Properties

Label 6013.2.a.c.1.5
Level $6013$
Weight $2$
Character 6013.1
Self dual yes
Analytic conductor $48.014$
Analytic rank $1$
Dimension $104$
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] = [6013,2,Mod(1,6013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6013, 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("6013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6013 = 7 \cdot 859 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6013.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: \(48.0140467354\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.68972 q^{2} +2.91852 q^{3} +5.23459 q^{4} +0.347371 q^{5} -7.85000 q^{6} -1.00000 q^{7} -8.70012 q^{8} +5.51776 q^{9} +O(q^{10})\) \(q-2.68972 q^{2} +2.91852 q^{3} +5.23459 q^{4} +0.347371 q^{5} -7.85000 q^{6} -1.00000 q^{7} -8.70012 q^{8} +5.51776 q^{9} -0.934329 q^{10} -5.00686 q^{11} +15.2772 q^{12} +1.86596 q^{13} +2.68972 q^{14} +1.01381 q^{15} +12.9317 q^{16} -2.63199 q^{17} -14.8412 q^{18} +4.88633 q^{19} +1.81834 q^{20} -2.91852 q^{21} +13.4671 q^{22} -0.974596 q^{23} -25.3915 q^{24} -4.87933 q^{25} -5.01891 q^{26} +7.34813 q^{27} -5.23459 q^{28} +1.26823 q^{29} -2.72686 q^{30} +8.76330 q^{31} -17.3824 q^{32} -14.6126 q^{33} +7.07931 q^{34} -0.347371 q^{35} +28.8832 q^{36} -8.53839 q^{37} -13.1429 q^{38} +5.44585 q^{39} -3.02217 q^{40} +6.41252 q^{41} +7.85000 q^{42} -9.81142 q^{43} -26.2089 q^{44} +1.91671 q^{45} +2.62139 q^{46} -11.5629 q^{47} +37.7415 q^{48} +1.00000 q^{49} +13.1240 q^{50} -7.68151 q^{51} +9.76754 q^{52} -11.6945 q^{53} -19.7644 q^{54} -1.73924 q^{55} +8.70012 q^{56} +14.2609 q^{57} -3.41119 q^{58} -8.80181 q^{59} +5.30687 q^{60} +2.06284 q^{61} -23.5708 q^{62} -5.51776 q^{63} +20.8904 q^{64} +0.648180 q^{65} +39.3039 q^{66} -4.30305 q^{67} -13.7774 q^{68} -2.84438 q^{69} +0.934329 q^{70} -13.4124 q^{71} -48.0052 q^{72} -9.89942 q^{73} +22.9659 q^{74} -14.2404 q^{75} +25.5779 q^{76} +5.00686 q^{77} -14.6478 q^{78} +10.6020 q^{79} +4.49210 q^{80} +4.89239 q^{81} -17.2479 q^{82} +6.24115 q^{83} -15.2772 q^{84} -0.914275 q^{85} +26.3900 q^{86} +3.70136 q^{87} +43.5603 q^{88} -0.489483 q^{89} -5.15540 q^{90} -1.86596 q^{91} -5.10161 q^{92} +25.5759 q^{93} +31.1011 q^{94} +1.69737 q^{95} -50.7309 q^{96} +4.93383 q^{97} -2.68972 q^{98} -27.6267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68972 −1.90192 −0.950959 0.309317i \(-0.899900\pi\)
−0.950959 + 0.309317i \(0.899900\pi\)
\(3\) 2.91852 1.68501 0.842504 0.538690i \(-0.181081\pi\)
0.842504 + 0.538690i \(0.181081\pi\)
\(4\) 5.23459 2.61729
\(5\) 0.347371 0.155349 0.0776744 0.996979i \(-0.475251\pi\)
0.0776744 + 0.996979i \(0.475251\pi\)
\(6\) −7.85000 −3.20475
\(7\) −1.00000 −0.377964
\(8\) −8.70012 −3.07596
\(9\) 5.51776 1.83925
\(10\) −0.934329 −0.295461
\(11\) −5.00686 −1.50963 −0.754813 0.655940i \(-0.772272\pi\)
−0.754813 + 0.655940i \(0.772272\pi\)
\(12\) 15.2772 4.41016
\(13\) 1.86596 0.517525 0.258762 0.965941i \(-0.416685\pi\)
0.258762 + 0.965941i \(0.416685\pi\)
\(14\) 2.68972 0.718858
\(15\) 1.01381 0.261764
\(16\) 12.9317 3.23293
\(17\) −2.63199 −0.638351 −0.319175 0.947696i \(-0.603406\pi\)
−0.319175 + 0.947696i \(0.603406\pi\)
\(18\) −14.8412 −3.49811
\(19\) 4.88633 1.12100 0.560501 0.828154i \(-0.310609\pi\)
0.560501 + 0.828154i \(0.310609\pi\)
\(20\) 1.81834 0.406593
\(21\) −2.91852 −0.636873
\(22\) 13.4671 2.87119
\(23\) −0.974596 −0.203217 −0.101609 0.994824i \(-0.532399\pi\)
−0.101609 + 0.994824i \(0.532399\pi\)
\(24\) −25.3915 −5.18302
\(25\) −4.87933 −0.975867
\(26\) −5.01891 −0.984289
\(27\) 7.34813 1.41415
\(28\) −5.23459 −0.989244
\(29\) 1.26823 0.235505 0.117753 0.993043i \(-0.462431\pi\)
0.117753 + 0.993043i \(0.462431\pi\)
\(30\) −2.72686 −0.497854
\(31\) 8.76330 1.57393 0.786967 0.616995i \(-0.211650\pi\)
0.786967 + 0.616995i \(0.211650\pi\)
\(32\) −17.3824 −3.07281
\(33\) −14.6126 −2.54373
\(34\) 7.07931 1.21409
\(35\) −0.347371 −0.0587164
\(36\) 28.8832 4.81386
\(37\) −8.53839 −1.40370 −0.701851 0.712324i \(-0.747643\pi\)
−0.701851 + 0.712324i \(0.747643\pi\)
\(38\) −13.1429 −2.13205
\(39\) 5.44585 0.872033
\(40\) −3.02217 −0.477847
\(41\) 6.41252 1.00147 0.500734 0.865601i \(-0.333063\pi\)
0.500734 + 0.865601i \(0.333063\pi\)
\(42\) 7.85000 1.21128
\(43\) −9.81142 −1.49623 −0.748114 0.663570i \(-0.769040\pi\)
−0.748114 + 0.663570i \(0.769040\pi\)
\(44\) −26.2089 −3.95113
\(45\) 1.91671 0.285726
\(46\) 2.62139 0.386503
\(47\) −11.5629 −1.68663 −0.843314 0.537421i \(-0.819399\pi\)
−0.843314 + 0.537421i \(0.819399\pi\)
\(48\) 37.7415 5.44751
\(49\) 1.00000 0.142857
\(50\) 13.1240 1.85602
\(51\) −7.68151 −1.07563
\(52\) 9.76754 1.35451
\(53\) −11.6945 −1.60636 −0.803180 0.595737i \(-0.796860\pi\)
−0.803180 + 0.595737i \(0.796860\pi\)
\(54\) −19.7644 −2.68959
\(55\) −1.73924 −0.234519
\(56\) 8.70012 1.16260
\(57\) 14.2609 1.88890
\(58\) −3.41119 −0.447911
\(59\) −8.80181 −1.14590 −0.572949 0.819591i \(-0.694201\pi\)
−0.572949 + 0.819591i \(0.694201\pi\)
\(60\) 5.30687 0.685113
\(61\) 2.06284 0.264119 0.132060 0.991242i \(-0.457841\pi\)
0.132060 + 0.991242i \(0.457841\pi\)
