Properties

Label 1045.6.a.h.1.18
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(167.601091705\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} +O(q^{10})\) \(q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} -15.2303 q^{10} +121.000 q^{11} -655.466 q^{12} -557.016 q^{13} +69.5563 q^{14} +518.092 q^{15} +988.508 q^{16} +1251.16 q^{17} -113.601 q^{18} +361.000 q^{19} -790.721 q^{20} -2366.10 q^{21} -73.7148 q^{22} +112.655 q^{23} +803.324 q^{24} +625.000 q^{25} +339.342 q^{26} -1171.49 q^{27} +3611.19 q^{28} +3058.85 q^{29} -315.629 q^{30} -2084.31 q^{31} -1842.65 q^{32} +2507.57 q^{33} -762.224 q^{34} -2854.35 q^{35} -5897.86 q^{36} -4134.99 q^{37} -219.926 q^{38} -11543.4 q^{39} +969.089 q^{40} +4338.04 q^{41} +1441.46 q^{42} -12533.9 q^{43} -3827.09 q^{44} +4661.77 q^{45} -68.6312 q^{46} -13727.7 q^{47} +20485.5 q^{48} -3771.31 q^{49} -380.758 q^{50} +25928.6 q^{51} +17617.8 q^{52} +2552.04 q^{53} +713.688 q^{54} +3025.00 q^{55} -4425.79 q^{56} +7481.25 q^{57} -1863.49 q^{58} +11558.1 q^{59} -16386.7 q^{60} +31983.1 q^{61} +1269.79 q^{62} -21290.1 q^{63} -30509.7 q^{64} -13925.4 q^{65} -1527.64 q^{66} +31684.8 q^{67} -39572.8 q^{68} +2334.63 q^{69} +1738.91 q^{70} +43305.0 q^{71} +7228.27 q^{72} -10784.1 q^{73} +2519.09 q^{74} +12952.3 q^{75} -11418.0 q^{76} -13815.0 q^{77} +7032.41 q^{78} -108908. q^{79} +24712.7 q^{80} -69590.0 q^{81} -2642.79 q^{82} +45563.6 q^{83} +74837.2 q^{84} +31279.0 q^{85} +7635.80 q^{86} +63390.6 q^{87} +4690.39 q^{88} +72026.0 q^{89} -2840.01 q^{90} +63596.7 q^{91} -3563.16 q^{92} -43194.7 q^{93} +8363.13 q^{94} +9025.00 q^{95} -38186.4 q^{96} +117684. q^{97} +2297.53 q^{98} +22563.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + O(q^{10}) \) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.609213 −0.107695 −0.0538474 0.998549i \(-0.517148\pi\)
−0.0538474 + 0.998549i \(0.517148\pi\)
\(3\) 20.7237 1.32942 0.664712 0.747099i \(-0.268554\pi\)
0.664712 + 0.747099i \(0.268554\pi\)
\(4\) −31.6289 −0.988402
\(5\) 25.0000 0.447214
\(6\) −12.6251 −0.143172
\(7\) −114.174 −0.880688 −0.440344 0.897829i \(-0.645143\pi\)
−0.440344 + 0.897829i \(0.645143\pi\)
\(8\) 38.7636 0.214140
\(9\) 186.471 0.767370
\(10\) −15.2303 −0.0481626
\(11\) 121.000 0.301511
\(12\) −655.466 −1.31401
\(13\) −557.016 −0.914133 −0.457066 0.889433i \(-0.651100\pi\)
−0.457066 + 0.889433i \(0.651100\pi\)
\(14\) 69.5563 0.0948454
\(15\) 518.092 0.594537
\(16\) 988.508 0.965340
\(17\) 1251.16 1.05000 0.525002 0.851101i \(-0.324065\pi\)
0.525002 + 0.851101i \(0.324065\pi\)
\(18\) −113.601 −0.0826417
\(19\) 361.000 0.229416
\(20\) −790.721 −0.442027
\(21\) −2366.10 −1.17081
\(22\) −73.7148 −0.0324712
\(23\) 112.655 0.0444051 0.0222025 0.999753i \(-0.492932\pi\)
0.0222025 + 0.999753i \(0.492932\pi\)
\(24\) 803.324 0.284684
\(25\) 625.000 0.200000
\(26\) 339.342 0.0984473
\(27\) −1171.49 −0.309264
\(28\) 3611.19 0.870473
\(29\) 3058.85 0.675404 0.337702 0.941253i \(-0.390350\pi\)
0.337702 + 0.941253i \(0.390350\pi\)
\(30\) −315.629 −0.0640285
\(31\) −2084.31 −0.389546 −0.194773 0.980848i \(-0.562397\pi\)
−0.194773 + 0.980848i \(0.562397\pi\)
\(32\) −1842.65 −0.318102
\(33\) 2507.57 0.400837
\(34\) −762.224 −0.113080
\(35\) −2854.35 −0.393856
\(36\) −5897.86 −0.758470
\(37\) −4134.99 −0.496558 −0.248279 0.968689i \(-0.579865\pi\)
−0.248279 + 0.968689i \(0.579865\pi\)
\(38\) −219.926 −0.0247069
\(39\) −11543.4 −1.21527
\(40\) 969.089 0.0957665
\(41\) 4338.04 0.403027 0.201513 0.979486i \(-0.435414\pi\)
0.201513 + 0.979486i \(0.435414\pi\)
\(42\) 1441.46 0.126090
\(43\) −12533.9 −1.03375 −0.516873 0.856062i \(-0.672904\pi\)
−0.516873 + 0.856062i \(0.672904\pi\)
\(44\) −3827.09 −0.298014
\(45\) 4661.77 0.343178
\(46\) −68.6312 −0.00478219
\(47\) −13727.7 −0.906472 −0.453236 0.891390i \(-0.649731\pi\)
−0.453236 + 0.891390i \(0.649731\pi\)
\(48\) 20485.5 1.28335
\(49\) −3771.31 −0.224389
\(50\) −380.758 −0.0215389
\(51\) 25928.6 1.39590
\(52\) 17617.8 0.903531
\(53\) 2552.04 0.124795 0.0623975 0.998051i \(-0.480125\pi\)
0.0623975 + 0.998051i \(0.480125\pi\)
\(54\) 713.688 0.0333061
\(55\) 3025.00 0.134840
\(56\) −4425.79 −0.188591
\(57\) 7481.25 0.304991
\(58\) −1863.49 −0.0727374
\(59\) 11558.1 0.432272 0.216136 0.976363i \(-0.430654\pi\)
0.216136 + 0.976363i \(0.430654\pi\)
\(60\) −16386.7 −0.587641
\(61\) 31983.1 1.10051 0.550257 0.834995i \(-0.314530\pi\)
0.550257 + 0.834995i \(0.314530\pi\)
\(62\) 1269.79 0.0419521
\(63\) −21290.1 −0.675813
\(64\) −30509.7 −0.931082
\(65\) −13925.4 −0.408813
\(66\) −1527.64 −0.0431680
\(67\) 31684.8 0.862312 0.431156 0.902277i \(-0.358106\pi\)
0.431156 + 0.902277i \(0.358106\pi\)
\(68\) −39572.8 −1.03782
\(69\) 2334.63 0.0590332
\(70\) 1738.91 0.0424162
\(71\) 43305.0 1.01951 0.509755 0.860319i \(-0.329736\pi\)
0.509755 + 0.860319i \(0.329736\pi\)
\(72\) 7228.27 0.164325
\(73\) −10784.1 −0.236852 −0.118426 0.992963i \(-0.537785\pi\)
−0.118426 + 0.992963i \(0.537785\pi\)
\(74\) 2519.09 0.0534767
\(75\) 12952.3 0.265885
\(76\) −11418.0 −0.226755
\(77\) −13815.0 −0.265537
\(78\) 7032.41 0.130878
\(79\) −108908. −1.96332 −0.981661 0.190636i \(-0.938945\pi\)
−0.981661 + 0.190636i \(0.938945\pi\)
\(80\) 24712.7 0.431713
