Properties

Label 6041.2.a.d.1.7
Level $6041$
Weight $2$
Character 6041.1
Self dual yes
Analytic conductor $48.238$
Analytic rank $1$
Dimension $101$
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] = [6041,2,Mod(1,6041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6041, 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("6041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.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: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.41856 q^{2} +2.09832 q^{3} +3.84945 q^{4} -1.02982 q^{5} -5.07493 q^{6} -1.00000 q^{7} -4.47302 q^{8} +1.40297 q^{9} +O(q^{10})\) \(q-2.41856 q^{2} +2.09832 q^{3} +3.84945 q^{4} -1.02982 q^{5} -5.07493 q^{6} -1.00000 q^{7} -4.47302 q^{8} +1.40297 q^{9} +2.49069 q^{10} +1.48551 q^{11} +8.07740 q^{12} +1.08201 q^{13} +2.41856 q^{14} -2.16090 q^{15} +3.11937 q^{16} -3.39749 q^{17} -3.39316 q^{18} -1.89904 q^{19} -3.96425 q^{20} -2.09832 q^{21} -3.59281 q^{22} -0.994082 q^{23} -9.38584 q^{24} -3.93947 q^{25} -2.61691 q^{26} -3.35110 q^{27} -3.84945 q^{28} +10.1257 q^{29} +5.22628 q^{30} +5.73591 q^{31} +1.40163 q^{32} +3.11709 q^{33} +8.21705 q^{34} +1.02982 q^{35} +5.40065 q^{36} +3.51074 q^{37} +4.59294 q^{38} +2.27041 q^{39} +4.60641 q^{40} -3.95945 q^{41} +5.07493 q^{42} -9.30767 q^{43} +5.71841 q^{44} -1.44481 q^{45} +2.40425 q^{46} -1.20677 q^{47} +6.54546 q^{48} +1.00000 q^{49} +9.52785 q^{50} -7.12904 q^{51} +4.16515 q^{52} +12.5017 q^{53} +8.10484 q^{54} -1.52981 q^{55} +4.47302 q^{56} -3.98480 q^{57} -24.4897 q^{58} -5.80890 q^{59} -8.31828 q^{60} +6.88980 q^{61} -13.8727 q^{62} -1.40297 q^{63} -9.62867 q^{64} -1.11428 q^{65} -7.53888 q^{66} +0.104871 q^{67} -13.0785 q^{68} -2.08591 q^{69} -2.49069 q^{70} -3.31842 q^{71} -6.27549 q^{72} +5.17255 q^{73} -8.49094 q^{74} -8.26628 q^{75} -7.31025 q^{76} -1.48551 q^{77} -5.49113 q^{78} -12.0716 q^{79} -3.21240 q^{80} -11.2406 q^{81} +9.57618 q^{82} -0.715863 q^{83} -8.07740 q^{84} +3.49881 q^{85} +22.5112 q^{86} +21.2470 q^{87} -6.64473 q^{88} -15.1763 q^{89} +3.49436 q^{90} -1.08201 q^{91} -3.82667 q^{92} +12.0358 q^{93} +2.91866 q^{94} +1.95567 q^{95} +2.94107 q^{96} -11.5352 q^{97} -2.41856 q^{98} +2.08413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41856 −1.71018 −0.855091 0.518477i \(-0.826499\pi\)
−0.855091 + 0.518477i \(0.826499\pi\)
\(3\) 2.09832 1.21147 0.605734 0.795667i \(-0.292880\pi\)
0.605734 + 0.795667i \(0.292880\pi\)
\(4\) 3.84945 1.92473
\(5\) −1.02982 −0.460550 −0.230275 0.973126i \(-0.573963\pi\)
−0.230275 + 0.973126i \(0.573963\pi\)
\(6\) −5.07493 −2.07183
\(7\) −1.00000 −0.377964
\(8\) −4.47302 −1.58145
\(9\) 1.40297 0.467655
\(10\) 2.49069 0.787626
\(11\) 1.48551 0.447899 0.223950 0.974601i \(-0.428105\pi\)
0.223950 + 0.974601i \(0.428105\pi\)
\(12\) 8.07740 2.33174
\(13\) 1.08201 0.300096 0.150048 0.988679i \(-0.452057\pi\)
0.150048 + 0.988679i \(0.452057\pi\)
\(14\) 2.41856 0.646388
\(15\) −2.16090 −0.557942
\(16\) 3.11937 0.779844
\(17\) −3.39749 −0.824013 −0.412006 0.911181i \(-0.635172\pi\)
−0.412006 + 0.911181i \(0.635172\pi\)
\(18\) −3.39316 −0.799776
\(19\) −1.89904 −0.435669 −0.217835 0.975986i \(-0.569899\pi\)
−0.217835 + 0.975986i \(0.569899\pi\)
\(20\) −3.96425 −0.886433
\(21\) −2.09832 −0.457892
\(22\) −3.59281 −0.765990
\(23\) −0.994082 −0.207280 −0.103640 0.994615i \(-0.533049\pi\)
−0.103640 + 0.994615i \(0.533049\pi\)
\(24\) −9.38584 −1.91588
\(25\) −3.93947 −0.787893
\(26\) −2.61691 −0.513219
\(27\) −3.35110 −0.644919
\(28\) −3.84945 −0.727478
\(29\) 10.1257 1.88030 0.940149 0.340762i \(-0.110685\pi\)
0.940149 + 0.340762i \(0.110685\pi\)
\(30\) 5.22628 0.954183
\(31\) 5.73591 1.03020 0.515100 0.857130i \(-0.327755\pi\)
0.515100 + 0.857130i \(0.327755\pi\)
\(32\) 1.40163 0.247775
\(33\) 3.11709 0.542616
\(34\) 8.21705 1.40921
\(35\) 1.02982 0.174072
\(36\) 5.40065 0.900109
\(37\) 3.51074 0.577162 0.288581 0.957456i \(-0.406817\pi\)
0.288581 + 0.957456i \(0.406817\pi\)
\(38\) 4.59294 0.745074
\(39\) 2.27041 0.363556
\(40\) 4.60641 0.728338
\(41\) −3.95945 −0.618362 −0.309181 0.951003i \(-0.600055\pi\)
−0.309181 + 0.951003i \(0.600055\pi\)
\(42\) 5.07493 0.783079
\(43\) −9.30767 −1.41941 −0.709703 0.704501i \(-0.751171\pi\)
−0.709703 + 0.704501i \(0.751171\pi\)
\(44\) 5.71841 0.862083
\(45\) −1.44481 −0.215379
\(46\) 2.40425 0.354487
\(47\) −1.20677 −0.176026 −0.0880130 0.996119i \(-0.528052\pi\)
−0.0880130 + 0.996119i \(0.528052\pi\)
\(48\) 6.54546 0.944756
\(49\) 1.00000 0.142857
\(50\) 9.52785 1.34744
\(51\) −7.12904 −0.998266
\(52\) 4.16515 0.577602
\(53\) 12.5017 1.71725 0.858623 0.512608i \(-0.171321\pi\)
0.858623 + 0.512608i \(0.171321\pi\)
\(54\) 8.10484 1.10293
\(55\) −1.52981 −0.206280
\(56\) 4.47302 0.597732
\(57\) −3.98480 −0.527799
\(58\) −24.4897 −3.21566
\(59\) −5.80890 −0.756255 −0.378127 0.925754i \(-0.623432\pi\)
−0.378127 + 0.925754i \(0.623432\pi\)
\(60\) −8.31828 −1.07389
\(61\) 6.88980 0.882148 0.441074 0.897471i \(-0.354598\pi\)
0.441074 + 0.897471i \(0.354598\pi\)
\(62\) −13.8727 −1.76183
\(63\) −1.40297 −0.176757
\(64\) −9.62867 −1.20358
