Properties

Label 4334.2.a.f.1.1
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, 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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.03203 q^{3} +1.00000 q^{4} +0.166109 q^{5} -3.03203 q^{6} -3.81414 q^{7} +1.00000 q^{8} +6.19318 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.03203 q^{3} +1.00000 q^{4} +0.166109 q^{5} -3.03203 q^{6} -3.81414 q^{7} +1.00000 q^{8} +6.19318 q^{9} +0.166109 q^{10} -1.00000 q^{11} -3.03203 q^{12} -0.0506337 q^{13} -3.81414 q^{14} -0.503646 q^{15} +1.00000 q^{16} -6.87105 q^{17} +6.19318 q^{18} +6.14963 q^{19} +0.166109 q^{20} +11.5646 q^{21} -1.00000 q^{22} +0.511723 q^{23} -3.03203 q^{24} -4.97241 q^{25} -0.0506337 q^{26} -9.68181 q^{27} -3.81414 q^{28} -2.35600 q^{29} -0.503646 q^{30} +8.10625 q^{31} +1.00000 q^{32} +3.03203 q^{33} -6.87105 q^{34} -0.633562 q^{35} +6.19318 q^{36} -6.88083 q^{37} +6.14963 q^{38} +0.153523 q^{39} +0.166109 q^{40} -11.6490 q^{41} +11.5646 q^{42} -3.00175 q^{43} -1.00000 q^{44} +1.02874 q^{45} +0.511723 q^{46} +0.127523 q^{47} -3.03203 q^{48} +7.54764 q^{49} -4.97241 q^{50} +20.8332 q^{51} -0.0506337 q^{52} -13.4512 q^{53} -9.68181 q^{54} -0.166109 q^{55} -3.81414 q^{56} -18.6458 q^{57} -2.35600 q^{58} -5.81311 q^{59} -0.503646 q^{60} +8.08229 q^{61} +8.10625 q^{62} -23.6216 q^{63} +1.00000 q^{64} -0.00841070 q^{65} +3.03203 q^{66} +10.7866 q^{67} -6.87105 q^{68} -1.55156 q^{69} -0.633562 q^{70} +6.76163 q^{71} +6.19318 q^{72} +16.3022 q^{73} -6.88083 q^{74} +15.0765 q^{75} +6.14963 q^{76} +3.81414 q^{77} +0.153523 q^{78} +12.7809 q^{79} +0.166109 q^{80} +10.7760 q^{81} -11.6490 q^{82} -3.92290 q^{83} +11.5646 q^{84} -1.14134 q^{85} -3.00175 q^{86} +7.14345 q^{87} -1.00000 q^{88} +6.40229 q^{89} +1.02874 q^{90} +0.193124 q^{91} +0.511723 q^{92} -24.5784 q^{93} +0.127523 q^{94} +1.02151 q^{95} -3.03203 q^{96} +2.08250 q^{97} +7.54764 q^{98} -6.19318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 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
\(3\) −3.03203 −1.75054 −0.875271 0.483634i \(-0.839317\pi\)
−0.875271 + 0.483634i \(0.839317\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.166109 0.0742861 0.0371431 0.999310i \(-0.488174\pi\)
0.0371431 + 0.999310i \(0.488174\pi\)
\(6\) −3.03203 −1.23782
\(7\) −3.81414 −1.44161 −0.720804 0.693139i \(-0.756227\pi\)
−0.720804 + 0.693139i \(0.756227\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.19318 2.06439
\(10\) 0.166109 0.0525282
\(11\) −1.00000 −0.301511
\(12\) −3.03203 −0.875271
\(13\) −0.0506337 −0.0140433 −0.00702163 0.999975i \(-0.502235\pi\)
−0.00702163 + 0.999975i \(0.502235\pi\)
\(14\) −3.81414 −1.01937
\(15\) −0.503646 −0.130041
\(16\) 1.00000 0.250000
\(17\) −6.87105 −1.66648 −0.833238 0.552915i \(-0.813515\pi\)
−0.833238 + 0.552915i \(0.813515\pi\)
\(18\) 6.19318 1.45975
\(19\) 6.14963 1.41082 0.705411 0.708798i \(-0.250762\pi\)
0.705411 + 0.708798i \(0.250762\pi\)
\(20\) 0.166109 0.0371431
\(21\) 11.5646 2.52359
\(22\) −1.00000 −0.213201
\(23\) 0.511723 0.106702 0.0533508 0.998576i \(-0.483010\pi\)
0.0533508 + 0.998576i \(0.483010\pi\)
\(24\) −3.03203 −0.618910
\(25\) −4.97241 −0.994482
\(26\) −0.0506337 −0.00993008
\(27\) −9.68181 −1.86327
\(28\) −3.81414 −0.720804
\(29\) −2.35600 −0.437498 −0.218749 0.975781i \(-0.570198\pi\)
−0.218749 + 0.975781i \(0.570198\pi\)
\(30\) −0.503646 −0.0919528
\(31\) 8.10625 1.45593 0.727963 0.685617i \(-0.240467\pi\)
0.727963 + 0.685617i \(0.240467\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.03203 0.527808
\(34\) −6.87105 −1.17838
\(35\) −0.633562 −0.107091
\(36\) 6.19318 1.03220
\(37\) −6.88083 −1.13120 −0.565601 0.824679i \(-0.691356\pi\)
−0.565601 + 0.824679i \(0.691356\pi\)
\(38\) 6.14963 0.997602
\(39\) 0.153523 0.0245833
\(40\) 0.166109 0.0262641
\(41\) −11.6490 −1.81927 −0.909635 0.415409i \(-0.863638\pi\)
−0.909635 + 0.415409i \(0.863638\pi\)
\(42\) 11.5646 1.78445
\(43\) −3.00175 −0.457763 −0.228882 0.973454i \(-0.573507\pi\)
−0.228882 + 0.973454i \(0.573507\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.02874 0.153356
\(46\) 0.511723 0.0754495
\(47\) 0.127523 0.0186012 0.00930058 0.999957i \(-0.497039\pi\)
0.00930058 + 0.999957i \(0.497039\pi\)
\(48\) −3.03203 −0.437635
\(49\) 7.54764 1.07823
\(50\) −4.97241 −0.703205
\(51\) 20.8332 2.91723
\(52\) −0.0506337 −0.00702163
\(53\) −13.4512 −1.84766 −0.923832 0.382798i \(-0.874961\pi\)
−0.923832 + 0.382798i \(0.874961\pi\)
\(54\) −9.68181 −1.31753
\(55\) −0.166109 −0.0223981
\(56\) −3.81414 −0.509686
\(57\) −18.6458 −2.46970
\(58\) −2.35600 −0.309358
\(59\) −5.81311 −0.756802 −0.378401 0.925642i \(-0.623526\pi\)
−0.378401 + 0.925642i \(0.623526\pi\)
\(60\) −0.503646 −0.0650204
\(61\) 8.08229 1.03483 0.517416 0.855734i \(-0.326894\pi\)
0.517416 + 0.855734i \(0.326894\pi\)
\(62\) 8.10625 1.02949
\(63\) −23.6216 −2.97605
\(64\) 1.00000 0.125000
\(65\) −0.00841070 −0.00104322
\(66\) 3.03203 0.373217
\(67\) 10.7866 1.31780 0.658899 0.752231i \(-0.271022\pi\)
0.658899 + 0.752231i \(0.271022\pi\)
\(68\) −6.87105 −0.833238
\(69\) −1.55156 −0.186786
\(70\) −0.633562 −0.0757251
