Properties

Label 4010.2.a.o.1.9
Level $4010$
Weight $2$
Character 4010.1
Self dual yes
Analytic conductor $32.020$
Analytic rank $0$
Dimension $22$
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] = [4010,2,Mod(1,4010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4010, 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("4010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4010.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: \(32.0200112105\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 4010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.18460 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.18460 q^{6} +4.68706 q^{7} +1.00000 q^{8} -1.59673 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.18460 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.18460 q^{6} +4.68706 q^{7} +1.00000 q^{8} -1.59673 q^{9} -1.00000 q^{10} +1.20462 q^{11} -1.18460 q^{12} +5.57551 q^{13} +4.68706 q^{14} +1.18460 q^{15} +1.00000 q^{16} +5.07141 q^{17} -1.59673 q^{18} +7.66277 q^{19} -1.00000 q^{20} -5.55227 q^{21} +1.20462 q^{22} -6.33980 q^{23} -1.18460 q^{24} +1.00000 q^{25} +5.57551 q^{26} +5.44527 q^{27} +4.68706 q^{28} -0.292065 q^{29} +1.18460 q^{30} -8.91920 q^{31} +1.00000 q^{32} -1.42699 q^{33} +5.07141 q^{34} -4.68706 q^{35} -1.59673 q^{36} -4.02531 q^{37} +7.66277 q^{38} -6.60473 q^{39} -1.00000 q^{40} -4.54836 q^{41} -5.55227 q^{42} +3.79335 q^{43} +1.20462 q^{44} +1.59673 q^{45} -6.33980 q^{46} -6.89121 q^{47} -1.18460 q^{48} +14.9685 q^{49} +1.00000 q^{50} -6.00757 q^{51} +5.57551 q^{52} -2.85791 q^{53} +5.44527 q^{54} -1.20462 q^{55} +4.68706 q^{56} -9.07728 q^{57} -0.292065 q^{58} +12.5998 q^{59} +1.18460 q^{60} +8.87868 q^{61} -8.91920 q^{62} -7.48398 q^{63} +1.00000 q^{64} -5.57551 q^{65} -1.42699 q^{66} -12.8489 q^{67} +5.07141 q^{68} +7.51010 q^{69} -4.68706 q^{70} +5.98862 q^{71} -1.59673 q^{72} -16.0837 q^{73} -4.02531 q^{74} -1.18460 q^{75} +7.66277 q^{76} +5.64614 q^{77} -6.60473 q^{78} +14.3384 q^{79} -1.00000 q^{80} -1.66024 q^{81} -4.54836 q^{82} +1.14337 q^{83} -5.55227 q^{84} -5.07141 q^{85} +3.79335 q^{86} +0.345979 q^{87} +1.20462 q^{88} -13.0424 q^{89} +1.59673 q^{90} +26.1327 q^{91} -6.33980 q^{92} +10.5656 q^{93} -6.89121 q^{94} -7.66277 q^{95} -1.18460 q^{96} +16.9850 q^{97} +14.9685 q^{98} -1.92346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.18460 −0.683927 −0.341963 0.939713i \(-0.611092\pi\)
−0.341963 + 0.939713i \(0.611092\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.18460 −0.483609
\(7\) 4.68706 1.77154 0.885770 0.464124i \(-0.153631\pi\)
0.885770 + 0.464124i \(0.153631\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.59673 −0.532244
\(10\) −1.00000 −0.316228
\(11\) 1.20462 0.363208 0.181604 0.983372i \(-0.441871\pi\)
0.181604 + 0.983372i \(0.441871\pi\)
\(12\) −1.18460 −0.341963
\(13\) 5.57551 1.54637 0.773185 0.634181i \(-0.218663\pi\)
0.773185 + 0.634181i \(0.218663\pi\)
\(14\) 4.68706 1.25267
\(15\) 1.18460 0.305861
\(16\) 1.00000 0.250000
\(17\) 5.07141 1.23000 0.614998 0.788528i \(-0.289157\pi\)
0.614998 + 0.788528i \(0.289157\pi\)
\(18\) −1.59673 −0.376354
\(19\) 7.66277 1.75796 0.878980 0.476859i \(-0.158225\pi\)
0.878980 + 0.476859i \(0.158225\pi\)
\(20\) −1.00000 −0.223607
\(21\) −5.55227 −1.21160
\(22\) 1.20462 0.256827
\(23\) −6.33980 −1.32194 −0.660970 0.750412i \(-0.729855\pi\)
−0.660970 + 0.750412i \(0.729855\pi\)
\(24\) −1.18460 −0.241805
\(25\) 1.00000 0.200000
\(26\) 5.57551 1.09345
\(27\) 5.44527 1.04794
\(28\) 4.68706 0.885770
\(29\) −0.292065 −0.0542351 −0.0271176 0.999632i \(-0.508633\pi\)
−0.0271176 + 0.999632i \(0.508633\pi\)
\(30\) 1.18460 0.216277
\(31\) −8.91920 −1.60194 −0.800968 0.598708i \(-0.795681\pi\)
−0.800968 + 0.598708i \(0.795681\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.42699 −0.248407
\(34\) 5.07141 0.869739
\(35\) −4.68706 −0.792257
\(36\) −1.59673 −0.266122
\(37\) −4.02531 −0.661757 −0.330879 0.943673i \(-0.607345\pi\)
−0.330879 + 0.943673i \(0.607345\pi\)
\(38\) 7.66277 1.24306
\(39\) −6.60473 −1.05760
\(40\) −1.00000 −0.158114
\(41\) −4.54836 −0.710335 −0.355168 0.934803i \(-0.615576\pi\)
−0.355168 + 0.934803i \(0.615576\pi\)
\(42\) −5.55227 −0.856733
\(43\) 3.79335 0.578480 0.289240 0.957257i \(-0.406597\pi\)
0.289240 + 0.957257i \(0.406597\pi\)
\(44\) 1.20462 0.181604
\(45\) 1.59673 0.238027
\(46\) −6.33980 −0.934753
\(47\) −6.89121 −1.00519 −0.502593 0.864523i \(-0.667621\pi\)
−0.502593 + 0.864523i \(0.667621\pi\)
\(48\) −1.18460 −0.170982
\(49\) 14.9685 2.13836
\(50\) 1.00000 0.141421
\(51\) −6.00757 −0.841228
\(52\) 5.57551 0.773185
\(53\) −2.85791 −0.392565 −0.196282 0.980547i \(-0.562887\pi\)
−0.196282 + 0.980547i \(0.562887\pi\)
\(54\) 5.44527 0.741007
\(55\) −1.20462 −0.162431
\(56\) 4.68706 0.626334
\(57\) −9.07728 −1.20232
\(58\) −0.292065 −0.0383500
\(59\) 12.5998 1.64035 0.820175 0.572113i \(-0.193876\pi\)
0.820175 + 0.572113i \(0.193876\pi\)
\(60\) 1.18460 0.152931
\(61\) 8.87868 1.13680 0.568400 0.822753i \(-0.307563\pi\)
0.568400 + 0.822753i \(0.307563\pi\)
\(62\) −8.91920 −1.13274
\(63\) −7.48398 −0.942893
\(64\) 1.00000 0.125000
