Properties

Label 6025.2.a.k.1.15
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $25$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(25\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
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)
 
\(f(q)\) \(=\) \(q+0.954311 q^{2} +0.726487 q^{3} -1.08929 q^{4} +0.693295 q^{6} +1.92977 q^{7} -2.94814 q^{8} -2.47222 q^{9} +O(q^{10})\) \(q+0.954311 q^{2} +0.726487 q^{3} -1.08929 q^{4} +0.693295 q^{6} +1.92977 q^{7} -2.94814 q^{8} -2.47222 q^{9} -2.82880 q^{11} -0.791355 q^{12} +6.44491 q^{13} +1.84160 q^{14} -0.634866 q^{16} +2.15771 q^{17} -2.35926 q^{18} +1.30556 q^{19} +1.40195 q^{21} -2.69956 q^{22} -1.78850 q^{23} -2.14179 q^{24} +6.15045 q^{26} -3.97549 q^{27} -2.10208 q^{28} +3.74238 q^{29} -8.69196 q^{31} +5.29043 q^{32} -2.05509 q^{33} +2.05912 q^{34} +2.69296 q^{36} +5.53981 q^{37} +1.24591 q^{38} +4.68214 q^{39} +2.83107 q^{41} +1.33790 q^{42} -4.52447 q^{43} +3.08139 q^{44} -1.70679 q^{46} +9.40445 q^{47} -0.461222 q^{48} -3.27600 q^{49} +1.56755 q^{51} -7.02038 q^{52} -4.21628 q^{53} -3.79386 q^{54} -5.68923 q^{56} +0.948471 q^{57} +3.57139 q^{58} -10.2699 q^{59} +12.2459 q^{61} -8.29484 q^{62} -4.77080 q^{63} +6.31845 q^{64} -1.96119 q^{66} +11.8281 q^{67} -2.35037 q^{68} -1.29932 q^{69} +9.42721 q^{71} +7.28845 q^{72} -16.8357 q^{73} +5.28670 q^{74} -1.42213 q^{76} -5.45893 q^{77} +4.46822 q^{78} +16.2958 q^{79} +4.52851 q^{81} +2.70172 q^{82} -5.44188 q^{83} -1.52713 q^{84} -4.31775 q^{86} +2.71879 q^{87} +8.33971 q^{88} +6.41711 q^{89} +12.4372 q^{91} +1.94820 q^{92} -6.31460 q^{93} +8.97477 q^{94} +3.84343 q^{96} -3.18370 q^{97} -3.12633 q^{98} +6.99341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.954311 0.674800 0.337400 0.941361i \(-0.390453\pi\)
0.337400 + 0.941361i \(0.390453\pi\)
\(3\) 0.726487 0.419437 0.209719 0.977762i \(-0.432745\pi\)
0.209719 + 0.977762i \(0.432745\pi\)
\(4\) −1.08929 −0.544645
\(5\) 0 0
\(6\) 0.693295 0.283036
\(7\) 1.92977 0.729383 0.364692 0.931128i \(-0.381174\pi\)
0.364692 + 0.931128i \(0.381174\pi\)
\(8\) −2.94814 −1.04233
\(9\) −2.47222 −0.824072
\(10\) 0 0
\(11\) −2.82880 −0.852916 −0.426458 0.904507i \(-0.640239\pi\)
−0.426458 + 0.904507i \(0.640239\pi\)
\(12\) −0.791355 −0.228445
\(13\) 6.44491 1.78750 0.893748 0.448570i \(-0.148066\pi\)
0.893748 + 0.448570i \(0.148066\pi\)
\(14\) 1.84160 0.492188
\(15\) 0 0
\(16\) −0.634866 −0.158717
\(17\) 2.15771 0.523321 0.261660 0.965160i \(-0.415730\pi\)
0.261660 + 0.965160i \(0.415730\pi\)
\(18\) −2.35926 −0.556084
\(19\) 1.30556 0.299516 0.149758 0.988723i \(-0.452151\pi\)
0.149758 + 0.988723i \(0.452151\pi\)
\(20\) 0 0
\(21\) 1.40195 0.305931
\(22\) −2.69956 −0.575547
\(23\) −1.78850 −0.372929 −0.186464 0.982462i \(-0.559703\pi\)
−0.186464 + 0.982462i \(0.559703\pi\)
\(24\) −2.14179 −0.437191
\(25\) 0 0
\(26\) 6.15045 1.20620
\(27\) −3.97549 −0.765084
\(28\) −2.10208 −0.397255
\(29\) 3.74238 0.694943 0.347471 0.937691i \(-0.387040\pi\)
0.347471 + 0.937691i \(0.387040\pi\)
\(30\) 0 0
\(31\) −8.69196 −1.56112 −0.780561 0.625079i \(-0.785067\pi\)
−0.780561 + 0.625079i \(0.785067\pi\)
\(32\) 5.29043 0.935224
\(33\) −2.05509 −0.357745
\(34\) 2.05912 0.353137
\(35\) 0 0
\(36\) 2.69296 0.448827
\(37\) 5.53981 0.910740 0.455370 0.890302i \(-0.349507\pi\)
0.455370 + 0.890302i \(0.349507\pi\)
\(38\) 1.24591 0.202113
\(39\) 4.68214 0.749743
\(40\) 0 0
\(41\) 2.83107 0.442139 0.221069 0.975258i \(-0.429045\pi\)
0.221069 + 0.975258i \(0.429045\pi\)
\(42\) 1.33790 0.206442
\(43\) −4.52447 −0.689975 −0.344987 0.938607i \(-0.612117\pi\)
−0.344987 + 0.938607i \(0.612117\pi\)
\(44\) 3.08139 0.464536
\(45\) 0 0
\(46\) −1.70679 −0.251652
\(47\) 9.40445 1.37178 0.685890 0.727705i \(-0.259413\pi\)
0.685890 + 0.727705i \(0.259413\pi\)
\(48\) −0.461222 −0.0665717
\(49\) −3.27600 −0.468000
\(50\) 0 0
\(51\) 1.56755 0.219500
\(52\) −7.02038 −0.973551
\(53\) −4.21628 −0.579151 −0.289576 0.957155i \(-0.593514\pi\)
−0.289576 + 0.957155i \(0.593514\pi\)
\(54\) −3.79386 −0.516279
\(55\) 0 0
\(56\) −5.68923 −0.760255
\(57\) 0.948471 0.125628
\(58\) 3.57139 0.468947
\(59\) −10.2699 −1.33702 −0.668512 0.743702i \(-0.733068\pi\)
−0.668512 + 0.743702i \(0.733068\pi\)
\(60\) 0 0
\(61\) 12.2459 1.56792 0.783962 0.620808i \(-0.213195\pi\)
0.783962 + 0.620808i \(0.213195\pi\)
\(62\) −8.29484 −1.05345
\(63\) −4.77080 −0.601064
\(64\) 6.31845 0.789806
\(65\) 0 0
\(66\) −1.96119 −0.241406
\(67\) 11.8281 1.44503 0.722514 0.691356i \(-0.242986\pi\)
0.722514 + 0.691356i \(0.242986\pi\)
\(68\) −2.35037 −0.285024
\(69\) −1.29932 −0.156420
\(70\) 0 0
\(71\) 9.42721 1.11880 0.559402 0.828897i \(-0.311031\pi\)
0.559402 + 0.828897i \(0.311031\pi\)
