Properties

Label 403.2.a.c.1.7
Level $403$
Weight $2$
Character 403.1
Self dual yes
Analytic conductor $3.218$
Analytic rank $0$
Dimension $7$
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] = [403,2,Mod(1,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, 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("403.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 2x^{6} - 9x^{5} + 12x^{4} + 22x^{3} - 18x^{2} - 13x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.0890306\) of defining polynomial
Character \(\chi\) \(=\) 403.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.58972 q^{2} +1.08903 q^{3} +4.70665 q^{4} -1.22264 q^{5} +2.82028 q^{6} -0.573038 q^{7} +7.00945 q^{8} -1.81401 q^{9} +O(q^{10})\) \(q+2.58972 q^{2} +1.08903 q^{3} +4.70665 q^{4} -1.22264 q^{5} +2.82028 q^{6} -0.573038 q^{7} +7.00945 q^{8} -1.81401 q^{9} -3.16629 q^{10} -1.53337 q^{11} +5.12568 q^{12} -1.00000 q^{13} -1.48401 q^{14} -1.33149 q^{15} +8.73922 q^{16} +3.04458 q^{17} -4.69778 q^{18} -0.170684 q^{19} -5.75452 q^{20} -0.624056 q^{21} -3.97100 q^{22} -1.04732 q^{23} +7.63351 q^{24} -3.50516 q^{25} -2.58972 q^{26} -5.24261 q^{27} -2.69709 q^{28} -0.554872 q^{29} -3.44819 q^{30} +1.00000 q^{31} +8.61322 q^{32} -1.66989 q^{33} +7.88460 q^{34} +0.700618 q^{35} -8.53791 q^{36} +5.10806 q^{37} -0.442022 q^{38} -1.08903 q^{39} -8.57002 q^{40} +3.94545 q^{41} -1.61613 q^{42} +3.89592 q^{43} -7.21703 q^{44} +2.21788 q^{45} -2.71225 q^{46} +6.79810 q^{47} +9.51728 q^{48} -6.67163 q^{49} -9.07737 q^{50} +3.31564 q^{51} -4.70665 q^{52} -7.17642 q^{53} -13.5769 q^{54} +1.87476 q^{55} -4.01668 q^{56} -0.185880 q^{57} -1.43696 q^{58} +7.05962 q^{59} -6.26685 q^{60} +7.06306 q^{61} +2.58972 q^{62} +1.03950 q^{63} +4.82738 q^{64} +1.22264 q^{65} -4.32454 q^{66} -8.47608 q^{67} +14.3297 q^{68} -1.14056 q^{69} +1.81440 q^{70} -3.61508 q^{71} -12.7152 q^{72} +3.02639 q^{73} +13.2284 q^{74} -3.81722 q^{75} -0.803347 q^{76} +0.878679 q^{77} -2.82028 q^{78} +5.15645 q^{79} -10.6849 q^{80} -0.267323 q^{81} +10.2176 q^{82} +13.5688 q^{83} -2.93721 q^{84} -3.72241 q^{85} +10.0893 q^{86} -0.604272 q^{87} -10.7481 q^{88} +6.51329 q^{89} +5.74369 q^{90} +0.573038 q^{91} -4.92935 q^{92} +1.08903 q^{93} +17.6052 q^{94} +0.208684 q^{95} +9.38006 q^{96} -18.1121 q^{97} -17.2776 q^{98} +2.78155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 5 q^{14} + 2 q^{16} + 7 q^{17} - 9 q^{18} + q^{19} - 2 q^{21} + 6 q^{22} + 6 q^{23} + 5 q^{24} + 10 q^{25} - 2 q^{26} + 11 q^{27} - 11 q^{28} - 2 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} + 6 q^{33} - 4 q^{34} - q^{35} - 20 q^{36} + 28 q^{37} - 8 q^{38} - 5 q^{39} - 5 q^{40} + 3 q^{41} + 13 q^{42} - q^{43} + 12 q^{44} + 9 q^{45} - 37 q^{46} - q^{47} + 11 q^{48} - 19 q^{49} + 21 q^{50} - 30 q^{51} - 8 q^{52} + 29 q^{53} + 2 q^{54} + 19 q^{55} - 20 q^{56} + 11 q^{57} + 3 q^{58} + 3 q^{59} - 43 q^{60} + 5 q^{61} + 2 q^{62} + q^{63} - 29 q^{64} - 11 q^{65} - 29 q^{66} - 32 q^{67} + 38 q^{68} + 17 q^{69} - 23 q^{70} + 5 q^{71} - 17 q^{72} + q^{73} - 4 q^{74} - 7 q^{75} - 12 q^{76} - 5 q^{77} - 6 q^{78} - 15 q^{79} - 11 q^{80} + 3 q^{81} - 36 q^{82} + 17 q^{83} + 2 q^{84} - q^{85} - 23 q^{86} - 42 q^{87} - 15 q^{88} + 26 q^{89} - 40 q^{90} - 4 q^{91} - 24 q^{92} + 5 q^{93} + 18 q^{94} - 21 q^{95} - 4 q^{96} + 11 q^{97} + 6 q^{98} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58972 1.83121 0.915604 0.402081i \(-0.131713\pi\)
0.915604 + 0.402081i \(0.131713\pi\)
\(3\) 1.08903 0.628752 0.314376 0.949299i \(-0.398205\pi\)
0.314376 + 0.949299i \(0.398205\pi\)
\(4\) 4.70665 2.35332
\(5\) −1.22264 −0.546780 −0.273390 0.961903i \(-0.588145\pi\)
−0.273390 + 0.961903i \(0.588145\pi\)
\(6\) 2.82028 1.15138
\(7\) −0.573038 −0.216588 −0.108294 0.994119i \(-0.534539\pi\)
−0.108294 + 0.994119i \(0.534539\pi\)
\(8\) 7.00945 2.47822
\(9\) −1.81401 −0.604671
\(10\) −3.16629 −1.00127
\(11\) −1.53337 −0.462328 −0.231164 0.972915i \(-0.574253\pi\)
−0.231164 + 0.972915i \(0.574253\pi\)
\(12\) 5.12568 1.47966
\(13\) −1.00000 −0.277350
\(14\) −1.48401 −0.396618
\(15\) −1.33149 −0.343789
\(16\) 8.73922 2.18480
\(17\) 3.04458 0.738418 0.369209 0.929346i \(-0.379629\pi\)
0.369209 + 0.929346i \(0.379629\pi\)
\(18\) −4.69778 −1.10728
\(19\) −0.170684 −0.0391575 −0.0195787 0.999808i \(-0.506233\pi\)
−0.0195787 + 0.999808i \(0.506233\pi\)
\(20\) −5.75452 −1.28675
\(21\) −0.624056 −0.136180
\(22\) −3.97100 −0.846620
\(23\) −1.04732 −0.218381 −0.109190 0.994021i \(-0.534826\pi\)
−0.109190 + 0.994021i \(0.534826\pi\)
\(24\) 7.63351 1.55818
\(25\) −3.50516 −0.701031
\(26\) −2.58972 −0.507886
\(27\) −5.24261 −1.00894
\(28\) −2.69709 −0.509701
\(29\) −0.554872 −0.103037 −0.0515185 0.998672i \(-0.516406\pi\)
−0.0515185 + 0.998672i \(0.516406\pi\)
\(30\) −3.44819 −0.629550
\(31\) 1.00000 0.179605
\(32\) 8.61322 1.52262
\(33\) −1.66989 −0.290690
\(34\) 7.88460 1.35220
\(35\) 0.700618 0.118426
\(36\) −8.53791 −1.42299
\(37\) 5.10806 0.839760 0.419880 0.907580i \(-0.362072\pi\)
0.419880 + 0.907580i \(0.362072\pi\)
\(38\) −0.442022 −0.0717055
\(39\) −1.08903 −0.174384
\(40\) −8.57002 −1.35504
\(41\) 3.94545 0.616176 0.308088 0.951358i \(-0.400311\pi\)
0.308088 + 0.951358i \(0.400311\pi\)
\(42\) −1.61613 −0.249374
