Properties

Label 495.6.a.e.1.1
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: 3.3.34253.1
Defining polynomial: \( x^{3} - x^{2} - 52x + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
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 1.1
Root \(-7.17710\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.17710 q^{2} -5.19759 q^{4} -25.0000 q^{5} -123.437 q^{7} +192.576 q^{8} +O(q^{10})\) \(q-5.17710 q^{2} -5.19759 q^{4} -25.0000 q^{5} -123.437 q^{7} +192.576 q^{8} +129.428 q^{10} +121.000 q^{11} -500.053 q^{13} +639.048 q^{14} -830.662 q^{16} +422.631 q^{17} -932.948 q^{19} +129.940 q^{20} -626.430 q^{22} +1225.18 q^{23} +625.000 q^{25} +2588.83 q^{26} +641.576 q^{28} +2111.62 q^{29} -159.612 q^{31} -1862.00 q^{32} -2188.00 q^{34} +3085.93 q^{35} +5414.46 q^{37} +4829.97 q^{38} -4814.40 q^{40} +18066.7 q^{41} +6815.47 q^{43} -628.908 q^{44} -6342.88 q^{46} +15098.9 q^{47} -1570.23 q^{49} -3235.69 q^{50} +2599.07 q^{52} -15367.7 q^{53} -3025.00 q^{55} -23771.0 q^{56} -10932.1 q^{58} -23400.5 q^{59} +10768.4 q^{61} +826.328 q^{62} +36221.0 q^{64} +12501.3 q^{65} +14507.1 q^{67} -2196.66 q^{68} -15976.2 q^{70} +28114.0 q^{71} -28836.7 q^{73} -28031.2 q^{74} +4849.08 q^{76} -14935.9 q^{77} -8150.52 q^{79} +20766.6 q^{80} -93533.0 q^{82} +109864. q^{83} -10565.8 q^{85} -35284.4 q^{86} +23301.7 q^{88} -69673.6 q^{89} +61725.2 q^{91} -6367.98 q^{92} -78168.5 q^{94} +23323.7 q^{95} +91551.4 q^{97} +8129.23 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 7 q^{2} + 25 q^{4} - 75 q^{5} - 172 q^{7} + 231 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 7 q^{2} + 25 q^{4} - 75 q^{5} - 172 q^{7} + 231 q^{8} - 175 q^{10} + 363 q^{11} - 654 q^{13} + 728 q^{14} - 415 q^{16} + 2366 q^{17} - 2872 q^{19} - 625 q^{20} + 847 q^{22} - 2272 q^{23} + 1875 q^{25} - 3422 q^{26} + 4592 q^{28} + 7738 q^{29} + 568 q^{31} - 1001 q^{32} + 2506 q^{34} + 4300 q^{35} - 9126 q^{37} - 13076 q^{38} - 5775 q^{40} + 8758 q^{41} - 14672 q^{43} + 3025 q^{44} - 28768 q^{46} + 19392 q^{47} - 26629 q^{49} + 4375 q^{50} - 61506 q^{52} + 4598 q^{53} - 9075 q^{55} - 2688 q^{56} + 8550 q^{58} + 9348 q^{59} - 60078 q^{61} + 14096 q^{62} - 7087 q^{64} + 16350 q^{65} - 38468 q^{67} - 59778 q^{68} - 18200 q^{70} + 74032 q^{71} - 44442 q^{73} - 82542 q^{74} - 98708 q^{76} - 20812 q^{77} - 108116 q^{79} + 10375 q^{80} - 92230 q^{82} + 81892 q^{83} - 59150 q^{85} - 126412 q^{86} + 27951 q^{88} - 167342 q^{89} - 31832 q^{91} - 72960 q^{92} + 12728 q^{94} + 71800 q^{95} + 159702 q^{97} - 163121 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.17710 −0.915191 −0.457596 0.889160i \(-0.651289\pi\)
−0.457596 + 0.889160i \(0.651289\pi\)
\(3\) 0 0
\(4\) −5.19759 −0.162425
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −123.437 −0.952141 −0.476071 0.879407i \(-0.657939\pi\)
−0.476071 + 0.879407i \(0.657939\pi\)
\(8\) 192.576 1.06384
\(9\) 0 0
\(10\) 129.428 0.409286
\(11\) 121.000 0.301511
\(12\) 0 0
\(13\) −500.053 −0.820649 −0.410324 0.911940i \(-0.634585\pi\)
−0.410324 + 0.911940i \(0.634585\pi\)
\(14\) 639.048 0.871392
\(15\) 0 0
\(16\) −830.662 −0.811194
\(17\) 422.631 0.354682 0.177341 0.984150i \(-0.443251\pi\)
0.177341 + 0.984150i \(0.443251\pi\)
\(18\) 0 0
\(19\) −932.948 −0.592889 −0.296445 0.955050i \(-0.595801\pi\)
−0.296445 + 0.955050i \(0.595801\pi\)
\(20\) 129.940 0.0726385
\(21\) 0 0
\(22\) −626.430 −0.275941
\(23\) 1225.18 0.482926 0.241463 0.970410i \(-0.422373\pi\)
0.241463 + 0.970410i \(0.422373\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 2588.83 0.751051
\(27\) 0 0
\(28\) 641.576 0.154651
\(29\) 2111.62 0.466251 0.233126 0.972447i \(-0.425105\pi\)
0.233126 + 0.972447i \(0.425105\pi\)
\(30\) 0 0
\(31\) −159.612 −0.0298306 −0.0149153 0.999889i \(-0.504748\pi\)
−0.0149153 + 0.999889i \(0.504748\pi\)
\(32\) −1862.00 −0.321444
\(33\) 0 0
\(34\) −2188.00 −0.324601
\(35\) 3085.93 0.425811
\(36\) 0 0
\(37\) 5414.46 0.650205 0.325103 0.945679i \(-0.394601\pi\)
0.325103 + 0.945679i \(0.394601\pi\)
\(38\) 4829.97 0.542607
\(39\) 0 0
\(40\) −4814.40 −0.475764
\(41\) 18066.7 1.67849 0.839244 0.543756i \(-0.182998\pi\)
0.839244 + 0.543756i \(0.182998\pi\)
\(42\) 0 0
\(43\) 6815.47 0.562114 0.281057 0.959691i \(-0.409315\pi\)
0.281057 + 0.959691i \(0.409315\pi\)
\(44\) −628.908 −0.0489729
\(45\) 0 0
\(46\) −6342.88 −0.441969
\(47\) 15098.9 0.997012 0.498506 0.866886i \(-0.333882\pi\)
0.498506 + 0.866886i \(0.333882\pi\)
\(48\) 0 0
\(49\) −1570.23 −0.0934270
\(50\) −3235.69 −0.183038
\(51\) 0 0
\(52\) 2599.07 0.133294
\(53\) −15367.7 −0.751484 −0.375742 0.926724i \(-0.622612\pi\)
−0.375742 + 0.926724i \(0.622612\pi\)
\(54\) 0 0
\(55\) −3025.00 −0.134840
