Properties

Label 6018.2.a.x.1.5
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $10$
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.580342\) 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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.580342 q^{5} +1.00000 q^{6} +4.77865 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.580342 q^{5} +1.00000 q^{6} +4.77865 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.580342 q^{10} +1.62859 q^{11} -1.00000 q^{12} +5.47999 q^{13} -4.77865 q^{14} -0.580342 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.16709 q^{19} +0.580342 q^{20} -4.77865 q^{21} -1.62859 q^{22} -7.82087 q^{23} +1.00000 q^{24} -4.66320 q^{25} -5.47999 q^{26} -1.00000 q^{27} +4.77865 q^{28} +1.14006 q^{29} +0.580342 q^{30} +7.10961 q^{31} -1.00000 q^{32} -1.62859 q^{33} -1.00000 q^{34} +2.77325 q^{35} +1.00000 q^{36} +1.66923 q^{37} -1.16709 q^{38} -5.47999 q^{39} -0.580342 q^{40} -0.211924 q^{41} +4.77865 q^{42} +9.35293 q^{43} +1.62859 q^{44} +0.580342 q^{45} +7.82087 q^{46} +4.12655 q^{47} -1.00000 q^{48} +15.8355 q^{49} +4.66320 q^{50} -1.00000 q^{51} +5.47999 q^{52} +6.63557 q^{53} +1.00000 q^{54} +0.945136 q^{55} -4.77865 q^{56} -1.16709 q^{57} -1.14006 q^{58} -1.00000 q^{59} -0.580342 q^{60} +1.75157 q^{61} -7.10961 q^{62} +4.77865 q^{63} +1.00000 q^{64} +3.18027 q^{65} +1.62859 q^{66} +0.972991 q^{67} +1.00000 q^{68} +7.82087 q^{69} -2.77325 q^{70} +0.225978 q^{71} -1.00000 q^{72} +1.96236 q^{73} -1.66923 q^{74} +4.66320 q^{75} +1.16709 q^{76} +7.78244 q^{77} +5.47999 q^{78} -8.26320 q^{79} +0.580342 q^{80} +1.00000 q^{81} +0.211924 q^{82} +8.22544 q^{83} -4.77865 q^{84} +0.580342 q^{85} -9.35293 q^{86} -1.14006 q^{87} -1.62859 q^{88} -1.59874 q^{89} -0.580342 q^{90} +26.1869 q^{91} -7.82087 q^{92} -7.10961 q^{93} -4.12655 q^{94} +0.677313 q^{95} +1.00000 q^{96} -7.65509 q^{97} -15.8355 q^{98} +1.62859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(5\) 0.580342 0.259537 0.129768 0.991544i \(-0.458577\pi\)
0.129768 + 0.991544i \(0.458577\pi\)
\(6\) 1.00000 0.408248
\(7\) 4.77865 1.80616 0.903080 0.429473i \(-0.141301\pi\)
0.903080 + 0.429473i \(0.141301\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −0.580342 −0.183520
\(11\) 1.62859 0.491037 0.245518 0.969392i \(-0.421042\pi\)
0.245518 + 0.969392i \(0.421042\pi\)
\(12\) −1.00000 −0.288675
\(13\) 5.47999 1.51988 0.759938 0.649996i \(-0.225229\pi\)
0.759938 + 0.649996i \(0.225229\pi\)
\(14\) −4.77865 −1.27715
\(15\) −0.580342 −0.149844
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 1.16709 0.267750 0.133875 0.990998i \(-0.457258\pi\)
0.133875 + 0.990998i \(0.457258\pi\)
\(20\) 0.580342 0.129768
\(21\) −4.77865 −1.04279
\(22\) −1.62859 −0.347216
\(23\) −7.82087 −1.63076 −0.815382 0.578923i \(-0.803473\pi\)
−0.815382 + 0.578923i \(0.803473\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.66320 −0.932641
\(26\) −5.47999 −1.07471
\(27\) −1.00000 −0.192450
\(28\) 4.77865 0.903080
\(29\) 1.14006 0.211704 0.105852 0.994382i \(-0.466243\pi\)
0.105852 + 0.994382i \(0.466243\pi\)
\(30\) 0.580342 0.105955
\(31\) 7.10961 1.27692 0.638461 0.769654i \(-0.279571\pi\)
0.638461 + 0.769654i \(0.279571\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.62859 −0.283500
\(34\) −1.00000 −0.171499
\(35\) 2.77325 0.468765
\(36\) 1.00000 0.166667
\(37\) 1.66923 0.274419 0.137209 0.990542i \(-0.456187\pi\)
0.137209 + 0.990542i \(0.456187\pi\)
\(38\) −1.16709 −0.189328
\(39\) −5.47999 −0.877501
\(40\) −0.580342 −0.0917601
\(41\) −0.211924 −0.0330970 −0.0165485 0.999863i \(-0.505268\pi\)
−0.0165485 + 0.999863i \(0.505268\pi\)
\(42\) 4.77865 0.737361
\(43\) 9.35293 1.42631 0.713154 0.701007i \(-0.247266\pi\)
0.713154 + 0.701007i \(0.247266\pi\)
\(44\) 1.62859 0.245518
\(45\) 0.580342 0.0865122
\(46\) 7.82087 1.15312
\(47\) 4.12655 0.601920 0.300960 0.953637i \(-0.402693\pi\)
0.300960 + 0.953637i \(0.402693\pi\)
\(48\) −1.00000 −0.144338
\(49\) 15.8355 2.26221
\(50\) 4.66320 0.659477
\(51\) −1.00000 −0.140028
\(52\) 5.47999 0.759938
\(53\) 6.63557 0.911465 0.455733 0.890117i \(-0.349377\pi\)
0.455733 + 0.890117i \(0.349377\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.945136 0.127442
\(56\) −4.77865 −0.638574
\(57\) −1.16709 −0.154585
\(58\) −1.14006 −0.149698
\(59\) −1.00000 −0.130189
\(60\) −0.580342 −0.0749218
\(61\) 1.75157 0.224266 0.112133 0.993693i \(-0.464232\pi\)
0.112133 + 0.993693i \(0.464232\pi\)
\(62\) −7.10961 −0.902921
\(63\) 4.77865 0.602053
\(64\) 1.00000 0.125000
\(65\) 3.18027 0.394463
\(66\) 1.62859 0.200465
\(67\) 0.972991 0.118870 0.0594349 0.998232i \(-0.481070\pi\)
0.0594349 + 0.998232i \(0.481070\pi\)
\(68\) 1.00000 0.121268
\(69\) 7.82087 0.941522
\(70\) −2.77325 −0.331467
\(71\) 0.225978 0.0268187 0.0134093 0.999910i \(-0.495732\pi\)
0.0134093 + 0.999910i \(0.495732\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.96236 0.229676 0.114838 0.993384i \(-0.463365\pi\)
0.114838 + 0.993384i \(0.463365\pi\)
\(74\) −1.66923 −0.194044
\(75\) 4.66320 0.538460
\(76\) 1.16709 0.133875
\(77\) 7.78244 0.886891
\(78\) 5.47999 0.620487
