i −0.412960 0.936894i
\(64\) −223.999 −0.437499
\(65\) 66.3854 0.126678
\(66\) 799.723 + 521.465i 1.49150 + 0.972544i
\(67\) 648.388i 1.18229i −0.806567 0.591143i \(-0.798677\pi\)
0.806567 0.591143i \(-0.201323\pi\)
\(68\) 1678.59i 2.99352i
\(69\) 829.846 + 541.106i 1.44785 + 0.944081i
\(70\) 1504.02i 2.56806i
\(71\) 809.977i 1.35390i 0.736031 + 0.676948i \(0.236698\pi\)
−0.736031 + 0.676948i \(0.763302\pi\)
\(72\) −505.248 1146.27i −0.827001 1.87624i
\(73\) 39.3227i 0.0630463i −0.999503 0.0315231i \(-0.989964\pi\)
0.999503 0.0315231i \(-0.0100358\pi\)
\(74\) 532.613i 0.836689i
\(75\) −540.989 352.756i −0.832907 0.543103i
\(76\) −761.005 −1.14859
\(77\) 693.547 1.02645
\(78\) 59.9459 91.9335i 0.0870197 0.133454i
\(79\) 595.268 0.847758 0.423879 0.905719i \(-0.360668\pi\)
0.423879 + 0.905719i \(0.360668\pi\)
\(80\) 1502.85i 2.10029i
\(81\) −491.816 + 538.106i −0.674644 + 0.738143i
\(82\) 1077.24i 1.45075i
\(83\) −642.266 −0.849372 −0.424686 0.905341i \(-0.639615\pi\)
−0.424686 + 0.905341i \(0.639615\pi\)
\(84\) −1422.55 927.582i −1.84777 1.20485i
\(85\) 1537.70 1.96220
\(86\) 1071.15i 1.34308i
\(87\) −371.826 + 570.236i −0.458206 + 0.702709i
\(88\) 1696.92 2.05560
\(89\) −258.723 −0.308141 −0.154070 0.988060i \(-0.549238\pi\)
−0.154070 + 0.988060i \(0.549238\pi\)
\(90\) −1959.62 + 863.753i −2.29513 + 1.01164i
\(91\) 79.7279i 0.0918434i
\(92\) 3286.08 3.72389
\(93\) −587.246 + 900.605i −0.654780 + 1.00418i
\(94\) 2231.65 2.44869
\(95\) 697.128i 0.752882i
\(96\) −465.685 303.653i −0.495092 0.322828i
\(97\) 1812.27i 1.89699i 0.316796 + 0.948494i \(0.397393\pi\)
−0.316796 + 0.948494i \(0.602607\pi\)
\(98\) −83.2344 −0.0857953
\(99\) −398.302 903.639i −0.404352 0.917365i
\(100\) −2142.25 −2.14225
\(101\) −614.895 −0.605785 −0.302893 0.953025i \(-0.597952\pi\)
−0.302893 + 0.953025i \(0.597952\pi\)
\(102\) 1388.54 2129.47i 1.34790 2.06715i
\(103\) 1232.80i 1.17933i −0.807648 0.589665i \(-0.799260\pi\)
0.807648 0.589665i \(-0.200740\pi\)
\(104\) 195.072i 0.183927i
\(105\) −849.723 + 1303.14i −0.789757 + 1.21118i
\(106\) 3139.25i 2.87652i
\(107\) 340.788i 0.307899i 0.988079 + 0.153950i \(0.0491994\pi\)
−0.988079 + 0.153950i \(0.950801\pi\)
\(108\) −391.602 + 2386.18i −0.348907 + 2.12602i
\(109\) 1023.05i 0.898991i −0.893283 0.449496i \(-0.851604\pi\)
0.893283 0.449496i \(-0.148396\pi\)
\(110\) 2900.99i 2.51453i
\(111\) −300.910 + 461.479i −0.257308 + 0.394609i
\(112\) −1804.90 −1.52274
\(113\) 2261.94 1.88306 0.941529 0.336932i \(-0.109389\pi\)
0.941529 + 0.336932i \(0.109389\pi\)
\(114\) 965.414 + 629.505i 0.793152 + 0.517180i
\(115\) 3010.26i 2.44094i
\(116\) 2258.06i 1.80738i
\(117\) −103.879 + 45.7875i −0.0820825 + 0.0361800i
\(118\) 1957.59 + 1162.21i 1.52721 + 0.906693i
\(119\) 1846.75i 1.42262i
\(120\) −2079.04 + 3188.44i −1.58158 + 2.42553i
\(121\) 6.73330 0.00505883
\(122\) 2199.66i 1.63236i
\(123\) −608.609 + 933.368i −0.446150 + 0.684219i
\(124\) 3566.28i 2.58276i
\(125\) 11.1875i 0.00800513i
\(126\) 1037.35 + 2353.47i 0.733451 + 1.66400i
\(127\) −781.993 −0.546383 −0.273192 0.961960i \(-0.588079\pi\)
−0.273192 + 0.961960i \(0.588079\pi\)
\(128\) 1981.19 1.36808
\(129\) −605.168 + 928.090i −0.413039 + 0.633440i
\(130\) −333.488 −0.224991
\(131\) −1870.92 −1.24781 −0.623904 0.781501i \(-0.714454\pi\)
−0.623904 + 0.781501i \(0.714454\pi\)
\(132\) −2743.85 1789.15i −1.80926 1.17974i
\(133\) 837.239 0.545849
\(134\) 3257.19i 2.09984i
\(135\) 2185.89 + 358.732i 1.39357 + 0.228702i
\(136\) 4518.50i 2.84895i
\(137\) 2056.20i 1.28228i −0.767422 0.641142i \(-0.778461\pi\)
0.767422 0.641142i \(-0.221539\pi\)
\(138\) −4168.74 2718.26i −2.57150 1.67676i
\(139\) −2117.28 −1.29198 −0.645991 0.763345i \(-0.723556\pi\)
−0.645991 + 0.763345i \(0.723556\pi\)
\(140\) 5160.28i 3.11517i
\(141\) −1933.59 1260.81i −1.15488 0.753047i
\(142\) 4068.93i 2.40463i
\(143\) 153.781i 0.0899290i
\(144\) 1036.55 + 2351.64i 0.599854 + 1.36090i
\(145\) 2068.53 1.18470
\(146\) 197.538i 0.111975i
\(147\) 72.1178 + 47.0249i 0.0404638 + 0.0263847i
\(148\) 1827.40i 1.01494i
\(149\) 174.373 0.0958737 0.0479368 0.998850i \(-0.484735\pi\)
