Properties

Label 6018.2.a.w.1.7
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $9$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - x^{8} - 22x^{7} + 20x^{6} + 129x^{5} - 106x^{4} - 126x^{3} + 48x^{2} + 24x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.44979\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.44979 q^{5} -1.00000 q^{6} +4.37806 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.44979 q^{5} -1.00000 q^{6} +4.37806 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.44979 q^{10} +5.18439 q^{11} +1.00000 q^{12} -1.77261 q^{13} -4.37806 q^{14} +1.44979 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.63563 q^{19} +1.44979 q^{20} +4.37806 q^{21} -5.18439 q^{22} +0.245496 q^{23} -1.00000 q^{24} -2.89810 q^{25} +1.77261 q^{26} +1.00000 q^{27} +4.37806 q^{28} +4.12193 q^{29} -1.44979 q^{30} -4.83360 q^{31} -1.00000 q^{32} +5.18439 q^{33} -1.00000 q^{34} +6.34728 q^{35} +1.00000 q^{36} +7.94495 q^{37} -1.63563 q^{38} -1.77261 q^{39} -1.44979 q^{40} -9.26927 q^{41} -4.37806 q^{42} -1.10770 q^{43} +5.18439 q^{44} +1.44979 q^{45} -0.245496 q^{46} +4.83205 q^{47} +1.00000 q^{48} +12.1674 q^{49} +2.89810 q^{50} +1.00000 q^{51} -1.77261 q^{52} -6.02547 q^{53} -1.00000 q^{54} +7.51629 q^{55} -4.37806 q^{56} +1.63563 q^{57} -4.12193 q^{58} +1.00000 q^{59} +1.44979 q^{60} +12.3248 q^{61} +4.83360 q^{62} +4.37806 q^{63} +1.00000 q^{64} -2.56992 q^{65} -5.18439 q^{66} +1.78528 q^{67} +1.00000 q^{68} +0.245496 q^{69} -6.34728 q^{70} +1.68929 q^{71} -1.00000 q^{72} -3.63143 q^{73} -7.94495 q^{74} -2.89810 q^{75} +1.63563 q^{76} +22.6975 q^{77} +1.77261 q^{78} -8.59258 q^{79} +1.44979 q^{80} +1.00000 q^{81} +9.26927 q^{82} +1.43522 q^{83} +4.37806 q^{84} +1.44979 q^{85} +1.10770 q^{86} +4.12193 q^{87} -5.18439 q^{88} +3.26823 q^{89} -1.44979 q^{90} -7.76060 q^{91} +0.245496 q^{92} -4.83360 q^{93} -4.83205 q^{94} +2.37133 q^{95} -1.00000 q^{96} -4.03329 q^{97} -12.1674 q^{98} +5.18439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9} - q^{10} + 6 q^{11} + 9 q^{12} + 2 q^{13} + q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 5 q^{19} + q^{20} - 6 q^{22} + 15 q^{23} - 9 q^{24} - 2 q^{26} + 9 q^{27} + 11 q^{29} - q^{30} - 5 q^{31} - 9 q^{32} + 6 q^{33} - 9 q^{34} + 22 q^{35} + 9 q^{36} + 9 q^{37} + 5 q^{38} + 2 q^{39} - q^{40} + q^{41} + 4 q^{43} + 6 q^{44} + q^{45} - 15 q^{46} + 14 q^{47} + 9 q^{48} - q^{49} + 9 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} + 4 q^{55} - 5 q^{57} - 11 q^{58} + 9 q^{59} + q^{60} + 10 q^{61} + 5 q^{62} + 9 q^{64} + 8 q^{65} - 6 q^{66} - q^{67} + 9 q^{68} + 15 q^{69} - 22 q^{70} + 14 q^{71} - 9 q^{72} - q^{73} - 9 q^{74} - 5 q^{76} + 30 q^{77} - 2 q^{78} + 4 q^{79} + q^{80} + 9 q^{81} - q^{82} + 22 q^{83} + q^{85} - 4 q^{86} + 11 q^{87} - 6 q^{88} + 22 q^{89} - q^{90} - 3 q^{91} + 15 q^{92} - 5 q^{93} - 14 q^{94} + 43 q^{95} - 9 q^{96} - 15 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) \) 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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.44979 0.648367 0.324184 0.945994i \(-0.394910\pi\)
0.324184 + 0.945994i \(0.394910\pi\)
\(6\) −1.00000 −0.408248
\(7\) 4.37806 1.65475 0.827375 0.561650i \(-0.189833\pi\)
0.827375 + 0.561650i \(0.189833\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.44979 −0.458465
\(11\) 5.18439 1.56315 0.781576 0.623810i \(-0.214416\pi\)
0.781576 + 0.623810i \(0.214416\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.77261 −0.491634 −0.245817 0.969316i \(-0.579056\pi\)
−0.245817 + 0.969316i \(0.579056\pi\)
\(14\) −4.37806 −1.17008
\(15\) 1.44979 0.374335
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 1.63563 0.375240 0.187620 0.982242i \(-0.439923\pi\)
0.187620 + 0.982242i \(0.439923\pi\)
\(20\) 1.44979 0.324184
\(21\) 4.37806 0.955370
\(22\) −5.18439 −1.10532
\(23\) 0.245496 0.0511895 0.0255948 0.999672i \(-0.491852\pi\)
0.0255948 + 0.999672i \(0.491852\pi\)
\(24\) −1.00000 −0.204124
\(25\) −2.89810 −0.579620
\(26\) 1.77261 0.347638
\(27\) 1.00000 0.192450
\(28\) 4.37806 0.827375
\(29\) 4.12193 0.765423 0.382711 0.923868i \(-0.374990\pi\)
0.382711 + 0.923868i \(0.374990\pi\)
\(30\) −1.44979 −0.264695
\(31\) −4.83360 −0.868140 −0.434070 0.900879i \(-0.642923\pi\)
−0.434070 + 0.900879i \(0.642923\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.18439 0.902486
\(34\) −1.00000 −0.171499
\(35\) 6.34728 1.07289
\(36\) 1.00000 0.166667
\(37\) 7.94495 1.30614 0.653071 0.757297i \(-0.273480\pi\)
0.653071 + 0.757297i \(0.273480\pi\)
\(38\) −1.63563 −0.265335
\(39\) −1.77261 −0.283845
\(40\) −1.44979 −0.229232
\(41\) −9.26927 −1.44762 −0.723809 0.690001i \(-0.757610\pi\)
−0.723809 + 0.690001i \(0.757610\pi\)
\(42\) −4.37806 −0.675549
\(43\) −1.10770 −0.168923 −0.0844614 0.996427i \(-0.526917\pi\)
−0.0844614 + 0.996427i \(0.526917\pi\)
\(44\) 5.18439 0.781576
\(45\) 1.44979 0.216122
\(46\) −0.245496 −0.0361965
\(47\) 4.83205 0.704827 0.352414 0.935844i \(-0.385361\pi\)
0.352414 + 0.935844i \(0.385361\pi\)
\(48\) 1.00000 0.144338
\(49\) 12.1674 1.73820
\(50\) 2.89810 0.409853
\(51\) 1.00000 0.140028
\(52\) −1.77261 −0.245817
\(53\) −6.02547 −0.827662 −0.413831 0.910354i \(-0.635809\pi\)
