Properties

Label 177.5.b.a.119.55
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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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [177,5,Mod(119,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.119");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 119.55
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.24

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.56380i q^{2} +(-1.54671 + 8.86610i) q^{3} +3.29930 q^{4} -32.9935i q^{5} +(-31.5970 - 5.51219i) q^{6} -48.4204 q^{7} +68.7789i q^{8} +(-76.2153 - 27.4266i) q^{9} +O(q^{10})\) \(q+3.56380i q^{2} +(-1.54671 + 8.86610i) q^{3} +3.29930 q^{4} -32.9935i q^{5} +(-31.5970 - 5.51219i) q^{6} -48.4204 q^{7} +68.7789i q^{8} +(-76.2153 - 27.4266i) q^{9} +117.582 q^{10} -143.870i q^{11} +(-5.10307 + 29.2519i) q^{12} +188.424 q^{13} -172.561i q^{14} +(292.524 + 51.0315i) q^{15} -192.326 q^{16} -314.784i q^{17} +(97.7432 - 271.617i) q^{18} -1.38992 q^{19} -108.855i q^{20} +(74.8926 - 429.300i) q^{21} +512.723 q^{22} -193.577i q^{23} +(-609.801 - 106.381i) q^{24} -463.571 q^{25} +671.508i q^{26} +(361.051 - 633.311i) q^{27} -159.753 q^{28} -1266.29i q^{29} +(-181.866 + 1042.50i) q^{30} +36.5072 q^{31} +415.051i q^{32} +(1275.56 + 222.525i) q^{33} +1121.83 q^{34} +1597.56i q^{35} +(-251.457 - 90.4886i) q^{36} +1485.40 q^{37} -4.95339i q^{38} +(-291.439 + 1670.59i) q^{39} +2269.26 q^{40} +1972.66i q^{41} +(1529.94 + 266.903i) q^{42} +203.989 q^{43} -474.668i q^{44} +(-904.901 + 2514.61i) q^{45} +689.872 q^{46} -934.292i q^{47} +(297.473 - 1705.18i) q^{48} -56.4629 q^{49} -1652.08i q^{50} +(2790.91 + 486.882i) q^{51} +621.668 q^{52} -3283.35i q^{53} +(2257.00 + 1286.71i) q^{54} -4746.76 q^{55} -3330.30i q^{56} +(2.14980 - 12.3231i) q^{57} +4512.83 q^{58} -453.188i q^{59} +(965.122 + 168.368i) q^{60} -5625.52 q^{61} +130.105i q^{62} +(3690.38 + 1328.01i) q^{63} -4556.37 q^{64} -6216.78i q^{65} +(-793.036 + 4545.85i) q^{66} -4794.66 q^{67} -1038.57i q^{68} +(1716.28 + 299.409i) q^{69} -5693.39 q^{70} +3643.38i q^{71} +(1886.38 - 5242.01i) q^{72} +2678.61 q^{73} +5293.67i q^{74} +(717.012 - 4110.07i) q^{75} -4.58574 q^{76} +6966.22i q^{77} +(-5953.66 - 1038.63i) q^{78} +7113.29 q^{79} +6345.50i q^{80} +(5056.56 + 4180.66i) q^{81} -7030.16 q^{82} -9846.88i q^{83} +(247.093 - 1416.39i) q^{84} -10385.8 q^{85} +726.977i q^{86} +(11227.1 + 1958.60i) q^{87} +9895.19 q^{88} -3149.01i q^{89} +(-8961.58 - 3224.89i) q^{90} -9123.59 q^{91} -638.669i q^{92} +(-56.4663 + 323.676i) q^{93} +3329.63 q^{94} +45.8582i q^{95} +(-3679.88 - 641.965i) q^{96} -13040.7 q^{97} -201.223i q^{98} +(-3945.86 + 10965.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.56380i 0.890951i 0.895294 + 0.445476i \(0.146965\pi\)
−0.895294 + 0.445476i \(0.853035\pi\)
\(3\) −1.54671 + 8.86610i −0.171857 + 0.985122i
\(4\) 3.29930 0.206206
\(5\) 32.9935i 1.31974i −0.751380 0.659870i \(-0.770611\pi\)
0.751380 0.659870i \(-0.229389\pi\)
\(6\) −31.5970 5.51219i −0.877695 0.153116i
\(7\) −48.4204 −0.988172 −0.494086 0.869413i \(-0.664497\pi\)
−0.494086 + 0.869413i \(0.664497\pi\)
\(8\) 68.7789i 1.07467i
\(9\) −76.2153 27.4266i −0.940930 0.338601i
\(10\) 117.582 1.17582
\(11\) 143.870i 1.18900i −0.804094 0.594502i \(-0.797349\pi\)
0.804094 0.594502i \(-0.202651\pi\)
\(12\) −5.10307 + 29.2519i −0.0354380 + 0.203138i
\(13\) 188.424 1.11494 0.557469 0.830198i \(-0.311773\pi\)
0.557469 + 0.830198i \(0.311773\pi\)
\(14\) 172.561i 0.880413i
\(15\) 292.524 + 51.0315i 1.30010 + 0.226807i
\(16\) −192.326 −0.751273
\(17\) 314.784i 1.08922i −0.838690 0.544610i \(-0.816678\pi\)
0.838690 0.544610i \(-0.183322\pi\)
\(18\) 97.7432 271.617i 0.301677 0.838323i
\(19\) −1.38992 −0.00385018 −0.00192509 0.999998i \(-0.500613\pi\)
−0.00192509 + 0.999998i \(0.500613\pi\)
\(20\) 108.855i 0.272138i
\(21\) 74.8926 429.300i 0.169824 0.973470i
\(22\) 512.723 1.05934
\(23\) 193.577i 0.365931i −0.983119 0.182965i \(-0.941430\pi\)
0.983119 0.182965i \(-0.0585697\pi\)
\(24\) −609.801 106.381i −1.05868 0.184690i
\(25\) −463.571 −0.741714
\(26\) 671.508i 0.993355i
\(27\) 361.051 633.311i 0.495268 0.868740i
\(28\) −159.753 −0.203767
\(29\) 1266.29i 1.50570i −0.658191 0.752851i \(-0.728678\pi\)
0.658191 0.752851i \(-0.271322\pi\)
\(30\) −181.866 + 1042.50i −0.202074 + 1.15833i
\(31\) 36.5072 0.0379888 0.0189944 0.999820i \(-0.493954\pi\)
0.0189944 + 0.999820i \(0.493954\pi\)
\(32\) 415.051i 0.405323i
\(33\) 1275.56 + 222.525i 1.17131 + 0.204339i
\(34\) 1121.83 0.970441
\(35\) 1597.56i 1.30413i
\(36\) −251.457 90.4886i −0.194025 0.0698215i
\(37\) 1485.40 1.08502 0.542512 0.840048i \(-0.317473\pi\)
0.542512 + 0.840048i \(0.317473\pi\)
\(38\) 4.95339i 0.00343032i
\(39\) −291.439 + 1670.59i −0.191610 + 1.09835i
\(40\) 2269.26 1.41829
\(41\) 1972.66i 1.17350i 0.809768 + 0.586750i \(0.199593\pi\)
−0.809768 + 0.586750i \(0.800407\pi\)
\(42\) 1529.94 + 266.903i 0.867314 + 0.151305i
\(43\) 203.989 0.110324 0.0551620 0.998477i \(-0.482432\pi\)
0.0551620 + 0.998477i \(0.482432\pi\)
\(44\) 474.668i 0.245180i
\(45\) −904.901 + 2514.61i −0.446865 + 1.24178i
\(46\) 689.872 0.326027
\(47\) 934.292i 0.422948i −0.977384 0.211474i \(-0.932174\pi\)
0.977384 0.211474i \(-0.0678263\pi\)
\(48\) 297.473 1705.18i 0.129112 0.740096i
\(49\) −56.4629 −0.0235164
\(50\) 1652.08i 0.660831i
\(51\) 2790.91 + 486.882i 1.07301 + 0.187190i
\(52\) 621.668 0.229907
\(53\) 3283.35i 1.16887i −0.811442 0.584433i \(-0.801317\pi\)
0.811442 0.584433i \(-0.198683\pi\)
\(54\) 2257.00 + 1286.71i 0.774005 + 0.441260i
\(55\) −4746.76 −1.56918
\(56\) 3330.30i 1.06196i
\(57\) 2.14980 12.3231i 0.000661682 0.00379290i
\(58\) 4512.83 1.34151
\(59\) 453.188i 0.130189i
\(60\) 965.122 + 168.368i 0.268089 + 0.0467689i
\(61\) −5625.52 −1.51183 −0.755914 0.654670i \(-0.772807\pi\)
−0.755914 + 0.654670i \(0.772807\pi\)
\(62\) 130.105i 0.0338461i
\(63\) 3690.38 + 1328.01i 0.929801 + 0.334596i
\(64\) −4556.37 −1.11240
\(65\) 6216.78i 1.47143i
\(66\) −793.036 + 4545.85i −0.182056 + 1.04358i
\(67\) −4794.66 −1.06809 −0.534045 0.845456i \(-0.679329\pi\)
−0.534045 + 0.845456i \(0.679329\pi\)
