Properties

Label 546.8.a.q.1.5
Level $546$
Weight $8$
Character 546.1
Self dual yes
Analytic conductor $170.562$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(170.562223914\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - x^{5} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(285.402\) of defining polynomial
Character \(\chi\) \(=\) 546.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\) \(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2299.22 q^{10} -3517.26 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -7759.86 q^{15} +4096.00 q^{16} +10914.5 q^{17} +5832.00 q^{18} -25836.8 q^{19} +18393.7 q^{20} -9261.00 q^{21} -28138.1 q^{22} +64084.6 q^{23} -13824.0 q^{24} +4475.01 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +216819. q^{29} -62078.9 q^{30} -190075. q^{31} +32768.0 q^{32} +94966.1 q^{33} +87316.4 q^{34} +98578.9 q^{35} +46656.0 q^{36} +107669. q^{37} -206695. q^{38} +59319.0 q^{39} +147150. q^{40} +561658. q^{41} -74088.0 q^{42} -277509. q^{43} -225105. q^{44} +209516. q^{45} +512677. q^{46} +511134. q^{47} -110592. q^{48} +117649. q^{49} +35800.1 q^{50} -294693. q^{51} -140608. q^{52} +1.28966e6 q^{53} -157464. q^{54} -1.01087e6 q^{55} +175616. q^{56} +697594. q^{57} +1.73455e6 q^{58} +611752. q^{59} -496631. q^{60} -620011. q^{61} -1.52060e6 q^{62} +250047. q^{63} +262144. q^{64} -631423. q^{65} +759729. q^{66} +1.99589e6 q^{67} +698531. q^{68} -1.73028e6 q^{69} +788632. q^{70} -3.28215e6 q^{71} +373248. q^{72} +2.89327e6 q^{73} +861355. q^{74} -120825. q^{75} -1.65356e6 q^{76} -1.20642e6 q^{77} +474552. q^{78} -2.70379e6 q^{79} +1.17720e6 q^{80} +531441. q^{81} +4.49327e6 q^{82} -3.10630e6 q^{83} -592704. q^{84} +3.13686e6 q^{85} -2.22007e6 q^{86} -5.85410e6 q^{87} -1.80084e6 q^{88} -30105.8 q^{89} +1.67613e6 q^{90} -753571. q^{91} +4.10141e6 q^{92} +5.13202e6 q^{93} +4.08907e6 q^{94} -7.42556e6 q^{95} -884736. q^{96} +9.04415e6 q^{97} +941192. q^{98} -2.56408e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.00000 0.707107
\(3\) −27.0000 −0.577350
\(4\) 64.0000 0.500000
\(5\) 287.402 1.02824 0.514121 0.857718i \(-0.328118\pi\)
0.514121 + 0.857718i \(0.328118\pi\)
\(6\) −216.000 −0.408248
\(7\) 343.000 0.377964
\(8\) 512.000 0.353553
\(9\) 729.000 0.333333
\(10\) 2299.22 0.727076
\(11\) −3517.26 −0.796765 −0.398383 0.917219i \(-0.630428\pi\)
−0.398383 + 0.917219i \(0.630428\pi\)
\(12\) −1728.00 −0.288675
\(13\) −2197.00 −0.277350
\(14\) 2744.00 0.267261
\(15\) −7759.86 −0.593655
\(16\) 4096.00 0.250000
\(17\) 10914.5 0.538808 0.269404 0.963027i \(-0.413173\pi\)
0.269404 + 0.963027i \(0.413173\pi\)
\(18\) 5832.00 0.235702
\(19\) −25836.8 −0.864175 −0.432087 0.901832i \(-0.642223\pi\)
−0.432087 + 0.901832i \(0.642223\pi\)
\(20\) 18393.7 0.514121
\(21\) −9261.00 −0.218218
\(22\) −28138.1 −0.563398
\(23\) 64084.6 1.09826 0.549131 0.835736i \(-0.314959\pi\)
0.549131 + 0.835736i \(0.314959\pi\)
\(24\) −13824.0 −0.204124
\(25\) 4475.01 0.0572801
\(26\) −17576.0 −0.196116
\(27\) −19683.0 −0.192450
\(28\) 21952.0 0.188982
\(29\) 216819. 1.65083 0.825417 0.564523i \(-0.190940\pi\)
0.825417 + 0.564523i \(0.190940\pi\)
\(30\) −62078.9 −0.419778
\(31\) −190075. −1.14593 −0.572966 0.819579i \(-0.694207\pi\)
−0.572966 + 0.819579i \(0.694207\pi\)
\(32\) 32768.0 0.176777
\(33\) 94966.1 0.460013
\(34\) 87316.4 0.380995
\(35\) 98578.9 0.388639
\(36\) 46656.0 0.166667
\(37\) 107669. 0.349451 0.174725 0.984617i \(-0.444096\pi\)
0.174725 + 0.984617i \(0.444096\pi\)
\(38\) −206695. −0.611064
\(39\) 59319.0 0.160128
\(40\) 147150. 0.363538
\(41\) 561658. 1.27271 0.636354 0.771397i \(-0.280442\pi\)
0.636354 + 0.771397i \(0.280442\pi\)
\(42\) −74088.0 −0.154303
\(43\) −277509. −0.532277 −0.266138 0.963935i \(-0.585748\pi\)
−0.266138 + 0.963935i \(0.585748\pi\)
\(44\) −225105. −0.398383
\(45\) 209516. 0.342747
\(46\) 512677. 0.776589
\(47\) 511134. 0.718112 0.359056 0.933316i \(-0.383099\pi\)
0.359056 + 0.933316i \(0.383099\pi\)
\(48\) −110592. −0.144338
\(49\) 117649. 0.142857
\(50\) 35800.1 0.0405032
\(51\) −294693. −0.311081
\(52\) −140608. −0.138675
\(53\) 1.28966e6 1.18990 0.594951 0.803762i \(-0.297172\pi\)
0.594951 + 0.803762i \(0.297172\pi\)
\(54\) −157464. −0.136083
\(55\) −1.01087e6 −0.819267
\(56\) 175616. 0.133631
\(57\) 697594. 0.498932
\(58\) 1.73455e6 1.16732
\(59\) 611752. 0.387787 0.193894 0.981023i \(-0.437888\pi\)
0.193894 + 0.981023i \(0.437888\pi\)
\(60\) −496631. −0.296828
\(61\) −620011. −0.349740 −0.174870 0.984592i \(-0.555950\pi\)
−0.174870 + 0.984592i \(0.555950\pi\)
\(62\) −1.52060e6 −0.810296
\(63\) 250047. 0.125988
\(64\) 262144. 0.125000
\(65\) −631423. −0.285183
\(66\) 759729. 0.325278
\(67\) 1.99589e6 0.810728 0.405364 0.914155i \(-0.367145\pi\)
0.405364 + 0.914155i \(0.367145\pi\)
\(68\) 698531. 0.269404
\(69\) −1.73028e6 −0.634082
\(70\) 788632. 0.274809
\(71\) −3.28215e6 −1.08831 −0.544157 0.838983i \(-0.683150\pi\)
−0.544157 + 0.838983i \(0.683150\pi\)
\(72\) 373248. 0.117851
\(73\) 2.89327e6 0.870480 0.435240 0.900314i \(-0.356664\pi\)
0.435240 + 0.900314i \(0.356664\pi\)
\(74\) 861355. 0.247099
\(75\) −120825. −0.0330707
\(76\) −1.65356e6 −0.432087
\(77\) −1.20642e6 −0.301149
\(78\) 474552. 0.113228
\(79\) −2.70379e6 −0.616989 −0.308495 0.951226i \(-0.599825\pi\)
−0.308495 + 0.951226i \(0.599825\pi\)