−0.413831 + 0.910354i \(0.635809\pi\)
\(54\) −1.00000 −0.136083
\(55\) 7.51629 1.01350
\(56\) −4.37806 −0.585042
\(57\) 1.63563 0.216645
\(58\) −4.12193 −0.541236
\(59\) 1.00000 0.130189
\(60\) 1.44979 0.187168
\(61\) 12.3248 1.57802 0.789012 0.614377i \(-0.210593\pi\)
0.789012 + 0.614377i \(0.210593\pi\)
\(62\) 4.83360 0.613868
\(63\) 4.37806 0.551583
\(64\) 1.00000 0.125000
\(65\) −2.56992 −0.318760
\(66\) −5.18439 −0.638154
\(67\) 1.78528 0.218107 0.109053 0.994036i \(-0.465218\pi\)
0.109053 + 0.994036i \(0.465218\pi\)
\(68\) 1.00000 0.121268
\(69\) 0.245496 0.0295543
\(70\) −6.34728 −0.758645
\(71\) 1.68929 0.200482 0.100241 0.994963i \(-0.468039\pi\)
0.100241 + 0.994963i \(0.468039\pi\)
\(72\) −1.00000 −0.117851
\(73\) −3.63143 −0.425026 −0.212513 0.977158i \(-0.568165\pi\)
−0.212513 + 0.977158i \(0.568165\pi\)
\(74\) −7.94495 −0.923582
\(75\) −2.89810 −0.334644
\(76\) 1.63563 0.187620
\(77\) 22.6975 2.58663
\(78\) 1.77261 0.200709
\(79\) −8.59258 −0.966741 −0.483371 0.875416i \(-0.660588\pi\)
−0.483371 + 0.875416i \(0.660588\pi\)
\(80\) 1.44979 0.162092
\(81\) 1.00000 0.111111
\(82\) 9.26927 1.02362
\(83\) 1.43522 0.157536 0.0787678 0.996893i \(-0.474901\pi\)
0.0787678 + 0.996893i \(0.474901\pi\)
\(84\) 4.37806 0.477685
\(85\) 1.44979 0.157252
\(86\) 1.10770 0.119446
\(87\) 4.12193 0.441917
\(88\) −5.18439 −0.552658
\(89\) 3.26823 0.346432 0.173216 0.984884i \(-0.444584\pi\)
0.173216 + 0.984884i \(0.444584\pi\)
\(90\) −1.44979 −0.152822
\(91\) −7.76060 −0.813532
\(92\) 0.245496 0.0255948
\(93\) −4.83360 −0.501221
\(94\) −4.83205 −0.498388
\(95\) 2.37133 0.243294
\(96\) −1.00000 −0.102062
\(97\) −4.03329 −0.409519 −0.204759 0.978812i \(-0.565641\pi\)
−0.204759 + 0.978812i \(0.565641\pi\)
\(98\) −12.1674 −1.22909
\(99\) 5.18439 0.521051
\(100\) −2.89810 −0.289810
\(101\) −2.07672 −0.206641 −0.103321 0.994648i \(-0.532947\pi\)
−0.103321 + 0.994648i \(0.532947\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −6.47581 −0.638080 −0.319040 0.947741i \(-0.603360\pi\)
−0.319040 + 0.947741i \(0.603360\pi\)
\(104\) 1.77261 0.173819
\(105\) 6.34728 0.619431
\(106\) 6.02547 0.585245
\(107\) 16.8654 1.63044 0.815221 0.579150i \(-0.196615\pi\)
0.815221 + 0.579150i \(0.196615\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.54545 −0.243810 −0.121905 0.992542i \(-0.538900\pi\)
−0.121905 + 0.992542i \(0.538900\pi\)
\(110\) −7.51629 −0.716651
\(111\) 7.94495 0.754101
\(112\) 4.37806 0.413687
\(113\) −0.191265 −0.0179927 −0.00899635 0.999960i \(-0.502864\pi\)
−0.00899635 + 0.999960i \(0.502864\pi\)
\(114\) −1.63563 −0.153191
\(115\) 0.355919 0.0331896
\(116\) 4.12193 0.382711
\(117\) −1.77261 −0.163878
\(118\) −1.00000 −0.0920575
\(119\) 4.37806 0.401336
\(120\) −1.44979 −0.132347
\(121\) 15.8779 1.44345
\(122\) −12.3248 −1.11583
\(123\) −9.26927 −0.835782
\(124\) −4.83360 −0.434070
\(125\) −11.4506 −1.02417
\(126\) −4.37806 −0.390028
\(127\) −16.0068 −1.42038 −0.710189 0.704011i \(-0.751390\pi\)
−0.710189 + 0.704011i \(0.751390\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.10770 −0.0975276
\(130\) 2.56992 0.225397
\(131\) 14.9695 1.30789 0.653945 0.756542i \(-0.273113\pi\)
0.653945 + 0.756542i \(0.273113\pi\)
\(132\) 5.18439 0.451243
\(133\) 7.16090 0.620929
\(134\) −1.78528 −0.154225
\(135\) 1.44979 0.124778
\(136\) −1.00000 −0.0857493
\(137\) 0.381874 0.0326257 0.0163128 0.999867i \(-0.494807\pi\)
0.0163128 + 0.999867i \(0.494807\pi\)
\(138\) −0.245496 −0.0208980
\(139\) 3.65947 0.310392 0.155196 0.987884i \(-0.450399\pi\)
0.155196 + 0.987884i \(0.450399\pi\)
\(140\) 6.34728 0.536443
\(141\) 4.83205 0.406932
\(142\) −1.68929 −0.141762
\(143\) −9.18992 −0.768500
\(144\) 1.00000 0.0833333
\(145\) 5.97594 0.496275
\(146\) 3.63143 0.300539
\(147\) 12.1674 1.00355
\(148\) 7.94495 0.653071
\(149\) 13.6599 1.11906 0.559531 0.828809i \(-0.310981\pi\)
0.559531 + 0.828809i \(0.310981\pi\)
\(150\) 2.89810 0.236629
\(151\) −19.2914 −1.56991 −0.784955 0.619553i \(-0.787314\pi\)
−0.784955 + 0.619553i \(0.787314\pi\)
\(152\) −1.63563 −0.132667
\(153\) 1.00000 0.0808452
\(154\) −22.6975 −1.82902
\(155\) −7.00772 −0.562874
\(156\) −1.77261 −0.141923
\(157\) 10.3290 0.824342 0.412171 0.911106i \(-0.364771\pi\)
0.412171 + 0.911106i \(0.364771\pi\)
\(158\) 8.59258 0.683589
\(159\) −6.02547 −0.477851
\(160\) −1.44979 −0.114616
\(161\) 1.07480 0.0847058
\(162\) −1.00000 −0.0785674
\(163\) −11.7369 −0.919306 −0.459653 0.888099i \(-0.652026\pi\)
−0.459653 + 0.888099i \(0.652026\pi\)
\(164\) −9.26927 −0.723809
\(165\) 7.51629 0.585143
\(166\) −1.43522 −0.111394
\(167\) 0.647953 0.0501401 0.0250701 0.999686i \(-0.492019\pi\)
0.0250701 + 0.999686i \(0.492019\pi\)
\(168\) −4.37806 −0.337774
\(169\) −9.85784 −0.758296
\(170\) −1.44979 −0.111194
\(171\) 1.63563 0.125080
\(172\) −1.10770 −0.0844614
\(173\) −2.21096 −0.168097 −0.0840483 0.996462i \(-0.526785\pi\)
−0.0840483 + 0.996462i \(0.526785\pi\)
\(174\) −4.12193 −0.312483
\(175\) −12.6880 −0.959125
\(176\) 5.18439 0.390788
\(177\) 1.00000 0.0751646
\(178\) −3.26823 −0.244964
\(179\) −2.20048 −0.164472 −0.0822359 0.996613i \(-0.526206\pi\)
−0.0822359 + 0.996613i \(0.526206\pi\)
\(180\) 1.44979 0.108061
\(181\) −16.8381 −1.25156 −0.625781 0.779999i \(-0.715220\pi\)
