Properties

Label 6025.2.a.n.1.10
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $40$
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] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.43348 q^{2} +2.46422 q^{3} +0.0548683 q^{4} -3.53241 q^{6} +5.17959 q^{7} +2.78831 q^{8} +3.07238 q^{9} +O(q^{10})\) \(q-1.43348 q^{2} +2.46422 q^{3} +0.0548683 q^{4} -3.53241 q^{6} +5.17959 q^{7} +2.78831 q^{8} +3.07238 q^{9} +2.79186 q^{11} +0.135207 q^{12} -1.04374 q^{13} -7.42485 q^{14} -4.10673 q^{16} -1.22801 q^{17} -4.40419 q^{18} -0.657935 q^{19} +12.7637 q^{21} -4.00208 q^{22} -5.23420 q^{23} +6.87101 q^{24} +1.49618 q^{26} +0.178351 q^{27} +0.284195 q^{28} +2.90874 q^{29} -0.0888286 q^{31} +0.310295 q^{32} +6.87975 q^{33} +1.76033 q^{34} +0.168576 q^{36} +8.62366 q^{37} +0.943138 q^{38} -2.57200 q^{39} +0.475889 q^{41} -18.2965 q^{42} -9.62961 q^{43} +0.153184 q^{44} +7.50313 q^{46} +11.2840 q^{47} -10.1199 q^{48} +19.8282 q^{49} -3.02608 q^{51} -0.0572681 q^{52} -4.33694 q^{53} -0.255663 q^{54} +14.4423 q^{56} -1.62130 q^{57} -4.16963 q^{58} +6.20571 q^{59} -2.05916 q^{61} +0.127334 q^{62} +15.9137 q^{63} +7.76865 q^{64} -9.86199 q^{66} +9.29073 q^{67} -0.0673787 q^{68} -12.8982 q^{69} +1.61695 q^{71} +8.56674 q^{72} -15.5909 q^{73} -12.3619 q^{74} -0.0360998 q^{76} +14.4607 q^{77} +3.68691 q^{78} -0.552668 q^{79} -8.77763 q^{81} -0.682178 q^{82} +2.67927 q^{83} +0.700320 q^{84} +13.8039 q^{86} +7.16778 q^{87} +7.78457 q^{88} +13.0002 q^{89} -5.40614 q^{91} -0.287192 q^{92} -0.218893 q^{93} -16.1754 q^{94} +0.764635 q^{96} +7.94354 q^{97} -28.4233 q^{98} +8.57764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.43348 −1.01362 −0.506812 0.862057i \(-0.669176\pi\)
−0.506812 + 0.862057i \(0.669176\pi\)
\(3\) 2.46422 1.42272 0.711359 0.702829i \(-0.248080\pi\)
0.711359 + 0.702829i \(0.248080\pi\)
\(4\) 0.0548683 0.0274341
\(5\) 0 0
\(6\) −3.53241 −1.44210
\(7\) 5.17959 1.95770 0.978851 0.204574i \(-0.0655807\pi\)
0.978851 + 0.204574i \(0.0655807\pi\)
\(8\) 2.78831 0.985816
\(9\) 3.07238 1.02413
\(10\) 0 0
\(11\) 2.79186 0.841777 0.420889 0.907112i \(-0.361718\pi\)
0.420889 + 0.907112i \(0.361718\pi\)
\(12\) 0.135207 0.0390310
\(13\) −1.04374 −0.289481 −0.144741 0.989470i \(-0.546235\pi\)
−0.144741 + 0.989470i \(0.546235\pi\)
\(14\) −7.42485 −1.98437
\(15\) 0 0
\(16\) −4.10673 −1.02668
\(17\) −1.22801 −0.297836 −0.148918 0.988850i \(-0.547579\pi\)
−0.148918 + 0.988850i \(0.547579\pi\)
\(18\) −4.40419 −1.03808
\(19\) −0.657935 −0.150941 −0.0754704 0.997148i \(-0.524046\pi\)
−0.0754704 + 0.997148i \(0.524046\pi\)
\(20\) 0 0
\(21\) 12.7637 2.78526
\(22\) −4.00208 −0.853246
\(23\) −5.23420 −1.09141 −0.545703 0.837978i \(-0.683737\pi\)
−0.545703 + 0.837978i \(0.683737\pi\)
\(24\) 6.87101 1.40254
\(25\) 0 0
\(26\) 1.49618 0.293425
\(27\) 0.178351 0.0343237
\(28\) 0.284195 0.0537079
\(29\) 2.90874 0.540140 0.270070 0.962841i \(-0.412953\pi\)
0.270070 + 0.962841i \(0.412953\pi\)
\(30\) 0 0
\(31\) −0.0888286 −0.0159541 −0.00797705 0.999968i \(-0.502539\pi\)
−0.00797705 + 0.999968i \(0.502539\pi\)
\(32\) 0.310295 0.0548529
\(33\) 6.87975 1.19761
\(34\) 1.76033 0.301894
\(35\) 0 0
\(36\) 0.168576 0.0280960
\(37\) 8.62366 1.41772 0.708861 0.705348i \(-0.249209\pi\)
0.708861 + 0.705348i \(0.249209\pi\)
\(38\) 0.943138 0.152997
\(39\) −2.57200 −0.411850
\(40\) 0 0
\(41\) 0.475889 0.0743214 0.0371607 0.999309i \(-0.488169\pi\)
0.0371607 + 0.999309i \(0.488169\pi\)
\(42\) −18.2965 −2.82320
\(43\) −9.62961 −1.46850 −0.734251 0.678878i \(-0.762466\pi\)
−0.734251 + 0.678878i \(0.762466\pi\)
\(44\) 0.153184 0.0230934
\(45\) 0 0
\(46\) 7.50313 1.10628
\(47\) 11.2840 1.64594 0.822969 0.568087i \(-0.192316\pi\)
0.822969 + 0.568087i \(0.192316\pi\)
\(48\) −10.1199 −1.46068
\(49\) 19.8282 2.83260
\(50\) 0 0
\(51\) −3.02608 −0.423736
\(52\) −0.0572681 −0.00794166
\(53\) −4.33694 −0.595725 −0.297862 0.954609i \(-0.596274\pi\)
−0.297862 + 0.954609i \(0.596274\pi\)
\(54\) −0.255663 −0.0347913
\(55\) 0 0
\(56\) 14.4423 1.92994
\(57\) −1.62130 −0.214746
\(58\) −4.16963 −0.547499
\(59\) 6.20571 0.807915 0.403957 0.914778i \(-0.367634\pi\)
0.403957 + 0.914778i \(0.367634\pi\)
\(60\) 0 0
\(61\) −2.05916 −0.263648 −0.131824 0.991273i \(-0.542083\pi\)
−0.131824 + 0.991273i \(0.542083\pi\)
\(62\) 0.127334 0.0161715
\(63\) 15.9137 2.00493
\(64\) 7.76865 0.971081
\(65\) 0 0
\(66\) −9.86199 −1.21393
\(67\) 9.29073 1.13504 0.567522 0.823358i \(-0.307902\pi\)
0.567522 + 0.823358i \(0.307902\pi\)
\(68\) −0.0673787 −0.00817087
\(69\) −12.8982 −1.55276
\(70\) 0 0
\(71\) 1.61695 0.191897 0.0959485 0.995386i \(-0.469412\pi\)
0.0959485 + 0.995386i \(0.469412\pi\)
\(72\) 8.56674 1.00960
\(73\) −15.5909 −1.82478 −0.912389 0.409324i \(-0.865765\pi\)