\(68\) 1038.57i 0.224604i
\(69\) 1716.28 + 299.409i 0.360487 + 0.0628879i
\(70\) −5693.39 −1.16192
\(71\) 3643.38i 0.722749i 0.932421 + 0.361375i \(0.117692\pi\)
−0.932421 + 0.361375i \(0.882308\pi\)
\(72\) 1886.38 5242.01i 0.363884 1.01119i
\(73\) 2678.61 0.502649 0.251324 0.967903i \(-0.419134\pi\)
0.251324 + 0.967903i \(0.419134\pi\)
\(74\) 5293.67i 0.966704i
\(75\) 717.012 4110.07i 0.127469 0.730678i
\(76\) −4.58574 −0.000793931
\(77\) 6966.22i 1.17494i
\(78\) −5953.66 1038.63i −0.978576 0.170715i
\(79\) 7113.29 1.13977 0.569884 0.821725i \(-0.306988\pi\)
0.569884 + 0.821725i \(0.306988\pi\)
\(80\) 6345.50i 0.991485i
\(81\) 5056.56 + 4180.66i 0.770699 + 0.637199i
\(82\) −7030.16 −1.04553
\(83\) 9846.88i 1.42936i −0.699450 0.714681i \(-0.746572\pi\)
0.699450 0.714681i \(-0.253428\pi\)
\(84\) 247.093 1416.39i 0.0350188 0.200735i
\(85\) −10385.8 −1.43749
\(86\) 726.977i 0.0982932i
\(87\) 11227.1 + 1958.60i 1.48330 + 0.258766i
\(88\) 9895.19 1.27779
\(89\) 3149.01i 0.397552i −0.980045 0.198776i \(-0.936303\pi\)
0.980045 0.198776i \(-0.0636967\pi\)
\(90\) −8961.58 3224.89i −1.10637 0.398135i
\(91\) −9123.59 −1.10175
\(92\) 638.669i 0.0754572i
\(93\) −56.4663 + 323.676i −0.00652864 + 0.0374236i
\(94\) 3329.63 0.376826
\(95\) 45.8582i 0.00508124i
\(96\) −3679.88 641.965i −0.399293 0.0696577i
\(97\) −13040.7 −1.38598 −0.692990 0.720947i \(-0.743707\pi\)
−0.692990 + 0.720947i \(0.743707\pi\)
\(98\) 201.223i 0.0209520i
\(99\) −3945.86 + 10965.1i −0.402598 + 1.11877i
\(100\) −1529.46 −0.152946
\(101\) 18350.4i 1.79888i −0.437042 0.899441i \(-0.643974\pi\)
0.437042 0.899441i \(-0.356026\pi\)
\(102\) −1735.15 + 9946.25i −0.166777 + 0.956003i
\(103\) 5773.21 0.544180 0.272090 0.962272i \(-0.412285\pi\)
0.272090 + 0.962272i \(0.412285\pi\)
\(104\) 12959.6i 1.19819i
\(105\) −14164.1 2470.97i −1.28473 0.224124i
\(106\) 11701.2 1.04140
\(107\) 1010.41i 0.0882531i −0.999026 0.0441265i \(-0.985950\pi\)
0.999026 0.0441265i \(-0.0140505\pi\)
\(108\) 1191.21 2089.48i 0.102127 0.179139i
\(109\) 3241.62 0.272841 0.136420 0.990651i \(-0.456440\pi\)
0.136420 + 0.990651i \(0.456440\pi\)
\(110\) 16916.5i 1.39806i
\(111\) −2297.49 + 13169.7i −0.186469 + 1.06888i
\(112\) 9312.50 0.742387
\(113\) 14844.0i 1.16250i −0.813724 0.581252i \(-0.802563\pi\)
0.813724 0.581252i \(-0.197437\pi\)
\(114\) 43.9172 + 7.66148i 0.00337929 + 0.000589526i
\(115\) −6386.80 −0.482934
\(116\) 4177.88i 0.310485i
\(117\) −14360.8 5167.85i −1.04908 0.377519i
\(118\) 1615.07 0.115992
\(119\) 15242.0i 1.07634i
\(120\) −3509.89 + 20119.5i −0.243743 + 1.39718i
\(121\) −6057.45 −0.413732
\(122\) 20048.2i 1.34697i
\(123\) −17489.8 3051.13i −1.15604 0.201675i
\(124\) 120.448 0.00783351
\(125\) 5326.10i 0.340871i
\(126\) −4732.77 + 13151.8i −0.298108 + 0.828407i
\(127\) −8624.34 −0.534710 −0.267355 0.963598i \(-0.586150\pi\)
−0.267355 + 0.963598i \(0.586150\pi\)
\(128\) 9597.22i 0.585768i
\(129\) −315.513 + 1808.59i −0.0189600 + 0.108683i
\(130\) 22155.4 1.31097
\(131\) 32219.3i 1.87747i 0.344635 + 0.938737i \(0.388003\pi\)
−0.344635 + 0.938737i \(0.611997\pi\)
\(132\) 4208.45 + 734.176i 0.241532 + 0.0421359i
\(133\) 67.3003 0.00380464
\(134\) 17087.2i 0.951617i
\(135\) −20895.2 11912.3i −1.14651 0.653626i
\(136\) 21650.5 1.17055
\(137\) 8355.56i 0.445179i 0.974912 + 0.222589i \(0.0714509\pi\)
−0.974912 + 0.222589i \(0.928549\pi\)
\(138\) −1067.04 + 6116.47i −0.0560300 + 0.321176i
\(139\) −6883.91 −0.356292 −0.178146 0.984004i \(-0.557010\pi\)
−0.178146 + 0.984004i \(0.557010\pi\)
\(140\) 5270.82i 0.268919i
\(141\) 8283.52 + 1445.08i 0.416655 + 0.0726866i
\(142\) −12984.3 −0.643934
\(143\) 27108.5i 1.32567i
\(144\) 14658.2 + 5274.85i 0.706896 + 0.254382i
\(145\) −41779.5 −1.98713
\(146\) 9546.06i 0.447835i
\(147\) 87.3320 500.606i 0.00404147 0.0231665i
\(148\) 4900.77 0.223739
\(149\) 31197.8i 1.40524i −0.711564 0.702622i \(-0.752013\pi\)
0.711564 0.702622i \(-0.247987\pi\)
\(150\) 14647.5 + 2555.29i 0.650999 + 0.113569i
\(151\) 10047.5 0.440661 0.220330 0.975425i \(-0.429286\pi\)
0.220330 + 0.975425i \(0.429286\pi\)
\(152\) 95.5969i 0.00413768i
\(153\) −8633.48 + 23991.4i −0.368810 + 1.02488i
\(154\) −24826.3 −1.04681
\(155\) 1204.50i 0.0501353i
\(156\) −961.544 + 5511.77i −0.0395112 + 0.226486i
\(157\) 33206.3 1.34717 0.673584 0.739111i \(-0.264754\pi\)
0.673584 + 0.739111i \(0.264754\pi\)
\(158\) 25350.4i 1.01548i
\(159\) 29110.5 + 5078.40i 1.15148 + 0.200878i
\(160\) 13694.0 0.534921
\(161\) 9373.10i 0.361603i
\(162\) −14899.1 + 18020.6i −0.567713 + 0.686655i
\(163\) 16842.0 0.633895 0.316947 0.948443i \(-0.397342\pi\)
0.316947 + 0.948443i \(0.397342\pi\)
\(164\) 6508.37i 0.241983i
\(165\) 7341.88 42085.2i 0.269674 1.54583i
\(166\) 35092.4 1.27349
\(167\) 47210.2i 1.69279i 0.532556 + 0.846395i \(0.321232\pi\)
−0.532556 + 0.846395i \(0.678768\pi\)
\(168\) 29526.8 + 5151.03i 1.04616 + 0.182505i
\(169\) 6942.79 0.243086
\(170\) 37013.1i 1.28073i
\(171\) 105.933 + 38.1207i 0.00362275 + 0.00130367i
\(172\) 673.020 0.0227495
\(173\) 44614.6i 1.49068i −0.666683 0.745341i \(-0.732287\pi\)
0.666683 0.745341i \(-0.267713\pi\)
\(174\) −6980.06 + 40011.2i −0.230548 + 1.32155i
\(175\) 22446.3 0.732941
\(176\) 27669.8i 0.893267i
\(177\) 4018.01 + 700.952i 0.128252 + 0.0223739i
\(178\) 11222.5 0.354200
\(179\) 42181.9i 1.31650i 0.752800 + 0.658249i \(0.228703\pi\)
−0.752800 + 0.658249i \(0.771297\pi\)
\(180\) −2985.54 + 8296.45i −0.0921462 + 0.256063i
\(181\) −60384.5 −1.84318 −0.921592 0.388160i \(-0.873111\pi\)
−0.921592 + 0.388160i \(0.873111\pi\)
\(182\) 32514.7i 0.981606i
\(183\) 8701.07 49876.4i 0.259819 1.48934i
\(184\) 13314.1 0.393255
\(185\) 49008.5i 1.43195i
\(186\) −1153.52 201.235i −0.0333426 0.00581670i
\(187\) −45287.9 −1.29509
\(188\) 3082.50i 0.0872144i
\(189\) −17482.2 + 30665.2i −0.489410 + 0.858464i
\(190\) −163.430 −0.00452714
\(191\) 51191.6i 1.40324i 0.712551 + 0.701621i \(0.247540\pi\)
−0.712551 + 0.701621i \(0.752460\pi\)
\(192\) 7047.41 40397.3i 0.191173 1.09585i
\(193\) −22027.7 −0.591364 −0.295682 0.955286i \(-0.595547\pi\)
−0.295682 + 0.955286i \(0.595547\pi\)
\(194\) 46474.5i 1.23484i
