Properties

Label 4001.2.a.b.1.40
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.40
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +O(q^{10})\) \(q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +7.52990 q^{10} -3.00578 q^{11} +3.54720 q^{12} +0.487304 q^{13} -9.43134 q^{14} -11.0993 q^{15} -4.89722 q^{16} +1.27456 q^{17} -7.68061 q^{18} +5.37940 q^{19} -5.45697 q^{20} +13.9021 q^{21} +5.47728 q^{22} -0.0884748 q^{23} +3.32545 q^{24} +12.0751 q^{25} -0.887990 q^{26} +3.26329 q^{27} +6.83496 q^{28} +2.32622 q^{29} +20.2257 q^{30} +7.57211 q^{31} +6.44788 q^{32} -8.07369 q^{33} -2.32256 q^{34} -21.3868 q^{35} +5.56619 q^{36} -4.84346 q^{37} -9.80261 q^{38} +1.30893 q^{39} -5.11583 q^{40} -1.44912 q^{41} -25.3331 q^{42} -10.7400 q^{43} -3.96943 q^{44} -17.4168 q^{45} +0.161223 q^{46} +1.02412 q^{47} -13.1542 q^{48} +19.7874 q^{49} -22.0038 q^{50} +3.42353 q^{51} +0.643532 q^{52} +2.55300 q^{53} -5.94654 q^{54} +12.4205 q^{55} +6.40767 q^{56} +14.4494 q^{57} -4.23896 q^{58} -0.415687 q^{59} -14.6577 q^{60} -4.77911 q^{61} -13.7983 q^{62} +21.8149 q^{63} -1.95521 q^{64} -2.01364 q^{65} +14.7123 q^{66} -3.55935 q^{67} +1.68318 q^{68} -0.237648 q^{69} +38.9721 q^{70} -5.50177 q^{71} +5.21822 q^{72} +4.20006 q^{73} +8.82599 q^{74} +32.4343 q^{75} +7.10402 q^{76} -15.5569 q^{77} -2.38519 q^{78} +16.6252 q^{79} +20.2363 q^{80} -3.87931 q^{81} +2.64065 q^{82} +11.0604 q^{83} +18.3591 q^{84} -5.26672 q^{85} +19.5710 q^{86} +6.24836 q^{87} -3.72128 q^{88} +7.34281 q^{89} +31.7378 q^{90} +2.52212 q^{91} -0.116840 q^{92} +20.3391 q^{93} -1.86621 q^{94} -22.2287 q^{95} +17.3194 q^{96} -16.7412 q^{97} -36.0576 q^{98} -12.6691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82225 −1.28853 −0.644263 0.764804i \(-0.722836\pi\)
−0.644263 + 0.764804i \(0.722836\pi\)
\(3\) 2.68606 1.55080 0.775398 0.631473i \(-0.217549\pi\)
0.775398 + 0.631473i \(0.217549\pi\)
\(4\) 1.32060 0.660299
\(5\) −4.13220 −1.84797 −0.923987 0.382423i \(-0.875090\pi\)
−0.923987 + 0.382423i \(0.875090\pi\)
\(6\) −4.89467 −1.99824
\(7\) 5.17565 1.95621 0.978107 0.208105i \(-0.0667294\pi\)
0.978107 + 0.208105i \(0.0667294\pi\)
\(8\) 1.23804 0.437714
\(9\) 4.21490 1.40497
\(10\) 7.52990 2.38116
\(11\) −3.00578 −0.906277 −0.453138 0.891440i \(-0.649696\pi\)
−0.453138 + 0.891440i \(0.649696\pi\)
\(12\) 3.54720 1.02399
\(13\) 0.487304 0.135154 0.0675769 0.997714i \(-0.478473\pi\)
0.0675769 + 0.997714i \(0.478473\pi\)
\(14\) −9.43134 −2.52063
\(15\) −11.0993 −2.86583
\(16\) −4.89722 −1.22430
\(17\) 1.27456 0.309125 0.154563 0.987983i \(-0.450603\pi\)
0.154563 + 0.987983i \(0.450603\pi\)
\(18\) −7.68061 −1.81034
\(19\) 5.37940 1.23412 0.617059 0.786917i \(-0.288324\pi\)
0.617059 + 0.786917i \(0.288324\pi\)
\(20\) −5.45697 −1.22022
\(21\) 13.9021 3.03369
\(22\) 5.47728 1.16776
\(23\) −0.0884748 −0.0184483 −0.00922413 0.999957i \(-0.502936\pi\)
−0.00922413 + 0.999957i \(0.502936\pi\)
\(24\) 3.32545 0.678804
\(25\) 12.0751 2.41501
\(26\) −0.887990 −0.174149
\(27\) 3.26329 0.628021
\(28\) 6.83496 1.29169
\(29\) 2.32622 0.431968 0.215984 0.976397i \(-0.430704\pi\)
0.215984 + 0.976397i \(0.430704\pi\)
\(30\) 20.2257 3.69270
\(31\) 7.57211 1.35999 0.679996 0.733216i \(-0.261982\pi\)
0.679996 + 0.733216i \(0.261982\pi\)
\(32\) 6.44788 1.13983
\(33\) −8.07369 −1.40545
\(34\) −2.32256 −0.398316
\(35\) −21.3868 −3.61503
\(36\) 5.56619 0.927698
\(37\) −4.84346 −0.796259 −0.398130 0.917329i \(-0.630341\pi\)
−0.398130 + 0.917329i \(0.630341\pi\)
\(38\) −9.80261 −1.59019
\(39\) 1.30893 0.209596
\(40\) −5.11583 −0.808884
\(41\) −1.44912 −0.226314 −0.113157 0.993577i \(-0.536096\pi\)
−0.113157 + 0.993577i \(0.536096\pi\)
\(42\) −25.3331 −3.90898
\(43\) −10.7400 −1.63784 −0.818919 0.573909i \(-0.805426\pi\)
−0.818919 + 0.573909i \(0.805426\pi\)
\(44\) −3.96943 −0.598413
\(45\) −17.4168 −2.59634
\(46\) 0.161223 0.0237711
\(47\) 1.02412 0.149384 0.0746920 0.997207i \(-0.476203\pi\)
0.0746920 + 0.997207i \(0.476203\pi\)
\(48\) −13.1542 −1.89865
\(49\) 19.7874 2.82677
\(50\) −22.0038 −3.11180
\(51\) 3.42353 0.479390
\(52\) 0.643532 0.0892419
\(53\) 2.55300 0.350681 0.175341 0.984508i \(-0.443897\pi\)
0.175341 + 0.984508i \(0.443897\pi\)
\(54\) −5.94654 −0.809222
\(55\) 12.4205 1.67478
\(56\) 6.40767 0.856261
\(57\) 14.4494 1.91387
\(58\) −4.23896 −0.556602
\(59\) −0.415687 −0.0541178 −0.0270589 0.999634i \(-0.508614\pi\)
−0.0270589 + 0.999634i \(0.508614\pi\)
\(60\) −14.6577 −1.89231
\(61\) −4.77911 −0.611902 −0.305951 0.952047i \(-0.598974\pi\)
−0.305951 + 0.952047i \(0.598974\pi\)
\(62\) −13.7983 −1.75238
\(63\) 21.8149 2.74842
\(64\) −1.95521 −0.244401
\(65\) −2.01364 −0.249761
\(66\) 14.7123 1.81096
\(67\) −3.55935 −0.434844 −0.217422 0.976078i \(-0.569765\pi\)
−0.217422 + 0.976078i \(0.569765\pi\)
\(68\) 1.68318 0.204115
\(69\) −0.237648 −0.0286095
\(70\) 38.9721 4.65806
\(71\) −5.50177 −0.652940 −0.326470 0.945208i \(-0.605859\pi\)
−0.326470 + 0.945208i \(0.605859\pi\)
\(72\) 5.21822 0.614973
\(73\) 4.20006 0.491580 0.245790 0.969323i \(-0.420953\pi\)
