Properties

Label 4026.2.a.y.1.5
Level $4026$
Weight $2$
Character 4026.1
Self dual yes
Analytic conductor $32.148$
Analytic rank $1$
Dimension $7$
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] = [4026,2,Mod(1,4026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4026, 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("4026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.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: \(32.1477718538\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 \) 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 1.5
Root \(-0.777182\) of defining polynomial
Character \(\chi\) \(=\) 4026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.777182 q^{5} +1.00000 q^{6} -3.79435 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.777182 q^{5} +1.00000 q^{6} -3.79435 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.777182 q^{10} -1.00000 q^{11} -1.00000 q^{12} -0.829389 q^{13} +3.79435 q^{14} -0.777182 q^{15} +1.00000 q^{16} +6.42418 q^{17} -1.00000 q^{18} +3.39222 q^{19} +0.777182 q^{20} +3.79435 q^{21} +1.00000 q^{22} -5.59479 q^{23} +1.00000 q^{24} -4.39599 q^{25} +0.829389 q^{26} -1.00000 q^{27} -3.79435 q^{28} -0.688882 q^{29} +0.777182 q^{30} -2.26002 q^{31} -1.00000 q^{32} +1.00000 q^{33} -6.42418 q^{34} -2.94890 q^{35} +1.00000 q^{36} +10.5891 q^{37} -3.39222 q^{38} +0.829389 q^{39} -0.777182 q^{40} -1.80120 q^{41} -3.79435 q^{42} +1.23959 q^{43} -1.00000 q^{44} +0.777182 q^{45} +5.59479 q^{46} +9.85707 q^{47} -1.00000 q^{48} +7.39710 q^{49} +4.39599 q^{50} -6.42418 q^{51} -0.829389 q^{52} +7.46497 q^{53} +1.00000 q^{54} -0.777182 q^{55} +3.79435 q^{56} -3.39222 q^{57} +0.688882 q^{58} -3.77758 q^{59} -0.777182 q^{60} -1.00000 q^{61} +2.26002 q^{62} -3.79435 q^{63} +1.00000 q^{64} -0.644586 q^{65} -1.00000 q^{66} -8.84367 q^{67} +6.42418 q^{68} +5.59479 q^{69} +2.94890 q^{70} -5.68617 q^{71} -1.00000 q^{72} +0.226192 q^{73} -10.5891 q^{74} +4.39599 q^{75} +3.39222 q^{76} +3.79435 q^{77} -0.829389 q^{78} -10.5300 q^{79} +0.777182 q^{80} +1.00000 q^{81} +1.80120 q^{82} +10.7814 q^{83} +3.79435 q^{84} +4.99276 q^{85} -1.23959 q^{86} +0.688882 q^{87} +1.00000 q^{88} -4.99276 q^{89} -0.777182 q^{90} +3.14699 q^{91} -5.59479 q^{92} +2.26002 q^{93} -9.85707 q^{94} +2.63637 q^{95} +1.00000 q^{96} +2.45363 q^{97} -7.39710 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) \) 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
\(5\) 0.777182 0.347566 0.173783 0.984784i \(-0.444401\pi\)
0.173783 + 0.984784i \(0.444401\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.79435 −1.43413 −0.717065 0.697006i \(-0.754515\pi\)
−0.717065 + 0.697006i \(0.754515\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −0.777182 −0.245767
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) −0.829389 −0.230031 −0.115016 0.993364i \(-0.536692\pi\)
−0.115016 + 0.993364i \(0.536692\pi\)
\(14\) 3.79435 1.01408
\(15\) −0.777182 −0.200668
\(16\) 1.00000 0.250000
\(17\) 6.42418 1.55809 0.779046 0.626967i \(-0.215704\pi\)
0.779046 + 0.626967i \(0.215704\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.39222 0.778228 0.389114 0.921190i \(-0.372781\pi\)
0.389114 + 0.921190i \(0.372781\pi\)
\(20\) 0.777182 0.173783
\(21\) 3.79435 0.827995
\(22\) 1.00000 0.213201
\(23\) −5.59479 −1.16659 −0.583297 0.812259i \(-0.698238\pi\)
−0.583297 + 0.812259i \(0.698238\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.39599 −0.879198
\(26\) 0.829389 0.162656
\(27\) −1.00000 −0.192450
\(28\) −3.79435 −0.717065
\(29\) −0.688882 −0.127922 −0.0639611 0.997952i \(-0.520373\pi\)
−0.0639611 + 0.997952i \(0.520373\pi\)
\(30\) 0.777182 0.141893
\(31\) −2.26002 −0.405911 −0.202956 0.979188i \(-0.565055\pi\)
−0.202956 + 0.979188i \(0.565055\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) −6.42418 −1.10174
\(35\) −2.94890 −0.498455
\(36\) 1.00000 0.166667
\(37\) 10.5891 1.74084 0.870418 0.492313i \(-0.163848\pi\)
0.870418 + 0.492313i \(0.163848\pi\)
\(38\) −3.39222 −0.550290
\(39\) 0.829389 0.132808
\(40\) −0.777182 −0.122883
\(41\) −1.80120 −0.281300 −0.140650 0.990059i \(-0.544919\pi\)
−0.140650 + 0.990059i \(0.544919\pi\)
\(42\) −3.79435 −0.585481
\(43\) 1.23959 0.189036 0.0945179 0.995523i \(-0.469869\pi\)
0.0945179 + 0.995523i \(0.469869\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0.777182 0.115855
\(46\) 5.59479 0.824907
\(47\) 9.85707 1.43780 0.718901 0.695113i \(-0.244646\pi\)
0.718901 + 0.695113i \(0.244646\pi\)
\(48\) −1.00000 −0.144338
\(49\) 7.39710 1.05673
\(50\) 4.39599 0.621687
\(51\) −6.42418 −0.899565
\(52\) −0.829389 −0.115016
\(53\) 7.46497 1.02539 0.512696 0.858570i \(-0.328647\pi\)
0.512696 + 0.858570i \(0.328647\pi\)
\(54\) 1.00000 0.136083
\(55\) −0.777182 −0.104795
\(56\) 3.79435 0.507041
\(57\) −3.39222 −0.449310
\(58\) 0.688882 0.0904547
\(59\) −3.77758 −0.491799 −0.245899 0.969295i \(-0.579083\pi\)
−0.245899 + 0.969295i \(0.579083\pi\)
\(60\) −0.777182 −0.100334
\(61\) −1.00000 −0.128037
\(62\) 2.26002 0.287023
\(63\) −3.79435 −0.478043
\(64\) 1.00000 0.125000
\(65\) −0.644586 −0.0799510
\(66\) −1.00000 −0.123091
\(67\) −8.84367 −1.08043 −0.540213 0.841528i \(-0.681656\pi\)
