Properties

Label 177.5.b.a.119.2
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.2
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.77

$q$-expansion

\(f(q)\) \(=\) \(q-7.73459i q^{2} +(-8.52815 - 2.87588i) q^{3} -43.8239 q^{4} -0.620129i q^{5} +(-22.2437 + 65.9618i) q^{6} +71.8012 q^{7} +215.207i q^{8} +(64.4587 + 49.0518i) q^{9} +O(q^{10})\) \(q-7.73459i q^{2} +(-8.52815 - 2.87588i) q^{3} -43.8239 q^{4} -0.620129i q^{5} +(-22.2437 + 65.9618i) q^{6} +71.8012 q^{7} +215.207i q^{8} +(64.4587 + 49.0518i) q^{9} -4.79645 q^{10} -63.2025i q^{11} +(373.737 + 126.032i) q^{12} +204.993 q^{13} -555.353i q^{14} +(-1.78341 + 5.28856i) q^{15} +963.353 q^{16} +443.362i q^{17} +(379.396 - 498.562i) q^{18} -526.936 q^{19} +27.1765i q^{20} +(-612.332 - 206.491i) q^{21} -488.846 q^{22} +966.597i q^{23} +(618.907 - 1835.31i) q^{24} +624.615 q^{25} -1585.54i q^{26} +(-408.646 - 603.696i) q^{27} -3146.61 q^{28} +559.951i q^{29} +(40.9048 + 13.7940i) q^{30} +1278.62 q^{31} -4007.84i q^{32} +(-181.763 + 539.001i) q^{33} +3429.22 q^{34} -44.5261i q^{35} +(-2824.83 - 2149.64i) q^{36} +362.114 q^{37} +4075.64i q^{38} +(-1748.21 - 589.535i) q^{39} +133.456 q^{40} -2028.46i q^{41} +(-1597.13 + 4736.14i) q^{42} -487.652 q^{43} +2769.78i q^{44} +(30.4185 - 39.9727i) q^{45} +7476.24 q^{46} -34.7038i q^{47} +(-8215.62 - 2770.48i) q^{48} +2754.42 q^{49} -4831.15i q^{50} +(1275.05 - 3781.05i) q^{51} -8983.61 q^{52} +1648.43i q^{53} +(-4669.34 + 3160.71i) q^{54} -39.1937 q^{55} +15452.1i q^{56} +(4493.79 + 1515.40i) q^{57} +4330.99 q^{58} -453.188i q^{59} +(78.1562 - 231.765i) q^{60} -2514.15 q^{61} -9889.62i q^{62} +(4628.21 + 3521.98i) q^{63} -15585.3 q^{64} -127.122i q^{65} +(4168.95 + 1405.86i) q^{66} -2378.22 q^{67} -19429.8i q^{68} +(2779.81 - 8243.29i) q^{69} -344.391 q^{70} -884.945i q^{71} +(-10556.3 + 13871.9i) q^{72} +7907.46 q^{73} -2800.80i q^{74} +(-5326.81 - 1796.32i) q^{75} +23092.4 q^{76} -4538.02i q^{77} +(-4559.82 + 13521.7i) q^{78} -3006.62 q^{79} -597.403i q^{80} +(1748.84 + 6323.63i) q^{81} -15689.3 q^{82} +4564.48i q^{83} +(26834.8 + 9049.26i) q^{84} +274.942 q^{85} +3771.79i q^{86} +(1610.35 - 4775.35i) q^{87} +13601.6 q^{88} -2010.89i q^{89} +(-309.173 - 235.274i) q^{90} +14718.8 q^{91} -42360.1i q^{92} +(-10904.3 - 3677.16i) q^{93} -268.420 q^{94} +326.769i q^{95} +(-11526.0 + 34179.4i) q^{96} +7872.26 q^{97} -21304.3i q^{98} +(3100.20 - 4073.95i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.73459i 1.93365i −0.255443 0.966824i \(-0.582221\pi\)
0.255443 0.966824i \(-0.417779\pi\)
\(3\) −8.52815 2.87588i −0.947572 0.319542i
\(4\) −43.8239 −2.73899
\(5\) 0.620129i 0.0248052i −0.999923 0.0124026i \(-0.996052\pi\)
0.999923 0.0124026i \(-0.00394797\pi\)
\(6\) −22.2437 + 65.9618i −0.617881 + 1.83227i
\(7\) 71.8012 1.46533 0.732666 0.680589i \(-0.238276\pi\)
0.732666 + 0.680589i \(0.238276\pi\)
\(8\) 215.207i 3.36260i
\(9\) 64.4587 + 49.0518i 0.795786 + 0.605578i
\(10\) −4.79645 −0.0479645
\(11\) 63.2025i 0.522335i −0.965294 0.261167i \(-0.915893\pi\)
0.965294 0.261167i \(-0.0841075\pi\)
\(12\) 373.737 + 126.032i 2.59540 + 0.875223i
\(13\) 204.993 1.21298 0.606489 0.795092i \(-0.292577\pi\)
0.606489 + 0.795092i \(0.292577\pi\)
\(14\) 555.353i 2.83344i
\(15\) −1.78341 + 5.28856i −0.00792629 + 0.0235047i
\(16\) 963.353 3.76310
\(17\) 443.362i 1.53412i 0.641573 + 0.767062i \(0.278282\pi\)
−0.641573 + 0.767062i \(0.721718\pi\)
\(18\) 379.396 498.562i 1.17097 1.53877i
\(19\) −526.936 −1.45966 −0.729829 0.683630i \(-0.760400\pi\)
−0.729829 + 0.683630i \(0.760400\pi\)
\(20\) 27.1765i 0.0679412i
\(21\) −612.332 206.491i −1.38851 0.468235i
\(22\) −488.846 −1.01001
\(23\) 966.597i 1.82722i 0.406596 + 0.913608i \(0.366716\pi\)
−0.406596 + 0.913608i \(0.633284\pi\)
\(24\) 618.907 1835.31i 1.07449 3.18631i
\(25\) 624.615 0.999385
\(26\) 1585.54i 2.34547i
\(27\) −408.646 603.696i −0.560558 0.828116i
\(28\) −3146.61 −4.01354
\(29\) 559.951i 0.665816i 0.942959 + 0.332908i \(0.108030\pi\)
−0.942959 + 0.332908i \(0.891970\pi\)
\(30\) 40.9048 + 13.7940i 0.0454498 + 0.0153267i
\(31\) 1278.62 1.33051 0.665256 0.746615i \(-0.268322\pi\)
0.665256 + 0.746615i \(0.268322\pi\)
\(32\) 4007.84i 3.91390i
\(33\) −181.763 + 539.001i −0.166908 + 0.494950i
\(34\) 3429.22 2.96645
\(35\) 44.5261i 0.0363478i
\(36\) −2824.83 2149.64i −2.17965 1.65867i
\(37\) 362.114 0.264510 0.132255 0.991216i \(-0.457778\pi\)
0.132255 + 0.991216i \(0.457778\pi\)
\(38\) 4075.64i 2.82246i
\(39\) −1748.21 589.535i −1.14938 0.387597i
\(40\) 133.456 0.0834100
\(41\) 2028.46i 1.20670i −0.797477 0.603349i \(-0.793833\pi\)
0.797477 0.603349i \(-0.206167\pi\)
\(42\) −1597.13 + 4736.14i −0.905401 + 2.68488i
\(43\) −487.652 −0.263738 −0.131869 0.991267i \(-0.542098\pi\)
−0.131869 + 0.991267i \(0.542098\pi\)
\(44\) 2769.78i 1.43067i
\(45\) 30.4185 39.9727i 0.0150215 0.0197396i
