Properties

Label 177.14.a.b.1.11
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} +O(q^{10})\) \(q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} -1.60362e6 q^{10} +9.00651e6 q^{11} +2.76778e6 q^{12} -3.09760e7 q^{13} +2.61909e7 q^{14} -1.76333e7 q^{15} -2.15917e7 q^{16} +5.93547e7 q^{17} -3.52331e7 q^{18} +1.66261e8 q^{19} -9.18353e7 q^{20} +2.87993e8 q^{21} -5.97107e8 q^{22} -1.38955e9 q^{23} -5.79421e8 q^{24} -6.35628e8 q^{25} +2.05362e9 q^{26} -3.87420e8 q^{27} +1.49989e9 q^{28} +2.71580e9 q^{29} +1.16904e9 q^{30} +4.57411e9 q^{31} -5.07966e9 q^{32} -6.56575e9 q^{33} -3.93505e9 q^{34} -9.55565e9 q^{35} -2.01771e9 q^{36} -9.75563e9 q^{37} -1.10227e10 q^{38} +2.25815e10 q^{39} +1.92253e10 q^{40} -1.59783e10 q^{41} -1.90931e10 q^{42} +6.97849e7 q^{43} -3.41949e10 q^{44} +1.28547e10 q^{45} +9.21231e10 q^{46} +1.45482e11 q^{47} +1.57403e10 q^{48} +5.91774e10 q^{49} +4.21404e10 q^{50} -4.32695e10 q^{51} +1.17606e11 q^{52} -3.12070e11 q^{53} +2.56849e10 q^{54} +2.17852e11 q^{55} -3.13994e11 q^{56} -1.21205e11 q^{57} -1.80050e11 q^{58} -4.21805e10 q^{59} +6.69479e10 q^{60} -3.14234e11 q^{61} -3.03251e11 q^{62} -2.09947e11 q^{63} +5.13647e11 q^{64} -7.49258e11 q^{65} +4.35291e11 q^{66} +1.17389e12 q^{67} -2.25351e11 q^{68} +1.01298e12 q^{69} +6.33513e11 q^{70} -9.67396e11 q^{71} +4.22398e11 q^{72} +2.15669e12 q^{73} +6.46771e11 q^{74} +4.63373e11 q^{75} -6.31241e11 q^{76} -3.55805e12 q^{77} -1.49709e12 q^{78} +2.07035e12 q^{79} -5.22266e11 q^{80} +2.82430e11 q^{81} +1.05932e12 q^{82} +3.77349e12 q^{83} -1.09342e12 q^{84} +1.43569e12 q^{85} -4.62654e9 q^{86} -1.97982e12 q^{87} +7.15852e12 q^{88} +1.92476e12 q^{89} -8.52228e11 q^{90} +1.22372e13 q^{91} +5.27567e12 q^{92} -3.33453e12 q^{93} -9.64504e12 q^{94} +4.02158e12 q^{95} +3.70308e12 q^{96} -7.77732e12 q^{97} -3.92330e12 q^{98} +4.78643e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −66.2972 −0.732488 −0.366244 0.930519i \(-0.619356\pi\)
−0.366244 + 0.930519i \(0.619356\pi\)
\(3\) −729.000 −0.577350
\(4\) −3796.68 −0.463462
\(5\) 24188.3 0.692310 0.346155 0.938177i \(-0.387487\pi\)
0.346155 + 0.938177i \(0.387487\pi\)
\(6\) 48330.7 0.422902
\(7\) −395052. −1.26916 −0.634582 0.772856i \(-0.718828\pi\)
−0.634582 + 0.772856i \(0.718828\pi\)
\(8\) 794816. 1.07197
\(9\) 531441. 0.333333
\(10\) −1.60362e6 −0.507109
\(11\) 9.00651e6 1.53287 0.766433 0.642324i \(-0.222030\pi\)
0.766433 + 0.642324i \(0.222030\pi\)
\(12\) 2.76778e6 0.267580
\(13\) −3.09760e7 −1.77989 −0.889947 0.456065i \(-0.849259\pi\)
−0.889947 + 0.456065i \(0.849259\pi\)
\(14\) 2.61909e7 0.929646
\(15\) −1.76333e7 −0.399705
\(16\) −2.15917e7 −0.321741
\(17\) 5.93547e7 0.596399 0.298199 0.954504i \(-0.403614\pi\)
0.298199 + 0.954504i \(0.403614\pi\)
\(18\) −3.52331e7 −0.244163
\(19\) 1.66261e8 0.810761 0.405381 0.914148i \(-0.367139\pi\)
0.405381 + 0.914148i \(0.367139\pi\)
\(20\) −9.18353e7 −0.320859
\(21\) 2.87993e8 0.732752
\(22\) −5.97107e8 −1.12281
\(23\) −1.38955e9 −1.95723 −0.978617 0.205693i \(-0.934055\pi\)
−0.978617 + 0.205693i \(0.934055\pi\)
\(24\) −5.79421e8 −0.618901
\(25\) −6.35628e8 −0.520707
\(26\) 2.05362e9 1.30375
\(27\) −3.87420e8 −0.192450
\(28\) 1.49989e9 0.588209
\(29\) 2.71580e9 0.847833 0.423916 0.905701i \(-0.360655\pi\)
0.423916 + 0.905701i \(0.360655\pi\)
\(30\) 1.16904e9 0.292779
\(31\) 4.57411e9 0.925669 0.462834 0.886445i \(-0.346832\pi\)
0.462834 + 0.886445i \(0.346832\pi\)
\(32\) −5.07966e9 −0.836296
\(33\) −6.56575e9 −0.885001
\(34\) −3.93505e9 −0.436855
\(35\) −9.55565e9 −0.878654
\(36\) −2.01771e9 −0.154487
\(37\) −9.75563e9 −0.625092 −0.312546 0.949903i \(-0.601182\pi\)
−0.312546 + 0.949903i \(0.601182\pi\)
\(38\) −1.10227e10 −0.593873
\(39\) 2.25815e10 1.02762
\(40\) 1.92253e10 0.742134
\(41\) −1.59783e10 −0.525333 −0.262667 0.964887i \(-0.584602\pi\)
−0.262667 + 0.964887i \(0.584602\pi\)
\(42\) −1.90931e10 −0.536732
\(43\) 6.97849e7 0.00168351 0.000841756 1.00000i \(-0.499732\pi\)
0.000841756 1.00000i \(0.499732\pi\)
\(44\) −3.41949e10 −0.710425
\(45\) 1.28547e10 0.230770
\(46\) 9.21231e10 1.43365
\(47\) 1.45482e11 1.96867 0.984334 0.176311i \(-0.0564165\pi\)
0.984334 + 0.176311i \(0.0564165\pi\)
\(48\) 1.57403e10 0.185757
\(49\) 5.91774e10 0.610775
\(50\) 4.21404e10 0.381411
\(51\) −4.32695e10 −0.344331
\(52\) 1.17606e11 0.824913
\(53\) −3.12070e11 −1.93401 −0.967004 0.254760i \(-0.918003\pi\)
−0.967004 + 0.254760i \(0.918003\pi\)
\(54\) 2.56849e10 0.140967
\(55\) 2.17852e11 1.06122
\(56\) −3.13994e11 −1.36050
\(57\) −1.21205e11 −0.468093
\(58\) −1.80050e11 −0.621027
\(59\) −4.21805e10 −0.130189
\(60\) 6.69479e10 0.185248
\(61\) −3.14234e11 −0.780925 −0.390463 0.920619i \(-0.627685\pi\)
−0.390463 + 0.920619i \(0.627685\pi\)
\(62\) −3.03251e11 −0.678041
\(63\) −2.09947e11 −0.423054
\(64\) 5.13647e11 0.934318
\(65\) −7.49258e11 −1.23224
\(66\) 4.35291e11 0.648252
\(67\) 1.17389e12 1.58541 0.792704 0.609607i \(-0.208673\pi\)
0.792704 + 0.609607i \(0.208673\pi\)
\(68\) −2.25351e11 −0.276408
\(69\) 1.01298e12 1.13001
\(70\) 6.33513e11 0.643604
\(71\) −9.67396e11 −0.896242 −0.448121 0.893973i \(-0.647907\pi\)
−0.448121 + 0.893973i \(0.647907\pi\)
\(72\) 4.22398e11 0.357323
\(73\) 2.15669e12 1.66797 0.833986 0.551785i \(-0.186053\pi\)
0.833986 + 0.551785i \(0.186053\pi\)
\(74\) 6.46771e11 0.457872
\(75\) 4.63373e11 0.300630
\(76\) −6.31241e11 −0.375757
\(77\) −3.55805e12 −1.94546
\(78\) −1.49709e12 −0.752720