\(56\) −23771.0 −1.01293
\(57\) 0 0
\(58\) −10932.1 −0.426709
\(59\) −23400.5 −0.875177 −0.437588 0.899175i \(-0.644167\pi\)
−0.437588 + 0.899175i \(0.644167\pi\)
\(60\) 0 0
\(61\) 10768.4 0.370532 0.185266 0.982688i \(-0.440685\pi\)
0.185266 + 0.982688i \(0.440685\pi\)
\(62\) 826.328 0.0273007
\(63\) 0 0
\(64\) 36221.0 1.10538
\(65\) 12501.3 0.367005
\(66\) 0 0
\(67\) 14507.1 0.394814 0.197407 0.980322i \(-0.436748\pi\)
0.197407 + 0.980322i \(0.436748\pi\)
\(68\) −2196.66 −0.0576090
\(69\) 0 0
\(70\) −15976.2 −0.389698
\(71\) 28114.0 0.661876 0.330938 0.943653i \(-0.392635\pi\)
0.330938 + 0.943653i \(0.392635\pi\)
\(72\) 0 0
\(73\) −28836.7 −0.633342 −0.316671 0.948536i \(-0.602565\pi\)
−0.316671 + 0.948536i \(0.602565\pi\)
\(74\) −28031.2 −0.595062
\(75\) 0 0
\(76\) 4849.08 0.0962998
\(77\) −14935.9 −0.287081
\(78\) 0 0
\(79\) −8150.52 −0.146932 −0.0734662 0.997298i \(-0.523406\pi\)
−0.0734662 + 0.997298i \(0.523406\pi\)
\(80\) 20766.6 0.362777
\(81\) 0 0
\(82\) −93533.0 −1.53614
\(83\) 109864. 1.75049 0.875246 0.483679i \(-0.160700\pi\)
0.875246 + 0.483679i \(0.160700\pi\)
\(84\) 0 0
\(85\) −10565.8 −0.158618
\(86\) −35284.4 −0.514442
\(87\) 0 0
\(88\) 23301.7 0.320760
\(89\) −69673.6 −0.932380 −0.466190 0.884685i \(-0.654374\pi\)
−0.466190 + 0.884685i \(0.654374\pi\)
\(90\) 0 0
\(91\) 61725.2 0.781374
\(92\) −6367.98 −0.0784390
\(93\) 0 0
\(94\) −78168.5 −0.912457
\(95\) 23323.7 0.265148
\(96\) 0 0
\(97\) 91551.4 0.987952 0.493976 0.869476i \(-0.335543\pi\)
0.493976 + 0.869476i \(0.335543\pi\)
\(98\) 8129.23 0.0855036
\(99\) 0 0
\(100\) −3248.49 −0.0324849
\(101\) −21299.3 −0.207760 −0.103880 0.994590i \(-0.533126\pi\)
−0.103880 + 0.994590i \(0.533126\pi\)
\(102\) 0 0
\(103\) −6548.06 −0.0608163 −0.0304081 0.999538i \(-0.509681\pi\)
−0.0304081 + 0.999538i \(0.509681\pi\)
\(104\) −96298.1 −0.873040
\(105\) 0 0
\(106\) 79560.3 0.687752
\(107\) −127171. −1.07381 −0.536905 0.843643i \(-0.680407\pi\)
−0.536905 + 0.843643i \(0.680407\pi\)
\(108\) 0 0
\(109\) 57285.2 0.461823 0.230912 0.972975i \(-0.425829\pi\)
0.230912 + 0.972975i \(0.425829\pi\)
\(110\) 15660.7 0.123404
\(111\) 0 0
\(112\) 102535. 0.772371
\(113\) 67774.2 0.499308 0.249654 0.968335i \(-0.419683\pi\)
0.249654 + 0.968335i \(0.419683\pi\)
\(114\) 0 0
\(115\) −30629.5 −0.215971
\(116\) −10975.3 −0.0757307
\(117\) 0 0
\(118\) 121147. 0.800954
\(119\) −52168.4 −0.337707
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) −55749.1 −0.339108
\(123\) 0 0
\(124\) 829.598 0.00484522
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −115352. −0.634622 −0.317311 0.948322i \(-0.602780\pi\)
−0.317311 + 0.948322i \(0.602780\pi\)
\(128\) −127936. −0.690187
\(129\) 0 0
\(130\) −64720.6 −0.335880
\(131\) −43276.4 −0.220329 −0.110165 0.993913i \(-0.535138\pi\)
−0.110165 + 0.993913i \(0.535138\pi\)
\(132\) 0 0
\(133\) 115161. 0.564514
\(134\) −75104.6 −0.361331
\(135\) 0 0
\(136\) 81388.4 0.377325
\(137\) −401439. −1.82734 −0.913668 0.406461i \(-0.866763\pi\)
−0.913668 + 0.406461i \(0.866763\pi\)
\(138\) 0 0
\(139\) −302018. −1.32586 −0.662928 0.748683i \(-0.730686\pi\)
−0.662928 + 0.748683i \(0.730686\pi\)
\(140\) −16039.4 −0.0691621
\(141\) 0 0
\(142\) −145549. −0.605743
\(143\) −60506.4 −0.247435
\(144\) 0 0
\(145\) −52790.4 −0.208514
\(146\) 149290. 0.579629
\(147\) 0 0
\(148\) −28142.1 −0.105609
\(149\) −326942. −1.20644 −0.603218 0.797576i \(-0.706115\pi\)
−0.603218 + 0.797576i \(0.706115\pi\)
\(150\) 0 0
\(151\) 164681. 0.587761 0.293881 0.955842i \(-0.405053\pi\)
0.293881 + 0.955842i \(0.405053\pi\)
\(152\) −179663. −0.630740
\(153\) 0 0
\(154\) 77324.8 0.262734
\(155\) 3990.30 0.0133406
\(156\) 0 0
\(157\) 248620. 0.804982 0.402491 0.915424i \(-0.368144\pi\)
0.402491 + 0.915424i \(0.368144\pi\)
\(158\) 42196.1 0.134471
\(159\) 0 0
\(160\) 46550.0 0.143754
\(161\) −151233. −0.459813
\(162\) 0 0
\(163\) −417656. −1.23126 −0.615629 0.788036i \(-0.711098\pi\)
−0.615629 + 0.788036i \(0.711098\pi\)
\(164\) −93903.0 −0.272628
\(165\) 0 0
\(166\) −568777. −1.60203
\(167\) −704955. −1.95601 −0.978004 0.208588i \(-0.933113\pi\)
−0.978004 + 0.208588i \(0.933113\pi\)
\(168\) 0 0
\(169\) −121240. −0.326535
\(170\) 54700.1 0.145166
\(171\) 0 0
\(172\) −35424.0 −0.0913012
\(173\) 171060. 0.434545 0.217272 0.976111i \(-0.430284\pi\)
0.217272 + 0.976111i \(0.430284\pi\)
\(174\) 0 0
\(175\) −77148.3 −0.190428
\(176\) −100510. −0.244584
\(177\) 0 0
\(178\) 360707. 0.853306
\(179\) 166327. 0.387999 0.193999 0.981002i \(-0.437854\pi\)
0.193999 + 0.981002i \(0.437854\pi\)
\(180\) 0 0
\(181\) −584391. −1.32589 −0.662945 0.748668i \(-0.730694\pi\)
−0.662945 + 0.748668i \(0.730694\pi\)
