Properties

Label 177.12.a.a.1.18
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} -238183. q^{10} +664138. q^{11} +317607. q^{12} -1.65425e6 q^{13} -1.85715e6 q^{14} +2.12625e6 q^{15} +190787. q^{16} +1.11788e7 q^{17} +1.60737e6 q^{18} -829403. q^{19} +1.14365e7 q^{20} +1.65787e7 q^{21} +1.80784e7 q^{22} +1.30559e6 q^{23} +2.21924e7 q^{24} +2.77345e7 q^{25} -4.50302e7 q^{26} -1.43489e7 q^{27} +8.91717e7 q^{28} -4.39688e7 q^{29} +5.78785e7 q^{30} +1.84585e8 q^{31} +1.92231e8 q^{32} -1.61385e8 q^{33} +3.04296e8 q^{34} +5.96969e8 q^{35} -7.71784e7 q^{36} +7.52080e7 q^{37} -2.25771e7 q^{38} +4.01983e8 q^{39} +7.99109e8 q^{40} -5.89404e8 q^{41} +4.51287e8 q^{42} +1.11165e9 q^{43} -8.68043e8 q^{44} -5.16679e8 q^{45} +3.55392e7 q^{46} -2.06811e9 q^{47} -4.63613e7 q^{48} +2.67733e9 q^{49} +7.54957e8 q^{50} -2.71644e9 q^{51} +2.16215e9 q^{52} -3.47306e9 q^{53} -3.90590e8 q^{54} -5.81121e9 q^{55} +6.23077e9 q^{56} +2.01545e8 q^{57} -1.19687e9 q^{58} +7.14924e8 q^{59} -2.77906e9 q^{60} -2.03845e9 q^{61} +5.02457e9 q^{62} -4.02862e9 q^{63} +4.84195e9 q^{64} +1.44747e10 q^{65} -4.39306e9 q^{66} -3.18226e9 q^{67} -1.46109e10 q^{68} -3.17258e8 q^{69} +1.62500e10 q^{70} +1.90460e10 q^{71} -5.39275e9 q^{72} +2.41193e10 q^{73} +2.04723e9 q^{74} -6.73947e9 q^{75} +1.08405e9 q^{76} -4.53108e10 q^{77} +1.09423e10 q^{78} +1.77091e10 q^{79} -1.66939e9 q^{80} +3.48678e9 q^{81} -1.60441e10 q^{82} -3.46150e10 q^{83} -2.16687e10 q^{84} -9.78144e10 q^{85} +3.02602e10 q^{86} +1.06844e10 q^{87} -6.06535e10 q^{88} -6.60387e10 q^{89} -1.40645e10 q^{90} +1.12861e11 q^{91} -1.70643e9 q^{92} -4.48541e10 q^{93} -5.62957e10 q^{94} +7.25728e9 q^{95} -4.67120e10 q^{96} +4.44981e10 q^{97} +7.28793e10 q^{98} +3.92167e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27.2209 0.601503 0.300751 0.953703i \(-0.402763\pi\)
0.300751 + 0.953703i \(0.402763\pi\)
\(3\) −243.000 −0.577350
\(4\) −1307.02 −0.638195
\(5\) −8750.00 −1.25220 −0.626099 0.779743i \(-0.715350\pi\)
−0.626099 + 0.779743i \(0.715350\pi\)
\(6\) −6614.68 −0.347278
\(7\) −68225.0 −1.53428 −0.767140 0.641480i \(-0.778321\pi\)
−0.767140 + 0.641480i \(0.778321\pi\)
\(8\) −91326.7 −0.985378
\(9\) 59049.0 0.333333
\(10\) −238183. −0.753201
\(11\) 664138. 1.24336 0.621682 0.783270i \(-0.286450\pi\)
0.621682 + 0.783270i \(0.286450\pi\)
\(12\) 317607. 0.368462
\(13\) −1.65425e6 −1.23570 −0.617850 0.786296i \(-0.711996\pi\)
−0.617850 + 0.786296i \(0.711996\pi\)
\(14\) −1.85715e6 −0.922873
\(15\) 2.12625e6 0.722957
\(16\) 190787. 0.0454873
\(17\) 1.11788e7 1.90952 0.954762 0.297370i \(-0.0961096\pi\)
0.954762 + 0.297370i \(0.0961096\pi\)
\(18\) 1.60737e6 0.200501
\(19\) −829403. −0.0768459 −0.0384229 0.999262i \(-0.512233\pi\)
−0.0384229 + 0.999262i \(0.512233\pi\)
\(20\) 1.14365e7 0.799147
\(21\) 1.65787e7 0.885817
\(22\) 1.80784e7 0.747887
\(23\) 1.30559e6 0.0422963 0.0211482 0.999776i \(-0.493268\pi\)
0.0211482 + 0.999776i \(0.493268\pi\)
\(24\) 2.21924e7 0.568908
\(25\) 2.77345e7 0.568002
\(26\) −4.50302e7 −0.743277
\(27\) −1.43489e7 −0.192450
\(28\) 8.91717e7 0.979169
\(29\) −4.39688e7 −0.398067 −0.199033 0.979993i \(-0.563780\pi\)
−0.199033 + 0.979993i \(0.563780\pi\)
\(30\) 5.78785e7 0.434861
\(31\) 1.84585e8 1.15800 0.578998 0.815329i \(-0.303444\pi\)
0.578998 + 0.815329i \(0.303444\pi\)
\(32\) 1.92231e8 1.01274
\(33\) −1.61385e8 −0.717857
\(34\) 3.04296e8 1.14858
\(35\) 5.96969e8 1.92122
\(36\) −7.71784e7 −0.212732
\(37\) 7.52080e7 0.178301 0.0891506 0.996018i \(-0.471585\pi\)
0.0891506 + 0.996018i \(0.471585\pi\)
\(38\) −2.25771e7 −0.0462230
\(39\) 4.01983e8 0.713432
\(40\) 7.99109e8 1.23389
\(41\) −5.89404e8 −0.794515 −0.397258 0.917707i \(-0.630038\pi\)
−0.397258 + 0.917707i \(0.630038\pi\)
\(42\) 4.51287e8 0.532821
\(43\) 1.11165e9 1.15317 0.576585 0.817037i \(-0.304385\pi\)
0.576585 + 0.817037i \(0.304385\pi\)
\(44\) −8.68043e8 −0.793509
\(45\) −5.16679e8 −0.417400
\(46\) 3.55392e7 0.0254413
\(47\) −2.06811e9 −1.31533 −0.657665 0.753310i \(-0.728456\pi\)
−0.657665 + 0.753310i \(0.728456\pi\)
\(48\) −4.63613e7 −0.0262621
\(49\) 2.67733e9 1.35401
\(50\) 7.54957e8 0.341654
\(51\) −2.71644e9 −1.10246
\(52\) 2.16215e9 0.788618
\(53\) −3.47306e9 −1.14076 −0.570381 0.821380i \(-0.693204\pi\)
−0.570381 + 0.821380i \(0.693204\pi\)
\(54\) −3.90590e8 −0.115759
\(55\) −5.81121e9 −1.55694
\(56\) 6.23077e9 1.51185
\(57\) 2.01545e8 0.0443670
\(58\) −1.19687e9 −0.239438
\(59\) 7.14924e8 0.130189
\(60\) −2.77906e9 −0.461388
\(61\) −2.03845e9 −0.309019 −0.154510 0.987991i \(-0.549380\pi\)
−0.154510 + 0.987991i \(0.549380\pi\)
\(62\) 5.02457e9 0.696537
\(63\) −4.02862e9 −0.511427
\(64\) 4.84195e9 0.563678
\(65\) 1.44747e10 1.54734
\(66\) −4.39306e9 −0.431793
\(67\) −3.18226e9 −0.287954 −0.143977 0.989581i \(-0.545989\pi\)
−0.143977 + 0.989581i \(0.545989\pi\)
\(68\) −1.46109e10 −1.21865
\(69\) −3.17258e8 −0.0244198
\(70\) 1.62500e10 1.15562
\(71\) 1.90460e10 1.25281 0.626403 0.779500i \(-0.284527\pi\)
0.626403 + 0.779500i \(0.284527\pi\)
\(72\) −5.39275e9 −0.328459
\(73\) 2.41193e10 1.36173 0.680863 0.732411i \(-0.261605\pi\)
0.680863 + 0.732411i \(0.261605\pi\)
\(74\) 2.04723e9 0.107249
\(75\) −6.73947e9 −0.327936
\(76\) 1.08405e9 0.0490426
\(77\) −4.53108e10 −1.90767
\(78\) 1.09423e10 0.429131
\(79\) 1.77091e10 0.647513 0.323756 0.946140i \(-0.395054\pi\)
0.323756 + 0.946140i \(0.395054\pi\)
\(80\) −1.66939e9 −0.0569591
\(81\) 3.48678e9 0.111111
