Properties

Label 43.10.a.a.1.14
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.1465409550\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(-35.4490\) of \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+33.4490 q^{2} +8.30450 q^{3} +606.833 q^{4} -752.925 q^{5} +277.777 q^{6} -7164.62 q^{7} +3172.07 q^{8} -19614.0 q^{9} +O(q^{10})\) \(q+33.4490 q^{2} +8.30450 q^{3} +606.833 q^{4} -752.925 q^{5} +277.777 q^{6} -7164.62 q^{7} +3172.07 q^{8} -19614.0 q^{9} -25184.6 q^{10} -30954.5 q^{11} +5039.45 q^{12} +41893.4 q^{13} -239649. q^{14} -6252.67 q^{15} -204596. q^{16} +187328. q^{17} -656069. q^{18} +668619. q^{19} -456900. q^{20} -59498.6 q^{21} -1.03540e6 q^{22} -2.17863e6 q^{23} +26342.4 q^{24} -1.38623e6 q^{25} +1.40129e6 q^{26} -326342. q^{27} -4.34773e6 q^{28} +2.40487e6 q^{29} -209145. q^{30} +8.05328e6 q^{31} -8.46763e6 q^{32} -257062. q^{33} +6.26594e6 q^{34} +5.39442e6 q^{35} -1.19024e7 q^{36} -1.64001e7 q^{37} +2.23646e7 q^{38} +347904. q^{39} -2.38833e6 q^{40} +1.13061e7 q^{41} -1.99017e6 q^{42} -3.41880e6 q^{43} -1.87842e7 q^{44} +1.47679e7 q^{45} -7.28730e7 q^{46} -4.31570e7 q^{47} -1.69907e6 q^{48} +1.09782e7 q^{49} -4.63679e7 q^{50} +1.55567e6 q^{51} +2.54223e7 q^{52} -3.13129e7 q^{53} -1.09158e7 q^{54} +2.33064e7 q^{55} -2.27267e7 q^{56} +5.55255e6 q^{57} +8.04403e7 q^{58} +4.51423e7 q^{59} -3.79433e6 q^{60} +7.25780e7 q^{61} +2.69374e8 q^{62} +1.40527e8 q^{63} -1.78480e8 q^{64} -3.15426e7 q^{65} -8.59845e6 q^{66} +2.83598e8 q^{67} +1.13677e8 q^{68} -1.80925e7 q^{69} +1.80438e8 q^{70} -1.90718e8 q^{71} -6.22170e7 q^{72} +2.75834e7 q^{73} -5.48567e8 q^{74} -1.15119e7 q^{75} +4.05740e8 q^{76} +2.21777e8 q^{77} +1.16370e7 q^{78} +2.64422e8 q^{79} +1.54046e8 q^{80} +3.83353e8 q^{81} +3.78177e8 q^{82} -5.42519e8 q^{83} -3.61057e7 q^{84} -1.41044e8 q^{85} -1.14355e8 q^{86} +1.99712e7 q^{87} -9.81898e7 q^{88} -2.40619e7 q^{89} +4.93971e8 q^{90} -3.00150e8 q^{91} -1.32207e9 q^{92} +6.68785e7 q^{93} -1.44356e9 q^{94} -5.03420e8 q^{95} -7.03194e7 q^{96} -1.30561e9 q^{97} +3.67209e8 q^{98} +6.07143e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 33.4490 1.47825 0.739125 0.673569i \(-0.235239\pi\)
0.739125 + 0.673569i \(0.235239\pi\)
\(3\) 8.30450 0.0591927 0.0295963 0.999562i \(-0.490578\pi\)
0.0295963 + 0.999562i \(0.490578\pi\)
\(4\) 606.833 1.18522
\(5\) −752.925 −0.538749 −0.269375 0.963035i \(-0.586817\pi\)
−0.269375 + 0.963035i \(0.586817\pi\)
\(6\) 277.777 0.0875015
\(7\) −7164.62 −1.12785 −0.563926 0.825825i \(-0.690710\pi\)
−0.563926 + 0.825825i \(0.690710\pi\)
\(8\) 3172.07 0.273803
\(9\) −19614.0 −0.996496
\(10\) −25184.6 −0.796406
\(11\) −30954.5 −0.637466 −0.318733 0.947845i \(-0.603257\pi\)
−0.318733 + 0.947845i \(0.603257\pi\)
\(12\) 5039.45 0.0701564
\(13\) 41893.4 0.406818 0.203409 0.979094i \(-0.434798\pi\)
0.203409 + 0.979094i \(0.434798\pi\)
\(14\) −239649. −1.66725
\(15\) −6252.67 −0.0318900
\(16\) −204596. −0.780472
\(17\) 187328. 0.543980 0.271990 0.962300i \(-0.412318\pi\)
0.271990 + 0.962300i \(0.412318\pi\)
\(18\) −656069. −1.47307
\(19\) 668619. 1.17703 0.588515 0.808486i \(-0.299713\pi\)
0.588515 + 0.808486i \(0.299713\pi\)
\(20\) −456900. −0.638537
\(21\) −59498.6 −0.0667606
\(22\) −1.03540e6 −0.942334
\(23\) −2.17863e6 −1.62334 −0.811669 0.584118i \(-0.801440\pi\)
−0.811669 + 0.584118i \(0.801440\pi\)
\(24\) 26342.4 0.0162071
\(25\) −1.38623e6 −0.709749
\(26\) 1.40129e6 0.601379
\(27\) −326342. −0.118178
\(28\) −4.34773e6 −1.33675
\(29\) 2.40487e6 0.631393 0.315697 0.948860i \(-0.397762\pi\)
0.315697 + 0.948860i \(0.397762\pi\)
\(30\) −209145. −0.0471414
\(31\) 8.05328e6 1.56619 0.783096 0.621901i \(-0.213639\pi\)
0.783096 + 0.621901i \(0.213639\pi\)
\(32\) −8.46763e6 −1.42754
\(33\) −257062. −0.0377333
\(34\) 6.26594e6 0.804138
\(35\) 5.39442e6 0.607629
\(36\) −1.19024e7 −1.18107
\(37\) −1.64001e7 −1.43860 −0.719299 0.694701i \(-0.755537\pi\)
−0.719299 + 0.694701i \(0.755537\pi\)
\(38\) 2.23646e7 1.73994
\(39\) 347904. 0.0240807
\(40\) −2.38833e6 −0.147511
\(41\) 1.13061e7 0.624863 0.312431 0.949940i \(-0.398857\pi\)
0.312431 + 0.949940i \(0.398857\pi\)
\(42\) −1.99017e6 −0.0986887
\(43\) −3.41880e6 −0.152499
\(44\) −1.87842e7 −0.755538
\(45\) 1.47679e7 0.536862
\(46\) −7.28730e7 −2.39970
\(47\) −4.31570e7 −1.29006 −0.645031 0.764156i \(-0.723156\pi\)
−0.645031 + 0.764156i \(0.723156\pi\)
\(48\) −1.69907e6 −0.0461983
\(49\) 1.09782e7 0.272049
\(50\) −4.63679e7 −1.04919
\(51\) 1.55567e6 0.0321996
\(52\) 2.54223e7 0.482169
\(53\) −3.13129e7 −0.545108 −0.272554 0.962141i \(-0.587868\pi\)
−0.272554 + 0.962141i \(0.587868\pi\)
\(54\) −1.09158e7 −0.174696
\(55\) 2.33064e7 0.343434
\(56\) −2.27267e7 −0.308809
\(57\) 5.55255e6 0.0696716
\(58\) 8.04403e7 0.933357
\(59\) 4.51423e7 0.485009 0.242504 0.970150i \(-0.422031\pi\)
0.242504 + 0.970150i \(0.422031\pi\)
\(60\) −3.79433e6 −0.0377967
\(61\) 7.25780e7 0.671152 0.335576 0.942013i \(-0.391069\pi\)
0.335576 + 0.942013i \(0.391069\pi\)
\(62\) 2.69374e8 2.31522
\(63\) 1.40527e8 1.12390
\(64\) −1.78480e8 −1.32978
\(65\) −3.15426e7 −0.219173
\(66\) −8.59845e6 −0.0557792
\(67\) 2.83598e8 1.71936 0.859678 0.510836i \(-0.170664\pi\)
0.859678 + 0.510836i \(0.170664\pi\)
\(68\) 1.13677e8 0.644737
\(69\) −1.80925e7 −0.0960897
\(70\) 1.80438e8 0.898228
\(71\) −1.90718e8 −0.890695 −0.445347 0.895358i \(-0.646920\pi\)
−0.445347 + 0.895358i \(0.646920\pi\)
\(72\) −6.22170e7 −0.272843
\(73\) 2.75834e7 0.113683 0.0568415 0.998383i \(-0.481897\pi\)