\(62\) −23.5708 −2.99349
\(63\) −5.51776 −0.695172
\(64\) 20.8904 2.61130
\(65\) 0.648180 0.0803969
\(66\) 39.3039 4.83797
\(67\) −4.30305 −0.525702 −0.262851 0.964837i \(-0.584663\pi\)
−0.262851 + 0.964837i \(0.584663\pi\)
\(68\) −13.7774 −1.67075
\(69\) −2.84438 −0.342423
\(70\) 0.934329 0.111674
\(71\) −13.4124 −1.59176 −0.795879 0.605456i \(-0.792991\pi\)
−0.795879 + 0.605456i \(0.792991\pi\)
\(72\) −48.0052 −5.65747
\(73\) −9.89942 −1.15864 −0.579320 0.815100i \(-0.696682\pi\)
−0.579320 + 0.815100i \(0.696682\pi\)
\(74\) 22.9659 2.66973
\(75\) −14.2404 −1.64434
\(76\) 25.5779 2.93399
\(77\) 5.00686 0.570585
\(78\) −14.6478 −1.65854
\(79\) 10.6020 1.19282 0.596411 0.802679i \(-0.296593\pi\)
0.596411 + 0.802679i \(0.296593\pi\)
\(80\) 4.49210 0.502232
\(81\) 4.89239 0.543599
\(82\) −17.2479 −1.90471
\(83\) 6.24115 0.685056 0.342528 0.939508i \(-0.388717\pi\)
0.342528 + 0.939508i \(0.388717\pi\)
\(84\) −15.2772 −1.66688
\(85\) −0.914275 −0.0991671
\(86\) 26.3900 2.84570
\(87\) 3.70136 0.396828
\(88\) 43.5603 4.64355
\(89\) −0.489483 −0.0518851 −0.0259425 0.999663i \(-0.508259\pi\)
−0.0259425 + 0.999663i \(0.508259\pi\)
\(90\) −5.15540 −0.543427
\(91\) −1.86596 −0.195606
\(92\) −5.10161 −0.531879
\(93\) 25.5759 2.65209
\(94\) 31.1011 3.20783
\(95\) 1.69737 0.174146
\(96\) −50.7309 −5.17771
\(97\) 4.93383 0.500954 0.250477 0.968122i \(-0.419412\pi\)
0.250477 + 0.968122i \(0.419412\pi\)
\(98\) −2.68972 −0.271703
\(99\) −27.6267 −2.77658
\(100\) −25.5413 −2.55413
\(101\) 11.8590 1.18002 0.590008 0.807398i \(-0.299125\pi\)
0.590008 + 0.807398i \(0.299125\pi\)
\(102\) 20.6611 2.04575
\(103\) −1.84566 −0.181858 −0.0909292 0.995857i \(-0.528984\pi\)
−0.0909292 + 0.995857i \(0.528984\pi\)
\(104\) −16.2341 −1.59188
\(105\) −1.01381 −0.0989375
\(106\) 31.4548 3.05516
\(107\) −1.62930 −0.157510 −0.0787550 0.996894i \(-0.525094\pi\)
−0.0787550 + 0.996894i \(0.525094\pi\)
\(108\) 38.4644 3.70124
\(109\) 2.27781 0.218175 0.109087 0.994032i \(-0.465207\pi\)
0.109087 + 0.994032i \(0.465207\pi\)
\(110\) 4.67806 0.446035
\(111\) −24.9195 −2.36525
\(112\) −12.9317 −1.22193
\(113\) 4.35334 0.409528 0.204764 0.978811i \(-0.434357\pi\)
0.204764 + 0.978811i \(0.434357\pi\)
\(114\) −38.3577 −3.59253
\(115\) −0.338546 −0.0315696
\(116\) 6.63868 0.616386
\(117\) 10.2959 0.951859
\(118\) 23.6744 2.17940
\(119\) 2.63199 0.241274
\(120\) −8.82026 −0.805176
\(121\) 14.0687 1.27897
\(122\) −5.54845 −0.502333
\(123\) 18.7151 1.68748
\(124\) 45.8722 4.11945
\(125\) −3.43179 −0.306949
\(126\) 14.8412 1.32216
\(127\) −0.392058 −0.0347895 −0.0173948 0.999849i \(-0.505537\pi\)
−0.0173948 + 0.999849i \(0.505537\pi\)
\(128\) −21.4244 −1.89367
\(129\) −28.6348 −2.52116
\(130\) −1.74342 −0.152908
\(131\) 20.8045 1.81770 0.908848 0.417128i \(-0.136963\pi\)
0.908848 + 0.417128i \(0.136963\pi\)
\(132\) −76.4911 −6.65769
\(133\) −4.88633 −0.423699
\(134\) 11.5740 0.999841
\(135\) 2.55252 0.219686
\(136\) 22.8986 1.96354
\(137\) −13.2735 −1.13403 −0.567014 0.823708i \(-0.691902\pi\)
−0.567014 + 0.823708i \(0.691902\pi\)
\(138\) 7.65058 0.651260
\(139\) −19.0691 −1.61742 −0.808710 0.588208i \(-0.799834\pi\)
−0.808710 + 0.588208i \(0.799834\pi\)
\(140\) −1.81834 −0.153678
\(141\) −33.7467 −2.84198
\(142\) 36.0755 3.02739
\(143\) −9.34261 −0.781269
\(144\) 71.3541 5.94617
\(145\) 0.440547 0.0365854
\(146\) 26.6267 2.20364
\(147\) 2.91852 0.240715
\(148\) −44.6949 −3.67390
\(149\) −3.85461 −0.315782 −0.157891 0.987457i \(-0.550470\pi\)
−0.157891 + 0.987457i \(0.550470\pi\)
\(150\) 38.3028 3.12741
\(151\) 12.3272 1.00317 0.501586 0.865108i \(-0.332750\pi\)
0.501586 + 0.865108i \(0.332750\pi\)
\(152\) −42.5117 −3.44815
\(153\) −14.5227 −1.17409
\(154\) −13.4671 −1.08521
\(155\) 3.04411 0.244509
\(156\) 28.5067 2.28237
\(157\) −4.76344 −0.380164 −0.190082 0.981768i \(-0.560875\pi\)
−0.190082 + 0.981768i \(0.560875\pi\)
\(158\) −28.5165 −2.26865
\(159\) −34.1305 −2.70673
\(160\) −6.03814 −0.477357
\(161\) 0.974596 0.0768089
\(162\) −13.1591 −1.03388
\(163\) 12.5149 0.980242 0.490121 0.871654i \(-0.336953\pi\)
0.490121 + 0.871654i \(0.336953\pi\)
\(164\) 33.5669 2.62113
\(165\) −5.07600 −0.395166
\(166\) −16.7869 −1.30292
\(167\) −23.4047 −1.81111 −0.905554 0.424232i \(-0.860544\pi\)
−0.905554 + 0.424232i \(0.860544\pi\)
\(168\) 25.3915 1.95900
\(169\) −9.51819 −0.732168
\(170\) 2.45914 0.188608
\(171\) 26.9616 2.06180
\(172\) −51.3587 −3.91607
\(173\) −1.24837 −0.0949120 −0.0474560 0.998873i \(-0.515111\pi\)
−0.0474560 + 0.998873i \(0.515111\pi\)
\(174\) −9.95563 −0.754734
\(175\) 4.87933 0.368843
\(176\) −64.7473 −4.88051
\(177\) −25.6883 −1.93085
\(178\) 1.31657 0.0986812
\(179\) 16.0148 1.19701 0.598503 0.801121i \(-0.295763\pi\)
0.598503 + 0.801121i \(0.295763\pi\)
\(180\) 10.0332 0.747828
\(181\) 3.08915 0.229615 0.114807 0.993388i \(-0.463375\pi\)
0.114807 + 0.993388i \(0.463375\pi\)
\(182\) 5.01891 0.372026
\(183\) 6.02043 0.445043
\(184\) 8.47911 0.625088
\(185\) −2.96599 −0.218064
\(186\) −68.7919 −5.04406
\(187\) 13.1780 0.963671
\(188\) −60.5272 −4.41440
\(189\) −7.34813 −0.534498
