Properties

Label 1045.2.a.d.1.1
Level $1045$
Weight $2$
Character 1045.1
Self dual yes
Analytic conductor $8.344$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1045,2,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(8.34436701122\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\Q(\zeta_{22})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) 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 1.1
Root \(0.284630\) of defining polynomial
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.39788 q^{2} -2.59435 q^{3} +3.74982 q^{4} +1.00000 q^{5} +6.22094 q^{6} -2.89389 q^{7} -4.19584 q^{8} +3.73066 q^{9} +O(q^{10})\) \(q-2.39788 q^{2} -2.59435 q^{3} +3.74982 q^{4} +1.00000 q^{5} +6.22094 q^{6} -2.89389 q^{7} -4.19584 q^{8} +3.73066 q^{9} -2.39788 q^{10} -1.00000 q^{11} -9.72834 q^{12} +4.73780 q^{13} +6.93920 q^{14} -2.59435 q^{15} +2.56149 q^{16} -5.65389 q^{17} -8.94566 q^{18} +1.00000 q^{19} +3.74982 q^{20} +7.50778 q^{21} +2.39788 q^{22} -4.00714 q^{23} +10.8855 q^{24} +1.00000 q^{25} -11.3607 q^{26} -1.89558 q^{27} -10.8516 q^{28} +9.32825 q^{29} +6.22094 q^{30} -6.60270 q^{31} +2.24955 q^{32} +2.59435 q^{33} +13.5573 q^{34} -2.89389 q^{35} +13.9893 q^{36} +6.07686 q^{37} -2.39788 q^{38} -12.2915 q^{39} -4.19584 q^{40} +5.47333 q^{41} -18.0027 q^{42} +10.9515 q^{43} -3.74982 q^{44} +3.73066 q^{45} +9.60863 q^{46} -0.295438 q^{47} -6.64540 q^{48} +1.37462 q^{49} -2.39788 q^{50} +14.6682 q^{51} +17.7659 q^{52} -3.81149 q^{53} +4.54538 q^{54} -1.00000 q^{55} +12.1423 q^{56} -2.59435 q^{57} -22.3680 q^{58} -5.54910 q^{59} -9.72834 q^{60} -1.01018 q^{61} +15.8325 q^{62} -10.7961 q^{63} -10.5171 q^{64} +4.73780 q^{65} -6.22094 q^{66} +6.98807 q^{67} -21.2010 q^{68} +10.3959 q^{69} +6.93920 q^{70} -1.02085 q^{71} -15.6533 q^{72} -0.202033 q^{73} -14.5716 q^{74} -2.59435 q^{75} +3.74982 q^{76} +2.89389 q^{77} +29.4735 q^{78} +7.28690 q^{79} +2.56149 q^{80} -6.27417 q^{81} -13.1244 q^{82} -13.7041 q^{83} +28.1528 q^{84} -5.65389 q^{85} -26.2603 q^{86} -24.2008 q^{87} +4.19584 q^{88} -15.8152 q^{89} -8.94566 q^{90} -13.7107 q^{91} -15.0260 q^{92} +17.1297 q^{93} +0.708423 q^{94} +1.00000 q^{95} -5.83613 q^{96} +4.81308 q^{97} -3.29618 q^{98} -3.73066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} - 11 q^{7} + 3 q^{8} + 8 q^{9} - 3 q^{10} - 5 q^{11} - 7 q^{12} + q^{13} - 7 q^{15} - 3 q^{16} - 3 q^{17} - 7 q^{18} + 5 q^{19} + 5 q^{20} + 11 q^{21} + 3 q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} - 16 q^{26} - 10 q^{27} - 22 q^{28} + 11 q^{29} + 2 q^{30} - 5 q^{31} - 2 q^{32} + 7 q^{33} + 4 q^{34} - 11 q^{35} - 3 q^{36} - 9 q^{37} - 3 q^{38} - 8 q^{39} + 3 q^{40} + 15 q^{41} + 11 q^{42} - 13 q^{43} - 5 q^{44} + 8 q^{45} + 18 q^{46} - 20 q^{47} - 20 q^{48} + 20 q^{49} - 3 q^{50} + 24 q^{51} + q^{52} - 5 q^{53} + 17 q^{54} - 5 q^{55} - 7 q^{57} - 33 q^{58} - 17 q^{59} - 7 q^{60} + 3 q^{61} + 14 q^{62} - 22 q^{63} - 17 q^{64} + q^{65} - 2 q^{66} - 28 q^{67} - 25 q^{68} - 2 q^{69} - 6 q^{71} - 26 q^{72} - 16 q^{73} - 21 q^{74} - 7 q^{75} + 5 q^{76} + 11 q^{77} + 29 q^{78} + 3 q^{79} - 3 q^{80} + q^{81} + 2 q^{82} - 33 q^{83} + 33 q^{84} - 3 q^{85} + 10 q^{86} - 3 q^{88} - 16 q^{89} - 7 q^{90} - 22 q^{91} - 19 q^{92} - 26 q^{93} - 10 q^{94} + 5 q^{95} + 5 q^{96} - 14 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39788 −1.69556 −0.847778 0.530352i \(-0.822060\pi\)
−0.847778 + 0.530352i \(0.822060\pi\)
\(3\) −2.59435 −1.49785 −0.748925 0.662655i \(-0.769430\pi\)
−0.748925 + 0.662655i \(0.769430\pi\)
\(4\) 3.74982 1.87491
\(5\) 1.00000 0.447214
\(6\) 6.22094 2.53969
\(7\) −2.89389 −1.09379 −0.546895 0.837201i \(-0.684190\pi\)
−0.546895 + 0.837201i \(0.684190\pi\)
\(8\) −4.19584 −1.48345
\(9\) 3.73066 1.24355
\(10\) −2.39788 −0.758275
\(11\) −1.00000 −0.301511
\(12\) −9.72834 −2.80833
\(13\) 4.73780 1.31403 0.657015 0.753878i \(-0.271819\pi\)
0.657015 + 0.753878i \(0.271819\pi\)
\(14\) 6.93920 1.85458
\(15\) −2.59435 −0.669859
\(16\) 2.56149 0.640372
\(17\) −5.65389 −1.37127 −0.685635 0.727946i \(-0.740475\pi\)
−0.685635 + 0.727946i \(0.740475\pi\)
\(18\) −8.94566 −2.10851
\(19\) 1.00000 0.229416
\(20\) 3.74982 0.838484
\(21\) 7.50778 1.63833
\(22\) 2.39788 0.511229
\(23\) −4.00714 −0.835547 −0.417773 0.908551i \(-0.637189\pi\)
−0.417773 + 0.908551i \(0.637189\pi\)
\(24\) 10.8855 2.22199
\(25\) 1.00000 0.200000
\(26\) −11.3607 −2.22801
\(27\) −1.89558 −0.364805
\(28\) −10.8516 −2.05075
\(29\) 9.32825 1.73221 0.866106 0.499860i \(-0.166615\pi\)
0.866106 + 0.499860i \(0.166615\pi\)
\(30\) 6.22094 1.13578
\(31\) −6.60270 −1.18588 −0.592940 0.805247i \(-0.702033\pi\)
−0.592940 + 0.805247i \(0.702033\pi\)
\(32\) 2.24955 0.397669
\(33\) 2.59435 0.451619
\(34\) 13.5573 2.32506
\(35\) −2.89389 −0.489157
\(36\) 13.9893 2.33155
\(37\) 6.07686 0.999029 0.499515 0.866305i \(-0.333512\pi\)
0.499515 + 0.866305i \(0.333512\pi\)
\(38\) −2.39788 −0.388987
\(39\) −12.2915 −1.96822
\(40\) −4.19584 −0.663421
\(41\) 5.47333 0.854791 0.427395 0.904065i \(-0.359431\pi\)
0.427395 + 0.904065i \(0.359431\pi\)
\(42\) −18.0027 −2.77788
\(43\) 10.9515 1.67009 0.835043 0.550185i \(-0.185443\pi\)
0.835043 + 0.550185i \(0.185443\pi\)
\(44\) −3.74982 −0.565306