\(46\) 7476.24 3.53319
\(47\) 34.7038i 0.0157102i −0.999969 0.00785510i \(-0.997500\pi\)
0.999969 0.00785510i \(-0.00250038\pi\)
\(48\) −8215.62 2770.48i −3.56581 1.20247i
\(49\) 2754.42 1.14720
\(50\) 4831.15i 1.93246i
\(51\) 1275.05 3781.05i 0.490216 1.45369i
\(52\) −8983.61 −3.32234
\(53\) 1648.43i 0.586840i 0.955984 + 0.293420i \(0.0947934\pi\)
−0.955984 + 0.293420i \(0.905207\pi\)
\(54\) −4669.34 + 3160.71i −1.60128 + 1.08392i
\(55\) −39.1937 −0.0129566
\(56\) 15452.1i 4.92733i
\(57\) 4493.79 + 1515.40i 1.38313 + 0.466422i
\(58\) 4330.99 1.28745
\(59\) 453.188i 0.130189i
\(60\) 78.1562 231.765i 0.0217101 0.0643792i
\(61\) −2514.15 −0.675664 −0.337832 0.941206i \(-0.609694\pi\)
−0.337832 + 0.941206i \(0.609694\pi\)
\(62\) 9889.62i 2.57274i
\(63\) 4628.21 + 3521.98i 1.16609 + 0.887372i
\(64\) −15585.3 −3.80501
\(65\) 127.122i 0.0300881i
\(66\) 4168.95 + 1405.86i 0.957059 + 0.322741i
\(67\) −2378.22 −0.529788 −0.264894 0.964277i \(-0.585337\pi\)
−0.264894 + 0.964277i \(0.585337\pi\)
\(68\) 19429.8i 4.20196i
\(69\) 2779.81 8243.29i 0.583872 1.73142i
\(70\) −344.391 −0.0702839
\(71\) 884.945i 0.175550i −0.996140 0.0877748i \(-0.972024\pi\)
0.996140 0.0877748i \(-0.0279756\pi\)
\(72\) −10556.3 + 13871.9i −2.03632 + 2.67591i
\(73\) 7907.46 1.48385 0.741927 0.670480i \(-0.233912\pi\)
0.741927 + 0.670480i \(0.233912\pi\)
\(74\) 2800.80i 0.511468i
\(75\) −5326.81 1796.32i −0.946989 0.319345i
\(76\) 23092.4 3.99800
\(77\) 4538.02i 0.765394i
\(78\) −4559.82 + 13521.7i −0.749477 + 2.22251i
\(79\) −3006.62 −0.481754 −0.240877 0.970556i \(-0.577435\pi\)
−0.240877 + 0.970556i \(0.577435\pi\)
\(80\) 597.403i 0.0933443i
\(81\) 1748.84 + 6323.63i 0.266551 + 0.963821i
\(82\) −15689.3 −2.33333
\(83\) 4564.48i 0.662576i 0.943530 + 0.331288i \(0.107483\pi\)
−0.943530 + 0.331288i \(0.892517\pi\)
\(84\) 26834.8 + 9049.26i 3.80311 + 1.28249i
\(85\) 274.942 0.0380542
\(86\) 3771.79i 0.509977i
\(87\) 1610.35 4775.35i 0.212756 0.630908i
\(88\) 13601.6 1.75641
\(89\) 2010.89i 0.253868i −0.991911 0.126934i \(-0.959486\pi\)
0.991911 0.126934i \(-0.0405137\pi\)
\(90\) −309.173 235.274i −0.0381695 0.0290462i
\(91\) 14718.8 1.77742
\(92\) 42360.1i 5.00474i
\(93\) −10904.3 3677.16i −1.26076 0.425154i
\(94\) −268.420 −0.0303780
\(95\) 326.769i 0.0362071i
\(96\) −11526.0 + 34179.4i −1.25065 + 3.70870i
\(97\) 7872.26 0.836673 0.418337 0.908292i \(-0.362613\pi\)
0.418337 + 0.908292i \(0.362613\pi\)
\(98\) 21304.3i 2.21827i
\(99\) 3100.20 4073.95i 0.316314 0.415667i
\(100\) −27373.1 −2.73731
\(101\) 4233.74i 0.415032i 0.978232 + 0.207516i \(0.0665380\pi\)
−0.978232 + 0.207516i \(0.933462\pi\)
\(102\) −29244.9 9862.01i −2.81093 0.947906i
\(103\) 10764.8 1.01468 0.507341 0.861745i \(-0.330628\pi\)
0.507341 + 0.861745i \(0.330628\pi\)
\(104\) 44115.9i 4.07877i
\(105\) −128.051 + 379.725i −0.0116146 + 0.0344422i
\(106\) 12750.0 1.13474
\(107\) 8243.20i 0.719993i 0.932954 + 0.359997i \(0.117222\pi\)
−0.932954 + 0.359997i \(0.882778\pi\)
\(108\) 17908.5 + 26456.3i 1.53536 + 2.26820i
\(109\) 4786.90 0.402903 0.201452 0.979498i \(-0.435434\pi\)
0.201452 + 0.979498i \(0.435434\pi\)
\(110\) 303.148i 0.0250535i
\(111\) −3088.16 1041.39i −0.250642 0.0845219i
\(112\) 69169.9 5.51418
\(113\) 2505.20i 0.196194i 0.995177 + 0.0980971i \(0.0312756\pi\)
−0.995177 + 0.0980971i \(0.968724\pi\)
\(114\) 11721.0 34757.7i 0.901895 2.67449i
\(115\) 599.415 0.0453244
\(116\) 24539.2i 1.82367i
\(117\) 13213.6 + 10055.3i 0.965272 + 0.734553i
\(118\) −3505.22 −0.251740
\(119\) 31833.9i 2.24800i
\(120\) −1138.13 383.803i −0.0790370 0.0266530i
\(121\) 10646.4 0.727166
\(122\) 19445.9i 1.30650i
\(123\) −5833.60 + 17299.0i −0.385590 + 1.14343i
\(124\) −56034.2 −3.64427
\(125\) 774.923i 0.0495951i
\(126\) 27241.1 35797.3i 1.71587 2.25481i
\(127\) 16718.1 1.03652 0.518262 0.855222i \(-0.326579\pi\)
0.518262 + 0.855222i \(0.326579\pi\)
\(128\) 56420.8i 3.44365i
\(129\) 4158.77 + 1402.43i 0.249911 + 0.0842754i
\(130\) −983.240 −0.0581799
\(131\) 36.1996i 0.00210941i −0.999999 0.00105470i \(-0.999664\pi\)
0.999999 0.00105470i \(-0.000335723\pi\)
\(132\) 7965.55 23621.1i 0.457160 1.35567i
\(133\) −37834.7 −2.13888
\(134\) 18394.6i 1.02442i
\(135\) −374.370 + 253.414i −0.0205416 + 0.0139047i
\(136\) −95414.4 −5.15865
\(137\) 976.041i 0.0520028i 0.999662 + 0.0260014i \(0.00827744\pi\)
−0.999662 + 0.0260014i \(0.991723\pi\)
\(138\) −63758.5 21500.7i −3.34796 1.12900i
\(139\) −5174.94 −0.267840 −0.133920 0.990992i \(-0.542757\pi\)
−0.133920 + 0.990992i \(0.542757\pi\)
\(140\) 1951.31i 0.0995564i
\(141\) −99.8039 + 295.959i −0.00502006 + 0.0148865i
\(142\) −6844.69 −0.339451
\(143\) 12956.1i 0.633581i
\(144\) 62096.5 + 47254.2i 2.99462 + 2.27885i
\(145\) 347.242 0.0165157
\(146\) 61161.0i 2.86925i
\(147\) −23490.1 7921.36i −1.08705 0.366577i
\(148\) −15869.2 −0.724490
