Properties

Label 5225.2.a.y.1.14
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $15$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(2.61792\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.61792 q^{2} +2.17802 q^{3} +4.85352 q^{4} +5.70188 q^{6} +4.94832 q^{7} +7.47030 q^{8} +1.74376 q^{9} +O(q^{10})\) \(q+2.61792 q^{2} +2.17802 q^{3} +4.85352 q^{4} +5.70188 q^{6} +4.94832 q^{7} +7.47030 q^{8} +1.74376 q^{9} +1.00000 q^{11} +10.5710 q^{12} -4.20557 q^{13} +12.9543 q^{14} +9.84962 q^{16} -6.38851 q^{17} +4.56502 q^{18} +1.00000 q^{19} +10.7775 q^{21} +2.61792 q^{22} +6.66227 q^{23} +16.2704 q^{24} -11.0099 q^{26} -2.73612 q^{27} +24.0168 q^{28} -6.65643 q^{29} -9.53855 q^{31} +10.8449 q^{32} +2.17802 q^{33} -16.7246 q^{34} +8.46336 q^{36} -3.69327 q^{37} +2.61792 q^{38} -9.15980 q^{39} -1.08046 q^{41} +28.2147 q^{42} +9.58018 q^{43} +4.85352 q^{44} +17.4413 q^{46} +2.90169 q^{47} +21.4526 q^{48} +17.4858 q^{49} -13.9143 q^{51} -20.4118 q^{52} -6.75151 q^{53} -7.16294 q^{54} +36.9654 q^{56} +2.17802 q^{57} -17.4260 q^{58} -0.613007 q^{59} +1.33665 q^{61} -24.9712 q^{62} +8.62866 q^{63} +8.69200 q^{64} +5.70188 q^{66} +0.386619 q^{67} -31.0067 q^{68} +14.5105 q^{69} +9.38483 q^{71} +13.0264 q^{72} -1.97456 q^{73} -9.66869 q^{74} +4.85352 q^{76} +4.94832 q^{77} -23.9797 q^{78} -6.61494 q^{79} -11.1906 q^{81} -2.82857 q^{82} -0.100761 q^{83} +52.3089 q^{84} +25.0802 q^{86} -14.4978 q^{87} +7.47030 q^{88} +2.48738 q^{89} -20.8105 q^{91} +32.3355 q^{92} -20.7751 q^{93} +7.59641 q^{94} +23.6205 q^{96} -17.3288 q^{97} +45.7766 q^{98} +1.74376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9} + 15 q^{11} + 11 q^{12} + 13 q^{13} + 9 q^{14} + 21 q^{16} + 17 q^{17} + 22 q^{18} + 15 q^{19} + 6 q^{21} + 5 q^{22} + 26 q^{23} + q^{24} + 3 q^{26} + q^{27} + 46 q^{28} + 9 q^{29} + 14 q^{31} + 18 q^{32} + 4 q^{33} - 13 q^{34} + 12 q^{36} + 9 q^{37} + 5 q^{38} - 22 q^{39} + 4 q^{41} - 6 q^{42} + 28 q^{43} + 17 q^{44} + 27 q^{46} + 14 q^{47} - 4 q^{48} + 32 q^{49} - 40 q^{51} + 14 q^{52} + 3 q^{53} - 39 q^{54} + 34 q^{56} + 4 q^{57} + 26 q^{58} + q^{59} + 2 q^{61} - 3 q^{62} + 45 q^{63} + 5 q^{64} - q^{66} + 37 q^{67} + 26 q^{68} - 7 q^{69} - 7 q^{71} + 16 q^{72} + 42 q^{73} - 43 q^{74} + 17 q^{76} + 21 q^{77} - 64 q^{78} - 10 q^{79} + 31 q^{81} + 22 q^{82} + 14 q^{83} - 32 q^{84} + 37 q^{86} + 29 q^{87} + 9 q^{88} + 15 q^{89} - 22 q^{91} + 26 q^{92} - 18 q^{93} - 44 q^{94} + 71 q^{96} + 8 q^{97} - 10 q^{98} + 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61792 1.85115 0.925575 0.378563i \(-0.123582\pi\)
0.925575 + 0.378563i \(0.123582\pi\)
\(3\) 2.17802 1.25748 0.628739 0.777616i \(-0.283571\pi\)
0.628739 + 0.777616i \(0.283571\pi\)
\(4\) 4.85352 2.42676
\(5\) 0 0
\(6\) 5.70188 2.32778
\(7\) 4.94832 1.87029 0.935144 0.354268i \(-0.115270\pi\)
0.935144 + 0.354268i \(0.115270\pi\)
\(8\) 7.47030 2.64115
\(9\) 1.74376 0.581253
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 10.5710 3.05160
\(13\) −4.20557 −1.16642 −0.583208 0.812323i \(-0.698203\pi\)
−0.583208 + 0.812323i \(0.698203\pi\)
\(14\) 12.9543 3.46218
\(15\) 0 0
\(16\) 9.84962 2.46240
\(17\) −6.38851 −1.54944 −0.774720 0.632304i \(-0.782109\pi\)
−0.774720 + 0.632304i \(0.782109\pi\)
\(18\) 4.56502 1.07599
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 10.7775 2.35185
\(22\) 2.61792 0.558143
\(23\) 6.66227 1.38918 0.694590 0.719406i \(-0.255586\pi\)
0.694590 + 0.719406i \(0.255586\pi\)
\(24\) 16.2704 3.32119
\(25\) 0 0
\(26\) −11.0099 −2.15921
\(27\) −2.73612 −0.526566
\(28\) 24.0168 4.53874
\(29\) −6.65643 −1.23607 −0.618034 0.786151i \(-0.712071\pi\)
−0.618034 + 0.786151i \(0.712071\pi\)
\(30\) 0 0
\(31\) −9.53855 −1.71317 −0.856587 0.516002i \(-0.827420\pi\)
−0.856587 + 0.516002i \(0.827420\pi\)
\(32\) 10.8449 1.91713
\(33\) 2.17802 0.379144
\(34\) −16.7246 −2.86825
\(35\) 0 0
\(36\) 8.46336 1.41056
\(37\) −3.69327 −0.607170 −0.303585 0.952804i \(-0.598184\pi\)
−0.303585 + 0.952804i \(0.598184\pi\)
\(38\) 2.61792 0.424683
\(39\) −9.15980 −1.46674
\(40\) 0 0
\(41\) −1.08046 −0.168740 −0.0843701 0.996434i \(-0.526888\pi\)
−0.0843701 + 0.996434i \(0.526888\pi\)
\(42\) 28.2147 4.35362
\(43\) 9.58018 1.46096 0.730482 0.682932i \(-0.239296\pi\)
0.730482 + 0.682932i \(0.239296\pi\)
\(44\) 4.85352 0.731696
\(45\) 0 0
\(46\) 17.4413 2.57158
\(47\) 2.90169 0.423256 0.211628 0.977350i \(-0.432124\pi\)
0.211628 + 0.977350i \(0.432124\pi\)
\(48\) 21.4526 3.09642
\(49\) 17.4858 2.49798
\(50\) 0 0
\(51\) −13.9143 −1.94839
\(52\) −20.4118 −2.83061
\(53\) −6.75151 −0.927391 −0.463695 0.885995i \(-0.653477\pi\)
−0.463695 + 0.885995i \(0.653477\pi\)
\(54\) −7.16294 −0.974753
\(55\) 0 0
\(56\) 36.9654 4.93971
\(57\) 2.17802 0.288485
\(58\) −17.4260 −2.28815
