Properties

Label 4031.2.a.b.1.18
Level $4031$
Weight $2$
Character 4031.1
Self dual yes
Analytic conductor $32.188$
Analytic rank $1$
Dimension $59$
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] = [4031,2,Mod(1,4031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4031, 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("4031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4031 = 29 \cdot 139 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4031.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: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.33108 q^{2} +2.24902 q^{3} -0.228227 q^{4} -0.768051 q^{5} -2.99362 q^{6} +2.32195 q^{7} +2.96595 q^{8} +2.05807 q^{9} +O(q^{10})\) \(q-1.33108 q^{2} +2.24902 q^{3} -0.228227 q^{4} -0.768051 q^{5} -2.99362 q^{6} +2.32195 q^{7} +2.96595 q^{8} +2.05807 q^{9} +1.02234 q^{10} +2.75683 q^{11} -0.513286 q^{12} -2.32328 q^{13} -3.09070 q^{14} -1.72736 q^{15} -3.49146 q^{16} -5.07020 q^{17} -2.73946 q^{18} +2.16559 q^{19} +0.175290 q^{20} +5.22210 q^{21} -3.66957 q^{22} -6.25765 q^{23} +6.67046 q^{24} -4.41010 q^{25} +3.09247 q^{26} -2.11841 q^{27} -0.529932 q^{28} +1.00000 q^{29} +2.29925 q^{30} +1.13865 q^{31} -1.28449 q^{32} +6.20016 q^{33} +6.74884 q^{34} -1.78338 q^{35} -0.469707 q^{36} -10.8474 q^{37} -2.88257 q^{38} -5.22510 q^{39} -2.27800 q^{40} -5.07743 q^{41} -6.95103 q^{42} +8.93812 q^{43} -0.629184 q^{44} -1.58070 q^{45} +8.32943 q^{46} -0.680566 q^{47} -7.85234 q^{48} -1.60855 q^{49} +5.87019 q^{50} -11.4030 q^{51} +0.530236 q^{52} +0.403466 q^{53} +2.81978 q^{54} -2.11739 q^{55} +6.88678 q^{56} +4.87044 q^{57} -1.33108 q^{58} -1.09579 q^{59} +0.394230 q^{60} -11.3179 q^{61} -1.51564 q^{62} +4.77874 q^{63} +8.69267 q^{64} +1.78440 q^{65} -8.25291 q^{66} -13.1384 q^{67} +1.15716 q^{68} -14.0735 q^{69} +2.37381 q^{70} +6.87462 q^{71} +6.10413 q^{72} -7.85139 q^{73} +14.4388 q^{74} -9.91838 q^{75} -0.494246 q^{76} +6.40123 q^{77} +6.95502 q^{78} -13.6784 q^{79} +2.68162 q^{80} -10.9386 q^{81} +6.75846 q^{82} -8.61588 q^{83} -1.19183 q^{84} +3.89417 q^{85} -11.8973 q^{86} +2.24902 q^{87} +8.17663 q^{88} +9.20872 q^{89} +2.10404 q^{90} -5.39455 q^{91} +1.42816 q^{92} +2.56085 q^{93} +0.905887 q^{94} -1.66328 q^{95} -2.88883 q^{96} +7.77949 q^{97} +2.14110 q^{98} +5.67376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33108 −0.941215 −0.470608 0.882343i \(-0.655965\pi\)
−0.470608 + 0.882343i \(0.655965\pi\)
\(3\) 2.24902 1.29847 0.649235 0.760588i \(-0.275089\pi\)
0.649235 + 0.760588i \(0.275089\pi\)
\(4\) −0.228227 −0.114114
\(5\) −0.768051 −0.343483 −0.171741 0.985142i \(-0.554939\pi\)
−0.171741 + 0.985142i \(0.554939\pi\)
\(6\) −2.99362 −1.22214
\(7\) 2.32195 0.877615 0.438807 0.898581i \(-0.355401\pi\)
0.438807 + 0.898581i \(0.355401\pi\)
\(8\) 2.96595 1.04862
\(9\) 2.05807 0.686023
\(10\) 1.02234 0.323291
\(11\) 2.75683 0.831217 0.415608 0.909544i \(-0.363569\pi\)
0.415608 + 0.909544i \(0.363569\pi\)
\(12\) −0.513286 −0.148173
\(13\) −2.32328 −0.644363 −0.322181 0.946678i \(-0.604416\pi\)
−0.322181 + 0.946678i \(0.604416\pi\)
\(14\) −3.09070 −0.826024
\(15\) −1.72736 −0.446002
\(16\) −3.49146 −0.872865
\(17\) −5.07020 −1.22970 −0.614852 0.788642i \(-0.710784\pi\)
−0.614852 + 0.788642i \(0.710784\pi\)
\(18\) −2.73946 −0.645696
\(19\) 2.16559 0.496820 0.248410 0.968655i \(-0.420092\pi\)
0.248410 + 0.968655i \(0.420092\pi\)
\(20\) 0.175290 0.0391960
\(21\) 5.22210 1.13956
\(22\) −3.66957 −0.782354
\(23\) −6.25765 −1.30481 −0.652405 0.757871i \(-0.726240\pi\)
−0.652405 + 0.757871i \(0.726240\pi\)
\(24\) 6.67046 1.36160
\(25\) −4.41010 −0.882020
\(26\) 3.09247 0.606484
\(27\) −2.11841 −0.407689
\(28\) −0.529932 −0.100148
\(29\) 1.00000 0.185695
\(30\) 2.29925 0.419784
\(31\) 1.13865 0.204508 0.102254 0.994758i \(-0.467395\pi\)
0.102254 + 0.994758i \(0.467395\pi\)
\(32\) −1.28449 −0.227067
\(33\) 6.20016 1.07931
\(34\) 6.74884 1.15742
\(35\) −1.78338 −0.301445
\(36\) −0.469707 −0.0782846
\(37\) −10.8474 −1.78331 −0.891653 0.452719i \(-0.850454\pi\)
−0.891653 + 0.452719i \(0.850454\pi\)
\(38\) −2.88257 −0.467614
\(39\) −5.22510 −0.836685
\(40\) −2.27800 −0.360183
\(41\) −5.07743 −0.792961 −0.396481 0.918043i \(-0.629769\pi\)
−0.396481 + 0.918043i \(0.629769\pi\)
\(42\) −6.95103 −1.07257
\(43\) 8.93812 1.36305 0.681525 0.731795i \(-0.261317\pi\)
0.681525 + 0.731795i \(0.261317\pi\)
\(44\) −0.629184 −0.0948531
\(45\) −1.58070 −0.235637
\(46\) 8.32943 1.22811
\(47\) −0.680566 −0.0992707 −0.0496353 0.998767i \(-0.515806\pi\)
−0.0496353 + 0.998767i \(0.515806\pi\)
\(48\) −7.85234 −1.13339
\(49\) −1.60855 −0.229792
\(50\) 5.87019 0.830170
\(51\) −11.4030 −1.59673
\(52\) 0.530236 0.0735305
\(53\) 0.403466 0.0554203 0.0277101 0.999616i \(-0.491178\pi\)
0.0277101 + 0.999616i \(0.491178\pi\)
\(54\) 2.81978 0.383723
\(55\) −2.11739 −0.285509
\(56\) 6.88678 0.920285
\(57\) 4.87044 0.645105
\(58\) −1.33108 −0.174779
\(59\) −1.09579 −0.142660 −0.0713301 0.997453i \(-0.522724\pi\)
−0.0713301 + 0.997453i \(0.522724\pi\)
\(60\) 0.394230 0.0508949
\(61\) −11.3179 −1.44911 −0.724554 0.689218i \(-0.757954\pi\)
−0.724554 + 0.689218i \(0.757954\pi\)