\(149\) 24593.4i 1.10776i −0.832596 0.553881i \(-0.813146\pi\)
0.832596 0.553881i \(-0.186854\pi\)
\(150\) −13893.8 + 41200.7i −0.617501 + 1.83114i
\(151\) 16890.9 0.740798 0.370399 0.928873i \(-0.379221\pi\)
0.370399 + 0.928873i \(0.379221\pi\)
\(152\) 113400.i 4.90825i
\(153\) −21747.7 + 28578.5i −0.929031 + 1.22083i
\(154\) −35099.7 −1.48000
\(155\) 792.911i 0.0330036i
\(156\) 76613.6 + 25835.8i 3.14816 + 1.06163i
\(157\) −16131.7 −0.654458 −0.327229 0.944945i \(-0.606115\pi\)
−0.327229 + 0.944945i \(0.606115\pi\)
\(158\) 23255.0i 0.931542i
\(159\) 4740.69 14058.1i 0.187520 0.556073i
\(160\) −2485.38 −0.0970850
\(161\) 69402.9i 2.67748i
\(162\) 48910.7 13526.6i 1.86369 0.515416i
\(163\) −40515.1 −1.52490 −0.762451 0.647046i \(-0.776004\pi\)
−0.762451 + 0.647046i \(0.776004\pi\)
\(164\) 88895.0i 3.30514i
\(165\) 334.250 + 112.716i 0.0122773 + 0.00414018i
\(166\) 35304.4 1.28119
\(167\) 20215.8i 0.724866i −0.932010 0.362433i \(-0.881946\pi\)
0.932010 0.362433i \(-0.118054\pi\)
\(168\) 44438.3 131778.i 1.57449 4.66900i
\(169\) 13461.3 0.471317
\(170\) 2126.56i 0.0735834i
\(171\) −33965.6 25847.2i −1.16158 0.883936i
\(172\) 21370.8 0.722378
\(173\) 49862.1i 1.66601i 0.553264 + 0.833006i \(0.313382\pi\)
−0.553264 + 0.833006i \(0.686618\pi\)
\(174\) −36935.3 12455.4i −1.21995 0.411395i
\(175\) 44848.2 1.46443
\(176\) 60886.3i 1.96560i
\(177\) −1303.31 + 3864.85i −0.0416008 + 0.123363i
\(178\) −15553.4 −0.490892
\(179\) 32152.1i 1.00347i 0.865022 + 0.501733i \(0.167304\pi\)
−0.865022 + 0.501733i \(0.832696\pi\)
\(180\) −1333.06 + 1751.76i −0.0411437 + 0.0540667i
\(181\) 26929.6 0.822003 0.411001 0.911635i \(-0.365179\pi\)
0.411001 + 0.911635i \(0.365179\pi\)
\(182\) 113844.i 3.43690i
\(183\) 21441.0 + 7230.37i 0.640240 + 0.215903i
\(184\) −208018. −6.14420
\(185\) 224.557i 0.00656121i
\(186\) −28441.3 + 84340.2i −0.822098 + 2.43786i
\(187\) 28021.6 0.801326
\(188\) 1520.86i 0.0430302i
\(189\) −29341.3 43346.1i −0.821403 1.21346i
\(190\) 2527.42 0.0700117
\(191\) 32685.5i 0.895958i −0.894044 0.447979i \(-0.852144\pi\)
0.894044 0.447979i \(-0.147856\pi\)
\(192\) 132914. + 44821.5i 3.60552 + 1.21586i
\(193\) 27244.8 0.731425 0.365712 0.930728i \(-0.380825\pi\)
0.365712 + 0.930728i \(0.380825\pi\)
\(194\) 60888.7i 1.61783i
\(195\) −365.588 + 1084.12i −0.00961442 + 0.0285107i
\(196\) −120709. −3.14216
\(197\) 32019.8i 0.825062i −0.910944 0.412531i \(-0.864645\pi\)
0.910944 0.412531i \(-0.135355\pi\)
\(198\) −31510.4 23978.8i −0.803753 0.611641i
\(199\) 25668.1 0.648169 0.324085 0.946028i \(-0.394944\pi\)
0.324085 + 0.946028i \(0.394944\pi\)
\(200\) 134421.i 3.36053i
\(201\) 20281.8 + 6839.47i 0.502013 + 0.169289i
\(202\) 32746.3 0.802526
\(203\) 40205.2i 0.975641i
\(204\) −55877.8 + 165701.i −1.34270 + 3.98166i
\(205\) −1257.91 −0.0299323
\(206\) 83261.0i 1.96204i
\(207\) −47413.3 + 62305.6i −1.10652 + 1.45407i
\(208\) 197481. 4.56456
\(209\) 33303.7i 0.762430i
\(210\) 2937.02 + 990.425i 0.0665990 + 0.0224586i
\(211\) −42406.1 −0.952497 −0.476249 0.879311i \(-0.658004\pi\)
−0.476249 + 0.879311i \(0.658004\pi\)
\(212\) 72240.8i 1.60735i
\(213\) −2544.99 + 7546.95i −0.0560954 + 0.166346i
\(214\) 63757.8 1.39221
\(215\) 302.408i 0.00654208i
\(216\) 129919. 87943.4i 2.78462 1.88493i
\(217\) 91806.7 1.94964
\(218\) 37024.7i 0.779073i
\(219\) −67436.0 22740.9i −1.40606 0.474153i
\(220\) 1717.62 0.0354881
\(221\) 90886.2i 1.86086i
\(222\) −8054.76 + 23885.7i −0.163436 + 0.484653i
\(223\) −53628.8 −1.07842 −0.539211 0.842171i \(-0.681277\pi\)
−0.539211 + 0.842171i \(0.681277\pi\)
\(224\) 287768.i 5.73516i
\(225\) 40261.9 + 30638.5i 0.795297 + 0.605205i
\(226\) 19376.7 0.379371
\(227\) 42594.5i 0.826613i −0.910592 0.413306i \(-0.864374\pi\)
0.910592 0.413306i \(-0.135626\pi\)
\(228\) −196936. 66410.9i −3.78839 1.27753i
\(229\) −15094.4 −0.287836 −0.143918 0.989590i \(-0.545970\pi\)
−0.143918 + 0.989590i \(0.545970\pi\)
\(230\) 4636.23i 0.0876415i
\(231\) −13050.8 + 38700.9i −0.244575 + 0.725266i
\(232\) −120505. −2.23887
\(233\) 1764.28i 0.0324979i −0.999868 0.0162489i \(-0.994828\pi\)
0.999868 0.0162489i \(-0.00517243\pi\)
\(234\) 77773.6 102202.i 1.42037 1.86650i
\(235\) −21.5209 −0.000389694
\(236\) 19860.5i 0.356587i
\(237\) 25640.9 + 8646.68i 0.456496 + 0.153940i
\(238\) 246222. 4.34684
\(239\) 99155.8i 1.73589i −0.496659 0.867946i \(-0.665440\pi\)
0.496659 0.867946i \(-0.334560\pi\)
\(240\) −1718.06 + 5094.75i −0.0298274 + 0.0884505i
\(241\) −73745.9 −1.26971 −0.634854 0.772632i \(-0.718940\pi\)
−0.634854 + 0.772632i \(0.718940\pi\)
\(242\) 82345.9i 1.40608i
\(243\) 3271.57 58958.3i 0.0554044 0.998464i
\(244\) 110180. 1.85064
\(245\) 1708.10i 0.0284564i
\(246\) 133801. + 45120.5i 2.21100 + 0.745596i
\(247\) −108018. −1.77053
\(248\) 275168.i 4.47398i
\(249\) 13126.9 38926.6i 0.211721 0.627838i
\(250\) −5993.72 −0.0958994