\(71\) 6.76163 0.802458 0.401229 0.915978i \(-0.368583\pi\)
0.401229 + 0.915978i \(0.368583\pi\)
\(72\) 6.19318 0.729874
\(73\) 16.3022 1.90802 0.954012 0.299768i \(-0.0969092\pi\)
0.954012 + 0.299768i \(0.0969092\pi\)
\(74\) −6.88083 −0.799880
\(75\) 15.0765 1.74088
\(76\) 6.14963 0.705411
\(77\) 3.81414 0.434661
\(78\) 0.153523 0.0173830
\(79\) 12.7809 1.43797 0.718983 0.695028i \(-0.244608\pi\)
0.718983 + 0.695028i \(0.244608\pi\)
\(80\) 0.166109 0.0185715
\(81\) 10.7760 1.19733
\(82\) −11.6490 −1.28642
\(83\) −3.92290 −0.430594 −0.215297 0.976549i \(-0.569072\pi\)
−0.215297 + 0.976549i \(0.569072\pi\)
\(84\) 11.5646 1.26180
\(85\) −1.14134 −0.123796
\(86\) −3.00175 −0.323688
\(87\) 7.14345 0.765858
\(88\) −1.00000 −0.106600
\(89\) 6.40229 0.678641 0.339321 0.940671i \(-0.389803\pi\)
0.339321 + 0.940671i \(0.389803\pi\)
\(90\) 1.02874 0.108439
\(91\) 0.193124 0.0202449
\(92\) 0.511723 0.0533508
\(93\) −24.5784 −2.54866
\(94\) 0.127523 0.0131530
\(95\) 1.02151 0.104804
\(96\) −3.03203 −0.309455
\(97\) 2.08250 0.211446 0.105723 0.994396i \(-0.466284\pi\)
0.105723 + 0.994396i \(0.466284\pi\)
\(98\) 7.54764 0.762427
\(99\) −6.19318 −0.622438
\(100\) −4.97241 −0.497241
\(101\) 14.9644 1.48901 0.744507 0.667615i \(-0.232685\pi\)
0.744507 + 0.667615i \(0.232685\pi\)
\(102\) 20.8332 2.06280
\(103\) −10.0999 −0.995177 −0.497588 0.867413i \(-0.665781\pi\)
−0.497588 + 0.867413i \(0.665781\pi\)
\(104\) −0.0506337 −0.00496504
\(105\) 1.92098 0.187468
\(106\) −13.4512 −1.30650
\(107\) −13.8018 −1.33427 −0.667137 0.744935i \(-0.732480\pi\)
−0.667137 + 0.744935i \(0.732480\pi\)
\(108\) −9.68181 −0.931633
\(109\) −3.10489 −0.297395 −0.148697 0.988883i \(-0.547508\pi\)
−0.148697 + 0.988883i \(0.547508\pi\)
\(110\) −0.166109 −0.0158379
\(111\) 20.8628 1.98021
\(112\) −3.81414 −0.360402
\(113\) −6.10115 −0.573948 −0.286974 0.957938i \(-0.592649\pi\)
−0.286974 + 0.957938i \(0.592649\pi\)
\(114\) −18.6458 −1.74634
\(115\) 0.0850017 0.00792645
\(116\) −2.35600 −0.218749
\(117\) −0.313584 −0.0289908
\(118\) −5.81311 −0.535140
\(119\) 26.2071 2.40240
\(120\) −0.503646 −0.0459764
\(121\) 1.00000 0.0909091
\(122\) 8.08229 0.731736
\(123\) 35.3201 3.18471
\(124\) 8.10625 0.727963
\(125\) −1.65650 −0.148162
\(126\) −23.6216 −2.10438
\(127\) 9.89255 0.877822 0.438911 0.898531i \(-0.355364\pi\)
0.438911 + 0.898531i \(0.355364\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.10140 0.801333
\(130\) −0.00841070 −0.000737667 0
\(131\) −10.7411 −0.938457 −0.469228 0.883077i \(-0.655468\pi\)
−0.469228 + 0.883077i \(0.655468\pi\)
\(132\) 3.03203 0.263904
\(133\) −23.4555 −2.03385
\(134\) 10.7866 0.931824
\(135\) −1.60823 −0.138415
\(136\) −6.87105 −0.589188
\(137\) 18.3506 1.56780 0.783899 0.620889i \(-0.213228\pi\)
0.783899 + 0.620889i \(0.213228\pi\)
\(138\) −1.55156 −0.132077
\(139\) 6.12724 0.519705 0.259853 0.965648i \(-0.416326\pi\)
0.259853 + 0.965648i \(0.416326\pi\)
\(140\) −0.633562 −0.0535457
\(141\) −0.386654 −0.0325621
\(142\) 6.76163 0.567423
\(143\) 0.0506337 0.00423420
\(144\) 6.19318 0.516099
\(145\) −0.391352 −0.0325000
\(146\) 16.3022 1.34918
\(147\) −22.8847 −1.88749
\(148\) −6.88083 −0.565601
\(149\) 3.56325 0.291913 0.145956 0.989291i \(-0.453374\pi\)
0.145956 + 0.989291i \(0.453374\pi\)
\(150\) 15.0765 1.23099
\(151\) 4.62966 0.376756 0.188378 0.982097i \(-0.439677\pi\)
0.188378 + 0.982097i \(0.439677\pi\)
\(152\) 6.14963 0.498801
\(153\) −42.5537 −3.44026
\(154\) 3.81414 0.307352
\(155\) 1.34652 0.108155
\(156\) 0.153523 0.0122916
\(157\) 21.9187 1.74930 0.874652 0.484751i \(-0.161090\pi\)
0.874652 + 0.484751i \(0.161090\pi\)
\(158\) 12.7809 1.01680
\(159\) 40.7844 3.23441
\(160\) 0.166109 0.0131321
\(161\) −1.95178 −0.153822
\(162\) 10.7760 0.846640
\(163\) 6.65441 0.521214 0.260607 0.965445i \(-0.416077\pi\)
0.260607 + 0.965445i \(0.416077\pi\)
\(164\) −11.6490 −0.909635
\(165\) 0.503646 0.0392088
\(166\) −3.92290 −0.304476
\(167\) −7.40584 −0.573081 −0.286540 0.958068i \(-0.592505\pi\)
−0.286540 + 0.958068i \(0.592505\pi\)
\(168\) 11.5646 0.892225
\(169\) −12.9974 −0.999803
\(170\) −1.14134 −0.0875370
\(171\) 38.0858 2.91249
\(172\) −3.00175 −0.228882
\(173\) −5.35677 −0.407268 −0.203634 0.979047i \(-0.565275\pi\)
−0.203634 + 0.979047i \(0.565275\pi\)
\(174\) 7.14345 0.541543
\(175\) 18.9654 1.43365
\(176\) −1.00000 −0.0753778
\(177\) 17.6255 1.32481
\(178\) 6.40229 0.479872
\(179\) 25.5696 1.91116 0.955579 0.294735i \(-0.0952314\pi\)
0.955579 + 0.294735i \(0.0952314\pi\)
\(180\) 1.02874 0.0766779
\(181\) −12.6905 −0.943275 −0.471637 0.881793i \(-0.656337\pi\)
−0.471637 + 0.881793i \(0.656337\pi\)
\(182\) 0.193124 0.0143153
\(183\) −24.5057 −1.81151
\(184\) 0.511723 0.0377247
\(185\) −1.14297 −0.0840325
\(186\) −24.5784 −1.80217
\(187\) 6.87105 0.502461
\(188\) 0.127523 0.00930058
\(189\) 36.9278 2.68610
\(190\) 1.02151 0.0741080
\(191\) 1.69359 0.122544 0.0612720 0.998121i \(-0.480484\pi\)
0.0612720 + 0.998121i \(0.480484\pi\)
\(192\) −3.03203 −0.218818
\(193\) −15.7527 −1.13391 −0.566953 0.823750i \(-0.691878\pi\)
−0.566953 + 0.823750i \(0.691878\pi\)
\(194\) 2.08250 0.149515
