Properties

Label 177.5.b.a.119.19
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 119.19
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.60

$q$-expansion

\(f(q)\) \(=\) \(q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} +O(q^{10})\) \(q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} -156.006 q^{10} +130.221i q^{11} +(-38.7533 + 29.7117i) q^{12} +134.782 q^{13} +417.419i q^{14} +(-184.558 - 240.721i) q^{15} -313.374 q^{16} +178.035i q^{17} +(-362.079 - 97.3314i) q^{18} +400.688 q^{19} +182.868i q^{20} +(-644.090 + 493.816i) q^{21} +602.768 q^{22} +68.8786i q^{23} +(-268.026 - 349.590i) q^{24} -510.908 q^{25} -623.878i q^{26} +(-278.163 - 673.845i) q^{27} +489.293 q^{28} -1463.81i q^{29} +(-1114.25 + 854.284i) q^{30} -240.021 q^{31} +667.412i q^{32} +(713.089 + 930.090i) q^{33} +824.088 q^{34} +3039.31i q^{35} +(-114.091 + 424.425i) q^{36} +223.236 q^{37} -1854.71i q^{38} +(962.663 - 738.062i) q^{39} -1649.63 q^{40} +200.831i q^{41} +(2285.78 + 2981.37i) q^{42} -3019.72 q^{43} -706.558i q^{44} +(-2636.37 - 708.689i) q^{45} +318.826 q^{46} -2568.51i q^{47} +(-2238.24 + 1716.03i) q^{48} +5731.18 q^{49} +2364.89i q^{50} +(974.915 + 1271.59i) q^{51} -731.302 q^{52} +3075.45i q^{53} +(-3119.09 + 1287.56i) q^{54} +4388.88 q^{55} +4413.86i q^{56} +(2861.87 - 2194.16i) q^{57} -6775.71 q^{58} -453.188i q^{59} +(1001.38 + 1306.11i) q^{60} +3522.17 q^{61} +1111.01i q^{62} +(-1896.22 + 7054.05i) q^{63} -1924.66 q^{64} -4542.58i q^{65} +(4305.20 - 3300.75i) q^{66} -5175.34 q^{67} -965.986i q^{68} +(377.178 + 491.957i) q^{69} +14068.4 q^{70} -3023.98i q^{71} +(-3828.69 - 1029.20i) q^{72} +4158.64 q^{73} -1033.32i q^{74} +(-3649.10 + 2797.72i) q^{75} -2174.06 q^{76} -11743.2i q^{77} +(-3416.34 - 4455.98i) q^{78} -11295.7 q^{79} +10561.7i q^{80} +(-5676.70 - 3289.65i) q^{81} +929.608 q^{82} -9462.92i q^{83} +(3494.72 - 2679.36i) q^{84} +6000.35 q^{85} +13977.7i q^{86} +(-8015.82 - 10455.1i) q^{87} +6373.78 q^{88} +3702.98i q^{89} +(-3280.38 + 12203.2i) q^{90} -12154.4 q^{91} -373.723i q^{92} +(-1714.32 + 1314.35i) q^{93} -11889.1 q^{94} -13504.5i q^{95} +(3654.74 + 4766.92i) q^{96} +8345.01 q^{97} -26528.5i q^{98} +(10186.3 + 2738.20i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.62880i 1.15720i −0.815611 0.578600i \(-0.803599\pi\)
0.815611 0.578600i \(-0.196401\pi\)
\(3\) 7.14239 5.47598i 0.793598 0.608442i
\(4\) −5.42582 −0.339114
\(5\) 33.7032i 1.34813i −0.738672 0.674065i \(-0.764547\pi\)
0.738672 0.674065i \(-0.235453\pi\)
\(6\) −25.3472 33.0607i −0.704090 0.918353i
\(7\) −90.1786 −1.84038 −0.920190 0.391472i \(-0.871966\pi\)
−0.920190 + 0.391472i \(0.871966\pi\)
\(8\) 48.9458i 0.764778i
\(9\) 21.0273 78.2231i 0.259597 0.965717i
\(10\) −156.006 −1.56006
\(11\) 130.221i 1.07621i 0.842878 + 0.538104i \(0.180859\pi\)
−0.842878 + 0.538104i \(0.819141\pi\)
\(12\) −38.7533 + 29.7117i −0.269120 + 0.206331i
\(13\) 134.782 0.797525 0.398763 0.917054i \(-0.369440\pi\)
0.398763 + 0.917054i \(0.369440\pi\)
\(14\) 417.419i 2.12969i
\(15\) −184.558 240.721i −0.820259 1.06987i
\(16\) −313.374 −1.22412
\(17\) 178.035i 0.616038i 0.951380 + 0.308019i \(0.0996660\pi\)
−0.951380 + 0.308019i \(0.900334\pi\)
\(18\) −362.079 97.3314i −1.11753 0.300406i
\(19\) 400.688 1.10994 0.554970 0.831871i \(-0.312730\pi\)
0.554970 + 0.831871i \(0.312730\pi\)
\(20\) 182.868i 0.457170i
\(21\) −644.090 + 493.816i −1.46052 + 1.11976i
\(22\) 602.768 1.24539
\(23\) 68.8786i 0.130205i 0.997879 + 0.0651026i \(0.0207375\pi\)
−0.997879 + 0.0651026i \(0.979263\pi\)
\(24\) −268.026 349.590i −0.465323 0.606926i
\(25\) −510.908 −0.817453
\(26\) 623.878i 0.922897i
\(27\) −278.163 673.845i −0.381567 0.924341i
\(28\) 489.293 0.624099
\(29\) 1463.81i 1.74056i −0.492553 0.870282i \(-0.663936\pi\)
0.492553 0.870282i \(-0.336064\pi\)
\(30\) −1114.25 + 854.284i −1.23806 + 0.949204i
\(31\) −240.021 −0.249761 −0.124881 0.992172i \(-0.539855\pi\)
−0.124881 + 0.992172i \(0.539855\pi\)
\(32\) 667.412i 0.651770i
\(33\) 713.089 + 930.090i 0.654810 + 0.854077i
\(34\) 824.088 0.712879
\(35\) 3039.31i 2.48107i
\(36\) −114.091 + 424.425i −0.0880329 + 0.327488i
\(37\) 223.236 0.163065 0.0815326 0.996671i \(-0.474019\pi\)
0.0815326 + 0.996671i \(0.474019\pi\)
\(38\) 1854.71i 1.28442i
\(39\) 962.663 738.062i 0.632915 0.485248i
\(40\) −1649.63 −1.03102
\(41\) 200.831i 0.119471i 0.998214 + 0.0597356i \(0.0190258\pi\)
−0.998214 + 0.0597356i \(0.980974\pi\)
\(42\) 2285.78 + 2981.37i 1.29579 + 1.69012i
\(43\) −3019.72 −1.63316 −0.816582 0.577229i \(-0.804134\pi\)
−0.816582 + 0.577229i \(0.804134\pi\)
\(44\) 706.558i 0.364957i
\(45\) −2636.37 708.689i −1.30191 0.349970i
\(46\) 318.826 0.150674
\(47\) 2568.51i 1.16275i −0.813637 0.581373i \(-0.802516\pi\)
0.813637 0.581373i \(-0.197484\pi\)
