Properties

Label 177.5.b.a.119.27
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 119.27
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.52

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.69145i q^{2} +(-5.71505 + 6.95257i) q^{3} +8.75607 q^{4} -3.65373i q^{5} +(18.7125 + 15.3818i) q^{6} +22.3529 q^{7} -66.6298i q^{8} +(-15.6765 - 79.4685i) q^{9} +O(q^{10})\) \(q-2.69145i q^{2} +(-5.71505 + 6.95257i) q^{3} +8.75607 q^{4} -3.65373i q^{5} +(18.7125 + 15.3818i) q^{6} +22.3529 q^{7} -66.6298i q^{8} +(-15.6765 - 79.4685i) q^{9} -9.83386 q^{10} +122.947i q^{11} +(-50.0414 + 60.8772i) q^{12} -0.917855 q^{13} -60.1618i q^{14} +(25.4028 + 20.8813i) q^{15} -39.2340 q^{16} -352.419i q^{17} +(-213.886 + 42.1925i) q^{18} +133.579 q^{19} -31.9924i q^{20} +(-127.748 + 155.410i) q^{21} +330.905 q^{22} +754.157i q^{23} +(463.249 + 380.793i) q^{24} +611.650 q^{25} +2.47036i q^{26} +(642.102 + 345.175i) q^{27} +195.724 q^{28} -1370.31i q^{29} +(56.2009 - 68.3706i) q^{30} +1455.10 q^{31} -960.481i q^{32} +(-854.795 - 702.646i) q^{33} -948.519 q^{34} -81.6716i q^{35} +(-137.264 - 695.832i) q^{36} +1869.95 q^{37} -359.523i q^{38} +(5.24558 - 6.38145i) q^{39} -243.448 q^{40} -1118.01i q^{41} +(418.280 + 343.828i) q^{42} +1275.10 q^{43} +1076.53i q^{44} +(-290.357 + 57.2777i) q^{45} +2029.78 q^{46} -1079.01i q^{47} +(224.224 - 272.777i) q^{48} -1901.35 q^{49} -1646.23i q^{50} +(2450.22 + 2014.09i) q^{51} -8.03681 q^{52} +990.574i q^{53} +(929.022 - 1728.19i) q^{54} +449.214 q^{55} -1489.37i q^{56} +(-763.413 + 928.720i) q^{57} -3688.12 q^{58} -453.188i q^{59} +(222.429 + 182.838i) q^{60} +3408.91 q^{61} -3916.32i q^{62} +(-350.415 - 1776.35i) q^{63} -3212.83 q^{64} +3.35360i q^{65} +(-1891.14 + 2300.64i) q^{66} -5369.84 q^{67} -3085.81i q^{68} +(-5243.33 - 4310.04i) q^{69} -219.815 q^{70} +104.981i q^{71} +(-5294.98 + 1044.52i) q^{72} +10170.8 q^{73} -5032.89i q^{74} +(-3495.61 + 4252.54i) q^{75} +1169.63 q^{76} +2748.22i q^{77} +(-17.1754 - 14.1183i) q^{78} +4028.36 q^{79} +143.350i q^{80} +(-6069.50 + 2491.57i) q^{81} -3009.07 q^{82} +13445.0i q^{83} +(-1118.57 + 1360.78i) q^{84} -1287.64 q^{85} -3431.88i q^{86} +(9527.17 + 7831.38i) q^{87} +8191.92 q^{88} -1161.48i q^{89} +(154.160 + 781.482i) q^{90} -20.5167 q^{91} +6603.45i q^{92} +(-8315.94 + 10116.7i) q^{93} -2904.11 q^{94} -488.064i q^{95} +(6677.81 + 5489.19i) q^{96} -3664.47 q^{97} +5117.39i q^{98} +(9770.39 - 1927.37i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69145i 0.672864i −0.941708 0.336432i \(-0.890780\pi\)
0.941708 0.336432i \(-0.109220\pi\)
\(3\) −5.71505 + 6.95257i −0.635005 + 0.772508i
\(4\) 8.75607 0.547255
\(5\) 3.65373i 0.146149i −0.997326 0.0730747i \(-0.976719\pi\)
0.997326 0.0730747i \(-0.0232811\pi\)
\(6\) 18.7125 + 15.3818i 0.519792 + 0.427272i
\(7\) 22.3529 0.456182 0.228091 0.973640i \(-0.426752\pi\)
0.228091 + 0.973640i \(0.426752\pi\)
\(8\) 66.6298i 1.04109i
\(9\) −15.6765 79.4685i −0.193537 0.981093i
\(10\) −9.83386 −0.0983386
\(11\) 122.947i 1.01609i 0.861331 + 0.508044i \(0.169631\pi\)
−0.861331 + 0.508044i \(0.830369\pi\)
\(12\) −50.0414 + 60.8772i −0.347510 + 0.422759i
\(13\) −0.917855 −0.00543109 −0.00271555 0.999996i \(-0.500864\pi\)
−0.00271555 + 0.999996i \(0.500864\pi\)
\(14\) 60.1618i 0.306948i
\(15\) 25.4028 + 20.8813i 0.112902 + 0.0928056i
\(16\) −39.2340 −0.153258
\(17\) 352.419i 1.21944i −0.792616 0.609721i \(-0.791281\pi\)
0.792616 0.609721i \(-0.208719\pi\)
\(18\) −213.886 + 42.1925i −0.660142 + 0.130224i
\(19\) 133.579 0.370026 0.185013 0.982736i \(-0.440767\pi\)
0.185013 + 0.982736i \(0.440767\pi\)
\(20\) 31.9924i 0.0799809i
\(21\) −127.748 + 155.410i −0.289678 + 0.352404i
\(22\) 330.905 0.683689
\(23\) 754.157i 1.42563i 0.701354 + 0.712813i \(0.252579\pi\)
−0.701354 + 0.712813i \(0.747421\pi\)
\(24\) 463.249 + 380.793i 0.804251 + 0.661098i
\(25\) 611.650 0.978640
\(26\) 2.47036i 0.00365439i
\(27\) 642.102 + 345.175i 0.880799 + 0.473490i
\(28\) 195.724 0.249648
\(29\) 1370.31i 1.62938i −0.579896 0.814690i \(-0.696907\pi\)
0.579896 0.814690i \(-0.303093\pi\)
\(30\) 56.2009 68.3706i 0.0624455 0.0759673i
\(31\) 1455.10 1.51415 0.757074 0.653330i \(-0.226628\pi\)
0.757074 + 0.653330i \(0.226628\pi\)
\(32\) 960.481i 0.937970i
\(33\) −854.795 702.646i −0.784936 0.645221i
\(34\) −948.519 −0.820518
\(35\) 81.6716i 0.0666707i
\(36\) −137.264 695.832i −0.105914 0.536908i
\(37\) 1869.95 1.36593 0.682963 0.730453i \(-0.260691\pi\)
0.682963 + 0.730453i \(0.260691\pi\)
\(38\) 359.523i 0.248977i
\(39\) 5.24558 6.38145i 0.00344877 0.00419556i
\(40\) −243.448 −0.152155
\(41\) 1118.01i 0.665085i −0.943088 0.332543i \(-0.892093\pi\)
0.943088 0.332543i \(-0.107907\pi\)
\(42\) 418.280 + 343.828i 0.237120 + 0.194914i
\(43\) 1275.10 0.689618 0.344809 0.938673i \(-0.387944\pi\)
0.344809 + 0.938673i \(0.387944\pi\)
\(44\) 1076.53i 0.556059i
\(45\) −290.357 + 57.2777i −0.143386 + 0.0282853i
\(46\) 2029.78 0.959252
\(47\) 1079.01i 0.488461i −0.969717 0.244231i \(-0.921465\pi\)
0.969717 0.244231i \(-0.0785354\pi\)
\(48\) 224.224 272.777i 0.0973194 0.118393i
\(49\) −1901.35 −0.791898
\(50\) 1646.23i 0.658491i
\(51\) 2450.22 + 2014.09i 0.942029 + 0.774352i
\(52\) −8.03681 −0.00297219
\(53\) 990.574i 0.352643i 0.984333 + 0.176322i \(0.0564198\pi\)
−0.984333 + 0.176322i \(0.943580\pi\)
\(54\) 929.022 1728.19i 0.318594 0.592657i
\(55\) 449.214 0.148501
\(56\) 1489.37i 0.474927i
\(57\) −763.413 + 928.720i −0.234969 + 0.285848i
\(58\) −3688.12 −1.09635
\(59\) 453.188i 0.130189i
\(60\) 222.429 + 182.838i 0.0617859 + 0.0507883i
\(61\) 3408.91 0.916127 0.458064 0.888919i \(-0.348543\pi\)
0.458064 + 0.888919i \(0.348543\pi\)
\(62\) 3916.32i 1.01881i
\(63\) −350.415 1776.35i −0.0882880 0.447557i
\(64\) −3212.83 −0.784383
\(65\) 3.35360i 0.000793751i
\(66\) −1891.14 + 2300.64i −0.434146 + 0.528155i
\(67\) −5369.84 −1.19622 −0.598111 0.801413i \(-0.704082\pi\)
−0.598111 + 0.801413i \(0.704082\pi\)
\(68\) 3085.81i 0.667345i
\(69\) −5243.33 4310.04i −1.10131 0.905281i
\(70\) −219.815 −0.0448603
\(71\) 104.981i 0.0208255i 0.999946 + 0.0104128i \(0.00331454\pi\)
−0.999946 + 0.0104128i \(0.996685\pi\)
