Properties

Label 4334.2.a.g.1.19
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $26$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.18604 q^{3} +1.00000 q^{4} +0.389300 q^{5} +2.18604 q^{6} +4.93283 q^{7} +1.00000 q^{8} +1.77878 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.18604 q^{3} +1.00000 q^{4} +0.389300 q^{5} +2.18604 q^{6} +4.93283 q^{7} +1.00000 q^{8} +1.77878 q^{9} +0.389300 q^{10} +1.00000 q^{11} +2.18604 q^{12} +0.775260 q^{13} +4.93283 q^{14} +0.851027 q^{15} +1.00000 q^{16} -5.68472 q^{17} +1.77878 q^{18} -1.12311 q^{19} +0.389300 q^{20} +10.7834 q^{21} +1.00000 q^{22} +7.98354 q^{23} +2.18604 q^{24} -4.84845 q^{25} +0.775260 q^{26} -2.66964 q^{27} +4.93283 q^{28} -9.93968 q^{29} +0.851027 q^{30} +3.43616 q^{31} +1.00000 q^{32} +2.18604 q^{33} -5.68472 q^{34} +1.92035 q^{35} +1.77878 q^{36} +6.94346 q^{37} -1.12311 q^{38} +1.69475 q^{39} +0.389300 q^{40} +5.59521 q^{41} +10.7834 q^{42} +7.79970 q^{43} +1.00000 q^{44} +0.692480 q^{45} +7.98354 q^{46} +2.14271 q^{47} +2.18604 q^{48} +17.3328 q^{49} -4.84845 q^{50} -12.4270 q^{51} +0.775260 q^{52} -6.84216 q^{53} -2.66964 q^{54} +0.389300 q^{55} +4.93283 q^{56} -2.45517 q^{57} -9.93968 q^{58} -2.55627 q^{59} +0.851027 q^{60} +0.705682 q^{61} +3.43616 q^{62} +8.77442 q^{63} +1.00000 q^{64} +0.301809 q^{65} +2.18604 q^{66} +3.66172 q^{67} -5.68472 q^{68} +17.4524 q^{69} +1.92035 q^{70} -5.92511 q^{71} +1.77878 q^{72} +6.54769 q^{73} +6.94346 q^{74} -10.5989 q^{75} -1.12311 q^{76} +4.93283 q^{77} +1.69475 q^{78} -16.3774 q^{79} +0.389300 q^{80} -11.1723 q^{81} +5.59521 q^{82} -12.4454 q^{83} +10.7834 q^{84} -2.21306 q^{85} +7.79970 q^{86} -21.7286 q^{87} +1.00000 q^{88} +13.1347 q^{89} +0.692480 q^{90} +3.82422 q^{91} +7.98354 q^{92} +7.51158 q^{93} +2.14271 q^{94} -0.437228 q^{95} +2.18604 q^{96} +1.45637 q^{97} +17.3328 q^{98} +1.77878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 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
\(3\) 2.18604 1.26211 0.631056 0.775737i \(-0.282622\pi\)
0.631056 + 0.775737i \(0.282622\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.389300 0.174100 0.0870502 0.996204i \(-0.472256\pi\)
0.0870502 + 0.996204i \(0.472256\pi\)
\(6\) 2.18604 0.892448
\(7\) 4.93283 1.86443 0.932216 0.361901i \(-0.117872\pi\)
0.932216 + 0.361901i \(0.117872\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.77878 0.592927
\(10\) 0.389300 0.123108
\(11\) 1.00000 0.301511
\(12\) 2.18604 0.631056
\(13\) 0.775260 0.215019 0.107509 0.994204i \(-0.465712\pi\)
0.107509 + 0.994204i \(0.465712\pi\)
\(14\) 4.93283 1.31835
\(15\) 0.851027 0.219734
\(16\) 1.00000 0.250000
\(17\) −5.68472 −1.37875 −0.689374 0.724406i \(-0.742114\pi\)
−0.689374 + 0.724406i \(0.742114\pi\)
\(18\) 1.77878 0.419263
\(19\) −1.12311 −0.257660 −0.128830 0.991667i \(-0.541122\pi\)
−0.128830 + 0.991667i \(0.541122\pi\)
\(20\) 0.389300 0.0870502
\(21\) 10.7834 2.35312
\(22\) 1.00000 0.213201
\(23\) 7.98354 1.66468 0.832342 0.554263i \(-0.187000\pi\)
0.832342 + 0.554263i \(0.187000\pi\)
\(24\) 2.18604 0.446224
\(25\) −4.84845 −0.969689
\(26\) 0.775260 0.152041
\(27\) −2.66964 −0.513772
\(28\) 4.93283 0.932216
\(29\) −9.93968 −1.84575 −0.922876 0.385097i \(-0.874168\pi\)
−0.922876 + 0.385097i \(0.874168\pi\)
\(30\) 0.851027 0.155376
\(31\) 3.43616 0.617152 0.308576 0.951200i \(-0.400148\pi\)
0.308576 + 0.951200i \(0.400148\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.18604 0.380541
\(34\) −5.68472 −0.974922
\(35\) 1.92035 0.324598
\(36\) 1.77878 0.296464
\(37\) 6.94346 1.14150 0.570749 0.821125i \(-0.306653\pi\)
0.570749 + 0.821125i \(0.306653\pi\)
\(38\) −1.12311 −0.182193
\(39\) 1.69475 0.271378
\(40\) 0.389300 0.0615538
\(41\) 5.59521 0.873824 0.436912 0.899504i \(-0.356072\pi\)
0.436912 + 0.899504i \(0.356072\pi\)
\(42\) 10.7834 1.66391
\(43\) 7.79970 1.18944 0.594721 0.803932i \(-0.297262\pi\)
0.594721 + 0.803932i \(0.297262\pi\)
\(44\) 1.00000 0.150756
\(45\) 0.692480 0.103229
\(46\) 7.98354 1.17711
\(47\) 2.14271 0.312547 0.156274 0.987714i \(-0.450052\pi\)
0.156274 + 0.987714i \(0.450052\pi\)
\(48\) 2.18604 0.315528
\(49\) 17.3328 2.47611
\(50\) −4.84845 −0.685674
\(51\) −12.4270 −1.74013
\(52\) 0.775260 0.107509
\(53\) −6.84216 −0.939844 −0.469922 0.882708i \(-0.655718\pi\)
−0.469922 + 0.882708i \(0.655718\pi\)
\(54\) −2.66964 −0.363291
\(55\) 0.389300 0.0524932
\(56\) 4.93283 0.659177
\(57\) −2.45517 −0.325195
\(58\) −9.93968 −1.30514
\(59\) −2.55627 −0.332798 −0.166399 0.986059i \(-0.553214\pi\)
−0.166399 + 0.986059i \(0.553214\pi\)
\(60\) 0.851027 0.109867
\(61\) 0.705682 0.0903533 0.0451767 0.998979i \(-0.485615\pi\)
0.0451767 + 0.998979i \(0.485615\pi\)
\(62\) 3.43616 0.436392
\(63\) 8.77442 1.10547
\(64\) 1.00000 0.125000
\(65\) 0.301809 0.0374348
\(66\) 2.18604 0.269083
\(67\) 3.66172 0.447350 0.223675 0.974664i \(-0.428195\pi\)
0.223675 + 0.974664i \(0.428195\pi\)
\(68\) −5.68472 −0.689374
\(69\) 17.4524 2.10102
\(70\) 1.92035 0.229526
\(71\) −5.92511 −0.703182 −0.351591 0.936154i \(-0.614359\pi\)
−0.351591 + 0.936154i \(0.614359\pi\)
