Properties

Label 6022.2.a.c.1.9
Level $6022$
Weight $2$
Character 6022.1
Self dual yes
Analytic conductor $48.086$
Analytic rank $0$
Dimension $61$
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] = [6022,2,Mod(1,6022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6022, 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("6022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6022 = 2 \cdot 3011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6022.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: \(48.0859120972\)
Analytic rank: \(0\)
Dimension: \(61\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6022.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.51016 q^{3} +1.00000 q^{4} +1.21389 q^{5} +2.51016 q^{6} +4.01976 q^{7} -1.00000 q^{8} +3.30092 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.51016 q^{3} +1.00000 q^{4} +1.21389 q^{5} +2.51016 q^{6} +4.01976 q^{7} -1.00000 q^{8} +3.30092 q^{9} -1.21389 q^{10} +4.67270 q^{11} -2.51016 q^{12} +3.24878 q^{13} -4.01976 q^{14} -3.04706 q^{15} +1.00000 q^{16} -6.81620 q^{17} -3.30092 q^{18} -6.37578 q^{19} +1.21389 q^{20} -10.0903 q^{21} -4.67270 q^{22} +2.73733 q^{23} +2.51016 q^{24} -3.52647 q^{25} -3.24878 q^{26} -0.755352 q^{27} +4.01976 q^{28} +1.51171 q^{29} +3.04706 q^{30} -2.65133 q^{31} -1.00000 q^{32} -11.7292 q^{33} +6.81620 q^{34} +4.87955 q^{35} +3.30092 q^{36} -4.72196 q^{37} +6.37578 q^{38} -8.15497 q^{39} -1.21389 q^{40} +5.91381 q^{41} +10.0903 q^{42} +7.72089 q^{43} +4.67270 q^{44} +4.00695 q^{45} -2.73733 q^{46} +12.9408 q^{47} -2.51016 q^{48} +9.15850 q^{49} +3.52647 q^{50} +17.1098 q^{51} +3.24878 q^{52} -10.7353 q^{53} +0.755352 q^{54} +5.67214 q^{55} -4.01976 q^{56} +16.0043 q^{57} -1.51171 q^{58} +2.48541 q^{59} -3.04706 q^{60} +11.0215 q^{61} +2.65133 q^{62} +13.2689 q^{63} +1.00000 q^{64} +3.94366 q^{65} +11.7292 q^{66} -5.99089 q^{67} -6.81620 q^{68} -6.87114 q^{69} -4.87955 q^{70} -6.95570 q^{71} -3.30092 q^{72} +11.9851 q^{73} +4.72196 q^{74} +8.85202 q^{75} -6.37578 q^{76} +18.7831 q^{77} +8.15497 q^{78} -0.820280 q^{79} +1.21389 q^{80} -8.00670 q^{81} -5.91381 q^{82} +6.75066 q^{83} -10.0903 q^{84} -8.27411 q^{85} -7.72089 q^{86} -3.79465 q^{87} -4.67270 q^{88} +2.03257 q^{89} -4.00695 q^{90} +13.0593 q^{91} +2.73733 q^{92} +6.65527 q^{93} -12.9408 q^{94} -7.73949 q^{95} +2.51016 q^{96} -8.73748 q^{97} -9.15850 q^{98} +15.4242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.51016 −1.44924 −0.724622 0.689147i \(-0.757985\pi\)
−0.724622 + 0.689147i \(0.757985\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.21389 0.542868 0.271434 0.962457i \(-0.412502\pi\)
0.271434 + 0.962457i \(0.412502\pi\)
\(6\) 2.51016 1.02477
\(7\) 4.01976 1.51933 0.759664 0.650316i \(-0.225363\pi\)
0.759664 + 0.650316i \(0.225363\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.30092 1.10031
\(10\) −1.21389 −0.383865
\(11\) 4.67270 1.40887 0.704436 0.709768i \(-0.251200\pi\)
0.704436 + 0.709768i \(0.251200\pi\)
\(12\) −2.51016 −0.724622
\(13\) 3.24878 0.901050 0.450525 0.892764i \(-0.351237\pi\)
0.450525 + 0.892764i \(0.351237\pi\)
\(14\) −4.01976 −1.07433
\(15\) −3.04706 −0.786747
\(16\) 1.00000 0.250000
\(17\) −6.81620 −1.65317 −0.826586 0.562811i \(-0.809720\pi\)
−0.826586 + 0.562811i \(0.809720\pi\)
\(18\) −3.30092 −0.778034
\(19\) −6.37578 −1.46270 −0.731352 0.682000i \(-0.761110\pi\)
−0.731352 + 0.682000i \(0.761110\pi\)
\(20\) 1.21389 0.271434
\(21\) −10.0903 −2.20188
\(22\) −4.67270 −0.996222
\(23\) 2.73733 0.570772 0.285386 0.958413i \(-0.407878\pi\)
0.285386 + 0.958413i \(0.407878\pi\)
\(24\) 2.51016 0.512385
\(25\) −3.52647 −0.705295
\(26\) −3.24878 −0.637138
\(27\) −0.755352 −0.145368
\(28\) 4.01976 0.759664
\(29\) 1.51171 0.280718 0.140359 0.990101i \(-0.455174\pi\)
0.140359 + 0.990101i \(0.455174\pi\)
\(30\) 3.04706 0.556314
\(31\) −2.65133 −0.476193 −0.238097 0.971241i \(-0.576523\pi\)
−0.238097 + 0.971241i \(0.576523\pi\)
\(32\) −1.00000 −0.176777
\(33\) −11.7292 −2.04180
\(34\) 6.81620 1.16897
\(35\) 4.87955 0.824794
\(36\) 3.30092 0.550153
\(37\) −4.72196 −0.776286 −0.388143 0.921599i \(-0.626883\pi\)
−0.388143 + 0.921599i \(0.626883\pi\)
\(38\) 6.37578 1.03429
\(39\) −8.15497 −1.30584
\(40\) −1.21389 −0.191933
\(41\) 5.91381 0.923582 0.461791 0.886989i \(-0.347207\pi\)
0.461791 + 0.886989i \(0.347207\pi\)
\(42\) 10.0903 1.55696
\(43\) 7.72089 1.17743 0.588713 0.808342i \(-0.299635\pi\)
0.588713 + 0.808342i \(0.299635\pi\)
\(44\) 4.67270 0.704436
\(45\) 4.00695 0.597321
\(46\) −2.73733 −0.403597
\(47\) 12.9408 1.88761 0.943804 0.330507i \(-0.107220\pi\)
0.943804 + 0.330507i \(0.107220\pi\)
\(48\) −2.51016 −0.362311
\(49\) 9.15850 1.30836
\(50\) 3.52647 0.498719
\(51\) 17.1098 2.39585
\(52\) 3.24878 0.450525
\(53\) −10.7353 −1.47460 −0.737301 0.675564i \(-0.763900\pi\)
−0.737301 + 0.675564i \(0.763900\pi\)
\(54\) 0.755352 0.102790
\(55\) 5.67214 0.764831
\(56\) −4.01976 −0.537164
\(57\) 16.0043 2.11981
\(58\) −1.51171 −0.198498
\(59\) 2.48541 0.323572 0.161786 0.986826i \(-0.448275\pi\)
0.161786 + 0.986826i \(0.448275\pi\)
\(60\) −3.04706 −0.393374