\(45\) 3.73066 0.556134
\(46\) 9.60863 1.41672
\(47\) −0.295438 −0.0430940 −0.0215470 0.999768i \(-0.506859\pi\)
−0.0215470 + 0.999768i \(0.506859\pi\)
\(48\) −6.64540 −0.959181
\(49\) 1.37462 0.196375
\(50\) −2.39788 −0.339111
\(51\) 14.6682 2.05395
\(52\) 17.7659 2.46368
\(53\) −3.81149 −0.523549 −0.261774 0.965129i \(-0.584308\pi\)
−0.261774 + 0.965129i \(0.584308\pi\)
\(54\) 4.54538 0.618547
\(55\) −1.00000 −0.134840
\(56\) 12.1423 1.62259
\(57\) −2.59435 −0.343630
\(58\) −22.3680 −2.93706
\(59\) −5.54910 −0.722431 −0.361215 0.932482i \(-0.617638\pi\)
−0.361215 + 0.932482i \(0.617638\pi\)
\(60\) −9.72834 −1.25592
\(61\) −1.01018 −0.129340 −0.0646700 0.997907i \(-0.520599\pi\)
−0.0646700 + 0.997907i \(0.520599\pi\)
\(62\) 15.8325 2.01073
\(63\) −10.7961 −1.36018
\(64\) −10.5171 −1.31464
\(65\) 4.73780 0.587652
\(66\) −6.22094 −0.765744
\(67\) 6.98807 0.853729 0.426864 0.904316i \(-0.359618\pi\)
0.426864 + 0.904316i \(0.359618\pi\)
\(68\) −21.2010 −2.57100
\(69\) 10.3959 1.25152
\(70\) 6.93920 0.829393
\(71\) −1.02085 −0.121152 −0.0605761 0.998164i \(-0.519294\pi\)
−0.0605761 + 0.998164i \(0.519294\pi\)
\(72\) −15.6533 −1.84475
\(73\) −0.202033 −0.0236462 −0.0118231 0.999930i \(-0.503763\pi\)
−0.0118231 + 0.999930i \(0.503763\pi\)
\(74\) −14.5716 −1.69391
\(75\) −2.59435 −0.299570
\(76\) 3.74982 0.430133
\(77\) 2.89389 0.329790
\(78\) 29.4735 3.33722
\(79\) 7.28690 0.819840 0.409920 0.912121i \(-0.365557\pi\)
0.409920 + 0.912121i \(0.365557\pi\)
\(80\) 2.56149 0.286383
\(81\) −6.27417 −0.697130
\(82\) −13.1244 −1.44935
\(83\) −13.7041 −1.50422 −0.752109 0.659039i \(-0.770963\pi\)
−0.752109 + 0.659039i \(0.770963\pi\)
\(84\) 28.1528 3.07172
\(85\) −5.65389 −0.613250
\(86\) −26.2603 −2.83172
\(87\) −24.2008 −2.59459
\(88\) 4.19584 0.447278
\(89\) −15.8152 −1.67641 −0.838203 0.545359i \(-0.816394\pi\)
−0.838203 + 0.545359i \(0.816394\pi\)
\(90\) −8.94566 −0.942955
\(91\) −13.7107 −1.43727
\(92\) −15.0260 −1.56657
\(93\) 17.1297 1.77627
\(94\) 0.708423 0.0730683
\(95\) 1.00000 0.102598
\(96\) −5.83613 −0.595648
\(97\) 4.81308 0.488694 0.244347 0.969688i \(-0.421426\pi\)
0.244347 + 0.969688i \(0.421426\pi\)
\(98\) −3.29618 −0.332964
\(99\) −3.73066 −0.374945
\(100\) 3.74982 0.374982
\(101\) 1.76221 0.175346 0.0876730 0.996149i \(-0.472057\pi\)
0.0876730 + 0.996149i \(0.472057\pi\)
\(102\) −35.1725 −3.48259
\(103\) −5.53571 −0.545450 −0.272725 0.962092i \(-0.587925\pi\)
−0.272725 + 0.962092i \(0.587925\pi\)
\(104\) −19.8791 −1.94930
\(105\) 7.50778 0.732684
\(106\) 9.13949 0.887706
\(107\) −4.32073 −0.417701 −0.208851 0.977948i \(-0.566972\pi\)
−0.208851 + 0.977948i \(0.566972\pi\)
\(108\) −7.10809 −0.683976
\(109\) −13.0039 −1.24555 −0.622776 0.782400i \(-0.713995\pi\)
−0.622776 + 0.782400i \(0.713995\pi\)
\(110\) 2.39788 0.228629
\(111\) −15.7655 −1.49640
\(112\) −7.41267 −0.700432
\(113\) −17.0047 −1.59967 −0.799833 0.600223i \(-0.795078\pi\)
−0.799833 + 0.600223i \(0.795078\pi\)
\(114\) 6.22094 0.582644
\(115\) −4.00714 −0.373668
\(116\) 34.9792 3.24774
\(117\) 17.6751 1.63406
\(118\) 13.3061 1.22492
\(119\) 16.3618 1.49988
\(120\) 10.8855 0.993705
\(121\) 1.00000 0.0909091
\(122\) 2.42228 0.219303
\(123\) −14.1997 −1.28035
\(124\) −24.7589 −2.22342
\(125\) 1.00000 0.0894427
\(126\) 25.8878 2.30627
\(127\) −9.80245 −0.869826 −0.434913 0.900472i \(-0.643221\pi\)
−0.434913 + 0.900472i \(0.643221\pi\)
\(128\) 20.7197 1.83138
\(129\) −28.4120 −2.50154
\(130\) −11.3607 −0.996396
\(131\) −13.4383 −1.17411 −0.587053 0.809549i \(-0.699712\pi\)
−0.587053 + 0.809549i \(0.699712\pi\)
\(132\) 9.72834 0.846743
\(133\) −2.89389 −0.250932
\(134\) −16.7565 −1.44754
\(135\) −1.89558 −0.163146
\(136\) 23.7228 2.03422
\(137\) −16.2122 −1.38510 −0.692549 0.721371i \(-0.743512\pi\)
−0.692549 + 0.721371i \(0.743512\pi\)
\(138\) −24.9282 −2.12203
\(139\) 19.0373 1.61472 0.807359 0.590060i \(-0.200896\pi\)
0.807359 + 0.590060i \(0.200896\pi\)
\(140\) −10.8516 −0.917125
\(141\) 0.766469 0.0645484
\(142\) 2.44787 0.205420
\(143\) −4.73780 −0.396195
\(144\) 9.55603 0.796336
\(145\) 9.32825 0.774669
\(146\) 0.484451 0.0400934
\(147\) −3.56626 −0.294140
\(148\) 22.7871 1.87309
\(149\) −15.3234 −1.25534 −0.627670 0.778480i \(-0.715991\pi\)
−0.627670 + 0.778480i \(0.715991\pi\)
\(150\) 6.22094 0.507937
\(151\) −1.25936 −0.102485 −0.0512426 0.998686i \(-0.516318\pi\)
−0.0512426 + 0.998686i \(0.516318\pi\)
\(152\) −4.19584 −0.340328
\(153\) −21.0927 −1.70525
\(154\) −6.93920 −0.559177
\(155\) −6.60270 −0.530342
\(156\) −46.0909 −3.69023
\(157\) 12.1861 0.972559 0.486279 0.873803i \(-0.338354\pi\)
0.486279 + 0.873803i \(0.338354\pi\)
\(158\) −17.4731 −1.39008
\(159\) 9.88835 0.784197
\(160\) 2.24955 0.177843
\(161\) 11.5962 0.913912
\(162\) 15.0447 1.18202
\(163\) 6.09722 0.477571 0.238786 0.971072i \(-0.423251\pi\)
0.238786 + 0.971072i \(0.423251\pi\)
\(164\) 20.5240 1.60265
\(165\) 2.59435 0.201970
\(166\) 32.8607 2.55048
\(167\) 1.06720 0.0825826 0.0412913 0.999147i \(-0.486853\pi\)
0.0412913 + 0.999147i \(0.486853\pi\)
\(168\) −31.5015 −2.43039
\(169\) 9.44675 0.726673
\(170\) 13.5573 1.03980
\(171\) 3.73066 0.285291
\(172\) 41.0661 3.13126
\(173\) −13.0289 −0.990571 −0.495286 0.868730i \(-0.664937\pi\)