\(72\) 1.77878 0.209631
\(73\) 6.54769 0.766349 0.383175 0.923676i \(-0.374831\pi\)
0.383175 + 0.923676i \(0.374831\pi\)
\(74\) 6.94346 0.807161
\(75\) −10.5989 −1.22386
\(76\) −1.12311 −0.128830
\(77\) 4.93283 0.562148
\(78\) 1.69475 0.191893
\(79\) −16.3774 −1.84260 −0.921302 0.388847i \(-0.872874\pi\)
−0.921302 + 0.388847i \(0.872874\pi\)
\(80\) 0.389300 0.0435251
\(81\) −11.1723 −1.24136
\(82\) 5.59521 0.617887
\(83\) −12.4454 −1.36605 −0.683027 0.730393i \(-0.739337\pi\)
−0.683027 + 0.730393i \(0.739337\pi\)
\(84\) 10.7834 1.17656
\(85\) −2.21306 −0.240041
\(86\) 7.79970 0.841063
\(87\) −21.7286 −2.32955
\(88\) 1.00000 0.106600
\(89\) 13.1347 1.39228 0.696138 0.717908i \(-0.254900\pi\)
0.696138 + 0.717908i \(0.254900\pi\)
\(90\) 0.692480 0.0729938
\(91\) 3.82422 0.400888
\(92\) 7.98354 0.832342
\(93\) 7.51158 0.778915
\(94\) 2.14271 0.221004
\(95\) −0.437228 −0.0448586
\(96\) 2.18604 0.223112
\(97\) 1.45637 0.147872 0.0739358 0.997263i \(-0.476444\pi\)
0.0739358 + 0.997263i \(0.476444\pi\)
\(98\) 17.3328 1.75087
\(99\) 1.77878 0.178774
\(100\) −4.84845 −0.484845
\(101\) −19.0906 −1.89958 −0.949792 0.312882i \(-0.898706\pi\)
−0.949792 + 0.312882i \(0.898706\pi\)
\(102\) −12.4270 −1.23046
\(103\) −18.8529 −1.85764 −0.928818 0.370536i \(-0.879174\pi\)
−0.928818 + 0.370536i \(0.879174\pi\)
\(104\) 0.775260 0.0760205
\(105\) 4.19797 0.409680
\(106\) −6.84216 −0.664570
\(107\) 4.43808 0.429046 0.214523 0.976719i \(-0.431180\pi\)
0.214523 + 0.976719i \(0.431180\pi\)
\(108\) −2.66964 −0.256886
\(109\) 3.10342 0.297254 0.148627 0.988893i \(-0.452515\pi\)
0.148627 + 0.988893i \(0.452515\pi\)
\(110\) 0.389300 0.0371183
\(111\) 15.1787 1.44070
\(112\) 4.93283 0.466108
\(113\) −1.47551 −0.138804 −0.0694022 0.997589i \(-0.522109\pi\)
−0.0694022 + 0.997589i \(0.522109\pi\)
\(114\) −2.45517 −0.229948
\(115\) 3.10799 0.289822
\(116\) −9.93968 −0.922876
\(117\) 1.37902 0.127490
\(118\) −2.55627 −0.235323
\(119\) −28.0417 −2.57058
\(120\) 0.851027 0.0776878
\(121\) 1.00000 0.0909091
\(122\) 0.705682 0.0638894
\(123\) 12.2314 1.10286
\(124\) 3.43616 0.308576
\(125\) −3.83400 −0.342924
\(126\) 8.77442 0.781687
\(127\) 15.6271 1.38668 0.693341 0.720610i \(-0.256138\pi\)
0.693341 + 0.720610i \(0.256138\pi\)
\(128\) 1.00000 0.0883883
\(129\) 17.0505 1.50121
\(130\) 0.301809 0.0264704
\(131\) −12.0105 −1.04937 −0.524683 0.851298i \(-0.675816\pi\)
−0.524683 + 0.851298i \(0.675816\pi\)
\(132\) 2.18604 0.190271
\(133\) −5.54012 −0.480389
\(134\) 3.66172 0.316324
\(135\) −1.03929 −0.0894479
\(136\) −5.68472 −0.487461
\(137\) −21.2914 −1.81904 −0.909522 0.415655i \(-0.863552\pi\)
−0.909522 + 0.415655i \(0.863552\pi\)
\(138\) 17.4524 1.48564
\(139\) −6.41890 −0.544444 −0.272222 0.962234i \(-0.587759\pi\)
−0.272222 + 0.962234i \(0.587759\pi\)
\(140\) 1.92035 0.162299
\(141\) 4.68406 0.394469
\(142\) −5.92511 −0.497224
\(143\) 0.775260 0.0648305
\(144\) 1.77878 0.148232
\(145\) −3.86952 −0.321346
\(146\) 6.54769 0.541891
\(147\) 37.8902 3.12513
\(148\) 6.94346 0.570749
\(149\) 12.3096 1.00844 0.504220 0.863575i \(-0.331780\pi\)
0.504220 + 0.863575i \(0.331780\pi\)
\(150\) −10.5989 −0.865397
\(151\) −12.2838 −0.999641 −0.499820 0.866129i \(-0.666601\pi\)
−0.499820 + 0.866129i \(0.666601\pi\)
\(152\) −1.12311 −0.0910964
\(153\) −10.1119 −0.817497
\(154\) 4.93283 0.397498
\(155\) 1.33770 0.107446
\(156\) 1.69475 0.135689
\(157\) 14.1766 1.13142 0.565709 0.824605i \(-0.308603\pi\)
0.565709 + 0.824605i \(0.308603\pi\)
\(158\) −16.3774 −1.30292
\(159\) −14.9573 −1.18619
\(160\) 0.389300 0.0307769
\(161\) 39.3814 3.10369
\(162\) −11.1723 −0.877777
\(163\) −1.04017 −0.0814722 −0.0407361 0.999170i \(-0.512970\pi\)
−0.0407361 + 0.999170i \(0.512970\pi\)
\(164\) 5.59521 0.436912
\(165\) 0.851027 0.0662524
\(166\) −12.4454 −0.965947
\(167\) 11.9099 0.921614 0.460807 0.887500i \(-0.347560\pi\)
0.460807 + 0.887500i \(0.347560\pi\)
\(168\) 10.7834 0.831955
\(169\) −12.3990 −0.953767
\(170\) −2.21306 −0.169734
\(171\) −1.99777 −0.152773
\(172\) 7.79970 0.594721
\(173\) −4.62647 −0.351744 −0.175872 0.984413i \(-0.556275\pi\)
−0.175872 + 0.984413i \(0.556275\pi\)
\(174\) −21.7286 −1.64724
\(175\) −23.9165 −1.80792
\(176\) 1.00000 0.0753778
\(177\) −5.58811 −0.420028
\(178\) 13.1347 0.984488
\(179\) 21.5158 1.60817 0.804085 0.594515i \(-0.202656\pi\)
0.804085 + 0.594515i \(0.202656\pi\)
\(180\) 0.692480 0.0516144
\(181\) 11.5012 0.854877 0.427439 0.904044i \(-0.359416\pi\)
0.427439 + 0.904044i \(0.359416\pi\)
\(182\) 3.82422 0.283470
\(183\) 1.54265 0.114036
\(184\) 7.98354 0.588554
\(185\) 2.70309 0.198735
\(186\) 7.51158 0.550776
\(187\) −5.68472 −0.415708
\(188\) 2.14271 0.156274
\(189\) −13.1689 −0.957893
\(190\) −0.437228 −0.0317199
\(191\) −14.2034 −1.02772 −0.513862 0.857873i \(-0.671786\pi\)
−0.513862 + 0.857873i \(0.671786\pi\)
\(192\) 2.18604 0.157764
\(193\) −8.33214 −0.599760 −0.299880 0.953977i \(-0.596947\pi\)
−0.299880 + 0.953977i \(0.596947\pi\)
\(194\) 1.45637 0.104561
\(195\) 0.659767 0.0472469
\(196\) 17.3328 1.23805
\(197\) 1.00000 0.0712470
