Properties

Label 6034.2.a.m.1.13
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
Dimension $21$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.402295 q^{3} +1.00000 q^{4} +1.29038 q^{5} +0.402295 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83816 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.402295 q^{3} +1.00000 q^{4} +1.29038 q^{5} +0.402295 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83816 q^{9} +1.29038 q^{10} -4.26945 q^{11} +0.402295 q^{12} +4.48732 q^{13} +1.00000 q^{14} +0.519113 q^{15} +1.00000 q^{16} -5.29141 q^{17} -2.83816 q^{18} -4.09738 q^{19} +1.29038 q^{20} +0.402295 q^{21} -4.26945 q^{22} +1.57271 q^{23} +0.402295 q^{24} -3.33492 q^{25} +4.48732 q^{26} -2.34866 q^{27} +1.00000 q^{28} -6.89951 q^{29} +0.519113 q^{30} +4.91518 q^{31} +1.00000 q^{32} -1.71758 q^{33} -5.29141 q^{34} +1.29038 q^{35} -2.83816 q^{36} +1.33586 q^{37} -4.09738 q^{38} +1.80523 q^{39} +1.29038 q^{40} -12.7678 q^{41} +0.402295 q^{42} -10.1930 q^{43} -4.26945 q^{44} -3.66230 q^{45} +1.57271 q^{46} -10.9210 q^{47} +0.402295 q^{48} +1.00000 q^{49} -3.33492 q^{50} -2.12871 q^{51} +4.48732 q^{52} +5.46626 q^{53} -2.34866 q^{54} -5.50921 q^{55} +1.00000 q^{56} -1.64836 q^{57} -6.89951 q^{58} -8.89097 q^{59} +0.519113 q^{60} +3.53783 q^{61} +4.91518 q^{62} -2.83816 q^{63} +1.00000 q^{64} +5.79035 q^{65} -1.71758 q^{66} +6.08722 q^{67} -5.29141 q^{68} +0.632695 q^{69} +1.29038 q^{70} +7.41357 q^{71} -2.83816 q^{72} +16.8789 q^{73} +1.33586 q^{74} -1.34162 q^{75} -4.09738 q^{76} -4.26945 q^{77} +1.80523 q^{78} +4.63855 q^{79} +1.29038 q^{80} +7.56962 q^{81} -12.7678 q^{82} +13.3622 q^{83} +0.402295 q^{84} -6.82793 q^{85} -10.1930 q^{86} -2.77563 q^{87} -4.26945 q^{88} -13.1678 q^{89} -3.66230 q^{90} +4.48732 q^{91} +1.57271 q^{92} +1.97735 q^{93} -10.9210 q^{94} -5.28718 q^{95} +0.402295 q^{96} -11.1611 q^{97} +1.00000 q^{98} +12.1174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 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
\(3\) 0.402295 0.232265 0.116132 0.993234i \(-0.462950\pi\)
0.116132 + 0.993234i \(0.462950\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.29038 0.577075 0.288538 0.957469i \(-0.406831\pi\)
0.288538 + 0.957469i \(0.406831\pi\)
\(6\) 0.402295 0.164236
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) −2.83816 −0.946053
\(10\) 1.29038 0.408054
\(11\) −4.26945 −1.28729 −0.643644 0.765325i \(-0.722578\pi\)
−0.643644 + 0.765325i \(0.722578\pi\)
\(12\) 0.402295 0.116132
\(13\) 4.48732 1.24456 0.622279 0.782795i \(-0.286207\pi\)
0.622279 + 0.782795i \(0.286207\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.519113 0.134034
\(16\) 1.00000 0.250000
\(17\) −5.29141 −1.28336 −0.641678 0.766975i \(-0.721761\pi\)
−0.641678 + 0.766975i \(0.721761\pi\)
\(18\) −2.83816 −0.668960
\(19\) −4.09738 −0.940004 −0.470002 0.882665i \(-0.655747\pi\)
−0.470002 + 0.882665i \(0.655747\pi\)
\(20\) 1.29038 0.288538
\(21\) 0.402295 0.0877879
\(22\) −4.26945 −0.910250
\(23\) 1.57271 0.327934 0.163967 0.986466i \(-0.447571\pi\)
0.163967 + 0.986466i \(0.447571\pi\)
\(24\) 0.402295 0.0821181
\(25\) −3.33492 −0.666984
\(26\) 4.48732 0.880036
\(27\) −2.34866 −0.452000
\(28\) 1.00000 0.188982
\(29\) −6.89951 −1.28121 −0.640603 0.767872i \(-0.721316\pi\)
−0.640603 + 0.767872i \(0.721316\pi\)
\(30\) 0.519113 0.0947766
\(31\) 4.91518 0.882792 0.441396 0.897313i \(-0.354483\pi\)
0.441396 + 0.897313i \(0.354483\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.71758 −0.298992
\(34\) −5.29141 −0.907469
\(35\) 1.29038 0.218114
\(36\) −2.83816 −0.473026
\(37\) 1.33586 0.219614 0.109807 0.993953i \(-0.464977\pi\)
0.109807 + 0.993953i \(0.464977\pi\)
\(38\) −4.09738 −0.664684
\(39\) 1.80523 0.289067
\(40\) 1.29038 0.204027
\(41\) −12.7678 −1.99400 −0.997001 0.0773897i \(-0.975341\pi\)
−0.997001 + 0.0773897i \(0.975341\pi\)
\(42\) 0.402295 0.0620754
\(43\) −10.1930 −1.55441 −0.777206 0.629246i \(-0.783364\pi\)
−0.777206 + 0.629246i \(0.783364\pi\)
\(44\) −4.26945 −0.643644
\(45\) −3.66230 −0.545944
\(46\) 1.57271 0.231884
\(47\) −10.9210 −1.59299 −0.796495 0.604646i \(-0.793315\pi\)
−0.796495 + 0.604646i \(0.793315\pi\)
\(48\) 0.402295 0.0580662
\(49\) 1.00000 0.142857
\(50\) −3.33492 −0.471629
\(51\) −2.12871 −0.298078
\(52\) 4.48732 0.622279
\(53\) 5.46626 0.750849 0.375424 0.926853i \(-0.377497\pi\)
0.375424 + 0.926853i \(0.377497\pi\)
\(54\) −2.34866 −0.319612
\(55\) −5.50921 −0.742862
\(56\) 1.00000 0.133631
\(57\) −1.64836 −0.218330
\(58\) −6.89951 −0.905949
\(59\) −8.89097 −1.15751 −0.578753 0.815503i \(-0.696460\pi\)
−0.578753 + 0.815503i \(0.696460\pi\)
\(60\) 0.519113 0.0670172
\(61\) 3.53783 0.452973 0.226487 0.974014i \(-0.427276\pi\)
0.226487 + 0.974014i \(0.427276\pi\)
\(62\) 4.91518 0.624228
\(63\) −2.83816 −0.357574
\(64\) 1.00000 0.125000
\(65\) 5.79035 0.718204
\(66\) −1.71758 −0.211419
\(67\) 6.08722 0.743672 0.371836 0.928298i \(-0.378728\pi\)
0.371836 + 0.928298i \(0.378728\pi\)
\(68\) −5.29141 −0.641678
\(69\) 0.632695 0.0761675
\(70\) 1.29038 0.154230
\(71\) 7.41357 0.879829 0.439915 0.898040i \(-0.355009\pi\)