−0.495286 + 0.868730i \(0.664937\pi\)
\(174\) 58.0304 4.39928
\(175\) −2.89389 −0.218758
\(176\) −2.56149 −0.193079
\(177\) 14.3963 1.08209
\(178\) 37.9229 2.84244
\(179\) 20.6273 1.54176 0.770878 0.636983i \(-0.219818\pi\)
0.770878 + 0.636983i \(0.219818\pi\)
\(180\) 13.9893 1.04270
\(181\) −20.5908 −1.53050 −0.765251 0.643732i \(-0.777385\pi\)
−0.765251 + 0.643732i \(0.777385\pi\)
\(182\) 32.8766 2.43697
\(183\) 2.62076 0.193732
\(184\) 16.8133 1.23950
\(185\) 6.07686 0.446779
\(186\) −41.0750 −3.01176
\(187\) 5.65389 0.413453
\(188\) −1.10784 −0.0807973
\(189\) 5.48562 0.399020
\(190\) −2.39788 −0.173960
\(191\) 8.40047 0.607837 0.303918 0.952698i \(-0.401705\pi\)
0.303918 + 0.952698i \(0.401705\pi\)
\(192\) 27.2851 1.96913
\(193\) 11.4982 0.827661 0.413830 0.910354i \(-0.364191\pi\)
0.413830 + 0.910354i \(0.364191\pi\)
\(194\) −11.5412 −0.828607
\(195\) −12.2915 −0.880214
\(196\) 5.15458 0.368185
\(197\) 27.0376 1.92635 0.963173 0.268883i \(-0.0866545\pi\)
0.963173 + 0.268883i \(0.0866545\pi\)
\(198\) 8.94566 0.635740
\(199\) −5.18460 −0.367526 −0.183763 0.982971i \(-0.558828\pi\)
−0.183763 + 0.982971i \(0.558828\pi\)
\(200\) −4.19584 −0.296691
\(201\) −18.1295 −1.27876
\(202\) −4.22555 −0.297309
\(203\) −26.9950 −1.89468
\(204\) 55.0029 3.85098
\(205\) 5.47333 0.382274
\(206\) 13.2740 0.924840
\(207\) −14.9493 −1.03905
\(208\) 12.1358 0.841467
\(209\) −1.00000 −0.0691714
\(210\) −18.0027 −1.24231
\(211\) −21.5427 −1.48306 −0.741529 0.670921i \(-0.765899\pi\)
−0.741529 + 0.670921i \(0.765899\pi\)
\(212\) −14.2924 −0.981606
\(213\) 2.64844 0.181468
\(214\) 10.3606 0.708235
\(215\) 10.9515 0.746885
\(216\) 7.95357 0.541172
\(217\) 19.1075 1.29710
\(218\) 31.1818 2.11190
\(219\) 0.524145 0.0354184
\(220\) −3.74982 −0.252813
\(221\) −26.7870 −1.80189
\(222\) 37.8037 2.53722
\(223\) −26.9600 −1.80537 −0.902687 0.430298i \(-0.858408\pi\)
−0.902687 + 0.430298i \(0.858408\pi\)
\(224\) −6.50997 −0.434966
\(225\) 3.73066 0.248711
\(226\) 40.7751 2.71232
\(227\) 9.02570 0.599057 0.299528 0.954087i \(-0.403171\pi\)
0.299528 + 0.954087i \(0.403171\pi\)
\(228\) −9.72834 −0.644275
\(229\) −13.7697 −0.909926 −0.454963 0.890510i \(-0.650347\pi\)
−0.454963 + 0.890510i \(0.650347\pi\)
\(230\) 9.60863 0.633575
\(231\) −7.50778 −0.493976
\(232\) −39.1399 −2.56966
\(233\) −2.45587 −0.160890 −0.0804448 0.996759i \(-0.525634\pi\)
−0.0804448 + 0.996759i \(0.525634\pi\)
\(234\) −42.3827 −2.77065
\(235\) −0.295438 −0.0192722
\(236\) −20.8081 −1.35449
\(237\) −18.9048 −1.22800
\(238\) −39.2335 −2.54313
\(239\) −22.8439 −1.47765 −0.738825 0.673897i \(-0.764619\pi\)
−0.738825 + 0.673897i \(0.764619\pi\)
\(240\) −6.64540 −0.428959
\(241\) 16.1181 1.03826 0.519129 0.854696i \(-0.326256\pi\)
0.519129 + 0.854696i \(0.326256\pi\)
\(242\) −2.39788 −0.154141
\(243\) 21.9641 1.40900
\(244\) −3.78798 −0.242501
\(245\) 1.37462 0.0878215
\(246\) 34.0492 2.17090
\(247\) 4.73780 0.301459
\(248\) 27.7039 1.75920
\(249\) 35.5532 2.25309
\(250\) −2.39788 −0.151655
\(251\) −18.8758 −1.19143 −0.595716 0.803195i \(-0.703132\pi\)
−0.595716 + 0.803195i \(0.703132\pi\)
\(252\) −40.4835 −2.55022
\(253\) 4.00714 0.251927
\(254\) 23.5051 1.47484
\(255\) 14.6682 0.918557
\(256\) −28.6490 −1.79056
\(257\) 7.48029 0.466608 0.233304 0.972404i \(-0.425046\pi\)
0.233304 + 0.972404i \(0.425046\pi\)
\(258\) 68.1285 4.24150
\(259\) −17.5858 −1.09273
\(260\) 17.7659 1.10179
\(261\) 34.8005 2.15410
\(262\) 32.2233 1.99076
\(263\) −17.7703 −1.09577 −0.547883 0.836555i \(-0.684566\pi\)
−0.547883 + 0.836555i \(0.684566\pi\)
\(264\) −10.8855 −0.669956
\(265\) −3.81149 −0.234138
\(266\) 6.93920 0.425470
\(267\) 41.0301 2.51100
\(268\) 26.2040 1.60066
\(269\) 25.9320 1.58110 0.790550 0.612398i \(-0.209795\pi\)
0.790550 + 0.612398i \(0.209795\pi\)
\(270\) 4.54538 0.276623
\(271\) −16.2686 −0.988248 −0.494124 0.869391i \(-0.664511\pi\)
−0.494124 + 0.869391i \(0.664511\pi\)
\(272\) −14.4824 −0.878122
\(273\) 35.5703 2.15282
\(274\) 38.8748 2.34851
\(275\) −1.00000 −0.0603023
\(276\) 38.9828 2.34649
\(277\) −17.9217 −1.07681 −0.538405 0.842686i \(-0.680973\pi\)
−0.538405 + 0.842686i \(0.680973\pi\)
\(278\) −45.6490 −2.73784
\(279\) −24.6324 −1.47470
\(280\) 12.1423 0.725643
\(281\) −28.8563 −1.72142 −0.860712 0.509093i \(-0.829981\pi\)
−0.860712 + 0.509093i \(0.829981\pi\)
\(282\) −1.83790 −0.109445
\(283\) −10.7620 −0.639736 −0.319868 0.947462i \(-0.603639\pi\)
−0.319868 + 0.947462i \(0.603639\pi\)
\(284\) −3.82799 −0.227149
\(285\) −2.59435 −0.153676
\(286\) 11.3607 0.671770
\(287\) −15.8392 −0.934961
\(288\) 8.39232 0.494522
\(289\) 14.9665 0.880380
\(290\) −22.3680 −1.31349
\(291\) −12.4868 −0.731990
\(292\) −0.757587 −0.0443345
\(293\) 5.14307 0.300462 0.150231 0.988651i \(-0.451998\pi\)
0.150231 + 0.988651i \(0.451998\pi\)
\(294\) 8.55144 0.498730
\(295\) −5.54910 −0.323081
\(296\) −25.4975 −1.48201
\(297\) 1.89558 0.109993
\(298\) 36.7436 2.12850
\(299\) −18.9850 −1.09793
\(300\) −9.72834 −0.561666
\(301\) −31.6924 −1.82672
\(302\) 3.01979 0.173769
\(303\) −4.57178 −0.262642
\(304\) 2.56149 0.146911
\(305\) −1.01018 −0.0578427
\(306\) 50.5778 2.89134
\(307\) 28.1017 1.60385 0.801925 0.597425i \(-0.203809\pi\)
0.801925 + 0.597425i \(0.203809\pi\)
