Properties

Label 4033.2.a.d.1.79
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $1$
Dimension $79$
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] = [4033,2,Mod(1,4033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4033, 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("4033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.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: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.79
Character \(\chi\) \(=\) 4033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.77530 q^{2} +0.714201 q^{3} +5.70227 q^{4} -2.27953 q^{5} +1.98212 q^{6} -4.78018 q^{7} +10.2749 q^{8} -2.48992 q^{9} +O(q^{10})\) \(q+2.77530 q^{2} +0.714201 q^{3} +5.70227 q^{4} -2.27953 q^{5} +1.98212 q^{6} -4.78018 q^{7} +10.2749 q^{8} -2.48992 q^{9} -6.32637 q^{10} +2.27334 q^{11} +4.07257 q^{12} -3.53419 q^{13} -13.2664 q^{14} -1.62804 q^{15} +17.1114 q^{16} -6.35164 q^{17} -6.91026 q^{18} -5.74978 q^{19} -12.9985 q^{20} -3.41401 q^{21} +6.30919 q^{22} +1.35354 q^{23} +7.33835 q^{24} +0.196253 q^{25} -9.80842 q^{26} -3.92090 q^{27} -27.2579 q^{28} -2.70705 q^{29} -4.51830 q^{30} +8.27203 q^{31} +26.9393 q^{32} +1.62362 q^{33} -17.6277 q^{34} +10.8966 q^{35} -14.1982 q^{36} -1.00000 q^{37} -15.9573 q^{38} -2.52412 q^{39} -23.4220 q^{40} +7.35264 q^{41} -9.47489 q^{42} +2.84117 q^{43} +12.9632 q^{44} +5.67584 q^{45} +3.75649 q^{46} -7.58798 q^{47} +12.2210 q^{48} +15.8501 q^{49} +0.544661 q^{50} -4.53635 q^{51} -20.1529 q^{52} -12.9859 q^{53} -10.8817 q^{54} -5.18214 q^{55} -49.1159 q^{56} -4.10650 q^{57} -7.51286 q^{58} +0.431054 q^{59} -9.28354 q^{60} -6.23767 q^{61} +22.9573 q^{62} +11.9023 q^{63} +40.5419 q^{64} +8.05628 q^{65} +4.50603 q^{66} +0.666623 q^{67} -36.2188 q^{68} +0.966702 q^{69} +30.2412 q^{70} +0.691721 q^{71} -25.5837 q^{72} -13.4129 q^{73} -2.77530 q^{74} +0.140164 q^{75} -32.7868 q^{76} -10.8670 q^{77} -7.00518 q^{78} -5.41458 q^{79} -39.0059 q^{80} +4.66944 q^{81} +20.4057 q^{82} -1.29394 q^{83} -19.4676 q^{84} +14.4787 q^{85} +7.88508 q^{86} -1.93338 q^{87} +23.3583 q^{88} +11.7089 q^{89} +15.7521 q^{90} +16.8941 q^{91} +7.71828 q^{92} +5.90789 q^{93} -21.0589 q^{94} +13.1068 q^{95} +19.2401 q^{96} -11.9401 q^{97} +43.9888 q^{98} -5.66042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77530 1.96243 0.981216 0.192914i \(-0.0617938\pi\)
0.981216 + 0.192914i \(0.0617938\pi\)
\(3\) 0.714201 0.412344 0.206172 0.978516i \(-0.433899\pi\)
0.206172 + 0.978516i \(0.433899\pi\)
\(4\) 5.70227 2.85114
\(5\) −2.27953 −1.01944 −0.509718 0.860341i \(-0.670250\pi\)
−0.509718 + 0.860341i \(0.670250\pi\)
\(6\) 1.98212 0.809197
\(7\) −4.78018 −1.80674 −0.903370 0.428863i \(-0.858914\pi\)
−0.903370 + 0.428863i \(0.858914\pi\)
\(8\) 10.2749 3.63273
\(9\) −2.48992 −0.829972
\(10\) −6.32637 −2.00057
\(11\) 2.27334 0.685437 0.342719 0.939438i \(-0.388652\pi\)
0.342719 + 0.939438i \(0.388652\pi\)
\(12\) 4.07257 1.17565
\(13\) −3.53419 −0.980207 −0.490104 0.871664i \(-0.663041\pi\)
−0.490104 + 0.871664i \(0.663041\pi\)
\(14\) −13.2664 −3.54560
\(15\) −1.62804 −0.420359
\(16\) 17.1114 4.27784
\(17\) −6.35164 −1.54050 −0.770249 0.637743i \(-0.779868\pi\)
−0.770249 + 0.637743i \(0.779868\pi\)
\(18\) −6.91026 −1.62876
\(19\) −5.74978 −1.31909 −0.659545 0.751665i \(-0.729251\pi\)
−0.659545 + 0.751665i \(0.729251\pi\)
\(20\) −12.9985 −2.90655
\(21\) −3.41401 −0.744998
\(22\) 6.30919 1.34512
\(23\) 1.35354 0.282233 0.141117 0.989993i \(-0.454931\pi\)
0.141117 + 0.989993i \(0.454931\pi\)
\(24\) 7.33835 1.49793
\(25\) 0.196253 0.0392506
\(26\) −9.80842 −1.92359
\(27\) −3.92090 −0.754578
\(28\) −27.2579 −5.15126
\(29\) −2.70705 −0.502686 −0.251343 0.967898i \(-0.580872\pi\)
−0.251343 + 0.967898i \(0.580872\pi\)
\(30\) −4.51830 −0.824925
\(31\) 8.27203 1.48570 0.742850 0.669457i \(-0.233473\pi\)
0.742850 + 0.669457i \(0.233473\pi\)
\(32\) 26.9393 4.76225
\(33\) 1.62362 0.282636
\(34\) −17.6277 −3.02312
\(35\) 10.8966 1.84186
\(36\) −14.1982 −2.36636
\(37\) −1.00000 −0.164399
\(38\) −15.9573 −2.58862
\(39\) −2.52412 −0.404183
\(40\) −23.4220 −3.70334
\(41\) 7.35264 1.14829 0.574144 0.818754i \(-0.305335\pi\)
0.574144 + 0.818754i \(0.305335\pi\)
\(42\) −9.47489 −1.46201
\(43\) 2.84117 0.433274 0.216637 0.976252i \(-0.430491\pi\)
0.216637 + 0.976252i \(0.430491\pi\)
\(44\) 12.9632 1.95428
\(45\) 5.67584 0.846104
\(46\) 3.75649 0.553864
\(47\) −7.58798 −1.10682 −0.553410 0.832909i \(-0.686674\pi\)
−0.553410 + 0.832909i \(0.686674\pi\)
\(48\) 12.2210 1.76394
\(49\) 15.8501 2.26431
\(50\) 0.544661 0.0770267
\(51\) −4.53635 −0.635216
\(52\) −20.1529 −2.79470
\(53\) −12.9859 −1.78375 −0.891875 0.452281i \(-0.850610\pi\)
−0.891875 + 0.452281i \(0.850610\pi\)
\(54\) −10.8817 −1.48081
\(55\) −5.18214 −0.698760
\(56\) −49.1159 −6.56339
\(57\) −4.10650 −0.543919
\(58\) −7.51286 −0.986487
\(59\) 0.431054 0.0561185 0.0280592 0.999606i \(-0.491067\pi\)
0.0280592 + 0.999606i \(0.491067\pi\)
\(60\) −9.28354 −1.19850
\(61\) −6.23767 −0.798652 −0.399326 0.916809i \(-0.630756\pi\)
−0.399326 + 0.916809i \(0.630756\pi\)