\(72\) −5294.98 + 1044.52i −1.02141 + 0.201489i
\(73\) 10170.8 1.90858 0.954292 0.298875i \(-0.0966113\pi\)
0.954292 + 0.298875i \(0.0966113\pi\)
\(74\) 5032.89i 0.919082i
\(75\) −3495.61 + 4252.54i −0.621442 + 0.756007i
\(76\) 1169.63 0.202499
\(77\) 2748.22i 0.463521i
\(78\) −17.1754 14.1183i −0.00282304 0.00232055i
\(79\) 4028.36 0.645467 0.322733 0.946490i \(-0.395398\pi\)
0.322733 + 0.946490i \(0.395398\pi\)
\(80\) 143.350i 0.0223985i
\(81\) −6069.50 + 2491.57i −0.925087 + 0.379755i
\(82\) −3009.07 −0.447512
\(83\) 13445.0i 1.95167i 0.218514 + 0.975834i \(0.429879\pi\)
−0.218514 + 0.975834i \(0.570121\pi\)
\(84\) −1118.57 + 1360.78i −0.158528 + 0.192855i
\(85\) −1287.64 −0.178221
\(86\) 3431.88i 0.464019i
\(87\) 9527.17 + 7831.38i 1.25871 + 1.03467i
\(88\) 8191.92 1.05784
\(89\) 1161.48i 0.146633i −0.997309 0.0733167i \(-0.976642\pi\)
0.997309 0.0733167i \(-0.0233584\pi\)
\(90\) 154.160 + 781.482i 0.0190321 + 0.0964793i
\(91\) −20.5167 −0.00247757
\(92\) 6603.45i 0.780181i
\(93\) −8315.94 + 10116.7i −0.961491 + 1.16969i
\(94\) −2904.11 −0.328668
\(95\) 488.064i 0.0540791i
\(96\) 6677.81 + 5489.19i 0.724589 + 0.595616i
\(97\) −3664.47 −0.389464 −0.194732 0.980856i \(-0.562384\pi\)
−0.194732 + 0.980856i \(0.562384\pi\)
\(98\) 5117.39i 0.532839i
\(99\) 9770.39 1927.37i 0.996877 0.196650i
\(100\) 5355.66 0.535566
\(101\) 1262.42i 0.123755i −0.998084 0.0618774i \(-0.980291\pi\)
0.998084 0.0618774i \(-0.0197088\pi\)
\(102\) 5420.83 6594.65i 0.521033 0.633857i
\(103\) −13300.7 −1.25372 −0.626861 0.779131i \(-0.715661\pi\)
−0.626861 + 0.779131i \(0.715661\pi\)
\(104\) 61.1565i 0.00565427i
\(105\) 567.827 + 466.757i 0.0515036 + 0.0423362i
\(106\) 2666.09 0.237281
\(107\) 8733.96i 0.762858i −0.924398 0.381429i \(-0.875432\pi\)
0.924398 0.381429i \(-0.124568\pi\)
\(108\) 5622.30 + 3022.37i 0.482021 + 0.259120i
\(109\) −14560.4 −1.22552 −0.612760 0.790269i \(-0.709941\pi\)
−0.612760 + 0.790269i \(0.709941\pi\)
\(110\) 1209.04i 0.0999206i
\(111\) −10686.9 + 13001.0i −0.867370 + 1.05519i
\(112\) −876.993 −0.0699134
\(113\) 4033.56i 0.315887i 0.987448 + 0.157943i \(0.0504864\pi\)
−0.987448 + 0.157943i \(0.949514\pi\)
\(114\) 2499.61 + 2054.69i 0.192337 + 0.158102i
\(115\) 2755.49 0.208354
\(116\) 11998.5i 0.891686i
\(117\) 14.3887 + 72.9406i 0.00105112 + 0.00532841i
\(118\) −1219.73 −0.0875994
\(119\) 7877.59i 0.556288i
\(120\) 1391.31 1692.59i 0.0966191 0.117541i
\(121\) −474.886 −0.0324353
\(122\) 9174.92i 0.616429i
\(123\) 7773.03 + 6389.47i 0.513784 + 0.422333i
\(124\) 12740.9 0.828624
\(125\) 4518.39i 0.289177i
\(126\) −4780.97 + 943.126i −0.301145 + 0.0594058i
\(127\) −21140.6 −1.31072 −0.655361 0.755316i \(-0.727484\pi\)
−0.655361 + 0.755316i \(0.727484\pi\)
\(128\) 6720.50i 0.410187i
\(129\) −7287.27 + 8865.25i −0.437911 + 0.532735i
\(130\) 9.02605 0.000534086
\(131\) 23279.6i 1.35654i 0.734812 + 0.678271i \(0.237270\pi\)
−0.734812 + 0.678271i \(0.762730\pi\)
\(132\) −7484.65 6152.42i −0.429560 0.353100i
\(133\) 2985.89 0.168799
\(134\) 14452.7i 0.804894i
\(135\) 1261.18 2346.07i 0.0692003 0.128728i
\(136\) −23481.6 −1.26955
\(137\) 119.342i 0.00635845i −0.999995 0.00317922i \(-0.998988\pi\)
0.999995 0.00317922i \(-0.00101198\pi\)
\(138\) −11600.3 + 14112.2i −0.609130 + 0.741030i
\(139\) −14867.4 −0.769494 −0.384747 0.923022i \(-0.625711\pi\)
−0.384747 + 0.923022i \(0.625711\pi\)
\(140\) 715.123i 0.0364858i
\(141\) 7501.90 + 6166.60i 0.377340 + 0.310175i
\(142\) 282.553 0.0140127
\(143\) 112.847i 0.00551847i
\(144\) 615.050 + 3117.87i 0.0296610 + 0.150360i
\(145\) −5006.74 −0.238133
\(146\) 27374.4i 1.28422i
\(147\) 10866.3 13219.3i 0.502859 0.611747i
\(148\) 16373.4 0.747509
\(149\) 29931.1i 1.34819i −0.738646 0.674093i \(-0.764535\pi\)
0.738646 0.674093i \(-0.235465\pi\)
\(150\) 11445.5 + 9408.27i 0.508690 + 0.418145i
\(151\) −17252.7 −0.756665 −0.378333 0.925670i \(-0.623502\pi\)
−0.378333 + 0.925670i \(0.623502\pi\)
\(152\) 8900.38i 0.385231i
\(153\) −28006.2 + 5524.69i −1.19639 + 0.236007i
\(154\) 7396.70 0.311886
\(155\) 5316.53i 0.221292i
\(156\) 45.9307 55.8765i 0.00188736 0.00229604i
\(157\) −34157.1 −1.38574 −0.692870 0.721063i \(-0.743654\pi\)
−0.692870 + 0.721063i \(0.743654\pi\)
\(158\) 10842.1i 0.434311i
\(159\) −6887.04 5661.18i −0.272420 0.223930i
\(160\) −3509.34 −0.137084
\(161\) 16857.6i 0.650345i
\(162\) 6705.96 + 16335.8i 0.255523 + 0.622457i
\(163\) 20800.0 0.782866 0.391433 0.920207i \(-0.371980\pi\)
0.391433 + 0.920207i \(0.371980\pi\)
\(164\) 9789.37i 0.363971i
\(165\) −2567.28 + 3123.19i −0.0942987 + 0.114718i
\(166\) 36186.7 1.31321
\(167\) 28532.1i 1.02306i −0.859265 0.511530i \(-0.829079\pi\)
0.859265 0.511530i \(-0.170921\pi\)
\(168\) 10355.0 + 8511.83i 0.366885 + 0.301581i
\(169\) −28560.2 −0.999971
\(170\) 3465.64i 0.119918i
\(171\) −2094.06 10615.4i −0.0716137 0.363030i
\(172\) 11164.9 0.377397
\(173\) 18222.1i 0.608843i 0.952537 + 0.304422i \(0.0984632\pi\)
−0.952537 + 0.304422i \(0.901537\pi\)
\(174\) 21077.8 25641.9i 0.696189 0.846940i
\(175\) 13672.2 0.446438
\(176\) 4823.69i 0.155723i
\(177\) 3150.82 + 2589.99i 0.100572 + 0.0826706i
\(178\) −3126.08 −0.0986643
\(179\) 38805.8i 1.21113i −0.795796 0.605565i \(-0.792947\pi\)
0.795796 0.605565i \(-0.207053\pi\)
\(180\) −2542.39 + 501.528i −0.0784687 + 0.0154792i
\(181\) 47165.8 1.43969 0.719847 0.694132i \(-0.244212\pi\)
0.719847 + 0.694132i \(0.244212\pi\)
\(182\) 55.2199i 0.00166706i
\(183\) −19482.1 + 23700.7i −0.581745 + 0.707715i
\(184\) 50249.3 1.48421
\(185\) 6832.31i 0.199629i
\(186\) 27228.5 + 22382.0i 0.787042 + 0.646953i
\(187\) 43328.7 1.23906
\(188\) 9447.90i 0.267313i
\(189\) 14352.9 + 7715.66i 0.401805 + 0.215998i
\(190\) −1313.60 −0.0363878
\(191\) 21370.2i 0.585790i −0.956145 0.292895i \(-0.905381\pi\)
0.956145 0.292895i \(-0.0946187\pi\)
\(192\) 18361.5 22337.5i 0.498087 0.605942i
\(193\) −65341.8 −1.75419 −0.877094 0.480318i \(-0.840521\pi\)
−0.877094 + 0.480318i \(0.840521\pi\)
\(194\) 9862.75i 0.262056i
\(195\) −23.3161 19.1660i −0.000613179 0.000504036i
\(196\) −16648.3 −0.433370
\(197\) 39380.4i 1.01472i 0.861733 + 0.507362i \(0.169379\pi\)
−0.861733 + 0.507362i \(0.830621\pi\)
