Properties

Label 6034.2.a.o.1.4
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
Dimension $25$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.89955 q^{3} +1.00000 q^{4} -3.35107 q^{5} +2.89955 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.40739 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.89955 q^{3} +1.00000 q^{4} -3.35107 q^{5} +2.89955 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.40739 q^{9} +3.35107 q^{10} +5.34965 q^{11} -2.89955 q^{12} +2.77854 q^{13} +1.00000 q^{14} +9.71661 q^{15} +1.00000 q^{16} -1.18328 q^{17} -5.40739 q^{18} -8.21463 q^{19} -3.35107 q^{20} +2.89955 q^{21} -5.34965 q^{22} +0.111080 q^{23} +2.89955 q^{24} +6.22970 q^{25} -2.77854 q^{26} -6.98035 q^{27} -1.00000 q^{28} -7.47496 q^{29} -9.71661 q^{30} -3.87355 q^{31} -1.00000 q^{32} -15.5116 q^{33} +1.18328 q^{34} +3.35107 q^{35} +5.40739 q^{36} +1.22307 q^{37} +8.21463 q^{38} -8.05653 q^{39} +3.35107 q^{40} -4.76950 q^{41} -2.89955 q^{42} +10.9734 q^{43} +5.34965 q^{44} -18.1206 q^{45} -0.111080 q^{46} -3.72068 q^{47} -2.89955 q^{48} +1.00000 q^{49} -6.22970 q^{50} +3.43098 q^{51} +2.77854 q^{52} +3.45969 q^{53} +6.98035 q^{54} -17.9271 q^{55} +1.00000 q^{56} +23.8187 q^{57} +7.47496 q^{58} +7.41617 q^{59} +9.71661 q^{60} -0.674429 q^{61} +3.87355 q^{62} -5.40739 q^{63} +1.00000 q^{64} -9.31111 q^{65} +15.5116 q^{66} -8.63322 q^{67} -1.18328 q^{68} -0.322082 q^{69} -3.35107 q^{70} -4.81812 q^{71} -5.40739 q^{72} +3.52593 q^{73} -1.22307 q^{74} -18.0633 q^{75} -8.21463 q^{76} -5.34965 q^{77} +8.05653 q^{78} -1.08915 q^{79} -3.35107 q^{80} +4.01770 q^{81} +4.76950 q^{82} +0.907057 q^{83} +2.89955 q^{84} +3.96526 q^{85} -10.9734 q^{86} +21.6740 q^{87} -5.34965 q^{88} +0.159247 q^{89} +18.1206 q^{90} -2.77854 q^{91} +0.111080 q^{92} +11.2316 q^{93} +3.72068 q^{94} +27.5278 q^{95} +2.89955 q^{96} +14.5975 q^{97} -1.00000 q^{98} +28.9276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.89955 −1.67406 −0.837028 0.547160i \(-0.815709\pi\)
−0.837028 + 0.547160i \(0.815709\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.35107 −1.49865 −0.749323 0.662205i \(-0.769621\pi\)
−0.749323 + 0.662205i \(0.769621\pi\)
\(6\) 2.89955 1.18374
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 5.40739 1.80246
\(10\) 3.35107 1.05970
\(11\) 5.34965 1.61298 0.806489 0.591249i \(-0.201365\pi\)
0.806489 + 0.591249i \(0.201365\pi\)
\(12\) −2.89955 −0.837028
\(13\) 2.77854 0.770630 0.385315 0.922785i \(-0.374093\pi\)
0.385315 + 0.922785i \(0.374093\pi\)
\(14\) 1.00000 0.267261
\(15\) 9.71661 2.50882
\(16\) 1.00000 0.250000
\(17\) −1.18328 −0.286988 −0.143494 0.989651i \(-0.545834\pi\)
−0.143494 + 0.989651i \(0.545834\pi\)
\(18\) −5.40739 −1.27453
\(19\) −8.21463 −1.88456 −0.942282 0.334819i \(-0.891325\pi\)
−0.942282 + 0.334819i \(0.891325\pi\)
\(20\) −3.35107 −0.749323
\(21\) 2.89955 0.632734
\(22\) −5.34965 −1.14055
\(23\) 0.111080 0.0231618 0.0115809 0.999933i \(-0.496314\pi\)
0.0115809 + 0.999933i \(0.496314\pi\)
\(24\) 2.89955 0.591868
\(25\) 6.22970 1.24594
\(26\) −2.77854 −0.544917
\(27\) −6.98035 −1.34337
\(28\) −1.00000 −0.188982
\(29\) −7.47496 −1.38806 −0.694032 0.719944i \(-0.744168\pi\)
−0.694032 + 0.719944i \(0.744168\pi\)
\(30\) −9.71661 −1.77400
\(31\) −3.87355 −0.695710 −0.347855 0.937548i \(-0.613090\pi\)
−0.347855 + 0.937548i \(0.613090\pi\)
\(32\) −1.00000 −0.176777
\(33\) −15.5116 −2.70022
\(34\) 1.18328 0.202931
\(35\) 3.35107 0.566435
\(36\) 5.40739 0.901232
\(37\) 1.22307 0.201072 0.100536 0.994933i \(-0.467944\pi\)
0.100536 + 0.994933i \(0.467944\pi\)
\(38\) 8.21463 1.33259
\(39\) −8.05653 −1.29008
\(40\) 3.35107 0.529851
\(41\) −4.76950 −0.744871 −0.372435 0.928058i \(-0.621477\pi\)
−0.372435 + 0.928058i \(0.621477\pi\)
\(42\) −2.89955 −0.447410
\(43\) 10.9734 1.67343 0.836716 0.547638i \(-0.184473\pi\)
0.836716 + 0.547638i \(0.184473\pi\)
\(44\) 5.34965 0.806489
\(45\) −18.1206 −2.70126
\(46\) −0.111080 −0.0163778
\(47\) −3.72068 −0.542716 −0.271358 0.962478i \(-0.587473\pi\)
−0.271358 + 0.962478i \(0.587473\pi\)
\(48\) −2.89955 −0.418514
\(49\) 1.00000 0.142857
\(50\) −6.22970 −0.881013
\(51\) 3.43098 0.480434
\(52\) 2.77854 0.385315
\(53\) 3.45969 0.475225 0.237612 0.971360i \(-0.423635\pi\)
0.237612 + 0.971360i \(0.423635\pi\)
\(54\) 6.98035 0.949905
\(55\) −17.9271 −2.41728
\(56\) 1.00000 0.133631
\(57\) 23.8187 3.15487
\(58\) 7.47496 0.981510
\(59\) 7.41617 0.965503 0.482751 0.875758i \(-0.339638\pi\)
0.482751 + 0.875758i \(0.339638\pi\)
\(60\) 9.71661 1.25441
\(61\) −0.674429 −0.0863518 −0.0431759 0.999067i \(-0.513748\pi\)
−0.0431759 + 0.999067i \(0.513748\pi\)
\(62\) 3.87355 0.491941
\(63\) −5.40739 −0.681267
\(64\) 1.00000 0.125000
\(65\) −9.31111 −1.15490
\(66\) 15.5116 1.90934
\(67\) −8.63322 −1.05472 −0.527358 0.849643i \(-0.676817\pi\)
−0.527358 + 0.849643i \(0.676817\pi\)
\(68\) −1.18328 −0.143494
\(69\) −0.322082 −0.0387741
\(70\) −3.35107 −0.400530
\(71\) −4.81812 −0.571806 −0.285903 0.958259i \(-0.592293\pi\)
−0.285903 + 0.958259i \(0.592293\pi\)
\(72\) −5.40739 −0.637267