\(62\) −1.51564 −0.192486
\(63\) 4.77874 0.602064
\(64\) 8.69267 1.08658
\(65\) 1.78440 0.221327
\(66\) −8.25291 −1.01586
\(67\) −13.1384 −1.60511 −0.802557 0.596576i \(-0.796527\pi\)
−0.802557 + 0.596576i \(0.796527\pi\)
\(68\) 1.15716 0.140326
\(69\) −14.0735 −1.69426
\(70\) 2.37381 0.283725
\(71\) 6.87462 0.815868 0.407934 0.913011i \(-0.366249\pi\)
0.407934 + 0.913011i \(0.366249\pi\)
\(72\) 6.10413 0.719379
\(73\) −7.85139 −0.918935 −0.459468 0.888195i \(-0.651960\pi\)
−0.459468 + 0.888195i \(0.651960\pi\)
\(74\) 14.4388 1.67848
\(75\) −9.91838 −1.14528
\(76\) −0.494246 −0.0566939
\(77\) 6.40123 0.729488
\(78\) 6.95502 0.787501
\(79\) −13.6784 −1.53894 −0.769471 0.638682i \(-0.779480\pi\)
−0.769471 + 0.638682i \(0.779480\pi\)
\(80\) 2.68162 0.299814
\(81\) −10.9386 −1.21540
\(82\) 6.75846 0.746347
\(83\) −8.61588 −0.945716 −0.472858 0.881139i \(-0.656778\pi\)
−0.472858 + 0.881139i \(0.656778\pi\)
\(84\) −1.19183 −0.130039
\(85\) 3.89417 0.422382
\(86\) −11.8973 −1.28292
\(87\) 2.24902 0.241120
\(88\) 8.17663 0.871631
\(89\) 9.20872 0.976122 0.488061 0.872809i \(-0.337704\pi\)
0.488061 + 0.872809i \(0.337704\pi\)
\(90\) 2.10404 0.221785
\(91\) −5.39455 −0.565502
\(92\) 1.42816 0.148896
\(93\) 2.56085 0.265548
\(94\) 0.905887 0.0934351
\(95\) −1.66328 −0.170649
\(96\) −2.88883 −0.294840
\(97\) 7.77949 0.789887 0.394944 0.918705i \(-0.370764\pi\)
0.394944 + 0.918705i \(0.370764\pi\)
\(98\) 2.14110 0.216284
\(99\) 5.67376 0.570234
\(100\) 1.00650 0.100650
\(101\) −2.00970 −0.199972 −0.0999861 0.994989i \(-0.531880\pi\)
−0.0999861 + 0.994989i \(0.531880\pi\)
\(102\) 15.1783 1.50287
\(103\) 15.6871 1.54569 0.772847 0.634592i \(-0.218832\pi\)
0.772847 + 0.634592i \(0.218832\pi\)
\(104\) −6.89073 −0.675692
\(105\) −4.01084 −0.391418
\(106\) −0.537045 −0.0521624
\(107\) 4.88257 0.472016 0.236008 0.971751i \(-0.424161\pi\)
0.236008 + 0.971751i \(0.424161\pi\)
\(108\) 0.483480 0.0465228
\(109\) 17.3395 1.66082 0.830410 0.557152i \(-0.188106\pi\)
0.830410 + 0.557152i \(0.188106\pi\)
\(110\) 2.81841 0.268725
\(111\) −24.3960 −2.31557
\(112\) −8.10699 −0.766039
\(113\) 10.0953 0.949687 0.474844 0.880070i \(-0.342505\pi\)
0.474844 + 0.880070i \(0.342505\pi\)
\(114\) −6.48294 −0.607183
\(115\) 4.80619 0.448180
\(116\) −0.228227 −0.0211904
\(117\) −4.78148 −0.442048
\(118\) 1.45859 0.134274
\(119\) −11.7728 −1.07921
\(120\) −5.12325 −0.467687
\(121\) −3.39987 −0.309079
\(122\) 15.0650 1.36392
\(123\) −11.4192 −1.02964
\(124\) −0.259872 −0.0233372
\(125\) 7.22743 0.646441
\(126\) −6.36088 −0.566672
\(127\) −0.124099 −0.0110120 −0.00550599 0.999985i \(-0.501753\pi\)
−0.00550599 + 0.999985i \(0.501753\pi\)
\(128\) −9.00166 −0.795642
\(129\) 20.1020 1.76988
\(130\) −2.37518 −0.208317
\(131\) 4.65193 0.406441 0.203220 0.979133i \(-0.434859\pi\)
0.203220 + 0.979133i \(0.434859\pi\)
\(132\) −1.41505 −0.123164
\(133\) 5.02838 0.436016
\(134\) 17.4883 1.51076
\(135\) 1.62705 0.140034
\(136\) −15.0380 −1.28949
\(137\) −9.87736 −0.843880 −0.421940 0.906624i \(-0.638651\pi\)
−0.421940 + 0.906624i \(0.638651\pi\)
\(138\) 18.7330 1.59466
\(139\) 1.00000 0.0848189
\(140\) 0.407015 0.0343990
\(141\) −1.53060 −0.128900
\(142\) −9.15067 −0.767907
\(143\) −6.40490 −0.535605
\(144\) −7.18567 −0.598806
\(145\) −0.768051 −0.0637831
\(146\) 10.4508 0.864916
\(147\) −3.61765 −0.298379
\(148\) 2.47568 0.203499
\(149\) −2.25689 −0.184892 −0.0924458 0.995718i \(-0.529469\pi\)
−0.0924458 + 0.995718i \(0.529469\pi\)
\(150\) 13.2022 1.07795
\(151\) 4.35064 0.354050 0.177025 0.984206i \(-0.443353\pi\)
0.177025 + 0.984206i \(0.443353\pi\)
\(152\) 6.42302 0.520975
\(153\) −10.4348 −0.843606
\(154\) −8.52055 −0.686605
\(155\) −0.874543 −0.0702450
\(156\) 1.19251 0.0954771
\(157\) 21.4917 1.71522 0.857612 0.514296i \(-0.171947\pi\)
0.857612 + 0.514296i \(0.171947\pi\)
\(158\) 18.2071 1.44848
\(159\) 0.907400 0.0719615
\(160\) 0.986551 0.0779937
\(161\) −14.5299 −1.14512
\(162\) 14.5601 1.14395
\(163\) 0.586869 0.0459672 0.0229836 0.999736i \(-0.492683\pi\)
0.0229836 + 0.999736i \(0.492683\pi\)
\(164\) 1.15881 0.0904876
\(165\) −4.76204 −0.370724
\(166\) 11.4684 0.890122
\(167\) 24.7861 1.91801 0.959003 0.283394i \(-0.0914605\pi\)
0.959003 + 0.283394i \(0.0914605\pi\)
\(168\) 15.4885 1.19496
\(169\) −7.60236 −0.584797
\(170\) −5.18345 −0.397553
\(171\) 4.45693 0.340830
\(172\) −2.03992 −0.155543
\(173\) −2.49813 −0.189929 −0.0949646 0.995481i \(-0.530274\pi\)
−0.0949646 + 0.995481i \(0.530274\pi\)
\(174\) −2.99362 −0.226946
\(175\) −10.2400 −0.774073
\(176\) −9.62537 −0.725540
\(177\) −2.46446 −0.185240
\(178\) −12.2575 −0.918741
\(179\) −17.6921 −1.32237 −0.661184 0.750224i \(-0.729946\pi\)
−0.661184 + 0.750224i \(0.729946\pi\)
\(180\) 0.360759 0.0268894
\(181\) −13.0882 −0.972838 −0.486419 0.873726i \(-0.661697\pi\)
−0.486419 + 0.873726i \(0.661697\pi\)
\(182\) 7.18057 0.532259
\(183\) −25.4541 −1.88162
\(184\) −18.5599 −1.36825
\(185\) 8.33138 0.612535
\(186\) −3.40869 −0.249938
\(187\) −13.9777 −1.02215
\(188\) 0.155323 0.0113281
\(189\) −4.91885 −0.357794
\(190\) 2.21396 0.160617
\(191\) 3.03234 0.219412 0.109706 0.993964i \(-0.465009\pi\)
