Properties

Label 4029.2.a.g.1.8
Level $4029$
Weight $2$
Character 4029.1
Self dual yes
Analytic conductor $32.172$
Analytic rank $1$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.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: \(32.1717269744\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 4029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.04848 q^{2} -1.00000 q^{3} -0.900691 q^{4} -0.0290827 q^{5} +1.04848 q^{6} +2.65326 q^{7} +3.04131 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.04848 q^{2} -1.00000 q^{3} -0.900691 q^{4} -0.0290827 q^{5} +1.04848 q^{6} +2.65326 q^{7} +3.04131 q^{8} +1.00000 q^{9} +0.0304926 q^{10} -4.86193 q^{11} +0.900691 q^{12} +5.69010 q^{13} -2.78189 q^{14} +0.0290827 q^{15} -1.38737 q^{16} -1.00000 q^{17} -1.04848 q^{18} -4.01215 q^{19} +0.0261945 q^{20} -2.65326 q^{21} +5.09763 q^{22} +6.54961 q^{23} -3.04131 q^{24} -4.99915 q^{25} -5.96595 q^{26} -1.00000 q^{27} -2.38977 q^{28} +2.20837 q^{29} -0.0304926 q^{30} -4.01939 q^{31} -4.62800 q^{32} +4.86193 q^{33} +1.04848 q^{34} -0.0771639 q^{35} -0.900691 q^{36} -9.08854 q^{37} +4.20666 q^{38} -5.69010 q^{39} -0.0884495 q^{40} +3.70009 q^{41} +2.78189 q^{42} -11.0541 q^{43} +4.37910 q^{44} -0.0290827 q^{45} -6.86713 q^{46} +10.4871 q^{47} +1.38737 q^{48} +0.0397868 q^{49} +5.24151 q^{50} +1.00000 q^{51} -5.12502 q^{52} +1.67145 q^{53} +1.04848 q^{54} +0.141398 q^{55} +8.06940 q^{56} +4.01215 q^{57} -2.31543 q^{58} -9.85933 q^{59} -0.0261945 q^{60} +10.0521 q^{61} +4.21425 q^{62} +2.65326 q^{63} +7.62711 q^{64} -0.165483 q^{65} -5.09763 q^{66} -5.10986 q^{67} +0.900691 q^{68} -6.54961 q^{69} +0.0809047 q^{70} +6.23056 q^{71} +3.04131 q^{72} -2.43967 q^{73} +9.52914 q^{74} +4.99915 q^{75} +3.61371 q^{76} -12.9000 q^{77} +5.96595 q^{78} -1.00000 q^{79} +0.0403485 q^{80} +1.00000 q^{81} -3.87947 q^{82} +9.03700 q^{83} +2.38977 q^{84} +0.0290827 q^{85} +11.5900 q^{86} -2.20837 q^{87} -14.7867 q^{88} -1.57190 q^{89} +0.0304926 q^{90} +15.0973 q^{91} -5.89917 q^{92} +4.01939 q^{93} -10.9955 q^{94} +0.116684 q^{95} +4.62800 q^{96} -4.85856 q^{97} -0.0417156 q^{98} -4.86193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04848 −0.741387 −0.370693 0.928755i \(-0.620880\pi\)
−0.370693 + 0.928755i \(0.620880\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.900691 −0.450346
\(5\) −0.0290827 −0.0130062 −0.00650308 0.999979i \(-0.502070\pi\)
−0.00650308 + 0.999979i \(0.502070\pi\)
\(6\) 1.04848 0.428040
\(7\) 2.65326 1.00284 0.501419 0.865205i \(-0.332812\pi\)
0.501419 + 0.865205i \(0.332812\pi\)
\(8\) 3.04131 1.07527
\(9\) 1.00000 0.333333
\(10\) 0.0304926 0.00964260
\(11\) −4.86193 −1.46593 −0.732963 0.680268i \(-0.761863\pi\)
−0.732963 + 0.680268i \(0.761863\pi\)
\(12\) 0.900691 0.260007
\(13\) 5.69010 1.57815 0.789074 0.614298i \(-0.210561\pi\)
0.789074 + 0.614298i \(0.210561\pi\)
\(14\) −2.78189 −0.743491
\(15\) 0.0290827 0.00750911
\(16\) −1.38737 −0.346843
\(17\) −1.00000 −0.242536
\(18\) −1.04848 −0.247129
\(19\) −4.01215 −0.920450 −0.460225 0.887802i \(-0.652231\pi\)
−0.460225 + 0.887802i \(0.652231\pi\)
\(20\) 0.0261945 0.00585727
\(21\) −2.65326 −0.578989
\(22\) 5.09763 1.08682
\(23\) 6.54961 1.36569 0.682844 0.730564i \(-0.260743\pi\)
0.682844 + 0.730564i \(0.260743\pi\)
\(24\) −3.04131 −0.620806
\(25\) −4.99915 −0.999831
\(26\) −5.96595 −1.17002
\(27\) −1.00000 −0.192450
\(28\) −2.38977 −0.451624
\(29\) 2.20837 0.410085 0.205042 0.978753i \(-0.434267\pi\)
0.205042 + 0.978753i \(0.434267\pi\)
\(30\) −0.0304926 −0.00556716
\(31\) −4.01939 −0.721903 −0.360952 0.932585i \(-0.617548\pi\)
−0.360952 + 0.932585i \(0.617548\pi\)
\(32\) −4.62800 −0.818122
\(33\) 4.86193 0.846353
\(34\) 1.04848 0.179813
\(35\) −0.0771639 −0.0130431
\(36\) −0.900691 −0.150115
\(37\) −9.08854 −1.49415 −0.747073 0.664742i \(-0.768541\pi\)
−0.747073 + 0.664742i \(0.768541\pi\)
\(38\) 4.20666 0.682410
\(39\) −5.69010 −0.911145
\(40\) −0.0884495 −0.0139851
\(41\) 3.70009 0.577857 0.288928 0.957351i \(-0.406701\pi\)
0.288928 + 0.957351i \(0.406701\pi\)
\(42\) 2.78189 0.429255
\(43\) −11.0541 −1.68573 −0.842867 0.538122i \(-0.819134\pi\)
−0.842867 + 0.538122i \(0.819134\pi\)
\(44\) 4.37910 0.660174
\(45\) −0.0290827 −0.00433539
\(46\) −6.86713 −1.01250
\(47\) 10.4871 1.52970 0.764849 0.644209i \(-0.222814\pi\)
0.764849 + 0.644209i \(0.222814\pi\)
\(48\) 1.38737 0.200250
\(49\) 0.0397868 0.00568383
\(50\) 5.24151 0.741261
\(51\) 1.00000 0.140028
\(52\) −5.12502 −0.710712
\(53\) 1.67145 0.229592 0.114796 0.993389i \(-0.463379\pi\)
0.114796 + 0.993389i \(0.463379\pi\)
\(54\) 1.04848 0.142680
\(55\) 0.141398 0.0190661
\(56\) 8.06940 1.07832
\(57\) 4.01215 0.531422
\(58\) −2.31543 −0.304031
\(59\) −9.85933 −1.28357 −0.641787 0.766883i \(-0.721807\pi\)
−0.641787 + 0.766883i \(0.721807\pi\)
\(60\) −0.0261945 −0.00338170
\(61\) 10.0521 1.28704 0.643519 0.765430i \(-0.277474\pi\)
0.643519 + 0.765430i \(0.277474\pi\)
\(62\) 4.21425 0.535210
\(63\) 2.65326 0.334279
\(64\) 7.62711 0.953388
\(65\) −0.165483 −0.0205257
\(66\) −5.09763 −0.627475
\(67\) −5.10986 −0.624268 −0.312134 0.950038i \(-0.601044\pi\)
−0.312134 + 0.950038i \(0.601044\pi\)