\(182\) −319558. −0.715107
\(183\) 0 0
\(184\) 235940. 0.513756
\(185\) −135361. −0.290781
\(186\) 0 0
\(187\) 51138.3 0.106941
\(188\) −78477.8 −0.161939
\(189\) 0 0
\(190\) −120749. −0.242661
\(191\) 715510. 1.41916 0.709581 0.704624i \(-0.248884\pi\)
0.709581 + 0.704624i \(0.248884\pi\)
\(192\) 0 0
\(193\) −922088. −1.78188 −0.890941 0.454118i \(-0.849954\pi\)
−0.890941 + 0.454118i \(0.849954\pi\)
\(194\) −473971. −0.904165
\(195\) 0 0
\(196\) 8161.40 0.0151749
\(197\) 613632. 1.12653 0.563265 0.826276i \(-0.309545\pi\)
0.563265 + 0.826276i \(0.309545\pi\)
\(198\) 0 0
\(199\) −378985. −0.678406 −0.339203 0.940713i \(-0.610157\pi\)
−0.339203 + 0.940713i \(0.610157\pi\)
\(200\) 120360. 0.212768
\(201\) 0 0
\(202\) 110269. 0.190140
\(203\) −260652. −0.443937
\(204\) 0 0
\(205\) −451666. −0.750642
\(206\) 33900.0 0.0556585
\(207\) 0 0
\(208\) 415375. 0.665705
\(209\) −112887. −0.178763
\(210\) 0 0
\(211\) −473721. −0.732515 −0.366257 0.930514i \(-0.619361\pi\)
−0.366257 + 0.930514i \(0.619361\pi\)
\(212\) 79875.1 0.122060
\(213\) 0 0
\(214\) 658376. 0.982741
\(215\) −170387. −0.251385
\(216\) 0 0
\(217\) 19702.1 0.0284029
\(218\) −296571. −0.422657
\(219\) 0 0
\(220\) 15722.7 0.0219013
\(221\) −211338. −0.291069
\(222\) 0 0
\(223\) −822747. −1.10791 −0.553954 0.832547i \(-0.686882\pi\)
−0.553954 + 0.832547i \(0.686882\pi\)
\(224\) 229840. 0.306060
\(225\) 0 0
\(226\) −350874. −0.456962
\(227\) 556097. 0.716285 0.358143 0.933667i \(-0.383410\pi\)
0.358143 + 0.933667i \(0.383410\pi\)
\(228\) 0 0
\(229\) −634919. −0.800073 −0.400036 0.916499i \(-0.631003\pi\)
−0.400036 + 0.916499i \(0.631003\pi\)
\(230\) 158572. 0.197655
\(231\) 0 0
\(232\) 406646. 0.496017
\(233\) 906561. 1.09397 0.546987 0.837141i \(-0.315775\pi\)
0.546987 + 0.837141i \(0.315775\pi\)
\(234\) 0 0
\(235\) −377472. −0.445877
\(236\) 121626. 0.142150
\(237\) 0 0
\(238\) 270081. 0.309066
\(239\) −662586. −0.750322 −0.375161 0.926960i \(-0.622413\pi\)
−0.375161 + 0.926960i \(0.622413\pi\)
\(240\) 0 0
\(241\) −1.31823e6 −1.46200 −0.731001 0.682376i \(-0.760947\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) −75798.0 −0.0831992
\(243\) 0 0
\(244\) −55969.6 −0.0601836
\(245\) 39255.7 0.0417818
\(246\) 0 0
\(247\) 466523. 0.486554
\(248\) −30737.4 −0.0317350
\(249\) 0 0
\(250\) 80892.3 0.0818572
\(251\) 11073.9 0.0110947 0.00554737 0.999985i \(-0.498234\pi\)
0.00554737 + 0.999985i \(0.498234\pi\)
\(252\) 0 0
\(253\) 148247. 0.145608
\(254\) 597188. 0.580800
\(255\) 0 0
\(256\) −496734. −0.473723
\(257\) 788596. 0.744769 0.372384 0.928079i \(-0.378540\pi\)
0.372384 + 0.928079i \(0.378540\pi\)
\(258\) 0 0
\(259\) −668346. −0.619087
\(260\) −64976.7 −0.0596107
\(261\) 0 0
\(262\) 224046. 0.201644
\(263\) −211325. −0.188391 −0.0941956 0.995554i \(-0.530028\pi\)
−0.0941956 + 0.995554i \(0.530028\pi\)
\(264\) 0 0
\(265\) 384193. 0.336074
\(266\) −596198. −0.516639
\(267\) 0 0
\(268\) −75401.8 −0.0641276
\(269\) −552342. −0.465401 −0.232701 0.972548i \(-0.574756\pi\)
−0.232701 + 0.972548i \(0.574756\pi\)
\(270\) 0 0
\(271\) −1.49255e6 −1.23454 −0.617271 0.786751i \(-0.711762\pi\)
−0.617271 + 0.786751i \(0.711762\pi\)
\(272\) −351063. −0.287715
\(273\) 0 0
\(274\) 2.07829e6 1.67236
\(275\) 75625.0 0.0603023
\(276\) 0 0
\(277\) 1.01431e6 0.794275 0.397138 0.917759i \(-0.370004\pi\)
0.397138 + 0.917759i \(0.370004\pi\)
\(278\) 1.56358e6 1.21341
\(279\) 0 0
\(280\) 594276. 0.452995
\(281\) 658216. 0.497282 0.248641 0.968596i \(-0.420016\pi\)
0.248641 + 0.968596i \(0.420016\pi\)
\(282\) 0 0
\(283\) 1.65981e6 1.23195 0.615974 0.787767i \(-0.288763\pi\)
0.615974 + 0.787767i \(0.288763\pi\)
\(284\) −146125. −0.107505
\(285\) 0 0
\(286\) 313248. 0.226450
\(287\) −2.23010e6 −1.59816
\(288\) 0 0
\(289\) −1.24124e6 −0.874201
\(290\) 273301. 0.190830
\(291\) 0 0
\(292\) 149881. 0.102870
\(293\) 410864. 0.279594 0.139797 0.990180i \(-0.455355\pi\)
0.139797 + 0.990180i \(0.455355\pi\)
\(294\) 0 0
\(295\) 585013. 0.391391
\(296\) 1.04269e6 0.691715
\(297\) 0 0
\(298\) 1.69261e6 1.10412
\(299\) −612654. −0.396312
\(300\) 0 0
\(301\) −841283. −0.535212
\(302\) −852570. −0.537914
\(303\) 0 0
\(304\) 774965. 0.480948
\(305\) −269210. −0.165707
\(306\) 0 0
\(307\) 1.34831e6 0.816477 0.408238 0.912875i \(-0.366143\pi\)
0.408238 + 0.912875i \(0.366143\pi\)
\(308\) 77630.7 0.0466291
\(309\) 0 0
\(310\) −20658.2 −0.0122092
\(311\) 2.52585e6 1.48083 0.740417 0.672148i \(-0.234628\pi\)
0.740417 + 0.672148i \(0.234628\pi\)
\(312\) 0 0
\(313\) 2.23061e6 1.28695 0.643476 0.765466i \(-0.277491\pi\)
0.643476 + 0.765466i \(0.277491\pi\)
\(314\) −1.28713e6 −0.736713
\(315\) 0 0
\(316\) 42363.0 0.0238654