0.439915 + 0.898040i \(0.355009\pi\)
\(72\) −2.83816 −0.334480
\(73\) 16.8789 1.97553 0.987763 0.155964i \(-0.0498485\pi\)
0.987763 + 0.155964i \(0.0498485\pi\)
\(74\) 1.33586 0.155291
\(75\) −1.34162 −0.154917
\(76\) −4.09738 −0.470002
\(77\) −4.26945 −0.486549
\(78\) 1.80523 0.204402
\(79\) 4.63855 0.521877 0.260939 0.965355i \(-0.415968\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(80\) 1.29038 0.144269
\(81\) 7.56962 0.841069
\(82\) −12.7678 −1.40997
\(83\) 13.3622 1.46670 0.733348 0.679854i \(-0.237957\pi\)
0.733348 + 0.679854i \(0.237957\pi\)
\(84\) 0.402295 0.0438940
\(85\) −6.82793 −0.740593
\(86\) −10.1930 −1.09914
\(87\) −2.77563 −0.297579
\(88\) −4.26945 −0.455125
\(89\) −13.1678 −1.39578 −0.697890 0.716205i \(-0.745878\pi\)
−0.697890 + 0.716205i \(0.745878\pi\)
\(90\) −3.66230 −0.386041
\(91\) 4.48732 0.470399
\(92\) 1.57271 0.163967
\(93\) 1.97735 0.205042
\(94\) −10.9210 −1.12641
\(95\) −5.28718 −0.542454
\(96\) 0.402295 0.0410590
\(97\) −11.1611 −1.13323 −0.566617 0.823981i \(-0.691748\pi\)
−0.566617 + 0.823981i \(0.691748\pi\)
\(98\) 1.00000 0.101015
\(99\) 12.1174 1.21784
\(100\) −3.33492 −0.333492
\(101\) −14.1440 −1.40739 −0.703693 0.710505i \(-0.748467\pi\)
−0.703693 + 0.710505i \(0.748467\pi\)
\(102\) −2.12871 −0.210773
\(103\) 8.10218 0.798331 0.399166 0.916879i \(-0.369300\pi\)
0.399166 + 0.916879i \(0.369300\pi\)
\(104\) 4.48732 0.440018
\(105\) 0.519113 0.0506602
\(106\) 5.46626 0.530930
\(107\) −8.03379 −0.776656 −0.388328 0.921521i \(-0.626947\pi\)
−0.388328 + 0.921521i \(0.626947\pi\)
\(108\) −2.34866 −0.226000
\(109\) −0.168957 −0.0161831 −0.00809155 0.999967i \(-0.502576\pi\)
−0.00809155 + 0.999967i \(0.502576\pi\)
\(110\) −5.50921 −0.525283
\(111\) 0.537410 0.0510087
\(112\) 1.00000 0.0944911
\(113\) 17.0693 1.60574 0.802872 0.596152i \(-0.203304\pi\)
0.802872 + 0.596152i \(0.203304\pi\)
\(114\) −1.64836 −0.154383
\(115\) 2.02940 0.189242
\(116\) −6.89951 −0.640603
\(117\) −12.7357 −1.17742
\(118\) −8.89097 −0.818480
\(119\) −5.29141 −0.485063
\(120\) 0.519113 0.0473883
\(121\) 7.22821 0.657110
\(122\) 3.53783 0.320301
\(123\) −5.13644 −0.463137
\(124\) 4.91518 0.441396
\(125\) −10.7552 −0.961976
\(126\) −2.83816 −0.252843
\(127\) −17.2185 −1.52789 −0.763947 0.645279i \(-0.776741\pi\)
−0.763947 + 0.645279i \(0.776741\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.10058 −0.361036
\(130\) 5.79035 0.507847
\(131\) −14.2327 −1.24352 −0.621759 0.783209i \(-0.713582\pi\)
−0.621759 + 0.783209i \(0.713582\pi\)
\(132\) −1.71758 −0.149496
\(133\) −4.09738 −0.355288
\(134\) 6.08722 0.525855
\(135\) −3.03066 −0.260838
\(136\) −5.29141 −0.453735
\(137\) −10.4057 −0.889019 −0.444510 0.895774i \(-0.646622\pi\)
−0.444510 + 0.895774i \(0.646622\pi\)
\(138\) 0.632695 0.0538585
\(139\) 0.839150 0.0711757 0.0355879 0.999367i \(-0.488670\pi\)
0.0355879 + 0.999367i \(0.488670\pi\)
\(140\) 1.29038 0.109057
\(141\) −4.39345 −0.369996
\(142\) 7.41357 0.622133
\(143\) −19.1584 −1.60211
\(144\) −2.83816 −0.236513
\(145\) −8.90298 −0.739353
\(146\) 16.8789 1.39691
\(147\) 0.402295 0.0331807
\(148\) 1.33586 0.109807
\(149\) 7.11269 0.582694 0.291347 0.956617i \(-0.405897\pi\)
0.291347 + 0.956617i \(0.405897\pi\)
\(150\) −1.34162 −0.109543
\(151\) 4.13649 0.336622 0.168311 0.985734i \(-0.446169\pi\)
0.168311 + 0.985734i \(0.446169\pi\)
\(152\) −4.09738 −0.332342
\(153\) 15.0179 1.21412
\(154\) −4.26945 −0.344042
\(155\) 6.34244 0.509437
\(156\) 1.80523 0.144534
\(157\) −20.8366 −1.66294 −0.831472 0.555566i \(-0.812502\pi\)
−0.831472 + 0.555566i \(0.812502\pi\)
\(158\) 4.63855 0.369023
\(159\) 2.19905 0.174396
\(160\) 1.29038 0.102013
\(161\) 1.57271 0.123947
\(162\) 7.56962 0.594726
\(163\) −10.3606 −0.811503 −0.405752 0.913983i \(-0.632990\pi\)
−0.405752 + 0.913983i \(0.632990\pi\)
\(164\) −12.7678 −0.997001
\(165\) −2.21633 −0.172541
\(166\) 13.3622 1.03711
\(167\) 6.98350 0.540400 0.270200 0.962804i \(-0.412910\pi\)
0.270200 + 0.962804i \(0.412910\pi\)
\(168\) 0.402295 0.0310377
\(169\) 7.13604 0.548926
\(170\) −6.82793 −0.523678
\(171\) 11.6290 0.889294
\(172\) −10.1930 −0.777206
\(173\) 8.61652 0.655102 0.327551 0.944833i \(-0.393777\pi\)
0.327551 + 0.944833i \(0.393777\pi\)
\(174\) −2.77563 −0.210420
\(175\) −3.33492 −0.252096
\(176\) −4.26945 −0.321822
\(177\) −3.57679 −0.268848
\(178\) −13.1678 −0.986966
\(179\) 6.07710 0.454224 0.227112 0.973869i \(-0.427072\pi\)
0.227112 + 0.973869i \(0.427072\pi\)
\(180\) −3.66230 −0.272972
\(181\) 24.2041 1.79907 0.899537 0.436844i \(-0.143904\pi\)
0.899537 + 0.436844i \(0.143904\pi\)
\(182\) 4.48732 0.332622
\(183\) 1.42325 0.105210
\(184\) 1.57271 0.115942
\(185\) 1.72377 0.126734
\(186\) 1.97735 0.144986
\(187\) 22.5914 1.65205
\(188\) −10.9210 −0.796495
\(189\) −2.34866 −0.170840
\(190\) −5.28718 −0.383573
\(191\) −18.9466 −1.37093 −0.685464 0.728106i \(-0.740401\pi\)
−0.685464 + 0.728106i \(0.740401\pi\)
\(192\) 0.402295 0.0290331
\(193\) 7.10269 0.511263 0.255631 0.966774i \(-0.417717\pi\)
0.255631 + 0.966774i \(0.417717\pi\)
\(194\) −11.1611 −0.801317
