Properties

Label 6010.2.a.f.1.3
Level $6010$
Weight $2$
Character 6010.1
Self dual yes
Analytic conductor $47.990$
Analytic rank $1$
Dimension $22$
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] = [6010,2,Mod(1,6010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6010, 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("6010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6010.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: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.63651 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.63651 q^{6} +2.17132 q^{7} +1.00000 q^{8} +3.95120 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.63651 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.63651 q^{6} +2.17132 q^{7} +1.00000 q^{8} +3.95120 q^{9} -1.00000 q^{10} -1.77623 q^{11} -2.63651 q^{12} +0.900529 q^{13} +2.17132 q^{14} +2.63651 q^{15} +1.00000 q^{16} -5.23605 q^{17} +3.95120 q^{18} +1.04540 q^{19} -1.00000 q^{20} -5.72472 q^{21} -1.77623 q^{22} +2.25167 q^{23} -2.63651 q^{24} +1.00000 q^{25} +0.900529 q^{26} -2.50784 q^{27} +2.17132 q^{28} +4.06145 q^{29} +2.63651 q^{30} -7.25058 q^{31} +1.00000 q^{32} +4.68306 q^{33} -5.23605 q^{34} -2.17132 q^{35} +3.95120 q^{36} -1.44375 q^{37} +1.04540 q^{38} -2.37426 q^{39} -1.00000 q^{40} +0.883837 q^{41} -5.72472 q^{42} +3.92508 q^{43} -1.77623 q^{44} -3.95120 q^{45} +2.25167 q^{46} -8.40218 q^{47} -2.63651 q^{48} -2.28536 q^{49} +1.00000 q^{50} +13.8049 q^{51} +0.900529 q^{52} +2.00171 q^{53} -2.50784 q^{54} +1.77623 q^{55} +2.17132 q^{56} -2.75621 q^{57} +4.06145 q^{58} +1.78596 q^{59} +2.63651 q^{60} -13.2270 q^{61} -7.25058 q^{62} +8.57932 q^{63} +1.00000 q^{64} -0.900529 q^{65} +4.68306 q^{66} -0.937044 q^{67} -5.23605 q^{68} -5.93657 q^{69} -2.17132 q^{70} +14.4146 q^{71} +3.95120 q^{72} +12.9522 q^{73} -1.44375 q^{74} -2.63651 q^{75} +1.04540 q^{76} -3.85677 q^{77} -2.37426 q^{78} +3.52563 q^{79} -1.00000 q^{80} -5.24163 q^{81} +0.883837 q^{82} -17.5229 q^{83} -5.72472 q^{84} +5.23605 q^{85} +3.92508 q^{86} -10.7081 q^{87} -1.77623 q^{88} -2.64012 q^{89} -3.95120 q^{90} +1.95534 q^{91} +2.25167 q^{92} +19.1163 q^{93} -8.40218 q^{94} -1.04540 q^{95} -2.63651 q^{96} +1.63106 q^{97} -2.28536 q^{98} -7.01825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.63651 −1.52219 −0.761096 0.648640i \(-0.775338\pi\)
−0.761096 + 0.648640i \(0.775338\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.63651 −1.07635
\(7\) 2.17132 0.820682 0.410341 0.911932i \(-0.365410\pi\)
0.410341 + 0.911932i \(0.365410\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.95120 1.31707
\(10\) −1.00000 −0.316228
\(11\) −1.77623 −0.535555 −0.267777 0.963481i \(-0.586289\pi\)
−0.267777 + 0.963481i \(0.586289\pi\)
\(12\) −2.63651 −0.761096
\(13\) 0.900529 0.249762 0.124881 0.992172i \(-0.460145\pi\)
0.124881 + 0.992172i \(0.460145\pi\)
\(14\) 2.17132 0.580310
\(15\) 2.63651 0.680745
\(16\) 1.00000 0.250000
\(17\) −5.23605 −1.26993 −0.634965 0.772541i \(-0.718985\pi\)
−0.634965 + 0.772541i \(0.718985\pi\)
\(18\) 3.95120 0.931306
\(19\) 1.04540 0.239831 0.119916 0.992784i \(-0.461738\pi\)
0.119916 + 0.992784i \(0.461738\pi\)
\(20\) −1.00000 −0.223607
\(21\) −5.72472 −1.24924
\(22\) −1.77623 −0.378694
\(23\) 2.25167 0.469506 0.234753 0.972055i \(-0.424572\pi\)
0.234753 + 0.972055i \(0.424572\pi\)
\(24\) −2.63651 −0.538176
\(25\) 1.00000 0.200000
\(26\) 0.900529 0.176608
\(27\) −2.50784 −0.482635
\(28\) 2.17132 0.410341
\(29\) 4.06145 0.754192 0.377096 0.926174i \(-0.376923\pi\)
0.377096 + 0.926174i \(0.376923\pi\)
\(30\) 2.63651 0.481359
\(31\) −7.25058 −1.30224 −0.651122 0.758973i \(-0.725701\pi\)
−0.651122 + 0.758973i \(0.725701\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.68306 0.815216
\(34\) −5.23605 −0.897976
\(35\) −2.17132 −0.367020
\(36\) 3.95120 0.658533
\(37\) −1.44375 −0.237351 −0.118676 0.992933i \(-0.537865\pi\)
−0.118676 + 0.992933i \(0.537865\pi\)
\(38\) 1.04540 0.169586
\(39\) −2.37426 −0.380185
\(40\) −1.00000 −0.158114
\(41\) 0.883837 0.138032 0.0690161 0.997616i \(-0.478014\pi\)
0.0690161 + 0.997616i \(0.478014\pi\)
\(42\) −5.72472 −0.883343
\(43\) 3.92508 0.598569 0.299284 0.954164i \(-0.403252\pi\)
0.299284 + 0.954164i \(0.403252\pi\)
\(44\) −1.77623 −0.267777
\(45\) −3.95120 −0.589010
\(46\) 2.25167 0.331991
\(47\) −8.40218 −1.22558 −0.612792 0.790244i \(-0.709954\pi\)
−0.612792 + 0.790244i \(0.709954\pi\)
\(48\) −2.63651 −0.380548
\(49\) −2.28536 −0.326480
\(50\) 1.00000 0.141421
\(51\) 13.8049 1.93308
\(52\) 0.900529 0.124881
\(53\) 2.00171 0.274956 0.137478 0.990505i \(-0.456100\pi\)
0.137478 + 0.990505i \(0.456100\pi\)
\(54\) −2.50784 −0.341274
\(55\) 1.77623 0.239507
\(56\) 2.17132 0.290155
\(57\) −2.75621 −0.365069
\(58\) 4.06145 0.533294
\(59\) 1.78596 0.232512 0.116256 0.993219i \(-0.462911\pi\)
0.116256 + 0.993219i \(0.462911\pi\)
\(60\) 2.63651 0.340372
\(61\) −13.2270 −1.69355 −0.846774 0.531953i \(-0.821458\pi\)
−0.846774 + 0.531953i \(0.821458\pi\)
\(62\) −7.25058 −0.920825
\(63\) 8.57932 1.08089
\(64\) 1.00000 0.125000
\(65\) −0.900529 −0.111697
\(66\) 4.68306 0.576445
