Properties

Label 6043.2.a.b.1.12
Level $6043$
Weight $2$
Character 6043.1
Self dual yes
Analytic conductor $48.254$
Analytic rank $1$
Dimension $243$
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] = [6043,2,Mod(1,6043)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6043, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6043.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6043 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6043.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: \(48.2535979415\)
Analytic rank: \(1\)
Dimension: \(243\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6043.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.70932 q^{2} +3.28141 q^{3} +5.34043 q^{4} -1.89583 q^{5} -8.89039 q^{6} +0.209771 q^{7} -9.05031 q^{8} +7.76762 q^{9} +O(q^{10})\) \(q-2.70932 q^{2} +3.28141 q^{3} +5.34043 q^{4} -1.89583 q^{5} -8.89039 q^{6} +0.209771 q^{7} -9.05031 q^{8} +7.76762 q^{9} +5.13641 q^{10} -5.16465 q^{11} +17.5241 q^{12} +2.75290 q^{13} -0.568338 q^{14} -6.22098 q^{15} +13.8394 q^{16} +2.29168 q^{17} -21.0450 q^{18} -4.02607 q^{19} -10.1245 q^{20} +0.688344 q^{21} +13.9927 q^{22} +4.05305 q^{23} -29.6977 q^{24} -1.40583 q^{25} -7.45849 q^{26} +15.6445 q^{27} +1.12027 q^{28} -3.59338 q^{29} +16.8547 q^{30} -3.60943 q^{31} -19.3947 q^{32} -16.9473 q^{33} -6.20890 q^{34} -0.397690 q^{35} +41.4825 q^{36} +10.2030 q^{37} +10.9079 q^{38} +9.03337 q^{39} +17.1578 q^{40} -11.0771 q^{41} -1.86495 q^{42} -5.57925 q^{43} -27.5815 q^{44} -14.7261 q^{45} -10.9810 q^{46} +4.13052 q^{47} +45.4125 q^{48} -6.95600 q^{49} +3.80885 q^{50} +7.51993 q^{51} +14.7017 q^{52} -9.80144 q^{53} -42.3860 q^{54} +9.79130 q^{55} -1.89849 q^{56} -13.2112 q^{57} +9.73562 q^{58} -10.6133 q^{59} -33.2227 q^{60} +2.91134 q^{61} +9.77910 q^{62} +1.62942 q^{63} +24.8677 q^{64} -5.21902 q^{65} +45.9158 q^{66} +5.60914 q^{67} +12.2386 q^{68} +13.2997 q^{69} +1.07747 q^{70} -9.53179 q^{71} -70.2994 q^{72} -5.74436 q^{73} -27.6433 q^{74} -4.61310 q^{75} -21.5010 q^{76} -1.08340 q^{77} -24.4743 q^{78} -10.9468 q^{79} -26.2371 q^{80} +28.0331 q^{81} +30.0115 q^{82} -8.59208 q^{83} +3.67606 q^{84} -4.34463 q^{85} +15.1160 q^{86} -11.7913 q^{87} +46.7417 q^{88} +11.4656 q^{89} +39.8977 q^{90} +0.577478 q^{91} +21.6451 q^{92} -11.8440 q^{93} -11.1909 q^{94} +7.63275 q^{95} -63.6418 q^{96} -5.66729 q^{97} +18.8460 q^{98} -40.1171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70932 −1.91578 −0.957890 0.287134i \(-0.907298\pi\)
−0.957890 + 0.287134i \(0.907298\pi\)
\(3\) 3.28141 1.89452 0.947260 0.320466i \(-0.103839\pi\)
0.947260 + 0.320466i \(0.103839\pi\)
\(4\) 5.34043 2.67022
\(5\) −1.89583 −0.847841 −0.423920 0.905700i \(-0.639346\pi\)
−0.423920 + 0.905700i \(0.639346\pi\)
\(6\) −8.89039 −3.62949
\(7\) 0.209771 0.0792860 0.0396430 0.999214i \(-0.487378\pi\)
0.0396430 + 0.999214i \(0.487378\pi\)
\(8\) −9.05031 −3.19977
\(9\) 7.76762 2.58921
\(10\) 5.13641 1.62428
\(11\) −5.16465 −1.55720 −0.778601 0.627520i \(-0.784070\pi\)
−0.778601 + 0.627520i \(0.784070\pi\)
\(12\) 17.5241 5.05878
\(13\) 2.75290 0.763516 0.381758 0.924262i \(-0.375319\pi\)
0.381758 + 0.924262i \(0.375319\pi\)
\(14\) −0.568338 −0.151895
\(15\) −6.22098 −1.60625
\(16\) 13.8394 3.45984
\(17\) 2.29168 0.555814 0.277907 0.960608i \(-0.410359\pi\)
0.277907 + 0.960608i \(0.410359\pi\)
\(18\) −21.0450 −4.96035
\(19\) −4.02607 −0.923644 −0.461822 0.886973i \(-0.652804\pi\)
−0.461822 + 0.886973i \(0.652804\pi\)
\(20\) −10.1245 −2.26392
\(21\) 0.688344 0.150209
\(22\) 13.9927 2.98326
\(23\) 4.05305 0.845120 0.422560 0.906335i \(-0.361132\pi\)
0.422560 + 0.906335i \(0.361132\pi\)
\(24\) −29.6977 −6.06203
\(25\) −1.40583 −0.281166
\(26\) −7.45849 −1.46273
\(27\) 15.6445 3.01079
\(28\) 1.12027 0.211711
\(29\) −3.59338 −0.667273 −0.333637 0.942702i \(-0.608276\pi\)
−0.333637 + 0.942702i \(0.608276\pi\)
\(30\) 16.8547 3.07723
\(31\) −3.60943 −0.648272 −0.324136 0.946011i \(-0.605074\pi\)
−0.324136 + 0.946011i \(0.605074\pi\)
\(32\) −19.3947 −3.42852
\(33\) −16.9473 −2.95015
\(34\) −6.20890 −1.06482
\(35\) −0.397690 −0.0672219
\(36\) 41.4825 6.91374
\(37\) 10.2030 1.67737 0.838685 0.544616i \(-0.183325\pi\)
0.838685 + 0.544616i \(0.183325\pi\)
\(38\) 10.9079 1.76950
\(39\) 9.03337 1.44650
\(40\) 17.1578 2.71289
\(41\) −11.0771 −1.72996 −0.864978 0.501809i \(-0.832668\pi\)
−0.864978 + 0.501809i \(0.832668\pi\)
\(42\) −1.86495 −0.287768
\(43\) −5.57925 −0.850827 −0.425414 0.904999i \(-0.639871\pi\)
−0.425414 + 0.904999i \(0.639871\pi\)
\(44\) −27.5815 −4.15806
\(45\) −14.7261 −2.19523
\(46\) −10.9810 −1.61907
\(47\) 4.13052 0.602499 0.301249 0.953545i \(-0.402596\pi\)
0.301249 + 0.953545i \(0.402596\pi\)
\(48\) 45.4125 6.55473
\(49\) −6.95600 −0.993714
\(50\) 3.80885 0.538653
\(51\) 7.51993 1.05300
\(52\) 14.7017 2.03875
\(53\) −9.80144 −1.34633 −0.673166 0.739491i \(-0.735066\pi\)
−0.673166 + 0.739491i \(0.735066\pi\)
\(54\) −42.3860 −5.76801
\(55\) 9.79130 1.32026
\(56\) −1.89849 −0.253697
\(57\) −13.2112 −1.74986
\(58\) 9.73562 1.27835
\(59\) −10.6133 −1.38173 −0.690866 0.722983i \(-0.742771\pi\)