\(68\) 0.900691 0.109225
\(69\) −6.54961 −0.788480
\(70\) 0.0809047 0.00966996
\(71\) 6.23056 0.739431 0.369716 0.929145i \(-0.379455\pi\)
0.369716 + 0.929145i \(0.379455\pi\)
\(72\) 3.04131 0.358422
\(73\) −2.43967 −0.285542 −0.142771 0.989756i \(-0.545601\pi\)
−0.142771 + 0.989756i \(0.545601\pi\)
\(74\) 9.52914 1.10774
\(75\) 4.99915 0.577253
\(76\) 3.61371 0.414521
\(77\) −12.9000 −1.47009
\(78\) 5.96595 0.675511
\(79\) −1.00000 −0.112509
\(80\) 0.0403485 0.00451110
\(81\) 1.00000 0.111111
\(82\) −3.87947 −0.428415
\(83\) 9.03700 0.991940 0.495970 0.868340i \(-0.334813\pi\)
0.495970 + 0.868340i \(0.334813\pi\)
\(84\) 2.38977 0.260745
\(85\) 0.0290827 0.00315446
\(86\) 11.5900 1.24978
\(87\) −2.20837 −0.236762
\(88\) −14.7867 −1.57626
\(89\) −1.57190 −0.166621 −0.0833104 0.996524i \(-0.526549\pi\)
−0.0833104 + 0.996524i \(0.526549\pi\)
\(90\) 0.0304926 0.00321420
\(91\) 15.0973 1.58263
\(92\) −5.89917 −0.615031
\(93\) 4.01939 0.416791
\(94\) −10.9955 −1.13410
\(95\) 0.116684 0.0119715
\(96\) 4.62800 0.472343
\(97\) −4.85856 −0.493312 −0.246656 0.969103i \(-0.579332\pi\)
−0.246656 + 0.969103i \(0.579332\pi\)
\(98\) −0.0417156 −0.00421391
\(99\) −4.86193 −0.488642
\(100\) 4.50269 0.450269
\(101\) 9.77685 0.972833 0.486416 0.873727i \(-0.338304\pi\)
0.486416 + 0.873727i \(0.338304\pi\)
\(102\) −1.04848 −0.103815
\(103\) 3.93988 0.388207 0.194104 0.980981i \(-0.437820\pi\)
0.194104 + 0.980981i \(0.437820\pi\)
\(104\) 17.3054 1.69693
\(105\) 0.0771639 0.00753042
\(106\) −1.75248 −0.170216
\(107\) −12.4093 −1.19965 −0.599825 0.800131i \(-0.704763\pi\)
−0.599825 + 0.800131i \(0.704763\pi\)
\(108\) 0.900691 0.0866690
\(109\) −6.91498 −0.662335 −0.331167 0.943572i \(-0.607442\pi\)
−0.331167 + 0.943572i \(0.607442\pi\)
\(110\) −0.148253 −0.0141353
\(111\) 9.08854 0.862646
\(112\) −3.68106 −0.347828
\(113\) −14.2593 −1.34140 −0.670702 0.741727i \(-0.734007\pi\)
−0.670702 + 0.741727i \(0.734007\pi\)
\(114\) −4.20666 −0.393989
\(115\) −0.190480 −0.0177624
\(116\) −1.98906 −0.184680
\(117\) 5.69010 0.526050
\(118\) 10.3373 0.951626
\(119\) −2.65326 −0.243224
\(120\) 0.0884495 0.00807430
\(121\) 12.6384 1.14894
\(122\) −10.5394 −0.954193
\(123\) −3.70009 −0.333626
\(124\) 3.62023 0.325106
\(125\) 0.290802 0.0260101
\(126\) −2.78189 −0.247830
\(127\) −0.354495 −0.0314564 −0.0157282 0.999876i \(-0.505007\pi\)
−0.0157282 + 0.999876i \(0.505007\pi\)
\(128\) 1.25913 0.111293
\(129\) 11.0541 0.973259
\(130\) 0.173506 0.0152175
\(131\) 6.11834 0.534562 0.267281 0.963619i \(-0.413875\pi\)
0.267281 + 0.963619i \(0.413875\pi\)
\(132\) −4.37910 −0.381151
\(133\) −10.6453 −0.923062
\(134\) 5.35758 0.462824
\(135\) 0.0290827 0.00250304
\(136\) −3.04131 −0.260791
\(137\) 8.20828 0.701281 0.350640 0.936510i \(-0.385964\pi\)
0.350640 + 0.936510i \(0.385964\pi\)
\(138\) 6.86713 0.584569
\(139\) 2.79349 0.236941 0.118471 0.992958i \(-0.462201\pi\)
0.118471 + 0.992958i \(0.462201\pi\)
\(140\) 0.0695008 0.00587389
\(141\) −10.4871 −0.883172
\(142\) −6.53261 −0.548204
\(143\) −27.6648 −2.31345
\(144\) −1.38737 −0.115614
\(145\) −0.0642254 −0.00533363
\(146\) 2.55795 0.211697
\(147\) −0.0397868 −0.00328156
\(148\) 8.18596 0.672882
\(149\) 13.1191 1.07476 0.537378 0.843342i \(-0.319415\pi\)
0.537378 + 0.843342i \(0.319415\pi\)
\(150\) −5.24151 −0.427967
\(151\) 1.38193 0.112460 0.0562299 0.998418i \(-0.482092\pi\)
0.0562299 + 0.998418i \(0.482092\pi\)
\(152\) −12.2022 −0.989730
\(153\) −1.00000 −0.0808452
\(154\) 13.5253 1.08990
\(155\) 0.116895 0.00938919
\(156\) 5.12502 0.410330
\(157\) 6.17154 0.492543 0.246271 0.969201i \(-0.420795\pi\)
0.246271 + 0.969201i \(0.420795\pi\)
\(158\) 1.04848 0.0834125
\(159\) −1.67145 −0.132555
\(160\) 0.134594 0.0106406
\(161\) 17.3778 1.36956
\(162\) −1.04848 −0.0823763
\(163\) −7.23385 −0.566599 −0.283300 0.959031i \(-0.591429\pi\)
−0.283300 + 0.959031i \(0.591429\pi\)
\(164\) −3.33264 −0.260235
\(165\) −0.141398 −0.0110078
\(166\) −9.47511 −0.735411
\(167\) −7.66967 −0.593497 −0.296749 0.954956i \(-0.595902\pi\)
−0.296749 + 0.954956i \(0.595902\pi\)
\(168\) −8.06940 −0.622568
\(169\) 19.3772 1.49055
\(170\) −0.0304926 −0.00233867
\(171\) −4.01215 −0.306817
\(172\) 9.95633 0.759163
\(173\) 4.59359 0.349244 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(174\) 2.31543 0.175533
\(175\) −13.2641 −1.00267
\(176\) 6.74531 0.508447
\(177\) 9.85933 0.741072
\(178\) 1.64810 0.123530
\(179\) −11.8850 −0.888325 −0.444162 0.895946i \(-0.646499\pi\)
−0.444162 + 0.895946i \(0.646499\pi\)
\(180\) 0.0261945 0.00195242
\(181\) 1.12907 0.0839232 0.0419616 0.999119i \(-0.486639\pi\)
0.0419616 + 0.999119i \(0.486639\pi\)
\(182\) −15.8292 −1.17334
\(183\) −10.0521 −0.743072
\(184\) 19.9194 1.46848
\(185\) 0.264319 0.0194331
\(186\) −4.21425 −0.309003
\(187\) 4.86193 0.355539
\(188\) −9.44562 −0.688893
\(189\) −2.65326 −0.192996
\(190\) −0.122341 −0.00887553
\(191\) −21.6882 −1.56931 −0.784653 0.619935i \(-0.787159\pi\)
−0.784653 + 0.619935i \(0.787159\pi\)
\(192\) −7.62711 −0.550439
\(193\) −21.2176 −1.52727 −0.763637 0.645646i \(-0.776588\pi\)
−0.763637 + 0.645646i \(0.776588\pi\)
\(194\) 5.09410 0.365735
\(195\) 0.165483 0.0118505