\(195\) 55118.6 + 9615.59i 1.44954 + 0.252876i
\(196\) −186.288 −0.00484923
\(197\) 22961.1i 0.591644i 0.955243 + 0.295822i \(0.0955936\pi\)
−0.955243 + 0.295822i \(0.904406\pi\)
\(198\) −39077.4 14062.3i −0.996770 0.358695i
\(199\) 38265.0 0.966263 0.483132 0.875548i \(-0.339499\pi\)
0.483132 + 0.875548i \(0.339499\pi\)
\(200\) 31883.9i 0.797098i
\(201\) 7415.97 42509.9i 0.183559 1.05220i
\(202\) 65397.2 1.60272
\(203\) 61314.5i 1.48789i
\(204\) 9208.03 + 1606.37i 0.221262 + 0.0385997i
\(205\) 65084.8 1.54872
\(206\) 20574.6i 0.484838i
\(207\) −5309.18 + 14753.6i −0.123904 + 0.344315i
\(208\) −36238.9 −0.837623
\(209\) 199.967i 0.00457788i
\(210\) 8806.05 50478.1i 0.199684 1.14463i
\(211\) 34607.7 0.777335 0.388668 0.921378i \(-0.372935\pi\)
0.388668 + 0.921378i \(0.372935\pi\)
\(212\) 10832.7i 0.241027i
\(213\) −32302.6 5635.27i −0.711996 0.124210i
\(214\) 3600.90 0.0786292
\(215\) 6730.31i 0.145599i
\(216\) 43558.5 + 24832.7i 0.933609 + 0.532251i
\(217\) −1767.69 −0.0375394
\(218\) 11552.5i 0.243088i
\(219\) −4143.05 + 23748.9i −0.0863838 + 0.495170i
\(220\) −15661.0 −0.323574
\(221\) 59313.1i 1.21441i
\(222\) −46934.2 8187.80i −0.952321 0.166135i
\(223\) 58364.2 1.17364 0.586822 0.809716i \(-0.300379\pi\)
0.586822 + 0.809716i \(0.300379\pi\)
\(224\) 20096.9i 0.400529i
\(225\) 35331.2 + 12714.2i 0.697901 + 0.251145i
\(226\) 52901.2 1.03573
\(227\) 18653.8i 0.362005i −0.983483 0.181003i \(-0.942066\pi\)
0.983483 0.181003i \(-0.0579343\pi\)
\(228\) 7.09284 40.6577i 0.000136443 0.000782119i
\(229\) −71930.2 −1.37164 −0.685820 0.727771i \(-0.740556\pi\)
−0.685820 + 0.727771i \(0.740556\pi\)
\(230\) 22761.3i 0.430270i
\(231\) −61763.2 10774.8i −1.15746 0.201922i
\(232\) 87094.4 1.61813
\(233\) 72712.2i 1.33935i 0.742653 + 0.669677i \(0.233567\pi\)
−0.742653 + 0.669677i \(0.766433\pi\)
\(234\) 18417.2 51179.2i 0.336351 0.934678i
\(235\) −30825.6 −0.558181
\(236\) 1495.20i 0.0268457i
\(237\) −11002.2 + 63067.2i −0.195877 + 1.12281i
\(238\) −54319.5 −0.958963
\(239\) 27801.0i 0.486703i −0.969938 0.243352i \(-0.921753\pi\)
0.969938 0.243352i \(-0.0782469\pi\)
\(240\) −56259.9 9814.69i −0.976734 0.170394i
\(241\) 48259.9 0.830907 0.415454 0.909614i \(-0.363623\pi\)
0.415454 + 0.909614i \(0.363623\pi\)
\(242\) 21587.6i 0.368615i
\(243\) −44887.2 + 38365.6i −0.760169 + 0.649725i
\(244\) −18560.2 −0.311748
\(245\) 1862.91i 0.0310356i
\(246\) 10873.6 62330.1i 0.179682 1.02998i
\(247\) −261.894 −0.00429271
\(248\) 2510.93i 0.0408254i
\(249\) 87303.4 + 15230.3i 1.40810 + 0.245646i
\(250\) 18981.2 0.303699
\(251\) 53937.3i 0.856134i −0.903747 0.428067i \(-0.859195\pi\)
0.903747 0.428067i \(-0.140805\pi\)
\(252\) 12175.7 + 4381.50i 0.191731 + 0.0689956i
\(253\) −27849.9 −0.435094
\(254\) 30735.5i 0.476401i
\(255\) 16063.9 92081.8i 0.247042 1.41610i
\(256\) −38699.4 −0.590506
\(257\) 69434.7i 1.05126i 0.850713 + 0.525630i \(0.176170\pi\)
−0.850713 + 0.525630i \(0.823830\pi\)
\(258\) −6445.45 1124.43i −0.0968308 0.0168924i
\(259\) −71923.6 −1.07219
\(260\) 20511.0i 0.303417i
\(261\) −34730.2 + 96511.1i −0.509831 + 1.41676i
\(262\) −114823. −1.67274
\(263\) 96388.7i 1.39352i 0.717302 + 0.696762i \(0.245377\pi\)
−0.717302 + 0.696762i \(0.754623\pi\)
\(264\) −15305.0 + 87731.7i −0.219597 + 1.25878i
\(265\) −108329. −1.54260
\(266\) 239.845i 0.00338975i
\(267\) 27919.5 + 4870.63i 0.391638 + 0.0683223i
\(268\) −15819.0 −0.220247
\(269\) 62174.8i 0.859230i 0.903012 + 0.429615i \(0.141351\pi\)
−0.903012 + 0.429615i \(0.858649\pi\)
\(270\) 42453.2 74466.3i 0.582349 1.02149i
\(271\) 31459.2 0.428360 0.214180 0.976794i \(-0.431292\pi\)
0.214180 + 0.976794i \(0.431292\pi\)
\(272\) 60541.2i 0.818301i
\(273\) 14111.6 80890.7i 0.189344 1.08536i
\(274\) −29777.6 −0.396632
\(275\) 66693.8i 0.881901i
\(276\) 5662.51 + 987.840i 0.0743345 + 0.0129679i
\(277\) 92427.3 1.20459 0.602297 0.798272i \(-0.294252\pi\)
0.602297 + 0.798272i \(0.294252\pi\)
\(278\) 24532.9i 0.317438i
\(279\) −2782.41 1001.27i −0.0357448 0.0128630i
\(280\) −109878. −1.40151
\(281\) 27532.2i 0.348681i 0.984685 + 0.174341i \(0.0557794\pi\)
−0.984685 + 0.174341i \(0.944221\pi\)
\(282\) −5149.99 + 29520.8i −0.0647602 + 0.371219i
\(283\) −93843.8 −1.17174 −0.585872 0.810404i \(-0.699248\pi\)
−0.585872 + 0.810404i \(0.699248\pi\)
\(284\) 12020.6i 0.149035i
\(285\) −406.583 70.9296i −0.00500564 0.000873248i
\(286\) 96609.6 1.18110
\(287\) 95516.8i 1.15962i
\(288\) 11383.5 31633.2i 0.137243 0.381381i
\(289\) −15568.2 −0.186399
\(290\) 148894.i 1.77044i
\(291\) 20170.2 115620.i 0.238191 1.36536i
\(292\) 8837.54 0.103649
\(293\) 95388.5i 1.11112i −0.831477 0.555560i \(-0.812504\pi\)
0.831477 0.555560i \(-0.187496\pi\)
\(294\) 1784.06 + 311.234i 0.0206403 + 0.00360075i
\(295\) −14952.2 −0.171816
\(296\) 102164.i 1.16604i
\(297\) −91114.2 51944.2i −1.03294 0.588876i
\(298\) 111183. 1.25200
\(299\) 36474.7i 0.407990i
\(300\) 2365.64 13560.3i 0.0262848 0.150670i
\(301\) −9877.23 −0.109019
\(302\) 35807.4i 0.392607i
\(303\) 162696. + 28382.8i 1.77212 + 0.309151i
\(304\) 267.317 0.00289254
\(305\) 185605.i 1.99522i
\(306\) −85500.7 30768.0i −0.913117 0.328592i
\(307\) −34270.2 −0.363613 −0.181807 0.983334i \(-0.558194\pi\)
−0.181807 + 0.983334i \(0.558194\pi\)
\(308\) 22983.6i 0.242280i
\(309\) −8929.50 + 51185.8i −0.0935213 + 0.536084i
\(310\) 4292.61 0.0446681
\(311\) 137459.i 1.42119i 0.703602 + 0.710594i \(0.251574\pi\)
−0.703602 + 0.710594i \(0.748426\pi\)
\(312\) −114901. 20044.9i −1.18036 0.205918i
\(313\) 147882. 1.50948 0.754739 0.656026i \(-0.227764\pi\)
0.754739 + 0.656026i \(0.227764\pi\)
\(314\) 118341.i 1.20026i
\(315\) 43815.7 121759.i 0.441579 1.22710i
\(316\) 23468.9 0.235027
\(317\) 105626.i 1.05112i 0.850758 + 0.525558i \(0.176143\pi\)
−0.850758 + 0.525558i \(0.823857\pi\)
\(318\) −18098.4 + 103744.i −0.178973 + 1.02591i
\(319\) −182181. −1.79029
\(320\) 150331.i 1.46807i
\(321\) 8958.39 + 1562.82i 0.0869400 + 0.0151669i
\(322\) −33403.9 −0.322170
\(323\) 437.524i 0.00419369i
\(324\) 16683.1 + 13793.2i 0.158923 + 0.131394i
\(325\) −87348.2 −0.826965
\(326\) 60021.4i 0.564769i
\(327\) −5013.87 + 28740.5i −0.0468897 + 0.268782i