\(65\) −1.11428 −0.138209
\(66\) −7.53888 −0.927972
\(67\) 0.104871 0.0128120 0.00640602 0.999979i \(-0.497961\pi\)
0.00640602 + 0.999979i \(0.497961\pi\)
\(68\) −13.0785 −1.58600
\(69\) −2.08591 −0.251114
\(70\) −2.49069 −0.297694
\(71\) −3.31842 −0.393824 −0.196912 0.980421i \(-0.563091\pi\)
−0.196912 + 0.980421i \(0.563091\pi\)
\(72\) −6.27549 −0.739574
\(73\) 5.17255 0.605401 0.302701 0.953086i \(-0.402112\pi\)
0.302701 + 0.953086i \(0.402112\pi\)
\(74\) −8.49094 −0.987052
\(75\) −8.26628 −0.954508
\(76\) −7.31025 −0.838544
\(77\) −1.48551 −0.169290
\(78\) −5.49113 −0.621748
\(79\) −12.0716 −1.35816 −0.679082 0.734063i \(-0.737622\pi\)
−0.679082 + 0.734063i \(0.737622\pi\)
\(80\) −3.21240 −0.359157
\(81\) −11.2406 −1.24895
\(82\) 9.57618 1.05751
\(83\) −0.715863 −0.0785761 −0.0392881 0.999228i \(-0.512509\pi\)
−0.0392881 + 0.999228i \(0.512509\pi\)
\(84\) −8.07740 −0.881317
\(85\) 3.49881 0.379500
\(86\) 22.5112 2.42745
\(87\) 21.2470 2.27792
\(88\) −6.64473 −0.708330
\(89\) −15.1763 −1.60868 −0.804341 0.594167i \(-0.797482\pi\)
−0.804341 + 0.594167i \(0.797482\pi\)
\(90\) 3.49436 0.368337
\(91\) −1.08201 −0.113426
\(92\) −3.82667 −0.398958
\(93\) 12.0358 1.24805
\(94\) 2.91866 0.301037
\(95\) 1.95567 0.200648
\(96\) 2.94107 0.300172
\(97\) −11.5352 −1.17122 −0.585611 0.810592i \(-0.699145\pi\)
−0.585611 + 0.810592i \(0.699145\pi\)
\(98\) −2.41856 −0.244312
\(99\) 2.08413 0.209463
\(100\) −15.1648 −1.51648
\(101\) 3.29800 0.328163 0.164081 0.986447i \(-0.447534\pi\)
0.164081 + 0.986447i \(0.447534\pi\)
\(102\) 17.2420 1.70722
\(103\) 1.26235 0.124383 0.0621915 0.998064i \(-0.480191\pi\)
0.0621915 + 0.998064i \(0.480191\pi\)
\(104\) −4.83985 −0.474586
\(105\) 2.16090 0.210882
\(106\) −30.2362 −2.93680
\(107\) 5.46590 0.528409 0.264204 0.964467i \(-0.414891\pi\)
0.264204 + 0.964467i \(0.414891\pi\)
\(108\) −12.8999 −1.24129
\(109\) 2.27962 0.218348 0.109174 0.994023i \(-0.465179\pi\)
0.109174 + 0.994023i \(0.465179\pi\)
\(110\) 3.69996 0.352777
\(111\) 7.36667 0.699213
\(112\) −3.11937 −0.294753
\(113\) 20.3751 1.91673 0.958364 0.285548i \(-0.0921758\pi\)
0.958364 + 0.285548i \(0.0921758\pi\)
\(114\) 9.63749 0.902633
\(115\) 1.02373 0.0954631
\(116\) 38.9785 3.61906
\(117\) 1.51802 0.140341
\(118\) 14.0492 1.29333
\(119\) 3.39749 0.311448
\(120\) 9.66575 0.882358
\(121\) −8.79325 −0.799386
\(122\) −16.6634 −1.50863
\(123\) −8.30821 −0.749126
\(124\) 22.0801 1.98285
\(125\) 9.20606 0.823415
\(126\) 3.39316 0.302287
\(127\) −15.6781 −1.39121 −0.695605 0.718425i \(-0.744863\pi\)
−0.695605 + 0.718425i \(0.744863\pi\)
\(128\) 20.4843 1.81057
\(129\) −19.5305 −1.71957
\(130\) 2.69495 0.236363
\(131\) −14.5064 −1.26743 −0.633713 0.773568i \(-0.718470\pi\)
−0.633713 + 0.773568i \(0.718470\pi\)
\(132\) 11.9991 1.04439
\(133\) 1.89904 0.164667
\(134\) −0.253637 −0.0219109
\(135\) 3.45103 0.297018
\(136\) 15.1970 1.30314
\(137\) 9.16330 0.782873 0.391437 0.920205i \(-0.371978\pi\)
0.391437 + 0.920205i \(0.371978\pi\)
\(138\) 5.04490 0.429450
\(139\) −12.9502 −1.09842 −0.549212 0.835683i \(-0.685072\pi\)
−0.549212 + 0.835683i \(0.685072\pi\)
\(140\) 3.96425 0.335040
\(141\) −2.53220 −0.213250
\(142\) 8.02582 0.673512
\(143\) 1.60734 0.134413
\(144\) 4.37638 0.364698
\(145\) −10.4277 −0.865973
\(146\) −12.5101 −1.03535
\(147\) 2.09832 0.173067
\(148\) 13.5144 1.11088
\(149\) 3.64635 0.298721 0.149360 0.988783i \(-0.452279\pi\)
0.149360 + 0.988783i \(0.452279\pi\)
\(150\) 19.9925 1.63238
\(151\) 14.0468 1.14311 0.571556 0.820563i \(-0.306340\pi\)
0.571556 + 0.820563i \(0.306340\pi\)
\(152\) 8.49443 0.688989
\(153\) −4.76657 −0.385354
\(154\) 3.59281 0.289517
\(155\) −5.90696 −0.474459
\(156\) 8.73983 0.699746
\(157\) 8.05538 0.642890 0.321445 0.946928i \(-0.395832\pi\)
0.321445 + 0.946928i \(0.395832\pi\)
\(158\) 29.1960 2.32271
\(159\) 26.2327 2.08039
\(160\) −1.44343 −0.114113
\(161\) 0.994082 0.0783446
\(162\) 27.1861 2.13594
\(163\) −7.61628 −0.596553 −0.298276 0.954480i \(-0.596412\pi\)
−0.298276 + 0.954480i \(0.596412\pi\)
\(164\) −15.2417 −1.19018
\(165\) −3.21005 −0.249902
\(166\) 1.73136 0.134380
\(167\) −17.2568 −1.33537 −0.667687 0.744442i \(-0.732715\pi\)
−0.667687 + 0.744442i \(0.732715\pi\)
\(168\) 9.38584 0.724133
\(169\) −11.8293 −0.909943
\(170\) −8.46210 −0.649014
\(171\) −2.66429 −0.203743
\(172\) −35.8294 −2.73197
\(173\) 10.0334 0.762826 0.381413 0.924405i \(-0.375438\pi\)
0.381413 + 0.924405i \(0.375438\pi\)
\(174\) −51.3873 −3.89566
\(175\) 3.93947 0.297796
\(176\) 4.63387 0.349291
\(177\) −12.1890 −0.916178
\(178\) 36.7048 2.75114
\(179\) −20.2444 −1.51314 −0.756569 0.653913i \(-0.773126\pi\)
−0.756569 + 0.653913i \(0.773126\pi\)
\(180\) −5.56171 −0.414545
\(181\) −19.0471 −1.41576 −0.707879 0.706334i \(-0.750348\pi\)
−0.707879 + 0.706334i \(0.750348\pi\)
\(182\) 2.61691 0.193978
\(183\) 14.4570 1.06869
\(184\) 4.44654 0.327804
\(185\) −3.61543 −0.265812
\(186\) −29.1093 −2.13440
\(187\) −5.04702 −0.369075
\(188\) −4.64542 −0.338802
\(189\) 3.35110 0.243756
\(190\) −4.72992 −0.343144
\(191\) −23.6796 −1.71340 −0.856700 0.515816i \(-0.827489\pi\)
