Properties

Label 4025.2.a.be.1.18
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $0$
Dimension $21$
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] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, 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("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.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: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.35921 q^{2} +2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} +1.00000 q^{7} +3.69426 q^{8} +3.28760 q^{9} +O(q^{10})\) \(q+2.35921 q^{2} +2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} +1.00000 q^{7} +3.69426 q^{8} +3.28760 q^{9} +2.70134 q^{11} +8.94150 q^{12} +2.80434 q^{13} +2.35921 q^{14} +1.58378 q^{16} -1.99885 q^{17} +7.75616 q^{18} -1.11683 q^{19} +2.50751 q^{21} +6.37305 q^{22} +1.00000 q^{23} +9.26340 q^{24} +6.61603 q^{26} +0.721167 q^{27} +3.56589 q^{28} -8.42950 q^{29} +2.48252 q^{31} -3.65206 q^{32} +6.77365 q^{33} -4.71571 q^{34} +11.7232 q^{36} +0.807977 q^{37} -2.63485 q^{38} +7.03190 q^{39} +6.79798 q^{41} +5.91575 q^{42} +3.15924 q^{43} +9.63269 q^{44} +2.35921 q^{46} -10.0740 q^{47} +3.97133 q^{48} +1.00000 q^{49} -5.01213 q^{51} +9.99995 q^{52} -4.86545 q^{53} +1.70139 q^{54} +3.69426 q^{56} -2.80047 q^{57} -19.8870 q^{58} -12.1768 q^{59} +9.43038 q^{61} +5.85680 q^{62} +3.28760 q^{63} -11.7835 q^{64} +15.9805 q^{66} +7.25984 q^{67} -7.12767 q^{68} +2.50751 q^{69} -2.44213 q^{71} +12.1453 q^{72} +1.70335 q^{73} +1.90619 q^{74} -3.98250 q^{76} +2.70134 q^{77} +16.5898 q^{78} +15.4751 q^{79} -8.05448 q^{81} +16.0379 q^{82} +10.7887 q^{83} +8.94150 q^{84} +7.45333 q^{86} -21.1371 q^{87} +9.97947 q^{88} -8.27944 q^{89} +2.80434 q^{91} +3.56589 q^{92} +6.22495 q^{93} -23.7668 q^{94} -9.15757 q^{96} -13.2465 q^{97} +2.35921 q^{98} +8.88095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9} + 7 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} + 56 q^{16} + 7 q^{17} + 24 q^{19} - q^{21} + 4 q^{22} + 21 q^{23} + 24 q^{24} - 2 q^{26} - 19 q^{27} + 30 q^{28} + 11 q^{29} + 46 q^{31} - 6 q^{32} - 3 q^{33} + 28 q^{34} + 58 q^{36} + 24 q^{37} - 4 q^{38} + 31 q^{39} + 14 q^{41} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 2 q^{46} - 25 q^{47} - 36 q^{48} + 21 q^{49} + 17 q^{51} - 8 q^{52} + 22 q^{53} - 6 q^{54} + 6 q^{56} + 40 q^{57} + 6 q^{58} + 10 q^{59} + 38 q^{61} - 54 q^{62} + 30 q^{63} + 100 q^{64} + 38 q^{66} + 12 q^{67} + 18 q^{68} - q^{69} + 56 q^{71} + 42 q^{72} - 40 q^{73} - 20 q^{74} + 60 q^{76} + 7 q^{77} + 38 q^{78} + 49 q^{79} + 57 q^{81} + 16 q^{82} - 2 q^{83} - 22 q^{84} + 16 q^{86} - 23 q^{87} + 12 q^{88} + 28 q^{89} - 3 q^{91} + 30 q^{92} - 30 q^{93} + 66 q^{94} + 46 q^{96} - q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.35921 1.66822 0.834108 0.551601i \(-0.185983\pi\)
0.834108 + 0.551601i \(0.185983\pi\)
\(3\) 2.50751 1.44771 0.723856 0.689952i \(-0.242368\pi\)
0.723856 + 0.689952i \(0.242368\pi\)
\(4\) 3.56589 1.78294
\(5\) 0 0
\(6\) 5.91575 2.41509
\(7\) 1.00000 0.377964
\(8\) 3.69426 1.30612
\(9\) 3.28760 1.09587
\(10\) 0 0
\(11\) 2.70134 0.814486 0.407243 0.913320i \(-0.366490\pi\)
0.407243 + 0.913320i \(0.366490\pi\)
\(12\) 8.94150 2.58119
\(13\) 2.80434 0.777783 0.388892 0.921283i \(-0.372858\pi\)
0.388892 + 0.921283i \(0.372858\pi\)
\(14\) 2.35921 0.630526
\(15\) 0 0
\(16\) 1.58378 0.395944
\(17\) −1.99885 −0.484792 −0.242396 0.970177i \(-0.577933\pi\)
−0.242396 + 0.970177i \(0.577933\pi\)
\(18\) 7.75616 1.82814
\(19\) −1.11683 −0.256219 −0.128110 0.991760i \(-0.540891\pi\)
−0.128110 + 0.991760i \(0.540891\pi\)
\(20\) 0 0
\(21\) 2.50751 0.547183
\(22\) 6.37305 1.35874
\(23\) 1.00000 0.208514
\(24\) 9.26340 1.89088
\(25\) 0 0
\(26\) 6.61603 1.29751
\(27\) 0.721167 0.138789
\(28\) 3.56589 0.673889
\(29\) −8.42950 −1.56532 −0.782659 0.622450i \(-0.786137\pi\)
−0.782659 + 0.622450i \(0.786137\pi\)
\(30\) 0 0
\(31\) 2.48252 0.445875 0.222937 0.974833i \(-0.428435\pi\)
0.222937 + 0.974833i \(0.428435\pi\)
\(32\) −3.65206 −0.645598
\(33\) 6.77365 1.17914
\(34\) −4.71571 −0.808738
\(35\) 0 0
\(36\) 11.7232 1.95387
\(37\) 0.807977 0.132831 0.0664153 0.997792i \(-0.478844\pi\)
0.0664153 + 0.997792i \(0.478844\pi\)
\(38\) −2.63485 −0.427429
\(39\) 7.03190 1.12601
\(40\) 0 0
\(41\) 6.79798 1.06167 0.530833 0.847477i \(-0.321879\pi\)
0.530833 + 0.847477i \(0.321879\pi\)
\(42\) 5.91575 0.912820
\(43\) 3.15924 0.481780 0.240890 0.970552i \(-0.422561\pi\)
0.240890 + 0.970552i \(0.422561\pi\)
\(44\) 9.63269 1.45218
\(45\) 0 0
\(46\) 2.35921 0.347847
\(47\) −10.0740 −1.46945 −0.734724 0.678366i \(-0.762688\pi\)
−0.734724 + 0.678366i \(0.762688\pi\)
\(48\) 3.97133 0.573213
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.01213 −0.701839
\(52\) 9.99995 1.38674