0.0479368 + 0.998850i \(0.484735\pi\)
\(150\) 2717.67 + 1772.07i 1.47931 + 0.964594i
\(151\) 2461.47i 1.32656i 0.748369 + 0.663282i \(0.230837\pi\)
−0.748369 + 0.663282i \(0.769163\pi\)
\(152\) 2048.50 1.09313
\(153\) −2406.17 + 1060.58i −1.27142 + 0.560413i
\(154\) −3484.04 −1.82307
\(155\) 3266.94 1.69295
\(156\) −205.674 + 315.424i −0.105559 + 0.161886i
\(157\) 171.463i 0.0871606i 0.999050 + 0.0435803i \(0.0138764\pi\)
−0.999050 + 0.0435803i \(0.986124\pi\)
\(158\) −2990.34 −1.50569
\(159\) 1773.58 2719.98i 0.884617 1.35666i
\(160\) 1689.27i 0.834678i
\(161\) −3615.27 −1.76971
\(162\) 2470.64 2703.18i 1.19822 1.31100i
\(163\) 1926.75 0.925858 0.462929 0.886395i \(-0.346798\pi\)
0.462929 + 0.886395i \(0.346798\pi\)
\(164\) 3696.02i 1.75982i
\(165\) −1638.97 + 2513.54i −0.773295 + 1.18593i
\(166\) 3226.43 1.50855
\(167\) 1091.39i 0.505712i 0.967504 + 0.252856i \(0.0813700\pi\)
−0.967504 + 0.252856i \(0.918630\pi\)
\(168\) 3829.26 + 2496.90i 1.75854 + 1.14667i
\(169\) 2179.32 0.991953
\(170\) −7724.64 −3.48502
\(171\) −480.825 1090.86i −0.215027 0.487837i
\(172\) 3675.12i 1.62922i
\(173\) 128.766 0.0565890 0.0282945 0.999600i \(-0.490992\pi\)
0.0282945 + 0.999600i \(0.490992\pi\)
\(174\) 1867.87 2864.59i 0.813811 1.24807i
\(175\) 2356.85 1.01806
\(176\) −3481.34 −1.49100
\(177\) −1039.53 2112.96i −0.441444 0.897289i
\(178\) 1299.70 0.547283
\(179\) −3323.70 −1.38785 −0.693924 0.720048i \(-0.744120\pi\)
−0.693924 + 0.720048i \(0.744120\pi\)
\(180\) 6723.45 2963.54i 2.78409 1.22716i
\(181\) 2547.84 1.04629 0.523147 0.852242i \(-0.324758\pi\)
0.523147 + 0.852242i \(0.324758\pi\)
\(182\) 400.514i 0.163121i
\(183\) −1242.74 + 1905.88i −0.502001 + 0.769873i
\(184\) −8845.59 −3.54405
\(185\) 1674.01 0.665274
\(186\) 2950.04 4524.20i 1.16294 1.78350i
\(187\) 3562.06i 1.39296i
\(188\) −7656.79 −2.97037
\(189\) 430.832 2625.22i 0.165812 1.01035i
\(190\) 3502.03i 1.33718i
\(191\) 677.105 0.256511 0.128255 0.991741i \(-0.459062\pi\)
0.128255 + 0.991741i \(0.459062\pi\)
\(192\) −974.976 635.740i −0.366473 0.238961i
\(193\) −133.205 −0.0496803 −0.0248402 0.999691i \(-0.507908\pi\)
−0.0248402 + 0.999691i \(0.507908\pi\)
\(194\) 9103.94i 3.36920i
\(195\) 288.948 + 188.411i 0.106113 + 0.0691916i
\(196\) 285.577 0.104073
\(197\) 1551.34i 0.561059i 0.959845 + 0.280530i \(0.0905101\pi\)
−0.959845 + 0.280530i \(0.909490\pi\)
\(198\) 2000.88 + 4539.44i 0.718162 + 1.62931i
\(199\) −1262.52 −0.449738 −0.224869 0.974389i \(-0.572195\pi\)
−0.224869 + 0.974389i \(0.572195\pi\)
\(200\) 5766.58 2.03879
\(201\) 1840.21 2822.16i 0.645763 0.990349i
\(202\) 3088.93 1.07592
\(203\) 2484.27i 0.858923i
\(204\) −4764.07 + 7306.22i −1.63506 + 2.50754i
\(205\) 3385.78 1.15353
\(206\) 6192.97i 2.09459i
\(207\) 2076.24 + 4710.42i 0.697144 + 1.58163i
\(208\) 400.203i 0.133409i
\(209\) 1614.89 0.534471
\(210\) 4268.60 6546.36i 1.40267 2.15115i
\(211\) 5221.63i 1.70366i −0.523819 0.851830i \(-0.675493\pi\)
0.523819 0.851830i \(-0.324507\pi\)
\(212\) 10770.8i 3.48934i
\(213\) −2298.82 + 3525.50i −0.739496 + 1.13410i
\(214\) 1711.95i 0.546854i
\(215\) 3366.64 1.06792
\(216\) 1054.13 6423.20i 0.332057 2.02335i
\(217\) 3923.54i 1.22741i
\(218\) 5139.29i 1.59668i
\(219\) 111.603 171.156i 0.0344358 0.0528111i
\(220\) 9953.30i 3.05023i
\(221\) −409.483 −0.124637
\(222\) 1511.63 2318.24i 0.456999 0.700858i
\(223\) −2152.45 −0.646362 −0.323181 0.946337i \(-0.604752\pi\)
−0.323181 + 0.946337i \(0.604752\pi\)
\(224\) 2028.79 0.605152
\(225\) −1353.53 3070.80i −0.401047 0.909866i
\(226\) −11362.9 −3.34446
\(227\) −3014.43 −0.881386 −0.440693 0.897658i \(-0.645267\pi\)
−0.440693 + 0.897658i \(0.645267\pi\)
\(228\) −3312.34 2159.83i −0.962127 0.627361i
\(229\) 4895.24i 1.41261i 0.707910 + 0.706303i \(0.249638\pi\)
−0.707910 + 0.706303i \(0.750362\pi\)
\(230\) 15122.1i 4.33530i
\(231\) 3018.72 + 1968.38i 0.859815 + 0.560648i
\(232\) 6078.33i 1.72009i
\(233\) 6412.16 1.80289 0.901447 0.432889i \(-0.142506\pi\)
0.901447 + 0.432889i \(0.142506\pi\)
\(234\) 521.839 230.014i 0.145785 0.0642586i
\(235\) 7014.09i 1.94702i
\(236\) −6716.49 3987.53i −1.85257 1.09986i
\(237\) 2590.95 + 1689.45i 0.710129 + 0.463044i