\(328\) −135677. −1.26113
\(329\) 45238.8i 0.417945i
\(330\) 149984. + 26165.0i 1.37726 + 0.240267i
\(331\) −142699. −1.30246 −0.651230 0.758880i \(-0.725747\pi\)
−0.651230 + 0.758880i \(0.725747\pi\)
\(332\) 32487.8i 0.294743i
\(333\) −113210. 40739.5i −1.02093 0.367390i
\(334\) −168248. −1.50819
\(335\) 158193.i 1.40960i
\(336\) −14403.8 + 82565.5i −0.127585 + 0.731342i
\(337\) −100324. −0.883377 −0.441689 0.897168i \(-0.645620\pi\)
−0.441689 + 0.897168i \(0.645620\pi\)
\(338\) 24742.8i 0.216578i
\(339\) 131608. + 22959.5i 1.14521 + 0.199785i
\(340\) −34266.0 −0.296418
\(341\) 5252.28i 0.0451688i
\(342\) −135.855 + 377.524i −0.00116151 + 0.00322770i
\(343\) 118991. 1.01141
\(344\) 14030.1i 0.118562i
\(345\) 9878.56 56626.0i 0.0829956 0.475749i
\(346\) 158998. 1.32813
\(347\) 181469.i 1.50710i −0.657388 0.753552i \(-0.728339\pi\)
0.657388 0.753552i \(-0.271661\pi\)
\(348\) 37041.5 + 6461.99i 0.305865 + 0.0533590i
\(349\) 149731. 1.22931 0.614656 0.788795i \(-0.289295\pi\)
0.614656 + 0.788795i \(0.289295\pi\)
\(350\) 79994.3i 0.653014i
\(351\) 68030.8 119331.i 0.552194 0.968591i
\(352\) 59713.2 0.481931
\(353\) 29293.1i 0.235080i −0.993068 0.117540i \(-0.962499\pi\)
0.993068 0.117540i \(-0.0375008\pi\)
\(354\) −2498.06 + 14319.4i −0.0199341 + 0.114266i
\(355\) 120208. 0.953841
\(356\) 10389.5i 0.0819777i
\(357\) −135137. 23575.0i −1.06032 0.184976i
\(358\) −150328. −1.17294
\(359\) 10042.8i 0.0779227i −0.999241 0.0389614i \(-0.987595\pi\)
0.999241 0.0389614i \(-0.0124049\pi\)
\(360\) −172952. 62238.1i −1.33451 0.480232i
\(361\) −130319. −0.999985
\(362\) 215199.i 1.64219i
\(363\) 9369.14 53705.9i 0.0711028 0.407576i
\(364\) −30101.4 −0.227188
\(365\) 88376.9i 0.663366i
\(366\) 177750. + 31008.9i 1.32693 + 0.231486i
\(367\) 139800. 1.03795 0.518974 0.854790i \(-0.326314\pi\)
0.518974 + 0.854790i \(0.326314\pi\)
\(368\) 37230.0i 0.274914i
\(369\) 54103.3 150347.i 0.397348 1.10418i
\(370\) 174657. 1.27580
\(371\) 158981.i 1.15504i
\(372\) −186.299 + 1067.90i −0.00134625 + 0.00771697i
\(373\) −120658. −0.867238 −0.433619 0.901096i \(-0.642764\pi\)
−0.433619 + 0.901096i \(0.642764\pi\)
\(374\) 161397.i 1.15386i
\(375\) 47221.8 + 8237.97i 0.335799 + 0.0585811i
\(376\) 64259.6 0.454530
\(377\) 238601.i 1.67876i
\(378\) −109285. 62303.2i −0.764850 0.436041i
\(379\) 160981. 1.12072 0.560358 0.828251i \(-0.310664\pi\)
0.560358 + 0.828251i \(0.310664\pi\)
\(380\) 151.300i 0.00104778i
\(381\) 13339.4 76464.2i 0.0918938 0.526755i
\(382\) −182437. −1.25022
\(383\) 267800.i 1.82563i −0.408374 0.912815i \(-0.633904\pi\)
0.408374 0.912815i \(-0.366096\pi\)
\(384\) 85089.8 + 14844.2i 0.577052 + 0.100668i
\(385\) 229840. 1.55062
\(386\) 78502.4i 0.526876i
\(387\) −15547.1 5594.73i −0.103807 0.0373558i
\(388\) −43025.1 −0.285797
\(389\) 2697.04i 0.0178233i 0.999960 + 0.00891165i \(0.00283670\pi\)
−0.999960 + 0.00891165i \(0.997163\pi\)
\(390\) −34268.1 + 196432.i −0.225300 + 1.29147i
\(391\) −60935.2 −0.398579
\(392\) 3883.46i 0.0252724i
\(393\) −285660. 49834.1i −1.84954 0.322657i
\(394\) −81829.0 −0.527126
\(395\) 234692.i 1.50420i
\(396\) −13018.6 + 36177.0i −0.0830181 + 0.230697i
\(397\) −34899.8 −0.221433 −0.110716 0.993852i \(-0.535314\pi\)
−0.110716 + 0.993852i \(0.535314\pi\)
\(398\) 136369.i 0.860893i
\(399\) −104.094 + 596.691i −0.000653855 + 0.00374804i
\(400\) 89156.7 0.557230
\(401\) 61105.8i 0.380009i −0.981783 0.190004i \(-0.939150\pi\)
0.981783 0.190004i \(-0.0608503\pi\)
\(402\) 151497. + 26429.1i 0.937459 + 0.163542i
\(403\) 6878.85 0.0423551
\(404\) 60543.4i 0.370940i
\(405\) 137935. 166834.i 0.840937 1.01712i
\(406\) −218513. −1.32564
\(407\) 213704.i 1.29010i
\(408\) −33487.2 + 191956.i −0.201168 + 1.15314i
\(409\) 245183. 1.46569 0.732847 0.680394i \(-0.238191\pi\)
0.732847 + 0.680394i \(0.238191\pi\)
\(410\) 231949.i 1.37983i
\(411\) −74081.2 12923.7i −0.438555 0.0765071i
\(412\) 19047.5 0.112213
\(413\) 21943.5i 0.128649i
\(414\) −52578.9 18920.9i −0.306768 0.110393i
\(415\) −324883. −1.88639
\(416\) 78205.7i 0.451910i
\(417\) 10647.4 61033.4i 0.0612313 0.350991i
\(418\) −712.642 −0.00407867
\(419\) 89352.9i 0.508956i 0.967079 + 0.254478i \(0.0819037\pi\)
−0.967079 + 0.254478i \(0.918096\pi\)
\(420\) −46731.6 8152.46i −0.264918 0.0462157i
\(421\) −137615. −0.776431 −0.388215 0.921569i \(-0.626908\pi\)
−0.388215 + 0.921569i \(0.626908\pi\)
\(422\) 123335.i 0.692568i
\(423\) −25624.5 + 71207.4i −0.143210 + 0.397964i
\(424\) 225825. 1.25615
\(425\) 145925.i 0.807889i
\(426\) 20083.0 115120.i 0.110665 0.634354i
\(427\) 272390. 1.49395
\(428\) 3333.64i 0.0181983i
\(429\) 240347. + 41929.2i 1.30594 + 0.227825i
\(430\) 23985.5 0.129722
\(431\) 260720.i 1.40353i 0.712411 + 0.701763i \(0.247603\pi\)
−0.712411 + 0.701763i \(0.752397\pi\)
\(432\) −69439.4 + 121802.i −0.372082 + 0.652661i
\(433\) 223240. 1.19068 0.595341 0.803473i \(-0.297017\pi\)
0.595341 + 0.803473i \(0.297017\pi\)
\(434\) 6299.72i 0.0334458i
\(435\) 64621.0 370421.i 0.341503 1.95757i
\(436\) 10695.1 0.0562614
\(437\) 269.056i 0.00140890i
\(438\) −84636.3 14765.0i −0.441172 0.0769637i
\(439\) 210890. 1.09428 0.547138 0.837042i \(-0.315717\pi\)
0.547138 + 0.837042i \(0.315717\pi\)
\(440\) 326477.i 1.68635i
\(441\) 4303.34 + 1548.59i 0.0221273 + 0.00796267i
\(442\) 211380. 1.08198
\(443\) 94013.2i 0.479051i −0.970890 0.239525i \(-0.923008\pi\)
0.970890 0.239525i \(-0.0769918\pi\)
\(444\) −7580.09 + 43450.7i −0.0384511 + 0.220410i
\(445\) −103897. −0.524666
\(446\) 207999.i 1.04566i
\(447\) 276603. + 48254.1i 1.38434 + 0.241501i
\(448\) 220622. 1.09924
\(449\) 251762.i 1.24881i 0.781100 + 0.624406i \(0.214659\pi\)
−0.781100 + 0.624406i \(0.785341\pi\)
\(450\) −45310.9 + 125914.i −0.223758 + 0.621796i
\(451\) 283805. 1.39530
\(452\) 48974.8i 0.239715i
\(453\) −15540.6 + 89082.2i −0.0757308 + 0.434105i
\(454\) 66478.4 0.322529
\(455\) 301019.i 1.45402i
\(456\) 847.572 + 147.861i 0.00407612 + 0.000711090i
\(457\) 202155. 0.967946 0.483973 0.875083i \(-0.339193\pi\)
0.483973 + 0.875083i \(0.339193\pi\)
\(458\) 256345.i 1.22206i
\(459\) −199357. 113653.i −0.946248 0.539456i
\(460\) −21071.9 −0.0995838