\(198\) −5187.43 26296.6i −0.132319 0.670762i
\(199\) 8277.96 0.209034 0.104517 0.994523i \(-0.466670\pi\)
0.104517 + 0.994523i \(0.466670\pi\)
\(200\) 40754.2i 1.01885i
\(201\) 30688.9 37334.2i 0.759607 0.924091i
\(202\) −3397.75 −0.0832701
\(203\) 30630.4i 0.743294i
\(204\) 21454.3 + 17635.5i 0.515530 + 0.423768i
\(205\) −4084.90 −0.0972018
\(206\) 35798.3i 0.843584i
\(207\) 59931.7 11822.5i 1.39867 0.275911i
\(208\) 36.0111 0.000832357
\(209\) 16423.1i 0.375979i
\(210\) 1256.25 1528.28i 0.0284865 0.0346549i
\(211\) 67639.6 1.51927 0.759637 0.650347i \(-0.225377\pi\)
0.759637 + 0.650347i \(0.225377\pi\)
\(212\) 8673.54i 0.192986i
\(213\) −729.891 599.974i −0.0160879 0.0132243i
\(214\) −23507.1 −0.513299
\(215\) 4658.89i 0.100787i
\(216\) 22998.9 42783.2i 0.492947 0.916992i
\(217\) 32525.6 0.690727
\(218\) 39188.6i 0.824607i
\(219\) −58126.9 + 70713.5i −1.21196 + 1.47440i
\(220\) 3933.35 0.0812677
\(221\) 323.469i 0.00662291i
\(222\) 34991.5 + 28763.2i 0.709998 + 0.583622i
\(223\) −15502.3 −0.311737 −0.155868 0.987778i \(-0.549818\pi\)
−0.155868 + 0.987778i \(0.549818\pi\)
\(224\) 21469.6i 0.427885i
\(225\) −9588.52 48606.9i −0.189403 0.960137i
\(226\) 10856.1 0.212549
\(227\) 90194.1i 1.75036i 0.483802 + 0.875178i \(0.339256\pi\)
−0.483802 + 0.875178i \(0.660744\pi\)
\(228\) −6684.50 + 8131.95i −0.128588 + 0.156432i
\(229\) 44735.6 0.853066 0.426533 0.904472i \(-0.359735\pi\)
0.426533 + 0.904472i \(0.359735\pi\)
\(230\) 7416.27i 0.140194i
\(231\) −19107.2 15706.2i −0.358074 0.294338i
\(232\) −91303.5 −1.69633
\(233\) 9980.66i 0.183843i −0.995766 0.0919216i \(-0.970699\pi\)
0.995766 0.0919216i \(-0.0293009\pi\)
\(234\) 196.316 38.7266i 0.00358529 0.000707258i
\(235\) −3942.42 −0.0713883
\(236\) 3968.14i 0.0712465i
\(237\) −23022.3 + 28007.5i −0.409875 + 0.498628i
\(238\) −21202.2 −0.374306
\(239\) 36063.8i 0.631357i 0.948866 + 0.315679i \(0.102232\pi\)
−0.948866 + 0.315679i \(0.897768\pi\)
\(240\) −996.654 819.254i −0.0173030 0.0142232i
\(241\) 16694.2 0.287430 0.143715 0.989619i \(-0.454095\pi\)
0.143715 + 0.989619i \(0.454095\pi\)
\(242\) 1278.13i 0.0218246i
\(243\) 17364.6 56438.1i 0.294071 0.955784i
\(244\) 29848.7 0.501355
\(245\) 6947.02i 0.115735i
\(246\) 17197.0 20920.8i 0.284172 0.345706i
\(247\) −122.607 −0.00200965
\(248\) 96952.8i 1.57637i
\(249\) −93477.6 76839.0i −1.50768 1.23932i
\(250\) −12161.0 −0.194577
\(251\) 75734.9i 1.20212i 0.799203 + 0.601061i \(0.205255\pi\)
−0.799203 + 0.601061i \(0.794745\pi\)
\(252\) −3068.26 15553.9i −0.0483160 0.244928i
\(253\) −92721.1 −1.44856
\(254\) 56899.1i 0.881937i
\(255\) 7358.95 8952.44i 0.113171 0.137677i
\(256\) −69493.3 −1.06038
\(257\) 124405.i 1.88353i 0.336269 + 0.941766i \(0.390835\pi\)
−0.336269 + 0.941766i \(0.609165\pi\)
\(258\) 23860.4 + 19613.4i 0.358458 + 0.294654i
\(259\) 41798.9 0.623111
\(260\) 29.3643i 0.000434384i
\(261\) −108896. + 21481.6i −1.59857 + 0.315345i
\(262\) 62656.0 0.912767
\(263\) 86024.0i 1.24368i −0.783145 0.621839i \(-0.786386\pi\)
0.783145 0.621839i \(-0.213614\pi\)
\(264\) −46817.2 + 56954.9i −0.671734 + 0.817190i
\(265\) 3619.29 0.0515385
\(266\) 8036.38i 0.113579i
\(267\) 8075.29 + 6637.93i 0.113275 + 0.0931130i
\(268\) −47018.7 −0.654638
\(269\) 13233.4i 0.182880i 0.995811 + 0.0914402i \(0.0291470\pi\)
−0.995811 + 0.0914402i \(0.970853\pi\)
\(270\) −6314.34 3394.40i −0.0866165 0.0465624i
\(271\) 73836.8 1.00539 0.502695 0.864464i \(-0.332342\pi\)
0.502695 + 0.864464i \(0.332342\pi\)
\(272\) 13826.8i 0.186889i
\(273\) 117.254 142.644i 0.00157327 0.00191394i
\(274\) −321.203 −0.00427837
\(275\) 75200.4i 0.994385i
\(276\) −45911.0 37739.0i −0.602696 0.495419i
\(277\) 8134.35 0.106014 0.0530070 0.998594i \(-0.483119\pi\)
0.0530070 + 0.998594i \(0.483119\pi\)
\(278\) 40014.9i 0.517764i
\(279\) −22810.8 115634.i −0.293043 1.48552i
\(280\) −5441.76 −0.0694103
\(281\) 121574.i 1.53967i −0.638242 0.769835i \(-0.720338\pi\)
0.638242 0.769835i \(-0.279662\pi\)
\(282\) 16597.1 20191.0i 0.208706 0.253898i
\(283\) −7329.56 −0.0915177 −0.0457588 0.998953i \(-0.514571\pi\)
−0.0457588 + 0.998953i \(0.514571\pi\)
\(284\) 919.225i 0.0113969i
\(285\) 3393.30 + 2789.31i 0.0417765 + 0.0343405i
\(286\) −303.723 −0.00371318
\(287\) 24990.8i 0.303400i
\(288\) −76328.0 + 15057.0i −0.920236 + 0.181532i
\(289\) −40678.0 −0.487039
\(290\) 13475.4i 0.160231i
\(291\) 20942.6 25477.5i 0.247312 0.300864i
\(292\) 89056.7 1.04448
\(293\) 85397.0i 0.994735i 0.867540 + 0.497368i \(0.165700\pi\)
−0.867540 + 0.497368i \(0.834300\pi\)
\(294\) −35579.0 29246.1i −0.411623 0.338356i
\(295\) −1655.83 −0.0190270
\(296\) 124595.i 1.42205i
\(297\) −42438.1 + 78944.4i −0.481108 + 0.894969i
\(298\) −80558.1 −0.907145
\(299\) 692.207i 0.00774272i
\(300\) −30607.8 + 37235.6i −0.340087 + 0.413729i
\(301\) 28502.3 0.314591
\(302\) 46434.9i 0.509132i
\(303\) 8777.08 + 7214.80i 0.0956015 + 0.0785849i
\(304\) −5240.85 −0.0567093
\(305\) 12455.2i 0.133891i
\(306\) 14869.4 + 75377.4i 0.158800 + 0.805005i
\(307\) 22581.6 0.239595 0.119797 0.992798i \(-0.461776\pi\)
0.119797 + 0.992798i \(0.461776\pi\)
\(308\) 24063.6i 0.253664i
\(309\) 76014.4 92474.4i 0.796120 0.968511i
\(310\) −14309.2 −0.148899
\(311\) 63130.8i 0.652710i 0.945247 + 0.326355i \(0.105821\pi\)
−0.945247 + 0.326355i \(0.894179\pi\)
\(312\) −425.195 349.512i −0.00436796 0.00359049i
\(313\) −177713. −1.81397 −0.906985 0.421163i \(-0.861622\pi\)
−0.906985 + 0.421163i \(0.861622\pi\)
\(314\) 91932.2i 0.932413i
\(315\) −6490.32 + 1280.32i −0.0654101 + 0.0129032i
\(316\) 35272.6 0.353235
\(317\) 68993.3i 0.686576i 0.939230 + 0.343288i \(0.111541\pi\)
−0.939230 + 0.343288i \(0.888459\pi\)
\(318\) −15236.8 + 18536.1i −0.150674 + 0.183301i
\(319\) 168475. 1.65559
\(320\) 11738.8i 0.114637i
\(321\) 60723.5 + 49915.0i 0.589314 + 0.484419i
\(322\) 45371.5 0.437594
\(323\) 47075.9i 0.451225i
\(324\) −53145.0 + 21816.4i −0.506258 + 0.207823i
\(325\) −561.406 −0.00531509
\(326\) 55982.1i 0.526762i
\(327\) 83213.3 101232.i 0.778211 0.946723i
\(328\) −74492.7 −0.692415
\(329\) 24119.0i 0.222827i
\(330\) 8405.93 + 6909.72i 0.0771895 + 0.0634501i