\(238\) 9277.17i 2.52668i
\(239\) 2716.85i 0.735308i 0.929963 + 0.367654i \(0.119839\pi\)
−0.929963 + 0.367654i \(0.880161\pi\)
\(240\) 4265.28 6541.28i 1.14718 1.75932i
\(241\) 3203.55 0.856260 0.428130 0.903717i \(-0.359173\pi\)
0.428130 + 0.903717i \(0.359173\pi\)
\(242\) −33.8248 −0.00898488
\(243\) −3667.89 + 946.317i −0.968292 + 0.249820i
\(244\) 7547.04i 1.98012i
\(245\) 261.607i 0.0682181i
\(246\) 3057.36 4688.79i 0.792398 1.21523i
\(247\) 185.643i 0.0478225i
\(248\) 9599.84i 2.45803i
\(249\) −2795.52 1822.84i −0.711481 0.463926i
\(250\) 56.2006i 0.0142178i
\(251\) 6998.29i 1.75987i 0.475091 + 0.879937i \(0.342415\pi\)
−0.475091 + 0.879937i \(0.657585\pi\)
\(252\) −3559.16 8074.76i −0.889707 2.01850i
\(253\) −6973.24 −1.73282
\(254\) 3928.35 0.970421
\(255\) 6692.96 + 4364.19i 1.64364 + 1.07175i
\(256\) −8160.53 −1.99232
\(257\) 4396.16i 1.06702i −0.845793 0.533512i \(-0.820872\pi\)
0.845793 0.533512i \(-0.179128\pi\)
\(258\) 3040.07 4662.27i 0.733590 1.12504i
\(259\) 2010.46i 0.482332i
\(260\) 1144.20 0.272924
\(261\) −3236.81 + 1426.71i −0.767638 + 0.338357i
\(262\) 9398.58 2.21621
\(263\) 4541.15i 1.06471i −0.846521 0.532356i \(-0.821307\pi\)
0.846521 0.532356i \(-0.178693\pi\)
\(264\) 7385.99 + 4816.09i 1.72188 + 1.12276i
\(265\) −9866.71 −2.28720
\(266\) −4205.88 −0.969471
\(267\) −1126.11 734.289i −0.258116 0.168306i
\(268\) 11175.4i 2.54719i
\(269\) −1074.56 −0.243559 −0.121779 0.992557i \(-0.538860\pi\)
−0.121779 + 0.992557i \(0.538860\pi\)
\(270\) −10980.8 1802.10i −2.47509 0.406193i
\(271\) −461.443 −0.103434 −0.0517171 0.998662i \(-0.516469\pi\)
−0.0517171 + 0.998662i \(0.516469\pi\)
\(272\) 9269.97i 2.06645i
\(273\) 226.278 347.022i 0.0501648 0.0769332i
\(274\) 10329.3i 2.27744i
\(275\) 4545.96 0.996843
\(276\) 14303.0 + 9326.34i 3.11934 + 2.03398i
\(277\) 517.812 0.112319 0.0561594 0.998422i \(-0.482114\pi\)
0.0561594 + 0.998422i \(0.482114\pi\)
\(278\) 10636.2 2.29466
\(279\) −5112.07 + 2253.28i −1.09696 + 0.483514i
\(280\) 13890.6i 2.96473i
\(281\) 4176.06i 0.886558i −0.896384 0.443279i \(-0.853815\pi\)
0.896384 0.443279i \(-0.146185\pi\)
\(282\) 9713.44 + 6333.71i 2.05116 + 1.33747i
\(283\) 1172.22i 0.246224i −0.992393 0.123112i \(-0.960712\pi\)
0.992393 0.123112i \(-0.0392875\pi\)
\(284\) 13960.5i 2.91692i
\(285\) −1978.54 + 3034.31i −0.411223 + 0.630656i
\(286\) 772.523i 0.159721i
\(287\) 4066.27i 0.836323i
\(288\) −1165.13 2643.35i −0.238388 0.540837i
\(289\) −4571.93 −0.930578
\(290\) −10391.3 −2.10413
\(291\) −5143.45 + 7888.04i −1.03613 + 1.58902i
\(292\) 677.755i 0.135831i
\(293\) 2489.88i 0.496451i 0.968702 + 0.248226i \(0.0798475\pi\)
−0.968702 + 0.248226i \(0.920153\pi\)
\(294\) −362.285 236.230i −0.0718669 0.0468613i
\(295\) −3652.83 + 6152.73i −0.720936 + 1.21432i
\(296\) 4919.05i 0.965925i
\(297\) 831.001 5063.60i 0.162355 0.989292i
\(298\) −875.964 −0.170279
\(299\) 801.621i 0.155047i
\(300\) −9324.32 6079.99i −1.79447 1.17009i
\(301\) 4043.28i 0.774256i
\(302\) 12365.2i 2.35608i
\(303\) −2676.38 1745.15i −0.507439 0.330879i
\(304\) −4202.62 −0.792884
\(305\) 6913.56 1.29793
\(306\) 12087.4 5327.86i 2.25815 0.995338i
\(307\) 4971.40 0.924210 0.462105 0.886825i \(-0.347094\pi\)
0.462105 + 0.886825i \(0.347094\pi\)
\(308\) 11953.8 2.21146
\(309\) 3498.84 5365.85i 0.644149 0.987873i
\(310\) −16411.5 −3.00681
\(311\) 2050.81i 0.373925i 0.982367 + 0.186963i \(0.0598643\pi\)
−0.982367 + 0.186963i \(0.940136\pi\)
\(312\) 553.642 849.070i 0.100461 0.154068i
\(313\) 926.601i 0.167331i −0.996494 0.0836655i \(-0.973337\pi\)
0.996494 0.0836655i \(-0.0266627\pi\)
\(314\) 861.345i 0.154804i
\(315\) −7396.99 + 3260.42i −1.32309 + 0.583186i
\(316\) 10259.8 1.82646
\(317\) 302.700i 0.0536319i −0.999640 0.0268160i \(-0.991463\pi\)
0.999640 0.0268160i \(-0.00853681\pi\)
\(318\) −8909.61 + 13663.9i −1.57115 + 2.40953i
\(319\) 4791.73i 0.841020i
\(320\) 3536.72i 0.617839i
\(321\) −967.202 + 1483.31i −0.168174 + 0.257914i
\(322\) 18161.4 3.14315
\(323\) 4300.07i 0.740750i
\(324\) −8476.78 + 9274.63i −1.45349 + 1.59030i
\(325\) 522.589i 0.0891939i
\(326\) −9679.07 −1.64440
