Properties

Label 1045.6.a.h.1.20
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 1.20
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +O(q^{10})\) \(q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +5.94602 q^{10} +121.000 q^{11} -447.932 q^{12} +762.757 q^{13} +3.19579 q^{14} +350.566 q^{15} +1018.57 q^{16} -2001.75 q^{17} -11.0275 q^{18} +361.000 q^{19} -798.586 q^{20} +188.418 q^{21} +28.7787 q^{22} +706.337 q^{23} -213.261 q^{24} +625.000 q^{25} +181.415 q^{26} -4057.67 q^{27} -429.214 q^{28} -3930.79 q^{29} +83.3789 q^{30} +8531.06 q^{31} +728.925 q^{32} +1696.74 q^{33} -476.098 q^{34} +335.918 q^{35} +1481.06 q^{36} +880.717 q^{37} +85.8605 q^{38} +10695.9 q^{39} -380.209 q^{40} +2489.76 q^{41} +44.8135 q^{42} +12748.2 q^{43} -3865.16 q^{44} -1159.13 q^{45} +167.996 q^{46} +2796.12 q^{47} +14283.1 q^{48} -16626.5 q^{49} +148.650 q^{50} -28069.9 q^{51} -24365.1 q^{52} -4387.76 q^{53} -965.078 q^{54} +3025.00 q^{55} -204.350 q^{56} +5062.18 q^{57} -934.901 q^{58} -29458.7 q^{59} -11198.3 q^{60} -18677.7 q^{61} +2029.03 q^{62} -622.994 q^{63} -32421.0 q^{64} +19068.9 q^{65} +403.554 q^{66} +16856.4 q^{67} +63942.8 q^{68} +9904.73 q^{69} +79.8948 q^{70} +72654.0 q^{71} +705.137 q^{72} +70264.7 q^{73} +209.470 q^{74} +8764.16 q^{75} -11531.6 q^{76} +1625.84 q^{77} +2543.92 q^{78} -33466.3 q^{79} +25464.3 q^{80} -45632.5 q^{81} +592.167 q^{82} -2916.82 q^{83} -6018.72 q^{84} -50043.8 q^{85} +3032.05 q^{86} -55120.0 q^{87} -1840.21 q^{88} -23748.6 q^{89} -275.688 q^{90} +10248.9 q^{91} -22562.8 q^{92} +119628. q^{93} +665.032 q^{94} +9025.00 q^{95} +10221.5 q^{96} -13529.3 q^{97} -3954.45 q^{98} -5610.18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + O(q^{10}) \) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.237841 0.0420447 0.0210223 0.999779i \(-0.493308\pi\)
0.0210223 + 0.999779i \(0.493308\pi\)
\(3\) 14.0227 0.899554 0.449777 0.893141i \(-0.351503\pi\)
0.449777 + 0.893141i \(0.351503\pi\)
\(4\) −31.9434 −0.998232
\(5\) 25.0000 0.447214
\(6\) 3.33516 0.0378215
\(7\) 13.4367 0.103645 0.0518224 0.998656i \(-0.483497\pi\)
0.0518224 + 0.998656i \(0.483497\pi\)
\(8\) −15.2083 −0.0840151
\(9\) −46.3651 −0.190803
\(10\) 5.94602 0.0188030
\(11\) 121.000 0.301511
\(12\) −447.932 −0.897964
\(13\) 762.757 1.25178 0.625890 0.779911i \(-0.284736\pi\)
0.625890 + 0.779911i \(0.284736\pi\)
\(14\) 3.19579 0.00435771
\(15\) 350.566 0.402293
\(16\) 1018.57 0.994700
\(17\) −2001.75 −1.67992 −0.839958 0.542651i \(-0.817421\pi\)
−0.839958 + 0.542651i \(0.817421\pi\)
\(18\) −11.0275 −0.00802225
\(19\) 361.000 0.229416
\(20\) −798.586 −0.446423
\(21\) 188.418 0.0932341
\(22\) 28.7787 0.0126770
\(23\) 706.337 0.278415 0.139207 0.990263i \(-0.455545\pi\)
0.139207 + 0.990263i \(0.455545\pi\)
\(24\) −213.261 −0.0755761
\(25\) 625.000 0.200000
\(26\) 181.415 0.0526307
\(27\) −4057.67 −1.07119
\(28\) −429.214 −0.103462
\(29\) −3930.79 −0.867929 −0.433965 0.900930i \(-0.642886\pi\)
−0.433965 + 0.900930i \(0.642886\pi\)
\(30\) 83.3789 0.0169143
\(31\) 8531.06 1.59441 0.797203 0.603711i \(-0.206312\pi\)
0.797203 + 0.603711i \(0.206312\pi\)
\(32\) 728.925 0.125837
\(33\) 1696.74 0.271226
\(34\) −476.098 −0.0706316
\(35\) 335.918 0.0463514
\(36\) 1481.06 0.190466
\(37\) 880.717 0.105763 0.0528813 0.998601i \(-0.483160\pi\)
0.0528813 + 0.998601i \(0.483160\pi\)
\(38\) 85.8605 0.00964571
\(39\) 10695.9 1.12604
\(40\) −380.209 −0.0375727
\(41\) 2489.76 0.231312 0.115656 0.993289i \(-0.463103\pi\)
0.115656 + 0.993289i \(0.463103\pi\)
\(42\) 44.8135 0.00392000
\(43\) 12748.2 1.05143 0.525713 0.850662i \(-0.323798\pi\)
0.525713 + 0.850662i \(0.323798\pi\)
\(44\) −3865.16 −0.300978
\(45\) −1159.13 −0.0853297
\(46\) 167.996 0.0117059
\(47\) 2796.12 0.184634 0.0923170 0.995730i \(-0.470573\pi\)
0.0923170 + 0.995730i \(0.470573\pi\)
\(48\) 14283.1 0.894786
\(49\) −16626.5 −0.989258
\(50\) 148.650 0.00840894
\(51\) −28069.9 −1.51118
\(52\) −24365.1 −1.24957
\(53\) −4387.76 −0.214562 −0.107281 0.994229i \(-0.534214\pi\)
−0.107281 + 0.994229i \(0.534214\pi\)
\(54\) −965.078 −0.0450379
\(55\) 3025.00 0.134840
\(56\) −204.350 −0.00870772
\(57\) 5062.18 0.206372
\(58\) −934.901 −0.0364918
\(59\) −29458.7 −1.10175 −0.550876 0.834587i \(-0.685706\pi\)
−0.550876 + 0.834587i \(0.685706\pi\)
\(60\) −11198.3 −0.401582
\(61\) −18677.7 −0.642686 −0.321343 0.946963i \(-0.604134\pi\)
−0.321343 + 0.946963i \(0.604134\pi\)
\(62\) 2029.03 0.0670363
\(63\) −622.994 −0.0197757
\(64\) −32421.0 −0.989409
\(65\) 19068.9 0.559813
\(66\) 403.554 0.0114036
\(67\) 16856.4 0.458753 0.229376 0.973338i \(-0.426331\pi\)
0.229376 + 0.973338i \(0.426331\pi\)
\(68\) 63942.8 1.67695
\(69\) 9904.73 0.250449
\(70\) 79.8948 0.00194883
\(71\) 72654.0 1.71046 0.855231 0.518247i \(-0.173415\pi\)
0.855231 + 0.518247i \(0.173415\pi\)
\(72\) 705.137 0.0160303
\(73\) 70264.7 1.54323 0.771614 0.636092i \(-0.219450\pi\)
0.771614 + 0.636092i \(0.219450\pi\)
\(74\) 209.470 0.00444675
\(75\) 8764.16 0.179911
\(76\) −11531.6 −0.229010
\(77\) 1625.84 0.0312501
\(78\) 2543.92 0.0473441
\(79\) −33466.3 −0.603309 −0.301654 0.953417i \(-0.597539\pi\)
−0.301654 + 0.953417i \(0.597539\pi\)
\(80\) 25464.3 0.444843