0.109706 + 0.993964i \(0.465009\pi\)
\(192\) 19.5499 1.41090
\(193\) 3.21536 0.231447 0.115723 0.993281i \(-0.463081\pi\)
0.115723 + 0.993281i \(0.463081\pi\)
\(194\) −10.3551 −0.743454
\(195\) 4.01314 0.287387
\(196\) 0.367114 0.0262224
\(197\) −14.9217 −1.06313 −0.531564 0.847018i \(-0.678396\pi\)
−0.531564 + 0.847018i \(0.678396\pi\)
\(198\) −7.55222 −0.536713
\(199\) −24.0928 −1.70789 −0.853945 0.520363i \(-0.825797\pi\)
−0.853945 + 0.520363i \(0.825797\pi\)
\(200\) −13.0801 −0.924904
\(201\) −29.5485 −2.08419
\(202\) 2.67507 0.188217
\(203\) 2.32195 0.162969
\(204\) 2.60247 0.182209
\(205\) 3.89972 0.272368
\(206\) −20.8808 −1.45483
\(207\) −12.8787 −0.895130
\(208\) 8.11164 0.562441
\(209\) 5.97016 0.412965
\(210\) 5.33875 0.368408
\(211\) 7.47712 0.514746 0.257373 0.966312i \(-0.417143\pi\)
0.257373 + 0.966312i \(0.417143\pi\)
\(212\) −0.0920818 −0.00632420
\(213\) 15.4611 1.05938
\(214\) −6.49909 −0.444269
\(215\) −6.86493 −0.468184
\(216\) −6.28311 −0.427511
\(217\) 2.64390 0.179479
\(218\) −23.0802 −1.56319
\(219\) −17.6579 −1.19321
\(220\) 0.483245 0.0325804
\(221\) 11.7795 0.792376
\(222\) 32.4731 2.17945
\(223\) −20.2984 −1.35928 −0.679642 0.733544i \(-0.737865\pi\)
−0.679642 + 0.733544i \(0.737865\pi\)
\(224\) −2.98251 −0.199278
\(225\) −9.07629 −0.605086
\(226\) −13.4377 −0.893860
\(227\) −12.0679 −0.800978 −0.400489 0.916302i \(-0.631160\pi\)
−0.400489 + 0.916302i \(0.631160\pi\)
\(228\) −1.11157 −0.0736152
\(229\) −3.51211 −0.232087 −0.116043 0.993244i \(-0.537021\pi\)
−0.116043 + 0.993244i \(0.537021\pi\)
\(230\) −6.39742 −0.421834
\(231\) 14.3965 0.947218
\(232\) 2.96595 0.194724
\(233\) 5.01658 0.328647 0.164324 0.986406i \(-0.447456\pi\)
0.164324 + 0.986406i \(0.447456\pi\)
\(234\) 6.36453 0.416062
\(235\) 0.522709 0.0340978
\(236\) 0.250090 0.0162795
\(237\) −30.7630 −1.99827
\(238\) 15.6705 1.01577
\(239\) 6.78054 0.438597 0.219298 0.975658i \(-0.429623\pi\)
0.219298 + 0.975658i \(0.429623\pi\)
\(240\) 6.03100 0.389299
\(241\) −3.39678 −0.218806 −0.109403 0.993997i \(-0.534894\pi\)
−0.109403 + 0.993997i \(0.534894\pi\)
\(242\) 4.52549 0.290910
\(243\) −18.2457 −1.17046
\(244\) 2.58305 0.165363
\(245\) 1.23545 0.0789297
\(246\) 15.1999 0.969110
\(247\) −5.03127 −0.320132
\(248\) 3.37719 0.214452
\(249\) −19.3772 −1.22798
\(250\) −9.62029 −0.608440
\(251\) −12.5444 −0.791793 −0.395896 0.918295i \(-0.629566\pi\)
−0.395896 + 0.918295i \(0.629566\pi\)
\(252\) −1.09064 −0.0687037
\(253\) −17.2513 −1.08458
\(254\) 0.165185 0.0103646
\(255\) 8.75805 0.548451
\(256\) −5.40341 −0.337713
\(257\) 3.42274 0.213505 0.106752 0.994286i \(-0.465955\pi\)
0.106752 + 0.994286i \(0.465955\pi\)
\(258\) −26.7573 −1.66584
\(259\) −25.1872 −1.56506
\(260\) −0.407248 −0.0252565
\(261\) 2.05807 0.127391
\(262\) −6.19208 −0.382548
\(263\) 18.9346 1.16756 0.583780 0.811912i \(-0.301573\pi\)
0.583780 + 0.811912i \(0.301573\pi\)
\(264\) 18.3894 1.13179
\(265\) −0.309882 −0.0190359
\(266\) −6.69318 −0.410385
\(267\) 20.7105 1.26746
\(268\) 2.99854 0.183165
\(269\) −7.14322 −0.435530 −0.217765 0.976001i \(-0.569877\pi\)
−0.217765 + 0.976001i \(0.569877\pi\)
\(270\) −2.16573 −0.131802
\(271\) 12.7937 0.777160 0.388580 0.921415i \(-0.372966\pi\)
0.388580 + 0.921415i \(0.372966\pi\)
\(272\) 17.7024 1.07337
\(273\) −12.1324 −0.734287
\(274\) 13.1476 0.794273
\(275\) −12.1579 −0.733150
\(276\) 3.21197 0.193338
\(277\) 4.10099 0.246404 0.123202 0.992382i \(-0.460684\pi\)
0.123202 + 0.992382i \(0.460684\pi\)
\(278\) −1.33108 −0.0798328
\(279\) 2.34343 0.140297
\(280\) −5.28940 −0.316102
\(281\) −24.4067 −1.45598 −0.727992 0.685585i \(-0.759546\pi\)
−0.727992 + 0.685585i \(0.759546\pi\)
\(282\) 2.03735 0.121323
\(283\) 12.1523 0.722380 0.361190 0.932492i \(-0.382371\pi\)
0.361190 + 0.932492i \(0.382371\pi\)
\(284\) −1.56898 −0.0931016
\(285\) −3.74074 −0.221582
\(286\) 8.52544 0.504120
\(287\) −11.7895 −0.695915
\(288\) −2.64356 −0.155773
\(289\) 8.70695 0.512173
\(290\) 1.02234 0.0600337
\(291\) 17.4962 1.02564
\(292\) 1.79190 0.104863
\(293\) 19.7255 1.15237 0.576187 0.817318i \(-0.304540\pi\)
0.576187 + 0.817318i \(0.304540\pi\)
\(294\) 4.81538 0.280838
\(295\) 0.841626 0.0490013
\(296\) −32.1729 −1.87001
\(297\) −5.84012 −0.338878
\(298\) 3.00410 0.174023
\(299\) 14.5383 0.840771
\(300\) 2.26364 0.130691
\(301\) 20.7539 1.19623
\(302\) −5.79105 −0.333237
\(303\) −4.51984 −0.259658
\(304\) −7.56106 −0.433656
\(305\) 8.69272 0.497744
\(306\) 13.8896 0.794015
\(307\) 0.274177 0.0156481 0.00782406 0.999969i \(-0.497509\pi\)
0.00782406 + 0.999969i \(0.497509\pi\)
\(308\) −1.46093 −0.0832445
\(309\) 35.2805 2.00704
\(310\) 1.16409 0.0661157
\(311\) −16.6056 −0.941617 −0.470808 0.882236i \(-0.656038\pi\)
−0.470808 + 0.882236i \(0.656038\pi\)
\(312\) −15.4974 −0.877366
\(313\) 10.4619 0.591341 0.295670 0.955290i \(-0.404457\pi\)
0.295670 + 0.955290i \(0.404457\pi\)
\(314\) −28.6072 −1.61440
\(315\) −3.67031 −0.206799
\(316\) 3.12179 0.175614
\(317\) 1.05127 0.0590449 0.0295225 0.999564i \(-0.490601\pi\)
0.0295225 + 0.999564i \(0.490601\pi\)
\(318\) −1.20782 −0.0677313
\(319\) 2.75683 0.154353
\(320\) −6.67641 −0.373223