\(72\) 7.28845 0.858952
\(73\) −16.8357 −1.97047 −0.985237 0.171198i \(-0.945236\pi\)
−0.985237 + 0.171198i \(0.945236\pi\)
\(74\) 5.28670 0.614567
\(75\) 0 0
\(76\) −1.42213 −0.163130
\(77\) −5.45893 −0.622102
\(78\) 4.46822 0.505926
\(79\) 16.2958 1.83342 0.916712 0.399548i \(-0.130833\pi\)
0.916712 + 0.399548i \(0.130833\pi\)
\(80\) 0 0
\(81\) 4.52851 0.503167
\(82\) 2.70172 0.298355
\(83\) −5.44188 −0.597324 −0.298662 0.954359i \(-0.596540\pi\)
−0.298662 + 0.954359i \(0.596540\pi\)
\(84\) −1.52713 −0.166624
\(85\) 0 0
\(86\) −4.31775 −0.465595
\(87\) 2.71879 0.291485
\(88\) 8.33971 0.889017
\(89\) 6.41711 0.680212 0.340106 0.940387i \(-0.389537\pi\)
0.340106 + 0.940387i \(0.389537\pi\)
\(90\) 0 0
\(91\) 12.4372 1.30377
\(92\) 1.94820 0.203114
\(93\) −6.31460 −0.654793
\(94\) 8.97477 0.925677
\(95\) 0 0
\(96\) 3.84343 0.392268
\(97\) −3.18370 −0.323256 −0.161628 0.986852i \(-0.551674\pi\)
−0.161628 + 0.986852i \(0.551674\pi\)
\(98\) −3.12633 −0.315807
\(99\) 6.99341 0.702864
\(100\) 0 0
\(101\) 11.1222 1.10670 0.553349 0.832949i \(-0.313349\pi\)
0.553349 + 0.832949i \(0.313349\pi\)
\(102\) 1.49593 0.148119
\(103\) −1.41993 −0.139910 −0.0699551 0.997550i \(-0.522286\pi\)
−0.0699551 + 0.997550i \(0.522286\pi\)
\(104\) −19.0005 −1.86315
\(105\) 0 0
\(106\) −4.02365 −0.390811
\(107\) 7.03950 0.680534 0.340267 0.940329i \(-0.389482\pi\)
0.340267 + 0.940329i \(0.389482\pi\)
\(108\) 4.33047 0.416699
\(109\) −8.60893 −0.824586 −0.412293 0.911051i \(-0.635272\pi\)
−0.412293 + 0.911051i \(0.635272\pi\)
\(110\) 0 0
\(111\) 4.02460 0.381998
\(112\) −1.22514 −0.115765
\(113\) 16.1383 1.51816 0.759081 0.650996i \(-0.225649\pi\)
0.759081 + 0.650996i \(0.225649\pi\)
\(114\) 0.905136 0.0847738
\(115\) 0 0
\(116\) −4.07654 −0.378497
\(117\) −15.9332 −1.47303
\(118\) −9.80065 −0.902223
\(119\) 4.16387 0.381701
\(120\) 0 0
\(121\) −2.99788 −0.272535
\(122\) 11.6864 1.05804
\(123\) 2.05673 0.185449
\(124\) 9.46807 0.850258
\(125\) 0 0
\(126\) −4.55283 −0.405598
\(127\) 8.33841 0.739914 0.369957 0.929049i \(-0.379372\pi\)
0.369957 + 0.929049i \(0.379372\pi\)
\(128\) −4.55109 −0.402264
\(129\) −3.28697 −0.289401
\(130\) 0 0
\(131\) 18.8414 1.64618 0.823088 0.567914i \(-0.192249\pi\)
0.823088 + 0.567914i \(0.192249\pi\)
\(132\) 2.23859 0.194844
\(133\) 2.51942 0.218462
\(134\) 11.2877 0.975105
\(135\) 0 0
\(136\) −6.36123 −0.545471
\(137\) 19.0380 1.62653 0.813263 0.581896i \(-0.197689\pi\)
0.813263 + 0.581896i \(0.197689\pi\)
\(138\) −1.23996 −0.105552
\(139\) 19.8989 1.68780 0.843902 0.536497i \(-0.180253\pi\)
0.843902 + 0.536497i \(0.180253\pi\)
\(140\) 0 0
\(141\) 6.83221 0.575376
\(142\) 8.99649 0.754969
\(143\) −18.2314 −1.52458
\(144\) 1.56953 0.130794
\(145\) 0 0
\(146\) −16.0665 −1.32968
\(147\) −2.37997 −0.196297
\(148\) −6.03446 −0.496030
\(149\) −19.4986 −1.59739 −0.798695 0.601736i \(-0.794476\pi\)
−0.798695 + 0.601736i \(0.794476\pi\)
\(150\) 0 0
\(151\) −7.24829 −0.589858 −0.294929 0.955519i \(-0.595296\pi\)
−0.294929 + 0.955519i \(0.595296\pi\)
\(152\) −3.84897 −0.312193
\(153\) −5.33432 −0.431254
\(154\) −5.20951 −0.419795
\(155\) 0 0
\(156\) −5.10021 −0.408344
\(157\) −5.22604 −0.417083 −0.208542 0.978014i \(-0.566872\pi\)
−0.208542 + 0.978014i \(0.566872\pi\)
\(158\) 15.5513 1.23719
\(159\) −3.06308 −0.242918
\(160\) 0 0
\(161\) −3.45139 −0.272008
\(162\) 4.32160 0.339537
\(163\) 5.26431 0.412332 0.206166 0.978517i \(-0.433901\pi\)
0.206166 + 0.978517i \(0.433901\pi\)
\(164\) −3.08386 −0.240809
\(165\) 0 0
\(166\) −5.19325 −0.403074
\(167\) 2.09327 0.161982 0.0809912 0.996715i \(-0.474191\pi\)
0.0809912 + 0.996715i \(0.474191\pi\)
\(168\) −4.13315 −0.318879
\(169\) 28.5368 2.19514
\(170\) 0 0
\(171\) −3.22762 −0.246822
\(172\) 4.92846 0.375791
\(173\) 15.6587 1.19051 0.595254 0.803538i \(-0.297051\pi\)
0.595254 + 0.803538i \(0.297051\pi\)
\(174\) 2.59457 0.196694
\(175\) 0 0
\(176\) 1.79591 0.135372
\(177\) −7.46093 −0.560798
\(178\) 6.12392 0.459007
\(179\) 15.6924 1.17291 0.586453 0.809983i \(-0.300524\pi\)
0.586453 + 0.809983i \(0.300524\pi\)
\(180\) 0 0
\(181\) −25.3735 −1.88600 −0.942999 0.332795i \(-0.892008\pi\)
−0.942999 + 0.332795i \(0.892008\pi\)
\(182\) 11.8689 0.879783
\(183\) 8.89648 0.657646
\(184\) 5.27276 0.388713
\(185\) 0 0
\(186\) −6.02609 −0.441854
\(187\) −6.10373 −0.446349
\(188\) −10.2442 −0.747133
\(189\) −7.67177 −0.558039
\(190\) 0 0
\(191\) 3.11508 0.225399 0.112700 0.993629i \(-0.464050\pi\)
0.112700 + 0.993629i \(0.464050\pi\)
\(192\) 4.59027 0.331274
\(193\) 1.60613 0.115612 0.0578058 0.998328i \(-0.481590\pi\)
0.0578058 + 0.998328i \(0.481590\pi\)
\(194\) −3.03824 −0.218133
\(195\) 0 0
\(196\) 3.56852 0.254894