\(81\) −69590.0 −1.17851
\(82\) −2642.79 −0.0434039
\(83\) 45563.6 0.725977 0.362988 0.931794i \(-0.381757\pi\)
0.362988 + 0.931794i \(0.381757\pi\)
\(84\) 74837.2 1.15723
\(85\) 31279.0 0.469576
\(86\) 7635.80 0.111329
\(87\) 63390.6 0.897898
\(88\) 4690.39 0.0645658
\(89\) 72026.0 0.963860 0.481930 0.876210i \(-0.339936\pi\)
0.481930 + 0.876210i \(0.339936\pi\)
\(90\) −2840.01 −0.0369585
\(91\) 63596.7 0.805066
\(92\) −3563.16 −0.0438901
\(93\) −43194.7 −0.517872
\(94\) 8363.13 0.0976223
\(95\) 9025.00 0.102598
\(96\) −38186.4 −0.422893
\(97\) 117684. 1.26995 0.634977 0.772531i \(-0.281010\pi\)
0.634977 + 0.772531i \(0.281010\pi\)
\(98\) 2297.53 0.0241655
\(99\) 22563.0 0.231371
\(100\) −19768.0 −0.197680
\(101\) −66340.4 −0.647105 −0.323552 0.946210i \(-0.604877\pi\)
−0.323552 + 0.946210i \(0.604877\pi\)
\(102\) −15796.1 −0.150331
\(103\) 150322. 1.39614 0.698071 0.716029i \(-0.254042\pi\)
0.698071 + 0.716029i \(0.254042\pi\)
\(104\) −21591.9 −0.195753
\(105\) −59152.6 −0.523601
\(106\) −1554.74 −0.0134398
\(107\) 216512. 1.82820 0.914098 0.405493i \(-0.132900\pi\)
0.914098 + 0.405493i \(0.132900\pi\)
\(108\) 37052.9 0.305677
\(109\) 41384.2 0.333633 0.166816 0.985988i \(-0.446651\pi\)
0.166816 + 0.985988i \(0.446651\pi\)
\(110\) −1842.87 −0.0145216
\(111\) −85692.2 −0.660137
\(112\) −112862. −0.850163
\(113\) 119837. 0.882867 0.441433 0.897294i \(-0.354470\pi\)
0.441433 + 0.897294i \(0.354470\pi\)
\(114\) −4557.68 −0.0328459
\(115\) 2816.39 0.0198585
\(116\) −96748.0 −0.667570
\(117\) −103867. −0.701478
\(118\) −7041.37 −0.0465535
\(119\) −142850. −0.924725
\(120\) 20083.1 0.127314
\(121\) 14641.0 0.0909091
\(122\) −19484.5 −0.118520
\(123\) 89900.2 0.535794
\(124\) 65924.5 0.385028
\(125\) 15625.0 0.0894427
\(126\) 12970.2 0.0727815
\(127\) 39095.9 0.215091 0.107545 0.994200i \(-0.465701\pi\)
0.107545 + 0.994200i \(0.465701\pi\)
\(128\) 77551.6 0.418375
\(129\) −259748. −1.37429
\(130\) 8483.54 0.0440270
\(131\) −27724.1 −0.141149 −0.0705747 0.997506i \(-0.522483\pi\)
−0.0705747 + 0.997506i \(0.522483\pi\)
\(132\) −79311.4 −0.396188
\(133\) −41216.8 −0.202044
\(134\) −19302.8 −0.0928665
\(135\) −29287.3 −0.138307
\(136\) 48499.4 0.224848
\(137\) 35413.7 0.161202 0.0806010 0.996746i \(-0.474316\pi\)
0.0806010 + 0.996746i \(0.474316\pi\)
\(138\) −1422.29 −0.00635756
\(139\) 173016. 0.759535 0.379768 0.925082i \(-0.376004\pi\)
0.379768 + 0.925082i \(0.376004\pi\)
\(140\) 90279.8 0.389288
\(141\) −284489. −1.20509
\(142\) −26382.0 −0.109796
\(143\) −67398.9 −0.275621
\(144\) 184328. 0.740773
\(145\) 76471.3 0.302050
\(146\) 6569.81 0.0255077
\(147\) −78155.4 −0.298308
\(148\) 130785. 0.490799
\(149\) −55220.4 −0.203767 −0.101883 0.994796i \(-0.532487\pi\)
−0.101883 + 0.994796i \(0.532487\pi\)
\(150\) −7890.72 −0.0286344
\(151\) 446154. 1.59236 0.796182 0.605058i \(-0.206850\pi\)
0.796182 + 0.605058i \(0.206850\pi\)
\(152\) 13993.6 0.0491272
\(153\) 233305. 0.805741
\(154\) 8416.31 0.0285970
\(155\) −52107.9 −0.174210
\(156\) 365105. 1.20118
\(157\) 282112. 0.913424 0.456712 0.889615i \(-0.349027\pi\)
0.456712 + 0.889615i \(0.349027\pi\)
\(158\) 66348.1 0.211439
\(159\) 52887.6 0.165906
\(160\) −46066.2 −0.142260
\(161\) −12862.3 −0.0391070
\(162\) 42395.2 0.126920
\(163\) 305803. 0.901515 0.450757 0.892647i \(-0.351154\pi\)
0.450757 + 0.892647i \(0.351154\pi\)
\(164\) −137207. −0.398352
\(165\) 62689.1 0.179260
\(166\) −27757.9 −0.0781839
\(167\) 156166. 0.433306 0.216653 0.976249i \(-0.430486\pi\)
0.216653 + 0.976249i \(0.430486\pi\)
\(168\) −91718.6 −0.250717
\(169\) −61026.2 −0.164361
\(170\) −19055.6 −0.0505708
\(171\) 67316.0 0.176047
\(172\) 396432. 1.02176
\(173\) 610359. 1.55050 0.775248 0.631657i \(-0.217625\pi\)
0.775248 + 0.631657i \(0.217625\pi\)
\(174\) −38618.4 −0.0966989
\(175\) −71358.7 −0.176138
\(176\) 119609. 0.291061
\(177\) 239527. 0.574674
\(178\) −43879.2 −0.103803
\(179\) 16828.2 0.0392560 0.0196280 0.999807i \(-0.493752\pi\)
0.0196280 + 0.999807i \(0.493752\pi\)
\(180\) −147447. −0.339198
\(181\) −417226. −0.946618 −0.473309 0.880896i \(-0.656941\pi\)
−0.473309 + 0.880896i \(0.656941\pi\)
\(182\) −38744.0 −0.0867013
\(183\) 662807. 1.46305
\(184\) 4366.93 0.00950892
\(185\) −103375. −0.222068
\(186\) 26314.8 0.0557721
\(187\) 151390. 0.316588
\(188\) 434193. 0.895959
\(189\) 133754. 0.272365
\(190\) −5498.15 −0.0110492
\(191\) 837287. 1.66070 0.830350 0.557242i \(-0.188141\pi\)
0.830350 + 0.557242i \(0.188141\pi\)
\(192\) −632273. −1.23780
\(193\) 108159. 0.209010 0.104505 0.994524i \(-0.466674\pi\)
0.104505 + 0.994524i \(0.466674\pi\)
\(194\) −71694.6 −0.136767
\(195\) −288586. −0.543486
\(196\) 119282. 0.221787
\(197\) −326694. −0.599757 −0.299879 0.953977i \(-0.596946\pi\)
−0.299879 + 0.953977i \(0.596946\pi\)
\(198\) −13745.7 −0.0249174
\(199\) 254361. 0.455321 0.227661 0.973741i \(-0.426892\pi\)
0.227661 + 0.973741i \(0.426892\pi\)
\(200\) 24227.2 0.0428281
\(201\) 656626. 1.14638
\(202\) 40415.5 0.0696898
\(203\) −349241. −0.594820
\(204\) −820093. −1.37971
\(205\) 108451. 0.180239
\(206\) −91578.2 −0.150357
\(207\) 21007.0 0.0340751
\(208\) −550615. −0.882449
\(209\) 43681.0 0.0691714
\(210\) 36036.6 0.0563891