\(67\) −0.937044 −0.114478 −0.0572391 0.998360i \(-0.518230\pi\)
−0.0572391 + 0.998360i \(0.518230\pi\)
\(68\) −5.23605 −0.634965
\(69\) −5.93657 −0.714679
\(70\) −2.17132 −0.259523
\(71\) 14.4146 1.71069 0.855347 0.518056i \(-0.173344\pi\)
0.855347 + 0.518056i \(0.173344\pi\)
\(72\) 3.95120 0.465653
\(73\) 12.9522 1.51594 0.757969 0.652290i \(-0.226192\pi\)
0.757969 + 0.652290i \(0.226192\pi\)
\(74\) −1.44375 −0.167833
\(75\) −2.63651 −0.304438
\(76\) 1.04540 0.119916
\(77\) −3.85677 −0.439520
\(78\) −2.37426 −0.268831
\(79\) 3.52563 0.396665 0.198332 0.980135i \(-0.436447\pi\)
0.198332 + 0.980135i \(0.436447\pi\)
\(80\) −1.00000 −0.111803
\(81\) −5.24163 −0.582403
\(82\) 0.883837 0.0976035
\(83\) −17.5229 −1.92339 −0.961693 0.274128i \(-0.911611\pi\)
−0.961693 + 0.274128i \(0.911611\pi\)
\(84\) −5.72472 −0.624618
\(85\) 5.23605 0.567930
\(86\) 3.92508 0.423252
\(87\) −10.7081 −1.14802
\(88\) −1.77623 −0.189347
\(89\) −2.64012 −0.279852 −0.139926 0.990162i \(-0.544686\pi\)
−0.139926 + 0.990162i \(0.544686\pi\)
\(90\) −3.95120 −0.416493
\(91\) 1.95534 0.204975
\(92\) 2.25167 0.234753
\(93\) 19.1163 1.98226
\(94\) −8.40218 −0.866618
\(95\) −1.04540 −0.107256
\(96\) −2.63651 −0.269088
\(97\) 1.63106 0.165609 0.0828045 0.996566i \(-0.473612\pi\)
0.0828045 + 0.996566i \(0.473612\pi\)
\(98\) −2.28536 −0.230856
\(99\) −7.01825 −0.705361
\(100\) 1.00000 0.100000
\(101\) 13.1673 1.31020 0.655099 0.755543i \(-0.272627\pi\)
0.655099 + 0.755543i \(0.272627\pi\)
\(102\) 13.8049 1.36689
\(103\) −2.58917 −0.255119 −0.127559 0.991831i \(-0.540714\pi\)
−0.127559 + 0.991831i \(0.540714\pi\)
\(104\) 0.900529 0.0883041
\(105\) 5.72472 0.558675
\(106\) 2.00171 0.194423
\(107\) 2.64733 0.255927 0.127963 0.991779i \(-0.459156\pi\)
0.127963 + 0.991779i \(0.459156\pi\)
\(108\) −2.50784 −0.241317
\(109\) 10.9027 1.04429 0.522143 0.852858i \(-0.325133\pi\)
0.522143 + 0.852858i \(0.325133\pi\)
\(110\) 1.77623 0.169357
\(111\) 3.80647 0.361294
\(112\) 2.17132 0.205171
\(113\) −10.5787 −0.995160 −0.497580 0.867418i \(-0.665778\pi\)
−0.497580 + 0.867418i \(0.665778\pi\)
\(114\) −2.75621 −0.258143
\(115\) −2.25167 −0.209970
\(116\) 4.06145 0.377096
\(117\) 3.55817 0.328953
\(118\) 1.78596 0.164411
\(119\) −11.3692 −1.04221
\(120\) 2.63651 0.240680
\(121\) −7.84499 −0.713181
\(122\) −13.2270 −1.19752
\(123\) −2.33025 −0.210111
\(124\) −7.25058 −0.651122
\(125\) −1.00000 −0.0894427
\(126\) 8.57932 0.764307
\(127\) 8.06671 0.715805 0.357902 0.933759i \(-0.383492\pi\)
0.357902 + 0.933759i \(0.383492\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.3485 −0.911136
\(130\) −0.900529 −0.0789816
\(131\) 1.41270 0.123428 0.0617140 0.998094i \(-0.480343\pi\)
0.0617140 + 0.998094i \(0.480343\pi\)
\(132\) 4.68306 0.407608
\(133\) 2.26990 0.196825
\(134\) −0.937044 −0.0809483
\(135\) 2.50784 0.215841
\(136\) −5.23605 −0.448988
\(137\) −3.87128 −0.330746 −0.165373 0.986231i \(-0.552883\pi\)
−0.165373 + 0.986231i \(0.552883\pi\)
\(138\) −5.93657 −0.505354
\(139\) −9.98899 −0.847255 −0.423628 0.905836i \(-0.639243\pi\)
−0.423628 + 0.905836i \(0.639243\pi\)
\(140\) −2.17132 −0.183510
\(141\) 22.1524 1.86557
\(142\) 14.4146 1.20964
\(143\) −1.59955 −0.133761
\(144\) 3.95120 0.329266
\(145\) −4.06145 −0.337285
\(146\) 12.9522 1.07193
\(147\) 6.02539 0.496965
\(148\) −1.44375 −0.118676
\(149\) 2.81037 0.230235 0.115117 0.993352i \(-0.463276\pi\)
0.115117 + 0.993352i \(0.463276\pi\)
\(150\) −2.63651 −0.215270
\(151\) −11.2886 −0.918650 −0.459325 0.888268i \(-0.651909\pi\)
−0.459325 + 0.888268i \(0.651909\pi\)
\(152\) 1.04540 0.0847932
\(153\) −20.6887 −1.67258
\(154\) −3.85677 −0.310788
\(155\) 7.25058 0.582381
\(156\) −2.37426 −0.190093
\(157\) −10.6219 −0.847719 −0.423859 0.905728i \(-0.639325\pi\)
−0.423859 + 0.905728i \(0.639325\pi\)
\(158\) 3.52563 0.280484
\(159\) −5.27753 −0.418536
\(160\) −1.00000 −0.0790569
\(161\) 4.88911 0.385316
\(162\) −5.24163 −0.411821
\(163\) −16.8717 −1.32149 −0.660746 0.750610i \(-0.729760\pi\)
−0.660746 + 0.750610i \(0.729760\pi\)
\(164\) 0.883837 0.0690161
\(165\) −4.68306 −0.364576
\(166\) −17.5229 −1.36004
\(167\) −7.27037 −0.562598 −0.281299 0.959620i \(-0.590765\pi\)
−0.281299 + 0.959620i \(0.590765\pi\)
\(168\) −5.72472 −0.441671
\(169\) −12.1890 −0.937619
\(170\) 5.23605 0.401587
\(171\) 4.13058 0.315874
\(172\) 3.92508 0.299284
\(173\) −15.6152 −1.18720 −0.593601 0.804760i \(-0.702294\pi\)
−0.593601 + 0.804760i \(0.702294\pi\)
\(174\) −10.7081 −0.811776
\(175\) 2.17132 0.164136
\(176\) −1.77623 −0.133889
\(177\) −4.70871 −0.353928
\(178\) −2.64012 −0.197885
\(179\) 20.0642 1.49967 0.749836 0.661624i \(-0.230133\pi\)
0.749836 + 0.661624i \(0.230133\pi\)
\(180\) −3.95120 −0.294505
\(181\) 18.1864 1.35178 0.675892 0.737001i \(-0.263759\pi\)
0.675892 + 0.737001i \(0.263759\pi\)
\(182\) 1.95534 0.144939
\(183\) 34.8732 2.57790
\(184\) 2.25167 0.165996
\(185\) 1.44375 0.106147
\(186\) 19.1163 1.40167
\(187\) 9.30046 0.680117
\(188\) −8.40218 −0.612792
\(189\) −5.44534 −0.396090
\(190\) −1.04540 −0.0758413
\(191\) −12.7274 −0.920922 −0.460461 0.887680i \(-0.652316\pi\)
−0.460461 + 0.887680i \(0.652316\pi\)
