Properties

Label 6046.2.a.e.1.4
Level $6046$
Weight $2$
Character 6046.1
Self dual yes
Analytic conductor $48.278$
Analytic rank $1$
Dimension $56$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6046,2,Mod(1,6046)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6046.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6046 = 2 \cdot 3023 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6046.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: \(48.2775530621\)
Analytic rank: \(1\)
Dimension: \(56\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6046.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.18186 q^{3} +1.00000 q^{4} +3.25833 q^{5} -3.18186 q^{6} +0.730955 q^{7} +1.00000 q^{8} +7.12426 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.18186 q^{3} +1.00000 q^{4} +3.25833 q^{5} -3.18186 q^{6} +0.730955 q^{7} +1.00000 q^{8} +7.12426 q^{9} +3.25833 q^{10} -5.75818 q^{11} -3.18186 q^{12} +6.39012 q^{13} +0.730955 q^{14} -10.3676 q^{15} +1.00000 q^{16} -3.49152 q^{17} +7.12426 q^{18} -4.71735 q^{19} +3.25833 q^{20} -2.32580 q^{21} -5.75818 q^{22} +3.36271 q^{23} -3.18186 q^{24} +5.61671 q^{25} +6.39012 q^{26} -13.1228 q^{27} +0.730955 q^{28} -8.76673 q^{29} -10.3676 q^{30} -2.41031 q^{31} +1.00000 q^{32} +18.3217 q^{33} -3.49152 q^{34} +2.38169 q^{35} +7.12426 q^{36} -1.65316 q^{37} -4.71735 q^{38} -20.3325 q^{39} +3.25833 q^{40} +9.18948 q^{41} -2.32580 q^{42} -10.1578 q^{43} -5.75818 q^{44} +23.2132 q^{45} +3.36271 q^{46} -5.76558 q^{47} -3.18186 q^{48} -6.46571 q^{49} +5.61671 q^{50} +11.1095 q^{51} +6.39012 q^{52} -12.3589 q^{53} -13.1228 q^{54} -18.7620 q^{55} +0.730955 q^{56} +15.0100 q^{57} -8.76673 q^{58} -3.29878 q^{59} -10.3676 q^{60} -3.47464 q^{61} -2.41031 q^{62} +5.20751 q^{63} +1.00000 q^{64} +20.8211 q^{65} +18.3217 q^{66} -6.19459 q^{67} -3.49152 q^{68} -10.6997 q^{69} +2.38169 q^{70} +3.91510 q^{71} +7.12426 q^{72} -13.0659 q^{73} -1.65316 q^{74} -17.8716 q^{75} -4.71735 q^{76} -4.20897 q^{77} -20.3325 q^{78} +5.70341 q^{79} +3.25833 q^{80} +20.3823 q^{81} +9.18948 q^{82} +5.97097 q^{83} -2.32580 q^{84} -11.3765 q^{85} -10.1578 q^{86} +27.8946 q^{87} -5.75818 q^{88} -6.76257 q^{89} +23.2132 q^{90} +4.67089 q^{91} +3.36271 q^{92} +7.66929 q^{93} -5.76558 q^{94} -15.3707 q^{95} -3.18186 q^{96} -18.9015 q^{97} -6.46571 q^{98} -41.0228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 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
\(3\) −3.18186 −1.83705 −0.918525 0.395363i \(-0.870619\pi\)
−0.918525 + 0.395363i \(0.870619\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.25833 1.45717 0.728585 0.684956i \(-0.240179\pi\)
0.728585 + 0.684956i \(0.240179\pi\)
\(6\) −3.18186 −1.29899
\(7\) 0.730955 0.276275 0.138137 0.990413i \(-0.455888\pi\)
0.138137 + 0.990413i \(0.455888\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.12426 2.37475
\(10\) 3.25833 1.03037
\(11\) −5.75818 −1.73616 −0.868078 0.496428i \(-0.834645\pi\)
−0.868078 + 0.496428i \(0.834645\pi\)
\(12\) −3.18186 −0.918525
\(13\) 6.39012 1.77230 0.886151 0.463397i \(-0.153370\pi\)
0.886151 + 0.463397i \(0.153370\pi\)
\(14\) 0.730955 0.195356
\(15\) −10.3676 −2.67689
\(16\) 1.00000 0.250000
\(17\) −3.49152 −0.846817 −0.423408 0.905939i \(-0.639166\pi\)
−0.423408 + 0.905939i \(0.639166\pi\)
\(18\) 7.12426 1.67920
\(19\) −4.71735 −1.08224 −0.541118 0.840947i \(-0.681999\pi\)
−0.541118 + 0.840947i \(0.681999\pi\)
\(20\) 3.25833 0.728585
\(21\) −2.32580 −0.507531
\(22\) −5.75818 −1.22765
\(23\) 3.36271 0.701173 0.350586 0.936530i \(-0.385982\pi\)
0.350586 + 0.936530i \(0.385982\pi\)
\(24\) −3.18186 −0.649495
\(25\) 5.61671 1.12334
\(26\) 6.39012 1.25321
\(27\) −13.1228 −2.52549
\(28\) 0.730955 0.138137
\(29\) −8.76673 −1.62794 −0.813971 0.580906i \(-0.802698\pi\)
−0.813971 + 0.580906i \(0.802698\pi\)
\(30\) −10.3676 −1.89285
\(31\) −2.41031 −0.432905 −0.216452 0.976293i \(-0.569449\pi\)
−0.216452 + 0.976293i \(0.569449\pi\)
\(32\) 1.00000 0.176777
\(33\) 18.3217 3.18940
\(34\) −3.49152 −0.598790
\(35\) 2.38169 0.402579
\(36\) 7.12426 1.18738
\(37\) −1.65316 −0.271778 −0.135889 0.990724i \(-0.543389\pi\)
−0.135889 + 0.990724i \(0.543389\pi\)
\(38\) −4.71735 −0.765256
\(39\) −20.3325 −3.25581
\(40\) 3.25833 0.515187
\(41\) 9.18948 1.43516 0.717578 0.696478i \(-0.245251\pi\)
0.717578 + 0.696478i \(0.245251\pi\)
\(42\) −2.32580 −0.358879
\(43\) −10.1578 −1.54904 −0.774522 0.632547i \(-0.782010\pi\)
−0.774522 + 0.632547i \(0.782010\pi\)
\(44\) −5.75818 −0.868078
\(45\) 23.2132 3.46042
\(46\) 3.36271 0.495804
\(47\) −5.76558 −0.840996 −0.420498 0.907293i \(-0.638145\pi\)
−0.420498 + 0.907293i \(0.638145\pi\)
\(48\) −3.18186 −0.459263
\(49\) −6.46571 −0.923672
\(50\) 5.61671 0.794323
\(51\) 11.1095 1.55565
\(52\) 6.39012 0.886151
\(53\) −12.3589 −1.69762 −0.848810 0.528698i \(-0.822680\pi\)
−0.848810 + 0.528698i \(0.822680\pi\)
\(54\) −13.1228 −1.78579
\(55\) −18.7620 −2.52987
\(56\) 0.730955 0.0976779
\(57\) 15.0100 1.98812
\(58\) −8.76673 −1.15113
\(59\) −3.29878 −0.429465 −0.214732 0.976673i \(-0.568888\pi\)
−0.214732 + 0.976673i \(0.568888\pi\)
