Properties

Label 495.6.a.e.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: 3.3.34253.1
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 1.2
Root \(0.921799\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.92180 q^{2} -23.4631 q^{4} -25.0000 q^{5} -85.0105 q^{7} -162.052 q^{8} +O(q^{10})\) \(q+2.92180 q^{2} -23.4631 q^{4} -25.0000 q^{5} -85.0105 q^{7} -162.052 q^{8} -73.0450 q^{10} +121.000 q^{11} +724.085 q^{13} -248.384 q^{14} +277.335 q^{16} +2098.75 q^{17} -6.40223 q^{19} +586.577 q^{20} +353.538 q^{22} -1569.80 q^{23} +625.000 q^{25} +2115.63 q^{26} +1994.61 q^{28} +5145.94 q^{29} -1031.88 q^{31} +5995.98 q^{32} +6132.14 q^{34} +2125.26 q^{35} -12641.6 q^{37} -18.7060 q^{38} +4051.30 q^{40} -13808.7 q^{41} -17012.0 q^{43} -2839.03 q^{44} -4586.64 q^{46} -8078.06 q^{47} -9580.22 q^{49} +1826.12 q^{50} -16989.3 q^{52} +22110.8 q^{53} -3025.00 q^{55} +13776.1 q^{56} +15035.4 q^{58} +16890.6 q^{59} -34398.6 q^{61} -3014.94 q^{62} +8644.32 q^{64} -18102.1 q^{65} -37306.5 q^{67} -49243.3 q^{68} +6209.59 q^{70} +56607.5 q^{71} -27777.9 q^{73} -36936.2 q^{74} +150.216 q^{76} -10286.3 q^{77} -12759.9 q^{79} -6933.39 q^{80} -40346.2 q^{82} +69258.6 q^{83} -52468.9 q^{85} -49705.6 q^{86} -19608.3 q^{88} -59029.2 q^{89} -61554.8 q^{91} +36832.4 q^{92} -23602.5 q^{94} +160.056 q^{95} +104905. q^{97} -27991.5 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 7 q^{2} + 25 q^{4} - 75 q^{5} - 172 q^{7} + 231 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.92180 0.516506 0.258253 0.966077i \(-0.416853\pi\)
0.258253 + 0.966077i \(0.416853\pi\)
\(3\) 0 0
\(4\) −23.4631 −0.733222
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −85.0105 −0.655734 −0.327867 0.944724i \(-0.606330\pi\)
−0.327867 + 0.944724i \(0.606330\pi\)
\(8\) −162.052 −0.895219
\(9\) 0 0
\(10\) −73.0450 −0.230988
\(11\) 121.000 0.301511
\(12\) 0 0
\(13\) 724.085 1.18831 0.594157 0.804349i \(-0.297486\pi\)
0.594157 + 0.804349i \(0.297486\pi\)
\(14\) −248.384 −0.338690
\(15\) 0 0
\(16\) 277.335 0.270835
\(17\) 2098.75 1.76132 0.880662 0.473745i \(-0.157098\pi\)
0.880662 + 0.473745i \(0.157098\pi\)
\(18\) 0 0
\(19\) −6.40223 −0.00406862 −0.00203431 0.999998i \(-0.500648\pi\)
−0.00203431 + 0.999998i \(0.500648\pi\)
\(20\) 586.577 0.327907
\(21\) 0 0
\(22\) 353.538 0.155732
\(23\) −1569.80 −0.618764 −0.309382 0.950938i \(-0.600122\pi\)
−0.309382 + 0.950938i \(0.600122\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 2115.63 0.613771
\(27\) 0 0
\(28\) 1994.61 0.480798
\(29\) 5145.94 1.13624 0.568119 0.822946i \(-0.307671\pi\)
0.568119 + 0.822946i \(0.307671\pi\)
\(30\) 0 0
\(31\) −1031.88 −0.192852 −0.0964259 0.995340i \(-0.530741\pi\)
−0.0964259 + 0.995340i \(0.530741\pi\)
\(32\) 5995.98 1.03511
\(33\) 0 0
\(34\) 6132.14 0.909735
\(35\) 2125.26 0.293253
\(36\) 0 0
\(37\) −12641.6 −1.51809 −0.759045 0.651039i \(-0.774334\pi\)
−0.759045 + 0.651039i \(0.774334\pi\)
\(38\) −18.7060 −0.00210147
\(39\) 0 0
\(40\) 4051.30 0.400354
\(41\) −13808.7 −1.28290 −0.641450 0.767165i \(-0.721667\pi\)
−0.641450 + 0.767165i \(0.721667\pi\)
\(42\) 0 0
\(43\) −17012.0 −1.40308 −0.701542 0.712628i \(-0.747505\pi\)
−0.701542 + 0.712628i \(0.747505\pi\)
\(44\) −2839.03 −0.221075
\(45\) 0 0
\(46\) −4586.64 −0.319595
\(47\) −8078.06 −0.533412 −0.266706 0.963778i \(-0.585935\pi\)
−0.266706 + 0.963778i \(0.585935\pi\)
\(48\) 0 0
\(49\) −9580.22 −0.570013
\(50\) 1826.12 0.103301
\(51\) 0 0
\(52\) −16989.3 −0.871297
\(53\) 22110.8 1.08122 0.540612 0.841272i \(-0.318193\pi\)
0.540612 + 0.841272i \(0.318193\pi\)
\(54\) 0 0
\(55\) −3025.00 −0.134840
\(56\) 13776.1 0.587025
\(57\) 0 0
\(58\) 15035.4 0.586874
\(59\) 16890.6 0.631706 0.315853 0.948808i \(-0.397709\pi\)
0.315853 + 0.948808i \(0.397709\pi\)
\(60\) 0 0
\(61\) −34398.6 −1.18363 −0.591816 0.806073i \(-0.701589\pi\)
−0.591816 + 0.806073i \(0.701589\pi\)
\(62\) −3014.94 −0.0996091
\(63\) 0 0
\(64\) 8644.32 0.263804
\(65\) −18102.1 −0.531430
\(66\) 0 0
\(67\) −37306.5 −1.01531 −0.507654 0.861561i \(-0.669487\pi\)
−0.507654 + 0.861561i \(0.669487\pi\)
\(68\) −49243.3 −1.29144
\(69\) 0 0
\(70\) 6209.59 0.151467
\(71\) 56607.5 1.33269 0.666344 0.745645i \(-0.267858\pi\)
0.666344 + 0.745645i \(0.267858\pi\)
\(72\) 0 0
\(73\) −27777.9 −0.610088 −0.305044 0.952338i \(-0.598671\pi\)
−0.305044 + 0.952338i \(0.598671\pi\)
\(74\) −36936.2 −0.784102
\(75\) 0 0
\(76\) 150.216 0.00298320
\(77\) −10286.3 −0.197711
\(78\) 0 0
\(79\) −12759.9 −0.230028 −0.115014 0.993364i \(-0.536691\pi\)
−0.115014 + 0.993364i \(0.536691\pi\)