0.0568415 + 0.998383i \(0.481897\pi\)
\(74\) −5.48567e8 −2.12661
\(75\) −1.15119e7 −0.0420120
\(76\) 4.05740e8 1.39504
\(77\) 2.21777e8 0.718967
\(78\) 1.16370e7 0.0355972
\(79\) 2.64422e8 0.763794 0.381897 0.924205i \(-0.375271\pi\)
0.381897 + 0.924205i \(0.375271\pi\)
\(80\) 1.54046e8 0.420479
\(81\) 3.83353e8 0.989501
\(82\) 3.78177e8 0.923703
\(83\) −5.42519e8 −1.25477 −0.627384 0.778710i \(-0.715874\pi\)
−0.627384 + 0.778710i \(0.715874\pi\)
\(84\) −3.61057e7 −0.0791260
\(85\) −1.41044e8 −0.293069
\(86\) −1.14355e8 −0.225431
\(87\) 1.99712e7 0.0373739
\(88\) −9.81898e7 −0.174540
\(89\) −2.40619e7 −0.0406513 −0.0203257 0.999793i \(-0.506470\pi\)
−0.0203257 + 0.999793i \(0.506470\pi\)
\(90\) 4.93971e8 0.793615
\(91\) −3.00150e8 −0.458830
\(92\) −1.32207e9 −1.92401
\(93\) 6.68785e7 0.0927071
\(94\) −1.44356e9 −1.90703
\(95\) −5.03420e8 −0.634124
\(96\) −7.03194e7 −0.0844996
\(97\) −1.30561e9 −1.49741 −0.748704 0.662905i \(-0.769323\pi\)
−0.748704 + 0.662905i \(0.769323\pi\)
\(98\) 3.67209e8 0.402157
\(99\) 6.07143e8 0.635232
\(100\) −8.41209e8 −0.841209
\(101\) 8.39059e8 0.802318 0.401159 0.916008i \(-0.368607\pi\)
0.401159 + 0.916008i \(0.368607\pi\)
\(102\) 5.20355e7 0.0475991
\(103\) −1.97091e9 −1.72544 −0.862720 0.505681i \(-0.831241\pi\)
−0.862720 + 0.505681i \(0.831241\pi\)
\(104\) 1.32889e8 0.111388
\(105\) 4.47980e7 0.0359672
\(106\) −1.04739e9 −0.805805
\(107\) 1.26639e9 0.933983 0.466991 0.884262i \(-0.345338\pi\)
0.466991 + 0.884262i \(0.345338\pi\)
\(108\) −1.98035e8 −0.140067
\(109\) −9.70279e8 −0.658381 −0.329191 0.944264i \(-0.606776\pi\)
−0.329191 + 0.944264i \(0.606776\pi\)
\(110\) 7.79576e8 0.507682
\(111\) −1.36195e8 −0.0851544
\(112\) 1.46585e9 0.880257
\(113\) −1.93357e9 −1.11559 −0.557797 0.829977i \(-0.688353\pi\)
−0.557797 + 0.829977i \(0.688353\pi\)
\(114\) 1.85727e8 0.102992
\(115\) 1.64035e9 0.874572
\(116\) 1.45935e9 0.748341
\(117\) −8.21698e8 −0.405393
\(118\) 1.50996e9 0.716964
\(119\) −1.34214e9 −0.613529
\(120\) −1.98339e7 −0.00873157
\(121\) −1.39977e9 −0.593637
\(122\) 2.42766e9 0.992130
\(123\) 9.38914e7 0.0369873
\(124\) 4.88700e9 1.85628
\(125\) 2.51428e9 0.921126
\(126\) 4.70049e9 1.66140
\(127\) −2.17278e9 −0.741137 −0.370569 0.928805i \(-0.620837\pi\)
−0.370569 + 0.928805i \(0.620837\pi\)
\(128\) −1.63455e9 −0.538212
\(129\) −2.83914e7 −0.00902680
\(130\) −1.05507e9 −0.323992
\(131\) −2.34464e9 −0.695594 −0.347797 0.937570i \(-0.613070\pi\)
−0.347797 + 0.937570i \(0.613070\pi\)
\(132\) −1.55994e8 −0.0447223
\(133\) −4.79040e9 −1.32752
\(134\) 9.48605e9 2.54164
\(135\) 2.45711e8 0.0636683
\(136\) 5.94218e8 0.148943
\(137\) 2.32762e9 0.564508 0.282254 0.959340i \(-0.408918\pi\)
0.282254 + 0.959340i \(0.408918\pi\)
\(138\) −6.05174e8 −0.142044
\(139\) −3.92528e9 −0.891875 −0.445937 0.895064i \(-0.647130\pi\)
−0.445937 + 0.895064i \(0.647130\pi\)
\(140\) 3.27351e9 0.720175
\(141\) −3.58397e8 −0.0763623
\(142\) −6.37932e9 −1.31667
\(143\) −1.29679e9 −0.259333
\(144\) 4.01296e9 0.777738
\(145\) −1.81068e9 −0.340163
\(146\) 9.22637e8 0.168052
\(147\) 9.11683e7 0.0161033
\(148\) −9.95214e9 −1.70506
\(149\) −3.42450e9 −0.569192 −0.284596 0.958648i \(-0.591859\pi\)
−0.284596 + 0.958648i \(0.591859\pi\)
\(150\) −3.85062e8 −0.0621041
\(151\) −2.21822e9 −0.347223 −0.173611 0.984814i \(-0.555544\pi\)
−0.173611 + 0.984814i \(0.555544\pi\)
\(152\) 2.12090e9 0.322274
\(153\) −3.67426e9 −0.542074
\(154\) 7.41822e9 1.06281
\(155\) −6.06352e9 −0.843785
\(156\) 2.11119e8 0.0285409
\(157\) −1.02245e9 −0.134306 −0.0671530 0.997743i \(-0.521392\pi\)
−0.0671530 + 0.997743i \(0.521392\pi\)
\(158\) 8.84465e9 1.12908
\(159\) −2.60038e8 −0.0322664
\(160\) 6.37549e9 0.769084
\(161\) 1.56091e10 1.83088
\(162\) 1.28228e10 1.46273
\(163\) 1.02522e10 1.13756 0.568778 0.822491i \(-0.307416\pi\)
0.568778 + 0.822491i \(0.307416\pi\)
\(164\) 6.86090e9 0.740601
\(165\) 1.93548e8 0.0203288
\(166\) −1.81467e10 −1.85486
\(167\) −1.77286e10 −1.76380 −0.881901 0.471436i \(-0.843736\pi\)
−0.881901 + 0.471436i \(0.843736\pi\)
\(168\) −1.88734e8 −0.0182792
\(169\) −8.84944e9 −0.834499
\(170\) −4.71778e9 −0.433229
\(171\) −1.31143e10 −1.17291
\(172\) −2.07464e9 −0.180744
\(173\) 1.17358e10 0.996104 0.498052 0.867147i \(-0.334049\pi\)
0.498052 + 0.867147i \(0.334049\pi\)
\(174\) 6.68017e8 0.0552479
\(175\) 9.93180e9 0.800492
\(176\) 6.33318e9 0.497525
\(177\) 3.74884e8 0.0287090
\(178\) −8.04846e8 −0.0600928
\(179\) 7.44591e9 0.542100 0.271050 0.962565i \(-0.412629\pi\)
0.271050 + 0.962565i \(0.412629\pi\)
\(180\) 8.96165e9 0.636300
\(181\) 8.28250e8 0.0573599 0.0286799 0.999589i \(-0.490870\pi\)
0.0286799 + 0.999589i \(0.490870\pi\)
\(182\) −1.00397e10 −0.678266
\(183\) 6.02724e8 0.0397273
\(184\) −6.91077e9 −0.444474
\(185\) 1.23481e10 0.775043
\(186\) 2.23702e9 0.137044
\(187\) −5.79866e9 −0.346769
\(188\) −2.61891e10 −1.52901
\(189\) 2.33812e9 0.133287
\(190\) −1.68389e10 −0.937394
\(191\) 1.78976e9 0.0973071 0.0486536 0.998816i \(-0.484507\pi\)
0.0486536 + 0.998816i \(0.484507\pi\)
\(192\) −1.48219e9 −0.0787133
\(193\) −1.53821e10 −0.798007 −0.399004 0.916949i \(-0.630644\pi\)
−0.399004 + 0.916949i \(0.630644\pi\)
\(194\) −4.36712e10 −2.21354
\(195\) −2.61945e8 −0.0129734
\(196\) 6.66192e9 0.322439
\(197\) 6.72162e9 0.317962 0.158981 0.987282i \(-0.449179\pi\)
0.158981 + 0.987282i \(0.449179\pi\)
\(198\) 2.03083e10 0.939032
\(199\) 2.38746e10 1.07919 0.539593 0.841926i \(-0.318578\pi\)