−0.690866 + 0.722983i \(0.742771\pi\)
\(60\) −33.2227 −4.28904
\(61\) 2.91134 0.372758 0.186379 0.982478i \(-0.440325\pi\)
0.186379 + 0.982478i \(0.440325\pi\)
\(62\) 9.77910 1.24195
\(63\) 1.62942 0.205288
\(64\) 24.8677 3.10846
\(65\) −5.21902 −0.647340
\(66\) 45.9158 5.65184
\(67\) 5.60914 0.685265 0.342633 0.939469i \(-0.388681\pi\)
0.342633 + 0.939469i \(0.388681\pi\)
\(68\) 12.2386 1.48414
\(69\) 13.2997 1.60110
\(70\) 1.07747 0.128782
\(71\) −9.53179 −1.13122 −0.565608 0.824674i \(-0.691358\pi\)
−0.565608 + 0.824674i \(0.691358\pi\)
\(72\) −70.2994 −8.28486
\(73\) −5.74436 −0.672327 −0.336163 0.941804i \(-0.609129\pi\)
−0.336163 + 0.941804i \(0.609129\pi\)
\(74\) −27.6433 −3.21347
\(75\) −4.61310 −0.532675
\(76\) −21.5010 −2.46633
\(77\) −1.08340 −0.123464
\(78\) −24.4743 −2.77117
\(79\) −10.9468 −1.23161 −0.615804 0.787899i \(-0.711169\pi\)
−0.615804 + 0.787899i \(0.711169\pi\)
\(80\) −26.2371 −2.93339
\(81\) 28.0331 3.11479
\(82\) 30.0115 3.31422
\(83\) −8.59208 −0.943104 −0.471552 0.881838i \(-0.656306\pi\)
−0.471552 + 0.881838i \(0.656306\pi\)
\(84\) 3.67606 0.401091
\(85\) −4.34463 −0.471241
\(86\) 15.1160 1.63000
\(87\) −11.7913 −1.26416
\(88\) 46.7417 4.98268
\(89\) 11.4656 1.21536 0.607678 0.794184i \(-0.292101\pi\)
0.607678 + 0.794184i \(0.292101\pi\)
\(90\) 39.8977 4.20559
\(91\) 0.577478 0.0605362
\(92\) 21.6451 2.25665
\(93\) −11.8440 −1.22816
\(94\) −11.1909 −1.15426
\(95\) 7.63275 0.783103
\(96\) −63.6418 −6.49541
\(97\) −5.66729 −0.575426 −0.287713 0.957717i \(-0.592895\pi\)
−0.287713 + 0.957717i \(0.592895\pi\)
\(98\) 18.8460 1.90374
\(99\) −40.1171 −4.03192
\(100\) −7.50775 −0.750775
\(101\) −0.295468 −0.0294002 −0.0147001 0.999892i \(-0.504679\pi\)
−0.0147001 + 0.999892i \(0.504679\pi\)
\(102\) −20.3739 −2.01732
\(103\) −2.69414 −0.265461 −0.132731 0.991152i \(-0.542374\pi\)
−0.132731 + 0.991152i \(0.542374\pi\)
\(104\) −24.9146 −2.44308
\(105\) −1.30498 −0.127353
\(106\) 26.5553 2.57928
\(107\) 0.320073 0.0309427 0.0154713 0.999880i \(-0.495075\pi\)
0.0154713 + 0.999880i \(0.495075\pi\)
\(108\) 83.5484 8.03945
\(109\) −4.01260 −0.384338 −0.192169 0.981362i \(-0.561552\pi\)
−0.192169 + 0.981362i \(0.561552\pi\)
\(110\) −26.5278 −2.52933
\(111\) 33.4803 3.17781
\(112\) 2.90310 0.274317
\(113\) 9.46731 0.890610 0.445305 0.895379i \(-0.353095\pi\)
0.445305 + 0.895379i \(0.353095\pi\)
\(114\) 35.7933 3.35235
\(115\) −7.68390 −0.716527
\(116\) −19.1902 −1.78176
\(117\) 21.3835 1.97690
\(118\) 28.7548 2.64710
\(119\) 0.480728 0.0440683
\(120\) 56.3018 5.13963
\(121\) 15.6736 1.42488
\(122\) −7.88775 −0.714123
\(123\) −36.3485 −3.27744
\(124\) −19.2759 −1.73103
\(125\) 12.1444 1.08622
\(126\) −4.41463 −0.393287
\(127\) 20.1483 1.78787 0.893935 0.448196i \(-0.147933\pi\)
0.893935 + 0.448196i \(0.147933\pi\)
\(128\) −28.5853 −2.52661
\(129\) −18.3078 −1.61191
\(130\) 14.1400 1.24016
\(131\) 0.686860 0.0600113 0.0300056 0.999550i \(-0.490447\pi\)
0.0300056 + 0.999550i \(0.490447\pi\)
\(132\) −90.5060 −7.87754
\(133\) −0.844554 −0.0732321
\(134\) −15.1970 −1.31282
\(135\) −29.6593 −2.55267
\(136\) −20.7404 −1.77848
\(137\) 16.3954 1.40075 0.700377 0.713773i \(-0.253015\pi\)
0.700377 + 0.713773i \(0.253015\pi\)
\(138\) −36.0332 −3.06735
\(139\) 16.7569 1.42130 0.710651 0.703545i \(-0.248401\pi\)
0.710651 + 0.703545i \(0.248401\pi\)
\(140\) −2.12384 −0.179497
\(141\) 13.5539 1.14145
\(142\) 25.8247 2.16716
\(143\) −14.2178 −1.18895
\(144\) 107.499 8.95824
\(145\) 6.81243 0.565741
\(146\) 15.5633 1.28803
\(147\) −22.8254 −1.88261
\(148\) 54.4887 4.47894
\(149\) −5.26544 −0.431362 −0.215681 0.976464i \(-0.569197\pi\)
−0.215681 + 0.976464i \(0.569197\pi\)
\(150\) 12.4984 1.02049
\(151\) −10.6145 −0.863793 −0.431897 0.901923i \(-0.642156\pi\)
−0.431897 + 0.901923i \(0.642156\pi\)
\(152\) 36.4372 2.95545
\(153\) 17.8009 1.43912
\(154\) 2.93527 0.236531
\(155\) 6.84285 0.549631
\(156\) 48.2421 3.86246
\(157\) 4.47300 0.356984 0.178492 0.983941i \(-0.442878\pi\)
0.178492 + 0.983941i \(0.442878\pi\)
\(158\) 29.6584 2.35949
\(159\) −32.1625 −2.55065
\(160\) 36.7690 2.90684
\(161\) 0.850214 0.0670062
\(162\) −75.9507 −5.96725
\(163\) 18.5835 1.45558 0.727788 0.685803i \(-0.240549\pi\)
0.727788 + 0.685803i \(0.240549\pi\)
\(164\) −59.1566 −4.61936
\(165\) 32.1292 2.50126
\(166\) 23.2787 1.80678
\(167\) −1.18642 −0.0918078 −0.0459039 0.998946i \(-0.514617\pi\)
−0.0459039 + 0.998946i \(0.514617\pi\)
\(168\) −6.22973 −0.480634
\(169\) −5.42156 −0.417043
\(170\) 11.7710 0.902795
\(171\) −31.2730 −2.39151
\(172\) −29.7956 −2.27189
\(173\) −22.3431 −1.69872 −0.849359 0.527816i \(-0.823011\pi\)
−0.849359 + 0.527816i \(0.823011\pi\)
\(174\) 31.9465 2.42186
\(175\) −0.294903 −0.0222926
\(176\) −71.4755 −5.38767
\(177\) −34.8265 −2.61772
\(178\) −31.0641 −2.32835
\(179\) −18.2940 −1.36736 −0.683680 0.729782i \(-0.739622\pi\)
−0.683680 + 0.729782i \(0.739622\pi\)
\(180\) −78.6437 −5.86175
\(181\) −12.2496 −0.910504 −0.455252 0.890363i \(-0.650451\pi\)
−0.455252 + 0.890363i \(0.650451\pi\)
\(182\) −1.56458 −0.115974
\(183\) 9.55327 0.706198
\(184\) −36.6814 −2.70419
