Properties

Label 7.10.a.a.1.2
Level $7$
Weight $10$
Character 7.1
Self dual yes
Analytic conductor $3.605$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.60525085315\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{193}) \)
Defining polynomial: \( x^{2} - x - 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-6.44622\) of defining polynomial
Character \(\chi\) \(=\) 7.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +O(q^{10})\) \(q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +2187.01 q^{10} +63864.3 q^{11} +77025.5 q^{12} -164679. q^{13} -26152.8 q^{14} -39316.5 q^{15} +93981.5 q^{16} -362910. q^{17} +203267. q^{18} -436498. q^{19} -78978.6 q^{20} +470156. q^{21} +695638. q^{22} +918199. q^{23} +1.93105e6 q^{24} -1.91281e6 q^{25} -1.79375e6 q^{26} +200076. q^{27} +944445. q^{28} -3.68643e6 q^{29} -428253. q^{30} +3.47629e6 q^{31} +6.07279e6 q^{32} -1.25057e7 q^{33} -3.95298e6 q^{34} -482078. q^{35} -7.34049e6 q^{36} +1.88149e7 q^{37} -4.75453e6 q^{38} +3.22469e7 q^{39} -1.98002e6 q^{40} +2.40714e6 q^{41} +5.12115e6 q^{42} -1.25306e7 q^{43} -2.51213e7 q^{44} +3.74685e6 q^{45} +1.00014e7 q^{46} -5.54509e7 q^{47} -1.84032e7 q^{48} +5.76480e6 q^{49} -2.08352e7 q^{50} +7.10639e7 q^{51} +6.47772e7 q^{52} -9.26889e7 q^{53} +2.17931e6 q^{54} +1.28228e7 q^{55} +2.36775e7 q^{56} +8.54737e7 q^{57} -4.01542e7 q^{58} -2.52600e7 q^{59} +1.54653e7 q^{60} +6.93275e7 q^{61} +3.78653e7 q^{62} -4.48057e7 q^{63} +1.80290e7 q^{64} -3.30646e7 q^{65} -1.36218e8 q^{66} -2.33494e7 q^{67} +1.42752e8 q^{68} -1.79799e8 q^{69} -5.25101e6 q^{70} -1.06194e8 q^{71} -1.84028e8 q^{72} -2.10115e8 q^{73} +2.04940e8 q^{74} +3.74561e8 q^{75} +1.71699e8 q^{76} -1.53338e8 q^{77} +3.51247e8 q^{78} -149606. q^{79} +1.88698e7 q^{80} -4.06488e8 q^{81} +2.62197e7 q^{82} +5.21565e8 q^{83} -1.84938e8 q^{84} -7.28659e7 q^{85} -1.36489e8 q^{86} +7.21865e8 q^{87} -6.29799e8 q^{88} +2.98587e8 q^{89} +4.08123e7 q^{90} +3.95394e8 q^{91} -3.61178e8 q^{92} -6.80716e8 q^{93} -6.03996e8 q^{94} -8.76410e7 q^{95} -1.18915e9 q^{96} -8.95983e8 q^{97} +6.27928e7 q^{98} +1.19179e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9} + 43384 q^{10} + 35316 q^{11} + 52136 q^{12} - 26530 q^{13} + 14406 q^{14} - 307136 q^{15} - 752 q^{16} - 463920 q^{17} + 332042 q^{18} - 925426 q^{19} + 473760 q^{20} + 206486 q^{21} + 1177888 q^{22} + 778128 q^{23} + 3301296 q^{24} + 2081722 q^{25} - 4127424 q^{26} - 2798612 q^{27} + 1488620 q^{28} - 10003584 q^{29} + 4095872 q^{30} + 2467260 q^{31} + 1284576 q^{32} - 15640784 q^{33} - 2246676 q^{34} + 5373438 q^{35} - 5612716 q^{36} + 30735552 q^{37} + 3504660 q^{38} + 47417944 q^{39} - 32409984 q^{40} - 19103448 q^{41} + 9575188 q^{42} + 4065100 q^{43} - 18650976 q^{44} + 22338298 q^{45} + 12367584 q^{46} - 82195020 q^{47} - 28806496 q^{48} + 11529602 q^{49} - 88312626 q^{50} + 59971356 q^{51} + 33466384 q^{52} - 55189812 q^{53} + 52834472 q^{54} + 82445816 q^{55} - 6281016 q^{56} + 31781116 q^{57} + 66558004 q^{58} - 7069218 q^{59} + 76165376 q^{60} + 44316386 q^{61} + 54910200 q^{62} - 26502238 q^{63} + 147417152 q^{64} - 369979260 q^{65} - 83258464 q^{66} - 241921336 q^{67} + 165645816 q^{68} - 195181152 q^{69} - 104164984 q^{70} + 206493816 q^{71} - 279147720 q^{72} - 499153188 q^{73} + 3571524 q^{74} + 813228014 q^{75} + 282511768 q^{76} - 84793716 q^{77} + 94970960 q^{78} + 468535096 q^{79} + 249904128 q^{80} - 585745634 q^{81} + 389586092 q^{82} + 444023958 q^{83} - 125178536 q^{84} + 173475060 q^{85} - 416830608 q^{86} + 28134340 q^{87} - 986010816 q^{88} + 636267396 q^{89} - 273242728 q^{90} + 63698530 q^{91} - 329431488 q^{92} - 791523960 q^{93} - 152223192 q^{94} + 1104747984 q^{95} - 1714981184 q^{96} - 1632716064 q^{97} - 34588806 q^{98} + 1409417860 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.8924 0.481383 0.240691 0.970602i \(-0.422626\pi\)
0.240691 + 0.970602i \(0.422626\pi\)
\(3\) −195.817 −1.39574 −0.697870 0.716225i \(-0.745869\pi\)
−0.697870 + 0.716225i \(0.745869\pi\)
\(4\) −393.355 −0.768271
\(5\) 200.782 0.143668 0.0718340 0.997417i \(-0.477115\pi\)
0.0718340 + 0.997417i \(0.477115\pi\)
\(6\) −2132.92 −0.671885
\(7\) −2401.00 −0.377964
\(8\) −9861.52 −0.851215
\(9\) 18661.3 0.948090
\(10\) 2187.01 0.0691593
\(11\) 63864.3 1.31520 0.657599 0.753369i \(-0.271572\pi\)
0.657599 + 0.753369i \(0.271572\pi\)
\(12\) 77025.5 1.07231
\(13\) −164679. −1.59916 −0.799581 0.600558i \(-0.794945\pi\)
−0.799581 + 0.600558i \(0.794945\pi\)
\(14\) −26152.8 −0.181946
\(15\) −39316.5 −0.200523
\(16\) 93981.5 0.358511
\(17\) −362910. −1.05385 −0.526925 0.849912i \(-0.676655\pi\)
−0.526925 + 0.849912i \(0.676655\pi\)
\(18\) 203267. 0.456394
\(19\) −436498. −0.768406 −0.384203 0.923249i \(-0.625524\pi\)
−0.384203 + 0.923249i \(0.625524\pi\)
\(20\) −78978.6 −0.110376
\(21\) 470156. 0.527540
\(22\) 695638. 0.633113
\(23\) 918199. 0.684166 0.342083 0.939670i \(-0.388868\pi\)
0.342083 + 0.939670i \(0.388868\pi\)
\(24\) 1.93105e6 1.18807
\(25\) −1.91281e6 −0.979359
\(26\) −1.79375e6 −0.769809
\(27\) 200076. 0.0724531
\(28\) 944445. 0.290379
\(29\) −3.68643e6 −0.967865 −0.483932 0.875105i \(-0.660792\pi\)
−0.483932 + 0.875105i \(0.660792\pi\)
\(30\) −428253. −0.0965284
\(31\) 3.47629e6 0.676064 0.338032 0.941135i \(-0.390239\pi\)
0.338032 + 0.941135i \(0.390239\pi\)
\(32\) 6.07279e6 1.02380
\(33\) −1.25057e7 −1.83567
\(34\) −3.95298e6 −0.507305
\(35\) −482078. −0.0543014
\(36\) −7.34049e6 −0.728390
\(37\) 1.88149e7 1.65042 0.825210 0.564826i \(-0.191057\pi\)
0.825210 + 0.564826i \(0.191057\pi\)
\(38\) −4.75453e6 −0.369897
\(39\) 3.22469e7 2.23201
\(40\) −1.98002e6 −0.122292
\(41\) 2.40714e6 0.133038 0.0665188 0.997785i \(-0.478811\pi\)
0.0665188 + 0.997785i \(0.478811\pi\)