\(321\) 10.9810 0.612898
\(322\) 19.3405 1.07780
\(323\) −10.9800 −0.610941
\(324\) 2.49648 0.138693
\(325\) 10.2459 0.568340
\(326\) −0.781170 −0.0432650
\(327\) 38.9968 2.15653
\(328\) −15.0594 −0.831516
\(329\) −1.58024 −0.0871214
\(330\) 6.33865 0.348931
\(331\) −30.7798 −1.69181 −0.845905 0.533333i \(-0.820939\pi\)
−0.845905 + 0.533333i \(0.820939\pi\)
\(332\) 1.96638 0.107919
\(333\) −22.3248 −1.22339
\(334\) −32.9923 −1.80526
\(335\) 10.0910 0.551329
\(336\) −18.2328 −0.994678
\(337\) 11.2395 0.612255 0.306127 0.951991i \(-0.400967\pi\)
0.306127 + 0.951991i \(0.400967\pi\)
\(338\) 10.1193 0.550420
\(339\) 22.7045 1.23314
\(340\) −0.888756 −0.0481995
\(341\) 3.13908 0.169991
\(342\) −5.93253 −0.320794
\(343\) −19.9886 −1.07928
\(344\) 26.5100 1.42932
\(345\) 10.8092 0.581948
\(346\) 3.32521 0.178764
\(347\) 31.2320 1.67662 0.838310 0.545194i \(-0.183544\pi\)
0.838310 + 0.545194i \(0.183544\pi\)
\(348\) −0.513286 −0.0275150
\(349\) 28.4236 1.52148 0.760740 0.649056i \(-0.224836\pi\)
0.760740 + 0.649056i \(0.224836\pi\)
\(350\) 13.6303 0.728570
\(351\) 4.92167 0.262700
\(352\) −3.54112 −0.188742
\(353\) −22.0558 −1.17391 −0.586956 0.809619i \(-0.699674\pi\)
−0.586956 + 0.809619i \(0.699674\pi\)
\(354\) 3.28039 0.174351
\(355\) −5.28006 −0.280236
\(356\) −2.10168 −0.111389
\(357\) −26.4771 −1.40132
\(358\) 23.5496 1.24463
\(359\) −1.53906 −0.0812282 −0.0406141 0.999175i \(-0.512931\pi\)
−0.0406141 + 0.999175i \(0.512931\pi\)
\(360\) −4.68828 −0.247094
\(361\) −14.3102 −0.753170
\(362\) 17.4214 0.915650
\(363\) −7.64635 −0.401329
\(364\) 1.23118 0.0645314
\(365\) 6.03026 0.315638
\(366\) 33.8815 1.77101
\(367\) −17.4613 −0.911471 −0.455736 0.890115i \(-0.650624\pi\)
−0.455736 + 0.890115i \(0.650624\pi\)
\(368\) 21.8483 1.13892
\(369\) −10.4497 −0.543990
\(370\) −11.0897 −0.576527
\(371\) 0.936827 0.0486376
\(372\) −0.584455 −0.0303026
\(373\) 13.6487 0.706701 0.353351 0.935491i \(-0.385042\pi\)
0.353351 + 0.935491i \(0.385042\pi\)
\(374\) 18.6054 0.962064
\(375\) 16.2546 0.839384
\(376\) −2.01852 −0.104097
\(377\) −2.32328 −0.119655
\(378\) 6.54738 0.336761
\(379\) −22.0759 −1.13396 −0.566982 0.823730i \(-0.691889\pi\)
−0.566982 + 0.823730i \(0.691889\pi\)
\(380\) 0.379606 0.0194734
\(381\) −0.279100 −0.0142987
\(382\) −4.03628 −0.206514
\(383\) −28.9119 −1.47733 −0.738665 0.674073i \(-0.764543\pi\)
−0.738665 + 0.674073i \(0.764543\pi\)
\(384\) −20.2449 −1.03312
\(385\) −4.91647 −0.250567
\(386\) −4.27991 −0.217841
\(387\) 18.3953 0.935085
\(388\) −1.77549 −0.0901369
\(389\) 3.82444 0.193907 0.0969535 0.995289i \(-0.469090\pi\)
0.0969535 + 0.995289i \(0.469090\pi\)
\(390\) −5.34181 −0.270493
\(391\) 31.7275 1.60453
\(392\) −4.77087 −0.240965
\(393\) 10.4623 0.527751
\(394\) 19.8620 1.00063
\(395\) 10.5057 0.528600
\(396\) −1.29491 −0.0650715
\(397\) −10.3270 −0.518295 −0.259148 0.965838i \(-0.583442\pi\)
−0.259148 + 0.965838i \(0.583442\pi\)
\(398\) 32.0694 1.60749
\(399\) 11.3089 0.566154
\(400\) 15.3977 0.769884
\(401\) 5.34790 0.267061 0.133531 0.991045i \(-0.457369\pi\)
0.133531 + 0.991045i \(0.457369\pi\)
\(402\) 39.3314 1.96167
\(403\) −2.64541 −0.131777
\(404\) 0.458667 0.0228195
\(405\) 8.40137 0.417467
\(406\) −3.09070 −0.153389
\(407\) −29.9046 −1.48231
\(408\) −33.8206 −1.67437
\(409\) −21.1204 −1.04434 −0.522168 0.852843i \(-0.674877\pi\)
−0.522168 + 0.852843i \(0.674877\pi\)
\(410\) −5.19084 −0.256357
\(411\) −22.2143 −1.09575
\(412\) −3.58022 −0.176385
\(413\) −2.54438 −0.125201
\(414\) 17.1426 0.842510
\(415\) 6.61743 0.324837
\(416\) 2.98422 0.146314
\(417\) 2.24902 0.110135
\(418\) −7.94676 −0.388689
\(419\) 7.62762 0.372634 0.186317 0.982490i \(-0.440345\pi\)
0.186317 + 0.982490i \(0.440345\pi\)
\(420\) 0.915382 0.0446661
\(421\) −2.98057 −0.145264 −0.0726321 0.997359i \(-0.523140\pi\)
−0.0726321 + 0.997359i \(0.523140\pi\)
\(422\) −9.95265 −0.484487
\(423\) −1.40065 −0.0681020
\(424\) 1.19666 0.0581148
\(425\) 22.3601 1.08462
\(426\) −20.5800 −0.997104
\(427\) −26.2796 −1.27176
\(428\) −1.11434 −0.0538634
\(429\) −14.4047 −0.695467
\(430\) 9.13777 0.440662
\(431\) −1.31983 −0.0635739 −0.0317870 0.999495i \(-0.510120\pi\)
−0.0317870 + 0.999495i \(0.510120\pi\)
\(432\) 7.39635 0.355857
\(433\) 22.2634 1.06991 0.534956 0.844880i \(-0.320328\pi\)
0.534956 + 0.844880i \(0.320328\pi\)
\(434\) −3.51924 −0.168929
\(435\) −1.72736 −0.0828205
\(436\) −3.95734 −0.189522
\(437\) −13.5515 −0.648255
\(438\) 23.5041 1.12307
\(439\) −10.5197 −0.502079 −0.251039 0.967977i \(-0.580772\pi\)
−0.251039 + 0.967977i \(0.580772\pi\)
\(440\) −6.28006 −0.299390
\(441\) −3.31050 −0.157643
\(442\) −15.6795 −0.745796
\(443\) 33.3116 1.58268 0.791342 0.611374i \(-0.209383\pi\)
0.791342 + 0.611374i \(0.209383\pi\)
\(444\) 5.56784 0.264238
\(445\) −7.07276 −0.335281
\(446\) 27.0188 1.27938
\(447\) −5.07578 −0.240076
\(448\) 20.1839 0.953602
\(449\) −2.78879 −0.131611 −0.0658056 0.997832i \(-0.520962\pi\)
−0.0658056 + 0.997832i \(0.520962\pi\)
\(450\) 12.0813 0.569516
\(451\) −13.9976 −0.659123
\(452\) −2.30402 −0.108372
\(453\) 9.78465 0.459723
\(454\) 16.0634 0.753892
\(455\) 4.14328 0.194240