0.539593 + 0.841926i \(0.318578\pi\)
\(200\) −4.39721e9 −0.194331
\(201\) 2.35514e9 0.101773
\(202\) 2.80657e10 1.18603
\(203\) −1.72300e10 −0.712118
\(204\) 9.44031e8 0.0381637
\(205\) −8.51263e9 −0.336645
\(206\) −6.59250e10 −2.55063
\(207\) 4.27318e10 1.61765
\(208\) −8.57122e9 −0.317510
\(209\) −2.06968e10 −0.750317
\(210\) 1.49845e9 0.0531685
\(211\) −9.62380e9 −0.334253 −0.167127 0.985935i \(-0.553449\pi\)
−0.167127 + 0.985935i \(0.553449\pi\)
\(212\) −1.90017e10 −0.646073
\(213\) −1.58382e9 −0.0527226
\(214\) 4.23593e10 1.38066
\(215\) 2.57410e9 0.0821585
\(216\) −1.03518e9 −0.0323574
\(217\) −5.76987e10 −1.76643
\(218\) −3.24548e10 −0.973251
\(219\) 2.29067e8 0.00672920
\(220\) 1.41431e10 0.407046
\(221\) 7.84781e9 0.221301
\(222\) −4.55558e9 −0.125879
\(223\) 3.02591e10 0.819378 0.409689 0.912225i \(-0.365637\pi\)
0.409689 + 0.912225i \(0.365637\pi\)
\(224\) 6.06673e10 1.61005
\(225\) 2.71895e10 0.707262
\(226\) −6.46758e10 −1.64913
\(227\) −1.66730e10 −0.416771 −0.208385 0.978047i \(-0.566821\pi\)
−0.208385 + 0.978047i \(0.566821\pi\)
\(228\) 3.36947e9 0.0825762
\(229\) 4.62782e10 1.11203 0.556015 0.831172i \(-0.312330\pi\)
0.556015 + 0.831172i \(0.312330\pi\)
\(230\) 5.48679e10 1.29284
\(231\) 1.84175e9 0.0425576
\(232\) 7.62840e9 0.172877
\(233\) 2.27489e10 0.505661 0.252830 0.967511i \(-0.418639\pi\)
0.252830 + 0.967511i \(0.418639\pi\)
\(234\) −2.74849e10 −0.599271
\(235\) 3.24940e10 0.695021
\(236\) 2.73938e10 0.574843
\(237\) 2.19590e9 0.0452110
\(238\) −4.48930e10 −0.906949
\(239\) 4.02770e10 0.798485 0.399242 0.916845i \(-0.369273\pi\)
0.399242 + 0.916845i \(0.369273\pi\)
\(240\) 1.27927e9 0.0248893
\(241\) −1.88067e10 −0.359118 −0.179559 0.983747i \(-0.557467\pi\)
−0.179559 + 0.983747i \(0.557467\pi\)
\(242\) −4.68207e10 −0.877544
\(243\) 9.60695e9 0.176749
\(244\) 4.40427e10 0.795463
\(245\) −8.26574e9 −0.146566
\(246\) 3.14057e9 0.0546765
\(247\) 2.80107e10 0.478837
\(248\) 2.55455e10 0.428827
\(249\) −4.50535e9 −0.0742731
\(250\) 8.41002e10 1.36165
\(251\) 6.83951e10 1.08766 0.543830 0.839195i \(-0.316973\pi\)
0.543830 + 0.839195i \(0.316973\pi\)
\(252\) 8.52765e10 1.33207
\(253\) 6.74385e10 1.03482
\(254\) −7.26772e10 −1.09559
\(255\) −1.17130e9 −0.0173475
\(256\) 3.67078e10 0.534169
\(257\) −8.21993e10 −1.17536 −0.587678 0.809095i \(-0.699958\pi\)
−0.587678 + 0.809095i \(0.699958\pi\)
\(258\) −9.49664e8 −0.0133439
\(259\) 1.17501e11 1.62252
\(260\) −1.91411e10 −0.259768
\(261\) −4.71691e10 −0.629181
\(262\) −7.84259e10 −1.02826
\(263\) −1.78524e10 −0.230089 −0.115044 0.993360i \(-0.536701\pi\)
−0.115044 + 0.993360i \(0.536701\pi\)
\(264\) −8.15418e8 −0.0103315
\(265\) 2.35763e10 0.293677
\(266\) −1.60234e11 −1.96240
\(267\) −1.99822e8 −0.00240626
\(268\) 1.72096e11 2.03782
\(269\) 1.12924e11 1.31492 0.657462 0.753488i \(-0.271630\pi\)
0.657462 + 0.753488i \(0.271630\pi\)
\(270\) 8.21879e9 0.0941176
\(271\) −1.05452e11 −1.18766 −0.593831 0.804590i \(-0.702385\pi\)
−0.593831 + 0.804590i \(0.702385\pi\)
\(272\) −3.83266e10 −0.424562
\(273\) −2.49260e9 −0.0271594
\(274\) 7.78565e10 0.834483
\(275\) 4.29101e10 0.452441
\(276\) −1.09791e10 −0.113887
\(277\) −7.65554e10 −0.781298 −0.390649 0.920540i \(-0.627749\pi\)
−0.390649 + 0.920540i \(0.627749\pi\)
\(278\) −1.31296e11 −1.31841
\(279\) −1.57957e11 −1.56070
\(280\) 1.71115e10 0.166370
\(281\) −1.62567e11 −1.55544 −0.777721 0.628610i \(-0.783624\pi\)
−0.777721 + 0.628610i \(0.783624\pi\)
\(282\) −1.19880e10 −0.112882
\(283\) 8.09281e10 0.749998 0.374999 0.927025i \(-0.377643\pi\)
0.374999 + 0.927025i \(0.377643\pi\)
\(284\) −1.15734e11 −1.05567
\(285\) −4.18065e9 −0.0375355
\(286\) −4.33763e10 −0.383358
\(287\) −8.10038e10 −0.704753
\(288\) 1.66084e11 1.42253
\(289\) −8.34960e10 −0.704085
\(290\) −6.05655e10 −0.502845
\(291\) −1.08424e10 −0.0886355
\(292\) 1.67385e10 0.134739
\(293\) −1.52458e11 −1.20849 −0.604247 0.796797i \(-0.706526\pi\)
−0.604247 + 0.796797i \(0.706526\pi\)
\(294\) 3.04948e9 0.0238047
\(295\) −3.39888e10 −0.261298
\(296\) −5.20223e10 −0.393892
\(297\) 1.01018e10 0.0753344
\(298\) −1.14546e11 −0.841408
\(299\) −9.12703e10 −0.660403
\(300\) −6.98583e9 −0.0497934
\(301\) 2.44944e10 0.171996
\(302\) −7.41972e10 −0.513282
\(303\) 6.96797e9 0.0474913
\(304\) −1.36797e11 −0.918640
\(305\) −5.46458e10 −0.361583
\(306\) −1.22900e11 −0.801321
\(307\) 2.31912e11 1.49005 0.745025 0.667037i \(-0.232438\pi\)
0.745025 + 0.667037i \(0.232438\pi\)
\(308\) 1.34582e11 0.852135
\(309\) −1.63675e10 −0.102133
\(310\) −2.02818e11 −1.24732
\(311\) 4.82364e10 0.292384 0.146192 0.989256i \(-0.453298\pi\)
0.146192 + 0.989256i \(0.453298\pi\)
\(312\) 1.10357e9 0.00659334
\(313\) 2.96278e11 1.74482 0.872408 0.488778i \(-0.162557\pi\)
0.872408 + 0.488778i \(0.162557\pi\)
\(314\) −3.42000e10 −0.198538
\(315\) −1.05806e11 −0.605500
\(316\) 1.60460e11 0.905264
\(317\) −4.42421e10 −0.246076 −0.123038 0.992402i \(-0.539264\pi\)
−0.123038 + 0.992402i \(0.539264\pi\)
\(318\) −8.69801e9 −0.0476978
\(319\) −7.44415e10 −0.402492
\(320\) 1.34382e11 0.716418
\(321\) 1.05167e10 0.0552849
\(322\) 5.22107e11 2.70650
\(323\) 1.25251e11 0.640281
\(324\) 2.32631e11 1.17278
\(325\) −5.80738e10 −0.288739
\(326\) 3.42925e11 1.68159
\(327\) −8.05768e9 −0.0389713
\(328\) 3.58637e10 0.171089
\(329\) 3.09204e11 1.45500
\(330\) 6.47399e9 0.0300510
\(331\) 1.85279e11 0.848399 0.424199 0.905569i \(-0.360556\pi\)
0.424199 + 0.905569i \(0.360556\pi\)
\(332\) −3.29218e11 −1.48718