\(48\) −2238.24 + 1716.03i −0.971456 + 0.744803i
\(49\) 5731.18 2.38700
\(50\) 2364.89i 0.945957i
\(51\) 974.915 + 1271.59i 0.374823 + 0.488886i
\(52\) −731.302 −0.270452
\(53\) 3075.45i 1.09486i 0.836852 + 0.547429i \(0.184393\pi\)
−0.836852 + 0.547429i \(0.815607\pi\)
\(54\) −3119.09 + 1287.56i −1.06965 + 0.441550i
\(55\) 4388.88 1.45087
\(56\) 4413.86i 1.40748i
\(57\) 2861.87 2194.16i 0.880846 0.675334i
\(58\) −6775.71 −2.01418
\(59\) 453.188i 0.130189i
\(60\) 1001.38 + 1306.11i 0.278161 + 0.362809i
\(61\) 3522.17 0.946566 0.473283 0.880910i \(-0.343069\pi\)
0.473283 + 0.880910i \(0.343069\pi\)
\(62\) 1111.01i 0.289024i
\(63\) −1896.22 + 7054.05i −0.477756 + 1.77729i
\(64\) −1924.66 −0.469887
\(65\) 4542.58i 1.07517i
\(66\) 4305.20 3300.75i 0.988339 0.757747i
\(67\) −5175.34 −1.15289 −0.576446 0.817135i \(-0.695561\pi\)
−0.576446 + 0.817135i \(0.695561\pi\)
\(68\) 965.986i 0.208907i
\(69\) 377.178 + 491.957i 0.0792224 + 0.103331i
\(70\) 14068.4 2.87110
\(71\) 3023.98i 0.599877i −0.953959 0.299939i \(-0.903034\pi\)
0.953959 0.299939i \(-0.0969662\pi\)
\(72\) −3828.69 1029.20i −0.738559 0.198534i
\(73\) 4158.64 0.780378 0.390189 0.920735i \(-0.372410\pi\)
0.390189 + 0.920735i \(0.372410\pi\)
\(74\) 1033.32i 0.188699i
\(75\) −3649.10 + 2797.72i −0.648729 + 0.497373i
\(76\) −2174.06 −0.376396
\(77\) 11743.2i 1.98063i
\(78\) −3416.34 4455.98i −0.561529 0.732409i
\(79\) −11295.7 −1.80991 −0.904956 0.425506i \(-0.860096\pi\)
−0.904956 + 0.425506i \(0.860096\pi\)
\(80\) 10561.7i 1.65027i
\(81\) −5676.70 3289.65i −0.865219 0.501394i
\(82\) 929.608 0.138252
\(83\) 9462.92i 1.37363i −0.726833 0.686814i \(-0.759009\pi\)
0.726833 0.686814i \(-0.240991\pi\)
\(84\) 3494.72 2679.36i 0.495284 0.379728i
\(85\) 6000.35 0.830498
\(86\) 13977.7i 1.88990i
\(87\) −8015.82 10455.1i −1.05903 1.38131i
\(88\) 6373.78 0.823060
\(89\) 3702.98i 0.467489i 0.972298 + 0.233744i \(0.0750979\pi\)
−0.972298 + 0.233744i \(0.924902\pi\)
\(90\) −3280.38 + 12203.2i −0.404986 + 1.50657i
\(91\) −12154.4 −1.46775
\(92\) 373.723i 0.0441544i
\(93\) −1714.32 + 1314.35i −0.198210 + 0.151965i
\(94\) −11889.1 −1.34553
\(95\) 13504.5i 1.49634i
\(96\) 3654.74 + 4766.92i 0.396564 + 0.517244i
\(97\) 8345.01 0.886917 0.443459 0.896295i \(-0.353751\pi\)
0.443459 + 0.896295i \(0.353751\pi\)
\(98\) 26528.5i 2.76224i
\(99\) 10186.3 + 2738.20i 1.03931 + 0.279380i
\(100\) 2772.10 0.277210
\(101\) 17854.1i 1.75023i −0.483914 0.875116i \(-0.660785\pi\)
0.483914 0.875116i \(-0.339215\pi\)
\(102\) 5885.96 4512.69i 0.565740 0.433746i
\(103\) −13628.6 −1.28463 −0.642314 0.766441i \(-0.722026\pi\)
−0.642314 + 0.766441i \(0.722026\pi\)
\(104\) 6597.00i 0.609930i
\(105\) 16643.2 + 21707.9i 1.50959 + 1.96897i
\(106\) 14235.7 1.26697
\(107\) 5939.18i 0.518751i 0.965777 + 0.259376i \(0.0835167\pi\)
−0.965777 + 0.259376i \(0.916483\pi\)
\(108\) 1509.26 + 3656.16i 0.129395 + 0.313457i
\(109\) 18993.4 1.59863 0.799317 0.600910i \(-0.205195\pi\)
0.799317 + 0.600910i \(0.205195\pi\)
\(110\) 20315.2i 1.67895i
\(111\) 1594.44 1222.44i 0.129408 0.0992157i
\(112\) 28259.6 2.25284
\(113\) 1215.68i 0.0952052i 0.998866 + 0.0476026i \(0.0151581\pi\)
−0.998866 + 0.0476026i \(0.984842\pi\)
\(114\) −10156.3 13247.0i −0.781497 1.01932i
\(115\) 2321.43 0.175534
\(116\) 7942.40i 0.590250i
\(117\) 2834.10 10543.0i 0.207035 0.770184i
\(118\) −2097.72 −0.150655
\(119\) 16054.9i 1.13374i
\(120\) −11782.3 + 9033.34i −0.818215 + 0.627316i
\(121\) −2316.57 −0.158225
\(122\) 16303.5i 1.09537i
\(123\) 1099.75 + 1434.41i 0.0726913 + 0.0948121i
\(124\) 1302.31 0.0846976
\(125\) 3845.27i 0.246097i
\(126\) 32651.8 + 8777.21i 2.05668 + 0.552860i
\(127\) 12112.2 0.750960 0.375480 0.926831i \(-0.377478\pi\)
0.375480 + 0.926831i \(0.377478\pi\)
\(128\) 19587.5i 1.19552i
\(129\) −21568.0 + 16535.9i −1.29608 + 0.993686i
\(130\) −21026.7 −1.24418
\(131\) 7500.56i 0.437070i −0.975829 0.218535i \(-0.929872\pi\)
0.975829 0.218535i \(-0.0701278\pi\)
\(132\) −3869.09 5046.51i −0.222055 0.289630i
\(133\) −36133.5 −2.04271
\(134\) 23955.6i 1.33413i
\(135\) −22710.7 + 9374.98i −1.24613 + 0.514402i
\(136\) 8714.06 0.471132
\(137\) 19710.8i 1.05018i 0.851048 + 0.525088i \(0.175968\pi\)
−0.851048 + 0.525088i \(0.824032\pi\)
\(138\) 2277.17 1745.88i 0.119574 0.0916762i
\(139\) 24368.1 1.26122 0.630612 0.776098i \(-0.282804\pi\)
0.630612 + 0.776098i \(0.282804\pi\)
\(140\) 16490.8i 0.841366i
\(141\) −14065.1 18345.3i −0.707463 0.922753i
\(142\) −13997.4 −0.694179
\(143\) 17551.4i 0.858303i
\(144\) −6589.41 + 24513.1i −0.317776 + 1.18215i
\(145\) −49335.3 −2.34651
\(146\) 19249.5i 0.903055i
\(147\) 40934.3 31383.8i 1.89432 1.45235i
\(148\) −1211.24 −0.0552977
\(149\) 4538.71i 0.204437i 0.994762 + 0.102219i \(0.0325941\pi\)
−0.994762 + 0.102219i \(0.967406\pi\)
\(150\) 12950.1 + 16891.0i 0.575560 + 0.750710i