\(80\) −6933.39 −0.121121
\(81\) 0 0
\(82\) −40346.2 −0.662625
\(83\) 69258.6 1.10352 0.551758 0.834004i \(-0.313957\pi\)
0.551758 + 0.834004i \(0.313957\pi\)
\(84\) 0 0
\(85\) −52468.9 −0.787688
\(86\) −49705.6 −0.724702
\(87\) 0 0
\(88\) −19608.3 −0.269919
\(89\) −59029.2 −0.789936 −0.394968 0.918695i \(-0.629244\pi\)
−0.394968 + 0.918695i \(0.629244\pi\)
\(90\) 0 0
\(91\) −61554.8 −0.779217
\(92\) 36832.4 0.453691
\(93\) 0 0
\(94\) −23602.5 −0.275510
\(95\) 160.056 0.00181954
\(96\) 0 0
\(97\) 104905. 1.13205 0.566027 0.824387i \(-0.308480\pi\)
0.566027 + 0.824387i \(0.308480\pi\)
\(98\) −27991.5 −0.294415
\(99\) 0 0
\(100\) −14664.4 −0.146644
\(101\) −135417. −1.32090 −0.660451 0.750869i \(-0.729635\pi\)
−0.660451 + 0.750869i \(0.729635\pi\)
\(102\) 0 0
\(103\) 167505. 1.55573 0.777867 0.628428i \(-0.216302\pi\)
0.777867 + 0.628428i \(0.216302\pi\)
\(104\) −117339. −1.06380
\(105\) 0 0
\(106\) 64603.4 0.558458
\(107\) −57989.6 −0.489656 −0.244828 0.969567i \(-0.578731\pi\)
−0.244828 + 0.969567i \(0.578731\pi\)
\(108\) 0 0
\(109\) −14956.1 −0.120574 −0.0602869 0.998181i \(-0.519202\pi\)
−0.0602869 + 0.998181i \(0.519202\pi\)
\(110\) −8838.44 −0.0696457
\(111\) 0 0
\(112\) −23576.4 −0.177596
\(113\) −198323. −1.46109 −0.730544 0.682866i \(-0.760733\pi\)
−0.730544 + 0.682866i \(0.760733\pi\)
\(114\) 0 0
\(115\) 39245.0 0.276720
\(116\) −120740. −0.833115
\(117\) 0 0
\(118\) 49351.0 0.326280
\(119\) −178416. −1.15496
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) −100506. −0.611353
\(123\) 0 0
\(124\) 24211.0 0.141403
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −40986.5 −0.225492 −0.112746 0.993624i \(-0.535965\pi\)
−0.112746 + 0.993624i \(0.535965\pi\)
\(128\) −166614. −0.898851
\(129\) 0 0
\(130\) −52890.8 −0.274487
\(131\) 238406. 1.21378 0.606889 0.794787i \(-0.292417\pi\)
0.606889 + 0.794787i \(0.292417\pi\)
\(132\) 0 0
\(133\) 544.257 0.00266793
\(134\) −109002. −0.524413
\(135\) 0 0
\(136\) −340107. −1.57677
\(137\) −149534. −0.680673 −0.340337 0.940304i \(-0.610541\pi\)
−0.340337 + 0.940304i \(0.610541\pi\)
\(138\) 0 0
\(139\) 167700. 0.736202 0.368101 0.929786i \(-0.380008\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(140\) −49865.2 −0.215019
\(141\) 0 0
\(142\) 165396. 0.688341
\(143\) 87614.3 0.358290
\(144\) 0 0
\(145\) −128648. −0.508142
\(146\) −81161.5 −0.315114
\(147\) 0 0
\(148\) 296611. 1.11310
\(149\) 272698. 1.00627 0.503136 0.864207i \(-0.332179\pi\)
0.503136 + 0.864207i \(0.332179\pi\)
\(150\) 0 0
\(151\) −448320. −1.60009 −0.800047 0.599937i \(-0.795192\pi\)
−0.800047 + 0.599937i \(0.795192\pi\)
\(152\) 1037.49 0.00364231
\(153\) 0 0
\(154\) −30054.4 −0.102119
\(155\) 25796.9 0.0862459
\(156\) 0 0
\(157\) −366634. −1.18709 −0.593545 0.804801i \(-0.702272\pi\)
−0.593545 + 0.804801i \(0.702272\pi\)
\(158\) −37281.9 −0.118811
\(159\) 0 0
\(160\) −149900. −0.462914
\(161\) 133450. 0.405744
\(162\) 0 0
\(163\) 501806. 1.47934 0.739668 0.672972i \(-0.234982\pi\)
0.739668 + 0.672972i \(0.234982\pi\)
\(164\) 323994. 0.940650
\(165\) 0 0
\(166\) 202360. 0.569973
\(167\) 195231. 0.541700 0.270850 0.962622i \(-0.412695\pi\)
0.270850 + 0.962622i \(0.412695\pi\)
\(168\) 0 0
\(169\) 153006. 0.412089
\(170\) −153303. −0.406846
\(171\) 0 0
\(172\) 399154. 1.02877
\(173\) −618180. −1.57036 −0.785181 0.619266i \(-0.787430\pi\)
−0.785181 + 0.619266i \(0.787430\pi\)
\(174\) 0 0
\(175\) −53131.6 −0.131147
\(176\) 33557.6 0.0816600
\(177\) 0 0
\(178\) −172471. −0.408007
\(179\) 88898.6 0.207378 0.103689 0.994610i \(-0.466935\pi\)
0.103689 + 0.994610i \(0.466935\pi\)
\(180\) 0 0
\(181\) −378128. −0.857911 −0.428956 0.903326i \(-0.641118\pi\)
−0.428956 + 0.903326i \(0.641118\pi\)
\(182\) −179851. −0.402470
\(183\) 0 0
\(184\) 254389. 0.553930
\(185\) 316040. 0.678910
\(186\) 0 0
\(187\) 253949. 0.531059
\(188\) 189536. 0.391109
\(189\) 0 0
\(190\) 467.651 0.000939805 0
\(191\) −125442. −0.248806 −0.124403 0.992232i \(-0.539701\pi\)
−0.124403 + 0.992232i \(0.539701\pi\)
\(192\) 0 0
\(193\) −928398. −1.79408 −0.897038 0.441953i \(-0.854286\pi\)
−0.897038 + 0.441953i \(0.854286\pi\)
\(194\) 306512. 0.584713
\(195\) 0 0
\(196\) 224781. 0.417946
\(197\) −1.03233e6 −1.89519 −0.947595 0.319473i \(-0.896494\pi\)
−0.947595 + 0.319473i \(0.896494\pi\)
\(198\) 0 0
\(199\) −155017. −0.277489 −0.138744 0.990328i \(-0.544307\pi\)
−0.138744 + 0.990328i \(0.544307\pi\)
\(200\) −101283. −0.179044
\(201\) 0 0
\(202\) −395662. −0.682254
\(203\) −437459. −0.745070
\(204\) 0 0
\(205\) 345217. 0.573730
\(206\) 489417. 0.803546