\(82\) −1.60441e10 −0.477903
\(83\) −3.46150e10 −0.964572 −0.482286 0.876014i \(-0.660193\pi\)
−0.482286 + 0.876014i \(0.660193\pi\)
\(84\) −2.16687e10 −0.565324
\(85\) −9.78144e10 −2.39110
\(86\) 3.02602e10 0.693634
\(87\) 1.06844e10 0.229824
\(88\) −6.06535e10 −1.22518
\(89\) −6.60387e10 −1.25358 −0.626792 0.779187i \(-0.715632\pi\)
−0.626792 + 0.779187i \(0.715632\pi\)
\(90\) −1.40645e10 −0.251067
\(91\) 1.12861e11 1.89591
\(92\) −1.70643e9 −0.0269933
\(93\) −4.48541e10 −0.668569
\(94\) −5.62957e10 −0.791175
\(95\) 7.25728e9 0.0962263
\(96\) −4.67120e10 −0.584705
\(97\) 4.44981e10 0.526135 0.263067 0.964777i \(-0.415266\pi\)
0.263067 + 0.964777i \(0.415266\pi\)
\(98\) 7.28793e10 0.814443
\(99\) 3.92167e10 0.414455
\(100\) −3.62496e10 −0.362496
\(101\) −6.89078e10 −0.652380 −0.326190 0.945304i \(-0.605765\pi\)
−0.326190 + 0.945304i \(0.605765\pi\)
\(102\) −7.39440e10 −0.663135
\(103\) 8.40518e9 0.0714401 0.0357201 0.999362i \(-0.488628\pi\)
0.0357201 + 0.999362i \(0.488628\pi\)
\(104\) 1.51077e11 1.21763
\(105\) −1.45064e11 −1.10922
\(106\) −9.45398e10 −0.686171
\(107\) 2.85129e11 1.96531 0.982655 0.185444i \(-0.0593722\pi\)
0.982655 + 0.185444i \(0.0593722\pi\)
\(108\) 1.87543e10 0.122821
\(109\) −6.32925e10 −0.394010 −0.197005 0.980403i \(-0.563121\pi\)
−0.197005 + 0.980403i \(0.563121\pi\)
\(110\) −1.58186e11 −0.936503
\(111\) −1.82755e10 −0.102942
\(112\) −1.30165e10 −0.0697902
\(113\) 2.13515e11 1.09017 0.545087 0.838379i \(-0.316496\pi\)
0.545087 + 0.838379i \(0.316496\pi\)
\(114\) 5.48623e9 0.0266869
\(115\) −1.14239e10 −0.0529634
\(116\) 5.74683e10 0.254044
\(117\) −9.76820e10 −0.411900
\(118\) 1.94609e10 0.0783090
\(119\) −7.62672e11 −2.92974
\(120\) −1.94184e11 −0.712386
\(121\) 1.55767e11 0.545955
\(122\) −5.54883e10 −0.185876
\(123\) 1.43225e11 0.458714
\(124\) −2.41257e11 −0.739027
\(125\) 1.84570e11 0.540948
\(126\) −1.09663e11 −0.307624
\(127\) −5.37182e11 −1.44278 −0.721391 0.692528i \(-0.756497\pi\)
−0.721391 + 0.692528i \(0.756497\pi\)
\(128\) −2.61886e11 −0.673685
\(129\) −2.70132e11 −0.665783
\(130\) 3.94015e11 0.930731
\(131\) 3.30858e11 0.749290 0.374645 0.927168i \(-0.377765\pi\)
0.374645 + 0.927168i \(0.377765\pi\)
\(132\) 2.10935e11 0.458132
\(133\) 5.65860e10 0.117903
\(134\) −8.66238e10 −0.173205
\(135\) 1.25553e11 0.240986
\(136\) −1.02092e12 −1.88160
\(137\) 6.30957e11 1.11696 0.558479 0.829519i \(-0.311385\pi\)
0.558479 + 0.829519i \(0.311385\pi\)
\(138\) −8.63603e9 −0.0146886
\(139\) 8.10012e11 1.32407 0.662033 0.749474i \(-0.269694\pi\)
0.662033 + 0.749474i \(0.269694\pi\)
\(140\) −7.80253e11 −1.22611
\(141\) 5.02550e11 0.759407
\(142\) 5.18450e11 0.753565
\(143\) −1.09865e12 −1.53643
\(144\) 1.12658e10 0.0151624
\(145\) 3.84728e11 0.498459
\(146\) 6.56550e11 0.819081
\(147\) −6.50591e11 −0.781740
\(148\) −9.82986e10 −0.113791
\(149\) −2.38458e11 −0.266004 −0.133002 0.991116i \(-0.542462\pi\)
−0.133002 + 0.991116i \(0.542462\pi\)
\(150\) −1.83455e11 −0.197254
\(151\) −2.44355e11 −0.253307 −0.126653 0.991947i \(-0.540424\pi\)
−0.126653 + 0.991947i \(0.540424\pi\)
\(152\) 7.57466e10 0.0757223
\(153\) 6.60096e11 0.636508
\(154\) −1.23340e12 −1.14747
\(155\) −1.61512e12 −1.45004
\(156\) −5.25401e11 −0.455309
\(157\) 3.50711e11 0.293428 0.146714 0.989179i \(-0.453130\pi\)
0.146714 + 0.989179i \(0.453130\pi\)
\(158\) 4.82058e11 0.389481
\(159\) 8.43954e11 0.658619
\(160\) −1.68202e12 −1.26815
\(161\) −8.90737e10 −0.0648944
\(162\) 9.49134e10 0.0668336
\(163\) 1.30317e12 0.887094 0.443547 0.896251i \(-0.353720\pi\)
0.443547 + 0.896251i \(0.353720\pi\)
\(164\) 7.70365e11 0.507055
\(165\) 1.41212e12 0.898899
\(166\) −9.42251e11 −0.580193
\(167\) −2.42144e12 −1.44256 −0.721278 0.692646i \(-0.756445\pi\)
−0.721278 + 0.692646i \(0.756445\pi\)
\(168\) −1.51408e12 −0.872865
\(169\) 9.44391e11 0.526957
\(170\) −2.66259e12 −1.43826
\(171\) −4.89754e10 −0.0256153
\(172\) −1.45296e12 −0.735947
\(173\) −1.37292e12 −0.673584 −0.336792 0.941579i \(-0.609342\pi\)
−0.336792 + 0.941579i \(0.609342\pi\)
\(174\) 2.90840e11 0.138240
\(175\) −1.89218e12 −0.871474
\(176\) 1.26709e11 0.0565573
\(177\) −1.73727e11 −0.0751646
\(178\) −1.79763e12 −0.754034
\(179\) 3.97937e11 0.161854 0.0809269 0.996720i \(-0.474212\pi\)
0.0809269 + 0.996720i \(0.474212\pi\)
\(180\) 6.75311e11 0.266382
\(181\) 2.56106e12 0.979913 0.489957 0.871747i \(-0.337013\pi\)
0.489957 + 0.871747i \(0.337013\pi\)
\(182\) 3.07219e12 1.14040
\(183\) 4.95342e11 0.178412
\(184\) −1.19235e11 −0.0416779
\(185\) −6.58070e11 −0.223269
\(186\) −1.22097e12 −0.402146
\(187\) 7.42425e12 2.37423
\(188\) 2.70306e12 0.839437
\(189\) 9.78955e11 0.295272
\(190\) 1.97550e11 0.0578804
\(191\) 2.33603e10 0.00664958 0.00332479 0.999994i \(-0.498942\pi\)
0.00332479 + 0.999994i \(0.498942\pi\)
\(192\) −1.17660e12 −0.325439
\(193\) −2.98688e12 −0.802883 −0.401441 0.915885i \(-0.631491\pi\)
−0.401441 + 0.915885i \(0.631491\pi\)
\(194\) 1.21128e12 0.316471
\(195\) −3.51736e12 −0.893359
\(196\) −3.49933e12 −0.864125
\(197\) 4.89501e12 1.17541 0.587705 0.809075i \(-0.300032\pi\)
0.587705 + 0.809075i \(0.300032\pi\)
\(198\) 1.06751e12 0.249296
\(199\) −5.23981e12 −1.19021 −0.595106 0.803648i \(-0.702890\pi\)
−0.595106 + 0.803648i \(0.702890\pi\)
\(200\) −2.53290e12 −0.559697
\(201\) 7.73288e11 0.166250
\(202\) −1.87573e12 −0.392408
\(203\) 2.99978e12 0.610746
\(204\) 3.55045e12 0.703587
\(205\) 5.15729e12 0.994891
\(206\) 2.28796e11 0.0429714