−0.540213 + 0.841528i \(0.681656\pi\)
\(68\) 6.42418 0.779046
\(69\) 5.59479 0.673533
\(70\) 2.94890 0.352461
\(71\) −5.68617 −0.674824 −0.337412 0.941357i \(-0.609552\pi\)
−0.337412 + 0.941357i \(0.609552\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.226192 0.0264737 0.0132369 0.999912i \(-0.495786\pi\)
0.0132369 + 0.999912i \(0.495786\pi\)
\(74\) −10.5891 −1.23096
\(75\) 4.39599 0.507605
\(76\) 3.39222 0.389114
\(77\) 3.79435 0.432406
\(78\) −0.829389 −0.0939098
\(79\) −10.5300 −1.18472 −0.592361 0.805673i \(-0.701804\pi\)
−0.592361 + 0.805673i \(0.701804\pi\)
\(80\) 0.777182 0.0868916
\(81\) 1.00000 0.111111
\(82\) 1.80120 0.198909
\(83\) 10.7814 1.18341 0.591704 0.806155i \(-0.298455\pi\)
0.591704 + 0.806155i \(0.298455\pi\)
\(84\) 3.79435 0.413998
\(85\) 4.99276 0.541540
\(86\) −1.23959 −0.133668
\(87\) 0.688882 0.0738559
\(88\) 1.00000 0.106600
\(89\) −4.99276 −0.529231 −0.264616 0.964354i \(-0.585245\pi\)
−0.264616 + 0.964354i \(0.585245\pi\)
\(90\) −0.777182 −0.0819222
\(91\) 3.14699 0.329894
\(92\) −5.59479 −0.583297
\(93\) 2.26002 0.234353
\(94\) −9.85707 −1.01668
\(95\) 2.63637 0.270486
\(96\) 1.00000 0.102062
\(97\) 2.45363 0.249128 0.124564 0.992212i \(-0.460247\pi\)
0.124564 + 0.992212i \(0.460247\pi\)
\(98\) −7.39710 −0.747219
\(99\) −1.00000 −0.100504
\(100\) −4.39599 −0.439599
\(101\) 1.13546 0.112982 0.0564912 0.998403i \(-0.482009\pi\)
0.0564912 + 0.998403i \(0.482009\pi\)
\(102\) 6.42418 0.636088
\(103\) 10.7380 1.05804 0.529021 0.848609i \(-0.322559\pi\)
0.529021 + 0.848609i \(0.322559\pi\)
\(104\) 0.829389 0.0813282
\(105\) 2.94890 0.287783
\(106\) −7.46497 −0.725062
\(107\) −11.3332 −1.09562 −0.547809 0.836603i \(-0.684538\pi\)
−0.547809 + 0.836603i \(0.684538\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −6.58859 −0.631072 −0.315536 0.948914i \(-0.602184\pi\)
−0.315536 + 0.948914i \(0.602184\pi\)
\(110\) 0.777182 0.0741014
\(111\) −10.5891 −1.00507
\(112\) −3.79435 −0.358532
\(113\) −8.50905 −0.800464 −0.400232 0.916414i \(-0.631070\pi\)
−0.400232 + 0.916414i \(0.631070\pi\)
\(114\) 3.39222 0.317710
\(115\) −4.34817 −0.405469
\(116\) −0.688882 −0.0639611
\(117\) −0.829389 −0.0766770
\(118\) 3.77758 0.347754
\(119\) −24.3756 −2.23451
\(120\) 0.777182 0.0709467
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 1.80120 0.162409
\(124\) −2.26002 −0.202956
\(125\) −7.30239 −0.653146
\(126\) 3.79435 0.338028
\(127\) −16.2682 −1.44357 −0.721785 0.692117i \(-0.756678\pi\)
−0.721785 + 0.692117i \(0.756678\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.23959 −0.109140
\(130\) 0.644586 0.0565339
\(131\) −7.36785 −0.643732 −0.321866 0.946785i \(-0.604310\pi\)
−0.321866 + 0.946785i \(0.604310\pi\)
\(132\) 1.00000 0.0870388
\(133\) −12.8713 −1.11608
\(134\) 8.84367 0.763977
\(135\) −0.777182 −0.0668892
\(136\) −6.42418 −0.550869
\(137\) −16.1360 −1.37859 −0.689296 0.724480i \(-0.742080\pi\)
−0.689296 + 0.724480i \(0.742080\pi\)
\(138\) −5.59479 −0.476260
\(139\) 3.58929 0.304440 0.152220 0.988347i \(-0.451358\pi\)
0.152220 + 0.988347i \(0.451358\pi\)
\(140\) −2.94890 −0.249228
\(141\) −9.85707 −0.830115
\(142\) 5.68617 0.477173
\(143\) 0.829389 0.0693570
\(144\) 1.00000 0.0833333
\(145\) −0.535387 −0.0444615
\(146\) −0.226192 −0.0187197
\(147\) −7.39710 −0.610102
\(148\) 10.5891 0.870418
\(149\) −8.50326 −0.696615 −0.348307 0.937380i \(-0.613243\pi\)
−0.348307 + 0.937380i \(0.613243\pi\)
\(150\) −4.39599 −0.358931
\(151\) 6.45800 0.525545 0.262772 0.964858i \(-0.415363\pi\)
0.262772 + 0.964858i \(0.415363\pi\)
\(152\) −3.39222 −0.275145
\(153\) 6.42418 0.519364
\(154\) −3.79435 −0.305757
\(155\) −1.75645 −0.141081
\(156\) 0.829389 0.0664042
\(157\) 21.4950 1.71549 0.857744 0.514077i \(-0.171865\pi\)
0.857744 + 0.514077i \(0.171865\pi\)
\(158\) 10.5300 0.837725
\(159\) −7.46497 −0.592010
\(160\) −0.777182 −0.0614416
\(161\) 21.2286 1.67305
\(162\) −1.00000 −0.0785674
\(163\) 24.3641 1.90834 0.954170 0.299265i \(-0.0967416\pi\)
0.954170 + 0.299265i \(0.0967416\pi\)
\(164\) −1.80120 −0.140650
\(165\) 0.777182 0.0605035
\(166\) −10.7814 −0.836796
\(167\) −15.8209 −1.22426 −0.612128 0.790759i \(-0.709686\pi\)
−0.612128 + 0.790759i \(0.709686\pi\)
\(168\) −3.79435 −0.292740
\(169\) −12.3121 −0.947086
\(170\) −4.99276 −0.382927
\(171\) 3.39222 0.259409
\(172\) 1.23959 0.0945179
\(173\) −0.495579 −0.0376782 −0.0188391 0.999823i \(-0.505997\pi\)
−0.0188391 + 0.999823i \(0.505997\pi\)
\(174\) −0.688882 −0.0522240
\(175\) 16.6799 1.26088
\(176\) −1.00000 −0.0753778
\(177\) 3.77758 0.283940
\(178\) 4.99276 0.374223
\(179\) −11.8556 −0.886129 −0.443065 0.896490i \(-0.646109\pi\)
−0.443065 + 0.896490i \(0.646109\pi\)
\(180\) 0.777182 0.0579277
\(181\) 18.2368 1.35553 0.677765 0.735279i \(-0.262949\pi\)
0.677765 + 0.735279i \(0.262949\pi\)
\(182\) −3.14699 −0.233270
\(183\) 1.00000 0.0739221
\(184\) 5.59479 0.412453
\(185\) 8.22966 0.605056
\(186\) −2.26002 −0.165713
\(187\) −6.42418 −0.469782
\(188\) 9.85707 0.718901
\(189\) 3.79435 0.275998
\(190\) −2.63637 −0.191262
\(191\) 5.85173 0.423416 0.211708 0.977333i \(-0.432097\pi\)