\(197\) 15.2199 1.08437 0.542187 0.840258i \(-0.317596\pi\)
0.542187 + 0.840258i \(0.317596\pi\)
\(198\) 6.67389 0.474293
\(199\) 3.89119 0.275839 0.137920 0.990443i \(-0.455958\pi\)
0.137920 + 0.990443i \(0.455958\pi\)
\(200\) 0 0
\(201\) 8.59293 0.606099
\(202\) 10.6140 0.746800
\(203\) 7.22192 0.506879
\(204\) −1.70751 −0.119550
\(205\) 0 0
\(206\) −1.35506 −0.0944114
\(207\) 4.42157 0.307320
\(208\) −4.09165 −0.283705
\(209\) −3.69317 −0.255462
\(210\) 0 0
\(211\) 23.3482 1.60735 0.803677 0.595066i \(-0.202874\pi\)
0.803677 + 0.595066i \(0.202874\pi\)
\(212\) 4.59276 0.315432
\(213\) 6.84874 0.469268
\(214\) 6.71788 0.459225
\(215\) 0 0
\(216\) 11.7203 0.797467
\(217\) −16.7735 −1.13866
\(218\) −8.21560 −0.556431
\(219\) −12.2309 −0.826490
\(220\) 0 0
\(221\) 13.9062 0.935434
\(222\) 3.84072 0.257772
\(223\) 24.7633 1.65827 0.829135 0.559048i \(-0.188833\pi\)
0.829135 + 0.559048i \(0.188833\pi\)
\(224\) 10.2093 0.682137
\(225\) 0 0
\(226\) 15.4009 1.02446
\(227\) −4.59488 −0.304973 −0.152486 0.988306i \(-0.548728\pi\)
−0.152486 + 0.988306i \(0.548728\pi\)
\(228\) −1.03316 −0.0684227
\(229\) 8.91085 0.588846 0.294423 0.955675i \(-0.404873\pi\)
0.294423 + 0.955675i \(0.404873\pi\)
\(230\) 0 0
\(231\) −3.96584 −0.260933
\(232\) −11.0331 −0.724357
\(233\) 11.1866 0.732858 0.366429 0.930446i \(-0.380580\pi\)
0.366429 + 0.930446i \(0.380580\pi\)
\(234\) −15.2052 −0.993998
\(235\) 0 0
\(236\) 11.1869 0.728203
\(237\) 11.8387 0.769007
\(238\) 3.97363 0.257572
\(239\) 9.02136 0.583543 0.291771 0.956488i \(-0.405755\pi\)
0.291771 + 0.956488i \(0.405755\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −2.86091 −0.183906
\(243\) 15.2164 0.976131
\(244\) −13.3393 −0.853963
\(245\) 0 0
\(246\) 1.96276 0.125141
\(247\) 8.41420 0.535383
\(248\) 25.6252 1.62720
\(249\) −3.95346 −0.250540
\(250\) 0 0
\(251\) 0.292167 0.0184414 0.00922072 0.999957i \(-0.497065\pi\)
0.00922072 + 0.999957i \(0.497065\pi\)
\(252\) 5.19679 0.327367
\(253\) 5.05932 0.318077
\(254\) 7.95744 0.499294
\(255\) 0 0
\(256\) −16.9801 −1.06125
\(257\) −1.33623 −0.0833516 −0.0416758 0.999131i \(-0.513270\pi\)
−0.0416758 + 0.999131i \(0.513270\pi\)
\(258\) −3.13679 −0.195288
\(259\) 10.6905 0.664278
\(260\) 0 0
\(261\) −9.25197 −0.572683
\(262\) 17.9805 1.11084
\(263\) 0.261451 0.0161218 0.00806089 0.999968i \(-0.497434\pi\)
0.00806089 + 0.999968i \(0.497434\pi\)
\(264\) 6.05869 0.372887
\(265\) 0 0
\(266\) 2.40431 0.147418
\(267\) 4.66195 0.285306
\(268\) −12.8842 −0.787027
\(269\) −31.1244 −1.89769 −0.948843 0.315748i \(-0.897744\pi\)
−0.948843 + 0.315748i \(0.897744\pi\)
\(270\) 0 0
\(271\) 6.21072 0.377274 0.188637 0.982047i \(-0.439593\pi\)
0.188637 + 0.982047i \(0.439593\pi\)
\(272\) −1.36986 −0.0830597
\(273\) 9.03544 0.546850
\(274\) 18.1682 1.09758
\(275\) 0 0
\(276\) 1.41534 0.0851935
\(277\) −31.1724 −1.87297 −0.936483 0.350712i \(-0.885940\pi\)
−0.936483 + 0.350712i \(0.885940\pi\)
\(278\) 18.9898 1.13893
\(279\) 21.4884 1.28648
\(280\) 0 0
\(281\) −30.3646 −1.81140 −0.905701 0.423916i \(-0.860655\pi\)
−0.905701 + 0.423916i \(0.860655\pi\)
\(282\) 6.52006 0.388264
\(283\) −32.8954 −1.95543 −0.977715 0.209937i \(-0.932674\pi\)
−0.977715 + 0.209937i \(0.932674\pi\)
\(284\) −10.2690 −0.609351
\(285\) 0 0
\(286\) −17.3984 −1.02879
\(287\) 5.46330 0.322488
\(288\) −13.0791 −0.770692
\(289\) −12.3443 −0.726135
\(290\) 0 0
\(291\) −2.31292 −0.135586
\(292\) 18.3390 1.07321
\(293\) 10.8629 0.634616 0.317308 0.948323i \(-0.397221\pi\)
0.317308 + 0.948323i \(0.397221\pi\)
\(294\) −2.27123 −0.132461
\(295\) 0 0
\(296\) −16.3322 −0.949288
\(297\) 11.2459 0.652552
\(298\) −18.6078 −1.07792
\(299\) −11.5267 −0.666608
\(300\) 0 0
\(301\) −8.73117 −0.503256
\(302\) −6.91713 −0.398036
\(303\) 8.08012 0.464191
\(304\) −0.828855 −0.0475381
\(305\) 0 0
\(306\) −5.09060 −0.291010
\(307\) 15.4972 0.884472 0.442236 0.896899i \(-0.354185\pi\)
0.442236 + 0.896899i \(0.354185\pi\)
\(308\) 5.94635 0.338825
\(309\) −1.03156 −0.0586836
\(310\) 0 0
\(311\) 10.0955 0.572465 0.286232 0.958160i \(-0.407597\pi\)
0.286232 + 0.958160i \(0.407597\pi\)
\(312\) −13.8036 −0.781477
\(313\) −24.5157 −1.38571 −0.692854 0.721078i \(-0.743647\pi\)
−0.692854 + 0.721078i \(0.743647\pi\)
\(314\) −4.98726 −0.281448
\(315\) 0 0
\(316\) −17.7509 −0.998566
\(317\) 21.3367 1.19839 0.599195 0.800603i \(-0.295487\pi\)
0.599195 + 0.800603i \(0.295487\pi\)
\(318\) −2.92313 −0.163921
\(319\) −10.5865 −0.592727
\(320\) 0 0
\(321\) 5.11411 0.285442
\(322\) −3.29370 −0.183551
\(323\) 2.81701 0.156743
\(324\) −4.93286 −0.274048
\(325\) 0 0
\(326\) 5.02379 0.278242
\(327\) −6.25428 −0.345862
\(328\) −8.34640 −0.460853
\(329\) 18.1484 1.00055
\(330\) 0 0