\(79\) −8.26320 −0.929682 −0.464841 0.885394i \(-0.653889\pi\)
−0.464841 + 0.885394i \(0.653889\pi\)
\(80\) 0.580342 0.0648842
\(81\) 1.00000 0.111111
\(82\) 0.211924 0.0234031
\(83\) 8.22544 0.902859 0.451429 0.892307i \(-0.350914\pi\)
0.451429 + 0.892307i \(0.350914\pi\)
\(84\) −4.77865 −0.521393
\(85\) 0.580342 0.0629469
\(86\) −9.35293 −1.00855
\(87\) −1.14006 −0.122228
\(88\) −1.62859 −0.173608
\(89\) −1.59874 −0.169466 −0.0847330 0.996404i \(-0.527004\pi\)
−0.0847330 + 0.996404i \(0.527004\pi\)
\(90\) −0.580342 −0.0611734
\(91\) 26.1869 2.74514
\(92\) −7.82087 −0.815382
\(93\) −7.10961 −0.737232
\(94\) −4.12655 −0.425622
\(95\) 0.677313 0.0694909
\(96\) 1.00000 0.102062
\(97\) −7.65509 −0.777257 −0.388628 0.921395i \(-0.627051\pi\)
−0.388628 + 0.921395i \(0.627051\pi\)
\(98\) −15.8355 −1.59962
\(99\) 1.62859 0.163679
\(100\) −4.66320 −0.466320
\(101\) 2.30869 0.229723 0.114861 0.993382i \(-0.463358\pi\)
0.114861 + 0.993382i \(0.463358\pi\)
\(102\) 1.00000 0.0990148
\(103\) −6.10597 −0.601639 −0.300819 0.953681i \(-0.597260\pi\)
−0.300819 + 0.953681i \(0.597260\pi\)
\(104\) −5.47999 −0.537357
\(105\) −2.77325 −0.270641
\(106\) −6.63557 −0.644503
\(107\) −0.192091 −0.0185701 −0.00928506 0.999957i \(-0.502956\pi\)
−0.00928506 + 0.999957i \(0.502956\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −0.690652 −0.0661525 −0.0330762 0.999453i \(-0.510530\pi\)
−0.0330762 + 0.999453i \(0.510530\pi\)
\(110\) −0.945136 −0.0901152
\(111\) −1.66923 −0.158436
\(112\) 4.77865 0.451540
\(113\) −18.0322 −1.69633 −0.848164 0.529733i \(-0.822292\pi\)
−0.848164 + 0.529733i \(0.822292\pi\)
\(114\) 1.16709 0.109308
\(115\) −4.53878 −0.423243
\(116\) 1.14006 0.105852
\(117\) 5.47999 0.506625
\(118\) 1.00000 0.0920575
\(119\) 4.77865 0.438058
\(120\) 0.580342 0.0529777
\(121\) −8.34771 −0.758883
\(122\) −1.75157 −0.158580
\(123\) 0.211924 0.0191085
\(124\) 7.10961 0.638461
\(125\) −5.60796 −0.501591
\(126\) −4.77865 −0.425716
\(127\) −4.20613 −0.373233 −0.186617 0.982433i \(-0.559752\pi\)
−0.186617 + 0.982433i \(0.559752\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.35293 −0.823479
\(130\) −3.18027 −0.278928
\(131\) 4.74754 0.414794 0.207397 0.978257i \(-0.433501\pi\)
0.207397 + 0.978257i \(0.433501\pi\)
\(132\) −1.62859 −0.141750
\(133\) 5.57713 0.483599
\(134\) −0.972991 −0.0840536
\(135\) −0.580342 −0.0499479
\(136\) −1.00000 −0.0857493
\(137\) −5.83732 −0.498716 −0.249358 0.968411i \(-0.580220\pi\)
−0.249358 + 0.968411i \(0.580220\pi\)
\(138\) −7.82087 −0.665757
\(139\) 1.62853 0.138130 0.0690651 0.997612i \(-0.477998\pi\)
0.0690651 + 0.997612i \(0.477998\pi\)
\(140\) 2.77325 0.234382
\(141\) −4.12655 −0.347519
\(142\) −0.225978 −0.0189637
\(143\) 8.92463 0.746315
\(144\) 1.00000 0.0833333
\(145\) 0.661626 0.0549450
\(146\) −1.96236 −0.162406
\(147\) −15.8355 −1.30609
\(148\) 1.66923 0.137209
\(149\) 5.84752 0.479047 0.239524 0.970891i \(-0.423009\pi\)
0.239524 + 0.970891i \(0.423009\pi\)
\(150\) −4.66320 −0.380749
\(151\) −0.333013 −0.0271002 −0.0135501 0.999908i \(-0.504313\pi\)
−0.0135501 + 0.999908i \(0.504313\pi\)
\(152\) −1.16709 −0.0946638
\(153\) 1.00000 0.0808452
\(154\) −7.78244 −0.627126
\(155\) 4.12600 0.331408
\(156\) −5.47999 −0.438750
\(157\) 13.5429 1.08084 0.540422 0.841394i \(-0.318265\pi\)
0.540422 + 0.841394i \(0.318265\pi\)
\(158\) 8.26320 0.657385
\(159\) −6.63557 −0.526235
\(160\) −0.580342 −0.0458800
\(161\) −37.3732 −2.94542
\(162\) −1.00000 −0.0785674
\(163\) −6.84383 −0.536050 −0.268025 0.963412i \(-0.586371\pi\)
−0.268025 + 0.963412i \(0.586371\pi\)
\(164\) −0.211924 −0.0165485
\(165\) −0.945136 −0.0735787
\(166\) −8.22544 −0.638418
\(167\) −5.73420 −0.443726 −0.221863 0.975078i \(-0.571214\pi\)
−0.221863 + 0.975078i \(0.571214\pi\)
\(168\) 4.77865 0.368681
\(169\) 17.0303 1.31002
\(170\) −0.580342 −0.0445102
\(171\) 1.16709 0.0892499
\(172\) 9.35293 0.713154
\(173\) 9.65505 0.734060 0.367030 0.930209i \(-0.380375\pi\)
0.367030 + 0.930209i \(0.380375\pi\)
\(174\) 1.14006 0.0864279
\(175\) −22.2838 −1.68450
\(176\) 1.62859 0.122759
\(177\) 1.00000 0.0751646
\(178\) 1.59874 0.119831
\(179\) 0.791546 0.0591629 0.0295815 0.999562i \(-0.490583\pi\)
0.0295815 + 0.999562i \(0.490583\pi\)
\(180\) 0.580342 0.0432561
\(181\) 1.53099 0.113797 0.0568987 0.998380i \(-0.481879\pi\)
0.0568987 + 0.998380i \(0.481879\pi\)
\(182\) −26.1869 −1.94110
\(183\) −1.75157 −0.129480
\(184\) 7.82087 0.576562
\(185\) 0.968721 0.0712218
\(186\) 7.10961 0.521302
\(187\) 1.62859 0.119094
\(188\) 4.12655 0.300960
\(189\) −4.77865 −0.347595
\(190\) −0.677313 −0.0491375
\(191\) −3.79389 −0.274516 −0.137258 0.990535i \(-0.543829\pi\)
−0.137258 + 0.990535i \(0.543829\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 8.98705 0.646902 0.323451 0.946245i \(-0.395157\pi\)
0.323451 + 0.946245i \(0.395157\pi\)
\(194\) 7.65509 0.549604
\(195\) −3.18027 −0.227744
\(196\) 15.8355 1.13111
\(197\) −5.73976 −0.408941 −0.204471 0.978873i \(-0.565547\pi\)
−0.204471 + 0.978873i \(0.565547\pi\)
\(198\) −1.62859 −0.115739
\(199\) 14.0439 0.995546 0.497773 0.867307i \(-0.334151\pi\)