\(195\) 2.32943 0.166814
\(196\) 1.00000 0.0714286
\(197\) 18.6519 1.32889 0.664447 0.747336i \(-0.268667\pi\)
0.664447 + 0.747336i \(0.268667\pi\)
\(198\) 12.1174 0.861145
\(199\) 18.6356 1.32104 0.660520 0.750808i \(-0.270336\pi\)
0.660520 + 0.750808i \(0.270336\pi\)
\(200\) −3.33492 −0.235814
\(201\) 2.44885 0.172729
\(202\) −14.1440 −0.995172
\(203\) −6.89951 −0.484250
\(204\) −2.12871 −0.149039
\(205\) −16.4754 −1.15069
\(206\) 8.10218 0.564506
\(207\) −4.46361 −0.310243
\(208\) 4.48732 0.311140
\(209\) 17.4936 1.21006
\(210\) 0.519113 0.0358222
\(211\) 15.4689 1.06493 0.532463 0.846454i \(-0.321267\pi\)
0.532463 + 0.846454i \(0.321267\pi\)
\(212\) 5.46626 0.375424
\(213\) 2.98244 0.204354
\(214\) −8.03379 −0.549179
\(215\) −13.1528 −0.897013
\(216\) −2.34866 −0.159806
\(217\) 4.91518 0.333664
\(218\) −0.168957 −0.0114432
\(219\) 6.79029 0.458845
\(220\) −5.50921 −0.371431
\(221\) −23.7442 −1.59721
\(222\) 0.537410 0.0360686
\(223\) 12.2261 0.818718 0.409359 0.912373i \(-0.365752\pi\)
0.409359 + 0.912373i \(0.365752\pi\)
\(224\) 1.00000 0.0668153
\(225\) 9.46503 0.631002
\(226\) 17.0693 1.13543
\(227\) 13.0966 0.869253 0.434626 0.900611i \(-0.356880\pi\)
0.434626 + 0.900611i \(0.356880\pi\)
\(228\) −1.64836 −0.109165
\(229\) 19.3324 1.27752 0.638760 0.769406i \(-0.279448\pi\)
0.638760 + 0.769406i \(0.279448\pi\)
\(230\) 2.02940 0.133815
\(231\) −1.71758 −0.113008
\(232\) −6.89951 −0.452975
\(233\) −17.6137 −1.15392 −0.576958 0.816774i \(-0.695760\pi\)
−0.576958 + 0.816774i \(0.695760\pi\)
\(234\) −12.7357 −0.832561
\(235\) −14.0922 −0.919275
\(236\) −8.89097 −0.578753
\(237\) 1.86606 0.121214
\(238\) −5.29141 −0.342991
\(239\) 13.4662 0.871057 0.435529 0.900175i \(-0.356561\pi\)
0.435529 + 0.900175i \(0.356561\pi\)
\(240\) 0.519113 0.0335086
\(241\) −25.3288 −1.63157 −0.815785 0.578355i \(-0.803695\pi\)
−0.815785 + 0.578355i \(0.803695\pi\)
\(242\) 7.22821 0.464647
\(243\) 10.0912 0.647351
\(244\) 3.53783 0.226487
\(245\) 1.29038 0.0824394
\(246\) −5.13644 −0.327487
\(247\) −18.3863 −1.16989
\(248\) 4.91518 0.312114
\(249\) 5.37555 0.340662
\(250\) −10.7552 −0.680219
\(251\) −1.58647 −0.100137 −0.0500684 0.998746i \(-0.515944\pi\)
−0.0500684 + 0.998746i \(0.515944\pi\)
\(252\) −2.83816 −0.178787
\(253\) −6.71463 −0.422145
\(254\) −17.2185 −1.08038
\(255\) −2.74684 −0.172014
\(256\) 1.00000 0.0625000
\(257\) 12.7615 0.796042 0.398021 0.917376i \(-0.369697\pi\)
0.398021 + 0.917376i \(0.369697\pi\)
\(258\) −4.10058 −0.255291
\(259\) 1.33586 0.0830065
\(260\) 5.79035 0.359102
\(261\) 19.5819 1.21209
\(262\) −14.2327 −0.879300
\(263\) −5.94191 −0.366394 −0.183197 0.983076i \(-0.558645\pi\)
−0.183197 + 0.983076i \(0.558645\pi\)
\(264\) −1.71758 −0.105710
\(265\) 7.05355 0.433296
\(266\) −4.09738 −0.251227
\(267\) −5.29732 −0.324191
\(268\) 6.08722 0.371836
\(269\) −22.8417 −1.39268 −0.696341 0.717711i \(-0.745190\pi\)
−0.696341 + 0.717711i \(0.745190\pi\)
\(270\) −3.03066 −0.184440
\(271\) 4.28619 0.260368 0.130184 0.991490i \(-0.458443\pi\)
0.130184 + 0.991490i \(0.458443\pi\)
\(272\) −5.29141 −0.320839
\(273\) 1.80523 0.109257
\(274\) −10.4057 −0.628631
\(275\) 14.2383 0.858600
\(276\) 0.632695 0.0380837
\(277\) −26.8331 −1.61224 −0.806122 0.591749i \(-0.798438\pi\)
−0.806122 + 0.591749i \(0.798438\pi\)
\(278\) 0.839150 0.0503289
\(279\) −13.9500 −0.835168
\(280\) 1.29038 0.0771150
\(281\) 5.11611 0.305202 0.152601 0.988288i \(-0.451235\pi\)
0.152601 + 0.988288i \(0.451235\pi\)
\(282\) −4.39345 −0.261626
\(283\) −26.1743 −1.55590 −0.777950 0.628326i \(-0.783740\pi\)
−0.777950 + 0.628326i \(0.783740\pi\)
\(284\) 7.41357 0.439915
\(285\) −2.12701 −0.125993
\(286\) −19.1584 −1.13286
\(287\) −12.7678 −0.753662
\(288\) −2.83816 −0.167240
\(289\) 10.9990 0.647000
\(290\) −8.90298 −0.522801
\(291\) −4.49004 −0.263211
\(292\) 16.8789 0.987763
\(293\) −13.5050 −0.788968 −0.394484 0.918903i \(-0.629077\pi\)
−0.394484 + 0.918903i \(0.629077\pi\)
\(294\) 0.402295 0.0234623
\(295\) −11.4727 −0.667968
\(296\) 1.33586 0.0776454
\(297\) 10.0275 0.581854
\(298\) 7.11269 0.412027
\(299\) 7.05727 0.408133
\(300\) −1.34162 −0.0774585
\(301\) −10.1930 −0.587513
\(302\) 4.13649 0.238028
\(303\) −5.69008 −0.326886
\(304\) −4.09738 −0.235001
\(305\) 4.56515 0.261400
\(306\) 15.0179 0.858514
\(307\) 18.7583 1.07059 0.535297 0.844664i \(-0.320200\pi\)
0.535297 + 0.844664i \(0.320200\pi\)
\(308\) −4.26945 −0.243275
\(309\) 3.25946 0.185424
\(310\) 6.34244 0.360227
\(311\) −3.76364 −0.213416 −0.106708 0.994290i \(-0.534031\pi\)
−0.106708 + 0.994290i \(0.534031\pi\)
\(312\) 1.80523 0.102201
\(313\) 14.3209 0.809466 0.404733 0.914435i \(-0.367365\pi\)
0.404733 + 0.914435i \(0.367365\pi\)
\(314\) −20.8366 −1.17588
\(315\) −3.66230 −0.206347
\(316\) 4.63855 0.260939
\(317\) −0.961763 −0.0540180 −0.0270090 0.999635i \(-0.508598\pi\)
−0.0270090 + 0.999635i \(0.508598\pi\)
\(318\) 2.19905 0.123316
\(319\) 29.4571 1.64928
\(320\) 1.29038 0.0721344
\(321\) −3.23195 −0.180390
\(322\) 1.57271 0.0876439
\(323\) 21.6809 1.20636
\(324\) 7.56962 0.420535
\(325\) −14.9649 −0.830101
\(326\) −10.3606 −0.573819