\(317\) 120908. 0.0675780 0.0337890 0.999429i \(-0.489243\pi\)
0.0337890 + 0.999429i \(0.489243\pi\)
\(318\) 0 0
\(319\) 255506. 0.140580
\(320\) −905524. −0.494339
\(321\) 0 0
\(322\) 782948. 0.420817
\(323\) −394292. −0.210287
\(324\) 0 0
\(325\) −312533. −0.164130
\(326\) 2.16225e6 1.12684
\(327\) 0 0
\(328\) 3.47920e6 1.78564
\(329\) −1.86377e6 −0.949296
\(330\) 0 0
\(331\) 578480. 0.290214 0.145107 0.989416i \(-0.453647\pi\)
0.145107 + 0.989416i \(0.453647\pi\)
\(332\) −571028. −0.284323
\(333\) 0 0
\(334\) 3.64963e6 1.79012
\(335\) −362677. −0.176566
\(336\) 0 0
\(337\) −1.78710e6 −0.857186 −0.428593 0.903498i \(-0.640991\pi\)
−0.428593 + 0.903498i \(0.640991\pi\)
\(338\) 627674. 0.298842
\(339\) 0 0
\(340\) 54916.5 0.0257635
\(341\) −19313.1 −0.00899425
\(342\) 0 0
\(343\) 2.26844e6 1.04110
\(344\) 1.31249e6 0.598000
\(345\) 0 0
\(346\) −885598. −0.397692
\(347\) 1.46282e6 0.652179 0.326089 0.945339i \(-0.394269\pi\)
0.326089 + 0.945339i \(0.394269\pi\)
\(348\) 0 0
\(349\) 1.48501e6 0.652627 0.326314 0.945262i \(-0.394193\pi\)
0.326314 + 0.945262i \(0.394193\pi\)
\(350\) 399405. 0.174278
\(351\) 0 0
\(352\) −225302. −0.0969189
\(353\) −1.34528e6 −0.574616 −0.287308 0.957838i \(-0.592760\pi\)
−0.287308 + 0.957838i \(0.592760\pi\)
\(354\) 0 0
\(355\) −702850. −0.296000
\(356\) 362135. 0.151442
\(357\) 0 0
\(358\) −861092. −0.355093
\(359\) 1.83956e6 0.753316 0.376658 0.926352i \(-0.377073\pi\)
0.376658 + 0.926352i \(0.377073\pi\)
\(360\) 0 0
\(361\) −1.60571e6 −0.648483
\(362\) 3.02546e6 1.21344
\(363\) 0 0
\(364\) −320822. −0.126914
\(365\) 720917. 0.283239
\(366\) 0 0
\(367\) −312079. −0.120948 −0.0604741 0.998170i \(-0.519261\pi\)
−0.0604741 + 0.998170i \(0.519261\pi\)
\(368\) −1.01771e6 −0.391746
\(369\) 0 0
\(370\) 700780. 0.266120
\(371\) 1.89695e6 0.715519
\(372\) 0 0
\(373\) 3.38658e6 1.26034 0.630172 0.776455i \(-0.282984\pi\)
0.630172 + 0.776455i \(0.282984\pi\)
\(374\) −264748. −0.0978710
\(375\) 0 0
\(376\) 2.90768e6 1.06066
\(377\) −1.05592e6 −0.382629
\(378\) 0 0
\(379\) −1.62370e6 −0.580641 −0.290321 0.956929i \(-0.593762\pi\)
−0.290321 + 0.956929i \(0.593762\pi\)
\(380\) −121227. −0.0430666
\(381\) 0 0
\(382\) −3.70427e6 −1.29881
\(383\) 3.06187e6 1.06657 0.533285 0.845935i \(-0.320957\pi\)
0.533285 + 0.845935i \(0.320957\pi\)
\(384\) 0 0
\(385\) 373398. 0.128387
\(386\) 4.77375e6 1.63076
\(387\) 0 0
\(388\) −475847. −0.160468
\(389\) −4.21840e6 −1.41343 −0.706715 0.707499i \(-0.749824\pi\)
−0.706715 + 0.707499i \(0.749824\pi\)
\(390\) 0 0
\(391\) 517798. 0.171285
\(392\) −302388. −0.0993915
\(393\) 0 0
\(394\) −3.17684e6 −1.03099
\(395\) 203763. 0.0657101
\(396\) 0 0
\(397\) 513185. 0.163417 0.0817085 0.996656i \(-0.473962\pi\)
0.0817085 + 0.996656i \(0.473962\pi\)
\(398\) 1.96205e6 0.620871
\(399\) 0 0
\(400\) −519164. −0.162239
\(401\) 2.18458e6 0.678432 0.339216 0.940709i \(-0.389838\pi\)
0.339216 + 0.940709i \(0.389838\pi\)
\(402\) 0 0
\(403\) 79814.5 0.0244804
\(404\) 110705. 0.0337453
\(405\) 0 0
\(406\) 1.34942e6 0.406287
\(407\) 655149. 0.196044
\(408\) 0 0
\(409\) 1.22307e6 0.361529 0.180764 0.983526i \(-0.442143\pi\)
0.180764 + 0.983526i \(0.442143\pi\)
\(410\) 2.33832e6 0.686981
\(411\) 0 0
\(412\) 34034.1 0.00987806
\(413\) 2.88850e6 0.833292
\(414\) 0 0
\(415\) −2.74660e6 −0.782844
\(416\) 931098. 0.263792
\(417\) 0 0
\(418\) 584426. 0.163602
\(419\) −2.42879e6 −0.675858 −0.337929 0.941172i \(-0.609726\pi\)
−0.337929 + 0.941172i \(0.609726\pi\)
\(420\) 0 0
\(421\) −727467. −0.200036 −0.100018 0.994986i \(-0.531890\pi\)
−0.100018 + 0.994986i \(0.531890\pi\)
\(422\) 2.45250e6 0.670391
\(423\) 0 0
\(424\) −2.95945e6 −0.799460
\(425\) 264144. 0.0709363
\(426\) 0 0
\(427\) −1.32922e6 −0.352799
\(428\) 660981. 0.174413
\(429\) 0 0
\(430\) 882110. 0.230066
\(431\) −6.18223e6 −1.60307 −0.801534 0.597949i \(-0.795982\pi\)
−0.801534 + 0.597949i \(0.795982\pi\)
\(432\) 0 0
\(433\) 2.42337e6 0.621154 0.310577 0.950548i \(-0.399478\pi\)
0.310577 + 0.950548i \(0.399478\pi\)
\(434\) −102000. −0.0259941
\(435\) 0 0
\(436\) −297745. −0.0750115
\(437\) −1.14303e6 −0.286321
\(438\) 0 0
\(439\) −3.79993e6 −0.941054 −0.470527 0.882385i \(-0.655936\pi\)
−0.470527 + 0.882385i \(0.655936\pi\)
\(440\) −582542. −0.143448
\(441\) 0 0
\(442\) 1.09412e6 0.266384
\(443\) 5.58044e6 1.35101 0.675506 0.737354i \(-0.263925\pi\)
0.675506 + 0.737354i \(0.263925\pi\)
\(444\) 0 0
\(445\) 1.74184e6 0.416973
\(446\) 4.25945e6 1.01395
\(447\) 0 0
\(448\) −4.47102e6 −1.05247
\(449\) −2.69609e6 −0.631130 −0.315565 0.948904i \(-0.602194\pi\)
−0.315565 + 0.948904i \(0.602194\pi\)
\(450\) 0 0
\(451\) 2.18607e6 0.506083
\(452\) −352263. −0.0810999
\(453\) 0 0