\(198\) 1.77878 0.126412
\(199\) −4.67312 −0.331269 −0.165635 0.986187i \(-0.552967\pi\)
−0.165635 + 0.986187i \(0.552967\pi\)
\(200\) −4.84845 −0.342837
\(201\) 8.00467 0.564606
\(202\) −19.0906 −1.34321
\(203\) −49.0307 −3.44128
\(204\) −12.4270 −0.870067
\(205\) 2.17822 0.152133
\(206\) −18.8529 −1.31355
\(207\) 14.2010 0.987036
\(208\) 0.775260 0.0537546
\(209\) −1.12311 −0.0776873
\(210\) 4.19797 0.289687
\(211\) 9.76819 0.672470 0.336235 0.941778i \(-0.390846\pi\)
0.336235 + 0.941778i \(0.390846\pi\)
\(212\) −6.84216 −0.469922
\(213\) −12.9525 −0.887494
\(214\) 4.43808 0.303381
\(215\) 3.03642 0.207082
\(216\) −2.66964 −0.181646
\(217\) 16.9500 1.15064
\(218\) 3.10342 0.210190
\(219\) 14.3135 0.967219
\(220\) 0.389300 0.0262466
\(221\) −4.40714 −0.296456
\(222\) 15.1787 1.01873
\(223\) −4.69464 −0.314376 −0.157188 0.987569i \(-0.550243\pi\)
−0.157188 + 0.987569i \(0.550243\pi\)
\(224\) 4.93283 0.329588
\(225\) −8.62432 −0.574955
\(226\) −1.47551 −0.0981496
\(227\) 27.9405 1.85448 0.927239 0.374471i \(-0.122176\pi\)
0.927239 + 0.374471i \(0.122176\pi\)
\(228\) −2.45517 −0.162598
\(229\) −6.53180 −0.431633 −0.215817 0.976434i \(-0.569241\pi\)
−0.215817 + 0.976434i \(0.569241\pi\)
\(230\) 3.10799 0.204935
\(231\) 10.7834 0.709493
\(232\) −9.93968 −0.652572
\(233\) 4.47438 0.293126 0.146563 0.989201i \(-0.453179\pi\)
0.146563 + 0.989201i \(0.453179\pi\)
\(234\) 1.37902 0.0901493
\(235\) 0.834159 0.0544146
\(236\) −2.55627 −0.166399
\(237\) −35.8018 −2.32557
\(238\) −28.0417 −1.81768
\(239\) −22.0632 −1.42715 −0.713573 0.700580i \(-0.752924\pi\)
−0.713573 + 0.700580i \(0.752924\pi\)
\(240\) 0.851027 0.0549336
\(241\) −9.29260 −0.598589 −0.299294 0.954161i \(-0.596751\pi\)
−0.299294 + 0.954161i \(0.596751\pi\)
\(242\) 1.00000 0.0642824
\(243\) −16.4142 −1.05297
\(244\) 0.705682 0.0451767
\(245\) 6.74765 0.431092
\(246\) 12.2314 0.779843
\(247\) −0.870705 −0.0554016
\(248\) 3.43616 0.218196
\(249\) −27.2061 −1.72411
\(250\) −3.83400 −0.242484
\(251\) 20.3196 1.28256 0.641281 0.767306i \(-0.278403\pi\)
0.641281 + 0.767306i \(0.278403\pi\)
\(252\) 8.77442 0.552736
\(253\) 7.98354 0.501921
\(254\) 15.6271 0.980532
\(255\) −4.83785 −0.302958
\(256\) 1.00000 0.0625000
\(257\) 1.26798 0.0790942 0.0395471 0.999218i \(-0.487408\pi\)
0.0395471 + 0.999218i \(0.487408\pi\)
\(258\) 17.0505 1.06152
\(259\) 34.2509 2.12825
\(260\) 0.301809 0.0187174
\(261\) −17.6805 −1.09440
\(262\) −12.0105 −0.742014
\(263\) 9.41962 0.580838 0.290419 0.956900i \(-0.406205\pi\)
0.290419 + 0.956900i \(0.406205\pi\)
\(264\) 2.18604 0.134542
\(265\) −2.66366 −0.163627
\(266\) −5.54012 −0.339686
\(267\) 28.7130 1.75721
\(268\) 3.66172 0.223675
\(269\) −4.91837 −0.299878 −0.149939 0.988695i \(-0.547908\pi\)
−0.149939 + 0.988695i \(0.547908\pi\)
\(270\) −1.03929 −0.0632492
\(271\) −26.7158 −1.62287 −0.811436 0.584442i \(-0.801314\pi\)
−0.811436 + 0.584442i \(0.801314\pi\)
\(272\) −5.68472 −0.344687
\(273\) 8.35992 0.505965
\(274\) −21.2914 −1.28626
\(275\) −4.84845 −0.292372
\(276\) 17.4524 1.05051
\(277\) 25.6570 1.54158 0.770789 0.637091i \(-0.219862\pi\)
0.770789 + 0.637091i \(0.219862\pi\)
\(278\) −6.41890 −0.384980
\(279\) 6.11217 0.365926
\(280\) 1.92035 0.114763
\(281\) 0.483127 0.0288210 0.0144105 0.999896i \(-0.495413\pi\)
0.0144105 + 0.999896i \(0.495413\pi\)
\(282\) 4.68406 0.278932
\(283\) −9.30471 −0.553107 −0.276554 0.960998i \(-0.589192\pi\)
−0.276554 + 0.960998i \(0.589192\pi\)
\(284\) −5.92511 −0.351591
\(285\) −0.955799 −0.0566166
\(286\) 0.775260 0.0458421
\(287\) 27.6002 1.62919
\(288\) 1.77878 0.104816
\(289\) 15.3161 0.900945
\(290\) −3.86952 −0.227226
\(291\) 3.18368 0.186631
\(292\) 6.54769 0.383175
\(293\) 4.60308 0.268915 0.134457 0.990919i \(-0.457071\pi\)
0.134457 + 0.990919i \(0.457071\pi\)
\(294\) 37.8902 2.20980
\(295\) −0.995156 −0.0579402
\(296\) 6.94346 0.403581
\(297\) −2.66964 −0.154908
\(298\) 12.3096 0.713075
\(299\) 6.18932 0.357938
\(300\) −10.5989 −0.611928
\(301\) 38.4745 2.21764
\(302\) −12.2838 −0.706853
\(303\) −41.7328 −2.39749
\(304\) −1.12311 −0.0644149
\(305\) 0.274722 0.0157305
\(306\) −10.1119 −0.578058
\(307\) 4.14367 0.236492 0.118246 0.992984i \(-0.462273\pi\)
0.118246 + 0.992984i \(0.462273\pi\)
\(308\) 4.93283 0.281074
\(309\) −41.2133 −2.34454
\(310\) 1.33770 0.0759761
\(311\) 32.5675 1.84673 0.923367 0.383919i \(-0.125426\pi\)
0.923367 + 0.383919i \(0.125426\pi\)
\(312\) 1.69475 0.0959464
\(313\) 11.0509 0.624635 0.312318 0.949978i \(-0.398895\pi\)
0.312318 + 0.949978i \(0.398895\pi\)
\(314\) 14.1766 0.800033
\(315\) 3.41588 0.192463
\(316\) −16.3774 −0.921302
\(317\) 7.53342 0.423119 0.211559 0.977365i \(-0.432146\pi\)
0.211559 + 0.977365i \(0.432146\pi\)
\(318\) −14.9573 −0.838762
\(319\) −9.93968 −0.556515
\(320\) 0.389300 0.0217625
\(321\) 9.70184 0.541504
\(322\) 39.3814 2.19464
\(323\) 6.38458 0.355248
\(324\) −11.1723 −0.620682
\(325\) −3.75881 −0.208501
\(326\) −1.04017 −0.0576095
\(327\) 6.78421 0.375168
\(328\) 5.59521 0.308944
\(329\) 10.5696 0.582723
\(330\) 0.851027 0.0468475