\(192\) −2.63651 −0.190274
\(193\) 2.05041 0.147591 0.0737957 0.997273i \(-0.476489\pi\)
0.0737957 + 0.997273i \(0.476489\pi\)
\(194\) 1.63106 0.117103
\(195\) 2.37426 0.170024
\(196\) −2.28536 −0.163240
\(197\) −17.8327 −1.27053 −0.635265 0.772295i \(-0.719109\pi\)
−0.635265 + 0.772295i \(0.719109\pi\)
\(198\) −7.01825 −0.498765
\(199\) −6.63145 −0.470091 −0.235046 0.971984i \(-0.575524\pi\)
−0.235046 + 0.971984i \(0.575524\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.47053 0.174258
\(202\) 13.1673 0.926449
\(203\) 8.81871 0.618952
\(204\) 13.8049 0.966538
\(205\) −0.883837 −0.0617299
\(206\) −2.58917 −0.180396
\(207\) 8.89681 0.618371
\(208\) 0.900529 0.0624404
\(209\) −1.85688 −0.128443
\(210\) 5.72472 0.395043
\(211\) 19.2458 1.32493 0.662467 0.749092i \(-0.269510\pi\)
0.662467 + 0.749092i \(0.269510\pi\)
\(212\) 2.00171 0.137478
\(213\) −38.0042 −2.60400
\(214\) 2.64733 0.180968
\(215\) −3.92508 −0.267688
\(216\) −2.50784 −0.170637
\(217\) −15.7434 −1.06873
\(218\) 10.9027 0.738421
\(219\) −34.1486 −2.30755
\(220\) 1.77623 0.119754
\(221\) −4.71522 −0.317180
\(222\) 3.80647 0.255474
\(223\) 8.59672 0.575679 0.287839 0.957679i \(-0.407063\pi\)
0.287839 + 0.957679i \(0.407063\pi\)
\(224\) 2.17132 0.145078
\(225\) 3.95120 0.263413
\(226\) −10.5787 −0.703685
\(227\) −3.91770 −0.260027 −0.130014 0.991512i \(-0.541502\pi\)
−0.130014 + 0.991512i \(0.541502\pi\)
\(228\) −2.75621 −0.182535
\(229\) 1.14916 0.0759389 0.0379695 0.999279i \(-0.487911\pi\)
0.0379695 + 0.999279i \(0.487911\pi\)
\(230\) −2.25167 −0.148471
\(231\) 10.1684 0.669034
\(232\) 4.06145 0.266647
\(233\) −24.9501 −1.63453 −0.817267 0.576259i \(-0.804512\pi\)
−0.817267 + 0.576259i \(0.804512\pi\)
\(234\) 3.55817 0.232605
\(235\) 8.40218 0.548098
\(236\) 1.78596 0.116256
\(237\) −9.29537 −0.603799
\(238\) −11.3692 −0.736953
\(239\) −23.5053 −1.52043 −0.760217 0.649669i \(-0.774908\pi\)
−0.760217 + 0.649669i \(0.774908\pi\)
\(240\) 2.63651 0.170186
\(241\) −22.9813 −1.48036 −0.740179 0.672410i \(-0.765259\pi\)
−0.740179 + 0.672410i \(0.765259\pi\)
\(242\) −7.84499 −0.504295
\(243\) 21.3432 1.36916
\(244\) −13.2270 −0.846774
\(245\) 2.28536 0.146006
\(246\) −2.33025 −0.148571
\(247\) 0.941413 0.0599007
\(248\) −7.25058 −0.460413
\(249\) 46.1993 2.92776
\(250\) −1.00000 −0.0632456
\(251\) −2.85163 −0.179993 −0.0899967 0.995942i \(-0.528686\pi\)
−0.0899967 + 0.995942i \(0.528686\pi\)
\(252\) 8.57932 0.540446
\(253\) −3.99950 −0.251446
\(254\) 8.06671 0.506150
\(255\) −13.8049 −0.864498
\(256\) 1.00000 0.0625000
\(257\) −3.55082 −0.221494 −0.110747 0.993849i \(-0.535324\pi\)
−0.110747 + 0.993849i \(0.535324\pi\)
\(258\) −10.3485 −0.644271
\(259\) −3.13485 −0.194790
\(260\) −0.900529 −0.0558484
\(261\) 16.0476 0.993320
\(262\) 1.41270 0.0872768
\(263\) −9.96034 −0.614181 −0.307090 0.951680i \(-0.599355\pi\)
−0.307090 + 0.951680i \(0.599355\pi\)
\(264\) 4.68306 0.288223
\(265\) −2.00171 −0.122964
\(266\) 2.26990 0.139177
\(267\) 6.96070 0.425988
\(268\) −0.937044 −0.0572391
\(269\) −29.9561 −1.82645 −0.913227 0.407451i \(-0.866418\pi\)
−0.913227 + 0.407451i \(0.866418\pi\)
\(270\) 2.50784 0.152623
\(271\) 26.1179 1.58655 0.793276 0.608863i \(-0.208374\pi\)
0.793276 + 0.608863i \(0.208374\pi\)
\(272\) −5.23605 −0.317482
\(273\) −5.15527 −0.312011
\(274\) −3.87128 −0.233873
\(275\) −1.77623 −0.107111
\(276\) −5.93657 −0.357339
\(277\) −31.1705 −1.87285 −0.936427 0.350861i \(-0.885889\pi\)
−0.936427 + 0.350861i \(0.885889\pi\)
\(278\) −9.98899 −0.599100
\(279\) −28.6485 −1.71514
\(280\) −2.17132 −0.129761
\(281\) −13.8505 −0.826250 −0.413125 0.910674i \(-0.635563\pi\)
−0.413125 + 0.910674i \(0.635563\pi\)
\(282\) 22.1524 1.31916
\(283\) −17.4713 −1.03856 −0.519280 0.854604i \(-0.673800\pi\)
−0.519280 + 0.854604i \(0.673800\pi\)
\(284\) 14.4146 0.855347
\(285\) 2.75621 0.163264
\(286\) −1.59955 −0.0945833
\(287\) 1.91910 0.113281
\(288\) 3.95120 0.232827
\(289\) 10.4163 0.612721
\(290\) −4.06145 −0.238496
\(291\) −4.30031 −0.252089
\(292\) 12.9522 0.757969
\(293\) −18.2160 −1.06419 −0.532096 0.846684i \(-0.678596\pi\)
−0.532096 + 0.846684i \(0.678596\pi\)
\(294\) 6.02539 0.351408
\(295\) −1.78596 −0.103983
\(296\) −1.44375 −0.0839164
\(297\) 4.45452 0.258477
\(298\) 2.81037 0.162801
\(299\) 2.02770 0.117265
\(300\) −2.63651 −0.152219
\(301\) 8.52261 0.491235
\(302\) −11.2886 −0.649584
\(303\) −34.7158 −1.99437
\(304\) 1.04540 0.0599578
\(305\) 13.2270 0.757377
\(306\) −20.6887 −1.18269
\(307\) 9.98595 0.569929 0.284964 0.958538i \(-0.408018\pi\)
0.284964 + 0.958538i \(0.408018\pi\)
\(308\) −3.85677 −0.219760
\(309\) 6.82638 0.388339
\(310\) 7.25058 0.411806
\(311\) 0.172246 0.00976720 0.00488360 0.999988i \(-0.498445\pi\)
0.00488360 + 0.999988i \(0.498445\pi\)
\(312\) −2.37426 −0.134416
\(313\) −27.8800 −1.57587 −0.787935 0.615758i \(-0.788850\pi\)
−0.787935 + 0.615758i \(0.788850\pi\)
\(314\) −10.6219 −0.599428
\(315\) −8.57932 −0.483390
\(316\) 3.52563 0.198332
\(317\) −30.3430 −1.70423 −0.852115 0.523354i \(-0.824680\pi\)
−0.852115 + 0.523354i \(0.824680\pi\)
\(318\) −5.27753 −0.295949
\(319\) −7.21408 −0.403911