\(53\) −4.86545 −0.668322 −0.334161 0.942516i \(-0.608453\pi\)
−0.334161 + 0.942516i \(0.608453\pi\)
\(54\) 1.70139 0.231530
\(55\) 0 0
\(56\) 3.69426 0.493666
\(57\) −2.80047 −0.370931
\(58\) −19.8870 −2.61129
\(59\) −12.1768 −1.58528 −0.792642 0.609688i \(-0.791295\pi\)
−0.792642 + 0.609688i \(0.791295\pi\)
\(60\) 0 0
\(61\) 9.43038 1.20744 0.603718 0.797198i \(-0.293685\pi\)
0.603718 + 0.797198i \(0.293685\pi\)
\(62\) 5.85680 0.743815
\(63\) 3.28760 0.414199
\(64\) −11.7835 −1.47294
\(65\) 0 0
\(66\) 15.9805 1.96706
\(67\) 7.25984 0.886930 0.443465 0.896292i \(-0.353749\pi\)
0.443465 + 0.896292i \(0.353749\pi\)
\(68\) −7.12767 −0.864357
\(69\) 2.50751 0.301869
\(70\) 0 0
\(71\) −2.44213 −0.289828 −0.144914 0.989444i \(-0.546290\pi\)
−0.144914 + 0.989444i \(0.546290\pi\)
\(72\) 12.1453 1.43133
\(73\) 1.70335 0.199362 0.0996808 0.995019i \(-0.468218\pi\)
0.0996808 + 0.995019i \(0.468218\pi\)
\(74\) 1.90619 0.221590
\(75\) 0 0
\(76\) −3.98250 −0.456824
\(77\) 2.70134 0.307847
\(78\) 16.5898 1.87842
\(79\) 15.4751 1.74108 0.870540 0.492098i \(-0.163770\pi\)
0.870540 + 0.492098i \(0.163770\pi\)
\(80\) 0 0
\(81\) −8.05448 −0.894942
\(82\) 16.0379 1.77109
\(83\) 10.7887 1.18421 0.592107 0.805860i \(-0.298296\pi\)
0.592107 + 0.805860i \(0.298296\pi\)
\(84\) 8.94150 0.975597
\(85\) 0 0
\(86\) 7.45333 0.803713
\(87\) −21.1371 −2.26613
\(88\) 9.97947 1.06382
\(89\) −8.27944 −0.877619 −0.438809 0.898580i \(-0.644600\pi\)
−0.438809 + 0.898580i \(0.644600\pi\)
\(90\) 0 0
\(91\) 2.80434 0.293974
\(92\) 3.56589 0.371769
\(93\) 6.22495 0.645498
\(94\) −23.7668 −2.45136
\(95\) 0 0
\(96\) −9.15757 −0.934640
\(97\) −13.2465 −1.34498 −0.672491 0.740106i \(-0.734776\pi\)
−0.672491 + 0.740106i \(0.734776\pi\)
\(98\) 2.35921 0.238317
\(99\) 8.88095 0.892569
\(100\) 0 0
\(101\) −13.4521 −1.33854 −0.669268 0.743021i \(-0.733392\pi\)
−0.669268 + 0.743021i \(0.733392\pi\)
\(102\) −11.8247 −1.17082
\(103\) −6.77042 −0.667109 −0.333554 0.942731i \(-0.608248\pi\)
−0.333554 + 0.942731i \(0.608248\pi\)
\(104\) 10.3600 1.01588
\(105\) 0 0
\(106\) −11.4786 −1.11490
\(107\) −10.0195 −0.968619 −0.484309 0.874897i \(-0.660929\pi\)
−0.484309 + 0.874897i \(0.660929\pi\)
\(108\) 2.57160 0.247452
\(109\) 15.5089 1.48548 0.742740 0.669580i \(-0.233526\pi\)
0.742740 + 0.669580i \(0.233526\pi\)
\(110\) 0 0
\(111\) 2.02601 0.192300
\(112\) 1.58378 0.149653
\(113\) −0.178511 −0.0167929 −0.00839645 0.999965i \(-0.502673\pi\)
−0.00839645 + 0.999965i \(0.502673\pi\)
\(114\) −6.60690 −0.618793
\(115\) 0 0
\(116\) −30.0586 −2.79088
\(117\) 9.21955 0.852348
\(118\) −28.7277 −2.64460
\(119\) −1.99885 −0.183234
\(120\) 0 0
\(121\) −3.70274 −0.336613
\(122\) 22.2483 2.01426
\(123\) 17.0460 1.53698
\(124\) 8.85240 0.794969
\(125\) 0 0
\(126\) 7.75616 0.690973
\(127\) 4.36340 0.387190 0.193595 0.981082i \(-0.437985\pi\)
0.193595 + 0.981082i \(0.437985\pi\)
\(128\) −20.4958 −1.81159
\(129\) 7.92183 0.697479
\(130\) 0 0
\(131\) −4.35393 −0.380405 −0.190202 0.981745i \(-0.560914\pi\)
−0.190202 + 0.981745i \(0.560914\pi\)
\(132\) 24.1541 2.10234
\(133\) −1.11683 −0.0968417
\(134\) 17.1275 1.47959
\(135\) 0 0
\(136\) −7.38427 −0.633196
\(137\) 10.7306 0.916780 0.458390 0.888751i \(-0.348426\pi\)
0.458390 + 0.888751i \(0.348426\pi\)
\(138\) 5.91575 0.503582
\(139\) 6.30819 0.535053 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(140\) 0 0
\(141\) −25.2607 −2.12734
\(142\) −5.76151 −0.483495
\(143\) 7.57548 0.633494
\(144\) 5.20683 0.433902
\(145\) 0 0
\(146\) 4.01856 0.332578
\(147\) 2.50751 0.206816
\(148\) 2.88116 0.236830
\(149\) −12.4249 −1.01789 −0.508943 0.860800i \(-0.669964\pi\)
−0.508943 + 0.860800i \(0.669964\pi\)
\(150\) 0 0
\(151\) −11.9899 −0.975727 −0.487864 0.872920i \(-0.662224\pi\)
−0.487864 + 0.872920i \(0.662224\pi\)
\(152\) −4.12587 −0.334653
\(153\) −6.57142 −0.531268
\(154\) 6.37305 0.513555
\(155\) 0 0
\(156\) 25.0750 2.00760
\(157\) 15.0216 1.19885 0.599427 0.800430i \(-0.295395\pi\)
0.599427 + 0.800430i \(0.295395\pi\)
\(158\) 36.5090 2.90450
\(159\) −12.2002 −0.967537
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) −19.0022 −1.49296
\(163\) 5.77178 0.452080 0.226040 0.974118i \(-0.427422\pi\)
0.226040 + 0.974118i \(0.427422\pi\)
\(164\) 24.2408 1.89289
\(165\) 0 0
\(166\) 25.4528 1.97552
\(167\) −0.00532684 −0.000412203 0 −0.000206101 1.00000i \(-0.500066\pi\)
−0.000206101 1.00000i \(0.500066\pi\)
\(168\) 9.26340 0.714686
\(169\) −5.13569 −0.395053
\(170\) 0 0
\(171\) −3.67170 −0.280782
\(172\) 11.2655 0.858987
\(173\) 20.7072 1.57434 0.787168 0.616739i \(-0.211546\pi\)
0.787168 + 0.616739i \(0.211546\pi\)
\(174\) −49.8668 −3.78039
\(175\) 0 0
\(176\) 4.27833 0.322491
\(177\) −30.5334 −2.29503
\(178\) −19.5330 −1.46406
\(179\) −12.1561 −0.908586 −0.454293 0.890852i \(-0.650108\pi\)
−0.454293 + 0.890852i \(0.650108\pi\)
