Properties

Label 8027.2.a.e.1.13
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $0$
Dimension $169$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(169\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.48779 q^{2} -1.56706 q^{3} +4.18912 q^{4} -0.470974 q^{5} +3.89852 q^{6} -0.335999 q^{7} -5.44607 q^{8} -0.544327 q^{9} +O(q^{10})\) \(q-2.48779 q^{2} -1.56706 q^{3} +4.18912 q^{4} -0.470974 q^{5} +3.89852 q^{6} -0.335999 q^{7} -5.44607 q^{8} -0.544327 q^{9} +1.17169 q^{10} +5.06537 q^{11} -6.56459 q^{12} -0.350034 q^{13} +0.835897 q^{14} +0.738043 q^{15} +5.17047 q^{16} -3.11361 q^{17} +1.35417 q^{18} +2.58200 q^{19} -1.97296 q^{20} +0.526530 q^{21} -12.6016 q^{22} -1.00000 q^{23} +8.53432 q^{24} -4.77818 q^{25} +0.870812 q^{26} +5.55417 q^{27} -1.40754 q^{28} -9.91707 q^{29} -1.83610 q^{30} -8.29672 q^{31} -1.97092 q^{32} -7.93773 q^{33} +7.74601 q^{34} +0.158247 q^{35} -2.28025 q^{36} +5.32250 q^{37} -6.42349 q^{38} +0.548524 q^{39} +2.56496 q^{40} -8.80884 q^{41} -1.30990 q^{42} -4.09651 q^{43} +21.2194 q^{44} +0.256364 q^{45} +2.48779 q^{46} +8.33840 q^{47} -8.10243 q^{48} -6.88710 q^{49} +11.8871 q^{50} +4.87920 q^{51} -1.46633 q^{52} +1.16674 q^{53} -13.8176 q^{54} -2.38565 q^{55} +1.82988 q^{56} -4.04615 q^{57} +24.6716 q^{58} +0.831949 q^{59} +3.09175 q^{60} +9.02470 q^{61} +20.6405 q^{62} +0.182893 q^{63} -5.43770 q^{64} +0.164857 q^{65} +19.7474 q^{66} +5.05580 q^{67} -13.0433 q^{68} +1.56706 q^{69} -0.393685 q^{70} +14.0398 q^{71} +2.96445 q^{72} -4.31779 q^{73} -13.2413 q^{74} +7.48769 q^{75} +10.8163 q^{76} -1.70196 q^{77} -1.36461 q^{78} -6.82411 q^{79} -2.43516 q^{80} -7.07073 q^{81} +21.9146 q^{82} -16.5666 q^{83} +2.20570 q^{84} +1.46643 q^{85} +10.1913 q^{86} +15.5406 q^{87} -27.5864 q^{88} -5.90829 q^{89} -0.637780 q^{90} +0.117611 q^{91} -4.18912 q^{92} +13.0014 q^{93} -20.7442 q^{94} -1.21606 q^{95} +3.08855 q^{96} +16.2984 q^{97} +17.1337 q^{98} -2.75722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48779 −1.75914 −0.879568 0.475773i \(-0.842168\pi\)
−0.879568 + 0.475773i \(0.842168\pi\)
\(3\) −1.56706 −0.904742 −0.452371 0.891830i \(-0.649422\pi\)
−0.452371 + 0.891830i \(0.649422\pi\)
\(4\) 4.18912 2.09456
\(5\) −0.470974 −0.210626 −0.105313 0.994439i \(-0.533584\pi\)
−0.105313 + 0.994439i \(0.533584\pi\)
\(6\) 3.89852 1.59156
\(7\) −0.335999 −0.126996 −0.0634979 0.997982i \(-0.520226\pi\)
−0.0634979 + 0.997982i \(0.520226\pi\)
\(8\) −5.44607 −1.92548
\(9\) −0.544327 −0.181442
\(10\) 1.17169 0.370519
\(11\) 5.06537 1.52727 0.763633 0.645651i \(-0.223414\pi\)
0.763633 + 0.645651i \(0.223414\pi\)
\(12\) −6.56459 −1.89503
\(13\) −0.350034 −0.0970819 −0.0485410 0.998821i \(-0.515457\pi\)
−0.0485410 + 0.998821i \(0.515457\pi\)
\(14\) 0.835897 0.223403
\(15\) 0.738043 0.190562
\(16\) 5.17047 1.29262
\(17\) −3.11361 −0.755160 −0.377580 0.925977i \(-0.623244\pi\)
−0.377580 + 0.925977i \(0.623244\pi\)
\(18\) 1.35417 0.319182
\(19\) 2.58200 0.592352 0.296176 0.955133i \(-0.404288\pi\)
0.296176 + 0.955133i \(0.404288\pi\)
\(20\) −1.97296 −0.441168
\(21\) 0.526530 0.114898
\(22\) −12.6016 −2.68667
\(23\) −1.00000 −0.208514
\(24\) 8.53432 1.74206
\(25\) −4.77818 −0.955637
\(26\) 0.870812 0.170780
\(27\) 5.55417 1.06890
\(28\) −1.40754 −0.266000
\(29\) −9.91707 −1.84155 −0.920777 0.390090i \(-0.872444\pi\)
−0.920777 + 0.390090i \(0.872444\pi\)
\(30\) −1.83610 −0.335224
\(31\) −8.29672 −1.49013 −0.745067 0.666989i \(-0.767583\pi\)
−0.745067 + 0.666989i \(0.767583\pi\)
\(32\) −1.97092 −0.348413
\(33\) −7.93773 −1.38178
\(34\) 7.74601 1.32843
\(35\) 0.158247 0.0267486
\(36\) −2.28025 −0.380042
\(37\) 5.32250 0.875013 0.437507 0.899215i \(-0.355862\pi\)
0.437507 + 0.899215i \(0.355862\pi\)
\(38\) −6.42349 −1.04203
\(39\) 0.548524 0.0878341
\(40\) 2.56496 0.405555
\(41\) −8.80884 −1.37571 −0.687855 0.725848i \(-0.741448\pi\)
−0.687855 + 0.725848i \(0.741448\pi\)
\(42\) −1.30990 −0.202122
\(43\) −4.09651 −0.624712 −0.312356 0.949965i \(-0.601118\pi\)
−0.312356 + 0.949965i \(0.601118\pi\)
\(44\) 21.2194 3.19895
\(45\) 0.256364 0.0382164
\(46\) 2.48779 0.366805
\(47\) 8.33840 1.21628 0.608140 0.793830i \(-0.291916\pi\)
0.608140 + 0.793830i \(0.291916\pi\)
\(48\) −8.10243 −1.16949
\(49\) −6.88710 −0.983872
\(50\) 11.8871 1.68109
\(51\) 4.87920 0.683225
\(52\) −1.46633 −0.203344
\(53\) 1.16674 0.160265 0.0801323 0.996784i \(-0.474466\pi\)
0.0801323 + 0.996784i \(0.474466\pi\)
\(54\) −13.8176 −1.88034
\(55\) −2.38565 −0.321681
\(56\) 1.82988 0.244528
\(57\) −4.04615 −0.535926
\(58\) 24.6716 3.23954
\(59\) 0.831949 0.108311 0.0541553 0.998533i \(-0.482753\pi\)
0.0541553 + 0.998533i \(0.482753\pi\)
\(60\) 3.09175 0.399143
\(61\) 9.02470 1.15549 0.577747 0.816216i \(-0.303932\pi\)
0.577747 + 0.816216i \(0.303932\pi\)
\(62\) 20.6405 2.62135
\(63\) 0.182893 0.0230424
\(64\) −5.43770 −0.679712
\(65\) 0.164857 0.0204480
\(66\) 19.7474 2.43074
\(67\) 5.05580 0.617664 0.308832 0.951117i \(-0.400062\pi\)
0.308832 + 0.951117i \(0.400062\pi\)
\(68\) −13.0433 −1.58173
\(69\) 1.56706 0.188652
\(70\) −0.393685 −0.0470544