\(42\) 5.12115e6 0.253949
\(43\) −1.25306e7 −0.558938 −0.279469 0.960155i \(-0.590158\pi\)
−0.279469 + 0.960155i \(0.590158\pi\)
\(44\) −2.51213e7 −1.01043
\(45\) 3.74685e6 0.136210
\(46\) 1.00014e7 0.329346
\(47\) −5.54509e7 −1.65756 −0.828779 0.559577i \(-0.810964\pi\)
−0.828779 + 0.559577i \(0.810964\pi\)
\(48\) −1.84032e7 −0.500388
\(49\) 5.76480e6 0.142857
\(50\) −2.08352e7 −0.471447
\(51\) 7.10639e7 1.47090
\(52\) 6.47772e7 1.22859
\(53\) −9.26889e7 −1.61356 −0.806782 0.590849i \(-0.798793\pi\)
−0.806782 + 0.590849i \(0.798793\pi\)
\(54\) 2.17931e6 0.0348777
\(55\) 1.28228e7 0.188952
\(56\) 2.36775e7 0.321729
\(57\) 8.54737e7 1.07250
\(58\) −4.01542e7 −0.465913
\(59\) −2.52600e7 −0.271393 −0.135696 0.990750i \(-0.543327\pi\)
−0.135696 + 0.990750i \(0.543327\pi\)
\(60\) 1.54653e7 0.154056
\(61\) 6.93275e7 0.641093 0.320547 0.947233i \(-0.396133\pi\)
0.320547 + 0.947233i \(0.396133\pi\)
\(62\) 3.78653e7 0.325446
\(63\) −4.48057e7 −0.358344
\(64\) 1.80290e7 0.134326
\(65\) −3.30646e7 −0.229748
\(66\) −1.36218e8 −0.883661
\(67\) −2.33494e7 −0.141559 −0.0707796 0.997492i \(-0.522549\pi\)
−0.0707796 + 0.997492i \(0.522549\pi\)
\(68\) 1.42752e8 0.809643
\(69\) −1.79799e8 −0.954918
\(70\) −5.25101e6 −0.0261398
\(71\) −1.06194e8 −0.495950 −0.247975 0.968766i \(-0.579765\pi\)
−0.247975 + 0.968766i \(0.579765\pi\)
\(72\) −1.84028e8 −0.807028
\(73\) −2.10115e8 −0.865974 −0.432987 0.901400i \(-0.642540\pi\)
−0.432987 + 0.901400i \(0.642540\pi\)
\(74\) 2.04940e8 0.794483
\(75\) 3.74561e8 1.36693
\(76\) 1.71699e8 0.590344
\(77\) −1.53338e8 −0.497098
\(78\) 3.51247e8 1.07445
\(79\) −149606. −0.000432144 0 −0.000216072 1.00000i \(-0.500069\pi\)
−0.000216072 1.00000i \(0.500069\pi\)
\(80\) 1.88698e7 0.0515066
\(81\) −4.06488e8 −1.04922
\(82\) 2.62197e7 0.0640420
\(83\) 5.21565e8 1.20630 0.603152 0.797626i \(-0.293911\pi\)
0.603152 + 0.797626i \(0.293911\pi\)
\(84\) −1.84938e8 −0.405294
\(85\) −7.28659e7 −0.151405
\(86\) −1.36489e8 −0.269063
\(87\) 7.21865e8 1.35089
\(88\) −6.29799e8 −1.11952
\(89\) 2.98587e8 0.504448 0.252224 0.967669i \(-0.418838\pi\)
0.252224 + 0.967669i \(0.418838\pi\)
\(90\) 4.08123e7 0.0655692
\(91\) 3.95394e8 0.604426
\(92\) −3.61178e8 −0.525625
\(93\) −6.80716e8 −0.943610
\(94\) −6.03996e8 −0.797919
\(95\) −8.76410e7 −0.110395
\(96\) −1.18915e9 −1.42895
\(97\) −8.95983e8 −1.02761 −0.513803 0.857908i \(-0.671764\pi\)
−0.513803 + 0.857908i \(0.671764\pi\)
\(98\) 6.27928e7 0.0687689
\(99\) 1.19179e9 1.24693
\(100\) 7.52413e8 0.752413
\(101\) −4.13043e7 −0.0394956 −0.0197478 0.999805i \(-0.506286\pi\)
−0.0197478 + 0.999805i \(0.506286\pi\)
\(102\) 7.74060e8 0.708066
\(103\) 4.29472e8 0.375982 0.187991 0.982171i \(-0.439802\pi\)
0.187991 + 0.982171i \(0.439802\pi\)
\(104\) 1.62398e9 1.36123
\(105\) 9.43990e7 0.0757906
\(106\) −1.00961e9 −0.776742
\(107\) 1.23287e9 0.909265 0.454632 0.890679i \(-0.349771\pi\)
0.454632 + 0.890679i \(0.349771\pi\)
\(108\) −7.87006e7 −0.0556636
\(109\) 1.69619e9 1.15095 0.575475 0.817820i \(-0.304817\pi\)
0.575475 + 0.817820i \(0.304817\pi\)
\(110\) 1.39672e8 0.0909581
\(111\) −3.68428e9 −2.30356
\(112\) −2.25650e8 −0.135504
\(113\) −1.42449e9 −0.821878 −0.410939 0.911663i \(-0.634799\pi\)
−0.410939 + 0.911663i \(0.634799\pi\)
\(114\) 9.31017e8 0.516281
\(115\) 1.84358e8 0.0982928
\(116\) 1.45007e9 0.743582
\(117\) −3.07311e9 −1.51615
\(118\) −2.75143e8 −0.130644
\(119\) 8.71347e8 0.398318
\(120\) 3.87721e8 0.170688
\(121\) 1.72070e9 0.729744
\(122\) 7.55146e8 0.308611
\(123\) −4.71359e8 −0.185686
\(124\) −1.36741e9 −0.519401
\(125\) −7.76211e8 −0.284371
\(126\) −4.88043e8 −0.172501
\(127\) −3.12858e9 −1.06716 −0.533581 0.845749i \(-0.679154\pi\)
−0.533581 + 0.845749i \(0.679154\pi\)
\(128\) −2.91289e9 −0.959133
\(129\) 2.45370e9 0.780132
\(130\) −3.60154e8 −0.110597
\(131\) 7.03123e8 0.208598 0.104299 0.994546i \(-0.466740\pi\)
0.104299 + 0.994546i \(0.466740\pi\)
\(132\) 4.91918e9 1.41029
\(133\) 1.04803e9 0.290430
\(134\) −2.54332e8 −0.0681442
\(135\) 4.01716e7 0.0104092
\(136\) 3.57885e9 0.897053
\(137\) −3.07310e9 −0.745306 −0.372653 0.927971i \(-0.621552\pi\)
−0.372653 + 0.927971i \(0.621552\pi\)
\(138\) −1.95845e9 −0.459681
\(139\) 5.07806e9 1.15380 0.576901 0.816814i \(-0.304262\pi\)
0.576901 + 0.816814i \(0.304262\pi\)
\(140\) 1.89628e8 0.0417182
\(141\) 1.08582e10 2.31352
\(142\) −1.15671e9 −0.238742
\(143\) −1.05171e10 −2.10321
\(144\) 1.75381e9 0.339901
\(145\) −7.40169e8 −0.139051
\(146\) −2.28867e9 −0.416865
\(147\) −1.12885e9 −0.199391
\(148\) −7.40093e9 −1.26797
\(149\) 2.13455e9 0.354788 0.177394 0.984140i \(-0.443233\pi\)
0.177394 + 0.984140i \(0.443233\pi\)
\(150\) 4.07988e9 0.658017
\(151\) −2.35298e9 −0.368318 −0.184159 0.982897i \(-0.558956\pi\)
−0.184159 + 0.982897i \(0.558956\pi\)
\(152\) 4.30454e9 0.654079
\(153\) −6.77236e9 −0.999145
\(154\) −1.67023e9 −0.239294
\(155\) 6.97977e8 0.0971288
\(156\) −1.26845e10 −1.71479
\(157\) −2.98482e9 −0.392075 −0.196038 0.980596i \(-0.562807\pi\)
−0.196038 + 0.980596i \(0.562807\pi\)
\(158\) −1.62958e6 −0.000208027 0
\(159\) 1.81501e10 2.25212
\(160\) 1.21931e9 0.147087
\(161\) −2.20460e9 −0.258591
\(162\) −4.42764e9 −0.505074
\(163\) 9.20745e9 1.02163 0.510817 0.859690i \(-0.329343\pi\)
0.510817 + 0.859690i \(0.329343\pi\)
\(164\) −9.46860e8 −0.102209
\(165\) −2.51092e9 −0.263728
\(166\) 5.68111e9 0.580694
\(167\) −4.95501e9 −0.492970 −0.246485 0.969147i \(-0.579276\pi\)
−0.246485 + 0.969147i \(0.579276\pi\)
\(168\) −4.63646e9 −0.449050
\(169\) 1.65146e10 1.55732
\(170\) −7.93688e8 −0.0728835
\(171\) −8.14560e9 −0.728518
\(172\) 4.92897e9 0.429416
\(173\) 3.77546e9 0.320452 0.160226 0.987080i \(-0.448778\pi\)
0.160226 + 0.987080i \(0.448778\pi\)
\(174\) 7.86287e9 0.650294
