Properties

Label 6018.2.a.bc.1.9
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $14$
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} + \cdots - 43744 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(1.26062\) 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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.26062 q^{5} -1.00000 q^{6} +3.87711 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.26062 q^{5} -1.00000 q^{6} +3.87711 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.26062 q^{10} -3.70558 q^{11} -1.00000 q^{12} +6.90495 q^{13} +3.87711 q^{14} -1.26062 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +2.11950 q^{19} +1.26062 q^{20} -3.87711 q^{21} -3.70558 q^{22} +2.51141 q^{23} -1.00000 q^{24} -3.41084 q^{25} +6.90495 q^{26} -1.00000 q^{27} +3.87711 q^{28} +6.32123 q^{29} -1.26062 q^{30} -2.19074 q^{31} +1.00000 q^{32} +3.70558 q^{33} +1.00000 q^{34} +4.88757 q^{35} +1.00000 q^{36} +5.33158 q^{37} +2.11950 q^{38} -6.90495 q^{39} +1.26062 q^{40} +8.42788 q^{41} -3.87711 q^{42} -9.26765 q^{43} -3.70558 q^{44} +1.26062 q^{45} +2.51141 q^{46} -0.566613 q^{47} -1.00000 q^{48} +8.03201 q^{49} -3.41084 q^{50} -1.00000 q^{51} +6.90495 q^{52} -10.4207 q^{53} -1.00000 q^{54} -4.67133 q^{55} +3.87711 q^{56} -2.11950 q^{57} +6.32123 q^{58} +1.00000 q^{59} -1.26062 q^{60} -2.78209 q^{61} -2.19074 q^{62} +3.87711 q^{63} +1.00000 q^{64} +8.70451 q^{65} +3.70558 q^{66} -0.453039 q^{67} +1.00000 q^{68} -2.51141 q^{69} +4.88757 q^{70} -12.4635 q^{71} +1.00000 q^{72} +11.3440 q^{73} +5.33158 q^{74} +3.41084 q^{75} +2.11950 q^{76} -14.3669 q^{77} -6.90495 q^{78} -12.9413 q^{79} +1.26062 q^{80} +1.00000 q^{81} +8.42788 q^{82} +14.6778 q^{83} -3.87711 q^{84} +1.26062 q^{85} -9.26765 q^{86} -6.32123 q^{87} -3.70558 q^{88} -1.22006 q^{89} +1.26062 q^{90} +26.7713 q^{91} +2.51141 q^{92} +2.19074 q^{93} -0.566613 q^{94} +2.67189 q^{95} -1.00000 q^{96} +8.86837 q^{97} +8.03201 q^{98} -3.70558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 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
\(5\) 1.26062 0.563767 0.281883 0.959449i \(-0.409041\pi\)
0.281883 + 0.959449i \(0.409041\pi\)
\(6\) −1.00000 −0.408248
\(7\) 3.87711 1.46541 0.732706 0.680546i \(-0.238257\pi\)
0.732706 + 0.680546i \(0.238257\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.26062 0.398643
\(11\) −3.70558 −1.11727 −0.558637 0.829412i \(-0.688675\pi\)
−0.558637 + 0.829412i \(0.688675\pi\)
\(12\) −1.00000 −0.288675
\(13\) 6.90495 1.91509 0.957544 0.288288i \(-0.0930862\pi\)
0.957544 + 0.288288i \(0.0930862\pi\)
\(14\) 3.87711 1.03620
\(15\) −1.26062 −0.325491
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) 2.11950 0.486247 0.243123 0.969995i \(-0.421828\pi\)
0.243123 + 0.969995i \(0.421828\pi\)
\(20\) 1.26062 0.281883
\(21\) −3.87711 −0.846056
\(22\) −3.70558 −0.790032
\(23\) 2.51141 0.523665 0.261832 0.965113i \(-0.415673\pi\)
0.261832 + 0.965113i \(0.415673\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.41084 −0.682167
\(26\) 6.90495 1.35417
\(27\) −1.00000 −0.192450
\(28\) 3.87711 0.732706
\(29\) 6.32123 1.17382 0.586911 0.809651i \(-0.300344\pi\)
0.586911 + 0.809651i \(0.300344\pi\)
\(30\) −1.26062 −0.230157
\(31\) −2.19074 −0.393468 −0.196734 0.980457i \(-0.563034\pi\)
−0.196734 + 0.980457i \(0.563034\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.70558 0.645058
\(34\) 1.00000 0.171499
\(35\) 4.88757 0.826150
\(36\) 1.00000 0.166667
\(37\) 5.33158 0.876507 0.438253 0.898851i \(-0.355597\pi\)
0.438253 + 0.898851i \(0.355597\pi\)
\(38\) 2.11950 0.343828
\(39\) −6.90495 −1.10568
\(40\) 1.26062 0.199322
\(41\) 8.42788 1.31621 0.658107 0.752925i \(-0.271357\pi\)
0.658107 + 0.752925i \(0.271357\pi\)
\(42\) −3.87711 −0.598252
\(43\) −9.26765 −1.41330 −0.706652 0.707561i \(-0.749795\pi\)
−0.706652 + 0.707561i \(0.749795\pi\)
\(44\) −3.70558 −0.558637
\(45\) 1.26062 0.187922
\(46\) 2.51141 0.370287
\(47\) −0.566613 −0.0826490 −0.0413245 0.999146i \(-0.513158\pi\)
−0.0413245 + 0.999146i \(0.513158\pi\)
\(48\) −1.00000 −0.144338
\(49\) 8.03201 1.14743
\(50\) −3.41084 −0.482365
\(51\) −1.00000 −0.140028
\(52\) 6.90495 0.957544
\(53\) −10.4207 −1.43139 −0.715696 0.698412i \(-0.753891\pi\)
−0.715696 + 0.698412i \(0.753891\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.67133 −0.629882
\(56\) 3.87711 0.518101
\(57\) −2.11950 −0.280735
\(58\) 6.32123 0.830018
\(59\) 1.00000 0.130189
\(60\) −1.26062 −0.162745
\(61\) −2.78209 −0.356210 −0.178105 0.984011i \(-0.556997\pi\)
−0.178105 + 0.984011i \(0.556997\pi\)
\(62\) −2.19074 −0.278224
\(63\) 3.87711 0.488470
\(64\) 1.00000 0.125000
\(65\) 8.70451 1.07966
\(66\) 3.70558 0.456125
\(67\) −0.453039 −0.0553475 −0.0276738 0.999617i \(-0.508810\pi\)
−0.0276738 + 0.999617i \(0.508810\pi\)
\(68\) 1.00000 0.121268
\(69\) −2.51141 −0.302338
\(70\) 4.88757 0.584176
\(71\) −12.4635 −1.47915 −0.739574 0.673075i \(-0.764973\pi\)
−0.739574 + 0.673075i \(0.764973\pi\)
\(72\) 1.00000 0.117851
\(73\) 11.3440 1.32771 0.663854 0.747862i \(-0.268919\pi\)
0.663854 + 0.747862i \(0.268919\pi\)
\(74\) 5.33158 0.619784
