Properties

Label 546.6.a.a.1.1
Level $546$
Weight $6$
Character 546.1
Self dual yes
Analytic conductor $87.570$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(87.5695656179\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 546.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +81.0000 q^{5} -36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +81.0000 q^{5} -36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} -324.000 q^{10} +191.000 q^{11} +144.000 q^{12} -169.000 q^{13} +196.000 q^{14} +729.000 q^{15} +256.000 q^{16} -871.000 q^{17} -324.000 q^{18} -479.000 q^{19} +1296.00 q^{20} -441.000 q^{21} -764.000 q^{22} +1387.00 q^{23} -576.000 q^{24} +3436.00 q^{25} +676.000 q^{26} +729.000 q^{27} -784.000 q^{28} -5295.00 q^{29} -2916.00 q^{30} +5940.00 q^{31} -1024.00 q^{32} +1719.00 q^{33} +3484.00 q^{34} -3969.00 q^{35} +1296.00 q^{36} +13543.0 q^{37} +1916.00 q^{38} -1521.00 q^{39} -5184.00 q^{40} +9464.00 q^{41} +1764.00 q^{42} +17387.0 q^{43} +3056.00 q^{44} +6561.00 q^{45} -5548.00 q^{46} -8112.00 q^{47} +2304.00 q^{48} +2401.00 q^{49} -13744.0 q^{50} -7839.00 q^{51} -2704.00 q^{52} +18038.0 q^{53} -2916.00 q^{54} +15471.0 q^{55} +3136.00 q^{56} -4311.00 q^{57} +21180.0 q^{58} +28784.0 q^{59} +11664.0 q^{60} +14773.0 q^{61} -23760.0 q^{62} -3969.00 q^{63} +4096.00 q^{64} -13689.0 q^{65} -6876.00 q^{66} -54354.0 q^{67} -13936.0 q^{68} +12483.0 q^{69} +15876.0 q^{70} +64608.0 q^{71} -5184.00 q^{72} +39461.0 q^{73} -54172.0 q^{74} +30924.0 q^{75} -7664.00 q^{76} -9359.00 q^{77} +6084.00 q^{78} -95554.0 q^{79} +20736.0 q^{80} +6561.00 q^{81} -37856.0 q^{82} -69634.0 q^{83} -7056.00 q^{84} -70551.0 q^{85} -69548.0 q^{86} -47655.0 q^{87} -12224.0 q^{88} -51906.0 q^{89} -26244.0 q^{90} +8281.00 q^{91} +22192.0 q^{92} +53460.0 q^{93} +32448.0 q^{94} -38799.0 q^{95} -9216.00 q^{96} +162654. q^{97} -9604.00 q^{98} +15471.0 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) 9.00000 0.577350
\(4\) 16.0000 0.500000
\(5\) 81.0000 1.44897 0.724486 0.689289i \(-0.242077\pi\)
0.724486 + 0.689289i \(0.242077\pi\)
\(6\) −36.0000 −0.408248
\(7\) −49.0000 −0.377964
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −324.000 −1.02458
\(11\) 191.000 0.475939 0.237970 0.971273i \(-0.423518\pi\)
0.237970 + 0.971273i \(0.423518\pi\)
\(12\) 144.000 0.288675
\(13\) −169.000 −0.277350
\(14\) 196.000 0.267261
\(15\) 729.000 0.836564
\(16\) 256.000 0.250000
\(17\) −871.000 −0.730964 −0.365482 0.930818i \(-0.619096\pi\)
−0.365482 + 0.930818i \(0.619096\pi\)
\(18\) −324.000 −0.235702
\(19\) −479.000 −0.304405 −0.152202 0.988349i \(-0.548637\pi\)
−0.152202 + 0.988349i \(0.548637\pi\)
\(20\) 1296.00 0.724486
\(21\) −441.000 −0.218218
\(22\) −764.000 −0.336540
\(23\) 1387.00 0.546710 0.273355 0.961913i \(-0.411867\pi\)
0.273355 + 0.961913i \(0.411867\pi\)
\(24\) −576.000 −0.204124
\(25\) 3436.00 1.09952
\(26\) 676.000 0.196116
\(27\) 729.000 0.192450
\(28\) −784.000 −0.188982
\(29\) −5295.00 −1.16915 −0.584576 0.811339i \(-0.698739\pi\)
−0.584576 + 0.811339i \(0.698739\pi\)
\(30\) −2916.00 −0.591540
\(31\) 5940.00 1.11015 0.555076 0.831800i \(-0.312689\pi\)
0.555076 + 0.831800i \(0.312689\pi\)
\(32\) −1024.00 −0.176777
\(33\) 1719.00 0.274784
\(34\) 3484.00 0.516869
\(35\) −3969.00 −0.547660
\(36\) 1296.00 0.166667
\(37\) 13543.0 1.62634 0.813169 0.582028i \(-0.197741\pi\)
0.813169 + 0.582028i \(0.197741\pi\)
\(38\) 1916.00 0.215247
\(39\) −1521.00 −0.160128
\(40\) −5184.00 −0.512289
\(41\) 9464.00 0.879255 0.439628 0.898180i \(-0.355110\pi\)
0.439628 + 0.898180i \(0.355110\pi\)
\(42\) 1764.00 0.154303
\(43\) 17387.0 1.43401 0.717007 0.697066i \(-0.245511\pi\)
0.717007 + 0.697066i \(0.245511\pi\)
\(44\) 3056.00 0.237970
\(45\) 6561.00 0.482991
\(46\) −5548.00 −0.386582
\(47\) −8112.00 −0.535653 −0.267826 0.963467i \(-0.586305\pi\)
−0.267826 + 0.963467i \(0.586305\pi\)
\(48\) 2304.00 0.144338
\(49\) 2401.00 0.142857
\(50\) −13744.0 −0.777478
\(51\) −7839.00 −0.422022
\(52\) −2704.00 −0.138675
\(53\) 18038.0 0.882061 0.441031 0.897492i \(-0.354613\pi\)
0.441031 + 0.897492i \(0.354613\pi\)
\(54\) −2916.00 −0.136083
\(55\) 15471.0 0.689623
\(56\) 3136.00 0.133631
\(57\) −4311.00 −0.175748
\(58\) 21180.0 0.826715
\(59\) 28784.0 1.07652 0.538259 0.842780i \(-0.319082\pi\)
0.538259 + 0.842780i \(0.319082\pi\)
\(60\) 11664.0 0.418282
\(61\) 14773.0 0.508328 0.254164 0.967161i \(-0.418200\pi\)
0.254164 + 0.967161i \(0.418200\pi\)
\(62\) −23760.0 −0.784996
\(63\) −3969.00 −0.125988
\(64\) 4096.00 0.125000
\(65\) −13689.0 −0.401873
\(66\) −6876.00 −0.194301
\(67\) −54354.0 −1.47926 −0.739630 0.673014i \(-0.764999\pi\)
−0.739630 + 0.673014i \(0.764999\pi\)
\(68\) −13936.0 −0.365482
\(69\) 12483.0 0.315643
\(70\) 15876.0 0.387254
\(71\) 64608.0 1.52104 0.760520 0.649315i \(-0.224944\pi\)
0.760520 + 0.649315i \(0.224944\pi\)
\(72\) −5184.00 −0.117851
\(73\) 39461.0 0.866684 0.433342 0.901229i \(-0.357334\pi\)
0.433342 + 0.901229i \(0.357334\pi\)
\(74\) −54172.0 −1.14999
\(75\) 30924.0 0.634808
\(76\) −7664.00 −0.152202
\(77\) −9359.00 −0.179888
\(78\) 6084.00 0.113228
\(79\) −95554.0 −1.72259 −0.861293 0.508108i \(-0.830345\pi\)
−0.861293 + 0.508108i \(0.830345\pi\)