\(454\) −2.87897e6 −0.655538
\(455\) −1.54313e6 −0.349441
\(456\) 0 0
\(457\) 1.14257e6 0.255912 0.127956 0.991780i \(-0.459158\pi\)
0.127956 + 0.991780i \(0.459158\pi\)
\(458\) 3.28704e6 0.732220
\(459\) 0 0
\(460\) 159199. 0.0350790
\(461\) −5.37091e6 −1.17705 −0.588526 0.808478i \(-0.700292\pi\)
−0.588526 + 0.808478i \(0.700292\pi\)
\(462\) 0 0
\(463\) −3.80227e6 −0.824311 −0.412155 0.911114i \(-0.635224\pi\)
−0.412155 + 0.911114i \(0.635224\pi\)
\(464\) −1.75404e6 −0.378220
\(465\) 0 0
\(466\) −4.69336e6 −1.00120
\(467\) −9.41694e6 −1.99810 −0.999051 0.0435609i \(-0.986130\pi\)
−0.999051 + 0.0435609i \(0.986130\pi\)
\(468\) 0 0
\(469\) −1.79071e6 −0.375919
\(470\) 1.95421e6 0.408063
\(471\) 0 0
\(472\) −4.50638e6 −0.931049
\(473\) 824672. 0.169484
\(474\) 0 0
\(475\) −583093. −0.118578
\(476\) 271150. 0.0548519
\(477\) 0 0
\(478\) 3.43028e6 0.686688
\(479\) 4.69047e6 0.934065 0.467033 0.884240i \(-0.345323\pi\)
0.467033 + 0.884240i \(0.345323\pi\)
\(480\) 0 0
\(481\) −2.70751e6 −0.533590
\(482\) 6.82461e6 1.33801
\(483\) 0 0
\(484\) −76097.9 −0.0147659
\(485\) −2.28879e6 −0.441825
\(486\) 0 0
\(487\) 7.07177e6 1.35116 0.675579 0.737288i \(-0.263894\pi\)
0.675579 + 0.737288i \(0.263894\pi\)
\(488\) 2.07373e6 0.394187
\(489\) 0 0
\(490\) −203231. −0.0382384
\(491\) −906051. −0.169609 −0.0848045 0.996398i \(-0.527027\pi\)
−0.0848045 + 0.996398i \(0.527027\pi\)
\(492\) 0 0
\(493\) 892434. 0.165371
\(494\) −2.41524e6 −0.445290
\(495\) 0 0
\(496\) 132584. 0.0241984
\(497\) −3.47031e6 −0.630199
\(498\) 0 0
\(499\) −7.13323e6 −1.28243 −0.641217 0.767360i \(-0.721570\pi\)
−0.641217 + 0.767360i \(0.721570\pi\)
\(500\) 81212.3 0.0145277
\(501\) 0 0
\(502\) −57330.9 −0.0101538
\(503\) 2.34927e6 0.414013 0.207006 0.978340i \(-0.433628\pi\)
0.207006 + 0.978340i \(0.433628\pi\)
\(504\) 0 0
\(505\) 532482. 0.0929131
\(506\) −767489. −0.133259
\(507\) 0 0
\(508\) 599551. 0.103078
\(509\) −1.97148e6 −0.337286 −0.168643 0.985677i \(-0.553938\pi\)
−0.168643 + 0.985677i \(0.553938\pi\)
\(510\) 0 0
\(511\) 3.55952e6 0.603031
\(512\) 6.66559e6 1.12373
\(513\) 0 0
\(514\) −4.08264e6 −0.681606
\(515\) 163702. 0.0271979
\(516\) 0 0
\(517\) 1.82697e6 0.300610
\(518\) 3.46010e6 0.566583
\(519\) 0 0
\(520\) 2.40745e6 0.390435
\(521\) −1.20074e7 −1.93801 −0.969004 0.247046i \(-0.920540\pi\)
−0.969004 + 0.247046i \(0.920540\pi\)
\(522\) 0 0
\(523\) 4.16772e6 0.666260 0.333130 0.942881i \(-0.391895\pi\)
0.333130 + 0.942881i \(0.391895\pi\)
\(524\) 224933. 0.0357869
\(525\) 0 0
\(526\) 1.09405e6 0.172414
\(527\) −67456.9 −0.0105804
\(528\) 0 0
\(529\) −4.93528e6 −0.766783
\(530\) −1.98901e6 −0.307572
\(531\) 0 0
\(532\) −598557. −0.0916910
\(533\) −9.03428e6 −1.37745
\(534\) 0 0
\(535\) 3.17927e6 0.480222
\(536\) 2.79371e6 0.420020
\(537\) 0 0
\(538\) 2.85953e6 0.425931
\(539\) −189998. −0.0281693
\(540\) 0 0
\(541\) 1.01106e7 1.48519 0.742594 0.669741i \(-0.233595\pi\)
0.742594 + 0.669741i \(0.233595\pi\)
\(542\) 7.72709e6 1.12984
\(543\) 0 0
\(544\) −786938. −0.114010
\(545\) −1.43213e6 −0.206534
\(546\) 0 0
\(547\) −7.39087e6 −1.05615 −0.528077 0.849196i \(-0.677087\pi\)
−0.528077 + 0.849196i \(0.677087\pi\)
\(548\) 2.08652e6 0.296805
\(549\) 0 0
\(550\) −391519. −0.0551881
\(551\) −1.97003e6 −0.276435
\(552\) 0 0
\(553\) 1.00608e6 0.139900
\(554\) −5.25119e6 −0.726914
\(555\) 0 0
\(556\) 1.56977e6 0.215352
\(557\) −1.52459e6 −0.208217 −0.104108 0.994566i \(-0.533199\pi\)
−0.104108 + 0.994566i \(0.533199\pi\)
\(558\) 0 0
\(559\) −3.40809e6 −0.461299
\(560\) −2.56337e6 −0.345415
\(561\) 0 0
\(562\) −3.40765e6 −0.455108
\(563\) 1.40845e7 1.87271 0.936353 0.351059i \(-0.114178\pi\)
0.936353 + 0.351059i \(0.114178\pi\)
\(564\) 0 0
\(565\) −1.69436e6 −0.223297
\(566\) −8.59301e6 −1.12747
\(567\) 0 0
\(568\) 5.41407e6 0.704131
\(569\) 1.30473e7 1.68942 0.844712 0.535221i \(-0.179772\pi\)
0.844712 + 0.535221i \(0.179772\pi\)
\(570\) 0 0
\(571\) −1.19873e7 −1.53862 −0.769312 0.638873i \(-0.779401\pi\)
−0.769312 + 0.638873i \(0.779401\pi\)
\(572\) 314487. 0.0401895
\(573\) 0 0
\(574\) 1.15455e7 1.46262
\(575\) 765737. 0.0965851
\(576\) 0 0
\(577\) 568904. 0.0711376 0.0355688 0.999367i \(-0.488676\pi\)
0.0355688 + 0.999367i \(0.488676\pi\)
\(578\) 6.42603e6 0.800061
\(579\) 0 0
\(580\) 274383. 0.0338678
\(581\) −1.35613e7 −1.66671
\(582\) 0 0
\(583\) −1.85949e6 −0.226581
\(584\) −5.55325e6 −0.673775
\(585\) 0 0
\(586\) −2.12708e6 −0.255882
\(587\) −2.93323e6 −0.351358 −0.175679 0.984447i \(-0.556212\pi\)
−0.175679 + 0.984447i \(0.556212\pi\)
\(588\) 0 0
\(589\) 148910. 0.0176862
\(590\) −3.02868e6 −0.358198
\(591\) 0 0
\(592\) −4.49758e6 −0.527442