0.497773 + 0.867307i \(0.334151\pi\)
\(200\) 4.66320 0.329738
\(201\) −0.972991 −0.0686295
\(202\) −2.30869 −0.162439
\(203\) 5.44796 0.382372
\(204\) −1.00000 −0.0700140
\(205\) −0.122988 −0.00858988
\(206\) 6.10597 0.425423
\(207\) −7.82087 −0.543588
\(208\) 5.47999 0.379969
\(209\) 1.90071 0.131475
\(210\) 2.77325 0.191372
\(211\) −25.2857 −1.74074 −0.870369 0.492401i \(-0.836119\pi\)
−0.870369 + 0.492401i \(0.836119\pi\)
\(212\) 6.63557 0.455733
\(213\) −0.225978 −0.0154838
\(214\) 0.192091 0.0131311
\(215\) 5.42789 0.370179
\(216\) 1.00000 0.0680414
\(217\) 33.9743 2.30633
\(218\) 0.690652 0.0467768
\(219\) −1.96236 −0.132604
\(220\) 0.945136 0.0637211
\(221\) 5.47999 0.368624
\(222\) 1.66923 0.112031
\(223\) −9.53502 −0.638512 −0.319256 0.947669i \(-0.603433\pi\)
−0.319256 + 0.947669i \(0.603433\pi\)
\(224\) −4.77865 −0.319287
\(225\) −4.66320 −0.310880
\(226\) 18.0322 1.19949
\(227\) 20.1882 1.33994 0.669969 0.742389i \(-0.266307\pi\)
0.669969 + 0.742389i \(0.266307\pi\)
\(228\) −1.16709 −0.0772927
\(229\) −2.84520 −0.188016 −0.0940079 0.995571i \(-0.529968\pi\)
−0.0940079 + 0.995571i \(0.529968\pi\)
\(230\) 4.53878 0.299278
\(231\) −7.78244 −0.512047
\(232\) −1.14006 −0.0748488
\(233\) −7.66783 −0.502336 −0.251168 0.967943i \(-0.580815\pi\)
−0.251168 + 0.967943i \(0.580815\pi\)
\(234\) −5.47999 −0.358238
\(235\) 2.39481 0.156220
\(236\) −1.00000 −0.0650945
\(237\) 8.26320 0.536752
\(238\) −4.77865 −0.309754
\(239\) −2.50181 −0.161829 −0.0809143 0.996721i \(-0.525784\pi\)
−0.0809143 + 0.996721i \(0.525784\pi\)
\(240\) −0.580342 −0.0374609
\(241\) 17.2582 1.11170 0.555849 0.831283i \(-0.312393\pi\)
0.555849 + 0.831283i \(0.312393\pi\)
\(242\) 8.34771 0.536611
\(243\) −1.00000 −0.0641500
\(244\) 1.75157 0.112133
\(245\) 9.18999 0.587127
\(246\) −0.211924 −0.0135118
\(247\) 6.39566 0.406946
\(248\) −7.10961 −0.451460
\(249\) −8.22544 −0.521266
\(250\) 5.60796 0.354679
\(251\) −19.8854 −1.25515 −0.627576 0.778555i \(-0.715953\pi\)
−0.627576 + 0.778555i \(0.715953\pi\)
\(252\) 4.77865 0.301027
\(253\) −12.7370 −0.800765
\(254\) 4.20613 0.263916
\(255\) −0.580342 −0.0363424
\(256\) 1.00000 0.0625000
\(257\) 8.13485 0.507438 0.253719 0.967278i \(-0.418346\pi\)
0.253719 + 0.967278i \(0.418346\pi\)
\(258\) 9.35293 0.582288
\(259\) 7.97664 0.495644
\(260\) 3.18027 0.197232
\(261\) 1.14006 0.0705681
\(262\) −4.74754 −0.293304
\(263\) 10.5725 0.651928 0.325964 0.945382i \(-0.394311\pi\)
0.325964 + 0.945382i \(0.394311\pi\)
\(264\) 1.62859 0.100232
\(265\) 3.85090 0.236559
\(266\) −5.57713 −0.341956
\(267\) 1.59874 0.0978412
\(268\) 0.972991 0.0594349
\(269\) −21.8410 −1.33167 −0.665834 0.746100i \(-0.731924\pi\)
−0.665834 + 0.746100i \(0.731924\pi\)
\(270\) 0.580342 0.0353185
\(271\) 25.2327 1.53278 0.766389 0.642376i \(-0.222051\pi\)
0.766389 + 0.642376i \(0.222051\pi\)
\(272\) 1.00000 0.0606339
\(273\) −26.1869 −1.58491
\(274\) 5.83732 0.352645
\(275\) −7.59442 −0.457961
\(276\) 7.82087 0.470761
\(277\) −14.1564 −0.850574 −0.425287 0.905058i \(-0.639827\pi\)
−0.425287 + 0.905058i \(0.639827\pi\)
\(278\) −1.62853 −0.0976728
\(279\) 7.10961 0.425641
\(280\) −2.77325 −0.165733
\(281\) −2.81297 −0.167808 −0.0839039 0.996474i \(-0.526739\pi\)
−0.0839039 + 0.996474i \(0.526739\pi\)
\(282\) 4.12655 0.245733
\(283\) −31.2649 −1.85851 −0.929253 0.369445i \(-0.879548\pi\)
−0.929253 + 0.369445i \(0.879548\pi\)
\(284\) 0.225978 0.0134093
\(285\) −0.677313 −0.0401206
\(286\) −8.92463 −0.527724
\(287\) −1.01271 −0.0597784
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −0.661626 −0.0388520
\(291\) 7.65509 0.448749
\(292\) 1.96236 0.114838
\(293\) 0.689982 0.0403092 0.0201546 0.999797i \(-0.493584\pi\)
0.0201546 + 0.999797i \(0.493584\pi\)
\(294\) 15.8355 0.923544
\(295\) −0.580342 −0.0337888
\(296\) −1.66923 −0.0970218
\(297\) −1.62859 −0.0945001
\(298\) −5.84752 −0.338738
\(299\) −42.8583 −2.47856
\(300\) 4.66320 0.269230
\(301\) 44.6943 2.57614
\(302\) 0.333013 0.0191627
\(303\) −2.30869 −0.132631
\(304\) 1.16709 0.0669374
\(305\) 1.01651 0.0582051
\(306\) −1.00000 −0.0571662
\(307\) 5.97982 0.341287 0.170643 0.985333i \(-0.445415\pi\)
0.170643 + 0.985333i \(0.445415\pi\)
\(308\) 7.78244 0.443445
\(309\) 6.10597 0.347356
\(310\) −4.12600 −0.234341
\(311\) 25.5624 1.44951 0.724756 0.689006i \(-0.241953\pi\)
0.724756 + 0.689006i \(0.241953\pi\)
\(312\) 5.47999 0.310243
\(313\) −21.2681 −1.20214 −0.601071 0.799195i \(-0.705259\pi\)
−0.601071 + 0.799195i \(0.705259\pi\)
\(314\) −13.5429 −0.764271
\(315\) 2.77325 0.156255
\(316\) −8.26320 −0.464841
\(317\) −27.9593 −1.57035 −0.785176 0.619273i \(-0.787428\pi\)
−0.785176 + 0.619273i \(0.787428\pi\)
\(318\) 6.63557 0.372104
\(319\) 1.85669 0.103955
\(320\) 0.580342 0.0324421
\(321\) 0.192091 0.0107215
\(322\) 37.3732 2.08273
\(323\) 1.16709 0.0649389
\(324\) 1.00000 0.0555556
\(325\) −25.5543 −1.41750
\(326\) 6.84383 0.379044
\(327\) 0.690652 0.0381931
\(328\) 0.211924 0.0117015
\(329\) 19.7194 1.08716
\(330\) 0.945136 0.0520280
\(331\) −17.4034 −0.956578 −0.478289 0.878203i \(-0.658743\pi\)
−0.478289 + 0.878203i \(0.658743\pi\)
\(332\) 8.22544 0.451429