\(80\) 20736.0 0.362243
\(81\) 6561.00 0.111111
\(82\) −37856.0 −0.621728
\(83\) −69634.0 −1.10950 −0.554748 0.832018i \(-0.687186\pi\)
−0.554748 + 0.832018i \(0.687186\pi\)
\(84\) −7056.00 −0.109109
\(85\) −70551.0 −1.05915
\(86\) −69548.0 −1.01400
\(87\) −47655.0 −0.675010
\(88\) −12224.0 −0.168270
\(89\) −51906.0 −0.694612 −0.347306 0.937752i \(-0.612904\pi\)
−0.347306 + 0.937752i \(0.612904\pi\)
\(90\) −26244.0 −0.341526
\(91\) 8281.00 0.104828
\(92\) 22192.0 0.273355
\(93\) 53460.0 0.640946
\(94\) 32448.0 0.378764
\(95\) −38799.0 −0.441074
\(96\) −9216.00 −0.102062
\(97\) 162654. 1.75524 0.877618 0.479361i \(-0.159132\pi\)
0.877618 + 0.479361i \(0.159132\pi\)
\(98\) −9604.00 −0.101015
\(99\) 15471.0 0.158646
\(100\) 54976.0 0.549760
\(101\) 30000.0 0.292629 0.146315 0.989238i \(-0.453259\pi\)
0.146315 + 0.989238i \(0.453259\pi\)
\(102\) 31356.0 0.298415
\(103\) 26549.0 0.246578 0.123289 0.992371i \(-0.460656\pi\)
0.123289 + 0.992371i \(0.460656\pi\)
\(104\) 10816.0 0.0980581
\(105\) −35721.0 −0.316192
\(106\) −72152.0 −0.623711
\(107\) −76686.0 −0.647525 −0.323763 0.946138i \(-0.604948\pi\)
−0.323763 + 0.946138i \(0.604948\pi\)
\(108\) 11664.0 0.0962250
\(109\) −121099. −0.976280 −0.488140 0.872765i \(-0.662324\pi\)
−0.488140 + 0.872765i \(0.662324\pi\)
\(110\) −61884.0 −0.487637
\(111\) 121887. 0.938966
\(112\) −12544.0 −0.0944911
\(113\) 155186. 1.14329 0.571645 0.820501i \(-0.306305\pi\)
0.571645 + 0.820501i \(0.306305\pi\)
\(114\) 17244.0 0.124273
\(115\) 112347. 0.792167
\(116\) −84720.0 −0.584576
\(117\) −13689.0 −0.0924500
\(118\) −115136. −0.761213
\(119\) 42679.0 0.276278
\(120\) −46656.0 −0.295770
\(121\) −124570. −0.773482
\(122\) −59092.0 −0.359442
\(123\) 85176.0 0.507638
\(124\) 95040.0 0.555076
\(125\) 25191.0 0.144202
\(126\) 15876.0 0.0890871
\(127\) −8354.00 −0.0459605 −0.0229803 0.999736i \(-0.507315\pi\)
−0.0229803 + 0.999736i \(0.507315\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 156483. 0.827929
\(130\) 54756.0 0.284167
\(131\) 332217. 1.69139 0.845695 0.533667i \(-0.179186\pi\)
0.845695 + 0.533667i \(0.179186\pi\)
\(132\) 27504.0 0.137392
\(133\) 23471.0 0.115054
\(134\) 217416. 1.04599
\(135\) 59049.0 0.278855
\(136\) 55744.0 0.258435
\(137\) 80385.0 0.365909 0.182955 0.983121i \(-0.441434\pi\)
0.182955 + 0.983121i \(0.441434\pi\)
\(138\) −49932.0 −0.223193
\(139\) −132656. −0.582358 −0.291179 0.956669i \(-0.594047\pi\)
−0.291179 + 0.956669i \(0.594047\pi\)
\(140\) −63504.0 −0.273830
\(141\) −73008.0 −0.309259
\(142\) −258432. −1.07554
\(143\) −32279.0 −0.132002
\(144\) 20736.0 0.0833333
\(145\) −428895. −1.69407
\(146\) −157844. −0.612838
\(147\) 21609.0 0.0824786
\(148\) 216688. 0.813169
\(149\) 149576. 0.551946 0.275973 0.961165i \(-0.411000\pi\)
0.275973 + 0.961165i \(0.411000\pi\)
\(150\) −123696. −0.448877
\(151\) 264571. 0.944278 0.472139 0.881524i \(-0.343482\pi\)
0.472139 + 0.881524i \(0.343482\pi\)
\(152\) 30656.0 0.107623
\(153\) −70551.0 −0.243655
\(154\) 37436.0 0.127200
\(155\) 481140. 1.60858
\(156\) −24336.0 −0.0800641
\(157\) 473873. 1.53431 0.767155 0.641462i \(-0.221672\pi\)
0.767155 + 0.641462i \(0.221672\pi\)
\(158\) 382216. 1.21805
\(159\) 162342. 0.509258
\(160\) −82944.0 −0.256144
\(161\) −67963.0 −0.206637
\(162\) −26244.0 −0.0785674
\(163\) 77866.0 0.229551 0.114775 0.993391i \(-0.463385\pi\)
0.114775 + 0.993391i \(0.463385\pi\)
\(164\) 151424. 0.439628
\(165\) 139239. 0.398154
\(166\) 278536. 0.784533
\(167\) 224669. 0.623379 0.311689 0.950184i \(-0.399105\pi\)
0.311689 + 0.950184i \(0.399105\pi\)
\(168\) 28224.0 0.0771517
\(169\) 28561.0 0.0769231
\(170\) 282204. 0.748929
\(171\) −38799.0 −0.101468
\(172\) 278192. 0.717007
\(173\) −268826. −0.682898 −0.341449 0.939900i \(-0.610918\pi\)
−0.341449 + 0.939900i \(0.610918\pi\)
\(174\) 190620. 0.477304
\(175\) −168364. −0.415579
\(176\) 48896.0 0.118985
\(177\) 259056. 0.621528
\(178\) 207624. 0.491165
\(179\) 171112. 0.399161 0.199580 0.979881i \(-0.436042\pi\)
0.199580 + 0.979881i \(0.436042\pi\)
\(180\) 104976. 0.241495
\(181\) −643850. −1.46079 −0.730396 0.683024i \(-0.760664\pi\)
−0.730396 + 0.683024i \(0.760664\pi\)
\(182\) −33124.0 −0.0741249
\(183\) 132957. 0.293483
\(184\) −88768.0 −0.193291
\(185\) 1.09698e6 2.35652
\(186\) −213840. −0.453217
\(187\) −166361. −0.347894
\(188\) −129792. −0.267826
\(189\) −35721.0 −0.0727393
\(190\) 155196. 0.311886
\(191\) 390891. 0.775304 0.387652 0.921806i \(-0.373286\pi\)
0.387652 + 0.921806i \(0.373286\pi\)
\(192\) 36864.0 0.0721688
\(193\) 507268. 0.980267 0.490133 0.871647i \(-0.336948\pi\)
0.490133 + 0.871647i \(0.336948\pi\)
\(194\) −650616. −1.24114
\(195\) −123201. −0.232021
\(196\) 38416.0 0.0714286
\(197\) −767200. −1.40846 −0.704228 0.709974i \(-0.748707\pi\)
−0.704228 + 0.709974i \(0.748707\pi\)
\(198\) −61884.0 −0.112180
\(199\) 476559. 0.853069 0.426534 0.904471i \(-0.359734\pi\)
0.426534 + 0.904471i \(0.359734\pi\)
\(200\) −219904. −0.388739
\(201\) −489186. −0.854051
\(202\) −120000. −0.206920
\(203\) 259455. 0.441898
\(204\) −125424. −0.211011
\(205\) 766584. 1.27402
\(206\) −106196. −0.174357
\(207\) 112347. 0.182237
\(208\) −43264.0 −0.0693375
\(209\) −91489.0 −0.144878
