Properties

Label 207.6.a.f.1.2
Level $207$
Weight $6$
Character 207.1
Self dual yes
Analytic conductor $33.199$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.1994507013\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 69)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-5.17654\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.27315 q^{2} +53.9914 q^{4} +37.4928 q^{5} +154.850 q^{7} -203.929 q^{8} +O(q^{10})\) \(q-9.27315 q^{2} +53.9914 q^{4} +37.4928 q^{5} +154.850 q^{7} -203.929 q^{8} -347.676 q^{10} -521.289 q^{11} -28.8511 q^{13} -1435.95 q^{14} +163.344 q^{16} +428.492 q^{17} -2563.67 q^{19} +2024.29 q^{20} +4834.00 q^{22} +529.000 q^{23} -1719.29 q^{25} +267.541 q^{26} +8360.58 q^{28} +2401.11 q^{29} -2130.21 q^{31} +5011.02 q^{32} -3973.47 q^{34} +5805.77 q^{35} +3651.58 q^{37} +23773.3 q^{38} -7645.87 q^{40} -16198.0 q^{41} +6503.63 q^{43} -28145.1 q^{44} -4905.50 q^{46} +20712.3 q^{47} +7171.64 q^{49} +15943.3 q^{50} -1557.71 q^{52} -34393.6 q^{53} -19544.6 q^{55} -31578.5 q^{56} -22265.9 q^{58} +18299.4 q^{59} -26509.8 q^{61} +19753.7 q^{62} -51695.0 q^{64} -1081.71 q^{65} -26313.7 q^{67} +23134.9 q^{68} -53837.8 q^{70} -39459.2 q^{71} -37484.5 q^{73} -33861.6 q^{74} -138416. q^{76} -80721.9 q^{77} +37368.8 q^{79} +6124.22 q^{80} +150206. q^{82} -76901.5 q^{83} +16065.3 q^{85} -60309.1 q^{86} +106306. q^{88} -62991.4 q^{89} -4467.60 q^{91} +28561.4 q^{92} -192068. q^{94} -96118.9 q^{95} +61484.7 q^{97} -66503.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8} - 172 q^{10} - 1100 q^{11} - 978 q^{13} + 344 q^{14} + 1218 q^{16} - 2522 q^{17} + 2060 q^{19} - 7720 q^{20} - 2572 q^{22} + 2645 q^{23} + 12035 q^{25} - 9280 q^{26} + 8072 q^{28} - 1526 q^{29} - 7392 q^{31} + 5086 q^{32} - 15608 q^{34} - 6056 q^{35} - 8210 q^{37} + 14276 q^{38} - 37472 q^{40} - 21250 q^{41} - 4548 q^{43} + 4260 q^{44} - 4232 q^{46} - 536 q^{47} - 27979 q^{49} + 81872 q^{50} - 76380 q^{52} + 11482 q^{53} - 77064 q^{55} + 28624 q^{56} - 79680 q^{58} - 74676 q^{59} - 44618 q^{61} - 64880 q^{62} - 137382 q^{64} + 24388 q^{65} - 1412 q^{67} - 80196 q^{68} - 222304 q^{70} - 37912 q^{71} + 46546 q^{73} - 111604 q^{74} - 79548 q^{76} - 157008 q^{77} + 50544 q^{79} - 69424 q^{80} - 233720 q^{82} - 89588 q^{83} + 147892 q^{85} - 77428 q^{86} + 54484 q^{88} - 280410 q^{89} - 27416 q^{91} + 62422 q^{92} + 113632 q^{94} - 203120 q^{95} + 90074 q^{97} - 32976 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.27315 −1.63928 −0.819639 0.572881i \(-0.805826\pi\)
−0.819639 + 0.572881i \(0.805826\pi\)
\(3\) 0 0
\(4\) 53.9914 1.68723
\(5\) 37.4928 0.670691 0.335345 0.942095i \(-0.391147\pi\)