\(151\) 21114.9 0.926052 0.463026 0.886345i \(-0.346764\pi\)
0.463026 + 0.886345i \(0.346764\pi\)
\(152\) 19612.0i 0.848857i
\(153\) 13926.4 + 3743.60i 0.594918 + 0.159921i
\(154\) −54356.8 −2.29199
\(155\) 8089.47i 0.336711i
\(156\) −5223.24 + 4004.59i −0.214630 + 0.164554i
\(157\) 35639.3 1.44587 0.722936 0.690915i \(-0.242792\pi\)
0.722936 + 0.690915i \(0.242792\pi\)
\(158\) 52285.4i 2.09443i
\(159\) 16841.1 + 21966.1i 0.666157 + 0.868877i
\(160\) 22494.0 0.878670
\(161\) 6211.38i 0.239627i
\(162\) −15227.1 + 26276.3i −0.580214 + 1.00123i
\(163\) −9162.59 −0.344860 −0.172430 0.985022i \(-0.555162\pi\)
−0.172430 + 0.985022i \(0.555162\pi\)
\(164\) 1089.67i 0.0405144i
\(165\) 31347.0 24033.4i 1.15141 0.882769i
\(166\) −43802.0 −1.58956
\(167\) 20236.1i 0.725593i 0.931868 + 0.362796i \(0.118178\pi\)
−0.931868 + 0.362796i \(0.881822\pi\)
\(168\) 24170.2 + 31525.5i 0.856371 + 1.11698i
\(169\) −10394.9 −0.363954
\(170\) 27774.4i 0.961053i
\(171\) 8425.40 31343.1i 0.288137 1.07189i
\(172\) 16384.5 0.553829
\(173\) 385.341i 0.0128752i 0.999979 + 0.00643758i \(0.00204916\pi\)
−0.999979 + 0.00643758i \(0.997951\pi\)
\(174\) −48394.7 + 37103.7i −1.59845 + 1.22551i
\(175\) 46073.0 1.50442
\(176\) 40807.9i 1.31740i
\(177\) −2481.65 3236.84i −0.0792124 0.103318i
\(178\) 17140.4 0.540978
\(179\) 38311.8i 1.19571i −0.801603 0.597857i \(-0.796019\pi\)
0.801603 0.597857i \(-0.203981\pi\)
\(180\) 14304.5 + 3845.22i 0.441497 + 0.118680i
\(181\) 10944.5 0.334071 0.167036 0.985951i \(-0.446581\pi\)
0.167036 + 0.985951i \(0.446581\pi\)
\(182\) 56260.5i 1.69848i
\(183\) 25156.7 19287.3i 0.751194 0.575931i
\(184\) 3371.32 0.0995781
\(185\) 7523.79i 0.219833i
\(186\) 6083.86 + 7935.25i 0.175854 + 0.229369i
\(187\) −23183.9 −0.662985
\(188\) 13936.3i 0.394303i
\(189\) 25084.3 + 60766.4i 0.702229 + 1.70114i
\(190\) −62509.6 −1.73157
\(191\) 7761.08i 0.212743i −0.994326 0.106372i \(-0.966077\pi\)
0.994326 0.106372i \(-0.0339233\pi\)
\(192\) −13746.6 + 10539.4i −0.372901 + 0.285899i
\(193\) −35665.8 −0.957497 −0.478749 0.877952i \(-0.658909\pi\)
−0.478749 + 0.877952i \(0.658909\pi\)
\(194\) 38627.4i 1.02634i
\(195\) −24875.1 32444.9i −0.654177 0.853251i
\(196\) −31096.4 −0.809464
\(197\) 70264.2i 1.81051i −0.424865 0.905257i \(-0.639679\pi\)
0.424865 0.905257i \(-0.360321\pi\)
\(198\) 12674.6 47150.4i 0.323299 1.20269i
\(199\) 13463.4 0.339978 0.169989 0.985446i \(-0.445627\pi\)
0.169989 + 0.985446i \(0.445627\pi\)
\(200\) 25006.8i 0.625170i
\(201\) −36964.2 + 28340.0i −0.914934 + 0.701468i
\(202\) −82643.2 −2.02537
\(203\) 132005.i 3.20330i
\(204\) −5289.72 6899.44i −0.127108 0.165788i
\(205\) 6768.66 0.161063
\(206\) 63084.2i 1.48657i
\(207\) 5387.90 + 1448.33i 0.125741 + 0.0338009i
\(208\) −42237.0 −0.976263
\(209\) 52178.1i 1.19453i
\(210\) 100482. 77038.1i 2.27850 1.74690i
\(211\) 39414.6 0.885303 0.442652 0.896694i \(-0.354038\pi\)
0.442652 + 0.896694i \(0.354038\pi\)
\(212\) 16686.9i 0.371282i
\(213\) −16559.3 21598.4i −0.364991 0.476062i
\(214\) 27491.3 0.600299
\(215\) 101774.i 2.20172i
\(216\) −32981.9 + 13614.9i −0.706916 + 0.291814i
\(217\) 21644.7 0.459656
\(218\) 87916.5i 1.84994i
\(219\) 29702.6 22772.6i 0.619307 0.474815i
\(220\) −23813.3 −0.492010
\(221\) 23995.8i 0.491305i
\(222\) −5658.42 7380.35i −0.114813 0.149751i
\(223\) 47200.5 0.949154 0.474577 0.880214i \(-0.342601\pi\)
0.474577 + 0.880214i \(0.342601\pi\)
\(224\) 60186.3i 1.19950i
\(225\) −10743.0 + 39964.8i −0.212208 + 0.789428i
\(226\) 5627.12 0.110172
\(227\) 39356.4i 0.763772i −0.924209 0.381886i \(-0.875275\pi\)
0.924209 0.381886i \(-0.124725\pi\)
\(228\) −15528.0 + 11905.1i −0.298707 + 0.229015i
\(229\) 46289.3 0.882693 0.441347 0.897337i \(-0.354501\pi\)
0.441347 + 0.897337i \(0.354501\pi\)
\(230\) 10745.5i 0.203128i
\(231\) −64305.3 83874.2i −1.20510 1.57183i
\(232\) −71647.6 −1.33115
\(233\) 33537.3i 0.617754i −0.951102 0.308877i \(-0.900047\pi\)
0.951102 0.308877i \(-0.0999532\pi\)
\(234\) −48801.7 13118.5i −0.891257 0.239581i
\(235\) −86566.9 −1.56753
\(236\) 2458.92i 0.0441489i
\(237\) −80677.9 + 61854.8i −1.43634 + 1.10123i
\(238\) −74315.1 −1.31197
\(239\) 49320.1i 0.863433i 0.902009 + 0.431716i \(0.142092\pi\)
−0.902009 + 0.431716i \(0.857908\pi\)
\(240\) 57835.7 + 75435.8i 1.00409 + 1.30965i
\(241\) 95764.7 1.64881 0.824406 0.565999i \(-0.191509\pi\)
0.824406 + 0.565999i \(0.191509\pi\)
\(242\) 10722.9i 0.183098i
\(243\) −58559.2 + 7589.58i −0.991706 + 0.128530i
\(244\) −19110.7 −0.320994
\(245\) 193159.i 3.21798i
\(246\) 6639.62 5090.51i 0.109717 0.0841184i
\(247\) 54005.4 0.885205
\(248\) 11748.0i 0.191012i
\(249\) −51818.7 67587.8i −0.835773 1.09011i
\(250\) −17799.0 −0.284784
\(251\) 54762.3i 0.869229i 0.900617 + 0.434614i \(0.143115\pi\)
−0.900617 + 0.434614i \(0.856885\pi\)
