Properties

Label 3525.2.a.bg.1.3
Level $3525$
Weight $2$
Character 3525.1
Self dual yes
Analytic conductor $28.147$
Analytic rank $1$
Dimension $10$
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] = [3525,2,Mod(1,3525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3525, 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("3525.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.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: \(28.1472667125\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 705)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.16553\) of defining polynomial
Character \(\chi\) \(=\) 3525.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.16553 q^{2} -1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} -4.15990 q^{7} +3.07879 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.16553 q^{2} -1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} -4.15990 q^{7} +3.07879 q^{8} +1.00000 q^{9} -3.81209 q^{11} +0.641537 q^{12} +4.61360 q^{13} +4.84850 q^{14} -2.30535 q^{16} +1.23057 q^{17} -1.16553 q^{18} -2.53013 q^{19} +4.15990 q^{21} +4.44310 q^{22} +2.58264 q^{23} -3.07879 q^{24} -5.37729 q^{26} -1.00000 q^{27} +2.66873 q^{28} -5.43386 q^{29} -6.09333 q^{31} -3.47062 q^{32} +3.81209 q^{33} -1.43427 q^{34} -0.641537 q^{36} +1.49075 q^{37} +2.94894 q^{38} -4.61360 q^{39} +5.04423 q^{41} -4.84850 q^{42} +12.3022 q^{43} +2.44560 q^{44} -3.01015 q^{46} +1.00000 q^{47} +2.30535 q^{48} +10.3048 q^{49} -1.23057 q^{51} -2.95979 q^{52} +6.27544 q^{53} +1.16553 q^{54} -12.8075 q^{56} +2.53013 q^{57} +6.33333 q^{58} +2.67129 q^{59} +12.7902 q^{61} +7.10197 q^{62} -4.15990 q^{63} +8.65583 q^{64} -4.44310 q^{66} +11.3306 q^{67} -0.789458 q^{68} -2.58264 q^{69} -3.49400 q^{71} +3.07879 q^{72} -14.2798 q^{73} -1.73752 q^{74} +1.62317 q^{76} +15.8579 q^{77} +5.37729 q^{78} +5.30405 q^{79} +1.00000 q^{81} -5.87921 q^{82} -5.94379 q^{83} -2.66873 q^{84} -14.3386 q^{86} +5.43386 q^{87} -11.7366 q^{88} -1.23460 q^{89} -19.1921 q^{91} -1.65686 q^{92} +6.09333 q^{93} -1.16553 q^{94} +3.47062 q^{96} -14.5416 q^{97} -12.0106 q^{98} -3.81209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16553 −0.824155 −0.412077 0.911149i \(-0.635197\pi\)
−0.412077 + 0.911149i \(0.635197\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.641537 −0.320769
\(5\) 0 0
\(6\) 1.16553 0.475826
\(7\) −4.15990 −1.57230 −0.786148 0.618038i \(-0.787928\pi\)
−0.786148 + 0.618038i \(0.787928\pi\)
\(8\) 3.07879 1.08852
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.81209 −1.14939 −0.574694 0.818369i \(-0.694879\pi\)
−0.574694 + 0.818369i \(0.694879\pi\)
\(12\) 0.641537 0.185196
\(13\) 4.61360 1.27958 0.639791 0.768549i \(-0.279021\pi\)
0.639791 + 0.768549i \(0.279021\pi\)
\(14\) 4.84850 1.29582
\(15\) 0 0
\(16\) −2.30535 −0.576339
\(17\) 1.23057 0.298457 0.149229 0.988803i \(-0.452321\pi\)
0.149229 + 0.988803i \(0.452321\pi\)
\(18\) −1.16553 −0.274718
\(19\) −2.53013 −0.580452 −0.290226 0.956958i \(-0.593730\pi\)
−0.290226 + 0.956958i \(0.593730\pi\)
\(20\) 0 0
\(21\) 4.15990 0.907766
\(22\) 4.44310 0.947273
\(23\) 2.58264 0.538517 0.269259 0.963068i \(-0.413221\pi\)
0.269259 + 0.963068i \(0.413221\pi\)
\(24\) −3.07879 −0.628456
\(25\) 0 0
\(26\) −5.37729 −1.05457
\(27\) −1.00000 −0.192450
\(28\) 2.66873 0.504343
\(29\) −5.43386 −1.00904 −0.504521 0.863399i \(-0.668331\pi\)
−0.504521 + 0.863399i \(0.668331\pi\)
\(30\) 0 0
\(31\) −6.09333 −1.09439 −0.547197 0.837004i \(-0.684305\pi\)
−0.547197 + 0.837004i \(0.684305\pi\)
\(32\) −3.47062 −0.613526
\(33\) 3.81209 0.663599
\(34\) −1.43427 −0.245975
\(35\) 0 0
\(36\) −0.641537 −0.106923
\(37\) 1.49075 0.245078 0.122539 0.992464i \(-0.460896\pi\)
0.122539 + 0.992464i \(0.460896\pi\)
\(38\) 2.94894 0.478382
\(39\) −4.61360 −0.738767
\(40\) 0 0
\(41\) 5.04423 0.787777 0.393888 0.919158i \(-0.371130\pi\)
0.393888 + 0.919158i \(0.371130\pi\)
\(42\) −4.84850 −0.748139
\(43\) 12.3022 1.87607 0.938037 0.346534i \(-0.112641\pi\)
0.938037 + 0.346534i \(0.112641\pi\)
\(44\) 2.44560 0.368687
\(45\) 0 0
\(46\) −3.01015 −0.443822
\(47\) 1.00000 0.145865
\(48\) 2.30535 0.332749
\(49\) 10.3048 1.47212
\(50\) 0 0
\(51\) −1.23057 −0.172314
\(52\) −2.95979 −0.410450
\(53\) 6.27544 0.861998 0.430999 0.902352i \(-0.358161\pi\)
0.430999 + 0.902352i \(0.358161\pi\)
\(54\) 1.16553 0.158609
\(55\) 0 0
\(56\) −12.8075 −1.71147
\(57\) 2.53013 0.335124
\(58\) 6.33333 0.831607
\(59\) 2.67129 0.347772 0.173886 0.984766i \(-0.444368\pi\)
0.173886 + 0.984766i \(0.444368\pi\)
\(60\) 0 0
\(61\) 12.7902 1.63762 0.818811 0.574064i \(-0.194634\pi\)
0.818811 + 0.574064i \(0.194634\pi\)
\(62\) 7.10197 0.901951
\(63\) −4.15990 −0.524099
\(64\) 8.65583 1.08198
\(65\) 0 0
\(66\) −4.44310 −0.546908