−0.856700 + 0.515816i \(0.827489\pi\)
\(192\) −20.2041 −1.45810
\(193\) −4.19935 −0.302276 −0.151138 0.988513i \(-0.548294\pi\)
−0.151138 + 0.988513i \(0.548294\pi\)
\(194\) 27.8986 2.00300
\(195\) −2.33812 −0.167436
\(196\) 3.84945 0.274961
\(197\) −5.81385 −0.414220 −0.207110 0.978318i \(-0.566406\pi\)
−0.207110 + 0.978318i \(0.566406\pi\)
\(198\) −5.04059 −0.358219
\(199\) −11.0846 −0.785769 −0.392885 0.919588i \(-0.628523\pi\)
−0.392885 + 0.919588i \(0.628523\pi\)
\(200\) 17.6213 1.24601
\(201\) 0.220053 0.0155214
\(202\) −7.97641 −0.561218
\(203\) −10.1257 −0.710686
\(204\) −27.4429 −1.92139
\(205\) 4.07753 0.284787
\(206\) −3.05308 −0.212718
\(207\) −1.39466 −0.0969358
\(208\) 3.37520 0.234028
\(209\) −2.82105 −0.195136
\(210\) −5.22628 −0.360647
\(211\) −1.57843 −0.108663 −0.0543317 0.998523i \(-0.517303\pi\)
−0.0543317 + 0.998523i \(0.517303\pi\)
\(212\) 48.1248 3.30523
\(213\) −6.96313 −0.477106
\(214\) −13.2196 −0.903676
\(215\) 9.58525 0.653708
\(216\) 14.9895 1.01991
\(217\) −5.73591 −0.389379
\(218\) −5.51342 −0.373416
\(219\) 10.8537 0.733424
\(220\) −5.88895 −0.397033
\(221\) −3.67612 −0.247283
\(222\) −17.8168 −1.19578
\(223\) −15.9116 −1.06552 −0.532761 0.846266i \(-0.678846\pi\)
−0.532761 + 0.846266i \(0.678846\pi\)
\(224\) −1.40163 −0.0936501
\(225\) −5.52694 −0.368463
\(226\) −49.2785 −3.27796
\(227\) −12.1747 −0.808064 −0.404032 0.914745i \(-0.632391\pi\)
−0.404032 + 0.914745i \(0.632391\pi\)
\(228\) −15.3393 −1.01587
\(229\) −26.5406 −1.75385 −0.876927 0.480624i \(-0.840410\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(230\) −2.47595 −0.163259
\(231\) −3.11709 −0.205089
\(232\) −45.2925 −2.97360
\(233\) 29.3076 1.92000 0.960001 0.279997i \(-0.0903334\pi\)
0.960001 + 0.279997i \(0.0903334\pi\)
\(234\) −3.67144 −0.240009
\(235\) 1.24276 0.0810689
\(236\) −22.3611 −1.45558
\(237\) −25.3302 −1.64537
\(238\) −8.21705 −0.532632
\(239\) −8.32212 −0.538313 −0.269157 0.963096i \(-0.586745\pi\)
−0.269157 + 0.963096i \(0.586745\pi\)
\(240\) −6.74066 −0.435108
\(241\) 9.98443 0.643154 0.321577 0.946884i \(-0.395787\pi\)
0.321577 + 0.946884i \(0.395787\pi\)
\(242\) 21.2670 1.36710
\(243\) −13.5331 −0.868149
\(244\) 26.5219 1.69789
\(245\) −1.02982 −0.0657929
\(246\) 20.0939 1.28114
\(247\) −2.05478 −0.130742
\(248\) −25.6568 −1.62921
\(249\) −1.50211 −0.0951925
\(250\) −22.2654 −1.40819
\(251\) 15.3489 0.968817 0.484408 0.874842i \(-0.339035\pi\)
0.484408 + 0.874842i \(0.339035\pi\)
\(252\) −5.40065 −0.340209
\(253\) −1.47672 −0.0928407
\(254\) 37.9186 2.37922
\(255\) 7.34164 0.459752
\(256\) −30.2853 −1.89283
\(257\) 20.1594 1.25751 0.628754 0.777605i \(-0.283565\pi\)
0.628754 + 0.777605i \(0.283565\pi\)
\(258\) 47.2358 2.94077
\(259\) −3.51074 −0.218147
\(260\) −4.28936 −0.266015
\(261\) 14.2060 0.879332
\(262\) 35.0845 2.16753
\(263\) −13.1857 −0.813064 −0.406532 0.913637i \(-0.633262\pi\)
−0.406532 + 0.913637i \(0.633262\pi\)
\(264\) −13.9428 −0.858120
\(265\) −12.8746 −0.790878
\(266\) −4.59294 −0.281611
\(267\) −31.8448 −1.94887
\(268\) 0.403696 0.0246597
\(269\) −24.0545 −1.46663 −0.733315 0.679889i \(-0.762028\pi\)
−0.733315 + 0.679889i \(0.762028\pi\)
\(270\) −8.34654 −0.507954
\(271\) 26.5726 1.61417 0.807084 0.590436i \(-0.201044\pi\)
0.807084 + 0.590436i \(0.201044\pi\)
\(272\) −10.5981 −0.642601
\(273\) −2.27041 −0.137411
\(274\) −22.1620 −1.33886
\(275\) −5.85213 −0.352897
\(276\) −8.02960 −0.483325
\(277\) −6.02419 −0.361958 −0.180979 0.983487i \(-0.557927\pi\)
−0.180979 + 0.983487i \(0.557927\pi\)
\(278\) 31.3210 1.87851
\(279\) 8.04728 0.481778
\(280\) −4.60641 −0.275286
\(281\) 22.9831 1.37106 0.685529 0.728045i \(-0.259571\pi\)
0.685529 + 0.728045i \(0.259571\pi\)
\(282\) 6.12429 0.364696
\(283\) −13.2858 −0.789758 −0.394879 0.918733i \(-0.629214\pi\)
−0.394879 + 0.918733i \(0.629214\pi\)
\(284\) −12.7741 −0.758004
\(285\) 4.10363 0.243078
\(286\) −3.88746 −0.229870
\(287\) 3.95945 0.233719
\(288\) 1.96644 0.115873
\(289\) −5.45705 −0.321003
\(290\) 25.2200 1.48097
\(291\) −24.2046 −1.41890
\(292\) 19.9115 1.16523
\(293\) 4.13869 0.241785 0.120893 0.992666i \(-0.461424\pi\)
0.120893 + 0.992666i \(0.461424\pi\)
\(294\) −5.07493 −0.295976
\(295\) 5.98214 0.348293
\(296\) −15.7036 −0.912752
\(297\) −4.97810 −0.288859
\(298\) −8.81894 −0.510867
\(299\) −1.07561 −0.0622039
\(300\) −31.8206 −1.83717
\(301\) 9.30767 0.536485
\(302\) −33.9731 −1.95493
\(303\) 6.92027 0.397559
\(304\) −5.92381 −0.339754
\(305\) −7.09526 −0.406274
\(306\) 11.5282 0.659026
\(307\) −6.72084 −0.383579 −0.191789 0.981436i \(-0.561429\pi\)
−0.191789 + 0.981436i \(0.561429\pi\)
\(308\) −5.71841 −0.325837
\(309\) 2.64882 0.150686
\(310\) 14.2864 0.811411
\(311\) 20.4775 1.16117 0.580587 0.814198i \(-0.302823\pi\)
0.580587 + 0.814198i \(0.302823\pi\)
\(312\) −10.1556 −0.574946
\(313\) 3.04133 0.171906 0.0859531 0.996299i \(-0.472606\pi\)
0.0859531 + 0.996299i \(0.472606\pi\)
\(314\) −19.4825 −1.09946
\(315\) 1.44481 0.0814056
\(316\) −46.4691 −2.61409
\(317\) −24.2259 −1.36066 −0.680330 0.732906i \(-0.738163\pi\)
−0.680330 + 0.732906i \(0.738163\pi\)
\(318\) −63.4455 −3.55784