−0.625781 + 0.779999i \(0.715220\pi\)
\(182\) 7.76060 0.575254
\(183\) 12.3248 0.911073
\(184\) −0.245496 −0.0180982
\(185\) 11.5185 0.846860
\(186\) 4.83360 0.354417
\(187\) 5.18439 0.379120
\(188\) 4.83205 0.352414
\(189\) 4.37806 0.318457
\(190\) −2.37133 −0.172035
\(191\) 7.42739 0.537427 0.268713 0.963220i \(-0.413402\pi\)
0.268713 + 0.963220i \(0.413402\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.61155 −0.331947 −0.165973 0.986130i \(-0.553077\pi\)
−0.165973 + 0.986130i \(0.553077\pi\)
\(194\) 4.03329 0.289573
\(195\) −2.56992 −0.184036
\(196\) 12.1674 0.869098
\(197\) −0.0799799 −0.00569834 −0.00284917 0.999996i \(-0.500907\pi\)
−0.00284917 + 0.999996i \(0.500907\pi\)
\(198\) −5.18439 −0.368439
\(199\) −14.5150 −1.02894 −0.514472 0.857507i \(-0.672012\pi\)
−0.514472 + 0.857507i \(0.672012\pi\)
\(200\) 2.89810 0.204927
\(201\) 1.78528 0.125924
\(202\) 2.07672 0.146118
\(203\) 18.0460 1.26658
\(204\) 1.00000 0.0700140
\(205\) −13.4385 −0.938588
\(206\) 6.47581 0.451191
\(207\) 0.245496 0.0170632
\(208\) −1.77261 −0.122909
\(209\) 8.47977 0.586558
\(210\) −6.34728 −0.438004
\(211\) −20.9886 −1.44491 −0.722456 0.691417i \(-0.756987\pi\)
−0.722456 + 0.691417i \(0.756987\pi\)
\(212\) −6.02547 −0.413831
\(213\) 1.68929 0.115748
\(214\) −16.8654 −1.15290
\(215\) −1.60594 −0.109524
\(216\) −1.00000 −0.0680414
\(217\) −21.1618 −1.43655
\(218\) 2.54545 0.172400
\(219\) −3.63143 −0.245389
\(220\) 7.51629 0.506748
\(221\) −1.77261 −0.119239
\(222\) −7.94495 −0.533230
\(223\) −5.05973 −0.338824 −0.169412 0.985545i \(-0.554187\pi\)
−0.169412 + 0.985545i \(0.554187\pi\)
\(224\) −4.37806 −0.292521
\(225\) −2.89810 −0.193207
\(226\) 0.191265 0.0127228
\(227\) −12.6609 −0.840332 −0.420166 0.907447i \(-0.638028\pi\)
−0.420166 + 0.907447i \(0.638028\pi\)
\(228\) 1.63563 0.108323
\(229\) 1.68676 0.111464 0.0557320 0.998446i \(-0.482251\pi\)
0.0557320 + 0.998446i \(0.482251\pi\)
\(230\) −0.355919 −0.0234686
\(231\) 22.6975 1.49339
\(232\) −4.12193 −0.270618
\(233\) 12.5530 0.822376 0.411188 0.911551i \(-0.365114\pi\)
0.411188 + 0.911551i \(0.365114\pi\)
\(234\) 1.77261 0.115879
\(235\) 7.00548 0.456987
\(236\) 1.00000 0.0650945
\(237\) −8.59258 −0.558148
\(238\) −4.37806 −0.283787
\(239\) 10.9851 0.710565 0.355283 0.934759i \(-0.384385\pi\)
0.355283 + 0.934759i \(0.384385\pi\)
\(240\) 1.44979 0.0935838
\(241\) −10.7798 −0.694386 −0.347193 0.937794i \(-0.612865\pi\)
−0.347193 + 0.937794i \(0.612865\pi\)
\(242\) −15.8779 −1.02067
\(243\) 1.00000 0.0641500
\(244\) 12.3248 0.789012
\(245\) 17.6402 1.12699
\(246\) 9.26927 0.590987
\(247\) −2.89935 −0.184481
\(248\) 4.83360 0.306934
\(249\) 1.43522 0.0909532
\(250\) 11.4506 0.724200
\(251\) −10.3017 −0.650238 −0.325119 0.945673i \(-0.605404\pi\)
−0.325119 + 0.945673i \(0.605404\pi\)
\(252\) 4.37806 0.275792
\(253\) 1.27275 0.0800170
\(254\) 16.0068 1.00436
\(255\) 1.44979 0.0907896
\(256\) 1.00000 0.0625000
\(257\) 15.2138 0.949014 0.474507 0.880252i \(-0.342626\pi\)
0.474507 + 0.880252i \(0.342626\pi\)
\(258\) 1.10770 0.0689624
\(259\) 34.7834 2.16134
\(260\) −2.56992 −0.159380
\(261\) 4.12193 0.255141
\(262\) −14.9695 −0.924818
\(263\) −24.4168 −1.50560 −0.752802 0.658247i \(-0.771298\pi\)
−0.752802 + 0.658247i \(0.771298\pi\)
\(264\) −5.18439 −0.319077
\(265\) −8.73568 −0.536629
\(266\) −7.16090 −0.439063
\(267\) 3.26823 0.200013
\(268\) 1.78528 0.109053
\(269\) 11.1815 0.681750 0.340875 0.940109i \(-0.389277\pi\)
0.340875 + 0.940109i \(0.389277\pi\)
\(270\) −1.44979 −0.0882316
\(271\) 7.52070 0.456850 0.228425 0.973562i \(-0.426642\pi\)
0.228425 + 0.973562i \(0.426642\pi\)
\(272\) 1.00000 0.0606339
\(273\) −7.76060 −0.469693
\(274\) −0.381874 −0.0230698
\(275\) −15.0249 −0.906034
\(276\) 0.245496 0.0147771
\(277\) 6.39054 0.383970 0.191985 0.981398i \(-0.438507\pi\)
0.191985 + 0.981398i \(0.438507\pi\)
\(278\) −3.65947 −0.219481
\(279\) −4.83360 −0.289380
\(280\) −6.34728 −0.379322
\(281\) −10.8901 −0.649646 −0.324823 0.945775i \(-0.605305\pi\)
−0.324823 + 0.945775i \(0.605305\pi\)
\(282\) −4.83205 −0.287745
\(283\) 5.70075 0.338874 0.169437 0.985541i \(-0.445805\pi\)
0.169437 + 0.985541i \(0.445805\pi\)
\(284\) 1.68929 0.100241
\(285\) 2.37133 0.140466
\(286\) 9.18992 0.543411
\(287\) −40.5814 −2.39544
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −5.97594 −0.350920
\(291\) −4.03329 −0.236436
\(292\) −3.63143 −0.212513
\(293\) 1.45272 0.0848690 0.0424345 0.999099i \(-0.486489\pi\)
0.0424345 + 0.999099i \(0.486489\pi\)
\(294\) −12.1674 −0.709615
\(295\) 1.44979 0.0844102
\(296\) −7.94495 −0.461791
\(297\) 5.18439 0.300829
\(298\) −13.6599 −0.791296
\(299\) −0.435170 −0.0251665
\(300\) −2.89810 −0.167322
\(301\) −4.84957 −0.279525
\(302\) 19.2914 1.11009
\(303\) −2.07672 −0.119304
\(304\) 1.63563 0.0938101
\(305\) 17.8684 1.02314
\(306\) −1.00000 −0.0571662
\(307\) −24.5574 −1.40156 −0.700781 0.713376i \(-0.747165\pi\)
−0.700781 + 0.713376i \(0.747165\pi\)
\(308\) 22.6975 1.29331
\(309\) −6.47581 −0.368396
\(310\) 7.00772 0.398012
\(311\) −4.47009 −0.253475 −0.126738 0.991936i \(-0.540451\pi\)
−0.126738 + 0.991936i \(0.540451\pi\)
\(312\) 1.77261 0.100354
\(313\) 31.5641 1.78411 0.892055 0.451927i \(-0.149263\pi\)
