Properties

Label 495.6.a.c.1.2
Level $495$
Weight $6$
Character 495.1
Self dual yes
Analytic conductor $79.390$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(79.3899908074\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.788.1
Defining polynomial: \( x^{3} - x^{2} - 7x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.35386\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.08127 q^{2} -30.8308 q^{4} -25.0000 q^{5} -139.508 q^{7} +67.9374 q^{8} +O(q^{10})\) \(q-1.08127 q^{2} -30.8308 q^{4} -25.0000 q^{5} -139.508 q^{7} +67.9374 q^{8} +27.0319 q^{10} +121.000 q^{11} -646.331 q^{13} +150.846 q^{14} +913.128 q^{16} +1378.32 q^{17} +1908.90 q^{19} +770.771 q^{20} -130.834 q^{22} -343.726 q^{23} +625.000 q^{25} +698.861 q^{26} +4301.15 q^{28} -53.5092 q^{29} +634.133 q^{31} -3161.34 q^{32} -1490.34 q^{34} +3487.70 q^{35} +11674.2 q^{37} -2064.04 q^{38} -1698.43 q^{40} -18866.5 q^{41} +13379.3 q^{43} -3730.53 q^{44} +371.662 q^{46} +2252.95 q^{47} +2655.48 q^{49} -675.796 q^{50} +19926.9 q^{52} +8900.71 q^{53} -3025.00 q^{55} -9477.80 q^{56} +57.8581 q^{58} +11276.7 q^{59} +11852.4 q^{61} -685.672 q^{62} -25801.8 q^{64} +16158.3 q^{65} -57333.6 q^{67} -42494.7 q^{68} -3771.16 q^{70} -31075.8 q^{71} +56010.8 q^{73} -12623.0 q^{74} -58853.0 q^{76} -16880.5 q^{77} -883.036 q^{79} -22828.2 q^{80} +20399.9 q^{82} -93986.3 q^{83} -34457.9 q^{85} -14466.7 q^{86} +8220.42 q^{88} -21739.9 q^{89} +90168.4 q^{91} +10597.4 q^{92} -2436.06 q^{94} -47722.5 q^{95} -158059. q^{97} -2871.30 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{2} - 20 q^{4} - 75 q^{5} + 152 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{2} - 20 q^{4} - 75 q^{5} + 152 q^{7} + 24 q^{8} + 50 q^{10} + 363 q^{11} - 546 q^{13} + 8 q^{14} - 1360 q^{16} + 314 q^{17} + 1808 q^{19} + 500 q^{20} - 242 q^{22} - 4288 q^{23} + 1875 q^{25} - 812 q^{26} + 5888 q^{28} - 5582 q^{29} + 6328 q^{31} + 736 q^{32} + 11596 q^{34} - 3800 q^{35} + 16866 q^{37} - 9584 q^{38} - 600 q^{40} - 23282 q^{41} + 20572 q^{43} - 2420 q^{44} + 16592 q^{46} - 3432 q^{47} + 11531 q^{49} - 1250 q^{50} + 21816 q^{52} - 16138 q^{53} - 9075 q^{55} - 15648 q^{56} + 17460 q^{58} - 21972 q^{59} + 8322 q^{61} - 5056 q^{62} + 22208 q^{64} + 13650 q^{65} - 84332 q^{67} - 59832 q^{68} - 200 q^{70} - 50528 q^{71} - 53838 q^{73} - 79212 q^{74} - 52448 q^{76} + 18392 q^{77} + 6364 q^{79} + 34000 q^{80} - 68020 q^{82} - 96272 q^{83} - 7850 q^{85} - 143152 q^{86} + 2904 q^{88} + 38938 q^{89} + 104968 q^{91} - 24000 q^{92} + 49088 q^{94} - 45200 q^{95} - 103242 q^{97} - 9554 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08127 −0.191144 −0.0955720 0.995423i \(-0.530468\pi\)
−0.0955720 + 0.995423i \(0.530468\pi\)
\(3\) 0 0
\(4\) −30.8308 −0.963464
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −139.508 −1.07610 −0.538052 0.842912i \(-0.680839\pi\)
−0.538052 + 0.842912i \(0.680839\pi\)
\(8\) 67.9374 0.375304
\(9\) 0 0
\(10\) 27.0319 0.0854822
\(11\) 121.000 0.301511
\(12\) 0 0
\(13\) −646.331 −1.06071 −0.530355 0.847776i \(-0.677941\pi\)
−0.530355 + 0.847776i \(0.677941\pi\)
\(14\) 150.846 0.205691
\(15\) 0 0
\(16\) 913.128 0.891727
\(17\) 1378.32 1.15672 0.578358 0.815783i \(-0.303694\pi\)
0.578358 + 0.815783i \(0.303694\pi\)
\(18\) 0 0
\(19\) 1908.90 1.21311 0.606553 0.795043i \(-0.292552\pi\)
0.606553 + 0.795043i \(0.292552\pi\)
\(20\) 770.771 0.430874
\(21\) 0 0
\(22\) −130.834 −0.0576321
\(23\) −343.726 −0.135485 −0.0677427 0.997703i \(-0.521580\pi\)
−0.0677427 + 0.997703i \(0.521580\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 698.861 0.202748
\(27\) 0 0
\(28\) 4301.15 1.03679
\(29\) −53.5092 −0.0118150 −0.00590750 0.999983i \(-0.501880\pi\)
−0.00590750 + 0.999983i \(0.501880\pi\)
\(30\) 0 0
\(31\) 634.133 0.118516 0.0592579 0.998243i \(-0.481127\pi\)
0.0592579 + 0.998243i \(0.481127\pi\)
\(32\) −3161.34 −0.545753
\(33\) 0 0
\(34\) −1490.34 −0.221099
\(35\) 3487.70 0.481248
\(36\) 0 0
\(37\) 11674.2 1.40192 0.700960 0.713201i \(-0.252755\pi\)
0.700960 + 0.713201i \(0.252755\pi\)
\(38\) −2064.04 −0.231878
\(39\) 0 0
\(40\) −1698.43 −0.167841
\(41\) −18866.5 −1.75280 −0.876399 0.481585i \(-0.840061\pi\)
−0.876399 + 0.481585i \(0.840061\pi\)
\(42\) 0 0
\(43\) 13379.3 1.10347 0.551736 0.834018i \(-0.313965\pi\)
0.551736 + 0.834018i \(0.313965\pi\)
\(44\) −3730.53 −0.290495
\(45\) 0 0
\(46\) 371.662 0.0258972
\(47\) 2252.95 0.148767 0.0743835 0.997230i \(-0.476301\pi\)
0.0743835 + 0.997230i \(0.476301\pi\)
\(48\) 0 0
\(49\) 2655.48 0.157998
\(50\) −675.796 −0.0382288
\(51\) 0 0
\(52\) 19926.9 1.02196
\(53\) 8900.71 0.435246 0.217623 0.976033i \(-0.430170\pi\)
0.217623 + 0.976033i \(0.430170\pi\)