\(80\) 1.17720e6 0.257060
\(81\) 531441. 0.111111
\(82\) 4.49327e6 0.899940
\(83\) −3.10630e6 −0.596308 −0.298154 0.954518i \(-0.596371\pi\)
−0.298154 + 0.954518i \(0.596371\pi\)
\(84\) −592704. −0.109109
\(85\) 3.13686e6 0.554025
\(86\) −2.22007e6 −0.376377
\(87\) −5.85410e6 −0.953110
\(88\) −1.80084e6 −0.281699
\(89\) −30105.8 −0.00452674 −0.00226337 0.999997i \(-0.500720\pi\)
−0.00226337 + 0.999997i \(0.500720\pi\)
\(90\) 1.67613e6 0.242359
\(91\) −753571. −0.104828
\(92\) 4.10141e6 0.549131
\(93\) 5.13202e6 0.661604
\(94\) 4.08907e6 0.507782
\(95\) −7.42556e6 −0.888580
\(96\) −884736. −0.102062
\(97\) 9.04415e6 1.00616 0.503080 0.864240i \(-0.332200\pi\)
0.503080 + 0.864240i \(0.332200\pi\)
\(98\) 941192. 0.101015
\(99\) −2.56408e6 −0.265588
\(100\) 286401. 0.0286401
\(101\) −2.61539e6 −0.252587 −0.126294 0.991993i \(-0.540308\pi\)
−0.126294 + 0.991993i \(0.540308\pi\)
\(102\) −2.35754e6 −0.219968
\(103\) −7.41803e6 −0.668895 −0.334448 0.942414i \(-0.608550\pi\)
−0.334448 + 0.942414i \(0.608550\pi\)
\(104\) −1.12486e6 −0.0980581
\(105\) −2.66163e6 −0.224381
\(106\) 1.03173e7 0.841387
\(107\) 1.42614e7 1.12543 0.562715 0.826651i \(-0.309757\pi\)
0.562715 + 0.826651i \(0.309757\pi\)
\(108\) −1.25971e6 −0.0962250
\(109\) −1.82390e7 −1.34899 −0.674493 0.738281i \(-0.735638\pi\)
−0.674493 + 0.738281i \(0.735638\pi\)
\(110\) −8.08695e6 −0.579309
\(111\) −2.90707e6 −0.201755
\(112\) 1.40493e6 0.0944911
\(113\) 2.88688e7 1.88215 0.941075 0.338198i \(-0.109817\pi\)
0.941075 + 0.338198i \(0.109817\pi\)
\(114\) 5.58076e6 0.352798
\(115\) 1.84180e7 1.12928
\(116\) 1.38764e7 0.825417
\(117\) −1.60161e6 −0.0924500
\(118\) 4.89402e6 0.274207
\(119\) 3.74369e6 0.203650
\(120\) −3.97305e6 −0.209889
\(121\) −7.11603e6 −0.365165
\(122\) −4.96009e6 −0.247303
\(123\) −1.51648e7 −0.734798
\(124\) −1.21648e7 −0.572966
\(125\) −2.11672e7 −0.969343
\(126\) 2.00038e6 0.0890871
\(127\) 3.03113e7 1.31308 0.656541 0.754291i \(-0.272019\pi\)
0.656541 + 0.754291i \(0.272019\pi\)
\(128\) 2.09715e6 0.0883883
\(129\) 7.49275e6 0.307310
\(130\) −5.05138e6 −0.201655
\(131\) 3.34282e7 1.29916 0.649581 0.760292i \(-0.274944\pi\)
0.649581 + 0.760292i \(0.274944\pi\)
\(132\) 6.07783e6 0.230006
\(133\) −8.86203e6 −0.326627
\(134\) 1.59671e7 0.573271
\(135\) −5.65694e6 −0.197885
\(136\) 5.58825e6 0.190498
\(137\) −2.80128e7 −0.930754 −0.465377 0.885113i \(-0.654081\pi\)
−0.465377 + 0.885113i \(0.654081\pi\)
\(138\) −1.38423e7 −0.448364
\(139\) −1.21769e7 −0.384578 −0.192289 0.981338i \(-0.561591\pi\)
−0.192289 + 0.981338i \(0.561591\pi\)
\(140\) 6.30905e6 0.194319
\(141\) −1.38006e7 −0.414602
\(142\) −2.62572e7 −0.769554
\(143\) 7.72743e6 0.220983
\(144\) 2.98598e6 0.0833333
\(145\) 6.23141e7 1.69746
\(146\) 2.31462e7 0.615522
\(147\) −3.17652e6 −0.0824786
\(148\) 6.89084e6 0.174725
\(149\) 7.04276e6 0.174418 0.0872089 0.996190i \(-0.472205\pi\)
0.0872089 + 0.996190i \(0.472205\pi\)
\(150\) −966602. −0.0233845
\(151\) −1.85979e7 −0.439586 −0.219793 0.975547i \(-0.570538\pi\)
−0.219793 + 0.975547i \(0.570538\pi\)
\(152\) −1.32285e7 −0.305532
\(153\) 7.95670e6 0.179603
\(154\) −9.65137e6 −0.212945
\(155\) −5.46279e7 −1.17829
\(156\) 3.79642e6 0.0800641
\(157\) 1.49954e6 0.0309250 0.0154625 0.999880i \(-0.495078\pi\)
0.0154625 + 0.999880i \(0.495078\pi\)
\(158\) −2.16303e7 −0.436277
\(159\) −3.48209e7 −0.686990
\(160\) 9.41759e6 0.181769
\(161\) 2.19810e7 0.415104
\(162\) 4.25153e6 0.0785674
\(163\) −3.53009e7 −0.638453 −0.319227 0.947678i \(-0.603423\pi\)
−0.319227 + 0.947678i \(0.603423\pi\)
\(164\) 3.59461e7 0.636354
\(165\) 2.72935e7 0.473004
\(166\) −2.48504e7 −0.421653
\(167\) 9.19470e7 1.52767 0.763836 0.645411i \(-0.223314\pi\)
0.763836 + 0.645411i \(0.223314\pi\)
\(168\) −4.74163e6 −0.0771517
\(169\) 4.82681e6 0.0769231
\(170\) 2.50949e7 0.391755
\(171\) −1.88350e7 −0.288058
\(172\) −1.77606e7 −0.266138
\(173\) 1.32661e8 1.94796 0.973981 0.226629i \(-0.0727704\pi\)
0.973981 + 0.226629i \(0.0727704\pi\)
\(174\) −4.68328e7 −0.673950
\(175\) 1.53493e6 0.0216499
\(176\) −1.44067e7 −0.199191
\(177\) −1.65173e7 −0.223889
\(178\) −240847. −0.00320089
\(179\) −1.16724e7 −0.152116 −0.0760582 0.997103i \(-0.524233\pi\)
−0.0760582 + 0.997103i \(0.524233\pi\)
\(180\) 1.34090e7 0.171374
\(181\) 9.37365e7 1.17499 0.587494 0.809228i \(-0.300114\pi\)
0.587494 + 0.809228i \(0.300114\pi\)
\(182\) −6.02857e6 −0.0741249
\(183\) 1.67403e7 0.201922
\(184\) 3.28113e7 0.388294
\(185\) 3.09444e7 0.359320
\(186\) 4.10562e7 0.467825
\(187\) −3.83893e7 −0.429304
\(188\) 3.27126e7 0.359056
\(189\) −6.75127e6 −0.0727393
\(190\) −5.94045e7 −0.628321
\(191\) 1.11753e8 1.16049 0.580245 0.814442i \(-0.302957\pi\)
0.580245 + 0.814442i \(0.302957\pi\)
\(192\) −7.07789e6 −0.0721688
\(193\) −2.11019e7 −0.211287 −0.105643 0.994404i \(-0.533690\pi\)
−0.105643 + 0.994404i \(0.533690\pi\)
\(194\) 7.23532e7 0.711462
\(195\) 1.70484e7 0.164650
\(196\) 7.52954e6 0.0714286
\(197\) 7.67918e7 0.715621 0.357810 0.933794i \(-0.383523\pi\)
0.357810 + 0.933794i \(0.383523\pi\)
\(198\) −2.05127e7 −0.187799
\(199\) 1.99509e8 1.79464 0.897321 0.441380i \(-0.145511\pi\)
0.897321 + 0.441380i \(0.145511\pi\)
\(200\) 2.29121e6 0.0202516
\(201\) −5.38891e7 −0.468074
\(202\) −2.09231e7 −0.178606
\(203\) 7.43688e7 0.623957
\(204\) −1.88603e7 −0.155541
\(205\) 1.61422e8 1.30865