\(593\) −5.90557e6 −0.689644 −0.344822 0.938668i \(-0.612061\pi\)
−0.344822 + 0.938668i \(0.612061\pi\)
\(594\) 0 0
\(595\) 1.30421e6 0.151027
\(596\) 1.69931e6 0.195955
\(597\) 0 0
\(598\) 3.17178e6 0.362702
\(599\) −1.07665e7 −1.22605 −0.613025 0.790064i \(-0.710047\pi\)
−0.613025 + 0.790064i \(0.710047\pi\)
\(600\) 0 0
\(601\) −1.19746e7 −1.35231 −0.676154 0.736760i \(-0.736355\pi\)
−0.676154 + 0.736760i \(0.736355\pi\)
\(602\) 4.35541e6 0.489822
\(603\) 0 0
\(604\) −855944. −0.0954669
\(605\) −366025. −0.0406558
\(606\) 0 0
\(607\) −3.45506e6 −0.380613 −0.190307 0.981725i \(-0.560948\pi\)
−0.190307 + 0.981725i \(0.560948\pi\)
\(608\) 1.73715e6 0.190580
\(609\) 0 0
\(610\) 1.39373e6 0.151654
\(611\) −7.55024e6 −0.818197
\(612\) 0 0
\(613\) −8.22419e6 −0.883979 −0.441990 0.897020i \(-0.645727\pi\)
−0.441990 + 0.897020i \(0.645727\pi\)
\(614\) −6.98034e6 −0.747233
\(615\) 0 0
\(616\) −2.87630e6 −0.305409
\(617\) −9.83567e6 −1.04014 −0.520069 0.854124i \(-0.674094\pi\)
−0.520069 + 0.854124i \(0.674094\pi\)
\(618\) 0 0
\(619\) 267648. 0.0280762 0.0140381 0.999901i \(-0.495531\pi\)
0.0140381 + 0.999901i \(0.495531\pi\)
\(620\) −20739.9 −0.00216685
\(621\) 0 0
\(622\) −1.30766e7 −1.35525
\(623\) 8.60032e6 0.887758
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) −1.15481e7 −1.17781
\(627\) 0 0
\(628\) −1.29222e6 −0.130749
\(629\) 2.28831e6 0.230616
\(630\) 0 0
\(631\) −4.17135e6 −0.417065 −0.208532 0.978015i \(-0.566869\pi\)
−0.208532 + 0.978015i \(0.566869\pi\)
\(632\) −1.56959e6 −0.156313
\(633\) 0 0
\(634\) −625951. −0.0618468
\(635\) 2.88379e6 0.283811
\(636\) 0 0
\(637\) 785197. 0.0766708
\(638\) −1.32278e6 −0.128658
\(639\) 0 0
\(640\) 3.19839e6 0.308661
\(641\) −8.24673e6 −0.792751 −0.396376 0.918088i \(-0.629732\pi\)
−0.396376 + 0.918088i \(0.629732\pi\)
\(642\) 0 0
\(643\) 1.07773e7 1.02797 0.513986 0.857799i \(-0.328168\pi\)
0.513986 + 0.857799i \(0.328168\pi\)
\(644\) 786046. 0.0746850
\(645\) 0 0
\(646\) 2.04129e6 0.192453
\(647\) −7.89194e6 −0.741179 −0.370590 0.928797i \(-0.620844\pi\)
−0.370590 + 0.928797i \(0.620844\pi\)
\(648\) 0 0
\(649\) −2.83147e6 −0.263876
\(650\) 1.61802e6 0.150210
\(651\) 0 0
\(652\) 2.17080e6 0.199987
\(653\) −1.47858e7 −1.35695 −0.678473 0.734625i \(-0.737358\pi\)
−0.678473 + 0.734625i \(0.737358\pi\)
\(654\) 0 0
\(655\) 1.08191e6 0.0985343
\(656\) −1.50073e7 −1.36158
\(657\) 0 0
\(658\) 9.64891e6 0.868788
\(659\) 475088. 0.0426148 0.0213074 0.999773i \(-0.493217\pi\)
0.0213074 + 0.999773i \(0.493217\pi\)
\(660\) 0 0
\(661\) 2.73604e6 0.243567 0.121784 0.992557i \(-0.461139\pi\)
0.121784 + 0.992557i \(0.461139\pi\)
\(662\) −2.99485e6 −0.265601
\(663\) 0 0
\(664\) 2.11571e7 1.86224
\(665\) −2.87902e6 −0.252458
\(666\) 0 0
\(667\) 2.58711e6 0.225165
\(668\) 3.66407e6 0.317704
\(669\) 0 0
\(670\) 1.87762e6 0.161592
\(671\) 1.30297e6 0.111720
\(672\) 0 0
\(673\) 1.52861e7 1.30094 0.650471 0.759531i \(-0.274572\pi\)
0.650471 + 0.759531i \(0.274572\pi\)
\(674\) 9.25202e6 0.784489
\(675\) 0 0
\(676\) 630157. 0.0530374
\(677\) 3.93225e6 0.329739 0.164869 0.986315i \(-0.447280\pi\)
0.164869 + 0.986315i \(0.447280\pi\)
\(678\) 0 0
\(679\) −1.13009e7 −0.940670
\(680\) −2.03471e6 −0.168745
\(681\) 0 0
\(682\) 99985.7 0.00823146
\(683\) −3.42591e6 −0.281011 −0.140506 0.990080i \(-0.544873\pi\)
−0.140506 + 0.990080i \(0.544873\pi\)
\(684\) 0 0
\(685\) 1.00360e7 0.817210
\(686\) −1.17439e7 −0.952803
\(687\) 0 0
\(688\) −5.66135e6 −0.455984
\(689\) 7.68467e6 0.616705
\(690\) 0 0
\(691\) 1.81896e7 1.44920 0.724599 0.689171i \(-0.242025\pi\)
0.724599 + 0.689171i \(0.242025\pi\)
\(692\) −889102. −0.0705808
\(693\) 0 0
\(694\) −7.57316e6 −0.596868
\(695\) 7.55046e6 0.592941
\(696\) 0 0
\(697\) 7.63552e6 0.595328
\(698\) −7.68804e6 −0.597279
\(699\) 0 0
\(700\) 400985. 0.0309302
\(701\) 1.15598e6 0.0888494 0.0444247 0.999013i \(-0.485855\pi\)
0.0444247 + 0.999013i \(0.485855\pi\)
\(702\) 0 0
\(703\) −5.05141e6 −0.385500
\(704\) 4.38274e6 0.333283
\(705\) 0 0
\(706\) 6.96468e6 0.525883
\(707\) 2.62913e6 0.197817
\(708\) 0 0
\(709\) 2.42664e7 1.81296 0.906481 0.422246i \(-0.138758\pi\)
0.906481 + 0.422246i \(0.138758\pi\)
\(710\) 3.63873e6 0.270897
\(711\) 0 0
\(712\) −1.34174e7 −0.991904
\(713\) −195553. −0.0144059
\(714\) 0 0
\(715\) 1.51266e6 0.110656
\(716\) −864499. −0.0630205
\(717\) 0 0
\(718\) −9.52359e6 −0.689429
\(719\) 2.25503e7 1.62679 0.813394 0.581714i \(-0.197618\pi\)
0.813394 + 0.581714i \(0.197618\pi\)
\(720\) 0 0
\(721\) 808276. 0.0579057
\(722\) 8.31291e6 0.593486
\(723\) 0 0
\(724\) 3.03743e6 0.215357
\(725\) 1.31976e6 0.0932503
\(726\) 0 0
\(727\) −2.17941e7 −1.52933 −0.764667 0.644425i \(-0.777097\pi\)