\(175\) 4.59266e9 0.370163
\(176\) 6.00206e9 0.471513
\(177\) 4.94633e9 0.378794
\(178\) 3.25235e9 0.242833
\(179\) −1.94362e10 −1.41505 −0.707526 0.706687i \(-0.750189\pi\)
−0.707526 + 0.706687i \(0.750189\pi\)
\(180\) −1.47384e9 −0.104646
\(181\) −9.81530e9 −0.679751 −0.339875 0.940470i \(-0.610385\pi\)
−0.339875 + 0.940470i \(0.610385\pi\)
\(182\) 4.30680e9 0.290960
\(183\) −1.35755e10 −0.894799
\(184\) −9.05485e9 −0.582373
\(185\) 3.77770e9 0.237113
\(186\) −7.41466e9 −0.454237
\(187\) −2.31770e10 −1.38602
\(188\) 2.18119e10 1.27345
\(189\) −4.80381e8 −0.0273847
\(190\) −9.54625e8 −0.0531424
\(191\) −1.84579e10 −1.00354 −0.501768 0.865002i \(-0.667317\pi\)
−0.501768 + 0.865002i \(0.667317\pi\)
\(192\) −3.53038e9 −0.187485
\(193\) 4.83605e9 0.250890 0.125445 0.992101i \(-0.459964\pi\)
0.125445 + 0.992101i \(0.459964\pi\)
\(194\) −9.75944e9 −0.494672
\(195\) 6.47460e9 0.320669
\(196\) −2.26761e9 −0.109753
\(197\) 2.70242e10 1.27836 0.639182 0.769056i \(-0.279273\pi\)
0.639182 + 0.769056i \(0.279273\pi\)
\(198\) 1.29815e10 0.600248
\(199\) 1.65772e10 0.749330 0.374665 0.927160i \(-0.377758\pi\)
0.374665 + 0.927160i \(0.377758\pi\)
\(200\) 1.88632e10 0.833645
\(201\) 4.57220e9 0.197580
\(202\) −4.49904e8 −0.0190125
\(203\) 8.85111e9 0.365819
\(204\) −2.79533e10 −1.13005
\(205\) 4.83311e8 0.0191132
\(206\) 4.67800e9 0.180991
\(207\) 1.71348e10 0.648651
\(208\) −1.54768e10 −0.573317
\(209\) −2.78766e10 −1.01061
\(210\) 1.02824e9 0.0364843
\(211\) −5.44866e10 −1.89243 −0.946213 0.323544i \(-0.895126\pi\)
−0.946213 + 0.323544i \(0.895126\pi\)
\(212\) 3.64596e10 1.23965
\(213\) 2.07946e10 0.692218
\(214\) 1.34290e10 0.437704
\(215\) −2.51592e9 −0.0803015
\(216\) −1.97305e9 −0.0616731
\(217\) −8.34657e9 −0.255528
\(218\) 1.84757e10 0.554047
\(219\) 4.11441e10 1.20867
\(220\) −5.04391e9 −0.145166
\(221\) 5.97636e10 1.68528
\(222\) −4.01308e10 −1.10889
\(223\) −2.05500e10 −0.556468 −0.278234 0.960513i \(-0.589749\pi\)
−0.278234 + 0.960513i \(0.589749\pi\)
\(224\) −1.45808e10 −0.386958
\(225\) −3.56955e10 −0.928521
\(226\) −1.55162e10 −0.395638
\(227\) −3.94058e10 −0.985017 −0.492509 0.870307i \(-0.663920\pi\)
−0.492509 + 0.870307i \(0.663920\pi\)
\(228\) −3.36215e10 −0.823967
\(229\) −1.82516e10 −0.438572 −0.219286 0.975661i \(-0.570373\pi\)
−0.219286 + 0.975661i \(0.570373\pi\)
\(230\) 2.00811e9 0.0473165
\(231\) 3.00262e10 0.693819
\(232\) 3.63538e10 0.823861
\(233\) −5.08161e10 −1.12953 −0.564767 0.825250i \(-0.691034\pi\)
−0.564767 + 0.825250i \(0.691034\pi\)
\(234\) −3.34737e10 −0.729848
\(235\) −1.11336e10 −0.238138
\(236\) 9.93612e9 0.208503
\(237\) 2.92955e7 0.000603160 0
\(238\) 9.49110e9 0.191743
\(239\) 3.80447e10 0.754230 0.377115 0.926166i \(-0.376916\pi\)
0.377115 + 0.926166i \(0.376916\pi\)
\(240\) −3.69503e9 −0.0718898
\(241\) 9.80077e10 1.87147 0.935737 0.352699i \(-0.114736\pi\)
0.935737 + 0.352699i \(0.114736\pi\)
\(242\) 1.87426e10 0.351286
\(243\) 7.56590e10 1.39198
\(244\) −2.72703e10 −0.492533
\(245\) 1.15747e9 0.0205240
\(246\) −5.13425e9 −0.0893859
\(247\) 7.18819e10 1.22881
\(248\) −3.42815e10 −0.575476
\(249\) −1.02131e11 −1.68369
\(250\) −8.45484e9 −0.136891
\(251\) 7.75125e10 1.23265 0.616325 0.787492i \(-0.288621\pi\)
0.616325 + 0.787492i \(0.288621\pi\)
\(252\) 1.76245e10 0.275305
\(253\) 5.86401e10 0.899814
\(254\) −3.40778e10 −0.513713
\(255\) 1.42684e10 0.211321
\(256\) −4.09593e10 −0.596036
\(257\) −1.07589e11 −1.53840 −0.769199 0.639009i \(-0.779345\pi\)
−0.769199 + 0.639009i \(0.779345\pi\)
\(258\) 2.67268e10 0.375542
\(259\) −4.51746e10 −0.623800
\(260\) 1.30061e10 0.176509
\(261\) −6.87934e10 −0.917623
\(262\) 7.65873e9 0.100416
\(263\) −1.21615e10 −0.156742 −0.0783708 0.996924i \(-0.524972\pi\)
−0.0783708 + 0.996924i \(0.524972\pi\)
\(264\) 1.23325e11 1.56255
\(265\) −1.86103e10 −0.231818
\(266\) 1.14156e10 0.139808
\(267\) −5.84685e10 −0.704078
\(268\) 9.18458e9 0.108756
\(269\) −1.23517e11 −1.43827 −0.719134 0.694872i \(-0.755461\pi\)
−0.719134 + 0.694872i \(0.755461\pi\)
\(270\) 4.37567e8 0.00501080
\(271\) 1.34305e11 1.51263 0.756313 0.654210i \(-0.226999\pi\)
0.756313 + 0.654210i \(0.226999\pi\)
\(272\) −3.41068e10 −0.377817
\(273\) −7.74248e10 −0.843622
\(274\) −3.34736e10 −0.358777
\(275\) −1.22160e11 −1.28805
\(276\) 7.07248e10 0.733636
\(277\) −2.16684e10 −0.221140 −0.110570 0.993868i \(-0.535268\pi\)
−0.110570 + 0.993868i \(0.535268\pi\)
\(278\) 5.53125e10 0.555420
\(279\) 6.48719e10 0.640970
\(280\) 4.75402e9 0.0462222
\(281\) 7.73283e9 0.0739878 0.0369939 0.999315i \(-0.488222\pi\)
0.0369939 + 0.999315i \(0.488222\pi\)
\(282\) 1.18273e11 1.11369
\(283\) −7.19601e10 −0.666888 −0.333444 0.942770i \(-0.608211\pi\)
−0.333444 + 0.942770i \(0.608211\pi\)
\(284\) 4.17720e10 0.381024
\(285\) 1.71616e10 0.154083
\(286\) −1.14557e11 −1.01245
\(287\) −5.77955e9 −0.0502835
\(288\) 1.13326e11 0.970650
\(289\) 1.31159e10 0.110601
\(290\) −8.06225e9 −0.0669368
\(291\) 1.75449e11 1.43427
\(292\) 8.26498e10 0.665303
\(293\) 1.73674e11 1.37667 0.688335 0.725393i \(-0.258342\pi\)
0.688335 + 0.725393i \(0.258342\pi\)
\(294\) −1.22959e10 −0.0959835
\(295\) −5.07175e9 −0.0389905
\(296\) −1.85544e11 −1.40486
\(297\) 1.27777e10 0.0952901
\(298\) 2.32505e10 0.170789
\(299\) −1.51208e11 −1.09409
\(300\) −1.47335e11 −1.05017
\(301\) 3.00860e10 0.211259
\(302\) −2.56297e10 −0.177302
\(303\) 8.08807e9 0.0551256
\(304\) −4.10227e10 −0.275482
\(305\) 1.39197e10 0.0921046
\(306\) −7.37675e10 −0.480971
\(307\) 2.27108e11 1.45918 0.729591 0.683884i \(-0.239710\pi\)
0.729591 + 0.683884i \(0.239710\pi\)
\(308\) 6.03163e10 0.381906
\(309\) −8.40978e10 −0.524773
\(310\) 7.60267e9 0.0467561
\(311\) −8.68962e10 −0.526719 −0.263360 0.964698i \(-0.584831\pi\)
−0.263360 + 0.964698i \(0.584831\pi\)