\(333\) 1.66923 0.0914730
\(334\) 5.73420 0.313762
\(335\) 0.564667 0.0308511
\(336\) −4.77865 −0.260697
\(337\) 19.7159 1.07399 0.536996 0.843585i \(-0.319559\pi\)
0.536996 + 0.843585i \(0.319559\pi\)
\(338\) −17.0303 −0.926325
\(339\) 18.0322 0.979376
\(340\) 0.580342 0.0314735
\(341\) 11.5786 0.627016
\(342\) −1.16709 −0.0631092
\(343\) 42.2216 2.27975
\(344\) −9.35293 −0.504276
\(345\) 4.53878 0.244360
\(346\) −9.65505 −0.519059
\(347\) −19.2525 −1.03353 −0.516765 0.856127i \(-0.672864\pi\)
−0.516765 + 0.856127i \(0.672864\pi\)
\(348\) −1.14006 −0.0611138
\(349\) −24.6206 −1.31791 −0.658955 0.752182i \(-0.729001\pi\)
−0.658955 + 0.752182i \(0.729001\pi\)
\(350\) 22.2838 1.19112
\(351\) −5.47999 −0.292500
\(352\) −1.62859 −0.0868039
\(353\) 21.4591 1.14216 0.571078 0.820896i \(-0.306526\pi\)
0.571078 + 0.820896i \(0.306526\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 0.131145 0.00696044
\(356\) −1.59874 −0.0847330
\(357\) −4.77865 −0.252913
\(358\) −0.791546 −0.0418345
\(359\) 33.9256 1.79053 0.895263 0.445538i \(-0.146988\pi\)
0.895263 + 0.445538i \(0.146988\pi\)
\(360\) −0.580342 −0.0305867
\(361\) −17.6379 −0.928310
\(362\) −1.53099 −0.0804669
\(363\) 8.34771 0.438141
\(364\) 26.1869 1.37257
\(365\) 1.13884 0.0596095
\(366\) 1.75157 0.0915560
\(367\) −2.51893 −0.131487 −0.0657434 0.997837i \(-0.520942\pi\)
−0.0657434 + 0.997837i \(0.520942\pi\)
\(368\) −7.82087 −0.407691
\(369\) −0.211924 −0.0110323
\(370\) −0.968721 −0.0503614
\(371\) 31.7090 1.64625
\(372\) −7.10961 −0.368616
\(373\) −17.7784 −0.920528 −0.460264 0.887782i \(-0.652245\pi\)
−0.460264 + 0.887782i \(0.652245\pi\)
\(374\) −1.62859 −0.0842121
\(375\) 5.60796 0.289594
\(376\) −4.12655 −0.212811
\(377\) 6.24753 0.321764
\(378\) 4.77865 0.245787
\(379\) 8.51794 0.437537 0.218769 0.975777i \(-0.429796\pi\)
0.218769 + 0.975777i \(0.429796\pi\)
\(380\) 0.677313 0.0347454
\(381\) 4.20613 0.215486
\(382\) 3.79389 0.194112
\(383\) 0.841850 0.0430165 0.0215083 0.999769i \(-0.493153\pi\)
0.0215083 + 0.999769i \(0.493153\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.51647 0.230181
\(386\) −8.98705 −0.457429
\(387\) 9.35293 0.475436
\(388\) −7.65509 −0.388628
\(389\) −0.461026 −0.0233749 −0.0116875 0.999932i \(-0.503720\pi\)
−0.0116875 + 0.999932i \(0.503720\pi\)
\(390\) 3.18027 0.161039
\(391\) −7.82087 −0.395518
\(392\) −15.8355 −0.799812
\(393\) −4.74754 −0.239482
\(394\) 5.73976 0.289165
\(395\) −4.79548 −0.241287
\(396\) 1.62859 0.0818395
\(397\) 7.85404 0.394183 0.197091 0.980385i \(-0.436850\pi\)
0.197091 + 0.980385i \(0.436850\pi\)
\(398\) −14.0439 −0.703958
\(399\) −5.57713 −0.279206
\(400\) −4.66320 −0.233160
\(401\) 22.4214 1.11967 0.559835 0.828604i \(-0.310864\pi\)
0.559835 + 0.828604i \(0.310864\pi\)
\(402\) 0.972991 0.0485284
\(403\) 38.9606 1.94076
\(404\) 2.30869 0.114861
\(405\) 0.580342 0.0288374
\(406\) −5.44796 −0.270378
\(407\) 2.71848 0.134750
\(408\) 1.00000 0.0495074
\(409\) 10.5913 0.523704 0.261852 0.965108i \(-0.415667\pi\)
0.261852 + 0.965108i \(0.415667\pi\)
\(410\) 0.122988 0.00607396
\(411\) 5.83732 0.287934
\(412\) −6.10597 −0.300819
\(413\) −4.77865 −0.235142
\(414\) 7.82087 0.384375
\(415\) 4.77356 0.234325
\(416\) −5.47999 −0.268679
\(417\) −1.62853 −0.0797495
\(418\) −1.90071 −0.0929669
\(419\) 33.0129 1.61279 0.806394 0.591379i \(-0.201416\pi\)
0.806394 + 0.591379i \(0.201416\pi\)
\(420\) −2.77325 −0.135321
\(421\) −12.7986 −0.623764 −0.311882 0.950121i \(-0.600959\pi\)
−0.311882 + 0.950121i \(0.600959\pi\)
\(422\) 25.2857 1.23089
\(423\) 4.12655 0.200640
\(424\) −6.63557 −0.322252
\(425\) −4.66320 −0.226199
\(426\) 0.225978 0.0109487
\(427\) 8.37014 0.405059
\(428\) −0.192091 −0.00928506
\(429\) −8.92463 −0.430885
\(430\) −5.42789 −0.261756
\(431\) −6.11123 −0.294368 −0.147184 0.989109i \(-0.547021\pi\)
−0.147184 + 0.989109i \(0.547021\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 9.07872 0.436296 0.218148 0.975916i \(-0.429999\pi\)
0.218148 + 0.975916i \(0.429999\pi\)
\(434\) −33.9743 −1.63082
\(435\) −0.661626 −0.0317225
\(436\) −0.690652 −0.0330762
\(437\) −9.12769 −0.436637
\(438\) 1.96236 0.0937650
\(439\) 4.51957 0.215707 0.107854 0.994167i \(-0.465602\pi\)
0.107854 + 0.994167i \(0.465602\pi\)
\(440\) −0.945136 −0.0450576
\(441\) 15.8355 0.754070
\(442\) −5.47999 −0.260656
\(443\) 9.45160 0.449059 0.224529 0.974467i \(-0.427915\pi\)
0.224529 + 0.974467i \(0.427915\pi\)
\(444\) −1.66923 −0.0792179
\(445\) −0.927815 −0.0439826
\(446\) 9.53502 0.451496
\(447\) −5.84752 −0.276578
\(448\) 4.77865 0.225770
\(449\) −7.59507 −0.358434 −0.179217 0.983810i \(-0.557356\pi\)
−0.179217 + 0.983810i \(0.557356\pi\)
\(450\) 4.66320 0.219826
\(451\) −0.345136 −0.0162518
\(452\) −18.0322 −0.848164
\(453\) 0.333013 0.0156463
\(454\) −20.1882 −0.947480
\(455\) 15.1974 0.712464
\(456\) 1.16709 0.0546542
\(457\) −9.84114 −0.460349 −0.230175 0.973149i \(-0.573930\pi\)
−0.230175 + 0.973149i \(0.573930\pi\)
\(458\) 2.84520 0.132947
\(459\) −1.00000 −0.0466760
\(460\) −4.53878 −0.211622
\(461\) −12.8726 −0.599538 −0.299769 0.954012i \(-0.596910\pi\)