\(59\) −0.613007 −0.0798067 −0.0399034 0.999204i \(-0.512705\pi\)
−0.0399034 + 0.999204i \(0.512705\pi\)
\(60\) 0 0
\(61\) 1.33665 0.171140 0.0855701 0.996332i \(-0.472729\pi\)
0.0855701 + 0.996332i \(0.472729\pi\)
\(62\) −24.9712 −3.17134
\(63\) 8.62866 1.08711
\(64\) 8.69200 1.08650
\(65\) 0 0
\(66\) 5.70188 0.701853
\(67\) 0.386619 0.0472330 0.0236165 0.999721i \(-0.492482\pi\)
0.0236165 + 0.999721i \(0.492482\pi\)
\(68\) −31.0067 −3.76012
\(69\) 14.5105 1.74686
\(70\) 0 0
\(71\) 9.38483 1.11377 0.556887 0.830588i \(-0.311996\pi\)
0.556887 + 0.830588i \(0.311996\pi\)
\(72\) 13.0264 1.53517
\(73\) −1.97456 −0.231105 −0.115552 0.993301i \(-0.536864\pi\)
−0.115552 + 0.993301i \(0.536864\pi\)
\(74\) −9.66869 −1.12396
\(75\) 0 0
\(76\) 4.85352 0.556737
\(77\) 4.94832 0.563913
\(78\) −23.9797 −2.71516
\(79\) −6.61494 −0.744238 −0.372119 0.928185i \(-0.621369\pi\)
−0.372119 + 0.928185i \(0.621369\pi\)
\(80\) 0 0
\(81\) −11.1906 −1.24340
\(82\) −2.82857 −0.312364
\(83\) −0.100761 −0.0110600 −0.00553000 0.999985i \(-0.501760\pi\)
−0.00553000 + 0.999985i \(0.501760\pi\)
\(84\) 52.3089 5.70737
\(85\) 0 0
\(86\) 25.0802 2.70446
\(87\) −14.4978 −1.55433
\(88\) 7.47030 0.796336
\(89\) 2.48738 0.263661 0.131831 0.991272i \(-0.457914\pi\)
0.131831 + 0.991272i \(0.457914\pi\)
\(90\) 0 0
\(91\) −20.8105 −2.18153
\(92\) 32.3355 3.37121
\(93\) −20.7751 −2.15428
\(94\) 7.59641 0.783510
\(95\) 0 0
\(96\) 23.6205 2.41075
\(97\) −17.3288 −1.75947 −0.879737 0.475461i \(-0.842281\pi\)
−0.879737 + 0.475461i \(0.842281\pi\)
\(98\) 45.7766 4.62413
\(99\) 1.74376 0.175254
\(100\) 0 0
\(101\) −9.71209 −0.966389 −0.483194 0.875513i \(-0.660524\pi\)
−0.483194 + 0.875513i \(0.660524\pi\)
\(102\) −36.4265 −3.60676
\(103\) 15.6212 1.53920 0.769602 0.638524i \(-0.220455\pi\)
0.769602 + 0.638524i \(0.220455\pi\)
\(104\) −31.4168 −3.08068
\(105\) 0 0
\(106\) −17.6749 −1.71674
\(107\) −5.49210 −0.530941 −0.265471 0.964119i \(-0.585527\pi\)
−0.265471 + 0.964119i \(0.585527\pi\)
\(108\) −13.2798 −1.27785
\(109\) 13.5177 1.29476 0.647378 0.762169i \(-0.275865\pi\)
0.647378 + 0.762169i \(0.275865\pi\)
\(110\) 0 0
\(111\) −8.04400 −0.763503
\(112\) 48.7390 4.60540
\(113\) −11.1897 −1.05264 −0.526318 0.850288i \(-0.676428\pi\)
−0.526318 + 0.850288i \(0.676428\pi\)
\(114\) 5.70188 0.534030
\(115\) 0 0
\(116\) −32.3071 −2.99964
\(117\) −7.33349 −0.677982
\(118\) −1.60481 −0.147734
\(119\) −31.6124 −2.89790
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 3.49924 0.316806
\(123\) −2.35327 −0.212187
\(124\) −46.2955 −4.15746
\(125\) 0 0
\(126\) 22.5892 2.01240
\(127\) 6.65255 0.590319 0.295159 0.955448i \(-0.404627\pi\)
0.295159 + 0.955448i \(0.404627\pi\)
\(128\) 1.06509 0.0941412
\(129\) 20.8658 1.83713
\(130\) 0 0
\(131\) 18.4455 1.61159 0.805797 0.592192i \(-0.201737\pi\)
0.805797 + 0.592192i \(0.201737\pi\)
\(132\) 10.5710 0.920092
\(133\) 4.94832 0.429073
\(134\) 1.01214 0.0874355
\(135\) 0 0
\(136\) −47.7240 −4.09230
\(137\) −15.3705 −1.31319 −0.656597 0.754242i \(-0.728005\pi\)
−0.656597 + 0.754242i \(0.728005\pi\)
\(138\) 37.9875 3.23371
\(139\) −2.38661 −0.202430 −0.101215 0.994865i \(-0.532273\pi\)
−0.101215 + 0.994865i \(0.532273\pi\)
\(140\) 0 0
\(141\) 6.31994 0.532235
\(142\) 24.5688 2.06176
\(143\) −4.20557 −0.351687
\(144\) 17.1753 1.43128
\(145\) 0 0
\(146\) −5.16924 −0.427809
\(147\) 38.0844 3.14115
\(148\) −17.9254 −1.47346
\(149\) −10.6114 −0.869317 −0.434659 0.900595i \(-0.643131\pi\)
−0.434659 + 0.900595i \(0.643131\pi\)
\(150\) 0 0
\(151\) 14.8914 1.21185 0.605923 0.795523i \(-0.292804\pi\)
0.605923 + 0.795523i \(0.292804\pi\)
\(152\) 7.47030 0.605921
\(153\) −11.1400 −0.900616
\(154\) 12.9543 1.04389
\(155\) 0 0
\(156\) −44.4573 −3.55943
\(157\) 5.84649 0.466601 0.233300 0.972405i \(-0.425047\pi\)
0.233300 + 0.972405i \(0.425047\pi\)
\(158\) −17.3174 −1.37770
\(159\) −14.7049 −1.16617
\(160\) 0 0
\(161\) 32.9670 2.59817
\(162\) −29.2961 −2.30172
\(163\) −3.65131 −0.285993 −0.142996 0.989723i \(-0.545674\pi\)
−0.142996 + 0.989723i \(0.545674\pi\)
\(164\) −5.24405 −0.409492
\(165\) 0 0
\(166\) −0.263785 −0.0204737
\(167\) −8.34211 −0.645532 −0.322766 0.946479i \(-0.604613\pi\)
−0.322766 + 0.946479i \(0.604613\pi\)
\(168\) 80.5112 6.21158
\(169\) 4.68682 0.360524
\(170\) 0 0
\(171\) 1.74376 0.133348
\(172\) 46.4976 3.54541
\(173\) 14.4715 1.10025 0.550124 0.835083i \(-0.314580\pi\)
0.550124 + 0.835083i \(0.314580\pi\)
\(174\) −37.9542 −2.87730
\(175\) 0 0
\(176\) 9.84962 0.742443
\(177\) −1.33514 −0.100355
\(178\) 6.51176 0.488077
\(179\) 23.2230 1.73577 0.867884 0.496766i \(-0.165479\pi\)
0.867884 + 0.496766i \(0.165479\pi\)
\(180\) 0 0
\(181\) 3.66090 0.272112 0.136056 0.990701i \(-0.456557\pi\)
0.136056 + 0.990701i \(0.456557\pi\)
\(182\) −54.4803 −4.03834