\(54\) 0 0
\(55\) −3025.00 −0.134840
\(56\) −9477.80 −0.403866
\(57\) 0 0
\(58\) 57.8581 0.00225837
\(59\) 11276.7 0.421746 0.210873 0.977514i \(-0.432369\pi\)
0.210873 + 0.977514i \(0.432369\pi\)
\(60\) 0 0
\(61\) 11852.4 0.407834 0.203917 0.978988i \(-0.434633\pi\)
0.203917 + 0.978988i \(0.434633\pi\)
\(62\) −685.672 −0.0226536
\(63\) 0 0
\(64\) −25801.8 −0.787409
\(65\) 16158.3 0.474364
\(66\) 0 0
\(67\) −57333.6 −1.56035 −0.780175 0.625561i \(-0.784870\pi\)
−0.780175 + 0.625561i \(0.784870\pi\)
\(68\) −42494.7 −1.11445
\(69\) 0 0
\(70\) −3771.16 −0.0919877
\(71\) −31075.8 −0.731605 −0.365803 0.930692i \(-0.619206\pi\)
−0.365803 + 0.930692i \(0.619206\pi\)
\(72\) 0 0
\(73\) 56010.8 1.23017 0.615084 0.788462i \(-0.289122\pi\)
0.615084 + 0.788462i \(0.289122\pi\)
\(74\) −12623.0 −0.267969
\(75\) 0 0
\(76\) −58853.0 −1.16878
\(77\) −16880.5 −0.324457
\(78\) 0 0
\(79\) −883.036 −0.0159188 −0.00795941 0.999968i \(-0.502534\pi\)
−0.00795941 + 0.999968i \(0.502534\pi\)
\(80\) −22828.2 −0.398792
\(81\) 0 0
\(82\) 20399.9 0.335037
\(83\) −93986.3 −1.49751 −0.748754 0.662848i \(-0.769348\pi\)
−0.748754 + 0.662848i \(0.769348\pi\)
\(84\) 0 0
\(85\) −34457.9 −0.517299
\(86\) −14466.7 −0.210922
\(87\) 0 0
\(88\) 8220.42 0.113159
\(89\) −21739.9 −0.290926 −0.145463 0.989364i \(-0.546467\pi\)
−0.145463 + 0.989364i \(0.546467\pi\)
\(90\) 0 0
\(91\) 90168.4 1.14143
\(92\) 10597.4 0.130535
\(93\) 0 0
\(94\) −2436.06 −0.0284359
\(95\) −47722.5 −0.542518
\(96\) 0 0
\(97\) −158059. −1.70565 −0.852825 0.522197i \(-0.825112\pi\)
−0.852825 + 0.522197i \(0.825112\pi\)
\(98\) −2871.30 −0.0302004
\(99\) 0 0
\(100\) −19269.3 −0.192693
\(101\) 156968. 1.53111 0.765556 0.643369i \(-0.222464\pi\)
0.765556 + 0.643369i \(0.222464\pi\)
\(102\) 0 0
\(103\) 169126. 1.57078 0.785391 0.618999i \(-0.212462\pi\)
0.785391 + 0.618999i \(0.212462\pi\)
\(104\) −43910.0 −0.398089
\(105\) 0 0
\(106\) −9624.11 −0.0831948
\(107\) 13538.5 0.114317 0.0571587 0.998365i \(-0.481796\pi\)
0.0571587 + 0.998365i \(0.481796\pi\)
\(108\) 0 0
\(109\) −74736.4 −0.602513 −0.301256 0.953543i \(-0.597406\pi\)
−0.301256 + 0.953543i \(0.597406\pi\)
\(110\) 3270.85 0.0257739
\(111\) 0 0
\(112\) −127389. −0.959590
\(113\) 205914. 1.51701 0.758507 0.651665i \(-0.225929\pi\)
0.758507 + 0.651665i \(0.225929\pi\)
\(114\) 0 0
\(115\) 8593.15 0.0605909
\(116\) 1649.73 0.0113833
\(117\) 0 0
\(118\) −12193.2 −0.0806142
\(119\) −192286. −1.24475
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) −12815.7 −0.0779550
\(123\) 0 0
\(124\) −19550.9 −0.114186
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −214682. −1.18110 −0.590550 0.807001i \(-0.701089\pi\)
−0.590550 + 0.807001i \(0.701089\pi\)
\(128\) 129062. 0.696261
\(129\) 0 0
\(130\) −17471.5 −0.0906719
\(131\) −253067. −1.28842 −0.644209 0.764849i \(-0.722813\pi\)
−0.644209 + 0.764849i \(0.722813\pi\)
\(132\) 0 0
\(133\) −266307. −1.30543
\(134\) 61993.3 0.298252
\(135\) 0 0
\(136\) 93639.2 0.434121
\(137\) −239398. −1.08973 −0.544865 0.838524i \(-0.683419\pi\)
−0.544865 + 0.838524i \(0.683419\pi\)
\(138\) 0 0
\(139\) −166398. −0.730484 −0.365242 0.930913i \(-0.619014\pi\)
−0.365242 + 0.930913i \(0.619014\pi\)
\(140\) −107529. −0.463665
\(141\) 0 0
\(142\) 33601.5 0.139842
\(143\) −78206.1 −0.319816
\(144\) 0 0
\(145\) 1337.73 0.00528383
\(146\) −60563.0 −0.235139
\(147\) 0 0
\(148\) −359926. −1.35070
\(149\) −295512. −1.09046 −0.545229 0.838287i \(-0.683557\pi\)
−0.545229 + 0.838287i \(0.683557\pi\)
\(150\) 0 0
\(151\) 428373. 1.52890 0.764452 0.644681i \(-0.223010\pi\)
0.764452 + 0.644681i \(0.223010\pi\)
\(152\) 129686. 0.455284
\(153\) 0 0
\(154\) 18252.4 0.0620181
\(155\) −15853.3 −0.0530019
\(156\) 0 0
\(157\) −289003. −0.935735 −0.467867 0.883799i \(-0.654978\pi\)
−0.467867 + 0.883799i \(0.654978\pi\)
\(158\) 954.804 0.00304279
\(159\) 0 0
\(160\) 79033.4 0.244068
\(161\) 47952.5 0.145796
\(162\) 0 0
\(163\) 288223. 0.849688 0.424844 0.905267i \(-0.360329\pi\)
0.424844 + 0.905267i \(0.360329\pi\)
\(164\) 581671. 1.68876
\(165\) 0 0
\(166\) 101625. 0.286240
\(167\) 180912. 0.501969 0.250985 0.967991i \(-0.419246\pi\)
0.250985 + 0.967991i \(0.419246\pi\)
\(168\) 0 0
\(169\) 46451.1 0.125106
\(170\) 37258.5 0.0988787
\(171\) 0 0
\(172\) −412495. −1.06316
\(173\) −218579. −0.555255 −0.277628 0.960689i \(-0.589548\pi\)
−0.277628 + 0.960689i \(0.589548\pi\)
\(174\) 0 0
\(175\) −87192.5 −0.215221
\(176\) 110489. 0.268866
\(177\) 0 0
\(178\) 23506.8 0.0556089
\(179\) −310916. −0.725287 −0.362643 0.931928i \(-0.618126\pi\)
−0.362643 + 0.931928i \(0.618126\pi\)
\(180\) 0 0
\(181\) −423637. −0.961163 −0.480582 0.876950i \(-0.659574\pi\)
−0.480582 + 0.876950i \(0.659574\pi\)