\(67\) 11.3306 1.38425 0.692127 0.721776i \(-0.256674\pi\)
0.692127 + 0.721776i \(0.256674\pi\)
\(68\) −0.789458 −0.0957358
\(69\) −2.58264 −0.310913
\(70\) 0 0
\(71\) −3.49400 −0.414661 −0.207331 0.978271i \(-0.566478\pi\)
−0.207331 + 0.978271i \(0.566478\pi\)
\(72\) 3.07879 0.362839
\(73\) −14.2798 −1.67132 −0.835662 0.549244i \(-0.814916\pi\)
−0.835662 + 0.549244i \(0.814916\pi\)
\(74\) −1.73752 −0.201982
\(75\) 0 0
\(76\) 1.62317 0.186191
\(77\) 15.8579 1.80718
\(78\) 5.37729 0.608858
\(79\) 5.30405 0.596752 0.298376 0.954448i \(-0.403555\pi\)
0.298376 + 0.954448i \(0.403555\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −5.87921 −0.649250
\(83\) −5.94379 −0.652415 −0.326208 0.945298i \(-0.605771\pi\)
−0.326208 + 0.945298i \(0.605771\pi\)
\(84\) −2.66873 −0.291183
\(85\) 0 0
\(86\) −14.3386 −1.54618
\(87\) 5.43386 0.582571
\(88\) −11.7366 −1.25113
\(89\) −1.23460 −0.130868 −0.0654338 0.997857i \(-0.520843\pi\)
−0.0654338 + 0.997857i \(0.520843\pi\)
\(90\) 0 0
\(91\) −19.1921 −2.01188
\(92\) −1.65686 −0.172740
\(93\) 6.09333 0.631849
\(94\) −1.16553 −0.120215
\(95\) 0 0
\(96\) 3.47062 0.354219
\(97\) −14.5416 −1.47647 −0.738236 0.674542i \(-0.764341\pi\)
−0.738236 + 0.674542i \(0.764341\pi\)
\(98\) −12.0106 −1.21325
\(99\) −3.81209 −0.383129
\(100\) 0 0
\(101\) −5.91317 −0.588382 −0.294191 0.955747i \(-0.595050\pi\)
−0.294191 + 0.955747i \(0.595050\pi\)
\(102\) 1.43427 0.142014
\(103\) −3.70244 −0.364813 −0.182406 0.983223i \(-0.558389\pi\)
−0.182406 + 0.983223i \(0.558389\pi\)
\(104\) 14.2043 1.39285
\(105\) 0 0
\(106\) −7.31422 −0.710420
\(107\) 18.6364 1.80165 0.900826 0.434181i \(-0.142962\pi\)
0.900826 + 0.434181i \(0.142962\pi\)
\(108\) 0.641537 0.0617320
\(109\) −11.8589 −1.13588 −0.567940 0.823070i \(-0.692259\pi\)
−0.567940 + 0.823070i \(0.692259\pi\)
\(110\) 0 0
\(111\) −1.49075 −0.141496
\(112\) 9.59006 0.906175
\(113\) 12.2064 1.14828 0.574142 0.818755i \(-0.305336\pi\)
0.574142 + 0.818755i \(0.305336\pi\)
\(114\) −2.94894 −0.276194
\(115\) 0 0
\(116\) 3.48602 0.323669
\(117\) 4.61360 0.426527
\(118\) −3.11347 −0.286618
\(119\) −5.11906 −0.469263
\(120\) 0 0
\(121\) 3.53200 0.321091
\(122\) −14.9074 −1.34965
\(123\) −5.04423 −0.454823
\(124\) 3.90910 0.351048
\(125\) 0 0
\(126\) 4.84850 0.431939
\(127\) −11.6492 −1.03370 −0.516850 0.856076i \(-0.672895\pi\)
−0.516850 + 0.856076i \(0.672895\pi\)
\(128\) −3.14739 −0.278193
\(129\) −12.3022 −1.08315
\(130\) 0 0
\(131\) −2.96872 −0.259378 −0.129689 0.991555i \(-0.541398\pi\)
−0.129689 + 0.991555i \(0.541398\pi\)
\(132\) −2.44560 −0.212862
\(133\) 10.5251 0.912642
\(134\) −13.2062 −1.14084
\(135\) 0 0
\(136\) 3.78868 0.324876
\(137\) 8.98119 0.767315 0.383658 0.923475i \(-0.374664\pi\)
0.383658 + 0.923475i \(0.374664\pi\)
\(138\) 3.01015 0.256241
\(139\) −15.3614 −1.30293 −0.651467 0.758677i \(-0.725846\pi\)
−0.651467 + 0.758677i \(0.725846\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) 4.07236 0.341745
\(143\) −17.5874 −1.47073
\(144\) −2.30535 −0.192113
\(145\) 0 0
\(146\) 16.6435 1.37743
\(147\) −10.3048 −0.849926
\(148\) −0.956372 −0.0786133
\(149\) 10.6569 0.873046 0.436523 0.899693i \(-0.356210\pi\)
0.436523 + 0.899693i \(0.356210\pi\)
\(150\) 0 0
\(151\) 5.11859 0.416545 0.208272 0.978071i \(-0.433216\pi\)
0.208272 + 0.978071i \(0.433216\pi\)
\(152\) −7.78975 −0.631832
\(153\) 1.23057 0.0994858
\(154\) −18.4829 −1.48939
\(155\) 0 0
\(156\) 2.95979 0.236973
\(157\) 11.5178 0.919221 0.459611 0.888121i \(-0.347989\pi\)
0.459611 + 0.888121i \(0.347989\pi\)
\(158\) −6.18204 −0.491816
\(159\) −6.27544 −0.497675
\(160\) 0 0
\(161\) −10.7435 −0.846709
\(162\) −1.16553 −0.0915728
\(163\) −6.71301 −0.525804 −0.262902 0.964823i \(-0.584680\pi\)
−0.262902 + 0.964823i \(0.584680\pi\)
\(164\) −3.23606 −0.252694
\(165\) 0 0
\(166\) 6.92767 0.537691
\(167\) −16.8981 −1.30761 −0.653806 0.756662i \(-0.726829\pi\)
−0.653806 + 0.756662i \(0.726829\pi\)
\(168\) 12.8075 0.988119
\(169\) 8.28526 0.637328
\(170\) 0 0
\(171\) −2.53013 −0.193484
\(172\) −7.89235 −0.601786
\(173\) 13.5026 1.02658 0.513292 0.858214i \(-0.328426\pi\)
0.513292 + 0.858214i \(0.328426\pi\)
\(174\) −6.33333 −0.480129
\(175\) 0 0
\(176\) 8.78821 0.662436
\(177\) −2.67129 −0.200787
\(178\) 1.43897 0.107855
\(179\) −5.85657 −0.437741 −0.218870 0.975754i \(-0.570237\pi\)
−0.218870 + 0.975754i \(0.570237\pi\)
\(180\) 0 0
\(181\) 18.2839 1.35903 0.679515 0.733662i \(-0.262190\pi\)
0.679515 + 0.733662i \(0.262190\pi\)
\(182\) 22.3690 1.65810
\(183\) −12.7902 −0.945481
\(184\) 7.95141 0.586186
\(185\) 0 0
\(186\) −7.10197 −0.520741
\(187\) −4.69104 −0.343043
\(188\) −0.641537 −0.0467889
\(189\) 4.15990 0.302589
\(190\) 0 0
\(191\) −5.42659 −0.392655 −0.196327 0.980538i \(-0.562902\pi\)
−0.196327 + 0.980538i \(0.562902\pi\)
