Properties

Label 287.2.a.c.1.2
Level $287$
Weight $2$
Character 287.1
Self dual yes
Analytic conductor $2.292$
Analytic rank $0$
Dimension $3$
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] = [287,2,Mod(1,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, 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("287.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 3 \) 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 1.2
Root \(0.713538\) of defining polynomial
Character \(\chi\) \(=\) 287.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.713538 q^{2} -3.20440 q^{3} -1.49086 q^{4} +2.00000 q^{5} -2.28646 q^{6} +1.00000 q^{7} -2.49086 q^{8} +7.26819 q^{9} +O(q^{10})\) \(q+0.713538 q^{2} -3.20440 q^{3} -1.49086 q^{4} +2.00000 q^{5} -2.28646 q^{6} +1.00000 q^{7} -2.49086 q^{8} +7.26819 q^{9} +1.42708 q^{10} -2.00000 q^{11} +4.77733 q^{12} +5.49086 q^{13} +0.713538 q^{14} -6.40880 q^{15} +1.20440 q^{16} +5.69527 q^{17} +5.18613 q^{18} +4.71354 q^{19} -2.98173 q^{20} -3.20440 q^{21} -1.42708 q^{22} -0.795598 q^{23} +7.98173 q^{24} -1.00000 q^{25} +3.91794 q^{26} -13.6770 q^{27} -1.49086 q^{28} +2.57292 q^{29} -4.57292 q^{30} -1.42708 q^{31} +5.84111 q^{32} +6.40880 q^{33} +4.06379 q^{34} +2.00000 q^{35} -10.8359 q^{36} -11.4543 q^{37} +3.36329 q^{38} -17.5949 q^{39} -4.98173 q^{40} -1.00000 q^{41} -2.28646 q^{42} +11.8228 q^{43} +2.98173 q^{44} +14.5364 q^{45} -0.567690 q^{46} +5.89967 q^{47} -3.85939 q^{48} +1.00000 q^{49} -0.713538 q^{50} -18.2499 q^{51} -8.18613 q^{52} -3.55465 q^{53} -9.75905 q^{54} -4.00000 q^{55} -2.49086 q^{56} -15.1041 q^{57} +1.83588 q^{58} -4.00000 q^{59} +9.55465 q^{60} -5.55465 q^{61} -1.01827 q^{62} +7.26819 q^{63} +1.75905 q^{64} +10.9817 q^{65} +4.57292 q^{66} +7.55465 q^{67} -8.49086 q^{68} +2.54942 q^{69} +1.42708 q^{70} +1.83588 q^{71} -18.1041 q^{72} +9.39053 q^{73} -8.17309 q^{74} +3.20440 q^{75} -7.02724 q^{76} -2.00000 q^{77} -12.5547 q^{78} +10.4088 q^{79} +2.40880 q^{80} +22.0220 q^{81} -0.713538 q^{82} +0.854152 q^{83} +4.77733 q^{84} +11.3905 q^{85} +8.43605 q^{86} -8.24468 q^{87} +4.98173 q^{88} +7.19917 q^{89} +10.3723 q^{90} +5.49086 q^{91} +1.18613 q^{92} +4.57292 q^{93} +4.20964 q^{94} +9.42708 q^{95} -18.7173 q^{96} +5.36852 q^{97} +0.713538 q^{98} -14.5364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - q^{3} + 3 q^{4} + 6 q^{5} - 8 q^{6} + 3 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - q^{3} + 3 q^{4} + 6 q^{5} - 8 q^{6} + 3 q^{7} + 8 q^{9} + 2 q^{10} - 6 q^{11} + 8 q^{12} + 9 q^{13} + q^{14} - 2 q^{15} - 5 q^{16} + q^{17} - 8 q^{18} + 13 q^{19} + 6 q^{20} - q^{21} - 2 q^{22} - 11 q^{23} + 9 q^{24} - 3 q^{25} + 2 q^{26} - 10 q^{27} + 3 q^{28} + 10 q^{29} - 16 q^{30} - 2 q^{31} + 6 q^{32} + 2 q^{33} + 7 q^{34} + 6 q^{35} - 13 q^{36} + 3 q^{37} + 13 q^{38} - 12 q^{39} - 3 q^{41} - 8 q^{42} + 9 q^{43} - 6 q^{44} + 16 q^{45} + 4 q^{46} - 7 q^{47} - 15 q^{48} + 3 q^{49} - q^{50} - 26 q^{51} - q^{52} + 2 q^{53} - 8 q^{54} - 12 q^{55} - 12 q^{57} - 14 q^{58} - 12 q^{59} + 16 q^{60} - 4 q^{61} - 18 q^{62} + 8 q^{63} - 16 q^{64} + 18 q^{65} + 16 q^{66} + 10 q^{67} - 18 q^{68} - 13 q^{69} + 2 q^{70} - 14 q^{71} - 21 q^{72} - 4 q^{73} + 6 q^{74} + q^{75} + 14 q^{76} - 6 q^{77} - 25 q^{78} + 14 q^{79} - 10 q^{80} + 23 q^{81} - q^{82} - 2 q^{83} + 8 q^{84} + 2 q^{85} - 27 q^{86} + 12 q^{87} + 5 q^{89} - 16 q^{90} + 9 q^{91} - 20 q^{92} + 16 q^{93} + 12 q^{94} + 26 q^{95} + 3 q^{96} + 27 q^{97} + q^{98} - 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.713538 0.504548 0.252274 0.967656i \(-0.418822\pi\)
0.252274 + 0.967656i \(0.418822\pi\)
\(3\) −3.20440 −1.85006 −0.925031 0.379892i \(-0.875961\pi\)
−0.925031 + 0.379892i \(0.875961\pi\)
\(4\) −1.49086 −0.745432
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −2.28646 −0.933444
\(7\) 1.00000 0.377964
\(8\) −2.49086 −0.880653
\(9\) 7.26819 2.42273
\(10\) 1.42708 0.451281
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 4.77733 1.37910
\(13\) 5.49086 1.52289 0.761446 0.648229i \(-0.224490\pi\)
0.761446 + 0.648229i \(0.224490\pi\)
\(14\) 0.713538 0.190701
\(15\) −6.40880 −1.65475
\(16\) 1.20440 0.301100
\(17\) 5.69527 1.38130 0.690652 0.723187i \(-0.257323\pi\)
0.690652 + 0.723187i \(0.257323\pi\)
\(18\) 5.18613 1.22238
\(19\) 4.71354 1.08136 0.540680 0.841228i \(-0.318167\pi\)
0.540680 + 0.841228i \(0.318167\pi\)
\(20\) −2.98173 −0.666734
\(21\) −3.20440 −0.699258
\(22\) −1.42708 −0.304254
\(23\) −0.795598 −0.165894 −0.0829469 0.996554i \(-0.526433\pi\)
−0.0829469 + 0.996554i \(0.526433\pi\)
\(24\) 7.98173 1.62926
\(25\) −1.00000 −0.200000
\(26\) 3.91794 0.768371
\(27\) −13.6770 −2.63214
\(28\) −1.49086 −0.281747
\(29\) 2.57292 0.477780 0.238890 0.971047i \(-0.423216\pi\)
0.238890 + 0.971047i \(0.423216\pi\)
\(30\) −4.57292 −0.834898
\(31\) −1.42708 −0.256310 −0.128155 0.991754i \(-0.540906\pi\)
−0.128155 + 0.991754i \(0.540906\pi\)
\(32\) 5.84111 1.03257
\(33\) 6.40880 1.11563
\(34\) 4.06379 0.696934
\(35\) 2.00000 0.338062
\(36\) −10.8359 −1.80598
\(37\) −11.4543 −1.88308 −0.941539 0.336904i \(-0.890620\pi\)
−0.941539 + 0.336904i \(0.890620\pi\)
\(38\) 3.36329 0.545597
\(39\) −17.5949 −2.81744
\(40\) −4.98173 −0.787680
\(41\) −1.00000 −0.156174
\(42\) −2.28646 −0.352809