\(43\) 3.89592 0.594122 0.297061 0.954858i \(-0.403993\pi\)
0.297061 + 0.954858i \(0.403993\pi\)
\(44\) −7.21703 −1.08801
\(45\) 2.21788 0.330622
\(46\) −2.71225 −0.399900
\(47\) 6.79810 0.991604 0.495802 0.868435i \(-0.334874\pi\)
0.495802 + 0.868435i \(0.334874\pi\)
\(48\) 9.51728 1.37370
\(49\) −6.67163 −0.953090
\(50\) −9.07737 −1.28373
\(51\) 3.31564 0.464282
\(52\) −4.70665 −0.652694
\(53\) −7.17642 −0.985757 −0.492879 0.870098i \(-0.664055\pi\)
−0.492879 + 0.870098i \(0.664055\pi\)
\(54\) −13.5769 −1.84758
\(55\) 1.87476 0.252792
\(56\) −4.01668 −0.536752
\(57\) −0.185880 −0.0246204
\(58\) −1.43696 −0.188682
\(59\) 7.05962 0.919084 0.459542 0.888156i \(-0.348014\pi\)
0.459542 + 0.888156i \(0.348014\pi\)
\(60\) −6.26685 −0.809047
\(61\) 7.06306 0.904332 0.452166 0.891934i \(-0.350651\pi\)
0.452166 + 0.891934i \(0.350651\pi\)
\(62\) 2.58972 0.328895
\(63\) 1.03950 0.130964
\(64\) 4.82738 0.603423
\(65\) 1.22264 0.151650
\(66\) −4.32454 −0.532314
\(67\) −8.47608 −1.03552 −0.517759 0.855526i \(-0.673234\pi\)
−0.517759 + 0.855526i \(0.673234\pi\)
\(68\) 14.3297 1.73774
\(69\) −1.14056 −0.137307
\(70\) 1.81440 0.216863
\(71\) −3.61508 −0.429032 −0.214516 0.976721i \(-0.568817\pi\)
−0.214516 + 0.976721i \(0.568817\pi\)
\(72\) −12.7152 −1.49850
\(73\) 3.02639 0.354212 0.177106 0.984192i \(-0.443326\pi\)
0.177106 + 0.984192i \(0.443326\pi\)
\(74\) 13.2284 1.53778
\(75\) −3.81722 −0.440775
\(76\) −0.803347 −0.0921502
\(77\) 0.878679 0.100135
\(78\) −2.82028 −0.319334
\(79\) 5.15645 0.580146 0.290073 0.957005i \(-0.406320\pi\)
0.290073 + 0.957005i \(0.406320\pi\)
\(80\) −10.6849 −1.19461
\(81\) −0.267323 −0.0297025
\(82\) 10.2176 1.12835
\(83\) 13.5688 1.48937 0.744685 0.667416i \(-0.232600\pi\)
0.744685 + 0.667416i \(0.232600\pi\)
\(84\) −2.93721 −0.320476
\(85\) −3.72241 −0.403753
\(86\) 10.0893 1.08796
\(87\) −0.604272 −0.0647848
\(88\) −10.7481 −1.14575
\(89\) 6.51329 0.690408 0.345204 0.938528i \(-0.387810\pi\)
0.345204 + 0.938528i \(0.387810\pi\)
\(90\) 5.74369 0.605438
\(91\) 0.573038 0.0600707
\(92\) −4.92935 −0.513920
\(93\) 1.08903 0.112927
\(94\) 17.6052 1.81583
\(95\) 0.208684 0.0214105
\(96\) 9.38006 0.957348
\(97\) −18.1121 −1.83900 −0.919500 0.393090i \(-0.871406\pi\)
−0.919500 + 0.393090i \(0.871406\pi\)
\(98\) −17.2776 −1.74531
\(99\) 2.78155 0.279556
\(100\) −16.4975 −1.64975
\(101\) 0.768329 0.0764516 0.0382258 0.999269i \(-0.487829\pi\)
0.0382258 + 0.999269i \(0.487829\pi\)
\(102\) 8.58657 0.850197
\(103\) −12.6231 −1.24379 −0.621897 0.783099i \(-0.713638\pi\)
−0.621897 + 0.783099i \(0.713638\pi\)
\(104\) −7.00945 −0.687333
\(105\) 0.762994 0.0744606
\(106\) −18.5849 −1.80513
\(107\) −6.76222 −0.653729 −0.326864 0.945071i \(-0.605992\pi\)
−0.326864 + 0.945071i \(0.605992\pi\)
\(108\) −24.6751 −2.37436
\(109\) 10.7442 1.02911 0.514556 0.857457i \(-0.327957\pi\)
0.514556 + 0.857457i \(0.327957\pi\)
\(110\) 4.85509 0.462915
\(111\) 5.56284 0.528001
\(112\) −5.00790 −0.473202
\(113\) 11.4364 1.07585 0.537924 0.842993i \(-0.319209\pi\)
0.537924 + 0.842993i \(0.319209\pi\)
\(114\) −0.481376 −0.0450850
\(115\) 1.28049 0.119406
\(116\) −2.61158 −0.242479
\(117\) 1.81401 0.167705
\(118\) 18.2824 1.68303
\(119\) −1.74466 −0.159933
\(120\) −9.33301 −0.851984
\(121\) −8.64878 −0.786252
\(122\) 18.2913 1.65602
\(123\) 4.29672 0.387422
\(124\) 4.70665 0.422669
\(125\) 10.3987 0.930090
\(126\) 2.69201 0.239823
\(127\) −3.13744 −0.278403 −0.139201 0.990264i \(-0.544454\pi\)
−0.139201 + 0.990264i \(0.544454\pi\)
\(128\) −4.72487 −0.417624
\(129\) 4.24278 0.373556
\(130\) 3.16629 0.277702
\(131\) 1.73537 0.151620 0.0758101 0.997122i \(-0.475846\pi\)
0.0758101 + 0.997122i \(0.475846\pi\)
\(132\) −7.85957 −0.684087
\(133\) 0.0978081 0.00848104
\(134\) −21.9507 −1.89625
\(135\) 6.40981 0.551669
\(136\) 21.3408 1.82996
\(137\) 8.66597 0.740384 0.370192 0.928955i \(-0.379292\pi\)
0.370192 + 0.928955i \(0.379292\pi\)
\(138\) −2.95373 −0.251438
\(139\) −11.8869 −1.00823 −0.504116 0.863636i \(-0.668182\pi\)
−0.504116 + 0.863636i \(0.668182\pi\)
\(140\) 3.29756 0.278695
\(141\) 7.40334 0.623473
\(142\) −9.36205 −0.785646
\(143\) 1.53337 0.128227
\(144\) −15.8530 −1.32109
\(145\) 0.678407 0.0563386
\(146\) 7.83749 0.648636
\(147\) −7.26561 −0.599257
\(148\) 24.0418 1.97623
\(149\) −7.07496 −0.579603 −0.289801 0.957087i \(-0.593589\pi\)
−0.289801 + 0.957087i \(0.593589\pi\)
\(150\) −9.88554 −0.807151
\(151\) 16.6729 1.35682 0.678412 0.734682i \(-0.262669\pi\)
0.678412 + 0.734682i \(0.262669\pi\)
\(152\) −1.19640 −0.0970407
\(153\) −5.52290 −0.446500
\(154\) 2.27553 0.183368
\(155\) −1.22264 −0.0982046
\(156\) −5.12568 −0.410383
\(157\) 16.5464 1.32055 0.660273 0.751026i \(-0.270441\pi\)
0.660273 + 0.751026i \(0.270441\pi\)
\(158\) 13.3538 1.06237
\(159\) −7.81534 −0.619797
\(160\) −10.5308 −0.832537
\(161\) 0.600152 0.0472986
\(162\) −0.692291 −0.0543915
\(163\) −15.3279 −1.20057 −0.600287 0.799785i \(-0.704947\pi\)
−0.600287 + 0.799785i \(0.704947\pi\)
\(164\) 18.5698 1.45006
\(165\) 2.04167 0.158944
\(166\) 35.1394 2.72735
\(167\) 19.2837 1.49222 0.746108 0.665825i \(-0.231920\pi\)
0.746108 + 0.665825i \(0.231920\pi\)
\(168\) −4.37429 −0.337484
\(169\) 1.00000 0.0769231
\(170\) −9.64001 −0.739355
\(171\) 0.309622 0.0236774
\(172\) 18.3367 1.39816