0.335345 + 0.942095i \(0.391147\pi\)
\(6\) 0 0
\(7\) 154.850 1.19445 0.597224 0.802075i \(-0.296270\pi\)
0.597224 + 0.802075i \(0.296270\pi\)
\(8\) −203.929 −1.12656
\(9\) 0 0
\(10\) −347.676 −1.09945
\(11\) −521.289 −1.29896 −0.649482 0.760377i \(-0.725014\pi\)
−0.649482 + 0.760377i \(0.725014\pi\)
\(12\) 0 0
\(13\) −28.8511 −0.0473483 −0.0236741 0.999720i \(-0.507536\pi\)
−0.0236741 + 0.999720i \(0.507536\pi\)
\(14\) −1435.95 −1.95803
\(15\) 0 0
\(16\) 163.344 0.159516
\(17\) 428.492 0.359601 0.179800 0.983703i \(-0.442455\pi\)
0.179800 + 0.983703i \(0.442455\pi\)
\(18\) 0 0
\(19\) −2563.67 −1.62921 −0.814606 0.580015i \(-0.803047\pi\)
−0.814606 + 0.580015i \(0.803047\pi\)
\(20\) 2024.29 1.13161
\(21\) 0 0
\(22\) 4834.00 2.12936
\(23\) 529.000 0.208514
\(24\) 0 0
\(25\) −1719.29 −0.550174
\(26\) 267.541 0.0776169
\(27\) 0 0
\(28\) 8360.58 2.01531
\(29\) 2401.11 0.530172 0.265086 0.964225i \(-0.414600\pi\)
0.265086 + 0.964225i \(0.414600\pi\)
\(30\) 0 0
\(31\) −2130.21 −0.398124 −0.199062 0.979987i \(-0.563789\pi\)
−0.199062 + 0.979987i \(0.563789\pi\)
\(32\) 5011.02 0.865071
\(33\) 0 0
\(34\) −3973.47 −0.589485
\(35\) 5805.77 0.801105
\(36\) 0 0
\(37\) 3651.58 0.438507 0.219253 0.975668i \(-0.429638\pi\)
0.219253 + 0.975668i \(0.429638\pi\)
\(38\) 23773.3 2.67073
\(39\) 0 0
\(40\) −7645.87 −0.755574
\(41\) −16198.0 −1.50488 −0.752440 0.658661i \(-0.771123\pi\)
−0.752440 + 0.658661i \(0.771123\pi\)
\(42\) 0 0
\(43\) 6503.63 0.536395 0.268197 0.963364i \(-0.413572\pi\)
0.268197 + 0.963364i \(0.413572\pi\)
\(44\) −28145.1 −2.19165
\(45\) 0 0
\(46\) −4905.50 −0.341813
\(47\) 20712.3 1.36768 0.683838 0.729633i \(-0.260309\pi\)
0.683838 + 0.729633i \(0.260309\pi\)
\(48\) 0 0
\(49\) 7171.64 0.426706
\(50\) 15943.3 0.901887
\(51\) 0 0
\(52\) −1557.71 −0.0798874
\(53\) −34393.6 −1.68185 −0.840926 0.541149i \(-0.817989\pi\)
−0.840926 + 0.541149i \(0.817989\pi\)
\(54\) 0 0
\(55\) −19544.6 −0.871203
\(56\) −31578.5 −1.34562
\(57\) 0 0
\(58\) −22265.9 −0.869099
\(59\) 18299.4 0.684393 0.342197 0.939628i \(-0.388829\pi\)
0.342197 + 0.939628i \(0.388829\pi\)
\(60\) 0 0
\(61\) −26509.8 −0.912183 −0.456092 0.889933i \(-0.650751\pi\)
−0.456092 + 0.889933i \(0.650751\pi\)
\(62\) 19753.7 0.652635
\(63\) 0 0
\(64\) −51695.0 −1.57761
\(65\) −1081.71 −0.0317560
\(66\) 0 0
\(67\) −26313.7 −0.716136 −0.358068 0.933696i \(-0.616564\pi\)
−0.358068 + 0.933696i \(0.616564\pi\)
\(68\) 23134.9 0.606729
\(69\) 0 0
\(70\) −53837.8 −1.31323
\(71\) −39459.2 −0.928971 −0.464486 0.885581i \(-0.653761\pi\)
−0.464486 + 0.885581i \(0.653761\pi\)
\(72\) 0 0
\(73\) −37484.5 −0.823273 −0.411637 0.911348i \(-0.635043\pi\)