\(319\) 15.0419 0.842184
\(320\) 9.91582 0.554311
\(321\) 11.4692 0.640151
\(322\) −2.40425 −0.133984
\(323\) 6.45197 0.358997
\(324\) −43.2701 −2.40389
\(325\) −4.26254 −0.236443
\(326\) 18.4204 1.02021
\(327\) 4.78339 0.264522
\(328\) 17.7107 0.977909
\(329\) 1.20677 0.0665316
\(330\) 7.76371 0.427378
\(331\) 20.4554 1.12433 0.562165 0.827025i \(-0.309969\pi\)
0.562165 + 0.827025i \(0.309969\pi\)
\(332\) −2.75568 −0.151238
\(333\) 4.92545 0.269913
\(334\) 41.7367 2.28373
\(335\) −0.107998 −0.00590059
\(336\) −6.54546 −0.357084
\(337\) 1.41685 0.0771805 0.0385903 0.999255i \(-0.487713\pi\)
0.0385903 + 0.999255i \(0.487713\pi\)
\(338\) 28.6098 1.55617
\(339\) 42.7536 2.32206
\(340\) 13.4685 0.730433
\(341\) 8.52077 0.461425
\(342\) 6.44375 0.348438
\(343\) −1.00000 −0.0539949
\(344\) 41.6334 2.24472
\(345\) 2.14811 0.115650
\(346\) −24.2664 −1.30457
\(347\) 5.24673 0.281659 0.140830 0.990034i \(-0.455023\pi\)
0.140830 + 0.990034i \(0.455023\pi\)
\(348\) 81.7895 4.38438
\(349\) −32.1140 −1.71902 −0.859512 0.511115i \(-0.829232\pi\)
−0.859512 + 0.511115i \(0.829232\pi\)
\(350\) −9.52785 −0.509285
\(351\) −3.62592 −0.193537
\(352\) 2.08214 0.110978
\(353\) −24.1244 −1.28401 −0.642007 0.766699i \(-0.721898\pi\)
−0.642007 + 0.766699i \(0.721898\pi\)
\(354\) 29.4798 1.56683
\(355\) 3.41739 0.181376
\(356\) −58.4204 −3.09627
\(357\) 7.12904 0.377309
\(358\) 48.9624 2.58774
\(359\) −16.7082 −0.881827 −0.440913 0.897550i \(-0.645345\pi\)
−0.440913 + 0.897550i \(0.645345\pi\)
\(360\) 6.46264 0.340611
\(361\) −15.3937 −0.810192
\(362\) 46.0666 2.42120
\(363\) −18.4511 −0.968431
\(364\) −4.16515 −0.218313
\(365\) −5.32681 −0.278818
\(366\) −34.9652 −1.82766
\(367\) −27.4628 −1.43354 −0.716772 0.697307i \(-0.754381\pi\)
−0.716772 + 0.697307i \(0.754381\pi\)
\(368\) −3.10091 −0.161646
\(369\) −5.55497 −0.289180
\(370\) 8.74416 0.454587
\(371\) −12.5017 −0.649058
\(372\) 46.3312 2.40216
\(373\) 8.86703 0.459117 0.229559 0.973295i \(-0.426272\pi\)
0.229559 + 0.973295i \(0.426272\pi\)
\(374\) 12.2065 0.631185
\(375\) 19.3173 0.997541
\(376\) 5.39792 0.278376
\(377\) 10.9561 0.564270
\(378\) −8.10484 −0.416868
\(379\) −19.3655 −0.994740 −0.497370 0.867539i \(-0.665701\pi\)
−0.497370 + 0.867539i \(0.665701\pi\)
\(380\) 7.52826 0.386192
\(381\) −32.8978 −1.68541
\(382\) 57.2707 2.93023
\(383\) 28.5629 1.45949 0.729747 0.683717i \(-0.239638\pi\)
0.729747 + 0.683717i \(0.239638\pi\)
\(384\) 42.9827 2.19345
\(385\) 1.52981 0.0779666
\(386\) 10.1564 0.516947
\(387\) −13.0584 −0.663793
\(388\) −44.4042 −2.25428
\(389\) 10.7195 0.543500 0.271750 0.962368i \(-0.412398\pi\)
0.271750 + 0.962368i \(0.412398\pi\)
\(390\) 5.65489 0.286346
\(391\) 3.37739 0.170802
\(392\) −4.47302 −0.225921
\(393\) −30.4390 −1.53545
\(394\) 14.0612 0.708392
\(395\) 12.4316 0.625503
\(396\) 8.02274 0.403158
\(397\) 16.2121 0.813660 0.406830 0.913504i \(-0.366634\pi\)
0.406830 + 0.913504i \(0.366634\pi\)
\(398\) 26.8089 1.34381
\(399\) 3.98480 0.199489
\(400\) −12.2887 −0.614434
\(401\) −15.6289 −0.780469 −0.390234 0.920716i \(-0.627606\pi\)
−0.390234 + 0.920716i \(0.627606\pi\)
\(402\) −0.532213 −0.0265444
\(403\) 6.20631 0.309158
\(404\) 12.6955 0.631623
\(405\) 11.5758 0.575206
\(406\) 24.4897 1.21540
\(407\) 5.21525 0.258510
\(408\) 31.8883 1.57871
\(409\) −23.4653 −1.16028 −0.580141 0.814516i \(-0.697003\pi\)
−0.580141 + 0.814516i \(0.697003\pi\)
\(410\) −9.86176 −0.487038
\(411\) 19.2276 0.948426
\(412\) 4.85936 0.239403
\(413\) 5.80890 0.285837
\(414\) 3.37308 0.165778
\(415\) 0.737211 0.0361883
\(416\) 1.51657 0.0743562
\(417\) −27.1738 −1.33071
\(418\) 6.82288 0.333718
\(419\) −0.0876217 −0.00428060 −0.00214030 0.999998i \(-0.500681\pi\)
−0.00214030 + 0.999998i \(0.500681\pi\)
\(420\) 8.31828 0.405891
\(421\) 7.89977 0.385011 0.192506 0.981296i \(-0.438339\pi\)
0.192506 + 0.981296i \(0.438339\pi\)
\(422\) 3.81753 0.185834
\(423\) −1.69306 −0.0823195
\(424\) −55.9205 −2.71574
\(425\) 13.3843 0.649234
\(426\) 16.8408 0.815938
\(427\) −6.88980 −0.333421
\(428\) 21.0407 1.01704
\(429\) 3.37272 0.162837
\(430\) −23.1825 −1.11796
\(431\) 18.8740 0.909130 0.454565 0.890714i \(-0.349795\pi\)
0.454565 + 0.890714i \(0.349795\pi\)
\(432\) −10.4533 −0.502936
\(433\) −7.88200 −0.378785 −0.189392 0.981901i \(-0.560652\pi\)
−0.189392 + 0.981901i \(0.560652\pi\)
\(434\) 13.8727 0.665909
\(435\) −21.8807 −1.04910
\(436\) 8.77530 0.420261
\(437\) 1.88780 0.0903057
\(438\) −26.2503 −1.25429
\(439\) 32.7339 1.56231 0.781153 0.624340i \(-0.214632\pi\)
0.781153 + 0.624340i \(0.214632\pi\)
\(440\) 6.84289 0.326222
\(441\) 1.40297 0.0668079
\(442\) 8.89094 0.422899
\(443\) 27.0414 1.28478 0.642389 0.766379i \(-0.277943\pi\)
0.642389 + 0.766379i \(0.277943\pi\)
\(444\) 28.3576 1.34579
\(445\) 15.6289 0.740880
\(446\) 38.4833 1.82224
\(447\) 7.65123 0.361891
\(448\) 9.62867 0.454912
\(449\) 23.5207 1.11001 0.555005 0.831847i \(-0.312716\pi\)
0.555005 + 0.831847i \(0.312716\pi\)
\(450\) 13.3673 0.630138
\(451\) −5.88181 −0.276964
\(452\) 78.4330 3.68918
\(453\) 29.4748 1.38484
\(454\) 29.4453 1.38194
\(455\) 1.11428 0.0522382