\(180\) 0 0
\(181\) −12.8574 −0.955683 −0.477842 0.878446i \(-0.658581\pi\)
−0.477842 + 0.878446i \(0.658581\pi\)
\(182\) 6.61603 0.490413
\(183\) 23.6468 1.74802
\(184\) 3.69426 0.272345
\(185\) 0 0
\(186\) 14.6860 1.07683
\(187\) −5.39958 −0.394856
\(188\) −35.9228 −2.61994
\(189\) 0.721167 0.0524572
\(190\) 0 0
\(191\) 12.9308 0.935639 0.467820 0.883824i \(-0.345040\pi\)
0.467820 + 0.883824i \(0.345040\pi\)
\(192\) −29.5473 −2.13239
\(193\) −0.302842 −0.0217991 −0.0108995 0.999941i \(-0.503469\pi\)
−0.0108995 + 0.999941i \(0.503469\pi\)
\(194\) −31.2514 −2.24372
\(195\) 0 0
\(196\) 3.56589 0.254706
\(197\) 10.3678 0.738672 0.369336 0.929296i \(-0.379585\pi\)
0.369336 + 0.929296i \(0.379585\pi\)
\(198\) 20.9520 1.48900
\(199\) −11.9825 −0.849414 −0.424707 0.905331i \(-0.639623\pi\)
−0.424707 + 0.905331i \(0.639623\pi\)
\(200\) 0 0
\(201\) 18.2041 1.28402
\(202\) −31.7364 −2.23297
\(203\) −8.42950 −0.591635
\(204\) −17.8727 −1.25134
\(205\) 0 0
\(206\) −15.9729 −1.11288
\(207\) 3.28760 0.228504
\(208\) 4.44144 0.307959
\(209\) −3.01695 −0.208687
\(210\) 0 0
\(211\) 28.1068 1.93495 0.967477 0.252960i \(-0.0814039\pi\)
0.967477 + 0.252960i \(0.0814039\pi\)
\(212\) −17.3497 −1.19158
\(213\) −6.12366 −0.419587
\(214\) −23.6381 −1.61586
\(215\) 0 0
\(216\) 2.66418 0.181275
\(217\) 2.48252 0.168525
\(218\) 36.5887 2.47810
\(219\) 4.27116 0.288618
\(220\) 0 0
\(221\) −5.60545 −0.377063
\(222\) 4.77979 0.320799
\(223\) −12.7655 −0.854844 −0.427422 0.904052i \(-0.640578\pi\)
−0.427422 + 0.904052i \(0.640578\pi\)
\(224\) −3.65206 −0.244013
\(225\) 0 0
\(226\) −0.421145 −0.0280142
\(227\) −1.81853 −0.120700 −0.0603499 0.998177i \(-0.519222\pi\)
−0.0603499 + 0.998177i \(0.519222\pi\)
\(228\) −9.98616 −0.661349
\(229\) 5.42321 0.358376 0.179188 0.983815i \(-0.442653\pi\)
0.179188 + 0.983815i \(0.442653\pi\)
\(230\) 0 0
\(231\) 6.77365 0.445673
\(232\) −31.1408 −2.04449
\(233\) 9.74067 0.638133 0.319066 0.947732i \(-0.396631\pi\)
0.319066 + 0.947732i \(0.396631\pi\)
\(234\) 21.7509 1.42190
\(235\) 0 0
\(236\) −43.4211 −2.82647
\(237\) 38.8039 2.52058
\(238\) −4.71571 −0.305674
\(239\) −21.1865 −1.37044 −0.685220 0.728336i \(-0.740294\pi\)
−0.685220 + 0.728336i \(0.740294\pi\)
\(240\) 0 0
\(241\) 13.8166 0.890008 0.445004 0.895529i \(-0.353202\pi\)
0.445004 + 0.895529i \(0.353202\pi\)
\(242\) −8.73555 −0.561543
\(243\) −22.3602 −1.43441
\(244\) 33.6277 2.15279
\(245\) 0 0
\(246\) 40.2151 2.56402
\(247\) −3.13198 −0.199283
\(248\) 9.17110 0.582365
\(249\) 27.0528 1.71440
\(250\) 0 0
\(251\) −11.9432 −0.753850 −0.376925 0.926244i \(-0.623019\pi\)
−0.376925 + 0.926244i \(0.623019\pi\)
\(252\) 11.7232 0.738494
\(253\) 2.70134 0.169832
\(254\) 10.2942 0.645916
\(255\) 0 0
\(256\) −24.7868 −1.54917
\(257\) −16.5580 −1.03286 −0.516431 0.856329i \(-0.672740\pi\)
−0.516431 + 0.856329i \(0.672740\pi\)
\(258\) 18.6893 1.16354
\(259\) 0.807977 0.0502053
\(260\) 0 0
\(261\) −27.7129 −1.71538
\(262\) −10.2719 −0.634597
\(263\) 17.5430 1.08175 0.540873 0.841104i \(-0.318094\pi\)
0.540873 + 0.841104i \(0.318094\pi\)
\(264\) 25.0236 1.54010
\(265\) 0 0
\(266\) −2.63485 −0.161553
\(267\) −20.7608 −1.27054
\(268\) 25.8878 1.58135
\(269\) 30.8143 1.87878 0.939389 0.342853i \(-0.111393\pi\)
0.939389 + 0.342853i \(0.111393\pi\)
\(270\) 0 0
\(271\) 20.4786 1.24398 0.621992 0.783023i \(-0.286324\pi\)
0.621992 + 0.783023i \(0.286324\pi\)
\(272\) −3.16573 −0.191951
\(273\) 7.03190 0.425590
\(274\) 25.3159 1.52939
\(275\) 0 0
\(276\) 8.94150 0.538215
\(277\) 31.9578 1.92016 0.960080 0.279727i \(-0.0902438\pi\)
0.960080 + 0.279727i \(0.0902438\pi\)
\(278\) 14.8824 0.892584
\(279\) 8.16156 0.488620
\(280\) 0 0
\(281\) 12.8548 0.766852 0.383426 0.923572i \(-0.374744\pi\)
0.383426 + 0.923572i \(0.374744\pi\)
\(282\) −59.5954 −3.54885
\(283\) −25.7504 −1.53070 −0.765351 0.643613i \(-0.777434\pi\)
−0.765351 + 0.643613i \(0.777434\pi\)
\(284\) −8.70836 −0.516746
\(285\) 0 0
\(286\) 17.8722 1.05680
\(287\) 6.79798 0.401272
\(288\) −12.0065 −0.707491
\(289\) −13.0046 −0.764977
\(290\) 0 0
\(291\) −33.2158 −1.94714
\(292\) 6.07394 0.355451
\(293\) −14.9716 −0.874651 −0.437325 0.899303i \(-0.644074\pi\)
−0.437325 + 0.899303i \(0.644074\pi\)
\(294\) 5.91575 0.345014
\(295\) 0 0
\(296\) 2.98488 0.173493
\(297\) 1.94812 0.113041
\(298\) −29.3130 −1.69805
\(299\) 2.80434 0.162179
\(300\) 0 0
\(301\) 3.15924 0.182096
\(302\) −28.2868 −1.62772
\(303\) −33.7313 −1.93781
\(304\) −1.76881 −0.101448
\(305\) 0 0
\(306\) −15.5034 −0.886270
\(307\) −29.1203 −1.66198 −0.830990 0.556287i \(-0.812226\pi\)
−0.830990 + 0.556287i \(0.812226\pi\)
\(308\) 9.63269 0.548873
\(309\) −16.9769 −0.965781
\(310\) 0 0
\(311\) 27.9131 1.58281 0.791405 0.611293i \(-0.209350\pi\)
0.791405 + 0.611293i \(0.209350\pi\)
\(312\) 25.9777 1.47070