\(183\) 2.91124 0.215205
\(184\) 49.7691 3.66903
\(185\) 0 0
\(186\) −54.3877 −3.98790
\(187\) −6.38851 −0.467174
\(188\) 14.0834 1.02714
\(189\) −13.5392 −0.984830
\(190\) 0 0
\(191\) 23.3590 1.69020 0.845099 0.534610i \(-0.179541\pi\)
0.845099 + 0.534610i \(0.179541\pi\)
\(192\) 18.9313 1.36625
\(193\) 25.1709 1.81184 0.905922 0.423445i \(-0.139179\pi\)
0.905922 + 0.423445i \(0.139179\pi\)
\(194\) −45.3655 −3.25705
\(195\) 0 0
\(196\) 84.8678 6.06199
\(197\) 6.98835 0.497899 0.248950 0.968516i \(-0.419915\pi\)
0.248950 + 0.968516i \(0.419915\pi\)
\(198\) 4.56502 0.324422
\(199\) 11.5381 0.817911 0.408955 0.912554i \(-0.365893\pi\)
0.408955 + 0.912554i \(0.365893\pi\)
\(200\) 0 0
\(201\) 0.842063 0.0593946
\(202\) −25.4255 −1.78893
\(203\) −32.9381 −2.31180
\(204\) −67.5332 −4.72827
\(205\) 0 0
\(206\) 40.8951 2.84930
\(207\) 11.6174 0.807464
\(208\) −41.4232 −2.87219
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 13.7660 0.947687 0.473844 0.880609i \(-0.342866\pi\)
0.473844 + 0.880609i \(0.342866\pi\)
\(212\) −32.7686 −2.25055
\(213\) 20.4403 1.40055
\(214\) −14.3779 −0.982853
\(215\) 0 0
\(216\) −20.4396 −1.39074
\(217\) −47.1998 −3.20413
\(218\) 35.3882 2.39679
\(219\) −4.30062 −0.290609
\(220\) 0 0
\(221\) 26.8673 1.80729
\(222\) −21.0586 −1.41336
\(223\) −18.7373 −1.25474 −0.627371 0.778720i \(-0.715869\pi\)
−0.627371 + 0.778720i \(0.715869\pi\)
\(224\) 53.6642 3.58559
\(225\) 0 0
\(226\) −29.2937 −1.94859
\(227\) −21.7922 −1.44640 −0.723199 0.690640i \(-0.757329\pi\)
−0.723199 + 0.690640i \(0.757329\pi\)
\(228\) 10.5710 0.700085
\(229\) −15.5530 −1.02777 −0.513886 0.857859i \(-0.671795\pi\)
−0.513886 + 0.857859i \(0.671795\pi\)
\(230\) 0 0
\(231\) 10.7775 0.709109
\(232\) −49.7255 −3.26464
\(233\) 27.0173 1.76996 0.884982 0.465625i \(-0.154170\pi\)
0.884982 + 0.465625i \(0.154170\pi\)
\(234\) −19.1985 −1.25505
\(235\) 0 0
\(236\) −2.97524 −0.193672
\(237\) −14.4074 −0.935864
\(238\) −82.7587 −5.36445
\(239\) −26.5139 −1.71504 −0.857521 0.514449i \(-0.827997\pi\)
−0.857521 + 0.514449i \(0.827997\pi\)
\(240\) 0 0
\(241\) −16.1879 −1.04275 −0.521377 0.853327i \(-0.674581\pi\)
−0.521377 + 0.853327i \(0.674581\pi\)
\(242\) 2.61792 0.168286
\(243\) −16.1649 −1.03698
\(244\) 6.48745 0.415316
\(245\) 0 0
\(246\) −6.16068 −0.392790
\(247\) −4.20557 −0.267594
\(248\) −71.2558 −4.52475
\(249\) −0.219460 −0.0139077
\(250\) 0 0
\(251\) 2.48202 0.156664 0.0783319 0.996927i \(-0.475041\pi\)
0.0783319 + 0.996927i \(0.475041\pi\)
\(252\) 41.8794 2.63815
\(253\) 6.66227 0.418853
\(254\) 17.4159 1.09277
\(255\) 0 0
\(256\) −14.5957 −0.912230
\(257\) −1.75270 −0.109330 −0.0546651 0.998505i \(-0.517409\pi\)
−0.0546651 + 0.998505i \(0.517409\pi\)
\(258\) 54.6250 3.40081
\(259\) −18.2755 −1.13558
\(260\) 0 0
\(261\) −11.6072 −0.718468
\(262\) 48.2890 2.98330
\(263\) −15.9328 −0.982460 −0.491230 0.871030i \(-0.663452\pi\)
−0.491230 + 0.871030i \(0.663452\pi\)
\(264\) 16.2704 1.00138
\(265\) 0 0
\(266\) 12.9543 0.794280
\(267\) 5.41755 0.331549
\(268\) 1.87646 0.114623
\(269\) −5.40061 −0.329281 −0.164641 0.986354i \(-0.552646\pi\)
−0.164641 + 0.986354i \(0.552646\pi\)
\(270\) 0 0
\(271\) −0.761668 −0.0462680 −0.0231340 0.999732i \(-0.507364\pi\)
−0.0231340 + 0.999732i \(0.507364\pi\)
\(272\) −62.9243 −3.81535
\(273\) −45.3256 −2.74323
\(274\) −40.2389 −2.43092
\(275\) 0 0
\(276\) 70.4272 4.23922
\(277\) 26.9579 1.61974 0.809872 0.586606i \(-0.199536\pi\)
0.809872 + 0.586606i \(0.199536\pi\)
\(278\) −6.24797 −0.374729
\(279\) −16.6329 −0.995787
\(280\) 0 0
\(281\) 18.4983 1.10352 0.551759 0.834004i \(-0.313957\pi\)
0.551759 + 0.834004i \(0.313957\pi\)
\(282\) 16.5451 0.985247
\(283\) 18.9028 1.12365 0.561827 0.827255i \(-0.310099\pi\)
0.561827 + 0.827255i \(0.310099\pi\)
\(284\) 45.5495 2.70286
\(285\) 0 0
\(286\) −11.0099 −0.651026
\(287\) −5.34648 −0.315593
\(288\) 18.9110 1.11434
\(289\) 23.8130 1.40077
\(290\) 0 0
\(291\) −37.7424 −2.21250
\(292\) −9.58356 −0.560835
\(293\) 13.8515 0.809214 0.404607 0.914491i \(-0.367408\pi\)
0.404607 + 0.914491i \(0.367408\pi\)
\(294\) 99.7021 5.81475
\(295\) 0 0
\(296\) −27.5898 −1.60363
\(297\) −2.73612 −0.158766
\(298\) −27.7797 −1.60924
\(299\) −28.0186 −1.62036
\(300\) 0 0
\(301\) 47.4057 2.73242
\(302\) 38.9846 2.24331
\(303\) −21.1531 −1.21521
\(304\) 9.84962 0.564914
\(305\) 0 0
\(306\) −29.1637 −1.66718
\(307\) 0.233341 0.0133175 0.00665874 0.999978i \(-0.497880\pi\)
0.00665874 + 0.999978i \(0.497880\pi\)
\(308\) 24.0168 1.36848
\(309\) 34.0233 1.93552
\(310\) 0 0
\(311\) 7.70278 0.436784 0.218392 0.975861i \(-0.429919\pi\)
0.218392 + 0.975861i \(0.429919\pi\)
\(312\) −68.4264 −3.87388
\(313\) 14.9273 0.843742 0.421871 0.906656i \(-0.361374\pi\)
0.421871 + 0.906656i \(0.361374\pi\)
\(314\) 15.3057 0.863749