\(60\) −10.3676 −1.33845
\(61\) −3.47464 −0.444882 −0.222441 0.974946i \(-0.571402\pi\)
−0.222441 + 0.974946i \(0.571402\pi\)
\(62\) −2.41031 −0.306110
\(63\) 5.20751 0.656085
\(64\) 1.00000 0.125000
\(65\) 20.8211 2.58254
\(66\) 18.3217 2.25525
\(67\) −6.19459 −0.756789 −0.378395 0.925644i \(-0.623524\pi\)
−0.378395 + 0.925644i \(0.623524\pi\)
\(68\) −3.49152 −0.423408
\(69\) −10.6997 −1.28809
\(70\) 2.38169 0.284667
\(71\) 3.91510 0.464637 0.232319 0.972640i \(-0.425369\pi\)
0.232319 + 0.972640i \(0.425369\pi\)
\(72\) 7.12426 0.839602
\(73\) −13.0659 −1.52925 −0.764626 0.644474i \(-0.777076\pi\)
−0.764626 + 0.644474i \(0.777076\pi\)
\(74\) −1.65316 −0.192176
\(75\) −17.8716 −2.06364
\(76\) −4.71735 −0.541118
\(77\) −4.20897 −0.479656
\(78\) −20.3325 −2.30220
\(79\) 5.70341 0.641684 0.320842 0.947133i \(-0.396034\pi\)
0.320842 + 0.947133i \(0.396034\pi\)
\(80\) 3.25833 0.364292
\(81\) 20.3823 2.26470
\(82\) 9.18948 1.01481
\(83\) 5.97097 0.655399 0.327700 0.944782i \(-0.393727\pi\)
0.327700 + 0.944782i \(0.393727\pi\)
\(84\) −2.32580 −0.253765
\(85\) −11.3765 −1.23396
\(86\) −10.1578 −1.09534
\(87\) 27.8946 2.99061
\(88\) −5.75818 −0.613824
\(89\) −6.76257 −0.716831 −0.358415 0.933562i \(-0.616683\pi\)
−0.358415 + 0.933562i \(0.616683\pi\)
\(90\) 23.2132 2.44689
\(91\) 4.67089 0.489642
\(92\) 3.36271 0.350586
\(93\) 7.66929 0.795268
\(94\) −5.76558 −0.594674
\(95\) −15.3707 −1.57700
\(96\) −3.18186 −0.324748
\(97\) −18.9015 −1.91916 −0.959579 0.281441i \(-0.909188\pi\)
−0.959579 + 0.281441i \(0.909188\pi\)
\(98\) −6.46571 −0.653135
\(99\) −41.0228 −4.12294
\(100\) 5.61671 0.561671
\(101\) 6.91866 0.688432 0.344216 0.938890i \(-0.388145\pi\)
0.344216 + 0.938890i \(0.388145\pi\)
\(102\) 11.1095 1.10001
\(103\) 10.4480 1.02947 0.514735 0.857349i \(-0.327890\pi\)
0.514735 + 0.857349i \(0.327890\pi\)
\(104\) 6.39012 0.626603
\(105\) −7.57822 −0.739558
\(106\) −12.3589 −1.20040
\(107\) 4.80472 0.464490 0.232245 0.972657i \(-0.425393\pi\)
0.232245 + 0.972657i \(0.425393\pi\)
\(108\) −13.1228 −1.26275
\(109\) 9.08343 0.870034 0.435017 0.900422i \(-0.356742\pi\)
0.435017 + 0.900422i \(0.356742\pi\)
\(110\) −18.7620 −1.78889
\(111\) 5.26014 0.499270
\(112\) 0.730955 0.0690687
\(113\) 15.9610 1.50149 0.750743 0.660594i \(-0.229696\pi\)
0.750743 + 0.660594i \(0.229696\pi\)
\(114\) 15.0100 1.40581
\(115\) 10.9568 1.02173
\(116\) −8.76673 −0.813971
\(117\) 45.5249 4.20878
\(118\) −3.29878 −0.303678
\(119\) −2.55214 −0.233954
\(120\) −10.3676 −0.946425
\(121\) 22.1566 2.01424
\(122\) −3.47464 −0.314579
\(123\) −29.2397 −2.63645
\(124\) −2.41031 −0.216452
\(125\) 2.00944 0.179730
\(126\) 5.20751 0.463922
\(127\) 14.8746 1.31991 0.659953 0.751307i \(-0.270576\pi\)
0.659953 + 0.751307i \(0.270576\pi\)
\(128\) 1.00000 0.0883883
\(129\) 32.3206 2.84567
\(130\) 20.8211 1.82613
\(131\) 1.43415 0.125303 0.0626513 0.998035i \(-0.480044\pi\)
0.0626513 + 0.998035i \(0.480044\pi\)
\(132\) 18.3217 1.59470
\(133\) −3.44817 −0.298994
\(134\) −6.19459 −0.535131
\(135\) −42.7585 −3.68007
\(136\) −3.49152 −0.299395
\(137\) 10.0698 0.860319 0.430159 0.902753i \(-0.358457\pi\)
0.430159 + 0.902753i \(0.358457\pi\)
\(138\) −10.6997 −0.910817
\(139\) −7.96726 −0.675774 −0.337887 0.941187i \(-0.609712\pi\)
−0.337887 + 0.941187i \(0.609712\pi\)
\(140\) 2.38169 0.201290
\(141\) 18.3453 1.54495
\(142\) 3.91510 0.328548
\(143\) −36.7955 −3.07699
\(144\) 7.12426 0.593688
\(145\) −28.5649 −2.37219
\(146\) −13.0659 −1.08135
\(147\) 20.5730 1.69683
\(148\) −1.65316 −0.135889
\(149\) 3.90248 0.319704 0.159852 0.987141i \(-0.448898\pi\)
0.159852 + 0.987141i \(0.448898\pi\)
\(150\) −17.8716 −1.45921
\(151\) 2.76698 0.225173 0.112587 0.993642i \(-0.464086\pi\)
0.112587 + 0.993642i \(0.464086\pi\)
\(152\) −4.71735 −0.382628
\(153\) −24.8745 −2.01098
\(154\) −4.20897 −0.339168
\(155\) −7.85359 −0.630816
\(156\) −20.3325 −1.62790
\(157\) −15.8994 −1.26891 −0.634454 0.772961i \(-0.718775\pi\)
−0.634454 + 0.772961i \(0.718775\pi\)
\(158\) 5.70341 0.453739
\(159\) 39.3242 3.11861
\(160\) 3.25833 0.257594
\(161\) 2.45799 0.193717
\(162\) 20.3823 1.60139
\(163\) −3.17193 −0.248444 −0.124222 0.992254i \(-0.539644\pi\)
−0.124222 + 0.992254i \(0.539644\pi\)
\(164\) 9.18948 0.717578
\(165\) 59.6983 4.64750
\(166\) 5.97097 0.463437
\(167\) −14.2730 −1.10448 −0.552239 0.833686i \(-0.686226\pi\)
−0.552239 + 0.833686i \(0.686226\pi\)
\(168\) −2.32580 −0.179439
\(169\) 27.8337 2.14105
\(170\) −11.3765 −0.872538
\(171\) −33.6077 −2.57004
\(172\) −10.1578 −0.774522
\(173\) −12.2135 −0.928574 −0.464287 0.885685i \(-0.653689\pi\)
−0.464287 + 0.885685i \(0.653689\pi\)
\(174\) 27.8946 2.11468
\(175\) 4.10556 0.310351
\(176\) −5.75818 −0.434039
\(177\) 10.4963 0.788949
\(178\) −6.76257 −0.506876
\(179\) 16.6232 1.24248 0.621238 0.783622i \(-0.286630\pi\)
0.621238 + 0.783622i \(0.286630\pi\)
\(180\) 23.2132 1.73021
\(181\) 4.65824 0.346244 0.173122 0.984900i \(-0.444614\pi\)
0.173122 + 0.984900i \(0.444614\pi\)
\(182\) 4.67089 0.346229
\(183\) 11.0558 0.817270
\(184\) 3.36271 0.247902
\(185\) −5.38655 −0.396027
\(186\) 7.66929 0.562339