\(79\) 2.07035e12 0.958224 0.479112 0.877754i \(-0.340959\pi\)
0.479112 + 0.877754i \(0.340959\pi\)
\(80\) −5.22266e11 −0.222745
\(81\) 2.82430e11 0.111111
\(82\) 1.05932e12 0.384800
\(83\) 3.77349e12 1.26688 0.633440 0.773791i \(-0.281642\pi\)
0.633440 + 0.773791i \(0.281642\pi\)
\(84\) −1.09342e12 −0.339603
\(85\) 1.43569e12 0.412893
\(86\) −4.62654e9 −0.00123315
\(87\) −1.97982e12 −0.489496
\(88\) 7.15852e12 1.64318
\(89\) 1.92476e12 0.410527 0.205264 0.978707i \(-0.434195\pi\)
0.205264 + 0.978707i \(0.434195\pi\)
\(90\) −8.52228e11 −0.169036
\(91\) 1.22372e13 2.25898
\(92\) 5.27567e12 0.907103
\(93\) −3.33453e12 −0.534435
\(94\) −9.64504e12 −1.44203
\(95\) 4.02158e12 0.561298
\(96\) 3.70308e12 0.482836
\(97\) −7.77732e12 −0.948011 −0.474006 0.880522i \(-0.657192\pi\)
−0.474006 + 0.880522i \(0.657192\pi\)
\(98\) −3.92330e12 −0.447385
\(99\) 4.78643e12 0.510955
\(100\) 2.41328e12 0.241328
\(101\) 1.79650e13 1.68398 0.841992 0.539490i \(-0.181383\pi\)
0.841992 + 0.539490i \(0.181383\pi\)
\(102\) 2.86865e12 0.252218
\(103\) −1.68871e12 −0.139352 −0.0696760 0.997570i \(-0.522197\pi\)
−0.0696760 + 0.997570i \(0.522197\pi\)
\(104\) −2.46202e13 −1.90799
\(105\) 6.96607e12 0.507291
\(106\) 2.06893e13 1.41664
\(107\) 8.61080e12 0.554688 0.277344 0.960771i \(-0.410546\pi\)
0.277344 + 0.960771i \(0.410546\pi\)
\(108\) 1.47091e12 0.0891933
\(109\) −1.80048e12 −0.102829 −0.0514146 0.998677i \(-0.516373\pi\)
−0.0514146 + 0.998677i \(0.516373\pi\)
\(110\) −1.44430e13 −0.777330
\(111\) 7.11186e12 0.360897
\(112\) 8.52985e12 0.408342
\(113\) 6.79997e11 0.0307254 0.0153627 0.999882i \(-0.495110\pi\)
0.0153627 + 0.999882i \(0.495110\pi\)
\(114\) 8.03552e12 0.342873
\(115\) −3.36108e13 −1.35501
\(116\) −1.03110e13 −0.392938
\(117\) −1.64619e13 −0.593298
\(118\) 2.79645e12 0.0953618
\(119\) −2.34482e13 −0.756927
\(120\) −1.40152e13 −0.428471
\(121\) 4.65946e13 1.34968
\(122\) 2.08328e13 0.572018
\(123\) 1.16482e13 0.303301
\(124\) −1.73664e13 −0.429012
\(125\) −4.49015e13 −1.05280
\(126\) 1.39189e13 0.309882
\(127\) 1.58988e13 0.336233 0.168116 0.985767i \(-0.446232\pi\)
0.168116 + 0.985767i \(0.446232\pi\)
\(128\) 7.55927e12 0.151920
\(129\) −5.08732e10 −0.000971976 0
\(130\) 4.96737e13 0.902599
\(131\) 7.45244e13 1.28835 0.644177 0.764876i \(-0.277200\pi\)
0.644177 + 0.764876i \(0.277200\pi\)
\(132\) 2.49280e13 0.410164
\(133\) −6.56820e13 −1.02899
\(134\) −7.78256e13 −1.16129
\(135\) −9.37105e12 −0.133235
\(136\) 4.71760e13 0.639320
\(137\) −6.74566e12 −0.0871647 −0.0435823 0.999050i \(-0.513877\pi\)
−0.0435823 + 0.999050i \(0.513877\pi\)
\(138\) −6.71578e13 −0.827718
\(139\) 2.71419e13 0.319186 0.159593 0.987183i \(-0.448982\pi\)
0.159593 + 0.987183i \(0.448982\pi\)
\(140\) 3.62798e13 0.407223
\(141\) −1.06056e14 −1.13661
\(142\) 6.41357e13 0.656486
\(143\) −2.78986e14 −2.72834
\(144\) −1.14747e13 −0.107247
\(145\) 6.56905e13 0.586963
\(146\) −1.42982e14 −1.22177
\(147\) −4.31403e13 −0.352631
\(148\) 3.70390e13 0.289707
\(149\) 1.25880e14 0.942423 0.471211 0.882020i \(-0.343817\pi\)
0.471211 + 0.882020i \(0.343817\pi\)
\(150\) −3.07203e13 −0.220208
\(151\) −1.69344e14 −1.16257 −0.581285 0.813700i \(-0.697450\pi\)
−0.581285 + 0.813700i \(0.697450\pi\)
\(152\) 1.32147e14 0.869110
\(153\) 3.15435e13 0.198800
\(154\) 2.35888e14 1.42502
\(155\) 1.10640e14 0.640850
\(156\) −8.57348e13 −0.476264
\(157\) 7.46180e13 0.397645 0.198823 0.980035i \(-0.436288\pi\)
0.198823 + 0.980035i \(0.436288\pi\)
\(158\) −1.37258e14 −0.701888
\(159\) 2.27499e14 1.11660
\(160\) −1.22869e14 −0.578976
\(161\) 5.48944e14 2.48405
\(162\) −1.87243e13 −0.0813875
\(163\) −1.71344e14 −0.715564 −0.357782 0.933805i \(-0.616467\pi\)
−0.357782 + 0.933805i \(0.616467\pi\)
\(164\) 6.06644e13 0.243472
\(165\) −1.58814e14 −0.612695
\(166\) −2.50172e14 −0.927975
\(167\) −3.04444e13 −0.108605 −0.0543025 0.998525i \(-0.517294\pi\)
−0.0543025 + 0.998525i \(0.517294\pi\)
\(168\) 2.28902e14 0.785486
\(169\) 6.56639e14 2.16802
\(170\) −9.51822e13 −0.302439
\(171\) 8.83581e13 0.270254
\(172\) −2.64951e11 −0.000780244 0
\(173\) 2.75315e14 0.780784 0.390392 0.920649i \(-0.372340\pi\)
0.390392 + 0.920649i \(0.372340\pi\)
\(174\) 1.31256e14 0.358550
\(175\) 2.51107e14 0.660862
\(176\) −1.94466e14 −0.493186
\(177\) 3.07496e13 0.0751646
\(178\) −1.27606e14 −0.300706
\(179\) −1.16652e14 −0.265063 −0.132531 0.991179i \(-0.542311\pi\)
−0.132531 + 0.991179i \(0.542311\pi\)
\(180\) −4.88050e13 −0.106953
\(181\) 4.23209e14 0.894631 0.447316 0.894376i \(-0.352380\pi\)
0.447316 + 0.894376i \(0.352380\pi\)
\(182\) −8.11289e14 −1.65467
\(183\) 2.29077e14 0.450867
\(184\) −1.10443e15 −2.09809
\(185\) −2.35972e14 −0.432758
\(186\) 2.21070e14 0.391467
\(187\) 5.34579e14 0.914200
\(188\) −5.52348e14 −0.912403
\(189\) 1.53051e14 0.244251
\(190\) −2.66620e14 −0.411144
\(191\) 3.91423e13 0.0583350 0.0291675 0.999575i \(-0.490714\pi\)
0.0291675 + 0.999575i \(0.490714\pi\)
\(192\) −3.74448e14 −0.539429
\(193\) −1.27389e15 −1.77423 −0.887114 0.461550i \(-0.847294\pi\)
−0.887114 + 0.461550i \(0.847294\pi\)
\(194\) 5.15614e14 0.694407
\(195\) 5.46209e14 0.711433
\(196\) −2.24678e14 −0.283071
\(197\) −1.36196e15 −1.66010 −0.830052 0.557686i \(-0.811689\pi\)
−0.830052 + 0.557686i \(0.811689\pi\)
\(198\) −3.17327e14 −0.374269
\(199\) −1.74517e13 −0.0199202 −0.00996010 0.999950i \(-0.503170\pi\)
−0.00996010 + 0.999950i \(0.503170\pi\)
\(200\) −5.05208e14 −0.558181
\(201\) −8.55765e14 −0.915336
\(202\) −1.19103e15 −1.23350