\(333\) 3.21673e11 1.43356
\(334\) −5.93002e11 −2.60734
\(335\) −2.13528e11 −0.926302
\(336\) 1.21732e10 0.0521048
\(337\) 3.97119e11 1.67720 0.838602 0.544744i \(-0.183373\pi\)
0.838602 + 0.544744i \(0.183373\pi\)
\(338\) −2.96005e11 −1.23360
\(339\) −1.60573e10 −0.0660350
\(340\) −8.55902e10 −0.347351
\(341\) −2.49285e11 −0.998394
\(342\) −4.38660e11 −1.73385
\(343\) 2.10464e11 0.821020
\(344\) −1.08447e10 −0.0417545
\(345\) 1.36223e10 0.0517682
\(346\) 3.92550e11 1.47249
\(347\) −3.90891e11 −1.44735 −0.723675 0.690141i \(-0.757548\pi\)
−0.723675 + 0.690141i \(0.757548\pi\)
\(348\) 1.21192e10 0.0442963
\(349\) 5.12370e10 0.184871 0.0924355 0.995719i \(-0.470535\pi\)
0.0924355 + 0.995719i \(0.470535\pi\)
\(350\) 3.32208e11 1.18333
\(351\) −1.36716e10 −0.0480769
\(352\) 2.62111e11 0.910005
\(353\) 4.84133e9 0.0165950 0.00829752 0.999966i \(-0.497359\pi\)
0.00829752 + 0.999966i \(0.497359\pi\)
\(354\) 1.25395e10 0.0424390
\(355\) 1.43596e11 0.479861
\(356\) −1.46016e10 −0.0481808
\(357\) −1.11458e10 −0.0363164
\(358\) 2.49058e11 0.801359
\(359\) −3.55635e11 −1.13000 −0.565001 0.825090i \(-0.691124\pi\)
−0.565001 + 0.825090i \(0.691124\pi\)
\(360\) 4.68448e10 0.146994
\(361\) 1.24364e11 0.385400
\(362\) 2.77041e10 0.0847922
\(363\) −1.16244e10 −0.0351390
\(364\) −1.82141e11 −0.543815
\(365\) −2.07683e10 −0.0612466
\(366\) 2.01605e10 0.0587268
\(367\) −3.97521e11 −1.14383 −0.571917 0.820312i \(-0.693800\pi\)
−0.571917 + 0.820312i \(0.693800\pi\)
\(368\) 4.45740e11 1.26697
\(369\) −2.21758e11 −0.622674
\(370\) 4.13030e11 1.14571
\(371\) 2.24345e11 0.614801
\(372\) 4.05841e10 0.109878
\(373\) −5.47884e11 −1.46554 −0.732772 0.680474i \(-0.761774\pi\)
−0.732772 + 0.680474i \(0.761774\pi\)
\(374\) −1.93959e11 −0.512611
\(375\) 2.08799e10 0.0545239
\(376\) −1.36897e11 −0.353222
\(377\) 1.00748e11 0.256862
\(378\) 7.82076e10 0.197032
\(379\) 6.83539e11 1.70171 0.850857 0.525397i \(-0.176083\pi\)
0.850857 + 0.525397i \(0.176083\pi\)
\(380\) −3.05492e11 −0.751577
\(381\) −1.80438e10 −0.0438699
\(382\) 5.98656e10 0.143844
\(383\) 5.16638e11 1.22685 0.613426 0.789753i \(-0.289791\pi\)
0.613426 + 0.789753i \(0.289791\pi\)
\(384\) −1.35741e10 −0.0318582
\(385\) −1.66982e11 −0.387343
\(386\) −5.14514e11 −1.17965
\(387\) 6.70565e10 0.151964
\(388\) −7.92286e11 −1.77476
\(389\) −4.39607e11 −0.973399 −0.486700 0.873569i \(-0.661799\pi\)
−0.486700 + 0.873569i \(0.661799\pi\)
\(390\) −8.76180e9 −0.0191780
\(391\) −4.08119e11 −0.883063
\(392\) 3.48235e10 0.0744878
\(393\) −1.94711e10 −0.0411741
\(394\) 2.24831e11 0.470028
\(395\) −1.99090e11 −0.411493
\(396\) 3.68434e11 0.752891
\(397\) 4.04283e11 0.816823 0.408411 0.912798i \(-0.366083\pi\)
0.408411 + 0.912798i \(0.366083\pi\)
\(398\) 7.98579e11 1.59531
\(399\) −3.97819e10 −0.0785792
\(400\) 2.83617e11 0.553940
\(401\) −8.05560e11 −1.55578 −0.777890 0.628400i \(-0.783710\pi\)
−0.777890 + 0.628400i \(0.783710\pi\)
\(402\) 7.87769e10 0.150446
\(403\) 3.37379e11 0.637155
\(404\) 5.09169e11 0.950924
\(405\) −2.88636e11 −0.533093
\(406\) −5.76324e11 −1.05269
\(407\) 5.07658e11 0.917057
\(408\) 4.93468e9 0.00881634
\(409\) −4.85519e11 −0.857929 −0.428965 0.903321i \(-0.641122\pi\)
−0.428965 + 0.903321i \(0.641122\pi\)
\(410\) −2.84739e11 −0.497644
\(411\) 1.93297e10 0.0334147
\(412\) −1.19602e12 −2.04503
\(413\) −3.23428e11 −0.547018
\(414\) 1.42933e12 2.39129
\(415\) 4.08476e11 0.676005
\(416\) −3.54737e11 −0.580747
\(417\) −3.25975e10 −0.0527925
\(418\) −6.92286e11 −1.10915
\(419\) 6.38311e11 1.01174 0.505871 0.862609i \(-0.331171\pi\)
0.505871 + 0.862609i \(0.331171\pi\)
\(420\) 2.71849e10 0.0426291
\(421\) −3.95759e11 −0.613991 −0.306995 0.951711i \(-0.599324\pi\)
−0.306995 + 0.951711i \(0.599324\pi\)
\(422\) −3.21906e11 −0.494110
\(423\) 8.46483e11 1.28554
\(424\) −9.93268e10 −0.149252
\(425\) −2.59680e11 −0.386090
\(426\) −5.29770e10 −0.0779371
\(427\) −5.19994e11 −0.756960
\(428\) 7.68485e11 1.10698
\(429\) −1.07692e10 −0.0153506
\(430\) 8.61010e10 0.121451
\(431\) 5.11706e11 0.714287 0.357144 0.934049i \(-0.383751\pi\)
0.357144 + 0.934049i \(0.383751\pi\)
\(432\) 6.67684e10 0.0922346
\(433\) 5.74450e11 0.785337 0.392669 0.919680i \(-0.371552\pi\)
0.392669 + 0.919680i \(0.371552\pi\)
\(434\) −1.92996e12 −2.61123
\(435\) −1.50368e10 −0.0201351
\(436\) −5.88797e11 −0.780327
\(437\) −1.45668e12 −1.91072
\(438\) 7.66204e9 0.00994743
\(439\) 7.80007e11 1.00232 0.501162 0.865353i \(-0.332906\pi\)
0.501162 + 0.865353i \(0.332906\pi\)
\(440\) 7.39296e10 0.0940332
\(441\) −2.15326e11 −0.271096
\(442\) 2.62501e11 0.327138
\(443\) 1.03032e12 1.27103 0.635517 0.772087i \(-0.280787\pi\)
0.635517 + 0.772087i \(0.280787\pi\)
\(444\) −8.26475e10 −0.100927
\(445\) 1.81168e10 0.0219009
\(446\) 1.01214e12 1.21124
\(447\) −2.84388e10 −0.0336920
\(448\) 1.27874e12 1.49980
\(449\) −5.64317e11 −0.655262 −0.327631 0.944806i \(-0.606250\pi\)
−0.327631 + 0.944806i \(0.606250\pi\)
\(450\) 9.09462e11 1.04551
\(451\) −3.49974e11 −0.398329
\(452\) −1.17335e12 −1.32223
\(453\) −1.84212e10 −0.0205531
\(454\) −5.57694e11 −0.616091
\(455\) 2.25991e11 0.247195
\(456\) 1.76131e10 0.0190762
\(457\) −2.62462e11 −0.281478 −0.140739 0.990047i \(-0.544948\pi\)
−0.140739 + 0.990047i \(0.544948\pi\)
\(458\) 1.54796e12 1.64386
\(459\) −6.11331e10 −0.0642865
\(460\) 9.95417e11 1.03656
\(461\) −7.04852e11 −0.726848 −0.363424 0.931624i \(-0.618392\pi\)
−0.363424 + 0.931624i \(0.618392\pi\)
\(462\) 6.16047e10 0.0629107