\(190\) −4.56544 −0.331212
\(191\) 0.102395 0.00740901 0.00370450 0.999993i \(-0.498821\pi\)
0.00370450 + 0.999993i \(0.498821\pi\)
\(192\) 60.9690 4.40006
\(193\) 7.13913 0.513886 0.256943 0.966427i \(-0.417285\pi\)
0.256943 + 0.966427i \(0.417285\pi\)
\(194\) −13.2706 −0.952774
\(195\) 1.89173 0.135469
\(196\) 5.23459 0.373899
\(197\) −17.8571 −1.27227 −0.636134 0.771579i \(-0.719467\pi\)
−0.636134 + 0.771579i \(0.719467\pi\)
\(198\) 74.3080 5.28084
\(199\) 6.29687 0.446373 0.223187 0.974776i \(-0.428354\pi\)
0.223187 + 0.974776i \(0.428354\pi\)
\(200\) 42.4508 3.00173
\(201\) −12.5585 −0.885811
\(202\) −31.8974 −2.24429
\(203\) −1.26823 −0.0890125
\(204\) −40.2095 −2.81523
\(205\) 2.22752 0.155577
\(206\) 4.96431 0.345880
\(207\) −5.37759 −0.373768
\(208\) 24.1301 1.67312
\(209\) −24.4652 −1.69229
\(210\) 2.72686 0.188171
\(211\) −4.70422 −0.323852 −0.161926 0.986803i \(-0.551771\pi\)
−0.161926 + 0.986803i \(0.551771\pi\)
\(212\) −61.2157 −4.20431
\(213\) −39.1443 −2.68212
\(214\) 4.38235 0.299571
\(215\) −3.40820 −0.232437
\(216\) −63.9297 −4.34986
\(217\) −8.76330 −0.594891
\(218\) −6.12667 −0.414950
\(219\) −28.8917 −1.95232
\(220\) −9.10419 −0.613804
\(221\) −4.91119 −0.330362
\(222\) 67.0263 4.49851
\(223\) −6.77620 −0.453768 −0.226884 0.973922i \(-0.572854\pi\)
−0.226884 + 0.973922i \(0.572854\pi\)
\(224\) 17.3824 1.16141
\(225\) −26.9230 −1.79487
\(226\) −11.7093 −0.778889
\(227\) 8.97012 0.595368 0.297684 0.954665i \(-0.403786\pi\)
0.297684 + 0.954665i \(0.403786\pi\)
\(228\) 74.6497 4.94379
\(229\) −20.5561 −1.35839 −0.679194 0.733959i \(-0.737670\pi\)
−0.679194 + 0.733959i \(0.737670\pi\)
\(230\) 0.910594 0.0600428
\(231\) 14.6126 0.961441
\(232\) −11.0338 −0.724404
\(233\) 22.0395 1.44386 0.721929 0.691967i \(-0.243256\pi\)
0.721929 + 0.691967i \(0.243256\pi\)
\(234\) −27.6931 −1.81036
\(235\) −4.01663 −0.262016
\(236\) −46.0738 −2.99915
\(237\) 30.9423 2.00992
\(238\) −7.07931 −0.458883
\(239\) −26.5936 −1.72020 −0.860099 0.510127i \(-0.829598\pi\)
−0.860099 + 0.510127i \(0.829598\pi\)
\(240\) 13.1103 0.846265
\(241\) −1.47059 −0.0947293 −0.0473646 0.998878i \(-0.515082\pi\)
−0.0473646 + 0.998878i \(0.515082\pi\)
\(242\) −37.8408 −2.43250
\(243\) −7.76586 −0.498180
\(244\) 10.7981 0.691277
\(245\) 0.347371 0.0221927
\(246\) −50.3383 −3.20945
\(247\) 9.11771 0.580146
\(248\) −76.2418 −4.84136
\(249\) 18.2149 1.15432
\(250\) 9.23055 0.583791
\(251\) 6.11694 0.386098 0.193049 0.981189i \(-0.438162\pi\)
0.193049 + 0.981189i \(0.438162\pi\)
\(252\) −28.8832 −1.81947
\(253\) 4.87967 0.306782
\(254\) 1.05453 0.0661669
\(255\) −2.66833 −0.167097
\(256\) 15.8449 0.990307
\(257\) 21.1245 1.31771 0.658856 0.752270i \(-0.271041\pi\)
0.658856 + 0.752270i \(0.271041\pi\)
\(258\) 77.0196 4.79503
\(259\) 8.53839 0.530550
\(260\) 3.39296 0.210422
\(261\) 6.99781 0.433153
\(262\) −55.9582 −3.45711
\(263\) 29.3611 1.81048 0.905241 0.424899i \(-0.139690\pi\)
0.905241 + 0.424899i \(0.139690\pi\)
\(264\) 127.132 7.82442
\(265\) −4.06232 −0.249546
\(266\) 13.1429 0.805840
\(267\) −1.42857 −0.0874268
\(268\) −22.5247 −1.37591
\(269\) −2.42218 −0.147683 −0.0738415 0.997270i \(-0.523526\pi\)
−0.0738415 + 0.997270i \(0.523526\pi\)
\(270\) −6.86557 −0.417825
\(271\) −29.0499 −1.76465 −0.882327 0.470637i \(-0.844024\pi\)
−0.882327 + 0.470637i \(0.844024\pi\)
\(272\) −34.0361 −2.06374
\(273\) −5.44585 −0.329598
\(274\) 35.7019 2.15683
\(275\) 24.4302 1.47319
\(276\) −14.8891 −0.896221
\(277\) 24.7085 1.48459 0.742294 0.670074i \(-0.233738\pi\)
0.742294 + 0.670074i \(0.233738\pi\)
\(278\) 51.2905 3.07620
\(279\) 48.3538 2.89486
\(280\) 3.02217 0.180609
\(281\) −20.3751 −1.21548 −0.607739 0.794137i \(-0.707923\pi\)
−0.607739 + 0.794137i \(0.707923\pi\)
\(282\) 90.7690 5.40522
\(283\) −16.9458 −1.00732 −0.503662 0.863901i \(-0.668014\pi\)
−0.503662 + 0.863901i \(0.668014\pi\)
\(284\) −70.2083 −4.16610
\(285\) 4.95380 0.293438
\(286\) 25.1290 1.48591
\(287\) −6.41252 −0.378519
\(288\) −95.9120 −5.65167
\(289\) −10.0726 −0.592508
\(290\) −1.18495 −0.0695825
\(291\) 14.3995 0.844112
\(292\) −51.8194 −3.03250
\(293\) −10.7707 −0.629232 −0.314616 0.949219i \(-0.601876\pi\)
−0.314616 + 0.949219i \(0.601876\pi\)
\(294\) −7.85000 −0.457821
\(295\) −3.05749 −0.178014
\(296\) 74.2850 4.31773
\(297\) −36.7911 −2.13484
\(298\) 10.3678 0.600592
\(299\) −1.81856 −0.105170
\(300\) −74.5428 −4.30373
\(301\) 9.81142 0.565521
\(302\) −33.1566 −1.90795
\(303\) 34.6107 1.98834
\(304\) 63.1886 3.62412
\(305\) 0.716569 0.0410306
\(306\) 39.0619 2.23302
\(307\) −32.8778 −1.87644 −0.938219 0.346042i \(-0.887525\pi\)
−0.938219 + 0.346042i \(0.887525\pi\)
\(308\) 26.2089 1.49339
\(309\) −5.38660 −0.306433
\(310\) −8.18780 −0.465036
\(311\) −17.2456 −0.977909 −0.488955 0.872309i \(-0.662622\pi\)
−0.488955 + 0.872309i \(0.662622\pi\)
\(312\) −47.3795 −2.68234
\(313\) −3.49902 −0.197776 −0.0988881 0.995099i \(-0.531529\pi\)
−0.0988881 + 0.995099i \(0.531529\pi\)
\(314\) 12.8123 0.723041
\(315\) −1.91671 −0.107994
\(316\) 55.4973 3.12196
\(317\) −16.1296 −0.905928 −0.452964 0.891529i \(-0.649633\pi\)