\(71\) 14.0398 1.66622 0.833110 0.553108i \(-0.186558\pi\)
0.833110 + 0.553108i \(0.186558\pi\)
\(72\) 2.96445 0.349363
\(73\) −4.31779 −0.505359 −0.252679 0.967550i \(-0.581312\pi\)
−0.252679 + 0.967550i \(0.581312\pi\)
\(74\) −13.2413 −1.53927
\(75\) 7.48769 0.864604
\(76\) 10.8163 1.24072
\(77\) −1.70196 −0.193956
\(78\) −1.36461 −0.154512
\(79\) −6.82411 −0.767772 −0.383886 0.923380i \(-0.625414\pi\)
−0.383886 + 0.923380i \(0.625414\pi\)
\(80\) −2.43516 −0.272259
\(81\) −7.07073 −0.785636
\(82\) 21.9146 2.42006
\(83\) −16.5666 −1.81842 −0.909209 0.416339i \(-0.863313\pi\)
−0.909209 + 0.416339i \(0.863313\pi\)
\(84\) 2.20570 0.240661
\(85\) 1.46643 0.159056
\(86\) 10.1913 1.09895
\(87\) 15.5406 1.66613
\(88\) −27.5864 −2.94072
\(89\) −5.90829 −0.626278 −0.313139 0.949707i \(-0.601381\pi\)
−0.313139 + 0.949707i \(0.601381\pi\)
\(90\) −0.637780 −0.0672279
\(91\) 0.117611 0.0123290
\(92\) −4.18912 −0.436746
\(93\) 13.0014 1.34819
\(94\) −20.7442 −2.13960
\(95\) −1.21606 −0.124765
\(96\) 3.08855 0.315224
\(97\) 16.2984 1.65486 0.827428 0.561572i \(-0.189803\pi\)
0.827428 + 0.561572i \(0.189803\pi\)
\(98\) 17.1337 1.73076
\(99\) −2.75722 −0.277111
\(100\) −20.0164 −2.00164
\(101\) −16.8293 −1.67458 −0.837289 0.546761i \(-0.815861\pi\)
−0.837289 + 0.546761i \(0.815861\pi\)
\(102\) −12.1385 −1.20189
\(103\) 18.4116 1.81415 0.907075 0.420970i \(-0.138310\pi\)
0.907075 + 0.420970i \(0.138310\pi\)
\(104\) 1.90631 0.186929
\(105\) −0.247982 −0.0242006
\(106\) −2.90262 −0.281927
\(107\) −6.11460 −0.591121 −0.295561 0.955324i \(-0.595506\pi\)
−0.295561 + 0.955324i \(0.595506\pi\)
\(108\) 23.2671 2.23887
\(109\) −18.9266 −1.81284 −0.906420 0.422377i \(-0.861196\pi\)
−0.906420 + 0.422377i \(0.861196\pi\)
\(110\) 5.93501 0.565881
\(111\) −8.34067 −0.791661
\(112\) −1.73727 −0.164157
\(113\) 4.06224 0.382144 0.191072 0.981576i \(-0.438804\pi\)
0.191072 + 0.981576i \(0.438804\pi\)
\(114\) 10.0660 0.942766
\(115\) 0.470974 0.0439185
\(116\) −41.5438 −3.85724
\(117\) 0.190533 0.0176148
\(118\) −2.06972 −0.190533
\(119\) 1.04617 0.0959021
\(120\) −4.01944 −0.366923
\(121\) 14.6579 1.33254
\(122\) −22.4516 −2.03267
\(123\) 13.8040 1.24466
\(124\) −34.7559 −3.12118
\(125\) 4.60527 0.411908
\(126\) −0.455001 −0.0405347
\(127\) −13.9328 −1.23634 −0.618168 0.786046i \(-0.712125\pi\)
−0.618168 + 0.786046i \(0.712125\pi\)
\(128\) 17.4697 1.54412
\(129\) 6.41947 0.565203
\(130\) −0.410129 −0.0359707
\(131\) 7.04555 0.615573 0.307786 0.951456i \(-0.400412\pi\)
0.307786 + 0.951456i \(0.400412\pi\)
\(132\) −33.2521 −2.89422
\(133\) −0.867551 −0.0752262
\(134\) −12.5778 −1.08655
\(135\) −2.61587 −0.225138
\(136\) 16.9569 1.45404
\(137\) 2.36941 0.202432 0.101216 0.994864i \(-0.467727\pi\)
0.101216 + 0.994864i \(0.467727\pi\)
\(138\) −3.89852 −0.331864
\(139\) 19.2979 1.63683 0.818415 0.574627i \(-0.194853\pi\)
0.818415 + 0.574627i \(0.194853\pi\)
\(140\) 0.662914 0.0560265
\(141\) −13.0668 −1.10042
\(142\) −34.9282 −2.93111
\(143\) −1.77305 −0.148270
\(144\) −2.81443 −0.234536
\(145\) 4.67068 0.387879
\(146\) 10.7418 0.888995
\(147\) 10.7925 0.890150
\(148\) 22.2966 1.83277
\(149\) −13.6893 −1.12147 −0.560736 0.827995i \(-0.689482\pi\)
−0.560736 + 0.827995i \(0.689482\pi\)
\(150\) −18.6278 −1.52096
\(151\) 14.1903 1.15479 0.577395 0.816465i \(-0.304069\pi\)
0.577395 + 0.816465i \(0.304069\pi\)
\(152\) −14.0618 −1.14056
\(153\) 1.69482 0.137018
\(154\) 4.23412 0.341195
\(155\) 3.90754 0.313861
\(156\) 2.29783 0.183974
\(157\) 19.8711 1.58589 0.792944 0.609295i \(-0.208547\pi\)
0.792944 + 0.609295i \(0.208547\pi\)
\(158\) 16.9770 1.35062
\(159\) −1.82836 −0.144998
\(160\) 0.928252 0.0733848
\(161\) 0.335999 0.0264804
\(162\) 17.5905 1.38204
\(163\) 14.4801 1.13417 0.567085 0.823659i \(-0.308071\pi\)
0.567085 + 0.823659i \(0.308071\pi\)
\(164\) −36.9013 −2.88151
\(165\) 3.73846 0.291039
\(166\) 41.2142 3.19885
\(167\) −8.90133 −0.688805 −0.344403 0.938822i \(-0.611919\pi\)
−0.344403 + 0.938822i \(0.611919\pi\)
\(168\) −2.86752 −0.221234
\(169\) −12.8775 −0.990575
\(170\) −3.64817 −0.279801
\(171\) −1.40545 −0.107478
\(172\) −17.1608 −1.30850
\(173\) 15.4942 1.17800 0.589001 0.808132i \(-0.299521\pi\)
0.589001 + 0.808132i \(0.299521\pi\)
\(174\) −38.6619 −2.93095
\(175\) 1.60547 0.121362
\(176\) 26.1903 1.97417
\(177\) −1.30371 −0.0979931
\(178\) 14.6986 1.10171
\(179\) −0.645088 −0.0482161 −0.0241081 0.999709i \(-0.507675\pi\)
−0.0241081 + 0.999709i \(0.507675\pi\)
\(180\) 1.07394 0.0800466
\(181\) −0.656289 −0.0487816 −0.0243908 0.999703i \(-0.507765\pi\)
−0.0243908 + 0.999703i \(0.507765\pi\)
\(182\) −0.292592 −0.0216884
\(183\) −14.1422 −1.04542
\(184\) 5.44607 0.401490
\(185\) −2.50676 −0.184300
\(186\) −32.3449 −2.37164
\(187\) −15.7716 −1.15333
\(188\) 34.9305 2.54757
\(189\) −1.86620 −0.135746
\(190\) 3.02529 0.219478
\(191\) 8.97318 0.649276 0.324638 0.945838i \(-0.394757\pi\)
0.324638 + 0.945838i \(0.394757\pi\)
\(192\) 8.52119 0.614964
\(193\) −5.87251 −0.422713 −0.211356 0.977409i \(-0.567788\pi\)
−0.211356 + 0.977409i \(0.567788\pi\)