\(203\) −1.07288e15 −1.07604
\(204\) 1.64281e14 0.159584
\(205\) −3.86488e14 −0.363694
\(206\) 1.11957e14 0.102074
\(207\) −7.38463e14 −0.652411
\(208\) 6.68825e14 0.572665
\(209\) 1.49744e15 1.24279
\(210\) −4.61831e14 −0.371585
\(211\) −1.31001e15 −1.02197 −0.510986 0.859589i \(-0.670720\pi\)
−0.510986 + 0.859589i \(0.670720\pi\)
\(212\) 1.18483e15 0.896339
\(213\) 7.05232e14 0.517445
\(214\) −5.70872e14 −0.406302
\(215\) 1.68798e12 0.00116551
\(216\) −3.07928e14 −0.206300
\(217\) −1.80701e15 −1.17482
\(218\) 1.19367e14 0.0753211
\(219\) −1.57223e15 −0.963004
\(220\) −8.27116e14 −0.491834
\(221\) −1.83857e15 −1.06153
\(222\) −4.71496e14 −0.264353
\(223\) −2.50006e15 −1.36135 −0.680675 0.732586i \(-0.738313\pi\)
−0.680675 + 0.732586i \(0.738313\pi\)
\(224\) 2.00673e15 1.06140
\(225\) −3.37799e14 −0.173569
\(226\) −4.50819e13 −0.0225060
\(227\) −3.09622e15 −1.50198 −0.750990 0.660313i \(-0.770424\pi\)
−0.750990 + 0.660313i \(0.770424\pi\)
\(228\) 4.60175e14 0.216943
\(229\) 2.26959e15 1.03996 0.519980 0.854179i \(-0.325940\pi\)
0.519980 + 0.854179i \(0.325940\pi\)
\(230\) 2.22830e15 0.992530
\(231\) 2.59381e15 1.12321
\(232\) 2.15856e15 0.908849
\(233\) −6.15223e14 −0.251895 −0.125947 0.992037i \(-0.540197\pi\)
−0.125947 + 0.992037i \(0.540197\pi\)
\(234\) 1.09138e15 0.434583
\(235\) 3.51896e15 1.36293
\(236\) 1.60146e14 0.0603376
\(237\) −1.50928e15 −0.553231
\(238\) 1.55455e15 0.554440
\(239\) −1.81888e15 −0.631272 −0.315636 0.948880i \(-0.602218\pi\)
−0.315636 + 0.948880i \(0.602218\pi\)
\(240\) 3.80732e14 0.128602
\(241\) 4.87508e15 1.60277 0.801384 0.598150i \(-0.204097\pi\)
0.801384 + 0.598150i \(0.204097\pi\)
\(242\) −3.08909e15 −0.988623
\(243\) −2.05891e14 −0.0641500
\(244\) 1.19305e15 0.361929
\(245\) 1.43140e15 0.422846
\(246\) −7.72241e14 −0.222165
\(247\) −5.15012e15 −1.44307
\(248\) 3.63558e15 0.992287
\(249\) −2.75088e15 −0.731434
\(250\) 2.97685e15 0.771163
\(251\) −3.95345e15 −0.997922 −0.498961 0.866624i \(-0.666285\pi\)
−0.498961 + 0.866624i \(0.666285\pi\)
\(252\) 7.97102e14 0.196070
\(253\) −1.25150e16 −3.00018
\(254\) −1.05405e15 −0.246286
\(255\) −1.04662e15 −0.238384
\(256\) −4.70895e15 −1.04560
\(257\) −3.43727e15 −0.744130 −0.372065 0.928207i \(-0.621350\pi\)
−0.372065 + 0.928207i \(0.621350\pi\)
\(258\) 3.37275e12 0.000711960 0
\(259\) 3.85399e15 0.793344
\(260\) 2.84469e15 0.571095
\(261\) 1.44329e15 0.282611
\(262\) −4.94076e15 −0.943704
\(263\) −9.04159e15 −1.68474 −0.842369 0.538901i \(-0.818840\pi\)
−0.842369 + 0.538901i \(0.818840\pi\)
\(264\) −5.21856e15 −0.948692
\(265\) −7.54844e15 −1.33893
\(266\) 4.35453e15 0.753721
\(267\) −1.40315e15 −0.237018
\(268\) −4.45688e15 −0.734776
\(269\) −9.00168e15 −1.44855 −0.724275 0.689511i \(-0.757826\pi\)
−0.724275 + 0.689511i \(0.757826\pi\)
\(270\) 6.21274e14 0.0975931
\(271\) 5.02090e14 0.0769984 0.0384992 0.999259i \(-0.487742\pi\)
0.0384992 + 0.999259i \(0.487742\pi\)
\(272\) −1.28157e15 −0.191886
\(273\) −8.92089e15 −1.30422
\(274\) 4.47218e14 0.0638470
\(275\) −5.72480e15 −0.798174
\(276\) −3.84596e15 −0.523716
\(277\) 8.16380e15 1.08586 0.542930 0.839778i \(-0.317315\pi\)
0.542930 + 0.839778i \(0.317315\pi\)
\(278\) −1.79943e15 −0.233800
\(279\) 2.43087e15 0.308556
\(280\) −7.59499e15 −0.941889
\(281\) 3.10827e15 0.376641 0.188320 0.982108i \(-0.439696\pi\)
0.188320 + 0.982108i \(0.439696\pi\)
\(282\) 7.03123e15 0.832554
\(283\) 1.18849e15 0.137525 0.0687626 0.997633i \(-0.478095\pi\)
0.0687626 + 0.997633i \(0.478095\pi\)
\(284\) 3.67289e15 0.415374
\(285\) −2.93173e15 −0.324066
\(286\) 1.84960e16 1.99847
\(287\) 6.31226e15 0.666734
\(288\) −2.69954e15 −0.278765
\(289\) −6.38160e15 −0.644308
\(290\) −4.35510e15 −0.429943
\(291\) 5.66966e15 0.547335
\(292\) −8.18826e15 −0.773042
\(293\) −1.32316e16 −1.22172 −0.610862 0.791737i \(-0.709177\pi\)
−0.610862 + 0.791737i \(0.709177\pi\)
\(294\) 2.86008e15 0.258298
\(295\) −1.02028e15 −0.0901311
\(296\) −7.75393e15 −0.670079
\(297\) −3.48931e15 −0.295000
\(298\) −8.34549e15 −0.690313
\(299\) 4.30427e16 3.48367
\(300\) −1.75928e15 −0.139331
\(301\) −2.75687e13 −0.00213665
\(302\) 1.12270e16 0.851568
\(303\) −1.30965e16 −0.972249
\(304\) −3.58986e15 −0.260855
\(305\) −7.60079e15 −0.540642
\(306\) −2.09125e15 −0.145618
\(307\) 6.62499e15 0.451633 0.225817 0.974170i \(-0.427495\pi\)
0.225817 + 0.974170i \(0.427495\pi\)
\(308\) 1.35088e16 0.901645
\(309\) 1.23107e15 0.0804549
\(310\) −7.33512e15 −0.469414
\(311\) −1.17605e16 −0.737029 −0.368514 0.929622i \(-0.620133\pi\)
−0.368514 + 0.929622i \(0.620133\pi\)
\(312\) 1.79482e16 1.10158
\(313\) −2.09100e15 −0.125695 −0.0628473 0.998023i \(-0.520018\pi\)
−0.0628473 + 0.998023i \(0.520018\pi\)
\(314\) −4.94696e15 −0.291270
\(315\) −5.07827e15 −0.292885
\(316\) −7.86045e15 −0.444101
\(317\) 9.00659e15 0.498512 0.249256 0.968438i \(-0.419814\pi\)
0.249256 + 0.968438i \(0.419814\pi\)
\(318\) −1.50825e16 −0.817896
\(319\) 2.44599e16 1.29961
\(320\) 1.24242e16 0.646838
\(321\) −6.27728e15 −0.320250
\(322\) −3.63935e16 −1.81953
\(323\) 9.86839e15 0.483537
\(324\) −1.07229e15 −0.0514958
\(325\) 1.96892e16 0.926802
\(326\) 1.13596e16 0.524141
\(327\) 1.31255e15 0.0593685
\(328\) −1.26998e16 −0.563140
\(329\) −5.74730e16 −2.49856
\(330\) 1.05290e16 0.448791
\(331\) −1.49381e16 −0.624330 −0.312165 0.950028i \(-0.601054\pi\)
−0.312165 + 0.950028i \(0.601054\pi\)
\(332\) −1.43267e16 −0.587151
\(333\) −5.18454e15 −0.208364