\(185\) −19.3432 −1.42214
\(186\) 32.0892 2.35289
\(187\) −11.8357 −0.865514
\(188\) 22.0588 1.60880
\(189\) 3.28176 0.238713
\(190\) −20.6796 −1.50025
\(191\) 4.85407 0.351228 0.175614 0.984459i \(-0.443809\pi\)
0.175614 + 0.984459i \(0.443809\pi\)
\(192\) 81.6010 5.88905
\(193\) −8.96655 −0.645426 −0.322713 0.946497i \(-0.604595\pi\)
−0.322713 + 0.946497i \(0.604595\pi\)
\(194\) 15.3545 1.10239
\(195\) −17.1257 −1.22640
\(196\) −37.1480 −2.65343
\(197\) −0.602301 −0.0429122 −0.0214561 0.999770i \(-0.506830\pi\)
−0.0214561 + 0.999770i \(0.506830\pi\)
\(198\) 108.690 7.72427
\(199\) −15.8168 −1.12123 −0.560613 0.828078i \(-0.689434\pi\)
−0.560613 + 0.828078i \(0.689434\pi\)
\(200\) 12.7232 0.899667
\(201\) 18.4059 1.29825
\(202\) 0.800519 0.0563243
\(203\) −0.753787 −0.0529055
\(204\) 40.1597 2.81174
\(205\) 21.0003 1.46673
\(206\) 7.29928 0.508565
\(207\) 31.4826 2.18819
\(208\) 38.0983 2.64164
\(209\) 20.7933 1.43830
\(210\) 3.53562 0.243981
\(211\) −16.4907 −1.13527 −0.567633 0.823282i \(-0.692141\pi\)
−0.567633 + 0.823282i \(0.692141\pi\)
\(212\) −52.3439 −3.59500
\(213\) −31.2777 −2.14311
\(214\) −0.867182 −0.0592794
\(215\) 10.5773 0.721366
\(216\) −141.588 −9.63382
\(217\) −0.757153 −0.0513989
\(218\) 10.8714 0.736307
\(219\) −18.8496 −1.27374
\(220\) 52.2898 3.52538
\(221\) 6.30876 0.424373
\(222\) −90.7090 −6.08799
\(223\) 22.1735 1.48484 0.742422 0.669932i \(-0.233677\pi\)
0.742422 + 0.669932i \(0.233677\pi\)
\(224\) −4.06844 −0.271834
\(225\) −10.9200 −0.727998
\(226\) −25.6500 −1.70621
\(227\) −14.3168 −0.950239 −0.475119 0.879921i \(-0.657595\pi\)
−0.475119 + 0.879921i \(0.657595\pi\)
\(228\) −70.5534 −4.67251
\(229\) −15.2184 −1.00566 −0.502832 0.864384i \(-0.667708\pi\)
−0.502832 + 0.864384i \(0.667708\pi\)
\(230\) 20.8182 1.37271
\(231\) −3.55506 −0.233906
\(232\) 32.5212 2.13512
\(233\) 21.7843 1.42714 0.713568 0.700586i \(-0.247078\pi\)
0.713568 + 0.700586i \(0.247078\pi\)
\(234\) −57.9347 −3.78731
\(235\) −7.83077 −0.510823
\(236\) −56.6795 −3.68952
\(237\) −35.9208 −2.33331
\(238\) −1.30245 −0.0844251
\(239\) −3.77638 −0.244274 −0.122137 0.992513i \(-0.538975\pi\)
−0.122137 + 0.992513i \(0.538975\pi\)
\(240\) −86.0944 −5.55737
\(241\) 8.82310 0.568346 0.284173 0.958773i \(-0.408281\pi\)
0.284173 + 0.958773i \(0.408281\pi\)
\(242\) −42.4649 −2.72975
\(243\) 45.0544 2.89024
\(244\) 15.5478 0.995346
\(245\) 13.1874 0.842511
\(246\) 98.4800 6.27885
\(247\) −11.0834 −0.705218
\(248\) 32.6664 2.07432
\(249\) −28.1941 −1.78673
\(250\) −32.9030 −2.08097
\(251\) −5.13955 −0.324406 −0.162203 0.986757i \(-0.551860\pi\)
−0.162203 + 0.986757i \(0.551860\pi\)
\(252\) 8.70182 0.548163
\(253\) −20.9326 −1.31602
\(254\) −54.5882 −3.42517
\(255\) −14.2565 −0.892776
\(256\) 27.7115 1.73197
\(257\) −23.8081 −1.48511 −0.742555 0.669785i \(-0.766386\pi\)
−0.742555 + 0.669785i \(0.766386\pi\)
\(258\) 49.6017 3.08807
\(259\) 2.14030 0.132992
\(260\) −27.8718 −1.72854
\(261\) −27.9120 −1.72771
\(262\) −1.86093 −0.114968
\(263\) −14.7079 −0.906927 −0.453464 0.891275i \(-0.649812\pi\)
−0.453464 + 0.891275i \(0.649812\pi\)
\(264\) 153.379 9.43980
\(265\) 18.5819 1.14147
\(266\) 2.28817 0.140297
\(267\) 37.6234 2.30251
\(268\) 29.9552 1.82981
\(269\) −32.6396 −1.99007 −0.995036 0.0995109i \(-0.968272\pi\)
−0.995036 + 0.0995109i \(0.968272\pi\)
\(270\) 80.3566 4.89035
\(271\) 2.59250 0.157483 0.0787417 0.996895i \(-0.474910\pi\)
0.0787417 + 0.996895i \(0.474910\pi\)
\(272\) 31.7154 1.92303
\(273\) 1.89494 0.114687
\(274\) −44.4205 −2.68354
\(275\) 7.26063 0.437833
\(276\) 71.0262 4.27528
\(277\) 20.8916 1.25525 0.627626 0.778515i \(-0.284027\pi\)
0.627626 + 0.778515i \(0.284027\pi\)
\(278\) −45.3999 −2.72290
\(279\) −28.0367 −1.67851
\(280\) 3.59922 0.215095
\(281\) 3.10100 0.184990 0.0924952 0.995713i \(-0.470516\pi\)
0.0924952 + 0.995713i \(0.470516\pi\)
\(282\) −36.7220 −2.18676
\(283\) −22.7565 −1.35274 −0.676368 0.736564i \(-0.736447\pi\)
−0.676368 + 0.736564i \(0.736447\pi\)
\(284\) −50.9039 −3.02059
\(285\) 25.0461 1.48360
\(286\) 38.5205 2.27777
\(287\) −2.32366 −0.137161
\(288\) −150.650 −8.87716
\(289\) −11.7482 −0.691071
\(290\) −18.4571 −1.08384
\(291\) −18.5967 −1.09016
\(292\) −30.6774 −1.79526
\(293\) −30.8413 −1.80177 −0.900884 0.434059i \(-0.857081\pi\)
−0.900884 + 0.434059i \(0.857081\pi\)
\(294\) 61.8415 3.60667
\(295\) 20.1210 1.17149
\(296\) −92.3407 −5.36720
\(297\) −80.7984 −4.68840
\(298\) 14.2658 0.826394
\(299\) 11.1576 0.645263
\(300\) −24.6360 −1.42236
\(301\) −1.17037 −0.0674587
\(302\) 28.7580 1.65484
\(303\) −0.969551 −0.0556993
\(304\) −55.7182 −3.19566
\(305\) −5.51940 −0.316040
\(306\) −48.2284 −2.75703
\(307\) 25.6319 1.46289 0.731444 0.681901i \(-0.238847\pi\)
0.731444 + 0.681901i \(0.238847\pi\)
\(308\) −5.78580 −0.329676
\(309\) −8.84055 −0.502921
\(310\) −18.5395 −1.05297
\(311\) 19.4166 1.10102 0.550508 0.834830i \(-0.314434\pi\)
0.550508 + 0.834830i \(0.314434\pi\)
\(312\) −81.7548 −4.62846
\(313\) 15.6980 0.887304 0.443652 0.896199i \(-0.353683\pi\)
0.443652 + 0.896199i \(0.353683\pi\)
\(314\) −12.1188 −0.683903
\(315\) −3.08911 −0.174051