\(463\) −1.58919e12 −1.60717 −0.803584 0.595191i \(-0.797076\pi\)
−0.803584 + 0.595191i \(0.797076\pi\)
\(464\) −4.92027e11 −0.492785
\(465\) −5.03545e10 −0.0499459
\(466\) 7.60928e11 0.747492
\(467\) −1.90216e12 −1.85063 −0.925317 0.379195i \(-0.876201\pi\)
−0.925317 + 0.379195i \(0.876201\pi\)
\(468\) −4.98634e11 −0.480480
\(469\) −2.03187e12 −1.93918
\(470\) 1.08689e12 1.02741
\(471\) −8.49098e9 −0.00794993
\(472\) 1.43194e11 0.132797
\(473\) 1.05827e11 0.0972127
\(474\) 7.34504e10 0.0668331
\(475\) −9.26859e11 −0.835396
\(476\) −8.14452e11 −0.727167
\(477\) 6.14173e11 0.543198
\(478\) 1.34722e12 1.18036
\(479\) −4.06033e11 −0.352412 −0.176206 0.984353i \(-0.556383\pi\)
−0.176206 + 0.984353i \(0.556383\pi\)
\(480\) 5.29453e10 0.0455241
\(481\) −6.87056e11 −0.585247
\(482\) −6.29066e11 −0.530866
\(483\) 1.29626e11 0.108375
\(484\) −8.49424e11 −0.703591
\(485\) 9.83025e11 0.806727
\(486\) 3.21343e11 0.261279
\(487\) −2.54024e11 −0.204642 −0.102321 0.994751i \(-0.532627\pi\)
−0.102321 + 0.994751i \(0.532627\pi\)
\(488\) 2.30222e11 0.183763
\(489\) 8.51394e10 0.0673350
\(490\) −2.76481e11 −0.216662
\(491\) 5.49800e11 0.426911 0.213456 0.976953i \(-0.431528\pi\)
0.213456 + 0.976953i \(0.431528\pi\)
\(492\) 5.69764e10 0.0438381
\(493\) 4.50499e11 0.343466
\(494\) 9.36929e11 0.707841
\(495\) −4.57133e11 −0.342231
\(496\) −1.64767e12 −1.22237
\(497\) 1.36642e12 1.00457
\(498\) −1.50699e11 −0.109794
\(499\) 2.09406e12 1.51195 0.755974 0.654601i \(-0.227164\pi\)
0.755974 + 0.654601i \(0.227164\pi\)
\(500\) 1.52575e12 1.09174
\(501\) −1.47227e11 −0.104404
\(502\) 2.28775e12 1.60783
\(503\) 2.16997e12 1.51146 0.755730 0.654883i \(-0.227282\pi\)
0.755730 + 0.654883i \(0.227282\pi\)
\(504\) 4.45761e11 0.307727
\(505\) −6.31749e11 −0.432248
\(506\) 2.25575e12 1.52973
\(507\) −7.34902e10 −0.0493962
\(508\) −1.31851e12 −0.878412
\(509\) −1.57264e12 −1.03848 −0.519242 0.854627i \(-0.673786\pi\)
−0.519242 + 0.854627i \(0.673786\pi\)
\(510\) −3.91788e10 −0.0256440
\(511\) −1.97625e11 −0.128217
\(512\) 2.06473e12 1.32785
\(513\) −2.18199e11 −0.139099
\(514\) −2.74948e12 −1.73747
\(515\) 1.48395e12 0.929580
\(516\) −1.72289e10 −0.0106987
\(517\) 1.33590e12 0.822371
\(518\) 3.93027e12 2.39850
\(519\) 9.74599e10 0.0589621
\(520\) −1.00055e11 −0.0600101
\(521\) 6.40632e11 0.380925 0.190462 0.981695i \(-0.439001\pi\)
0.190462 + 0.981695i \(0.439001\pi\)
\(522\) −1.57776e12 −0.930087
\(523\) 1.66251e12 0.971642 0.485821 0.874058i \(-0.338521\pi\)
0.485821 + 0.874058i \(0.338521\pi\)
\(524\) −1.42281e12 −0.824433
\(525\) 8.24787e10 0.0473833
\(526\) −5.97144e11 −0.340129
\(527\) 1.50861e12 0.851978
\(528\) 5.25939e10 0.0294498
\(529\) 2.94529e12 1.63522
\(530\) 7.88603e11 0.434127
\(531\) −8.85423e11 −0.483310
\(532\) −2.90697e12 −1.57340
\(533\) 4.73650e11 0.254206
\(534\) −6.68384e9 −0.00355706
\(535\) −9.53493e11 −0.503183
\(536\) 8.99591e11 0.470764
\(537\) 6.18346e10 0.0320883
\(538\) 3.77719e12 1.94379
\(539\) −3.39824e11 −0.173422
\(540\) 1.49106e11 0.0754610
\(541\) −3.01359e12 −1.51250 −0.756251 0.654282i \(-0.772971\pi\)
−0.756251 + 0.654282i \(0.772971\pi\)
\(542\) −3.52726e12 −1.75566
\(543\) 6.87821e9 0.00339528
\(544\) −1.58623e12 −0.776551
\(545\) 7.30547e11 0.354702
\(546\) −8.33748e10 −0.0401484
\(547\) 5.31804e11 0.253985 0.126993 0.991904i \(-0.459468\pi\)
0.126993 + 0.991904i \(0.459468\pi\)
\(548\) 1.41248e12 0.669066
\(549\) −1.42355e12 −0.668800
\(550\) 1.43530e12 0.668820
\(551\) 1.60794e12 0.743169
\(552\) −5.73905e10 −0.0263096
\(553\) −1.89448e12 −0.861446
\(554\) −2.56070e12 −1.15495
\(555\) 1.02545e11 0.0458769
\(556\) −2.38199e12 −1.05707
\(557\) −4.53326e12 −1.99555 −0.997775 0.0666751i \(-0.978761\pi\)
−0.997775 + 0.0666751i \(0.978761\pi\)
\(558\) −5.28351e12 −2.30711
\(559\) −1.43225e11 −0.0620392
\(560\) −1.10368e12 −0.474238
\(561\) −4.81550e10 −0.0205262
\(562\) −5.43770e12 −2.29933
\(563\) 1.58678e12 0.665623 0.332811 0.942993i \(-0.392003\pi\)
0.332811 + 0.942993i \(0.392003\pi\)
\(564\) −2.17487e11 −0.0905062
\(565\) 1.45583e12 0.601025
\(566\) 2.70696e12 1.10868
\(567\) −2.74658e12 −1.11601
\(568\) −6.04970e11 −0.243874
\(569\) −1.94543e12 −0.778054 −0.389027 0.921226i \(-0.627189\pi\)
−0.389027 + 0.921226i \(0.627189\pi\)
\(570\) −1.39839e11 −0.0554868
\(571\) 5.49369e11 0.216273 0.108136 0.994136i \(-0.465512\pi\)
0.108136 + 0.994136i \(0.465512\pi\)
\(572\) −7.86935e11 −0.307367
\(573\) 1.48631e10 0.00575987
\(574\) −2.70949e12 −1.04180
\(575\) 3.02008e12 1.15216
\(576\) 3.50072e12 1.32512
\(577\) 1.70113e12 0.638922 0.319461 0.947599i \(-0.396498\pi\)
0.319461 + 0.947599i \(0.396498\pi\)
\(578\) −2.79285e12 −1.04081
\(579\) −1.27740e11 −0.0472362
\(580\) −1.09878e12 −0.403168
\(581\) 3.88694e12 1.41519
\(582\) −3.62668e11 −0.131025
\(583\) 9.69277e11 0.347488
\(584\) 8.74965e10 0.0311267
\(585\) 6.18677e11 0.218405
\(586\) −5.09955e12 −1.78646
\(587\) −3.76857e12 −1.31010 −0.655051 0.755585i \(-0.727353\pi\)
−0.655051 + 0.755585i \(0.727353\pi\)
\(588\) 5.53239e10 0.0190860
\(589\) 5.38458e12 1.84346
\(590\) −1.13689e12 −0.386264
\(591\) 5.58197e10 0.0188211
\(592\) 3.35540e12 1.12279
\(593\) 2.20370e12 0.731823 0.365912 0.930650i \(-0.380757\pi\)
0.365912 + 0.930650i \(0.380757\pi\)
\(594\) 3.37894e11 0.111363
\(595\) 1.01053e12 0.330538
\(596\) −2.07810e12 −0.674619
\(597\) 1.98266e11 0.0638799
\(598\) −3.05290e12 −0.976240
\(599\) 2.10006e12 0.666515 0.333258 0.942836i \(-0.391852\pi\)
