Properties

Label 320.6.a.r.1.1
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 1
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{70}) \)
Defining polynomial: \(x^{2} - 70\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-8.36660\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-20.7332 q^{3} -25.0000 q^{5} +35.2668 q^{7} +186.866 q^{9} +O(q^{10})\) \(q-20.7332 q^{3} -25.0000 q^{5} +35.2668 q^{7} +186.866 q^{9} +7.33201 q^{11} -619.328 q^{13} +518.330 q^{15} +959.328 q^{17} +309.328 q^{19} -731.194 q^{21} +2467.12 q^{23} +625.000 q^{25} +1163.85 q^{27} +1284.66 q^{29} +7095.32 q^{31} -152.016 q^{33} -881.670 q^{35} +6100.59 q^{37} +12840.7 q^{39} -18830.4 q^{41} -3147.48 q^{43} -4671.64 q^{45} +20556.8 q^{47} -15563.3 q^{49} -19889.9 q^{51} -33741.9 q^{53} -183.300 q^{55} -6413.36 q^{57} -15065.3 q^{59} +7542.11 q^{61} +6590.15 q^{63} +15483.2 q^{65} -25574.9 q^{67} -51151.3 q^{69} -56232.3 q^{71} +58657.5 q^{73} -12958.3 q^{75} +258.576 q^{77} +32238.7 q^{79} -69538.6 q^{81} -31173.4 q^{83} -23983.2 q^{85} -26635.0 q^{87} -75258.9 q^{89} -21841.7 q^{91} -147109. q^{93} -7733.20 q^{95} -176059. q^{97} +1370.10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 8q^{3} - 50q^{5} + 104q^{7} + 106q^{9} + O(q^{10}) \) \( 2q - 8q^{3} - 50q^{5} + 104q^{7} + 106q^{9} - 320q^{11} + 100q^{13} + 200q^{15} + 580q^{17} - 720q^{19} + 144q^{21} + 1688q^{23} + 1250q^{25} - 2960q^{27} - 108q^{29} + 9840q^{31} - 4320q^{33} - 2600q^{35} - 6540q^{37} + 22000q^{39} - 10620q^{41} - 25672q^{43} - 2650q^{45} + 28296q^{47} - 27646q^{49} - 24720q^{51} - 31340q^{53} + 8000q^{55} - 19520q^{57} - 30800q^{59} - 24540q^{61} + 1032q^{63} - 2500q^{65} - 34584q^{67} - 61072q^{69} - 12400q^{71} - 7180q^{73} - 5000q^{75} - 22240q^{77} + 71840q^{79} - 102398q^{81} + 31928q^{83} - 14500q^{85} - 44368q^{87} - 40748q^{89} + 27600q^{91} - 112160q^{93} + 18000q^{95} - 190140q^{97} + 27840q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −20.7332 −1.33004 −0.665018 0.746828i \(-0.731576\pi\)
−0.665018 + 0.746828i \(0.731576\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 35.2668 0.272033 0.136016 0.990707i \(-0.456570\pi\)
0.136016 + 0.990707i \(0.456570\pi\)
\(8\) 0 0
\(9\) 186.866 0.768994
\(10\) 0 0
\(11\) 7.33201 0.0182701 0.00913505 0.999958i \(-0.497092\pi\)
0.00913505 + 0.999958i \(0.497092\pi\)
\(12\) 0 0
\(13\) −619.328 −1.01639 −0.508197 0.861241i \(-0.669688\pi\)
−0.508197 + 0.861241i \(0.669688\pi\)
\(14\) 0 0
\(15\) 518.330 0.594810
\(16\) 0 0
\(17\) 959.328 0.805091 0.402545 0.915400i \(-0.368126\pi\)
0.402545 + 0.915400i \(0.368126\pi\)
\(18\) 0 0
\(19\) 309.328 0.196578 0.0982891 0.995158i \(-0.468663\pi\)
0.0982891 + 0.995158i \(0.468663\pi\)
\(20\) 0 0
\(21\) −731.194 −0.361813
\(22\) 0 0
\(23\) 2467.12 0.972458 0.486229 0.873831i \(-0.338372\pi\)
0.486229 + 0.873831i \(0.338372\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 1163.85 0.307246
\(28\) 0 0
\(29\) 1284.66 0.283656 0.141828 0.989891i \(-0.454702\pi\)
0.141828 + 0.989891i \(0.454702\pi\)
\(30\) 0 0
\(31\) 7095.32 1.32607 0.663037 0.748587i \(-0.269267\pi\)
0.663037 + 0.748587i \(0.269267\pi\)
\(32\) 0 0
\(33\) −152.016 −0.0242999
\(34\) 0 0
\(35\) −881.670 −0.121657
\(36\) 0 0
\(37\) 6100.59 0.732601 0.366301 0.930497i \(-0.380624\pi\)
0.366301 + 0.930497i \(0.380624\pi\)
\(38\) 0 0
\(39\) 12840.7 1.35184
\(40\) 0 0
\(41\) −18830.4 −1.74945 −0.874723 0.484623i \(-0.838957\pi\)
−0.874723 + 0.484623i \(0.838957\pi\)
\(42\) 0 0
\(43\) −3147.48 −0.259592 −0.129796 0.991541i \(-0.541432\pi\)
−0.129796 + 0.991541i \(0.541432\pi\)
\(44\) 0 0
\(45\) −4671.64 −0.343905
\(46\) 0 0
\(47\) 20556.8 1.35741 0.678705 0.734411i \(-0.262541\pi\)
0.678705 + 0.734411i \(0.262541\pi\)
\(48\) 0 0
\(49\) −15563.3 −0.925998
\(50\) 0 0
\(51\) −19889.9 −1.07080
\(52\) 0 0
\(53\) −33741.9 −1.64998 −0.824991 0.565146i \(-0.808820\pi\)
−0.824991 + 0.565146i \(0.808820\pi\)
\(54\) 0 0
\(55\) −183.300 −0.00817064
\(56\) 0 0
\(57\) −6413.36 −0.261456
\(58\) 0 0
\(59\) −15065.3 −0.563441 −0.281721 0.959496i \(-0.590905\pi\)
−0.281721 + 0.959496i \(0.590905\pi\)
\(60\) 0 0
\(61\) 7542.11 0.259518 0.129759 0.991546i \(-0.458580\pi\)
0.129759 + 0.991546i \(0.458580\pi\)
\(62\) 0 0
\(63\) 6590.15 0.209192
\(64\) 0 0
\(65\) 15483.2 0.454545
\(66\) 0 0