\(206\) −5.93442e7 −0.472980
\(207\) 4.67177e7 0.366087
\(208\) −8.99891e6 −0.0693375
\(209\) 9.08749e7 0.688545
\(210\) −2.12931e7 −0.158661
\(211\) 1.74866e8 1.28149 0.640747 0.767752i \(-0.278625\pi\)
0.640747 + 0.767752i \(0.278625\pi\)
\(212\) 8.25385e7 0.594951
\(213\) 8.86181e7 0.628339
\(214\) 1.14091e8 0.795799
\(215\) −7.97567e7 −0.547309
\(216\) −1.00777e7 −0.0680414
\(217\) −6.51957e7 −0.433122
\(218\) −1.45912e8 −0.953877
\(219\) −7.81183e7 −0.502572
\(220\) −6.46956e7 −0.409634
\(221\) −2.39793e7 −0.149439
\(222\) −2.32566e7 −0.142663
\(223\) −2.34627e8 −1.41681 −0.708404 0.705808i \(-0.750584\pi\)
−0.708404 + 0.705808i \(0.750584\pi\)
\(224\) 1.12394e7 0.0668153
\(225\) 3.26228e6 0.0190934
\(226\) 2.30950e8 1.33088
\(227\) 2.48898e8 1.41231 0.706157 0.708056i \(-0.250427\pi\)
0.706157 + 0.708056i \(0.250427\pi\)
\(228\) 4.46460e7 0.249466
\(229\) 2.28854e8 1.25932 0.629659 0.776872i \(-0.283195\pi\)
0.629659 + 0.776872i \(0.283195\pi\)
\(230\) 1.47344e8 0.798521
\(231\) 3.25734e7 0.173868
\(232\) 1.11011e8 0.583658
\(233\) 3.63509e8 1.88265 0.941325 0.337501i \(-0.109582\pi\)
0.941325 + 0.337501i \(0.109582\pi\)
\(234\) −1.28129e7 −0.0653720
\(235\) 1.46901e8 0.738392
\(236\) 3.91522e7 0.193894
\(237\) 7.30023e7 0.356219
\(238\) 2.99495e7 0.144003
\(239\) −1.96099e8 −0.929142 −0.464571 0.885536i \(-0.653791\pi\)
−0.464571 + 0.885536i \(0.653791\pi\)
\(240\) −3.17844e7 −0.148414
\(241\) −9.03845e7 −0.415943 −0.207972 0.978135i \(-0.566686\pi\)
−0.207972 + 0.978135i \(0.566686\pi\)
\(242\) −5.69282e7 −0.258211
\(243\) −1.43489e7 −0.0641500
\(244\) −3.96807e7 −0.174870
\(245\) 3.38126e7 0.146892
\(246\) −1.21318e8 −0.519581
\(247\) 5.67635e7 0.239679
\(248\) −9.73184e7 −0.405148
\(249\) 8.38702e7 0.344279
\(250\) −1.69337e8 −0.685429
\(251\) −3.02094e7 −0.120582 −0.0602911 0.998181i \(-0.519203\pi\)
−0.0602911 + 0.998181i \(0.519203\pi\)
\(252\) 1.60030e7 0.0629941
\(253\) −2.25402e8 −0.875058
\(254\) 2.42490e8 0.928489
\(255\) −8.46953e7 −0.319867
\(256\) 1.67772e7 0.0625000
\(257\) −3.72951e8 −1.37052 −0.685261 0.728298i \(-0.740312\pi\)
−0.685261 + 0.728298i \(0.740312\pi\)
\(258\) 5.99420e7 0.217301
\(259\) 3.69306e7 0.132080
\(260\) −4.04110e7 −0.142591
\(261\) 1.58061e8 0.550278
\(262\) 2.67426e8 0.918646
\(263\) 1.64651e8 0.558110 0.279055 0.960275i \(-0.409979\pi\)
0.279055 + 0.960275i \(0.409979\pi\)
\(264\) 4.86226e7 0.162639
\(265\) 3.70652e8 1.22351
\(266\) −7.08963e7 −0.230960
\(267\) 812857. 0.00261351
\(268\) 1.27737e8 0.405364
\(269\) −4.31852e8 −1.35270 −0.676351 0.736579i \(-0.736440\pi\)
−0.676351 + 0.736579i \(0.736440\pi\)
\(270\) −4.52555e7 −0.139926
\(271\) −5.71179e7 −0.174333 −0.0871665 0.996194i \(-0.527781\pi\)
−0.0871665 + 0.996194i \(0.527781\pi\)
\(272\) 4.47060e7 0.134702
\(273\) 2.03464e7 0.0605228
\(274\) −2.24103e8 −0.658142
\(275\) −1.57398e7 −0.0456388
\(276\) −1.10738e8 −0.317041
\(277\) 2.63212e8 0.744091 0.372045 0.928215i \(-0.378657\pi\)
0.372045 + 0.928215i \(0.378657\pi\)
\(278\) −9.74150e7 −0.271938
\(279\) −1.38565e8 −0.381977
\(280\) 5.04724e7 0.137405
\(281\) 4.49585e8 1.20876 0.604380 0.796696i \(-0.293421\pi\)
0.604380 + 0.796696i \(0.293421\pi\)
\(282\) −1.10405e8 −0.293168
\(283\) −4.77230e8 −1.25163 −0.625814 0.779972i \(-0.715233\pi\)
−0.625814 + 0.779972i \(0.715233\pi\)
\(284\) −2.10058e8 −0.544157
\(285\) 2.00490e8 0.513022
\(286\) 6.18194e7 0.156259
\(287\) 1.92649e8 0.481038
\(288\) 2.38879e7 0.0589256
\(289\) −2.91211e8 −0.709685
\(290\) 4.98513e8 1.20028
\(291\) −2.44192e8 −0.580906
\(292\) 1.85169e8 0.435240
\(293\) 5.25029e6 0.0121940 0.00609701 0.999981i \(-0.498059\pi\)
0.00609701 + 0.999981i \(0.498059\pi\)
\(294\) −2.54122e7 −0.0583212
\(295\) 1.75819e8 0.398739
\(296\) 5.51267e7 0.123549
\(297\) 6.92303e7 0.153338
\(298\) 5.63421e7 0.123332
\(299\) −1.40794e8 −0.304603
\(300\) −7.73282e6 −0.0165354
\(301\) −9.51856e7 −0.201182
\(302\) −1.48783e8 −0.310834
\(303\) 7.06155e7 0.145831
\(304\) −1.05828e8 −0.216044
\(305\) −1.78193e8 −0.359617
\(306\) 6.36536e7 0.126998
\(307\) 1.91174e7 0.0377090 0.0188545 0.999822i \(-0.493998\pi\)
0.0188545 + 0.999822i \(0.493998\pi\)
\(308\) −7.72110e7 −0.150575
\(309\) 2.00287e8 0.386187
\(310\) −4.37024e8 −0.833180
\(311\) −3.00942e8 −0.567312 −0.283656 0.958926i \(-0.591547\pi\)
−0.283656 + 0.958926i \(0.591547\pi\)
\(312\) 3.03713e7 0.0566139
\(313\) 2.75131e8 0.507147 0.253574 0.967316i \(-0.418394\pi\)
0.253574 + 0.967316i \(0.418394\pi\)
\(314\) 1.19963e7 0.0218673
\(315\) 7.18641e7 0.129546
\(316\) −1.73042e8 −0.308495
\(317\) −3.48501e8 −0.614464 −0.307232 0.951635i \(-0.599403\pi\)
−0.307232 + 0.951635i \(0.599403\pi\)
\(318\) −2.78567e8 −0.485775
\(319\) −7.62608e8 −1.31533
\(320\) 7.53408e7 0.128530
\(321\) −3.85057e8 −0.649767
\(322\) 1.75848e8 0.293523
\(323\) −2.81997e8 −0.465625
\(324\) 3.40122e7 0.0555556
\(325\) −9.83160e6 −0.0158867
\(326\) −2.82407e8 −0.451455
\(327\) 4.92452e8 0.778837
\(328\) 2.87569e8 0.449970
\(329\) 1.75319e8 0.271421
\(330\) 2.18348e8 0.334464
\(331\) 4.63729e8 0.702855 0.351428 0.936215i \(-0.385696\pi\)
0.351428 + 0.936215i \(0.385696\pi\)
\(332\) −1.98803e8 −0.298154
\(333\) 7.84909e7 0.116484
\(334\) 7.35576e8 1.08023
\(335\) 5.73624e8 0.833624
\(336\) −3.79331e7 −0.0545545