−0.299769 + 0.954012i \(0.596910\pi\)
\(462\) 7.78244 0.362072
\(463\) −3.67175 −0.170641 −0.0853204 0.996354i \(-0.527191\pi\)
−0.0853204 + 0.996354i \(0.527191\pi\)
\(464\) 1.14006 0.0529261
\(465\) −4.12600 −0.191339
\(466\) 7.66783 0.355205
\(467\) 9.76462 0.451853 0.225926 0.974144i \(-0.427459\pi\)
0.225926 + 0.974144i \(0.427459\pi\)
\(468\) 5.47999 0.253313
\(469\) 4.64958 0.214698
\(470\) −2.39481 −0.110464
\(471\) −13.5429 −0.624025
\(472\) 1.00000 0.0460287
\(473\) 15.2320 0.700370
\(474\) −8.26320 −0.379541
\(475\) −5.44240 −0.249714
\(476\) 4.77865 0.219029
\(477\) 6.63557 0.303822
\(478\) 2.50181 0.114430
\(479\) 5.99020 0.273699 0.136850 0.990592i \(-0.456302\pi\)
0.136850 + 0.990592i \(0.456302\pi\)
\(480\) 0.580342 0.0264889
\(481\) 9.14734 0.417083
\(482\) −17.2582 −0.786089
\(483\) 37.3732 1.70054
\(484\) −8.34771 −0.379441
\(485\) −4.44257 −0.201727
\(486\) 1.00000 0.0453609
\(487\) 19.1635 0.868383 0.434192 0.900821i \(-0.357034\pi\)
0.434192 + 0.900821i \(0.357034\pi\)
\(488\) −1.75157 −0.0792898
\(489\) 6.84383 0.309489
\(490\) −9.18999 −0.415161
\(491\) −35.5803 −1.60572 −0.802859 0.596169i \(-0.796689\pi\)
−0.802859 + 0.596169i \(0.796689\pi\)
\(492\) 0.211924 0.00955427
\(493\) 1.14006 0.0513458
\(494\) −6.39566 −0.287754
\(495\) 0.945136 0.0424807
\(496\) 7.10961 0.319231
\(497\) 1.07987 0.0484388
\(498\) 8.22544 0.368591
\(499\) 37.3473 1.67190 0.835948 0.548809i \(-0.184918\pi\)
0.835948 + 0.548809i \(0.184918\pi\)
\(500\) −5.60796 −0.250796
\(501\) 5.73420 0.256185
\(502\) 19.8854 0.887527
\(503\) −40.2022 −1.79253 −0.896264 0.443521i \(-0.853729\pi\)
−0.896264 + 0.443521i \(0.853729\pi\)
\(504\) −4.77865 −0.212858
\(505\) 1.33983 0.0596215
\(506\) 12.7370 0.566227
\(507\) −17.0303 −0.756341
\(508\) −4.20613 −0.186617
\(509\) −30.0994 −1.33413 −0.667066 0.744998i \(-0.732450\pi\)
−0.667066 + 0.744998i \(0.732450\pi\)
\(510\) 0.580342 0.0256980
\(511\) 9.37741 0.414832
\(512\) −1.00000 −0.0441942
\(513\) −1.16709 −0.0515285
\(514\) −8.13485 −0.358813
\(515\) −3.54355 −0.156147
\(516\) −9.35293 −0.411740
\(517\) 6.72045 0.295565
\(518\) −7.97664 −0.350473
\(519\) −9.65505 −0.423810
\(520\) −3.18027 −0.139464
\(521\) 38.2781 1.67700 0.838498 0.544905i \(-0.183434\pi\)
0.838498 + 0.544905i \(0.183434\pi\)
\(522\) −1.14006 −0.0498992
\(523\) 39.3589 1.72105 0.860523 0.509412i \(-0.170137\pi\)
0.860523 + 0.509412i \(0.170137\pi\)
\(524\) 4.74754 0.207397
\(525\) 22.2838 0.972545
\(526\) −10.5725 −0.460983
\(527\) 7.10961 0.309699
\(528\) −1.62859 −0.0708751
\(529\) 38.1660 1.65939
\(530\) −3.85090 −0.167272
\(531\) −1.00000 −0.0433963
\(532\) 5.57713 0.241799
\(533\) −1.16134 −0.0503033
\(534\) −1.59874 −0.0691842
\(535\) −0.111478 −0.00481963
\(536\) −0.972991 −0.0420268
\(537\) −0.791546 −0.0341577
\(538\) 21.8410 0.941631
\(539\) 25.7894 1.11083
\(540\) −0.580342 −0.0249739
\(541\) 17.1469 0.737201 0.368601 0.929588i \(-0.379837\pi\)
0.368601 + 0.929588i \(0.379837\pi\)
\(542\) −25.2327 −1.08384
\(543\) −1.53099 −0.0657010
\(544\) −1.00000 −0.0428746
\(545\) −0.400814 −0.0171690
\(546\) 26.1869 1.12070
\(547\) −33.9397 −1.45116 −0.725578 0.688140i \(-0.758428\pi\)
−0.725578 + 0.688140i \(0.758428\pi\)
\(548\) −5.83732 −0.249358
\(549\) 1.75157 0.0747552
\(550\) 7.59442 0.323827
\(551\) 1.33056 0.0566838
\(552\) −7.82087 −0.332878
\(553\) −39.4869 −1.67915
\(554\) 14.1564 0.601447
\(555\) −0.968721 −0.0411199
\(556\) 1.62853 0.0690651
\(557\) 16.7397 0.709286 0.354643 0.935002i \(-0.384602\pi\)
0.354643 + 0.935002i \(0.384602\pi\)
\(558\) −7.10961 −0.300974
\(559\) 51.2539 2.16781
\(560\) 2.77325 0.117191
\(561\) −1.62859 −0.0687589
\(562\) 2.81297 0.118658
\(563\) 35.6193 1.50117 0.750586 0.660772i \(-0.229771\pi\)
0.750586 + 0.660772i \(0.229771\pi\)
\(564\) −4.12655 −0.173759
\(565\) −10.4648 −0.440260
\(566\) 31.2649 1.31416
\(567\) 4.77865 0.200684
\(568\) −0.225978 −0.00948184
\(569\) −4.63130 −0.194154 −0.0970772 0.995277i \(-0.530949\pi\)
−0.0970772 + 0.995277i \(0.530949\pi\)
\(570\) 0.677313 0.0283695
\(571\) −7.01576 −0.293600 −0.146800 0.989166i \(-0.546897\pi\)
−0.146800 + 0.989166i \(0.546897\pi\)
\(572\) 8.92463 0.373157
\(573\) 3.79389 0.158492
\(574\) 1.01271 0.0422697
\(575\) 36.4703 1.52092
\(576\) 1.00000 0.0416667
\(577\) 14.7211 0.612847 0.306423 0.951895i \(-0.400868\pi\)
0.306423 + 0.951895i \(0.400868\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −8.98705 −0.373489
\(580\) 0.661626 0.0274725
\(581\) 39.3065 1.63071
\(582\) −7.65509 −0.317314
\(583\) 10.8066 0.447563
\(584\) −1.96236 −0.0812029
\(585\) 3.18027 0.131488
\(586\) −0.689982 −0.0285029
\(587\) −5.22657 −0.215724 −0.107862 0.994166i \(-0.534400\pi\)
−0.107862 + 0.994166i \(0.534400\pi\)
\(588\) −15.8355 −0.653044
\(589\) 8.29758 0.341896
\(590\) 0.580342 0.0238923
\(591\) 5.73976 0.236102
\(592\) 1.66923 0.0686047
\(593\) −3.08693 −0.126765 −0.0633824 0.997989i \(-0.520189\pi\)
−0.0633824 + 0.997989i \(0.520189\pi\)
\(594\) 1.62859 0.0668217
\(595\) 2.77325 0.113692
\(596\) 5.84752 0.239524
\(597\) −14.0439 −0.574779
\(598\) 42.8583 1.75261