\(75\) 3.41084 0.393849
\(76\) 2.11950 0.243123
\(77\) −14.3669 −1.63727
\(78\) −6.90495 −0.781831
\(79\) −12.9413 −1.45601 −0.728007 0.685570i \(-0.759553\pi\)
−0.728007 + 0.685570i \(0.759553\pi\)
\(80\) 1.26062 0.140942
\(81\) 1.00000 0.111111
\(82\) 8.42788 0.930704
\(83\) 14.6778 1.61110 0.805550 0.592528i \(-0.201870\pi\)
0.805550 + 0.592528i \(0.201870\pi\)
\(84\) −3.87711 −0.423028
\(85\) 1.26062 0.136733
\(86\) −9.26765 −0.999357
\(87\) −6.32123 −0.677706
\(88\) −3.70558 −0.395016
\(89\) −1.22006 −0.129326 −0.0646630 0.997907i \(-0.520597\pi\)
−0.0646630 + 0.997907i \(0.520597\pi\)
\(90\) 1.26062 0.132881
\(91\) 26.7713 2.80639
\(92\) 2.51141 0.261832
\(93\) 2.19074 0.227169
\(94\) −0.566613 −0.0584417
\(95\) 2.67189 0.274130
\(96\) −1.00000 −0.102062
\(97\) 8.86837 0.900446 0.450223 0.892916i \(-0.351344\pi\)
0.450223 + 0.892916i \(0.351344\pi\)
\(98\) 8.03201 0.811355
\(99\) −3.70558 −0.372425
\(100\) −3.41084 −0.341084
\(101\) −4.60470 −0.458185 −0.229093 0.973405i \(-0.573576\pi\)
−0.229093 + 0.973405i \(0.573576\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 8.13422 0.801489 0.400744 0.916190i \(-0.368752\pi\)
0.400744 + 0.916190i \(0.368752\pi\)
\(104\) 6.90495 0.677086
\(105\) −4.88757 −0.476978
\(106\) −10.4207 −1.01215
\(107\) 3.07336 0.297113 0.148556 0.988904i \(-0.452537\pi\)
0.148556 + 0.988904i \(0.452537\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 4.24379 0.406481 0.203241 0.979129i \(-0.434853\pi\)
0.203241 + 0.979129i \(0.434853\pi\)
\(110\) −4.67133 −0.445394
\(111\) −5.33158 −0.506052
\(112\) 3.87711 0.366353
\(113\) −4.70750 −0.442844 −0.221422 0.975178i \(-0.571070\pi\)
−0.221422 + 0.975178i \(0.571070\pi\)
\(114\) −2.11950 −0.198509
\(115\) 3.16593 0.295225
\(116\) 6.32123 0.586911
\(117\) 6.90495 0.638362
\(118\) 1.00000 0.0920575
\(119\) 3.87711 0.355414
\(120\) −1.26062 −0.115078
\(121\) 2.73131 0.248301
\(122\) −2.78209 −0.251879
\(123\) −8.42788 −0.759916
\(124\) −2.19074 −0.196734
\(125\) −10.6029 −0.948350
\(126\) 3.87711 0.345401
\(127\) 6.08214 0.539703 0.269852 0.962902i \(-0.413025\pi\)
0.269852 + 0.962902i \(0.413025\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.26765 0.815971
\(130\) 8.70451 0.763436
\(131\) −18.8906 −1.65048 −0.825241 0.564780i \(-0.808961\pi\)
−0.825241 + 0.564780i \(0.808961\pi\)
\(132\) 3.70558 0.322529
\(133\) 8.21754 0.712551
\(134\) −0.453039 −0.0391366
\(135\) −1.26062 −0.108497
\(136\) 1.00000 0.0857493
\(137\) −7.31949 −0.625347 −0.312673 0.949861i \(-0.601224\pi\)
−0.312673 + 0.949861i \(0.601224\pi\)
\(138\) −2.51141 −0.213785
\(139\) 11.0123 0.934048 0.467024 0.884245i \(-0.345326\pi\)
0.467024 + 0.884245i \(0.345326\pi\)
\(140\) 4.88757 0.413075
\(141\) 0.566613 0.0477174
\(142\) −12.4635 −1.04592
\(143\) −25.5868 −2.13968
\(144\) 1.00000 0.0833333
\(145\) 7.96866 0.661762
\(146\) 11.3440 0.938832
\(147\) −8.03201 −0.662469
\(148\) 5.33158 0.438253
\(149\) −4.08706 −0.334825 −0.167412 0.985887i \(-0.553541\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(150\) 3.41084 0.278494
\(151\) −3.48477 −0.283587 −0.141793 0.989896i \(-0.545287\pi\)
−0.141793 + 0.989896i \(0.545287\pi\)
\(152\) 2.11950 0.171914
\(153\) 1.00000 0.0808452
\(154\) −14.3669 −1.15772
\(155\) −2.76169 −0.221824
\(156\) −6.90495 −0.552838
\(157\) 6.18739 0.493808 0.246904 0.969040i \(-0.420587\pi\)
0.246904 + 0.969040i \(0.420587\pi\)
\(158\) −12.9413 −1.02956
\(159\) 10.4207 0.826415
\(160\) 1.26062 0.0996608
\(161\) 9.73702 0.767384
\(162\) 1.00000 0.0785674
\(163\) −10.2176 −0.800306 −0.400153 0.916448i \(-0.631043\pi\)
−0.400153 + 0.916448i \(0.631043\pi\)
\(164\) 8.42788 0.658107
\(165\) 4.67133 0.363662
\(166\) 14.6778 1.13922
\(167\) −20.7844 −1.60834 −0.804171 0.594398i \(-0.797390\pi\)
−0.804171 + 0.594398i \(0.797390\pi\)
\(168\) −3.87711 −0.299126
\(169\) 34.6783 2.66756
\(170\) 1.26062 0.0966852
\(171\) 2.11950 0.162082
\(172\) −9.26765 −0.706652
\(173\) 13.8913 1.05613 0.528067 0.849203i \(-0.322917\pi\)
0.528067 + 0.849203i \(0.322917\pi\)
\(174\) −6.32123 −0.479211
\(175\) −13.2242 −0.999656
\(176\) −3.70558 −0.279318
\(177\) −1.00000 −0.0751646
\(178\) −1.22006 −0.0914473
\(179\) −9.01354 −0.673704 −0.336852 0.941558i \(-0.609362\pi\)
−0.336852 + 0.941558i \(0.609362\pi\)
\(180\) 1.26062 0.0939611
\(181\) −3.59465 −0.267189 −0.133594 0.991036i \(-0.542652\pi\)
−0.133594 + 0.991036i \(0.542652\pi\)
\(182\) 26.7713 1.98442
\(183\) 2.78209 0.205658
\(184\) 2.51141 0.185144
\(185\) 6.72110 0.494145
\(186\) 2.19074 0.160633
\(187\) −3.70558 −0.270979
\(188\) −0.566613 −0.0413245
\(189\) −3.87711 −0.282019
\(190\) 2.67189 0.193839
\(191\) −6.31625 −0.457028 −0.228514 0.973541i \(-0.573387\pi\)
−0.228514 + 0.973541i \(0.573387\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −13.5834 −0.977753 −0.488877 0.872353i \(-0.662593\pi\)
−0.488877 + 0.872353i \(0.662593\pi\)
\(194\) 8.86837 0.636712
\(195\) −8.70451 −0.623343
\(196\) 8.03201 0.573715
\(197\) −27.2147 −1.93897 −0.969484 0.245156i \(-0.921161\pi\)
−0.969484 + 0.245156i \(0.921161\pi\)