\(331\) 11.5271 0.633584 0.316792 0.948495i \(-0.397394\pi\)
0.316792 + 0.948495i \(0.397394\pi\)
\(332\) −12.4454 −0.683027
\(333\) 12.3509 0.676825
\(334\) 11.9099 0.651679
\(335\) 1.42551 0.0778838
\(336\) 10.7834 0.588281
\(337\) 16.1314 0.878732 0.439366 0.898308i \(-0.355203\pi\)
0.439366 + 0.898308i \(0.355203\pi\)
\(338\) −12.3990 −0.674415
\(339\) −3.22553 −0.175187
\(340\) −2.21306 −0.120020
\(341\) 3.43616 0.186078
\(342\) −1.99777 −0.108027
\(343\) 50.9697 2.75211
\(344\) 7.79970 0.420531
\(345\) 6.79421 0.365788
\(346\) −4.62647 −0.248721
\(347\) −0.902306 −0.0484383 −0.0242192 0.999707i \(-0.507710\pi\)
−0.0242192 + 0.999707i \(0.507710\pi\)
\(348\) −21.7286 −1.16477
\(349\) 20.8256 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(350\) −23.9165 −1.27839
\(351\) −2.06966 −0.110470
\(352\) 1.00000 0.0533002
\(353\) −19.4315 −1.03424 −0.517118 0.855914i \(-0.672995\pi\)
−0.517118 + 0.855914i \(0.672995\pi\)
\(354\) −5.58811 −0.297005
\(355\) −2.30665 −0.122424
\(356\) 13.1347 0.696138
\(357\) −61.3004 −3.24436
\(358\) 21.5158 1.13715
\(359\) −13.6692 −0.721433 −0.360717 0.932675i \(-0.617468\pi\)
−0.360717 + 0.932675i \(0.617468\pi\)
\(360\) 0.692480 0.0364969
\(361\) −17.7386 −0.933612
\(362\) 11.5012 0.604489
\(363\) 2.18604 0.114737
\(364\) 3.82422 0.200444
\(365\) 2.54902 0.133422
\(366\) 1.54265 0.0806356
\(367\) 13.1334 0.685556 0.342778 0.939416i \(-0.388632\pi\)
0.342778 + 0.939416i \(0.388632\pi\)
\(368\) 7.98354 0.416171
\(369\) 9.95265 0.518114
\(370\) 2.70309 0.140527
\(371\) −33.7512 −1.75228
\(372\) 7.51158 0.389457
\(373\) −18.4840 −0.957063 −0.478532 0.878070i \(-0.658831\pi\)
−0.478532 + 0.878070i \(0.658831\pi\)
\(374\) −5.68472 −0.293950
\(375\) −8.38129 −0.432808
\(376\) 2.14271 0.110502
\(377\) −7.70584 −0.396871
\(378\) −13.1689 −0.677333
\(379\) −22.5634 −1.15901 −0.579503 0.814970i \(-0.696753\pi\)
−0.579503 + 0.814970i \(0.696753\pi\)
\(380\) −0.437228 −0.0224293
\(381\) 34.1615 1.75015
\(382\) −14.2034 −0.726710
\(383\) −33.1128 −1.69198 −0.845992 0.533196i \(-0.820991\pi\)
−0.845992 + 0.533196i \(0.820991\pi\)
\(384\) 2.18604 0.111556
\(385\) 1.92035 0.0978701
\(386\) −8.33214 −0.424095
\(387\) 13.8740 0.705253
\(388\) 1.45637 0.0739358
\(389\) −23.0986 −1.17115 −0.585574 0.810619i \(-0.699131\pi\)
−0.585574 + 0.810619i \(0.699131\pi\)
\(390\) 0.659767 0.0334086
\(391\) −45.3842 −2.29518
\(392\) 17.3328 0.875437
\(393\) −26.2556 −1.32442
\(394\) 1.00000 0.0503793
\(395\) −6.37574 −0.320798
\(396\) 1.77878 0.0893871
\(397\) −1.24697 −0.0625834 −0.0312917 0.999510i \(-0.509962\pi\)
−0.0312917 + 0.999510i \(0.509962\pi\)
\(398\) −4.67312 −0.234243
\(399\) −12.1109 −0.606305
\(400\) −4.84845 −0.242422
\(401\) 1.76907 0.0883431 0.0441715 0.999024i \(-0.485935\pi\)
0.0441715 + 0.999024i \(0.485935\pi\)
\(402\) 8.00467 0.399237
\(403\) 2.66392 0.132699
\(404\) −19.0906 −0.949792
\(405\) −4.34937 −0.216122
\(406\) −49.0307 −2.43335
\(407\) 6.94346 0.344175
\(408\) −12.4270 −0.615230
\(409\) 19.8592 0.981973 0.490986 0.871167i \(-0.336636\pi\)
0.490986 + 0.871167i \(0.336636\pi\)
\(410\) 2.17822 0.107574
\(411\) −46.5438 −2.29584
\(412\) −18.8529 −0.928818
\(413\) −12.6096 −0.620479
\(414\) 14.2010 0.697940
\(415\) −4.84498 −0.237831
\(416\) 0.775260 0.0380103
\(417\) −14.0320 −0.687150
\(418\) −1.12311 −0.0549332
\(419\) −32.6124 −1.59322 −0.796609 0.604495i \(-0.793375\pi\)
−0.796609 + 0.604495i \(0.793375\pi\)
\(420\) 4.19797 0.204840
\(421\) 16.3556 0.797124 0.398562 0.917141i \(-0.369509\pi\)
0.398562 + 0.917141i \(0.369509\pi\)
\(422\) 9.76819 0.475508
\(423\) 3.81142 0.185318
\(424\) −6.84216 −0.332285
\(425\) 27.5621 1.33696
\(426\) −12.9525 −0.627553
\(427\) 3.48101 0.168458
\(428\) 4.43808 0.214523
\(429\) 1.69475 0.0818234
\(430\) 3.03642 0.146429
\(431\) −27.6455 −1.33164 −0.665819 0.746113i \(-0.731918\pi\)
−0.665819 + 0.746113i \(0.731918\pi\)
\(432\) −2.66964 −0.128443
\(433\) 28.8663 1.38723 0.693614 0.720347i \(-0.256018\pi\)
0.693614 + 0.720347i \(0.256018\pi\)
\(434\) 16.9500 0.813624
\(435\) −8.45894 −0.405575
\(436\) 3.10342 0.148627
\(437\) −8.96641 −0.428922
\(438\) 14.3135 0.683927
\(439\) −30.2827 −1.44531 −0.722657 0.691207i \(-0.757079\pi\)
−0.722657 + 0.691207i \(0.757079\pi\)
\(440\) 0.389300 0.0185592
\(441\) 30.8312 1.46815
\(442\) −4.40714 −0.209626
\(443\) −17.5265 −0.832711 −0.416356 0.909202i \(-0.636693\pi\)
−0.416356 + 0.909202i \(0.636693\pi\)
\(444\) 15.1787 0.720349
\(445\) 5.11334 0.242396
\(446\) −4.69464 −0.222298
\(447\) 26.9093 1.27276
\(448\) 4.93283 0.233054
\(449\) −0.319442 −0.0150754 −0.00753770 0.999972i \(-0.502399\pi\)
−0.00753770 + 0.999972i \(0.502399\pi\)
\(450\) −8.62432 −0.406554
\(451\) 5.59521 0.263468
\(452\) −1.47551 −0.0694022
\(453\) −26.8529 −1.26166
\(454\) 27.9405 1.31131
\(455\) 1.48877 0.0697947
\(456\) −2.45517 −0.114974
\(457\) −13.8474 −0.647755 −0.323878 0.946099i \(-0.604987\pi\)
−0.323878 + 0.946099i \(0.604987\pi\)
\(458\) −6.53180 −0.305211
\(459\) 15.1761 0.708362
\(460\) 3.10799 0.144911
\(461\) −20.5144 −0.955451 −0.477726 0.878509i \(-0.658539\pi\)