\(327\) −0.0679703 −0.00375877
\(328\) −12.7678 −0.704986
\(329\) −10.9210 −0.602093
\(330\) −2.21633 −0.122005
\(331\) 17.1265 0.941360 0.470680 0.882304i \(-0.344009\pi\)
0.470680 + 0.882304i \(0.344009\pi\)
\(332\) 13.3622 0.733348
\(333\) −3.79139 −0.207767
\(334\) 6.98350 0.382120
\(335\) 7.85482 0.429155
\(336\) 0.402295 0.0219470
\(337\) −11.3371 −0.617570 −0.308785 0.951132i \(-0.599922\pi\)
−0.308785 + 0.951132i \(0.599922\pi\)
\(338\) 7.13604 0.388150
\(339\) 6.86688 0.372958
\(340\) −6.82793 −0.370296
\(341\) −20.9851 −1.13641
\(342\) 11.6290 0.628826
\(343\) 1.00000 0.0539949
\(344\) −10.1930 −0.549568
\(345\) 0.816416 0.0439544
\(346\) 8.61652 0.463227
\(347\) −18.6999 −1.00386 −0.501931 0.864908i \(-0.667377\pi\)
−0.501931 + 0.864908i \(0.667377\pi\)
\(348\) −2.77563 −0.148790
\(349\) 23.4872 1.25724 0.628620 0.777713i \(-0.283620\pi\)
0.628620 + 0.777713i \(0.283620\pi\)
\(350\) −3.33492 −0.178259
\(351\) −10.5392 −0.562540
\(352\) −4.26945 −0.227563
\(353\) 19.2863 1.02650 0.513252 0.858238i \(-0.328441\pi\)
0.513252 + 0.858238i \(0.328441\pi\)
\(354\) −3.57679 −0.190104
\(355\) 9.56633 0.507728
\(356\) −13.1678 −0.697890
\(357\) −2.12871 −0.112663
\(358\) 6.07710 0.321185
\(359\) 8.66200 0.457163 0.228581 0.973525i \(-0.426591\pi\)
0.228581 + 0.973525i \(0.426591\pi\)
\(360\) −3.66230 −0.193020
\(361\) −2.21144 −0.116392
\(362\) 24.2041 1.27214
\(363\) 2.90787 0.152624
\(364\) 4.48732 0.235199
\(365\) 21.7802 1.14003
\(366\) 1.42325 0.0743946
\(367\) −0.608611 −0.0317692 −0.0158846 0.999874i \(-0.505056\pi\)
−0.0158846 + 0.999874i \(0.505056\pi\)
\(368\) 1.57271 0.0819834
\(369\) 36.2372 1.88643
\(370\) 1.72377 0.0896146
\(371\) 5.46626 0.283794
\(372\) 1.97735 0.102521
\(373\) −28.4115 −1.47109 −0.735546 0.677475i \(-0.763074\pi\)
−0.735546 + 0.677475i \(0.763074\pi\)
\(374\) 22.5914 1.16817
\(375\) −4.32677 −0.223433
\(376\) −10.9210 −0.563207
\(377\) −30.9603 −1.59454
\(378\) −2.34866 −0.120802
\(379\) 13.6763 0.702504 0.351252 0.936281i \(-0.385756\pi\)
0.351252 + 0.936281i \(0.385756\pi\)
\(380\) −5.28718 −0.271227
\(381\) −6.92691 −0.354876
\(382\) −18.9466 −0.969393
\(383\) −17.9619 −0.917810 −0.458905 0.888485i \(-0.651758\pi\)
−0.458905 + 0.888485i \(0.651758\pi\)
\(384\) 0.402295 0.0205295
\(385\) −5.50921 −0.280776
\(386\) 7.10269 0.361517
\(387\) 28.9293 1.47056
\(388\) −11.1611 −0.566617
\(389\) −5.82184 −0.295179 −0.147590 0.989049i \(-0.547151\pi\)
−0.147590 + 0.989049i \(0.547151\pi\)
\(390\) 2.32943 0.117955
\(391\) −8.32187 −0.420855
\(392\) 1.00000 0.0505076
\(393\) −5.72574 −0.288826
\(394\) 18.6519 0.939670
\(395\) 5.98549 0.301163
\(396\) 12.1174 0.608921
\(397\) −33.0817 −1.66032 −0.830162 0.557522i \(-0.811752\pi\)
−0.830162 + 0.557522i \(0.811752\pi\)
\(398\) 18.6356 0.934117
\(399\) −1.64836 −0.0825210
\(400\) −3.33492 −0.166746
\(401\) −32.8107 −1.63849 −0.819245 0.573444i \(-0.805607\pi\)
−0.819245 + 0.573444i \(0.805607\pi\)
\(402\) 2.44885 0.122138
\(403\) 22.0560 1.09869
\(404\) −14.1440 −0.703693
\(405\) 9.76769 0.485360
\(406\) −6.89951 −0.342417
\(407\) −5.70340 −0.282707
\(408\) −2.12871 −0.105387
\(409\) 24.4040 1.20670 0.603349 0.797477i \(-0.293833\pi\)
0.603349 + 0.797477i \(0.293833\pi\)
\(410\) −16.4754 −0.813660
\(411\) −4.18616 −0.206488
\(412\) 8.10218 0.399166
\(413\) −8.89097 −0.437496
\(414\) −4.46361 −0.219375
\(415\) 17.2424 0.846394
\(416\) 4.48732 0.220009
\(417\) 0.337585 0.0165316
\(418\) 17.4936 0.855639
\(419\) −32.2470 −1.57537 −0.787685 0.616078i \(-0.788720\pi\)
−0.787685 + 0.616078i \(0.788720\pi\)
\(420\) 0.519113 0.0253301
\(421\) −19.6786 −0.959076 −0.479538 0.877521i \(-0.659196\pi\)
−0.479538 + 0.877521i \(0.659196\pi\)
\(422\) 15.4689 0.753016
\(423\) 30.9955 1.50705
\(424\) 5.46626 0.265465
\(425\) 17.6464 0.855977
\(426\) 2.98244 0.144500
\(427\) 3.53783 0.171208
\(428\) −8.03379 −0.388328
\(429\) −7.70732 −0.372113
\(430\) −13.1528 −0.634284
\(431\) −1.00000 −0.0481683
\(432\) −2.34866 −0.113000
\(433\) −1.99480 −0.0958640 −0.0479320 0.998851i \(-0.515263\pi\)
−0.0479320 + 0.998851i \(0.515263\pi\)
\(434\) 4.91518 0.235936
\(435\) −3.58162 −0.171726
\(436\) −0.168957 −0.00809155
\(437\) −6.44401 −0.308259
\(438\) 6.79029 0.324453
\(439\) −35.9660 −1.71656 −0.858281 0.513180i \(-0.828467\pi\)
−0.858281 + 0.513180i \(0.828467\pi\)
\(440\) −5.50921 −0.262641
\(441\) −2.83816 −0.135150
\(442\) −23.7442 −1.12940
\(443\) −34.2598 −1.62773 −0.813866 0.581053i \(-0.802641\pi\)
−0.813866 + 0.581053i \(0.802641\pi\)
\(444\) 0.537410 0.0255044
\(445\) −16.9914 −0.805471
\(446\) 12.2261 0.578921
\(447\) 2.86140 0.135339
\(448\) 1.00000 0.0472456
\(449\) 3.00677 0.141898 0.0709492 0.997480i \(-0.477397\pi\)
0.0709492 + 0.997480i \(0.477397\pi\)
\(450\) 9.46503 0.446186
\(451\) 54.5117 2.56685
\(452\) 17.0693 0.802872
\(453\) 1.66409 0.0781856
\(454\) 13.0966 0.614654
\(455\) 5.79035 0.271456
\(456\) −1.64836 −0.0771913
\(457\) −19.5362 −0.913863 −0.456931 0.889502i \(-0.651052\pi\)
−0.456931 + 0.889502i \(0.651052\pi\)
\(458\) 19.3324 0.903343
\(459\) 12.4277 0.580076