0.333258 + 0.942836i \(0.391852\pi\)
\(600\) −3.65166e10 −0.0115030
\(601\) −1.35259e12 −0.422892 −0.211446 0.977390i \(-0.567817\pi\)
−0.211446 + 0.977390i \(0.567817\pi\)
\(602\) 8.19313e11 0.254253
\(603\) −5.56249e12 −1.71333
\(604\) −1.34609e12 −0.411536
\(605\) 1.05392e12 0.319822
\(606\) 2.33071e11 0.0702040
\(607\) 4.40577e12 1.31726 0.658631 0.752466i \(-0.271136\pi\)
0.658631 + 0.752466i \(0.271136\pi\)
\(608\) −5.66162e12 −1.68025
\(609\) −1.43086e11 −0.0421522
\(610\) −1.82785e12 −0.534509
\(611\) −1.80799e12 −0.524821
\(612\) −2.22966e12 −0.642478
\(613\) 2.69654e12 0.771320 0.385660 0.922641i \(-0.373974\pi\)
0.385660 + 0.922641i \(0.373974\pi\)
\(614\) 7.75722e12 2.20267
\(615\) −7.06932e10 −0.0199269
\(616\) 7.03493e11 0.196855
\(617\) −2.92929e12 −0.813727 −0.406863 0.913489i \(-0.633377\pi\)
−0.406863 + 0.913489i \(0.633377\pi\)
\(618\) −5.47474e11 −0.150979
\(619\) 5.71068e12 1.56343 0.781717 0.623633i \(-0.214344\pi\)
0.781717 + 0.623633i \(0.214344\pi\)
\(620\) −3.67954e12 −1.00007
\(621\) 7.10980e11 0.191843
\(622\) 1.61346e12 0.432216
\(623\) 1.72394e11 0.0458487
\(624\) −7.11797e10 −0.0187943
\(625\) 8.14411e11 0.213493
\(626\) 9.91019e12 2.57927
\(627\) −1.71876e11 −0.0444133
\(628\) −6.20459e11 −0.159182
\(629\) −3.07221e12 −0.782569
\(630\) −3.53911e12 −0.895080
\(631\) 6.26095e12 1.57220 0.786101 0.618099i \(-0.212097\pi\)
0.786101 + 0.618099i \(0.212097\pi\)
\(632\) 8.38765e11 0.209129
\(633\) −7.99209e10 −0.0197853
\(634\) −1.47985e12 −0.363762
\(635\) 1.63594e12 0.399287
\(636\) −1.57800e11 −0.0382428
\(637\) 4.59913e11 0.110675
\(638\) −2.48999e12 −0.594983
\(639\) 3.74075e12 0.887574
\(640\) 1.23069e12 0.289961
\(641\) −7.96482e12 −1.86344 −0.931718 0.363181i \(-0.881691\pi\)
−0.931718 + 0.363181i \(0.881691\pi\)
\(642\) 3.51773e11 0.0817249
\(643\) 5.28675e12 1.21966 0.609831 0.792532i \(-0.291237\pi\)
0.609831 + 0.792532i \(0.291237\pi\)
\(644\) 9.47210e12 2.17000
\(645\) 2.13766e10 0.00486318
\(646\) 4.18952e12 0.946495
\(647\) 2.49240e12 0.559176 0.279588 0.960120i \(-0.409802\pi\)
0.279588 + 0.960120i \(0.409802\pi\)
\(648\) 1.21602e12 0.270928
\(649\) −1.39736e12 −0.309177
\(650\) −1.94251e12 −0.426828
\(651\) −4.79159e11 −0.104560
\(652\) 6.22137e12 1.34825
\(653\) −4.23455e12 −0.911376 −0.455688 0.890140i \(-0.650607\pi\)
−0.455688 + 0.890140i \(0.650607\pi\)
\(654\) −2.69521e11 −0.0576093
\(655\) 1.76534e12 0.374751
\(656\) −2.31318e12 −0.487688
\(657\) −5.41022e11 −0.113285
\(658\) 1.03425e13 2.15085
\(659\) 9.53023e11 0.196843 0.0984213 0.995145i \(-0.468621\pi\)
0.0984213 + 0.995145i \(0.468621\pi\)
\(660\) 1.17452e11 0.0240941
\(661\) −6.93404e12 −1.41280 −0.706399 0.707814i \(-0.749681\pi\)
−0.706399 + 0.707814i \(0.749681\pi\)
\(662\) 6.19739e12 1.25414
\(663\) 6.51722e10 0.0130994
\(664\) −1.72091e12 −0.343559
\(665\) 3.60681e12 0.715198
\(666\) 1.07596e13 2.11915
\(667\) −5.23932e12 −1.02496
\(668\) −1.07583e13 −2.09049
\(669\) 2.51287e11 0.0485012
\(670\) −7.14228e12 −1.36931
\(671\) −2.24662e12 −0.427837
\(672\) 5.03812e11 0.0953031
\(673\) −9.52595e11 −0.178995 −0.0894974 0.995987i \(-0.528526\pi\)
−0.0894974 + 0.995987i \(0.528526\pi\)
\(674\) 1.32832e13 2.47933
\(675\) 4.52385e11 0.0838767
\(676\) −5.37014e12 −0.989066
\(677\) −9.34347e12 −1.70946 −0.854731 0.519072i \(-0.826278\pi\)
−0.854731 + 0.519072i \(0.826278\pi\)
\(678\) −5.37100e11 −0.0976162
\(679\) 9.35418e12 1.68885
\(680\) −4.47401e11 −0.0802430
\(681\) −1.38461e11 −0.0246698
\(682\) −8.33834e12 −1.47588
\(683\) −6.37568e12 −1.12107 −0.560535 0.828130i \(-0.689405\pi\)
−0.560535 + 0.828130i \(0.689405\pi\)
\(684\) −7.95820e12 −1.39015
\(685\) −1.75252e12 −0.304128
\(686\) 7.03980e12 1.21367
\(687\) 3.84317e11 0.0658241
\(688\) 6.99474e11 0.119021
\(689\) −1.31180e12 −0.221760
\(690\) 4.55651e11 0.0765264
\(691\) 6.11546e12 1.02042 0.510208 0.860051i \(-0.329568\pi\)
0.510208 + 0.860051i \(0.329568\pi\)
\(692\) 7.12166e12 1.18060
\(693\) −4.34995e12 −0.716448
\(694\) −1.30749e13 −2.13954
\(695\) 2.95544e12 0.480497
\(696\) 6.33501e10 0.0102331
\(697\) 2.11795e12 0.339913
\(698\) 1.71382e12 0.273286
\(699\) 1.88918e11 0.0299314
\(700\) 6.02695e12 0.948760
\(701\) 3.82093e12 0.597638 0.298819 0.954310i \(-0.403407\pi\)
0.298819 + 0.954310i \(0.403407\pi\)
\(702\) −4.57300e11 −0.0710697
\(703\) −1.09654e13 −1.69327
\(704\) 5.52477e12 0.847690
\(705\) 2.69846e11 0.0411401
\(706\) 1.61937e11 0.0245316
\(707\) −6.01154e12 −0.904896
\(708\) 2.27492e11 0.0340265
\(709\) −6.49775e11 −0.0965728 −0.0482864 0.998834i \(-0.515376\pi\)
−0.0482864 + 0.998834i \(0.515376\pi\)
\(710\) 4.80315e12 0.709354
\(711\) −5.18639e12 −0.761118
\(712\) −7.63260e10 −0.0111304
\(713\) −1.75451e13 −2.54246
\(714\) −3.72814e11 −0.0536847
\(715\) 9.76385e11 0.139715
\(716\) 4.51843e12 0.642508
\(717\) 3.34480e11 0.0472644
\(718\) −1.18956e13 −1.67042
\(719\) 3.00170e12 0.418878 0.209439 0.977822i \(-0.432836\pi\)
0.209439 + 0.977822i \(0.432836\pi\)
\(720\) −3.02146e12 −0.419006
\(721\) 1.41208e13 1.94604
\(722\) 4.15984e12 0.569717
\(723\) −1.56181e11 −0.0212571
\(724\) 5.02610e11 0.0679841
\(725\) −3.33370e12 −0.448131
\(726\) −3.88823e11 −0.0519442
\(727\) −1.31825e13 −1.75022 −0.875109 0.483925i \(-0.839211\pi\)
−0.875109 + 0.483925i \(0.839211\pi\)
\(728\) −9.52096e11 −0.125629
\(729\) −7.46576e12 −0.979039
\(730\) −6.94676e11 −0.0905377
\(731\) −6.40438e11 −0.0829562
\(732\) 3.65753e11 0.0470856