−0.411637 + 0.911348i \(0.635043\pi\)
\(74\) −33861.6 −0.718834
\(75\) 0 0
\(76\) −138416. −2.74886
\(77\) −80721.9 −1.55154
\(78\) 0 0
\(79\) 37368.8 0.673660 0.336830 0.941565i \(-0.390645\pi\)
0.336830 + 0.941565i \(0.390645\pi\)
\(80\) 6124.22 0.106986
\(81\) 0 0
\(82\) 150206. 2.46691
\(83\) −76901.5 −1.22529 −0.612646 0.790357i \(-0.709895\pi\)
−0.612646 + 0.790357i \(0.709895\pi\)
\(84\) 0 0
\(85\) 16065.3 0.241181
\(86\) −60309.1 −0.879300
\(87\) 0 0
\(88\) 106306. 1.46336
\(89\) −62991.4 −0.842959 −0.421480 0.906838i \(-0.638489\pi\)
−0.421480 + 0.906838i \(0.638489\pi\)
\(90\) 0 0
\(91\) −4467.60 −0.0565550
\(92\) 28561.4 0.351812
\(93\) 0 0
\(94\) −192068. −2.24200
\(95\) −96118.9 −1.09270
\(96\) 0 0
\(97\) 61484.7 0.663495 0.331748 0.943368i \(-0.392362\pi\)
0.331748 + 0.943368i \(0.392362\pi\)
\(98\) −66503.7 −0.699489
\(99\) 0 0
\(100\) −92827.0 −0.928270
\(101\) 89228.8 0.870365 0.435183 0.900342i \(-0.356684\pi\)
0.435183 + 0.900342i \(0.356684\pi\)
\(102\) 0 0
\(103\) 76234.9 0.708045 0.354023 0.935237i \(-0.384814\pi\)
0.354023 + 0.935237i \(0.384814\pi\)
\(104\) 5883.59 0.0533407
\(105\) 0 0
\(106\) 318937. 2.75702
\(107\) 98757.7 0.833895 0.416947 0.908931i \(-0.363100\pi\)
0.416947 + 0.908931i \(0.363100\pi\)
\(108\) 0 0
\(109\) 242295. 1.95334 0.976672 0.214738i \(-0.0688898\pi\)
0.976672 + 0.214738i \(0.0688898\pi\)
\(110\) 181240. 1.42814
\(111\) 0 0
\(112\) 25293.9 0.190533
\(113\) −218460. −1.60945 −0.804723 0.593650i \(-0.797686\pi\)
−0.804723 + 0.593650i \(0.797686\pi\)
\(114\) 0 0
\(115\) 19833.7 0.139849
\(116\) 129639. 0.894523
\(117\) 0 0
\(118\) −169693. −1.12191
\(119\) 66352.1 0.429524
\(120\) 0 0
\(121\) 110692. 0.687307
\(122\) 245830. 1.49532
\(123\) 0 0
\(124\) −115013. −0.671726
\(125\) −181626. −1.03969
\(126\) 0 0
\(127\) −199105. −1.09540 −0.547700 0.836675i \(-0.684496\pi\)
−0.547700 + 0.836675i \(0.684496\pi\)
\(128\) 319023. 1.72106
\(129\) 0 0
\(130\) 10030.8 0.0520570
\(131\) −236710. −1.20514 −0.602572 0.798064i \(-0.705858\pi\)
−0.602572 + 0.798064i \(0.705858\pi\)
\(132\) 0 0
\(133\) −396985. −1.94601
\(134\) 244011. 1.17395
\(135\) 0 0
\(136\) −87382.1 −0.405112
\(137\) 308407. 1.40386 0.701929 0.712247i \(-0.252322\pi\)
0.701929 + 0.712247i \(0.252322\pi\)
\(138\) 0 0
\(139\) −99198.8 −0.435481 −0.217741 0.976007i \(-0.569869\pi\)
−0.217741 + 0.976007i \(0.569869\pi\)
\(140\) 313461. 1.35165
\(141\) 0 0
\(142\) 365911. 1.52284
\(143\) 15039.8 0.0615037
\(144\) 0 0
\(145\) 90024.2 0.355582
\(146\) 347599. 1.34957
\(147\) 0 0
\(148\) 197154. 0.739862
\(149\) 10925.0 0.0403140 0.0201570 0.999797i \(-0.493583\pi\)
0.0201570 + 0.999797i \(0.493583\pi\)