\(194\) −40.5471 −2.91112
\(195\) −0.258340 −0.0185001
\(196\) −28.8509 −2.06078
\(197\) −19.5731 −1.39453 −0.697263 0.716816i \(-0.745599\pi\)
−0.697263 + 0.716816i \(0.745599\pi\)
\(198\) 6.85938 0.487475
\(199\) 25.5399 1.81048 0.905238 0.424905i \(-0.139693\pi\)
0.905238 + 0.424905i \(0.139693\pi\)
\(200\) 26.0223 1.84006
\(201\) −7.92273 −0.558826
\(202\) 41.8678 2.94581
\(203\) 3.33213 0.233869
\(204\) 20.4396 1.43106
\(205\) 4.14873 0.289760
\(206\) −45.8043 −3.19133
\(207\) 0.544327 0.0378333
\(208\) −1.80984 −0.125490
\(209\) 13.0788 0.904679
\(210\) 0.616928 0.0425721
\(211\) −9.28151 −0.638965 −0.319483 0.947592i \(-0.603509\pi\)
−0.319483 + 0.947592i \(0.603509\pi\)
\(212\) 4.88763 0.335684
\(213\) −22.0012 −1.50750
\(214\) 15.2119 1.03986
\(215\) 1.92935 0.131580
\(216\) −30.2484 −2.05814
\(217\) 2.78769 0.189241
\(218\) 47.0855 3.18903
\(219\) 6.76623 0.457219
\(220\) −9.99378 −0.673781
\(221\) 1.08987 0.0733124
\(222\) 20.7499 1.39264
\(223\) 16.8445 1.12799 0.563994 0.825779i \(-0.309264\pi\)
0.563994 + 0.825779i \(0.309264\pi\)
\(224\) 0.662228 0.0442470
\(225\) 2.60089 0.173393
\(226\) −10.1060 −0.672242
\(227\) 1.37966 0.0915713 0.0457857 0.998951i \(-0.485421\pi\)
0.0457857 + 0.998951i \(0.485421\pi\)
\(228\) −16.9498 −1.12253
\(229\) −19.7876 −1.30760 −0.653802 0.756665i \(-0.726827\pi\)
−0.653802 + 0.756665i \(0.726827\pi\)
\(230\) −1.17169 −0.0772586
\(231\) 2.66707 0.175480
\(232\) 54.0091 3.54587
\(233\) −17.7548 −1.16316 −0.581578 0.813490i \(-0.697565\pi\)
−0.581578 + 0.813490i \(0.697565\pi\)
\(234\) −0.474007 −0.0309868
\(235\) −3.92716 −0.256180
\(236\) 3.48513 0.226863
\(237\) 10.6938 0.694636
\(238\) −2.60265 −0.168705
\(239\) −8.75121 −0.566069 −0.283034 0.959110i \(-0.591341\pi\)
−0.283034 + 0.959110i \(0.591341\pi\)
\(240\) 3.81603 0.246324
\(241\) −9.47928 −0.610614 −0.305307 0.952254i \(-0.598759\pi\)
−0.305307 + 0.952254i \(0.598759\pi\)
\(242\) −36.4659 −2.34412
\(243\) −5.58226 −0.358102
\(244\) 37.8055 2.42025
\(245\) 3.24364 0.207229
\(246\) −34.3414 −2.18953
\(247\) −0.903788 −0.0575067
\(248\) 45.1845 2.86922
\(249\) 25.9608 1.64520
\(250\) −11.4570 −0.724601
\(251\) −7.74307 −0.488738 −0.244369 0.969682i \(-0.578581\pi\)
−0.244369 + 0.969682i \(0.578581\pi\)
\(252\) 0.766162 0.0482637
\(253\) −5.06537 −0.318457
\(254\) 34.6619 2.17488
\(255\) −2.29798 −0.143905
\(256\) −32.5857 −2.03660
\(257\) −20.1148 −1.25472 −0.627362 0.778728i \(-0.715865\pi\)
−0.627362 + 0.778728i \(0.715865\pi\)
\(258\) −15.9703 −0.994269
\(259\) −1.78836 −0.111123
\(260\) 0.690604 0.0428294
\(261\) 5.39813 0.334136
\(262\) −17.5279 −1.08288
\(263\) 9.84468 0.607049 0.303524 0.952824i \(-0.401837\pi\)
0.303524 + 0.952824i \(0.401837\pi\)
\(264\) 43.2294 2.66059
\(265\) −0.549506 −0.0337559
\(266\) 2.15829 0.132333
\(267\) 9.25864 0.566619
\(268\) 21.1793 1.29373
\(269\) −22.3874 −1.36498 −0.682492 0.730893i \(-0.739104\pi\)
−0.682492 + 0.730893i \(0.739104\pi\)
\(270\) 6.50774 0.396048
\(271\) 8.77313 0.532930 0.266465 0.963845i \(-0.414144\pi\)
0.266465 + 0.963845i \(0.414144\pi\)
\(272\) −16.0988 −0.976134
\(273\) −0.184303 −0.0111546
\(274\) −5.89460 −0.356106
\(275\) −24.2033 −1.45951
\(276\) 6.56459 0.395142
\(277\) −8.98312 −0.539743 −0.269872 0.962896i \(-0.586981\pi\)
−0.269872 + 0.962896i \(0.586981\pi\)
\(278\) −48.0093 −2.87941
\(279\) 4.51613 0.270374
\(280\) −0.861823 −0.0515038
\(281\) 6.10871 0.364415 0.182207 0.983260i \(-0.441676\pi\)
0.182207 + 0.983260i \(0.441676\pi\)
\(282\) 32.5074 1.93579
\(283\) −6.13832 −0.364885 −0.182443 0.983216i \(-0.558400\pi\)
−0.182443 + 0.983216i \(0.558400\pi\)
\(284\) 58.8144 3.48999
\(285\) 1.90563 0.112880
\(286\) 4.41098 0.260827
\(287\) 2.95976 0.174709
\(288\) 1.07283 0.0632169
\(289\) −7.30546 −0.429733
\(290\) −11.6197 −0.682331
\(291\) −25.5406 −1.49722
\(292\) −18.0877 −1.05850
\(293\) −0.664082 −0.0387961 −0.0193980 0.999812i \(-0.506175\pi\)
−0.0193980 + 0.999812i \(0.506175\pi\)
\(294\) −26.8495 −1.56590
\(295\) −0.391826 −0.0228130
\(296\) −28.9867 −1.68482
\(297\) 28.1339 1.63249
\(298\) 34.0562 1.97282
\(299\) 0.350034 0.0202430
\(300\) 31.3668 1.81097
\(301\) 1.37642 0.0793357
\(302\) −35.3026 −2.03143
\(303\) 26.3725 1.51506
\(304\) 13.3502 0.765685
\(305\) −4.25039 −0.243377
\(306\) −4.21636 −0.241033
\(307\) 19.5257 1.11439 0.557195 0.830382i \(-0.311878\pi\)
0.557195 + 0.830382i \(0.311878\pi\)
\(308\) −7.12971 −0.406253
\(309\) −28.8521 −1.64134
\(310\) −9.72114 −0.552124
\(311\) −0.522895 −0.0296507 −0.0148253 0.999890i \(-0.504719\pi\)
−0.0148253 + 0.999890i \(0.504719\pi\)
\(312\) −2.98730 −0.169123
\(313\) 21.3409 1.20626 0.603128 0.797644i \(-0.293921\pi\)
0.603128 + 0.797644i \(0.293921\pi\)
\(314\) −49.4352 −2.78979
\(315\) −0.0861380 −0.00485333
\(316\) −28.5870 −1.60814
\(317\) −0.420362 −0.0236099 −0.0118049 0.999930i \(-0.503758\pi\)
−0.0118049 + 0.999930i \(0.503758\pi\)
\(318\) 4.54857 0.255071
\(319\) −50.2336 −2.81254
\(320\) 2.56101 0.143165
\(321\) 9.58194 0.534812
\(322\) −0.835897 −0.0465827
\(323\) −8.03934 −0.447321