\(192\) −8.65583 −0.624681
\(193\) −17.7710 −1.27918 −0.639592 0.768715i \(-0.720896\pi\)
−0.639592 + 0.768715i \(0.720896\pi\)
\(194\) 16.9487 1.21684
\(195\) 0 0
\(196\) −6.61092 −0.472208
\(197\) 2.41574 0.172114 0.0860571 0.996290i \(-0.472573\pi\)
0.0860571 + 0.996290i \(0.472573\pi\)
\(198\) 4.44310 0.315758
\(199\) −7.71405 −0.546834 −0.273417 0.961896i \(-0.588154\pi\)
−0.273417 + 0.961896i \(0.588154\pi\)
\(200\) 0 0
\(201\) −11.3306 −0.799200
\(202\) 6.89198 0.484918
\(203\) 22.6043 1.58651
\(204\) 0.789458 0.0552731
\(205\) 0 0
\(206\) 4.31531 0.300662
\(207\) 2.58264 0.179506
\(208\) −10.6360 −0.737472
\(209\) 9.64507 0.667164
\(210\) 0 0
\(211\) 1.21651 0.0837481 0.0418740 0.999123i \(-0.486667\pi\)
0.0418740 + 0.999123i \(0.486667\pi\)
\(212\) −4.02593 −0.276502
\(213\) 3.49400 0.239405
\(214\) −21.7213 −1.48484
\(215\) 0 0
\(216\) −3.07879 −0.209485
\(217\) 25.3477 1.72071
\(218\) 13.8220 0.936141
\(219\) 14.2798 0.964939
\(220\) 0 0
\(221\) 5.67736 0.381901
\(222\) 1.73752 0.116614
\(223\) −28.0985 −1.88161 −0.940806 0.338945i \(-0.889930\pi\)
−0.940806 + 0.338945i \(0.889930\pi\)
\(224\) 14.4375 0.964644
\(225\) 0 0
\(226\) −14.2270 −0.946365
\(227\) −25.5840 −1.69807 −0.849034 0.528339i \(-0.822815\pi\)
−0.849034 + 0.528339i \(0.822815\pi\)
\(228\) −1.62317 −0.107497
\(229\) −28.8181 −1.90435 −0.952176 0.305550i \(-0.901160\pi\)
−0.952176 + 0.305550i \(0.901160\pi\)
\(230\) 0 0
\(231\) −15.8579 −1.04337
\(232\) −16.7297 −1.09836
\(233\) −7.58573 −0.496957 −0.248479 0.968637i \(-0.579931\pi\)
−0.248479 + 0.968637i \(0.579931\pi\)
\(234\) −5.37729 −0.351524
\(235\) 0 0
\(236\) −1.71373 −0.111555
\(237\) −5.30405 −0.344535
\(238\) 5.96642 0.386746
\(239\) −6.26770 −0.405424 −0.202712 0.979238i \(-0.564976\pi\)
−0.202712 + 0.979238i \(0.564976\pi\)
\(240\) 0 0
\(241\) 3.08604 0.198790 0.0993948 0.995048i \(-0.468309\pi\)
0.0993948 + 0.995048i \(0.468309\pi\)
\(242\) −4.11665 −0.264628
\(243\) −1.00000 −0.0641500
\(244\) −8.20541 −0.525298
\(245\) 0 0
\(246\) 5.87921 0.374845
\(247\) −11.6730 −0.742735
\(248\) −18.7601 −1.19127
\(249\) 5.94379 0.376672
\(250\) 0 0
\(251\) −28.3257 −1.78790 −0.893950 0.448166i \(-0.852077\pi\)
−0.893950 + 0.448166i \(0.852077\pi\)
\(252\) 2.66873 0.168114
\(253\) −9.84524 −0.618965
\(254\) 13.5775 0.851928
\(255\) 0 0
\(256\) −13.6433 −0.852705
\(257\) 31.1489 1.94301 0.971506 0.237015i \(-0.0761689\pi\)
0.971506 + 0.237015i \(0.0761689\pi\)
\(258\) 14.3386 0.892685
\(259\) −6.20138 −0.385335
\(260\) 0 0
\(261\) −5.43386 −0.336348
\(262\) 3.46014 0.213768
\(263\) 20.2925 1.25129 0.625643 0.780109i \(-0.284836\pi\)
0.625643 + 0.780109i \(0.284836\pi\)
\(264\) 11.7366 0.722339
\(265\) 0 0
\(266\) −12.2673 −0.752158
\(267\) 1.23460 0.0755565
\(268\) −7.26901 −0.444025
\(269\) −12.3091 −0.750498 −0.375249 0.926924i \(-0.622443\pi\)
−0.375249 + 0.926924i \(0.622443\pi\)
\(270\) 0 0
\(271\) 4.15010 0.252101 0.126050 0.992024i \(-0.459770\pi\)
0.126050 + 0.992024i \(0.459770\pi\)
\(272\) −2.83690 −0.172013
\(273\) 19.1921 1.16156
\(274\) −10.4679 −0.632387
\(275\) 0 0
\(276\) 1.65686 0.0997312
\(277\) −26.8137 −1.61108 −0.805541 0.592540i \(-0.798125\pi\)
−0.805541 + 0.592540i \(0.798125\pi\)
\(278\) 17.9042 1.07382
\(279\) −6.09333 −0.364798
\(280\) 0 0
\(281\) −6.98903 −0.416930 −0.208465 0.978030i \(-0.566847\pi\)
−0.208465 + 0.978030i \(0.566847\pi\)
\(282\) 1.16553 0.0694064
\(283\) 20.1757 1.19932 0.599660 0.800255i \(-0.295303\pi\)
0.599660 + 0.800255i \(0.295303\pi\)
\(284\) 2.24153 0.133010
\(285\) 0 0
\(286\) 20.4987 1.21211
\(287\) −20.9835 −1.23862
\(288\) −3.47062 −0.204509
\(289\) −15.4857 −0.910923
\(290\) 0 0
\(291\) 14.5416 0.852442
\(292\) 9.16102 0.536108
\(293\) 2.10609 0.123039 0.0615196 0.998106i \(-0.480405\pi\)
0.0615196 + 0.998106i \(0.480405\pi\)
\(294\) 12.0106 0.700471
\(295\) 0 0
\(296\) 4.58971 0.266772
\(297\) 3.81209 0.221200
\(298\) −12.4209 −0.719525
\(299\) 11.9153 0.689077
\(300\) 0 0
\(301\) −51.1762 −2.94975
\(302\) −5.96587 −0.343297
\(303\) 5.91317 0.339703
\(304\) 5.83285 0.334537
\(305\) 0 0
\(306\) −1.43427 −0.0819917
\(307\) −17.1013 −0.976020 −0.488010 0.872838i \(-0.662277\pi\)
−0.488010 + 0.872838i \(0.662277\pi\)
\(308\) −10.1734 −0.579686
\(309\) 3.70244 0.210625
\(310\) 0 0
\(311\) 30.7032 1.74102 0.870510 0.492150i \(-0.163789\pi\)
0.870510 + 0.492150i \(0.163789\pi\)
\(312\) −14.2043 −0.804161
\(313\) −1.89191 −0.106937 −0.0534686 0.998570i \(-0.517028\pi\)
−0.0534686 + 0.998570i \(0.517028\pi\)
\(314\) −13.4244 −0.757581
\(315\) 0 0
\(316\) −3.40275 −0.191420
\(317\) 18.9576 1.06476 0.532382 0.846504i \(-0.321297\pi\)
0.532382 + 0.846504i \(0.321297\pi\)
\(318\) 7.31422 0.410161
\(319\) 20.7143 1.15978
\(320\) 0 0
\(321\) −18.6364 −1.04018