0.892055 + 0.451927i \(0.149263\pi\)
\(314\) −10.3290 −0.582898
\(315\) 6.34728 0.357629
\(316\) −8.59258 −0.483371
\(317\) 16.7785 0.942375 0.471187 0.882033i \(-0.343826\pi\)
0.471187 + 0.882033i \(0.343826\pi\)
\(318\) 6.02547 0.337891
\(319\) 21.3697 1.19647
\(320\) 1.44979 0.0810459
\(321\) 16.8654 0.941337
\(322\) −1.07480 −0.0598961
\(323\) 1.63563 0.0910091
\(324\) 1.00000 0.0555556
\(325\) 5.13721 0.284961
\(326\) 11.7369 0.650048
\(327\) −2.54545 −0.140764
\(328\) 9.26927 0.511810
\(329\) 21.1550 1.16631
\(330\) −7.51629 −0.413758
\(331\) 8.17673 0.449434 0.224717 0.974424i \(-0.427854\pi\)
0.224717 + 0.974424i \(0.427854\pi\)
\(332\) 1.43522 0.0787678
\(333\) 7.94495 0.435381
\(334\) −0.647953 −0.0354544
\(335\) 2.58829 0.141413
\(336\) 4.37806 0.238843
\(337\) 6.57262 0.358033 0.179017 0.983846i \(-0.442708\pi\)
0.179017 + 0.983846i \(0.442708\pi\)
\(338\) 9.85784 0.536196
\(339\) −0.191265 −0.0103881
\(340\) 1.44979 0.0786261
\(341\) −25.0593 −1.35704
\(342\) −1.63563 −0.0884450
\(343\) 22.6230 1.22153
\(344\) 1.10770 0.0597232
\(345\) 0.355919 0.0191620
\(346\) 2.21096 0.118862
\(347\) 12.2280 0.656432 0.328216 0.944603i \(-0.393553\pi\)
0.328216 + 0.944603i \(0.393553\pi\)
\(348\) 4.12193 0.220959
\(349\) 3.69015 0.197529 0.0987645 0.995111i \(-0.468511\pi\)
0.0987645 + 0.995111i \(0.468511\pi\)
\(350\) 12.6880 0.678204
\(351\) −1.77261 −0.0946151
\(352\) −5.18439 −0.276329
\(353\) −10.4464 −0.556007 −0.278004 0.960580i \(-0.589673\pi\)
−0.278004 + 0.960580i \(0.589673\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 2.44912 0.129986
\(356\) 3.26823 0.173216
\(357\) 4.37806 0.231711
\(358\) 2.20048 0.116299
\(359\) −27.4693 −1.44977 −0.724887 0.688867i \(-0.758108\pi\)
−0.724887 + 0.688867i \(0.758108\pi\)
\(360\) −1.44979 −0.0764108
\(361\) −16.3247 −0.859195
\(362\) 16.8381 0.884988
\(363\) 15.8779 0.833373
\(364\) −7.76060 −0.406766
\(365\) −5.26482 −0.275573
\(366\) −12.3248 −0.644226
\(367\) −23.1923 −1.21063 −0.605315 0.795986i \(-0.706953\pi\)
−0.605315 + 0.795986i \(0.706953\pi\)
\(368\) 0.245496 0.0127974
\(369\) −9.26927 −0.482539
\(370\) −11.5185 −0.598820
\(371\) −26.3798 −1.36957
\(372\) −4.83360 −0.250610
\(373\) −7.72058 −0.399757 −0.199878 0.979821i \(-0.564055\pi\)
−0.199878 + 0.979821i \(0.564055\pi\)
\(374\) −5.18439 −0.268078
\(375\) −11.4506 −0.591307
\(376\) −4.83205 −0.249194
\(377\) −7.30658 −0.376308
\(378\) −4.37806 −0.225183
\(379\) −8.20322 −0.421371 −0.210686 0.977554i \(-0.567570\pi\)
−0.210686 + 0.977554i \(0.567570\pi\)
\(380\) 2.37133 0.121647
\(381\) −16.0068 −0.820055
\(382\) −7.42739 −0.380018
\(383\) 22.7157 1.16072 0.580359 0.814361i \(-0.302912\pi\)
0.580359 + 0.814361i \(0.302912\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 32.9068 1.67708
\(386\) 4.61155 0.234722
\(387\) −1.10770 −0.0563076
\(388\) −4.03329 −0.204759
\(389\) −3.21475 −0.162994 −0.0814972 0.996674i \(-0.525970\pi\)
−0.0814972 + 0.996674i \(0.525970\pi\)
\(390\) 2.56992 0.130133
\(391\) 0.245496 0.0124153
\(392\) −12.1674 −0.614545
\(393\) 14.9695 0.755111
\(394\) 0.0799799 0.00402933
\(395\) −12.4575 −0.626803
\(396\) 5.18439 0.260525
\(397\) 36.4680 1.83027 0.915137 0.403143i \(-0.132082\pi\)
0.915137 + 0.403143i \(0.132082\pi\)
\(398\) 14.5150 0.727573
\(399\) 7.16090 0.358493
\(400\) −2.89810 −0.144905
\(401\) 1.86893 0.0933299 0.0466650 0.998911i \(-0.485141\pi\)
0.0466650 + 0.998911i \(0.485141\pi\)
\(402\) −1.78528 −0.0890418
\(403\) 8.56810 0.426808
\(404\) −2.07672 −0.103321
\(405\) 1.44979 0.0720408
\(406\) −18.0460 −0.895609
\(407\) 41.1897 2.04170
\(408\) −1.00000 −0.0495074
\(409\) −25.4421 −1.25803 −0.629016 0.777392i \(-0.716542\pi\)
−0.629016 + 0.777392i \(0.716542\pi\)
\(410\) 13.4385 0.663682
\(411\) 0.381874 0.0188364
\(412\) −6.47581 −0.319040
\(413\) 4.37806 0.215430
\(414\) −0.245496 −0.0120655
\(415\) 2.08077 0.102141
\(416\) 1.77261 0.0869095
\(417\) 3.65947 0.179205
\(418\) −8.47977 −0.414759
\(419\) −16.7336 −0.817491 −0.408746 0.912648i \(-0.634034\pi\)
−0.408746 + 0.912648i \(0.634034\pi\)
\(420\) 6.34728 0.309715
\(421\) 3.56961 0.173972 0.0869861 0.996210i \(-0.472276\pi\)
0.0869861 + 0.996210i \(0.472276\pi\)
\(422\) 20.9886 1.02171
\(423\) 4.83205 0.234942
\(424\) 6.02547 0.292623
\(425\) −2.89810 −0.140578
\(426\) −1.68929 −0.0818464
\(427\) 53.9585 2.61124
\(428\) 16.8654 0.815221
\(429\) −9.18992 −0.443693
\(430\) 1.60594 0.0774452
\(431\) −12.8508 −0.619000 −0.309500 0.950899i \(-0.600162\pi\)
−0.309500 + 0.950899i \(0.600162\pi\)
\(432\) 1.00000 0.0481125
\(433\) −7.89068 −0.379202 −0.189601 0.981861i \(-0.560719\pi\)
−0.189601 + 0.981861i \(0.560719\pi\)
\(434\) 21.1618 1.01580
\(435\) 5.97594 0.286525
\(436\) −2.54545 −0.121905
\(437\) 0.401542 0.0192084
\(438\) 3.63143 0.173516
\(439\) −0.241284 −0.0115159 −0.00575793 0.999983i \(-0.501833\pi\)
−0.00575793 + 0.999983i \(0.501833\pi\)
\(440\) −7.51629 −0.358325
\(441\) 12.1674 0.579399
\(442\) 1.77261 0.0843146
\(443\) −11.3111 −0.537406 −0.268703 0.963223i \(-0.586595\pi\)
−0.268703 + 0.963223i \(0.586595\pi\)
\(444\) 7.94495 0.377051
\(445\) 4.73826 0.224615
\(446\) 5.05973 0.239585
\(447\) 13.6599 0.646091
\(448\) 4.37806 0.206844