\(207\) 0 0
\(208\) 200814. 0.321837
\(209\) −774.670 −0.00122674
\(210\) 0 0
\(211\) −364263. −0.563259 −0.281630 0.959523i \(-0.590875\pi\)
−0.281630 + 0.959523i \(0.590875\pi\)
\(212\) −518789. −0.792777
\(213\) 0 0
\(214\) −169434. −0.252910
\(215\) 425300. 0.627478
\(216\) 0 0
\(217\) 87720.4 0.126459
\(218\) −43698.8 −0.0622771
\(219\) 0 0
\(220\) 70975.8 0.0988676
\(221\) 1.51968e6 2.09301
\(222\) 0 0
\(223\) −74806.0 −0.100734 −0.0503668 0.998731i \(-0.516039\pi\)
−0.0503668 + 0.998731i \(0.516039\pi\)
\(224\) −509721. −0.678755
\(225\) 0 0
\(226\) −579459. −0.754661
\(227\) −1.22677e6 −1.58015 −0.790075 0.613010i \(-0.789958\pi\)
−0.790075 + 0.613010i \(0.789958\pi\)
\(228\) 0 0
\(229\) −440852. −0.555526 −0.277763 0.960650i \(-0.589593\pi\)
−0.277763 + 0.960650i \(0.589593\pi\)
\(230\) 114666. 0.142927
\(231\) 0 0
\(232\) −833910. −1.01718
\(233\) 514549. 0.620922 0.310461 0.950586i \(-0.399517\pi\)
0.310461 + 0.950586i \(0.399517\pi\)
\(234\) 0 0
\(235\) 201952. 0.238549
\(236\) −396306. −0.463181
\(237\) 0 0
\(238\) −521296. −0.596544
\(239\) 984315. 1.11465 0.557326 0.830294i \(-0.311827\pi\)
0.557326 + 0.830294i \(0.311827\pi\)
\(240\) 0 0
\(241\) 284794. 0.315855 0.157927 0.987451i \(-0.449519\pi\)
0.157927 + 0.987451i \(0.449519\pi\)
\(242\) 42778.1 0.0469551
\(243\) 0 0
\(244\) 807098. 0.867865
\(245\) 239505. 0.254918
\(246\) 0 0
\(247\) −4635.76 −0.00483480
\(248\) 167218. 0.172645
\(249\) 0 0
\(250\) −45653.1 −0.0461977
\(251\) −134529. −0.134782 −0.0673911 0.997727i \(-0.521468\pi\)
−0.0673911 + 0.997727i \(0.521468\pi\)
\(252\) 0 0
\(253\) −189946. −0.186564
\(254\) −119754. −0.116468
\(255\) 0 0
\(256\) −763432. −0.728066
\(257\) −2.06732e6 −1.95242 −0.976212 0.216817i \(-0.930433\pi\)
−0.976212 + 0.216817i \(0.930433\pi\)
\(258\) 0 0
\(259\) 1.07467e6 0.995462
\(260\) 424732. 0.389656
\(261\) 0 0
\(262\) 696575. 0.626924
\(263\) 661739. 0.589926 0.294963 0.955509i \(-0.404693\pi\)
0.294963 + 0.955509i \(0.404693\pi\)
\(264\) 0 0
\(265\) −552771. −0.483538
\(266\) 1590.21 0.00137800
\(267\) 0 0
\(268\) 875327. 0.744446
\(269\) −703008. −0.592351 −0.296176 0.955133i \(-0.595711\pi\)
−0.296176 + 0.955133i \(0.595711\pi\)
\(270\) 0 0
\(271\) −1.33847e6 −1.10710 −0.553549 0.832817i \(-0.686727\pi\)
−0.553549 + 0.832817i \(0.686727\pi\)
\(272\) 582059. 0.477029
\(273\) 0 0
\(274\) −436908. −0.351572
\(275\) 75625.0 0.0603023
\(276\) 0 0
\(277\) −33171.1 −0.0259753 −0.0129877 0.999916i \(-0.504134\pi\)
−0.0129877 + 0.999916i \(0.504134\pi\)
\(278\) 489987. 0.380253
\(279\) 0 0
\(280\) −344403. −0.262526
\(281\) 321114. 0.242601 0.121301 0.992616i \(-0.461293\pi\)
0.121301 + 0.992616i \(0.461293\pi\)
\(282\) 0 0
\(283\) −1.90591e6 −1.41461 −0.707305 0.706908i \(-0.750089\pi\)
−0.707305 + 0.706908i \(0.750089\pi\)
\(284\) −1.32819e6 −0.977155
\(285\) 0 0
\(286\) 255991. 0.185059
\(287\) 1.17388e6 0.841240
\(288\) 0 0
\(289\) 2.98491e6 2.10226
\(290\) −375885. −0.262458
\(291\) 0 0
\(292\) 651756. 0.447330
\(293\) −272957. −0.185748 −0.0928742 0.995678i \(-0.529605\pi\)
−0.0928742 + 0.995678i \(0.529605\pi\)
\(294\) 0 0
\(295\) −422265. −0.282508
\(296\) 2.04859e6 1.35902
\(297\) 0 0
\(298\) 796768. 0.519746
\(299\) −1.13667e6 −0.735286
\(300\) 0 0
\(301\) 1.44620e6 0.920050
\(302\) −1.30990e6 −0.826459
\(303\) 0 0
\(304\) −1775.57 −0.00110193
\(305\) 859966. 0.529336
\(306\) 0 0
\(307\) −843806. −0.510971 −0.255486 0.966813i \(-0.582235\pi\)
−0.255486 + 0.966813i \(0.582235\pi\)
\(308\) 241348. 0.144966
\(309\) 0 0
\(310\) 75373.4 0.0445465
\(311\) −2.06909e6 −1.21305 −0.606523 0.795066i \(-0.707436\pi\)
−0.606523 + 0.795066i \(0.707436\pi\)
\(312\) 0 0
\(313\) 603113. 0.347967 0.173983 0.984749i \(-0.444336\pi\)
0.173983 + 0.984749i \(0.444336\pi\)
\(314\) −1.07123e6 −0.613139
\(315\) 0 0
\(316\) 299387. 0.168661
\(317\) 1.67334e6 0.935268 0.467634 0.883922i \(-0.345107\pi\)
0.467634 + 0.883922i \(0.345107\pi\)
\(318\) 0 0
\(319\) 622659. 0.342589
\(320\) −216108. −0.117977
\(321\) 0 0
\(322\) 389913. 0.209569
\(323\) −13436.7 −0.00716616
\(324\) 0 0
\(325\) 452553. 0.237663
\(326\) 1.46618e6 0.764086
\(327\) 0 0
\(328\) 2.23772e6 1.14848
\(329\) 686720. 0.349776
\(330\) 0 0
\(331\) −2.20421e6 −1.10582 −0.552909 0.833242i \(-0.686482\pi\)
−0.552909 + 0.833242i \(0.686482\pi\)
\(332\) −1.62502e6 −0.809122
\(333\) 0 0
\(334\) 570427. 0.279791
\(335\) 932663. 0.454060
\(336\) 0 0
\(337\) 1.07377e6 0.515036 0.257518 0.966273i \(-0.417095\pi\)
0.257518 + 0.966273i \(0.417095\pi\)
\(338\) 447052. 0.212847