\(324\) −29.6201 −1.64556
\(325\) 1.67253 0.0927751
\(326\) −36.0236 −1.99516
\(327\) 29.6591 1.64015
\(328\) 47.9736 2.64890
\(329\) −2.80169 −0.154462
\(330\) −9.30052 −0.511977
\(331\) 26.2070 1.44047 0.720234 0.693731i \(-0.244034\pi\)
0.720234 + 0.693731i \(0.244034\pi\)
\(332\) −69.3994 −3.80879
\(333\) −2.89718 −0.158765
\(334\) 22.1447 1.21170
\(335\) −2.38115 −0.130096
\(336\) 2.72241 0.148520
\(337\) 9.00093 0.490312 0.245156 0.969484i \(-0.421161\pi\)
0.245156 + 0.969484i \(0.421161\pi\)
\(338\) 32.0365 1.74256
\(339\) −6.36577 −0.345741
\(340\) 6.14303 0.333153
\(341\) −42.0259 −2.27583
\(342\) 3.49648 0.189068
\(343\) 4.66606 0.251943
\(344\) 22.3099 1.20287
\(345\) −0.738043 −0.0397349
\(346\) −38.5464 −2.07226
\(347\) 7.33953 0.394007 0.197003 0.980403i \(-0.436879\pi\)
0.197003 + 0.980403i \(0.436879\pi\)
\(348\) 65.1015 3.48981
\(349\) 1.00000 0.0535288
\(350\) −3.99407 −0.213492
\(351\) −1.94415 −0.103771
\(352\) −9.98344 −0.532119
\(353\) −6.87289 −0.365807 −0.182904 0.983131i \(-0.558550\pi\)
−0.182904 + 0.983131i \(0.558550\pi\)
\(354\) 3.24337 0.172383
\(355\) −6.61238 −0.350949
\(356\) −24.7505 −1.31178
\(357\) −1.63941 −0.0867667
\(358\) 1.60485 0.0848188
\(359\) −13.2408 −0.698822 −0.349411 0.936970i \(-0.613618\pi\)
−0.349411 + 0.936970i \(0.613618\pi\)
\(360\) −1.39618 −0.0735849
\(361\) −12.3333 −0.649119
\(362\) 1.63271 0.0858134
\(363\) −22.9698 −1.20560
\(364\) 0.492687 0.0258238
\(365\) 2.03356 0.106442
\(366\) 35.1830 1.83904
\(367\) 22.2551 1.16171 0.580855 0.814007i \(-0.302719\pi\)
0.580855 + 0.814007i \(0.302719\pi\)
\(368\) −5.17047 −0.269530
\(369\) 4.79489 0.249612
\(370\) 6.23629 0.324209
\(371\) −0.392025 −0.0203529
\(372\) 54.4646 2.82386
\(373\) −19.0422 −0.985966 −0.492983 0.870039i \(-0.664094\pi\)
−0.492983 + 0.870039i \(0.664094\pi\)
\(374\) 39.2364 2.02886
\(375\) −7.21672 −0.372670
\(376\) −45.4115 −2.34192
\(377\) 3.47131 0.178782
\(378\) 4.64271 0.238795
\(379\) −7.15989 −0.367779 −0.183889 0.982947i \(-0.558869\pi\)
−0.183889 + 0.982947i \(0.558869\pi\)
\(380\) −5.09420 −0.261327
\(381\) 21.8335 1.11856
\(382\) −22.3234 −1.14217
\(383\) −13.1827 −0.673603 −0.336801 0.941576i \(-0.609345\pi\)
−0.336801 + 0.941576i \(0.609345\pi\)
\(384\) −27.3761 −1.39703
\(385\) 0.801578 0.0408522
\(386\) 14.6096 0.743609
\(387\) 2.22984 0.113349
\(388\) 68.2761 3.46619
\(389\) 19.4173 0.984496 0.492248 0.870455i \(-0.336175\pi\)
0.492248 + 0.870455i \(0.336175\pi\)
\(390\) 0.642697 0.0325442
\(391\) 3.11361 0.157462
\(392\) 37.5077 1.89442
\(393\) −11.0408 −0.556934
\(394\) 48.6938 2.45316
\(395\) 3.21398 0.161713
\(396\) −11.5503 −0.580425
\(397\) −12.5470 −0.629714 −0.314857 0.949139i \(-0.601957\pi\)
−0.314857 + 0.949139i \(0.601957\pi\)
\(398\) −63.5380 −3.18487
\(399\) 1.35950 0.0680603
\(400\) −24.7055 −1.23527
\(401\) −14.7606 −0.737108 −0.368554 0.929606i \(-0.620147\pi\)
−0.368554 + 0.929606i \(0.620147\pi\)
\(402\) 19.7101 0.983051
\(403\) 2.90413 0.144665
\(404\) −70.4999 −3.50750
\(405\) 3.33013 0.165475
\(406\) −8.28964 −0.411408
\(407\) 26.9604 1.33638
\(408\) −26.5725 −1.31553
\(409\) 24.8020 1.22638 0.613191 0.789935i \(-0.289886\pi\)
0.613191 + 0.789935i \(0.289886\pi\)
\(410\) −10.3212 −0.509727
\(411\) −3.71300 −0.183149
\(412\) 77.1284 3.79984
\(413\) −0.279534 −0.0137550
\(414\) −1.35417 −0.0665540
\(415\) 7.80242 0.383006
\(416\) 0.689889 0.0338246
\(417\) −30.2410 −1.48091
\(418\) −32.5373 −1.59145
\(419\) 7.75564 0.378888 0.189444 0.981892i \(-0.439331\pi\)
0.189444 + 0.981892i \(0.439331\pi\)
\(420\) −1.03883 −0.0506895
\(421\) −22.3424 −1.08890 −0.544450 0.838793i \(-0.683262\pi\)
−0.544450 + 0.838793i \(0.683262\pi\)
\(422\) 23.0905 1.12403
\(423\) −4.53882 −0.220685
\(424\) −6.35417 −0.308586
\(425\) 14.8774 0.721659
\(426\) 54.7345 2.65189
\(427\) −3.03229 −0.146743
\(428\) −25.6148 −1.23814
\(429\) 2.77847 0.134146
\(430\) −4.79982 −0.231468
\(431\) −11.6119 −0.559325 −0.279663 0.960098i \(-0.590223\pi\)
−0.279663 + 0.960098i \(0.590223\pi\)
\(432\) 28.7177 1.38168
\(433\) −5.55487 −0.266950 −0.133475 0.991052i \(-0.542614\pi\)
−0.133475 + 0.991052i \(0.542614\pi\)
\(434\) −6.93520 −0.332900
\(435\) −7.31922 −0.350930
\(436\) −79.2858 −3.79710
\(437\) −2.58200 −0.123514
\(438\) −16.8330 −0.804311
\(439\) −10.5959 −0.505716 −0.252858 0.967503i \(-0.581371\pi\)
−0.252858 + 0.967503i \(0.581371\pi\)
\(440\) 12.9924 0.619391
\(441\) 3.74884 0.178516
\(442\) −2.71137 −0.128966
\(443\) 31.3152 1.48783 0.743916 0.668273i \(-0.232966\pi\)
0.743916 + 0.668273i \(0.232966\pi\)
\(444\) −34.9400 −1.65818
\(445\) 2.78265 0.131910
\(446\) −41.9055 −1.98428
\(447\) 21.4520 1.01464
\(448\) 1.82706 0.0863206
\(449\) 25.1815 1.18839 0.594195 0.804321i \(-0.297471\pi\)
0.594195 + 0.804321i \(0.297471\pi\)
\(450\) −6.47049 −0.305022
\(451\) −44.6200 −2.10107
\(452\) 17.0172 0.800422
\(453\) −22.2370 −1.04479
\(454\) −3.43231 −0.161086
\(455\) −0.0553917 −0.00259680
\(456\) 22.0356 1.03191
\(457\) 4.20332 0.196623 0.0983114 0.995156i \(-0.468656\pi\)
0.0983114 + 0.995156i \(0.468656\pi\)