\(460\) 2.02940 0.0946212
\(461\) 24.2117 1.12765 0.563825 0.825895i \(-0.309329\pi\)
0.563825 + 0.825895i \(0.309329\pi\)
\(462\) −1.71758 −0.0799089
\(463\) 35.4816 1.64897 0.824486 0.565883i \(-0.191465\pi\)
0.824486 + 0.565883i \(0.191465\pi\)
\(464\) −6.89951 −0.320301
\(465\) 2.55153 0.118324
\(466\) −17.6137 −0.815941
\(467\) 25.0107 1.15736 0.578679 0.815555i \(-0.303568\pi\)
0.578679 + 0.815555i \(0.303568\pi\)
\(468\) −12.7357 −0.588709
\(469\) 6.08722 0.281082
\(470\) −14.0922 −0.650026
\(471\) −8.38247 −0.386244
\(472\) −8.89097 −0.409240
\(473\) 43.5184 2.00098
\(474\) 1.86606 0.0857111
\(475\) 13.6644 0.626968
\(476\) −5.29141 −0.242531
\(477\) −15.5141 −0.710343
\(478\) 13.4662 0.615930
\(479\) 2.45113 0.111995 0.0559974 0.998431i \(-0.482166\pi\)
0.0559974 + 0.998431i \(0.482166\pi\)
\(480\) 0.519113 0.0236942
\(481\) 5.99444 0.273323
\(482\) −25.3288 −1.15369
\(483\) 0.632695 0.0287886
\(484\) 7.22821 0.328555
\(485\) −14.4020 −0.653962
\(486\) 10.0912 0.457746
\(487\) −32.6827 −1.48099 −0.740497 0.672060i \(-0.765410\pi\)
−0.740497 + 0.672060i \(0.765410\pi\)
\(488\) 3.53783 0.160150
\(489\) −4.16801 −0.188484
\(490\) 1.29038 0.0582934
\(491\) 40.8488 1.84348 0.921741 0.387805i \(-0.126767\pi\)
0.921741 + 0.387805i \(0.126767\pi\)
\(492\) −5.13644 −0.231568
\(493\) 36.5081 1.64424
\(494\) −18.3863 −0.827238
\(495\) 15.6360 0.702787
\(496\) 4.91518 0.220698
\(497\) 7.41357 0.332544
\(498\) 5.37555 0.240884
\(499\) 21.8637 0.978753 0.489376 0.872073i \(-0.337224\pi\)
0.489376 + 0.872073i \(0.337224\pi\)
\(500\) −10.7552 −0.480988
\(501\) 2.80943 0.125516
\(502\) −1.58647 −0.0708074
\(503\) −20.5702 −0.917182 −0.458591 0.888648i \(-0.651646\pi\)
−0.458591 + 0.888648i \(0.651646\pi\)
\(504\) −2.83816 −0.126422
\(505\) −18.2512 −0.812168
\(506\) −6.71463 −0.298502
\(507\) 2.87079 0.127496
\(508\) −17.2185 −0.763947
\(509\) −28.1182 −1.24632 −0.623158 0.782096i \(-0.714151\pi\)
−0.623158 + 0.782096i \(0.714151\pi\)
\(510\) −2.74684 −0.121632
\(511\) 16.8789 0.746678
\(512\) 1.00000 0.0441942
\(513\) 9.62336 0.424882
\(514\) 12.7615 0.562887
\(515\) 10.4549 0.460697
\(516\) −4.10058 −0.180518
\(517\) 46.6266 2.05064
\(518\) 1.33586 0.0586944
\(519\) 3.46638 0.152157
\(520\) 5.79035 0.253924
\(521\) −20.0445 −0.878167 −0.439083 0.898446i \(-0.644697\pi\)
−0.439083 + 0.898446i \(0.644697\pi\)
\(522\) 19.5819 0.857076
\(523\) 32.6174 1.42626 0.713131 0.701031i \(-0.247277\pi\)
0.713131 + 0.701031i \(0.247277\pi\)
\(524\) −14.2327 −0.621759
\(525\) −1.34162 −0.0585531
\(526\) −5.94191 −0.259079
\(527\) −26.0082 −1.13293
\(528\) −1.71758 −0.0747480
\(529\) −20.5266 −0.892460
\(530\) 7.05355 0.306387
\(531\) 25.2340 1.09506
\(532\) −4.09738 −0.177644
\(533\) −57.2934 −2.48165
\(534\) −5.29732 −0.229238
\(535\) −10.3666 −0.448189
\(536\) 6.08722 0.262928
\(537\) 2.44478 0.105500
\(538\) −22.8417 −0.984775
\(539\) −4.26945 −0.183898
\(540\) −3.03066 −0.130419
\(541\) −45.8958 −1.97322 −0.986608 0.163112i \(-0.947847\pi\)
−0.986608 + 0.163112i \(0.947847\pi\)
\(542\) 4.28619 0.184108
\(543\) 9.73717 0.417862
\(544\) −5.29141 −0.226867
\(545\) −0.218018 −0.00933887
\(546\) 1.80523 0.0772565
\(547\) 7.14405 0.305457 0.152729 0.988268i \(-0.451194\pi\)
0.152729 + 0.988268i \(0.451194\pi\)
\(548\) −10.4057 −0.444510
\(549\) −10.0409 −0.428537
\(550\) 14.2383 0.607122
\(551\) 28.2699 1.20434
\(552\) 0.632695 0.0269293
\(553\) 4.63855 0.197251
\(554\) −26.8331 −1.14003
\(555\) 0.693464 0.0294359
\(556\) 0.839150 0.0355879
\(557\) 43.0882 1.82570 0.912852 0.408290i \(-0.133875\pi\)
0.912852 + 0.408290i \(0.133875\pi\)
\(558\) −13.9500 −0.590553
\(559\) −45.7391 −1.93456
\(560\) 1.29038 0.0545285
\(561\) 9.08840 0.383713
\(562\) 5.11611 0.215810
\(563\) 0.116114 0.00489361 0.00244681 0.999997i \(-0.499221\pi\)
0.00244681 + 0.999997i \(0.499221\pi\)
\(564\) −4.39345 −0.184998
\(565\) 22.0259 0.926635
\(566\) −26.1743 −1.10019
\(567\) 7.56962 0.317894
\(568\) 7.41357 0.311067
\(569\) −7.70421 −0.322977 −0.161489 0.986875i \(-0.551630\pi\)
−0.161489 + 0.986875i \(0.551630\pi\)
\(570\) −2.12701 −0.0890905
\(571\) 9.71404 0.406520 0.203260 0.979125i \(-0.434846\pi\)
0.203260 + 0.979125i \(0.434846\pi\)
\(572\) −19.1584 −0.801053
\(573\) −7.62212 −0.318419
\(574\) −12.7678 −0.532919
\(575\) −5.24488 −0.218726
\(576\) −2.83816 −0.118257
\(577\) −38.7478 −1.61309 −0.806547 0.591170i \(-0.798666\pi\)
−0.806547 + 0.591170i \(0.798666\pi\)
\(578\) 10.9990 0.457498
\(579\) 2.85737 0.118748
\(580\) −8.90298 −0.369676
\(581\) 13.3622 0.554359
\(582\) −4.49004 −0.186118
\(583\) −23.3379 −0.966558
\(584\) 16.8789 0.698454
\(585\) −16.4339 −0.679459
\(586\) −13.5050 −0.557885
\(587\) 16.5051 0.681240 0.340620 0.940201i \(-0.389363\pi\)
0.340620 + 0.940201i \(0.389363\pi\)
\(588\) 0.402295 0.0165904
\(589\) −20.1394 −0.829828
\(590\) −11.4727 −0.472325
\(591\) 7.50356 0.308655
\(592\) 1.33586 0.0549036
\(593\) 7.74850 0.318193 0.159096 0.987263i \(-0.449142\pi\)
0.159096 + 0.987263i \(0.449142\pi\)
\(594\) 10.0275 0.411433
\(595\) −6.82793 −0.279918