\(456\) 17.8241 0.834688
\(457\) 16.0734 0.751884 0.375942 0.926643i \(-0.377319\pi\)
0.375942 + 0.926643i \(0.377319\pi\)
\(458\) 64.1902 2.99941
\(459\) 11.3853 0.531421
\(460\) 3.94079 0.183740
\(461\) −10.6683 −0.496874 −0.248437 0.968648i \(-0.579917\pi\)
−0.248437 + 0.968648i \(0.579917\pi\)
\(462\) 7.53888 0.350741
\(463\) 5.19512 0.241438 0.120719 0.992687i \(-0.461480\pi\)
0.120719 + 0.992687i \(0.461480\pi\)
\(464\) 31.5859 1.46634
\(465\) −12.3947 −0.574792
\(466\) −70.8822 −3.28355
\(467\) 1.15133 0.0532770 0.0266385 0.999645i \(-0.491520\pi\)
0.0266385 + 0.999645i \(0.491520\pi\)
\(468\) 5.84356 0.270119
\(469\) −0.104871 −0.00484249
\(470\) −3.00570 −0.138643
\(471\) 16.9028 0.778840
\(472\) 25.9833 1.19598
\(473\) −13.8267 −0.635751
\(474\) 61.2627 2.81389
\(475\) 7.48119 0.343261
\(476\) 13.0785 0.599451
\(477\) 17.5395 0.803079
\(478\) 20.1276 0.920614
\(479\) 22.7050 1.03742 0.518708 0.854951i \(-0.326413\pi\)
0.518708 + 0.854951i \(0.326413\pi\)
\(480\) −3.02878 −0.138244
\(481\) 3.79865 0.173204
\(482\) −24.1480 −1.09991
\(483\) 2.08591 0.0949120
\(484\) −33.8492 −1.53860
\(485\) 11.8792 0.539407
\(486\) 32.7307 1.48469
\(487\) 9.30730 0.421754 0.210877 0.977513i \(-0.432368\pi\)
0.210877 + 0.977513i \(0.432368\pi\)
\(488\) −30.8182 −1.39507
\(489\) −15.9814 −0.722705
\(490\) 2.49069 0.112518
\(491\) 31.2996 1.41253 0.706265 0.707947i \(-0.250379\pi\)
0.706265 + 0.707947i \(0.250379\pi\)
\(492\) −31.9820 −1.44186
\(493\) −34.4021 −1.54939
\(494\) 4.96961 0.223593
\(495\) −2.14628 −0.0964681
\(496\) 17.8924 0.803394
\(497\) 3.31842 0.148852
\(498\) 3.63295 0.162797
\(499\) −43.2064 −1.93418 −0.967091 0.254431i \(-0.918112\pi\)
−0.967091 + 0.254431i \(0.918112\pi\)
\(500\) 35.4383 1.58485
\(501\) −36.2104 −1.61776
\(502\) −37.1224 −1.65685
\(503\) −35.9591 −1.60334 −0.801668 0.597769i \(-0.796054\pi\)
−0.801668 + 0.597769i \(0.796054\pi\)
\(504\) 6.27549 0.279533
\(505\) −3.39635 −0.151136
\(506\) 3.57155 0.158775
\(507\) −24.8216 −1.10237
\(508\) −60.3522 −2.67770
\(509\) 24.2796 1.07617 0.538087 0.842889i \(-0.319147\pi\)
0.538087 + 0.842889i \(0.319147\pi\)
\(510\) −17.7562 −0.786259
\(511\) −5.17255 −0.228820
\(512\) 32.2782 1.42651
\(513\) 6.36386 0.280971
\(514\) −48.7567 −2.15057
\(515\) −1.30000 −0.0572847
\(516\) −75.1818 −3.30969
\(517\) −1.79268 −0.0788419
\(518\) 8.49094 0.373071
\(519\) 21.0533 0.924139
\(520\) 4.98419 0.218571
\(521\) −4.53090 −0.198502 −0.0992511 0.995062i \(-0.531645\pi\)
−0.0992511 + 0.995062i \(0.531645\pi\)
\(522\) −34.3582 −1.50382
\(523\) −39.9600 −1.74733 −0.873665 0.486528i \(-0.838263\pi\)
−0.873665 + 0.486528i \(0.838263\pi\)
\(524\) −55.8415 −2.43945
\(525\) 8.26628 0.360770
\(526\) 31.8904 1.39049
\(527\) −19.4877 −0.848897
\(528\) 9.72337 0.423155
\(529\) −22.0118 −0.957035
\(530\) 31.1380 1.35255
\(531\) −8.14969 −0.353667
\(532\) 7.31025 0.316940
\(533\) −4.28416 −0.185568
\(534\) 77.0186 3.33292
\(535\) −5.62891 −0.243359
\(536\) −0.469090 −0.0202616
\(537\) −42.4794 −1.83312
\(538\) 58.1774 2.50821
\(539\) 1.48551 0.0639856
\(540\) 13.2846 0.571677
\(541\) 5.93881 0.255330 0.127665 0.991817i \(-0.459252\pi\)
0.127665 + 0.991817i \(0.459252\pi\)
\(542\) −64.2674 −2.76052
\(543\) −39.9669 −1.71515
\(544\) −4.76202 −0.204170
\(545\) −2.34761 −0.100560
\(546\) 5.49113 0.234999
\(547\) −17.7257 −0.757898 −0.378949 0.925418i \(-0.623714\pi\)
−0.378949 + 0.925418i \(0.623714\pi\)
\(548\) 35.2737 1.50682
\(549\) 9.66615 0.412541
\(550\) 14.1538 0.603518
\(551\) −19.2291 −0.819188
\(552\) 9.33029 0.397124
\(553\) 12.0716 0.513338
\(554\) 14.5699 0.619015
\(555\) −7.58636 −0.322023
\(556\) −49.8513 −2.11417
\(557\) −31.7621 −1.34580 −0.672901 0.739732i \(-0.734952\pi\)
−0.672901 + 0.739732i \(0.734952\pi\)
\(558\) −19.4629 −0.823929
\(559\) −10.0710 −0.425958
\(560\) 3.21240 0.135749
\(561\) −10.5903 −0.447122
\(562\) −55.5862 −2.34476
\(563\) −28.6635 −1.20802 −0.604011 0.796976i \(-0.706432\pi\)
−0.604011 + 0.796976i \(0.706432\pi\)
\(564\) −9.74759 −0.410448
\(565\) −20.9827 −0.882750
\(566\) 32.1325 1.35063
\(567\) 11.2406 0.472060
\(568\) 14.8434 0.622814
\(569\) −13.0571 −0.547384 −0.273692 0.961817i \(-0.588245\pi\)
−0.273692 + 0.961817i \(0.588245\pi\)
\(570\) −9.92490 −0.415708
\(571\) 11.8830 0.497288 0.248644 0.968595i \(-0.420015\pi\)
0.248644 + 0.968595i \(0.420015\pi\)
\(572\) 6.18738 0.258707
\(573\) −49.6876 −2.07573
\(574\) −9.57618 −0.399702
\(575\) 3.91615 0.163315
\(576\) −13.5087 −0.562863
\(577\) 25.3055 1.05348 0.526741 0.850026i \(-0.323414\pi\)
0.526741 + 0.850026i \(0.323414\pi\)
\(578\) 13.1982 0.548973
\(579\) −8.81160 −0.366198
\(580\) −40.1409 −1.66676
\(581\) 0.715863 0.0296990
\(582\) 58.5403 2.42657
\(583\) 18.5715 0.769153
\(584\) −23.1369 −0.957412
\(585\) −1.56329 −0.0646343
\(586\) −10.0097 −0.413497
\(587\) −8.79091 −0.362840 −0.181420 0.983406i \(-0.558069\pi\)
−0.181420 + 0.983406i \(0.558069\pi\)
\(588\) 8.07740 0.333106
\(589\) −10.8927 −0.448826
\(590\) −14.4682 −0.595645
\(591\) −12.1993 −0.501814
\(592\) 10.9513 0.450096