−0.452964 + 0.891529i \(0.649633\pi\)
\(318\) 91.8016 5.14798
\(319\) −6.34987 −0.355525
\(320\) 7.25671 0.405662
\(321\) −4.75513 −0.265406
\(322\) −2.62139 −0.146084
\(323\) −12.8608 −0.715592
\(324\) 25.6096 1.42276
\(325\) −9.10465 −0.505035
\(326\) −33.6615 −1.86434
\(327\) 6.64783 0.367626
\(328\) −55.7898 −3.08047
\(329\) 11.5629 0.637485
\(330\) 13.6530 0.751573
\(331\) −7.42416 −0.408069 −0.204034 0.978964i \(-0.565405\pi\)
−0.204034 + 0.978964i \(0.565405\pi\)
\(332\) 32.6699 1.79299
\(333\) −47.1128 −2.58176
\(334\) 62.9520 3.44458
\(335\) −1.49475 −0.0816671
\(336\) −37.7415 −2.05897
\(337\) −18.0698 −0.984325 −0.492162 0.870503i \(-0.663793\pi\)
−0.492162 + 0.870503i \(0.663793\pi\)
\(338\) 25.6012 1.39252
\(339\) 12.7053 0.690058
\(340\) −4.78585 −0.259549
\(341\) −43.8766 −2.37605
\(342\) −72.5191 −3.92138
\(343\) −1.00000 −0.0539949
\(344\) 85.3606 4.60233
\(345\) −0.988054 −0.0531950
\(346\) 3.35777 0.180515
\(347\) −4.36326 −0.234232 −0.117116 0.993118i \(-0.537365\pi\)
−0.117116 + 0.993118i \(0.537365\pi\)
\(348\) 19.3751 1.03861
\(349\) 5.28185 0.282731 0.141365 0.989957i \(-0.454851\pi\)
0.141365 + 0.989957i \(0.454851\pi\)
\(350\) −13.1240 −0.701509
\(351\) 13.7113 0.731857
\(352\) 87.0314 4.63879
\(353\) 4.17885 0.222418 0.111209 0.993797i \(-0.464528\pi\)
0.111209 + 0.993797i \(0.464528\pi\)
\(354\) 69.0942 3.67231
\(355\) −4.65907 −0.247278
\(356\) −2.56224 −0.135798
\(357\) 7.68151 0.406549
\(358\) −43.0754 −2.27661
\(359\) 31.3208 1.65305 0.826524 0.562902i \(-0.190315\pi\)
0.826524 + 0.562902i \(0.190315\pi\)
\(360\) −16.6756 −0.878881
\(361\) 4.87623 0.256644
\(362\) −8.30895 −0.436709
\(363\) 41.0597 2.15508
\(364\) −9.76754 −0.511958
\(365\) −3.43877 −0.179993
\(366\) −16.1933 −0.846435
\(367\) 5.68976 0.297003 0.148501 0.988912i \(-0.452555\pi\)
0.148501 + 0.988912i \(0.452555\pi\)
\(368\) −12.6032 −0.656987
\(369\) 35.3828 1.84195
\(370\) 7.97767 0.414739
\(371\) 11.6945 0.607147
\(372\) 133.879 6.94130
\(373\) 28.8233 1.49241 0.746206 0.665715i \(-0.231873\pi\)
0.746206 + 0.665715i \(0.231873\pi\)
\(374\) −35.4451 −1.83282
\(375\) −10.0157 −0.517211
\(376\) 100.599 5.18800
\(377\) 2.36647 0.121880
\(378\) 19.7644 1.01657
\(379\) 16.8685 0.866478 0.433239 0.901279i \(-0.357371\pi\)
0.433239 + 0.901279i \(0.357371\pi\)
\(380\) 8.88502 0.455792
\(381\) −1.14423 −0.0586207
\(382\) −0.275412 −0.0140913
\(383\) −7.40623 −0.378440 −0.189220 0.981935i \(-0.560596\pi\)
−0.189220 + 0.981935i \(0.560596\pi\)
\(384\) −62.5276 −3.19085
\(385\) 1.73924 0.0886397
\(386\) −19.2022 −0.977368
\(387\) −54.1371 −2.75194
\(388\) 25.8265 1.31114
\(389\) −20.1315 −1.02071 −0.510353 0.859965i \(-0.670485\pi\)
−0.510353 + 0.859965i \(0.670485\pi\)
\(390\) −5.08821 −0.257652
\(391\) 2.56513 0.129724
\(392\) −8.70012 −0.439423
\(393\) 60.7183 3.06283
\(394\) 48.0306 2.41975
\(395\) 3.68284 0.185304
\(396\) −144.614 −7.26713
\(397\) −11.9766 −0.601086 −0.300543 0.953768i \(-0.597168\pi\)
−0.300543 + 0.953768i \(0.597168\pi\)
\(398\) −16.9368 −0.848966
\(399\) −14.2609 −0.713936
\(400\) −63.0981 −3.15491
\(401\) −2.05154 −0.102449 −0.0512245 0.998687i \(-0.516312\pi\)
−0.0512245 + 0.998687i \(0.516312\pi\)
\(402\) 33.7790 1.68474
\(403\) 16.3520 0.814550
\(404\) 62.0770 3.08844
\(405\) 1.69947 0.0844475
\(406\) 3.41119 0.169295
\(407\) 42.7505 2.11907
\(408\) 66.8301 3.30858
\(409\) 4.28821 0.212038 0.106019 0.994364i \(-0.466189\pi\)
0.106019 + 0.994364i \(0.466189\pi\)
\(410\) −5.99141 −0.295895
\(411\) −38.7389 −1.91085
\(412\) −9.66127 −0.475977
\(413\) 8.80181 0.433109
\(414\) 14.4642 0.710876
\(415\) 2.16799 0.106423
\(416\) −32.4349 −1.59025
\(417\) −55.6535 −2.72537
\(418\) 65.8045 3.21860
\(419\) 24.9168 1.21726 0.608632 0.793453i \(-0.291719\pi\)
0.608632 + 0.793453i \(0.291719\pi\)
\(420\) −5.30687 −0.258949
\(421\) 15.3529 0.748256 0.374128 0.927377i \(-0.377942\pi\)
0.374128 + 0.927377i \(0.377942\pi\)
\(422\) 12.6530 0.615940
\(423\) −63.8015 −3.10214
\(424\) 101.743 4.94109
\(425\) 12.8423 0.622945
\(426\) 105.287 5.10118
\(427\) −2.06284 −0.0998276
\(428\) −8.52869 −0.412250
\(429\) −27.2666 −1.31644
\(430\) 9.16710 0.442077
\(431\) 30.5469 1.47139 0.735696 0.677312i \(-0.236855\pi\)
0.735696 + 0.677312i \(0.236855\pi\)
\(432\) 95.0239 4.57184
\(433\) 27.3984 1.31668 0.658342 0.752719i \(-0.271258\pi\)
0.658342 + 0.752719i \(0.271258\pi\)
\(434\) 23.5708 1.13143
\(435\) 1.28575 0.0616468
\(436\) 11.9234 0.571027
\(437\) −4.76220 −0.227807
\(438\) 77.7104 3.71315
\(439\) −40.2473 −1.92090 −0.960450 0.278452i \(-0.910179\pi\)
−0.960450 + 0.278452i \(0.910179\pi\)
\(440\) 15.1316 0.721370
\(441\) 5.51776 0.262750
\(442\) 13.2097 0.628322
\(443\) −15.0260 −0.713905 −0.356952 0.934123i \(-0.616184\pi\)
−0.356952 + 0.934123i \(0.616184\pi\)
\(444\) −130.443 −6.19055
\(445\) −0.170032 −0.00806029
\(446\) 18.2261 0.863029
\(447\) −11.2498 −0.532096
\(448\) −20.8904 −0.986978
\(449\) −21.6326 −1.02091 −0.510453 0.859906i \(-0.670522\pi\)
−0.510453 + 0.859906i \(0.670522\pi\)
\(450\) 72.4153 3.41369
\(451\) −32.1066 −1.51184