\(596\) 7.11269 0.291347
\(597\) 7.49699 0.306831
\(598\) 7.05727 0.288593
\(599\) −1.24804 −0.0509934 −0.0254967 0.999675i \(-0.508117\pi\)
−0.0254967 + 0.999675i \(0.508117\pi\)
\(600\) −1.34162 −0.0547714
\(601\) 18.1173 0.739018 0.369509 0.929227i \(-0.379526\pi\)
0.369509 + 0.929227i \(0.379526\pi\)
\(602\) −10.1930 −0.415434
\(603\) −17.2765 −0.703553
\(604\) 4.13649 0.168311
\(605\) 9.32714 0.379202
\(606\) −5.69008 −0.231144
\(607\) 7.48701 0.303888 0.151944 0.988389i \(-0.451447\pi\)
0.151944 + 0.988389i \(0.451447\pi\)
\(608\) −4.09738 −0.166171
\(609\) −2.77563 −0.112474
\(610\) 4.56515 0.184838
\(611\) −49.0060 −1.98257
\(612\) 15.0179 0.607061
\(613\) −22.1711 −0.895484 −0.447742 0.894163i \(-0.647772\pi\)
−0.447742 + 0.894163i \(0.647772\pi\)
\(614\) 18.7583 0.757024
\(615\) −6.62795 −0.267265
\(616\) −4.26945 −0.172021
\(617\) −27.2472 −1.09693 −0.548466 0.836173i \(-0.684788\pi\)
−0.548466 + 0.836173i \(0.684788\pi\)
\(618\) 3.25946 0.131115
\(619\) −26.9935 −1.08496 −0.542480 0.840069i \(-0.682514\pi\)
−0.542480 + 0.840069i \(0.682514\pi\)
\(620\) 6.34244 0.254719
\(621\) −3.69377 −0.148226
\(622\) −3.76364 −0.150908
\(623\) −13.1678 −0.527556
\(624\) 1.80523 0.0722668
\(625\) 2.79629 0.111851
\(626\) 14.3209 0.572379
\(627\) 7.03758 0.281054
\(628\) −20.8366 −0.831472
\(629\) −7.06859 −0.281843
\(630\) −3.66230 −0.145910
\(631\) 28.3347 1.12799 0.563993 0.825780i \(-0.309264\pi\)
0.563993 + 0.825780i \(0.309264\pi\)
\(632\) 4.63855 0.184511
\(633\) 6.22307 0.247345
\(634\) −0.961763 −0.0381965
\(635\) −22.2184 −0.881710
\(636\) 2.19905 0.0871979
\(637\) 4.48732 0.177794
\(638\) 29.4571 1.16622
\(639\) −21.0409 −0.832365
\(640\) 1.29038 0.0510067
\(641\) 10.1810 0.402127 0.201063 0.979578i \(-0.435560\pi\)
0.201063 + 0.979578i \(0.435560\pi\)
\(642\) −3.23195 −0.127555
\(643\) −26.1316 −1.03053 −0.515264 0.857031i \(-0.672306\pi\)
−0.515264 + 0.857031i \(0.672306\pi\)
\(644\) 1.57271 0.0619736
\(645\) −5.29130 −0.208345
\(646\) 21.6809 0.853025
\(647\) −9.77741 −0.384390 −0.192195 0.981357i \(-0.561561\pi\)
−0.192195 + 0.981357i \(0.561561\pi\)
\(648\) 7.56962 0.297363
\(649\) 37.9596 1.49004
\(650\) −14.9649 −0.586970
\(651\) 1.97735 0.0774984
\(652\) −10.3606 −0.405752
\(653\) 4.35039 0.170244 0.0851219 0.996371i \(-0.472872\pi\)
0.0851219 + 0.996371i \(0.472872\pi\)
\(654\) −0.0679703 −0.00265785
\(655\) −18.3656 −0.717604
\(656\) −12.7678 −0.498500
\(657\) −47.9050 −1.86895
\(658\) −10.9210 −0.425744
\(659\) 30.0844 1.17192 0.585961 0.810339i \(-0.300717\pi\)
0.585961 + 0.810339i \(0.300717\pi\)
\(660\) −2.21633 −0.0862704
\(661\) 4.34251 0.168904 0.0844521 0.996428i \(-0.473086\pi\)
0.0844521 + 0.996428i \(0.473086\pi\)
\(662\) 17.1265 0.665642
\(663\) −9.55218 −0.370976
\(664\) 13.3622 0.518555
\(665\) −5.28718 −0.205028
\(666\) −3.79139 −0.146913
\(667\) −10.8509 −0.420150
\(668\) 6.98350 0.270200
\(669\) 4.91848 0.190159
\(670\) 7.85482 0.303458
\(671\) −15.1046 −0.583107
\(672\) 0.402295 0.0155189
\(673\) 35.1476 1.35484 0.677421 0.735596i \(-0.263098\pi\)
0.677421 + 0.735596i \(0.263098\pi\)
\(674\) −11.3371 −0.436688
\(675\) 7.83259 0.301477
\(676\) 7.13604 0.274463
\(677\) 44.3919 1.70612 0.853061 0.521812i \(-0.174744\pi\)
0.853061 + 0.521812i \(0.174744\pi\)
\(678\) 6.86688 0.263721
\(679\) −11.1611 −0.428322
\(680\) −6.82793 −0.261839
\(681\) 5.26870 0.201897
\(682\) −20.9851 −0.803561
\(683\) −22.0053 −0.842011 −0.421006 0.907058i \(-0.638323\pi\)
−0.421006 + 0.907058i \(0.638323\pi\)
\(684\) 11.6290 0.444647
\(685\) −13.4273 −0.513031
\(686\) 1.00000 0.0381802
\(687\) 7.77731 0.296723
\(688\) −10.1930 −0.388603
\(689\) 24.5289 0.934475
\(690\) 0.816416 0.0310804
\(691\) 45.8748 1.74516 0.872580 0.488471i \(-0.162445\pi\)
0.872580 + 0.488471i \(0.162445\pi\)
\(692\) 8.61652 0.327551
\(693\) 12.1174 0.460301
\(694\) −18.6999 −0.709837
\(695\) 1.08282 0.0410738
\(696\) −2.77563 −0.105210
\(697\) 67.5599 2.55901
\(698\) 23.4872 0.889002
\(699\) −7.08592 −0.268014
\(700\) −3.33492 −0.126048
\(701\) −3.27195 −0.123580 −0.0617900 0.998089i \(-0.519681\pi\)
−0.0617900 + 0.998089i \(0.519681\pi\)
\(702\) −10.5392 −0.397776
\(703\) −5.47354 −0.206439
\(704\) −4.26945 −0.160911
\(705\) −5.66923 −0.213515
\(706\) 19.2863 0.725848
\(707\) −14.1440 −0.531942
\(708\) −3.57679 −0.134424
\(709\) −35.3918 −1.32917 −0.664584 0.747214i \(-0.731391\pi\)
−0.664584 + 0.747214i \(0.731391\pi\)
\(710\) 9.56633 0.359018
\(711\) −13.1649 −0.493724
\(712\) −13.1678 −0.493483
\(713\) 7.73017 0.289497
\(714\) −2.12871 −0.0796648
\(715\) −24.7216 −0.924536
\(716\) 6.07710 0.227112
\(717\) 5.41739 0.202316
\(718\) 8.66200 0.323263
\(719\) −36.9034 −1.37626 −0.688132 0.725586i \(-0.741569\pi\)
−0.688132 + 0.725586i \(0.741569\pi\)
\(720\) −3.66230 −0.136486
\(721\) 8.10218 0.301741
\(722\) −2.21144 −0.0823013
\(723\) −10.1896 −0.378956
\(724\) 24.2041 0.899537
\(725\) 23.0093 0.854544
\(726\) 2.90787 0.107921
\(727\) 47.9409 1.77803 0.889014 0.457880i \(-0.151391\pi\)
0.889014 + 0.457880i \(0.151391\pi\)
\(728\) 4.48732 0.166311
\(729\) −18.6492 −0.690712