\(211\) 845329. 1.30713 0.653566 0.756869i \(-0.273272\pi\)
0.653566 + 0.756869i \(0.273272\pi\)
\(212\) −80718.0 −0.123348
\(213\) 897438. 1.35536
\(214\) −131902. −0.196887
\(215\) −313347. −0.462306
\(216\) −45411.2 −0.0662260
\(217\) 237974. 0.343069
\(218\) −25211.8 −0.0359305
\(219\) −223486. −0.314876
\(220\) −95677.3 −0.133276
\(221\) −696916. −0.959842
\(222\) 52204.8 0.0710932
\(223\) −809537. −1.09012 −0.545060 0.838397i \(-0.683493\pi\)
−0.545060 + 0.838397i \(0.683493\pi\)
\(224\) 210382. 0.280149
\(225\) 116544. 0.153474
\(226\) −73006.4 −0.0950801
\(227\) −309805. −0.399047 −0.199523 0.979893i \(-0.563939\pi\)
−0.199523 + 0.979893i \(0.563939\pi\)
\(228\) −236623. −0.301454
\(229\) −1.19087e6 −1.50064 −0.750319 0.661076i \(-0.770100\pi\)
−0.750319 + 0.661076i \(0.770100\pi\)
\(230\) −1715.78 −0.00213866
\(231\) −286299. −0.353012
\(232\) 118572. 0.144631
\(233\) −60940.3 −0.0735385 −0.0367692 0.999324i \(-0.511707\pi\)
−0.0367692 + 0.999324i \(0.511707\pi\)
\(234\) 63277.3 0.0755455
\(235\) −343194. −0.405387
\(236\) −365570. −0.427259
\(237\) −2.25697e6 −2.61009
\(238\) 87026.1 0.0995880
\(239\) −855678. −0.968982 −0.484491 0.874796i \(-0.660995\pi\)
−0.484491 + 0.874796i \(0.660995\pi\)
\(240\) 512138. 0.573930
\(241\) 1.55896e6 1.72898 0.864492 0.502646i \(-0.167640\pi\)
0.864492 + 0.502646i \(0.167640\pi\)
\(242\) −8919.49 −0.00979043
\(243\) −1.15749e6 −1.25748
\(244\) −1.01159e6 −1.08775
\(245\) −94282.7 −0.100350
\(246\) −54768.4 −0.0577022
\(247\) −201083. −0.209716
\(248\) −80795.4 −0.0834176
\(249\) 944245. 0.965131
\(250\) −9518.96 −0.00963251
\(251\) −1.64608e6 −1.64918 −0.824588 0.565734i \(-0.808593\pi\)
−0.824588 + 0.565734i \(0.808593\pi\)
\(252\) 673382. 0.667975
\(253\) 13631.3 0.0133886
\(254\) −23817.7 −0.0231641
\(255\) 648216. 0.624265
\(256\) 929065. 0.886025
\(257\) −615662. −0.581447 −0.290723 0.956807i \(-0.593896\pi\)
−0.290723 + 0.956807i \(0.593896\pi\)
\(258\) 158242. 0.148004
\(259\) 472108. 0.437313
\(260\) 440445. 0.404071
\(261\) 570387. 0.518284
\(262\) 16889.9 0.0152011
\(263\) 550187. 0.490480 0.245240 0.969462i \(-0.421133\pi\)
0.245240 + 0.969462i \(0.421133\pi\)
\(264\) 97202.2 0.0858353
\(265\) 63800.9 0.0558100
\(266\) 25109.8 0.0217590
\(267\) 1.49264e6 1.28138
\(268\) −1.00216e6 −0.852311
\(269\) −187673. −0.158132 −0.0790661 0.996869i \(-0.525194\pi\)
−0.0790661 + 0.996869i \(0.525194\pi\)
\(270\) 17842.2 0.0148950
\(271\) 1.22230e6 1.01101 0.505505 0.862824i \(-0.331306\pi\)
0.505505 + 0.862824i \(0.331306\pi\)
\(272\) 1.23678e6 1.01361
\(273\) 1.31796e6 1.07027
\(274\) −21574.5 −0.0173606
\(275\) 75625.0 0.0603023
\(276\) −73841.8 −0.0583485
\(277\) −838965. −0.656968 −0.328484 0.944509i \(-0.606538\pi\)
−0.328484 + 0.944509i \(0.606538\pi\)
\(278\) −105403. −0.0817980
\(279\) −388664. −0.298926
\(280\) −110645. −0.0843404
\(281\) 1.12952e6 0.853349 0.426675 0.904405i \(-0.359685\pi\)
0.426675 + 0.904405i \(0.359685\pi\)
\(282\) 173315. 0.129781
\(283\) 700626. 0.520020 0.260010 0.965606i \(-0.416274\pi\)
0.260010 + 0.965606i \(0.416274\pi\)
\(284\) −1.36969e6 −1.00769
\(285\) 187031. 0.136396
\(286\) 41060.3 0.0296830
\(287\) −495291. −0.354941
\(288\) −343600. −0.244102
\(289\) 145545. 0.102506
\(290\) −46587.3 −0.0325292
\(291\) 2.43884e6 1.68831
\(292\) 341088. 0.234105
\(293\) 163837. 0.111492 0.0557459 0.998445i \(-0.482246\pi\)
0.0557459 + 0.998445i \(0.482246\pi\)
\(294\) 47613.3 0.0321263
\(295\) 288953. 0.193318
\(296\) −160287. −0.106333
\(297\) −141750. −0.0932467
\(298\) 33641.0 0.0219446
\(299\) −62750.9 −0.0405921
\(300\) −409666. −0.262801
\(301\) 1.43104e6 0.910408
\(302\) −271803. −0.171489
\(303\) −1.37482e6 −0.860277
\(304\) 356851. 0.221464
\(305\) 799577. 0.492165
\(306\) −142132. −0.0867740
\(307\) −1.46111e6 −0.884785 −0.442393 0.896822i \(-0.645870\pi\)
−0.442393 + 0.896822i \(0.645870\pi\)
\(308\) 436954. 0.262458
\(309\) 3.11522e6 1.85606
\(310\) 31744.8 0.0187615
\(311\) −412561. −0.241873 −0.120936 0.992660i \(-0.538590\pi\)
−0.120936 + 0.992660i \(0.538590\pi\)
\(312\) −447464. −0.260239
\(313\) 2.78479e6 1.60669 0.803344 0.595516i \(-0.203052\pi\)
0.803344 + 0.595516i \(0.203052\pi\)
\(314\) −171867. −0.0983710
\(315\) −532253. −0.302233
\(316\) 3.44463e6 1.94055
\(317\) −1.13553e6 −0.634674 −0.317337 0.948313i \(-0.602789\pi\)
−0.317337 + 0.948313i \(0.602789\pi\)
\(318\) −32219.8 −0.0178672
\(319\) 370121. 0.203642
\(320\) −762742. −0.416393
\(321\) 4.48693e6 2.43045
\(322\) 7835.90 0.00421162
\(323\) 451669. 0.240887
\(324\) 2.20105e6 1.16484
\(325\) −348135. −0.182827
\(326\) −186299. −0.0970884
\(327\) 857633. 0.443539
\(328\) 168158. 0.0863043
\(329\) 1.56735e6 0.798319
\(330\) −38191.1 −0.0193053
\(331\) 62356.8 0.0312834 0.0156417 0.999878i \(-0.495021\pi\)
0.0156417 + 0.999878i \(0.495021\pi\)
\(332\) −1.44112e6 −0.717557
\(333\) −771055. −0.381044
\(334\) −95138.3 −0.0466648
\(335\) 792121. 0.385638
\(336\) −2.33891e6 −1.13023
\(337\) −1.12521e6 −0.539706 −0.269853 0.962902i \(-0.586975\pi\)
−0.269853 + 0.962902i \(0.586975\pi\)
\(338\) 37178.0 0.0177008
\(339\) 2.48347e6 1.17370
\(340\) −989319. −0.464129
\(341\) −252202. −0.117453