−0.764667 + 0.644425i \(0.777097\pi\)
\(728\) 1.18868e7 0.831257
\(729\) 0 0
\(730\) −3.73226e6 −0.259218
\(731\) 2.88043e6 0.199372
\(732\) 0 0
\(733\) 1.73565e7 1.19317 0.596583 0.802551i \(-0.296524\pi\)
0.596583 + 0.802551i \(0.296524\pi\)
\(734\) 1.61567e6 0.110691
\(735\) 0 0
\(736\) −2.28129e6 −0.155233
\(737\) 1.75536e6 0.119041
\(738\) 0 0
\(739\) 1.16961e6 0.0787825 0.0393912 0.999224i \(-0.487458\pi\)
0.0393912 + 0.999224i \(0.487458\pi\)
\(740\) 703553. 0.0472300
\(741\) 0 0
\(742\) −9.82071e6 −0.654837
\(743\) −2.98047e6 −0.198067 −0.0990336 0.995084i \(-0.531575\pi\)
−0.0990336 + 0.995084i \(0.531575\pi\)
\(744\) 0 0
\(745\) 8.17354e6 0.539535
\(746\) −1.75327e7 −1.15346
\(747\) 0 0
\(748\) −265796. −0.0173698
\(749\) 1.56976e7 1.02242
\(750\) 0 0
\(751\) −1.83578e7 −1.18774 −0.593868 0.804563i \(-0.702400\pi\)
−0.593868 + 0.804563i \(0.702400\pi\)
\(752\) −1.25421e7 −0.808770
\(753\) 0 0
\(754\) 5.46661e6 0.350178
\(755\) −4.11702e6 −0.262855
\(756\) 0 0
\(757\) 1.60050e7 1.01511 0.507557 0.861618i \(-0.330549\pi\)
0.507557 + 0.861618i \(0.330549\pi\)
\(758\) 8.40607e6 0.531398
\(759\) 0 0
\(760\) 4.49158e6 0.282075
\(761\) 1.67436e7 1.04807 0.524033 0.851698i \(-0.324427\pi\)
0.524033 + 0.851698i \(0.324427\pi\)
\(762\) 0 0
\(763\) −7.07113e6 −0.439721
\(764\) −3.71892e6 −0.230507
\(765\) 0 0
\(766\) −1.58516e7 −0.976116
\(767\) 1.17015e7 0.718213
\(768\) 0 0
\(769\) −1.73863e7 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(770\) −1.93312e6 −0.117498
\(771\) 0 0
\(772\) 4.79263e6 0.289422
\(773\) −1.79095e7 −1.07804 −0.539021 0.842292i \(-0.681206\pi\)
−0.539021 + 0.842292i \(0.681206\pi\)
\(774\) 0 0
\(775\) −99757.5 −0.00596611
\(776\) 1.76306e7 1.05102
\(777\) 0 0
\(778\) 2.18391e7 1.29356
\(779\) −1.68552e7 −0.995157
\(780\) 0 0
\(781\) 3.40179e6 0.199563
\(782\) −2.68070e6 −0.156758
\(783\) 0 0
\(784\) 1.30433e6 0.0757874
\(785\) −6.21549e6 −0.359999
\(786\) 0 0
\(787\) −3.01291e7 −1.73400 −0.867000 0.498308i \(-0.833955\pi\)
−0.867000 + 0.498308i \(0.833955\pi\)
\(788\) −3.18941e6 −0.182976
\(789\) 0 0
\(790\) −1.05490e6 −0.0601374
\(791\) −8.36587e6 −0.475412
\(792\) 0 0
\(793\) −5.38476e6 −0.304077
\(794\) −2.65681e6 −0.149558
\(795\) 0 0
\(796\) 1.96981e6 0.110190
\(797\) 5.51251e6 0.307400 0.153700 0.988118i \(-0.450881\pi\)
0.153700 + 0.988118i \(0.450881\pi\)
\(798\) 0 0
\(799\) 6.38125e6 0.353622
\(800\) −1.16375e6 −0.0642887
\(801\) 0 0
\(802\) −1.13098e7 −0.620895
\(803\) −3.48924e6 −0.190960
\(804\) 0 0
\(805\) 3.78082e6 0.205635
\(806\) −413208. −0.0224043
\(807\) 0 0
\(808\) −4.10173e6 −0.221024
\(809\) −3.11564e7 −1.67369 −0.836847 0.547436i \(-0.815604\pi\)
−0.836847 + 0.547436i \(0.815604\pi\)
\(810\) 0 0
\(811\) −1.11336e7 −0.594406 −0.297203 0.954814i \(-0.596054\pi\)
−0.297203 + 0.954814i \(0.596054\pi\)
\(812\) 1.35476e6 0.0721063
\(813\) 0 0
\(814\) −3.39178e6 −0.179418
\(815\) 1.04414e7 0.550636
\(816\) 0 0
\(817\) −6.35848e6 −0.333271
\(818\) −6.33195e6 −0.330868
\(819\) 0 0
\(820\) 2.34758e6 0.121923
\(821\) 3.44603e7 1.78427 0.892136 0.451767i \(-0.149206\pi\)
0.892136 + 0.451767i \(0.149206\pi\)
\(822\) 0 0
\(823\) −9.74417e6 −0.501470 −0.250735 0.968056i \(-0.580672\pi\)
−0.250735 + 0.968056i \(0.580672\pi\)
\(824\) −1.26100e6 −0.0646989
\(825\) 0 0
\(826\) −1.49541e7 −0.762622
\(827\) 9.63214e6 0.489733 0.244866 0.969557i \(-0.421256\pi\)
0.244866 + 0.969557i \(0.421256\pi\)
\(828\) 0 0
\(829\) −2.79310e7 −1.41156 −0.705780 0.708431i \(-0.749403\pi\)
−0.705780 + 0.708431i \(0.749403\pi\)
\(830\) 1.42194e7 0.716452
\(831\) 0 0
\(832\) −1.81124e7 −0.907126
\(833\) −663626. −0.0331368
\(834\) 0 0
\(835\) 1.76239e7 0.874753
\(836\) 586739. 0.0290355
\(837\) 0 0
\(838\) 1.25741e7 0.618540
\(839\) 3.51475e7 1.72381 0.861906 0.507068i \(-0.169271\pi\)
0.861906 + 0.507068i \(0.169271\pi\)
\(840\) 0 0
\(841\) −1.60522e7 −0.782610
\(842\) 3.76617e6 0.183071
\(843\) 0 0
\(844\) 2.46221e6 0.118978
\(845\) 3.03101e6 0.146031
\(846\) 0 0
\(847\) −1.80725e6 −0.0865583
\(848\) 1.27654e7 0.609599
\(849\) 0 0
\(850\) −1.36750e6 −0.0649203
\(851\) 6.63368e6 0.314001
\(852\) 0 0
\(853\) 2.50498e7 1.17878 0.589389 0.807849i \(-0.299369\pi\)
0.589389 + 0.807849i \(0.299369\pi\)
\(854\) 6.88152e6 0.322879
\(855\) 0 0
\(856\) −2.44900e7 −1.14236
\(857\) 1.89631e7 0.881975 0.440987 0.897513i \(-0.354628\pi\)
0.440987 + 0.897513i \(0.354628\pi\)
\(858\) 0 0
\(859\) −3.04605e7 −1.40849 −0.704245 0.709957i \(-0.748714\pi\)
−0.704245 + 0.709957i \(0.748714\pi\)
\(860\) 885600. 0.0408312
\(861\) 0 0
\(862\) 3.20060e7 1.46711
\(863\) −3.46176e7 −1.58223 −0.791115 0.611667i \(-0.790499\pi\)
−0.791115 + 0.611667i \(0.790499\pi\)