\(43\) 11.8228 1.80297 0.901483 0.432814i \(-0.142479\pi\)
0.901483 + 0.432814i \(0.142479\pi\)
\(44\) 2.98173 0.449512
\(45\) 14.5364 2.16696
\(46\) −0.567690 −0.0837013
\(47\) 5.89967 0.860555 0.430277 0.902697i \(-0.358416\pi\)
0.430277 + 0.902697i \(0.358416\pi\)
\(48\) −3.85939 −0.557054
\(49\) 1.00000 0.142857
\(50\) −0.713538 −0.100910
\(51\) −18.2499 −2.55550
\(52\) −8.18613 −1.13521
\(53\) −3.55465 −0.488269 −0.244134 0.969741i \(-0.578504\pi\)
−0.244134 + 0.969741i \(0.578504\pi\)
\(54\) −9.75905 −1.32804
\(55\) −4.00000 −0.539360
\(56\) −2.49086 −0.332856
\(57\) −15.1041 −2.00058
\(58\) 1.83588 0.241063
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 9.55465 1.23350
\(61\) −5.55465 −0.711200 −0.355600 0.934638i \(-0.615723\pi\)
−0.355600 + 0.934638i \(0.615723\pi\)
\(62\) −1.01827 −0.129321
\(63\) 7.26819 0.915706
\(64\) 1.75905 0.219882
\(65\) 10.9817 1.36212
\(66\) 4.57292 0.562888
\(67\) 7.55465 0.922948 0.461474 0.887154i \(-0.347321\pi\)
0.461474 + 0.887154i \(0.347321\pi\)
\(68\) −8.49086 −1.02967
\(69\) 2.54942 0.306914
\(70\) 1.42708 0.170568
\(71\) 1.83588 0.217879 0.108939 0.994048i \(-0.465255\pi\)
0.108939 + 0.994048i \(0.465255\pi\)
\(72\) −18.1041 −2.13358
\(73\) 9.39053 1.09908 0.549539 0.835468i \(-0.314803\pi\)
0.549539 + 0.835468i \(0.314803\pi\)
\(74\) −8.17309 −0.950102
\(75\) 3.20440 0.370012
\(76\) −7.02724 −0.806080
\(77\) −2.00000 −0.227921
\(78\) −12.5547 −1.42153
\(79\) 10.4088 1.17108 0.585541 0.810643i \(-0.300882\pi\)
0.585541 + 0.810643i \(0.300882\pi\)
\(80\) 2.40880 0.269312
\(81\) 22.0220 2.44689
\(82\) −0.713538 −0.0787971
\(83\) 0.854152 0.0937553 0.0468777 0.998901i \(-0.485073\pi\)
0.0468777 + 0.998901i \(0.485073\pi\)
\(84\) 4.77733 0.521249
\(85\) 11.3905 1.23548
\(86\) 8.43605 0.909682
\(87\) −8.24468 −0.883923
\(88\) 4.98173 0.531054
\(89\) 7.19917 0.763110 0.381555 0.924346i \(-0.375389\pi\)
0.381555 + 0.924346i \(0.375389\pi\)
\(90\) 10.3723 1.09333
\(91\) 5.49086 0.575599
\(92\) 1.18613 0.123662
\(93\) 4.57292 0.474190
\(94\) 4.20964 0.434191
\(95\) 9.42708 0.967198
\(96\) −18.7173 −1.91032
\(97\) 5.36852 0.545091 0.272545 0.962143i \(-0.412134\pi\)
0.272545 + 0.962143i \(0.412134\pi\)
\(98\) 0.713538 0.0720782
\(99\) −14.5364 −1.46096
\(100\) 1.49086 0.149086
\(101\) −9.74078 −0.969244 −0.484622 0.874724i \(-0.661043\pi\)
−0.484622 + 0.874724i \(0.661043\pi\)
\(102\) −13.0220 −1.28937
\(103\) 12.8542 1.26656 0.633279 0.773924i \(-0.281709\pi\)
0.633279 + 0.773924i \(0.281709\pi\)
\(104\) −13.6770 −1.34114
\(105\) −6.40880 −0.625435
\(106\) −2.53638 −0.246355
\(107\) −14.9582 −1.44607 −0.723033 0.690814i \(-0.757252\pi\)
−0.723033 + 0.690814i \(0.757252\pi\)
\(108\) 20.3905 1.96208
\(109\) −14.0910 −1.34968 −0.674838 0.737966i \(-0.735786\pi\)
−0.674838 + 0.737966i \(0.735786\pi\)
\(110\) −2.85415 −0.272133
\(111\) 36.7042 3.48381
\(112\) 1.20440 0.113805
\(113\) −5.04028 −0.474150 −0.237075 0.971491i \(-0.576189\pi\)
−0.237075 + 0.971491i \(0.576189\pi\)
\(114\) −10.7773 −1.00939
\(115\) −1.59120 −0.148380
\(116\) −3.83588 −0.356152
\(117\) 39.9086 3.68955
\(118\) −2.85415 −0.262746
\(119\) 5.69527 0.522084
\(120\) 15.9635 1.45726
\(121\) −7.00000 −0.636364
\(122\) −3.96345 −0.358834
\(123\) 3.20440 0.288931
\(124\) 2.12758 0.191062
\(125\) −12.0000 −1.07331
\(126\) 5.18613 0.462017
\(127\) 4.75382 0.421833 0.210917 0.977504i \(-0.432355\pi\)
0.210917 + 0.977504i \(0.432355\pi\)
\(128\) −10.4271 −0.921632
\(129\) −37.8851 −3.33560
\(130\) 7.83588 0.687252
\(131\) −15.8359 −1.38359 −0.691794 0.722095i \(-0.743179\pi\)
−0.691794 + 0.722095i \(0.743179\pi\)
\(132\) −9.55465 −0.831626
\(133\) 4.71354 0.408716
\(134\) 5.39053 0.465671
\(135\) −27.3540 −2.35426
\(136\) −14.1861 −1.21645
\(137\) 15.9635 1.36385 0.681925 0.731422i \(-0.261143\pi\)
0.681925 + 0.731422i \(0.261143\pi\)
\(138\) 1.81911 0.154853
\(139\) −7.26295 −0.616036 −0.308018 0.951381i \(-0.599666\pi\)
−0.308018 + 0.951381i \(0.599666\pi\)
\(140\) −2.98173 −0.252002
\(141\) −18.9049 −1.59208
\(142\) 1.30997 0.109930
\(143\) −10.9817 −0.918338
\(144\) 8.75382 0.729485
\(145\) 5.14585 0.427339
\(146\) 6.70050 0.554537
\(147\) −3.20440 −0.264295
\(148\) 17.0768 1.40371
\(149\) −22.3723 −1.83281 −0.916403 0.400256i \(-0.868921\pi\)
−0.916403 + 0.400256i \(0.868921\pi\)
\(150\) 2.28646 0.186689
\(151\) −19.3905 −1.57798 −0.788989 0.614407i \(-0.789395\pi\)
−0.788989 + 0.614407i \(0.789395\pi\)
\(152\) −11.7408 −0.952303
\(153\) 41.3943 3.34653
\(154\) −1.42708 −0.114997
\(155\) −2.85415 −0.229251
\(156\) 26.2316 2.10021
\(157\) 7.65872 0.611232 0.305616 0.952155i \(-0.401138\pi\)
0.305616 + 0.952155i \(0.401138\pi\)
\(158\) 7.42708 0.590866
\(159\) 11.3905 0.903328
\(160\) 11.6822 0.923561
\(161\) −0.795598 −0.0627019
\(162\) 15.7135 1.23457
\(163\) 1.35805 0.106371 0.0531855 0.998585i \(-0.483063\pi\)
0.0531855 + 0.998585i \(0.483063\pi\)
\(164\) 1.49086 0.116417
\(165\) 12.8176 0.997849
\(166\) 0.609470 0.0473040
\(167\) −13.5311 −1.04707 −0.523536 0.852004i \(-0.675387\pi\)
−0.523536 + 0.852004i \(0.675387\pi\)
\(168\) 7.98173 0.615804
\(169\) 17.1496 1.31920
\(170\) 8.12758 0.623357
\(171\) 34.2589 2.61984
\(172\) −17.6262 −1.34399
\(173\) 3.01827 0.229475 0.114738 0.993396i \(-0.463397\pi\)