\(65\) −5.57551 −0.691557
\(66\) −1.42699 −0.175651
\(67\) −12.8489 −1.56974 −0.784872 0.619658i \(-0.787271\pi\)
−0.784872 + 0.619658i \(0.787271\pi\)
\(68\) 5.07141 0.614998
\(69\) 7.51010 0.904110
\(70\) −4.68706 −0.560210
\(71\) 5.98862 0.710719 0.355359 0.934730i \(-0.384358\pi\)
0.355359 + 0.934730i \(0.384358\pi\)
\(72\) −1.59673 −0.188177
\(73\) −16.0837 −1.88245 −0.941225 0.337780i \(-0.890324\pi\)
−0.941225 + 0.337780i \(0.890324\pi\)
\(74\) −4.02531 −0.467933
\(75\) −1.18460 −0.136785
\(76\) 7.66277 0.878980
\(77\) 5.64614 0.643438
\(78\) −6.60473 −0.747838
\(79\) 14.3384 1.61320 0.806598 0.591100i \(-0.201306\pi\)
0.806598 + 0.591100i \(0.201306\pi\)
\(80\) −1.00000 −0.111803
\(81\) −1.66024 −0.184471
\(82\) −4.54836 −0.502283
\(83\) 1.14337 0.125501 0.0627505 0.998029i \(-0.480013\pi\)
0.0627505 + 0.998029i \(0.480013\pi\)
\(84\) −5.55227 −0.605802
\(85\) −5.07141 −0.550071
\(86\) 3.79335 0.409047
\(87\) 0.345979 0.0370928
\(88\) 1.20462 0.128413
\(89\) −13.0424 −1.38250 −0.691248 0.722618i \(-0.742939\pi\)
−0.691248 + 0.722618i \(0.742939\pi\)
\(90\) 1.59673 0.168310
\(91\) 26.1327 2.73946
\(92\) −6.33980 −0.660970
\(93\) 10.5656 1.09561
\(94\) −6.89121 −0.710774
\(95\) −7.66277 −0.786183
\(96\) −1.18460 −0.120902
\(97\) 16.9850 1.72456 0.862281 0.506430i \(-0.169035\pi\)
0.862281 + 0.506430i \(0.169035\pi\)
\(98\) 14.9685 1.51205
\(99\) −1.92346 −0.193315
\(100\) 1.00000 0.100000
\(101\) 8.26350 0.822249 0.411124 0.911579i \(-0.365136\pi\)
0.411124 + 0.911579i \(0.365136\pi\)
\(102\) −6.00757 −0.594838
\(103\) 3.12024 0.307447 0.153723 0.988114i \(-0.450874\pi\)
0.153723 + 0.988114i \(0.450874\pi\)
\(104\) 5.57551 0.546724
\(105\) 5.55227 0.541846
\(106\) −2.85791 −0.277585
\(107\) −10.8774 −1.05155 −0.525777 0.850623i \(-0.676225\pi\)
−0.525777 + 0.850623i \(0.676225\pi\)
\(108\) 5.44527 0.523971
\(109\) −2.49420 −0.238901 −0.119450 0.992840i \(-0.538113\pi\)
−0.119450 + 0.992840i \(0.538113\pi\)
\(110\) −1.20462 −0.114856
\(111\) 4.76837 0.452593
\(112\) 4.68706 0.442885
\(113\) 2.93612 0.276207 0.138103 0.990418i \(-0.455899\pi\)
0.138103 + 0.990418i \(0.455899\pi\)
\(114\) −9.07728 −0.850165
\(115\) 6.33980 0.591189
\(116\) −0.292065 −0.0271176
\(117\) −8.90261 −0.823046
\(118\) 12.5998 1.15990
\(119\) 23.7700 2.17899
\(120\) 1.18460 0.108138
\(121\) −9.54888 −0.868080
\(122\) 8.87868 0.803838
\(123\) 5.38797 0.485817
\(124\) −8.91920 −0.800968
\(125\) −1.00000 −0.0894427
\(126\) −7.48398 −0.666726
\(127\) 3.65155 0.324023 0.162011 0.986789i \(-0.448202\pi\)
0.162011 + 0.986789i \(0.448202\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.49358 −0.395638
\(130\) −5.57551 −0.489005
\(131\) 15.9192 1.39087 0.695435 0.718589i \(-0.255212\pi\)
0.695435 + 0.718589i \(0.255212\pi\)
\(132\) −1.42699 −0.124204
\(133\) 35.9158 3.11430
\(134\) −12.8489 −1.10998
\(135\) −5.44527 −0.468654
\(136\) 5.07141 0.434870
\(137\) 1.83255 0.156565 0.0782827 0.996931i \(-0.475056\pi\)
0.0782827 + 0.996931i \(0.475056\pi\)
\(138\) 7.51010 0.639302
\(139\) −1.09285 −0.0926946 −0.0463473 0.998925i \(-0.514758\pi\)
−0.0463473 + 0.998925i \(0.514758\pi\)
\(140\) −4.68706 −0.396129
\(141\) 8.16330 0.687474
\(142\) 5.98862 0.502554
\(143\) 6.71640 0.561653
\(144\) −1.59673 −0.133061
\(145\) 0.292065 0.0242547
\(146\) −16.0837 −1.33109
\(147\) −17.7316 −1.46248
\(148\) −4.02531 −0.330879
\(149\) −12.2217 −1.00124 −0.500621 0.865667i \(-0.666895\pi\)
−0.500621 + 0.865667i \(0.666895\pi\)
\(150\) −1.18460 −0.0967218
\(151\) 3.85740 0.313911 0.156955 0.987606i \(-0.449832\pi\)
0.156955 + 0.987606i \(0.449832\pi\)
\(152\) 7.66277 0.621532
\(153\) −8.09769 −0.654659
\(154\) 5.64614 0.454979
\(155\) 8.91920 0.716407
\(156\) −6.60473 −0.528801
\(157\) 23.1416 1.84690 0.923449 0.383721i \(-0.125357\pi\)
0.923449 + 0.383721i \(0.125357\pi\)
\(158\) 14.3384 1.14070
\(159\) 3.38547 0.268485
\(160\) −1.00000 −0.0790569
\(161\) −29.7150 −2.34187
\(162\) −1.66024 −0.130441
\(163\) 11.2345 0.879952 0.439976 0.898010i \(-0.354987\pi\)
0.439976 + 0.898010i \(0.354987\pi\)
\(164\) −4.54836 −0.355168
\(165\) 1.42699 0.111091
\(166\) 1.14337 0.0887427
\(167\) 17.0849 1.32207 0.661036 0.750354i \(-0.270117\pi\)
0.661036 + 0.750354i \(0.270117\pi\)
\(168\) −5.55227 −0.428367
\(169\) 18.0863 1.39126
\(170\) −5.07141 −0.388959
\(171\) −12.2354 −0.935664
\(172\) 3.79335 0.289240
\(173\) 10.9413 0.831851 0.415925 0.909399i \(-0.363458\pi\)
0.415925 + 0.909399i \(0.363458\pi\)
\(174\) 0.345979 0.0262286
\(175\) 4.68706 0.354308
\(176\) 1.20462 0.0908020
\(177\) −14.9256 −1.12188
\(178\) −13.0424 −0.977572
\(179\) −17.3319 −1.29545 −0.647724 0.761875i \(-0.724279\pi\)
−0.647724 + 0.761875i \(0.724279\pi\)
\(180\) 1.59673 0.119013
\(181\) −23.4315 −1.74165 −0.870823 0.491597i \(-0.836413\pi\)
−0.870823 + 0.491597i \(0.836413\pi\)
\(182\) 26.1327 1.93709
\(183\) −10.5176 −0.777487
\(184\) −6.33980 −0.467376
\(185\) 4.02531 0.295947
\(186\) 10.5656 0.774710
\(187\) 6.10914 0.446745
\(188\) −6.89121 −0.502593
\(189\) 25.5223 1.85647
\(190\) −7.66277 −0.555916
\(191\) −1.46888 −0.106285 −0.0531423 0.998587i \(-0.516924\pi\)