\(316\) −58.4605 −3.28866
\(317\) −13.8845 −0.779831 −0.389915 0.920851i \(-0.627496\pi\)
−0.389915 + 0.920851i \(0.627496\pi\)
\(318\) 87.1386 4.88649
\(319\) 18.5585 1.03908
\(320\) −47.1449 −2.63548
\(321\) 1.05029 0.0586215
\(322\) −2.30350 −0.128369
\(323\) −9.22646 −0.513374
\(324\) 149.709 8.31716
\(325\) −3.87011 −0.214675
\(326\) −50.3488 −2.78856
\(327\) −13.1670 −0.728136
\(328\) 100.251 5.53546
\(329\) 0.866465 0.0477697
\(330\) −87.0484 −4.79186
\(331\) −30.4171 −1.67187 −0.835937 0.548826i \(-0.815075\pi\)
−0.835937 + 0.548826i \(0.815075\pi\)
\(332\) −45.8854 −2.51829
\(333\) 79.2534 4.34306
\(334\) 3.21439 0.175884
\(335\) −10.6340 −0.580996
\(336\) 9.52624 0.519699
\(337\) −29.4203 −1.60262 −0.801312 0.598247i \(-0.795864\pi\)
−0.801312 + 0.598247i \(0.795864\pi\)
\(338\) 14.6887 0.798962
\(339\) 31.0661 1.68728
\(340\) −23.2022 −1.25832
\(341\) 18.6414 1.00949
\(342\) 84.7287 4.58160
\(343\) −2.92757 −0.158074
\(344\) 50.4939 2.72245
\(345\) −25.2140 −1.35748
\(346\) 60.5348 3.25437
\(347\) 30.3090 1.62707 0.813536 0.581515i \(-0.197540\pi\)
0.813536 + 0.581515i \(0.197540\pi\)
\(348\) −62.9708 −3.37559
\(349\) 9.41165 0.503794 0.251897 0.967754i \(-0.418946\pi\)
0.251897 + 0.967754i \(0.418946\pi\)
\(350\) 0.798987 0.0427077
\(351\) 43.0677 2.29878
\(352\) 100.167 5.33890
\(353\) −11.1145 −0.591568 −0.295784 0.955255i \(-0.595581\pi\)
−0.295784 + 0.955255i \(0.595581\pi\)
\(354\) 94.3563 5.01498
\(355\) 18.0707 0.959091
\(356\) 61.2315 3.24526
\(357\) 1.57746 0.0834882
\(358\) 49.5644 2.61956
\(359\) 34.8111 1.83726 0.918631 0.395117i \(-0.129296\pi\)
0.918631 + 0.395117i \(0.129296\pi\)
\(360\) 133.276 7.02424
\(361\) −2.79074 −0.146881
\(362\) 33.1881 1.74433
\(363\) 51.4316 2.69946
\(364\) 3.08398 0.161645
\(365\) 10.8903 0.570026
\(366\) −25.8829 −1.35292
\(367\) −18.8522 −0.984078 −0.492039 0.870573i \(-0.663748\pi\)
−0.492039 + 0.870573i \(0.663748\pi\)
\(368\) 56.0917 2.92398
\(369\) −86.0429 −4.47922
\(370\) 52.4071 2.72451
\(371\) −2.05606 −0.106745
\(372\) −63.2520 −3.27946
\(373\) −36.6470 −1.89751 −0.948755 0.316012i \(-0.897656\pi\)
−0.948755 + 0.316012i \(0.897656\pi\)
\(374\) 32.0668 1.65813
\(375\) 39.8506 2.05788
\(376\) −37.3825 −1.92786
\(377\) −9.89220 −0.509474
\(378\) −8.89136 −0.457322
\(379\) 32.8260 1.68616 0.843080 0.537789i \(-0.180740\pi\)
0.843080 + 0.537789i \(0.180740\pi\)
\(380\) 40.7622 2.09105
\(381\) 66.1147 3.38716
\(382\) −13.1512 −0.672876
\(383\) 12.3381 0.630446 0.315223 0.949018i \(-0.397921\pi\)
0.315223 + 0.949018i \(0.397921\pi\)
\(384\) −93.8000 −4.78671
\(385\) 2.05393 0.104678
\(386\) 24.2933 1.23650
\(387\) −43.3375 −2.20297
\(388\) −30.2658 −1.53651
\(389\) 9.17177 0.465027 0.232514 0.972593i \(-0.425305\pi\)
0.232514 + 0.972593i \(0.425305\pi\)
\(390\) 46.3991 2.34951
\(391\) 9.28830 0.469729
\(392\) 62.9539 3.17965
\(393\) 2.25387 0.113693
\(394\) 1.63183 0.0822104
\(395\) 20.7532 1.04421
\(396\) −214.242 −10.7661
\(397\) 12.5377 0.629248 0.314624 0.949216i \(-0.398122\pi\)
0.314624 + 0.949216i \(0.398122\pi\)
\(398\) 42.8529 2.14802
\(399\) −2.77132 −0.138740
\(400\) −19.4558 −0.972790
\(401\) 23.7631 1.18667 0.593337 0.804954i \(-0.297810\pi\)
0.593337 + 0.804954i \(0.297810\pi\)
\(402\) −49.8674 −2.48716
\(403\) −9.93638 −0.494966
\(404\) −1.57793 −0.0785049
\(405\) −53.1459 −2.64084
\(406\) 2.04225 0.101355
\(407\) −52.6952 −2.61200
\(408\) −68.0577 −3.36936
\(409\) 16.2292 0.802481 0.401240 0.915973i \(-0.368579\pi\)
0.401240 + 0.915973i \(0.368579\pi\)
\(410\) −56.8967 −2.80993
\(411\) 53.8000 2.65376
\(412\) −14.3879 −0.708839
\(413\) −2.22636 −0.109552
\(414\) −85.2965 −4.19210
\(415\) 16.2891 0.799602
\(416\) −53.3915 −2.61773
\(417\) 54.9862 2.69269
\(418\) −56.3357 −2.75547
\(419\) 1.41667 0.0692089 0.0346045 0.999401i \(-0.488983\pi\)
0.0346045 + 0.999401i \(0.488983\pi\)
\(420\) −6.96917 −0.340061
\(421\) −22.1382 −1.07895 −0.539475 0.842002i \(-0.681377\pi\)
−0.539475 + 0.842002i \(0.681377\pi\)
\(422\) 44.6786 2.17492
\(423\) 32.0843 1.55999
\(424\) 88.7061 4.30795
\(425\) −3.22172 −0.156276
\(426\) 84.7413 4.10573
\(427\) 0.610714 0.0295545
\(428\) 1.70933 0.0826236
\(429\) −46.6542 −2.25249
\(430\) −28.6573 −1.38198
\(431\) −9.06906 −0.436841 −0.218421 0.975855i \(-0.570090\pi\)
−0.218421 + 0.975855i \(0.570090\pi\)
\(432\) 216.510 10.4168
\(433\) −18.0098 −0.865496 −0.432748 0.901515i \(-0.642456\pi\)
−0.432748 + 0.901515i \(0.642456\pi\)
\(434\) 2.05137 0.0984691
\(435\) 22.3543 1.07181
\(436\) −21.4290 −1.02626
\(437\) −16.3179 −0.780591
\(438\) 51.0696 2.44020
\(439\) −6.81076 −0.325060 −0.162530 0.986704i \(-0.551965\pi\)
−0.162530 + 0.986704i \(0.551965\pi\)
\(440\) −88.6143 −4.22452
\(441\) −54.0315 −2.57293
\(442\) −17.0925 −0.813005
\(443\) −5.18584 −0.246387 −0.123193 0.992383i \(-0.539314\pi\)
−0.123193 + 0.992383i \(0.539314\pi\)
\(444\) 178.799 8.48545
\(445\) −21.7369 −1.03043
\(446\) −60.0751 −2.84464
\(447\) −17.2780 −0.817223
\(448\) 5.21653 0.246458
\(449\) −9.34671 −0.441099 −0.220549 0.975376i \(-0.570785\pi\)
−0.220549 + 0.975376i \(0.570785\pi\)