\(81\) −45632.5 −0.772791
\(82\) 592.167 0.00972545
\(83\) −2916.82 −0.0464745 −0.0232373 0.999730i \(-0.507397\pi\)
−0.0232373 + 0.999730i \(0.507397\pi\)
\(84\) −6018.72 −0.0930693
\(85\) −50043.8 −0.751281
\(86\) 3032.05 0.0442069
\(87\) −55120.0 −0.780749
\(88\) −1840.21 −0.0253315
\(89\) −23748.6 −0.317807 −0.158904 0.987294i \(-0.550796\pi\)
−0.158904 + 0.987294i \(0.550796\pi\)
\(90\) −275.688 −0.00358766
\(91\) 10248.9 0.129740
\(92\) −22562.8 −0.277923
\(93\) 119628. 1.43425
\(94\) 665.032 0.00776288
\(95\) 9025.00 0.102598
\(96\) 10221.5 0.113197
\(97\) −13529.3 −0.145997 −0.0729986 0.997332i \(-0.523257\pi\)
−0.0729986 + 0.997332i \(0.523257\pi\)
\(98\) −3954.45 −0.0415930
\(99\) −5610.18 −0.0575293
\(100\) −19964.6 −0.199646
\(101\) 141198. 1.37729 0.688645 0.725098i \(-0.258206\pi\)
0.688645 + 0.725098i \(0.258206\pi\)
\(102\) −6676.15 −0.0635369
\(103\) −135486. −1.25835 −0.629174 0.777265i \(-0.716607\pi\)
−0.629174 + 0.777265i \(0.716607\pi\)
\(104\) −11600.3 −0.105168
\(105\) 4710.46 0.0416955
\(106\) −1043.59 −0.00902120
\(107\) 60023.8 0.506832 0.253416 0.967357i \(-0.418446\pi\)
0.253416 + 0.967357i \(0.418446\pi\)
\(108\) 129616. 1.06930
\(109\) 81401.3 0.656244 0.328122 0.944635i \(-0.393584\pi\)
0.328122 + 0.944635i \(0.393584\pi\)
\(110\) 719.468 0.00566930
\(111\) 12350.0 0.0951391
\(112\) 13686.3 0.103095
\(113\) 134294. 0.989371 0.494685 0.869072i \(-0.335283\pi\)
0.494685 + 0.869072i \(0.335283\pi\)
\(114\) 1203.99 0.00867684
\(115\) 17658.4 0.124511
\(116\) 125563. 0.866395
\(117\) −35365.3 −0.238843
\(118\) −7006.49 −0.0463229
\(119\) −26896.9 −0.174115
\(120\) −5331.54 −0.0337986
\(121\) 14641.0 0.0909091
\(122\) −4442.32 −0.0270215
\(123\) 34913.1 0.208078
\(124\) −272511. −1.59159
\(125\) 15625.0 0.0894427
\(126\) −148.173 −0.000831465 0
\(127\) −232790. −1.28072 −0.640361 0.768074i \(-0.721215\pi\)
−0.640361 + 0.768074i \(0.721215\pi\)
\(128\) −31036.6 −0.167436
\(129\) 178764. 0.945815
\(130\) 4535.37 0.0235372
\(131\) 148739. 0.757262 0.378631 0.925548i \(-0.376395\pi\)
0.378631 + 0.925548i \(0.376395\pi\)
\(132\) −54199.7 −0.270746
\(133\) 4850.65 0.0237777
\(134\) 4009.15 0.0192881
\(135\) −101442. −0.479051
\(136\) 30443.3 0.141138
\(137\) 286694. 1.30502 0.652510 0.757780i \(-0.273716\pi\)
0.652510 + 0.757780i \(0.273716\pi\)
\(138\) 2355.75 0.0105301
\(139\) 15407.2 0.0676374 0.0338187 0.999428i \(-0.489233\pi\)
0.0338187 + 0.999428i \(0.489233\pi\)
\(140\) −10730.4 −0.0462694
\(141\) 39209.1 0.166088
\(142\) 17280.1 0.0719158
\(143\) 92293.6 0.377426
\(144\) −47226.3 −0.189792
\(145\) −98269.6 −0.388150
\(146\) 16711.8 0.0648845
\(147\) −233147. −0.889891
\(148\) −28133.1 −0.105576
\(149\) −58380.9 −0.215430 −0.107715 0.994182i \(-0.534353\pi\)
−0.107715 + 0.994182i \(0.534353\pi\)
\(150\) 2084.47 0.00756429
\(151\) 361236. 1.28928 0.644641 0.764485i \(-0.277007\pi\)
0.644641 + 0.764485i \(0.277007\pi\)
\(152\) −5490.21 −0.0192744
\(153\) 92811.4 0.320533
\(154\) 386.691 0.00131390
\(155\) 213277. 0.713040
\(156\) −341663. −1.12405
\(157\) 426364. 1.38048 0.690241 0.723579i \(-0.257504\pi\)
0.690241 + 0.723579i \(0.257504\pi\)
\(158\) −7959.64 −0.0253659
\(159\) −61528.0 −0.193010
\(160\) 18223.1 0.0562760
\(161\) 9490.84 0.0288563
\(162\) −10853.3 −0.0324918
\(163\) −238502. −0.703110 −0.351555 0.936167i \(-0.614347\pi\)
−0.351555 + 0.936167i \(0.614347\pi\)
\(164\) −79531.6 −0.230903
\(165\) 42418.5 0.121296
\(166\) −693.739 −0.00195401
\(167\) 412948. 1.14579 0.572894 0.819629i \(-0.305821\pi\)
0.572894 + 0.819629i \(0.305821\pi\)
\(168\) −2865.53 −0.00783307
\(169\) 210506. 0.566953
\(170\) −11902.4 −0.0315874
\(171\) −16737.8 −0.0437732
\(172\) −407222. −1.04957
\(173\) 107449. 0.272951 0.136476 0.990643i \(-0.456422\pi\)
0.136476 + 0.990643i \(0.456422\pi\)
\(174\) −13109.8 −0.0328263
\(175\) 8397.94 0.0207290
\(176\) 123247. 0.299913
\(177\) −413090. −0.991086
\(178\) −5648.39 −0.0133621
\(179\) 359439. 0.838480 0.419240 0.907875i \(-0.362297\pi\)
0.419240 + 0.907875i \(0.362297\pi\)
\(180\) 37026.5 0.0851788
\(181\) −146510. −0.332407 −0.166204 0.986091i \(-0.553151\pi\)
−0.166204 + 0.986091i \(0.553151\pi\)
\(182\) 2437.61 0.00545490
\(183\) −261911. −0.578131
\(184\) −10742.2 −0.0233910
\(185\) 22017.9 0.0472985
\(186\) 28452.4 0.0603028
\(187\) −242212. −0.506514
\(188\) −89317.8 −0.184308
\(189\) −54521.7 −0.111023
\(190\) 2146.51 0.00431369
\(191\) 581639. 1.15364 0.576820 0.816871i \(-0.304294\pi\)
0.576820 + 0.816871i \(0.304294\pi\)
\(192\) −454628. −0.890027
\(193\) 795485. 1.53723 0.768615 0.639712i \(-0.220946\pi\)
0.768615 + 0.639712i \(0.220946\pi\)
\(194\) −3217.81 −0.00613841
\(195\) 267397. 0.503582
\(196\) 531106. 0.987509
\(197\) 563252. 1.03404 0.517020 0.855973i \(-0.327041\pi\)
0.517020 + 0.855973i \(0.327041\pi\)
\(198\) −1334.33 −0.00241880
\(199\) −431989. −0.773287 −0.386643 0.922229i \(-0.626366\pi\)
−0.386643 + 0.922229i \(0.626366\pi\)
\(200\) −9505.22 −0.0168030
\(201\) 236372. 0.412673
\(202\) 33582.7 0.0579078
\(203\) −52816.8 −0.0899564
\(204\) 896648. 1.50850
\(205\) 62244.1 0.103446
\(206\) −32224.0 −0.0529068
\(207\) −32749.4 −0.0531224
\(208\) 776924. 1.24515