\(315\) 0 0
\(316\) −32.1057 −1.80609
\(317\) −3.39011 −0.190408 −0.0952038 0.995458i \(-0.530350\pi\)
−0.0952038 + 0.995458i \(0.530350\pi\)
\(318\) −38.4963 −2.15876
\(319\) −6.65643 −0.372689
\(320\) 0 0
\(321\) −11.9619 −0.667648
\(322\) 86.3051 4.80960
\(323\) −6.38851 −0.355466
\(324\) −54.3137 −3.01743
\(325\) 0 0
\(326\) −9.55885 −0.529416
\(327\) 29.4417 1.62813
\(328\) −8.07139 −0.445668
\(329\) 14.3585 0.791610
\(330\) 0 0
\(331\) −8.10646 −0.445571 −0.222786 0.974867i \(-0.571515\pi\)
−0.222786 + 0.974867i \(0.571515\pi\)
\(332\) −0.489047 −0.0268399
\(333\) −6.44017 −0.352919
\(334\) −21.8390 −1.19498
\(335\) 0 0
\(336\) 106.154 5.79120
\(337\) 13.4558 0.732984 0.366492 0.930421i \(-0.380559\pi\)
0.366492 + 0.930421i \(0.380559\pi\)
\(338\) 12.2697 0.667385
\(339\) −24.3713 −1.32367
\(340\) 0 0
\(341\) −9.53855 −0.516541
\(342\) 4.56502 0.246848
\(343\) 51.8872 2.80165
\(344\) 71.5667 3.85862
\(345\) 0 0
\(346\) 37.8853 2.03673
\(347\) −15.8117 −0.848819 −0.424409 0.905470i \(-0.639518\pi\)
−0.424409 + 0.905470i \(0.639518\pi\)
\(348\) −70.3654 −3.77198
\(349\) −7.24809 −0.387981 −0.193991 0.981003i \(-0.562143\pi\)
−0.193991 + 0.981003i \(0.562143\pi\)
\(350\) 0 0
\(351\) 11.5069 0.614194
\(352\) 10.8449 0.578038
\(353\) −11.6864 −0.622005 −0.311003 0.950409i \(-0.600665\pi\)
−0.311003 + 0.950409i \(0.600665\pi\)
\(354\) −3.49529 −0.185773
\(355\) 0 0
\(356\) 12.0725 0.639843
\(357\) −68.8522 −3.64405
\(358\) 60.7960 3.21317
\(359\) 27.1065 1.43063 0.715313 0.698804i \(-0.246284\pi\)
0.715313 + 0.698804i \(0.246284\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 9.58395 0.503721
\(363\) 2.17802 0.114316
\(364\) −101.004 −5.29405
\(365\) 0 0
\(366\) 7.62140 0.398377
\(367\) −12.9734 −0.677207 −0.338604 0.940929i \(-0.609955\pi\)
−0.338604 + 0.940929i \(0.609955\pi\)
\(368\) 65.6208 3.42072
\(369\) −1.88407 −0.0980806
\(370\) 0 0
\(371\) −33.4086 −1.73449
\(372\) −100.832 −5.22792
\(373\) −25.2889 −1.30941 −0.654704 0.755885i \(-0.727207\pi\)
−0.654704 + 0.755885i \(0.727207\pi\)
\(374\) −16.7246 −0.864809
\(375\) 0 0
\(376\) 21.6765 1.11788
\(377\) 27.9941 1.44177
\(378\) −35.4445 −1.82307
\(379\) −25.0016 −1.28425 −0.642123 0.766602i \(-0.721946\pi\)
−0.642123 + 0.766602i \(0.721946\pi\)
\(380\) 0 0
\(381\) 14.4894 0.742313
\(382\) 61.1521 3.12881
\(383\) −2.66127 −0.135985 −0.0679923 0.997686i \(-0.521659\pi\)
−0.0679923 + 0.997686i \(0.521659\pi\)
\(384\) 2.31978 0.118381
\(385\) 0 0
\(386\) 65.8956 3.35400
\(387\) 16.7055 0.849189
\(388\) −84.1057 −4.26982
\(389\) 6.77412 0.343462 0.171731 0.985144i \(-0.445064\pi\)
0.171731 + 0.985144i \(0.445064\pi\)
\(390\) 0 0
\(391\) −42.5620 −2.15245
\(392\) 130.624 6.59753
\(393\) 40.1747 2.02654
\(394\) 18.2949 0.921686
\(395\) 0 0
\(396\) 8.46336 0.425300
\(397\) 20.9430 1.05110 0.525550 0.850763i \(-0.323860\pi\)
0.525550 + 0.850763i \(0.323860\pi\)
\(398\) 30.2057 1.51408
\(399\) 10.7775 0.539551
\(400\) 0 0
\(401\) 15.8352 0.790774 0.395387 0.918515i \(-0.370611\pi\)
0.395387 + 0.918515i \(0.370611\pi\)
\(402\) 2.20446 0.109948
\(403\) 40.1150 1.99827
\(404\) −47.1378 −2.34519
\(405\) 0 0
\(406\) −86.2295 −4.27950
\(407\) −3.69327 −0.183069
\(408\) −103.944 −5.14598
\(409\) −1.16027 −0.0573715 −0.0286857 0.999588i \(-0.509132\pi\)
−0.0286857 + 0.999588i \(0.509132\pi\)
\(410\) 0 0
\(411\) −33.4773 −1.65131
\(412\) 75.8178 3.73528
\(413\) −3.03335 −0.149262
\(414\) 30.4134 1.49474
\(415\) 0 0
\(416\) −45.6092 −2.23617
\(417\) −5.19809 −0.254551
\(418\) 2.61792 0.128047
\(419\) 0.923724 0.0451269 0.0225634 0.999745i \(-0.492817\pi\)
0.0225634 + 0.999745i \(0.492817\pi\)
\(420\) 0 0
\(421\) 13.0507 0.636054 0.318027 0.948082i \(-0.396980\pi\)
0.318027 + 0.948082i \(0.396980\pi\)
\(422\) 36.0382 1.75431
\(423\) 5.05985 0.246018
\(424\) −50.4357 −2.44938
\(425\) 0 0
\(426\) 53.5112 2.59263
\(427\) 6.61415 0.320081
\(428\) −26.6560 −1.28847
\(429\) −9.15980 −0.442239
\(430\) 0 0
\(431\) 20.3251 0.979025 0.489513 0.871996i \(-0.337175\pi\)
0.489513 + 0.871996i \(0.337175\pi\)
\(432\) −26.9497 −1.29662
\(433\) −20.5451 −0.987333 −0.493666 0.869651i \(-0.664344\pi\)
−0.493666 + 0.869651i \(0.664344\pi\)
\(434\) −123.565 −5.93133
\(435\) 0 0
\(436\) 65.6082 3.14206
\(437\) 6.66227 0.318700
\(438\) −11.2587 −0.537961
\(439\) −7.67668 −0.366388 −0.183194 0.983077i \(-0.558644\pi\)
−0.183194 + 0.983077i \(0.558644\pi\)
\(440\) 0 0
\(441\) 30.4911 1.45196
\(442\) 70.3365 3.34557
\(443\) 9.04317 0.429654 0.214827 0.976652i \(-0.431081\pi\)
0.214827 + 0.976652i \(0.431081\pi\)
\(444\) −39.0417 −1.85284
\(445\) 0 0
\(446\) −49.0528 −2.32272
\(447\) −23.1117 −1.09315
\(448\) 43.0107 2.03207
\(449\) −9.97433 −0.470718 −0.235359 0.971909i \(-0.575627\pi\)