\(327\) 2903.54 4452.90i 0.491028 0.753045i
\(328\) 9949.07i 1.67483i
\(329\) 8423.82 1.41161
\(330\) 8233.39 12626.8i 1.37343 2.10631i
\(331\) 884.721 0.146914 0.0734572 0.997298i \(-0.476597\pi\)
0.0734572 + 0.997298i \(0.476597\pi\)
\(332\) −11069.9 −1.82994
\(333\) −2619.48 + 1154.60i −0.431070 + 0.190005i
\(334\) 5482.59i 0.898186i
\(335\) −10237.4 −1.66963
\(336\) −7855.97 5122.54i −1.27553 0.831718i
\(337\) 1782.59i 0.288142i −0.989567 0.144071i \(-0.953981\pi\)
0.989567 0.144071i \(-0.0460194\pi\)
\(338\) −10947.9 −1.76179
\(339\) 9845.29 + 6419.69i 1.57735 + 1.02852i
\(340\) 26503.3 4.22747
\(341\) 7567.84i 1.20182i
\(342\) 2415.43 + 5479.94i 0.381905 + 0.866437i
\(343\) 6189.88 0.974409
\(344\) 9892.81i 1.55054i
\(345\) 8543.51 13102.4i 1.33324 2.04467i
\(346\) −646.858 −0.100507
\(347\) −2878.22 −0.445277 −0.222638 0.974901i \(-0.571467\pi\)
−0.222638 + 0.974901i \(0.571467\pi\)
\(348\) −6408.68 + 9828.41i −0.987188 + 1.51396i
\(349\) 1591.36i 0.244079i −0.992525 0.122040i \(-0.961056\pi\)
0.992525 0.122040i \(-0.0389435\pi\)
\(350\) −11839.7 −1.80816
\(351\) −582.095 95.5291i −0.0885183 0.0145270i
\(352\) 3913.18 0.592538
\(353\) 8834.08 1.33198 0.665992 0.745959i \(-0.268008\pi\)
0.665992 + 0.745959i \(0.268008\pi\)
\(354\) 5222.08 + 10614.5i 0.784041 + 1.59366i
\(355\) 12788.7 1.91198
\(356\) −4459.26 −0.663878
\(357\) 5241.32 8038.14i 0.777031 1.19166i
\(358\) 16696.6 2.46493
\(359\) 2254.31i 0.331414i −0.986175 0.165707i \(-0.947009\pi\)
0.986175 0.165707i \(-0.0529906\pi\)
\(360\) −18098.4 + 7977.35i −2.64964 + 1.16790i
\(361\) −4909.53 −0.715779
\(362\) −12799.1 −1.85830
\(363\) 29.3073 + 19.1100i 0.00423755 + 0.00276313i
\(364\) 1374.16i 0.197873i
\(365\) −620.865 −0.0890345
\(366\) 6242.93 9574.22i 0.891594 1.36736i
\(367\) 7324.96i 1.04185i 0.853602 + 0.520926i \(0.174413\pi\)
−0.853602 + 0.520926i \(0.825587\pi\)
\(368\) 18147.3 2.57063
\(369\) −5298.04 + 2335.25i −0.747440 + 0.329454i
\(370\) −8409.41 −1.18158
\(371\) 11849.8i 1.65825i
\(372\) −10121.6 + 15522.6i −1.41070 + 2.16346i
\(373\) −12190.8 −1.69226 −0.846131 0.532975i \(-0.821074\pi\)
−0.846131 + 0.532975i \(0.821074\pi\)
\(374\) 17894.1i 2.47401i
\(375\) 31.7516 48.6946i 0.00437239 0.00670554i
\(376\) 20610.8 2.82692
\(377\) −550.841 −0.0752514
\(378\) −2164.29 + 13187.8i −0.294495 + 1.79447i
\(379\) −12783.7 −1.73260 −0.866298 0.499528i \(-0.833507\pi\)
−0.866298 + 0.499528i \(0.833507\pi\)
\(380\) 12015.5i 1.62205i
\(381\) −3403.69 2219.40i −0.457681 0.298434i
\(382\) −3401.45 −0.455584
\(383\) 8079.16i 1.07787i 0.842346 + 0.538937i \(0.181174\pi\)
−0.842346 + 0.538937i \(0.818826\pi\)
\(384\) 8623.29 + 5622.87i 1.14598 + 0.747242i
\(385\) 10950.4i 1.44957i
\(386\) 669.157 0.0882362
\(387\) −5268.09 + 2322.05i −0.691969 + 0.305003i
\(388\) 31235.7i 4.08699i
\(389\) 4699.78i 0.612566i −0.951940 0.306283i \(-0.900915\pi\)
0.951940 0.306283i \(-0.0990855\pi\)
\(390\) −1451.54 946.483i −0.188465 0.122890i
\(391\) 18568.1i 2.40161i
\(392\) −768.727 −0.0990474
\(393\) −8143.33 5309.91i −1.04523 0.681551i
\(394\) 7793.20i 0.996486i
\(395\) 9398.66i 1.19721i
\(396\) −6865.02 15574.8i −0.871162 1.97643i
\(397\) 3284.57i 0.415234i 0.978210 + 0.207617i \(0.0665708\pi\)
−0.978210 + 0.207617i \(0.933429\pi\)
\(398\) 6342.30 0.798770
\(399\) 3644.16 + 2376.20i 0.457233 + 0.298142i
\(400\) −11830.5 −1.47881
\(401\) 10745.7 1.33819 0.669097 0.743175i \(-0.266681\pi\)
0.669097 + 0.743175i \(0.266681\pi\)
\(402\) −9244.32 + 14177.2i −1.14693 + 1.75894i
\(403\) −869.974 −0.107535
\(404\) −10598.1 −1.30514
\(405\) 8496.14 + 7765.26i 1.04241 + 0.952738i
\(406\) 12479.8i 1.52552i
\(407\) 3877.83i 0.472278i
\(408\) 12824.1 19667.1i 1.55610 2.38644i
\(409\) 608.438i 0.0735583i −0.999323 0.0367791i \(-0.988290\pi\)
0.999323 0.0367791i \(-0.0117098\pi\)
\(410\) −17008.5 −2.04876
\(411\) 5835.77 8949.78i 0.700382 1.07411i
\(412\) 21248.1i 2.54082i
\(413\) 7389.33 + 4386.99i 0.880400 + 0.522687i
\(414\) −10430.0 23662.9i −1.23818 2.80910i
\(415\) 10140.7i 1.19949i
\(416\) 449.847i 0.0530181i
\(417\) −9215.65 6009.12i −1.08224 0.705679i
\(418\) −8112.43 −0.949263