\(195\) 0.0255015 0.00182620
\(196\) 7.54764 0.539117
\(197\) −1.00000 −0.0712470
\(198\) −6.19318 −0.440130
\(199\) −12.3738 −0.877157 −0.438579 0.898693i \(-0.644518\pi\)
−0.438579 + 0.898693i \(0.644518\pi\)
\(200\) −4.97241 −0.351602
\(201\) −32.7054 −2.30686
\(202\) 14.9644 1.05289
\(203\) 8.98610 0.630701
\(204\) 20.8332 1.45862
\(205\) −1.93500 −0.135146
\(206\) −10.0999 −0.703696
\(207\) 3.16920 0.220274
\(208\) −0.0506337 −0.00351081
\(209\) −6.14963 −0.425379
\(210\) 1.92098 0.132560
\(211\) 16.7813 1.15527 0.577636 0.816294i \(-0.303975\pi\)
0.577636 + 0.816294i \(0.303975\pi\)
\(212\) −13.4512 −0.923832
\(213\) −20.5014 −1.40474
\(214\) −13.8018 −0.943474
\(215\) −0.498618 −0.0340055
\(216\) −9.68181 −0.658764
\(217\) −30.9183 −2.09887
\(218\) −3.10489 −0.210290
\(219\) −49.4286 −3.34008
\(220\) −0.166109 −0.0111991
\(221\) 0.347907 0.0234027
\(222\) 20.8628 1.40022
\(223\) 12.1229 0.811809 0.405905 0.913915i \(-0.366957\pi\)
0.405905 + 0.913915i \(0.366957\pi\)
\(224\) −3.81414 −0.254843
\(225\) −30.7950 −2.05300
\(226\) −6.10115 −0.405842
\(227\) 29.0275 1.92662 0.963310 0.268390i \(-0.0864917\pi\)
0.963310 + 0.268390i \(0.0864917\pi\)
\(228\) −18.6458 −1.23485
\(229\) 14.6144 0.965750 0.482875 0.875689i \(-0.339593\pi\)
0.482875 + 0.875689i \(0.339593\pi\)
\(230\) 0.0850017 0.00560485
\(231\) −11.5646 −0.760892
\(232\) −2.35600 −0.154679
\(233\) 21.4191 1.40321 0.701605 0.712566i \(-0.252467\pi\)
0.701605 + 0.712566i \(0.252467\pi\)
\(234\) −0.313584 −0.0204996
\(235\) 0.0211827 0.00138181
\(236\) −5.81311 −0.378401
\(237\) −38.7521 −2.51722
\(238\) 26.2071 1.69876
\(239\) −1.92035 −0.124217 −0.0621084 0.998069i \(-0.519782\pi\)
−0.0621084 + 0.998069i \(0.519782\pi\)
\(240\) −0.503646 −0.0325102
\(241\) 13.0050 0.837726 0.418863 0.908049i \(-0.362429\pi\)
0.418863 + 0.908049i \(0.362429\pi\)
\(242\) 1.00000 0.0642824
\(243\) −3.62756 −0.232708
\(244\) 8.08229 0.517416
\(245\) 1.25373 0.0800979
\(246\) 35.3201 2.25193
\(247\) −0.311378 −0.0198125
\(248\) 8.10625 0.514747
\(249\) 11.8943 0.753773
\(250\) −1.65650 −0.104767
\(251\) 25.9958 1.64084 0.820421 0.571760i \(-0.193739\pi\)
0.820421 + 0.571760i \(0.193739\pi\)
\(252\) −23.6216 −1.48802
\(253\) −0.511723 −0.0321718
\(254\) 9.89255 0.620714
\(255\) 3.46058 0.216710
\(256\) 1.00000 0.0625000
\(257\) 20.9429 1.30638 0.653190 0.757194i \(-0.273430\pi\)
0.653190 + 0.757194i \(0.273430\pi\)
\(258\) 9.10140 0.566628
\(259\) 26.2444 1.63075
\(260\) −0.00841070 −0.000521609 0
\(261\) −14.5911 −0.903168
\(262\) −10.7411 −0.663589
\(263\) 25.4745 1.57083 0.785413 0.618972i \(-0.212451\pi\)
0.785413 + 0.618972i \(0.212451\pi\)
\(264\) 3.03203 0.186608
\(265\) −2.23436 −0.137256
\(266\) −23.4555 −1.43815
\(267\) −19.4119 −1.18799
\(268\) 10.7866 0.658899
\(269\) −15.3961 −0.938719 −0.469360 0.883007i \(-0.655515\pi\)
−0.469360 + 0.883007i \(0.655515\pi\)
\(270\) −1.60823 −0.0978740
\(271\) 2.54931 0.154860 0.0774299 0.996998i \(-0.475329\pi\)
0.0774299 + 0.996998i \(0.475329\pi\)
\(272\) −6.87105 −0.416619
\(273\) −0.585556 −0.0354395
\(274\) 18.3506 1.10860
\(275\) 4.97241 0.299847
\(276\) −1.55156 −0.0933928
\(277\) 11.0873 0.666169 0.333084 0.942897i \(-0.391911\pi\)
0.333084 + 0.942897i \(0.391911\pi\)
\(278\) 6.12724 0.367487
\(279\) 50.2035 3.00560
\(280\) −0.633562 −0.0378626
\(281\) −14.2505 −0.850112 −0.425056 0.905167i \(-0.639746\pi\)
−0.425056 + 0.905167i \(0.639746\pi\)
\(282\) −0.386654 −0.0230249
\(283\) 9.22982 0.548656 0.274328 0.961636i \(-0.411545\pi\)
0.274328 + 0.961636i \(0.411545\pi\)
\(284\) 6.76163 0.401229
\(285\) −3.09724 −0.183465
\(286\) 0.0506337 0.00299403
\(287\) 44.4309 2.62267
\(288\) 6.19318 0.364937
\(289\) 30.2114 1.77714
\(290\) −0.391352 −0.0229810
\(291\) −6.31420 −0.370145
\(292\) 16.3022 0.954012
\(293\) 8.18464 0.478152 0.239076 0.971001i \(-0.423155\pi\)
0.239076 + 0.971001i \(0.423155\pi\)
\(294\) −22.8847 −1.33466
\(295\) −0.965608 −0.0562199
\(296\) −6.88083 −0.399940
\(297\) 9.68181 0.561796
\(298\) 3.56325 0.206414
\(299\) −0.0259104 −0.00149844
\(300\) 15.0765 0.870440
\(301\) 11.4491 0.659915
\(302\) 4.62966 0.266407
\(303\) −45.3725 −2.60658
\(304\) 6.14963 0.352706
\(305\) 1.34254 0.0768736
\(306\) −42.5537 −2.43263
\(307\) 20.3784 1.16305 0.581527 0.813527i \(-0.302455\pi\)
0.581527 + 0.813527i \(0.302455\pi\)
\(308\) 3.81414 0.217331
\(309\) 30.6233 1.74210
\(310\) 1.34652 0.0764771
\(311\) −30.4710 −1.72785 −0.863926 0.503619i \(-0.832001\pi\)
−0.863926 + 0.503619i \(0.832001\pi\)
\(312\) 0.153523 0.00869151
\(313\) 17.8210 1.00730 0.503652 0.863907i \(-0.331990\pi\)
0.503652 + 0.863907i \(0.331990\pi\)
\(314\) 21.9187 1.23694
\(315\) −3.92376 −0.221079
\(316\) 12.7809 0.718983
\(317\) −25.2830 −1.42004 −0.710018 0.704184i \(-0.751313\pi\)
−0.710018 + 0.704184i \(0.751313\pi\)
\(318\) 40.7844 2.28707
\(319\) 2.35600 0.131911
\(320\) 0.166109 0.00928576
\(321\) 41.8475 2.33570
\(322\) −1.95178 −0.108769
\(323\) −42.2545 −2.35110
\(324\) 10.7760 0.598665
\(325\) 0.251771 0.0139658
\(326\) 6.65441 0.368554
\(327\) 9.41412 0.520602
\(328\) −11.6490 −0.643209