\(62\) 22.9573 2.91559
\(63\) 11.9023 1.49954
\(64\) 40.5419 5.06774
\(65\) 8.05628 0.999259
\(66\) 4.50603 0.554654
\(67\) 0.666623 0.0814409 0.0407205 0.999171i \(-0.487035\pi\)
0.0407205 + 0.999171i \(0.487035\pi\)
\(68\) −36.2188 −4.39217
\(69\) 0.966702 0.116377
\(70\) 30.2412 3.61452
\(71\) 0.691721 0.0820922 0.0410461 0.999157i \(-0.486931\pi\)
0.0410461 + 0.999157i \(0.486931\pi\)
\(72\) −25.5837 −3.01506
\(73\) −13.4129 −1.56986 −0.784931 0.619583i \(-0.787302\pi\)
−0.784931 + 0.619583i \(0.787302\pi\)
\(74\) −2.77530 −0.322622
\(75\) 0.140164 0.0161848
\(76\) −32.7868 −3.76090
\(77\) −10.8670 −1.23841
\(78\) −7.00518 −0.793181
\(79\) −5.41458 −0.609188 −0.304594 0.952482i \(-0.598521\pi\)
−0.304594 + 0.952482i \(0.598521\pi\)
\(80\) −39.0059 −4.36099
\(81\) 4.66944 0.518826
\(82\) 20.4057 2.25344
\(83\) −1.29394 −0.142028 −0.0710141 0.997475i \(-0.522624\pi\)
−0.0710141 + 0.997475i \(0.522624\pi\)
\(84\) −19.4676 −2.12409
\(85\) 14.4787 1.57044
\(86\) 7.88508 0.850270
\(87\) −1.93338 −0.207280
\(88\) 23.3583 2.49001
\(89\) 11.7089 1.24114 0.620571 0.784150i \(-0.286901\pi\)
0.620571 + 0.784150i \(0.286901\pi\)
\(90\) 15.7521 1.66042
\(91\) 16.8941 1.77098
\(92\) 7.71828 0.804686
\(93\) 5.90789 0.612620
\(94\) −21.0589 −2.17206
\(95\) 13.1068 1.34473
\(96\) 19.2401 1.96368
\(97\) −11.9401 −1.21233 −0.606165 0.795339i \(-0.707293\pi\)
−0.606165 + 0.795339i \(0.707293\pi\)
\(98\) 43.9888 4.44354
\(99\) −5.66042 −0.568894
\(100\) 1.11909 0.111909
\(101\) 18.0764 1.79867 0.899337 0.437257i \(-0.144050\pi\)
0.899337 + 0.437257i \(0.144050\pi\)
\(102\) −12.5897 −1.24657
\(103\) 11.2106 1.10461 0.552304 0.833643i \(-0.313749\pi\)
0.552304 + 0.833643i \(0.313749\pi\)
\(104\) −36.3134 −3.56083
\(105\) 7.78234 0.759478
\(106\) −36.0397 −3.50049
\(107\) 7.70623 0.744989 0.372494 0.928034i \(-0.378503\pi\)
0.372494 + 0.928034i \(0.378503\pi\)
\(108\) −22.3581 −2.15141
\(109\) −1.00000 −0.0957826
\(110\) −14.3820 −1.37127
\(111\) −0.714201 −0.0677890
\(112\) −81.7955 −7.72895
\(113\) 2.59623 0.244232 0.122116 0.992516i \(-0.461032\pi\)
0.122116 + 0.992516i \(0.461032\pi\)
\(114\) −11.3967 −1.06740
\(115\) −3.08544 −0.287719
\(116\) −15.4363 −1.43323
\(117\) 8.79983 0.813545
\(118\) 1.19630 0.110129
\(119\) 30.3620 2.78328
\(120\) −16.7280 −1.52705
\(121\) −5.83193 −0.530176
\(122\) −17.3114 −1.56730
\(123\) 5.25126 0.473490
\(124\) 47.1694 4.23594
\(125\) 10.9503 0.979423
\(126\) 33.0323 2.94275
\(127\) −3.27414 −0.290533 −0.145266 0.989393i \(-0.546404\pi\)
−0.145266 + 0.989393i \(0.546404\pi\)
\(128\) 58.6371 5.18284
\(129\) 2.02916 0.178658
\(130\) 22.3586 1.96098
\(131\) −5.05540 −0.441692 −0.220846 0.975309i \(-0.570882\pi\)
−0.220846 + 0.975309i \(0.570882\pi\)
\(132\) 9.25833 0.805834
\(133\) 27.4850 2.38325
\(134\) 1.85008 0.159822
\(135\) 8.93781 0.769245
\(136\) −65.2625 −5.59621
\(137\) −16.9417 −1.44743 −0.723714 0.690100i \(-0.757567\pi\)
−0.723714 + 0.690100i \(0.757567\pi\)
\(138\) 2.68289 0.228382
\(139\) 16.2835 1.38115 0.690573 0.723263i \(-0.257359\pi\)
0.690573 + 0.723263i \(0.257359\pi\)
\(140\) 62.1352 5.25138
\(141\) −5.41934 −0.456391
\(142\) 1.91973 0.161100
\(143\) −8.03440 −0.671871
\(144\) −42.6059 −3.55049
\(145\) 6.17080 0.512457
\(146\) −37.2248 −3.08075
\(147\) 11.3202 0.933673
\(148\) −5.70227 −0.468724
\(149\) 2.89005 0.236762 0.118381 0.992968i \(-0.462230\pi\)
0.118381 + 0.992968i \(0.462230\pi\)
\(150\) 0.388997 0.0317615
\(151\) 16.1526 1.31448 0.657240 0.753682i \(-0.271724\pi\)
0.657240 + 0.753682i \(0.271724\pi\)
\(152\) −59.0784 −4.79189
\(153\) 15.8151 1.27857
\(154\) −30.1591 −2.43029
\(155\) −18.8563 −1.51458
\(156\) −14.3932 −1.15238
\(157\) −16.6431 −1.32827 −0.664134 0.747614i \(-0.731199\pi\)
−0.664134 + 0.747614i \(0.731199\pi\)
\(158\) −15.0271 −1.19549
\(159\) −9.27454 −0.735519
\(160\) −61.4090 −4.85481
\(161\) −6.47018 −0.509922
\(162\) 12.9591 1.01816
\(163\) 0.322726 0.0252779 0.0126389 0.999920i \(-0.495977\pi\)
0.0126389 + 0.999920i \(0.495977\pi\)
\(164\) 41.9267 3.27393
\(165\) −3.70109 −0.288130
\(166\) −3.59107 −0.278721
\(167\) −17.7694 −1.37504 −0.687521 0.726165i \(-0.741301\pi\)
−0.687521 + 0.726165i \(0.741301\pi\)
\(168\) −35.0786 −2.70638
\(169\) −0.509521 −0.0391939
\(170\) 40.1828 3.08188
\(171\) 14.3165 1.09481
\(172\) 16.2011 1.23532
\(173\) −3.73205 −0.283743 −0.141871 0.989885i \(-0.545312\pi\)
−0.141871 + 0.989885i \(0.545312\pi\)
\(174\) −5.36569 −0.406772
\(175\) −0.938126 −0.0709157
\(176\) 38.9000 2.93219
\(177\) 0.307859 0.0231401
\(178\) 32.4957 2.43566
\(179\) 23.6743 1.76950 0.884749 0.466067i \(-0.154330\pi\)
0.884749 + 0.466067i \(0.154330\pi\)
\(180\) 32.3652 2.41236
\(181\) −23.6607 −1.75868 −0.879341 0.476192i \(-0.842017\pi\)
−0.879341 + 0.476192i \(0.842017\pi\)
\(182\) 46.8860 3.47542
\(183\) −4.45495 −0.329319
\(184\) 13.9075 1.02528
\(185\) 2.27953 0.167594
\(186\) 16.3962 1.20222
\(187\) −14.4394 −1.05592
\(188\) −43.2687 −3.15570
\(189\) 18.7426 1.36333
\(190\) 36.3752 2.63894
\(191\) −8.26889 −0.598316 −0.299158 0.954204i \(-0.596706\pi\)
−0.299158 + 0.954204i \(0.596706\pi\)
