Properties

Label 15.8.a.c.1.1
Level 15
Weight 8
Character 15.1
Self dual Yes
Analytic conductor 4.686
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 15.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.68577538226\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{601}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(12.7577\)
Character \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} +O(q^{10})\) \(q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} -1094.71 q^{10} +7411.55 q^{11} -1385.20 q^{12} -14594.3 q^{13} -11721.5 q^{14} +3375.00 q^{15} -7185.09 q^{16} +14414.7 q^{17} -6384.33 q^{18} +409.730 q^{19} -6412.94 q^{20} +36137.6 q^{21} -64907.8 q^{22} -17913.8 q^{23} +42397.5 q^{24} +15625.0 q^{25} +127812. q^{26} +19683.0 q^{27} -68666.1 q^{28} -10705.4 q^{29} -29557.1 q^{30} +178691. q^{31} -138071. q^{32} +200112. q^{33} -126239. q^{34} +167304. q^{35} -37400.3 q^{36} -427962. q^{37} -3588.27 q^{38} -394046. q^{39} +196285. q^{40} +53370.3 q^{41} -316480. q^{42} +89349.4 q^{43} -380239. q^{44} +91125.0 q^{45} +156883. q^{46} -161273. q^{47} -193997. q^{48} +967848. q^{49} -136838. q^{50} +389197. q^{51} +748740. q^{52} -121833. q^{53} -172377. q^{54} +926444. q^{55} +2.10170e6 q^{56} +11062.7 q^{57} +93754.2 q^{58} -1.69229e6 q^{59} -173149. q^{60} -1.23924e6 q^{61} -1.56491e6 q^{62} +975714. q^{63} +2.12887e6 q^{64} -1.82429e6 q^{65} -1.75251e6 q^{66} -944402. q^{67} -739526. q^{68} -483674. q^{69} -1.46519e6 q^{70} -936943. q^{71} +1.14473e6 q^{72} -5.49712e6 q^{73} +3.74794e6 q^{74} +421875. q^{75} -21020.6 q^{76} +9.91983e6 q^{77} +3.45092e6 q^{78} -3.29987e6 q^{79} -898136. q^{80} +531441. q^{81} -467399. q^{82} -4.16260e6 q^{83} -1.85399e6 q^{84} +1.80184e6 q^{85} -782491. q^{86} -289046. q^{87} +1.16382e7 q^{88} +8.50941e6 q^{89} -798041. q^{90} -1.95334e7 q^{91} +919044. q^{92} +4.82465e6 q^{93} +1.41237e6 q^{94} +51216.2 q^{95} -3.72792e6 q^{96} +6.61583e6 q^{97} -8.47607e6 q^{98} +5.40302e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 7q^{2} + 54q^{3} + 69q^{4} + 250q^{5} + 189q^{6} + 1304q^{7} + 1449q^{8} + 1458q^{9} + O(q^{10}) \) \( 2q + 7q^{2} + 54q^{3} + 69q^{4} + 250q^{5} + 189q^{6} + 1304q^{7} + 1449q^{8} + 1458q^{9} + 875q^{10} + 3448q^{11} + 1863q^{12} - 8988q^{13} - 12264q^{14} + 6750q^{15} - 24495q^{16} - 5492q^{17} + 5103q^{18} - 49584q^{19} + 8625q^{20} + 35208q^{21} - 127364q^{22} + 91848q^{23} + 39123q^{24} + 31250q^{25} + 216154q^{26} + 39366q^{27} - 72808q^{28} + 181772q^{29} + 23625q^{30} + 304232q^{31} - 395311q^{32} + 93096q^{33} - 439922q^{34} + 163000q^{35} + 50301q^{36} - 502316q^{37} - 791372q^{38} - 242676q^{39} + 181125q^{40} + 631172q^{41} - 331128q^{42} + 353640q^{43} - 857068q^{44} + 182250q^{45} + 1886472q^{46} - 467480q^{47} - 661365q^{48} + 145490q^{49} + 109375q^{50} - 148284q^{51} + 1423198q^{52} - 568052q^{53} + 137781q^{54} + 431000q^{55} + 2105880q^{56} - 1338768q^{57} + 3126746q^{58} + 287224q^{59} + 232875q^{60} - 2514180q^{61} + 413328q^{62} + 950616q^{63} + 291041q^{64} - 1123500q^{65} - 3438828q^{66} - 5073832q^{67} - 3134374q^{68} + 2479896q^{69} - 1533000q^{70} - 3748816q^{71} + 1056321q^{72} - 1477212q^{73} + 2576306q^{74} + 843750q^{75} - 6035444q^{76} + 10056288q^{77} + 5836158q^{78} - 4627720q^{79} - 3061875q^{80} + 1062882q^{81} + 8637398q^{82} - 6072936q^{83} - 1965816q^{84} - 686500q^{85} + 3382108q^{86} + 4907844q^{87} + 12118884q^{88} + 16516356q^{89} + 637875q^{90} - 19726448q^{91} + 14123784q^{92} + 8214264q^{93} - 3412736q^{94} - 6198000q^{95} - 10673397q^{96} + 2723428q^{97} - 21434497q^{98} + 2513592q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.75765 −0.774074 −0.387037 0.922064i \(-0.626501\pi\)
−0.387037 + 0.922064i \(0.626501\pi\)
\(3\) 27.0000 0.577350
\(4\) −51.3036 −0.400809
\(5\) 125.000 0.447214
\(6\) −236.457 −0.446912
\(7\) 1338.43 1.47486 0.737432 0.675421i \(-0.236038\pi\)
0.737432 + 0.675421i \(0.236038\pi\)
\(8\) 1570.28 1.08433
\(9\) 729.000 0.333333
\(10\) −1094.71 −0.346177
\(11\) 7411.55 1.67894 0.839469 0.543408i \(-0.182866\pi\)
0.839469 + 0.543408i \(0.182866\pi\)
\(12\) −1385.20 −0.231407
\(13\) −14594.3 −1.84239 −0.921195 0.389101i \(-0.872786\pi\)
−0.921195 + 0.389101i \(0.872786\pi\)
\(14\) −11721.5 −1.14165
\(15\) 3375.00 0.258199
\(16\) −7185.09 −0.438543
\(17\) 14414.7 0.711598 0.355799 0.934563i \(-0.384209\pi\)
0.355799 + 0.934563i \(0.384209\pi\)
\(18\) −6384.33 −0.258025
\(19\) 409.730 0.0137044 0.00685220 0.999977i \(-0.497819\pi\)
0.00685220 + 0.999977i \(0.497819\pi\)
\(20\) −6412.94 −0.179247
\(21\) 36137.6 0.851513
\(22\) −64907.8 −1.29962
\(23\) −17913.8 −0.307002 −0.153501 0.988148i \(-0.549055\pi\)
−0.153501 + 0.988148i \(0.549055\pi\)
\(24\) 42397.5 0.626038
\(25\) 15625.0 0.200000
\(26\) 127812. 1.42615
\(27\) 19683.0 0.192450
\(28\) −68666.1 −0.591139
\(29\) −10705.4 −0.0815099 −0.0407549 0.999169i \(-0.512976\pi\)
−0.0407549 + 0.999169i \(0.512976\pi\)
\(30\) −29557.1 −0.199865
\(31\) 178691. 1.07730 0.538649 0.842530i \(-0.318935\pi\)
0.538649 + 0.842530i \(0.318935\pi\)
\(32\) −138071. −0.744865
\(33\) 200112. 0.969335
\(34\) −126239. −0.550830
\(35\) 167304. 0.659579
\(36\) −37400.3 −0.133603
\(37\) −427962. −1.38899 −0.694496 0.719497i \(-0.744372\pi\)
−0.694496 + 0.719497i \(0.744372\pi\)
\(38\) −3588.27 −0.0106082
\(39\) −394046. −1.06370
\(40\) 196285. 0.484927
\(41\) 53370.3 0.120936 0.0604681 0.998170i \(-0.480741\pi\)
0.0604681 + 0.998170i \(0.480741\pi\)
\(42\) −316480. −0.659134