\(209\) 43681.0 0.0691714
\(210\) 1120.34 0.00175308
\(211\) −660940. −1.02201 −0.511006 0.859577i \(-0.670727\pi\)
−0.511006 + 0.859577i \(0.670727\pi\)
\(212\) 140160. 0.214183
\(213\) 1.01880e6 1.53865
\(214\) 14276.1 0.0213096
\(215\) 318706. 0.470212
\(216\) 61710.4 0.0899962
\(217\) 114629. 0.165252
\(218\) 19360.5 0.0275916
\(219\) 985297. 1.38822
\(220\) −96628.9 −0.134602
\(221\) −1.52685e6 −2.10289
\(222\) 2937.33 0.00400009
\(223\) −460376. −0.619942 −0.309971 0.950746i \(-0.600319\pi\)
−0.309971 + 0.950746i \(0.600319\pi\)
\(224\) 9794.35 0.0130423
\(225\) −28978.2 −0.0381606
\(226\) 31940.5 0.0415978
\(227\) −416351. −0.536285 −0.268142 0.963379i \(-0.586410\pi\)
−0.268142 + 0.963379i \(0.586410\pi\)
\(228\) −161703. −0.206007
\(229\) 833444. 1.05024 0.525119 0.851029i \(-0.324021\pi\)
0.525119 + 0.851029i \(0.324021\pi\)
\(230\) 4199.89 0.00523502
\(231\) 22798.6 0.0281111
\(232\) 59780.8 0.0729191
\(233\) −835699. −1.00846 −0.504232 0.863568i \(-0.668224\pi\)
−0.504232 + 0.863568i \(0.668224\pi\)
\(234\) −8411.32 −0.0100421
\(235\) 69903.1 0.0825709
\(236\) 941013. 1.09981
\(237\) −469286. −0.542709
\(238\) −6397.18 −0.00732059
\(239\) 1.25316e6 1.41910 0.709550 0.704655i \(-0.248898\pi\)
0.709550 + 0.704655i \(0.248898\pi\)
\(240\) 357077. 0.400160
\(241\) 203482. 0.225675 0.112838 0.993613i \(-0.464006\pi\)
0.112838 + 0.993613i \(0.464006\pi\)
\(242\) 3482.23 0.00382224
\(243\) 346124. 0.376024
\(244\) 596630. 0.641550
\(245\) −415661. −0.442410
\(246\) 8303.75 0.00874856
\(247\) 275355. 0.287178
\(248\) −129743. −0.133954
\(249\) −40901.6 −0.0418063
\(250\) 3716.26 0.00376059
\(251\) 594133. 0.595250 0.297625 0.954683i \(-0.403806\pi\)
0.297625 + 0.954683i \(0.403806\pi\)
\(252\) 19900.6 0.0197408
\(253\) 85466.8 0.0839453
\(254\) −55367.0 −0.0538476
\(255\) −701746. −0.675818
\(256\) 1.03009e6 0.982369
\(257\) 1.19242e6 1.12615 0.563076 0.826405i \(-0.309618\pi\)
0.563076 + 0.826405i \(0.309618\pi\)
\(258\) 42517.4 0.0397665
\(259\) 11833.9 0.0109617
\(260\) −609127. −0.558823
\(261\) 182251. 0.165603
\(262\) 35376.2 0.0318389
\(263\) 735505. 0.655687 0.327843 0.944732i \(-0.393678\pi\)
0.327843 + 0.944732i \(0.393678\pi\)
\(264\) −25804.6 −0.0227870
\(265\) −109694. −0.0959551
\(266\) 1153.68 0.000999728 0
\(267\) −333019. −0.285885
\(268\) −538452. −0.457942
\(269\) 1.17187e6 0.987410 0.493705 0.869629i \(-0.335642\pi\)
0.493705 + 0.869629i \(0.335642\pi\)
\(270\) −24127.0 −0.0201416
\(271\) −1.88984e6 −1.56315 −0.781576 0.623810i \(-0.785584\pi\)
−0.781576 + 0.623810i \(0.785584\pi\)
\(272\) −2.03893e6 −1.67101
\(273\) 143717. 0.116709
\(274\) 68187.5 0.0548692
\(275\) 75625.0 0.0603023
\(276\) −316391. −0.250007
\(277\) −48565.1 −0.0380298 −0.0190149 0.999819i \(-0.506053\pi\)
−0.0190149 + 0.999819i \(0.506053\pi\)
\(278\) 3664.46 0.00284379
\(279\) −395544. −0.304217
\(280\) −5108.75 −0.00389421
\(281\) −379736. −0.286890 −0.143445 0.989658i \(-0.545818\pi\)
−0.143445 + 0.989658i \(0.545818\pi\)
\(282\) 9325.52 0.00698313
\(283\) −2.61231e6 −1.93891 −0.969457 0.245263i \(-0.921126\pi\)
−0.969457 + 0.245263i \(0.921126\pi\)
\(284\) −2.32082e6 −1.70744
\(285\) 126554. 0.0922923
\(286\) 21951.2 0.0158688
\(287\) 33454.2 0.0239743
\(288\) −33796.7 −0.0240101
\(289\) 2.58715e6 1.82212
\(290\) −23372.5 −0.0163196
\(291\) −189716. −0.131332
\(292\) −2.24449e6 −1.54050
\(293\) 1.56047e6 1.06191 0.530954 0.847401i \(-0.321834\pi\)
0.530954 + 0.847401i \(0.321834\pi\)
\(294\) −55451.9 −0.0374152
\(295\) −736469. −0.492719
\(296\) −13394.2 −0.00888565
\(297\) −490978. −0.322976
\(298\) −13885.4 −0.00905767
\(299\) 538764. 0.348514
\(300\) −279957. −0.179593
\(301\) 171294. 0.108975
\(302\) 85916.5 0.0542075
\(303\) 1.97997e6 1.23895
\(304\) 367705. 0.228200
\(305\) −466943. −0.287418
\(306\) 22074.3 0.0134767
\(307\) 2.63622e6 1.59638 0.798189 0.602407i \(-0.205792\pi\)
0.798189 + 0.602407i \(0.205792\pi\)
\(308\) −51934.9 −0.0311948
\(309\) −1.89987e6 −1.13195
\(310\) 50725.9 0.0299796
\(311\) 2.44311e6 1.43233 0.716163 0.697933i \(-0.245897\pi\)
0.716163 + 0.697933i \(0.245897\pi\)
\(312\) −162667. −0.0946046
\(313\) −3.05748e6 −1.76402 −0.882008 0.471234i \(-0.843809\pi\)
−0.882008 + 0.471234i \(0.843809\pi\)
\(314\) 101407. 0.0580420
\(315\) −15574.9 −0.00884398
\(316\) 1.06903e6 0.602242
\(317\) 1.87160e6 1.04608 0.523041 0.852307i \(-0.324797\pi\)
0.523041 + 0.852307i \(0.324797\pi\)
\(318\) −14633.9 −0.00811505
\(319\) −475625. −0.261691
\(320\) −810524. −0.442477
\(321\) 841693. 0.455923
\(322\) 2257.31 0.00121325
\(323\) −722632. −0.385399
\(324\) 1.45766e6 0.771425
\(325\) 476723. 0.250356
\(326\) −56725.5 −0.0295620
\(327\) 1.14146e6 0.590327
\(328\) −37865.2 −0.0194337
\(329\) 37570.7 0.0191364
\(330\) 10088.9 0.00509984
\(331\) 2.95191e6 1.48093 0.740463 0.672097i \(-0.234606\pi\)
0.740463 + 0.672097i \(0.234606\pi\)
\(332\) 93173.4 0.0463924
\(333\) −40834.5 −0.0201798
\(334\) 98215.9 0.0481743
\(335\) 421411. 0.205161
\(336\) 191918. 0.0927399
\(337\) −1.09405e6 −0.524761 −0.262381 0.964964i \(-0.584508\pi\)
−0.262381 + 0.964964i \(0.584508\pi\)
\(338\) 50066.8 0.0238374
\(339\) 1.88315e6 0.889992
\(340\) 1.59857e6 0.749953