\(192\) 28.9551 2.08965
\(193\) −3.84462 −0.276741 −0.138371 0.990381i \(-0.544187\pi\)
−0.138371 + 0.990381i \(0.544187\pi\)
\(194\) −33.1372 −2.37912
\(195\) 5.75380 0.412039
\(196\) 90.3818 6.45585
\(197\) 3.99863 0.284890 0.142445 0.989803i \(-0.454504\pi\)
0.142445 + 0.989803i \(0.454504\pi\)
\(198\) −15.7094 −1.11642
\(199\) −0.637214 −0.0451709 −0.0225854 0.999745i \(-0.507190\pi\)
−0.0225854 + 0.999745i \(0.507190\pi\)
\(200\) 2.01648 0.142587
\(201\) 0.476102 0.0335817
\(202\) 50.1675 3.52977
\(203\) 12.9402 0.908223
\(204\) −25.8675 −1.81109
\(205\) −16.7605 −1.17061
\(206\) 31.1126 2.16772
\(207\) −3.37021 −0.234246
\(208\) −60.4748 −4.19317
\(209\) −13.0712 −0.904153
\(210\) 21.5983 1.49042
\(211\) 2.06981 0.142492 0.0712460 0.997459i \(-0.477302\pi\)
0.0712460 + 0.997459i \(0.477302\pi\)
\(212\) −74.0492 −5.08572
\(213\) 0.494028 0.0338502
\(214\) 21.3871 1.46199
\(215\) −6.47652 −0.441695
\(216\) −40.2869 −2.74118
\(217\) −39.5418 −2.68427
\(218\) −2.77530 −0.187967
\(219\) −9.57951 −0.647323
\(220\) −29.5500 −1.99226
\(221\) 22.4479 1.51001
\(222\) −1.98212 −0.133031
\(223\) −6.48010 −0.433940 −0.216970 0.976178i \(-0.569617\pi\)
−0.216970 + 0.976178i \(0.569617\pi\)
\(224\) −128.775 −8.60414
\(225\) −0.488654 −0.0325769
\(226\) 7.20530 0.479289
\(227\) −21.5329 −1.42919 −0.714593 0.699540i \(-0.753388\pi\)
−0.714593 + 0.699540i \(0.753388\pi\)
\(228\) −23.4164 −1.55079
\(229\) 2.52407 0.166795 0.0833977 0.996516i \(-0.473423\pi\)
0.0833977 + 0.996516i \(0.473423\pi\)
\(230\) −8.56302 −0.564629
\(231\) −7.76120 −0.510650
\(232\) −27.8147 −1.82612
\(233\) −2.09896 −0.137508 −0.0687538 0.997634i \(-0.521902\pi\)
−0.0687538 + 0.997634i \(0.521902\pi\)
\(234\) 24.4221 1.59653
\(235\) 17.2970 1.12833
\(236\) 2.45799 0.160001
\(237\) −3.86710 −0.251195
\(238\) 84.2635 5.46199
\(239\) 28.8245 1.86450 0.932252 0.361809i \(-0.117841\pi\)
0.932252 + 0.361809i \(0.117841\pi\)
\(240\) −27.8580 −1.79823
\(241\) −9.11602 −0.587215 −0.293607 0.955926i \(-0.594856\pi\)
−0.293607 + 0.955926i \(0.594856\pi\)
\(242\) −16.1853 −1.04043
\(243\) 15.0976 0.968513
\(244\) −35.5689 −2.27707
\(245\) −36.1309 −2.30832
\(246\) 14.5738 0.929192
\(247\) 20.3208 1.29298
\(248\) 84.9944 5.39715
\(249\) −0.924133 −0.0585645
\(250\) 30.3903 1.92205
\(251\) −10.9599 −0.691781 −0.345890 0.938275i \(-0.612423\pi\)
−0.345890 + 0.938275i \(0.612423\pi\)
\(252\) 67.8699 4.27540
\(253\) 3.07706 0.193453
\(254\) −9.08671 −0.570151
\(255\) 10.3407 0.647562
\(256\) 81.6517 5.10323
\(257\) −31.1095 −1.94056 −0.970278 0.241991i \(-0.922200\pi\)
−0.970278 + 0.241991i \(0.922200\pi\)
\(258\) 5.63153 0.350604
\(259\) 4.78018 0.297026
\(260\) 45.9391 2.84902
\(261\) 6.74033 0.417216
\(262\) −14.0302 −0.866791
\(263\) −3.26479 −0.201316 −0.100658 0.994921i \(-0.532095\pi\)
−0.100658 + 0.994921i \(0.532095\pi\)
\(264\) 16.6826 1.02674
\(265\) 29.6017 1.81842
\(266\) 76.2790 4.67697
\(267\) 8.36252 0.511778
\(268\) 3.80126 0.232199
\(269\) 3.18715 0.194324 0.0971621 0.995269i \(-0.469023\pi\)
0.0971621 + 0.995269i \(0.469023\pi\)
\(270\) 24.8051 1.50959
\(271\) −9.84695 −0.598160 −0.299080 0.954228i \(-0.596680\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(272\) −108.685 −6.59001
\(273\) 12.0658 0.730253
\(274\) −47.0183 −2.84048
\(275\) 0.446150 0.0269039
\(276\) 5.51240 0.331807
\(277\) 11.3928 0.684527 0.342264 0.939604i \(-0.388806\pi\)
0.342264 + 0.939604i \(0.388806\pi\)
\(278\) 45.1914 2.71040
\(279\) −20.5967 −1.23309
\(280\) 111.961 6.69096
\(281\) 4.67462 0.278864 0.139432 0.990232i \(-0.455472\pi\)
0.139432 + 0.990232i \(0.455472\pi\)
\(282\) −15.0403 −0.895635
\(283\) 20.4781 1.21730 0.608648 0.793440i \(-0.291712\pi\)
0.608648 + 0.793440i \(0.291712\pi\)
\(284\) 3.94438 0.234056
\(285\) 9.36088 0.554491
\(286\) −22.2979 −1.31850
\(287\) −35.1469 −2.07466
\(288\) −67.0767 −3.95253
\(289\) 23.3433 1.37314
\(290\) 17.1258 1.00566
\(291\) −8.52761 −0.499897
\(292\) −76.4841 −4.47589
\(293\) −5.18021 −0.302631 −0.151316 0.988485i \(-0.548351\pi\)
−0.151316 + 0.988485i \(0.548351\pi\)
\(294\) 31.4169 1.83227
\(295\) −0.982601 −0.0572092
\(296\) −10.2749 −0.597217
\(297\) −8.91354 −0.517216
\(298\) 8.02075 0.464630
\(299\) −4.78368 −0.276647
\(300\) 0.799255 0.0461450
\(301\) −13.5813 −0.782813
\(302\) 44.8282 2.57958
\(303\) 12.9102 0.741672
\(304\) −98.3866 −5.64286
\(305\) 14.2189 0.814175
\(306\) 43.8915 2.50911
\(307\) 24.8472 1.41810 0.709052 0.705156i \(-0.249123\pi\)
0.709052 + 0.705156i \(0.249123\pi\)
\(308\) −61.9665 −3.53087
\(309\) 8.00659 0.455479
\(310\) −52.3319 −2.97225
\(311\) −9.91826 −0.562413 −0.281206 0.959647i \(-0.590735\pi\)
−0.281206 + 0.959647i \(0.590735\pi\)
\(312\) −25.9351 −1.46829
\(313\) 24.4577 1.38243 0.691215 0.722649i \(-0.257076\pi\)
0.691215 + 0.722649i \(0.257076\pi\)
\(314\) −46.1897 −2.60663
\(315\) −27.1315 −1.52869
\(316\) −30.8754 −1.73688
\(317\) −25.4916 −1.43175 −0.715875 0.698229i \(-0.753972\pi\)
−0.715875 + 0.698229i \(0.753972\pi\)
\(318\) −25.7396 −1.44341
\(319\) −6.15404 −0.344560