\(419\) 2140.32 0.249551 0.124775 0.992185i \(-0.460179\pi\)
0.124775 + 0.992185i \(0.460179\pi\)
\(420\) −14645.6 + 22460.6i −1.70150 + 2.60944i
\(421\) 6114.20i 0.707809i −0.935281 0.353905i \(-0.884854\pi\)
0.935281 0.353905i \(-0.115146\pi\)
\(422\) 26230.9i 3.02584i
\(423\) −4837.78 10975.6i −0.556078 1.26159i
\(424\) 28993.1i 3.32083i
\(425\) 12104.8i 1.38158i
\(426\) 11548.2 17710.4i 1.31340 2.01425i
\(427\) 8303.08i 0.941017i
\(428\) 5873.72i 0.663357i
\(429\) 436.452 669.347i 0.0491191 0.0753295i
\(430\) −16912.4 −1.89671
\(431\) 5957.62 0.665820 0.332910 0.942959i \(-0.391969\pi\)
0.332910 + 0.942959i \(0.391969\pi\)
\(432\) −2162.61 + 13177.6i −0.240853 + 1.46761i
\(433\) 5929.89 0.658135 0.329067 0.944306i \(-0.393266\pi\)
0.329067 + 0.944306i \(0.393266\pi\)
\(434\) 19710.0i 2.17997i
\(435\) 9003.44 + 5870.75i 0.992372 + 0.647083i
\(436\) 17632.9i 1.93684i
\(437\) −8417.99 −0.921481
\(438\) −560.640 + 859.803i −0.0611608 + 0.0937967i
\(439\) 2601.68 0.282851 0.141425 0.989949i \(-0.454831\pi\)
0.141425 + 0.989949i \(0.454831\pi\)
\(440\) 26792.6i 2.90293i
\(441\) 180.436 + 409.360i 0.0194834 + 0.0442025i
\(442\) 2057.04 0.221366
\(443\) −4968.72 −0.532892 −0.266446 0.963850i \(-0.585849\pi\)
−0.266446 + 0.963850i \(0.585849\pi\)
\(444\) −5186.40 + 7953.90i −0.554359 + 0.850170i
\(445\) 4084.96i 0.435159i
\(446\) 10812.9 1.14799
\(447\) 758.972 + 494.893i 0.0803091 + 0.0523661i
\(448\) 4247.54 0.447941
\(449\) 10888.3i 1.14443i 0.820102 + 0.572217i \(0.193916\pi\)
−0.820102 + 0.572217i \(0.806084\pi\)
\(450\) 6799.50 + 15426.2i 0.712292 + 1.61600i
\(451\) 7843.15i 0.818890i
\(452\) 38986.1 4.05697
\(453\) −6985.97 + 10713.7i −0.724568 + 1.11120i
\(454\) 15143.0 1.56541
\(455\) −1258.82 −0.129702
\(456\) 8916.26 + 5813.91i 0.915663 + 0.597064i
\(457\) 11335.6i 1.16030i 0.814511 + 0.580149i \(0.197006\pi\)
−0.814511 + 0.580149i \(0.802994\pi\)
\(458\) 24591.3i 2.50890i
\(459\) −13483.2 2212.76i −1.37111 0.225017i
\(460\) 51883.9i 5.25891i
\(461\) 2047.70i 0.206878i −0.994636 0.103439i \(-0.967015\pi\)
0.994636 0.103439i \(-0.0329846\pi\)
\(462\) −15164.6 9888.17i −1.52710 0.995757i
\(463\) 8560.90i 0.859306i −0.902994 0.429653i \(-0.858636\pi\)
0.902994 0.429653i \(-0.141364\pi\)
\(464\) 12470.1i 1.24765i
\(465\) 14219.6 + 9272.00i 1.41811 + 0.924686i
\(466\) −32211.6 −3.20209
\(467\) −12235.6 −1.21241 −0.606204 0.795309i \(-0.707308\pi\)
−0.606204 + 0.795309i \(0.707308\pi\)
\(468\) −1790.43 + 789.180i −0.176843 + 0.0779484i
\(469\) 12294.9i 1.21051i
\(470\) 35235.4i 3.45806i
\(471\) −486.634 + 746.306i −0.0476070 + 0.0730105i
\(472\) 18079.7 + 10733.8i 1.76310 + 1.04674i
\(473\) 7798.80i 0.758117i
\(474\) −13015.7 8486.97i −1.26125 0.822404i
\(475\) 5487.82 0.530102
\(476\) 31830.0i 3.06497i
\(477\) 15439.3 6805.29i 1.48201 0.653234i
\(478\) 13648.2i 1.30597i
\(479\) 20219.0i 1.92866i 0.264701 + 0.964331i \(0.414727\pi\)
−0.264701 + 0.964331i \(0.585273\pi\)
\(480\) −4794.37 + 7352.69i −0.455900 + 0.699173i
\(481\) −445.783 −0.0422577
\(482\) −16093.1 −1.52079
\(483\) −15735.8 10260.6i −1.48241 0.966614i
\(484\) 116.053 0.0108990
\(485\) 28613.8 2.67894
\(486\) 18425.7 4753.83i 1.71976 0.443700i
\(487\) 3590.52 0.334091 0.167045 0.985949i \(-0.446577\pi\)
0.167045 + 0.985949i \(0.446577\pi\)
\(488\) 20315.4i 1.88450i
\(489\) 8386.35 + 5468.38i 0.775550 + 0.505703i
\(490\) 1314.18i 0.121161i
\(491\) 11912.8i 1.09494i 0.836824 + 0.547472i \(0.184410\pi\)
−0.836824 + 0.547472i \(0.815590\pi\)
\(492\) −10489.8 + 16087.2i −0.961212 + 1.47412i
\(493\) −12759.2 −1.16561
\(494\) 932.578i 0.0849366i
\(495\) −14267.5 + 6288.78i −1.29551 + 0.571030i
\(496\) 19694.7i 1.78290i
\(497\) 15359.0i 1.38621i
\(498\) 14043.3 + 9157.04i 1.26365 + 0.823969i
\(499\) −12240.9 −1.09815 −0.549074 0.835773i \(-0.685020\pi\)
−0.549074 + 0.835773i \(0.685020\pi\)
\(500\) 192.825i 0.0172467i
\(501\) −3097.50 + 4750.35i −0.276220 + 0.423613i
\(502\) 35156.0i 3.12568i
\(503\) 21730.3 1.92626 0.963128 0.269044i \(-0.0867078\pi\)
0.963128 + 0.269044i \(0.0867078\pi\)
\(504\) 9580.67 + 21735.9i 0.846740 + 1.92102i
\(505\) 9708.55i 0.855495i