\(320\) −1.00000 −0.0559017
\(321\) −6.97971 −0.389569
\(322\) 4.88911 0.272459
\(323\) −5.47377 −0.304569
\(324\) −5.24163 −0.291202
\(325\) 0.900529 0.0499523
\(326\) −16.8717 −0.934436
\(327\) −28.7450 −1.58960
\(328\) 0.883837 0.0488018
\(329\) −18.2438 −1.00581
\(330\) −4.68306 −0.257794
\(331\) 27.0931 1.48917 0.744587 0.667526i \(-0.232647\pi\)
0.744587 + 0.667526i \(0.232647\pi\)
\(332\) −17.5229 −0.961693
\(333\) −5.70455 −0.312607
\(334\) −7.27037 −0.397817
\(335\) 0.937044 0.0511962
\(336\) −5.72472 −0.312309
\(337\) 24.6657 1.34363 0.671814 0.740720i \(-0.265516\pi\)
0.671814 + 0.740720i \(0.265516\pi\)
\(338\) −12.1890 −0.662997
\(339\) 27.8909 1.51482
\(340\) 5.23605 0.283965
\(341\) 12.8787 0.697422
\(342\) 4.13058 0.223356
\(343\) −20.1615 −1.08862
\(344\) 3.92508 0.211626
\(345\) 5.93657 0.319614
\(346\) −15.6152 −0.839478
\(347\) 25.1247 1.34876 0.674382 0.738383i \(-0.264410\pi\)
0.674382 + 0.738383i \(0.264410\pi\)
\(348\) −10.7081 −0.574012
\(349\) 23.8129 1.27467 0.637337 0.770585i \(-0.280036\pi\)
0.637337 + 0.770585i \(0.280036\pi\)
\(350\) 2.17132 0.116062
\(351\) −2.25839 −0.120544
\(352\) −1.77623 −0.0946736
\(353\) 12.0812 0.643016 0.321508 0.946907i \(-0.395810\pi\)
0.321508 + 0.946907i \(0.395810\pi\)
\(354\) −4.70871 −0.250265
\(355\) −14.4146 −0.765046
\(356\) −2.64012 −0.139926
\(357\) 29.9749 1.58644
\(358\) 20.0642 1.06043
\(359\) −24.6600 −1.30150 −0.650752 0.759290i \(-0.725546\pi\)
−0.650752 + 0.759290i \(0.725546\pi\)
\(360\) −3.95120 −0.208246
\(361\) −17.9071 −0.942481
\(362\) 18.1864 0.955855
\(363\) 20.6834 1.08560
\(364\) 1.95534 0.102488
\(365\) −12.9522 −0.677948
\(366\) 34.8732 1.82285
\(367\) 7.31637 0.381911 0.190956 0.981599i \(-0.438841\pi\)
0.190956 + 0.981599i \(0.438841\pi\)
\(368\) 2.25167 0.117377
\(369\) 3.49222 0.181798
\(370\) 1.44375 0.0750571
\(371\) 4.34636 0.225652
\(372\) 19.1163 0.991132
\(373\) −13.8046 −0.714776 −0.357388 0.933956i \(-0.616333\pi\)
−0.357388 + 0.933956i \(0.616333\pi\)
\(374\) 9.30046 0.480915
\(375\) 2.63651 0.136149
\(376\) −8.40218 −0.433309
\(377\) 3.65745 0.188368
\(378\) −5.44534 −0.280078
\(379\) 19.7863 1.01636 0.508178 0.861252i \(-0.330319\pi\)
0.508178 + 0.861252i \(0.330319\pi\)
\(380\) −1.04540 −0.0536279
\(381\) −21.2680 −1.08959
\(382\) −12.7274 −0.651190
\(383\) −29.8608 −1.52582 −0.762908 0.646507i \(-0.776229\pi\)
−0.762908 + 0.646507i \(0.776229\pi\)
\(384\) −2.63651 −0.134544
\(385\) 3.85677 0.196559
\(386\) 2.05041 0.104363
\(387\) 15.5088 0.788355
\(388\) 1.63106 0.0828045
\(389\) −18.9990 −0.963289 −0.481644 0.876367i \(-0.659960\pi\)
−0.481644 + 0.876367i \(0.659960\pi\)
\(390\) 2.37426 0.120225
\(391\) −11.7899 −0.596240
\(392\) −2.28536 −0.115428
\(393\) −3.72460 −0.187881
\(394\) −17.8327 −0.898400
\(395\) −3.52563 −0.177394
\(396\) −7.01825 −0.352680
\(397\) 6.87745 0.345169 0.172585 0.984995i \(-0.444788\pi\)
0.172585 + 0.984995i \(0.444788\pi\)
\(398\) −6.63145 −0.332405
\(399\) −5.98462 −0.299606
\(400\) 1.00000 0.0500000
\(401\) −8.89445 −0.444168 −0.222084 0.975028i \(-0.571286\pi\)
−0.222084 + 0.975028i \(0.571286\pi\)
\(402\) 2.47053 0.123219
\(403\) −6.52936 −0.325251
\(404\) 13.1673 0.655099
\(405\) 5.24163 0.260459
\(406\) 8.81871 0.437665
\(407\) 2.56444 0.127115
\(408\) 13.8049 0.683445
\(409\) −10.7251 −0.530323 −0.265162 0.964204i \(-0.585425\pi\)
−0.265162 + 0.964204i \(0.585425\pi\)
\(410\) −0.883837 −0.0436496
\(411\) 10.2067 0.503459
\(412\) −2.58917 −0.127559
\(413\) 3.87790 0.190819
\(414\) 8.89681 0.437254
\(415\) 17.5229 0.860165
\(416\) 0.900529 0.0441521
\(417\) 26.3361 1.28968
\(418\) −1.85688 −0.0908227
\(419\) −24.4326 −1.19361 −0.596805 0.802386i \(-0.703563\pi\)
−0.596805 + 0.802386i \(0.703563\pi\)
\(420\) 5.72472 0.279338
\(421\) 31.6170 1.54092 0.770459 0.637489i \(-0.220027\pi\)
0.770459 + 0.637489i \(0.220027\pi\)
\(422\) 19.2458 0.936869
\(423\) −33.1987 −1.61417
\(424\) 2.00171 0.0972116
\(425\) −5.23605 −0.253986
\(426\) −38.0042 −1.84131
\(427\) −28.7201 −1.38986
\(428\) 2.64733 0.127963
\(429\) 4.21723 0.203610
\(430\) −3.92508 −0.189284
\(431\) −38.0324 −1.83196 −0.915979 0.401226i \(-0.868584\pi\)
−0.915979 + 0.401226i \(0.868584\pi\)
\(432\) −2.50784 −0.120659
\(433\) 28.5182 1.37050 0.685248 0.728310i \(-0.259694\pi\)
0.685248 + 0.728310i \(0.259694\pi\)
\(434\) −15.7434 −0.755705
\(435\) 10.7081 0.513412
\(436\) 10.9027 0.522143
\(437\) 2.35390 0.112602
\(438\) −34.1486 −1.63168
\(439\) −2.50649 −0.119628 −0.0598141 0.998210i \(-0.519051\pi\)
−0.0598141 + 0.998210i \(0.519051\pi\)
\(440\) 1.77623 0.0846786
\(441\) −9.02992 −0.429996
\(442\) −4.71522 −0.224280
\(443\) −35.3204 −1.67812 −0.839061 0.544038i \(-0.816895\pi\)
−0.839061 + 0.544038i \(0.816895\pi\)
\(444\) 3.80647 0.180647
\(445\) 2.64012 0.125154
\(446\) 8.59672 0.407066
\(447\) −7.40958 −0.350461
\(448\) 2.17132 0.102585
\(449\) −24.4328 −1.15306 −0.576528 0.817077i \(-0.695593\pi\)
−0.576528 + 0.817077i \(0.695593\pi\)
\(450\) 3.95120 0.186261
\(451\) −1.56990 −0.0739238
\(452\) −10.5787 −0.497580
\(453\) 29.7624 1.39836
\(454\) −3.91770 −0.183867