\(196\) −0.0358356 −0.00255969
\(197\) 1.92916 0.137447 0.0687236 0.997636i \(-0.478107\pi\)
0.0687236 + 0.997636i \(0.478107\pi\)
\(198\) 5.09763 0.362273
\(199\) −11.8049 −0.836824 −0.418412 0.908257i \(-0.637413\pi\)
−0.418412 + 0.908257i \(0.637413\pi\)
\(200\) −15.2040 −1.07509
\(201\) 5.10986 0.360421
\(202\) −10.2508 −0.721245
\(203\) 5.85939 0.411248
\(204\) −0.900691 −0.0630610
\(205\) −0.107608 −0.00751570
\(206\) −4.13088 −0.287812
\(207\) 6.54961 0.455229
\(208\) −7.89429 −0.547370
\(209\) 19.5068 1.34931
\(210\) −0.0809047 −0.00558296
\(211\) 6.25806 0.430823 0.215411 0.976523i \(-0.430891\pi\)
0.215411 + 0.976523i \(0.430891\pi\)
\(212\) −1.50546 −0.103396
\(213\) −6.23056 −0.426911
\(214\) 13.0109 0.889405
\(215\) 0.321483 0.0219249
\(216\) −3.04131 −0.206935
\(217\) −10.6645 −0.723952
\(218\) 7.25021 0.491046
\(219\) 2.43967 0.164858
\(220\) −0.127356 −0.00858633
\(221\) −5.69010 −0.382757
\(222\) −9.52914 −0.639554
\(223\) −19.3188 −1.29368 −0.646840 0.762626i \(-0.723910\pi\)
−0.646840 + 0.762626i \(0.723910\pi\)
\(224\) −12.2793 −0.820444
\(225\) −4.99915 −0.333277
\(226\) 14.9506 0.994499
\(227\) 4.30211 0.285541 0.142771 0.989756i \(-0.454399\pi\)
0.142771 + 0.989756i \(0.454399\pi\)
\(228\) −3.61371 −0.239324
\(229\) −22.8035 −1.50690 −0.753450 0.657505i \(-0.771612\pi\)
−0.753450 + 0.657505i \(0.771612\pi\)
\(230\) 0.199714 0.0131688
\(231\) 12.9000 0.848755
\(232\) 6.71636 0.440950
\(233\) 16.3679 1.07230 0.536148 0.844124i \(-0.319879\pi\)
0.536148 + 0.844124i \(0.319879\pi\)
\(234\) −5.96595 −0.390006
\(235\) −0.304992 −0.0198955
\(236\) 8.88021 0.578052
\(237\) 1.00000 0.0649570
\(238\) 2.78189 0.180323
\(239\) −12.4023 −0.802238 −0.401119 0.916026i \(-0.631379\pi\)
−0.401119 + 0.916026i \(0.631379\pi\)
\(240\) −0.0403485 −0.00260449
\(241\) 7.49506 0.482800 0.241400 0.970426i \(-0.422393\pi\)
0.241400 + 0.970426i \(0.422393\pi\)
\(242\) −13.2511 −0.851810
\(243\) −1.00000 −0.0641500
\(244\) −9.05382 −0.579612
\(245\) −0.00115711 −7.39248e−5 0
\(246\) 3.87947 0.247346
\(247\) −22.8295 −1.45261
\(248\) −12.2242 −0.776239
\(249\) −9.03700 −0.572697
\(250\) −0.304900 −0.0192836
\(251\) −27.1669 −1.71476 −0.857380 0.514684i \(-0.827909\pi\)
−0.857380 + 0.514684i \(0.827909\pi\)
\(252\) −2.38977 −0.150541
\(253\) −31.8437 −2.00200
\(254\) 0.371681 0.0233213
\(255\) −0.0290827 −0.00182123
\(256\) −16.5744 −1.03590
\(257\) 17.1018 1.06678 0.533390 0.845870i \(-0.320918\pi\)
0.533390 + 0.845870i \(0.320918\pi\)
\(258\) −11.5900 −0.721561
\(259\) −24.1142 −1.49839
\(260\) 0.149049 0.00924364
\(261\) 2.20837 0.136695
\(262\) −6.41495 −0.396317
\(263\) −24.1366 −1.48832 −0.744162 0.667999i \(-0.767151\pi\)
−0.744162 + 0.667999i \(0.767151\pi\)
\(264\) 14.7867 0.910056
\(265\) −0.0486103 −0.00298611
\(266\) 11.1613 0.684346
\(267\) 1.57190 0.0961986
\(268\) 4.60240 0.281136
\(269\) −4.48564 −0.273494 −0.136747 0.990606i \(-0.543665\pi\)
−0.136747 + 0.990606i \(0.543665\pi\)
\(270\) −0.0304926 −0.00185572
\(271\) 26.4955 1.60949 0.804743 0.593624i \(-0.202303\pi\)
0.804743 + 0.593624i \(0.202303\pi\)
\(272\) 1.38737 0.0841219
\(273\) −15.0973 −0.913730
\(274\) −8.60621 −0.519920
\(275\) 24.3055 1.46568
\(276\) 5.89917 0.355089
\(277\) −1.86292 −0.111932 −0.0559661 0.998433i \(-0.517824\pi\)
−0.0559661 + 0.998433i \(0.517824\pi\)
\(278\) −2.92892 −0.175665
\(279\) −4.01939 −0.240634
\(280\) −0.234680 −0.0140248
\(281\) −6.81221 −0.406382 −0.203191 0.979139i \(-0.565131\pi\)
−0.203191 + 0.979139i \(0.565131\pi\)
\(282\) 10.9955 0.654772
\(283\) −14.4451 −0.858673 −0.429337 0.903145i \(-0.641253\pi\)
−0.429337 + 0.903145i \(0.641253\pi\)
\(284\) −5.61181 −0.332999
\(285\) −0.116684 −0.00691176
\(286\) 29.0060 1.71516
\(287\) 9.81729 0.579497
\(288\) −4.62800 −0.272707
\(289\) 1.00000 0.0588235
\(290\) 0.0673390 0.00395428
\(291\) 4.85856 0.284814
\(292\) 2.19739 0.128593
\(293\) −12.8907 −0.753084 −0.376542 0.926400i \(-0.622887\pi\)
−0.376542 + 0.926400i \(0.622887\pi\)
\(294\) 0.0417156 0.00243290
\(295\) 0.286735 0.0166944
\(296\) −27.6411 −1.60661
\(297\) 4.86193 0.282118
\(298\) −13.7551 −0.796809
\(299\) 37.2679 2.15526
\(300\) −4.50269 −0.259963
\(301\) −29.3294 −1.69052
\(302\) −1.44892 −0.0833761
\(303\) −9.77685 −0.561665
\(304\) 5.56635 0.319252
\(305\) −0.292341 −0.0167394
\(306\) 1.04848 0.0599376
\(307\) −32.5298 −1.85658 −0.928288 0.371862i \(-0.878719\pi\)
−0.928288 + 0.371862i \(0.878719\pi\)
\(308\) 11.6189 0.662047
\(309\) −3.93988 −0.224132
\(310\) −0.122561 −0.00696102
\(311\) 28.1002 1.59342 0.796709 0.604363i \(-0.206572\pi\)
0.796709 + 0.604363i \(0.206572\pi\)
\(312\) −17.3054 −0.979724
\(313\) 4.42249 0.249974 0.124987 0.992158i \(-0.460111\pi\)
0.124987 + 0.992158i \(0.460111\pi\)
\(314\) −6.47074 −0.365165
\(315\) −0.0771639 −0.00434769
\(316\) 0.900691 0.0506678
\(317\) −26.9923 −1.51604 −0.758019 0.652233i \(-0.773832\pi\)
−0.758019 + 0.652233i \(0.773832\pi\)
\(318\) 1.75248 0.0982744
\(319\) −10.7370 −0.601154
\(320\) −0.221817 −0.0123999
\(321\) 12.4093 0.692619
\(322\) −18.2203 −1.01538
\(323\) 4.01215 0.223242
\(324\) −0.900691 −0.0500384
\(325\) −28.4457 −1.57788