\(210\) 142884. 0.223581
\(211\) −95231.0 −0.147256 −0.0736279 0.997286i \(-0.523458\pi\)
−0.0736279 + 0.997286i \(0.523458\pi\)
\(212\) 288608. 0.441031
\(213\) 581472. 0.878172
\(214\) 306744. 0.457869
\(215\) 1.40835e6 2.07785
\(216\) −46656.0 −0.0680414
\(217\) −291060. −0.419598
\(218\) 484396. 0.690334
\(219\) 355149. 0.500380
\(220\) 247536. 0.344811
\(221\) 147199. 0.202733
\(222\) −487548. −0.663949
\(223\) −860014. −1.15809 −0.579046 0.815295i \(-0.696575\pi\)
−0.579046 + 0.815295i \(0.696575\pi\)
\(224\) 50176.0 0.0668153
\(225\) 278316. 0.366507
\(226\) −620744. −0.808428
\(227\) −264390. −0.340550 −0.170275 0.985397i \(-0.554466\pi\)
−0.170275 + 0.985397i \(0.554466\pi\)
\(228\) −68976.0 −0.0878741
\(229\) −82854.0 −0.104406 −0.0522029 0.998636i \(-0.516624\pi\)
−0.0522029 + 0.998636i \(0.516624\pi\)
\(230\) −449388. −0.560147
\(231\) −84231.0 −0.103858
\(232\) 338880. 0.413358
\(233\) −588276. −0.709890 −0.354945 0.934887i \(-0.615500\pi\)
−0.354945 + 0.934887i \(0.615500\pi\)
\(234\) 54756.0 0.0653720
\(235\) −657072. −0.776146
\(236\) 460544. 0.538259
\(237\) −859986. −0.994536
\(238\) −170716. −0.195358
\(239\) 1.68226e6 1.90501 0.952507 0.304515i \(-0.0984945\pi\)
0.952507 + 0.304515i \(0.0984945\pi\)
\(240\) 186624. 0.209141
\(241\) −264906. −0.293798 −0.146899 0.989151i \(-0.546929\pi\)
−0.146899 + 0.989151i \(0.546929\pi\)
\(242\) 498280. 0.546934
\(243\) 59049.0 0.0641500
\(244\) 236368. 0.254164
\(245\) 194481. 0.206996
\(246\) −340704. −0.358955
\(247\) 80951.0 0.0844267
\(248\) −380160. −0.392498
\(249\) −626706. −0.640568
\(250\) −100764. −0.101966
\(251\) 1.91551e6 1.91911 0.959555 0.281521i \(-0.0908389\pi\)
0.959555 + 0.281521i \(0.0908389\pi\)
\(252\) −63504.0 −0.0629941
\(253\) 264917. 0.260201
\(254\) 33416.0 0.0324990
\(255\) −634959. −0.611498
\(256\) 65536.0 0.0625000
\(257\) 222734. 0.210355 0.105178 0.994453i \(-0.466459\pi\)
0.105178 + 0.994453i \(0.466459\pi\)
\(258\) −625932. −0.585434
\(259\) −663607. −0.614698
\(260\) −219024. −0.200936
\(261\) −428895. −0.389717
\(262\) −1.32887e6 −1.19599
\(263\) 1.28672e6 1.14708 0.573540 0.819178i \(-0.305570\pi\)
0.573540 + 0.819178i \(0.305570\pi\)
\(264\) −110016. −0.0971507
\(265\) 1.46108e6 1.27808
\(266\) −93884.0 −0.0813556
\(267\) −467154. −0.401035
\(268\) −869664. −0.739630
\(269\) −134666. −0.113469 −0.0567345 0.998389i \(-0.518069\pi\)
−0.0567345 + 0.998389i \(0.518069\pi\)
\(270\) −236196. −0.197180
\(271\) 1.45917e6 1.20693 0.603466 0.797389i \(-0.293786\pi\)
0.603466 + 0.797389i \(0.293786\pi\)
\(272\) −222976. −0.182741
\(273\) 74529.0 0.0605228
\(274\) −321540. −0.258737
\(275\) 656276. 0.523305
\(276\) 199728. 0.157822
\(277\) −1.11879e6 −0.876088 −0.438044 0.898954i \(-0.644329\pi\)
−0.438044 + 0.898954i \(0.644329\pi\)
\(278\) 530624. 0.411789
\(279\) 481140. 0.370050
\(280\) 254016. 0.193627
\(281\) 2.14775e6 1.62263 0.811314 0.584611i \(-0.198753\pi\)
0.811314 + 0.584611i \(0.198753\pi\)
\(282\) 292032. 0.218679
\(283\) −2.13321e6 −1.58331 −0.791657 0.610966i \(-0.790781\pi\)
−0.791657 + 0.610966i \(0.790781\pi\)
\(284\) 1.03373e6 0.760520
\(285\) −349191. −0.254654
\(286\) 129116. 0.0933394
\(287\) −463736. −0.332327
\(288\) −82944.0 −0.0589256
\(289\) −661216. −0.465692
\(290\) 1.71558e6 1.19789
\(291\) 1.46389e6 1.01339
\(292\) 631376. 0.433342
\(293\) −1.20629e6 −0.820888 −0.410444 0.911886i \(-0.634626\pi\)
−0.410444 + 0.911886i \(0.634626\pi\)
\(294\) −86436.0 −0.0583212
\(295\) 2.33150e6 1.55984
\(296\) −866752. −0.574997
\(297\) 139239. 0.0915946
\(298\) −598304. −0.390284
\(299\) −234403. −0.151630
\(300\) 494784. 0.317404
\(301\) −851963. −0.542007
\(302\) −1.05828e6 −0.667705
\(303\) 270000. 0.168950
\(304\) −122624. −0.0761012
\(305\) 1.19661e6 0.736553
\(306\) 282204. 0.172290
\(307\) −529472. −0.320625 −0.160312 0.987066i \(-0.551250\pi\)
−0.160312 + 0.987066i \(0.551250\pi\)
\(308\) −149744. −0.0899441
\(309\) 238941. 0.142362
\(310\) −1.92456e6 −1.13744
\(311\) 2.66970e6 1.56517 0.782584 0.622545i \(-0.213901\pi\)
0.782584 + 0.622545i \(0.213901\pi\)
\(312\) 97344.0 0.0566139
\(313\) −1.39360e6 −0.804037 −0.402019 0.915632i \(-0.631691\pi\)
−0.402019 + 0.915632i \(0.631691\pi\)
\(314\) −1.89549e6 −1.08492
\(315\) −321489. −0.182553
\(316\) −1.52886e6 −0.861293
\(317\) 963472. 0.538506 0.269253 0.963069i \(-0.413223\pi\)
0.269253 + 0.963069i \(0.413223\pi\)
\(318\) −649368. −0.360100
\(319\) −1.01134e6 −0.556445
\(320\) 331776. 0.181122
\(321\) −690174. −0.373849
\(322\) 271852. 0.146114
\(323\) 417209. 0.222509
\(324\) 104976. 0.0555556
\(325\) −580684. −0.304952
\(326\) −311464. −0.162317
\(327\) −1.08989e6 −0.563655
\(328\) −605696. −0.310864
\(329\) 397488. 0.202458
\(330\) −556956. −0.281537
\(331\) 2.52824e6 1.26838 0.634189 0.773178i \(-0.281334\pi\)
0.634189 + 0.773178i \(0.281334\pi\)
\(332\) −1.11414e6 −0.554748
\(333\) 1.09698e6 0.542112
\(334\) −898676. −0.440795
\(335\) −4.40267e6 −2.14341
\(336\) −112896. −0.0545545
\(337\) 487563. 0.233860 0.116930 0.993140i \(-0.462695\pi\)
0.116930 + 0.993140i \(0.462695\pi\)
\(338\) −114244. −0.0543928
\(339\) 1.39667e6 0.660079
\(340\) −1.12882e6 −0.529573
\(341\) 1.13454e6 0.528365