\(334\) 2.01838e15 0.0795518
\(335\) 2.83944e16 1.09759
\(336\) −6.21826e15 −0.235756
\(337\) −7.32859e15 −0.272537 −0.136269 0.990672i \(-0.543511\pi\)
−0.136269 + 0.990672i \(0.543511\pi\)
\(338\) −4.35334e16 −1.58805
\(339\) −4.95718e14 −0.0177393
\(340\) −5.45085e15 −0.191360
\(341\) 4.11968e16 1.41893
\(342\) −5.85790e15 −0.197958
\(343\) 1.48981e16 0.493990
\(344\) 5.54661e13 0.00180467
\(345\) 2.45023e16 0.782317
\(346\) −1.82526e16 −0.571914
\(347\) 5.06850e16 1.55861 0.779306 0.626643i \(-0.215572\pi\)
0.779306 + 0.626643i \(0.215572\pi\)
\(348\) 7.51672e15 0.226863
\(349\) −4.77340e15 −0.141404 −0.0707022 0.997497i \(-0.522524\pi\)
−0.0707022 + 0.997497i \(0.522524\pi\)
\(350\) −1.66477e16 −0.484073
\(351\) 1.20007e16 0.342541
\(352\) −4.57501e16 −1.28193
\(353\) 2.66414e16 0.732860 0.366430 0.930446i \(-0.380580\pi\)
0.366430 + 0.930446i \(0.380580\pi\)
\(354\) −2.03861e15 −0.0550571
\(355\) −2.33997e16 −0.620477
\(356\) −7.30771e15 −0.190264
\(357\) 1.70937e16 0.437012
\(358\) 7.73372e15 0.194155
\(359\) 2.90946e16 0.717296 0.358648 0.933473i \(-0.383238\pi\)
0.358648 + 0.933473i \(0.383238\pi\)
\(360\) 1.02171e16 0.247378
\(361\) −1.44101e16 −0.342666
\(362\) −2.80576e16 −0.655306
\(363\) −3.39674e16 −0.779238
\(364\) −4.64606e16 −1.04695
\(365\) 5.21667e16 1.15475
\(366\) −1.51871e16 −0.330255
\(367\) 4.94440e16 1.05629 0.528147 0.849153i \(-0.322887\pi\)
0.528147 + 0.849153i \(0.322887\pi\)
\(368\) 3.00027e16 0.629722
\(369\) −8.49151e15 −0.175111
\(370\) 1.56443e16 0.316990
\(371\) 1.23284e17 2.45457
\(372\) 1.26601e16 0.247690
\(373\) −1.42386e16 −0.273754 −0.136877 0.990588i \(-0.543707\pi\)
−0.136877 + 0.990588i \(0.543707\pi\)
\(374\) −3.54411e16 −0.669640
\(375\) 3.27332e16 0.607835
\(376\) 1.15631e17 2.11035
\(377\) −8.41246e16 −1.50905
\(378\) −1.01469e16 −0.178911
\(379\) −1.01224e17 −1.75440 −0.877201 0.480123i \(-0.840592\pi\)
−0.877201 + 0.480123i \(0.840592\pi\)
\(380\) −1.52687e16 −0.260140
\(381\) −1.15902e16 −0.194124
\(382\) −2.59502e15 −0.0427297
\(383\) −1.79418e15 −0.0290452 −0.0145226 0.999895i \(-0.504623\pi\)
−0.0145226 + 0.999895i \(0.504623\pi\)
\(384\) −5.51071e15 −0.0877111
\(385\) −8.60631e16 −1.34686
\(386\) 8.44554e16 1.29960
\(387\) 3.70865e13 0.000561171 0
\(388\) 2.95280e16 0.439367
\(389\) 6.66866e16 0.975812 0.487906 0.872896i \(-0.337761\pi\)
0.487906 + 0.872896i \(0.337761\pi\)
\(390\) −3.62121e16 −0.521116
\(391\) −8.24761e16 −1.16729
\(392\) 4.70352e16 0.654731
\(393\) −5.43283e16 −0.743832
\(394\) 9.02944e16 1.21601
\(395\) 5.00782e16 0.663388
\(396\) −1.81725e16 −0.236808
\(397\) 1.14660e17 1.46985 0.734927 0.678146i \(-0.237216\pi\)
0.734927 + 0.678146i \(0.237216\pi\)
\(398\) 1.15700e15 0.0145913
\(399\) 4.78822e16 0.594087
\(400\) 1.37243e16 0.167533
\(401\) −1.18945e17 −1.42859 −0.714295 0.699845i \(-0.753252\pi\)
−0.714295 + 0.699845i \(0.753252\pi\)
\(402\) 5.67349e16 0.670472
\(403\) −1.41688e17 −1.64759
\(404\) −6.82073e16 −0.780462
\(405\) 6.83150e15 0.0769233
\(406\) 7.11291e16 0.788185
\(407\) −8.78642e16 −0.958183
\(408\) −3.43913e16 −0.369112
\(409\) 9.34144e16 0.986762 0.493381 0.869813i \(-0.335761\pi\)
0.493381 + 0.869813i \(0.335761\pi\)
\(410\) 2.56231e16 0.266401
\(411\) 4.91758e15 0.0503245
\(412\) 6.41149e15 0.0645843
\(413\) 1.66635e16 0.165231
\(414\) 4.89580e16 0.477883
\(415\) 9.12744e16 0.877074
\(416\) 1.57348e17 1.48852
\(417\) −1.97864e16 −0.184282
\(418\) −9.92758e16 −0.910327
\(419\) −3.90001e16 −0.352107 −0.176053 0.984381i \(-0.556333\pi\)
−0.176053 + 0.984381i \(0.556333\pi\)
\(420\) −2.64479e16 −0.235110
\(421\) 8.00151e16 0.700388 0.350194 0.936677i \(-0.386116\pi\)
0.350194 + 0.936677i \(0.386116\pi\)
\(422\) 8.68501e16 0.748582
\(423\) 7.73150e16 0.656223
\(424\) −2.48038e17 −2.07319
\(425\) −3.77275e16 −0.310549
\(426\) −4.67549e16 −0.379022
\(427\) 1.24139e17 0.991121
\(428\) −3.26925e16 −0.257077
\(429\) 2.03381e17 1.57521
\(430\) −1.11908e14 −0.000853723 0
\(431\) −2.40571e16 −0.180776 −0.0903881 0.995907i \(-0.528811\pi\)
−0.0903881 + 0.995907i \(0.528811\pi\)
\(432\) 8.36506e15 0.0619191
\(433\) 7.32442e16 0.534075 0.267037 0.963686i \(-0.413955\pi\)
0.267037 + 0.963686i \(0.413955\pi\)
\(434\) 1.19800e17 0.860544
\(435\) −4.78884e16 −0.338883
\(436\) 6.83586e15 0.0476574
\(437\) −2.31028e17 −1.58685
\(438\) 1.04234e17 0.705389
\(439\) 1.59228e16 0.106169 0.0530847 0.998590i \(-0.483095\pi\)
0.0530847 + 0.998590i \(0.483095\pi\)
\(440\) 1.73153e17 1.13759
\(441\) 3.14493e16 0.203592
\(442\) 1.21892e17 0.777555
\(443\) 1.43251e16 0.0900480 0.0450240 0.998986i \(-0.485664\pi\)
0.0450240 + 0.998986i \(0.485664\pi\)
\(444\) −2.70014e16 −0.167262
\(445\) 4.65568e16 0.284212
\(446\) 1.65747e17 0.997171
\(447\) −9.17665e16 −0.544108
\(448\) −2.02917e17 −1.18580
\(449\) −2.20473e17 −1.26986 −0.634928 0.772572i \(-0.718970\pi\)
−0.634928 + 0.772572i \(0.718970\pi\)
\(450\) 2.23951e16 0.127137
\(451\) −1.43909e17 −0.805266
\(452\) −2.58173e15 −0.0142400
\(453\) 1.23452e17 0.671210
\(454\) 2.05271e17 1.10018
\(455\) 2.95996e17 1.56391
\(456\) −9.63353e16 −0.501781
\(457\) −1.42337e17 −0.730906 −0.365453 0.930830i \(-0.619086\pi\)
−0.365453 + 0.930830i \(0.619086\pi\)
\(458\) −1.50467e17 −0.761757
\(459\) −2.29952e16 −0.114777
\(460\) 1.27610e17 0.627997
\(461\) 1.91520e17 0.929302 0.464651 0.885494i \(-0.346180\pi\)
0.464651 + 0.885494i \(0.346180\pi\)
\(462\) −1.71963e17 −0.822738