\(312\) −3.18003e11 −1.89992
\(313\) −5.25289e10 −0.309349 −0.154674 0.987965i \(-0.549433\pi\)
−0.154674 + 0.987965i \(0.549433\pi\)
\(314\) −3.25120e10 −0.188738
\(315\) −8.99618e9 −0.0514826
\(316\) 5.88484e7 0.000332004 0
\(317\) 2.63784e11 1.46718 0.733588 0.679595i \(-0.237844\pi\)
0.733588 + 0.679595i \(0.237844\pi\)
\(318\) 1.97698e11 1.08413
\(319\) −2.35431e11 −1.27293
\(320\) 3.61990e9 0.0192984
\(321\) −2.41417e11 −1.26910
\(322\) −2.40134e10 −0.124481
\(323\) 1.58410e11 0.809786
\(324\) 1.59894e11 0.806082
\(325\) 3.14999e11 1.56615
\(326\) 1.00292e11 0.491797
\(327\) −3.32143e11 −1.60643
\(328\) −2.37381e10 −0.113244
\(329\) 1.33138e11 0.626498
\(330\) −2.73501e10 −0.126954
\(331\) −2.11350e11 −0.967780 −0.483890 0.875129i \(-0.660776\pi\)
−0.483890 + 0.875129i \(0.660776\pi\)
\(332\) −2.05160e11 −0.926768
\(333\) 3.51110e11 1.56475
\(334\) −5.39722e10 −0.237307
\(335\) −4.68813e9 −0.0203375
\(336\) 4.41860e10 0.189129
\(337\) −3.67482e11 −1.55203 −0.776017 0.630712i \(-0.782763\pi\)
−0.776017 + 0.630712i \(0.782763\pi\)
\(338\) 1.79884e11 0.749666
\(339\) 2.78940e11 1.14713
\(340\) 2.86621e10 0.116320
\(341\) 2.22011e11 0.889158
\(342\) −8.87255e10 −0.350696
\(343\) −1.38413e10 −0.0539949
\(344\) 1.23571e11 0.475776
\(345\) −3.61004e10 −0.137191
\(346\) 4.11240e10 0.154260
\(347\) 4.33866e11 1.60647 0.803235 0.595662i \(-0.203110\pi\)
0.803235 + 0.595662i \(0.203110\pi\)
\(348\) −2.83949e11 −1.03785
\(349\) 1.04086e11 0.375559 0.187780 0.982211i \(-0.439871\pi\)
0.187780 + 0.982211i \(0.439871\pi\)
\(350\) 5.00253e10 0.178190
\(351\) −3.29482e10 −0.115864
\(352\) 3.87834e11 1.34649
\(353\) −4.46890e11 −1.53184 −0.765922 0.642934i \(-0.777717\pi\)
−0.765922 + 0.642934i \(0.777717\pi\)
\(354\) 5.38776e10 0.182345
\(355\) −2.13219e10 −0.0712522
\(356\) −1.17451e11 −0.387553
\(357\) −1.70625e11 −0.555948
\(358\) −2.11708e11 −0.681182
\(359\) −1.96551e11 −0.624526 −0.312263 0.949996i \(-0.601087\pi\)
−0.312263 + 0.949996i \(0.601087\pi\)
\(360\) −3.69496e10 −0.115944
\(361\) −1.32157e11 −0.409551
\(362\) −1.06913e11 −0.327220
\(363\) −3.36942e11 −1.01853
\(364\) −1.55530e11 −0.464363
\(365\) −4.21874e10 −0.124413
\(366\) −1.47870e11 −0.430741
\(367\) −2.25518e11 −0.648908 −0.324454 0.945901i \(-0.605181\pi\)
−0.324454 + 0.945901i \(0.605181\pi\)
\(368\) 8.62937e10 0.245281
\(369\) 4.49203e10 0.126132
\(370\) 4.11484e10 0.114142
\(371\) 2.22546e11 0.609870
\(372\) 2.67763e11 0.724948
\(373\) −2.04414e11 −0.546791 −0.273395 0.961902i \(-0.588147\pi\)
−0.273395 + 0.961902i \(0.588147\pi\)
\(374\) −2.52454e11 −0.667206
\(375\) 1.51995e11 0.396908
\(376\) 5.46831e11 1.41094
\(377\) 6.07076e11 1.54777
\(378\) −5.23253e9 −0.0131825
\(379\) 4.03306e10 0.100406 0.0502029 0.998739i \(-0.484013\pi\)
0.0502029 + 0.998739i \(0.484013\pi\)
\(380\) 3.44740e10 0.0848136
\(381\) 6.12628e11 1.48948
\(382\) −2.01052e11 −0.483084
\(383\) −3.98325e11 −0.945895 −0.472947 0.881091i \(-0.656810\pi\)
−0.472947 + 0.881091i \(0.656810\pi\)
\(384\) 5.70393e11 1.33870
\(385\) −3.07876e10 −0.0714171
\(386\) 5.26764e10 0.120774
\(387\) −2.33837e11 −0.529923
\(388\) 3.52439e11 0.789480
\(389\) −4.22504e11 −0.935531 −0.467765 0.883853i \(-0.654941\pi\)
−0.467765 + 0.883853i \(0.654941\pi\)
\(390\) 7.05242e10 0.154365
\(391\) −3.33224e11 −0.721009
\(392\) −5.68497e10 −0.121602
\(393\) −1.37683e11 −0.291149
\(394\) 2.94359e11 0.615382
\(395\) −3.00383e7 −6.20853e−5 0
\(396\) −4.68795e11 −0.957976
\(397\) 6.50999e11 1.31529 0.657647 0.753326i \(-0.271552\pi\)
0.657647 + 0.753326i \(0.271552\pi\)
\(398\) 1.80567e11 0.360714
\(399\) −2.05222e11 −0.405365
\(400\) −1.79769e11 −0.351111
\(401\) −3.10509e11 −0.599687 −0.299843 0.953988i \(-0.596934\pi\)
−0.299843 + 0.953988i \(0.596934\pi\)
\(402\) 4.98024e10 0.0951115
\(403\) −5.72471e11 −1.08114
\(404\) 1.62472e10 0.0303433
\(405\) −8.16155e10 −0.150739
\(406\) 9.64102e10 0.176099
\(407\) 1.20160e12 2.17063
\(408\) −7.00799e11 −1.25205
\(409\) 2.99519e11 0.529261 0.264630 0.964350i \(-0.414750\pi\)
0.264630 + 0.964350i \(0.414750\pi\)
\(410\) 5.26444e9 0.00920078
\(411\) 6.01766e11 1.04025
\(412\) −1.68935e11 −0.288856
\(413\) 6.06492e10 0.102577
\(414\) 1.86639e11 0.312249
\(415\) 1.04721e11 0.173307
\(416\) −1.00006e12 −1.63722
\(417\) −9.94370e11 −1.61041
\(418\) −3.03645e11 −0.486488
\(419\) −4.35217e11 −0.689832 −0.344916 0.938634i \(-0.612093\pi\)
−0.344916 + 0.938634i \(0.612093\pi\)
\(420\) −3.71323e10 −0.0582277
\(421\) −2.07600e11 −0.322076 −0.161038 0.986948i \(-0.551484\pi\)
−0.161038 + 0.986948i \(0.551484\pi\)
\(422\) −5.93493e11 −0.910981
\(423\) −1.03478e12 −1.57151
\(424\) 9.14054e11 1.37349
\(425\) 6.94179e11 1.03210
\(426\) 2.26504e11 0.333222
\(427\) −1.66455e11 −0.242310
\(428\) −4.84955e11 −0.698562
\(429\) 2.05942e12 2.93554
\(430\) −2.74045e10 −0.0386557
\(431\) 8.61584e11 1.20268 0.601340 0.798993i \(-0.294634\pi\)
0.601340 + 0.798993i \(0.294634\pi\)
\(432\) 1.88034e10 0.0259752
\(433\) 1.45840e11 0.199379 0.0996896 0.995019i \(-0.468215\pi\)
0.0996896 + 0.995019i \(0.468215\pi\)
\(434\) −9.09145e10 −0.123007
\(435\) 1.44938e11 0.194079
\(436\) −6.67206e11 −0.884241
\(437\) −4.00792e11 −0.525718
\(438\) 4.48160e11 0.581835
\(439\) −1.07131e11 −0.137665 −0.0688324 0.997628i \(-0.521927\pi\)
−0.0688324 + 0.997628i \(0.521927\pi\)
\(440\) −1.26452e11 −0.160839
\(441\) 1.07578e11 0.135441
\(442\) 6.50972e11 0.811263
\(443\) −1.36838e11 −0.168806 −0.0844031 0.996432i \(-0.526898\pi\)
−0.0844031 + 0.996432i \(0.526898\pi\)
\(444\) 1.44923e12 1.76976
\(445\) 5.99510e10 0.0724731
\(446\) −2.23840e11 −0.267874
\(447\) −4.17981e11 −0.495191
\(448\) −4.32876e10 −0.0507706
\(449\) −7.65671e11 −0.889065 −0.444532 0.895763i \(-0.646630\pi\)