\(182\) −97496.7 −0.218178
\(183\) 0 0
\(184\) −23351.8 −0.0508483
\(185\) −291855. −0.626957
\(186\) 0 0
\(187\) 166776. 0.348763
\(188\) −69460.3 −0.143332
\(189\) 0 0
\(190\) 51601.1 0.103699
\(191\) −861089. −1.70791 −0.853954 0.520348i \(-0.825802\pi\)
−0.853954 + 0.520348i \(0.825802\pi\)
\(192\) 0 0
\(193\) 430583. 0.832077 0.416038 0.909347i \(-0.363418\pi\)
0.416038 + 0.909347i \(0.363418\pi\)
\(194\) 170905. 0.326025
\(195\) 0 0
\(196\) −81870.6 −0.152226
\(197\) 184755. 0.339181 0.169590 0.985515i \(-0.445756\pi\)
0.169590 + 0.985515i \(0.445756\pi\)
\(198\) 0 0
\(199\) 322993. 0.578177 0.289089 0.957302i \(-0.406648\pi\)
0.289089 + 0.957302i \(0.406648\pi\)
\(200\) 42460.9 0.0750609
\(201\) 0 0
\(202\) −169725. −0.292663
\(203\) 7464.96 0.0127142
\(204\) 0 0
\(205\) 471663. 0.783875
\(206\) −182871. −0.300246
\(207\) 0 0
\(208\) −590183. −0.945864
\(209\) 230977. 0.365765
\(210\) 0 0
\(211\) −394106. −0.609406 −0.304703 0.952447i \(-0.598557\pi\)
−0.304703 + 0.952447i \(0.598557\pi\)
\(212\) −274417. −0.419344
\(213\) 0 0
\(214\) −14638.9 −0.0218511
\(215\) −334482. −0.493488
\(216\) 0 0
\(217\) −88466.6 −0.127535
\(218\) 80810.6 0.115167
\(219\) 0 0
\(220\) 93263.3 0.129913
\(221\) −890849. −1.22694
\(222\) 0 0
\(223\) 445038. 0.599287 0.299643 0.954051i \(-0.403132\pi\)
0.299643 + 0.954051i \(0.403132\pi\)
\(224\) 441032. 0.587286
\(225\) 0 0
\(226\) −222649. −0.289968
\(227\) −1.15887e6 −1.49270 −0.746349 0.665555i \(-0.768195\pi\)
−0.746349 + 0.665555i \(0.768195\pi\)
\(228\) 0 0
\(229\) 885853. 1.11628 0.558140 0.829747i \(-0.311515\pi\)
0.558140 + 0.829747i \(0.311515\pi\)
\(230\) −9291.55 −0.0115816
\(231\) 0 0
\(232\) −3635.27 −0.00443422
\(233\) −750392. −0.905520 −0.452760 0.891632i \(-0.649561\pi\)
−0.452760 + 0.891632i \(0.649561\pi\)
\(234\) 0 0
\(235\) −56323.7 −0.0665306
\(236\) −347669. −0.406337
\(237\) 0 0
\(238\) 207914. 0.237926
\(239\) −617415. −0.699169 −0.349585 0.936905i \(-0.613677\pi\)
−0.349585 + 0.936905i \(0.613677\pi\)
\(240\) 0 0
\(241\) 1.20275e6 1.33393 0.666966 0.745088i \(-0.267593\pi\)
0.666966 + 0.745088i \(0.267593\pi\)
\(242\) −15830.9 −0.0173767
\(243\) 0 0
\(244\) −365421. −0.392933
\(245\) −66386.9 −0.0706589
\(246\) 0 0
\(247\) −1.23378e6 −1.28675
\(248\) 43081.3 0.0444795
\(249\) 0 0
\(250\) 16894.9 0.0170964
\(251\) −1.55775e6 −1.56068 −0.780338 0.625358i \(-0.784953\pi\)
−0.780338 + 0.625358i \(0.784953\pi\)
\(252\) 0 0
\(253\) −41590.8 −0.0408504
\(254\) 232130. 0.225760
\(255\) 0 0
\(256\) 686107. 0.654323
\(257\) −92156.0 −0.0870344 −0.0435172 0.999053i \(-0.513856\pi\)
−0.0435172 + 0.999053i \(0.513856\pi\)
\(258\) 0 0
\(259\) −1.62865e6 −1.50861
\(260\) −498173. −0.457033
\(261\) 0 0
\(262\) 273635. 0.246274
\(263\) 862122. 0.768563 0.384281 0.923216i \(-0.374449\pi\)
0.384281 + 0.923216i \(0.374449\pi\)
\(264\) 0 0
\(265\) −222518. −0.194648
\(266\) 287950. 0.249525
\(267\) 0 0
\(268\) 1.76764e6 1.50334
\(269\) 1.25052e6 1.05368 0.526841 0.849964i \(-0.323376\pi\)
0.526841 + 0.849964i \(0.323376\pi\)
\(270\) 0 0
\(271\) 844654. 0.698644 0.349322 0.937003i \(-0.386412\pi\)
0.349322 + 0.937003i \(0.386412\pi\)
\(272\) 1.25858e6 1.03147
\(273\) 0 0
\(274\) 258855. 0.208295
\(275\) 75625.0 0.0603023
\(276\) 0 0
\(277\) −1.52990e6 −1.19802 −0.599008 0.800743i \(-0.704438\pi\)
−0.599008 + 0.800743i \(0.704438\pi\)
\(278\) 179922. 0.139628
\(279\) 0 0
\(280\) 236945. 0.180615
\(281\) −1.13284e6 −0.855858 −0.427929 0.903812i \(-0.640757\pi\)
−0.427929 + 0.903812i \(0.640757\pi\)
\(282\) 0 0
\(283\) −411138. −0.305156 −0.152578 0.988291i \(-0.548758\pi\)
−0.152578 + 0.988291i \(0.548758\pi\)
\(284\) 958094. 0.704875
\(285\) 0 0
\(286\) 84562.2 0.0611310
\(287\) 2.63203e6 1.88619
\(288\) 0 0
\(289\) 479901. 0.337993
\(290\) −1446.45 −0.00100997
\(291\) 0 0
\(292\) −1.72686e6 −1.18522
\(293\) −314013. −0.213687 −0.106843 0.994276i \(-0.534074\pi\)
−0.106843 + 0.994276i \(0.534074\pi\)
\(294\) 0 0
\(295\) −281917. −0.188610
\(296\) 793115. 0.526147
\(297\) 0 0
\(298\) 319529. 0.208435
\(299\) 222161. 0.143711
\(300\) 0 0
\(301\) −1.86652e6 −1.18745
\(302\) −463189. −0.292241
\(303\) 0 0
\(304\) 1.74307e6 1.08176
\(305\) −296311. −0.182389
\(306\) 0 0
\(307\) 797600. 0.482991 0.241496 0.970402i \(-0.422362\pi\)
0.241496 + 0.970402i \(0.422362\pi\)
\(308\) 520439. 0.312603
\(309\) 0 0
\(310\) 17141.8 0.0101310
\(311\) 618368. 0.362532 0.181266 0.983434i \(-0.441980\pi\)
0.181266 + 0.983434i \(0.441980\pi\)
\(312\) 0 0
\(313\) −2.60175e6 −1.50108 −0.750541 0.660824i \(-0.770207\pi\)
−0.750541 + 0.660824i \(0.770207\pi\)
\(314\) 312491. 0.178860
\(315\) 0 0
\(316\) 27224.7 0.0153372