−0.0531423 + 0.998587i \(0.516924\pi\)
\(192\) −1.18460 −0.0854908
\(193\) −5.91331 −0.425649 −0.212825 0.977090i \(-0.568266\pi\)
−0.212825 + 0.977090i \(0.568266\pi\)
\(194\) 16.9850 1.21945
\(195\) 6.60473 0.472974
\(196\) 14.9685 1.06918
\(197\) −18.2523 −1.30042 −0.650211 0.759754i \(-0.725319\pi\)
−0.650211 + 0.759754i \(0.725319\pi\)
\(198\) −1.92346 −0.136695
\(199\) 18.6917 1.32502 0.662511 0.749053i \(-0.269491\pi\)
0.662511 + 0.749053i \(0.269491\pi\)
\(200\) 1.00000 0.0707107
\(201\) 15.2208 1.07359
\(202\) 8.26350 0.581418
\(203\) −1.36893 −0.0960797
\(204\) −6.00757 −0.420614
\(205\) 4.54836 0.317672
\(206\) 3.12024 0.217398
\(207\) 10.1230 0.703595
\(208\) 5.57551 0.386592
\(209\) 9.23075 0.638505
\(210\) 5.55227 0.383143
\(211\) −0.232000 −0.0159715 −0.00798577 0.999968i \(-0.502542\pi\)
−0.00798577 + 0.999968i \(0.502542\pi\)
\(212\) −2.85791 −0.196282
\(213\) −7.09410 −0.486080
\(214\) −10.8774 −0.743561
\(215\) −3.79335 −0.258704
\(216\) 5.44527 0.370504
\(217\) −41.8048 −2.83789
\(218\) −2.49420 −0.168928
\(219\) 19.0526 1.28746
\(220\) −1.20462 −0.0812157
\(221\) 28.2757 1.90203
\(222\) 4.76837 0.320032
\(223\) 21.6531 1.45000 0.724999 0.688750i \(-0.241840\pi\)
0.724999 + 0.688750i \(0.241840\pi\)
\(224\) 4.68706 0.313167
\(225\) −1.59673 −0.106449
\(226\) 2.93612 0.195308
\(227\) −16.5630 −1.09933 −0.549663 0.835387i \(-0.685244\pi\)
−0.549663 + 0.835387i \(0.685244\pi\)
\(228\) −9.07728 −0.601158
\(229\) −9.48459 −0.626760 −0.313380 0.949628i \(-0.601461\pi\)
−0.313380 + 0.949628i \(0.601461\pi\)
\(230\) 6.33980 0.418034
\(231\) −6.68839 −0.440064
\(232\) −0.292065 −0.0191750
\(233\) 22.7987 1.49359 0.746796 0.665053i \(-0.231591\pi\)
0.746796 + 0.665053i \(0.231591\pi\)
\(234\) −8.90261 −0.581982
\(235\) 6.89121 0.449533
\(236\) 12.5998 0.820175
\(237\) −16.9852 −1.10331
\(238\) 23.7700 1.54078
\(239\) −5.11597 −0.330925 −0.165462 0.986216i \(-0.552912\pi\)
−0.165462 + 0.986216i \(0.552912\pi\)
\(240\) 1.18460 0.0764653
\(241\) −19.7206 −1.27032 −0.635158 0.772382i \(-0.719065\pi\)
−0.635158 + 0.772382i \(0.719065\pi\)
\(242\) −9.54888 −0.613825
\(243\) −14.3691 −0.921778
\(244\) 8.87868 0.568400
\(245\) −14.9685 −0.956302
\(246\) 5.38797 0.343525
\(247\) 42.7239 2.71845
\(248\) −8.91920 −0.566370
\(249\) −1.35443 −0.0858335
\(250\) −1.00000 −0.0632456
\(251\) −9.93945 −0.627372 −0.313686 0.949527i \(-0.601564\pi\)
−0.313686 + 0.949527i \(0.601564\pi\)
\(252\) −7.48398 −0.471446
\(253\) −7.63708 −0.480139
\(254\) 3.65155 0.229119
\(255\) 6.00757 0.376208
\(256\) 1.00000 0.0625000
\(257\) 3.61811 0.225691 0.112846 0.993613i \(-0.464003\pi\)
0.112846 + 0.993613i \(0.464003\pi\)
\(258\) −4.49358 −0.279758
\(259\) −18.8669 −1.17233
\(260\) −5.57551 −0.345779
\(261\) 0.466350 0.0288663
\(262\) 15.9192 0.983494
\(263\) −26.6289 −1.64201 −0.821003 0.570924i \(-0.806585\pi\)
−0.821003 + 0.570924i \(0.806585\pi\)
\(264\) −1.42699 −0.0878253
\(265\) 2.85791 0.175560
\(266\) 35.9158 2.20214
\(267\) 15.4500 0.945525
\(268\) −12.8489 −0.784872
\(269\) −18.7041 −1.14041 −0.570204 0.821503i \(-0.693136\pi\)
−0.570204 + 0.821503i \(0.693136\pi\)
\(270\) −5.44527 −0.331389
\(271\) −26.8851 −1.63316 −0.816578 0.577235i \(-0.804132\pi\)
−0.816578 + 0.577235i \(0.804132\pi\)
\(272\) 5.07141 0.307499
\(273\) −30.9567 −1.87359
\(274\) 1.83255 0.110708
\(275\) 1.20462 0.0726416
\(276\) 7.51010 0.452055
\(277\) 2.71702 0.163250 0.0816248 0.996663i \(-0.473989\pi\)
0.0816248 + 0.996663i \(0.473989\pi\)
\(278\) −1.09285 −0.0655450
\(279\) 14.2416 0.852621
\(280\) −4.68706 −0.280105
\(281\) 25.7351 1.53523 0.767614 0.640912i \(-0.221444\pi\)
0.767614 + 0.640912i \(0.221444\pi\)
\(282\) 8.16330 0.486118
\(283\) −9.30846 −0.553330 −0.276665 0.960966i \(-0.589229\pi\)
−0.276665 + 0.960966i \(0.589229\pi\)
\(284\) 5.98862 0.355359
\(285\) 9.07728 0.537692
\(286\) 6.71640 0.397149
\(287\) −21.3184 −1.25839
\(288\) −1.59673 −0.0940884
\(289\) 8.71917 0.512893
\(290\) 0.292065 0.0171506
\(291\) −20.1203 −1.17947
\(292\) −16.0837 −0.941225
\(293\) 17.9029 1.04590 0.522948 0.852365i \(-0.324832\pi\)
0.522948 + 0.852365i \(0.324832\pi\)
\(294\) −17.7316 −1.03413
\(295\) −12.5998 −0.733587
\(296\) −4.02531 −0.233966
\(297\) 6.55950 0.380621
\(298\) −12.2217 −0.707985
\(299\) −35.3476 −2.04421
\(300\) −1.18460 −0.0683927
\(301\) 17.7796 1.02480
\(302\) 3.85740 0.221968
\(303\) −9.78890 −0.562358
\(304\) 7.66277 0.439490
\(305\) −8.87868 −0.508392
\(306\) −8.09769 −0.462914
\(307\) −3.00095 −0.171273 −0.0856366 0.996326i \(-0.527292\pi\)
−0.0856366 + 0.996326i \(0.527292\pi\)
\(308\) 5.64614 0.321719
\(309\) −3.69623 −0.210271
\(310\) 8.91920 0.506576
\(311\) −21.9134 −1.24260 −0.621298 0.783575i \(-0.713394\pi\)
−0.621298 + 0.783575i \(0.713394\pi\)
\(312\) −6.60473 −0.373919
\(313\) 29.3208 1.65731 0.828655 0.559759i \(-0.189106\pi\)
0.828655 + 0.559759i \(0.189106\pi\)
\(314\) 23.1416 1.30595
\(315\) 7.48398 0.421674
\(316\) 14.3384 0.806598
\(317\) −14.9234 −0.838182 −0.419091 0.907944i \(-0.637651\pi\)
−0.419091 + 0.907944i \(0.637651\pi\)
\(318\) 3.38547 0.189848
\(319\) −0.351829 −0.0196986