\(450\) 29.5857 1.39468
\(451\) 57.2095 2.69389
\(452\) 50.5595 2.37812
\(453\) −34.8304 −1.63647
\(454\) 38.7888 1.82045
\(455\) −1.09480 −0.0513250
\(456\) 119.565 5.59916
\(457\) 27.7641 1.29875 0.649374 0.760469i \(-0.275031\pi\)
0.649374 + 0.760469i \(0.275031\pi\)
\(458\) 41.2317 1.92663
\(459\) 35.8522 1.67344
\(460\) −41.0353 −1.91328
\(461\) −22.1977 −1.03385 −0.516924 0.856031i \(-0.672923\pi\)
−0.516924 + 0.856031i \(0.672923\pi\)
\(462\) 9.63180 0.448112
\(463\) −14.5578 −0.676557 −0.338278 0.941046i \(-0.609845\pi\)
−0.338278 + 0.941046i \(0.609845\pi\)
\(464\) −49.7300 −2.30866
\(465\) 22.4542 1.04129
\(466\) −59.0206 −2.73408
\(467\) 25.2113 1.16664 0.583320 0.812242i \(-0.301753\pi\)
0.583320 + 0.812242i \(0.301753\pi\)
\(468\) 114.197 5.27876
\(469\) 1.17663 0.0543320
\(470\) 21.2161 0.978625
\(471\) 14.6777 0.676313
\(472\) 96.0536 4.42122
\(473\) 28.8149 1.32491
\(474\) 97.3211 4.47011
\(475\) 5.65998 0.259698
\(476\) 2.56730 0.117672
\(477\) −76.1339 −3.48593
\(478\) 10.2314 0.467976
\(479\) −26.7187 −1.22081 −0.610404 0.792090i \(-0.708993\pi\)
−0.610404 + 0.792090i \(0.708993\pi\)
\(480\) 120.654 5.50707
\(481\) 28.0879 1.28070
\(482\) −23.9046 −1.08883
\(483\) 2.78990 0.126945
\(484\) 83.7040 3.80473
\(485\) 10.7442 0.487870
\(486\) −122.067 −5.53707
\(487\) 9.58729 0.434442 0.217221 0.976122i \(-0.430301\pi\)
0.217221 + 0.976122i \(0.430301\pi\)
\(488\) −26.3485 −1.19274
\(489\) 60.9801 2.75762
\(490\) −35.7289 −1.61407
\(491\) −19.3437 −0.872969 −0.436485 0.899712i \(-0.643777\pi\)
−0.436485 + 0.899712i \(0.643777\pi\)
\(492\) −194.117 −8.75147
\(493\) −8.23487 −0.370880
\(494\) 30.0284 1.35104
\(495\) 76.0551 3.41842
\(496\) −49.9521 −2.24292
\(497\) −1.99950 −0.0896896
\(498\) 76.3870 3.42298
\(499\) −0.905302 −0.0405269 −0.0202634 0.999795i \(-0.506450\pi\)
−0.0202634 + 0.999795i \(0.506450\pi\)
\(500\) 64.8562 2.90046
\(501\) −3.89312 −0.173932
\(502\) 13.9247 0.621490
\(503\) 15.2979 0.682098 0.341049 0.940045i \(-0.389218\pi\)
0.341049 + 0.940045i \(0.389218\pi\)
\(504\) −14.7468 −0.656874
\(505\) 0.560157 0.0249267
\(506\) 56.7132 2.52121
\(507\) −17.7903 −0.790096
\(508\) 107.601 4.77400
\(509\) −14.8703 −0.659114 −0.329557 0.944136i \(-0.606899\pi\)
−0.329557 + 0.944136i \(0.606899\pi\)
\(510\) 38.6255 1.71036
\(511\) −1.20500 −0.0533061
\(512\) −17.9087 −0.791459
\(513\) −62.9859 −2.78089
\(514\) 64.5039 2.84515
\(515\) 5.10762 0.225069
\(516\) −97.7715 −4.30415
\(517\) −21.3327 −0.938212
\(518\) −5.79878 −0.254784
\(519\) −73.3169 −3.21826
\(520\) 47.2338 2.07134
\(521\) −15.2271 −0.667113 −0.333556 0.942730i \(-0.608249\pi\)
−0.333556 + 0.942730i \(0.608249\pi\)
\(522\) 75.6226 3.30991
\(523\) −12.2771 −0.536840 −0.268420 0.963302i \(-0.586502\pi\)
−0.268420 + 0.963302i \(0.586502\pi\)
\(524\) 3.66813 0.160243
\(525\) −0.967696 −0.0422337
\(526\) 39.8484 1.73747
\(527\) −8.27164 −0.360318
\(528\) −234.540 −10.2070
\(529\) −6.57275 −0.285772
\(530\) −50.3443 −2.18682
\(531\) −82.4400 −3.57759
\(532\) −4.51028 −0.195546
\(533\) −30.4942 −1.32085
\(534\) −101.934 −4.41111
\(535\) −0.606804 −0.0262344
\(536\) −50.7644 −2.19269
\(537\) −60.0301 −2.59049
\(538\) 88.4313 3.81254
\(539\) 35.9253 1.54741
\(540\) −158.393 −6.81617
\(541\) −34.0267 −1.46292 −0.731462 0.681882i \(-0.761162\pi\)
−0.731462 + 0.681882i \(0.761162\pi\)
\(542\) −7.02393 −0.301704
\(543\) −40.1958 −1.72497
\(544\) −44.4463 −1.90562
\(545\) 7.60721 0.325857
\(546\) −5.13401 −0.219715
\(547\) −37.5998 −1.60765 −0.803826 0.594865i \(-0.797205\pi\)
−0.803826 + 0.594865i \(0.797205\pi\)
\(548\) 87.5586 3.74032
\(549\) 22.6142 0.965149
\(550\) −19.6714 −0.838791
\(551\) 14.4672 0.616323
\(552\) −120.367 −5.12314
\(553\) −2.29632 −0.0976494
\(554\) −56.6020 −2.40479
\(555\) −63.4730 −2.69428
\(556\) 89.4891 3.79518
\(557\) −6.86733 −0.290978 −0.145489 0.989360i \(-0.546476\pi\)
−0.145489 + 0.989360i \(0.546476\pi\)
\(558\) 75.9604 3.21566
\(559\) −15.3591 −0.649621
\(560\) −5.50378 −0.232577
\(561\) −38.8378 −1.63973
\(562\) −8.40162 −0.354401
\(563\) −0.799100 −0.0336781 −0.0168390 0.999858i \(-0.505360\pi\)
−0.0168390 + 0.999858i \(0.505360\pi\)
\(564\) 72.3838 3.04791
\(565\) −17.9484 −0.755095
\(566\) 61.6548 2.59155
\(567\) 5.88053 0.246959
\(568\) 86.2657 3.61963
\(569\) 7.21890 0.302632 0.151316 0.988485i \(-0.451649\pi\)
0.151316 + 0.988485i \(0.451649\pi\)
\(570\) −67.8581 −2.84226
\(571\) 18.7072 0.782871 0.391436 0.920205i \(-0.371979\pi\)
0.391436 + 0.920205i \(0.371979\pi\)
\(572\) −75.9290 −3.17475
\(573\) 15.9282 0.665409
\(574\) 6.29555 0.262771
\(575\) −5.69791 −0.237619
\(576\) 193.163 8.04845
\(577\) 4.96673 0.206768 0.103384 0.994642i \(-0.467033\pi\)
0.103384 + 0.994642i \(0.467033\pi\)
\(578\) 31.8297 1.32394
\(579\) −29.4229 −1.22277
\(580\) 36.3813 1.51065
\(581\) −1.80237 −0.0747750
\(582\) 50.3844 2.08850
\(583\) 50.6211 2.09651
\(584\) 51.9883 2.15129
\(585\) −40.5394 −1.67610
\(586\) 83.5591 3.45179
\(587\) 26.1577 1.07964 0.539821 0.841780i \(-0.318492\pi\)
0.539821 + 0.841780i \(0.318492\pi\)
\(588\) −121.898 −5.02698
\(589\) 14.5318 0.598773