\(251\) 34624.4i 0.549585i −0.961504 0.274793i \(-0.911391\pi\)
0.961504 0.274793i \(-0.0886092\pi\)
\(252\) −202826. 154347.i −3.19392 2.43051i
\(253\) 61091.4 0.954419
\(254\) 129308.i 2.00427i
\(255\) −2344.74 790.698i −0.0360591 0.0121599i
\(256\) 187026. 2.85380
\(257\) 85104.8i 1.28851i 0.764811 + 0.644255i \(0.222832\pi\)
−0.764811 + 0.644255i \(0.777168\pi\)
\(258\) 10847.2 32166.4i 0.162959 0.483240i
\(259\) 26000.2 0.387594
\(260\) 5571.00i 0.0824113i
\(261\) −27466.6 + 36093.7i −0.403203 + 0.529847i
\(262\) −279.989 −0.00407885
\(263\) 112176.i 1.62176i −0.585210 0.810882i \(-0.698988\pi\)
0.585210 0.810882i \(-0.301012\pi\)
\(264\) −115997. 39116.5i −1.66432 0.561245i
\(265\) 1022.24 0.0145567
\(266\) 292636.i 4.13585i
\(267\) −5783.07 + 17149.2i −0.0811215 + 0.240558i
\(268\) 104223. 1.45109
\(269\) 26041.8i 0.359887i 0.983677 + 0.179944i \(0.0575915\pi\)
−0.983677 + 0.179944i \(0.942408\pi\)
\(270\) 1960.05 + 2895.60i 0.0268868 + 0.0397201i
\(271\) −122251. −1.66461 −0.832307 0.554315i \(-0.812980\pi\)
−0.832307 + 0.554315i \(0.812980\pi\)
\(272\) 427114.i 5.77306i
\(273\) −125524. 42329.4i −1.68423 0.567958i
\(274\) 7549.28 0.100555
\(275\) 39477.3i 0.522014i
\(276\) −121822. + 361253.i −1.59922 + 4.74235i
\(277\) 27696.8 0.360969 0.180485 0.983578i \(-0.442233\pi\)
0.180485 + 0.983578i \(0.442233\pi\)
\(278\) 40026.0i 0.517909i
\(279\) 82418.3 + 62718.7i 1.05880 + 0.805728i
\(280\) 9582.30 0.122223
\(281\) 138592.i 1.75520i 0.479396 + 0.877599i \(0.340856\pi\)
−0.479396 + 0.877599i \(0.659144\pi\)
\(282\) 2289.13 + 771.942i 0.0287853 + 0.00970704i
\(283\) 34002.8 0.424563 0.212281 0.977209i \(-0.431911\pi\)
0.212281 + 0.977209i \(0.431911\pi\)
\(284\) 38781.8i 0.480829i
\(285\) 939.746 2786.73i 0.0115697 0.0343088i
\(286\) −100210. −1.22512
\(287\) 145646.i 1.76821i
\(288\) 196592. 258340.i 2.37017 3.11463i
\(289\) −113049. −1.35353
\(290\) 2685.78i 0.0319355i
\(291\) −67135.8 22639.6i −0.792808 0.267352i
\(292\) −346536. −4.06427
\(293\) 85177.2i 0.992175i 0.868272 + 0.496088i \(0.165231\pi\)
−0.868272 + 0.496088i \(0.834769\pi\)
\(294\) −61268.5 + 181686.i −0.708831 + 2.10197i
\(295\) −281.035 −0.00322936
\(296\) 77929.3i 0.889441i
\(297\) −38155.1 + 25827.5i −0.432554 + 0.292799i
\(298\) −190220. −2.14202
\(299\) 198146.i 2.21637i
\(300\) 233442. + 78721.6i 2.59380 + 0.874685i
\(301\) −35014.0 −0.386464
\(302\) 130644.i 1.43244i
\(303\) 12175.7 36106.0i 0.132620 0.393273i
\(304\) −507626. −5.49283
\(305\) 1559.10i 0.0167600i
\(306\) 221043. + 168209.i 2.36066 + 1.79642i
\(307\) 181337. 1.92402 0.962011 0.273009i \(-0.0880190\pi\)
0.962011 + 0.273009i \(0.0880190\pi\)
\(308\) 198874.i 2.09641i
\(309\) −91803.5 30958.1i −0.961485 0.324233i
\(310\) −6132.84 −0.0638173
\(311\) 54923.1i 0.567851i −0.958846 0.283925i \(-0.908363\pi\)
0.958846 0.283925i \(-0.0916368\pi\)
\(312\) 126872. 376227.i 1.30334 3.86493i
\(313\) 54353.5 0.554803 0.277401 0.960754i \(-0.410527\pi\)
0.277401 + 0.960754i \(0.410527\pi\)
\(314\) 124772.i 1.26549i
\(315\) 2184.08 2870.09i 0.0220114 0.0289251i
\(316\) 131762. 1.31952
\(317\) 22871.8i 0.227605i 0.993503 + 0.113802i \(0.0363031\pi\)
−0.993503 + 0.113802i \(0.963697\pi\)
\(318\) −108734. 36667.3i −1.07525 0.362597i
\(319\) 35390.3 0.347779
\(320\) 9664.92i 0.0943840i
\(321\) 23706.4 70299.3i 0.230068 0.682246i
\(322\) 536803. 5.17730
\(323\) 233623.i 2.23930i
\(324\) −76641.1 277126.i −0.730082 2.63990i
\(325\) 128042. 1.21223
\(326\) 313368.i 2.94862i
\(327\) −40823.4 13766.5i −0.381780 0.128744i
\(328\) 436538. 4.05765
\(329\) 2491.78i 0.0230206i
\(330\) 871.815 2585.29i 0.00800565 0.0237400i
\(331\) −77310.0 −0.705634 −0.352817 0.935692i \(-0.614776\pi\)
−0.352817 + 0.935692i \(0.614776\pi\)
\(332\) 200034.i 1.81479i
\(333\) 23341.4 + 17762.3i 0.210493 + 0.160181i
\(334\) −156361. −1.40164
\(335\) 1474.80i 0.0131415i
\(336\) −589892. 198924.i −5.22509 1.76201i
\(337\) 4371.86 0.0384952 0.0192476 0.999815i \(-0.493873\pi\)
0.0192476 + 0.999815i \(0.493873\pi\)
\(338\) 104118.i 0.911361i
\(339\) 7204.65 21364.8i 0.0626922 0.185908i
\(340\) −12049.0 −0.104230
\(341\) 80812.1i 0.694973i
\(342\) −199917. + 262710.i −1.70922 + 2.24608i
\(343\) 25375.9 0.215692
\(344\) 104946.i 0.886848i
\(345\) −5111.90 1723.84i −0.0429482 0.0144830i
\(346\) 385663. 3.22148
\(347\) 71853.0i 0.596741i −0.954450 0.298370i \(-0.903557\pi\)
0.954450 0.298370i \(-0.0964431\pi\)
\(348\) −70571.8 + 209274.i −0.582737 + 1.72805i
\(349\) 185348. 1.52173 0.760863 0.648913i \(-0.224776\pi\)
0.760863 + 0.648913i \(0.224776\pi\)
\(350\) 346882.i 2.83169i
\(351\) −83769.8 123754.i −0.679944 1.00449i
\(352\) −253305. −2.04437
\(353\) 146210.i 1.17335i 0.809822 + 0.586676i \(0.199564\pi\)
−0.809822 + 0.586676i \(0.800436\pi\)
\(354\) 29893.1 + 10080.6i 0.238541 + 0.0804413i
\(355\) −548.781 −0.00435454