\(43\) 89349.4 0.171377 0.0856884 0.996322i \(-0.472691\pi\)
0.0856884 + 0.996322i \(0.472691\pi\)
\(44\) −380239. −0.672933
\(45\) 91125.0 0.149071
\(46\) 156883. 0.237642
\(47\) −161273. −0.226578 −0.113289 0.993562i \(-0.536139\pi\)
−0.113289 + 0.993562i \(0.536139\pi\)
\(48\) −193997. −0.253193
\(49\) 967848. 1.17522
\(50\) −136838. −0.154815
\(51\) 389197. 0.410841
\(52\) 748740. 0.738447
\(53\) −121833. −0.112408 −0.0562042 0.998419i \(-0.517900\pi\)
−0.0562042 + 0.998419i \(0.517900\pi\)
\(54\) −172377. −0.148971
\(55\) 926444. 0.750844
\(56\) 2.10170e6 1.59924
\(57\) 11062.7 0.00791224
\(58\) 93754.2 0.0630947
\(59\) −1.69229e6 −1.07274 −0.536368 0.843984i \(-0.680204\pi\)
−0.536368 + 0.843984i \(0.680204\pi\)
\(60\) −173149. −0.103488
\(61\) −1.23924e6 −0.699040 −0.349520 0.936929i \(-0.613655\pi\)
−0.349520 + 0.936929i \(0.613655\pi\)
\(62\) −1.56491e6 −0.833908
\(63\) 975714. 0.491621
\(64\) 2.12887e6 1.01512
\(65\) −1.82429e6 −0.823942
\(66\) −1.75251e6 −0.750337
\(67\) −944402. −0.383615 −0.191807 0.981433i \(-0.561435\pi\)
−0.191807 + 0.981433i \(0.561435\pi\)
\(68\) −739526. −0.285215
\(69\) −483674. −0.177248
\(70\) −1.46519e6 −0.510563
\(71\) −936943. −0.310677 −0.155338 0.987861i \(-0.549647\pi\)
−0.155338 + 0.987861i \(0.549647\pi\)
\(72\) 1.14473e6 0.361443
\(73\) −5.49712e6 −1.65389 −0.826943 0.562286i \(-0.809922\pi\)
−0.826943 + 0.562286i \(0.809922\pi\)
\(74\) 3.74794e6 1.07518
\(75\) 421875. 0.115470
\(76\) −21020.6 −0.00549285
\(77\) 9.91983e6 2.47621
\(78\) 3.45092e6 0.823386
\(79\) −3.29987e6 −0.753011 −0.376506 0.926414i \(-0.622874\pi\)
−0.376506 + 0.926414i \(0.622874\pi\)
\(80\) −898136. −0.196122
\(81\) 531441. 0.111111
\(82\) −467399. −0.0936136
\(83\) −4.16260e6 −0.799083 −0.399541 0.916715i \(-0.630831\pi\)
−0.399541 + 0.916715i \(0.630831\pi\)
\(84\) −1.85399e6 −0.341294
\(85\) 1.80184e6 0.318236
\(86\) −782491. −0.132658
\(87\) −289046. −0.0470598
\(88\) 1.16382e7 1.82052
\(89\) 8.50941e6 1.27948 0.639741 0.768590i \(-0.279041\pi\)
0.639741 + 0.768590i \(0.279041\pi\)
\(90\) −798041. −0.115392
\(91\) −1.95334e7 −2.71728
\(92\) 919044. 0.123049
\(93\) 4.82465e6 0.621978
\(94\) 1.41237e6 0.175389
\(95\) 51216.2 0.00612879
\(96\) −3.72792e6 −0.430048
\(97\) 6.61583e6 0.736010 0.368005 0.929824i \(-0.380041\pi\)
0.368005 + 0.929824i \(0.380041\pi\)
\(98\) −8.47607e6 −0.909711
\(99\) 5.40302e6 0.559646
\(100\) −801618. −0.0801618
\(101\) 1.05637e7 1.02022 0.510108 0.860110i \(-0.329605\pi\)
0.510108 + 0.860110i \(0.329605\pi\)
\(102\) −3.40845e6 −0.318022
\(103\) 8.46118e6 0.762958 0.381479 0.924377i \(-0.375415\pi\)
0.381479 + 0.924377i \(0.375415\pi\)
\(104\) −2.29171e7 −1.99776
\(105\) 4.51720e6 0.380808
\(106\) 1.06697e6 0.0870124
\(107\) −2.74027e6 −0.216247 −0.108123 0.994137i \(-0.534484\pi\)
−0.108123 + 0.994137i \(0.534484\pi\)
\(108\) −1.00981e6 −0.0771357
\(109\) 2.66853e6 0.197369 0.0986846 0.995119i \(-0.468536\pi\)
0.0986846 + 0.995119i \(0.468536\pi\)
\(110\) −8.11347e6 −0.581209
\(111\) −1.15550e7 −0.801935
\(112\) −9.61673e6 −0.646792
\(113\) −1.77381e7 −1.15646 −0.578232 0.815872i \(-0.696257\pi\)
−0.578232 + 0.815872i \(0.696257\pi\)
\(114\) −96883.3 −0.00612466
\(115\) −2.23923e6 −0.137296
\(116\) 549226. 0.0326699
\(117\) −1.06392e7 −0.614130
\(118\) 1.48205e7 0.830377
\(119\) 1.92931e7 1.04951
\(120\) 5.29969e6 0.279973
\(121\) 3.54439e7 1.81883
\(122\) 1.08529e7 0.541109
\(123\) 1.44100e6 0.0698226
\(124\) −9.16746e6 −0.431791
\(125\) 1.95313e6 0.0894427
\(126\) −8.54497e6 −0.380551
\(127\) −1.39230e7 −0.603142 −0.301571 0.953444i \(-0.597511\pi\)
−0.301571 + 0.953444i \(0.597511\pi\)
\(128\) −970801. −0.0409162
\(129\) 2.41243e6 0.0989445
\(130\) 1.59765e7 0.637792
\(131\) 4.73774e7 1.84129 0.920644 0.390403i \(-0.127664\pi\)
0.920644 + 0.390403i \(0.127664\pi\)
\(132\) −1.02664e7 −0.388518
\(133\) 548394. 0.0202121
\(134\) 8.27074e6 0.296946
\(135\) 2.46037e6 0.0860663
\(136\) 2.26351e7 0.771607
\(137\) −1.37766e7 −0.457740 −0.228870 0.973457i \(-0.573503\pi\)
−0.228870 + 0.973457i \(0.573503\pi\)
\(138\) 4.23585e6 0.137203
\(139\) −2.99177e7 −0.944881 −0.472440 0.881363i \(-0.656627\pi\)
−0.472440 + 0.881363i \(0.656627\pi\)
\(140\) −8.58327e6 −0.264365
\(141\) −4.35436e6 −0.130815
\(142\) 8.20542e6 0.240487
\(143\) −1.08166e8 −3.09326
\(144\) −5.23793e6 −0.146181
\(145\) −1.33818e6 −0.0364523
\(146\) 4.81419e7 1.28023
\(147\) 2.61319e7 0.678516
\(148\) 2.19560e7 0.556720
\(149\) 1.53461e7 0.380056 0.190028 0.981779i \(-0.439142\pi\)
0.190028 + 0.981779i \(0.439142\pi\)
\(150\) −3.69463e6 −0.0893824
\(151\) −8.10081e7 −1.91474 −0.957368 0.288871i \(-0.906720\pi\)
−0.957368 + 0.288871i \(0.906720\pi\)
\(152\) 643390. 0.0148601
\(153\) 1.05083e7 0.237199
\(154\) −8.68744e7 −1.91677
\(155\) 2.23363e7 0.481782
\(156\) 2.02160e7 0.426342
\(157\) −4.04242e7 −0.833667 −0.416834 0.908983i \(-0.636860\pi\)
−0.416834 + 0.908983i \(0.636860\pi\)
\(158\) 2.88991e7 0.582887
\(159\) −3.28948e6 −0.0648990
\(160\) −1.72589e7 −0.333114
\(161\) −2.39764e7 −0.452786
\(162\) −4.65417e6 −0.0860083
\(163\) 2.71649e7 0.491305 0.245652 0.969358i \(-0.420998\pi\)
0.245652 + 0.969358i \(0.420998\pi\)
\(164\) −2.73809e6 −0.0484723
\(165\) 2.50140e7 0.433500
\(166\) 3.64546e7 0.618549
\(167\) −4.96738e7 −0.825315 −0.412658 0.910886i \(-0.635399\pi\)
−0.412658 + 0.910886i \(0.635399\pi\)
\(168\) 5.67460e7 0.923322
\(169\) 1.50245e8 2.39440
\(170\) −1.57799e7 −0.246339
\(171\) 298693. 0.00456813
\(172\) −4.58394e6 −0.0686894
\(173\) 1.18247e8 1.73632 0.868161 0.496283i \(-0.165302\pi\)