\(590\) −54.5142 −2.24432
\(591\) −1.97640 −0.0812980
\(592\) 141.204 5.80343
\(593\) 1.93002 0.0792565 0.0396282 0.999214i \(-0.487383\pi\)
0.0396282 + 0.999214i \(0.487383\pi\)
\(594\) 218.909 8.98195
\(595\) −0.911378 −0.0373629
\(596\) −28.1197 −1.15183
\(597\) −51.9014 −2.12418
\(598\) −30.2297 −1.23618
\(599\) 42.7468 1.74659 0.873293 0.487195i \(-0.161980\pi\)
0.873293 + 0.487195i \(0.161980\pi\)
\(600\) 41.7500 1.70444
\(601\) −7.94266 −0.323988 −0.161994 0.986792i \(-0.551792\pi\)
−0.161994 + 0.986792i \(0.551792\pi\)
\(602\) 3.17090 0.129236
\(603\) 43.5697 1.77429
\(604\) −56.6859 −2.30652
\(605\) −29.7145 −1.20807
\(606\) 2.62683 0.106708
\(607\) −5.03411 −0.204328 −0.102164 0.994768i \(-0.532577\pi\)
−0.102164 + 0.994768i \(0.532577\pi\)
\(608\) 78.0843 3.16674
\(609\) −2.47348 −0.100230
\(610\) 14.9538 0.605463
\(611\) 11.3709 0.460018
\(612\) 95.0645 3.84275
\(613\) 22.6503 0.914835 0.457418 0.889252i \(-0.348774\pi\)
0.457418 + 0.889252i \(0.348774\pi\)
\(614\) −69.4450 −2.80257
\(615\) 68.9106 2.77874
\(616\) 9.80506 0.395057
\(617\) −31.8408 −1.28186 −0.640931 0.767598i \(-0.721452\pi\)
−0.640931 + 0.767598i \(0.721452\pi\)
\(618\) 23.9519 0.963487
\(619\) 32.3649 1.30086 0.650428 0.759568i \(-0.274590\pi\)
0.650428 + 0.759568i \(0.274590\pi\)
\(620\) 36.5438 1.46763
\(621\) 63.4080 2.54448
\(622\) −52.6059 −2.10930
\(623\) 2.40516 0.0963607
\(624\) 125.016 5.00465
\(625\) −15.9945 −0.639779
\(626\) −42.5310 −1.69988
\(627\) 68.2311 2.72489
\(628\) 23.8877 0.953224
\(629\) 23.3821 0.932306
\(630\) 8.36939 0.333445
\(631\) −35.1277 −1.39841 −0.699206 0.714920i \(-0.746463\pi\)
−0.699206 + 0.714920i \(0.746463\pi\)
\(632\) 99.0718 3.94086
\(633\) −54.1126 −2.15078
\(634\) 37.6176 1.49399
\(635\) −38.1977 −1.51583
\(636\) −171.762 −6.81080
\(637\) −19.1491 −0.758717
\(638\) −50.2811 −1.99065
\(639\) −74.0394 −2.92895
\(640\) 54.1929 2.14216
\(641\) −1.04563 −0.0413000 −0.0206500 0.999787i \(-0.506574\pi\)
−0.0206500 + 0.999787i \(0.506574\pi\)
\(642\) −2.84558 −0.112306
\(643\) −34.5026 −1.36065 −0.680324 0.732911i \(-0.738161\pi\)
−0.680324 + 0.732911i \(0.738161\pi\)
\(644\) 4.54051 0.178921
\(645\) 34.7084 1.36664
\(646\) 24.9975 0.983512
\(647\) 23.9717 0.942423 0.471212 0.882020i \(-0.343817\pi\)
0.471212 + 0.882020i \(0.343817\pi\)
\(648\) −253.708 −9.96660
\(649\) 54.8139 2.15164
\(650\) 10.4854 0.411271
\(651\) −2.48453 −0.0973763
\(652\) 99.2442 3.88670
\(653\) 38.0668 1.48967 0.744835 0.667249i \(-0.232528\pi\)
0.744835 + 0.667249i \(0.232528\pi\)
\(654\) 35.6736 1.39495
\(655\) −1.30217 −0.0508800
\(656\) −153.300 −5.98537
\(657\) −44.6200 −1.74079
\(658\) −2.34753 −0.0915164
\(659\) −23.5942 −0.919098 −0.459549 0.888152i \(-0.651989\pi\)
−0.459549 + 0.888152i \(0.651989\pi\)
\(660\) 171.584 6.67890
\(661\) 18.1139 0.704547 0.352274 0.935897i \(-0.385409\pi\)
0.352274 + 0.935897i \(0.385409\pi\)
\(662\) 82.4097 3.20294
\(663\) 20.7016 0.803983
\(664\) 77.7610 3.01771
\(665\) 1.60113 0.0620891
\(666\) −214.723 −8.32035
\(667\) −14.5642 −0.563926
\(668\) −6.33599 −0.245147
\(669\) 72.7601 2.81307
\(670\) 28.8108 1.11306
\(671\) −15.0360 −0.580460
\(672\) −13.3502 −0.514995
\(673\) −23.9047 −0.921457 −0.460729 0.887541i \(-0.652412\pi\)
−0.460729 + 0.887541i \(0.652412\pi\)
\(674\) 79.7090 3.07027
\(675\) −21.9935 −0.846532
\(676\) −28.9534 −1.11359
\(677\) −10.0892 −0.387758 −0.193879 0.981025i \(-0.562107\pi\)
−0.193879 + 0.981025i \(0.562107\pi\)
\(678\) −84.1681 −3.23246
\(679\) −1.18883 −0.0456233
\(680\) 39.3203 1.50786
\(681\) −46.9792 −1.80025
\(682\) −50.5057 −1.93396
\(683\) 29.6675 1.13520 0.567598 0.823306i \(-0.307873\pi\)
0.567598 + 0.823306i \(0.307873\pi\)
\(684\) −167.011 −6.38584
\(685\) −31.0829 −1.18762
\(686\) 7.93172 0.302835
\(687\) −49.9379 −1.90525
\(688\) −77.2132 −2.94373
\(689\) −26.9824 −1.02795
\(690\) 68.3128 2.60063
\(691\) −18.1269 −0.689581 −0.344790 0.938680i \(-0.612050\pi\)
−0.344790 + 0.938680i \(0.612050\pi\)
\(692\) −119.322 −4.53594
\(693\) −8.41540 −0.319675
\(694\) −82.1168 −3.11711
\(695\) −31.7682 −1.20504
\(696\) 106.715 4.04503
\(697\) −25.3852 −0.961534
\(698\) −25.4992 −0.965159
\(699\) 71.4830 2.70374
\(700\) −1.57491 −0.0595260
\(701\) 4.53335 0.171222 0.0856112 0.996329i \(-0.472716\pi\)
0.0856112 + 0.996329i \(0.472716\pi\)
\(702\) −116.684 −4.40397
\(703\) −41.0782 −1.54929
\(704\) −128.433 −4.84050
\(705\) −25.6959 −0.967764
\(706\) 30.1129 1.13331
\(707\) −0.0619807 −0.00233102
\(708\) −185.989 −6.98988
\(709\) 30.4848 1.14488 0.572441 0.819946i \(-0.305997\pi\)
0.572441 + 0.819946i \(0.305997\pi\)
\(710\) −48.9592 −1.83741
\(711\) −85.0304 −3.18889
\(712\) −103.768 −3.88885
\(713\) −14.6292 −0.547868
\(714\) −4.27386 −0.159945
\(715\) 26.9544 1.00804
\(716\) −97.6980 −3.65115
\(717\) −12.3919 −0.462782
\(718\) −94.3146 −3.51979
\(719\) 21.6069 0.805802 0.402901 0.915243i \(-0.368002\pi\)
0.402901 + 0.915243i \(0.368002\pi\)
\(720\) −203.800 −7.59516
\(721\) −0.565152 −0.0210474
\(722\) 7.56102 0.281392
\(723\) 28.9522 1.07674
\(724\) −65.4181 −2.43124
\(725\) 5.05168 0.187615
\(726\) −139.345 −5.17157