\(341\) 1.03226e6 0.480732
\(342\) −3980.93 −0.00184043
\(343\) −449235. −0.206176
\(344\) −193880. −0.0883357
\(345\) 247618. 0.112004
\(346\) 25555.6 0.0114762
\(347\) −3.39515e6 −1.51368 −0.756841 0.653599i \(-0.773259\pi\)
−0.756841 + 0.653599i \(0.773259\pi\)
\(348\) 1.76072e6 0.779369
\(349\) 3.42781e6 1.50644 0.753221 0.657767i \(-0.228499\pi\)
0.753221 + 0.657767i \(0.228499\pi\)
\(350\) 1997.37 0.000871543 0
\(351\) −3.09502e6 −1.34090
\(352\) 88199.9 0.0379413
\(353\) −535037. −0.228532 −0.114266 0.993450i \(-0.536452\pi\)
−0.114266 + 0.993450i \(0.536452\pi\)
\(354\) −98249.6 −0.0416699
\(355\) 1.81635e6 0.764942
\(356\) 758613. 0.317245
\(357\) −377166. −0.156625
\(358\) 85489.2 0.0352536
\(359\) −725648. −0.297160 −0.148580 0.988900i \(-0.547470\pi\)
−0.148580 + 0.988900i \(0.547470\pi\)
\(360\) 17628.4 0.00716898
\(361\) 130321. 0.0526316
\(362\) −34846.0 −0.0139760
\(363\) 205306. 0.0817776
\(364\) −327386. −0.129511
\(365\) 1.75662e6 0.690152
\(366\) −62293.1 −0.0243073
\(367\) 2.75169e6 1.06644 0.533218 0.845978i \(-0.320982\pi\)
0.533218 + 0.845978i \(0.320982\pi\)
\(368\) 719456. 0.276939
\(369\) −115438. −0.0441350
\(370\) 5236.76 0.00198865
\(371\) −58957.0 −0.0222383
\(372\) −3.82133e6 −1.43172
\(373\) 1.67257e6 0.622463 0.311231 0.950334i \(-0.399259\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(374\) −57607.8 −0.0212962
\(375\) 219104. 0.0804585
\(376\) −42524.4 −0.0155120
\(377\) −2.99823e6 −1.08646
\(378\) −12967.5 −0.00466795
\(379\) −3.18070e6 −1.13743 −0.568715 0.822535i \(-0.692559\pi\)
−0.568715 + 0.822535i \(0.692559\pi\)
\(380\) −288289. −0.102416
\(381\) −3.26434e6 −1.15208
\(382\) 138337. 0.0485044
\(383\) −1.98368e6 −0.690994 −0.345497 0.938420i \(-0.612290\pi\)
−0.345497 + 0.938420i \(0.612290\pi\)
\(384\) −435216. −0.150618
\(385\) 40646.0 0.0139755
\(386\) 189199. 0.0646323
\(387\) −591074. −0.200615
\(388\) 432171. 0.145739
\(389\) 3.25286e6 1.08991 0.544956 0.838464i \(-0.316546\pi\)
0.544956 + 0.838464i \(0.316546\pi\)
\(390\) 63597.9 0.0211729
\(391\) −1.41391e6 −0.467714
\(392\) 252861. 0.0831125
\(393\) 2.08571e6 0.681198
\(394\) 133964. 0.0434759
\(395\) −836657. −0.269808
\(396\) 179208. 0.0574276
\(397\) 2.96793e6 0.945100 0.472550 0.881304i \(-0.343334\pi\)
0.472550 + 0.881304i \(0.343334\pi\)
\(398\) −102745. −0.0325126
\(399\) 68019.0 0.0213894
\(400\) 636608. 0.198940
\(401\) −2.20884e6 −0.685966 −0.342983 0.939342i \(-0.611437\pi\)
−0.342983 + 0.939342i \(0.611437\pi\)
\(402\) 56218.9 0.0173507
\(403\) 6.50713e6 1.99585
\(404\) −4.51035e6 −1.37486
\(405\) −1.14081e6 −0.345603
\(406\) −12562.0 −0.00378219
\(407\) 106567. 0.0318886
\(408\) 426896. 0.126961
\(409\) −3.01941e6 −0.892510 −0.446255 0.894906i \(-0.647243\pi\)
−0.446255 + 0.894906i \(0.647243\pi\)
\(410\) 14804.2 0.00434935
\(411\) 4.02021e6 1.17394
\(412\) 4.32788e6 1.25612
\(413\) −395828. −0.114191
\(414\) −7789.14 −0.00223352
\(415\) −72920.6 −0.0207840
\(416\) 555993. 0.157520
\(417\) 216050. 0.0608435
\(418\) 10389.1 0.00290829
\(419\) 4.61737e6 1.28487 0.642436 0.766339i \(-0.277924\pi\)
0.642436 + 0.766339i \(0.277924\pi\)
\(420\) −150468. −0.0416218
\(421\) 3.73590e6 1.02728 0.513642 0.858005i \(-0.328296\pi\)
0.513642 + 0.858005i \(0.328296\pi\)
\(422\) −157198. −0.0429702
\(423\) −129643. −0.0352287
\(424\) 66730.6 0.0180265
\(425\) −1.25109e6 −0.335983
\(426\) 242312. 0.0646922
\(427\) −250967. −0.0666111
\(428\) −1.91737e6 −0.505936
\(429\) 1.29420e6 0.339515
\(430\) 75801.2 0.0197699
\(431\) 3.42690e6 0.888604 0.444302 0.895877i \(-0.353452\pi\)
0.444302 + 0.895877i \(0.353452\pi\)
\(432\) −4.13303e6 −1.06551
\(433\) −3.40551e6 −0.872897 −0.436448 0.899729i \(-0.643764\pi\)
−0.436448 + 0.899729i \(0.643764\pi\)
\(434\) 27263.5 0.00694797
\(435\) −1.37800e6 −0.349162
\(436\) −2.60024e6 −0.655084
\(437\) 254988. 0.0638728
\(438\) 234344. 0.0583671
\(439\) 2.01604e6 0.499274 0.249637 0.968340i \(-0.419689\pi\)
0.249637 + 0.968340i \(0.419689\pi\)
\(440\) −46005.3 −0.0113286
\(441\) 770888. 0.188753
\(442\) −363147. −0.0884152
\(443\) 2.62765e6 0.636147 0.318074 0.948066i \(-0.396964\pi\)
0.318074 + 0.948066i \(0.396964\pi\)
\(444\) −394501. −0.0949709
\(445\) −593716. −0.142128
\(446\) −109496. −0.0260653
\(447\) −818655. −0.193790
\(448\) −435631. −0.102547
\(449\) 501196. 0.117325 0.0586626 0.998278i \(-0.481316\pi\)
0.0586626 + 0.998278i \(0.481316\pi\)
\(450\) −6892.20 −0.00160445
\(451\) 301261. 0.0697432
\(452\) −4.28980e6 −0.987622
\(453\) 5.06548e6 1.15978
\(454\) −99025.3 −0.0225479
\(455\) 256224. 0.0580217
\(456\) −76987.4 −0.0173383
\(457\) −1.95026e6 −0.436820 −0.218410 0.975857i \(-0.570087\pi\)
−0.218410 + 0.975857i \(0.570087\pi\)
\(458\) 198227. 0.0441570
\(459\) 8.12244e6 1.79951
\(460\) −564071. −0.124291
\(461\) −14514.4 −0.00318087 −0.00159043 0.999999i \(-0.500506\pi\)
−0.00159043 + 0.999999i \(0.500506\pi\)
\(462\) 5422.44 0.00118192
\(463\) 6.72963e6 1.45894 0.729472 0.684011i \(-0.239766\pi\)
0.729472 + 0.684011i \(0.239766\pi\)
\(464\) −4.00379e6 −0.863329
\(465\) 2.99070e6 0.641418
\(466\) −198763. −0.0424005
\(467\) −4.14046e6 −0.878530 −0.439265 0.898357i \(-0.644761\pi\)