\(342\) 155196. 0.0717489
\(343\) −117649. −0.0539949
\(344\) −1.11277e6 −0.507001
\(345\) 1.01112e6 0.457358
\(346\) 1.07530e6 0.482882
\(347\) 1.30149e6 0.580252 0.290126 0.956988i \(-0.406303\pi\)
0.290126 + 0.956988i \(0.406303\pi\)
\(348\) −762480. −0.337505
\(349\) −3.03469e6 −1.33368 −0.666839 0.745202i \(-0.732353\pi\)
−0.666839 + 0.745202i \(0.732353\pi\)
\(350\) 673456. 0.293859
\(351\) −123201. −0.0533761
\(352\) −195584. −0.0841350
\(353\) −3.35440e6 −1.43277 −0.716387 0.697703i \(-0.754206\pi\)
−0.716387 + 0.697703i \(0.754206\pi\)
\(354\) −1.03622e6 −0.439486
\(355\) 5.23325e6 2.20394
\(356\) −830496. −0.347306
\(357\) 384111. 0.159509
\(358\) −684448. −0.282249
\(359\) −2.15602e6 −0.882909 −0.441454 0.897284i \(-0.645537\pi\)
−0.441454 + 0.897284i \(0.645537\pi\)
\(360\) −419904. −0.170763
\(361\) −2.24666e6 −0.907338
\(362\) 2.57540e6 1.03294
\(363\) −1.12113e6 −0.446570
\(364\) 132496. 0.0524142
\(365\) 3.19634e6 1.25580
\(366\) −531828. −0.207524
\(367\) −2.70477e6 −1.04825 −0.524125 0.851641i \(-0.675608\pi\)
−0.524125 + 0.851641i \(0.675608\pi\)
\(368\) 355072. 0.136677
\(369\) 766584. 0.293085
\(370\) −4.38793e6 −1.66631
\(371\) −883862. −0.333388
\(372\) 855360. 0.320473
\(373\) −64248.0 −0.0239104 −0.0119552 0.999929i \(-0.503806\pi\)
−0.0119552 + 0.999929i \(0.503806\pi\)
\(374\) 665444. 0.245999
\(375\) 226719. 0.0832549
\(376\) 519168. 0.189382
\(377\) 894855. 0.324264
\(378\) 142884. 0.0514344
\(379\) −2.62394e6 −0.938329 −0.469165 0.883111i \(-0.655445\pi\)
−0.469165 + 0.883111i \(0.655445\pi\)
\(380\) −620784. −0.220537
\(381\) −75186.0 −0.0265353
\(382\) −1.56356e6 −0.548223
\(383\) −5.62688e6 −1.96007 −0.980034 0.198832i \(-0.936285\pi\)
−0.980034 + 0.198832i \(0.936285\pi\)
\(384\) −147456. −0.0510310
\(385\) −758079. −0.260653
\(386\) −2.02907e6 −0.693153
\(387\) 1.40835e6 0.478005
\(388\) 2.60246e6 0.877618
\(389\) −75010.0 −0.0251330 −0.0125665 0.999921i \(-0.504000\pi\)
−0.0125665 + 0.999921i \(0.504000\pi\)
\(390\) 492804. 0.164064
\(391\) −1.20808e6 −0.399625
\(392\) −153664. −0.0505076
\(393\) 2.98995e6 0.976524
\(394\) 3.06880e6 0.995928
\(395\) −7.73987e6 −2.49598
\(396\) 247536. 0.0793232
\(397\) −1.33959e6 −0.426574 −0.213287 0.976990i \(-0.568417\pi\)
−0.213287 + 0.976990i \(0.568417\pi\)
\(398\) −1.90624e6 −0.603211
\(399\) 211239. 0.0664266
\(400\) 879616. 0.274880
\(401\) −1.66502e6 −0.517082 −0.258541 0.966000i \(-0.583242\pi\)
−0.258541 + 0.966000i \(0.583242\pi\)
\(402\) 1.95674e6 0.603905
\(403\) −1.00386e6 −0.307901
\(404\) 480000. 0.146315
\(405\) 531441. 0.160997
\(406\) −1.03782e6 −0.312469
\(407\) 2.58671e6 0.774038
\(408\) 501696. 0.149207
\(409\) 1.59142e6 0.470409 0.235204 0.971946i \(-0.424424\pi\)
0.235204 + 0.971946i \(0.424424\pi\)
\(410\) −3.06634e6 −0.900866
\(411\) 723465. 0.211258
\(412\) 424784. 0.123289
\(413\) −1.41042e6 −0.406885
\(414\) −449388. −0.128861
\(415\) −5.64035e6 −1.60763
\(416\) 173056. 0.0490290
\(417\) −1.19390e6 −0.336224
\(418\) 365956. 0.102444
\(419\) −2.39338e6 −0.666004 −0.333002 0.942926i \(-0.608062\pi\)
−0.333002 + 0.942926i \(0.608062\pi\)
\(420\) −571536. −0.158096
\(421\) −4.67244e6 −1.28481 −0.642404 0.766366i \(-0.722063\pi\)
−0.642404 + 0.766366i \(0.722063\pi\)
\(422\) 380924. 0.104126
\(423\) −657072. −0.178551
\(424\) −1.15443e6 −0.311856
\(425\) −2.99276e6 −0.803709
\(426\) −2.32589e6 −0.620962
\(427\) −723877. −0.192130
\(428\) −1.22698e6 −0.323763
\(429\) −290511. −0.0762113
\(430\) −5.63339e6 −1.46926
\(431\) −3.49069e6 −0.905146 −0.452573 0.891727i \(-0.649494\pi\)
−0.452573 + 0.891727i \(0.649494\pi\)
\(432\) 186624. 0.0481125
\(433\) 608356. 0.155933 0.0779665 0.996956i \(-0.475157\pi\)
0.0779665 + 0.996956i \(0.475157\pi\)
\(434\) 1.16424e6 0.296700
\(435\) −3.86006e6 −0.978071
\(436\) −1.93758e6 −0.488140
\(437\) −664373. −0.166421
\(438\) −1.42060e6 −0.353822
\(439\) 3.43334e6 0.850267 0.425133 0.905131i \(-0.360227\pi\)
0.425133 + 0.905131i \(0.360227\pi\)
\(440\) −990144. −0.243819
\(441\) 194481. 0.0476190
\(442\) −588796. −0.143354
\(443\) −858506. −0.207842 −0.103921 0.994586i \(-0.533139\pi\)
−0.103921 + 0.994586i \(0.533139\pi\)
\(444\) 1.95019e6 0.469483
\(445\) −4.20439e6 −1.00647
\(446\) 3.44006e6 0.818895
\(447\) 1.34618e6 0.318666
\(448\) −200704. −0.0472456
\(449\) −4.88344e6 −1.14317 −0.571584 0.820543i \(-0.693671\pi\)
−0.571584 + 0.820543i \(0.693671\pi\)
\(450\) −1.11326e6 −0.259159
\(451\) 1.80762e6 0.418472
\(452\) 2.48298e6 0.571645
\(453\) 2.38114e6 0.545179
\(454\) 1.05756e6 0.240805
\(455\) 670761. 0.151894
\(456\) 275904. 0.0621364
\(457\) 2.72506e6 0.610360 0.305180 0.952295i \(-0.401283\pi\)
0.305180 + 0.952295i \(0.401283\pi\)
\(458\) 331416. 0.0738261
\(459\) −634959. −0.140674
\(460\) 1.79755e6 0.396084
\(461\) 3.36299e6 0.737009 0.368505 0.929626i \(-0.379870\pi\)
0.368505 + 0.929626i \(0.379870\pi\)
\(462\) 336924. 0.0734390
\(463\) −664525. −0.144065 −0.0720326 0.997402i \(-0.522949\pi\)
−0.0720326 + 0.997402i \(0.522949\pi\)
\(464\) −1.35552e6 −0.292288
\(465\) 4.33026e6 0.928713
\(466\) 2.35310e6 0.501968
\(467\) 1.92580e6 0.408620 0.204310 0.978906i \(-0.434505\pi\)
0.204310 + 0.978906i \(0.434505\pi\)