\(455\) −1.95534 −0.0916676
\(456\) −2.75621 −0.129071
\(457\) −20.9258 −0.978865 −0.489433 0.872041i \(-0.662796\pi\)
−0.489433 + 0.872041i \(0.662796\pi\)
\(458\) 1.14916 0.0536969
\(459\) 13.1312 0.612912
\(460\) −2.25167 −0.104985
\(461\) 8.09838 0.377179 0.188590 0.982056i \(-0.439608\pi\)
0.188590 + 0.982056i \(0.439608\pi\)
\(462\) 10.1684 0.473078
\(463\) −33.1924 −1.54258 −0.771291 0.636483i \(-0.780389\pi\)
−0.771291 + 0.636483i \(0.780389\pi\)
\(464\) 4.06145 0.188548
\(465\) −19.1163 −0.886495
\(466\) −24.9501 −1.15579
\(467\) 0.450355 0.0208399 0.0104200 0.999946i \(-0.496683\pi\)
0.0104200 + 0.999946i \(0.496683\pi\)
\(468\) 3.55817 0.164476
\(469\) −2.03462 −0.0939502
\(470\) 8.40218 0.387564
\(471\) 28.0047 1.29039
\(472\) 1.78596 0.0822055
\(473\) −6.97186 −0.320566
\(474\) −9.29537 −0.426951
\(475\) 1.04540 0.0479663
\(476\) −11.3692 −0.521104
\(477\) 7.90915 0.362135
\(478\) −23.5053 −1.07511
\(479\) 20.8688 0.953518 0.476759 0.879034i \(-0.341811\pi\)
0.476759 + 0.879034i \(0.341811\pi\)
\(480\) 2.63651 0.120340
\(481\) −1.30014 −0.0592813
\(482\) −22.9813 −1.04677
\(483\) −12.8902 −0.586524
\(484\) −7.84499 −0.356591
\(485\) −1.63106 −0.0740626
\(486\) 21.3432 0.968145
\(487\) 30.3844 1.37685 0.688425 0.725308i \(-0.258302\pi\)
0.688425 + 0.725308i \(0.258302\pi\)
\(488\) −13.2270 −0.598759
\(489\) 44.4824 2.01156
\(490\) 2.28536 0.103242
\(491\) 25.3306 1.14316 0.571578 0.820548i \(-0.306331\pi\)
0.571578 + 0.820548i \(0.306331\pi\)
\(492\) −2.33025 −0.105056
\(493\) −21.2660 −0.957771
\(494\) 0.941413 0.0423562
\(495\) 7.01825 0.315447
\(496\) −7.25058 −0.325561
\(497\) 31.2987 1.40394
\(498\) 46.1993 2.07024
\(499\) 0.774573 0.0346747 0.0173373 0.999850i \(-0.494481\pi\)
0.0173373 + 0.999850i \(0.494481\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 19.1684 0.856381
\(502\) −2.85163 −0.127275
\(503\) 21.7716 0.970749 0.485375 0.874306i \(-0.338683\pi\)
0.485375 + 0.874306i \(0.338683\pi\)
\(504\) 8.57932 0.382153
\(505\) −13.1673 −0.585938
\(506\) −3.99950 −0.177799
\(507\) 32.1366 1.42724
\(508\) 8.06671 0.357902
\(509\) −10.5944 −0.469590 −0.234795 0.972045i \(-0.575442\pi\)
−0.234795 + 0.972045i \(0.575442\pi\)
\(510\) −13.8049 −0.611292
\(511\) 28.1234 1.24410
\(512\) 1.00000 0.0441942
\(513\) −2.62170 −0.115751
\(514\) −3.55082 −0.156620
\(515\) 2.58917 0.114093
\(516\) −10.3485 −0.455568
\(517\) 14.9242 0.656367
\(518\) −3.13485 −0.137737
\(519\) 41.1697 1.80715
\(520\) −0.900529 −0.0394908
\(521\) −2.62266 −0.114901 −0.0574504 0.998348i \(-0.518297\pi\)
−0.0574504 + 0.998348i \(0.518297\pi\)
\(522\) 16.0476 0.702384
\(523\) 29.2273 1.27802 0.639009 0.769199i \(-0.279345\pi\)
0.639009 + 0.769199i \(0.279345\pi\)
\(524\) 1.41270 0.0617140
\(525\) −5.72472 −0.249847
\(526\) −9.96034 −0.434292
\(527\) 37.9645 1.65376
\(528\) 4.68306 0.203804
\(529\) −17.9300 −0.779564
\(530\) −2.00171 −0.0869487
\(531\) 7.05669 0.306234
\(532\) 2.26990 0.0984127
\(533\) 0.795921 0.0344752
\(534\) 6.96070 0.301219
\(535\) −2.64733 −0.114454
\(536\) −0.937044 −0.0404742
\(537\) −52.8996 −2.28279
\(538\) −29.9561 −1.29150
\(539\) 4.05934 0.174848
\(540\) 2.50784 0.107920
\(541\) 6.36416 0.273616 0.136808 0.990598i \(-0.456316\pi\)
0.136808 + 0.990598i \(0.456316\pi\)
\(542\) 26.1179 1.12186
\(543\) −47.9486 −2.05767
\(544\) −5.23605 −0.224494
\(545\) −10.9027 −0.467018
\(546\) −5.15527 −0.220625
\(547\) −23.9127 −1.02243 −0.511216 0.859452i \(-0.670805\pi\)
−0.511216 + 0.859452i \(0.670805\pi\)
\(548\) −3.87128 −0.165373
\(549\) −52.2626 −2.23051
\(550\) −1.77623 −0.0757389
\(551\) 4.24584 0.180879
\(552\) −5.93657 −0.252677
\(553\) 7.65528 0.325536
\(554\) −31.1705 −1.32431
\(555\) −3.80647 −0.161576
\(556\) −9.98899 −0.423628
\(557\) 25.9381 1.09903 0.549516 0.835483i \(-0.314812\pi\)
0.549516 + 0.835483i \(0.314812\pi\)
\(558\) −28.6485 −1.21279
\(559\) 3.53465 0.149500
\(560\) −2.17132 −0.0917551
\(561\) −24.5208 −1.03527
\(562\) −13.8505 −0.584247
\(563\) −11.0540 −0.465869 −0.232934 0.972492i \(-0.574833\pi\)
−0.232934 + 0.972492i \(0.574833\pi\)
\(564\) 22.1524 0.932786
\(565\) 10.5787 0.445049
\(566\) −17.4713 −0.734373
\(567\) −11.3813 −0.477968
\(568\) 14.4146 0.604822
\(569\) −0.786619 −0.0329768 −0.0164884 0.999864i \(-0.505249\pi\)
−0.0164884 + 0.999864i \(0.505249\pi\)
\(570\) 2.75621 0.115445
\(571\) 27.4530 1.14887 0.574435 0.818550i \(-0.305222\pi\)
0.574435 + 0.818550i \(0.305222\pi\)
\(572\) −1.59955 −0.0668805
\(573\) 33.5559 1.40182
\(574\) 1.91910 0.0801015
\(575\) 2.25167 0.0939013
\(576\) 3.95120 0.164633
\(577\) 0.759900 0.0316350 0.0158175 0.999875i \(-0.494965\pi\)
0.0158175 + 0.999875i \(0.494965\pi\)
\(578\) 10.4163 0.433259
\(579\) −5.40592 −0.224662
\(580\) −4.06145 −0.168642
\(581\) −38.0478 −1.57849
\(582\) −4.30031 −0.178254
\(583\) −3.55550 −0.147254
\(584\) 12.9522 0.535965
\(585\) −3.55817 −0.147112
\(586\) −18.2160 −0.752498
\(587\) −20.6196 −0.851063 −0.425531 0.904944i \(-0.639913\pi\)
−0.425531 + 0.904944i \(0.639913\pi\)
\(588\) 6.02539 0.248483
\(589\) −7.57976 −0.312319
\(590\) −1.78596 −0.0735269
\(591\) 47.0162 1.93399