\(463\) −2.76794e16 −0.130581 −0.0652904 0.997866i \(-0.520797\pi\)
−0.0652904 + 0.997866i \(0.520797\pi\)
\(464\) −5.86386e16 −0.272783
\(465\) −8.06566e16 −0.369995
\(466\) 4.07876e16 0.184510
\(467\) −5.95978e16 −0.265871 −0.132935 0.991125i \(-0.542440\pi\)
−0.132935 + 0.991125i \(0.542440\pi\)
\(468\) 6.25007e16 0.274971
\(469\) −4.63748e17 −2.01214
\(470\) −2.33297e17 −0.998329
\(471\) −5.43965e16 −0.229581
\(472\) −3.35258e16 −0.139558
\(473\) 6.28518e14 0.00258060
\(474\) 1.00061e17 0.405235
\(475\) −1.05680e17 −0.422169
\(476\) 8.90253e16 0.350807
\(477\) −1.65847e17 −0.644669
\(478\) 1.20586e17 0.462399
\(479\) −1.29801e17 −0.491019 −0.245509 0.969394i \(-0.578955\pi\)
−0.245509 + 0.969394i \(0.578955\pi\)
\(480\) 8.95712e16 0.334272
\(481\) 3.02191e17 1.11260
\(482\) −3.23204e17 −1.17401
\(483\) −4.00180e17 −1.43417
\(484\) −1.76905e17 −0.625525
\(485\) −1.88120e17 −0.656318
\(486\) 1.36500e16 0.0469891
\(487\) −1.65002e17 −0.560469 −0.280235 0.959932i \(-0.590412\pi\)
−0.280235 + 0.959932i \(0.590412\pi\)
\(488\) −2.49758e17 −0.837127
\(489\) 1.24909e17 0.413131
\(490\) −9.48980e16 −0.309729
\(491\) 3.60927e17 1.16249 0.581245 0.813729i \(-0.302566\pi\)
0.581245 + 0.813729i \(0.302566\pi\)
\(492\) −4.42244e16 −0.140569
\(493\) 1.61195e17 0.505646
\(494\) 3.41438e17 1.05703
\(495\) 1.15776e17 0.353740
\(496\) −9.87627e16 −0.297826
\(497\) 3.82172e17 1.13748
\(498\) 1.82375e17 0.535766
\(499\) −1.29018e16 −0.0374109 −0.0187054 0.999825i \(-0.505954\pi\)
−0.0187054 + 0.999825i \(0.505954\pi\)
\(500\) 1.70477e17 0.487933
\(501\) 2.21939e16 0.0627031
\(502\) 2.62103e17 0.730966
\(503\) 5.41825e17 1.49165 0.745825 0.666142i \(-0.232056\pi\)
0.745825 + 0.666142i \(0.232056\pi\)
\(504\) −1.66869e17 −0.453501
\(505\) 4.34543e17 1.16584
\(506\) 8.29708e17 2.19759
\(507\) −4.78690e17 −1.25171
\(508\) −6.03626e16 −0.155831
\(509\) −9.65207e16 −0.246011 −0.123006 0.992406i \(-0.539253\pi\)
−0.123006 + 0.992406i \(0.539253\pi\)
\(510\) 6.93878e16 0.174613
\(511\) −8.52005e17 −2.11693
\(512\) 2.50265e17 0.613967
\(513\) −6.44131e16 −0.156031
\(514\) 2.27882e17 0.545066
\(515\) −4.08470e16 −0.0964748
\(516\) 1.93149e14 0.000450474 0
\(517\) 1.31028e18 3.01771
\(518\) −2.55509e17 −0.581115
\(519\) −2.00705e17 −0.450786
\(520\) −5.95522e17 −1.32092
\(521\) −2.36741e17 −0.518596 −0.259298 0.965797i \(-0.583491\pi\)
−0.259298 + 0.965797i \(0.583491\pi\)
\(522\) −9.56858e16 −0.207009
\(523\) −9.65494e16 −0.206295 −0.103148 0.994666i \(-0.532891\pi\)
−0.103148 + 0.994666i \(0.532891\pi\)
\(524\) −2.82945e17 −0.597103
\(525\) −1.83057e17 −0.381549
\(526\) 5.99432e17 1.23405
\(527\) 2.71495e17 0.552068
\(528\) 1.41766e17 0.284741
\(529\) 1.42681e18 2.83076
\(530\) 5.00440e17 0.980752
\(531\) −2.24165e16 −0.0433963
\(532\) 2.49373e17 0.476897
\(533\) 4.94944e17 0.935037
\(534\) 9.30250e16 0.173613
\(535\) 2.08281e17 0.384016
\(536\) 9.33026e17 1.69951
\(537\) 8.50395e16 0.153034
\(538\) 5.96786e17 1.06105
\(539\) 5.32982e17 0.936237
\(540\) 3.55789e16 0.0617494
\(541\) −5.17097e17 −0.886727 −0.443363 0.896342i \(-0.646215\pi\)
−0.443363 + 0.896342i \(0.646215\pi\)
\(542\) −3.32872e16 −0.0564003
\(543\) −3.08519e17 −0.516516
\(544\) −3.01502e17 −0.498766
\(545\) −4.35506e16 −0.0711897
\(546\) 5.91430e17 0.955325
\(547\) −1.17641e18 −1.87776 −0.938879 0.344246i \(-0.888135\pi\)
−0.938879 + 0.344246i \(0.888135\pi\)
\(548\) 2.56111e16 0.0403975
\(549\) −1.66997e17 −0.260308
\(550\) 3.79538e17 0.584652
\(551\) 4.51532e17 0.687390
\(552\) 8.05133e17 1.21133
\(553\) −8.17896e17 −1.21614
\(554\) −5.41237e17 −0.795379
\(555\) 1.72024e17 0.249853
\(556\) −1.03049e17 −0.147930
\(557\) −6.58364e17 −0.934130 −0.467065 0.884223i \(-0.654689\pi\)
−0.467065 + 0.884223i \(0.654689\pi\)
\(558\) −1.61160e17 −0.226014
\(559\) −2.16166e15 −0.00299647
\(560\) 2.06323e17 0.282699
\(561\) −3.89708e17 −0.527813
\(562\) −2.06069e17 −0.275885
\(563\) 7.46468e16 0.0987885 0.0493943 0.998779i \(-0.484271\pi\)
0.0493943 + 0.998779i \(0.484271\pi\)
\(564\) 4.02662e17 0.526776
\(565\) 1.64480e16 0.0212715
\(566\) −7.87933e16 −0.100736
\(567\) −1.11574e17 −0.141018
\(568\) −7.68902e17 −0.960742
\(569\) −1.32614e16 −0.0163818 −0.00819088 0.999966i \(-0.502607\pi\)
−0.00819088 + 0.999966i \(0.502607\pi\)
\(570\) 1.94366e17 0.237374
\(571\) −8.32634e17 −1.00535 −0.502677 0.864474i \(-0.667652\pi\)
−0.502677 + 0.864474i \(0.667652\pi\)
\(572\) 1.05922e18 1.26448
\(573\) −2.85347e16 −0.0336797
\(574\) −4.18485e17 −0.488374
\(575\) 8.83236e17 1.01914
\(576\) 2.72973e17 0.311439
\(577\) 1.45763e18 1.64439 0.822196 0.569205i \(-0.192749\pi\)
0.822196 + 0.569205i \(0.192749\pi\)
\(578\) 4.23082e17 0.471948
\(579\) 9.28666e17 1.02435
\(580\) −2.49406e17 −0.272035
\(581\) −1.49073e18 −1.60788
\(582\) −3.75883e17 −0.400916
\(583\) −2.81066e18 −2.96458
\(584\) 1.71417e18 1.78801
\(585\) −3.98186e17 −0.410746
\(586\) 8.77219e17 0.894898
\(587\) −1.61649e18 −1.63089 −0.815444 0.578836i \(-0.803507\pi\)
−0.815444 + 0.578836i \(0.803507\pi\)
\(588\) 1.63790e17 0.163431
\(589\) 7.60498e17 0.750496
\(590\) 6.76415e16 0.0660199
\(591\) 9.92872e17 0.958461
\(592\) 2.10641e17 0.201118
\(593\) 1.67586e18 1.58264 0.791321 0.611401i \(-0.209394\pi\)
0.791321 + 0.611401i \(0.209394\pi\)
\(594\) 2.31331e17 0.216084
\(595\) −5.67173e17 −0.524029
\(596\) −4.77926e17 −0.436777
\(597\) 1.27223e16 0.0115009
\(598\) −2.85361e18 −2.55174
\(599\) −1.11637e18 −0.987490 −0.493745 0.869607i \(-0.664372\pi\)