\(337\) −4.28582e8 −0.610000 −0.305000 0.952352i \(-0.598656\pi\)
−0.305000 + 0.952352i \(0.598656\pi\)
\(338\) 3.86145e7 0.0543928
\(339\) −7.79458e8 −1.08666
\(340\) 2.00759e8 0.277013
\(341\) 6.68544e8 0.913039
\(342\) −1.50680e8 −0.203688
\(343\) 4.03536e7 0.0539949
\(344\) −1.42085e8 −0.188188
\(345\) −4.97287e8 −0.651989
\(346\) 1.06128e9 1.37742
\(347\) 8.76369e8 1.12599 0.562994 0.826461i \(-0.309649\pi\)
0.562994 + 0.826461i \(0.309649\pi\)
\(348\) −3.74663e8 −0.476555
\(349\) −1.20567e9 −1.51824 −0.759121 0.650950i \(-0.774371\pi\)
−0.759121 + 0.650950i \(0.774371\pi\)
\(350\) 1.22794e7 0.0153088
\(351\) 4.32436e7 0.0533761
\(352\) −1.15254e8 −0.140850
\(353\) −8.95397e8 −1.08344 −0.541719 0.840560i \(-0.682226\pi\)
−0.541719 + 0.840560i \(0.682226\pi\)
\(354\) −1.32139e8 −0.158314
\(355\) −9.43297e8 −1.11905
\(356\) −1.92677e6 −0.00226337
\(357\) −1.01080e8 −0.117578
\(358\) −9.33795e7 −0.107563
\(359\) −4.94478e8 −0.564048 −0.282024 0.959407i \(-0.591006\pi\)
−0.282024 + 0.959407i \(0.591006\pi\)
\(360\) 1.07272e8 0.121179
\(361\) −2.26330e8 −0.253202
\(362\) 7.49892e8 0.830842
\(363\) 1.92133e8 0.210828
\(364\) −4.82285e7 −0.0524142
\(365\) 8.31532e8 0.895063
\(366\) 1.33922e8 0.142781
\(367\) 4.93677e8 0.521329 0.260664 0.965429i \(-0.416058\pi\)
0.260664 + 0.965429i \(0.416058\pi\)
\(368\) 2.62490e8 0.274566
\(369\) 4.09449e8 0.424236
\(370\) 2.47555e8 0.254077
\(371\) 4.42355e8 0.449741
\(372\) 3.28449e8 0.330802
\(373\) 1.72228e9 1.71840 0.859198 0.511643i \(-0.170963\pi\)
0.859198 + 0.511643i \(0.170963\pi\)
\(374\) −3.07115e8 −0.303564
\(375\) 5.71514e8 0.559651
\(376\) 2.61701e8 0.253891
\(377\) −4.76351e8 −0.457859
\(378\) −5.40102e7 −0.0514344
\(379\) 6.09310e8 0.574912 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(380\) −4.75236e8 −0.444290
\(381\) −8.18405e8 −0.758108
\(382\) 8.94021e8 0.820590
\(383\) −6.40183e8 −0.582248 −0.291124 0.956685i \(-0.594029\pi\)
−0.291124 + 0.956685i \(0.594029\pi\)
\(384\) −5.66231e7 −0.0510310
\(385\) −3.46728e8 −0.309654
\(386\) −1.68816e8 −0.149402
\(387\) −2.02304e8 −0.177426
\(388\) 5.78826e8 0.503080
\(389\) −8.23729e7 −0.0709514 −0.0354757 0.999371i \(-0.511295\pi\)
−0.0354757 + 0.999371i \(0.511295\pi\)
\(390\) 1.36387e8 0.116425
\(391\) 6.99454e8 0.591753
\(392\) 6.02363e7 0.0505076
\(393\) −9.02561e8 −0.750072
\(394\) 6.14334e8 0.506020
\(395\) −7.77074e8 −0.634414
\(396\) −1.64101e8 −0.132794
\(397\) 2.61533e7 0.0209778 0.0104889 0.999945i \(-0.496661\pi\)
0.0104889 + 0.999945i \(0.496661\pi\)
\(398\) 1.59608e9 1.26900
\(399\) 2.39275e8 0.188578
\(400\) 1.83296e7 0.0143200
\(401\) 1.57626e9 1.22074 0.610368 0.792118i \(-0.291022\pi\)
0.610368 + 0.792118i \(0.291022\pi\)
\(402\) −4.31113e8 −0.330978
\(403\) 4.17595e8 0.317824
\(404\) −1.67385e8 −0.126294
\(405\) 1.52737e8 0.114249
\(406\) 5.94950e8 0.441204
\(407\) −3.78701e8 −0.278430
\(408\) −1.50883e8 −0.109984
\(409\) −1.97505e9 −1.42740 −0.713701 0.700450i \(-0.752983\pi\)
−0.713701 + 0.700450i \(0.752983\pi\)
\(410\) 1.29137e9 0.925356
\(411\) 7.56346e8 0.537371
\(412\) −4.74754e8 −0.334448
\(413\) 2.09831e8 0.146570
\(414\) 3.73741e8 0.258863
\(415\) −8.92759e8 −0.613149
\(416\) −7.19913e7 −0.0490290
\(417\) 3.28776e8 0.222036
\(418\) 7.26999e8 0.486875
\(419\) −1.58753e9 −1.05432 −0.527162 0.849765i \(-0.676744\pi\)
−0.527162 + 0.849765i \(0.676744\pi\)
\(420\) −1.70344e8 −0.112190
\(421\) −2.14716e9 −1.40242 −0.701210 0.712955i \(-0.747356\pi\)
−0.701210 + 0.712955i \(0.747356\pi\)
\(422\) 1.39893e9 0.906153
\(423\) 3.72617e8 0.239371
\(424\) 6.60308e8 0.420694
\(425\) 4.88427e7 0.0308630
\(426\) 7.08945e8 0.444302
\(427\) −2.12664e8 −0.132189
\(428\) 9.12729e8 0.562715
\(429\) −2.08641e8 −0.127585
\(430\) −6.38054e8 −0.387006
\(431\) −5.97101e7 −0.0359234 −0.0179617 0.999839i \(-0.505718\pi\)
−0.0179617 + 0.999839i \(0.505718\pi\)
\(432\) −8.06216e7 −0.0481125
\(433\) 2.72594e9 1.61365 0.806823 0.590794i \(-0.201185\pi\)
0.806823 + 0.590794i \(0.201185\pi\)
\(434\) −5.21566e8 −0.306263
\(435\) −1.68248e9 −0.980027
\(436\) −1.16729e9 −0.674493
\(437\) −1.65574e9 −0.949091
\(438\) −6.24946e8 −0.355372
\(439\) −1.53065e9 −0.863474 −0.431737 0.902000i \(-0.642099\pi\)
−0.431737 + 0.902000i \(0.642099\pi\)
\(440\) −5.17565e8 −0.289655
\(441\) 8.57661e7 0.0476190
\(442\) −1.91834e8 −0.105669
\(443\) 1.54984e9 0.846981 0.423490 0.905901i \(-0.360805\pi\)
0.423490 + 0.905901i \(0.360805\pi\)
\(444\) −1.86053e8 −0.100878
\(445\) −8.65248e6 −0.00465458
\(446\) −1.87702e9 −1.00183
\(447\) −1.90154e8 −0.100700
\(448\) 8.99154e7 0.0472456
\(449\) 2.25662e9 1.17651 0.588257 0.808674i \(-0.299814\pi\)
0.588257 + 0.808674i \(0.299814\pi\)
\(450\) 2.60983e7 0.0135011
\(451\) −1.97550e9 −1.01405
\(452\) 1.84760e9 0.941075
\(453\) 5.02142e8 0.253795
\(454\) 1.99118e9 0.998656
\(455\) −2.16578e8 −0.107789
\(456\) 3.57168e8 0.176399
\(457\) −9.22071e8 −0.451916 −0.225958 0.974137i \(-0.572551\pi\)
−0.225958 + 0.974137i \(0.572551\pi\)
\(458\) 1.83084e9 0.890472
\(459\) −2.14831e8 −0.103694
\(460\) 1.17876e9 0.564639
\(461\) 3.40218e9 1.61735 0.808676 0.588255i \(-0.200185\pi\)
0.808676 + 0.588255i \(0.200185\pi\)
\(462\) 2.60587e8 0.122944
\(463\) −1.27583e9 −0.597394 −0.298697 0.954348i \(-0.596552\pi\)
−0.298697 + 0.954348i \(0.596552\pi\)
\(464\) 8.88089e8 0.412709
\(465\) 1.47495e9 0.680289