0.245790 + 0.969323i \(0.420953\pi\)
\(74\) 8.82599 1.02600
\(75\) 32.4343 3.74519
\(76\) 7.10402 0.814887
\(77\) −15.5569 −1.77287
\(78\) −2.38519 −0.270070
\(79\) 16.6252 1.87048 0.935239 0.354016i \(-0.115184\pi\)
0.935239 + 0.354016i \(0.115184\pi\)
\(80\) 20.2363 2.26248
\(81\) −3.87931 −0.431034
\(82\) 2.64065 0.291611
\(83\) 11.0604 1.21403 0.607017 0.794689i \(-0.292366\pi\)
0.607017 + 0.794689i \(0.292366\pi\)
\(84\) 18.3591 2.00314
\(85\) −5.26672 −0.571256
\(86\) 19.5710 2.11040
\(87\) 6.24836 0.669894
\(88\) −3.72128 −0.396690
\(89\) 7.34281 0.778336 0.389168 0.921167i \(-0.372762\pi\)
0.389168 + 0.921167i \(0.372762\pi\)
\(90\) 31.7378 3.34546
\(91\) 2.52212 0.264390
\(92\) −0.116840 −0.0121814
\(93\) 20.3391 2.10907
\(94\) −1.86621 −0.192485
\(95\) −22.2287 −2.28062
\(96\) 17.3194 1.76765
\(97\) −16.7412 −1.69981 −0.849906 0.526934i \(-0.823342\pi\)
−0.849906 + 0.526934i \(0.823342\pi\)
\(98\) −36.0576 −3.64237
\(99\) −12.6691 −1.27329
\(100\) 15.9463 1.59463
\(101\) −7.01632 −0.698150 −0.349075 0.937095i \(-0.613504\pi\)
−0.349075 + 0.937095i \(0.613504\pi\)
\(102\) −6.23853 −0.617707
\(103\) −0.948146 −0.0934236 −0.0467118 0.998908i \(-0.514874\pi\)
−0.0467118 + 0.998908i \(0.514874\pi\)
\(104\) 0.603302 0.0591586
\(105\) −57.4462 −5.60618
\(106\) −4.65220 −0.451862
\(107\) 1.51759 0.146711 0.0733554 0.997306i \(-0.476629\pi\)
0.0733554 + 0.997306i \(0.476629\pi\)
\(108\) 4.30950 0.414682
\(109\) 14.3328 1.37283 0.686416 0.727209i \(-0.259183\pi\)
0.686416 + 0.727209i \(0.259183\pi\)
\(110\) −22.6332 −2.15799
\(111\) −13.0098 −1.23484
\(112\) −25.3463 −2.39500
\(113\) 13.4796 1.26806 0.634028 0.773310i \(-0.281401\pi\)
0.634028 + 0.773310i \(0.281401\pi\)
\(114\) −26.3304 −2.46607
\(115\) 0.365595 0.0340919
\(116\) 3.07200 0.285228
\(117\) 2.05394 0.189887
\(118\) 0.757486 0.0697322
\(119\) 6.59666 0.604715
\(120\) −13.7414 −1.25441
\(121\) −1.96529 −0.178663
\(122\) 8.70873 0.788452
\(123\) −3.89241 −0.350967
\(124\) 9.99971 0.898001
\(125\) −29.2355 −2.61490
\(126\) −39.7522 −3.54140
\(127\) 3.88226 0.344495 0.172248 0.985054i \(-0.444897\pi\)
0.172248 + 0.985054i \(0.444897\pi\)
\(128\) −9.33286 −0.824916
\(129\) −28.8483 −2.53995
\(130\) 3.66935 0.321823
\(131\) 11.6225 1.01547 0.507733 0.861515i \(-0.330484\pi\)
0.507733 + 0.861515i \(0.330484\pi\)
\(132\) −10.6621 −0.928017
\(133\) 27.8419 2.41420
\(134\) 6.48602 0.560307
\(135\) −13.4846 −1.16057
\(136\) 1.57795 0.135308
\(137\) −13.7634 −1.17589 −0.587945 0.808901i \(-0.700063\pi\)
−0.587945 + 0.808901i \(0.700063\pi\)
\(138\) 0.433055 0.0368641
\(139\) 18.7351 1.58909 0.794545 0.607205i \(-0.207709\pi\)
0.794545 + 0.607205i \(0.207709\pi\)
\(140\) −28.2434 −2.38700
\(141\) 2.75086 0.231664
\(142\) 10.0256 0.841330
\(143\) −1.46473 −0.122487
\(144\) −20.6413 −1.72011
\(145\) −9.61240 −0.798266
\(146\) −7.65356 −0.633413
\(147\) 53.1501 4.38374
\(148\) −6.39626 −0.525769
\(149\) 17.0987 1.40078 0.700390 0.713760i \(-0.253009\pi\)
0.700390 + 0.713760i \(0.253009\pi\)
\(150\) −59.1034 −4.82577
\(151\) 0.102087 0.00830775 0.00415387 0.999991i \(-0.498678\pi\)
0.00415387 + 0.999991i \(0.498678\pi\)
\(152\) 6.65992 0.540191
\(153\) 5.37213 0.434311
\(154\) 28.3485 2.28439
\(155\) −31.2895 −2.51323
\(156\) 1.72856 0.138396
\(157\) 6.49465 0.518329 0.259165 0.965833i \(-0.416553\pi\)
0.259165 + 0.965833i \(0.416553\pi\)
\(158\) −30.2952 −2.41016
\(159\) 6.85750 0.543835
\(160\) −26.6439 −2.10638
\(161\) −0.457915 −0.0360887
\(162\) 7.06908 0.555399
\(163\) 6.35927 0.498096 0.249048 0.968491i \(-0.419882\pi\)
0.249048 + 0.968491i \(0.419882\pi\)
\(164\) −1.91370 −0.149435
\(165\) 33.3621 2.59724
\(166\) −20.1548 −1.56431
\(167\) −6.02781 −0.466446 −0.233223 0.972423i \(-0.574927\pi\)
−0.233223 + 0.972423i \(0.574927\pi\)
\(168\) 17.2114 1.32789
\(169\) −12.7625 −0.981733
\(170\) 9.59728 0.736078
\(171\) 22.6736 1.73390
\(172\) −14.1833 −1.08146
\(173\) −21.1629 −1.60898 −0.804491 0.593965i \(-0.797562\pi\)
−0.804491 + 0.593965i \(0.797562\pi\)
\(174\) −11.3861 −0.863176
\(175\) 62.4963 4.72427
\(176\) 14.7200 1.10956
\(177\) −1.11656 −0.0839257
\(178\) −13.3804 −1.00291
\(179\) 15.5515 1.16237 0.581186 0.813771i \(-0.302589\pi\)
0.581186 + 0.813771i \(0.302589\pi\)
\(180\) −23.0006 −1.71436
\(181\) −6.44125 −0.478774 −0.239387 0.970924i \(-0.576946\pi\)
−0.239387 + 0.970924i \(0.576946\pi\)
\(182\) −4.59593 −0.340673
\(183\) −12.8370 −0.948935
\(184\) −0.109535 −0.00807506
\(185\) 20.0141 1.47147
\(186\) −37.0630 −2.71759
\(187\) −3.83103 −0.280153
\(188\) 1.35246 0.0986381
\(189\) 16.8897 1.22854
\(190\) 40.5063 2.93864
\(191\) 5.65605 0.409257 0.204629 0.978840i \(-0.434401\pi\)
0.204629 + 0.978840i \(0.434401\pi\)
\(192\) −5.25181 −0.379017
\(193\) −8.10006 −0.583055 −0.291528 0.956562i \(-0.594163\pi\)
−0.291528 + 0.956562i \(0.594163\pi\)
\(194\) 30.5067 2.19025
\(195\) −5.40874 −0.387328
\(196\) 26.1312 1.86651
\(197\) −10.5838 −0.754062 −0.377031 0.926201i \(-0.623055\pi\)
−0.377031 + 0.926201i \(0.623055\pi\)