\(329\) −0.486391 −0.0268156
\(330\) 0.503646 0.0277248
\(331\) −20.1374 −1.10685 −0.553427 0.832898i \(-0.686680\pi\)
−0.553427 + 0.832898i \(0.686680\pi\)
\(332\) −3.92290 −0.215297
\(333\) −42.6142 −2.33524
\(334\) −7.40584 −0.405229
\(335\) 1.79176 0.0978941
\(336\) 11.5646 0.630899
\(337\) 9.66620 0.526551 0.263276 0.964721i \(-0.415197\pi\)
0.263276 + 0.964721i \(0.415197\pi\)
\(338\) −12.9974 −0.706967
\(339\) 18.4988 1.00472
\(340\) −1.14134 −0.0618980
\(341\) −8.10625 −0.438978
\(342\) 38.0858 2.05944
\(343\) −2.08879 −0.112784
\(344\) −3.00175 −0.161844
\(345\) −0.257727 −0.0138756
\(346\) −5.35677 −0.287982
\(347\) 9.15792 0.491623 0.245812 0.969318i \(-0.420946\pi\)
0.245812 + 0.969318i \(0.420946\pi\)
\(348\) 7.14345 0.382929
\(349\) −1.35630 −0.0726009 −0.0363005 0.999341i \(-0.511557\pi\)
−0.0363005 + 0.999341i \(0.511557\pi\)
\(350\) 18.9654 1.01375
\(351\) 0.490226 0.0261663
\(352\) −1.00000 −0.0533002
\(353\) −5.33642 −0.284029 −0.142015 0.989865i \(-0.545358\pi\)
−0.142015 + 0.989865i \(0.545358\pi\)
\(354\) 17.6255 0.936785
\(355\) 1.12317 0.0596115
\(356\) 6.40229 0.339321
\(357\) −79.4607 −4.20551
\(358\) 25.5696 1.35139
\(359\) 18.9002 0.997516 0.498758 0.866741i \(-0.333790\pi\)
0.498758 + 0.866741i \(0.333790\pi\)
\(360\) 1.02874 0.0542195
\(361\) 18.8180 0.990420
\(362\) −12.6905 −0.666996
\(363\) −3.03203 −0.159140
\(364\) 0.193124 0.0101224
\(365\) 2.70793 0.141740
\(366\) −24.5057 −1.28093
\(367\) −19.7230 −1.02953 −0.514765 0.857331i \(-0.672121\pi\)
−0.514765 + 0.857331i \(0.672121\pi\)
\(368\) 0.511723 0.0266754
\(369\) −72.1444 −3.75569
\(370\) −1.14297 −0.0594200
\(371\) 51.3047 2.66361
\(372\) −24.5784 −1.27433
\(373\) −9.58095 −0.496083 −0.248042 0.968749i \(-0.579787\pi\)
−0.248042 + 0.968749i \(0.579787\pi\)
\(374\) 6.87105 0.355294
\(375\) 5.02257 0.259364
\(376\) 0.127523 0.00657651
\(377\) 0.119293 0.00614389
\(378\) 36.9278 1.89936
\(379\) 14.0487 0.721633 0.360817 0.932637i \(-0.382498\pi\)
0.360817 + 0.932637i \(0.382498\pi\)
\(380\) 1.02151 0.0524022
\(381\) −29.9945 −1.53666
\(382\) 1.69359 0.0866517
\(383\) −6.02899 −0.308067 −0.154034 0.988066i \(-0.549226\pi\)
−0.154034 + 0.988066i \(0.549226\pi\)
\(384\) −3.03203 −0.154727
\(385\) 0.633562 0.0322893
\(386\) −15.7527 −0.801793
\(387\) −18.5904 −0.945004
\(388\) 2.08250 0.105723
\(389\) −32.8783 −1.66700 −0.833499 0.552522i \(-0.813666\pi\)
−0.833499 + 0.552522i \(0.813666\pi\)
\(390\) 0.0255015 0.00129132
\(391\) −3.51608 −0.177816
\(392\) 7.54764 0.381214
\(393\) 32.5674 1.64281
\(394\) −1.00000 −0.0503793
\(395\) 2.12302 0.106821
\(396\) −6.19318 −0.311219
\(397\) 18.7499 0.941031 0.470515 0.882392i \(-0.344068\pi\)
0.470515 + 0.882392i \(0.344068\pi\)
\(398\) −12.3738 −0.620244
\(399\) 71.1178 3.56034
\(400\) −4.97241 −0.248620
\(401\) −3.76413 −0.187972 −0.0939858 0.995574i \(-0.529961\pi\)
−0.0939858 + 0.995574i \(0.529961\pi\)
\(402\) −32.7054 −1.63120
\(403\) −0.410449 −0.0204459
\(404\) 14.9644 0.744507
\(405\) 1.78998 0.0889449
\(406\) 8.98610 0.445973
\(407\) 6.88083 0.341070
\(408\) 20.8332 1.03140
\(409\) −9.61873 −0.475616 −0.237808 0.971312i \(-0.576429\pi\)
−0.237808 + 0.971312i \(0.576429\pi\)
\(410\) −1.93500 −0.0955629
\(411\) −55.6395 −2.74449
\(412\) −10.0999 −0.497588
\(413\) 22.1720 1.09101
\(414\) 3.16920 0.155757
\(415\) −0.651628 −0.0319872
\(416\) −0.0506337 −0.00248252
\(417\) −18.5779 −0.909766
\(418\) −6.14963 −0.300788
\(419\) −29.9972 −1.46546 −0.732730 0.680519i \(-0.761754\pi\)
−0.732730 + 0.680519i \(0.761754\pi\)
\(420\) 1.92098 0.0937340
\(421\) 0.643680 0.0313710 0.0156855 0.999877i \(-0.495007\pi\)
0.0156855 + 0.999877i \(0.495007\pi\)
\(422\) 16.7813 0.816901
\(423\) 0.789774 0.0384001
\(424\) −13.4512 −0.653248
\(425\) 34.1657 1.65728
\(426\) −20.5014 −0.993298
\(427\) −30.8270 −1.49182
\(428\) −13.8018 −0.667137
\(429\) −0.153523 −0.00741214
\(430\) −0.498618 −0.0240455
\(431\) −32.5274 −1.56679 −0.783396 0.621523i \(-0.786514\pi\)
−0.783396 + 0.621523i \(0.786514\pi\)
\(432\) −9.68181 −0.465816
\(433\) 27.5766 1.32525 0.662624 0.748953i \(-0.269443\pi\)
0.662624 + 0.748953i \(0.269443\pi\)
\(434\) −30.9183 −1.48413
\(435\) 1.18659 0.0568926
\(436\) −3.10489 −0.148697
\(437\) 3.14691 0.150537
\(438\) −49.4286 −2.36179
\(439\) −6.52532 −0.311437 −0.155718 0.987801i \(-0.549769\pi\)
−0.155718 + 0.987801i \(0.549769\pi\)
\(440\) −0.166109 −0.00791893
\(441\) 46.7439 2.22590
\(442\) 0.347907 0.0165482
\(443\) −40.7089 −1.93414 −0.967068 0.254517i \(-0.918084\pi\)
−0.967068 + 0.254517i \(0.918084\pi\)
\(444\) 20.8628 0.990107
\(445\) 1.06348 0.0504136
\(446\) 12.1229 0.574036
\(447\) −10.8039 −0.511006
\(448\) −3.81414 −0.180201
\(449\) 8.56754 0.404327 0.202164 0.979352i \(-0.435203\pi\)
0.202164 + 0.979352i \(0.435203\pi\)
\(450\) −30.7950 −1.45169
\(451\) 11.6490 0.548530
\(452\) −6.10115 −0.286974
\(453\) −14.0373 −0.659528
\(454\) 29.0275 1.36233
\(455\) 0.0320795 0.00150391
\(456\) −18.6458 −0.873172
\(457\) −19.1190 −0.894350 −0.447175 0.894446i \(-0.647570\pi\)
−0.447175 + 0.894446i \(0.647570\pi\)
\(458\) 14.6144 0.682888