\(198\) −3.70558 −0.263344
\(199\) −11.0485 −0.783207 −0.391604 0.920134i \(-0.628080\pi\)
−0.391604 + 0.920134i \(0.628080\pi\)
\(200\) −3.41084 −0.241183
\(201\) 0.453039 0.0319549
\(202\) −4.60470 −0.323986
\(203\) 24.5081 1.72013
\(204\) −1.00000 −0.0700140
\(205\) 10.6244 0.742037
\(206\) 8.13422 0.566738
\(207\) 2.51141 0.174555
\(208\) 6.90495 0.478772
\(209\) −7.85397 −0.543271
\(210\) −4.88757 −0.337274
\(211\) 23.7933 1.63800 0.819001 0.573793i \(-0.194528\pi\)
0.819001 + 0.573793i \(0.194528\pi\)
\(212\) −10.4207 −0.715696
\(213\) 12.4635 0.853986
\(214\) 3.07336 0.210091
\(215\) −11.6830 −0.796773
\(216\) −1.00000 −0.0680414
\(217\) −8.49375 −0.576593
\(218\) 4.24379 0.287426
\(219\) −11.3440 −0.766553
\(220\) −4.67133 −0.314941
\(221\) 6.90495 0.464477
\(222\) −5.33158 −0.357832
\(223\) 14.5096 0.971637 0.485818 0.874060i \(-0.338522\pi\)
0.485818 + 0.874060i \(0.338522\pi\)
\(224\) 3.87711 0.259051
\(225\) −3.41084 −0.227389
\(226\) −4.70750 −0.313138
\(227\) −11.2613 −0.747440 −0.373720 0.927542i \(-0.621918\pi\)
−0.373720 + 0.927542i \(0.621918\pi\)
\(228\) −2.11950 −0.140367
\(229\) −14.7592 −0.975312 −0.487656 0.873036i \(-0.662148\pi\)
−0.487656 + 0.873036i \(0.662148\pi\)
\(230\) 3.16593 0.208755
\(231\) 14.3669 0.945276
\(232\) 6.32123 0.415009
\(233\) −14.1530 −0.927192 −0.463596 0.886047i \(-0.653441\pi\)
−0.463596 + 0.886047i \(0.653441\pi\)
\(234\) 6.90495 0.451390
\(235\) −0.714284 −0.0465948
\(236\) 1.00000 0.0650945
\(237\) 12.9413 0.840630
\(238\) 3.87711 0.251316
\(239\) 19.0349 1.23127 0.615634 0.788032i \(-0.288900\pi\)
0.615634 + 0.788032i \(0.288900\pi\)
\(240\) −1.26062 −0.0813727
\(241\) 13.6413 0.878711 0.439355 0.898313i \(-0.355207\pi\)
0.439355 + 0.898313i \(0.355207\pi\)
\(242\) 2.73131 0.175575
\(243\) −1.00000 −0.0641500
\(244\) −2.78209 −0.178105
\(245\) 10.1253 0.646882
\(246\) −8.42788 −0.537342
\(247\) 14.6350 0.931205
\(248\) −2.19074 −0.139112
\(249\) −14.6778 −0.930169
\(250\) −10.6029 −0.670584
\(251\) 23.9674 1.51281 0.756404 0.654105i \(-0.226954\pi\)
0.756404 + 0.654105i \(0.226954\pi\)
\(252\) 3.87711 0.244235
\(253\) −9.30622 −0.585077
\(254\) 6.08214 0.381628
\(255\) −1.26062 −0.0789431
\(256\) 1.00000 0.0625000
\(257\) −23.0284 −1.43647 −0.718235 0.695800i \(-0.755050\pi\)
−0.718235 + 0.695800i \(0.755050\pi\)
\(258\) 9.26765 0.576979
\(259\) 20.6712 1.28444
\(260\) 8.70451 0.539831
\(261\) 6.32123 0.391274
\(262\) −18.8906 −1.16707
\(263\) 2.30569 0.142175 0.0710874 0.997470i \(-0.477353\pi\)
0.0710874 + 0.997470i \(0.477353\pi\)
\(264\) 3.70558 0.228063
\(265\) −13.1365 −0.806971
\(266\) 8.21754 0.503850
\(267\) 1.22006 0.0746664
\(268\) −0.453039 −0.0276738
\(269\) 19.7737 1.20562 0.602811 0.797884i \(-0.294047\pi\)
0.602811 + 0.797884i \(0.294047\pi\)
\(270\) −1.26062 −0.0767189
\(271\) 27.5096 1.67109 0.835544 0.549423i \(-0.185153\pi\)
0.835544 + 0.549423i \(0.185153\pi\)
\(272\) 1.00000 0.0606339
\(273\) −26.7713 −1.62027
\(274\) −7.31949 −0.442187
\(275\) 12.6391 0.762168
\(276\) −2.51141 −0.151169
\(277\) 13.5731 0.815527 0.407763 0.913088i \(-0.366309\pi\)
0.407763 + 0.913088i \(0.366309\pi\)
\(278\) 11.0123 0.660472
\(279\) −2.19074 −0.131156
\(280\) 4.88757 0.292088
\(281\) 10.0237 0.597964 0.298982 0.954259i \(-0.403353\pi\)
0.298982 + 0.954259i \(0.403353\pi\)
\(282\) 0.566613 0.0337413
\(283\) 4.03872 0.240077 0.120039 0.992769i \(-0.461698\pi\)
0.120039 + 0.992769i \(0.461698\pi\)
\(284\) −12.4635 −0.739574
\(285\) −2.67189 −0.158269
\(286\) −25.5868 −1.51298
\(287\) 32.6758 1.92879
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 7.96866 0.467936
\(291\) −8.86837 −0.519873
\(292\) 11.3440 0.663854
\(293\) 30.3238 1.77154 0.885769 0.464127i \(-0.153632\pi\)
0.885769 + 0.464127i \(0.153632\pi\)
\(294\) −8.03201 −0.468436
\(295\) 1.26062 0.0733961
\(296\) 5.33158 0.309892
\(297\) 3.70558 0.215019
\(298\) −4.08706 −0.236757
\(299\) 17.3411 1.00286
\(300\) 3.41084 0.196925
\(301\) −35.9317 −2.07107
\(302\) −3.48477 −0.200526
\(303\) 4.60470 0.264533
\(304\) 2.11950 0.121562
\(305\) −3.50716 −0.200819
\(306\) 1.00000 0.0571662
\(307\) 5.03826 0.287549 0.143774 0.989611i \(-0.454076\pi\)
0.143774 + 0.989611i \(0.454076\pi\)
\(308\) −14.3669 −0.818633
\(309\) −8.13422 −0.462740
\(310\) −2.76169 −0.156853
\(311\) 14.5697 0.826170 0.413085 0.910692i \(-0.364451\pi\)
0.413085 + 0.910692i \(0.364451\pi\)
\(312\) −6.90495 −0.390916
\(313\) 15.0211 0.849044 0.424522 0.905418i \(-0.360442\pi\)
0.424522 + 0.905418i \(0.360442\pi\)
\(314\) 6.18739 0.349175
\(315\) 4.88757 0.275383
\(316\) −12.9413 −0.728007
\(317\) 25.7537 1.44647 0.723237 0.690600i \(-0.242653\pi\)
0.723237 + 0.690600i \(0.242653\pi\)
\(318\) 10.4207 0.584364
\(319\) −23.4238 −1.31148
\(320\) 1.26062 0.0704708
\(321\) −3.07336 −0.171538
\(322\) 9.73702 0.542623
\(323\) 2.11950 0.117932
\(324\) 1.00000 0.0555556
\(325\) −23.5516 −1.30641
\(326\) −10.2176 −0.565902
\(327\) −4.24379 −0.234682
\(328\) 8.42788 0.465352
\(329\) −2.19682 −0.121115
\(330\) 4.67133 0.257148
\(331\) 9.58716 0.526958 0.263479 0.964665i \(-0.415130\pi\)