−0.235359 + 0.971909i \(0.575627\pi\)
\(450\) 0 0
\(451\) −1.08046 −0.0508771
\(452\) −54.3093 −2.55449
\(453\) 32.4338 1.52387
\(454\) −57.0502 −2.67750
\(455\) 0 0
\(456\) 16.2704 0.761933
\(457\) 18.7284 0.876077 0.438038 0.898956i \(-0.355673\pi\)
0.438038 + 0.898956i \(0.355673\pi\)
\(458\) −40.7166 −1.90256
\(459\) 17.4797 0.815883
\(460\) 0 0
\(461\) −26.5036 −1.23440 −0.617198 0.786808i \(-0.711732\pi\)
−0.617198 + 0.786808i \(0.711732\pi\)
\(462\) 28.2147 1.31267
\(463\) 18.1944 0.845564 0.422782 0.906231i \(-0.361054\pi\)
0.422782 + 0.906231i \(0.361054\pi\)
\(464\) −65.5633 −3.04370
\(465\) 0 0
\(466\) 70.7293 3.27647
\(467\) 13.5114 0.625234 0.312617 0.949879i \(-0.398794\pi\)
0.312617 + 0.949879i \(0.398794\pi\)
\(468\) −35.5933 −1.64530
\(469\) 1.91311 0.0883394
\(470\) 0 0
\(471\) 12.7338 0.586741
\(472\) −4.57934 −0.210781
\(473\) 9.58018 0.440497
\(474\) −37.7176 −1.73243
\(475\) 0 0
\(476\) −153.431 −7.03251
\(477\) −11.7730 −0.539048
\(478\) −69.4114 −3.17480
\(479\) −15.0739 −0.688743 −0.344371 0.938833i \(-0.611908\pi\)
−0.344371 + 0.938833i \(0.611908\pi\)
\(480\) 0 0
\(481\) 15.5323 0.708212
\(482\) −42.3786 −1.93029
\(483\) 71.8027 3.26714
\(484\) 4.85352 0.220615
\(485\) 0 0
\(486\) −42.3185 −1.91961
\(487\) −41.3382 −1.87321 −0.936607 0.350381i \(-0.886052\pi\)
−0.936607 + 0.350381i \(0.886052\pi\)
\(488\) 9.98515 0.452007
\(489\) −7.95262 −0.359630
\(490\) 0 0
\(491\) −29.4695 −1.32994 −0.664970 0.746870i \(-0.731556\pi\)
−0.664970 + 0.746870i \(0.731556\pi\)
\(492\) −11.4216 −0.514927
\(493\) 42.5246 1.91521
\(494\) −11.0099 −0.495357
\(495\) 0 0
\(496\) −93.9511 −4.21853
\(497\) 46.4391 2.08308
\(498\) −0.574529 −0.0257453
\(499\) 0.211110 0.00945058 0.00472529 0.999989i \(-0.498496\pi\)
0.00472529 + 0.999989i \(0.498496\pi\)
\(500\) 0 0
\(501\) −18.1693 −0.811743
\(502\) 6.49774 0.290008
\(503\) −7.94133 −0.354086 −0.177043 0.984203i \(-0.556653\pi\)
−0.177043 + 0.984203i \(0.556653\pi\)
\(504\) 64.4587 2.87122
\(505\) 0 0
\(506\) 17.4413 0.775361
\(507\) 10.2080 0.453352
\(508\) 32.2883 1.43256
\(509\) 7.40748 0.328331 0.164165 0.986433i \(-0.447507\pi\)
0.164165 + 0.986433i \(0.447507\pi\)
\(510\) 0 0
\(511\) −9.77074 −0.432232
\(512\) −40.3405 −1.78282
\(513\) −2.73612 −0.120803
\(514\) −4.58842 −0.202387
\(515\) 0 0
\(516\) 101.273 4.45827
\(517\) 2.90169 0.127616
\(518\) −47.8438 −2.10213
\(519\) 31.5192 1.38354
\(520\) 0 0
\(521\) 14.9680 0.655760 0.327880 0.944719i \(-0.393666\pi\)
0.327880 + 0.944719i \(0.393666\pi\)
\(522\) −30.3868 −1.32999
\(523\) 6.78937 0.296878 0.148439 0.988922i \(-0.452575\pi\)
0.148439 + 0.988922i \(0.452575\pi\)
\(524\) 89.5257 3.91095
\(525\) 0 0
\(526\) −41.7109 −1.81868
\(527\) 60.9371 2.65446
\(528\) 21.4526 0.933606
\(529\) 21.3859 0.929820
\(530\) 0 0
\(531\) −1.06894 −0.0463879
\(532\) 24.0168 1.04126
\(533\) 4.54397 0.196821
\(534\) 14.1827 0.613746
\(535\) 0 0
\(536\) 2.88816 0.124749
\(537\) 50.5801 2.18269
\(538\) −14.1384 −0.609549
\(539\) 17.4858 0.753168
\(540\) 0 0
\(541\) −21.8957 −0.941368 −0.470684 0.882302i \(-0.655993\pi\)
−0.470684 + 0.882302i \(0.655993\pi\)
\(542\) −1.99399 −0.0856491
\(543\) 7.97350 0.342176
\(544\) −69.2830 −2.97048
\(545\) 0 0
\(546\) −118.659 −5.07813
\(547\) −16.7053 −0.714266 −0.357133 0.934054i \(-0.616246\pi\)
−0.357133 + 0.934054i \(0.616246\pi\)
\(548\) −74.6012 −3.18681
\(549\) 2.33079 0.0994757
\(550\) 0 0
\(551\) −6.65643 −0.283573
\(552\) 108.398 4.61373
\(553\) −32.7328 −1.39194
\(554\) 70.5738 2.99839
\(555\) 0 0
\(556\) −11.5835 −0.491249
\(557\) −23.8953 −1.01248 −0.506238 0.862394i \(-0.668964\pi\)
−0.506238 + 0.862394i \(0.668964\pi\)
\(558\) −43.5437 −1.84335
\(559\) −40.2901 −1.70409
\(560\) 0 0
\(561\) −13.9143 −0.587461
\(562\) 48.4272 2.04278
\(563\) −17.6090 −0.742129 −0.371065 0.928607i \(-0.621007\pi\)
−0.371065 + 0.928607i \(0.621007\pi\)
\(564\) 30.6739 1.29161
\(565\) 0 0
\(566\) 49.4860 2.08005
\(567\) −55.3745 −2.32551
\(568\) 70.1075 2.94164
\(569\) 38.1265 1.59835 0.799174 0.601100i \(-0.205271\pi\)
0.799174 + 0.601100i \(0.205271\pi\)
\(570\) 0 0
\(571\) −6.37976 −0.266985 −0.133492 0.991050i \(-0.542619\pi\)
−0.133492 + 0.991050i \(0.542619\pi\)
\(572\) −20.4118 −0.853461
\(573\) 50.8763 2.12539
\(574\) −13.9967 −0.584210
\(575\) 0 0
\(576\) 15.1567 0.631531
\(577\) −19.3120 −0.803969 −0.401985 0.915646i \(-0.631679\pi\)
−0.401985 + 0.915646i \(0.631679\pi\)
\(578\) 62.3406 2.59303
\(579\) 54.8227 2.27835
\(580\) 0 0
\(581\) −0.498599 −0.0206854
\(582\) −98.8068 −4.09567
\(583\) −6.75151 −0.279619
\(584\) −14.7505 −0.610381
\(585\) 0 0
\(586\) 36.2622 1.49798
\(587\) −10.2671 −0.423769 −0.211884 0.977295i \(-0.567960\pi\)
−0.211884 + 0.977295i \(0.567960\pi\)
\(588\) 184.844 7.62282
\(589\) −9.53855 −0.393029