\(456\) 14.4455 0.676471
\(457\) 1.33846 0.0626104 0.0313052 0.999510i \(-0.490034\pi\)
0.0313052 + 0.999510i \(0.490034\pi\)
\(458\) 4.67490 0.218444
\(459\) 10.7408 0.501337
\(460\) −1.09690 −0.0511434
\(461\) −14.9902 −0.698164 −0.349082 0.937092i \(-0.613507\pi\)
−0.349082 + 0.937092i \(0.613507\pi\)
\(462\) −19.1628 −0.891536
\(463\) 0.0783710 0.00364221 0.00182110 0.999998i \(-0.499420\pi\)
0.00182110 + 0.999998i \(0.499420\pi\)
\(464\) −3.49146 −0.162087
\(465\) −1.96686 −0.0912110
\(466\) −6.67747 −0.309328
\(467\) −14.9284 −0.690802 −0.345401 0.938455i \(-0.612257\pi\)
−0.345401 + 0.938455i \(0.612257\pi\)
\(468\) 1.09126 0.0504436
\(469\) −30.5068 −1.40867
\(470\) −0.695767 −0.0320933
\(471\) 48.3352 2.22717
\(472\) −3.25007 −0.149597
\(473\) 24.6409 1.13299
\(474\) 40.9480 1.88080
\(475\) −9.55045 −0.438205
\(476\) 2.68686 0.123152
\(477\) 0.830361 0.0380196
\(478\) −9.02544 −0.412814
\(479\) 11.5980 0.529926 0.264963 0.964259i \(-0.414640\pi\)
0.264963 + 0.964259i \(0.414640\pi\)
\(480\) 2.21877 0.101272
\(481\) 25.2016 1.14910
\(482\) 4.52138 0.205943
\(483\) −32.6781 −1.48690
\(484\) 0.775941 0.0352701
\(485\) −5.97504 −0.271313
\(486\) 24.2865 1.10166
\(487\) −41.8745 −1.89751 −0.948756 0.316008i \(-0.897657\pi\)
−0.948756 + 0.316008i \(0.897657\pi\)
\(488\) −33.5683 −1.51957
\(489\) 1.31988 0.0596870
\(490\) −1.64448 −0.0742899
\(491\) 15.0652 0.679884 0.339942 0.940446i \(-0.389593\pi\)
0.339942 + 0.940446i \(0.389593\pi\)
\(492\) 2.60618 0.117495
\(493\) −5.07020 −0.228350
\(494\) 6.69702 0.301313
\(495\) −4.35773 −0.195866
\(496\) −3.97556 −0.178508
\(497\) 15.9625 0.716018
\(498\) 25.7927 1.15580
\(499\) −7.40967 −0.331703 −0.165851 0.986151i \(-0.553037\pi\)
−0.165851 + 0.986151i \(0.553037\pi\)
\(500\) −1.64950 −0.0737677
\(501\) 55.7443 2.49047
\(502\) 16.6975 0.745248
\(503\) 38.4356 1.71376 0.856880 0.515516i \(-0.172400\pi\)
0.856880 + 0.515516i \(0.172400\pi\)
\(504\) 14.1735 0.631337
\(505\) 1.54355 0.0686870
\(506\) 22.9629 1.02082
\(507\) −17.0978 −0.759341
\(508\) 0.0283227 0.00125662
\(509\) 41.5698 1.84255 0.921275 0.388912i \(-0.127149\pi\)
0.921275 + 0.388912i \(0.127149\pi\)
\(510\) −11.6577 −0.516210
\(511\) −18.2305 −0.806471
\(512\) 25.1957 1.11350
\(513\) −4.58761 −0.202548
\(514\) −4.55594 −0.200954
\(515\) −12.0485 −0.530919
\(516\) −4.58781 −0.201967
\(517\) −1.87621 −0.0825155
\(518\) 33.5262 1.47305
\(519\) −5.61833 −0.246617
\(520\) 5.29243 0.232088
\(521\) −8.79559 −0.385342 −0.192671 0.981263i \(-0.561715\pi\)
−0.192671 + 0.981263i \(0.561715\pi\)
\(522\) −2.73946 −0.119903
\(523\) −38.1154 −1.66667 −0.833336 0.552767i \(-0.813572\pi\)
−0.833336 + 0.552767i \(0.813572\pi\)
\(524\) −1.06170 −0.0463804
\(525\) −23.0300 −1.00511
\(526\) −25.2035 −1.09893
\(527\) −5.77320 −0.251485
\(528\) −21.6476 −0.942091
\(529\) 16.1582 0.702529
\(530\) 0.412478 0.0179169
\(531\) −2.25522 −0.0978683
\(532\) −1.14761 −0.0497554
\(533\) 11.7963 0.510955
\(534\) −27.5674 −1.19296
\(535\) −3.75006 −0.162129
\(536\) −38.9679 −1.68316
\(537\) −39.7898 −1.71705
\(538\) 9.50819 0.409927
\(539\) −4.43450 −0.191007
\(540\) −0.371337 −0.0159798
\(541\) −21.8880 −0.941039 −0.470520 0.882390i \(-0.655934\pi\)
−0.470520 + 0.882390i \(0.655934\pi\)
\(542\) −17.0294 −0.731475
\(543\) −29.4356 −1.26320
\(544\) 6.51261 0.279226
\(545\) −13.3176 −0.570463
\(546\) 16.1492 0.691122
\(547\) 11.1549 0.476950 0.238475 0.971149i \(-0.423353\pi\)
0.238475 + 0.971149i \(0.423353\pi\)
\(548\) 2.25428 0.0962981
\(549\) −23.2930 −0.994123
\(550\) 16.1831 0.690052
\(551\) 2.16559 0.0922571
\(552\) −41.7414 −1.77663
\(553\) −31.7606 −1.35060
\(554\) −5.45874 −0.231920
\(555\) 18.7374 0.795358
\(556\) −0.228227 −0.00967898
\(557\) 18.4574 0.782064 0.391032 0.920377i \(-0.372118\pi\)
0.391032 + 0.920377i \(0.372118\pi\)
\(558\) −3.11929 −0.132050
\(559\) −20.7658 −0.878299
\(560\) 6.22658 0.263121
\(561\) −31.4361 −1.32723
\(562\) 32.4873 1.37039
\(563\) −0.376010 −0.0158469 −0.00792346 0.999969i \(-0.502522\pi\)
−0.00792346 + 0.999969i \(0.502522\pi\)
\(564\) 0.349325 0.0147092
\(565\) −7.75371 −0.326201
\(566\) −16.1757 −0.679915
\(567\) −25.3988 −1.06665
\(568\) 20.3898 0.855536
\(569\) 45.5041 1.90763 0.953816 0.300391i \(-0.0971171\pi\)
0.953816 + 0.300391i \(0.0971171\pi\)
\(570\) 4.97923 0.208557
\(571\) −39.3056 −1.64489 −0.822444 0.568846i \(-0.807390\pi\)
−0.822444 + 0.568846i \(0.807390\pi\)
\(572\) 1.46177 0.0611198
\(573\) 6.81977 0.284900
\(574\) 15.6928 0.655005
\(575\) 27.5968 1.15087
\(576\) 17.8901 0.745422
\(577\) −35.6677 −1.48487 −0.742433 0.669920i \(-0.766328\pi\)
−0.742433 + 0.669920i \(0.766328\pi\)
\(578\) −11.5896 −0.482066
\(579\) 7.23140 0.300527
\(580\) 0.175290 0.00727852
\(581\) −20.0056 −0.829974
\(582\) −23.2888 −0.965353
\(583\) 1.11229 0.0460662
\(584\) −23.2868 −0.963615
\(585\) 3.67242 0.151836
\(586\) −26.2562 −1.08463
\(587\) 7.52414 0.310555 0.155277 0.987871i \(-0.450373\pi\)
0.155277 + 0.987871i \(0.450373\pi\)
\(588\) 0.825645 0.0340490
\(589\) 2.46585 0.101604
\(590\) −1.12027 −0.0461208
\(591\) −33.5592 −1.38044
\(592\) 37.8733 1.55658