−0.444532 + 0.895763i \(0.646630\pi\)
\(450\) −3.88811e11 −0.446974
\(451\) 1.53730e11 0.174971
\(452\) 5.60331e11 0.631425
\(453\) 4.60754e11 0.514076
\(454\) −4.29226e11 −0.474170
\(455\) 7.93880e10 0.0868368
\(456\) −8.42901e11 −0.912924
\(457\) 5.41842e11 0.581099 0.290549 0.956860i \(-0.406162\pi\)
0.290549 + 0.956860i \(0.406162\pi\)
\(458\) −1.98805e11 −0.211121
\(459\) −7.26094e10 −0.0763547
\(460\) −7.25181e10 −0.0755155
\(461\) −7.10838e11 −0.733021 −0.366510 0.930414i \(-0.619448\pi\)
−0.366510 + 0.930414i \(0.619448\pi\)
\(462\) 3.27059e11 0.333992
\(463\) 7.96272e11 0.805280 0.402640 0.915358i \(-0.368093\pi\)
0.402640 + 0.915358i \(0.368093\pi\)
\(464\) −3.46456e11 −0.346990
\(465\) −1.36676e11 −0.135567
\(466\) −5.53511e11 −0.543738
\(467\) −1.67673e12 −1.63132 −0.815658 0.578535i \(-0.803625\pi\)
−0.815658 + 0.578535i \(0.803625\pi\)
\(468\) 1.20882e12 1.16481
\(469\) 5.60618e10 0.0535044
\(470\) −1.21272e11 −0.114635
\(471\) 5.84478e11 0.547235
\(472\) 2.49102e11 0.231014
\(473\) −8.00257e11 −0.735114
\(474\) 3.19099e8 0.000290351 0
\(475\) 8.34938e11 0.752546
\(476\) −3.42749e11 −0.306016
\(477\) −1.72969e12 −1.52980
\(478\) 4.14400e11 0.363073
\(479\) 1.17129e12 1.01661 0.508305 0.861177i \(-0.330272\pi\)
0.508305 + 0.861177i \(0.330272\pi\)
\(480\) −2.38761e11 −0.205295
\(481\) −3.09842e12 −2.63929
\(482\) 1.06754e12 0.900895
\(483\) 4.31697e11 0.360925
\(484\) −6.76844e11 −0.560641
\(485\) −1.79897e11 −0.147634
\(486\) 8.24112e11 0.670074
\(487\) 4.49797e11 0.362357 0.181178 0.983450i \(-0.442009\pi\)
0.181178 + 0.983450i \(0.442009\pi\)
\(488\) −6.83675e11 −0.545708
\(489\) −1.80297e12 −1.42594
\(490\) 1.26077e10 0.00987990
\(491\) 2.25034e12 1.74735 0.873677 0.486506i \(-0.161729\pi\)
0.873677 + 0.486506i \(0.161729\pi\)
\(492\) 1.85411e11 0.142657
\(493\) 1.33784e12 1.01998
\(494\) 7.82970e11 0.591526
\(495\) 2.39290e11 0.179143
\(496\) 3.26707e11 0.242376
\(497\) 2.54972e11 0.187452
\(498\) −1.11246e12 −0.810497
\(499\) 1.59712e10 0.0115315 0.00576574 0.999983i \(-0.498165\pi\)
0.00576574 + 0.999983i \(0.498165\pi\)
\(500\) 3.05326e11 0.218474
\(501\) 9.70275e11 0.688058
\(502\) 8.44300e11 0.593376
\(503\) 1.73375e12 1.20762 0.603811 0.797127i \(-0.293648\pi\)
0.603811 + 0.797127i \(0.293648\pi\)
\(504\) 4.41852e11 0.305028
\(505\) −8.29316e9 −0.00567425
\(506\) 6.38734e11 0.433155
\(507\) −3.23384e12 −2.17361
\(508\) 1.23064e12 0.819869
\(509\) 9.77460e11 0.645460 0.322730 0.946491i \(-0.395399\pi\)
0.322730 + 0.946491i \(0.395399\pi\)
\(510\) 1.55417e11 0.101726
\(511\) 5.04487e11 0.327307
\(512\) 1.04525e12 0.672212
\(513\) −8.73326e10 −0.0556734
\(514\) −1.17191e12 −0.740558
\(515\) 8.62303e10 0.0540166
\(516\) −9.65175e11 −0.599353
\(517\) −3.54133e12 −2.18001
\(518\) −4.92062e11 −0.300286
\(519\) −7.39300e11 −0.447268
\(520\) 3.26067e11 0.195565
\(521\) 5.89223e11 0.350356 0.175178 0.984537i \(-0.443950\pi\)
0.175178 + 0.984537i \(0.443950\pi\)
\(522\) −7.49328e11 −0.441728
\(523\) 1.43218e12 0.837027 0.418513 0.908211i \(-0.362551\pi\)
0.418513 + 0.908211i \(0.362551\pi\)
\(524\) −2.76577e11 −0.160260
\(525\) −8.99320e11 −0.516651
\(526\) −1.32468e11 −0.0754527
\(527\) −1.26158e12 −0.712471
\(528\) −1.17530e12 −0.658109
\(529\) −9.58063e11 −0.531916
\(530\) −2.02711e11 −0.111593
\(531\) −4.71382e11 −0.257305
\(532\) −4.12248e11 −0.223129
\(533\) −3.96405e11 −0.212749
\(534\) −6.36865e11 −0.338931
\(535\) 2.47538e11 0.130632
\(536\) 2.30260e11 0.120497
\(537\) 3.80594e12 1.97505
\(538\) −1.34540e12 −0.692357
\(539\) 3.68165e11 0.187885
\(540\) −1.58017e10 −0.00799708
\(541\) 1.17323e12 0.588839 0.294419 0.955676i \(-0.404874\pi\)
0.294419 + 0.955676i \(0.404874\pi\)
\(542\) 1.46291e12 0.728152
\(543\) 1.92200e12 0.948755
\(544\) −2.20388e12 −1.07893
\(545\) 3.40565e11 0.165355
\(546\) −8.43345e11 −0.406105
\(547\) 2.59515e11 0.123942 0.0619712 0.998078i \(-0.480261\pi\)
0.0619712 + 0.998078i \(0.480261\pi\)
\(548\) 1.20882e12 0.572597
\(549\) 1.29374e12 0.607814
\(550\) −1.33062e12 −0.620045
\(551\) 1.60912e12 0.743714
\(552\) 1.77309e12 0.812841
\(553\) 3.59205e8 0.000163335 0
\(554\) −2.36022e11 −0.106453
\(555\) −7.39737e11 −0.330947
\(556\) −1.99748e12 −0.886432
\(557\) −2.36651e12 −1.04174 −0.520871 0.853635i \(-0.674393\pi\)
−0.520871 + 0.853635i \(0.674393\pi\)
\(558\) 7.06613e11 0.308552
\(559\) 2.06352e12 0.893832
\(560\) −4.53064e10 −0.0194676
\(561\) 4.53845e12 1.93453
\(562\) 8.42294e10 0.0356164
\(563\) −2.42400e12 −1.01682 −0.508410 0.861115i \(-0.669767\pi\)
−0.508410 + 0.861115i \(0.669767\pi\)
\(564\) −4.27113e12 −1.77741
\(565\) −2.86013e11 −0.118078
\(566\) −7.83821e11 −0.321028
\(567\) 9.75977e11 0.396566
\(568\) 1.04724e12 0.422160
\(569\) −2.11854e12 −0.847290 −0.423645 0.905828i \(-0.639250\pi\)
−0.423645 + 0.905828i \(0.639250\pi\)
\(570\) 1.86932e11 0.0741730
\(571\) −7.50992e11 −0.295646 −0.147823 0.989014i \(-0.547227\pi\)
−0.147823 + 0.989014i \(0.547227\pi\)
\(572\) 4.13695e12 1.61584
\(573\) 3.61437e12 1.40067
\(574\) −6.29534e10 −0.0242056
\(575\) −1.75634e12 −0.670045
\(576\) 3.36444e11 0.127354
\(577\) 4.35951e12 1.63737 0.818685 0.574243i \(-0.194704\pi\)
0.818685 + 0.574243i \(0.194704\pi\)
\(578\) 1.42864e11 0.0532413
\(579\) −9.46981e11 −0.350177
\(580\) 2.91149e11 0.106829
\(581\) −1.25228e12 −0.455940
\(582\) 1.91106e12 0.690433
\(583\) −5.91951e12 −2.12216
\(584\) 2.07206e12 0.737130
\(585\) −6.17026e11 −0.217822
\(586\) 1.89173e12 0.662704
\(587\) −2.20056e12 −0.765002 −0.382501 0.923955i \(-0.624937\pi\)
−0.382501 + 0.923955i \(0.624937\pi\)
\(588\) 4.44037e11 0.153187
\(589\) −1.51739e12 −0.519492
\(590\) −5.52438e10 −0.0187693
\(591\) −5.29179e12 −1.78426
\(592\) 1.76825e12 0.591693