\(320\) −92.4164 −5.16624
\(321\) 5.50379 0.307192
\(322\) −17.9567 −1.00069
\(323\) 36.5205 2.03206
\(324\) 26.6264 1.47925
\(325\) −0.693595 −0.0384738
\(326\) 0.895661 0.0496061
\(327\) −0.714201 −0.0394954
\(328\) 75.5477 4.17142
\(329\) 36.2719 1.99974
\(330\) −10.2716 −0.565434
\(331\) −23.1540 −1.27266 −0.636329 0.771418i \(-0.719548\pi\)
−0.636329 + 0.771418i \(0.719548\pi\)
\(332\) −7.37840 −0.404942
\(333\) 2.48992 0.136447
\(334\) −49.3155 −2.69842
\(335\) −1.51959 −0.0830238
\(336\) −58.4184 −3.18699
\(337\) 9.33003 0.508239 0.254119 0.967173i \(-0.418214\pi\)
0.254119 + 0.967173i \(0.418214\pi\)
\(338\) −1.41407 −0.0769154
\(339\) 1.85423 0.100708
\(340\) 82.5618 4.47754
\(341\) 18.8051 1.01835
\(342\) 39.7325 2.14849
\(343\) −42.3053 −2.28427
\(344\) 29.1927 1.57397
\(345\) −2.20363 −0.118639
\(346\) −10.3576 −0.556826
\(347\) 12.8462 0.689618 0.344809 0.938673i \(-0.387944\pi\)
0.344809 + 0.938673i \(0.387944\pi\)
\(348\) −11.0246 −0.590983
\(349\) −31.8799 −1.70649 −0.853246 0.521508i \(-0.825370\pi\)
−0.853246 + 0.521508i \(0.825370\pi\)
\(350\) −2.60358 −0.139167
\(351\) 13.8572 0.739643
\(352\) 61.2422 3.26422
\(353\) −32.1816 −1.71285 −0.856426 0.516269i \(-0.827320\pi\)
−0.856426 + 0.516269i \(0.827320\pi\)
\(354\) 0.854401 0.0454109
\(355\) −1.57680 −0.0836878
\(356\) 66.7675 3.53867
\(357\) 21.6846 1.14767
\(358\) 65.7031 3.47252
\(359\) 5.62295 0.296768 0.148384 0.988930i \(-0.452593\pi\)
0.148384 + 0.988930i \(0.452593\pi\)
\(360\) 58.3187 3.07367
\(361\) 14.0600 0.739998
\(362\) −65.6654 −3.45129
\(363\) −4.16517 −0.218615
\(364\) 96.3345 5.04930
\(365\) 30.5751 1.60037
\(366\) −12.3638 −0.646267
\(367\) −15.5485 −0.811624 −0.405812 0.913957i \(-0.633011\pi\)
−0.405812 + 0.913957i \(0.633011\pi\)
\(368\) 23.1610 1.20735
\(369\) −18.3075 −0.953048
\(370\) 6.32637 0.328892
\(371\) 62.0750 3.22277
\(372\) 33.6884 1.74666
\(373\) −8.46974 −0.438546 −0.219273 0.975663i \(-0.570369\pi\)
−0.219273 + 0.975663i \(0.570369\pi\)
\(374\) −40.0737 −2.07216
\(375\) 7.82070 0.403859
\(376\) −77.9658 −4.02078
\(377\) 9.56722 0.492737
\(378\) 52.0164 2.67543
\(379\) 21.3493 1.09664 0.548320 0.836269i \(-0.315268\pi\)
0.548320 + 0.836269i \(0.315268\pi\)
\(380\) 74.7385 3.83400
\(381\) −2.33839 −0.119800
\(382\) −22.9486 −1.17415
\(383\) 3.76037 0.192146 0.0960730 0.995374i \(-0.469372\pi\)
0.0960730 + 0.995374i \(0.469372\pi\)
\(384\) 41.8787 2.13711
\(385\) 24.7716 1.26248
\(386\) −10.6699 −0.543086
\(387\) −7.07427 −0.359605
\(388\) −68.0856 −3.45652
\(389\) −11.8710 −0.601885 −0.300942 0.953642i \(-0.597301\pi\)
−0.300942 + 0.953642i \(0.597301\pi\)
\(390\) 15.9685 0.808597
\(391\) −8.59722 −0.434780
\(392\) 162.859 8.22561
\(393\) −3.61057 −0.182129
\(394\) 11.0974 0.559078
\(395\) 12.3427 0.621028
\(396\) −32.2773 −1.62199
\(397\) −19.3858 −0.972944 −0.486472 0.873696i \(-0.661717\pi\)
−0.486472 + 0.873696i \(0.661717\pi\)
\(398\) −1.76846 −0.0886448
\(399\) 19.6298 0.982719
\(400\) 3.35816 0.167908
\(401\) 37.5886 1.87709 0.938544 0.345160i \(-0.112175\pi\)
0.938544 + 0.345160i \(0.112175\pi\)
\(402\) 1.32133 0.0659017
\(403\) −29.2349 −1.45629
\(404\) 103.077 5.12826
\(405\) −10.6441 −0.528911
\(406\) 35.9129 1.78233
\(407\) −2.27334 −0.112685
\(408\) −46.6105 −2.30757
\(409\) −29.3979 −1.45363 −0.726816 0.686832i \(-0.759001\pi\)
−0.726816 + 0.686832i \(0.759001\pi\)
\(410\) −46.5155 −2.29724
\(411\) −12.0998 −0.596839
\(412\) 63.9256 3.14939
\(413\) −2.06052 −0.101391
\(414\) −9.35334 −0.459691
\(415\) 2.94957 0.144789
\(416\) −95.2086 −4.66799
\(417\) 11.6297 0.569507
\(418\) −36.2764 −1.77434
\(419\) 25.1072 1.22657 0.613283 0.789863i \(-0.289848\pi\)
0.613283 + 0.789863i \(0.289848\pi\)
\(420\) 44.3770 2.16538
\(421\) −16.0196 −0.780746 −0.390373 0.920657i \(-0.627654\pi\)
−0.390373 + 0.920657i \(0.627654\pi\)
\(422\) 5.74435 0.279631
\(423\) 18.8934 0.918630
\(424\) −133.429 −6.47988
\(425\) −1.24653 −0.0604656
\(426\) 1.37107 0.0664288
\(427\) 29.8172 1.44296
\(428\) 43.9430 2.12407
\(429\) −5.73818 −0.277042
\(430\) −17.9743 −0.866797
\(431\) −8.45458 −0.407243 −0.203621 0.979050i \(-0.565271\pi\)
−0.203621 + 0.979050i \(0.565271\pi\)
\(432\) −67.0921 −3.22797
\(433\) −5.64365 −0.271216 −0.135608 0.990763i \(-0.543299\pi\)
−0.135608 + 0.990763i \(0.543299\pi\)
\(434\) −109.740 −5.26770
\(435\) 4.40719 0.211309
\(436\) −5.70227 −0.273089
\(437\) −7.78258 −0.372291
\(438\) −26.5860 −1.27033
\(439\) −11.2605 −0.537433 −0.268716 0.963219i \(-0.586599\pi\)
−0.268716 + 0.963219i \(0.586599\pi\)
\(440\) −53.2460 −2.53840
\(441\) −39.4655 −1.87931
\(442\) 62.2995 2.96329
\(443\) −4.74032 −0.225219 −0.112610 0.993639i \(-0.535921\pi\)
−0.112610 + 0.993639i \(0.535921\pi\)
\(444\) −4.07257 −0.193276
\(445\) −26.6908 −1.26527
\(446\) −17.9842 −0.851577
\(447\) 2.06408 0.0976275
\(448\) −193.798 −9.15608
\(449\) 3.26679 0.154169 0.0770847 0.997025i \(-0.475439\pi\)
0.0770847 + 0.997025i \(0.475439\pi\)
\(450\) −1.35616 −0.0639300
\(451\) 16.7150 0.787080
\(452\) 14.8044 0.696340
\(453\) 11.5362 0.542018
\(454\) −59.7601 −2.80468