\(313\) −34.6962 −1.96115 −0.980573 0.196152i \(-0.937155\pi\)
−0.980573 + 0.196152i \(0.937155\pi\)
\(314\) 35.4391 1.99995
\(315\) 0 0
\(316\) 55.1823 3.10425
\(317\) −22.9724 −1.29026 −0.645130 0.764073i \(-0.723197\pi\)
−0.645130 + 0.764073i \(0.723197\pi\)
\(318\) −28.7828 −1.61406
\(319\) −22.7710 −1.27493
\(320\) 0 0
\(321\) −25.1239 −1.40228
\(322\) 2.35921 0.131474
\(323\) 2.23238 0.124213
\(324\) −28.7213 −1.59563
\(325\) 0 0
\(326\) 13.6168 0.754167
\(327\) 38.8886 2.15055
\(328\) 25.1135 1.38666
\(329\) −10.0740 −0.555399
\(330\) 0 0
\(331\) −14.4248 −0.792858 −0.396429 0.918065i \(-0.629751\pi\)
−0.396429 + 0.918065i \(0.629751\pi\)
\(332\) 38.4713 2.11139
\(333\) 2.65631 0.145565
\(334\) −0.0125671 −0.000687643 0
\(335\) 0 0
\(336\) 3.97133 0.216654
\(337\) −3.73562 −0.203492 −0.101746 0.994810i \(-0.532443\pi\)
−0.101746 + 0.994810i \(0.532443\pi\)
\(338\) −12.1162 −0.659034
\(339\) −0.447618 −0.0243113
\(340\) 0 0
\(341\) 6.70615 0.363159
\(342\) −8.66233 −0.468405
\(343\) 1.00000 0.0539949
\(344\) 11.6711 0.629262
\(345\) 0 0
\(346\) 48.8526 2.62633
\(347\) 15.9464 0.856045 0.428023 0.903768i \(-0.359210\pi\)
0.428023 + 0.903768i \(0.359210\pi\)
\(348\) −75.3723 −4.04038
\(349\) 3.27234 0.175164 0.0875821 0.996157i \(-0.472086\pi\)
0.0875821 + 0.996157i \(0.472086\pi\)
\(350\) 0 0
\(351\) 2.02240 0.107948
\(352\) −9.86546 −0.525831
\(353\) 10.3265 0.549623 0.274812 0.961498i \(-0.411385\pi\)
0.274812 + 0.961498i \(0.411385\pi\)
\(354\) −72.0349 −3.82861
\(355\) 0 0
\(356\) −29.5235 −1.56474
\(357\) −5.01213 −0.265270
\(358\) −28.6787 −1.51572
\(359\) 15.5797 0.822263 0.411131 0.911576i \(-0.365134\pi\)
0.411131 + 0.911576i \(0.365134\pi\)
\(360\) 0 0
\(361\) −17.7527 −0.934352
\(362\) −30.3334 −1.59429
\(363\) −9.28466 −0.487318
\(364\) 9.99995 0.524140
\(365\) 0 0
\(366\) 55.7878 2.91607
\(367\) −21.5509 −1.12495 −0.562475 0.826814i \(-0.690151\pi\)
−0.562475 + 0.826814i \(0.690151\pi\)
\(368\) 1.58378 0.0825601
\(369\) 22.3490 1.16344
\(370\) 0 0
\(371\) −4.86545 −0.252602
\(372\) 22.1975 1.15089
\(373\) −20.5515 −1.06412 −0.532059 0.846707i \(-0.678582\pi\)
−0.532059 + 0.846707i \(0.678582\pi\)
\(374\) −12.7388 −0.658706
\(375\) 0 0
\(376\) −37.2161 −1.91927
\(377\) −23.6392 −1.21748
\(378\) 1.70139 0.0875099
\(379\) 13.3073 0.683552 0.341776 0.939781i \(-0.388972\pi\)
0.341776 + 0.939781i \(0.388972\pi\)
\(380\) 0 0
\(381\) 10.9413 0.560539
\(382\) 30.5065 1.56085
\(383\) 10.7300 0.548277 0.274139 0.961690i \(-0.411607\pi\)
0.274139 + 0.961690i \(0.411607\pi\)
\(384\) −51.3933 −2.62265
\(385\) 0 0
\(386\) −0.714469 −0.0363655
\(387\) 10.3863 0.527967
\(388\) −47.2356 −2.39803
\(389\) −29.3543 −1.48832 −0.744161 0.668001i \(-0.767150\pi\)
−0.744161 + 0.668001i \(0.767150\pi\)
\(390\) 0 0
\(391\) −1.99885 −0.101086
\(392\) 3.69426 0.186588
\(393\) −10.9175 −0.550716
\(394\) 24.4598 1.23226
\(395\) 0 0
\(396\) 31.6685 1.59140
\(397\) −7.32590 −0.367676 −0.183838 0.982957i \(-0.558852\pi\)
−0.183838 + 0.982957i \(0.558852\pi\)
\(398\) −28.2692 −1.41701
\(399\) −2.80047 −0.140199
\(400\) 0 0
\(401\) 11.7248 0.585510 0.292755 0.956187i \(-0.405428\pi\)
0.292755 + 0.956187i \(0.405428\pi\)
\(402\) 42.9474 2.14202
\(403\) 6.96184 0.346794
\(404\) −47.9688 −2.38653
\(405\) 0 0
\(406\) −19.8870 −0.986975
\(407\) 2.18262 0.108189
\(408\) −18.5161 −0.916685
\(409\) 9.34310 0.461987 0.230993 0.972955i \(-0.425802\pi\)
0.230993 + 0.972955i \(0.425802\pi\)
\(410\) 0 0
\(411\) 26.9072 1.32723
\(412\) −24.1425 −1.18942
\(413\) −12.1768 −0.599181
\(414\) 7.75616 0.381194
\(415\) 0 0
\(416\) −10.2416 −0.502136
\(417\) 15.8178 0.774603
\(418\) −7.11763 −0.348135
\(419\) 22.0474 1.07709 0.538543 0.842598i \(-0.318975\pi\)
0.538543 + 0.842598i \(0.318975\pi\)
\(420\) 0 0
\(421\) 5.11313 0.249199 0.124599 0.992207i \(-0.460235\pi\)
0.124599 + 0.992207i \(0.460235\pi\)
\(422\) 66.3100 3.22792
\(423\) −33.1194 −1.61032
\(424\) −17.9743 −0.872907
\(425\) 0 0
\(426\) −14.4470 −0.699961
\(427\) 9.43038 0.456368
\(428\) −35.7283 −1.72699
\(429\) 18.9956 0.917116
\(430\) 0 0
\(431\) 8.08201 0.389296 0.194648 0.980873i \(-0.437643\pi\)
0.194648 + 0.980873i \(0.437643\pi\)
\(432\) 1.14217 0.0549526
\(433\) 38.6561 1.85769 0.928847 0.370464i \(-0.120801\pi\)
0.928847 + 0.370464i \(0.120801\pi\)
\(434\) 5.85680 0.281136
\(435\) 0 0
\(436\) 55.3028 2.64853
\(437\) −1.11683 −0.0534254
\(438\) 10.0766 0.481477
\(439\) 2.29718 0.109638 0.0548192 0.998496i \(-0.482542\pi\)
0.0548192 + 0.998496i \(0.482542\pi\)
\(440\) 0 0
\(441\) 3.28760 0.156553
\(442\) −13.2245 −0.629023
\(443\) −29.1842 −1.38658 −0.693292 0.720657i \(-0.743840\pi\)
−0.693292 + 0.720657i \(0.743840\pi\)
\(444\) 7.22452 0.342861
\(445\) 0 0
\(446\) −30.1166 −1.42606
\(447\) −31.1555 −1.47361
\(448\) −11.7835 −0.556720