\(308\) 10.8516 0.618326
\(309\) 14.3616 0.817002
\(310\) 15.8325 0.899224
\(311\) −14.1909 −0.804692 −0.402346 0.915488i \(-0.631805\pi\)
−0.402346 + 0.915488i \(0.631805\pi\)
\(312\) 51.5733 2.91976
\(313\) −9.46083 −0.534758 −0.267379 0.963591i \(-0.586158\pi\)
−0.267379 + 0.963591i \(0.586158\pi\)
\(314\) −29.2208 −1.64903
\(315\) −10.7961 −0.608293
\(316\) 27.3245 1.53712
\(317\) −23.8673 −1.34052 −0.670260 0.742126i \(-0.733818\pi\)
−0.670260 + 0.742126i \(0.733818\pi\)
\(318\) −23.7111 −1.32965
\(319\) −9.32825 −0.522282
\(320\) −10.5171 −0.587926
\(321\) 11.2095 0.625653
\(322\) −27.8064 −1.54959
\(323\) −5.65389 −0.314591
\(324\) −23.5270 −1.30705
\(325\) 4.73780 0.262806
\(326\) −14.6204 −0.809748
\(327\) 33.7368 1.86565
\(328\) −22.9652 −1.26804
\(329\) 0.854966 0.0471358
\(330\) −6.22094 −0.342451
\(331\) −13.1843 −0.724674 −0.362337 0.932047i \(-0.618021\pi\)
−0.362337 + 0.932047i \(0.618021\pi\)
\(332\) −51.3877 −2.82027
\(333\) 22.6707 1.24235
\(334\) −2.55902 −0.140023
\(335\) 6.98807 0.381799
\(336\) 19.2311 1.04914
\(337\) 17.0148 0.926854 0.463427 0.886135i \(-0.346620\pi\)
0.463427 + 0.886135i \(0.346620\pi\)
\(338\) −22.6521 −1.23211
\(339\) 44.1161 2.39606
\(340\) −21.2010 −1.14979
\(341\) 6.60270 0.357556
\(342\) −8.94566 −0.483726
\(343\) 16.2792 0.878997
\(344\) −45.9507 −2.47750
\(345\) 10.3959 0.559698
\(346\) 31.2418 1.67957
\(347\) −30.2606 −1.62447 −0.812236 0.583329i \(-0.801750\pi\)
−0.812236 + 0.583329i \(0.801750\pi\)
\(348\) −90.7484 −4.86462
\(349\) 5.13463 0.274851 0.137425 0.990512i \(-0.456117\pi\)
0.137425 + 0.990512i \(0.456117\pi\)
\(350\) 6.93920 0.370916
\(351\) −8.98089 −0.479365
\(352\) −2.24955 −0.119902
\(353\) −10.5661 −0.562376 −0.281188 0.959653i \(-0.590728\pi\)
−0.281188 + 0.959653i \(0.590728\pi\)
\(354\) −34.5206 −1.83475
\(355\) −1.02085 −0.0541809
\(356\) −59.3040 −3.14311
\(357\) −42.4481 −2.24659
\(358\) −49.4617 −2.61413
\(359\) 16.5178 0.871778 0.435889 0.900000i \(-0.356434\pi\)
0.435889 + 0.900000i \(0.356434\pi\)
\(360\) −15.6533 −0.824999
\(361\) 1.00000 0.0526316
\(362\) 49.3742 2.59505
\(363\) −2.59435 −0.136168
\(364\) −51.4126 −2.69475
\(365\) −0.202033 −0.0105749
\(366\) −6.28426 −0.328483
\(367\) 19.8761 1.03752 0.518762 0.854919i \(-0.326393\pi\)
0.518762 + 0.854919i \(0.326393\pi\)
\(368\) −10.2642 −0.535061
\(369\) 20.4191 1.06298
\(370\) −14.5716 −0.757539
\(371\) 11.0301 0.572652
\(372\) 64.2333 3.33034
\(373\) −11.4151 −0.591052 −0.295526 0.955335i \(-0.595495\pi\)
−0.295526 + 0.955335i \(0.595495\pi\)
\(374\) −13.5573 −0.701033
\(375\) −2.59435 −0.133972
\(376\) 1.23961 0.0639280
\(377\) 44.1954 2.27618
\(378\) −13.1538 −0.676560
\(379\) 1.99925 0.102695 0.0513474 0.998681i \(-0.483648\pi\)
0.0513474 + 0.998681i \(0.483648\pi\)
\(380\) 3.74982 0.192362
\(381\) 25.4310 1.30287
\(382\) −20.1433 −1.03062
\(383\) −7.07007 −0.361264 −0.180632 0.983551i \(-0.557814\pi\)
−0.180632 + 0.983551i \(0.557814\pi\)
\(384\) −53.7541 −2.74313
\(385\) 2.89389 0.147487
\(386\) −27.5713 −1.40334
\(387\) 40.8563 2.07684
\(388\) 18.0481 0.916256
\(389\) 17.0237 0.863135 0.431568 0.902081i \(-0.357961\pi\)
0.431568 + 0.902081i \(0.357961\pi\)
\(390\) 29.4735 1.49245
\(391\) 22.6559 1.14576
\(392\) −5.76771 −0.291313
\(393\) 34.8636 1.75863
\(394\) −64.8327 −3.26623
\(395\) 7.28690 0.366644
\(396\) −13.9893 −0.702988
\(397\) −25.3590 −1.27273 −0.636366 0.771387i \(-0.719563\pi\)
−0.636366 + 0.771387i \(0.719563\pi\)
\(398\) 12.4320 0.623161
\(399\) 7.50778 0.375859
\(400\) 2.56149 0.128074
\(401\) 19.6449 0.981019 0.490509 0.871436i \(-0.336811\pi\)
0.490509 + 0.871436i \(0.336811\pi\)
\(402\) 43.4723 2.16820
\(403\) −31.2823 −1.55828
\(404\) 6.60795 0.328758
\(405\) −6.27417 −0.311766
\(406\) 64.7306 3.21253
\(407\) −6.07686 −0.301219
\(408\) −61.5454 −3.04695
\(409\) −28.6527 −1.41678 −0.708392 0.705819i \(-0.750579\pi\)
−0.708392 + 0.705819i \(0.750579\pi\)
\(410\) −13.1244 −0.648167
\(411\) 42.0600 2.07467
\(412\) −20.7579 −1.02267
\(413\) 16.0585 0.790187
\(414\) 35.8465 1.76176
\(415\) −13.7041 −0.672706
\(416\) 10.6579 0.522548
\(417\) −49.3893 −2.41861
\(418\) 2.39788 0.117284
\(419\) −2.80518 −0.137042 −0.0685211 0.997650i \(-0.521828\pi\)
−0.0685211 + 0.997650i \(0.521828\pi\)
\(420\) 28.1528 1.37372
\(421\) 3.26165 0.158963 0.0794815 0.996836i \(-0.474674\pi\)
0.0794815 + 0.996836i \(0.474674\pi\)
\(422\) 51.6566 2.51461
\(423\) −1.10218 −0.0535897
\(424\) 15.9924 0.776661
\(425\) −5.65389 −0.274254
\(426\) −6.35062 −0.307689
\(427\) 2.92335 0.141471
\(428\) −16.2020 −0.783151
\(429\) 12.2915 0.593440
\(430\) −26.2603 −1.26639
\(431\) 32.7606 1.57802 0.789012 0.614378i \(-0.210593\pi\)
0.789012 + 0.614378i \(0.210593\pi\)
\(432\) −4.85551 −0.233611
\(433\) −21.8656 −1.05079 −0.525396 0.850858i \(-0.676083\pi\)
−0.525396 + 0.850858i \(0.676083\pi\)
\(434\) −45.8175 −2.19931
\(435\) −24.2008 −1.16034
\(436\) −48.7624 −2.33529
\(437\) −4.00714 −0.191688
\(438\) −1.25684 −0.0600539
\(439\) 30.6280 1.46180 0.730898 0.682486i \(-0.239101\pi\)
0.730898 + 0.682486i \(0.239101\pi\)
\(440\) 4.19584 0.200029
\(441\) 5.12825 0.244202
\(442\) 64.2319 3.05520
\(443\) 4.54914 0.216136 0.108068 0.994144i \(-0.465534\pi\)