\(461\) 180886.i 0.851143i 0.904925 + 0.425572i \(0.139927\pi\)
−0.904925 + 0.425572i \(0.860073\pi\)
\(462\) 38399.1 220112.i 0.179903 1.03124i
\(463\) −121417. −0.566394 −0.283197 0.959062i \(-0.591395\pi\)
−0.283197 + 0.959062i \(0.591395\pi\)
\(464\) 243541.i 1.13119i
\(465\) 10679.2 + 1863.02i 0.0493894 + 0.00861611i
\(466\) −259132. −1.19330
\(467\) 220885.i 1.01282i −0.862293 0.506409i \(-0.830973\pi\)
0.862293 0.506409i \(-0.169027\pi\)
\(468\) −47380.7 17050.3i −0.216326 0.0778466i
\(469\) 232159. 1.05546
\(470\) 109856.i 0.497312i
\(471\) −51360.7 + 294411.i −0.231520 + 1.32712i
\(472\) 31169.8 0.139910
\(473\) 29347.8i 0.131176i
\(474\) −224759. 39209.8i −1.00037 0.174517i
\(475\) 644.325 0.00285573
\(476\) 50287.8i 0.221947i
\(477\) −90051.2 + 250241.i −0.395779 + 1.09982i
\(478\) 99077.2 0.433629
\(479\) 9680.62i 0.0421922i 0.999777 + 0.0210961i \(0.00671559\pi\)
−0.999777 + 0.0210961i \(0.993284\pi\)
\(480\) −21180.7 + 121412.i −0.0919300 + 0.526962i
\(481\) 279885. 1.20973
\(482\) 171989.i 0.740298i
\(483\) −83102.8 14497.5i −0.356223 0.0621440i
\(484\) −19985.3 −0.0853140
\(485\) 430258.i 1.82913i
\(486\) −136728. 159969.i −0.578874 0.677273i
\(487\) 431822. 1.82074 0.910368 0.413799i \(-0.135798\pi\)
0.910368 + 0.413799i \(0.135798\pi\)
\(488\) 386917.i 1.62472i
\(489\) −26049.7 + 149322.i −0.108939 + 0.624464i
\(490\) −6639.04 −0.0276512
\(491\) 25060.0i 0.103948i −0.998648 0.0519742i \(-0.983449\pi\)
0.998648 0.0519742i \(-0.0165514\pi\)
\(492\) −57703.9 10066.6i −0.238383 0.0415865i
\(493\) −398610. −1.64004
\(494\) 933.340i 0.00382460i
\(495\) 361776. + 130188.i 1.47649 + 0.531324i
\(496\) −7021.28 −0.0285399
\(497\) 176414.i 0.714201i
\(498\) −54277.9 + 311132.i −0.218859 + 1.25455i
\(499\) 172187. 0.691511 0.345755 0.938325i \(-0.387623\pi\)
0.345755 + 0.938325i \(0.387623\pi\)
\(500\) 17572.4i 0.0702896i
\(501\) −418570. 73020.8i −1.66760 0.290918i
\(502\) 192222. 0.762773
\(503\) 451517.i 1.78459i 0.451455 + 0.892294i \(0.350905\pi\)
−0.451455 + 0.892294i \(0.649095\pi\)
\(504\) −91339.1 + 253820.i −0.359580 + 0.999230i
\(505\) −605444. −2.37406
\(506\) 99251.6i 0.387647i
\(507\) −10738.5 + 61555.5i −0.0417762 + 0.239470i
\(508\) −28454.2 −0.110260
\(509\) 171453.i 0.661773i 0.943670 + 0.330887i \(0.107348\pi\)
−0.943670 + 0.330887i \(0.892652\pi\)
\(510\) 328162. + 57248.7i 1.26168 + 0.220103i
\(511\) −129700. −0.496703
\(512\) 291473.i 1.11188i
\(513\) −501.830 + 880.250i −0.00190687 + 0.00334481i
\(514\) −247452. −0.936622
\(515\) 190478.i 0.718176i
\(516\) −1040.97 + 5967.06i −0.00390966 + 0.0224110i
\(517\) −134416. −0.502887
\(518\) 256322.i 0.955270i
\(519\) 395558. + 69006.1i 1.46850 + 0.256185i
\(520\) 427584. 1.58130
\(521\) 497867.i 1.83416i −0.398701 0.917081i \(-0.630539\pi\)
0.398701 0.917081i \(-0.369461\pi\)
\(522\) −343947. 123772.i −1.26226 0.454235i
\(523\) 93268.9 0.340984 0.170492 0.985359i \(-0.445464\pi\)
0.170492 + 0.985359i \(0.445464\pi\)
\(524\) 106301.i 0.387146i
\(525\) −34718.0 + 199011.i −0.125961 + 0.722036i
\(526\) −343511. −1.24156
\(527\) 11491.9i 0.0413781i
\(528\) −245323. 42797.4i −0.879977 0.153514i
\(529\) 242369. 0.866095
\(530\) 386064.i 1.37438i
\(531\) −12429.4 + 34539.8i −0.0440820 + 0.122499i
\(532\) 222.044 0.000784540
\(533\) 371697.i 1.30838i
\(534\) −17358.0 + 99499.5i −0.0608718 + 0.348930i
\(535\) −33336.9 −0.116471
\(536\) 329772.i 1.14785i
\(537\) −373989. 65243.4i −1.29691 0.226250i
\(538\) −221579. −0.765532
\(539\) 8123.29i 0.0279611i
\(540\) −68939.3 39302.3i −0.236417 0.134782i
\(541\) −239967. −0.819891 −0.409946 0.912110i \(-0.634452\pi\)
−0.409946 + 0.912110i \(0.634452\pi\)
\(542\) 112114.i 0.381648i
\(543\) 93397.7 535375.i 0.316764 1.81576i
\(544\) 130652. 0.441486
\(545\) 106953.i 0.360079i
\(546\) 288279. + 50291.0i 0.967001 + 0.168696i
\(547\) −305510. −1.02106 −0.510529 0.859860i \(-0.670551\pi\)
−0.510529 + 0.859860i \(0.670551\pi\)
\(548\) 27567.5i 0.0917985i
\(549\) 428751. + 154289.i 1.42253 + 0.511906i
\(550\) −237684. −0.785731
\(551\) 1760.04i 0.00579723i
\(552\) −20593.0 + 118044.i −0.0675838 + 0.387404i
\(553\) −344429. −1.12629
\(554\) 329393.i 1.07323i
\(555\) 434514. + 75802.2i 1.41065 + 0.246091i
\(556\) −22712.1 −0.0734695
\(557\) 351391.i 1.13261i −0.824196 0.566305i \(-0.808373\pi\)
0.824196 0.566305i \(-0.191627\pi\)
\(558\) 3568.33 9915.97i 0.0114603 0.0318469i
\(559\) 38436.5 0.123004
\(560\) 307252.i 0.979758i
\(561\) 70047.4 401527.i 0.222570 1.27582i
\(562\) −98119.5 −0.310658
\(563\) 234536.i 0.739934i −0.929045 0.369967i \(-0.879369\pi\)
0.929045 0.369967i \(-0.120631\pi\)
\(564\) 27329.8 + 4767.76i 0.0859168 + 0.0149884i
\(565\) −489756. −1.53420
\(566\) 334441.i 1.04397i
\(567\) −244841. 202429.i −0.761583 0.629662i
\(568\) −250588. −0.776718
\(569\) 111484.i 0.344340i −0.985067 0.172170i \(-0.944922\pi\)
0.985067 0.172170i \(-0.0550778\pi\)
\(570\) 252.779 1448.98i 0.000778021 0.00445978i
\(571\) 12151.4 0.0372696 0.0186348 0.999826i \(-0.494068\pi\)
0.0186348 + 0.999826i \(0.494068\pi\)
\(572\) 89439.1i 0.273360i
\(573\) −453870. 79178.9i −1.38236 0.241157i
\(574\) 340403. 1.03317
\(575\) 89736.9i 0.271416i
\(576\) 347266. + 124966.i 1.04669 + 0.376658i
\(577\) 414975. 1.24644 0.623218 0.782048i \(-0.285825\pi\)
0.623218 + 0.782048i \(0.285825\pi\)
\(578\) 55482.0i 0.166072i
\(579\) 34070.6 195300.i 0.101630 0.582565i
\(580\) −137843. −0.409759
\(581\) 476790.i 1.41246i
\(582\) 412047. + 71882.7i 1.21647 + 0.212216i
\(583\) −472374. −1.38979
\(584\) 184232.i 0.540182i
\(585\) −170506. + 473814.i −0.498226 + 1.38451i
\(586\) 339946. 0.989953
\(587\) 325482.i 0.944606i −0.881436 0.472303i \(-0.843423\pi\)
0.881436 0.472303i \(-0.156577\pi\)
\(588\) 288.134 1651.65i 0.000833375 0.00477708i
\(589\) −50.7420 −0.000146264
\(590\) 53286.9i 0.153079i
\(591\) −203576. 35514.3i −0.582842 0.101678i
\(592\) −285681. −0.815150
\(593\) 208866.i 0.593962i −0.954883 0.296981i \(-0.904020\pi\)
0.954883 0.296981i \(-0.0959798\pi\)
\(594\) 185119. 324713.i 0.524660 0.920295i
\(595\) 502887. 1.42048
\(596\) 102931.i 0.289770i