\(590\) 0 0
\(591\) 15.2207 0.626097
\(592\) −36.3773 −1.49510
\(593\) 28.6849 1.17795 0.588975 0.808151i \(-0.299532\pi\)
0.588975 + 0.808151i \(0.299532\pi\)
\(594\) −7.16294 −0.293899
\(595\) 0 0
\(596\) −51.5025 −2.10962
\(597\) 25.1301 1.02851
\(598\) −73.3507 −2.99953
\(599\) −21.3984 −0.874315 −0.437158 0.899385i \(-0.644015\pi\)
−0.437158 + 0.899385i \(0.644015\pi\)
\(600\) 0 0
\(601\) −36.6616 −1.49546 −0.747729 0.664004i \(-0.768856\pi\)
−0.747729 + 0.664004i \(0.768856\pi\)
\(602\) 124.105 5.05812
\(603\) 0.674170 0.0274543
\(604\) 72.2758 2.94086
\(605\) 0 0
\(606\) −55.3772 −2.24954
\(607\) 47.9867 1.94772 0.973860 0.227150i \(-0.0729408\pi\)
0.973860 + 0.227150i \(0.0729408\pi\)
\(608\) 10.8449 0.439821
\(609\) −71.7398 −2.90704
\(610\) 0 0
\(611\) −12.2033 −0.493692
\(612\) −54.0682 −2.18558
\(613\) 25.0991 1.01374 0.506872 0.862021i \(-0.330802\pi\)
0.506872 + 0.862021i \(0.330802\pi\)
\(614\) 0.610869 0.0246527
\(615\) 0 0
\(616\) 36.9654 1.48938
\(617\) −7.05585 −0.284058 −0.142029 0.989863i \(-0.545363\pi\)
−0.142029 + 0.989863i \(0.545363\pi\)
\(618\) 89.0703 3.58293
\(619\) 15.8586 0.637410 0.318705 0.947854i \(-0.396752\pi\)
0.318705 + 0.947854i \(0.396752\pi\)
\(620\) 0 0
\(621\) −18.2288 −0.731495
\(622\) 20.1653 0.808554
\(623\) 12.3083 0.493123
\(624\) −90.2205 −3.61171
\(625\) 0 0
\(626\) 39.0786 1.56189
\(627\) 2.17802 0.0869816
\(628\) 28.3761 1.13233
\(629\) 23.5945 0.940773
\(630\) 0 0
\(631\) 3.11637 0.124061 0.0620303 0.998074i \(-0.480242\pi\)
0.0620303 + 0.998074i \(0.480242\pi\)
\(632\) −49.4155 −1.96564
\(633\) 29.9825 1.19170
\(634\) −8.87505 −0.352473
\(635\) 0 0
\(636\) −71.3705 −2.83002
\(637\) −73.5379 −2.91368
\(638\) −17.4260 −0.689903
\(639\) 16.3649 0.647384
\(640\) 0 0
\(641\) −23.2203 −0.917147 −0.458573 0.888657i \(-0.651639\pi\)
−0.458573 + 0.888657i \(0.651639\pi\)
\(642\) −31.3153 −1.23592
\(643\) 17.3300 0.683428 0.341714 0.939804i \(-0.388993\pi\)
0.341714 + 0.939804i \(0.388993\pi\)
\(644\) 160.006 6.30512
\(645\) 0 0
\(646\) −16.7246 −0.658021
\(647\) −33.8000 −1.32881 −0.664407 0.747371i \(-0.731316\pi\)
−0.664407 + 0.747371i \(0.731316\pi\)
\(648\) −83.5970 −3.28400
\(649\) −0.613007 −0.0240626
\(650\) 0 0
\(651\) −102.802 −4.02912
\(652\) −17.7217 −0.694036
\(653\) 23.8491 0.933289 0.466644 0.884445i \(-0.345463\pi\)
0.466644 + 0.884445i \(0.345463\pi\)
\(654\) 77.0761 3.01391
\(655\) 0 0
\(656\) −10.6422 −0.415506
\(657\) −3.44315 −0.134330
\(658\) 37.5894 1.46539
\(659\) −34.8028 −1.35572 −0.677862 0.735189i \(-0.737093\pi\)
−0.677862 + 0.735189i \(0.737093\pi\)
\(660\) 0 0
\(661\) −41.3984 −1.61021 −0.805105 0.593132i \(-0.797891\pi\)
−0.805105 + 0.593132i \(0.797891\pi\)
\(662\) −21.2221 −0.824820
\(663\) 58.5175 2.27263
\(664\) −0.752717 −0.0292111
\(665\) 0 0
\(666\) −16.8599 −0.653306
\(667\) −44.3469 −1.71712
\(668\) −40.4886 −1.56655
\(669\) −40.8102 −1.57781
\(670\) 0 0
\(671\) 1.33665 0.0516007
\(672\) 116.882 4.50880
\(673\) 49.3984 1.90417 0.952085 0.305835i \(-0.0989354\pi\)
0.952085 + 0.305835i \(0.0989354\pi\)
\(674\) 35.2262 1.35686
\(675\) 0 0
\(676\) 22.7476 0.874906
\(677\) 36.6932 1.41023 0.705117 0.709091i \(-0.250895\pi\)
0.705117 + 0.709091i \(0.250895\pi\)
\(678\) −63.8022 −2.45031
\(679\) −85.7484 −3.29072
\(680\) 0 0
\(681\) −47.4637 −1.81881
\(682\) −24.9712 −0.956196
\(683\) −26.3703 −1.00903 −0.504516 0.863403i \(-0.668329\pi\)
−0.504516 + 0.863403i \(0.668329\pi\)
\(684\) 8.46336 0.323605
\(685\) 0 0
\(686\) 135.837 5.18627
\(687\) −33.8747 −1.29240
\(688\) 94.3611 3.59748
\(689\) 28.3939 1.08172
\(690\) 0 0
\(691\) 13.3427 0.507581 0.253791 0.967259i \(-0.418323\pi\)
0.253791 + 0.967259i \(0.418323\pi\)
\(692\) 70.2378 2.67004
\(693\) 8.62866 0.327776
\(694\) −41.3939 −1.57129
\(695\) 0 0
\(696\) −108.303 −4.10521
\(697\) 6.90255 0.261453
\(698\) −18.9749 −0.718212
\(699\) 58.8442 2.22569
\(700\) 0 0
\(701\) −7.00399 −0.264537 −0.132268 0.991214i \(-0.542226\pi\)
−0.132268 + 0.991214i \(0.542226\pi\)
\(702\) 30.1243 1.13697
\(703\) −3.69327 −0.139294
\(704\) 8.69200 0.327592
\(705\) 0 0
\(706\) −30.5941 −1.15143
\(707\) −48.0585 −1.80743
\(708\) −6.48013 −0.243538
\(709\) −30.5543 −1.14749 −0.573745 0.819034i \(-0.694510\pi\)
−0.573745 + 0.819034i \(0.694510\pi\)
\(710\) 0 0
\(711\) −11.5348 −0.432591
\(712\) 18.5814 0.696369
\(713\) −63.5484 −2.37991
\(714\) −180.250 −6.74568
\(715\) 0 0
\(716\) 112.713 4.21229
\(717\) −57.7478 −2.15663
\(718\) 70.9627 2.64831
\(719\) −29.1224 −1.08608 −0.543042 0.839706i \(-0.682727\pi\)
−0.543042 + 0.839706i \(0.682727\pi\)
\(720\) 0 0
\(721\) 77.2987 2.87875
\(722\) 2.61792 0.0974290
\(723\) −35.2575 −1.31124
\(724\) 17.7682 0.660351
\(725\) 0 0
\(726\) 5.70188 0.211617