0.108068 + 0.994144i \(0.465534\pi\)
\(444\) −59.1177 −2.80560
\(445\) −15.8152 −0.749711
\(446\) 64.6467 3.06111
\(447\) 39.7542 1.88031
\(448\) 30.4355 1.43794
\(449\) 11.5308 0.544172 0.272086 0.962273i \(-0.412286\pi\)
0.272086 + 0.962273i \(0.412286\pi\)
\(450\) −8.94566 −0.421702
\(451\) −5.47333 −0.257729
\(452\) −63.7644 −2.99923
\(453\) 3.26722 0.153507
\(454\) −21.6425 −1.01573
\(455\) −13.7107 −0.642767
\(456\) 10.8855 0.509760
\(457\) 11.3778 0.532231 0.266115 0.963941i \(-0.414260\pi\)
0.266115 + 0.963941i \(0.414260\pi\)
\(458\) 33.0180 1.54283
\(459\) 10.7174 0.500246
\(460\) −15.0260 −0.700593
\(461\) 4.37265 0.203655 0.101827 0.994802i \(-0.467531\pi\)
0.101827 + 0.994802i \(0.467531\pi\)
\(462\) 18.0027 0.837563
\(463\) −9.31982 −0.433129 −0.216564 0.976268i \(-0.569485\pi\)
−0.216564 + 0.976268i \(0.569485\pi\)
\(464\) 23.8942 1.10926
\(465\) 17.1297 0.794372
\(466\) 5.88888 0.272797
\(467\) −28.0711 −1.29897 −0.649487 0.760372i \(-0.725016\pi\)
−0.649487 + 0.760372i \(0.725016\pi\)
\(468\) 66.2784 3.06372
\(469\) −20.2227 −0.933799
\(470\) 0.708423 0.0326771
\(471\) −31.6151 −1.45675
\(472\) 23.2831 1.07169
\(473\) −10.9515 −0.503550
\(474\) 45.3313 2.08214
\(475\) 1.00000 0.0458831
\(476\) 61.3536 2.81214
\(477\) −14.2194 −0.651060
\(478\) 54.7769 2.50544
\(479\) −5.65184 −0.258239 −0.129120 0.991629i \(-0.541215\pi\)
−0.129120 + 0.991629i \(0.541215\pi\)
\(480\) −5.83613 −0.266382
\(481\) 28.7909 1.31275
\(482\) −38.6492 −1.76042
\(483\) −30.0847 −1.36890
\(484\) 3.74982 0.170446
\(485\) 4.81308 0.218550
\(486\) −52.6673 −2.38904
\(487\) −6.09349 −0.276122 −0.138061 0.990424i \(-0.544087\pi\)
−0.138061 + 0.990424i \(0.544087\pi\)
\(488\) 4.23855 0.191870
\(489\) −15.8183 −0.715330
\(490\) −3.29618 −0.148906
\(491\) 8.56286 0.386436 0.193218 0.981156i \(-0.438107\pi\)
0.193218 + 0.981156i \(0.438107\pi\)
\(492\) −53.2464 −2.40053
\(493\) −52.7409 −2.37533
\(494\) −11.3607 −0.511140
\(495\) −3.73066 −0.167681
\(496\) −16.9127 −0.759404
\(497\) 2.95422 0.132515
\(498\) −85.2522 −3.82024
\(499\) −1.35537 −0.0606749 −0.0303374 0.999540i \(-0.509658\pi\)
−0.0303374 + 0.999540i \(0.509658\pi\)
\(500\) 3.74982 0.167697
\(501\) −2.76870 −0.123696
\(502\) 45.2619 2.02014
\(503\) 13.9030 0.619903 0.309952 0.950752i \(-0.399687\pi\)
0.309952 + 0.950752i \(0.399687\pi\)
\(504\) 45.2989 2.01777
\(505\) 1.76221 0.0784172
\(506\) −9.60863 −0.427156
\(507\) −24.5082 −1.08845
\(508\) −36.7574 −1.63084
\(509\) −3.21978 −0.142714 −0.0713572 0.997451i \(-0.522733\pi\)
−0.0713572 + 0.997451i \(0.522733\pi\)
\(510\) −35.1725 −1.55746
\(511\) 0.584663 0.0258640
\(512\) 27.2574 1.20462
\(513\) −1.89558 −0.0836920
\(514\) −17.9368 −0.791160
\(515\) −5.53571 −0.243933
\(516\) −106.540 −4.69015
\(517\) 0.295438 0.0129933
\(518\) 42.1686 1.85278
\(519\) 33.8016 1.48373
\(520\) −19.8791 −0.871755
\(521\) 3.09750 0.135704 0.0678520 0.997695i \(-0.478385\pi\)
0.0678520 + 0.997695i \(0.478385\pi\)
\(522\) −83.4474 −3.65239
\(523\) 13.2007 0.577228 0.288614 0.957446i \(-0.406806\pi\)
0.288614 + 0.957446i \(0.406806\pi\)
\(524\) −50.3910 −2.20134
\(525\) 7.50778 0.327666
\(526\) 42.6111 1.85793
\(527\) 37.3309 1.62616
\(528\) 6.64540 0.289204
\(529\) −6.94281 −0.301861
\(530\) 9.13949 0.396994
\(531\) −20.7018 −0.898381
\(532\) −10.8516 −0.470475
\(533\) 25.9316 1.12322
\(534\) −98.3852 −4.25755
\(535\) −4.32073 −0.186802
\(536\) −29.3209 −1.26647
\(537\) −53.5144 −2.30932
\(538\) −62.1817 −2.68084
\(539\) −1.37462 −0.0592092
\(540\) −7.10809 −0.305883
\(541\) −6.57608 −0.282728 −0.141364 0.989958i \(-0.545149\pi\)
−0.141364 + 0.989958i \(0.545149\pi\)
\(542\) 39.0102 1.67563
\(543\) 53.4198 2.29246
\(544\) −12.7187 −0.545311
\(545\) −13.0039 −0.557028
\(546\) −85.2933 −3.65022
\(547\) −23.9559 −1.02428 −0.512139 0.858902i \(-0.671147\pi\)
−0.512139 + 0.858902i \(0.671147\pi\)
\(548\) −60.7926 −2.59693
\(549\) −3.76863 −0.160841
\(550\) 2.39788 0.102246
\(551\) 9.32825 0.397397
\(552\) −43.6197 −1.85658
\(553\) −21.0875 −0.896732
\(554\) 42.9740 1.82579
\(555\) −15.7655 −0.669208
\(556\) 71.3862 3.02745
\(557\) −11.2404 −0.476271 −0.238135 0.971232i \(-0.576536\pi\)
−0.238135 + 0.971232i \(0.576536\pi\)
\(558\) 59.0655 2.50044
\(559\) 51.8860 2.19454
\(560\) −7.41267 −0.313243
\(561\) −14.6682 −0.619291
\(562\) 69.1939 2.91877
\(563\) 44.9880 1.89602 0.948009 0.318242i \(-0.103093\pi\)
0.948009 + 0.318242i \(0.103093\pi\)
\(564\) 2.87412 0.121022
\(565\) −17.0047 −0.715392
\(566\) 25.8060 1.08471
\(567\) 18.1568 0.762513
\(568\) 4.28331 0.179724
\(569\) 33.2099 1.39223 0.696115 0.717930i \(-0.254910\pi\)
0.696115 + 0.717930i \(0.254910\pi\)
\(570\) 6.22094 0.260566
\(571\) −44.6440 −1.86829 −0.934146 0.356891i \(-0.883837\pi\)
−0.934146 + 0.356891i \(0.883837\pi\)
\(572\) −17.7659 −0.742829
\(573\) −21.7938 −0.910448
\(574\) 37.9806 1.58528
\(575\) −4.00714 −0.167109
\(576\) −39.2358 −1.63483
\(577\) −45.6776 −1.90158 −0.950792 0.309831i \(-0.899728\pi\)
−0.950792 + 0.309831i \(0.899728\pi\)
\(578\) −35.8877 −1.49273
\(579\) −29.8304 −1.23971
\(580\) 34.9792 1.45243
\(581\) 39.6581 1.64530
\(582\) 29.9418 1.24113
\(583\) 3.81149 0.157856
\(584\) 0.847700 0.0350781