\(73\) 3.52593 0.412679 0.206340 0.978480i \(-0.433845\pi\)
0.206340 + 0.978480i \(0.433845\pi\)
\(74\) −1.22307 −0.142179
\(75\) −18.0633 −2.08577
\(76\) −8.21463 −0.942282
\(77\) −5.34965 −0.609649
\(78\) 8.05653 0.912222
\(79\) −1.08915 −0.122538 −0.0612692 0.998121i \(-0.519515\pi\)
−0.0612692 + 0.998121i \(0.519515\pi\)
\(80\) −3.35107 −0.374662
\(81\) 4.01770 0.446411
\(82\) 4.76950 0.526703
\(83\) 0.907057 0.0995624 0.0497812 0.998760i \(-0.484148\pi\)
0.0497812 + 0.998760i \(0.484148\pi\)
\(84\) 2.89955 0.316367
\(85\) 3.96526 0.430093
\(86\) −10.9734 −1.18329
\(87\) 21.6740 2.32370
\(88\) −5.34965 −0.570274
\(89\) 0.159247 0.0168801 0.00844006 0.999964i \(-0.497313\pi\)
0.00844006 + 0.999964i \(0.497313\pi\)
\(90\) 18.1206 1.91008
\(91\) −2.77854 −0.291271
\(92\) 0.111080 0.0115809
\(93\) 11.2316 1.16466
\(94\) 3.72068 0.383758
\(95\) 27.5278 2.82430
\(96\) 2.89955 0.295934
\(97\) 14.5975 1.48215 0.741076 0.671421i \(-0.234316\pi\)
0.741076 + 0.671421i \(0.234316\pi\)
\(98\) −1.00000 −0.101015
\(99\) 28.9276 2.90734
\(100\) 6.22970 0.622970
\(101\) 7.37963 0.734300 0.367150 0.930162i \(-0.380334\pi\)
0.367150 + 0.930162i \(0.380334\pi\)
\(102\) −3.43098 −0.339718
\(103\) 5.22762 0.515093 0.257546 0.966266i \(-0.417086\pi\)
0.257546 + 0.966266i \(0.417086\pi\)
\(104\) −2.77854 −0.272459
\(105\) −9.71661 −0.948244
\(106\) −3.45969 −0.336035
\(107\) 10.9803 1.06150 0.530751 0.847528i \(-0.321910\pi\)
0.530751 + 0.847528i \(0.321910\pi\)
\(108\) −6.98035 −0.671684
\(109\) 15.2126 1.45711 0.728553 0.684989i \(-0.240193\pi\)
0.728553 + 0.684989i \(0.240193\pi\)
\(110\) 17.9271 1.70928
\(111\) −3.54636 −0.336605
\(112\) −1.00000 −0.0944911
\(113\) 13.8700 1.30478 0.652391 0.757882i \(-0.273766\pi\)
0.652391 + 0.757882i \(0.273766\pi\)
\(114\) −23.8187 −2.23083
\(115\) −0.372237 −0.0347113
\(116\) −7.47496 −0.694032
\(117\) 15.0247 1.38903
\(118\) −7.41617 −0.682713
\(119\) 1.18328 0.108471
\(120\) −9.71661 −0.887001
\(121\) 17.6187 1.60170
\(122\) 0.674429 0.0610599
\(123\) 13.8294 1.24696
\(124\) −3.87355 −0.347855
\(125\) −4.12083 −0.368578
\(126\) 5.40739 0.481729
\(127\) 8.34294 0.740317 0.370158 0.928969i \(-0.379303\pi\)
0.370158 + 0.928969i \(0.379303\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −31.8180 −2.80142
\(130\) 9.31111 0.816638
\(131\) −18.0094 −1.57349 −0.786745 0.617279i \(-0.788235\pi\)
−0.786745 + 0.617279i \(0.788235\pi\)
\(132\) −15.5116 −1.35011
\(133\) 8.21463 0.712299
\(134\) 8.63322 0.745797
\(135\) 23.3917 2.01323
\(136\) 1.18328 0.101465
\(137\) 4.30484 0.367787 0.183894 0.982946i \(-0.441130\pi\)
0.183894 + 0.982946i \(0.441130\pi\)
\(138\) 0.322082 0.0274174
\(139\) 17.2429 1.46252 0.731261 0.682098i \(-0.238932\pi\)
0.731261 + 0.682098i \(0.238932\pi\)
\(140\) 3.35107 0.283218
\(141\) 10.7883 0.908537
\(142\) 4.81812 0.404328
\(143\) 14.8642 1.24301
\(144\) 5.40739 0.450616
\(145\) 25.0491 2.08022
\(146\) −3.52593 −0.291808
\(147\) −2.89955 −0.239151
\(148\) 1.22307 0.100536
\(149\) −21.2617 −1.74182 −0.870912 0.491439i \(-0.836471\pi\)
−0.870912 + 0.491439i \(0.836471\pi\)
\(150\) 18.0633 1.47487
\(151\) −12.2728 −0.998749 −0.499375 0.866386i \(-0.666437\pi\)
−0.499375 + 0.866386i \(0.666437\pi\)
\(152\) 8.21463 0.666294
\(153\) −6.39846 −0.517285
\(154\) 5.34965 0.431087
\(155\) 12.9806 1.04262
\(156\) −8.05653 −0.645039
\(157\) −1.28169 −0.102290 −0.0511451 0.998691i \(-0.516287\pi\)
−0.0511451 + 0.998691i \(0.516287\pi\)
\(158\) 1.08915 0.0866478
\(159\) −10.0315 −0.795553
\(160\) 3.35107 0.264926
\(161\) −0.111080 −0.00875432
\(162\) −4.01770 −0.315660
\(163\) 1.62246 0.127081 0.0635406 0.997979i \(-0.479761\pi\)
0.0635406 + 0.997979i \(0.479761\pi\)
\(164\) −4.76950 −0.372435
\(165\) 51.9804 4.04667
\(166\) −0.907057 −0.0704012
\(167\) −13.7556 −1.06444 −0.532222 0.846605i \(-0.678643\pi\)
−0.532222 + 0.846605i \(0.678643\pi\)
\(168\) −2.89955 −0.223705
\(169\) −5.27969 −0.406130
\(170\) −3.96526 −0.304122
\(171\) −44.4197 −3.39686
\(172\) 10.9734 0.836716
\(173\) 3.09879 0.235597 0.117798 0.993038i \(-0.462416\pi\)
0.117798 + 0.993038i \(0.462416\pi\)
\(174\) −21.6740 −1.64310
\(175\) −6.22970 −0.470921
\(176\) 5.34965 0.403245
\(177\) −21.5035 −1.61631
\(178\) −0.159247 −0.0119361
\(179\) 3.55238 0.265517 0.132759 0.991148i \(-0.457616\pi\)
0.132759 + 0.991148i \(0.457616\pi\)
\(180\) −18.1206 −1.35063
\(181\) −13.5674 −1.00845 −0.504227 0.863571i \(-0.668223\pi\)
−0.504227 + 0.863571i \(0.668223\pi\)
\(182\) 2.77854 0.205959
\(183\) 1.95554 0.144558
\(184\) −0.111080 −0.00818892
\(185\) −4.09860 −0.301335
\(186\) −11.2316 −0.823537
\(187\) −6.33013 −0.462905
\(188\) −3.72068 −0.271358
\(189\) 6.98035 0.507746
\(190\) −27.5278 −1.99708
\(191\) −15.6436 −1.13193 −0.565965 0.824429i \(-0.691496\pi\)
−0.565965 + 0.824429i \(0.691496\pi\)
\(192\) −2.89955 −0.209257
\(193\) −27.3651 −1.96978 −0.984890 0.173181i \(-0.944595\pi\)
−0.984890 + 0.173181i \(0.944595\pi\)
\(194\) −14.5975 −1.04804
\(195\) 26.9980 1.93337
\(196\) 1.00000 0.0714286