−0.912389 + 0.409324i \(0.865765\pi\)
\(74\) −12.3619 −1.43704
\(75\) 0 0
\(76\) −0.0360998 −0.00414093
\(77\) 14.4607 1.64795
\(78\) 3.68691 0.417461
\(79\) −0.552668 −0.0621800 −0.0310900 0.999517i \(-0.509898\pi\)
−0.0310900 + 0.999517i \(0.509898\pi\)
\(80\) 0 0
\(81\) −8.77763 −0.975293
\(82\) −0.682178 −0.0753340
\(83\) 2.67927 0.294088 0.147044 0.989130i \(-0.453024\pi\)
0.147044 + 0.989130i \(0.453024\pi\)
\(84\) 0.700320 0.0764111
\(85\) 0 0
\(86\) 13.8039 1.48851
\(87\) 7.16778 0.768467
\(88\) 7.78457 0.829838
\(89\) 13.0002 1.37802 0.689011 0.724750i \(-0.258045\pi\)
0.689011 + 0.724750i \(0.258045\pi\)
\(90\) 0 0
\(91\) −5.40614 −0.566718
\(92\) −0.287192 −0.0299418
\(93\) −0.218893 −0.0226982
\(94\) −16.1754 −1.66836
\(95\) 0 0
\(96\) 0.764635 0.0780402
\(97\) 7.94354 0.806545 0.403272 0.915080i \(-0.367873\pi\)
0.403272 + 0.915080i \(0.367873\pi\)
\(98\) −28.4233 −2.87119
\(99\) 8.57764 0.862085
\(100\) 0 0
\(101\) 10.2339 1.01831 0.509155 0.860675i \(-0.329958\pi\)
0.509155 + 0.860675i \(0.329958\pi\)
\(102\) 4.33783 0.429509
\(103\) 15.7121 1.54816 0.774078 0.633091i \(-0.218214\pi\)
0.774078 + 0.633091i \(0.218214\pi\)
\(104\) −2.91027 −0.285375
\(105\) 0 0
\(106\) 6.21693 0.603841
\(107\) 19.3889 1.87439 0.937196 0.348803i \(-0.113412\pi\)
0.937196 + 0.348803i \(0.113412\pi\)
\(108\) 0.00978582 0.000941641 0
\(109\) 6.76288 0.647767 0.323883 0.946097i \(-0.395011\pi\)
0.323883 + 0.946097i \(0.395011\pi\)
\(110\) 0 0
\(111\) 21.2506 2.01702
\(112\) −21.2712 −2.00994
\(113\) 9.10124 0.856173 0.428086 0.903738i \(-0.359188\pi\)
0.428086 + 0.903738i \(0.359188\pi\)
\(114\) 2.32410 0.217672
\(115\) 0 0
\(116\) 0.159598 0.0148183
\(117\) −3.20676 −0.296465
\(118\) −8.89577 −0.818922
\(119\) −6.36059 −0.583074
\(120\) 0 0
\(121\) −3.20553 −0.291411
\(122\) 2.95176 0.267240
\(123\) 1.17270 0.105738
\(124\) −0.00487387 −0.000437687 0
\(125\) 0 0
\(126\) −22.8119 −2.03225
\(127\) −0.727223 −0.0645306 −0.0322653 0.999479i \(-0.510272\pi\)
−0.0322653 + 0.999479i \(0.510272\pi\)
\(128\) −11.7568 −1.03916
\(129\) −23.7295 −2.08926
\(130\) 0 0
\(131\) −0.525880 −0.0459464 −0.0229732 0.999736i \(-0.507313\pi\)
−0.0229732 + 0.999736i \(0.507313\pi\)
\(132\) 0.377480 0.0328554
\(133\) −3.40784 −0.295497
\(134\) −13.3181 −1.15051
\(135\) 0 0
\(136\) −3.42407 −0.293612
\(137\) −6.88081 −0.587868 −0.293934 0.955826i \(-0.594965\pi\)
−0.293934 + 0.955826i \(0.594965\pi\)
\(138\) 18.4894 1.57392
\(139\) 2.59618 0.220205 0.110103 0.993920i \(-0.464882\pi\)
0.110103 + 0.993920i \(0.464882\pi\)
\(140\) 0 0
\(141\) 27.8062 2.34170
\(142\) −2.31787 −0.194512
\(143\) −2.91397 −0.243678
\(144\) −12.6174 −1.05145
\(145\) 0 0
\(146\) 22.3493 1.84964
\(147\) 48.8610 4.02999
\(148\) 0.473166 0.0388940
\(149\) −17.9601 −1.47135 −0.735675 0.677335i \(-0.763135\pi\)
−0.735675 + 0.677335i \(0.763135\pi\)
\(150\) 0 0
\(151\) −21.0714 −1.71476 −0.857382 0.514681i \(-0.827910\pi\)
−0.857382 + 0.514681i \(0.827910\pi\)
\(152\) −1.83453 −0.148800
\(153\) −3.77291 −0.305021
\(154\) −20.7291 −1.67040
\(155\) 0 0
\(156\) −0.141121 −0.0112987
\(157\) −10.0807 −0.804529 −0.402265 0.915523i \(-0.631777\pi\)
−0.402265 + 0.915523i \(0.631777\pi\)
\(158\) 0.792239 0.0630272
\(159\) −10.6872 −0.847548
\(160\) 0 0
\(161\) −27.1110 −2.13665
\(162\) 12.5826 0.988580
\(163\) 15.6749 1.22776 0.613878 0.789401i \(-0.289609\pi\)
0.613878 + 0.789401i \(0.289609\pi\)
\(164\) 0.0261112 0.00203894
\(165\) 0 0
\(166\) −3.84068 −0.298095
\(167\) −2.23696 −0.173101 −0.0865505 0.996247i \(-0.527584\pi\)
−0.0865505 + 0.996247i \(0.527584\pi\)
\(168\) 35.5890 2.74575
\(169\) −11.9106 −0.916201
\(170\) 0 0
\(171\) −2.02143 −0.154582
\(172\) −0.528360 −0.0402871
\(173\) 10.8730 0.826658 0.413329 0.910582i \(-0.364366\pi\)
0.413329 + 0.910582i \(0.364366\pi\)
\(174\) −10.2749 −0.778936
\(175\) 0 0
\(176\) −11.4654 −0.864237
\(177\) 15.2922 1.14943
\(178\) −18.6356 −1.39680
\(179\) 4.70527 0.351688 0.175844 0.984418i \(-0.443735\pi\)
0.175844 + 0.984418i \(0.443735\pi\)
\(180\) 0 0
\(181\) −5.72151 −0.425277 −0.212638 0.977131i \(-0.568206\pi\)
−0.212638 + 0.977131i \(0.568206\pi\)
\(182\) 7.74960 0.574439
\(183\) −5.07422 −0.375097
\(184\) −14.5946 −1.07593
\(185\) 0 0
\(186\) 0.313779 0.0230074
\(187\) −3.42843 −0.250711
\(188\) 0.619132 0.0451549
\(189\) 0.923787 0.0671956
\(190\) 0 0
\(191\) 19.5048 1.41132 0.705660 0.708551i \(-0.250651\pi\)
0.705660 + 0.708551i \(0.250651\pi\)
\(192\) 19.1437 1.38157
\(193\) 21.3217 1.53477 0.767384 0.641187i \(-0.221558\pi\)
0.767384 + 0.641187i \(0.221558\pi\)
\(194\) −11.3869 −0.817533
\(195\) 0 0
\(196\) 1.08794 0.0777099
\(197\) −22.8070 −1.62493 −0.812465 0.583010i \(-0.801875\pi\)