\(317\) 729701. 0.407846 0.203923 0.978987i \(-0.434631\pi\)
0.203923 + 0.978987i \(0.434631\pi\)
\(318\) 0 0
\(319\) −6474.61 −0.00356235
\(320\) 645046. 0.352140
\(321\) 0 0
\(322\) −51849.8 −0.0278681
\(323\) 2.63107e6 1.40322
\(324\) 0 0
\(325\) −403957. −0.212142
\(326\) −311648. −0.162413
\(327\) 0 0
\(328\) −1.28174e6 −0.657833
\(329\) −314304. −0.160089
\(330\) 0 0
\(331\) 2.87129e6 1.44048 0.720239 0.693726i \(-0.244032\pi\)
0.720239 + 0.693726i \(0.244032\pi\)
\(332\) 2.89768e6 1.44280
\(333\) 0 0
\(334\) −195616. −0.0959484
\(335\) 1.43334e6 0.697810
\(336\) 0 0
\(337\) 2.16558e6 1.03872 0.519361 0.854555i \(-0.326170\pi\)
0.519361 + 0.854555i \(0.326170\pi\)
\(338\) −50226.3 −0.0239133
\(339\) 0 0
\(340\) 1.06237e6 0.498399
\(341\) 76730.1 0.0357338
\(342\) 0 0
\(343\) 1.97425e6 0.906081
\(344\) 908953. 0.414138
\(345\) 0 0
\(346\) 236343. 0.106134
\(347\) −392930. −0.175183 −0.0875913 0.996156i \(-0.527917\pi\)
−0.0875913 + 0.996156i \(0.527917\pi\)
\(348\) 0 0
\(349\) 247840. 0.108920 0.0544601 0.998516i \(-0.482656\pi\)
0.0544601 + 0.998516i \(0.482656\pi\)
\(350\) 94279.0 0.0411381
\(351\) 0 0
\(352\) −382522. −0.164551
\(353\) 2.90847e6 1.24230 0.621151 0.783691i \(-0.286665\pi\)
0.621151 + 0.783691i \(0.286665\pi\)
\(354\) 0 0
\(355\) 776896. 0.327184
\(356\) 670261. 0.280297
\(357\) 0 0
\(358\) 336185. 0.138634
\(359\) −758403. −0.310573 −0.155287 0.987869i \(-0.549630\pi\)
−0.155287 + 0.987869i \(0.549630\pi\)
\(360\) 0 0
\(361\) 1.16779e6 0.471627
\(362\) 458067. 0.183721
\(363\) 0 0
\(364\) −2.77997e6 −1.09973
\(365\) −1.40027e6 −0.550148
\(366\) 0 0
\(367\) −2.29924e6 −0.891085 −0.445542 0.895261i \(-0.646989\pi\)
−0.445542 + 0.895261i \(0.646989\pi\)
\(368\) −313866. −0.120816
\(369\) 0 0
\(370\) 315575. 0.119839
\(371\) −1.24172e6 −0.468370
\(372\) 0 0
\(373\) −19163.9 −0.00713203 −0.00356601 0.999994i \(-0.501135\pi\)
−0.00356601 + 0.999994i \(0.501135\pi\)
\(374\) −180331. −0.0666640
\(375\) 0 0
\(376\) 153059. 0.0558329
\(377\) 34584.7 0.0125323
\(378\) 0 0
\(379\) 346535. 0.123922 0.0619610 0.998079i \(-0.480265\pi\)
0.0619610 + 0.998079i \(0.480265\pi\)
\(380\) 1.47132e6 0.522696
\(381\) 0 0
\(382\) 931073. 0.326457
\(383\) 5.25066e6 1.82901 0.914507 0.404571i \(-0.132579\pi\)
0.914507 + 0.404571i \(0.132579\pi\)
\(384\) 0 0
\(385\) 422012. 0.145102
\(386\) −465578. −0.159047
\(387\) 0 0
\(388\) 4.87309e6 1.64333
\(389\) 4.34474e6 1.45576 0.727880 0.685704i \(-0.240506\pi\)
0.727880 + 0.685704i \(0.240506\pi\)
\(390\) 0 0
\(391\) −473763. −0.156718
\(392\) 180406. 0.0592974
\(393\) 0 0
\(394\) −199771. −0.0648324
\(395\) 22075.9 0.00711911
\(396\) 0 0
\(397\) 3.90748e6 1.24429 0.622144 0.782903i \(-0.286262\pi\)
0.622144 + 0.782903i \(0.286262\pi\)
\(398\) −349244. −0.110515
\(399\) 0 0
\(400\) 570705. 0.178345
\(401\) 3.05315e6 0.948171 0.474085 0.880479i \(-0.342779\pi\)
0.474085 + 0.880479i \(0.342779\pi\)
\(402\) 0 0
\(403\) −409860. −0.125711
\(404\) −4.83945e6 −1.47517
\(405\) 0 0
\(406\) −8071.67 −0.00243023
\(407\) 1.41258e6 0.422695
\(408\) 0 0
\(409\) −5.46050e6 −1.61408 −0.807038 0.590499i \(-0.798931\pi\)
−0.807038 + 0.590499i \(0.798931\pi\)
\(410\) −509997. −0.149833
\(411\) 0 0
\(412\) −5.21428e6 −1.51339
\(413\) −1.57318e6 −0.453842
\(414\) 0 0
\(415\) 2.34966e6 0.669706
\(416\) 2.04327e6 0.578886
\(417\) 0 0
\(418\) −249749. −0.0699139
\(419\) −3.02804e6 −0.842609 −0.421305 0.906919i \(-0.638428\pi\)
−0.421305 + 0.906919i \(0.638428\pi\)
\(420\) 0 0
\(421\) −3.31510e6 −0.911572 −0.455786 0.890089i \(-0.650642\pi\)
−0.455786 + 0.890089i \(0.650642\pi\)
\(422\) 426136. 0.116484
\(423\) 0 0
\(424\) 604691. 0.163350
\(425\) 861448. 0.231343
\(426\) 0 0
\(427\) −1.65351e6 −0.438871
\(428\) −417404. −0.110141
\(429\) 0 0
\(430\) 361667. 0.0943273
\(431\) 3.02139e6 0.783455 0.391728 0.920081i \(-0.371878\pi\)
0.391728 + 0.920081i \(0.371878\pi\)
\(432\) 0 0
\(433\) −739663. −0.189589 −0.0947947 0.995497i \(-0.530219\pi\)
−0.0947947 + 0.995497i \(0.530219\pi\)
\(434\) 95656.7 0.0243776
\(435\) 0 0
\(436\) 2.30419e6 0.580499
\(437\) −656138. −0.164358
\(438\) 0 0
\(439\) 89371.4 0.0221329 0.0110664 0.999939i \(-0.496477\pi\)
0.0110664 + 0.999939i \(0.496477\pi\)
\(440\) −205511. −0.0506060
\(441\) 0 0
\(442\) 963252. 0.234522
\(443\) −5.06164e6 −1.22541 −0.612706 0.790311i \(-0.709919\pi\)
−0.612706 + 0.790311i \(0.709919\pi\)
\(444\) 0 0
\(445\) 543498. 0.130106
\(446\) −481208. −0.114550
\(447\) 0 0
\(448\) 3.59956e6 0.847334
\(449\) −6.64598e6 −1.55576 −0.777881 0.628411i \(-0.783706\pi\)
−0.777881 + 0.628411i \(0.783706\pi\)
\(450\) 0 0
\(451\) −2.28285e6 −0.528489
\(452\) −6.34850e6 −1.46159
\(453\) 0 0
\(454\) 1.25306e6 0.285320