\(468\) −219024. −0.0462250
\(469\) 2.66335e6 0.559108
\(470\) 2.62829e6 0.548818
\(471\) 4.26486e6 0.885834
\(472\) −1.84218e6 −0.380606
\(473\) 3.32092e6 0.682504
\(474\) 3.43994e6 0.703243
\(475\) −1.64584e6 −0.334699
\(476\) 682864. 0.138139
\(477\) 1.46108e6 0.294020
\(478\) −6.72904e6 −1.34705
\(479\) 2.21923e6 0.441940 0.220970 0.975281i \(-0.429078\pi\)
0.220970 + 0.975281i \(0.429078\pi\)
\(480\) −746496. −0.147885
\(481\) −2.28877e6 −0.451065
\(482\) 1.05962e6 0.207747
\(483\) −611667. −0.119302
\(484\) −1.99312e6 −0.386741
\(485\) 1.31750e7 2.54329
\(486\) −236196. −0.0453609
\(487\) −4.73622e6 −0.904918 −0.452459 0.891785i \(-0.649453\pi\)
−0.452459 + 0.891785i \(0.649453\pi\)
\(488\) −945472. −0.179721
\(489\) 700794. 0.132531
\(490\) −777924. −0.146368
\(491\) −90374.0 −0.0169176 −0.00845882 0.999964i \(-0.502693\pi\)
−0.00845882 + 0.999964i \(0.502693\pi\)
\(492\) 1.36282e6 0.253819
\(493\) 4.61195e6 0.854608
\(494\) −323804. −0.0596987
\(495\) 1.25315e6 0.229874
\(496\) 1.52064e6 0.277538
\(497\) −3.16579e6 −0.574899
\(498\) 2.50682e6 0.452950
\(499\) 1.07570e7 1.93393 0.966964 0.254914i \(-0.0820473\pi\)
0.966964 + 0.254914i \(0.0820473\pi\)
\(500\) 403056. 0.0721008
\(501\) 2.02202e6 0.359908
\(502\) −7.66204e6 −1.35702
\(503\) 5.32408e6 0.938263 0.469132 0.883128i \(-0.344567\pi\)
0.469132 + 0.883128i \(0.344567\pi\)
\(504\) 254016. 0.0445435
\(505\) 2.43000e6 0.424012
\(506\) −1.05967e6 −0.183990
\(507\) 257049. 0.0444116
\(508\) −133664. −0.0229803
\(509\) 1.09148e6 0.186732 0.0933661 0.995632i \(-0.470237\pi\)
0.0933661 + 0.995632i \(0.470237\pi\)
\(510\) 2.53984e6 0.432395
\(511\) −1.93359e6 −0.327576
\(512\) −262144. −0.0441942
\(513\) −349191. −0.0585827
\(514\) −890936. −0.148744
\(515\) 2.15047e6 0.357285
\(516\) 2.50373e6 0.413964
\(517\) −1.54939e6 −0.254938
\(518\) 2.65443e6 0.434657
\(519\) −2.41943e6 −0.394271
\(520\) 876096. 0.142083
\(521\) −5.67635e6 −0.916167 −0.458084 0.888909i \(-0.651464\pi\)
−0.458084 + 0.888909i \(0.651464\pi\)
\(522\) 1.71558e6 0.275572
\(523\) 2.40814e6 0.384971 0.192486 0.981300i \(-0.438345\pi\)
0.192486 + 0.981300i \(0.438345\pi\)
\(524\) 5.31547e6 0.845695
\(525\) −1.51528e6 −0.239935
\(526\) −5.14686e6 −0.811107
\(527\) −5.17374e6 −0.811480
\(528\) 440064. 0.0686959
\(529\) −4.51257e6 −0.701108
\(530\) −5.84431e6 −0.903740
\(531\) 2.33150e6 0.358839
\(532\) 375536. 0.0575271
\(533\) −1.59942e6 −0.243862
\(534\) 1.86862e6 0.283574
\(535\) −6.21157e6 −0.938246
\(536\) 3.47866e6 0.522997
\(537\) 1.54001e6 0.230456
\(538\) 538664. 0.0802347
\(539\) 458591. 0.0679913
\(540\) 944784. 0.139427
\(541\) 3.90368e6 0.573432 0.286716 0.958016i \(-0.407436\pi\)
0.286716 + 0.958016i \(0.407436\pi\)
\(542\) −5.83668e6 −0.853430
\(543\) −5.79465e6 −0.843388
\(544\) 891904. 0.129217
\(545\) −9.80902e6 −1.41460
\(546\) −298116. −0.0427960
\(547\) 1.07447e7 1.53541 0.767707 0.640801i \(-0.221398\pi\)
0.767707 + 0.640801i \(0.221398\pi\)
\(548\) 1.28616e6 0.182955
\(549\) 1.19661e6 0.169443
\(550\) −2.62510e6 −0.370032
\(551\) 2.53630e6 0.355895
\(552\) −798912. −0.111597
\(553\) 4.68215e6 0.651077
\(554\) 4.47514e6 0.619488
\(555\) 9.87285e6 1.36054
\(556\) −2.12250e6 −0.291179
\(557\) 4.77566e6 0.652222 0.326111 0.945331i \(-0.394262\pi\)
0.326111 + 0.945331i \(0.394262\pi\)
\(558\) −1.92456e6 −0.261665
\(559\) −2.93840e6 −0.397724
\(560\) −1.01606e6 −0.136915
\(561\) −1.49725e6 −0.200857
\(562\) −8.59102e6 −1.14737
\(563\) −2.51090e6 −0.333855 −0.166927 0.985969i \(-0.553385\pi\)
−0.166927 + 0.985969i \(0.553385\pi\)
\(564\) −1.16813e6 −0.154630
\(565\) 1.25701e7 1.65660
\(566\) 8.53283e6 1.11957
\(567\) −321489. −0.0419961
\(568\) −4.13491e6 −0.537769
\(569\) 5.10788e6 0.661394 0.330697 0.943737i \(-0.392716\pi\)
0.330697 + 0.943737i \(0.392716\pi\)
\(570\) 1.39676e6 0.180068
\(571\) −4.53217e6 −0.581722 −0.290861 0.956765i \(-0.593942\pi\)
−0.290861 + 0.956765i \(0.593942\pi\)
\(572\) −516464. −0.0660009
\(573\) 3.51802e6 0.447622
\(574\) 1.85494e6 0.234991
\(575\) 4.76573e6 0.601118
\(576\) 331776. 0.0416667
\(577\) −8.72842e6 −1.09143 −0.545715 0.837971i \(-0.683742\pi\)
−0.545715 + 0.837971i \(0.683742\pi\)
\(578\) 2.64486e6 0.329294
\(579\) 4.56541e6 0.565957
\(580\) −6.86232e6 −0.847034
\(581\) 3.41207e6 0.419350
\(582\) −5.85554e6 −0.716572
\(583\) 3.44526e6 0.419808
\(584\) −2.52550e6 −0.306419
\(585\) −1.10881e6 −0.133958
\(586\) 4.82518e6 0.580456
\(587\) 1.38534e7 1.65944 0.829721 0.558178i \(-0.188500\pi\)
0.829721 + 0.558178i \(0.188500\pi\)
\(588\) 345744. 0.0412393
\(589\) −2.84526e6 −0.337935
\(590\) −9.32602e6 −1.10298
\(591\) −6.90480e6 −0.813172
\(592\) 3.46701e6 0.406584
\(593\) −2.52117e6 −0.294419 −0.147209 0.989105i \(-0.547029\pi\)
−0.147209 + 0.989105i \(0.547029\pi\)
\(594\) −556956. −0.0647671
\(595\) 3.45700e6 0.400320
\(596\) 2.39322e6 0.275973
\(597\) 4.28903e6 0.492519
\(598\) 937612. 0.107219
\(599\) −2.90068e6 −0.330318 −0.165159 0.986267i \(-0.552814\pi\)
−0.165159 + 0.986267i \(0.552814\pi\)
\(600\) −1.97914e6 −0.224439
\(601\) 2.15686e6 0.243577 0.121788 0.992556i \(-0.461137\pi\)
0.121788 + 0.992556i \(0.461137\pi\)
\(602\) 3.40785e6 0.383256
\(603\) −4.40267e6 −0.493087