0.114738 + 0.993396i \(0.463397\pi\)
\(174\) −5.88289 −0.445981
\(175\) −1.00000 −0.0755929
\(176\) −2.40880 −0.181570
\(177\) 12.8176 0.963430
\(178\) 5.13688 0.385025
\(179\) −10.8176 −0.808546 −0.404273 0.914638i \(-0.632475\pi\)
−0.404273 + 0.914638i \(0.632475\pi\)
\(180\) −21.6718 −1.61532
\(181\) 15.3320 1.13962 0.569808 0.821778i \(-0.307017\pi\)
0.569808 + 0.821778i \(0.307017\pi\)
\(182\) 3.91794 0.290417
\(183\) 17.7993 1.31576
\(184\) 1.98173 0.146095
\(185\) −22.9086 −1.68428
\(186\) 3.26295 0.239251
\(187\) −11.3905 −0.832958
\(188\) −8.79560 −0.641485
\(189\) −13.6770 −0.994855
\(190\) 6.72658 0.487997
\(191\) −3.01827 −0.218395 −0.109197 0.994020i \(-0.534828\pi\)
−0.109197 + 0.994020i \(0.534828\pi\)
\(192\) −5.63671 −0.406795
\(193\) 1.01827 0.0732969 0.0366484 0.999328i \(-0.488332\pi\)
0.0366484 + 0.999328i \(0.488332\pi\)
\(194\) 3.83064 0.275024
\(195\) −35.1899 −2.52000
\(196\) −1.49086 −0.106490
\(197\) 14.8411 1.05739 0.528693 0.848813i \(-0.322682\pi\)
0.528693 + 0.848813i \(0.322682\pi\)
\(198\) −10.3723 −0.737124
\(199\) 9.77209 0.692725 0.346363 0.938101i \(-0.387417\pi\)
0.346363 + 0.938101i \(0.387417\pi\)
\(200\) 2.49086 0.176131
\(201\) −24.2081 −1.70751
\(202\) −6.95042 −0.489030
\(203\) 2.57292 0.180584
\(204\) 27.2081 1.90495
\(205\) −2.00000 −0.139686
\(206\) 9.17192 0.639038
\(207\) −5.78256 −0.401916
\(208\) 6.61320 0.458543
\(209\) −9.42708 −0.652084
\(210\) −4.57292 −0.315562
\(211\) 10.6640 0.734137 0.367068 0.930194i \(-0.380361\pi\)
0.367068 + 0.930194i \(0.380361\pi\)
\(212\) 5.29950 0.363971
\(213\) −5.88289 −0.403089
\(214\) −10.6733 −0.729609
\(215\) 23.6457 1.61262
\(216\) 34.0675 2.31800
\(217\) −1.42708 −0.0968762
\(218\) −10.0545 −0.680976
\(219\) −30.0910 −2.03336
\(220\) 5.96345 0.402056
\(221\) 31.2719 2.10358
\(222\) 26.1899 1.75775
\(223\) −24.4998 −1.64063 −0.820315 0.571912i \(-0.806202\pi\)
−0.820315 + 0.571912i \(0.806202\pi\)
\(224\) 5.84111 0.390276
\(225\) −7.26819 −0.484546
\(226\) −3.59643 −0.239231
\(227\) −10.8542 −0.720415 −0.360208 0.932872i \(-0.617294\pi\)
−0.360208 + 0.932872i \(0.617294\pi\)
\(228\) 22.5181 1.49130
\(229\) 3.07683 0.203322 0.101661 0.994819i \(-0.467584\pi\)
0.101661 + 0.994819i \(0.467584\pi\)
\(230\) −1.13538 −0.0748647
\(231\) 6.40880 0.421668
\(232\) −6.40880 −0.420759
\(233\) 16.3827 1.07327 0.536634 0.843815i \(-0.319696\pi\)
0.536634 + 0.843815i \(0.319696\pi\)
\(234\) 28.4763 1.86156
\(235\) 11.7993 0.769704
\(236\) 5.96345 0.388188
\(237\) −33.3540 −2.16657
\(238\) 4.06379 0.263416
\(239\) −14.8281 −0.959148 −0.479574 0.877501i \(-0.659209\pi\)
−0.479574 + 0.877501i \(0.659209\pi\)
\(240\) −7.71877 −0.498245
\(241\) −14.7811 −0.952132 −0.476066 0.879410i \(-0.657938\pi\)
−0.476066 + 0.879410i \(0.657938\pi\)
\(242\) −4.99477 −0.321076
\(243\) −29.5364 −1.89476
\(244\) 8.28123 0.530151
\(245\) 2.00000 0.127775
\(246\) 2.28646 0.145779
\(247\) 25.8814 1.64679
\(248\) 3.55465 0.225721
\(249\) −2.73705 −0.173453
\(250\) −8.56246 −0.541537
\(251\) −10.2812 −0.648945 −0.324473 0.945895i \(-0.605187\pi\)
−0.324473 + 0.945895i \(0.605187\pi\)
\(252\) −10.8359 −0.682596
\(253\) 1.59120 0.100038
\(254\) 3.39203 0.212835
\(255\) −36.4998 −2.28571
\(256\) −10.9582 −0.684889
\(257\) −1.48563 −0.0926710 −0.0463355 0.998926i \(-0.514754\pi\)
−0.0463355 + 0.998926i \(0.514754\pi\)
\(258\) −27.0325 −1.68297
\(259\) −11.4543 −0.711737
\(260\) −16.3723 −1.01536
\(261\) 18.7005 1.15753
\(262\) −11.2995 −0.698085
\(263\) 28.3357 1.74725 0.873627 0.486595i \(-0.161761\pi\)
0.873627 + 0.486595i \(0.161761\pi\)
\(264\) −15.9635 −0.982483
\(265\) −7.10930 −0.436721
\(266\) 3.36329 0.206216
\(267\) −23.0690 −1.41180
\(268\) −11.2630 −0.687994
\(269\) 15.8098 0.963941 0.481970 0.876188i \(-0.339921\pi\)
0.481970 + 0.876188i \(0.339921\pi\)
\(270\) −19.5181 −1.18783
\(271\) 16.3357 0.992324 0.496162 0.868230i \(-0.334742\pi\)
0.496162 + 0.868230i \(0.334742\pi\)
\(272\) 6.85939 0.415911
\(273\) −17.5949 −1.06489
\(274\) 11.3905 0.688127
\(275\) 2.00000 0.120605
\(276\) −3.80083 −0.228783
\(277\) −1.93098 −0.116021 −0.0580106 0.998316i \(-0.518476\pi\)
−0.0580106 + 0.998316i \(0.518476\pi\)
\(278\) −5.18239 −0.310819
\(279\) −10.3723 −0.620971
\(280\) −4.98173 −0.297715
\(281\) −29.5181 −1.76090 −0.880451 0.474137i \(-0.842760\pi\)
−0.880451 + 0.474137i \(0.842760\pi\)
\(282\) −13.4894 −0.803280
\(283\) 8.03655 0.477723 0.238862 0.971054i \(-0.423226\pi\)
0.238862 + 0.971054i \(0.423226\pi\)
\(284\) −2.73705 −0.162414
\(285\) −30.2081 −1.78938
\(286\) −7.83588 −0.463345
\(287\) −1.00000 −0.0590281
\(288\) 42.4543 2.50164
\(289\) 15.4360 0.908003
\(290\) 3.67176 0.215613
\(291\) −17.2029 −1.00845
\(292\) −14.0000 −0.819288
\(293\) −6.56246 −0.383383 −0.191691 0.981455i \(-0.561397\pi\)
−0.191691 + 0.981455i \(0.561397\pi\)
\(294\) −2.28646 −0.133349
\(295\) −8.00000 −0.465778
\(296\) 28.5311 1.65834
\(297\) 27.3540 1.58724
\(298\) −15.9635 −0.924738
\(299\) −4.36852 −0.252638
\(300\) −4.77733 −0.275819
\(301\) 11.8228 0.681457
\(302\) −13.8359 −0.796165
\(303\) 31.2134 1.79316
\(304\) 5.67699 0.325598
\(305\) −11.1093 −0.636117
\(306\) 29.5364 1.68848
\(307\) −19.6457 −1.12124 −0.560619 0.828074i \(-0.689437\pi\)