\(331\) 58531.4 0.534236 0.267118 0.963664i \(-0.413929\pi\)
0.267118 + 0.963664i \(0.413929\pi\)
\(332\) 117726.i 1.06806i
\(333\) −29314.3 148602.i −0.264357 1.34010i
\(334\) −76792.9 −0.688380
\(335\) 19620.0i 0.174827i
\(336\) 5012.06 6097.36i 0.0443954 0.0540086i
\(337\) −169918. −1.49616 −0.748081 0.663608i \(-0.769024\pi\)
−0.748081 + 0.663608i \(0.769024\pi\)
\(338\) 76868.4i 0.672844i
\(339\) −28043.6 23052.0i −0.244025 0.200590i
\(340\) −11274.7 −0.0975321
\(341\) 178899.i 1.53851i
\(342\) −28570.8 + 5636.05i −0.244270 + 0.0481862i
\(343\) −96170.0 −0.817432
\(344\) 84959.9i 0.717955i
\(345\) −15747.7 + 19157.7i −0.132306 + 0.160955i
\(346\) 49043.9 0.409668
\(347\) 61581.2i 0.511434i 0.966752 + 0.255717i \(0.0823115\pi\)
−0.966752 + 0.255717i \(0.917688\pi\)
\(348\) 83420.6 + 68572.2i 0.688835 + 0.566225i
\(349\) 215132. 1.76626 0.883128 0.469132i \(-0.155433\pi\)
0.883128 + 0.469132i \(0.155433\pi\)
\(350\) 36798.0i 0.300392i
\(351\) −589.357 316.820i −0.00478370 0.00257157i
\(352\) 118088. 0.953060
\(353\) 47015.6i 0.377305i 0.982044 + 0.188653i \(0.0604120\pi\)
−0.982044 + 0.188653i \(0.939588\pi\)
\(354\) 6970.83 8480.28i 0.0556261 0.0676712i
\(355\) 383.574 0.00304364
\(356\) 10170.0i 0.0802458i
\(357\) 54769.5 + 45020.8i 0.429736 + 0.353245i
\(358\) −104444. −0.814926
\(359\) 36472.1i 0.282990i 0.989939 + 0.141495i \(0.0451910\pi\)
−0.989939 + 0.141495i \(0.954809\pi\)
\(360\) 3816.40 + 19346.4i 0.0294475 + 0.149278i
\(361\) −112478. −0.863081
\(362\) 126945.i 0.968718i
\(363\) 2713.99 3301.68i 0.0205966 0.0250565i
\(364\) −179.646 −0.00135586
\(365\) 37161.6i 0.278938i
\(366\) 63789.3 + 52435.1i 0.476196 + 0.391435i
\(367\) −97416.3 −0.723269 −0.361634 0.932320i \(-0.617781\pi\)
−0.361634 + 0.932320i \(0.617781\pi\)
\(368\) 29588.6i 0.218488i
\(369\) −88846.5 + 17526.4i −0.652511 + 0.128718i
\(370\) −18388.8 −0.134323
\(371\) 22142.2i 0.160869i
\(372\) −72815.0 + 88582.2i −0.526181 + 0.640119i
\(373\) 124860. 0.897440 0.448720 0.893672i \(-0.351880\pi\)
0.448720 + 0.893672i \(0.351880\pi\)
\(374\) 116617.i 0.833719i
\(375\) 31414.4 + 25822.8i 0.223391 + 0.183629i
\(376\) −71894.3 −0.508533
\(377\) 1257.75i 0.00884932i
\(378\) 20766.3 38630.1i 0.145337 0.270360i
\(379\) −133641. −0.930381 −0.465191 0.885211i \(-0.654014\pi\)
−0.465191 + 0.885211i \(0.654014\pi\)
\(380\) 4273.52i 0.0295950i
\(381\) 120820. 146982.i 0.832315 1.01254i
\(382\) −57516.9 −0.394157
\(383\) 22401.1i 0.152711i 0.997081 + 0.0763557i \(0.0243285\pi\)
−0.997081 + 0.0763557i \(0.975672\pi\)
\(384\) 46724.8 + 38408.0i 0.316873 + 0.260471i
\(385\) 10041.3 0.0677433
\(386\) 175864.i 1.18033i
\(387\) −19989.1 101331.i −0.133466 0.676579i
\(388\) −32086.4 −0.213136
\(389\) 128505.i 0.849218i −0.905377 0.424609i \(-0.860412\pi\)
0.905377 0.424609i \(-0.139588\pi\)
\(390\) −51.5843 + 62.7543i −0.000339147 + 0.000412586i
\(391\) 265779. 1.73847
\(392\) 126686.i 0.824438i
\(393\) −161853. 133044.i −1.04794 0.861411i
\(394\) 105991. 0.682771
\(395\) 14718.5i 0.0943346i
\(396\) 85550.3 16876.2i 0.545546 0.107618i
\(397\) 109933. 0.697501 0.348751 0.937216i \(-0.386606\pi\)
0.348751 + 0.937216i \(0.386606\pi\)
\(398\) 22279.7i 0.140651i
\(399\) −17064.5 + 20759.6i −0.107188 + 0.130399i
\(400\) −23997.5 −0.149984
\(401\) 196757.i 1.22361i 0.791010 + 0.611803i \(0.209555\pi\)
−0.791010 + 0.611803i \(0.790445\pi\)
\(402\) −100483. 82597.8i −0.621787 0.511112i
\(403\) −1335.57 −0.00822348
\(404\) 11053.9i 0.0677254i
\(405\) 9103.55 + 22176.3i 0.0555010 + 0.135201i
\(406\) −82440.3 −0.500135
\(407\) 229904.i 1.38790i
\(408\) 134198. 163258.i 0.806171 0.980738i
\(409\) 269066. 1.60847 0.804233 0.594315i \(-0.202577\pi\)
0.804233 + 0.594315i \(0.202577\pi\)
\(410\) 10994.3i 0.0654035i
\(411\) 829.732 + 682.044i 0.00491195 + 0.00403765i
\(412\) −116462. −0.686106
\(413\) 10130.1i 0.0593898i
\(414\) −31819.8 161303.i −0.185651 0.941116i
\(415\) 49124.6 0.285235
\(416\) 881.582i 0.00509420i
\(417\) 84967.8 103367.i 0.488633 0.594440i
\(418\) 44202.1 0.252983
\(419\) 209827.i 1.19518i −0.801802 0.597590i \(-0.796125\pi\)
0.801802 0.597590i \(-0.203875\pi\)
\(420\) 4971.94 + 4086.96i 0.0281856 + 0.0231687i
\(421\) −117308. −0.661854 −0.330927 0.943656i \(-0.607361\pi\)
−0.330927 + 0.943656i \(0.607361\pi\)
\(422\) 182049.i 1.02226i
\(423\) −85747.4 + 16915.1i −0.479226 + 0.0945352i
\(424\) 66001.8 0.367134
\(425\) 215557.i 1.19340i
\(426\) −1614.80 + 1964.47i −0.00889816 + 0.0108249i
\(427\) 76199.1 0.417921
\(428\) 76475.2i 0.417478i
\(429\) 784.578 + 644.927i 0.00426306 + 0.00350426i
\(430\) −12539.2 −0.0678160
\(431\) 160861.i 0.865959i −0.901404 0.432979i \(-0.857462\pi\)
0.901404 0.432979i \(-0.142538\pi\)
\(432\) −25192.2 13542.6i −0.134989 0.0725660i
\(433\) 83767.1 0.446784 0.223392 0.974729i \(-0.428287\pi\)
0.223392 + 0.974729i \(0.428287\pi\)
\(434\) 87541.2i 0.464765i
\(435\) 28613.8 34809.7i 0.151216 0.183960i
\(436\) −127492. −0.670671
\(437\) 100740.i 0.527519i
\(438\) 190322. + 156446.i 0.992068 + 0.815484i
\(439\) −100136. −0.519589 −0.259794 0.965664i \(-0.583655\pi\)
−0.259794 + 0.965664i \(0.583655\pi\)
\(440\) 29931.1i 0.154603i
\(441\) 29806.4 + 151097.i 0.153261 + 0.776926i
\(442\) 870.603 0.00445631
\(443\) 27661.8i 0.140953i 0.997513 + 0.0704764i \(0.0224519\pi\)
−0.997513 + 0.0704764i \(0.977548\pi\)
\(444\) −93575.0 + 113838.i −0.474672 + 0.577457i
\(445\) −4243.75 −0.0214304
\(446\) 41723.9i 0.209756i
\(447\) 208098. + 171058.i 1.04148 + 0.856105i
\(448\) −71816.2 −0.357822
\(449\) 215392.i 1.06840i 0.845357 + 0.534202i \(0.179388\pi\)
−0.845357 + 0.534202i \(0.820612\pi\)
\(450\) −130823. + 25807.1i −0.646041 + 0.127442i
\(451\) 137455. 0.675785
\(452\) 35318.1i 0.172871i
\(453\) 98600.1 119951.i 0.480486 0.584530i
\(454\) 242753. 1.17775
\(455\) 74.9627i 0.000362095i
\(456\) 61880.5 + 50866.1i 0.297594 + 0.244624i
\(457\) 47885.4 0.229282 0.114641 0.993407i \(-0.463428\pi\)
0.114641 + 0.993407i \(0.463428\pi\)
\(458\) 120404.i 0.573997i
\(459\) 121646. 226289.i 0.577394 1.07408i
\(460\) 24127.3 0.114023
\(461\) 61515.5i 0.289456i −0.989471 0.144728i \(-0.953769\pi\)
0.989471 0.144728i \(-0.0462308\pi\)