\(455\) −2.25421e6 −0.510465
\(456\) 0 0
\(457\) −176313. −0.0394905 −0.0197453 0.999805i \(-0.506286\pi\)
−0.0197453 + 0.999805i \(0.506286\pi\)
\(458\) −957850. −0.213370
\(459\) 0 0
\(460\) −264934. −0.0583772
\(461\) −8.43740e6 −1.84908 −0.924542 0.381081i \(-0.875552\pi\)
−0.924542 + 0.381081i \(0.875552\pi\)
\(462\) 0 0
\(463\) 5.65739e6 1.22649 0.613244 0.789893i \(-0.289864\pi\)
0.613244 + 0.789893i \(0.289864\pi\)
\(464\) −48860.8 −0.0105357
\(465\) 0 0
\(466\) 811379. 0.173085
\(467\) 2.54278e6 0.539532 0.269766 0.962926i \(-0.413054\pi\)
0.269766 + 0.962926i \(0.413054\pi\)
\(468\) 0 0
\(469\) 7.99850e6 1.67910
\(470\) 60901.4 0.0127169
\(471\) 0 0
\(472\) 766107. 0.158283
\(473\) 1.61889e6 0.332710
\(474\) 0 0
\(475\) 1.19306e6 0.242621
\(476\) 5.92835e6 1.19927
\(477\) 0 0
\(478\) 667594. 0.133642
\(479\) −6.89136e6 −1.37235 −0.686177 0.727434i \(-0.740713\pi\)
−0.686177 + 0.727434i \(0.740713\pi\)
\(480\) 0 0
\(481\) −7.54540e6 −1.48703
\(482\) −1.30051e6 −0.254973
\(483\) 0 0
\(484\) −451394. −0.0875876
\(485\) 3.95147e6 0.762790
\(486\) 0 0
\(487\) 7.89949e6 1.50930 0.754652 0.656125i \(-0.227806\pi\)
0.754652 + 0.656125i \(0.227806\pi\)
\(488\) 805223. 0.153062
\(489\) 0 0
\(490\) 71782.4 0.0135060
\(491\) 2.29000e6 0.428679 0.214340 0.976759i \(-0.431240\pi\)
0.214340 + 0.976759i \(0.431240\pi\)
\(492\) 0 0
\(493\) −73752.6 −0.0136666
\(494\) 1.33406e6 0.245955
\(495\) 0 0
\(496\) 579045. 0.105684
\(497\) 4.33533e6 0.787283
\(498\) 0 0
\(499\) −5.96310e6 −1.07206 −0.536032 0.844198i \(-0.680077\pi\)
−0.536032 + 0.844198i \(0.680077\pi\)
\(500\) 481732. 0.0861748
\(501\) 0 0
\(502\) 1.68435e6 0.298314
\(503\) −2.17453e6 −0.383218 −0.191609 0.981471i \(-0.561371\pi\)
−0.191609 + 0.981471i \(0.561371\pi\)
\(504\) 0 0
\(505\) −3.92420e6 −0.684734
\(506\) 44971.1 0.00780831
\(507\) 0 0
\(508\) 6.61883e6 1.13795
\(509\) 3.33531e6 0.570613 0.285307 0.958436i \(-0.407905\pi\)
0.285307 + 0.958436i \(0.407905\pi\)
\(510\) 0 0
\(511\) −7.81395e6 −1.32379
\(512\) −4.87184e6 −0.821331
\(513\) 0 0
\(514\) 99645.9 0.0166361
\(515\) −4.22814e6 −0.702475
\(516\) 0 0
\(517\) 272607. 0.0448549
\(518\) 1.76101e6 0.288362
\(519\) 0 0
\(520\) 1.09775e6 0.178031
\(521\) −9.81327e6 −1.58387 −0.791935 0.610605i \(-0.790926\pi\)
−0.791935 + 0.610605i \(0.790926\pi\)
\(522\) 0 0
\(523\) 7.96466e6 1.27325 0.636624 0.771175i \(-0.280330\pi\)
0.636624 + 0.771175i \(0.280330\pi\)
\(524\) 7.80227e6 1.24134
\(525\) 0 0
\(526\) −932190. −0.146906
\(527\) 874036. 0.137089
\(528\) 0 0
\(529\) −6.31820e6 −0.981644
\(530\) 240603. 0.0372058
\(531\) 0 0
\(532\) 8.21046e6 1.25773
\(533\) 1.21940e7 1.85921
\(534\) 0 0
\(535\) −338463. −0.0511243
\(536\) −3.89509e6 −0.585607
\(537\) 0 0
\(538\) −1.35215e6 −0.201405
\(539\) 321313. 0.0476383
\(540\) 0 0
\(541\) −5.50616e6 −0.808827 −0.404413 0.914576i \(-0.632524\pi\)
−0.404413 + 0.914576i \(0.632524\pi\)
\(542\) −913303. −0.133542
\(543\) 0 0
\(544\) −4.35733e6 −0.631281
\(545\) 1.86841e6 0.269452
\(546\) 0 0
\(547\) 2.92918e6 0.418580 0.209290 0.977854i \(-0.432885\pi\)
0.209290 + 0.977854i \(0.432885\pi\)
\(548\) 7.38084e6 1.04992
\(549\) 0 0
\(550\) −81771.4 −0.0115264
\(551\) −102144. −0.0143328
\(552\) 0 0
\(553\) 123191. 0.0171303
\(554\) 1.65424e6 0.228994
\(555\) 0 0
\(556\) 5.13018e6 0.703795
\(557\) −4.05453e6 −0.553736 −0.276868 0.960908i \(-0.589296\pi\)
−0.276868 + 0.960908i \(0.589296\pi\)
\(558\) 0 0
\(559\) −8.64745e6 −1.17047
\(560\) 3.18472e6 0.429142
\(561\) 0 0
\(562\) 1.22491e6 0.163592
\(563\) 1.65845e6 0.220512 0.110256 0.993903i \(-0.464833\pi\)
0.110256 + 0.993903i \(0.464833\pi\)
\(564\) 0 0
\(565\) −5.14785e6 −0.678430
\(566\) 444553. 0.0583288
\(567\) 0 0
\(568\) −2.11121e6 −0.274575
\(569\) −1.05475e7 −1.36575 −0.682873 0.730537i \(-0.739270\pi\)
−0.682873 + 0.730537i \(0.739270\pi\)
\(570\) 0 0
\(571\) −1.46769e7 −1.88384 −0.941918 0.335843i \(-0.890979\pi\)
−0.941918 + 0.335843i \(0.890979\pi\)
\(572\) 2.41116e6 0.308131
\(573\) 0 0
\(574\) −2.84595e6 −0.360534
\(575\) −214829. −0.0270971
\(576\) 0 0
\(577\) −8.25271e6 −1.03195 −0.515973 0.856605i \(-0.672570\pi\)
−0.515973 + 0.856605i \(0.672570\pi\)
\(578\) −518905. −0.0646053
\(579\) 0 0
\(580\) −41243.3 −0.00509078
\(581\) 1.31118e7 1.61147
\(582\) 0 0
\(583\) 1.07699e6 0.131232
\(584\) 3.80522e6 0.461687
\(585\) 0 0
\(586\) 339534. 0.0408450
\(587\) −1.01063e7 −1.21059 −0.605296 0.796000i \(-0.706945\pi\)
−0.605296 + 0.796000i \(0.706945\pi\)
\(588\) 0 0
\(589\) 1.21050e6 0.143772
\(590\) 304829. 0.0360517
\(591\) 0 0
\(592\) 1.06600e7 1.25013
\(593\) −1.48922e7 −1.73909 −0.869543 0.493857i \(-0.835587\pi\)
−0.869543 + 0.493857i \(0.835587\pi\)