\(342\) −41009.8 −0.0189593
\(343\) 2.34951e6 1.07830
\(344\) −485858. −0.221367
\(345\) 58365.9 0.0264004
\(346\) −371839. −0.166980
\(347\) −122496. −0.0546135 −0.0273067 0.999627i \(-0.508693\pi\)
−0.0273067 + 0.999627i \(0.508693\pi\)
\(348\) −2.00497e6 −0.887484
\(349\) 3.69774e6 1.62507 0.812536 0.582911i \(-0.198087\pi\)
0.812536 + 0.582911i \(0.198087\pi\)
\(350\) 43472.7 0.0189691
\(351\) 652540. 0.282709
\(352\) −222960. −0.0959115
\(353\) −2.44140e6 −1.04280 −0.521401 0.853312i \(-0.674590\pi\)
−0.521401 + 0.853312i \(0.674590\pi\)
\(354\) −145923. −0.0618893
\(355\) 1.08262e6 0.455939
\(356\) −2.27810e6 −0.952681
\(357\) −2.96038e6 −1.22935
\(358\) −10252.0 −0.00422767
\(359\) −3.74687e6 −1.53438 −0.767188 0.641422i \(-0.778345\pi\)
−0.767188 + 0.641422i \(0.778345\pi\)
\(360\) 180707. 0.0734883
\(361\) 130321. 0.0526316
\(362\) 254180. 0.101946
\(363\) 303415. 0.120857
\(364\) −2.01149e6 −0.795728
\(365\) −269602. −0.105923
\(366\) −403791. −0.157563
\(367\) −135654. −0.0525738 −0.0262869 0.999654i \(-0.508368\pi\)
−0.0262869 + 0.999654i \(0.508368\pi\)
\(368\) 111361. 0.0428660
\(369\) 808918. 0.309271
\(370\) 62977.3 0.0239155
\(371\) −291376. −0.109905
\(372\) 1.36620e6 0.511866
\(373\) 3.31430e6 1.23344 0.616722 0.787181i \(-0.288460\pi\)
0.616722 + 0.787181i \(0.288460\pi\)
\(374\) −92229.1 −0.0340948
\(375\) 323807. 0.118907
\(376\) −532136. −0.194112
\(377\) −1.70383e6 −0.617409
\(378\) −81484.6 −0.0293323
\(379\) 2.96745e6 1.06117 0.530585 0.847631i \(-0.321972\pi\)
0.530585 + 0.847631i \(0.321972\pi\)
\(380\) −285450. −0.101408
\(381\) 810211. 0.285947
\(382\) −510087. −0.178849
\(383\) −40599.5 −0.0141424 −0.00707121 0.999975i \(-0.502251\pi\)
−0.00707121 + 0.999975i \(0.502251\pi\)
\(384\) 1.60715e6 0.556198
\(385\) −345376. −0.118752
\(386\) −65891.7 −0.0225093
\(387\) −2.33720e6 −0.793266
\(388\) −3.72221e6 −1.25522
\(389\) 1.75224e6 0.587109 0.293555 0.955942i \(-0.405162\pi\)
0.293555 + 0.955942i \(0.405162\pi\)
\(390\) 175810. 0.0585305
\(391\) 140950. 0.0466255
\(392\) −146189. −0.0480508
\(393\) −574545. −0.187648
\(394\) 199026. 0.0645907
\(395\) −2.72270e6 −0.878024
\(396\) −713641. −0.228687
\(397\) 663352. 0.211236 0.105618 0.994407i \(-0.466318\pi\)
0.105618 + 0.994407i \(0.466318\pi\)
\(398\) −154960. −0.0490357
\(399\) −854164. −0.268602
\(400\) 617818. 0.193068
\(401\) −2.03063e6 −0.630624 −0.315312 0.948988i \(-0.602109\pi\)
−0.315312 + 0.948988i \(0.602109\pi\)
\(402\) −400026. −0.123459
\(403\) 1.16100e6 0.356097
\(404\) 2.09827e6 0.639599
\(405\) −1.73975e6 −0.527047
\(406\) 212762. 0.0640589
\(407\) −500334. −0.149718
\(408\) 1.00509e6 0.298919
\(409\) 4.46219e6 1.31898 0.659492 0.751712i \(-0.270772\pi\)
0.659492 + 0.751712i \(0.270772\pi\)
\(410\) −66069.8 −0.0194108
\(411\) 733903. 0.214306
\(412\) −4.75451e6 −1.37995
\(413\) −1.31964e6 −0.380697
\(414\) −12797.7 −0.00366971
\(415\) 1.13909e6 0.324667
\(416\) 1.02638e6 0.290788
\(417\) 3.58552e6 1.00975
\(418\) −26611.1 −0.00744940
\(419\) 1.44867e6 0.403121 0.201561 0.979476i \(-0.435399\pi\)
0.201561 + 0.979476i \(0.435399\pi\)
\(420\) 1.87093e6 0.517528
\(421\) −3.16817e6 −0.871171 −0.435585 0.900147i \(-0.643459\pi\)
−0.435585 + 0.900147i \(0.643459\pi\)
\(422\) −514986. −0.140771
\(423\) −2.55982e6 −0.695600
\(424\) 98926.0 0.0267237
\(425\) 781975. 0.210001
\(426\) −546731. −0.145965
\(427\) −3.65164e6 −0.969210
\(428\) −6.84803e6 −1.80699
\(429\) −1.39675e6 −0.366418
\(430\) 190895. 0.0497879
\(431\) 6.58226e6 1.70680 0.853398 0.521260i \(-0.174538\pi\)
0.853398 + 0.521260i \(0.174538\pi\)
\(432\) −1.15803e6 −0.298545
\(433\) 76748.9 0.0196722 0.00983609 0.999952i \(-0.496869\pi\)
0.00983609 + 0.999952i \(0.496869\pi\)
\(434\) −144977. −0.0369467
\(435\) 1.58477e6 0.401552
\(436\) −1.30894e6 −0.329763
\(437\) 40668.6 0.0101872
\(438\) 136151. 0.0339105
\(439\) −1.53842e6 −0.380989 −0.190495 0.981688i \(-0.561009\pi\)
−0.190495 + 0.981688i \(0.561009\pi\)
\(440\) 117260. 0.0288747
\(441\) −703239. −0.172189
\(442\) 424571. 0.103370
\(443\) 7.10213e6 1.71941 0.859705 0.510791i \(-0.170647\pi\)
0.859705 + 0.510791i \(0.170647\pi\)
\(444\) 2.71035e6 0.652480
\(445\) 1.80065e6 0.431051
\(446\) 493181. 0.117400
\(447\) −1.14437e6 −0.270893
\(448\) 3.48341e6 0.819993
\(449\) 4.40451e6 1.03105 0.515527 0.856873i \(-0.327596\pi\)
0.515527 + 0.856873i \(0.327596\pi\)
\(450\) −71000.4 −0.0165283
\(451\) 524903. 0.121517
\(452\) −3.79031e6 −0.872627
\(453\) 9.24595e6 2.11693
\(454\) 188737. 0.0429752
\(455\) 1.58992e6 0.360036
\(456\) 290000. 0.0653109
\(457\) 1.11602e6 0.249966 0.124983 0.992159i \(-0.460112\pi\)
0.124983 + 0.992159i \(0.460112\pi\)
\(458\) 725494. 0.161611
\(459\) −1.46572e6 −0.324728
\(460\) −89079.1 −0.0196282
\(461\) 6.20830e6 1.36057 0.680284 0.732949i \(-0.261856\pi\)
0.680284 + 0.732949i \(0.261856\pi\)
\(462\) 174417. 0.0380175
\(463\) 3.42480e6 0.742476 0.371238 0.928538i \(-0.378933\pi\)
0.371238 + 0.928538i \(0.378933\pi\)
\(464\) 3.02370e6 0.651994
\(465\) −1.07987e6 −0.231600
\(466\) 37125.6 0.00791971
\(467\) 93071.3 0.0197480 0.00987401 0.999951i \(-0.496857\pi\)
0.00987401 + 0.999951i \(0.496857\pi\)
\(468\) 3.28520e6 0.693342