\(452\) 22.7880 1.07186
\(453\) 35.9771 1.69035
\(454\) −24.1271 −1.13234
\(455\) −0.648180 −0.0303872
\(456\) −124.071 −5.81017
\(457\) 13.1071 0.613123 0.306562 0.951851i \(-0.400821\pi\)
0.306562 + 0.951851i \(0.400821\pi\)
\(458\) 55.2902 2.58354
\(459\) −19.3402 −0.902723
\(460\) −1.77215 −0.0826269
\(461\) −9.36134 −0.436001 −0.218000 0.975949i \(-0.569953\pi\)
−0.218000 + 0.975949i \(0.569953\pi\)
\(462\) −39.3039 −1.82858
\(463\) 29.3049 1.36192 0.680958 0.732322i \(-0.261564\pi\)
0.680958 + 0.732322i \(0.261564\pi\)
\(464\) 16.4004 0.761371
\(465\) 8.88430 0.412000
\(466\) −59.2802 −2.74610
\(467\) −36.7073 −1.69861 −0.849305 0.527903i \(-0.822978\pi\)
−0.849305 + 0.527903i \(0.822978\pi\)
\(468\) 53.8949 2.49129
\(469\) 4.30305 0.198697
\(470\) 10.8036 0.498333
\(471\) −13.9022 −0.640579
\(472\) 76.5768 3.52473
\(473\) 49.1244 2.25874
\(474\) −83.2260 −3.82269
\(475\) −23.8420 −1.09395
\(476\) 13.7774 0.631484
\(477\) −64.5273 −2.95450
\(478\) 71.5293 3.27168
\(479\) 4.72072 0.215695 0.107848 0.994167i \(-0.465604\pi\)
0.107848 + 0.994167i \(0.465604\pi\)
\(480\) −17.6224 −0.804351
\(481\) −15.9323 −0.726450
\(482\) 3.95548 0.180167
\(483\) 2.84438 0.129424
\(484\) 73.6437 3.34744
\(485\) 1.71387 0.0778227
\(486\) 20.8880 0.947498
\(487\) 37.8401 1.71470 0.857350 0.514734i \(-0.172109\pi\)
0.857350 + 0.514734i \(0.172109\pi\)
\(488\) −17.9469 −0.812419
\(489\) 36.5250 1.65172
\(490\) −0.934329 −0.0422087
\(491\) −8.58180 −0.387291 −0.193646 0.981072i \(-0.562031\pi\)
−0.193646 + 0.981072i \(0.562031\pi\)
\(492\) 97.9657 4.41663
\(493\) −3.33797 −0.150335
\(494\) −24.5241 −1.10339
\(495\) −9.59669 −0.431339
\(496\) 113.324 5.08842
\(497\) 13.4124 0.601628
\(498\) −48.9930 −2.19543
\(499\) −25.1559 −1.12613 −0.563066 0.826412i \(-0.690378\pi\)
−0.563066 + 0.826412i \(0.690378\pi\)
\(500\) −17.9640 −0.803375
\(501\) −68.3070 −3.05173
\(502\) −16.4528 −0.734326
\(503\) −4.60886 −0.205499 −0.102749 0.994707i \(-0.532764\pi\)
−0.102749 + 0.994707i \(0.532764\pi\)
\(504\) 48.0052 2.13832
\(505\) 4.11947 0.183314
\(506\) −13.1249 −0.583475
\(507\) −27.7790 −1.23371
\(508\) −2.05226 −0.0910544
\(509\) −17.3466 −0.768875 −0.384437 0.923151i \(-0.625605\pi\)
−0.384437 + 0.923151i \(0.625605\pi\)
\(510\) 7.17706 0.317805
\(511\) 9.89942 0.437925
\(512\) 0.230524 0.0101878
\(513\) 35.9054 1.58526
\(514\) −56.8190 −2.50618
\(515\) −0.641128 −0.0282515
\(516\) −149.891 −6.59860
\(517\) 57.8941 2.54618
\(518\) −22.9659 −1.00906
\(519\) −3.64340 −0.159928
\(520\) −5.63925 −0.247297
\(521\) 39.1629 1.71576 0.857879 0.513852i \(-0.171782\pi\)
0.857879 + 0.513852i \(0.171782\pi\)
\(522\) −18.8221 −0.823822
\(523\) −4.70539 −0.205752 −0.102876 0.994694i \(-0.532805\pi\)
−0.102876 + 0.994694i \(0.532805\pi\)
\(524\) 108.903 4.75744
\(525\) 14.2404 0.621503
\(526\) −78.9730 −3.44339
\(527\) −23.0649 −1.00472
\(528\) −188.966 −8.22371
\(529\) −22.0502 −0.958703
\(530\) 10.9265 0.474616
\(531\) −48.5663 −2.10760
\(532\) −25.5779 −1.10894
\(533\) 11.9655 0.518284
\(534\) 3.84244 0.166279
\(535\) −0.565970 −0.0244690
\(536\) 37.4371 1.61704
\(537\) 46.7396 2.01696
\(538\) 6.51499 0.280881
\(539\) −5.00686 −0.215661
\(540\) 13.3614 0.574984
\(541\) 2.30598 0.0991416 0.0495708 0.998771i \(-0.484215\pi\)
0.0495708 + 0.998771i \(0.484215\pi\)
\(542\) 78.1360 3.35623
\(543\) 9.01576 0.386903
\(544\) 45.7503 1.96153
\(545\) 0.791244 0.0338932
\(546\) 14.6478 0.626868
\(547\) −6.01663 −0.257253 −0.128626 0.991693i \(-0.541057\pi\)
−0.128626 + 0.991693i \(0.541057\pi\)
\(548\) −69.4811 −2.96808
\(549\) 11.3822 0.485782
\(550\) −65.7102 −2.80189
\(551\) 6.19701 0.264001
\(552\) 24.7464 1.05328
\(553\) −10.6020 −0.450844
\(554\) −66.4588 −2.82357
\(555\) −8.65629 −0.367439
\(556\) −99.8188 −4.23326
\(557\) −7.45288 −0.315789 −0.157894 0.987456i \(-0.550471\pi\)
−0.157894 + 0.987456i \(0.550471\pi\)
\(558\) −130.058 −5.50579
\(559\) −18.3077 −0.774335
\(560\) −4.49210 −0.189826
\(561\) 38.4603 1.62379
\(562\) 54.8033 2.31174
\(563\) 32.1826 1.35633 0.678167 0.734908i \(-0.262775\pi\)
0.678167 + 0.734908i \(0.262775\pi\)
\(564\) −176.650 −7.43830
\(565\) 1.51222 0.0636197
\(566\) 45.5794 1.91585
\(567\) −4.89239 −0.205461
\(568\) 116.689 4.89618
\(569\) −12.0767 −0.506280 −0.253140 0.967430i \(-0.581463\pi\)
−0.253140 + 0.967430i \(0.581463\pi\)
\(570\) −13.3243 −0.558095
\(571\) −14.3032 −0.598571 −0.299286 0.954164i \(-0.596748\pi\)
−0.299286 + 0.954164i \(0.596748\pi\)
\(572\) −48.9047 −2.04481
\(573\) 0.298840 0.0124842
\(574\) 17.2479 0.719913
\(575\) 4.75538 0.198313
\(576\) 115.268 4.80284
\(577\) −14.7782 −0.615225 −0.307612 0.951512i \(-0.599530\pi\)
−0.307612 + 0.951512i \(0.599530\pi\)
\(578\) 27.0926 1.12690
\(579\) 20.8357 0.865902
\(580\) 2.30608 0.0957548
\(581\) −6.24115 −0.258927
\(582\) −38.7305 −1.60543
\(583\) 58.5526 2.42500
\(584\) 86.1262 3.56393
\(585\) 3.57650 0.147870
\(586\) 28.9702 1.19675
\(587\) −38.8881 −1.60509 −0.802543 0.596595i \(-0.796520\pi\)
−0.802543 + 0.596595i \(0.796520\pi\)
\(588\) 15.2772 0.630023
\(589\) 42.8204 1.76438
\(590\) 8.22379 0.338568