\(339\) 0 0
\(340\) 1.23108e6 0.577550
\(341\) −124857. −0.0581470
\(342\) 0 0
\(343\) 2.24319e6 1.02951
\(344\) 2.75683e6 1.25607
\(345\) 0 0
\(346\) −1.80620e6 −0.811101
\(347\) 1.39783e6 0.623203 0.311601 0.950213i \(-0.399135\pi\)
0.311601 + 0.950213i \(0.399135\pi\)
\(348\) 0 0
\(349\) −2.66674e6 −1.17197 −0.585985 0.810322i \(-0.699292\pi\)
−0.585985 + 0.810322i \(0.699292\pi\)
\(350\) −155240. −0.0677381
\(351\) 0 0
\(352\) 725514. 0.312097
\(353\) 594048. 0.253738 0.126869 0.991920i \(-0.459507\pi\)
0.126869 + 0.991920i \(0.459507\pi\)
\(354\) 0 0
\(355\) −1.41519e6 −0.595996
\(356\) 1.38501e6 0.579198
\(357\) 0 0
\(358\) 259744. 0.107112
\(359\) 3.35774e6 1.37503 0.687513 0.726172i \(-0.258702\pi\)
0.687513 + 0.726172i \(0.258702\pi\)
\(360\) 0 0
\(361\) −2.47606e6 −0.999983
\(362\) −1.10481e6 −0.443116
\(363\) 0 0
\(364\) 1.44427e6 0.571339
\(365\) 694448. 0.272840
\(366\) 0 0
\(367\) 2.58775e6 1.00290 0.501450 0.865187i \(-0.332800\pi\)
0.501450 + 0.865187i \(0.332800\pi\)
\(368\) −435362. −0.167583
\(369\) 0 0
\(370\) 923404. 0.350661
\(371\) −1.87965e6 −0.708995
\(372\) 0 0
\(373\) −1.07376e6 −0.399608 −0.199804 0.979836i \(-0.564031\pi\)
−0.199804 + 0.979836i \(0.564031\pi\)
\(374\) 741989. 0.274295
\(375\) 0 0
\(376\) 1.30907e6 0.477520
\(377\) 3.72610e6 1.35021
\(378\) 0 0
\(379\) 5.16745e6 1.84790 0.923949 0.382516i \(-0.124942\pi\)
0.923949 + 0.382516i \(0.124942\pi\)
\(380\) −3755.40 −0.00133413
\(381\) 0 0
\(382\) −366517. −0.128510
\(383\) −2.42092e6 −0.843302 −0.421651 0.906758i \(-0.638549\pi\)
−0.421651 + 0.906758i \(0.638549\pi\)
\(384\) 0 0
\(385\) 257157. 0.0884191
\(386\) −2.71259e6 −0.926651
\(387\) 0 0
\(388\) −2.46140e6 −0.830047
\(389\) −1.92154e6 −0.643835 −0.321918 0.946768i \(-0.604327\pi\)
−0.321918 + 0.946768i \(0.604327\pi\)
\(390\) 0 0
\(391\) −3.29463e6 −1.08984
\(392\) 1.55249e6 0.510287
\(393\) 0 0
\(394\) −3.01626e6 −0.978877
\(395\) 318998. 0.102871
\(396\) 0 0
\(397\) 4.09572e6 1.30423 0.652114 0.758121i \(-0.273882\pi\)
0.652114 + 0.758121i \(0.273882\pi\)
\(398\) −452928. −0.143325
\(399\) 0 0
\(400\) 173335. 0.0541671
\(401\) −5.97525e6 −1.85565 −0.927823 0.373022i \(-0.878322\pi\)
−0.927823 + 0.373022i \(0.878322\pi\)
\(402\) 0 0
\(403\) −747167. −0.229168
\(404\) 3.17731e6 0.968514
\(405\) 0 0
\(406\) −1.27817e6 −0.384833
\(407\) −1.52963e6 −0.457721
\(408\) 0 0
\(409\) −1.92665e6 −0.569500 −0.284750 0.958602i \(-0.591911\pi\)
−0.284750 + 0.958602i \(0.591911\pi\)
\(410\) 1.00865e6 0.296335
\(411\) 0 0
\(412\) −3.93019e6 −1.14070
\(413\) −1.43588e6 −0.414231
\(414\) 0 0
\(415\) −1.73147e6 −0.493507
\(416\) 4.34160e6 1.23003
\(417\) 0 0
\(418\) −2263.43 −0.000633616 0
\(419\) 1.47857e6 0.411441 0.205720 0.978611i \(-0.434046\pi\)
0.205720 + 0.978611i \(0.434046\pi\)
\(420\) 0 0
\(421\) 4.82644e6 1.32715 0.663577 0.748108i \(-0.269037\pi\)
0.663577 + 0.748108i \(0.269037\pi\)
\(422\) −1.06430e6 −0.290927
\(423\) 0 0
\(424\) −3.58311e6 −0.967932
\(425\) 1.31172e6 0.352265
\(426\) 0 0
\(427\) 2.92425e6 0.776147
\(428\) 1.36062e6 0.359026
\(429\) 0 0
\(430\) 1.24264e6 0.324096
\(431\) −2.89229e6 −0.749978 −0.374989 0.927029i \(-0.622353\pi\)
−0.374989 + 0.927029i \(0.622353\pi\)
\(432\) 0 0
\(433\) 2.36700e6 0.606706 0.303353 0.952878i \(-0.401894\pi\)
0.303353 + 0.952878i \(0.401894\pi\)
\(434\) 256301. 0.0653170
\(435\) 0 0
\(436\) 350917. 0.0884073
\(437\) 10050.2 0.00251752
\(438\) 0 0
\(439\) 3.22037e6 0.797525 0.398762 0.917054i \(-0.369440\pi\)
0.398762 + 0.917054i \(0.369440\pi\)
\(440\) 490207. 0.120711
\(441\) 0 0
\(442\) 4.44019e6 1.08105
\(443\) 3.80335e6 0.920782 0.460391 0.887716i \(-0.347709\pi\)
0.460391 + 0.887716i \(0.347709\pi\)
\(444\) 0 0
\(445\) 1.47573e6 0.353270
\(446\) −218568. −0.0520295
\(447\) 0 0
\(448\) −734858. −0.172985
\(449\) 6.55303e6 1.53400 0.767001 0.641646i \(-0.221748\pi\)
0.767001 + 0.641646i \(0.221748\pi\)
\(450\) 0 0
\(451\) −1.67085e6 −0.386809
\(452\) 4.65326e6 1.07130
\(453\) 0 0
\(454\) −3.58437e6 −0.816157
\(455\) 1.53887e6 0.348477
\(456\) 0 0
\(457\) −7.41470e6 −1.66074 −0.830372 0.557209i \(-0.811872\pi\)
−0.830372 + 0.557209i \(0.811872\pi\)
\(458\) −1.28808e6 −0.286932
\(459\) 0 0
\(460\) −920810. −0.202897
\(461\) −409525. −0.0897487 −0.0448743 0.998993i \(-0.514289\pi\)
−0.0448743 + 0.998993i \(0.514289\pi\)
\(462\) 0 0
\(463\) 7.07192e6 1.53315 0.766575 0.642154i \(-0.221959\pi\)
0.766575 + 0.642154i \(0.221959\pi\)
\(464\) 1.42715e6 0.307734
\(465\) 0 0
\(466\) 1.50341e6 0.320710
\(467\) 6.35423e6 1.34825 0.674125 0.738617i \(-0.264521\pi\)