\(173\) −14.0195 −1.06588 −0.532942 0.846152i \(-0.678914\pi\)
−0.532942 + 0.846152i \(0.678914\pi\)
\(174\) −1.56490 −0.118634
\(175\) 2.00859 0.151835
\(176\) −13.4005 −1.01010
\(177\) 7.68814 0.577876
\(178\) 16.8676 1.26428
\(179\) −22.7717 −1.70203 −0.851017 0.525137i \(-0.824014\pi\)
−0.851017 + 0.525137i \(0.824014\pi\)
\(180\) 10.4388 0.778060
\(181\) 15.8733 1.17985 0.589926 0.807457i \(-0.299157\pi\)
0.589926 + 0.807457i \(0.299157\pi\)
\(182\) 1.48401 0.110002
\(183\) 7.69189 0.568601
\(184\) −7.34111 −0.541194
\(185\) −6.24531 −0.459164
\(186\) 2.82028 0.206793
\(187\) −4.66846 −0.341392
\(188\) 31.9962 2.33357
\(189\) 3.00421 0.218524
\(190\) 0.540433 0.0392072
\(191\) −8.17952 −0.591849 −0.295925 0.955211i \(-0.595628\pi\)
−0.295925 + 0.955211i \(0.595628\pi\)
\(192\) 5.25717 0.379403
\(193\) −14.7608 −1.06251 −0.531253 0.847213i \(-0.678279\pi\)
−0.531253 + 0.847213i \(0.678279\pi\)
\(194\) −46.9051 −3.36759
\(195\) 1.33149 0.0953500
\(196\) −31.4010 −2.24293
\(197\) 10.2450 0.729929 0.364965 0.931021i \(-0.381081\pi\)
0.364965 + 0.931021i \(0.381081\pi\)
\(198\) 7.20344 0.511926
\(199\) −8.45228 −0.599166 −0.299583 0.954070i \(-0.596848\pi\)
−0.299583 + 0.954070i \(0.596848\pi\)
\(200\) −24.5692 −1.73731
\(201\) −9.23071 −0.651084
\(202\) 1.98976 0.139999
\(203\) 0.317962 0.0223166
\(204\) 15.6055 1.09261
\(205\) −4.82386 −0.336913
\(206\) −32.6903 −2.27764
\(207\) 1.89984 0.132048
\(208\) −8.73922 −0.605956
\(209\) 0.261721 0.0181036
\(210\) 1.97594 0.136353
\(211\) 17.8589 1.22946 0.614729 0.788738i \(-0.289265\pi\)
0.614729 + 0.788738i \(0.289265\pi\)
\(212\) −33.7769 −2.31980
\(213\) −3.93694 −0.269755
\(214\) −17.5123 −1.19711
\(215\) −4.76330 −0.324854
\(216\) −36.7478 −2.50037
\(217\) −0.573038 −0.0389003
\(218\) 27.8246 1.88452
\(219\) 3.29583 0.222712
\(220\) 8.82381 0.594901
\(221\) −3.04458 −0.204800
\(222\) 14.4062 0.966880
\(223\) −13.0448 −0.873547 −0.436773 0.899572i \(-0.643879\pi\)
−0.436773 + 0.899572i \(0.643879\pi\)
\(224\) −4.93570 −0.329780
\(225\) 6.35840 0.423893
\(226\) 29.6171 1.97010
\(227\) 12.3606 0.820400 0.410200 0.911996i \(-0.365459\pi\)
0.410200 + 0.911996i \(0.365459\pi\)
\(228\) −0.874869 −0.0579396
\(229\) 6.65491 0.439769 0.219884 0.975526i \(-0.429432\pi\)
0.219884 + 0.975526i \(0.429432\pi\)
\(230\) 3.31611 0.218658
\(231\) 0.956909 0.0629600
\(232\) −3.88935 −0.255348
\(233\) −18.4220 −1.20686 −0.603432 0.797415i \(-0.706200\pi\)
−0.603432 + 0.797415i \(0.706200\pi\)
\(234\) 4.69778 0.307104
\(235\) −8.31161 −0.542190
\(236\) 33.2271 2.16290
\(237\) 5.61553 0.364768
\(238\) −4.51817 −0.292870
\(239\) −24.7696 −1.60221 −0.801107 0.598521i \(-0.795755\pi\)
−0.801107 + 0.598521i \(0.795755\pi\)
\(240\) −11.6362 −0.751112
\(241\) 16.7239 1.07728 0.538641 0.842536i \(-0.318938\pi\)
0.538641 + 0.842536i \(0.318938\pi\)
\(242\) −22.3979 −1.43979
\(243\) 15.4367 0.990265
\(244\) 33.2433 2.12819
\(245\) 8.15698 0.521131
\(246\) 11.1273 0.709451
\(247\) 0.170684 0.0108603
\(248\) 7.00945 0.445101
\(249\) 14.7768 0.936444
\(250\) 26.9298 1.70319
\(251\) −14.3980 −0.908794 −0.454397 0.890799i \(-0.650145\pi\)
−0.454397 + 0.890799i \(0.650145\pi\)
\(252\) 4.89255 0.308202
\(253\) 1.60592 0.100964
\(254\) −8.12509 −0.509814
\(255\) −4.05382 −0.253860
\(256\) −21.8909 −1.36818
\(257\) 26.7350 1.66768 0.833841 0.552005i \(-0.186137\pi\)
0.833841 + 0.552005i \(0.186137\pi\)
\(258\) 10.9876 0.684058
\(259\) −2.92711 −0.181882
\(260\) 5.75452 0.356880
\(261\) 1.00654 0.0623035
\(262\) 4.49413 0.277648
\(263\) 13.1232 0.809213 0.404606 0.914491i \(-0.367409\pi\)
0.404606 + 0.914491i \(0.367409\pi\)
\(264\) −11.7050 −0.720392
\(265\) 8.77416 0.538993
\(266\) 0.253296 0.0155305
\(267\) 7.09318 0.434095
\(268\) −39.8939 −2.43691
\(269\) 16.7183 1.01933 0.509666 0.860372i \(-0.329769\pi\)
0.509666 + 0.860372i \(0.329769\pi\)
\(270\) 16.5996 1.01022
\(271\) −11.6958 −0.710469 −0.355235 0.934777i \(-0.615599\pi\)
−0.355235 + 0.934777i \(0.615599\pi\)
\(272\) 26.6072 1.61330
\(273\) 0.624056 0.0377696
\(274\) 22.4424 1.35580
\(275\) 5.37470 0.324107
\(276\) −5.36821 −0.323128
\(277\) 21.4797 1.29059 0.645295 0.763934i \(-0.276735\pi\)
0.645295 + 0.763934i \(0.276735\pi\)
\(278\) −30.7837 −1.84628
\(279\) −1.81401 −0.108602
\(280\) 4.91095 0.293485
\(281\) 4.91202 0.293026 0.146513 0.989209i \(-0.453195\pi\)
0.146513 + 0.989209i \(0.453195\pi\)
\(282\) 19.1726 1.14171
\(283\) −8.94867 −0.531943 −0.265972 0.963981i \(-0.585693\pi\)
−0.265972 + 0.963981i \(0.585693\pi\)
\(284\) −17.0149 −1.00965
\(285\) 0.227263 0.0134619
\(286\) 3.97100 0.234810
\(287\) −2.26089 −0.133456
\(288\) −15.6245 −0.920682
\(289\) −7.73055 −0.454738
\(290\) 1.75688 0.103168
\(291\) −19.7246 −1.15628
\(292\) 14.2441 0.833575
\(293\) 5.86850 0.342842 0.171421 0.985198i \(-0.445164\pi\)
0.171421 + 0.985198i \(0.445164\pi\)
\(294\) −18.8159 −1.09736
\(295\) −8.63136 −0.502537
\(296\) 35.8047 2.08111
\(297\) 8.03886 0.466462
\(298\) −18.3221 −1.06137
\(299\) 1.04732 0.0605679
\(300\) −17.9663 −1.03729
\(301\) −2.23251 −0.128680
\(302\) 43.1782 2.48463
\(303\) 0.836734 0.0480691
\(304\) −1.49164 −0.0855515
\(305\) −8.63557 −0.494471
\(306\) −14.3028 −0.817634
\(307\) −30.0293 −1.71386 −0.856931 0.515432i \(-0.827632\pi\)
