Properties

Label 6014.2.a.e.1.17
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.a (trivial)

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: yes
Analytic conductor: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.56192 q^{3} +1.00000 q^{4} -3.75184 q^{5} +1.56192 q^{6} -2.39374 q^{7} +1.00000 q^{8} -0.560398 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.56192 q^{3} +1.00000 q^{4} -3.75184 q^{5} +1.56192 q^{6} -2.39374 q^{7} +1.00000 q^{8} -0.560398 q^{9} -3.75184 q^{10} +2.24392 q^{11} +1.56192 q^{12} +2.57839 q^{13} -2.39374 q^{14} -5.86008 q^{15} +1.00000 q^{16} +0.0983609 q^{17} -0.560398 q^{18} +5.94294 q^{19} -3.75184 q^{20} -3.73884 q^{21} +2.24392 q^{22} -1.87367 q^{23} +1.56192 q^{24} +9.07630 q^{25} +2.57839 q^{26} -5.56107 q^{27} -2.39374 q^{28} -7.16628 q^{29} -5.86008 q^{30} +1.00000 q^{31} +1.00000 q^{32} +3.50483 q^{33} +0.0983609 q^{34} +8.98093 q^{35} -0.560398 q^{36} +0.543246 q^{37} +5.94294 q^{38} +4.02725 q^{39} -3.75184 q^{40} +7.44368 q^{41} -3.73884 q^{42} -5.45549 q^{43} +2.24392 q^{44} +2.10252 q^{45} -1.87367 q^{46} -8.90482 q^{47} +1.56192 q^{48} -1.27001 q^{49} +9.07630 q^{50} +0.153632 q^{51} +2.57839 q^{52} +2.87792 q^{53} -5.56107 q^{54} -8.41883 q^{55} -2.39374 q^{56} +9.28242 q^{57} -7.16628 q^{58} -8.47404 q^{59} -5.86008 q^{60} -7.57710 q^{61} +1.00000 q^{62} +1.34145 q^{63} +1.00000 q^{64} -9.67370 q^{65} +3.50483 q^{66} -11.3966 q^{67} +0.0983609 q^{68} -2.92652 q^{69} +8.98093 q^{70} +3.15399 q^{71} -0.560398 q^{72} -9.85978 q^{73} +0.543246 q^{74} +14.1765 q^{75} +5.94294 q^{76} -5.37136 q^{77} +4.02725 q^{78} -8.19488 q^{79} -3.75184 q^{80} -7.00476 q^{81} +7.44368 q^{82} +5.49596 q^{83} -3.73884 q^{84} -0.369034 q^{85} -5.45549 q^{86} -11.1932 q^{87} +2.24392 q^{88} +8.25650 q^{89} +2.10252 q^{90} -6.17199 q^{91} -1.87367 q^{92} +1.56192 q^{93} -8.90482 q^{94} -22.2970 q^{95} +1.56192 q^{96} -1.00000 q^{97} -1.27001 q^{98} -1.25749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.56192 0.901776 0.450888 0.892580i \(-0.351107\pi\)
0.450888 + 0.892580i \(0.351107\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.75184 −1.67787 −0.838937 0.544229i \(-0.816822\pi\)
−0.838937 + 0.544229i \(0.816822\pi\)
\(6\) 1.56192 0.637652
\(7\) −2.39374 −0.904749 −0.452374 0.891828i \(-0.649423\pi\)
−0.452374 + 0.891828i \(0.649423\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.560398 −0.186799
\(10\) −3.75184 −1.18644
\(11\) 2.24392 0.676568 0.338284 0.941044i \(-0.390154\pi\)
0.338284 + 0.941044i \(0.390154\pi\)
\(12\) 1.56192 0.450888
\(13\) 2.57839 0.715117 0.357558 0.933891i \(-0.383609\pi\)
0.357558 + 0.933891i \(0.383609\pi\)
\(14\) −2.39374 −0.639754
\(15\) −5.86008 −1.51307
\(16\) 1.00000 0.250000
\(17\) 0.0983609 0.0238560 0.0119280 0.999929i \(-0.496203\pi\)
0.0119280 + 0.999929i \(0.496203\pi\)
\(18\) −0.560398 −0.132087
\(19\) 5.94294 1.36341 0.681703 0.731629i \(-0.261240\pi\)
0.681703 + 0.731629i \(0.261240\pi\)
\(20\) −3.75184 −0.838937
\(21\) −3.73884 −0.815881
\(22\) 2.24392 0.478406
\(23\) −1.87367 −0.390686 −0.195343 0.980735i \(-0.562582\pi\)
−0.195343 + 0.980735i \(0.562582\pi\)
\(24\) 1.56192 0.318826
\(25\) 9.07630 1.81526
\(26\) 2.57839 0.505664
\(27\) −5.56107 −1.07023
\(28\) −2.39374 −0.452374
\(29\) −7.16628 −1.33074 −0.665372 0.746512i \(-0.731727\pi\)
−0.665372 + 0.746512i \(0.731727\pi\)
\(30\) −5.86008 −1.06990
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) 3.50483 0.610113
\(34\) 0.0983609 0.0168687
\(35\) 8.98093 1.51805
\(36\) −0.560398 −0.0933996
\(37\) 0.543246 0.0893091 0.0446545 0.999002i \(-0.485781\pi\)
0.0446545 + 0.999002i \(0.485781\pi\)
\(38\) 5.94294 0.964073
\(39\) 4.02725 0.644875
\(40\) −3.75184 −0.593218
\(41\) 7.44368 1.16251 0.581253 0.813723i \(-0.302562\pi\)
0.581253 + 0.813723i \(0.302562\pi\)
\(42\) −3.73884 −0.576915
\(43\) −5.45549 −0.831954 −0.415977 0.909375i \(-0.636560\pi\)
−0.415977 + 0.909375i \(0.636560\pi\)
\(44\) 2.24392 0.338284
\(45\) 2.10252 0.313426
\(46\) −1.87367 −0.276257
\(47\) −8.90482 −1.29890 −0.649451 0.760404i \(-0.725001\pi\)
−0.649451 + 0.760404i \(0.725001\pi\)
\(48\) 1.56192 0.225444
\(49\) −1.27001 −0.181430
\(50\) 9.07630 1.28358
\(51\) 0.153632 0.0215128
\(52\) 2.57839 0.357558
\(53\) 2.87792 0.395312 0.197656 0.980271i \(-0.436667\pi\)
0.197656 + 0.980271i \(0.436667\pi\)
\(54\) −5.56107 −0.756765
\(55\) −8.41883 −1.13519
\(56\) −2.39374 −0.319877
\(57\) 9.28242 1.22949
\(58\) −7.16628 −0.940978
\(59\) −8.47404 −1.10323 −0.551613 0.834100i \(-0.685987\pi\)
−0.551613 + 0.834100i \(0.685987\pi\)
\(60\) −5.86008 −0.756533
\(61\) −7.57710 −0.970149 −0.485074 0.874473i \(-0.661207\pi\)
−0.485074 + 0.874473i \(0.661207\pi\)
\(62\) 1.00000 0.127000
\(63\) 1.34145 0.169006
\(64\) 1.00000 0.125000
\(65\) −9.67370 −1.19988
\(66\) 3.50483 0.431415
\(67\) −11.3966 −1.39232 −0.696158 0.717888i \(-0.745109\pi\)
−0.696158 + 0.717888i \(0.745109\pi\)
\(68\) 0.0983609 0.0119280
\(69\) −2.92652 −0.352312
\(70\) 8.98093 1.07343
\(71\) 3.15399 0.374310 0.187155 0.982330i \(-0.440073\pi\)
0.187155 + 0.982330i \(0.440073\pi\)