\(455\) −38.5105 −1.80540
\(456\) −42.1939 −1.97591
\(457\) 20.6589 0.966381 0.483190 0.875515i \(-0.339478\pi\)
0.483190 + 0.875515i \(0.339478\pi\)
\(458\) 7.00505 0.327324
\(459\) 24.9042 1.16243
\(460\) −17.5940 −0.820326
\(461\) −16.0370 −0.746918 −0.373459 0.927647i \(-0.621828\pi\)
−0.373459 + 0.927647i \(0.621828\pi\)
\(462\) −21.5396 −1.00211
\(463\) −16.2860 −0.756875 −0.378438 0.925627i \(-0.623539\pi\)
−0.378438 + 0.925627i \(0.623539\pi\)
\(464\) −46.3213 −2.15041
\(465\) −13.4672 −0.624527
\(466\) −5.82524 −0.269849
\(467\) 18.2679 0.845339 0.422670 0.906284i \(-0.361093\pi\)
0.422670 + 0.906284i \(0.361093\pi\)
\(468\) 50.1791 2.31953
\(469\) −3.18658 −0.147142
\(470\) 48.0043 2.21428
\(471\) −11.8865 −0.547703
\(472\) 4.42904 0.203863
\(473\) 6.45894 0.296982
\(474\) −10.7323 −0.492953
\(475\) −1.12841 −0.0517751
\(476\) 173.132 7.93551
\(477\) 32.3338 1.48046
\(478\) 79.9967 3.65896
\(479\) 24.5562 1.12200 0.561001 0.827815i \(-0.310416\pi\)
0.561001 + 0.827815i \(0.310416\pi\)
\(480\) −43.8584 −2.00185
\(481\) 3.53419 0.161145
\(482\) −25.2997 −1.15237
\(483\) −4.62101 −0.210263
\(484\) −33.2553 −1.51160
\(485\) 27.2177 1.23589
\(486\) 41.9004 1.90064
\(487\) −6.65037 −0.301357 −0.150679 0.988583i \(-0.548146\pi\)
−0.150679 + 0.988583i \(0.548146\pi\)
\(488\) −64.0915 −2.90129
\(489\) 0.230491 0.0104232
\(490\) −100.274 −4.52991
\(491\) −7.73292 −0.348982 −0.174491 0.984659i \(-0.555828\pi\)
−0.174491 + 0.984659i \(0.555828\pi\)
\(492\) 29.9441 1.34999
\(493\) 17.1942 0.774388
\(494\) 56.3962 2.53739
\(495\) 12.9031 0.579951
\(496\) 141.546 6.35560
\(497\) −3.30655 −0.148319
\(498\) −2.56474 −0.114929
\(499\) −24.9461 −1.11674 −0.558370 0.829592i \(-0.688573\pi\)
−0.558370 + 0.829592i \(0.688573\pi\)
\(500\) 62.4415 2.79247
\(501\) −12.6910 −0.566990
\(502\) −30.4169 −1.35757
\(503\) 0.704072 0.0313930 0.0156965 0.999877i \(-0.495003\pi\)
0.0156965 + 0.999877i \(0.495003\pi\)
\(504\) 122.295 5.44743
\(505\) −41.2058 −1.83363
\(506\) 8.53976 0.379639
\(507\) −0.363900 −0.0161614
\(508\) −18.6700 −0.828349
\(509\) −6.52617 −0.289267 −0.144634 0.989485i \(-0.546200\pi\)
−0.144634 + 0.989485i \(0.546200\pi\)
\(510\) 28.6986 1.27080
\(511\) 64.1161 2.83633
\(512\) 109.333 4.83190
\(513\) 22.5443 0.995356
\(514\) −86.3381 −3.80821
\(515\) −25.5548 −1.12608
\(516\) 11.5709 0.509378
\(517\) −17.2500 −0.758656
\(518\) 13.2664 0.582893
\(519\) −2.66544 −0.117000
\(520\) 82.7776 3.63004
\(521\) 23.3605 1.02344 0.511721 0.859151i \(-0.329008\pi\)
0.511721 + 0.859151i \(0.329008\pi\)
\(522\) 18.7064 0.818757
\(523\) −44.8106 −1.95943 −0.979714 0.200398i \(-0.935776\pi\)
−0.979714 + 0.200398i \(0.935776\pi\)
\(524\) −28.8273 −1.25933
\(525\) −0.670010 −0.0292417
\(526\) −9.06077 −0.395068
\(527\) −52.5410 −2.28872
\(528\) 27.7824 1.20907
\(529\) −21.1679 −0.920344
\(530\) 82.1536 3.56853
\(531\) −1.07329 −0.0465768
\(532\) 156.727 6.79497
\(533\) −25.9856 −1.12556
\(534\) 23.2085 1.00433
\(535\) −17.5666 −0.759469
\(536\) 6.84949 0.295853
\(537\) 16.9082 0.729642
\(538\) 8.84530 0.381348
\(539\) 36.0327 1.55204
\(540\) 50.9659 2.19322
\(541\) 12.6920 0.545671 0.272835 0.962061i \(-0.412039\pi\)
0.272835 + 0.962061i \(0.412039\pi\)
\(542\) −27.3282 −1.17385
\(543\) −16.8985 −0.725183
\(544\) −171.109 −7.33623
\(545\) 2.27953 0.0976443
\(546\) 33.4860 1.43307
\(547\) −29.0607 −1.24255 −0.621274 0.783593i \(-0.713385\pi\)
−0.621274 + 0.783593i \(0.713385\pi\)
\(548\) −96.6063 −4.12682
\(549\) 15.5313 0.662859
\(550\) 1.23820 0.0527970
\(551\) 15.5649 0.663088
\(552\) 9.93277 0.422767
\(553\) 25.8827 1.10064
\(554\) 31.6184 1.34334
\(555\) 1.62804 0.0691065
\(556\) 92.8527 3.93783
\(557\) 39.5149 1.67430 0.837151 0.546972i \(-0.184220\pi\)
0.837151 + 0.546972i \(0.184220\pi\)
\(558\) −57.1619 −2.41986
\(559\) −10.0412 −0.424698
\(560\) 186.455 7.87917
\(561\) −10.3127 −0.435401
\(562\) 12.9735 0.547252
\(563\) 33.5395 1.41352 0.706760 0.707454i \(-0.250156\pi\)
0.706760 + 0.707454i \(0.250156\pi\)
\(564\) −30.9026 −1.30123
\(565\) −5.91817 −0.248979
\(566\) 56.8328 2.38886
\(567\) −22.3208 −0.937384
\(568\) 7.10737 0.298219
\(569\) −31.3312 −1.31347 −0.656735 0.754121i \(-0.728063\pi\)
−0.656735 + 0.754121i \(0.728063\pi\)
\(570\) 25.9792 1.08815
\(571\) 4.31388 0.180530 0.0902652 0.995918i \(-0.471229\pi\)
0.0902652 + 0.995918i \(0.471229\pi\)
\(572\) −45.8144 −1.91560
\(573\) −5.90565 −0.246712
\(574\) −97.5432 −4.07137
\(575\) 0.265637 0.0110778
\(576\) −100.946 −4.20608
\(577\) 17.2498 0.718118 0.359059 0.933315i \(-0.383098\pi\)
0.359059 + 0.933315i \(0.383098\pi\)
\(578\) 64.7846 2.69469
\(579\) −2.74583 −0.114113
\(580\) 35.1876 1.46108
\(581\) 6.18527 0.256608
\(582\) −23.6667 −0.981014
\(583\) −29.5214 −1.22265
\(584\) −137.816 −5.70288
\(585\) −20.0595 −0.829357
\(586\) −14.3766 −0.593893
\(587\) 0.501336 0.0206924 0.0103462 0.999946i \(-0.496707\pi\)
0.0103462 + 0.999946i \(0.496707\pi\)
\(588\) 64.5508 2.66203
\(589\) −47.5624 −1.95977
\(590\) −2.72701 −0.112269
\(591\) 2.85582 0.117473
\(592\) −17.1114 −0.703273