\(593\) 6.90701 0.283637 0.141818 0.989893i \(-0.454705\pi\)
0.141818 + 0.989893i \(0.454705\pi\)
\(594\) 7.77366 0.318957
\(595\) 9.04207 0.370689
\(596\) 0.515084 0.0210986
\(597\) −54.1850 −2.21764
\(598\) −19.3516 −0.791346
\(599\) 18.0988 0.739496 0.369748 0.929132i \(-0.379444\pi\)
0.369748 + 0.929132i \(0.379444\pi\)
\(600\) −29.4174 −1.20096
\(601\) 6.71850 0.274053 0.137027 0.990567i \(-0.456245\pi\)
0.137027 + 0.990567i \(0.456245\pi\)
\(602\) −27.6251 −1.12591
\(603\) −27.0398 −1.10115
\(604\) −0.992934 −0.0404019
\(605\) 2.61127 0.106163
\(606\) 6.01626 0.244394
\(607\) −36.9855 −1.50119 −0.750597 0.660760i \(-0.770234\pi\)
−0.750597 + 0.660760i \(0.770234\pi\)
\(608\) −2.78167 −0.112811
\(609\) 5.22210 0.211610
\(610\) −11.5707 −0.468484
\(611\) 1.58115 0.0639663
\(612\) 2.38151 0.0962669
\(613\) 5.87449 0.237268 0.118634 0.992938i \(-0.462148\pi\)
0.118634 + 0.992938i \(0.462148\pi\)
\(614\) −0.364952 −0.0147283
\(615\) 8.77054 0.353662
\(616\) 18.9857 0.764956
\(617\) 34.6078 1.39326 0.696628 0.717432i \(-0.254683\pi\)
0.696628 + 0.717432i \(0.254683\pi\)
\(618\) −46.9612 −1.88906
\(619\) −40.2200 −1.61658 −0.808290 0.588785i \(-0.799607\pi\)
−0.808290 + 0.588785i \(0.799607\pi\)
\(620\) 0.199594 0.00801591
\(621\) 13.2563 0.531957
\(622\) 22.1034 0.886264
\(623\) 21.3822 0.856659
\(624\) 18.2432 0.730313
\(625\) 16.4995 0.659978
\(626\) −13.9256 −0.556579
\(627\) 13.4270 0.536222
\(628\) −4.90499 −0.195730
\(629\) 54.9987 2.19294
\(630\) 4.88548 0.194642
\(631\) −0.439056 −0.0174785 −0.00873927 0.999962i \(-0.502782\pi\)
−0.00873927 + 0.999962i \(0.502782\pi\)
\(632\) −40.5695 −1.61377
\(633\) 16.8162 0.668382
\(634\) −1.39932 −0.0555740
\(635\) 0.0953141 0.00378242
\(636\) −0.207093 −0.00821178
\(637\) 3.73711 0.148070
\(638\) −3.66957 −0.145280
\(639\) 14.1485 0.559704
\(640\) 6.91373 0.273289
\(641\) 22.0670 0.871592 0.435796 0.900045i \(-0.356467\pi\)
0.435796 + 0.900045i \(0.356467\pi\)
\(642\) −14.6166 −0.576870
\(643\) −38.1072 −1.50280 −0.751401 0.659846i \(-0.770622\pi\)
−0.751401 + 0.659846i \(0.770622\pi\)
\(644\) 3.31613 0.130674
\(645\) −15.4393 −0.607923
\(646\) 14.6152 0.575027
\(647\) 37.6194 1.47897 0.739485 0.673173i \(-0.235069\pi\)
0.739485 + 0.673173i \(0.235069\pi\)
\(648\) −32.4432 −1.27449
\(649\) −3.02092 −0.118582
\(650\) −13.6381 −0.534931
\(651\) 5.94616 0.233049
\(652\) −0.133940 −0.00524548
\(653\) 22.7015 0.888378 0.444189 0.895933i \(-0.353492\pi\)
0.444189 + 0.895933i \(0.353492\pi\)
\(654\) −51.9078 −2.02975
\(655\) −3.57291 −0.139605
\(656\) 17.7276 0.692148
\(657\) −16.1587 −0.630411
\(658\) 2.10342 0.0820000
\(659\) −27.6992 −1.07901 −0.539505 0.841983i \(-0.681388\pi\)
−0.539505 + 0.841983i \(0.681388\pi\)
\(660\) 1.08683 0.0423047
\(661\) −14.7929 −0.575379 −0.287689 0.957724i \(-0.592887\pi\)
−0.287689 + 0.957724i \(0.592887\pi\)
\(662\) 40.9704 1.59236
\(663\) 26.4923 1.02888
\(664\) −25.5543 −0.991697
\(665\) −3.86205 −0.149764
\(666\) 29.7161 1.15147
\(667\) −6.25765 −0.242297
\(668\) −5.65686 −0.218871
\(669\) −45.6515 −1.76499
\(670\) −13.4319 −0.518919
\(671\) −31.2016 −1.20452
\(672\) −6.70772 −0.258756
\(673\) −21.4452 −0.826651 −0.413325 0.910583i \(-0.635633\pi\)
−0.413325 + 0.910583i \(0.635633\pi\)
\(674\) −14.9607 −0.576264
\(675\) 9.34241 0.359590
\(676\) 1.73506 0.0667333
\(677\) −51.6540 −1.98522 −0.992612 0.121329i \(-0.961284\pi\)
−0.992612 + 0.121329i \(0.961284\pi\)
\(678\) −30.2215 −1.16065
\(679\) 18.0636 0.693217
\(680\) 11.5499 0.442919
\(681\) −27.1410 −1.04005
\(682\) −4.17836 −0.159998
\(683\) −33.1623 −1.26892 −0.634459 0.772956i \(-0.718777\pi\)
−0.634459 + 0.772956i \(0.718777\pi\)
\(684\) −1.01719 −0.0388933
\(685\) 7.58631 0.289858
\(686\) 26.6064 1.01584
\(687\) −7.89879 −0.301358
\(688\) −31.2071 −1.18976
\(689\) −0.937364 −0.0357107
\(690\) −14.3879 −0.547738
\(691\) −13.2094 −0.502508 −0.251254 0.967921i \(-0.580843\pi\)
−0.251254 + 0.967921i \(0.580843\pi\)
\(692\) 0.570141 0.0216735
\(693\) 13.1742 0.500446
\(694\) −41.5722 −1.57806
\(695\) −0.768051 −0.0291338
\(696\) 6.67046 0.252843
\(697\) 25.7436 0.975108
\(698\) −37.8341 −1.43204
\(699\) 11.2824 0.426738
\(700\) 2.33705 0.0883323
\(701\) 9.98297 0.377051 0.188526 0.982068i \(-0.439629\pi\)
0.188526 + 0.982068i \(0.439629\pi\)
\(702\) −6.55114 −0.247257
\(703\) −23.4910 −0.885982
\(704\) 23.9643 0.903187
\(705\) 1.17558 0.0442749
\(706\) 29.3580 1.10490
\(707\) −4.66641 −0.175499
\(708\) 0.562456 0.0211384
\(709\) 33.4638 1.25676 0.628380 0.777906i \(-0.283718\pi\)
0.628380 + 0.777906i \(0.283718\pi\)
\(710\) 7.02818 0.263763
\(711\) −28.1511 −1.05575
\(712\) 27.3126 1.02358
\(713\) −7.12529 −0.266844
\(714\) 35.2431 1.31894
\(715\) 4.91929 0.183971
\(716\) 4.03781 0.150900
\(717\) 15.2495 0.569505
\(718\) 2.04861 0.0764533
\(719\) 15.6418 0.583341 0.291670 0.956519i \(-0.405789\pi\)
0.291670 + 0.956519i \(0.405789\pi\)
\(720\) 5.51896 0.205679
\(721\) 36.4246 1.35652
\(722\) 19.0481 0.708895
\(723\) −7.63941 −0.284113
\(724\) 2.98708 0.111014
\(725\) −4.41010 −0.163787
\(726\) 10.1779 0.377737
\(727\) 16.4733 0.610962 0.305481 0.952198i \(-0.401183\pi\)