\(198\) 23.0862 1.64067
\(199\) −21.1551 −1.49964 −0.749822 0.661640i \(-0.769861\pi\)
−0.749822 + 0.661640i \(0.769861\pi\)
\(200\) 14.9494 1.05708
\(201\) −9.56061 −0.674353
\(202\) 12.7855 0.899585
\(203\) 12.0397 0.845022
\(204\) 4.52111 0.316541
\(205\) 5.98803 0.418222
\(206\) 1.72776 0.120379
\(207\) −0.372913 −0.0259192
\(208\) −2.38643 −0.165469
\(209\) −16.1693 −1.11845
\(210\) 104.681 7.22370
\(211\) −0.592362 −0.0407799 −0.0203899 0.999792i \(-0.506491\pi\)
−0.0203899 + 0.999792i \(0.506491\pi\)
\(212\) 3.37148 0.231554
\(213\) −14.7781 −1.01258
\(214\) −2.76543 −0.189041
\(215\) 44.3799 3.02668
\(216\) 4.04009 0.274893
\(217\) 39.1906 2.66043
\(218\) −26.1179 −1.76893
\(219\) 11.2816 0.762340
\(220\) 16.4024 1.10585
\(221\) 0.621096 0.0417794
\(222\) 23.7071 1.59112
\(223\) 12.4349 0.832705 0.416352 0.909203i \(-0.363308\pi\)
0.416352 + 0.909203i \(0.363308\pi\)
\(224\) 33.3720 2.22976
\(225\) 50.8952 3.39301
\(226\) −24.5632 −1.63392
\(227\) 15.8638 1.05292 0.526458 0.850201i \(-0.323520\pi\)
0.526458 + 0.850201i \(0.323520\pi\)
\(228\) 19.0818 1.26372
\(229\) 9.32802 0.616413 0.308206 0.951320i \(-0.400271\pi\)
0.308206 + 0.951320i \(0.400271\pi\)
\(230\) −0.666206 −0.0439283
\(231\) −41.7866 −2.74936
\(232\) 2.87996 0.189078
\(233\) 21.0202 1.37708 0.688540 0.725199i \(-0.258252\pi\)
0.688540 + 0.725199i \(0.258252\pi\)
\(234\) −3.74279 −0.244674
\(235\) −4.23188 −0.276058
\(236\) −0.548955 −0.0357339
\(237\) 44.6562 2.90073
\(238\) −12.0208 −0.779191
\(239\) −8.07536 −0.522352 −0.261176 0.965291i \(-0.584110\pi\)
−0.261176 + 0.965291i \(0.584110\pi\)
\(240\) 54.3558 3.50865
\(241\) 16.0756 1.03552 0.517760 0.855526i \(-0.326766\pi\)
0.517760 + 0.855526i \(0.326766\pi\)
\(242\) 3.58125 0.230212
\(243\) −20.2099 −1.29647
\(244\) −6.31128 −0.404038
\(245\) −81.7654 −5.22380
\(246\) 7.09294 0.452230
\(247\) 2.62140 0.166796
\(248\) 9.37458 0.595287
\(249\) 29.7088 1.88272
\(250\) 53.2744 3.36937
\(251\) 3.30727 0.208753 0.104377 0.994538i \(-0.466715\pi\)
0.104377 + 0.994538i \(0.466715\pi\)
\(252\) 28.8087 1.81478
\(253\) 0.265936 0.0167192
\(254\) −7.07446 −0.443891
\(255\) −14.1467 −0.885901
\(256\) 20.9172 1.30733
\(257\) −2.73397 −0.170541 −0.0852703 0.996358i \(-0.527175\pi\)
−0.0852703 + 0.996358i \(0.527175\pi\)
\(258\) 52.5689 3.27280
\(259\) −25.0681 −1.55765
\(260\) −2.65920 −0.164917
\(261\) 9.80479 0.606901
\(262\) −21.1792 −1.30845
\(263\) 23.8280 1.46930 0.734648 0.678448i \(-0.237347\pi\)
0.734648 + 0.678448i \(0.237347\pi\)
\(264\) −9.99556 −0.615184
\(265\) −10.5495 −0.648050
\(266\) −50.7349 −3.11076
\(267\) 19.7232 1.20704
\(268\) −4.70047 −0.287127
\(269\) 12.1682 0.741910 0.370955 0.928651i \(-0.379030\pi\)
0.370955 + 0.928651i \(0.379030\pi\)
\(270\) 24.5723 1.49542
\(271\) −20.3384 −1.23547 −0.617736 0.786386i \(-0.711950\pi\)
−0.617736 + 0.786386i \(0.711950\pi\)
\(272\) −6.24178 −0.378463
\(273\) 6.77455 0.410014
\(274\) 25.0804 1.51516
\(275\) −36.2949 −2.18867
\(276\) −0.313838 −0.0188908
\(277\) 9.70253 0.582968 0.291484 0.956576i \(-0.405851\pi\)
0.291484 + 0.956576i \(0.405851\pi\)
\(278\) −34.1400 −2.04758
\(279\) 31.9157 1.91074
\(280\) −26.4778 −1.58235
\(281\) 26.2637 1.56676 0.783380 0.621544i \(-0.213494\pi\)
0.783380 + 0.621544i \(0.213494\pi\)
\(282\) −5.01275 −0.298505
\(283\) 8.58208 0.510152 0.255076 0.966921i \(-0.417900\pi\)
0.255076 + 0.966921i \(0.417900\pi\)
\(284\) −7.26563 −0.431136
\(285\) −59.7076 −3.53678
\(286\) 2.66910 0.157827
\(287\) −7.50012 −0.442718
\(288\) 27.1772 1.60143
\(289\) −15.3755 −0.904442
\(290\) 17.5162 1.02859
\(291\) −44.9679 −2.63606
\(292\) 5.54659 0.324589
\(293\) −0.133318 −0.00778854 −0.00389427 0.999992i \(-0.501240\pi\)
−0.00389427 + 0.999992i \(0.501240\pi\)
\(294\) −96.8527 −5.64857
\(295\) 1.71770 0.100008
\(296\) −5.99640 −0.348534
\(297\) −9.80874 −0.569161
\(298\) −31.1581 −1.80494
\(299\) −0.0431141 −0.00249335
\(300\) 42.8326 2.47294
\(301\) −55.5867 −3.20396
\(302\) −0.186029 −0.0107047
\(303\) −18.8462 −1.08269
\(304\) −26.3441 −1.51094
\(305\) 19.7482 1.13078
\(306\) −9.78937 −0.559621
\(307\) −26.5823 −1.51713 −0.758567 0.651595i \(-0.774100\pi\)
−0.758567 + 0.651595i \(0.774100\pi\)
\(308\) −20.5444 −1.17062
\(309\) −2.54678 −0.144881
\(310\) 57.0172 3.23836
\(311\) 19.4255 1.10152 0.550759 0.834664i \(-0.314338\pi\)
0.550759 + 0.834664i \(0.314338\pi\)
\(312\) 1.62050 0.0917430
\(313\) −5.80086 −0.327884 −0.163942 0.986470i \(-0.552421\pi\)
−0.163942 + 0.986470i \(0.552421\pi\)
\(314\) −11.8349 −0.667881
\(315\) −90.1433 −5.07900
\(316\) 21.9552 1.23508
\(317\) 31.4424 1.76598 0.882990 0.469392i \(-0.155527\pi\)
0.882990 + 0.469392i \(0.155527\pi\)
\(318\) −12.4961 −0.700745
\(319\) −6.99210 −0.391483
\(320\) 8.07932 0.451648
\(321\) 4.07633 0.227518
\(322\) 0.834436 0.0465013
\(323\) 6.85635 0.381497
\(324\) −5.12301 −0.284612
\(325\) 5.88422 0.326398
\(326\) −11.5882 −0.641810
\(327\) 38.4987 2.12898
\(328\) −1.79407 −0.0990607
\(329\) 5.30051 0.292227
\(330\) −60.7941 −3.34661