\(72\) −0.560398 −0.0660435
\(73\) −9.85978 −1.15400 −0.577000 0.816744i \(-0.695777\pi\)
−0.577000 + 0.816744i \(0.695777\pi\)
\(74\) 0.543246 0.0631511
\(75\) 14.1765 1.63696
\(76\) 5.94294 0.681703
\(77\) −5.37136 −0.612124
\(78\) 4.02725 0.455996
\(79\) −8.19488 −0.921997 −0.460998 0.887401i \(-0.652509\pi\)
−0.460998 + 0.887401i \(0.652509\pi\)
\(80\) −3.75184 −0.419468
\(81\) −7.00476 −0.778307
\(82\) 7.44368 0.822016
\(83\) 5.49596 0.603260 0.301630 0.953425i \(-0.402469\pi\)
0.301630 + 0.953425i \(0.402469\pi\)
\(84\) −3.73884 −0.407940
\(85\) −0.369034 −0.0400274
\(86\) −5.45549 −0.588281
\(87\) −11.1932 −1.20003
\(88\) 2.24392 0.239203
\(89\) 8.25650 0.875187 0.437593 0.899173i \(-0.355831\pi\)
0.437593 + 0.899173i \(0.355831\pi\)
\(90\) 2.10252 0.221625
\(91\) −6.17199 −0.647001
\(92\) −1.87367 −0.195343
\(93\) 1.56192 0.161964
\(94\) −8.90482 −0.918462
\(95\) −22.2970 −2.28762
\(96\) 1.56192 0.159413
\(97\) −1.00000 −0.101535
\(98\) −1.27001 −0.128290
\(99\) −1.25749 −0.126382
\(100\) 9.07630 0.907630
\(101\) −8.27408 −0.823302 −0.411651 0.911342i \(-0.635048\pi\)
−0.411651 + 0.911342i \(0.635048\pi\)
\(102\) 0.153632 0.0152118
\(103\) −10.9834 −1.08223 −0.541115 0.840949i \(-0.681997\pi\)
−0.541115 + 0.840949i \(0.681997\pi\)
\(104\) 2.57839 0.252832
\(105\) 14.0275 1.36895
\(106\) 2.87792 0.279528
\(107\) 0.540399 0.0522423 0.0261212 0.999659i \(-0.491684\pi\)
0.0261212 + 0.999659i \(0.491684\pi\)
\(108\) −5.56107 −0.535114
\(109\) −12.4265 −1.19024 −0.595122 0.803635i \(-0.702896\pi\)
−0.595122 + 0.803635i \(0.702896\pi\)
\(110\) −8.41883 −0.802704
\(111\) 0.848508 0.0805368
\(112\) −2.39374 −0.226187
\(113\) 2.36848 0.222808 0.111404 0.993775i \(-0.464465\pi\)
0.111404 + 0.993775i \(0.464465\pi\)
\(114\) 9.28242 0.869378
\(115\) 7.02969 0.655522
\(116\) −7.16628 −0.665372
\(117\) −1.44492 −0.133583
\(118\) −8.47404 −0.780099
\(119\) −0.235450 −0.0215837
\(120\) −5.86008 −0.534950
\(121\) −5.96482 −0.542256
\(122\) −7.57710 −0.685999
\(123\) 11.6264 1.04832
\(124\) 1.00000 0.0898027
\(125\) −15.2936 −1.36790
\(126\) 1.34145 0.119506
\(127\) −8.95664 −0.794773 −0.397387 0.917651i \(-0.630083\pi\)
−0.397387 + 0.917651i \(0.630083\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.52105 −0.750237
\(130\) −9.67370 −0.848440
\(131\) −1.81408 −0.158497 −0.0792486 0.996855i \(-0.525252\pi\)
−0.0792486 + 0.996855i \(0.525252\pi\)
\(132\) 3.50483 0.305056
\(133\) −14.2259 −1.23354
\(134\) −11.3966 −0.984516
\(135\) 20.8642 1.79571
\(136\) 0.0983609 0.00843437
\(137\) 8.60658 0.735310 0.367655 0.929962i \(-0.380161\pi\)
0.367655 + 0.929962i \(0.380161\pi\)
\(138\) −2.92652 −0.249122
\(139\) −1.22561 −0.103955 −0.0519773 0.998648i \(-0.516552\pi\)
−0.0519773 + 0.998648i \(0.516552\pi\)
\(140\) 8.98093 0.759027
\(141\) −13.9086 −1.17132
\(142\) 3.15399 0.264677
\(143\) 5.78570 0.483825
\(144\) −0.560398 −0.0466998
\(145\) 26.8867 2.23282
\(146\) −9.85978 −0.816001
\(147\) −1.98366 −0.163609
\(148\) 0.543246 0.0446545
\(149\) 4.91409 0.402578 0.201289 0.979532i \(-0.435487\pi\)
0.201289 + 0.979532i \(0.435487\pi\)
\(150\) 14.1765 1.15750
\(151\) 5.25936 0.428001 0.214000 0.976834i \(-0.431351\pi\)
0.214000 + 0.976834i \(0.431351\pi\)
\(152\) 5.94294 0.482036
\(153\) −0.0551212 −0.00445629
\(154\) −5.37136 −0.432837
\(155\) −3.75184 −0.301355
\(156\) 4.02725 0.322438
\(157\) −15.9814 −1.27545 −0.637726 0.770263i \(-0.720125\pi\)
−0.637726 + 0.770263i \(0.720125\pi\)
\(158\) −8.19488 −0.651950
\(159\) 4.49508 0.356483
\(160\) −3.75184 −0.296609
\(161\) 4.48507 0.353473
\(162\) −7.00476 −0.550346
\(163\) 20.6002 1.61353 0.806766 0.590872i \(-0.201216\pi\)
0.806766 + 0.590872i \(0.201216\pi\)
\(164\) 7.44368 0.581253
\(165\) −13.1496 −1.02369
\(166\) 5.49596 0.426569
\(167\) 6.52617 0.505010 0.252505 0.967596i \(-0.418746\pi\)
0.252505 + 0.967596i \(0.418746\pi\)
\(168\) −3.73884 −0.288457
\(169\) −6.35191 −0.488608
\(170\) −0.369034 −0.0283036
\(171\) −3.33041 −0.254683
\(172\) −5.45549 −0.415977
\(173\) 2.24208 0.170462 0.0852311 0.996361i \(-0.472837\pi\)
0.0852311 + 0.996361i \(0.472837\pi\)
\(174\) −11.1932 −0.848552
\(175\) −21.7263 −1.64235
\(176\) 2.24392 0.169142
\(177\) −13.2358 −0.994863
\(178\) 8.25650 0.618851
\(179\) 11.9848 0.895784 0.447892 0.894088i \(-0.352175\pi\)
0.447892 + 0.894088i \(0.352175\pi\)
\(180\) 2.10252 0.156713
\(181\) 15.6727 1.16494 0.582471 0.812852i \(-0.302086\pi\)
0.582471 + 0.812852i \(0.302086\pi\)
\(182\) −6.17199 −0.457499
\(183\) −11.8348 −0.874857
\(184\) −1.87367 −0.138128
\(185\) −2.03817 −0.149849
\(186\) 1.56192 0.114526
\(187\) 0.220714 0.0161402
\(188\) −8.90482 −0.649451
\(189\) 13.3117 0.968287
\(190\) −22.2970 −1.61759
\(191\) −2.91679 −0.211052 −0.105526 0.994417i \(-0.533653\pi\)
−0.105526 + 0.994417i \(0.533653\pi\)
\(192\) 1.56192 0.112722
\(193\) −6.67285 −0.480322 −0.240161 0.970733i \(-0.577200\pi\)
−0.240161 + 0.970733i \(0.577200\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −15.1096 −1.08202
\(196\) −1.27001 −0.0907150
\(197\) 0.343230 0.0244541 0.0122270 0.999925i \(-0.496108\pi\)