\(67\) −25574.9 −0.696029 −0.348015 0.937489i \(-0.613144\pi\)
−0.348015 + 0.937489i \(0.613144\pi\)
\(68\) 0 0
\(69\) −51151.3 −1.29340
\(70\) 0 0
\(71\) −56232.3 −1.32385 −0.661926 0.749569i \(-0.730261\pi\)
−0.661926 + 0.749569i \(0.730261\pi\)
\(72\) 0 0
\(73\) 58657.5 1.28830 0.644149 0.764900i \(-0.277212\pi\)
0.644149 + 0.764900i \(0.277212\pi\)
\(74\) 0 0
\(75\) −12958.3 −0.266007
\(76\) 0 0
\(77\) 258.576 0.00497006
\(78\) 0 0
\(79\) 32238.7 0.581179 0.290589 0.956848i \(-0.406149\pi\)
0.290589 + 0.956848i \(0.406149\pi\)
\(80\) 0 0
\(81\) −69538.6 −1.17764
\(82\) 0 0
\(83\) −31173.4 −0.496694 −0.248347 0.968671i \(-0.579887\pi\)
−0.248347 + 0.968671i \(0.579887\pi\)
\(84\) 0 0
\(85\) −23983.2 −0.360048
\(86\) 0 0
\(87\) −26635.0 −0.377272
\(88\) 0 0
\(89\) −75258.9 −1.00712 −0.503562 0.863959i \(-0.667977\pi\)
−0.503562 + 0.863959i \(0.667977\pi\)
\(90\) 0 0
\(91\) −21841.7 −0.276492
\(92\) 0 0
\(93\) −147109. −1.76372
\(94\) 0 0
\(95\) −7733.20 −0.0879124
\(96\) 0 0
\(97\) −176059. −1.89989 −0.949944 0.312419i \(-0.898861\pi\)
−0.949944 + 0.312419i \(0.898861\pi\)
\(98\) 0 0
\(99\) 1370.10 0.0140496
\(100\) 0 0
\(101\) 102454. 0.999370 0.499685 0.866207i \(-0.333449\pi\)
0.499685 + 0.866207i \(0.333449\pi\)
\(102\) 0 0
\(103\) −150320. −1.39612 −0.698062 0.716038i \(-0.745954\pi\)
−0.698062 + 0.716038i \(0.745954\pi\)
\(104\) 0 0
\(105\) 18279.8 0.161808
\(106\) 0 0
\(107\) 220857. 1.86488 0.932441 0.361321i \(-0.117674\pi\)
0.932441 + 0.361321i \(0.117674\pi\)
\(108\) 0 0
\(109\) 24621.0 0.198490 0.0992450 0.995063i \(-0.468357\pi\)
0.0992450 + 0.995063i \(0.468357\pi\)
\(110\) 0 0
\(111\) −126485. −0.974386
\(112\) 0 0
\(113\) −64568.7 −0.475692 −0.237846 0.971303i \(-0.576441\pi\)
−0.237846 + 0.971303i \(0.576441\pi\)
\(114\) 0 0
\(115\) −61678.0 −0.434896
\(116\) 0 0
\(117\) −115731. −0.781602
\(118\) 0 0
\(119\) 33832.4 0.219011
\(120\) 0 0
\(121\) −160997. −0.999666
\(122\) 0 0
\(123\) 390415. 2.32682
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 159599. 0.878054 0.439027 0.898474i \(-0.355323\pi\)
0.439027 + 0.898474i \(0.355323\pi\)
\(128\) 0 0
\(129\) 65257.3 0.345267
\(130\) 0 0
\(131\) −116112. −0.591153 −0.295577 0.955319i \(-0.595512\pi\)
−0.295577 + 0.955319i \(0.595512\pi\)
\(132\) 0 0
\(133\) 10909.0 0.0534757
\(134\) 0 0
\(135\) −29096.1 −0.137405
\(136\) 0 0
\(137\) −1446.13 −0.00658272 −0.00329136 0.999995i \(-0.501048\pi\)
−0.00329136 + 0.999995i \(0.501048\pi\)
\(138\) 0 0
\(139\) 135055. 0.592891 0.296446 0.955050i \(-0.404199\pi\)
0.296446 + 0.955050i \(0.404199\pi\)
\(140\) 0 0
\(141\) −426209. −1.80540
\(142\) 0 0
\(143\) −4540.92 −0.0185696
\(144\) 0 0
\(145\) −32116.4 −0.126855
\(146\) 0 0
\(147\) 322676. 1.23161
\(148\) 0 0
\(149\) −16097.8 −0.0594019 −0.0297010 0.999559i \(-0.509455\pi\)
−0.0297010 + 0.999559i \(0.509455\pi\)
\(150\) 0 0
\(151\) −467353. −1.66802 −0.834012 0.551746i \(-0.813962\pi\)
−0.834012 + 0.551746i \(0.813962\pi\)
\(152\) 0 0
\(153\) 179265. 0.619110
\(154\) 0 0
\(155\) −177383. −0.593038
\(156\) 0 0
\(157\) −210478. −0.681487 −0.340743 0.940156i \(-0.610679\pi\)
−0.340743 + 0.940156i \(0.610679\pi\)
\(158\) 0 0
\(159\) 699577. 2.19454
\(160\) 0 0
\(161\) 87007.4 0.264540
\(162\) 0 0
\(163\) 136230. 0.401610 0.200805 0.979631i \(-0.435644\pi\)
0.200805 + 0.979631i \(0.435644\pi\)
\(164\) 0 0
\(165\) 3800.40 0.0108672
\(166\) 0 0
\(167\) 246713. 0.684542 0.342271 0.939601i \(-0.388804\pi\)
0.342271 + 0.939601i \(0.388804\pi\)
\(168\) 0 0
\(169\) 12274.2 0.0330580
\(170\) 0 0
\(171\) 57802.8 0.151167
\(172\) 0 0
\(173\) 652180. 1.65673 0.828366 0.560187i \(-0.189271\pi\)
0.828366 + 0.560187i \(0.189271\pi\)
\(174\) 0 0
\(175\) 22041.7 0.0544065
\(176\) 0 0
\(177\) 312353. 0.749397
\(178\) 0 0
\(179\) −786542. −1.83480 −0.917402 0.397962i \(-0.869718\pi\)
−0.917402 + 0.397962i \(0.869718\pi\)
\(180\) 0 0
\(181\) 974.027 0.00220991 0.00110495 0.999999i \(-0.499648\pi\)
0.00110495 + 0.999999i \(0.499648\pi\)
\(182\) 0 0
\(183\) −156372. −0.345169
\(184\) 0 0
\(185\) −152515. −0.327629
\(186\) 0 0
\(187\) 7033.80 0.0147091
\(188\) 0 0
\(189\) 41045.1 0.0835809
\(190\) 0 0
\(191\) −469675. −0.931567 −0.465783 0.884899i \(-0.654227\pi\)
−0.465783 + 0.884899i \(0.654227\pi\)
\(192\) 0 0
\(193\) −644811. −1.24606 −0.623030 0.782198i \(-0.714099\pi\)
−0.623030 + 0.782198i \(0.714099\pi\)