\(197\) −24.6276 −1.75464 −0.877320 0.479905i \(-0.840671\pi\)
−0.877320 + 0.479905i \(0.840671\pi\)
\(198\) −28.9276 −2.05580
\(199\) 17.8996 1.26887 0.634436 0.772975i \(-0.281232\pi\)
0.634436 + 0.772975i \(0.281232\pi\)
\(200\) −6.22970 −0.440507
\(201\) 25.0325 1.76565
\(202\) −7.37963 −0.519229
\(203\) 7.47496 0.524639
\(204\) 3.43098 0.240217
\(205\) 15.9830 1.11630
\(206\) −5.22762 −0.364226
\(207\) 0.600652 0.0417482
\(208\) 2.77854 0.192657
\(209\) −43.9453 −3.03976
\(210\) 9.71661 0.670510
\(211\) 18.6795 1.28595 0.642975 0.765887i \(-0.277700\pi\)
0.642975 + 0.765887i \(0.277700\pi\)
\(212\) 3.45969 0.237612
\(213\) 13.9704 0.957235
\(214\) −10.9803 −0.750595
\(215\) −36.7728 −2.50788
\(216\) 6.98035 0.474953
\(217\) 3.87355 0.262954
\(218\) −15.2126 −1.03033
\(219\) −10.2236 −0.690848
\(220\) −17.9271 −1.20864
\(221\) −3.28780 −0.221161
\(222\) 3.54636 0.238016
\(223\) −20.2817 −1.35816 −0.679081 0.734063i \(-0.737621\pi\)
−0.679081 + 0.734063i \(0.737621\pi\)
\(224\) 1.00000 0.0668153
\(225\) 33.6864 2.24576
\(226\) −13.8700 −0.922621
\(227\) 15.7833 1.04758 0.523788 0.851849i \(-0.324519\pi\)
0.523788 + 0.851849i \(0.324519\pi\)
\(228\) 23.8187 1.57743
\(229\) 9.01082 0.595452 0.297726 0.954651i \(-0.403772\pi\)
0.297726 + 0.954651i \(0.403772\pi\)
\(230\) 0.372237 0.0245446
\(231\) 15.5116 1.02059
\(232\) 7.47496 0.490755
\(233\) 13.8008 0.904121 0.452060 0.891987i \(-0.350689\pi\)
0.452060 + 0.891987i \(0.350689\pi\)
\(234\) −15.0247 −0.982194
\(235\) 12.4683 0.813340
\(236\) 7.41617 0.482751
\(237\) 3.15803 0.205136
\(238\) −1.18328 −0.0767007
\(239\) −8.98950 −0.581482 −0.290741 0.956802i \(-0.593902\pi\)
−0.290741 + 0.956802i \(0.593902\pi\)
\(240\) 9.71661 0.627204
\(241\) 29.0628 1.87210 0.936050 0.351867i \(-0.114453\pi\)
0.936050 + 0.351867i \(0.114453\pi\)
\(242\) −17.6187 −1.13257
\(243\) 9.29152 0.596052
\(244\) −0.674429 −0.0431759
\(245\) −3.35107 −0.214092
\(246\) −13.8294 −0.881731
\(247\) −22.8247 −1.45230
\(248\) 3.87355 0.245971
\(249\) −2.63006 −0.166673
\(250\) 4.12083 0.260624
\(251\) −0.476213 −0.0300583 −0.0150291 0.999887i \(-0.504784\pi\)
−0.0150291 + 0.999887i \(0.504784\pi\)
\(252\) −5.40739 −0.340634
\(253\) 0.594238 0.0373594
\(254\) −8.34294 −0.523483
\(255\) −11.4975 −0.720000
\(256\) 1.00000 0.0625000
\(257\) −6.69576 −0.417670 −0.208835 0.977951i \(-0.566967\pi\)
−0.208835 + 0.977951i \(0.566967\pi\)
\(258\) 31.8180 1.98090
\(259\) −1.22307 −0.0759980
\(260\) −9.31111 −0.577451
\(261\) −40.4200 −2.50194
\(262\) 18.0094 1.11262
\(263\) 27.4036 1.68978 0.844888 0.534943i \(-0.179667\pi\)
0.844888 + 0.534943i \(0.179667\pi\)
\(264\) 15.5116 0.954671
\(265\) −11.5937 −0.712194
\(266\) −8.21463 −0.503671
\(267\) −0.461744 −0.0282583
\(268\) −8.63322 −0.527358
\(269\) 19.5892 1.19437 0.597187 0.802102i \(-0.296285\pi\)
0.597187 + 0.802102i \(0.296285\pi\)
\(270\) −23.3917 −1.42357
\(271\) −1.99730 −0.121327 −0.0606636 0.998158i \(-0.519322\pi\)
−0.0606636 + 0.998158i \(0.519322\pi\)
\(272\) −1.18328 −0.0717469
\(273\) 8.05653 0.487603
\(274\) −4.30484 −0.260065
\(275\) 33.3267 2.00968
\(276\) −0.322082 −0.0193870
\(277\) 0.800922 0.0481227 0.0240614 0.999710i \(-0.492340\pi\)
0.0240614 + 0.999710i \(0.492340\pi\)
\(278\) −17.2429 −1.03416
\(279\) −20.9458 −1.25399
\(280\) −3.35107 −0.200265
\(281\) 9.16859 0.546952 0.273476 0.961879i \(-0.411827\pi\)
0.273476 + 0.961879i \(0.411827\pi\)
\(282\) −10.7883 −0.642433
\(283\) 10.0066 0.594833 0.297417 0.954748i \(-0.403875\pi\)
0.297417 + 0.954748i \(0.403875\pi\)
\(284\) −4.81812 −0.285903
\(285\) −79.8183 −4.72803
\(286\) −14.8642 −0.878940
\(287\) 4.76950 0.281535
\(288\) −5.40739 −0.318634
\(289\) −15.5998 −0.917638
\(290\) −25.0491 −1.47094
\(291\) −42.3262 −2.48121
\(292\) 3.52593 0.206340
\(293\) 16.0734 0.939018 0.469509 0.882928i \(-0.344431\pi\)
0.469509 + 0.882928i \(0.344431\pi\)
\(294\) 2.89955 0.169105
\(295\) −24.8521 −1.44695
\(296\) −1.22307 −0.0710896
\(297\) −37.3424 −2.16683
\(298\) 21.2617 1.23166
\(299\) 0.308640 0.0178491
\(300\) −18.0633 −1.04289
\(301\) −10.9734 −0.632498
\(302\) 12.2728 0.706222
\(303\) −21.3976 −1.22926
\(304\) −8.21463 −0.471141
\(305\) 2.26006 0.129411
\(306\) 6.39846 0.365776
\(307\) −22.7974 −1.30112 −0.650559 0.759456i \(-0.725465\pi\)
−0.650559 + 0.759456i \(0.725465\pi\)
\(308\) −5.34965 −0.304824
\(309\) −15.1577 −0.862294
\(310\) −12.9806 −0.737246
\(311\) −10.1888 −0.577755 −0.288877 0.957366i \(-0.593282\pi\)
−0.288877 + 0.957366i \(0.593282\pi\)
\(312\) 8.05653 0.456111
\(313\) 21.3794 1.20843 0.604217 0.796820i \(-0.293486\pi\)
0.604217 + 0.796820i \(0.293486\pi\)
\(314\) 1.28169 0.0723301
\(315\) 18.1206 1.02098
\(316\) −1.08915 −0.0612692
\(317\) 6.92557 0.388979 0.194489 0.980905i \(-0.437695\pi\)
0.194489 + 0.980905i \(0.437695\pi\)
\(318\) 10.0315 0.562541
\(319\) −39.9884 −2.23892
\(320\) −3.35107 −0.187331
\(321\) −31.8378 −1.77701
\(322\) 0.111080 0.00619024
\(323\) 9.72021 0.540847
\(324\) 4.01770 0.223206
\(325\) 17.3095 0.960159
\(326\) −1.62246 −0.0898600
\(327\) −44.1098 −2.43928