\(356\) 88125.1i 0.695344i
\(357\) 91550.4 271484.i 0.718330 2.13014i
\(358\) 248683. 1.94035
\(359\) 71968.3i 0.558409i 0.960232 + 0.279205i \(0.0900708\pi\)
−0.960232 + 0.279205i \(0.909929\pi\)
\(360\) 8602.39 + 6546.25i 0.0663765 + 0.0505112i
\(361\) 147341. 1.13060
\(362\) 208290.i 1.58946i
\(363\) −90794.4 30617.8i −0.689043 0.232360i
\(364\) −645035. −4.86833
\(365\) 4903.65i 0.0368073i
\(366\) 55924.0 165837.i 0.417480 1.23800i
\(367\) 263314. 1.95498 0.977489 0.210988i \(-0.0676681\pi\)
0.977489 + 0.210988i \(0.0676681\pi\)
\(368\) 931174.i 6.87599i
\(369\) 99499.6 130752.i 0.730749 0.960273i
\(370\) −1736.86 −0.0126871
\(371\) 118360.i 0.859915i
\(372\) 477868. + 161147.i 3.45320 + 1.16449i
\(373\) 94196.4 0.677043 0.338522 0.940959i \(-0.390073\pi\)
0.338522 + 0.940959i \(0.390073\pi\)
\(374\) 216735.i 1.54948i
\(375\) −2228.58 + 6608.66i −0.0158477 + 0.0469949i
\(376\) 7468.49 0.0528272
\(377\) 114786.i 0.807620i
\(378\) −335265. + 226943.i −2.34641 + 1.58830i
\(379\) 102807. 0.715720 0.357860 0.933775i \(-0.383507\pi\)
0.357860 + 0.933775i \(0.383507\pi\)
\(380\) 14320.3i 0.0991710i
\(381\) −142574. 48079.2i −0.982182 0.331213i
\(382\) −252809. −1.73247
\(383\) 58900.9i 0.401536i 0.979639 + 0.200768i \(0.0643437\pi\)
−0.979639 + 0.200768i \(0.935656\pi\)
\(384\) 162259. 481165.i 1.10039 3.26311i
\(385\) −2814.16 −0.0189857
\(386\) 210728.i 1.41432i
\(387\) −31433.4 23920.2i −0.209879 0.159714i
\(388\) −344993. −2.29164
\(389\) 179102.i 1.18359i −0.806088 0.591795i \(-0.798419\pi\)
0.806088 0.591795i \(-0.201581\pi\)
\(390\) 8385.22 + 2827.68i 0.0551296 + 0.0185909i
\(391\) −428552. −2.80318
\(392\) 592769.i 3.85757i
\(393\) −104.105 + 308.715i −0.000674044 + 0.00199882i
\(394\) −247660. −1.59538
\(395\) 1864.50i 0.0119500i
\(396\) −135863. + 178536.i −0.866383 + 1.13851i
\(397\) 45669.8 0.289767 0.144883 0.989449i \(-0.453719\pi\)
0.144883 + 0.989449i \(0.453719\pi\)
\(398\) 198533.i 1.25333i
\(399\) 322660. + 108808.i 2.02675 + 0.683462i
\(400\) 601725. 3.76078
\(401\) 54669.9i 0.339985i −0.985445 0.169992i \(-0.945626\pi\)
0.985445 0.169992i \(-0.0543743\pi\)
\(402\) 52900.5 156872.i 0.327346 0.970716i
\(403\) 262109. 1.61388
\(404\) 185539.i 1.13677i
\(405\) 3921.47 1084.51i 0.0239077 0.00661185i
\(406\) 310971. 1.88655
\(407\) 22886.5i 0.138163i
\(408\) 813708. + 274400.i 4.88819 + 1.64840i
\(409\) 259180. 1.54937 0.774684 0.632348i \(-0.217909\pi\)
0.774684 + 0.632348i \(0.217909\pi\)
\(410\) 9729.40i 0.0578786i
\(411\) 2806.97 8323.83i 0.0166171 0.0492764i
\(412\) −471754. −2.77921
\(413\) 32539.4i 0.190770i
\(414\) 481908. + 366723.i 2.81167 + 2.13962i
\(415\) 2830.57 0.0164353
\(416\) 821580.i 4.74748i
\(417\) 44132.7 + 14882.5i 0.253798 + 0.0855861i
\(418\) 257591. 1.47427
\(419\) 102683.i 0.584888i 0.956283 + 0.292444i \(0.0944685\pi\)
−0.956283 + 0.292444i \(0.905532\pi\)
\(420\) 5611.71 16641.0i 0.0318124 0.0943369i
\(421\) −216357. −1.22069 −0.610346 0.792135i \(-0.708970\pi\)
−0.610346 + 0.792135i \(0.708970\pi\)
\(422\) 327994.i 1.84179i
\(423\) 1702.29 2236.96i 0.00951375 0.0125020i
\(424\) −354754. −1.97331
\(425\) 276931.i 1.53318i
\(426\) 58372.5 + 19684.5i 0.321654 + 0.108469i
\(427\) −180519. −0.990072
\(428\) 361249.i 1.97206i
\(429\) −37260.1 + 110492.i −0.202456 + 0.600364i
\(430\) 2339.00 0.0126501
\(431\) 140988.i 0.758976i −0.925197 0.379488i \(-0.876100\pi\)
0.925197 0.379488i \(-0.123900\pi\)
\(432\) −393671. 581572.i −2.10943 3.11628i
\(433\) 133663. 0.712911 0.356455 0.934312i \(-0.383985\pi\)
0.356455 + 0.934312i \(0.383985\pi\)
\(434\) 710087.i 3.76992i
\(435\) −2961.33 998.625i −0.0156498 0.00527745i
\(436\) −209780. −1.10355
\(437\) 509335.i 2.66711i
\(438\) −175891. + 521590.i −0.916846 + 2.71882i
\(439\) −13250.2 −0.0687531 −0.0343765 0.999409i \(-0.510945\pi\)
−0.0343765 + 0.999409i \(0.510945\pi\)
\(440\) 8434.75i 0.0435679i
\(441\) 177546. + 135109.i 0.912923 + 0.694717i
\(442\) 702968. 3.59825
\(443\) 195021.i 0.993743i 0.867824 + 0.496871i \(0.165518\pi\)
−0.867824 + 0.496871i \(0.834482\pi\)
\(444\) 135335. + 45638.0i 0.686507 + 0.231505i
\(445\) −1247.01 −0.00629725
\(446\) 414797.i 2.08529i
\(447\) −70727.6 + 209736.i −0.353976 + 1.04968i
\(448\) −1.11905e6 −5.57560
\(449\) 62270.2i 0.308879i 0.988002 + 0.154439i \(0.0493571\pi\)
−0.988002 + 0.154439i \(0.950643\pi\)
\(450\) 236976. 311409.i 1.17025 1.53782i
\(451\) −128204. −0.630300
\(452\) 109788.i 0.537375i
\(453\) −144048. 48576.2i −0.701960 0.236716i
\(454\) −329451. −1.59838
\(455\) 9127.55i 0.0440891i
\(456\) −326125. + 967094.i −1.56839 + 4.65092i
\(457\) −178424. −0.854319 −0.427159 0.904176i \(-0.640486\pi\)
−0.427159 + 0.904176i \(0.640486\pi\)
\(458\) 116749.i 0.556574i
\(459\) 267656. 181178.i 1.27043 0.859964i
\(460\) −26268.7 −0.124143
\(461\) 37707.0i 0.177427i 0.996057 + 0.0887135i \(0.0282756\pi\)