\(194\) 0 0
\(195\) −321016. −0.604562
\(196\) 0 0
\(197\) 521778. 0.957899 0.478950 0.877842i \(-0.341018\pi\)
0.478950 + 0.877842i \(0.341018\pi\)
\(198\) 0 0
\(199\) 394042. 0.705358 0.352679 0.935744i \(-0.385271\pi\)
0.352679 + 0.935744i \(0.385271\pi\)
\(200\) 0 0
\(201\) 530250. 0.925744
\(202\) 0 0
\(203\) 45305.7 0.0771637
\(204\) 0 0
\(205\) 470761. 0.782376
\(206\) 0 0
\(207\) 461020. 0.747814
\(208\) 0 0
\(209\) 2267.99 0.00359150
\(210\) 0 0
\(211\) −750041. −1.15979 −0.579894 0.814692i \(-0.696906\pi\)
−0.579894 + 0.814692i \(0.696906\pi\)
\(212\) 0 0
\(213\) 1.16587e6 1.76077
\(214\) 0 0
\(215\) 78686.9 0.116093
\(216\) 0 0
\(217\) 250229. 0.360735
\(218\) 0 0
\(219\) −1.21616e6 −1.71348
\(220\) 0 0
\(221\) −594139. −0.818290
\(222\) 0 0
\(223\) −1.00328e6 −1.35102 −0.675509 0.737351i \(-0.736076\pi\)
−0.675509 + 0.737351i \(0.736076\pi\)
\(224\) 0 0
\(225\) 116791. 0.153799
\(226\) 0 0
\(227\) −385367. −0.496375 −0.248188 0.968712i \(-0.579835\pi\)
−0.248188 + 0.968712i \(0.579835\pi\)
\(228\) 0 0
\(229\) 16601.6 0.0209200 0.0104600 0.999945i \(-0.496670\pi\)
0.0104600 + 0.999945i \(0.496670\pi\)
\(230\) 0 0
\(231\) −5361.12 −0.00661036
\(232\) 0 0
\(233\) 933464. 1.12644 0.563219 0.826307i \(-0.309563\pi\)
0.563219 + 0.826307i \(0.309563\pi\)
\(234\) 0 0
\(235\) −513920. −0.607052
\(236\) 0 0
\(237\) −668411. −0.772988
\(238\) 0 0
\(239\) 1.34120e6 1.51880 0.759398 0.650626i \(-0.225493\pi\)
0.759398 + 0.650626i \(0.225493\pi\)
\(240\) 0 0
\(241\) 390139. 0.432690 0.216345 0.976317i \(-0.430586\pi\)
0.216345 + 0.976317i \(0.430586\pi\)
\(242\) 0 0
\(243\) 1.15894e6 1.25906
\(244\) 0 0
\(245\) 389081. 0.414119
\(246\) 0 0
\(247\) −191576. −0.199801
\(248\) 0 0
\(249\) 646325. 0.660621
\(250\) 0 0
\(251\) −805856. −0.807371 −0.403686 0.914898i \(-0.632271\pi\)
−0.403686 + 0.914898i \(0.632271\pi\)
\(252\) 0 0
\(253\) 18088.9 0.0177669
\(254\) 0 0
\(255\) 497249. 0.478876
\(256\) 0 0
\(257\) 153621. 0.145084 0.0725419 0.997365i \(-0.476889\pi\)
0.0725419 + 0.997365i \(0.476889\pi\)
\(258\) 0 0
\(259\) 215148. 0.199291
\(260\) 0 0
\(261\) 240058. 0.218130
\(262\) 0 0
\(263\) −28007.0 −0.0249676 −0.0124838 0.999922i \(-0.503974\pi\)
−0.0124838 + 0.999922i \(0.503974\pi\)
\(264\) 0 0
\(265\) 843546. 0.737895
\(266\) 0 0
\(267\) 1.56036e6 1.33951
\(268\) 0 0
\(269\) −715607. −0.602968 −0.301484 0.953471i \(-0.597482\pi\)
−0.301484 + 0.953471i \(0.597482\pi\)
\(270\) 0 0
\(271\) −1.35674e6 −1.12221 −0.561104 0.827745i \(-0.689623\pi\)
−0.561104 + 0.827745i \(0.689623\pi\)
\(272\) 0 0
\(273\) 452849. 0.367745
\(274\) 0 0
\(275\) 4582.50 0.00365402
\(276\) 0 0
\(277\) 791037. 0.619437 0.309719 0.950828i \(-0.399765\pi\)
0.309719 + 0.950828i \(0.399765\pi\)
\(278\) 0 0
\(279\) 1.32587e6 1.01974
\(280\) 0 0
\(281\) −191136. −0.144403 −0.0722016 0.997390i \(-0.523002\pi\)
−0.0722016 + 0.997390i \(0.523002\pi\)
\(282\) 0 0
\(283\) 1.16924e6 0.867834 0.433917 0.900953i \(-0.357131\pi\)
0.433917 + 0.900953i \(0.357131\pi\)
\(284\) 0 0
\(285\) 160334. 0.116927
\(286\) 0 0
\(287\) −664089. −0.475906
\(288\) 0 0
\(289\) −499547. −0.351829
\(290\) 0 0
\(291\) 3.65026e6 2.52692
\(292\) 0 0
\(293\) 932811. 0.634782 0.317391 0.948295i \(-0.397193\pi\)
0.317391 + 0.948295i \(0.397193\pi\)
\(294\) 0 0
\(295\) 376633. 0.251979
\(296\) 0 0
\(297\) 8533.32 0.00561341
\(298\) 0 0
\(299\) −1.52796e6 −0.988401
\(300\) 0 0
\(301\) −111001. −0.0706175
\(302\) 0 0
\(303\) −2.12420e6 −1.32920
\(304\) 0 0
\(305\) −188553. −0.116060
\(306\) 0 0
\(307\) 678740. 0.411015 0.205507 0.978656i \(-0.434116\pi\)
0.205507 + 0.978656i \(0.434116\pi\)
\(308\) 0 0
\(309\) 3.11662e6 1.85689
\(310\) 0 0
\(311\) 1.25645e6 0.736621 0.368311 0.929703i \(-0.379936\pi\)
0.368311 + 0.929703i \(0.379936\pi\)
\(312\) 0 0
\(313\) 3.13670e6 1.80972 0.904861 0.425708i \(-0.139975\pi\)
0.904861 + 0.425708i \(0.139975\pi\)
\(314\) 0 0
\(315\) −164754. −0.0935533
\(316\) 0 0
\(317\) −353375. −0.197510 −0.0987548 0.995112i \(-0.531486\pi\)
−0.0987548 + 0.995112i \(0.531486\pi\)
\(318\) 0 0
\(319\) 9419.10 0.00518242
\(320\) 0 0
\(321\) −4.57907e6 −2.48036
\(322\) 0 0
\(323\) 296747. 0.158263
\(324\) 0 0
\(325\) −387080. −0.203279
\(326\) 0 0
\(327\) −510471. −0.263999
\(328\) 0 0
\(329\) 724973. 0.369260
\(330\) 0 0
\(331\) 2.91561e6 1.46271 0.731356 0.681996i \(-0.238888\pi\)