\(252\) 10288.5 38274.0i 0.162014 0.602703i
\(253\) −8969.46 −0.140128
\(254\) 56065.1i 0.869011i
\(255\) 42856.8 32857.8i 0.659082 0.505310i
\(256\) 59872.0 0.913574
\(257\) 85189.9i 1.28980i 0.764267 + 0.644899i \(0.223101\pi\)
−0.764267 + 0.644899i \(0.776899\pi\)
\(258\) 76541.5 + 99834.1i 1.14989 + 1.49982i
\(259\) −20131.1 −0.300102
\(260\) 24647.2i 0.364604i
\(261\) −114504. 30780.1i −1.68089 0.451845i
\(262\) −34718.6 −0.505778
\(263\) 64508.2i 0.932617i −0.884622 0.466309i \(-0.845584\pi\)
0.884622 0.466309i \(-0.154416\pi\)
\(264\) 45524.0 34902.7i 0.653179 0.500784i
\(265\) 103653. 1.47601
\(266\) 167255.i 2.36383i
\(267\) 20277.4 + 26448.1i 0.284440 + 0.370998i
\(268\) 28080.5 0.390962
\(269\) 11006.7i 0.152108i 0.997104 + 0.0760542i \(0.0242322\pi\)
−0.997104 + 0.0760542i \(0.975768\pi\)
\(270\) 43394.9 + 105124.i 0.595267 + 1.44202i
\(271\) −2180.15 −0.0296858 −0.0148429 0.999890i \(-0.504725\pi\)
−0.0148429 + 0.999890i \(0.504725\pi\)
\(272\) 55791.4i 0.754101i
\(273\) −86811.6 + 66557.4i −1.16480 + 0.893040i
\(274\) 91237.3 1.21527
\(275\) 66531.1i 0.879750i
\(276\) −2046.50 2669.28i −0.0268654 0.0350409i
\(277\) −11249.7 −0.146615 −0.0733077 0.997309i \(-0.523356\pi\)
−0.0733077 + 0.997309i \(0.523356\pi\)
\(278\) 112795.i 1.45949i
\(279\) −5046.99 + 18775.2i −0.0648372 + 0.241199i
\(280\) 148761. 1.89747
\(281\) 83004.0i 1.05120i 0.850731 + 0.525601i \(0.176160\pi\)
−0.850731 + 0.525601i \(0.823840\pi\)
\(282\) −84916.6 + 65104.5i −1.06781 + 0.818677i
\(283\) 52296.8 0.652983 0.326492 0.945200i \(-0.394134\pi\)
0.326492 + 0.945200i \(0.394134\pi\)
\(284\) 16407.6i 0.203427i
\(285\) −73950.3 96454.3i −0.910437 1.18749i
\(286\) 81242.2 0.993229
\(287\) 18110.7i 0.219872i
\(288\) 52207.1 + 14033.9i 0.629425 + 0.169197i
\(289\) 51824.6 0.620498
\(290\) 228363.i 2.71538i
\(291\) 59603.2 45697.1i 0.703856 0.539638i
\(292\) −22564.0 −0.264637
\(293\) 27668.3i 0.322290i −0.986931 0.161145i \(-0.948481\pi\)
0.986931 0.161145i \(-0.0515187\pi\)
\(294\) −145270. 189477.i −1.68066 2.19211i
\(295\) −15273.9 −0.175511
\(296\) 10926.5i 0.124709i
\(297\) 87748.9 36222.7i 0.994784 0.410646i
\(298\) 21008.8 0.236575
\(299\) 9283.58i 0.103842i
\(300\) 19799.4 15179.9i 0.219993 0.168666i
\(301\) 272314. 3.00564
\(302\) 97736.7i 1.07163i
\(303\) −97768.7 127521.i −1.06491 1.38898i
\(304\) −125565. −1.35869
\(305\) 118709.i 1.27609i
\(306\) 17328.4 64462.7i 0.185061 0.688440i
\(307\) 46064.3 0.488751 0.244376 0.969681i \(-0.421417\pi\)
0.244376 + 0.969681i \(0.421417\pi\)
\(308\) 63716.4i 0.671660i
\(309\) −97340.9 + 74630.0i −1.01948 + 0.781622i
\(310\) 37444.6 0.389642
\(311\) 4093.35i 0.0423212i −0.999776 0.0211606i \(-0.993264\pi\)
0.999776 0.0211606i \(-0.00673613\pi\)
\(312\) −36125.0 47118.3i −0.371107 0.484039i
\(313\) 38229.6 0.390221 0.195110 0.980781i \(-0.437493\pi\)
0.195110 + 0.980781i \(0.437493\pi\)
\(314\) 164967.i 1.67316i
\(315\) 237744. + 63908.6i 2.39601 + 0.644078i
\(316\) 61288.2 0.613766
\(317\) 35832.0i 0.356577i 0.983978 + 0.178288i \(0.0570560\pi\)
−0.983978 + 0.178288i \(0.942944\pi\)
\(318\) 101677. 77954.2i 1.00547 0.770878i
\(319\) 190620. 1.87321
\(320\) 64867.1i 0.633468i
\(321\) 32522.8 + 42419.9i 0.315630 + 0.411680i
\(322\) −28751.2 −0.277297
\(323\) 71336.5i 0.683764i
\(324\) 30800.8 + 17849.0i 0.293408 + 0.170030i
\(325\) −68861.1 −0.651939
\(326\) 42411.8i 0.399073i
\(327\) 135658. 104007.i 1.26867 0.972676i
\(328\) 9829.83 0.0913689
\(329\) 231624.i 2.13989i
\(330\) −111246. 145099.i −1.02154 1.33241i
\(331\) −50899.9 −0.464580 −0.232290 0.972647i \(-0.574622\pi\)
−0.232290 + 0.972647i \(0.574622\pi\)
\(332\) 51344.2i 0.465816i
\(333\) 4694.06 17462.2i 0.0423312 0.157475i
\(334\) 93668.7 0.839656
\(335\) 174426.i 1.55425i
\(336\) 201841. 154749.i 1.78785 1.37072i
\(337\) −219364. −1.93155 −0.965774 0.259384i \(-0.916481\pi\)
−0.965774 + 0.259384i \(0.916481\pi\)
\(338\) 48115.9i 0.421168i
\(339\) 6657.01 + 8682.82i 0.0579269 + 0.0755547i
\(340\) −32556.8 −0.281634
\(341\) 31255.8i 0.268795i
\(342\) −145081. 38999.5i −1.24039 0.333432i
\(343\) −300311. −2.55260
\(344\) 147803.i 1.24901i
\(345\) 16580.6 12712.1i 0.139303 0.106802i
\(346\) 1783.67 0.0148991
\(347\) 18664.6i 0.155010i −0.996992 0.0775051i \(-0.975305\pi\)
0.996992 0.0775051i \(-0.0246954\pi\)
\(348\) 43492.4 + 56727.7i 0.359133 + 0.468421i
\(349\) 129387. 1.06228 0.531141 0.847284i \(-0.321763\pi\)
0.531141 + 0.847284i \(0.321763\pi\)
\(350\) 213263.i 1.74092i
\(351\) −37491.2 90821.9i −0.304310 0.737185i
\(352\) −86911.3 −0.701440
\(353\) 187137.i 1.50180i 0.660418 + 0.750898i \(0.270379\pi\)
−0.660418 + 0.750898i \(0.729621\pi\)
\(354\) −14982.7 + 11487.0i −0.119559 + 0.0916647i
\(355\) −101918. −0.808712
\(356\) 20091.7i 0.158532i
\(357\) −87916.5 114671.i −0.689817 0.899737i