\(320\) −1.00000 −0.0559017
\(321\) 12.8853 0.719185
\(322\) −29.7150 −1.65595
\(323\) 38.8610 2.16228
\(324\) −1.66024 −0.0922357
\(325\) 5.57551 0.309274
\(326\) 11.2345 0.622220
\(327\) 2.95462 0.163391
\(328\) −4.54836 −0.251141
\(329\) −32.2995 −1.78073
\(330\) 1.42699 0.0785533
\(331\) −15.9878 −0.878769 −0.439385 0.898299i \(-0.644803\pi\)
−0.439385 + 0.898299i \(0.644803\pi\)
\(332\) 1.14337 0.0627505
\(333\) 6.42735 0.352217
\(334\) 17.0849 0.934846
\(335\) 12.8489 0.702011
\(336\) −5.55227 −0.302901
\(337\) −3.70069 −0.201590 −0.100795 0.994907i \(-0.532139\pi\)
−0.100795 + 0.994907i \(0.532139\pi\)
\(338\) 18.0863 0.983768
\(339\) −3.47811 −0.188905
\(340\) −5.07141 −0.275036
\(341\) −10.7443 −0.581835
\(342\) −12.2354 −0.661614
\(343\) 37.3488 2.01665
\(344\) 3.79335 0.204524
\(345\) −7.51010 −0.404330
\(346\) 10.9413 0.588207
\(347\) −33.9042 −1.82007 −0.910036 0.414529i \(-0.863946\pi\)
−0.910036 + 0.414529i \(0.863946\pi\)
\(348\) 0.345979 0.0185464
\(349\) 6.93106 0.371011 0.185506 0.982643i \(-0.440608\pi\)
0.185506 + 0.982643i \(0.440608\pi\)
\(350\) 4.68706 0.250534
\(351\) 30.3602 1.62051
\(352\) 1.20462 0.0642067
\(353\) 15.2625 0.812340 0.406170 0.913798i \(-0.366864\pi\)
0.406170 + 0.913798i \(0.366864\pi\)
\(354\) −14.9256 −0.793288
\(355\) −5.98862 −0.317843
\(356\) −13.0424 −0.691248
\(357\) −28.1578 −1.49027
\(358\) −17.3319 −0.916020
\(359\) 30.4397 1.60655 0.803274 0.595610i \(-0.203090\pi\)
0.803274 + 0.595610i \(0.203090\pi\)
\(360\) 1.59673 0.0841552
\(361\) 39.7180 2.09042
\(362\) −23.4315 −1.23153
\(363\) 11.3116 0.593703
\(364\) 26.1327 1.36973
\(365\) 16.0837 0.841857
\(366\) −10.5176 −0.549766
\(367\) −5.26652 −0.274910 −0.137455 0.990508i \(-0.543892\pi\)
−0.137455 + 0.990508i \(0.543892\pi\)
\(368\) −6.33980 −0.330485
\(369\) 7.26253 0.378072
\(370\) 4.02531 0.209266
\(371\) −13.3952 −0.695445
\(372\) 10.5656 0.547803
\(373\) 26.4681 1.37047 0.685233 0.728324i \(-0.259700\pi\)
0.685233 + 0.728324i \(0.259700\pi\)
\(374\) 6.10914 0.315896
\(375\) 1.18460 0.0611723
\(376\) −6.89121 −0.355387
\(377\) −1.62841 −0.0838675
\(378\) 25.5223 1.31272
\(379\) 22.3660 1.14886 0.574432 0.818552i \(-0.305223\pi\)
0.574432 + 0.818552i \(0.305223\pi\)
\(380\) −7.66277 −0.393092
\(381\) −4.32561 −0.221608
\(382\) −1.46888 −0.0751545
\(383\) 14.5128 0.741571 0.370786 0.928718i \(-0.379088\pi\)
0.370786 + 0.928718i \(0.379088\pi\)
\(384\) −1.18460 −0.0604511
\(385\) −5.64614 −0.287754
\(386\) −5.91331 −0.300979
\(387\) −6.05697 −0.307893
\(388\) 16.9850 0.862281
\(389\) 7.81183 0.396076 0.198038 0.980194i \(-0.436543\pi\)
0.198038 + 0.980194i \(0.436543\pi\)
\(390\) 6.60473 0.334443
\(391\) −32.1517 −1.62598
\(392\) 14.9685 0.756023
\(393\) −18.8579 −0.951253
\(394\) −18.2523 −0.919537
\(395\) −14.3384 −0.721443
\(396\) −1.92346 −0.0966577
\(397\) 0.904128 0.0453769 0.0226884 0.999743i \(-0.492777\pi\)
0.0226884 + 0.999743i \(0.492777\pi\)
\(398\) 18.6917 0.936931
\(399\) −42.5457 −2.12995
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 15.2208 0.759142
\(403\) −49.7291 −2.47718
\(404\) 8.26350 0.411124
\(405\) 1.66024 0.0824981
\(406\) −1.36893 −0.0679386
\(407\) −4.84899 −0.240355
\(408\) −6.00757 −0.297419
\(409\) 17.0960 0.845344 0.422672 0.906283i \(-0.361092\pi\)
0.422672 + 0.906283i \(0.361092\pi\)
\(410\) 4.54836 0.224628
\(411\) −2.17083 −0.107079
\(412\) 3.12024 0.153723
\(413\) 59.0558 2.90595
\(414\) 10.1230 0.497517
\(415\) −1.14337 −0.0561258
\(416\) 5.57551 0.273362
\(417\) 1.29459 0.0633963
\(418\) 9.23075 0.451491
\(419\) 24.7515 1.20919 0.604595 0.796533i \(-0.293335\pi\)
0.604595 + 0.796533i \(0.293335\pi\)
\(420\) 5.55227 0.270923
\(421\) 13.3166 0.649011 0.324506 0.945884i \(-0.394802\pi\)
0.324506 + 0.945884i \(0.394802\pi\)
\(422\) −0.232000 −0.0112936
\(423\) 11.0034 0.535005
\(424\) −2.85791 −0.138793
\(425\) 5.07141 0.245999
\(426\) −7.09410 −0.343710
\(427\) 41.6149 2.01389
\(428\) −10.8774 −0.525777
\(429\) −7.95621 −0.384130
\(430\) −3.79335 −0.182932
\(431\) 12.8500 0.618963 0.309482 0.950905i \(-0.399844\pi\)
0.309482 + 0.950905i \(0.399844\pi\)
\(432\) 5.44527 0.261986
\(433\) 18.4111 0.884780 0.442390 0.896823i \(-0.354131\pi\)
0.442390 + 0.896823i \(0.354131\pi\)
\(434\) −41.8048 −2.00669
\(435\) −0.345979 −0.0165884
\(436\) −2.49420 −0.119450
\(437\) −48.5804 −2.32392
\(438\) 19.0526 0.910370
\(439\) −16.7436 −0.799126 −0.399563 0.916706i \(-0.630838\pi\)
−0.399563 + 0.916706i \(0.630838\pi\)
\(440\) −1.20462 −0.0574282
\(441\) −23.9007 −1.13813
\(442\) 28.2757 1.34494
\(443\) −1.70027 −0.0807823 −0.0403912 0.999184i \(-0.512860\pi\)
−0.0403912 + 0.999184i \(0.512860\pi\)
\(444\) 4.76837 0.226297
\(445\) 13.0424 0.618271
\(446\) 21.6531 1.02530
\(447\) 14.4778 0.684776
\(448\) 4.68706 0.221443
\(449\) −33.7537 −1.59293 −0.796467 0.604682i \(-0.793300\pi\)
−0.796467 + 0.604682i \(0.793300\pi\)
\(450\) −1.59673 −0.0752707
\(451\) −5.47907 −0.257999
\(452\) 2.93612 0.138103
\(453\) −4.56946 −0.214692
\(454\) −16.5630 −0.777341
\(455\) −26.1327 −1.22512
\(456\) −9.07728 −0.425083
\(457\) 20.4483 0.956533 0.478266 0.878215i \(-0.341265\pi\)