\(331\) 11.4177 0.627575 0.313788 0.949493i \(-0.398402\pi\)
0.313788 + 0.949493i \(0.398402\pi\)
\(332\) 14.6063 0.801625
\(333\) −20.4147 −1.11872
\(334\) 10.9842 0.601027
\(335\) 14.7079 0.803580
\(336\) −68.0816 −3.71416
\(337\) 26.1871 1.42650 0.713251 0.700909i \(-0.247222\pi\)
0.713251 + 0.700909i \(0.247222\pi\)
\(338\) 23.2565 1.26499
\(339\) 36.2070 1.96649
\(340\) −6.95521 −0.377199
\(341\) −22.7601 −1.23253
\(342\) −41.3171 −2.23417
\(343\) 66.1831 3.57355
\(344\) −13.2966 −0.716904
\(345\) 0.982010 0.0528696
\(346\) 38.5640 2.07321
\(347\) −28.5805 −1.53428 −0.767142 0.641478i \(-0.778322\pi\)
−0.767142 + 0.641478i \(0.778322\pi\)
\(348\) 8.25157 0.442330
\(349\) 24.1301 1.29165 0.645826 0.763484i \(-0.276513\pi\)
0.645826 + 0.763484i \(0.276513\pi\)
\(350\) −113.884 −6.08735
\(351\) 1.59022 0.0848794
\(352\) −19.3809 −1.03300
\(353\) −33.3389 −1.77445 −0.887224 0.461338i \(-0.847369\pi\)
−0.887224 + 0.461338i \(0.847369\pi\)
\(354\) 2.03465 0.108140
\(355\) 22.7344 1.20662
\(356\) 9.69690 0.513935
\(357\) 17.7190 0.937789
\(358\) −28.3387 −1.49775
\(359\) 21.5536 1.13755 0.568777 0.822492i \(-0.307417\pi\)
0.568777 + 0.822492i \(0.307417\pi\)
\(360\) −21.5627 −1.13645
\(361\) 9.93793 0.523049
\(362\) 11.7376 0.616913
\(363\) −5.27888 −0.277070
\(364\) 3.33070 0.174576
\(365\) −17.3555 −0.908427
\(366\) 23.3922 1.22273
\(367\) 17.4807 0.912487 0.456244 0.889855i \(-0.349195\pi\)
0.456244 + 0.889855i \(0.349195\pi\)
\(368\) 0.433280 0.0225863
\(369\) −6.10788 −0.317964
\(370\) −36.4707 −1.89602
\(371\) 13.2134 0.686007
\(372\) 26.8598 1.39262
\(373\) 4.90780 0.254116 0.127058 0.991895i \(-0.459447\pi\)
0.127058 + 0.991895i \(0.459447\pi\)
\(374\) 6.98111 0.360984
\(375\) −78.5282 −4.05518
\(376\) 1.26791 0.0653874
\(377\) 1.13358 0.0583821
\(378\) −30.7772 −1.58301
\(379\) −22.6574 −1.16383 −0.581917 0.813248i \(-0.697697\pi\)
−0.581917 + 0.813248i \(0.697697\pi\)
\(380\) −29.3552 −1.50589
\(381\) 10.4280 0.534242
\(382\) −10.3067 −0.527339
\(383\) −5.15569 −0.263443 −0.131722 0.991287i \(-0.542051\pi\)
−0.131722 + 0.991287i \(0.542051\pi\)
\(384\) −25.0686 −1.27928
\(385\) 64.2841 3.27622
\(386\) 14.7603 0.751282
\(387\) −45.2682 −2.30111
\(388\) −22.1084 −1.12238
\(389\) −27.0339 −1.37067 −0.685336 0.728227i \(-0.740345\pi\)
−0.685336 + 0.728227i \(0.740345\pi\)
\(390\) 9.85608 0.499082
\(391\) −0.112766 −0.00570283
\(392\) 24.4976 1.23732
\(393\) 31.2188 1.57478
\(394\) 19.2863 0.971629
\(395\) −68.6985 −3.45660
\(396\) −16.7307 −0.840751
\(397\) 20.3480 1.02124 0.510619 0.859807i \(-0.329416\pi\)
0.510619 + 0.859807i \(0.329416\pi\)
\(398\) 38.5499 1.93233
\(399\) 74.7849 3.74393
\(400\) −59.1341 −2.95671
\(401\) −37.3694 −1.86614 −0.933068 0.359699i \(-0.882879\pi\)
−0.933068 + 0.359699i \(0.882879\pi\)
\(402\) 17.4218 0.868922
\(403\) 3.68992 0.183808
\(404\) −9.26574 −0.460988
\(405\) 16.0301 0.796541
\(406\) −21.9394 −1.08883
\(407\) 14.5584 0.721631
\(408\) 4.23847 0.209836
\(409\) 30.4801 1.50715 0.753573 0.657364i \(-0.228329\pi\)
0.753573 + 0.657364i \(0.228329\pi\)
\(410\) −10.9117 −0.538890
\(411\) −36.9694 −1.82356
\(412\) −1.25212 −0.0616875
\(413\) −2.15145 −0.105866
\(414\) 0.679540 0.0333976
\(415\) −45.7036 −2.24350
\(416\) 3.14207 0.154053
\(417\) 50.3235 2.46435
\(418\) 29.4645 1.44116
\(419\) 21.6303 1.05671 0.528354 0.849024i \(-0.322809\pi\)
0.528354 + 0.849024i \(0.322809\pi\)
\(420\) −75.8633 −3.70175
\(421\) −22.1290 −1.07850 −0.539251 0.842145i \(-0.681293\pi\)
−0.539251 + 0.842145i \(0.681293\pi\)
\(422\) 1.07943 0.0525459
\(423\) 4.31658 0.209880
\(424\) 3.16072 0.153498
\(425\) 15.3903 0.746541
\(426\) 26.9294 1.30473
\(427\) −24.7350 −1.19701
\(428\) 2.00412 0.0968730
\(429\) −3.93434 −0.189952
\(430\) −80.8713 −3.89996
\(431\) 30.4676 1.46757 0.733786 0.679380i \(-0.237751\pi\)
0.733786 + 0.679380i \(0.237751\pi\)
\(432\) −15.9811 −0.768889
\(433\) 20.3753 0.979175 0.489588 0.871954i \(-0.337147\pi\)
0.489588 + 0.871954i \(0.337147\pi\)
\(434\) −71.4151 −3.42804
\(435\) −25.8194 −1.23795
\(436\) 18.9278 0.906479
\(437\) −0.475941 −0.0227674
\(438\) −20.5579 −0.982294
\(439\) 27.8037 1.32700 0.663499 0.748177i \(-0.269071\pi\)
0.663499 + 0.748177i \(0.269071\pi\)
\(440\) 15.3771 0.733072
\(441\) 83.4019 3.97152
\(442\) −1.13179 −0.0538339
\(443\) −13.0379 −0.619450 −0.309725 0.950826i \(-0.600237\pi\)
−0.309725 + 0.950826i \(0.600237\pi\)
\(444\) −17.1807 −0.815360
\(445\) −30.3419 −1.43835
\(446\) −22.6596 −1.07296
\(447\) 45.9281 2.17232
\(448\) −10.1195 −0.478101
\(449\) 2.12159 0.100124 0.0500620 0.998746i \(-0.484058\pi\)
0.0500620 + 0.998746i \(0.484058\pi\)
\(450\) −92.7437 −4.37198
\(451\) 4.35572 0.205103
\(452\) 17.8011 0.837296
\(453\) 0.274212 0.0128836
\(454\) −28.9078 −1.35671
\(455\) −10.4219 −0.488585
\(456\) 17.8889 0.837725
\(457\) 31.2174 1.46029 0.730144 0.683294i \(-0.239453\pi\)
0.730144 + 0.683294i \(0.239453\pi\)
\(458\) −16.9980 −0.794264
\(459\) 4.15925 0.194137
\(460\) 0.482804 0.0225109
\(461\) 15.8163 0.736636 0.368318 0.929700i \(-0.379934\pi\)