\(593\) 17.6922 0.726531 0.363265 0.931686i \(-0.381662\pi\)
0.363265 + 0.931686i \(0.381662\pi\)
\(594\) 12.0398 0.494001
\(595\) −3.49881 −0.143437
\(596\) 14.0365 0.574956
\(597\) −23.2592 −0.951935
\(598\) 2.60142 0.106380
\(599\) −19.2824 −0.787858 −0.393929 0.919141i \(-0.628884\pi\)
−0.393929 + 0.919141i \(0.628884\pi\)
\(600\) 36.9752 1.50951
\(601\) −20.0154 −0.816444 −0.408222 0.912883i \(-0.633851\pi\)
−0.408222 + 0.912883i \(0.633851\pi\)
\(602\) −22.5112 −0.917488
\(603\) 0.147131 0.00599162
\(604\) 54.0725 2.20018
\(605\) 9.05548 0.368158
\(606\) −16.7371 −0.679898
\(607\) 27.4368 1.11362 0.556812 0.830638i \(-0.312024\pi\)
0.556812 + 0.830638i \(0.312024\pi\)
\(608\) −2.66174 −0.107948
\(609\) −21.2470 −0.860974
\(610\) 17.1603 0.694802
\(611\) −1.30574 −0.0528246
\(612\) −18.3487 −0.741701
\(613\) 8.68507 0.350787 0.175393 0.984498i \(-0.443880\pi\)
0.175393 + 0.984498i \(0.443880\pi\)
\(614\) 16.2548 0.655990
\(615\) 8.55598 0.345010
\(616\) 6.64473 0.267724
\(617\) −16.4522 −0.662341 −0.331170 0.943571i \(-0.607444\pi\)
−0.331170 + 0.943571i \(0.607444\pi\)
\(618\) −6.40634 −0.257701
\(619\) −27.2271 −1.09435 −0.547175 0.837018i \(-0.684297\pi\)
−0.547175 + 0.837018i \(0.684297\pi\)
\(620\) −22.7386 −0.913203
\(621\) 3.33126 0.133679
\(622\) −49.5262 −1.98582
\(623\) 15.1763 0.608025
\(624\) 7.08226 0.283517
\(625\) 10.2167 0.408669
\(626\) −7.35565 −0.293991
\(627\) −5.91947 −0.236401
\(628\) 31.0088 1.23739
\(629\) −11.9277 −0.475589
\(630\) −3.49436 −0.139218
\(631\) −41.3731 −1.64704 −0.823518 0.567289i \(-0.807992\pi\)
−0.823518 + 0.567289i \(0.807992\pi\)
\(632\) 53.9966 2.14787
\(633\) −3.31205 −0.131642
\(634\) 58.5918 2.32698
\(635\) 16.1457 0.640722
\(636\) 100.982 4.00418
\(637\) 1.08201 0.0428708
\(638\) −36.3798 −1.44029
\(639\) −4.65564 −0.184174
\(640\) −21.0952 −0.833861
\(641\) 45.3067 1.78951 0.894754 0.446560i \(-0.147351\pi\)
0.894754 + 0.446560i \(0.147351\pi\)
\(642\) −27.7391 −1.09477
\(643\) 5.71604 0.225418 0.112709 0.993628i \(-0.464047\pi\)
0.112709 + 0.993628i \(0.464047\pi\)
\(644\) 3.82667 0.150792
\(645\) 20.1130 0.791947
\(646\) −15.6045 −0.613951
\(647\) −7.42167 −0.291776 −0.145888 0.989301i \(-0.546604\pi\)
−0.145888 + 0.989301i \(0.546604\pi\)
\(648\) 50.2793 1.97516
\(649\) −8.62920 −0.338726
\(650\) 10.3092 0.404361
\(651\) −12.0358 −0.471720
\(652\) −29.3185 −1.14820
\(653\) −43.2905 −1.69409 −0.847044 0.531523i \(-0.821620\pi\)
−0.847044 + 0.531523i \(0.821620\pi\)
\(654\) −11.5689 −0.452381
\(655\) 14.9390 0.583713
\(656\) −12.3510 −0.482226
\(657\) 7.25691 0.283119
\(658\) −2.91866 −0.113781
\(659\) −3.31724 −0.129221 −0.0646107 0.997911i \(-0.520581\pi\)
−0.0646107 + 0.997911i \(0.520581\pi\)
\(660\) −12.3569 −0.480993
\(661\) 35.2547 1.37125 0.685625 0.727955i \(-0.259529\pi\)
0.685625 + 0.727955i \(0.259529\pi\)
\(662\) −49.4727 −1.92281
\(663\) −7.71370 −0.299575
\(664\) 3.20207 0.124264
\(665\) −1.95567 −0.0758377
\(666\) −11.9125 −0.461600
\(667\) −10.0658 −0.389749
\(668\) −66.4293 −2.57023
\(669\) −33.3878 −1.29085
\(670\) 0.261201 0.0100911
\(671\) 10.2349 0.395113
\(672\) −2.94107 −0.113454
\(673\) 12.7403 0.491103 0.245552 0.969384i \(-0.421031\pi\)
0.245552 + 0.969384i \(0.421031\pi\)
\(674\) −3.42673 −0.131993
\(675\) 13.2015 0.508127
\(676\) −45.5361 −1.75139
\(677\) −41.8809 −1.60961 −0.804806 0.593538i \(-0.797731\pi\)
−0.804806 + 0.593538i \(0.797731\pi\)
\(678\) −103.402 −3.97114
\(679\) 11.5352 0.442680
\(680\) −15.6502 −0.600160
\(681\) −25.5465 −0.978943
\(682\) −20.6080 −0.789122
\(683\) 23.1358 0.885268 0.442634 0.896702i \(-0.354044\pi\)
0.442634 + 0.896702i \(0.354044\pi\)
\(684\) −10.2560 −0.392149
\(685\) −9.43657 −0.360553
\(686\) 2.41856 0.0923412
\(687\) −55.6908 −2.12474
\(688\) −29.0341 −1.10692
\(689\) 13.5270 0.515338
\(690\) −5.19535 −0.197783
\(691\) −33.2244 −1.26392 −0.631959 0.775002i \(-0.717749\pi\)
−0.631959 + 0.775002i \(0.717749\pi\)
\(692\) 38.6231 1.46823
\(693\) −2.08413 −0.0791694
\(694\) −12.6896 −0.481689
\(695\) 13.3364 0.505880
\(696\) −95.0384 −3.60242
\(697\) 13.4522 0.509538
\(698\) 77.6698 2.93985
\(699\) 61.4968 2.32602
\(700\) 15.1648 0.573175
\(701\) −24.2115 −0.914455 −0.457227 0.889350i \(-0.651157\pi\)
−0.457227 + 0.889350i \(0.651157\pi\)
\(702\) 8.76952 0.330984
\(703\) −6.66702 −0.251451
\(704\) −14.3035 −0.539084
\(705\) 2.60772 0.0982123
\(706\) 58.3465 2.19590
\(707\) −3.29800 −0.124034
\(708\) −46.9208 −1.76339
\(709\) −1.17792 −0.0442378 −0.0221189 0.999755i \(-0.507041\pi\)
−0.0221189 + 0.999755i \(0.507041\pi\)
\(710\) −8.26516 −0.310186
\(711\) −16.9361 −0.635153
\(712\) 67.8838 2.54405
\(713\) −5.70196 −0.213540
\(714\) −17.2420 −0.645267
\(715\) −1.65528 −0.0619038
\(716\) −77.9299 −2.91238
\(717\) −17.4625 −0.652149
\(718\) 40.4099 1.50808
\(719\) −25.2437 −0.941430 −0.470715 0.882285i \(-0.656004\pi\)
−0.470715 + 0.882285i \(0.656004\pi\)
\(720\) −4.50689 −0.167962
\(721\) −1.26235 −0.0470124
\(722\) 37.2305 1.38558
\(723\) 20.9506 0.779160
\(724\) −73.3208 −2.72494
\(725\) −39.8899 −1.48147
\(726\) 44.6251 1.65619
\(727\) −31.3492 −1.16268 −0.581339 0.813662i \(-0.697471\pi\)