\(591\) −52.1164 −2.14378
\(592\) −110.416 −4.53807
\(593\) −14.6422 −0.601284 −0.300642 0.953737i \(-0.597201\pi\)
−0.300642 + 0.953737i \(0.597201\pi\)
\(594\) 98.9577 4.06028
\(595\) 0.914275 0.0374816
\(596\) −20.1773 −0.826495
\(597\) 18.3775 0.752143
\(598\) 4.89141 0.200025
\(599\) −42.7007 −1.74470 −0.872351 0.488880i \(-0.837405\pi\)
−0.872351 + 0.488880i \(0.837405\pi\)
\(600\) 123.894 5.05793
\(601\) 37.3644 1.52412 0.762062 0.647504i \(-0.224187\pi\)
0.762062 + 0.647504i \(0.224187\pi\)
\(602\) −26.3900 −1.07557
\(603\) −23.7432 −0.966898
\(604\) 64.5277 2.62559
\(605\) 4.88705 0.198687
\(606\) −93.0932 −3.78165
\(607\) −0.633414 −0.0257095 −0.0128547 0.999917i \(-0.504092\pi\)
−0.0128547 + 0.999917i \(0.504092\pi\)
\(608\) −84.9363 −3.44462
\(609\) −3.70136 −0.149987
\(610\) −1.92737 −0.0780368
\(611\) −21.5760 −0.872871
\(612\) −76.0202 −3.07293
\(613\) 15.6251 0.631090 0.315545 0.948911i \(-0.397813\pi\)
0.315545 + 0.948911i \(0.397813\pi\)
\(614\) 88.4321 3.56883
\(615\) 6.50107 0.262148
\(616\) −43.5603 −1.75510
\(617\) −16.5528 −0.666392 −0.333196 0.942858i \(-0.608127\pi\)
−0.333196 + 0.942858i \(0.608127\pi\)
\(618\) 14.4884 0.582810
\(619\) 30.7945 1.23774 0.618868 0.785495i \(-0.287592\pi\)
0.618868 + 0.785495i \(0.287592\pi\)
\(620\) 15.9347 0.639952
\(621\) −7.16146 −0.287380
\(622\) 46.3858 1.85990
\(623\) 0.489483 0.0196107
\(624\) 70.4241 2.81922
\(625\) 23.2046 0.928183
\(626\) 9.41137 0.376154
\(627\) −71.4022 −2.85153
\(628\) −24.9346 −0.995000
\(629\) 22.4729 0.896054
\(630\) 5.15540 0.205396
\(631\) −35.1859 −1.40073 −0.700364 0.713785i \(-0.746979\pi\)
−0.700364 + 0.713785i \(0.746979\pi\)
\(632\) −92.2390 −3.66907
\(633\) −13.7294 −0.545693
\(634\) 43.3841 1.72300
\(635\) −0.136190 −0.00540452
\(636\) −178.659 −7.08430
\(637\) 1.86596 0.0739321
\(638\) 17.0794 0.676179
\(639\) −74.0063 −2.92764
\(640\) −7.44222 −0.294180
\(641\) 14.0078 0.553275 0.276637 0.960974i \(-0.410780\pi\)
0.276637 + 0.960974i \(0.410780\pi\)
\(642\) 12.7900 0.504780
\(643\) 6.58680 0.259758 0.129879 0.991530i \(-0.458541\pi\)
0.129879 + 0.991530i \(0.458541\pi\)
\(644\) 5.10161 0.201032
\(645\) −9.94690 −0.391659
\(646\) 34.5918 1.36100
\(647\) −4.05178 −0.159292 −0.0796460 0.996823i \(-0.525379\pi\)
−0.0796460 + 0.996823i \(0.525379\pi\)
\(648\) −42.5644 −1.67209
\(649\) 44.0695 1.72988
\(650\) 24.4889 0.960535
\(651\) −25.5759 −1.00240
\(652\) 65.5103 2.56558
\(653\) 27.8418 1.08953 0.544767 0.838587i \(-0.316618\pi\)
0.544767 + 0.838587i \(0.316618\pi\)
\(654\) −17.8808 −0.699195
\(655\) 7.22687 0.282377
\(656\) 82.9249 3.23767
\(657\) −54.6226 −2.13103
\(658\) −31.1011 −1.21245
\(659\) −16.5191 −0.643491 −0.321745 0.946826i \(-0.604270\pi\)
−0.321745 + 0.946826i \(0.604270\pi\)
\(660\) −26.5708 −1.03427
\(661\) −1.52023 −0.0591301 −0.0295651 0.999563i \(-0.509412\pi\)
−0.0295651 + 0.999563i \(0.509412\pi\)
\(662\) 19.9689 0.776114
\(663\) −14.3334 −0.556663
\(664\) −54.2988 −2.10720
\(665\) −1.69737 −0.0658211
\(666\) 126.720 4.91030
\(667\) −1.23602 −0.0478587
\(668\) −122.514 −4.74020
\(669\) −19.7765 −0.764602
\(670\) 4.02047 0.155324
\(671\) −10.3283 −0.398721
\(672\) 50.7309 1.95699
\(673\) 14.8227 0.571371 0.285686 0.958323i \(-0.407779\pi\)
0.285686 + 0.958323i \(0.407779\pi\)
\(674\) 48.6027 1.87211
\(675\) −35.8540 −1.38002
\(676\) −49.8238 −1.91630
\(677\) −18.1691 −0.698297 −0.349148 0.937067i \(-0.613529\pi\)
−0.349148 + 0.937067i \(0.613529\pi\)
\(678\) −34.1737 −1.31243
\(679\) −4.93383 −0.189343
\(680\) 7.95431 0.305034
\(681\) 26.1795 1.00320
\(682\) 118.016 4.51906
\(683\) −1.32417 −0.0506678 −0.0253339 0.999679i \(-0.508065\pi\)
−0.0253339 + 0.999679i \(0.508065\pi\)
\(684\) 141.133 5.39635
\(685\) −4.61081 −0.176170
\(686\) 2.68972 0.102694
\(687\) −59.9935 −2.28889
\(688\) −126.878 −4.83720
\(689\) −21.8214 −0.831330
\(690\) 2.65759 0.101173
\(691\) −23.5124 −0.894452 −0.447226 0.894421i \(-0.647588\pi\)
−0.447226 + 0.894421i \(0.647588\pi\)
\(692\) −6.53471 −0.248413
\(693\) 27.6267 1.04945
\(694\) 11.7359 0.445490
\(695\) −6.62404 −0.251264
\(696\) −32.2023 −1.22063
\(697\) −16.8777 −0.639288
\(698\) −14.2067 −0.537731
\(699\) 64.3228 2.43291
\(700\) 25.5413 0.965370
\(701\) −38.8990 −1.46919 −0.734597 0.678504i \(-0.762629\pi\)
−0.734597 + 0.678504i \(0.762629\pi\)
\(702\) −36.8796 −1.39193
\(703\) −41.7214 −1.57355
\(704\) −104.595 −3.94209
\(705\) −11.7226 −0.441499
\(706\) −11.2399 −0.423020
\(707\) −11.8590 −0.446004
\(708\) −134.467 −5.05359
\(709\) 7.05569 0.264982 0.132491 0.991184i \(-0.457702\pi\)
0.132491 + 0.991184i \(0.457702\pi\)
\(710\) 12.5316 0.470302
\(711\) 58.4995 2.19390
\(712\) 4.25856 0.159596
\(713\) −8.54068 −0.319851
\(714\) −20.6611 −0.773222
\(715\) −3.24535 −0.121369
\(716\) 83.8311 3.13291
\(717\) −77.6140 −2.89855
\(718\) −84.2441 −3.14396
\(719\) −11.9386 −0.445236 −0.222618 0.974906i \(-0.571460\pi\)
−0.222618 + 0.974906i \(0.571460\pi\)
\(720\) 24.7863 0.923731
\(721\) 1.84566 0.0687360
\(722\) −13.1157 −0.488115
\(723\) −4.29196 −0.159620
\(724\) 16.1704 0.600970
\(725\) −6.18813 −0.229821