\(150\) 0 0
\(151\) −488685. −1.74416 −0.872081 0.489362i \(-0.837230\pi\)
−0.872081 + 0.489362i \(0.837230\pi\)
\(152\) 522807. 1.83541
\(153\) 0 0
\(154\) 748546. 2.54341
\(155\) −79867.4 −0.267018
\(156\) 0 0
\(157\) −589168. −1.90761 −0.953806 0.300423i \(-0.902872\pi\)
−0.953806 + 0.300423i \(0.902872\pi\)
\(158\) −346526. −1.10432
\(159\) 0 0
\(160\) 187877. 0.580195
\(161\) 81915.9 0.249060
\(162\) 0 0
\(163\) 598674. 1.76490 0.882452 0.470402i \(-0.155891\pi\)
0.882452 + 0.470402i \(0.155891\pi\)
\(164\) −874552. −2.53908
\(165\) 0 0
\(166\) 713119. 2.00859
\(167\) −222576. −0.617570 −0.308785 0.951132i \(-0.599922\pi\)
−0.308785 + 0.951132i \(0.599922\pi\)
\(168\) 0 0
\(169\) −370461. −0.997758
\(170\) −148976. −0.395362
\(171\) 0 0
\(172\) 351140. 0.905021
\(173\) −438731. −1.11451 −0.557253 0.830343i \(-0.688145\pi\)
−0.557253 + 0.830343i \(0.688145\pi\)
\(174\) 0 0
\(175\) −266233. −0.657154
\(176\) −85149.5 −0.207205
\(177\) 0 0
\(178\) 584129. 1.38184
\(179\) −159561. −0.372216 −0.186108 0.982529i \(-0.559587\pi\)
−0.186108 + 0.982529i \(0.559587\pi\)
\(180\) 0 0
\(181\) 448958. 1.01861 0.509306 0.860585i \(-0.329902\pi\)
0.509306 + 0.860585i \(0.329902\pi\)
\(182\) 41428.8 0.0927094
\(183\) 0 0
\(184\) −107879. −0.234904
\(185\) 136908. 0.294103
\(186\) 0 0
\(187\) −223368. −0.467108
\(188\) 1.11829e6 2.30759
\(189\) 0 0
\(190\) 891326. 1.79123
\(191\) −170763. −0.338696 −0.169348 0.985556i \(-0.554166\pi\)
−0.169348 + 0.985556i \(0.554166\pi\)
\(192\) 0 0
\(193\) 211013. 0.407771 0.203885 0.978995i \(-0.434643\pi\)
0.203885 + 0.978995i \(0.434643\pi\)
\(194\) −570157. −1.08765
\(195\) 0 0
\(196\) 387207. 0.719951
\(197\) 429130. 0.787813 0.393906 0.919151i \(-0.371123\pi\)
0.393906 + 0.919151i \(0.371123\pi\)
\(198\) 0 0
\(199\) −646856. −1.15791 −0.578955 0.815359i \(-0.696539\pi\)
−0.578955 + 0.815359i \(0.696539\pi\)
\(200\) 350614. 0.619804
\(201\) 0 0
\(202\) −827432. −1.42677
\(203\) 371813. 0.633263
\(204\) 0 0
\(205\) −607308. −1.00931
\(206\) −706938. −1.16068
\(207\) 0 0
\(208\) −4712.66 −0.00755279
\(209\) 1.33641e6 2.11629
\(210\) 0 0
\(211\) 282510. 0.436845 0.218422 0.975854i \(-0.429909\pi\)
0.218422 + 0.975854i \(0.429909\pi\)
\(212\) −1.85696e6 −2.83767
\(213\) 0 0
\(214\) −915795. −1.36699
\(215\) 243839. 0.359755
\(216\) 0 0
\(217\) −329864. −0.475538
\(218\) −2.24684e6 −3.20207
\(219\) 0 0
\(220\) −1.05524e6 −1.46992
\(221\) −12362.5 −0.0170265
\(222\) 0 0
\(223\) −637440. −0.858375 −0.429187 0.903215i \(-0.641200\pi\)
−0.429187 + 0.903215i \(0.641200\pi\)
\(224\) 775959. 1.03328
\(225\) 0 0
\(226\) 2.02582e6 2.63833
\(227\) −687712. −0.885813 −0.442906 0.896568i \(-0.646053\pi\)