−0.812465 + 0.583010i \(0.801875\pi\)
\(198\) −12.2959 −0.873831
\(199\) −18.7857 −1.33168 −0.665840 0.746095i \(-0.731927\pi\)
−0.665840 + 0.746095i \(0.731927\pi\)
\(200\) 0 0
\(201\) 22.8944 1.61485
\(202\) −14.6701 −1.03218
\(203\) 15.0661 1.05743
\(204\) −0.166036 −0.0116248
\(205\) 0 0
\(206\) −22.5229 −1.56925
\(207\) −16.0814 −1.11774
\(208\) 4.28635 0.297205
\(209\) −1.83686 −0.127058
\(210\) 0 0
\(211\) −0.886722 −0.0610445 −0.0305222 0.999534i \(-0.509717\pi\)
−0.0305222 + 0.999534i \(0.509717\pi\)
\(212\) −0.237961 −0.0163432
\(213\) 3.98453 0.273015
\(214\) −27.7936 −1.89993
\(215\) 0 0
\(216\) 0.497298 0.0338369
\(217\) −0.460096 −0.0312334
\(218\) −9.69447 −0.656592
\(219\) −38.4194 −2.59614
\(220\) 0 0
\(221\) 1.28172 0.0862178
\(222\) −30.4623 −2.04450
\(223\) −8.77254 −0.587452 −0.293726 0.955890i \(-0.594895\pi\)
−0.293726 + 0.955890i \(0.594895\pi\)
\(224\) 1.60720 0.107386
\(225\) 0 0
\(226\) −13.0465 −0.867837
\(227\) −1.76117 −0.116893 −0.0584465 0.998291i \(-0.518615\pi\)
−0.0584465 + 0.998291i \(0.518615\pi\)
\(228\) −0.0889578 −0.00589137
\(229\) 1.91528 0.126565 0.0632827 0.997996i \(-0.479843\pi\)
0.0632827 + 0.997996i \(0.479843\pi\)
\(230\) 0 0
\(231\) 35.6343 2.34457
\(232\) 8.11048 0.532479
\(233\) −19.2871 −1.26354 −0.631771 0.775155i \(-0.717672\pi\)
−0.631771 + 0.775155i \(0.717672\pi\)
\(234\) 4.59683 0.300504
\(235\) 0 0
\(236\) 0.340497 0.0221645
\(237\) −1.36189 −0.0884646
\(238\) 9.11778 0.591018
\(239\) −16.0031 −1.03515 −0.517577 0.855636i \(-0.673166\pi\)
−0.517577 + 0.855636i \(0.673166\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 4.59506 0.295382
\(243\) −22.1651 −1.42189
\(244\) −0.112982 −0.00723296
\(245\) 0 0
\(246\) −1.68104 −0.107179
\(247\) 0.686713 0.0436945
\(248\) −0.247682 −0.0157278
\(249\) 6.60231 0.418404
\(250\) 0 0
\(251\) 4.12210 0.260185 0.130092 0.991502i \(-0.458473\pi\)
0.130092 + 0.991502i \(0.458473\pi\)
\(252\) 0.873155 0.0550036
\(253\) −14.6132 −0.918721
\(254\) 1.04246 0.0654098
\(255\) 0 0
\(256\) 1.31586 0.0822410
\(257\) −20.2865 −1.26543 −0.632717 0.774383i \(-0.718060\pi\)
−0.632717 + 0.774383i \(0.718060\pi\)
\(258\) 34.0158 2.11773
\(259\) 44.6671 2.77548
\(260\) 0 0
\(261\) 8.93675 0.553171
\(262\) 0.753839 0.0465723
\(263\) −5.48083 −0.337962 −0.168981 0.985619i \(-0.554048\pi\)
−0.168981 + 0.985619i \(0.554048\pi\)
\(264\) 19.1829 1.18062
\(265\) 0 0
\(266\) 4.88507 0.299523
\(267\) 32.0354 1.96054
\(268\) 0.509766 0.0311389
\(269\) −8.66729 −0.528454 −0.264227 0.964460i \(-0.585117\pi\)
−0.264227 + 0.964460i \(0.585117\pi\)
\(270\) 0 0
\(271\) 6.56471 0.398778 0.199389 0.979920i \(-0.436104\pi\)
0.199389 + 0.979920i \(0.436104\pi\)
\(272\) 5.04310 0.305783
\(273\) −13.3219 −0.806279
\(274\) 9.86352 0.595877
\(275\) 0 0
\(276\) −0.707703 −0.0425987
\(277\) 11.5757 0.695515 0.347758 0.937584i \(-0.386943\pi\)
0.347758 + 0.937584i \(0.386943\pi\)
\(278\) −3.72158 −0.223206
\(279\) −0.272915 −0.0163390
\(280\) 0 0
\(281\) 23.1853 1.38312 0.691560 0.722319i \(-0.256924\pi\)
0.691560 + 0.722319i \(0.256924\pi\)
\(282\) −39.8597 −2.37361
\(283\) −17.3530 −1.03153 −0.515766 0.856730i \(-0.672493\pi\)
−0.515766 + 0.856730i \(0.672493\pi\)
\(284\) 0.0887194 0.00526453
\(285\) 0 0
\(286\) 4.17712 0.246998
\(287\) 2.46491 0.145499
\(288\) 0.953343 0.0561763
\(289\) −15.4920 −0.911294
\(290\) 0 0
\(291\) 19.5746 1.14749
\(292\) −0.855447 −0.0500612
\(293\) 13.0688 0.763487 0.381744 0.924268i \(-0.375324\pi\)
0.381744 + 0.924268i \(0.375324\pi\)
\(294\) −70.0413 −4.08489
\(295\) 0 0
\(296\) 24.0454 1.39761
\(297\) 0.497931 0.0288929
\(298\) 25.7455 1.49140
\(299\) 5.46314 0.315941
\(300\) 0 0
\(301\) −49.8775 −2.87489
\(302\) 30.2054 1.73813
\(303\) 25.2185 1.44877
\(304\) 2.70196 0.154968
\(305\) 0 0
\(306\) 5.40839 0.309177
\(307\) 12.8961 0.736018 0.368009 0.929822i \(-0.380040\pi\)
0.368009 + 0.929822i \(0.380040\pi\)
\(308\) 0.793433 0.0452101
\(309\) 38.7180 2.20259
\(310\) 0 0
\(311\) 21.1630 1.20004 0.600022 0.799983i \(-0.295158\pi\)
0.600022 + 0.799983i \(0.295158\pi\)
\(312\) −7.17154 −0.406008
\(313\) 8.30818 0.469606 0.234803 0.972043i \(-0.424556\pi\)
0.234803 + 0.972043i \(0.424556\pi\)
\(314\) 14.4505 0.815491
\(315\) 0 0
\(316\) −0.0303239 −0.00170585
\(317\) 6.88752 0.386842 0.193421 0.981116i \(-0.438042\pi\)
0.193421 + 0.981116i \(0.438042\pi\)
\(318\) 15.3199 0.859095
\(319\) 8.12080 0.454677
\(320\) 0 0
\(321\) 47.7784 2.66673
\(322\) 38.8632 2.16576
\(323\) 0.807951 0.0449556
\(324\) −0.481614 −0.0267563
\(325\) 0 0
\(326\) −22.4697 −1.24448
\(327\) 16.6652 0.921589
\(328\) 1.32693 0.0732673
\(329\) 58.4464 3.22226
\(330\) 0 0
\(331\) −18.7637 −1.03135 −0.515674 0.856785i \(-0.672459\pi\)