\(187\) 20.1048 1.47021
\(188\) −5.76558 −0.420498
\(189\) −9.59220 −0.697730
\(190\) −15.3707 −1.11511
\(191\) −16.9489 −1.22638 −0.613190 0.789936i \(-0.710114\pi\)
−0.613190 + 0.789936i \(0.710114\pi\)
\(192\) −3.18186 −0.229631
\(193\) 17.4848 1.25858 0.629291 0.777170i \(-0.283345\pi\)
0.629291 + 0.777170i \(0.283345\pi\)
\(194\) −18.9015 −1.35705
\(195\) −66.2500 −4.74426
\(196\) −6.46571 −0.461836
\(197\) −13.3981 −0.954576 −0.477288 0.878747i \(-0.658380\pi\)
−0.477288 + 0.878747i \(0.658380\pi\)
\(198\) −41.0228 −2.91536
\(199\) −3.66238 −0.259619 −0.129810 0.991539i \(-0.541437\pi\)
−0.129810 + 0.991539i \(0.541437\pi\)
\(200\) 5.61671 0.397161
\(201\) 19.7103 1.39026
\(202\) 6.91866 0.486795
\(203\) −6.40808 −0.449759
\(204\) 11.1095 0.777823
\(205\) 29.9423 2.09126
\(206\) 10.4480 0.727946
\(207\) 23.9568 1.66511
\(208\) 6.39012 0.443075
\(209\) 27.1634 1.87893
\(210\) −7.57822 −0.522947
\(211\) 16.6422 1.14569 0.572847 0.819662i \(-0.305839\pi\)
0.572847 + 0.819662i \(0.305839\pi\)
\(212\) −12.3589 −0.848810
\(213\) −12.4573 −0.853562
\(214\) 4.80472 0.328444
\(215\) −33.0973 −2.25722
\(216\) −13.1228 −0.892896
\(217\) −1.76183 −0.119601
\(218\) 9.08343 0.615207
\(219\) 41.5741 2.80931
\(220\) −18.7620 −1.26494
\(221\) −22.3112 −1.50081
\(222\) 5.26014 0.353037
\(223\) −15.6933 −1.05090 −0.525452 0.850823i \(-0.676104\pi\)
−0.525452 + 0.850823i \(0.676104\pi\)
\(224\) 0.730955 0.0488390
\(225\) 40.0149 2.66766
\(226\) 15.9610 1.06171
\(227\) −21.4540 −1.42395 −0.711974 0.702205i \(-0.752199\pi\)
−0.711974 + 0.702205i \(0.752199\pi\)
\(228\) 15.0100 0.994060
\(229\) −0.269337 −0.0177983 −0.00889913 0.999960i \(-0.502833\pi\)
−0.00889913 + 0.999960i \(0.502833\pi\)
\(230\) 10.9568 0.722470
\(231\) 13.3924 0.881153
\(232\) −8.76673 −0.575564
\(233\) −24.5826 −1.61046 −0.805230 0.592962i \(-0.797958\pi\)
−0.805230 + 0.592962i \(0.797958\pi\)
\(234\) 45.5249 2.97606
\(235\) −18.7862 −1.22547
\(236\) −3.29878 −0.214732
\(237\) −18.1475 −1.17881
\(238\) −2.55214 −0.165431
\(239\) −23.0023 −1.48789 −0.743947 0.668239i \(-0.767049\pi\)
−0.743947 + 0.668239i \(0.767049\pi\)
\(240\) −10.3676 −0.669223
\(241\) −7.66395 −0.493679 −0.246839 0.969056i \(-0.579392\pi\)
−0.246839 + 0.969056i \(0.579392\pi\)
\(242\) 22.1566 1.42428
\(243\) −25.4852 −1.63488
\(244\) −3.47464 −0.222441
\(245\) −21.0674 −1.34595
\(246\) −29.2397 −1.86425
\(247\) −30.1445 −1.91805
\(248\) −2.41031 −0.153055
\(249\) −18.9988 −1.20400
\(250\) 2.00944 0.127088
\(251\) −2.40741 −0.151955 −0.0759773 0.997110i \(-0.524208\pi\)
−0.0759773 + 0.997110i \(0.524208\pi\)
\(252\) 5.20751 0.328042
\(253\) −19.3631 −1.21735
\(254\) 14.8746 0.933315
\(255\) 36.1985 2.26684
\(256\) 1.00000 0.0625000
\(257\) 16.2530 1.01384 0.506918 0.861994i \(-0.330785\pi\)
0.506918 + 0.861994i \(0.330785\pi\)
\(258\) 32.3206 2.01219
\(259\) −1.20839 −0.0750855
\(260\) 20.8211 1.29127
\(261\) −62.4565 −3.86596
\(262\) 1.43415 0.0886024
\(263\) −8.95933 −0.552456 −0.276228 0.961092i \(-0.589085\pi\)
−0.276228 + 0.961092i \(0.589085\pi\)
\(264\) 18.3217 1.12762
\(265\) −40.2692 −2.47372
\(266\) −3.44817 −0.211421
\(267\) 21.5176 1.31685
\(268\) −6.19459 −0.378395
\(269\) −11.0489 −0.673661 −0.336831 0.941565i \(-0.609355\pi\)
−0.336831 + 0.941565i \(0.609355\pi\)
\(270\) −42.7585 −2.60220
\(271\) 20.2615 1.23080 0.615399 0.788216i \(-0.288995\pi\)
0.615399 + 0.788216i \(0.288995\pi\)
\(272\) −3.49152 −0.211704
\(273\) −14.8621 −0.899498
\(274\) 10.0698 0.608337
\(275\) −32.3420 −1.95030
\(276\) −10.6997 −0.644045
\(277\) −16.0554 −0.964678 −0.482339 0.875985i \(-0.660213\pi\)
−0.482339 + 0.875985i \(0.660213\pi\)
\(278\) −7.96726 −0.477845
\(279\) −17.1717 −1.02804
\(280\) 2.38169 0.142333
\(281\) 14.6147 0.871842 0.435921 0.899985i \(-0.356423\pi\)
0.435921 + 0.899985i \(0.356423\pi\)
\(282\) 18.3453 1.09245
\(283\) 18.9708 1.12769 0.563847 0.825879i \(-0.309321\pi\)
0.563847 + 0.825879i \(0.309321\pi\)
\(284\) 3.91510 0.232319
\(285\) 48.9075 2.89703
\(286\) −36.7955 −2.17576
\(287\) 6.71709 0.396497
\(288\) 7.12426 0.419801
\(289\) −4.80932 −0.282901
\(290\) −28.5649 −1.67739
\(291\) 60.1420 3.52559
\(292\) −13.0659 −0.764626
\(293\) −11.3485 −0.662988 −0.331494 0.943457i \(-0.607553\pi\)
−0.331494 + 0.943457i \(0.607553\pi\)
\(294\) 20.5730 1.19984
\(295\) −10.7485 −0.625803
\(296\) −1.65316 −0.0960881
\(297\) 75.5636 4.38465
\(298\) 3.90248 0.226065
\(299\) 21.4881 1.24269
\(300\) −17.8716 −1.03182
\(301\) −7.42487 −0.427962
\(302\) 2.76698 0.159222
\(303\) −22.0142 −1.26469
\(304\) −4.71735 −0.270559
\(305\) −11.3215 −0.648268
\(306\) −24.8745 −1.42198
\(307\) 33.8698 1.93305 0.966527 0.256564i \(-0.0825905\pi\)
0.966527 + 0.256564i \(0.0825905\pi\)
\(308\) −4.20897 −0.239828
\(309\) −33.2441 −1.89119
\(310\) −7.85359 −0.446054
\(311\) 4.54087 0.257489 0.128745 0.991678i \(-0.458905\pi\)
0.128745 + 0.991678i \(0.458905\pi\)
\(312\) −20.3325 −1.15110
\(313\) 9.53960 0.539210 0.269605 0.962971i \(-0.413107\pi\)
0.269605 + 0.962971i \(0.413107\pi\)
\(314\) −15.8994 −0.897254
\(315\) 16.9678 0.956027
\(316\) 5.70341 0.320842