\(459\) 66.5243 3.10509
\(460\) 0.0850017 0.00396323
\(461\) 32.9517 1.53471 0.767356 0.641221i \(-0.221572\pi\)
0.767356 + 0.641221i \(0.221572\pi\)
\(462\) −11.5646 −0.538032
\(463\) −23.3372 −1.08457 −0.542285 0.840195i \(-0.682441\pi\)
−0.542285 + 0.840195i \(0.682441\pi\)
\(464\) −2.35600 −0.109374
\(465\) −4.08268 −0.189330
\(466\) 21.4191 0.992220
\(467\) 35.7040 1.65218 0.826091 0.563536i \(-0.190559\pi\)
0.826091 + 0.563536i \(0.190559\pi\)
\(468\) −0.313584 −0.0144954
\(469\) −41.1417 −1.89975
\(470\) 0.0211827 0.000977086 0
\(471\) −66.4581 −3.06223
\(472\) −5.81311 −0.267570
\(473\) 3.00175 0.138021
\(474\) −38.7521 −1.77994
\(475\) −30.5785 −1.40304
\(476\) 26.2071 1.20120
\(477\) −83.3057 −3.81431
\(478\) −1.92035 −0.0878346
\(479\) 15.6255 0.713945 0.356973 0.934115i \(-0.383809\pi\)
0.356973 + 0.934115i \(0.383809\pi\)
\(480\) −0.503646 −0.0229882
\(481\) 0.348401 0.0158857
\(482\) 13.0050 0.592362
\(483\) 5.91786 0.269272
\(484\) 1.00000 0.0454545
\(485\) 0.345922 0.0157075
\(486\) −3.62756 −0.164550
\(487\) −39.5206 −1.79085 −0.895425 0.445213i \(-0.853128\pi\)
−0.895425 + 0.445213i \(0.853128\pi\)
\(488\) 8.08229 0.365868
\(489\) −20.1763 −0.912406
\(490\) 1.25373 0.0566377
\(491\) 32.0955 1.44845 0.724224 0.689565i \(-0.242198\pi\)
0.724224 + 0.689565i \(0.242198\pi\)
\(492\) 35.3201 1.59235
\(493\) 16.1882 0.729080
\(494\) −0.311378 −0.0140096
\(495\) −1.02874 −0.0462385
\(496\) 8.10625 0.363981
\(497\) −25.7898 −1.15683
\(498\) 11.8943 0.532998
\(499\) −43.8293 −1.96207 −0.981034 0.193836i \(-0.937907\pi\)
−0.981034 + 0.193836i \(0.937907\pi\)
\(500\) −1.65650 −0.0740811
\(501\) 22.4547 1.00320
\(502\) 25.9958 1.16025
\(503\) 30.0284 1.33890 0.669450 0.742857i \(-0.266530\pi\)
0.669450 + 0.742857i \(0.266530\pi\)
\(504\) −23.6216 −1.05219
\(505\) 2.48572 0.110613
\(506\) −0.511723 −0.0227489
\(507\) 39.4086 1.75020
\(508\) 9.89255 0.438911
\(509\) −13.7211 −0.608176 −0.304088 0.952644i \(-0.598352\pi\)
−0.304088 + 0.952644i \(0.598352\pi\)
\(510\) 3.46058 0.153237
\(511\) −62.1787 −2.75062
\(512\) 1.00000 0.0441942
\(513\) −59.5396 −2.62874
\(514\) 20.9429 0.923751
\(515\) −1.67769 −0.0739278
\(516\) 9.10140 0.400667
\(517\) −0.127523 −0.00560846
\(518\) 26.2444 1.15311
\(519\) 16.2419 0.712939
\(520\) −0.00841070 −0.000368833 0
\(521\) −19.4234 −0.850954 −0.425477 0.904969i \(-0.639894\pi\)
−0.425477 + 0.904969i \(0.639894\pi\)
\(522\) −14.5911 −0.638636
\(523\) −26.4242 −1.15545 −0.577725 0.816231i \(-0.696059\pi\)
−0.577725 + 0.816231i \(0.696059\pi\)
\(524\) −10.7411 −0.469228
\(525\) −57.5037 −2.50967
\(526\) 25.4745 1.11074
\(527\) −55.6985 −2.42626
\(528\) 3.03203 0.131952
\(529\) −22.7381 −0.988615
\(530\) −2.23436 −0.0970545
\(531\) −36.0016 −1.56234
\(532\) −23.4555 −1.01693
\(533\) 0.589832 0.0255485
\(534\) −19.4119 −0.840035
\(535\) −2.29261 −0.0991180
\(536\) 10.7866 0.465912
\(537\) −77.5275 −3.34556
\(538\) −15.3961 −0.663775
\(539\) −7.54764 −0.325100
\(540\) −1.60823 −0.0692074
\(541\) −38.7122 −1.66437 −0.832183 0.554501i \(-0.812909\pi\)
−0.832183 + 0.554501i \(0.812909\pi\)
\(542\) 2.54931 0.109502
\(543\) 38.4778 1.65124
\(544\) −6.87105 −0.294594
\(545\) −0.515750 −0.0220923
\(546\) −0.585556 −0.0250595
\(547\) −2.28442 −0.0976748 −0.0488374 0.998807i \(-0.515552\pi\)
−0.0488374 + 0.998807i \(0.515552\pi\)
\(548\) 18.3506 0.783899
\(549\) 50.0551 2.13630
\(550\) 4.97241 0.212024
\(551\) −14.4885 −0.617232
\(552\) −1.55156 −0.0660387
\(553\) −48.7482 −2.07298
\(554\) 11.0873 0.471052
\(555\) 3.46550 0.147102
\(556\) 6.12724 0.259853
\(557\) 13.6862 0.579904 0.289952 0.957041i \(-0.406361\pi\)
0.289952 + 0.957041i \(0.406361\pi\)
\(558\) 50.2035 2.12528
\(559\) 0.151990 0.00642848
\(560\) −0.633562 −0.0267729
\(561\) −20.8332 −0.879579
\(562\) −14.2505 −0.601120
\(563\) 42.1715 1.77732 0.888659 0.458569i \(-0.151638\pi\)
0.888659 + 0.458569i \(0.151638\pi\)
\(564\) −0.386654 −0.0162811
\(565\) −1.01345 −0.0426363
\(566\) 9.22982 0.387958
\(567\) −41.1010 −1.72608
\(568\) 6.76163 0.283712
\(569\) −27.1028 −1.13621 −0.568104 0.822957i \(-0.692323\pi\)
−0.568104 + 0.822957i \(0.692323\pi\)
\(570\) −3.09724 −0.129729
\(571\) 3.74835 0.156863 0.0784317 0.996919i \(-0.475009\pi\)
0.0784317 + 0.996919i \(0.475009\pi\)
\(572\) 0.0506337 0.00211710
\(573\) −5.13501 −0.214518
\(574\) 44.4309 1.85451
\(575\) −2.54450 −0.106113
\(576\) 6.19318 0.258049
\(577\) 9.27951 0.386311 0.193155 0.981168i \(-0.438128\pi\)
0.193155 + 0.981168i \(0.438128\pi\)
\(578\) 30.2114 1.25663
\(579\) 47.7627 1.98495
\(580\) −0.391352 −0.0162500
\(581\) 14.9625 0.620748
\(582\) −6.31420 −0.261732
\(583\) 13.4512 0.557092
\(584\) 16.3022 0.674588
\(585\) −0.0520890 −0.00215361
\(586\) 8.18464 0.338105
\(587\) 1.99899 0.0825071 0.0412535 0.999149i \(-0.486865\pi\)
0.0412535 + 0.999149i \(0.486865\pi\)
\(588\) −22.8847 −0.943747
\(589\) 49.8504 2.05405
\(590\) −0.965608 −0.0397535
\(591\) 3.03203 0.124721
\(592\) −6.88083 −0.282800
\(593\) 5.13124 0.210715 0.105357 0.994434i \(-0.466401\pi\)
0.105357 + 0.994434i \(0.466401\pi\)
\(594\) 9.68181 0.397250
\(595\) 4.35324 0.178465