−0.439265 + 0.898357i \(0.644761\pi\)
\(468\) 1.12969e6 0.238421
\(469\) 226495. 0.0475474
\(470\) 16625.8 0.00347167
\(471\) 5.97875e6 1.24182
\(472\) 448019. 0.0925638
\(473\) 1.54254e6 0.317017
\(474\) −111615. −0.0228180
\(475\) 225625. 0.0458831
\(476\) 859180. 0.173807
\(477\) 203439. 0.0409391
\(478\) 298053. 0.0596657
\(479\) 1.99457e6 0.397202 0.198601 0.980080i \(-0.436360\pi\)
0.198601 + 0.980080i \(0.436360\pi\)
\(480\) 255537. 0.0506233
\(481\) 671773. 0.132391
\(482\) 48396.4 0.00948845
\(483\) 133087. 0.0259578
\(484\) −467684. −0.0907484
\(485\) −338231. −0.0652919
\(486\) 82322.3 0.0158098
\(487\) −832253. −0.159013 −0.0795065 0.996834i \(-0.525334\pi\)
−0.0795065 + 0.996834i \(0.525334\pi\)
\(488\) 284057. 0.0539953
\(489\) −3.34443e6 −0.632485
\(490\) −98861.2 −0.0186010
\(491\) −2.73598e6 −0.512165 −0.256082 0.966655i \(-0.582432\pi\)
−0.256082 + 0.966655i \(0.582432\pi\)
\(492\) −1.11524e6 −0.207710
\(493\) 7.86845e6 1.45805
\(494\) 65490.7 0.0120743
\(495\) −140255. −0.0257279
\(496\) 8.68951e6 1.58596
\(497\) 976229. 0.177280
\(498\) −9728.07 −0.00175773
\(499\) −3.85719e6 −0.693458 −0.346729 0.937965i \(-0.612708\pi\)
−0.346729 + 0.937965i \(0.612708\pi\)
\(500\) −499116. −0.0892846
\(501\) 5.79063e6 1.03070
\(502\) 141309. 0.0250271
\(503\) 1.84439e6 0.325038 0.162519 0.986705i \(-0.448038\pi\)
0.162519 + 0.986705i \(0.448038\pi\)
\(504\) 9474.72 0.00166146
\(505\) 3.52995e6 0.615943
\(506\) 20327.5 0.00352945
\(507\) 2.95185e6 0.510004
\(508\) 7.43611e6 1.27846
\(509\) 7.89689e6 1.35102 0.675509 0.737351i \(-0.263924\pi\)
0.675509 + 0.737351i \(0.263924\pi\)
\(510\) −166904. −0.0284146
\(511\) 944125. 0.159947
\(512\) 1.23817e6 0.208740
\(513\) −1.46482e6 −0.245748
\(514\) 283606. 0.0473487
\(515\) −3.38714e6 −0.562750
\(516\) −5.71034e6 −0.944143
\(517\) 338331. 0.0556693
\(518\) 2814.59 0.000460883 0
\(519\) 1.50671e6 0.245534
\(520\) −290007. −0.0470327
\(521\) 6.41862e6 1.03597 0.517986 0.855389i \(-0.326682\pi\)
0.517986 + 0.855389i \(0.326682\pi\)
\(522\) 43346.8 0.00696275
\(523\) −2.64741e6 −0.423220 −0.211610 0.977354i \(-0.567871\pi\)
−0.211610 + 0.977354i \(0.567871\pi\)
\(524\) −4.75123e6 −0.755924
\(525\) 117761. 0.0186468
\(526\) 174933. 0.0275681
\(527\) −1.70771e7 −2.67847
\(528\) 1.72825e6 0.269788
\(529\) −5.93743e6 −0.922485
\(530\) −26089.7 −0.00403440
\(531\) 1.36586e6 0.210218
\(532\) −154946. −0.0237357
\(533\) 1.89908e6 0.289552
\(534\) −79205.4 −0.0120199
\(535\) 1.50059e6 0.226662
\(536\) −256359. −0.0385421
\(537\) 5.04029e6 0.754258
\(538\) 278718. 0.0415154
\(539\) −2.01180e6 −0.298272
\(540\) 3.24040e6 0.478204
\(541\) 9.91923e6 1.45708 0.728542 0.685001i \(-0.240198\pi\)
0.728542 + 0.685001i \(0.240198\pi\)
\(542\) −449480. −0.0657222
\(543\) −2.05446e6 −0.299018
\(544\) −1.45913e6 −0.211395
\(545\) 2.03503e6 0.293481
\(546\) 34181.8 0.00490697
\(547\) −9.93545e6 −1.41977 −0.709887 0.704315i \(-0.751254\pi\)
−0.709887 + 0.704315i \(0.751254\pi\)
\(548\) −9.15799e6 −1.30271
\(549\) 865994. 0.122626
\(550\) 17986.7 0.00253539
\(551\) −1.41901e6 −0.199117
\(552\) −150635. −0.0210415
\(553\) −449676. −0.0625298
\(554\) −11550.7 −0.00159895
\(555\) 308750. 0.0425475
\(556\) −492159. −0.0675179
\(557\) −3.13866e6 −0.428653 −0.214327 0.976762i \(-0.568756\pi\)
−0.214327 + 0.976762i \(0.568756\pi\)
\(558\) −94076.4 −0.0127907
\(559\) 9.72381e6 1.31615
\(560\) 342156. 0.0461057
\(561\) −3.39645e6 −0.455636
\(562\) −90316.6 −0.0120622
\(563\) 6.58190e6 0.875145 0.437572 0.899183i \(-0.355838\pi\)
0.437572 + 0.899183i \(0.355838\pi\)
\(564\) −1.25247e6 −0.165795
\(565\) 3.35734e6 0.442460
\(566\) −621313. −0.0815210
\(567\) −613151. −0.0800958
\(568\) −1.10495e6 −0.143705
\(569\) −2.23838e6 −0.289837 −0.144918 0.989444i \(-0.546292\pi\)
−0.144918 + 0.989444i \(0.546292\pi\)
\(570\) 30099.8 0.00388040
\(571\) 1.00359e7 1.28815 0.644077 0.764961i \(-0.277242\pi\)
0.644077 + 0.764961i \(0.277242\pi\)
\(572\) −2.94818e6 −0.376759
\(573\) 8.15612e6 1.03776
\(574\) 7956.77 0.00100799
\(575\) 441461. 0.0556830
\(576\) 1.50320e6 0.188782
\(577\) −1.31917e7 −1.64953 −0.824764 0.565477i \(-0.808692\pi\)
−0.824764 + 0.565477i \(0.808692\pi\)
\(578\) 615329. 0.0766104
\(579\) 1.11548e7 1.38282
\(580\) 3.13907e6 0.387464
\(581\) −39192.5 −0.00481684
\(582\) −45122.2 −0.00552183
\(583\) −530919. −0.0646929
\(584\) −1.06861e6 −0.129654
\(585\) −884133. −0.106814
\(586\) 371143. 0.0446476
\(587\) −2.64077e6 −0.316326 −0.158163 0.987413i \(-0.550557\pi\)
−0.158163 + 0.987413i \(0.550557\pi\)
\(588\) 7.44752e6 0.888317
\(589\) 3.07971e6 0.365782
\(590\) −175162. −0.0207162
\(591\) 7.89829e6 0.930175
\(592\) 897074. 0.105202
\(593\) −3.07163e6 −0.358701 −0.179351 0.983785i \(-0.557400\pi\)
−0.179351 + 0.983785i \(0.557400\pi\)
\(594\) −116774. −0.0135794
\(595\) −672423. −0.0778664
\(596\) 1.86489e6 0.215049
\(597\) −6.05764e6 −0.695613
\(598\) 128140. 0.0146532
\(599\) −9.95471e6 −1.13360 −0.566802 0.823854i \(-0.691820\pi\)
−0.566802 + 0.823854i \(0.691820\pi\)
\(600\) −133288. −0.0151152
\(601\) 2.54692e6 0.287627 0.143813 0.989605i \(-0.454064\pi\)
0.143813 + 0.989605i \(0.454064\pi\)
\(602\) 40740.7 0.00458182
\(603\) −781551. −0.0875314