\(604\) 4.23314e6 0.472139
\(605\) −1.00902e7 −1.12075
\(606\) −1.08000e6 −0.119465
\(607\) 5.21923e6 0.574956 0.287478 0.957787i \(-0.407183\pi\)
0.287478 + 0.957787i \(0.407183\pi\)
\(608\) 490496. 0.0538117
\(609\) 2.33510e6 0.255130
\(610\) −4.78645e6 −0.520822
\(611\) 1.37093e6 0.148563
\(612\) −1.12882e6 −0.121827
\(613\) −1.24585e7 −1.33911 −0.669555 0.742763i \(-0.733515\pi\)
−0.669555 + 0.742763i \(0.733515\pi\)
\(614\) 2.11789e6 0.226716
\(615\) 6.89926e6 0.735554
\(616\) 598976. 0.0636001
\(617\) 1.57862e7 1.66942 0.834711 0.550689i \(-0.185635\pi\)
0.834711 + 0.550689i \(0.185635\pi\)
\(618\) −955764. −0.100665
\(619\) −2.20272e6 −0.231064 −0.115532 0.993304i \(-0.536857\pi\)
−0.115532 + 0.993304i \(0.536857\pi\)
\(620\) 7.69824e6 0.804289
\(621\) 1.01112e6 0.105214
\(622\) −1.06788e7 −1.10674
\(623\) 2.54339e6 0.262539
\(624\) −389376. −0.0400320
\(625\) −8.69703e6 −0.890576
\(626\) 5.57438e6 0.568540
\(627\) −823401. −0.0836455
\(628\) 7.58197e6 0.767155
\(629\) −1.17960e7 −1.18879
\(630\) 1.28596e6 0.129085
\(631\) −6.26899e6 −0.626793 −0.313397 0.949622i \(-0.601467\pi\)
−0.313397 + 0.949622i \(0.601467\pi\)
\(632\) 6.11546e6 0.609026
\(633\) −857079. −0.0850181
\(634\) −3.85389e6 −0.380782
\(635\) −676674. −0.0665955
\(636\) 2.59747e6 0.254629
\(637\) −405769. −0.0396214
\(638\) 4.04538e6 0.393466
\(639\) 5.23325e6 0.507013
\(640\) −1.32710e6 −0.128072
\(641\) 1.21894e6 0.117176 0.0585879 0.998282i \(-0.481340\pi\)
0.0585879 + 0.998282i \(0.481340\pi\)
\(642\) 2.76070e6 0.264351
\(643\) −1.77027e7 −1.68854 −0.844272 0.535914i \(-0.819967\pi\)
−0.844272 + 0.535914i \(0.819967\pi\)
\(644\) −1.08741e6 −0.103318
\(645\) 1.26751e7 1.19965
\(646\) −1.66884e6 −0.157338
\(647\) −1.12733e7 −1.05875 −0.529373 0.848389i \(-0.677573\pi\)
−0.529373 + 0.848389i \(0.677573\pi\)
\(648\) −419904. −0.0392837
\(649\) 5.49774e6 0.512357
\(650\) 2.32274e6 0.215634
\(651\) −2.61954e6 −0.242255
\(652\) 1.24586e6 0.114775
\(653\) 1.08510e7 0.995837 0.497918 0.867224i \(-0.334098\pi\)
0.497918 + 0.867224i \(0.334098\pi\)
\(654\) 4.35956e6 0.398565
\(655\) 2.69096e7 2.45078
\(656\) 2.42278e6 0.219814
\(657\) 3.19634e6 0.288895
\(658\) −1.58995e6 −0.143159
\(659\) 3.02513e6 0.271351 0.135675 0.990753i \(-0.456680\pi\)
0.135675 + 0.990753i \(0.456680\pi\)
\(660\) 2.22782e6 0.199077
\(661\) 9.79315e6 0.871804 0.435902 0.899994i \(-0.356429\pi\)
0.435902 + 0.899994i \(0.356429\pi\)
\(662\) −1.01130e7 −0.896879
\(663\) 1.32479e6 0.117048
\(664\) 4.45658e6 0.392266
\(665\) 1.90115e6 0.166710
\(666\) −4.38793e6 −0.383331
\(667\) −7.34416e6 −0.639187
\(668\) 3.59470e6 0.311689
\(669\) −7.74013e6 −0.668625
\(670\) 1.76107e7 1.51562
\(671\) 2.82164e6 0.241933
\(672\) 451584. 0.0385758
\(673\) −1.03000e7 −0.876598 −0.438299 0.898829i \(-0.644419\pi\)
−0.438299 + 0.898829i \(0.644419\pi\)
\(674\) −1.95025e6 −0.165364
\(675\) 2.50484e6 0.211603
\(676\) 456976. 0.0384615
\(677\) 1.04319e7 0.874764 0.437382 0.899276i \(-0.355906\pi\)
0.437382 + 0.899276i \(0.355906\pi\)
\(678\) −5.58670e6 −0.466746
\(679\) −7.97005e6 −0.663417
\(680\) 4.51526e6 0.374465
\(681\) −2.37951e6 −0.196616
\(682\) −4.53816e6 −0.373610
\(683\) −4.91629e6 −0.403261 −0.201630 0.979462i \(-0.564624\pi\)
−0.201630 + 0.979462i \(0.564624\pi\)
\(684\) −620784. −0.0507341
\(685\) 6.51119e6 0.530193
\(686\) 470596. 0.0381802
\(687\) −745686. −0.0602787
\(688\) 4.45107e6 0.358504
\(689\) −3.04842e6 −0.244640
\(690\) −4.04449e6 −0.323401
\(691\) −9.03610e6 −0.719923 −0.359961 0.932967i \(-0.617210\pi\)
−0.359961 + 0.932967i \(0.617210\pi\)
\(692\) −4.30122e6 −0.341449
\(693\) −758079. −0.0599627
\(694\) −5.20595e6 −0.410300
\(695\) −1.07451e7 −0.843820
\(696\) 3.04992e6 0.238652
\(697\) −8.24314e6 −0.642704
\(698\) 1.21388e7 0.943052
\(699\) −5.29448e6 −0.409855
\(700\) −2.69382e6 −0.207790
\(701\) 4.72375e6 0.363071 0.181535 0.983384i \(-0.441893\pi\)
0.181535 + 0.983384i \(0.441893\pi\)
\(702\) 492804. 0.0377426
\(703\) −6.48710e6 −0.495065
\(704\) 782336. 0.0594924
\(705\) −5.91365e6 −0.448108
\(706\) 1.34176e7 1.01312
\(707\) −1.47000e6 −0.110603
\(708\) 4.14490e6 0.310764
\(709\) −1.57179e7 −1.17430 −0.587149 0.809479i \(-0.699750\pi\)
−0.587149 + 0.809479i \(0.699750\pi\)
\(710\) −2.09330e7 −1.55842
\(711\) −7.73987e6 −0.574196
\(712\) 3.32198e6 0.245583
\(713\) 8.23878e6 0.606931
\(714\) −1.53644e6 −0.112790
\(715\) −2.61460e6 −0.191267
\(716\) 2.73779e6 0.199580
\(717\) 1.51403e7 1.09986
\(718\) 8.62406e6 0.624311
\(719\) −2.20514e6 −0.159079 −0.0795396 0.996832i \(-0.525345\pi\)
−0.0795396 + 0.996832i \(0.525345\pi\)
\(720\) 1.67962e6 0.120748
\(721\) −1.30090e6 −0.0931979
\(722\) 8.98663e6 0.641585
\(723\) −2.38415e6 −0.169624
\(724\) −1.03016e7 −0.730396
\(725\) −1.81936e7 −1.28551
\(726\) 4.48452e6 0.315773
\(727\) 4.55650e6 0.319739 0.159869 0.987138i \(-0.448893\pi\)
0.159869 + 0.987138i \(0.448893\pi\)
\(728\) −529984. −0.0370625
\(729\) 531441. 0.0370370
\(730\) −1.27854e7 −0.887986
\(731\) −1.51441e7 −1.04821
\(732\) 2.12731e6 0.146742
\(733\) −6.91692e6 −0.475503 −0.237751 0.971326i \(-0.576410\pi\)
−0.237751 + 0.971326i \(0.576410\pi\)
\(734\) 1.08191e7 0.741225