−0.856931 + 0.515432i \(0.827632\pi\)
\(308\) 4.13563 0.235649
\(309\) −13.7470 −0.782038
\(310\) −3.16629 −0.179833
\(311\) 11.6620 0.661290 0.330645 0.943755i \(-0.392734\pi\)
0.330645 + 0.943755i \(0.392734\pi\)
\(312\) −7.63351 −0.432162
\(313\) −20.7436 −1.17250 −0.586248 0.810131i \(-0.699396\pi\)
−0.586248 + 0.810131i \(0.699396\pi\)
\(314\) 42.8505 2.41819
\(315\) −1.27093 −0.0716088
\(316\) 24.2696 1.36527
\(317\) 20.3042 1.14040 0.570198 0.821507i \(-0.306866\pi\)
0.570198 + 0.821507i \(0.306866\pi\)
\(318\) −20.2395 −1.13498
\(319\) 0.850823 0.0476370
\(320\) −5.90214 −0.329940
\(321\) −7.36427 −0.411033
\(322\) 1.55422 0.0866136
\(323\) −0.519659 −0.0289146
\(324\) −1.25819 −0.0698996
\(325\) 3.50516 0.194431
\(326\) −39.6949 −2.19850
\(327\) 11.7008 0.647056
\(328\) 27.6555 1.52702
\(329\) −3.89557 −0.214770
\(330\) 5.28734 0.291059
\(331\) −24.9050 −1.36890 −0.684452 0.729058i \(-0.739958\pi\)
−0.684452 + 0.729058i \(0.739958\pi\)
\(332\) 63.8636 3.50497
\(333\) −9.26609 −0.507779
\(334\) 49.9393 2.73256
\(335\) 10.3632 0.566201
\(336\) −5.45376 −0.297527
\(337\) 4.24298 0.231130 0.115565 0.993300i \(-0.463132\pi\)
0.115565 + 0.993300i \(0.463132\pi\)
\(338\) 2.58972 0.140862
\(339\) 12.4546 0.676442
\(340\) −17.5201 −0.950160
\(341\) −1.53337 −0.0830366
\(342\) 0.801834 0.0433582
\(343\) 7.83436 0.423016
\(344\) 27.3083 1.47236
\(345\) 1.39449 0.0750769
\(346\) −36.3066 −1.95186
\(347\) −27.8347 −1.49424 −0.747122 0.664687i \(-0.768565\pi\)
−0.747122 + 0.664687i \(0.768565\pi\)
\(348\) −2.84409 −0.152459
\(349\) −15.2791 −0.817873 −0.408937 0.912563i \(-0.634100\pi\)
−0.408937 + 0.912563i \(0.634100\pi\)
\(350\) 5.20168 0.278041
\(351\) 5.24261 0.279830
\(352\) −13.2073 −0.703949
\(353\) 15.7131 0.836327 0.418163 0.908372i \(-0.362674\pi\)
0.418163 + 0.908372i \(0.362674\pi\)
\(354\) 19.9101 1.05821
\(355\) 4.41994 0.234586
\(356\) 30.6558 1.62475
\(357\) −1.89999 −0.100558
\(358\) −58.9722 −3.11678
\(359\) 10.0405 0.529918 0.264959 0.964260i \(-0.414642\pi\)
0.264959 + 0.964260i \(0.414642\pi\)
\(360\) 15.5461 0.819353
\(361\) −18.9709 −0.998467
\(362\) 41.1073 2.16055
\(363\) −9.41878 −0.494358
\(364\) 2.69709 0.141366
\(365\) −3.70018 −0.193676
\(366\) 19.9198 1.04123
\(367\) −2.39645 −0.125094 −0.0625469 0.998042i \(-0.519922\pi\)
−0.0625469 + 0.998042i \(0.519922\pi\)
\(368\) −9.15272 −0.477119
\(369\) −7.15710 −0.372584
\(370\) −16.1736 −0.840826
\(371\) 4.11236 0.213503
\(372\) 5.12568 0.265754
\(373\) −29.7360 −1.53967 −0.769835 0.638243i \(-0.779661\pi\)
−0.769835 + 0.638243i \(0.779661\pi\)
\(374\) −12.0900 −0.625159
\(375\) 11.3245 0.584796
\(376\) 47.6509 2.45741
\(377\) 0.554872 0.0285773
\(378\) 7.78007 0.400163
\(379\) −0.122804 −0.00630802 −0.00315401 0.999995i \(-0.501004\pi\)
−0.00315401 + 0.999995i \(0.501004\pi\)
\(380\) 0.982202 0.0503859
\(381\) −3.41677 −0.175046
\(382\) −21.1827 −1.08380
\(383\) −35.9159 −1.83522 −0.917608 0.397487i \(-0.869882\pi\)
−0.917608 + 0.397487i \(0.869882\pi\)
\(384\) −5.14553 −0.262582
\(385\) −1.07431 −0.0547517
\(386\) −38.2263 −1.94567
\(387\) −7.06725 −0.359248
\(388\) −85.2470 −4.32776
\(389\) 6.97889 0.353844 0.176922 0.984225i \(-0.443386\pi\)
0.176922 + 0.984225i \(0.443386\pi\)
\(390\) 3.44819 0.174606
\(391\) −3.18863 −0.161256
\(392\) −46.7644 −2.36196
\(393\) 1.88987 0.0953315
\(394\) 26.5318 1.33665
\(395\) −6.30447 −0.317212
\(396\) 13.0918 0.657887
\(397\) −5.41099 −0.271570 −0.135785 0.990738i \(-0.543356\pi\)
−0.135785 + 0.990738i \(0.543356\pi\)
\(398\) −21.8890 −1.09720
\(399\) 0.106516 0.00533247
\(400\) −30.6323 −1.53162
\(401\) 6.50195 0.324692 0.162346 0.986734i \(-0.448094\pi\)
0.162346 + 0.986734i \(0.448094\pi\)
\(402\) −23.9050 −1.19227
\(403\) −1.00000 −0.0498135
\(404\) 3.61625 0.179915
\(405\) 0.326839 0.0162408
\(406\) 0.823433 0.0408663
\(407\) −7.83255 −0.388245
\(408\) 23.2408 1.15059
\(409\) −32.5096 −1.60750 −0.803749 0.594969i \(-0.797164\pi\)
−0.803749 + 0.594969i \(0.797164\pi\)
\(410\) −12.4924 −0.616958
\(411\) 9.43750 0.465518
\(412\) −59.4126 −2.92705
\(413\) −4.04543 −0.199063
\(414\) 4.92006 0.241808
\(415\) −16.5897 −0.814358
\(416\) −8.61322 −0.422298
\(417\) −12.9452 −0.633928
\(418\) 0.677784 0.0331515
\(419\) 9.90498 0.483890 0.241945 0.970290i \(-0.422215\pi\)
0.241945 + 0.970290i \(0.422215\pi\)
\(420\) 3.59114 0.175230
\(421\) −18.3445 −0.894057 −0.447029 0.894520i \(-0.647518\pi\)
−0.447029 + 0.894520i \(0.647518\pi\)
\(422\) 46.2496 2.25140
\(423\) −12.3318 −0.599594
\(424\) −50.3028 −2.44292
\(425\) −10.6717 −0.517654
\(426\) −10.1956 −0.493977
\(427\) −4.04740 −0.195867
\(428\) −31.8274 −1.53843
\(429\) 1.66989 0.0806229
\(430\) −12.3356 −0.594876
\(431\) −4.17716 −0.201207 −0.100603 0.994927i \(-0.532077\pi\)
−0.100603 + 0.994927i \(0.532077\pi\)
\(432\) −45.8163 −2.20434
\(433\) 11.2781 0.541989 0.270995 0.962581i \(-0.412647\pi\)
0.270995 + 0.962581i \(0.412647\pi\)
\(434\) −1.48401 −0.0712346
\(435\) 0.738806 0.0354230
\(436\) 50.5693 2.42183
\(437\) 0.178760 0.00855123
\(438\) 8.53527 0.407831
\(439\) −32.7529 −1.56321 −0.781606 0.623772i \(-0.785599\pi\)
−0.781606 + 0.623772i \(0.785599\pi\)
\(440\) 13.1410 0.626473
\(441\) 12.1024 0.576305
\(442\) −7.88460 −0.375032