0.211708 + 0.977333i \(0.432097\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 23.2053 1.67035 0.835176 0.549982i \(-0.185366\pi\)
0.835176 + 0.549982i \(0.185366\pi\)
\(194\) −2.45363 −0.176160
\(195\) 0.644586 0.0461598
\(196\) 7.39710 0.528364
\(197\) −11.6762 −0.831898 −0.415949 0.909388i \(-0.636550\pi\)
−0.415949 + 0.909388i \(0.636550\pi\)
\(198\) 1.00000 0.0710669
\(199\) −6.10189 −0.432552 −0.216276 0.976332i \(-0.569391\pi\)
−0.216276 + 0.976332i \(0.569391\pi\)
\(200\) 4.39599 0.310843
\(201\) 8.84367 0.623785
\(202\) −1.13546 −0.0798907
\(203\) 2.61386 0.183457
\(204\) −6.42418 −0.449782
\(205\) −1.39986 −0.0977704
\(206\) −10.7380 −0.748149
\(207\) −5.59479 −0.388865
\(208\) −0.829389 −0.0575078
\(209\) −3.39222 −0.234645
\(210\) −2.94890 −0.203493
\(211\) −3.15597 −0.217266 −0.108633 0.994082i \(-0.534647\pi\)
−0.108633 + 0.994082i \(0.534647\pi\)
\(212\) 7.46497 0.512696
\(213\) 5.68617 0.389610
\(214\) 11.3332 0.774719
\(215\) 0.963387 0.0657025
\(216\) 1.00000 0.0680414
\(217\) 8.57530 0.582129
\(218\) 6.58859 0.446235
\(219\) −0.226192 −0.0152846
\(220\) −0.777182 −0.0523976
\(221\) −5.32814 −0.358409
\(222\) 10.5891 0.710694
\(223\) 12.5155 0.838100 0.419050 0.907963i \(-0.362363\pi\)
0.419050 + 0.907963i \(0.362363\pi\)
\(224\) 3.79435 0.253521
\(225\) −4.39599 −0.293066
\(226\) 8.50905 0.566013
\(227\) −4.01934 −0.266773 −0.133387 0.991064i \(-0.542585\pi\)
−0.133387 + 0.991064i \(0.542585\pi\)
\(228\) −3.39222 −0.224655
\(229\) −15.5815 −1.02966 −0.514828 0.857293i \(-0.672144\pi\)
−0.514828 + 0.857293i \(0.672144\pi\)
\(230\) 4.34817 0.286710
\(231\) −3.79435 −0.249650
\(232\) 0.688882 0.0452273
\(233\) −20.1974 −1.32317 −0.661587 0.749868i \(-0.730117\pi\)
−0.661587 + 0.749868i \(0.730117\pi\)
\(234\) 0.829389 0.0542188
\(235\) 7.66074 0.499731
\(236\) −3.77758 −0.245899
\(237\) 10.5300 0.684000
\(238\) 24.3756 1.58003
\(239\) −16.3488 −1.05752 −0.528759 0.848772i \(-0.677342\pi\)
−0.528759 + 0.848772i \(0.677342\pi\)
\(240\) −0.777182 −0.0501669
\(241\) −15.8848 −1.02323 −0.511614 0.859216i \(-0.670952\pi\)
−0.511614 + 0.859216i \(0.670952\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 5.74889 0.367283
\(246\) −1.80120 −0.114840
\(247\) −2.81347 −0.179017
\(248\) 2.26002 0.143511
\(249\) −10.7814 −0.683241
\(250\) 7.30239 0.461844
\(251\) 0.930521 0.0587340 0.0293670 0.999569i \(-0.490651\pi\)
0.0293670 + 0.999569i \(0.490651\pi\)
\(252\) −3.79435 −0.239022
\(253\) 5.59479 0.351741
\(254\) 16.2682 1.02076
\(255\) −4.99276 −0.312658
\(256\) 1.00000 0.0625000
\(257\) 12.1287 0.756568 0.378284 0.925690i \(-0.376514\pi\)
0.378284 + 0.925690i \(0.376514\pi\)
\(258\) 1.23959 0.0771735
\(259\) −40.1787 −2.49659
\(260\) −0.644586 −0.0399755
\(261\) −0.688882 −0.0426407
\(262\) 7.36785 0.455188
\(263\) −30.6916 −1.89252 −0.946262 0.323401i \(-0.895174\pi\)
−0.946262 + 0.323401i \(0.895174\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 5.80164 0.356392
\(266\) 12.8713 0.789188
\(267\) 4.99276 0.305552
\(268\) −8.84367 −0.540213
\(269\) −12.9720 −0.790915 −0.395457 0.918484i \(-0.629414\pi\)
−0.395457 + 0.918484i \(0.629414\pi\)
\(270\) 0.777182 0.0472978
\(271\) −12.6657 −0.769385 −0.384692 0.923045i \(-0.625692\pi\)
−0.384692 + 0.923045i \(0.625692\pi\)
\(272\) 6.42418 0.389523
\(273\) −3.14699 −0.190465
\(274\) 16.1360 0.974812
\(275\) 4.39599 0.265088
\(276\) 5.59479 0.336767
\(277\) 14.3557 0.862548 0.431274 0.902221i \(-0.358064\pi\)
0.431274 + 0.902221i \(0.358064\pi\)
\(278\) −3.58929 −0.215271
\(279\) −2.26002 −0.135304
\(280\) 2.94890 0.176231
\(281\) −27.3160 −1.62953 −0.814767 0.579788i \(-0.803135\pi\)
−0.814767 + 0.579788i \(0.803135\pi\)
\(282\) 9.85707 0.586980
\(283\) −32.9040 −1.95594 −0.977969 0.208750i \(-0.933061\pi\)
−0.977969 + 0.208750i \(0.933061\pi\)
\(284\) −5.68617 −0.337412
\(285\) −2.63637 −0.156165
\(286\) −0.829389 −0.0490428
\(287\) 6.83438 0.403421
\(288\) −1.00000 −0.0589256
\(289\) 24.2701 1.42765
\(290\) 0.535387 0.0314390
\(291\) −2.45363 −0.143834
\(292\) 0.226192 0.0132369
\(293\) −9.74062 −0.569053 −0.284526 0.958668i \(-0.591836\pi\)
−0.284526 + 0.958668i \(0.591836\pi\)
\(294\) 7.39710 0.431407
\(295\) −2.93587 −0.170933
\(296\) −10.5891 −0.615479
\(297\) 1.00000 0.0580259
\(298\) 8.50326 0.492581
\(299\) 4.64025 0.268353
\(300\) 4.39599 0.253802
\(301\) −4.70344 −0.271102
\(302\) −6.45800 −0.371616
\(303\) −1.13546 −0.0652305
\(304\) 3.39222 0.194557
\(305\) −0.777182 −0.0445013
\(306\) −6.42418 −0.367246
\(307\) −8.60709 −0.491232 −0.245616 0.969367i \(-0.578990\pi\)
−0.245616 + 0.969367i \(0.578990\pi\)
\(308\) 3.79435 0.216203
\(309\) −10.7380 −0.610861
\(310\) 1.75645 0.0997594
\(311\) 5.85160 0.331814 0.165907 0.986141i \(-0.446945\pi\)
0.165907 + 0.986141i \(0.446945\pi\)
\(312\) −0.829389 −0.0469549
\(313\) 6.45719 0.364982 0.182491 0.983208i \(-0.441584\pi\)
0.182491 + 0.983208i \(0.441584\pi\)
\(314\) −21.4950 −1.21303
\(315\) −2.94890 −0.166152
\(316\) −10.5300 −0.592361
\(317\) 11.2731 0.633160 0.316580 0.948566i \(-0.397465\pi\)
0.316580 + 0.948566i \(0.397465\pi\)
\(318\) 7.46497 0.418615
\(319\) 0.688882 0.0385700
\(320\) 0.777182 0.0434458
\(321\) 11.3332 0.632555