\(328\) 4.76950 0.263352
\(329\) 3.72068 0.205127
\(330\) −51.9804 −2.86143
\(331\) −16.7005 −0.917943 −0.458971 0.888451i \(-0.651782\pi\)
−0.458971 + 0.888451i \(0.651782\pi\)
\(332\) 0.907057 0.0497812
\(333\) 6.61363 0.362424
\(334\) 13.7556 0.752675
\(335\) 28.9306 1.58065
\(336\) 2.89955 0.158183
\(337\) 11.0483 0.601841 0.300921 0.953649i \(-0.402706\pi\)
0.300921 + 0.953649i \(0.402706\pi\)
\(338\) 5.27969 0.287177
\(339\) −40.2168 −2.18428
\(340\) 3.96526 0.215047
\(341\) −20.7221 −1.12217
\(342\) 44.4197 2.40194
\(343\) −1.00000 −0.0539949
\(344\) −10.9734 −0.591647
\(345\) 1.07932 0.0581086
\(346\) −3.09879 −0.166592
\(347\) −20.6926 −1.11084 −0.555419 0.831571i \(-0.687442\pi\)
−0.555419 + 0.831571i \(0.687442\pi\)
\(348\) 21.6740 1.16185
\(349\) −6.06856 −0.324843 −0.162421 0.986721i \(-0.551930\pi\)
−0.162421 + 0.986721i \(0.551930\pi\)
\(350\) 6.22970 0.332992
\(351\) −19.3952 −1.03524
\(352\) −5.34965 −0.285137
\(353\) 2.63860 0.140438 0.0702192 0.997532i \(-0.477630\pi\)
0.0702192 + 0.997532i \(0.477630\pi\)
\(354\) 21.5035 1.14290
\(355\) 16.1459 0.856935
\(356\) 0.159247 0.00844006
\(357\) −3.43098 −0.181587
\(358\) −3.55238 −0.187749
\(359\) −20.8998 −1.10305 −0.551525 0.834158i \(-0.685954\pi\)
−0.551525 + 0.834158i \(0.685954\pi\)
\(360\) 18.1206 0.955038
\(361\) 48.4801 2.55159
\(362\) 13.5674 0.713085
\(363\) −51.0863 −2.68134
\(364\) −2.77854 −0.145635
\(365\) −11.8157 −0.618460
\(366\) −1.95554 −0.102218
\(367\) −3.30242 −0.172385 −0.0861924 0.996279i \(-0.527470\pi\)
−0.0861924 + 0.996279i \(0.527470\pi\)
\(368\) 0.111080 0.00579044
\(369\) −25.7906 −1.34260
\(370\) 4.09860 0.213076
\(371\) −3.45969 −0.179618
\(372\) 11.2316 0.582329
\(373\) 30.3078 1.56928 0.784640 0.619952i \(-0.212848\pi\)
0.784640 + 0.619952i \(0.212848\pi\)
\(374\) 6.33013 0.327323
\(375\) 11.9485 0.617020
\(376\) 3.72068 0.191879
\(377\) −20.7695 −1.06968
\(378\) −6.98035 −0.359030
\(379\) 18.4903 0.949781 0.474890 0.880045i \(-0.342488\pi\)
0.474890 + 0.880045i \(0.342488\pi\)
\(380\) 27.5278 1.41215
\(381\) −24.1908 −1.23933
\(382\) 15.6436 0.800396
\(383\) −33.1678 −1.69479 −0.847397 0.530960i \(-0.821831\pi\)
−0.847397 + 0.530960i \(0.821831\pi\)
\(384\) 2.89955 0.147967
\(385\) 17.9271 0.913648
\(386\) 27.3651 1.39284
\(387\) 59.3376 3.01630
\(388\) 14.5975 0.741076
\(389\) 34.9633 1.77271 0.886355 0.463005i \(-0.153229\pi\)
0.886355 + 0.463005i \(0.153229\pi\)
\(390\) −26.9980 −1.36710
\(391\) −0.131439 −0.00664714
\(392\) −1.00000 −0.0505076
\(393\) 52.2192 2.63411
\(394\) 24.6276 1.24072
\(395\) 3.64981 0.183642
\(396\) 28.9276 1.45367
\(397\) 26.5591 1.33296 0.666481 0.745522i \(-0.267800\pi\)
0.666481 + 0.745522i \(0.267800\pi\)
\(398\) −17.8996 −0.897228
\(399\) −23.8187 −1.19243
\(400\) 6.22970 0.311485
\(401\) −25.0671 −1.25179 −0.625896 0.779907i \(-0.715267\pi\)
−0.625896 + 0.779907i \(0.715267\pi\)
\(402\) −25.0325 −1.24851
\(403\) −10.7628 −0.536135
\(404\) 7.37963 0.367150
\(405\) −13.4636 −0.669012
\(406\) −7.47496 −0.370976
\(407\) 6.54300 0.324324
\(408\) −3.43098 −0.169859
\(409\) 3.80485 0.188138 0.0940690 0.995566i \(-0.470013\pi\)
0.0940690 + 0.995566i \(0.470013\pi\)
\(410\) −15.9830 −0.789342
\(411\) −12.4821 −0.615696
\(412\) 5.22762 0.257546
\(413\) −7.41617 −0.364926
\(414\) −0.600652 −0.0295204
\(415\) −3.03961 −0.149209
\(416\) −2.77854 −0.136229
\(417\) −49.9966 −2.44834
\(418\) 43.9453 2.14944
\(419\) −12.5299 −0.612126 −0.306063 0.952011i \(-0.599012\pi\)
−0.306063 + 0.952011i \(0.599012\pi\)
\(420\) −9.71661 −0.474122
\(421\) −21.5252 −1.04907 −0.524537 0.851388i \(-0.675762\pi\)
−0.524537 + 0.851388i \(0.675762\pi\)
\(422\) −18.6795 −0.909304
\(423\) −20.1191 −0.978226
\(424\) −3.45969 −0.168017
\(425\) −7.37149 −0.357570
\(426\) −13.9704 −0.676867
\(427\) 0.674429 0.0326379
\(428\) 10.9803 0.530751
\(429\) −43.0996 −2.08087
\(430\) 36.7728 1.77334
\(431\) −1.00000 −0.0481683
\(432\) −6.98035 −0.335842
\(433\) 7.94016 0.381580 0.190790 0.981631i \(-0.438895\pi\)
0.190790 + 0.981631i \(0.438895\pi\)
\(434\) −3.87355 −0.185936
\(435\) −72.6312 −3.48240
\(436\) 15.2126 0.728553
\(437\) −0.912480 −0.0436498
\(438\) 10.2236 0.488503
\(439\) 4.78946 0.228588 0.114294 0.993447i \(-0.463539\pi\)
0.114294 + 0.993447i \(0.463539\pi\)
\(440\) 17.9271 0.854639
\(441\) 5.40739 0.257495
\(442\) 3.28780 0.156385
\(443\) 36.7286 1.74503 0.872514 0.488590i \(-0.162489\pi\)
0.872514 + 0.488590i \(0.162489\pi\)
\(444\) −3.54636 −0.168303
\(445\) −0.533648 −0.0252973
\(446\) 20.2817 0.960365
\(447\) 61.6493 2.91591
\(448\) −1.00000 −0.0472456
\(449\) −21.2727 −1.00392 −0.501960 0.864891i \(-0.667387\pi\)
−0.501960 + 0.864891i \(0.667387\pi\)
\(450\) −33.6864 −1.58799
\(451\) −25.5151 −1.20146
\(452\) 13.8700 0.652391
\(453\) 35.5857 1.67196
\(454\) −15.7833 −0.740748
\(455\) 9.31111 0.436512
\(456\) −23.8187 −1.11541
\(457\) −1.75027 −0.0818742 −0.0409371 0.999162i \(-0.513034\pi\)
−0.0409371 + 0.999162i \(0.513034\pi\)
\(458\) −9.01082 −0.421048
\(459\) 8.25971 0.385530
\(460\) −0.372237 −0.0173556