−0.996057 + 0.0887135i \(0.971724\pi\)
\(462\) 299336. + 100942.i 1.40241 + 0.472922i
\(463\) −234321. −1.09308 −0.546538 0.837435i \(-0.684054\pi\)
−0.546538 + 0.837435i \(0.684054\pi\)
\(464\) 539430.i 2.50553i
\(465\) −2280.31 + 6762.07i −0.0105460 + 0.0312733i
\(466\) −13646.0 −0.0628395
\(467\) 254624.i 1.16753i −0.811924 0.583763i \(-0.801580\pi\)
0.811924 0.583763i \(-0.198420\pi\)
\(468\) −579072. 440662.i −2.64387 2.01194i
\(469\) −170759. −0.776316
\(470\) 166.455i 0.000753532i
\(471\) 137574. + 46392.8i 0.620146 + 0.209127i
\(472\) 97529.0 0.437774
\(473\) 30820.9i 0.137760i
\(474\) 66878.5 198322.i 0.297667 0.882703i
\(475\) −329133. −1.45876
\(476\) 1.39509e6i 6.15726i
\(477\) −80858.6 + 106256.i −0.355377 + 0.466999i
\(478\) −766930. −3.35660
\(479\) 157553.i 0.686680i 0.939211 + 0.343340i \(0.111558\pi\)
−0.939211 + 0.343340i \(0.888442\pi\)
\(480\) 21195.7 + 7147.63i 0.0919951 + 0.0310227i
\(481\) 74230.9 0.320844
\(482\) 570394.i 2.45517i
\(483\) 199594. 591878.i 0.855566 2.53710i
\(484\) −466569. −1.99170
\(485\) 4881.82i 0.0207538i
\(486\) −456018. 25304.3i −1.93068 0.107133i
\(487\) −9062.55 −0.0382114 −0.0191057 0.999817i \(-0.506082\pi\)
−0.0191057 + 0.999817i \(0.506082\pi\)
\(488\) 541061.i 2.27199i
\(489\) 345519. + 116516.i 1.44495 + 0.487270i
\(490\) −13211.4 −0.0550247
\(491\) 200856.i 0.833148i −0.909102 0.416574i \(-0.863231\pi\)
0.909102 0.416574i \(-0.136769\pi\)
\(492\) 255651. 758110.i 1.05613 3.13186i
\(493\) −248261. −1.02144
\(494\) 835479.i 3.42359i
\(495\) −2526.38 1922.52i −0.0103107 0.00784623i
\(496\) 1.23176e6 5.00685
\(497\) 63540.2i 0.257238i
\(498\) −301081. 101531.i −1.21402 0.409393i
\(499\) 280290. 1.12566 0.562829 0.826573i \(-0.309713\pi\)
0.562829 + 0.826573i \(0.309713\pi\)
\(500\) 33960.2i 0.135841i
\(501\) −58138.1 + 172403.i −0.231625 + 0.686863i
\(502\) −267806. −1.06270
\(503\) 254469.i 1.00577i 0.864353 + 0.502886i \(0.167728\pi\)
−0.864353 + 0.502886i \(0.832272\pi\)
\(504\) −757953. + 996022.i −2.98388 + 3.92110i
\(505\) 2625.47 0.0102949
\(506\) 472517.i 1.84551i
\(507\) −114800. 38713.0i −0.446607 0.150605i
\(508\) −732653. −2.83904
\(509\) 250109.i 0.965370i 0.875794 + 0.482685i \(0.160338\pi\)
−0.875794 + 0.482685i \(0.839662\pi\)
\(510\) −6115.73 + 18135.6i −0.0235130 + 0.0697256i
\(511\) 567766. 2.17434
\(512\) 543841.i 2.07459i
\(513\) 215331. + 318110.i 0.818222 + 1.20877i
\(514\) 658251. 2.49153
\(515\) 6675.55i 0.0251694i
\(516\) −182254. 61459.9i −0.684505 0.230830i
\(517\) −2193.37 −0.00820599
\(518\) 201101.i 0.749471i
\(519\) 143397. 425231.i 0.532360 1.57867i
\(520\) 27357.6 0.101175
\(521\) 190802.i 0.702924i 0.936202 + 0.351462i \(0.114315\pi\)
−0.936202 + 0.351462i \(0.885685\pi\)
\(522\) 279170. + 212443.i 1.02454 + 0.779653i
\(523\) −397545. −1.45339 −0.726697 0.686958i \(-0.758946\pi\)
−0.726697 + 0.686958i \(0.758946\pi\)
\(524\) 1586.41i 0.00577766i
\(525\) −382472. 128978.i −1.38765 0.467946i
\(526\) −867634. −3.13592
\(527\) 566892.i 2.04117i
\(528\) −175102. + 519248.i −0.628090 + 1.86255i
\(529\) −654469. −2.33872
\(530\) 7906.62i 0.0281475i
\(531\) 22229.7 29211.9i 0.0788395 0.103603i
\(532\) 1.65806e6 5.85839
\(533\) 415821.i 1.46370i
\(534\) 132642. + 44729.7i 0.465155 + 0.156860i
\(535\) 5111.85 0.0178596
\(536\) 511809.i 1.78147i
\(537\) 92465.4 274198.i 0.320649 0.950857i
\(538\) 201423. 0.695895
\(539\) 174086.i 0.599221i
\(540\) 16406.3 11105.6i 0.0562632 0.0380850i
\(541\) 43502.7 0.148635 0.0743177 0.997235i \(-0.476322\pi\)
0.0743177 + 0.997235i \(0.476322\pi\)
\(542\) 945561.i 3.21878i
\(543\) −229660. 77446.3i −0.778907 0.262664i
\(544\) 1.77692e6 6.00441
\(545\) 2968.49i 0.00999409i
\(546\) −327400. + 970877.i −1.09823 + 3.25671i
\(547\) −11223.2 −0.0375095 −0.0187547 0.999824i \(-0.505970\pi\)
−0.0187547 + 0.999824i \(0.505970\pi\)
\(548\) 42773.9i 0.142435i
\(549\) −162059. 123323.i −0.537684 0.409167i
\(550\) −305341. −1.00939
\(551\) 295059.i 0.971863i
\(552\) 1.77401e6 + 598234.i 5.82208 + 1.96333i
\(553\) −215879. −0.705929
\(554\) 214224.i 0.697988i
\(555\) −645.799 + 1915.06i −0.00209658 + 0.00621722i
\(556\) 226786. 0.733613
\(557\) 142448.i 0.459140i −0.973292 0.229570i \(-0.926268\pi\)
0.973292 0.229570i \(-0.0737320\pi\)
\(558\) 485104. 637472.i 1.55800 2.04735i
\(559\) −99965.5 −0.319909
\(560\) 42894.3i 0.136780i
\(561\) −238972. 80586.6i −0.759314 0.256057i
\(562\) 1.07195e6 3.39393
\(563\) 80736.3i 0.254714i −0.991857 0.127357i \(-0.959351\pi\)
0.991857 0.127357i \(-0.0406493\pi\)
\(564\) 4373.80 12970.1i 0.0137499 0.0407742i
\(565\) 1553.55 0.00486663
\(566\) 262998.i 0.820955i
\(567\) 125569. + 454044.i 0.390586 + 1.41232i
\(568\) 190446. 0.590304
\(569\) 597848.i 1.84657i −0.384112 0.923287i \(-0.625492\pi\)
0.384112 0.923287i \(-0.374508\pi\)