0.263479 + 0.964665i \(0.415130\pi\)
\(332\) 14.6778 0.805550
\(333\) 5.33158 0.292169
\(334\) −20.7844 −1.13727
\(335\) −0.571110 −0.0312031
\(336\) −3.87711 −0.211514
\(337\) −12.3053 −0.670313 −0.335156 0.942163i \(-0.608789\pi\)
−0.335156 + 0.942163i \(0.608789\pi\)
\(338\) 34.6783 1.88625
\(339\) 4.70750 0.255676
\(340\) 1.26062 0.0683667
\(341\) 8.11796 0.439612
\(342\) 2.11950 0.114609
\(343\) 4.00121 0.216045
\(344\) −9.26765 −0.499678
\(345\) −3.16593 −0.170448
\(346\) 13.8913 0.746800
\(347\) −33.7675 −1.81273 −0.906367 0.422491i \(-0.861156\pi\)
−0.906367 + 0.422491i \(0.861156\pi\)
\(348\) −6.32123 −0.338853
\(349\) 26.2330 1.40422 0.702110 0.712069i \(-0.252241\pi\)
0.702110 + 0.712069i \(0.252241\pi\)
\(350\) −13.2242 −0.706863
\(351\) −6.90495 −0.368559
\(352\) −3.70558 −0.197508
\(353\) −22.4187 −1.19323 −0.596614 0.802528i \(-0.703488\pi\)
−0.596614 + 0.802528i \(0.703488\pi\)
\(354\) −1.00000 −0.0531494
\(355\) −15.7118 −0.833894
\(356\) −1.22006 −0.0646630
\(357\) −3.87711 −0.205199
\(358\) −9.01354 −0.476381
\(359\) 17.3542 0.915918 0.457959 0.888973i \(-0.348581\pi\)
0.457959 + 0.888973i \(0.348581\pi\)
\(360\) 1.26062 0.0664405
\(361\) −14.5077 −0.763564
\(362\) −3.59465 −0.188931
\(363\) −2.73131 −0.143357
\(364\) 26.7713 1.40320
\(365\) 14.3004 0.748518
\(366\) 2.78209 0.145422
\(367\) −2.01352 −0.105105 −0.0525524 0.998618i \(-0.516736\pi\)
−0.0525524 + 0.998618i \(0.516736\pi\)
\(368\) 2.51141 0.130916
\(369\) 8.42788 0.438738
\(370\) 6.72110 0.349413
\(371\) −40.4022 −2.09758
\(372\) 2.19074 0.113585
\(373\) 36.9804 1.91477 0.957386 0.288813i \(-0.0932605\pi\)
0.957386 + 0.288813i \(0.0932605\pi\)
\(374\) −3.70558 −0.191611
\(375\) 10.6029 0.547530
\(376\) −0.566613 −0.0292208
\(377\) 43.6477 2.24797
\(378\) −3.87711 −0.199417
\(379\) −19.1842 −0.985427 −0.492713 0.870192i \(-0.663995\pi\)
−0.492713 + 0.870192i \(0.663995\pi\)
\(380\) 2.67189 0.137065
\(381\) −6.08214 −0.311598
\(382\) −6.31625 −0.323167
\(383\) −14.5579 −0.743875 −0.371938 0.928258i \(-0.621306\pi\)
−0.371938 + 0.928258i \(0.621306\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −18.1113 −0.923035
\(386\) −13.5834 −0.691376
\(387\) −9.26765 −0.471101
\(388\) 8.86837 0.450223
\(389\) 0.644984 0.0327020 0.0163510 0.999866i \(-0.494795\pi\)
0.0163510 + 0.999866i \(0.494795\pi\)
\(390\) −8.70451 −0.440770
\(391\) 2.51141 0.127007
\(392\) 8.03201 0.405678
\(393\) 18.8906 0.952907
\(394\) −27.2147 −1.37106
\(395\) −16.3141 −0.820852
\(396\) −3.70558 −0.186212
\(397\) −34.7272 −1.74291 −0.871454 0.490477i \(-0.836823\pi\)
−0.871454 + 0.490477i \(0.836823\pi\)
\(398\) −11.0485 −0.553811
\(399\) −8.21754 −0.411392
\(400\) −3.41084 −0.170542
\(401\) −12.8048 −0.639442 −0.319721 0.947512i \(-0.603589\pi\)
−0.319721 + 0.947512i \(0.603589\pi\)
\(402\) 0.453039 0.0225955
\(403\) −15.1269 −0.753526
\(404\) −4.60470 −0.229093
\(405\) 1.26062 0.0626407
\(406\) 24.5081 1.21632
\(407\) −19.7566 −0.979298
\(408\) −1.00000 −0.0495074
\(409\) 30.5691 1.51154 0.755772 0.654835i \(-0.227262\pi\)
0.755772 + 0.654835i \(0.227262\pi\)
\(410\) 10.6244 0.524700
\(411\) 7.31949 0.361044
\(412\) 8.13422 0.400744
\(413\) 3.87711 0.190780
\(414\) 2.51141 0.123429
\(415\) 18.5032 0.908284
\(416\) 6.90495 0.338543
\(417\) −11.0123 −0.539273
\(418\) −7.85397 −0.384150
\(419\) −9.79506 −0.478520 −0.239260 0.970956i \(-0.576905\pi\)
−0.239260 + 0.970956i \(0.576905\pi\)
\(420\) −4.88757 −0.238489
\(421\) −7.50279 −0.365663 −0.182832 0.983144i \(-0.558526\pi\)
−0.182832 + 0.983144i \(0.558526\pi\)
\(422\) 23.7933 1.15824
\(423\) −0.566613 −0.0275497
\(424\) −10.4207 −0.506074
\(425\) −3.41084 −0.165450
\(426\) 12.4635 0.603860
\(427\) −10.7865 −0.521994
\(428\) 3.07336 0.148556
\(429\) 25.5868 1.23534
\(430\) −11.6830 −0.563404
\(431\) −2.08543 −0.100452 −0.0502259 0.998738i \(-0.515994\pi\)
−0.0502259 + 0.998738i \(0.515994\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 7.45018 0.358033 0.179016 0.983846i \(-0.442708\pi\)
0.179016 + 0.983846i \(0.442708\pi\)
\(434\) −8.49375 −0.407713
\(435\) −7.96866 −0.382068
\(436\) 4.24379 0.203241
\(437\) 5.32293 0.254630
\(438\) −11.3440 −0.542035
\(439\) −19.2809 −0.920226 −0.460113 0.887860i \(-0.652191\pi\)
−0.460113 + 0.887860i \(0.652191\pi\)
\(440\) −4.67133 −0.222697
\(441\) 8.03201 0.382477
\(442\) 6.90495 0.328435
\(443\) −23.5618 −1.11946 −0.559728 0.828676i \(-0.689095\pi\)
−0.559728 + 0.828676i \(0.689095\pi\)
\(444\) −5.33158 −0.253026
\(445\) −1.53803 −0.0729096
\(446\) 14.5096 0.687051
\(447\) 4.08706 0.193311
\(448\) 3.87711 0.183176
\(449\) −2.41928 −0.114173 −0.0570865 0.998369i \(-0.518181\pi\)
−0.0570865 + 0.998369i \(0.518181\pi\)
\(450\) −3.41084 −0.160788
\(451\) −31.2302 −1.47057
\(452\) −4.70750 −0.221422
\(453\) 3.48477 0.163729
\(454\) −11.2613 −0.528520
\(455\) 33.7484 1.58215
\(456\) −2.11950 −0.0992547
\(457\) 4.67152 0.218524 0.109262 0.994013i \(-0.465151\pi\)
0.109262 + 0.994013i \(0.465151\pi\)
\(458\) −14.7592 −0.689650
\(459\) −1.00000 −0.0466760
\(460\) 3.16593 0.147612
\(461\) 31.4436 1.46447 0.732237 0.681050i \(-0.238476\pi\)