\(317\) −24.1254 −1.35502 −0.677510 0.735514i \(-0.736941\pi\)
−0.677510 + 0.735514i \(0.736941\pi\)
\(318\) 39.3242 2.20519
\(319\) 50.4804 2.82636
\(320\) 3.25833 0.182146
\(321\) −15.2880 −0.853291
\(322\) 2.45799 0.136978
\(323\) 16.4707 0.916455
\(324\) 20.3823 1.13235
\(325\) 35.8915 1.99090
\(326\) −3.17193 −0.175677
\(327\) −28.9022 −1.59830
\(328\) 9.18948 0.507404
\(329\) −4.21438 −0.232346
\(330\) 59.6983 3.28628
\(331\) −27.3148 −1.50136 −0.750679 0.660667i \(-0.770273\pi\)
−0.750679 + 0.660667i \(0.770273\pi\)
\(332\) 5.97097 0.327700
\(333\) −11.7776 −0.645406
\(334\) −14.2730 −0.780984
\(335\) −20.1840 −1.10277
\(336\) −2.32580 −0.126883
\(337\) 3.25159 0.177125 0.0885627 0.996071i \(-0.471773\pi\)
0.0885627 + 0.996071i \(0.471773\pi\)
\(338\) 27.8337 1.51395
\(339\) −50.7858 −2.75831
\(340\) −11.3765 −0.616978
\(341\) 13.8790 0.751590
\(342\) −33.6077 −1.81729
\(343\) −9.84282 −0.531462
\(344\) −10.1578 −0.547670
\(345\) −34.8631 −1.87696
\(346\) −12.2135 −0.656601
\(347\) 6.76218 0.363013 0.181506 0.983390i \(-0.441903\pi\)
0.181506 + 0.983390i \(0.441903\pi\)
\(348\) 27.8946 1.49530
\(349\) −21.6154 −1.15704 −0.578522 0.815667i \(-0.696370\pi\)
−0.578522 + 0.815667i \(0.696370\pi\)
\(350\) 4.10556 0.219451
\(351\) −83.8566 −4.47593
\(352\) −5.75818 −0.306912
\(353\) 13.4774 0.717331 0.358666 0.933466i \(-0.383232\pi\)
0.358666 + 0.933466i \(0.383232\pi\)
\(354\) 10.4963 0.557871
\(355\) 12.7567 0.677055
\(356\) −6.76257 −0.358415
\(357\) 8.12056 0.429786
\(358\) 16.6232 0.878563
\(359\) 6.90181 0.364264 0.182132 0.983274i \(-0.441700\pi\)
0.182132 + 0.983274i \(0.441700\pi\)
\(360\) 23.2132 1.22344
\(361\) 3.25343 0.171233
\(362\) 4.65824 0.244832
\(363\) −70.4993 −3.70025
\(364\) 4.67089 0.244821
\(365\) −42.5731 −2.22838
\(366\) 11.0558 0.577897
\(367\) 13.5564 0.707641 0.353820 0.935313i \(-0.384882\pi\)
0.353820 + 0.935313i \(0.384882\pi\)
\(368\) 3.36271 0.175293
\(369\) 65.4682 3.40814
\(370\) −5.38655 −0.280033
\(371\) −9.03376 −0.469010
\(372\) 7.66929 0.397634
\(373\) −16.4605 −0.852291 −0.426145 0.904655i \(-0.640129\pi\)
−0.426145 + 0.904655i \(0.640129\pi\)
\(374\) 20.1048 1.03959
\(375\) −6.39378 −0.330173
\(376\) −5.76558 −0.297337
\(377\) −56.0205 −2.88520
\(378\) −9.59220 −0.493370
\(379\) −35.4651 −1.82172 −0.910860 0.412716i \(-0.864580\pi\)
−0.910860 + 0.412716i \(0.864580\pi\)
\(380\) −15.3707 −0.788500
\(381\) −47.3289 −2.42473
\(382\) −16.9489 −0.867181
\(383\) 28.2598 1.44401 0.722004 0.691889i \(-0.243221\pi\)
0.722004 + 0.691889i \(0.243221\pi\)
\(384\) −3.18186 −0.162374
\(385\) −13.7142 −0.698940
\(386\) 17.4848 0.889951
\(387\) −72.3666 −3.67860
\(388\) −18.9015 −0.959579
\(389\) −28.6301 −1.45160 −0.725801 0.687905i \(-0.758531\pi\)
−0.725801 + 0.687905i \(0.758531\pi\)
\(390\) −66.2500 −3.35470
\(391\) −11.7409 −0.593765
\(392\) −6.46571 −0.326567
\(393\) −4.56329 −0.230187
\(394\) −13.3981 −0.674987
\(395\) 18.5836 0.935043
\(396\) −41.0228 −2.06147
\(397\) 29.1457 1.46278 0.731390 0.681960i \(-0.238872\pi\)
0.731390 + 0.681960i \(0.238872\pi\)
\(398\) −3.66238 −0.183579
\(399\) 10.9716 0.549268
\(400\) 5.61671 0.280836
\(401\) 2.03995 0.101870 0.0509352 0.998702i \(-0.483780\pi\)
0.0509352 + 0.998702i \(0.483780\pi\)
\(402\) 19.7103 0.983062
\(403\) −15.4022 −0.767238
\(404\) 6.91866 0.344216
\(405\) 66.4123 3.30005
\(406\) −6.40808 −0.318028
\(407\) 9.51920 0.471849
\(408\) 11.1095 0.550004
\(409\) 13.0344 0.644509 0.322254 0.946653i \(-0.395559\pi\)
0.322254 + 0.946653i \(0.395559\pi\)
\(410\) 29.9423 1.47875
\(411\) −32.0406 −1.58045
\(412\) 10.4480 0.514735
\(413\) −2.41126 −0.118650
\(414\) 23.9568 1.17741
\(415\) 19.4554 0.955028
\(416\) 6.39012 0.313302
\(417\) 25.3508 1.24143
\(418\) 27.1634 1.32860
\(419\) 10.4099 0.508558 0.254279 0.967131i \(-0.418162\pi\)
0.254279 + 0.967131i \(0.418162\pi\)
\(420\) −7.57822 −0.369779
\(421\) 2.74094 0.133585 0.0667927 0.997767i \(-0.478723\pi\)
0.0667927 + 0.997767i \(0.478723\pi\)
\(422\) 16.6422 0.810129
\(423\) −41.0755 −1.99716
\(424\) −12.3589 −0.600199
\(425\) −19.6108 −0.951265
\(426\) −12.4573 −0.603559
\(427\) −2.53980 −0.122910
\(428\) 4.80472 0.232245
\(429\) 117.078 5.65259
\(430\) −33.0973 −1.59610
\(431\) −18.7175 −0.901588 −0.450794 0.892628i \(-0.648859\pi\)
−0.450794 + 0.892628i \(0.648859\pi\)
\(432\) −13.1228 −0.631373
\(433\) 33.0512 1.58834 0.794170 0.607696i \(-0.207906\pi\)
0.794170 + 0.607696i \(0.207906\pi\)
\(434\) −1.76183 −0.0845705
\(435\) 90.8896 4.35782
\(436\) 9.08343 0.435017
\(437\) −15.8631 −0.758834
\(438\) 41.5741 1.98649
\(439\) −16.9884 −0.810812 −0.405406 0.914137i \(-0.632870\pi\)
−0.405406 + 0.914137i \(0.632870\pi\)
\(440\) −18.7620 −0.894445
\(441\) −46.0634 −2.19349
\(442\) −22.3112 −1.06124
\(443\) 8.95033 0.425243 0.212621 0.977135i \(-0.431800\pi\)
0.212621 + 0.977135i \(0.431800\pi\)
\(444\) 5.26014 0.249635
\(445\) −22.0347 −1.04454
\(446\) −15.6933 −0.743101
\(447\) −12.4172 −0.587312
\(448\) 0.730955 0.0345344
\(449\) −40.1425 −1.89444 −0.947221 0.320583i \(-0.896121\pi\)
−0.947221 + 0.320583i \(0.896121\pi\)
\(450\) 40.0149 1.88632