\(331\) 18.3486 1.00853 0.504266 0.863548i \(-0.331763\pi\)
0.504266 + 0.863548i \(0.331763\pi\)
\(332\) 5.92779 0.325330
\(333\) −13.6956 −0.750515
\(334\) 1.99763 0.109306
\(335\) 0 0
\(336\) −0.890051 −0.0485562
\(337\) −23.5672 −1.28379 −0.641893 0.766794i \(-0.721851\pi\)
−0.641893 + 0.766794i \(0.721851\pi\)
\(338\) 27.2330 1.48128
\(339\) 11.7243 0.636774
\(340\) 0 0
\(341\) 24.5878 1.33151
\(342\) −3.08016 −0.166556
\(343\) −19.8303 −1.07073
\(344\) 13.3388 0.719179
\(345\) 0 0
\(346\) 14.9433 0.803355
\(347\) 29.9357 1.60703 0.803516 0.595284i \(-0.202960\pi\)
0.803516 + 0.595284i \(0.202960\pi\)
\(348\) −2.96155 −0.158756
\(349\) −14.2722 −0.763973 −0.381987 0.924168i \(-0.624760\pi\)
−0.381987 + 0.924168i \(0.624760\pi\)
\(350\) 0 0
\(351\) −25.6217 −1.36758
\(352\) −14.9656 −0.797668
\(353\) 7.32451 0.389844 0.194922 0.980819i \(-0.437555\pi\)
0.194922 + 0.980819i \(0.437555\pi\)
\(354\) −7.12005 −0.378426
\(355\) 0 0
\(356\) −6.99009 −0.370474
\(357\) 3.02500 0.160100
\(358\) 14.9755 0.791477
\(359\) 1.92275 0.101479 0.0507394 0.998712i \(-0.483842\pi\)
0.0507394 + 0.998712i \(0.483842\pi\)
\(360\) 0 0
\(361\) −17.2955 −0.910290
\(362\) −24.2142 −1.27267
\(363\) −2.17792 −0.114311
\(364\) −13.5477 −0.710092
\(365\) 0 0
\(366\) 8.49001 0.443780
\(367\) −10.6190 −0.554305 −0.277153 0.960826i \(-0.589391\pi\)
−0.277153 + 0.960826i \(0.589391\pi\)
\(368\) 1.13546 0.0591899
\(369\) −6.99901 −0.364354
\(370\) 0 0
\(371\) −8.13644 −0.422423
\(372\) 6.87843 0.356630
\(373\) −21.9835 −1.13826 −0.569132 0.822246i \(-0.692721\pi\)
−0.569132 + 0.822246i \(0.692721\pi\)
\(374\) −5.82485 −0.301196
\(375\) 0 0
\(376\) −27.7257 −1.42984
\(377\) 24.1193 1.24221
\(378\) −7.32126 −0.376565
\(379\) 11.7937 0.605801 0.302901 0.953022i \(-0.402045\pi\)
0.302901 + 0.953022i \(0.402045\pi\)
\(380\) 0 0
\(381\) 6.05775 0.310348
\(382\) 2.97275 0.152099
\(383\) −3.77603 −0.192946 −0.0964731 0.995336i \(-0.530756\pi\)
−0.0964731 + 0.995336i \(0.530756\pi\)
\(384\) −3.30631 −0.168724
\(385\) 0 0
\(386\) 1.53275 0.0780147
\(387\) 11.1855 0.568589
\(388\) 3.46798 0.176060
\(389\) −5.79768 −0.293954 −0.146977 0.989140i \(-0.546954\pi\)
−0.146977 + 0.989140i \(0.546954\pi\)
\(390\) 0 0
\(391\) −3.85907 −0.195161
\(392\) 9.65813 0.487809
\(393\) 13.6880 0.690468
\(394\) 14.5245 0.731735
\(395\) 0 0
\(396\) −7.61785 −0.382812
\(397\) −10.3725 −0.520583 −0.260291 0.965530i \(-0.583819\pi\)
−0.260291 + 0.965530i \(0.583819\pi\)
\(398\) 3.71341 0.186136
\(399\) 1.83033 0.0916310
\(400\) 0 0
\(401\) 14.1753 0.707880 0.353940 0.935268i \(-0.384842\pi\)
0.353940 + 0.935268i \(0.384842\pi\)
\(402\) 8.20033 0.408995
\(403\) −56.0189 −2.79050
\(404\) −12.1153 −0.602758
\(405\) 0 0
\(406\) 6.89196 0.342042
\(407\) −15.6710 −0.776784
\(408\) −4.62135 −0.228791
\(409\) −36.9371 −1.82642 −0.913212 0.407485i \(-0.866406\pi\)
−0.913212 + 0.407485i \(0.866406\pi\)
\(410\) 0 0
\(411\) 13.8309 0.682226
\(412\) 1.54672 0.0762014
\(413\) −19.8185 −0.975202
\(414\) 4.21955 0.207380
\(415\) 0 0
\(416\) 34.0963 1.67171
\(417\) 14.4563 0.707928
\(418\) −3.52443 −0.172385
\(419\) 23.1100 1.12899 0.564497 0.825435i \(-0.309070\pi\)
0.564497 + 0.825435i \(0.309070\pi\)
\(420\) 0 0
\(421\) −18.5538 −0.904255 −0.452127 0.891953i \(-0.649335\pi\)
−0.452127 + 0.891953i \(0.649335\pi\)
\(422\) 22.2814 1.08464
\(423\) −23.2498 −1.13045
\(424\) 12.4302 0.603664
\(425\) 0 0
\(426\) 6.53583 0.316662
\(427\) 23.6317 1.14362
\(428\) −7.66806 −0.370650
\(429\) −13.2448 −0.639467
\(430\) 0 0
\(431\) −9.98236 −0.480833 −0.240417 0.970670i \(-0.577284\pi\)
−0.240417 + 0.970670i \(0.577284\pi\)
\(432\) 2.52391 0.121432
\(433\) −15.6993 −0.754459 −0.377230 0.926120i \(-0.623123\pi\)
−0.377230 + 0.926120i \(0.623123\pi\)
\(434\) −16.0071 −0.768365
\(435\) 0 0
\(436\) 9.37763 0.449107
\(437\) −2.33499 −0.111698
\(438\) −11.6721 −0.557716
\(439\) 3.10402 0.148147 0.0740733 0.997253i \(-0.476400\pi\)
0.0740733 + 0.997253i \(0.476400\pi\)
\(440\) 0 0
\(441\) 8.09899 0.385666
\(442\) 13.2709 0.631231
\(443\) −1.81863 −0.0864058 −0.0432029 0.999066i \(-0.513756\pi\)
−0.0432029 + 0.999066i \(0.513756\pi\)
\(444\) −4.38396 −0.208053
\(445\) 0 0
\(446\) 23.6318 1.11900
\(447\) −14.1655 −0.670005
\(448\) 12.1931 0.576071
\(449\) −8.38120 −0.395533 −0.197767 0.980249i \(-0.563369\pi\)
−0.197767 + 0.980249i \(0.563369\pi\)
\(450\) 0 0
\(451\) −8.00853 −0.377107
\(452\) −17.5793 −0.826859
\(453\) −5.26579 −0.247408
\(454\) −4.38494 −0.205796
\(455\) 0 0
\(456\) −2.79623 −0.130945
\(457\) 34.0456 1.59259 0.796294 0.604910i \(-0.206791\pi\)
0.796294 + 0.604910i \(0.206791\pi\)
\(458\) 8.50372 0.397353
\(459\) −8.57795 −0.400385
\(460\) 0 0