−0.515674 + 0.856785i \(0.672459\pi\)
\(332\) 0.147007 0.00806805
\(333\) 26.4951 1.45192
\(334\) 3.20664 0.175459
\(335\) 0 0
\(336\) −52.4168 −2.85957
\(337\) −1.51865 −0.0827260 −0.0413630 0.999144i \(-0.513170\pi\)
−0.0413630 + 0.999144i \(0.513170\pi\)
\(338\) 17.0736 0.928683
\(339\) 22.4274 1.21809
\(340\) 0 0
\(341\) −0.247997 −0.0134298
\(342\) 2.89768 0.156688
\(343\) 66.4448 3.58768
\(344\) −26.8503 −1.44767
\(345\) 0 0
\(346\) −15.5862 −0.837920
\(347\) 30.3377 1.62861 0.814307 0.580435i \(-0.197117\pi\)
0.814307 + 0.580435i \(0.197117\pi\)
\(348\) 0.393284 0.0210822
\(349\) −12.8971 −0.690363 −0.345182 0.938536i \(-0.612183\pi\)
−0.345182 + 0.938536i \(0.612183\pi\)
\(350\) 0 0
\(351\) −0.186152 −0.00993606
\(352\) 0.866300 0.0461739
\(353\) −14.8812 −0.792046 −0.396023 0.918241i \(-0.629610\pi\)
−0.396023 + 0.918241i \(0.629610\pi\)
\(354\) −21.9211 −1.16510
\(355\) 0 0
\(356\) 0.713301 0.0378049
\(357\) −15.6739 −0.829550
\(358\) −6.74491 −0.356480
\(359\) −6.68516 −0.352829 −0.176415 0.984316i \(-0.556450\pi\)
−0.176415 + 0.984316i \(0.556450\pi\)
\(360\) 0 0
\(361\) −18.5671 −0.977217
\(362\) 8.20168 0.431071
\(363\) −7.89912 −0.414596
\(364\) −0.296626 −0.0155474
\(365\) 0 0
\(366\) 7.27379 0.380207
\(367\) −15.3030 −0.798811 −0.399405 0.916774i \(-0.630783\pi\)
−0.399405 + 0.916774i \(0.630783\pi\)
\(368\) 21.4954 1.12053
\(369\) 1.46211 0.0761144
\(370\) 0 0
\(371\) −22.4636 −1.16625
\(372\) −0.0120103 −0.000622705 0
\(373\) 12.1156 0.627324 0.313662 0.949535i \(-0.398444\pi\)
0.313662 + 0.949535i \(0.398444\pi\)
\(374\) 4.91459 0.254127
\(375\) 0 0
\(376\) 31.4632 1.62259
\(377\) −3.03597 −0.156360
\(378\) −1.32423 −0.0681111
\(379\) −7.60280 −0.390530 −0.195265 0.980751i \(-0.562557\pi\)
−0.195265 + 0.980751i \(0.562557\pi\)
\(380\) 0 0
\(381\) −1.79204 −0.0918088
\(382\) −27.9598 −1.43055
\(383\) −5.69888 −0.291199 −0.145600 0.989344i \(-0.546511\pi\)
−0.145600 + 0.989344i \(0.546511\pi\)
\(384\) −28.9713 −1.47844
\(385\) 0 0
\(386\) −30.5642 −1.55568
\(387\) −29.5858 −1.50393
\(388\) 0.435849 0.0221269
\(389\) 22.6246 1.14711 0.573557 0.819166i \(-0.305563\pi\)
0.573557 + 0.819166i \(0.305563\pi\)
\(390\) 0 0
\(391\) 6.42765 0.325060
\(392\) 55.2871 2.79242
\(393\) −1.29588 −0.0653687
\(394\) 32.6934 1.64707
\(395\) 0 0
\(396\) 0.470640 0.0236506
\(397\) 6.33449 0.317919 0.158959 0.987285i \(-0.449186\pi\)
0.158959 + 0.987285i \(0.449186\pi\)
\(398\) 26.9289 1.34982
\(399\) −8.39766 −0.420409
\(400\) 0 0
\(401\) 10.3255 0.515633 0.257817 0.966194i \(-0.416997\pi\)
0.257817 + 0.966194i \(0.416997\pi\)
\(402\) −32.8187 −1.63685
\(403\) 0.0927139 0.00461841
\(404\) 0.561515 0.0279364
\(405\) 0 0
\(406\) −21.5970 −1.07184
\(407\) 24.0761 1.19341
\(408\) −8.43766 −0.417726
\(409\) 29.2410 1.44587 0.722937 0.690914i \(-0.242792\pi\)
0.722937 + 0.690914i \(0.242792\pi\)
\(410\) 0 0
\(411\) −16.9558 −0.836369
\(412\) 0.862094 0.0424723
\(413\) 32.1431 1.58166
\(414\) 23.0524 1.13297
\(415\) 0 0
\(416\) −0.323867 −0.0158789
\(417\) 6.39757 0.313290
\(418\) 2.63311 0.128790
\(419\) −16.1489 −0.788928 −0.394464 0.918911i \(-0.629070\pi\)
−0.394464 + 0.918911i \(0.629070\pi\)
\(420\) 0 0
\(421\) −3.71549 −0.181082 −0.0905410 0.995893i \(-0.528860\pi\)
−0.0905410 + 0.995893i \(0.528860\pi\)
\(422\) 1.27110 0.0618761
\(423\) 34.6686 1.68565
\(424\) −12.0927 −0.587275
\(425\) 0 0
\(426\) −5.71175 −0.276735
\(427\) −10.6656 −0.516145
\(428\) 1.06383 0.0514223
\(429\) −7.18066 −0.346686
\(430\) 0 0
\(431\) −6.70077 −0.322765 −0.161382 0.986892i \(-0.551595\pi\)
−0.161382 + 0.986892i \(0.551595\pi\)
\(432\) −0.732440 −0.0352395
\(433\) 39.5127 1.89886 0.949428 0.313983i \(-0.101664\pi\)
0.949428 + 0.313983i \(0.101664\pi\)
\(434\) 0.659539 0.0316589
\(435\) 0 0
\(436\) 0.371068 0.0177709
\(437\) 3.44377 0.164738
\(438\) 55.0735 2.63152
\(439\) −30.3954 −1.45069 −0.725346 0.688384i \(-0.758320\pi\)
−0.725346 + 0.688384i \(0.758320\pi\)
\(440\) 0 0
\(441\) 60.9197 2.90094
\(442\) −1.83732 −0.0873925
\(443\) −24.9368 −1.18479 −0.592393 0.805649i \(-0.701817\pi\)
−0.592393 + 0.805649i \(0.701817\pi\)
\(444\) 1.16598 0.0553351
\(445\) 0 0
\(446\) 12.5753 0.595456
\(447\) −44.2577 −2.09332
\(448\) 40.2385 1.90109
\(449\) 16.5391 0.780530 0.390265 0.920703i \(-0.372383\pi\)
0.390265 + 0.920703i \(0.372383\pi\)
\(450\) 0 0
\(451\) 1.32862 0.0625621
\(452\) 0.499369 0.0234884
\(453\) −51.9245 −2.43962
\(454\) 2.52460 0.118486
\(455\) 0 0
\(456\) −4.52068 −0.211700
\(457\) −28.7826 −1.34639 −0.673197 0.739463i \(-0.735080\pi\)
−0.673197 + 0.739463i \(0.735080\pi\)
\(458\) −2.74552 −0.128290
\(459\) −0.219017 −0.0102228
\(460\) 0 0
\(461\) −30.9485 −1.44142 −0.720708 0.693238i \(-0.756183\pi\)