\(596\) 3.56325 0.145956
\(597\) 37.5178 1.53550
\(598\) −0.0259104 −0.00105956
\(599\) −5.97253 −0.244031 −0.122016 0.992528i \(-0.538936\pi\)
−0.122016 + 0.992528i \(0.538936\pi\)
\(600\) 15.0765 0.615494
\(601\) −20.2190 −0.824750 −0.412375 0.911014i \(-0.635301\pi\)
−0.412375 + 0.911014i \(0.635301\pi\)
\(602\) 11.4491 0.466631
\(603\) 66.8036 2.72045
\(604\) 4.62966 0.188378
\(605\) 0.166109 0.00675328
\(606\) −45.3725 −1.84313
\(607\) 5.55943 0.225650 0.112825 0.993615i \(-0.464010\pi\)
0.112825 + 0.993615i \(0.464010\pi\)
\(608\) 6.14963 0.249401
\(609\) −27.2461 −1.10407
\(610\) 1.34254 0.0543578
\(611\) −0.00645696 −0.000261221 0
\(612\) −42.5537 −1.72013
\(613\) −3.79740 −0.153376 −0.0766878 0.997055i \(-0.524434\pi\)
−0.0766878 + 0.997055i \(0.524434\pi\)
\(614\) 20.3784 0.822404
\(615\) 5.86698 0.236579
\(616\) 3.81414 0.153676
\(617\) −3.92954 −0.158197 −0.0790986 0.996867i \(-0.525204\pi\)
−0.0790986 + 0.996867i \(0.525204\pi\)
\(618\) 30.6233 1.23185
\(619\) 17.6742 0.710388 0.355194 0.934793i \(-0.384415\pi\)
0.355194 + 0.934793i \(0.384415\pi\)
\(620\) 1.34652 0.0540775
\(621\) −4.95441 −0.198814
\(622\) −30.4710 −1.22178
\(623\) −24.4192 −0.978335
\(624\) 0.153523 0.00614582
\(625\) 24.5869 0.983475
\(626\) 17.8210 0.712271
\(627\) 18.6458 0.744643
\(628\) 21.9187 0.874652
\(629\) 47.2785 1.88512
\(630\) −3.92376 −0.156326
\(631\) 0.316869 0.0126144 0.00630718 0.999980i \(-0.497992\pi\)
0.00630718 + 0.999980i \(0.497992\pi\)
\(632\) 12.7809 0.508398
\(633\) −50.8813 −2.02235
\(634\) −25.2830 −1.00412
\(635\) 1.64324 0.0652100
\(636\) 40.7844 1.61721
\(637\) −0.382165 −0.0151419
\(638\) 2.35600 0.0932749
\(639\) 41.8760 1.65659
\(640\) 0.166109 0.00656603
\(641\) −0.517942 −0.0204575 −0.0102287 0.999948i \(-0.503256\pi\)
−0.0102287 + 0.999948i \(0.503256\pi\)
\(642\) 41.8475 1.65159
\(643\) −19.5342 −0.770352 −0.385176 0.922843i \(-0.625859\pi\)
−0.385176 + 0.922843i \(0.625859\pi\)
\(644\) −1.95178 −0.0769110
\(645\) 1.51182 0.0595279
\(646\) −42.2545 −1.66248
\(647\) 27.5050 1.08133 0.540666 0.841237i \(-0.318172\pi\)
0.540666 + 0.841237i \(0.318172\pi\)
\(648\) 10.7760 0.423320
\(649\) 5.81311 0.228184
\(650\) 0.251771 0.00987528
\(651\) 93.7452 3.67417
\(652\) 6.65441 0.260607
\(653\) −10.5515 −0.412912 −0.206456 0.978456i \(-0.566193\pi\)
−0.206456 + 0.978456i \(0.566193\pi\)
\(654\) 9.41412 0.368121
\(655\) −1.78420 −0.0697143
\(656\) −11.6490 −0.454817
\(657\) 100.962 3.93891
\(658\) −0.486391 −0.0189615
\(659\) 11.6989 0.455724 0.227862 0.973693i \(-0.426827\pi\)
0.227862 + 0.973693i \(0.426827\pi\)
\(660\) 0.503646 0.0196044
\(661\) 38.8021 1.50923 0.754614 0.656169i \(-0.227824\pi\)
0.754614 + 0.656169i \(0.227824\pi\)
\(662\) −20.1374 −0.782664
\(663\) −1.05486 −0.0409674
\(664\) −3.92290 −0.152238
\(665\) −3.89617 −0.151087
\(666\) −42.6142 −1.65127
\(667\) −1.20562 −0.0466818
\(668\) −7.40584 −0.286540
\(669\) −36.7569 −1.42111
\(670\) 1.79176 0.0692216
\(671\) −8.08229 −0.312013
\(672\) 11.5646 0.446113
\(673\) 13.2547 0.510930 0.255465 0.966818i \(-0.417771\pi\)
0.255465 + 0.966818i \(0.417771\pi\)
\(674\) 9.66620 0.372328
\(675\) 48.1419 1.85298
\(676\) −12.9974 −0.499901
\(677\) 37.2988 1.43351 0.716755 0.697325i \(-0.245626\pi\)
0.716755 + 0.697325i \(0.245626\pi\)
\(678\) 18.4988 0.710444
\(679\) −7.94295 −0.304823
\(680\) −1.14134 −0.0437685
\(681\) −88.0120 −3.37263
\(682\) −8.10625 −0.310404
\(683\) −37.2642 −1.42588 −0.712938 0.701227i \(-0.752636\pi\)
−0.712938 + 0.701227i \(0.752636\pi\)
\(684\) 38.0858 1.45625
\(685\) 3.04820 0.116466
\(686\) −2.08879 −0.0797503
\(687\) −44.3114 −1.69058
\(688\) −3.00175 −0.114441
\(689\) 0.681083 0.0259472
\(690\) −0.257727 −0.00981152
\(691\) 35.3757 1.34576 0.672878 0.739753i \(-0.265058\pi\)
0.672878 + 0.739753i \(0.265058\pi\)
\(692\) −5.35677 −0.203634
\(693\) 23.6216 0.897312
\(694\) 9.15792 0.347630
\(695\) 1.01779 0.0386069
\(696\) 7.14345 0.270772
\(697\) 80.0409 3.03177
\(698\) −1.35630 −0.0513366
\(699\) −64.9432 −2.45638
\(700\) 18.9654 0.716826
\(701\) −18.8161 −0.710674 −0.355337 0.934738i \(-0.615634\pi\)
−0.355337 + 0.934738i \(0.615634\pi\)
\(702\) 0.490226 0.0185024
\(703\) −42.3146 −1.59592
\(704\) −1.00000 −0.0376889
\(705\) −0.0642266 −0.00241891
\(706\) −5.33642 −0.200839
\(707\) −57.0763 −2.14657
\(708\) 17.6255 0.662407
\(709\) 19.3600 0.727079 0.363540 0.931579i \(-0.381568\pi\)
0.363540 + 0.931579i \(0.381568\pi\)
\(710\) 1.12317 0.0421517
\(711\) 79.1546 2.96853
\(712\) 6.40229 0.239936
\(713\) 4.14816 0.155350
\(714\) −79.4607 −2.97374
\(715\) 0.00841070 0.000314542 0
\(716\) 25.5696 0.955579
\(717\) 5.82254 0.217447
\(718\) 18.9002 0.705351
\(719\) 13.3509 0.497903 0.248952 0.968516i \(-0.419914\pi\)
0.248952 + 0.968516i \(0.419914\pi\)
\(720\) 1.02874 0.0383390
\(721\) 38.5226 1.43466
\(722\) 18.8180 0.700332
\(723\) −39.4315 −1.46647
\(724\) −12.6905 −0.471637
\(725\) 11.7150 0.435084
\(726\) −3.03203 −0.112529
\(727\) −27.2684 −1.01133 −0.505665 0.862730i \(-0.668753\pi\)
−0.505665 + 0.862730i \(0.668753\pi\)
\(728\) 0.193124 0.00715764
\(729\) −21.3290 −0.789964