\(592\) −1.44375 −0.0593378
\(593\) −46.5255 −1.91057 −0.955286 0.295682i \(-0.904453\pi\)
−0.955286 + 0.295682i \(0.904453\pi\)
\(594\) 4.45452 0.182771
\(595\) 11.3692 0.466090
\(596\) 2.81037 0.115117
\(597\) 17.4839 0.715569
\(598\) 2.02770 0.0829187
\(599\) 2.85734 0.116748 0.0583740 0.998295i \(-0.481408\pi\)
0.0583740 + 0.998295i \(0.481408\pi\)
\(600\) −2.63651 −0.107635
\(601\) 1.00000 0.0407909
\(602\) 8.52261 0.347356
\(603\) −3.70245 −0.150775
\(604\) −11.2886 −0.459325
\(605\) 7.84499 0.318944
\(606\) −34.7158 −1.41023
\(607\) −4.60050 −0.186728 −0.0933642 0.995632i \(-0.529762\pi\)
−0.0933642 + 0.995632i \(0.529762\pi\)
\(608\) 1.04540 0.0423966
\(609\) −23.2506 −0.942163
\(610\) 13.2270 0.535547
\(611\) −7.56640 −0.306104
\(612\) −20.6887 −0.836291
\(613\) 8.65659 0.349636 0.174818 0.984601i \(-0.444066\pi\)
0.174818 + 0.984601i \(0.444066\pi\)
\(614\) 9.98595 0.403000
\(615\) 2.33025 0.0939647
\(616\) −3.85677 −0.155394
\(617\) 31.2527 1.25819 0.629093 0.777330i \(-0.283426\pi\)
0.629093 + 0.777330i \(0.283426\pi\)
\(618\) 6.82638 0.274597
\(619\) −6.63931 −0.266856 −0.133428 0.991058i \(-0.542599\pi\)
−0.133428 + 0.991058i \(0.542599\pi\)
\(620\) 7.25058 0.291190
\(621\) −5.64685 −0.226600
\(622\) 0.172246 0.00690645
\(623\) −5.73254 −0.229670
\(624\) −2.37426 −0.0950463
\(625\) 1.00000 0.0400000
\(626\) −27.8800 −1.11431
\(627\) 4.89568 0.195514
\(628\) −10.6219 −0.423859
\(629\) 7.55956 0.301420
\(630\) −8.57932 −0.341808
\(631\) 23.2236 0.924519 0.462259 0.886745i \(-0.347039\pi\)
0.462259 + 0.886745i \(0.347039\pi\)
\(632\) 3.52563 0.140242
\(633\) −50.7417 −2.01680
\(634\) −30.3430 −1.20507
\(635\) −8.06671 −0.320118
\(636\) −5.27753 −0.209268
\(637\) −2.05803 −0.0815423
\(638\) −7.21408 −0.285608
\(639\) 56.9548 2.25310
\(640\) −1.00000 −0.0395285
\(641\) 2.38410 0.0941663 0.0470831 0.998891i \(-0.485007\pi\)
0.0470831 + 0.998891i \(0.485007\pi\)
\(642\) −6.97971 −0.275467
\(643\) 30.8278 1.21573 0.607864 0.794041i \(-0.292026\pi\)
0.607864 + 0.794041i \(0.292026\pi\)
\(644\) 4.88911 0.192658
\(645\) 10.3485 0.407472
\(646\) −5.47377 −0.215363
\(647\) 14.0342 0.551742 0.275871 0.961195i \(-0.411034\pi\)
0.275871 + 0.961195i \(0.411034\pi\)
\(648\) −5.24163 −0.205911
\(649\) −3.17228 −0.124523
\(650\) 0.900529 0.0353216
\(651\) 41.5075 1.62681
\(652\) −16.8717 −0.660746
\(653\) 3.78451 0.148099 0.0740497 0.997255i \(-0.476408\pi\)
0.0740497 + 0.997255i \(0.476408\pi\)
\(654\) −28.7450 −1.12402
\(655\) −1.41270 −0.0551987
\(656\) 0.883837 0.0345081
\(657\) 51.1766 1.99659
\(658\) −18.2438 −0.711218
\(659\) 35.2237 1.37212 0.686061 0.727544i \(-0.259338\pi\)
0.686061 + 0.727544i \(0.259338\pi\)
\(660\) −4.68306 −0.182288
\(661\) 27.7448 1.07915 0.539575 0.841938i \(-0.318585\pi\)
0.539575 + 0.841938i \(0.318585\pi\)
\(662\) 27.0931 1.05300
\(663\) 12.4317 0.482808
\(664\) −17.5229 −0.680020
\(665\) −2.26990 −0.0880230
\(666\) −5.70455 −0.221047
\(667\) 9.14506 0.354098
\(668\) −7.27037 −0.281299
\(669\) −22.6654 −0.876293
\(670\) 0.937044 0.0362012
\(671\) 23.4943 0.906987
\(672\) −5.72472 −0.220836
\(673\) 37.6678 1.45199 0.725994 0.687702i \(-0.241380\pi\)
0.725994 + 0.687702i \(0.241380\pi\)
\(674\) 24.6657 0.950088
\(675\) −2.50784 −0.0965270
\(676\) −12.1890 −0.468810
\(677\) −22.2553 −0.855341 −0.427671 0.903935i \(-0.640666\pi\)
−0.427671 + 0.903935i \(0.640666\pi\)
\(678\) 27.8909 1.07114
\(679\) 3.54156 0.135912
\(680\) 5.23605 0.200794
\(681\) 10.3291 0.395811
\(682\) 12.8787 0.493152
\(683\) −23.4223 −0.896228 −0.448114 0.893976i \(-0.647904\pi\)
−0.448114 + 0.893976i \(0.647904\pi\)
\(684\) 4.13058 0.157937
\(685\) 3.87128 0.147914
\(686\) −20.1615 −0.769770
\(687\) −3.02979 −0.115594
\(688\) 3.92508 0.149642
\(689\) 1.80260 0.0686735
\(690\) 5.93657 0.226001
\(691\) 4.84037 0.184136 0.0920681 0.995753i \(-0.470652\pi\)
0.0920681 + 0.995753i \(0.470652\pi\)
\(692\) −15.6152 −0.593601
\(693\) −15.2389 −0.578877
\(694\) 25.1247 0.953720
\(695\) 9.98899 0.378904
\(696\) −10.7081 −0.405888
\(697\) −4.62782 −0.175291
\(698\) 23.8129 0.901331
\(699\) 65.7812 2.48807
\(700\) 2.17132 0.0820682
\(701\) 4.91616 0.185681 0.0928404 0.995681i \(-0.470405\pi\)
0.0928404 + 0.995681i \(0.470405\pi\)
\(702\) −2.25839 −0.0852373
\(703\) −1.50930 −0.0569243
\(704\) −1.77623 −0.0669443
\(705\) −22.1524 −0.834309
\(706\) 12.0812 0.454681
\(707\) 28.5905 1.07526
\(708\) −4.70871 −0.176964
\(709\) 27.7789 1.04326 0.521629 0.853173i \(-0.325325\pi\)
0.521629 + 0.853173i \(0.325325\pi\)
\(710\) −14.4146 −0.540969
\(711\) 13.9305 0.522433
\(712\) −2.64012 −0.0989426
\(713\) −16.3260 −0.611412
\(714\) 29.9749 1.12178
\(715\) 1.59955 0.0598198
\(716\) 20.0642 0.749836
\(717\) 61.9721 2.31439
\(718\) −24.6600 −0.920303
\(719\) 30.6066 1.14143 0.570716 0.821147i \(-0.306666\pi\)
0.570716 + 0.821147i \(0.306666\pi\)
\(720\) −3.95120 −0.147252
\(721\) −5.62193 −0.209371
\(722\) −17.9071 −0.666435
\(723\) 60.5906 2.25339
\(724\) 18.1864 0.675892
\(725\) 4.06145 0.150838
\(726\) 20.6834 0.767634
\(727\) −18.2848 −0.678147 −0.339074 0.940760i \(-0.610114\pi\)
−0.339074 + 0.940760i \(0.610114\pi\)