\(593\) −2.83604e12 −0.941815 −0.470907 0.882183i \(-0.656073\pi\)
−0.470907 + 0.882183i \(0.656073\pi\)
\(594\) 1.39180e11 0.0458710
\(595\) 1.74951e11 0.0572256
\(596\) −8.39636e11 −0.272573
\(597\) −3.24610e12 −1.04587
\(598\) −1.64702e12 −0.526677
\(599\) −8.29286e11 −0.263199 −0.131599 0.991303i \(-0.542011\pi\)
−0.131599 + 0.991303i \(0.542011\pi\)
\(600\) −3.69374e12 −1.16355
\(601\) 5.62459e12 1.75855 0.879277 0.476311i \(-0.158026\pi\)
0.879277 + 0.476311i \(0.158026\pi\)
\(602\) 3.27710e11 0.101696
\(603\) −4.35728e11 −0.134211
\(604\) 9.25557e11 0.282968
\(605\) 3.45485e11 0.104841
\(606\) 8.80989e10 0.0265365
\(607\) −4.68777e11 −0.140158 −0.0700789 0.997541i \(-0.522325\pi\)
−0.0700789 + 0.997541i \(0.522325\pi\)
\(608\) −2.65076e12 −0.786691
\(609\) −1.73320e12 −0.510588
\(610\) 1.51620e11 0.0443375
\(611\) 9.13159e12 2.65070
\(612\) 2.66394e12 0.767614
\(613\) 5.58394e12 1.59723 0.798617 0.601840i \(-0.205566\pi\)
0.798617 + 0.601840i \(0.205566\pi\)
\(614\) 2.47376e12 0.702425
\(615\) −9.46405e10 −0.0266771
\(616\) 1.51215e12 0.423137
\(617\) −3.36717e12 −0.935367 −0.467683 0.883896i \(-0.654911\pi\)
−0.467683 + 0.883896i \(0.654911\pi\)
\(618\) −9.16031e11 −0.252617
\(619\) −5.66928e12 −1.55210 −0.776051 0.630671i \(-0.782780\pi\)
−0.776051 + 0.630671i \(0.782780\pi\)
\(620\) −2.74552e11 −0.0746212
\(621\) 1.83709e11 0.0495700
\(622\) −9.46512e11 −0.253553
\(623\) −7.16909e11 −0.190663
\(624\) 3.03061e12 0.800201
\(625\) 3.58011e12 0.938505
\(626\) −5.72168e11 −0.148915
\(627\) 5.45871e12 1.41054
\(628\) 1.17409e12 0.301220
\(629\) −6.82812e12 −1.73930
\(630\) −9.79904e10 −0.0247828
\(631\) −1.06685e12 −0.267899 −0.133950 0.990988i \(-0.542766\pi\)
−0.133950 + 0.990988i \(0.542766\pi\)
\(632\) 1.47535e9 0.000367847 0
\(633\) 1.06694e13 2.64133
\(634\) 2.87325e12 0.706273
\(635\) −6.28163e11 −0.153317
\(636\) −7.13941e12 −1.73024
\(637\) −9.49340e11 −0.228452
\(638\) −2.56442e12 −0.612768
\(639\) −1.98172e12 −0.470205
\(640\) −5.84856e11 −0.137797
\(641\) −7.83632e12 −1.83337 −0.916686 0.399607i \(-0.869147\pi\)
−0.916686 + 0.399607i \(0.869147\pi\)
\(642\) −2.62962e12 −0.610921
\(643\) 7.05971e12 1.62869 0.814343 0.580383i \(-0.197097\pi\)
0.814343 + 0.580383i \(0.197097\pi\)
\(644\) 8.67188e11 0.198668
\(645\) 4.92660e11 0.112080
\(646\) 1.72547e12 0.389817
\(647\) 2.77314e12 0.622161 0.311081 0.950384i \(-0.399309\pi\)
0.311081 + 0.950384i \(0.399309\pi\)
\(648\) 4.00859e12 0.893108
\(649\) −1.61321e12 −0.356935
\(650\) 3.43111e12 0.753919
\(651\) 1.63440e12 0.356651
\(652\) −3.62179e12 −0.784891
\(653\) 3.09564e12 0.666257 0.333128 0.942882i \(-0.391896\pi\)
0.333128 + 0.942882i \(0.391896\pi\)
\(654\) −3.61785e12 −0.773305
\(655\) 1.41175e11 0.0299689
\(656\) 2.26227e11 0.0476954
\(657\) −3.92102e12 −0.821021
\(658\) 1.45019e12 0.301585
\(659\) −4.80261e12 −0.991958 −0.495979 0.868335i \(-0.665191\pi\)
−0.495979 + 0.868335i \(0.665191\pi\)
\(660\) 9.87683e11 0.202614
\(661\) −5.13389e12 −1.04602 −0.523010 0.852327i \(-0.675191\pi\)
−0.523010 + 0.852327i \(0.675191\pi\)
\(662\) −2.30212e12 −0.465872
\(663\) −1.17027e13 −2.35221
\(664\) −5.14342e12 −1.02682
\(665\) 2.10426e11 0.0417256
\(666\) 3.82444e12 0.753241
\(667\) −3.38488e12 −0.662181
\(668\) 1.94908e12 0.378735
\(669\) 4.02404e12 0.776685
\(670\) −5.10652e10 −0.00979014
\(671\) 4.42755e12 0.843164
\(672\) 2.85516e12 0.540093
\(673\) 4.43802e12 0.833915 0.416957 0.908926i \(-0.363096\pi\)
0.416957 + 0.908926i \(0.363096\pi\)
\(674\) −4.00277e12 −0.747122
\(675\) −3.82707e11 −0.0709576
\(676\) −6.49609e12 −1.19644
\(677\) −4.70675e12 −0.861136 −0.430568 0.902558i \(-0.641687\pi\)
−0.430568 + 0.902558i \(0.641687\pi\)
\(678\) 3.03834e12 0.552207
\(679\) 2.15126e12 0.388399
\(680\) 7.18569e11 0.128878
\(681\) 7.71632e12 1.37483
\(682\) 2.41824e12 0.428025
\(683\) 6.12667e11 0.107729 0.0538644 0.998548i \(-0.482846\pi\)
0.0538644 + 0.998548i \(0.482846\pi\)
\(684\) 3.20411e12 0.559699
\(685\) −6.17025e11 −0.107077
\(686\) −1.50765e11 −0.0259922
\(687\) 3.57397e12 0.612133
\(688\) −1.17764e12 −0.200385
\(689\) 1.52639e13 2.58035
\(690\) −3.93222e11 −0.0660415
\(691\) 2.69919e12 0.450383 0.225191 0.974315i \(-0.427699\pi\)
0.225191 + 0.974315i \(0.427699\pi\)
\(692\) −1.48510e12 −0.246194
\(693\) −2.86148e12 −0.471293
\(694\) 4.72586e12 0.773327
\(695\) 1.01958e12 0.165764
\(696\) −7.11869e12 −1.14990
\(697\) −8.73576e11 −0.140202
\(698\) 1.13375e12 0.180788
\(699\) 9.95064e12 1.57654
\(700\) −1.80654e12 −0.284386
\(701\) −5.78506e12 −0.904850 −0.452425 0.891802i \(-0.649441\pi\)
−0.452425 + 0.891802i \(0.649441\pi\)
\(702\) −3.58886e11 −0.0557750
\(703\) −8.21267e12 −1.26819
\(704\) 1.15141e12 0.176666
\(705\) 2.18014e12 0.332379
\(706\) −4.86772e12 −0.737403
\(707\) 9.91715e10 0.0149279
\(708\) −1.94566e12 −0.291016
\(709\) −3.72656e12 −0.553860 −0.276930 0.960890i \(-0.589317\pi\)
−0.276930 + 0.960890i \(0.589317\pi\)
\(710\) −2.32248e11 −0.0342996
\(711\) −2.79184e9 −0.000409711 0
\(712\) −2.94453e12 −0.429394
\(713\) 3.19192e12 0.462541
\(714\) −1.85852e12 −0.267624
\(715\) −2.11164e12 −0.302165
\(716\) 7.64532e12 1.08714
\(717\) −7.44980e12 −1.05271
\(718\) −2.14092e12 −0.300636
\(719\) 1.33255e13 1.85953 0.929765 0.368154i \(-0.120010\pi\)
0.929765 + 0.368154i \(0.120010\pi\)
\(720\) 3.52134e11 0.0488328
\(721\) −1.03116e12 −0.142108
\(722\) −1.43952e12 −0.197151
\(723\) −1.91916e13 −2.61209
\(724\) 3.86089e12 0.522233
\(725\) 7.05144e12 0.947888
\(726\) −3.67012e12 −0.490304
\(727\) −2.39852e12 −0.318448 −0.159224 0.987242i \(-0.550899\pi\)
−0.159224 + 0.987242i \(0.550899\pi\)
\(728\) −3.89918e12 −0.514497
\(729\) −6.81442e12 −0.893625
\(730\) −4.59524e11 −0.0598901
\(731\) 4.54748e12 0.589037