\(322\) −21.2286 −1.18302
\(323\) 21.7922 1.21255
\(324\) 1.00000 0.0555556
\(325\) 3.64598 0.202243
\(326\) −24.3641 −1.34940
\(327\) 6.58859 0.364350
\(328\) 1.80120 0.0994546
\(329\) −37.4012 −2.06199
\(330\) −0.777182 −0.0427825
\(331\) −32.4487 −1.78354 −0.891770 0.452489i \(-0.850536\pi\)
−0.891770 + 0.452489i \(0.850536\pi\)
\(332\) 10.7814 0.591704
\(333\) 10.5891 0.580279
\(334\) 15.8209 0.865680
\(335\) −6.87314 −0.375520
\(336\) 3.79435 0.206999
\(337\) −8.74285 −0.476253 −0.238127 0.971234i \(-0.576533\pi\)
−0.238127 + 0.971234i \(0.576533\pi\)
\(338\) 12.3121 0.669691
\(339\) 8.50905 0.462148
\(340\) 4.99276 0.270770
\(341\) 2.26002 0.122387
\(342\) −3.39222 −0.183430
\(343\) −1.50672 −0.0813552
\(344\) −1.23959 −0.0668342
\(345\) 4.34817 0.234098
\(346\) 0.495579 0.0266425
\(347\) −25.9734 −1.39432 −0.697161 0.716914i \(-0.745554\pi\)
−0.697161 + 0.716914i \(0.745554\pi\)
\(348\) 0.688882 0.0369280
\(349\) −16.2802 −0.871457 −0.435729 0.900078i \(-0.643509\pi\)
−0.435729 + 0.900078i \(0.643509\pi\)
\(350\) −16.6799 −0.891579
\(351\) 0.829389 0.0442695
\(352\) 1.00000 0.0533002
\(353\) −27.7773 −1.47843 −0.739217 0.673467i \(-0.764804\pi\)
−0.739217 + 0.673467i \(0.764804\pi\)
\(354\) −3.77758 −0.200776
\(355\) −4.41919 −0.234546
\(356\) −4.99276 −0.264616
\(357\) 24.3756 1.29009
\(358\) 11.8556 0.626588
\(359\) 11.6724 0.616048 0.308024 0.951379i \(-0.400332\pi\)
0.308024 + 0.951379i \(0.400332\pi\)
\(360\) −0.777182 −0.0409611
\(361\) −7.49285 −0.394361
\(362\) −18.2368 −0.958504
\(363\) −1.00000 −0.0524864
\(364\) 3.14699 0.164947
\(365\) 0.175792 0.00920137
\(366\) −1.00000 −0.0522708
\(367\) 26.9833 1.40852 0.704259 0.709943i \(-0.251279\pi\)
0.704259 + 0.709943i \(0.251279\pi\)
\(368\) −5.59479 −0.291649
\(369\) −1.80120 −0.0937667
\(370\) −8.22966 −0.427839
\(371\) −28.3247 −1.47055
\(372\) 2.26002 0.117177
\(373\) −3.69371 −0.191253 −0.0956265 0.995417i \(-0.530485\pi\)
−0.0956265 + 0.995417i \(0.530485\pi\)
\(374\) 6.42418 0.332186
\(375\) 7.30239 0.377094
\(376\) −9.85707 −0.508340
\(377\) 0.571351 0.0294261
\(378\) −3.79435 −0.195160
\(379\) −38.5449 −1.97992 −0.989960 0.141347i \(-0.954857\pi\)
−0.989960 + 0.141347i \(0.954857\pi\)
\(380\) 2.63637 0.135243
\(381\) 16.2682 0.833446
\(382\) −5.85173 −0.299401
\(383\) −13.6304 −0.696483 −0.348242 0.937405i \(-0.613221\pi\)
−0.348242 + 0.937405i \(0.613221\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.94890 0.150290
\(386\) −23.2053 −1.18112
\(387\) 1.23959 0.0630119
\(388\) 2.45363 0.124564
\(389\) −29.5694 −1.49923 −0.749614 0.661875i \(-0.769761\pi\)
−0.749614 + 0.661875i \(0.769761\pi\)
\(390\) −0.644586 −0.0326399
\(391\) −35.9419 −1.81766
\(392\) −7.39710 −0.373610
\(393\) 7.36785 0.371659
\(394\) 11.6762 0.588241
\(395\) −8.18376 −0.411770
\(396\) −1.00000 −0.0502519
\(397\) 32.3149 1.62184 0.810920 0.585157i \(-0.198967\pi\)
0.810920 + 0.585157i \(0.198967\pi\)
\(398\) 6.10189 0.305860
\(399\) 12.8713 0.644369
\(400\) −4.39599 −0.219799
\(401\) 9.61472 0.480136 0.240068 0.970756i \(-0.422830\pi\)
0.240068 + 0.970756i \(0.422830\pi\)
\(402\) −8.84367 −0.441082
\(403\) 1.87443 0.0933722
\(404\) 1.13546 0.0564912
\(405\) 0.777182 0.0386185
\(406\) −2.61386 −0.129724
\(407\) −10.5891 −0.524882
\(408\) 6.42418 0.318044
\(409\) −19.8458 −0.981313 −0.490656 0.871353i \(-0.663243\pi\)
−0.490656 + 0.871353i \(0.663243\pi\)
\(410\) 1.39986 0.0691341
\(411\) 16.1360 0.795931
\(412\) 10.7380 0.529021
\(413\) 14.3335 0.705303
\(414\) 5.59479 0.274969
\(415\) 8.37908 0.411313
\(416\) 0.829389 0.0406641
\(417\) −3.58929 −0.175768
\(418\) 3.39222 0.165919
\(419\) 21.0434 1.02804 0.514018 0.857779i \(-0.328156\pi\)
0.514018 + 0.857779i \(0.328156\pi\)
\(420\) 2.94890 0.143892
\(421\) −12.1741 −0.593331 −0.296666 0.954981i \(-0.595875\pi\)
−0.296666 + 0.954981i \(0.595875\pi\)
\(422\) 3.15597 0.153630
\(423\) 9.85707 0.479267
\(424\) −7.46497 −0.362531
\(425\) −28.2406 −1.36987
\(426\) −5.68617 −0.275496
\(427\) 3.79435 0.183621
\(428\) −11.3332 −0.547809
\(429\) −0.829389 −0.0400433
\(430\) −0.963387 −0.0464587
\(431\) −7.06839 −0.340473 −0.170236 0.985403i \(-0.554453\pi\)
−0.170236 + 0.985403i \(0.554453\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −7.60525 −0.365485 −0.182742 0.983161i \(-0.558497\pi\)
−0.182742 + 0.983161i \(0.558497\pi\)
\(434\) −8.57530 −0.411628
\(435\) 0.535387 0.0256698
\(436\) −6.58859 −0.315536
\(437\) −18.9787 −0.907877
\(438\) 0.226192 0.0108078
\(439\) 18.6709 0.891111 0.445556 0.895254i \(-0.353006\pi\)
0.445556 + 0.895254i \(0.353006\pi\)
\(440\) 0.777182 0.0370507
\(441\) 7.39710 0.352243
\(442\) 5.32814 0.253434
\(443\) −10.7433 −0.510432 −0.255216 0.966884i \(-0.582147\pi\)
−0.255216 + 0.966884i \(0.582147\pi\)
\(444\) −10.5891 −0.502536
\(445\) −3.88028 −0.183943
\(446\) −12.5155 −0.592626
\(447\) 8.50326 0.402191
\(448\) −3.79435 −0.179266
\(449\) 36.3330 1.71466 0.857330 0.514767i \(-0.172122\pi\)
0.857330 + 0.514767i \(0.172122\pi\)
\(450\) 4.39599 0.207229
\(451\) 1.80120 0.0848151
\(452\) −8.50905 −0.400232
\(453\) −6.45800 −0.303424
\(454\) 4.01934 0.188637
\(455\) 2.44578 0.114660