\(585\) 17.6751 0.730776
\(586\) −12.3325 −0.509449
\(587\) −17.5933 −0.726155 −0.363078 0.931759i \(-0.618274\pi\)
−0.363078 + 0.931759i \(0.618274\pi\)
\(588\) −13.3728 −0.551485
\(589\) −6.60270 −0.272060
\(590\) 13.3061 0.547802
\(591\) −70.1449 −2.88538
\(592\) 15.5658 0.639750
\(593\) 32.4709 1.33342 0.666710 0.745317i \(-0.267702\pi\)
0.666710 + 0.745317i \(0.267702\pi\)
\(594\) −4.54538 −0.186499
\(595\) 16.3618 0.670767
\(596\) −57.4598 −2.35365
\(597\) 13.4507 0.550499
\(598\) 45.5238 1.86161
\(599\) 1.31594 0.0537679 0.0268839 0.999639i \(-0.491442\pi\)
0.0268839 + 0.999639i \(0.491442\pi\)
\(600\) 10.8855 0.444398
\(601\) −4.53331 −0.184918 −0.0924588 0.995717i \(-0.529473\pi\)
−0.0924588 + 0.995717i \(0.529473\pi\)
\(602\) 75.9946 3.09731
\(603\) 26.0701 1.06166
\(604\) −4.72236 −0.192150
\(605\) 1.00000 0.0406558
\(606\) 10.9626 0.445324
\(607\) −14.2654 −0.579016 −0.289508 0.957176i \(-0.593492\pi\)
−0.289508 + 0.957176i \(0.593492\pi\)
\(608\) 2.24955 0.0912315
\(609\) 70.0344 2.83794
\(610\) 2.42228 0.0980754
\(611\) −1.39972 −0.0566268
\(612\) −79.0938 −3.19718
\(613\) 5.06662 0.204639 0.102319 0.994752i \(-0.467374\pi\)
0.102319 + 0.994752i \(0.467374\pi\)
\(614\) −67.3845 −2.71942
\(615\) −14.1997 −0.572589
\(616\) −12.1423 −0.489228
\(617\) 19.5460 0.786893 0.393446 0.919348i \(-0.371283\pi\)
0.393446 + 0.919348i \(0.371283\pi\)
\(618\) −34.4373 −1.38527
\(619\) 8.78654 0.353161 0.176580 0.984286i \(-0.443496\pi\)
0.176580 + 0.984286i \(0.443496\pi\)
\(620\) −24.7589 −0.994342
\(621\) 7.59587 0.304812
\(622\) 34.0280 1.36440
\(623\) 45.7675 1.83363
\(624\) −31.4846 −1.26039
\(625\) 1.00000 0.0400000
\(626\) 22.6859 0.906712
\(627\) 2.59435 0.103608
\(628\) 45.6957 1.82346
\(629\) −34.3579 −1.36994
\(630\) 25.8878 1.03139
\(631\) −0.0559751 −0.00222833 −0.00111417 0.999999i \(-0.500355\pi\)
−0.00111417 + 0.999999i \(0.500355\pi\)
\(632\) −30.5747 −1.21620
\(633\) 55.8892 2.22140
\(634\) 57.2308 2.27293
\(635\) −9.80245 −0.388998
\(636\) 37.0795 1.47030
\(637\) 6.51269 0.258042
\(638\) 22.3680 0.885558
\(639\) −3.80843 −0.150659
\(640\) 20.7197 0.819017
\(641\) 4.49262 0.177448 0.0887239 0.996056i \(-0.471721\pi\)
0.0887239 + 0.996056i \(0.471721\pi\)
\(642\) −26.8790 −1.06083
\(643\) −5.48669 −0.216374 −0.108187 0.994131i \(-0.534505\pi\)
−0.108187 + 0.994131i \(0.534505\pi\)
\(644\) 43.4838 1.71350
\(645\) −28.4120 −1.11872
\(646\) 13.5573 0.533406
\(647\) −34.5798 −1.35947 −0.679736 0.733456i \(-0.737906\pi\)
−0.679736 + 0.733456i \(0.737906\pi\)
\(648\) 26.3254 1.03416
\(649\) 5.54910 0.217821
\(650\) −11.3607 −0.445602
\(651\) −49.5716 −1.94286
\(652\) 22.8635 0.895402
\(653\) 11.3537 0.444304 0.222152 0.975012i \(-0.428692\pi\)
0.222152 + 0.975012i \(0.428692\pi\)
\(654\) −80.8967 −3.16331
\(655\) −13.4383 −0.525076
\(656\) 14.0199 0.547384
\(657\) −0.753717 −0.0294053
\(658\) −2.05010 −0.0799213
\(659\) 27.1448 1.05741 0.528706 0.848805i \(-0.322677\pi\)
0.528706 + 0.848805i \(0.322677\pi\)
\(660\) 9.72834 0.378675
\(661\) 5.01901 0.195217 0.0976084 0.995225i \(-0.468881\pi\)
0.0976084 + 0.995225i \(0.468881\pi\)
\(662\) 31.6143 1.22873
\(663\) 69.4949 2.69896
\(664\) 57.5002 2.23144
\(665\) −2.89389 −0.112220
\(666\) −54.3615 −2.10647
\(667\) −37.3796 −1.44734
\(668\) 4.00181 0.154835
\(669\) 69.9436 2.70418
\(670\) −16.7565 −0.647362
\(671\) 1.01018 0.0389975
\(672\) 16.8892 0.651513
\(673\) −38.5035 −1.48420 −0.742100 0.670289i \(-0.766170\pi\)
−0.742100 + 0.670289i \(0.766170\pi\)
\(674\) −40.7994 −1.57153
\(675\) −1.89558 −0.0729610
\(676\) 35.4236 1.36244
\(677\) 17.8660 0.686647 0.343324 0.939217i \(-0.388447\pi\)
0.343324 + 0.939217i \(0.388447\pi\)
\(678\) −105.785 −4.06265
\(679\) −13.9285 −0.534528
\(680\) 23.7228 0.909729
\(681\) −23.4158 −0.897297
\(682\) −15.8325 −0.606257
\(683\) 44.9512 1.72001 0.860005 0.510286i \(-0.170460\pi\)
0.860005 + 0.510286i \(0.170460\pi\)
\(684\) 13.9893 0.534894
\(685\) −16.2122 −0.619435
\(686\) −39.0356 −1.49039
\(687\) 35.7234 1.36293
\(688\) 28.0521 1.06948
\(689\) −18.0581 −0.687958
\(690\) −24.9282 −0.948999
\(691\) 24.1309 0.917983 0.458991 0.888441i \(-0.348211\pi\)
0.458991 + 0.888441i \(0.348211\pi\)
\(692\) −48.8561 −1.85723
\(693\) 10.7961 0.410111
\(694\) 72.5611 2.75438
\(695\) 19.0373 0.722124
\(696\) 101.543 3.84896
\(697\) −30.9456 −1.17215
\(698\) −12.3122 −0.466024
\(699\) 6.37139 0.240988
\(700\) −10.8516 −0.410151
\(701\) −1.53772 −0.0580789 −0.0290395 0.999578i \(-0.509245\pi\)
−0.0290395 + 0.999578i \(0.509245\pi\)
\(702\) 21.5351 0.812789
\(703\) 6.07686 0.229193
\(704\) 10.5171 0.396379
\(705\) 0.766469 0.0288669
\(706\) 25.3362 0.953540
\(707\) −5.09964 −0.191792
\(708\) 53.9835 2.02882
\(709\) 5.19348 0.195045 0.0975226 0.995233i \(-0.468908\pi\)
0.0975226 + 0.995233i \(0.468908\pi\)
\(710\) 2.44787 0.0918668
\(711\) 27.1849 1.01951
\(712\) 66.3580 2.48687
\(713\) 26.4580 0.990858
\(714\) 101.785 3.80922
\(715\) −4.73780 −0.177184
\(716\) 77.3485 2.89065
\(717\) 59.2652 2.21330
\(718\) −39.6077 −1.47815
\(719\) −37.4841 −1.39792 −0.698960 0.715160i \(-0.746354\pi\)
−0.698960 + 0.715160i \(0.746354\pi\)
\(720\) 9.55603 0.356132
\(721\) 16.0198 0.596607
\(722\) −2.39788 −0.0892398