−0.560619 + 0.828074i \(0.689437\pi\)
\(308\) 2.98173 0.169900
\(309\) −41.1899 −2.34321
\(310\) −2.03655 −0.115668
\(311\) −1.32301 −0.0750209 −0.0375104 0.999296i \(-0.511943\pi\)
−0.0375104 + 0.999296i \(0.511943\pi\)
\(312\) 43.8266 2.48119
\(313\) −17.6222 −0.996064 −0.498032 0.867159i \(-0.665944\pi\)
−0.498032 + 0.867159i \(0.665944\pi\)
\(314\) 5.46479 0.308396
\(315\) 14.5364 0.819032
\(316\) −15.5181 −0.872962
\(317\) −22.7811 −1.27951 −0.639756 0.768578i \(-0.720965\pi\)
−0.639756 + 0.768578i \(0.720965\pi\)
\(318\) 8.12758 0.455772
\(319\) −5.14585 −0.288112
\(320\) 3.51811 0.196668
\(321\) 47.9321 2.67531
\(322\) −0.567690 −0.0316361
\(323\) 26.8448 1.49369
\(324\) −32.8318 −1.82399
\(325\) −5.49086 −0.304578
\(326\) 0.969023 0.0536692
\(327\) 45.1533 2.49698
\(328\) 2.49086 0.137535
\(329\) 5.89967 0.325259
\(330\) 9.14585 0.503462
\(331\) 22.0000 1.20923 0.604615 0.796518i \(-0.293327\pi\)
0.604615 + 0.796518i \(0.293327\pi\)
\(332\) −1.27342 −0.0698882
\(333\) −83.2522 −4.56219
\(334\) −9.65498 −0.528297
\(335\) 15.1093 0.825509
\(336\) −3.85939 −0.210547
\(337\) 6.63148 0.361240 0.180620 0.983553i \(-0.442190\pi\)
0.180620 + 0.983553i \(0.442190\pi\)
\(338\) 12.2369 0.665598
\(339\) 16.1511 0.877206
\(340\) −16.9817 −0.920963
\(341\) 2.85415 0.154561
\(342\) 24.4450 1.32184
\(343\) 1.00000 0.0539949
\(344\) −29.4491 −1.58779
\(345\) 5.09883 0.274512
\(346\) 2.15365 0.115781
\(347\) −18.0000 −0.966291 −0.483145 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 12.2917 0.658904
\(349\) 34.6274 1.85356 0.926781 0.375601i \(-0.122564\pi\)
0.926781 + 0.375601i \(0.122564\pi\)
\(350\) −0.713538 −0.0381402
\(351\) −75.0985 −4.00846
\(352\) −11.6822 −0.622665
\(353\) −27.9635 −1.48834 −0.744172 0.667988i \(-0.767156\pi\)
−0.744172 + 0.667988i \(0.767156\pi\)
\(354\) 9.14585 0.486096
\(355\) 3.67176 0.194877
\(356\) −10.7330 −0.568847
\(357\) −18.2499 −0.965888
\(358\) −7.71877 −0.407950
\(359\) 11.9907 0.632845 0.316422 0.948618i \(-0.397518\pi\)
0.316422 + 0.948618i \(0.397518\pi\)
\(360\) −36.2081 −1.90834
\(361\) 3.21744 0.169339
\(362\) 10.9399 0.574991
\(363\) 22.4308 1.17731
\(364\) −8.18613 −0.429070
\(365\) 18.7811 0.983046
\(366\) 12.7005 0.663866
\(367\) 28.4998 1.48768 0.743840 0.668358i \(-0.233003\pi\)
0.743840 + 0.668358i \(0.233003\pi\)
\(368\) −0.958220 −0.0499507
\(369\) −7.26819 −0.378367
\(370\) −16.3462 −0.849797
\(371\) −3.55465 −0.184548
\(372\) −6.81761 −0.353476
\(373\) −14.8411 −0.768444 −0.384222 0.923241i \(-0.625530\pi\)
−0.384222 + 0.923241i \(0.625530\pi\)
\(374\) −8.12758 −0.420267
\(375\) 38.4528 1.98570
\(376\) −14.6953 −0.757850
\(377\) 14.1276 0.727607
\(378\) −9.75905 −0.501952
\(379\) 7.20440 0.370065 0.185033 0.982732i \(-0.440761\pi\)
0.185033 + 0.982732i \(0.440761\pi\)
\(380\) −14.0545 −0.720980
\(381\) −15.2331 −0.780418
\(382\) −2.15365 −0.110190
\(383\) −5.16786 −0.264065 −0.132033 0.991245i \(-0.542150\pi\)
−0.132033 + 0.991245i \(0.542150\pi\)
\(384\) 33.4125 1.70508
\(385\) −4.00000 −0.203859
\(386\) 0.726576 0.0369818
\(387\) 85.9306 4.36810
\(388\) −8.00373 −0.406328
\(389\) −4.34502 −0.220301 −0.110151 0.993915i \(-0.535133\pi\)
−0.110151 + 0.993915i \(0.535133\pi\)
\(390\) −25.1093 −1.27146
\(391\) −4.53114 −0.229150
\(392\) −2.49086 −0.125808
\(393\) 50.7445 2.55972
\(394\) 10.5897 0.533501
\(395\) 20.8176 1.04745
\(396\) 21.6718 1.08905
\(397\) 19.7083 0.989131 0.494566 0.869140i \(-0.335327\pi\)
0.494566 + 0.869140i \(0.335327\pi\)
\(398\) 6.97276 0.349513
\(399\) −15.1041 −0.756149
\(400\) −1.20440 −0.0602201
\(401\) −28.3995 −1.41820 −0.709102 0.705106i \(-0.750899\pi\)
−0.709102 + 0.705106i \(0.750899\pi\)
\(402\) −17.2734 −0.861520
\(403\) −7.83588 −0.390333
\(404\) 14.5222 0.722505
\(405\) 44.0440 2.18856
\(406\) 1.83588 0.0911131
\(407\) 22.9086 1.13554
\(408\) 45.4581 2.25051
\(409\) 19.2734 0.953009 0.476505 0.879172i \(-0.341904\pi\)
0.476505 + 0.879172i \(0.341904\pi\)
\(410\) −1.42708 −0.0704783
\(411\) −51.1533 −2.52321
\(412\) −19.1638 −0.944132
\(413\) −4.00000 −0.196827
\(414\) −4.12608 −0.202786
\(415\) 1.70830 0.0838573
\(416\) 32.0728 1.57250
\(417\) 23.2734 1.13970
\(418\) −6.72658 −0.329008
\(419\) −15.9530 −0.779354 −0.389677 0.920952i \(-0.627413\pi\)
−0.389677 + 0.920952i \(0.627413\pi\)
\(420\) 9.55465 0.466219
\(421\) −38.0806 −1.85593 −0.927966 0.372664i \(-0.878445\pi\)
−0.927966 + 0.372664i \(0.878445\pi\)
\(422\) 7.60914 0.370407
\(423\) 42.8799 2.08489
\(424\) 8.85415 0.429996
\(425\) −5.69527 −0.276261
\(426\) −4.19767 −0.203378
\(427\) −5.55465 −0.268808
\(428\) 22.3007 1.07794
\(429\) 35.1899 1.69898
\(430\) 16.8721 0.813644
\(431\) −10.2917 −0.495734 −0.247867 0.968794i \(-0.579730\pi\)
−0.247867 + 0.968794i \(0.579730\pi\)
\(432\) −16.4726 −0.792538
\(433\) 9.98953 0.480066 0.240033 0.970765i \(-0.422842\pi\)
0.240033 + 0.970765i \(0.422842\pi\)
\(434\) −1.01827 −0.0488787
\(435\) −16.4894 −0.790604
\(436\) 21.0078 1.00609
\(437\) −3.75008 −0.179391
\(438\) −21.4711 −1.02593
\(439\) 1.61320 0.0769941 0.0384970 0.999259i \(-0.487743\pi\)
0.0384970 + 0.999259i \(0.487743\pi\)
\(440\) 9.96345 0.474989
\(441\) 7.26819 0.346104
\(442\) 22.3137 1.06135
\(443\) 21.2096 1.00770 0.503850 0.863791i \(-0.331916\pi\)