\(727\) −24.8759 −0.922597 −0.461299 0.887245i \(-0.652616\pi\)
−0.461299 + 0.887245i \(0.652616\pi\)
\(728\) −5.22636 −0.193702
\(729\) 63.7426 2.36084
\(730\) −29.5054 −1.09204
\(731\) −12.7858 −0.472902
\(732\) 51.0186 1.88570
\(733\) −40.7721 −1.50595 −0.752976 0.658048i \(-0.771383\pi\)
−0.752976 + 0.658048i \(0.771383\pi\)
\(734\) 51.0768 1.88528
\(735\) 43.2731 1.59615
\(736\) −78.6076 −2.89752
\(737\) −28.9692 −1.06710
\(738\) 233.118 8.58120
\(739\) 21.5673 0.793364 0.396682 0.917956i \(-0.370162\pi\)
0.396682 + 0.917956i \(0.370162\pi\)
\(740\) −103.301 −3.79743
\(741\) −36.3690 −1.33605
\(742\) 5.57053 0.204501
\(743\) 41.4941 1.52227 0.761136 0.648593i \(-0.224642\pi\)
0.761136 + 0.648593i \(0.224642\pi\)
\(744\) 107.192 3.92984
\(745\) 9.98237 0.365726
\(746\) 99.2886 3.63521
\(747\) −66.7401 −2.44189
\(748\) −63.2079 −2.31111
\(749\) 0.0671421 0.00245332
\(750\) −107.968 −3.94244
\(751\) −2.04360 −0.0745721 −0.0372860 0.999305i \(-0.511871\pi\)
−0.0372860 + 0.999305i \(0.511871\pi\)
\(752\) 57.1638 2.08455
\(753\) −16.8650 −0.614593
\(754\) 26.8012 0.976041
\(755\) 20.1232 0.732359
\(756\) 17.5260 0.637416
\(757\) −22.3884 −0.813720 −0.406860 0.913490i \(-0.633376\pi\)
−0.406860 + 0.913490i \(0.633376\pi\)
\(758\) −88.9363 −3.23031
\(759\) −68.6884 −2.49323
\(760\) −69.0787 −2.50575
\(761\) −0.615377 −0.0223074 −0.0111537 0.999938i \(-0.503550\pi\)
−0.0111537 + 0.999938i \(0.503550\pi\)
\(762\) −179.126 −6.48905
\(763\) −0.841728 −0.0304726
\(764\) 25.9228 0.937855
\(765\) −33.7475 −1.22014
\(766\) −33.4278 −1.20780
\(767\) −29.2173 −1.05498
\(768\) 90.9325 3.28125
\(769\) 52.3955 1.88943 0.944714 0.327894i \(-0.106339\pi\)
0.944714 + 0.327894i \(0.106339\pi\)
\(770\) −5.56477 −0.200540
\(771\) −78.1242 −2.81357
\(772\) −47.8853 −1.72343
\(773\) 29.1928 1.04999 0.524997 0.851104i \(-0.324067\pi\)
0.524997 + 0.851104i \(0.324067\pi\)
\(774\) 117.415 4.22041
\(775\) 5.07425 0.182272
\(776\) 51.2907 1.84123
\(777\) 7.02321 0.251956
\(778\) −24.8493 −0.890890
\(779\) 44.5973 1.59786
\(780\) −91.4588 −3.27475
\(781\) 49.2284 1.76153
\(782\) −25.1650 −0.899899
\(783\) −56.2166 −2.00902
\(784\) −96.2665 −3.43809
\(785\) −8.48004 −0.302666
\(786\) −6.10645 −0.217810
\(787\) 32.4773 1.15769 0.578845 0.815438i \(-0.303504\pi\)
0.578845 + 0.815438i \(0.303504\pi\)
\(788\) −3.21655 −0.114585
\(789\) −48.2625 −1.71819
\(790\) −56.2272 −2.00047
\(791\) 1.98597 0.0706129
\(792\) 363.072 12.9012
\(793\) 8.01461 0.284607
\(794\) −33.9686 −1.20550
\(795\) 60.9746 2.16255
\(796\) −84.4687 −2.99391
\(797\) −6.58537 −0.233266 −0.116633 0.993175i \(-0.537210\pi\)
−0.116633 + 0.993175i \(0.537210\pi\)
\(798\) 7.50841 0.265795
\(799\) 9.46583 0.334877
\(800\) 27.2656 0.963986
\(801\) 89.0607 3.14681
\(802\) −64.3820 −2.27341
\(803\) 29.6676 1.04695
\(804\) 98.2952 3.46660
\(805\) −1.61186 −0.0568106
\(806\) 26.9209 0.948247
\(807\) −107.104 −3.77023
\(808\) 2.67408 0.0940738
\(809\) −25.4573 −0.895030 −0.447515 0.894276i \(-0.647691\pi\)
−0.447515 + 0.894276i \(0.647691\pi\)
\(810\) 143.990 5.05928
\(811\) −1.06088 −0.0372524 −0.0186262 0.999827i \(-0.505929\pi\)
−0.0186262 + 0.999827i \(0.505929\pi\)
\(812\) −4.02555 −0.141269
\(813\) 8.50706 0.298356
\(814\) 142.768 5.00403
\(815\) −35.2312 −1.23410
\(816\) 104.071 3.64321
\(817\) 22.4625 0.785862
\(818\) −43.9701 −1.53738
\(819\) 4.48563 0.156741
\(820\) 112.151 3.91648
\(821\) 38.7114 1.35104 0.675519 0.737342i \(-0.263919\pi\)
0.675519 + 0.737342i \(0.263919\pi\)
\(822\) −145.762 −5.08402
\(823\) −9.58475 −0.334103 −0.167052 0.985948i \(-0.553425\pi\)
−0.167052 + 0.985948i \(0.553425\pi\)
\(824\) 24.3828 0.849414
\(825\) 23.8251 0.829483
\(826\) 6.03193 0.209878
\(827\) 21.5016 0.747684 0.373842 0.927492i \(-0.378040\pi\)
0.373842 + 0.927492i \(0.378040\pi\)
\(828\) 168.131 5.84295
\(829\) 12.3253 0.428076 0.214038 0.976825i \(-0.431338\pi\)
0.214038 + 0.976825i \(0.431338\pi\)
\(830\) −44.1325 −1.53186
\(831\) 68.5537 2.37810
\(832\) 68.4582 2.37336
\(833\) −15.9409 −0.552320
\(834\) −148.975 −5.15859
\(835\) 2.24925 0.0778384
\(836\) 111.045 3.84057
\(837\) −56.4677 −1.95181
\(838\) −3.83822 −0.132589
\(839\) −39.2827 −1.35619 −0.678095 0.734975i \(-0.737194\pi\)
−0.678095 + 0.734975i \(0.737194\pi\)
\(840\) 11.8105 0.407501
\(841\) −16.0876 −0.554746
\(842\) 59.9795 2.06703
\(843\) 10.1757 0.350468
\(844\) −88.0673 −3.03140
\(845\) 10.2783 0.353586
\(846\) −86.9269 −2.98861
\(847\) 3.28788 0.112973
\(848\) −135.646 −4.65809
\(849\) −74.6734 −2.56279
\(850\) 8.72867 0.299391
\(851\) 41.3535 1.41758
\(852\) −167.036 −5.72257
\(853\) −47.0050 −1.60942 −0.804710 0.593668i \(-0.797679\pi\)
−0.804710 + 0.593668i \(0.797679\pi\)
\(854\) −1.65462 −0.0566200
\(855\) 59.2883 2.02762
\(856\) −2.89676 −0.0990093
\(857\) −6.82617 −0.233177 −0.116589 0.993180i \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(858\) 126.401 4.31527
\(859\) 28.5434 0.973887 0.486943 0.873434i \(-0.338112\pi\)
0.486943 + 0.873434i \(0.338112\pi\)
\(860\) 56.4874 1.92620
\(861\) −7.62488 −0.259855
\(862\) 24.5710 0.836892