\(207\) 7.70936e10 0.0140988
\(208\) −3.15611e11 −0.0562087
\(209\) −5.50838e11 −0.0955474
\(210\) −3.94876e12 −0.667198
\(211\) 1.28415e12 0.211380 0.105690 0.994399i \(-0.466295\pi\)
0.105690 + 0.994399i \(0.466295\pi\)
\(212\) 4.53937e12 0.728028
\(213\) −4.62818e12 −0.723307
\(214\) 7.76147e12 1.18214
\(215\) −9.72698e12 −1.44400
\(216\) 1.31044e12 0.189636
\(217\) −1.25933e13 −1.77669
\(218\) −1.72288e12 −0.236998
\(219\) −5.86100e12 −0.786192
\(220\) 7.59538e12 0.993631
\(221\) −1.84925e13 −2.35960
\(222\) −4.97477e11 −0.0619201
\(223\) −7.57568e11 −0.0919909 −0.0459955 0.998942i \(-0.514646\pi\)
−0.0459955 + 0.998942i \(0.514646\pi\)
\(224\) −1.31149e13 −1.55382
\(225\) 1.63769e12 0.189334
\(226\) 5.81206e12 0.655743
\(227\) 2.35281e12 0.259087 0.129543 0.991574i \(-0.458649\pi\)
0.129543 + 0.991574i \(0.458649\pi\)
\(228\) −2.63424e11 −0.0283148
\(229\) −9.82529e12 −1.03098 −0.515490 0.856896i \(-0.672390\pi\)
−0.515490 + 0.856896i \(0.672390\pi\)
\(230\) −3.10969e11 −0.0318576
\(231\) 1.10105e13 1.10139
\(232\) 4.01553e12 0.392246
\(233\) −1.72545e13 −1.64606 −0.823028 0.568000i \(-0.807717\pi\)
−0.823028 + 0.568000i \(0.807717\pi\)
\(234\) −2.65899e12 −0.247759
\(235\) 1.80960e13 1.64706
\(236\) −9.34422e11 −0.0830859
\(237\) −4.30332e12 −0.373842
\(238\) −2.07606e13 −1.76225
\(239\) −2.07219e13 −1.71887 −0.859433 0.511249i \(-0.829183\pi\)
−0.859433 + 0.511249i \(0.829183\pi\)
\(240\) 4.05662e11 0.0328854
\(241\) −2.16204e13 −1.71305 −0.856524 0.516107i \(-0.827381\pi\)
−0.856524 + 0.516107i \(0.827381\pi\)
\(242\) 4.24013e12 0.328393
\(243\) −8.47289e11 −0.0641500
\(244\) 2.66430e12 0.197214
\(245\) −2.34266e13 −1.69549
\(246\) 3.89872e12 0.275917
\(247\) 1.37204e12 0.0949585
\(248\) −1.68575e13 −1.14106
\(249\) 8.41144e12 0.556896
\(250\) 5.02415e12 0.325381
\(251\) 2.18129e12 0.138200 0.0691001 0.997610i \(-0.477987\pi\)
0.0691001 + 0.997610i \(0.477987\pi\)
\(252\) 5.26550e12 0.326390
\(253\) 8.67089e11 0.0525897
\(254\) −1.46226e13 −0.867837
\(255\) 2.37689e13 1.38050
\(256\) −1.70451e13 −0.968901
\(257\) 2.66641e13 1.48352 0.741761 0.670664i \(-0.233991\pi\)
0.741761 + 0.670664i \(0.233991\pi\)
\(258\) −7.35323e12 −0.400470
\(259\) −5.13107e12 −0.273564
\(260\) −1.89188e13 −0.987506
\(261\) −2.59632e12 −0.132689
\(262\) 9.00626e12 0.450700
\(263\) −7.43238e12 −0.364226 −0.182113 0.983278i \(-0.558294\pi\)
−0.182113 + 0.983278i \(0.558294\pi\)
\(264\) 1.47388e13 0.707360
\(265\) 3.03893e13 1.42846
\(266\) 1.54032e12 0.0709190
\(267\) 1.60474e13 0.723757
\(268\) 4.15928e12 0.183771
\(269\) −6.93975e11 −0.0300404 −0.0150202 0.999887i \(-0.504781\pi\)
−0.0150202 + 0.999887i \(0.504781\pi\)
\(270\) 3.41767e12 0.144954
\(271\) 2.12225e13 0.881993 0.440997 0.897509i \(-0.354625\pi\)
0.440997 + 0.897509i \(0.354625\pi\)
\(272\) 2.13277e12 0.0868591
\(273\) −2.74253e13 −1.09460
\(274\) 1.71752e13 0.671853
\(275\) 1.84195e13 0.706233
\(276\) 4.14663e11 0.0155846
\(277\) −2.67735e13 −0.986430 −0.493215 0.869907i \(-0.664178\pi\)
−0.493215 + 0.869907i \(0.664178\pi\)
\(278\) 2.20492e13 0.796429
\(279\) 1.08996e13 0.385999
\(280\) −5.45193e13 −1.89313
\(281\) −3.05388e12 −0.103984 −0.0519921 0.998647i \(-0.516557\pi\)
−0.0519921 + 0.998647i \(0.516557\pi\)
\(282\) 1.36799e13 0.456785
\(283\) −1.73422e13 −0.567908 −0.283954 0.958838i \(-0.591646\pi\)
−0.283954 + 0.958838i \(0.591646\pi\)
\(284\) −2.48936e13 −0.799534
\(285\) −1.76352e12 −0.0555563
\(286\) −2.99063e13 −0.924164
\(287\) 4.02121e13 1.21901
\(288\) 1.13510e13 0.337580
\(289\) 9.06932e13 2.64628
\(290\) 1.04726e13 0.299824
\(291\) −1.08130e13 −0.303764
\(292\) −3.15245e13 −0.869046
\(293\) −2.92304e13 −0.790792 −0.395396 0.918511i \(-0.629393\pi\)
−0.395396 + 0.918511i \(0.629393\pi\)
\(294\) −1.77097e13 −0.470219
\(295\) −6.25559e12 −0.163022
\(296\) −6.86850e12 −0.175694
\(297\) −9.52965e12 −0.239286
\(298\) −6.49105e12 −0.160002
\(299\) −2.15977e12 −0.0522656
\(300\) 8.80865e12 0.209287
\(301\) −7.58426e13 −1.76928
\(302\) −6.65155e12 −0.152365
\(303\) 1.67446e13 0.376652
\(304\) −1.58240e11 −0.00349551
\(305\) 1.78364e13 0.386953
\(306\) 1.79684e13 0.382861
\(307\) −2.63689e13 −0.551862 −0.275931 0.961177i \(-0.588986\pi\)
−0.275931 + 0.961177i \(0.588986\pi\)
\(308\) 5.92223e13 1.21746
\(309\) −2.04246e12 −0.0412460
\(310\) −4.39650e13 −0.872203
\(311\) 7.04786e13 1.37365 0.686823 0.726824i \(-0.259005\pi\)
0.686823 + 0.726824i \(0.259005\pi\)
\(312\) −3.67118e13 −0.703001
\(313\) 4.84770e13 0.912099 0.456049 0.889954i \(-0.349264\pi\)
0.456049 + 0.889954i \(0.349264\pi\)
\(314\) 9.54667e12 0.176498
\(315\) 3.52504e13 0.640408
\(316\) −2.31462e13 −0.413239
\(317\) 5.95063e13 1.04409 0.522044 0.852919i \(-0.325170\pi\)
0.522044 + 0.852919i \(0.325170\pi\)
\(318\) 2.29732e13 0.396161
\(319\) −2.92014e13 −0.494942
\(320\) −4.23671e13 −0.705837
\(321\) −6.92864e13 −1.13467
\(322\) −2.42467e12 −0.0390341
\(323\) −9.27171e12 −0.146739
\(324\) −4.55731e12 −0.0709105
\(325\) −4.58798e13 −0.701880
\(326\) 3.54735e13 0.533589
\(327\) 1.53801e13 0.227482
\(328\) 5.38284e13 0.782898
\(329\) 1.41097e14 2.01809
\(330\) 3.84393e13 0.540690
\(331\) 1.15288e14 1.59489 0.797443 0.603395i \(-0.206186\pi\)
0.797443 + 0.603395i \(0.206186\pi\)
\(332\) 4.52426e13 0.615585
\(333\) 4.44096e12 0.0594338
\(334\) −6.59137e13 −0.867701
\(335\) 2.78447e13 0.360576
\(336\) 3.16300e12 0.0402934