\(449\) −2.53121 −0.119455 −0.0597277 0.998215i \(-0.519023\pi\)
−0.0597277 + 0.998215i \(0.519023\pi\)
\(450\) 2.89810 0.136618
\(451\) −48.0555 −2.26285
\(452\) −0.191265 −0.00899635
\(453\) −19.2914 −0.906388
\(454\) 12.6609 0.594204
\(455\) −11.2513 −0.527468
\(456\) −1.63563 −0.0765956
\(457\) −30.7641 −1.43909 −0.719543 0.694448i \(-0.755649\pi\)
−0.719543 + 0.694448i \(0.755649\pi\)
\(458\) −1.68676 −0.0788169
\(459\) 1.00000 0.0466760
\(460\) 0.355919 0.0165948
\(461\) −17.1603 −0.799233 −0.399617 0.916682i \(-0.630857\pi\)
−0.399617 + 0.916682i \(0.630857\pi\)
\(462\) −22.6975 −1.05599
\(463\) 8.00799 0.372163 0.186081 0.982534i \(-0.440421\pi\)
0.186081 + 0.982534i \(0.440421\pi\)
\(464\) 4.12193 0.191356
\(465\) −7.00772 −0.324975
\(466\) −12.5530 −0.581507
\(467\) 20.3714 0.942676 0.471338 0.881953i \(-0.343771\pi\)
0.471338 + 0.881953i \(0.343771\pi\)
\(468\) −1.77261 −0.0819391
\(469\) 7.81607 0.360912
\(470\) −7.00548 −0.323139
\(471\) 10.3290 0.475934
\(472\) −1.00000 −0.0460287
\(473\) −5.74275 −0.264052
\(474\) 8.59258 0.394670
\(475\) −4.74023 −0.217497
\(476\) 4.37806 0.200668
\(477\) −6.02547 −0.275887
\(478\) −10.9851 −0.502446
\(479\) 41.9139 1.91509 0.957547 0.288278i \(-0.0930827\pi\)
0.957547 + 0.288278i \(0.0930827\pi\)
\(480\) −1.44979 −0.0661737
\(481\) −14.0833 −0.642144
\(482\) 10.7798 0.491005
\(483\) 1.07480 0.0489049
\(484\) 15.8779 0.721723
\(485\) −5.84744 −0.265519
\(486\) −1.00000 −0.0453609
\(487\) −17.0648 −0.773280 −0.386640 0.922231i \(-0.626364\pi\)
−0.386640 + 0.922231i \(0.626364\pi\)
\(488\) −12.3248 −0.557916
\(489\) −11.7369 −0.530762
\(490\) −17.6402 −0.796902
\(491\) 29.0665 1.31175 0.655877 0.754868i \(-0.272299\pi\)
0.655877 + 0.754868i \(0.272299\pi\)
\(492\) −9.26927 −0.417891
\(493\) 4.12193 0.185642
\(494\) 2.89935 0.130448
\(495\) 7.51629 0.337832
\(496\) −4.83360 −0.217035
\(497\) 7.39581 0.331748
\(498\) −1.43522 −0.0643136
\(499\) 13.3167 0.596137 0.298069 0.954544i \(-0.403658\pi\)
0.298069 + 0.954544i \(0.403658\pi\)
\(500\) −11.4506 −0.512087
\(501\) 0.647953 0.0289484
\(502\) 10.3017 0.459788
\(503\) −1.86807 −0.0832932 −0.0416466 0.999132i \(-0.513260\pi\)
−0.0416466 + 0.999132i \(0.513260\pi\)
\(504\) −4.37806 −0.195014
\(505\) −3.01082 −0.133980
\(506\) −1.27275 −0.0565806
\(507\) −9.85784 −0.437802
\(508\) −16.0068 −0.710189
\(509\) 23.2264 1.02949 0.514746 0.857342i \(-0.327886\pi\)
0.514746 + 0.857342i \(0.327886\pi\)
\(510\) −1.44979 −0.0641979
\(511\) −15.8986 −0.703312
\(512\) −1.00000 −0.0441942
\(513\) 1.63563 0.0722150
\(514\) −15.2138 −0.671054
\(515\) −9.38858 −0.413710
\(516\) −1.10770 −0.0487638
\(517\) 25.0512 1.10175
\(518\) −34.7834 −1.52830
\(519\) −2.21096 −0.0970506
\(520\) 2.56992 0.112699
\(521\) 33.7971 1.48068 0.740339 0.672234i \(-0.234665\pi\)
0.740339 + 0.672234i \(0.234665\pi\)
\(522\) −4.12193 −0.180412
\(523\) −28.9913 −1.26770 −0.633851 0.773455i \(-0.718527\pi\)
−0.633851 + 0.773455i \(0.718527\pi\)
\(524\) 14.9695 0.653945
\(525\) −12.6880 −0.553751
\(526\) 24.4168 1.06462
\(527\) −4.83360 −0.210555
\(528\) 5.18439 0.225622
\(529\) −22.9397 −0.997380
\(530\) 8.73568 0.379454
\(531\) 1.00000 0.0433963
\(532\) 7.16090 0.310464
\(533\) 16.4308 0.711698
\(534\) −3.26823 −0.141430
\(535\) 24.4514 1.05713
\(536\) −1.78528 −0.0771125
\(537\) −2.20048 −0.0949579
\(538\) −11.1815 −0.482070
\(539\) 63.0804 2.71706
\(540\) 1.44979 0.0623892
\(541\) 40.4523 1.73918 0.869590 0.493774i \(-0.164383\pi\)
0.869590 + 0.493774i \(0.164383\pi\)
\(542\) −7.52070 −0.323042
\(543\) −16.8381 −0.722590
\(544\) −1.00000 −0.0428746
\(545\) −3.69038 −0.158079
\(546\) 7.76060 0.332123
\(547\) 37.6258 1.60876 0.804381 0.594114i \(-0.202497\pi\)
0.804381 + 0.594114i \(0.202497\pi\)
\(548\) 0.381874 0.0163128
\(549\) 12.3248 0.526008
\(550\) 15.0249 0.640663
\(551\) 6.74197 0.287217
\(552\) −0.245496 −0.0104490
\(553\) −37.6188 −1.59971
\(554\) −6.39054 −0.271508
\(555\) 11.5185 0.488935
\(556\) 3.65947 0.155196
\(557\) 30.0412 1.27289 0.636443 0.771324i \(-0.280405\pi\)
0.636443 + 0.771324i \(0.280405\pi\)
\(558\) 4.83360 0.204623
\(559\) 1.96352 0.0830482
\(560\) 6.34728 0.268221
\(561\) 5.18439 0.218885
\(562\) 10.8901 0.459369
\(563\) 2.98074 0.125623 0.0628116 0.998025i \(-0.479993\pi\)
0.0628116 + 0.998025i \(0.479993\pi\)
\(564\) 4.83205 0.203466
\(565\) −0.277295 −0.0116659
\(566\) −5.70075 −0.239620
\(567\) 4.37806 0.183861
\(568\) −1.68929 −0.0708811
\(569\) 9.68369 0.405962 0.202981 0.979183i \(-0.434937\pi\)
0.202981 + 0.979183i \(0.434937\pi\)
\(570\) −2.37133 −0.0993242
\(571\) −7.37647 −0.308696 −0.154348 0.988017i \(-0.549328\pi\)
−0.154348 + 0.988017i \(0.549328\pi\)
\(572\) −9.18992 −0.384250
\(573\) 7.42739 0.310284
\(574\) 40.5814 1.69383
\(575\) −0.711473 −0.0296705
\(576\) 1.00000 0.0416667
\(577\) 38.6927 1.61080 0.805400 0.592732i \(-0.201950\pi\)
0.805400 + 0.592732i \(0.201950\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −4.61155 −0.191650
\(580\) 5.97594 0.248138
\(581\) 6.28346 0.260682
\(582\) 4.03329 0.167185
\(583\) −31.2384 −1.29376
\(584\) 3.63143 0.150269
\(585\) −2.56992 −0.106253
\(586\) −1.45272 −0.0600114
\(587\) −20.2520 −0.835891 −0.417946 0.908472i \(-0.637250\pi\)