\(469\) −3.61758e6 −0.759428
\(470\) 209078. 0.0436580
\(471\) 5.84640e6 1.21433
\(472\) 448034. 0.0925670
\(473\) −1.51660e6 −0.311686
\(474\) 1.37498e6 0.281093
\(475\) 225625. 0.0458831
\(476\) 4.51818e6 0.914000
\(477\) 475880. 0.0957639
\(478\) 521291. 0.104354
\(479\) −5.98996e6 −1.19285 −0.596424 0.802670i \(-0.703412\pi\)
−0.596424 + 0.802670i \(0.703412\pi\)
\(480\) −954660. −0.189124
\(481\) 2.30326e6 0.453920
\(482\) −949737. −0.186203
\(483\) −266554. −0.0519898
\(484\) −463078. −0.0898547
\(485\) 2.94210e6 0.567940
\(486\) 705158. 0.135424
\(487\) 4.39175e6 0.839103 0.419551 0.907732i \(-0.362187\pi\)
0.419551 + 0.907732i \(0.362187\pi\)
\(488\) 1.23978e6 0.235665
\(489\) 6.33736e6 1.19850
\(490\) 57438.3 0.0108072
\(491\) 1.21644e6 0.227713 0.113856 0.993497i \(-0.463680\pi\)
0.113856 + 0.993497i \(0.463680\pi\)
\(492\) −2.84344e6 −0.529580
\(493\) 3.82711e6 0.709176
\(494\) 122502. 0.0225854
\(495\) 564074. 0.103472
\(496\) −2.06036e6 −0.376045
\(497\) −4.94430e6 −0.897870
\(498\) −575247. −0.103940
\(499\) 162759. 0.0292613 0.0146307 0.999893i \(-0.495343\pi\)
0.0146307 + 0.999893i \(0.495343\pi\)
\(500\) −494201. −0.0884053
\(501\) 3.23633e6 0.576048
\(502\) 1.00281e6 0.177607
\(503\) 4.48157e6 0.789788 0.394894 0.918727i \(-0.370781\pi\)
0.394894 + 0.918727i \(0.370781\pi\)
\(504\) −825281. −0.144719
\(505\) −1.65851e6 −0.289394
\(506\) −8304.38 −0.00144189
\(507\) −1.26469e6 −0.218506
\(508\) −1.23656e6 −0.212596
\(509\) −6.49298e6 −1.11084 −0.555418 0.831571i \(-0.687442\pi\)
−0.555418 + 0.831571i \(0.687442\pi\)
\(510\) −394902. −0.0672301
\(511\) 1.23126e6 0.208592
\(512\) −3.04765e6 −0.513795
\(513\) −422908. −0.0709501
\(514\) 375070. 0.0626187
\(515\) 3.75805e6 0.624373
\(516\) 8.21553e6 1.35835
\(517\) −1.66106e6 −0.273312
\(518\) −287615. −0.0470963
\(519\) 1.26489e7 2.06127
\(520\) −539798. −0.0875433
\(521\) −3.01994e6 −0.487421 −0.243710 0.969848i \(-0.578365\pi\)
−0.243710 + 0.969848i \(0.578365\pi\)
\(522\) −347487. −0.0558165
\(523\) 661888. 0.105811 0.0529055 0.998600i \(-0.483152\pi\)
0.0529055 + 0.998600i \(0.483152\pi\)
\(524\) 876881. 0.139512
\(525\) −1.47882e6 −0.234162
\(526\) −335181. −0.0528221
\(527\) −2.60781e6 −0.409025
\(528\) 2.47875e6 0.386944
\(529\) −6.42365e6 −0.998028
\(530\) −38868.4 −0.00601045
\(531\) 2.15525e6 0.331713
\(532\) 1.30364e6 0.199700
\(533\) −2.41636e6 −0.368420
\(534\) −909338. −0.137998
\(535\) 5.41280e6 0.817594
\(536\) 1.22822e6 0.184656
\(537\) 348743. 0.0521879
\(538\) 114333. 0.0170300
\(539\) −456328. −0.0676559
\(540\) 926323. 0.136703
\(541\) −4.71067e6 −0.691974 −0.345987 0.938239i \(-0.612456\pi\)
−0.345987 + 0.938239i \(0.612456\pi\)
\(542\) −744643. −0.108880
\(543\) −8.64646e6 −1.25846
\(544\) −2.30545e6 −0.334009
\(545\) 1.03461e6 0.149205
\(546\) −802918. −0.115263
\(547\) 7.59966e6 1.08599 0.542995 0.839736i \(-0.317290\pi\)
0.542995 + 0.839736i \(0.317290\pi\)
\(548\) −1.12010e6 −0.159332
\(549\) 5.96392e6 0.844502
\(550\) −46071.8 −0.00649424
\(551\) 1.10425e6 0.154948
\(552\) 90498.8 0.0126414
\(553\) 1.24344e7 1.72907
\(554\) 511109. 0.0707520
\(555\) −2.14230e6 −0.295222
\(556\) −5.47228e6 −0.750726
\(557\) −1.25435e7 −1.71309 −0.856546 0.516070i \(-0.827394\pi\)
−0.856546 + 0.516070i \(0.827394\pi\)
\(558\) 236779. 0.0321928
\(559\) 6.98157e6 0.944982
\(560\) −2.82155e6 −0.380204
\(561\) 3.13737e6 0.420880
\(562\) −688117. −0.0919013
\(563\) 1.28593e7 1.70980 0.854901 0.518792i \(-0.173618\pi\)
0.854901 + 0.518792i \(0.173618\pi\)
\(564\) 8.99807e6 1.19111
\(565\) 2.99593e6 0.394830
\(566\) −426831. −0.0560035
\(567\) 7.94537e6 1.03790
\(568\) 1.67865e6 0.218318
\(569\) −9.15727e6 −1.18573 −0.592865 0.805302i \(-0.702003\pi\)
−0.592865 + 0.805302i \(0.702003\pi\)
\(570\) −113942. −0.0146891
\(571\) −1.21179e6 −0.155538 −0.0777691 0.996971i \(-0.524780\pi\)
−0.0777691 + 0.996971i \(0.524780\pi\)
\(572\) 2.13175e6 0.272425
\(573\) 1.73517e7 2.20777
\(574\) 301738. 0.0382253
\(575\) 70409.6 0.00888101
\(576\) −5.68917e6 −0.714484
\(577\) 6.20841e6 0.776321 0.388160 0.921592i \(-0.373111\pi\)
0.388160 + 0.921592i \(0.373111\pi\)
\(578\) −88667.7 −0.0110394
\(579\) 2.24145e6 0.277864
\(580\) −2.41870e6 −0.298546
\(581\) −5.20217e6 −0.639359
\(582\) −1.48578e6 −0.181822
\(583\) 308796. 0.0376271
\(584\) −418030. −0.0507195
\(585\) −2.59668e6 −0.313710
\(586\) −99811.6 −0.0120071
\(587\) −1.08448e7 −1.29906 −0.649528 0.760338i \(-0.725033\pi\)
−0.649528 + 0.760338i \(0.725033\pi\)
\(588\) 2.47197e6 0.294849
\(589\) −752437. −0.0893680
\(590\) −176034. −0.0208193
\(591\) −6.77030e6 −0.797332
\(592\) −4.08747e6 −0.479347
\(593\) −1.09447e7 −1.27811 −0.639054 0.769162i \(-0.720674\pi\)
−0.639054 + 0.769162i \(0.720674\pi\)
\(594\) 86356.3 0.0100422
\(595\) −3.57125e6 −0.413549
\(596\) 1.74656e6 0.201404
\(597\) 5.27130e6 0.605316
\(598\) 38228.7 0.00437156
\(599\) −1.27587e7 −1.45292 −0.726459 0.687210i \(-0.758835\pi\)
−0.726459 + 0.687210i \(0.758835\pi\)
\(600\) 502077. 0.0569367
\(601\) −6.73618e6 −0.760725 −0.380363 0.924837i \(-0.624201\pi\)
−0.380363 + 0.924837i \(0.624201\pi\)
\(602\) −871810. −0.0980462
\(603\) 5.90830e6 0.661712
\(604\) −1.41113e7 −1.57389