\(337\) 1.33412e14 1.67198 0.835990 0.548745i \(-0.184894\pi\)
0.835990 + 0.548745i \(0.184894\pi\)
\(338\) 2.57072e13 0.316966
\(339\) −5.18840e13 −0.629413
\(340\) 1.27846e14 1.52599
\(341\) 1.22590e14 1.43981
\(342\) −1.33315e12 −0.0154077
\(343\) −4.77577e13 −0.543157
\(344\) −1.01524e14 −1.13631
\(345\) 2.77601e12 0.0305784
\(346\) −3.73721e13 −0.405162
\(347\) −9.01792e13 −0.962264 −0.481132 0.876648i \(-0.659774\pi\)
−0.481132 + 0.876648i \(0.659774\pi\)
\(348\) −1.39648e13 −0.146672
\(349\) 2.10940e13 0.218082 0.109041 0.994037i \(-0.465222\pi\)
0.109041 + 0.994037i \(0.465222\pi\)
\(350\) −5.15070e13 −0.524194
\(351\) 2.37367e13 0.237811
\(352\) 1.27668e14 1.25920
\(353\) −1.47536e14 −1.43264 −0.716322 0.697769i \(-0.754176\pi\)
−0.716322 + 0.697769i \(0.754176\pi\)
\(354\) −4.72899e12 −0.0452117
\(355\) −1.66653e14 −1.56876
\(356\) 8.63141e13 0.800031
\(357\) 1.85329e14 1.69149
\(358\) 1.08322e13 0.0973555
\(359\) 6.40285e13 0.566701 0.283350 0.959016i \(-0.408554\pi\)
0.283350 + 0.959016i \(0.408554\pi\)
\(360\) 4.71866e13 0.411296
\(361\) −1.15802e14 −0.994095
\(362\) 6.97143e13 0.589420
\(363\) −3.78515e13 −0.315207
\(364\) −1.47512e14 −1.20996
\(365\) −2.11044e14 −1.70515
\(366\) 1.34837e13 0.107315
\(367\) 1.63466e14 1.28164 0.640818 0.767693i \(-0.278595\pi\)
0.640818 + 0.767693i \(0.278595\pi\)
\(368\) 2.49090e11 0.00192394
\(369\) −3.48037e13 −0.264838
\(370\) −1.79133e13 −0.134297
\(371\) 2.36950e14 1.75025
\(372\) 5.86254e13 0.426677
\(373\) −1.66447e14 −1.19365 −0.596827 0.802370i \(-0.703572\pi\)
−0.596827 + 0.802370i \(0.703572\pi\)
\(374\) 2.02095e14 1.42811
\(375\) −4.48504e13 −0.312316
\(376\) 1.88874e14 1.29610
\(377\) 7.27356e13 0.491892
\(378\) 2.66480e13 0.177607
\(379\) 1.95984e14 1.28737 0.643687 0.765289i \(-0.277404\pi\)
0.643687 + 0.765289i \(0.277404\pi\)
\(380\) −9.48543e12 −0.0614111
\(381\) 1.30535e14 0.832991
\(382\) 6.35888e11 0.00399974
\(383\) −1.90371e14 −1.18034 −0.590172 0.807278i \(-0.700940\pi\)
−0.590172 + 0.807278i \(0.700940\pi\)
\(384\) 6.36382e13 0.388952
\(385\) 3.96470e14 2.38878
\(386\) −8.13055e13 −0.482936
\(387\) 6.56420e13 0.384390
\(388\) −5.81600e13 −0.335776
\(389\) 2.88431e14 1.64180 0.820899 0.571073i \(-0.193473\pi\)
0.820899 + 0.571073i \(0.193473\pi\)
\(390\) −9.57456e13 −0.537358
\(391\) 1.45949e13 0.0807659
\(392\) −2.44512e14 −1.33422
\(393\) −8.03986e13 −0.432603
\(394\) 1.33247e14 0.707012
\(395\) −1.54955e14 −0.810815
\(396\) −5.12571e13 −0.264503
\(397\) 2.38162e14 1.21206 0.606030 0.795441i \(-0.292761\pi\)
0.606030 + 0.795441i \(0.292761\pi\)
\(398\) −1.42632e14 −0.715915
\(399\) −1.37504e13 −0.0680714
\(400\) 5.29139e12 0.0258368
\(401\) −8.38112e13 −0.403653 −0.201826 0.979421i \(-0.564688\pi\)
−0.201826 + 0.979421i \(0.564688\pi\)
\(402\) 2.10496e13 0.100000
\(403\) −3.05350e14 −1.43094
\(404\) 9.00640e13 0.416346
\(405\) −3.05094e13 −0.139133
\(406\) 8.16566e13 0.367365
\(407\) 4.99485e13 0.221693
\(408\) 2.48084e14 1.08634
\(409\) −4.14093e14 −1.78904 −0.894520 0.447028i \(-0.852483\pi\)
−0.894520 + 0.447028i \(0.852483\pi\)
\(410\) 1.40386e14 0.598429
\(411\) −1.53323e14 −0.644876
\(412\) −1.09858e13 −0.0455927
\(413\) −4.87757e13 −0.199746
\(414\) 2.09856e12 0.00848045
\(415\) 3.02881e14 1.20784
\(416\) −3.17998e14 −1.25144
\(417\) −1.96833e14 −0.764450
\(418\) −1.49943e13 −0.0574720
\(419\) 4.99942e14 1.89122 0.945610 0.325301i \(-0.105466\pi\)
0.945610 + 0.325301i \(0.105466\pi\)
\(420\) 1.89601e14 0.707898
\(421\) 1.98871e14 0.732857 0.366428 0.930446i \(-0.380580\pi\)
0.366428 + 0.930446i \(0.380580\pi\)
\(422\) 3.49558e13 0.127146
\(423\) −1.22120e14 −0.438444
\(424\) 3.17183e14 1.12408
\(425\) 3.10037e14 1.08461
\(426\) −1.25983e14 −0.435071
\(427\) 1.39073e14 0.474122
\(428\) −3.72670e14 −1.25425
\(429\) 2.66972e14 0.887056
\(430\) −2.64777e14 −0.868568
\(431\) −2.31495e14 −0.749749 −0.374874 0.927076i \(-0.622314\pi\)
−0.374874 + 0.927076i \(0.622314\pi\)
\(432\) −2.73759e12 −0.00875403
\(433\) −1.23881e13 −0.0391131 −0.0195565 0.999809i \(-0.506225\pi\)
−0.0195565 + 0.999809i \(0.506225\pi\)
\(434\) −3.42801e14 −1.06868
\(435\) −9.34888e13 −0.287785
\(436\) 8.27248e13 0.251455
\(437\) −1.08286e12 −0.00325030
\(438\) −1.59542e14 −0.472897
\(439\) −2.24804e14 −0.658036 −0.329018 0.944324i \(-0.606718\pi\)
−0.329018 + 0.944324i \(0.606718\pi\)
\(440\) 5.30719e14 1.53417
\(441\) 1.58094e14 0.451338
\(442\) −5.03383e14 −1.41931
\(443\) −1.11592e14 −0.310750 −0.155375 0.987856i \(-0.549659\pi\)
−0.155375 + 0.987856i \(0.549659\pi\)
\(444\) 2.38866e13 0.0656972
\(445\) 5.77839e14 1.56974
\(446\) −2.06217e13 −0.0553328
\(447\) 5.79453e13 0.153577
\(448\) −3.30343e14 −0.864839
\(449\) −3.55719e14 −0.919924 −0.459962 0.887939i \(-0.652137\pi\)
−0.459962 + 0.887939i \(0.652137\pi\)
\(450\) 4.45794e13 0.113885
\(451\) −3.91446e14 −0.987872
\(452\) −2.79068e14 −0.695744
\(453\) 5.93781e13 0.146247
\(454\) 6.40457e13 0.155841
\(455\) −9.87538e14 −2.37406
\(456\) −1.84064e13 −0.0437183
\(457\) −1.75577e13 −0.0412030 −0.0206015 0.999788i \(-0.506558\pi\)
−0.0206015 + 0.999788i \(0.506558\pi\)
\(458\) −2.67453e14 −0.620137
\(459\) −1.60403e14 −0.367488
\(460\) 1.49313e13 0.0338010
\(461\) 3.32355e14 0.743441 0.371720 0.928345i \(-0.378768\pi\)
0.371720 + 0.928345i \(0.378768\pi\)
\(462\) 2.99717e14 0.662491
\(463\) −3.59705e14 −0.785689 −0.392845 0.919605i \(-0.628509\pi\)
−0.392845 + 0.919605i \(0.628509\pi\)