\(61\) 11.0215 1.41115 0.705577 0.708633i \(-0.250688\pi\)
0.705577 + 0.708633i \(0.250688\pi\)
\(62\) 2.65133 0.336719
\(63\) 13.2689 1.67173
\(64\) 1.00000 0.125000
\(65\) 3.94366 0.489151
\(66\) 11.7292 1.44377
\(67\) −5.99089 −0.731903 −0.365952 0.930634i \(-0.619256\pi\)
−0.365952 + 0.930634i \(0.619256\pi\)
\(68\) −6.81620 −0.826586
\(69\) −6.87114 −0.827188
\(70\) −4.87955 −0.583218
\(71\) −6.95570 −0.825490 −0.412745 0.910847i \(-0.635430\pi\)
−0.412745 + 0.910847i \(0.635430\pi\)
\(72\) −3.30092 −0.389017
\(73\) 11.9851 1.40275 0.701377 0.712791i \(-0.252569\pi\)
0.701377 + 0.712791i \(0.252569\pi\)
\(74\) 4.72196 0.548917
\(75\) 8.85202 1.02214
\(76\) −6.37578 −0.731352
\(77\) 18.7831 2.14054
\(78\) 8.15497 0.923368
\(79\) −0.820280 −0.0922887 −0.0461444 0.998935i \(-0.514693\pi\)
−0.0461444 + 0.998935i \(0.514693\pi\)
\(80\) 1.21389 0.135717
\(81\) −8.00670 −0.889633
\(82\) −5.91381 −0.653071
\(83\) 6.75066 0.740981 0.370490 0.928836i \(-0.379190\pi\)
0.370490 + 0.928836i \(0.379190\pi\)
\(84\) −10.0903 −1.10094
\(85\) −8.27411 −0.897454
\(86\) −7.72089 −0.832565
\(87\) −3.79465 −0.406829
\(88\) −4.67270 −0.498111
\(89\) 2.03257 0.215452 0.107726 0.994181i \(-0.465643\pi\)
0.107726 + 0.994181i \(0.465643\pi\)
\(90\) −4.00695 −0.422369
\(91\) 13.0593 1.36899
\(92\) 2.73733 0.285386
\(93\) 6.65527 0.690120
\(94\) −12.9408 −1.33474
\(95\) −7.73949 −0.794055
\(96\) 2.51016 0.256192
\(97\) −8.73748 −0.887157 −0.443578 0.896236i \(-0.646291\pi\)
−0.443578 + 0.896236i \(0.646291\pi\)
\(98\) −9.15850 −0.925148
\(99\) 15.4242 1.55019
\(100\) −3.52647 −0.352647
\(101\) 4.95801 0.493341 0.246670 0.969099i \(-0.420663\pi\)
0.246670 + 0.969099i \(0.420663\pi\)
\(102\) −17.1098 −1.69412
\(103\) 6.96802 0.686579 0.343290 0.939230i \(-0.388459\pi\)
0.343290 + 0.939230i \(0.388459\pi\)
\(104\) −3.24878 −0.318569
\(105\) −12.2485 −1.19533
\(106\) 10.7353 1.04270
\(107\) −7.43212 −0.718490 −0.359245 0.933243i \(-0.616966\pi\)
−0.359245 + 0.933243i \(0.616966\pi\)
\(108\) −0.755352 −0.0726838
\(109\) 13.7246 1.31458 0.657289 0.753639i \(-0.271703\pi\)
0.657289 + 0.753639i \(0.271703\pi\)
\(110\) −5.67214 −0.540817
\(111\) 11.8529 1.12503
\(112\) 4.01976 0.379832
\(113\) 10.6786 1.00455 0.502277 0.864707i \(-0.332496\pi\)
0.502277 + 0.864707i \(0.332496\pi\)
\(114\) −16.0043 −1.49894
\(115\) 3.32281 0.309854
\(116\) 1.51171 0.140359
\(117\) 10.7240 0.991430
\(118\) −2.48541 −0.228800
\(119\) −27.3995 −2.51171
\(120\) 3.04706 0.278157
\(121\) 10.8341 0.984918
\(122\) −11.0215 −0.997837
\(123\) −14.8446 −1.33849
\(124\) −2.65133 −0.238097
\(125\) −10.3502 −0.925749
\(126\) −13.2689 −1.18209
\(127\) −6.74879 −0.598858 −0.299429 0.954119i \(-0.596796\pi\)
−0.299429 + 0.954119i \(0.596796\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −19.3807 −1.70638
\(130\) −3.94366 −0.345882
\(131\) −15.4181 −1.34709 −0.673545 0.739146i \(-0.735229\pi\)
−0.673545 + 0.739146i \(0.735229\pi\)
\(132\) −11.7292 −1.02090
\(133\) −25.6291 −2.22233
\(134\) 5.99089 0.517534
\(135\) −0.916913 −0.0789153
\(136\) 6.81620 0.584484
\(137\) −4.39322 −0.375338 −0.187669 0.982232i \(-0.560093\pi\)
−0.187669 + 0.982232i \(0.560093\pi\)
\(138\) 6.87114 0.584910
\(139\) −19.2144 −1.62974 −0.814872 0.579642i \(-0.803193\pi\)
−0.814872 + 0.579642i \(0.803193\pi\)
\(140\) 4.87955 0.412397
\(141\) −32.4835 −2.73560
\(142\) 6.95570 0.583709
\(143\) 15.1806 1.26946
\(144\) 3.30092 0.275076
\(145\) 1.83505 0.152393
\(146\) −11.9851 −0.991897
\(147\) −22.9893 −1.89613
\(148\) −4.72196 −0.388143
\(149\) 13.2134 1.08249 0.541243 0.840866i \(-0.317954\pi\)
0.541243 + 0.840866i \(0.317954\pi\)
\(150\) −8.85202 −0.722765
\(151\) 21.3556 1.73790 0.868948 0.494904i \(-0.164797\pi\)
0.868948 + 0.494904i \(0.164797\pi\)
\(152\) 6.37578 0.517144
\(153\) −22.4997 −1.81899
\(154\) −18.7831 −1.51359
\(155\) −3.21842 −0.258510
\(156\) −8.15497 −0.652920
\(157\) 18.0969 1.44429 0.722145 0.691742i \(-0.243156\pi\)
0.722145 + 0.691742i \(0.243156\pi\)
\(158\) 0.820280 0.0652580
\(159\) 26.9473 2.13706
\(160\) −1.21389 −0.0959664
\(161\) 11.0034 0.867190
\(162\) 8.00670 0.629065
\(163\) 15.4959 1.21373 0.606867 0.794803i \(-0.292426\pi\)
0.606867 + 0.794803i \(0.292426\pi\)
\(164\) 5.91381 0.461791
\(165\) −14.2380 −1.10843
\(166\) −6.75066 −0.523953
\(167\) 11.2723 0.872278 0.436139 0.899879i \(-0.356346\pi\)
0.436139 + 0.899879i \(0.356346\pi\)
\(168\) 10.0903 0.778481
\(169\) −2.44542 −0.188110
\(170\) 8.27411 0.634596
\(171\) −21.0459 −1.60942
\(172\) 7.72089 0.588713
\(173\) 1.11114 0.0844787 0.0422393 0.999108i \(-0.486551\pi\)
0.0422393 + 0.999108i \(0.486551\pi\)
\(174\) 3.79465 0.287671
\(175\) −14.1756 −1.07157
\(176\) 4.67270 0.352218
\(177\) −6.23878 −0.468935
\(178\) −2.03257 −0.152347
\(179\) 9.19618 0.687355 0.343677 0.939088i \(-0.388327\pi\)
0.343677 + 0.939088i \(0.388327\pi\)
\(180\) 4.00695 0.298660
\(181\) −17.9710 −1.33578 −0.667888 0.744262i \(-0.732801\pi\)
−0.667888 + 0.744262i \(0.732801\pi\)
\(182\) −13.0593 −0.968022
\(183\) −27.6657 −2.04511
\(184\) −2.73733 −0.201798
\(185\) −5.73194 −0.421420
\(186\) −6.65527 −0.487988