\(358\) −177338. −1.38368
\(359\) 11341.9i 0.0880030i −0.999031 0.0440015i \(-0.985989\pi\)
0.999031 0.0440015i \(-0.0140106\pi\)
\(360\) −34687.3 + 129039.i −0.267649 + 0.995673i
\(361\) 30230.0 0.231966
\(362\) 50660.0i 0.386588i
\(363\) −16545.8 + 12685.5i −0.125567 + 0.0962705i
\(364\) 65947.8 0.497734
\(365\) 140159.i 1.05205i
\(366\) −89277.3 116446.i −0.666468 0.869282i
\(367\) −246051. −1.82681 −0.913403 0.407055i \(-0.866556\pi\)
−0.913403 + 0.407055i \(0.866556\pi\)
\(368\) 21584.7i 0.159386i
\(369\) 15709.6 + 4222.94i 0.115375 + 0.0310143i
\(370\) −34826.1 −0.254391
\(371\) 277340.i 2.01495i
\(372\) 9301.60 7131.42i 0.0672158 0.0515336i
\(373\) 128003. 0.920032 0.460016 0.887911i \(-0.347844\pi\)
0.460016 + 0.887911i \(0.347844\pi\)
\(374\) 107314.i 0.767207i
\(375\) −21056.6 27464.4i −0.149736 0.195302i
\(376\) −125718. −0.889242
\(377\) 197296.i 1.38814i
\(378\) 281276. 116110.i 1.96856 0.812620i
\(379\) 250015. 1.74055 0.870277 0.492563i \(-0.163940\pi\)
0.870277 + 0.492563i \(0.163940\pi\)
\(380\) 73273.0i 0.507431i
\(381\) 86510.2 66326.3i 0.595960 0.456915i
\(382\) −35924.5 −0.246187
\(383\) 218308.i 1.48823i 0.668049 + 0.744117i \(0.267130\pi\)
−0.668049 + 0.744117i \(0.732870\pi\)
\(384\) 107260. + 139901.i 0.727407 + 0.948765i
\(385\) −395783. −2.67015
\(386\) 165090.i 1.10802i
\(387\) −63496.7 + 236212.i −0.423964 + 1.57717i
\(388\) −45278.5 −0.300766
\(389\) 114908.i 0.759365i −0.925117 0.379683i \(-0.876033\pi\)
0.925117 0.379683i \(-0.123967\pi\)
\(390\) −150181. + 115142.i −0.987383 + 0.757014i
\(391\) −12262.8 −0.0802113
\(392\) 280517.i 1.82552i
\(393\) −41072.9 53571.9i −0.265932 0.346858i
\(394\) −325239. −2.09513
\(395\) 380700.i 2.43999i
\(396\) −55269.1 14857.0i −0.352446 0.0947417i
\(397\) −81107.2 −0.514610 −0.257305 0.966330i \(-0.582835\pi\)
−0.257305 + 0.966330i \(0.582835\pi\)
\(398\) 62319.7i 0.393422i
\(399\) −258079. + 197866.i −1.62109 + 1.24287i
\(400\) 160105. 1.00066
\(401\) 92221.4i 0.573513i −0.958004 0.286756i \(-0.907423\pi\)
0.958004 0.286756i \(-0.0925770\pi\)
\(402\) 131180. + 171100.i 0.811740 + 1.05876i
\(403\) −32350.4 −0.199191
\(404\) 96873.3i 0.593528i
\(405\) −110872. + 191323.i −0.675944 + 1.16643i
\(406\) 611024. 3.70686
\(407\) 29070.1i 0.175492i
\(408\) 62239.1 47718.0i 0.373889 0.286656i
\(409\) −184450. −1.10264 −0.551319 0.834295i \(-0.685875\pi\)
−0.551319 + 0.834295i \(0.685875\pi\)
\(410\) 31330.8i 0.186382i
\(411\) 107936. + 140782.i 0.638972 + 0.833419i
\(412\) 73946.5 0.435636
\(413\) 40867.8i 0.239597i
\(414\) 6704.05 24939.5i 0.0391144 0.145508i
\(415\) −318931. −1.85183
\(416\) 89955.0i 0.519803i
\(417\) 174046. 133439.i 1.00091 0.767382i
\(418\) 241522. 1.38231
\(419\) 137728.i 0.784499i −0.919859 0.392250i \(-0.871697\pi\)
0.919859 0.392250i \(-0.128303\pi\)
\(420\) −90303.1 117783.i −0.511922 0.667706i
\(421\) −208082. −1.17401 −0.587003 0.809585i \(-0.699692\pi\)
−0.587003 + 0.809585i \(0.699692\pi\)
\(422\) 182442.i 1.02447i
\(423\) −200916. 54008.8i −1.12288 0.301845i
\(424\) 150531. 0.837323
\(425\) 90959.4i 0.503582i
\(426\) −99974.9 + 76649.5i −0.550899 + 0.422367i
\(427\) −317625. −1.74204
\(428\) 32225.0i 0.175916i
\(429\) 96111.3 + 125359.i 0.522228 + 0.681148i
\(430\) 471093. 2.54783
\(431\) 182971.i 0.984981i 0.870318 + 0.492491i \(0.163913\pi\)
−0.870318 + 0.492491i \(0.836087\pi\)
\(432\) 87168.8 + 211165.i 0.467083 + 1.13150i
\(433\) −123677. −0.659649 −0.329825 0.944042i \(-0.606990\pi\)
−0.329825 + 0.944042i \(0.606990\pi\)
\(434\) 100189.i 0.531914i
\(435\) −352372. + 270159.i −1.86218 + 1.42771i
\(436\) −103055. −0.542119
\(437\) 27598.8i 0.144520i
\(438\) −105410. 137487.i −0.549456 0.716663i
\(439\) 23268.2 0.120735 0.0603675 0.998176i \(-0.480773\pi\)
0.0603675 + 0.998176i \(0.480773\pi\)
\(440\) 214817.i 1.10959i
\(441\) 120511. 448311.i 0.619657 2.30516i
\(442\) 111072. 0.568539
\(443\) 207356.i 1.05660i 0.849059 + 0.528298i \(0.177170\pi\)
−0.849059 + 0.528298i \(0.822830\pi\)
\(444\) −8651.15 + 6632.73i −0.0438842 + 0.0336455i
\(445\) 124802. 0.630235
\(446\) 218482.i 1.09836i
\(447\) 24853.9 + 32417.2i 0.124388 + 0.162241i
\(448\) 173563. 0.864770
\(449\) 269010.i 1.33437i 0.744892 + 0.667185i \(0.232501\pi\)
−0.744892 + 0.667185i \(0.767499\pi\)
\(450\) 184989. + 49727.4i 0.913527 + 0.245567i
\(451\) −26152.5 −0.128576
\(452\) 6596.04i 0.0322854i
\(453\) 150811. 115625.i 0.734913 0.563449i
\(454\) −182173. −0.883838
\(455\) 409644.i 1.97872i
\(456\) −107395. 140076.i −0.516480 0.673652i
\(457\) −265318. −1.27038 −0.635190 0.772356i \(-0.719078\pi\)
−0.635190 + 0.772356i \(0.719078\pi\)
\(458\) 214264.i 1.02145i
\(459\) 119968. 49522.6i 0.569429 0.235060i
\(460\) −12595.7 −0.0595259
\(461\) 135910.i 0.639514i −0.947500 0.319757i \(-0.896399\pi\)