\(730\) 21.7802 0.806121
\(731\) 53.9351 1.99486
\(732\) 1.42325 0.0526049
\(733\) −7.47973 −0.276270 −0.138135 0.990413i \(-0.544111\pi\)
−0.138135 + 0.990413i \(0.544111\pi\)
\(734\) −0.608611 −0.0224642
\(735\) 0.519113 0.0191478
\(736\) 1.57271 0.0579710
\(737\) −25.9891 −0.957320
\(738\) 36.2372 1.33391
\(739\) −21.5957 −0.794410 −0.397205 0.917730i \(-0.630020\pi\)
−0.397205 + 0.917730i \(0.630020\pi\)
\(740\) 1.72377 0.0633671
\(741\) −7.39670 −0.271725
\(742\) 5.46626 0.200673
\(743\) −29.2867 −1.07443 −0.537213 0.843447i \(-0.680523\pi\)
−0.537213 + 0.843447i \(0.680523\pi\)
\(744\) 1.97735 0.0724931
\(745\) 9.17807 0.336258
\(746\) −28.4115 −1.04022
\(747\) −37.9241 −1.38757
\(748\) 22.5914 0.826024
\(749\) −8.03379 −0.293548
\(750\) −4.32677 −0.157991
\(751\) −15.1490 −0.552795 −0.276397 0.961043i \(-0.589141\pi\)
−0.276397 + 0.961043i \(0.589141\pi\)
\(752\) −10.9210 −0.398247
\(753\) −0.638227 −0.0232583
\(754\) −30.9603 −1.12751
\(755\) 5.33764 0.194257
\(756\) −2.34866 −0.0854200
\(757\) 8.37899 0.304539 0.152270 0.988339i \(-0.451342\pi\)
0.152270 + 0.988339i \(0.451342\pi\)
\(758\) 13.6763 0.496745
\(759\) −2.70126 −0.0980495
\(760\) −5.28718 −0.191786
\(761\) 25.4673 0.923190 0.461595 0.887091i \(-0.347277\pi\)
0.461595 + 0.887091i \(0.347277\pi\)
\(762\) −6.92691 −0.250935
\(763\) −0.168957 −0.00611664
\(764\) −18.9466 −0.685464
\(765\) 19.3787 0.700640
\(766\) −17.9619 −0.648990
\(767\) −39.8966 −1.44058
\(768\) 0.402295 0.0145166
\(769\) −1.98243 −0.0714884 −0.0357442 0.999361i \(-0.511380\pi\)
−0.0357442 + 0.999361i \(0.511380\pi\)
\(770\) −5.50921 −0.198538
\(771\) 5.13389 0.184893
\(772\) 7.10269 0.255631
\(773\) −26.3293 −0.947000 −0.473500 0.880794i \(-0.657010\pi\)
−0.473500 + 0.880794i \(0.657010\pi\)
\(774\) 28.9293 1.03984
\(775\) −16.3917 −0.588808
\(776\) −11.1611 −0.400659
\(777\) 0.537410 0.0192795
\(778\) −5.82184 −0.208723
\(779\) 52.3148 1.87437
\(780\) 2.32943 0.0834068
\(781\) −31.6519 −1.13259
\(782\) −8.32187 −0.297590
\(783\) 16.2046 0.579105
\(784\) 1.00000 0.0357143
\(785\) −26.8872 −0.959645
\(786\) −5.72574 −0.204231
\(787\) 25.6165 0.913131 0.456566 0.889690i \(-0.349079\pi\)
0.456566 + 0.889690i \(0.349079\pi\)
\(788\) 18.6519 0.664447
\(789\) −2.39040 −0.0851004
\(790\) 5.98549 0.212954
\(791\) 17.0693 0.606914
\(792\) 12.1174 0.430572
\(793\) 15.8754 0.563752
\(794\) −33.0817 −1.17403
\(795\) 2.83761 0.100640
\(796\) 18.6356 0.660520
\(797\) 23.1954 0.821623 0.410812 0.911720i \(-0.365245\pi\)
0.410812 + 0.911720i \(0.365245\pi\)
\(798\) −1.64836 −0.0583512
\(799\) 57.7874 2.04437
\(800\) −3.33492 −0.117907
\(801\) 37.3722 1.32048
\(802\) −32.8107 −1.15859
\(803\) −72.0636 −2.54307
\(804\) 2.44885 0.0863645
\(805\) 2.02940 0.0715269
\(806\) 22.0560 0.776888
\(807\) −9.18909 −0.323471
\(808\) −14.1440 −0.497586
\(809\) 34.2529 1.20427 0.602134 0.798395i \(-0.294317\pi\)
0.602134 + 0.798395i \(0.294317\pi\)
\(810\) 9.76769 0.343202
\(811\) −13.4307 −0.471614 −0.235807 0.971800i \(-0.575773\pi\)
−0.235807 + 0.971800i \(0.575773\pi\)
\(812\) −6.89951 −0.242125
\(813\) 1.72431 0.0604743
\(814\) −5.70340 −0.199904
\(815\) −13.3691 −0.468299
\(816\) −2.12871 −0.0745196
\(817\) 41.7645 1.46115
\(818\) 24.4040 0.853264
\(819\) −12.7357 −0.445022
\(820\) −16.4754 −0.575345
\(821\) 49.7187 1.73520 0.867598 0.497267i \(-0.165663\pi\)
0.867598 + 0.497267i \(0.165663\pi\)
\(822\) −4.18616 −0.146009
\(823\) 8.01807 0.279492 0.139746 0.990187i \(-0.455371\pi\)
0.139746 + 0.990187i \(0.455371\pi\)
\(824\) 8.10218 0.282253
\(825\) 5.72798 0.199423
\(826\) −8.89097 −0.309356
\(827\) −46.1060 −1.60326 −0.801631 0.597819i \(-0.796034\pi\)
−0.801631 + 0.597819i \(0.796034\pi\)
\(828\) −4.46361 −0.155121
\(829\) 20.0871 0.697655 0.348828 0.937187i \(-0.386580\pi\)
0.348828 + 0.937187i \(0.386580\pi\)
\(830\) 17.2424 0.598491
\(831\) −10.7948 −0.374468
\(832\) 4.48732 0.155570
\(833\) −5.29141 −0.183336
\(834\) 0.337585 0.0116896
\(835\) 9.01137 0.311851
\(836\) 17.4936 0.605028
\(837\) −11.5441 −0.399022
\(838\) −32.2470 −1.11395
\(839\) 8.72624 0.301263 0.150632 0.988590i \(-0.451869\pi\)
0.150632 + 0.988590i \(0.451869\pi\)
\(840\) 0.519113 0.0179111
\(841\) 18.6032 0.641489
\(842\) −19.6786 −0.678169
\(843\) 2.05819 0.0708877
\(844\) 15.4689 0.532463
\(845\) 9.20821 0.316772
\(846\) 30.9955 1.06565
\(847\) 7.22821 0.248364
\(848\) 5.46626 0.187712
\(849\) −10.5298 −0.361381
\(850\) 17.6464 0.605267
\(851\) 2.10093 0.0720190
\(852\) 2.98244 0.102177
\(853\) 16.1417 0.552683 0.276341 0.961060i \(-0.410878\pi\)
0.276341 + 0.961060i \(0.410878\pi\)
\(854\) 3.53783 0.121062
\(855\) 15.0059 0.513190
\(856\) −8.03379 −0.274589
\(857\) −17.8085 −0.608327 −0.304163 0.952620i \(-0.598377\pi\)
−0.304163 + 0.952620i \(0.598377\pi\)
\(858\) −7.70732 −0.263124
\(859\) −0.288568 −0.00984582 −0.00492291 0.999988i \(-0.501567\pi\)
−0.00492291 + 0.999988i \(0.501567\pi\)
\(860\) −13.1528 −0.448507
\(861\) −5.13644 −0.175049
\(862\) −1.00000 −0.0340601
\(863\) −3.94842 −0.134406 −0.0672029 0.997739i \(-0.521407\pi\)