\(451\) −52.9146 −2.49165
\(452\) 15.9610 0.750743
\(453\) −8.80414 −0.413655
\(454\) −21.4540 −1.00688
\(455\) 15.2193 0.713492
\(456\) 15.0100 0.702907
\(457\) 7.34381 0.343529 0.171764 0.985138i \(-0.445053\pi\)
0.171764 + 0.985138i \(0.445053\pi\)
\(458\) −0.269337 −0.0125853
\(459\) 45.8186 2.13863
\(460\) 10.9568 0.510864
\(461\) −28.4444 −1.32479 −0.662395 0.749155i \(-0.730460\pi\)
−0.662395 + 0.749155i \(0.730460\pi\)
\(462\) 13.3924 0.623069
\(463\) −18.5267 −0.861008 −0.430504 0.902589i \(-0.641664\pi\)
−0.430504 + 0.902589i \(0.641664\pi\)
\(464\) −8.76673 −0.406985
\(465\) 24.9891 1.15884
\(466\) −24.5826 −1.13877
\(467\) −7.41094 −0.342937 −0.171469 0.985190i \(-0.554851\pi\)
−0.171469 + 0.985190i \(0.554851\pi\)
\(468\) 45.5249 2.10439
\(469\) −4.52796 −0.209082
\(470\) −18.7862 −0.866541
\(471\) 50.5896 2.33105
\(472\) −3.29878 −0.151839
\(473\) 58.4902 2.68938
\(474\) −18.1475 −0.833542
\(475\) −26.4960 −1.21572
\(476\) −2.55214 −0.116977
\(477\) −88.0477 −4.03143
\(478\) −23.0023 −1.05210
\(479\) 40.0605 1.83041 0.915206 0.402987i \(-0.132028\pi\)
0.915206 + 0.402987i \(0.132028\pi\)
\(480\) −10.3676 −0.473212
\(481\) −10.5639 −0.481673
\(482\) −7.66395 −0.349084
\(483\) −7.82098 −0.355867
\(484\) 22.1566 1.00712
\(485\) −61.5873 −2.79654
\(486\) −25.4852 −1.15603
\(487\) −23.3099 −1.05627 −0.528137 0.849159i \(-0.677109\pi\)
−0.528137 + 0.849159i \(0.677109\pi\)
\(488\) −3.47464 −0.157290
\(489\) 10.0926 0.456405
\(490\) −21.0674 −0.951728
\(491\) −20.7248 −0.935295 −0.467648 0.883915i \(-0.654898\pi\)
−0.467648 + 0.883915i \(0.654898\pi\)
\(492\) −29.2397 −1.31823
\(493\) 30.6092 1.37857
\(494\) −30.1445 −1.35626
\(495\) −133.666 −6.00782
\(496\) −2.41031 −0.108226
\(497\) 2.86176 0.128368
\(498\) −18.9988 −0.851358
\(499\) 32.6856 1.46321 0.731604 0.681730i \(-0.238772\pi\)
0.731604 + 0.681730i \(0.238772\pi\)
\(500\) 2.00944 0.0898651
\(501\) 45.4147 2.02898
\(502\) −2.40741 −0.107448
\(503\) −22.8957 −1.02087 −0.510434 0.859917i \(-0.670515\pi\)
−0.510434 + 0.859917i \(0.670515\pi\)
\(504\) 5.20751 0.231961
\(505\) 22.5433 1.00316
\(506\) −19.3631 −0.860793
\(507\) −88.5630 −3.93322
\(508\) 14.8746 0.659953
\(509\) −21.0881 −0.934715 −0.467357 0.884068i \(-0.654794\pi\)
−0.467357 + 0.884068i \(0.654794\pi\)
\(510\) 36.1985 1.60290
\(511\) −9.55061 −0.422494
\(512\) 1.00000 0.0441942
\(513\) 61.9051 2.73318
\(514\) 16.2530 0.716891
\(515\) 34.0430 1.50011
\(516\) 32.3206 1.42284
\(517\) 33.1992 1.46010
\(518\) −1.20839 −0.0530935
\(519\) 38.8616 1.70584
\(520\) 20.8211 0.913067
\(521\) −30.1264 −1.31986 −0.659931 0.751326i \(-0.729415\pi\)
−0.659931 + 0.751326i \(0.729415\pi\)
\(522\) −62.4565 −2.73365
\(523\) 36.4701 1.59472 0.797362 0.603501i \(-0.206228\pi\)
0.797362 + 0.603501i \(0.206228\pi\)
\(524\) 1.43415 0.0626513
\(525\) −13.0633 −0.570131
\(526\) −8.95933 −0.390646
\(527\) 8.41564 0.366591
\(528\) 18.3217 0.797351
\(529\) −11.6922 −0.508357
\(530\) −40.2692 −1.74918
\(531\) −23.5014 −1.01987
\(532\) −3.44817 −0.149497
\(533\) 58.7219 2.54353
\(534\) 21.5176 0.931157
\(535\) 15.6554 0.676840
\(536\) −6.19459 −0.267565
\(537\) −52.8927 −2.28249
\(538\) −11.0489 −0.476350
\(539\) 37.2307 1.60364
\(540\) −42.7585 −1.84003
\(541\) 14.1947 0.610277 0.305138 0.952308i \(-0.401297\pi\)
0.305138 + 0.952308i \(0.401297\pi\)
\(542\) 20.2615 0.870306
\(543\) −14.8219 −0.636068
\(544\) −3.49152 −0.149697
\(545\) 29.5968 1.26779
\(546\) −14.8621 −0.636041
\(547\) 11.1207 0.475486 0.237743 0.971328i \(-0.423592\pi\)
0.237743 + 0.971328i \(0.423592\pi\)
\(548\) 10.0698 0.430159
\(549\) −24.7542 −1.05649
\(550\) −32.3420 −1.37907
\(551\) 41.3558 1.76182
\(552\) −10.6997 −0.455409
\(553\) 4.16894 0.177281
\(554\) −16.0554 −0.682130
\(555\) 17.1393 0.727521
\(556\) −7.96726 −0.337887
\(557\) −2.95092 −0.125034 −0.0625172 0.998044i \(-0.519913\pi\)
−0.0625172 + 0.998044i \(0.519913\pi\)
\(558\) −17.1717 −0.726936
\(559\) −64.9094 −2.74537
\(560\) 2.38169 0.100645
\(561\) −63.9706 −2.70084
\(562\) 14.6147 0.616485
\(563\) −9.11591 −0.384190 −0.192095 0.981376i \(-0.561528\pi\)
−0.192095 + 0.981376i \(0.561528\pi\)
\(564\) 18.3453 0.772476
\(565\) 52.0063 2.18792
\(566\) 18.9708 0.797400
\(567\) 14.8986 0.625680
\(568\) 3.91510 0.164274
\(569\) 14.0235 0.587894 0.293947 0.955822i \(-0.405031\pi\)
0.293947 + 0.955822i \(0.405031\pi\)
\(570\) 48.9075 2.04851
\(571\) 32.8245 1.37366 0.686831 0.726817i \(-0.259001\pi\)
0.686831 + 0.726817i \(0.259001\pi\)
\(572\) −36.7955 −1.53850
\(573\) 53.9291 2.25292
\(574\) 6.71709 0.280366
\(575\) 18.8874 0.787657
\(576\) 7.12426 0.296844
\(577\) 24.8871 1.03607 0.518033 0.855361i \(-0.326665\pi\)
0.518033 + 0.855361i \(0.326665\pi\)
\(578\) −4.80932 −0.200041
\(579\) −55.6342 −2.31208
\(580\) −28.5649 −1.18609
\(581\) 4.36451 0.181070
\(582\) 60.1420 2.49297
\(583\) 71.1645 2.94733
\(584\) −13.0659 −0.540673
\(585\) 148.335 6.13290
\(586\) −11.3485 −0.468804
\(587\) 37.7809 1.55938 0.779692 0.626163i \(-0.215376\pi\)
0.779692 + 0.626163i \(0.215376\pi\)
\(588\) 20.5730 0.848416
\(589\) 11.3703 0.468505