\(605\) 366025. 0.0406558
\(606\) 837557. 0.0926473
\(607\) −4.75731e6 −0.524071 −0.262035 0.965058i \(-0.584394\pi\)
−0.262035 + 0.965058i \(0.584394\pi\)
\(608\) −665195. −0.0729777
\(609\) −7.23756e6 −0.790768
\(610\) −487113. −0.0530036
\(611\) 7.64657e6 0.828636
\(612\) −7.37917e6 −0.796396
\(613\) 266874. 0.0286850 0.0143425 0.999897i \(-0.495434\pi\)
0.0143425 + 0.999897i \(0.495434\pi\)
\(614\) 890130. 0.0952867
\(615\) 2.24750e6 0.239614
\(616\) −535520. −0.0568623
\(617\) −2.11758e6 −0.223937 −0.111969 0.993712i \(-0.535716\pi\)
−0.111969 + 0.993712i \(0.535716\pi\)
\(618\) −1.89784e6 −0.199888
\(619\) 1.96652e6 0.206287 0.103144 0.994666i \(-0.467110\pi\)
0.103144 + 0.994666i \(0.467110\pi\)
\(620\) 1.64811e6 0.172190
\(621\) −131975. −0.0137329
\(622\) 251338. 0.0260484
\(623\) −8.22349e6 −0.848860
\(624\) −1.14108e7 −1.17315
\(625\) 390625. 0.0400000
\(626\) −1.69653e6 −0.173032
\(627\) 905231. 0.0919582
\(628\) −8.92288e6 −0.902830
\(629\) −5.17353e6 −0.521388
\(630\) 324256. 0.0325489
\(631\) 1.73409e7 1.73379 0.866896 0.498489i \(-0.166112\pi\)
0.866896 + 0.498489i \(0.166112\pi\)
\(632\) −4.22166e6 −0.420427
\(633\) 1.75183e7 1.73773
\(634\) 691781. 0.0683511
\(635\) 977397. 0.0961915
\(636\) −1.67277e6 −0.163981
\(637\) 2.10068e6 0.205122
\(638\) −225483. −0.0219312
\(639\) 8.07511e6 0.782342
\(640\) 1.93879e6 0.187103
\(641\) −3.94482e6 −0.379212 −0.189606 0.981860i \(-0.560721\pi\)
−0.189606 + 0.981860i \(0.560721\pi\)
\(642\) −2.73350e6 −0.261747
\(643\) −1.81584e7 −1.73201 −0.866005 0.500035i \(-0.833321\pi\)
−0.866005 + 0.500035i \(0.833321\pi\)
\(644\) 406820. 0.0386534
\(645\) −6.49370e6 −0.614600
\(646\) −275163. −0.0259423
\(647\) 1.17027e7 1.09907 0.549537 0.835469i \(-0.314804\pi\)
0.549537 + 0.835469i \(0.314804\pi\)
\(648\) −2.69756e6 −0.252367
\(649\) 1.39853e6 0.130335
\(650\) 212089. 0.0196895
\(651\) 4.93171e6 0.456084
\(652\) −9.67220e6 −0.891059
\(653\) −3.95039e6 −0.362541 −0.181271 0.983433i \(-0.558021\pi\)
−0.181271 + 0.983433i \(0.558021\pi\)
\(654\) −522482. −0.0477669
\(655\) −693102. −0.0631239
\(656\) 4.28819e6 0.389058
\(657\) −2.01092e6 −0.181753
\(658\) −954851. −0.0859748
\(659\) 1.24284e7 1.11481 0.557406 0.830240i \(-0.311797\pi\)
0.557406 + 0.830240i \(0.311797\pi\)
\(660\) −1.98279e6 −0.177180
\(661\) −4.42595e6 −0.394006 −0.197003 0.980403i \(-0.563121\pi\)
−0.197003 + 0.980403i \(0.563121\pi\)
\(662\) −37988.6 −0.00336905
\(663\) −1.44427e7 −1.27604
\(664\) 1.76621e6 0.155461
\(665\) −1.03042e6 −0.0903567
\(666\) 469737. 0.0410364
\(667\) 344596. 0.0299913
\(668\) −4.93935e6 −0.428281
\(669\) −1.67766e7 −1.44923
\(670\) −482571. −0.0415311
\(671\) 3.86995e6 0.331818
\(672\) 4.35989e6 0.372437
\(673\) 1.16679e6 0.0993011 0.0496506 0.998767i \(-0.484189\pi\)
0.0496506 + 0.998767i \(0.484189\pi\)
\(674\) 685491. 0.0581235
\(675\) −732182. −0.0618529
\(676\) 1.93019e6 0.162455
\(677\) 1.01941e6 0.0854822 0.0427411 0.999086i \(-0.486391\pi\)
0.0427411 + 0.999086i \(0.486391\pi\)
\(678\) −1.51296e6 −0.126402
\(679\) −1.34364e7 −1.11843
\(680\) 1.21249e6 0.100555
\(681\) −6.42030e6 −0.530503
\(682\) 153645. 0.0126490
\(683\) −1.53024e7 −1.25519 −0.627594 0.778541i \(-0.715960\pi\)
−0.627594 + 0.778541i \(0.715960\pi\)
\(684\) −2.12913e6 −0.174005
\(685\) 885344. 0.0720917
\(686\) −1.43135e6 −0.116128
\(687\) −2.46792e7 −1.99498
\(688\) −1.23898e7 −0.997917
\(689\) −1.42153e6 −0.114079
\(690\) −35557.3 −0.00284319
\(691\) 1.44395e7 1.15042 0.575211 0.818005i \(-0.304920\pi\)
0.575211 + 0.818005i \(0.304920\pi\)
\(692\) −1.93050e7 −1.53251
\(693\) −2.57610e6 −0.203765
\(694\) 74626.5 0.00588158
\(695\) 4.32539e6 0.339675
\(696\) 2.45725e6 0.192276
\(697\) 5.42758e6 0.423179
\(698\) −2.25271e6 −0.175012
\(699\) −1.26291e6 −0.0977638
\(700\) 2.25699e6 0.174095
\(701\) 1.06826e7 0.821074 0.410537 0.911844i \(-0.365341\pi\)
0.410537 + 0.911844i \(0.365341\pi\)
\(702\) −397536. −0.0304462
\(703\) −1.49273e6 −0.113918
\(704\) −3.69167e6 −0.280732
\(705\) −7.11223e6 −0.538931
\(706\) 1.48733e6 0.112304
\(707\) 7.57434e6 0.569897
\(708\) −7.57597e6 −0.568009
\(709\) −4.42131e6 −0.330321 −0.165160 0.986267i \(-0.552814\pi\)
−0.165160 + 0.986267i \(0.552814\pi\)
\(710\) −659549. −0.0491022
\(711\) −2.03081e7 −1.50659
\(712\) 2.79198e6 0.206401
\(713\) −234809. −0.0172978
\(714\) 1.80350e6 0.132395
\(715\) −1.68497e6 −0.123262
\(716\) −532258. −0.0388007
\(717\) −1.77328e7 −1.28819
\(718\) 2.28264e6 0.165244
\(719\) −1.95698e7 −1.41177 −0.705885 0.708326i \(-0.749451\pi\)
−0.705885 + 0.708326i \(0.749451\pi\)
\(720\) 4.60820e6 0.331284
\(721\) −1.71629e7 −1.22956
\(722\) −79393.3 −0.00566814
\(723\) 3.23073e7 2.29856
\(724\) 1.31964e7 0.935639
\(725\) 1.91178e6 0.135081
\(726\) −184845. −0.0130156
\(727\) −2.24777e7 −1.57731 −0.788654 0.614837i \(-0.789222\pi\)
−0.788654 + 0.614837i \(0.789222\pi\)
\(728\) 2.46524e6 0.172397
\(729\) −7.07705e6 −0.493212
\(730\) 164245. 0.0114074
\(731\) −1.56819e7 −1.08544
\(732\) −2.09638e7 −1.44608
\(733\) −1.36016e7 −0.935040 −0.467520 0.883982i \(-0.654852\pi\)
−0.467520 + 0.883982i \(0.654852\pi\)
\(734\) 82642.5 0.00566192
\(735\) −1.95388e6 −0.133408
\(736\) −207584. −0.0141254