\(456\) 3.39222 0.158855
\(457\) −21.9436 −1.02648 −0.513238 0.858246i \(-0.671554\pi\)
−0.513238 + 0.858246i \(0.671554\pi\)
\(458\) 15.5815 0.728077
\(459\) −6.42418 −0.299855
\(460\) −4.34817 −0.202734
\(461\) 19.7455 0.919639 0.459820 0.888012i \(-0.347914\pi\)
0.459820 + 0.888012i \(0.347914\pi\)
\(462\) 3.79435 0.176529
\(463\) 36.6840 1.70485 0.852426 0.522848i \(-0.175130\pi\)
0.852426 + 0.522848i \(0.175130\pi\)
\(464\) −0.688882 −0.0319806
\(465\) 1.75645 0.0814532
\(466\) 20.1974 0.935625
\(467\) −36.7614 −1.70111 −0.850557 0.525883i \(-0.823735\pi\)
−0.850557 + 0.525883i \(0.823735\pi\)
\(468\) −0.829389 −0.0383385
\(469\) 33.5560 1.54947
\(470\) −7.66074 −0.353364
\(471\) −21.4950 −0.990438
\(472\) 3.77758 0.173877
\(473\) −1.23959 −0.0569964
\(474\) −10.5300 −0.483661
\(475\) −14.9122 −0.684216
\(476\) −24.3756 −1.11725
\(477\) 7.46497 0.341797
\(478\) 16.3488 0.747778
\(479\) −16.0940 −0.735356 −0.367678 0.929953i \(-0.619847\pi\)
−0.367678 + 0.929953i \(0.619847\pi\)
\(480\) 0.777182 0.0354733
\(481\) −8.78248 −0.400446
\(482\) 15.8848 0.723531
\(483\) −21.2286 −0.965934
\(484\) 1.00000 0.0454545
\(485\) 1.90692 0.0865886
\(486\) 1.00000 0.0453609
\(487\) 19.4585 0.881747 0.440873 0.897569i \(-0.354669\pi\)
0.440873 + 0.897569i \(0.354669\pi\)
\(488\) 1.00000 0.0452679
\(489\) −24.3641 −1.10178
\(490\) −5.74889 −0.259708
\(491\) 18.8815 0.852108 0.426054 0.904698i \(-0.359903\pi\)
0.426054 + 0.904698i \(0.359903\pi\)
\(492\) 1.80120 0.0812043
\(493\) −4.42550 −0.199315
\(494\) 2.81347 0.126584
\(495\) −0.777182 −0.0349317
\(496\) −2.26002 −0.101478
\(497\) 21.5753 0.967785
\(498\) 10.7814 0.483124
\(499\) 8.27868 0.370605 0.185302 0.982682i \(-0.440674\pi\)
0.185302 + 0.982682i \(0.440674\pi\)
\(500\) −7.30239 −0.326573
\(501\) 15.8209 0.706824
\(502\) −0.930521 −0.0415312
\(503\) 7.73269 0.344784 0.172392 0.985028i \(-0.444850\pi\)
0.172392 + 0.985028i \(0.444850\pi\)
\(504\) 3.79435 0.169014
\(505\) 0.882459 0.0392689
\(506\) −5.59479 −0.248719
\(507\) 12.3121 0.546800
\(508\) −16.2682 −0.721785
\(509\) 7.99538 0.354389 0.177195 0.984176i \(-0.443298\pi\)
0.177195 + 0.984176i \(0.443298\pi\)
\(510\) 4.99276 0.221083
\(511\) −0.858250 −0.0379667
\(512\) −1.00000 −0.0441942
\(513\) −3.39222 −0.149770
\(514\) −12.1287 −0.534974
\(515\) 8.34535 0.367740
\(516\) −1.23959 −0.0545699
\(517\) −9.85707 −0.433514
\(518\) 40.1787 1.76535
\(519\) 0.495579 0.0217535
\(520\) 0.644586 0.0282670
\(521\) −12.1788 −0.533562 −0.266781 0.963757i \(-0.585960\pi\)
−0.266781 + 0.963757i \(0.585960\pi\)
\(522\) 0.688882 0.0301516
\(523\) 27.3315 1.19512 0.597561 0.801824i \(-0.296137\pi\)
0.597561 + 0.801824i \(0.296137\pi\)
\(524\) −7.36785 −0.321866
\(525\) −16.6799 −0.727971
\(526\) 30.6916 1.33822
\(527\) −14.5188 −0.632447
\(528\) 1.00000 0.0435194
\(529\) 8.30167 0.360942
\(530\) −5.80164 −0.252007
\(531\) −3.77758 −0.163933
\(532\) −12.8713 −0.558040
\(533\) 1.49389 0.0647077
\(534\) −4.99276 −0.216058
\(535\) −8.80793 −0.380800
\(536\) 8.84367 0.381988
\(537\) 11.8556 0.511607
\(538\) 12.9720 0.559261
\(539\) −7.39710 −0.318615
\(540\) −0.777182 −0.0334446
\(541\) −22.7153 −0.976608 −0.488304 0.872674i \(-0.662384\pi\)
−0.488304 + 0.872674i \(0.662384\pi\)
\(542\) 12.6657 0.544037
\(543\) −18.2368 −0.782615
\(544\) −6.42418 −0.275434
\(545\) −5.12053 −0.219339
\(546\) 3.14699 0.134679
\(547\) 13.3654 0.571463 0.285732 0.958310i \(-0.407763\pi\)
0.285732 + 0.958310i \(0.407763\pi\)
\(548\) −16.1360 −0.689296
\(549\) −1.00000 −0.0426790
\(550\) −4.39599 −0.187446
\(551\) −2.33684 −0.0995527
\(552\) −5.59479 −0.238130
\(553\) 39.9547 1.69905
\(554\) −14.3557 −0.609913
\(555\) −8.22966 −0.349329
\(556\) 3.58929 0.152220
\(557\) 42.2260 1.78917 0.894586 0.446897i \(-0.147471\pi\)
0.894586 + 0.446897i \(0.147471\pi\)
\(558\) 2.26002 0.0956742
\(559\) −1.02810 −0.0434841
\(560\) −2.94890 −0.124614
\(561\) 6.42418 0.271229
\(562\) 27.3160 1.15226
\(563\) −27.9142 −1.17644 −0.588221 0.808700i \(-0.700171\pi\)
−0.588221 + 0.808700i \(0.700171\pi\)
\(564\) −9.85707 −0.415058
\(565\) −6.61308 −0.278214
\(566\) 32.9040 1.38306
\(567\) −3.79435 −0.159348
\(568\) 5.68617 0.238586
\(569\) −17.7914 −0.745854 −0.372927 0.927861i \(-0.621646\pi\)
−0.372927 + 0.927861i \(0.621646\pi\)
\(570\) 2.63637 0.110425
\(571\) 3.42938 0.143515 0.0717575 0.997422i \(-0.477139\pi\)
0.0717575 + 0.997422i \(0.477139\pi\)
\(572\) 0.829389 0.0346785
\(573\) −5.85173 −0.244460
\(574\) −6.83438 −0.285261
\(575\) 24.5946 1.02567
\(576\) 1.00000 0.0416667
\(577\) −5.76799 −0.240124 −0.120062 0.992766i \(-0.538309\pi\)
−0.120062 + 0.992766i \(0.538309\pi\)
\(578\) −24.2701 −1.00950
\(579\) −23.2053 −0.964378
\(580\) −0.535387 −0.0222307
\(581\) −40.9083 −1.69716
\(582\) 2.45363 0.101706
\(583\) −7.46497 −0.309167
\(584\) −0.226192 −0.00935987
\(585\) −0.644586 −0.0266503
\(586\) 9.74062 0.402381
\(587\) −5.56488 −0.229687 −0.114844 0.993384i \(-0.536637\pi\)
−0.114844 + 0.993384i \(0.536637\pi\)
\(588\) −7.39710 −0.305051
\(589\) −7.66648 −0.315892
\(590\) 2.93587 0.120868
\(591\) 11.6762 0.480296
\(592\) 10.5891 0.435209
\(593\) 7.02105 0.288320 0.144160 0.989554i \(-0.453952\pi\)