\(466\) 2.90807e9 1.33123
\(467\) 4.23326e9 1.92338 0.961692 0.274132i \(-0.0883904\pi\)
0.961692 + 0.274132i \(0.0883904\pi\)
\(468\) −1.02503e8 −0.0462250
\(469\) 6.84591e8 0.306426
\(470\) 1.17521e9 0.522122
\(471\) −4.04876e7 −0.0178546
\(472\) 3.13217e8 0.137104
\(473\) 9.76073e8 0.424100
\(474\) 5.84018e8 0.251885
\(475\) −1.15620e8 −0.0495001
\(476\) 2.39596e8 0.101825
\(477\) 9.40165e8 0.396634
\(478\) −1.56879e9 −0.657003
\(479\) −3.66335e9 −1.52301 −0.761507 0.648156i \(-0.775540\pi\)
−0.761507 + 0.648156i \(0.775540\pi\)
\(480\) −2.54275e8 −0.104944
\(481\) −2.36550e8 −0.0969202
\(482\) −7.23076e8 −0.294116
\(483\) −5.93487e8 −0.239661
\(484\) −4.55426e8 −0.182582
\(485\) 2.59931e9 1.03457
\(486\) −1.14791e8 −0.0453609
\(487\) −6.70678e8 −0.263125 −0.131563 0.991308i \(-0.541999\pi\)
−0.131563 + 0.991308i \(0.541999\pi\)
\(488\) −3.17446e8 −0.123652
\(489\) 9.53124e8 0.368611
\(490\) 2.70501e8 0.103868
\(491\) −2.84339e9 −1.08406 −0.542028 0.840360i \(-0.682343\pi\)
−0.542028 + 0.840360i \(0.682343\pi\)
\(492\) −9.70546e8 −0.367399
\(493\) 2.36648e9 0.889484
\(494\) 4.54108e8 0.169479
\(495\) −7.36924e8 −0.273089
\(496\) −7.78547e8 −0.286483
\(497\) −1.12578e9 −0.411344
\(498\) 6.70962e8 0.243442
\(499\) 3.14281e9 1.13231 0.566156 0.824298i \(-0.308430\pi\)
0.566156 + 0.824298i \(0.308430\pi\)
\(500\) −1.35470e9 −0.484672
\(501\) −2.48257e9 −0.882002
\(502\) −2.41675e8 −0.0852645
\(503\) 6.79858e8 0.238194 0.119097 0.992883i \(-0.462000\pi\)
0.119097 + 0.992883i \(0.462000\pi\)
\(504\) 1.28024e8 0.0445435
\(505\) −7.51669e8 −0.259721
\(506\) −1.80322e9 −0.618759
\(507\) −1.30324e8 −0.0444116
\(508\) 1.93992e9 0.656541
\(509\) 1.56897e9 0.527355 0.263678 0.964611i \(-0.415064\pi\)
0.263678 + 0.964611i \(0.415064\pi\)
\(510\) −6.77563e8 −0.226180
\(511\) 9.92391e8 0.329011
\(512\) 1.34218e8 0.0441942
\(513\) 5.08546e8 0.166311
\(514\) −2.98361e9 −0.969105
\(515\) −2.13196e9 −0.687786
\(516\) 4.79536e8 0.153655
\(517\) −1.79779e9 −0.572167
\(518\) 2.95445e8 0.0933946
\(519\) −3.58184e9 −1.12466
\(520\) −3.23288e8 −0.100827
\(521\) −5.47294e9 −1.69547 −0.847733 0.530424i \(-0.822033\pi\)
−0.847733 + 0.530424i \(0.822033\pi\)
\(522\) 1.26449e9 0.389105
\(523\) −3.72307e9 −1.13801 −0.569004 0.822335i \(-0.692671\pi\)
−0.569004 + 0.822335i \(0.692671\pi\)
\(524\) 2.13940e9 0.649581
\(525\) −4.14431e7 −0.0124996
\(526\) 1.31721e9 0.394643
\(527\) −2.07458e9 −0.617438
\(528\) 3.88981e8 0.115003
\(529\) 7.02009e8 0.206181
\(530\) 2.96522e9 0.865149
\(531\) 4.45967e8 0.129262
\(532\) −5.67170e8 −0.163314
\(533\) −1.23396e9 −0.352986
\(534\) 6.50286e6 0.00184803
\(535\) 4.09875e9 1.15721
\(536\) 1.02190e9 0.286636
\(537\) 3.15156e8 0.0878244
\(538\) −3.45482e9 −0.956505
\(539\) −4.13803e8 −0.113824
\(540\) −3.62044e8 −0.0989426
\(541\) 4.22328e9 1.14673 0.573363 0.819301i \(-0.305638\pi\)
0.573363 + 0.819301i \(0.305638\pi\)
\(542\) −4.56943e8 −0.123272
\(543\) −2.53089e9 −0.678380
\(544\) 3.57648e8 0.0952488
\(545\) −5.24192e9 −1.38708
\(546\) 1.62771e8 0.0427960
\(547\) −3.72289e9 −0.972579 −0.486290 0.873798i \(-0.661650\pi\)
−0.486290 + 0.873798i \(0.661650\pi\)
\(548\) −1.79282e9 −0.465377
\(549\) −4.51988e8 −0.116580
\(550\) −1.25918e8 −0.0322715
\(551\) −5.60191e9 −1.42661
\(552\) −8.85905e8 −0.224182
\(553\) −9.27399e8 −0.233200
\(554\) 2.10569e9 0.526152
\(555\) −8.35499e8 −0.207453
\(556\) −7.79320e8 −0.192289
\(557\) −1.51634e9 −0.371794 −0.185897 0.982569i \(-0.559519\pi\)
−0.185897 + 0.982569i \(0.559519\pi\)
\(558\) −1.10852e9 −0.270099
\(559\) 6.09687e8 0.147627
\(560\) 4.03779e8 0.0971597
\(561\) 1.03651e9 0.247859
\(562\) 3.59668e9 0.854722
\(563\) −1.12443e9 −0.265553 −0.132777 0.991146i \(-0.542389\pi\)
−0.132777 + 0.991146i \(0.542389\pi\)
\(564\) −8.83239e8 −0.207301
\(565\) 8.29696e9 1.93530
\(566\) −3.81784e9 −0.885035
\(567\) 1.82284e8 0.0419961
\(568\) −1.68046e9 −0.384777
\(569\) 4.73165e9 1.07676 0.538381 0.842701i \(-0.319036\pi\)
0.538381 + 0.842701i \(0.319036\pi\)
\(570\) 1.60392e9 0.362761
\(571\) −3.52395e8 −0.0792142 −0.0396071 0.999215i \(-0.512611\pi\)
−0.0396071 + 0.999215i \(0.512611\pi\)
\(572\) 4.94555e8 0.110491
\(573\) −3.01732e9 −0.670009
\(574\) 1.54119e9 0.340145
\(575\) 2.86779e8 0.0629086
\(576\) 1.91103e8 0.0416667
\(577\) −3.04877e9 −0.660707 −0.330354 0.943857i \(-0.607168\pi\)
−0.330354 + 0.943857i \(0.607168\pi\)
\(578\) −2.32969e9 −0.501823
\(579\) 5.69753e8 0.121986
\(580\) 3.98811e9 0.848728
\(581\) −1.06546e9 −0.225383
\(582\) −1.95354e9 −0.410763
\(583\) −4.53609e9 −0.948072
\(584\) 1.48135e9 0.307761
\(585\) −4.60307e8 −0.0950609
\(586\) 4.20023e7 0.00862247
\(587\) −2.10059e9 −0.428655 −0.214327 0.976762i \(-0.568756\pi\)
−0.214327 + 0.976762i \(0.568756\pi\)
\(588\) −2.03297e8 −0.0412393
\(589\) 4.91093e9 0.990286
\(590\) 1.40655e9 0.281951
\(591\) −2.07338e9 −0.413164
\(592\) 4.41014e8 0.0873627
\(593\) 2.27623e9 0.448255 0.224128 0.974560i \(-0.428047\pi\)
0.224128 + 0.974560i \(0.428047\pi\)
\(594\) 5.53842e8 0.108426
\(595\) 1.07594e9 0.209402
\(596\) 4.50736e8 0.0872089
\(597\) −5.38675e9 −1.03614
\(598\) −1.12635e9 −0.215387
\(599\) −1.02748e7 −0.00195334 −0.000976672 1.00000i \(-0.500311\pi\)
−0.000976672 1.00000i \(0.500311\pi\)
\(600\) −6.18625e7 −0.0116923
\(601\) −1.02256e10 −1.92144 −0.960722 0.277513i \(-0.910490\pi\)