0.947500 0.319757i \(-0.103601\pi\)
\(462\) −388237. + 297657.i −1.81892 + 1.39454i
\(463\) −79162.9 −0.369283 −0.184642 0.982806i \(-0.559112\pi\)
−0.184642 + 0.982806i \(0.559112\pi\)
\(464\) 458721.i 2.13065i
\(465\) 44297.8 + 57778.1i 0.204869 + 0.267213i
\(466\) −155237. −0.714866
\(467\) 264929.i 1.21478i 0.794405 + 0.607388i \(0.207783\pi\)
−0.794405 + 0.607388i \(0.792217\pi\)
\(468\) −15377.3 + 57204.7i −0.0702084 + 0.261180i
\(469\) 466705. 2.12176
\(470\) 400701.i 1.81395i
\(471\) 254550. 195160.i 1.14744 0.879729i
\(472\) −22181.6 −0.0995656
\(473\) 393232.i 1.75762i
\(474\) 286314. + 373442.i 1.27434 + 1.66214i
\(475\) −204715. −0.907323
\(476\) 87111.3i 0.384468i
\(477\) 240572. + 64668.6i 1.05732 + 0.284221i
\(478\) 228293. 0.999165
\(479\) 256028.i 1.11588i 0.829883 + 0.557938i \(0.188407\pi\)
−0.829883 + 0.557938i \(0.811593\pi\)
\(480\) 160661. 123176.i 0.697311 0.534620i
\(481\) 30088.2 0.130049
\(482\) 443276.i 1.90801i
\(483\) −34013.4 44364.0i −0.145799 0.190168i
\(484\) 12569.3 0.0536562
\(485\) 281254.i 1.19568i
\(486\) 35130.7 + 271059.i 0.148735 + 1.14760i
\(487\) 118044. 0.497720 0.248860 0.968540i \(-0.419944\pi\)
0.248860 + 0.968540i \(0.419944\pi\)
\(488\) 172396.i 0.723913i
\(489\) −65442.8 + 50174.2i −0.273681 + 0.209827i
\(490\) −894097. −3.72385
\(491\) 262067.i 1.08705i −0.839393 0.543525i \(-0.817089\pi\)
0.839393 0.543525i \(-0.182911\pi\)
\(492\) −5967.03 7782.87i −0.0246506 0.0321521i
\(493\) 260610. 1.07225
\(494\) 249981.i 1.02436i
\(495\) 92286.4 343311.i 0.376641 1.40113i
\(496\) 75216.1 0.305737
\(497\) 272698.i 1.10400i
\(498\) −312851. + 239859.i −1.26147 + 0.967157i
\(499\) 434790. 1.74614 0.873069 0.487597i \(-0.162127\pi\)
0.873069 + 0.487597i \(0.162127\pi\)
\(500\) 20863.8i 0.0834551i
\(501\) 110812. + 144534.i 0.441481 + 0.575829i
\(502\) 253484. 1.00587
\(503\) 40412.2i 0.159726i 0.996806 + 0.0798632i \(0.0254483\pi\)
−0.996806 + 0.0798632i \(0.974552\pi\)
\(504\) 345266. + 92811.7i 1.35923 + 0.365378i
\(505\) −601741. −2.35954
\(506\) 41517.8i 0.162156i
\(507\) −74244.3 + 56922.2i −0.288833 + 0.221445i
\(508\) −65718.8 −0.254661
\(509\) 8123.63i 0.0313556i −0.999877 0.0156778i \(-0.995009\pi\)
0.999877 0.0156778i \(-0.00499060\pi\)
\(510\) −152092. 198376.i −0.584745 0.762690i
\(511\) −375020. −1.43619
\(512\) 36263.6i 0.138335i
\(513\) −111456. 270002.i −0.423517 1.02596i
\(514\) 394327. 1.49256
\(515\) 459329.i 1.73185i
\(516\) 117024. 89721.0i 0.439518 0.336973i
\(517\) 334474. 1.25136
\(518\) 93183.1i 0.347278i
\(519\) 2110.12 + 2752.25i 0.00783378 + 0.0102177i
\(520\) −222340. −0.822264
\(521\) 349679.i 1.28823i 0.764928 + 0.644116i \(0.222774\pi\)
−0.764928 + 0.644116i \(0.777226\pi\)
\(522\) −142475. + 530017.i −0.522875 + 1.94513i
\(523\) −33077.4 −0.120928 −0.0604641 0.998170i \(-0.519258\pi\)
−0.0604641 + 0.998170i \(0.519258\pi\)
\(524\) 40696.7i 0.148217i
\(525\) 329071. 252295.i 1.19391 0.915354i
\(526\) −298596. −1.07923
\(527\) 42732.0i 0.153862i
\(528\) −223463. 291466.i −0.801564 1.04549i
\(529\) 275097. 0.983047
\(530\) 479788.i 1.70804i
\(531\) −35449.7 9529.33i −0.125726 0.0337966i
\(532\) 196054. 0.692712
\(533\) 27068.4i 0.0952813i
\(534\) 122423. 93860.2i 0.429320 0.329154i
\(535\) 200170. 0.699344
\(536\) 253311.i 0.881707i
\(537\) −209795. 273638.i −0.727522 0.948916i
\(538\) 50947.9 0.176020
\(539\) 746321.i 2.56891i
\(540\) 123225. 50867.0i 0.422581 0.174441i
\(541\) 347488. 1.18726 0.593630 0.804738i \(-0.297694\pi\)
0.593630 + 0.804738i \(0.297694\pi\)
\(542\) 10091.5i 0.0343524i
\(543\) 78169.9 59931.9i 0.265118 0.203263i
\(544\) −118823. −0.401515
\(545\) 640138.i 2.15516i
\(546\) 308081. + 401834.i 1.03343 + 1.34791i
\(547\) −115572. −0.386260 −0.193130 0.981173i \(-0.561864\pi\)
−0.193130 + 0.981173i \(0.561864\pi\)
\(548\) 106947.i 0.356130i
\(549\) 74061.9 275515.i 0.245726 0.914115i
\(550\) −307959. −1.01805
\(551\) 586533.i 1.93192i
\(552\) 24079.2 18461.3i 0.0790250 0.0605875i
\(553\) 1.01863e6 3.33092
\(554\) 52072.4i 0.169663i
\(555\) −41200.1 53737.8i −0.133756 0.174459i
\(556\) −132217. −0.427699
\(557\) 407655.i 1.31396i −0.753908 0.656980i \(-0.771834\pi\)
0.753908 0.656980i \(-0.228166\pi\)
\(558\) 86906.5 + 23361.5i 0.279115 + 0.0750297i
\(559\) −407003. −1.30249
\(560\) 952440.i 3.03712i
\(561\) −165588. + 126955.i −0.526144 + 0.403388i
\(562\) 384209. 1.21645
\(563\) 169358.i 0.534304i −0.963654 0.267152i \(-0.913917\pi\)
0.963654 0.267152i \(-0.0860826\pi\)
\(564\) 76314.7 + 99538.1i 0.239911 + 0.312919i
\(565\) 40972.2 0.128349
\(566\) 242071.i 0.755633i
\(567\) 511917. + 296656.i 1.59233 + 0.922755i
\(568\) −148011. −0.458773
\(569\) 304678.i 0.941057i 0.882385 + 0.470529i \(0.155937\pi\)
−0.882385 + 0.470529i \(0.844063\pi\)
\(570\) −446468. + 342301.i −1.37417 + 1.05356i