\(735\) 1.75033e6 0.119509
\(736\) −1.42029e6 −0.0966456
\(737\) −1.03816e7 −0.704038
\(738\) −3.06634e6 −0.207243
\(739\) −1.69329e7 −1.14057 −0.570283 0.821448i \(-0.693166\pi\)
−0.570283 + 0.821448i \(0.693166\pi\)
\(740\) 1.75517e7 1.17826
\(741\) 728559. 0.0487438
\(742\) 3.53545e6 0.235741
\(743\) −1.65904e7 −1.10252 −0.551258 0.834335i \(-0.685852\pi\)
−0.551258 + 0.834335i \(0.685852\pi\)
\(744\) −3.42144e6 −0.226609
\(745\) 1.21157e7 0.799754
\(746\) 256992. 0.0169072
\(747\) −5.64035e6 −0.369832
\(748\) −2.66178e6 −0.173947
\(749\) 3.75761e6 0.244742
\(750\) −906876. −0.0588701
\(751\) 1.51165e7 0.978029 0.489014 0.872276i \(-0.337357\pi\)
0.489014 + 0.872276i \(0.337357\pi\)
\(752\) −2.07667e6 −0.133913
\(753\) 1.72396e7 1.10800
\(754\) −3.57942e6 −0.229290
\(755\) 2.14303e7 1.36823
\(756\) −571536. −0.0363696
\(757\) 1.61932e6 0.102705 0.0513526 0.998681i \(-0.483647\pi\)
0.0513526 + 0.998681i \(0.483647\pi\)
\(758\) 1.04957e7 0.663499
\(759\) 2.38425e6 0.150227
\(760\) 2.48314e6 0.155943
\(761\) 9.14101e6 0.572180 0.286090 0.958203i \(-0.407644\pi\)
0.286090 + 0.958203i \(0.407644\pi\)
\(762\) 300744. 0.0187633
\(763\) 5.93385e6 0.368999
\(764\) 6.25426e6 0.387652
\(765\) −5.71463e6 −0.353049
\(766\) 2.25075e7 1.38598
\(767\) −4.86450e6 −0.298572
\(768\) 589824. 0.0360844
\(769\) −2.63234e7 −1.60519 −0.802594 0.596525i \(-0.796548\pi\)
−0.802594 + 0.596525i \(0.796548\pi\)
\(770\) 3.03232e6 0.184309
\(771\) 2.00461e6 0.121449
\(772\) 8.11629e6 0.490133
\(773\) −2.59047e7 −1.55930 −0.779649 0.626216i \(-0.784603\pi\)
−0.779649 + 0.626216i \(0.784603\pi\)
\(774\) −5.63339e6 −0.338000
\(775\) 2.04098e7 1.22063
\(776\) −1.04099e7 −0.620569
\(777\) −5.97246e6 −0.354896
\(778\) 300040. 0.0177717
\(779\) −4.53326e6 −0.267650
\(780\) −1.97122e6 −0.116011
\(781\) 1.23401e7 0.723923
\(782\) 4.83231e6 0.282578
\(783\) −3.86006e6 −0.225003
\(784\) 614656. 0.0357143
\(785\) 3.83837e7 2.22317
\(786\) −1.19598e7 −0.690507
\(787\) 2.64728e7 1.52357 0.761785 0.647830i \(-0.224323\pi\)
0.761785 + 0.647830i \(0.224323\pi\)
\(788\) −1.22752e7 −0.704228
\(789\) 1.15804e7 0.662266
\(790\) 3.09595e7 1.76492
\(791\) −7.60411e6 −0.432123
\(792\) −990144. −0.0560900
\(793\) −2.49664e6 −0.140985
\(794\) 5.35834e6 0.301633
\(795\) 1.31497e7 0.737901
\(796\) 7.62494e6 0.426534
\(797\) −1.81480e7 −1.01200 −0.506002 0.862532i \(-0.668877\pi\)
−0.506002 + 0.862532i \(0.668877\pi\)
\(798\) −844956. −0.0469707
\(799\) 7.06555e6 0.391543
\(800\) −3.51846e6 −0.194370
\(801\) −4.20439e6 −0.231537
\(802\) 6.66009e6 0.365632
\(803\) 7.53705e6 0.412489
\(804\) −7.82698e6 −0.427026
\(805\) −5.50500e6 −0.299411
\(806\) 4.01544e6 0.217719
\(807\) −1.21199e6 −0.0655114
\(808\) −1.92000e6 −0.103460
\(809\) 8.58811e6 0.461346 0.230673 0.973031i \(-0.425907\pi\)
0.230673 + 0.973031i \(0.425907\pi\)
\(810\) −2.12576e6 −0.113842
\(811\) −2.36211e6 −0.126109 −0.0630547 0.998010i \(-0.520084\pi\)
−0.0630547 + 0.998010i \(0.520084\pi\)
\(812\) 4.15128e6 0.220949
\(813\) 1.31325e7 0.696822
\(814\) −1.03469e7 −0.547327
\(815\) 6.30715e6 0.332613
\(816\) −2.00678e6 −0.105506
\(817\) −8.32837e6 −0.436521
\(818\) −6.36566e6 −0.332629
\(819\) 670761. 0.0349428
\(820\) 1.22653e7 0.637008
\(821\) −3.01415e7 −1.56066 −0.780329 0.625370i \(-0.784948\pi\)
−0.780329 + 0.625370i \(0.784948\pi\)
\(822\) −2.89386e6 −0.149382
\(823\) −2.85577e7 −1.46968 −0.734841 0.678239i \(-0.762743\pi\)
−0.734841 + 0.678239i \(0.762743\pi\)
\(824\) −1.69914e6 −0.0871786
\(825\) 5.90648e6 0.302130
\(826\) 5.64166e6 0.287711
\(827\) −1.20087e7 −0.610568 −0.305284 0.952261i \(-0.598751\pi\)
−0.305284 + 0.952261i \(0.598751\pi\)
\(828\) 1.79755e6 0.0911183
\(829\) 4.34077e6 0.219372 0.109686 0.993966i \(-0.465016\pi\)
0.109686 + 0.993966i \(0.465016\pi\)
\(830\) 2.25614e7 1.13677
\(831\) −1.00691e7 −0.505809
\(832\) −692224. −0.0346688
\(833\) −2.09127e6 −0.104423
\(834\) 4.77562e6 0.237747
\(835\) 1.81982e7 0.903258
\(836\) −1.46382e6 −0.0724391
\(837\) 4.33026e6 0.213649
\(838\) 9.57352e6 0.470936
\(839\) −3.99079e7 −1.95728 −0.978642 0.205572i \(-0.934095\pi\)
−0.978642 + 0.205572i \(0.934095\pi\)
\(840\) 2.28614e6 0.111791
\(841\) 7.52588e6 0.366916
\(842\) 1.86898e7 0.908497
\(843\) 1.93298e7 0.936824
\(844\) −1.52370e6 −0.0736279
\(845\) 2.31344e6 0.111459
\(846\) 2.62829e6 0.126255
\(847\) 6.10393e6 0.292349
\(848\) 4.61773e6 0.220515
\(849\) −1.91989e7 −0.914127
\(850\) 1.19710e7 0.568308
\(851\) 1.87841e7 0.889134
\(852\) 9.30355e6 0.439086
\(853\) −1.62889e7 −0.766510 −0.383255 0.923643i \(-0.625197\pi\)
−0.383255 + 0.923643i \(0.625197\pi\)
\(854\) 2.89551e6 0.135856
\(855\) −3.14272e6 −0.147025
\(856\) 4.90790e6 0.228935
\(857\) −3.50248e7 −1.62901 −0.814504 0.580158i \(-0.802991\pi\)
−0.814504 + 0.580158i \(0.802991\pi\)
\(858\) 1.16204e6 0.0538895
\(859\) 1.56483e7 0.723576 0.361788 0.932260i \(-0.382166\pi\)
0.361788 + 0.932260i \(0.382166\pi\)
\(860\) 2.25336e7 1.03892
\(861\) −4.17362e6 −0.191869
\(862\) 1.39628e7 0.640035
\(863\) 2.17260e7 0.993007 0.496504 0.868035i \(-0.334617\pi\)
0.496504 + 0.868035i \(0.334617\pi\)
\(864\) −746496. −0.0340207
\(865\) −2.17749e7 −0.989501
\(866\) −2.43342e6 −0.110261