\(187\) −31.8500 −2.32911
\(188\) 12.9408 0.943804
\(189\) −3.03634 −0.220861
\(190\) 7.73949 0.561482
\(191\) 24.2424 1.75412 0.877060 0.480380i \(-0.159501\pi\)
0.877060 + 0.480380i \(0.159501\pi\)
\(192\) −2.51016 −0.181155
\(193\) 8.80361 0.633697 0.316849 0.948476i \(-0.397375\pi\)
0.316849 + 0.948476i \(0.397375\pi\)
\(194\) 8.73748 0.627314
\(195\) −9.89923 −0.708898
\(196\) 9.15850 0.654179
\(197\) 22.5605 1.60737 0.803684 0.595056i \(-0.202870\pi\)
0.803684 + 0.595056i \(0.202870\pi\)
\(198\) −15.4242 −1.09615
\(199\) −12.7595 −0.904494 −0.452247 0.891893i \(-0.649377\pi\)
−0.452247 + 0.891893i \(0.649377\pi\)
\(200\) 3.52647 0.249359
\(201\) 15.0381 1.06071
\(202\) −4.95801 −0.348845
\(203\) 6.07673 0.426503
\(204\) 17.1098 1.19792
\(205\) 7.17871 0.501383
\(206\) −6.96802 −0.485485
\(207\) 9.03569 0.628024
\(208\) 3.24878 0.225262
\(209\) −29.7921 −2.06076
\(210\) 12.2485 0.845224
\(211\) −21.9026 −1.50784 −0.753920 0.656966i \(-0.771840\pi\)
−0.753920 + 0.656966i \(0.771840\pi\)
\(212\) −10.7353 −0.737301
\(213\) 17.4599 1.19634
\(214\) 7.43212 0.508049
\(215\) 9.37231 0.639186
\(216\) 0.755352 0.0513952
\(217\) −10.6577 −0.723493
\(218\) −13.7246 −0.929547
\(219\) −30.0846 −2.03293
\(220\) 5.67214 0.382415
\(221\) −22.1443 −1.48959
\(222\) −11.8529 −0.795514
\(223\) −16.3532 −1.09509 −0.547547 0.836775i \(-0.684438\pi\)
−0.547547 + 0.836775i \(0.684438\pi\)
\(224\) −4.01976 −0.268582
\(225\) −11.6406 −0.776040
\(226\) −10.6786 −0.710327
\(227\) 12.4998 0.829640 0.414820 0.909903i \(-0.363844\pi\)
0.414820 + 0.909903i \(0.363844\pi\)
\(228\) 16.0043 1.05991
\(229\) 18.2669 1.20711 0.603556 0.797321i \(-0.293750\pi\)
0.603556 + 0.797321i \(0.293750\pi\)
\(230\) −3.32281 −0.219100
\(231\) −47.1487 −3.10216
\(232\) −1.51171 −0.0992489
\(233\) 11.4372 0.749279 0.374639 0.927171i \(-0.377767\pi\)
0.374639 + 0.927171i \(0.377767\pi\)
\(234\) −10.7240 −0.701047
\(235\) 15.7087 1.02472
\(236\) 2.48541 0.161786
\(237\) 2.05904 0.133749
\(238\) 27.3995 1.77605
\(239\) −9.03889 −0.584677 −0.292339 0.956315i \(-0.594433\pi\)
−0.292339 + 0.956315i \(0.594433\pi\)
\(240\) −3.04706 −0.196687
\(241\) −13.9464 −0.898368 −0.449184 0.893439i \(-0.648285\pi\)
−0.449184 + 0.893439i \(0.648285\pi\)
\(242\) −10.8341 −0.696442
\(243\) 22.3642 1.43466
\(244\) 11.0215 0.705577
\(245\) 11.1174 0.710265
\(246\) 14.8446 0.946459
\(247\) −20.7135 −1.31797
\(248\) 2.65133 0.168360
\(249\) −16.9452 −1.07386
\(250\) 10.3502 0.654604
\(251\) −13.1105 −0.827525 −0.413763 0.910385i \(-0.635786\pi\)
−0.413763 + 0.910385i \(0.635786\pi\)
\(252\) 13.2689 0.835863
\(253\) 12.7907 0.804144
\(254\) 6.74879 0.423457
\(255\) 20.7694 1.30063
\(256\) 1.00000 0.0625000
\(257\) 17.8690 1.11464 0.557318 0.830299i \(-0.311830\pi\)
0.557318 + 0.830299i \(0.311830\pi\)
\(258\) 19.3807 1.20659
\(259\) −18.9812 −1.17943
\(260\) 3.94366 0.244575
\(261\) 4.99004 0.308876
\(262\) 15.4181 0.952536
\(263\) −5.81471 −0.358551 −0.179275 0.983799i \(-0.557375\pi\)
−0.179275 + 0.983799i \(0.557375\pi\)
\(264\) 11.7292 0.721884
\(265\) −13.0314 −0.800514
\(266\) 25.6291 1.57142
\(267\) −5.10207 −0.312242
\(268\) −5.99089 −0.365952
\(269\) 24.5522 1.49697 0.748487 0.663150i \(-0.230781\pi\)
0.748487 + 0.663150i \(0.230781\pi\)
\(270\) 0.916913 0.0558016
\(271\) 13.9621 0.848136 0.424068 0.905630i \(-0.360602\pi\)
0.424068 + 0.905630i \(0.360602\pi\)
\(272\) −6.81620 −0.413293
\(273\) −32.7810 −1.98400
\(274\) 4.39322 0.265404
\(275\) −16.4781 −0.993669
\(276\) −6.87114 −0.413594
\(277\) −6.71887 −0.403698 −0.201849 0.979417i \(-0.564695\pi\)
−0.201849 + 0.979417i \(0.564695\pi\)
\(278\) 19.2144 1.15240
\(279\) −8.75182 −0.523958
\(280\) −4.87955 −0.291609
\(281\) −5.63094 −0.335913 −0.167957 0.985794i \(-0.553717\pi\)
−0.167957 + 0.985794i \(0.553717\pi\)
\(282\) 32.4835 1.93436
\(283\) −15.3746 −0.913924 −0.456962 0.889486i \(-0.651063\pi\)
−0.456962 + 0.889486i \(0.651063\pi\)
\(284\) −6.95570 −0.412745
\(285\) 19.4274 1.15078
\(286\) −15.1806 −0.897646
\(287\) 23.7721 1.40322
\(288\) −3.30092 −0.194508
\(289\) 29.4606 1.73298
\(290\) −1.83505 −0.107758
\(291\) 21.9325 1.28571
\(292\) 11.9851 0.701377
\(293\) −5.87022 −0.342942 −0.171471 0.985189i \(-0.554852\pi\)
−0.171471 + 0.985189i \(0.554852\pi\)
\(294\) 22.9893 1.34076
\(295\) 3.01701 0.175657
\(296\) 4.72196 0.274458
\(297\) −3.52953 −0.204804
\(298\) −13.2134 −0.765433
\(299\) 8.89297 0.514294
\(300\) 8.85202 0.511072
\(301\) 31.0362 1.78889
\(302\) −21.3556 −1.22888
\(303\) −12.4454 −0.714971
\(304\) −6.37578 −0.365676
\(305\) 13.3788 0.766070
\(306\) 22.4997 1.28622
\(307\) −12.0524 −0.687868 −0.343934 0.938994i \(-0.611760\pi\)
−0.343934 + 0.938994i \(0.611760\pi\)
\(308\) 18.7831 1.07027
\(309\) −17.4909 −0.995020
\(310\) 3.21842 0.182794
\(311\) 29.3871 1.66639 0.833196 0.552978i \(-0.186509\pi\)
0.833196 + 0.552978i \(0.186509\pi\)
\(312\) 8.15497 0.461684
\(313\) −1.93762 −0.109521 −0.0547603 0.998500i \(-0.517439\pi\)
−0.0547603 + 0.998500i \(0.517439\pi\)
\(314\) −18.0969 −1.02127
\(315\) 16.1070 0.907526
\(316\) −0.820280 −0.0461444
\(317\) 14.8682 0.835080 0.417540 0.908658i \(-0.362892\pi\)