\(570\) −21554.2 7268.55i −0.0663412 0.0223717i
\(571\) 84790.5 0.260061 0.130030 0.991510i \(-0.458492\pi\)
0.130030 + 0.991510i \(0.458492\pi\)
\(572\) 567787.i 1.73538i
\(573\) −93999.3 + 278746.i −0.286296 + 0.848985i
\(574\) −1.12651e6 −3.41910
\(575\) 603752.i 1.82609i
\(576\) −1.00461e6 764488.i −3.02798 2.30423i
\(577\) −315750. −0.948402 −0.474201 0.880417i \(-0.657263\pi\)
−0.474201 + 0.880417i \(0.657263\pi\)
\(578\) 874385.i 2.61726i
\(579\) −232348. 78352.8i −0.693078 0.233721i
\(580\) −15217.5 −0.0452363
\(581\) 327736.i 0.970893i
\(582\) −175108. + 519268.i −0.516965 + 1.53301i
\(583\) 104185. 0.306527
\(584\) 1.70174e6i 4.98961i
\(585\) 6235.58 8194.14i 0.0182207 0.0239437i
\(586\) 658811. 1.91852
\(587\) 255826.i 0.742454i −0.928542 0.371227i \(-0.878937\pi\)
0.928542 0.371227i \(-0.121063\pi\)
\(588\) 1.02943e6 + 347145.i 2.97743 + 1.00405i
\(589\) −673753. −1.94209
\(590\) 2173.69i 0.00624444i
\(591\) −92085.0 + 273070.i −0.263642 + 0.781806i
\(592\) 348843. 0.995375
\(593\) 469997.i 1.33655i 0.743914 + 0.668275i \(0.232967\pi\)
−0.743914 + 0.668275i \(0.767033\pi\)
\(594\) 199765. + 295114.i 0.566170 + 0.836407i
\(595\) 19741.1 0.0557620
\(596\) 1.07778e6i 3.03415i
\(597\) −218902. 73818.4i −0.614187 0.207117i
\(598\) 1.53258e6 4.28569
\(599\) 407616.i 1.13605i −0.823011 0.568025i \(-0.807708\pi\)
0.823011 0.568025i \(-0.192292\pi\)
\(600\) 386579. 1.14637e6i 1.07383 3.18435i
\(601\) −222294. −0.615431 −0.307715 0.951478i \(-0.599564\pi\)
−0.307715 + 0.951478i \(0.599564\pi\)
\(602\) 270819.i 0.747286i
\(603\) −153297. 116656.i −0.421598 0.320828i
\(604\) −740227. −2.02904
\(605\) 6602.17i 0.0180375i
\(606\) −279265. 94174.2i −0.760452 0.256441i
\(607\) −163249. −0.443071 −0.221535 0.975152i \(-0.571107\pi\)
−0.221535 + 0.975152i \(0.571107\pi\)
\(608\) 2.11187e6i 5.71296i
\(609\) 115625. 342876.i 0.311758 0.924490i
\(610\) 12059.0 0.0324079
\(611\) 7114.06i 0.0190561i
\(612\) 953069. 1.25242e6i 2.54461 3.34386i
\(613\) −288936. −0.768919 −0.384459 0.923142i \(-0.625612\pi\)
−0.384459 + 0.923142i \(0.625612\pi\)
\(614\) 1.40257e6i 3.72038i
\(615\) 10727.6 + 3617.58i 0.0283631 + 0.00956463i
\(616\) 976612. 2.57372
\(617\) 412795.i 1.08434i 0.840270 + 0.542168i \(0.182396\pi\)
−0.840270 + 0.542168i \(0.817604\pi\)
\(618\) −239448. + 710063.i −0.626953 + 1.85917i
\(619\) 499803. 1.30442 0.652211 0.758038i \(-0.273842\pi\)
0.652211 + 0.758038i \(0.273842\pi\)
\(620\) 34748.5i 0.0903966i
\(621\) 583531. 394997.i 1.51315 1.02426i
\(622\) −424808. −1.09802
\(623\) 144384.i 0.372001i
\(624\) −1.68415e6 567931.i −4.32525 1.45857i
\(625\) 389904. 0.998154
\(626\) 420402.i 1.07279i
\(627\) 95777.3 284019.i 0.243628 0.722458i
\(628\) 706955. 1.79256
\(629\) 160547.i 0.405790i
\(630\) −22199.0 16893.0i −0.0559309 0.0425623i
\(631\) −689137. −1.73080 −0.865400 0.501081i \(-0.832936\pi\)
−0.865400 + 0.501081i \(0.832936\pi\)
\(632\) 647045.i 1.61995i
\(633\) 361646. + 121955.i 0.902560 + 0.304363i
\(634\) 176904. 0.440108
\(635\) 10367.4i 0.0257112i
\(636\) −207756. + 616080.i −0.513616 + 1.52308i
\(637\) 564638. 1.39152
\(638\) 273730.i 0.672482i
\(639\) 43408.2 57042.4i 0.106309 0.139700i
\(640\) 34988.2 0.0854204
\(641\) 250518.i 0.609710i 0.952399 + 0.304855i \(0.0986081\pi\)
−0.952399 + 0.304855i \(0.901392\pi\)
\(642\) −543736. 183360.i −1.31922 0.444870i
\(643\) 277817. 0.671950 0.335975 0.941871i \(-0.390934\pi\)
0.335975 + 0.941871i \(0.390934\pi\)
\(644\) 3.04151e6i 7.33360i
\(645\) 869.687 2578.98i 0.00209047 0.00619909i
\(646\) −1.80698e6 −4.33001
\(647\) 705078.i 1.68434i −0.539215 0.842168i \(-0.681279\pi\)
0.539215 0.842168i \(-0.318721\pi\)
\(648\) −1.36089e6 + 376363.i −3.24095 + 0.896306i
\(649\) −28642.6 −0.0680022
\(650\) 990353.i 2.34403i
\(651\) −782941. 264025.i −1.84743 0.622992i
\(652\) 1.77553e6 4.17670
\(653\) 58074.5i 0.136194i −0.997679 0.0680972i \(-0.978307\pi\)
0.997679 0.0680972i \(-0.0216928\pi\)
\(654\) −106478. + 315752.i −0.248946 + 0.738228i
\(655\) −22.4484 −5.23242e−5
\(656\) 1.95412e6i 4.54092i
\(657\) 509705. + 387875.i 1.18083 + 0.898589i
\(658\) −19272.9 −0.0445138
\(659\) 745763.i 1.71724i 0.512615 + 0.858619i \(0.328677\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(660\) −14648.1 4939.67i −0.0336275 0.0113399i
\(661\) 226416. 0.518209 0.259104 0.965849i \(-0.416573\pi\)
0.259104 + 0.965849i \(0.416573\pi\)
\(662\) 597961.i 1.36445i
\(663\) 261377. 775091.i 0.594622 1.76330i
\(664\) −982307. −2.22798
\(665\) 23462.4i 0.0530554i
\(666\) 137384. 180536.i 0.309734 0.407020i
\(667\) −541247. −1.21659
\(668\) 885935.i 1.98540i
\(669\) 457354. + 154230.i 1.02188 + 0.344601i
\(670\) 11407.0 0.0254110
\(671\) 158900.i 0.352923i
\(672\) −827584. + 2.45412e6i −1.83262 + 5.43448i
\(673\) −515622. −1.13842 −0.569208 0.822194i \(-0.692750\pi\)
−0.569208 + 0.822194i \(0.692750\pi\)