0.144160 + 0.989554i \(0.453952\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −18.9443 −0.776639
\(596\) −8.50326 −0.348307
\(597\) 6.10189 0.249734
\(598\) −4.64025 −0.189754
\(599\) 1.00712 0.0411498 0.0205749 0.999788i \(-0.493450\pi\)
0.0205749 + 0.999788i \(0.493450\pi\)
\(600\) −4.39599 −0.179465
\(601\) −37.9811 −1.54928 −0.774640 0.632402i \(-0.782069\pi\)
−0.774640 + 0.632402i \(0.782069\pi\)
\(602\) 4.70344 0.191698
\(603\) −8.84367 −0.360142
\(604\) 6.45800 0.262772
\(605\) 0.777182 0.0315969
\(606\) 1.13546 0.0461249
\(607\) −44.4593 −1.80455 −0.902274 0.431164i \(-0.858103\pi\)
−0.902274 + 0.431164i \(0.858103\pi\)
\(608\) −3.39222 −0.137573
\(609\) −2.61386 −0.105919
\(610\) 0.777182 0.0314672
\(611\) −8.17534 −0.330739
\(612\) 6.42418 0.259682
\(613\) 40.8749 1.65092 0.825461 0.564459i \(-0.190915\pi\)
0.825461 + 0.564459i \(0.190915\pi\)
\(614\) 8.60709 0.347354
\(615\) 1.39986 0.0564478
\(616\) −3.79435 −0.152879
\(617\) −33.2297 −1.33778 −0.668888 0.743363i \(-0.733230\pi\)
−0.668888 + 0.743363i \(0.733230\pi\)
\(618\) 10.7380 0.431944
\(619\) 34.7437 1.39647 0.698233 0.715871i \(-0.253970\pi\)
0.698233 + 0.715871i \(0.253970\pi\)
\(620\) −1.75645 −0.0705406
\(621\) 5.59479 0.224511
\(622\) −5.85160 −0.234628
\(623\) 18.9443 0.758986
\(624\) 0.829389 0.0332021
\(625\) 16.3047 0.652186
\(626\) −6.45719 −0.258081
\(627\) 3.39222 0.135472
\(628\) 21.4950 0.857744
\(629\) 68.0262 2.71238
\(630\) 2.94890 0.117487
\(631\) −7.89540 −0.314311 −0.157155 0.987574i \(-0.550232\pi\)
−0.157155 + 0.987574i \(0.550232\pi\)
\(632\) 10.5300 0.418863
\(633\) 3.15597 0.125439
\(634\) −11.2731 −0.447712
\(635\) −12.6434 −0.501737
\(636\) −7.46497 −0.296005
\(637\) −6.13507 −0.243080
\(638\) −0.688882 −0.0272731
\(639\) −5.68617 −0.224941
\(640\) −0.777182 −0.0307208
\(641\) 30.1269 1.18994 0.594971 0.803747i \(-0.297164\pi\)
0.594971 + 0.803747i \(0.297164\pi\)
\(642\) −11.3332 −0.447284
\(643\) −33.6686 −1.32776 −0.663879 0.747840i \(-0.731091\pi\)
−0.663879 + 0.747840i \(0.731091\pi\)
\(644\) 21.2286 0.836524
\(645\) −0.963387 −0.0379333
\(646\) −21.7922 −0.857403
\(647\) 46.0336 1.80977 0.904884 0.425657i \(-0.139957\pi\)
0.904884 + 0.425657i \(0.139957\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 3.77758 0.148283
\(650\) −3.64598 −0.143007
\(651\) −8.57530 −0.336093
\(652\) 24.3641 0.954170
\(653\) −27.5881 −1.07961 −0.539803 0.841791i \(-0.681501\pi\)
−0.539803 + 0.841791i \(0.681501\pi\)
\(654\) −6.58859 −0.257634
\(655\) −5.72616 −0.223740
\(656\) −1.80120 −0.0703250
\(657\) 0.226192 0.00882457
\(658\) 37.4012 1.45805
\(659\) 34.4549 1.34217 0.671087 0.741379i \(-0.265828\pi\)
0.671087 + 0.741379i \(0.265828\pi\)
\(660\) 0.777182 0.0302518
\(661\) 5.39462 0.209826 0.104913 0.994481i \(-0.466544\pi\)
0.104913 + 0.994481i \(0.466544\pi\)
\(662\) 32.4487 1.26115
\(663\) 5.32814 0.206928
\(664\) −10.7814 −0.418398
\(665\) −10.0033 −0.387912
\(666\) −10.5891 −0.410319
\(667\) 3.85415 0.149233
\(668\) −15.8209 −0.612128
\(669\) −12.5155 −0.483877
\(670\) 6.87314 0.265533
\(671\) 1.00000 0.0386046
\(672\) −3.79435 −0.146370
\(673\) −33.7794 −1.30210 −0.651051 0.759034i \(-0.725672\pi\)
−0.651051 + 0.759034i \(0.725672\pi\)
\(674\) 8.74285 0.336762
\(675\) 4.39599 0.169202
\(676\) −12.3121 −0.473543
\(677\) 3.09741 0.119043 0.0595215 0.998227i \(-0.481043\pi\)
0.0595215 + 0.998227i \(0.481043\pi\)
\(678\) −8.50905 −0.326788
\(679\) −9.30992 −0.357282
\(680\) −4.99276 −0.191463
\(681\) 4.01934 0.154021
\(682\) −2.26002 −0.0865406
\(683\) −34.7936 −1.33134 −0.665670 0.746246i \(-0.731854\pi\)
−0.665670 + 0.746246i \(0.731854\pi\)
\(684\) 3.39222 0.129705
\(685\) −12.5406 −0.479152
\(686\) 1.50672 0.0575268
\(687\) 15.5815 0.594473
\(688\) 1.23959 0.0472589
\(689\) −6.19136 −0.235872
\(690\) −4.34817 −0.165532
\(691\) −15.8352 −0.602401 −0.301200 0.953561i \(-0.597387\pi\)
−0.301200 + 0.953561i \(0.597387\pi\)
\(692\) −0.495579 −0.0188391
\(693\) 3.79435 0.144135
\(694\) 25.9734 0.985935
\(695\) 2.78953 0.105813
\(696\) −0.688882 −0.0261120
\(697\) −11.5712 −0.438291
\(698\) 16.2802 0.616213
\(699\) 20.1974 0.763935
\(700\) 16.6799 0.630442
\(701\) 23.9830 0.905825 0.452913 0.891555i \(-0.350385\pi\)
0.452913 + 0.891555i \(0.350385\pi\)
\(702\) −0.829389 −0.0313033
\(703\) 35.9205 1.35477
\(704\) −1.00000 −0.0376889
\(705\) −7.66074 −0.288520
\(706\) 27.7773 1.04541
\(707\) −4.30833 −0.162031
\(708\) 3.77758 0.141970
\(709\) 21.1200 0.793178 0.396589 0.917996i \(-0.370194\pi\)
0.396589 + 0.917996i \(0.370194\pi\)
\(710\) 4.41919 0.165849
\(711\) −10.5300 −0.394907
\(712\) 4.99276 0.187111
\(713\) 12.6443 0.473534
\(714\) −24.3756 −0.912233
\(715\) 0.644586 0.0241061
\(716\) −11.8556 −0.443065
\(717\) 16.3488 0.610558
\(718\) −11.6724 −0.435612
\(719\) −26.3527 −0.982789 −0.491394 0.870937i \(-0.663513\pi\)
−0.491394 + 0.870937i \(0.663513\pi\)
\(720\) 0.777182 0.0289639
\(721\) −40.7436 −1.51737
\(722\) 7.49285 0.278855
\(723\) 15.8848 0.590761
\(724\) 18.2368 0.677765
\(725\) 3.02832 0.112469
\(726\) 1.00000 0.0371135
\(727\) 34.8656 1.29310 0.646548 0.762874i \(-0.276212\pi\)