\(732\) 5.33998e12 0.687448
\(733\) 7.93815e12 1.01567 0.507834 0.861455i \(-0.330446\pi\)
0.507834 + 0.861455i \(0.330446\pi\)
\(734\) −2.45644e12 −0.312373
\(735\) −2.26652e11 −0.0286462
\(736\) 5.57603e12 0.700447
\(737\) −1.49119e12 −0.186178
\(738\) 4.89292e11 0.0607175
\(739\) −2.20371e12 −0.271803 −0.135902 0.990722i \(-0.543393\pi\)
−0.135902 + 0.990722i \(0.543393\pi\)
\(740\) −1.48598e12 −0.182167
\(741\) −1.40757e13 −1.71509
\(742\) 2.42407e12 0.293581
\(743\) −1.09079e12 −0.131308 −0.0656540 0.997842i \(-0.520913\pi\)
−0.0656540 + 0.997842i \(0.520913\pi\)
\(744\) 6.71290e12 0.803215
\(745\) 4.28580e11 0.0509716
\(746\) −2.22657e12 −0.263215
\(747\) 9.73305e12 1.14368
\(748\) 9.11678e12 1.06484
\(749\) −2.96012e12 −0.343670
\(750\) 1.65560e12 0.191064
\(751\) −3.09647e11 −0.0355212 −0.0177606 0.999842i \(-0.505654\pi\)
−0.0177606 + 0.999842i \(0.505654\pi\)
\(752\) −5.21136e12 −0.594252
\(753\) −1.51783e13 −1.72046
\(754\) 6.61254e12 0.745071
\(755\) −4.72437e11 −0.0529155
\(756\) 1.88960e11 0.0210389
\(757\) 1.44340e12 0.159755 0.0798777 0.996805i \(-0.474547\pi\)
0.0798777 + 0.996805i \(0.474547\pi\)
\(758\) 4.39299e11 0.0483336
\(759\) −1.14827e13 −1.25591
\(760\) 8.64274e11 0.0939702
\(761\) −2.27862e12 −0.246287 −0.123143 0.992389i \(-0.539297\pi\)
−0.123143 + 0.992389i \(0.539297\pi\)
\(762\) 6.67302e12 0.717010
\(763\) −4.07256e12 −0.435018
\(764\) 7.26051e12 0.770987
\(765\) −1.35977e12 −0.143545
\(766\) −4.33873e12 −0.455337
\(767\) 4.15978e12 0.434001
\(768\) 8.02053e12 0.831912
\(769\) 1.09547e13 1.12962 0.564809 0.825221i \(-0.308950\pi\)
0.564809 + 0.825221i \(0.308950\pi\)
\(770\) −3.35352e11 −0.0343789
\(771\) 2.10677e13 2.14720
\(772\) −1.90228e12 −0.192751
\(773\) 7.52114e12 0.757663 0.378831 0.925466i \(-0.376326\pi\)
0.378831 + 0.925466i \(0.376326\pi\)
\(774\) −2.54705e12 −0.255096
\(775\) −6.64948e12 −0.662110
\(776\) 8.83576e12 0.874714
\(777\) 8.84595e12 0.870662
\(778\) −4.60211e12 −0.450348
\(779\) −1.05071e12 −0.102227
\(780\) −2.54681e12 −0.246361
\(781\) −6.78201e12 −0.652272
\(782\) −3.62962e12 −0.347081
\(783\) −7.37564e11 −0.0701248
\(784\) 5.41785e11 0.0512158
\(785\) −5.99298e11 −0.0563287
\(786\) −1.49971e12 −0.140154
\(787\) 1.85303e12 0.172185 0.0860926 0.996287i \(-0.472562\pi\)
0.0860926 + 0.996287i \(0.472562\pi\)
\(788\) −1.06301e13 −0.982129
\(789\) 2.38142e12 0.218771
\(790\) −3.27191e8 −2.98868e−5 0
\(791\) 3.42021e12 0.310641
\(792\) −1.17528e13 −1.06140
\(793\) −1.14168e13 −1.02521
\(794\) 7.09097e12 0.633159
\(795\) 3.64421e12 0.323557
\(796\) −6.52073e12 −0.575688
\(797\) −1.84378e13 −1.61863 −0.809314 0.587377i \(-0.800161\pi\)
−0.809314 + 0.587377i \(0.800161\pi\)
\(798\) −2.23537e12 −0.195136
\(799\) 2.01237e13 1.74682
\(800\) −1.16161e13 −1.00266
\(801\) 5.57202e12 0.478262
\(802\) −3.38220e12 −0.288679
\(803\) −1.34189e13 −1.13893
\(804\) −1.79850e12 −0.151795
\(805\) −4.42644e11 −0.0371512
\(806\) −6.23560e12 −0.520440
\(807\) 2.41866e13 2.00745
\(808\) 4.07323e11 0.0336192
\(809\) −1.03419e13 −0.848856 −0.424428 0.905462i \(-0.639525\pi\)
−0.424428 + 0.905462i \(0.639525\pi\)
\(810\) −8.88992e11 −0.0725630
\(811\) −2.31795e13 −1.88153 −0.940764 0.339062i \(-0.889890\pi\)
−0.940764 + 0.339062i \(0.889890\pi\)
\(812\) −3.48163e12 −0.281048
\(813\) −2.62993e13 −2.11123
\(814\) 1.30884e13 1.04490
\(815\) 1.84869e12 0.146776
\(816\) 6.67869e12 0.527334
\(817\) 5.46958e12 0.429492
\(818\) 3.26250e12 0.254777
\(819\) 7.37854e12 0.573051
\(820\) −1.90113e11 −0.0146842
\(821\) 1.10059e13 0.845436 0.422718 0.906261i \(-0.361076\pi\)
0.422718 + 0.906261i \(0.361076\pi\)
\(822\) 6.55470e12 0.500760
\(823\) 2.30119e13 1.74845 0.874224 0.485523i \(-0.161371\pi\)
0.874224 + 0.485523i \(0.161371\pi\)
\(824\) −4.23525e12 −0.320041
\(825\) 2.39211e13 1.79778
\(826\) 6.60618e11 0.0493787
\(827\) 6.58898e12 0.489827 0.244914 0.969545i \(-0.421240\pi\)
0.244914 + 0.969545i \(0.421240\pi\)
\(828\) −6.74003e12 −0.498340
\(829\) −1.32427e13 −0.973829 −0.486915 0.873450i \(-0.661878\pi\)
−0.486915 + 0.873450i \(0.661878\pi\)
\(830\) 1.14067e12 0.0834271
\(831\) 4.24304e12 0.308654
\(832\) −2.96899e12 −0.214810
\(833\) −2.09210e12 −0.150550
\(834\) −1.08311e13 −0.775222
\(835\) −9.94878e11 −0.0708240
\(836\) 1.09654e13 0.776419
\(837\) 6.95520e11 0.0489830
\(838\) −4.74058e12 −0.332073
\(839\) −5.05558e12 −0.352243 −0.176122 0.984368i \(-0.556355\pi\)
−0.176122 + 0.984368i \(0.556355\pi\)
\(840\) −9.30918e11 −0.0645141
\(841\) −9.17397e11 −0.0632376
\(842\) −2.26127e12 −0.155042
\(843\) −1.51422e12 −0.103268
\(844\) 2.14326e13 1.45390
\(845\) 3.31584e12 0.223737
\(846\) −1.12713e13 −0.756499
\(847\) −4.13139e12 −0.275817
\(848\) −8.71104e12 −0.578480
\(849\) 1.40910e13 0.930802
\(850\) 7.56130e12 0.496834
\(851\) 1.72758e13 1.12916
\(852\) −8.17966e12 −0.531811
\(853\) 1.03049e13 0.666456 0.333228 0.942846i \(-0.391862\pi\)
0.333228 + 0.942846i \(0.391862\pi\)
\(854\) −1.81310e12 −0.116644
\(855\) −1.63549e12 −0.104665
\(856\) −1.21580e13 −0.773979
\(857\) −1.66788e13 −1.05621 −0.528105 0.849179i \(-0.677097\pi\)
−0.528105 + 0.849179i \(0.677097\pi\)
\(858\) 2.24322e13 1.41312
\(859\) −2.36677e13 −1.48316 −0.741579 0.670865i \(-0.765923\pi\)
−0.741579 + 0.670865i \(0.765923\pi\)
\(860\) 9.89649e11 0.0616933
\(861\) 1.13173e12 0.0701827
\(862\) 9.38476e12 0.578949
\(863\) 1.26428e13 0.775880 0.387940 0.921685i \(-0.373187\pi\)
0.387940 + 0.921685i \(0.373187\pi\)
\(864\) 1.21502e12 0.0741772
\(865\) 7.58046e11 0.0460387
\(866\) 1.58855e12 0.0959776
\(867\) −2.56832e12 −0.154370
\(868\) 3.28316e12 0.196315
\(869\) −9.55450e9 −0.000568354 0
\(870\) 1.57872e12 0.0934264
\(871\) 3.84514e12 0.226376
\(872\) −1.67271e13 −0.979705
\(873\) −1.67202e13 −0.974264