−0.581339 + 0.813662i \(0.697471\pi\)
\(728\) 4.83985 0.179377
\(729\) 5.32489 0.197218
\(730\) 12.8832 0.476829
\(731\) 31.6227 1.16961
\(732\) 55.6516 2.05694
\(733\) −23.6872 −0.874907 −0.437454 0.899241i \(-0.644120\pi\)
−0.437454 + 0.899241i \(0.644120\pi\)
\(734\) 66.4205 2.45162
\(735\) −2.16090 −0.0797060
\(736\) −1.39333 −0.0513589
\(737\) 0.155787 0.00573850
\(738\) 13.4351 0.494551
\(739\) 53.7040 1.97553 0.987767 0.155940i \(-0.0498406\pi\)
0.987767 + 0.155940i \(0.0498406\pi\)
\(740\) −13.9174 −0.511615
\(741\) −4.31159 −0.158390
\(742\) 30.2362 1.11001
\(743\) −6.56075 −0.240690 −0.120345 0.992732i \(-0.538400\pi\)
−0.120345 + 0.992732i \(0.538400\pi\)
\(744\) −53.8363 −1.97373
\(745\) −3.75510 −0.137576
\(746\) −21.4455 −0.785175
\(747\) −1.00433 −0.0367466
\(748\) −19.4283 −0.710368
\(749\) −5.46590 −0.199720
\(750\) −46.7201 −1.70598
\(751\) −20.3400 −0.742216 −0.371108 0.928590i \(-0.621022\pi\)
−0.371108 + 0.928590i \(0.621022\pi\)
\(752\) −3.76438 −0.137273
\(753\) 32.2071 1.17369
\(754\) −26.4981 −0.965004
\(755\) −14.4657 −0.526461
\(756\) 12.8999 0.469164
\(757\) 45.4955 1.65356 0.826781 0.562525i \(-0.190170\pi\)
0.826781 + 0.562525i \(0.190170\pi\)
\(758\) 46.8367 1.70119
\(759\) −3.09864 −0.112474
\(760\) −8.74775 −0.317314
\(761\) 44.8309 1.62512 0.812560 0.582878i \(-0.198074\pi\)
0.812560 + 0.582878i \(0.198074\pi\)
\(762\) 79.5655 2.88235
\(763\) −2.27962 −0.0825279
\(764\) −91.1537 −3.29782
\(765\) 4.90872 0.177475
\(766\) −69.0811 −2.49600
\(767\) −6.28529 −0.226949
\(768\) −63.5483 −2.29310
\(769\) 43.3073 1.56170 0.780851 0.624717i \(-0.214786\pi\)
0.780851 + 0.624717i \(0.214786\pi\)
\(770\) −3.69996 −0.133337
\(771\) 42.3009 1.52343
\(772\) −16.1652 −0.581798
\(773\) 13.2332 0.475964 0.237982 0.971270i \(-0.423514\pi\)
0.237982 + 0.971270i \(0.423514\pi\)
\(774\) 31.5825 1.13521
\(775\) −22.5964 −0.811687
\(776\) 51.5971 1.85223
\(777\) −7.36667 −0.264278
\(778\) −25.9258 −0.929484
\(779\) 7.51914 0.269401
\(780\) −9.00047 −0.322269
\(781\) −4.92956 −0.176394
\(782\) −8.16842 −0.292102
\(783\) −33.9322 −1.21264
\(784\) 3.11937 0.111406
\(785\) −8.29561 −0.296083
\(786\) 73.6187 2.62589
\(787\) 20.9538 0.746924 0.373462 0.927646i \(-0.378171\pi\)
0.373462 + 0.927646i \(0.378171\pi\)
\(788\) −22.3801 −0.797259
\(789\) −27.6678 −0.985001
\(790\) −30.0667 −1.06972
\(791\) −20.3751 −0.724455
\(792\) −9.32233 −0.331255
\(793\) 7.45483 0.264729
\(794\) −39.2099 −1.39151
\(795\) −27.0150 −0.958124
\(796\) −42.6698 −1.51239
\(797\) −38.8134 −1.37484 −0.687420 0.726260i \(-0.741257\pi\)
−0.687420 + 0.726260i \(0.741257\pi\)
\(798\) −9.63749 −0.341163
\(799\) 4.10000 0.145048
\(800\) −5.52166 −0.195220
\(801\) −21.2918 −0.752309
\(802\) 37.7994 1.33474
\(803\) 7.68389 0.271159
\(804\) 0.847085 0.0298744
\(805\) −1.02373 −0.0360817
\(806\) −15.0104 −0.528717
\(807\) −50.4742 −1.77678
\(808\) −14.7520 −0.518973
\(809\) −43.5265 −1.53031 −0.765156 0.643845i \(-0.777338\pi\)
−0.765156 + 0.643845i \(0.777338\pi\)
\(810\) −27.9968 −0.983708
\(811\) −19.7701 −0.694222 −0.347111 0.937824i \(-0.612837\pi\)
−0.347111 + 0.937824i \(0.612837\pi\)
\(812\) −38.9785 −1.36788
\(813\) 55.7579 1.95551
\(814\) −12.6134 −0.442100
\(815\) 7.84341 0.274743
\(816\) −22.2382 −0.778491
\(817\) 17.6756 0.618392
\(818\) 56.7523 1.98430
\(819\) −1.51802 −0.0530441
\(820\) 15.6962 0.548137
\(821\) 8.08980 0.282336 0.141168 0.989986i \(-0.454914\pi\)
0.141168 + 0.989986i \(0.454914\pi\)
\(822\) −46.5031 −1.62198
\(823\) −3.15390 −0.109938 −0.0549691 0.998488i \(-0.517506\pi\)
−0.0549691 + 0.998488i \(0.517506\pi\)
\(824\) −5.64652 −0.196706
\(825\) −12.2797 −0.427523
\(826\) −14.0492 −0.488834
\(827\) 21.4195 0.744829 0.372415 0.928066i \(-0.378530\pi\)
0.372415 + 0.928066i \(0.378530\pi\)
\(828\) −5.36869 −0.186575
\(829\) −48.7102 −1.69178 −0.845888 0.533360i \(-0.820929\pi\)
−0.845888 + 0.533360i \(0.820929\pi\)
\(830\) −1.78299 −0.0618886
\(831\) −12.6407 −0.438501
\(832\) −10.4183 −0.361190
\(833\) −3.39749 −0.117716
\(834\) 65.7215 2.27575
\(835\) 17.7715 0.615007
\(836\) −10.8595 −0.375583
\(837\) −19.2216 −0.664395
\(838\) 0.211919 0.00732061
\(839\) 4.02063 0.138808 0.0694038 0.997589i \(-0.477890\pi\)
0.0694038 + 0.997589i \(0.477890\pi\)
\(840\) −9.66575 −0.333500
\(841\) 73.5302 2.53552
\(842\) −19.1061 −0.658440
\(843\) 48.2261 1.66099
\(844\) −6.07608 −0.209147
\(845\) 12.1820 0.419074
\(846\) 4.09478 0.140781
\(847\) 8.79325 0.302140
\(848\) 38.9976 1.33918
\(849\) −27.8779 −0.956767
\(850\) −32.3708 −1.11031
\(851\) −3.48996 −0.119634
\(852\) −26.8042 −0.918298
\(853\) 34.4443 1.17935 0.589675 0.807641i \(-0.299256\pi\)
0.589675 + 0.807641i \(0.299256\pi\)
\(854\) 16.6634 0.570210
\(855\) 2.74374 0.0938340
\(856\) −24.4491 −0.835652
\(857\) −53.3128 −1.82113 −0.910565 0.413367i \(-0.864353\pi\)
−0.910565 + 0.413367i \(0.864353\pi\)
\(858\) −8.15715 −0.278480
\(859\) 19.6093 0.669062 0.334531 0.942385i \(-0.391422\pi\)
0.334531 + 0.942385i \(0.391422\pi\)
\(860\) 36.8979 1.25821
\(861\) 8.30821 0.283143
\(862\) −45.6480 −1.55478