−0.960722 + 0.277513i \(0.910490\pi\)
\(602\) −7.61485e8 −0.142257
\(603\) 1.45501e9 0.270243
\(604\) −1.19026e9 −0.219793
\(605\) −2.04516e9 −0.375478
\(606\) 5.64924e8 0.103118
\(607\) −9.02774e7 −0.0163840 −0.00819198 0.999966i \(-0.502608\pi\)
−0.00819198 + 0.999966i \(0.502608\pi\)
\(608\) −8.46621e8 −0.152766
\(609\) −2.00796e9 −0.360242
\(610\) −1.42554e9 −0.254287
\(611\) −1.12296e9 −0.199168
\(612\) 5.09229e8 0.0898014
\(613\) −6.23451e9 −1.09318 −0.546588 0.837401i \(-0.684074\pi\)
−0.546588 + 0.837401i \(0.684074\pi\)
\(614\) 1.52940e8 0.0266643
\(615\) −4.35839e9 −0.755550
\(616\) −6.17688e8 −0.106472
\(617\) 6.17858e9 1.05899 0.529494 0.848314i \(-0.322382\pi\)
0.529494 + 0.848314i \(0.322382\pi\)
\(618\) 1.60229e9 0.273075
\(619\) −2.29126e9 −0.388291 −0.194145 0.980973i \(-0.562193\pi\)
−0.194145 + 0.980973i \(0.562193\pi\)
\(620\) −3.49619e9 −0.589147
\(621\) −1.26138e9 −0.211361
\(622\) −2.40754e9 −0.401150
\(623\) −1.03263e7 −0.00171095
\(624\) 2.42971e8 0.0400320
\(625\) −6.43310e9 −1.05400
\(626\) 2.20105e9 0.358607
\(627\) −2.45362e9 −0.397531
\(628\) 9.59707e7 0.0154625
\(629\) 1.17516e9 0.188287
\(630\) 5.74912e8 0.0916030
\(631\) 3.63119e9 0.575368 0.287684 0.957725i \(-0.407115\pi\)
0.287684 + 0.957725i \(0.407115\pi\)
\(632\) −1.38434e9 −0.218139
\(633\) −4.72138e9 −0.739871
\(634\) −2.78801e9 −0.434492
\(635\) 8.71153e9 1.35016
\(636\) −2.22854e9 −0.343495
\(637\) −2.58475e8 −0.0396214
\(638\) −6.10087e9 −0.930077
\(639\) −2.39269e9 −0.362771
\(640\) 6.02726e8 0.0908845
\(641\) 7.55654e9 1.13323 0.566617 0.823981i \(-0.308252\pi\)
0.566617 + 0.823981i \(0.308252\pi\)
\(642\) −3.08046e9 −0.459455
\(643\) 6.07377e9 0.900990 0.450495 0.892779i \(-0.351248\pi\)
0.450495 + 0.892779i \(0.351248\pi\)
\(644\) 1.40678e9 0.207552
\(645\) 2.15343e9 0.315989
\(646\) −2.25598e9 −0.329246
\(647\) −9.06304e9 −1.31555 −0.657777 0.753213i \(-0.728503\pi\)
−0.657777 + 0.753213i \(0.728503\pi\)
\(648\) 2.72098e8 0.0392837
\(649\) −2.15169e9 −0.308976
\(650\) −7.86528e7 −0.0112336
\(651\) 1.76028e9 0.250063
\(652\) −2.25926e9 −0.319227
\(653\) 5.11882e9 0.719405 0.359703 0.933067i \(-0.382878\pi\)
0.359703 + 0.933067i \(0.382878\pi\)
\(654\) 3.93962e9 0.550721
\(655\) 9.60733e9 1.33585
\(656\) 2.30055e9 0.318177
\(657\) 2.10919e9 0.290160
\(658\) 1.40255e9 0.191924
\(659\) −7.01319e9 −0.954589 −0.477295 0.878743i \(-0.658383\pi\)
−0.477295 + 0.878743i \(0.658383\pi\)
\(660\) 1.74678e9 0.236502
\(661\) 2.47324e9 0.333089 0.166545 0.986034i \(-0.446739\pi\)
0.166545 + 0.986034i \(0.446739\pi\)
\(662\) 3.70983e9 0.496994
\(663\) 6.47440e8 0.0862784
\(664\) −1.59043e9 −0.210827
\(665\) −2.54697e9 −0.335852
\(666\) 6.27927e8 0.0823663
\(667\) 1.38947e10 1.81305
\(668\) 5.88461e9 0.763836
\(669\) 6.33493e9 0.817994
\(670\) 4.58899e9 0.589461
\(671\) 2.18074e9 0.278661
\(672\) −3.03464e8 −0.0385758
\(673\) 8.63601e8 0.109209 0.0546047 0.998508i \(-0.482610\pi\)
0.0546047 + 0.998508i \(0.482610\pi\)
\(674\) −3.42866e9 −0.431335
\(675\) −8.80816e7 −0.0110236
\(676\) 3.08916e8 0.0384615
\(677\) 3.19919e8 0.0396259 0.0198130 0.999804i \(-0.493693\pi\)
0.0198130 + 0.999804i \(0.493693\pi\)
\(678\) −6.23566e9 −0.768384
\(679\) 3.10214e9 0.380292
\(680\) 1.60607e9 0.195877
\(681\) −6.72025e9 −0.815399
\(682\) 5.34835e9 0.645616
\(683\) −1.10213e10 −1.32361 −0.661804 0.749677i \(-0.730209\pi\)
−0.661804 + 0.749677i \(0.730209\pi\)
\(684\) −1.20544e9 −0.144029
\(685\) −8.05094e9 −0.957039
\(686\) 3.22829e8 0.0381802
\(687\) −6.17907e9 −0.727067
\(688\) −1.13668e9 −0.133069
\(689\) −2.83339e9 −0.330019
\(690\) −3.97830e9 −0.461026
\(691\) −1.56486e10 −1.80428 −0.902138 0.431448i \(-0.858003\pi\)
−0.902138 + 0.431448i \(0.858003\pi\)
\(692\) 8.49028e9 0.973981
\(693\) −8.79481e8 −0.100383
\(694\) 7.01095e9 0.796194
\(695\) −3.49966e9 −0.395439
\(696\) −2.99730e9 −0.336975
\(697\) 6.13024e9 0.685746
\(698\) −9.64539e9 −1.07356
\(699\) −9.81475e9 −1.08695
\(700\) 9.82354e7 0.0108249
\(701\) −7.67098e9 −0.841081 −0.420540 0.907274i \(-0.638160\pi\)
−0.420540 + 0.907274i \(0.638160\pi\)
\(702\) 3.45948e8 0.0377426
\(703\) −2.78183e9 −0.301987
\(704\) −9.22029e8 −0.0995957
\(705\) −3.96633e9 −0.426311
\(706\) −7.16317e9 −0.766106
\(707\) −8.97079e8 −0.0954691
\(708\) −1.05711e9 −0.111945
\(709\) −1.15081e10 −1.21266 −0.606332 0.795212i \(-0.707360\pi\)
−0.606332 + 0.795212i \(0.707360\pi\)
\(710\) −7.54638e9 −0.791288
\(711\) −1.97106e9 −0.205663
\(712\) −1.54142e7 −0.00160044
\(713\) −1.21809e10 −1.25853
\(714\) −8.08637e8 −0.0831399
\(715\) 2.22088e9 0.227224
\(716\) −7.47036e8 −0.0760582
\(717\) 5.29466e9 0.536440
\(718\) −3.95582e9 −0.398842
\(719\) −1.49179e10 −1.49678 −0.748389 0.663260i \(-0.769172\pi\)
−0.748389 + 0.663260i \(0.769172\pi\)
\(720\) 8.58178e8 0.0856868
\(721\) −2.54438e9 −0.252819
\(722\) −1.81064e9 −0.179041
\(723\) 2.44038e9 0.240145
\(724\) 5.99914e9 0.587494
\(725\) 9.70266e8 0.0945600
\(726\) 1.53706e9 0.149078
\(727\) −2.24015e9 −0.216226 −0.108113 0.994139i \(-0.534481\pi\)
−0.108113 + 0.994139i \(0.534481\pi\)
\(728\) −3.85828e8 −0.0370625
\(729\) 3.87420e8 0.0370370
\(730\) 6.65225e9 0.632905
\(731\) −3.02889e9 −0.286795
\(732\) 1.07138e9 0.100961
\(733\) 7.57707e9 0.710620 0.355310 0.934748i \(-0.384375\pi\)
0.355310 + 0.934748i \(0.384375\pi\)