\(458\) 49.2276 2.30025
\(459\) −17.2935 −0.807191
\(460\) 1.97296 0.0919899
\(461\) −31.5623 −1.47001 −0.735003 0.678064i \(-0.762819\pi\)
−0.735003 + 0.678064i \(0.762819\pi\)
\(462\) −6.63512 −0.308694
\(463\) −9.68047 −0.449890 −0.224945 0.974372i \(-0.572220\pi\)
−0.224945 + 0.974372i \(0.572220\pi\)
\(464\) −51.2759 −2.38042
\(465\) −6.12334 −0.283963
\(466\) 44.1703 2.04615
\(467\) −10.4946 −0.485631 −0.242815 0.970073i \(-0.578071\pi\)
−0.242815 + 0.970073i \(0.578071\pi\)
\(468\) 0.798165 0.0368952
\(469\) −1.69874 −0.0784407
\(470\) 9.76998 0.450655
\(471\) −31.1392 −1.43482
\(472\) −4.53086 −0.208550
\(473\) −20.7503 −0.954101
\(474\) −26.6039 −1.22196
\(475\) −12.3373 −0.566073
\(476\) 4.38252 0.200873
\(477\) −0.635090 −0.0290788
\(478\) 21.7712 0.995792
\(479\) −9.34130 −0.426815 −0.213407 0.976963i \(-0.568456\pi\)
−0.213407 + 0.976963i \(0.568456\pi\)
\(480\) −1.45463 −0.0663943
\(481\) −1.86305 −0.0849480
\(482\) 23.5825 1.07415
\(483\) −0.526530 −0.0239580
\(484\) 61.4038 2.79108
\(485\) −7.67613 −0.348555
\(486\) 13.8875 0.629951
\(487\) 0.228229 0.0103420 0.00517102 0.999987i \(-0.498354\pi\)
0.00517102 + 0.999987i \(0.498354\pi\)
\(488\) −49.1492 −2.22488
\(489\) −22.6912 −1.02613
\(490\) −8.06952 −0.364544
\(491\) −11.1342 −0.502480 −0.251240 0.967925i \(-0.580838\pi\)
−0.251240 + 0.967925i \(0.580838\pi\)
\(492\) 57.8265 2.60702
\(493\) 30.8778 1.39067
\(494\) 2.24844 0.101162
\(495\) 1.29858 0.0583666
\(496\) −42.8980 −1.92618
\(497\) −4.71737 −0.211603
\(498\) −64.5851 −2.89413
\(499\) 5.02082 0.224763 0.112381 0.993665i \(-0.464152\pi\)
0.112381 + 0.993665i \(0.464152\pi\)
\(500\) 19.2920 0.862765
\(501\) 13.9489 0.623191
\(502\) 19.2632 0.859757
\(503\) 5.18423 0.231153 0.115577 0.993299i \(-0.463128\pi\)
0.115577 + 0.993299i \(0.463128\pi\)
\(504\) −0.996051 −0.0443676
\(505\) 7.92615 0.352709
\(506\) 12.6016 0.560209
\(507\) 20.1798 0.896215
\(508\) −58.3661 −2.58958
\(509\) 2.54684 0.112887 0.0564434 0.998406i \(-0.482024\pi\)
0.0564434 + 0.998406i \(0.482024\pi\)
\(510\) 5.71689 0.253148
\(511\) 1.45077 0.0641784
\(512\) 46.1269 2.03854
\(513\) 14.3409 0.633165
\(514\) 50.0414 2.20723
\(515\) −8.67138 −0.382107
\(516\) 26.8919 1.18385
\(517\) 42.2370 1.85758
\(518\) 4.44906 0.195480
\(519\) −24.2803 −1.06579
\(520\) −0.897822 −0.0393721
\(521\) 12.6274 0.553217 0.276608 0.960983i \(-0.410790\pi\)
0.276608 + 0.960983i \(0.410790\pi\)
\(522\) −13.4294 −0.587790
\(523\) −25.0533 −1.09550 −0.547751 0.836641i \(-0.684516\pi\)
−0.547751 + 0.836641i \(0.684516\pi\)
\(524\) 29.5146 1.28935
\(525\) −2.51586 −0.109801
\(526\) −24.4915 −1.06788
\(527\) 25.8327 1.12529
\(528\) −41.0418 −1.78611
\(529\) 1.00000 0.0434783
\(530\) 1.36706 0.0593812
\(531\) −0.452853 −0.0196521
\(532\) −3.63427 −0.157566
\(533\) 3.08339 0.133557
\(534\) −23.0336 −0.996761
\(535\) 2.87982 0.124505
\(536\) −27.5342 −1.18930
\(537\) 1.01089 0.0436232
\(538\) 55.6952 2.40119
\(539\) −34.8857 −1.50263
\(540\) −10.9582 −0.471565
\(541\) 2.55159 0.109701 0.0548506 0.998495i \(-0.482532\pi\)
0.0548506 + 0.998495i \(0.482532\pi\)
\(542\) −21.8257 −0.937496
\(543\) 1.02844 0.0441347
\(544\) 6.13667 0.263108
\(545\) 8.91393 0.381831
\(546\) 0.458509 0.0196224
\(547\) 2.55567 0.109273 0.0546364 0.998506i \(-0.482600\pi\)
0.0546364 + 0.998506i \(0.482600\pi\)
\(548\) 9.92574 0.424006
\(549\) −4.91239 −0.209656
\(550\) 60.2127 2.56748
\(551\) −25.6059 −1.09085
\(552\) −8.53432 −0.363245
\(553\) 2.29290 0.0975038
\(554\) 22.3481 0.949481
\(555\) 3.92823 0.166744
\(556\) 80.8414 3.42844
\(557\) 15.6981 0.665151 0.332575 0.943077i \(-0.392082\pi\)
0.332575 + 0.943077i \(0.392082\pi\)
\(558\) −11.2352 −0.475624
\(559\) 1.43392 0.0606482
\(560\) 0.818210 0.0345757
\(561\) 24.7149 1.04347
\(562\) −15.1972 −0.641055
\(563\) 37.3544 1.57430 0.787150 0.616761i \(-0.211556\pi\)
0.787150 + 0.616761i \(0.211556\pi\)
\(564\) −54.7382 −2.30489
\(565\) −1.91321 −0.0804893
\(566\) 15.2709 0.641883
\(567\) 2.37576 0.0997725
\(568\) −76.4619 −3.20827
\(569\) −27.1803 −1.13946 −0.569728 0.821833i \(-0.692951\pi\)
−0.569728 + 0.821833i \(0.692951\pi\)
\(570\) −4.74081 −0.198571
\(571\) 40.4782 1.69396 0.846980 0.531624i \(-0.178418\pi\)
0.846980 + 0.531624i \(0.178418\pi\)
\(572\) −7.42751 −0.310560
\(573\) −14.0615 −0.587427
\(574\) −7.36328 −0.307337
\(575\) 4.77818 0.199264
\(576\) 2.95989 0.123329
\(577\) 10.7852 0.448992 0.224496 0.974475i \(-0.427926\pi\)
0.224496 + 0.974475i \(0.427926\pi\)
\(578\) 18.1745 0.755959
\(579\) 9.20257 0.382446
\(580\) 19.5660 0.812434
\(581\) 5.56636 0.230931
\(582\) 63.5398 2.63381
\(583\) 5.90999 0.244767
\(584\) 23.5150 0.973057
\(585\) −0.0897360 −0.00371013
\(586\) 1.65210 0.0682476
\(587\) 5.48151 0.226246 0.113123 0.993581i \(-0.463915\pi\)
0.113123 + 0.993581i \(0.463915\pi\)
\(588\) 45.2110 1.86447
\(589\) −21.4222 −0.882685
\(590\) 0.974783 0.0401312
\(591\) 30.6722 1.26169
\(592\) 27.5198 1.13106
\(593\) 25.9759 1.06670 0.533352 0.845894i \(-0.320932\pi\)
0.533352 + 0.845894i \(0.320932\pi\)
\(594\) −69.9913 −2.87178