\(462\) −42272.5 + 51426.1i −0.198050 + 0.240935i
\(463\) 104362. 0.486833 0.243416 0.969922i \(-0.421732\pi\)
0.243416 + 0.969922i \(0.421732\pi\)
\(464\) 53762.7i 0.249715i
\(465\) 36963.6 + 30384.2i 0.170950 + 0.140521i
\(466\) −26862.5 −0.123701
\(467\) 262028.i 1.20147i −0.799447 0.600737i \(-0.794874\pi\)
0.799447 0.600737i \(-0.205126\pi\)
\(468\) 125.989 + 638.673i 0.000575228 + 0.00291600i
\(469\) −120032. −0.545695
\(470\) 10610.8i 0.0480346i
\(471\) 195209. 237480.i 0.879952 1.07049i
\(472\) −30195.8 −0.135539
\(473\) 156770.i 0.700712i
\(474\) 75380.8 + 61963.4i 0.335509 + 0.275790i
\(475\) 81703.9 0.362122
\(476\) 68976.7i 0.304431i
\(477\) 78719.5 15528.7i 0.345976 0.0682494i
\(478\) 97064.0 0.424817
\(479\) 191629.i 0.835198i 0.908631 + 0.417599i \(0.137128\pi\)
−0.908631 + 0.417599i \(0.862872\pi\)
\(480\) 20056.0 24398.9i 0.0870488 0.105898i
\(481\) −1716.35 −0.00741847
\(482\) 44931.7i 0.193401i
\(483\) −117204. 96342.0i −0.502397 0.412973i
\(484\) −4158.13 −0.0177504
\(485\) 13389.0i 0.0569199i
\(486\) −151900. 46736.1i −0.643112 0.197870i
\(487\) −244922. −1.03269 −0.516344 0.856381i \(-0.672708\pi\)
−0.516344 + 0.856381i \(0.672708\pi\)
\(488\) 227135.i 0.953772i
\(489\) −118873. + 144613.i −0.497124 + 0.604770i
\(490\) 18697.6 0.0778741
\(491\) 276138.i 1.14542i −0.819760 0.572708i \(-0.805893\pi\)
0.819760 0.572708i \(-0.194107\pi\)
\(492\) 68061.3 + 55946.7i 0.281171 + 0.231124i
\(493\) −482923. −1.98694
\(494\) 329.990i 0.00135222i
\(495\) −7042.10 35698.4i −0.0287403 0.145693i
\(496\) −57089.2 −0.232055
\(497\) 2346.64i 0.00950022i
\(498\) −206809. + 251591.i −0.833893 + 1.01446i
\(499\) −205373. −0.824786 −0.412393 0.911006i \(-0.635307\pi\)
−0.412393 + 0.911006i \(0.635307\pi\)
\(500\) 39563.4i 0.158253i
\(501\) 198372. + 163062.i 0.790322 + 0.649649i
\(502\) 203837. 0.808864
\(503\) 226075.i 0.893544i −0.894648 0.446772i \(-0.852573\pi\)
0.894648 0.446772i \(-0.147427\pi\)
\(504\) −118358. + 23348.1i −0.465948 + 0.0919159i
\(505\) −4612.55 −0.0180867
\(506\) 249554.i 0.974685i
\(507\) 163223. 198567.i 0.634986 0.772485i
\(508\) −185109. −0.717299
\(509\) 91546.0i 0.353349i 0.984269 + 0.176674i \(0.0565340\pi\)
−0.984269 + 0.176674i \(0.943466\pi\)
\(510\) −24095.1 19806.3i −0.0926377 0.0761487i
\(511\) 227348. 0.870662
\(512\) 79509.9i 0.303306i
\(513\) 85771.7 + 46108.2i 0.325919 + 0.175204i
\(514\) 334831. 1.26736
\(515\) 48597.4i 0.183231i
\(516\) −63807.9 + 77624.7i −0.239649 + 0.291542i
\(517\) 132661. 0.496320
\(518\) 112500.i 0.419268i
\(519\) −126690. 104140.i −0.470336 0.386619i
\(520\) 223.450 0.000826367
\(521\) 422512.i 1.55655i −0.627923 0.778276i \(-0.716095\pi\)
0.627923 0.778276i \(-0.283905\pi\)
\(522\) 57816.8 + 293090.i 0.212184 + 1.07562i
\(523\) −68616.0 −0.250855 −0.125427 0.992103i \(-0.540030\pi\)
−0.125427 + 0.992103i \(0.540030\pi\)
\(524\) 203838.i 0.742373i
\(525\) −78137.1 + 95056.7i −0.283491 + 0.344877i
\(526\) −231530. −0.836826
\(527\) 512803.i 1.84642i
\(528\) 33537.0 + 27567.6i 0.120297 + 0.0988851i
\(529\) −288911. −1.03241
\(530\) 9741.16i 0.0346784i
\(531\) −36014.2 + 7104.39i −0.127727 + 0.0251963i
\(532\) 26144.7 0.0923762
\(533\) 1026.17i 0.00361214i
\(534\) 17865.7 21734.3i 0.0626523 0.0762189i
\(535\) −31911.6 −0.111491
\(536\) 357792.i 1.24538i
\(537\) 269800. + 221777.i 0.935608 + 0.769074i
\(538\) 35617.1 0.123053
\(539\) 233764.i 0.804638i
\(540\) 11042.9 20542.4i 0.0378702 0.0704471i
\(541\) −12212.0 −0.0417245 −0.0208623 0.999782i \(-0.506641\pi\)
−0.0208623 + 0.999782i \(0.506641\pi\)
\(542\) 198728.i 0.676490i
\(543\) −269555. + 327924.i −0.914214 + 1.11218i
\(544\) −338492. −1.14380
\(545\) 53199.8i 0.179109i
\(546\) −383.920 315.584i −0.00128782 0.00105859i
\(547\) 249969. 0.835434 0.417717 0.908577i \(-0.362830\pi\)
0.417717 + 0.908577i \(0.362830\pi\)
\(548\) 1044.97i 0.00347969i
\(549\) −53439.7 270901.i −0.177304 0.898806i
\(550\) 202398. 0.669085
\(551\) 183045.i 0.602913i
\(552\) −287177. + 349362.i −0.942480 + 1.14656i
\(553\) 90045.6 0.294450
\(554\) 21893.2i 0.0713330i
\(555\) 47502.1 + 39047.0i 0.154215 + 0.126766i
\(556\) −130180. −0.421109
\(557\) 291658.i 0.940076i 0.882646 + 0.470038i \(0.155760\pi\)
−0.882646 + 0.470038i \(0.844240\pi\)
\(558\) −311224. + 61394.2i −0.999552 + 0.197178i
\(559\) −1170.36 −0.00374538
\(560\) 3204.30i 0.0102178i
\(561\) −247626. + 301246.i −0.786810 + 0.957184i
\(562\) −327211. −1.03599
\(563\) 564661.i 1.78144i 0.454553 + 0.890720i \(0.349799\pi\)
−0.454553 + 0.890720i \(0.650201\pi\)
\(564\) 65687.2 + 53995.2i 0.206501 + 0.169745i
\(565\) 14737.5 0.0461666
\(566\) 19727.2i 0.0615789i
\(567\) −135671. + 55693.9i −0.422008 + 0.173237i
\(568\) 6994.90 0.0216813
\(569\) 426831.i 1.31835i −0.751989 0.659175i \(-0.770905\pi\)
0.751989 0.659175i \(-0.229095\pi\)
\(570\) 7507.29 9132.90i 0.0231065 0.0281099i
\(571\) −410430. −1.25883 −0.629414 0.777070i \(-0.716705\pi\)
−0.629414 + 0.777070i \(0.716705\pi\)
\(572\) 988.099i 0.00302001i
\(573\) 148578. + 122132.i 0.452528 + 0.371980i
\(574\) −67261.5 −0.204147
\(575\) 461280.i 1.39518i
\(576\) 50365.9 + 255319.i 0.151807 + 0.769553i
\(577\) −7045.07 −0.0211609 −0.0105804 0.999944i \(-0.503368\pi\)
−0.0105804 + 0.999944i \(0.503368\pi\)
\(578\) 109483.i 0.327711i
\(579\) 373431. 454293.i 1.11392 1.35512i
\(580\) −43839.4 −0.130319
\(581\) 300536.i 0.890315i
\(582\) −68571.5 56366.1i −0.202441 0.166407i
\(583\) −121788. −0.358316
\(584\) 677682.i 1.98701i
\(585\) 266.505 52.5726i 0.000778743 0.000153620i
\(586\) 229842. 0.669321
\(587\) 93808.0i 0.272247i 0.990692 + 0.136124i \(0.0434645\pi\)
−0.990692 + 0.136124i \(0.956536\pi\)
\(588\) 95146.0 115749.i 0.275192 0.334782i
\(589\) 194371. 0.560274
\(590\) 4456.58i 0.0128026i
\(591\) −273795. 225061.i −0.783883 0.644355i
\(592\) −73365.6 −0.209339
\(593\) 364567.i 1.03674i 0.855158 + 0.518368i \(0.173460\pi\)
−0.855158 + 0.518368i \(0.826540\pi\)
\(594\) 212475. + 114220.i 0.602192 + 0.323720i
\(595\) −28782.6 −0.0813010
\(596\) 262079.i 0.737801i
\(597\) −47308.9 + 57553.1i −0.132738 + 0.161480i
\(598\) −1863.04 −0.00520979