\(571\) −451694. −1.38539 −0.692695 0.721230i \(-0.743577\pi\)
−0.692695 + 0.721230i \(0.743577\pi\)
\(572\) 95231.1i 0.291063i
\(573\) −42499.5 55432.6i −0.129442 0.168833i
\(574\) −83830.7 −0.254436
\(575\) 35190.6i 0.106437i
\(576\) −40470.4 + 150553.i −0.121981 + 0.453778i
\(577\) −459751. −1.38093 −0.690464 0.723366i \(-0.742594\pi\)
−0.690464 + 0.723366i \(0.742594\pi\)
\(578\) 239886.i 0.718041i
\(579\) −254739. + 195305.i −0.759868 + 0.582582i
\(580\) 267685. 0.795733
\(581\) 853353.i 2.52800i
\(582\) −211523. 275892.i −0.624469 0.814503i
\(583\) −400489. −1.17829
\(584\) 203548.i 0.596816i
\(585\) −355335. 95518.3i −1.03831 0.279110i
\(586\) −128071. −0.372954
\(587\) 537822.i 1.56085i −0.625247 0.780427i \(-0.715002\pi\)
0.625247 0.780427i \(-0.284998\pi\)
\(588\) −222102. + 170283.i −0.642390 + 0.492512i
\(589\) −96173.4 −0.277220
\(590\) 70699.8i 0.203102i
\(591\) −384765. 501854.i −1.10159 1.43682i
\(592\) −69956.4 −0.199611
\(593\) 87783.0i 0.249632i 0.992180 + 0.124816i \(0.0398341\pi\)
−0.992180 + 0.124816i \(0.960166\pi\)
\(594\) −167668. 406172.i −0.475200 1.15116i
\(595\) −541103. −1.52843
\(596\) 24626.2i 0.0693275i
\(597\) 96161.1 73725.6i 0.269806 0.206857i
\(598\) 42971.9 0.120166
\(599\) 10152.6i 0.0282960i 0.999900 + 0.0141480i \(0.00450361\pi\)
−0.999900 + 0.0141480i \(0.995496\pi\)
\(600\) 136937. + 178608.i 0.380380 + 0.496134i
\(601\) 537739. 1.48875 0.744376 0.667761i \(-0.232747\pi\)
0.744376 + 0.667761i \(0.232747\pi\)
\(602\) 1.26049e6i 3.47813i
\(603\) −108824. + 404831.i −0.299287 + 1.11337i
\(604\) −114566. −0.314037
\(605\) 78075.8i 0.213307i
\(606\) −590269. + 452552.i −1.60733 + 1.23232i
\(607\) 334916. 0.908989 0.454494 0.890750i \(-0.349820\pi\)
0.454494 + 0.890750i \(0.349820\pi\)
\(608\) 267424.i 0.723425i
\(609\) 722855. + 942829.i 1.94902 + 2.54213i
\(610\) −549479. −1.47670
\(611\) 346188.i 0.927319i
\(612\) −75562.4 20312.1i −0.201745 0.0542316i
\(613\) 193709. 0.515500 0.257750 0.966212i \(-0.417019\pi\)
0.257750 + 0.966212i \(0.417019\pi\)
\(614\) 213223.i 0.565584i
\(615\) 48344.4 37065.0i 0.127819 0.0979973i
\(616\) −574779. −1.51474
\(617\) 397810.i 1.04497i −0.852647 0.522487i \(-0.825004\pi\)
0.852647 0.522487i \(-0.174996\pi\)
\(618\) 345448. + 450572.i 0.904494 + 1.17974i
\(619\) −53881.4 −0.140624 −0.0703118 0.997525i \(-0.522399\pi\)
−0.0703118 + 0.997525i \(0.522399\pi\)
\(620\) 43892.1i 0.114183i
\(621\) 46413.5 19159.4i 0.120354 0.0496821i
\(622\) −18947.3 −0.0489741
\(623\) 333929.i 0.860357i
\(624\) −301673. + 231289.i −0.774761 + 0.593999i
\(625\) −448916. −1.14922
\(626\) 176957.i 0.451564i
\(627\) 285726. + 372676.i 0.726800 + 0.947974i
\(628\) −193373. −0.490316
\(629\) 39743.8i 0.100454i
\(630\) 295820. 1.10047e6i 0.745327 2.77267i
\(631\) 742614. 1.86511 0.932555 0.361029i \(-0.117574\pi\)
0.932555 + 0.361029i \(0.117574\pi\)
\(632\) 552875.i 1.38418i
\(633\) 281514. 215833.i 0.702575 0.538656i
\(634\) 165859. 0.412631
\(635\) 408221.i 1.01239i
\(636\) −91377.0 119184.i −0.225903 0.294648i
\(637\) 772458. 1.90369
\(638\) 882342.i 2.16768i
\(639\) −236545. 63586.3i −0.579312 0.155726i
\(640\) 660161. 1.61172
\(641\) 378409.i 0.920969i −0.887668 0.460485i \(-0.847676\pi\)
0.887668 0.460485i \(-0.152324\pi\)
\(642\) 196353. 150542.i 0.476396 0.365247i
\(643\) 809650. 1.95828 0.979141 0.203182i \(-0.0651284\pi\)
0.979141 + 0.203182i \(0.0651284\pi\)
\(644\) 33701.8i 0.0812609i
\(645\) 557314. + 726912.i 1.33962 + 1.74728i
\(646\) 330202. 0.791253
\(647\) 158470.i 0.378563i −0.981923 0.189282i \(-0.939384\pi\)
0.981923 0.189282i \(-0.0606159\pi\)
\(648\) −161014. + 277851.i −0.383455 + 0.661700i
\(649\) 59014.6 0.140110
\(650\) 318744.i 0.754425i
\(651\) 154595. 118526.i 0.364782 0.279674i
\(652\) 49714.6 0.116947
\(653\) 145679.i 0.341641i 0.985302 + 0.170820i \(0.0546418\pi\)
−0.985302 + 0.170820i \(0.945358\pi\)
\(654\) −481429. 627934.i −1.12558 1.46811i
\(655\) −252793. −0.589227
\(656\) 62935.2i 0.146247i
\(657\) 87445.0 325301.i 0.202584 0.753625i
\(658\) 1.07214e6 2.47629
\(659\) 288401.i 0.664088i −0.943264 0.332044i \(-0.892262\pi\)
0.943264 0.332044i \(-0.107738\pi\)
\(660\) −170084. + 130401.i −0.390458 + 0.299359i
\(661\) −292254. −0.668894 −0.334447 0.942415i \(-0.608550\pi\)
−0.334447 + 0.942415i \(0.608550\pi\)
\(662\) 235605.i 0.537612i
\(663\) 131401. + 171388.i 0.298931 + 0.389899i
\(664\) −463170. −1.05052
\(665\) 1.21782e6i 2.75384i
\(666\) −80829.3 21727.9i −0.182230 0.0489857i
\(667\) 100826. 0.226631
\(668\) 109797.i 0.246059i
\(669\) 337124. 258469.i 0.753247 0.577505i
\(670\) 807382. 1.79858
\(671\) 458662.i 1.01870i
\(672\) −329579. 429874.i −0.729829 0.951925i
\(673\) −65987.4 −0.145690 −0.0728452 0.997343i \(-0.523208\pi\)
−0.0728452 + 0.997343i \(0.523208\pi\)