0.0122270 + 0.999925i \(0.496108\pi\)
\(198\) −1.25749 −0.0893658
\(199\) −18.6347 −1.32098 −0.660491 0.750834i \(-0.729652\pi\)
−0.660491 + 0.750834i \(0.729652\pi\)
\(200\) 9.07630 0.641791
\(201\) −17.8006 −1.25556
\(202\) −8.27408 −0.582162
\(203\) 17.1542 1.20399
\(204\) 0.153632 0.0107564
\(205\) −27.9275 −1.95054
\(206\) −10.9834 −0.765251
\(207\) 1.05000 0.0729799
\(208\) 2.57839 0.178779
\(209\) 13.3355 0.922436
\(210\) 14.0275 0.967990
\(211\) −16.8159 −1.15765 −0.578827 0.815450i \(-0.696490\pi\)
−0.578827 + 0.815450i \(0.696490\pi\)
\(212\) 2.87792 0.197656
\(213\) 4.92629 0.337544
\(214\) 0.540399 0.0369409
\(215\) 20.4681 1.39591
\(216\) −5.56107 −0.378383
\(217\) −2.39374 −0.162498
\(218\) −12.4265 −0.841630
\(219\) −15.4002 −1.04065
\(220\) −8.41883 −0.567597
\(221\) 0.253613 0.0170598
\(222\) 0.848508 0.0569481
\(223\) −7.80316 −0.522538 −0.261269 0.965266i \(-0.584141\pi\)
−0.261269 + 0.965266i \(0.584141\pi\)
\(224\) −2.39374 −0.159938
\(225\) −5.08634 −0.339089
\(226\) 2.36848 0.157549
\(227\) −15.0215 −0.997009 −0.498505 0.866887i \(-0.666117\pi\)
−0.498505 + 0.866887i \(0.666117\pi\)
\(228\) 9.28242 0.614743
\(229\) −10.1878 −0.673226 −0.336613 0.941643i \(-0.609281\pi\)
−0.336613 + 0.941643i \(0.609281\pi\)
\(230\) 7.02969 0.463524
\(231\) −8.38965 −0.551999
\(232\) −7.16628 −0.470489
\(233\) 24.7094 1.61876 0.809382 0.587282i \(-0.199802\pi\)
0.809382 + 0.587282i \(0.199802\pi\)
\(234\) −1.44492 −0.0944576
\(235\) 33.4094 2.17939
\(236\) −8.47404 −0.551613
\(237\) −12.7998 −0.831435
\(238\) −0.235450 −0.0152620
\(239\) −10.9021 −0.705200 −0.352600 0.935774i \(-0.614702\pi\)
−0.352600 + 0.935774i \(0.614702\pi\)
\(240\) −5.86008 −0.378267
\(241\) −15.2459 −0.982074 −0.491037 0.871139i \(-0.663382\pi\)
−0.491037 + 0.871139i \(0.663382\pi\)
\(242\) −5.96482 −0.383433
\(243\) 5.74230 0.368369
\(244\) −7.57710 −0.485074
\(245\) 4.76487 0.304416
\(246\) 11.6264 0.741275
\(247\) 15.3232 0.974994
\(248\) 1.00000 0.0635001
\(249\) 8.58427 0.544006
\(250\) −15.2936 −0.967253
\(251\) −0.275802 −0.0174085 −0.00870423 0.999962i \(-0.502771\pi\)
−0.00870423 + 0.999962i \(0.502771\pi\)
\(252\) 1.34145 0.0845032
\(253\) −4.20436 −0.264326
\(254\) −8.95664 −0.561990
\(255\) −0.576403 −0.0360957
\(256\) 1.00000 0.0625000
\(257\) 5.99659 0.374057 0.187028 0.982354i \(-0.440114\pi\)
0.187028 + 0.982354i \(0.440114\pi\)
\(258\) −8.52105 −0.530498
\(259\) −1.30039 −0.0808023
\(260\) −9.67370 −0.599938
\(261\) 4.01597 0.248582
\(262\) −1.81408 −0.112074
\(263\) −14.5509 −0.897245 −0.448623 0.893721i \(-0.648085\pi\)
−0.448623 + 0.893721i \(0.648085\pi\)
\(264\) 3.50483 0.215707
\(265\) −10.7975 −0.663284
\(266\) −14.2259 −0.872244
\(267\) 12.8960 0.789223
\(268\) −11.3966 −0.696158
\(269\) 10.1366 0.618039 0.309019 0.951056i \(-0.399999\pi\)
0.309019 + 0.951056i \(0.399999\pi\)
\(270\) 20.8642 1.26976
\(271\) 12.2040 0.741340 0.370670 0.928765i \(-0.379128\pi\)
0.370670 + 0.928765i \(0.379128\pi\)
\(272\) 0.0983609 0.00596400
\(273\) −9.64018 −0.583450
\(274\) 8.60658 0.519943
\(275\) 20.3665 1.22815
\(276\) −2.92652 −0.176156
\(277\) −21.7743 −1.30829 −0.654147 0.756368i \(-0.726972\pi\)
−0.654147 + 0.756368i \(0.726972\pi\)
\(278\) −1.22561 −0.0735070
\(279\) −0.560398 −0.0335501
\(280\) 8.98093 0.536713
\(281\) −7.70986 −0.459932 −0.229966 0.973199i \(-0.573861\pi\)
−0.229966 + 0.973199i \(0.573861\pi\)
\(282\) −13.9086 −0.828247
\(283\) 16.7327 0.994655 0.497328 0.867563i \(-0.334315\pi\)
0.497328 + 0.867563i \(0.334315\pi\)
\(284\) 3.15399 0.187155
\(285\) −34.8261 −2.06292
\(286\) 5.78570 0.342116
\(287\) −17.8182 −1.05178
\(288\) −0.560398 −0.0330218
\(289\) −16.9903 −0.999431
\(290\) 26.8867 1.57884
\(291\) −1.56192 −0.0915615
\(292\) −9.85978 −0.577000
\(293\) 25.5368 1.49187 0.745937 0.666017i \(-0.232002\pi\)
0.745937 + 0.666017i \(0.232002\pi\)
\(294\) −1.98366 −0.115689
\(295\) 31.7932 1.85107
\(296\) 0.543246 0.0315755
\(297\) −12.4786 −0.724081
\(298\) 4.91409 0.284666
\(299\) −4.83104 −0.279386
\(300\) 14.1765 0.818479
\(301\) 13.0590 0.752710
\(302\) 5.25936 0.302642
\(303\) −12.9235 −0.742434
\(304\) 5.94294 0.340851
\(305\) 28.4281 1.62779
\(306\) −0.0551212 −0.00315107
\(307\) 9.96450 0.568704 0.284352 0.958720i \(-0.408222\pi\)
0.284352 + 0.958720i \(0.408222\pi\)
\(308\) −5.37136 −0.306062
\(309\) −17.1553 −0.975929
\(310\) −3.75184 −0.213090
\(311\) 16.3760 0.928599 0.464299 0.885678i \(-0.346306\pi\)
0.464299 + 0.885678i \(0.346306\pi\)
\(312\) 4.02725 0.227998
\(313\) −30.9221 −1.74782 −0.873910 0.486087i \(-0.838424\pi\)
−0.873910 + 0.486087i \(0.838424\pi\)
\(314\) −15.9814 −0.901881
\(315\) −5.03289 −0.283571
\(316\) −8.19488 −0.460998
\(317\) −2.71329 −0.152394 −0.0761968 0.997093i \(-0.524278\pi\)
−0.0761968 + 0.997093i \(0.524278\pi\)
\(318\) 4.49508 0.252072
\(319\) −16.0806 −0.900339
\(320\) −3.75184 −0.209734
\(321\) 0.844061 0.0471109
\(322\) 4.48507 0.249943
\(323\) 0.584553 0.0325254
\(324\) −7.00476 −0.389153
\(325\) 23.4022 1.29812
\(326\) 20.6002 1.14094
\(327\) −19.4093 −1.07333
\(328\) 7.44368 0.411008