\(322\) 12.5219 0.697819
\(323\) −3.11351 −0.173240
\(324\) −0.641537 −0.0356410
\(325\) 0 0
\(326\) 7.82422 0.433344
\(327\) 11.8589 0.655801
\(328\) 15.5302 0.857509
\(329\) −4.15990 −0.229343
\(330\) 0 0
\(331\) −34.7036 −1.90748 −0.953742 0.300626i \(-0.902804\pi\)
−0.953742 + 0.300626i \(0.902804\pi\)
\(332\) 3.81316 0.209274
\(333\) 1.49075 0.0816926
\(334\) 19.6952 1.07768
\(335\) 0 0
\(336\) −9.59006 −0.523180
\(337\) 0.0144912 0.000789386 0 0.000394693 1.00000i \(-0.499874\pi\)
0.000394693 1.00000i \(0.499874\pi\)
\(338\) −9.65673 −0.525257
\(339\) −12.2064 −0.662963
\(340\) 0 0
\(341\) 23.2283 1.25788
\(342\) 2.94894 0.159461
\(343\) −13.7477 −0.742305
\(344\) 37.8761 2.04214
\(345\) 0 0
\(346\) −15.7377 −0.846064
\(347\) −30.3323 −1.62832 −0.814162 0.580638i \(-0.802803\pi\)
−0.814162 + 0.580638i \(0.802803\pi\)
\(348\) −3.48602 −0.186871
\(349\) −4.89284 −0.261908 −0.130954 0.991388i \(-0.541804\pi\)
−0.130954 + 0.991388i \(0.541804\pi\)
\(350\) 0 0
\(351\) −4.61360 −0.246256
\(352\) 13.2303 0.705178
\(353\) −24.2132 −1.28874 −0.644369 0.764715i \(-0.722880\pi\)
−0.644369 + 0.764715i \(0.722880\pi\)
\(354\) 3.11347 0.165479
\(355\) 0 0
\(356\) 0.792044 0.0419783
\(357\) 5.11906 0.270929
\(358\) 6.82602 0.360766
\(359\) −8.29577 −0.437834 −0.218917 0.975743i \(-0.570252\pi\)
−0.218917 + 0.975743i \(0.570252\pi\)
\(360\) 0 0
\(361\) −12.5984 −0.663076
\(362\) −21.3104 −1.12005
\(363\) −3.53200 −0.185382
\(364\) 12.3125 0.645348
\(365\) 0 0
\(366\) 14.9074 0.779223
\(367\) 11.0837 0.578564 0.289282 0.957244i \(-0.406583\pi\)
0.289282 + 0.957244i \(0.406583\pi\)
\(368\) −5.95390 −0.310368
\(369\) 5.04423 0.262592
\(370\) 0 0
\(371\) −26.1052 −1.35532
\(372\) −3.90910 −0.202677
\(373\) −1.43233 −0.0741634 −0.0370817 0.999312i \(-0.511806\pi\)
−0.0370817 + 0.999312i \(0.511806\pi\)
\(374\) 5.46756 0.282721
\(375\) 0 0
\(376\) 3.07879 0.158777
\(377\) −25.0696 −1.29115
\(378\) −4.84850 −0.249380
\(379\) −12.1820 −0.625749 −0.312874 0.949795i \(-0.601292\pi\)
−0.312874 + 0.949795i \(0.601292\pi\)
\(380\) 0 0
\(381\) 11.6492 0.596807
\(382\) 6.32486 0.323608
\(383\) 22.4757 1.14846 0.574228 0.818696i \(-0.305302\pi\)
0.574228 + 0.818696i \(0.305302\pi\)
\(384\) 3.14739 0.160615
\(385\) 0 0
\(386\) 20.7126 1.05425
\(387\) 12.3022 0.625358
\(388\) 9.32896 0.473606
\(389\) 7.90866 0.400985 0.200492 0.979695i \(-0.435746\pi\)
0.200492 + 0.979695i \(0.435746\pi\)
\(390\) 0 0
\(391\) 3.17812 0.160725
\(392\) 31.7264 1.60242
\(393\) 2.96872 0.149752
\(394\) −2.81562 −0.141849
\(395\) 0 0
\(396\) 2.44560 0.122896
\(397\) −22.6540 −1.13697 −0.568486 0.822693i \(-0.692471\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(398\) 8.99096 0.450676
\(399\) −10.5251 −0.526914
\(400\) 0 0
\(401\) 33.4361 1.66972 0.834859 0.550464i \(-0.185549\pi\)
0.834859 + 0.550464i \(0.185549\pi\)
\(402\) 13.2062 0.658664
\(403\) −28.1122 −1.40037
\(404\) 3.79352 0.188735
\(405\) 0 0
\(406\) −26.3461 −1.30753
\(407\) −5.68287 −0.281689
\(408\) −3.78868 −0.187567
\(409\) 14.3473 0.709430 0.354715 0.934974i \(-0.384578\pi\)
0.354715 + 0.934974i \(0.384578\pi\)
\(410\) 0 0
\(411\) −8.98119 −0.443010
\(412\) 2.37526 0.117020
\(413\) −11.1123 −0.546801
\(414\) −3.01015 −0.147941
\(415\) 0 0
\(416\) −16.0121 −0.785056
\(417\) 15.3614 0.752250
\(418\) −11.2416 −0.549846
\(419\) −8.05906 −0.393711 −0.196855 0.980433i \(-0.563073\pi\)
−0.196855 + 0.980433i \(0.563073\pi\)
\(420\) 0 0
\(421\) 0.407998 0.0198846 0.00994231 0.999951i \(-0.496835\pi\)
0.00994231 + 0.999951i \(0.496835\pi\)
\(422\) −1.41788 −0.0690214
\(423\) 1.00000 0.0486217
\(424\) 19.3208 0.938301
\(425\) 0 0
\(426\) −4.07236 −0.197307
\(427\) −53.2061 −2.57483
\(428\) −11.9560 −0.577913
\(429\) 17.5874 0.849129
\(430\) 0 0
\(431\) −11.7588 −0.566402 −0.283201 0.959061i \(-0.591396\pi\)
−0.283201 + 0.959061i \(0.591396\pi\)
\(432\) 2.30535 0.110916
\(433\) −4.25415 −0.204442 −0.102221 0.994762i \(-0.532595\pi\)
−0.102221 + 0.994762i \(0.532595\pi\)
\(434\) −29.5435 −1.41813
\(435\) 0 0
\(436\) 7.60795 0.364355
\(437\) −6.53441 −0.312583
\(438\) −16.6435 −0.795259
\(439\) −4.77103 −0.227709 −0.113854 0.993497i \(-0.536320\pi\)
−0.113854 + 0.993497i \(0.536320\pi\)
\(440\) 0 0
\(441\) 10.3048 0.490705
\(442\) −6.61714 −0.314745
\(443\) 6.80236 0.323190 0.161595 0.986857i \(-0.448336\pi\)
0.161595 + 0.986857i \(0.448336\pi\)
\(444\) 0.956372 0.0453874
\(445\) 0 0
\(446\) 32.7496 1.55074
\(447\) −10.6569 −0.504053
\(448\) −36.0074 −1.70119
\(449\) −1.56203 −0.0737165 −0.0368583 0.999321i \(-0.511735\pi\)
−0.0368583 + 0.999321i \(0.511735\pi\)
\(450\) 0 0
\(451\) −19.2291 −0.905461
\(452\) −7.83088 −0.368334
\(453\) −5.11859 −0.240492
\(454\) 29.8189 1.39947
\(455\) 0 0
\(456\) 7.78975 0.364788