−0.493745 + 0.869607i \(0.664372\pi\)
\(600\) 3.68296e17 0.322266
\(601\) −1.51121e18 −1.30810 −0.654050 0.756451i \(-0.726931\pi\)
−0.654050 + 0.756451i \(0.726931\pi\)
\(602\) 1.82773e15 0.00156507
\(603\) 6.23853e17 0.528469
\(604\) 6.42944e17 0.538807
\(605\) 1.12704e18 0.934396
\(606\) 8.68260e17 0.712160
\(607\) −1.94403e18 −1.57753 −0.788765 0.614695i \(-0.789279\pi\)
−0.788765 + 0.614695i \(0.789279\pi\)
\(608\) −8.44552e17 −0.678037
\(609\) 7.82131e17 0.621251
\(610\) 5.03911e17 0.396014
\(611\) −4.50645e18 −3.50402
\(612\) −1.19761e17 −0.0921360
\(613\) −1.24029e18 −0.944124 −0.472062 0.881565i \(-0.656490\pi\)
−0.472062 + 0.881565i \(0.656490\pi\)
\(614\) −4.39219e17 −0.330816
\(615\) 2.81750e17 0.209979
\(616\) −2.82799e18 −2.08547
\(617\) 4.04176e15 0.00294929 0.00147464 0.999999i \(-0.499531\pi\)
0.00147464 + 0.999999i \(0.499531\pi\)
\(618\) −8.16165e16 −0.0589322
\(619\) 3.05627e17 0.218374 0.109187 0.994021i \(-0.465175\pi\)
0.109187 + 0.994021i \(0.465175\pi\)
\(620\) −4.20065e17 −0.297009
\(621\) 5.38339e17 0.376670
\(622\) 7.79690e17 0.539864
\(623\) −7.60382e17 −0.521026
\(624\) −4.87573e17 −0.330628
\(625\) −3.10179e17 −0.208158
\(626\) 1.38628e17 0.0920697
\(627\) −1.09163e18 −0.717524
\(628\) −2.83301e17 −0.184293
\(629\) −5.79042e17 −0.372804
\(630\) 3.36675e17 0.214535
\(631\) 1.46562e18 0.924337 0.462168 0.886792i \(-0.347072\pi\)
0.462168 + 0.886792i \(0.347072\pi\)
\(632\) 1.64555e18 1.02719
\(633\) 9.54999e17 0.590036
\(634\) −5.97112e17 −0.365154
\(635\) 3.84565e17 0.232777
\(636\) −8.63740e17 −0.517502
\(637\) −1.83308e18 −1.08711
\(638\) −1.62162e18 −0.951951
\(639\) −5.14114e17 −0.298747
\(640\) 1.82846e17 0.105176
\(641\) −1.04197e18 −0.593307 −0.296653 0.954985i \(-0.595871\pi\)
−0.296653 + 0.954985i \(0.595871\pi\)
\(642\) 4.16166e17 0.234579
\(643\) 3.04390e17 0.169847 0.0849237 0.996387i \(-0.472935\pi\)
0.0849237 + 0.996387i \(0.472935\pi\)
\(644\) −2.08417e18 −1.15126
\(645\) −1.23054e15 −0.000672909 0
\(646\) −6.54247e17 −0.354185
\(647\) −2.96662e18 −1.58995 −0.794976 0.606641i \(-0.792517\pi\)
−0.794976 + 0.606641i \(0.792517\pi\)
\(648\) 2.24480e17 0.119108
\(649\) −3.79900e17 −0.199562
\(650\) −1.30534e18 −0.678871
\(651\) 1.31731e18 0.678285
\(652\) 6.50537e17 0.331636
\(653\) −1.67294e18 −0.844394 −0.422197 0.906504i \(-0.638741\pi\)
−0.422197 + 0.906504i \(0.638741\pi\)
\(654\) −8.70185e16 −0.0434867
\(655\) 1.80262e18 0.891941
\(656\) 3.44998e17 0.169021
\(657\) 1.14615e18 0.555991
\(658\) 3.81030e18 1.83017
\(659\) −2.51358e18 −1.19547 −0.597733 0.801695i \(-0.703932\pi\)
−0.597733 + 0.801695i \(0.703932\pi\)
\(660\) 6.02968e17 0.283961
\(661\) 2.08332e18 0.971507 0.485753 0.874096i \(-0.338545\pi\)
0.485753 + 0.874096i \(0.338545\pi\)
\(662\) 9.90356e17 0.457314
\(663\) 1.34032e18 0.612872
\(664\) 2.99923e18 1.35806
\(665\) −1.58874e18 −0.712379
\(666\) 3.43721e17 0.152624
\(667\) −3.77373e18 −1.65941
\(668\) 1.15587e17 0.0503343
\(669\) 1.82255e18 0.785975
\(670\) −1.88247e18 −0.803974
\(671\) −2.83015e18 −1.19705
\(672\) −1.46291e18 −0.612798
\(673\) 1.90322e18 0.789570 0.394785 0.918774i \(-0.370819\pi\)
0.394785 + 0.918774i \(0.370819\pi\)
\(674\) 4.85865e17 0.199630
\(675\) 2.46255e17 0.100210
\(676\) −2.49305e18 −1.00479
\(677\) 2.04877e18 0.817838 0.408919 0.912571i \(-0.365906\pi\)
0.408919 + 0.912571i \(0.365906\pi\)
\(678\) 3.28647e16 0.0129938
\(679\) 3.07245e18 1.20318
\(680\) 1.14111e18 0.442608
\(681\) 2.25715e18 0.867169
\(682\) −2.73123e18 −1.03935
\(683\) −1.53611e18 −0.579012 −0.289506 0.957176i \(-0.593491\pi\)
−0.289506 + 0.957176i \(0.593491\pi\)
\(684\) −3.35468e17 −0.125252
\(685\) −1.63166e17 −0.0603450
\(686\) −9.87700e17 −0.361841
\(687\) −1.65453e18 −0.600421
\(688\) −1.50677e15 −0.000541655 0
\(689\) 9.66668e18 3.44233
\(690\) −1.62443e18 −0.573037
\(691\) 7.30668e17 0.255336 0.127668 0.991817i \(-0.459251\pi\)
0.127668 + 0.991817i \(0.459251\pi\)
\(692\) −1.04528e18 −0.361863
\(693\) −1.89089e18 −0.648486
\(694\) −3.36028e18 −1.14166
\(695\) 6.56516e17 0.220976
\(696\) −1.57359e18 −0.524724
\(697\) −9.48385e17 −0.313308
\(698\) 3.16463e17 0.103577
\(699\) 4.48498e17 0.145431
\(700\) −9.53371e17 −0.306284
\(701\) −5.29959e18 −1.68684 −0.843422 0.537251i \(-0.819463\pi\)
−0.843422 + 0.537251i \(0.819463\pi\)
\(702\) −7.95616e17 −0.250907
\(703\) −1.62199e18 −0.506801
\(704\) 4.62617e18 1.43218
\(705\) −2.56532e18 −0.786888
\(706\) −1.76625e18 −0.536811
\(707\) −7.09711e18 −2.13725
\(708\) −1.16746e17 −0.0348359
\(709\) −3.40661e17 −0.100722 −0.0503608 0.998731i \(-0.516037\pi\)
−0.0503608 + 0.998731i \(0.516037\pi\)
\(710\) 1.55133e18 0.454492
\(711\) 1.10027e18 0.319408
\(712\) 1.52983e18 0.440072
\(713\) −6.35594e18 −1.81175
\(714\) −1.13327e18 −0.320106
\(715\) −6.74820e18 −1.88886
\(716\) 4.42892e17 0.122846
\(717\) 1.32596e18 0.364465
\(718\) −1.92889e18 −0.525411
\(719\) 3.22541e18 0.870656 0.435328 0.900272i \(-0.356632\pi\)
0.435328 + 0.900272i \(0.356632\pi\)
\(720\) −2.77554e17 −0.0742482
\(721\) 6.67129e17 0.176860
\(722\) 9.55352e17 0.250999
\(723\) −3.55393e18 −0.925359
\(724\) −1.60679e18 −0.414628
\(725\) −1.72624e18 −0.441472
\(726\) 2.25195e18 0.570782
\(727\) −4.66127e18 −1.17093 −0.585465 0.810698i \(-0.699088\pi\)
−0.585465 + 0.810698i \(0.699088\pi\)
\(728\) 9.72629e18 2.42155
\(729\) 1.50095e17 0.0370370
\(730\) −3.45850e18 −0.845843
\(731\) 4.14206e15 0.00100404
\(732\) −8.69731e17 −0.208960