\(449\) 20.8373 0.983374 0.491687 0.870772i \(-0.336380\pi\)
0.491687 + 0.870772i \(0.336380\pi\)
\(450\) 0 0
\(451\) 18.3637 0.864712
\(452\) −0.636550 −0.0299408
\(453\) −30.0649 −1.41257
\(454\) −4.29029 −0.201353
\(455\) 0 0
\(456\) −10.3457 −0.484480
\(457\) 13.4806 0.630596 0.315298 0.948993i \(-0.397895\pi\)
0.315298 + 0.948993i \(0.397895\pi\)
\(458\) 12.7945 0.597849
\(459\) −1.44151 −0.0672837
\(460\) 0 0
\(461\) −34.2227 −1.59391 −0.796954 0.604040i \(-0.793557\pi\)
−0.796954 + 0.604040i \(0.793557\pi\)
\(462\) 15.9805 0.743479
\(463\) 28.0881 1.30536 0.652681 0.757632i \(-0.273644\pi\)
0.652681 + 0.757632i \(0.273644\pi\)
\(464\) −13.3504 −0.619779
\(465\) 0 0
\(466\) 22.9803 1.06454
\(467\) −27.6544 −1.27969 −0.639846 0.768503i \(-0.721002\pi\)
−0.639846 + 0.768503i \(0.721002\pi\)
\(468\) 32.8759 1.51969
\(469\) 7.25984 0.335228
\(470\) 0 0
\(471\) 37.6668 1.73559
\(472\) −44.9843 −2.07057
\(473\) 8.53421 0.392403
\(474\) 91.5466 4.20487
\(475\) 0 0
\(476\) −7.12767 −0.326696
\(477\) −15.9957 −0.732392
\(478\) −49.9834 −2.28619
\(479\) −7.07484 −0.323258 −0.161629 0.986852i \(-0.551675\pi\)
−0.161629 + 0.986852i \(0.551675\pi\)
\(480\) 0 0
\(481\) 2.26584 0.103313
\(482\) 32.5964 1.48473
\(483\) 2.50751 0.114096
\(484\) −13.2036 −0.600162
\(485\) 0 0
\(486\) −52.7524 −2.39290
\(487\) −41.7092 −1.89002 −0.945012 0.327037i \(-0.893950\pi\)
−0.945012 + 0.327037i \(0.893950\pi\)
\(488\) 34.8383 1.57706
\(489\) 14.4728 0.654482
\(490\) 0 0
\(491\) 2.60678 0.117642 0.0588212 0.998269i \(-0.481266\pi\)
0.0588212 + 0.998269i \(0.481266\pi\)
\(492\) 60.7841 2.74036
\(493\) 16.8493 0.758854
\(494\) −7.38900 −0.332447
\(495\) 0 0
\(496\) 3.93176 0.176541
\(497\) −2.44213 −0.109545
\(498\) 63.8232 2.85999
\(499\) 35.7391 1.59990 0.799951 0.600066i \(-0.204859\pi\)
0.799951 + 0.600066i \(0.204859\pi\)
\(500\) 0 0
\(501\) −0.0133571 −0.000596751 0
\(502\) −28.1766 −1.25758
\(503\) −26.8250 −1.19607 −0.598033 0.801472i \(-0.704051\pi\)
−0.598033 + 0.801472i \(0.704051\pi\)
\(504\) 12.1453 0.540993
\(505\) 0 0
\(506\) 6.37305 0.283316
\(507\) −12.8778 −0.571923
\(508\) 15.5594 0.690337
\(509\) −10.6497 −0.472038 −0.236019 0.971748i \(-0.575843\pi\)
−0.236019 + 0.971748i \(0.575843\pi\)
\(510\) 0 0
\(511\) 1.70335 0.0753516
\(512\) −17.4858 −0.772771
\(513\) −0.805424 −0.0355603
\(514\) −39.0639 −1.72304
\(515\) 0 0
\(516\) 28.2484 1.24357
\(517\) −27.2134 −1.19684
\(518\) 1.90619 0.0837532
\(519\) 51.9234 2.27918
\(520\) 0 0
\(521\) −10.9869 −0.481346 −0.240673 0.970606i \(-0.577368\pi\)
−0.240673 + 0.970606i \(0.577368\pi\)
\(522\) −65.3805 −2.86163
\(523\) −28.5035 −1.24637 −0.623185 0.782074i \(-0.714162\pi\)
−0.623185 + 0.782074i \(0.714162\pi\)
\(524\) −15.5256 −0.678240
\(525\) 0 0
\(526\) 41.3876 1.80459
\(527\) −4.96219 −0.216157
\(528\) 10.7279 0.466874
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −40.0325 −1.73726
\(532\) −3.98250 −0.172663
\(533\) 19.0638 0.825746
\(534\) −48.9791 −2.11953
\(535\) 0 0
\(536\) 26.8197 1.15844
\(537\) −30.4814 −1.31537
\(538\) 72.6974 3.13421
\(539\) 2.70134 0.116355
\(540\) 0 0
\(541\) −16.2056 −0.696735 −0.348367 0.937358i \(-0.613264\pi\)
−0.348367 + 0.937358i \(0.613264\pi\)
\(542\) 48.3133 2.07523
\(543\) −32.2401 −1.38355
\(544\) 7.29991 0.312981
\(545\) 0 0
\(546\) 16.5898 0.709976
\(547\) 1.49191 0.0637895 0.0318948 0.999491i \(-0.489846\pi\)
0.0318948 + 0.999491i \(0.489846\pi\)
\(548\) 38.2643 1.63457
\(549\) 31.0033 1.32319
\(550\) 0 0
\(551\) 9.41434 0.401065
\(552\) 9.26340 0.394276
\(553\) 15.4751 0.658066
\(554\) 75.3953 3.20324
\(555\) 0 0
\(556\) 22.4943 0.953970
\(557\) 21.1267 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(558\) 19.2548 0.815123
\(559\) 8.85959 0.374721
\(560\) 0 0
\(561\) −13.5395 −0.571638
\(562\) 30.3272 1.27927
\(563\) −11.4806 −0.483851 −0.241926 0.970295i \(-0.577779\pi\)
−0.241926 + 0.970295i \(0.577779\pi\)
\(564\) −90.0768 −3.79292
\(565\) 0 0
\(566\) −60.7506 −2.55354
\(567\) −8.05448 −0.338256
\(568\) −9.02187 −0.378549
\(569\) 19.7215 0.826768 0.413384 0.910557i \(-0.364347\pi\)
0.413384 + 0.910557i \(0.364347\pi\)
\(570\) 0 0
\(571\) 22.6321 0.947126 0.473563 0.880760i \(-0.342968\pi\)
0.473563 + 0.880760i \(0.342968\pi\)
\(572\) 27.0133 1.12948
\(573\) 32.4241 1.35454
\(574\) 16.0379 0.669408
\(575\) 0 0
\(576\) −38.7396 −1.61415
\(577\) −1.42011 −0.0591199 −0.0295599 0.999563i \(-0.509411\pi\)
−0.0295599 + 0.999563i \(0.509411\pi\)
\(578\) −30.6806 −1.27615
\(579\) −0.759379 −0.0315587
\(580\) 0 0
\(581\) 10.7887 0.447590
\(582\) −78.3632 −3.24826
\(583\) −13.1433 −0.544338
\(584\) 6.29261 0.260390
\(585\) 0 0
\(586\) −35.3212 −1.45911
\(587\) −12.0482 −0.497281 −0.248640 0.968596i \(-0.579984\pi\)
−0.248640 + 0.968596i \(0.579984\pi\)
\(588\) 8.94150 0.368741
\(589\) −2.77257 −0.114242