−0.442906 + 0.896568i \(0.646053\pi\)
\(228\) 0 0
\(229\) −606450. −0.764199 −0.382100 0.924121i \(-0.624799\pi\)
−0.382100 + 0.924121i \(0.624799\pi\)
\(230\) −183921. −0.229251
\(231\) 0 0
\(232\) −489657. −0.597271
\(233\) −1.44933e6 −1.74895 −0.874475 0.485070i \(-0.838794\pi\)
−0.874475 + 0.485070i \(0.838794\pi\)
\(234\) 0 0
\(235\) 776561. 0.917289
\(236\) 988007. 1.15473
\(237\) 0 0
\(238\) −615294. −0.704109
\(239\) −1.10668e6 −1.25322 −0.626610 0.779333i \(-0.715558\pi\)
−0.626610 + 0.779333i \(0.715558\pi\)
\(240\) 0 0
\(241\) −1.02594e6 −1.13784 −0.568919 0.822394i \(-0.692638\pi\)
−0.568919 + 0.822394i \(0.692638\pi\)
\(242\) −1.02646e6 −1.12669
\(243\) 0 0
\(244\) −1.43130e6 −1.53906
\(245\) 268885. 0.286188
\(246\) 0 0
\(247\) 73964.6 0.0771403
\(248\) 434412. 0.448510
\(249\) 0 0
\(250\) 1.68424e6 1.70434
\(251\) 1.07943e6 1.08146 0.540730 0.841196i \(-0.318148\pi\)
0.540730 + 0.841196i \(0.318148\pi\)
\(252\) 0 0
\(253\) −275762. −0.270853
\(254\) 1.84633e6 1.79566
\(255\) 0 0
\(256\) −1.30411e6 −1.24369
\(257\) −1.24866e6 −1.17926 −0.589631 0.807673i \(-0.700727\pi\)
−0.589631 + 0.807673i \(0.700727\pi\)
\(258\) 0 0
\(259\) 565448. 0.523774
\(260\) −58402.9 −0.0535798
\(261\) 0 0
\(262\) 2.19505e6 1.97557
\(263\) −53460.0 −0.0476584 −0.0238292 0.999716i \(-0.507586\pi\)
−0.0238292 + 0.999716i \(0.507586\pi\)
\(264\) 0 0
\(265\) −1.28951e6 −1.12800
\(266\) 3.68130e6 3.19005
\(267\) 0 0
\(268\) −1.42071e6 −1.20829
\(269\) 1.19910e6 1.01035 0.505177 0.863016i \(-0.331427\pi\)
0.505177 + 0.863016i \(0.331427\pi\)
\(270\) 0 0
\(271\) 595615. 0.492654 0.246327 0.969187i \(-0.420776\pi\)
0.246327 + 0.969187i \(0.420776\pi\)
\(272\) 69991.6 0.0573619
\(273\) 0 0
\(274\) −2.85991e6 −2.30131
\(275\) 896249. 0.714656
\(276\) 0 0
\(277\) 2.14463e6 1.67940 0.839698 0.543053i \(-0.182732\pi\)
0.839698 + 0.543053i \(0.182732\pi\)
\(278\) 919886. 0.713875
\(279\) 0 0
\(280\) −1.18397e6 −0.902494
\(281\) 1.27455e6 0.962921 0.481461 0.876468i \(-0.340106\pi\)
0.481461 + 0.876468i \(0.340106\pi\)
\(282\) 0 0
\(283\) 1.33116e6 0.988014 0.494007 0.869458i \(-0.335532\pi\)
0.494007 + 0.869458i \(0.335532\pi\)
\(284\) −2.13046e6 −1.56739
\(285\) 0 0
\(286\) −139466. −0.100822
\(287\) −2.50827e6 −1.79750
\(288\) 0 0
\(289\) −1.23625e6 −0.870687
\(290\) −834808. −0.582897
\(291\) 0 0
\(292\) −2.02384e6 −1.38905
\(293\) 543720. 0.370004 0.185002 0.982738i \(-0.440771\pi\)
0.185002 + 0.982738i \(0.440771\pi\)
\(294\) 0 0
\(295\) 686093. 0.459016
\(296\) −744664. −0.494005
\(297\) 0 0
\(298\) −101309. −0.0660858
\(299\) −15262.2 −0.00987279
\(300\) 0 0
\(301\) 1.00709e6 0.640695