−0.720708 + 0.693238i \(0.756183\pi\)
\(462\) −51.0811 −2.37651
\(463\) −18.7109 −0.869570 −0.434785 0.900534i \(-0.643176\pi\)
−0.434785 + 0.900534i \(0.643176\pi\)
\(464\) −11.9454 −0.554552
\(465\) 0 0
\(466\) 27.6477 1.28076
\(467\) 7.89229 0.365212 0.182606 0.983186i \(-0.441547\pi\)
0.182606 + 0.983186i \(0.441547\pi\)
\(468\) −0.175949 −0.00813326
\(469\) 48.1222 2.22208
\(470\) 0 0
\(471\) −24.8411 −1.14462
\(472\) 17.3034 0.796456
\(473\) −26.8845 −1.23615
\(474\) 1.95225 0.0896698
\(475\) 0 0
\(476\) −0.348994 −0.0159961
\(477\) −13.3247 −0.610097
\(478\) 22.9402 1.04926
\(479\) −26.2048 −1.19733 −0.598665 0.801000i \(-0.704302\pi\)
−0.598665 + 0.801000i \(0.704302\pi\)
\(480\) 0 0
\(481\) −9.00085 −0.410404
\(482\) −1.43348 −0.0652933
\(483\) −66.8075 −3.03985
\(484\) −0.175882 −0.00799462
\(485\) 0 0
\(486\) 31.7732 1.44126
\(487\) −8.82039 −0.399690 −0.199845 0.979827i \(-0.564044\pi\)
−0.199845 + 0.979827i \(0.564044\pi\)
\(488\) −5.74157 −0.259909
\(489\) 38.6265 1.74675
\(490\) 0 0
\(491\) −20.1268 −0.908309 −0.454155 0.890923i \(-0.650059\pi\)
−0.454155 + 0.890923i \(0.650059\pi\)
\(492\) 0.0643438 0.00290084
\(493\) −3.57196 −0.160873
\(494\) −0.984390 −0.0442898
\(495\) 0 0
\(496\) 0.364795 0.0163798
\(497\) 8.37516 0.375677
\(498\) −9.46428 −0.424105
\(499\) −23.4769 −1.05097 −0.525485 0.850803i \(-0.676116\pi\)
−0.525485 + 0.850803i \(0.676116\pi\)
\(500\) 0 0
\(501\) −5.51235 −0.246274
\(502\) −5.90896 −0.263730
\(503\) 22.5386 1.00495 0.502474 0.864592i \(-0.332423\pi\)
0.502474 + 0.864592i \(0.332423\pi\)
\(504\) 44.3722 1.97650
\(505\) 0 0
\(506\) 20.9477 0.931238
\(507\) −29.3504 −1.30349
\(508\) −0.0399015 −0.00177034
\(509\) 3.72385 0.165057 0.0825283 0.996589i \(-0.473701\pi\)
0.0825283 + 0.996589i \(0.473701\pi\)
\(510\) 0 0
\(511\) −80.7546 −3.57237
\(512\) 21.6274 0.955803
\(513\) −0.117344 −0.00518085
\(514\) 29.0803 1.28267
\(515\) 0 0
\(516\) −1.30200 −0.0573172
\(517\) 31.5033 1.38551
\(518\) −64.0294 −2.81329
\(519\) 26.7934 1.17610
\(520\) 0 0
\(521\) 22.2014 0.972659 0.486330 0.873775i \(-0.338335\pi\)
0.486330 + 0.873775i \(0.338335\pi\)
\(522\) −12.8107 −0.560708
\(523\) 0.231478 0.0101218 0.00506091 0.999987i \(-0.498389\pi\)
0.00506091 + 0.999987i \(0.498389\pi\)
\(524\) −0.0288541 −0.00126050
\(525\) 0 0
\(526\) 7.85666 0.342567
\(527\) 0.109082 0.00475170
\(528\) −28.2533 −1.22957
\(529\) 4.39687 0.191168
\(530\) 0 0
\(531\) 19.0663 0.827406
\(532\) −0.186982 −0.00810671
\(533\) −0.496704 −0.0215146
\(534\) −45.9222 −1.98725
\(535\) 0 0
\(536\) 25.9054 1.11894
\(537\) 11.5948 0.500353
\(538\) 12.4244 0.535654
\(539\) 55.3575 2.38442
\(540\) 0 0
\(541\) −13.5420 −0.582215 −0.291107 0.956690i \(-0.594024\pi\)
−0.291107 + 0.956690i \(0.594024\pi\)
\(542\) −9.41038 −0.404211
\(543\) −14.0991 −0.605048
\(544\) −0.381045 −0.0163372
\(545\) 0 0
\(546\) 19.0967 0.817264
\(547\) −18.4978 −0.790909 −0.395455 0.918485i \(-0.629413\pi\)
−0.395455 + 0.918485i \(0.629413\pi\)
\(548\) −0.377538 −0.0161276
\(549\) −6.32651 −0.270009
\(550\) 0 0
\(551\) −1.91377 −0.0815291
\(552\) −35.9642 −1.53074
\(553\) −2.86260 −0.121730
\(554\) −16.5935 −0.704991
\(555\) 0 0
\(556\) 0.142448 0.00604115
\(557\) 21.1410 0.895771 0.447886 0.894091i \(-0.352177\pi\)
0.447886 + 0.894091i \(0.352177\pi\)
\(558\) 0.391219 0.0165616
\(559\) 10.0508 0.425104
\(560\) 0 0
\(561\) −8.44840 −0.356692
\(562\) −33.2357 −1.40196
\(563\) 33.7297 1.42154 0.710769 0.703426i \(-0.248347\pi\)
0.710769 + 0.703426i \(0.248347\pi\)
\(564\) 1.52568 0.0642426
\(565\) 0 0
\(566\) 24.8753 1.04559
\(567\) −45.4646 −1.90933
\(568\) 4.50857 0.189175
\(569\) 11.0670 0.463953 0.231976 0.972721i \(-0.425481\pi\)
0.231976 + 0.972721i \(0.425481\pi\)
\(570\) 0 0
\(571\) 9.61172 0.402238 0.201119 0.979567i \(-0.435542\pi\)
0.201119 + 0.979567i \(0.435542\pi\)
\(572\) −0.159885 −0.00668511
\(573\) 48.0642 2.00791
\(574\) −3.53341 −0.147482
\(575\) 0 0
\(576\) 23.8682 0.994509
\(577\) 11.8334 0.492632 0.246316 0.969190i \(-0.420780\pi\)
0.246316 + 0.969190i \(0.420780\pi\)
\(578\) 22.2075 0.923709
\(579\) 52.5413 2.18354
\(580\) 0 0
\(581\) 13.8775 0.575737
\(582\) −28.0599 −1.16312
\(583\) −12.1081 −0.501468
\(584\) −43.4723 −1.79890
\(585\) 0 0
\(586\) −18.7339 −0.773889
\(587\) −29.0431 −1.19874 −0.599369 0.800473i \(-0.704582\pi\)
−0.599369 + 0.800473i \(0.704582\pi\)
\(588\) 2.68092 0.110559
\(589\) 0.0584435 0.00240812
\(590\) 0 0
\(591\) −56.2014 −2.31182
\(592\) −35.4150 −1.45555
\(593\) −10.5632 −0.433780 −0.216890 0.976196i \(-0.569591\pi\)
−0.216890 + 0.976196i \(0.569591\pi\)
\(594\) −0.713775 −0.0292866
\(595\) 0 0
\(596\) −0.985441 −0.0403652
\(597\) −46.2920 −1.89460
\(598\) −7.83131 −0.320246