\(590\) 0 0
\(591\) 25.9973 1.06938
\(592\) 1.27966 0.0525935
\(593\) −13.4535 −0.552471 −0.276235 0.961090i \(-0.589087\pi\)
−0.276235 + 0.961090i \(0.589087\pi\)
\(594\) 4.59603 0.188578
\(595\) 0 0
\(596\) −44.3057 −1.81483
\(597\) −30.0461 −1.22971
\(598\) 6.61603 0.270550
\(599\) 43.1777 1.76419 0.882096 0.471069i \(-0.156132\pi\)
0.882096 + 0.471069i \(0.156132\pi\)
\(600\) 0 0
\(601\) −20.3297 −0.829266 −0.414633 0.909989i \(-0.636090\pi\)
−0.414633 + 0.909989i \(0.636090\pi\)
\(602\) 7.45333 0.303775
\(603\) 23.8675 0.971958
\(604\) −42.7548 −1.73967
\(605\) 0 0
\(606\) −79.5794 −3.23269
\(607\) −0.793889 −0.0322230 −0.0161115 0.999870i \(-0.505129\pi\)
−0.0161115 + 0.999870i \(0.505129\pi\)
\(608\) 4.07874 0.165415
\(609\) −21.1371 −0.856516
\(610\) 0 0
\(611\) −28.2510 −1.14291
\(612\) −23.4330 −0.947221
\(613\) 1.43440 0.0579349 0.0289674 0.999580i \(-0.490778\pi\)
0.0289674 + 0.999580i \(0.490778\pi\)
\(614\) −68.7009 −2.77254
\(615\) 0 0
\(616\) 9.97947 0.402084
\(617\) 46.1995 1.85992 0.929960 0.367660i \(-0.119841\pi\)
0.929960 + 0.367660i \(0.119841\pi\)
\(618\) −40.0521 −1.61113
\(619\) 2.94224 0.118259 0.0591294 0.998250i \(-0.481168\pi\)
0.0591294 + 0.998250i \(0.481168\pi\)
\(620\) 0 0
\(621\) 0.721167 0.0289395
\(622\) 65.8531 2.64047
\(623\) −8.27944 −0.331709
\(624\) 11.1370 0.445835
\(625\) 0 0
\(626\) −81.8558 −3.27162
\(627\) −7.56503 −0.302118
\(628\) 53.5653 2.13749
\(629\) −1.61502 −0.0643953
\(630\) 0 0
\(631\) 28.4317 1.13185 0.565924 0.824458i \(-0.308520\pi\)
0.565924 + 0.824458i \(0.308520\pi\)
\(632\) 57.1689 2.27406
\(633\) 70.4781 2.80125
\(634\) −54.1968 −2.15243
\(635\) 0 0
\(636\) −43.5044 −1.72506
\(637\) 2.80434 0.111112
\(638\) −53.7216 −2.12686
\(639\) −8.02875 −0.317613
\(640\) 0 0
\(641\) 44.8580 1.77178 0.885892 0.463892i \(-0.153547\pi\)
0.885892 + 0.463892i \(0.153547\pi\)
\(642\) −59.2727 −2.33931
\(643\) −0.903492 −0.0356302 −0.0178151 0.999841i \(-0.505671\pi\)
−0.0178151 + 0.999841i \(0.505671\pi\)
\(644\) 3.56589 0.140516
\(645\) 0 0
\(646\) 5.26666 0.207214
\(647\) 17.0363 0.669765 0.334882 0.942260i \(-0.391303\pi\)
0.334882 + 0.942260i \(0.391303\pi\)
\(648\) −29.7553 −1.16890
\(649\) −32.8937 −1.29119
\(650\) 0 0
\(651\) 6.22495 0.243975
\(652\) 20.5815 0.806034
\(653\) −23.1721 −0.906793 −0.453397 0.891309i \(-0.649788\pi\)
−0.453397 + 0.891309i \(0.649788\pi\)
\(654\) 91.7465 3.58757
\(655\) 0 0
\(656\) 10.7665 0.420360
\(657\) 5.59993 0.218474
\(658\) −23.7668 −0.926525
\(659\) −25.0481 −0.975737 −0.487868 0.872917i \(-0.662225\pi\)
−0.487868 + 0.872917i \(0.662225\pi\)
\(660\) 0 0
\(661\) −8.53827 −0.332100 −0.166050 0.986117i \(-0.553101\pi\)
−0.166050 + 0.986117i \(0.553101\pi\)
\(662\) −34.0311 −1.32266
\(663\) −14.0557 −0.545879
\(664\) 39.8563 1.54672
\(665\) 0 0
\(666\) 6.26680 0.242833
\(667\) −8.42950 −0.326392
\(668\) −0.0189949 −0.000734934 0
\(669\) −32.0097 −1.23757
\(670\) 0 0
\(671\) 25.4747 0.983440
\(672\) −9.15757 −0.353261
\(673\) 23.9052 0.921477 0.460738 0.887536i \(-0.347585\pi\)
0.460738 + 0.887536i \(0.347585\pi\)
\(674\) −8.81313 −0.339469
\(675\) 0 0
\(676\) −18.3133 −0.704357
\(677\) 29.3023 1.12618 0.563090 0.826395i \(-0.309612\pi\)
0.563090 + 0.826395i \(0.309612\pi\)
\(678\) −1.05603 −0.0405564
\(679\) −13.2465 −0.508355
\(680\) 0 0
\(681\) −4.55997 −0.174739
\(682\) 15.8212 0.605827
\(683\) 28.8697 1.10467 0.552334 0.833623i \(-0.313737\pi\)
0.552334 + 0.833623i \(0.313737\pi\)
\(684\) −13.0929 −0.500619
\(685\) 0 0
\(686\) 2.35921 0.0900752
\(687\) 13.5988 0.518825
\(688\) 5.00354 0.190758
\(689\) −13.6444 −0.519809
\(690\) 0 0
\(691\) 13.1773 0.501290 0.250645 0.968079i \(-0.419357\pi\)
0.250645 + 0.968079i \(0.419357\pi\)
\(692\) 73.8394 2.80695
\(693\) 8.88095 0.337359
\(694\) 37.6208 1.42807
\(695\) 0 0
\(696\) −78.0858 −2.95983
\(697\) −13.5881 −0.514687
\(698\) 7.72014 0.292212
\(699\) 24.4248 0.923832
\(700\) 0 0
\(701\) 32.1209 1.21319 0.606595 0.795011i \(-0.292535\pi\)
0.606595 + 0.795011i \(0.292535\pi\)
\(702\) 4.77127 0.180080
\(703\) −0.902376 −0.0340337
\(704\) −31.8314 −1.19969
\(705\) 0 0
\(706\) 24.3624 0.916890
\(707\) −13.4521 −0.505919
\(708\) −108.879 −4.09191
\(709\) 39.6975 1.49087 0.745435 0.666578i \(-0.232242\pi\)
0.745435 + 0.666578i \(0.232242\pi\)
\(710\) 0 0
\(711\) 50.8758 1.90799
\(712\) −30.5864 −1.14627
\(713\) 2.48252 0.0929713
\(714\) −11.8247 −0.442528
\(715\) 0 0
\(716\) −43.3471 −1.61996
\(717\) −53.1253 −1.98400
\(718\) 36.7557 1.37171
\(719\) 28.5811 1.06590 0.532948 0.846148i \(-0.321084\pi\)
0.532948 + 0.846148i \(0.321084\pi\)
\(720\) 0 0
\(721\) −6.77042 −0.252143
\(722\) −41.8824 −1.55870
\(723\) 34.6454 1.28847
\(724\) −45.8481 −1.70393
\(725\) 0 0
\(726\) −21.9045 −0.812952
\(727\) −9.67378 −0.358781 −0.179390 0.983778i \(-0.557412\pi\)