0.417540 + 0.908658i \(0.362892\pi\)
\(318\) −26.9473 −1.51113
\(319\) 7.06378 0.395496
\(320\) 1.21389 0.0678585
\(321\) 18.6558 1.04127
\(322\) −11.0034 −0.613196
\(323\) 43.4586 2.41810
\(324\) −8.00670 −0.444816
\(325\) −11.4567 −0.635505
\(326\) −15.4959 −0.858239
\(327\) −34.4510 −1.90514
\(328\) −5.91381 −0.326535
\(329\) 52.0189 2.86789
\(330\) 14.2380 0.783775
\(331\) 5.44635 0.299358 0.149679 0.988735i \(-0.452176\pi\)
0.149679 + 0.988735i \(0.452176\pi\)
\(332\) 6.75066 0.370490
\(333\) −15.5868 −0.854152
\(334\) −11.2723 −0.616793
\(335\) −7.27227 −0.397327
\(336\) −10.0903 −0.550469
\(337\) −23.5626 −1.28354 −0.641768 0.766899i \(-0.721799\pi\)
−0.641768 + 0.766899i \(0.721799\pi\)
\(338\) 2.44542 0.133014
\(339\) −26.8049 −1.45584
\(340\) −8.27411 −0.448727
\(341\) −12.3889 −0.670895
\(342\) 21.0459 1.13803
\(343\) 8.67666 0.468496
\(344\) −7.72089 −0.416283
\(345\) −8.34080 −0.449053
\(346\) −1.11114 −0.0597354
\(347\) 26.3506 1.41457 0.707286 0.706928i \(-0.249919\pi\)
0.707286 + 0.706928i \(0.249919\pi\)
\(348\) −3.79465 −0.203414
\(349\) −0.161549 −0.00864752 −0.00432376 0.999991i \(-0.501376\pi\)
−0.00432376 + 0.999991i \(0.501376\pi\)
\(350\) 14.1756 0.757717
\(351\) −2.45397 −0.130983
\(352\) −4.67270 −0.249056
\(353\) 21.0100 1.11825 0.559124 0.829084i \(-0.311138\pi\)
0.559124 + 0.829084i \(0.311138\pi\)
\(354\) 6.23878 0.331587
\(355\) −8.44345 −0.448132
\(356\) 2.03257 0.107726
\(357\) 68.7773 3.64008
\(358\) −9.19618 −0.486033
\(359\) −32.9008 −1.73644 −0.868218 0.496183i \(-0.834734\pi\)
−0.868218 + 0.496183i \(0.834734\pi\)
\(360\) −4.00695 −0.211185
\(361\) 21.6506 1.13951
\(362\) 17.9710 0.944536
\(363\) −27.1954 −1.42739
\(364\) 13.0593 0.684495
\(365\) 14.5486 0.761510
\(366\) 27.6657 1.44611
\(367\) −8.81948 −0.460373 −0.230187 0.973146i \(-0.573934\pi\)
−0.230187 + 0.973146i \(0.573934\pi\)
\(368\) 2.73733 0.142693
\(369\) 19.5210 1.01622
\(370\) 5.73194 0.297989
\(371\) −43.1532 −2.24040
\(372\) 6.65527 0.345060
\(373\) −28.0095 −1.45028 −0.725139 0.688603i \(-0.758224\pi\)
−0.725139 + 0.688603i \(0.758224\pi\)
\(374\) 31.8500 1.64693
\(375\) 25.9807 1.34164
\(376\) −12.9408 −0.667370
\(377\) 4.91123 0.252941
\(378\) 3.03634 0.156172
\(379\) 9.41084 0.483403 0.241701 0.970351i \(-0.422295\pi\)
0.241701 + 0.970351i \(0.422295\pi\)
\(380\) −7.73949 −0.397028
\(381\) 16.9406 0.867891
\(382\) −24.2424 −1.24035
\(383\) 23.1857 1.18473 0.592367 0.805668i \(-0.298193\pi\)
0.592367 + 0.805668i \(0.298193\pi\)
\(384\) 2.51016 0.128096
\(385\) 22.8006 1.16203
\(386\) −8.80361 −0.448092
\(387\) 25.4860 1.29553
\(388\) −8.73748 −0.443578
\(389\) 10.2703 0.520726 0.260363 0.965511i \(-0.416158\pi\)
0.260363 + 0.965511i \(0.416158\pi\)
\(390\) 9.89923 0.501267
\(391\) −18.6582 −0.943584
\(392\) −9.15850 −0.462574
\(393\) 38.7021 1.95226
\(394\) −22.5605 −1.13658
\(395\) −0.995729 −0.0501006
\(396\) 15.4242 0.775095
\(397\) 22.5607 1.13229 0.566145 0.824306i \(-0.308434\pi\)
0.566145 + 0.824306i \(0.308434\pi\)
\(398\) 12.7595 0.639574
\(399\) 64.3333 3.22069
\(400\) −3.52647 −0.176324
\(401\) −0.914761 −0.0456810 −0.0228405 0.999739i \(-0.507271\pi\)
−0.0228405 + 0.999739i \(0.507271\pi\)
\(402\) −15.0381 −0.750032
\(403\) −8.61359 −0.429074
\(404\) 4.95801 0.246670
\(405\) −9.71924 −0.482953
\(406\) −6.07673 −0.301583
\(407\) −22.0643 −1.09369
\(408\) −17.1098 −0.847060
\(409\) 3.49032 0.172585 0.0862927 0.996270i \(-0.472498\pi\)
0.0862927 + 0.996270i \(0.472498\pi\)
\(410\) −7.17871 −0.354531
\(411\) 11.0277 0.543957
\(412\) 6.96802 0.343290
\(413\) 9.99075 0.491613
\(414\) −9.03569 −0.444080
\(415\) 8.19455 0.402255
\(416\) −3.24878 −0.159285
\(417\) 48.2312 2.36189
\(418\) 29.7921 1.45718
\(419\) −10.2557 −0.501023 −0.250512 0.968114i \(-0.580599\pi\)
−0.250512 + 0.968114i \(0.580599\pi\)
\(420\) −12.2485 −0.597664
\(421\) 7.17374 0.349627 0.174813 0.984602i \(-0.444068\pi\)
0.174813 + 0.984602i \(0.444068\pi\)
\(422\) 21.9026 1.06620
\(423\) 42.7165 2.07695
\(424\) 10.7353 0.521351
\(425\) 24.0371 1.16597
\(426\) −17.4599 −0.845937
\(427\) 44.3037 2.14401
\(428\) −7.43212 −0.359245
\(429\) −38.1057 −1.83976
\(430\) −9.37231 −0.451973
\(431\) −25.5762 −1.23196 −0.615982 0.787760i \(-0.711241\pi\)
−0.615982 + 0.787760i \(0.711241\pi\)
\(432\) −0.755352 −0.0363419
\(433\) 14.5028 0.696958 0.348479 0.937317i \(-0.386698\pi\)
0.348479 + 0.937317i \(0.386698\pi\)
\(434\) 10.6577 0.511587
\(435\) −4.60628 −0.220854
\(436\) 13.7246 0.657289
\(437\) −17.4526 −0.834871
\(438\) 30.0846 1.43750
\(439\) −20.7583 −0.990739 −0.495370 0.868682i \(-0.664967\pi\)
−0.495370 + 0.868682i \(0.664967\pi\)
\(440\) −5.67214 −0.270409
\(441\) 30.2315 1.43959
\(442\) 22.1443 1.05330
\(443\) −24.5702 −1.16736 −0.583682 0.811982i \(-0.698388\pi\)
−0.583682 + 0.811982i \(0.698388\pi\)
\(444\) 11.8529 0.562513
\(445\) 2.46731 0.116962
\(446\) 16.3532 0.774348
\(447\) −33.1678 −1.56878
\(448\) 4.01976 0.189916
\(449\) −37.6451 −1.77658 −0.888292 0.459279i \(-0.848108\pi\)
−0.888292 + 0.459279i \(0.848108\pi\)
\(450\) 11.6406 0.548743
\(451\) 27.6334 1.30121