\(733\) −3.40711e18 −0.811355 −0.405677 0.914016i \(-0.632964\pi\)
−0.405677 + 0.914016i \(0.632964\pi\)
\(734\) −3.27800e18 −0.773722
\(735\) −1.04349e18 −0.244130
\(736\) 7.05844e18 1.63683
\(737\) 1.05727e19 2.43022
\(738\) 5.62964e17 0.128267
\(739\) 2.73641e18 0.618005 0.309003 0.951061i \(-0.400005\pi\)
0.309003 + 0.951061i \(0.400005\pi\)
\(740\) 8.95912e17 0.200567
\(741\) 3.75444e18 0.833156
\(742\) −8.17338e18 −1.79794
\(743\) 1.64585e18 0.358892 0.179446 0.983768i \(-0.442569\pi\)
0.179446 + 0.983768i \(0.442569\pi\)
\(744\) −2.65033e18 −0.572897
\(745\) 3.04482e18 0.652449
\(746\) 9.43982e17 0.200522
\(747\) 2.00539e18 0.422294
\(748\) −2.02962e18 −0.423697
\(749\) −3.40172e18 −0.703990
\(750\) −2.17012e18 −0.445231
\(751\) −8.27237e18 −1.68256 −0.841280 0.540600i \(-0.818197\pi\)
−0.841280 + 0.540600i \(0.818197\pi\)
\(752\) −3.14120e18 −0.633402
\(753\) 2.88206e18 0.576151
\(754\) 5.57722e18 1.10536
\(755\) −4.09614e18 −0.804859
\(756\) −5.81087e17 −0.113201
\(757\) −7.54897e18 −1.45802 −0.729012 0.684501i \(-0.760020\pi\)
−0.729012 + 0.684501i \(0.760020\pi\)
\(758\) 6.71088e18 1.28508
\(759\) 9.12342e18 1.73215
\(760\) 3.19642e18 0.601694
\(761\) 7.12996e18 1.33072 0.665360 0.746522i \(-0.268278\pi\)
0.665360 + 0.746522i \(0.268278\pi\)
\(762\) 7.68399e17 0.142193
\(763\) 7.11285e17 0.130507
\(764\) −1.48611e17 −0.0270361
\(765\) 7.62984e17 0.137631
\(766\) 1.18949e17 0.0212752
\(767\) 1.30659e18 0.231722
\(768\) 3.43283e18 0.603676
\(769\) 7.42916e18 1.29544 0.647722 0.761877i \(-0.275722\pi\)
0.647722 + 0.761877i \(0.275722\pi\)
\(770\) 5.70575e18 0.986558
\(771\) 2.50577e18 0.429624
\(772\) 4.83655e18 0.822287
\(773\) −5.54036e18 −0.934052 −0.467026 0.884244i \(-0.654675\pi\)
−0.467026 + 0.884244i \(0.654675\pi\)
\(774\) −2.45873e15 −0.000411051 0
\(775\) −2.90743e18 −0.482002
\(776\) −6.18154e18 −1.01624
\(777\) −2.80956e18 −0.458038
\(778\) −4.42114e18 −0.714771
\(779\) −2.65657e18 −0.425920
\(780\) −2.07378e18 −0.329722
\(781\) −8.71287e18 −1.37382
\(782\) 5.46794e18 0.855027
\(783\) −1.05215e18 −0.163165
\(784\) −1.27774e18 −0.196512
\(785\) 1.80488e18 0.275294
\(786\) 3.60182e18 0.544848
\(787\) −4.81562e18 −0.722465 −0.361232 0.932476i \(-0.617644\pi\)
−0.361232 + 0.932476i \(0.617644\pi\)
\(788\) 5.17094e18 0.769395
\(789\) 6.59132e18 0.972684
\(790\) −3.32005e18 −0.485924
\(791\) −2.68635e17 −0.0389955
\(792\) 3.80433e18 0.547728
\(793\) 9.73373e18 1.38996
\(794\) −7.60165e18 −1.07665
\(795\) 5.50281e18 0.773034
\(796\) 6.62586e16 0.00923225
\(797\) −8.01513e18 −1.10772 −0.553862 0.832608i \(-0.686847\pi\)
−0.553862 + 0.832608i \(0.686847\pi\)
\(798\) −3.17445e18 −0.435161
\(799\) 8.63502e18 1.17411
\(800\) 3.22878e18 0.435465
\(801\) 1.02290e18 0.136842
\(802\) 7.88572e18 1.04642
\(803\) 1.94242e19 2.55678
\(804\) 3.24907e18 0.424223
\(805\) 1.32780e19 1.71973
\(806\) 9.39350e18 1.20684
\(807\) 6.56222e18 0.836321
\(808\) 1.42789e19 1.80518
\(809\) −9.80201e18 −1.22928 −0.614638 0.788809i \(-0.710698\pi\)
−0.614638 + 0.788809i \(0.710698\pi\)
\(810\) −4.52909e17 −0.0563454
\(811\) −5.22975e18 −0.645425 −0.322712 0.946497i \(-0.604595\pi\)
−0.322712 + 0.946497i \(0.604595\pi\)
\(812\) 4.07339e18 0.498703
\(813\) −3.66024e17 −0.0444550
\(814\) 5.82515e18 0.701857
\(815\) −4.14451e18 −0.495392
\(816\) 9.34262e17 0.110785
\(817\) 1.16025e16 0.00136493
\(818\) −6.19312e18 −0.722791
\(819\) 6.50333e18 0.752992
\(820\) 1.46737e18 0.168558
\(821\) 2.56010e18 0.291761 0.145880 0.989302i \(-0.453399\pi\)
0.145880 + 0.989302i \(0.453399\pi\)
\(822\) −3.26022e17 −0.0368621
\(823\) −8.71139e18 −0.977211 −0.488605 0.872505i \(-0.662494\pi\)
−0.488605 + 0.872505i \(0.662494\pi\)
\(824\) −1.34221e18 −0.149381
\(825\) 4.17338e18 0.460826
\(826\) −1.10475e18 −0.121030
\(827\) 1.03968e19 1.13009 0.565043 0.825061i \(-0.308859\pi\)
0.565043 + 0.825061i \(0.308859\pi\)
\(828\) 2.80371e18 0.302368
\(829\) −1.16199e19 −1.24336 −0.621682 0.783270i \(-0.713550\pi\)
−0.621682 + 0.783270i \(0.713550\pi\)
\(830\) −6.05124e18 −0.642446
\(831\) −5.95141e18 −0.626922
\(832\) −1.59107e19 −1.66299
\(833\) 3.51245e18 0.364266
\(834\) 1.31178e18 0.134984
\(835\) −7.36398e17 −0.0751883
\(836\) −5.68528e18 −0.575985
\(837\) −1.77210e18 −0.178145
\(838\) 2.58560e18 0.257914
\(839\) −1.03399e19 −1.02344 −0.511720 0.859152i \(-0.670991\pi\)
−0.511720 + 0.859152i \(0.670991\pi\)
\(840\) 5.53675e18 0.543800
\(841\) −2.88508e18 −0.281180
\(842\) −5.30478e18 −0.513025
\(843\) −2.26593e18 −0.217454
\(844\) 4.97370e18 0.473645
\(845\) 1.58830e19 1.50094
\(846\) −5.12577e18 −0.480675
\(847\) −1.84073e19 −1.71296
\(848\) 6.73811e18 0.622250
\(849\) −8.66407e17 −0.0794002
\(850\) 2.50123e18 0.227473
\(851\) 1.35559e19 1.22345
\(852\) −2.67754e18 −0.239816
\(853\) −1.83597e19 −1.63192 −0.815958 0.578111i \(-0.803790\pi\)
−0.815958 + 0.578111i \(0.803790\pi\)
\(854\) −8.23007e18 −0.725984
\(855\) 2.13723e18 0.187099
\(856\) 6.84400e18 0.594608
\(857\) −7.25793e18 −0.625802 −0.312901 0.949786i \(-0.601301\pi\)
−0.312901 + 0.949786i \(0.601301\pi\)
\(858\) −1.34836e19 −1.15382
\(859\) −3.54601e18 −0.301151 −0.150576 0.988599i \(-0.548113\pi\)
−0.150576 + 0.988599i \(0.548113\pi\)
\(860\) −6.40871e15 −0.000540171 0
\(861\) −4.60164e18 −0.384939
\(862\) 1.59492e18 0.132416
\(863\) −2.11515e18 −0.174289 −0.0871446 0.996196i \(-0.527774\pi\)
−0.0871446 + 0.996196i \(0.527774\pi\)
\(864\) 1.96797e18 0.160945