\(329\) 21.3158 1.17518
\(330\) −13.1496 −0.723860
\(331\) −26.5667 −1.46024 −0.730118 0.683321i \(-0.760535\pi\)
−0.730118 + 0.683321i \(0.760535\pi\)
\(332\) 5.49596 0.301630
\(333\) −0.304434 −0.0166829
\(334\) 6.52617 0.357096
\(335\) 42.7582 2.33613
\(336\) −3.73884 −0.203970
\(337\) 32.3828 1.76401 0.882003 0.471244i \(-0.156195\pi\)
0.882003 + 0.471244i \(0.156195\pi\)
\(338\) −6.35191 −0.345498
\(339\) 3.69938 0.200923
\(340\) −0.369034 −0.0200137
\(341\) 2.24392 0.121515
\(342\) −3.33041 −0.180088
\(343\) 19.7963 1.06890
\(344\) −5.45549 −0.294140
\(345\) 10.9798 0.591134
\(346\) 2.24208 0.120535
\(347\) 21.7246 1.16624 0.583119 0.812386i \(-0.301832\pi\)
0.583119 + 0.812386i \(0.301832\pi\)
\(348\) −11.1932 −0.600017
\(349\) 17.4429 0.933697 0.466849 0.884337i \(-0.345389\pi\)
0.466849 + 0.884337i \(0.345389\pi\)
\(350\) −21.7263 −1.16132
\(351\) −14.3386 −0.765338
\(352\) 2.24392 0.119601
\(353\) −17.0303 −0.906434 −0.453217 0.891400i \(-0.649724\pi\)
−0.453217 + 0.891400i \(0.649724\pi\)
\(354\) −13.2358 −0.703474
\(355\) −11.8333 −0.628044
\(356\) 8.25650 0.437593
\(357\) −0.367755 −0.0194637
\(358\) 11.9848 0.633415
\(359\) −6.88917 −0.363596 −0.181798 0.983336i \(-0.558192\pi\)
−0.181798 + 0.983336i \(0.558192\pi\)
\(360\) 2.10252 0.110813
\(361\) 16.3186 0.858873
\(362\) 15.6727 0.823738
\(363\) −9.31658 −0.488994
\(364\) −6.17199 −0.323500
\(365\) 36.9923 1.93627
\(366\) −11.8348 −0.618618
\(367\) 28.0593 1.46468 0.732342 0.680937i \(-0.238427\pi\)
0.732342 + 0.680937i \(0.238427\pi\)
\(368\) −1.87367 −0.0976715
\(369\) −4.17142 −0.217155
\(370\) −2.03817 −0.105960
\(371\) −6.88898 −0.357658
\(372\) 1.56192 0.0809819
\(373\) 17.7996 0.921630 0.460815 0.887496i \(-0.347557\pi\)
0.460815 + 0.887496i \(0.347557\pi\)
\(374\) 0.220714 0.0114128
\(375\) −23.8874 −1.23354
\(376\) −8.90482 −0.459231
\(377\) −18.4775 −0.951637
\(378\) 13.3117 0.684682
\(379\) −12.7562 −0.655240 −0.327620 0.944810i \(-0.606247\pi\)
−0.327620 + 0.944810i \(0.606247\pi\)
\(380\) −22.2970 −1.14381
\(381\) −13.9896 −0.716708
\(382\) −2.91679 −0.149236
\(383\) −25.5429 −1.30518 −0.652590 0.757711i \(-0.726317\pi\)
−0.652590 + 0.757711i \(0.726317\pi\)
\(384\) 1.56192 0.0797065
\(385\) 20.1525 1.02707
\(386\) −6.67285 −0.339639
\(387\) 3.05724 0.155408
\(388\) −1.00000 −0.0507673
\(389\) 5.01300 0.254169 0.127085 0.991892i \(-0.459438\pi\)
0.127085 + 0.991892i \(0.459438\pi\)
\(390\) −15.1096 −0.765103
\(391\) −0.184295 −0.00932021
\(392\) −1.27001 −0.0641452
\(393\) −2.83346 −0.142929
\(394\) 0.343230 0.0172917
\(395\) 30.7459 1.54699
\(396\) −1.25749 −0.0631912
\(397\) −28.8266 −1.44676 −0.723382 0.690448i \(-0.757413\pi\)
−0.723382 + 0.690448i \(0.757413\pi\)
\(398\) −18.6347 −0.934076
\(399\) −22.2197 −1.11238
\(400\) 9.07630 0.453815
\(401\) 15.1201 0.755064 0.377532 0.925997i \(-0.376773\pi\)
0.377532 + 0.925997i \(0.376773\pi\)
\(402\) −17.8006 −0.887814
\(403\) 2.57839 0.128439
\(404\) −8.27408 −0.411651
\(405\) 26.2807 1.30590
\(406\) 17.1542 0.851349
\(407\) 1.21900 0.0604236
\(408\) 0.153632 0.00760592
\(409\) −13.3584 −0.660532 −0.330266 0.943888i \(-0.607138\pi\)
−0.330266 + 0.943888i \(0.607138\pi\)
\(410\) −27.9275 −1.37924
\(411\) 13.4428 0.663085
\(412\) −10.9834 −0.541115
\(413\) 20.2846 0.998142
\(414\) 1.05000 0.0516046
\(415\) −20.6200 −1.01219
\(416\) 2.57839 0.126416
\(417\) −1.91430 −0.0937438
\(418\) 13.3355 0.652261
\(419\) −11.4278 −0.558285 −0.279143 0.960250i \(-0.590050\pi\)
−0.279143 + 0.960250i \(0.590050\pi\)
\(420\) 14.0275 0.684473
\(421\) −34.7650 −1.69434 −0.847172 0.531319i \(-0.821697\pi\)
−0.847172 + 0.531319i \(0.821697\pi\)
\(422\) −16.8159 −0.818586
\(423\) 4.99024 0.242634
\(424\) 2.87792 0.139764
\(425\) 0.892752 0.0433049
\(426\) 4.92629 0.238679
\(427\) 18.1376 0.877741
\(428\) 0.540399 0.0261212
\(429\) 9.03682 0.436302
\(430\) 20.4681 0.987060
\(431\) 10.8643 0.523313 0.261657 0.965161i \(-0.415731\pi\)
0.261657 + 0.965161i \(0.415731\pi\)
\(432\) −5.56107 −0.267557
\(433\) 39.8552 1.91532 0.957659 0.287903i \(-0.0929582\pi\)
0.957659 + 0.287903i \(0.0929582\pi\)
\(434\) −2.39374 −0.114903
\(435\) 41.9950 2.01350
\(436\) −12.4265 −0.595122
\(437\) −11.1351 −0.532664
\(438\) −15.4002 −0.735851
\(439\) 1.11217 0.0530809 0.0265405 0.999648i \(-0.491551\pi\)
0.0265405 + 0.999648i \(0.491551\pi\)
\(440\) −8.41883 −0.401352
\(441\) 0.711711 0.0338910
\(442\) 0.253613 0.0120631
\(443\) −20.0217 −0.951259 −0.475629 0.879646i \(-0.657780\pi\)
−0.475629 + 0.879646i \(0.657780\pi\)
\(444\) 0.848508 0.0402684
\(445\) −30.9771 −1.46845
\(446\) −7.80316 −0.369490
\(447\) 7.67543 0.363035
\(448\) −2.39374 −0.113094
\(449\) −11.6894 −0.551657 −0.275828 0.961207i \(-0.588952\pi\)
−0.275828 + 0.961207i \(0.588952\pi\)
\(450\) −5.08634 −0.239772
\(451\) 16.7030 0.786515
\(452\) 2.36848 0.111404
\(453\) 8.21472 0.385961
\(454\) −15.0215 −0.704992
\(455\) 23.1563 1.08559
\(456\) 9.28242 0.434689
\(457\) 14.8909 0.696567 0.348284 0.937389i \(-0.386765\pi\)
0.348284 + 0.937389i \(0.386765\pi\)
\(458\) −10.1878 −0.476042
\(459\) −0.546991 −0.0255314