0.868161 + 0.496283i \(0.165302\pi\)
\(174\) 2.53136e6 0.0364277
\(175\) 2.09129e7 0.294973
\(176\) −5.32527e7 −0.736287
\(177\) −4.56918e7 −0.619344
\(178\) −7.45224e7 −0.990415
\(179\) −9.22014e6 −0.120158 −0.0600789 0.998194i \(-0.519135\pi\)
−0.0600789 + 0.998194i \(0.519135\pi\)
\(180\) −4.67504e6 −0.0597491
\(181\) −7.95194e7 −0.996778 −0.498389 0.866954i \(-0.666075\pi\)
−0.498389 + 0.866954i \(0.666075\pi\)
\(182\) 1.71067e8 2.10337
\(183\) −3.34596e7 −0.403591
\(184\) −2.81297e7 −0.332892
\(185\) −5.34953e7 −0.621176
\(186\) −4.22526e7 −0.481457
\(187\) 1.06835e8 1.19473
\(188\) 8.27387e6 0.0908147
\(189\) 2.63443e7 0.283838
\(190\) −448534. −0.00474414
\(191\) −7.45248e6 −0.0773899 −0.0386950 0.999251i \(-0.512320\pi\)
−0.0386950 + 0.999251i \(0.512320\pi\)
\(192\) 5.74795e7 0.586082
\(193\) −5.72075e7 −0.572800 −0.286400 0.958110i \(-0.592459\pi\)
−0.286400 + 0.958110i \(0.592459\pi\)
\(194\) −5.79392e7 −0.569726
\(195\) −4.92558e7 −0.475703
\(196\) −4.96540e7 −0.471040
\(197\) −6.10094e7 −0.568545 −0.284273 0.958743i \(-0.591752\pi\)
−0.284273 + 0.958743i \(0.591752\pi\)
\(198\) −4.73178e7 −0.433208
\(199\) 1.51883e8 1.36622 0.683112 0.730313i \(-0.260626\pi\)
0.683112 + 0.730313i \(0.260626\pi\)
\(200\) 2.45356e7 0.216866
\(201\) −2.54989e7 −0.221480
\(202\) −9.25135e7 −0.789724
\(203\) −1.43284e7 −0.120216
\(204\) −1.99672e7 −0.164669
\(205\) 6.67129e6 0.0540843
\(206\) −7.41001e7 −0.590586
\(207\) −1.30592e7 −0.102334
\(208\) 1.04861e8 0.807968
\(209\) 3.03673e6 0.0230088
\(210\) −3.95600e7 −0.294774
\(211\) 3.14356e7 0.230374 0.115187 0.993344i \(-0.463253\pi\)
0.115187 + 0.993344i \(0.463253\pi\)
\(212\) 6.25045e6 0.0450543
\(213\) −2.52975e7 −0.179369
\(214\) 2.39983e7 0.167391
\(215\) 1.11687e7 0.0766420
\(216\) 3.09078e7 0.208679
\(217\) 2.39165e8 1.58887
\(218\) −2.33701e7 −0.152778
\(219\) −1.48422e8 −0.954871
\(220\) −4.75299e7 −0.300945
\(221\) −2.10373e8 −1.31104
\(222\) 1.01195e8 0.620757
\(223\) −1.55318e8 −0.937899 −0.468949 0.883225i \(-0.655367\pi\)
−0.468949 + 0.883225i \(0.655367\pi\)
\(224\) −1.84798e8 −1.09858
\(225\) 1.13906e7 0.0666667
\(226\) 1.55344e8 0.895189
\(227\) 1.06573e8 0.604721 0.302361 0.953194i \(-0.402225\pi\)
0.302361 + 0.953194i \(0.402225\pi\)
\(228\) −567556. −0.00317130
\(229\) 3.09602e7 0.170365 0.0851825 0.996365i \(-0.472853\pi\)
0.0851825 + 0.996365i \(0.472853\pi\)
\(230\) 1.96104e7 0.106277
\(231\) 2.67835e8 1.42964
\(232\) −1.68105e7 −0.0883836
\(233\) 1.29584e8 0.671128 0.335564 0.942017i \(-0.391073\pi\)
0.335564 + 0.942017i \(0.391073\pi\)
\(234\) 9.31748e7 0.475382
\(235\) −2.01591e7 −0.101329
\(236\) 8.68205e7 0.429962
\(237\) −8.90964e7 −0.434751
\(238\) −1.68962e8 −0.812399
\(239\) 3.32406e8 1.57498 0.787492 0.616325i \(-0.211379\pi\)
0.787492 + 0.616325i \(0.211379\pi\)
\(240\) −2.42497e7 −0.113231
\(241\) 2.28413e8 1.05114 0.525570 0.850750i \(-0.323852\pi\)
0.525570 + 0.850750i \(0.323852\pi\)
\(242\) −3.10405e8 −1.40791
\(243\) 1.43489e7 0.0641500
\(244\) 6.35776e7 0.280182
\(245\) 1.20981e8 0.525576
\(246\) −1.26198e7 −0.0540479
\(247\) −5.97972e6 −0.0252488
\(248\) 2.80594e8 1.16815
\(249\) −1.12390e8 −0.461351
\(250\) −1.71048e7 −0.0692353
\(251\) −9.68540e7 −0.386598 −0.193299 0.981140i \(-0.561919\pi\)
−0.193299 + 0.981140i \(0.561919\pi\)
\(252\) −5.00576e7 −0.197046
\(253\) −1.32769e8 −0.515438
\(254\) 1.21933e8 0.466876
\(255\) 4.86496e7 0.183734
\(256\) −2.63993e8 −0.983452
\(257\) −3.58302e8 −1.31669 −0.658345 0.752717i \(-0.728743\pi\)
−0.658345 + 0.752717i \(0.728743\pi\)
\(258\) −2.11273e7 −0.0765904
\(259\) −5.72797e8 −2.04857
\(260\) 9.35925e7 0.330243
\(261\) −7.80424e6 −0.0271700
\(262\) −4.14915e8 −1.42529
\(263\) 3.55854e8 1.20622 0.603111 0.797657i \(-0.293928\pi\)
0.603111 + 0.797657i \(0.293928\pi\)
\(264\) 3.14231e8 1.05108
\(265\) −1.52291e7 −0.0502705
\(266\) −4.80264e6 −0.0156457
\(267\) 2.29754e8 0.738710
\(268\) 4.84512e7 0.153756
\(269\) −6.05263e8 −1.89588 −0.947941 0.318445i \(-0.896839\pi\)
−0.947941 + 0.318445i \(0.896839\pi\)
\(270\) −2.15471e7 −0.0666217
\(271\) −1.40319e8 −0.428277 −0.214138 0.976803i \(-0.568694\pi\)
−0.214138 + 0.976803i \(0.568694\pi\)
\(272\) −1.03571e8 −0.312066
\(273\) −5.27403e8 −1.56882
\(274\) 1.20650e8 0.354325
\(275\) 1.15805e8 0.335788
\(276\) 2.48142e7 0.0710425
\(277\) −2.91107e8 −0.822950 −0.411475 0.911421i \(-0.634986\pi\)
−0.411475 + 0.911421i \(0.634986\pi\)
\(278\) 2.62009e8 0.731408
\(279\) 1.30265e8 0.359099
\(280\) 2.62713e8 0.715202
\(281\) 5.10230e8 1.37181 0.685905 0.727691i \(-0.259406\pi\)
0.685905 + 0.727691i \(0.259406\pi\)
\(282\) 3.81340e7 0.101261
\(283\) 2.28117e8 0.598281 0.299141 0.954209i \(-0.403300\pi\)
0.299141 + 0.954209i \(0.403300\pi\)
\(284\) 4.80685e7 0.124522
\(285\) 1.38284e6 0.00353846
\(286\) 9.47284e8 2.39441
\(287\) 7.14324e7 0.178365
\(288\) −1.00654e8 −0.248288
\(289\) −2.02555e8 −0.493628
\(290\) 1.17193e7 0.0282168
\(291\) 1.78628e8 0.424935
\(292\) 2.82022e8 0.662892
\(293\) −1.68215e8 −0.390687 −0.195343 0.980735i \(-0.562582\pi\)
−0.195343 + 0.980735i \(0.562582\pi\)
\(294\) −2.28854e8 −0.525222
\(295\) −2.11536e8 −0.479742
\(296\) −6.72020e8 −1.50613
\(297\) 1.45882e8 0.323112
\(298\) −1.34396e8 −0.294191
\(299\) 2.61440e8 0.565618
\(300\) −2.16437e7 −0.0462814
\(301\) 1.19588e8 0.252758
\(302\) 7.09440e8 1.48215
\(303\) 2.85221e8 0.589023
\(304\) −2.94395e6 −0.00600997
\(305\) −1.54905e8 −0.312620
\(306\) −9.20282e7 −0.183610
\(307\) 5.67876e8 1.12013 0.560066 0.828448i \(-0.310776\pi\)