\(597\) −59185.0 + 339261.i −0.166059 + 0.951887i
\(598\) 129989. 0.363499
\(599\) 199894.i 0.557116i −0.960419 0.278558i \(-0.910144\pi\)
0.960419 0.278558i \(-0.0898565\pi\)
\(600\) 282686. + 49315.3i 0.785239 + 0.136987i
\(601\) 110370. 0.305565 0.152782 0.988260i \(-0.451177\pi\)
0.152782 + 0.988260i \(0.451177\pi\)
\(602\) 35200.5i 0.0971306i
\(603\) 365427. + 131501.i 1.00500 + 0.361656i
\(604\) 33149.7 0.0908669
\(605\) 199856.i 0.546018i
\(606\) −101151. + 579818.i −0.275438 + 1.57887i
\(607\) −671627. −1.82285 −0.911425 0.411466i \(-0.865017\pi\)
−0.911425 + 0.411466i \(0.865017\pi\)
\(608\) 576.886i 0.00156057i
\(609\) −543621. 94836.1i −1.46575 0.255705i
\(610\) −661462. −1.77764
\(611\) 176043.i 0.471560i
\(612\) −28484.4 + 79154.7i −0.0760509 + 0.211336i
\(613\) 400715. 1.06639 0.533193 0.845993i \(-0.320992\pi\)
0.533193 + 0.845993i \(0.320992\pi\)
\(614\) 122132.i 0.323961i
\(615\) −100668. + 577048.i −0.266158 + 1.52567i
\(616\) −479129. −1.26267
\(617\) 353491.i 0.928556i 0.885690 + 0.464278i \(0.153686\pi\)
−0.885690 + 0.464278i \(0.846314\pi\)
\(618\) −182416. 31823.0i −0.477624 0.0833229i
\(619\) 106626. 0.278279 0.139139 0.990273i \(-0.455566\pi\)
0.139139 + 0.990273i \(0.455566\pi\)
\(620\) 3974.00i 0.0103382i
\(621\) −122595. 69891.3i −0.317899 0.181234i
\(622\) −489876. −1.26621
\(623\) 152477.i 0.392850i
\(624\) 56051.3 321298.i 0.143952 0.825161i
\(625\) −465459. −1.19157
\(626\) 527022.i 1.34487i
\(627\) −1772.92 309.291i −0.00450977 0.000786742i
\(628\) 109558. 0.277794
\(629\) 467580.i 1.18183i
\(630\) 433924. + 156151.i 1.09328 + 0.393425i
\(631\) −699848. −1.75770 −0.878851 0.477097i \(-0.841689\pi\)
−0.878851 + 0.477097i \(0.841689\pi\)
\(632\) 489245.i 1.22488i
\(633\) −53528.3 + 306836.i −0.133591 + 0.765770i
\(634\) −376429. −0.936492
\(635\) 284547.i 0.705678i
\(636\) 96044.1 + 16755.2i 0.237441 + 0.0414223i
\(637\) −10639.0 −0.0262193
\(638\) 649258.i 1.59506i
\(639\) 99925.7 277681.i 0.244723 0.680057i
\(640\) −316646. −0.773061
\(641\) 300253.i 0.730754i 0.930860 + 0.365377i \(0.119060\pi\)
−0.930860 + 0.365377i \(0.880940\pi\)
\(642\) −5569.57 + 31925.9i −0.0135130 + 0.0774593i
\(643\) 466427. 1.12814 0.564069 0.825728i \(-0.309235\pi\)
0.564069 + 0.825728i \(0.309235\pi\)
\(644\) 30924.6i 0.0745646i
\(645\) 59671.6 + 10409.9i 0.143433 + 0.0250222i
\(646\) −1559.25 −0.00373638
\(647\) 107628.i 0.257109i −0.991702 0.128554i \(-0.958966\pi\)
0.991702 0.128554i \(-0.0410336\pi\)
\(648\) −287541. + 347785.i −0.684779 + 0.828248i
\(649\) −65199.9 −0.154795
\(650\) 311292.i 0.736785i
\(651\) 2734.12 15672.6i 0.00645142 0.0369809i
\(652\) 55566.6 0.130713
\(653\) 509956.i 1.19593i 0.801522 + 0.597966i \(0.204024\pi\)
−0.801522 + 0.597966i \(0.795976\pi\)
\(654\) −102426. 17868.4i −0.239471 0.0417764i
\(655\) 1.06303e6 2.47778
\(656\) 379393.i 0.881620i
\(657\) −204152. 73465.4i −0.472957 0.170197i
\(658\) −161222. −0.372369
\(659\) 547617.i 1.26097i −0.776200 0.630486i \(-0.782855\pi\)
0.776200 0.630486i \(-0.217145\pi\)
\(660\) 24223.1 138852.i 0.0556085 0.318760i
\(661\) 341882. 0.782480 0.391240 0.920289i \(-0.372046\pi\)
0.391240 + 0.920289i \(0.372046\pi\)
\(662\) 508551.i 1.16043i
\(663\) 525876. + 91740.4i 1.19634 + 0.208705i
\(664\) 677258. 1.53609
\(665\) 2220.47i 0.00502114i
\(666\) 145188. 403459.i 0.327326 0.909601i
\(667\) −245126. −0.550983
\(668\) 155761.i 0.349064i
\(669\) −90272.7 + 517462.i −0.201699 + 1.15618i
\(670\) −563768. −1.25589
\(671\) 809340.i 1.79757i
\(672\) 178181. + 31084.2i 0.394570 + 0.0688338i
\(673\) −318066. −0.702244 −0.351122 0.936330i \(-0.614200\pi\)
−0.351122 + 0.936330i \(0.614200\pi\)
\(674\) 357536.i 0.787046i
\(675\) −167373. + 293585.i −0.367347 + 0.644356i
\(676\) 22906.3 0.0501259
\(677\) 793472.i 1.73123i −0.500711 0.865615i \(-0.666928\pi\)
0.500711 0.865615i \(-0.333072\pi\)
\(678\) −81823.0 + 469027.i −0.177998 + 1.02032i
\(679\) 631435. 1.36959
\(680\) 714327.i 1.54482i
\(681\) 165386. + 28852.1i 0.356619 + 0.0622132i
\(682\) 18718.1 0.0402432
\(683\) 208408.i 0.446759i 0.974732 + 0.223379i \(0.0717089\pi\)
−0.974732 + 0.223379i \(0.928291\pi\)
\(684\) 349.504 + 125.772i 0.000747034 + 0.000268825i
\(685\) 275679. 0.587520
\(686\) 424062.i 0.901117i
\(687\) 111255. 637740.i 0.235726 1.35123i
\(688\) −39232.4 −0.0828834
\(689\) 618663.i 1.30321i
\(690\) 201804. + 35205.2i 0.423869 + 0.0739451i
\(691\) 543662. 1.13860 0.569302 0.822128i \(-0.307213\pi\)
0.569302 + 0.822128i \(0.307213\pi\)
\(692\) 147197.i 0.307388i
\(693\) 191060. 530933.i 0.397836 1.10554i
\(694\) 646720. 1.34276
\(695\) 227124.i 0.470212i
\(696\) −134710. + 772187.i −0.278088 + 1.59406i
\(697\) 620961. 1.27820
\(698\) 533614.i 1.09526i
\(699\) −644673. 112465.i −1.31943 0.230178i
\(700\) 74057.0 0.151137
\(701\) 72520.4i 0.147579i 0.997274 + 0.0737894i \(0.0235093\pi\)
−0.997274 + 0.0737894i \(0.976491\pi\)
\(702\) 425274. + 242448.i 0.862967 + 0.491978i
\(703\) −2064.58 −0.00417754
\(704\) 655524.i 1.32264i
\(705\) 47678.3 273302.i 0.0959274 0.549876i
\(706\) 104395. 0.209445
\(707\) 888534.i 1.77761i
\(708\) 13256.6 + 2312.65i 0.0264463 + 0.00461363i
\(709\) 112277. 0.223356 0.111678 0.993744i \(-0.464378\pi\)
0.111678 + 0.993744i \(0.464378\pi\)
\(710\) 428397.i 0.849826i
\(711\) −542142. 195094.i −1.07244 0.385926i
\(712\) 216586. 0.427238
\(713\) 7066.97i 0.0139013i
\(714\) 84016.7 481602.i 0.164805 0.944695i
\(715\) −894406. −1.74953
\(716\) 139171.i 0.271470i
\(717\) 246486. + 43000.2i 0.479462 + 0.0836434i
\(718\) 35790.4 0.0694254
\(719\) 315016.i 0.609361i 0.952455 + 0.304681i \(0.0985498\pi\)
−0.952455 + 0.304681i \(0.901450\pi\)
\(720\) 174036. 483625.i 0.335717 0.932918i
\(721\) −279541. −0.537743
\(722\) 464432.i 0.890938i
\(723\) −74644.3 + 427877.i −0.142797 + 0.818545i
\(724\) −199226. −0.380076
\(725\) 587018.i 1.11680i
\(726\) 191397. + 33389.8i 0.363130 + 0.0633491i
\(727\) −886179. −1.67669 −0.838345 0.545141i \(-0.816476\pi\)
−0.838345 + 0.545141i \(0.816476\pi\)
\(728\) 627511.i 1.18402i
\(729\) −270726. 457315.i −0.509418 0.860519i
\(730\) 314958. 0.591026
\(731\) 64212.5i 0.120167i