\(464\) −8.38870e12 −0.0181070
\(465\) 3.92474e14 0.837182
\(466\) −4.69683e14 −0.990107
\(467\) −7.51804e14 −1.56625 −0.783126 0.621863i \(-0.786376\pi\)
−0.783126 + 0.621863i \(0.786376\pi\)
\(468\) 1.27673e14 0.262873
\(469\) 2.17109e14 0.441802
\(470\) 4.92588e14 0.990708
\(471\) −8.52228e13 −0.169411
\(472\) −6.52917e13 −0.128285
\(473\) 7.38291e14 1.43381
\(474\) −1.17140e14 −0.224867
\(475\) −2.30030e13 −0.0436486
\(476\) 9.96830e14 1.86975
\(477\) −2.05081e14 −0.380254
\(478\) −5.64070e14 −1.03390
\(479\) 9.00575e14 1.63183 0.815914 0.578173i \(-0.196234\pi\)
0.815914 + 0.578173i \(0.196234\pi\)
\(480\) 4.08730e14 0.732167
\(481\) −1.24413e14 −0.220327
\(482\) −5.88526e14 −1.03040
\(483\) 2.16449e13 0.0374668
\(484\) −2.03592e14 −0.348426
\(485\) −3.89359e14 −0.658825
\(486\) −2.30640e13 −0.0385864
\(487\) −6.74263e14 −1.11537 −0.557686 0.830052i \(-0.688311\pi\)
−0.557686 + 0.830052i \(0.688311\pi\)
\(488\) 1.86165e14 0.304501
\(489\) −3.16671e14 −0.512164
\(490\) −6.37694e14 −1.01984
\(491\) 6.05535e14 0.957615 0.478808 0.877920i \(-0.341069\pi\)
0.478808 + 0.877920i \(0.341069\pi\)
\(492\) −1.87199e14 −0.292749
\(493\) −4.91518e14 −0.760118
\(494\) 3.73482e13 0.0571178
\(495\) −3.43146e14 −0.518980
\(496\) 3.52165e13 0.0526741
\(497\) −1.29942e15 −1.92215
\(498\) 2.28967e14 0.334974
\(499\) −9.33233e14 −1.35032 −0.675161 0.737671i \(-0.735926\pi\)
−0.675161 + 0.737671i \(0.735926\pi\)
\(500\) −2.41237e14 −0.345230
\(501\) 5.88409e14 0.832860
\(502\) 5.93768e13 0.0831278
\(503\) 8.39570e14 1.16261 0.581303 0.813687i \(-0.302543\pi\)
0.581303 + 0.813687i \(0.302543\pi\)
\(504\) 3.67921e14 0.503949
\(505\) 6.02943e14 0.816910
\(506\) 2.36030e13 0.0316329
\(507\) −2.29487e14 −0.304239
\(508\) 7.02109e14 0.920776
\(509\) 7.03132e14 0.912198 0.456099 0.889929i \(-0.349246\pi\)
0.456099 + 0.889929i \(0.349246\pi\)
\(510\) 6.47010e14 0.830377
\(511\) −1.64554e15 −2.08927
\(512\) 7.23595e13 0.0908889
\(513\) 1.19010e13 0.0147890
\(514\) 7.25819e14 0.892342
\(515\) −7.35453e13 −0.0894572
\(516\) 3.53069e14 0.424899
\(517\) −1.37351e15 −1.63544
\(518\) −1.39672e14 −0.164549
\(519\) 3.33620e14 0.388894
\(520\) −1.32193e15 −1.52472
\(521\) 7.78604e14 0.888606 0.444303 0.895877i \(-0.353451\pi\)
0.444303 + 0.895877i \(0.353451\pi\)
\(522\) −7.06741e13 −0.0798127
\(523\) 1.20304e15 1.34438 0.672189 0.740379i \(-0.265354\pi\)
0.672189 + 0.740379i \(0.265354\pi\)
\(524\) −4.32440e14 −0.478193
\(525\) 4.59801e14 0.503145
\(526\) −2.02316e14 −0.219083
\(527\) 2.06343e15 2.21122
\(528\) −3.07903e13 −0.0326533
\(529\) −9.51105e14 −0.998211
\(530\) 8.27224e14 0.859223
\(531\) 4.22156e13 0.0433963
\(532\) −7.39592e13 −0.0752451
\(533\) 9.75024e14 0.981783
\(534\) 4.36825e14 0.435342
\(535\) −2.49488e15 −2.46096
\(536\) 2.90625e14 0.283744
\(537\) −9.66988e13 −0.0934464
\(538\) −1.88906e13 −0.0180694
\(539\) 1.77812e15 1.68353
\(540\) −1.64101e14 −0.153796
\(541\) −5.14851e14 −0.477635 −0.238818 0.971064i \(-0.576760\pi\)
−0.238818 + 0.971064i \(0.576760\pi\)
\(542\) 5.77695e14 0.530521
\(543\) −6.22338e14 −0.565753
\(544\) 2.14890e15 1.93385
\(545\) 5.53810e14 0.493378
\(546\) −7.46542e14 −0.658407
\(547\) −1.50647e15 −1.31531 −0.657657 0.753317i \(-0.728452\pi\)
−0.657657 + 0.753317i \(0.728452\pi\)
\(548\) −8.24675e14 −0.712837
\(549\) −1.20368e14 −0.103006
\(550\) 5.01395e14 0.424801
\(551\) 3.64679e13 0.0305898
\(552\) 2.89741e13 0.0240627
\(553\) −1.20821e15 −0.993466
\(554\) −7.28799e14 −0.593340
\(555\) 1.59911e14 0.128904
\(556\) −1.05870e15 −0.845012
\(557\) −1.78211e15 −1.40841 −0.704206 0.709995i \(-0.748697\pi\)
−0.704206 + 0.709995i \(0.748697\pi\)
\(558\) 2.96696e14 0.232179
\(559\) −1.83896e15 −1.42497
\(560\) 1.13894e14 0.0873912
\(561\) −1.80409e15 −1.37077
\(562\) −8.31294e13 −0.0625468
\(563\) −1.93847e15 −1.44432 −0.722158 0.691728i \(-0.756850\pi\)
−0.722158 + 0.691728i \(0.756850\pi\)
\(564\) −6.56845e14 −0.484649
\(565\) −1.86825e15 −1.36512
\(566\) −4.72069e14 −0.341598
\(567\) −2.37886e14 −0.170476
\(568\) −1.73941e15 −1.23449
\(569\) 1.21352e15 0.852964 0.426482 0.904496i \(-0.359753\pi\)
0.426482 + 0.904496i \(0.359753\pi\)
\(570\) −4.80045e13 −0.0334172
\(571\) −1.68489e15 −1.16164 −0.580820 0.814032i \(-0.697268\pi\)
−0.580820 + 0.814032i \(0.697268\pi\)
\(572\) 1.43596e15 0.980539
\(573\) −5.67655e12 −0.00383914
\(574\) 1.09461e15 0.733237
\(575\) 3.62097e13 0.0240244
\(576\) 2.85913e14 0.187893
\(577\) −5.11907e14 −0.333215 −0.166607 0.986023i \(-0.553281\pi\)
−0.166607 + 0.986023i \(0.553281\pi\)
\(578\) 2.46875e15 1.59175
\(579\) 7.25811e14 0.463545
\(580\) −5.02848e14 −0.318114
\(581\) 2.36161e15 1.47992
\(582\) −2.94341e14 −0.182715
\(583\) −2.30659e15 −1.41838
\(584\) −2.20274e15 −1.34181
\(585\) 8.54718e14 0.515781
\(586\) −7.95677e14 −0.475664
\(587\) −1.36053e15 −0.805745 −0.402873 0.915256i \(-0.631988\pi\)
−0.402873 + 0.915256i \(0.631988\pi\)
\(588\) 8.50337e14 0.498903
\(589\) −1.53095e14 −0.0889872
\(590\) −1.70283e14 −0.0980584
\(591\) −1.18949e15 −0.678623
\(592\) 1.43487e13 0.00811044
\(593\) −2.90584e15 −1.62731 −0.813656 0.581346i \(-0.802526\pi\)
−0.813656 + 0.581346i \(0.802526\pi\)
\(594\) −2.59406e14 −0.143931
\(595\) 6.67339e15 3.66862
\(596\) 3.11670e14 0.169762
\(597\) 1.27328e15 0.687169
\(598\) −5.87909e13 −0.0314379
\(599\) 3.99294e14 0.211566 0.105783 0.994389i \(-0.466265\pi\)
0.105783 + 0.994389i \(0.466265\pi\)
\(600\) 6.15494e14 0.323141