\(604\) −1.15391e7 −1.28700
\(605\) 366025. 0.0406558
\(606\) 470918. 0.0520912
\(607\) 1.26844e7 1.39733 0.698664 0.715450i \(-0.253778\pi\)
0.698664 + 0.715450i \(0.253778\pi\)
\(608\) 263142. 0.0288690
\(609\) −740632. −0.0809206
\(610\) −111058. −0.0120844
\(611\) 2.13276e6 0.231121
\(612\) −2.96472e6 −0.319966
\(613\) −7.37808e6 −0.793035 −0.396518 0.918027i \(-0.629781\pi\)
−0.396518 + 0.918027i \(0.629781\pi\)
\(614\) 627000. 0.0671192
\(615\) 872827. 0.0930552
\(616\) −24726.4 −0.00262548
\(617\) 9.02256e6 0.954151 0.477075 0.878862i \(-0.341697\pi\)
0.477075 + 0.878862i \(0.341697\pi\)
\(618\) −451866. −0.0475925
\(619\) −2.58008e6 −0.270649 −0.135325 0.990801i \(-0.543208\pi\)
−0.135325 + 0.990801i \(0.543208\pi\)
\(620\) −6.81279e6 −0.711780
\(621\) −2.86608e6 −0.298236
\(622\) 581071. 0.0602217
\(623\) −319103. −0.0329391
\(624\) 1.08945e7 1.12008
\(625\) 390625. 0.0400000
\(626\) −727193. −0.0741675
\(627\) 612524. 0.0622234
\(628\) −1.36195e7 −1.37804
\(629\) −1.76298e6 −0.177672
\(630\) −3704.33 −0.000371842 0
\(631\) −1.31123e7 −1.31101 −0.655504 0.755192i \(-0.727544\pi\)
−0.655504 + 0.755192i \(0.727544\pi\)
\(632\) 508967. 0.0506870
\(633\) −9.26813e6 −0.919355
\(634\) 445144. 0.0439822
\(635\) −5.81975e6 −0.572757
\(636\) 1.96542e6 0.192669
\(637\) −1.26819e7 −1.23833
\(638\) −113123. −0.0110027
\(639\) −3.36861e6 −0.326361
\(640\) −775916. −0.0748798
\(641\) −1.64330e7 −1.57969 −0.789845 0.613306i \(-0.789839\pi\)
−0.789845 + 0.613306i \(0.789839\pi\)
\(642\) 200189. 0.0191691
\(643\) −4.28158e6 −0.408392 −0.204196 0.978930i \(-0.565458\pi\)
−0.204196 + 0.978930i \(0.565458\pi\)
\(644\) −303170. −0.0288053
\(645\) 4.46910e6 0.422981
\(646\) −171871. −0.0162040
\(647\) −1.04162e7 −0.978251 −0.489125 0.872213i \(-0.662684\pi\)
−0.489125 + 0.872213i \(0.662684\pi\)
\(648\) 693996. 0.0649261
\(649\) −3.56451e6 −0.332191
\(650\) 113384. 0.0105261
\(651\) 1.60741e6 0.148653
\(652\) 7.61857e6 0.701867
\(653\) 4.78986e6 0.439582 0.219791 0.975547i \(-0.429463\pi\)
0.219791 + 0.975547i \(0.429463\pi\)
\(654\) 271486. 0.0248201
\(655\) 3.71847e6 0.338658
\(656\) 2.53600e6 0.230086
\(657\) −3.25783e6 −0.294452
\(658\) 8935.84 0.000804582 0
\(659\) −6.78319e6 −0.608444 −0.304222 0.952601i \(-0.598397\pi\)
−0.304222 + 0.952601i \(0.598397\pi\)
\(660\) −1.35499e6 −0.121081
\(661\) 2.77654e6 0.247172 0.123586 0.992334i \(-0.460560\pi\)
0.123586 + 0.992334i \(0.460560\pi\)
\(662\) 702085. 0.0622651
\(663\) −2.14105e7 −1.89166
\(664\) 44360.1 0.00390456
\(665\) 121266. 0.0106337
\(666\) −9712.12 −0.000848454 0
\(667\) −2.77646e6 −0.241644
\(668\) −1.31910e7 −1.14376
\(669\) −6.45570e6 −0.557671
\(670\) 100229. 0.00862591
\(671\) −2.26000e6 −0.193777
\(672\) 137343. 0.0117323
\(673\) −1.59547e7 −1.35785 −0.678923 0.734209i \(-0.737553\pi\)
−0.678923 + 0.734209i \(0.737553\pi\)
\(674\) −260209. −0.0220634
\(675\) −2.53604e6 −0.214238
\(676\) −6.72427e6 −0.565950
\(677\) 9566.55 0.000802202 0 0.000401101 1.00000i \(-0.499872\pi\)
0.000401101 1.00000i \(0.499872\pi\)
\(678\) 447890. 0.0374195
\(679\) −181789. −0.0151318
\(680\) 761083. 0.0631189
\(681\) −5.83835e6 −0.482417
\(682\) 245513. 0.0202122
\(683\) −1.92293e7 −1.57729 −0.788644 0.614850i \(-0.789217\pi\)
−0.788644 + 0.614850i \(0.789217\pi\)
\(684\) 534663. 0.0436958
\(685\) 7.16735e6 0.583623
\(686\) −106846. −0.00866862
\(687\) 1.16871e7 0.944746
\(688\) 1.29850e7 1.04585
\(689\) −3.34680e6 −0.268585
\(690\) 58893.7 0.00470919
\(691\) −3.69107e6 −0.294074 −0.147037 0.989131i \(-0.546974\pi\)
−0.147037 + 0.989131i \(0.546974\pi\)
\(692\) −3.43227e6 −0.272469
\(693\) −75382.3 −0.00596261
\(694\) −807504. −0.0636423
\(695\) 385180. 0.0302484
\(696\) 838285. 0.0655947
\(697\) −4.98388e6 −0.388585
\(698\) 815272. 0.0633379
\(699\) −1.17187e7 −0.907167
\(700\) −268259. −0.0206923
\(701\) −6.16999e6 −0.474230 −0.237115 0.971482i \(-0.576202\pi\)
−0.237115 + 0.971482i \(0.576202\pi\)
\(702\) −736121. −0.0563775
\(703\) 317939. 0.0242636
\(704\) −3.92294e6 −0.298318
\(705\) 980227. 0.0742769
\(706\) −127254. −0.00960857
\(707\) 1.89724e6 0.142749
\(708\) 1.31955e7 0.989334
\(709\) −1.61376e7 −1.20565 −0.602827 0.797872i \(-0.705959\pi\)
−0.602827 + 0.797872i \(0.705959\pi\)
\(710\) 432002. 0.0321617
\(711\) 1.55167e6 0.115113
\(712\) 361178. 0.0267006
\(713\) 6.02581e6 0.443907
\(714\) −89705.5 −0.00658527
\(715\) 2.30734e6 0.168790
\(716\) −1.14817e7 −0.836998
\(717\) 1.75727e7 1.27656
\(718\) −172589. −0.0124940
\(719\) 2.06581e7 1.49028 0.745142 0.666906i \(-0.232382\pi\)
0.745142 + 0.666906i \(0.232382\pi\)
\(720\) −1.18066e6 −0.0848774
\(721\) −1.82048e6 −0.130421
\(722\) 30995.6 0.00221288
\(723\) 2.85336e6 0.203007
\(724\) 4.68003e6 0.331820
\(725\) −2.45674e6 −0.173586
\(726\) 48830.0 0.00343831
\(727\) −1.80431e7 −1.26612 −0.633060 0.774103i \(-0.718201\pi\)
−0.633060 + 0.774103i \(0.718201\pi\)
\(728\) −155869. −0.0109002
\(729\) 1.59423e7 1.11105
\(730\) 417795. 0.0290172
\(731\) −2.55188e7 −1.76631
\(732\) 8.36634e6 0.577109
\(733\) −3.18991e6 −0.219290 −0.109645 0.993971i \(-0.534971\pi\)
−0.109645 + 0.993971i \(0.534971\pi\)
\(734\) 654465. 0.0448380
\(735\) −5.82868e6 −0.397971