\(599\) −18.1055 −0.739771 −0.369885 0.929077i \(-0.620603\pi\)
−0.369885 + 0.929077i \(0.620603\pi\)
\(600\) −4.66320 −0.190374
\(601\) 24.7259 1.00859 0.504296 0.863531i \(-0.331752\pi\)
0.504296 + 0.863531i \(0.331752\pi\)
\(602\) −44.6943 −1.82161
\(603\) 0.972991 0.0396233
\(604\) −0.333013 −0.0135501
\(605\) −4.84452 −0.196958
\(606\) 2.30869 0.0937839
\(607\) 47.5956 1.93184 0.965922 0.258833i \(-0.0833379\pi\)
0.965922 + 0.258833i \(0.0833379\pi\)
\(608\) −1.16709 −0.0473319
\(609\) −5.44796 −0.220762
\(610\) −1.01651 −0.0411573
\(611\) 22.6135 0.914843
\(612\) 1.00000 0.0404226
\(613\) −6.03601 −0.243792 −0.121896 0.992543i \(-0.538897\pi\)
−0.121896 + 0.992543i \(0.538897\pi\)
\(614\) −5.97982 −0.241326
\(615\) 0.122988 0.00495937
\(616\) −7.78244 −0.313563
\(617\) 17.3761 0.699536 0.349768 0.936836i \(-0.386260\pi\)
0.349768 + 0.936836i \(0.386260\pi\)
\(618\) −6.10597 −0.245618
\(619\) −41.2754 −1.65900 −0.829500 0.558507i \(-0.811374\pi\)
−0.829500 + 0.558507i \(0.811374\pi\)
\(620\) 4.12600 0.165704
\(621\) 7.82087 0.313841
\(622\) −25.5624 −1.02496
\(623\) −7.63981 −0.306082
\(624\) −5.47999 −0.219375
\(625\) 20.0615 0.802459
\(626\) 21.2681 0.850043
\(627\) −1.90071 −0.0759071
\(628\) 13.5429 0.540422
\(629\) 1.66923 0.0665564
\(630\) −2.77325 −0.110489
\(631\) −6.56631 −0.261401 −0.130700 0.991422i \(-0.541723\pi\)
−0.130700 + 0.991422i \(0.541723\pi\)
\(632\) 8.26320 0.328692
\(633\) 25.2857 1.00502
\(634\) 27.9593 1.11041
\(635\) −2.44099 −0.0968678
\(636\) −6.63557 −0.263117
\(637\) 86.7782 3.43828
\(638\) −1.85669 −0.0735070
\(639\) 0.225978 0.00893957
\(640\) −0.580342 −0.0229400
\(641\) −13.1408 −0.519029 −0.259515 0.965739i \(-0.583563\pi\)
−0.259515 + 0.965739i \(0.583563\pi\)
\(642\) −0.192091 −0.00758122
\(643\) 27.1713 1.07153 0.535766 0.844366i \(-0.320023\pi\)
0.535766 + 0.844366i \(0.320023\pi\)
\(644\) −37.3732 −1.47271
\(645\) −5.42789 −0.213723
\(646\) −1.16709 −0.0459187
\(647\) 2.94678 0.115850 0.0579250 0.998321i \(-0.481552\pi\)
0.0579250 + 0.998321i \(0.481552\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −1.62859 −0.0639276
\(650\) 25.5543 1.00232
\(651\) −33.9743 −1.33156
\(652\) −6.84383 −0.268025
\(653\) 0.487703 0.0190853 0.00954264 0.999954i \(-0.496962\pi\)
0.00954264 + 0.999954i \(0.496962\pi\)
\(654\) −0.690652 −0.0270066
\(655\) 2.75519 0.107654
\(656\) −0.211924 −0.00827424
\(657\) 1.96236 0.0765588
\(658\) −19.7194 −0.768740
\(659\) 8.26188 0.321837 0.160919 0.986968i \(-0.448554\pi\)
0.160919 + 0.986968i \(0.448554\pi\)
\(660\) −0.945136 −0.0367894
\(661\) 12.3243 0.479359 0.239679 0.970852i \(-0.422958\pi\)
0.239679 + 0.970852i \(0.422958\pi\)
\(662\) 17.4034 0.676402
\(663\) −5.47999 −0.212825
\(664\) −8.22544 −0.319209
\(665\) 3.23664 0.125512
\(666\) −1.66923 −0.0646812
\(667\) −8.91628 −0.345240
\(668\) −5.73420 −0.221863
\(669\) 9.53502 0.368645
\(670\) −0.564667 −0.0218150
\(671\) 2.85258 0.110123
\(672\) 4.77865 0.184340
\(673\) −12.2900 −0.473745 −0.236873 0.971541i \(-0.576122\pi\)
−0.236873 + 0.971541i \(0.576122\pi\)
\(674\) −19.7159 −0.759427
\(675\) 4.66320 0.179487
\(676\) 17.0303 0.655011
\(677\) 36.1627 1.38985 0.694923 0.719085i \(-0.255439\pi\)
0.694923 + 0.719085i \(0.255439\pi\)
\(678\) −18.0322 −0.692523
\(679\) −36.5810 −1.40385
\(680\) −0.580342 −0.0222551
\(681\) −20.1882 −0.773614
\(682\) −11.5786 −0.443367
\(683\) 17.0937 0.654073 0.327037 0.945012i \(-0.393950\pi\)
0.327037 + 0.945012i \(0.393950\pi\)
\(684\) 1.16709 0.0446250
\(685\) −3.38764 −0.129435
\(686\) −42.2216 −1.61203
\(687\) 2.84520 0.108551
\(688\) 9.35293 0.356577
\(689\) 36.3628 1.38531
\(690\) −4.53878 −0.172788
\(691\) −30.2593 −1.15112 −0.575558 0.817761i \(-0.695215\pi\)
−0.575558 + 0.817761i \(0.695215\pi\)
\(692\) 9.65505 0.367030
\(693\) 7.78244 0.295630
\(694\) 19.2525 0.730816
\(695\) 0.945105 0.0358499
\(696\) 1.14006 0.0432139
\(697\) −0.211924 −0.00802719
\(698\) 24.6206 0.931904
\(699\) 7.66783 0.290024
\(700\) −22.2838 −0.842249
\(701\) −28.6279 −1.08126 −0.540631 0.841260i \(-0.681814\pi\)
−0.540631 + 0.841260i \(0.681814\pi\)
\(702\) 5.47999 0.206829
\(703\) 1.94814 0.0734756
\(704\) 1.62859 0.0613796
\(705\) −2.39481 −0.0901938
\(706\) −21.4591 −0.807626
\(707\) 11.0324 0.414916
\(708\) 1.00000 0.0375823
\(709\) −1.67588 −0.0629389 −0.0314695 0.999505i \(-0.510019\pi\)
−0.0314695 + 0.999505i \(0.510019\pi\)
\(710\) −0.131145 −0.00492177
\(711\) −8.26320 −0.309894
\(712\) 1.59874 0.0599153
\(713\) −55.6033 −2.08236
\(714\) 4.77865 0.178836
\(715\) 5.17933 0.193696
\(716\) 0.791546 0.0295815
\(717\) 2.50181 0.0934318
\(718\) −33.9256 −1.26609
\(719\) −28.3153 −1.05598 −0.527991 0.849250i \(-0.677054\pi\)
−0.527991 + 0.849250i \(0.677054\pi\)
\(720\) 0.580342 0.0216281
\(721\) −29.1783 −1.08666
\(722\) 17.6379 0.656414
\(723\) −17.2582 −0.641839
\(724\) 1.53099 0.0568987
\(725\) −5.31634 −0.197444
\(726\) −8.34771 −0.309813
\(727\) 17.4072 0.645597 0.322798 0.946468i \(-0.395376\pi\)
0.322798 + 0.946468i \(0.395376\pi\)
\(728\) −26.1869 −0.970552
\(729\) 1.00000 0.0370370
\(730\) −1.13884 −0.0421503
\(731\) 9.35293 0.345930