\(590\) −10.7485 −0.442510
\(591\) 42.6310 1.75360
\(592\) −1.65316 −0.0679445
\(593\) 13.2399 0.543696 0.271848 0.962340i \(-0.412365\pi\)
0.271848 + 0.962340i \(0.412365\pi\)
\(594\) 75.5636 3.10041
\(595\) −8.31571 −0.340911
\(596\) 3.90248 0.159852
\(597\) 11.6532 0.476934
\(598\) 21.4881 0.878714
\(599\) −7.42702 −0.303460 −0.151730 0.988422i \(-0.548484\pi\)
−0.151730 + 0.988422i \(0.548484\pi\)
\(600\) −17.8716 −0.729605
\(601\) −40.0027 −1.63174 −0.815872 0.578232i \(-0.803743\pi\)
−0.815872 + 0.578232i \(0.803743\pi\)
\(602\) −7.42487 −0.302615
\(603\) −44.1318 −1.79719
\(604\) 2.76698 0.112587
\(605\) 72.1935 2.93508
\(606\) −22.0142 −0.894267
\(607\) −29.1085 −1.18148 −0.590740 0.806862i \(-0.701164\pi\)
−0.590740 + 0.806862i \(0.701164\pi\)
\(608\) −4.71735 −0.191314
\(609\) 20.3897 0.826231
\(610\) −11.3215 −0.458395
\(611\) −36.8428 −1.49050
\(612\) −24.8745 −1.00549
\(613\) 26.7990 1.08240 0.541200 0.840894i \(-0.317970\pi\)
0.541200 + 0.840894i \(0.317970\pi\)
\(614\) 33.8698 1.36688
\(615\) −95.2725 −3.84176
\(616\) −4.20897 −0.169584
\(617\) 21.8951 0.881465 0.440733 0.897638i \(-0.354719\pi\)
0.440733 + 0.897638i \(0.354719\pi\)
\(618\) −33.2441 −1.33727
\(619\) 23.6420 0.950254 0.475127 0.879917i \(-0.342402\pi\)
0.475127 + 0.879917i \(0.342402\pi\)
\(620\) −7.85359 −0.315408
\(621\) −44.1283 −1.77081
\(622\) 4.54087 0.182072
\(623\) −4.94313 −0.198042
\(624\) −20.3325 −0.813952
\(625\) −21.5361 −0.861445
\(626\) 9.53960 0.381279
\(627\) −86.4301 −3.45169
\(628\) −15.8994 −0.634454
\(629\) 5.77204 0.230146
\(630\) 16.9678 0.676013
\(631\) −21.5790 −0.859047 −0.429523 0.903056i \(-0.641318\pi\)
−0.429523 + 0.903056i \(0.641318\pi\)
\(632\) 5.70341 0.226870
\(633\) −52.9532 −2.10470
\(634\) −24.1254 −0.958144
\(635\) 48.4663 1.92333
\(636\) 39.3242 1.55931
\(637\) −41.3167 −1.63703
\(638\) 50.4804 1.99854
\(639\) 27.8922 1.10340
\(640\) 3.25833 0.128797
\(641\) 22.2160 0.877479 0.438740 0.898614i \(-0.355425\pi\)
0.438740 + 0.898614i \(0.355425\pi\)
\(642\) −15.2880 −0.603368
\(643\) −16.4214 −0.647597 −0.323799 0.946126i \(-0.604960\pi\)
−0.323799 + 0.946126i \(0.604960\pi\)
\(644\) 2.45799 0.0968583
\(645\) 105.311 4.14663
\(646\) 16.4707 0.648032
\(647\) 8.67949 0.341226 0.170613 0.985338i \(-0.445425\pi\)
0.170613 + 0.985338i \(0.445425\pi\)
\(648\) 20.3823 0.800693
\(649\) 18.9950 0.745618
\(650\) 35.8915 1.40778
\(651\) 5.60590 0.219713
\(652\) −3.17193 −0.124222
\(653\) −29.1413 −1.14039 −0.570194 0.821510i \(-0.693132\pi\)
−0.570194 + 0.821510i \(0.693132\pi\)
\(654\) −28.9022 −1.13017
\(655\) 4.67295 0.182587
\(656\) 9.18948 0.358789
\(657\) −93.0852 −3.63160
\(658\) −4.21438 −0.164294
\(659\) −19.0624 −0.742568 −0.371284 0.928519i \(-0.621082\pi\)
−0.371284 + 0.928519i \(0.621082\pi\)
\(660\) 59.6983 2.32375
\(661\) 31.8226 1.23776 0.618879 0.785486i \(-0.287587\pi\)
0.618879 + 0.785486i \(0.287587\pi\)
\(662\) −27.3148 −1.06162
\(663\) 70.9913 2.75707
\(664\) 5.97097 0.231719
\(665\) −11.2353 −0.435686
\(666\) −11.7776 −0.456371
\(667\) −29.4800 −1.14147
\(668\) −14.2730 −0.552239
\(669\) 49.9341 1.93056
\(670\) −20.1840 −0.779776
\(671\) 20.0076 0.772384
\(672\) −2.32580 −0.0897196
\(673\) 5.18110 0.199717 0.0998584 0.995002i \(-0.468161\pi\)
0.0998584 + 0.995002i \(0.468161\pi\)
\(674\) 3.25159 0.125247
\(675\) −73.7072 −2.83699
\(676\) 27.8337 1.07053
\(677\) 48.9104 1.87978 0.939890 0.341479i \(-0.110928\pi\)
0.939890 + 0.341479i \(0.110928\pi\)
\(678\) −50.7858 −1.95042
\(679\) −13.8161 −0.530215
\(680\) −11.3765 −0.436269
\(681\) 68.2636 2.61587
\(682\) 13.8790 0.531454
\(683\) 13.7576 0.526419 0.263209 0.964739i \(-0.415219\pi\)
0.263209 + 0.964739i \(0.415219\pi\)
\(684\) −33.6077 −1.28502
\(685\) 32.8106 1.25363
\(686\) −9.84282 −0.375801
\(687\) 0.856993 0.0326963
\(688\) −10.1578 −0.387261
\(689\) −78.9746 −3.00869
\(690\) −34.8631 −1.32721
\(691\) 1.79712 0.0683658 0.0341829 0.999416i \(-0.489117\pi\)
0.0341829 + 0.999416i \(0.489117\pi\)
\(692\) −12.2135 −0.464287
\(693\) −29.9858 −1.13907
\(694\) 6.76218 0.256689
\(695\) −25.9600 −0.984718
\(696\) 27.8946 1.05734
\(697\) −32.0852 −1.21531
\(698\) −21.6154 −0.818153
\(699\) 78.2185 2.95850
\(700\) 4.10556 0.155176
\(701\) −6.07857 −0.229585 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(702\) −83.8566 −3.16496
\(703\) 7.79855 0.294128
\(704\) −5.75818 −0.217019
\(705\) 59.7750 2.25126
\(706\) 13.4774 0.507230
\(707\) 5.05723 0.190197
\(708\) 10.4963 0.394474
\(709\) 19.9584 0.749553 0.374777 0.927115i \(-0.377719\pi\)
0.374777 + 0.927115i \(0.377719\pi\)
\(710\) 12.7567 0.478750
\(711\) 40.6326 1.52384
\(712\) −6.76257 −0.253438
\(713\) −8.10517 −0.303541
\(714\) 8.12056 0.303904
\(715\) −119.892 −4.48370
\(716\) 16.6232 0.621238
\(717\) 73.1901 2.73334
\(718\) 6.90181 0.257573
\(719\) −38.2316 −1.42580 −0.712898 0.701267i \(-0.752618\pi\)
−0.712898 + 0.701267i \(0.752618\pi\)
\(720\) 23.2132 0.865105
\(721\) 7.63700 0.284417
\(722\) 3.25343 0.121080
\(723\) 24.3857 0.906912
\(724\) 4.65824 0.173122
\(725\) −49.2402 −1.82873
\(726\) −70.4993 −2.61647