\(595\) −0.492718 −0.0201995
\(596\) −57.3461 −2.34899
\(597\) −40.0225 −1.63801
\(598\) −0.870812 −0.0356102
\(599\) 11.3592 0.464123 0.232061 0.972701i \(-0.425453\pi\)
0.232061 + 0.972701i \(0.425453\pi\)
\(600\) −40.7785 −1.66478
\(601\) 36.5995 1.49293 0.746463 0.665427i \(-0.231750\pi\)
0.746463 + 0.665427i \(0.231750\pi\)
\(602\) −3.42426 −0.139562
\(603\) −2.75201 −0.112070
\(604\) 59.4449 2.41878
\(605\) −6.90350 −0.280667
\(606\) −65.6093 −2.66520
\(607\) −28.9238 −1.17398 −0.586991 0.809593i \(-0.699688\pi\)
−0.586991 + 0.809593i \(0.699688\pi\)
\(608\) −5.08893 −0.206383
\(609\) −5.22164 −0.211591
\(610\) 10.5741 0.428133
\(611\) −2.91872 −0.118079
\(612\) 7.09980 0.286992
\(613\) 19.8061 0.799961 0.399980 0.916524i \(-0.369017\pi\)
0.399980 + 0.916524i \(0.369017\pi\)
\(614\) −48.5759 −1.96036
\(615\) −6.50131 −0.262158
\(616\) 9.26899 0.373458
\(617\) −1.36172 −0.0548207 −0.0274104 0.999624i \(-0.508726\pi\)
−0.0274104 + 0.999624i \(0.508726\pi\)
\(618\) 71.7780 2.88733
\(619\) 14.1234 0.567668 0.283834 0.958873i \(-0.408394\pi\)
0.283834 + 0.958873i \(0.408394\pi\)
\(620\) 16.3691 0.657400
\(621\) −5.55417 −0.222881
\(622\) 1.30086 0.0521596
\(623\) 1.98518 0.0795346
\(624\) 2.83613 0.113536
\(625\) 21.7220 0.868878
\(626\) −53.0916 −2.12197
\(627\) −20.4952 −0.818501
\(628\) 83.2424 3.32173
\(629\) −16.5722 −0.660775
\(630\) 0.214294 0.00853766
\(631\) 32.0582 1.27622 0.638109 0.769946i \(-0.279717\pi\)
0.638109 + 0.769946i \(0.279717\pi\)
\(632\) 37.1646 1.47833
\(633\) 14.5447 0.578099
\(634\) 1.04577 0.0415330
\(635\) 6.56198 0.260404
\(636\) −7.65920 −0.303707
\(637\) 2.41072 0.0955162
\(638\) 124.971 4.94764
\(639\) −7.64225 −0.302323
\(640\) −8.22777 −0.325231
\(641\) −1.51282 −0.0597527 −0.0298764 0.999554i \(-0.509511\pi\)
−0.0298764 + 0.999554i \(0.509511\pi\)
\(642\) −23.8379 −0.940807
\(643\) −44.9863 −1.77409 −0.887043 0.461687i \(-0.847244\pi\)
−0.887043 + 0.461687i \(0.847244\pi\)
\(644\) 1.40754 0.0554649
\(645\) −3.02340 −0.119046
\(646\) 20.0002 0.786898
\(647\) −2.30366 −0.0905661 −0.0452831 0.998974i \(-0.514419\pi\)
−0.0452831 + 0.998974i \(0.514419\pi\)
\(648\) 38.5077 1.51273
\(649\) 4.21413 0.165419
\(650\) −4.16090 −0.163204
\(651\) −4.36848 −0.171214
\(652\) 60.6589 2.37559
\(653\) −3.63855 −0.142387 −0.0711937 0.997463i \(-0.522681\pi\)
−0.0711937 + 0.997463i \(0.522681\pi\)
\(654\) −73.7857 −2.88525
\(655\) −3.31827 −0.129655
\(656\) −45.5459 −1.77827
\(657\) 2.35029 0.0916935
\(658\) 6.97004 0.271720
\(659\) 20.3199 0.791550 0.395775 0.918347i \(-0.370476\pi\)
0.395775 + 0.918347i \(0.370476\pi\)
\(660\) 15.6608 0.609598
\(661\) 8.06801 0.313809 0.156905 0.987614i \(-0.449848\pi\)
0.156905 + 0.987614i \(0.449848\pi\)
\(662\) −65.1977 −2.53398
\(663\) −1.70789 −0.0663288
\(664\) 90.2228 3.50132
\(665\) 0.408594 0.0158446
\(666\) 7.20759 0.279288
\(667\) 9.91707 0.383990
\(668\) −37.2887 −1.44274
\(669\) −26.3962 −1.02054
\(670\) 5.92380 0.228856
\(671\) 45.7134 1.76475
\(672\) −1.03775 −0.0400321
\(673\) 13.5378 0.521844 0.260922 0.965360i \(-0.415973\pi\)
0.260922 + 0.965360i \(0.415973\pi\)
\(674\) −22.3925 −0.862525
\(675\) −26.5388 −1.02148
\(676\) −53.9453 −2.07482
\(677\) −23.3595 −0.897777 −0.448889 0.893588i \(-0.648180\pi\)
−0.448889 + 0.893588i \(0.648180\pi\)
\(678\) 15.8367 0.608206
\(679\) −5.47626 −0.210160
\(680\) −7.98626 −0.306259
\(681\) −2.16201 −0.0828484
\(682\) 104.552 4.00350
\(683\) 9.00578 0.344597 0.172298 0.985045i \(-0.444881\pi\)
0.172298 + 0.985045i \(0.444881\pi\)
\(684\) −5.88761 −0.225119
\(685\) −1.11593 −0.0426375
\(686\) −11.6082 −0.443203
\(687\) 31.0084 1.18304
\(688\) −21.1809 −0.807514
\(689\) −0.408400 −0.0155588
\(690\) 1.83610 0.0698991
\(691\) −19.5090 −0.742156 −0.371078 0.928602i \(-0.621012\pi\)
−0.371078 + 0.928602i \(0.621012\pi\)
\(692\) 64.9070 2.46739
\(693\) 0.926422 0.0351919
\(694\) −18.2592 −0.693112
\(695\) −9.08882 −0.344759
\(696\) −84.6354 −3.20810
\(697\) 27.4273 1.03888
\(698\) −2.48779 −0.0941644
\(699\) 27.8228 1.05236
\(700\) 6.72549 0.254199
\(701\) 25.5272 0.964150 0.482075 0.876130i \(-0.339883\pi\)
0.482075 + 0.876130i \(0.339883\pi\)
\(702\) 4.83664 0.182547
\(703\) 13.7427 0.518316
\(704\) −27.5439 −1.03810
\(705\) 6.15410 0.231777
\(706\) 17.0983 0.643504
\(707\) 5.65463 0.212664
\(708\) −5.46141 −0.205252
\(709\) −33.2523 −1.24882 −0.624408 0.781098i \(-0.714660\pi\)
−0.624408 + 0.781098i \(0.714660\pi\)
\(710\) 16.4502 0.617366
\(711\) 3.71455 0.139306
\(712\) 32.1770 1.20588
\(713\) 8.29672 0.310715
\(714\) 4.07851 0.152634
\(715\) 0.835060 0.0312295
\(716\) −2.70235 −0.100992
\(717\) 13.7137 0.512146
\(718\) 32.9403 1.22932
\(719\) −28.6719 −1.06928 −0.534642 0.845079i \(-0.679553\pi\)
−0.534642 + 0.845079i \(0.679553\pi\)
\(720\) 1.32552 0.0493993
\(721\) −6.18628 −0.230389
\(722\) 30.6826 1.14189
\(723\) 14.8546 0.552448
\(724\) −2.74927 −0.102176
\(725\) 47.3856 1.75986
\(726\) 57.1442 2.12082
\(727\) −42.9821 −1.59412 −0.797058 0.603902i \(-0.793612\pi\)
−0.797058 + 0.603902i \(0.793612\pi\)