\(593\) 41.5671 1.70696 0.853478 0.521128i \(-0.174489\pi\)
0.853478 + 0.521128i \(0.174489\pi\)
\(594\) −24.7377 −1.01500
\(595\) −69.2110 −2.83738
\(596\) 16.4799 0.675042
\(597\) −0.455099 −0.0186260
\(598\) −13.2761 −0.542901
\(599\) −36.8908 −1.50732 −0.753659 0.657265i \(-0.771713\pi\)
−0.753659 + 0.657265i \(0.771713\pi\)
\(600\) 1.44017 0.0587949
\(601\) 25.5938 1.04399 0.521997 0.852947i \(-0.325187\pi\)
0.521997 + 0.852947i \(0.325187\pi\)
\(602\) −37.6921 −1.53622
\(603\) −1.65983 −0.0675937
\(604\) 92.1065 3.74776
\(605\) 13.2941 0.540480
\(606\) 35.8297 1.45548
\(607\) 19.2017 0.779372 0.389686 0.920948i \(-0.372584\pi\)
0.389686 + 0.920948i \(0.372584\pi\)
\(608\) −154.895 −6.28183
\(609\) 9.24189 0.374500
\(610\) 39.4618 1.59776
\(611\) 26.8173 1.08491
\(612\) 90.1818 3.64538
\(613\) −15.1564 −0.612161 −0.306080 0.952006i \(-0.599018\pi\)
−0.306080 + 0.952006i \(0.599018\pi\)
\(614\) 68.9584 2.78293
\(615\) −11.9704 −0.482693
\(616\) −111.657 −4.49879
\(617\) 8.14996 0.328105 0.164053 0.986452i \(-0.447543\pi\)
0.164053 + 0.986452i \(0.447543\pi\)
\(618\) 22.2207 0.893846
\(619\) 37.5309 1.50849 0.754246 0.656591i \(-0.228002\pi\)
0.754246 + 0.656591i \(0.228002\pi\)
\(620\) −107.524 −4.31827
\(621\) −5.30711 −0.212967
\(622\) −27.5261 −1.10370
\(623\) −55.9708 −2.24242
\(624\) −43.1912 −1.72903
\(625\) −25.9428 −1.03771
\(626\) 67.8774 2.71292
\(627\) −9.33546 −0.372822
\(628\) −94.9037 −3.78707
\(629\) 6.35164 0.253256
\(630\) −75.2981 −2.99995
\(631\) −14.3127 −0.569779 −0.284890 0.958560i \(-0.591957\pi\)
−0.284890 + 0.958560i \(0.591957\pi\)
\(632\) −55.6343 −2.21301
\(633\) 1.47826 0.0587557
\(634\) −70.7467 −2.80971
\(635\) 7.46350 0.296180
\(636\) −52.8860 −2.09707
\(637\) −56.0174 −2.21949
\(638\) −17.0793 −0.676175
\(639\) −1.72233 −0.0681343
\(640\) −133.665 −5.28358
\(641\) 5.64811 0.223087 0.111543 0.993760i \(-0.464421\pi\)
0.111543 + 0.993760i \(0.464421\pi\)
\(642\) 15.2747 0.602843
\(643\) −15.2476 −0.601307 −0.300653 0.953734i \(-0.597205\pi\)
−0.300653 + 0.953734i \(0.597205\pi\)
\(644\) −36.8948 −1.45386
\(645\) −4.62554 −0.182130
\(646\) 101.355 3.98777
\(647\) −1.55911 −0.0612949 −0.0306475 0.999530i \(-0.509757\pi\)
−0.0306475 + 0.999530i \(0.509757\pi\)
\(648\) 47.9780 1.88476
\(649\) 0.979932 0.0384657
\(650\) −1.92493 −0.0755021
\(651\) −28.2408 −1.10684
\(652\) 1.84027 0.0720707
\(653\) 22.7942 0.892007 0.446003 0.895031i \(-0.352847\pi\)
0.446003 + 0.895031i \(0.352847\pi\)
\(654\) −1.98212 −0.0775070
\(655\) 11.5239 0.450277
\(656\) 125.814 4.91220
\(657\) 33.3970 1.30294
\(658\) 100.665 3.92434
\(659\) −38.2210 −1.48888 −0.744440 0.667689i \(-0.767283\pi\)
−0.744440 + 0.667689i \(0.767283\pi\)
\(660\) −21.1046 −0.821497
\(661\) −30.1739 −1.17363 −0.586815 0.809721i \(-0.699618\pi\)
−0.586815 + 0.809721i \(0.699618\pi\)
\(662\) −64.2592 −2.49750
\(663\) 16.0323 0.622643
\(664\) −13.2951 −0.515950
\(665\) −62.6528 −2.42957
\(666\) 6.91026 0.267767
\(667\) −3.66411 −0.141875
\(668\) −101.326 −3.92043
\(669\) −4.62810 −0.178933
\(670\) −4.21730 −0.162929
\(671\) −14.1803 −0.547426
\(672\) −91.9712 −3.54786
\(673\) 7.45780 0.287477 0.143739 0.989616i \(-0.454088\pi\)
0.143739 + 0.989616i \(0.454088\pi\)
\(674\) 25.8936 0.997384
\(675\) −0.769490 −0.0296177
\(676\) −2.90543 −0.111747
\(677\) 3.48593 0.133975 0.0669876 0.997754i \(-0.478661\pi\)
0.0669876 + 0.997754i \(0.478661\pi\)
\(678\) 5.14603 0.197632
\(679\) 57.0757 2.19036
\(680\) 148.768 5.70498
\(681\) −15.3788 −0.589317
\(682\) 52.1898 1.99845
\(683\) −33.1191 −1.26727 −0.633634 0.773633i \(-0.718438\pi\)
−0.633634 + 0.773633i \(0.718438\pi\)
\(684\) 81.6364 3.12145
\(685\) 38.6191 1.47556
\(686\) −117.410 −4.48272
\(687\) 1.80269 0.0687771
\(688\) 48.6163 1.85348
\(689\) 45.8946 1.74845
\(690\) −6.11572 −0.232821
\(691\) −22.6571 −0.861916 −0.430958 0.902372i \(-0.641824\pi\)
−0.430958 + 0.902372i \(0.641824\pi\)
\(692\) −21.2812 −0.808989
\(693\) 27.0579 1.02784
\(694\) 35.6519 1.35333
\(695\) −37.1186 −1.40799
\(696\) −19.8653 −0.752991
\(697\) −46.7013 −1.76894
\(698\) −88.4762 −3.34887
\(699\) −1.49908 −0.0567004
\(700\) −5.34945 −0.202190
\(701\) −32.2047 −1.21635 −0.608177 0.793802i \(-0.708099\pi\)
−0.608177 + 0.793802i \(0.708099\pi\)
\(702\) 38.4579 1.45150
\(703\) 5.74978 0.216857
\(704\) 92.1655 3.47362
\(705\) 12.3535 0.465261
\(706\) −89.3134 −3.36136
\(707\) −86.4087 −3.24973
\(708\) 1.75550 0.0659757
\(709\) 18.8350 0.707363 0.353682 0.935366i \(-0.384930\pi\)
0.353682 + 0.935366i \(0.384930\pi\)
\(710\) −4.37609 −0.164232
\(711\) 13.4819 0.505609
\(712\) 120.308 4.50874
\(713\) 11.1966 0.419314
\(714\) 60.1811 2.25222
\(715\) 18.3147 0.684929
\(716\) 134.997 5.04508
\(717\) 20.5865 0.768817
\(718\) 15.6053 0.582386
\(719\) −3.77422 −0.140755 −0.0703773 0.997520i \(-0.522420\pi\)
−0.0703773 + 0.997520i \(0.522420\pi\)
\(720\) 97.1214 3.61950
\(721\) −53.5885 −1.99574
\(722\) 39.0205 1.45219
\(723\) −6.51067 −0.242134
\(724\) −134.920 −5.01425
\(725\) −0.531267 −0.0197308
\(726\) −11.5596 −0.429016
\(727\) −41.5073 −1.53942 −0.769710 0.638393i \(-0.779599\pi\)