0.560066 + 0.828448i \(0.310776\pi\)
\(308\) −5.08922e8 −0.992485
\(309\) 2.28452e8 0.440494
\(310\) −1.95614e8 −0.372935
\(311\) −6.68026e8 −1.25931 −0.629654 0.776876i \(-0.716803\pi\)
−0.629654 + 0.776876i \(0.716803\pi\)
\(312\) −6.18762e8 −1.15341
\(313\) 2.41610e8 0.445358 0.222679 0.974892i \(-0.428520\pi\)
0.222679 + 0.974892i \(0.428520\pi\)
\(314\) 3.54021e8 0.645321
\(315\) 1.21964e8 0.219860
\(316\) 1.69295e8 0.301814
\(317\) −9.73867e8 −1.71709 −0.858544 0.512740i \(-0.828630\pi\)
−0.858544 + 0.512740i \(0.828630\pi\)
\(318\) 2.88082e7 0.0502366
\(319\) −7.93437e7 −0.136850
\(320\) 2.66109e8 0.453977
\(321\) −7.39872e7 −0.124850
\(322\) 2.09977e8 0.350490
\(323\) 5.90614e6 0.00975202
\(324\) −2.72648e7 −0.0445343
\(325\) −2.28036e8 −0.368478
\(326\) −2.37901e8 −0.380307
\(327\) 7.20504e7 0.113951
\(328\) 8.38063e7 0.131135
\(329\) −2.15852e8 −0.334172
\(330\) −2.19064e8 −0.335561
\(331\) −4.25946e8 −0.645590 −0.322795 0.946469i \(-0.604622\pi\)
−0.322795 + 0.946469i \(0.604622\pi\)
\(332\) 2.13556e8 0.320280
\(333\) −3.11985e8 −0.462997
\(334\) 4.35026e8 0.638855
\(335\) −1.18050e8 −0.171558
\(336\) −2.59652e8 −0.373425
\(337\) 8.64429e8 1.23034 0.615170 0.788395i \(-0.289088\pi\)
0.615170 + 0.788395i \(0.289088\pi\)
\(338\) −1.31579e9 −1.85345
\(339\) −4.78928e8 −0.667685
\(340\) −9.24407e7 −0.127552
\(341\) 1.32437e9 1.80872
\(342\) −2.61585e6 −0.00353607
\(343\) 1.93141e8 0.258432
\(344\) 1.40303e8 0.185829
\(345\) −6.04592e7 −0.0792676
\(346\) −1.03557e9 −1.34404
\(347\) 8.95674e8 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(348\) 1.48291e7 0.0188620
\(349\) 2.98991e8 0.376503 0.188252 0.982121i \(-0.439718\pi\)
0.188252 + 0.982121i \(0.439718\pi\)
\(350\) −1.83148e8 −0.228331
\(351\) −2.87260e8 −0.354568
\(352\) −1.02332e9 −1.25058
\(353\) 9.92149e8 1.20051 0.600254 0.799809i \(-0.295066\pi\)
0.600254 + 0.799809i \(0.295066\pi\)
\(354\) 4.00153e8 0.479418
\(355\) −1.17118e8 −0.138939
\(356\) −4.36563e8 −0.512828
\(357\) 5.20913e8 0.605935
\(358\) 8.07468e7 0.0930111
\(359\) 7.94667e8 0.906473 0.453236 0.891390i \(-0.350269\pi\)
0.453236 + 0.891390i \(0.350269\pi\)
\(360\) 1.43092e8 0.161642
\(361\) −8.93704e8 −0.999812
\(362\) 6.96403e8 0.771580
\(363\) 9.56985e8 1.05010
\(364\) 1.00213e9 1.08911
\(365\) −6.87141e8 −0.739640
\(366\) 2.93027e8 0.312409
\(367\) −5.76769e8 −0.609074 −0.304537 0.952500i \(-0.598502\pi\)
−0.304537 + 0.952500i \(0.598502\pi\)
\(368\) 1.28713e8 0.134634
\(369\) 3.89070e7 0.0403121
\(370\) 4.68493e8 0.480836
\(371\) −1.63064e8 −0.165787
\(372\) −2.47521e8 −0.249294
\(373\) 7.49247e8 0.747557 0.373779 0.927518i \(-0.378062\pi\)
0.373779 + 0.927518i \(0.378062\pi\)
\(374\) −9.35627e8 −0.924809
\(375\) 5.27344e7 0.0516398
\(376\) −2.53243e8 −0.245686
\(377\) 1.56238e8 0.150173
\(378\) −2.30714e8 −0.219711
\(379\) −1.93999e9 −1.83047 −0.915233 0.402926i \(-0.867993\pi\)
−0.915233 + 0.402926i \(0.867993\pi\)
\(380\) −2.62757e6 −0.00245648
\(381\) −3.75921e8 −0.348224
\(382\) 6.52663e7 0.0599055
\(383\) 1.08549e9 0.987254 0.493627 0.869674i \(-0.335671\pi\)
0.493627 + 0.869674i \(0.335671\pi\)
\(384\) −2.62116e7 −0.0236230
\(385\) 1.23998e9 1.10739
\(386\) 5.01004e8 0.443389
\(387\) 6.51357e7 0.0571256
\(388\) −3.39416e8 −0.294999
\(389\) −7.18963e8 −0.619274 −0.309637 0.950855i \(-0.600208\pi\)
−0.309637 + 0.950855i \(0.600208\pi\)
\(390\) 4.31365e8 0.368230
\(391\) −2.58223e8 −0.218462
\(392\) 1.51979e9 1.27433
\(393\) 1.27919e9 1.06307
\(394\) 5.34299e8 0.440096
\(395\) −4.12483e8 −0.336757
\(396\) −2.77194e8 −0.224311
\(397\) −7.87080e7 −0.0631324 −0.0315662 0.999502i \(-0.510049\pi\)
−0.0315662 + 0.999502i \(0.510049\pi\)
\(398\) −1.33013e9 −1.05756
\(399\) 1.48066e7 0.0116695
\(400\) −1.12267e8 −0.0877086
\(401\) 4.28246e8 0.331656 0.165828 0.986155i \(-0.446970\pi\)
0.165828 + 0.986155i \(0.446970\pi\)
\(402\) 2.23310e8 0.171442
\(403\) −2.60786e9 −1.98480
\(404\) −5.41957e8 −0.408912
\(405\) 6.64301e7 0.0496904
\(406\) 1.25483e8 0.0930561
\(407\) −3.17186e9 −2.33203
\(408\) 6.11148e8 0.445488
\(409\) 4.98651e8 0.360384 0.180192 0.983631i \(-0.442328\pi\)
0.180192 + 0.983631i \(0.442328\pi\)
\(410\) −5.84248e7 −0.0418653
\(411\) −3.71967e8 −0.264276
\(412\) −4.34089e8 −0.305800
\(413\) −2.26501e9 −1.58214
\(414\) 1.14368e8 0.0792141
\(415\) −5.20325e8 −0.357361
\(416\) 2.01505e9 1.37233
\(417\) −8.07779e8 −0.545527
\(418\) −2.65946e7 −0.0178105
\(419\) 2.31115e9 1.53489 0.767447 0.641112i \(-0.221527\pi\)
0.767447 + 0.641112i \(0.221527\pi\)
\(420\) −2.31748e8 −0.152631
\(421\) 1.06460e9 0.695344 0.347672 0.937616i \(-0.386972\pi\)
0.347672 + 0.937616i \(0.386972\pi\)
\(422\) −2.75302e8 −0.178326
\(423\) −1.17568e8 −0.0755261
\(424\) −1.91311e8 −0.121888
\(425\) 2.25230e8 0.142320
\(426\) 2.21546e8 0.138845
\(427\) −1.65864e9 −1.03099
\(428\) 1.40586e8 0.0866737
\(429\) −2.92049e9 −1.78589
\(430\) −9.78114e7 −0.0593266
\(431\) 2.79013e9 1.67863 0.839313 0.543649i \(-0.182958\pi\)
0.839313 + 0.543649i \(0.182958\pi\)
\(432\) −1.41424e8 −0.0843977
\(433\) 2.27098e9 1.34433 0.672164 0.740403i \(-0.265365\pi\)
0.672164 + 0.740403i \(0.265365\pi\)
\(434\) −2.09452e9 −1.22990
\(435\) −3.61308e7 −0.0210458
\(436\) −1.36905e8 −0.0791074
\(437\) −7.33984e6 −0.00420728
\(438\) 1.29983e9 0.739141
\(439\) 2.10307e9 1.18639 0.593195 0.805059i \(-0.297866\pi\)
0.593195 + 0.805059i \(0.297866\pi\)
\(440\) 1.45477e9 0.814163
\(441\) 7.05561e8 0.391741
\(442\) 1.84237e9 1.01484
\(443\) −2.70576e9 −1.47869 −0.739343 0.673329i \(-0.764864\pi\)