\(728\) −0.640519 −0.0237392
\(729\) 29.9599 1.10963
\(730\) −5.05909 −0.187245
\(731\) 12.7549 0.471758
\(732\) −59.2435 −2.18970
\(733\) −25.1275 −0.928106 −0.464053 0.885807i \(-0.653605\pi\)
−0.464053 + 0.885807i \(0.653605\pi\)
\(734\) −55.3662 −2.04360
\(735\) −5.08298 −0.187489
\(736\) 1.97092 0.0726491
\(737\) 25.6095 0.943337
\(738\) −11.9287 −0.439102
\(739\) −2.84812 −0.104770 −0.0523849 0.998627i \(-0.516682\pi\)
−0.0523849 + 0.998627i \(0.516682\pi\)
\(740\) −10.5011 −0.386028
\(741\) 1.41629 0.0520287
\(742\) 0.975278 0.0358036
\(743\) 8.99408 0.329961 0.164980 0.986297i \(-0.447244\pi\)
0.164980 + 0.986297i \(0.447244\pi\)
\(744\) −70.8068 −2.59590
\(745\) 6.44730 0.236211
\(746\) 47.3730 1.73445
\(747\) 9.01764 0.329938
\(748\) −66.0689 −2.41572
\(749\) 2.05450 0.0750699
\(750\) 17.9537 0.655577
\(751\) 18.9189 0.690362 0.345181 0.938536i \(-0.387818\pi\)
0.345181 + 0.938536i \(0.387818\pi\)
\(752\) 43.1135 1.57219
\(753\) 12.1338 0.442182
\(754\) −8.63590 −0.314501
\(755\) −6.68326 −0.243229
\(756\) −7.81772 −0.284328
\(757\) 23.9906 0.871953 0.435976 0.899958i \(-0.356403\pi\)
0.435976 + 0.899958i \(0.356403\pi\)
\(758\) 17.8123 0.646973
\(759\) 7.93773 0.288121
\(760\) 6.62273 0.240232
\(761\) 31.3449 1.13625 0.568125 0.822942i \(-0.307669\pi\)
0.568125 + 0.822942i \(0.307669\pi\)
\(762\) −54.3173 −1.96771
\(763\) 6.35932 0.230223
\(764\) 37.5897 1.35995
\(765\) −0.798215 −0.0288595
\(766\) 32.7957 1.18496
\(767\) −0.291210 −0.0105150
\(768\) 51.0636 1.84260
\(769\) 46.2211 1.66678 0.833388 0.552688i \(-0.186398\pi\)
0.833388 + 0.552688i \(0.186398\pi\)
\(770\) −1.99416 −0.0718645
\(771\) 31.5210 1.13520
\(772\) −24.6007 −0.885397
\(773\) −10.6969 −0.384741 −0.192370 0.981322i \(-0.561617\pi\)
−0.192370 + 0.981322i \(0.561617\pi\)
\(774\) −5.54738 −0.199397
\(775\) 39.6433 1.42403
\(776\) −88.7625 −3.18639
\(777\) 2.80246 0.100538
\(778\) −48.3062 −1.73186
\(779\) −22.7445 −0.814905
\(780\) −1.08222 −0.0387496
\(781\) 71.1168 2.54476
\(782\) −7.74601 −0.276997
\(783\) −55.0811 −1.96844
\(784\) −35.6096 −1.27177
\(785\) −9.35877 −0.334029
\(786\) 27.4672 0.979723
\(787\) −16.4830 −0.587557 −0.293778 0.955874i \(-0.594913\pi\)
−0.293778 + 0.955874i \(0.594913\pi\)
\(788\) −81.9940 −2.92092
\(789\) −15.4272 −0.549222
\(790\) −7.99571 −0.284475
\(791\) −1.36491 −0.0485306
\(792\) 15.0160 0.533570
\(793\) −3.15895 −0.112178
\(794\) 31.2142 1.10775
\(795\) 0.861108 0.0305403
\(796\) 106.990 3.79215
\(797\) 20.2229 0.716332 0.358166 0.933658i \(-0.383402\pi\)
0.358166 + 0.933658i \(0.383402\pi\)
\(798\) −3.38216 −0.119727
\(799\) −25.9625 −0.918486
\(800\) 9.41743 0.332956
\(801\) 3.21604 0.113633
\(802\) 36.7213 1.29667
\(803\) −21.8712 −0.771817
\(804\) −33.1892 −1.17049
\(805\) −0.158247 −0.00557746
\(806\) −7.22488 −0.254486
\(807\) 35.0824 1.23496
\(808\) 91.6536 3.22436
\(809\) 30.4746 1.07143 0.535715 0.844399i \(-0.320042\pi\)
0.535715 + 0.844399i \(0.320042\pi\)
\(810\) −8.28467 −0.291093
\(811\) −36.2133 −1.27162 −0.635811 0.771845i \(-0.719334\pi\)
−0.635811 + 0.771845i \(0.719334\pi\)
\(812\) 13.9587 0.489853
\(813\) −13.7480 −0.482164
\(814\) −67.0719 −2.35087
\(815\) −6.81976 −0.238886
\(816\) 25.2278 0.883149
\(817\) −10.5772 −0.370049
\(818\) −61.7023 −2.15737
\(819\) −0.0640189 −0.00223700
\(820\) 17.3795 0.606919
\(821\) 24.4959 0.854912 0.427456 0.904036i \(-0.359410\pi\)
0.427456 + 0.904036i \(0.359410\pi\)
\(822\) 9.23719 0.322184
\(823\) 19.6961 0.686562 0.343281 0.939233i \(-0.388462\pi\)
0.343281 + 0.939233i \(0.388462\pi\)
\(824\) −100.271 −3.49310
\(825\) 37.9279 1.32048
\(826\) 0.695424 0.0241969
\(827\) 2.02743 0.0705006 0.0352503 0.999379i \(-0.488777\pi\)
0.0352503 + 0.999379i \(0.488777\pi\)
\(828\) 2.28025 0.0792442
\(829\) 20.9975 0.729273 0.364637 0.931150i \(-0.381193\pi\)
0.364637 + 0.931150i \(0.381193\pi\)
\(830\) −19.4108 −0.673759
\(831\) 14.0771 0.488328
\(832\) 1.90338 0.0659878
\(833\) 21.4437 0.742981
\(834\) 75.2334 2.60512
\(835\) 4.19229 0.145080
\(836\) 54.7886 1.89490
\(837\) −46.0814 −1.59281
\(838\) −19.2944 −0.666515
\(839\) 15.7053 0.542209 0.271104 0.962550i \(-0.412611\pi\)
0.271104 + 0.962550i \(0.412611\pi\)
\(840\) 1.35053 0.0465976
\(841\) 69.3482 2.39132
\(842\) 55.5832 1.91552
\(843\) −9.57270 −0.329701
\(844\) −38.8813 −1.33835
\(845\) 6.06495 0.208641
\(846\) 11.2916 0.388214
\(847\) −4.92505 −0.169227
\(848\) 6.03262 0.207161
\(849\) 9.61911 0.330127
\(850\) −37.0119 −1.26950
\(851\) −5.32250 −0.182453
\(852\) −92.1657 −3.15754
\(853\) −5.75815 −0.197155 −0.0985776 0.995129i \(-0.531429\pi\)
−0.0985776 + 0.995129i \(0.531429\pi\)
\(854\) 7.54371 0.258141
\(855\) 0.661932 0.0226376
\(856\) 33.3006 1.13819
\(857\) 13.2855 0.453822 0.226911 0.973915i \(-0.427137\pi\)
0.226911 + 0.973915i \(0.427137\pi\)
\(858\) −6.91227 −0.235981
\(859\) 53.0647 1.81054 0.905272 0.424832i \(-0.139667\pi\)
0.905272 + 0.424832i \(0.139667\pi\)
\(860\) 8.08226 0.275603
\(861\) −4.63812 −0.158067
\(862\) 28.8880 0.983929
\(863\) 20.3099 0.691355 0.345678 0.938353i \(-0.387649\pi\)