\(457\) −4.03564 −0.188779 −0.0943896 0.995535i \(-0.530090\pi\)
−0.0943896 + 0.995535i \(0.530090\pi\)
\(458\) 33.5884 1.56948
\(459\) −1.23057 −0.0574382
\(460\) 0 0
\(461\) 18.7992 0.875567 0.437784 0.899080i \(-0.355764\pi\)
0.437784 + 0.899080i \(0.355764\pi\)
\(462\) 18.4829 0.859902
\(463\) −35.4554 −1.64775 −0.823876 0.566771i \(-0.808193\pi\)
−0.823876 + 0.566771i \(0.808193\pi\)
\(464\) 12.5270 0.581550
\(465\) 0 0
\(466\) 8.84140 0.409570
\(467\) −41.6376 −1.92676 −0.963379 0.268143i \(-0.913590\pi\)
−0.963379 + 0.268143i \(0.913590\pi\)
\(468\) −2.95979 −0.136817
\(469\) −47.1343 −2.17646
\(470\) 0 0
\(471\) −11.5178 −0.530713
\(472\) 8.22435 0.378557
\(473\) −46.8972 −2.15634
\(474\) 6.18204 0.283950
\(475\) 0 0
\(476\) 3.28407 0.150525
\(477\) 6.27544 0.287333
\(478\) 7.30520 0.334132
\(479\) −23.2251 −1.06118 −0.530591 0.847628i \(-0.678030\pi\)
−0.530591 + 0.847628i \(0.678030\pi\)
\(480\) 0 0
\(481\) 6.87772 0.313597
\(482\) −3.59688 −0.163833
\(483\) 10.7435 0.488848
\(484\) −2.26591 −0.102996
\(485\) 0 0
\(486\) 1.16553 0.0528696
\(487\) 4.25601 0.192858 0.0964291 0.995340i \(-0.469258\pi\)
0.0964291 + 0.995340i \(0.469258\pi\)
\(488\) 39.3785 1.78258
\(489\) 6.71301 0.303573
\(490\) 0 0
\(491\) 29.2980 1.32220 0.661101 0.750297i \(-0.270089\pi\)
0.661101 + 0.750297i \(0.270089\pi\)
\(492\) 3.23606 0.145893
\(493\) −6.68675 −0.301156
\(494\) 13.6052 0.612129
\(495\) 0 0
\(496\) 14.0473 0.630742
\(497\) 14.5347 0.651971
\(498\) −6.92767 −0.310436
\(499\) 28.3988 1.27130 0.635651 0.771976i \(-0.280732\pi\)
0.635651 + 0.771976i \(0.280732\pi\)
\(500\) 0 0
\(501\) 16.8981 0.754950
\(502\) 33.0145 1.47351
\(503\) 23.0789 1.02904 0.514518 0.857480i \(-0.327971\pi\)
0.514518 + 0.857480i \(0.327971\pi\)
\(504\) −12.8075 −0.570491
\(505\) 0 0
\(506\) 11.4749 0.510123
\(507\) −8.28526 −0.367961
\(508\) 7.47340 0.331578
\(509\) 34.4963 1.52902 0.764510 0.644612i \(-0.222981\pi\)
0.764510 + 0.644612i \(0.222981\pi\)
\(510\) 0 0
\(511\) 59.4026 2.62782
\(512\) 22.1964 0.980954
\(513\) 2.53013 0.111708
\(514\) −36.3050 −1.60134
\(515\) 0 0
\(516\) 7.89235 0.347441
\(517\) −3.81209 −0.167655
\(518\) 7.22790 0.317576
\(519\) −13.5026 −0.592698
\(520\) 0 0
\(521\) −28.8601 −1.26438 −0.632191 0.774813i \(-0.717844\pi\)
−0.632191 + 0.774813i \(0.717844\pi\)
\(522\) 6.33333 0.277202
\(523\) 2.81087 0.122911 0.0614553 0.998110i \(-0.480426\pi\)
0.0614553 + 0.998110i \(0.480426\pi\)
\(524\) 1.90455 0.0832005
\(525\) 0 0
\(526\) −23.6515 −1.03125
\(527\) −7.49828 −0.326630
\(528\) −8.78821 −0.382458
\(529\) −16.3300 −0.709999
\(530\) 0 0
\(531\) 2.67129 0.115924
\(532\) −6.75224 −0.292747
\(533\) 23.2721 1.00802
\(534\) −1.43897 −0.0622702
\(535\) 0 0
\(536\) 34.8846 1.50679
\(537\) 5.85657 0.252730
\(538\) 14.3466 0.618526
\(539\) −39.2828 −1.69203
\(540\) 0 0
\(541\) −9.59709 −0.412611 −0.206305 0.978488i \(-0.566144\pi\)
−0.206305 + 0.978488i \(0.566144\pi\)
\(542\) −4.83707 −0.207770
\(543\) −18.2839 −0.784636
\(544\) −4.27085 −0.183111
\(545\) 0 0
\(546\) −22.3690 −0.957305
\(547\) −36.0808 −1.54270 −0.771352 0.636409i \(-0.780419\pi\)
−0.771352 + 0.636409i \(0.780419\pi\)
\(548\) −5.76177 −0.246131
\(549\) 12.7902 0.545874
\(550\) 0 0
\(551\) 13.7484 0.585700
\(552\) −7.95141 −0.338435
\(553\) −22.0644 −0.938272
\(554\) 31.2523 1.32778
\(555\) 0 0
\(556\) 9.85489 0.417941
\(557\) 21.1230 0.895008 0.447504 0.894282i \(-0.352313\pi\)
0.447504 + 0.894282i \(0.352313\pi\)
\(558\) 7.10197 0.300650
\(559\) 56.7576 2.40059
\(560\) 0 0
\(561\) 4.69104 0.198056
\(562\) 8.14593 0.343615
\(563\) 11.8546 0.499612 0.249806 0.968296i \(-0.419633\pi\)
0.249806 + 0.968296i \(0.419633\pi\)
\(564\) 0.641537 0.0270136
\(565\) 0 0
\(566\) −23.5154 −0.988425
\(567\) −4.15990 −0.174700
\(568\) −10.7573 −0.451366
\(569\) 6.36909 0.267006 0.133503 0.991048i \(-0.457377\pi\)
0.133503 + 0.991048i \(0.457377\pi\)
\(570\) 0 0
\(571\) 40.2702 1.68526 0.842628 0.538496i \(-0.181007\pi\)
0.842628 + 0.538496i \(0.181007\pi\)
\(572\) 11.2830 0.471765
\(573\) 5.42659 0.226699
\(574\) 24.4570 1.02081
\(575\) 0 0
\(576\) 8.65583 0.360660
\(577\) −26.1825 −1.08999 −0.544996 0.838438i \(-0.683469\pi\)
−0.544996 + 0.838438i \(0.683469\pi\)
\(578\) 18.0491 0.750742
\(579\) 17.7710 0.738537
\(580\) 0 0
\(581\) 24.7256 1.02579
\(582\) −16.9487 −0.702544
\(583\) −23.9225 −0.990770
\(584\) −43.9646 −1.81927
\(585\) 0 0
\(586\) −2.45472 −0.101403
\(587\) −4.54659 −0.187658 −0.0938289 0.995588i \(-0.529911\pi\)
−0.0938289 + 0.995588i \(0.529911\pi\)
\(588\) 6.61092 0.272630
\(589\) 15.4169 0.635243
\(590\) 0 0
\(591\) −2.41574 −0.0993702
\(592\) −3.43671 −0.141248
\(593\) 23.1314 0.949891 0.474946 0.880015i \(-0.342468\pi\)
0.474946 + 0.880015i \(0.342468\pi\)
\(594\) −4.44310 −0.182303