−0.739343 + 0.673329i \(0.764864\pi\)
\(444\) 5.92812e8 0.321423
\(445\) 1.06368e9 0.572202
\(446\) 1.36022e9 0.726003
\(447\) 4.14346e8 0.219425
\(448\) 2.84934e9 1.49717
\(449\) 2.11008e9 1.10011 0.550055 0.835128i \(-0.314607\pi\)
0.550055 + 0.835128i \(0.314607\pi\)
\(450\) −9.97551e7 −0.0516050
\(451\) 3.95557e8 0.203044
\(452\) 9.10027e8 0.463521
\(453\) −2.18722e9 −1.10547
\(454\) −9.33326e8 −0.468099
\(455\) −2.44168e9 −1.21520
\(456\) 1.73715e7 0.00857948
\(457\) −2.27404e8 −0.111453 −0.0557264 0.998446i \(-0.517747\pi\)
−0.0557264 + 0.998446i \(0.517747\pi\)
\(458\) −2.71139e8 −0.131875
\(459\) 2.83725e8 0.136947
\(460\) 1.14880e8 0.0550293
\(461\) −5.48876e8 −0.260928 −0.130464 0.991453i \(-0.541647\pi\)
−0.130464 + 0.991453i \(0.541647\pi\)
\(462\) −2.34561e9 −1.10665
\(463\) 4.99899e8 0.234072 0.117036 0.993128i \(-0.462661\pi\)
0.117036 + 0.993128i \(0.462661\pi\)
\(464\) 7.69193e7 0.0357456
\(465\) 6.03081e8 0.278157
\(466\) −1.13485e9 −0.519503
\(467\) 2.23313e9 1.01462 0.507311 0.861763i \(-0.330639\pi\)
0.507311 + 0.861763i \(0.330639\pi\)
\(468\) 5.45831e8 0.246149
\(469\) −1.26401e9 −0.565779
\(470\) 1.76546e8 0.0784361
\(471\) −1.09145e9 −0.481318
\(472\) −2.65737e9 −1.16320
\(473\) 6.62218e8 0.287731
\(474\) 7.80275e8 0.336530
\(475\) 6.40203e6 0.00274088
\(476\) −9.89803e8 −0.420653
\(477\) −8.88161e7 −0.0374694
\(478\) −2.91109e9 −1.21915
\(479\) −3.53414e9 −1.46929 −0.734647 0.678449i \(-0.762652\pi\)
−0.734647 + 0.678449i \(0.762652\pi\)
\(480\) −4.65990e8 −0.192323
\(481\) 6.24581e9 2.55906
\(482\) −2.00036e9 −0.813660
\(483\) −6.47363e8 −0.261416
\(484\) −1.81840e9 −0.729004
\(485\) 8.26979e8 0.329154
\(486\) −1.25663e8 −0.0496569
\(487\) 2.72597e9 1.06947 0.534737 0.845019i \(-0.320411\pi\)
0.534737 + 0.845019i \(0.320411\pi\)
\(488\) −1.94596e9 −0.757990
\(489\) 7.33452e8 0.283655
\(490\) −1.05951e9 −0.406835
\(491\) −4.86034e9 −1.85302 −0.926512 0.376265i \(-0.877208\pi\)
−0.926512 + 0.376265i \(0.877208\pi\)
\(492\) −7.39284e7 −0.0279855
\(493\) −1.54315e8 −0.0580023
\(494\) 5.23683e7 0.0195445
\(495\) 6.75377e8 0.250281
\(496\) −1.28391e9 −0.472441
\(497\) −1.25403e9 −0.458206
\(498\) 9.84275e8 0.357120
\(499\) 2.41002e8 0.0868297 0.0434149 0.999057i \(-0.486176\pi\)
0.0434149 + 0.999057i \(0.486176\pi\)
\(500\) −1.00202e8 −0.0358494
\(501\) −1.34119e9 −0.476496
\(502\) 8.48214e8 0.299256
\(503\) 3.91762e9 1.37257 0.686285 0.727333i \(-0.259240\pi\)
0.686285 + 0.727333i \(0.259240\pi\)
\(504\) 1.53214e9 0.533080
\(505\) 1.32047e9 0.456255
\(506\) 1.16275e9 0.398987
\(507\) 4.05662e9 1.38241
\(508\) 7.14299e8 0.241745
\(509\) 1.53452e9 0.515775 0.257888 0.966175i \(-0.416974\pi\)
0.257888 + 0.966175i \(0.416974\pi\)
\(510\) −4.26057e8 −0.142224
\(511\) −7.35751e9 −2.43926
\(512\) 2.43622e9 0.802181
\(513\) 8.06471e6 0.00263741
\(514\) 3.13788e9 1.01922
\(515\) 1.05765e9 0.341205
\(516\) −1.23766e8 −0.0396578
\(517\) −1.19528e9 −0.380411
\(518\) 5.01636e9 1.58575
\(519\) 3.19268e9 1.00247
\(520\) −2.86464e9 −0.893425
\(521\) −2.45259e9 −0.759790 −0.379895 0.925030i \(-0.624040\pi\)
−0.379895 + 0.925030i \(0.624040\pi\)
\(522\) 6.83468e7 0.0210316
\(523\) −2.27819e8 −0.0696362 −0.0348181 0.999394i \(-0.511085\pi\)
−0.0348181 + 0.999394i \(0.511085\pi\)
\(524\) −2.43063e9 −0.738005
\(525\) 5.64649e8 0.170303
\(526\) −3.11645e9 −0.933706
\(527\) 2.57577e9 0.766603
\(528\) −1.43782e9 −0.425095
\(529\) −3.08392e9 −0.905750
\(530\) 1.33371e8 0.0389131
\(531\) −1.23368e9 −0.357579
\(532\) −2.81346e7 −0.00810120
\(533\) −7.78903e8 −0.222812
\(534\) −2.01211e9 −0.571816
\(535\) −3.42534e8 −0.0967086
\(536\) −1.48297e9 −0.415965
\(537\) −2.48944e8 −0.0693731
\(538\) 5.30069e9 1.46755
\(539\) 7.17325e9 1.97313
\(540\) −1.26226e8 −0.0344961
\(541\) 3.79946e9 1.03165 0.515824 0.856694i \(-0.327486\pi\)
0.515824 + 0.856694i \(0.327486\pi\)
\(542\) 1.22887e9 0.331518
\(543\) −2.14702e9 −0.575490
\(544\) −1.99025e9 −0.530045
\(545\) 3.33566e8 0.0882662
\(546\) 4.61881e9 1.21438
\(547\) 5.31117e9 1.38751 0.693753 0.720213i \(-0.255956\pi\)
0.693753 + 0.720213i \(0.255956\pi\)
\(548\) 7.06787e8 0.183466
\(549\) −9.03408e8 −0.233013
\(550\) −1.01418e9 −0.259925
\(551\) −4.38632e6 −0.00111704
\(552\) −7.59502e8 −0.192195
\(553\) −4.41663e9 −1.11059
\(554\) 2.54941e9 0.637024
\(555\) −1.44437e9 −0.358636
\(556\) 1.53489e9 0.378717
\(557\) −7.38937e9 −1.81182 −0.905909 0.423473i \(-0.860811\pi\)
−0.905909 + 0.423473i \(0.860811\pi\)
\(558\) −1.14082e9 −0.277969
\(559\) −1.30399e9 −0.315743
\(560\) −1.20209e9 −0.289254
\(561\) 2.88455e9 0.689777
\(562\) −4.46842e9 −1.06188
\(563\) −2.33548e9 −0.551564 −0.275782 0.961220i \(-0.588937\pi\)
−0.275782 + 0.961220i \(0.588937\pi\)
\(564\) 2.23394e8 0.0524319
\(565\) −2.21726e9 −0.517187
\(566\) −1.99777e9 −0.463114
\(567\) 7.11296e8 0.163874
\(568\) −1.47126e9 −0.336876
\(569\) 6.66096e9 1.51581 0.757903 0.652367i \(-0.226224\pi\)
0.757903 + 0.652367i \(0.226224\pi\)
\(570\) −1.21104e7 −0.00273903
\(571\) −2.11804e9 −0.476110 −0.238055 0.971252i \(-0.576510\pi\)
−0.238055 + 0.971252i \(0.576510\pi\)
\(572\) 5.54932e9 1.23981
\(573\) −2.01217e8 −0.0446811
\(574\) −6.25580e8 −0.138067
\(575\) −2.79904e8 −0.0614004
\(576\) 1.55195e9 0.338375
\(577\) 4.63211e9 1.00384 0.501919 0.864915i \(-0.332628\pi\)
0.501919 + 0.864915i \(0.332628\pi\)
\(578\) 1.77390e9 0.382105
\(579\) −1.54460e9 −0.330706
\(580\) 6.86532e7 0.0146104
\(581\) −5.57135e9 −1.17854
\(582\) −1.56436e9 −0.328932
\(583\) −9.02970e8 −0.188727
\(584\) −8.63201e9 −1.79336