\(733\) 1.12951e13 1.44519 0.722593 0.691274i \(-0.242950\pi\)
0.722593 + 0.691274i \(0.242950\pi\)
\(734\) −1.32967e13 −1.69087
\(735\) −6.86429e10 −0.00867566
\(736\) 1.84479e13 2.31737
\(737\) −8.77863e12 −1.09603
\(738\) −7.41757e12 −0.920467
\(739\) −1.22652e13 −1.51278 −0.756388 0.654124i \(-0.773038\pi\)
−0.756388 + 0.654124i \(0.773038\pi\)
\(740\) 7.49321e12 0.918598
\(741\) 2.32615e11 0.0283437
\(742\) 7.50412e12 0.908829
\(743\) −1.25794e13 −1.51430 −0.757149 0.653242i \(-0.773408\pi\)
−0.757149 + 0.653242i \(0.773408\pi\)
\(744\) 2.12143e11 0.0253834
\(745\) 2.57839e12 0.306652
\(746\) −1.83262e13 −2.16644
\(747\) 1.06410e13 1.25037
\(748\) −3.51882e12 −0.410998
\(749\) −9.07317e12 −1.05339
\(750\) 6.98410e11 0.0806000
\(751\) 1.42829e13 1.63846 0.819231 0.573463i \(-0.194400\pi\)
0.819231 + 0.573463i \(0.194400\pi\)
\(752\) 8.82976e12 1.00686
\(753\) 5.67988e11 0.0643816
\(754\) 3.36992e12 0.379706
\(755\) 1.67015e12 0.187066
\(756\) 1.41885e12 0.157975
\(757\) −1.33564e12 −0.147828 −0.0739142 0.997265i \(-0.523549\pi\)
−0.0739142 + 0.997265i \(0.523549\pi\)
\(758\) 2.28637e13 2.51556
\(759\) 5.60043e11 0.0612539
\(760\) −1.59688e12 −0.173625
\(761\) 1.24325e13 1.34378 0.671888 0.740653i \(-0.265484\pi\)
0.671888 + 0.740653i \(0.265484\pi\)
\(762\) −6.03548e11 −0.0648507
\(763\) 6.95168e12 0.742556
\(764\) 1.08609e12 0.115330
\(765\) 2.76644e12 0.292042
\(766\) 1.72810e13 1.81359
\(767\) 1.89116e12 0.197310
\(768\) 3.04840e11 0.0316189
\(769\) −1.49843e13 −1.54514 −0.772569 0.634931i \(-0.781028\pi\)
−0.772569 + 0.634931i \(0.781028\pi\)
\(770\) −5.58537e12 −0.572590
\(771\) −6.82624e11 −0.0695724
\(772\) −9.33435e12 −0.945815
\(773\) 8.29355e12 0.835473 0.417737 0.908568i \(-0.362823\pi\)
0.417737 + 0.908568i \(0.362823\pi\)
\(774\) 2.24297e12 0.224641
\(775\) −1.11637e13 −1.11160
\(776\) −4.14148e12 −0.409994
\(777\) 9.75784e11 0.0960416
\(778\) −1.47044e13 −1.43893
\(779\) 7.55946e12 0.735482
\(780\) −1.58957e11 −0.0153764
\(781\) 5.90358e12 0.567788
\(782\) −1.36512e13 −1.30539
\(783\) −7.84810e11 −0.0746168
\(784\) −2.24609e12 −0.212327
\(785\) 7.69832e11 0.0723573
\(786\) −6.51288e11 −0.0608656
\(787\) −1.33986e12 −0.124501 −0.0622505 0.998061i \(-0.519828\pi\)
−0.0622505 + 0.998061i \(0.519828\pi\)
\(788\) 4.07890e12 0.376856
\(789\) −1.48255e11 −0.0136196
\(790\) −6.65936e12 −0.608290
\(791\) 1.38533e13 1.25822
\(792\) 1.92590e12 0.173928
\(793\) 3.04054e12 0.273037
\(794\) 1.35228e13 1.20747
\(795\) 1.95789e11 0.0173835
\(796\) 1.44879e13 1.27907
\(797\) −3.09254e12 −0.271489 −0.135745 0.990744i \(-0.543343\pi\)
−0.135745 + 0.990744i \(0.543343\pi\)
\(798\) −1.33066e12 −0.116160
\(799\) −8.08453e12 −0.701769
\(800\) 1.17381e13 1.01319
\(801\) 4.71951e11 0.0405089
\(802\) −2.69452e13 −2.29983
\(803\) −8.53832e11 −0.0724690
\(804\) 1.42917e12 0.120624
\(805\) −1.17525e13 −0.986387
\(806\) 1.12850e13 0.941874
\(807\) 9.37777e11 0.0778339
\(808\) 2.66155e12 0.219677
\(809\) −1.40195e13 −1.15071 −0.575353 0.817905i \(-0.695135\pi\)
−0.575353 + 0.817905i \(0.695135\pi\)
\(810\) −9.65458e12 −0.788044
\(811\) −2.03904e13 −1.65513 −0.827565 0.561370i \(-0.810274\pi\)
−0.827565 + 0.561370i \(0.810274\pi\)
\(812\) −1.04557e13 −0.844017
\(813\) −8.75726e11 −0.0703009
\(814\) 1.69806e13 1.35564
\(815\) −7.71914e12 −0.612857
\(816\) −3.18284e11 −0.0251309
\(817\) −2.28588e12 −0.179495
\(818\) −1.62401e13 −1.26823
\(819\) 5.88715e12 0.457223
\(820\) −5.16575e12 −0.398998
\(821\) 2.45678e13 1.88721 0.943607 0.331067i \(-0.107408\pi\)
0.943607 + 0.331067i \(0.107408\pi\)
\(822\) 6.46560e11 0.0493953
\(823\) −1.21005e13 −0.919399 −0.459699 0.888075i \(-0.652043\pi\)
−0.459699 + 0.888075i \(0.652043\pi\)
\(824\) −6.25187e12 −0.472430
\(825\) 3.56347e11 0.0267812
\(826\) −1.08183e13 −0.808629
\(827\) −4.05700e12 −0.301599 −0.150800 0.988564i \(-0.548185\pi\)
−0.150800 + 0.988564i \(0.548185\pi\)
\(828\) 2.59311e13 1.91727
\(829\) 1.18554e13 0.871809 0.435904 0.899993i \(-0.356429\pi\)
0.435904 + 0.899993i \(0.356429\pi\)
\(830\) 1.36631e13 0.999305
\(831\) −6.35754e11 −0.0462471
\(832\) −7.47713e12 −0.540979
\(833\) 2.05652e12 0.147990
\(834\) −1.09035e12 −0.0780404
\(835\) 1.33483e13 0.950247
\(836\) −1.25595e13 −0.889291
\(837\) −2.62813e12 −0.185089
\(838\) 2.13508e13 1.49561
\(839\) −1.24519e13 −0.867575 −0.433787 0.901015i \(-0.642823\pi\)
−0.433787 + 0.901015i \(0.642823\pi\)
\(840\) 1.42102e11 0.00984791
\(841\) −8.72376e12 −0.601342
\(842\) −1.32377e13 −0.907632
\(843\) −1.35004e12 −0.0920708
\(844\) −5.84004e12 −0.396164
\(845\) 6.66297e12 0.449586
\(846\) 2.83140e13 1.90035
\(847\) 1.00288e13 0.669535
\(848\) 6.40651e12 0.425442
\(849\) 6.72067e11 0.0443944
\(850\) −8.68602e12 −0.570737
\(851\) 3.57298e13 2.33533
\(852\) −9.61113e11 −0.0624879
\(853\) 7.48447e12 0.484050 0.242025 0.970270i \(-0.422188\pi\)
0.242025 + 0.970270i \(0.422188\pi\)
\(854\) −1.73933e13 −1.11898
\(855\) 9.87410e12 0.631902
\(856\) 4.01706e12 0.255727
\(857\) 1.28244e13 0.812129 0.406064 0.913844i \(-0.366901\pi\)
0.406064 + 0.913844i \(0.366901\pi\)
\(858\) −3.60218e11 −0.0226920
\(859\) 1.30938e13 0.820536 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(860\) 1.56205e12 0.0973760
\(861\) −6.72696e11 −0.0417162
\(862\) 1.71160e13 1.05589
\(863\) −2.48587e13 −1.52556 −0.762780 0.646658i \(-0.776166\pi\)
−0.762780 + 0.646658i \(0.776166\pi\)
\(864\) 2.76335e12 0.168703
\(865\) −8.83617e12 −0.536650
\(866\) 1.92147e13 1.16092