\(443\) −15.3591 −0.729731 −0.364865 0.931060i \(-0.618885\pi\)
−0.364865 + 0.931060i \(0.618885\pi\)
\(444\) 26.1823 1.24256
\(445\) −7.96340 −0.377501
\(446\) −33.7825 −1.59965
\(447\) −7.70484 −0.364427
\(448\) −2.76627 −0.130694
\(449\) 6.85235 0.323382 0.161691 0.986841i \(-0.448305\pi\)
0.161691 + 0.986841i \(0.448305\pi\)
\(450\) 16.4665 0.776236
\(451\) −6.04984 −0.284876
\(452\) 53.8272 2.53182
\(453\) 18.1573 0.853106
\(454\) 32.0104 1.50232
\(455\) −0.700618 −0.0328455
\(456\) −1.30291 −0.0610145
\(457\) 11.6216 0.543634 0.271817 0.962349i \(-0.412375\pi\)
0.271817 + 0.962349i \(0.412375\pi\)
\(458\) 17.2344 0.805308
\(459\) −15.9615 −0.745020
\(460\) 6.02680 0.281001
\(461\) 22.0155 1.02536 0.512681 0.858579i \(-0.328652\pi\)
0.512681 + 0.858579i \(0.328652\pi\)
\(462\) 2.47812 0.115293
\(463\) −12.6323 −0.587074 −0.293537 0.955948i \(-0.594832\pi\)
−0.293537 + 0.955948i \(0.594832\pi\)
\(464\) −4.84914 −0.225116
\(465\) −1.33149 −0.0617464
\(466\) −47.7077 −2.21002
\(467\) −8.71567 −0.403313 −0.201657 0.979456i \(-0.564633\pi\)
−0.201657 + 0.979456i \(0.564633\pi\)
\(468\) 8.53791 0.394665
\(469\) 4.85712 0.224281
\(470\) −21.5247 −0.992862
\(471\) 18.0195 0.830296
\(472\) 49.4840 2.27769
\(473\) −5.97389 −0.274680
\(474\) 14.5427 0.667966
\(475\) 0.598272 0.0274506
\(476\) −8.21149 −0.376373
\(477\) 13.0181 0.596059
\(478\) −64.1464 −2.93399
\(479\) 16.9032 0.772325 0.386162 0.922431i \(-0.373800\pi\)
0.386162 + 0.922431i \(0.373800\pi\)
\(480\) −11.4684 −0.523459
\(481\) −5.10806 −0.232908
\(482\) 43.3102 1.97273
\(483\) 0.653584 0.0297391
\(484\) −40.7067 −1.85031
\(485\) 22.1445 1.00553
\(486\) 39.9767 1.81338
\(487\) −0.0858727 −0.00389127 −0.00194563 0.999998i \(-0.500619\pi\)
−0.00194563 + 0.999998i \(0.500619\pi\)
\(488\) 49.5082 2.24113
\(489\) −16.6925 −0.754863
\(490\) 21.1243 0.954299
\(491\) −39.9349 −1.80224 −0.901118 0.433574i \(-0.857252\pi\)
−0.901118 + 0.433574i \(0.857252\pi\)
\(492\) 20.2231 0.911729
\(493\) −1.68935 −0.0760845
\(494\) 0.442022 0.0198875
\(495\) −3.40083 −0.152856
\(496\) 8.73922 0.392402
\(497\) 2.07158 0.0929231
\(498\) 38.2679 1.71482
\(499\) 9.38080 0.419942 0.209971 0.977708i \(-0.432663\pi\)
0.209971 + 0.977708i \(0.432663\pi\)
\(500\) 48.9431 2.18880
\(501\) 21.0005 0.938234
\(502\) −37.2868 −1.66419
\(503\) −27.4528 −1.22406 −0.612031 0.790834i \(-0.709647\pi\)
−0.612031 + 0.790834i \(0.709647\pi\)
\(504\) 7.28631 0.324558
\(505\) −0.939388 −0.0418022
\(506\) 4.15889 0.184885
\(507\) 1.08903 0.0483655
\(508\) −14.7668 −0.655172
\(509\) 10.8524 0.481026 0.240513 0.970646i \(-0.422684\pi\)
0.240513 + 0.970646i \(0.422684\pi\)
\(510\) −10.4983 −0.464871
\(511\) −1.73424 −0.0767180
\(512\) −47.2414 −2.08780
\(513\) 0.894827 0.0395076
\(514\) 69.2361 3.05387
\(515\) 15.4335 0.680082
\(516\) 19.9692 0.879097
\(517\) −10.4240 −0.458447
\(518\) −7.58040 −0.333064
\(519\) −15.2677 −0.670177
\(520\) 8.57002 0.375820
\(521\) 9.07911 0.397763 0.198882 0.980024i \(-0.436269\pi\)
0.198882 + 0.980024i \(0.436269\pi\)
\(522\) 2.60667 0.114091
\(523\) 3.83179 0.167552 0.0837762 0.996485i \(-0.473302\pi\)
0.0837762 + 0.996485i \(0.473302\pi\)
\(524\) 8.16778 0.356811
\(525\) 2.18741 0.0954666
\(526\) 33.9855 1.48184
\(527\) 3.04458 0.132624
\(528\) −14.5935 −0.635101
\(529\) −21.9031 −0.952310
\(530\) 22.7226 0.987008
\(531\) −12.8062 −0.555743
\(532\) 0.460348 0.0199586
\(533\) −3.94545 −0.170897
\(534\) 18.3693 0.794919
\(535\) 8.26775 0.357446
\(536\) −59.4127 −2.56624
\(537\) −24.7991 −1.07016
\(538\) 43.2957 1.86661
\(539\) 10.2301 0.440640
\(540\) 30.1687 1.29825
\(541\) 40.1608 1.72665 0.863324 0.504650i \(-0.168378\pi\)
0.863324 + 0.504650i \(0.168378\pi\)
\(542\) −30.2888 −1.30102
\(543\) 17.2865 0.741834
\(544\) 26.2236 1.12433
\(545\) −13.1363 −0.562698
\(546\) 1.61613 0.0691640
\(547\) 38.1661 1.63186 0.815931 0.578149i \(-0.196225\pi\)
0.815931 + 0.578149i \(0.196225\pi\)
\(548\) 40.7876 1.74236
\(549\) −12.8125 −0.546823
\(550\) 13.9190 0.593507
\(551\) 0.0947074 0.00403467
\(552\) −7.99469 −0.340277
\(553\) −2.95484 −0.125653
\(554\) 55.6263 2.36334
\(555\) −6.80134 −0.288701
\(556\) −55.9473 −2.37269
\(557\) 41.3959 1.75400 0.877001 0.480489i \(-0.159541\pi\)
0.877001 + 0.480489i \(0.159541\pi\)
\(558\) −4.69778 −0.198873
\(559\) −3.89592 −0.164780
\(560\) 6.12285 0.258738
\(561\) −5.08410 −0.214651
\(562\) 12.7207 0.536592
\(563\) 16.6148 0.700232 0.350116 0.936706i \(-0.386142\pi\)
0.350116 + 0.936706i \(0.386142\pi\)
\(564\) 34.8449 1.46723
\(565\) −13.9826 −0.588253
\(566\) −23.1745 −0.974098
\(567\) 0.153186 0.00643321
\(568\) −25.3398 −1.06323
\(569\) 44.4229 1.86230 0.931152 0.364631i \(-0.118805\pi\)
0.931152 + 0.364631i \(0.118805\pi\)
\(570\) 0.588548 0.0246516
\(571\) 11.7168 0.490332 0.245166 0.969481i \(-0.421157\pi\)
0.245166 + 0.969481i \(0.421157\pi\)
\(572\) 7.21703 0.301759
\(573\) −8.90775 −0.372127
\(574\) −5.85508 −0.244386
\(575\) 3.67101 0.153092
\(576\) −8.75693 −0.364872
\(577\) −9.27400 −0.386082 −0.193041 0.981191i \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(578\) −20.0200 −0.832721
\(579\) −16.0750 −0.668053
\(580\) 3.19302 0.132583
\(581\) −7.77544 −0.322580
\(582\) −51.0811 −2.11738
\(583\) 11.0041 0.455744
\(584\) 21.2133 0.877813
\(585\) −2.21788 −0.0916981