0.345678 + 0.938353i \(0.387649\pi\)
\(864\) −10.9468 −0.372419
\(865\) −7.29735 −0.248118
\(866\) 13.8194 0.469601
\(867\) 11.4481 0.388797
\(868\) 11.6780 0.396376
\(869\) −34.5666 −1.17259
\(870\) 18.2087 0.617333
\(871\) −1.76970 −0.0599640
\(872\) 103.076 3.49058
\(873\) −8.87168 −0.300261
\(874\) 6.42349 0.217278
\(875\) −1.54737 −0.0523105
\(876\) 28.3445 0.957673
\(877\) 54.6432 1.84517 0.922586 0.385792i \(-0.126072\pi\)
0.922586 + 0.385792i \(0.126072\pi\)
\(878\) 26.3605 0.889624
\(879\) 1.04066 0.0351004
\(880\) −12.3350 −0.415811
\(881\) −44.3072 −1.49275 −0.746374 0.665527i \(-0.768207\pi\)
−0.746374 + 0.665527i \(0.768207\pi\)
\(882\) −9.32633 −0.314034
\(883\) 13.2858 0.447101 0.223551 0.974692i \(-0.428235\pi\)
0.223551 + 0.974692i \(0.428235\pi\)
\(884\) 4.56558 0.153557
\(885\) 0.614015 0.0206399
\(886\) −77.9059 −2.61730
\(887\) −0.473815 −0.0159092 −0.00795458 0.999968i \(-0.502532\pi\)
−0.00795458 + 0.999968i \(0.502532\pi\)
\(888\) 45.4239 1.52433
\(889\) 4.68141 0.157009
\(890\) −6.92266 −0.232048
\(891\) −35.8158 −1.19988
\(892\) 70.5634 2.36264
\(893\) 21.5298 0.720466
\(894\) −53.3680 −1.78489
\(895\) 0.303819 0.0101556
\(896\) −5.86981 −0.196097
\(897\) −0.548524 −0.0183147
\(898\) −62.6465 −2.09054
\(899\) 82.2791 2.74416
\(900\) 10.8955 0.363182
\(901\) −3.63278 −0.121025
\(902\) 111.005 3.69608
\(903\) −2.15694 −0.0717784
\(904\) −22.1233 −0.735809
\(905\) 0.309095 0.0102747
\(906\) 55.3212 1.83792
\(907\) 47.3641 1.57270 0.786350 0.617781i \(-0.211968\pi\)
0.786350 + 0.617781i \(0.211968\pi\)
\(908\) 5.77956 0.191802
\(909\) 9.16064 0.303839
\(910\) 0.137803 0.00456813
\(911\) 17.7875 0.589325 0.294662 0.955601i \(-0.404793\pi\)
0.294662 + 0.955601i \(0.404793\pi\)
\(912\) −20.9205 −0.692747
\(913\) −83.9158 −2.77721
\(914\) −10.4570 −0.345886
\(915\) 6.66062 0.220193
\(916\) −82.8928 −2.73885
\(917\) −2.36730 −0.0781751
\(918\) 43.0226 1.41996
\(919\) −18.3646 −0.605793 −0.302897 0.953023i \(-0.597954\pi\)
−0.302897 + 0.953023i \(0.597954\pi\)
\(920\) −2.56496 −0.0845641
\(921\) −30.5979 −1.00823
\(922\) 78.5206 2.58594
\(923\) −4.91441 −0.161760
\(924\) 11.1727 0.367554
\(925\) −25.4319 −0.836195
\(926\) 24.0830 0.791417
\(927\) −10.0219 −0.329163
\(928\) 19.5458 0.641621
\(929\) −41.5224 −1.36231 −0.681153 0.732141i \(-0.738521\pi\)
−0.681153 + 0.732141i \(0.738521\pi\)
\(930\) 15.2336 0.499529
\(931\) −17.7825 −0.582799
\(932\) −74.3770 −2.43630
\(933\) 0.819408 0.0268262
\(934\) 26.1083 0.854291
\(935\) 7.42798 0.242921
\(936\) −1.03766 −0.0339169
\(937\) 48.9662 1.59966 0.799828 0.600229i \(-0.204924\pi\)
0.799828 + 0.600229i \(0.204924\pi\)
\(938\) 4.22612 0.137988
\(939\) −33.4424 −1.09135
\(940\) −16.4514 −0.536584
\(941\) 27.8976 0.909437 0.454719 0.890635i \(-0.349740\pi\)
0.454719 + 0.890635i \(0.349740\pi\)
\(942\) 77.4679 2.52404
\(943\) 8.80884 0.286855
\(944\) 4.30157 0.140004
\(945\) 0.878929 0.0285916
\(946\) 51.6225 1.67839
\(947\) 21.8444 0.709847 0.354924 0.934895i \(-0.384507\pi\)
0.354924 + 0.934895i \(0.384507\pi\)
\(948\) 44.7975 1.45496
\(949\) 1.51137 0.0490612
\(950\) 30.6926 0.995800
\(951\) 0.658732 0.0213608
\(952\) −5.69751 −0.184657
\(953\) 13.3513 0.432491 0.216246 0.976339i \(-0.430619\pi\)
0.216246 + 0.976339i \(0.430619\pi\)
\(954\) 1.57997 0.0511536
\(955\) −4.22613 −0.136754
\(956\) −36.6599 −1.18566
\(957\) 78.7190 2.54462
\(958\) 23.2392 0.750825
\(959\) −0.796120 −0.0257080
\(960\) −4.01326 −0.129527
\(961\) 37.8356 1.22050
\(962\) 4.63490 0.149435
\(963\) 3.32834 0.107254
\(964\) −39.7098 −1.27897
\(965\) 2.76580 0.0890342
\(966\) 1.30990 0.0421453
\(967\) 18.0686 0.581046 0.290523 0.956868i \(-0.406171\pi\)
0.290523 + 0.956868i \(0.406171\pi\)
\(968\) −79.8282 −2.56578
\(969\) 12.5981 0.404710
\(970\) 19.0966 0.613156
\(971\) −14.7636 −0.473788 −0.236894 0.971536i \(-0.576129\pi\)
−0.236894 + 0.971536i \(0.576129\pi\)
\(972\) −23.3848 −0.750066
\(973\) −6.48409 −0.207871
\(974\) −0.567786 −0.0181931
\(975\) −2.62095 −0.0839375
\(976\) 46.6619 1.49361
\(977\) 44.1532 1.41259 0.706293 0.707920i \(-0.250366\pi\)
0.706293 + 0.707920i \(0.250366\pi\)
\(978\) 56.4510 1.80511
\(979\) −29.9277 −0.956492
\(980\) 13.5880 0.434053
\(981\) 10.3023 0.328926
\(982\) 27.6997 0.883931
\(983\) −50.2940 −1.60413 −0.802064 0.597238i \(-0.796265\pi\)
−0.802064 + 0.597238i \(0.796265\pi\)
\(984\) −75.1775 −2.39657
\(985\) 9.21841 0.293723
\(986\) −76.8177 −2.44637
\(987\) 4.39042 0.139749
\(988\) −3.78608 −0.120451
\(989\) 4.09651 0.130261
\(990\) −3.23059 −0.102675
\(991\) 34.2725 1.08870 0.544351 0.838857i \(-0.316776\pi\)
0.544351 + 0.838857i \(0.316776\pi\)
\(992\) 16.3522 0.519182
\(993\) −41.0679 −1.30325
\(994\) 11.7358 0.372238
\(995\) −12.0286 −0.381333
\(996\) 108.753 3.44597
\(997\) −12.4521 −0.394361 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(998\) −12.4908 −0.395389
\(999\) 29.5621 0.935302
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 8027.2.a.e.1.13 169
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.e.1.13 169 1.1 even 1 trivial