\(732\) 28707.4 164557.i 0.0535762 0.307110i
\(733\) 530184. 0.986775 0.493388 0.869810i \(-0.335758\pi\)
0.493388 + 0.869810i \(0.335758\pi\)
\(734\) 498220.i 0.924760i
\(735\) −16516.7 2881.39i −0.0305738 0.00533368i
\(736\) 80344.5 0.148320
\(737\) 689806.i 1.26996i
\(738\) 535806. + 192814.i 0.983773 + 0.354018i
\(739\) 703143. 1.28752 0.643761 0.765226i \(-0.277373\pi\)
0.643761 + 0.765226i \(0.277373\pi\)
\(740\) 161694.i 0.295277i
\(741\) 405.076 2321.98i 0.000737734 0.00422885i
\(742\) −566577. −1.02909
\(743\) 201327.i 0.364690i −0.983235 0.182345i \(-0.941631\pi\)
0.983235 0.182345i \(-0.0583688\pi\)
\(744\) −22262.1 3883.69i −0.0402180 0.00701614i
\(745\) −1.02932e6 −1.85456
\(746\) 430001.i 0.772666i
\(747\) −270067. + 750483.i −0.483983 + 1.34493i
\(748\) −149418. −0.267055
\(749\) 48924.4i 0.0872092i
\(750\) −29358.5 + 168289.i −0.0521929 + 0.299181i
\(751\) 362775. 0.643217 0.321609 0.946873i \(-0.395776\pi\)
0.321609 + 0.946873i \(0.395776\pi\)
\(752\) 179688.i 0.317749i
\(753\) 478213. + 83425.6i 0.843396 + 0.147133i
\(754\) 850327. 1.49570
\(755\) 331503.i 0.581558i
\(756\) −57679.0 + 101174.i −0.100919 + 0.177021i
\(757\) 494359. 0.862682 0.431341 0.902189i \(-0.358041\pi\)
0.431341 + 0.902189i \(0.358041\pi\)
\(758\) 573704.i 0.998503i
\(759\) 43075.9 246920.i 0.0747740 0.428620i
\(760\) −3154.08 −0.00546066
\(761\) 1.04816e6i 1.80992i −0.425498 0.904959i \(-0.639901\pi\)
0.425498 0.904959i \(-0.360099\pi\)
\(762\) 272504. + 47539.0i 0.469313 + 0.0818729i
\(763\) −156961. −0.269614
\(764\) 168896.i 0.289357i
\(765\) 791560. + 284849.i 1.35257 + 0.486734i
\(766\) 954386. 1.62655
\(767\) 85391.6i 0.145153i
\(768\) 59856.9 343113.i 0.101483 0.581720i
\(769\) −145986. −0.246865 −0.123432 0.992353i \(-0.539390\pi\)
−0.123432 + 0.992353i \(0.539390\pi\)
\(770\) 819105.i 1.38152i
\(771\) −615615. 107396.i −1.03562 0.180667i
\(772\) −72675.9 −0.121943
\(773\) 929338.i 1.55530i 0.628696 + 0.777651i \(0.283589\pi\)
−0.628696 + 0.777651i \(0.716411\pi\)
\(774\) 19938.5 55406.8i 0.0332822 0.0924871i
\(775\) −16923.7 −0.0281768
\(776\) 896924.i 1.48947i
\(777\) 111245. 637682.i 0.184264 1.05624i
\(778\) −9611.72 −0.0158797
\(779\) 2741.82i 0.00451819i
\(780\) 181853. + 31724.7i 0.298903 + 0.0521445i
\(781\) 524171. 0.859352
\(782\) 217161.i 0.355114i
\(783\) −801959. 457197.i −1.30806 0.745726i
\(784\) 10859.3 0.0176672
\(785\) 1.09559e6i 1.77791i
\(786\) 177599. 1.01804e6i 0.287472 1.64785i
\(787\) 1.09920e6 1.77470 0.887352 0.461092i \(-0.152542\pi\)
0.887352 + 0.461092i \(0.152542\pi\)
\(788\) 75755.6i 0.122001i
\(789\) −854592. 149086.i −1.37279 0.239487i
\(790\) 836398. 1.34017
\(791\) 718753.i 1.14875i
\(792\) −754166. 271392.i −1.20231 0.432660i
\(793\) −1.05998e6 −1.68560
\(794\) 124376.i 0.197286i
\(795\) 167554. 960456.i 0.265107 1.51965i
\(796\) 126248. 0.199249
\(797\) 871729.i 1.37235i 0.727437 + 0.686175i \(0.240711\pi\)
−0.727437 + 0.686175i \(0.759289\pi\)
\(798\) −2126.49 370.972i −0.00333932 0.000582553i
\(799\) −294100. −0.460683
\(800\) 192406.i 0.300634i
\(801\) −86366.9 + 240003.i −0.134612 + 0.374069i
\(802\) 217769. 0.338569
\(803\) 385371.i 0.597651i
\(804\) 24467.5 140253.i 0.0378510 0.216970i
\(805\) 309251. 0.477222
\(806\) 24514.9i 0.0377363i
\(807\) −551248. 96166.6i −0.846447 0.147665i
\(808\) 1.26212e6 1.93321
\(809\) 631887.i 0.965478i 0.875764 + 0.482739i \(0.160358\pi\)
−0.875764 + 0.482739i \(0.839642\pi\)
\(810\) 594562. + 491572.i 0.906207 + 0.749234i
\(811\) −1.25367e6 −1.90608 −0.953042 0.302839i \(-0.902065\pi\)
−0.953042 + 0.302839i \(0.902065\pi\)
\(812\) 202295.i 0.306812i
\(813\) −48658.4 + 278920.i −0.0736168 + 0.421987i
\(814\) 761598. 1.14942
\(815\) 555675.i 0.836576i
\(816\) −536764. 93640.0i −0.806126 0.140631i
\(817\) −283.528 −0.000424767
\(818\) 873783.i 1.30586i
\(819\) 695358. + 250230.i 1.03667 + 0.373053i
\(820\) 214734. 0.319355
\(821\) 891043.i 1.32194i −0.750411 0.660971i \(-0.770145\pi\)
0.750411 0.660971i \(-0.229855\pi\)
\(822\) 46057.4 264011.i 0.0681641 0.390731i
\(823\) −577380. −0.852436 −0.426218 0.904620i \(-0.640154\pi\)
−0.426218 + 0.904620i \(0.640154\pi\)
\(824\) 397075.i 0.584814i
\(825\) −591313. 103156.i −0.868780 0.151561i
\(826\) −78202.5 −0.114620
\(827\) 978522.i 1.43074i −0.698747 0.715368i \(-0.746259\pi\)
0.698747 0.715368i \(-0.253741\pi\)
\(828\) −17516.6 + 48676.4i −0.0255498 + 0.0709999i
\(829\) −1.22664e6 −1.78488 −0.892439 0.451169i \(-0.851007\pi\)
−0.892439 + 0.451169i \(0.851007\pi\)
\(830\) 1.15782e6i 1.68068i
\(831\) −142959. + 819469.i −0.207018 + 1.18667i
\(832\) −858533. −1.24025
\(833\) 17773.6i 0.0256145i
\(834\) 217511. + 37945.4i 0.312715 + 0.0545541i
\(835\) 1.55763e6 2.23404
\(836\) 659.749i 0.000943987i
\(837\) 13181.0 23120.4i 0.0188146 0.0330024i
\(838\) −318436. −0.453455
\(839\) 221493.i 0.314657i 0.987546 + 0.157328i \(0.0502881\pi\)
−0.987546 + 0.157328i \(0.949712\pi\)
\(840\) 169951. 974193.i 0.240860 1.38066i
\(841\) −896222. −1.26714
\(842\) 490434.i 0.691762i
\(843\) −244103. 42584.5i −0.343494 0.0599234i
\(844\) 114181. 0.160291
\(845\) 229067.i 0.320811i
\(846\) −253769. 91320.7i −0.354567 0.127593i
\(847\) 293304. 0.408838
\(848\) 631473.i 0.878138i
\(849\) 145150. 832028.i 0.201373 1.15431i
\(850\) −520048. −0.719790
\(851\) 287540.i 0.397044i
\(852\) −106576. 18592.4i −0.146818 0.0256128i
\(853\) 1.07567e6 1.47836 0.739179 0.673509i \(-0.235214\pi\)
0.739179 + 0.673509i \(0.235214\pi\)
\(854\) 970744.i 1.33103i
\(855\) 1257.74 3495.10i 0.00172051 0.00478109i
\(856\) 69494.9 0.0948430
\(857\) 967907.i 1.31787i −0.752200 0.658934i \(-0.771007\pi\)
0.752200 0.658934i \(-0.228993\pi\)
\(858\) −149427. + 856550.i −0.202981 + 1.16353i
\(859\) 476618. 0.645928 0.322964 0.946411i \(-0.395321\pi\)
0.322964 + 0.946411i \(0.395321\pi\)
\(860\) 22205.3i 0.0300234i
\(861\) 846861. + 147737.i 1.14237 + 0.199289i
\(862\) −929156. −1.25047
\(863\) 682724.i 0.916692i −0.888774 0.458346i \(-0.848442\pi\)
0.888774 0.458346i \(-0.151558\pi\)
\(864\) 262856. + 149854.i 0.352120 + 0.200744i
\(865\) −1.47199e6 −1.96731
\(866\) 795584.i 1.06084i