\(461\) −9.45946 −0.440571 −0.220286 0.975435i \(-0.570699\pi\)
−0.220286 + 0.975435i \(0.570699\pi\)
\(462\) −15.5116 −0.721663
\(463\) −4.01164 −0.186437 −0.0932183 0.995646i \(-0.529715\pi\)
−0.0932183 + 0.995646i \(0.529715\pi\)
\(464\) −7.47496 −0.347016
\(465\) −37.6378 −1.74541
\(466\) −13.8008 −0.639310
\(467\) 8.52792 0.394625 0.197313 0.980341i \(-0.436779\pi\)
0.197313 + 0.980341i \(0.436779\pi\)
\(468\) 15.0247 0.694516
\(469\) 8.63322 0.398645
\(470\) −12.4683 −0.575118
\(471\) 3.71633 0.171239
\(472\) −7.41617 −0.341357
\(473\) 58.7039 2.69921
\(474\) −3.15803 −0.145053
\(475\) −51.1747 −2.34806
\(476\) 1.18328 0.0542356
\(477\) 18.7079 0.856576
\(478\) 8.98950 0.411170
\(479\) −24.0773 −1.10012 −0.550061 0.835125i \(-0.685395\pi\)
−0.550061 + 0.835125i \(0.685395\pi\)
\(480\) −9.71661 −0.443501
\(481\) 3.39836 0.154952
\(482\) −29.0628 −1.32377
\(483\) 0.322082 0.0146552
\(484\) 17.6187 0.800850
\(485\) −48.9173 −2.22122
\(486\) −9.29152 −0.421472
\(487\) −4.92742 −0.223283 −0.111641 0.993749i \(-0.535611\pi\)
−0.111641 + 0.993749i \(0.535611\pi\)
\(488\) 0.674429 0.0305300
\(489\) −4.70442 −0.212741
\(490\) 3.35107 0.151386
\(491\) −37.0739 −1.67312 −0.836561 0.547874i \(-0.815437\pi\)
−0.836561 + 0.547874i \(0.815437\pi\)
\(492\) 13.8294 0.623478
\(493\) 8.84497 0.398358
\(494\) 22.8247 1.02693
\(495\) −96.9386 −4.35707
\(496\) −3.87355 −0.173928
\(497\) 4.81812 0.216122
\(498\) 2.63006 0.117856
\(499\) 32.5784 1.45841 0.729205 0.684295i \(-0.239890\pi\)
0.729205 + 0.684295i \(0.239890\pi\)
\(500\) −4.12083 −0.184289
\(501\) 39.8852 1.78194
\(502\) 0.476213 0.0212544
\(503\) −15.6439 −0.697526 −0.348763 0.937211i \(-0.613398\pi\)
−0.348763 + 0.937211i \(0.613398\pi\)
\(504\) 5.40739 0.240864
\(505\) −24.7297 −1.10046
\(506\) −0.594238 −0.0264171
\(507\) 15.3087 0.679884
\(508\) 8.34294 0.370158
\(509\) 15.5276 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(510\) 11.4975 0.509117
\(511\) −3.52593 −0.155978
\(512\) −1.00000 −0.0441942
\(513\) 57.3410 2.53167
\(514\) 6.69576 0.295337
\(515\) −17.5181 −0.771942
\(516\) −31.8180 −1.40071
\(517\) −19.9043 −0.875390
\(518\) 1.22307 0.0537387
\(519\) −8.98510 −0.394402
\(520\) 9.31111 0.408319
\(521\) −5.11431 −0.224062 −0.112031 0.993705i \(-0.535736\pi\)
−0.112031 + 0.993705i \(0.535736\pi\)
\(522\) 40.4200 1.76914
\(523\) −15.2652 −0.667499 −0.333750 0.942662i \(-0.608314\pi\)
−0.333750 + 0.942662i \(0.608314\pi\)
\(524\) −18.0094 −0.786745
\(525\) 18.0633 0.788349
\(526\) −27.4036 −1.19485
\(527\) 4.58350 0.199660
\(528\) −15.5116 −0.675054
\(529\) −22.9877 −0.999464
\(530\) 11.5937 0.503597
\(531\) 40.1021 1.74028
\(532\) 8.21463 0.356149
\(533\) −13.2523 −0.574020
\(534\) 0.461744 0.0199816
\(535\) −36.7957 −1.59082
\(536\) 8.63322 0.372898
\(537\) −10.3003 −0.444491
\(538\) −19.5892 −0.844550
\(539\) 5.34965 0.230426
\(540\) 23.3917 1.00662
\(541\) 42.2533 1.81661 0.908306 0.418307i \(-0.137376\pi\)
0.908306 + 0.418307i \(0.137376\pi\)
\(542\) 1.99730 0.0857912
\(543\) 39.3393 1.68821
\(544\) 1.18328 0.0507327
\(545\) −50.9787 −2.18369
\(546\) −8.05653 −0.344788
\(547\) −32.9417 −1.40849 −0.704243 0.709959i \(-0.748713\pi\)
−0.704243 + 0.709959i \(0.748713\pi\)
\(548\) 4.30484 0.183894
\(549\) −3.64690 −0.155646
\(550\) −33.3267 −1.42106
\(551\) 61.4040 2.61590
\(552\) 0.322082 0.0137087
\(553\) 1.08915 0.0463152
\(554\) −0.800922 −0.0340279
\(555\) 11.8841 0.504452
\(556\) 17.2429 0.731261
\(557\) −37.7321 −1.59876 −0.799381 0.600825i \(-0.794839\pi\)
−0.799381 + 0.600825i \(0.794839\pi\)
\(558\) 20.9458 0.886706
\(559\) 30.4901 1.28960
\(560\) 3.35107 0.141609
\(561\) 18.3545 0.774929
\(562\) −9.16859 −0.386753
\(563\) −25.5532 −1.07694 −0.538470 0.842645i \(-0.680997\pi\)
−0.538470 + 0.842645i \(0.680997\pi\)
\(564\) 10.7883 0.454269
\(565\) −46.4795 −1.95541
\(566\) −10.0066 −0.420611
\(567\) −4.01770 −0.168728
\(568\) 4.81812 0.202164
\(569\) −19.8398 −0.831728 −0.415864 0.909427i \(-0.636521\pi\)
−0.415864 + 0.909427i \(0.636521\pi\)
\(570\) 79.8183 3.34322
\(571\) 22.0403 0.922358 0.461179 0.887307i \(-0.347427\pi\)
0.461179 + 0.887307i \(0.347427\pi\)
\(572\) 14.8642 0.621505
\(573\) 45.3594 1.89492
\(574\) −4.76950 −0.199075
\(575\) 0.691994 0.0288582
\(576\) 5.40739 0.225308
\(577\) 28.1623 1.17241 0.586205 0.810162i \(-0.300621\pi\)
0.586205 + 0.810162i \(0.300621\pi\)
\(578\) 15.5998 0.648868
\(579\) 79.3464 3.29752
\(580\) 25.0491 1.04011
\(581\) −0.907057 −0.0376310
\(582\) 42.3262 1.75448
\(583\) 18.5081 0.766528
\(584\) −3.52593 −0.145904
\(585\) −50.3488 −2.08167
\(586\) −16.0734 −0.663986
\(587\) −20.0591 −0.827926 −0.413963 0.910294i \(-0.635856\pi\)
−0.413963 + 0.910294i \(0.635856\pi\)
\(588\) −2.89955 −0.119575
\(589\) 31.8198 1.31111
\(590\) 24.8521 1.02315
\(591\) 71.4088 2.93737
\(592\) 1.22307 0.0502679
\(593\) 13.5893 0.558044 0.279022 0.960285i \(-0.409990\pi\)
0.279022 + 0.960285i \(0.409990\pi\)
\(594\) 37.3424 1.53218
\(595\) −3.96526 −0.162560
\(596\) −21.2617 −0.870912
\(597\) −51.9009 −2.12416
\(598\) −0.308640 −0.0126212