\(452\) 10.6786 0.502277
\(453\) −53.6061 −2.51863
\(454\) −12.4998 −0.586644
\(455\) 15.8526 0.743180
\(456\) −16.0043 −0.749468
\(457\) 7.18013 0.335872 0.167936 0.985798i \(-0.446290\pi\)
0.167936 + 0.985798i \(0.446290\pi\)
\(458\) −18.2669 −0.853557
\(459\) 5.14863 0.240317
\(460\) 3.32281 0.154927
\(461\) −30.2705 −1.40984 −0.704918 0.709288i \(-0.749016\pi\)
−0.704918 + 0.709288i \(0.749016\pi\)
\(462\) 47.1487 2.19356
\(463\) −28.2538 −1.31307 −0.656533 0.754297i \(-0.727978\pi\)
−0.656533 + 0.754297i \(0.727978\pi\)
\(464\) 1.51171 0.0701795
\(465\) 8.07876 0.374644
\(466\) −11.4372 −0.529820
\(467\) −8.30473 −0.384297 −0.192148 0.981366i \(-0.561546\pi\)
−0.192148 + 0.981366i \(0.561546\pi\)
\(468\) 10.7240 0.495715
\(469\) −24.0820 −1.11200
\(470\) −15.7087 −0.724587
\(471\) −45.4262 −2.09313
\(472\) −2.48541 −0.114400
\(473\) 36.0774 1.65884
\(474\) −2.05904 −0.0945747
\(475\) 22.4840 1.03164
\(476\) −27.3995 −1.25585
\(477\) −35.4362 −1.62251
\(478\) 9.03889 0.413429
\(479\) −22.1687 −1.01291 −0.506456 0.862266i \(-0.669045\pi\)
−0.506456 + 0.862266i \(0.669045\pi\)
\(480\) 3.04706 0.139079
\(481\) −15.3406 −0.699472
\(482\) 13.9464 0.635242
\(483\) −27.6203 −1.25677
\(484\) 10.8341 0.492459
\(485\) −10.6063 −0.481609
\(486\) −22.3642 −1.01446
\(487\) −28.0909 −1.27292 −0.636460 0.771309i \(-0.719602\pi\)
−0.636460 + 0.771309i \(0.719602\pi\)
\(488\) −11.0215 −0.498918
\(489\) −38.8973 −1.75900
\(490\) −11.1174 −0.502233
\(491\) 12.7026 0.573258 0.286629 0.958042i \(-0.407465\pi\)
0.286629 + 0.958042i \(0.407465\pi\)
\(492\) −14.8446 −0.669247
\(493\) −10.3041 −0.464075
\(494\) 20.7135 0.931945
\(495\) 18.7233 0.841548
\(496\) −2.65133 −0.119048
\(497\) −27.9603 −1.25419
\(498\) 16.9452 0.759335
\(499\) 41.7976 1.87112 0.935560 0.353168i \(-0.114896\pi\)
0.935560 + 0.353168i \(0.114896\pi\)
\(500\) −10.3502 −0.462875
\(501\) −28.2953 −1.26414
\(502\) 13.1105 0.585149
\(503\) 28.8523 1.28646 0.643231 0.765672i \(-0.277593\pi\)
0.643231 + 0.765672i \(0.277593\pi\)
\(504\) −13.2689 −0.591044
\(505\) 6.01848 0.267819
\(506\) −12.7907 −0.568616
\(507\) 6.13841 0.272616
\(508\) −6.74879 −0.299429
\(509\) 39.8489 1.76627 0.883135 0.469118i \(-0.155428\pi\)
0.883135 + 0.469118i \(0.155428\pi\)
\(510\) −20.7694 −0.919683
\(511\) 48.1774 2.13124
\(512\) −1.00000 −0.0441942
\(513\) 4.81596 0.212630
\(514\) −17.8690 −0.788167
\(515\) 8.45840 0.372722
\(516\) −19.3807 −0.853188
\(517\) 60.4684 2.65940
\(518\) 18.9812 0.833985
\(519\) −2.78915 −0.122430
\(520\) −3.94366 −0.172941
\(521\) −22.2964 −0.976822 −0.488411 0.872614i \(-0.662423\pi\)
−0.488411 + 0.872614i \(0.662423\pi\)
\(522\) −4.99004 −0.218408
\(523\) −14.8565 −0.649629 −0.324815 0.945778i \(-0.605302\pi\)
−0.324815 + 0.945778i \(0.605302\pi\)
\(524\) −15.4181 −0.673545
\(525\) 35.5830 1.55297
\(526\) 5.81471 0.253534
\(527\) 18.0720 0.787229
\(528\) −11.7292 −0.510449
\(529\) −15.5070 −0.674219
\(530\) 13.0314 0.566049
\(531\) 8.20412 0.356029
\(532\) −25.6291 −1.11116
\(533\) 19.2127 0.832193
\(534\) 5.10207 0.220788
\(535\) −9.02177 −0.390045
\(536\) 5.99089 0.258767
\(537\) −23.0839 −0.996144
\(538\) −24.5522 −1.05852
\(539\) 42.7949 1.84331
\(540\) −0.916913 −0.0394577
\(541\) 22.9543 0.986882 0.493441 0.869779i \(-0.335739\pi\)
0.493441 + 0.869779i \(0.335739\pi\)
\(542\) −13.9621 −0.599723
\(543\) 45.1102 1.93586
\(544\) 6.81620 0.292242
\(545\) 16.6601 0.713642
\(546\) 32.7810 1.40290
\(547\) −5.38432 −0.230217 −0.115109 0.993353i \(-0.536722\pi\)
−0.115109 + 0.993353i \(0.536722\pi\)
\(548\) −4.39322 −0.187669
\(549\) 36.3809 1.55270
\(550\) 16.4781 0.702630
\(551\) −9.63836 −0.410608
\(552\) 6.87114 0.292455
\(553\) −3.29733 −0.140217
\(554\) 6.71887 0.285458
\(555\) 14.3881 0.610741
\(556\) −19.2144 −0.814872
\(557\) 2.39840 0.101623 0.0508117 0.998708i \(-0.483819\pi\)
0.0508117 + 0.998708i \(0.483819\pi\)
\(558\) 8.75182 0.370494
\(559\) 25.0835 1.06092
\(560\) 4.87955 0.206199
\(561\) 79.9488 3.37544
\(562\) 5.63094 0.237527
\(563\) 45.7260 1.92712 0.963560 0.267492i \(-0.0861950\pi\)
0.963560 + 0.267492i \(0.0861950\pi\)
\(564\) −32.4835 −1.36780
\(565\) 12.9626 0.545340
\(566\) 15.3746 0.646242
\(567\) −32.1850 −1.35164
\(568\) 6.95570 0.291855
\(569\) 0.792583 0.0332268 0.0166134 0.999862i \(-0.494712\pi\)
0.0166134 + 0.999862i \(0.494712\pi\)
\(570\) −19.4274 −0.813724
\(571\) 12.8133 0.536218 0.268109 0.963389i \(-0.413601\pi\)
0.268109 + 0.963389i \(0.413601\pi\)
\(572\) 15.1806 0.634731
\(573\) −60.8524 −2.54215
\(574\) −23.7721 −0.992229
\(575\) −9.65311 −0.402562
\(576\) 3.30092 0.137538
\(577\) 1.21451 0.0505607 0.0252804 0.999680i \(-0.491952\pi\)
0.0252804 + 0.999680i \(0.491952\pi\)
\(578\) −29.4606 −1.22540
\(579\) −22.0985 −0.918382
\(580\) 1.83505 0.0761964
\(581\) 27.1360 1.12579
\(582\) −21.9325 −0.909131
\(583\) −50.1627 −2.07752
\(584\) −11.9851 −0.495948
\(585\) 13.0177 0.538215
\(586\) 5.87022 0.242497
\(587\) −1.74261 −0.0719251 −0.0359625 0.999353i \(-0.511450\pi\)
−0.0359625 + 0.999353i \(0.511450\pi\)
\(588\) −22.9893 −0.948064
\(589\) 16.9043 0.696530
\(590\) −3.01701 −0.124208