−0.179390 + 0.983778i \(0.557412\pi\)
\(728\) 10.3600 0.383966
\(729\) −31.9049 −1.18166
\(730\) 0 0
\(731\) −6.31485 −0.233563
\(732\) 84.3217 3.11662
\(733\) −23.1744 −0.855966 −0.427983 0.903787i \(-0.640776\pi\)
−0.427983 + 0.903787i \(0.640776\pi\)
\(734\) −50.8433 −1.87666
\(735\) 0 0
\(736\) −3.65206 −0.134617
\(737\) 19.6113 0.722392
\(738\) 52.7262 1.94088
\(739\) −29.2997 −1.07781 −0.538904 0.842367i \(-0.681161\pi\)
−0.538904 + 0.842367i \(0.681161\pi\)
\(740\) 0 0
\(741\) −7.85346 −0.288504
\(742\) −11.4786 −0.421394
\(743\) 36.8301 1.35116 0.675582 0.737285i \(-0.263892\pi\)
0.675582 + 0.737285i \(0.263892\pi\)
\(744\) 22.9966 0.843097
\(745\) 0 0
\(746\) −48.4855 −1.77518
\(747\) 35.4689 1.29774
\(748\) −19.2543 −0.704007
\(749\) −10.0195 −0.366103
\(750\) 0 0
\(751\) 37.5423 1.36994 0.684969 0.728572i \(-0.259816\pi\)
0.684969 + 0.728572i \(0.259816\pi\)
\(752\) −15.9550 −0.581819
\(753\) −29.9478 −1.09136
\(754\) −55.7698 −2.03102
\(755\) 0 0
\(756\) 2.57160 0.0935282
\(757\) 17.3405 0.630250 0.315125 0.949050i \(-0.397954\pi\)
0.315125 + 0.949050i \(0.397954\pi\)
\(758\) 31.3948 1.14031
\(759\) 6.77365 0.245868
\(760\) 0 0
\(761\) −44.6219 −1.61754 −0.808771 0.588123i \(-0.799867\pi\)
−0.808771 + 0.588123i \(0.799867\pi\)
\(762\) 25.8128 0.935099
\(763\) 15.5089 0.561458
\(764\) 46.1097 1.66819
\(765\) 0 0
\(766\) 25.3143 0.914644
\(767\) −34.1478 −1.23301
\(768\) −62.1531 −2.24276
\(769\) 38.4931 1.38810 0.694048 0.719929i \(-0.255826\pi\)
0.694048 + 0.719929i \(0.255826\pi\)
\(770\) 0 0
\(771\) −41.5194 −1.49528
\(772\) −1.07990 −0.0388665
\(773\) −54.2437 −1.95101 −0.975505 0.219976i \(-0.929402\pi\)
−0.975505 + 0.219976i \(0.929402\pi\)
\(774\) 24.5036 0.880763
\(775\) 0 0
\(776\) −48.9362 −1.75671
\(777\) 2.02601 0.0726827
\(778\) −69.2530 −2.48284
\(779\) −7.59220 −0.272019
\(780\) 0 0
\(781\) −6.59703 −0.236060
\(782\) −4.71571 −0.168634
\(783\) −6.07908 −0.217249
\(784\) 1.58378 0.0565635
\(785\) 0 0
\(786\) −25.7568 −0.918714
\(787\) 4.83401 0.172314 0.0861570 0.996282i \(-0.472541\pi\)
0.0861570 + 0.996282i \(0.472541\pi\)
\(788\) 36.9703 1.31701
\(789\) 43.9892 1.56606
\(790\) 0 0
\(791\) −0.178511 −0.00634712
\(792\) 32.8085 1.16580
\(793\) 26.4460 0.939124
\(794\) −17.2834 −0.613363
\(795\) 0 0
\(796\) −42.7281 −1.51446
\(797\) 44.4895 1.57590 0.787950 0.615739i \(-0.211143\pi\)
0.787950 + 0.615739i \(0.211143\pi\)
\(798\) −6.60690 −0.233882
\(799\) 20.1365 0.712377
\(800\) 0 0
\(801\) −27.2195 −0.961754
\(802\) 27.6614 0.976757
\(803\) 4.60133 0.162377
\(804\) 64.9138 2.28933
\(805\) 0 0
\(806\) 16.4245 0.578527
\(807\) 77.2670 2.71993
\(808\) −49.6957 −1.74829
\(809\) −19.7547 −0.694540 −0.347270 0.937765i \(-0.612891\pi\)
−0.347270 + 0.937765i \(0.612891\pi\)
\(810\) 0 0
\(811\) 11.3167 0.397382 0.198691 0.980062i \(-0.436331\pi\)
0.198691 + 0.980062i \(0.436331\pi\)
\(812\) −30.0586 −1.05485
\(813\) 51.3502 1.80093
\(814\) 5.14928 0.180482
\(815\) 0 0
\(816\) −7.93810 −0.277889
\(817\) −3.52835 −0.123441
\(818\) 22.0424 0.770694
\(819\) 9.21955 0.322157
\(820\) 0 0
\(821\) −17.5446 −0.612310 −0.306155 0.951982i \(-0.599043\pi\)
−0.306155 + 0.951982i \(0.599043\pi\)
\(822\) 63.4798 2.21411
\(823\) −47.0147 −1.63883 −0.819415 0.573201i \(-0.805701\pi\)
−0.819415 + 0.573201i \(0.805701\pi\)
\(824\) −25.0117 −0.871323
\(825\) 0 0
\(826\) −28.7277 −0.999563
\(827\) 1.29703 0.0451022 0.0225511 0.999746i \(-0.492821\pi\)
0.0225511 + 0.999746i \(0.492821\pi\)
\(828\) 11.7232 0.407410
\(829\) 57.4555 1.99551 0.997757 0.0669420i \(-0.0213243\pi\)
0.997757 + 0.0669420i \(0.0213243\pi\)
\(830\) 0 0
\(831\) 80.1345 2.77984
\(832\) −33.0450 −1.14563
\(833\) −1.99885 −0.0692560
\(834\) 37.3176 1.29220
\(835\) 0 0
\(836\) −10.7581 −0.372077
\(837\) 1.79032 0.0618824
\(838\) 52.0145 1.79681
\(839\) −53.3764 −1.84276 −0.921379 0.388664i \(-0.872937\pi\)
−0.921379 + 0.388664i \(0.872937\pi\)
\(840\) 0 0
\(841\) 42.0565 1.45022
\(842\) 12.0630 0.415717
\(843\) 32.2335 1.11018
\(844\) 100.226 3.44991
\(845\) 0 0
\(846\) −78.1357 −2.68636
\(847\) −3.70274 −0.127228
\(848\) −7.70579 −0.264618
\(849\) −64.5693 −2.21601
\(850\) 0 0
\(851\) 0.807977 0.0276971
\(852\) −21.8363 −0.748099
\(853\) −20.9398 −0.716966 −0.358483 0.933536i \(-0.616706\pi\)
−0.358483 + 0.933536i \(0.616706\pi\)
\(854\) 22.2483 0.761320
\(855\) 0 0
\(856\) −37.0145 −1.26513
\(857\) 12.5261 0.427883 0.213941 0.976846i \(-0.431370\pi\)
0.213941 + 0.976846i \(0.431370\pi\)
\(858\) 44.8147 1.52995
\(859\) 39.2473 1.33910 0.669550 0.742767i \(-0.266487\pi\)
0.669550 + 0.742767i \(0.266487\pi\)
\(860\) 0 0
\(861\) 17.0460 0.580926
\(862\) 19.0672 0.649431
\(863\) −50.8955 −1.73250 −0.866251 0.499608i \(-0.833477\pi\)
−0.866251 + 0.499608i \(0.833477\pi\)
\(864\) −2.63374 −0.0896018
\(865\) 0 0