\(863\) −1.00000 −0.0340404
\(864\) −4.69699 −0.159795
\(865\) −10.3326 −0.351320
\(866\) 19.0631 0.647791
\(867\) −11.4507 −0.388885
\(868\) −22.0801 −0.749447
\(869\) −17.9326 −0.608320
\(870\) 52.9198 1.79415
\(871\) 0.113472 0.00384484
\(872\) −10.1968 −0.345307
\(873\) −16.1835 −0.547728
\(874\) −4.56576 −0.154439
\(875\) −9.20606 −0.311222
\(876\) 41.7807 1.41164
\(877\) 33.6985 1.13792 0.568960 0.822365i \(-0.307346\pi\)
0.568960 + 0.822365i \(0.307346\pi\)
\(878\) −79.1691 −2.67183
\(879\) 8.68433 0.292915
\(880\) −4.77207 −0.160866
\(881\) 42.2511 1.42348 0.711738 0.702445i \(-0.247908\pi\)
0.711738 + 0.702445i \(0.247908\pi\)
\(882\) −3.39316 −0.114254
\(883\) −47.5207 −1.59920 −0.799600 0.600533i \(-0.794955\pi\)
−0.799600 + 0.600533i \(0.794955\pi\)
\(884\) −14.1511 −0.475951
\(885\) 12.5525 0.421946
\(886\) −65.4015 −2.19720
\(887\) 16.8097 0.564414 0.282207 0.959354i \(-0.408934\pi\)
0.282207 + 0.959354i \(0.408934\pi\)
\(888\) −32.9512 −1.10577
\(889\) 15.6781 0.525828
\(890\) −37.7994 −1.26704
\(891\) −16.6980 −0.559405
\(892\) −61.2511 −2.05084
\(893\) 2.29171 0.0766891
\(894\) −18.5050 −0.618900
\(895\) 20.8481 0.696877
\(896\) −20.4843 −0.684333
\(897\) −2.25697 −0.0753581
\(898\) −56.8863 −1.89832
\(899\) 58.0802 1.93708
\(900\) −21.2757 −0.709189
\(901\) −42.4745 −1.41503
\(902\) 14.2255 0.473659
\(903\) 19.5305 0.649935
\(904\) −91.1382 −3.03121
\(905\) 19.6151 0.652028
\(906\) −71.2866 −2.36834
\(907\) 53.3866 1.77267 0.886336 0.463042i \(-0.153242\pi\)
0.886336 + 0.463042i \(0.153242\pi\)
\(908\) −46.8659 −1.55530
\(909\) 4.62698 0.153467
\(910\) −2.69495 −0.0893368
\(911\) −10.8268 −0.358707 −0.179353 0.983785i \(-0.557401\pi\)
−0.179353 + 0.983785i \(0.557401\pi\)
\(912\) −12.4301 −0.411601
\(913\) −1.06342 −0.0351942
\(914\) −38.8746 −1.28586
\(915\) −14.8882 −0.492188
\(916\) −102.167 −3.37569
\(917\) 14.5064 0.479042
\(918\) −27.5361 −0.908827
\(919\) −53.8490 −1.77631 −0.888157 0.459541i \(-0.848014\pi\)
−0.888157 + 0.459541i \(0.848014\pi\)
\(920\) −4.57915 −0.150970
\(921\) −14.1025 −0.464694
\(922\) 25.8020 0.849745
\(923\) −3.59057 −0.118185
\(924\) −11.9991 −0.394741
\(925\) −13.8304 −0.454742
\(926\) −12.5647 −0.412903
\(927\) 1.77104 0.0581684
\(928\) 14.1925 0.465891
\(929\) −56.5111 −1.85407 −0.927035 0.374974i \(-0.877651\pi\)
−0.927035 + 0.374974i \(0.877651\pi\)
\(930\) 29.9774 0.982999
\(931\) −1.89904 −0.0622384
\(932\) 112.818 3.69548
\(933\) 42.9685 1.40672
\(934\) −2.78456 −0.0911135
\(935\) 5.19753 0.169978
\(936\) −6.79015 −0.221943
\(937\) −26.7929 −0.875287 −0.437643 0.899149i \(-0.644187\pi\)
−0.437643 + 0.899149i \(0.644187\pi\)
\(938\) 0.253637 0.00828155
\(939\) 6.38170 0.208259
\(940\) 4.78395 0.156035
\(941\) 16.3860 0.534169 0.267084 0.963673i \(-0.413940\pi\)
0.267084 + 0.963673i \(0.413940\pi\)
\(942\) −40.8805 −1.33196
\(943\) 3.93602 0.128174
\(944\) −18.1201 −0.589760
\(945\) −3.45103 −0.112262
\(946\) 33.4407 1.08725
\(947\) 11.2918 0.366935 0.183467 0.983026i \(-0.441268\pi\)
0.183467 + 0.983026i \(0.441268\pi\)
\(948\) −97.5073 −3.16689
\(949\) 5.59675 0.181678
\(950\) −18.0937 −0.587039
\(951\) −50.8337 −1.64840
\(952\) −15.1970 −0.492539
\(953\) 49.5611 1.60544 0.802721 0.596355i \(-0.203385\pi\)
0.802721 + 0.596355i \(0.203385\pi\)
\(954\) −42.4204 −1.37341
\(955\) 24.3858 0.789107
\(956\) −32.0356 −1.03611
\(957\) 31.5628 1.02028
\(958\) −54.9134 −1.77417
\(959\) −9.16330 −0.295898
\(960\) 20.8066 0.671531
\(961\) 1.90062 0.0613103
\(962\) −9.18729 −0.296210
\(963\) 7.66848 0.247113
\(964\) 38.4346 1.23789
\(965\) 4.32459 0.139213
\(966\) −5.04490 −0.162317
\(967\) 2.95115 0.0949024 0.0474512 0.998874i \(-0.484890\pi\)
0.0474512 + 0.998874i \(0.484890\pi\)
\(968\) 39.3324 1.26419
\(969\) 13.5383 0.434913
\(970\) −28.7306 −0.922484
\(971\) −46.4932 −1.49204 −0.746019 0.665925i \(-0.768037\pi\)
−0.746019 + 0.665925i \(0.768037\pi\)
\(972\) −52.0951 −1.67095
\(973\) 12.9502 0.415165
\(974\) −22.5103 −0.721277
\(975\) −8.94420 −0.286444
\(976\) 21.4919 0.687937
\(977\) −24.2919 −0.777168 −0.388584 0.921413i \(-0.627036\pi\)
−0.388584 + 0.921413i \(0.627036\pi\)
\(978\) 38.6521 1.23596
\(979\) −22.5446 −0.720528
\(980\) −3.96425 −0.126633
\(981\) 3.19824 0.102112
\(982\) −75.7001 −2.41569
\(983\) 17.3581 0.553638 0.276819 0.960922i \(-0.410720\pi\)
0.276819 + 0.960922i \(0.410720\pi\)
\(984\) 37.1628 1.18471
\(985\) 5.98723 0.190769
\(986\) 83.2036 2.64974
\(987\) 2.53220 0.0806009
\(988\) −7.90977 −0.251643
\(989\) 9.25259 0.294215
\(990\) 5.19091 0.164978
\(991\) −2.14789 −0.0682300 −0.0341150 0.999418i \(-0.510861\pi\)
−0.0341150 + 0.999418i \(0.510861\pi\)
\(992\) 8.03960 0.255258
\(993\) 42.9220 1.36209
\(994\) −8.02582 −0.254563
\(995\) 11.4152 0.361886
\(996\) −5.78231 −0.183219
\(997\) 28.3117 0.896641 0.448321 0.893873i \(-0.352022\pi\)
0.448321 + 0.893873i \(0.352022\pi\)
\(998\) 104.497 3.30781
\(999\) −11.7648 −0.372222
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 6041.2.a.d.1.7 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6041.2.a.d.1.7 101 1.1 even 1 trivial