\(730\) 2.70793 0.100225
\(731\) 20.6252 0.762851
\(732\) −24.5057 −0.905757
\(733\) −31.8139 −1.17507 −0.587537 0.809198i \(-0.699902\pi\)
−0.587537 + 0.809198i \(0.699902\pi\)
\(734\) −19.7230 −0.727988
\(735\) −3.80134 −0.140215
\(736\) 0.511723 0.0188624
\(737\) −10.7866 −0.397331
\(738\) −72.1444 −2.65567
\(739\) 19.4469 0.715366 0.357683 0.933843i \(-0.383567\pi\)
0.357683 + 0.933843i \(0.383567\pi\)
\(740\) −1.14297 −0.0420163
\(741\) 0.944107 0.0346827
\(742\) 51.3047 1.88346
\(743\) 12.8043 0.469745 0.234872 0.972026i \(-0.424533\pi\)
0.234872 + 0.972026i \(0.424533\pi\)
\(744\) −24.5784 −0.901086
\(745\) 0.591887 0.0216851
\(746\) −9.58095 −0.350784
\(747\) −24.2952 −0.888916
\(748\) 6.87105 0.251231
\(749\) 52.6421 1.92350
\(750\) 5.02257 0.183398
\(751\) 30.6629 1.11890 0.559452 0.828863i \(-0.311012\pi\)
0.559452 + 0.828863i \(0.311012\pi\)
\(752\) 0.127523 0.00465029
\(753\) −78.8200 −2.87236
\(754\) 0.119293 0.00434439
\(755\) 0.769027 0.0279878
\(756\) 36.9278 1.34305
\(757\) −20.9154 −0.760182 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(758\) 14.0487 0.510272
\(759\) 1.55156 0.0563180
\(760\) 1.02151 0.0370540
\(761\) 1.90068 0.0688997 0.0344499 0.999406i \(-0.489032\pi\)
0.0344499 + 0.999406i \(0.489032\pi\)
\(762\) −29.9945 −1.08658
\(763\) 11.8425 0.428727
\(764\) 1.69359 0.0612720
\(765\) −7.06854 −0.255564
\(766\) −6.02899 −0.217836
\(767\) 0.294339 0.0106280
\(768\) −3.03203 −0.109409
\(769\) −17.2441 −0.621840 −0.310920 0.950436i \(-0.600637\pi\)
−0.310920 + 0.950436i \(0.600637\pi\)
\(770\) 0.633562 0.0228320
\(771\) −63.4993 −2.28687
\(772\) −15.7527 −0.566953
\(773\) 46.3368 1.66662 0.833309 0.552807i \(-0.186443\pi\)
0.833309 + 0.552807i \(0.186443\pi\)
\(774\) −18.5904 −0.668219
\(775\) −40.3076 −1.44789
\(776\) 2.08250 0.0747575
\(777\) −79.5738 −2.85469
\(778\) −32.8783 −1.17875
\(779\) −71.6371 −2.56667
\(780\) 0.0255015 0.000913098 0
\(781\) −6.76163 −0.241950
\(782\) −3.51608 −0.125735
\(783\) 22.8103 0.815175
\(784\) 7.54764 0.269559
\(785\) 3.64089 0.129949
\(786\) 32.5674 1.16164
\(787\) 6.64678 0.236932 0.118466 0.992958i \(-0.462202\pi\)
0.118466 + 0.992958i \(0.462202\pi\)
\(788\) −1.00000 −0.0356235
\(789\) −77.2394 −2.74980
\(790\) 2.12302 0.0755338
\(791\) 23.2706 0.827408
\(792\) −6.19318 −0.220065
\(793\) −0.409236 −0.0145324
\(794\) 18.7499 0.665409
\(795\) 6.77464 0.240272
\(796\) −12.3738 −0.438579
\(797\) −20.9608 −0.742470 −0.371235 0.928539i \(-0.621066\pi\)
−0.371235 + 0.928539i \(0.621066\pi\)
\(798\) 71.1178 2.51754
\(799\) −0.876219 −0.0309984
\(800\) −4.97241 −0.175801
\(801\) 39.6505 1.40098
\(802\) −3.76413 −0.132916
\(803\) −16.3022 −0.575291
\(804\) −32.7054 −1.15343
\(805\) −0.324208 −0.0114268
\(806\) −0.410449 −0.0144575
\(807\) 46.6815 1.64327
\(808\) 14.9644 0.526446
\(809\) −15.1008 −0.530917 −0.265458 0.964122i \(-0.585523\pi\)
−0.265458 + 0.964122i \(0.585523\pi\)
\(810\) 1.78998 0.0628936
\(811\) 44.6558 1.56808 0.784038 0.620713i \(-0.213157\pi\)
0.784038 + 0.620713i \(0.213157\pi\)
\(812\) 8.98610 0.315350
\(813\) −7.72959 −0.271088
\(814\) 6.88083 0.241173
\(815\) 1.10536 0.0387189
\(816\) 20.8332 0.729308
\(817\) −18.4597 −0.645823
\(818\) −9.61873 −0.336311
\(819\) 1.19605 0.0417934
\(820\) −1.93500 −0.0675732
\(821\) 7.56295 0.263949 0.131974 0.991253i \(-0.457868\pi\)
0.131974 + 0.991253i \(0.457868\pi\)
\(822\) −55.6395 −1.94065
\(823\) −38.3827 −1.33794 −0.668968 0.743291i \(-0.733264\pi\)
−0.668968 + 0.743291i \(0.733264\pi\)
\(824\) −10.0999 −0.351848
\(825\) −15.0765 −0.524895
\(826\) 22.1720 0.771462
\(827\) −15.6983 −0.545882 −0.272941 0.962031i \(-0.587996\pi\)
−0.272941 + 0.962031i \(0.587996\pi\)
\(828\) 3.16920 0.110137
\(829\) 39.2791 1.36422 0.682110 0.731250i \(-0.261063\pi\)
0.682110 + 0.731250i \(0.261063\pi\)
\(830\) −0.651628 −0.0226183
\(831\) −33.6168 −1.16616
\(832\) −0.0506337 −0.00175541
\(833\) −51.8603 −1.79685
\(834\) −18.5779 −0.643302
\(835\) −1.23017 −0.0425719
\(836\) −6.14963 −0.212689
\(837\) −78.4832 −2.71278
\(838\) −29.9972 −1.03624
\(839\) 22.9830 0.793461 0.396730 0.917935i \(-0.370145\pi\)
0.396730 + 0.917935i \(0.370145\pi\)
\(840\) 1.92098 0.0662800
\(841\) −23.4493 −0.808596
\(842\) 0.643680 0.0221827
\(843\) 43.2078 1.48816
\(844\) 16.7813 0.577636
\(845\) −2.15899 −0.0742715
\(846\) 0.789774 0.0271530
\(847\) −3.81414 −0.131055
\(848\) −13.4512 −0.461916
\(849\) −27.9851 −0.960445
\(850\) 34.1657 1.17187
\(851\) −3.52108 −0.120701
\(852\) −20.5014 −0.702368
\(853\) 30.7087 1.05145 0.525723 0.850656i \(-0.323795\pi\)
0.525723 + 0.850656i \(0.323795\pi\)
\(854\) −30.8270 −1.05488
\(855\) 6.32638 0.216358
\(856\) −13.8018 −0.471737
\(857\) −28.8363 −0.985029 −0.492515 0.870304i \(-0.663922\pi\)
−0.492515 + 0.870304i \(0.663922\pi\)
\(858\) −0.153523 −0.00524117
\(859\) 31.3542 1.06979 0.534895 0.844918i \(-0.320351\pi\)
0.534895 + 0.844918i \(0.320351\pi\)
\(860\) −0.498618 −0.0170027
\(861\) −134.716 −4.59110
\(862\) −32.5274 −1.10789
\(863\) 9.48537 0.322886 0.161443 0.986882i \(-0.448385\pi\)
0.161443 + 0.986882i \(0.448385\pi\)