\(736\) 514867. 0.0350349
\(737\) 2.03963e6 0.138319
\(738\) −27455.9 −0.00185564
\(739\) 5.03450e6 0.339114 0.169557 0.985520i \(-0.445766\pi\)
0.169557 + 0.985520i \(0.445766\pi\)
\(740\) −703328. −0.0472148
\(741\) 3.86121e6 0.258332
\(742\) −14022.4 −0.000935001 0
\(743\) 1.29496e7 0.860569 0.430284 0.902693i \(-0.358413\pi\)
0.430284 + 0.902693i \(0.358413\pi\)
\(744\) −1.81935e6 −0.120499
\(745\) −1.45952e6 −0.0963430
\(746\) 397806. 0.0261712
\(747\) 135239. 0.00886748
\(748\) 7.73708e6 0.505618
\(749\) 806522. 0.0525305
\(750\) 52111.8 0.00338285
\(751\) −2.56649e7 −1.66050 −0.830251 0.557390i \(-0.811803\pi\)
−0.830251 + 0.557390i \(0.811803\pi\)
\(752\) 2.84806e6 0.183655
\(753\) 8.33132e6 0.535459
\(754\) −713102. −0.0456797
\(755\) 9.03089e6 0.576585
\(756\) 1.74161e6 0.110827
\(757\) −9.78629e6 −0.620695 −0.310347 0.950623i \(-0.600445\pi\)
−0.310347 + 0.950623i \(0.600445\pi\)
\(758\) −756500. −0.0478229
\(759\) 1.19847e6 0.0755133
\(760\) −137255. −0.00861976
\(761\) 1.22546e7 0.767073 0.383536 0.923526i \(-0.374706\pi\)
0.383536 + 0.923526i \(0.374706\pi\)
\(762\) −776392. −0.0484388
\(763\) 1.09377e6 0.0680163
\(764\) −1.85795e7 −1.15160
\(765\) 2.32029e6 0.143347
\(766\) −471799. −0.0290526
\(767\) −2.24699e7 −1.37915
\(768\) 1.44446e7 0.883694
\(769\) −3.08185e7 −1.87930 −0.939650 0.342138i \(-0.888849\pi\)
−0.939650 + 0.342138i \(0.888849\pi\)
\(770\) 9667.28 0.000587594 0
\(771\) 1.67209e7 1.01303
\(772\) −2.54105e7 −1.53451
\(773\) −2.39580e7 −1.44212 −0.721061 0.692871i \(-0.756345\pi\)
−0.721061 + 0.692871i \(0.756345\pi\)
\(774\) −140581. −0.00843481
\(775\) 5.33192e6 0.318881
\(776\) 205758. 0.0122660
\(777\) 165943. 0.00986068
\(778\) 773663. 0.0458250
\(779\) 898804. 0.0530666
\(780\) −8.54158e6 −0.502692
\(781\) 8.79113e6 0.515724
\(782\) −336286. −0.0196649
\(783\) 1.59498e7 0.929718
\(784\) −1.69353e7 −0.984015
\(785\) 1.06591e7 0.617371
\(786\) 496068. 0.0286408
\(787\) −1.06543e7 −0.613178 −0.306589 0.951842i \(-0.599188\pi\)
−0.306589 + 0.951842i \(0.599188\pi\)
\(788\) −1.79922e7 −1.03221
\(789\) 1.03137e7 0.589825
\(790\) −198991. −0.0113440
\(791\) 1.80446e6 0.102543
\(792\) 85321.6 0.00483332
\(793\) −1.42466e7 −0.804502
\(794\) 705895. 0.0397364
\(795\) −1.53820e6 −0.0863168
\(796\) 1.37992e7 0.771920
\(797\) −2.29416e7 −1.27932 −0.639658 0.768660i \(-0.720924\pi\)
−0.639658 + 0.768660i \(0.720924\pi\)
\(798\) 16177.7 0.000899309 0
\(799\) −5.59714e6 −0.310170
\(800\) 455578. 0.0251674
\(801\) 1.10111e6 0.0606385
\(802\) −525351. −0.0288412
\(803\) 8.50202e6 0.465300
\(804\) −7.55053e6 −0.411943
\(805\) 237271. 0.0129049
\(806\) 1.54766e6 0.0839147
\(807\) 1.64327e7 0.888229
\(808\) −2.14739e6 −0.115713
\(809\) −2.22454e7 −1.19500 −0.597501 0.801868i \(-0.703840\pi\)
−0.597501 + 0.801868i \(0.703840\pi\)
\(810\) −271332. −0.0145308
\(811\) −3.11364e7 −1.66232 −0.831162 0.556030i \(-0.812324\pi\)
−0.831162 + 0.556030i \(0.812324\pi\)
\(812\) 1.68715e6 0.0897973
\(813\) −2.65005e7 −1.40614
\(814\) 25345.9 0.00134075
\(815\) −5.96255e6 −0.314440
\(816\) −2.85912e7 −1.50317
\(817\) 4.60211e6 0.241214
\(818\) −718138. −0.0375253
\(819\) −475193. −0.0247549
\(820\) −1.98829e6 −0.103263
\(821\) −2.75160e7 −1.42471 −0.712357 0.701817i \(-0.752372\pi\)
−0.712357 + 0.701817i \(0.752372\pi\)
\(822\) 956170. 0.0493578
\(823\) 1.81038e7 0.931690 0.465845 0.884866i \(-0.345750\pi\)
0.465845 + 0.884866i \(0.345750\pi\)
\(824\) 2.06051e6 0.105720
\(825\) 1.06046e6 0.0542451
\(826\) −94144.1 −0.00480112
\(827\) 2.27756e7 1.15799 0.578996 0.815330i \(-0.303445\pi\)
0.578996 + 0.815330i \(0.303445\pi\)
\(828\) 1.04613e6 0.0530285
\(829\) −9.39704e6 −0.474903 −0.237451 0.971399i \(-0.576312\pi\)
−0.237451 + 0.971399i \(0.576312\pi\)
\(830\) −17343.5 −0.000873858 0
\(831\) −681011. −0.0342099
\(832\) −2.47293e7 −1.23852
\(833\) 3.32820e7 1.66187
\(834\) 51385.5 0.00255815
\(835\) 1.03237e7 0.512412
\(836\) −1.39532e6 −0.0690492
\(837\) −3.46162e7 −1.70791
\(838\) 1.09820e6 0.0540220
\(839\) 3.68860e7 1.80907 0.904537 0.426395i \(-0.140216\pi\)
0.904537 + 0.426395i \(0.140216\pi\)
\(840\) −71638.3 −0.00350305
\(841\) −5.06008e6 −0.246699
\(842\) 888550. 0.0431918
\(843\) −5.32490e6 −0.258073
\(844\) 2.11127e7 1.02021
\(845\) 5.26264e6 0.253549
\(846\) −30834.3 −0.00148118
\(847\) 196727. 0.00942225
\(848\) −4.46925e6 −0.213425
\(849\) −3.66315e7 −1.74416
\(850\) −297561. −0.0141263
\(851\) 622083. 0.0294459
\(852\) −3.25440e7 −1.53593
\(853\) 1.29325e7 0.608570 0.304285 0.952581i \(-0.401583\pi\)
0.304285 + 0.952581i \(0.401583\pi\)
\(854\) −59690.1 −0.00280064
\(855\) −418445. −0.0195760
\(856\) −912863. −0.0425815
\(857\) 3.74701e7 1.74274 0.871371 0.490624i \(-0.163231\pi\)
0.871371 + 0.490624i \(0.163231\pi\)
\(858\) 307814. 0.0142748
\(859\) 3.07350e6 0.142118 0.0710592 0.997472i \(-0.477362\pi\)
0.0710592 + 0.997472i \(0.477362\pi\)
\(860\) −1.01806e7 −0.469381
\(861\) 469117. 0.0215662
\(862\) 815057. 0.0373611
\(863\) 7.51629e6 0.343539 0.171770 0.985137i \(-0.445052\pi\)
0.171770 + 0.985137i \(0.445052\pi\)
\(864\) −2.95774e6 −0.134795
\(865\) 2.68621e6 0.122068
\(866\) −809970. −0.0367007
\(867\) 3.62787e7 1.63909