0.731356 + 0.681996i \(0.238888\pi\)
\(332\) 0 0
\(333\) 1.13999e6 0.563366
\(334\) 0 0
\(335\) 639373. 0.311274
\(336\) 0 0
\(337\) −3.11496e6 −1.49409 −0.747046 0.664772i \(-0.768529\pi\)
−0.747046 + 0.664772i \(0.768529\pi\)
\(338\) 0 0
\(339\) 1.33871e6 0.632687
\(340\) 0 0
\(341\) 52022.9 0.0242275
\(342\) 0 0
\(343\) −1.14160e6 −0.523934
\(344\) 0 0
\(345\) 1.27878e6 0.578428
\(346\) 0 0
\(347\) −4.09755e6 −1.82684 −0.913419 0.407020i \(-0.866568\pi\)
−0.913419 + 0.407020i \(0.866568\pi\)
\(348\) 0 0
\(349\) −2.46309e6 −1.08247 −0.541237 0.840870i \(-0.682044\pi\)
−0.541237 + 0.840870i \(0.682044\pi\)
\(350\) 0 0
\(351\) −720802. −0.312283
\(352\) 0 0
\(353\) 3.56682e6 1.52350 0.761752 0.647868i \(-0.224339\pi\)
0.761752 + 0.647868i \(0.224339\pi\)
\(354\) 0 0
\(355\) 1.40581e6 0.592045
\(356\) 0 0
\(357\) −701455. −0.291292
\(358\) 0 0
\(359\) −648318. −0.265492 −0.132746 0.991150i \(-0.542380\pi\)
−0.132746 + 0.991150i \(0.542380\pi\)
\(360\) 0 0
\(361\) −2.38042e6 −0.961357
\(362\) 0 0
\(363\) 3.33799e6 1.32959
\(364\) 0 0
\(365\) −1.46644e6 −0.576145
\(366\) 0 0
\(367\) −3.84494e6 −1.49013 −0.745065 0.666992i \(-0.767581\pi\)
−0.745065 + 0.666992i \(0.767581\pi\)
\(368\) 0 0
\(369\) −3.51876e6 −1.34531
\(370\) 0 0
\(371\) −1.18997e6 −0.448849
\(372\) 0 0
\(373\) −2.40550e6 −0.895228 −0.447614 0.894227i \(-0.647726\pi\)
−0.447614 + 0.894227i \(0.647726\pi\)
\(374\) 0 0
\(375\) 323956. 0.118962
\(376\) 0 0
\(377\) −795623. −0.288306
\(378\) 0 0
\(379\) −5.03689e6 −1.80121 −0.900605 0.434638i \(-0.856876\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(380\) 0 0
\(381\) −3.30900e6 −1.16784
\(382\) 0 0
\(383\) −1.61371e6 −0.562121 −0.281060 0.959690i \(-0.590686\pi\)
−0.281060 + 0.959690i \(0.590686\pi\)
\(384\) 0 0
\(385\) −6464.41 −0.00222268
\(386\) 0 0
\(387\) −588155. −0.199625
\(388\) 0 0
\(389\) −1.99508e6 −0.668477 −0.334238 0.942489i \(-0.608479\pi\)
−0.334238 + 0.942489i \(0.608479\pi\)
\(390\) 0 0
\(391\) 2.36678e6 0.782917
\(392\) 0 0
\(393\) 2.40738e6 0.786255
\(394\) 0 0
\(395\) −805967. −0.259911
\(396\) 0 0
\(397\) −3.61674e6 −1.15170 −0.575852 0.817554i \(-0.695329\pi\)
−0.575852 + 0.817554i \(0.695329\pi\)
\(398\) 0 0
\(399\) −226179. −0.0711245
\(400\) 0 0
\(401\) −2.64534e6 −0.821525 −0.410763 0.911742i \(-0.634738\pi\)
−0.410763 + 0.911742i \(0.634738\pi\)
\(402\) 0 0
\(403\) −4.39433e6 −1.34781
\(404\) 0 0
\(405\) 1.73846e6 0.526658
\(406\) 0 0
\(407\) 44729.6 0.0133847
\(408\) 0 0
\(409\) 2.86360e6 0.846456 0.423228 0.906023i \(-0.360897\pi\)
0.423228 + 0.906023i \(0.360897\pi\)
\(410\) 0 0
\(411\) 29982.9 0.00875525
\(412\) 0 0
\(413\) −531306. −0.153274
\(414\) 0 0
\(415\) 779336. 0.222129
\(416\) 0 0
\(417\) −2.80013e6 −0.788566
\(418\) 0 0
\(419\) −1.09856e6 −0.305695 −0.152847 0.988250i \(-0.548844\pi\)
−0.152847 + 0.988250i \(0.548844\pi\)
\(420\) 0 0
\(421\) −2.31987e6 −0.637909 −0.318955 0.947770i \(-0.603332\pi\)
−0.318955 + 0.947770i \(0.603332\pi\)
\(422\) 0 0
\(423\) 3.84136e6 1.04384
\(424\) 0 0
\(425\) 599580. 0.161018
\(426\) 0 0
\(427\) 265986. 0.0705975
\(428\) 0 0
\(429\) 94147.7 0.0246983
\(430\) 0 0
\(431\) 5.05072e6 1.30967 0.654833 0.755774i \(-0.272739\pi\)
0.654833 + 0.755774i \(0.272739\pi\)
\(432\) 0 0
\(433\) −1.01025e6 −0.258946 −0.129473 0.991583i \(-0.541329\pi\)
−0.129473 + 0.991583i \(0.541329\pi\)
\(434\) 0 0
\(435\) 665876. 0.168721
\(436\) 0 0
\(437\) 763149. 0.191164
\(438\) 0 0
\(439\) −5.14635e6 −1.27450 −0.637248 0.770659i \(-0.719927\pi\)
−0.637248 + 0.770659i \(0.719927\pi\)
\(440\) 0 0
\(441\) −2.90824e6 −0.712087
\(442\) 0 0
\(443\) −5.25603e6 −1.27247 −0.636236 0.771494i \(-0.719510\pi\)
−0.636236 + 0.771494i \(0.719510\pi\)
\(444\) 0 0
\(445\) 1.88147e6 0.450399
\(446\) 0 0
\(447\) 333759. 0.0790067
\(448\) 0 0
\(449\) −4.10261e6 −0.960384 −0.480192 0.877163i \(-0.659433\pi\)
−0.480192 + 0.877163i \(0.659433\pi\)
\(450\) 0 0
\(451\) −138065. −0.0319626
\(452\) 0 0
\(453\) 9.68972e6 2.21853
\(454\) 0 0
\(455\) 546043. 0.123651
\(456\) 0 0
\(457\) −4.01053e6 −0.898278 −0.449139 0.893462i \(-0.648269\pi\)
−0.449139 + 0.893462i \(0.648269\pi\)
\(458\) 0 0
\(459\) 1.11651e6 0.247361
\(460\) 0 0
\(461\) −3.83280e6 −0.839971 −0.419986 0.907531i \(-0.637965\pi\)
−0.419986 + 0.907531i \(0.637965\pi\)
\(462\) 0 0