\(726\) −110.439 −4.09878
\(727\) −47.3986 −1.75792 −0.878958 0.476899i \(-0.841761\pi\)
−0.878958 + 0.476899i \(0.841761\pi\)
\(728\) 16.2341 0.601676
\(729\) −37.3420 −1.38304
\(730\) 9.24932 0.342333
\(731\) 25.8235 0.955118
\(732\) 31.5144 1.16481
\(733\) 15.4114 0.569234 0.284617 0.958641i \(-0.408134\pi\)
0.284617 + 0.958641i \(0.408134\pi\)
\(734\) −15.3038 −0.564875
\(735\) 1.01381 0.0373949
\(736\) 16.9408 0.624448
\(737\) 21.5448 0.793613
\(738\) −95.1697 −3.50324
\(739\) −42.0082 −1.54530 −0.772649 0.634833i \(-0.781069\pi\)
−0.772649 + 0.634833i \(0.781069\pi\)
\(740\) −15.5257 −0.570736
\(741\) 26.6102 0.977550
\(742\) −31.4548 −1.15474
\(743\) −40.2222 −1.47561 −0.737805 0.675014i \(-0.764137\pi\)
−0.737805 + 0.675014i \(0.764137\pi\)
\(744\) −222.513 −8.15773
\(745\) −1.33898 −0.0490564
\(746\) −77.5265 −2.83845
\(747\) 34.4372 1.25999
\(748\) 68.9814 2.52221
\(749\) 1.62930 0.0595332
\(750\) 26.9395 0.983693
\(751\) −15.0609 −0.549580 −0.274790 0.961504i \(-0.588608\pi\)
−0.274790 + 0.961504i \(0.588608\pi\)
\(752\) −149.529 −5.45275
\(753\) 17.8524 0.650578
\(754\) −6.36515 −0.231805
\(755\) 4.28210 0.155842
\(756\) −38.4644 −1.39894
\(757\) −16.0338 −0.582759 −0.291380 0.956607i \(-0.594114\pi\)
−0.291380 + 0.956607i \(0.594114\pi\)
\(758\) −45.3716 −1.64797
\(759\) 14.2414 0.516931
\(760\) −14.7673 −0.535667
\(761\) −46.9757 −1.70287 −0.851433 0.524463i \(-0.824266\pi\)
−0.851433 + 0.524463i \(0.824266\pi\)
\(762\) 3.07766 0.111492
\(763\) −2.27781 −0.0824622
\(764\) 0.535993 0.0193915
\(765\) −5.04475 −0.182393
\(766\) 19.9207 0.719763
\(767\) −16.4238 −0.593030
\(768\) 46.2437 1.66868
\(769\) −6.41739 −0.231417 −0.115709 0.993283i \(-0.536914\pi\)
−0.115709 + 0.993283i \(0.536914\pi\)
\(770\) −4.67806 −0.168586
\(771\) 61.6523 2.22035
\(772\) 37.3704 1.34499
\(773\) 31.5449 1.13459 0.567296 0.823514i \(-0.307990\pi\)
0.567296 + 0.823514i \(0.307990\pi\)
\(774\) 145.613 5.23397
\(775\) −42.7590 −1.53595
\(776\) −42.9249 −1.54092
\(777\) 24.9195 0.893980
\(778\) 54.1480 1.94130
\(779\) 31.3337 1.12265
\(780\) 9.90241 0.354563
\(781\) 67.1540 2.40296
\(782\) −6.89946 −0.246724
\(783\) 9.31914 0.333039
\(784\) 12.9317 0.461847
\(785\) −1.65468 −0.0590580
\(786\) −163.315 −5.82526
\(787\) 40.5997 1.44722 0.723612 0.690207i \(-0.242480\pi\)
0.723612 + 0.690207i \(0.242480\pi\)
\(788\) −93.4746 −3.32990
\(789\) 85.6909 3.05068
\(790\) −9.90579 −0.352432
\(791\) −4.35334 −0.154787
\(792\) 240.355 8.54066
\(793\) 3.84917 0.136688
\(794\) 32.2136 1.14322
\(795\) −11.8559 −0.420487
\(796\) 32.9615 1.16829
\(797\) 53.8734 1.90830 0.954148 0.299336i \(-0.0967652\pi\)
0.954148 + 0.299336i \(0.0967652\pi\)
\(798\) 38.3577 1.35785
\(799\) 30.4335 1.07666
\(800\) 84.8146 2.99865
\(801\) −2.70085 −0.0954298
\(802\) 5.51807 0.194850
\(803\) 49.5650 1.74911
\(804\) −65.7388 −2.31843
\(805\) 0.338546 0.0119322
\(806\) −43.9822 −1.54921
\(807\) −7.06918 −0.248847
\(808\) −103.175 −3.62968
\(809\) 3.71273 0.130533 0.0652663 0.997868i \(-0.479210\pi\)
0.0652663 + 0.997868i \(0.479210\pi\)
\(810\) −4.57110 −0.160612
\(811\) 3.54436 0.124459 0.0622296 0.998062i \(-0.480179\pi\)
0.0622296 + 0.998062i \(0.480179\pi\)
\(812\) −6.63868 −0.232972
\(813\) −84.7826 −2.97346
\(814\) −114.987 −4.03029
\(815\) 4.34731 0.152280
\(816\) −99.3351 −3.47742
\(817\) −47.9418 −1.67727
\(818\) −11.5341 −0.403280
\(819\) −10.2959 −0.359769
\(820\) 11.6602 0.407190
\(821\) 13.1491 0.458908 0.229454 0.973319i \(-0.426306\pi\)
0.229454 + 0.973319i \(0.426306\pi\)
\(822\) 104.197 3.63427
\(823\) −18.9164 −0.659383 −0.329691 0.944089i \(-0.606945\pi\)
−0.329691 + 0.944089i \(0.606945\pi\)
\(824\) 16.0575 0.559389
\(825\) 71.2999 2.48234
\(826\) −23.6744 −0.823737
\(827\) −17.2239 −0.598935 −0.299468 0.954106i \(-0.596809\pi\)
−0.299468 + 0.954106i \(0.596809\pi\)
\(828\) −28.1494 −0.978261
\(829\) 26.1463 0.908099 0.454049 0.890977i \(-0.349979\pi\)
0.454049 + 0.890977i \(0.349979\pi\)
\(830\) −5.83129 −0.202407
\(831\) 72.1122 2.50154
\(832\) 38.9807 1.35141
\(833\) −2.63199 −0.0911930
\(834\) 149.692 5.18342
\(835\) −8.13009 −0.281353
\(836\) −128.065 −4.42923
\(837\) 64.3938 2.22578
\(838\) −67.0191 −2.31513
\(839\) 43.4920 1.50151 0.750756 0.660580i \(-0.229690\pi\)
0.750756 + 0.660580i \(0.229690\pi\)
\(840\) 8.82026 0.304328
\(841\) −27.3916 −0.944537
\(842\) −41.2951 −1.42312
\(843\) −59.4652 −2.04809
\(844\) −24.6247 −0.847616
\(845\) −3.30634 −0.113742
\(846\) 171.608 5.90001
\(847\) −14.0687 −0.483406
\(848\) −151.230 −5.19324
\(849\) −49.4567 −1.69735
\(850\) −34.5423 −1.18479
\(851\) 8.32148 0.285257
\(852\) −204.904 −7.01991
\(853\) −48.2745 −1.65289 −0.826443 0.563020i \(-0.809639\pi\)
−0.826443 + 0.563020i \(0.809639\pi\)
\(854\) 5.54845 0.189864
\(855\) 9.36567 0.320299
\(856\) 14.1751 0.484494
\(857\) 36.8858 1.26000 0.629998 0.776597i \(-0.283056\pi\)
0.629998 + 0.776597i \(0.283056\pi\)
\(858\) 73.3395 2.50377
\(859\) −1.00000 −0.0341196
\(860\) −17.8405 −0.608356
\(861\) −18.7151 −0.637808
\(862\) −82.1626 −2.79847
\(863\) 34.5982 1.17774 0.588868 0.808229i \(-0.299574\pi\)