\(595\) 0 0
\(596\) −6.83679 −0.280046
\(597\) 7.71405 0.315715
\(598\) −13.8876 −0.567906
\(599\) −41.6490 −1.70173 −0.850866 0.525383i \(-0.823922\pi\)
−0.850866 + 0.525383i \(0.823922\pi\)
\(600\) 0 0
\(601\) 8.66645 0.353512 0.176756 0.984255i \(-0.443440\pi\)
0.176756 + 0.984255i \(0.443440\pi\)
\(602\) 59.6474 2.43105
\(603\) 11.3306 0.461418
\(604\) −3.28376 −0.133614
\(605\) 0 0
\(606\) −6.89198 −0.279968
\(607\) 11.3275 0.459771 0.229885 0.973218i \(-0.426165\pi\)
0.229885 + 0.973218i \(0.426165\pi\)
\(608\) 8.78113 0.356122
\(609\) −22.6043 −0.915974
\(610\) 0 0
\(611\) 4.61360 0.186646
\(612\) −0.789458 −0.0319119
\(613\) −22.4281 −0.905863 −0.452931 0.891545i \(-0.649622\pi\)
−0.452931 + 0.891545i \(0.649622\pi\)
\(614\) 19.9320 0.804392
\(615\) 0 0
\(616\) 48.8232 1.96714
\(617\) 42.5696 1.71379 0.856893 0.515494i \(-0.172392\pi\)
0.856893 + 0.515494i \(0.172392\pi\)
\(618\) −4.31531 −0.173587
\(619\) 19.1959 0.771549 0.385774 0.922593i \(-0.373934\pi\)
0.385774 + 0.922593i \(0.373934\pi\)
\(620\) 0 0
\(621\) −2.58264 −0.103638
\(622\) −35.7856 −1.43487
\(623\) 5.13583 0.205763
\(624\) 10.6360 0.425780
\(625\) 0 0
\(626\) 2.20508 0.0881328
\(627\) −9.64507 −0.385187
\(628\) −7.38910 −0.294857
\(629\) 1.83448 0.0731453
\(630\) 0 0
\(631\) −30.0498 −1.19627 −0.598133 0.801397i \(-0.704090\pi\)
−0.598133 + 0.801397i \(0.704090\pi\)
\(632\) 16.3301 0.649576
\(633\) −1.21651 −0.0483520
\(634\) −22.0957 −0.877531
\(635\) 0 0
\(636\) 4.02593 0.159639
\(637\) 47.5422 1.88369
\(638\) −24.1432 −0.955839
\(639\) −3.49400 −0.138220
\(640\) 0 0
\(641\) 21.0046 0.829631 0.414815 0.909906i \(-0.363846\pi\)
0.414815 + 0.909906i \(0.363846\pi\)
\(642\) 21.7213 0.857273
\(643\) 12.2565 0.483351 0.241675 0.970357i \(-0.422303\pi\)
0.241675 + 0.970357i \(0.422303\pi\)
\(644\) 6.89238 0.271598
\(645\) 0 0
\(646\) 3.62889 0.142777
\(647\) 12.9252 0.508143 0.254072 0.967185i \(-0.418230\pi\)
0.254072 + 0.967185i \(0.418230\pi\)
\(648\) 3.07879 0.120946
\(649\) −10.1832 −0.399725
\(650\) 0 0
\(651\) −25.3477 −0.993454
\(652\) 4.30665 0.168661
\(653\) 2.34399 0.0917276 0.0458638 0.998948i \(-0.485396\pi\)
0.0458638 + 0.998948i \(0.485396\pi\)
\(654\) −13.8220 −0.540481
\(655\) 0 0
\(656\) −11.6287 −0.454026
\(657\) −14.2798 −0.557108
\(658\) 4.84850 0.189014
\(659\) −12.3566 −0.481345 −0.240672 0.970606i \(-0.577368\pi\)
−0.240672 + 0.970606i \(0.577368\pi\)
\(660\) 0 0
\(661\) 34.5750 1.34481 0.672405 0.740184i \(-0.265261\pi\)
0.672405 + 0.740184i \(0.265261\pi\)
\(662\) 40.4482 1.57206
\(663\) −5.67736 −0.220490
\(664\) −18.2997 −0.710166
\(665\) 0 0
\(666\) −1.73752 −0.0673274
\(667\) −14.0337 −0.543387
\(668\) 10.8407 0.419441
\(669\) 28.0985 1.08635
\(670\) 0 0
\(671\) −48.7574 −1.88226
\(672\) −14.4375 −0.556937
\(673\) 21.9687 0.846831 0.423416 0.905936i \(-0.360831\pi\)
0.423416 + 0.905936i \(0.360831\pi\)
\(674\) −0.0168899 −0.000650576 0
\(675\) 0 0
\(676\) −5.31531 −0.204435
\(677\) −12.3690 −0.475379 −0.237689 0.971341i \(-0.576390\pi\)
−0.237689 + 0.971341i \(0.576390\pi\)
\(678\) 14.2270 0.546384
\(679\) 60.4915 2.32145
\(680\) 0 0
\(681\) 25.5840 0.980380
\(682\) −27.0733 −1.03669
\(683\) −7.40119 −0.283198 −0.141599 0.989924i \(-0.545224\pi\)
−0.141599 + 0.989924i \(0.545224\pi\)
\(684\) 1.62317 0.0620636
\(685\) 0 0
\(686\) 16.0233 0.611774
\(687\) 28.8181 1.09948
\(688\) −28.3610 −1.08125
\(689\) 28.9523 1.10300
\(690\) 0 0
\(691\) 30.0653 1.14374 0.571869 0.820345i \(-0.306219\pi\)
0.571869 + 0.820345i \(0.306219\pi\)
\(692\) −8.66242 −0.329296
\(693\) 15.8579 0.602392
\(694\) 35.3533 1.34199
\(695\) 0 0
\(696\) 16.7297 0.634139
\(697\) 6.20729 0.235118
\(698\) 5.70276 0.215853
\(699\) 7.58573 0.286918
\(700\) 0 0
\(701\) −3.69687 −0.139629 −0.0698144 0.997560i \(-0.522241\pi\)
−0.0698144 + 0.997560i \(0.522241\pi\)
\(702\) 5.37729 0.202953
\(703\) −3.77179 −0.142256
\(704\) −32.9968 −1.24361
\(705\) 0 0
\(706\) 28.2212 1.06212
\(707\) 24.5982 0.925111
\(708\) 1.71373 0.0644060
\(709\) −27.5176 −1.03345 −0.516723 0.856153i \(-0.672848\pi\)
−0.516723 + 0.856153i \(0.672848\pi\)
\(710\) 0 0
\(711\) 5.30405 0.198917
\(712\) −3.80109 −0.142452
\(713\) −15.7369 −0.589351
\(714\) −5.96642 −0.223288
\(715\) 0 0
\(716\) 3.75721 0.140414
\(717\) 6.26770 0.234072
\(718\) 9.66898 0.360843
\(719\) −25.3414 −0.945074 −0.472537 0.881311i \(-0.656662\pi\)
−0.472537 + 0.881311i \(0.656662\pi\)
\(720\) 0 0
\(721\) 15.4018 0.573593
\(722\) 14.6839 0.546477
\(723\) −3.08604 −0.114771
\(724\) −11.7298 −0.435934
\(725\) 0 0
\(726\) 4.11665 0.152783
\(727\) 35.6248 1.32125 0.660625 0.750716i \(-0.270291\pi\)
0.660625 + 0.750716i \(0.270291\pi\)
\(728\) −59.0886 −2.18997
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.1388 0.559928