\(461\) 37.0441 1.72532 0.862659 0.505786i \(-0.168797\pi\)
0.862659 + 0.505786i \(0.168797\pi\)
\(462\) −3.78464 −0.176078
\(463\) −17.9429 −0.833876 −0.416938 0.908935i \(-0.636897\pi\)
−0.416938 + 0.908935i \(0.636897\pi\)
\(464\) −2.37591 −0.110299
\(465\) 0 0
\(466\) 10.6755 0.494532
\(467\) −22.5460 −1.04330 −0.521652 0.853158i \(-0.674684\pi\)
−0.521652 + 0.853158i \(0.674684\pi\)
\(468\) 17.3559 0.802276
\(469\) 22.8254 1.05398
\(470\) 0 0
\(471\) −3.79665 −0.174940
\(472\) 30.2771 1.39361
\(473\) 12.7988 0.588490
\(474\) 11.2978 0.518926
\(475\) 0 0
\(476\) −4.53566 −0.207892
\(477\) 10.4236 0.477262
\(478\) 8.60918 0.393775
\(479\) −6.58124 −0.300705 −0.150352 0.988632i \(-0.548041\pi\)
−0.150352 + 0.988632i \(0.548041\pi\)
\(480\) 0 0
\(481\) 35.7036 1.62794
\(482\) 0.954311 0.0434677
\(483\) −2.50739 −0.114090
\(484\) 3.26556 0.148435
\(485\) 0 0
\(486\) 14.5212 0.658693
\(487\) −30.3973 −1.37743 −0.688717 0.725031i \(-0.741826\pi\)
−0.688717 + 0.725031i \(0.741826\pi\)
\(488\) −36.1026 −1.63429
\(489\) 3.82445 0.172948
\(490\) 0 0
\(491\) −6.16398 −0.278176 −0.139088 0.990280i \(-0.544417\pi\)
−0.139088 + 0.990280i \(0.544417\pi\)
\(492\) −2.24038 −0.101004
\(493\) 8.07496 0.363678
\(494\) 8.02977 0.361276
\(495\) 0 0
\(496\) 5.51823 0.247776
\(497\) 18.1923 0.816036
\(498\) −3.77283 −0.169064
\(499\) 10.2121 0.457157 0.228579 0.973525i \(-0.426592\pi\)
0.228579 + 0.973525i \(0.426592\pi\)
\(500\) 0 0
\(501\) 1.52074 0.0679415
\(502\) 0.278819 0.0124443
\(503\) 33.2347 1.48186 0.740930 0.671582i \(-0.234385\pi\)
0.740930 + 0.671582i \(0.234385\pi\)
\(504\) 14.0650 0.626505
\(505\) 0 0
\(506\) 4.82816 0.214638
\(507\) 20.7316 0.920724
\(508\) −9.08295 −0.402991
\(509\) 32.8944 1.45802 0.729009 0.684504i \(-0.239981\pi\)
0.729009 + 0.684504i \(0.239981\pi\)
\(510\) 0 0
\(511\) −32.4890 −1.43723
\(512\) −7.10207 −0.313870
\(513\) −5.19024 −0.229155
\(514\) −1.27518 −0.0562457
\(515\) 0 0
\(516\) 3.58046 0.157621
\(517\) −26.6033 −1.17001
\(518\) 10.2021 0.448255
\(519\) 11.3758 0.499344
\(520\) 0 0
\(521\) −16.7379 −0.733302 −0.366651 0.930359i \(-0.619496\pi\)
−0.366651 + 0.930359i \(0.619496\pi\)
\(522\) −8.82926 −0.386446
\(523\) −1.77831 −0.0777599 −0.0388799 0.999244i \(-0.512379\pi\)
−0.0388799 + 0.999244i \(0.512379\pi\)
\(524\) −20.5237 −0.896582
\(525\) 0 0
\(526\) 0.249506 0.0108790
\(527\) −18.7547 −0.816968
\(528\) 1.30471 0.0567800
\(529\) −19.8013 −0.860924
\(530\) 0 0
\(531\) 25.3894 1.10180
\(532\) −2.74438 −0.118984
\(533\) 18.2460 0.790321
\(534\) 4.44895 0.192525
\(535\) 0 0
\(536\) −34.8708 −1.50619
\(537\) 11.4003 0.491961
\(538\) −29.7023 −1.28056
\(539\) 9.26716 0.399165
\(540\) 0 0
\(541\) 16.6472 0.715718 0.357859 0.933776i \(-0.383507\pi\)
0.357859 + 0.933776i \(0.383507\pi\)
\(542\) 5.92696 0.254585
\(543\) −18.4335 −0.791058
\(544\) 11.4152 0.489423
\(545\) 0 0
\(546\) 8.62262 0.369014
\(547\) −19.0159 −0.813060 −0.406530 0.913637i \(-0.633261\pi\)
−0.406530 + 0.913637i \(0.633261\pi\)
\(548\) −20.7379 −0.885880
\(549\) −30.2745 −1.29208
\(550\) 0 0
\(551\) 4.88590 0.208146
\(552\) 3.83059 0.163041
\(553\) 31.4472 1.33727
\(554\) −29.7482 −1.26388
\(555\) 0 0
\(556\) −21.6757 −0.919254
\(557\) −20.6747 −0.876017 −0.438008 0.898971i \(-0.644316\pi\)
−0.438008 + 0.898971i \(0.644316\pi\)
\(558\) 20.5066 0.868115
\(559\) −29.1598 −1.23333
\(560\) 0 0
\(561\) −4.43428 −0.187215
\(562\) −28.9773 −1.22233
\(563\) 33.3776 1.40670 0.703349 0.710845i \(-0.251687\pi\)
0.703349 + 0.710845i \(0.251687\pi\)
\(564\) −7.44226 −0.313376
\(565\) 0 0
\(566\) −31.3925 −1.31952
\(567\) 8.73896 0.367002
\(568\) −27.7928 −1.16616
\(569\) 28.2188 1.18299 0.591496 0.806308i \(-0.298538\pi\)
0.591496 + 0.806308i \(0.298538\pi\)
\(570\) 0 0
\(571\) −14.6813 −0.614392 −0.307196 0.951646i \(-0.599391\pi\)
−0.307196 + 0.951646i \(0.599391\pi\)
\(572\) 19.8592 0.830357
\(573\) 2.26306 0.0945408
\(574\) 5.21369 0.217615
\(575\) 0 0
\(576\) −15.6206 −0.650857
\(577\) 5.06714 0.210948 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(578\) −11.7803 −0.489996
\(579\) 1.16683 0.0484918
\(580\) 0 0
\(581\) −10.5016 −0.435678
\(582\) −2.20724 −0.0914932
\(583\) 11.9270 0.493967
\(584\) 49.6342 2.05388
\(585\) 0 0
\(586\) 10.3666 0.428239
\(587\) −37.9278 −1.56545 −0.782725 0.622368i \(-0.786171\pi\)
−0.782725 + 0.622368i \(0.786171\pi\)
\(588\) 2.59248 0.106912
\(589\) −11.3479 −0.467581
\(590\) 0 0
\(591\) 11.0571 0.454827
\(592\) −3.51704 −0.144549
\(593\) −15.7405 −0.646385 −0.323193 0.946333i \(-0.604756\pi\)
−0.323193 + 0.946333i \(0.604756\pi\)
\(594\) 10.7321 0.440342
\(595\) 0 0
\(596\) 21.2397 0.870011
\(597\) 2.82690 0.115697
\(598\) −11.0001 −0.449827