\(734\) 3.94942e9 0.368635
\(735\) −9.12940e8 −0.0848079
\(736\) 2.09992e9 0.194147
\(737\) −7.02008e9 −0.645960
\(738\) 3.27559e9 0.299980
\(739\) −4.16117e9 −0.379280 −0.189640 0.981854i \(-0.560732\pi\)
−0.189640 + 0.981854i \(0.560732\pi\)
\(740\) 1.98044e9 0.179660
\(741\) −1.53261e9 −0.138379
\(742\) 3.53884e9 0.318015
\(743\) −1.87849e10 −1.68015 −0.840077 0.542467i \(-0.817490\pi\)
−0.840077 + 0.542467i \(0.817490\pi\)
\(744\) 2.62760e9 0.233912
\(745\) 2.02410e9 0.179344
\(746\) 1.37783e10 1.21509
\(747\) −2.26450e9 −0.198769
\(748\) −2.45692e9 −0.214652
\(749\) 4.89165e9 0.425373
\(750\) 4.57211e9 0.395733
\(751\) −3.05552e9 −0.263236 −0.131618 0.991301i \(-0.542017\pi\)
−0.131618 + 0.991301i \(0.542017\pi\)
\(752\) 2.09360e9 0.179528
\(753\) 8.15653e8 0.0696182
\(754\) −3.81080e9 −0.323755
\(755\) −5.34506e9 −0.452000
\(756\) −4.32081e8 −0.0363696
\(757\) −2.34720e9 −0.196659 −0.0983295 0.995154i \(-0.531350\pi\)
−0.0983295 + 0.995154i \(0.531350\pi\)
\(758\) 4.87448e9 0.406524
\(759\) 6.08586e9 0.505215
\(760\) −3.80189e9 −0.314161
\(761\) −1.64745e10 −1.35509 −0.677544 0.735483i \(-0.736955\pi\)
−0.677544 + 0.735483i \(0.736955\pi\)
\(762\) −6.54724e9 −0.536063
\(763\) −6.25597e9 −0.509869
\(764\) 7.15217e9 0.580245
\(765\) 2.28677e9 0.184675
\(766\) −5.12146e9 −0.411712
\(767\) −1.34402e9 −0.107553
\(768\) −4.52985e8 −0.0360844
\(769\) −1.04854e10 −0.831465 −0.415732 0.909487i \(-0.636475\pi\)
−0.415732 + 0.909487i \(0.636475\pi\)
\(770\) −2.77382e9 −0.218958
\(771\) 1.00697e10 0.791271
\(772\) −1.35052e9 −0.105643
\(773\) −7.53799e9 −0.586985 −0.293493 0.955961i \(-0.594818\pi\)
−0.293493 + 0.955961i \(0.594818\pi\)
\(774\) −1.61843e9 −0.125459
\(775\) −8.50587e8 −0.0656392
\(776\) 4.63060e9 0.355731
\(777\) −9.97126e8 −0.0762564
\(778\) −6.58983e8 −0.0501702
\(779\) −1.45115e10 −1.09984
\(780\) 1.09110e9 0.0823252
\(781\) 1.15442e10 0.867131
\(782\) 5.59563e9 0.418433
\(783\) −4.26764e9 −0.317703
\(784\) 4.81890e8 0.0357143
\(785\) 4.30972e8 0.0317984
\(786\) −7.22049e9 −0.530381
\(787\) 2.27545e10 1.66401 0.832005 0.554768i \(-0.187193\pi\)
0.832005 + 0.554768i \(0.187193\pi\)
\(788\) 4.91467e9 0.357810
\(789\) −4.44558e9 −0.322225
\(790\) −6.21659e9 −0.448598
\(791\) 9.90200e9 0.711386
\(792\) −1.31281e9 −0.0938997
\(793\) 1.36216e9 0.0970003
\(794\) 2.09226e8 0.0148335
\(795\) −1.00076e10 −0.706391
\(796\) 1.27686e10 0.897321
\(797\) 5.92842e8 0.0414796 0.0207398 0.999785i \(-0.493398\pi\)
0.0207398 + 0.999785i \(0.493398\pi\)
\(798\) 1.91420e9 0.133345
\(799\) 5.57879e9 0.386925
\(800\) 1.46637e8 0.0101258
\(801\) −2.19472e7 −0.00150891
\(802\) 1.26101e10 0.863191
\(803\) −1.01764e10 −0.693568
\(804\) −3.44890e9 −0.234037
\(805\) 6.31739e9 0.426827
\(806\) 3.34076e9 0.224736
\(807\) 1.16600e10 0.780983
\(808\) −1.33908e9 −0.0893031
\(809\) −2.10016e10 −1.39454 −0.697272 0.716806i \(-0.745603\pi\)
−0.697272 + 0.716806i \(0.745603\pi\)
\(810\) 1.22190e9 0.0807863
\(811\) 2.26623e10 1.49187 0.745936 0.666017i \(-0.232002\pi\)
0.745936 + 0.666017i \(0.232002\pi\)
\(812\) 4.75960e9 0.311978
\(813\) 1.54218e9 0.100651
\(814\) −3.02961e9 −0.196880
\(815\) −1.01456e10 −0.656484
\(816\) −1.20706e9 −0.0777703
\(817\) 7.16996e9 0.459980
\(818\) −1.58004e10 −1.00933
\(819\) −5.49353e8 −0.0349428
\(820\) 1.03310e10 0.654325
\(821\) 6.69701e9 0.422357 0.211179 0.977447i \(-0.432270\pi\)
0.211179 + 0.977447i \(0.432270\pi\)
\(822\) 6.05077e9 0.379979
\(823\) 6.85362e9 0.428569 0.214285 0.976771i \(-0.431258\pi\)
0.214285 + 0.976771i \(0.431258\pi\)
\(824\) −3.79803e9 −0.236490
\(825\) 4.24974e8 0.0263496
\(826\) 1.67865e9 0.103641
\(827\) 8.71864e9 0.536018 0.268009 0.963416i \(-0.413634\pi\)
0.268009 + 0.963416i \(0.413634\pi\)
\(828\) 2.98993e9 0.183044
\(829\) 1.73628e10 1.05847 0.529235 0.848475i \(-0.322479\pi\)
0.529235 + 0.848475i \(0.322479\pi\)
\(830\) −7.14207e9 −0.433561
\(831\) −7.10671e9 −0.429601
\(832\) −5.75930e8 −0.0346688
\(833\) 1.28409e9 0.0769726
\(834\) 2.63021e9 0.157003
\(835\) 2.64258e10 1.57081
\(836\) 5.81600e9 0.344272
\(837\) 3.74124e9 0.220535
\(838\) −1.27003e10 −0.745520
\(839\) −2.28163e10 −1.33376 −0.666882 0.745164i \(-0.732371\pi\)
−0.666882 + 0.745164i \(0.732371\pi\)
\(840\) −1.36276e9 −0.0793305
\(841\) 2.97604e10 1.72526
\(842\) −1.71773e10 −0.991660
\(843\) −1.21388e10 −0.697878
\(844\) 1.11914e10 0.640747
\(845\) 1.38724e9 0.0790955
\(846\) 2.98093e9 0.169261
\(847\) −2.44080e9 −0.138019
\(848\) 5.28246e9 0.297475
\(849\) 1.28852e10 0.722628
\(850\) 3.90742e8 0.0218235
\(851\) 6.89994e9 0.383789
\(852\) 5.67156e9 0.314169
\(853\) −1.38482e10 −0.763962 −0.381981 0.924170i \(-0.624758\pi\)
−0.381981 + 0.924170i \(0.624758\pi\)
\(854\) −1.70131e9 −0.0934719
\(855\) −5.41323e9 −0.296193
\(856\) 7.30183e9 0.397900
\(857\) 1.62737e10 0.883188 0.441594 0.897215i \(-0.354413\pi\)
0.441594 + 0.897215i \(0.354413\pi\)
\(858\) −1.66912e9 −0.0902159
\(859\) −1.05712e10 −0.569047 −0.284524 0.958669i \(-0.591835\pi\)
−0.284524 + 0.958669i \(0.591835\pi\)
\(860\) −5.10443e9 −0.273655
\(861\) −5.20152e9 −0.277728
\(862\) −4.77681e8 −0.0254017
\(863\) −1.49720e8 −0.00792941 −0.00396470 0.999992i \(-0.501262\pi\)
−0.00396470 + 0.999992i \(0.501262\pi\)
\(864\) −6.44973e8 −0.0340207
\(865\) 3.81269e10 2.00298
\(866\) 2.18075e10 1.14102