0.503850 + 0.863791i \(0.331916\pi\)
\(444\) −54.7210 −2.59694
\(445\) 14.3983 0.682546
\(446\) −17.4816 −0.827776
\(447\) 71.6897 3.39081
\(448\) 1.75905 0.0831074
\(449\) 12.0325 0.567848 0.283924 0.958847i \(-0.408364\pi\)
0.283924 + 0.958847i \(0.408364\pi\)
\(450\) −5.18613 −0.244476
\(451\) 2.00000 0.0941763
\(452\) 7.51437 0.353446
\(453\) 62.1350 2.91936
\(454\) −7.74485 −0.363484
\(455\) 10.9817 0.514831
\(456\) 37.6222 1.76182
\(457\) −0.908636 −0.0425042 −0.0212521 0.999774i \(-0.506765\pi\)
−0.0212521 + 0.999774i \(0.506765\pi\)
\(458\) 2.19543 0.102586
\(459\) −77.8941 −3.63579
\(460\) 2.37226 0.110607
\(461\) −13.4010 −0.624147 −0.312073 0.950058i \(-0.601023\pi\)
−0.312073 + 0.950058i \(0.601023\pi\)
\(462\) 4.57292 0.212752
\(463\) −7.29950 −0.339237 −0.169618 0.985510i \(-0.554253\pi\)
−0.169618 + 0.985510i \(0.554253\pi\)
\(464\) 3.09883 0.143860
\(465\) 9.14585 0.424129
\(466\) 11.6897 0.541515
\(467\) −4.54685 −0.210403 −0.105202 0.994451i \(-0.533549\pi\)
−0.105202 + 0.994451i \(0.533549\pi\)
\(468\) −59.4983 −2.75031
\(469\) 7.55465 0.348841
\(470\) 8.41927 0.388352
\(471\) −24.5416 −1.13082
\(472\) 9.96345 0.458605
\(473\) −23.6457 −1.08723
\(474\) −23.7993 −1.09314
\(475\) −4.71354 −0.216272
\(476\) −8.49086 −0.389178
\(477\) −25.8359 −1.18294
\(478\) −10.5804 −0.483936
\(479\) 13.3581 0.610345 0.305173 0.952297i \(-0.401286\pi\)
0.305173 + 0.952297i \(0.401286\pi\)
\(480\) −37.4345 −1.70865
\(481\) −62.8941 −2.86772
\(482\) −10.5468 −0.480396
\(483\) 2.54942 0.116002
\(484\) 10.4360 0.474366
\(485\) 10.7370 0.487544
\(486\) −21.0753 −0.955996
\(487\) 2.11454 0.0958188 0.0479094 0.998852i \(-0.484744\pi\)
0.0479094 + 0.998852i \(0.484744\pi\)
\(488\) 13.8359 0.626321
\(489\) −4.35175 −0.196793
\(490\) 1.42708 0.0644687
\(491\) −15.5767 −0.702965 −0.351482 0.936194i \(-0.614322\pi\)
−0.351482 + 0.936194i \(0.614322\pi\)
\(492\) −4.77733 −0.215378
\(493\) 14.6535 0.659960
\(494\) 18.4674 0.830886
\(495\) −29.0728 −1.30672
\(496\) −1.71877 −0.0771752
\(497\) 1.83588 0.0823504
\(498\) −1.95299 −0.0875154
\(499\) −12.5729 −0.562841 −0.281421 0.959584i \(-0.590806\pi\)
−0.281421 + 0.959584i \(0.590806\pi\)
\(500\) 17.8904 0.800081
\(501\) 43.3592 1.93715
\(502\) −7.33605 −0.327424
\(503\) −34.4308 −1.53519 −0.767597 0.640933i \(-0.778548\pi\)
−0.767597 + 0.640933i \(0.778548\pi\)
\(504\) −18.1041 −0.806419
\(505\) −19.4816 −0.866918
\(506\) 1.13538 0.0504738
\(507\) −54.9542 −2.44060
\(508\) −7.08729 −0.314448
\(509\) 25.6184 1.13552 0.567759 0.823195i \(-0.307811\pi\)
0.567759 + 0.823195i \(0.307811\pi\)
\(510\) −26.0440 −1.15325
\(511\) 9.39053 0.415413
\(512\) 13.0350 0.576073
\(513\) −64.4670 −2.84629
\(514\) −1.06005 −0.0467569
\(515\) 25.7083 1.13284
\(516\) 56.4816 2.48646
\(517\) −11.7993 −0.518934
\(518\) −8.17309 −0.359105
\(519\) −9.67176 −0.424543
\(520\) −27.3540 −1.19955
\(521\) 28.1988 1.23541 0.617707 0.786409i \(-0.288062\pi\)
0.617707 + 0.786409i \(0.288062\pi\)
\(522\) 13.3435 0.584030
\(523\) −5.54418 −0.242430 −0.121215 0.992626i \(-0.538679\pi\)
−0.121215 + 0.992626i \(0.538679\pi\)
\(524\) 23.6091 1.03137
\(525\) 3.20440 0.139852
\(526\) 20.2186 0.881573
\(527\) −8.12758 −0.354043
\(528\) 7.71877 0.335916
\(529\) −22.3670 −0.972479
\(530\) −5.07276 −0.220346
\(531\) −29.0728 −1.26165
\(532\) −7.02724 −0.304670
\(533\) −5.49086 −0.237836
\(534\) −16.4606 −0.712321
\(535\) −29.9164 −1.29340
\(536\) −18.8176 −0.812797
\(537\) 34.6640 1.49586
\(538\) 11.2809 0.486354
\(539\) −2.00000 −0.0861461
\(540\) 40.7811 1.75494
\(541\) −7.40357 −0.318304 −0.159152 0.987254i \(-0.550876\pi\)
−0.159152 + 0.987254i \(0.550876\pi\)
\(542\) 11.6562 0.500675
\(543\) −49.1298 −2.10836
\(544\) 33.2667 1.42630
\(545\) −28.1821 −1.20719
\(546\) −12.5547 −0.537289
\(547\) 36.4633 1.55906 0.779529 0.626366i \(-0.215459\pi\)
0.779529 + 0.626366i \(0.215459\pi\)
\(548\) −23.7993 −1.01666
\(549\) −40.3723 −1.72305
\(550\) 1.42708 0.0608507
\(551\) 12.1276 0.516652
\(552\) −6.35025 −0.270285
\(553\) 10.4088 0.442627
\(554\) −1.37783 −0.0585382
\(555\) 73.4085 3.11602
\(556\) 10.8281 0.459213
\(557\) −22.0545 −0.934478 −0.467239 0.884131i \(-0.654751\pi\)
−0.467239 + 0.884131i \(0.654751\pi\)
\(558\) −7.40100 −0.313309
\(559\) 64.9176 2.74572
\(560\) 2.40880 0.101791
\(561\) 36.4998 1.54102
\(562\) −21.0623 −0.888459
\(563\) −40.7538 −1.71757 −0.858784 0.512337i \(-0.828780\pi\)
−0.858784 + 0.512337i \(0.828780\pi\)
\(564\) 28.1846 1.18679
\(565\) −10.0806 −0.424092
\(566\) 5.73438 0.241034
\(567\) 22.0220 0.924837
\(568\) −4.57292 −0.191876
\(569\) 30.5860 1.28223 0.641115 0.767445i \(-0.278472\pi\)
0.641115 + 0.767445i \(0.278472\pi\)
\(570\) −21.5547 −0.902825
\(571\) −14.2007 −0.594279 −0.297140 0.954834i \(-0.596033\pi\)
−0.297140 + 0.954834i \(0.596033\pi\)
\(572\) 16.3723 0.684558
\(573\) 9.67176 0.404043
\(574\) −0.713538 −0.0297825
\(575\) 0.795598 0.0331787
\(576\) 12.7851 0.532714
\(577\) 14.5144 0.604241 0.302121 0.953270i \(-0.402305\pi\)
0.302121 + 0.953270i \(0.402305\pi\)
\(578\) 11.0142 0.458130
\(579\) −3.26295 −0.135604
\(580\) −7.67176 −0.318552
\(581\) 0.854152 0.0354362
\(582\) −12.2749 −0.508812
\(583\) 7.10930 0.294437
\(584\) −23.3905 −0.967907
\(585\) 79.8173 3.30004