\(599\) −19.7226 −0.805842 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(600\) 0 0
\(601\) 16.4315 0.670255 0.335127 0.942173i \(-0.391221\pi\)
0.335127 + 0.942173i \(0.391221\pi\)
\(602\) −8.33225 −0.339597
\(603\) −29.2415 −1.19081
\(604\) 7.89550 0.321263
\(605\) 0 0
\(606\) 7.71095 0.313236
\(607\) −3.48612 −0.141497 −0.0707487 0.997494i \(-0.522539\pi\)
−0.0707487 + 0.997494i \(0.522539\pi\)
\(608\) 6.90696 0.280114
\(609\) 5.24663 0.212604
\(610\) 0 0
\(611\) 60.6108 2.45205
\(612\) 5.81062 0.234881
\(613\) 26.4960 1.07016 0.535081 0.844801i \(-0.320281\pi\)
0.535081 + 0.844801i \(0.320281\pi\)
\(614\) 14.7892 0.596842
\(615\) 0 0
\(616\) 16.0937 0.648434
\(617\) −38.4572 −1.54823 −0.774115 0.633045i \(-0.781805\pi\)
−0.774115 + 0.633045i \(0.781805\pi\)
\(618\) −0.984433 −0.0395997
\(619\) 36.4591 1.46542 0.732708 0.680544i \(-0.238256\pi\)
0.732708 + 0.680544i \(0.238256\pi\)
\(620\) 0 0
\(621\) 7.11018 0.285322
\(622\) 9.63427 0.386299
\(623\) 12.3835 0.496135
\(624\) −2.97253 −0.118997
\(625\) 0 0
\(626\) −23.3956 −0.935076
\(627\) −2.68304 −0.107150
\(628\) 5.69267 0.227162
\(629\) 11.9533 0.476609
\(630\) 0 0
\(631\) 29.7324 1.18363 0.591814 0.806074i \(-0.298412\pi\)
0.591814 + 0.806074i \(0.298412\pi\)
\(632\) −48.0425 −1.91103
\(633\) 16.9621 0.674184
\(634\) 20.3619 0.808674
\(635\) 0 0
\(636\) 3.33658 0.132304
\(637\) −21.1135 −0.836549
\(638\) −10.1028 −0.399972
\(639\) −23.3061 −0.921975
\(640\) 0 0
\(641\) 18.7422 0.740274 0.370137 0.928977i \(-0.379311\pi\)
0.370137 + 0.928977i \(0.379311\pi\)
\(642\) 4.88045 0.192616
\(643\) −29.5989 −1.16727 −0.583633 0.812018i \(-0.698369\pi\)
−0.583633 + 0.812018i \(0.698369\pi\)
\(644\) 3.75957 0.148148
\(645\) 0 0
\(646\) 2.68831 0.105770
\(647\) 37.4655 1.47292 0.736460 0.676481i \(-0.236496\pi\)
0.736460 + 0.676481i \(0.236496\pi\)
\(648\) −13.3507 −0.524465
\(649\) 29.0514 1.14037
\(650\) 0 0
\(651\) −12.1857 −0.477595
\(652\) −5.73436 −0.224575
\(653\) −19.4784 −0.762249 −0.381124 0.924524i \(-0.624463\pi\)
−0.381124 + 0.924524i \(0.624463\pi\)
\(654\) −5.96853 −0.233388
\(655\) 0 0
\(656\) −1.79735 −0.0701747
\(657\) 41.6216 1.62381
\(658\) 17.3192 0.675173
\(659\) 27.6813 1.07831 0.539155 0.842206i \(-0.318744\pi\)
0.539155 + 0.842206i \(0.318744\pi\)
\(660\) 0 0
\(661\) 34.3354 1.33549 0.667745 0.744390i \(-0.267260\pi\)
0.667745 + 0.744390i \(0.267260\pi\)
\(662\) 17.5103 0.680558
\(663\) 10.1027 0.392356
\(664\) 16.0435 0.622607
\(665\) 0 0
\(666\) −13.0699 −0.506448
\(667\) −6.69326 −0.259164
\(668\) −2.28018 −0.0882229
\(669\) 17.9902 0.695541
\(670\) 0 0
\(671\) −34.6412 −1.33731
\(672\) 7.41692 0.286114
\(673\) 11.8998 0.458702 0.229351 0.973344i \(-0.426340\pi\)
0.229351 + 0.973344i \(0.426340\pi\)
\(674\) −22.4904 −0.866299
\(675\) 0 0
\(676\) −31.0849 −1.19557
\(677\) −22.0197 −0.846288 −0.423144 0.906063i \(-0.639073\pi\)
−0.423144 + 0.906063i \(0.639073\pi\)
\(678\) 11.1886 0.429695
\(679\) −6.14380 −0.235777
\(680\) 0 0
\(681\) −3.33812 −0.127917
\(682\) 23.4645 0.898500
\(683\) 47.4084 1.81403 0.907016 0.421096i \(-0.138355\pi\)
0.907016 + 0.421096i \(0.138355\pi\)
\(684\) 3.51582 0.134431
\(685\) 0 0
\(686\) −18.9243 −0.722532
\(687\) 6.47362 0.246984
\(688\) 2.87243 0.109510
\(689\) −27.1736 −1.03523
\(690\) 0 0
\(691\) −32.9505 −1.25350 −0.626748 0.779222i \(-0.715614\pi\)
−0.626748 + 0.779222i \(0.715614\pi\)
\(692\) −17.0569 −0.648404
\(693\) 13.4956 0.512657
\(694\) 28.5679 1.08442
\(695\) 0 0
\(696\) −8.01539 −0.303822
\(697\) 6.10862 0.231380
\(698\) −13.6201 −0.515529
\(699\) 8.12691 0.307388
\(700\) 0 0
\(701\) −21.4743 −0.811072 −0.405536 0.914079i \(-0.632915\pi\)
−0.405536 + 0.914079i \(0.632915\pi\)
\(702\) −24.4511 −0.922846
\(703\) 7.23255 0.272781
\(704\) −17.8736 −0.673638
\(705\) 0 0
\(706\) 6.98986 0.263067
\(707\) 21.4632 0.807207
\(708\) 8.12712 0.305436
\(709\) 19.2938 0.724593 0.362296 0.932063i \(-0.381993\pi\)
0.362296 + 0.932063i \(0.381993\pi\)
\(710\) 0 0
\(711\) −40.2868 −1.51087
\(712\) −18.9186 −0.709003
\(713\) 15.5456 0.582187
\(714\) 2.88679 0.108035
\(715\) 0 0
\(716\) −17.0936 −0.638818
\(717\) 6.55390 0.244760
\(718\) 1.83490 0.0684779
\(719\) −2.49526 −0.0930574 −0.0465287 0.998917i \(-0.514816\pi\)
−0.0465287 + 0.998917i \(0.514816\pi\)
\(720\) 0 0
\(721\) −2.74014 −0.102048
\(722\) −16.5053 −0.614264
\(723\) 0.726487 0.0270183
\(724\) 27.6391 1.02720
\(725\) 0 0
\(726\) −2.07842 −0.0771372
\(727\) −24.6994 −0.916048 −0.458024 0.888940i \(-0.651443\pi\)
−0.458024 + 0.888940i \(0.651443\pi\)
\(728\) −36.6666 −1.35895
\(729\) −2.53101 −0.0937412
\(730\) 0 0
\(731\) −9.76248 −0.361078
\(732\) −9.69084 −0.358184
\(733\) 8.47061 0.312869 0.156435 0.987688i \(-0.450000\pi\)