\(727\) 20.4576 0.758731 0.379366 0.925247i \(-0.376142\pi\)
0.379366 + 0.925247i \(0.376142\pi\)
\(728\) −155.460 −5.76175
\(729\) −1.63574 −0.0605829
\(730\) 0 0
\(731\) −61.2030 −2.26368
\(732\) 14.1298 0.522251
\(733\) −43.2636 −1.59798 −0.798989 0.601346i \(-0.794631\pi\)
−0.798989 + 0.601346i \(0.794631\pi\)
\(734\) −33.9634 −1.25361
\(735\) 0 0
\(736\) 72.2520 2.66324
\(737\) 0.386619 0.0142413
\(738\) −4.93234 −0.181562
\(739\) −31.1858 −1.14719 −0.573595 0.819139i \(-0.694452\pi\)
−0.573595 + 0.819139i \(0.694452\pi\)
\(740\) 0 0
\(741\) −9.15980 −0.336494
\(742\) −87.4611 −3.21080
\(743\) −45.0080 −1.65118 −0.825592 0.564268i \(-0.809158\pi\)
−0.825592 + 0.564268i \(0.809158\pi\)
\(744\) −155.196 −5.68977
\(745\) 0 0
\(746\) −66.2043 −2.42391
\(747\) −0.175703 −0.00642865
\(748\) −31.0067 −1.13372
\(749\) −27.1767 −0.993013
\(750\) 0 0
\(751\) −29.7716 −1.08638 −0.543191 0.839609i \(-0.682784\pi\)
−0.543191 + 0.839609i \(0.682784\pi\)
\(752\) 28.5806 1.04223
\(753\) 5.40588 0.197001
\(754\) 73.2863 2.66893
\(755\) 0 0
\(756\) −65.7126 −2.38995
\(757\) −32.1474 −1.16842 −0.584209 0.811603i \(-0.698595\pi\)
−0.584209 + 0.811603i \(0.698595\pi\)
\(758\) −65.4522 −2.37733
\(759\) 14.5105 0.526699
\(760\) 0 0
\(761\) −2.83297 −0.102695 −0.0513475 0.998681i \(-0.516352\pi\)
−0.0513475 + 0.998681i \(0.516352\pi\)
\(762\) 37.9321 1.37413
\(763\) 66.8896 2.42157
\(764\) 113.373 4.10170
\(765\) 0 0
\(766\) −6.96700 −0.251728
\(767\) 2.57804 0.0930878
\(768\) −31.7896 −1.14711
\(769\) −0.197238 −0.00711259 −0.00355630 0.999994i \(-0.501132\pi\)
−0.00355630 + 0.999994i \(0.501132\pi\)
\(770\) 0 0
\(771\) −3.81740 −0.137480
\(772\) 122.168 4.39691
\(773\) 39.5489 1.42247 0.711237 0.702952i \(-0.248135\pi\)
0.711237 + 0.702952i \(0.248135\pi\)
\(774\) 43.7337 1.57198
\(775\) 0 0
\(776\) −129.451 −4.64703
\(777\) −39.8043 −1.42797
\(778\) 17.7341 0.635799
\(779\) −1.08046 −0.0387116
\(780\) 0 0
\(781\) 9.38483 0.335816
\(782\) −111.424 −3.98451
\(783\) 18.2128 0.650871
\(784\) 172.229 6.15103
\(785\) 0 0
\(786\) 105.174 3.75144
\(787\) 20.2522 0.721912 0.360956 0.932583i \(-0.382450\pi\)
0.360956 + 0.932583i \(0.382450\pi\)
\(788\) 33.9181 1.20828
\(789\) −34.7019 −1.23542
\(790\) 0 0
\(791\) −55.3700 −1.96873
\(792\) 13.0264 0.462872
\(793\) −5.62136 −0.199620
\(794\) 54.8272 1.94574
\(795\) 0 0
\(796\) 56.0002 1.98487
\(797\) 24.5195 0.868524 0.434262 0.900787i \(-0.357009\pi\)
0.434262 + 0.900787i \(0.357009\pi\)
\(798\) 28.2147 0.998790
\(799\) −18.5375 −0.655809
\(800\) 0 0
\(801\) 4.33738 0.153254
\(802\) 41.4554 1.46384
\(803\) −1.97456 −0.0696806
\(804\) 4.08697 0.144136
\(805\) 0 0
\(806\) 105.018 3.69910
\(807\) −11.7626 −0.414064
\(808\) −72.5522 −2.55238
\(809\) 18.8544 0.662885 0.331442 0.943475i \(-0.392465\pi\)
0.331442 + 0.943475i \(0.392465\pi\)
\(810\) 0 0
\(811\) 30.8152 1.08207 0.541034 0.841001i \(-0.318033\pi\)
0.541034 + 0.841001i \(0.318033\pi\)
\(812\) −159.866 −5.61019
\(813\) −1.65893 −0.0581811
\(814\) −9.66869 −0.338888
\(815\) 0 0
\(816\) −137.050 −4.79772
\(817\) 9.58018 0.335168
\(818\) −3.03749 −0.106203
\(819\) −36.2884 −1.26802
\(820\) 0 0
\(821\) −3.91462 −0.136621 −0.0683106 0.997664i \(-0.521761\pi\)
−0.0683106 + 0.997664i \(0.521761\pi\)
\(822\) −87.6410 −3.05683
\(823\) 30.0384 1.04707 0.523537 0.852003i \(-0.324612\pi\)
0.523537 + 0.852003i \(0.324612\pi\)
\(824\) 116.695 4.06526
\(825\) 0 0
\(826\) −7.94108 −0.276306
\(827\) −19.0520 −0.662504 −0.331252 0.943542i \(-0.607471\pi\)
−0.331252 + 0.943542i \(0.607471\pi\)
\(828\) 56.3852 1.95952
\(829\) −2.78078 −0.0965806 −0.0482903 0.998833i \(-0.515377\pi\)
−0.0482903 + 0.998833i \(0.515377\pi\)
\(830\) 0 0
\(831\) 58.7148 2.03679
\(832\) −36.5548 −1.26731
\(833\) −111.708 −3.87047
\(834\) −13.6082 −0.471213
\(835\) 0 0
\(836\) 4.85352 0.167862
\(837\) 26.0986 0.902099
\(838\) 2.41824 0.0835367
\(839\) −12.1680 −0.420087 −0.210044 0.977692i \(-0.567361\pi\)
−0.210044 + 0.977692i \(0.567361\pi\)
\(840\) 0 0
\(841\) 15.3081 0.527864
\(842\) 34.1658 1.17743
\(843\) 40.2897 1.38765
\(844\) 66.8133 2.29981
\(845\) 0 0
\(846\) 13.2463 0.455417
\(847\) 4.94832 0.170026
\(848\) −66.4997 −2.28361
\(849\) 41.1706 1.41297
\(850\) 0 0
\(851\) −24.6056 −0.843468
\(852\) 99.2075 3.39879
\(853\) 30.8061 1.05478 0.527390 0.849623i \(-0.323171\pi\)
0.527390 + 0.849623i \(0.323171\pi\)
\(854\) 17.3153 0.592519
\(855\) 0 0
\(856\) −41.0276 −1.40229
\(857\) −5.90481 −0.201705 −0.100852 0.994901i \(-0.532157\pi\)
−0.100852 + 0.994901i \(0.532157\pi\)
\(858\) −23.9797 −0.818652
\(859\) 28.0485 0.957003 0.478502 0.878087i \(-0.341180\pi\)
0.478502 + 0.878087i \(0.341180\pi\)
\(860\) 0 0
\(861\) −11.6447 −0.396851
\(862\) 53.2095 1.81232
\(863\) −24.0412 −0.818374 −0.409187 0.912451i \(-0.634188\pi\)