\(586\) −4.68256 −0.193435
\(587\) 30.3958 1.25457 0.627284 0.778791i \(-0.284167\pi\)
0.627284 + 0.778791i \(0.284167\pi\)
\(588\) 4.77733 0.197014
\(589\) −6.72658 −0.277164
\(590\) −5.70830 −0.235007
\(591\) −47.5569 −1.95623
\(592\) −13.7956 −0.566996
\(593\) 4.54568 0.186669 0.0933344 0.995635i \(-0.470247\pi\)
0.0933344 + 0.995635i \(0.470247\pi\)
\(594\) 19.5181 0.800838
\(595\) 11.3905 0.466966
\(596\) 33.3540 1.36623
\(597\) −31.3137 −1.28158
\(598\) −3.11711 −0.127468
\(599\) −29.9542 −1.22389 −0.611947 0.790899i \(-0.709613\pi\)
−0.611947 + 0.790899i \(0.709613\pi\)
\(600\) −7.98173 −0.325853
\(601\) 19.9399 0.813367 0.406684 0.913569i \(-0.366685\pi\)
0.406684 + 0.913569i \(0.366685\pi\)
\(602\) 8.43605 0.343828
\(603\) 54.9086 2.23605
\(604\) 28.9086 1.17628
\(605\) −14.0000 −0.569181
\(606\) 22.2719 0.904735
\(607\) −31.0623 −1.26078 −0.630390 0.776279i \(-0.717105\pi\)
−0.630390 + 0.776279i \(0.717105\pi\)
\(608\) 27.5323 1.11658
\(609\) −8.24468 −0.334091
\(610\) −7.92691 −0.320951
\(611\) 32.3943 1.31053
\(612\) −61.7132 −2.49461
\(613\) 3.77733 0.152565 0.0762824 0.997086i \(-0.475695\pi\)
0.0762824 + 0.997086i \(0.475695\pi\)
\(614\) −14.0179 −0.565718
\(615\) 6.40880 0.258428
\(616\) 4.98173 0.200720
\(617\) −24.8046 −0.998594 −0.499297 0.866431i \(-0.666408\pi\)
−0.499297 + 0.866431i \(0.666408\pi\)
\(618\) −29.3905 −1.18226
\(619\) −1.54418 −0.0620659 −0.0310330 0.999518i \(-0.509880\pi\)
−0.0310330 + 0.999518i \(0.509880\pi\)
\(620\) 4.25515 0.170891
\(621\) 10.8814 0.436655
\(622\) −0.944016 −0.0378516
\(623\) 7.19917 0.288429
\(624\) −21.1914 −0.848333
\(625\) −19.0000 −0.760000
\(626\) −12.5741 −0.502562
\(627\) 30.2081 1.20640
\(628\) −11.4181 −0.455632
\(629\) −65.2354 −2.60110
\(630\) 10.3723 0.413241
\(631\) 13.4438 0.535191 0.267596 0.963531i \(-0.413771\pi\)
0.267596 + 0.963531i \(0.413771\pi\)
\(632\) −25.9269 −1.03132
\(633\) −34.1716 −1.35820
\(634\) −16.2552 −0.645575
\(635\) 9.50764 0.377299
\(636\) −16.9817 −0.673369
\(637\) 5.49086 0.217556
\(638\) −3.67176 −0.145366
\(639\) 13.3435 0.527861
\(640\) −20.8542 −0.824333
\(641\) −6.31777 −0.249537 −0.124769 0.992186i \(-0.539819\pi\)
−0.124769 + 0.992186i \(0.539819\pi\)
\(642\) 34.2014 1.34982
\(643\) 39.1522 1.54401 0.772005 0.635616i \(-0.219254\pi\)
0.772005 + 0.635616i \(0.219254\pi\)
\(644\) 1.18613 0.0467400
\(645\) −75.7703 −2.98345
\(646\) 19.1548 0.753636
\(647\) −29.6897 −1.16722 −0.583611 0.812033i \(-0.698361\pi\)
−0.583611 + 0.812033i \(0.698361\pi\)
\(648\) −54.8538 −2.15486
\(649\) 8.00000 0.314027
\(650\) −3.91794 −0.153674
\(651\) 4.57292 0.179227
\(652\) −2.02467 −0.0792923
\(653\) −4.39833 −0.172120 −0.0860601 0.996290i \(-0.527428\pi\)
−0.0860601 + 0.996290i \(0.527428\pi\)
\(654\) 32.2186 1.25985
\(655\) −31.6718 −1.23752
\(656\) −1.20440 −0.0470240
\(657\) 68.2522 2.66277
\(658\) 4.20964 0.164109
\(659\) 14.3178 0.557741 0.278871 0.960329i \(-0.410040\pi\)
0.278871 + 0.960329i \(0.410040\pi\)
\(660\) −19.1093 −0.743829
\(661\) 1.26295 0.0491232 0.0245616 0.999698i \(-0.492181\pi\)
0.0245616 + 0.999698i \(0.492181\pi\)
\(662\) 15.6978 0.610114
\(663\) −100.208 −3.89175
\(664\) −2.12758 −0.0825659
\(665\) 9.42708 0.365566
\(666\) −59.4036 −2.30184
\(667\) −2.04701 −0.0792607
\(668\) 20.1731 0.780520
\(669\) 78.5073 3.03527
\(670\) 10.7811 0.416509
\(671\) 11.1093 0.428870
\(672\) −18.7173 −0.722034
\(673\) −30.7080 −1.18371 −0.591853 0.806046i \(-0.701603\pi\)
−0.591853 + 0.806046i \(0.701603\pi\)
\(674\) 4.73181 0.182263
\(675\) 13.6770 0.526428
\(676\) −25.5677 −0.983373
\(677\) 13.8098 0.530754 0.265377 0.964145i \(-0.414504\pi\)
0.265377 + 0.964145i \(0.414504\pi\)
\(678\) 11.5244 0.442592
\(679\) 5.36852 0.206025
\(680\) −28.3723 −1.08803
\(681\) 34.7811 1.33281
\(682\) 2.03655 0.0779834
\(683\) 40.5073 1.54997 0.774984 0.631980i \(-0.217758\pi\)
0.774984 + 0.631980i \(0.217758\pi\)
\(684\) −51.0753 −1.95291
\(685\) 31.9269 1.21986
\(686\) 0.713538 0.0272430
\(687\) −9.85939 −0.376159
\(688\) 14.2394 0.542874
\(689\) −19.5181 −0.743581
\(690\) 3.63821 0.138504
\(691\) 17.2096 0.654685 0.327343 0.944906i \(-0.393847\pi\)
0.327343 + 0.944906i \(0.393847\pi\)
\(692\) −4.49983 −0.171058
\(693\) −14.5364 −0.552191
\(694\) −12.8437 −0.487540
\(695\) −14.5259 −0.550999
\(696\) 20.5364 0.778429
\(697\) −5.69527 −0.215724
\(698\) 24.7080 0.935210
\(699\) −52.4968 −1.98561
\(700\) 1.49086 0.0563493
\(701\) 24.9620 0.942800 0.471400 0.881920i \(-0.343749\pi\)
0.471400 + 0.881920i \(0.343749\pi\)
\(702\) −53.5856 −2.02246
\(703\) −53.9904 −2.03629
\(704\) −3.51811 −0.132594
\(705\) −37.8098 −1.42400
\(706\) −19.9530 −0.750941
\(707\) −9.74078 −0.366340
\(708\) −19.1093 −0.718172
\(709\) 5.89036 0.221217 0.110609 0.993864i \(-0.464720\pi\)
0.110609 + 0.993864i \(0.464720\pi\)
\(710\) 2.61994 0.0983245
\(711\) 75.6532 2.83721
\(712\) −17.9321 −0.672035
\(713\) 1.13538 0.0425203
\(714\) −13.0220 −0.487336
\(715\) −21.9635 −0.821387
\(716\) 16.1276 0.602716
\(717\) 47.5151 1.77448
\(718\) 8.55582 0.319300
\(719\) 22.2917 0.831340 0.415670 0.909516i \(-0.363547\pi\)
0.415670 + 0.909516i \(0.363547\pi\)
\(720\) 17.5076 0.652471
\(721\) 12.8542 0.478714
\(722\) 2.29577 0.0854395
\(723\) 47.3645 1.76150
\(724\) −22.8579 −0.849507