\(594\) 0 0
\(595\) 4.80716e6 0.556667
\(596\) 9.11088e6 1.05062
\(597\) 0 0
\(598\) −240217. −0.0274695
\(599\) −1.59013e7 −1.81078 −0.905390 0.424580i \(-0.860422\pi\)
−0.905390 + 0.424580i \(0.860422\pi\)
\(600\) 0 0
\(601\) −2.84828e6 −0.321660 −0.160830 0.986982i \(-0.551417\pi\)
−0.160830 + 0.986982i \(0.551417\pi\)
\(602\) 2.01822e6 0.226974
\(603\) 0 0
\(604\) −1.32071e7 −1.47304
\(605\) −366025. −0.0406558
\(606\) 0 0
\(607\) 1.32016e6 0.145430 0.0727149 0.997353i \(-0.476834\pi\)
0.0727149 + 0.997353i \(0.476834\pi\)
\(608\) −6.03467e6 −0.662056
\(609\) 0 0
\(610\) 320393. 0.0348625
\(611\) −1.45615e6 −0.157799
\(612\) 0 0
\(613\) −978527. −0.105177 −0.0525886 0.998616i \(-0.516747\pi\)
−0.0525886 + 0.998616i \(0.516747\pi\)
\(614\) −862424. −0.0923209
\(615\) 0 0
\(616\) −1.14681e6 −0.121770
\(617\) −1.29643e7 −1.37100 −0.685500 0.728073i \(-0.740416\pi\)
−0.685500 + 0.728073i \(0.740416\pi\)
\(618\) 0 0
\(619\) 1.27406e7 1.33648 0.668240 0.743946i \(-0.267048\pi\)
0.668240 + 0.743946i \(0.267048\pi\)
\(620\) 488771. 0.0510654
\(621\) 0 0
\(622\) −668626. −0.0692958
\(623\) 3.03289e6 0.313067
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 2.81320e6 0.286923
\(627\) 0 0
\(628\) 8.91020e6 0.901547
\(629\) 1.60908e7 1.62162
\(630\) 0 0
\(631\) −1.93988e7 −1.93955 −0.969775 0.243999i \(-0.921541\pi\)
−0.969775 + 0.243999i \(0.921541\pi\)
\(632\) −59991.1 −0.00597440
\(633\) 0 0
\(634\) −789006. −0.0779574
\(635\) 5.36706e6 0.528204
\(636\) 0 0
\(637\) −1.71632e6 −0.167590
\(638\) 7000.83 0.000680923 0
\(639\) 0 0
\(640\) −3.22654e6 −0.311378
\(641\) −6.77844e6 −0.651605 −0.325803 0.945438i \(-0.605634\pi\)
−0.325803 + 0.945438i \(0.605634\pi\)
\(642\) 0 0
\(643\) −1.74257e7 −1.66212 −0.831060 0.556182i \(-0.812266\pi\)
−0.831060 + 0.556182i \(0.812266\pi\)
\(644\) −1.47842e6 −0.140470
\(645\) 0 0
\(646\) −2.84491e6 −0.268217
\(647\) −792517. −0.0744300 −0.0372150 0.999307i \(-0.511849\pi\)
−0.0372150 + 0.999307i \(0.511849\pi\)
\(648\) 0 0
\(649\) 1.36448e6 0.127161
\(650\) 436788. 0.0405497
\(651\) 0 0
\(652\) −8.88616e6 −0.818644
\(653\) 9.09663e6 0.834829 0.417414 0.908716i \(-0.362936\pi\)
0.417414 + 0.908716i \(0.362936\pi\)
\(654\) 0 0
\(655\) 6.32667e6 0.576198
\(656\) −1.72275e7 −1.56302
\(657\) 0 0
\(658\) 339849. 0.0306000
\(659\) 8.15992e6 0.731935 0.365968 0.930628i \(-0.380738\pi\)
0.365968 + 0.930628i \(0.380738\pi\)
\(660\) 0 0
\(661\) −1.85172e6 −0.164843 −0.0824216 0.996598i \(-0.526265\pi\)
−0.0824216 + 0.996598i \(0.526265\pi\)
\(662\) −3.10465e6 −0.275339
\(663\) 0 0
\(664\) −6.38518e6 −0.562022
\(665\) 6.65766e6 0.583805
\(666\) 0 0
\(667\) 18392.5 0.00160076
\(668\) −5.57768e6 −0.483629
\(669\) 0 0
\(670\) −1.54983e6 −0.133382
\(671\) 1.43414e6 0.122966
\(672\) 0 0
\(673\) 1.42740e6 0.121481 0.0607405 0.998154i \(-0.480654\pi\)
0.0607405 + 0.998154i \(0.480654\pi\)
\(674\) −2.34158e6 −0.198545
\(675\) 0 0
\(676\) −1.43213e6 −0.120535
\(677\) −941868. −0.0789802 −0.0394901 0.999220i \(-0.512573\pi\)
−0.0394901 + 0.999220i \(0.512573\pi\)
\(678\) 0 0
\(679\) 2.20505e7 1.83545
\(680\) −2.34098e6 −0.194145
\(681\) 0 0
\(682\) −82966.3 −0.00683031
\(683\) −9.56089e6 −0.784236 −0.392118 0.919915i \(-0.628257\pi\)
−0.392118 + 0.919915i \(0.628257\pi\)
\(684\) 0 0
\(685\) 5.98494e6 0.487342
\(686\) −2.13471e6 −0.173192
\(687\) 0 0
\(688\) 1.22170e7 0.983996
\(689\) −5.75281e6 −0.461670
\(690\) 0 0
\(691\) −1.53765e7 −1.22507 −0.612536 0.790443i \(-0.709851\pi\)
−0.612536 + 0.790443i \(0.709851\pi\)
\(692\) 6.73897e6 0.534968
\(693\) 0 0
\(694\) 424865. 0.0334851
\(695\) 4.15994e6 0.326682
\(696\) 0 0
\(697\) −2.60040e7 −2.02749
\(698\) −267983. −0.0208194
\(699\) 0 0
\(700\) 2.68822e6 0.207357
\(701\) −1.72261e7 −1.32401 −0.662006 0.749499i \(-0.730295\pi\)
−0.662006 + 0.749499i \(0.730295\pi\)
\(702\) 0 0
\(703\) 2.22849e7 1.70068
\(704\) −3.12202e6 −0.237413
\(705\) 0 0
\(706\) −3.14485e6 −0.237459
\(707\) −2.18983e7 −1.64764
\(708\) 0 0
\(709\) 2.47878e7 1.85192 0.925959 0.377625i \(-0.123259\pi\)
0.925959 + 0.377625i \(0.123259\pi\)
\(710\) −840037. −0.0625393
\(711\) 0 0
\(712\) −1.47695e6 −0.109186
\(713\) −217968. −0.0160572
\(714\) 0 0
\(715\) 1.95515e6 0.143026
\(716\) 9.58579e6 0.698788
\(717\) 0 0
\(718\) 820042. 0.0593642
\(719\) −7.44502e6 −0.537086 −0.268543 0.963268i \(-0.586542\pi\)
−0.268543 + 0.963268i \(0.586542\pi\)
\(720\) 0 0
\(721\) −2.35944e7 −1.69032
\(722\) −1.26271e6 −0.0901486
\(723\) 0 0
\(724\) 1.30611e7 0.926046
\(725\) −33443.2 −0.00236300
\(726\) 0 0
\(727\) 3.56658e6 0.250274 0.125137 0.992139i \(-0.460063\pi\)
0.125137 + 0.992139i \(0.460063\pi\)
\(728\) 6.12580e6 0.428385