\(737\) 3.83386e6 0.259997
\(738\) −492804. −0.0333068
\(739\) 9.16190e6 0.617127 0.308563 0.951204i \(-0.400152\pi\)
0.308563 + 0.951204i \(0.400152\pi\)
\(740\) 3.26962e6 0.219492
\(741\) −4.16717e6 −0.278802
\(742\) 177510. 0.0118362
\(743\) 1.23617e7 0.821500 0.410750 0.911748i \(-0.365267\pi\)
0.410750 + 0.911748i \(0.365267\pi\)
\(744\) −1.67438e6 −0.110897
\(745\) −1.38051e6 −0.0911273
\(746\) −2.01912e6 −0.132836
\(747\) 8.49628e6 0.557093
\(748\) −4.78830e6 −0.312916
\(749\) −2.47201e7 −1.61007
\(750\) −197268. −0.0128057
\(751\) 9.61270e6 0.621936 0.310968 0.950420i \(-0.399347\pi\)
0.310968 + 0.950420i \(0.399347\pi\)
\(752\) −1.35700e7 −0.875054
\(753\) −3.41128e7 −2.19245
\(754\) 1.03800e6 0.0664917
\(755\) 1.11538e7 0.712127
\(756\) −4.23048e6 −0.269206
\(757\) −2.55706e6 −0.162182 −0.0810908 0.996707i \(-0.525840\pi\)
−0.0810908 + 0.996707i \(0.525840\pi\)
\(758\) −1.80781e6 −0.114283
\(759\) 282491. 0.0177992
\(760\) 349841. 0.0219703
\(761\) 6.00751e6 0.376039 0.188019 0.982165i \(-0.439793\pi\)
0.188019 + 0.982165i \(0.439793\pi\)
\(762\) −493591. −0.0307950
\(763\) −4.72500e6 −0.293826
\(764\) −2.64824e7 −1.64144
\(765\) 5.83262e6 0.360338
\(766\) 24733.8 0.00152307
\(767\) −6.43806e6 −0.395154
\(768\) 1.92536e7 1.17790
\(769\) −1.76926e7 −1.07889 −0.539443 0.842022i \(-0.681365\pi\)
−0.539443 + 0.842022i \(0.681365\pi\)
\(770\) 210408. 0.0127890
\(771\) −1.27588e7 −0.772989
\(772\) −3.42093e6 −0.206586
\(773\) −2.65637e7 −1.59897 −0.799485 0.600686i \(-0.794894\pi\)
−0.799485 + 0.600686i \(0.794894\pi\)
\(774\) 1.42386e6 0.0854306
\(775\) −1.30270e6 −0.0779092
\(776\) 4.56185e6 0.271948
\(777\) 9.78382e6 0.581374
\(778\) −1.06749e6 −0.0632286
\(779\) 1.56603e6 0.0924607
\(780\) 9.12763e6 0.537182
\(781\) 5.23990e6 0.307394
\(782\) −85868.6 −0.00502132
\(783\) −3.58342e6 −0.208878
\(784\) −3.72797e6 −0.216612
\(785\) 7.05280e6 0.408496
\(786\) 350021. 0.0202087
\(787\) 2.44560e7 1.40750 0.703751 0.710446i \(-0.251507\pi\)
0.703751 + 0.710446i \(0.251507\pi\)
\(788\) 1.03330e7 0.592801
\(789\) 1.14019e7 0.652056
\(790\) 1.65870e6 0.0945586
\(791\) −1.36823e7 −0.777530
\(792\) 874621. 0.0495458
\(793\) −1.78151e7 −1.00602
\(794\) −404123. −0.0227490
\(795\) 1.32219e6 0.0741952
\(796\) −8.04515e6 −0.450041
\(797\) 1.74911e6 0.0975376 0.0487688 0.998810i \(-0.484470\pi\)
0.0487688 + 0.998810i \(0.484470\pi\)
\(798\) 520368. 0.0289270
\(799\) −1.71756e7 −0.951799
\(800\) −1.15165e6 −0.0636205
\(801\) 1.34307e7 0.739637
\(802\) 1.23709e6 0.0679149
\(803\) −1.30487e6 −0.0714134
\(804\) −2.07683e7 −1.13308
\(805\) −321558. −0.0174892
\(806\) −707295. −0.0383498
\(807\) −3.88927e6 −0.210225
\(808\) −2.57159e6 −0.138571
\(809\) −9.47251e6 −0.508855 −0.254427 0.967092i \(-0.581887\pi\)
−0.254427 + 0.967092i \(0.581887\pi\)
\(810\) 1.05988e6 0.0567602
\(811\) −8.05797e6 −0.430203 −0.215101 0.976592i \(-0.569008\pi\)
−0.215101 + 0.976592i \(0.569008\pi\)
\(812\) 1.10461e7 0.587921
\(813\) 2.53306e7 1.34406
\(814\) 304810. 0.0161238
\(815\) 7.64507e6 0.403170
\(816\) 2.56307e7 1.34752
\(817\) −4.52473e6 −0.237158
\(818\) −2.71842e6 −0.142048
\(819\) 1.18589e7 0.617783
\(820\) −3.43018e6 −0.178149
\(821\) −2.53676e7 −1.31347 −0.656736 0.754121i \(-0.728063\pi\)
−0.656736 + 0.754121i \(0.728063\pi\)
\(822\) −447104. −0.0230796
\(823\) −2.45044e7 −1.26109 −0.630544 0.776154i \(-0.717168\pi\)
−0.630544 + 0.776154i \(0.717168\pi\)
\(824\) 5.82702e6 0.298970
\(825\) 1.56723e6 0.0801673
\(826\) 803941. 0.0409991
\(827\) 2.50859e6 0.127546 0.0637729 0.997964i \(-0.479687\pi\)
0.0637729 + 0.997964i \(0.479687\pi\)
\(828\) −664426. −0.0336799
\(829\) 2.57470e7 1.30119 0.650594 0.759426i \(-0.274520\pi\)
0.650594 + 0.759426i \(0.274520\pi\)
\(830\) −693949. −0.0349649
\(831\) −1.73864e7 −0.873390
\(832\) 1.69944e7 0.851133
\(833\) −4.71851e6 −0.235609
\(834\) −2.18435e6 −0.108744
\(835\) 3.90415e6 0.193780
\(836\) −1.38158e6 −0.0683692
\(837\) 2.44176e6 0.120473
\(838\) −882552. −0.0434140
\(839\) 4.72133e6 0.231558 0.115779 0.993275i \(-0.463064\pi\)
0.115779 + 0.993275i \(0.463064\pi\)
\(840\) −2.29297e6 −0.112124
\(841\) −1.11546e7 −0.543830
\(842\) 1.93009e6 0.0938205
\(843\) 2.34077e7 1.13446
\(844\) −2.67368e7 −1.29197
\(845\) −1.52565e6 −0.0735046
\(846\) 1.55948e6 0.0749124
\(847\) −1.67162e6 −0.0800625
\(848\) 2.52271e6 0.120470
\(849\) 1.45196e7 0.691328
\(850\) −476390. −0.0226160
\(851\) −465829. −0.0220497
\(852\) −2.83849e7 −1.33964
\(853\) 3.31831e7 1.56151 0.780754 0.624839i \(-0.214835\pi\)
0.780754 + 0.624839i \(0.214835\pi\)
\(854\) 2.22463e6 0.104379
\(855\) 1.68290e6 0.0787305
\(856\) 8.39278e6 0.391491
\(857\) −1.51606e7 −0.705124 −0.352562 0.935788i \(-0.614689\pi\)
−0.352562 + 0.935788i \(0.614689\pi\)
\(858\) 850921. 0.0394613
\(859\) −3.64591e7 −1.68586 −0.842932 0.538020i \(-0.819172\pi\)
−0.842932 + 0.538020i \(0.819172\pi\)
\(860\) 9.91080e6 0.456944
\(861\) −1.02643e7 −0.471867
\(862\) −4.01000e6 −0.183813
\(863\) −2.98273e7 −1.36328 −0.681642 0.731685i \(-0.738734\pi\)
−0.681642 + 0.731685i \(0.738734\pi\)
\(864\) 2.15864e6 0.0983777
\(865\) 1.52590e7 0.693403
\(866\) −46756.5 −0.00211859
\(867\) 3.01622e6 0.136275