\(585\) −1.32991e9 −0.274647
\(586\) 1.47317e9 0.302420
\(587\) −7.08115e9 −1.44501 −0.722504 0.691367i \(-0.757009\pi\)
−0.722504 + 0.691367i \(0.757009\pi\)
\(588\) −1.34066e9 −0.271955
\(589\) 7.32149e7 0.0147637
\(590\) 1.85256e9 0.371356
\(591\) −1.64725e9 −0.328250
\(592\) 3.07495e9 0.609133
\(593\) 2.25289e9 0.443657 0.221829 0.975086i \(-0.428797\pi\)
0.221829 + 0.975086i \(0.428797\pi\)
\(594\) −1.27758e9 −0.250112
\(595\) 2.41163e9 0.469355
\(596\) −7.87312e8 −0.152330
\(597\) 4.10083e9 0.788790
\(598\) −2.28960e9 −0.437830
\(599\) −4.50218e9 −0.855912 −0.427956 0.903799i \(-0.640766\pi\)
−0.427956 + 0.903799i \(0.640766\pi\)
\(600\) 6.62461e8 0.125208
\(601\) 5.26755e9 0.989802 0.494901 0.868949i \(-0.335204\pi\)
0.494901 + 0.868949i \(0.335204\pi\)
\(602\) −1.04731e9 −0.195653
\(603\) −6.88469e8 −0.127872
\(604\) 4.15600e9 0.767444
\(605\) 4.43049e9 0.813407
\(606\) −2.49786e9 −0.455947
\(607\) −2.39522e9 −0.434696 −0.217348 0.976094i \(-0.569741\pi\)
−0.217348 + 0.976094i \(0.569741\pi\)
\(608\) −5.65718e7 −0.0102079
\(609\) −3.86867e8 −0.0694067
\(610\) 1.35661e9 0.241991
\(611\) 2.35366e9 0.417446
\(612\) −5.39114e8 −0.0950716
\(613\) −9.90842e9 −1.73737 −0.868686 0.495363i \(-0.835035\pi\)
−0.868686 + 0.495363i \(0.835035\pi\)
\(614\) −4.97326e9 −0.867066
\(615\) 1.80125e8 0.0312256
\(616\) 1.55769e10 2.68502
\(617\) −2.05272e9 −0.351829 −0.175915 0.984405i \(-0.556288\pi\)
−0.175915 + 0.984405i \(0.556288\pi\)
\(618\) −2.00070e9 −0.340975
\(619\) 8.57333e9 1.45289 0.726444 0.687225i \(-0.241172\pi\)
0.726444 + 0.687225i \(0.241172\pi\)
\(620\) −1.14593e9 −0.193103
\(621\) −3.52598e8 −0.0590826
\(622\) 5.85034e9 0.974798
\(623\) 1.13892e10 1.88706
\(624\) 2.83126e9 0.466480
\(625\) 2.44141e8 0.0400000
\(626\) −2.11593e9 −0.344740
\(627\) 8.19918e7 0.0132842
\(628\) 2.07391e9 0.334141
\(629\) −6.16895e9 −0.988403
\(630\) −1.06812e9 −0.170188
\(631\) −2.15662e9 −0.341720 −0.170860 0.985295i \(-0.554655\pi\)
−0.170860 + 0.985295i \(0.554655\pi\)
\(632\) −5.18171e9 −0.816513
\(633\) 8.48761e8 0.133006
\(634\) 8.52879e9 1.32915
\(635\) −1.74037e9 −0.269733
\(636\) 1.68762e8 0.0260121
\(637\) −1.41251e10 −2.16522
\(638\) 6.94864e8 0.105932
\(639\) −6.83031e8 −0.103559
\(640\) −1.21350e8 −0.0182983
\(641\) 1.09316e10 1.63938 0.819689 0.572809i \(-0.194146\pi\)
0.819689 + 0.572809i \(0.194146\pi\)
\(642\) 6.47954e8 0.0966433
\(643\) 5.34196e9 0.792432 0.396216 0.918157i \(-0.370323\pi\)
0.396216 + 0.918157i \(0.370323\pi\)
\(644\) 1.23007e9 0.181481
\(645\) 3.01554e8 0.0442493
\(646\) −5.17239e7 −0.00754879
\(647\) 4.77656e9 0.693346 0.346673 0.937986i \(-0.387311\pi\)
0.346673 + 0.937986i \(0.387311\pi\)
\(648\) 8.34510e8 0.120481
\(649\) −1.25425e10 −1.80106
\(650\) 1.99706e9 0.285229
\(651\) 6.45744e9 0.917333
\(652\) −1.39365e9 −0.196919
\(653\) −1.50855e9 −0.212013 −0.106006 0.994365i \(-0.533806\pi\)
−0.106006 + 0.994365i \(0.533806\pi\)
\(654\) −6.30992e8 −0.0882067
\(655\) 5.92218e9 0.823449
\(656\) −3.83471e8 −0.0530358
\(657\) −4.00740e9 −0.551295
\(658\) 1.89036e9 0.258674
\(659\) 2.78418e9 0.378965 0.189482 0.981884i \(-0.439319\pi\)
0.189482 + 0.981884i \(0.439319\pi\)
\(660\) −1.28331e9 −0.173751
\(661\) −9.29515e9 −1.25185 −0.625924 0.779884i \(-0.715278\pi\)
−0.625924 + 0.779884i \(0.715278\pi\)
\(662\) 3.73029e9 0.499735
\(663\) −5.68006e9 −0.756930
\(664\) −6.53644e9 −0.866469
\(665\) 6.85492e7 0.00903914
\(666\) 2.73225e9 0.358394
\(667\) 1.91775e8 0.0250237
\(668\) 2.54844e9 0.330794
\(669\) −4.19360e9 −0.541496
\(670\) 1.03384e9 0.132798
\(671\) −9.18471e9 −1.17364
\(672\) −4.98955e9 −0.634263
\(673\) −7.87291e9 −0.995595 −0.497798 0.867293i \(-0.665858\pi\)
−0.497798 + 0.867293i \(0.665858\pi\)
\(674\) −7.57037e9 −0.952374
\(675\) 3.07547e8 0.0384900
\(676\) −7.70811e9 −0.959698
\(677\) −7.50679e9 −0.929810 −0.464905 0.885361i \(-0.653911\pi\)
−0.464905 + 0.885361i \(0.653911\pi\)
\(678\) 4.19429e9 0.516838
\(679\) 8.85482e9 1.08551
\(680\) 2.82939e9 0.345073
\(681\) 2.87746e9 0.349136
\(682\) −1.15984e10 −1.40008
\(683\) 7.93522e9 0.952985 0.476493 0.879178i \(-0.341908\pi\)
0.476493 + 0.879178i \(0.341908\pi\)
\(684\) −1.53240e7 −0.00183095
\(685\) −1.72207e9 −0.204708
\(686\) −1.69147e9 −0.200046
\(687\) 8.35927e8 0.0983603
\(688\) −6.41984e8 −0.0751561
\(689\) 1.77806e9 0.207100
\(690\) 5.29481e8 0.0613590
\(691\) −7.23622e8 −0.0834332 −0.0417166 0.999129i \(-0.513283\pi\)
−0.0417166 + 0.999129i \(0.513283\pi\)
\(692\) −6.06651e9 −0.695934
\(693\) 7.23156e9 0.825402
\(694\) −7.84400e9 −0.890799
\(695\) −3.73972e9 −0.422564
\(696\) −4.53883e8 −0.0510283
\(697\) 7.69318e8 0.0860580
\(698\) −2.61846e9 −0.291442
\(699\) 3.49876e9 0.387476
\(700\) −1.07291e9 −0.118228
\(701\) 1.37209e10 1.50442 0.752211 0.658923i \(-0.228988\pi\)
0.752211 + 0.658923i \(0.228988\pi\)
\(702\) 2.51572e9 0.274462
\(703\) −1.75349e8 −0.0190353
\(704\) 1.57782e10 1.70433
\(705\) −5.44296e8 −0.0585023
\(706\) −8.68889e9 −0.929283
\(707\) 1.41388e10 1.50468
\(708\) 2.34415e9 0.248239
\(709\) 1.20390e10 1.26861 0.634304 0.773084i \(-0.281287\pi\)
0.634304 + 0.773084i \(0.281287\pi\)
\(710\) 1.02568e9 0.107549
\(711\) −2.40560e9 −0.251004
\(712\) 1.33621e10 1.38738
\(713\) −3.20104e9 −0.330733
\(714\) −4.56197e9 −0.469039
\(715\) −1.35208e10 −1.38335
\(716\) 4.73026e8 0.0481603
\(717\) 8.97496e9 0.909317
\(718\) −6.95942e9 −0.701677
\(719\) −1.84411e8 −0.0185027 −0.00925137 0.999957i \(-0.502945\pi\)
−0.00925137 + 0.999957i \(0.502945\pi\)
\(720\) −6.54741e8 −0.0653741