\(591\) −56.6305 −2.32947
\(592\) −4.72196 −0.194071
\(593\) 34.7229 1.42590 0.712949 0.701216i \(-0.247359\pi\)
0.712949 + 0.701216i \(0.247359\pi\)
\(594\) 3.52953 0.144818
\(595\) −33.2600 −1.36353
\(596\) 13.2134 0.541243
\(597\) 32.0283 1.31083
\(598\) −8.89297 −0.363661
\(599\) 3.51978 0.143814 0.0719071 0.997411i \(-0.477091\pi\)
0.0719071 + 0.997411i \(0.477091\pi\)
\(600\) −8.85202 −0.361382
\(601\) 5.77629 0.235620 0.117810 0.993036i \(-0.462413\pi\)
0.117810 + 0.993036i \(0.462413\pi\)
\(602\) −31.0362 −1.26494
\(603\) −19.7754 −0.805318
\(604\) 21.3556 0.868948
\(605\) 13.1514 0.534680
\(606\) 12.4454 0.505561
\(607\) 12.3287 0.500407 0.250203 0.968193i \(-0.419503\pi\)
0.250203 + 0.968193i \(0.419503\pi\)
\(608\) 6.37578 0.258572
\(609\) −15.2536 −0.618107
\(610\) −13.3788 −0.541693
\(611\) 42.0418 1.70083
\(612\) −22.4997 −0.909497
\(613\) −0.349047 −0.0140979 −0.00704894 0.999975i \(-0.502244\pi\)
−0.00704894 + 0.999975i \(0.502244\pi\)
\(614\) 12.0524 0.486396
\(615\) −18.0197 −0.726626
\(616\) −18.7831 −0.756794
\(617\) 39.1621 1.57661 0.788303 0.615288i \(-0.210960\pi\)
0.788303 + 0.615288i \(0.210960\pi\)
\(618\) 17.4909 0.703586
\(619\) −41.8362 −1.68154 −0.840769 0.541394i \(-0.817897\pi\)
−0.840769 + 0.541394i \(0.817897\pi\)
\(620\) −3.21842 −0.129255
\(621\) −2.06764 −0.0829717
\(622\) −29.3871 −1.17832
\(623\) 8.17044 0.327342
\(624\) −8.15497 −0.326460
\(625\) 5.06838 0.202735
\(626\) 1.93762 0.0774427
\(627\) 74.7830 2.98655
\(628\) 18.0969 0.722145
\(629\) 32.1858 1.28333
\(630\) −16.1070 −0.641718
\(631\) −28.8787 −1.14964 −0.574821 0.818280i \(-0.694928\pi\)
−0.574821 + 0.818280i \(0.694928\pi\)
\(632\) 0.820280 0.0326290
\(633\) 54.9792 2.18523
\(634\) −14.8682 −0.590491
\(635\) −8.19229 −0.325101
\(636\) 26.9473 1.06853
\(637\) 29.7540 1.17889
\(638\) −7.06378 −0.279658
\(639\) −22.9602 −0.908291
\(640\) −1.21389 −0.0479832
\(641\) −1.86176 −0.0735351 −0.0367675 0.999324i \(-0.511706\pi\)
−0.0367675 + 0.999324i \(0.511706\pi\)
\(642\) −18.6558 −0.736287
\(643\) 25.2592 0.996127 0.498064 0.867140i \(-0.334045\pi\)
0.498064 + 0.867140i \(0.334045\pi\)
\(644\) 11.0034 0.433595
\(645\) −23.5260 −0.926336
\(646\) −43.4586 −1.70986
\(647\) −7.39753 −0.290827 −0.145413 0.989371i \(-0.546451\pi\)
−0.145413 + 0.989371i \(0.546451\pi\)
\(648\) 8.00670 0.314533
\(649\) 11.6136 0.455872
\(650\) 11.4567 0.449370
\(651\) 26.7526 1.04852
\(652\) 15.4959 0.606867
\(653\) −27.1383 −1.06200 −0.531002 0.847370i \(-0.678184\pi\)
−0.531002 + 0.847370i \(0.678184\pi\)
\(654\) 34.4510 1.34714
\(655\) −18.7159 −0.731291
\(656\) 5.91381 0.230895
\(657\) 39.5619 1.54346
\(658\) −52.0189 −2.02791
\(659\) 2.22998 0.0868679 0.0434339 0.999056i \(-0.486170\pi\)
0.0434339 + 0.999056i \(0.486170\pi\)
\(660\) −14.2380 −0.554213
\(661\) −3.14096 −0.122169 −0.0610846 0.998133i \(-0.519456\pi\)
−0.0610846 + 0.998133i \(0.519456\pi\)
\(662\) −5.44635 −0.211678
\(663\) 55.5859 2.15878
\(664\) −6.75066 −0.261976
\(665\) −31.1109 −1.20643
\(666\) 15.5868 0.603976
\(667\) 4.13805 0.160226
\(668\) 11.2723 0.436139
\(669\) 41.0493 1.58706
\(670\) 7.27227 0.280952
\(671\) 51.5000 1.98813
\(672\) 10.0903 0.389240
\(673\) 31.9422 1.23128 0.615640 0.788027i \(-0.288897\pi\)
0.615640 + 0.788027i \(0.288897\pi\)
\(674\) 23.5626 0.907597
\(675\) 2.66373 0.102527
\(676\) −2.44542 −0.0940548
\(677\) 38.5252 1.48064 0.740322 0.672253i \(-0.234673\pi\)
0.740322 + 0.672253i \(0.234673\pi\)
\(678\) 26.8049 1.02944
\(679\) −35.1226 −1.34788
\(680\) 8.27411 0.317298
\(681\) −31.3765 −1.20235
\(682\) 12.3889 0.474394
\(683\) 33.7516 1.29147 0.645734 0.763563i \(-0.276552\pi\)
0.645734 + 0.763563i \(0.276552\pi\)
\(684\) −21.0459 −0.804711
\(685\) −5.33289 −0.203759
\(686\) −8.67666 −0.331276
\(687\) −45.8529 −1.74940
\(688\) 7.72089 0.294356
\(689\) −34.8765 −1.32869
\(690\) 8.34080 0.317529
\(691\) 27.7046 1.05393 0.526965 0.849887i \(-0.323330\pi\)
0.526965 + 0.849887i \(0.323330\pi\)
\(692\) 1.11114 0.0422393
\(693\) 62.0016 2.35525
\(694\) −26.3506 −1.00025
\(695\) −23.3241 −0.884735
\(696\) 3.79465 0.143836
\(697\) −40.3097 −1.52684
\(698\) 0.161549 0.00611472
\(699\) −28.7093 −1.08589
\(700\) −14.1756 −0.535787
\(701\) 8.97566 0.339006 0.169503 0.985530i \(-0.445784\pi\)
0.169503 + 0.985530i \(0.445784\pi\)
\(702\) 2.45397 0.0926192
\(703\) 30.1062 1.13548
\(704\) 4.67270 0.176109
\(705\) −39.4313 −1.48507
\(706\) −21.0100 −0.790721
\(707\) 19.9300 0.749547
\(708\) −6.23878 −0.234468
\(709\) −11.0200 −0.413866 −0.206933 0.978355i \(-0.566348\pi\)
−0.206933 + 0.978355i \(0.566348\pi\)
\(710\) 8.44345 0.316877
\(711\) −2.70768 −0.101546
\(712\) −2.03257 −0.0761736
\(713\) −7.25756 −0.271798
\(714\) −68.7773 −2.57392
\(715\) 18.4275 0.689150
\(716\) 9.19618 0.343677
\(717\) 22.6891 0.847340
\(718\) 32.9008 1.22785
\(719\) −1.19184 −0.0444480 −0.0222240 0.999753i \(-0.507075\pi\)
−0.0222240 + 0.999753i \(0.507075\pi\)
\(720\) 4.00695 0.149330
\(721\) 28.0098 1.04314
\(722\) −21.6506 −0.805752
\(723\) 35.0078 1.30195
\(724\) −17.9710 −0.667888
\(725\) −5.33102 −0.197989
\(726\) 27.1954 1.00931