−0.477726 + 0.878509i \(0.658539\pi\)
\(462\) 10.7834 0.501688
\(463\) −19.8953 −0.924613 −0.462306 0.886720i \(-0.652978\pi\)
−0.462306 + 0.886720i \(0.652978\pi\)
\(464\) −9.93968 −0.461438
\(465\) 2.92426 0.135609
\(466\) 4.47438 0.207271
\(467\) 21.9574 1.01607 0.508034 0.861337i \(-0.330372\pi\)
0.508034 + 0.861337i \(0.330372\pi\)
\(468\) 1.37902 0.0637452
\(469\) 18.0626 0.834054
\(470\) 0.834159 0.0384769
\(471\) 30.9907 1.42798
\(472\) −2.55627 −0.117662
\(473\) 7.79970 0.358630
\(474\) −35.8018 −1.64443
\(475\) 5.44535 0.249850
\(476\) −28.0417 −1.28529
\(477\) −12.1707 −0.557259
\(478\) −22.0632 −1.00915
\(479\) −7.94047 −0.362809 −0.181405 0.983409i \(-0.558064\pi\)
−0.181405 + 0.983409i \(0.558064\pi\)
\(480\) 0.851027 0.0388439
\(481\) 5.38299 0.245443
\(482\) −9.29260 −0.423266
\(483\) 86.0894 3.91720
\(484\) 1.00000 0.0454545
\(485\) 0.566964 0.0257445
\(486\) −16.4142 −0.744562
\(487\) 13.9288 0.631172 0.315586 0.948897i \(-0.397799\pi\)
0.315586 + 0.948897i \(0.397799\pi\)
\(488\) 0.705682 0.0319447
\(489\) −2.27385 −0.102827
\(490\) 6.74765 0.304828
\(491\) −9.36573 −0.422670 −0.211335 0.977414i \(-0.567781\pi\)
−0.211335 + 0.977414i \(0.567781\pi\)
\(492\) 12.2314 0.551432
\(493\) 56.5043 2.54483
\(494\) −0.870705 −0.0391748
\(495\) 0.692480 0.0311247
\(496\) 3.43616 0.154288
\(497\) −29.2275 −1.31103
\(498\) −27.2061 −1.21913
\(499\) −2.10961 −0.0944391 −0.0472195 0.998885i \(-0.515036\pi\)
−0.0472195 + 0.998885i \(0.515036\pi\)
\(500\) −3.83400 −0.171462
\(501\) 26.0355 1.16318
\(502\) 20.3196 0.906909
\(503\) 12.7055 0.566508 0.283254 0.959045i \(-0.408586\pi\)
0.283254 + 0.959045i \(0.408586\pi\)
\(504\) 8.77442 0.390844
\(505\) −7.43197 −0.330718
\(506\) 7.98354 0.354912
\(507\) −27.1047 −1.20376
\(508\) 15.6271 0.693341
\(509\) 20.5922 0.912731 0.456366 0.889792i \(-0.349151\pi\)
0.456366 + 0.889792i \(0.349151\pi\)
\(510\) −4.83785 −0.214224
\(511\) 32.2986 1.42881
\(512\) 1.00000 0.0441942
\(513\) 2.99830 0.132378
\(514\) 1.26798 0.0559281
\(515\) −7.33946 −0.323415
\(516\) 17.0505 0.750605
\(517\) 2.14271 0.0942365
\(518\) 34.2509 1.50490
\(519\) −10.1137 −0.443941
\(520\) 0.301809 0.0132352
\(521\) −7.09017 −0.310626 −0.155313 0.987865i \(-0.549639\pi\)
−0.155313 + 0.987865i \(0.549639\pi\)
\(522\) −17.6805 −0.773855
\(523\) −8.26602 −0.361448 −0.180724 0.983534i \(-0.557844\pi\)
−0.180724 + 0.983534i \(0.557844\pi\)
\(524\) −12.0105 −0.524683
\(525\) −52.2826 −2.28180
\(526\) 9.41962 0.410715
\(527\) −19.5336 −0.850897
\(528\) 2.18604 0.0951353
\(529\) 40.7369 1.77117
\(530\) −2.66366 −0.115702
\(531\) −4.54704 −0.197325
\(532\) −5.54012 −0.240195
\(533\) 4.33774 0.187888
\(534\) 28.7130 1.24253
\(535\) 1.72775 0.0746970
\(536\) 3.66172 0.158162
\(537\) 47.0345 2.02969
\(538\) −4.91837 −0.212046
\(539\) 17.3328 0.746575
\(540\) −1.03929 −0.0447239
\(541\) −1.71185 −0.0735982 −0.0367991 0.999323i \(-0.511716\pi\)
−0.0367991 + 0.999323i \(0.511716\pi\)
\(542\) −26.7158 −1.14754
\(543\) 25.1421 1.07895
\(544\) −5.68472 −0.243730
\(545\) 1.20816 0.0517520
\(546\) 8.35992 0.357771
\(547\) −28.6175 −1.22360 −0.611799 0.791013i \(-0.709554\pi\)
−0.611799 + 0.791013i \(0.709554\pi\)
\(548\) −21.2914 −0.909522
\(549\) 1.25525 0.0535729
\(550\) −4.84845 −0.206738
\(551\) 11.1634 0.475576
\(552\) 17.4524 0.742822
\(553\) −80.7870 −3.43541
\(554\) 25.6570 1.09006
\(555\) 5.90907 0.250826
\(556\) −6.41890 −0.272222
\(557\) 14.9097 0.631744 0.315872 0.948802i \(-0.397703\pi\)
0.315872 + 0.948802i \(0.397703\pi\)
\(558\) 6.11217 0.258749
\(559\) 6.04680 0.255752
\(560\) 1.92035 0.0811496
\(561\) −12.4270 −0.524670
\(562\) 0.483127 0.0203795
\(563\) −25.6860 −1.08254 −0.541268 0.840850i \(-0.682056\pi\)
−0.541268 + 0.840850i \(0.682056\pi\)
\(564\) 4.68406 0.197235
\(565\) −0.574417 −0.0241659
\(566\) −9.30471 −0.391106
\(567\) −55.1109 −2.31444
\(568\) −5.92511 −0.248612
\(569\) −30.8376 −1.29278 −0.646389 0.763008i \(-0.723722\pi\)
−0.646389 + 0.763008i \(0.723722\pi\)
\(570\) −0.955799 −0.0400340
\(571\) −23.7625 −0.994429 −0.497214 0.867628i \(-0.665644\pi\)
−0.497214 + 0.867628i \(0.665644\pi\)
\(572\) 0.775260 0.0324153
\(573\) −31.0493 −1.29710
\(574\) 27.6002 1.15201
\(575\) −38.7078 −1.61423
\(576\) 1.77878 0.0741159
\(577\) 36.5603 1.52202 0.761012 0.648738i \(-0.224703\pi\)
0.761012 + 0.648738i \(0.224703\pi\)
\(578\) 15.3161 0.637065
\(579\) −18.2144 −0.756965
\(580\) −3.86952 −0.160673
\(581\) −61.3907 −2.54692
\(582\) 3.18368 0.131968
\(583\) −6.84216 −0.283373
\(584\) 6.54769 0.270945
\(585\) 0.536852 0.0221961
\(586\) 4.60308 0.190151
\(587\) −19.7982 −0.817159 −0.408580 0.912723i \(-0.633976\pi\)
−0.408580 + 0.912723i \(0.633976\pi\)
\(588\) 37.8902 1.56256
\(589\) −3.85919 −0.159015
\(590\) −0.995156 −0.0409699
\(591\) 2.18604 0.0899218
\(592\) 6.94346 0.285375
\(593\) 3.89133 0.159798 0.0798988 0.996803i \(-0.474540\pi\)
0.0798988 + 0.996803i \(0.474540\pi\)
\(594\) −2.66964 −0.109537
\(595\) −10.9167 −0.447539
\(596\) 12.3096 0.504220
\(597\) −10.2156 −0.418099