\(326\) 7.58455 0.420069
\(327\) 6.91498 0.382399
\(328\) 11.2531 0.621350
\(329\) 27.8250 1.53404
\(330\) 0.148253 0.00816104
\(331\) −23.4339 −1.28804 −0.644021 0.765008i \(-0.722735\pi\)
−0.644021 + 0.765008i \(0.722735\pi\)
\(332\) −8.13955 −0.446716
\(333\) −9.08854 −0.498049
\(334\) 8.04150 0.440011
\(335\) 0.148608 0.00811934
\(336\) 3.68106 0.200818
\(337\) −6.05229 −0.329689 −0.164845 0.986320i \(-0.552712\pi\)
−0.164845 + 0.986320i \(0.552712\pi\)
\(338\) −20.3166 −1.10508
\(339\) 14.2593 0.774460
\(340\) −0.0261945 −0.00142060
\(341\) 19.5420 1.05826
\(342\) 4.20666 0.227470
\(343\) −18.4673 −0.997138
\(344\) −33.6190 −1.81261
\(345\) 0.190480 0.0102551
\(346\) −4.81628 −0.258925
\(347\) −22.5338 −1.20968 −0.604839 0.796347i \(-0.706763\pi\)
−0.604839 + 0.796347i \(0.706763\pi\)
\(348\) 1.98906 0.106625
\(349\) −2.38801 −0.127827 −0.0639137 0.997955i \(-0.520358\pi\)
−0.0639137 + 0.997955i \(0.520358\pi\)
\(350\) 13.9071 0.743365
\(351\) −5.69010 −0.303715
\(352\) 22.5010 1.19931
\(353\) 20.0148 1.06528 0.532640 0.846342i \(-0.321200\pi\)
0.532640 + 0.846342i \(0.321200\pi\)
\(354\) −10.3373 −0.549421
\(355\) −0.181201 −0.00961716
\(356\) 1.41579 0.0750369
\(357\) 2.65326 0.140425
\(358\) 12.4611 0.658592
\(359\) −23.8118 −1.25674 −0.628368 0.777916i \(-0.716277\pi\)
−0.628368 + 0.777916i \(0.716277\pi\)
\(360\) −0.0884495 −0.00466170
\(361\) −2.90266 −0.152771
\(362\) −1.18381 −0.0622195
\(363\) −12.6384 −0.663341
\(364\) −13.5980 −0.712729
\(365\) 0.0709522 0.00371381
\(366\) 10.5394 0.550903
\(367\) 21.0106 1.09674 0.548372 0.836234i \(-0.315248\pi\)
0.548372 + 0.836234i \(0.315248\pi\)
\(368\) −9.08675 −0.473680
\(369\) 3.70009 0.192619
\(370\) −0.277133 −0.0144074
\(371\) 4.43480 0.230243
\(372\) −3.62023 −0.187700
\(373\) −36.7765 −1.90422 −0.952108 0.305761i \(-0.901089\pi\)
−0.952108 + 0.305761i \(0.901089\pi\)
\(374\) −5.09763 −0.263592
\(375\) −0.290802 −0.0150170
\(376\) 31.8945 1.64483
\(377\) 12.5659 0.647175
\(378\) 2.78189 0.143085
\(379\) 28.9867 1.48894 0.744472 0.667653i \(-0.232701\pi\)
0.744472 + 0.667653i \(0.232701\pi\)
\(380\) −0.105096 −0.00539132
\(381\) 0.354495 0.0181613
\(382\) 22.7397 1.16346
\(383\) −10.3087 −0.526752 −0.263376 0.964693i \(-0.584836\pi\)
−0.263376 + 0.964693i \(0.584836\pi\)
\(384\) −1.25913 −0.0642548
\(385\) 0.375165 0.0191202
\(386\) 22.2462 1.13230
\(387\) −11.0541 −0.561911
\(388\) 4.37607 0.222161
\(389\) −12.0478 −0.610847 −0.305423 0.952217i \(-0.598798\pi\)
−0.305423 + 0.952217i \(0.598798\pi\)
\(390\) −0.173506 −0.00878580
\(391\) −6.54961 −0.331228
\(392\) 0.121004 0.00611163
\(393\) −6.11834 −0.308629
\(394\) −2.02269 −0.101902
\(395\) 0.0290827 0.00146331
\(396\) 4.37910 0.220058
\(397\) −14.4500 −0.725227 −0.362614 0.931940i \(-0.618115\pi\)
−0.362614 + 0.931940i \(0.618115\pi\)
\(398\) 12.3771 0.620410
\(399\) 10.6453 0.532930
\(400\) 6.93569 0.346785
\(401\) −28.3766 −1.41706 −0.708531 0.705680i \(-0.750642\pi\)
−0.708531 + 0.705680i \(0.750642\pi\)
\(402\) −5.35758 −0.267212
\(403\) −22.8707 −1.13927
\(404\) −8.80592 −0.438111
\(405\) −0.0290827 −0.00144513
\(406\) −6.14345 −0.304894
\(407\) 44.1878 2.19031
\(408\) 3.04131 0.150568
\(409\) −3.27719 −0.162046 −0.0810232 0.996712i \(-0.525819\pi\)
−0.0810232 + 0.996712i \(0.525819\pi\)
\(410\) 0.112825 0.00557204
\(411\) −8.20828 −0.404885
\(412\) −3.54861 −0.174827
\(413\) −26.1594 −1.28722
\(414\) −6.86713 −0.337501
\(415\) −0.262820 −0.0129013
\(416\) −26.3338 −1.29112
\(417\) −2.79349 −0.136798
\(418\) −20.4525 −1.00036
\(419\) −18.3150 −0.894747 −0.447373 0.894347i \(-0.647640\pi\)
−0.447373 + 0.894347i \(0.647640\pi\)
\(420\) −0.0695008 −0.00339129
\(421\) −3.92987 −0.191530 −0.0957651 0.995404i \(-0.530530\pi\)
−0.0957651 + 0.995404i \(0.530530\pi\)
\(422\) −6.56145 −0.319406
\(423\) 10.4871 0.509899
\(424\) 5.08342 0.246872
\(425\) 4.99915 0.242495
\(426\) 6.53261 0.316506
\(427\) 26.6708 1.29069
\(428\) 11.1769 0.540257
\(429\) 27.6648 1.33567
\(430\) −0.337068 −0.0162549
\(431\) 17.8750 0.861007 0.430503 0.902589i \(-0.358336\pi\)
0.430503 + 0.902589i \(0.358336\pi\)
\(432\) 1.38737 0.0667500
\(433\) 31.2642 1.50246 0.751231 0.660040i \(-0.229461\pi\)
0.751231 + 0.660040i \(0.229461\pi\)
\(434\) 11.1815 0.536729
\(435\) 0.0642254 0.00307937
\(436\) 6.22826 0.298280
\(437\) −26.2780 −1.25705
\(438\) −2.55795 −0.122223
\(439\) −7.50935 −0.358402 −0.179201 0.983813i \(-0.557351\pi\)
−0.179201 + 0.983813i \(0.557351\pi\)
\(440\) 0.430035 0.0205011
\(441\) 0.0397868 0.00189461
\(442\) 5.96595 0.283771
\(443\) 13.1677 0.625617 0.312809 0.949816i \(-0.398730\pi\)
0.312809 + 0.949816i \(0.398730\pi\)
\(444\) −8.18596 −0.388489
\(445\) 0.0457150 0.00216710
\(446\) 20.2553 0.959117
\(447\) −13.1191 −0.620510
\(448\) 20.2367 0.956094
\(449\) 13.3870 0.631771 0.315885 0.948797i \(-0.397698\pi\)
0.315885 + 0.948797i \(0.397698\pi\)
\(450\) 5.24151 0.247087
\(451\) −17.9896 −0.847096
\(452\) 12.8432 0.604095
\(453\) −1.38193 −0.0649286
\(454\) −4.51068 −0.211697
\(455\) −0.439070 −0.0205839
\(456\) 12.2022 0.571421
\(457\) 0.813175 0.0380387 0.0190194 0.999819i \(-0.493946\pi\)
0.0190194 + 0.999819i \(0.493946\pi\)