0.368318 + 0.929700i \(0.379934\pi\)
\(462\) 76.1457 3.54262
\(463\) −2.89470 −0.134528 −0.0672640 0.997735i \(-0.521427\pi\)
−0.0672640 + 0.997735i \(0.521427\pi\)
\(464\) −11.3920 −0.528860
\(465\) −84.0452 −3.89750
\(466\) −38.3041 −1.77440
\(467\) 8.96153 0.414690 0.207345 0.978268i \(-0.433518\pi\)
0.207345 + 0.978268i \(0.433518\pi\)
\(468\) 2.71243 0.125382
\(469\) −18.4220 −0.850647
\(470\) 7.71156 0.355708
\(471\) 17.4450 0.803823
\(472\) −0.514637 −0.0236881
\(473\) 32.2821 1.48433
\(474\) −81.3747 −3.73767
\(475\) 64.9565 2.98041
\(476\) 8.71154 0.399293
\(477\) 10.7606 0.492696
\(478\) 14.7153 0.673064
\(479\) −35.2623 −1.61117 −0.805587 0.592477i \(-0.798150\pi\)
−0.805587 + 0.592477i \(0.798150\pi\)
\(480\) −71.5670 −3.26657
\(481\) −2.36023 −0.107617
\(482\) −29.2938 −1.33430
\(483\) −1.22999 −0.0559663
\(484\) −2.59536 −0.117971
\(485\) 69.1780 3.14121
\(486\) 36.8276 1.67053
\(487\) −9.78816 −0.443544 −0.221772 0.975099i \(-0.571184\pi\)
−0.221772 + 0.975099i \(0.571184\pi\)
\(488\) −5.91673 −0.267838
\(489\) 17.0814 0.772445
\(490\) 148.997 6.73100
\(491\) 10.2068 0.460628 0.230314 0.973116i \(-0.426025\pi\)
0.230314 + 0.973116i \(0.426025\pi\)
\(492\) −5.14031 −0.231743
\(493\) 2.96490 0.133532
\(494\) −4.77685 −0.214921
\(495\) 52.3511 2.35301
\(496\) −37.0823 −1.66504
\(497\) −28.4753 −1.27729
\(498\) −54.1369 −2.42593
\(499\) −7.89886 −0.353601 −0.176801 0.984247i \(-0.556575\pi\)
−0.176801 + 0.984247i \(0.556575\pi\)
\(500\) −38.6083 −1.72662
\(501\) −16.1910 −0.723362
\(502\) −6.02668 −0.268984
\(503\) 42.0662 1.87564 0.937821 0.347120i \(-0.112840\pi\)
0.937821 + 0.347120i \(0.112840\pi\)
\(504\) 27.0077 1.20302
\(505\) 28.9928 1.29016
\(506\) −0.484602 −0.0215432
\(507\) −34.2809 −1.52247
\(508\) 5.12691 0.227470
\(509\) −20.1333 −0.892394 −0.446197 0.894935i \(-0.647222\pi\)
−0.446197 + 0.894935i \(0.647222\pi\)
\(510\) 25.7788 1.14151
\(511\) 21.7380 0.961634
\(512\) −19.4507 −0.859609
\(513\) 17.5546 0.775053
\(514\) 4.98198 0.219746
\(515\) 3.91793 0.172645
\(516\) −38.0970 −1.67713
\(517\) −3.07829 −0.135383
\(518\) 45.6803 2.00708
\(519\) −56.8446 −2.49520
\(520\) −2.49296 −0.109324
\(521\) −16.0105 −0.701434 −0.350717 0.936482i \(-0.614062\pi\)
−0.350717 + 0.936482i \(0.614062\pi\)
\(522\) −17.8668 −0.782008
\(523\) 1.35515 0.0592564 0.0296282 0.999561i \(-0.490568\pi\)
0.0296282 + 0.999561i \(0.490568\pi\)
\(524\) 15.3487 0.670511
\(525\) 167.869 7.32638
\(526\) −43.4206 −1.89323
\(527\) 9.65108 0.420408
\(528\) 39.5386 1.72070
\(529\) −22.9922 −0.999660
\(530\) 19.2238 0.835029
\(531\) −1.75208 −0.0760338
\(532\) 36.7680 1.59409
\(533\) −0.706160 −0.0305872
\(534\) −35.9406 −1.55530
\(535\) −6.27097 −0.271118
\(536\) −4.40662 −0.190337
\(537\) 41.7722 1.80260
\(538\) −22.1736 −0.955970
\(539\) −59.4765 −2.56184
\(540\) −17.8077 −0.766321
\(541\) 33.1080 1.42343 0.711713 0.702471i \(-0.247920\pi\)
0.711713 + 0.702471i \(0.247920\pi\)
\(542\) 37.0617 1.59194
\(543\) −17.3016 −0.742481
\(544\) 8.21818 0.352352
\(545\) −59.2259 −2.53696
\(546\) −12.3449 −0.528314
\(547\) −26.3531 −1.12678 −0.563388 0.826192i \(-0.690502\pi\)
−0.563388 + 0.826192i \(0.690502\pi\)
\(548\) −18.1760 −0.776439
\(549\) −20.1435 −0.859702
\(550\) 66.1385 2.82015
\(551\) 12.5137 0.533100
\(552\) −0.294218 −0.0125228
\(553\) 86.0462 3.65906
\(554\) −17.6804 −0.751170
\(555\) 53.7590 2.28194
\(556\) 24.7415 1.04927
\(557\) 24.1858 1.02478 0.512392 0.858752i \(-0.328760\pi\)
0.512392 + 0.858752i \(0.328760\pi\)
\(558\) −58.1584 −2.46204
\(559\) −5.23366 −0.221360
\(560\) 104.736 4.42590
\(561\) −10.2904 −0.434460
\(562\) −47.8590 −2.01881
\(563\) −19.5434 −0.823657 −0.411828 0.911261i \(-0.635110\pi\)
−0.411828 + 0.911261i \(0.635110\pi\)
\(564\) 3.63278 0.152967
\(565\) −55.7004 −2.34333
\(566\) −15.6387 −0.657344
\(567\) −20.0780 −0.843195
\(568\) −6.81142 −0.285801
\(569\) −10.0091 −0.419603 −0.209802 0.977744i \(-0.567282\pi\)
−0.209802 + 0.977744i \(0.567282\pi\)
\(570\) 108.802 4.55723
\(571\) −8.28534 −0.346731 −0.173365 0.984858i \(-0.555464\pi\)
−0.173365 + 0.984858i \(0.555464\pi\)
\(572\) −1.93432 −0.0808778
\(573\) 15.1925 0.634674
\(574\) 13.6671 0.570454
\(575\) −1.06834 −0.0445528
\(576\) −8.24102 −0.343376
\(577\) 9.42953 0.392556 0.196278 0.980548i \(-0.437114\pi\)
0.196278 + 0.980548i \(0.437114\pi\)
\(578\) 28.0180 1.16540
\(579\) −21.7572 −0.904199
\(580\) −12.6941 −0.527094
\(581\) 57.2447 2.37491
\(582\) 81.9427 3.39663
\(583\) −7.67375 −0.317814
\(584\) 5.19984 0.215171
\(585\) −8.48727 −0.350906
\(586\) 0.242939 0.0100357
\(587\) −21.8257 −0.900844 −0.450422 0.892816i \(-0.648727\pi\)
−0.450422 + 0.892816i \(0.648727\pi\)
\(588\) 70.1898 2.89458
\(589\) 40.7334 1.67839
\(590\) −3.13008 −0.128863
\(591\) −28.4286 −1.16940
\(592\) 23.7195 0.974864
\(593\) 39.5962 1.62602 0.813010 0.582250i \(-0.197828\pi\)
0.813010 + 0.582250i \(0.197828\pi\)
\(594\) 17.8740 0.733379
\(595\) −27.2587 −1.11750
\(596\) 22.5805 0.924934
\(597\) −56.8237 −2.32564
\(598\) 0.0785647 0.00321275