\(506\) 35030.2 3.07763
\(507\) 9485.69 + 6185.20i 0.830915 + 0.541804i
\(508\) −13478.2 −1.17716
\(509\) 8351.63 0.727268 0.363634 0.931542i \(-0.381536\pi\)
0.363634 + 0.931542i \(0.381536\pi\)
\(510\) −33622.2 21923.6i −2.91924 1.90351i
\(511\) 745.650i 0.0645511i
\(512\) 25145.0 2.17044
\(513\) 1003.17 6112.70i 0.0863375 0.526086i
\(514\) 22084.2i 1.89512i
\(515\) −19464.6 −1.66546
\(516\) −10430.5 + 15996.3i −0.889876 + 1.36472i
\(517\) 16248.1 1.38219
\(518\) 10099.6i 0.856660i
\(519\) 560.465 + 365.455i 0.0474021 + 0.0309088i
\(520\) −3079.99 −0.259743
\(521\) 1641.69i 0.138050i 0.997615 + 0.0690248i \(0.0219887\pi\)
−0.997615 + 0.0690248i \(0.978011\pi\)
\(522\) 16260.2 7167.09i 1.36339 0.600949i
\(523\) 2499.37 0.208967 0.104483 0.994527i \(-0.466681\pi\)
0.104483 + 0.994527i \(0.466681\pi\)
\(524\) −32246.5 −2.68835
\(525\) 10258.4 + 6689.06i 0.852787 + 0.556066i
\(526\) 22812.5i 1.89101i
\(527\) −20151.4 −1.66567
\(528\) −15152.8 9880.50i −1.24894 0.814382i
\(529\) 24182.6 1.98756
\(530\) 49565.5 4.06224
\(531\) 1472.24 12147.2i 0.120320 0.992735i
\(532\) 14430.4 1.17601
\(533\) −901.622 −0.0732713
\(534\) 5657.04 + 3688.71i 0.458435 + 0.298925i
\(535\) 5380.69 0.434818
\(536\) 30082.3i 2.42418i
\(537\) −14466.7 9433.09i −1.16254 0.758041i
\(538\) 5398.09 0.432580
\(539\) −606.010 −0.0484280
\(540\) 37675.3 + 6183.00i 3.00238 + 0.492729i
\(541\) 8763.50i 0.696437i −0.937413 0.348218i \(-0.886787\pi\)
0.937413 0.348218i \(-0.113213\pi\)
\(542\) 2318.06 0.183707
\(543\) 11089.7 + 7231.10i 0.876434 + 0.571485i
\(544\) 10419.9i 0.821228i
\(545\) −16152.8 −1.26956
\(546\) −1136.71 + 1743.27i −0.0890967 + 0.136639i
\(547\) −8486.37 −0.663348 −0.331674 0.943394i \(-0.607613\pi\)
−0.331674 + 0.943394i \(0.607613\pi\)
\(548\) 35440.0i 2.76263i
\(549\) −10818.3 + 4768.44i −0.841007 + 0.370696i
\(550\) −22836.7 −1.77047
\(551\) 5784.50i 0.447238i
\(552\) −38501.2 25105.0i −2.96870 1.93576i
\(553\) −11287.6 −0.867992
\(554\) −2601.24 −0.199487
\(555\) 7286.27 + 4751.06i 0.557270 + 0.363372i
\(556\) −36492.8 −2.78352
\(557\) 4363.80i 0.331958i −0.986129 0.165979i \(-0.946922\pi\)
0.986129 0.165979i \(-0.0530783\pi\)
\(558\) 25680.6 11319.4i 1.94829 0.858760i
\(559\) −896.524 −0.0678335
\(560\) 28497.5i 2.15042i
\(561\) 10109.6 15504.2i 0.760834 1.16682i
\(562\) 20978.5i 1.57460i
\(563\) −14160.7 −1.06004 −0.530020 0.847985i \(-0.677816\pi\)
−0.530020 + 0.847985i \(0.677816\pi\)
\(564\) −33326.8 21731.0i −2.48814 1.62241i
\(565\) 35713.7i 2.65927i
\(566\) 5888.68i 0.437314i
\(567\) 9325.95 10203.7i 0.690747 0.755761i
\(568\) 37579.4i 2.77605i
\(569\) −23427.8 −1.72609 −0.863044 0.505129i \(-0.831445\pi\)
−0.863044 + 0.505129i \(0.831445\pi\)
\(570\) 9939.23 15242.9i 0.730365 1.12010i
\(571\) 3642.83i 0.266983i 0.991050 + 0.133492i \(0.0426190\pi\)
−0.991050 + 0.133492i \(0.957381\pi\)
\(572\) 2650.53i 0.193749i
\(573\) 2947.16 + 1921.71i 0.214868 + 0.140106i
\(574\) 20427.0i 1.48538i
\(575\) −23696.9 −1.71866
\(576\) −2439.35 5534.22i −0.176458 0.400335i
\(577\) −1937.25 −0.139773 −0.0698863 0.997555i \(-0.522264\pi\)
−0.0698863 + 0.997555i \(0.522264\pi\)
\(578\) 22967.1 1.65278
\(579\) −579.786 378.053i −0.0416150 0.0271353i
\(580\) 35652.5 2.55239
\(581\) 12178.8 0.869644
\(582\) 25838.2 39625.7i 1.84025 2.82223i
\(583\) 22856.2i 1.62368i
\(584\) 1824.40i 0.129271i
\(585\) 722.938 + 1640.15i 0.0510937 + 0.115918i
\(586\) 12507.9i 0.881737i
\(587\) 7040.82 0.495070 0.247535 0.968879i \(-0.420380\pi\)
0.247535 + 0.968879i \(0.420380\pi\)
\(588\) 1243.00 + 810.506i 0.0871777 + 0.0568448i
\(589\) 9135.78i 0.639106i
\(590\) 18350.0 30908.3i 1.28044 2.15674i
\(591\) −4402.92 + 6752.36i −0.306450 + 0.469974i
\(592\) 10091.7i 0.700621i
\(593\) 20860.2i 1.44457i −0.691598 0.722283i \(-0.743093\pi\)
0.691598 0.722283i \(-0.256907\pi\)
\(594\) −4174.54 + 25437.1i −0.288356 + 1.75706i
\(595\) −29158.3 −2.00903
\(596\) 3005.43 0.206556
\(597\) −5495.24 3583.21i −0.376725 0.245646i
\(598\) 4026.95i 0.275375i
\(599\) 25414.9i 1.73359i −0.498661 0.866797i \(-0.666175\pi\)
0.498661 0.866797i \(-0.333825\pi\)
\(600\) 25099.5 + 16366.3i 1.70781 + 1.11359i