\(864\) −9.68181 −0.329382
\(865\) −0.889807 −0.0302543
\(866\) 27.5766 0.937091
\(867\) −91.6017 −3.11096
\(868\) −30.9183 −1.04944
\(869\) −12.7809 −0.433563
\(870\) 1.18659 0.0402292
\(871\) −0.546167 −0.0185062
\(872\) −3.10489 −0.105145
\(873\) 12.8973 0.436508
\(874\) 3.14691 0.106446
\(875\) 6.31814 0.213592
\(876\) −49.4286 −1.67004
\(877\) −43.3408 −1.46352 −0.731758 0.681564i \(-0.761300\pi\)
−0.731758 + 0.681564i \(0.761300\pi\)
\(878\) −6.52532 −0.220219
\(879\) −24.8161 −0.837025
\(880\) −0.166109 −0.00559953
\(881\) −26.2998 −0.886062 −0.443031 0.896506i \(-0.646097\pi\)
−0.443031 + 0.896506i \(0.646097\pi\)
\(882\) 46.7439 1.57395
\(883\) 1.37722 0.0463473 0.0231736 0.999731i \(-0.492623\pi\)
0.0231736 + 0.999731i \(0.492623\pi\)
\(884\) 0.347907 0.0117014
\(885\) 2.92775 0.0984152
\(886\) −40.7089 −1.36764
\(887\) −0.276896 −0.00929726 −0.00464863 0.999989i \(-0.501480\pi\)
−0.00464863 + 0.999989i \(0.501480\pi\)
\(888\) 20.8628 0.700111
\(889\) −37.7315 −1.26548
\(890\) 1.06348 0.0356478
\(891\) −10.7760 −0.361008
\(892\) 12.1229 0.405905
\(893\) 0.784221 0.0262429
\(894\) −10.8039 −0.361335
\(895\) 4.24733 0.141972
\(896\) −3.81414 −0.127421
\(897\) 0.0785611 0.00262308
\(898\) 8.56754 0.285903
\(899\) −19.0983 −0.636964
\(900\) −30.7950 −1.02650
\(901\) 92.4239 3.07909
\(902\) 11.6490 0.387869
\(903\) −34.7140 −1.15521
\(904\) −6.10115 −0.202921
\(905\) −2.10800 −0.0700722
\(906\) −14.0373 −0.466356
\(907\) −9.51101 −0.315808 −0.157904 0.987454i \(-0.550474\pi\)
−0.157904 + 0.987454i \(0.550474\pi\)
\(908\) 29.0275 0.963310
\(909\) 92.6773 3.07391
\(910\) 0.0320795 0.00106343
\(911\) −22.3222 −0.739567 −0.369783 0.929118i \(-0.620568\pi\)
−0.369783 + 0.929118i \(0.620568\pi\)
\(912\) −18.6458 −0.617426
\(913\) 3.92290 0.129829
\(914\) −19.1190 −0.632401
\(915\) −4.07062 −0.134570
\(916\) 14.6144 0.482875
\(917\) 40.9681 1.35289
\(918\) 66.5243 2.19563
\(919\) −31.2461 −1.03072 −0.515358 0.856975i \(-0.672341\pi\)
−0.515358 + 0.856975i \(0.672341\pi\)
\(920\) 0.0850017 0.00280242
\(921\) −61.7877 −2.03597
\(922\) 32.9517 1.08521
\(923\) −0.342366 −0.0112691
\(924\) −11.5646 −0.380446
\(925\) 34.2143 1.12496
\(926\) −23.3372 −0.766906
\(927\) −62.5508 −2.05444
\(928\) −2.35600 −0.0773394
\(929\) −32.8420 −1.07751 −0.538755 0.842463i \(-0.681105\pi\)
−0.538755 + 0.842463i \(0.681105\pi\)
\(930\) −4.08268 −0.133876
\(931\) 46.4152 1.52120
\(932\) 21.4191 0.701605
\(933\) 92.3888 3.02467
\(934\) 35.7040 1.16827
\(935\) 1.14134 0.0373259
\(936\) −0.313584 −0.0102498
\(937\) −21.2236 −0.693345 −0.346672 0.937986i \(-0.612688\pi\)
−0.346672 + 0.937986i \(0.612688\pi\)
\(938\) −41.1417 −1.34333
\(939\) −54.0338 −1.76333
\(940\) 0.0211827 0.000690904 0
\(941\) 50.3176 1.64031 0.820154 0.572143i \(-0.193888\pi\)
0.820154 + 0.572143i \(0.193888\pi\)
\(942\) −66.4581 −2.16532
\(943\) −5.96107 −0.194119
\(944\) −5.81311 −0.189201
\(945\) 6.13403 0.199540
\(946\) 3.00175 0.0975955
\(947\) 38.2254 1.24216 0.621079 0.783748i \(-0.286695\pi\)
0.621079 + 0.783748i \(0.286695\pi\)
\(948\) −38.7521 −1.25861
\(949\) −0.825438 −0.0267949
\(950\) −30.5785 −0.992097
\(951\) 76.6588 2.48583
\(952\) 26.2071 0.849378
\(953\) 46.5777 1.50880 0.754401 0.656414i \(-0.227928\pi\)
0.754401 + 0.656414i \(0.227928\pi\)
\(954\) −83.3057 −2.69712
\(955\) 0.281320 0.00910331
\(956\) −1.92035 −0.0621084
\(957\) −7.14345 −0.230915
\(958\) 15.6255 0.504836
\(959\) −69.9917 −2.26015
\(960\) −0.503646 −0.0162551
\(961\) 34.7113 1.11972
\(962\) 0.348401 0.0112329
\(963\) −85.4773 −2.75447
\(964\) 13.0050 0.418863
\(965\) −2.61667 −0.0842335
\(966\) 5.91786 0.190404
\(967\) −4.65602 −0.149727 −0.0748637 0.997194i \(-0.523852\pi\)
−0.0748637 + 0.997194i \(0.523852\pi\)
\(968\) 1.00000 0.0321412
\(969\) 128.117 4.11570
\(970\) 0.345922 0.0111069
\(971\) −34.2132 −1.09795 −0.548977 0.835837i \(-0.684983\pi\)
−0.548977 + 0.835837i \(0.684983\pi\)
\(972\) −3.62756 −0.116354
\(973\) −23.3701 −0.749212
\(974\) −39.5206 −1.26632
\(975\) −0.763377 −0.0244476
\(976\) 8.08229 0.258708
\(977\) −39.2707 −1.25638 −0.628190 0.778060i \(-0.716204\pi\)
−0.628190 + 0.778060i \(0.716204\pi\)
\(978\) −20.1763 −0.645168
\(979\) −6.40229 −0.204618
\(980\) 1.25373 0.0400489
\(981\) −19.2292 −0.613940
\(982\) 32.0955 1.02421
\(983\) −11.9472 −0.381057 −0.190529 0.981682i \(-0.561020\pi\)
−0.190529 + 0.981682i \(0.561020\pi\)
\(984\) 35.3201 1.12596
\(985\) −0.166109 −0.00529267
\(986\) 16.1882 0.515537
\(987\) 1.47475 0.0469418
\(988\) −0.311378 −0.00990627
\(989\) −1.53607 −0.0488441
\(990\) −1.02874 −0.0326956
\(991\) 43.8508 1.39297 0.696483 0.717573i \(-0.254747\pi\)
0.696483 + 0.717573i \(0.254747\pi\)
\(992\) 8.10625 0.257374
\(993\) 61.0572 1.93759
\(994\) −25.7898 −0.818002
\(995\) −2.05540 −0.0651606
\(996\) 11.8943 0.376886
\(997\) −0.622649 −0.0197195 −0.00985974 0.999951i \(-0.503139\pi\)
−0.00985974 + 0.999951i \(0.503139\pi\)
\(998\) −43.8293 −1.38739
\(999\) 66.6189 2.10773
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 4334.2.a.f.1.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.f.1.1 24 1.1 even 1 trivial