0.478266 + 0.878215i \(0.341265\pi\)
\(458\) −9.48459 −0.443186
\(459\) 27.6152 1.28897
\(460\) 6.33980 0.295595
\(461\) 1.18525 0.0552025 0.0276013 0.999619i \(-0.491213\pi\)
0.0276013 + 0.999619i \(0.491213\pi\)
\(462\) −6.68839 −0.311172
\(463\) −10.3889 −0.482814 −0.241407 0.970424i \(-0.577609\pi\)
−0.241407 + 0.970424i \(0.577609\pi\)
\(464\) −0.292065 −0.0135588
\(465\) −10.5656 −0.489970
\(466\) 22.7987 1.05613
\(467\) −13.1057 −0.606459 −0.303230 0.952918i \(-0.598065\pi\)
−0.303230 + 0.952918i \(0.598065\pi\)
\(468\) −8.90261 −0.411523
\(469\) −60.2235 −2.78086
\(470\) 6.89121 0.317868
\(471\) −27.4134 −1.26314
\(472\) 12.5998 0.579951
\(473\) 4.56956 0.210109
\(474\) −16.9852 −0.780156
\(475\) 7.66277 0.351592
\(476\) 23.7700 1.08949
\(477\) 4.56333 0.208940
\(478\) −5.11597 −0.233999
\(479\) −8.41221 −0.384363 −0.192182 0.981359i \(-0.561556\pi\)
−0.192182 + 0.981359i \(0.561556\pi\)
\(480\) 1.18460 0.0540691
\(481\) −22.4432 −1.02332
\(482\) −19.7206 −0.898249
\(483\) 35.2003 1.60167
\(484\) −9.54888 −0.434040
\(485\) −16.9850 −0.771248
\(486\) −14.3691 −0.651795
\(487\) 27.3511 1.23940 0.619698 0.784840i \(-0.287255\pi\)
0.619698 + 0.784840i \(0.287255\pi\)
\(488\) 8.87868 0.401919
\(489\) −13.3083 −0.601822
\(490\) −14.9685 −0.676208
\(491\) −12.8040 −0.577835 −0.288918 0.957354i \(-0.593295\pi\)
−0.288918 + 0.957354i \(0.593295\pi\)
\(492\) 5.38797 0.242909
\(493\) −1.48118 −0.0667090
\(494\) 42.7239 1.92224
\(495\) 1.92346 0.0864533
\(496\) −8.91920 −0.400484
\(497\) 28.0690 1.25907
\(498\) −1.35443 −0.0606935
\(499\) −30.6213 −1.37080 −0.685398 0.728168i \(-0.740372\pi\)
−0.685398 + 0.728168i \(0.740372\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −20.2387 −0.904200
\(502\) −9.93945 −0.443619
\(503\) 0.215284 0.00959906 0.00479953 0.999988i \(-0.498472\pi\)
0.00479953 + 0.999988i \(0.498472\pi\)
\(504\) −7.48398 −0.333363
\(505\) −8.26350 −0.367721
\(506\) −7.63708 −0.339509
\(507\) −21.4250 −0.951518
\(508\) 3.65155 0.162011
\(509\) −10.4650 −0.463853 −0.231926 0.972733i \(-0.574503\pi\)
−0.231926 + 0.972733i \(0.574503\pi\)
\(510\) 6.00757 0.266020
\(511\) −75.3850 −3.33484
\(512\) 1.00000 0.0441942
\(513\) 41.7258 1.84224
\(514\) 3.61811 0.159588
\(515\) −3.12024 −0.137494
\(516\) −4.49358 −0.197819
\(517\) −8.30132 −0.365092
\(518\) −18.8669 −0.828962
\(519\) −12.9610 −0.568925
\(520\) −5.57551 −0.244502
\(521\) −25.7634 −1.12871 −0.564357 0.825531i \(-0.690876\pi\)
−0.564357 + 0.825531i \(0.690876\pi\)
\(522\) 0.466350 0.0204116
\(523\) −10.5026 −0.459245 −0.229622 0.973280i \(-0.573749\pi\)
−0.229622 + 0.973280i \(0.573749\pi\)
\(524\) 15.9192 0.695435
\(525\) −5.55227 −0.242321
\(526\) −26.6289 −1.16107
\(527\) −45.2329 −1.97038
\(528\) −1.42699 −0.0621019
\(529\) 17.1931 0.747525
\(530\) 2.85791 0.124140
\(531\) −20.1185 −0.873067
\(532\) 35.9158 1.55715
\(533\) −25.3595 −1.09844
\(534\) 15.4500 0.668587
\(535\) 10.8774 0.470269
\(536\) −12.8489 −0.554988
\(537\) 20.5313 0.885991
\(538\) −18.7041 −0.806390
\(539\) 18.0314 0.776668
\(540\) −5.44527 −0.234327
\(541\) 6.91127 0.297139 0.148569 0.988902i \(-0.452533\pi\)
0.148569 + 0.988902i \(0.452533\pi\)
\(542\) −26.8851 −1.15482
\(543\) 27.7568 1.19116
\(544\) 5.07141 0.217435
\(545\) 2.49420 0.106840
\(546\) −30.9567 −1.32483
\(547\) −29.1689 −1.24717 −0.623587 0.781754i \(-0.714325\pi\)
−0.623587 + 0.781754i \(0.714325\pi\)
\(548\) 1.83255 0.0782827
\(549\) −14.1769 −0.605055
\(550\) 1.20462 0.0513653
\(551\) −2.23803 −0.0953431
\(552\) 7.51010 0.319651
\(553\) 67.2049 2.85784
\(554\) 2.71702 0.115435
\(555\) −4.76837 −0.202406
\(556\) −1.09285 −0.0463473
\(557\) 34.2643 1.45182 0.725912 0.687788i \(-0.241418\pi\)
0.725912 + 0.687788i \(0.241418\pi\)
\(558\) 14.2416 0.602894
\(559\) 21.1499 0.894544
\(560\) −4.68706 −0.198064
\(561\) −7.23686 −0.305540
\(562\) 25.7351 1.08557
\(563\) −29.8364 −1.25745 −0.628727 0.777626i \(-0.716424\pi\)
−0.628727 + 0.777626i \(0.716424\pi\)
\(564\) 8.16330 0.343737
\(565\) −2.93612 −0.123523
\(566\) −9.30846 −0.391264
\(567\) −7.78165 −0.326799
\(568\) 5.98862 0.251277
\(569\) 6.27332 0.262991 0.131496 0.991317i \(-0.458022\pi\)
0.131496 + 0.991317i \(0.458022\pi\)
\(570\) 9.07728 0.380205
\(571\) −2.18579 −0.0914723 −0.0457362 0.998954i \(-0.514563\pi\)
−0.0457362 + 0.998954i \(0.514563\pi\)
\(572\) 6.71640 0.280827
\(573\) 1.74003 0.0726908
\(574\) −21.3184 −0.889815
\(575\) −6.33980 −0.264388
\(576\) −1.59673 −0.0665306
\(577\) −46.4721 −1.93466 −0.967330 0.253519i \(-0.918412\pi\)
−0.967330 + 0.253519i \(0.918412\pi\)
\(578\) 8.71917 0.362670
\(579\) 7.00488 0.291113
\(580\) 0.292065 0.0121273
\(581\) 5.35904 0.222330
\(582\) −20.1203 −0.834014
\(583\) −3.44271 −0.142583
\(584\) −16.0837 −0.665547
\(585\) 8.90261 0.368078
\(586\) 17.9029 0.739560
\(587\) −4.77144 −0.196939 −0.0984693 0.995140i \(-0.531395\pi\)
−0.0984693 + 0.995140i \(0.531395\pi\)
\(588\) −17.7316 −0.731240
\(589\) −68.3457 −2.81614
\(590\) −12.5998 −0.518724
\(591\) 21.6216 0.889393
\(592\) −4.02531 −0.165439
\(593\) −37.2715 −1.53056 −0.765278 0.643700i \(-0.777398\pi\)