\(601\) 11780.0i 0.799527i −0.916618 0.399763i \(-0.869092\pi\)
0.916618 0.399763i \(-0.130908\pi\)
\(602\) 20311.5i 1.37514i
\(603\) 16019.3 7060.95i 1.08185 0.476856i
\(604\) 42425.0i 2.85803i
\(605\) 106.312i 0.00714412i
\(606\) 13444.8 + 8766.80i 0.901253 + 0.587668i
\(607\) −10681.0 −0.714214 −0.357107 0.934064i \(-0.616237\pi\)
−0.357107 + 0.934064i \(0.616237\pi\)
\(608\) 4723.93 0.315100
\(609\) 7050.68 10813.0i 0.469143 0.719482i
\(610\) −34730.4 −2.30523
\(611\) 1867.83i 0.123673i
\(612\) −41472.1 + 18279.9i −2.73923 + 1.20739i
\(613\) 20194.4i 1.33058i 0.746585 + 0.665290i \(0.231692\pi\)
−0.746585 + 0.665290i \(0.768308\pi\)
\(614\) −24973.9 −1.64147
\(615\) 14736.9 + 9609.30i 0.966260 + 0.630056i
\(616\) −32177.5 −2.10466
\(617\) 15263.6i 0.995929i 0.867197 + 0.497964i \(0.165919\pi\)
−0.867197 + 0.497964i \(0.834081\pi\)
\(618\) −17576.5 + 26955.4i −1.14406 + 1.75454i
\(619\) 23507.2 1.52639 0.763194 0.646169i \(-0.223630\pi\)
0.763194 + 0.646169i \(0.223630\pi\)
\(620\) 56307.9 3.64739
\(621\) −4331.78 + 26395.2i −0.279917 + 1.70564i
\(622\) 10302.3i 0.664121i
\(623\) 4905.98 0.315496
\(624\) −1135.83 + 1741.92i −0.0728679 + 0.111751i
\(625\) −15713.1 −1.00564
\(626\) 4654.79i 0.297193i
\(627\) 7028.95 + 4583.28i 0.447702 + 0.291927i
\(628\) 2955.28i 0.187784i
\(629\) −10325.7 −0.654554
\(630\) 37158.9 16378.7i 2.34991 1.03579i
\(631\) 1583.44 0.0998982 0.0499491 0.998752i \(-0.484094\pi\)
0.0499491 + 0.998752i \(0.484094\pi\)
\(632\) −27617.8 −1.73826
\(633\) 14819.7 22727.6i 0.930537 1.42708i
\(634\) 1520.62i 0.0952546i
\(635\) 12346.9i 0.771607i
\(636\) 30568.9 46880.7i 1.90587 2.92287i
\(637\) 69.6649i 0.00433316i
\(638\) 24071.3i 1.49372i
\(639\) −20011.6 + 8820.66i −1.23889 + 0.546072i
\(640\) 31280.9i 1.93201i
\(641\) 20497.2i 1.26301i 0.775371 + 0.631506i \(0.217563\pi\)
−0.775371 + 0.631506i \(0.782437\pi\)
\(642\) 4858.75 7451.43i 0.298691 0.458075i
\(643\) −4515.90 −0.276967 −0.138483 0.990365i \(-0.544223\pi\)
−0.138483 + 0.990365i \(0.544223\pi\)
\(644\) −62311.7 −3.81277
\(645\) 14653.6 + 9554.97i 0.894550 + 0.583297i
\(646\) 21601.5i 1.31563i
\(647\) 7206.18i 0.437873i 0.975739 + 0.218937i \(0.0702588\pi\)
−0.975739 + 0.218937i \(0.929741\pi\)
\(648\) 22818.1 24965.8i 1.38330 1.51350i
\(649\) 14252.8 + 8461.76i 0.862049 + 0.511792i
\(650\) 2625.23i 0.158416i
\(651\) 11135.5 17077.6i 0.670408 1.02814i
\(652\) 33208.9 1.99473
\(653\) 1838.01i 0.110148i 0.998482 + 0.0550742i \(0.0175395\pi\)
−0.998482 + 0.0550742i \(0.982460\pi\)
\(654\) −14586.0 + 22369.2i −0.872105 + 1.33747i
\(655\) 29539.8i 1.76216i
\(656\) 20411.1i 1.21482i
\(657\) 971.525 428.225i 0.0576907 0.0254287i
\(658\) −42317.2 −2.50714
\(659\) −5231.00 −0.309212 −0.154606 0.987976i \(-0.549411\pi\)
−0.154606 + 0.987976i \(0.549411\pi\)
\(660\) −28248.8 + 43322.6i −1.66603 + 2.55504i
\(661\) −1527.63 −0.0898910 −0.0449455 0.998989i \(-0.514311\pi\)
−0.0449455 + 0.998989i \(0.514311\pi\)
\(662\) −4444.41 −0.260932
\(663\) −1782.31 1162.17i −0.104403 0.0680767i
\(664\) 29798.3 1.74156
\(665\) 13219.1i 0.770852i
\(666\) 13159.0 5800.16i 0.765615 0.337465i
\(667\) 24978.0i 1.45000i
\(668\) 18810.8i 1.08954i
\(669\) −9368.72 6108.94i −0.541429 0.353042i
\(670\) 51427.6 2.96540
\(671\) 16015.2i 0.921402i
\(672\) 8830.47 + 5757.96i 0.506909 + 0.330533i
\(673\) 13657.3i 0.782242i −0.920339 0.391121i \(-0.872087\pi\)
0.920339 0.391121i \(-0.127913\pi\)
\(674\) 8954.88i 0.511764i
\(675\) 2823.96 17207.4i 0.161028 0.981206i
\(676\) 37562.1 2.13713
\(677\) 11537.8i 0.655000i 0.944851 + 0.327500i \(0.106206\pi\)
−0.944851 + 0.327500i \(0.893794\pi\)
\(678\) −49458.0 32249.4i −2.80151 1.82674i
\(679\) 34364.7i 1.94226i
\(680\) −71342.4 −4.02332
\(681\) −13120.6 8555.35i −0.738298 0.481412i
\(682\) 38017.1i 2.13453i
\(683\) 20558.2 1.15174 0.575869 0.817542i \(-0.304664\pi\)
0.575869 + 0.817542i \(0.304664\pi\)
\(684\) −8287.34 18801.7i −0.463267 1.05103i
\(685\) −32465.3 −1.81085
\(686\) −31095.0 −1.73063
\(687\) −13893.3 + 21307.0i −0.771563 + 1.18328i
\(688\) 20295.7i 1.12466i
\(689\) 2627.47 0.145281