\(729\) 0 0
\(730\) 1.51407e6 0.105157
\(731\) 1.84409e7 1.27641
\(732\) 0 0
\(733\) 1.38091e7 0.949305 0.474652 0.880173i \(-0.342574\pi\)
0.474652 + 0.880173i \(0.342574\pi\)
\(734\) 2.48611e6 0.170326
\(735\) 0 0
\(736\) 1.08663e6 0.0739416
\(737\) −6.93737e6 −0.470463
\(738\) 0 0
\(739\) −7.18607e6 −0.484039 −0.242020 0.970271i \(-0.577810\pi\)
−0.242020 + 0.970271i \(0.577810\pi\)
\(740\) 8.99814e6 0.604051
\(741\) 0 0
\(742\) 1.34264e6 0.0895261
\(743\) −2.18843e6 −0.145432 −0.0727161 0.997353i \(-0.523167\pi\)
−0.0727161 + 0.997353i \(0.523167\pi\)
\(744\) 0 0
\(745\) 7.38780e6 0.487668
\(746\) 20721.5 0.00136324
\(747\) 0 0
\(748\) −5.14186e6 −0.336021
\(749\) −1.88873e6 −0.123017
\(750\) 0 0
\(751\) −1.41771e6 −0.0917250 −0.0458625 0.998948i \(-0.514604\pi\)
−0.0458625 + 0.998948i \(0.514604\pi\)
\(752\) 2.05723e6 0.132660
\(753\) 0 0
\(754\) −37395.5 −0.00239547
\(755\) −1.07093e7 −0.683746
\(756\) 0 0
\(757\) −2.05513e7 −1.30347 −0.651734 0.758448i \(-0.725958\pi\)
−0.651734 + 0.758448i \(0.725958\pi\)
\(758\) −374699. −0.0236870
\(759\) 0 0
\(760\) −3.24214e6 −0.203609
\(761\) 1.30587e7 0.817409 0.408705 0.912667i \(-0.365981\pi\)
0.408705 + 0.912667i \(0.365981\pi\)
\(762\) 0 0
\(763\) 1.04263e7 0.648366
\(764\) 2.65481e7 1.64551
\(765\) 0 0
\(766\) −5.67740e6 −0.349605
\(767\) −7.28846e6 −0.447350
\(768\) 0 0
\(769\) 1.82667e7 1.11389 0.556946 0.830549i \(-0.311973\pi\)
0.556946 + 0.830549i \(0.311973\pi\)
\(770\) −456310. −0.0277353
\(771\) 0 0
\(772\) −1.32752e7 −0.801676
\(773\) 1.49182e7 0.897981 0.448990 0.893537i \(-0.351784\pi\)
0.448990 + 0.893537i \(0.351784\pi\)
\(774\) 0 0
\(775\) 396333. 0.0237032
\(776\) −1.07381e7 −0.640138
\(777\) 0 0
\(778\) −4.69786e6 −0.278260
\(779\) −3.60143e7 −2.12633
\(780\) 0 0
\(781\) −3.76018e6 −0.220587
\(782\) 512268. 0.0299558
\(783\) 0 0
\(784\) 2.42479e6 0.140891
\(785\) 7.22507e6 0.418473
\(786\) 0 0
\(787\) −1.60565e7 −0.924087 −0.462043 0.886857i \(-0.652884\pi\)
−0.462043 + 0.886857i \(0.652884\pi\)
\(788\) −5.69616e6 −0.326788
\(789\) 0 0
\(790\) −23870.1 −0.00136078
\(791\) −2.87266e7 −1.63246
\(792\) 0 0
\(793\) −7.66060e6 −0.432593
\(794\) −4.22506e6 −0.237838
\(795\) 0 0
\(796\) −9.95816e6 −0.557053
\(797\) −2.10741e7 −1.17518 −0.587588 0.809160i \(-0.699922\pi\)
−0.587588 + 0.809160i \(0.699922\pi\)
\(798\) 0 0
\(799\) 3.10528e6 0.172081
\(800\) −1.97584e6 −0.109151
\(801\) 0 0
\(802\) −3.30129e6 −0.181237
\(803\) 6.77730e6 0.370909
\(804\) 0 0
\(805\) −1.19881e6 −0.0652021
\(806\) 443171. 0.0240289
\(807\) 0 0
\(808\) 1.06640e7 0.574633
\(809\) −2.38181e7 −1.27949 −0.639744 0.768588i \(-0.720960\pi\)
−0.639744 + 0.768588i \(0.720960\pi\)
\(810\) 0 0
\(811\) 2.93046e7 1.56453 0.782264 0.622947i \(-0.214065\pi\)
0.782264 + 0.622947i \(0.214065\pi\)
\(812\) −230151. −0.0122496
\(813\) 0 0
\(814\) −1.52739e6 −0.0807956
\(815\) −7.20557e6 −0.379992
\(816\) 0 0
\(817\) 2.55397e7 1.33863
\(818\) 5.90430e6 0.308521
\(819\) 0 0
\(820\) −1.45418e7 −0.755236
\(821\) 3.14594e6 0.162889 0.0814446 0.996678i \(-0.474047\pi\)
0.0814446 + 0.996678i \(0.474047\pi\)
\(822\) 0 0
\(823\) 2.44990e7 1.26081 0.630404 0.776267i \(-0.282889\pi\)
0.630404 + 0.776267i \(0.282889\pi\)
\(824\) 1.14899e7 0.589522
\(825\) 0 0
\(826\) 1.70104e6 0.0867492
\(827\) −1.34163e7 −0.682135 −0.341067 0.940039i \(-0.610788\pi\)
−0.341067 + 0.940039i \(0.610788\pi\)
\(828\) 0 0
\(829\) 1.42349e7 0.719394 0.359697 0.933069i \(-0.382880\pi\)
0.359697 + 0.933069i \(0.382880\pi\)
\(830\) −2.54062e6 −0.128010
\(831\) 0 0
\(832\) 1.66765e7 0.835213
\(833\) 3.66009e6 0.182759
\(834\) 0 0
\(835\) −4.52281e6 −0.224487
\(836\) −7.12121e6 −0.352402
\(837\) 0 0
\(838\) 3.27414e6 0.161060
\(839\) −1.15794e7 −0.567913 −0.283957 0.958837i \(-0.591647\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(840\) 0 0
\(841\) −2.05083e7 −0.999860
\(842\) 3.58453e6 0.174242
\(843\) 0 0
\(844\) 1.21506e7 0.587140
\(845\) −1.16128e6 −0.0559492
\(846\) 0 0
\(847\) −2.04254e6 −0.0978276
\(848\) 8.12749e6 0.388121
\(849\) 0 0
\(850\) −931462. −0.0442199
\(851\) −4.01273e6 −0.189940
\(852\) 0 0
\(853\) 6.61595e6 0.311329 0.155664 0.987810i \(-0.450248\pi\)
0.155664 + 0.987810i \(0.450248\pi\)
\(854\) 1.78790e6 0.0838876
\(855\) 0 0
\(856\) 919772. 0.0429038
\(857\) 9.97147e6 0.463775 0.231887 0.972743i \(-0.425510\pi\)
0.231887 + 0.972743i \(0.425510\pi\)
\(858\) 0 0
\(859\) −3.79757e7 −1.75599 −0.877996 0.478667i \(-0.841120\pi\)
−0.877996 + 0.478667i \(0.841120\pi\)
\(860\) 1.03124e7 0.475458
\(861\) 0 0
\(862\) −3.26695e6 −0.149753
\(863\) −8.18531e6 −0.374118 −0.187059 0.982349i \(-0.559896\pi\)
−0.187059 + 0.982349i \(0.559896\pi\)
\(864\) 0 0