0.732237 + 0.681050i \(0.238476\pi\)
\(462\) 14.3669 0.668411
\(463\) 3.38202 0.157176 0.0785879 0.996907i \(-0.474959\pi\)
0.0785879 + 0.996907i \(0.474959\pi\)
\(464\) 6.32123 0.293456
\(465\) 2.76169 0.128070
\(466\) −14.1530 −0.655623
\(467\) 23.5843 1.09135 0.545675 0.837997i \(-0.316273\pi\)
0.545675 + 0.837997i \(0.316273\pi\)
\(468\) 6.90495 0.319181
\(469\) −1.75648 −0.0811069
\(470\) −0.714284 −0.0329475
\(471\) −6.18739 −0.285100
\(472\) 1.00000 0.0460287
\(473\) 34.3420 1.57905
\(474\) 12.9413 0.594415
\(475\) −7.22927 −0.331702
\(476\) 3.87711 0.177707
\(477\) −10.4207 −0.477131
\(478\) 19.0349 0.870638
\(479\) 11.2885 0.515785 0.257892 0.966174i \(-0.416972\pi\)
0.257892 + 0.966174i \(0.416972\pi\)
\(480\) −1.26062 −0.0575392
\(481\) 36.8143 1.67859
\(482\) 13.6413 0.621342
\(483\) −9.73702 −0.443050
\(484\) 2.73131 0.124150
\(485\) 11.1796 0.507641
\(486\) −1.00000 −0.0453609
\(487\) 10.3474 0.468885 0.234443 0.972130i \(-0.424673\pi\)
0.234443 + 0.972130i \(0.424673\pi\)
\(488\) −2.78209 −0.125939
\(489\) 10.2176 0.462057
\(490\) 10.1253 0.457415
\(491\) −7.75497 −0.349977 −0.174988 0.984571i \(-0.555989\pi\)
−0.174988 + 0.984571i \(0.555989\pi\)
\(492\) −8.42788 −0.379958
\(493\) 6.32123 0.284694
\(494\) 14.6350 0.658461
\(495\) −4.67133 −0.209961
\(496\) −2.19074 −0.0983671
\(497\) −48.3225 −2.16756
\(498\) −14.6778 −0.657729
\(499\) 9.95739 0.445754 0.222877 0.974847i \(-0.428455\pi\)
0.222877 + 0.974847i \(0.428455\pi\)
\(500\) −10.6029 −0.474175
\(501\) 20.7844 0.928577
\(502\) 23.9674 1.06972
\(503\) −4.70643 −0.209849 −0.104925 0.994480i \(-0.533460\pi\)
−0.104925 + 0.994480i \(0.533460\pi\)
\(504\) 3.87711 0.172700
\(505\) −5.80478 −0.258309
\(506\) −9.30622 −0.413712
\(507\) −34.6783 −1.54012
\(508\) 6.08214 0.269852
\(509\) −20.0388 −0.888206 −0.444103 0.895976i \(-0.646478\pi\)
−0.444103 + 0.895976i \(0.646478\pi\)
\(510\) −1.26062 −0.0558212
\(511\) 43.9818 1.94564
\(512\) 1.00000 0.0441942
\(513\) −2.11950 −0.0935782
\(514\) −23.0284 −1.01574
\(515\) 10.2542 0.451852
\(516\) 9.26765 0.407986
\(517\) 2.09963 0.0923416
\(518\) 20.6712 0.908238
\(519\) −13.8913 −0.609759
\(520\) 8.70451 0.381718
\(521\) 7.61921 0.333804 0.166902 0.985974i \(-0.446624\pi\)
0.166902 + 0.985974i \(0.446624\pi\)
\(522\) 6.32123 0.276673
\(523\) 2.14711 0.0938864 0.0469432 0.998898i \(-0.485052\pi\)
0.0469432 + 0.998898i \(0.485052\pi\)
\(524\) −18.8906 −0.825241
\(525\) 13.2242 0.577151
\(526\) 2.30569 0.100533
\(527\) −2.19074 −0.0954301
\(528\) 3.70558 0.161265
\(529\) −16.6928 −0.725775
\(530\) −13.1365 −0.570615
\(531\) 1.00000 0.0433963
\(532\) 8.21754 0.356276
\(533\) 58.1940 2.52066
\(534\) 1.22006 0.0527971
\(535\) 3.87434 0.167502
\(536\) −0.453039 −0.0195683
\(537\) 9.01354 0.388963
\(538\) 19.7737 0.852503
\(539\) −29.7632 −1.28199
\(540\) −1.26062 −0.0542485
\(541\) −0.386441 −0.0166144 −0.00830720 0.999965i \(-0.502644\pi\)
−0.00830720 + 0.999965i \(0.502644\pi\)
\(542\) 27.5096 1.18164
\(543\) 3.59465 0.154261
\(544\) 1.00000 0.0428746
\(545\) 5.34981 0.229161
\(546\) −26.7713 −1.14570
\(547\) 30.4805 1.30325 0.651627 0.758540i \(-0.274087\pi\)
0.651627 + 0.758540i \(0.274087\pi\)
\(548\) −7.31949 −0.312673
\(549\) −2.78209 −0.118737
\(550\) 12.6391 0.538934
\(551\) 13.3978 0.570767
\(552\) −2.51141 −0.106893
\(553\) −50.1750 −2.13366
\(554\) 13.5731 0.576664
\(555\) −6.72110 −0.285295
\(556\) 11.0123 0.467024
\(557\) −44.9059 −1.90272 −0.951362 0.308074i \(-0.900316\pi\)
−0.951362 + 0.308074i \(0.900316\pi\)
\(558\) −2.19074 −0.0927414
\(559\) −63.9926 −2.70660
\(560\) 4.88757 0.206537
\(561\) 3.70558 0.156450
\(562\) 10.0237 0.422825
\(563\) 1.23125 0.0518912 0.0259456 0.999663i \(-0.491740\pi\)
0.0259456 + 0.999663i \(0.491740\pi\)
\(564\) 0.566613 0.0238587
\(565\) −5.93437 −0.249661
\(566\) 4.03872 0.169760
\(567\) 3.87711 0.162823
\(568\) −12.4635 −0.522958
\(569\) −10.0696 −0.422139 −0.211070 0.977471i \(-0.567695\pi\)
−0.211070 + 0.977471i \(0.567695\pi\)
\(570\) −2.67189 −0.111913
\(571\) −36.4471 −1.52526 −0.762631 0.646833i \(-0.776093\pi\)
−0.762631 + 0.646833i \(0.776093\pi\)
\(572\) −25.5868 −1.06984
\(573\) 6.31625 0.263865
\(574\) 32.6758 1.36386
\(575\) −8.56600 −0.357227
\(576\) 1.00000 0.0416667
\(577\) −16.6992 −0.695198 −0.347599 0.937643i \(-0.613003\pi\)
−0.347599 + 0.937643i \(0.613003\pi\)
\(578\) 1.00000 0.0415945
\(579\) 13.5834 0.564506
\(580\) 7.96866 0.330881
\(581\) 56.9076 2.36092
\(582\) −8.86837 −0.367606
\(583\) 38.6147 1.59926
\(584\) 11.3440 0.469416
\(585\) 8.70451 0.359887
\(586\) 30.3238 1.25267
\(587\) −21.6517 −0.893661 −0.446831 0.894619i \(-0.647447\pi\)
−0.446831 + 0.894619i \(0.647447\pi\)
\(588\) −8.03201 −0.331234
\(589\) −4.64327 −0.191323
\(590\) 1.26062 0.0518989
\(591\) 27.2147 1.11946
\(592\) 5.33158 0.219127
\(593\) 1.02945 0.0422744 0.0211372 0.999777i \(-0.493271\pi\)
0.0211372 + 0.999777i \(0.493271\pi\)
\(594\) 3.70558 0.152042
\(595\) 4.88757 0.200371
\(596\) −4.08706 −0.167412
\(597\) 11.0485 0.452185
\(598\) 17.3411 0.709132