\(867\) 7.86271e9 0.409737
\(868\) −4.17252e9 −0.216561
\(869\) 9.50993e9 0.491596
\(870\) −1.34599e10 −0.692984
\(871\) −4.38497e9 −0.224856
\(872\) −9.33835e9 −0.476939
\(873\) 6.59318e9 0.335386
\(874\) −1.32459e10 −0.671109
\(875\) −7.26034e9 −0.366377
\(876\) −4.99957e9 −0.251286
\(877\) 2.82110e10 1.41228 0.706138 0.708074i \(-0.250436\pi\)
0.706138 + 0.708074i \(0.250436\pi\)
\(878\) −1.22452e10 −0.610568
\(879\) −1.41758e8 −0.00704022
\(880\) −4.14052e9 −0.204817
\(881\) 1.13329e10 0.558373 0.279187 0.960237i \(-0.409935\pi\)
0.279187 + 0.960237i \(0.409935\pi\)
\(882\) 6.86129e8 0.0336718
\(883\) −5.55367e9 −0.271467 −0.135734 0.990745i \(-0.543339\pi\)
−0.135734 + 0.990745i \(0.543339\pi\)
\(884\) −1.53467e9 −0.0747193
\(885\) −4.74711e9 −0.230212
\(886\) 1.23987e10 0.598906
\(887\) −4.16027e9 −0.200165 −0.100083 0.994979i \(-0.531911\pi\)
−0.100083 + 0.994979i \(0.531911\pi\)
\(888\) −1.48842e9 −0.0713313
\(889\) 1.03968e10 0.496298
\(890\) −6.92199e7 −0.00329129
\(891\) −1.86922e9 −0.0885295
\(892\) −1.50161e10 −0.708404
\(893\) −1.32061e10 −0.620574
\(894\) −1.52124e9 −0.0712058
\(895\) −3.35468e9 −0.156412
\(896\) 7.19323e8 0.0334077
\(897\) 3.80143e9 0.175863
\(898\) 1.80530e10 0.831921
\(899\) −4.12118e10 −1.89174
\(900\) 2.08786e8 0.00954669
\(901\) 1.40761e10 0.641129
\(902\) −1.58040e10 −0.717041
\(903\) 2.57001e9 0.116152
\(904\) 1.47808e10 0.665440
\(905\) 2.69401e10 1.20817
\(906\) 4.01714e9 0.179460
\(907\) 2.52488e10 1.12361 0.561804 0.827271i \(-0.310108\pi\)
0.561804 + 0.827271i \(0.310108\pi\)
\(908\) 1.59295e10 0.706157
\(909\) −1.90662e9 −0.0841958
\(910\) −1.73262e9 −0.0762183
\(911\) −4.60044e9 −0.201597 −0.100799 0.994907i \(-0.532140\pi\)
−0.100799 + 0.994907i \(0.532140\pi\)
\(912\) 2.85735e9 0.124733
\(913\) 1.09257e10 0.475118
\(914\) −7.37657e9 −0.319553
\(915\) 4.81120e9 0.207625
\(916\) 1.46467e10 0.629659
\(917\) 1.14659e10 0.491037
\(918\) −1.71865e9 −0.0733225
\(919\) 1.41325e10 0.600640 0.300320 0.953839i \(-0.402907\pi\)
0.300320 + 0.953839i \(0.402907\pi\)
\(920\) 9.43004e9 0.399260
\(921\) −5.16171e8 −0.0217713
\(922\) 2.72175e10 1.14364
\(923\) 7.21089e9 0.301844
\(924\) 2.08470e9 0.0869342
\(925\) 4.81821e8 0.0200166
\(926\) −1.02067e10 −0.422421
\(927\) −5.40774e9 −0.222965
\(928\) 7.10471e9 0.291829
\(929\) −4.45261e9 −0.182205 −0.0911024 0.995842i \(-0.529039\pi\)
−0.0911024 + 0.995842i \(0.529039\pi\)
\(930\) 1.17996e10 0.481037
\(931\) −3.03968e9 −0.123454
\(932\) 2.32646e10 0.941325
\(933\) 8.12544e9 0.327538
\(934\) 3.38661e10 1.36004
\(935\) −1.10332e10 −0.441428
\(936\) −8.20026e8 −0.0326860
\(937\) 1.52816e10 0.606849 0.303425 0.952855i \(-0.401870\pi\)
0.303425 + 0.952855i \(0.401870\pi\)
\(938\) 5.47673e9 0.216676
\(939\) −7.42853e9 −0.292802
\(940\) 9.40166e9 0.369196
\(941\) −1.62754e10 −0.636747 −0.318374 0.947965i \(-0.603137\pi\)
−0.318374 + 0.947965i \(0.603137\pi\)
\(942\) −3.23901e8 −0.0126251
\(943\) 3.59936e10 1.39777
\(944\) 2.50574e9 0.0969468
\(945\) −1.94033e9 −0.0747935
\(946\) 7.80858e9 0.299884
\(947\) 1.76582e10 0.675648 0.337824 0.941209i \(-0.390309\pi\)
0.337824 + 0.941209i \(0.390309\pi\)
\(948\) 4.67214e9 0.178109
\(949\) −6.35651e9 −0.241428
\(950\) −9.24961e8 −0.0350018
\(951\) 9.40952e9 0.354761
\(952\) 1.91677e9 0.0720013
\(953\) 2.02839e10 0.759147 0.379574 0.925162i \(-0.376071\pi\)
0.379574 + 0.925162i \(0.376071\pi\)
\(954\) 7.52132e9 0.280462
\(955\) 3.21180e10 1.19326
\(956\) −1.25503e10 −0.464571
\(957\) 2.05904e10 0.759405
\(958\) −2.93068e10 −1.07693
\(959\) −9.60840e9 −0.351792
\(960\) −2.03420e9 −0.0742069
\(961\) 8.61586e9 0.313160
\(962\) −1.89240e9 −0.0685329
\(963\) 1.03965e10 0.375143
\(964\) −5.78461e9 −0.207972
\(965\) −6.06475e9 −0.217254
\(966\) −4.74790e9 −0.169466
\(967\) 1.37829e10 0.490171 0.245086 0.969501i \(-0.421184\pi\)
0.245086 + 0.969501i \(0.421184\pi\)
\(968\) −3.64341e9 −0.129105
\(969\) 7.61392e9 0.268829
\(970\) 2.07945e10 0.731554
\(971\) −4.58501e10 −1.60721 −0.803606 0.595161i \(-0.797088\pi\)
−0.803606 + 0.595161i \(0.797088\pi\)
\(972\) −9.18330e8 −0.0320750
\(973\) −4.17667e9 −0.145357
\(974\) −5.36543e9 −0.186058
\(975\) 2.65453e8 0.00917216
\(976\) −2.53957e9 −0.0874349
\(977\) −1.35238e10 −0.463945 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(978\) 7.62499e9 0.260647
\(979\) 1.05890e8 0.00360675
\(980\) 2.16401e9 0.0734458
\(981\) −1.32962e10 −0.449662
\(982\) −2.27471e10 −0.766543
\(983\) −2.37303e10 −0.796831 −0.398415 0.917205i \(-0.630440\pi\)
−0.398415 + 0.917205i \(0.630440\pi\)
\(984\) −7.76436e9 −0.259790
\(985\) 2.20701e10 0.735831
\(986\) 1.89318e10 0.628960
\(987\) −4.73361e9 −0.156705
\(988\) 3.63286e9 0.119839
\(989\) −1.77841e10 −0.584580
\(990\) −5.89539e9 −0.193103
\(991\) 5.70744e9 0.186288 0.0931438 0.995653i \(-0.470308\pi\)
0.0931438 + 0.995653i \(0.470308\pi\)
\(992\) −6.22838e9 −0.202574
\(993\) −1.25207e10 −0.405794
\(994\) −9.00622e9 −0.290864
\(995\) 5.73394e10 1.84532
\(996\) 5.36769e9 0.172139
\(997\) −1.53823e9 −0.0491572 −0.0245786 0.999698i \(-0.507824\pi\)
−0.0245786 + 0.999698i \(0.507824\pi\)
\(998\) 2.51425e10 0.800666
\(999\) −2.11926e9 −0.0672518
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 546.8.a.q.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.8.a.q.1.5 6 1.1 even 1 trivial