\(863\) 3.32469 0.113174 0.0565870 0.998398i \(-0.481978\pi\)
0.0565870 + 0.998398i \(0.481978\pi\)
\(864\) −303.420 −10.3226
\(865\) 42.3588 1.44024
\(866\) 48.7944 1.65810
\(867\) −38.5506 −1.30925
\(868\) −4.04353 −0.137246
\(869\) 56.5363 1.91786
\(870\) −60.5651 −2.05335
\(871\) 15.4414 0.523211
\(872\) 36.3153 1.22979
\(873\) −44.0214 −1.48990
\(874\) 44.2104 1.49544
\(875\) 2.54754 0.0861225
\(876\) −100.665 −3.40115
\(877\) 2.00812 0.0678093 0.0339046 0.999425i \(-0.489206\pi\)
0.0339046 + 0.999425i \(0.489206\pi\)
\(878\) 18.4526 0.622744
\(879\) −101.203 −3.41349
\(880\) 135.505 4.56788
\(881\) −50.4691 −1.70035 −0.850174 0.526501i \(-0.823504\pi\)
−0.850174 + 0.526501i \(0.823504\pi\)
\(882\) 146.389 4.92917
\(883\) 48.5004 1.63217 0.816085 0.577932i \(-0.196140\pi\)
0.816085 + 0.577932i \(0.196140\pi\)
\(884\) 33.6915 1.13317
\(885\) 66.0251 2.21941
\(886\) 14.0501 0.472023
\(887\) 4.20922 0.141332 0.0706659 0.997500i \(-0.477488\pi\)
0.0706659 + 0.997500i \(0.477488\pi\)
\(888\) −303.007 −10.1683
\(889\) 4.22653 0.141753
\(890\) 58.8923 1.97407
\(891\) −144.781 −4.85035
\(892\) 118.416 3.96486
\(893\) −16.6298 −0.556495
\(894\) 46.8118 1.56562
\(895\) 34.6823 1.15930
\(896\) −5.99637 −0.200325
\(897\) 36.6128 1.22246
\(898\) 25.3233 0.845048
\(899\) 12.9700 0.432575
\(900\) −58.3174 −1.94391
\(901\) −22.4618 −0.748310
\(902\) −154.999 −5.16090
\(903\) −3.84044 −0.127802
\(904\) −85.6821 −2.84975
\(905\) 23.2231 0.771962
\(906\) 94.3668 3.13513
\(907\) 5.84708 0.194149 0.0970745 0.995277i \(-0.469051\pi\)
0.0970745 + 0.995277i \(0.469051\pi\)
\(908\) −76.4579 −2.53734
\(909\) −2.29509 −0.0761232
\(910\) 2.96617 0.0983275
\(911\) 35.3269 1.17043 0.585216 0.810877i \(-0.301010\pi\)
0.585216 + 0.810877i \(0.301010\pi\)
\(912\) −182.834 −6.05424
\(913\) 44.3751 1.46860
\(914\) −75.2218 −2.48812
\(915\) −18.1114 −0.598744
\(916\) −81.2731 −2.68534
\(917\) 0.144083 0.00475806
\(918\) −97.1351 −3.20594
\(919\) −36.4202 −1.20139 −0.600696 0.799477i \(-0.705110\pi\)
−0.600696 + 0.799477i \(0.705110\pi\)
\(920\) 69.5417 2.29272
\(921\) 84.1086 2.77147
\(922\) 60.1407 1.98063
\(923\) −26.2400 −0.863702
\(924\) −18.9856 −0.624579
\(925\) −14.3438 −0.471620
\(926\) 39.4417 1.29613
\(927\) −20.9270 −0.687334
\(928\) 69.6923 2.28776
\(929\) 5.15251 0.169048 0.0845242 0.996421i \(-0.473063\pi\)
0.0845242 + 0.996421i \(0.473063\pi\)
\(930\) −60.8356 −1.99488
\(931\) 28.0053 0.917838
\(932\) 116.337 3.81076
\(933\) 63.7138 2.08590
\(934\) −68.3056 −2.23503
\(935\) 22.4385 0.733818
\(936\) −193.527 −6.32563
\(937\) −26.8558 −0.877341 −0.438671 0.898648i \(-0.644551\pi\)
−0.438671 + 0.898648i \(0.644551\pi\)
\(938\) −3.18788 −0.104088
\(939\) 51.5115 1.68102
\(940\) −41.8197 −1.36401
\(941\) 18.9305 0.617118 0.308559 0.951205i \(-0.400153\pi\)
0.308559 + 0.951205i \(0.400153\pi\)
\(942\) −39.7667 −1.29567
\(943\) −44.8962 −1.46202
\(944\) −146.881 −4.78057
\(945\) −6.22167 −0.202391
\(946\) −78.0688 −2.53824
\(947\) 21.6729 0.704274 0.352137 0.935948i \(-0.385455\pi\)
0.352137 + 0.935948i \(0.385455\pi\)
\(948\) −191.833 −6.23044
\(949\) −15.8136 −0.513332
\(950\) −15.3347 −0.497524
\(951\) −45.5607 −1.47741
\(952\) −4.35074 −0.141008
\(953\) 46.3982 1.50299 0.751493 0.659741i \(-0.229334\pi\)
0.751493 + 0.659741i \(0.229334\pi\)
\(954\) 206.271 6.67828
\(955\) −9.20248 −0.297785
\(956\) −20.1675 −0.652264
\(957\) 60.8981 1.96856
\(958\) 72.3896 2.33880
\(959\) 3.43928 0.111060
\(960\) −154.702 −4.99297
\(961\) −17.9720 −0.579743
\(962\) −76.0993 −2.45354
\(963\) 2.48621 0.0801170
\(964\) 47.1192 1.51761
\(965\) 16.9990 0.547219
\(966\) −7.55873 −0.243198
\(967\) −22.2626 −0.715916 −0.357958 0.933738i \(-0.616527\pi\)
−0.357958 + 0.933738i \(0.616527\pi\)
\(968\) −141.851 −4.55927
\(969\) −30.2758 −0.972598
\(970\) −29.1095 −0.934651
\(971\) 34.7524 1.11526 0.557629 0.830091i \(-0.311711\pi\)
0.557629 + 0.830091i \(0.311711\pi\)
\(972\) 240.610 7.71757
\(973\) 3.51511 0.112689
\(974\) −25.9751 −0.832295
\(975\) −12.6994 −0.406706
\(976\) 40.2910 1.28968
\(977\) 47.6648 1.52493 0.762465 0.647029i \(-0.223989\pi\)
0.762465 + 0.647029i \(0.223989\pi\)
\(978\) −165.215 −5.28299
\(979\) −59.2160 −1.89255
\(980\) 70.4263 2.24969
\(981\) −31.1684 −0.995130
\(982\) 52.4084 1.67242
\(983\) −10.7104 −0.341609 −0.170805 0.985305i \(-0.554637\pi\)
−0.170805 + 0.985305i \(0.554637\pi\)
\(984\) 328.966 10.4870
\(985\) 1.14186 0.0363827
\(986\) 22.3109 0.710524
\(987\) 2.84322 0.0905008
\(988\) −59.1900 −1.88308
\(989\) −22.6130 −0.719052
\(990\) −206.058 −6.54895
\(991\) 12.9717 0.412060 0.206030 0.978546i \(-0.433946\pi\)
0.206030 + 0.978546i \(0.433946\pi\)
\(992\) 70.0036 2.22262
\(993\) −99.8107 −3.16740
\(994\) 5.41728 0.171826
\(995\) 29.9860 0.950620
\(996\) −150.569 −4.77095
\(997\) −33.2909 −1.05433 −0.527167 0.849762i \(-0.676746\pi\)
−0.527167 + 0.849762i \(0.676746\pi\)
\(998\) 2.45276 0.0776406
\(999\) 159.622 5.05020
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 6043.2.a.b.1.12 243
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6043.2.a.b.1.12 243 1.1 even 1 trivial