−0.765278 + 0.643700i \(0.777398\pi\)
\(594\) 6.55950 0.269140
\(595\) −23.7700 −0.974474
\(596\) −12.2217 −0.500621
\(597\) −22.1421 −0.906217
\(598\) −35.3476 −1.44547
\(599\) 13.3274 0.544544 0.272272 0.962220i \(-0.412225\pi\)
0.272272 + 0.962220i \(0.412225\pi\)
\(600\) −1.18460 −0.0483609
\(601\) 4.28792 0.174908 0.0874540 0.996169i \(-0.472127\pi\)
0.0874540 + 0.996169i \(0.472127\pi\)
\(602\) 17.7796 0.724644
\(603\) 20.5163 0.835487
\(604\) 3.85740 0.156955
\(605\) 9.54888 0.388217
\(606\) −9.78890 −0.397647
\(607\) −14.5854 −0.592003 −0.296001 0.955188i \(-0.595653\pi\)
−0.296001 + 0.955188i \(0.595653\pi\)
\(608\) 7.66277 0.310766
\(609\) 1.62162 0.0657115
\(610\) −8.87868 −0.359487
\(611\) −38.4221 −1.55439
\(612\) −8.09769 −0.327330
\(613\) −9.89125 −0.399504 −0.199752 0.979847i \(-0.564014\pi\)
−0.199752 + 0.979847i \(0.564014\pi\)
\(614\) −3.00095 −0.121108
\(615\) −5.38797 −0.217264
\(616\) 5.64614 0.227490
\(617\) −13.1860 −0.530846 −0.265423 0.964132i \(-0.585512\pi\)
−0.265423 + 0.964132i \(0.585512\pi\)
\(618\) −3.69623 −0.148684
\(619\) −27.7389 −1.11492 −0.557460 0.830204i \(-0.688224\pi\)
−0.557460 + 0.830204i \(0.688224\pi\)
\(620\) 8.91920 0.358204
\(621\) −34.5219 −1.38532
\(622\) −21.9134 −0.878648
\(623\) −61.1306 −2.44915
\(624\) −6.60473 −0.264401
\(625\) 1.00000 0.0400000
\(626\) 29.3208 1.17190
\(627\) −10.9347 −0.436690
\(628\) 23.1416 0.923449
\(629\) −20.4140 −0.813959
\(630\) 7.48398 0.298169
\(631\) 2.70915 0.107850 0.0539248 0.998545i \(-0.482827\pi\)
0.0539248 + 0.998545i \(0.482827\pi\)
\(632\) 14.3384 0.570351
\(633\) 0.274826 0.0109234
\(634\) −14.9234 −0.592684
\(635\) −3.65155 −0.144907
\(636\) 3.38547 0.134243
\(637\) 83.4571 3.30669
\(638\) −0.351829 −0.0139290
\(639\) −9.56224 −0.378276
\(640\) −1.00000 −0.0395285
\(641\) −2.54312 −0.100447 −0.0502237 0.998738i \(-0.515993\pi\)
−0.0502237 + 0.998738i \(0.515993\pi\)
\(642\) 12.8853 0.508541
\(643\) −24.8187 −0.978752 −0.489376 0.872073i \(-0.662775\pi\)
−0.489376 + 0.872073i \(0.662775\pi\)
\(644\) −29.7150 −1.17094
\(645\) 4.49358 0.176935
\(646\) 38.8610 1.52897
\(647\) 0.270701 0.0106423 0.00532117 0.999986i \(-0.498306\pi\)
0.00532117 + 0.999986i \(0.498306\pi\)
\(648\) −1.66024 −0.0652205
\(649\) 15.1780 0.595788
\(650\) 5.57551 0.218690
\(651\) 49.5218 1.94091
\(652\) 11.2345 0.439976
\(653\) −11.1525 −0.436429 −0.218215 0.975901i \(-0.570023\pi\)
−0.218215 + 0.975901i \(0.570023\pi\)
\(654\) 2.95462 0.115535
\(655\) −15.9192 −0.622016
\(656\) −4.54836 −0.177584
\(657\) 25.6813 1.00192
\(658\) −32.2995 −1.25917
\(659\) 16.5271 0.643805 0.321903 0.946773i \(-0.395678\pi\)
0.321903 + 0.946773i \(0.395678\pi\)
\(660\) 1.42699 0.0555456
\(661\) −2.99653 −0.116551 −0.0582757 0.998301i \(-0.518560\pi\)
−0.0582757 + 0.998301i \(0.518560\pi\)
\(662\) −15.9878 −0.621384
\(663\) −33.4953 −1.30085
\(664\) 1.14337 0.0443713
\(665\) −35.9158 −1.39276
\(666\) 6.42735 0.249055
\(667\) 1.85163 0.0716955
\(668\) 17.0849 0.661036
\(669\) −25.6502 −0.991693
\(670\) 12.8489 0.496396
\(671\) 10.6955 0.412894
\(672\) −5.55227 −0.214183
\(673\) −2.88930 −0.111374 −0.0556872 0.998448i \(-0.517735\pi\)
−0.0556872 + 0.998448i \(0.517735\pi\)
\(674\) −3.70069 −0.142545
\(675\) 5.44527 0.209589
\(676\) 18.0863 0.695629
\(677\) −7.70902 −0.296282 −0.148141 0.988966i \(-0.547329\pi\)
−0.148141 + 0.988966i \(0.547329\pi\)
\(678\) −3.47811 −0.133576
\(679\) 79.6095 3.05513
\(680\) −5.07141 −0.194480
\(681\) 19.6205 0.751858
\(682\) −10.7443 −0.411420
\(683\) 7.21850 0.276208 0.138104 0.990418i \(-0.455899\pi\)
0.138104 + 0.990418i \(0.455899\pi\)
\(684\) −12.2354 −0.467832
\(685\) −1.83255 −0.0700182
\(686\) 37.3488 1.42598
\(687\) 11.2354 0.428658
\(688\) 3.79335 0.144620
\(689\) −15.9343 −0.607050
\(690\) −7.51010 −0.285905
\(691\) 11.8567 0.451050 0.225525 0.974237i \(-0.427590\pi\)
0.225525 + 0.974237i \(0.427590\pi\)
\(692\) 10.9413 0.415925
\(693\) −9.01538 −0.342466
\(694\) −33.9042 −1.28699
\(695\) 1.09285 0.0414543
\(696\) 0.345979 0.0131143
\(697\) −23.0666 −0.873710
\(698\) 6.93106 0.262345
\(699\) −27.0072 −1.02151
\(700\) 4.68706 0.177154
\(701\) −41.8618 −1.58110 −0.790549 0.612399i \(-0.790205\pi\)
−0.790549 + 0.612399i \(0.790205\pi\)
\(702\) 30.3602 1.14587
\(703\) −30.8450 −1.16334
\(704\) 1.20462 0.0454010
\(705\) −8.16330 −0.307448
\(706\) 15.2625 0.574411
\(707\) 38.7315 1.45665
\(708\) −14.9256 −0.560939
\(709\) −3.07129 −0.115345 −0.0576724 0.998336i \(-0.518368\pi\)
−0.0576724 + 0.998336i \(0.518368\pi\)
\(710\) −5.98862 −0.224749
\(711\) −22.8946 −0.858615
\(712\) −13.0424 −0.488786
\(713\) 56.5459 2.11766
\(714\) −28.1578 −1.05378
\(715\) −6.71640 −0.251179
\(716\) −17.3319 −0.647724
\(717\) 6.06036 0.226328
\(718\) 30.4397 1.13600
\(719\) 27.6940 1.03281 0.516407 0.856343i \(-0.327269\pi\)
0.516407 + 0.856343i \(0.327269\pi\)
\(720\) 1.59673 0.0595067
\(721\) 14.6248 0.544654
\(722\) 39.7180 1.47815
\(723\) 23.3609 0.868803
\(724\) −23.4315 −0.870823
\(725\) −0.292065 −0.0108470
\(726\) 11.3116 0.419811
\(727\) −31.2593 −1.15934 −0.579671 0.814851i \(-0.696819\pi\)
−0.579671 + 0.814851i \(0.696819\pi\)