\(460\) 7.02969 0.327761
\(461\) −26.1101 −1.21607 −0.608035 0.793910i \(-0.708042\pi\)
−0.608035 + 0.793910i \(0.708042\pi\)
\(462\) −8.38965 −0.390322
\(463\) −5.62200 −0.261277 −0.130638 0.991430i \(-0.541703\pi\)
−0.130638 + 0.991430i \(0.541703\pi\)
\(464\) −7.16628 −0.332686
\(465\) −5.86008 −0.271755
\(466\) 24.7094 1.14464
\(467\) −38.7588 −1.79354 −0.896771 0.442494i \(-0.854094\pi\)
−0.896771 + 0.442494i \(0.854094\pi\)
\(468\) −1.44492 −0.0667916
\(469\) 27.2805 1.25970
\(470\) 33.4094 1.54106
\(471\) −24.9617 −1.15017
\(472\) −8.47404 −0.390049
\(473\) −12.2417 −0.562873
\(474\) −12.7998 −0.587913
\(475\) 53.9399 2.47493
\(476\) −0.235450 −0.0107918
\(477\) −1.61278 −0.0738440
\(478\) −10.9021 −0.498651
\(479\) 14.2225 0.649843 0.324921 0.945741i \(-0.394662\pi\)
0.324921 + 0.945741i \(0.394662\pi\)
\(480\) −5.86008 −0.267475
\(481\) 1.40070 0.0638664
\(482\) −15.2459 −0.694431
\(483\) 7.00533 0.318753
\(484\) −5.96482 −0.271128
\(485\) 3.75184 0.170362
\(486\) 5.74230 0.260476
\(487\) 37.2537 1.68812 0.844062 0.536245i \(-0.180158\pi\)
0.844062 + 0.536245i \(0.180158\pi\)
\(488\) −7.57710 −0.342999
\(489\) 32.1759 1.45504
\(490\) 4.76487 0.215255
\(491\) 36.7869 1.66017 0.830085 0.557637i \(-0.188292\pi\)
0.830085 + 0.557637i \(0.188292\pi\)
\(492\) 11.6264 0.524161
\(493\) −0.704881 −0.0317463
\(494\) 15.3232 0.689425
\(495\) 4.71789 0.212054
\(496\) 1.00000 0.0449013
\(497\) −7.54983 −0.338656
\(498\) 8.58427 0.384670
\(499\) 4.29955 0.192474 0.0962372 0.995358i \(-0.469319\pi\)
0.0962372 + 0.995358i \(0.469319\pi\)
\(500\) −15.2936 −0.683951
\(501\) 10.1934 0.455406
\(502\) −0.275802 −0.0123096
\(503\) 26.5264 1.18275 0.591377 0.806395i \(-0.298585\pi\)
0.591377 + 0.806395i \(0.298585\pi\)
\(504\) 1.34145 0.0597528
\(505\) 31.0430 1.38140
\(506\) −4.20436 −0.186906
\(507\) −9.92119 −0.440615
\(508\) −8.95664 −0.397387
\(509\) 0.727766 0.0322577 0.0161288 0.999870i \(-0.494866\pi\)
0.0161288 + 0.999870i \(0.494866\pi\)
\(510\) −0.576403 −0.0255235
\(511\) 23.6017 1.04408
\(512\) 1.00000 0.0441942
\(513\) −33.0491 −1.45915
\(514\) 5.99659 0.264498
\(515\) 41.2080 1.81584
\(516\) −8.52105 −0.375118
\(517\) −19.9817 −0.878794
\(518\) −1.30039 −0.0571358
\(519\) 3.50196 0.153719
\(520\) −9.67370 −0.424220
\(521\) 12.4453 0.545237 0.272618 0.962122i \(-0.412110\pi\)
0.272618 + 0.962122i \(0.412110\pi\)
\(522\) 4.01597 0.175774
\(523\) 16.9889 0.742871 0.371435 0.928459i \(-0.378866\pi\)
0.371435 + 0.928459i \(0.378866\pi\)
\(524\) −1.81408 −0.0792486
\(525\) −33.9348 −1.48104
\(526\) −14.5509 −0.634448
\(527\) 0.0983609 0.00428467
\(528\) 3.50483 0.152528
\(529\) −19.4894 −0.847364
\(530\) −10.7975 −0.469013
\(531\) 4.74883 0.206082
\(532\) −14.2259 −0.616769
\(533\) 19.1927 0.831328
\(534\) 12.8960 0.558065
\(535\) −2.02749 −0.0876560
\(536\) −11.3966 −0.492258
\(537\) 18.7193 0.807797
\(538\) 10.1366 0.437019
\(539\) −2.84980 −0.122750
\(540\) 20.8642 0.897853
\(541\) −2.19717 −0.0944636 −0.0472318 0.998884i \(-0.515040\pi\)
−0.0472318 + 0.998884i \(0.515040\pi\)
\(542\) 12.2040 0.524207
\(543\) 24.4795 1.05052
\(544\) 0.0983609 0.00421719
\(545\) 46.6223 1.99708
\(546\) −9.64018 −0.412561
\(547\) 17.2689 0.738364 0.369182 0.929357i \(-0.379638\pi\)
0.369182 + 0.929357i \(0.379638\pi\)
\(548\) 8.60658 0.367655
\(549\) 4.24619 0.181223
\(550\) 20.3665 0.868430
\(551\) −42.5888 −1.81434
\(552\) −2.92652 −0.124561
\(553\) 19.6164 0.834175
\(554\) −21.7743 −0.925103
\(555\) −3.18347 −0.135131
\(556\) −1.22561 −0.0519773
\(557\) −17.7728 −0.753058 −0.376529 0.926405i \(-0.622883\pi\)
−0.376529 + 0.926405i \(0.622883\pi\)
\(558\) −0.560398 −0.0237235
\(559\) −14.0664 −0.594944
\(560\) 8.98093 0.379513
\(561\) 0.344738 0.0145549
\(562\) −7.70986 −0.325221
\(563\) −23.9880 −1.01097 −0.505486 0.862835i \(-0.668687\pi\)
−0.505486 + 0.862835i \(0.668687\pi\)
\(564\) −13.9086 −0.585659
\(565\) −8.88616 −0.373844
\(566\) 16.7327 0.703328
\(567\) 16.7676 0.704172
\(568\) 3.15399 0.132338
\(569\) −42.9240 −1.79947 −0.899735 0.436437i \(-0.856240\pi\)
−0.899735 + 0.436437i \(0.856240\pi\)
\(570\) −34.8261 −1.45871
\(571\) 9.53021 0.398827 0.199413 0.979915i \(-0.436096\pi\)
0.199413 + 0.979915i \(0.436096\pi\)
\(572\) 5.78570 0.241912
\(573\) −4.55580 −0.190321
\(574\) −17.8182 −0.743718
\(575\) −17.0059 −0.709197
\(576\) −0.560398 −0.0233499
\(577\) −9.93712 −0.413688 −0.206844 0.978374i \(-0.566319\pi\)
−0.206844 + 0.978374i \(0.566319\pi\)
\(578\) −16.9903 −0.706704
\(579\) −10.4225 −0.433143
\(580\) 26.8867 1.11641
\(581\) −13.1559 −0.545799
\(582\) −1.56192 −0.0647438
\(583\) 6.45782 0.267455
\(584\) −9.85978 −0.408001
\(585\) 5.42112 0.224136
\(586\) 25.5368 1.05491
\(587\) 0.481022 0.0198539 0.00992695 0.999951i \(-0.496840\pi\)
0.00992695 + 0.999951i \(0.496840\pi\)
\(588\) −1.98366 −0.0818046
\(589\) 5.94294 0.244875
\(590\) 31.7932 1.30891
\(591\) 0.536098 0.0220521
\(592\) 0.543246 0.0223273
\(593\) 28.4099 1.16666 0.583328 0.812237i \(-0.301750\pi\)
0.583328 + 0.812237i \(0.301750\pi\)
\(594\) −12.4786 −0.512003
\(595\) 0.883372 0.0362147