0.674125 + 0.738617i \(0.264521\pi\)
\(468\) 0 0
\(469\) 3.17145e6 0.665772
\(470\) 590062. 0.123212
\(471\) 0 0
\(472\) −2.73716e6 −0.565516
\(473\) −2.05845e6 −0.423046
\(474\) 0 0
\(475\) −4001.39 −0.000813724 0
\(476\) 4.18619e6 0.846841
\(477\) 0 0
\(478\) 2.87597e6 0.575725
\(479\) −6.36751e6 −1.26803 −0.634017 0.773319i \(-0.718595\pi\)
−0.634017 + 0.773319i \(0.718595\pi\)
\(480\) 0 0
\(481\) −9.15358e6 −1.80397
\(482\) 832109. 0.163141
\(483\) 0 0
\(484\) −343523. −0.0666565
\(485\) −2.62263e6 −0.506270
\(486\) 0 0
\(487\) −2.94280e6 −0.562261 −0.281130 0.959670i \(-0.590709\pi\)
−0.281130 + 0.959670i \(0.590709\pi\)
\(488\) 5.57437e6 1.05961
\(489\) 0 0
\(490\) 699787. 0.131667
\(491\) 501628. 0.0939027 0.0469513 0.998897i \(-0.485049\pi\)
0.0469513 + 0.998897i \(0.485049\pi\)
\(492\) 0 0
\(493\) 1.08001e7 2.00129
\(494\) −13544.8 −0.00249720
\(495\) 0 0
\(496\) −286176. −0.0522311
\(497\) −4.81224e6 −0.873888
\(498\) 0 0
\(499\) −9.19784e6 −1.65362 −0.826808 0.562484i \(-0.809846\pi\)
−0.826808 + 0.562484i \(0.809846\pi\)
\(500\) 366611. 0.0655813
\(501\) 0 0
\(502\) −393068. −0.0696158
\(503\) 6.53811e6 1.15221 0.576106 0.817375i \(-0.304572\pi\)
0.576106 + 0.817375i \(0.304572\pi\)
\(504\) 0 0
\(505\) 3.38543e6 0.590726
\(506\) −554984. −0.0963616
\(507\) 0 0
\(508\) 961669. 0.165336
\(509\) 1.49017e6 0.254942 0.127471 0.991842i \(-0.459314\pi\)
0.127471 + 0.991842i \(0.459314\pi\)
\(510\) 0 0
\(511\) 2.36141e6 0.400055
\(512\) 3.10107e6 0.522801
\(513\) 0 0
\(514\) −6.04029e6 −1.00844
\(515\) −4.18763e6 −0.695746
\(516\) 0 0
\(517\) −977445. −0.160830
\(518\) 3.13996e6 0.514162
\(519\) 0 0
\(520\) 2.93349e6 0.475746
\(521\) −3.82163e6 −0.616814 −0.308407 0.951255i \(-0.599796\pi\)
−0.308407 + 0.951255i \(0.599796\pi\)
\(522\) 0 0
\(523\) −4.18273e6 −0.668660 −0.334330 0.942456i \(-0.608510\pi\)
−0.334330 + 0.942456i \(0.608510\pi\)
\(524\) −5.59375e6 −0.889968
\(525\) 0 0
\(526\) 1.93347e6 0.304700
\(527\) −2.16566e6 −0.339675
\(528\) 0 0
\(529\) −3.97207e6 −0.617131
\(530\) −1.61509e6 −0.249750
\(531\) 0 0
\(532\) −12769.9 −0.00195619
\(533\) −9.99866e6 −1.52449
\(534\) 0 0
\(535\) 1.44974e6 0.218981
\(536\) 6.04560e6 0.908923
\(537\) 0 0
\(538\) −2.05405e6 −0.305953
\(539\) −1.15921e6 −0.171866
\(540\) 0 0
\(541\) 2.80424e6 0.411928 0.205964 0.978560i \(-0.433967\pi\)
0.205964 + 0.978560i \(0.433967\pi\)
\(542\) −3.91075e6 −0.571823
\(543\) 0 0
\(544\) 1.25841e7 1.82316
\(545\) 373903. 0.0539222
\(546\) 0 0
\(547\) −8.42403e6 −1.20379 −0.601896 0.798574i \(-0.705588\pi\)
−0.601896 + 0.798574i \(0.705588\pi\)
\(548\) 3.50853e6 0.499084
\(549\) 0 0
\(550\) 220961. 0.0311465
\(551\) −32945.5 −0.00462293
\(552\) 0 0
\(553\) 1.08473e6 0.150837
\(554\) −96919.4 −0.0134164
\(555\) 0 0
\(556\) −3.93477e6 −0.539799
\(557\) 3.56702e6 0.487155 0.243577 0.969881i \(-0.421679\pi\)
0.243577 + 0.969881i \(0.421679\pi\)
\(558\) 0 0
\(559\) −1.23181e7 −1.66730
\(560\) 589411. 0.0794233
\(561\) 0 0
\(562\) 938231. 0.125305
\(563\) −4.70552e6 −0.625658 −0.312829 0.949810i \(-0.601277\pi\)
−0.312829 + 0.949810i \(0.601277\pi\)
\(564\) 0 0
\(565\) 4.95807e6 0.653418
\(566\) −5.56869e6 −0.730655
\(567\) 0 0
\(568\) −9.17337e6 −1.19305
\(569\) −2.60879e6 −0.337799 −0.168900 0.985633i \(-0.554021\pi\)
−0.168900 + 0.985633i \(0.554021\pi\)
\(570\) 0 0
\(571\) 1.13036e6 0.145086 0.0725431 0.997365i \(-0.476889\pi\)
0.0725431 + 0.997365i \(0.476889\pi\)
\(572\) −2.05570e6 −0.262706
\(573\) 0 0
\(574\) 3.42985e6 0.434506
\(575\) −981126. −0.123753
\(576\) 0 0
\(577\) 1.12075e7 1.40142 0.700710 0.713446i \(-0.252867\pi\)
0.700710 + 0.713446i \(0.252867\pi\)
\(578\) 8.72132e6 1.08583
\(579\) 0 0
\(580\) 3.01849e6 0.372580
\(581\) −5.88771e6 −0.723613
\(582\) 0 0
\(583\) 2.67541e6 0.326001
\(584\) 4.50147e6 0.546162
\(585\) 0 0
\(586\) −797526. −0.0959402
\(587\) −9.05798e6 −1.08502 −0.542508 0.840051i \(-0.682525\pi\)
−0.542508 + 0.840051i \(0.682525\pi\)
\(588\) 0 0
\(589\) 6606.31 0.000784641 0
\(590\) −1.23377e6 −0.145917
\(591\) 0 0
\(592\) −3.50596e6 −0.411152
\(593\) −1.00907e7 −1.17837 −0.589186 0.807997i \(-0.700552\pi\)
−0.589186 + 0.807997i \(0.700552\pi\)
\(594\) 0 0
\(595\) 4.46040e6 0.516514
\(596\) −6.39833e6 −0.737821
\(597\) 0 0
\(598\) −3.32112e6 −0.379780
\(599\) 1.29126e7 1.47044 0.735222 0.677827i \(-0.237078\pi\)
0.735222 + 0.677827i \(0.237078\pi\)
\(600\) 0 0
\(601\) 1.82591e6 0.206202 0.103101 0.994671i \(-0.467124\pi\)
0.103101 + 0.994671i \(0.467124\pi\)
\(602\) 4.22550e6 0.475211
\(603\) 0 0