\(463\) 1.14398e6 0.248009 0.124004 0.992282i \(-0.460426\pi\)
0.124004 + 0.992282i \(0.460426\pi\)
\(464\) 0 0
\(465\) 3.67772e6 0.788762
\(466\) 0 0
\(467\) −7.12577e6 −1.51196 −0.755979 0.654596i \(-0.772839\pi\)
−0.755979 + 0.654596i \(0.772839\pi\)
\(468\) 0 0
\(469\) −901946. −0.189343
\(470\) 0 0
\(471\) 4.36388e6 0.906401
\(472\) 0 0
\(473\) −23077.3 −0.00474277
\(474\) 0 0
\(475\) 193330. 0.0393156
\(476\) 0 0
\(477\) −6.30519e6 −1.26883
\(478\) 0 0
\(479\) 6.45039e6 1.28454 0.642269 0.766479i \(-0.277993\pi\)
0.642269 + 0.766479i \(0.277993\pi\)
\(480\) 0 0
\(481\) −3.77827e6 −0.744612
\(482\) 0 0
\(483\) −1.80394e6 −0.351848
\(484\) 0 0
\(485\) 4.40147e6 0.849656
\(486\) 0 0
\(487\) −1.46947e6 −0.280762 −0.140381 0.990098i \(-0.544833\pi\)
−0.140381 + 0.990098i \(0.544833\pi\)
\(488\) 0 0
\(489\) −2.82449e6 −0.534155
\(490\) 0 0
\(491\) 5.19488e6 0.972460 0.486230 0.873831i \(-0.338372\pi\)
0.486230 + 0.873831i \(0.338372\pi\)
\(492\) 0 0
\(493\) 1.23241e6 0.228369
\(494\) 0 0
\(495\) −34252.5 −0.00628317
\(496\) 0 0
\(497\) −1.98313e6 −0.360131
\(498\) 0 0
\(499\) 7.07689e6 1.27230 0.636152 0.771564i \(-0.280525\pi\)
0.636152 + 0.771564i \(0.280525\pi\)
\(500\) 0 0
\(501\) −5.11514e6 −0.910465
\(502\) 0 0
\(503\) 8.92098e6 1.57215 0.786073 0.618134i \(-0.212111\pi\)
0.786073 + 0.618134i \(0.212111\pi\)
\(504\) 0 0
\(505\) −2.56135e6 −0.446932
\(506\) 0 0
\(507\) −254483. −0.0439683
\(508\) 0 0
\(509\) −5.79714e6 −0.991789 −0.495895 0.868383i \(-0.665160\pi\)
−0.495895 + 0.868383i \(0.665160\pi\)
\(510\) 0 0
\(511\) 2.06866e6 0.350459
\(512\) 0 0
\(513\) 360010. 0.0603978
\(514\) 0 0
\(515\) 3.75800e6 0.624365
\(516\) 0 0
\(517\) 150723. 0.0248000
\(518\) 0 0
\(519\) −1.35218e7 −2.20351
\(520\) 0 0
\(521\) 7.45721e6 1.20360 0.601800 0.798647i \(-0.294450\pi\)
0.601800 + 0.798647i \(0.294450\pi\)
\(522\) 0 0
\(523\) 1.01015e7 1.61485 0.807424 0.589971i \(-0.200861\pi\)
0.807424 + 0.589971i \(0.200861\pi\)
\(524\) 0 0
\(525\) −456996. −0.0723626
\(526\) 0 0
\(527\) 6.80674e6 1.06761
\(528\) 0 0
\(529\) −349660. −0.0543258
\(530\) 0 0
\(531\) −2.81519e6 −0.433283
\(532\) 0 0
\(533\) 1.16622e7 1.77813
\(534\) 0 0
\(535\) −5.52142e6 −0.834001
\(536\) 0 0
\(537\) 1.63075e7 2.44035
\(538\) 0 0
\(539\) −114110. −0.0169181
\(540\) 0 0
\(541\) −1.23616e7 −1.81585 −0.907925 0.419132i \(-0.862334\pi\)
−0.907925 + 0.419132i \(0.862334\pi\)
\(542\) 0 0
\(543\) −20194.7 −0.00293926
\(544\) 0 0
\(545\) −615524. −0.0887675
\(546\) 0 0
\(547\) 3.72735e6 0.532637 0.266319 0.963885i \(-0.414193\pi\)
0.266319 + 0.963885i \(0.414193\pi\)
\(548\) 0 0
\(549\) 1.40936e6 0.199568
\(550\) 0 0
\(551\) 397380. 0.0557606
\(552\) 0 0
\(553\) 1.13696e6 0.158100
\(554\) 0 0
\(555\) 3.16212e6 0.435759
\(556\) 0 0
\(557\) 1.68294e6 0.229842 0.114921 0.993375i \(-0.463338\pi\)
0.114921 + 0.993375i \(0.463338\pi\)
\(558\) 0 0
\(559\) 1.94932e6 0.263848
\(560\) 0 0
\(561\) −145833. −0.0195636
\(562\) 0 0
\(563\) −1.31501e7 −1.74848 −0.874238 0.485498i \(-0.838638\pi\)
−0.874238 + 0.485498i \(0.838638\pi\)
\(564\) 0 0
\(565\) 1.61422e6 0.212736
\(566\) 0 0
\(567\) −2.45240e6 −0.320357
\(568\) 0 0
\(569\) 6.91087e6 0.894854 0.447427 0.894320i \(-0.352340\pi\)
0.447427 + 0.894320i \(0.352340\pi\)
\(570\) 0 0
\(571\) −1.49642e6 −0.192072 −0.0960361 0.995378i \(-0.530616\pi\)
−0.0960361 + 0.995378i \(0.530616\pi\)
\(572\) 0 0
\(573\) 9.73787e6 1.23902
\(574\) 0 0
\(575\) 1.54195e6 0.194492
\(576\) 0 0
\(577\) −2.81857e6 −0.352444 −0.176222 0.984350i \(-0.556388\pi\)
−0.176222 + 0.984350i \(0.556388\pi\)
\(578\) 0 0
\(579\) 1.33690e7 1.65730
\(580\) 0 0
\(581\) −1.09939e6 −0.135117
\(582\) 0 0
\(583\) −247395. −0.0301454
\(584\) 0 0
\(585\) 2.89328e6 0.349543
\(586\) 0 0
\(587\) 9.61995e6 1.15233 0.576166 0.817333i \(-0.304548\pi\)
0.576166 + 0.817333i \(0.304548\pi\)
\(588\) 0 0
\(589\) 2.19478e6 0.260677
\(590\) 0 0
\(591\) −1.08181e7 −1.27404
\(592\) 0 0
\(593\) 7.39724e6 0.863839 0.431920 0.901912i \(-0.357836\pi\)
0.431920 + 0.901912i \(0.357836\pi\)
\(594\) 0 0
\(595\) −845811. −0.0979447
\(596\) 0 0
\(597\) −8.16975e6 −0.938152
\(598\) 0 0
\(599\) −1.14938e7 −1.30887 −0.654434 0.756119i \(-0.727093\pi\)
−0.654434 + 0.756119i \(0.727093\pi\)
\(600\) 0 0
\(601\) −7.58526e6 −0.856612 −0.428306 0.903634i \(-0.640889\pi\)
−0.428306 + 0.903634i \(0.640889\pi\)
\(602\) 0 0