\(599\) −31.7146 −1.29582 −0.647912 0.761716i \(-0.724357\pi\)
−0.647912 + 0.761716i \(0.724357\pi\)
\(600\) 3.41084 0.139247
\(601\) −6.06629 −0.247449 −0.123725 0.992317i \(-0.539484\pi\)
−0.123725 + 0.992317i \(0.539484\pi\)
\(602\) −35.9317 −1.46447
\(603\) −0.453039 −0.0184492
\(604\) −3.48477 −0.141793
\(605\) 3.44314 0.139984
\(606\) 4.60470 0.187053
\(607\) −15.9535 −0.647533 −0.323767 0.946137i \(-0.604949\pi\)
−0.323767 + 0.946137i \(0.604949\pi\)
\(608\) 2.11950 0.0859571
\(609\) −24.5081 −0.993119
\(610\) −3.50716 −0.142001
\(611\) −3.91243 −0.158280
\(612\) 1.00000 0.0404226
\(613\) 14.7853 0.597171 0.298586 0.954383i \(-0.403485\pi\)
0.298586 + 0.954383i \(0.403485\pi\)
\(614\) 5.03826 0.203328
\(615\) −10.6244 −0.428415
\(616\) −14.3669 −0.578861
\(617\) −28.4699 −1.14615 −0.573077 0.819501i \(-0.694250\pi\)
−0.573077 + 0.819501i \(0.694250\pi\)
\(618\) −8.13422 −0.327206
\(619\) 11.4895 0.461803 0.230901 0.972977i \(-0.425833\pi\)
0.230901 + 0.972977i \(0.425833\pi\)
\(620\) −2.76169 −0.110912
\(621\) −2.51141 −0.100779
\(622\) 14.5697 0.584191
\(623\) −4.73031 −0.189516
\(624\) −6.90495 −0.276419
\(625\) 3.68799 0.147520
\(626\) 15.0211 0.600365
\(627\) 7.85397 0.313658
\(628\) 6.18739 0.246904
\(629\) 5.33158 0.212584
\(630\) 4.88757 0.194725
\(631\) 43.2240 1.72072 0.860361 0.509685i \(-0.170238\pi\)
0.860361 + 0.509685i \(0.170238\pi\)
\(632\) −12.9413 −0.514779
\(633\) −23.7933 −0.945701
\(634\) 25.7537 1.02281
\(635\) 7.66728 0.304267
\(636\) 10.4207 0.413207
\(637\) 55.4606 2.19743
\(638\) −23.4238 −0.927357
\(639\) −12.4635 −0.493049
\(640\) 1.26062 0.0498304
\(641\) 13.1489 0.519349 0.259674 0.965696i \(-0.416385\pi\)
0.259674 + 0.965696i \(0.416385\pi\)
\(642\) −3.07336 −0.121296
\(643\) 11.4488 0.451495 0.225748 0.974186i \(-0.427517\pi\)
0.225748 + 0.974186i \(0.427517\pi\)
\(644\) 9.73702 0.383692
\(645\) 11.6830 0.460017
\(646\) 2.11950 0.0833906
\(647\) −19.1471 −0.752749 −0.376374 0.926468i \(-0.622829\pi\)
−0.376374 + 0.926468i \(0.622829\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.70558 −0.145457
\(650\) −23.5516 −0.923771
\(651\) 8.49375 0.332896
\(652\) −10.2176 −0.400153
\(653\) 9.71651 0.380236 0.190118 0.981761i \(-0.439113\pi\)
0.190118 + 0.981761i \(0.439113\pi\)
\(654\) −4.24379 −0.165945
\(655\) −23.8139 −0.930487
\(656\) 8.42788 0.329053
\(657\) 11.3440 0.442570
\(658\) −2.19682 −0.0856411
\(659\) 26.5758 1.03524 0.517622 0.855609i \(-0.326817\pi\)
0.517622 + 0.855609i \(0.326817\pi\)
\(660\) 4.67133 0.181831
\(661\) −2.12483 −0.0826462 −0.0413231 0.999146i \(-0.513157\pi\)
−0.0413231 + 0.999146i \(0.513157\pi\)
\(662\) 9.58716 0.372615
\(663\) −6.90495 −0.268166
\(664\) 14.6778 0.569610
\(665\) 10.3592 0.401713
\(666\) 5.33158 0.206595
\(667\) 15.8752 0.614689
\(668\) −20.7844 −0.804171
\(669\) −14.5096 −0.560975
\(670\) −0.571110 −0.0220639
\(671\) 10.3093 0.397984
\(672\) −3.87711 −0.149563
\(673\) −41.2886 −1.59156 −0.795780 0.605586i \(-0.792939\pi\)
−0.795780 + 0.605586i \(0.792939\pi\)
\(674\) −12.3053 −0.473983
\(675\) 3.41084 0.131283
\(676\) 34.6783 1.33378
\(677\) 20.5424 0.789510 0.394755 0.918786i \(-0.370829\pi\)
0.394755 + 0.918786i \(0.370829\pi\)
\(678\) 4.70750 0.180790
\(679\) 34.3837 1.31952
\(680\) 1.26062 0.0483426
\(681\) 11.2613 0.431535
\(682\) 8.11796 0.310853
\(683\) −38.2641 −1.46413 −0.732067 0.681233i \(-0.761444\pi\)
−0.732067 + 0.681233i \(0.761444\pi\)
\(684\) 2.11950 0.0810411
\(685\) −9.22710 −0.352549
\(686\) 4.00121 0.152767
\(687\) 14.7592 0.563097
\(688\) −9.26765 −0.353326
\(689\) −71.9543 −2.74124
\(690\) −3.16593 −0.120525
\(691\) 2.85437 0.108585 0.0542926 0.998525i \(-0.482710\pi\)
0.0542926 + 0.998525i \(0.482710\pi\)
\(692\) 13.8913 0.528067
\(693\) −14.3669 −0.545755
\(694\) −33.7675 −1.28180
\(695\) 13.8823 0.526585
\(696\) −6.32123 −0.239605
\(697\) 8.42788 0.319229
\(698\) 26.2330 0.992933
\(699\) 14.1530 0.535314
\(700\) −13.2242 −0.499828
\(701\) 24.2546 0.916083 0.458042 0.888931i \(-0.348551\pi\)
0.458042 + 0.888931i \(0.348551\pi\)
\(702\) −6.90495 −0.260610
\(703\) 11.3003 0.426199
\(704\) −3.70558 −0.139659
\(705\) 0.714284 0.0269015
\(706\) −22.4187 −0.843740
\(707\) −17.8530 −0.671430
\(708\) −1.00000 −0.0375823
\(709\) 24.1237 0.905984 0.452992 0.891515i \(-0.350357\pi\)
0.452992 + 0.891515i \(0.350357\pi\)
\(710\) −15.7118 −0.589652
\(711\) −12.9413 −0.485338
\(712\) −1.22006 −0.0457236
\(713\) −5.50184 −0.206046
\(714\) −3.87711 −0.145097
\(715\) −32.2553 −1.20628
\(716\) −9.01354 −0.336852
\(717\) −19.0349 −0.710873
\(718\) 17.3542 0.647652
\(719\) −18.2711 −0.681397 −0.340699 0.940173i \(-0.610664\pi\)
−0.340699 + 0.940173i \(0.610664\pi\)
\(720\) 1.26062 0.0469805
\(721\) 31.5373 1.17451
\(722\) −14.5077 −0.539921
\(723\) −13.6413 −0.507324
\(724\) −3.59465 −0.133594
\(725\) −21.5607 −0.800743
\(726\) −2.73131 −0.101368
\(727\) −32.7924 −1.21620 −0.608102 0.793859i \(-0.708069\pi\)
−0.608102 + 0.793859i \(0.708069\pi\)
\(728\) 26.7713 0.992209
\(729\) 1.00000 0.0370370
\(730\) 14.3004 0.529282
\(731\) −9.26765 −0.342776
\(732\) 2.78209 0.102829