\(599\) −31.4306 −1.28422 −0.642110 0.766612i \(-0.721941\pi\)
−0.642110 + 0.766612i \(0.721941\pi\)
\(600\) 18.0633 0.737433
\(601\) −20.4441 −0.833934 −0.416967 0.908922i \(-0.636907\pi\)
−0.416967 + 0.908922i \(0.636907\pi\)
\(602\) 10.9734 0.447243
\(603\) −46.6832 −1.90109
\(604\) −12.2728 −0.499375
\(605\) −59.0416 −2.40038
\(606\) 21.3976 0.869218
\(607\) −0.628313 −0.0255024 −0.0127512 0.999919i \(-0.504059\pi\)
−0.0127512 + 0.999919i \(0.504059\pi\)
\(608\) 8.21463 0.333147
\(609\) −21.6740 −0.878275
\(610\) −2.26006 −0.0915072
\(611\) −10.3381 −0.418233
\(612\) −6.39846 −0.258642
\(613\) −2.50434 −0.101149 −0.0505746 0.998720i \(-0.516105\pi\)
−0.0505746 + 0.998720i \(0.516105\pi\)
\(614\) 22.7974 0.920029
\(615\) −46.3434 −1.86875
\(616\) 5.34965 0.215543
\(617\) −12.6270 −0.508344 −0.254172 0.967159i \(-0.581803\pi\)
−0.254172 + 0.967159i \(0.581803\pi\)
\(618\) 15.1577 0.609734
\(619\) −38.7800 −1.55870 −0.779349 0.626590i \(-0.784450\pi\)
−0.779349 + 0.626590i \(0.784450\pi\)
\(620\) 12.9806 0.521312
\(621\) −0.775376 −0.0311148
\(622\) 10.1888 0.408534
\(623\) −0.159247 −0.00638009
\(624\) −8.05653 −0.322519
\(625\) −17.3393 −0.693573
\(626\) −21.3794 −0.854492
\(627\) 127.422 5.08873
\(628\) −1.28169 −0.0511451
\(629\) −1.44724 −0.0577051
\(630\) −18.1206 −0.721941
\(631\) −19.3148 −0.768910 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(632\) 1.08915 0.0433239
\(633\) −54.1622 −2.15275
\(634\) −6.92557 −0.275049
\(635\) −27.9578 −1.10947
\(636\) −10.0315 −0.397777
\(637\) 2.77854 0.110090
\(638\) 39.9884 1.58315
\(639\) −26.0535 −1.03066
\(640\) 3.35107 0.132463
\(641\) −43.3826 −1.71351 −0.856755 0.515724i \(-0.827523\pi\)
−0.856755 + 0.515724i \(0.827523\pi\)
\(642\) 31.8378 1.25654
\(643\) 40.5360 1.59858 0.799292 0.600942i \(-0.205208\pi\)
0.799292 + 0.600942i \(0.205208\pi\)
\(644\) −0.111080 −0.00437716
\(645\) 106.624 4.19833
\(646\) −9.72021 −0.382437
\(647\) 41.4339 1.62893 0.814466 0.580211i \(-0.197030\pi\)
0.814466 + 0.580211i \(0.197030\pi\)
\(648\) −4.01770 −0.157830
\(649\) 39.6739 1.55733
\(650\) −17.3095 −0.678935
\(651\) −11.2316 −0.440199
\(652\) 1.62246 0.0635406
\(653\) −37.3521 −1.46170 −0.730850 0.682538i \(-0.760876\pi\)
−0.730850 + 0.682538i \(0.760876\pi\)
\(654\) 44.1098 1.72483
\(655\) 60.3509 2.35810
\(656\) −4.76950 −0.186218
\(657\) 19.0661 0.743839
\(658\) −3.72068 −0.145047
\(659\) −17.0881 −0.665657 −0.332829 0.942987i \(-0.608003\pi\)
−0.332829 + 0.942987i \(0.608003\pi\)
\(660\) 51.9804 2.02333
\(661\) 8.16677 0.317650 0.158825 0.987307i \(-0.449229\pi\)
0.158825 + 0.987307i \(0.449229\pi\)
\(662\) 16.7005 0.649083
\(663\) 9.53314 0.370236
\(664\) −0.907057 −0.0352006
\(665\) −27.5278 −1.06748
\(666\) −6.61363 −0.256273
\(667\) −0.830317 −0.0321500
\(668\) −13.7556 −0.532222
\(669\) 58.8078 2.27364
\(670\) −28.9306 −1.11769
\(671\) −3.60796 −0.139284
\(672\) −2.89955 −0.111853
\(673\) −7.31793 −0.282086 −0.141043 0.990004i \(-0.545046\pi\)
−0.141043 + 0.990004i \(0.545046\pi\)
\(674\) −11.0483 −0.425566
\(675\) −43.4855 −1.67376
\(676\) −5.27969 −0.203065
\(677\) 18.8622 0.724935 0.362467 0.931996i \(-0.381934\pi\)
0.362467 + 0.931996i \(0.381934\pi\)
\(678\) 40.2168 1.54452
\(679\) −14.5975 −0.560201
\(680\) −3.96526 −0.152061
\(681\) −45.7645 −1.75370
\(682\) 20.7221 0.793491
\(683\) −23.2750 −0.890595 −0.445297 0.895383i \(-0.646902\pi\)
−0.445297 + 0.895383i \(0.646902\pi\)
\(684\) −44.4197 −1.69843
\(685\) −14.4258 −0.551183
\(686\) 1.00000 0.0381802
\(687\) −26.1273 −0.996820
\(688\) 10.9734 0.418358
\(689\) 9.61290 0.366222
\(690\) −1.07932 −0.0410890
\(691\) −35.2859 −1.34234 −0.671169 0.741304i \(-0.734208\pi\)
−0.671169 + 0.741304i \(0.734208\pi\)
\(692\) 3.09879 0.117798
\(693\) −28.9276 −1.09887
\(694\) 20.6926 0.785481
\(695\) −57.7821 −2.19180
\(696\) −21.6740 −0.821551
\(697\) 5.64366 0.213769
\(698\) 6.06856 0.229698
\(699\) −40.0161 −1.51355
\(700\) −6.22970 −0.235461
\(701\) −9.72151 −0.367176 −0.183588 0.983003i \(-0.558771\pi\)
−0.183588 + 0.983003i \(0.558771\pi\)
\(702\) 19.3952 0.732025
\(703\) −10.0471 −0.378933
\(704\) 5.34965 0.201622
\(705\) −36.1523 −1.36158
\(706\) −2.63860 −0.0993049
\(707\) −7.37963 −0.277539
\(708\) −21.5035 −0.808153
\(709\) 32.1634 1.20792 0.603961 0.797014i \(-0.293588\pi\)
0.603961 + 0.797014i \(0.293588\pi\)
\(710\) −16.1459 −0.605944
\(711\) −5.88944 −0.220871
\(712\) −0.159247 −0.00596803
\(713\) −0.430273 −0.0161139
\(714\) 3.43098 0.128401
\(715\) −49.8111 −1.86283
\(716\) 3.55238 0.132759
\(717\) 26.0655 0.973434
\(718\) 20.8998 0.779975
\(719\) −22.1291 −0.825275 −0.412637 0.910895i \(-0.635392\pi\)
−0.412637 + 0.910895i \(0.635392\pi\)
\(720\) −18.1206 −0.675314
\(721\) −5.22762 −0.194687
\(722\) −48.4801 −1.80424
\(723\) −84.2691 −3.13400
\(724\) −13.5674 −0.504227
\(725\) −46.5668 −1.72945
\(726\) 51.0863 1.89599
\(727\) 7.76586 0.288020 0.144010 0.989576i \(-0.454000\pi\)
0.144010 + 0.989576i \(0.454000\pi\)
\(728\) 2.77854 0.102980
\(729\) −38.9943 −1.44423
\(730\) 11.8157 0.437317