\(603\) −4.77908e6 −0.535243
\(604\) 0 0
\(605\) 4.02493e6 0.447064
\(606\) 0 0
\(607\) −2.36915e6 −0.260988 −0.130494 0.991449i \(-0.541656\pi\)
−0.130494 + 0.991449i \(0.541656\pi\)
\(608\) 0 0
\(609\) −939332. −0.102630
\(610\) 0 0
\(611\) −1.27314e7 −1.37966
\(612\) 0 0
\(613\) 1.05992e7 1.13926 0.569629 0.821902i \(-0.307087\pi\)
0.569629 + 0.821902i \(0.307087\pi\)
\(614\) 0 0
\(615\) −9.76037e6 −1.04059
\(616\) 0 0
\(617\) −1.22009e7 −1.29026 −0.645131 0.764072i \(-0.723197\pi\)
−0.645131 + 0.764072i \(0.723197\pi\)
\(618\) 0 0
\(619\) 1.46019e7 1.53173 0.765865 0.643001i \(-0.222311\pi\)
0.765865 + 0.643001i \(0.222311\pi\)
\(620\) 0 0
\(621\) 2.87135e6 0.298784
\(622\) 0 0
\(623\) −2.65414e6 −0.273970
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −47022.8 −0.00477683
\(628\) 0 0
\(629\) 5.85247e6 0.589811
\(630\) 0 0
\(631\) −9.40997e6 −0.940838 −0.470419 0.882443i \(-0.655897\pi\)
−0.470419 + 0.882443i \(0.655897\pi\)
\(632\) 0 0
\(633\) 1.55507e7 1.54256
\(634\) 0 0
\(635\) −3.98998e6 −0.392678
\(636\) 0 0
\(637\) 9.63876e6 0.941180
\(638\) 0 0
\(639\) −1.05079e7 −1.01804
\(640\) 0 0
\(641\) −8.44166e6 −0.811489 −0.405744 0.913987i \(-0.632988\pi\)
−0.405744 + 0.913987i \(0.632988\pi\)
\(642\) 0 0
\(643\) −1.03157e7 −0.983942 −0.491971 0.870612i \(-0.663723\pi\)
−0.491971 + 0.870612i \(0.663723\pi\)
\(644\) 0 0
\(645\) −1.63143e6 −0.154408
\(646\) 0 0
\(647\) 3.52118e6 0.330695 0.165348 0.986235i \(-0.447125\pi\)
0.165348 + 0.986235i \(0.447125\pi\)
\(648\) 0 0
\(649\) −110459. −0.0102941
\(650\) 0 0
\(651\) −5.18805e6 −0.479791
\(652\) 0 0
\(653\) 2.20492e6 0.202354 0.101177 0.994868i \(-0.467739\pi\)
0.101177 + 0.994868i \(0.467739\pi\)
\(654\) 0 0
\(655\) 2.90281e6 0.264372
\(656\) 0 0
\(657\) 1.09611e7 0.990694
\(658\) 0 0
\(659\) 1.26903e7 1.13830 0.569152 0.822232i \(-0.307271\pi\)
0.569152 + 0.822232i \(0.307271\pi\)
\(660\) 0 0
\(661\) −2.20351e6 −0.196160 −0.0980801 0.995179i \(-0.531270\pi\)
−0.0980801 + 0.995179i \(0.531270\pi\)
\(662\) 0 0
\(663\) 1.23184e7 1.08835
\(664\) 0 0
\(665\) −272725. −0.0239150
\(666\) 0 0
\(667\) 3.16940e6 0.275843
\(668\) 0 0
\(669\) 2.08013e7 1.79690
\(670\) 0 0
\(671\) 55298.8 0.00474143
\(672\) 0 0
\(673\) 2.02905e6 0.172685 0.0863424 0.996266i \(-0.472482\pi\)
0.0863424 + 0.996266i \(0.472482\pi\)
\(674\) 0 0
\(675\) 727404. 0.0614492
\(676\) 0 0
\(677\) 1.33080e7 1.11594 0.557971 0.829860i \(-0.311580\pi\)
0.557971 + 0.829860i \(0.311580\pi\)
\(678\) 0 0
\(679\) −6.20903e6 −0.516832
\(680\) 0 0
\(681\) 7.98989e6 0.660196
\(682\) 0 0
\(683\) 5.95063e6 0.488102 0.244051 0.969762i \(-0.421524\pi\)
0.244051 + 0.969762i \(0.421524\pi\)
\(684\) 0 0
\(685\) 36153.2 0.00294388
\(686\) 0 0
\(687\) −344204. −0.0278243
\(688\) 0 0
\(689\) 2.08973e7 1.67703
\(690\) 0 0
\(691\) −1.95555e7 −1.55802 −0.779010 0.627011i \(-0.784278\pi\)
−0.779010 + 0.627011i \(0.784278\pi\)
\(692\) 0 0
\(693\) 48319.0 0.00382195
\(694\) 0 0
\(695\) −3.37639e6 −0.265149
\(696\) 0 0
\(697\) −1.80646e7 −1.40846
\(698\) 0 0
\(699\) −1.93537e7 −1.49820
\(700\) 0 0
\(701\) 1.70838e7 1.31308 0.656538 0.754293i \(-0.272020\pi\)
0.656538 + 0.754293i \(0.272020\pi\)
\(702\) 0 0
\(703\) 1.88708e6 0.144013
\(704\) 0 0
\(705\) 1.06552e7 0.807401
\(706\) 0 0
\(707\) 3.61323e6 0.271861
\(708\) 0 0
\(709\) −2.47096e7 −1.84608 −0.923038 0.384710i \(-0.874301\pi\)
−0.923038 + 0.384710i \(0.874301\pi\)
\(710\) 0 0
\(711\) 6.02430e6 0.446923
\(712\) 0 0
\(713\) 1.75050e7 1.28955
\(714\) 0 0
\(715\) 113523. 0.00830459
\(716\) 0 0
\(717\) −2.78074e7 −2.02005
\(718\) 0 0
\(719\) 2.02894e7 1.46369 0.731843 0.681474i \(-0.238661\pi\)
0.731843 + 0.681474i \(0.238661\pi\)
\(720\) 0 0
\(721\) −5.30131e6 −0.379791
\(722\) 0 0
\(723\) −8.08882e6 −0.575492
\(724\) 0 0
\(725\) 802910. 0.0567312
\(726\) 0 0
\(727\) 2.59786e7 1.82297 0.911486 0.411331i \(-0.134936\pi\)
0.911486 + 0.411331i \(0.134936\pi\)
\(728\) 0 0
\(729\) −7.13072e6 −0.496952
\(730\) 0 0
\(731\) −3.01946e6 −0.208995
\(732\) 0 0
\(733\) −1.75705e7 −1.20788 −0.603940 0.797030i \(-0.706403\pi\)
−0.603940 + 0.797030i \(0.706403\pi\)
\(734\) 0 0
\(735\) −8.06690e6 −0.550793
\(736\) 0 0
\(737\) −187516. −0.0127165
\(738\) 0 0
\(739\) 2.26188e7 1.52356 0.761779 0.647837i \(-0.224326\pi\)
0.761779 + 0.647837i \(0.224326\pi\)
\(740\) 0 0
\(741\) 3.97197e6 0.265742