−0.417946 + 0.908472i \(0.637250\pi\)
\(588\) 12.1674 0.501774
\(589\) −7.90600 −0.325761
\(590\) −1.44979 −0.0596871
\(591\) −0.0799799 −0.00328994
\(592\) 7.94495 0.326535
\(593\) 7.92828 0.325576 0.162788 0.986661i \(-0.447951\pi\)
0.162788 + 0.986661i \(0.447951\pi\)
\(594\) −5.18439 −0.212718
\(595\) 6.34728 0.260213
\(596\) 13.6599 0.559531
\(597\) −14.5150 −0.594061
\(598\) 0.435170 0.0177954
\(599\) 12.5467 0.512646 0.256323 0.966591i \(-0.417489\pi\)
0.256323 + 0.966591i \(0.417489\pi\)
\(600\) 2.89810 0.118314
\(601\) 9.91921 0.404613 0.202307 0.979322i \(-0.435156\pi\)
0.202307 + 0.979322i \(0.435156\pi\)
\(602\) 4.84957 0.197654
\(603\) 1.78528 0.0727023
\(604\) −19.2914 −0.784955
\(605\) 23.0197 0.935883
\(606\) 2.07672 0.0843610
\(607\) −29.9474 −1.21553 −0.607763 0.794119i \(-0.707933\pi\)
−0.607763 + 0.794119i \(0.707933\pi\)
\(608\) −1.63563 −0.0663337
\(609\) 18.0460 0.731262
\(610\) −17.8684 −0.723469
\(611\) −8.56536 −0.346517
\(612\) 1.00000 0.0404226
\(613\) 4.40182 0.177788 0.0888939 0.996041i \(-0.471667\pi\)
0.0888939 + 0.996041i \(0.471667\pi\)
\(614\) 24.5574 0.991054
\(615\) −13.4385 −0.541894
\(616\) −22.6975 −0.914510
\(617\) −33.9438 −1.36653 −0.683263 0.730172i \(-0.739440\pi\)
−0.683263 + 0.730172i \(0.739440\pi\)
\(618\) 6.47581 0.260495
\(619\) 30.0777 1.20892 0.604462 0.796634i \(-0.293388\pi\)
0.604462 + 0.796634i \(0.293388\pi\)
\(620\) −7.00772 −0.281437
\(621\) 0.245496 0.00985143
\(622\) 4.47009 0.179234
\(623\) 14.3085 0.573258
\(624\) −1.77261 −0.0709613
\(625\) −2.11053 −0.0844212
\(626\) −31.5641 −1.26156
\(627\) 8.47977 0.338649
\(628\) 10.3290 0.412171
\(629\) 7.94495 0.316786
\(630\) −6.34728 −0.252882
\(631\) 17.1407 0.682362 0.341181 0.939998i \(-0.389173\pi\)
0.341181 + 0.939998i \(0.389173\pi\)
\(632\) 8.59258 0.341795
\(633\) −20.9886 −0.834221
\(634\) −16.7785 −0.666360
\(635\) −23.2066 −0.920927
\(636\) −6.02547 −0.238925
\(637\) −21.5680 −0.854557
\(638\) −21.3697 −0.846034
\(639\) 1.68929 0.0668273
\(640\) −1.44979 −0.0573081
\(641\) −17.7927 −0.702769 −0.351385 0.936231i \(-0.614289\pi\)
−0.351385 + 0.936231i \(0.614289\pi\)
\(642\) −16.8654 −0.665625
\(643\) 9.89663 0.390285 0.195142 0.980775i \(-0.437483\pi\)
0.195142 + 0.980775i \(0.437483\pi\)
\(644\) 1.07480 0.0423529
\(645\) −1.60594 −0.0632337
\(646\) −1.63563 −0.0643532
\(647\) −31.6652 −1.24489 −0.622443 0.782665i \(-0.713860\pi\)
−0.622443 + 0.782665i \(0.713860\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 5.18439 0.203505
\(650\) −5.13721 −0.201498
\(651\) −21.1618 −0.829395
\(652\) −11.7369 −0.459653
\(653\) −26.7297 −1.04601 −0.523007 0.852328i \(-0.675190\pi\)
−0.523007 + 0.852328i \(0.675190\pi\)
\(654\) 2.54545 0.0995351
\(655\) 21.7027 0.847993
\(656\) −9.26927 −0.361904
\(657\) −3.63143 −0.141675
\(658\) −21.1550 −0.824708
\(659\) −9.01170 −0.351046 −0.175523 0.984475i \(-0.556162\pi\)
−0.175523 + 0.984475i \(0.556162\pi\)
\(660\) 7.51629 0.292571
\(661\) −28.0363 −1.09049 −0.545244 0.838278i \(-0.683563\pi\)
−0.545244 + 0.838278i \(0.683563\pi\)
\(662\) −8.17673 −0.317798
\(663\) −1.77261 −0.0688426
\(664\) −1.43522 −0.0556972
\(665\) 10.3818 0.402590
\(666\) −7.94495 −0.307861
\(667\) 1.01192 0.0391816
\(668\) 0.647953 0.0250701
\(669\) −5.05973 −0.195620
\(670\) −2.58829 −0.0999944
\(671\) 63.8964 2.46669
\(672\) −4.37806 −0.168887
\(673\) 36.1961 1.39526 0.697628 0.716461i \(-0.254239\pi\)
0.697628 + 0.716461i \(0.254239\pi\)
\(674\) −6.57262 −0.253168
\(675\) −2.89810 −0.111548
\(676\) −9.85784 −0.379148
\(677\) 28.7139 1.10356 0.551782 0.833988i \(-0.313948\pi\)
0.551782 + 0.833988i \(0.313948\pi\)
\(678\) 0.191265 0.00734549
\(679\) −17.6580 −0.677651
\(680\) −1.44979 −0.0555970
\(681\) −12.6609 −0.485166
\(682\) 25.0593 0.959569
\(683\) 12.7428 0.487589 0.243795 0.969827i \(-0.421608\pi\)
0.243795 + 0.969827i \(0.421608\pi\)
\(684\) 1.63563 0.0625400
\(685\) 0.553638 0.0211534
\(686\) −22.6230 −0.863752
\(687\) 1.68676 0.0643538
\(688\) −1.10770 −0.0422307
\(689\) 10.6808 0.406907
\(690\) −0.355919 −0.0135496
\(691\) −14.4289 −0.548900 −0.274450 0.961601i \(-0.588496\pi\)
−0.274450 + 0.961601i \(0.588496\pi\)
\(692\) −2.21096 −0.0840483
\(693\) 22.6975 0.862208
\(694\) −12.2280 −0.464167
\(695\) 5.30548 0.201248
\(696\) −4.12193 −0.156241
\(697\) −9.26927 −0.351099
\(698\) −3.69015 −0.139674
\(699\) 12.5530 0.474799
\(700\) −12.6880 −0.479563
\(701\) −24.4740 −0.924371 −0.462186 0.886783i \(-0.652935\pi\)
−0.462186 + 0.886783i \(0.652935\pi\)
\(702\) 1.77261 0.0669030
\(703\) 12.9950 0.490117
\(704\) 5.18439 0.195394
\(705\) 7.00548 0.263842
\(706\) 10.4464 0.393156
\(707\) −9.09200 −0.341940
\(708\) 1.00000 0.0375823
\(709\) −36.4391 −1.36850 −0.684249 0.729248i \(-0.739870\pi\)
−0.684249 + 0.729248i \(0.739870\pi\)
\(710\) −2.44912 −0.0919140
\(711\) −8.59258 −0.322247
\(712\) −3.26823 −0.122482
\(713\) −1.18663 −0.0444397
\(714\) −4.37806 −0.163845
\(715\) −13.3235 −0.498270
\(716\) −2.20048 −0.0822359
\(717\) 10.9851 0.410245
\(718\) 27.4693 1.02515
\(719\) −40.9091 −1.52565 −0.762826 0.646604i \(-0.776188\pi\)
−0.762826 + 0.646604i \(0.776188\pi\)
\(720\) 1.44979 0.0540306
\(721\) −28.3514 −1.05586
\(722\) 16.3247 0.607542