\(458\) 23.9090 1.11720
\(459\) 1.00000 0.0466760
\(460\) 0.171564 0.00799920
\(461\) −21.8646 −1.01834 −0.509169 0.860667i \(-0.670047\pi\)
−0.509169 + 0.860667i \(0.670047\pi\)
\(462\) −13.5253 −0.629256
\(463\) 13.5844 0.631322 0.315661 0.948872i \(-0.397774\pi\)
0.315661 + 0.948872i \(0.397774\pi\)
\(464\) −3.06384 −0.142235
\(465\) −0.116895 −0.00542085
\(466\) −17.1614 −0.794986
\(467\) −9.89268 −0.457779 −0.228889 0.973452i \(-0.573509\pi\)
−0.228889 + 0.973452i \(0.573509\pi\)
\(468\) −5.12502 −0.236904
\(469\) −13.5578 −0.626040
\(470\) 0.319778 0.0147503
\(471\) −6.17154 −0.284370
\(472\) −29.9853 −1.38019
\(473\) 53.7442 2.47116
\(474\) −1.04848 −0.0481582
\(475\) 20.0574 0.920294
\(476\) 2.38977 0.109535
\(477\) 1.67145 0.0765306
\(478\) 13.0036 0.594769
\(479\) 8.67265 0.396263 0.198132 0.980175i \(-0.436513\pi\)
0.198132 + 0.980175i \(0.436513\pi\)
\(480\) −0.134594 −0.00614337
\(481\) −51.7147 −2.35799
\(482\) −7.85842 −0.357941
\(483\) −17.3778 −0.790718
\(484\) −11.3833 −0.517421
\(485\) 0.141300 0.00641610
\(486\) 1.04848 0.0475600
\(487\) 7.14346 0.323701 0.161850 0.986815i \(-0.448254\pi\)
0.161850 + 0.986815i \(0.448254\pi\)
\(488\) 30.5716 1.38391
\(489\) 7.23385 0.327126
\(490\) 0.00121320 5.48069e−5 0
\(491\) −13.8187 −0.623628 −0.311814 0.950143i \(-0.600937\pi\)
−0.311814 + 0.950143i \(0.600937\pi\)
\(492\) 3.33264 0.150247
\(493\) −2.20837 −0.0994601
\(494\) 23.9363 1.07694
\(495\) 0.141398 0.00635536
\(496\) 5.57639 0.250387
\(497\) 16.5313 0.741529
\(498\) 9.47511 0.424590
\(499\) −9.30638 −0.416611 −0.208305 0.978064i \(-0.566795\pi\)
−0.208305 + 0.978064i \(0.566795\pi\)
\(500\) −0.261923 −0.0117135
\(501\) 7.66967 0.342656
\(502\) 28.4839 1.27130
\(503\) 30.5367 1.36157 0.680783 0.732486i \(-0.261640\pi\)
0.680783 + 0.732486i \(0.261640\pi\)
\(504\) 8.06940 0.359440
\(505\) −0.284337 −0.0126528
\(506\) 33.3875 1.48426
\(507\) −19.3772 −0.860572
\(508\) 0.319291 0.0141662
\(509\) 22.1835 0.983267 0.491634 0.870802i \(-0.336400\pi\)
0.491634 + 0.870802i \(0.336400\pi\)
\(510\) 0.0304926 0.00135023
\(511\) −6.47309 −0.286352
\(512\) 14.8596 0.656709
\(513\) 4.01215 0.177141
\(514\) −17.9309 −0.790896
\(515\) −0.114582 −0.00504909
\(516\) −9.95633 −0.438303
\(517\) −50.9874 −2.24243
\(518\) 25.2833 1.11088
\(519\) −4.59359 −0.201636
\(520\) −0.503286 −0.0220706
\(521\) −1.90747 −0.0835679 −0.0417840 0.999127i \(-0.513304\pi\)
−0.0417840 + 0.999127i \(0.513304\pi\)
\(522\) −2.31543 −0.101344
\(523\) −20.9029 −0.914020 −0.457010 0.889462i \(-0.651080\pi\)
−0.457010 + 0.889462i \(0.651080\pi\)
\(524\) −5.51073 −0.240738
\(525\) 13.2641 0.578891
\(526\) 25.3067 1.10342
\(527\) 4.01939 0.175087
\(528\) −6.74531 −0.293552
\(529\) 19.8974 0.865103
\(530\) 0.0509669 0.00221386
\(531\) −9.85933 −0.427858
\(532\) 9.58810 0.415697
\(533\) 21.0539 0.911944
\(534\) −1.64810 −0.0713203
\(535\) 0.360895 0.0156029
\(536\) −15.5407 −0.671255
\(537\) 11.8850 0.512874
\(538\) 4.70310 0.202765
\(539\) −0.193441 −0.00833207
\(540\) −0.0261945 −0.00112723
\(541\) 39.8925 1.71511 0.857556 0.514391i \(-0.171982\pi\)
0.857556 + 0.514391i \(0.171982\pi\)
\(542\) −27.7799 −1.19325
\(543\) −1.12907 −0.0484531
\(544\) 4.62800 0.198424
\(545\) 0.201106 0.00861443
\(546\) 15.8292 0.677428
\(547\) −26.5623 −1.13572 −0.567860 0.823125i \(-0.692229\pi\)
−0.567860 + 0.823125i \(0.692229\pi\)
\(548\) −7.39313 −0.315819
\(549\) 10.0521 0.429013
\(550\) −25.4838 −1.08663
\(551\) −8.86032 −0.377462
\(552\) −19.9194 −0.847827
\(553\) −2.65326 −0.112828
\(554\) 1.95324 0.0829850
\(555\) −0.264319 −0.0112197
\(556\) −2.51607 −0.106705
\(557\) 7.69438 0.326021 0.163011 0.986624i \(-0.447879\pi\)
0.163011 + 0.986624i \(0.447879\pi\)
\(558\) 4.21425 0.178403
\(559\) −62.8989 −2.66034
\(560\) 0.107055 0.00452390
\(561\) −4.86193 −0.205271
\(562\) 7.14246 0.301286
\(563\) 11.7260 0.494191 0.247095 0.968991i \(-0.420524\pi\)
0.247095 + 0.968991i \(0.420524\pi\)
\(564\) 9.44562 0.397732
\(565\) 0.414699 0.0174465
\(566\) 15.1454 0.636609
\(567\) 2.65326 0.111426
\(568\) 18.9491 0.795086
\(569\) −22.9170 −0.960732 −0.480366 0.877068i \(-0.659496\pi\)
−0.480366 + 0.877068i \(0.659496\pi\)
\(570\) 0.122341 0.00512429
\(571\) −34.9908 −1.46432 −0.732160 0.681133i \(-0.761488\pi\)
−0.732160 + 0.681133i \(0.761488\pi\)
\(572\) 24.9175 1.04185
\(573\) 21.6882 0.906039
\(574\) −10.2932 −0.429631
\(575\) −32.7425 −1.36546
\(576\) 7.62711 0.317796
\(577\) −28.8737 −1.20203 −0.601014 0.799239i \(-0.705236\pi\)
−0.601014 + 0.799239i \(0.705236\pi\)
\(578\) −1.04848 −0.0436110
\(579\) 21.2176 0.881772
\(580\) 0.0578472 0.00240198
\(581\) 23.9775 0.994755
\(582\) −5.09410 −0.211157
\(583\) −8.12649 −0.336565
\(584\) −7.41981 −0.307034
\(585\) −0.165483 −0.00684189
\(586\) 13.5157 0.558327
\(587\) 27.8908 1.15118 0.575588 0.817740i \(-0.304773\pi\)
0.575588 + 0.817740i \(0.304773\pi\)
\(588\) 0.0358356 0.00147784
\(589\) 16.1264 0.664476
\(590\) −0.300636 −0.0123770
\(591\) −1.92916 −0.0793552
\(592\) 12.6092 0.518235
\(593\) 43.4134 1.78277 0.891387 0.453242i \(-0.149733\pi\)
0.891387 + 0.453242i \(0.149733\pi\)
\(594\) −5.09763 −0.209158