\(586\) 15.1978 0.627814
\(587\) −26.9865 −1.11385 −0.556927 0.830562i \(-0.688020\pi\)
−0.556927 + 0.830562i \(0.688020\pi\)
\(588\) −34.1966 −1.41025
\(589\) −0.170684 −0.00703289
\(590\) −22.3528 −0.920250
\(591\) 11.1572 0.458945
\(592\) 44.6405 1.83471
\(593\) 12.8406 0.527299 0.263649 0.964619i \(-0.415074\pi\)
0.263649 + 0.964619i \(0.415074\pi\)
\(594\) 20.8184 0.854188
\(595\) 2.13308 0.0874480
\(596\) −33.2993 −1.36399
\(597\) −9.20479 −0.376727
\(598\) 2.71225 0.110912
\(599\) −33.5314 −1.37006 −0.685029 0.728516i \(-0.740210\pi\)
−0.685029 + 0.728516i \(0.740210\pi\)
\(600\) −26.7566 −1.09234
\(601\) −36.7391 −1.49862 −0.749310 0.662220i \(-0.769615\pi\)
−0.749310 + 0.662220i \(0.769615\pi\)
\(602\) −5.78157 −0.235639
\(603\) 15.3757 0.626148
\(604\) 78.4735 3.19304
\(605\) 10.5743 0.429907
\(606\) 2.16691 0.0880245
\(607\) 6.49000 0.263421 0.131710 0.991288i \(-0.457953\pi\)
0.131710 + 0.991288i \(0.457953\pi\)
\(608\) −1.47013 −0.0596218
\(609\) 0.346271 0.0140316
\(610\) −22.3637 −0.905479
\(611\) −6.79810 −0.275022
\(612\) −25.9943 −1.05076
\(613\) −23.9687 −0.968088 −0.484044 0.875044i \(-0.660833\pi\)
−0.484044 + 0.875044i \(0.660833\pi\)
\(614\) −77.7674 −3.13844
\(615\) −5.25333 −0.211835
\(616\) 6.15906 0.248156
\(617\) −31.1849 −1.25546 −0.627729 0.778432i \(-0.716015\pi\)
−0.627729 + 0.778432i \(0.716015\pi\)
\(618\) −35.6008 −1.43207
\(619\) −3.32672 −0.133712 −0.0668561 0.997763i \(-0.521297\pi\)
−0.0668561 + 0.997763i \(0.521297\pi\)
\(620\) −5.75452 −0.231107
\(621\) 5.49067 0.220333
\(622\) 30.2012 1.21096
\(623\) −3.73236 −0.149534
\(624\) −9.51728 −0.380996
\(625\) 4.81191 0.192476
\(626\) −53.7201 −2.14709
\(627\) 0.285022 0.0113827
\(628\) 77.8780 3.10767
\(629\) 15.5519 0.620094
\(630\) −3.29135 −0.131131
\(631\) 26.4173 1.05166 0.525829 0.850590i \(-0.323755\pi\)
0.525829 + 0.850590i \(0.323755\pi\)
\(632\) 36.1439 1.43773
\(633\) 19.4489 0.773025
\(634\) 52.5821 2.08830
\(635\) 3.83595 0.152225
\(636\) −36.7840 −1.45858
\(637\) 6.67163 0.264340
\(638\) 2.20339 0.0872332
\(639\) 6.55781 0.259423
\(640\) 5.77681 0.228348
\(641\) 30.9803 1.22365 0.611825 0.790993i \(-0.290436\pi\)
0.611825 + 0.790993i \(0.290436\pi\)
\(642\) −19.0714 −0.752687
\(643\) −34.9166 −1.37698 −0.688488 0.725248i \(-0.741725\pi\)
−0.688488 + 0.725248i \(0.741725\pi\)
\(644\) 2.82470 0.111309
\(645\) −5.18738 −0.204253
\(646\) −1.34577 −0.0529487
\(647\) 46.6829 1.83529 0.917647 0.397396i \(-0.130086\pi\)
0.917647 + 0.397396i \(0.130086\pi\)
\(648\) −1.87378 −0.0736092
\(649\) −10.8250 −0.424919
\(650\) 9.07737 0.356044
\(651\) −0.624056 −0.0244587
\(652\) −72.1430 −2.82534
\(653\) 25.1719 0.985053 0.492526 0.870297i \(-0.336073\pi\)
0.492526 + 0.870297i \(0.336073\pi\)
\(654\) 30.3018 1.18489
\(655\) −2.12173 −0.0829029
\(656\) 34.4802 1.34622
\(657\) −5.48990 −0.214182
\(658\) −10.0884 −0.393288
\(659\) −22.6064 −0.880620 −0.440310 0.897846i \(-0.645131\pi\)
−0.440310 + 0.897846i \(0.645131\pi\)
\(660\) 9.60940 0.374045
\(661\) 28.2947 1.10054 0.550268 0.834988i \(-0.314525\pi\)
0.550268 + 0.834988i \(0.314525\pi\)
\(662\) −64.4970 −2.50675
\(663\) −3.31564 −0.128769
\(664\) 95.1099 3.69098
\(665\) −0.119584 −0.00463727
\(666\) −23.9966 −0.929848
\(667\) 0.581126 0.0225013
\(668\) 90.7614 3.51166
\(669\) −14.2062 −0.549244
\(670\) 26.8377 1.03683
\(671\) −10.8303 −0.418099
\(672\) −5.37513 −0.207350
\(673\) −15.4671 −0.596212 −0.298106 0.954533i \(-0.596355\pi\)
−0.298106 + 0.954533i \(0.596355\pi\)
\(674\) 10.9881 0.423247
\(675\) 18.3762 0.707299
\(676\) 4.70665 0.181025
\(677\) −5.14548 −0.197757 −0.0988785 0.995100i \(-0.531526\pi\)
−0.0988785 + 0.995100i \(0.531526\pi\)
\(678\) 32.2540 1.23871
\(679\) 10.3789 0.398305
\(680\) −26.0921 −1.00059
\(681\) 13.4610 0.515828
\(682\) −3.97100 −0.152057
\(683\) 48.3922 1.85168 0.925838 0.377920i \(-0.123361\pi\)
0.925838 + 0.377920i \(0.123361\pi\)
\(684\) 1.45728 0.0557205
\(685\) −10.5953 −0.404827
\(686\) 20.2888 0.774630
\(687\) 7.24740 0.276506
\(688\) 34.0473 1.29804
\(689\) 7.17642 0.273400
\(690\) 3.61134 0.137481
\(691\) 26.0413 0.990658 0.495329 0.868705i \(-0.335047\pi\)
0.495329 + 0.868705i \(0.335047\pi\)
\(692\) −65.9849 −2.50837
\(693\) −1.59393 −0.0605486
\(694\) −72.0840 −2.73627
\(695\) 14.5333 0.551281
\(696\) −4.23562 −0.160551
\(697\) 12.0122 0.454996
\(698\) −39.5687 −1.49770
\(699\) −20.0621 −0.758818
\(700\) 9.45371 0.357317
\(701\) 29.0404 1.09684 0.548420 0.836203i \(-0.315230\pi\)
0.548420 + 0.836203i \(0.315230\pi\)
\(702\) 13.5769 0.512426
\(703\) −0.871862 −0.0328829
\(704\) −7.40216 −0.278980
\(705\) −9.05160 −0.340903
\(706\) 40.6926 1.53149
\(707\) −0.440282 −0.0165585
\(708\) 36.1853 1.35993
\(709\) 8.70581 0.326953 0.163477 0.986547i \(-0.447729\pi\)
0.163477 + 0.986547i \(0.447729\pi\)
\(710\) 11.4464 0.429576
\(711\) −9.35387 −0.350797
\(712\) 45.6546 1.71098
\(713\) −1.04732 −0.0392223
\(714\) −4.92043 −0.184142
\(715\) −1.87476 −0.0701119
\(716\) −107.178 −4.00544
\(717\) −26.9749 −1.00740
\(718\) 26.0021 0.970389
\(719\) 20.1480 0.751392 0.375696 0.926743i \(-0.377404\pi\)
0.375696 + 0.926743i \(0.377404\pi\)
\(720\) 19.3825 0.722345
\(721\) 7.23353 0.269391
\(722\) −49.1292 −1.82840
\(723\) 18.2128 0.677343