\(721\) 1.13247e10 1.12526
\(722\) 7.82675e9 0.773929
\(723\) 6.16714e9 0.606876
\(724\) 4.07963e9 0.399517
\(725\) −1.67272e8 −0.0163020
\(726\) −8.38094e9 −0.812858
\(727\) 1.10078e10 1.06250 0.531251 0.847215i \(-0.321722\pi\)
0.531251 + 0.847215i \(0.321722\pi\)
\(728\) −3.06729e10 −2.94642
\(729\) 3.87420e8 0.0370370
\(730\) 6.01774e9 0.572536
\(731\) 1.28795e9 0.121951
\(732\) 1.71659e9 0.161763
\(733\) 1.57261e10 1.47488 0.737439 0.675414i \(-0.236035\pi\)
0.737439 + 0.675414i \(0.236035\pi\)
\(734\) 5.05114e9 0.471469
\(735\) 3.26649e9 0.303442
\(736\) 2.47338e9 0.228675
\(737\) −6.99948e9 −0.644065
\(738\) −3.40734e8 −0.0312045
\(739\) −1.66376e10 −1.51647 −0.758236 0.651980i \(-0.773939\pi\)
−0.758236 + 0.651980i \(0.773939\pi\)
\(740\) 2.74450e9 0.248973
\(741\) −1.61452e8 −0.0145774
\(742\) 1.42806e9 0.128331
\(743\) −1.32975e10 −1.18935 −0.594673 0.803967i \(-0.702719\pi\)
−0.594673 + 0.803967i \(0.702719\pi\)
\(744\) 7.57603e9 0.674430
\(745\) 1.91827e9 0.169966
\(746\) −6.56165e9 −0.578665
\(747\) −3.03454e9 −0.266361
\(748\) −5.48103e9 −0.478858
\(749\) −3.66765e9 −0.318935
\(750\) −4.61829e8 −0.0399730
\(751\) −4.12057e8 −0.0354991 −0.0177495 0.999842i \(-0.505650\pi\)
−0.0177495 + 0.999842i \(0.505650\pi\)
\(752\) 1.15876e9 0.0993644
\(753\) −2.61506e9 −0.223202
\(754\) −1.36828e9 −0.116245
\(755\) −1.01260e10 −0.856296
\(756\) −1.35156e9 −0.113765
\(757\) −6.86113e9 −0.574857 −0.287428 0.957802i \(-0.592800\pi\)
−0.287428 + 0.957802i \(0.592800\pi\)
\(758\) 1.69897e10 1.41692
\(759\) −3.58477e9 −0.297588
\(760\) 8.04237e7 0.00664564
\(761\) −6.71798e9 −0.552576 −0.276288 0.961075i \(-0.589104\pi\)
−0.276288 + 0.961075i \(0.589104\pi\)
\(762\) 3.29218e9 0.269551
\(763\) 3.57164e9 0.291093
\(764\) 3.82339e8 0.0310186
\(765\) 1.31354e9 0.106079
\(766\) −9.50632e9 −0.764208
\(767\) 2.46978e10 1.97640
\(768\) −7.12782e9 −0.567796
\(769\) 2.89464e9 0.229537 0.114768 0.993392i \(-0.463387\pi\)
0.114768 + 0.993392i \(0.463387\pi\)
\(770\) −1.08593e10 −0.857204
\(771\) −9.67416e9 −0.760191
\(772\) 2.93495e9 0.229583
\(773\) 8.52286e9 0.663677 0.331839 0.943336i \(-0.392331\pi\)
0.331839 + 0.943336i \(0.392331\pi\)
\(774\) −5.70436e8 −0.0442195
\(775\) 2.79204e9 0.215460
\(776\) 1.03887e10 0.798077
\(777\) −1.54655e10 −1.18274
\(778\) 6.29643e9 0.479364
\(779\) 2.18674e7 0.00165736
\(780\) 2.52700e9 0.190666
\(781\) −6.94420e9 −0.521607
\(782\) 2.26143e9 0.169106
\(783\) −2.10715e8 −0.0156866
\(784\) −6.95407e9 −0.515386
\(785\) −5.05303e9 −0.372827
\(786\) −1.12027e10 −0.822894
\(787\) 7.66305e9 0.560390 0.280195 0.959943i \(-0.409601\pi\)
0.280195 + 0.959943i \(0.409601\pi\)
\(788\) 3.13000e9 0.227878
\(789\) 9.60807e9 0.696413
\(790\) 3.61238e9 0.260675
\(791\) −2.37412e10 −1.70563
\(792\) 8.48424e9 0.606841
\(793\) 1.80859e10 1.28790
\(794\) 6.89297e8 0.0488691
\(795\) −4.11186e8 −0.0290237
\(796\) −7.79211e9 −0.547595
\(797\) −1.16737e10 −0.816780 −0.408390 0.912807i \(-0.633910\pi\)
−0.408390 + 0.912807i \(0.633910\pi\)
\(798\) −1.29671e8 −0.00903304
\(799\) −2.32470e9 −0.161233
\(800\) −2.15736e9 −0.148973
\(801\) 6.20336e9 0.426494
\(802\) −3.75043e9 −0.256726
\(803\) −4.07422e10 −2.77677
\(804\) 1.30818e9 0.0887712
\(805\) −2.99705e9 −0.202492
\(806\) 2.28388e10 1.53638
\(807\) −1.63421e10 −1.09459
\(808\) 1.65880e10 1.10625
\(809\) 2.70449e8 0.0179583 0.00897917 0.999960i \(-0.497142\pi\)
0.00897917 + 0.999960i \(0.497142\pi\)
\(810\) −5.81772e8 −0.0384641
\(811\) −1.73776e9 −0.114398 −0.0571989 0.998363i \(-0.518217\pi\)
−0.0571989 + 0.998363i \(0.518217\pi\)
\(812\) 7.35099e8 0.0481837
\(813\) −3.78862e9 −0.247266
\(814\) 2.77781e10 1.80516
\(815\) 3.39561e9 0.219718
\(816\) −2.79642e9 −0.180172
\(817\) 3.66091e7 0.00234862
\(818\) −4.36701e9 −0.278964
\(819\) −1.42399e10 −0.905759
\(820\) −3.42261e8 −0.0216775
\(821\) 2.90103e10 1.82958 0.914791 0.403928i \(-0.132355\pi\)
0.914791 + 0.403928i \(0.132355\pi\)
\(822\) 3.25756e9 0.204570
\(823\) 1.99700e10 1.24876 0.624379 0.781122i \(-0.285352\pi\)
0.624379 + 0.781122i \(0.285352\pi\)
\(824\) 1.32864e10 0.827299
\(825\) 3.12675e9 0.193867
\(826\) 1.98362e10 1.22469
\(827\) −1.04944e10 −0.645193 −0.322597 0.946537i \(-0.604556\pi\)
−0.322597 + 0.946537i \(0.604556\pi\)
\(828\) 6.69983e8 0.0410164
\(829\) −2.15421e10 −1.31325 −0.656625 0.754218i \(-0.728016\pi\)
−0.656625 + 0.754218i \(0.728016\pi\)
\(830\) 4.55683e9 0.276624
\(831\) −7.85988e9 −0.475130
\(832\) −3.10694e10 −1.87026
\(833\) 1.39512e10 0.836287
\(834\) 7.07425e9 0.422279
\(835\) −6.20923e9 −0.369092
\(836\) −1.55795e8 −0.00922215
\(837\) 3.51717e9 0.207326
\(838\) −2.02402e10 −1.18812
\(839\) −1.14187e10 −0.667498 −0.333749 0.942662i \(-0.608314\pi\)
−0.333749 + 0.942662i \(0.608314\pi\)
\(840\) 7.09325e9 0.412922
\(841\) −1.71353e10 −0.993356
\(842\) −9.32340e9 −0.538248
\(843\) 1.37762e10 0.792015
\(844\) −1.61276e9 −0.0923358
\(845\) 1.87806e10 1.07081
\(846\) 1.02962e9 0.0584628
\(847\) 4.74391e10 2.68253
\(848\) 8.75379e8 0.0492959
\(849\) 6.15916e9 0.345418
\(850\) −1.97248e9 −0.110166
\(851\) 7.66645e9 0.426423
\(852\) 1.29785e9 0.0718929
\(853\) 9.38139e9 0.517542 0.258771 0.965939i \(-0.416682\pi\)
0.258771 + 0.965939i \(0.416682\pi\)
\(854\) 1.45258e10 0.798062
\(855\) 3.73366e7 0.00204293
\(856\) −4.30298e9 −0.234483
\(857\) 1.57142e10 0.852826 0.426413 0.904529i \(-0.359777\pi\)
0.426413 + 0.904529i \(0.359777\pi\)
\(858\) 2.55767e10 1.38241
\(859\) −8.67241e9 −0.466835 −0.233418 0.972377i \(-0.574991\pi\)
−0.233418 + 0.972377i \(0.574991\pi\)