\(599\) 29.4004 1.20127 0.600634 0.799524i \(-0.294915\pi\)
0.600634 + 0.799524i \(0.294915\pi\)
\(600\) 40.1550 1.63932
\(601\) −24.8580 −1.01398 −0.506989 0.861953i \(-0.669241\pi\)
−0.506989 + 0.861953i \(0.669241\pi\)
\(602\) 101.293 4.12839
\(603\) −15.0023 −0.610941
\(604\) 0.134816 0.00548560
\(605\) 8.12097 0.330164
\(606\) 34.3426 1.39507
\(607\) 24.2523 0.984372 0.492186 0.870490i \(-0.336198\pi\)
0.492186 + 0.870490i \(0.336198\pi\)
\(608\) 34.6857 1.40669
\(609\) 32.3393 1.31046
\(610\) −35.9862 −1.45704
\(611\) 0.499060 0.0201898
\(612\) 7.09442 0.286775
\(613\) −17.9999 −0.727009 −0.363504 0.931593i \(-0.618420\pi\)
−0.363504 + 0.931593i \(0.618420\pi\)
\(614\) 48.4397 1.95487
\(615\) 16.0842 0.648577
\(616\) −19.2600 −0.776009
\(617\) −30.0696 −1.21056 −0.605278 0.796014i \(-0.706938\pi\)
−0.605278 + 0.796014i \(0.706938\pi\)
\(618\) 4.64086 0.186683
\(619\) −43.5036 −1.74856 −0.874279 0.485425i \(-0.838665\pi\)
−0.874279 + 0.485425i \(0.838665\pi\)
\(620\) −41.3208 −1.65948
\(621\) −0.288719 −0.0115859
\(622\) −35.3981 −1.41934
\(623\) 38.0038 1.52259
\(624\) −6.41009 −0.256609
\(625\) 60.4316 2.41726
\(626\) 10.5706 0.422487
\(627\) −43.4316 −1.73449
\(628\) 8.57682 0.342252
\(629\) −6.17326 −0.246144
\(630\) 164.264 6.54443
\(631\) −32.6888 −1.30132 −0.650660 0.759369i \(-0.725508\pi\)
−0.650660 + 0.759369i \(0.725508\pi\)
\(632\) 20.5827 0.818734
\(633\) −1.59112 −0.0632412
\(634\) −57.2959 −2.27551
\(635\) −16.0423 −0.636618
\(636\) 9.05600 0.359094
\(637\) 9.64247 0.382049
\(638\) 12.7414 0.504435
\(639\) −23.1894 −0.917360
\(640\) 38.5652 1.52442
\(641\) 28.3515 1.11982 0.559908 0.828555i \(-0.310837\pi\)
0.559908 + 0.828555i \(0.310837\pi\)
\(642\) −7.42809 −0.293163
\(643\) −5.78843 −0.228273 −0.114137 0.993465i \(-0.536410\pi\)
−0.114137 + 0.993465i \(0.536410\pi\)
\(644\) −0.604721 −0.0238294
\(645\) 119.207 4.69377
\(646\) −12.4940 −0.491569
\(647\) 25.4787 1.00167 0.500836 0.865542i \(-0.333026\pi\)
0.500836 + 0.865542i \(0.333026\pi\)
\(648\) −4.80274 −0.188670
\(649\) 1.24946 0.0490457
\(650\) −10.7225 −0.420572
\(651\) 105.268 4.12579
\(652\) 8.39803 0.328892
\(653\) 23.0587 0.902355 0.451178 0.892434i \(-0.351004\pi\)
0.451178 + 0.892434i \(0.351004\pi\)
\(654\) −70.1542 −2.74325
\(655\) −48.0266 −1.87655
\(656\) 7.09664 0.277077
\(657\) 17.7028 0.690653
\(658\) −9.65887 −0.376542
\(659\) −24.6113 −0.958721 −0.479360 0.877618i \(-0.659131\pi\)
−0.479360 + 0.877618i \(0.659131\pi\)
\(660\) 44.0579 1.71495
\(661\) −19.8608 −0.772497 −0.386249 0.922395i \(-0.626229\pi\)
−0.386249 + 0.922395i \(0.626229\pi\)
\(662\) −20.8060 −0.808647
\(663\) 1.66830 0.0647914
\(664\) 13.6932 0.531399
\(665\) −115.048 −4.46138
\(666\) 37.2007 1.44150
\(667\) −0.205812 −0.00796906
\(668\) −7.96031 −0.307994
\(669\) 33.4009 1.29135
\(670\) −26.8015 −1.03543
\(671\) 14.3649 0.554552
\(672\) 89.6390 3.45790
\(673\) −26.9327 −1.03818 −0.519090 0.854719i \(-0.673729\pi\)
−0.519090 + 0.854719i \(0.673729\pi\)
\(674\) −47.7195 −1.83809
\(675\) 39.4044 1.51668
\(676\) −16.8542 −0.648238
\(677\) −18.9289 −0.727496 −0.363748 0.931497i \(-0.618503\pi\)
−0.363748 + 0.931497i \(0.618503\pi\)
\(678\) −65.9782 −2.53388
\(679\) −86.6467 −3.32520
\(680\) −6.52041 −0.250046
\(681\) 42.6110 1.63286
\(682\) 41.4746 1.58814
\(683\) −38.8590 −1.48690 −0.743448 0.668794i \(-0.766811\pi\)
−0.743448 + 0.668794i \(0.766811\pi\)
\(684\) 29.9428 1.14489
\(685\) 56.8732 2.17301
\(686\) −120.602 −4.60461
\(687\) 25.0556 0.955930
\(688\) 52.5962 2.00521
\(689\) 1.24409 0.0473959
\(690\) −1.78947 −0.0681239
\(691\) −43.6266 −1.65964 −0.829818 0.558034i \(-0.811556\pi\)
−0.829818 + 0.558034i \(0.811556\pi\)
\(692\) −27.9476 −1.06241
\(693\) −65.5707 −2.49082
\(694\) 52.0809 1.97696
\(695\) −77.4171 −2.93660
\(696\) 7.73572 0.293222
\(697\) −1.84698 −0.0699593
\(698\) −43.9710 −1.66433
\(699\) 56.4615 2.13557
\(700\) 82.5325 3.11943
\(701\) −46.1568 −1.74332 −0.871660 0.490111i \(-0.836956\pi\)
−0.871660 + 0.490111i \(0.836956\pi\)
\(702\) −2.89777 −0.109369
\(703\) −26.0549 −0.982678
\(704\) 5.87693 0.221495
\(705\) −11.3671 −0.428109
\(706\) 60.7518 2.28642
\(707\) −36.3141 −1.36573
\(708\) −1.47452 −0.0554160
\(709\) −8.25597 −0.310060 −0.155030 0.987910i \(-0.549547\pi\)
−0.155030 + 0.987910i \(0.549547\pi\)
\(710\) −41.4278 −1.55476
\(711\) 70.0735 2.62796
\(712\) 9.09070 0.340688
\(713\) −0.669941 −0.0250895
\(714\) −32.2885 −1.20837
\(715\) 6.05254 0.226352
\(716\) 20.5373 0.767513
\(717\) −21.6909 −0.810061
\(718\) −39.2760 −1.46577
\(719\) 8.86749 0.330702 0.165351 0.986235i \(-0.447124\pi\)
0.165351 + 0.986235i \(0.447124\pi\)
\(720\) 85.2939 3.17871
\(721\) −4.90728 −0.182757
\(722\) −18.1094 −0.673962
\(723\) 43.1800 1.60588
\(724\) −8.50630 −0.316134
\(725\) 28.0892 1.04321
\(726\) 9.61945 0.357011
\(727\) −31.0127 −1.15020 −0.575098 0.818085i \(-0.695036\pi\)
−0.575098 + 0.818085i \(0.695036\pi\)
\(728\) 3.12248 0.115727
\(729\) −42.6471 −1.57952
\(730\) 31.6260 1.17053
\(731\) −13.6888 −0.506297