\(727\) 22.7654 0.844323 0.422162 0.906521i \(-0.361271\pi\)
0.422162 + 0.906521i \(0.361271\pi\)
\(728\) 4.67089 0.173115
\(729\) 19.9436 0.738653
\(730\) −42.5731 −1.57570
\(731\) 35.4660 1.31176
\(732\) 11.0558 0.408635
\(733\) 16.0169 0.591599 0.295800 0.955250i \(-0.404414\pi\)
0.295800 + 0.955250i \(0.404414\pi\)
\(734\) 13.5564 0.500378
\(735\) 67.0336 2.47257
\(736\) 3.36271 0.123951
\(737\) 35.6695 1.31390
\(738\) 65.4682 2.40992
\(739\) −31.9413 −1.17498 −0.587490 0.809231i \(-0.699884\pi\)
−0.587490 + 0.809231i \(0.699884\pi\)
\(740\) −5.38655 −0.198013
\(741\) 95.9156 3.52355
\(742\) −9.03376 −0.331640
\(743\) −35.4020 −1.29877 −0.649387 0.760458i \(-0.724975\pi\)
−0.649387 + 0.760458i \(0.724975\pi\)
\(744\) 7.66929 0.281170
\(745\) 12.7156 0.465862
\(746\) −16.4605 −0.602661
\(747\) 42.5388 1.55641
\(748\) 20.1048 0.735103
\(749\) 3.51203 0.128327
\(750\) −6.39378 −0.233468
\(751\) 39.5106 1.44176 0.720881 0.693059i \(-0.243737\pi\)
0.720881 + 0.693059i \(0.243737\pi\)
\(752\) −5.76558 −0.210249
\(753\) 7.66006 0.279148
\(754\) −56.0205 −2.04015
\(755\) 9.01572 0.328116
\(756\) −9.59220 −0.348865
\(757\) 30.7188 1.11649 0.558247 0.829675i \(-0.311474\pi\)
0.558247 + 0.829675i \(0.311474\pi\)
\(758\) −35.4651 −1.28815
\(759\) 61.6106 2.23632
\(760\) −15.3707 −0.557554
\(761\) −35.7388 −1.29553 −0.647765 0.761840i \(-0.724296\pi\)
−0.647765 + 0.761840i \(0.724296\pi\)
\(762\) −47.3289 −1.71455
\(763\) 6.63957 0.240369
\(764\) −16.9489 −0.613190
\(765\) −81.0492 −2.93034
\(766\) 28.2598 1.02107
\(767\) −21.0796 −0.761141
\(768\) −3.18186 −0.114816
\(769\) −19.3434 −0.697540 −0.348770 0.937208i \(-0.613401\pi\)
−0.348770 + 0.937208i \(0.613401\pi\)
\(770\) −13.7142 −0.494225
\(771\) −51.7150 −1.86247
\(772\) 17.4848 0.629291
\(773\) 1.06919 0.0384560 0.0192280 0.999815i \(-0.493879\pi\)
0.0192280 + 0.999815i \(0.493879\pi\)
\(774\) −72.3666 −2.60116
\(775\) −13.5380 −0.486300
\(776\) −18.9015 −0.678525
\(777\) 3.84492 0.137936
\(778\) −28.6301 −1.02644
\(779\) −43.3500 −1.55318
\(780\) −66.2500 −2.37213
\(781\) −22.5438 −0.806682
\(782\) −11.7409 −0.419855
\(783\) 115.044 4.11135
\(784\) −6.46571 −0.230918
\(785\) −51.8054 −1.84901
\(786\) −4.56329 −0.162767
\(787\) −8.53703 −0.304312 −0.152156 0.988356i \(-0.548622\pi\)
−0.152156 + 0.988356i \(0.548622\pi\)
\(788\) −13.3981 −0.477288
\(789\) 28.5074 1.01489
\(790\) 18.5836 0.661175
\(791\) 11.6668 0.414823
\(792\) −41.0228 −1.45768
\(793\) −22.2034 −0.788465
\(794\) 29.1457 1.03434
\(795\) 128.131 4.54435
\(796\) −3.66238 −0.129810
\(797\) 1.34500 0.0476422 0.0238211 0.999716i \(-0.492417\pi\)
0.0238211 + 0.999716i \(0.492417\pi\)
\(798\) 10.9716 0.388391
\(799\) 20.1306 0.712170
\(800\) 5.61671 0.198581
\(801\) −48.1783 −1.70230
\(802\) 2.03995 0.0720333
\(803\) 75.2360 2.65502
\(804\) 19.7103 0.695130
\(805\) 8.00893 0.282278
\(806\) −15.4022 −0.542519
\(807\) 35.1560 1.23755
\(808\) 6.91866 0.243398
\(809\) 8.94182 0.314378 0.157189 0.987569i \(-0.449757\pi\)
0.157189 + 0.987569i \(0.449757\pi\)
\(810\) 66.4123 2.33349
\(811\) 44.0342 1.54625 0.773125 0.634254i \(-0.218693\pi\)
0.773125 + 0.634254i \(0.218693\pi\)
\(812\) −6.40808 −0.224880
\(813\) −64.4693 −2.26104
\(814\) 9.51920 0.333648
\(815\) −10.3352 −0.362026
\(816\) 11.1095 0.388911
\(817\) 47.9178 1.67643
\(818\) 13.0344 0.455737
\(819\) 33.2767 1.16278
\(820\) 29.9423 1.04563
\(821\) −45.8981 −1.60185 −0.800927 0.598761i \(-0.795660\pi\)
−0.800927 + 0.598761i \(0.795660\pi\)
\(822\) −32.0406 −1.11755
\(823\) −23.5201 −0.819860 −0.409930 0.912117i \(-0.634447\pi\)
−0.409930 + 0.912117i \(0.634447\pi\)
\(824\) 10.4480 0.363973
\(825\) 102.908 3.58279
\(826\) −2.41126 −0.0838985
\(827\) −33.6472 −1.17003 −0.585014 0.811023i \(-0.698911\pi\)
−0.585014 + 0.811023i \(0.698911\pi\)
\(828\) 23.9568 0.832557
\(829\) 26.0962 0.906359 0.453179 0.891419i \(-0.350290\pi\)
0.453179 + 0.891419i \(0.350290\pi\)
\(830\) 19.4554 0.675307
\(831\) 51.0862 1.77216
\(832\) 6.39012 0.221538
\(833\) 22.5751 0.782181
\(834\) 25.3508 0.877825
\(835\) −46.5061 −1.60941
\(836\) 27.1634 0.939464
\(837\) 31.6301 1.09330
\(838\) 10.4099 0.359605
\(839\) 36.8689 1.27286 0.636428 0.771336i \(-0.280411\pi\)
0.636428 + 0.771336i \(0.280411\pi\)
\(840\) −7.57822 −0.261473
\(841\) 47.8556 1.65019
\(842\) 2.74094 0.0944591
\(843\) −46.5021 −1.60162
\(844\) 16.6422 0.572847
\(845\) 90.6913 3.11988
\(846\) −41.0755 −1.41220
\(847\) 16.1955 0.556483
\(848\) −12.3589 −0.424405
\(849\) −60.3624 −2.07163
\(850\) −19.6108 −0.672646
\(851\) −5.55910 −0.190563
\(852\) −12.4573 −0.426781
\(853\) −22.5089 −0.770689 −0.385344 0.922773i \(-0.625917\pi\)
−0.385344 + 0.922773i \(0.625917\pi\)
\(854\) −2.53980 −0.0869103
\(855\) −109.505 −3.74499
\(856\) 4.80472 0.164222
\(857\) −23.3086 −0.796207 −0.398104 0.917340i \(-0.630332\pi\)
−0.398104 + 0.917340i \(0.630332\pi\)
\(858\) 117.078 3.99698
\(859\) 46.6021 1.59004 0.795022 0.606581i \(-0.207459\pi\)
0.795022 + 0.606581i \(0.207459\pi\)
\(860\) −33.0973 −1.12861
\(861\) −21.3729 −0.728386
\(862\) −18.7175 −0.637519
\(863\) 30.1422 1.02605 0.513026 0.858373i \(-0.328524\pi\)