\(742\) 0 0
\(743\) 1.75610e7 1.16701 0.583507 0.812108i \(-0.301680\pi\)
0.583507 + 0.812108i \(0.301680\pi\)
\(744\) 0 0
\(745\) 402445. 0.0265653
\(746\) 0 0
\(747\) −5.82524e6 −0.381955
\(748\) 0 0
\(749\) 7.78892e6 0.507309
\(750\) 0 0
\(751\) 1.36472e6 0.0882967 0.0441483 0.999025i \(-0.485943\pi\)
0.0441483 + 0.999025i \(0.485943\pi\)
\(752\) 0 0
\(753\) 1.67080e7 1.07383
\(754\) 0 0
\(755\) 1.16838e7 0.745963
\(756\) 0 0
\(757\) 2.89968e6 0.183912 0.0919560 0.995763i \(-0.470688\pi\)
0.0919560 + 0.995763i \(0.470688\pi\)
\(758\) 0 0
\(759\) −375042. −0.0236306
\(760\) 0 0
\(761\) −9.33991e6 −0.584630 −0.292315 0.956322i \(-0.594426\pi\)
−0.292315 + 0.956322i \(0.594426\pi\)
\(762\) 0 0
\(763\) 868303. 0.0539958
\(764\) 0 0
\(765\) −4.48164e6 −0.276874
\(766\) 0 0
\(767\) 9.33038e6 0.572679
\(768\) 0 0
\(769\) −1.86030e7 −1.13440 −0.567200 0.823580i \(-0.691974\pi\)
−0.567200 + 0.823580i \(0.691974\pi\)
\(770\) 0 0
\(771\) −3.18506e6 −0.192967
\(772\) 0 0
\(773\) −2.71314e7 −1.63314 −0.816570 0.577247i \(-0.804127\pi\)
−0.816570 + 0.577247i \(0.804127\pi\)
\(774\) 0 0
\(775\) 4.43457e6 0.265215
\(776\) 0 0
\(777\) −4.46071e6 −0.265065
\(778\) 0 0
\(779\) −5.82478e6 −0.343903
\(780\) 0 0
\(781\) −412295. −0.0241869
\(782\) 0 0
\(783\) 1.49514e6 0.0871521
\(784\) 0 0
\(785\) 5.26195e6 0.304770
\(786\) 0 0
\(787\) 9.16693e6 0.527579 0.263789 0.964580i \(-0.415028\pi\)
0.263789 + 0.964580i \(0.415028\pi\)
\(788\) 0 0
\(789\) 580674. 0.0332078
\(790\) 0 0
\(791\) −2.27713e6 −0.129404
\(792\) 0 0
\(793\) −4.67104e6 −0.263773
\(794\) 0 0
\(795\) −1.74894e7 −0.981426
\(796\) 0 0
\(797\) 1.90109e7 1.06012 0.530062 0.847959i \(-0.322169\pi\)
0.530062 + 0.847959i \(0.322169\pi\)
\(798\) 0 0
\(799\) 1.97207e7 1.09284
\(800\) 0 0
\(801\) −1.40633e7 −0.774472
\(802\) 0 0
\(803\) 430077. 0.0235373
\(804\) 0 0
\(805\) −2.17519e6 −0.118306
\(806\) 0 0
\(807\) 1.48368e7 0.801969
\(808\) 0 0
\(809\) −4.04747e6 −0.217426 −0.108713 0.994073i \(-0.534673\pi\)
−0.108713 + 0.994073i \(0.534673\pi\)
\(810\) 0 0
\(811\) −984765. −0.0525752 −0.0262876 0.999654i \(-0.508369\pi\)
−0.0262876 + 0.999654i \(0.508369\pi\)
\(812\) 0 0
\(813\) 2.81296e7 1.49258
\(814\) 0 0
\(815\) −3.40575e6 −0.179605
\(816\) 0 0
\(817\) −973603. −0.0510301
\(818\) 0 0
\(819\) −4.08147e6 −0.212621
\(820\) 0 0
\(821\) −3.53595e6 −0.183083 −0.0915415 0.995801i \(-0.529179\pi\)
−0.0915415 + 0.995801i \(0.529179\pi\)
\(822\) 0 0
\(823\) 9.27174e6 0.477157 0.238579 0.971123i \(-0.423319\pi\)
0.238579 + 0.971123i \(0.423319\pi\)
\(824\) 0 0
\(825\) −95010.0 −0.00485998
\(826\) 0 0
\(827\) −3.88822e6 −0.197691 −0.0988456 0.995103i \(-0.531515\pi\)
−0.0988456 + 0.995103i \(0.531515\pi\)
\(828\) 0 0
\(829\) −2.20046e7 −1.11206 −0.556028 0.831163i \(-0.687675\pi\)
−0.556028 + 0.831163i \(0.687675\pi\)
\(830\) 0 0
\(831\) −1.64007e7 −0.823874
\(832\) 0 0
\(833\) −1.49303e7 −0.745513
\(834\) 0 0
\(835\) −6.16781e6 −0.306136
\(836\) 0 0
\(837\) 8.25785e6 0.407430
\(838\) 0 0
\(839\) 888779. 0.0435902 0.0217951 0.999762i \(-0.493062\pi\)
0.0217951 + 0.999762i \(0.493062\pi\)
\(840\) 0 0
\(841\) −1.88608e7 −0.919539
\(842\) 0 0
\(843\) 3.96286e6 0.192061
\(844\) 0 0
\(845\) −306855. −0.0147840
\(846\) 0 0
\(847\) −5.67786e6 −0.271942
\(848\) 0 0
\(849\) −2.42420e7 −1.15425
\(850\) 0 0
\(851\) 1.50509e7 0.712424
\(852\) 0 0
\(853\) −2.03265e7 −0.956511 −0.478255 0.878221i \(-0.658731\pi\)
−0.478255 + 0.878221i \(0.658731\pi\)
\(854\) 0 0
\(855\) −1.44507e6 −0.0676041
\(856\) 0 0
\(857\) 1.96142e6 0.0912258 0.0456129 0.998959i \(-0.485476\pi\)
0.0456129 + 0.998959i \(0.485476\pi\)
\(858\) 0 0
\(859\) −1.54216e7 −0.713095 −0.356548 0.934277i \(-0.616046\pi\)
−0.356548 + 0.934277i \(0.616046\pi\)
\(860\) 0 0
\(861\) 1.37687e7 0.632972
\(862\) 0 0
\(863\) −2.79115e7 −1.27572 −0.637860 0.770152i \(-0.720180\pi\)
−0.637860 + 0.770152i \(0.720180\pi\)
\(864\) 0 0
\(865\) −1.63045e7 −0.740913
\(866\) 0 0
\(867\) 1.03572e7 0.467945
\(868\) 0 0
\(869\) 236374. 0.0106182
\(870\) 0 0
\(871\) 1.58393e7 0.707440
\(872\) 0 0
\(873\) −3.28993e7 −1.46100
\(874\) 0 0
\(875\) −551044. −0.0243313
\(876\) 0 0
\(877\) −1.72191e7 −0.755980 −0.377990 0.925810i \(-0.623385\pi\)
−0.377990 + 0.925810i \(0.623385\pi\)
\(878\) 0 0
\(879\) −1.93402e7 −0.844282
\(880\) 0 0