\(601\) 1.25221e15 0.651431 0.325716 0.945468i \(-0.394395\pi\)
0.325716 + 0.945468i \(0.394395\pi\)
\(602\) −2.06450e15 −1.06423
\(603\) −1.87909e14 −0.0959848
\(604\) 3.19377e14 0.161659
\(605\) −1.36297e15 −0.683644
\(606\) 4.55803e14 0.226557
\(607\) −3.11779e14 −0.153571 −0.0767856 0.997048i \(-0.524466\pi\)
−0.0767856 + 0.997048i \(0.524466\pi\)
\(608\) −1.59437e14 −0.0778248
\(609\) −7.28946e14 −0.352614
\(610\) 4.85523e14 0.232753
\(611\) 3.42117e15 1.62536
\(612\) −8.62760e14 −0.406216
\(613\) 4.85794e14 0.226683 0.113342 0.993556i \(-0.463845\pi\)
0.113342 + 0.993556i \(0.463845\pi\)
\(614\) −7.17785e14 −0.331947
\(615\) −1.25322e15 −0.574401
\(616\) 4.13809e15 1.87978
\(617\) −2.01403e15 −0.906769 −0.453385 0.891315i \(-0.649784\pi\)
−0.453385 + 0.891315i \(0.649784\pi\)
\(618\) −5.55975e13 −0.0248096
\(619\) −2.87650e15 −1.27223 −0.636114 0.771595i \(-0.719459\pi\)
−0.636114 + 0.771595i \(0.719459\pi\)
\(620\) 2.11100e15 0.925408
\(621\) −1.87337e13 −0.00813993
\(622\) 1.91849e15 0.826252
\(623\) 4.50549e15 1.92335
\(624\) 7.66934e13 0.0324521
\(625\) −2.96921e15 −1.24538
\(626\) 1.31959e15 0.548630
\(627\) 1.33854e14 0.0551643
\(628\) −4.58387e14 −0.187264
\(629\) 8.40733e14 0.340471
\(630\) 9.59549e14 0.385207
\(631\) 3.57834e15 1.42403 0.712017 0.702162i \(-0.247782\pi\)
0.712017 + 0.702162i \(0.247782\pi\)
\(632\) −1.61732e15 −0.638045
\(633\) −3.12050e14 −0.122040
\(634\) 1.61981e15 0.628021
\(635\) 4.70034e15 1.80665
\(636\) −1.10307e15 −0.420327
\(637\) −4.42898e15 −1.67316
\(638\) −7.94888e14 −0.297709
\(639\) 1.12465e15 0.417602
\(640\) 2.29150e15 0.843588
\(641\) 1.79966e15 0.656856 0.328428 0.944529i \(-0.393481\pi\)
0.328428 + 0.944529i \(0.393481\pi\)
\(642\) −1.88604e15 −0.682508
\(643\) −2.88174e15 −1.03394 −0.516970 0.856004i \(-0.672940\pi\)
−0.516970 + 0.856004i \(0.672940\pi\)
\(644\) 1.16421e14 0.0414153
\(645\) 2.36366e15 0.833692
\(646\) −2.52384e14 −0.0882639
\(647\) −3.67263e15 −1.27351 −0.636756 0.771065i \(-0.719724\pi\)
−0.636756 + 0.771065i \(0.719724\pi\)
\(648\) −3.18437e14 −0.109486
\(649\) 4.74808e14 0.161872
\(650\) −1.24889e15 −0.422183
\(651\) 3.06018e15 1.02577
\(652\) −1.70328e15 −0.566139
\(653\) −4.94676e15 −1.63041 −0.815207 0.579170i \(-0.803377\pi\)
−0.815207 + 0.579170i \(0.803377\pi\)
\(654\) 4.18660e14 0.136831
\(655\) −2.89501e15 −0.938260
\(656\) −1.12451e14 −0.0361403
\(657\) 1.42422e15 0.453908
\(658\) 3.84078e15 1.21388
\(659\) −5.20368e15 −1.63095 −0.815475 0.578793i \(-0.803524\pi\)
−0.815475 + 0.578793i \(0.803524\pi\)
\(660\) −1.84568e15 −0.573673
\(661\) 7.86702e14 0.242495 0.121247 0.992622i \(-0.461311\pi\)
0.121247 + 0.992622i \(0.461311\pi\)
\(662\) 3.13824e15 0.959327
\(663\) 4.49368e15 1.36232
\(664\) 3.16127e15 0.950468
\(665\) −4.95128e14 −0.147638
\(666\) 1.20887e14 0.0357496
\(667\) −5.74051e13 −0.0168368
\(668\) 3.16487e15 0.920631
\(669\) 1.84089e14 0.0531110
\(670\) 7.57959e14 0.216887
\(671\) −1.35381e15 −0.384223
\(672\) 3.18693e15 0.897101
\(673\) 1.34979e15 0.376863 0.188432 0.982086i \(-0.439660\pi\)
0.188432 + 0.982086i \(0.439660\pi\)
\(674\) 3.63160e15 1.00570
\(675\) −3.97959e14 −0.109312
\(676\) −1.23434e15 −0.336301
\(677\) −5.70336e15 −1.54132 −0.770661 0.637245i \(-0.780074\pi\)
−0.770661 + 0.637245i \(0.780074\pi\)
\(678\) −1.41233e15 −0.378593
\(679\) −3.03589e15 −0.807238
\(680\) 8.93306e15 2.35614
\(681\) −5.71734e14 −0.149584
\(682\) 3.33701e15 0.866050
\(683\) 2.68427e15 0.691054 0.345527 0.938409i \(-0.387700\pi\)
0.345527 + 0.938409i \(0.387700\pi\)
\(684\) 6.40120e13 0.0163475
\(685\) −5.52088e15 −1.39865
\(686\) −1.30001e15 −0.326710
\(687\) 2.38755e15 0.595237
\(688\) 2.12090e14 0.0524545
\(689\) 5.74532e15 1.40964
\(690\) 7.55653e13 0.0183930
\(691\) −2.29109e15 −0.553240 −0.276620 0.960979i \(-0.589214\pi\)
−0.276620 + 0.960979i \(0.589214\pi\)
\(692\) 1.79444e15 0.429878
\(693\) −2.67556e15 −0.635890
\(694\) −2.45476e15 −0.578804
\(695\) −7.08760e15 −1.65799
\(696\) −9.75774e14 −0.226464
\(697\) −6.58882e15 −1.51715
\(698\) 5.74199e14 0.131177
\(699\) 4.19284e15 0.950351
\(700\) 2.47313e15 0.556170
\(701\) 6.08661e15 1.35808 0.679041 0.734100i \(-0.262396\pi\)
0.679041 + 0.734100i \(0.262396\pi\)
\(702\) 6.46135e14 0.143044
\(703\) −6.23777e13 −0.0137017
\(704\) 3.21573e15 0.700857
\(705\) −4.39732e15 −0.950928
\(706\) −4.01608e15 −0.861740
\(707\) 4.70124e15 1.00093
\(708\) 2.27065e14 0.0479697
\(709\) 2.23119e15 0.467716 0.233858 0.972271i \(-0.424865\pi\)
0.233858 + 0.972271i \(0.424865\pi\)
\(710\) −4.53644e15 −0.943614
\(711\) 1.04571e15 0.215838
\(712\) 6.03110e15 1.23525
\(713\) 2.40992e14 0.0489790
\(714\) 5.04483e15 1.01743
\(715\) 9.61321e15 1.92391
\(716\) −5.20113e14 −0.103294
\(717\) 5.03543e15 0.992388
\(718\) 1.74291e15 0.340872
\(719\) 2.77472e15 0.538530 0.269265 0.963066i \(-0.413219\pi\)
0.269265 + 0.963066i \(0.413219\pi\)
\(720\) −9.85759e13 −0.0189864
\(721\) −5.73444e14 −0.109609
\(722\) −3.15224e15 −0.597950
\(723\) 5.25375e15 0.989029
\(724\) −3.34736e15 −0.625375
\(725\) −1.21945e15 −0.226103
\(726\) −1.03035e15 −0.189598
\(727\) −8.74528e15 −1.59711 −0.798554 0.601923i \(-0.794402\pi\)
−0.798554 + 0.601923i \(0.794402\pi\)
\(728\) −1.03073e16 −1.86819
\(729\) 2.05891e14 0.0370370
\(730\) −5.74481e15 −1.02565
\(731\) 1.24269e16 2.20200
\(732\) −6.47424e14 −0.113862
\(733\) −7.84581e15 −1.36951 −0.684756 0.728772i \(-0.740091\pi\)