\(732\) −16.9525 −0.626581
\(733\) −6.91323 −0.255346 −0.127673 0.991816i \(-0.540751\pi\)
−0.127673 + 0.991816i \(0.540751\pi\)
\(734\) −31.8543 −1.17576
\(735\) −219.626 −8.10105
\(736\) −0.570474 −0.0210280
\(737\) 10.6986 0.394088
\(738\) 11.1301 0.409704
\(739\) 32.2320 1.18568 0.592838 0.805322i \(-0.298008\pi\)
0.592838 + 0.805322i \(0.298008\pi\)
\(740\) 26.4306 0.971608
\(741\) 7.04123 0.258666
\(742\) −24.0782 −0.883938
\(743\) −46.5143 −1.70644 −0.853222 0.521547i \(-0.825355\pi\)
−0.853222 + 0.521547i \(0.825355\pi\)
\(744\) 25.1807 0.923168
\(745\) −70.6552 −2.58861
\(746\) −8.94324 −0.327435
\(747\) 46.6184 1.70568
\(748\) −5.05926 −0.184985
\(749\) 7.85451 0.286998
\(750\) 143.098 5.22520
\(751\) 41.3671 1.50951 0.754754 0.656008i \(-0.227756\pi\)
0.754754 + 0.656008i \(0.227756\pi\)
\(752\) −5.01536 −0.182891
\(753\) 8.88352 0.323733
\(754\) −2.06566 −0.0752269
\(755\) −0.421845 −0.0153525
\(756\) 22.3045 0.811206
\(757\) −3.99613 −0.145242 −0.0726208 0.997360i \(-0.523136\pi\)
−0.0726208 + 0.997360i \(0.523136\pi\)
\(758\) 41.2875 1.49963
\(759\) 0.714318 0.0259281
\(760\) −27.5201 −0.998258
\(761\) 18.3632 0.665666 0.332833 0.942986i \(-0.391996\pi\)
0.332833 + 0.942986i \(0.391996\pi\)
\(762\) −19.0024 −0.688384
\(763\) 74.1815 2.68555
\(764\) 7.46937 0.270232
\(765\) −22.1987 −0.802595
\(766\) 9.39496 0.339454
\(767\) −0.202566 −0.00731423
\(768\) 56.1849 2.02740
\(769\) −18.2658 −0.658683 −0.329341 0.944211i \(-0.606827\pi\)
−0.329341 + 0.944211i \(0.606827\pi\)
\(770\) −117.142 −4.22149
\(771\) −7.34361 −0.264474
\(772\) −10.6969 −0.384991
\(773\) −13.0559 −0.469588 −0.234794 0.972045i \(-0.575442\pi\)
−0.234794 + 0.972045i \(0.575442\pi\)
\(774\) 82.4899 2.96504
\(775\) 91.4336 3.28439
\(776\) −20.7263 −0.744031
\(777\) −67.3342 −2.41560
\(778\) 49.2625 1.76615
\(779\) −7.79537 −0.279298
\(780\) −7.14277 −0.255752
\(781\) 16.5371 0.591744
\(782\) 0.205488 0.00734824
\(783\) 7.59114 0.271285
\(784\) −96.9031 −3.46083
\(785\) −26.8372 −0.957859
\(786\) −56.8885 −2.02914
\(787\) −42.3411 −1.50930 −0.754648 0.656130i \(-0.772192\pi\)
−0.754648 + 0.656130i \(0.772192\pi\)
\(788\) −13.9769 −0.497906
\(789\) 64.0033 2.27858
\(790\) 125.186 4.45391
\(791\) 69.7658 2.48059
\(792\) −15.6848 −0.557336
\(793\) −2.32888 −0.0827008
\(794\) −37.0792 −1.31589
\(795\) −28.3365 −1.00499
\(796\) −27.9373 −0.990213
\(797\) 54.0030 1.91288 0.956442 0.291921i \(-0.0942945\pi\)
0.956442 + 0.291921i \(0.0942945\pi\)
\(798\) −136.277 −4.82415
\(799\) 1.30530 0.0461784
\(800\) 77.8584 2.75271
\(801\) 30.9492 1.09354
\(802\) 68.0963 2.40457
\(803\) −12.6244 −0.445507
\(804\) −12.6257 −0.445275
\(805\) 1.89219 0.0666911
\(806\) −6.72396 −0.236841
\(807\) 32.6846 1.15055
\(808\) −8.68650 −0.305590
\(809\) 18.9901 0.667655 0.333828 0.942634i \(-0.391660\pi\)
0.333828 + 0.942634i \(0.391660\pi\)
\(810\) −29.2108 −1.02636
\(811\) −1.99008 −0.0698810 −0.0349405 0.999389i \(-0.511124\pi\)
−0.0349405 + 0.999389i \(0.511124\pi\)
\(812\) 15.8996 0.557967
\(813\) −54.6302 −1.91596
\(814\) −26.5290 −0.929840
\(815\) −26.2777 −0.920469
\(816\) −16.7658 −0.586919
\(817\) −57.7749 −2.02129
\(818\) −55.5424 −1.94200
\(819\) 10.6305 0.371459
\(820\) 7.90778 0.276152
\(821\) −13.6320 −0.475759 −0.237879 0.971295i \(-0.576452\pi\)
−0.237879 + 0.971295i \(0.576452\pi\)
\(822\) 67.3675 2.34971
\(823\) −21.4172 −0.746557 −0.373279 0.927719i \(-0.621766\pi\)
−0.373279 + 0.927719i \(0.621766\pi\)
\(824\) −1.17384 −0.0408928
\(825\) −97.4903 −3.39418
\(826\) 3.92048 0.136411
\(827\) −9.71569 −0.337848 −0.168924 0.985629i \(-0.554029\pi\)
−0.168924 + 0.985629i \(0.554029\pi\)
\(828\) −0.492467 −0.0171144
\(829\) −32.0851 −1.11436 −0.557181 0.830391i \(-0.688117\pi\)
−0.557181 + 0.830391i \(0.688117\pi\)
\(830\) 83.2835 2.89081
\(831\) 26.0615 0.904065
\(832\) −0.952782 −0.0330318
\(833\) 25.2201 0.873826
\(834\) −91.7021 −3.17538
\(835\) 24.9081 0.861980
\(836\) −21.3531 −0.738513
\(837\) 24.7100 0.854103
\(838\) −39.4158 −1.36160
\(839\) 2.52233 0.0870804 0.0435402 0.999052i \(-0.486136\pi\)
0.0435402 + 0.999052i \(0.486136\pi\)
\(840\) −71.1208 −2.45390
\(841\) −23.5887 −0.813404
\(842\) 40.3246 1.38968
\(843\) 70.5457 2.42972
\(844\) −0.782272 −0.0269269
\(845\) 52.7373 1.81422
\(846\) −7.86590 −0.270435
\(847\) −10.1717 −0.349503
\(848\) −12.5026 −0.429340
\(849\) 23.0520 0.791141
\(850\) −28.0450 −0.961937
\(851\) 0.428524 0.0146896
\(852\) −19.5159 −0.668603
\(853\) −28.3783 −0.971654 −0.485827 0.874055i \(-0.661482\pi\)
−0.485827 + 0.874055i \(0.661482\pi\)
\(854\) 45.0734 1.54238
\(855\) −93.6919 −3.20420
\(856\) 1.87884 0.0642173
\(857\) 20.0013 0.683231 0.341616 0.939840i \(-0.389026\pi\)
0.341616 + 0.939840i \(0.389026\pi\)
\(858\) 7.16936 0.244758
\(859\) −55.8459 −1.90544 −0.952719 0.303853i \(-0.901727\pi\)
−0.952719 + 0.303853i \(0.901727\pi\)
\(860\) 58.6080 1.99852
\(861\) −20.1458 −0.686565
\(862\) −55.5196 −1.89101
\(863\) −10.7654 −0.366457 −0.183229 0.983070i \(-0.558655\pi\)
−0.183229 + 0.983070i \(0.558655\pi\)