\(595\) 0.0771639 0.00316341
\(596\) −11.8162 −0.484011
\(597\) 11.8049 0.483140
\(598\) −39.0746 −1.59788
\(599\) 15.2412 0.622739 0.311370 0.950289i \(-0.399212\pi\)
0.311370 + 0.950289i \(0.399212\pi\)
\(600\) 15.2040 0.620701
\(601\) 28.8790 1.17800 0.589000 0.808133i \(-0.299522\pi\)
0.589000 + 0.808133i \(0.299522\pi\)
\(602\) 30.7513 1.25333
\(603\) −5.10986 −0.208089
\(604\) −1.24469 −0.0506457
\(605\) −0.367557 −0.0149433
\(606\) 10.2508 0.416411
\(607\) −20.3652 −0.826599 −0.413300 0.910595i \(-0.635624\pi\)
−0.413300 + 0.910595i \(0.635624\pi\)
\(608\) 18.5682 0.753041
\(609\) −5.85939 −0.237434
\(610\) 0.306514 0.0124104
\(611\) 59.6725 2.41409
\(612\) 0.900691 0.0364083
\(613\) 41.0433 1.65772 0.828862 0.559454i \(-0.188989\pi\)
0.828862 + 0.559454i \(0.188989\pi\)
\(614\) 34.1069 1.37644
\(615\) 0.107608 0.00433919
\(616\) −39.2328 −1.58074
\(617\) −42.7053 −1.71925 −0.859626 0.510923i \(-0.829304\pi\)
−0.859626 + 0.510923i \(0.829304\pi\)
\(618\) 4.13088 0.166168
\(619\) −9.35159 −0.375872 −0.187936 0.982181i \(-0.560180\pi\)
−0.187936 + 0.982181i \(0.560180\pi\)
\(620\) −0.105286 −0.00422838
\(621\) −6.54961 −0.262827
\(622\) −29.4625 −1.18134
\(623\) −4.17065 −0.167094
\(624\) 7.89429 0.316024
\(625\) 24.9873 0.999493
\(626\) −4.63689 −0.185327
\(627\) −19.5068 −0.779026
\(628\) −5.55866 −0.221815
\(629\) 9.08854 0.362384
\(630\) 0.0809047 0.00322332
\(631\) 7.16286 0.285149 0.142575 0.989784i \(-0.454462\pi\)
0.142575 + 0.989784i \(0.454462\pi\)
\(632\) −3.04131 −0.120977
\(633\) −6.25806 −0.248736
\(634\) 28.3008 1.12397
\(635\) 0.0103097 0.000409127 0
\(636\) 1.50546 0.0596955
\(637\) 0.226391 0.00896993
\(638\) 11.2575 0.445688
\(639\) 6.23056 0.246477
\(640\) −0.0366189 −0.00144749
\(641\) −31.4710 −1.24303 −0.621515 0.783402i \(-0.713483\pi\)
−0.621515 + 0.783402i \(0.713483\pi\)
\(642\) −13.0109 −0.513498
\(643\) 7.95454 0.313696 0.156848 0.987623i \(-0.449867\pi\)
0.156848 + 0.987623i \(0.449867\pi\)
\(644\) −15.6520 −0.616777
\(645\) −0.321483 −0.0126584
\(646\) −4.20666 −0.165509
\(647\) −25.2224 −0.991594 −0.495797 0.868438i \(-0.665124\pi\)
−0.495797 + 0.868438i \(0.665124\pi\)
\(648\) 3.04131 0.119474
\(649\) 47.9353 1.88163
\(650\) 29.8247 1.16982
\(651\) 10.6645 0.417974
\(652\) 6.51547 0.255165
\(653\) 30.1848 1.18122 0.590612 0.806956i \(-0.298886\pi\)
0.590612 + 0.806956i \(0.298886\pi\)
\(654\) −7.25021 −0.283506
\(655\) −0.177938 −0.00695260
\(656\) −5.13340 −0.200426
\(657\) −2.43967 −0.0951807
\(658\) −29.1739 −1.13732
\(659\) −15.2520 −0.594133 −0.297067 0.954857i \(-0.596008\pi\)
−0.297067 + 0.954857i \(0.596008\pi\)
\(660\) 0.127356 0.00495732
\(661\) 43.6528 1.69790 0.848948 0.528477i \(-0.177237\pi\)
0.848948 + 0.528477i \(0.177237\pi\)
\(662\) 24.5699 0.954937
\(663\) 5.69010 0.220985
\(664\) 27.4844 1.06660
\(665\) 0.309593 0.0120055
\(666\) 9.52914 0.369247
\(667\) 14.4640 0.560047
\(668\) 6.90801 0.267279
\(669\) 19.3188 0.746906
\(670\) −0.155813 −0.00601957
\(671\) −48.8725 −1.88670
\(672\) 12.2793 0.473683
\(673\) −17.1600 −0.661470 −0.330735 0.943724i \(-0.607297\pi\)
−0.330735 + 0.943724i \(0.607297\pi\)
\(674\) 6.34570 0.244427
\(675\) 4.99915 0.192418
\(676\) −17.4529 −0.671264
\(677\) −14.7120 −0.565429 −0.282714 0.959204i \(-0.591235\pi\)
−0.282714 + 0.959204i \(0.591235\pi\)
\(678\) −14.9506 −0.574174
\(679\) −12.8910 −0.494712
\(680\) 0.0884495 0.00339188
\(681\) −4.30211 −0.164857
\(682\) −20.4894 −0.784578
\(683\) 23.3629 0.893958 0.446979 0.894544i \(-0.352500\pi\)
0.446979 + 0.894544i \(0.352500\pi\)
\(684\) 3.61371 0.138174
\(685\) −0.238719 −0.00912097
\(686\) 19.3625 0.739265
\(687\) 22.8035 0.870009
\(688\) 15.3362 0.584685
\(689\) 9.51073 0.362330
\(690\) −0.199714 −0.00760300
\(691\) 10.7717 0.409775 0.204888 0.978786i \(-0.434317\pi\)
0.204888 + 0.978786i \(0.434317\pi\)
\(692\) −4.13740 −0.157280
\(693\) −12.9000 −0.490029
\(694\) 23.6262 0.896840
\(695\) −0.0812422 −0.00308169
\(696\) −6.71636 −0.254583
\(697\) −3.70009 −0.140151
\(698\) 2.50378 0.0947696
\(699\) −16.3679 −0.619091
\(700\) 11.9468 0.451547
\(701\) −30.9481 −1.16889 −0.584446 0.811433i \(-0.698688\pi\)
−0.584446 + 0.811433i \(0.698688\pi\)
\(702\) 5.96595 0.225170
\(703\) 36.4646 1.37529
\(704\) −37.0824 −1.39760
\(705\) 0.304992 0.0114867
\(706\) −20.9851 −0.789785
\(707\) 25.9405 0.975593
\(708\) −8.88021 −0.333739
\(709\) −8.41122 −0.315890 −0.157945 0.987448i \(-0.550487\pi\)
−0.157945 + 0.987448i \(0.550487\pi\)
\(710\) 0.189986 0.00713004
\(711\) −1.00000 −0.0375029
\(712\) −4.78063 −0.179162
\(713\) −26.3254 −0.985895
\(714\) −2.78189 −0.104110
\(715\) 0.804567 0.0300891
\(716\) 10.7047 0.400053
\(717\) 12.4023 0.463172
\(718\) 24.9661 0.931728
\(719\) 16.5780 0.618256 0.309128 0.951021i \(-0.399963\pi\)
0.309128 + 0.951021i \(0.399963\pi\)
\(720\) 0.0403485 0.00150370
\(721\) 10.4535 0.389309
\(722\) 3.04338 0.113263
\(723\) −7.49506 −0.278744
\(724\) −1.01694 −0.0377944
\(725\) −11.0400 −0.410015
\(726\) 13.2511 0.491793
\(727\) −8.39259 −0.311264 −0.155632 0.987815i \(-0.549741\pi\)
−0.155632 + 0.987815i \(0.549741\pi\)
\(728\) 45.9157 1.70175
\(729\) 1.00000 0.0370370