\(604\) 1.05190e7 1.17322
\(605\) −366025. −0.0406558
\(606\) 0 0
\(607\) −1.26409e6 −0.139253 −0.0696267 0.997573i \(-0.522181\pi\)
−0.0696267 + 0.997573i \(0.522181\pi\)
\(608\) −38387.7 −0.00421146
\(609\) 0 0
\(610\) 2.51265e6 0.273405
\(611\) −5.84920e6 −0.633860
\(612\) 0 0
\(613\) 1.59125e7 1.71036 0.855180 0.518332i \(-0.173447\pi\)
0.855180 + 0.518332i \(0.173447\pi\)
\(614\) −2.46543e6 −0.263920
\(615\) 0 0
\(616\) 1.66691e6 0.176995
\(617\) −85225.6 −0.00901274 −0.00450637 0.999990i \(-0.501434\pi\)
−0.00450637 + 0.999990i \(0.501434\pi\)
\(618\) 0 0
\(619\) −1.20387e7 −1.26285 −0.631425 0.775437i \(-0.717530\pi\)
−0.631425 + 0.775437i \(0.717530\pi\)
\(620\) −605276. −0.0632374
\(621\) 0 0
\(622\) −6.04545e6 −0.626546
\(623\) 5.01810e6 0.517987
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 1.76218e6 0.179727
\(627\) 0 0
\(628\) 8.60236e6 0.870400
\(629\) −2.65316e7 −2.67385
\(630\) 0 0
\(631\) 121417. 0.0121396 0.00606981 0.999982i \(-0.498068\pi\)
0.00606981 + 0.999982i \(0.498068\pi\)
\(632\) 2.06777e6 0.205925
\(633\) 0 0
\(634\) 4.88916e6 0.483071
\(635\) 1.02466e6 0.100843
\(636\) 0 0
\(637\) −6.93689e6 −0.677355
\(638\) 1.81928e6 0.176949
\(639\) 0 0
\(640\) 4.16536e6 0.401978
\(641\) −1.25328e7 −1.20477 −0.602385 0.798206i \(-0.705783\pi\)
−0.602385 + 0.798206i \(0.705783\pi\)
\(642\) 0 0
\(643\) −3.45380e6 −0.329435 −0.164717 0.986341i \(-0.552671\pi\)
−0.164717 + 0.986341i \(0.552671\pi\)
\(644\) −3.13114e6 −0.297501
\(645\) 0 0
\(646\) −39259.4 −0.00370137
\(647\) −1.71115e7 −1.60704 −0.803521 0.595276i \(-0.797043\pi\)
−0.803521 + 0.595276i \(0.797043\pi\)
\(648\) 0 0
\(649\) 2.04376e6 0.190467
\(650\) 1.32227e6 0.122754
\(651\) 0 0
\(652\) −1.17739e7 −1.08468
\(653\) −1.61622e7 −1.48326 −0.741630 0.670809i \(-0.765947\pi\)
−0.741630 + 0.670809i \(0.765947\pi\)
\(654\) 0 0
\(655\) −5.96015e6 −0.542818
\(656\) −3.82964e6 −0.347455
\(657\) 0 0
\(658\) 2.00646e6 0.180661
\(659\) −9.54805e6 −0.856449 −0.428224 0.903672i \(-0.640861\pi\)
−0.428224 + 0.903672i \(0.640861\pi\)
\(660\) 0 0
\(661\) −1.24374e7 −1.10720 −0.553599 0.832784i \(-0.686746\pi\)
−0.553599 + 0.832784i \(0.686746\pi\)
\(662\) −6.44027e6 −0.571162
\(663\) 0 0
\(664\) −1.12235e7 −0.987889
\(665\) −13606.4 −0.00119314
\(666\) 0 0
\(667\) −8.07810e6 −0.703064
\(668\) −4.58073e6 −0.397186
\(669\) 0 0
\(670\) 2.72505e6 0.234525
\(671\) −4.16224e6 −0.356878
\(672\) 0 0
\(673\) 1.37772e7 1.17253 0.586266 0.810119i \(-0.300597\pi\)
0.586266 + 0.810119i \(0.300597\pi\)
\(674\) 3.13735e6 0.266019
\(675\) 0 0
\(676\) −3.58999e6 −0.302153
\(677\) 1.06456e6 0.0892683 0.0446341 0.999003i \(-0.485788\pi\)
0.0446341 + 0.999003i \(0.485788\pi\)
\(678\) 0 0
\(679\) −8.91804e6 −0.742326
\(680\) 8.50268e6 0.705154
\(681\) 0 0
\(682\) −364807. −0.0300333
\(683\) 1.48070e7 1.21455 0.607275 0.794492i \(-0.292263\pi\)
0.607275 + 0.794492i \(0.292263\pi\)
\(684\) 0 0
\(685\) 3.73835e6 0.304406
\(686\) 6.55415e6 0.531748
\(687\) 0 0
\(688\) −4.71803e6 −0.380005
\(689\) 1.60101e7 1.28483
\(690\) 0 0
\(691\) 1.56554e7 1.24729 0.623646 0.781707i \(-0.285651\pi\)
0.623646 + 0.781707i \(0.285651\pi\)
\(692\) 1.45044e7 1.15142
\(693\) 0 0
\(694\) 4.08417e6 0.321888
\(695\) −4.19251e6 −0.329240
\(696\) 0 0
\(697\) −2.89810e7 −2.25960
\(698\) −7.79167e6 −0.605330
\(699\) 0 0
\(700\) 1.24663e6 0.0961596
\(701\) −1.56474e7 −1.20267 −0.601334 0.798998i \(-0.705364\pi\)
−0.601334 + 0.798998i \(0.705364\pi\)
\(702\) 0 0
\(703\) 80934.4 0.00617653
\(704\) 1.04596e6 0.0795398
\(705\) 0 0
\(706\) 1.73569e6 0.131057
\(707\) 1.15119e7 0.866160
\(708\) 0 0
\(709\) −635875. −0.0475068 −0.0237534 0.999718i \(-0.507562\pi\)
−0.0237534 + 0.999718i \(0.507562\pi\)
\(710\) −4.13490e6 −0.307836
\(711\) 0 0
\(712\) 9.56580e6 0.707166
\(713\) 1.61984e6 0.119330
\(714\) 0 0
\(715\) −2.19036e6 −0.160232
\(716\) −2.08584e6 −0.152054
\(717\) 0 0
\(718\) 9.81064e6 0.710209
\(719\) 2.50359e6 0.180610 0.0903048 0.995914i \(-0.471216\pi\)
0.0903048 + 0.995914i \(0.471216\pi\)
\(720\) 0 0
\(721\) −1.42397e7 −1.02015
\(722\) −7.23454e6 −0.516497
\(723\) 0 0
\(724\) 8.87205e6 0.629039
\(725\) 3.21621e6 0.227248
\(726\) 0 0
\(727\) 8.82888e6 0.619540 0.309770 0.950811i \(-0.399748\pi\)
0.309770 + 0.950811i \(0.399748\pi\)
\(728\) 9.97508e6 0.697570
\(729\) 0 0
\(730\) 2.02904e6 0.140923
\(731\) −3.57040e7 −2.47129
\(732\) 0 0
\(733\) −2.93960e6 −0.202082 −0.101041 0.994882i \(-0.532217\pi\)
−0.101041 + 0.994882i \(0.532217\pi\)
\(734\) 7.56089e6 0.518004
\(735\) 0 0
\(736\) −9.41250e6 −0.640487