−0.769710 + 0.638393i \(0.779599\pi\)
\(728\) 173.585 6.43348
\(729\) −3.22557 −0.119466
\(730\) 84.8550 3.14063
\(731\) −18.0461 −0.667458
\(732\) −25.4033 −0.938934
\(733\) −10.2931 −0.380185 −0.190093 0.981766i \(-0.560879\pi\)
−0.190093 + 0.981766i \(0.560879\pi\)
\(734\) −43.1516 −1.59276
\(735\) −25.8047 −0.951820
\(736\) 36.4636 1.34406
\(737\) 1.51546 0.0558226
\(738\) −50.8086 −1.87029
\(739\) 15.7578 0.579660 0.289830 0.957078i \(-0.406401\pi\)
0.289830 + 0.957078i \(0.406401\pi\)
\(740\) 12.9985 0.477834
\(741\) 14.5131 0.533153
\(742\) 172.276 6.32447
\(743\) 19.7268 0.723708 0.361854 0.932235i \(-0.382144\pi\)
0.361854 + 0.932235i \(0.382144\pi\)
\(744\) 60.7031 2.22548
\(745\) −6.58796 −0.241364
\(746\) −23.5060 −0.860617
\(747\) 3.22180 0.117880
\(748\) −82.3376 −3.01056
\(749\) −36.8372 −1.34600
\(750\) 21.7048 0.792546
\(751\) −15.4840 −0.565019 −0.282510 0.959264i \(-0.591167\pi\)
−0.282510 + 0.959264i \(0.591167\pi\)
\(752\) −129.841 −4.73480
\(753\) −7.82755 −0.285252
\(754\) 26.5519 0.966962
\(755\) −36.8203 −1.34003
\(756\) 106.876 3.88703
\(757\) 4.68563 0.170302 0.0851511 0.996368i \(-0.472863\pi\)
0.0851511 + 0.996368i \(0.472863\pi\)
\(758\) 59.2506 2.15208
\(759\) 2.19764 0.0797693
\(760\) 134.671 4.88503
\(761\) 18.2788 0.662605 0.331303 0.943525i \(-0.392512\pi\)
0.331303 + 0.943525i \(0.392512\pi\)
\(762\) −6.48974 −0.235098
\(763\) 4.78018 0.173054
\(764\) −47.1515 −1.70588
\(765\) −36.0509 −1.30342
\(766\) 10.4361 0.377073
\(767\) −1.52343 −0.0550077
\(768\) 58.3157 2.10429
\(769\) −15.7087 −0.566471 −0.283236 0.959050i \(-0.591408\pi\)
−0.283236 + 0.959050i \(0.591408\pi\)
\(770\) 68.7485 2.47752
\(771\) −22.2184 −0.800177
\(772\) −21.9230 −0.789028
\(773\) 5.33431 0.191862 0.0959310 0.995388i \(-0.469417\pi\)
0.0959310 + 0.995388i \(0.469417\pi\)
\(774\) −19.6332 −0.705701
\(775\) 1.62341 0.0583147
\(776\) −122.683 −4.40407
\(777\) 3.41401 0.122477
\(778\) −32.9456 −1.18116
\(779\) −42.2760 −1.51470
\(780\) 32.8098 1.17478
\(781\) 1.57252 0.0562691
\(782\) −23.8598 −0.853226
\(783\) 10.6141 0.379316
\(784\) 271.218 9.68635
\(785\) 37.9385 1.35408
\(786\) −10.0204 −0.357416
\(787\) 51.6176 1.83997 0.919985 0.391953i \(-0.128201\pi\)
0.919985 + 0.391953i \(0.128201\pi\)
\(788\) 22.8013 0.812261
\(789\) −2.33172 −0.0830114
\(790\) 34.2546 1.21872
\(791\) −12.4104 −0.441264
\(792\) −58.1603 −2.06664
\(793\) 22.0451 0.782844
\(794\) −53.8013 −1.90934
\(795\) 21.1416 0.749815
\(796\) −3.63357 −0.128788
\(797\) −54.5486 −1.93221 −0.966105 0.258151i \(-0.916887\pi\)
−0.966105 + 0.258151i \(0.916887\pi\)
\(798\) 54.4785 1.92852
\(799\) 48.1961 1.70505
\(800\) 5.28693 0.186921
\(801\) −29.1542 −1.03011
\(802\) 104.320 3.68366
\(803\) −30.4921 −1.07604
\(804\) 2.71487 0.0957460
\(805\) 14.7490 0.519833
\(806\) −81.1356 −2.85788
\(807\) 2.27627 0.0801285
\(808\) 185.734 6.53409
\(809\) 15.6349 0.549693 0.274846 0.961488i \(-0.411373\pi\)
0.274846 + 0.961488i \(0.411373\pi\)
\(810\) −29.5406 −1.03795
\(811\) 39.6254 1.39143 0.695717 0.718316i \(-0.255087\pi\)
0.695717 + 0.718316i \(0.255087\pi\)
\(812\) 73.7885 2.58947
\(813\) −7.03270 −0.246648
\(814\) −6.30919 −0.221137
\(815\) −0.735664 −0.0257692
\(816\) −77.6231 −2.71735
\(817\) −16.3361 −0.571527
\(818\) −81.5878 −2.85265
\(819\) −42.0648 −1.46986
\(820\) −95.5732 −3.33756
\(821\) −34.7967 −1.21441 −0.607206 0.794545i \(-0.707710\pi\)
−0.607206 + 0.794545i \(0.707710\pi\)
\(822\) −33.5805 −1.17125
\(823\) 42.2634 1.47321 0.736604 0.676324i \(-0.236428\pi\)
0.736604 + 0.676324i \(0.236428\pi\)
\(824\) 115.187 4.01274
\(825\) 0.318641 0.0110936
\(826\) −5.71855 −0.198974
\(827\) −49.4228 −1.71860 −0.859300 0.511472i \(-0.829101\pi\)
−0.859300 + 0.511472i \(0.829101\pi\)
\(828\) −19.2179 −0.667867
\(829\) −51.4919 −1.78839 −0.894193 0.447682i \(-0.852250\pi\)
−0.894193 + 0.447682i \(0.852250\pi\)
\(830\) 8.18594 0.284138
\(831\) 8.13675 0.282261
\(832\) −143.283 −4.96743
\(833\) −100.674 −3.48816
\(834\) 32.2758 1.11762
\(835\) 40.5060 1.40177
\(836\) −74.5355 −2.57786
\(837\) −32.4338 −1.12108
\(838\) 69.6799 2.40705
\(839\) 11.5186 0.397668 0.198834 0.980033i \(-0.436285\pi\)
0.198834 + 0.980033i \(0.436285\pi\)
\(840\) 79.9628 2.75898
\(841\) −21.6719 −0.747306
\(842\) −44.4591 −1.53216
\(843\) 3.33862 0.114988
\(844\) 11.8026 0.406264
\(845\) 1.16147 0.0399557
\(846\) 52.4349 1.80275
\(847\) 27.8777 0.957889
\(848\) −222.207 −7.63061
\(849\) 14.6255 0.501945
\(850\) −3.45949 −0.118660
\(851\) −1.35354 −0.0463989
\(852\) 2.81708 0.0965117
\(853\) 7.90139 0.270539 0.135269 0.990809i \(-0.456810\pi\)
0.135269 + 0.990809i \(0.456810\pi\)
\(854\) 82.7516 2.83170
\(855\) −32.6348 −1.11609
\(856\) 79.1808 2.70634
\(857\) 37.8937 1.29443 0.647213 0.762310i \(-0.275935\pi\)
0.647213 + 0.762310i \(0.275935\pi\)
\(858\) −15.9252 −0.543676
\(859\) 51.8909 1.77049 0.885247 0.465121i \(-0.153989\pi\)
0.885247 + 0.465121i \(0.153989\pi\)
\(860\) −36.9309 −1.25933
\(861\) −25.1020 −0.855473
\(862\) −23.4640 −0.799186
\(863\) −9.77648 −0.332795 −0.166398 0.986059i \(-0.553214\pi\)