\(724\) 74.7099 2.77657
\(725\) 1.94491 0.0722322
\(726\) −24.3920 −0.905272
\(727\) 10.3774 0.384876 0.192438 0.981309i \(-0.438361\pi\)
0.192438 + 0.981309i \(0.438361\pi\)
\(728\) 4.01668 0.148868
\(729\) 17.6130 0.652334
\(730\) −9.58242 −0.354661
\(731\) 11.8614 0.438711
\(732\) 36.2030 1.33810
\(733\) 50.8688 1.87888 0.939441 0.342712i \(-0.111345\pi\)
0.939441 + 0.342712i \(0.111345\pi\)
\(734\) −6.20614 −0.229073
\(735\) 8.88321 0.327662
\(736\) −9.02076 −0.332510
\(737\) 12.9970 0.478749
\(738\) −18.5349 −0.682278
\(739\) 35.0783 1.29038 0.645189 0.764023i \(-0.276779\pi\)
0.645189 + 0.764023i \(0.276779\pi\)
\(740\) −29.3945 −1.08056
\(741\) 0.185880 0.00682846
\(742\) 10.6499 0.390969
\(743\) 22.5151 0.825998 0.412999 0.910732i \(-0.364481\pi\)
0.412999 + 0.910732i \(0.364481\pi\)
\(744\) 7.63351 0.279858
\(745\) 8.65011 0.316915
\(746\) −77.0078 −2.81946
\(747\) −24.6140 −0.900578
\(748\) −21.9728 −0.803405
\(749\) 3.87501 0.141590
\(750\) 29.3274 1.07088
\(751\) −43.8171 −1.59891 −0.799454 0.600727i \(-0.794878\pi\)
−0.799454 + 0.600727i \(0.794878\pi\)
\(752\) 59.4101 2.16646
\(753\) −15.6799 −0.571406
\(754\) 1.43696 0.0523311
\(755\) −20.3849 −0.741884
\(756\) 14.1398 0.514258
\(757\) 42.2912 1.53710 0.768550 0.639790i \(-0.220979\pi\)
0.768550 + 0.639790i \(0.220979\pi\)
\(758\) −0.318028 −0.0115513
\(759\) 1.74890 0.0634810
\(760\) 1.46276 0.0530599
\(761\) −42.8193 −1.55220 −0.776099 0.630611i \(-0.782804\pi\)
−0.776099 + 0.630611i \(0.782804\pi\)
\(762\) −8.84847 −0.320546
\(763\) −6.15685 −0.222893
\(764\) −38.4981 −1.39281
\(765\) 6.75251 0.244137
\(766\) −93.0120 −3.36066
\(767\) −7.05962 −0.254908
\(768\) −23.8398 −0.860245
\(769\) 25.3392 0.913754 0.456877 0.889530i \(-0.348968\pi\)
0.456877 + 0.889530i \(0.348968\pi\)
\(770\) −2.78215 −0.100262
\(771\) 29.1152 1.04856
\(772\) −69.4739 −2.50042
\(773\) −11.6925 −0.420551 −0.210276 0.977642i \(-0.567436\pi\)
−0.210276 + 0.977642i \(0.567436\pi\)
\(774\) −18.3022 −0.657859
\(775\) −3.50516 −0.125909
\(776\) −126.956 −4.55744
\(777\) −3.18772 −0.114359
\(778\) 18.0734 0.647961
\(779\) −0.673424 −0.0241279
\(780\) 6.26685 0.224389
\(781\) 5.54326 0.198354
\(782\) −8.25767 −0.295294
\(783\) 2.90897 0.103958
\(784\) −58.3048 −2.08231
\(785\) −20.2302 −0.722048
\(786\) 4.89424 0.174572
\(787\) 18.3689 0.654782 0.327391 0.944889i \(-0.393831\pi\)
0.327391 + 0.944889i \(0.393831\pi\)
\(788\) 48.2198 1.71776
\(789\) 14.2916 0.508794
\(790\) −16.3268 −0.580882
\(791\) −6.55351 −0.233016
\(792\) 19.4972 0.692801
\(793\) −7.06306 −0.250817
\(794\) −14.0129 −0.497301
\(795\) 9.55533 0.338893
\(796\) −39.7819 −1.41003
\(797\) 11.0461 0.391272 0.195636 0.980677i \(-0.437323\pi\)
0.195636 + 0.980677i \(0.437323\pi\)
\(798\) 0.275847 0.00976487
\(799\) 20.6973 0.732219
\(800\) −30.1907 −1.06740
\(801\) −11.8152 −0.417469
\(802\) 16.8382 0.594578
\(803\) −4.64057 −0.163762
\(804\) −43.4457 −1.53221
\(805\) −0.733768 −0.0258619
\(806\) −2.58972 −0.0912190
\(807\) 18.2067 0.640907
\(808\) 5.38557 0.189464
\(809\) −25.8647 −0.909355 −0.454678 0.890656i \(-0.650246\pi\)
−0.454678 + 0.890656i \(0.650246\pi\)
\(810\) 0.846421 0.0297402
\(811\) 41.7130 1.46474 0.732372 0.680905i \(-0.238413\pi\)
0.732372 + 0.680905i \(0.238413\pi\)
\(812\) 1.49654 0.0525181
\(813\) −12.7371 −0.446709
\(814\) −20.2841 −0.710958
\(815\) 18.7405 0.656450
\(816\) 28.9761 1.01437
\(817\) −0.664969 −0.0232643
\(818\) −84.1908 −2.94366
\(819\) −1.03950 −0.0363230
\(820\) −22.7042 −0.792865
\(821\) 42.4540 1.48166 0.740828 0.671695i \(-0.234434\pi\)
0.740828 + 0.671695i \(0.234434\pi\)
\(822\) 24.4405 0.852460
\(823\) −29.0780 −1.01359 −0.506797 0.862065i \(-0.669171\pi\)
−0.506797 + 0.862065i \(0.669171\pi\)
\(824\) −88.4812 −3.08239
\(825\) 5.85322 0.203783
\(826\) −10.4765 −0.364525
\(827\) −36.4739 −1.26832 −0.634161 0.773201i \(-0.718654\pi\)
−0.634161 + 0.773201i \(0.718654\pi\)
\(828\) 8.94189 0.310752
\(829\) −43.6715 −1.51678 −0.758388 0.651804i \(-0.774013\pi\)
−0.758388 + 0.651804i \(0.774013\pi\)
\(830\) −42.9628 −1.49126
\(831\) 23.3920 0.811461
\(832\) −4.82738 −0.167359
\(833\) −20.3123 −0.703779
\(834\) −33.5244 −1.16085
\(835\) −23.5770 −0.815914
\(836\) 1.23183 0.0426037
\(837\) −5.24261 −0.181211
\(838\) 25.6511 0.886103
\(839\) 1.66526 0.0574912 0.0287456 0.999587i \(-0.490849\pi\)
0.0287456 + 0.999587i \(0.490849\pi\)
\(840\) 5.34817 0.184529
\(841\) −28.6921 −0.989383
\(842\) −47.5072 −1.63721
\(843\) 5.34934 0.184241
\(844\) 84.0556 2.89331
\(845\) −1.22264 −0.0420600
\(846\) −31.9360 −1.09798
\(847\) 4.95608 0.170293
\(848\) −62.7163 −2.15369
\(849\) −9.74537 −0.334460
\(850\) −27.6368 −0.947933
\(851\) −5.34976 −0.183387
\(852\) −18.5298 −0.634819
\(853\) 43.2903 1.48223 0.741116 0.671377i \(-0.234297\pi\)
0.741116 + 0.671377i \(0.234297\pi\)
\(854\) −10.4816 −0.358674
\(855\) −0.378556 −0.0129463
\(856\) −47.3995 −1.62008
\(857\) 49.8064 1.70135 0.850677 0.525688i \(-0.176192\pi\)
0.850677 + 0.525688i \(0.176192\pi\)
\(858\) 4.32454 0.147637
\(859\) −29.5928 −1.00969 −0.504846 0.863209i \(-0.668451\pi\)
−0.504846 + 0.863209i \(0.668451\pi\)
\(860\) −22.4192 −0.764487
\(861\) −2.46218 −0.0839110
\(862\) −10.8177 −0.368451
\(863\) 6.55697 0.223202 0.111601 0.993753i \(-0.464402\pi\)