\(732\) −1.75157 −0.0647399
\(733\) −39.9094 −1.47409 −0.737044 0.675845i \(-0.763779\pi\)
−0.737044 + 0.675845i \(0.763779\pi\)
\(734\) 2.51893 0.0929752
\(735\) −9.18999 −0.338978
\(736\) 7.82087 0.288281
\(737\) 1.58460 0.0583695
\(738\) 0.211924 0.00780103
\(739\) 17.7834 0.654174 0.327087 0.944994i \(-0.393933\pi\)
0.327087 + 0.944994i \(0.393933\pi\)
\(740\) 0.968721 0.0356109
\(741\) −6.39566 −0.234951
\(742\) −31.7090 −1.16408
\(743\) 9.66656 0.354632 0.177316 0.984154i \(-0.443259\pi\)
0.177316 + 0.984154i \(0.443259\pi\)
\(744\) 7.10961 0.260651
\(745\) 3.39356 0.124330
\(746\) 17.7784 0.650912
\(747\) 8.22544 0.300953
\(748\) 1.62859 0.0595470
\(749\) −0.917935 −0.0335406
\(750\) −5.60796 −0.204774
\(751\) −11.3917 −0.415689 −0.207844 0.978162i \(-0.566645\pi\)
−0.207844 + 0.978162i \(0.566645\pi\)
\(752\) 4.12655 0.150480
\(753\) 19.8854 0.724663
\(754\) −6.24753 −0.227522
\(755\) −0.193261 −0.00703349
\(756\) −4.77865 −0.173798
\(757\) 38.4001 1.39568 0.697839 0.716255i \(-0.254145\pi\)
0.697839 + 0.716255i \(0.254145\pi\)
\(758\) −8.51794 −0.309386
\(759\) 12.7370 0.462322
\(760\) −0.677313 −0.0245687
\(761\) −47.6314 −1.72664 −0.863318 0.504659i \(-0.831618\pi\)
−0.863318 + 0.504659i \(0.831618\pi\)
\(762\) −4.20613 −0.152372
\(763\) −3.30038 −0.119482
\(764\) −3.79389 −0.137258
\(765\) 0.580342 0.0209823
\(766\) −0.841850 −0.0304173
\(767\) −5.47999 −0.197871
\(768\) −1.00000 −0.0360844
\(769\) −38.9500 −1.40457 −0.702287 0.711894i \(-0.747838\pi\)
−0.702287 + 0.711894i \(0.747838\pi\)
\(770\) −4.51647 −0.162762
\(771\) −8.13485 −0.292969
\(772\) 8.98705 0.323451
\(773\) −46.0313 −1.65563 −0.827815 0.561001i \(-0.810416\pi\)
−0.827815 + 0.561001i \(0.810416\pi\)
\(774\) −9.35293 −0.336184
\(775\) −33.1535 −1.19091
\(776\) 7.65509 0.274802
\(777\) −7.97664 −0.286160
\(778\) 0.461026 0.0165286
\(779\) −0.247335 −0.00886170
\(780\) −3.18027 −0.113872
\(781\) 0.368025 0.0131690
\(782\) 7.82087 0.279674
\(783\) −1.14006 −0.0407425
\(784\) 15.8355 0.565553
\(785\) 7.85952 0.280518
\(786\) 4.74754 0.169339
\(787\) 19.5827 0.698049 0.349025 0.937114i \(-0.386513\pi\)
0.349025 + 0.937114i \(0.386513\pi\)
\(788\) −5.73976 −0.204471
\(789\) −10.5725 −0.376391
\(790\) 4.79548 0.170615
\(791\) −86.1696 −3.06384
\(792\) −1.62859 −0.0578693
\(793\) 9.59858 0.340856
\(794\) −7.85404 −0.278729
\(795\) −3.85090 −0.136577
\(796\) 14.0439 0.497773
\(797\) −4.14326 −0.146762 −0.0733809 0.997304i \(-0.523379\pi\)
−0.0733809 + 0.997304i \(0.523379\pi\)
\(798\) 5.57713 0.197428
\(799\) 4.12655 0.145987
\(800\) 4.66320 0.164869
\(801\) −1.59874 −0.0564887
\(802\) −22.4214 −0.791727
\(803\) 3.19587 0.112780
\(804\) −0.972991 −0.0343148
\(805\) −21.6892 −0.764444
\(806\) −38.9606 −1.37233
\(807\) 21.8410 0.768838
\(808\) −2.30869 −0.0812193
\(809\) −16.6699 −0.586084 −0.293042 0.956100i \(-0.594668\pi\)
−0.293042 + 0.956100i \(0.594668\pi\)
\(810\) −0.580342 −0.0203911
\(811\) 10.8325 0.380379 0.190190 0.981747i \(-0.439090\pi\)
0.190190 + 0.981747i \(0.439090\pi\)
\(812\) 5.44796 0.191186
\(813\) −25.2327 −0.884950
\(814\) −2.71848 −0.0952825
\(815\) −3.97176 −0.139125
\(816\) −1.00000 −0.0350070
\(817\) 10.9157 0.381894
\(818\) −10.5913 −0.370314
\(819\) 26.1869 0.915046
\(820\) −0.122988 −0.00429494
\(821\) −53.1173 −1.85381 −0.926903 0.375302i \(-0.877539\pi\)
−0.926903 + 0.375302i \(0.877539\pi\)
\(822\) −5.83732 −0.203600
\(823\) −54.7971 −1.91011 −0.955053 0.296434i \(-0.904202\pi\)
−0.955053 + 0.296434i \(0.904202\pi\)
\(824\) 6.10597 0.212711
\(825\) 7.59442 0.264404
\(826\) 4.77865 0.166270
\(827\) −6.84173 −0.237910 −0.118955 0.992900i \(-0.537954\pi\)
−0.118955 + 0.992900i \(0.537954\pi\)
\(828\) −7.82087 −0.271794
\(829\) 20.4322 0.709638 0.354819 0.934935i \(-0.384542\pi\)
0.354819 + 0.934935i \(0.384542\pi\)
\(830\) −4.77356 −0.165693
\(831\) 14.1564 0.491079
\(832\) 5.47999 0.189984
\(833\) 15.8355 0.548667
\(834\) 1.62853 0.0563914
\(835\) −3.32780 −0.115163
\(836\) 1.90071 0.0657375
\(837\) −7.10961 −0.245744
\(838\) −33.0129 −1.14041
\(839\) −5.68351 −0.196216 −0.0981082 0.995176i \(-0.531279\pi\)
−0.0981082 + 0.995176i \(0.531279\pi\)
\(840\) 2.77325 0.0956862
\(841\) −27.7003 −0.955181
\(842\) 12.7986 0.441068
\(843\) 2.81297 0.0968839
\(844\) −25.2857 −0.870369
\(845\) 9.88338 0.339999
\(846\) −4.12655 −0.141874
\(847\) −39.8908 −1.37066
\(848\) 6.63557 0.227866
\(849\) 31.2649 1.07301
\(850\) 4.66320 0.159947
\(851\) −13.0548 −0.447513
\(852\) −0.225978 −0.00774189
\(853\) −24.8870 −0.852116 −0.426058 0.904696i \(-0.640098\pi\)
−0.426058 + 0.904696i \(0.640098\pi\)
\(854\) −8.37014 −0.286420
\(855\) 0.677313 0.0231636
\(856\) 0.192091 0.00656553
\(857\) 29.4230 1.00507 0.502536 0.864556i \(-0.332400\pi\)
0.502536 + 0.864556i \(0.332400\pi\)
\(858\) 8.92463 0.304682
\(859\) 2.31173 0.0788751 0.0394375 0.999222i \(-0.487443\pi\)
0.0394375 + 0.999222i \(0.487443\pi\)
\(860\) 5.42789 0.185090
\(861\) 1.01271 0.0345131
\(862\) 6.11123 0.208149
\(863\) 16.3119 0.555265 0.277632 0.960687i \(-0.410450\pi\)
0.277632 + 0.960687i \(0.410450\pi\)