\(731\) −12.9846 −0.480254
\(732\) 1.95554 0.0722788
\(733\) 21.7272 0.802511 0.401256 0.915966i \(-0.368574\pi\)
0.401256 + 0.915966i \(0.368574\pi\)
\(734\) 3.30242 0.121894
\(735\) 9.71661 0.358403
\(736\) −0.111080 −0.00409446
\(737\) −46.1847 −1.70123
\(738\) 25.7906 0.949363
\(739\) 28.1868 1.03687 0.518435 0.855117i \(-0.326515\pi\)
0.518435 + 0.855117i \(0.326515\pi\)
\(740\) −4.09860 −0.150668
\(741\) 66.1814 2.43123
\(742\) 3.45969 0.127009
\(743\) −2.98384 −0.109467 −0.0547333 0.998501i \(-0.517431\pi\)
−0.0547333 + 0.998501i \(0.517431\pi\)
\(744\) −11.2316 −0.411769
\(745\) 71.2495 2.61038
\(746\) −30.3078 −1.10965
\(747\) 4.90481 0.179458
\(748\) −6.33013 −0.231453
\(749\) −10.9803 −0.401210
\(750\) −11.9485 −0.436299
\(751\) −27.8884 −1.01766 −0.508831 0.860867i \(-0.669922\pi\)
−0.508831 + 0.860867i \(0.669922\pi\)
\(752\) −3.72068 −0.135679
\(753\) 1.38080 0.0503192
\(754\) 20.7695 0.756381
\(755\) 41.1272 1.49677
\(756\) 6.98035 0.253873
\(757\) 21.7298 0.789784 0.394892 0.918727i \(-0.370782\pi\)
0.394892 + 0.918727i \(0.370782\pi\)
\(758\) −18.4903 −0.671596
\(759\) −1.72302 −0.0625417
\(760\) −27.5278 −0.998540
\(761\) −29.5943 −1.07279 −0.536396 0.843967i \(-0.680214\pi\)
−0.536396 + 0.843967i \(0.680214\pi\)
\(762\) 24.1908 0.876340
\(763\) −15.2126 −0.550734
\(764\) −15.6436 −0.565965
\(765\) 21.4417 0.775227
\(766\) 33.1678 1.19840
\(767\) 20.6061 0.744045
\(768\) −2.89955 −0.104628
\(769\) −23.1609 −0.835203 −0.417601 0.908630i \(-0.637129\pi\)
−0.417601 + 0.908630i \(0.637129\pi\)
\(770\) −17.9271 −0.646046
\(771\) 19.4147 0.699203
\(772\) −27.3651 −0.984890
\(773\) 12.5669 0.452001 0.226001 0.974127i \(-0.427435\pi\)
0.226001 + 0.974127i \(0.427435\pi\)
\(774\) −59.3376 −2.13285
\(775\) −24.1311 −0.866814
\(776\) −14.5975 −0.524020
\(777\) 3.54636 0.127225
\(778\) −34.9633 −1.25350
\(779\) 39.1797 1.40376
\(780\) 26.9980 0.966685
\(781\) −25.7752 −0.922311
\(782\) 0.131439 0.00470024
\(783\) 52.1778 1.86468
\(784\) 1.00000 0.0357143
\(785\) 4.29505 0.153297
\(786\) −52.2192 −1.86260
\(787\) −17.1128 −0.610007 −0.305003 0.952351i \(-0.598658\pi\)
−0.305003 + 0.952351i \(0.598658\pi\)
\(788\) −24.6276 −0.877320
\(789\) −79.4580 −2.82878
\(790\) −3.64981 −0.129854
\(791\) −13.8700 −0.493161
\(792\) −28.9276 −1.02790
\(793\) −1.87393 −0.0665452
\(794\) −26.5591 −0.942546
\(795\) 33.6165 1.19225
\(796\) 17.8996 0.634436
\(797\) −17.9195 −0.634741 −0.317371 0.948302i \(-0.602800\pi\)
−0.317371 + 0.948302i \(0.602800\pi\)
\(798\) 23.8187 0.843174
\(799\) 4.40260 0.155753
\(800\) −6.22970 −0.220253
\(801\) 0.861110 0.0304258
\(802\) 25.0671 0.885150
\(803\) 18.8625 0.665643
\(804\) 25.0325 0.882827
\(805\) 0.372237 0.0131196
\(806\) 10.7628 0.379105
\(807\) −56.7998 −1.99945
\(808\) −7.37963 −0.259614
\(809\) 18.7742 0.660065 0.330032 0.943970i \(-0.392940\pi\)
0.330032 + 0.943970i \(0.392940\pi\)
\(810\) 13.4636 0.473063
\(811\) 24.5643 0.862568 0.431284 0.902216i \(-0.358061\pi\)
0.431284 + 0.902216i \(0.358061\pi\)
\(812\) 7.47496 0.262320
\(813\) 5.79126 0.203108
\(814\) −6.54300 −0.229332
\(815\) −5.43700 −0.190450
\(816\) 3.43098 0.120108
\(817\) −90.1426 −3.15369
\(818\) −3.80485 −0.133034
\(819\) −15.0247 −0.525005
\(820\) 15.9830 0.558149
\(821\) 16.8467 0.587953 0.293977 0.955813i \(-0.405021\pi\)
0.293977 + 0.955813i \(0.405021\pi\)
\(822\) 12.4821 0.435363
\(823\) −7.56628 −0.263744 −0.131872 0.991267i \(-0.542099\pi\)
−0.131872 + 0.991267i \(0.542099\pi\)
\(824\) −5.22762 −0.182113
\(825\) −96.6324 −3.36431
\(826\) 7.41617 0.258041
\(827\) −0.204095 −0.00709707 −0.00354854 0.999994i \(-0.501130\pi\)
−0.00354854 + 0.999994i \(0.501130\pi\)
\(828\) 0.600652 0.0208741
\(829\) 24.8892 0.864439 0.432219 0.901769i \(-0.357731\pi\)
0.432219 + 0.901769i \(0.357731\pi\)
\(830\) 3.03961 0.105507
\(831\) −2.32231 −0.0805602
\(832\) 2.77854 0.0963287
\(833\) −1.18328 −0.0409983
\(834\) 49.9966 1.73124
\(835\) 46.0962 1.59522
\(836\) −43.9453 −1.51988
\(837\) 27.0387 0.934595
\(838\) 12.5299 0.432839
\(839\) 32.8301 1.13342 0.566710 0.823918i \(-0.308216\pi\)
0.566710 + 0.823918i \(0.308216\pi\)
\(840\) 9.71661 0.335255
\(841\) 26.8750 0.926724
\(842\) 21.5252 0.741808
\(843\) −26.5848 −0.915628
\(844\) 18.6795 0.642975
\(845\) 17.6926 0.608645
\(846\) 20.1191 0.691710
\(847\) −17.6187 −0.605386
\(848\) 3.45969 0.118806
\(849\) −29.0148 −0.995784
\(850\) 7.37149 0.252840
\(851\) 0.135859 0.00465717
\(852\) 13.9704 0.478617
\(853\) 7.00241 0.239758 0.119879 0.992789i \(-0.461749\pi\)
0.119879 + 0.992789i \(0.461749\pi\)
\(854\) −0.674429 −0.0230785
\(855\) 148.854 5.09069
\(856\) −10.9803 −0.375298
\(857\) −25.9672 −0.887023 −0.443511 0.896269i \(-0.646267\pi\)
−0.443511 + 0.896269i \(0.646267\pi\)
\(858\) 43.0996 1.47140
\(859\) −29.2579 −0.998266 −0.499133 0.866525i \(-0.666348\pi\)
−0.499133 + 0.866525i \(0.666348\pi\)
\(860\) −36.7728 −1.25394
\(861\) −13.8294 −0.471305
\(862\) 1.00000 0.0340601
\(863\) −18.0305 −0.613764 −0.306882 0.951748i \(-0.599286\pi\)
−0.306882 + 0.951748i \(0.599286\pi\)