\(874\) −4.36561e12 −0.253071
\(875\) 1.86368e12 0.107482
\(876\) −1.61842e13 −0.928589
\(877\) 2.21629e13 1.26511 0.632555 0.774515i \(-0.282006\pi\)
0.632555 + 0.774515i \(0.282006\pi\)
\(878\) −1.16691e12 −0.0662695
\(879\) −3.40082e13 −1.92147
\(880\) 1.20511e12 0.0677413
\(881\) −1.87132e13 −1.04654 −0.523272 0.852166i \(-0.675289\pi\)
−0.523272 + 0.852166i \(0.675289\pi\)
\(882\) 1.17179e12 0.0651991
\(883\) −1.66483e13 −0.921611 −0.460805 0.887501i \(-0.652439\pi\)
−0.460805 + 0.887501i \(0.652439\pi\)
\(884\) −2.35083e13 −1.29475
\(885\) 9.93134e11 0.0544206
\(886\) −1.49050e12 −0.0812604
\(887\) −1.58859e13 −0.861698 −0.430849 0.902424i \(-0.641786\pi\)
−0.430849 + 0.902424i \(0.641786\pi\)
\(888\) 3.63326e13 1.96082
\(889\) 7.51171e12 0.403349
\(890\) 6.53013e11 0.0348873
\(891\) −2.59600e13 −1.37993
\(892\) 8.08344e12 0.427518
\(893\) 2.42042e13 1.27368
\(894\) −4.55284e12 −0.238376
\(895\) −3.90244e12 −0.203298
\(896\) 6.99384e12 0.362518
\(897\) 2.96091e13 1.52707
\(898\) −8.34003e12 −0.427980
\(899\) −1.28151e13 −0.654339
\(900\) 1.40410e13 0.713355
\(901\) 3.36377e13 1.70046
\(902\) 1.67450e12 0.0842278
\(903\) −5.89134e12 −0.294862
\(904\) 1.40477e13 0.699595
\(905\) −1.97074e12 −0.0976585
\(906\) 5.01873e12 0.247467
\(907\) −3.65370e13 −1.79267 −0.896333 0.443381i \(-0.853779\pi\)
−0.896333 + 0.443381i \(0.853779\pi\)
\(908\) 1.55005e13 0.756760
\(909\) −7.70789e11 −0.0374454
\(910\) 8.64729e11 0.0418017
\(911\) 2.09138e13 1.00600 0.503002 0.864286i \(-0.332229\pi\)
0.503002 + 0.864286i \(0.332229\pi\)
\(912\) 8.03294e12 0.384501
\(913\) 3.33093e13 1.58653
\(914\) 5.90199e12 0.279731
\(915\) −2.72572e12 −0.128554
\(916\) 7.17935e12 0.336942
\(917\) −1.68820e12 −0.0788427
\(918\) −7.90894e11 −0.0367558
\(919\) −1.22511e12 −0.0566571 −0.0283286 0.999599i \(-0.509018\pi\)
−0.0283286 + 0.999599i \(0.509018\pi\)
\(920\) −1.81805e12 −0.0836683
\(921\) −4.44716e13 −2.03664
\(922\) −7.74276e12 −0.352863
\(923\) 1.74879e13 0.793105
\(924\) −1.18109e13 −0.533041
\(925\) −3.59894e13 −1.61635
\(926\) 8.67335e12 0.387648
\(927\) 8.01448e12 0.356465
\(928\) −2.23869e13 −0.990896
\(929\) 9.53162e12 0.419852 0.209926 0.977717i \(-0.432678\pi\)
0.209926 + 0.977717i \(0.432678\pi\)
\(930\) −1.48873e12 −0.0652594
\(931\) −2.51632e12 −0.109772
\(932\) 1.99887e13 0.867788
\(933\) 1.70157e13 0.735163
\(934\) −1.82637e13 −0.785287
\(935\) −4.65353e12 −0.199127
\(936\) 3.03056e13 1.29057
\(937\) −9.70345e12 −0.411242 −0.205621 0.978632i \(-0.565921\pi\)
−0.205621 + 0.978632i \(0.565921\pi\)
\(938\) 6.10650e11 0.0257561
\(939\) 1.02860e13 0.431770
\(940\) 4.37944e12 0.182954
\(941\) −2.29625e13 −0.954698 −0.477349 0.878714i \(-0.658402\pi\)
−0.477349 + 0.878714i \(0.658402\pi\)
\(942\) 6.36639e12 0.263429
\(943\) 2.21024e12 0.0910198
\(944\) −2.37397e12 −0.0972973
\(945\) −9.64520e10 −0.00393431
\(946\) −8.71676e12 −0.353871
\(947\) 1.40763e13 0.568738 0.284369 0.958715i \(-0.408216\pi\)
0.284369 + 0.958715i \(0.408216\pi\)
\(948\) −1.15235e10 −0.000463391 0
\(949\) 3.46015e13 1.38483
\(950\) 9.09452e12 0.362263
\(951\) −5.16534e13 −2.04780
\(952\) −8.59281e12 −0.339054
\(953\) 9.86435e12 0.387392 0.193696 0.981062i \(-0.437953\pi\)
0.193696 + 0.981062i \(0.437953\pi\)
\(954\) −1.88406e13 −0.736421
\(955\) −3.70602e12 −0.144176
\(956\) −1.49651e13 −0.579453
\(957\) 4.61014e13 1.77668
\(958\) 1.27582e13 0.489378
\(959\) 7.37852e12 0.281699
\(960\) −7.08838e11 −0.0269356
\(961\) −1.43550e13 −0.542937
\(962\) −3.37493e13 −1.27051
\(963\) 2.30069e13 0.862065
\(964\) −3.85518e13 −1.43780
\(965\) 9.70993e11 0.0360449
\(966\) 4.70224e12 0.173743
\(967\) −2.37375e12 −0.0873002 −0.0436501 0.999047i \(-0.513899\pi\)
−0.0436501 + 0.999047i \(0.513899\pi\)
\(968\) −1.69687e13 −0.621168
\(969\) −3.10193e13 −1.13025
\(970\) −1.95952e12 −0.0710686
\(971\) 4.45895e13 1.60970 0.804852 0.593476i \(-0.202245\pi\)
0.804852 + 0.593476i \(0.202245\pi\)
\(972\) −2.97608e13 −1.06942
\(973\) −1.21924e13 −0.436096
\(974\) 4.89939e12 0.174432
\(975\) −6.16822e13 −2.18594
\(976\) 6.51550e12 0.229839
\(977\) 8.90599e11 0.0312721 0.0156360 0.999878i \(-0.495023\pi\)
0.0156360 + 0.999878i \(0.495023\pi\)
\(978\) −1.96388e13 −0.686420
\(979\) 1.90691e13 0.663449
\(980\) −4.55296e11 −0.0157680
\(981\) 3.16531e13 1.09120
\(982\) 2.45117e13 0.841146
\(983\) 8.23794e12 0.281402 0.140701 0.990052i \(-0.455064\pi\)
0.140701 + 0.990052i \(0.455064\pi\)
\(984\) 4.64832e12 0.158059
\(985\) 5.42597e12 0.183660
\(986\) 1.45724e13 0.491003
\(987\) −2.60706e13 −0.874428
\(988\) −2.82751e13 −0.944056
\(989\) −1.15056e13 −0.382407
\(990\) 2.60645e12 0.0862364
\(991\) 8.90224e12 0.293203 0.146601 0.989196i \(-0.453167\pi\)
0.146601 + 0.989196i \(0.453167\pi\)
\(992\) 2.11108e13 0.692152
\(993\) 4.13859e13 1.35077
\(994\) 2.77727e12 0.0902359
\(995\) 3.32841e12 0.107655
\(996\) 4.01738e13 1.29353
\(997\) 1.45450e13 0.466216 0.233108 0.972451i \(-0.425110\pi\)
0.233108 + 0.972451i \(0.425110\pi\)
\(998\) 1.73965e11 0.00555106
\(999\) 3.76440e12 0.119578
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 7.10.a.a.1.2 2
3.2 odd 2 63.10.a.d.1.1 2
4.3 odd 2 112.10.a.e.1.2 2
5.2 odd 4 175.10.b.b.99.3 4
5.3 odd 4 175.10.b.b.99.2 4
5.4 even 2 175.10.a.b.1.1 2
7.2 even 3 49.10.c.c.18.1 4
7.3 odd 6 49.10.c.b.30.1 4
7.4 even 3 49.10.c.c.30.1 4
7.5 odd 6 49.10.c.b.18.1 4
7.6 odd 2 49.10.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.10.a.a.1.2 2 1.1 even 1 trivial
49.10.a.b.1.2 2 7.6 odd 2
49.10.c.b.18.1 4 7.5 odd 6
49.10.c.b.30.1 4 7.3 odd 6
49.10.c.c.18.1 4 7.2 even 3
49.10.c.c.30.1 4 7.4 even 3
63.10.a.d.1.1 2 3.2 odd 2
112.10.a.e.1.2 2 4.3 odd 2
175.10.a.b.1.1 2 5.4 even 2
175.10.b.b.99.2 4 5.3 odd 4
175.10.b.b.99.3 4 5.2 odd 4