\(864\) 21.0413 0.715840
\(865\) 87.4491 2.97336
\(866\) −37.1289 −1.26169
\(867\) −41.2995 −1.40260
\(868\) 51.7551 1.75668
\(869\) −49.9716 −1.69517
\(870\) 47.0495 1.59513
\(871\) −1.73448 −0.0587707
\(872\) 17.7446 0.600907
\(873\) −70.5626 −2.38818
\(874\) 0.867284 0.0293363
\(875\) −151.313 −5.11531
\(876\) 14.8984 0.503372
\(877\) −13.8207 −0.466692 −0.233346 0.972394i \(-0.574968\pi\)
−0.233346 + 0.972394i \(0.574968\pi\)
\(878\) −50.6653 −1.70987
\(879\) −0.358101 −0.0120784
\(880\) −60.8257 −2.05044
\(881\) −5.26645 −0.177431 −0.0887157 0.996057i \(-0.528276\pi\)
−0.0887157 + 0.996057i \(0.528276\pi\)
\(882\) −151.979 −5.11741
\(883\) −5.43937 −0.183049 −0.0915247 0.995803i \(-0.529174\pi\)
−0.0915247 + 0.995803i \(0.529174\pi\)
\(884\) 0.820218 0.0275869
\(885\) 4.61384 0.155093
\(886\) 23.7583 0.798177
\(887\) 25.5993 0.859542 0.429771 0.902938i \(-0.358594\pi\)
0.429771 + 0.902938i \(0.358594\pi\)
\(888\) −16.1067 −0.540504
\(889\) 20.0932 0.673906
\(890\) 55.2906 1.85335
\(891\) 11.6603 0.390636
\(892\) 16.4215 0.549834
\(893\) 5.50918 0.184358
\(894\) −83.6925 −2.79910
\(895\) −64.2618 −2.14804
\(896\) −48.3037 −1.61371
\(897\) −0.115807 −0.00386668
\(898\) −3.86607 −0.129012
\(899\) 17.6144 0.587473
\(900\) 67.2120 2.24040
\(901\) 3.25394 0.108404
\(902\) −7.93722 −0.264280
\(903\) −149.309 −4.96869
\(904\) 16.6883 0.555045
\(905\) 26.6165 0.884763
\(906\) −0.499684 −0.0166009
\(907\) −22.5912 −0.750129 −0.375064 0.926999i \(-0.622379\pi\)
−0.375064 + 0.926999i \(0.622379\pi\)
\(908\) 20.9497 0.695239
\(909\) −29.5731 −0.980878
\(910\) 18.9913 0.629555
\(911\) 40.5238 1.34261 0.671307 0.741179i \(-0.265733\pi\)
0.671307 + 0.741179i \(0.265733\pi\)
\(912\) −70.7617 −2.34315
\(913\) −33.2450 −1.10025
\(914\) −56.8859 −1.88162
\(915\) 53.0448 1.75361
\(916\) 12.3186 0.407017
\(917\) 60.1542 1.98647
\(918\) −7.57920 −0.250151
\(919\) 56.5294 1.86473 0.932367 0.361514i \(-0.117740\pi\)
0.932367 + 0.361514i \(0.117740\pi\)
\(920\) 0.452622 0.0149225
\(921\) −71.4017 −2.35277
\(922\) −28.8212 −0.949175
\(923\) −2.68103 −0.0882473
\(924\) −55.1834 −1.81540
\(925\) −58.4850 −1.92297
\(926\) 5.27486 0.173343
\(927\) −3.99634 −0.131257
\(928\) 14.9992 0.492372
\(929\) −24.7082 −0.810650 −0.405325 0.914173i \(-0.632842\pi\)
−0.405325 + 0.914173i \(0.632842\pi\)
\(930\) 153.152 5.02204
\(931\) 106.444 3.48857
\(932\) 27.7592 0.909284
\(933\) 52.1780 1.70823
\(934\) −16.3301 −0.534339
\(935\) 15.8306 0.517716
\(936\) 2.54286 0.0831159
\(937\) 40.6915 1.32933 0.664667 0.747139i \(-0.268573\pi\)
0.664667 + 0.747139i \(0.268573\pi\)
\(938\) 33.5694 1.09608
\(939\) −15.5814 −0.508481
\(940\) −5.58862 −0.182281
\(941\) 25.7501 0.839429 0.419715 0.907656i \(-0.362130\pi\)
0.419715 + 0.907656i \(0.362130\pi\)
\(942\) −31.7892 −1.03575
\(943\) 0.128210 0.00417510
\(944\) 2.03571 0.0662567
\(945\) −69.7915 −2.27032
\(946\) −58.8262 −1.91260
\(947\) 53.0653 1.72439 0.862196 0.506575i \(-0.169089\pi\)
0.862196 + 0.506575i \(0.169089\pi\)
\(948\) 58.9728 1.91535
\(949\) 2.04670 0.0664388
\(950\) −118.367 −3.84033
\(951\) 84.4560 2.73867
\(952\) 8.16694 0.264692
\(953\) 17.7978 0.576528 0.288264 0.957551i \(-0.406922\pi\)
0.288264 + 0.957551i \(0.406922\pi\)
\(954\) −19.6086 −0.634851
\(955\) −23.3719 −0.756297
\(956\) −10.6643 −0.344908
\(957\) −18.7812 −0.607109
\(958\) 64.2567 2.07604
\(959\) −71.2348 −2.30029
\(960\) 21.7015 0.700413
\(961\) 26.3369 0.849576
\(962\) 4.30094 0.138668
\(963\) 6.39648 0.206124
\(964\) 21.2294 0.683753
\(965\) 33.4710 1.07747
\(966\) 2.24134 0.0721140
\(967\) −33.3758 −1.07329 −0.536647 0.843807i \(-0.680309\pi\)
−0.536647 + 0.843807i \(0.680309\pi\)
\(968\) −2.43311 −0.0782031
\(969\) 18.4165 0.591624
\(970\) −126.060 −4.04753
\(971\) −18.5427 −0.595064 −0.297532 0.954712i \(-0.596163\pi\)
−0.297532 + 0.954712i \(0.596163\pi\)
\(972\) −26.6892 −0.856056
\(973\) 96.9664 3.10860
\(974\) 17.8365 0.571518
\(975\) 15.8053 0.506176
\(976\) 23.4043 0.749154
\(977\) 32.6089 1.04325 0.521626 0.853174i \(-0.325326\pi\)
0.521626 + 0.853174i \(0.325326\pi\)
\(978\) −31.1265 −0.995316
\(979\) −22.0709 −0.705388
\(980\) −107.979 −3.44927
\(981\) 60.4112 1.92878
\(982\) −18.5994 −0.593531
\(983\) −59.8324 −1.90836 −0.954179 0.299237i \(-0.903268\pi\)
−0.954179 + 0.299237i \(0.903268\pi\)
\(984\) −4.81896 −0.153623
\(985\) 43.7342 1.39349
\(986\) −5.40279 −0.172060
\(987\) 14.2375 0.453184
\(988\) 3.46182 0.110135
\(989\) 0.950222 0.0302153
\(990\) −95.3968 −3.03191
\(991\) −28.0661 −0.891551 −0.445775 0.895145i \(-0.647072\pi\)
−0.445775 + 0.895145i \(0.647072\pi\)
\(992\) 48.8240 1.55016
\(993\) 30.6687 0.973241
\(994\) 51.8891 1.64582
\(995\) 87.4169 2.77130
\(996\) 39.2334 1.24316
\(997\) −40.7160 −1.28949 −0.644744 0.764399i \(-0.723036\pi\)
−0.644744 + 0.764399i \(0.723036\pi\)
\(998\) 14.3937 0.455625
\(999\) −15.8056 −0.500068
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 4001.2.a.b.1.40 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.40 184 1.1 even 1 trivial