\(864\) 0 0
\(865\) −4.27651e6 −0.194334
\(866\) −1.25460e7 −0.568475
\(867\) 0 0
\(868\) −102403. −0.00461333
\(869\) −986213. −0.0443018
\(870\) 0 0
\(871\) −7.25430e6 −0.324004
\(872\) 1.10317e7 0.491307
\(873\) 0 0
\(874\) 5.91758e6 0.262039
\(875\) 1.92871e6 0.0851621
\(876\) 0 0
\(877\) −3.61979e7 −1.58922 −0.794611 0.607119i \(-0.792325\pi\)
−0.794611 + 0.607119i \(0.792325\pi\)
\(878\) 1.96727e7 0.861245
\(879\) 0 0
\(880\) 2.51275e6 0.109381
\(881\) −2.40371e7 −1.04338 −0.521690 0.853135i \(-0.674698\pi\)
−0.521690 + 0.853135i \(0.674698\pi\)
\(882\) 0 0
\(883\) 3.64938e7 1.57513 0.787567 0.616229i \(-0.211341\pi\)
0.787567 + 0.616229i \(0.211341\pi\)
\(884\) 1.09845e6 0.0472768
\(885\) 0 0
\(886\) −2.88905e7 −1.23644
\(887\) −2.29197e7 −0.978137 −0.489069 0.872245i \(-0.662663\pi\)
−0.489069 + 0.872245i \(0.662663\pi\)
\(888\) 0 0
\(889\) 1.42387e7 0.604250
\(890\) −9.01768e6 −0.381610
\(891\) 0 0
\(892\) 4.27630e6 0.179952
\(893\) −1.40865e7 −0.591117
\(894\) 0 0
\(895\) −4.15817e6 −0.173518
\(896\) 1.57920e7 0.657156
\(897\) 0 0
\(898\) 1.39579e7 0.577605
\(899\) −337039. −0.0139085
\(900\) 0 0
\(901\) −6.49487e6 −0.266538
\(902\) −1.13175e7 −0.463163
\(903\) 0 0
\(904\) 1.30517e7 0.531184
\(905\) 1.46098e7 0.592956
\(906\) 0 0
\(907\) −2.66664e7 −1.07633 −0.538167 0.842838i \(-0.680883\pi\)
−0.538167 + 0.842838i \(0.680883\pi\)
\(908\) −2.89036e6 −0.116342
\(909\) 0 0
\(910\) 7.98894e6 0.319805
\(911\) −1.73286e7 −0.691778 −0.345889 0.938276i \(-0.612423\pi\)
−0.345889 + 0.938276i \(0.612423\pi\)
\(912\) 0 0
\(913\) 1.32935e7 0.527793
\(914\) −5.91518e6 −0.234208
\(915\) 0 0
\(916\) 3.30005e6 0.129952
\(917\) 5.34192e6 0.209785
\(918\) 0 0
\(919\) −1.72198e7 −0.672573 −0.336286 0.941760i \(-0.609171\pi\)
−0.336286 + 0.941760i \(0.609171\pi\)
\(920\) −5.89850e6 −0.229759
\(921\) 0 0
\(922\) 2.78058e7 1.07723
\(923\) −1.40585e7 −0.543168
\(924\) 0 0
\(925\) 3.38404e6 0.130041
\(926\) 1.96848e7 0.754402
\(927\) 0 0
\(928\) −3.93183e6 −0.149874
\(929\) −5.47137e6 −0.207997 −0.103998 0.994577i \(-0.533164\pi\)
−0.103998 + 0.994577i \(0.533164\pi\)
\(930\) 0 0
\(931\) 1.46494e6 0.0553919
\(932\) −4.71193e6 −0.177688
\(933\) 0 0
\(934\) 4.87525e7 1.82865
\(935\) −1.27846e6 −0.0478252
\(936\) 0 0
\(937\) 8.04892e6 0.299494 0.149747 0.988724i \(-0.452154\pi\)
0.149747 + 0.988724i \(0.452154\pi\)
\(938\) 9.27072e6 0.344038
\(939\) 0 0
\(940\) 1.96195e6 0.0724215
\(941\) 1.13721e7 0.418665 0.209333 0.977844i \(-0.432871\pi\)
0.209333 + 0.977844i \(0.432871\pi\)
\(942\) 0 0
\(943\) 2.21349e7 0.810584
\(944\) 1.94379e7 0.709938
\(945\) 0 0
\(946\) −4.26941e6 −0.155110
\(947\) −4.97017e7 −1.80093 −0.900463 0.434932i \(-0.856772\pi\)
−0.900463 + 0.434932i \(0.856772\pi\)
\(948\) 0 0
\(949\) 1.44199e7 0.519751
\(950\) 3.01873e6 0.108521
\(951\) 0 0
\(952\) −1.00464e7 −0.359266
\(953\) −2.95809e7 −1.05507 −0.527533 0.849534i \(-0.676883\pi\)
−0.527533 + 0.849534i \(0.676883\pi\)
\(954\) 0 0
\(955\) −1.78877e7 −0.634669
\(956\) 3.44385e6 0.121871
\(957\) 0 0
\(958\) −2.42830e7 −0.854849
\(959\) 4.95526e7 1.73988
\(960\) 0 0
\(961\) −2.86037e7 −0.999110
\(962\) 1.40171e7 0.488337
\(963\) 0 0
\(964\) 6.85161e6 0.237465
\(965\) 2.30522e7 0.796882
\(966\) 0 0
\(967\) 3.10475e7 1.06773 0.533863 0.845571i \(-0.320740\pi\)
0.533863 + 0.845571i \(0.320740\pi\)
\(968\) 2.81950e6 0.0967128
\(969\) 0 0
\(970\) 1.18493e7 0.404355
\(971\) 1.89426e7 0.644751 0.322376 0.946612i \(-0.395519\pi\)
0.322376 + 0.946612i \(0.395519\pi\)
\(972\) 0 0
\(973\) 3.72803e7 1.26240
\(974\) −3.66113e7 −1.23657
\(975\) 0 0
\(976\) −8.94489e6 −0.300573
\(977\) −5.49466e7 −1.84164 −0.920819 0.389989i \(-0.872479\pi\)
−0.920819 + 0.389989i \(0.872479\pi\)
\(978\) 0 0
\(979\) −8.43050e6 −0.281123
\(980\) −204035. −0.00678640
\(981\) 0 0
\(982\) 4.69072e6 0.155225
\(983\) 4.72203e7 1.55864 0.779318 0.626628i \(-0.215565\pi\)
0.779318 + 0.626628i \(0.215565\pi\)
\(984\) 0 0
\(985\) −1.53408e7 −0.503799
\(986\) −4.62022e6 −0.151346
\(987\) 0 0
\(988\) −2.42480e6 −0.0790283
\(989\) 8.35018e6 0.271459
\(990\) 0 0
\(991\) 4.48844e7 1.45182 0.725908 0.687792i \(-0.241420\pi\)
0.725908 + 0.687792i \(0.241420\pi\)
\(992\) 297198. 0.00958885
\(993\) 0 0
\(994\) 1.79662e7 0.576753
\(995\) 9.47463e6 0.303392
\(996\) 0 0
\(997\) 5.08797e7 1.62109 0.810543 0.585679i \(-0.199172\pi\)
0.810543 + 0.585679i \(0.199172\pi\)
\(998\) 3.69295e7 1.17367
\(999\) 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.e.1.1 3
3.2 odd 2 165.6.a.a.1.3 3
15.14 odd 2 825.6.a.j.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.a.1.3 3 3.2 odd 2
495.6.a.e.1.1 3 1.1 even 1 trivial
825.6.a.j.1.1 3 15.14 odd 2