\(860\) −5.72993e8 −0.0307188
\(861\) 1.92867e9 0.102979
\(862\) −2.44350e10 −1.29938
\(863\) −1.44436e10 −0.764961 −0.382480 0.923964i \(-0.624930\pi\)
−0.382480 + 0.923964i \(0.624930\pi\)
\(864\) −2.71765e9 −0.143349
\(865\) 1.47809e10 0.776507
\(866\) −1.98884e10 −1.04061
\(867\) −5.46898e9 −0.284996
\(868\) −1.22700e10 −0.636833
\(869\) −2.44571e10 −1.26426
\(870\) 3.16421e8 0.0162910
\(871\) 1.37829e10 0.706768
\(872\) 4.19034e9 0.214013
\(873\) 4.82294e9 0.245337
\(874\) 6.42797e7 0.00325675
\(875\) 2.61412e9 0.131916
\(876\) 7.61459e9 0.382721
\(877\) −3.05357e10 −1.52865 −0.764327 0.644829i \(-0.776929\pi\)
−0.764327 + 0.644829i \(0.776929\pi\)
\(878\) −1.84179e10 −0.918354
\(879\) −4.54181e9 −0.225563
\(880\) −6.65658e9 −0.329277
\(881\) 1.64615e10 0.811063 0.405532 0.914081i \(-0.367086\pi\)
0.405532 + 0.914081i \(0.367086\pi\)
\(882\) −6.17906e9 −0.303237
\(883\) 6.48699e8 0.0317089 0.0158544 0.999874i \(-0.494953\pi\)
0.0158544 + 0.999874i \(0.494953\pi\)
\(884\) 1.07929e10 0.525477
\(885\) −5.71148e9 −0.276979
\(886\) 2.36961e10 1.14461
\(887\) −3.02429e10 −1.45509 −0.727547 0.686058i \(-0.759340\pi\)
−0.727547 + 0.686058i \(0.759340\pi\)
\(888\) −1.81445e10 −0.869562
\(889\) −1.86349e10 −0.889552
\(890\) −9.31531e9 −0.442927
\(891\) 3.93880e9 0.186549
\(892\) 7.96839e9 0.375918
\(893\) −6.60783e7 −0.00310512
\(894\) −3.62870e9 −0.169851
\(895\) −1.15252e9 −0.0537362
\(896\) −1.29935e9 −0.0603459
\(897\) 7.05888e9 0.326560
\(898\) −1.84793e10 −0.851567
\(899\) −1.91296e9 −0.0878104
\(900\) −5.84380e8 −0.0267206
\(901\) −1.75618e9 −0.0799896
\(902\) −3.46415e9 −0.157171
\(903\) 3.22887e9 0.145930
\(904\) −2.78537e10 −1.25399
\(905\) −9.93993e9 −0.445772
\(906\) 1.91549e10 0.855719
\(907\) −3.51061e10 −1.56227 −0.781136 0.624361i \(-0.785359\pi\)
−0.781136 + 0.624361i \(0.785359\pi\)
\(908\) −5.46755e9 −0.242378
\(909\) 7.70096e9 0.340072
\(910\) 2.13834e10 0.940657
\(911\) 1.98834e10 0.871318 0.435659 0.900112i \(-0.356515\pi\)
0.435659 + 0.900112i \(0.356515\pi\)
\(912\) −7.94865e7 −0.00346986
\(913\) −3.08513e10 −1.34161
\(914\) 1.99152e9 0.0862727
\(915\) −4.18244e9 −0.180491
\(916\) −1.58837e9 −0.0682838
\(917\) 6.34113e10 2.71565
\(918\) −2.48476e9 −0.106007
\(919\) 3.04145e10 1.29263 0.646317 0.763069i \(-0.276308\pi\)
0.646317 + 0.763069i \(0.276308\pi\)
\(920\) −3.51621e9 −0.148874
\(921\) 1.53327e10 0.646709
\(922\) 4.80686e9 0.201978
\(923\) 1.36740e10 0.572388
\(924\) −1.37409e10 −0.573012
\(925\) −6.68691e9 −0.277798
\(926\) −4.37794e9 −0.181189
\(927\) 6.16820e9 0.254319
\(928\) 1.47811e9 0.0607139
\(929\) −1.54054e10 −0.630402 −0.315201 0.949025i \(-0.602072\pi\)
−0.315201 + 0.949025i \(0.602072\pi\)
\(930\) −5.28157e9 −0.215314
\(931\) 3.96556e8 0.0161057
\(932\) −6.64811e9 −0.268994
\(933\) −1.80367e10 −0.727062
\(934\) −1.95570e10 −0.785393
\(935\) 1.33544e10 0.534299
\(936\) −1.67066e10 −0.665920
\(937\) 1.59155e10 0.632022 0.316011 0.948755i \(-0.397656\pi\)
0.316011 + 0.948755i \(0.397656\pi\)
\(938\) 1.10698e10 0.437955
\(939\) 6.52346e9 0.257128
\(940\) 1.03423e9 0.0406136
\(941\) 2.40112e10 0.939400 0.469700 0.882826i \(-0.344362\pi\)
0.469700 + 0.882826i \(0.344362\pi\)
\(942\) 9.55857e9 0.372576
\(943\) −9.56068e8 −0.0371277
\(944\) 1.21593e10 0.470441
\(945\) 3.29304e9 0.126936
\(946\) −5.79947e9 −0.222725
\(947\) 8.05811e8 0.0308325 0.0154162 0.999881i \(-0.495093\pi\)
0.0154162 + 0.999881i \(0.495093\pi\)
\(948\) 4.57096e9 0.174252
\(949\) 8.02267e10 3.04710
\(950\) −5.60667e7 −0.00212164
\(951\) −2.62944e10 −0.991361
\(952\) 3.02955e10 1.13802
\(953\) 2.64373e10 0.989447 0.494723 0.869050i \(-0.335269\pi\)
0.494723 + 0.869050i \(0.335269\pi\)
\(954\) 7.77820e8 0.0290041
\(955\) −9.31561e8 −0.0346098
\(956\) −1.70536e10 −0.631268
\(957\) −2.14228e9 −0.0790104
\(958\) 3.09507e10 1.13734
\(959\) −1.84390e10 −0.675105
\(960\) 7.18494e9 0.262104
\(961\) 4.41771e9 0.160570
\(962\) −5.46986e10 −1.98091
\(963\) −1.99766e9 −0.0720823
\(964\) −1.17184e10 −0.421306
\(965\) −7.15094e9 −0.256164
\(966\) 5.66938e9 0.202356
\(967\) −5.21065e10 −1.85310 −0.926552 0.376167i \(-0.877242\pi\)
−0.926552 + 0.376167i \(0.877242\pi\)
\(968\) 5.56568e10 1.97222
\(969\) 1.59466e8 0.00563033
\(970\) −7.24239e9 −0.254789
\(971\) 7.86045e9 0.275537 0.137769 0.990464i \(-0.456007\pi\)
0.137769 + 0.990464i \(0.456007\pi\)
\(972\) −7.36150e8 −0.0257119
\(973\) −4.00428e10 −1.39357
\(974\) −2.38731e10 −0.827852
\(975\) −6.15697e9 −0.212741
\(976\) 8.90407e9 0.306559
\(977\) −1.16546e10 −0.399822 −0.199911 0.979814i \(-0.564065\pi\)
−0.199911 + 0.979814i \(0.564065\pi\)
\(978\) −6.42331e9 −0.219570
\(979\) 6.30679e10 2.14817
\(980\) −6.20675e9 −0.210656
\(981\) 1.94536e9 0.0657898
\(982\) 4.25651e10 1.43438
\(983\) 1.58904e10 0.533576 0.266788 0.963755i \(-0.414038\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(984\) 2.26277e9 0.0757107
\(985\) −7.62618e9 −0.254261
\(986\) 1.35144e9 0.0448981
\(987\) −5.82801e9 −0.192935
\(988\) 3.06781e8 0.0101200
\(989\) −1.60059e9 −0.0526130
\(990\) −5.91472e9 −0.193736
\(991\) −3.50706e10 −1.14468 −0.572342 0.820015i \(-0.693965\pi\)
−0.572342 + 0.820015i \(0.693965\pi\)
\(992\) −2.46720e10 −0.802442
\(993\) −1.15006e10 −0.372732
\(994\) 1.09824e10 0.354686
\(995\) 1.89853e10 0.610994
\(996\) 5.76602e9 0.184913
\(997\) 5.92011e10 1.89189 0.945947 0.324322i \(-0.105136\pi\)
0.945947 + 0.324322i \(0.105136\pi\)
\(998\) −2.11061e9 −0.0672126
\(999\) −8.42358e9 −0.267312
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 \(a_p\))