\(733\) −23.1275 −0.854233 −0.427117 0.904197i \(-0.640471\pi\)
−0.427117 + 0.904197i \(0.640471\pi\)
\(734\) −2.01352 −0.0743204
\(735\) −10.1253 −0.373478
\(736\) 2.51141 0.0925718
\(737\) 1.67877 0.0618384
\(738\) 8.42788 0.310235
\(739\) −10.6500 −0.391768 −0.195884 0.980627i \(-0.562758\pi\)
−0.195884 + 0.980627i \(0.562758\pi\)
\(740\) 6.72110 0.247073
\(741\) −14.6350 −0.537631
\(742\) −40.4022 −1.48321
\(743\) −29.5531 −1.08420 −0.542099 0.840315i \(-0.682370\pi\)
−0.542099 + 0.840315i \(0.682370\pi\)
\(744\) 2.19074 0.0803164
\(745\) −5.15223 −0.188763
\(746\) 36.9804 1.35395
\(747\) 14.6778 0.537033
\(748\) −3.70558 −0.135489
\(749\) 11.9158 0.435393
\(750\) 10.6029 0.387162
\(751\) −18.0328 −0.658025 −0.329012 0.944326i \(-0.606716\pi\)
−0.329012 + 0.944326i \(0.606716\pi\)
\(752\) −0.566613 −0.0206623
\(753\) −23.9674 −0.873420
\(754\) 43.6477 1.58956
\(755\) −4.39297 −0.159877
\(756\) −3.87711 −0.141009
\(757\) −46.8493 −1.70277 −0.851383 0.524544i \(-0.824236\pi\)
−0.851383 + 0.524544i \(0.824236\pi\)
\(758\) −19.1842 −0.696802
\(759\) 9.30622 0.337794
\(760\) 2.67189 0.0969195
\(761\) −21.8281 −0.791267 −0.395634 0.918408i \(-0.629475\pi\)
−0.395634 + 0.918408i \(0.629475\pi\)
\(762\) −6.08214 −0.220333
\(763\) 16.4537 0.595662
\(764\) −6.31625 −0.228514
\(765\) 1.26062 0.0455778
\(766\) −14.5579 −0.525999
\(767\) 6.90495 0.249323
\(768\) −1.00000 −0.0360844
\(769\) 17.0243 0.613911 0.306955 0.951724i \(-0.400690\pi\)
0.306955 + 0.951724i \(0.400690\pi\)
\(770\) −18.1113 −0.652685
\(771\) 23.0284 0.829347
\(772\) −13.5834 −0.488877
\(773\) −8.84541 −0.318147 −0.159074 0.987267i \(-0.550851\pi\)
−0.159074 + 0.987267i \(0.550851\pi\)
\(774\) −9.26765 −0.333119
\(775\) 7.47225 0.268411
\(776\) 8.86837 0.318356
\(777\) −20.6712 −0.741574
\(778\) 0.644984 0.0231238
\(779\) 17.8629 0.640005
\(780\) −8.70451 −0.311672
\(781\) 46.1846 1.65261
\(782\) 2.51141 0.0898078
\(783\) −6.32123 −0.225902
\(784\) 8.03201 0.286857
\(785\) 7.79995 0.278392
\(786\) 18.8906 0.673807
\(787\) −37.0025 −1.31900 −0.659498 0.751707i \(-0.729231\pi\)
−0.659498 + 0.751707i \(0.729231\pi\)
\(788\) −27.2147 −0.969484
\(789\) −2.30569 −0.0820846
\(790\) −16.3141 −0.580430
\(791\) −18.2515 −0.648949
\(792\) −3.70558 −0.131672
\(793\) −19.2102 −0.682174
\(794\) −34.7272 −1.23242
\(795\) 13.1365 0.465905
\(796\) −11.0485 −0.391604
\(797\) −5.65890 −0.200449 −0.100224 0.994965i \(-0.531956\pi\)
−0.100224 + 0.994965i \(0.531956\pi\)
\(798\) −8.21754 −0.290898
\(799\) −0.566613 −0.0200453
\(800\) −3.41084 −0.120591
\(801\) −1.22006 −0.0431086
\(802\) −12.8048 −0.452154
\(803\) −42.0359 −1.48341
\(804\) 0.453039 0.0159775
\(805\) 12.2747 0.432626
\(806\) −15.1269 −0.532824
\(807\) −19.7737 −0.696066
\(808\) −4.60470 −0.161993
\(809\) −16.4805 −0.579422 −0.289711 0.957114i \(-0.593559\pi\)
−0.289711 + 0.957114i \(0.593559\pi\)
\(810\) 1.26062 0.0442937
\(811\) −24.5225 −0.861100 −0.430550 0.902567i \(-0.641680\pi\)
−0.430550 + 0.902567i \(0.641680\pi\)
\(812\) 24.5081 0.860066
\(813\) −27.5096 −0.964803
\(814\) −19.7566 −0.692468
\(815\) −12.8805 −0.451186
\(816\) −1.00000 −0.0350070
\(817\) −19.6428 −0.687214
\(818\) 30.5691 1.06882
\(819\) 26.7713 0.935463
\(820\) 10.6244 0.371019
\(821\) −15.2085 −0.530782 −0.265391 0.964141i \(-0.585501\pi\)
−0.265391 + 0.964141i \(0.585501\pi\)
\(822\) 7.31949 0.255297
\(823\) 54.4027 1.89636 0.948179 0.317737i \(-0.102923\pi\)
0.948179 + 0.317737i \(0.102923\pi\)
\(824\) 8.13422 0.283369
\(825\) −12.6391 −0.440038
\(826\) 3.87711 0.134902
\(827\) −12.2446 −0.425787 −0.212893 0.977075i \(-0.568289\pi\)
−0.212893 + 0.977075i \(0.568289\pi\)
\(828\) 2.51141 0.0872775
\(829\) −11.1674 −0.387861 −0.193930 0.981015i \(-0.562124\pi\)
−0.193930 + 0.981015i \(0.562124\pi\)
\(830\) 18.5032 0.642254
\(831\) −13.5731 −0.470844
\(832\) 6.90495 0.239386
\(833\) 8.03201 0.278293
\(834\) −11.0123 −0.381324
\(835\) −26.2012 −0.906729
\(836\) −7.85397 −0.271635
\(837\) 2.19074 0.0757230
\(838\) −9.79506 −0.338365
\(839\) −21.5815 −0.745076 −0.372538 0.928017i \(-0.621512\pi\)
−0.372538 + 0.928017i \(0.621512\pi\)
\(840\) −4.88757 −0.168637
\(841\) 10.9579 0.377858
\(842\) −7.50279 −0.258563
\(843\) −10.0237 −0.345235
\(844\) 23.7933 0.819001
\(845\) 43.7161 1.50388
\(846\) −0.566613 −0.0194806
\(847\) 10.5896 0.363863
\(848\) −10.4207 −0.357848
\(849\) −4.03872 −0.138609
\(850\) −3.41084 −0.116991
\(851\) 13.3898 0.458996
\(852\) 12.4635 0.426993
\(853\) −32.5547 −1.11465 −0.557326 0.830294i \(-0.688172\pi\)
−0.557326 + 0.830294i \(0.688172\pi\)
\(854\) −10.7865 −0.369106
\(855\) 2.67189 0.0913765
\(856\) 3.07336 0.105045
\(857\) −32.9809 −1.12661 −0.563304 0.826250i \(-0.690470\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(858\) 25.5868 0.873519
\(859\) 9.08126 0.309849 0.154924 0.987926i \(-0.450487\pi\)
0.154924 + 0.987926i \(0.450487\pi\)
\(860\) −11.6830 −0.398387
\(861\) −32.6758 −1.11359
\(862\) −2.08543 −0.0710301
\(863\) 2.19803 0.0748218 0.0374109 0.999300i \(-0.488089\pi\)
0.0374109 + 0.999300i \(0.488089\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 17.5116 0.595413