\(730\) −0.0743919 −0.00275337
\(731\) 11.0541 0.408850
\(732\) 9.05382 0.334639
\(733\) −33.9614 −1.25439 −0.627196 0.778862i \(-0.715797\pi\)
−0.627196 + 0.778862i \(0.715797\pi\)
\(734\) −22.0292 −0.813112
\(735\) 0.00115711 4.26805e−5 0
\(736\) −30.3116 −1.11730
\(737\) 24.8438 0.915132
\(738\) −3.87947 −0.142805
\(739\) 44.9041 1.65183 0.825913 0.563798i \(-0.190660\pi\)
0.825913 + 0.563798i \(0.190660\pi\)
\(740\) −0.238070 −0.00875161
\(741\) 22.8295 0.838663
\(742\) −4.64980 −0.170699
\(743\) 16.9651 0.622389 0.311194 0.950346i \(-0.399271\pi\)
0.311194 + 0.950346i \(0.399271\pi\)
\(744\) 12.2242 0.448162
\(745\) −0.381537 −0.0139784
\(746\) 38.5594 1.41176
\(747\) 9.03700 0.330647
\(748\) −4.37910 −0.160116
\(749\) −32.9250 −1.20305
\(750\) 0.304900 0.0111334
\(751\) −53.5372 −1.95360 −0.976800 0.214152i \(-0.931301\pi\)
−0.976800 + 0.214152i \(0.931301\pi\)
\(752\) −14.5495 −0.530566
\(753\) 27.1669 0.990017
\(754\) −13.1750 −0.479807
\(755\) −0.0401901 −0.00146267
\(756\) 2.38977 0.0869150
\(757\) 10.9325 0.397348 0.198674 0.980066i \(-0.436337\pi\)
0.198674 + 0.980066i \(0.436337\pi\)
\(758\) −30.3919 −1.10388
\(759\) 31.8437 1.15585
\(760\) 0.354873 0.0128726
\(761\) 0.300100 0.0108786 0.00543932 0.999985i \(-0.498269\pi\)
0.00543932 + 0.999985i \(0.498269\pi\)
\(762\) −0.371681 −0.0134646
\(763\) −18.3472 −0.664214
\(764\) 19.5344 0.706730
\(765\) 0.0290827 0.00105149
\(766\) 10.8085 0.390527
\(767\) −56.1005 −2.02567
\(768\) 16.5744 0.598077
\(769\) 18.8122 0.678385 0.339192 0.940717i \(-0.389846\pi\)
0.339192 + 0.940717i \(0.389846\pi\)
\(770\) −0.393353 −0.0141755
\(771\) −17.1018 −0.615905
\(772\) 19.1105 0.687801
\(773\) −12.1872 −0.438343 −0.219172 0.975686i \(-0.570335\pi\)
−0.219172 + 0.975686i \(0.570335\pi\)
\(774\) 11.5900 0.416594
\(775\) 20.0935 0.721781
\(776\) −14.7764 −0.530443
\(777\) 24.1142 0.865094
\(778\) 12.6318 0.452874
\(779\) −14.8453 −0.531888
\(780\) −0.149049 −0.00533682
\(781\) −30.2925 −1.08395
\(782\) 6.86713 0.245568
\(783\) −2.20837 −0.0789208
\(784\) −0.0551991 −0.00197140
\(785\) −0.179485 −0.00640609
\(786\) 6.41495 0.228814
\(787\) −19.1493 −0.682598 −0.341299 0.939955i \(-0.610867\pi\)
−0.341299 + 0.939955i \(0.610867\pi\)
\(788\) −1.73758 −0.0618988
\(789\) 24.1366 0.859284
\(790\) −0.0304926 −0.00108488
\(791\) −37.8337 −1.34521
\(792\) −14.7867 −0.525421
\(793\) 57.1973 2.03114
\(794\) 15.1506 0.537674
\(795\) 0.0486103 0.00172403
\(796\) 10.6325 0.376860
\(797\) −52.5098 −1.85999 −0.929996 0.367570i \(-0.880190\pi\)
−0.929996 + 0.367570i \(0.880190\pi\)
\(798\) −11.1613 −0.395107
\(799\) −10.4871 −0.371006
\(800\) 23.1361 0.817984
\(801\) −1.57190 −0.0555403
\(802\) 29.7523 1.05059
\(803\) 11.8615 0.418584
\(804\) −4.60240 −0.162314
\(805\) −0.505393 −0.0178128
\(806\) 23.9795 0.844641
\(807\) 4.48564 0.157902
\(808\) 29.7345 1.04605
\(809\) −3.93181 −0.138235 −0.0691176 0.997609i \(-0.522018\pi\)
−0.0691176 + 0.997609i \(0.522018\pi\)
\(810\) 0.0304926 0.00107140
\(811\) 22.5161 0.790646 0.395323 0.918542i \(-0.370633\pi\)
0.395323 + 0.918542i \(0.370633\pi\)
\(812\) −5.27750 −0.185204
\(813\) −26.4955 −0.929237
\(814\) −46.3300 −1.62387
\(815\) 0.210380 0.00736928
\(816\) −1.38737 −0.0485678
\(817\) 44.3507 1.55163
\(818\) 3.43606 0.120139
\(819\) 15.0973 0.527543
\(820\) 0.0969219 0.00338466
\(821\) 34.2935 1.19685 0.598426 0.801178i \(-0.295793\pi\)
0.598426 + 0.801178i \(0.295793\pi\)
\(822\) 8.60621 0.300176
\(823\) 7.00859 0.244304 0.122152 0.992511i \(-0.461020\pi\)
0.122152 + 0.992511i \(0.461020\pi\)
\(824\) 11.9824 0.417427
\(825\) −24.3055 −0.846210
\(826\) 27.4275 0.954326
\(827\) 4.13520 0.143795 0.0718976 0.997412i \(-0.477095\pi\)
0.0718976 + 0.997412i \(0.477095\pi\)
\(828\) −5.89917 −0.205010
\(829\) −40.4100 −1.40350 −0.701749 0.712424i \(-0.747597\pi\)
−0.701749 + 0.712424i \(0.747597\pi\)
\(830\) 0.275561 0.00956488
\(831\) 1.86292 0.0646241
\(832\) 43.3990 1.50459
\(833\) −0.0397868 −0.00137853
\(834\) 2.92892 0.101420
\(835\) 0.223055 0.00771912
\(836\) −17.5696 −0.607657
\(837\) 4.01939 0.138930
\(838\) 19.2029 0.663354
\(839\) −50.9701 −1.75968 −0.879841 0.475267i \(-0.842351\pi\)
−0.879841 + 0.475267i \(0.842351\pi\)
\(840\) 0.234680 0.00809721
\(841\) −24.1231 −0.831831
\(842\) 4.12039 0.141998
\(843\) 6.81221 0.234625
\(844\) −5.63658 −0.194019
\(845\) −0.563541 −0.0193864
\(846\) −10.9955 −0.378033
\(847\) 33.5328 1.15220
\(848\) −2.31893 −0.0796324
\(849\) 14.4451 0.495755
\(850\) −5.24151 −0.179782
\(851\) −59.5264 −2.04054
\(852\) 5.61181 0.192257
\(853\) −26.7903 −0.917282 −0.458641 0.888622i \(-0.651664\pi\)
−0.458641 + 0.888622i \(0.651664\pi\)
\(854\) −27.9638 −0.956901
\(855\) 0.116684 0.00399051
\(856\) −37.7405 −1.28994
\(857\) 2.44333 0.0834625 0.0417313 0.999129i \(-0.486713\pi\)
0.0417313 + 0.999129i \(0.486713\pi\)
\(858\) −29.0060 −0.990249
\(859\) 2.59589 0.0885705 0.0442852 0.999019i \(-0.485899\pi\)
0.0442852 + 0.999019i \(0.485899\pi\)
\(860\) −0.289556 −0.00987379
\(861\) −9.81729 −0.334572
\(862\) −18.7415 −0.638339
\(863\) −29.6027 −1.00769 −0.503844 0.863795i \(-0.668081\pi\)
−0.503844 + 0.863795i \(0.668081\pi\)