\(864\) 6.98035 0.237476
\(865\) −10.3843 −0.353076
\(866\) −7.94016 −0.269818
\(867\) 45.2325 1.53618
\(868\) 3.87355 0.131477
\(869\) −5.82654 −0.197652
\(870\) 72.6312 2.46243
\(871\) −23.9878 −0.812796
\(872\) −15.2126 −0.515165
\(873\) 78.9344 2.67153
\(874\) 0.912480 0.0308651
\(875\) 4.12083 0.139309
\(876\) −10.2236 −0.345424
\(877\) −36.5108 −1.23288 −0.616442 0.787401i \(-0.711426\pi\)
−0.616442 + 0.787401i \(0.711426\pi\)
\(878\) −4.78946 −0.161636
\(879\) −46.6056 −1.57197
\(880\) −17.9271 −0.604321
\(881\) 28.2687 0.952398 0.476199 0.879337i \(-0.342014\pi\)
0.476199 + 0.879337i \(0.342014\pi\)
\(882\) −5.40739 −0.182076
\(883\) −14.6824 −0.494103 −0.247051 0.969002i \(-0.579462\pi\)
−0.247051 + 0.969002i \(0.579462\pi\)
\(884\) −3.28780 −0.110581
\(885\) 72.0600 2.42227
\(886\) −36.7286 −1.23392
\(887\) −50.4856 −1.69514 −0.847570 0.530684i \(-0.821935\pi\)
−0.847570 + 0.530684i \(0.821935\pi\)
\(888\) 3.54636 0.119008
\(889\) −8.34294 −0.279813
\(890\) 0.533648 0.0178879
\(891\) 21.4933 0.720052
\(892\) −20.2817 −0.679081
\(893\) 30.5640 1.02278
\(894\) −61.6493 −2.06186
\(895\) −11.9043 −0.397917
\(896\) 1.00000 0.0334077
\(897\) −0.894918 −0.0298804
\(898\) 21.2727 0.709878
\(899\) 28.9546 0.965691
\(900\) 33.6864 1.12288
\(901\) −4.09378 −0.136384
\(902\) 25.5151 0.849561
\(903\) 31.8180 1.05884
\(904\) −13.8700 −0.461310
\(905\) 45.4653 1.51132
\(906\) −35.5857 −1.18226
\(907\) 46.3852 1.54020 0.770098 0.637926i \(-0.220208\pi\)
0.770098 + 0.637926i \(0.220208\pi\)
\(908\) 15.7833 0.523788
\(909\) 39.9045 1.32355
\(910\) −9.31111 −0.308660
\(911\) 18.4009 0.609648 0.304824 0.952409i \(-0.401402\pi\)
0.304824 + 0.952409i \(0.401402\pi\)
\(912\) 23.8187 0.788717
\(913\) 4.85243 0.160592
\(914\) 1.75027 0.0578938
\(915\) −6.55316 −0.216641
\(916\) 9.01082 0.297726
\(917\) 18.0094 0.594723
\(918\) −8.25971 −0.272611
\(919\) 14.0594 0.463777 0.231889 0.972742i \(-0.425509\pi\)
0.231889 + 0.972742i \(0.425509\pi\)
\(920\) 0.372237 0.0122723
\(921\) 66.1023 2.17814
\(922\) 9.45946 0.311531
\(923\) −13.3874 −0.440650
\(924\) 15.5116 0.510293
\(925\) 7.61937 0.250523
\(926\) 4.01164 0.131831
\(927\) 28.2678 0.928436
\(928\) 7.47496 0.245378
\(929\) −34.6751 −1.13765 −0.568827 0.822457i \(-0.692603\pi\)
−0.568827 + 0.822457i \(0.692603\pi\)
\(930\) 37.6378 1.23419
\(931\) −8.21463 −0.269224
\(932\) 13.8008 0.452060
\(933\) 29.5430 0.967194
\(934\) −8.52792 −0.279042
\(935\) 21.2127 0.693731
\(936\) −15.0247 −0.491097
\(937\) 35.5973 1.16291 0.581457 0.813577i \(-0.302483\pi\)
0.581457 + 0.813577i \(0.302483\pi\)
\(938\) −8.63322 −0.281885
\(939\) −61.9906 −2.02299
\(940\) 12.4683 0.406670
\(941\) 40.6357 1.32469 0.662343 0.749201i \(-0.269562\pi\)
0.662343 + 0.749201i \(0.269562\pi\)
\(942\) −3.71633 −0.121085
\(943\) −0.529795 −0.0172525
\(944\) 7.41617 0.241376
\(945\) −23.3917 −0.760931
\(946\) −58.7039 −1.90863
\(947\) 12.4476 0.404491 0.202246 0.979335i \(-0.435176\pi\)
0.202246 + 0.979335i \(0.435176\pi\)
\(948\) 3.15803 0.102568
\(949\) 9.79696 0.318023
\(950\) 51.1747 1.66033
\(951\) −20.0810 −0.651172
\(952\) −1.18328 −0.0383504
\(953\) 3.88437 0.125827 0.0629136 0.998019i \(-0.479961\pi\)
0.0629136 + 0.998019i \(0.479961\pi\)
\(954\) −18.7079 −0.605690
\(955\) 52.4229 1.69636
\(956\) −8.98950 −0.290741
\(957\) 115.948 3.74808
\(958\) 24.0773 0.777903
\(959\) −4.30484 −0.139011
\(960\) 9.71661 0.313602
\(961\) −15.9956 −0.515987
\(962\) −3.39836 −0.109567
\(963\) 59.3746 1.91332
\(964\) 29.0628 0.936050
\(965\) 91.7024 2.95200
\(966\) −0.322082 −0.0103628
\(967\) −36.3245 −1.16812 −0.584058 0.811712i \(-0.698536\pi\)
−0.584058 + 0.811712i \(0.698536\pi\)
\(968\) −17.6187 −0.566287
\(969\) −28.1842 −0.905408
\(970\) 48.9173 1.57064
\(971\) −44.3366 −1.42283 −0.711415 0.702772i \(-0.751945\pi\)
−0.711415 + 0.702772i \(0.751945\pi\)
\(972\) 9.29152 0.298026
\(973\) −17.2429 −0.552781
\(974\) 4.92742 0.157885
\(975\) −50.1898 −1.60736
\(976\) −0.674429 −0.0215879
\(977\) −27.6645 −0.885064 −0.442532 0.896753i \(-0.645920\pi\)
−0.442532 + 0.896753i \(0.645920\pi\)
\(978\) 4.70442 0.150431
\(979\) 0.851914 0.0272273
\(980\) −3.35107 −0.107046
\(981\) 82.2606 2.62638
\(982\) 37.0739 1.18308
\(983\) −32.2099 −1.02734 −0.513668 0.857989i \(-0.671714\pi\)
−0.513668 + 0.857989i \(0.671714\pi\)
\(984\) −13.8294 −0.440865
\(985\) 82.5288 2.62959
\(986\) −8.84497 −0.281681
\(987\) −10.7883 −0.343395
\(988\) −22.8247 −0.726151
\(989\) 1.21893 0.0387596
\(990\) 96.9386 3.08091
\(991\) −0.938694 −0.0298186 −0.0149093 0.999889i \(-0.504746\pi\)
−0.0149093 + 0.999889i \(0.504746\pi\)
\(992\) 3.87355 0.122985
\(993\) 48.4239 1.53669
\(994\) −4.81812 −0.152822
\(995\) −59.9831 −1.90159
\(996\) −2.63006 −0.0833365
\(997\) 52.3283 1.65725 0.828627 0.559801i \(-0.189122\pi\)
0.828627 + 0.559801i \(0.189122\pi\)
\(998\) −32.5784 −1.03125
\(999\) −8.53747 −0.270114
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 6034.2.a.o.1.4 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.o.1.4 25 1.1 even 1 trivial