\(727\) 15.5597 0.577079 0.288539 0.957468i \(-0.406830\pi\)
0.288539 + 0.957468i \(0.406830\pi\)
\(728\) −13.0593 −0.484011
\(729\) −32.1176 −1.18954
\(730\) −14.5486 −0.538469
\(731\) −52.6272 −1.94649
\(732\) −27.6657 −1.02255
\(733\) 8.18329 0.302257 0.151128 0.988514i \(-0.451709\pi\)
0.151128 + 0.988514i \(0.451709\pi\)
\(734\) 8.81948 0.325533
\(735\) −27.9065 −1.02935
\(736\) −2.73733 −0.100899
\(737\) −27.9936 −1.03116
\(738\) −19.5210 −0.718578
\(739\) 2.99978 0.110349 0.0551744 0.998477i \(-0.482429\pi\)
0.0551744 + 0.998477i \(0.482429\pi\)
\(740\) −5.73194 −0.210710
\(741\) 51.9943 1.91006
\(742\) 43.1532 1.58421
\(743\) 8.31764 0.305145 0.152572 0.988292i \(-0.451244\pi\)
0.152572 + 0.988292i \(0.451244\pi\)
\(744\) −6.65527 −0.243994
\(745\) 16.0396 0.587646
\(746\) 28.0095 1.02550
\(747\) 22.2834 0.815306
\(748\) −31.8500 −1.16455
\(749\) −29.8754 −1.09162
\(750\) −25.9807 −0.948680
\(751\) 18.7289 0.683429 0.341714 0.939804i \(-0.388992\pi\)
0.341714 + 0.939804i \(0.388992\pi\)
\(752\) 12.9408 0.471902
\(753\) 32.9094 1.19928
\(754\) −4.91123 −0.178856
\(755\) 25.9234 0.943447
\(756\) −3.03634 −0.110430
\(757\) 42.9718 1.56183 0.780917 0.624634i \(-0.214752\pi\)
0.780917 + 0.624634i \(0.214752\pi\)
\(758\) −9.41084 −0.341817
\(759\) −32.1067 −1.16540
\(760\) 7.73949 0.280741
\(761\) 8.40161 0.304558 0.152279 0.988338i \(-0.451339\pi\)
0.152279 + 0.988338i \(0.451339\pi\)
\(762\) −16.9406 −0.613692
\(763\) 55.1696 1.99728
\(764\) 24.2424 0.877060
\(765\) −27.3122 −0.987473
\(766\) −23.1857 −0.837734
\(767\) 8.07454 0.291555
\(768\) −2.51016 −0.0905777
\(769\) −19.8721 −0.716608 −0.358304 0.933605i \(-0.616645\pi\)
−0.358304 + 0.933605i \(0.616645\pi\)
\(770\) −22.8006 −0.821678
\(771\) −44.8540 −1.61538
\(772\) 8.80361 0.316849
\(773\) −25.9813 −0.934482 −0.467241 0.884130i \(-0.654752\pi\)
−0.467241 + 0.884130i \(0.654752\pi\)
\(774\) −25.4860 −0.916076
\(775\) 9.34985 0.335856
\(776\) 8.73748 0.313657
\(777\) 47.6458 1.70928
\(778\) −10.2703 −0.368209
\(779\) −37.7052 −1.35093
\(780\) −9.89923 −0.354449
\(781\) −32.5019 −1.16301
\(782\) 18.6582 0.667215
\(783\) −1.14188 −0.0408073
\(784\) 9.15850 0.327089
\(785\) 21.9676 0.784059
\(786\) −38.7021 −1.38046
\(787\) −6.96333 −0.248216 −0.124108 0.992269i \(-0.539607\pi\)
−0.124108 + 0.992269i \(0.539607\pi\)
\(788\) 22.5605 0.803684
\(789\) 14.5959 0.519627
\(790\) 0.995729 0.0354264
\(791\) 42.9253 1.52625
\(792\) −15.4242 −0.548075
\(793\) 35.8063 1.27152
\(794\) −22.5607 −0.800650
\(795\) 32.7110 1.16014
\(796\) −12.7595 −0.452247
\(797\) 41.5681 1.47242 0.736209 0.676754i \(-0.236614\pi\)
0.736209 + 0.676754i \(0.236614\pi\)
\(798\) −64.3333 −2.27737
\(799\) −88.2070 −3.12054
\(800\) 3.52647 0.124680
\(801\) 6.70933 0.237063
\(802\) 0.914761 0.0323013
\(803\) 56.0029 1.97630
\(804\) 15.0381 0.530353
\(805\) 13.3569 0.470769
\(806\) 8.61359 0.303401
\(807\) −61.6300 −2.16948
\(808\) −4.95801 −0.174422
\(809\) 13.0635 0.459289 0.229644 0.973275i \(-0.426244\pi\)
0.229644 + 0.973275i \(0.426244\pi\)
\(810\) 9.71924 0.341499
\(811\) 14.6307 0.513752 0.256876 0.966444i \(-0.417307\pi\)
0.256876 + 0.966444i \(0.417307\pi\)
\(812\) 6.07673 0.213251
\(813\) −35.0471 −1.22916
\(814\) 22.0643 0.773353
\(815\) 18.8103 0.658897
\(816\) 17.1098 0.598962
\(817\) −49.2267 −1.72223
\(818\) −3.49032 −0.122036
\(819\) 43.1078 1.50631
\(820\) 7.17871 0.250691
\(821\) −47.8079 −1.66851 −0.834254 0.551381i \(-0.814101\pi\)
−0.834254 + 0.551381i \(0.814101\pi\)
\(822\) −11.0277 −0.384635
\(823\) 0.993723 0.0346390 0.0173195 0.999850i \(-0.494487\pi\)
0.0173195 + 0.999850i \(0.494487\pi\)
\(824\) −6.96802 −0.242742
\(825\) 41.3628 1.44007
\(826\) −9.99075 −0.347623
\(827\) 20.9711 0.729238 0.364619 0.931157i \(-0.381199\pi\)
0.364619 + 0.931157i \(0.381199\pi\)
\(828\) 9.03569 0.314012
\(829\) 42.3902 1.47227 0.736136 0.676834i \(-0.236648\pi\)
0.736136 + 0.676834i \(0.236648\pi\)
\(830\) −8.19455 −0.284437
\(831\) 16.8655 0.585057
\(832\) 3.24878 0.112631
\(833\) −62.4262 −2.16294
\(834\) −48.2312 −1.67011
\(835\) 13.6833 0.473531
\(836\) −29.7921 −1.03038
\(837\) 2.00269 0.0692230
\(838\) 10.2557 0.354277
\(839\) 5.84310 0.201726 0.100863 0.994900i \(-0.467840\pi\)
0.100863 + 0.994900i \(0.467840\pi\)
\(840\) 12.2485 0.422612
\(841\) −26.7147 −0.921197
\(842\) −7.17374 −0.247223
\(843\) 14.1346 0.486820
\(844\) −21.9026 −0.753920
\(845\) −2.96847 −0.102119
\(846\) −42.7165 −1.46862
\(847\) 43.5505 1.49641
\(848\) −10.7353 −0.368651
\(849\) 38.5927 1.32450
\(850\) −24.0371 −0.824467
\(851\) −12.9256 −0.443082
\(852\) 17.4599 0.598168
\(853\) 13.5369 0.463495 0.231748 0.972776i \(-0.425556\pi\)
0.231748 + 0.972776i \(0.425556\pi\)
\(854\) −44.3037 −1.51604
\(855\) −25.5474 −0.873704
\(856\) 7.43212 0.254025
\(857\) 0.00897015 0.000306414 0 0.000153207 1.00000i \(-0.499951\pi\)
0.000153207 1.00000i \(0.499951\pi\)
\(858\) 38.1057 1.30091
\(859\) −53.3826 −1.82139 −0.910695 0.413080i \(-0.864453\pi\)
−0.910695 + 0.413080i \(0.864453\pi\)
\(860\) 9.37231 0.319593
\(861\) −59.6719 −2.03361
\(862\) 25.5762 0.871130
\(863\) 33.9617 1.15607 0.578034 0.816013i \(-0.303820\pi\)