\(674\) 1.01539e6i 2.23519i
\(675\) 142115. + 344273.i 0.311913 + 0.755605i
\(676\) 56400.8 0.123422
\(677\) 556849.i 1.21496i −0.794337 0.607478i \(-0.792181\pi\)
0.794337 0.607478i \(-0.207819\pi\)
\(678\) 40191.1 30814.0i 0.0874320 0.0670330i
\(679\) −752541. −1.63226
\(680\) 293692.i 0.635147i
\(681\) −215515. 281099.i −0.464711 0.606129i
\(682\) −144677. −0.311050
\(683\) 726005.i 1.55632i 0.628068 + 0.778158i \(0.283846\pi\)
−0.628068 + 0.778158i \(0.716154\pi\)
\(684\) −45714.8 + 170062.i −0.0977112 + 0.363492i
\(685\) 664317. 1.41577
\(686\) 1.39008e6i 2.95387i
\(687\) 330616. 253479.i 0.700504 0.537068i
\(688\) 946301. 1.99918
\(689\) 414515.i 0.873176i
\(690\) −58841.9 76748.1i −0.123591 0.161202i
\(691\) −273276. −0.572329 −0.286165 0.958180i \(-0.592380\pi\)
−0.286165 + 0.958180i \(0.592380\pi\)
\(692\) 2090.79i 0.00436615i
\(693\) −918587. 246927.i −1.91273 0.514166i
\(694\) −86394.9 −0.179378
\(695\) 821284.i 1.70029i
\(696\) −511735. + 392341.i −1.05639 + 0.809925i
\(697\) −35754.9 −0.0735987
\(698\) 598907.i 1.22927i
\(699\) −183649. 239536.i −0.375868 0.490249i
\(700\) −249984. −0.510171
\(701\) 122895.i 0.250090i −0.992151 0.125045i \(-0.960092\pi\)
0.992151 0.125045i \(-0.0399076\pi\)
\(702\) −420397. + 173540.i −0.853071 + 0.352147i
\(703\) 89448.2 0.180993
\(704\) 250631.i 0.505696i
\(705\) −618294. + 474039.i −1.24399 + 0.953752i
\(706\) 866222. 1.73788
\(707\) 1.61006e6i 3.22109i
\(708\) 13465.0 + 17562.5i 0.0268620 + 0.0350365i
\(709\) −649498. −1.29207 −0.646034 0.763309i \(-0.723574\pi\)
−0.646034 + 0.763309i \(0.723574\pi\)
\(710\) 471758.i 0.935842i
\(711\) −237518. + 883581.i −0.469847 + 1.74786i
\(712\) 181245. 0.357525
\(713\) 16532.3i 0.0325202i
\(714\) −530787. + 406948.i −1.04118 + 0.798257i
\(715\) 591540. 1.15710
\(716\) 207873.i 0.405483i
\(717\) 270076. + 352263.i 0.525349 + 0.685219i
\(718\) −52499.5 −0.101837
\(719\) 531825.i 1.02875i −0.857565 0.514376i \(-0.828023\pi\)
0.857565 0.514376i \(-0.171977\pi\)
\(720\) 826169. + 222084.i 1.59369 + 0.428404i
\(721\) 1.22901e6 2.36420
\(722\) 139929.i 0.268431i
\(723\) 683988. 524405.i 1.30849 1.00321i
\(724\) −59383.0 −0.113288
\(725\) 747875.i 1.42283i
\(726\) 58718.5 + 76587.3i 0.111404 + 0.145306i
\(727\) −549128. −1.03897 −0.519487 0.854478i \(-0.673877\pi\)
−0.519487 + 0.854478i \(0.673877\pi\)
\(728\) 594908.i 1.12250i
\(729\) −376692. + 374877.i −0.708813 + 0.705397i
\(730\) −648771. −1.21743
\(731\) 537615.i 1.00609i
\(732\) −136496. + 104650.i −0.254740 + 0.195306i
\(733\) 62572.4 0.116460 0.0582298 0.998303i \(-0.481454\pi\)
0.0582298 + 0.998303i \(0.481454\pi\)
\(734\) 1.13892e6i 2.11398i
\(735\) −1.05774e6 1.37962e6i −1.95795 2.55378i
\(736\) −45970.4 −0.0848639
\(737\) 673939.i 1.24075i
\(738\) 19547.2 72716.8i 0.0358898 0.133512i
\(739\) 180670. 0.330823 0.165412 0.986225i \(-0.447105\pi\)
0.165412 + 0.986225i \(0.447105\pi\)
\(740\) 40822.7i 0.0745485i
\(741\) 385728. 295733.i 0.702497 0.538596i
\(742\) −1.28375e6 −2.33171
\(743\) 678464.i 1.22899i 0.788920 + 0.614497i \(0.210641\pi\)
−0.788920 + 0.614497i \(0.789359\pi\)
\(744\) 64331.8 + 83908.7i 0.116220 + 0.151587i
\(745\) 152969. 0.275608
\(746\) 592502.i 1.06466i
\(747\) −740219. 198980.i −1.32654 0.356589i
\(748\) 125792. 0.224827
\(749\) 535587.i 0.954699i
\(750\) −127127. + 97466.9i −0.226004 + 0.173275i
\(751\) 11030.3 0.0195572 0.00977858 0.999952i \(-0.496887\pi\)
0.00977858 + 0.999952i \(0.496887\pi\)
\(752\) 804902.i 1.42334i
\(753\) 299877. + 391133.i 0.528875 + 0.689819i
\(754\) −913242. −1.60636
\(755\) 711640.i 1.24844i
\(756\) −136103. 329708.i −0.238136 0.576880i
\(757\) −248825. −0.434213 −0.217106 0.976148i \(-0.569662\pi\)
−0.217106 + 0.976148i \(0.569662\pi\)
\(758\) 1.15727e6i 2.01417i
\(759\) −64063.3 + 49116.5i −0.111205 + 0.0852598i
\(760\) −660988. −1.14437
\(761\) 29077.7i 0.0502100i 0.999685 + 0.0251050i \(0.00799201\pi\)
−0.999685 + 0.0251050i \(0.992008\pi\)
\(762\) −307011. 400439.i −0.528743 0.689646i
\(763\) −1.71279e6 −2.94209
\(764\) 42110.3i 0.0721442i
\(765\) 126171. 469366.i 0.215595 0.802026i
\(766\) 1.01050e6 1.72219
\(767\) 61081.4i 0.103829i
\(768\) 427629. 327858.i 0.725011 0.555857i
\(769\) −85639.0 −0.144817 −0.0724084 0.997375i \(-0.523069\pi\)
−0.0724084 + 0.997375i \(0.523069\pi\)
\(770\) 1.83200e6i 3.08990i
\(771\) 466498. + 608459.i 0.784768 + 1.02358i
\(772\) 193516. 0.324701
\(773\) 380679.i 0.637089i −0.947908 0.318544i \(-0.896806\pi\)
0.947908 0.318544i \(-0.103194\pi\)
\(774\) 1.09338e6 + 293914.i 1.82511 + 0.490612i
\(775\) 122628. 0.204168
\(776\) 408453.i 0.678295i
\(777\) −143784. + 110238.i −0.238160 + 0.182595i
\(778\) −531886. −0.878738
\(779\) 80470.6i 0.132606i
\(780\) 134968. + 176040.i 0.221841 + 0.289349i
\(781\) 393787. 0.645593
\(782\) 56762.1i