\(596\) 4.91409 0.201289
\(597\) −29.1060 −1.19123
\(598\) −4.83104 −0.197556
\(599\) 25.1564 1.02786 0.513932 0.857831i \(-0.328188\pi\)
0.513932 + 0.857831i \(0.328188\pi\)
\(600\) 14.1765 0.578752
\(601\) −4.95961 −0.202307 −0.101153 0.994871i \(-0.532253\pi\)
−0.101153 + 0.994871i \(0.532253\pi\)
\(602\) 13.0590 0.532246
\(603\) 6.38663 0.260084
\(604\) 5.25936 0.214000
\(605\) 22.3790 0.909837
\(606\) −12.9235 −0.524980
\(607\) 33.7791 1.37105 0.685525 0.728049i \(-0.259573\pi\)
0.685525 + 0.728049i \(0.259573\pi\)
\(608\) 5.94294 0.241018
\(609\) 26.7935 1.08573
\(610\) 28.4281 1.15102
\(611\) −22.9601 −0.928866
\(612\) −0.0551212 −0.00222814
\(613\) 19.3378 0.781045 0.390523 0.920593i \(-0.372294\pi\)
0.390523 + 0.920593i \(0.372294\pi\)
\(614\) 9.96450 0.402135
\(615\) −43.6206 −1.75895
\(616\) −5.37136 −0.216418
\(617\) 44.3819 1.78675 0.893374 0.449314i \(-0.148331\pi\)
0.893374 + 0.449314i \(0.148331\pi\)
\(618\) −17.1553 −0.690086
\(619\) 0.993756 0.0399424 0.0199712 0.999801i \(-0.493643\pi\)
0.0199712 + 0.999801i \(0.493643\pi\)
\(620\) −3.75184 −0.150677
\(621\) 10.4196 0.418123
\(622\) 16.3760 0.656619
\(623\) −19.7639 −0.791824
\(624\) 4.02725 0.161219
\(625\) 11.9977 0.479908
\(626\) −30.9221 −1.23590
\(627\) 20.8290 0.831831
\(628\) −15.9814 −0.637726
\(629\) 0.0534341 0.00213056
\(630\) −5.03289 −0.200515
\(631\) 5.90755 0.235176 0.117588 0.993062i \(-0.462484\pi\)
0.117588 + 0.993062i \(0.462484\pi\)
\(632\) −8.19488 −0.325975
\(633\) −26.2651 −1.04395
\(634\) −2.71329 −0.107759
\(635\) 33.6039 1.33353
\(636\) 4.49508 0.178242
\(637\) −3.27458 −0.129744
\(638\) −16.0806 −0.636635
\(639\) −1.76749 −0.0699208
\(640\) −3.75184 −0.148304
\(641\) 21.3085 0.841634 0.420817 0.907146i \(-0.361743\pi\)
0.420817 + 0.907146i \(0.361743\pi\)
\(642\) 0.844061 0.0333124
\(643\) −4.76022 −0.187725 −0.0938623 0.995585i \(-0.529921\pi\)
−0.0938623 + 0.995585i \(0.529921\pi\)
\(644\) 4.48507 0.176736
\(645\) 31.9696 1.25880
\(646\) 0.584553 0.0229989
\(647\) −27.2597 −1.07169 −0.535845 0.844316i \(-0.680007\pi\)
−0.535845 + 0.844316i \(0.680007\pi\)
\(648\) −7.00476 −0.275173
\(649\) −19.0151 −0.746407
\(650\) 23.4022 0.917911
\(651\) −3.73884 −0.146537
\(652\) 20.6002 0.806766
\(653\) 38.1641 1.49348 0.746738 0.665118i \(-0.231619\pi\)
0.746738 + 0.665118i \(0.231619\pi\)
\(654\) −19.4093 −0.758962
\(655\) 6.80614 0.265938
\(656\) 7.44368 0.290627
\(657\) 5.52540 0.215566
\(658\) 21.3158 0.830977
\(659\) 23.1460 0.901640 0.450820 0.892615i \(-0.351132\pi\)
0.450820 + 0.892615i \(0.351132\pi\)
\(660\) −13.1496 −0.511846
\(661\) 24.0712 0.936259 0.468130 0.883660i \(-0.344928\pi\)
0.468130 + 0.883660i \(0.344928\pi\)
\(662\) −26.5667 −1.03254
\(663\) 0.396123 0.0153842
\(664\) 5.49596 0.213285
\(665\) 53.3732 2.06972
\(666\) −0.304434 −0.0117966
\(667\) 13.4272 0.519903
\(668\) 6.52617 0.252505
\(669\) −12.1879 −0.471212
\(670\) 42.7582 1.65189
\(671\) −17.0024 −0.656371
\(672\) −3.73884 −0.144229
\(673\) −21.7421 −0.838097 −0.419048 0.907964i \(-0.637636\pi\)
−0.419048 + 0.907964i \(0.637636\pi\)
\(674\) 32.3828 1.24734
\(675\) −50.4739 −1.94274
\(676\) −6.35191 −0.244304
\(677\) 6.56881 0.252460 0.126230 0.992001i \(-0.459712\pi\)
0.126230 + 0.992001i \(0.459712\pi\)
\(678\) 3.69938 0.142074
\(679\) 2.39374 0.0918633
\(680\) −0.369034 −0.0141518
\(681\) −23.4624 −0.899079
\(682\) 2.24392 0.0859242
\(683\) 8.44591 0.323174 0.161587 0.986859i \(-0.448339\pi\)
0.161587 + 0.986859i \(0.448339\pi\)
\(684\) −3.33041 −0.127342
\(685\) −32.2905 −1.23376
\(686\) 19.7963 0.755824
\(687\) −15.9125 −0.607099
\(688\) −5.45549 −0.207989
\(689\) 7.42039 0.282694
\(690\) 10.9798 0.417995
\(691\) 28.1775 1.07192 0.535960 0.844243i \(-0.319950\pi\)
0.535960 + 0.844243i \(0.319950\pi\)
\(692\) 2.24208 0.0852311
\(693\) 3.01010 0.114344
\(694\) 21.7246 0.824655
\(695\) 4.59828 0.174423
\(696\) −11.1932 −0.424276
\(697\) 0.732166 0.0277328
\(698\) 17.4429 0.660224
\(699\) 38.5941 1.45976
\(700\) −21.7263 −0.821177
\(701\) −37.2466 −1.40678 −0.703392 0.710802i \(-0.748332\pi\)
−0.703392 + 0.710802i \(0.748332\pi\)
\(702\) −14.3386 −0.541175
\(703\) 3.22848 0.121764
\(704\) 2.24392 0.0845710
\(705\) 52.1830 1.96532
\(706\) −17.0303 −0.640945
\(707\) 19.8060 0.744881
\(708\) −13.2358 −0.497432
\(709\) 38.7576 1.45557 0.727786 0.685805i \(-0.240550\pi\)
0.727786 + 0.685805i \(0.240550\pi\)
\(710\) −11.8333 −0.444094
\(711\) 4.59240 0.172228
\(712\) 8.25650 0.309425
\(713\) −1.87367 −0.0701693
\(714\) −0.367755 −0.0137629
\(715\) −21.7070 −0.811797
\(716\) 11.9848 0.447892
\(717\) −17.0283 −0.635932
\(718\) −6.88917 −0.257101
\(719\) −40.1264 −1.49646 −0.748231 0.663438i \(-0.769097\pi\)
−0.748231 + 0.663438i \(0.769097\pi\)
\(720\) 2.10252 0.0783564
\(721\) 26.2915 0.979145
\(722\) 16.3186 0.607315
\(723\) −23.8129 −0.885611
\(724\) 15.6727 0.582471
\(725\) −65.0433 −2.41565
\(726\) −9.31658 −0.345771
\(727\) 22.4005 0.830787 0.415394 0.909642i \(-0.363644\pi\)
0.415394 + 0.909642i \(0.363644\pi\)
\(728\) −6.17199 −0.228749
\(729\) 29.9833 1.11049
\(730\) 36.9923 1.36915