0.588868 + 0.808229i \(0.299574\pi\)
\(864\) −127.728 −4.34541
\(865\) −0.433648 −0.0147445
\(866\) −73.6940 −2.50423
\(867\) −29.3972 −0.998382
\(868\) −45.8722 −1.55700
\(869\) −53.0829 −1.80072
\(870\) −3.45829 −0.117247
\(871\) −8.02933 −0.272063
\(872\) −19.8172 −0.671096
\(873\) 27.2237 0.921382
\(874\) 12.8090 0.433270
\(875\) 3.43179 0.116016
\(876\) −151.236 −5.10979
\(877\) 15.8976 0.536825 0.268413 0.963304i \(-0.413501\pi\)
0.268413 + 0.963304i \(0.413501\pi\)
\(878\) 108.254 3.65340
\(879\) −31.4346 −1.06026
\(880\) −22.4913 −0.758182
\(881\) 26.0363 0.877186 0.438593 0.898686i \(-0.355477\pi\)
0.438593 + 0.898686i \(0.355477\pi\)
\(882\) −14.8412 −0.499730
\(883\) −34.6382 −1.16567 −0.582835 0.812591i \(-0.698057\pi\)
−0.582835 + 0.812591i \(0.698057\pi\)
\(884\) −25.7080 −0.864655
\(885\) −8.92335 −0.299955
\(886\) 40.4156 1.35779
\(887\) 39.8386 1.33765 0.668824 0.743421i \(-0.266798\pi\)
0.668824 + 0.743421i \(0.266798\pi\)
\(888\) 216.802 7.27541
\(889\) 0.392058 0.0131492
\(890\) 0.457338 0.0153300
\(891\) −24.4955 −0.820631
\(892\) −35.4706 −1.18764
\(893\) −56.5003 −1.89071
\(894\) 30.2587 1.01200
\(895\) 5.56309 0.185953
\(896\) 21.4244 0.715740
\(897\) −5.30750 −0.177212
\(898\) 58.1856 1.94168
\(899\) 11.1139 0.370669
\(900\) −140.931 −4.69769
\(901\) 30.7797 1.02542
\(902\) 86.3578 2.87540
\(903\) 28.6348 0.952907
\(904\) −37.8746 −1.25969
\(905\) 1.07308 0.0356704
\(906\) −96.7683 −3.21491
\(907\) −6.99072 −0.232123 −0.116062 0.993242i \(-0.537027\pi\)
−0.116062 + 0.993242i \(0.537027\pi\)
\(908\) 46.9548 1.55825
\(909\) 65.4351 2.17035
\(910\) 1.74342 0.0577939
\(911\) 51.2228 1.69709 0.848544 0.529125i \(-0.177480\pi\)
0.848544 + 0.529125i \(0.177480\pi\)
\(912\) 184.417 6.10667
\(913\) −31.2486 −1.03418
\(914\) −35.2544 −1.16611
\(915\) 2.09132 0.0691369
\(916\) −107.603 −3.55530
\(917\) −20.8045 −0.687024
\(918\) 52.0197 1.71690
\(919\) 17.7559 0.585715 0.292857 0.956156i \(-0.405394\pi\)
0.292857 + 0.956156i \(0.405394\pi\)
\(920\) 2.94539 0.0971068
\(921\) −95.9546 −3.16181
\(922\) 25.1794 0.829238
\(923\) −25.0270 −0.823774
\(924\) 76.4911 2.51637
\(925\) 41.6616 1.36983
\(926\) −78.8221 −2.59025
\(927\) −10.1839 −0.334484
\(928\) −22.0450 −0.723661
\(929\) −13.4118 −0.440027 −0.220013 0.975497i \(-0.570610\pi\)
−0.220013 + 0.975497i \(0.570610\pi\)
\(930\) −23.8963 −0.783590
\(931\) 4.88633 0.160143
\(932\) 115.368 3.77900
\(933\) −50.3317 −1.64778
\(934\) 98.7322 3.23062
\(935\) 4.57765 0.149705
\(936\) −89.5758 −2.92788
\(937\) −22.5056 −0.735225 −0.367612 0.929979i \(-0.619825\pi\)
−0.367612 + 0.929979i \(0.619825\pi\)
\(938\) −11.5740 −0.377904
\(939\) −10.2120 −0.333255
\(940\) −21.0254 −0.685772
\(941\) 35.2001 1.14749 0.573746 0.819033i \(-0.305490\pi\)
0.573746 + 0.819033i \(0.305490\pi\)
\(942\) 37.3930 1.21833
\(943\) −6.24962 −0.203516
\(944\) −113.822 −3.70461
\(945\) −2.55252 −0.0830336
\(946\) −132.131 −4.29595
\(947\) 3.48739 0.113325 0.0566624 0.998393i \(-0.481954\pi\)
0.0566624 + 0.998393i \(0.481954\pi\)
\(948\) 161.970 5.26054
\(949\) −18.4719 −0.599624
\(950\) 64.1284 2.08060
\(951\) −47.0746 −1.52650
\(952\) −22.8986 −0.742148
\(953\) −44.5458 −1.44298 −0.721490 0.692425i \(-0.756543\pi\)
−0.721490 + 0.692425i \(0.756543\pi\)
\(954\) 173.560 5.61922
\(955\) 0.0355689 0.00115098
\(956\) −139.207 −4.50226
\(957\) −18.5322 −0.599062
\(958\) −12.6974 −0.410234
\(959\) 13.2735 0.428622
\(960\) 21.1789 0.683545
\(961\) 45.7954 1.47727
\(962\) 42.8534 1.38165
\(963\) −8.99006 −0.289701
\(964\) −7.69795 −0.247934
\(965\) 2.47992 0.0798316
\(966\) −7.65058 −0.246153
\(967\) −23.4187 −0.753095 −0.376547 0.926397i \(-0.622889\pi\)
−0.376547 + 0.926397i \(0.622889\pi\)
\(968\) −122.399 −3.93406
\(969\) −37.5344 −1.20578
\(970\) −4.60982 −0.148012
\(971\) 9.96733 0.319867 0.159933 0.987128i \(-0.448872\pi\)
0.159933 + 0.987128i \(0.448872\pi\)
\(972\) −40.6510 −1.30388
\(973\) 19.0691 0.611327
\(974\) −101.779 −3.26122
\(975\) −26.5721 −0.850988
\(976\) 26.6760 0.853878
\(977\) 14.7814 0.472899 0.236449 0.971644i \(-0.424016\pi\)
0.236449 + 0.971644i \(0.424016\pi\)
\(978\) −98.2419 −3.14143
\(979\) 2.45077 0.0783271
\(980\) 1.81834 0.0580848
\(981\) 12.5684 0.401278
\(982\) 23.0826 0.736596
\(983\) 48.6850 1.55281 0.776405 0.630234i \(-0.217041\pi\)
0.776405 + 0.630234i \(0.217041\pi\)
\(984\) −162.824 −5.19062
\(985\) −6.20304 −0.197645
\(986\) 8.97821 0.285924
\(987\) 33.7467 1.07417
\(988\) 47.7274 1.51841
\(989\) 9.56217 0.304059
\(990\) 25.8124 0.820372
\(991\) 48.7125 1.54740 0.773701 0.633551i \(-0.218403\pi\)
0.773701 + 0.633551i \(0.218403\pi\)
\(992\) −152.327 −4.83640
\(993\) −21.6676 −0.687600
\(994\) −36.0755 −1.14425
\(995\) 2.18735 0.0693436
\(996\) 95.3476 3.02120
\(997\) 32.9908 1.04483 0.522414 0.852692i \(-0.325031\pi\)
0.522414 + 0.852692i \(0.325031\pi\)
\(998\) 67.6622 2.14181
\(999\) −62.7412 −1.98504
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 6013.2.a.c.1.5 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6013.2.a.c.1.5 104 1.1 even 1 trivial