\(868\) −3.66166e6 −0.164960
\(869\) −4.04942e6 −0.181904
\(870\) −327745. −0.0146804
\(871\) 1.28574e7 0.574258
\(872\) −1.23798e6 −0.0551344
\(873\) 627286. 0.0278567
\(874\) 60646.5 0.00268551
\(875\) 209948. 0.00927027
\(876\) −3.14738e7 −1.38576
\(877\) 6.35147e6 0.278853 0.139427 0.990232i \(-0.455474\pi\)
0.139427 + 0.990232i \(0.455474\pi\)
\(878\) 479497. 0.0209918
\(879\) 2.18819e7 0.955243
\(880\) 3.08118e6 0.134125
\(881\) −4.09407e7 −1.77711 −0.888556 0.458767i \(-0.848291\pi\)
−0.888556 + 0.458767i \(0.848291\pi\)
\(882\) 183348. 0.00793608
\(883\) −3.72230e7 −1.60661 −0.803303 0.595570i \(-0.796926\pi\)
−0.803303 + 0.595570i \(0.796926\pi\)
\(884\) 4.87728e7 2.09917
\(885\) −1.03272e7 −0.443227
\(886\) 624961. 0.0267466
\(887\) 6.01716e6 0.256792 0.128396 0.991723i \(-0.459017\pi\)
0.128396 + 0.991723i \(0.459017\pi\)
\(888\) −187823. −0.00799312
\(889\) −3.12793e6 −0.132740
\(890\) −141210. −0.00597571
\(891\) −5.52154e6 −0.233005
\(892\) 1.47060e7 0.618846
\(893\) 1.00940e6 0.0423580
\(894\) −194710. −0.00814786
\(895\) 8.98598e6 0.374980
\(896\) −417030. −0.0173539
\(897\) 7.55490e6 0.313507
\(898\) 119205. 0.00493290
\(899\) −3.35338e7 −1.38383
\(900\) 925663. 0.0380931
\(901\) 8.78320e6 0.360446
\(902\) 71652.2 0.00293233
\(903\) 2.40200e6 0.0980288
\(904\) −2.04238e6 −0.0831220
\(905\) −3.66275e6 −0.148657
\(906\) 1.20478e6 0.0487626
\(907\) −3.16493e7 −1.27746 −0.638728 0.769432i \(-0.720539\pi\)
−0.638728 + 0.769432i \(0.720539\pi\)
\(908\) 1.32997e7 0.535337
\(909\) −6.54667e6 −0.262791
\(910\) 60940.4 0.00243950
\(911\) −1.65255e7 −0.659719 −0.329860 0.944030i \(-0.607001\pi\)
−0.329860 + 0.944030i \(0.607001\pi\)
\(912\) 5.15620e6 0.205278
\(913\) −352936. −0.0140126
\(914\) −463851. −0.0183660
\(915\) −6.54778e6 −0.258548
\(916\) −2.66231e7 −1.04838
\(917\) 1.99856e6 0.0784863
\(918\) 1.93185e6 0.0756599
\(919\) 3.77434e6 0.147419 0.0737093 0.997280i \(-0.476516\pi\)
0.0737093 + 0.997280i \(0.476516\pi\)
\(920\) −268556. −0.0104608
\(921\) 3.69668e7 1.43603
\(922\) −3452.11 −0.000133739 0
\(923\) 5.54173e7 2.14112
\(924\) −728266. −0.0280614
\(925\) 550448. 0.0211525
\(926\) 1.60058e6 0.0613408
\(927\) 6.28181e6 0.240096
\(928\) −2.86525e6 −0.109218
\(929\) −1.04084e7 −0.395679 −0.197840 0.980234i \(-0.563392\pi\)
−0.197840 + 0.980234i \(0.563392\pi\)
\(930\) 711311. 0.0269682
\(931\) −6.00215e6 −0.226951
\(932\) 2.66951e7 1.00668
\(933\) 3.42589e7 1.28845
\(934\) −984771. −0.0369375
\(935\) −6.05530e6 −0.226520
\(936\) 537848. 0.0200664
\(937\) 5.23121e7 1.94649 0.973247 0.229763i \(-0.0737950\pi\)
0.973247 + 0.229763i \(0.0737950\pi\)
\(938\) 53869.7 0.00199911
\(939\) −4.28740e7 −1.58683
\(940\) −2.23295e6 −0.0824249
\(941\) −991679. −0.0365088 −0.0182544 0.999833i \(-0.505811\pi\)
−0.0182544 + 0.999833i \(0.505811\pi\)
\(942\) 1.42199e6 0.0522119
\(943\) 1.75861e6 0.0644008
\(944\) −3.00059e7 −1.09591
\(945\) −1.36304e6 −0.0496512
\(946\) 366878. 0.0133289
\(947\) −2.12854e7 −0.771269 −0.385635 0.922652i \(-0.626017\pi\)
−0.385635 + 0.922652i \(0.626017\pi\)
\(948\) 1.49906e7 0.541749
\(949\) 5.35949e7 1.93178
\(950\) 53662.8 0.00192914
\(951\) 2.62449e7 0.941008
\(952\) 409058. 0.0146282
\(953\) 3.99471e6 0.142480 0.0712398 0.997459i \(-0.477304\pi\)
0.0712398 + 0.997459i \(0.477304\pi\)
\(954\) 48386.1 0.00172127
\(955\) 1.45410e7 0.515923
\(956\) −4.00304e7 −1.41659
\(957\) −6.66953e6 −0.235405
\(958\) 474390. 0.0167002
\(959\) 3.85222e6 0.135259
\(960\) −1.13657e7 −0.398032
\(961\) 4.41499e7 1.54213
\(962\) 159775. 0.00556636
\(963\) −2.78301e6 −0.0967050
\(964\) −6.49993e6 −0.225277
\(965\) 1.98871e7 0.687470
\(966\) 31653.5 0.00109139
\(967\) 3.18059e7 1.09381 0.546905 0.837195i \(-0.315806\pi\)
0.546905 + 0.837195i \(0.315806\pi\)
\(968\) −222665. −0.00763773
\(969\) −1.01332e7 −0.346687
\(970\) −80445.2 −0.00274518
\(971\) −6.42176e6 −0.218578 −0.109289 0.994010i \(-0.534857\pi\)
−0.109289 + 0.994010i \(0.534857\pi\)
\(972\) −1.10564e7 −0.375359
\(973\) 207022. 0.00701027
\(974\) −197944. −0.00668565
\(975\) 6.68493e6 0.225209
\(976\) −1.90246e7 −0.639280
\(977\) 7.63925e6 0.256044 0.128022 0.991771i \(-0.459137\pi\)
0.128022 + 0.991771i \(0.459137\pi\)
\(978\) −795442. −0.0265926
\(979\) −2.87358e6 −0.0958224
\(980\) 1.32777e7 0.441627
\(981\) −3.77418e6 −0.125213
\(982\) −650728. −0.0215338
\(983\) −4.54880e7 −1.50146 −0.750728 0.660611i \(-0.770297\pi\)
−0.750728 + 0.660611i \(0.770297\pi\)
\(984\) −530970. −0.0174817
\(985\) 1.40813e7 0.462437
\(986\) 1.87144e6 0.0613032
\(987\) 526841. 0.0172142
\(988\) −8.79580e6 −0.286670
\(989\) 9.00455e6 0.292733
\(990\) −33358.2 −0.00108172
\(991\) 3.14083e7 1.01592 0.507961 0.861380i \(-0.330399\pi\)
0.507961 + 0.861380i \(0.330399\pi\)
\(992\) 6.21851e6 0.200635
\(993\) 4.13936e7 1.33217
\(994\) 232187. 0.00745370
\(995\) −1.07997e7 −0.345824
\(996\) 1.30654e6 0.0417324
\(997\) 3.37727e7 1.07604 0.538019 0.842933i \(-0.319173\pi\)
0.538019 + 0.842933i \(0.319173\pi\)
\(998\) −917397. −0.0291562
\(999\) −3.57366e6 −0.113292
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.1.20 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.20 40 1.1 even 1 trivial