\(599\) 42.4874 1.73599 0.867995 0.496573i \(-0.165409\pi\)
0.867995 + 0.496573i \(0.165409\pi\)
\(600\) 0 0
\(601\) −13.6920 −0.558510 −0.279255 0.960217i \(-0.590087\pi\)
−0.279255 + 0.960217i \(0.590087\pi\)
\(602\) 71.4984 2.91406
\(603\) 28.5446 1.16243
\(604\) −1.15615 −0.0470431
\(605\) 0 0
\(606\) −36.1503 −1.46850
\(607\) −29.5482 −1.19932 −0.599662 0.800253i \(-0.704698\pi\)
−0.599662 + 0.800253i \(0.704698\pi\)
\(608\) −0.204154 −0.00827954
\(609\) 37.1262 1.50443
\(610\) 0 0
\(611\) −11.7775 −0.476468
\(612\) −0.207013 −0.00836800
\(613\) −6.84948 −0.276648 −0.138324 0.990387i \(-0.544172\pi\)
−0.138324 + 0.990387i \(0.544172\pi\)
\(614\) −18.4863 −0.746046
\(615\) 0 0
\(616\) 40.3209 1.62458
\(617\) 18.9353 0.762306 0.381153 0.924512i \(-0.375527\pi\)
0.381153 + 0.924512i \(0.375527\pi\)
\(618\) −55.5015 −2.23260
\(619\) 3.23449 0.130005 0.0650026 0.997885i \(-0.479294\pi\)
0.0650026 + 0.997885i \(0.479294\pi\)
\(620\) 0 0
\(621\) −0.933526 −0.0374611
\(622\) −30.3368 −1.21639
\(623\) 67.3360 2.69776
\(624\) 10.5625 0.422839
\(625\) 0 0
\(626\) −11.9096 −0.476004
\(627\) −4.52643 −0.180768
\(628\) −0.553112 −0.0220716
\(629\) −10.5899 −0.422248
\(630\) 0 0
\(631\) −33.4292 −1.33080 −0.665398 0.746488i \(-0.731738\pi\)
−0.665398 + 0.746488i \(0.731738\pi\)
\(632\) −1.54101 −0.0612981
\(633\) −2.18508 −0.0868490
\(634\) −9.87313 −0.392112
\(635\) 0 0
\(636\) −0.586387 −0.0232518
\(637\) −20.6955 −0.819984
\(638\) −11.6410 −0.460872
\(639\) 4.96789 0.196527
\(640\) 0 0
\(641\) 15.4442 0.610010 0.305005 0.952351i \(-0.401342\pi\)
0.305005 + 0.952351i \(0.401342\pi\)
\(642\) −68.4895 −2.70306
\(643\) −14.7173 −0.580394 −0.290197 0.956967i \(-0.593721\pi\)
−0.290197 + 0.956967i \(0.593721\pi\)
\(644\) −1.48754 −0.0586171
\(645\) 0 0
\(646\) −1.15818 −0.0455681
\(647\) 35.6625 1.40204 0.701019 0.713142i \(-0.252729\pi\)
0.701019 + 0.713142i \(0.252729\pi\)
\(648\) −24.4748 −0.961459
\(649\) 17.3255 0.680084
\(650\) 0 0
\(651\) −1.13378 −0.0444363
\(652\) 0.860057 0.0336824
\(653\) −43.0253 −1.68371 −0.841854 0.539705i \(-0.818536\pi\)
−0.841854 + 0.539705i \(0.818536\pi\)
\(654\) −23.8893 −0.934145
\(655\) 0 0
\(656\) −1.95435 −0.0763044
\(657\) −47.9012 −1.86880
\(658\) −83.7818 −3.26616
\(659\) −11.3198 −0.440955 −0.220478 0.975392i \(-0.570762\pi\)
−0.220478 + 0.975392i \(0.570762\pi\)
\(660\) 0 0
\(661\) 41.1612 1.60099 0.800493 0.599342i \(-0.204571\pi\)
0.800493 + 0.599342i \(0.204571\pi\)
\(662\) 26.8975 1.04540
\(663\) 3.15844 0.122664
\(664\) 7.47063 0.289917
\(665\) 0 0
\(666\) −37.9803 −1.47171
\(667\) −15.2249 −0.589512
\(668\) −0.122738 −0.00474888
\(669\) −21.6175 −0.835779
\(670\) 0 0
\(671\) −5.74888 −0.221933
\(672\) 3.96050 0.152780
\(673\) −27.0152 −1.04136 −0.520680 0.853752i \(-0.674322\pi\)
−0.520680 + 0.853752i \(0.674322\pi\)
\(674\) 2.17695 0.0838531
\(675\) 0 0
\(676\) −0.653515 −0.0251352
\(677\) −51.7906 −1.99047 −0.995237 0.0974881i \(-0.968919\pi\)
−0.995237 + 0.0974881i \(0.968919\pi\)
\(678\) −32.1493 −1.23469
\(679\) 41.1443 1.57897
\(680\) 0 0
\(681\) −4.33991 −0.166306
\(682\) 0.355499 0.0136128
\(683\) −21.7709 −0.833039 −0.416520 0.909127i \(-0.636750\pi\)
−0.416520 + 0.909127i \(0.636750\pi\)
\(684\) −0.110912 −0.00424083
\(685\) 0 0
\(686\) −95.2474 −3.63656
\(687\) 4.71967 0.180067
\(688\) 39.5462 1.50768
\(689\) 4.52663 0.172451
\(690\) 0 0
\(691\) −39.9459 −1.51961 −0.759807 0.650148i \(-0.774707\pi\)
−0.759807 + 0.650148i \(0.774707\pi\)
\(692\) 0.596582 0.0226786
\(693\) 44.4287 1.68771
\(694\) −43.4885 −1.65080
\(695\) 0 0
\(696\) 19.9860 0.757567
\(697\) −0.584396 −0.0221356
\(698\) 18.4877 0.699769
\(699\) −47.5277 −1.79766
\(700\) 0 0
\(701\) 10.8929 0.411419 0.205710 0.978613i \(-0.434050\pi\)
0.205710 + 0.978613i \(0.434050\pi\)
\(702\) 0.266846 0.0100714
\(703\) −5.67382 −0.213992
\(704\) 21.6890 0.817434
\(705\) 0 0
\(706\) 21.3319 0.802837
\(707\) 53.0073 1.99355
\(708\) 0.839059 0.0315338
\(709\) −39.0384 −1.46612 −0.733060 0.680164i \(-0.761908\pi\)
−0.733060 + 0.680164i \(0.761908\pi\)
\(710\) 0 0
\(711\) −1.69800 −0.0636801
\(712\) 36.2487 1.35848
\(713\) 0.464947 0.0174124
\(714\) 22.4682 0.840852
\(715\) 0 0
\(716\) 0.258170 0.00964827
\(717\) −39.4352 −1.47273
\(718\) 9.58305 0.357636
\(719\) −51.9115 −1.93597 −0.967986 0.251006i \(-0.919239\pi\)
−0.967986 + 0.251006i \(0.919239\pi\)
\(720\) 0 0
\(721\) 81.3821 3.03083
\(722\) 26.6156 0.990531
\(723\) 2.46422 0.0916453
\(724\) −0.313929 −0.0116671
\(725\) 0 0
\(726\) 11.3232 0.420245
\(727\) 38.9182 1.44340 0.721699 0.692207i \(-0.243362\pi\)
0.721699 + 0.692207i \(0.243362\pi\)
\(728\) −15.0740 −0.558680
\(729\) −28.2867 −1.04765
\(730\) 0 0
\(731\) 11.8252 0.437373