\(599\) 100121.i 0.279043i 0.990219 + 0.139521i \(0.0445564\pi\)
−0.990219 + 0.139521i \(0.955444\pi\)
\(600\) 283346. + 232912.i 0.787073 + 0.646978i
\(601\) −148652. −0.411549 −0.205774 0.978599i \(-0.565971\pi\)
−0.205774 + 0.978599i \(0.565971\pi\)
\(602\) 76712.6i 0.211677i
\(603\) 84180.2 + 426733.i 0.231513 + 1.17361i
\(604\) −151066. −0.414089
\(605\) 1735.11i 0.00474040i
\(606\) 19418.3 23623.1i 0.0528769 0.0643268i
\(607\) 222267. 0.603251 0.301626 0.953426i \(-0.402471\pi\)
0.301626 + 0.953426i \(0.402471\pi\)
\(608\) 128301.i 0.347073i
\(609\) 212960. + 175054.i 0.574201 + 0.471996i
\(610\) −33522.7 −0.0900906
\(611\) 990.375i 0.00265288i
\(612\) −245224. + 48374.6i −0.654728 + 0.129156i
\(613\) 164165. 0.436877 0.218439 0.975851i \(-0.429904\pi\)
0.218439 + 0.975851i \(0.429904\pi\)
\(614\) 60777.2i 0.161215i
\(615\) 23345.4 28400.6i 0.0617236 0.0750891i
\(616\) 183113. 0.482568
\(617\) 382686.i 1.00524i 0.864506 + 0.502622i \(0.167631\pi\)
−0.864506 + 0.502622i \(0.832369\pi\)
\(618\) −248891. 204589.i −0.651675 0.535680i
\(619\) −329349. −0.859557 −0.429779 0.902934i \(-0.641408\pi\)
−0.429779 + 0.902934i \(0.641408\pi\)
\(620\) 46551.9i 0.121103i
\(621\) −260316. + 484246.i −0.675021 + 1.25569i
\(622\) 169914. 0.439185
\(623\) 25962.5i 0.0668915i
\(624\) −205.805 + 250.370i −0.000528551 + 0.000643002i
\(625\) 365772. 0.936377
\(626\) 478306.i 1.22055i
\(627\) −114183. 93859.1i −0.290447 0.238749i
\(628\) −299082. −0.758352
\(629\) 659006.i 1.66567i
\(630\) 3445.93 + 17468.4i 0.00868211 + 0.0440121i
\(631\) −208873. −0.524594 −0.262297 0.964987i \(-0.584480\pi\)
−0.262297 + 0.964987i \(0.584480\pi\)
\(632\) 268409.i 0.671990i
\(633\) −386563. + 470269.i −0.964747 + 1.17365i
\(634\) 185692. 0.461972
\(635\) 77242.3i 0.191561i
\(636\) −60303.4 49569.7i −0.149083 0.122547i
\(637\) 1745.16 0.00430087
\(638\) 453443.i 1.11399i
\(639\) 8342.72 1645.74i 0.0204318 0.00403050i
\(640\) −24554.9 −0.0599485
\(641\) 232155.i 0.565017i −0.959265 0.282509i \(-0.908833\pi\)
0.959265 0.282509i \(-0.0911665\pi\)
\(642\) 134344. 163434.i 0.325948 0.396528i
\(643\) 209174. 0.505924 0.252962 0.967476i \(-0.418595\pi\)
0.252962 + 0.967476i \(0.418595\pi\)
\(644\) 147606.i 0.355905i
\(645\) 32391.2 + 26625.8i 0.0778589 + 0.0640004i
\(646\) −126703. −0.303613
\(647\) 81749.3i 0.195288i 0.995221 + 0.0976440i \(0.0311307\pi\)
−0.995221 + 0.0976440i \(0.968869\pi\)
\(648\) 166013. + 404410.i 0.395360 + 0.963100i
\(649\) 55717.9 0.132283
\(650\) 1511.00i 0.00357633i
\(651\) −185885. + 226137.i −0.438615 + 0.533592i
\(652\) 182126. 0.428427
\(653\) 356530.i 0.836122i 0.908419 + 0.418061i \(0.137290\pi\)
−0.908419 + 0.418061i \(0.862710\pi\)
\(654\) −272462. 223965.i −0.637015 0.523630i
\(655\) 85057.5 0.198258
\(656\) 43863.9i 0.101929i
\(657\) −159443. 808262.i −0.369381 1.87250i
\(658\) −64915.3 −0.149932
\(659\) 455548.i 1.04897i −0.851420 0.524485i \(-0.824258\pi\)
0.851420 0.524485i \(-0.175742\pi\)
\(660\) −22479.3 + 27346.9i −0.0516054 + 0.0627799i
\(661\) −361402. −0.827156 −0.413578 0.910469i \(-0.635721\pi\)
−0.413578 + 0.910469i \(0.635721\pi\)
\(662\) 157535.i 0.359468i
\(663\) −2248.94 1848.64i −0.00511625 0.00420558i
\(664\) 895841. 2.03186
\(665\) 10909.6i 0.0246699i
\(666\) −399956. + 78898.0i −0.901705 + 0.177876i
\(667\) 1.03343e6 2.32289
\(668\) 249829.i 0.559874i
\(669\) 88596.6 107781.i 0.197954 0.240819i
\(670\) 52806.2 0.117635
\(671\) 419114.i 0.930866i
\(672\) 149269. + 122699.i 0.330544 + 0.271709i
\(673\) −116443. −0.257089 −0.128544 0.991704i \(-0.541030\pi\)
−0.128544 + 0.991704i \(0.541030\pi\)
\(674\) 457325.i 1.00671i
\(675\) 392742. + 211126.i 0.861985 + 0.463377i
\(676\) −250075. −0.547239
\(677\) 476770.i 1.04024i 0.854094 + 0.520118i \(0.174112\pi\)
−0.854094 + 0.520118i \(0.825888\pi\)
\(678\) −62043.3 + 75478.1i −0.134970 + 0.164196i
\(679\) −81911.6 −0.177667
\(680\) 85795.5i 0.185544i
\(681\) −627081. 515463.i −1.35216 1.11148i
\(682\) 481499. 1.03521
\(683\) 526531.i 1.12871i −0.825532 0.564356i \(-0.809125\pi\)
0.825532 0.564356i \(-0.190875\pi\)
\(684\) −18335.7 92948.9i −0.0391909 0.198670i
\(685\) −436.043 −0.000929283
\(686\) 258837.i 0.550020i
\(687\) −255666. + 311028.i −0.541701 + 0.659000i
\(688\) −50027.4 −0.105689
\(689\) 909.204i 0.00191524i
\(690\) 51562.1 + 42384.3i 0.108301 + 0.0890240i
\(691\) 155810. 0.326316 0.163158 0.986600i \(-0.447832\pi\)
0.163158 + 0.986600i \(0.447832\pi\)
\(692\) 159554.i 0.333192i
\(693\) 218397. 43082.4i 0.454757 0.0897084i
\(694\) 165743. 0.344125
\(695\) 54321.5i 0.112461i
\(696\) 521804. 634794.i 1.07718 1.31043i
\(697\) −394007. −0.811033
\(698\) 579017.i 1.18845i
\(699\) 69391.2 + 57039.9i 0.142020 + 0.116741i
\(700\) 119715. 0.244315
\(701\) 229962.i 0.467972i −0.972240 0.233986i \(-0.924823\pi\)
0.972240 0.233986i \(-0.0751770\pi\)
\(702\) −852.707 + 1586.23i −0.00173032 + 0.00321878i
\(703\) 249787. 0.505428
\(704\) 395007.i 0.797003i
\(705\) 22531.1 27409.9i 0.0453319 0.0551480i
\(706\) 126540. 0.253875
\(707\) 28218.8i 0.0564547i
\(708\) 27588.8 + 22678.1i 0.0550385 + 0.0452419i
\(709\) −947919. −1.88573 −0.942864 0.333178i \(-0.891879\pi\)
−0.942864 + 0.333178i \(0.891879\pi\)
\(710\) 1032.37i 0.00204795i
\(711\) −63150.5 320128.i −0.124922 0.633263i
\(712\) −77389.4 −0.152659
\(713\) 1.09737e6i 2.15861i
\(714\) 121171. 147410.i 0.237686 0.289154i
\(715\) −412.314 −0.000806521
\(716\) 339787.i 0.662797i
\(717\) −250736. 206106.i −0.487728 0.400915i
\(718\) 98162.9 0.190414
\(719\) 37919.1i 0.0733500i −0.999327 0.0366750i \(-0.988323\pi\)
0.999327 0.0366750i \(-0.0116766\pi\)
\(720\) 11391.8 2247.23i 0.0219750 0.00433493i
\(721\) −297310. −0.571926
\(722\) 302728.i 0.580736i
\(723\) −95408.2 + 116068.i −0.182519 + 0.222042i
\(724\) 412988. 0.787880
\(725\) 838150.i 1.59458i
\(726\) −8886.31 7304.59i −0.0168596 0.0138587i
\(727\) −632730. −1.19715 −0.598577 0.801065i \(-0.704267\pi\)
−0.598577 + 0.801065i \(0.704267\pi\)
\(728\) 1367.03i 0.00257937i
\(729\) 293150. + 443275.i 0.551614 + 0.834100i
\(730\) −100019. −0.187687
\(731\) 449370.i 0.840949i
\(732\) −170586. + 207525.i −0.318363 + 0.387301i