\(728\) 1.95534 0.0724696
\(729\) −40.5466 −1.50173
\(730\) −12.9522 −0.479382
\(731\) −20.5519 −0.760140
\(732\) 34.8732 1.28895
\(733\) 20.8955 0.771791 0.385896 0.922542i \(-0.373892\pi\)
0.385896 + 0.922542i \(0.373892\pi\)
\(734\) 7.31637 0.270052
\(735\) −6.02539 −0.222250
\(736\) 2.25167 0.0829978
\(737\) 1.66441 0.0613093
\(738\) 3.49222 0.128550
\(739\) −15.9178 −0.585546 −0.292773 0.956182i \(-0.594578\pi\)
−0.292773 + 0.956182i \(0.594578\pi\)
\(740\) 1.44375 0.0530734
\(741\) −2.48205 −0.0911803
\(742\) 4.34636 0.159560
\(743\) 19.6056 0.719258 0.359629 0.933095i \(-0.382903\pi\)
0.359629 + 0.933095i \(0.382903\pi\)
\(744\) 19.1163 0.700836
\(745\) −2.81037 −0.102964
\(746\) −13.8046 −0.505423
\(747\) −69.2364 −2.53323
\(748\) 9.30046 0.340058
\(749\) 5.74820 0.210035
\(750\) 2.63651 0.0962718
\(751\) 47.6108 1.73734 0.868672 0.495387i \(-0.164974\pi\)
0.868672 + 0.495387i \(0.164974\pi\)
\(752\) −8.40218 −0.306396
\(753\) 7.51836 0.273984
\(754\) 3.65745 0.133196
\(755\) 11.2886 0.410833
\(756\) −5.44534 −0.198045
\(757\) 9.83741 0.357547 0.178773 0.983890i \(-0.442787\pi\)
0.178773 + 0.983890i \(0.442787\pi\)
\(758\) 19.7863 0.718672
\(759\) 10.5447 0.382749
\(760\) −1.04540 −0.0379207
\(761\) −31.8608 −1.15495 −0.577477 0.816407i \(-0.695963\pi\)
−0.577477 + 0.816407i \(0.695963\pi\)
\(762\) −21.2680 −0.770458
\(763\) 23.6732 0.857026
\(764\) −12.7274 −0.460461
\(765\) 20.6887 0.748001
\(766\) −29.8608 −1.07891
\(767\) 1.60831 0.0580727
\(768\) −2.63651 −0.0951369
\(769\) −23.7125 −0.855093 −0.427546 0.903993i \(-0.640622\pi\)
−0.427546 + 0.903993i \(0.640622\pi\)
\(770\) 3.85677 0.138989
\(771\) 9.36177 0.337156
\(772\) 2.05041 0.0737957
\(773\) −16.9672 −0.610269 −0.305135 0.952309i \(-0.598701\pi\)
−0.305135 + 0.952309i \(0.598701\pi\)
\(774\) 15.5088 0.557451
\(775\) −7.25058 −0.260449
\(776\) 1.63106 0.0585516
\(777\) 8.26507 0.296508
\(778\) −18.9990 −0.681148
\(779\) 0.923964 0.0331044
\(780\) 2.37426 0.0850120
\(781\) −25.6036 −0.916170
\(782\) −11.7899 −0.421606
\(783\) −10.1855 −0.363999
\(784\) −2.28536 −0.0816201
\(785\) 10.6219 0.379111
\(786\) −3.72460 −0.132852
\(787\) 21.8966 0.780528 0.390264 0.920703i \(-0.372384\pi\)
0.390264 + 0.920703i \(0.372384\pi\)
\(788\) −17.8327 −0.635265
\(789\) 26.2606 0.934901
\(790\) −3.52563 −0.125436
\(791\) −22.9698 −0.816711
\(792\) −7.01825 −0.249383
\(793\) −11.9113 −0.422983
\(794\) 6.87745 0.244071
\(795\) 5.27753 0.187175
\(796\) −6.63145 −0.235046
\(797\) −12.2229 −0.432956 −0.216478 0.976287i \(-0.569457\pi\)
−0.216478 + 0.976287i \(0.569457\pi\)
\(798\) −5.98462 −0.211853
\(799\) 43.9943 1.55640
\(800\) 1.00000 0.0353553
\(801\) −10.4316 −0.368583
\(802\) −8.89445 −0.314074
\(803\) −23.0061 −0.811868
\(804\) 2.47053 0.0871288
\(805\) −4.88911 −0.172318
\(806\) −6.52936 −0.229987
\(807\) 78.9796 2.78021
\(808\) 13.1673 0.463225
\(809\) −24.7125 −0.868846 −0.434423 0.900709i \(-0.643048\pi\)
−0.434423 + 0.900709i \(0.643048\pi\)
\(810\) 5.24163 0.184172
\(811\) 48.0885 1.68862 0.844309 0.535857i \(-0.180011\pi\)
0.844309 + 0.535857i \(0.180011\pi\)
\(812\) 8.81871 0.309476
\(813\) −68.8603 −2.41503
\(814\) 2.56444 0.0898836
\(815\) 16.8717 0.590989
\(816\) 13.8049 0.483269
\(817\) 4.10328 0.143556
\(818\) −10.7251 −0.374995
\(819\) 7.72592 0.269966
\(820\) −0.883837 −0.0308649
\(821\) 8.96380 0.312839 0.156419 0.987691i \(-0.450005\pi\)
0.156419 + 0.987691i \(0.450005\pi\)
\(822\) 10.2067 0.355999
\(823\) 23.8389 0.830973 0.415486 0.909599i \(-0.363611\pi\)
0.415486 + 0.909599i \(0.363611\pi\)
\(824\) −2.58917 −0.0901981
\(825\) 4.68306 0.163043
\(826\) 3.87790 0.134929
\(827\) 1.26283 0.0439128 0.0219564 0.999759i \(-0.493011\pi\)
0.0219564 + 0.999759i \(0.493011\pi\)
\(828\) 8.89681 0.309185
\(829\) −8.90497 −0.309282 −0.154641 0.987971i \(-0.549422\pi\)
−0.154641 + 0.987971i \(0.549422\pi\)
\(830\) 17.5229 0.608228
\(831\) 82.1815 2.85084
\(832\) 0.900529 0.0312202
\(833\) 11.9663 0.414607
\(834\) 26.3361 0.911944
\(835\) 7.27037 0.251601
\(836\) −1.85688 −0.0642214
\(837\) 18.1833 0.628508
\(838\) −24.4326 −0.844009
\(839\) 12.5029 0.431649 0.215824 0.976432i \(-0.430756\pi\)
0.215824 + 0.976432i \(0.430756\pi\)
\(840\) 5.72472 0.197521
\(841\) −12.5046 −0.431195
\(842\) 31.6170 1.08959
\(843\) 36.5170 1.25771
\(844\) 19.2458 0.662467
\(845\) 12.1890 0.419316
\(846\) −33.1987 −1.14139
\(847\) −17.0340 −0.585295
\(848\) 2.00171 0.0687390
\(849\) 46.0632 1.58089
\(850\) −5.23605 −0.179595
\(851\) −3.25086 −0.111438
\(852\) −38.0042 −1.30200
\(853\) −40.3463 −1.38143 −0.690716 0.723126i \(-0.742705\pi\)
−0.690716 + 0.723126i \(0.742705\pi\)
\(854\) −28.7201 −0.982783
\(855\) −4.13058 −0.141263
\(856\) 2.64733 0.0904838
\(857\) 17.1256 0.584999 0.292500 0.956266i \(-0.405513\pi\)
0.292500 + 0.956266i \(0.405513\pi\)
\(858\) 4.21723 0.143974
\(859\) −4.28665 −0.146259 −0.0731293 0.997322i \(-0.523299\pi\)
−0.0731293 + 0.997322i \(0.523299\pi\)
\(860\) −3.92508 −0.133844
\(861\) −5.05972 −0.172435
\(862\) −38.0324 −1.29539
\(863\) 23.5022 0.800025 0.400013 0.916510i \(-0.369006\pi\)