−0.684756 + 0.728772i \(0.740091\pi\)
\(734\) 4.44970e15 0.770907
\(735\) 5.69267e15 0.978894
\(736\) 2.50974e14 0.0428351
\(737\) −2.11346e15 −0.358032
\(738\) −9.47389e14 −0.159301
\(739\) 5.26678e15 0.879024 0.439512 0.898237i \(-0.355151\pi\)
0.439512 + 0.898237i \(0.355151\pi\)
\(740\) 8.60113e14 0.142489
\(741\) −3.33406e14 −0.0548243
\(742\) 6.44998e15 1.05278
\(743\) 8.32342e13 0.0134854 0.00674269 0.999977i \(-0.497854\pi\)
0.00674269 + 0.999977i \(0.497854\pi\)
\(744\) 4.09638e15 0.658794
\(745\) 2.08651e15 0.333090
\(746\) −4.53085e15 −0.717986
\(747\) −2.04398e15 −0.321524
\(748\) −9.70366e15 −1.51522
\(749\) −1.94530e16 −3.01534
\(750\) −1.22087e15 −0.187859
\(751\) 1.04791e16 1.60069 0.800343 0.599542i \(-0.204651\pi\)
0.800343 + 0.599542i \(0.204651\pi\)
\(752\) −3.94569e14 −0.0598308
\(753\) −5.30055e14 −0.0797900
\(754\) 1.97993e15 0.295874
\(755\) 2.13810e15 0.317191
\(756\) −1.27952e15 −0.188441
\(757\) −4.74174e15 −0.693282 −0.346641 0.937998i \(-0.612678\pi\)
−0.346641 + 0.937998i \(0.612678\pi\)
\(758\) 5.33486e15 0.774359
\(759\) −2.10703e14 −0.0303627
\(760\) −6.62783e14 −0.0948193
\(761\) −3.54806e15 −0.503935 −0.251968 0.967736i \(-0.581078\pi\)
−0.251968 + 0.967736i \(0.581078\pi\)
\(762\) 3.55328e15 0.501046
\(763\) 4.31814e15 0.604521
\(764\) −3.05324e13 −0.00424373
\(765\) −5.77584e15 −0.797035
\(766\) −5.18208e15 −0.709980
\(767\) −1.18267e15 −0.160875
\(768\) 4.14196e15 0.559395
\(769\) −1.03550e16 −1.38853 −0.694263 0.719721i \(-0.744270\pi\)
−0.694263 + 0.719721i \(0.744270\pi\)
\(770\) 1.07923e16 1.43686
\(771\) −6.47937e15 −0.856512
\(772\) 3.90392e15 0.512396
\(773\) −4.02175e15 −0.524116 −0.262058 0.965052i \(-0.584401\pi\)
−0.262058 + 0.965052i \(0.584401\pi\)
\(774\) 1.78684e15 0.231211
\(775\) 5.11936e15 0.657744
\(776\) −4.06387e15 −0.518442
\(777\) 1.24685e15 0.157942
\(778\) 7.85136e15 0.987546
\(779\) 4.88854e14 0.0610552
\(780\) 4.59727e15 0.570137
\(781\) 1.26492e16 1.55769
\(782\) 3.97285e14 0.0485809
\(783\) 6.30905e14 0.0766080
\(784\) 5.10801e14 0.0615904
\(785\) −3.06872e15 −0.367430
\(786\) −2.18852e15 −0.260212
\(787\) −5.58523e15 −0.659447 −0.329724 0.944077i \(-0.606956\pi\)
−0.329724 + 0.944077i \(0.606956\pi\)
\(788\) −6.39789e15 −0.750140
\(789\) 1.80607e15 0.210286
\(790\) −4.21801e15 −0.487707
\(791\) −1.45670e16 −1.67263
\(792\) −3.58153e15 −0.408395
\(793\) 3.37211e15 0.381855
\(794\) 6.48298e15 0.729058
\(795\) −7.38460e15 −0.824722
\(796\) 6.84856e15 0.759587
\(797\) 1.12022e16 1.23390 0.616952 0.787000i \(-0.288367\pi\)
0.616952 + 0.787000i \(0.288367\pi\)
\(798\) −3.74298e14 −0.0409451
\(799\) −2.31189e16 −2.51166
\(800\) 5.33141e15 0.575237
\(801\) −3.89952e15 −0.417861
\(802\) −2.28141e15 −0.242798
\(803\) 1.60186e16 1.69312
\(804\) −1.01071e15 −0.106100
\(805\) 7.79395e14 0.0812607
\(806\) −8.31190e15 −0.860712
\(807\) 1.68636e14 0.0173439
\(808\) 6.29312e15 0.642841
\(809\) −1.42853e16 −1.44935 −0.724675 0.689091i \(-0.758010\pi\)
−0.724675 + 0.689091i \(0.758010\pi\)
\(810\) −8.30493e14 −0.0836890
\(811\) −9.38781e15 −0.939614 −0.469807 0.882769i \(-0.655677\pi\)
−0.469807 + 0.882769i \(0.655677\pi\)
\(812\) −3.92078e15 −0.389775
\(813\) −5.15706e15 −0.509219
\(814\) 1.35964e15 0.133349
\(815\) −1.14028e16 −1.11082
\(816\) −5.18263e14 −0.0501481
\(817\) −9.22009e14 −0.0886163
\(818\) −1.12720e16 −1.07611
\(819\) 6.66436e15 0.631970
\(820\) −6.74070e15 −0.634934
\(821\) 1.93523e16 1.81069 0.905347 0.424672i \(-0.139611\pi\)
0.905347 + 0.424672i \(0.139611\pi\)
\(822\) −4.17358e15 −0.387894
\(823\) 1.83381e16 1.69299 0.846495 0.532397i \(-0.178708\pi\)
0.846495 + 0.532397i \(0.178708\pi\)
\(824\) −7.67617e14 −0.0703955
\(825\) −4.47594e15 −0.407744
\(826\) −1.32772e15 −0.120148
\(827\) 6.01570e15 0.540761 0.270381 0.962754i \(-0.412850\pi\)
0.270381 + 0.962754i \(0.412850\pi\)
\(828\) −1.00763e14 −0.00899776
\(829\) 1.05787e16 0.938384 0.469192 0.883096i \(-0.344545\pi\)
0.469192 + 0.883096i \(0.344545\pi\)
\(830\) 8.24470e15 0.726516
\(831\) 6.50596e15 0.569516
\(832\) −8.00982e15 −0.696537
\(833\) 2.99293e16 2.58552
\(834\) −5.35797e15 −0.459819
\(835\) 2.11876e16 1.80637
\(836\) 7.19957e14 0.0609779
\(837\) −2.64859e15 −0.222856
\(838\) 1.36089e16 1.13757
\(839\) −1.18712e16 −0.985837 −0.492919 0.870075i \(-0.664070\pi\)
−0.492919 + 0.870075i \(0.664070\pi\)
\(840\) 1.32482e16 1.09300
\(841\) −1.02673e16 −0.841543
\(842\) 5.41344e15 0.440815
\(843\) 7.42093e14 0.0600353
\(844\) −1.67842e15 −0.134902
\(845\) −8.26343e15 −0.659855
\(846\) −3.32421e15 −0.263725
\(847\) −1.06272e16 −0.837648
\(848\) −6.62616e14 −0.0518902
\(849\) 4.21414e15 0.327882
\(850\) 8.43949e15 0.652398
\(851\) 9.81905e13 0.00754149
\(852\) 6.04914e15 0.461611
\(853\) 5.71978e15 0.433670 0.216835 0.976208i \(-0.430427\pi\)
0.216835 + 0.976208i \(0.430427\pi\)
\(854\) 3.78569e15 0.285185
\(855\) 4.28535e14 0.0320754
\(856\) −2.60399e16 −1.93657
\(857\) 1.98359e16 1.46574 0.732870 0.680368i \(-0.238180\pi\)
0.732870 + 0.680368i \(0.238180\pi\)
\(858\) 7.26723e15 0.533567
\(859\) −1.28081e16 −0.934380 −0.467190 0.884157i \(-0.654734\pi\)
−0.467190 + 0.884157i \(0.654734\pi\)
\(860\) 1.27134e16 0.921551
\(861\) −9.77155e15 −0.703795
\(862\) −6.30149e15 −0.450976
\(863\) −1.09758e16 −0.780506 −0.390253 0.920708i \(-0.627612\pi\)
−0.390253 + 0.920708i \(0.627612\pi\)
\(864\) −2.75830e15 −0.194902
\(865\) 1.20131e16 0.843461