\(723\) −41.8160 −1.55515
\(724\) −77.2117 −2.86955
\(725\) 9.32825 0.346443
\(726\) 6.22094 0.230881
\(727\) 28.1916 1.04557 0.522785 0.852464i \(-0.324893\pi\)
0.522785 + 0.852464i \(0.324893\pi\)
\(728\) 57.5279 2.13213
\(729\) −38.1602 −1.41334
\(730\) 0.484451 0.0179303
\(731\) −61.9185 −2.29014
\(732\) 9.82736 0.363230
\(733\) −18.1906 −0.671884 −0.335942 0.941883i \(-0.609055\pi\)
−0.335942 + 0.941883i \(0.609055\pi\)
\(734\) −47.6604 −1.75918
\(735\) −3.56626 −0.131543
\(736\) −9.01428 −0.332271
\(737\) −6.98807 −0.257409
\(738\) −48.9626 −1.80234
\(739\) 5.65484 0.208017 0.104008 0.994576i \(-0.466833\pi\)
0.104008 + 0.994576i \(0.466833\pi\)
\(740\) 22.7871 0.837670
\(741\) −12.2915 −0.451540
\(742\) −26.4487 −0.970963
\(743\) −44.5565 −1.63462 −0.817310 0.576198i \(-0.804536\pi\)
−0.817310 + 0.576198i \(0.804536\pi\)
\(744\) −71.8737 −2.63502
\(745\) −15.3234 −0.561405
\(746\) 27.3720 1.00216
\(747\) −51.1252 −1.87057
\(748\) 21.2010 0.775187
\(749\) 12.5037 0.456877
\(750\) 6.22094 0.227156
\(751\) −18.8205 −0.686769 −0.343384 0.939195i \(-0.611573\pi\)
−0.343384 + 0.939195i \(0.611573\pi\)
\(752\) −0.756760 −0.0275962
\(753\) 48.9705 1.78459
\(754\) −105.975 −3.85939
\(755\) −1.25936 −0.0458328
\(756\) 20.5701 0.748126
\(757\) 2.97780 0.108230 0.0541150 0.998535i \(-0.482766\pi\)
0.0541150 + 0.998535i \(0.482766\pi\)
\(758\) −4.79397 −0.174125
\(759\) −10.3959 −0.377348
\(760\) −4.19584 −0.152199
\(761\) −41.9642 −1.52120 −0.760601 0.649219i \(-0.775096\pi\)
−0.760601 + 0.649219i \(0.775096\pi\)
\(762\) −60.9804 −2.20909
\(763\) 37.6320 1.36237
\(764\) 31.5002 1.13964
\(765\) −21.0927 −0.762609
\(766\) 16.9532 0.612542
\(767\) −26.2905 −0.949295
\(768\) 74.3256 2.68199
\(769\) −2.33683 −0.0842683 −0.0421341 0.999112i \(-0.513416\pi\)
−0.0421341 + 0.999112i \(0.513416\pi\)
\(770\) −6.93920 −0.250072
\(771\) −19.4065 −0.698908
\(772\) 43.1162 1.55179
\(773\) 4.40125 0.158302 0.0791509 0.996863i \(-0.474779\pi\)
0.0791509 + 0.996863i \(0.474779\pi\)
\(774\) −97.9683 −3.52140
\(775\) −6.60270 −0.237176
\(776\) −20.1949 −0.724955
\(777\) 45.6237 1.63674
\(778\) −40.8207 −1.46349
\(779\) 5.47333 0.196102
\(780\) −46.0909 −1.65032
\(781\) 1.02085 0.0365288
\(782\) −54.3262 −1.94270
\(783\) −17.6825 −0.631920
\(784\) 3.52108 0.125753
\(785\) 12.1861 0.434942
\(786\) −83.5985 −2.98186
\(787\) −13.1902 −0.470180 −0.235090 0.971974i \(-0.575539\pi\)
−0.235090 + 0.971974i \(0.575539\pi\)
\(788\) 101.386 3.61172
\(789\) 46.1025 1.64129
\(790\) −17.4731 −0.621664
\(791\) 49.2097 1.74970
\(792\) 15.6533 0.556214
\(793\) −4.78602 −0.169957
\(794\) 60.8078 2.15799
\(795\) 9.88835 0.350704
\(796\) −19.4413 −0.689078
\(797\) −39.1687 −1.38743 −0.693713 0.720252i \(-0.744026\pi\)
−0.693713 + 0.720252i \(0.744026\pi\)
\(798\) −18.0027 −0.637290
\(799\) 1.67037 0.0590935
\(800\) 2.24955 0.0795338
\(801\) −59.0010 −2.08470
\(802\) −47.1060 −1.66337
\(803\) 0.202033 0.00712960
\(804\) −67.9823 −2.39755
\(805\) 11.5962 0.408714
\(806\) 75.0111 2.64215
\(807\) −67.2766 −2.36825
\(808\) −7.39394 −0.260118
\(809\) 18.2003 0.639887 0.319944 0.947437i \(-0.396336\pi\)
0.319944 + 0.947437i \(0.396336\pi\)
\(810\) 15.0447 0.528616
\(811\) −54.6434 −1.91879 −0.959395 0.282065i \(-0.908981\pi\)
−0.959395 + 0.282065i \(0.908981\pi\)
\(812\) −101.226 −3.55234
\(813\) 42.2065 1.48025
\(814\) 14.5716 0.510733
\(815\) 6.09722 0.213576
\(816\) 37.5723 1.31530
\(817\) 10.9515 0.383144
\(818\) 68.7056 2.40224
\(819\) −51.1499 −1.78732
\(820\) 20.5240 0.716729
\(821\) 18.3540 0.640560 0.320280 0.947323i \(-0.396223\pi\)
0.320280 + 0.947323i \(0.396223\pi\)
\(822\) −100.855 −3.51772
\(823\) 9.63416 0.335826 0.167913 0.985802i \(-0.446297\pi\)
0.167913 + 0.985802i \(0.446297\pi\)
\(824\) 23.2270 0.809150
\(825\) 2.59435 0.0903237
\(826\) −38.5063 −1.33981
\(827\) 26.2829 0.913947 0.456973 0.889480i \(-0.348933\pi\)
0.456973 + 0.889480i \(0.348933\pi\)
\(828\) −56.0570 −1.94812
\(829\) −45.2690 −1.57226 −0.786128 0.618064i \(-0.787917\pi\)
−0.786128 + 0.618064i \(0.787917\pi\)
\(830\) 32.8607 1.14061
\(831\) 46.4952 1.61290
\(832\) −49.8281 −1.72748
\(833\) −7.77197 −0.269283
\(834\) 118.430 4.10088
\(835\) 1.06720 0.0369321
\(836\) −3.74982 −0.129690
\(837\) 12.5160 0.432615
\(838\) 6.72648 0.232362
\(839\) 23.0656 0.796315 0.398157 0.917317i \(-0.369650\pi\)
0.398157 + 0.917317i \(0.369650\pi\)
\(840\) −31.5015 −1.08690
\(841\) 58.0162 2.00056
\(842\) −7.82104 −0.269531
\(843\) 74.8634 2.57843
\(844\) −80.7810 −2.78060
\(845\) 9.44675 0.324978
\(846\) 2.64289 0.0908643
\(847\) −2.89389 −0.0994354
\(848\) −9.76309 −0.335266
\(849\) 27.9205 0.958228
\(850\) 13.5573 0.465013
\(851\) −24.3508 −0.834736
\(852\) 9.93115 0.340235
\(853\) −10.1175 −0.346418 −0.173209 0.984885i \(-0.555414\pi\)
−0.173209 + 0.984885i \(0.555414\pi\)
\(854\) −7.00983 −0.239872
\(855\) 3.73066 0.127586
\(856\) 18.1291 0.619641
\(857\) 17.5975 0.601119 0.300559 0.953763i \(-0.402827\pi\)
0.300559 + 0.953763i \(0.402827\pi\)
\(858\) −29.4735 −1.00621
\(859\) 51.9873 1.77378 0.886891 0.461978i \(-0.152860\pi\)
0.886891 + 0.461978i \(0.152860\pi\)
\(860\) 41.0661 1.40034
\(861\) 41.0926 1.40043
\(862\) −78.5560 −2.67563