0.111601 + 0.993753i \(0.464402\pi\)
\(864\) −45.1557 −1.53623
\(865\) 17.1408 0.582805
\(866\) 29.2070 0.992495
\(867\) −8.41881 −0.285918
\(868\) −2.69709 −0.0915451
\(869\) −7.90675 −0.268218
\(870\) 1.91330 0.0648669
\(871\) 8.47608 0.287201
\(872\) 75.3112 2.55036
\(873\) 32.8555 1.11199
\(874\) 0.462937 0.0156591
\(875\) −5.95886 −0.201446
\(876\) 15.5123 0.524112
\(877\) −9.40850 −0.317703 −0.158851 0.987303i \(-0.550779\pi\)
−0.158851 + 0.987303i \(0.550779\pi\)
\(878\) −84.8209 −2.86257
\(879\) 6.39098 0.215562
\(880\) 16.3839 0.552301
\(881\) −42.2031 −1.42186 −0.710930 0.703263i \(-0.751726\pi\)
−0.710930 + 0.703263i \(0.751726\pi\)
\(882\) 31.3419 1.05534
\(883\) 24.4614 0.823192 0.411596 0.911366i \(-0.364971\pi\)
0.411596 + 0.911366i \(0.364971\pi\)
\(884\) −14.3297 −0.481961
\(885\) −9.39981 −0.315971
\(886\) −39.7756 −1.33629
\(887\) 22.2383 0.746690 0.373345 0.927693i \(-0.378211\pi\)
0.373345 + 0.927693i \(0.378211\pi\)
\(888\) 38.9924 1.30850
\(889\) 1.79787 0.0602987
\(890\) −20.6230 −0.691283
\(891\) 0.409905 0.0137323
\(892\) −61.3974 −2.05574
\(893\) −1.16032 −0.0388287
\(894\) −19.9534 −0.667341
\(895\) 27.8415 0.930639
\(896\) 2.70753 0.0904523
\(897\) 1.14056 0.0380822
\(898\) 17.7457 0.592180
\(899\) −0.554872 −0.0185060
\(900\) 29.9267 0.997557
\(901\) −21.8492 −0.727901
\(902\) −15.6674 −0.521667
\(903\) −2.43127 −0.0809077
\(904\) 80.1631 2.66618
\(905\) −19.4073 −0.645120
\(906\) 47.0224 1.56221
\(907\) 47.7520 1.58558 0.792790 0.609495i \(-0.208628\pi\)
0.792790 + 0.609495i \(0.208628\pi\)
\(908\) 58.1768 1.93067
\(909\) −1.39376 −0.0462280
\(910\) −1.81440 −0.0601469
\(911\) −0.138448 −0.00458697 −0.00229349 0.999997i \(-0.500730\pi\)
−0.00229349 + 0.999997i \(0.500730\pi\)
\(912\) −1.62444 −0.0537907
\(913\) −20.8060 −0.688578
\(914\) 30.0966 0.995507
\(915\) −9.40440 −0.310900
\(916\) 31.3223 1.03492
\(917\) −0.994434 −0.0328391
\(918\) −41.3358 −1.36429
\(919\) 9.66845 0.318933 0.159466 0.987203i \(-0.449023\pi\)
0.159466 + 0.987203i \(0.449023\pi\)
\(920\) 8.97552 0.295914
\(921\) −32.7028 −1.07759
\(922\) 57.0139 1.87765
\(923\) 3.61508 0.118992
\(924\) 4.50383 0.148165
\(925\) −17.9046 −0.588698
\(926\) −32.7142 −1.07505
\(927\) 22.8985 0.752085
\(928\) −4.77923 −0.156886
\(929\) −11.9193 −0.391061 −0.195531 0.980698i \(-0.562643\pi\)
−0.195531 + 0.980698i \(0.562643\pi\)
\(930\) −3.44819 −0.113070
\(931\) 1.13874 0.0373206
\(932\) −86.7057 −2.84014
\(933\) 12.7002 0.415787
\(934\) −22.5711 −0.738550
\(935\) 5.70784 0.186666
\(936\) 12.7152 0.415610
\(937\) 9.05049 0.295667 0.147833 0.989012i \(-0.452770\pi\)
0.147833 + 0.989012i \(0.452770\pi\)
\(938\) 12.5786 0.410705
\(939\) −22.5904 −0.737210
\(940\) −39.1198 −1.27595
\(941\) 17.7185 0.577607 0.288804 0.957388i \(-0.406743\pi\)
0.288804 + 0.957388i \(0.406743\pi\)
\(942\) 46.6655 1.52044
\(943\) −4.13214 −0.134561
\(944\) 61.6955 2.00802
\(945\) −3.67306 −0.119485
\(946\) −15.4707 −0.502996
\(947\) 57.5147 1.86898 0.934489 0.355993i \(-0.115857\pi\)
0.934489 + 0.355993i \(0.115857\pi\)
\(948\) 26.4303 0.858417
\(949\) −3.02639 −0.0982407
\(950\) 1.54936 0.0502678
\(951\) 22.1119 0.717026
\(952\) −12.2291 −0.396347
\(953\) 4.03295 0.130640 0.0653201 0.997864i \(-0.479193\pi\)
0.0653201 + 0.997864i \(0.479193\pi\)
\(954\) 33.7133 1.09151
\(955\) 10.0006 0.323612
\(956\) −116.582 −3.77053
\(957\) 0.926573 0.0299518
\(958\) 43.7744 1.41429
\(959\) −4.96593 −0.160358
\(960\) −6.42761 −0.207450
\(961\) 1.00000 0.0322581
\(962\) −13.2284 −0.426502
\(963\) 12.2668 0.395291
\(964\) 78.7135 2.53519
\(965\) 18.0471 0.580957
\(966\) 1.69260 0.0544585
\(967\) −12.5674 −0.404141 −0.202071 0.979371i \(-0.564767\pi\)
−0.202071 + 0.979371i \(0.564767\pi\)
\(968\) −60.6232 −1.94850
\(969\) −0.565925 −0.0181801
\(970\) 57.3480 1.84133
\(971\) −12.9635 −0.416018 −0.208009 0.978127i \(-0.566698\pi\)
−0.208009 + 0.978127i \(0.566698\pi\)
\(972\) 72.6551 2.33041
\(973\) 6.81163 0.218371
\(974\) −0.222386 −0.00712572
\(975\) 3.81722 0.122249
\(976\) 61.7256 1.97579
\(977\) 52.5757 1.68205 0.841024 0.540999i \(-0.181954\pi\)
0.841024 + 0.540999i \(0.181954\pi\)
\(978\) −43.2290 −1.38231
\(979\) −9.98729 −0.319195
\(980\) 38.3920 1.22639
\(981\) −19.4902 −0.622273
\(982\) −103.420 −3.30027
\(983\) 7.56545 0.241300 0.120650 0.992695i \(-0.461502\pi\)
0.120650 + 0.992695i \(0.461502\pi\)
\(984\) 30.1176 0.960115
\(985\) −12.5260 −0.399111
\(986\) −4.37494 −0.139326
\(987\) −4.24239 −0.135037
\(988\) 0.803347 0.0255579
\(989\) −4.08026 −0.129745
\(990\) −8.80720 −0.279911
\(991\) 39.4600 1.25349 0.626745 0.779225i \(-0.284387\pi\)
0.626745 + 0.779225i \(0.284387\pi\)
\(992\) 8.61322 0.273470
\(993\) −27.1223 −0.860701
\(994\) 5.36481 0.170162
\(995\) 10.3341 0.327612
\(996\) 69.5494 2.20376
\(997\) 39.6484 1.25568 0.627839 0.778344i \(-0.283940\pi\)
0.627839 + 0.778344i \(0.283940\pi\)
\(998\) 24.2936 0.769002
\(999\) −26.7796 −0.847268
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 403.2.a.c.1.7 7
3.2 odd 2 3627.2.a.n.1.1 7
4.3 odd 2 6448.2.a.ba.1.4 7
13.12 even 2 5239.2.a.h.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.a.c.1.7 7 1.1 even 1 trivial
3627.2.a.n.1.1 7 3.2 odd 2
5239.2.a.h.1.1 7 13.12 even 2
6448.2.a.ba.1.4 7 4.3 odd 2