0.156435 + 0.987688i \(0.450000\pi\)
\(734\) −10.1338 −0.374045
\(735\) 0 0
\(736\) −9.46194 −0.348772
\(737\) −33.4592 −1.23249
\(738\) −6.67924 −0.245866
\(739\) 25.6575 0.943825 0.471913 0.881645i \(-0.343564\pi\)
0.471913 + 0.881645i \(0.343564\pi\)
\(740\) 0 0
\(741\) 6.11281 0.224560
\(742\) −7.76470 −0.285051
\(743\) −3.16313 −0.116044 −0.0580221 0.998315i \(-0.518479\pi\)
−0.0580221 + 0.998315i \(0.518479\pi\)
\(744\) 18.6163 0.682508
\(745\) 0 0
\(746\) −20.9791 −0.768100
\(747\) 13.4535 0.492238
\(748\) 6.64873 0.243102
\(749\) 13.5846 0.496370
\(750\) 0 0
\(751\) −29.3697 −1.07171 −0.535857 0.844309i \(-0.680012\pi\)
−0.535857 + 0.844309i \(0.680012\pi\)
\(752\) −5.97057 −0.217724
\(753\) 0.212256 0.00773503
\(754\) 23.0173 0.838241
\(755\) 0 0
\(756\) 8.35679 0.303933
\(757\) 0.0845371 0.00307255 0.00153628 0.999999i \(-0.499511\pi\)
0.00153628 + 0.999999i \(0.499511\pi\)
\(758\) 11.2549 0.408795
\(759\) 3.67553 0.133413
\(760\) 0 0
\(761\) 0.857810 0.0310956 0.0155478 0.999879i \(-0.495051\pi\)
0.0155478 + 0.999879i \(0.495051\pi\)
\(762\) 5.78098 0.209423
\(763\) −16.6132 −0.601439
\(764\) −3.39322 −0.122762
\(765\) 0 0
\(766\) −3.60351 −0.130200
\(767\) −66.1884 −2.38992
\(768\) −12.3358 −0.445129
\(769\) 35.8091 1.29131 0.645655 0.763629i \(-0.276584\pi\)
0.645655 + 0.763629i \(0.276584\pi\)
\(770\) 0 0
\(771\) −0.970752 −0.0349608
\(772\) −1.74954 −0.0629673
\(773\) −22.4083 −0.805970 −0.402985 0.915207i \(-0.632027\pi\)
−0.402985 + 0.915207i \(0.632027\pi\)
\(774\) 10.6744 0.383684
\(775\) 0 0
\(776\) 9.38602 0.336938
\(777\) 7.76654 0.278623
\(778\) −5.53279 −0.198360
\(779\) 3.69612 0.132427
\(780\) 0 0
\(781\) −26.6677 −0.954245
\(782\) −3.68275 −0.131695
\(783\) −14.8778 −0.531690
\(784\) 2.07982 0.0742794
\(785\) 0 0
\(786\) 13.0626 0.465928
\(787\) 41.4843 1.47875 0.739377 0.673291i \(-0.235120\pi\)
0.739377 + 0.673291i \(0.235120\pi\)
\(788\) −16.5789 −0.590599
\(789\) 0.189941 0.00676208
\(790\) 0 0
\(791\) 31.1431 1.10732
\(792\) −20.6176 −0.732614
\(793\) 78.9236 2.80266
\(794\) −9.89863 −0.351289
\(795\) 0 0
\(796\) −4.23864 −0.150235
\(797\) 14.2759 0.505679 0.252840 0.967508i \(-0.418636\pi\)
0.252840 + 0.967508i \(0.418636\pi\)
\(798\) 1.74670 0.0618326
\(799\) 20.2921 0.717881
\(800\) 0 0
\(801\) −15.8645 −0.560544
\(802\) 13.5276 0.477678
\(803\) 47.6249 1.68065
\(804\) −9.36020 −0.330109
\(805\) 0 0
\(806\) −53.4595 −1.88303
\(807\) −22.6114 −0.795961
\(808\) −32.7898 −1.15354
\(809\) 28.2967 0.994858 0.497429 0.867505i \(-0.334277\pi\)
0.497429 + 0.867505i \(0.334277\pi\)
\(810\) 0 0
\(811\) 27.7290 0.973696 0.486848 0.873487i \(-0.338147\pi\)
0.486848 + 0.873487i \(0.338147\pi\)
\(812\) −7.86677 −0.276069
\(813\) 4.51200 0.158243
\(814\) −14.9550 −0.524174
\(815\) 0 0
\(816\) −0.995182 −0.0348384
\(817\) −5.90696 −0.206658
\(818\) −35.2495 −1.23247
\(819\) −30.7474 −1.07440
\(820\) 0 0
\(821\) −2.87351 −0.100286 −0.0501431 0.998742i \(-0.515968\pi\)
−0.0501431 + 0.998742i \(0.515968\pi\)
\(822\) 13.1989 0.460366
\(823\) 44.3438 1.54573 0.772865 0.634571i \(-0.218823\pi\)
0.772865 + 0.634571i \(0.218823\pi\)
\(824\) 4.18617 0.145832
\(825\) 0 0
\(826\) −18.9130 −0.658066
\(827\) −28.5124 −0.991474 −0.495737 0.868473i \(-0.665102\pi\)
−0.495737 + 0.868473i \(0.665102\pi\)
\(828\) −4.81637 −0.167380
\(829\) −20.2274 −0.702527 −0.351264 0.936277i \(-0.614248\pi\)
−0.351264 + 0.936277i \(0.614248\pi\)
\(830\) 0 0
\(831\) −22.6463 −0.785592
\(832\) 40.7218 1.41177
\(833\) −7.06866 −0.244914
\(834\) 13.7958 0.477710
\(835\) 0 0
\(836\) 4.02293 0.139136
\(837\) 34.5549 1.19439
\(838\) 22.0541 0.761846
\(839\) −29.7728 −1.02787 −0.513935 0.857829i \(-0.671813\pi\)
−0.513935 + 0.857829i \(0.671813\pi\)
\(840\) 0 0
\(841\) −14.9946 −0.517055
\(842\) −17.7061 −0.610191
\(843\) −22.0595 −0.759770
\(844\) −25.4329 −0.875437
\(845\) 0 0
\(846\) −22.1876 −0.762825
\(847\) −5.78521 −0.198782
\(848\) 2.67678 0.0919209
\(849\) −23.8981 −0.820180
\(850\) 0 0
\(851\) −9.90797 −0.339641
\(852\) −7.46027 −0.255585
\(853\) −23.5214 −0.805356 −0.402678 0.915342i \(-0.631921\pi\)
−0.402678 + 0.915342i \(0.631921\pi\)
\(854\) 22.5520 0.771713
\(855\) 0 0
\(856\) −20.7535 −0.709339
\(857\) −0.198145 −0.00676851 −0.00338426 0.999994i \(-0.501077\pi\)
−0.00338426 + 0.999994i \(0.501077\pi\)
\(858\) −12.6397 −0.431512
\(859\) 3.33604 0.113824 0.0569121 0.998379i \(-0.481875\pi\)
0.0569121 + 0.998379i \(0.481875\pi\)
\(860\) 0 0
\(861\) 3.96902 0.135264
\(862\) −9.52627 −0.324466
\(863\) −38.9081 −1.32445 −0.662223 0.749307i \(-0.730387\pi\)
−0.662223 + 0.749307i \(0.730387\pi\)
\(864\) −21.0321 −0.715525
\(865\) 0 0
\(866\) −14.9820 −0.509109