\(866\) 91.1980 3.09903
\(867\) −32.6092 −1.10747
\(868\) 8.85240 0.300470
\(869\) 41.8035 1.41809
\(870\) 0 0
\(871\) 20.3590 0.689840
\(872\) 57.2938 1.94021
\(873\) −43.5493 −1.47392
\(874\) −2.63485 −0.0891250
\(875\) 0 0
\(876\) 15.2305 0.514590
\(877\) 48.7836 1.64730 0.823652 0.567095i \(-0.191933\pi\)
0.823652 + 0.567095i \(0.191933\pi\)
\(878\) 5.41953 0.182900
\(879\) −37.5414 −1.26624
\(880\) 0 0
\(881\) 18.7616 0.632093 0.316047 0.948744i \(-0.397644\pi\)
0.316047 + 0.948744i \(0.397644\pi\)
\(882\) 7.75616 0.261163
\(883\) 24.0146 0.808157 0.404078 0.914724i \(-0.367592\pi\)
0.404078 + 0.914724i \(0.367592\pi\)
\(884\) −19.9884 −0.672283
\(885\) 0 0
\(886\) −68.8518 −2.31312
\(887\) −1.47725 −0.0496012 −0.0248006 0.999692i \(-0.507895\pi\)
−0.0248006 + 0.999692i \(0.507895\pi\)
\(888\) 7.48461 0.251167
\(889\) 4.36340 0.146344
\(890\) 0 0
\(891\) −21.7579 −0.728917
\(892\) −45.5205 −1.52414
\(893\) 11.2510 0.376500
\(894\) −73.5025 −2.45829
\(895\) 0 0
\(896\) −20.4958 −0.684715
\(897\) 7.03190 0.234788
\(898\) 49.1597 1.64048
\(899\) −20.9264 −0.697936
\(900\) 0 0
\(901\) 9.72531 0.323997
\(902\) 43.3238 1.44253
\(903\) 7.92183 0.263622
\(904\) −0.659466 −0.0219335
\(905\) 0 0
\(906\) −70.9295 −2.35647
\(907\) 17.3795 0.577077 0.288539 0.957468i \(-0.406831\pi\)
0.288539 + 0.957468i \(0.406831\pi\)
\(908\) −6.48466 −0.215201
\(909\) −44.2252 −1.46686
\(910\) 0 0
\(911\) −52.6898 −1.74569 −0.872846 0.487996i \(-0.837728\pi\)
−0.872846 + 0.487996i \(0.837728\pi\)
\(912\) −4.43532 −0.146868
\(913\) 29.1440 0.964525
\(914\) 31.8036 1.05197
\(915\) 0 0
\(916\) 19.3386 0.638964
\(917\) −4.35393 −0.143780
\(918\) −3.40082 −0.112244
\(919\) −3.45752 −0.114053 −0.0570266 0.998373i \(-0.518162\pi\)
−0.0570266 + 0.998373i \(0.518162\pi\)
\(920\) 0 0
\(921\) −73.0193 −2.40607
\(922\) −80.7386 −2.65898
\(923\) −6.84856 −0.225423
\(924\) 24.1541 0.794610
\(925\) 0 0
\(926\) 66.2657 2.17763
\(927\) −22.2584 −0.731063
\(928\) 30.7850 1.01057
\(929\) −12.8336 −0.421057 −0.210529 0.977588i \(-0.567519\pi\)
−0.210529 + 0.977588i \(0.567519\pi\)
\(930\) 0 0
\(931\) −1.11683 −0.0366027
\(932\) 34.7341 1.13775
\(933\) 69.9925 2.29145
\(934\) −65.2426 −2.13480
\(935\) 0 0
\(936\) 34.0594 1.11327
\(937\) −32.5335 −1.06282 −0.531411 0.847114i \(-0.678338\pi\)
−0.531411 + 0.847114i \(0.678338\pi\)
\(938\) 17.1275 0.559233
\(939\) −87.0011 −2.83917
\(940\) 0 0
\(941\) 44.7486 1.45876 0.729381 0.684108i \(-0.239808\pi\)
0.729381 + 0.684108i \(0.239808\pi\)
\(942\) 88.8640 2.89534
\(943\) 6.79798 0.221373
\(944\) −19.2853 −0.627684
\(945\) 0 0
\(946\) 20.1340 0.654613
\(947\) −13.4275 −0.436336 −0.218168 0.975911i \(-0.570008\pi\)
−0.218168 + 0.975911i \(0.570008\pi\)
\(948\) 138.370 4.49405
\(949\) 4.77676 0.155060
\(950\) 0 0
\(951\) −57.6035 −1.86792
\(952\) −7.38427 −0.239326
\(953\) −7.99902 −0.259114 −0.129557 0.991572i \(-0.541355\pi\)
−0.129557 + 0.991572i \(0.541355\pi\)
\(954\) −37.7372 −1.22179
\(955\) 0 0
\(956\) −75.5486 −2.44342
\(957\) −57.0984 −1.84573
\(958\) −16.6910 −0.539263
\(959\) 10.7306 0.346510
\(960\) 0 0
\(961\) −24.8371 −0.801196
\(962\) 5.34560 0.172349
\(963\) −32.9400 −1.06148
\(964\) 49.2686 1.58683
\(965\) 0 0
\(966\) 5.91575 0.190336
\(967\) 43.6769 1.40455 0.702277 0.711904i \(-0.252167\pi\)
0.702277 + 0.711904i \(0.252167\pi\)
\(968\) −13.6789 −0.439656
\(969\) 5.59772 0.179825
\(970\) 0 0
\(971\) 7.16184 0.229834 0.114917 0.993375i \(-0.463340\pi\)
0.114917 + 0.993375i \(0.463340\pi\)
\(972\) −79.7339 −2.55746
\(973\) 6.30819 0.202231
\(974\) −98.4009 −3.15297
\(975\) 0 0
\(976\) 14.9356 0.478077
\(977\) 15.6590 0.500977 0.250488 0.968120i \(-0.419409\pi\)
0.250488 + 0.968120i \(0.419409\pi\)
\(978\) 34.1444 1.09182
\(979\) −22.3656 −0.714808
\(980\) 0 0
\(981\) 50.9870 1.62789
\(982\) 6.14996 0.196253
\(983\) −41.2674 −1.31623 −0.658113 0.752919i \(-0.728645\pi\)
−0.658113 + 0.752919i \(0.728645\pi\)
\(984\) 62.9723 2.00748
\(985\) 0 0
\(986\) 39.7511 1.26593
\(987\) −25.2607 −0.804057
\(988\) −11.1683 −0.355310
\(989\) 3.15924 0.100458
\(990\) 0 0
\(991\) 55.1091 1.75060 0.875300 0.483581i \(-0.160664\pi\)
0.875300 + 0.483581i \(0.160664\pi\)
\(992\) −9.06632 −0.287856
\(993\) −36.1703 −1.14783
\(994\) −5.76151 −0.182744
\(995\) 0 0
\(996\) 96.4671 3.05668
\(997\) 4.56403 0.144544 0.0722721 0.997385i \(-0.476975\pi\)
0.0722721 + 0.997385i \(0.476975\pi\)
\(998\) 84.3161 2.66898
\(999\) 0.582687 0.0184354
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 4025.2.a.be.1.18 21
5.2 odd 4 805.2.c.c.484.36 yes 42
5.3 odd 4 805.2.c.c.484.7 42
5.4 even 2 4025.2.a.bd.1.4 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
805.2.c.c.484.7 42 5.3 odd 4
805.2.c.c.484.36 yes 42 5.2 odd 4
4025.2.a.bd.1.4 21 5.4 even 2
4025.2.a.be.1.18 21 1.1 even 1 trivial