\(737\) −4.51409e6 −0.306127
\(738\) 0 0
\(739\) −1.51762e6 −0.102224 −0.0511120 0.998693i \(-0.516277\pi\)
−0.0511120 + 0.998693i \(0.516277\pi\)
\(740\) −7.41527e6 −0.497792
\(741\) 0 0
\(742\) −5.49197e6 −0.366200
\(743\) 1.07165e7 0.712168 0.356084 0.934454i \(-0.384112\pi\)
0.356084 + 0.934454i \(0.384112\pi\)
\(744\) 0 0
\(745\) −6.81744e6 −0.450019
\(746\) −3.13731e6 −0.206400
\(747\) 0 0
\(748\) −5.95844e6 −0.389384
\(749\) 4.92973e6 0.321084
\(750\) 0 0
\(751\) −2.69694e7 −1.74490 −0.872452 0.488700i \(-0.837471\pi\)
−0.872452 + 0.488700i \(0.837471\pi\)
\(752\) −2.24033e6 −0.144467
\(753\) 0 0
\(754\) 1.08869e7 0.697391
\(755\) 1.12080e7 0.715584
\(756\) 0 0
\(757\) −2.81995e7 −1.78855 −0.894275 0.447518i \(-0.852308\pi\)
−0.894275 + 0.447518i \(0.852308\pi\)
\(758\) 1.50982e7 0.954450
\(759\) 0 0
\(760\) −25937.4 −0.00162889
\(761\) −5.29643e6 −0.331529 −0.165764 0.986165i \(-0.553009\pi\)
−0.165764 + 0.986165i \(0.553009\pi\)
\(762\) 0 0
\(763\) 1.27143e6 0.0790643
\(764\) 2.94326e6 0.182430
\(765\) 0 0
\(766\) −7.07344e6 −0.435571
\(767\) 1.22302e7 0.750665
\(768\) 0 0
\(769\) 6.09571e6 0.371714 0.185857 0.982577i \(-0.440494\pi\)
0.185857 + 0.982577i \(0.440494\pi\)
\(770\) 751360. 0.0456690
\(771\) 0 0
\(772\) 2.17831e7 1.31546
\(773\) −1.02486e7 −0.616901 −0.308451 0.951240i \(-0.599810\pi\)
−0.308451 + 0.951240i \(0.599810\pi\)
\(774\) 0 0
\(775\) −644923. −0.0385704
\(776\) −1.70001e7 −1.01344
\(777\) 0 0
\(778\) −5.61434e6 −0.332545
\(779\) 88406.4 0.00521963
\(780\) 0 0
\(781\) 6.84951e6 0.401820
\(782\) −9.62624e6 −0.562911
\(783\) 0 0
\(784\) −2.65693e6 −0.154380
\(785\) 9.16585e6 0.530883
\(786\) 0 0
\(787\) −1.62333e7 −0.934267 −0.467133 0.884187i \(-0.654713\pi\)
−0.467133 + 0.884187i \(0.654713\pi\)
\(788\) 2.42217e7 1.38959
\(789\) 0 0
\(790\) 932048. 0.0531337
\(791\) 1.68595e7 0.958084
\(792\) 0 0
\(793\) −2.49075e7 −1.40653
\(794\) 1.19669e7 0.673642
\(795\) 0 0
\(796\) 3.63717e6 0.203461
\(797\) −1.29153e7 −0.720211 −0.360105 0.932912i \(-0.617259\pi\)
−0.360105 + 0.932912i \(0.617259\pi\)
\(798\) 0 0
\(799\) −1.69539e7 −0.939511
\(800\) 3.74749e6 0.207021
\(801\) 0 0
\(802\) −1.74585e7 −0.958452
\(803\) −3.36113e6 −0.183948
\(804\) 0 0
\(805\) −3.33624e6 −0.181454
\(806\) −2.18307e6 −0.118367
\(807\) 0 0
\(808\) 2.19447e7 1.18250
\(809\) −1.40361e6 −0.0754007 −0.0377004 0.999289i \(-0.512003\pi\)
−0.0377004 + 0.999289i \(0.512003\pi\)
\(810\) 0 0
\(811\) −1.27909e7 −0.682887 −0.341444 0.939902i \(-0.610916\pi\)
−0.341444 + 0.939902i \(0.610916\pi\)
\(812\) 1.02641e7 0.546301
\(813\) 0 0
\(814\) −4.46928e6 −0.236416
\(815\) −1.25452e7 −0.661580
\(816\) 0 0
\(817\) 108915. 0.00570862
\(818\) −5.62928e6 −0.294150
\(819\) 0 0
\(820\) −8.09986e6 −0.420671
\(821\) 5.20603e6 0.269556 0.134778 0.990876i \(-0.456968\pi\)
0.134778 + 0.990876i \(0.456968\pi\)
\(822\) 0 0
\(823\) 3.77702e7 1.94379 0.971896 0.235409i \(-0.0756429\pi\)
0.971896 + 0.235409i \(0.0756429\pi\)
\(824\) −2.71446e7 −1.39272
\(825\) 0 0
\(826\) −4.19535e6 −0.213953
\(827\) 2.54890e7 1.29595 0.647976 0.761661i \(-0.275616\pi\)
0.647976 + 0.761661i \(0.275616\pi\)
\(828\) 0 0
\(829\) 1.71410e7 0.866262 0.433131 0.901331i \(-0.357409\pi\)
0.433131 + 0.901331i \(0.357409\pi\)
\(830\) −5.05900e6 −0.254900
\(831\) 0 0
\(832\) 6.25922e6 0.313482
\(833\) −2.01065e7 −1.00398
\(834\) 0 0
\(835\) −4.88079e6 −0.242255
\(836\) 18176.1 0.000899469 0
\(837\) 0 0
\(838\) 4.32009e6 0.212512
\(839\) 1.01094e7 0.495818 0.247909 0.968783i \(-0.420257\pi\)
0.247909 + 0.968783i \(0.420257\pi\)
\(840\) 0 0
\(841\) 5.96954e6 0.291039
\(842\) 1.41019e7 0.685483
\(843\) 0 0
\(844\) 8.54672e6 0.412994
\(845\) −3.82515e6 −0.184292
\(846\) 0 0
\(847\) −1.24464e6 −0.0596121
\(848\) 6.13212e6 0.292834
\(849\) 0 0
\(850\) 3.83259e6 0.181947
\(851\) 1.98448e7 0.939339
\(852\) 0 0
\(853\) 3.29141e7 1.54885 0.774425 0.632666i \(-0.218039\pi\)
0.774425 + 0.632666i \(0.218039\pi\)
\(854\) 8.54406e6 0.400885
\(855\) 0 0
\(856\) 9.39734e6 0.438349
\(857\) −6.94241e6 −0.322893 −0.161446 0.986881i \(-0.551616\pi\)
−0.161446 + 0.986881i \(0.551616\pi\)
\(858\) 0 0
\(859\) −1.84275e7 −0.852085 −0.426042 0.904703i \(-0.640093\pi\)
−0.426042 + 0.904703i \(0.640093\pi\)
\(860\) −9.97884e6 −0.460081
\(861\) 0 0
\(862\) −8.45068e6 −0.387368
\(863\) 2.60648e7 1.19131 0.595657 0.803239i \(-0.296892\pi\)
0.595657 + 0.803239i \(0.296892\pi\)
\(864\) 0 0
\(865\) 1.54545e7 0.702287
\(866\) 6.91589e6 0.313367
\(867\) 0 0
\(868\) −2.05819e6 −0.0927228
\(869\) −1.54395e6 −0.0693559