\(725\) −2.57292 −0.0955560
\(726\) 16.0052 0.594010
\(727\) −21.1768 −0.785405 −0.392702 0.919666i \(-0.628460\pi\)
−0.392702 + 0.919666i \(0.628460\pi\)
\(728\) −13.6770 −0.506903
\(729\) 28.5804 1.05853
\(730\) 13.4010 0.495993
\(731\) 67.3342 2.49045
\(732\) −26.5364 −0.980813
\(733\) −30.6900 −1.13356 −0.566781 0.823868i \(-0.691811\pi\)
−0.566781 + 0.823868i \(0.691811\pi\)
\(734\) 20.3357 0.750605
\(735\) −6.40880 −0.236392
\(736\) −4.64718 −0.171297
\(737\) −15.1093 −0.556558
\(738\) −5.18613 −0.190904
\(739\) −39.9176 −1.46839 −0.734196 0.678937i \(-0.762441\pi\)
−0.734196 + 0.678937i \(0.762441\pi\)
\(740\) 34.1537 1.25551
\(741\) −82.9344 −3.04667
\(742\) −2.53638 −0.0931134
\(743\) 24.9478 0.915244 0.457622 0.889147i \(-0.348701\pi\)
0.457622 + 0.889147i \(0.348701\pi\)
\(744\) −11.3905 −0.417597
\(745\) −44.7445 −1.63931
\(746\) −10.5897 −0.387716
\(747\) 6.20814 0.227144
\(748\) 16.9817 0.620913
\(749\) −14.9582 −0.546561
\(750\) 27.4375 1.00188
\(751\) −35.1899 −1.28410 −0.642048 0.766664i \(-0.721915\pi\)
−0.642048 + 0.766664i \(0.721915\pi\)
\(752\) 7.10557 0.259113
\(753\) 32.9452 1.20059
\(754\) 10.0806 0.367112
\(755\) −38.7811 −1.41139
\(756\) 20.3905 0.741596
\(757\) 12.8542 0.467192 0.233596 0.972334i \(-0.424951\pi\)
0.233596 + 0.972334i \(0.424951\pi\)
\(758\) 5.14061 0.186716
\(759\) −5.09883 −0.185076
\(760\) −23.4816 −0.851766
\(761\) 29.3645 1.06446 0.532230 0.846600i \(-0.321354\pi\)
0.532230 + 0.846600i \(0.321354\pi\)
\(762\) −10.8694 −0.393758
\(763\) −14.0910 −0.510130
\(764\) 4.49983 0.162798
\(765\) 82.7885 2.99323
\(766\) −3.68746 −0.133233
\(767\) −21.9635 −0.793054
\(768\) 35.1145 1.26709
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) −2.85415 −0.102856
\(771\) 4.76055 0.171447
\(772\) −1.51811 −0.0546378
\(773\) −28.1220 −1.01148 −0.505739 0.862686i \(-0.668780\pi\)
−0.505739 + 0.862686i \(0.668780\pi\)
\(774\) 61.3148 2.20391
\(775\) 1.42708 0.0512621
\(776\) −13.3723 −0.480036
\(777\) 36.7042 1.31676
\(778\) −3.10033 −0.111152
\(779\) −4.71354 −0.168880
\(780\) 52.4633 1.87849
\(781\) −3.67176 −0.131386
\(782\) −3.23314 −0.115617
\(783\) −35.1899 −1.25758
\(784\) 1.20440 0.0430143
\(785\) 15.3174 0.546703
\(786\) 36.2081 1.29150
\(787\) −5.51811 −0.196699 −0.0983496 0.995152i \(-0.531356\pi\)
−0.0983496 + 0.995152i \(0.531356\pi\)
\(788\) −22.1261 −0.788209
\(789\) −90.7990 −3.23253
\(790\) 14.8542 0.528487
\(791\) −5.04028 −0.179212
\(792\) 36.2081 1.28660
\(793\) −30.4998 −1.08308
\(794\) 14.0626 0.499064
\(795\) 22.7811 0.807961
\(796\) −14.5689 −0.516379
\(797\) 37.5256 1.32922 0.664612 0.747189i \(-0.268597\pi\)
0.664612 + 0.747189i \(0.268597\pi\)
\(798\) −10.7773 −0.381513
\(799\) 33.6002 1.18869
\(800\) −5.84111 −0.206515
\(801\) 52.3249 1.84881
\(802\) −20.2641 −0.715551
\(803\) −18.7811 −0.662769
\(804\) 36.0910 1.27283
\(805\) −1.59120 −0.0560823
\(806\) −5.59120 −0.196942
\(807\) −50.6610 −1.78335
\(808\) 24.2630 0.853568
\(809\) 14.8281 0.521327 0.260664 0.965430i \(-0.416059\pi\)
0.260664 + 0.965430i \(0.416059\pi\)
\(810\) 31.4271 1.10423
\(811\) −19.4271 −0.682177 −0.341088 0.940031i \(-0.610796\pi\)
−0.341088 + 0.940031i \(0.610796\pi\)
\(812\) −3.83588 −0.134613
\(813\) −52.3462 −1.83586
\(814\) 16.3462 0.572933
\(815\) 2.71611 0.0951411
\(816\) −21.9802 −0.769462
\(817\) 55.7274 1.94966
\(818\) 13.7523 0.480839
\(819\) 39.9086 1.39452
\(820\) 2.98173 0.104126
\(821\) −16.0130 −0.558859 −0.279429 0.960166i \(-0.590145\pi\)
−0.279429 + 0.960166i \(0.590145\pi\)
\(822\) −36.4998 −1.27308
\(823\) 18.9086 0.659114 0.329557 0.944136i \(-0.393101\pi\)
0.329557 + 0.944136i \(0.393101\pi\)
\(824\) −32.0179 −1.11540
\(825\) −6.40880 −0.223126
\(826\) −2.85415 −0.0993086
\(827\) −16.6640 −0.579462 −0.289731 0.957108i \(-0.593566\pi\)
−0.289731 + 0.957108i \(0.593566\pi\)
\(828\) 8.62101 0.299601
\(829\) 5.06229 0.175821 0.0879103 0.996128i \(-0.471981\pi\)
0.0879103 + 0.996128i \(0.471981\pi\)
\(830\) 1.21894 0.0423100
\(831\) 6.18763 0.214646
\(832\) 9.65872 0.334856
\(833\) 5.69527 0.197329
\(834\) 16.6065 0.575035
\(835\) −27.0623 −0.936529
\(836\) 14.0545 0.486085
\(837\) 19.5181 0.674644
\(838\) −11.3831 −0.393221
\(839\) 8.86869 0.306181 0.153091 0.988212i \(-0.451077\pi\)
0.153091 + 0.988212i \(0.451077\pi\)
\(840\) 15.9635 0.550792
\(841\) −22.3801 −0.771726
\(842\) −27.1719 −0.936406
\(843\) 94.5879 3.25778
\(844\) −15.8985 −0.547249
\(845\) 34.2992 1.17993
\(846\) 30.5964 1.05193
\(847\) −7.00000 −0.240523
\(848\) −4.28123 −0.147018
\(849\) −25.7523 −0.883817
\(850\) −4.06379 −0.139387
\(851\) 9.11304 0.312391
\(852\) 8.77059 0.300476
\(853\) −22.5729 −0.772882 −0.386441 0.922314i \(-0.626296\pi\)
−0.386441 + 0.922314i \(0.626296\pi\)
\(854\) −3.96345 −0.135627
\(855\) 68.5178 2.34326
\(856\) 37.2589 1.27348
\(857\) 44.7811 1.52969 0.764846 0.644213i \(-0.222815\pi\)
0.764846 + 0.644213i \(0.222815\pi\)
\(858\) 25.1093 0.857217
\(859\) −39.6352 −1.35234 −0.676168 0.736747i \(-0.736361\pi\)
−0.676168 + 0.736747i \(0.736361\pi\)
\(860\) −35.2525 −1.20210
\(861\) 3.20440 0.109206
\(862\) −7.34352 −0.250121
\(863\) 6.21861 0.211684 0.105842 0.994383i \(-0.466246\pi\)
0.105842 + 0.994383i \(0.466246\pi\)
\(864\) −79.8889 −2.71787