0.305481 + 0.952198i \(0.401183\pi\)
\(728\) −15.9999 −0.592997
\(729\) −8.21928 −0.304418
\(730\) −8.02676 −0.297084
\(731\) −45.3181 −1.67615
\(732\) 5.80932 0.214719
\(733\) 1.68644 0.0622901 0.0311450 0.999515i \(-0.490085\pi\)
0.0311450 + 0.999515i \(0.490085\pi\)
\(734\) 23.2424 0.857891
\(735\) 2.77854 0.102488
\(736\) 8.03787 0.296280
\(737\) −36.2204 −1.33420
\(738\) 13.9094 0.512012
\(739\) 42.4536 1.56168 0.780840 0.624731i \(-0.214791\pi\)
0.780840 + 0.624731i \(0.214791\pi\)
\(740\) −1.90145 −0.0698985
\(741\) −11.3154 −0.415682
\(742\) −1.24699 −0.0457785
\(743\) 10.2889 0.377462 0.188731 0.982029i \(-0.439563\pi\)
0.188731 + 0.982029i \(0.439563\pi\)
\(744\) 7.59534 0.278459
\(745\) 1.73341 0.0635071
\(746\) −18.1675 −0.665158
\(747\) −17.7321 −0.648783
\(748\) 3.19009 0.116641
\(749\) 11.3371 0.414248
\(750\) −21.6362 −0.790041
\(751\) 45.9257 1.67585 0.837927 0.545782i \(-0.183767\pi\)
0.837927 + 0.545782i \(0.183767\pi\)
\(752\) 2.37617 0.0866499
\(753\) −28.2125 −1.02812
\(754\) 3.09247 0.112621
\(755\) −3.34151 −0.121610
\(756\) 1.12262 0.0408291
\(757\) 33.5253 1.21850 0.609249 0.792979i \(-0.291471\pi\)
0.609249 + 0.792979i \(0.291471\pi\)
\(758\) 29.3848 1.06730
\(759\) −38.7984 −1.40829
\(760\) −4.93320 −0.178946
\(761\) 36.3243 1.31676 0.658378 0.752688i \(-0.271243\pi\)
0.658378 + 0.752688i \(0.271243\pi\)
\(762\) 0.371504 0.0134582
\(763\) 40.2614 1.45756
\(764\) −0.692061 −0.0250379
\(765\) 8.01448 0.289764
\(766\) 38.4840 1.39049
\(767\) 2.54584 0.0919249
\(768\) −12.1524 −0.438510
\(769\) 50.3839 1.81689 0.908444 0.418006i \(-0.137271\pi\)
0.908444 + 0.418006i \(0.137271\pi\)
\(770\) 6.54421 0.235837
\(771\) 7.69779 0.277229
\(772\) −0.733833 −0.0264112
\(773\) −8.49018 −0.305371 −0.152685 0.988275i \(-0.548792\pi\)
−0.152685 + 0.988275i \(0.548792\pi\)
\(774\) −24.4856 −0.880116
\(775\) −5.02157 −0.180380
\(776\) 23.0736 0.828292
\(777\) −56.6464 −2.03218
\(778\) −5.09064 −0.182508
\(779\) −10.9956 −0.393959
\(780\) −0.915907 −0.0327947
\(781\) 18.9522 0.678163
\(782\) −42.2319 −1.51021
\(783\) −2.11841 −0.0757059
\(784\) 5.61618 0.200578
\(785\) −16.5067 −0.589150
\(786\) −13.9261 −0.496727
\(787\) −0.537361 −0.0191548 −0.00957742 0.999954i \(-0.503049\pi\)
−0.00957742 + 0.999954i \(0.503049\pi\)
\(788\) 3.40554 0.121317
\(789\) 42.5843 1.51604
\(790\) −13.9839 −0.497527
\(791\) 23.4408 0.833460
\(792\) 16.8281 0.597959
\(793\) 26.2947 0.933751
\(794\) 13.7460 0.487827
\(795\) −0.696929 −0.0247175
\(796\) 5.49862 0.194893
\(797\) −0.203016 −0.00719119 −0.00359559 0.999994i \(-0.501145\pi\)
−0.00359559 + 0.999994i \(0.501145\pi\)
\(798\) −15.0531 −0.532873
\(799\) 3.45060 0.122074
\(800\) 5.66471 0.200278
\(801\) 18.9522 0.669643
\(802\) −7.11848 −0.251362
\(803\) −21.6450 −0.763834
\(804\) 6.74377 0.237834
\(805\) 11.1597 0.393329
\(806\) 3.52125 0.124031
\(807\) −16.0652 −0.565522
\(808\) −5.96065 −0.209695
\(809\) −30.5469 −1.07397 −0.536985 0.843592i \(-0.680437\pi\)
−0.536985 + 0.843592i \(0.680437\pi\)
\(810\) −11.1829 −0.392927
\(811\) 43.2311 1.51805 0.759024 0.651063i \(-0.225677\pi\)
0.759024 + 0.651063i \(0.225677\pi\)
\(812\) −0.529932 −0.0185970
\(813\) 28.7732 1.00912
\(814\) 39.8054 1.39518
\(815\) −0.450745 −0.0157889
\(816\) 39.8130 1.39373
\(817\) 19.3563 0.677190
\(818\) 28.1129 0.982945
\(819\) −11.1024 −0.387948
\(820\) −0.890023 −0.0310809
\(821\) −16.2042 −0.565530 −0.282765 0.959189i \(-0.591252\pi\)
−0.282765 + 0.959189i \(0.591252\pi\)
\(822\) 29.5690 1.03134
\(823\) −1.15493 −0.0402583 −0.0201292 0.999797i \(-0.506408\pi\)
−0.0201292 + 0.999797i \(0.506408\pi\)
\(824\) 46.5271 1.62085
\(825\) −27.3433 −0.951972
\(826\) 3.38677 0.117841
\(827\) 43.7846 1.52254 0.761270 0.648436i \(-0.224576\pi\)
0.761270 + 0.648436i \(0.224576\pi\)
\(828\) 2.93926 0.102146
\(829\) −31.7976 −1.10437 −0.552187 0.833720i \(-0.686207\pi\)
−0.552187 + 0.833720i \(0.686207\pi\)
\(830\) −8.80833 −0.305742
\(831\) 9.22318 0.319949
\(832\) −20.1955 −0.700154
\(833\) 8.15566 0.282577
\(834\) −2.99362 −0.103661
\(835\) −19.0370 −0.658802
\(836\) −1.36255 −0.0471249
\(837\) −2.41214 −0.0833757
\(838\) −10.1530 −0.350728
\(839\) −4.37059 −0.150889 −0.0754447 0.997150i \(-0.524038\pi\)
−0.0754447 + 0.997150i \(0.524038\pi\)
\(840\) −11.8959 −0.410449
\(841\) 1.00000 0.0344828
\(842\) 3.96738 0.136725
\(843\) −54.8911 −1.89055
\(844\) −1.70648 −0.0587395
\(845\) 5.83900 0.200868
\(846\) 1.86438 0.0640987
\(847\) −7.89432 −0.271252
\(848\) −1.40868 −0.0483744
\(849\) 27.3307 0.937988
\(850\) −29.7631 −1.02086
\(851\) 67.8794 2.32688
\(852\) −3.52865 −0.120890
\(853\) −12.8251 −0.439125 −0.219562 0.975598i \(-0.570463\pi\)
−0.219562 + 0.975598i \(0.570463\pi\)
\(854\) 34.9802 1.19700
\(855\) −3.42315 −0.117069
\(856\) 14.4815 0.494966
\(857\) 5.10036 0.174225 0.0871125 0.996198i \(-0.472236\pi\)
0.0871125 + 0.996198i \(0.472236\pi\)
\(858\) 19.1738 0.654584
\(859\) −21.9547 −0.749085 −0.374543 0.927210i \(-0.622200\pi\)
−0.374543 + 0.927210i \(0.622200\pi\)
\(860\) 1.56676 0.0534262
\(861\) −26.5149 −0.903624
\(862\) 1.75680 0.0598368
\(863\) 57.2311 1.94817 0.974085 0.226181i \(-0.0726242\pi\)