\(723\) −10.7798 −0.400904
\(724\) −16.8381 −0.625781
\(725\) −11.9458 −0.443654
\(726\) −15.8779 −0.589284
\(727\) 6.40377 0.237503 0.118751 0.992924i \(-0.462111\pi\)
0.118751 + 0.992924i \(0.462111\pi\)
\(728\) 7.76060 0.287627
\(729\) 1.00000 0.0370370
\(730\) 5.26482 0.194860
\(731\) −1.10770 −0.0409698
\(732\) 12.3248 0.455537
\(733\) −33.1848 −1.22571 −0.612854 0.790196i \(-0.709979\pi\)
−0.612854 + 0.790196i \(0.709979\pi\)
\(734\) 23.1923 0.856045
\(735\) 17.6402 0.650668
\(736\) −0.245496 −0.00904912
\(737\) 9.25560 0.340934
\(738\) 9.26927 0.341207
\(739\) 8.59928 0.316329 0.158165 0.987413i \(-0.449442\pi\)
0.158165 + 0.987413i \(0.449442\pi\)
\(740\) 11.5185 0.423430
\(741\) −2.89935 −0.106510
\(742\) 26.3798 0.968434
\(743\) 35.4072 1.29896 0.649482 0.760377i \(-0.274986\pi\)
0.649482 + 0.760377i \(0.274986\pi\)
\(744\) 4.83360 0.177208
\(745\) 19.8040 0.725563
\(746\) 7.72058 0.282671
\(747\) 1.43522 0.0525119
\(748\) 5.18439 0.189560
\(749\) 73.8378 2.69797
\(750\) 11.4506 0.418117
\(751\) 14.3082 0.522113 0.261056 0.965324i \(-0.415929\pi\)
0.261056 + 0.965324i \(0.415929\pi\)
\(752\) 4.83205 0.176207
\(753\) −10.3017 −0.375415
\(754\) 7.30658 0.266090
\(755\) −27.9685 −1.01788
\(756\) 4.37806 0.159228
\(757\) 24.2300 0.880654 0.440327 0.897837i \(-0.354863\pi\)
0.440327 + 0.897837i \(0.354863\pi\)
\(758\) 8.20322 0.297954
\(759\) 1.27275 0.0461979
\(760\) −2.37133 −0.0860173
\(761\) 1.99312 0.0722507 0.0361253 0.999347i \(-0.488498\pi\)
0.0361253 + 0.999347i \(0.488498\pi\)
\(762\) 16.0068 0.579867
\(763\) −11.1441 −0.403445
\(764\) 7.42739 0.268713
\(765\) 1.44979 0.0524174
\(766\) −22.7157 −0.820752
\(767\) −1.77261 −0.0640054
\(768\) 1.00000 0.0360844
\(769\) −29.2753 −1.05570 −0.527848 0.849339i \(-0.677001\pi\)
−0.527848 + 0.849339i \(0.677001\pi\)
\(770\) −32.9068 −1.18588
\(771\) 15.2138 0.547913
\(772\) −4.61155 −0.165973
\(773\) −40.5864 −1.45979 −0.729896 0.683559i \(-0.760431\pi\)
−0.729896 + 0.683559i \(0.760431\pi\)
\(774\) 1.10770 0.0398155
\(775\) 14.0082 0.503191
\(776\) 4.03329 0.144787
\(777\) 34.7834 1.24785
\(778\) 3.21475 0.115255
\(779\) −15.1611 −0.543204
\(780\) −2.56992 −0.0920180
\(781\) 8.75795 0.313384
\(782\) −0.245496 −0.00877893
\(783\) 4.12193 0.147306
\(784\) 12.1674 0.434549
\(785\) 14.9749 0.534477
\(786\) −14.9695 −0.533944
\(787\) 12.9698 0.462324 0.231162 0.972915i \(-0.425747\pi\)
0.231162 + 0.972915i \(0.425747\pi\)
\(788\) −0.0799799 −0.00284917
\(789\) −24.4168 −0.869261
\(790\) 12.4575 0.443217
\(791\) −0.837369 −0.0297734
\(792\) −5.18439 −0.184219
\(793\) −21.8470 −0.775811
\(794\) −36.4680 −1.29420
\(795\) −8.73568 −0.309823
\(796\) −14.5150 −0.514472
\(797\) 4.50661 0.159632 0.0798161 0.996810i \(-0.474567\pi\)
0.0798161 + 0.996810i \(0.474567\pi\)
\(798\) −7.16090 −0.253493
\(799\) 4.83205 0.170946
\(800\) 2.89810 0.102463
\(801\) 3.26823 0.115477
\(802\) −1.86893 −0.0659942
\(803\) −18.8267 −0.664381
\(804\) 1.78528 0.0629621
\(805\) 1.55823 0.0549205
\(806\) −8.56810 −0.301798
\(807\) 11.1815 0.393609
\(808\) 2.07672 0.0730588
\(809\) −7.80597 −0.274443 −0.137222 0.990540i \(-0.543817\pi\)
−0.137222 + 0.990540i \(0.543817\pi\)
\(810\) −1.44979 −0.0509406
\(811\) 20.5255 0.720748 0.360374 0.932808i \(-0.382649\pi\)
0.360374 + 0.932808i \(0.382649\pi\)
\(812\) 18.0460 0.633291
\(813\) 7.52070 0.263762
\(814\) −41.1897 −1.44370
\(815\) −17.0161 −0.596048
\(816\) 1.00000 0.0350070
\(817\) −1.81179 −0.0633866
\(818\) 25.4421 0.889563
\(819\) −7.76060 −0.271177
\(820\) −13.4385 −0.469294
\(821\) 17.0975 0.596707 0.298354 0.954455i \(-0.403563\pi\)
0.298354 + 0.954455i \(0.403563\pi\)
\(822\) −0.381874 −0.0133194
\(823\) 51.5166 1.79576 0.897878 0.440244i \(-0.145108\pi\)
0.897878 + 0.440244i \(0.145108\pi\)
\(824\) 6.47581 0.225595
\(825\) −15.0249 −0.523099
\(826\) −4.37806 −0.152332
\(827\) 25.4308 0.884316 0.442158 0.896937i \(-0.354213\pi\)
0.442158 + 0.896937i \(0.354213\pi\)
\(828\) 0.245496 0.00853159
\(829\) −6.78146 −0.235530 −0.117765 0.993042i \(-0.537573\pi\)
−0.117765 + 0.993042i \(0.537573\pi\)
\(830\) −2.08077 −0.0722245
\(831\) 6.39054 0.221685
\(832\) −1.77261 −0.0614543
\(833\) 12.1674 0.421574
\(834\) −3.65947 −0.126717
\(835\) 0.939398 0.0325092
\(836\) 8.47977 0.293279
\(837\) −4.83360 −0.167074
\(838\) 16.7336 0.578053
\(839\) 41.9267 1.44747 0.723736 0.690077i \(-0.242423\pi\)
0.723736 + 0.690077i \(0.242423\pi\)
\(840\) −6.34728 −0.219002
\(841\) −12.0097 −0.414128
\(842\) −3.56961 −0.123017
\(843\) −10.8901 −0.375073
\(844\) −20.9886 −0.722456
\(845\) −14.2918 −0.491654
\(846\) −4.83205 −0.166129
\(847\) 69.5143 2.38854
\(848\) −6.02547 −0.206915
\(849\) 5.70075 0.195649
\(850\) 2.89810 0.0994040
\(851\) 1.95046 0.0668608
\(852\) 1.68929 0.0578742
\(853\) −34.0677 −1.16646 −0.583228 0.812309i \(-0.698211\pi\)
−0.583228 + 0.812309i \(0.698211\pi\)
\(854\) −53.9585 −1.84642
\(855\) 2.37133 0.0810979
\(856\) −16.8654 −0.576449
\(857\) −14.9956 −0.512239 −0.256119 0.966645i \(-0.582444\pi\)
−0.256119 + 0.966645i \(0.582444\pi\)
\(858\) 9.18992 0.313739
\(859\) 40.9152 1.39601 0.698004 0.716094i \(-0.254072\pi\)
0.698004 + 0.716094i \(0.254072\pi\)
\(860\) −1.60594 −0.0547620
\(861\) −40.5814 −1.38301