−0.0672029 + 0.997739i \(0.521407\pi\)
\(864\) −2.34866 −0.0799031
\(865\) 11.1186 0.378043
\(866\) −1.99480 −0.0677861
\(867\) 4.42484 0.150275
\(868\) 4.91518 0.166832
\(869\) −19.8040 −0.671806
\(870\) −3.58162 −0.121428
\(871\) 27.3153 0.925543
\(872\) −0.168957 −0.00572159
\(873\) 31.6769 1.07210
\(874\) −6.44401 −0.217972
\(875\) −10.7552 −0.363593
\(876\) 6.79029 0.229423
\(877\) −45.1598 −1.52494 −0.762469 0.647024i \(-0.776013\pi\)
−0.762469 + 0.647024i \(0.776013\pi\)
\(878\) −35.9660 −1.21379
\(879\) −5.43297 −0.183250
\(880\) −5.50921 −0.185716
\(881\) −27.4688 −0.925449 −0.462724 0.886502i \(-0.653128\pi\)
−0.462724 + 0.886502i \(0.653128\pi\)
\(882\) −2.83816 −0.0955658
\(883\) −31.3245 −1.05415 −0.527076 0.849818i \(-0.676712\pi\)
−0.527076 + 0.849818i \(0.676712\pi\)
\(884\) −23.7442 −0.798605
\(885\) −4.61542 −0.155146
\(886\) −34.2598 −1.15098
\(887\) 44.9727 1.51004 0.755019 0.655703i \(-0.227628\pi\)
0.755019 + 0.655703i \(0.227628\pi\)
\(888\) 0.537410 0.0180343
\(889\) −17.2185 −0.577490
\(890\) −16.9914 −0.569554
\(891\) −32.3181 −1.08270
\(892\) 12.2261 0.409359
\(893\) 44.7475 1.49742
\(894\) 2.86140 0.0956994
\(895\) 7.84177 0.262121
\(896\) 1.00000 0.0334077
\(897\) 2.83910 0.0947949
\(898\) 3.00677 0.100337
\(899\) −33.9123 −1.13104
\(900\) 9.46503 0.315501
\(901\) −28.9242 −0.963606
\(902\) 54.5117 1.81504
\(903\) −4.10058 −0.136459
\(904\) 17.0693 0.567716
\(905\) 31.2325 1.03820
\(906\) 1.66409 0.0552856
\(907\) −19.6842 −0.653602 −0.326801 0.945093i \(-0.605971\pi\)
−0.326801 + 0.945093i \(0.605971\pi\)
\(908\) 13.0966 0.434626
\(909\) 40.1431 1.33146
\(910\) 5.79035 0.191948
\(911\) 35.4480 1.17444 0.587222 0.809426i \(-0.300222\pi\)
0.587222 + 0.809426i \(0.300222\pi\)
\(912\) −1.64836 −0.0545825
\(913\) −57.0494 −1.88806
\(914\) −19.5362 −0.646199
\(915\) 1.83654 0.0607140
\(916\) 19.3324 0.638760
\(917\) −14.2327 −0.470005
\(918\) 12.4277 0.410176
\(919\) 48.4550 1.59838 0.799191 0.601077i \(-0.205261\pi\)
0.799191 + 0.601077i \(0.205261\pi\)
\(920\) 2.02940 0.0669073
\(921\) 7.54637 0.248661
\(922\) 24.2117 0.797368
\(923\) 33.2671 1.09500
\(924\) −1.71758 −0.0565042
\(925\) −4.45499 −0.146479
\(926\) 35.4816 1.16600
\(927\) −22.9953 −0.755264
\(928\) −6.89951 −0.226487
\(929\) 9.57160 0.314034 0.157017 0.987596i \(-0.449812\pi\)
0.157017 + 0.987596i \(0.449812\pi\)
\(930\) 2.55153 0.0836680
\(931\) −4.09738 −0.134286
\(932\) −17.6137 −0.576958
\(933\) −1.51409 −0.0495692
\(934\) 25.0107 0.818376
\(935\) 29.1515 0.953356
\(936\) −12.7357 −0.416280
\(937\) −16.1334 −0.527055 −0.263527 0.964652i \(-0.584886\pi\)
−0.263527 + 0.964652i \(0.584886\pi\)
\(938\) 6.08722 0.198755
\(939\) 5.76123 0.188011
\(940\) −14.0922 −0.459638
\(941\) 52.1665 1.70058 0.850289 0.526316i \(-0.176427\pi\)
0.850289 + 0.526316i \(0.176427\pi\)
\(942\) −8.38247 −0.273116
\(943\) −20.0802 −0.653900
\(944\) −8.89097 −0.289376
\(945\) −3.03066 −0.0985875
\(946\) 43.5184 1.41490
\(947\) 16.6449 0.540885 0.270443 0.962736i \(-0.412830\pi\)
0.270443 + 0.962736i \(0.412830\pi\)
\(948\) 1.86606 0.0606069
\(949\) 75.7410 2.45866
\(950\) 13.6644 0.443333
\(951\) −0.386912 −0.0125465
\(952\) −5.29141 −0.171496
\(953\) 25.1333 0.814147 0.407073 0.913395i \(-0.366549\pi\)
0.407073 + 0.913395i \(0.366549\pi\)
\(954\) −15.5141 −0.502288
\(955\) −24.4483 −0.791129
\(956\) 13.4662 0.435529
\(957\) 11.8504 0.383070
\(958\) 2.45113 0.0791923
\(959\) −10.4057 −0.336018
\(960\) 0.519113 0.0167543
\(961\) −6.84105 −0.220679
\(962\) 5.99444 0.193269
\(963\) 22.8012 0.734758
\(964\) −25.3288 −0.815785
\(965\) 9.16517 0.295037
\(966\) 0.632695 0.0203566
\(967\) −45.4028 −1.46006 −0.730028 0.683418i \(-0.760493\pi\)
−0.730028 + 0.683418i \(0.760493\pi\)
\(968\) 7.22821 0.232324
\(969\) 8.72213 0.280195
\(970\) −14.4020 −0.462421
\(971\) 40.6123 1.30331 0.651656 0.758515i \(-0.274075\pi\)
0.651656 + 0.758515i \(0.274075\pi\)
\(972\) 10.0912 0.323675
\(973\) 0.839150 0.0269019
\(974\) −32.6827 −1.04722
\(975\) −6.02028 −0.192803
\(976\) 3.53783 0.113243
\(977\) 51.8364 1.65839 0.829197 0.558957i \(-0.188798\pi\)
0.829197 + 0.558957i \(0.188798\pi\)
\(978\) −4.16801 −0.133278
\(979\) 56.2192 1.79677
\(980\) 1.29038 0.0412197
\(981\) 0.479526 0.0153101
\(982\) 40.8488 1.30354
\(983\) −14.8605 −0.473978 −0.236989 0.971512i \(-0.576160\pi\)
−0.236989 + 0.971512i \(0.576160\pi\)
\(984\) −5.13644 −0.163744
\(985\) 24.0681 0.766872
\(986\) 36.5081 1.16265
\(987\) −4.39345 −0.139845
\(988\) −18.3863 −0.584945
\(989\) −16.0306 −0.509744
\(990\) 15.6360 0.496946
\(991\) −28.0159 −0.889954 −0.444977 0.895542i \(-0.646788\pi\)
−0.444977 + 0.895542i \(0.646788\pi\)
\(992\) 4.91518 0.156057
\(993\) 6.88992 0.218645
\(994\) 7.41357 0.235144
\(995\) 24.0470 0.762340
\(996\) 5.37555 0.170331
\(997\) −6.69582 −0.212059 −0.106029 0.994363i \(-0.533814\pi\)
−0.106029 + 0.994363i \(0.533814\pi\)
\(998\) 21.8637 0.692083
\(999\) −3.13749 −0.0992657
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 6034.2.a.m.1.13 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.m.1.13 21 1.1 even 1 trivial