\(598\) 6.18932 0.253100
\(599\) 47.0370 1.92188 0.960939 0.276761i \(-0.0892609\pi\)
0.960939 + 0.276761i \(0.0892609\pi\)
\(600\) −10.5989 −0.432699
\(601\) 33.3486 1.36032 0.680158 0.733065i \(-0.261911\pi\)
0.680158 + 0.733065i \(0.261911\pi\)
\(602\) 38.4745 1.56811
\(603\) 6.51340 0.265246
\(604\) −12.2838 −0.499820
\(605\) 0.389300 0.0158273
\(606\) −41.7328 −1.69528
\(607\) −25.9755 −1.05431 −0.527157 0.849768i \(-0.676742\pi\)
−0.527157 + 0.849768i \(0.676742\pi\)
\(608\) −1.12311 −0.0455482
\(609\) −107.183 −4.34328
\(610\) 0.274722 0.0111232
\(611\) 1.66116 0.0672034
\(612\) −10.1119 −0.408748
\(613\) −24.4618 −0.988005 −0.494002 0.869461i \(-0.664467\pi\)
−0.494002 + 0.869461i \(0.664467\pi\)
\(614\) 4.14367 0.167225
\(615\) 4.76167 0.192009
\(616\) 4.93283 0.198749
\(617\) −25.8086 −1.03902 −0.519508 0.854465i \(-0.673885\pi\)
−0.519508 + 0.854465i \(0.673885\pi\)
\(618\) −41.2133 −1.65784
\(619\) 42.1127 1.69265 0.846326 0.532666i \(-0.178810\pi\)
0.846326 + 0.532666i \(0.178810\pi\)
\(620\) 1.33770 0.0537232
\(621\) −21.3131 −0.855267
\(622\) 32.5675 1.30584
\(623\) 64.7912 2.59580
\(624\) 1.69475 0.0678444
\(625\) 22.7496 0.909986
\(626\) 11.0509 0.441684
\(627\) −2.45517 −0.0980501
\(628\) 14.1766 0.565709
\(629\) −39.4717 −1.57384
\(630\) 3.41588 0.136092
\(631\) 15.3047 0.609270 0.304635 0.952469i \(-0.401466\pi\)
0.304635 + 0.952469i \(0.401466\pi\)
\(632\) −16.3774 −0.651459
\(633\) 21.3537 0.848732
\(634\) 7.53342 0.299190
\(635\) 6.08364 0.241422
\(636\) −14.9573 −0.593094
\(637\) 13.4374 0.532409
\(638\) −9.93968 −0.393516
\(639\) −10.5395 −0.416935
\(640\) 0.389300 0.0153884
\(641\) 15.4150 0.608855 0.304428 0.952535i \(-0.401535\pi\)
0.304428 + 0.952535i \(0.401535\pi\)
\(642\) 9.70184 0.382901
\(643\) 42.3479 1.67004 0.835020 0.550220i \(-0.185456\pi\)
0.835020 + 0.550220i \(0.185456\pi\)
\(644\) 39.3814 1.55184
\(645\) 6.63775 0.261361
\(646\) 6.38458 0.251198
\(647\) −22.5470 −0.886414 −0.443207 0.896419i \(-0.646159\pi\)
−0.443207 + 0.896419i \(0.646159\pi\)
\(648\) −11.1723 −0.438889
\(649\) −2.55627 −0.100342
\(650\) −3.75881 −0.147433
\(651\) 37.0533 1.45223
\(652\) −1.04017 −0.0407361
\(653\) −23.1557 −0.906154 −0.453077 0.891471i \(-0.649674\pi\)
−0.453077 + 0.891471i \(0.649674\pi\)
\(654\) 6.78421 0.265284
\(655\) −4.67571 −0.182695
\(656\) 5.59521 0.218456
\(657\) 11.6469 0.454389
\(658\) 10.5696 0.412047
\(659\) 43.3685 1.68940 0.844699 0.535242i \(-0.179780\pi\)
0.844699 + 0.535242i \(0.179780\pi\)
\(660\) 0.851027 0.0331262
\(661\) 27.2414 1.05957 0.529784 0.848132i \(-0.322273\pi\)
0.529784 + 0.848132i \(0.322273\pi\)
\(662\) 11.5271 0.448012
\(663\) −9.63420 −0.374161
\(664\) −12.4454 −0.482973
\(665\) −2.15677 −0.0836359
\(666\) 12.3509 0.478588
\(667\) −79.3538 −3.07259
\(668\) 11.9099 0.460807
\(669\) −10.2627 −0.396778
\(670\) 1.42551 0.0550722
\(671\) 0.705682 0.0272425
\(672\) 10.7834 0.415977
\(673\) −49.4379 −1.90569 −0.952845 0.303458i \(-0.901859\pi\)
−0.952845 + 0.303458i \(0.901859\pi\)
\(674\) 16.1314 0.621357
\(675\) 12.9436 0.498199
\(676\) −12.3990 −0.476884
\(677\) 24.6273 0.946504 0.473252 0.880927i \(-0.343080\pi\)
0.473252 + 0.880927i \(0.343080\pi\)
\(678\) −3.22553 −0.123876
\(679\) 7.18400 0.275697
\(680\) −2.21306 −0.0848671
\(681\) 61.0792 2.34056
\(682\) 3.43616 0.131577
\(683\) 18.4662 0.706588 0.353294 0.935512i \(-0.385062\pi\)
0.353294 + 0.935512i \(0.385062\pi\)
\(684\) −1.99777 −0.0763867
\(685\) −8.28874 −0.316696
\(686\) 50.9697 1.94603
\(687\) −14.2788 −0.544770
\(688\) 7.79970 0.297361
\(689\) −5.30446 −0.202084
\(690\) 6.79421 0.258651
\(691\) −48.7834 −1.85581 −0.927904 0.372818i \(-0.878392\pi\)
−0.927904 + 0.372818i \(0.878392\pi\)
\(692\) −4.62647 −0.175872
\(693\) 8.77442 0.333313
\(694\) −0.902306 −0.0342511
\(695\) −2.49888 −0.0947880
\(696\) −21.7286 −0.823619
\(697\) −31.8072 −1.20478
\(698\) 20.8256 0.788261
\(699\) 9.78117 0.369958
\(700\) −23.9165 −0.903960
\(701\) 23.4917 0.887268 0.443634 0.896208i \(-0.353689\pi\)
0.443634 + 0.896208i \(0.353689\pi\)
\(702\) −2.06966 −0.0781144
\(703\) −7.79829 −0.294118
\(704\) 1.00000 0.0376889
\(705\) 1.82351 0.0686773
\(706\) −19.4315 −0.731315
\(707\) −94.1705 −3.54165
\(708\) −5.58811 −0.210014
\(709\) −42.2792 −1.58783 −0.793915 0.608029i \(-0.791961\pi\)
−0.793915 + 0.608029i \(0.791961\pi\)
\(710\) −2.30665 −0.0865670
\(711\) −29.1319 −1.09253
\(712\) 13.1347 0.492244
\(713\) 27.4327 1.02736
\(714\) −61.3004 −2.29411
\(715\) 0.301809 0.0112870
\(716\) 21.5158 0.804085
\(717\) −48.2310 −1.80122
\(718\) −13.6692 −0.510130
\(719\) −11.8908 −0.443454 −0.221727 0.975109i \(-0.571169\pi\)
−0.221727 + 0.975109i \(0.571169\pi\)
\(720\) 0.692480 0.0258072
\(721\) −92.9983 −3.46344
\(722\) −17.7386 −0.660163
\(723\) −20.3140 −0.755486
\(724\) 11.5012 0.427439
\(725\) 48.1920 1.78981
\(726\) 2.18604 0.0811316
\(727\) 24.3114 0.901660 0.450830 0.892610i \(-0.351128\pi\)
0.450830 + 0.892610i \(0.351128\pi\)
\(728\) 3.82422 0.141735
\(729\) −2.36523 −0.0876010
\(730\) 2.54902 0.0943434
\(731\) −44.3391 −1.63994