\(864\) 4.62800 0.157448
\(865\) −0.133594 −0.00454232
\(866\) −32.7799 −1.11391
\(867\) −1.00000 −0.0339618
\(868\) 9.60540 0.326029
\(869\) 4.86193 0.164930
\(870\) −0.0673390 −0.00228300
\(871\) −29.0756 −0.985188
\(872\) −21.0306 −0.712187
\(873\) −4.85856 −0.164437
\(874\) 27.5519 0.931959
\(875\) 0.771573 0.0260839
\(876\) −2.19739 −0.0742430
\(877\) −0.898159 −0.0303287 −0.0151643 0.999885i \(-0.504827\pi\)
−0.0151643 + 0.999885i \(0.504827\pi\)
\(878\) 7.87340 0.265714
\(879\) 12.8907 0.434793
\(880\) −0.196172 −0.00661294
\(881\) −5.79109 −0.195107 −0.0975534 0.995230i \(-0.531102\pi\)
−0.0975534 + 0.995230i \(0.531102\pi\)
\(882\) −0.0417156 −0.00140464
\(883\) −40.9805 −1.37910 −0.689551 0.724237i \(-0.742192\pi\)
−0.689551 + 0.724237i \(0.742192\pi\)
\(884\) 5.12502 0.172373
\(885\) −0.286735 −0.00963851
\(886\) −13.8061 −0.463824
\(887\) −22.2927 −0.748516 −0.374258 0.927325i \(-0.622103\pi\)
−0.374258 + 0.927325i \(0.622103\pi\)
\(888\) 27.6411 0.927574
\(889\) −0.940568 −0.0315457
\(890\) −0.0479312 −0.00160666
\(891\) −4.86193 −0.162881
\(892\) 17.4002 0.582603
\(893\) −42.0757 −1.40801
\(894\) 13.7551 0.460038
\(895\) 0.345647 0.0115537
\(896\) 3.34080 0.111608
\(897\) −37.2679 −1.24434
\(898\) −14.0360 −0.468387
\(899\) −8.87631 −0.296041
\(900\) 4.50269 0.150090
\(901\) −1.67145 −0.0556842
\(902\) 18.8617 0.628025
\(903\) 29.3294 0.976021
\(904\) −43.3671 −1.44237
\(905\) −0.0328364 −0.00109152
\(906\) 1.44892 0.0481372
\(907\) −54.4677 −1.80857 −0.904285 0.426929i \(-0.859595\pi\)
−0.904285 + 0.426929i \(0.859595\pi\)
\(908\) −3.87488 −0.128592
\(909\) 9.77685 0.324278
\(910\) 0.460356 0.0152606
\(911\) −31.1586 −1.03233 −0.516165 0.856489i \(-0.672641\pi\)
−0.516165 + 0.856489i \(0.672641\pi\)
\(912\) −5.56635 −0.184320
\(913\) −43.9373 −1.45411
\(914\) −0.852597 −0.0282014
\(915\) 0.292341 0.00966451
\(916\) 20.5389 0.678626
\(917\) 16.2335 0.536079
\(918\) −1.04848 −0.0346050
\(919\) 35.6814 1.17702 0.588510 0.808490i \(-0.299715\pi\)
0.588510 + 0.808490i \(0.299715\pi\)
\(920\) −0.579310 −0.0190993
\(921\) 32.5298 1.07189
\(922\) 22.9246 0.754982
\(923\) 35.4525 1.16693
\(924\) −11.6189 −0.382233
\(925\) 45.4350 1.49389
\(926\) −14.2430 −0.468054
\(927\) 3.93988 0.129402
\(928\) −10.2203 −0.335499
\(929\) −42.4484 −1.39269 −0.696344 0.717708i \(-0.745191\pi\)
−0.696344 + 0.717708i \(0.745191\pi\)
\(930\) 0.122561 0.00401895
\(931\) −0.159631 −0.00523168
\(932\) −14.7424 −0.482904
\(933\) −28.1002 −0.919960
\(934\) 10.3723 0.339391
\(935\) −0.141398 −0.00462420
\(936\) 17.3054 0.565644
\(937\) 36.4609 1.19112 0.595562 0.803309i \(-0.296929\pi\)
0.595562 + 0.803309i \(0.296929\pi\)
\(938\) 14.2150 0.464138
\(939\) −4.42249 −0.144323
\(940\) 0.274704 0.00895985
\(941\) 28.0671 0.914961 0.457480 0.889220i \(-0.348752\pi\)
0.457480 + 0.889220i \(0.348752\pi\)
\(942\) 6.47074 0.210828
\(943\) 24.2341 0.789172
\(944\) 13.6786 0.445199
\(945\) 0.0771639 0.00251014
\(946\) −56.3497 −1.83209
\(947\) −11.1419 −0.362063 −0.181031 0.983477i \(-0.557944\pi\)
−0.181031 + 0.983477i \(0.557944\pi\)
\(948\) −0.900691 −0.0292531
\(949\) −13.8820 −0.450628
\(950\) −21.0297 −0.682294
\(951\) 26.9923 0.875285
\(952\) −8.06940 −0.261531
\(953\) 36.5558 1.18416 0.592080 0.805880i \(-0.298307\pi\)
0.592080 + 0.805880i \(0.298307\pi\)
\(954\) −1.75248 −0.0567388
\(955\) 0.630752 0.0204107
\(956\) 11.1706 0.361284
\(957\) 10.7370 0.347076
\(958\) −9.09309 −0.293784
\(959\) 21.7787 0.703271
\(960\) 0.221817 0.00715910
\(961\) −14.8445 −0.478855
\(962\) 54.2217 1.74818
\(963\) −12.4093 −0.399884
\(964\) −6.75074 −0.217427
\(965\) 0.617063 0.0198640
\(966\) 18.2203 0.586228
\(967\) 52.0779 1.67471 0.837357 0.546657i \(-0.184100\pi\)
0.837357 + 0.546657i \(0.184100\pi\)
\(968\) 38.4372 1.23542
\(969\) −4.01215 −0.128889
\(970\) −0.148150 −0.00475681
\(971\) −38.2043 −1.22604 −0.613018 0.790069i \(-0.710045\pi\)
−0.613018 + 0.790069i \(0.710045\pi\)
\(972\) 0.900691 0.0288897
\(973\) 7.41186 0.237613
\(974\) −7.48977 −0.239988
\(975\) 28.4457 0.910991
\(976\) −13.9460 −0.446400
\(977\) −25.0880 −0.802636 −0.401318 0.915939i \(-0.631448\pi\)
−0.401318 + 0.915939i \(0.631448\pi\)
\(978\) −7.58455 −0.242527
\(979\) 7.64245 0.244254
\(980\) 0.00104219 3.32917e−5 0
\(981\) −6.91498 −0.220778
\(982\) 14.4886 0.462350
\(983\) 23.8926 0.762054 0.381027 0.924564i \(-0.375570\pi\)
0.381027 + 0.924564i \(0.375570\pi\)
\(984\) −11.2531 −0.358737
\(985\) −0.0561052 −0.00178766
\(986\) 2.31543 0.0737384
\(987\) −27.8250 −0.885678
\(988\) 20.5623 0.654175
\(989\) −72.4000 −2.30219
\(990\) −0.148253 −0.00471178
\(991\) 25.3724 0.805981 0.402991 0.915204i \(-0.367971\pi\)
0.402991 + 0.915204i \(0.367971\pi\)
\(992\) 18.6017 0.590605
\(993\) 23.4339 0.743651
\(994\) −17.3327 −0.549760
\(995\) 0.343317 0.0108839
\(996\) 8.13955 0.257911
\(997\) −10.2375 −0.324226 −0.162113 0.986772i \(-0.551831\pi\)
−0.162113 + 0.986772i \(0.551831\pi\)
\(998\) 9.75754 0.308870
\(999\) 9.08854 0.287549
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 4029.2.a.g.1.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.g.1.8 22 1.1 even 1 trivial