\(731\) −0.536607 −0.0198471
\(732\) −11.8348 −0.437429
\(733\) 23.5236 0.868862 0.434431 0.900705i \(-0.356949\pi\)
0.434431 + 0.900705i \(0.356949\pi\)
\(734\) 28.0593 1.03569
\(735\) 7.44236 0.274516
\(736\) −1.87367 −0.0690642
\(737\) −25.5731 −0.941996
\(738\) −4.17142 −0.153552
\(739\) −3.74419 −0.137732 −0.0688661 0.997626i \(-0.521938\pi\)
−0.0688661 + 0.997626i \(0.521938\pi\)
\(740\) −2.03817 −0.0749247
\(741\) 23.9337 0.879226
\(742\) −6.88898 −0.252903
\(743\) −30.1601 −1.10647 −0.553233 0.833026i \(-0.686606\pi\)
−0.553233 + 0.833026i \(0.686606\pi\)
\(744\) 1.56192 0.0572629
\(745\) −18.4369 −0.675475
\(746\) 17.7996 0.651691
\(747\) −3.07992 −0.112689
\(748\) 0.220714 0.00807010
\(749\) −1.29357 −0.0472662
\(750\) −23.8874 −0.872246
\(751\) −48.6350 −1.77472 −0.887358 0.461082i \(-0.847461\pi\)
−0.887358 + 0.461082i \(0.847461\pi\)
\(752\) −8.90482 −0.324725
\(753\) −0.430781 −0.0156985
\(754\) −18.4775 −0.672909
\(755\) −19.7323 −0.718131
\(756\) 13.3117 0.484143
\(757\) −42.7839 −1.55501 −0.777504 0.628878i \(-0.783515\pi\)
−0.777504 + 0.628878i \(0.783515\pi\)
\(758\) −12.7562 −0.463324
\(759\) −6.56688 −0.238363
\(760\) −22.2970 −0.808796
\(761\) −23.4138 −0.848748 −0.424374 0.905487i \(-0.639506\pi\)
−0.424374 + 0.905487i \(0.639506\pi\)
\(762\) −13.9896 −0.506789
\(763\) 29.7458 1.07687
\(764\) −2.91679 −0.105526
\(765\) 0.206806 0.00747708
\(766\) −25.5429 −0.922901
\(767\) −21.8494 −0.788935
\(768\) 1.56192 0.0563610
\(769\) −8.73251 −0.314902 −0.157451 0.987527i \(-0.550328\pi\)
−0.157451 + 0.987527i \(0.550328\pi\)
\(770\) 20.1525 0.726245
\(771\) 9.36621 0.337316
\(772\) −6.67285 −0.240161
\(773\) −19.6191 −0.705650 −0.352825 0.935689i \(-0.614779\pi\)
−0.352825 + 0.935689i \(0.614779\pi\)
\(774\) 3.05724 0.109890
\(775\) 9.07630 0.326030
\(776\) −1.00000 −0.0358979
\(777\) −2.03111 −0.0728656
\(778\) 5.01300 0.179725
\(779\) 44.2374 1.58497
\(780\) −15.1096 −0.541010
\(781\) 7.07730 0.253246
\(782\) −0.184295 −0.00659039
\(783\) 39.8521 1.42420
\(784\) −1.27001 −0.0453575
\(785\) 59.9596 2.14005
\(786\) −2.83346 −0.101066
\(787\) −11.4801 −0.409221 −0.204611 0.978843i \(-0.565593\pi\)
−0.204611 + 0.978843i \(0.565593\pi\)
\(788\) 0.343230 0.0122270
\(789\) −22.7273 −0.809115
\(790\) 30.7459 1.09389
\(791\) −5.66953 −0.201585
\(792\) −1.25749 −0.0446829
\(793\) −19.5367 −0.693769
\(794\) −28.8266 −1.02302
\(795\) −16.8648 −0.598134
\(796\) −18.6347 −0.660491
\(797\) −12.9066 −0.457175 −0.228588 0.973523i \(-0.573411\pi\)
−0.228588 + 0.973523i \(0.573411\pi\)
\(798\) −22.2197 −0.786569
\(799\) −0.875885 −0.0309866
\(800\) 9.07630 0.320896
\(801\) −4.62692 −0.163484
\(802\) 15.1201 0.533911
\(803\) −22.1246 −0.780759
\(804\) −17.8006 −0.627779
\(805\) −16.8273 −0.593083
\(806\) 2.57839 0.0908199
\(807\) 15.8326 0.557333
\(808\) −8.27408 −0.291081
\(809\) −32.3221 −1.13638 −0.568191 0.822896i \(-0.692357\pi\)
−0.568191 + 0.822896i \(0.692357\pi\)
\(810\) 26.2807 0.923411
\(811\) 45.8968 1.61165 0.805827 0.592151i \(-0.201721\pi\)
0.805827 + 0.592151i \(0.201721\pi\)
\(812\) 17.1542 0.601995
\(813\) 19.0617 0.668523
\(814\) 1.21900 0.0427260
\(815\) −77.2886 −2.70730
\(816\) 0.153632 0.00537820
\(817\) −32.4217 −1.13429
\(818\) −13.3584 −0.467067
\(819\) 3.45877 0.120859
\(820\) −27.9275 −0.975270
\(821\) 4.74026 0.165436 0.0827182 0.996573i \(-0.473640\pi\)
0.0827182 + 0.996573i \(0.473640\pi\)
\(822\) 13.4428 0.468872
\(823\) 31.3979 1.09446 0.547231 0.836981i \(-0.315682\pi\)
0.547231 + 0.836981i \(0.315682\pi\)
\(824\) −10.9834 −0.382626
\(825\) 31.8109 1.10751
\(826\) 20.2846 0.705793
\(827\) −6.81237 −0.236889 −0.118445 0.992961i \(-0.537791\pi\)
−0.118445 + 0.992961i \(0.537791\pi\)
\(828\) 1.05000 0.0364900
\(829\) −16.8112 −0.583878 −0.291939 0.956437i \(-0.594300\pi\)
−0.291939 + 0.956437i \(0.594300\pi\)
\(830\) −20.6200 −0.715729
\(831\) −34.0098 −1.17979
\(832\) 2.57839 0.0893896
\(833\) −0.124919 −0.00432819
\(834\) −1.91430 −0.0662869
\(835\) −24.4851 −0.847343
\(836\) 13.3355 0.461218
\(837\) −5.56107 −0.192219
\(838\) −11.4278 −0.394767
\(839\) −1.04239 −0.0359875 −0.0179937 0.999838i \(-0.505728\pi\)
−0.0179937 + 0.999838i \(0.505728\pi\)
\(840\) 14.0275 0.483995
\(841\) 22.3555 0.770880
\(842\) −34.7650 −1.19808
\(843\) −12.0422 −0.414756
\(844\) −16.8159 −0.578827
\(845\) 23.8313 0.819823
\(846\) 4.99024 0.171568
\(847\) 14.2782 0.490606
\(848\) 2.87792 0.0988281
\(849\) 26.1352 0.896957
\(850\) 0.892752 0.0306212
\(851\) −1.01786 −0.0348918
\(852\) 4.92629 0.168772
\(853\) −26.5391 −0.908682 −0.454341 0.890828i \(-0.650125\pi\)
−0.454341 + 0.890828i \(0.650125\pi\)
\(854\) 18.1376 0.620656
\(855\) 12.4952 0.427326
\(856\) 0.540399 0.0184704
\(857\) −45.5640 −1.55644 −0.778218 0.627994i \(-0.783876\pi\)
−0.778218 + 0.627994i \(0.783876\pi\)
\(858\) 9.03682 0.308512
\(859\) −36.2295 −1.23613 −0.618067 0.786126i \(-0.712084\pi\)
−0.618067 + 0.786126i \(0.712084\pi\)
\(860\) 20.4681 0.697957
\(861\) −27.8307 −0.948467
\(862\) 10.8643 0.370038
\(863\) 14.3389 0.488100 0.244050 0.969763i \(-0.421524\pi\)