\(867\) −6.93393e11 −0.0416767
\(868\) −3.50135e13 −2.09361
\(869\) −8.18506e12 −0.486893
\(870\) −5.02967e11 −0.0297648
\(871\) 1.18809e13 0.699465
\(872\) −3.07779e12 −0.180266
\(873\) 2.56082e13 1.49216
\(874\) −4.87243e13 −2.82452
\(875\) −1.80139e13 −1.03889
\(876\) 1.39005e11 0.00797558
\(877\) 2.55056e13 1.45592 0.727959 0.685621i \(-0.240469\pi\)
0.727959 + 0.685621i \(0.240469\pi\)
\(878\) 2.60904e13 1.48168
\(879\) −1.26608e12 −0.0715340
\(880\) −4.76841e12 −0.268041
\(881\) −4.40986e12 −0.246623 −0.123311 0.992368i \(-0.539351\pi\)
−0.123311 + 0.992368i \(0.539351\pi\)
\(882\) −7.20244e12 −0.400748
\(883\) 7.48100e12 0.414130 0.207065 0.978327i \(-0.433609\pi\)
0.207065 + 0.978327i \(0.433609\pi\)
\(884\) 4.76231e12 0.262291
\(885\) −2.82260e11 −0.0154669
\(886\) 3.44633e13 1.87890
\(887\) 1.64901e13 0.894473 0.447237 0.894416i \(-0.352408\pi\)
0.447237 + 0.894416i \(0.352408\pi\)
\(888\) −4.32019e11 −0.0233155
\(889\) 1.55671e13 0.835893
\(890\) 6.05989e11 0.0323750
\(891\) −1.18665e13 −0.630773
\(892\) 1.83622e13 0.971144
\(893\) −2.88556e13 −1.51844
\(894\) −9.51247e11 −0.0498052
\(895\) −5.60621e12 −0.292056
\(896\) 1.17109e13 0.607023
\(897\) −7.57954e11 −0.0390910
\(898\) −1.88758e13 −0.968641
\(899\) 1.93671e13 0.988884
\(900\) 1.64995e13 0.838262
\(901\) −5.86580e12 −0.296528
\(902\) −1.17063e13 −0.588829
\(903\) 2.03414e11 0.0101809
\(904\) −6.13340e12 −0.305452
\(905\) −6.23610e11 −0.0309026
\(906\) −6.16171e11 −0.0303825
\(907\) −2.16035e13 −1.05997 −0.529983 0.848008i \(-0.677802\pi\)
−0.529983 + 0.848008i \(0.677802\pi\)
\(908\) −1.01177e13 −0.493965
\(909\) −1.64573e13 −0.799507
\(910\) 7.55915e12 0.365415
\(911\) −6.95722e12 −0.334659 −0.167330 0.985901i \(-0.553514\pi\)
−0.167330 + 0.985901i \(0.553514\pi\)
\(912\) −1.13603e12 −0.0543767
\(913\) 1.67934e13 0.799872
\(914\) −8.77910e12 −0.416095
\(915\) −4.53806e11 −0.0214030
\(916\) 2.80831e13 1.31800
\(917\) 1.67985e13 0.784527
\(918\) −2.04484e12 −0.0950314
\(919\) 8.46725e12 0.391582 0.195791 0.980646i \(-0.437273\pi\)
0.195791 + 0.980646i \(0.437273\pi\)
\(920\) 5.20329e12 0.239460
\(921\) 1.92592e12 0.0882001
\(922\) −2.35766e13 −1.07446
\(923\) −7.98982e12 −0.362351
\(924\) 1.11764e12 0.0504401
\(925\) 2.27343e13 1.02104
\(926\) −5.31568e13 −2.37580
\(927\) 3.86576e13 1.71940
\(928\) −2.03635e13 −0.901336
\(929\) −3.72600e13 −1.64124 −0.820619 0.571475i \(-0.806371\pi\)
−0.820619 + 0.571475i \(0.806371\pi\)
\(930\) −1.68431e12 −0.0738325
\(931\) 7.34022e12 0.320210
\(932\) 1.38048e13 0.599319
\(933\) 4.00579e11 0.0173070
\(934\) −6.36252e13 −2.73570
\(935\) 4.36595e12 0.186822
\(936\) −2.60648e12 −0.110998
\(937\) −1.23351e13 −0.522774 −0.261387 0.965234i \(-0.584180\pi\)
−0.261387 + 0.965234i \(0.584180\pi\)
\(938\) −6.79639e13 −2.86659
\(939\) 2.46044e12 0.103280
\(940\) 1.97184e13 0.823753
\(941\) −1.46321e13 −0.608348 −0.304174 0.952617i \(-0.598380\pi\)
−0.304174 + 0.952617i \(0.598380\pi\)
\(942\) −2.84014e11 −0.0117520
\(943\) −2.46318e13 −1.01436
\(944\) −9.23594e12 −0.378536
\(945\) −1.76043e12 −0.0718084
\(946\) 3.53982e12 0.143705
\(947\) −1.11462e13 −0.450353 −0.225176 0.974318i \(-0.572296\pi\)
−0.225176 + 0.974318i \(0.572296\pi\)
\(948\) 1.33254e12 0.0535850
\(949\) 1.15556e12 0.0462483
\(950\) −3.10025e13 −1.23492
\(951\) −3.67409e11 −0.0145659
\(952\) −4.25734e12 −0.167986
\(953\) 3.70196e13 1.45383 0.726915 0.686728i \(-0.240954\pi\)
0.726915 + 0.686728i \(0.240954\pi\)
\(954\) 2.05435e13 0.802982
\(955\) −1.34756e12 −0.0524242
\(956\) 2.44414e13 0.946381
\(957\) −6.18200e11 −0.0238246
\(958\) −1.35814e13 −0.520953
\(959\) −1.66765e13 −0.636681
\(960\) 1.11598e12 0.0424067
\(961\) 3.84157e13 1.45296
\(962\) −2.29813e13 −0.865142
\(963\) −2.48389e13 −0.930710
\(964\) −1.14126e13 −0.425634
\(965\) 1.15815e13 0.429926
\(966\) 4.33584e12 0.160205
\(967\) −2.16109e13 −0.794792 −0.397396 0.917647i \(-0.630086\pi\)
−0.397396 + 0.917647i \(0.630086\pi\)
\(968\) −4.44015e12 −0.162539
\(969\) 1.04015e12 0.0379000
\(970\) 3.28812e13 1.19254
\(971\) 1.75506e13 0.633586 0.316793 0.948495i \(-0.397394\pi\)
0.316793 + 0.948495i \(0.397394\pi\)
\(972\) 5.82982e12 0.209487
\(973\) 2.81231e13 1.00590
\(974\) −8.49684e12 −0.302512
\(975\) −4.82274e11 −0.0170912
\(976\) −1.48492e13 −0.523816
\(977\) −2.50109e13 −0.878219 −0.439110 0.898433i \(-0.644706\pi\)
−0.439110 + 0.898433i \(0.644706\pi\)
\(978\) 2.84782e12 0.0995379
\(979\) 7.44825e11 0.0259139
\(980\) −5.01593e12 −0.173714
\(981\) 1.90311e13 0.656074
\(982\) 1.83902e13 0.631081
\(983\) −2.10182e13 −0.717966 −0.358983 0.933344i \(-0.616876\pi\)
−0.358983 + 0.933344i \(0.616876\pi\)
\(984\) 2.97830e11 0.0101272
\(985\) −5.06088e12 −0.171302
\(986\) 1.50687e13 0.507728
\(987\) 2.56778e12 0.0861253
\(988\) 1.69978e13 0.567528
\(989\) 7.44831e12 0.247557
\(990\) −1.52906e13 −0.505903
\(991\) −5.45177e13 −1.79559 −0.897793 0.440417i \(-0.854830\pi\)
−0.897793 + 0.440417i \(0.854830\pi\)
\(992\) −6.81922e13 −2.23580
\(993\) 1.53865e12 0.0502190
\(994\) 4.57054e13 1.48501
\(995\) −1.79757e13 −0.581411
\(996\) −2.73399e12 −0.0880300
\(997\) −6.06106e13 −1.94276 −0.971382 0.237522i \(-0.923665\pi\)
−0.971382 + 0.237522i \(0.923665\pi\)
\(998\) 7.00442e13 2.23504
\(999\) 5.35205e12 0.170011
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 43.10.a.a.1.14 15
3.2 odd 2 387.10.a.c.1.2 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.14 15 1.1 even 1 trivial
387.10.a.c.1.2 15 3.2 odd 2