\(867\) −5.95094e6 −0.268867
\(868\) −4.65696e6 −0.209799
\(869\) −1.82508e7 −0.819847
\(870\) 1.54402e7 0.691601
\(871\) 9.18583e6 0.410273
\(872\) 7.75034e6 0.345167
\(873\) 1.31750e7 0.585079
\(874\) 2.65749e6 0.117677
\(875\) −1.23436e6 −0.0545031
\(876\) 5.68238e6 0.250190
\(877\) −2.54991e7 −1.11951 −0.559753 0.828660i \(-0.689104\pi\)
−0.559753 + 0.828660i \(0.689104\pi\)
\(878\) −1.37333e7 −0.601229
\(879\) −1.08566e7 −0.473940
\(880\) 3.96058e6 0.172406
\(881\) −2.16980e6 −0.0941846 −0.0470923 0.998891i \(-0.514995\pi\)
−0.0470923 + 0.998891i \(0.514995\pi\)
\(882\) −777924. −0.0336718
\(883\) 2.38447e7 1.02918 0.514589 0.857437i \(-0.327945\pi\)
0.514589 + 0.857437i \(0.327945\pi\)
\(884\) 2.35518e6 0.101366
\(885\) 2.09835e7 0.900576
\(886\) 3.43402e6 0.146967
\(887\) 3.48915e7 1.48905 0.744526 0.667593i \(-0.232675\pi\)
0.744526 + 0.667593i \(0.232675\pi\)
\(888\) −7.80077e6 −0.331975
\(889\) 409346. 0.0173715
\(890\) 1.68175e7 0.711685
\(891\) 1.25315e6 0.0528822
\(892\) −1.37602e7 −0.579046
\(893\) 3.88565e6 0.163055
\(894\) −5.38474e6 −0.225331
\(895\) 1.38601e7 0.578373
\(896\) 802816. 0.0334077
\(897\) −2.10963e6 −0.0875436
\(898\) 1.95338e7 0.808342
\(899\) −3.14523e7 −1.29794
\(900\) 4.45306e6 0.183253
\(901\) −1.57111e7 −0.644755
\(902\) −7.23050e6 −0.295905
\(903\) −7.66767e6 −0.312928
\(904\) −9.93190e6 −0.404214
\(905\) −5.21519e7 −2.11665
\(906\) −9.52456e6 −0.385500
\(907\) −2.41854e6 −0.0976192 −0.0488096 0.998808i \(-0.515543\pi\)
−0.0488096 + 0.998808i \(0.515543\pi\)
\(908\) −4.23024e6 −0.170275
\(909\) 2.43000e6 0.0975431
\(910\) −2.68304e6 −0.107405
\(911\) 4.40197e7 1.75732 0.878660 0.477447i \(-0.158438\pi\)
0.878660 + 0.477447i \(0.158438\pi\)
\(912\) −1.10362e6 −0.0439370
\(913\) −1.33001e7 −0.528053
\(914\) −1.09003e7 −0.431590
\(915\) 1.07695e7 0.425249
\(916\) −1.32566e6 −0.0522029
\(917\) −1.62786e7 −0.639285
\(918\) 2.53984e6 0.0994716
\(919\) −1.56948e7 −0.613010 −0.306505 0.951869i \(-0.599160\pi\)
−0.306505 + 0.951869i \(0.599160\pi\)
\(920\) −7.19021e6 −0.280073
\(921\) −4.76525e6 −0.185113
\(922\) −1.34519e7 −0.521144
\(923\) −1.09188e7 −0.421860
\(924\) −1.34770e6 −0.0519292
\(925\) 4.65337e7 1.78819
\(926\) 2.65810e6 0.101869
\(927\) 2.15047e6 0.0821928
\(928\) 5.42208e6 0.206679
\(929\) −2.00533e7 −0.762337 −0.381169 0.924505i \(-0.624478\pi\)
−0.381169 + 0.924505i \(0.624478\pi\)
\(930\) −1.73210e7 −0.656699
\(931\) −1.15008e6 −0.0434864
\(932\) −9.41242e6 −0.354945
\(933\) 2.40273e7 0.903651
\(934\) −7.70322e6 −0.288938
\(935\) −1.34752e7 −0.504089
\(936\) 876096. 0.0326860
\(937\) −2.98075e7 −1.10912 −0.554558 0.832145i \(-0.687113\pi\)
−0.554558 + 0.832145i \(0.687113\pi\)
\(938\) −1.06534e7 −0.395349
\(939\) −1.25424e7 −0.464211
\(940\) −1.05132e7 −0.388073
\(941\) −3.46281e7 −1.27484 −0.637418 0.770518i \(-0.719998\pi\)
−0.637418 + 0.770518i \(0.719998\pi\)
\(942\) −1.70594e7 −0.626379
\(943\) 1.31266e7 0.480698
\(944\) 7.36870e6 0.269129
\(945\) −2.89340e6 −0.105397
\(946\) −1.32837e7 −0.482603
\(947\) −4.31021e7 −1.56179 −0.780897 0.624660i \(-0.785238\pi\)
−0.780897 + 0.624660i \(0.785238\pi\)
\(948\) −1.37598e7 −0.497268
\(949\) −6.66891e6 −0.240375
\(950\) 6.58338e6 0.236668
\(951\) 8.67125e6 0.310907
\(952\) −2.73146e6 −0.0976791
\(953\) −9.55352e6 −0.340746 −0.170373 0.985380i \(-0.554497\pi\)
−0.170373 + 0.985380i \(0.554497\pi\)
\(954\) −5.84431e6 −0.207904
\(955\) 3.16622e7 1.12339
\(956\) 2.69162e7 0.952507
\(957\) −9.10210e6 −0.321264
\(958\) −8.87692e6 −0.312499
\(959\) −3.93886e6 −0.138301
\(960\) 2.98598e6 0.104571
\(961\) 6.65445e6 0.232436
\(962\) 9.15507e6 0.318951
\(963\) −6.21157e6 −0.215842
\(964\) −4.23850e6 −0.146899
\(965\) 4.10887e7 1.42038
\(966\) 2.44667e6 0.0843592
\(967\) 3.22474e7 1.10899 0.554496 0.832186i \(-0.312911\pi\)
0.554496 + 0.832186i \(0.312911\pi\)
\(968\) 7.97248e6 0.273467
\(969\) 3.75488e6 0.128466
\(970\) −5.26999e7 −1.79838
\(971\) 4.83425e7 1.64544 0.822718 0.568450i \(-0.192457\pi\)
0.822718 + 0.568450i \(0.192457\pi\)
\(972\) 944784. 0.0320750
\(973\) 6.50014e6 0.220111
\(974\) 1.89449e7 0.639873
\(975\) −5.22616e6 −0.176064
\(976\) 3.78189e6 0.127082
\(977\) 1.13176e7 0.379332 0.189666 0.981849i \(-0.439259\pi\)
0.189666 + 0.981849i \(0.439259\pi\)
\(978\) −2.80318e6 −0.0937137
\(979\) −9.91405e6 −0.330593
\(980\) 3.11170e6 0.103498
\(981\) −9.80902e6 −0.325427
\(982\) 361496. 0.0119626
\(983\) 9.69274e6 0.319936 0.159968 0.987122i \(-0.448861\pi\)
0.159968 + 0.987122i \(0.448861\pi\)
\(984\) −5.45126e6 −0.179477
\(985\) −6.21432e7 −2.04081
\(986\) −1.84478e7 −0.604299
\(987\) 3.57739e6 0.116889
\(988\) 1.29522e6 0.0422134
\(989\) 2.41158e7 0.783990
\(990\) −5.01260e6 −0.162546
\(991\) −4.74954e7 −1.53627 −0.768135 0.640287i \(-0.778815\pi\)
−0.768135 + 0.640287i \(0.778815\pi\)
\(992\) −6.08256e6 −0.196249
\(993\) 2.27542e7 0.732298
\(994\) 1.26632e7 0.406515
\(995\) 3.86013e7 1.23607
\(996\) −1.00273e7 −0.320284
\(997\) 2.40841e7 0.767349 0.383675 0.923468i \(-0.374658\pi\)
0.383675 + 0.923468i \(0.374658\pi\)
\(998\) −4.30280e7 −1.36749
\(999\) 9.87285e6 0.312989
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.6.a.a.1.1 1 1.1 even 1 trivial