\(863\) −42.2968 −1.43980 −0.719900 0.694078i \(-0.755812\pi\)
−0.719900 + 0.694078i \(0.755812\pi\)
\(864\) −4.26422 −0.145072
\(865\) −13.0289 −0.442997
\(866\) 52.4310 1.78168
\(867\) −38.8282 −1.31868
\(868\) 71.6497 2.43195
\(869\) −7.28690 −0.247191
\(870\) 58.0304 1.96742
\(871\) 33.1081 1.12182
\(872\) 54.5625 1.84772
\(873\) 17.9559 0.607716
\(874\) 9.60863 0.325017
\(875\) −2.89389 −0.0978315
\(876\) 1.96545 0.0664063
\(877\) −4.60606 −0.155535 −0.0777677 0.996972i \(-0.524779\pi\)
−0.0777677 + 0.996972i \(0.524779\pi\)
\(878\) −73.4423 −2.47856
\(879\) −13.3429 −0.450046
\(880\) −2.56149 −0.0863477
\(881\) 45.1124 1.51987 0.759937 0.649997i \(-0.225230\pi\)
0.759937 + 0.649997i \(0.225230\pi\)
\(882\) −12.2969 −0.414059
\(883\) −40.3849 −1.35906 −0.679530 0.733648i \(-0.737816\pi\)
−0.679530 + 0.733648i \(0.737816\pi\)
\(884\) −100.446 −3.37837
\(885\) 14.3963 0.483927
\(886\) −10.9083 −0.366471
\(887\) 50.2462 1.68710 0.843551 0.537050i \(-0.180461\pi\)
0.843551 + 0.537050i \(0.180461\pi\)
\(888\) 66.1496 2.21984
\(889\) 28.3672 0.951407
\(890\) 37.9229 1.27118
\(891\) 6.27417 0.210192
\(892\) −101.095 −3.38491
\(893\) −0.295438 −0.00988645
\(894\) −95.3257 −3.18817
\(895\) 20.6273 0.689494
\(896\) −59.9606 −2.00314
\(897\) 49.2538 1.64454
\(898\) −27.6495 −0.922674
\(899\) −61.5916 −2.05420
\(900\) 13.9893 0.466309
\(901\) 21.5498 0.717926
\(902\) 13.1244 0.436994
\(903\) 82.2213 2.73615
\(904\) 71.3490 2.37303
\(905\) −20.5908 −0.684462
\(906\) −7.83439 −0.260280
\(907\) 58.4194 1.93979 0.969893 0.243532i \(-0.0783062\pi\)
0.969893 + 0.243532i \(0.0783062\pi\)
\(908\) 33.8447 1.12318
\(909\) 6.57419 0.218052
\(910\) 32.8766 1.08985
\(911\) −39.2409 −1.30011 −0.650054 0.759888i \(-0.725254\pi\)
−0.650054 + 0.759888i \(0.725254\pi\)
\(912\) −6.64540 −0.220051
\(913\) 13.7041 0.453539
\(914\) −27.2826 −0.902427
\(915\) 2.62076 0.0866396
\(916\) −51.6337 −1.70603
\(917\) 38.8889 1.28422
\(918\) −25.6990 −0.848195
\(919\) 18.4113 0.607334 0.303667 0.952778i \(-0.401789\pi\)
0.303667 + 0.952778i \(0.401789\pi\)
\(920\) 16.8133 0.554319
\(921\) −72.9057 −2.40233
\(922\) −10.4851 −0.345308
\(923\) −4.83657 −0.159198
\(924\) −28.1528 −0.926159
\(925\) 6.07686 0.199806
\(926\) 22.3478 0.734393
\(927\) −20.6518 −0.678296
\(928\) 20.9844 0.688847
\(929\) −32.8679 −1.07836 −0.539180 0.842191i \(-0.681266\pi\)
−0.539180 + 0.842191i \(0.681266\pi\)
\(930\) −41.0750 −1.34690
\(931\) 1.37462 0.0450515
\(932\) −9.20907 −0.301653
\(933\) 36.8162 1.20531
\(934\) 67.3110 2.20248
\(935\) 5.65389 0.184902
\(936\) −74.1620 −2.42406
\(937\) 4.34616 0.141983 0.0709914 0.997477i \(-0.477384\pi\)
0.0709914 + 0.997477i \(0.477384\pi\)
\(938\) 48.4917 1.58331
\(939\) 24.5447 0.800987
\(940\) −1.10784 −0.0361337
\(941\) −55.1238 −1.79699 −0.898493 0.438989i \(-0.855337\pi\)
−0.898493 + 0.438989i \(0.855337\pi\)
\(942\) 75.8091 2.46999
\(943\) −21.9324 −0.714218
\(944\) −14.2139 −0.462625
\(945\) 5.48562 0.178447
\(946\) 26.2603 0.853797
\(947\) 16.6794 0.542007 0.271004 0.962578i \(-0.412644\pi\)
0.271004 + 0.962578i \(0.412644\pi\)
\(948\) −70.8894 −2.30238
\(949\) −0.957193 −0.0310718
\(950\) −2.39788 −0.0777974
\(951\) 61.9201 2.00790
\(952\) −68.6514 −2.22500
\(953\) 51.8274 1.67885 0.839427 0.543472i \(-0.182891\pi\)
0.839427 + 0.543472i \(0.182891\pi\)
\(954\) 34.0963 1.10391
\(955\) 8.40047 0.271833
\(956\) −85.6605 −2.77046
\(957\) 24.2008 0.782299
\(958\) 13.5524 0.437859
\(959\) 46.9163 1.51501
\(960\) 27.2851 0.880624
\(961\) 12.5957 0.406312
\(962\) −69.0371 −2.22585
\(963\) −16.1192 −0.519433
\(964\) 60.4399 1.94664
\(965\) 11.4982 0.370141
\(966\) 72.1395 2.32105
\(967\) −28.7146 −0.923398 −0.461699 0.887037i \(-0.652760\pi\)
−0.461699 + 0.887037i \(0.652760\pi\)
\(968\) −4.19584 −0.134860
\(969\) 14.6682 0.471210
\(970\) −11.5412 −0.370564
\(971\) 43.9744 1.41121 0.705603 0.708607i \(-0.250676\pi\)
0.705603 + 0.708607i \(0.250676\pi\)
\(972\) 82.3615 2.64175
\(973\) −55.0918 −1.76616
\(974\) 14.6114 0.468180
\(975\) −12.2915 −0.393644
\(976\) −2.58756 −0.0828258
\(977\) 19.2496 0.615848 0.307924 0.951411i \(-0.400366\pi\)
0.307924 + 0.951411i \(0.400366\pi\)
\(978\) 37.9304 1.21288
\(979\) 15.8152 0.505455
\(980\) 5.15458 0.164657
\(981\) −48.5132 −1.54891
\(982\) −20.5327 −0.655224
\(983\) −12.7410 −0.406373 −0.203187 0.979140i \(-0.565130\pi\)
−0.203187 + 0.979140i \(0.565130\pi\)
\(984\) 59.5799 1.89934
\(985\) 27.0376 0.861488
\(986\) 126.466 4.02750
\(987\) −2.21808 −0.0706023
\(988\) 17.7659 0.565208
\(989\) −43.8842 −1.39544
\(990\) 8.94566 0.284312
\(991\) 27.9827 0.888900 0.444450 0.895804i \(-0.353399\pi\)
0.444450 + 0.895804i \(0.353399\pi\)
\(992\) −14.8531 −0.471588
\(993\) 34.2047 1.08545
\(994\) −7.08387 −0.224687
\(995\) −5.18460 −0.164363
\(996\) 133.318 4.22434
\(997\) −47.7121 −1.51106 −0.755528 0.655116i \(-0.772620\pi\)
−0.755528 + 0.655116i \(0.772620\pi\)
\(998\) 3.25002 0.102878
\(999\) −11.5192 −0.364451
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 1045.2.a.d.1.1 5
3.2 odd 2 9405.2.a.v.1.5 5
5.4 even 2 5225.2.a.j.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.d.1.1 5 1.1 even 1 trivial
5225.2.a.j.1.5 5 5.4 even 2
9405.2.a.v.1.5 5 3.2 odd 2