0.578034 + 0.816013i \(0.303820\pi\)
\(864\) 0.755352 0.0256976
\(865\) 1.34881 0.0458607
\(866\) −14.5028 −0.492824
\(867\) −73.9509 −2.51150
\(868\) −10.6577 −0.361747
\(869\) −3.83292 −0.130023
\(870\) 4.60628 0.156168
\(871\) −19.4631 −0.659481
\(872\) −13.7246 −0.464774
\(873\) −28.8417 −0.976144
\(874\) 17.4526 0.590343
\(875\) −41.6053 −1.40652
\(876\) −30.0846 −1.01647
\(877\) −44.9270 −1.51708 −0.758538 0.651629i \(-0.774086\pi\)
−0.758538 + 0.651629i \(0.774086\pi\)
\(878\) 20.7583 0.700559
\(879\) 14.7352 0.497006
\(880\) 5.67214 0.191208
\(881\) 26.1150 0.879835 0.439918 0.898038i \(-0.355008\pi\)
0.439918 + 0.898038i \(0.355008\pi\)
\(882\) −30.2315 −1.01795
\(883\) −0.528881 −0.0177983 −0.00889913 0.999960i \(-0.502833\pi\)
−0.00889913 + 0.999960i \(0.502833\pi\)
\(884\) −22.1443 −0.744795
\(885\) −7.57318 −0.254570
\(886\) 24.5702 0.825451
\(887\) −22.5205 −0.756165 −0.378083 0.925772i \(-0.623416\pi\)
−0.378083 + 0.925772i \(0.623416\pi\)
\(888\) −11.8529 −0.397757
\(889\) −27.1285 −0.909862
\(890\) −2.46731 −0.0827044
\(891\) −37.4129 −1.25338
\(892\) −16.3532 −0.547547
\(893\) −82.5076 −2.76101
\(894\) 33.1678 1.10930
\(895\) 11.1631 0.373143
\(896\) −4.01976 −0.134291
\(897\) −22.3228 −0.745337
\(898\) 37.6451 1.25623
\(899\) −4.00805 −0.133676
\(900\) −11.6406 −0.388020
\(901\) 73.1737 2.43777
\(902\) −27.6334 −0.920093
\(903\) −77.9058 −2.59254
\(904\) −10.6786 −0.355164
\(905\) −21.8148 −0.725149
\(906\) 53.6061 1.78094
\(907\) 9.43735 0.313362 0.156681 0.987649i \(-0.449921\pi\)
0.156681 + 0.987649i \(0.449921\pi\)
\(908\) 12.4998 0.414820
\(909\) 16.3660 0.542826
\(910\) −15.8526 −0.525508
\(911\) 27.0224 0.895291 0.447646 0.894211i \(-0.352263\pi\)
0.447646 + 0.894211i \(0.352263\pi\)
\(912\) 16.0043 0.529954
\(913\) 31.5438 1.04395
\(914\) −7.18013 −0.237497
\(915\) −33.5831 −1.11022
\(916\) 18.2669 0.603556
\(917\) −61.9773 −2.04667
\(918\) −5.14863 −0.169930
\(919\) −49.0794 −1.61898 −0.809491 0.587133i \(-0.800257\pi\)
−0.809491 + 0.587133i \(0.800257\pi\)
\(920\) −3.32281 −0.109550
\(921\) 30.2535 0.996887
\(922\) 30.2705 0.996905
\(923\) −22.5975 −0.743807
\(924\) −47.1487 −1.55108
\(925\) 16.6519 0.547510
\(926\) 28.2538 0.928478
\(927\) 23.0009 0.755447
\(928\) −1.51171 −0.0496244
\(929\) 51.3861 1.68592 0.842962 0.537974i \(-0.180810\pi\)
0.842962 + 0.537974i \(0.180810\pi\)
\(930\) −8.07876 −0.264913
\(931\) −58.3926 −1.91374
\(932\) 11.4372 0.374639
\(933\) −73.7665 −2.41501
\(934\) 8.30473 0.271739
\(935\) −38.6624 −1.26440
\(936\) −10.7240 −0.350523
\(937\) 37.4451 1.22328 0.611639 0.791137i \(-0.290511\pi\)
0.611639 + 0.791137i \(0.290511\pi\)
\(938\) 24.0820 0.786304
\(939\) 4.86373 0.158722
\(940\) 15.7087 0.512361
\(941\) −6.20414 −0.202249 −0.101125 0.994874i \(-0.532244\pi\)
−0.101125 + 0.994874i \(0.532244\pi\)
\(942\) 45.4262 1.48006
\(943\) 16.1880 0.527155
\(944\) 2.48541 0.0808931
\(945\) −3.68578 −0.119898
\(946\) −36.0774 −1.17298
\(947\) −19.2298 −0.624885 −0.312442 0.949937i \(-0.601147\pi\)
−0.312442 + 0.949937i \(0.601147\pi\)
\(948\) 2.05904 0.0668744
\(949\) 38.9371 1.26395
\(950\) −22.4840 −0.729478
\(951\) −37.3216 −1.21023
\(952\) 27.3995 0.888023
\(953\) −13.7065 −0.443997 −0.221998 0.975047i \(-0.571258\pi\)
−0.221998 + 0.975047i \(0.571258\pi\)
\(954\) 35.4362 1.14729
\(955\) 29.4276 0.952256
\(956\) −9.03889 −0.292339
\(957\) −17.7312 −0.573170
\(958\) 22.1687 0.716238
\(959\) −17.6597 −0.570262
\(960\) −3.04706 −0.0983434
\(961\) −23.9704 −0.773240
\(962\) 15.3406 0.494601
\(963\) −24.5328 −0.790559
\(964\) −13.9464 −0.449184
\(965\) 10.6866 0.344014
\(966\) 27.6203 0.888670
\(967\) −15.8001 −0.508098 −0.254049 0.967191i \(-0.581762\pi\)
−0.254049 + 0.967191i \(0.581762\pi\)
\(968\) −10.8341 −0.348221
\(969\) −109.088 −3.50442
\(970\) 10.6063 0.340549
\(971\) 51.7045 1.65928 0.829638 0.558302i \(-0.188547\pi\)
0.829638 + 0.558302i \(0.188547\pi\)
\(972\) 22.3642 0.717331
\(973\) −77.2373 −2.47611
\(974\) 28.0909 0.900091
\(975\) 28.7583 0.921002
\(976\) 11.0215 0.352789
\(977\) −58.0074 −1.85582 −0.927911 0.372802i \(-0.878397\pi\)
−0.927911 + 0.372802i \(0.878397\pi\)
\(978\) 38.8973 1.24380
\(979\) 9.49757 0.303544
\(980\) 11.1174 0.355132
\(981\) 45.3038 1.44644
\(982\) −12.7026 −0.405355
\(983\) −15.8172 −0.504490 −0.252245 0.967663i \(-0.581169\pi\)
−0.252245 + 0.967663i \(0.581169\pi\)
\(984\) 14.8446 0.473229
\(985\) 27.3859 0.872589
\(986\) 10.3041 0.328151
\(987\) −130.576 −4.15628
\(988\) −20.7135 −0.658985
\(989\) 21.1346 0.672041
\(990\) −18.7233 −0.595064
\(991\) 18.7579 0.595865 0.297932 0.954587i \(-0.403703\pi\)
0.297932 + 0.954587i \(0.403703\pi\)
\(992\) 2.65133 0.0841798
\(993\) −13.6712 −0.433843
\(994\) 27.9603 0.886846
\(995\) −15.4886 −0.491021
\(996\) −16.9452 −0.536931
\(997\) −13.3493 −0.422777 −0.211389 0.977402i \(-0.567799\pi\)
−0.211389 + 0.977402i \(0.567799\pi\)
\(998\) −41.7976 −1.32308
\(999\) 3.56674 0.112847
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 6022.2.a.c.1.9 61
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6022.2.a.c.1.9 61 1.1 even 1 trivial