\(865\) 6.03655 0.205249
\(866\) 7.12791 0.242216
\(867\) −49.4633 −1.67986
\(868\) 2.12758 0.0722146
\(869\) −20.8176 −0.706189
\(870\) −11.7658 −0.398898
\(871\) 41.4816 1.40555
\(872\) 35.0988 1.18860
\(873\) 39.0194 1.32061
\(874\) −2.67583 −0.0905112
\(875\) −12.0000 −0.405674
\(876\) 44.8616 1.51573
\(877\) 4.08463 0.137928 0.0689641 0.997619i \(-0.478031\pi\)
0.0689641 + 0.997619i \(0.478031\pi\)
\(878\) 1.15108 0.0388472
\(879\) 21.0287 0.709282
\(880\) −4.81761 −0.162401
\(881\) 58.3537 1.96598 0.982992 0.183647i \(-0.0587904\pi\)
0.982992 + 0.183647i \(0.0587904\pi\)
\(882\) 5.18613 0.174626
\(883\) 31.8724 1.07259 0.536296 0.844030i \(-0.319823\pi\)
0.536296 + 0.844030i \(0.319823\pi\)
\(884\) −46.6222 −1.56807
\(885\) 25.6352 0.861718
\(886\) 15.1339 0.508433
\(887\) 13.0821 0.439253 0.219626 0.975584i \(-0.429516\pi\)
0.219626 + 0.975584i \(0.429516\pi\)
\(888\) −91.4252 −3.06803
\(889\) 4.75382 0.159438
\(890\) 10.2738 0.344377
\(891\) −44.0440 −1.47553
\(892\) 36.5259 1.22298
\(893\) 27.8083 0.930569
\(894\) 51.1533 1.71082
\(895\) −21.6352 −0.723185
\(896\) −10.4271 −0.348344
\(897\) 13.9985 0.467396
\(898\) 8.58563 0.286506
\(899\) −3.67176 −0.122460
\(900\) 10.8359 0.361196
\(901\) −20.2447 −0.674448
\(902\) 1.42708 0.0475164
\(903\) −37.8851 −1.26074
\(904\) 12.5547 0.417561
\(905\) 30.6640 1.01930
\(906\) 44.3357 1.47296
\(907\) −44.4256 −1.47513 −0.737564 0.675278i \(-0.764024\pi\)
−0.737564 + 0.675278i \(0.764024\pi\)
\(908\) 16.1821 0.537021
\(909\) −70.7978 −2.34822
\(910\) 7.83588 0.259757
\(911\) −24.0310 −0.796182 −0.398091 0.917346i \(-0.630327\pi\)
−0.398091 + 0.917346i \(0.630327\pi\)
\(912\) −18.1914 −0.602376
\(913\) −1.70830 −0.0565366
\(914\) −0.648346 −0.0214454
\(915\) 35.5987 1.17686
\(916\) −4.58713 −0.151563
\(917\) −15.8359 −0.522947
\(918\) −55.5804 −1.83443
\(919\) −26.4453 −0.872352 −0.436176 0.899861i \(-0.643667\pi\)
−0.436176 + 0.899861i \(0.643667\pi\)
\(920\) 3.96345 0.130671
\(921\) 62.9527 2.07436
\(922\) −9.56212 −0.314912
\(923\) 10.0806 0.331806
\(924\) −9.55465 −0.314325
\(925\) 11.4543 0.376616
\(926\) −5.20847 −0.171161
\(927\) 93.4264 3.06853
\(928\) 15.0287 0.493343
\(929\) −34.3032 −1.12545 −0.562726 0.826643i \(-0.690248\pi\)
−0.562726 + 0.826643i \(0.690248\pi\)
\(930\) 6.52591 0.213993
\(931\) 4.71354 0.154480
\(932\) −24.4244 −0.800048
\(933\) 4.23945 0.138793
\(934\) −3.24435 −0.106158
\(935\) −22.7811 −0.745020
\(936\) −99.4070 −3.24922
\(937\) 58.5427 1.91251 0.956253 0.292541i \(-0.0945007\pi\)
0.956253 + 0.292541i \(0.0945007\pi\)
\(938\) 5.39053 0.176007
\(939\) 56.4685 1.84278
\(940\) −17.5912 −0.573762
\(941\) −0.382726 −0.0124765 −0.00623826 0.999981i \(-0.501986\pi\)
−0.00623826 + 0.999981i \(0.501986\pi\)
\(942\) −17.5114 −0.570551
\(943\) 0.795598 0.0259083
\(944\) −4.81761 −0.156800
\(945\) −27.3540 −0.889825
\(946\) −16.8721 −0.548559
\(947\) −28.5323 −0.927175 −0.463588 0.886051i \(-0.653438\pi\)
−0.463588 + 0.886051i \(0.653438\pi\)
\(948\) 49.7262 1.61503
\(949\) 51.5621 1.67378
\(950\) −3.36329 −0.109119
\(951\) 72.9997 2.36718
\(952\) −14.1861 −0.459775
\(953\) 18.9440 0.613657 0.306828 0.951765i \(-0.400732\pi\)
0.306828 + 0.951765i \(0.400732\pi\)
\(954\) −18.4349 −0.596851
\(955\) −6.03655 −0.195338
\(956\) 22.1066 0.714980
\(957\) 16.4894 0.533025
\(958\) 9.53148 0.307948
\(959\) 15.9635 0.515487
\(960\) −11.2734 −0.363848
\(961\) −28.9635 −0.934305
\(962\) −44.8773 −1.44690
\(963\) −108.719 −3.50343
\(964\) 22.0365 0.709749
\(965\) 2.03655 0.0655587
\(966\) 1.81911 0.0585288
\(967\) −5.93738 −0.190933 −0.0954666 0.995433i \(-0.530434\pi\)
−0.0954666 + 0.995433i \(0.530434\pi\)
\(968\) 17.4360 0.560416
\(969\) −86.0217 −2.76341
\(970\) 7.66129 0.245989
\(971\) −43.7288 −1.40332 −0.701662 0.712510i \(-0.747558\pi\)
−0.701662 + 0.712510i \(0.747558\pi\)
\(972\) 44.0347 1.41241
\(973\) −7.26295 −0.232840
\(974\) 1.50880 0.0483452
\(975\) 17.5949 0.563489
\(976\) −6.69003 −0.214143
\(977\) −43.4920 −1.39143 −0.695717 0.718316i \(-0.744913\pi\)
−0.695717 + 0.718316i \(0.744913\pi\)
\(978\) −3.10514 −0.0992914
\(979\) −14.3983 −0.460173
\(980\) −2.98173 −0.0952478
\(981\) −102.416 −3.26990
\(982\) −11.1145 −0.354679
\(983\) −40.6640 −1.29698 −0.648489 0.761224i \(-0.724599\pi\)
−0.648489 + 0.761224i \(0.724599\pi\)
\(984\) −7.98173 −0.254448
\(985\) 29.6822 0.945754
\(986\) 10.4558 0.332981
\(987\) −18.9049 −0.601750
\(988\) −38.5856 −1.22757
\(989\) −9.40623 −0.299101
\(990\) −20.7445 −0.659304
\(991\) −49.9164 −1.58565 −0.792824 0.609451i \(-0.791390\pi\)
−0.792824 + 0.609451i \(0.791390\pi\)
\(992\) −8.33571 −0.264659
\(993\) −70.4968 −2.23715
\(994\) 1.30997 0.0415497
\(995\) 19.5442 0.619592
\(996\) 4.08056 0.129298
\(997\) 1.06122 0.0336091 0.0168046 0.999859i \(-0.494651\pi\)
0.0168046 + 0.999859i \(0.494651\pi\)
\(998\) −8.97126 −0.283980
\(999\) 156.661 4.95652
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 287.2.a.c.1.2 3
3.2 odd 2 2583.2.a.m.1.2 3
4.3 odd 2 4592.2.a.t.1.3 3
5.4 even 2 7175.2.a.k.1.2 3
7.6 odd 2 2009.2.a.j.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.a.c.1.2 3 1.1 even 1 trivial
2009.2.a.j.1.2 3 7.6 odd 2
2583.2.a.m.1.2 3 3.2 odd 2
4592.2.a.t.1.3 3 4.3 odd 2
7175.2.a.k.1.2 3 5.4 even 2