\(867\) −8.96797 −0.304568
\(868\) 18.2712 0.620164
\(869\) −46.0977 −1.56376
\(870\) 0 0
\(871\) 76.2308 2.58298
\(872\) 25.3804 0.859488
\(873\) 7.87080 0.266386
\(874\) −2.22831 −0.0753737
\(875\) 0 0
\(876\) 13.3230 0.450144
\(877\) −29.5938 −0.999311 −0.499655 0.866224i \(-0.666540\pi\)
−0.499655 + 0.866224i \(0.666540\pi\)
\(878\) 2.96220 0.0999693
\(879\) 7.89174 0.266182
\(880\) 0 0
\(881\) −34.5670 −1.16459 −0.582296 0.812977i \(-0.697846\pi\)
−0.582296 + 0.812977i \(0.697846\pi\)
\(882\) 7.72895 0.260247
\(883\) −26.9745 −0.907765 −0.453883 0.891061i \(-0.649961\pi\)
−0.453883 + 0.891061i \(0.649961\pi\)
\(884\) −15.1479 −0.509480
\(885\) 0 0
\(886\) −1.73554 −0.0583066
\(887\) −49.5386 −1.66334 −0.831672 0.555267i \(-0.812616\pi\)
−0.831672 + 0.555267i \(0.812616\pi\)
\(888\) −11.8651 −0.398167
\(889\) 16.0912 0.539681
\(890\) 0 0
\(891\) −12.8102 −0.429159
\(892\) −26.9744 −0.903169
\(893\) 12.2781 0.410870
\(894\) −13.5183 −0.452120
\(895\) 0 0
\(896\) −8.78254 −0.293404
\(897\) −8.37402 −0.279600
\(898\) −7.99827 −0.266906
\(899\) −32.5286 −1.08489
\(900\) 0 0
\(901\) −9.09751 −0.303082
\(902\) −7.64263 −0.254472
\(903\) −6.34308 −0.211084
\(904\) −47.5780 −1.58242
\(905\) 0 0
\(906\) −5.02520 −0.166951
\(907\) −44.9401 −1.49221 −0.746106 0.665827i \(-0.768079\pi\)
−0.746106 + 0.665827i \(0.768079\pi\)
\(908\) 5.00516 0.166102
\(909\) −27.4965 −0.912000
\(910\) 0 0
\(911\) 0.879323 0.0291333 0.0145666 0.999894i \(-0.495363\pi\)
0.0145666 + 0.999894i \(0.495363\pi\)
\(912\) −0.602152 −0.0199393
\(913\) 15.3940 0.509467
\(914\) 32.4901 1.07468
\(915\) 0 0
\(916\) −9.70650 −0.320712
\(917\) 36.3594 1.20069
\(918\) −8.18604 −0.270179
\(919\) −31.1511 −1.02758 −0.513789 0.857916i \(-0.671759\pi\)
−0.513789 + 0.857916i \(0.671759\pi\)
\(920\) 0 0
\(921\) 11.2585 0.370981
\(922\) 35.3516 1.16424
\(923\) 60.7575 1.99986
\(924\) 4.31995 0.142116
\(925\) 0 0
\(926\) −17.1231 −0.562699
\(927\) 3.51039 0.115296
\(928\) 19.7988 0.649927
\(929\) −14.7760 −0.484785 −0.242393 0.970178i \(-0.577932\pi\)
−0.242393 + 0.970178i \(0.577932\pi\)
\(930\) 0 0
\(931\) −4.27701 −0.140173
\(932\) −12.1854 −0.399147
\(933\) 7.33427 0.240113
\(934\) −21.5159 −0.704022
\(935\) 0 0
\(936\) 46.9734 1.53537
\(937\) −4.98095 −0.162720 −0.0813602 0.996685i \(-0.525926\pi\)
−0.0813602 + 0.996685i \(0.525926\pi\)
\(938\) 21.7825 0.711225
\(939\) −17.8103 −0.581218
\(940\) 0 0
\(941\) −26.6282 −0.868053 −0.434026 0.900900i \(-0.642908\pi\)
−0.434026 + 0.900900i \(0.642908\pi\)
\(942\) −3.62318 −0.118050
\(943\) −5.06337 −0.164886
\(944\) 6.52000 0.212208
\(945\) 0 0
\(946\) 12.2141 0.397113
\(947\) 34.7075 1.12784 0.563921 0.825829i \(-0.309292\pi\)
0.563921 + 0.825829i \(0.309292\pi\)
\(948\) −12.8958 −0.418836
\(949\) −108.505 −3.52221
\(950\) 0 0
\(951\) 15.5009 0.502650
\(952\) −12.2757 −0.397857
\(953\) −7.26177 −0.235232 −0.117616 0.993059i \(-0.537525\pi\)
−0.117616 + 0.993059i \(0.537525\pi\)
\(954\) 9.94733 0.322057
\(955\) 0 0
\(956\) −9.82687 −0.317824
\(957\) −7.69092 −0.248612
\(958\) −6.28055 −0.202916
\(959\) 36.7389 1.18636
\(960\) 0 0
\(961\) 44.5502 1.43710
\(962\) 34.0723 1.09854
\(963\) −17.4032 −0.560809
\(964\) −1.08929 −0.0350837
\(965\) 0 0
\(966\) −2.39283 −0.0769881
\(967\) −8.56893 −0.275558 −0.137779 0.990463i \(-0.543996\pi\)
−0.137779 + 0.990463i \(0.543996\pi\)
\(968\) 8.83819 0.284070
\(969\) 2.04652 0.0657438
\(970\) 0 0
\(971\) 12.8300 0.411733 0.205867 0.978580i \(-0.433999\pi\)
0.205867 + 0.978580i \(0.433999\pi\)
\(972\) −16.5751 −0.531645
\(973\) 38.4003 1.23106
\(974\) −29.0085 −0.929492
\(975\) 0 0
\(976\) −7.77450 −0.248856
\(977\) 11.6047 0.371267 0.185633 0.982619i \(-0.440566\pi\)
0.185633 + 0.982619i \(0.440566\pi\)
\(978\) 3.64972 0.116705
\(979\) −18.1527 −0.580164
\(980\) 0 0
\(981\) 21.2832 0.679519
\(982\) −5.88235 −0.187713
\(983\) −15.5809 −0.496953 −0.248476 0.968638i \(-0.579930\pi\)
−0.248476 + 0.968638i \(0.579930\pi\)
\(984\) −6.06355 −0.193299
\(985\) 0 0
\(986\) 7.70603 0.245410
\(987\) 13.1846 0.419670
\(988\) −9.16551 −0.291594
\(989\) 8.09202 0.257311
\(990\) 0 0
\(991\) −24.9277 −0.791854 −0.395927 0.918282i \(-0.629577\pi\)
−0.395927 + 0.918282i \(0.629577\pi\)
\(992\) −45.9842 −1.46000
\(993\) 13.3300 0.423016
\(994\) 17.3611 0.550661
\(995\) 0 0
\(996\) 4.30646 0.136455
\(997\) 11.4849 0.363730 0.181865 0.983324i \(-0.441787\pi\)
0.181865 + 0.983324i \(0.441787\pi\)
\(998\) 9.74554 0.308490
\(999\) −22.0235 −0.696792
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.k.1.15 25
5.4 even 2 1205.2.a.d.1.11 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.d.1.11 25 5.4 even 2
6025.2.a.k.1.15 25 1.1 even 1 trivial