\(870\) 0 0
\(871\) −2.70131e7 −1.20650
\(872\) 2.42367e6 0.107940
\(873\) 0 0
\(874\) 29364.8 0.00130031
\(875\) 1.32829e6 0.0586506
\(876\) 0 0
\(877\) 1.86288e6 0.0817875 0.0408937 0.999164i \(-0.486979\pi\)
0.0408937 + 0.999164i \(0.486979\pi\)
\(878\) 9.40927e6 0.411926
\(879\) 0 0
\(880\) −838940. −0.0365194
\(881\) −1.01838e7 −0.442051 −0.221025 0.975268i \(-0.570940\pi\)
−0.221025 + 0.975268i \(0.570940\pi\)
\(882\) 0 0
\(883\) 6.25954e6 0.270172 0.135086 0.990834i \(-0.456869\pi\)
0.135086 + 0.990834i \(0.456869\pi\)
\(884\) −3.56563e7 −1.53464
\(885\) 0 0
\(886\) 1.11126e7 0.475589
\(887\) −1.80319e7 −0.769540 −0.384770 0.923012i \(-0.625719\pi\)
−0.384770 + 0.923012i \(0.625719\pi\)
\(888\) 0 0
\(889\) 3.48428e6 0.147863
\(890\) 4.31179e6 0.182466
\(891\) 0 0
\(892\) 1.75518e6 0.0738600
\(893\) 51717.6 0.00217025
\(894\) 0 0
\(895\) −2.22247e6 −0.0927422
\(896\) 1.41640e7 0.589407
\(897\) 0 0
\(898\) 1.91466e7 0.792321
\(899\) −5.30998e6 −0.219126
\(900\) 0 0
\(901\) 4.64052e7 1.90439
\(902\) −4.88189e6 −0.199789
\(903\) 0 0
\(904\) 3.21386e7 1.30799
\(905\) 9.45320e6 0.383670
\(906\) 0 0
\(907\) 2.69733e7 1.08872 0.544360 0.838852i \(-0.316772\pi\)
0.544360 + 0.838852i \(0.316772\pi\)
\(908\) 2.87838e7 1.15860
\(909\) 0 0
\(910\) 4.49627e6 0.179990
\(911\) 4.31660e7 1.72324 0.861621 0.507553i \(-0.169450\pi\)
0.861621 + 0.507553i \(0.169450\pi\)
\(912\) 0 0
\(913\) 8.38029e6 0.332723
\(914\) −2.16643e7 −0.857784
\(915\) 0 0
\(916\) 1.03438e7 0.407323
\(917\) −2.02670e7 −0.795915
\(918\) 0 0
\(919\) −3.69944e7 −1.44493 −0.722465 0.691407i \(-0.756991\pi\)
−0.722465 + 0.691407i \(0.756991\pi\)
\(920\) −6.35974e6 −0.247725
\(921\) 0 0
\(922\) −1.19655e6 −0.0463557
\(923\) 4.09887e7 1.58365
\(924\) 0 0
\(925\) −7.90099e6 −0.303618
\(926\) 2.06627e7 0.791882
\(927\) 0 0
\(928\) 3.08550e7 1.17613
\(929\) −1.63853e6 −0.0622895 −0.0311447 0.999515i \(-0.509915\pi\)
−0.0311447 + 0.999515i \(0.509915\pi\)
\(930\) 0 0
\(931\) 61334.7 0.00231917
\(932\) −1.20729e7 −0.455273
\(933\) 0 0
\(934\) 1.85658e7 0.696380
\(935\) −6.34873e6 −0.237497
\(936\) 0 0
\(937\) −2.02831e7 −0.754719 −0.377360 0.926067i \(-0.623168\pi\)
−0.377360 + 0.926067i \(0.623168\pi\)
\(938\) 9.26633e6 0.343875
\(939\) 0 0
\(940\) −4.73841e6 −0.174909
\(941\) 1.83342e7 0.674975 0.337487 0.941330i \(-0.390423\pi\)
0.337487 + 0.941330i \(0.390423\pi\)
\(942\) 0 0
\(943\) 2.16769e7 0.793812
\(944\) 4.68436e6 0.171088
\(945\) 0 0
\(946\) −6.01438e6 −0.218506
\(947\) 6.09095e6 0.220704 0.110352 0.993893i \(-0.464802\pi\)
0.110352 + 0.993893i \(0.464802\pi\)
\(948\) 0 0
\(949\) −2.01136e7 −0.724976
\(950\) −11691.3 −0.000420293 0
\(951\) 0 0
\(952\) 2.89127e7 1.03394
\(953\) 5.31211e7 1.89467 0.947337 0.320238i \(-0.103763\pi\)
0.947337 + 0.320238i \(0.103763\pi\)
\(954\) 0 0
\(955\) 3.13605e6 0.111269
\(956\) −2.30951e7 −0.817287
\(957\) 0 0
\(958\) −1.86046e7 −0.654947
\(959\) 1.27120e7 0.446340
\(960\) 0 0
\(961\) −2.75644e7 −0.962808
\(962\) −2.67449e7 −0.931759
\(963\) 0 0
\(964\) −6.68214e6 −0.231592
\(965\) 2.32099e7 0.802335
\(966\) 0 0
\(967\) −2.17670e6 −0.0748570 −0.0374285 0.999299i \(-0.511917\pi\)
−0.0374285 + 0.999299i \(0.511917\pi\)
\(968\) −2.37260e6 −0.0813836
\(969\) 0 0
\(970\) −7.66279e6 −0.261492
\(971\) −4.83305e7 −1.64503 −0.822514 0.568745i \(-0.807429\pi\)
−0.822514 + 0.568745i \(0.807429\pi\)
\(972\) 0 0
\(973\) −1.42563e7 −0.482753
\(974\) −8.59826e6 −0.290411
\(975\) 0 0
\(976\) −9.53996e6 −0.320569
\(977\) 3.84816e7 1.28978 0.644892 0.764274i \(-0.276902\pi\)
0.644892 + 0.764274i \(0.276902\pi\)
\(978\) 0 0
\(979\) −7.14253e6 −0.238175
\(980\) −5.61954e6 −0.186911
\(981\) 0 0
\(982\) 1.46566e6 0.0485013
\(983\) 1.53385e7 0.506288 0.253144 0.967429i \(-0.418535\pi\)
0.253144 + 0.967429i \(0.418535\pi\)
\(984\) 0 0
\(985\) 2.58082e7 0.847555
\(986\) 3.15556e7 1.03368
\(987\) 0 0
\(988\) 108769. 0.00354498
\(989\) 2.67054e7 0.868178
\(990\) 0 0
\(991\) −4.29143e7 −1.38809 −0.694046 0.719931i \(-0.744174\pi\)
−0.694046 + 0.719931i \(0.744174\pi\)
\(992\) −6.18712e6 −0.199622
\(993\) 0 0
\(994\) −1.40604e7 −0.451368
\(995\) 3.87542e6 0.124097
\(996\) 0 0
\(997\) 6.10887e7 1.94636 0.973180 0.230044i \(-0.0738869\pi\)
0.973180 + 0.230044i \(0.0738869\pi\)
\(998\) −2.68742e7 −0.854102
\(999\) 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.1.2 3
3.2 odd 2 165.6.a.a.1.2 3
15.14 odd 2 825.6.a.j.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.a.1.2 3 3.2 odd 2
495.6.a.e.1.2 3 1.1 even 1 trivial
825.6.a.j.1.2 3 15.14 odd 2