\(866\) 7.45018 0.253167
\(867\) −1.00000 −0.0339618
\(868\) −8.49375 −0.288297
\(869\) 47.9551 1.62677
\(870\) −7.96866 −0.270163
\(871\) −3.12821 −0.105995
\(872\) 4.24379 0.143713
\(873\) 8.86837 0.300149
\(874\) 5.32293 0.180051
\(875\) −41.1085 −1.38972
\(876\) −11.3440 −0.383277
\(877\) −1.01349 −0.0342233 −0.0171116 0.999854i \(-0.505447\pi\)
−0.0171116 + 0.999854i \(0.505447\pi\)
\(878\) −19.2809 −0.650698
\(879\) −30.3238 −1.02280
\(880\) −4.67133 −0.157470
\(881\) 34.3745 1.15811 0.579053 0.815290i \(-0.303422\pi\)
0.579053 + 0.815290i \(0.303422\pi\)
\(882\) 8.03201 0.270452
\(883\) −3.37694 −0.113643 −0.0568215 0.998384i \(-0.518097\pi\)
−0.0568215 + 0.998384i \(0.518097\pi\)
\(884\) 6.90495 0.232238
\(885\) −1.26062 −0.0423753
\(886\) −23.5618 −0.791575
\(887\) 34.9691 1.17415 0.587073 0.809534i \(-0.300280\pi\)
0.587073 + 0.809534i \(0.300280\pi\)
\(888\) −5.33158 −0.178916
\(889\) 23.5812 0.790887
\(890\) −1.53803 −0.0515549
\(891\) −3.70558 −0.124142
\(892\) 14.5096 0.485818
\(893\) −1.20094 −0.0401878
\(894\) 4.08706 0.136692
\(895\) −11.3627 −0.379812
\(896\) 3.87711 0.129525
\(897\) −17.3411 −0.579004
\(898\) −2.41928 −0.0807325
\(899\) −13.8482 −0.461862
\(900\) −3.41084 −0.113695
\(901\) −10.4207 −0.347164
\(902\) −31.2302 −1.03985
\(903\) 35.9317 1.19573
\(904\) −4.70750 −0.156569
\(905\) −4.53149 −0.150632
\(906\) 3.48477 0.115774
\(907\) −44.6523 −1.48266 −0.741328 0.671143i \(-0.765804\pi\)
−0.741328 + 0.671143i \(0.765804\pi\)
\(908\) −11.2613 −0.373720
\(909\) −4.60470 −0.152728
\(910\) 33.7484 1.11875
\(911\) 23.7187 0.785835 0.392918 0.919574i \(-0.371466\pi\)
0.392918 + 0.919574i \(0.371466\pi\)
\(912\) −2.11950 −0.0701837
\(913\) −54.3898 −1.80004
\(914\) 4.67152 0.154520
\(915\) 3.50716 0.115943
\(916\) −14.7592 −0.487656
\(917\) −73.2412 −2.41864
\(918\) −1.00000 −0.0330049
\(919\) −34.6832 −1.14409 −0.572046 0.820221i \(-0.693850\pi\)
−0.572046 + 0.820221i \(0.693850\pi\)
\(920\) 3.16593 0.104378
\(921\) −5.03826 −0.166016
\(922\) 31.4436 1.03554
\(923\) −86.0599 −2.83270
\(924\) 14.3669 0.472638
\(925\) −18.1852 −0.597924
\(926\) 3.38202 0.111140
\(927\) 8.13422 0.267163
\(928\) 6.32123 0.207504
\(929\) 24.7481 0.811959 0.405979 0.913882i \(-0.366931\pi\)
0.405979 + 0.913882i \(0.366931\pi\)
\(930\) 2.76169 0.0905594
\(931\) 17.0238 0.557934
\(932\) −14.1530 −0.463596
\(933\) −14.5697 −0.476990
\(934\) 23.5843 0.771701
\(935\) −4.67133 −0.152769
\(936\) 6.90495 0.225695
\(937\) 5.35962 0.175091 0.0875455 0.996161i \(-0.472098\pi\)
0.0875455 + 0.996161i \(0.472098\pi\)
\(938\) −1.75648 −0.0573512
\(939\) −15.0211 −0.490196
\(940\) −0.714284 −0.0232974
\(941\) −0.725685 −0.0236567 −0.0118283 0.999930i \(-0.503765\pi\)
−0.0118283 + 0.999930i \(0.503765\pi\)
\(942\) −6.18739 −0.201596
\(943\) 21.1659 0.689255
\(944\) 1.00000 0.0325472
\(945\) −4.88757 −0.158993
\(946\) 34.3420 1.11656
\(947\) 23.4403 0.761708 0.380854 0.924635i \(-0.375630\pi\)
0.380854 + 0.924635i \(0.375630\pi\)
\(948\) 12.9413 0.420315
\(949\) 78.3294 2.54268
\(950\) −7.22927 −0.234548
\(951\) −25.7537 −0.835122
\(952\) 3.87711 0.125658
\(953\) −4.73220 −0.153291 −0.0766455 0.997058i \(-0.524421\pi\)
−0.0766455 + 0.997058i \(0.524421\pi\)
\(954\) −10.4207 −0.337382
\(955\) −7.96239 −0.257657
\(956\) 19.0349 0.615634
\(957\) 23.4238 0.757184
\(958\) 11.2885 0.364715
\(959\) −28.3785 −0.916390
\(960\) −1.26062 −0.0406863
\(961\) −26.2007 −0.845183
\(962\) 36.8143 1.18694
\(963\) 3.07336 0.0990377
\(964\) 13.6413 0.439355
\(965\) −17.1235 −0.551224
\(966\) −9.73702 −0.313283
\(967\) 38.8462 1.24921 0.624605 0.780941i \(-0.285260\pi\)
0.624605 + 0.780941i \(0.285260\pi\)
\(968\) 2.73131 0.0877876
\(969\) −2.11950 −0.0680882
\(970\) 11.1796 0.358957
\(971\) 11.2007 0.359449 0.179725 0.983717i \(-0.442479\pi\)
0.179725 + 0.983717i \(0.442479\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 42.6958 1.36876
\(974\) 10.3474 0.331552
\(975\) 23.5516 0.754256
\(976\) −2.78209 −0.0890526
\(977\) −11.2555 −0.360095 −0.180048 0.983658i \(-0.557625\pi\)
−0.180048 + 0.983658i \(0.557625\pi\)
\(978\) 10.2176 0.326724
\(979\) 4.52102 0.144492
\(980\) 10.1253 0.323441
\(981\) 4.24379 0.135494
\(982\) −7.75497 −0.247471
\(983\) 52.4257 1.67212 0.836061 0.548637i \(-0.184853\pi\)
0.836061 + 0.548637i \(0.184853\pi\)
\(984\) −8.42788 −0.268671
\(985\) −34.3074 −1.09312
\(986\) 6.32123 0.201309
\(987\) 2.19682 0.0699257
\(988\) 14.6350 0.465602
\(989\) −23.2749 −0.740098
\(990\) −4.67133 −0.148465
\(991\) −28.7659 −0.913780 −0.456890 0.889523i \(-0.651037\pi\)
−0.456890 + 0.889523i \(0.651037\pi\)
\(992\) −2.19074 −0.0695561
\(993\) −9.58716 −0.304239
\(994\) −48.3225 −1.53270
\(995\) −13.9280 −0.441546
\(996\) −14.6778 −0.465085
\(997\) 21.2788 0.673907 0.336954 0.941521i \(-0.390603\pi\)
0.336954 + 0.941521i \(0.390603\pi\)
\(998\) 9.95739 0.315196
\(999\) −5.33158 −0.168684
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.bc.1.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.bc.1.9 14 1.1 even 1 trivial