\(867\) 24079.6 138029.i 0.0320340 0.183625i
\(868\) −5832.15 −0.00774086
\(869\) 1.02339e6i 1.35519i
\(870\) 1.32011e6 + 230297.i 1.74410 + 0.304263i
\(871\) −903431. −1.19085
\(872\) 222955.i 0.293214i
\(873\) 993900. + 357662.i 1.30411 + 0.469294i
\(874\) −958.865 −0.00125526
\(875\) 257892.i 0.336839i
\(876\) −13669.2 + 78354.5i −0.0178129 + 0.102107i
\(877\) −716340. −0.931365 −0.465683 0.884952i \(-0.654191\pi\)
−0.465683 + 0.884952i \(0.654191\pi\)
\(878\) 751571.i 0.974947i
\(879\) 845724. + 147539.i 1.09459 + 0.190954i
\(880\) 912925. 1.17888
\(881\) 304540.i 0.392367i −0.980567 0.196183i \(-0.937145\pi\)
0.980567 0.196183i \(-0.0628548\pi\)
\(882\) −5518.87 + 15336.3i −0.00709435 + 0.0197143i
\(883\) 408396. 0.523794 0.261897 0.965096i \(-0.415652\pi\)
0.261897 + 0.965096i \(0.415652\pi\)
\(884\) 195691.i 0.250419i
\(885\) 23126.9 132568.i 0.0295277 0.169259i
\(886\) 335045. 0.426811
\(887\) 657288.i 0.835427i 0.908579 + 0.417713i \(0.137168\pi\)
−0.908579 + 0.417713i \(0.862832\pi\)
\(888\) −905797. 158019.i −1.14870 0.200393i
\(889\) 417594. 0.528385
\(890\) 370269.i 0.467452i
\(891\) 601470. 727485.i 0.757633 0.916365i
\(892\) 192561. 0.242013
\(893\) 1298.59i 0.00162843i
\(894\) −171968. + 985758.i −0.215166 + 1.23338i
\(895\) 1.39173e6 1.73744
\(896\) 464701.i 0.578839i
\(897\) 323389. + 56416.0i 0.401920 + 0.0701161i
\(898\) −897229. −1.11263
\(899\) 46228.9i 0.0571998i
\(900\) 116568. + 41947.9i 0.143911 + 0.0517876i
\(901\) −1.03355e6 −1.27315
\(902\) 1.01143e6i 1.24314i
\(903\) 15277.3 87572.5i 0.0187357 0.107397i
\(904\) 1.02096e6 1.24931
\(905\) 1.99230e6i 2.43252i
\(906\) −317472. 55383.8i −0.386766 0.0674724i
\(907\) 1.35437e6 1.64636 0.823179 0.567783i \(-0.192199\pi\)
0.823179 + 0.567783i \(0.192199\pi\)
\(908\) 61544.3i 0.0746477i
\(909\) −503290. + 1.39858e6i −0.609103 + 1.69262i
\(910\) −1.07277e6 −1.29546
\(911\) 29604.9i 0.0356719i 0.999841 + 0.0178360i \(0.00567766\pi\)
−0.999841 + 0.0178360i \(0.994322\pi\)
\(912\) −413.463 + 2370.06i −0.000497104 + 0.00284950i
\(913\) −1.41667e6 −1.69952
\(914\) 720439.i 0.862393i
\(915\) −1.64560e6 287079.i −1.96554 0.342893i
\(916\) −237319. −0.282840
\(917\) 1.56007e6i 1.85527i
\(918\) 405038. 710468.i 0.480629 0.843061i
\(919\) −792378. −0.938213 −0.469106 0.883142i \(-0.655424\pi\)
−0.469106 + 0.883142i \(0.655424\pi\)
\(920\) 439277.i 0.518995i
\(921\) 53006.2 303843.i 0.0624895 0.358203i
\(922\) −644642. −0.758327
\(923\) 686502.i 0.805821i
\(924\) −203775. 35549.1i −0.238675 0.0416375i
\(925\) −688588. −0.804778
\(926\) 432708.i 0.504630i
\(927\) −440007. 158340.i −0.512035 0.184260i
\(928\) 525577. 0.610295
\(929\) 678039.i 0.785639i 0.919616 + 0.392820i \(0.128500\pi\)
−0.919616 + 0.392820i \(0.871500\pi\)
\(930\) −6639.44 + 38058.7i −0.00767654 + 0.0440035i
\(931\) 78.4787 9.05425e−5
\(932\) 239899.i 0.276183i
\(933\) −1.21872e6 212610.i −1.40004 0.244242i
\(934\) 787189. 0.902372
\(935\) 1.49421e6i 1.70918i
\(936\) 355439. 987723.i 0.405708 1.12741i
\(937\) −1.48025e6 −1.68599 −0.842996 0.537920i \(-0.819210\pi\)
−0.842996 + 0.537920i \(0.819210\pi\)
\(938\) 827371.i 0.940361i
\(939\) −228731. + 1.31114e6i −0.259415 + 1.48702i
\(940\) −101703. −0.115100
\(941\) 149475.i 0.168807i 0.996432 + 0.0844034i \(0.0268984\pi\)
−0.996432 + 0.0844034i \(0.973102\pi\)
\(942\) −1.04922e6 183040.i −1.18240 0.206273i
\(943\) 381862. 0.429420
\(944\) 87159.7i 0.0978074i
\(945\) 1.01175e6 + 576800.i 1.13295 + 0.645894i
\(946\) 104590. 0.116871
\(947\) 533086.i 0.594425i 0.954811 + 0.297213i \(0.0960570\pi\)
−0.954811 + 0.297213i \(0.903943\pi\)
\(948\) −36299.6 + 208077.i −0.0403911 + 0.231530i
\(949\) 504717. 0.560422
\(950\) 2296.25i 0.00254432i
\(951\) −936486. 163373.i −1.03548 0.180642i
\(952\) −1.04833e6 −1.15671
\(953\) 551784.i 0.607552i −0.952743 0.303776i \(-0.901753\pi\)
0.952743 0.303776i \(-0.0982475\pi\)
\(954\) −891812. 320925.i −0.979888 0.352620i
\(955\) 1.68899e6 1.85191
\(956\) 91723.6i 0.100361i
\(957\) 281782. 1.61524e6i 0.307674 1.76365i
\(958\) −34499.8 −0.0375912
\(959\) 404580.i 0.439913i
\(960\) −1.33285e6 232519.i −1.44623 0.252299i
\(961\) −922188. −0.998557
\(962\) 997457.i 1.07781i
\(963\) −27712.1 + 77008.7i −0.0298825 + 0.0830400i
\(964\) 159224. 0.171338
\(965\) 726771.i 0.780446i
\(966\) 51666.3 296162.i 0.0553673 0.317377i
\(967\) 436427. 0.466723 0.233361 0.972390i \(-0.425027\pi\)
0.233361 + 0.972390i \(0.425027\pi\)
\(968\) 416625.i 0.444625i
\(969\) −3879.13 676.725i −0.00413130 0.000720716i
\(970\) −1.53335e6 −1.62967
\(971\) 61610.5i 0.0653456i −0.999466 0.0326728i \(-0.989598\pi\)
0.999466 0.0326728i \(-0.0104019\pi\)
\(972\) −148096. + 126580.i −0.156751 + 0.133977i
\(973\) 333322. 0.352077
\(974\) 1.53893e6i 1.62219i
\(975\) 135103. 774437.i 0.142120 0.814661i
\(976\) 1.08193e6 1.13580
\(977\) 432087.i 0.452671i 0.974049 + 0.226335i \(0.0726745\pi\)
−0.974049 + 0.226335i \(0.927325\pi\)
\(978\) −532156. 92836.0i −0.556367 0.0970597i
\(979\) −453047. −0.472692
\(980\) 6146.29i 0.00639972i
\(981\) −247061. 88906.9i −0.256724 0.0923841i
\(982\) 89308.9 0.0926130
\(983\) 901970.i 0.933437i −0.884406 0.466718i \(-0.845436\pi\)
0.884406 0.466718i \(-0.154564\pi\)
\(984\) 209854. 1.20293e6i 0.216734 1.24236i
\(985\) 757568. 0.780817
\(986\) 1.42057e6i 1.46119i
\(987\) −401092. 69971.5i −0.411727 0.0718269i
\(988\) −864.067 −0.000885184
\(989\) 39487.7i 0.0403709i
\(990\) −463964. + 1.28930e6i −0.473384 + 1.31548i
\(991\) 310140. 0.315799 0.157899 0.987455i \(-0.449528\pi\)
0.157899 + 0.987455i \(0.449528\pi\)
\(992\) 15152.3i 0.0153977i
\(993\) 220714. 1.26518e6i 0.223837 1.28308i
\(994\) 628705. 0.636318
\(995\) 1.26250e6i 1.27522i
\(996\) 288040. + 50249.3i 0.290358 + 0.0506537i
\(997\) 922449. 0.928008 0.464004 0.885833i \(-0.346412\pi\)
0.464004 + 0.885833i \(0.346412\pi\)
\(998\) 613641.i 0.616103i
\(999\) 536304. 940720.i 0.537378 0.942604i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.5.b.a.119.55 yes 78
3.2 odd 2 inner 177.5.b.a.119.24 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.5.b.a.119.24 78 3.2 odd 2 inner
177.5.b.a.119.55 yes 78 1.1 even 1 trivial