\(868\) −7.52686e6 −0.339090
\(869\) −1.31779e7 −0.591964
\(870\) −965461. −0.0432451
\(871\) −1.76490e7 −0.788268
\(872\) 1.60420e6 0.0714442
\(873\) 2.19446e7 0.974524
\(874\) −24775.9 −0.00109711
\(875\) −1.78397e6 −0.0787711
\(876\) 7.06861e6 0.311224
\(877\) −916487. −0.0402372 −0.0201186 0.999798i \(-0.506404\pi\)
−0.0201186 + 0.999798i \(0.506404\pi\)
\(878\) 937225. 0.0410306
\(879\) 3.39530e6 0.148220
\(880\) 2.99024e6 0.130166
\(881\) 3.07967e7 1.33680 0.668398 0.743804i \(-0.266981\pi\)
0.668398 + 0.743804i \(0.266981\pi\)
\(882\) 428423. 0.0185439
\(883\) −4.44832e6 −0.191997 −0.0959984 0.995381i \(-0.530604\pi\)
−0.0959984 + 0.995381i \(0.530604\pi\)
\(884\) 2.20427e7 0.948710
\(885\) 5.98817e6 0.257002
\(886\) −4.32671e6 −0.185171
\(887\) −2.81458e7 −1.20117 −0.600584 0.799561i \(-0.705065\pi\)
−0.600584 + 0.799561i \(0.705065\pi\)
\(888\) −3.32173e6 −0.141362
\(889\) −4.46373e6 −0.189428
\(890\) −1.09698e6 −0.0464220
\(891\) −8.42039e6 −0.355335
\(892\) 2.56047e7 1.07748
\(893\) −4.95572e6 −0.207959
\(894\) 697165. 0.0291737
\(895\) 420706. 0.0175558
\(896\) −8.85437e6 −0.368458
\(897\) −1.30043e6 −0.0539642
\(898\) −2.68329e6 −0.111039
\(899\) −6.37561e6 −0.263101
\(900\) −3.68616e6 −0.151694
\(901\) 3.19301e6 0.131035
\(902\) −319778. −0.0130868
\(903\) 2.96565e7 1.21032
\(904\) 4.64531e6 0.189057
\(905\) −1.04306e7 −0.423341
\(906\) −5.63276e6 −0.227982
\(907\) 8.55681e6 0.345377 0.172689 0.984976i \(-0.444755\pi\)
0.172689 + 0.984976i \(0.444755\pi\)
\(908\) 9.79878e6 0.394419
\(909\) −1.23705e7 −0.496569
\(910\) −968599. −0.0387740
\(911\) 1.10075e7 0.439434 0.219717 0.975564i \(-0.429487\pi\)
0.219717 + 0.975564i \(0.429487\pi\)
\(912\) 7.39528e6 0.294420
\(913\) 5.51319e6 0.218890
\(914\) −679893. −0.0269200
\(915\) 1.65702e7 0.654297
\(916\) 3.76659e7 1.48323
\(917\) 3.16537e6 0.124309
\(918\) 892938. 0.0349715
\(919\) 2.27983e7 0.890458 0.445229 0.895417i \(-0.353122\pi\)
0.445229 + 0.895417i \(0.353122\pi\)
\(920\) 109173. 0.00425252
\(921\) −3.02796e7 −1.17626
\(922\) −3.78218e6 −0.146526
\(923\) −2.41216e7 −0.931968
\(924\) 9.05530e6 0.348918
\(925\) −2.58437e6 −0.0993116
\(926\) −2.08643e6 −0.0799607
\(927\) 2.80307e7 1.07136
\(928\) −5.63638e6 −0.214848
\(929\) −1.70404e7 −0.647799 −0.323900 0.946091i \(-0.604994\pi\)
−0.323900 + 0.946091i \(0.604994\pi\)
\(930\) 657869. 0.0249421
\(931\) −1.36144e6 −0.0514784
\(932\) 1.92747e6 0.0726855
\(933\) −8.54978e6 −0.321552
\(934\) −56700.3 −0.00212676
\(935\) 3.78476e6 0.141582
\(936\) −4.02626e6 −0.150215
\(937\) 1.60954e7 0.598898 0.299449 0.954112i \(-0.403197\pi\)
0.299449 + 0.954112i \(0.403197\pi\)
\(938\) 2.20388e6 0.0817864
\(939\) 5.77111e7 2.13597
\(940\) 1.08548e7 0.400685
\(941\) −4.32347e7 −1.59169 −0.795844 0.605501i \(-0.792973\pi\)
−0.795844 + 0.605501i \(0.792973\pi\)
\(942\) −3.56171e6 −0.130777
\(943\) 488704. 0.0178964
\(944\) 1.14253e7 0.417290
\(945\) 3.34385e6 0.121805
\(946\) 923932. 0.0335670
\(947\) −3.07297e7 −1.11348 −0.556741 0.830686i \(-0.687948\pi\)
−0.556741 + 0.830686i \(0.687948\pi\)
\(948\) 7.13854e7 2.57982
\(949\) 6.00691e6 0.216514
\(950\) −137454. −0.00494137
\(951\) −2.35324e7 −0.843752
\(952\) −5.53737e6 −0.198021
\(953\) 3.57437e7 1.27487 0.637437 0.770502i \(-0.279995\pi\)
0.637437 + 0.770502i \(0.279995\pi\)
\(954\) −289913. −0.0103133
\(955\) 2.09322e7 0.742687
\(956\) 2.70641e7 0.957744
\(957\) 7.67027e6 0.270726
\(958\) 3.64916e6 0.128463
\(959\) −4.04333e6 −0.141969
\(960\) −1.58068e7 −0.553563
\(961\) −2.42848e7 −0.848254
\(962\) −1.40317e6 −0.0488848
\(963\) 4.03732e7 1.40290
\(964\) −4.93080e7 −1.70893
\(965\) 2.70397e6 0.0934723
\(966\) 162389. 0.00559903
\(967\) −2.23534e7 −0.768738 −0.384369 0.923180i \(-0.625581\pi\)
−0.384369 + 0.923180i \(0.625581\pi\)
\(968\) 567537. 0.0194673
\(969\) 9.36024e6 0.320241
\(970\) −1.79237e6 −0.0611642
\(971\) 2.85203e7 0.970747 0.485374 0.874307i \(-0.338684\pi\)
0.485374 + 0.874307i \(0.338684\pi\)
\(972\) 3.66101e7 1.24290
\(973\) −1.97539e7 −0.668914
\(974\) −2.67551e6 −0.0903670
\(975\) −7.21464e6 −0.243054
\(976\) 3.16156e7 1.06237
\(977\) −1.27850e7 −0.428514 −0.214257 0.976777i \(-0.568733\pi\)
−0.214257 + 0.976777i \(0.568733\pi\)
\(978\) −3.86081e6 −0.129072
\(979\) 8.71514e6 0.290615
\(980\) 2.98205e6 0.0991860
\(981\) 7.71695e6 0.256020
\(982\) −741072. −0.0245235
\(983\) 3.98081e7 1.31398 0.656988 0.753901i \(-0.271830\pi\)
0.656988 + 0.753901i \(0.271830\pi\)
\(984\) 3.48485e6 0.114735
\(985\) −8.16735e6 −0.268220
\(986\) −2.33153e6 −0.0763745
\(987\) 3.24813e7 1.06130
\(988\) 6.36002e6 0.207284
\(989\) −1.41201e6 −0.0459036
\(990\) −343642. −0.0111434
\(991\) −1.86602e7 −0.603576 −0.301788 0.953375i \(-0.597583\pi\)
−0.301788 + 0.953375i \(0.597583\pi\)
\(992\) 3.84065e6 0.123916
\(993\) 1.29226e6 0.0415889
\(994\) 3.01213e6 0.0966959
\(995\) 6.35903e6 0.203626
\(996\) −2.98654e7 −0.953937
\(997\) 4.30330e7 1.37108 0.685541 0.728034i \(-0.259566\pi\)
0.685541 + 0.728034i \(0.259566\pi\)
\(998\) −99155.0 −0.00315129
\(999\) 4.84410e6 0.153568
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 1045.6.a.h.1.18 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.18 40 1.1 even 1 trivial