\(864\) 1.00000 0.0340207
\(865\) 5.60323 0.190516
\(866\) −9.07872 −0.308508
\(867\) −1.00000 −0.0339618
\(868\) 33.9743 1.15316
\(869\) −13.4573 −0.456508
\(870\) 0.661626 0.0224312
\(871\) 5.33198 0.180667
\(872\) 0.690652 0.0233884
\(873\) −7.65509 −0.259086
\(874\) 9.12769 0.308749
\(875\) −26.7985 −0.905954
\(876\) −1.96236 −0.0663019
\(877\) 30.0760 1.01560 0.507798 0.861476i \(-0.330460\pi\)
0.507798 + 0.861476i \(0.330460\pi\)
\(878\) −4.51957 −0.152528
\(879\) −0.689982 −0.0232725
\(880\) 0.945136 0.0318605
\(881\) 54.3583 1.83138 0.915690 0.401886i \(-0.131645\pi\)
0.915690 + 0.401886i \(0.131645\pi\)
\(882\) −15.8355 −0.533208
\(883\) 24.5535 0.826292 0.413146 0.910665i \(-0.364430\pi\)
0.413146 + 0.910665i \(0.364430\pi\)
\(884\) 5.47999 0.184312
\(885\) 0.580342 0.0195080
\(886\) −9.45160 −0.317533
\(887\) −8.10195 −0.272037 −0.136018 0.990706i \(-0.543431\pi\)
−0.136018 + 0.990706i \(0.543431\pi\)
\(888\) 1.66923 0.0560155
\(889\) −20.0996 −0.674119
\(890\) 0.927815 0.0311004
\(891\) 1.62859 0.0545597
\(892\) −9.53502 −0.319256
\(893\) 4.81608 0.161164
\(894\) 5.84752 0.195570
\(895\) 0.459367 0.0153550
\(896\) −4.77865 −0.159643
\(897\) 42.8583 1.43100
\(898\) 7.59507 0.253451
\(899\) 8.10539 0.270330
\(900\) −4.66320 −0.155440
\(901\) 6.63557 0.221063
\(902\) 0.345136 0.0114918
\(903\) −44.6943 −1.48733
\(904\) 18.0322 0.599743
\(905\) 0.888496 0.0295346
\(906\) −0.333013 −0.0110636
\(907\) 11.0364 0.366458 0.183229 0.983070i \(-0.441345\pi\)
0.183229 + 0.983070i \(0.441345\pi\)
\(908\) 20.1882 0.669969
\(909\) 2.30869 0.0765743
\(910\) −15.1974 −0.503788
\(911\) −1.78247 −0.0590559 −0.0295280 0.999564i \(-0.509400\pi\)
−0.0295280 + 0.999564i \(0.509400\pi\)
\(912\) −1.16709 −0.0386463
\(913\) 13.3958 0.443337
\(914\) 9.84114 0.325516
\(915\) −1.01651 −0.0336048
\(916\) −2.84520 −0.0940079
\(917\) 22.6868 0.749184
\(918\) 1.00000 0.0330049
\(919\) 6.91066 0.227962 0.113981 0.993483i \(-0.463640\pi\)
0.113981 + 0.993483i \(0.463640\pi\)
\(920\) 4.53878 0.149639
\(921\) −5.97982 −0.197042
\(922\) 12.8726 0.423937
\(923\) 1.23836 0.0407611
\(924\) −7.78244 −0.256023
\(925\) −7.78394 −0.255934
\(926\) 3.67175 0.120661
\(927\) −6.10597 −0.200546
\(928\) −1.14006 −0.0374244
\(929\) 21.1989 0.695513 0.347756 0.937585i \(-0.386944\pi\)
0.347756 + 0.937585i \(0.386944\pi\)
\(930\) 4.12600 0.135297
\(931\) 18.4815 0.605706
\(932\) −7.66783 −0.251168
\(933\) −25.5624 −0.836876
\(934\) −9.76462 −0.319508
\(935\) 0.945136 0.0309093
\(936\) −5.47999 −0.179119
\(937\) 47.8982 1.56477 0.782383 0.622798i \(-0.214004\pi\)
0.782383 + 0.622798i \(0.214004\pi\)
\(938\) −4.64958 −0.151814
\(939\) 21.2681 0.694057
\(940\) 2.39481 0.0781102
\(941\) −50.5950 −1.64935 −0.824675 0.565607i \(-0.808642\pi\)
−0.824675 + 0.565607i \(0.808642\pi\)
\(942\) 13.5429 0.441252
\(943\) 1.65743 0.0539733
\(944\) −1.00000 −0.0325472
\(945\) −2.77325 −0.0902138
\(946\) −15.2320 −0.495236
\(947\) 14.8078 0.481190 0.240595 0.970626i \(-0.422657\pi\)
0.240595 + 0.970626i \(0.422657\pi\)
\(948\) 8.26320 0.268376
\(949\) 10.7537 0.349080
\(950\) 5.44240 0.176575
\(951\) 27.9593 0.906643
\(952\) −4.77865 −0.154877
\(953\) −48.4740 −1.57023 −0.785113 0.619352i \(-0.787395\pi\)
−0.785113 + 0.619352i \(0.787395\pi\)
\(954\) −6.63557 −0.214834
\(955\) −2.20175 −0.0712470
\(956\) −2.50181 −0.0809143
\(957\) −1.85669 −0.0600182
\(958\) −5.99020 −0.193535
\(959\) −27.8945 −0.900760
\(960\) −0.580342 −0.0187304
\(961\) 19.5465 0.630532
\(962\) −9.14734 −0.294922
\(963\) −0.192091 −0.00619004
\(964\) 17.2582 0.555849
\(965\) 5.21556 0.167895
\(966\) −37.3732 −1.20246
\(967\) 53.9593 1.73522 0.867608 0.497250i \(-0.165657\pi\)
0.867608 + 0.497250i \(0.165657\pi\)
\(968\) 8.34771 0.268306
\(969\) −1.16709 −0.0374925
\(970\) 4.44257 0.142642
\(971\) 38.0035 1.21959 0.609795 0.792560i \(-0.291252\pi\)
0.609795 + 0.792560i \(0.291252\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 7.78218 0.249485
\(974\) −19.1635 −0.614040
\(975\) 25.5543 0.818393
\(976\) 1.75157 0.0560664
\(977\) −17.6360 −0.564224 −0.282112 0.959381i \(-0.591035\pi\)
−0.282112 + 0.959381i \(0.591035\pi\)
\(978\) −6.84383 −0.218841
\(979\) −2.60368 −0.0832140
\(980\) 9.18999 0.293563
\(981\) −0.690652 −0.0220508
\(982\) 35.5803 1.13541
\(983\) 60.0008 1.91373 0.956864 0.290535i \(-0.0938331\pi\)
0.956864 + 0.290535i \(0.0938331\pi\)
\(984\) −0.211924 −0.00675589
\(985\) −3.33102 −0.106135
\(986\) −1.14006 −0.0363070
\(987\) −19.7194 −0.627674
\(988\) 6.39566 0.203473
\(989\) −73.1480 −2.32597
\(990\) −0.945136 −0.0300384
\(991\) −1.80378 −0.0572991 −0.0286496 0.999590i \(-0.509121\pi\)
−0.0286496 + 0.999590i \(0.509121\pi\)
\(992\) −7.10961 −0.225730
\(993\) 17.4034 0.552280
\(994\) −1.07987 −0.0342514
\(995\) 8.15027 0.258381
\(996\) −8.22544 −0.260633
\(997\) −24.8694 −0.787623 −0.393812 0.919191i \(-0.628844\pi\)
−0.393812 + 0.919191i \(0.628844\pi\)
\(998\) −37.3473 −1.18221
\(999\) −1.66923 −0.0528120
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.x.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.x.1.5 10 1.1 even 1 trivial