\(732\) 1.54265 0.0570180
\(733\) 23.7766 0.878210 0.439105 0.898436i \(-0.355296\pi\)
0.439105 + 0.898436i \(0.355296\pi\)
\(734\) 13.1334 0.484762
\(735\) 14.7507 0.544086
\(736\) 7.98354 0.294277
\(737\) 3.66172 0.134881
\(738\) 9.95265 0.366362
\(739\) 5.71016 0.210052 0.105026 0.994469i \(-0.466507\pi\)
0.105026 + 0.994469i \(0.466507\pi\)
\(740\) 2.70309 0.0993676
\(741\) −1.90340 −0.0699230
\(742\) −33.7512 −1.23905
\(743\) 25.5682 0.938006 0.469003 0.883197i \(-0.344613\pi\)
0.469003 + 0.883197i \(0.344613\pi\)
\(744\) 7.51158 0.275388
\(745\) 4.79212 0.175570
\(746\) −18.4840 −0.676746
\(747\) −22.1376 −0.809971
\(748\) −5.68472 −0.207854
\(749\) 21.8923 0.799927
\(750\) −8.38129 −0.306042
\(751\) −13.7750 −0.502658 −0.251329 0.967902i \(-0.580868\pi\)
−0.251329 + 0.967902i \(0.580868\pi\)
\(752\) 2.14271 0.0781368
\(753\) 44.4195 1.61874
\(754\) −7.70584 −0.280630
\(755\) −4.78208 −0.174038
\(756\) −13.1689 −0.478946
\(757\) −7.81397 −0.284003 −0.142002 0.989866i \(-0.545354\pi\)
−0.142002 + 0.989866i \(0.545354\pi\)
\(758\) −22.5634 −0.819541
\(759\) 17.4524 0.633480
\(760\) −0.437228 −0.0158599
\(761\) 25.4522 0.922641 0.461321 0.887234i \(-0.347376\pi\)
0.461321 + 0.887234i \(0.347376\pi\)
\(762\) 34.1615 1.23754
\(763\) 15.3086 0.554210
\(764\) −14.2034 −0.513862
\(765\) −3.93656 −0.142327
\(766\) −33.1128 −1.19641
\(767\) −1.98177 −0.0715577
\(768\) 2.18604 0.0788820
\(769\) −2.16932 −0.0782277 −0.0391139 0.999235i \(-0.512454\pi\)
−0.0391139 + 0.999235i \(0.512454\pi\)
\(770\) 1.92035 0.0692046
\(771\) 2.77185 0.0998258
\(772\) −8.33214 −0.299880
\(773\) 53.0166 1.90688 0.953438 0.301589i \(-0.0975170\pi\)
0.953438 + 0.301589i \(0.0975170\pi\)
\(774\) 13.8740 0.498689
\(775\) −16.6600 −0.598445
\(776\) 1.45637 0.0522805
\(777\) 74.8739 2.68609
\(778\) −23.0986 −0.828126
\(779\) −6.28404 −0.225149
\(780\) 0.659767 0.0236235
\(781\) −5.92511 −0.212017
\(782\) −45.3842 −1.62294
\(783\) 26.5353 0.948296
\(784\) 17.3328 0.619027
\(785\) 5.51896 0.196980
\(786\) −26.2556 −0.936505
\(787\) −17.3658 −0.619024 −0.309512 0.950896i \(-0.600166\pi\)
−0.309512 + 0.950896i \(0.600166\pi\)
\(788\) 1.00000 0.0356235
\(789\) 20.5917 0.733083
\(790\) −6.37574 −0.226839
\(791\) −7.27844 −0.258792
\(792\) 1.77878 0.0632062
\(793\) 0.547087 0.0194276
\(794\) −1.24697 −0.0442531
\(795\) −5.82287 −0.206516
\(796\) −4.67312 −0.165635
\(797\) 5.17702 0.183380 0.0916898 0.995788i \(-0.470773\pi\)
0.0916898 + 0.995788i \(0.470773\pi\)
\(798\) −12.1109 −0.428722
\(799\) −12.1807 −0.430924
\(800\) −4.84845 −0.171418
\(801\) 23.3638 0.825518
\(802\) 1.76907 0.0624680
\(803\) 6.54769 0.231063
\(804\) 8.00467 0.282303
\(805\) 15.3312 0.540354
\(806\) 2.66392 0.0938324
\(807\) −10.7518 −0.378480
\(808\) −19.0906 −0.671604
\(809\) −52.5823 −1.84870 −0.924348 0.381551i \(-0.875390\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(810\) −4.34937 −0.152821
\(811\) −14.0755 −0.494256 −0.247128 0.968983i \(-0.579487\pi\)
−0.247128 + 0.968983i \(0.579487\pi\)
\(812\) −49.0307 −1.72064
\(813\) −58.4019 −2.04825
\(814\) 6.94346 0.243368
\(815\) −0.404937 −0.0141843
\(816\) −12.4270 −0.435034
\(817\) −8.75994 −0.306471
\(818\) 19.8592 0.694360
\(819\) 6.80246 0.237697
\(820\) 2.17822 0.0760666
\(821\) −0.748229 −0.0261134 −0.0130567 0.999915i \(-0.504156\pi\)
−0.0130567 + 0.999915i \(0.504156\pi\)
\(822\) −46.5438 −1.62340
\(823\) 18.1188 0.631581 0.315790 0.948829i \(-0.397730\pi\)
0.315790 + 0.948829i \(0.397730\pi\)
\(824\) −18.8529 −0.656773
\(825\) −10.5989 −0.369007
\(826\) −12.6096 −0.438745
\(827\) 39.5905 1.37670 0.688348 0.725380i \(-0.258336\pi\)
0.688348 + 0.725380i \(0.258336\pi\)
\(828\) 14.2010 0.493518
\(829\) −33.1881 −1.15267 −0.576334 0.817214i \(-0.695517\pi\)
−0.576334 + 0.817214i \(0.695517\pi\)
\(830\) −4.84498 −0.168172
\(831\) 56.0872 1.94564
\(832\) 0.775260 0.0268773
\(833\) −98.5320 −3.41393
\(834\) −14.0320 −0.485888
\(835\) 4.63652 0.160453
\(836\) −1.12311 −0.0388437
\(837\) −9.17329 −0.317075
\(838\) −32.6124 −1.12658
\(839\) −1.85772 −0.0641356 −0.0320678 0.999486i \(-0.510209\pi\)
−0.0320678 + 0.999486i \(0.510209\pi\)
\(840\) 4.19797 0.144844
\(841\) 69.7973 2.40680
\(842\) 16.3556 0.563652
\(843\) 1.05614 0.0363753
\(844\) 9.76819 0.336235
\(845\) −4.82692 −0.166051
\(846\) 3.81142 0.131039
\(847\) 4.93283 0.169494
\(848\) −6.84216 −0.234961
\(849\) −20.3405 −0.698084
\(850\) 27.5621 0.945371
\(851\) 55.4334 1.90023
\(852\) −12.9525 −0.443747
\(853\) 33.5899 1.15010 0.575048 0.818120i \(-0.304983\pi\)
0.575048 + 0.818120i \(0.304983\pi\)
\(854\) 3.48101 0.119118
\(855\) −0.777733 −0.0265979
\(856\) 4.43808 0.151691
\(857\) −30.9089 −1.05583 −0.527914 0.849298i \(-0.677026\pi\)
−0.527914 + 0.849298i \(0.677026\pi\)
\(858\) 1.69475 0.0578579
\(859\) 1.76822 0.0603308 0.0301654 0.999545i \(-0.490397\pi\)
0.0301654 + 0.999545i \(0.490397\pi\)
\(860\) 3.03642 0.103541
\(861\) 60.3351 2.05622
\(862\) −27.6455 −0.941610
\(863\) −9.88514 −0.336494 −0.168247 0.985745i \(-0.553811\pi\)
−0.168247 + 0.985745i \(0.553811\pi\)