\(690\) −42918.4 + 65820.1i −2.36794 + 3.63149i
\(691\) 10360.1i 0.570358i 0.958474 + 0.285179i \(0.0920531\pi\)
−0.958474 + 0.285179i \(0.907947\pi\)
\(692\) 2219.37 0.121919
\(693\) 7552.73 + 17135.1i 0.414004 + 0.939260i
\(694\) 14458.8 0.790847
\(695\) 33429.7i 1.82455i
\(696\) 17251.1 26456.4i 0.939514 1.44085i
\(697\) −20884.4 −1.13494
\(698\) 7994.23i 0.433505i
\(699\) 27909.5 + 18198.6i 1.51020 + 0.984739i
\(700\) 40622.0 2.19338
\(701\) −15053.3 −0.811064 −0.405532 0.914081i \(-0.632914\pi\)
−0.405532 + 0.914081i \(0.632914\pi\)
\(702\) 2924.16 + 479.892i 0.157216 + 0.0258011i
\(703\) 4681.26i 0.251148i
\(704\) 8192.78 0.438604
\(705\) −19906.9 + 30529.5i −1.06346 + 1.63093i
\(706\) −44378.1 −2.36571
\(707\) 11659.8 0.620244
\(708\) −17917.0 36418.4i −0.951075 1.93317i
\(709\) 6457.43 0.342051 0.171025 0.985267i \(-0.445292\pi\)
0.171025 + 0.985267i \(0.445292\pi\)
\(710\) −64244.2 −3.39583
\(711\) 6482.47 + 14706.9i 0.341929 + 0.775743i
\(712\) 12003.6 0.631817
\(713\) 39449.1i 2.07206i
\(714\) −26329.8 + 40379.7i −1.38007 + 2.11649i
\(715\) −2428.05 −0.126998
\(716\) −57286.2 −2.99006
\(717\) −7710.79 + 11825.3i −0.401625 + 0.615935i
\(718\) 11324.5i 0.588618i
\(719\) 3504.48 0.181773 0.0908866 0.995861i \(-0.471030\pi\)
0.0908866 + 0.995861i \(0.471030\pi\)
\(720\) 37130.0 16366.0i 1.92188 0.847119i
\(721\) 23376.7i 1.20748i
\(722\) 24663.1 1.27128
\(723\) 13943.7 + 9092.09i 0.717251 + 0.467688i
\(724\) 43913.7 2.25420
\(725\) 16283.5i 0.834145i
\(726\) −147.225 95.9993i −0.00752624 0.00490753i
\(727\) 21316.2 1.08745 0.543723 0.839265i \(-0.317014\pi\)
0.543723 + 0.839265i \(0.317014\pi\)
\(728\) 3699.02i 0.188317i
\(729\) −18650.6 6291.02i −0.947547 0.319617i
\(730\) 3118.93 0.158132
\(731\) −20766.3 −1.05071
\(732\) −21419.5 + 32849.2i −1.08154 + 1.65866i
\(733\) 503.085 0.0253504 0.0126752 0.999920i \(-0.495965\pi\)
0.0126752 + 0.999920i \(0.495965\pi\)
\(734\) 36797.1i 1.85041i
\(735\) 742.474 1138.67i 0.0372607 0.0571433i
\(736\) −20398.4 −1.02159
\(737\) 23714.8i 1.18527i
\(738\) 26614.8 11731.2i 1.32751 0.585136i
\(739\) 12261.2i 0.610332i −0.952299 0.305166i \(-0.901288\pi\)
0.952299 0.305166i \(-0.0987119\pi\)
\(740\) 28852.7 1.43331
\(741\) 526.878 808.025i 0.0261206 0.0400588i
\(742\) 59527.4i 2.94518i
\(743\) 10092.6i 0.498335i 0.968460 + 0.249168i \(0.0801570\pi\)
−0.968460 + 0.249168i \(0.919843\pi\)
\(744\) 27245.6 41784.1i 1.34257 2.05898i
\(745\) 2753.17i 0.135394i
\(746\) 61240.5 3.00559
\(747\) −6994.28 15868.1i −0.342580 0.777220i
\(748\) 61394.6i 3.00108i
\(749\) 6462.13i 0.315248i
\(750\) −159.505 + 244.618i −0.00776572 + 0.0119096i
\(751\) 12579.2i 0.611213i 0.952158 + 0.305606i \(0.0988591\pi\)
−0.952158 + 0.305606i \(0.901141\pi\)
\(752\) −42284.3 −2.05047
\(753\) −19862.1 + 30460.7i −0.961241 + 1.47417i
\(754\) 2767.16 0.133652
\(755\) 38864.0 1.87338
\(756\) 7425.68 45247.5i 0.357235 2.17677i
\(757\) 25539.6 1.22623 0.613114 0.789995i \(-0.289917\pi\)
0.613114 + 0.789995i \(0.289917\pi\)
\(758\) 64219.0 3.07723
\(759\) −30351.6 19791.0i −1.45151 0.946466i
\(760\) 32343.7i 1.54372i
\(761\) 1308.83i 0.0623457i 0.999514 + 0.0311729i \(0.00992424\pi\)
−0.999514 + 0.0311729i \(0.990076\pi\)
\(762\) 17098.5 + 11149.2i 0.812878 + 0.530043i
\(763\) 19399.3i 0.920449i
\(764\) 11670.4 0.552643
\(765\) 16745.5 + 37991.0i 0.791419 + 1.79551i
\(766\) 40585.8i 1.91439i
\(767\) 972.736 1638.45i 0.0457933 0.0771330i
\(768\) −35519.4 23160.7i −1.66888 1.08820i
\(769\) 36500.3i 1.71162i −0.517293 0.855808i \(-0.673060\pi\)
0.517293 0.855808i \(-0.326940\pi\)
\(770\) 55009.4i 2.57455i
\(771\) 12476.9 19134.7i 0.582807 0.893798i
\(772\) −2295.88 −0.107034
\(773\) −8733.49 −0.406367 −0.203184 0.979141i \(-0.565129\pi\)
−0.203184 + 0.979141i \(0.565129\pi\)
\(774\) 26464.3 11664.8i 1.22899 0.541710i
\(775\) 25717.5i 1.19200i
\(776\) 84081.2i 3.88961i
\(777\) 5705.95 8750.70i 0.263449 0.404028i
\(778\) 23609.4i 1.08797i
\(779\) 9468.13i 0.435470i
\(780\) 4980.22 + 3247.39i 0.228616 + 0.149071i
\(781\) 29624.9i 1.35732i
\(782\) 93277.0i 4.26545i
\(783\) −18137.7 2976.62i −0.827826 0.135857i
\(784\) 1577.09 0.0718427