\(728\) 26.1327 0.968544
\(729\) 22.0023 0.814900
\(730\) 16.0837 0.595283
\(731\) 19.2376 0.711529
\(732\) −10.5176 −0.388744
\(733\) 16.7522 0.618757 0.309379 0.950939i \(-0.399879\pi\)
0.309379 + 0.950939i \(0.399879\pi\)
\(734\) −5.26652 −0.194391
\(735\) 17.7316 0.654041
\(736\) −6.33980 −0.233688
\(737\) −15.4781 −0.570143
\(738\) 7.26253 0.267337
\(739\) −0.974682 −0.0358542 −0.0179271 0.999839i \(-0.505707\pi\)
−0.0179271 + 0.999839i \(0.505707\pi\)
\(740\) 4.02531 0.147973
\(741\) −50.6105 −1.85922
\(742\) −13.3952 −0.491754
\(743\) −25.1796 −0.923751 −0.461876 0.886945i \(-0.652823\pi\)
−0.461876 + 0.886945i \(0.652823\pi\)
\(744\) 10.5656 0.387355
\(745\) 12.2217 0.447769
\(746\) 26.4681 0.969066
\(747\) −1.82566 −0.0667973
\(748\) 6.10914 0.223372
\(749\) −50.9828 −1.86287
\(750\) 1.18460 0.0432553
\(751\) 24.3111 0.887125 0.443563 0.896243i \(-0.353714\pi\)
0.443563 + 0.896243i \(0.353714\pi\)
\(752\) −6.89121 −0.251297
\(753\) 11.7742 0.429077
\(754\) −1.62841 −0.0593033
\(755\) −3.85740 −0.140385
\(756\) 25.5223 0.928237
\(757\) 18.8631 0.685590 0.342795 0.939410i \(-0.388626\pi\)
0.342795 + 0.939410i \(0.388626\pi\)
\(758\) 22.3660 0.812369
\(759\) 9.04685 0.328380
\(760\) −7.66277 −0.277958
\(761\) 21.2166 0.769102 0.384551 0.923104i \(-0.374356\pi\)
0.384551 + 0.923104i \(0.374356\pi\)
\(762\) −4.32561 −0.156700
\(763\) −11.6904 −0.423223
\(764\) −1.46888 −0.0531423
\(765\) 8.09769 0.292772
\(766\) 14.5128 0.524370
\(767\) 70.2502 2.53659
\(768\) −1.18460 −0.0427454
\(769\) −1.90537 −0.0687093 −0.0343546 0.999410i \(-0.510938\pi\)
−0.0343546 + 0.999410i \(0.510938\pi\)
\(770\) −5.64614 −0.203473
\(771\) −4.28600 −0.154356
\(772\) −5.91331 −0.212825
\(773\) −14.7132 −0.529197 −0.264598 0.964359i \(-0.585239\pi\)
−0.264598 + 0.964359i \(0.585239\pi\)
\(774\) −6.05697 −0.217713
\(775\) −8.91920 −0.320387
\(776\) 16.9850 0.609725
\(777\) 22.3496 0.801787
\(778\) 7.81183 0.280068
\(779\) −34.8531 −1.24874
\(780\) 6.60473 0.236487
\(781\) 7.21404 0.258139
\(782\) −32.1517 −1.14974
\(783\) −1.59037 −0.0568353
\(784\) 14.9685 0.534589
\(785\) −23.1416 −0.825958
\(786\) −18.8579 −0.672638
\(787\) −1.05492 −0.0376038 −0.0188019 0.999823i \(-0.505985\pi\)
−0.0188019 + 0.999823i \(0.505985\pi\)
\(788\) −18.2523 −0.650211
\(789\) 31.5444 1.12301
\(790\) −14.3384 −0.510137
\(791\) 13.7617 0.489311
\(792\) −1.92346 −0.0683473
\(793\) 49.5032 1.75791
\(794\) 0.904128 0.0320863
\(795\) −3.38547 −0.120070
\(796\) 18.6917 0.662511
\(797\) 35.6101 1.26137 0.630687 0.776037i \(-0.282773\pi\)
0.630687 + 0.776037i \(0.282773\pi\)
\(798\) −42.5457 −1.50610
\(799\) −34.9482 −1.23638
\(800\) 1.00000 0.0353553
\(801\) 20.8253 0.735825
\(802\) −1.00000 −0.0353112
\(803\) −19.3748 −0.683721
\(804\) 15.2208 0.536795
\(805\) 29.7150 1.04732
\(806\) −49.7291 −1.75163
\(807\) 22.1568 0.779955
\(808\) 8.26350 0.290709
\(809\) 1.01998 0.0358607 0.0179304 0.999839i \(-0.494292\pi\)
0.0179304 + 0.999839i \(0.494292\pi\)
\(810\) 1.66024 0.0583350
\(811\) 5.54965 0.194874 0.0974372 0.995242i \(-0.468935\pi\)
0.0974372 + 0.995242i \(0.468935\pi\)
\(812\) −1.36893 −0.0480399
\(813\) 31.8480 1.11696
\(814\) −4.84899 −0.169957
\(815\) −11.2345 −0.393526
\(816\) −6.00757 −0.210307
\(817\) 29.0675 1.01694
\(818\) 17.0960 0.597749
\(819\) −41.7270 −1.45806
\(820\) 4.54836 0.158836
\(821\) −37.7565 −1.31771 −0.658856 0.752269i \(-0.728959\pi\)
−0.658856 + 0.752269i \(0.728959\pi\)
\(822\) −2.17083 −0.0757164
\(823\) −40.4823 −1.41113 −0.705563 0.708647i \(-0.749306\pi\)
−0.705563 + 0.708647i \(0.749306\pi\)
\(824\) 3.12024 0.108699
\(825\) −1.42699 −0.0496815
\(826\) 59.0558 2.05481
\(827\) −15.9936 −0.556154 −0.278077 0.960559i \(-0.589697\pi\)
−0.278077 + 0.960559i \(0.589697\pi\)
\(828\) 10.1230 0.351798
\(829\) 24.8958 0.864666 0.432333 0.901714i \(-0.357690\pi\)
0.432333 + 0.901714i \(0.357690\pi\)
\(830\) −1.14337 −0.0396869
\(831\) −3.21856 −0.111651
\(832\) 5.57551 0.193296
\(833\) 75.9114 2.63017
\(834\) 1.29459 0.0448280
\(835\) −17.0849 −0.591248
\(836\) 9.23075 0.319252
\(837\) −48.5674 −1.67874
\(838\) 24.7515 0.855027
\(839\) −29.2328 −1.00923 −0.504615 0.863345i \(-0.668365\pi\)
−0.504615 + 0.863345i \(0.668365\pi\)
\(840\) 5.55227 0.191571
\(841\) −28.9147 −0.997059
\(842\) 13.3166 0.458920
\(843\) −30.4857 −1.04998
\(844\) −0.232000 −0.00798577
\(845\) −18.0863 −0.622189
\(846\) 11.0034 0.378306
\(847\) −44.7561 −1.53784
\(848\) −2.85791 −0.0981412
\(849\) 11.0268 0.378437
\(850\) 5.07141 0.173948
\(851\) 25.5197 0.874803
\(852\) −7.09410 −0.243040
\(853\) −17.8351 −0.610662 −0.305331 0.952246i \(-0.598767\pi\)
−0.305331 + 0.952246i \(0.598767\pi\)
\(854\) 41.6149 1.42403
\(855\) 12.2354 0.418442
\(856\) −10.8774 −0.371780
\(857\) −43.6215 −1.49008 −0.745042 0.667018i \(-0.767571\pi\)
−0.745042 + 0.667018i \(0.767571\pi\)
\(858\) −7.95621 −0.271621
\(859\) −18.5409 −0.632608 −0.316304 0.948658i \(-0.602442\pi\)
−0.316304 + 0.948658i \(0.602442\pi\)
\(860\) −3.79335 −0.129352
\(861\) 25.2537 0.860645
\(862\) 12.8500 0.437673
\(863\) −29.5342 −1.00535 −0.502677 0.864474i \(-0.667652\pi\)