\(732\) −0.278413 −0.0102905
\(733\) 41.2969 1.52534 0.762668 0.646790i \(-0.223889\pi\)
0.762668 + 0.646790i \(0.223889\pi\)
\(734\) 21.9366 0.809694
\(735\) 0 0
\(736\) −1.62415 −0.0598668
\(737\) 25.9384 0.955454
\(738\) −2.09591 −0.0771514
\(739\) −44.7870 −1.64752 −0.823758 0.566941i \(-0.808127\pi\)
−0.823758 + 0.566941i \(0.808127\pi\)
\(740\) 0 0
\(741\) 1.69221 0.0621649
\(742\) 32.2011 1.18214
\(743\) 22.3140 0.818622 0.409311 0.912395i \(-0.365769\pi\)
0.409311 + 0.912395i \(0.365769\pi\)
\(744\) −0.610342 −0.0223762
\(745\) 0 0
\(746\) −17.3675 −0.635871
\(747\) 8.23172 0.301183
\(748\) −0.188112 −0.00687805
\(749\) 100.426 3.66950
\(750\) 0 0
\(751\) −7.54056 −0.275159 −0.137580 0.990491i \(-0.543932\pi\)
−0.137580 + 0.990491i \(0.543932\pi\)
\(752\) −46.3402 −1.68985
\(753\) 10.1578 0.370170
\(754\) 4.35200 0.158491
\(755\) 0 0
\(756\) 0.0506866 0.00184345
\(757\) 36.8147 1.33805 0.669026 0.743239i \(-0.266711\pi\)
0.669026 + 0.743239i \(0.266711\pi\)
\(758\) 10.8985 0.395850
\(759\) −36.0100 −1.30708
\(760\) 0 0
\(761\) 45.4086 1.64606 0.823030 0.567998i \(-0.192282\pi\)
0.823030 + 0.567998i \(0.192282\pi\)
\(762\) 2.56885 0.0930596
\(763\) 35.0290 1.26813
\(764\) 1.07020 0.0387183
\(765\) 0 0
\(766\) 8.16924 0.295166
\(767\) −6.47714 −0.233876
\(768\) 3.24256 0.117006
\(769\) −36.7641 −1.32575 −0.662873 0.748732i \(-0.730663\pi\)
−0.662873 + 0.748732i \(0.730663\pi\)
\(770\) 0 0
\(771\) −49.9903 −1.80036
\(772\) 1.16988 0.0421051
\(773\) −8.78587 −0.316006 −0.158003 0.987439i \(-0.550506\pi\)
−0.158003 + 0.987439i \(0.550506\pi\)
\(774\) 42.4107 1.52442
\(775\) 0 0
\(776\) 22.1491 0.795105
\(777\) 110.069 3.94872
\(778\) −32.4319 −1.16274
\(779\) −0.313104 −0.0112181
\(780\) 0 0
\(781\) 4.51431 0.161535
\(782\) −9.21391 −0.329489
\(783\) 0.518778 0.0185396
\(784\) −81.4289 −2.90818
\(785\) 0 0
\(786\) 1.85762 0.0662593
\(787\) −42.6718 −1.52108 −0.760542 0.649289i \(-0.775067\pi\)
−0.760542 + 0.649289i \(0.775067\pi\)
\(788\) −1.25138 −0.0445785
\(789\) −13.5060 −0.480825
\(790\) 0 0
\(791\) 47.1407 1.67613
\(792\) 23.9171 0.849858
\(793\) 2.14922 0.0763211
\(794\) −9.08037 −0.322250
\(795\) 0 0
\(796\) −1.03074 −0.0365335
\(797\) 45.6410 1.61669 0.808343 0.588711i \(-0.200365\pi\)
0.808343 + 0.588711i \(0.200365\pi\)
\(798\) 12.0379 0.426137
\(799\) −13.8568 −0.490219
\(800\) 0 0
\(801\) 39.9416 1.41127
\(802\) −14.8015 −0.522658
\(803\) −43.5276 −1.53606
\(804\) 1.25618 0.0443019
\(805\) 0 0
\(806\) −0.132904 −0.00468133
\(807\) −21.3581 −0.751841
\(808\) 28.5352 1.00387
\(809\) 16.3698 0.575532 0.287766 0.957701i \(-0.407088\pi\)
0.287766 + 0.957701i \(0.407088\pi\)
\(810\) 0 0
\(811\) 50.1149 1.75977 0.879886 0.475184i \(-0.157619\pi\)
0.879886 + 0.475184i \(0.157619\pi\)
\(812\) 0.826651 0.0290098
\(813\) 16.1769 0.567348
\(814\) −34.5126 −1.20966
\(815\) 0 0
\(816\) 12.4273 0.435042
\(817\) 6.33566 0.221657
\(818\) −41.9164 −1.46557
\(819\) −16.6097 −0.580390
\(820\) 0 0
\(821\) 5.41793 0.189087 0.0945436 0.995521i \(-0.469861\pi\)
0.0945436 + 0.995521i \(0.469861\pi\)
\(822\) 24.3059 0.847764
\(823\) 18.4024 0.641468 0.320734 0.947169i \(-0.396071\pi\)
0.320734 + 0.947169i \(0.396071\pi\)
\(824\) 43.8101 1.52620
\(825\) 0 0
\(826\) −46.0765 −1.60321
\(827\) −33.6753 −1.17101 −0.585503 0.810670i \(-0.699103\pi\)
−0.585503 + 0.810670i \(0.699103\pi\)
\(828\) −0.882361 −0.0306642
\(829\) 10.5634 0.366881 0.183440 0.983031i \(-0.441277\pi\)
0.183440 + 0.983031i \(0.441277\pi\)
\(830\) 0 0
\(831\) 28.5250 0.989522
\(832\) −8.10844 −0.281110
\(833\) −24.3492 −0.843650
\(834\) −9.17079 −0.317559
\(835\) 0 0
\(836\) −0.100785 −0.00348574
\(837\) −0.0158427 −0.000547604 0
\(838\) 23.1492 0.799676
\(839\) 30.4519 1.05132 0.525658 0.850696i \(-0.323819\pi\)
0.525658 + 0.850696i \(0.323819\pi\)
\(840\) 0 0
\(841\) −20.5392 −0.708249
\(842\) 5.32609 0.183549
\(843\) 57.1337 1.96779
\(844\) −0.0486529 −0.00167470
\(845\) 0 0
\(846\) −49.6968 −1.70861
\(847\) −16.6033 −0.570497
\(848\) 17.8106 0.611620
\(849\) −42.7617 −1.46758
\(850\) 0 0
\(851\) −45.1380 −1.54731
\(852\) 0.218624 0.00748994
\(853\) −10.3766 −0.355287 −0.177644 0.984095i \(-0.556847\pi\)
−0.177644 + 0.984095i \(0.556847\pi\)
\(854\) 15.2889 0.523177
\(855\) 0 0
\(856\) 54.0622 1.84781
\(857\) 37.3240 1.27496 0.637482 0.770466i \(-0.279976\pi\)
0.637482 + 0.770466i \(0.279976\pi\)
\(858\) 10.2933 0.351409
\(859\) −23.8640 −0.814231 −0.407115 0.913377i \(-0.633465\pi\)
−0.407115 + 0.913377i \(0.633465\pi\)
\(860\) 0 0
\(861\) 6.07409 0.207004
\(862\) 9.60543 0.327162
\(863\) 38.6590 1.31597 0.657984 0.753032i \(-0.271409\pi\)
0.657984 + 0.753032i \(0.271409\pi\)
\(864\) 0.0553415 0.00188276
\(865\) 0 0
\(866\) −56.6406 −1.92473