−0.166398 + 0.986059i \(0.553214\pi\)
\(864\) −105.627 −3.59349
\(865\) 8.50732 0.289258
\(866\) −15.6628 −0.532244
\(867\) 16.6718 0.566205
\(868\) −225.478 −7.65323
\(869\) −12.3092 −0.417560
\(870\) 12.2313 0.414678
\(871\) −2.35597 −0.0798290
\(872\) −10.2749 −0.347952
\(873\) 29.7298 1.00620
\(874\) −21.5990 −0.730596
\(875\) −52.3443 −1.76956
\(876\) −54.6250 −1.84561
\(877\) 29.4725 0.995216 0.497608 0.867402i \(-0.334212\pi\)
0.497608 + 0.867402i \(0.334212\pi\)
\(878\) −31.2511 −1.05467
\(879\) −3.69971 −0.124788
\(880\) −88.6736 −2.98919
\(881\) −15.2632 −0.514229 −0.257114 0.966381i \(-0.582772\pi\)
−0.257114 + 0.966381i \(0.582772\pi\)
\(882\) −109.529 −3.68802
\(883\) 37.0330 1.24626 0.623130 0.782118i \(-0.285861\pi\)
0.623130 + 0.782118i \(0.285861\pi\)
\(884\) 128.004 4.30524
\(885\) −0.701774 −0.0235899
\(886\) −13.1558 −0.441978
\(887\) −25.9964 −0.872875 −0.436437 0.899735i \(-0.643760\pi\)
−0.436437 + 0.899735i \(0.643760\pi\)
\(888\) −7.33835 −0.246259
\(889\) 15.6510 0.524917
\(890\) −74.0750 −2.48300
\(891\) 10.6152 0.355623
\(892\) −36.9513 −1.23722
\(893\) 43.6292 1.45999
\(894\) 5.72843 0.191587
\(895\) −53.9662 −1.80389
\(896\) −280.296 −9.36404
\(897\) −3.41651 −0.114074
\(898\) 9.06631 0.302547
\(899\) −22.3928 −0.746841
\(900\) −2.78644 −0.0928813
\(901\) 82.4818 2.74787
\(902\) 46.3892 1.54459
\(903\) −9.69978 −0.322788
\(904\) 26.6760 0.887230
\(905\) 53.9352 1.79287
\(906\) 32.0164 1.06367
\(907\) −20.9225 −0.694719 −0.347359 0.937732i \(-0.612922\pi\)
−0.347359 + 0.937732i \(0.612922\pi\)
\(908\) −122.786 −4.07481
\(909\) −45.0088 −1.49285
\(910\) −106.878 −3.54297
\(911\) −37.0236 −1.22665 −0.613324 0.789832i \(-0.710168\pi\)
−0.613324 + 0.789832i \(0.710168\pi\)
\(912\) −70.2678 −2.32680
\(913\) −2.94156 −0.0973515
\(914\) 57.3345 1.89646
\(915\) 10.1552 0.335720
\(916\) 14.3929 0.475556
\(917\) 24.1657 0.798023
\(918\) 69.1165 2.28118
\(919\) −28.5293 −0.941096 −0.470548 0.882374i \(-0.655944\pi\)
−0.470548 + 0.882374i \(0.655944\pi\)
\(920\) −31.7026 −1.04520
\(921\) 17.7459 0.584747
\(922\) −44.5075 −1.46578
\(923\) −2.44467 −0.0804674
\(924\) −44.2565 −1.45593
\(925\) −0.196253 −0.00645276
\(926\) −45.1985 −1.48532
\(927\) −27.9133 −0.916794
\(928\) −72.9261 −2.39392
\(929\) 14.9398 0.490158 0.245079 0.969503i \(-0.421186\pi\)
0.245079 + 0.969503i \(0.421186\pi\)
\(930\) −37.3755 −1.22559
\(931\) −91.1348 −2.98682
\(932\) −11.9689 −0.392053
\(933\) −7.08363 −0.231908
\(934\) 50.6990 1.65892
\(935\) 32.9151 1.07644
\(936\) 90.4175 2.95539
\(937\) 14.9470 0.488296 0.244148 0.969738i \(-0.421492\pi\)
0.244148 + 0.969738i \(0.421492\pi\)
\(938\) −8.84370 −0.288757
\(939\) 17.4677 0.570037
\(940\) 98.6323 3.21703
\(941\) 17.3025 0.564046 0.282023 0.959408i \(-0.408995\pi\)
0.282023 + 0.959408i \(0.408995\pi\)
\(942\) −32.9887 −1.07483
\(943\) 9.95211 0.324085
\(944\) 7.37593 0.240066
\(945\) −42.7244 −1.38982
\(946\) 17.9255 0.582807
\(947\) 3.07936 0.100066 0.0500330 0.998748i \(-0.484067\pi\)
0.0500330 + 0.998748i \(0.484067\pi\)
\(948\) −22.0512 −0.716191
\(949\) 47.4037 1.53879
\(950\) −3.13168 −0.101605
\(951\) −18.2061 −0.590373
\(952\) 311.967 10.1109
\(953\) 51.1464 1.65679 0.828397 0.560142i \(-0.189253\pi\)
0.828397 + 0.560142i \(0.189253\pi\)
\(954\) 89.7359 2.90531
\(955\) 18.8492 0.609945
\(956\) 164.365 5.31596
\(957\) −4.39522 −0.142077
\(958\) 68.1508 2.20185
\(959\) 80.9845 2.61513
\(960\) −66.0039 −2.13027
\(961\) 37.4265 1.20731
\(962\) 9.80842 0.316236
\(963\) −19.1879 −0.618320
\(964\) −51.9821 −1.67423
\(965\) 8.76391 0.282120
\(966\) −12.8247 −0.412627
\(967\) −1.55344 −0.0499554 −0.0249777 0.999688i \(-0.507951\pi\)
−0.0249777 + 0.999688i \(0.507951\pi\)
\(968\) −59.9226 −1.92598
\(969\) 26.0830 0.837906
\(970\) 75.5373 2.42536
\(971\) −13.2256 −0.424431 −0.212215 0.977223i \(-0.568068\pi\)
−0.212215 + 0.977223i \(0.568068\pi\)
\(972\) 86.0908 2.76136
\(973\) −77.8379 −2.49537
\(974\) −18.4568 −0.591393
\(975\) −0.495367 −0.0158644
\(976\) −106.735 −3.41651
\(977\) 20.7097 0.662560 0.331280 0.943532i \(-0.392519\pi\)
0.331280 + 0.943532i \(0.392519\pi\)
\(978\) 0.639682 0.0204548
\(979\) 26.6183 0.850726
\(980\) −206.028 −6.58132
\(981\) 2.48992 0.0794969
\(982\) −21.4611 −0.684853
\(983\) 45.0770 1.43773 0.718866 0.695149i \(-0.244662\pi\)
0.718866 + 0.695149i \(0.244662\pi\)
\(984\) 53.9562 1.72006
\(985\) −9.11498 −0.290428
\(986\) 47.7190 1.51968
\(987\) 25.9054 0.824579
\(988\) 115.875 3.68647
\(989\) 3.84564 0.122284
\(990\) 35.8099 1.13811
\(991\) 39.5977 1.25786 0.628932 0.777461i \(-0.283492\pi\)
0.628932 + 0.777461i \(0.283492\pi\)
\(992\) 222.843 7.07527
\(993\) −16.5366 −0.524773
\(994\) −9.17667 −0.291066
\(995\) 1.45255 0.0460489
\(996\) −5.26966 −0.166975
\(997\) 25.1944 0.797915 0.398957 0.916969i \(-0.369372\pi\)
0.398957 + 0.916969i \(0.369372\pi\)
\(998\) −69.2328 −2.19153
\(999\) 3.92090 0.124052
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 4033.2.a.d.1.79 79
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.d.1.79 79 1.1 even 1 trivial