\(732\) 8.20541 0.303281
\(733\) −26.4007 −0.975131 −0.487565 0.873086i \(-0.662115\pi\)
−0.487565 + 0.873086i \(0.662115\pi\)
\(734\) −12.9184 −0.476827
\(735\) 0 0
\(736\) −8.96337 −0.330394
\(737\) −43.1933 −1.59104
\(738\) −5.87921 −0.216417
\(739\) −2.48916 −0.0915652 −0.0457826 0.998951i \(-0.514578\pi\)
−0.0457826 + 0.998951i \(0.514578\pi\)
\(740\) 0 0
\(741\) 11.6730 0.428818
\(742\) 30.4265 1.11699
\(743\) −44.8468 −1.64527 −0.822634 0.568571i \(-0.807496\pi\)
−0.822634 + 0.568571i \(0.807496\pi\)
\(744\) 18.7601 0.687779
\(745\) 0 0
\(746\) 1.66943 0.0611221
\(747\) −5.94379 −0.217472
\(748\) 3.00948 0.110037
\(749\) −77.5258 −2.83273
\(750\) 0 0
\(751\) −38.4960 −1.40474 −0.702370 0.711812i \(-0.747875\pi\)
−0.702370 + 0.711812i \(0.747875\pi\)
\(752\) −2.30535 −0.0840676
\(753\) 28.3257 1.03224
\(754\) 29.2194 1.06411
\(755\) 0 0
\(756\) −2.66873 −0.0970609
\(757\) −1.70387 −0.0619284 −0.0309642 0.999520i \(-0.509858\pi\)
−0.0309642 + 0.999520i \(0.509858\pi\)
\(758\) 14.1985 0.515714
\(759\) 9.84524 0.357360
\(760\) 0 0
\(761\) −17.2211 −0.624263 −0.312132 0.950039i \(-0.601043\pi\)
−0.312132 + 0.950039i \(0.601043\pi\)
\(762\) −13.5775 −0.491861
\(763\) 49.3320 1.78594
\(764\) 3.48136 0.125951
\(765\) 0 0
\(766\) −26.1961 −0.946505
\(767\) 12.3243 0.445003
\(768\) 13.6433 0.492310
\(769\) 1.47987 0.0533656 0.0266828 0.999644i \(-0.491506\pi\)
0.0266828 + 0.999644i \(0.491506\pi\)
\(770\) 0 0
\(771\) −31.1489 −1.12180
\(772\) 11.4007 0.410322
\(773\) 33.0531 1.18884 0.594418 0.804156i \(-0.297383\pi\)
0.594418 + 0.804156i \(0.297383\pi\)
\(774\) −14.3386 −0.515392
\(775\) 0 0
\(776\) −44.7705 −1.60717
\(777\) 6.20138 0.222473
\(778\) −9.21779 −0.330474
\(779\) −12.7626 −0.457266
\(780\) 0 0
\(781\) 13.3194 0.476606
\(782\) −3.70420 −0.132462
\(783\) 5.43386 0.194190
\(784\) −23.7562 −0.848437
\(785\) 0 0
\(786\) −3.46014 −0.123419
\(787\) −2.79404 −0.0995968 −0.0497984 0.998759i \(-0.515858\pi\)
−0.0497984 + 0.998759i \(0.515858\pi\)
\(788\) −1.54979 −0.0552089
\(789\) −20.2925 −0.722431
\(790\) 0 0
\(791\) −50.7776 −1.80544
\(792\) −11.7366 −0.417043
\(793\) 59.0089 2.09547
\(794\) 26.4039 0.937041
\(795\) 0 0
\(796\) 4.94885 0.175407
\(797\) −31.7140 −1.12337 −0.561684 0.827352i \(-0.689846\pi\)
−0.561684 + 0.827352i \(0.689846\pi\)
\(798\) 12.2673 0.434259
\(799\) 1.23057 0.0435345
\(800\) 0 0
\(801\) −1.23460 −0.0436226
\(802\) −38.9708 −1.37611
\(803\) 54.4358 1.92100
\(804\) 7.26901 0.256358
\(805\) 0 0
\(806\) 32.7656 1.15412
\(807\) 12.3091 0.433300
\(808\) −18.2054 −0.640465
\(809\) 12.9229 0.454344 0.227172 0.973855i \(-0.427052\pi\)
0.227172 + 0.973855i \(0.427052\pi\)
\(810\) 0 0
\(811\) −20.0140 −0.702786 −0.351393 0.936228i \(-0.614292\pi\)
−0.351393 + 0.936228i \(0.614292\pi\)
\(812\) −14.5015 −0.508904
\(813\) −4.15010 −0.145550
\(814\) 6.62356 0.232156
\(815\) 0 0
\(816\) 2.83690 0.0993115
\(817\) −31.1263 −1.08897
\(818\) −16.7223 −0.584680
\(819\) −19.1921 −0.670627
\(820\) 0 0
\(821\) −35.9297 −1.25396 −0.626978 0.779037i \(-0.715708\pi\)
−0.626978 + 0.779037i \(0.715708\pi\)
\(822\) 10.4679 0.365109
\(823\) −19.8583 −0.692217 −0.346108 0.938195i \(-0.612497\pi\)
−0.346108 + 0.938195i \(0.612497\pi\)
\(824\) −11.3991 −0.397105
\(825\) 0 0
\(826\) 12.9517 0.450649
\(827\) 15.4529 0.537350 0.268675 0.963231i \(-0.413414\pi\)
0.268675 + 0.963231i \(0.413414\pi\)
\(828\) −1.65686 −0.0575799
\(829\) −18.2545 −0.634004 −0.317002 0.948425i \(-0.602676\pi\)
−0.317002 + 0.948425i \(0.602676\pi\)
\(830\) 0 0
\(831\) 26.8137 0.930159
\(832\) 39.9345 1.38448
\(833\) 12.6808 0.439364
\(834\) −17.9042 −0.619970
\(835\) 0 0
\(836\) −6.18767 −0.214005
\(837\) 6.09333 0.210616
\(838\) 9.39308 0.324479
\(839\) 42.3886 1.46342 0.731709 0.681617i \(-0.238723\pi\)
0.731709 + 0.681617i \(0.238723\pi\)
\(840\) 0 0
\(841\) 0.526840 0.0181669
\(842\) −0.475535 −0.0163880
\(843\) 6.98903 0.240715
\(844\) −0.780437 −0.0268638
\(845\) 0 0
\(846\) −1.16553 −0.0400718
\(847\) −14.6928 −0.504850
\(848\) −14.4671 −0.496803
\(849\) −20.1757 −0.692427
\(850\) 0 0
\(851\) 3.85007 0.131979
\(852\) −2.24153 −0.0767936
\(853\) −24.4161 −0.835993 −0.417997 0.908449i \(-0.637268\pi\)
−0.417997 + 0.908449i \(0.637268\pi\)
\(854\) 62.0134 2.12205
\(855\) 0 0
\(856\) 57.3777 1.96113
\(857\) −29.3860 −1.00381 −0.501904 0.864923i \(-0.667367\pi\)
−0.501904 + 0.864923i \(0.667367\pi\)
\(858\) −20.4987 −0.699814
\(859\) 15.1898 0.518268 0.259134 0.965841i \(-0.416563\pi\)
0.259134 + 0.965841i \(0.416563\pi\)
\(860\) 0 0
\(861\) 20.9835 0.715117
\(862\) 13.7053 0.466803
\(863\) 23.3323 0.794240 0.397120 0.917767i \(-0.370010\pi\)
0.397120 + 0.917767i \(0.370010\pi\)
\(864\) 3.47062 0.118073
\(865\) 0 0
\(866\) 4.95835 0.168492
\(867\) 15.4857 0.525922