0.974085 + 0.226181i \(0.0726242\pi\)
\(864\) 2.72107 0.0925728
\(865\) 1.91869 0.0652374
\(866\) −29.6344 −1.00702
\(867\) 19.5821 0.665042
\(868\) −0.603409 −0.0204810
\(869\) −37.7091 −1.27919
\(870\) 2.29925 0.0779519
\(871\) 30.5243 1.03427
\(872\) 51.4280 1.74157
\(873\) 16.0107 0.541881
\(874\) 18.0381 0.610148
\(875\) 16.7817 0.567326
\(876\) 4.03001 0.136161
\(877\) −51.6800 −1.74511 −0.872554 0.488517i \(-0.837538\pi\)
−0.872554 + 0.488517i \(0.837538\pi\)
\(878\) 14.0026 0.472564
\(879\) 44.3629 1.49632
\(880\) 7.39277 0.249210
\(881\) 16.1283 0.543377 0.271688 0.962385i \(-0.412418\pi\)
0.271688 + 0.962385i \(0.412418\pi\)
\(882\) 4.40654 0.148376
\(883\) −41.0614 −1.38182 −0.690912 0.722939i \(-0.742791\pi\)
−0.690912 + 0.722939i \(0.742791\pi\)
\(884\) −2.68840 −0.0904208
\(885\) 1.89283 0.0636268
\(886\) −44.3404 −1.48965
\(887\) −23.6138 −0.792874 −0.396437 0.918062i \(-0.629753\pi\)
−0.396437 + 0.918062i \(0.629753\pi\)
\(888\) −72.3574 −2.42815
\(889\) −0.288151 −0.00966427
\(890\) 9.41441 0.315572
\(891\) −30.1558 −1.01026
\(892\) 4.63265 0.155113
\(893\) −1.47382 −0.0493196
\(894\) 6.75627 0.225963
\(895\) 13.5884 0.454211
\(896\) −20.9014 −0.698267
\(897\) 32.6968 1.09172
\(898\) 3.71210 0.123875
\(899\) 1.13865 0.0379762
\(900\) 2.07146 0.0690485
\(901\) −2.04565 −0.0681505
\(902\) 18.6320 0.620377
\(903\) 46.6758 1.55327
\(904\) 29.9422 0.995862
\(905\) 10.0524 0.334153
\(906\) −13.0242 −0.432698
\(907\) −16.5452 −0.549375 −0.274688 0.961534i \(-0.588574\pi\)
−0.274688 + 0.961534i \(0.588574\pi\)
\(908\) 2.75423 0.0914024
\(909\) −4.13610 −0.137186
\(910\) −5.51504 −0.182822
\(911\) −6.74786 −0.223567 −0.111783 0.993733i \(-0.535656\pi\)
−0.111783 + 0.993733i \(0.535656\pi\)
\(912\) −17.0049 −0.563090
\(913\) −23.7526 −0.786095
\(914\) −1.78159 −0.0589298
\(915\) 19.5501 0.646305
\(916\) 0.801558 0.0264842
\(917\) 10.8015 0.356698
\(918\) −14.2968 −0.471866
\(919\) −25.1667 −0.830172 −0.415086 0.909782i \(-0.636248\pi\)
−0.415086 + 0.909782i \(0.636248\pi\)
\(920\) 14.2549 0.469970
\(921\) 0.616629 0.0203186
\(922\) 19.9532 0.657123
\(923\) −15.9717 −0.525715
\(924\) −3.28566 −0.108090
\(925\) 47.8382 1.57291
\(926\) −0.104318 −0.00342810
\(927\) 32.2851 1.06038
\(928\) −1.28449 −0.0421653
\(929\) 14.1028 0.462699 0.231349 0.972871i \(-0.425686\pi\)
0.231349 + 0.972871i \(0.425686\pi\)
\(930\) 2.61805 0.0858492
\(931\) −3.48345 −0.114165
\(932\) −1.14492 −0.0375031
\(933\) −37.3462 −1.22266
\(934\) 19.8708 0.650193
\(935\) 10.7356 0.351091
\(936\) −14.1816 −0.463541
\(937\) −16.0094 −0.523005 −0.261503 0.965203i \(-0.584218\pi\)
−0.261503 + 0.965203i \(0.584218\pi\)
\(938\) 40.6069 1.32586
\(939\) 23.5289 0.767838
\(940\) −0.119296 −0.00389102
\(941\) −17.6384 −0.574995 −0.287498 0.957781i \(-0.592823\pi\)
−0.287498 + 0.957781i \(0.592823\pi\)
\(942\) −64.3380 −2.09624
\(943\) 31.7728 1.03466
\(944\) 3.82592 0.124523
\(945\) 3.77793 0.122896
\(946\) −32.7990 −1.06639
\(947\) −18.8627 −0.612957 −0.306478 0.951878i \(-0.599151\pi\)
−0.306478 + 0.951878i \(0.599151\pi\)
\(948\) 7.02094 0.228030
\(949\) 18.2410 0.592127
\(950\) 12.7124 0.412445
\(951\) 2.36431 0.0766680
\(952\) −34.9174 −1.13168
\(953\) −7.39553 −0.239565 −0.119782 0.992800i \(-0.538220\pi\)
−0.119782 + 0.992800i \(0.538220\pi\)
\(954\) −1.10528 −0.0357846
\(955\) −2.32899 −0.0753643
\(956\) −1.54750 −0.0500498
\(957\) 6.20016 0.200423
\(958\) −15.4379 −0.498774
\(959\) −22.9347 −0.740601
\(960\) −15.0154 −0.484618
\(961\) −29.7035 −0.958176
\(962\) −33.5454 −1.08155
\(963\) 10.0487 0.323814
\(964\) 0.775237 0.0249687
\(965\) −2.46956 −0.0794980
\(966\) 43.4971 1.39950
\(967\) 7.49708 0.241090 0.120545 0.992708i \(-0.461536\pi\)
0.120545 + 0.992708i \(0.461536\pi\)
\(968\) −10.0838 −0.324106
\(969\) −24.6941 −0.793289
\(970\) 7.95326 0.255364
\(971\) −10.0837 −0.323602 −0.161801 0.986823i \(-0.551730\pi\)
−0.161801 + 0.986823i \(0.551730\pi\)
\(972\) 4.16417 0.133566
\(973\) 2.32195 0.0744383
\(974\) 55.7382 1.78597
\(975\) 23.0432 0.737973
\(976\) 39.5160 1.26488
\(977\) −18.4119 −0.589048 −0.294524 0.955644i \(-0.595161\pi\)
−0.294524 + 0.955644i \(0.595161\pi\)
\(978\) −1.75686 −0.0561783
\(979\) 25.3869 0.811369
\(980\) −0.281962 −0.00900695
\(981\) 35.6859 1.13936
\(982\) −20.0530 −0.639917
\(983\) 20.7157 0.660729 0.330364 0.943853i \(-0.392828\pi\)
0.330364 + 0.943853i \(0.392828\pi\)
\(984\) −33.8688 −1.07970
\(985\) 11.4606 0.365166
\(986\) 6.74884 0.214927
\(987\) −3.55398 −0.113125
\(988\) 1.14827 0.0365314
\(989\) −55.9316 −1.77852
\(990\) 5.80049 0.184352
\(991\) −7.41403 −0.235514 −0.117757 0.993042i \(-0.537570\pi\)
−0.117757 + 0.993042i \(0.537570\pi\)
\(992\) −1.46258 −0.0464371
\(993\) −69.2242 −2.19676
\(994\) −21.2474 −0.673927
\(995\) 18.5045 0.586631
\(996\) 4.42241 0.140130
\(997\) 14.7768 0.467985 0.233992 0.972238i \(-0.424821\pi\)
0.233992 + 0.972238i \(0.424821\pi\)
\(998\) 9.86287 0.312204
\(999\) 22.9793 0.727034
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 4031.2.a.b.1.18 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4031.2.a.b.1.18 59 1.1 even 1 trivial