\(674\) 33814.5i 0.0744361i
\(675\) −255247. 377078.i −0.560213 0.827606i
\(676\) −589926. −1.29093
\(677\) 722728.i 1.57688i −0.615114 0.788438i \(-0.710890\pi\)
0.615114 0.788438i \(-0.289110\pi\)
\(678\) −165248. 55725.1i −0.359481 0.121225i
\(679\) 565238. 1.22600
\(680\) 59169.3i 0.127961i
\(681\) −122497. + 363253.i −0.264137 + 0.783275i
\(682\) −625049. −1.34383
\(683\) 821439.i 1.76090i 0.474142 + 0.880448i \(0.342758\pi\)
−0.474142 + 0.880448i \(0.657242\pi\)
\(684\) 1.48851e6 + 1.13272e6i 3.18155 + 2.42110i
\(685\) 605.272 0.00128994
\(686\) 196272.i 0.417071i
\(687\) 128727. + 43409.7i 0.272745 + 0.0919756i
\(688\) −469781. −0.992473
\(689\) 337918.i 0.711824i
\(690\) −13333.2 + 39538.5i −0.0280051 + 0.0830466i
\(691\) −506557. −1.06089 −0.530447 0.847718i \(-0.677976\pi\)
−0.530447 + 0.847718i \(0.677976\pi\)
\(692\) 2.18515e6i 4.56320i
\(693\) 222598. 292515.i 0.463505 0.609090i
\(694\) −555753. −1.15389
\(695\) 3209.13i 0.00664382i
\(696\) 1.02769e6 + 346558.i 2.12149 + 0.715414i
\(697\) 899341. 1.85122
\(698\) 1.43359e6i 2.94248i
\(699\) −5073.84 + 15046.0i −0.0103844 + 0.0307941i
\(700\) −1.96542e6 −4.01107
\(701\) 831341.i 1.69178i 0.533360 + 0.845888i \(0.320929\pi\)
−0.533360 + 0.845888i \(0.679071\pi\)
\(702\) −957185. + 647925.i −1.94232 + 1.31477i
\(703\) −190811. −0.386094
\(704\) 985032.i 1.98749i
\(705\) 183.533 + 61.8913i 0.000369263 + 0.000124524i
\(706\) 1.13088e6 2.26885
\(707\) 303988.i 0.608160i
\(708\) 57116.2 169373.i 0.113944 0.337892i
\(709\) −417159. −0.829869 −0.414935 0.909851i \(-0.636196\pi\)
−0.414935 + 0.909851i \(0.636196\pi\)
\(710\) 4244.59i 0.00842014i
\(711\) −193803. 147480.i −0.383373 0.291739i
\(712\) 432757. 0.853658
\(713\) 1.23591e6i 2.43113i
\(714\) −2.09982e6 708105.i −4.11894 1.38900i
\(715\) −8034.46 −0.0157161
\(716\) 1.40903e6i 2.74849i
\(717\) −285160. + 845616.i −0.554690 + 1.64488i
\(718\) 556646. 1.07977
\(719\) 150325.i 0.290787i 0.989374 + 0.145393i \(0.0464448\pi\)
−0.989374 + 0.145393i \(0.953555\pi\)
\(720\) 29303.7 38507.8i 0.0565272 0.0742821i
\(721\) 772923. 1.48685
\(722\) 1.13962e6i 2.18618i
\(723\) 628916. + 212084.i 1.20314 + 0.405725i
\(724\) −1.18016e6 −2.25146
\(725\) 349754.i 0.665406i
\(726\) −236816. + 702258.i −0.449302 + 1.33237i
\(727\) −479152. −0.906577 −0.453289 0.891364i \(-0.649749\pi\)
−0.453289 + 0.891364i \(0.649749\pi\)
\(728\) 3.16758e6i 5.97674i
\(729\) −197457. + 493397.i −0.371551 + 0.928413i
\(730\) −37927.7 −0.0711723
\(731\) 216206.i 0.404607i
\(732\) −939629. 316863.i −1.75362 0.591357i
\(733\) 1.03624e6 1.92865 0.964325 0.264720i \(-0.0852796\pi\)
0.964325 + 0.264720i \(0.0852796\pi\)
\(734\) 2.03663e6i 3.78024i
\(735\) −4912.27 + 14566.9i −0.00909301 + 0.0269645i
\(736\) 3.87396e6 7.15154
\(737\) 150310.i 0.276727i
\(738\) −1.01131e6 769588.i −1.85683 1.41301i
\(739\) −900360. −1.64865 −0.824323 0.566120i \(-0.808444\pi\)
−0.824323 + 0.566120i \(0.808444\pi\)
\(740\) 9840.98i 0.0179711i
\(741\) 921198. + 310648.i 1.67771 + 0.565759i
\(742\) 915463. 1.66277
\(743\) 464398.i 0.841226i −0.907240 0.420613i \(-0.861815\pi\)
0.907240 0.420613i \(-0.138185\pi\)
\(744\) 791349. 2.34667e6i 1.42962 4.23942i
\(745\) −15251.1 −0.0274782
\(746\) 728571.i 1.30916i
\(747\) −223896. + 294221.i −0.401241 + 0.527269i
\(748\) −1.22802e6 −2.19483
\(749\) 591872.i 1.05503i
\(750\) 51115.3 + 17237.2i 0.0908716 + 0.0306439i
\(751\) −469386. −0.832243 −0.416121 0.909309i \(-0.636611\pi\)
−0.416121 + 0.909309i \(0.636611\pi\)
\(752\) 33432.0i 0.0591190i
\(753\) −99575.5 + 295282.i −0.175615 + 0.520772i
\(754\) 887825. 1.56165
\(755\) 10474.6i 0.0183756i
\(756\) 1.28585e6 + 1.89960e6i 2.24982 + 3.32367i
\(757\) −162448. −0.283480 −0.141740 0.989904i \(-0.545270\pi\)
−0.141740 + 0.989904i \(0.545270\pi\)
\(758\) 795168.i 1.38395i
\(759\) −520997. 175691.i −0.904381 0.304977i
\(760\) −70322.8 −0.121750
\(761\) 863476.i 1.49101i −0.666499 0.745506i \(-0.732208\pi\)
0.666499 0.745506i \(-0.267792\pi\)
\(762\) −371873. + 1.10276e6i −0.640449 + 1.89919i
\(763\) 343705. 0.590387
\(764\) 1.43240e6i 2.45402i
\(765\) 17722.4 + 13486.4i 0.0302830 + 0.0230448i
\(766\) 455575. 0.776429
\(767\) 92900.5i 0.157916i
\(768\) −1.59499e6 537865.i −2.70418 0.911907i
\(769\) −899906. −1.52175 −0.760877 0.648896i \(-0.775231\pi\)
−0.760877 + 0.648896i \(0.775231\pi\)
\(770\) 21766.4i 0.0367117i
\(771\) 244751. 725787.i 0.411733 1.22096i
\(772\) −1.19398e6 −2.00337
\(773\) 736093.i 1.23189i −0.787787 0.615947i \(-0.788773\pi\)
0.787787 0.615947i \(-0.211227\pi\)
\(774\) −185013. + 243125.i −0.308831 + 0.405833i
\(775\) 798647. 1.32969
\(776\) 1.69416e6i 2.81340i
\(777\) −221734. 74773.4i −0.367274 0.123853i
\(778\) −1.38528e6 −2.28865
\(779\) 1.06887e6i 1.76137i
\(780\) 16021.5 47510.3i 0.0263338 0.0780906i
\(781\) −55930.8 −0.0916957
\(782\) 3.31468e6i