0.400013 + 0.916510i \(0.369006\pi\)
\(864\) −2.50784 −0.0853186
\(865\) 15.6152 0.530933
\(866\) 28.5182 0.969087
\(867\) −27.4626 −0.932679
\(868\) −15.7434 −0.534364
\(869\) −6.26234 −0.212435
\(870\) 10.7081 0.363037
\(871\) −0.843835 −0.0285923
\(872\) 10.9027 0.369211
\(873\) 6.44464 0.218118
\(874\) 2.35390 0.0796219
\(875\) −2.17132 −0.0734041
\(876\) −34.1486 −1.15377
\(877\) −40.4065 −1.36443 −0.682215 0.731152i \(-0.738983\pi\)
−0.682215 + 0.731152i \(0.738983\pi\)
\(878\) −2.50649 −0.0845899
\(879\) 48.0268 1.61990
\(880\) 1.77623 0.0598768
\(881\) −23.8372 −0.803094 −0.401547 0.915838i \(-0.631527\pi\)
−0.401547 + 0.915838i \(0.631527\pi\)
\(882\) −9.02992 −0.304053
\(883\) 16.9901 0.571763 0.285881 0.958265i \(-0.407714\pi\)
0.285881 + 0.958265i \(0.407714\pi\)
\(884\) −4.71522 −0.158590
\(885\) 4.70871 0.158282
\(886\) −35.3204 −1.18661
\(887\) 30.9578 1.03946 0.519730 0.854331i \(-0.326033\pi\)
0.519730 + 0.854331i \(0.326033\pi\)
\(888\) 3.80647 0.127737
\(889\) 17.5154 0.587448
\(890\) 2.64012 0.0884969
\(891\) 9.31036 0.311909
\(892\) 8.59672 0.287839
\(893\) −8.78364 −0.293933
\(894\) −7.40958 −0.247814
\(895\) −20.0642 −0.670673
\(896\) 2.17132 0.0725388
\(897\) −5.34605 −0.178499
\(898\) −24.4328 −0.815334
\(899\) −29.4479 −0.982141
\(900\) 3.95120 0.131707
\(901\) −10.4811 −0.349175
\(902\) −1.56990 −0.0522720
\(903\) −22.4700 −0.747753
\(904\) −10.5787 −0.351842
\(905\) −18.1864 −0.604536
\(906\) 29.7624 0.988791
\(907\) −33.2719 −1.10478 −0.552388 0.833587i \(-0.686283\pi\)
−0.552388 + 0.833587i \(0.686283\pi\)
\(908\) −3.91770 −0.130014
\(909\) 52.0267 1.72562
\(910\) −1.95534 −0.0648188
\(911\) 29.7923 0.987064 0.493532 0.869728i \(-0.335706\pi\)
0.493532 + 0.869728i \(0.335706\pi\)
\(912\) −2.75621 −0.0912673
\(913\) 31.1247 1.03008
\(914\) −20.9258 −0.692162
\(915\) −34.8732 −1.15287
\(916\) 1.14916 0.0379695
\(917\) 3.06742 0.101295
\(918\) 13.1312 0.433394
\(919\) 24.9119 0.821769 0.410885 0.911687i \(-0.365220\pi\)
0.410885 + 0.911687i \(0.365220\pi\)
\(920\) −2.25167 −0.0742355
\(921\) −26.3281 −0.867540
\(922\) 8.09838 0.266706
\(923\) 12.9807 0.427266
\(924\) 10.1684 0.334517
\(925\) −1.44375 −0.0474703
\(926\) −33.1924 −1.09077
\(927\) −10.2303 −0.336008
\(928\) 4.06145 0.133324
\(929\) 21.3235 0.699603 0.349801 0.936824i \(-0.386249\pi\)
0.349801 + 0.936824i \(0.386249\pi\)
\(930\) −19.1163 −0.626847
\(931\) −2.38912 −0.0783002
\(932\) −24.9501 −0.817267
\(933\) −0.454130 −0.0148675
\(934\) 0.450355 0.0147361
\(935\) −9.30046 −0.304157
\(936\) 3.55817 0.116302
\(937\) −10.3958 −0.339616 −0.169808 0.985477i \(-0.554315\pi\)
−0.169808 + 0.985477i \(0.554315\pi\)
\(938\) −2.03462 −0.0664329
\(939\) 73.5060 2.39878
\(940\) 8.40218 0.274049
\(941\) 31.5844 1.02962 0.514811 0.857304i \(-0.327862\pi\)
0.514811 + 0.857304i \(0.327862\pi\)
\(942\) 28.0047 0.912443
\(943\) 1.99011 0.0648070
\(944\) 1.78596 0.0581281
\(945\) 5.44534 0.177137
\(946\) −6.97186 −0.226675
\(947\) −33.6642 −1.09394 −0.546970 0.837152i \(-0.684219\pi\)
−0.546970 + 0.837152i \(0.684219\pi\)
\(948\) −9.29537 −0.301900
\(949\) 11.6638 0.378623
\(950\) 1.04540 0.0339173
\(951\) 79.9996 2.59416
\(952\) −11.3692 −0.368477
\(953\) −10.7582 −0.348491 −0.174246 0.984702i \(-0.555749\pi\)
−0.174246 + 0.984702i \(0.555749\pi\)
\(954\) 7.90915 0.256068
\(955\) 12.7274 0.411849
\(956\) −23.5053 −0.760217
\(957\) 19.0200 0.614830
\(958\) 20.8688 0.674239
\(959\) −8.40580 −0.271437
\(960\) 2.63651 0.0850931
\(961\) 21.5710 0.695838
\(962\) −1.30014 −0.0419182
\(963\) 10.4601 0.337072
\(964\) −22.9813 −0.740179
\(965\) −2.05041 −0.0660049
\(966\) −12.8902 −0.414735
\(967\) −22.0062 −0.707673 −0.353837 0.935307i \(-0.615123\pi\)
−0.353837 + 0.935307i \(0.615123\pi\)
\(968\) −7.84499 −0.252148
\(969\) 14.4317 0.463612
\(970\) −1.63106 −0.0523702
\(971\) −7.05416 −0.226379 −0.113189 0.993573i \(-0.536107\pi\)
−0.113189 + 0.993573i \(0.536107\pi\)
\(972\) 21.3432 0.684582
\(973\) −21.6893 −0.695327
\(974\) 30.3844 0.973580
\(975\) −2.37426 −0.0760370
\(976\) −13.2270 −0.423387
\(977\) −18.2423 −0.583624 −0.291812 0.956476i \(-0.594258\pi\)
−0.291812 + 0.956476i \(0.594258\pi\)
\(978\) 44.4824 1.42239
\(979\) 4.68947 0.149876
\(980\) 2.28536 0.0730032
\(981\) 43.0785 1.37539
\(982\) 25.3306 0.808333
\(983\) −39.7802 −1.26879 −0.634396 0.773008i \(-0.718751\pi\)
−0.634396 + 0.773008i \(0.718751\pi\)
\(984\) −2.33025 −0.0742856
\(985\) 17.8327 0.568198
\(986\) −21.2660 −0.677246
\(987\) 48.1001 1.53104
\(988\) 0.941413 0.0299503
\(989\) 8.83800 0.281032
\(990\) 7.01825 0.223055
\(991\) −49.8743 −1.58431 −0.792155 0.610320i \(-0.791041\pi\)
−0.792155 + 0.610320i \(0.791041\pi\)
\(992\) −7.25058 −0.230206
\(993\) −71.4314 −2.26681
\(994\) 31.2987 0.992733
\(995\) 6.63145 0.210231
\(996\) 46.1993 1.46388
\(997\) 42.5584 1.34784 0.673919 0.738805i \(-0.264610\pi\)
0.673919 + 0.738805i \(0.264610\pi\)
\(998\) 0.774573 0.0245187
\(999\) 3.62071 0.114554
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 6010.2.a.f.1.3 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6010.2.a.f.1.3 22 1.1 even 1 trivial