0.646548 + 0.762874i \(0.276212\pi\)
\(728\) −3.14699 −0.116635
\(729\) 1.00000 0.0370370
\(730\) −0.175792 −0.00650635
\(731\) 7.96335 0.294535
\(732\) 1.00000 0.0369611
\(733\) −15.0496 −0.555871 −0.277936 0.960600i \(-0.589650\pi\)
−0.277936 + 0.960600i \(0.589650\pi\)
\(734\) −26.9833 −0.995972
\(735\) −5.74889 −0.212051
\(736\) 5.59479 0.206227
\(737\) 8.84367 0.325761
\(738\) 1.80120 0.0663030
\(739\) 2.72565 0.100265 0.0501324 0.998743i \(-0.484036\pi\)
0.0501324 + 0.998743i \(0.484036\pi\)
\(740\) 8.22966 0.302528
\(741\) 2.81347 0.103355
\(742\) 28.3247 1.03983
\(743\) −35.2118 −1.29179 −0.645897 0.763425i \(-0.723516\pi\)
−0.645897 + 0.763425i \(0.723516\pi\)
\(744\) −2.26002 −0.0828563
\(745\) −6.60858 −0.242120
\(746\) 3.69371 0.135236
\(747\) 10.7814 0.394469
\(748\) −6.42418 −0.234891
\(749\) 43.0020 1.57126
\(750\) −7.30239 −0.266646
\(751\) 17.3514 0.633161 0.316580 0.948566i \(-0.397465\pi\)
0.316580 + 0.948566i \(0.397465\pi\)
\(752\) 9.85707 0.359450
\(753\) −0.930521 −0.0339101
\(754\) −0.571351 −0.0208074
\(755\) 5.01905 0.182662
\(756\) 3.79435 0.137999
\(757\) −16.4900 −0.599341 −0.299670 0.954043i \(-0.596877\pi\)
−0.299670 + 0.954043i \(0.596877\pi\)
\(758\) 38.5449 1.40002
\(759\) −5.59479 −0.203078
\(760\) −2.63637 −0.0956312
\(761\) −1.73716 −0.0629721 −0.0314860 0.999504i \(-0.510024\pi\)
−0.0314860 + 0.999504i \(0.510024\pi\)
\(762\) −16.2682 −0.589335
\(763\) 24.9994 0.905039
\(764\) 5.85173 0.211708
\(765\) 4.99276 0.180513
\(766\) 13.6304 0.492488
\(767\) 3.13308 0.113129
\(768\) −1.00000 −0.0360844
\(769\) 48.7609 1.75836 0.879182 0.476485i \(-0.158089\pi\)
0.879182 + 0.476485i \(0.158089\pi\)
\(770\) −2.94890 −0.106271
\(771\) −12.1287 −0.436805
\(772\) 23.2053 0.835176
\(773\) 16.0776 0.578271 0.289135 0.957288i \(-0.406632\pi\)
0.289135 + 0.957288i \(0.406632\pi\)
\(774\) −1.23959 −0.0445561
\(775\) 9.93501 0.356876
\(776\) −2.45363 −0.0880801
\(777\) 40.1787 1.44140
\(778\) 29.5694 1.06011
\(779\) −6.11006 −0.218916
\(780\) 0.644586 0.0230799
\(781\) 5.68617 0.203467
\(782\) 35.9419 1.28528
\(783\) 0.688882 0.0246186
\(784\) 7.39710 0.264182
\(785\) 16.7055 0.596246
\(786\) −7.36785 −0.262803
\(787\) −24.7989 −0.883985 −0.441992 0.897019i \(-0.645728\pi\)
−0.441992 + 0.897019i \(0.645728\pi\)
\(788\) −11.6762 −0.415949
\(789\) 30.6916 1.09265
\(790\) 8.18376 0.291165
\(791\) 32.2863 1.14797
\(792\) 1.00000 0.0355335
\(793\) 0.829389 0.0294525
\(794\) −32.3149 −1.14681
\(795\) −5.80164 −0.205763
\(796\) −6.10189 −0.216276
\(797\) 22.2114 0.786767 0.393384 0.919374i \(-0.371304\pi\)
0.393384 + 0.919374i \(0.371304\pi\)
\(798\) −12.8713 −0.455638
\(799\) 63.3236 2.24023
\(800\) 4.39599 0.155422
\(801\) −4.99276 −0.176410
\(802\) −9.61472 −0.339507
\(803\) −0.226192 −0.00798213
\(804\) 8.84367 0.311892
\(805\) 16.4985 0.581495
\(806\) −1.87443 −0.0660241
\(807\) 12.9720 0.456635
\(808\) −1.13546 −0.0399453
\(809\) −38.3358 −1.34781 −0.673907 0.738816i \(-0.735385\pi\)
−0.673907 + 0.738816i \(0.735385\pi\)
\(810\) −0.777182 −0.0273074
\(811\) −12.6512 −0.444242 −0.222121 0.975019i \(-0.571298\pi\)
−0.222121 + 0.975019i \(0.571298\pi\)
\(812\) 2.61386 0.0917285
\(813\) 12.6657 0.444204
\(814\) 10.5891 0.371148
\(815\) 18.9353 0.663275
\(816\) −6.42418 −0.224891
\(817\) 4.20496 0.147113
\(818\) 19.8458 0.693893
\(819\) 3.14699 0.109965
\(820\) −1.39986 −0.0488852
\(821\) −27.8160 −0.970784 −0.485392 0.874297i \(-0.661323\pi\)
−0.485392 + 0.874297i \(0.661323\pi\)
\(822\) −16.1360 −0.562808
\(823\) −22.1749 −0.772969 −0.386485 0.922296i \(-0.626311\pi\)
−0.386485 + 0.922296i \(0.626311\pi\)
\(824\) −10.7380 −0.374074
\(825\) −4.39599 −0.153049
\(826\) −14.3335 −0.498725
\(827\) 25.2864 0.879296 0.439648 0.898170i \(-0.355103\pi\)
0.439648 + 0.898170i \(0.355103\pi\)
\(828\) −5.59479 −0.194432
\(829\) 0.481347 0.0167179 0.00835893 0.999965i \(-0.497339\pi\)
0.00835893 + 0.999965i \(0.497339\pi\)
\(830\) −8.37908 −0.290842
\(831\) −14.3557 −0.497992
\(832\) −0.829389 −0.0287539
\(833\) 47.5203 1.64648
\(834\) 3.58929 0.124287
\(835\) −12.2957 −0.425510
\(836\) −3.39222 −0.117322
\(837\) 2.26002 0.0781177
\(838\) −21.0434 −0.726931
\(839\) −37.0881 −1.28042 −0.640212 0.768198i \(-0.721153\pi\)
−0.640212 + 0.768198i \(0.721153\pi\)
\(840\) −2.94890 −0.101747
\(841\) −28.5254 −0.983636
\(842\) 12.1741 0.419549
\(843\) 27.3160 0.940812
\(844\) −3.15597 −0.108633
\(845\) −9.56875 −0.329175
\(846\) −9.85707 −0.338893
\(847\) −3.79435 −0.130375
\(848\) 7.46497 0.256348
\(849\) 32.9040 1.12926
\(850\) 28.2406 0.968645
\(851\) −59.2438 −2.03085
\(852\) 5.68617 0.194805
\(853\) −50.6840 −1.73539 −0.867693 0.497100i \(-0.834398\pi\)
−0.867693 + 0.497100i \(0.834398\pi\)
\(854\) −3.79435 −0.129840
\(855\) 2.63637 0.0901620
\(856\) 11.3332 0.387360
\(857\) −9.07769 −0.310088 −0.155044 0.987908i \(-0.549552\pi\)
−0.155044 + 0.987908i \(0.549552\pi\)
\(858\) 0.829389 0.0283149
\(859\) 26.3285 0.898316 0.449158 0.893452i \(-0.351724\pi\)
0.449158 + 0.893452i \(0.351724\pi\)
\(860\) 0.963387 0.0328512
\(861\) −6.83438 −0.232915
\(862\) 7.06839 0.240750
\(863\) −24.4367 −0.831836 −0.415918 0.909402i \(-0.636540\pi\)