\(865\) 6.65941e18 0.540544
\(866\) −4.85589e18 −0.391203
\(867\) 4.65219e18 0.371992
\(868\) 6.86065e18 0.544486
\(869\) 1.86466e19 1.46883
\(870\) 3.17487e18 0.248228
\(871\) −3.63624e19 −2.82186
\(872\) −1.43105e18 −0.110230
\(873\) −4.13319e18 −0.316004
\(874\) 1.53165e19 1.16235
\(875\) 1.77385e19 1.33618
\(876\) 5.96924e18 0.446316
\(877\) 9.33642e18 0.692920 0.346460 0.938065i \(-0.387384\pi\)
0.346460 + 0.938065i \(0.387384\pi\)
\(878\) −1.05563e18 −0.0777677
\(879\) 9.64585e18 0.705363
\(880\) −4.70380e18 −0.341438
\(881\) 3.84401e18 0.276975 0.138488 0.990364i \(-0.455776\pi\)
0.138488 + 0.990364i \(0.455776\pi\)
\(882\) −2.08500e18 −0.149128
\(883\) −4.87356e17 −0.0346020 −0.0173010 0.999850i \(-0.505507\pi\)
−0.0173010 + 0.999850i \(0.505507\pi\)
\(884\) 6.98047e18 0.491977
\(885\) 7.43781e17 0.0520372
\(886\) −9.49716e17 −0.0659591
\(887\) 2.16616e19 1.49344 0.746718 0.665140i \(-0.231628\pi\)
0.746718 + 0.665140i \(0.231628\pi\)
\(888\) 5.65262e18 0.386870
\(889\) −6.28085e18 −0.426734
\(890\) −3.08658e18 −0.208182
\(891\) 2.54371e18 0.170318
\(892\) 9.49194e18 0.630934
\(893\) 2.41880e19 1.59612
\(894\) 6.08386e18 0.398552
\(895\) −2.82162e18 −0.183506
\(896\) −2.98631e18 −0.192811
\(897\) −3.13781e19 −2.01130
\(898\) 1.46167e19 0.930153
\(899\) 1.24223e19 0.784812
\(900\) 1.28251e18 0.0804426
\(901\) −1.85228e19 −1.15344
\(902\) 9.54074e18 0.589847
\(903\) 2.00976e16 0.00123360
\(904\) 5.40473e17 0.0329366
\(905\) 1.02367e19 0.619362
\(906\) −8.18450e18 −0.491653
\(907\) 2.90941e19 1.73523 0.867616 0.497235i \(-0.165651\pi\)
0.867616 + 0.497235i \(0.165651\pi\)
\(908\) 1.17554e19 0.696111
\(909\) 9.54733e18 0.561328
\(910\) −1.96237e19 −1.14555
\(911\) −9.46913e18 −0.548834 −0.274417 0.961611i \(-0.588485\pi\)
−0.274417 + 0.961611i \(0.588485\pi\)
\(912\) 2.61701e18 0.150605
\(913\) 3.39860e19 1.94196
\(914\) 9.43652e18 0.535379
\(915\) 5.54098e18 0.312140
\(916\) −8.61690e18 −0.481981
\(917\) −2.94411e19 −1.63513
\(918\) 1.52452e18 0.0840727
\(919\) 2.29731e19 1.25797 0.628984 0.777419i \(-0.283471\pi\)
0.628984 + 0.777419i \(0.283471\pi\)
\(920\) −2.67144e19 −1.45253
\(921\) −4.82962e18 −0.260751
\(922\) −1.26972e19 −0.680702
\(923\) 2.99661e19 1.59521
\(924\) −9.84789e18 −0.520565
\(925\) 6.20096e18 0.325490
\(926\) 1.83506e18 0.0956489
\(927\) −8.97450e17 −0.0464506
\(928\) −1.37953e19 −0.709039
\(929\) −2.32058e19 −1.18439 −0.592194 0.805796i \(-0.701738\pi\)
−0.592194 + 0.805796i \(0.701738\pi\)
\(930\) 5.34731e18 0.271017
\(931\) 9.83892e18 0.495193
\(932\) 2.33581e18 0.116744
\(933\) 8.57343e18 0.425524
\(934\) 3.95117e18 0.194747
\(935\) 1.29306e19 0.632910
\(936\) −1.30842e19 −0.635996
\(937\) −1.05355e19 −0.508568 −0.254284 0.967130i \(-0.581840\pi\)
−0.254284 + 0.967130i \(0.581840\pi\)
\(938\) 3.07452e19 1.47387
\(939\) 1.52434e18 0.0725698
\(940\) −1.33604e19 −0.631666
\(941\) −9.40380e18 −0.441541 −0.220770 0.975326i \(-0.570857\pi\)
−0.220770 + 0.975326i \(0.570857\pi\)
\(942\) 3.60634e18 0.168165
\(943\) 2.22026e19 1.02820
\(944\) 9.10749e17 0.0418871
\(945\) 3.70206e18 0.169097
\(946\) −4.16690e16 −0.00189026
\(947\) −4.17865e19 −1.88261 −0.941307 0.337551i \(-0.890402\pi\)
−0.941307 + 0.337551i \(0.890402\pi\)
\(948\) 5.73027e18 0.256402
\(949\) −6.68056e19 −2.96881
\(950\) 7.00632e18 0.309233
\(951\) −6.56581e18 −0.287816
\(952\) −1.86370e19 −0.811402
\(953\) −1.17614e18 −0.0508576 −0.0254288 0.999677i \(-0.508095\pi\)
−0.0254288 + 0.999677i \(0.508095\pi\)
\(954\) 1.09952e19 0.472212
\(955\) 9.46786e17 0.0403859
\(956\) 6.90569e18 0.292571
\(957\) −1.78312e19 −0.750333
\(958\) 8.60546e18 0.359665
\(959\) 2.66489e18 0.110626
\(960\) −9.05728e18 −0.373452
\(961\) −3.49507e18 −0.143138
\(962\) −2.00344e19 −0.814964
\(963\) 4.57613e18 0.184896
\(964\) −1.85091e19 −0.742822
\(965\) −3.08133e19 −1.22832
\(966\) 2.65308e19 1.05051
\(967\) −1.96858e19 −0.774248 −0.387124 0.922028i \(-0.626531\pi\)
−0.387124 + 0.922028i \(0.626531\pi\)
\(968\) 3.70341e19 1.44681
\(969\) −7.19405e18 −0.279170
\(970\) 1.24718e19 0.480745
\(971\) −1.81593e19 −0.695302 −0.347651 0.937624i \(-0.613021\pi\)
−0.347651 + 0.937624i \(0.613021\pi\)
\(972\) 7.81703e17 0.0297311
\(973\) −1.07225e19 −0.405099
\(974\) 1.09392e19 0.410537
\(975\) −1.43535e19 −0.535090
\(976\) 6.78484e18 0.251256
\(977\) 3.12787e19 1.15062 0.575312 0.817934i \(-0.304881\pi\)
0.575312 + 0.817934i \(0.304881\pi\)
\(978\) −8.28115e18 −0.302613
\(979\) 1.73354e19 0.629283
\(980\) −5.43458e18 −0.195973
\(981\) −9.56850e17 −0.0342764
\(982\) −2.39284e19 −0.851509
\(983\) 1.23581e19 0.436872 0.218436 0.975851i \(-0.429904\pi\)
0.218436 + 0.975851i \(0.429904\pi\)
\(984\) 9.25815e18 0.325129
\(985\) −3.29436e19 −1.14931
\(986\) −1.06868e19 −0.370380
\(987\) 4.18978e19 1.44255
\(988\) 1.95533e19 0.668807
\(989\) −9.69694e16 −0.00329503
\(990\) −7.67561e18 −0.259110
\(991\) −2.03024e18 −0.0680875 −0.0340438 0.999420i \(-0.510839\pi\)
−0.0340438 + 0.999420i \(0.510839\pi\)
\(992\) −2.32349e19 −0.774133
\(993\) 1.08899e19 0.360457
\(994\) −2.53370e19 −0.833188
\(995\) −4.22128e17 −0.0137910
\(996\) 1.04442e19 0.338992
\(997\) −3.18071e19 −1.02566 −0.512832 0.858489i \(-0.671404\pi\)
−0.512832 + 0.858489i \(0.671404\pi\)
\(998\) 8.55356e17 0.0274030
\(999\) 3.77953e18 0.120299
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 177.14.a.b.1.11 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.11 31 1.1 even 1 trivial