\(867\) −38.1757 −1.29651
\(868\) −0.0252447 −0.000856861 0
\(869\) −1.54297 −0.0523417
\(870\) 0 0
\(871\) −9.69710 −0.328574
\(872\) 18.8570 0.638579
\(873\) 24.4056 0.826003
\(874\) −4.93658 −0.166982
\(875\) 0 0
\(876\) −2.10801 −0.0712230
\(877\) −28.9135 −0.976341 −0.488170 0.872748i \(-0.662335\pi\)
−0.488170 + 0.872748i \(0.662335\pi\)
\(878\) 43.5712 1.47046
\(879\) 32.2044 1.08623
\(880\) 0 0
\(881\) 14.1236 0.475835 0.237918 0.971285i \(-0.423535\pi\)
0.237918 + 0.971285i \(0.423535\pi\)
\(882\) −87.3272 −2.94046
\(883\) 18.6110 0.626310 0.313155 0.949702i \(-0.398614\pi\)
0.313155 + 0.949702i \(0.398614\pi\)
\(884\) 0.0703258 0.00236531
\(885\) 0 0
\(886\) 35.7465 1.20093
\(887\) 4.35743 0.146308 0.0731541 0.997321i \(-0.476693\pi\)
0.0731541 + 0.997321i \(0.476693\pi\)
\(888\) 59.2533 1.98841
\(889\) −3.76672 −0.126332
\(890\) 0 0
\(891\) −24.5059 −0.820979
\(892\) −0.481334 −0.0161163
\(893\) −7.42413 −0.248439
\(894\) 63.4425 2.12184
\(895\) 0 0
\(896\) −60.8955 −2.03437
\(897\) 13.4624 0.449496
\(898\) −23.7085 −0.791164
\(899\) −0.258380 −0.00861744
\(900\) 0 0
\(901\) 5.32580 0.177428
\(902\) −1.90455 −0.0634144
\(903\) −122.909 −4.09016
\(904\) 25.3771 0.844029
\(905\) 0 0
\(906\) 74.4327 2.47286
\(907\) 53.9300 1.79072 0.895359 0.445345i \(-0.146919\pi\)
0.895359 + 0.445345i \(0.146919\pi\)
\(908\) −0.0966324 −0.00320686
\(909\) 31.4423 1.04288
\(910\) 0 0
\(911\) 2.92385 0.0968714 0.0484357 0.998826i \(-0.484576\pi\)
0.0484357 + 0.998826i \(0.484576\pi\)
\(912\) 6.65822 0.220476
\(913\) 7.48014 0.247557
\(914\) 41.2594 1.36474
\(915\) 0 0
\(916\) 0.105088 0.00347221
\(917\) −2.72384 −0.0899493
\(918\) 0.313957 0.0103621
\(919\) −51.8138 −1.70918 −0.854590 0.519303i \(-0.826192\pi\)
−0.854590 + 0.519303i \(0.826192\pi\)
\(920\) 0 0
\(921\) 31.7788 1.04715
\(922\) 44.3641 1.46106
\(923\) −1.68768 −0.0555506
\(924\) 1.95519 0.0643211
\(925\) 0 0
\(926\) 26.8217 0.881417
\(927\) 48.2734 1.58551
\(928\) 0.902568 0.0296283
\(929\) −4.04344 −0.132661 −0.0663306 0.997798i \(-0.521129\pi\)
−0.0663306 + 0.997798i \(0.521129\pi\)
\(930\) 0 0
\(931\) −13.0457 −0.427555
\(932\) −1.05825 −0.0346642
\(933\) 52.1503 1.70732
\(934\) −11.3135 −0.370188
\(935\) 0 0
\(936\) −8.94143 −0.292260
\(937\) 30.4753 0.995586 0.497793 0.867296i \(-0.334144\pi\)
0.497793 + 0.867296i \(0.334144\pi\)
\(938\) −68.9823 −2.25235
\(939\) 20.4732 0.668117
\(940\) 0 0
\(941\) −31.1342 −1.01495 −0.507473 0.861668i \(-0.669420\pi\)
−0.507473 + 0.861668i \(0.669420\pi\)
\(942\) 35.6093 1.16021
\(943\) −2.49090 −0.0811149
\(944\) −25.4852 −0.829471
\(945\) 0 0
\(946\) 38.5384 1.25299
\(947\) 6.66732 0.216659 0.108329 0.994115i \(-0.465450\pi\)
0.108329 + 0.994115i \(0.465450\pi\)
\(948\) −0.0747248 −0.00242695
\(949\) 16.2728 0.528239
\(950\) 0 0
\(951\) 16.9724 0.550367
\(952\) −17.7353 −0.574804
\(953\) −48.4890 −1.57071 −0.785356 0.619045i \(-0.787520\pi\)
−0.785356 + 0.619045i \(0.787520\pi\)
\(954\) 19.1007 0.618409
\(955\) 0 0
\(956\) −0.878063 −0.0283986
\(957\) 20.0114 0.646878
\(958\) 37.5641 1.21364
\(959\) −35.6398 −1.15087
\(960\) 0 0
\(961\) −30.9921 −0.999745
\(962\) 12.9026 0.415995
\(963\) 59.5699 1.91961
\(964\) 0.0548683 0.00176719
\(965\) 0 0
\(966\) 95.7674 3.08126
\(967\) 36.4511 1.17219 0.586094 0.810243i \(-0.300665\pi\)
0.586094 + 0.810243i \(0.300665\pi\)
\(968\) −8.93800 −0.287278
\(969\) 1.99097 0.0639591
\(970\) 0 0
\(971\) −6.64815 −0.213349 −0.106675 0.994294i \(-0.534020\pi\)
−0.106675 + 0.994294i \(0.534020\pi\)
\(972\) −1.21616 −0.0390083
\(973\) 13.4472 0.431097
\(974\) 12.6439 0.405136
\(975\) 0 0
\(976\) 8.45640 0.270683
\(977\) −41.3101 −1.32163 −0.660814 0.750550i \(-0.729789\pi\)
−0.660814 + 0.750550i \(0.729789\pi\)
\(978\) −55.3704 −1.77055
\(979\) 36.2948 1.15999
\(980\) 0 0
\(981\) 20.7781 0.663394
\(982\) 28.8514 0.920684
\(983\) 1.36032 0.0433874 0.0216937 0.999765i \(-0.493094\pi\)
0.0216937 + 0.999765i \(0.493094\pi\)
\(984\) 3.26984 0.104239
\(985\) 0 0
\(986\) 5.12034 0.163065
\(987\) 144.025 4.58436
\(988\) 0.0376787 0.00119872
\(989\) 50.4033 1.60273
\(990\) 0 0
\(991\) −48.3616 −1.53626 −0.768128 0.640296i \(-0.778811\pi\)
−0.768128 + 0.640296i \(0.778811\pi\)
\(992\) −0.0275631 −0.000875129 0
\(993\) −46.2380 −1.46732
\(994\) −12.0056 −0.380796
\(995\) 0 0
\(996\) 0.362257 0.0114786
\(997\) 40.6531 1.28750 0.643748 0.765238i \(-0.277379\pi\)
0.643748 + 0.765238i \(0.277379\pi\)
\(998\) 33.6537 1.06529
\(999\) 1.53804 0.0486615
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 6025.2.a.n.1.10 yes 40
5.4 even 2 6025.2.a.m.1.31 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6025.2.a.m.1.31 40 5.4 even 2
6025.2.a.n.1.10 yes 40 1.1 even 1 trivial