−0.415918 + 0.909402i \(0.636540\pi\)
\(864\) 1.00000 0.0340207
\(865\) −0.385155 −0.0130957
\(866\) 7.60525 0.258437
\(867\) −24.2701 −0.824255
\(868\) 8.57530 0.291065
\(869\) 10.5300 0.357207
\(870\) −0.535387 −0.0181513
\(871\) 7.33484 0.248532
\(872\) 6.58859 0.223118
\(873\) 2.45363 0.0830427
\(874\) 18.9787 0.641966
\(875\) 27.7078 0.936696
\(876\) −0.226192 −0.00764230
\(877\) 30.1107 1.01677 0.508384 0.861131i \(-0.330243\pi\)
0.508384 + 0.861131i \(0.330243\pi\)
\(878\) −18.6709 −0.630111
\(879\) 9.74062 0.328543
\(880\) −0.777182 −0.0261988
\(881\) 30.5699 1.02992 0.514962 0.857213i \(-0.327806\pi\)
0.514962 + 0.857213i \(0.327806\pi\)
\(882\) −7.39710 −0.249073
\(883\) 25.9570 0.873523 0.436761 0.899577i \(-0.356125\pi\)
0.436761 + 0.899577i \(0.356125\pi\)
\(884\) −5.32814 −0.179205
\(885\) 2.93587 0.0986880
\(886\) 10.7433 0.360930
\(887\) 6.81823 0.228934 0.114467 0.993427i \(-0.463484\pi\)
0.114467 + 0.993427i \(0.463484\pi\)
\(888\) 10.5891 0.355347
\(889\) 61.7273 2.07027
\(890\) 3.88028 0.130067
\(891\) −1.00000 −0.0335013
\(892\) 12.5155 0.419050
\(893\) 33.4373 1.11894
\(894\) −8.50326 −0.284392
\(895\) −9.21396 −0.307989
\(896\) 3.79435 0.126760
\(897\) −4.64025 −0.154934
\(898\) −36.3330 −1.21245
\(899\) 1.55689 0.0519251
\(900\) −4.39599 −0.146533
\(901\) 47.9563 1.59766
\(902\) −1.80120 −0.0599734
\(903\) 4.70344 0.156521
\(904\) 8.50905 0.283007
\(905\) 14.1733 0.471136
\(906\) 6.45800 0.214553
\(907\) 2.04272 0.0678274 0.0339137 0.999425i \(-0.489203\pi\)
0.0339137 + 0.999425i \(0.489203\pi\)
\(908\) −4.01934 −0.133387
\(909\) 1.13546 0.0376608
\(910\) −2.44578 −0.0810770
\(911\) −46.0830 −1.52680 −0.763398 0.645928i \(-0.776471\pi\)
−0.763398 + 0.645928i \(0.776471\pi\)
\(912\) −3.39222 −0.112328
\(913\) −10.7814 −0.356811
\(914\) 21.9436 0.725829
\(915\) 0.777182 0.0256928
\(916\) −15.5815 −0.514828
\(917\) 27.9562 0.923196
\(918\) 6.42418 0.212029
\(919\) 4.13868 0.136522 0.0682612 0.997667i \(-0.478255\pi\)
0.0682612 + 0.997667i \(0.478255\pi\)
\(920\) 4.34817 0.143355
\(921\) 8.60709 0.283613
\(922\) −19.7455 −0.650283
\(923\) 4.71604 0.155230
\(924\) −3.79435 −0.124825
\(925\) −46.5495 −1.53054
\(926\) −36.6840 −1.20551
\(927\) 10.7380 0.352681
\(928\) 0.688882 0.0226137
\(929\) 31.4418 1.03157 0.515785 0.856718i \(-0.327500\pi\)
0.515785 + 0.856718i \(0.327500\pi\)
\(930\) −1.75645 −0.0575961
\(931\) 25.0926 0.822376
\(932\) −20.1974 −0.661587
\(933\) −5.85160 −0.191573
\(934\) 36.7614 1.20287
\(935\) −4.99276 −0.163281
\(936\) 0.829389 0.0271094
\(937\) 49.1285 1.60496 0.802479 0.596680i \(-0.203514\pi\)
0.802479 + 0.596680i \(0.203514\pi\)
\(938\) −33.5560 −1.09564
\(939\) −6.45719 −0.210723
\(940\) 7.66074 0.249866
\(941\) 42.3067 1.37916 0.689580 0.724210i \(-0.257795\pi\)
0.689580 + 0.724210i \(0.257795\pi\)
\(942\) 21.4950 0.700345
\(943\) 10.0773 0.328163
\(944\) −3.77758 −0.122950
\(945\) 2.94890 0.0959278
\(946\) 1.23959 0.0403026
\(947\) 0.991701 0.0322260 0.0161130 0.999870i \(-0.494871\pi\)
0.0161130 + 0.999870i \(0.494871\pi\)
\(948\) 10.5300 0.342000
\(949\) −0.187601 −0.00608978
\(950\) 14.9122 0.483814
\(951\) −11.2731 −0.365555
\(952\) 24.3756 0.790017
\(953\) 0.570606 0.0184837 0.00924187 0.999957i \(-0.497058\pi\)
0.00924187 + 0.999957i \(0.497058\pi\)
\(954\) −7.46497 −0.241687
\(955\) 4.54786 0.147165
\(956\) −16.3488 −0.528759
\(957\) −0.688882 −0.0222684
\(958\) 16.0940 0.519975
\(959\) 61.2257 1.97708
\(960\) −0.777182 −0.0250834
\(961\) −25.8923 −0.835236
\(962\) 8.78248 0.283158
\(963\) −11.3332 −0.365206
\(964\) −15.8848 −0.511614
\(965\) 18.0347 0.580558
\(966\) 21.2286 0.683019
\(967\) 42.4682 1.36569 0.682843 0.730565i \(-0.260743\pi\)
0.682843 + 0.730565i \(0.260743\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −21.7922 −0.700067
\(970\) −1.90692 −0.0612274
\(971\) 6.39066 0.205086 0.102543 0.994729i \(-0.467302\pi\)
0.102543 + 0.994729i \(0.467302\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −13.6190 −0.436606
\(974\) −19.4585 −0.623489
\(975\) −3.64598 −0.116765
\(976\) −1.00000 −0.0320092
\(977\) 9.10943 0.291436 0.145718 0.989326i \(-0.453451\pi\)
0.145718 + 0.989326i \(0.453451\pi\)
\(978\) 24.3641 0.779076
\(979\) 4.99276 0.159569
\(980\) 5.74889 0.183642
\(981\) −6.58859 −0.210357
\(982\) −18.8815 −0.602532
\(983\) −15.7771 −0.503210 −0.251605 0.967830i \(-0.580958\pi\)
−0.251605 + 0.967830i \(0.580958\pi\)
\(984\) −1.80120 −0.0574201
\(985\) −9.07456 −0.289140
\(986\) 4.42550 0.140937
\(987\) 37.4012 1.19049
\(988\) −2.81347 −0.0895083
\(989\) −6.93525 −0.220528
\(990\) 0.777182 0.0247005
\(991\) 55.1508 1.75192 0.875962 0.482380i \(-0.160228\pi\)
0.875962 + 0.482380i \(0.160228\pi\)
\(992\) 2.26002 0.0717557
\(993\) 32.4487 1.02973
\(994\) −21.5753 −0.684327
\(995\) −4.74228 −0.150340
\(996\) −10.7814 −0.341620
\(997\) −14.8620 −0.470686 −0.235343 0.971912i \(-0.575621\pi\)
−0.235343 + 0.971912i \(0.575621\pi\)
\(998\) −8.27868 −0.262057
\(999\) −10.5891 −0.335024
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 4026.2.a.y.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.y.1.5 7 1.1 even 1 trivial