\(862\) 12.8508 0.437699
\(863\) 43.3752 1.47651 0.738255 0.674522i \(-0.235650\pi\)
0.738255 + 0.674522i \(0.235650\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −3.20544 −0.108988
\(866\) 7.89068 0.268136
\(867\) 1.00000 0.0339618
\(868\) −21.1618 −0.718277
\(869\) −44.5473 −1.51116
\(870\) −5.97594 −0.202603
\(871\) −3.16462 −0.107229
\(872\) 2.54545 0.0861999
\(873\) −4.03329 −0.136506
\(874\) −0.401542 −0.0135824
\(875\) −50.1314 −1.69475
\(876\) −3.63143 −0.122694
\(877\) 13.5089 0.456162 0.228081 0.973642i \(-0.426755\pi\)
0.228081 + 0.973642i \(0.426755\pi\)
\(878\) 0.241284 0.00814294
\(879\) 1.45272 0.0489991
\(880\) 7.51629 0.253374
\(881\) 0.499198 0.0168184 0.00840921 0.999965i \(-0.497323\pi\)
0.00840921 + 0.999965i \(0.497323\pi\)
\(882\) −12.1674 −0.409697
\(883\) −26.2013 −0.881744 −0.440872 0.897570i \(-0.645331\pi\)
−0.440872 + 0.897570i \(0.645331\pi\)
\(884\) −1.77261 −0.0596194
\(885\) 1.44979 0.0487343
\(886\) 11.3111 0.380003
\(887\) 23.0467 0.773832 0.386916 0.922115i \(-0.373540\pi\)
0.386916 + 0.922115i \(0.373540\pi\)
\(888\) −7.94495 −0.266615
\(889\) −70.0788 −2.35037
\(890\) −4.73826 −0.158827
\(891\) 5.18439 0.173684
\(892\) −5.05973 −0.169412
\(893\) 7.90347 0.264480
\(894\) −13.6599 −0.456855
\(895\) −3.19025 −0.106638
\(896\) −4.37806 −0.146261
\(897\) −0.435170 −0.0145299
\(898\) 2.53121 0.0844677
\(899\) −19.9237 −0.664494
\(900\) −2.89810 −0.0966033
\(901\) −6.02547 −0.200737
\(902\) 48.0555 1.60007
\(903\) −4.84957 −0.161384
\(904\) 0.191265 0.00636138
\(905\) −24.4117 −0.811472
\(906\) 19.2914 0.640913
\(907\) 27.7324 0.920838 0.460419 0.887702i \(-0.347699\pi\)
0.460419 + 0.887702i \(0.347699\pi\)
\(908\) −12.6609 −0.420166
\(909\) −2.07672 −0.0688805
\(910\) 11.2513 0.372976
\(911\) 10.8254 0.358660 0.179330 0.983789i \(-0.442607\pi\)
0.179330 + 0.983789i \(0.442607\pi\)
\(912\) 1.63563 0.0541613
\(913\) 7.44073 0.246252
\(914\) 30.7641 1.01759
\(915\) 17.8684 0.590710
\(916\) 1.68676 0.0557320
\(917\) 65.5373 2.16423
\(918\) −1.00000 −0.0330049
\(919\) 51.7151 1.70592 0.852961 0.521974i \(-0.174804\pi\)
0.852961 + 0.521974i \(0.174804\pi\)
\(920\) −0.355919 −0.0117343
\(921\) −24.5574 −0.809192
\(922\) 17.1603 0.565143
\(923\) −2.99446 −0.0985639
\(924\) 22.6975 0.746694
\(925\) −23.0252 −0.757065
\(926\) −8.00799 −0.263159
\(927\) −6.47581 −0.212693
\(928\) −4.12193 −0.135309
\(929\) −34.4693 −1.13090 −0.565450 0.824782i \(-0.691298\pi\)
−0.565450 + 0.824782i \(0.691298\pi\)
\(930\) 7.00772 0.229792
\(931\) 19.9014 0.652241
\(932\) 12.5530 0.411188
\(933\) −4.47009 −0.146344
\(934\) −20.3714 −0.666573
\(935\) 7.51629 0.245809
\(936\) 1.77261 0.0579397
\(937\) −51.0063 −1.66630 −0.833151 0.553045i \(-0.813466\pi\)
−0.833151 + 0.553045i \(0.813466\pi\)
\(938\) −7.81607 −0.255204
\(939\) 31.5641 1.03006
\(940\) 7.00548 0.228494
\(941\) 49.2787 1.60644 0.803219 0.595683i \(-0.203119\pi\)
0.803219 + 0.595683i \(0.203119\pi\)
\(942\) −10.3290 −0.336536
\(943\) −2.27557 −0.0741028
\(944\) 1.00000 0.0325472
\(945\) 6.34728 0.206477
\(946\) 5.74275 0.186713
\(947\) 30.2193 0.981997 0.490998 0.871160i \(-0.336632\pi\)
0.490998 + 0.871160i \(0.336632\pi\)
\(948\) −8.59258 −0.279074
\(949\) 6.43711 0.208958
\(950\) 4.74023 0.153793
\(951\) 16.7785 0.544080
\(952\) −4.37806 −0.141894
\(953\) 17.2028 0.557254 0.278627 0.960399i \(-0.410121\pi\)
0.278627 + 0.960399i \(0.410121\pi\)
\(954\) 6.02547 0.195082
\(955\) 10.7682 0.348450
\(956\) 10.9851 0.355283
\(957\) 21.3697 0.690784
\(958\) −41.9139 −1.35418
\(959\) 1.67186 0.0539873
\(960\) 1.44979 0.0467919
\(961\) −7.63632 −0.246333
\(962\) 14.0833 0.454065
\(963\) 16.8654 0.543481
\(964\) −10.7798 −0.347193
\(965\) −6.68580 −0.215223
\(966\) −1.07480 −0.0345810
\(967\) 4.96745 0.159743 0.0798713 0.996805i \(-0.474549\pi\)
0.0798713 + 0.996805i \(0.474549\pi\)
\(968\) −15.8779 −0.510335
\(969\) 1.63563 0.0525441
\(970\) 5.84744 0.187750
\(971\) −40.7526 −1.30781 −0.653906 0.756576i \(-0.726871\pi\)
−0.653906 + 0.756576i \(0.726871\pi\)
\(972\) 1.00000 0.0320750
\(973\) 16.0214 0.513622
\(974\) 17.0648 0.546792
\(975\) 5.13721 0.164522
\(976\) 12.3248 0.394506
\(977\) −42.7449 −1.36753 −0.683765 0.729703i \(-0.739659\pi\)
−0.683765 + 0.729703i \(0.739659\pi\)
\(978\) 11.7369 0.375305
\(979\) 16.9438 0.541526
\(980\) 17.6402 0.563495
\(981\) −2.54545 −0.0812700
\(982\) −29.0665 −0.927550
\(983\) 1.37125 0.0437359 0.0218680 0.999761i \(-0.493039\pi\)
0.0218680 + 0.999761i \(0.493039\pi\)
\(984\) 9.26927 0.295494
\(985\) −0.115954 −0.00369461
\(986\) −4.12193 −0.131269
\(987\) 21.1550 0.673371
\(988\) −2.89935 −0.0922405
\(989\) −0.271936 −0.00864707
\(990\) −7.51629 −0.238884
\(991\) 4.24426 0.134823 0.0674117 0.997725i \(-0.478526\pi\)
0.0674117 + 0.997725i \(0.478526\pi\)
\(992\) 4.83360 0.153467
\(993\) 8.17673 0.259481
\(994\) −7.39581 −0.234581
\(995\) −21.0438 −0.667134
\(996\) 1.43522 0.0454766
\(997\) 52.8359 1.67333 0.836664 0.547716i \(-0.184503\pi\)
0.836664 + 0.547716i \(0.184503\pi\)
\(998\) −13.3167 −0.421533
\(999\) 7.94495 0.251367
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 6018.2.a.w.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.w.1.7 9 1.1 even 1 trivial