\(866\) −3.37216e14 −0.0235266
\(867\) −2.20384e16 −1.52783
\(868\) 1.64597e16 1.13387
\(869\) 1.17613e16 0.805094
\(870\) −2.54485e15 −0.173104
\(871\) 5.26425e15 0.355825
\(872\) 5.78030e15 0.388248
\(873\) 2.62757e15 0.175378
\(874\) −2.94763e13 −0.00195506
\(875\) −1.25923e16 −0.829965
\(876\) 7.66046e15 0.501744
\(877\) 1.89070e16 1.23062 0.615312 0.788284i \(-0.289030\pi\)
0.615312 + 0.788284i \(0.289030\pi\)
\(878\) −6.11938e15 −0.395811
\(879\) 7.10298e15 0.456564
\(880\) −1.10871e15 −0.0708209
\(881\) 2.73060e15 0.173337 0.0866684 0.996237i \(-0.472378\pi\)
0.0866684 + 0.996237i \(0.472378\pi\)
\(882\) 4.30345e15 0.271481
\(883\) 1.90415e16 1.19376 0.596881 0.802330i \(-0.296407\pi\)
0.596881 + 0.802330i \(0.296407\pi\)
\(884\) 2.41701e16 1.50589
\(885\) 1.52011e15 0.0941210
\(886\) −3.03763e15 −0.186917
\(887\) −7.35165e15 −0.449578 −0.224789 0.974407i \(-0.572169\pi\)
−0.224789 + 0.974407i \(0.572169\pi\)
\(888\) 1.66905e15 0.101437
\(889\) 3.66492e16 2.21363
\(890\) 1.57293e16 0.944200
\(891\) 2.31571e15 0.138152
\(892\) 9.90159e14 0.0587081
\(893\) 1.71529e15 0.101078
\(894\) 1.57732e15 0.0923772
\(895\) −3.48195e15 −0.202673
\(896\) 1.78672e16 1.03362
\(897\) 5.24824e14 0.0301756
\(898\) −9.68299e15 −0.553337
\(899\) −8.11599e15 −0.460960
\(900\) −2.14050e15 −0.120832
\(901\) −3.88246e16 −2.17831
\(902\) −1.06555e16 −0.594207
\(903\) 1.84298e16 1.02150
\(904\) −1.94996e16 −1.07423
\(905\) −2.24093e16 −1.22705
\(906\) 1.61633e15 0.0879678
\(907\) −2.98228e15 −0.161327 −0.0806637 0.996741i \(-0.525704\pi\)
−0.0806637 + 0.996741i \(0.525704\pi\)
\(908\) −3.07518e15 −0.165348
\(909\) −4.06894e15 −0.217460
\(910\) −2.68817e16 −1.42800
\(911\) −2.38748e16 −1.26063 −0.630317 0.776338i \(-0.717075\pi\)
−0.630317 + 0.776338i \(0.717075\pi\)
\(912\) 3.84522e13 0.00201813
\(913\) −2.29891e16 −1.19931
\(914\) −4.77937e14 −0.0247837
\(915\) −4.33425e15 −0.223408
\(916\) 1.28419e16 0.657966
\(917\) −2.25728e16 −1.14962
\(918\) −4.36632e15 −0.221045
\(919\) 3.24634e16 1.63365 0.816826 0.576885i \(-0.195732\pi\)
0.816826 + 0.576885i \(0.195732\pi\)
\(920\) 1.04331e15 0.0521890
\(921\) 6.40764e15 0.318618
\(922\) 9.04699e15 0.447182
\(923\) −3.15069e16 −1.54809
\(924\) −1.43910e16 −0.702903
\(925\) 2.08585e15 0.101275
\(926\) −9.79149e15 −0.472594
\(927\) 4.96317e14 0.0238134
\(928\) −8.45215e15 −0.403138
\(929\) −2.26731e16 −1.07504 −0.537521 0.843250i \(-0.680639\pi\)
−0.537521 + 0.843250i \(0.680639\pi\)
\(930\) 1.06835e16 0.503567
\(931\) −2.22058e15 −0.104050
\(932\) 2.25520e16 1.05050
\(933\) −1.71263e16 −0.793075
\(934\) −2.04648e16 −0.942104
\(935\) −6.49622e16 −2.97301
\(936\) 8.92097e15 0.405878
\(937\) −2.84366e16 −1.28621 −0.643103 0.765780i \(-0.722353\pi\)
−0.643103 + 0.765780i \(0.722353\pi\)
\(938\) 5.90991e15 0.265745
\(939\) −1.17799e16 −0.526601
\(940\) −2.36518e16 −1.05114
\(941\) −3.16014e16 −1.39625 −0.698124 0.715977i \(-0.745982\pi\)
−0.698124 + 0.715977i \(0.745982\pi\)
\(942\) −2.31984e15 −0.101901
\(943\) −7.69519e14 −0.0336051
\(944\) 1.36399e14 0.00592194
\(945\) −8.56586e15 −0.369740
\(946\) 2.00970e16 0.862440
\(947\) −1.87145e16 −0.798460 −0.399230 0.916851i \(-0.630723\pi\)
−0.399230 + 0.916851i \(0.630723\pi\)
\(948\) 5.62454e15 0.238584
\(949\) −3.98995e16 −1.68268
\(950\) −6.26163e14 −0.0262547
\(951\) −1.44600e16 −0.602804
\(952\) 6.96524e16 2.88691
\(953\) 3.18697e15 0.131331 0.0656654 0.997842i \(-0.479083\pi\)
0.0656654 + 0.997842i \(0.479083\pi\)
\(954\) −5.58248e15 −0.228724
\(955\) −2.04403e14 −0.00832660
\(956\) 2.70840e16 1.09697
\(957\) 7.09593e15 0.285755
\(958\) 2.45144e16 0.981548
\(959\) −4.30471e16 −1.71373
\(960\) 1.02952e16 0.407515
\(961\) 8.66313e15 0.340954
\(962\) −3.38663e15 −0.132527
\(963\) 1.68366e16 0.655103
\(964\) 2.82583e16 1.09326
\(965\) 2.61352e16 1.00537
\(966\) 5.89194e14 0.0225364
\(967\) −2.85691e16 −1.08655 −0.543277 0.839553i \(-0.682817\pi\)
−0.543277 + 0.839553i \(0.682817\pi\)
\(968\) −1.42257e16 −0.537972
\(969\) 2.25302e15 0.0847199
\(970\) −1.05987e16 −0.396285
\(971\) −2.35784e16 −0.876615 −0.438307 0.898825i \(-0.644422\pi\)
−0.438307 + 0.898825i \(0.644422\pi\)
\(972\) 1.10743e15 0.0409402
\(973\) −5.52631e16 −2.03149
\(974\) −1.83540e16 −0.670899
\(975\) 1.11488e16 0.405231
\(976\) −3.88910e14 −0.0140564
\(977\) −1.01719e16 −0.365581 −0.182790 0.983152i \(-0.558513\pi\)
−0.182790 + 0.983152i \(0.558513\pi\)
\(978\) −8.62006e15 −0.308068
\(979\) −4.38588e16 −1.55866
\(980\) 3.06192e16 1.08206
\(981\) −3.73736e15 −0.131337
\(982\) 1.64832e16 0.576008
\(983\) −1.37295e16 −0.477101 −0.238551 0.971130i \(-0.576672\pi\)
−0.238551 + 0.971130i \(0.576672\pi\)
\(984\) −1.30803e16 −0.452006
\(985\) −4.28314e16 −1.47185
\(986\) −1.33796e16 −0.457213
\(987\) −3.42865e16 −1.16514
\(988\) −1.79329e15 −0.0606020
\(989\) 1.45136e15 0.0487748
\(990\) −9.34074e15 −0.312168
\(991\) 3.58942e16 1.19294 0.596471 0.802635i \(-0.296569\pi\)
0.596471 + 0.802635i \(0.296569\pi\)
\(992\) 3.54829e16 1.17275
\(993\) −2.80149e16 −0.920807
\(994\) −3.53713e16 −1.15618
\(995\) 4.58484e16 1.49038
\(996\) −1.09939e16 −0.355408
\(997\) −1.47560e16 −0.474402 −0.237201 0.971461i \(-0.576230\pi\)
−0.237201 + 0.971461i \(0.576230\pi\)
\(998\) −2.54034e16 −0.812222
\(999\) −1.07915e15 −0.0343141
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 177.12.a.a.1.18 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.18 26 1.1 even 1 trivial