\(865\) 5.46447e6 0.248318
\(866\) 799779. 0.0362389
\(867\) 0 0
\(868\) 2.72750e6 0.122876
\(869\) −106847. −0.00479970
\(870\) 0 0
\(871\) 3.70565e7 1.65508
\(872\) −5.07740e6 −0.226126
\(873\) 0 0
\(874\) 709465. 0.0314161
\(875\) 2.17981e6 0.0962496
\(876\) 0 0
\(877\) −3.02517e7 −1.32816 −0.664081 0.747660i \(-0.731177\pi\)
−0.664081 + 0.747660i \(0.731177\pi\)
\(878\) −96635.0 −0.00423056
\(879\) 0 0
\(880\) −2.76221e6 −0.120240
\(881\) −6.11414e6 −0.265397 −0.132698 0.991156i \(-0.542364\pi\)
−0.132698 + 0.991156i \(0.542364\pi\)
\(882\) 0 0
\(883\) −7.72672e6 −0.333498 −0.166749 0.985999i \(-0.553327\pi\)
−0.166749 + 0.985999i \(0.553327\pi\)
\(884\) 2.74656e7 1.18211
\(885\) 0 0
\(886\) 5.47302e6 0.234230
\(887\) 2.48274e7 1.05955 0.529775 0.848138i \(-0.322276\pi\)
0.529775 + 0.848138i \(0.322276\pi\)
\(888\) 0 0
\(889\) 2.99499e7 1.27099
\(890\) −587671. −0.0248690
\(891\) 0 0
\(892\) −1.37209e7 −0.577391
\(893\) 4.30065e6 0.180470
\(894\) 0 0
\(895\) 7.77289e6 0.324358
\(896\) −1.80051e7 −0.749249
\(897\) 0 0
\(898\) 7.18613e6 0.297375
\(899\) −33931.9 −0.00140026
\(900\) 0 0
\(901\) 1.22680e7 0.503457
\(902\) 2.46838e6 0.101017
\(903\) 0 0
\(904\) 1.39893e7 0.569342
\(905\) 1.05909e7 0.429845
\(906\) 0 0
\(907\) −3.64608e6 −0.147166 −0.0735831 0.997289i \(-0.523443\pi\)
−0.0735831 + 0.997289i \(0.523443\pi\)
\(908\) 3.57291e7 1.43816
\(909\) 0 0
\(910\) 2.43742e6 0.0975723
\(911\) 1.15898e7 0.462678 0.231339 0.972873i \(-0.425689\pi\)
0.231339 + 0.972873i \(0.425689\pi\)
\(912\) 0 0
\(913\) −1.13723e7 −0.451516
\(914\) 190642. 0.00754838
\(915\) 0 0
\(916\) −2.73116e7 −1.07550
\(917\) 3.53048e7 1.38647
\(918\) 0 0
\(919\) −3.48544e7 −1.36135 −0.680674 0.732586i \(-0.738313\pi\)
−0.680674 + 0.732586i \(0.738313\pi\)
\(920\) 583796. 0.0227401
\(921\) 0 0
\(922\) 9.12314e6 0.353441
\(923\) 2.00853e7 0.776021
\(924\) 0 0
\(925\) 7.29638e6 0.280384
\(926\) −6.11719e6 −0.234436
\(927\) 0 0
\(928\) 169161. 0.00644806
\(929\) 4.11213e7 1.56325 0.781624 0.623750i \(-0.214392\pi\)
0.781624 + 0.623750i \(0.214392\pi\)
\(930\) 0 0
\(931\) 5.06903e6 0.191669
\(932\) 2.31352e7 0.872436
\(933\) 0 0
\(934\) −2.74945e6 −0.103128
\(935\) −4.16941e6 −0.155972
\(936\) 0 0
\(937\) −1.53222e6 −0.0570126 −0.0285063 0.999594i \(-0.509075\pi\)
−0.0285063 + 0.999594i \(0.509075\pi\)
\(938\) −8.64857e6 −0.320950
\(939\) 0 0
\(940\) 1.73651e6 0.0640999
\(941\) 1.91551e7 0.705196 0.352598 0.935775i \(-0.385298\pi\)
0.352598 + 0.935775i \(0.385298\pi\)
\(942\) 0 0
\(943\) 6.48491e6 0.237479
\(944\) 1.02970e7 0.376082
\(945\) 0 0
\(946\) −1.75047e6 −0.0635955
\(947\) −2.83184e7 −1.02611 −0.513054 0.858356i \(-0.671486\pi\)
−0.513054 + 0.858356i \(0.671486\pi\)
\(948\) 0 0
\(949\) −3.62015e7 −1.30485
\(950\) −1.29003e6 −0.0463756
\(951\) 0 0
\(952\) −1.30634e7 −0.467159
\(953\) 5.47682e7 1.95342 0.976711 0.214559i \(-0.0688313\pi\)
0.976711 + 0.214559i \(0.0688313\pi\)
\(954\) 0 0
\(955\) 2.15272e7 0.763800
\(956\) 1.90354e7 0.673624
\(957\) 0 0
\(958\) 7.45145e6 0.262318
\(959\) 3.33979e7 1.17266
\(960\) 0 0
\(961\) −2.82270e7 −0.985954
\(962\) 8.15865e6 0.284237
\(963\) 0 0
\(964\) −3.70819e7 −1.28520
\(965\) −1.07646e7 −0.372116
\(966\) 0 0
\(967\) 2.29671e7 0.789843 0.394922 0.918715i \(-0.370772\pi\)
0.394922 + 0.918715i \(0.370772\pi\)
\(968\) 994671. 0.0341186
\(969\) 0 0
\(970\) −4.27263e6 −0.145803
\(971\) −1.46281e7 −0.497898 −0.248949 0.968517i \(-0.580085\pi\)
−0.248949 + 0.968517i \(0.580085\pi\)
\(972\) 0 0
\(973\) 2.32138e7 0.786076
\(974\) −8.54152e6 −0.288495
\(975\) 0 0
\(976\) 1.08228e7 0.363676
\(977\) 1.54714e7 0.518552 0.259276 0.965803i \(-0.416516\pi\)
0.259276 + 0.965803i \(0.416516\pi\)
\(978\) 0 0
\(979\) −2.63053e6 −0.0877176
\(980\) 2.04676e6 0.0680773
\(981\) 0 0
\(982\) −2.47612e6 −0.0819395
\(983\) −2.02694e7 −0.669047 −0.334524 0.942387i \(-0.608575\pi\)
−0.334524 + 0.942387i \(0.608575\pi\)
\(984\) 0 0
\(985\) −4.61888e6 −0.151686
\(986\) 79746.8 0.00261229
\(987\) 0 0
\(988\) 3.80385e7 1.23974
\(989\) −4.59881e6 −0.149505
\(990\) 0 0
\(991\) −4.43452e7 −1.43437 −0.717187 0.696881i \(-0.754570\pi\)
−0.717187 + 0.696881i \(0.754570\pi\)
\(992\) −2.00471e6 −0.0646803
\(993\) 0 0
\(994\) −4.68768e6 −0.150484
\(995\) −8.07483e6 −0.258569
\(996\) 0 0
\(997\) 2.32293e7 0.740112 0.370056 0.929009i \(-0.379338\pi\)
0.370056 + 0.929009i \(0.379338\pi\)
\(998\) 6.44775e6 0.204919
\(999\) 0 0
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 495.6.a.c.1.2 3
3.2 odd 2 165.6.a.d.1.2 3
15.14 odd 2 825.6.a.h.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.d.1.2 3 3.2 odd 2
495.6.a.c.1.2 3 1.1 even 1 trivial
825.6.a.h.1.2 3 15.14 odd 2