\(881\) 3.57166e7 1.55035 0.775177 0.631745i \(-0.217661\pi\)
0.775177 + 0.631745i \(0.217661\pi\)
\(882\) 0 0
\(883\) −3.78278e6 −0.163271 −0.0816356 0.996662i \(-0.526014\pi\)
−0.0816356 + 0.996662i \(0.526014\pi\)
\(884\) 0 0
\(885\) −7.80882e6 −0.335141
\(886\) 0 0
\(887\) −2.45768e7 −1.04886 −0.524428 0.851455i \(-0.675721\pi\)
−0.524428 + 0.851455i \(0.675721\pi\)
\(888\) 0 0
\(889\) 5.62855e6 0.238859
\(890\) 0 0
\(891\) −509857. −0.0215156
\(892\) 0 0
\(893\) 6.35880e6 0.266837
\(894\) 0 0
\(895\) 1.96636e7 0.820549
\(896\) 0 0
\(897\) 3.16794e7 1.31461
\(898\) 0 0
\(899\) 9.11504e6 0.376149
\(900\) 0 0
\(901\) −3.23695e7 −1.32839
\(902\) 0 0
\(903\) 2.30142e6 0.0939238
\(904\) 0 0
\(905\) −24350.7 −0.000988301 0
\(906\) 0 0
\(907\) 1.47776e6 0.0596467 0.0298234 0.999555i \(-0.490506\pi\)
0.0298234 + 0.999555i \(0.490506\pi\)
\(908\) 0 0
\(909\) 1.91452e7 0.768510
\(910\) 0 0
\(911\) −2.62169e7 −1.04661 −0.523305 0.852146i \(-0.675301\pi\)
−0.523305 + 0.852146i \(0.675301\pi\)
\(912\) 0 0
\(913\) −228564. −0.00907466
\(914\) 0 0
\(915\) 3.90930e6 0.154364
\(916\) 0 0
\(917\) −4.09491e6 −0.160813
\(918\) 0 0
\(919\) 1.10734e6 0.0432507 0.0216254 0.999766i \(-0.493116\pi\)
0.0216254 + 0.999766i \(0.493116\pi\)
\(920\) 0 0
\(921\) −1.40724e7 −0.546664
\(922\) 0 0
\(923\) 3.48262e7 1.34556
\(924\) 0 0
\(925\) 3.81287e6 0.146520
\(926\) 0 0
\(927\) −2.80896e7 −1.07361
\(928\) 0 0
\(929\) 2.36543e7 0.899229 0.449615 0.893223i \(-0.351561\pi\)
0.449615 + 0.893223i \(0.351561\pi\)
\(930\) 0 0
\(931\) −4.81415e6 −0.182031
\(932\) 0 0
\(933\) −2.60502e7 −0.979732
\(934\) 0 0
\(935\) −175845. −0.00657811
\(936\) 0 0
\(937\) −3.28168e7 −1.22109 −0.610544 0.791983i \(-0.709049\pi\)
−0.610544 + 0.791983i \(0.709049\pi\)
\(938\) 0 0
\(939\) −6.50338e7 −2.40699
\(940\) 0 0
\(941\) −3.66896e7 −1.35073 −0.675366 0.737483i \(-0.736014\pi\)
−0.675366 + 0.737483i \(0.736014\pi\)
\(942\) 0 0
\(943\) −4.64569e7 −1.70126
\(944\) 0 0
\(945\) −1.02613e6 −0.0373785
\(946\) 0 0
\(947\) −8.63334e6 −0.312827 −0.156413 0.987692i \(-0.549993\pi\)
−0.156413 + 0.987692i \(0.549993\pi\)
\(948\) 0 0
\(949\) −3.63282e7 −1.30942
\(950\) 0 0
\(951\) 7.32660e6 0.262695
\(952\) 0 0
\(953\) −1.76257e7 −0.628659 −0.314329 0.949314i \(-0.601780\pi\)
−0.314329 + 0.949314i \(0.601780\pi\)
\(954\) 0 0
\(955\) 1.17419e7 0.416609
\(956\) 0 0
\(957\) −195288. −0.00689281
\(958\) 0 0
\(959\) −51000.3 −0.00179071
\(960\) 0 0
\(961\) 2.17144e7 0.758470
\(962\) 0 0
\(963\) 4.12706e7 1.43408
\(964\) 0 0
\(965\) 1.61203e7 0.557255
\(966\) 0 0
\(967\) −4.87856e7 −1.67774 −0.838871 0.544330i \(-0.816784\pi\)
−0.838871 + 0.544330i \(0.816784\pi\)
\(968\) 0 0
\(969\) −6.15252e6 −0.210496
\(970\) 0 0
\(971\) 3.81830e7 1.29964 0.649818 0.760090i \(-0.274845\pi\)
0.649818 + 0.760090i \(0.274845\pi\)
\(972\) 0 0
\(973\) 4.76297e6 0.161286
\(974\) 0 0
\(975\) 8.02541e6 0.270368
\(976\) 0 0
\(977\) 3.64067e7 1.22024 0.610120 0.792309i \(-0.291121\pi\)
0.610120 + 0.792309i \(0.291121\pi\)
\(978\) 0 0
\(979\) −551799. −0.0184003
\(980\) 0 0
\(981\) 4.60081e6 0.152638
\(982\) 0 0
\(983\) −4.61248e7 −1.52248 −0.761239 0.648472i \(-0.775408\pi\)
−0.761239 + 0.648472i \(0.775408\pi\)
\(984\) 0 0
\(985\) −1.30444e7 −0.428386
\(986\) 0 0
\(987\) −1.50310e7 −0.491129
\(988\) 0 0
\(989\) −7.76520e6 −0.252442
\(990\) 0 0
\(991\) 2.77541e7 0.897725 0.448862 0.893601i \(-0.351829\pi\)
0.448862 + 0.893601i \(0.351829\pi\)
\(992\) 0 0
\(993\) −6.04499e7 −1.94546
\(994\) 0 0
\(995\) −9.85105e6 −0.315446
\(996\) 0 0
\(997\) −2.50394e7 −0.797784 −0.398892 0.916998i \(-0.630605\pi\)
−0.398892 + 0.916998i \(0.630605\pi\)
\(998\) 0 0
\(999\) 7.10015e6 0.225089
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 320.6.a.r.1.1 2
4.3 odd 2 320.6.a.v.1.2 2
8.3 odd 2 160.6.a.a.1.1 2
8.5 even 2 160.6.a.e.1.2 yes 2
40.3 even 4 800.6.c.f.449.1 4
40.13 odd 4 800.6.c.g.449.4 4
40.19 odd 2 800.6.a.l.1.2 2
40.27 even 4 800.6.c.f.449.4 4
40.29 even 2 800.6.a.g.1.1 2
40.37 odd 4 800.6.c.g.449.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.a.1.1 2 8.3 odd 2
160.6.a.e.1.2 yes 2 8.5 even 2
320.6.a.r.1.1 2 1.1 even 1 trivial
320.6.a.v.1.2 2 4.3 odd 2
800.6.a.g.1.1 2 40.29 even 2
800.6.a.l.1.2 2 40.19 odd 2
800.6.c.f.449.1 4 40.3 even 4
800.6.c.f.449.4 4 40.27 even 4
800.6.c.g.449.1 4 40.37 odd 4
800.6.c.g.449.4 4 40.13 odd 4