\(864\) −2.66964 −0.0908229
\(865\) −1.80109 −0.0612388
\(866\) 28.8663 0.980918
\(867\) 33.4816 1.13709
\(868\) 16.9500 0.575319
\(869\) −16.3774 −0.555566
\(870\) −8.45894 −0.286785
\(871\) 2.83879 0.0961886
\(872\) 3.10342 0.105095
\(873\) 2.59056 0.0876771
\(874\) −8.96641 −0.303293
\(875\) −18.9125 −0.639358
\(876\) 14.3135 0.483609
\(877\) 14.3047 0.483034 0.241517 0.970397i \(-0.422355\pi\)
0.241517 + 0.970397i \(0.422355\pi\)
\(878\) −30.2827 −1.02199
\(879\) 10.0625 0.339401
\(880\) 0.389300 0.0131233
\(881\) 13.5867 0.457747 0.228873 0.973456i \(-0.426496\pi\)
0.228873 + 0.973456i \(0.426496\pi\)
\(882\) 30.8312 1.03814
\(883\) 28.2712 0.951401 0.475700 0.879607i \(-0.342195\pi\)
0.475700 + 0.879607i \(0.342195\pi\)
\(884\) −4.40714 −0.148228
\(885\) −2.17545 −0.0731270
\(886\) −17.5265 −0.588816
\(887\) 28.8603 0.969034 0.484517 0.874782i \(-0.338995\pi\)
0.484517 + 0.874782i \(0.338995\pi\)
\(888\) 15.1787 0.509364
\(889\) 77.0858 2.58538
\(890\) 5.11334 0.171400
\(891\) −11.1723 −0.374286
\(892\) −4.69464 −0.157188
\(893\) −2.40651 −0.0805308
\(894\) 26.9093 0.899980
\(895\) 8.37612 0.279983
\(896\) 4.93283 0.164794
\(897\) 13.5301 0.451758
\(898\) −0.319442 −0.0106599
\(899\) −34.1543 −1.13911
\(900\) −8.62432 −0.287477
\(901\) 38.8958 1.29581
\(902\) 5.59521 0.186300
\(903\) 84.1070 2.79891
\(904\) −1.47551 −0.0490748
\(905\) 4.47742 0.148834
\(906\) −26.8529 −0.892127
\(907\) 39.5765 1.31412 0.657058 0.753840i \(-0.271801\pi\)
0.657058 + 0.753840i \(0.271801\pi\)
\(908\) 27.9405 0.927239
\(909\) −33.9580 −1.12631
\(910\) 1.48877 0.0493523
\(911\) 34.5285 1.14398 0.571990 0.820260i \(-0.306172\pi\)
0.571990 + 0.820260i \(0.306172\pi\)
\(912\) −2.45517 −0.0812988
\(913\) −12.4454 −0.411881
\(914\) −13.8474 −0.458032
\(915\) 0.600554 0.0198537
\(916\) −6.53180 −0.215817
\(917\) −59.2459 −1.95647
\(918\) 15.1761 0.500887
\(919\) 28.8019 0.950087 0.475044 0.879962i \(-0.342432\pi\)
0.475044 + 0.879962i \(0.342432\pi\)
\(920\) 3.10799 0.102468
\(921\) 9.05825 0.298479
\(922\) −20.5144 −0.675606
\(923\) −4.59351 −0.151197
\(924\) 10.7834 0.354747
\(925\) −33.6650 −1.10690
\(926\) −19.8953 −0.653800
\(927\) −33.5353 −1.10144
\(928\) −9.93968 −0.326286
\(929\) −36.9290 −1.21160 −0.605801 0.795616i \(-0.707147\pi\)
−0.605801 + 0.795616i \(0.707147\pi\)
\(930\) 2.92426 0.0958903
\(931\) −19.4666 −0.637993
\(932\) 4.47438 0.146563
\(933\) 71.1939 2.33078
\(934\) 21.9574 0.718468
\(935\) −2.21306 −0.0723749
\(936\) 1.37902 0.0450746
\(937\) 4.93365 0.161175 0.0805876 0.996748i \(-0.474320\pi\)
0.0805876 + 0.996748i \(0.474320\pi\)
\(938\) 18.0626 0.589765
\(939\) 24.1578 0.788360
\(940\) 0.834159 0.0272073
\(941\) 2.18510 0.0712323 0.0356162 0.999366i \(-0.488661\pi\)
0.0356162 + 0.999366i \(0.488661\pi\)
\(942\) 30.9907 1.00973
\(943\) 44.6695 1.45464
\(944\) −2.55627 −0.0831994
\(945\) −5.12664 −0.166770
\(946\) 7.79970 0.253590
\(947\) 22.0405 0.716219 0.358109 0.933680i \(-0.383421\pi\)
0.358109 + 0.933680i \(0.383421\pi\)
\(948\) −35.8018 −1.16279
\(949\) 5.07616 0.164779
\(950\) 5.44535 0.176670
\(951\) 16.4684 0.534023
\(952\) −28.0417 −0.908838
\(953\) −8.09447 −0.262206 −0.131103 0.991369i \(-0.541852\pi\)
−0.131103 + 0.991369i \(0.541852\pi\)
\(954\) −12.1707 −0.394041
\(955\) −5.52939 −0.178927
\(956\) −22.0632 −0.713573
\(957\) −21.7286 −0.702385
\(958\) −7.94047 −0.256545
\(959\) −105.027 −3.39149
\(960\) 0.851027 0.0274668
\(961\) −19.1928 −0.619124
\(962\) 5.38299 0.173555
\(963\) 7.89438 0.254393
\(964\) −9.29260 −0.299294
\(965\) −3.24370 −0.104419
\(966\) 86.0894 2.76988
\(967\) −18.0109 −0.579190 −0.289595 0.957149i \(-0.593521\pi\)
−0.289595 + 0.957149i \(0.593521\pi\)
\(968\) 1.00000 0.0321412
\(969\) 13.9570 0.448362
\(970\) 0.566964 0.0182041
\(971\) 4.49226 0.144163 0.0720817 0.997399i \(-0.477036\pi\)
0.0720817 + 0.997399i \(0.477036\pi\)
\(972\) −16.4142 −0.526485
\(973\) −31.6633 −1.01508
\(974\) 13.9288 0.446306
\(975\) −8.21691 −0.263152
\(976\) 0.705682 0.0225883
\(977\) −19.0488 −0.609425 −0.304712 0.952444i \(-0.598560\pi\)
−0.304712 + 0.952444i \(0.598560\pi\)
\(978\) −2.27385 −0.0727097
\(979\) 13.1347 0.419787
\(980\) 6.74765 0.215546
\(981\) 5.52031 0.176250
\(982\) −9.36573 −0.298873
\(983\) −58.8520 −1.87709 −0.938544 0.345159i \(-0.887825\pi\)
−0.938544 + 0.345159i \(0.887825\pi\)
\(984\) 12.2314 0.389921
\(985\) 0.389300 0.0124041
\(986\) 56.5043 1.79946
\(987\) 23.1057 0.735462
\(988\) −0.870705 −0.0277008
\(989\) 62.2692 1.98005
\(990\) 0.692480 0.0220085
\(991\) 25.3312 0.804673 0.402337 0.915492i \(-0.368198\pi\)
0.402337 + 0.915492i \(0.368198\pi\)
\(992\) 3.43616 0.109098
\(993\) 25.1986 0.799655
\(994\) −29.2275 −0.927042
\(995\) −1.81925 −0.0576741
\(996\) −27.2061 −0.862057
\(997\) 52.7205 1.66968 0.834838 0.550496i \(-0.185561\pi\)
0.834838 + 0.550496i \(0.185561\pi\)
\(998\) −2.10961 −0.0667785
\(999\) −18.5365 −0.586470
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 4334.2.a.g.1.19 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.g.1.19 26 1.1 even 1 trivial