−0.502677 + 0.864474i \(0.667652\pi\)
\(864\) 5.44527 0.185252
\(865\) −10.9413 −0.372015
\(866\) 18.4111 0.625634
\(867\) −10.3287 −0.350781
\(868\) −41.8048 −1.41895
\(869\) 17.2724 0.585925
\(870\) −0.345979 −0.0117298
\(871\) −71.6392 −2.42740
\(872\) −2.49420 −0.0844642
\(873\) −27.1205 −0.917889
\(874\) −48.5804 −1.64326
\(875\) −4.68706 −0.158451
\(876\) 19.0526 0.643729
\(877\) 52.7471 1.78114 0.890572 0.454843i \(-0.150305\pi\)
0.890572 + 0.454843i \(0.150305\pi\)
\(878\) −16.7436 −0.565068
\(879\) −21.2076 −0.715316
\(880\) −1.20462 −0.0406079
\(881\) 18.4412 0.621301 0.310651 0.950524i \(-0.399453\pi\)
0.310651 + 0.950524i \(0.399453\pi\)
\(882\) −23.9007 −0.804779
\(883\) −44.0880 −1.48368 −0.741840 0.670577i \(-0.766046\pi\)
−0.741840 + 0.670577i \(0.766046\pi\)
\(884\) 28.2757 0.951015
\(885\) 14.9256 0.501719
\(886\) −1.70027 −0.0571217
\(887\) −0.646874 −0.0217199 −0.0108600 0.999941i \(-0.503457\pi\)
−0.0108600 + 0.999941i \(0.503457\pi\)
\(888\) 4.76837 0.160016
\(889\) 17.1150 0.574020
\(890\) 13.0424 0.437183
\(891\) −1.99997 −0.0670014
\(892\) 21.6531 0.724999
\(893\) −52.8058 −1.76708
\(894\) 14.4778 0.484210
\(895\) 17.3319 0.579342
\(896\) 4.68706 0.156584
\(897\) 41.8727 1.39809
\(898\) −33.7537 −1.12637
\(899\) 2.60499 0.0868811
\(900\) −1.59673 −0.0532244
\(901\) −14.4937 −0.482853
\(902\) −5.47907 −0.182433
\(903\) −21.0617 −0.700889
\(904\) 2.93612 0.0976538
\(905\) 23.4315 0.778888
\(906\) −4.56946 −0.151810
\(907\) −27.7674 −0.922001 −0.461001 0.887400i \(-0.652509\pi\)
−0.461001 + 0.887400i \(0.652509\pi\)
\(908\) −16.5630 −0.549663
\(909\) −13.1946 −0.437637
\(910\) −26.1327 −0.866292
\(911\) 24.2328 0.802867 0.401434 0.915888i \(-0.368512\pi\)
0.401434 + 0.915888i \(0.368512\pi\)
\(912\) −9.07728 −0.300579
\(913\) 1.37733 0.0455830
\(914\) 20.4483 0.676371
\(915\) 10.5176 0.347703
\(916\) −9.48459 −0.313380
\(917\) 74.6144 2.46398
\(918\) 27.6152 0.911437
\(919\) −24.4364 −0.806084 −0.403042 0.915181i \(-0.632047\pi\)
−0.403042 + 0.915181i \(0.632047\pi\)
\(920\) 6.33980 0.209017
\(921\) 3.55491 0.117138
\(922\) 1.18525 0.0390341
\(923\) 33.3897 1.09903
\(924\) −6.68839 −0.220032
\(925\) −4.02531 −0.132351
\(926\) −10.3889 −0.341401
\(927\) −4.98220 −0.163637
\(928\) −0.292065 −0.00958750
\(929\) −14.2019 −0.465949 −0.232974 0.972483i \(-0.574846\pi\)
−0.232974 + 0.972483i \(0.574846\pi\)
\(930\) −10.5656 −0.346461
\(931\) 114.700 3.75914
\(932\) 22.7987 0.746796
\(933\) 25.9585 0.849844
\(934\) −13.1057 −0.428831
\(935\) −6.10914 −0.199790
\(936\) −8.90261 −0.290991
\(937\) −12.5103 −0.408695 −0.204348 0.978898i \(-0.565507\pi\)
−0.204348 + 0.978898i \(0.565507\pi\)
\(938\) −60.2235 −1.96637
\(939\) −34.7333 −1.13348
\(940\) 6.89121 0.224767
\(941\) −2.05386 −0.0669540 −0.0334770 0.999439i \(-0.510658\pi\)
−0.0334770 + 0.999439i \(0.510658\pi\)
\(942\) −27.4134 −0.893177
\(943\) 28.8357 0.939020
\(944\) 12.5998 0.410087
\(945\) −25.5223 −0.830240
\(946\) 4.56956 0.148569
\(947\) 44.3966 1.44269 0.721347 0.692574i \(-0.243523\pi\)
0.721347 + 0.692574i \(0.243523\pi\)
\(948\) −16.9852 −0.551654
\(949\) −89.6747 −2.91096
\(950\) 7.66277 0.248613
\(951\) 17.6782 0.573255
\(952\) 23.7700 0.770389
\(953\) 35.0284 1.13468 0.567340 0.823484i \(-0.307973\pi\)
0.567340 + 0.823484i \(0.307973\pi\)
\(954\) 4.56333 0.147743
\(955\) 1.46888 0.0475319
\(956\) −5.11597 −0.165462
\(957\) 0.416775 0.0134724
\(958\) −8.41221 −0.271786
\(959\) 8.58927 0.277362
\(960\) 1.18460 0.0382327
\(961\) 48.5521 1.56620
\(962\) −22.4432 −0.723597
\(963\) 17.3682 0.559683
\(964\) −19.7206 −0.635158
\(965\) 5.91331 0.190356
\(966\) 35.2003 1.13255
\(967\) 19.8609 0.638685 0.319342 0.947639i \(-0.396538\pi\)
0.319342 + 0.947639i \(0.396538\pi\)
\(968\) −9.54888 −0.306913
\(969\) −46.0346 −1.47884
\(970\) −16.9850 −0.545355
\(971\) −52.9437 −1.69904 −0.849522 0.527554i \(-0.823109\pi\)
−0.849522 + 0.527554i \(0.823109\pi\)
\(972\) −14.3691 −0.460889
\(973\) −5.12227 −0.164212
\(974\) 27.3511 0.876385
\(975\) −6.60473 −0.211521
\(976\) 8.87868 0.284200
\(977\) 15.7034 0.502395 0.251197 0.967936i \(-0.419176\pi\)
0.251197 + 0.967936i \(0.419176\pi\)
\(978\) −13.3083 −0.425553
\(979\) −15.7112 −0.502133
\(980\) −14.9685 −0.478151
\(981\) 3.98257 0.127154
\(982\) −12.8040 −0.408591
\(983\) 30.9448 0.986987 0.493493 0.869749i \(-0.335720\pi\)
0.493493 + 0.869749i \(0.335720\pi\)
\(984\) 5.38797 0.171762
\(985\) 18.2523 0.581566
\(986\) −1.48118 −0.0471704
\(987\) 38.2619 1.21789
\(988\) 42.7239 1.35923
\(989\) −24.0491 −0.764716
\(990\) 1.92346 0.0611317
\(991\) −35.9669 −1.14252 −0.571262 0.820768i \(-0.693546\pi\)
−0.571262 + 0.820768i \(0.693546\pi\)
\(992\) −8.91920 −0.283185
\(993\) 18.9391 0.601013
\(994\) 28.0690 0.890295
\(995\) −18.6917 −0.592567
\(996\) −1.35443 −0.0429168
\(997\) −55.3819 −1.75396 −0.876982 0.480524i \(-0.840447\pi\)
−0.876982 + 0.480524i \(0.840447\pi\)
\(998\) −30.6213 −0.969300
\(999\) −21.9189 −0.693483
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 4010.2.a.o.1.9 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.o.1.9 22 1.1 even 1 trivial