\(868\) −16.2615 −0.551951
\(869\) −20.2195 −0.685900
\(870\) 0 0
\(871\) 52.2749 1.77127
\(872\) −36.5112 −1.23643
\(873\) −14.5416 −0.492158
\(874\) 7.61606 0.257617
\(875\) 0 0
\(876\) −9.16102 −0.309522
\(877\) 29.0676 0.981543 0.490771 0.871288i \(-0.336715\pi\)
0.490771 + 0.871288i \(0.336715\pi\)
\(878\) 5.56078 0.187667
\(879\) −2.10609 −0.0710367
\(880\) 0 0
\(881\) −1.61823 −0.0545196 −0.0272598 0.999628i \(-0.508678\pi\)
−0.0272598 + 0.999628i \(0.508678\pi\)
\(882\) −12.0106 −0.404417
\(883\) 13.6728 0.460125 0.230063 0.973176i \(-0.426107\pi\)
0.230063 + 0.973176i \(0.426107\pi\)
\(884\) −3.64224 −0.122502
\(885\) 0 0
\(886\) −7.92837 −0.266359
\(887\) −5.09087 −0.170935 −0.0854673 0.996341i \(-0.527238\pi\)
−0.0854673 + 0.996341i \(0.527238\pi\)
\(888\) −4.58971 −0.154021
\(889\) 48.4596 1.62528
\(890\) 0 0
\(891\) −3.81209 −0.127710
\(892\) 18.0262 0.603562
\(893\) −2.53013 −0.0846676
\(894\) 12.4209 0.415418
\(895\) 0 0
\(896\) 13.0928 0.437401
\(897\) −11.9153 −0.397839
\(898\) 1.82059 0.0607538
\(899\) 33.1103 1.10429
\(900\) 0 0
\(901\) 7.72238 0.257270
\(902\) 22.4121 0.746240
\(903\) 51.1762 1.70304
\(904\) 37.5811 1.24993
\(905\) 0 0
\(906\) 5.96587 0.198203
\(907\) −18.3464 −0.609181 −0.304591 0.952483i \(-0.598520\pi\)
−0.304591 + 0.952483i \(0.598520\pi\)
\(908\) 16.4131 0.544687
\(909\) −5.91317 −0.196127
\(910\) 0 0
\(911\) −27.6570 −0.916316 −0.458158 0.888871i \(-0.651491\pi\)
−0.458158 + 0.888871i \(0.651491\pi\)
\(912\) −5.83285 −0.193145
\(913\) 22.6582 0.749878
\(914\) 4.70366 0.155583
\(915\) 0 0
\(916\) 18.4879 0.610857
\(917\) 12.3496 0.407820
\(918\) 1.43427 0.0473379
\(919\) 7.19193 0.237240 0.118620 0.992940i \(-0.462153\pi\)
0.118620 + 0.992940i \(0.462153\pi\)
\(920\) 0 0
\(921\) 17.1013 0.563505
\(922\) −21.9111 −0.721603
\(923\) −16.1199 −0.530593
\(924\) 10.1734 0.334682
\(925\) 0 0
\(926\) 41.3243 1.35800
\(927\) −3.70244 −0.121604
\(928\) 18.8589 0.619073
\(929\) −26.7260 −0.876852 −0.438426 0.898767i \(-0.644464\pi\)
−0.438426 + 0.898767i \(0.644464\pi\)
\(930\) 0 0
\(931\) −26.0725 −0.854492
\(932\) 4.86653 0.159408
\(933\) −30.7032 −1.00518
\(934\) 48.5299 1.58795
\(935\) 0 0
\(936\) 14.2043 0.464282
\(937\) 27.4610 0.897112 0.448556 0.893755i \(-0.351939\pi\)
0.448556 + 0.893755i \(0.351939\pi\)
\(938\) 54.9364 1.79374
\(939\) 1.89191 0.0617402
\(940\) 0 0
\(941\) −44.1964 −1.44076 −0.720381 0.693579i \(-0.756033\pi\)
−0.720381 + 0.693579i \(0.756033\pi\)
\(942\) 13.4244 0.437389
\(943\) 13.0274 0.424232
\(944\) −6.15827 −0.200435
\(945\) 0 0
\(946\) 54.6602 1.77715
\(947\) 42.5524 1.38277 0.691384 0.722487i \(-0.257001\pi\)
0.691384 + 0.722487i \(0.257001\pi\)
\(948\) 3.40275 0.110516
\(949\) −65.8812 −2.13859
\(950\) 0 0
\(951\) −18.9576 −0.614742
\(952\) −15.7605 −0.510802
\(953\) 35.9045 1.16306 0.581530 0.813525i \(-0.302454\pi\)
0.581530 + 0.813525i \(0.302454\pi\)
\(954\) −7.31422 −0.236807
\(955\) 0 0
\(956\) 4.02097 0.130047
\(957\) −20.7143 −0.669600
\(958\) 27.0696 0.874578
\(959\) −37.3609 −1.20645
\(960\) 0 0
\(961\) 6.12868 0.197699
\(962\) −8.01620 −0.258453
\(963\) 18.6364 0.600550
\(964\) −1.97981 −0.0637655
\(965\) 0 0
\(966\) −12.5219 −0.402886
\(967\) 38.1824 1.22786 0.613932 0.789359i \(-0.289587\pi\)
0.613932 + 0.789359i \(0.289587\pi\)
\(968\) 10.8743 0.349513
\(969\) 3.11351 0.100020
\(970\) 0 0
\(971\) 26.5718 0.852731 0.426365 0.904551i \(-0.359794\pi\)
0.426365 + 0.904551i \(0.359794\pi\)
\(972\) 0.641537 0.0205773
\(973\) 63.9018 2.04860
\(974\) −4.96051 −0.158945
\(975\) 0 0
\(976\) −29.4860 −0.943824
\(977\) −41.8510 −1.33893 −0.669466 0.742843i \(-0.733477\pi\)
−0.669466 + 0.742843i \(0.733477\pi\)
\(978\) −7.82422 −0.250191
\(979\) 4.70641 0.150418
\(980\) 0 0
\(981\) −11.8589 −0.378627
\(982\) −34.1478 −1.08970
\(983\) −23.7688 −0.758108 −0.379054 0.925375i \(-0.623751\pi\)
−0.379054 + 0.925375i \(0.623751\pi\)
\(984\) −15.5302 −0.495083
\(985\) 0 0
\(986\) 7.79362 0.248199
\(987\) 4.15990 0.132411
\(988\) 7.48866 0.238246
\(989\) 31.7723 1.01030
\(990\) 0 0
\(991\) 29.2351 0.928685 0.464342 0.885656i \(-0.346291\pi\)
0.464342 + 0.885656i \(0.346291\pi\)
\(992\) 21.1477 0.671439
\(993\) 34.7036 1.10129
\(994\) −16.9406 −0.537325
\(995\) 0 0
\(996\) −3.81316 −0.120825
\(997\) 6.57182 0.208132 0.104066 0.994570i \(-0.466815\pi\)
0.104066 + 0.994570i \(0.466815\pi\)
\(998\) −33.0996 −1.04775
\(999\) −1.49075 −0.0471653
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 3525.2.a.bg.1.3 10
5.2 odd 4 705.2.c.b.424.7 20
5.3 odd 4 705.2.c.b.424.14 yes 20
5.4 even 2 3525.2.a.bf.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
705.2.c.b.424.7 20 5.2 odd 4
705.2.c.b.424.14 yes 20 5.3 odd 4
3525.2.a.bf.1.8 10 5.4 even 2
3525.2.a.bg.1.3 10 1.1 even 1 trivial