0.244050 + 0.969763i \(0.421524\pi\)
\(864\) −5.56107 −0.189191
\(865\) −8.41193 −0.286014
\(866\) 39.8552 1.35434
\(867\) −26.5376 −0.901263
\(868\) −2.39374 −0.0812488
\(869\) −18.3887 −0.623793
\(870\) 41.9950 1.42376
\(871\) −29.3849 −0.995669
\(872\) −12.4265 −0.420815
\(873\) 0.560398 0.0189666
\(874\) −11.1351 −0.376650
\(875\) 36.6089 1.23761
\(876\) −15.4002 −0.520325
\(877\) −30.5967 −1.03318 −0.516589 0.856233i \(-0.672799\pi\)
−0.516589 + 0.856233i \(0.672799\pi\)
\(878\) 1.11217 0.0375339
\(879\) 39.8864 1.34534
\(880\) −8.41883 −0.283799
\(881\) 9.82117 0.330884 0.165442 0.986220i \(-0.447095\pi\)
0.165442 + 0.986220i \(0.447095\pi\)
\(882\) 0.711711 0.0239645
\(883\) 40.5589 1.36492 0.682458 0.730925i \(-0.260911\pi\)
0.682458 + 0.730925i \(0.260911\pi\)
\(884\) 0.253613 0.00852992
\(885\) 49.6586 1.66925
\(886\) −20.0217 −0.672642
\(887\) 18.6428 0.625963 0.312982 0.949759i \(-0.398672\pi\)
0.312982 + 0.949759i \(0.398672\pi\)
\(888\) 0.848508 0.0284741
\(889\) 21.4399 0.719070
\(890\) −30.9771 −1.03835
\(891\) −15.7181 −0.526577
\(892\) −7.80316 −0.261269
\(893\) −52.9208 −1.77093
\(894\) 7.67543 0.256705
\(895\) −44.9649 −1.50301
\(896\) −2.39374 −0.0799692
\(897\) −7.54571 −0.251944
\(898\) −11.6894 −0.390080
\(899\) −7.16628 −0.239009
\(900\) −5.08634 −0.169545
\(901\) 0.283074 0.00943057
\(902\) 16.7030 0.556150
\(903\) 20.3972 0.678776
\(904\) 2.36848 0.0787745
\(905\) −58.8014 −1.95462
\(906\) 8.21472 0.272916
\(907\) 46.1852 1.53355 0.766777 0.641913i \(-0.221859\pi\)
0.766777 + 0.641913i \(0.221859\pi\)
\(908\) −15.0215 −0.498505
\(909\) 4.63678 0.153792
\(910\) 23.1563 0.767625
\(911\) 27.5874 0.914011 0.457006 0.889464i \(-0.348922\pi\)
0.457006 + 0.889464i \(0.348922\pi\)
\(912\) 9.28242 0.307372
\(913\) 12.3325 0.408146
\(914\) 14.8909 0.492547
\(915\) 44.4025 1.46790
\(916\) −10.1878 −0.336613
\(917\) 4.34244 0.143400
\(918\) −0.546991 −0.0180534
\(919\) −52.9597 −1.74698 −0.873490 0.486842i \(-0.838149\pi\)
−0.873490 + 0.486842i \(0.838149\pi\)
\(920\) 7.02969 0.231762
\(921\) 15.5638 0.512844
\(922\) −26.1101 −0.859891
\(923\) 8.13221 0.267675
\(924\) −8.38965 −0.275999
\(925\) 4.93066 0.162119
\(926\) −5.62200 −0.184750
\(927\) 6.15509 0.202160
\(928\) −7.16628 −0.235245
\(929\) 40.9581 1.34379 0.671896 0.740645i \(-0.265480\pi\)
0.671896 + 0.740645i \(0.265480\pi\)
\(930\) −5.86008 −0.192160
\(931\) −7.54760 −0.247362
\(932\) 24.7094 0.809382
\(933\) 25.5781 0.837389
\(934\) −38.7588 −1.26823
\(935\) −0.828083 −0.0270812
\(936\) −1.44492 −0.0472288
\(937\) −32.6865 −1.06782 −0.533911 0.845541i \(-0.679278\pi\)
−0.533911 + 0.845541i \(0.679278\pi\)
\(938\) 27.2805 0.890740
\(939\) −48.2979 −1.57614
\(940\) 33.4094 1.08970
\(941\) −44.9518 −1.46539 −0.732694 0.680558i \(-0.761737\pi\)
−0.732694 + 0.680558i \(0.761737\pi\)
\(942\) −24.9617 −0.813295
\(943\) −13.9470 −0.454175
\(944\) −8.47404 −0.275806
\(945\) −49.9435 −1.62466
\(946\) −12.2417 −0.398012
\(947\) 24.3199 0.790289 0.395145 0.918619i \(-0.370694\pi\)
0.395145 + 0.918619i \(0.370694\pi\)
\(948\) −12.7998 −0.415717
\(949\) −25.4224 −0.825245
\(950\) 53.9399 1.75004
\(951\) −4.23795 −0.137425
\(952\) −0.235450 −0.00763099
\(953\) −27.9528 −0.905479 −0.452740 0.891643i \(-0.649553\pi\)
−0.452740 + 0.891643i \(0.649553\pi\)
\(954\) −1.61278 −0.0522156
\(955\) 10.9433 0.354118
\(956\) −10.9021 −0.352600
\(957\) −25.1166 −0.811904
\(958\) 14.2225 0.459508
\(959\) −20.6019 −0.665271
\(960\) −5.86008 −0.189133
\(961\) 1.00000 0.0322581
\(962\) 1.40070 0.0451604
\(963\) −0.302838 −0.00975883
\(964\) −15.2459 −0.491037
\(965\) 25.0354 0.805919
\(966\) 7.00533 0.225393
\(967\) 17.2667 0.555260 0.277630 0.960688i \(-0.410451\pi\)
0.277630 + 0.960688i \(0.410451\pi\)
\(968\) −5.96482 −0.191717
\(969\) 0.913027 0.0293306
\(970\) 3.75184 0.120464
\(971\) 39.9411 1.28177 0.640885 0.767637i \(-0.278567\pi\)
0.640885 + 0.767637i \(0.278567\pi\)
\(972\) 5.74230 0.184184
\(973\) 2.93378 0.0940528
\(974\) 37.2537 1.19368
\(975\) 36.5525 1.17062
\(976\) −7.57710 −0.242537
\(977\) −3.10021 −0.0991846 −0.0495923 0.998770i \(-0.515792\pi\)
−0.0495923 + 0.998770i \(0.515792\pi\)
\(978\) 32.1759 1.02887
\(979\) 18.5269 0.592123
\(980\) 4.76487 0.152208
\(981\) 6.96379 0.222337
\(982\) 36.7869 1.17392
\(983\) 32.6254 1.04059 0.520294 0.853987i \(-0.325823\pi\)
0.520294 + 0.853987i \(0.325823\pi\)
\(984\) 11.6264 0.370638
\(985\) −1.28774 −0.0410309
\(986\) −0.704881 −0.0224480
\(987\) 33.2937 1.05975
\(988\) 15.3232 0.487497
\(989\) 10.2218 0.325033
\(990\) 4.71789 0.149945
\(991\) −37.0927 −1.17829 −0.589145 0.808028i \(-0.700535\pi\)
−0.589145 + 0.808028i \(0.700535\pi\)
\(992\) 1.00000 0.0317500
\(993\) −41.4951 −1.31681
\(994\) −7.54983 −0.239466
\(995\) 69.9146 2.21644
\(996\) 8.58427 0.272003
\(997\) −26.0630 −0.825423 −0.412711 0.910862i \(-0.635418\pi\)
−0.412711 + 0.910862i \(0.635418\pi\)
\(998\) 4.29955 0.136100
\(999\) −3.02103 −0.0955811
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 6014.2.a.e.1.17 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.e.1.17 21 1.1 even 1 trivial