\(733\) −473944. −0.882103 −0.441051 0.897482i \(-0.645394\pi\)
−0.441051 + 0.897482i \(0.645394\pi\)
\(734\) 262192.i 0.486661i
\(735\) −48299.6 39702.5i −0.0894065 0.0734926i
\(736\) 724353. 1.33719
\(737\) 660204.i 1.21547i
\(738\) 47171.6 + 239126.i 0.0866100 + 0.439051i
\(739\) −490032. −0.897295 −0.448647 0.893709i \(-0.648094\pi\)
−0.448647 + 0.893709i \(0.648094\pi\)
\(740\) 59824.2i 0.109248i
\(741\) 700.702 852.431i 0.00127614 0.00155247i
\(742\) 59594.8 0.108243
\(743\) 429957.i 0.778838i −0.921061 0.389419i \(-0.872676\pi\)
0.921061 0.389419i \(-0.127324\pi\)
\(744\) 674071. + 554090.i 1.21775 + 1.00100i
\(745\) −109360. −0.197036
\(746\) 336055.i 0.603855i
\(747\) 1.06846e6 210771.i 1.91477 0.377719i
\(748\) 379390. 0.678082
\(749\) 195230.i 0.348002i
\(750\) 69500.9 84550.5i 0.123557 0.150312i
\(751\) 259444. 0.460007 0.230003 0.973190i \(-0.426126\pi\)
0.230003 + 0.973190i \(0.426126\pi\)
\(752\) 42333.9i 0.0748604i
\(753\) −526552. 432829.i −0.928649 0.763354i
\(754\) 3385.16 0.00595439
\(755\) 63036.9i 0.110586i
\(756\) 125675. + 67558.9i 0.219889 + 0.118206i
\(757\) 103286. 0.180240 0.0901200 0.995931i \(-0.471275\pi\)
0.0901200 + 0.995931i \(0.471275\pi\)
\(758\) 359688.i 0.626019i
\(759\) 529905. 644650.i 0.919845 1.11903i
\(760\) −32519.6 −0.0563012
\(761\) 815782.i 1.40866i 0.709875 + 0.704328i \(0.248751\pi\)
−0.709875 + 0.704328i \(0.751249\pi\)
\(762\) −395595. 325181.i −0.681303 0.560035i
\(763\) −325467. −0.559060
\(764\) 187119.i 0.320576i
\(765\) 20185.7 + 102327.i 0.0344923 + 0.174851i
\(766\) 60291.5 0.102754
\(767\) 415.961i 0.000707068i
\(768\) 397157. 483157.i 0.673349 0.819154i
\(769\) 188165. 0.318190 0.159095 0.987263i \(-0.449142\pi\)
0.159095 + 0.987263i \(0.449142\pi\)
\(770\) 27025.6i 0.0455820i
\(771\) −864937. 710983.i −1.45504 1.19605i
\(772\) −572137. −0.959988
\(773\) 706818.i 1.18290i −0.806341 0.591451i \(-0.798555\pi\)
0.806341 0.591451i \(-0.201445\pi\)
\(774\) −272727. + 53799.8i −0.455245 + 0.0898047i
\(775\) 890010. 1.48181
\(776\) 244163.i 0.405468i
\(777\) −238883. + 290610.i −0.395679 + 0.481358i
\(778\) −345864. −0.571408
\(779\) 149343.i 0.246099i
\(780\) −204.158 167.819i −0.000335565 0.000275836i
\(781\) −12907.1 −0.0211606
\(782\) 715332.i 1.16975i
\(783\) 472996. 879879.i 0.771496 1.43516i
\(784\) 74597.4 0.121364
\(785\) 124801.i 0.202525i
\(786\) −358082. + 435620.i −0.579612 + 0.705120i
\(787\) −29122.5 −0.0470196 −0.0235098 0.999724i \(-0.507484\pi\)
−0.0235098 + 0.999724i \(0.507484\pi\)
\(788\) 344818.i 0.555313i
\(789\) 598088. + 491631.i 0.960751 + 0.789742i
\(790\) −39614.3 −0.0634743
\(791\) 90161.8i 0.144102i
\(792\) −128420. 651000.i −0.204731 1.03784i
\(793\) −3128.88 −0.00497557
\(794\) 295878.i 0.469323i
\(795\) −20684.4 + 25163.4i −0.0327272 + 0.0398139i
\(796\) 72482.4 0.114395
\(797\) 456766.i 0.719079i 0.933130 + 0.359540i \(0.117066\pi\)
−0.933130 + 0.359540i \(0.882934\pi\)
\(798\) 55873.5 + 45928.3i 0.0877406 + 0.0721232i
\(799\) −380264. −0.595650
\(800\) 587478.i 0.917935i
\(801\) −92301.4 + 18208.0i −0.143861 + 0.0283790i
\(802\) 529563. 0.823320
\(803\) 1.25047e6i 1.93929i
\(804\) 268714. 326901.i 0.415699 0.505713i
\(805\) 61593.2 0.0950475
\(806\) 3594.62i 0.00553328i
\(807\) −92006.2 75629.5i −0.141276 0.116130i
\(808\) −84115.0 −0.128840
\(809\) 153327.i 0.234272i 0.993116 + 0.117136i \(0.0373713\pi\)
−0.993116 + 0.117136i \(0.962629\pi\)
\(810\) 59686.5 24501.8i 0.0909717 0.0373446i
\(811\) −127155. −0.193327 −0.0966635 0.995317i \(-0.530817\pi\)
−0.0966635 + 0.995317i \(0.530817\pi\)
\(812\) 268202.i 0.406771i
\(813\) −421981. + 513356.i −0.638428 + 0.776671i
\(814\) 618777. 0.933868
\(815\) 75997.5i 0.114415i
\(816\) −96131.7 79020.7i −0.144373 0.118675i
\(817\) 170328. 0.255177
\(818\) 724178.i 1.08228i
\(819\) 321.630 + 1630.43i 0.000479500 + 0.00243072i
\(820\) −35767.7 −0.0531941
\(821\) 319929.i 0.474643i 0.971431 + 0.237321i \(0.0762694\pi\)
−0.971431 + 0.237321i \(0.923731\pi\)
\(822\) 1835.69 2233.19i 0.00271679 0.00330507i
\(823\) 1.24453e6 1.83741 0.918706 0.394942i \(-0.129235\pi\)
0.918706 + 0.394942i \(0.129235\pi\)
\(824\) 886226.i 1.30524i
\(825\) −522836. 429774.i −0.768170 0.631440i
\(826\) −27264.6 −0.0399613
\(827\) 735008.i 1.07469i 0.843364 + 0.537343i \(0.180572\pi\)
−0.843364 + 0.537343i \(0.819428\pi\)
\(828\) 524767. 103519.i 0.765430 0.150994i
\(829\) 462547. 0.673049 0.336525 0.941675i \(-0.390748\pi\)
0.336525 + 0.941675i \(0.390748\pi\)
\(830\) 132217.i 0.191924i
\(831\) −46488.2 + 56554.6i −0.0673195 + 0.0818967i
\(832\) 2948.92 0.00426006
\(833\) 670070.i 0.965674i
\(834\) −278206. 228687.i −0.399977 0.328783i
\(835\) −104249. −0.149520
\(836\) 143802.i 0.205756i
\(837\) 934320. + 502262.i 1.33366 + 0.716934i
\(838\) −564739. −0.804193
\(839\) 113693.i 0.161514i 0.996734 + 0.0807568i \(0.0257337\pi\)
−0.996734 + 0.0807568i \(0.974266\pi\)
\(840\) 31099.9 37834.3i 0.0440759 0.0536200i
\(841\) −1.17047e6 −1.65488
\(842\) 315728.i 0.445337i
\(843\) 845252. + 694801.i 1.18941 + 0.977699i
\(844\) 592257. 0.831430
\(845\) 104351.i 0.146145i
\(846\) 45526.2 + 230785.i 0.0636093 + 0.322454i
\(847\) −10615.1 −0.0147964
\(848\) 38864.2i 0.0540452i
\(849\) 41888.8 50959.3i 0.0581142 0.0706981i
\(850\) −580162. −0.802992
\(851\) 1.41024e6i 1.94730i
\(852\) −6390.98 5253.42i −0.00880416 0.00723707i
\(853\) −26560.1 −0.0365032 −0.0182516 0.999833i \(-0.505810\pi\)
−0.0182516 + 0.999833i \(0.505810\pi\)
\(854\) 205086.i 0.281204i
\(855\) −38785.7 + 7651.12i −0.0530566 + 0.0104663i
\(856\) −581942. −0.794205
\(857\) 500794.i 0.681864i −0.940088 0.340932i \(-0.889257\pi\)
0.940088 0.340932i \(-0.110743\pi\)
\(858\) 1735.79 2111.66i 0.00235789 0.00286846i
\(859\) 374009. 0.506869 0.253434 0.967353i \(-0.418440\pi\)
0.253434 + 0.967353i \(0.418440\pi\)
\(860\) 40793.6i 0.0551562i
\(861\) 173750. + 142823.i 0.234379 + 0.192661i
\(862\) −432951. −0.582672
\(863\) 622632.i 0.836007i 0.908445 + 0.418004i \(0.137270\pi\)
−0.908445 + 0.418004i \(0.862730\pi\)
\(864\) 331534. 616727.i 0.444120 0.826163i
\(865\) 66578.6 0.0889820
\(866\) 225455.i 0.300625i