0.513026 + 0.858373i \(0.328524\pi\)
\(864\) −13.1228 −0.446448
\(865\) −39.7955 −1.35309
\(866\) 33.0512 1.12313
\(867\) 15.3026 0.519704
\(868\) −1.76183 −0.0598004
\(869\) −32.8413 −1.11406
\(870\) 90.8896 3.08145
\(871\) −39.5842 −1.34126
\(872\) 9.08343 0.307604
\(873\) −134.659 −4.55753
\(874\) −15.8631 −0.536577
\(875\) 1.46881 0.0496550
\(876\) 41.5741 1.40466
\(877\) −33.3570 −1.12639 −0.563193 0.826325i \(-0.690427\pi\)
−0.563193 + 0.826325i \(0.690427\pi\)
\(878\) −16.9884 −0.573331
\(879\) 36.1095 1.21794
\(880\) −18.7620 −0.632468
\(881\) −16.7938 −0.565797 −0.282899 0.959150i \(-0.591296\pi\)
−0.282899 + 0.959150i \(0.591296\pi\)
\(882\) −46.0634 −1.55103
\(883\) −20.8750 −0.702501 −0.351251 0.936281i \(-0.614243\pi\)
−0.351251 + 0.936281i \(0.614243\pi\)
\(884\) −22.3112 −0.750407
\(885\) 34.2003 1.14963
\(886\) 8.95033 0.300692
\(887\) −46.8678 −1.57367 −0.786833 0.617166i \(-0.788280\pi\)
−0.786833 + 0.617166i \(0.788280\pi\)
\(888\) 5.26014 0.176519
\(889\) 10.8727 0.364657
\(890\) −22.0347 −0.738604
\(891\) −117.365 −3.93187
\(892\) −15.6933 −0.525452
\(893\) 27.1983 0.910156
\(894\) −12.4172 −0.415292
\(895\) 54.1638 1.81050
\(896\) 0.730955 0.0244195
\(897\) −68.3723 −2.28288
\(898\) −40.1425 −1.33957
\(899\) 21.1306 0.704744
\(900\) 40.0149 1.33383
\(901\) 43.1511 1.43757
\(902\) −52.9146 −1.76186
\(903\) 23.6249 0.786188
\(904\) 15.9610 0.530856
\(905\) 15.1781 0.504537
\(906\) −8.80414 −0.292498
\(907\) −13.8963 −0.461419 −0.230710 0.973023i \(-0.574105\pi\)
−0.230710 + 0.973023i \(0.574105\pi\)
\(908\) −21.4540 −0.711974
\(909\) 49.2903 1.63486
\(910\) 15.2193 0.504515
\(911\) 28.4412 0.942301 0.471150 0.882053i \(-0.343839\pi\)
0.471150 + 0.882053i \(0.343839\pi\)
\(912\) 15.0100 0.497030
\(913\) −34.3819 −1.13788
\(914\) 7.34381 0.242912
\(915\) 36.0235 1.19090
\(916\) −0.269337 −0.00889913
\(917\) 1.04830 0.0346180
\(918\) 45.8186 1.51224
\(919\) 26.7449 0.882232 0.441116 0.897450i \(-0.354583\pi\)
0.441116 + 0.897450i \(0.354583\pi\)
\(920\) 10.9568 0.361235
\(921\) −107.769 −3.55112
\(922\) −28.4444 −0.936767
\(923\) 25.0180 0.823477
\(924\) 13.3924 0.440576
\(925\) −9.28533 −0.305300
\(926\) −18.5267 −0.608825
\(927\) 74.4342 2.44474
\(928\) −8.76673 −0.287782
\(929\) 14.6015 0.479059 0.239530 0.970889i \(-0.423007\pi\)
0.239530 + 0.970889i \(0.423007\pi\)
\(930\) 24.9891 0.819424
\(931\) 30.5010 0.999631
\(932\) −24.5826 −0.805230
\(933\) −14.4484 −0.473020
\(934\) −7.41094 −0.242493
\(935\) 65.5079 2.14234
\(936\) 45.5249 1.48803
\(937\) −36.1515 −1.18102 −0.590509 0.807031i \(-0.701073\pi\)
−0.590509 + 0.807031i \(0.701073\pi\)
\(938\) −4.52796 −0.147843
\(939\) −30.3537 −0.990556
\(940\) −18.7862 −0.612737
\(941\) −36.2444 −1.18153 −0.590767 0.806843i \(-0.701175\pi\)
−0.590767 + 0.806843i \(0.701175\pi\)
\(942\) 50.5896 1.64830
\(943\) 30.9015 1.00629
\(944\) −3.29878 −0.107366
\(945\) −31.2546 −1.01671
\(946\) 58.4902 1.90168
\(947\) 14.0773 0.457451 0.228725 0.973491i \(-0.426544\pi\)
0.228725 + 0.973491i \(0.426544\pi\)
\(948\) −18.1475 −0.589403
\(949\) −83.4930 −2.71030
\(950\) −26.4960 −0.859644
\(951\) 76.7639 2.48924
\(952\) −2.55214 −0.0827153
\(953\) 26.9547 0.873150 0.436575 0.899668i \(-0.356191\pi\)
0.436575 + 0.899668i \(0.356191\pi\)
\(954\) −88.0477 −2.85065
\(955\) −55.2251 −1.78704
\(956\) −23.0023 −0.743947
\(957\) −160.622 −5.19216
\(958\) 40.0605 1.29430
\(959\) 7.36055 0.237684
\(960\) −10.3676 −0.334612
\(961\) −25.1904 −0.812593
\(962\) −10.5639 −0.340594
\(963\) 34.2301 1.10305
\(964\) −7.66395 −0.246839
\(965\) 56.9711 1.83397
\(966\) −7.82098 −0.251636
\(967\) −53.5070 −1.72067 −0.860334 0.509731i \(-0.829745\pi\)
−0.860334 + 0.509731i \(0.829745\pi\)
\(968\) 22.1566 0.712140
\(969\) −52.4076 −1.68357
\(970\) −61.5873 −1.97745
\(971\) −39.4960 −1.26749 −0.633744 0.773543i \(-0.718483\pi\)
−0.633744 + 0.773543i \(0.718483\pi\)
\(972\) −25.4852 −0.817440
\(973\) −5.82371 −0.186700
\(974\) −23.3099 −0.746898
\(975\) −114.202 −3.65738
\(976\) −3.47464 −0.111220
\(977\) 29.3663 0.939513 0.469756 0.882796i \(-0.344342\pi\)
0.469756 + 0.882796i \(0.344342\pi\)
\(978\) 10.0926 0.322727
\(979\) 38.9401 1.24453
\(980\) −21.0674 −0.672973
\(981\) 64.7127 2.06612
\(982\) −20.7248 −0.661354
\(983\) 13.6426 0.435131 0.217565 0.976046i \(-0.430189\pi\)
0.217565 + 0.976046i \(0.430189\pi\)
\(984\) −29.2397 −0.932127
\(985\) −43.6555 −1.39098
\(986\) 30.6092 0.974795
\(987\) 13.4096 0.426832
\(988\) −30.1445 −0.959024
\(989\) −34.1576 −1.08615
\(990\) −133.666 −4.24817
\(991\) −51.5061 −1.63614 −0.818072 0.575115i \(-0.804957\pi\)
−0.818072 + 0.575115i \(0.804957\pi\)
\(992\) −2.41031 −0.0765275
\(993\) 86.9120 2.75807
\(994\) 2.86176 0.0907696
\(995\) −11.9333 −0.378310
\(996\) −18.9988 −0.602001
\(997\) −12.0060 −0.380233 −0.190117 0.981762i \(-0.560887\pi\)
−0.190117 + 0.981762i \(0.560887\pi\)
\(998\) 32.6856 1.03464
\(999\) 21.6942 0.686373
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 6046.2.a.e.1.4 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6046.2.a.e.1.4 56 1.1 even 1 trivial