−0.409187 + 0.912451i \(0.634188\pi\)
\(864\) −29.6730 −1.00950
\(865\) 0 0
\(866\) −53.7854 −1.82770
\(867\) 51.8652 1.76143
\(868\) −229.085 −7.77565
\(869\) −6.61494 −0.224396
\(870\) 0 0
\(871\) −1.62595 −0.0550933
\(872\) 100.981 3.41964
\(873\) −30.2172 −1.02270
\(874\) 17.4413 0.589961
\(875\) 0 0
\(876\) −20.8731 −0.705238
\(877\) −46.1837 −1.55951 −0.779757 0.626083i \(-0.784657\pi\)
−0.779757 + 0.626083i \(0.784657\pi\)
\(878\) −20.0970 −0.678240
\(879\) 30.1688 1.01757
\(880\) 0 0
\(881\) −16.5583 −0.557863 −0.278931 0.960311i \(-0.589980\pi\)
−0.278931 + 0.960311i \(0.589980\pi\)
\(882\) 79.8232 2.68779
\(883\) 39.6210 1.33335 0.666676 0.745347i \(-0.267716\pi\)
0.666676 + 0.745347i \(0.267716\pi\)
\(884\) 130.401 4.38586
\(885\) 0 0
\(886\) 23.6743 0.795354
\(887\) 2.31838 0.0778436 0.0389218 0.999242i \(-0.487608\pi\)
0.0389218 + 0.999242i \(0.487608\pi\)
\(888\) −60.0911 −2.01652
\(889\) 32.9189 1.10407
\(890\) 0 0
\(891\) −11.1906 −0.374899
\(892\) −90.9419 −3.04496
\(893\) 2.90169 0.0971015
\(894\) −60.5048 −2.02358
\(895\) 0 0
\(896\) 5.27038 0.176071
\(897\) −61.0251 −2.03757
\(898\) −26.1120 −0.871370
\(899\) 63.4927 2.11760
\(900\) 0 0
\(901\) 43.1320 1.43694
\(902\) −2.82857 −0.0941811
\(903\) 103.251 3.43596
\(904\) −83.5901 −2.78017
\(905\) 0 0
\(906\) 84.9091 2.82092
\(907\) 3.05923 0.101580 0.0507900 0.998709i \(-0.483826\pi\)
0.0507900 + 0.998709i \(0.483826\pi\)
\(908\) −105.769 −3.51006
\(909\) −16.9355 −0.561716
\(910\) 0 0
\(911\) −51.4953 −1.70611 −0.853057 0.521817i \(-0.825254\pi\)
−0.853057 + 0.521817i \(0.825254\pi\)
\(912\) 21.4526 0.710368
\(913\) −0.100761 −0.00333471
\(914\) 49.0295 1.62175
\(915\) 0 0
\(916\) −75.4868 −2.49416
\(917\) 91.2743 3.01414
\(918\) 45.7605 1.51032
\(919\) 47.9995 1.58336 0.791678 0.610938i \(-0.209208\pi\)
0.791678 + 0.610938i \(0.209208\pi\)
\(920\) 0 0
\(921\) 0.508221 0.0167464
\(922\) −69.3844 −2.28505
\(923\) −39.4686 −1.29912
\(924\) 52.3089 1.72084
\(925\) 0 0
\(926\) 47.6315 1.56527
\(927\) 27.2396 0.894666
\(928\) −72.1886 −2.36971
\(929\) 27.5397 0.903548 0.451774 0.892132i \(-0.350791\pi\)
0.451774 + 0.892132i \(0.350791\pi\)
\(930\) 0 0
\(931\) 17.4858 0.573075
\(932\) 131.129 4.29528
\(933\) 16.7768 0.549247
\(934\) 35.3719 1.15740
\(935\) 0 0
\(936\) −54.7834 −1.79065
\(937\) 7.50039 0.245027 0.122513 0.992467i \(-0.460905\pi\)
0.122513 + 0.992467i \(0.460905\pi\)
\(938\) 5.00838 0.163530
\(939\) 32.5119 1.06099
\(940\) 0 0
\(941\) −42.0396 −1.37045 −0.685226 0.728330i \(-0.740297\pi\)
−0.685226 + 0.728330i \(0.740297\pi\)
\(942\) 33.3360 1.08615
\(943\) −7.19835 −0.234410
\(944\) −6.03789 −0.196516
\(945\) 0 0
\(946\) 25.0802 0.815426
\(947\) 20.1743 0.655576 0.327788 0.944751i \(-0.393697\pi\)
0.327788 + 0.944751i \(0.393697\pi\)
\(948\) −69.9268 −2.27112
\(949\) 8.30414 0.269564
\(950\) 0 0
\(951\) −7.38372 −0.239434
\(952\) −236.154 −7.65378
\(953\) −1.49342 −0.0483766 −0.0241883 0.999707i \(-0.507700\pi\)
−0.0241883 + 0.999707i \(0.507700\pi\)
\(954\) −30.8208 −0.997860
\(955\) 0 0
\(956\) −128.686 −4.16200
\(957\) −14.4978 −0.468648
\(958\) −39.4622 −1.27497
\(959\) −76.0583 −2.45605
\(960\) 0 0
\(961\) 59.9839 1.93497
\(962\) 40.6624 1.31101
\(963\) −9.57689 −0.308611
\(964\) −78.5682 −2.53051
\(965\) 0 0
\(966\) 187.974 6.04797
\(967\) 37.4587 1.20459 0.602295 0.798274i \(-0.294253\pi\)
0.602295 + 0.798274i \(0.294253\pi\)
\(968\) 7.47030 0.240104
\(969\) −13.9143 −0.446991
\(970\) 0 0
\(971\) −8.24513 −0.264599 −0.132299 0.991210i \(-0.542236\pi\)
−0.132299 + 0.991210i \(0.542236\pi\)
\(972\) −78.4568 −2.51650
\(973\) −11.8097 −0.378602
\(974\) −108.220 −3.46760
\(975\) 0 0
\(976\) 13.1655 0.421416
\(977\) 29.8558 0.955171 0.477586 0.878585i \(-0.341512\pi\)
0.477586 + 0.878585i \(0.341512\pi\)
\(978\) −20.8193 −0.665729
\(979\) 2.48738 0.0794969
\(980\) 0 0
\(981\) 23.5715 0.752581
\(982\) −77.1489 −2.46192
\(983\) 25.9753 0.828484 0.414242 0.910167i \(-0.364047\pi\)
0.414242 + 0.910167i \(0.364047\pi\)
\(984\) −17.5796 −0.560418
\(985\) 0 0
\(986\) 111.326 3.54535
\(987\) 31.2731 0.995432
\(988\) −20.4118 −0.649386
\(989\) 63.8257 2.02954
\(990\) 0 0
\(991\) −33.3837 −1.06047 −0.530235 0.847851i \(-0.677896\pi\)
−0.530235 + 0.847851i \(0.677896\pi\)
\(992\) −103.445 −3.28438
\(993\) −17.6560 −0.560297
\(994\) 121.574 3.85609
\(995\) 0 0
\(996\) −1.06515 −0.0337507
\(997\) 11.8321 0.374725 0.187363 0.982291i \(-0.440006\pi\)
0.187363 + 0.982291i \(0.440006\pi\)
\(998\) 0.552670 0.0174945
\(999\) 10.1052 0.319715
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 5225.2.a.y.1.14 yes 15
5.4 even 2 5225.2.a.r.1.2 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5225.2.a.r.1.2 15 5.4 even 2
5225.2.a.y.1.14 yes 15 1.1 even 1 trivial