\(867\) 232477. 282817.i 0.309273 0.376242i
\(868\) 284797. 0.378003
\(869\) 495273.i 0.655851i
\(870\) −93688.8 77012.7i −0.123780 0.101747i
\(871\) 4928.74 0.00649680
\(872\) 970157.i 1.27588i
\(873\) 57446.0 + 291210.i 0.0753757 + 0.382101i
\(874\) 271137. 0.354948
\(875\) 100999.i 0.131917i
\(876\) −508963. + 619173.i −0.663251 + 0.806870i
\(877\) 1.47961e6 1.92375 0.961873 0.273497i \(-0.0881804\pi\)
0.961873 + 0.273497i \(0.0881804\pi\)
\(878\) 269511.i 0.349612i
\(879\) −593729. 488048.i −0.768441 0.631662i
\(880\) −17624.5 −0.0227589
\(881\) 868848.i 1.11942i −0.828689 0.559709i \(-0.810913\pi\)
0.828689 0.559709i \(-0.189087\pi\)
\(882\) 406671. 80222.6i 0.522765 0.103124i
\(883\) −1.11196e6 −1.42616 −0.713080 0.701083i \(-0.752700\pi\)
−0.713080 + 0.701083i \(0.752700\pi\)
\(884\) 2832.32i 0.00362442i
\(885\) 9463.13 11512.3i 0.0120823 0.0146985i
\(886\) 74450.5 0.0948419
\(887\) 1.31641e6i 1.67319i 0.547822 + 0.836595i \(0.315457\pi\)
−0.547822 + 0.836595i \(0.684543\pi\)
\(888\) 866253. + 712064.i 1.09855 + 0.903011i
\(889\) −472555. −0.597928
\(890\) 11421.9i 0.0144197i
\(891\) −306331. 746224.i −0.385865 0.939970i
\(892\) −135740. −0.170599
\(893\) 144134.i 0.180743i
\(894\) 460393. 560086.i 0.576042 0.700777i
\(895\) −141786. −0.177006
\(896\) 150223.i 0.187120i
\(897\) 4812.61 + 3955.99i 0.00598131 + 0.00491666i
\(898\) 579716. 0.718891
\(899\) 1.99393e6i 2.46712i
\(900\) −83957.8 425606.i −0.103652 0.525440i
\(901\) 349097. 0.430028
\(902\) 369955.i 0.454711i
\(903\) −162892. + 198164.i −0.199767 + 0.243024i
\(904\) 268755. 0.328867
\(905\) 172331.i 0.210410i
\(906\) −322842. 265378.i −0.393309 0.323302i
\(907\) −1.15372e6 −1.40244 −0.701221 0.712944i \(-0.747361\pi\)
−0.701221 + 0.712944i \(0.747361\pi\)
\(908\) 789746.i 0.957890i
\(909\) −100323. + 19790.3i −0.121415 + 0.0239511i
\(910\) 201.759 0.000243640
\(911\) 827151.i 0.996662i 0.866987 + 0.498331i \(0.166054\pi\)
−0.866987 + 0.498331i \(0.833946\pi\)
\(912\) 29951.7 36437.4i 0.0360107 0.0438084i
\(913\) −1.65302e6 −1.98307
\(914\) 128881.i 0.154276i
\(915\) 86596.0 + 71182.3i 0.103432 + 0.0850217i
\(916\) 391709. 0.466844
\(917\) 520367.i 0.618830i
\(918\) −609046. 327405.i −0.722712 0.388508i
\(919\) 614145. 0.727176 0.363588 0.931560i \(-0.381552\pi\)
0.363588 + 0.931560i \(0.381552\pi\)
\(920\) 183598.i 0.216916i
\(921\) −129055. + 157000.i −0.152144 + 0.185089i
\(922\) −165566. −0.194765
\(923\) 96.3577i 0.000113105i
\(924\) −167304. 137525.i −0.195958 0.161078i
\(925\) 1.14376e6 1.33675
\(926\) 280885.i 0.327572i
\(927\) 208509. + 1.05699e6i 0.242641 + 1.23002i
\(928\) −1.31616e6 −1.52831
\(929\) 141985.i 0.164517i −0.996611 0.0822584i \(-0.973787\pi\)
0.996611 0.0822584i \(-0.0262133\pi\)
\(930\) 81777.7 99485.7i 0.0945517 0.115026i
\(931\) −253981. −0.293023
\(932\) 87391.4i 0.100609i
\(933\) −438921. 360795.i −0.504224 0.414474i
\(934\) −705237. −0.808428
\(935\) 158312.i 0.181088i
\(936\) 4860.02 958.719i 0.00554736 0.00109431i
\(937\) −884504. −1.00744 −0.503722 0.863866i \(-0.668036\pi\)
−0.503722 + 0.863866i \(0.668036\pi\)
\(938\) 323060.i 0.367178i
\(939\) 1.01564e6 1.23556e6i 1.15188 1.40131i
\(940\) −34520.1 −0.0390676
\(941\) 736405.i 0.831644i −0.909446 0.415822i \(-0.863494\pi\)
0.909446 0.415822i \(-0.136506\pi\)
\(942\) −639165. 525397.i −0.720297 0.592087i
\(943\) 843154. 0.948164
\(944\) 17780.3i 0.0199524i
\(945\) 28191.0 52441.5i 0.0315679 0.0587235i
\(946\) 421938. 0.471484
\(947\) 23491.8i 0.0261948i −0.999914 0.0130974i \(-0.995831\pi\)
0.999914 0.0130974i \(-0.00416916\pi\)
\(948\) −201585. + 245235.i −0.224306 + 0.272877i
\(949\) −9335.36 −0.0103657
\(950\) 219902.i 0.243659i
\(951\) −479681. 394300.i −0.530385 0.435979i
\(952\) −524882. −0.579146
\(953\) 266400.i 0.293324i 0.989187 + 0.146662i \(0.0468530\pi\)
−0.989187 + 0.146662i \(0.953147\pi\)
\(954\) −41794.8 211870.i −0.0459225 0.232794i
\(955\) −78081.0 −0.0856128
\(956\) 315777.i 0.345513i
\(957\) −962842. + 1.17133e6i −1.05131 + 1.27896i
\(958\) 515760. 0.561974
\(959\) 2667.64i 0.00290061i
\(960\) −81615.1 67088.0i −0.0885581 0.0727951i
\(961\) 1.19378e6 1.29264
\(962\) 4619.46i 0.00499162i
\(963\) −694075. + 136918.i −0.748435 + 0.147641i
\(964\) 146176. 0.157297
\(965\) 238741.i 0.256373i
\(966\) −259300. + 315448.i −0.277874 + 0.338045i
\(967\) −900514. −0.963025 −0.481513 0.876439i \(-0.659912\pi\)
−0.481513 + 0.876439i \(0.659912\pi\)
\(968\) 31641.6i 0.0337681i
\(969\) 327299. + 269041.i 0.348575 + 0.286531i
\(970\) 36035.9 0.0382994
\(971\) 282724.i 0.299864i 0.988696 + 0.149932i \(0.0479055\pi\)
−0.988696 + 0.149932i \(0.952094\pi\)
\(972\) 152046. 494176.i 0.160932 0.523057i
\(973\) −332329. −0.351029
\(974\) 659196.i 0.694859i
\(975\) 3208.46 3903.22i 0.00337511 0.00410595i
\(976\) −133745. −0.140404
\(977\) 522927.i 0.547837i 0.961753 + 0.273919i \(0.0883199\pi\)
−0.961753 + 0.273919i \(0.911680\pi\)
\(978\) 389220. + 319941.i 0.406928 + 0.334496i
\(979\) 142800. 0.148992
\(980\) 60828.6i 0.0633367i
\(981\) 228256. + 1.15709e6i 0.237183 + 1.20235i
\(982\) −743212. −0.770708
\(983\) 784774.i 0.812152i −0.913839 0.406076i \(-0.866897\pi\)
0.913839 0.406076i \(-0.133103\pi\)
\(984\) 425729. 517916.i 0.439687 0.534896i
\(985\) 143886. 0.148301
\(986\) 1.29976e6i 1.33694i
\(987\) 167689. + 137841.i 0.172136 + 0.141496i
\(988\) −1073.55 −0.00109979
\(989\) 961628.i 0.983138i
\(990\) −96080.6 + 18953.5i −0.0980314 + 0.0193383i
\(991\) −1.39542e6 −1.42088 −0.710439 0.703758i \(-0.751504\pi\)
−0.710439 + 0.703758i \(0.751504\pi\)
\(992\) 1.39759e6i 1.42022i
\(993\) −334510. + 406944.i −0.339243 + 0.412702i
\(994\) 6315.88 0.00639235
\(995\) 30245.4i 0.0305502i
\(996\) −818497. 672808.i −0.825084 0.678223i
\(997\) −1.73135e6 −1.74179 −0.870893 0.491472i \(-0.836459\pi\)
−0.870893 + 0.491472i \(0.836459\pi\)
\(998\) 552751.i 0.554969i
\(999\) 1.20070e6 + 645460.i 1.20311 + 0.646753i
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.119.27 78
3.2 odd 2 inner 177.5.b.a.119.52 yes 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.5.b.a.119.27 78 1.1 even 1 trivial
177.5.b.a.119.52 yes 78 3.2 odd 2 inner