\(302\) 4.53165e6 2.85917
\(303\) 0 0
\(304\) −418760. −0.259885
\(305\) −993926. −0.611793
\(306\) 0 0
\(307\) 2.16140e6 1.30885 0.654424 0.756127i \(-0.272911\pi\)
0.654424 + 0.756127i \(0.272911\pi\)
\(308\) −4.35828e6 −2.61781
\(309\) 0 0
\(310\) 740623. 0.437716
\(311\) 2.27827e6 1.33569 0.667843 0.744302i \(-0.267218\pi\)
0.667843 + 0.744302i \(0.267218\pi\)
\(312\) 0 0
\(313\) −2.34170e6 −1.35105 −0.675524 0.737338i \(-0.736083\pi\)
−0.675524 + 0.737338i \(0.736083\pi\)
\(314\) 5.46345e6 3.12711
\(315\) 0 0
\(316\) 2.01759e6 1.13662
\(317\) −1.70927e6 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(318\) 0 0
\(319\) −1.25167e6 −0.688675
\(320\) −1.93819e6 −1.05809
\(321\) 0 0
\(322\) −759618. −0.408278
\(323\) −1.09851e6 −0.585865
\(324\) 0 0
\(325\) 49603.5 0.0260498
\(326\) −5.55159e6 −2.89317
\(327\) 0 0
\(328\) 3.30325e6 1.69534
\(329\) 3.20731e6 1.63362
\(330\) 0 0
\(331\) 3.09295e6 1.55168 0.775840 0.630930i \(-0.217326\pi\)
0.775840 + 0.630930i \(0.217326\pi\)
\(332\) −4.15202e6 −2.06735
\(333\) 0 0
\(334\) 2.06398e6 1.01237
\(335\) −986575. −0.480306
\(336\) 0 0
\(337\) −691524. −0.331690 −0.165845 0.986152i \(-0.553035\pi\)
−0.165845 + 0.986152i \(0.553035\pi\)
\(338\) 3.43534e6 1.63560
\(339\) 0 0
\(340\) 867390. 0.406928
\(341\) 1.11045e6 0.517148
\(342\) 0 0
\(343\) −1.49204e6 −0.684770
\(344\) −1.32628e6 −0.604281
\(345\) 0 0
\(346\) 4.06842e6 1.82699
\(347\) 4.15931e6 1.85437 0.927187 0.374599i \(-0.122220\pi\)
0.927187 + 0.374599i \(0.122220\pi\)
\(348\) 0 0
\(349\) −3.44531e6 −1.51414 −0.757068 0.653337i \(-0.773369\pi\)
−0.757068 + 0.653337i \(0.773369\pi\)
\(350\) 2.46882e6 1.07726
\(351\) 0 0
\(352\) −2.61219e6 −1.12370
\(353\) 2.27651e6 0.972373 0.486186 0.873855i \(-0.338388\pi\)
0.486186 + 0.873855i \(0.338388\pi\)
\(354\) 0 0
\(355\) −1.47943e6 −0.623053
\(356\) −3.40099e6 −1.42227
\(357\) 0 0
\(358\) 1.47964e6 0.610165
\(359\) 602616. 0.246777 0.123388 0.992358i \(-0.460624\pi\)
0.123388 + 0.992358i \(0.460624\pi\)
\(360\) 0 0
\(361\) 4.09629e6 1.65433
\(362\) −4.16326e6 −1.66979
\(363\) 0 0
\(364\) −241212. −0.0954214
\(365\) −1.40540e6 −0.552162
\(366\) 0 0
\(367\) 2.69133e6 1.04304 0.521521 0.853238i \(-0.325365\pi\)
0.521521 + 0.853238i \(0.325365\pi\)
\(368\) 86409.0 0.0332613
\(369\) 0 0
\(370\) −1.26957e6 −0.482116
\(371\) −5.32586e6 −2.00889
\(372\) 0 0
\(373\) −2.93803e6 −1.09341 −0.546707 0.837324i \(-0.684119\pi\)
−0.546707 + 0.837324i \(0.684119\pi\)
\(374\) 2.07133e6 0.765720
\(375\) 0 0
\(376\) −4.22384e6 −1.54077
\(377\) −69274.6 −0.0251027
\(378\) 0 0
\(379\) 2.78962e6 0.997578 0.498789 0.866723i \(-0.333778\pi\)
0.498789 + 0.866723i \(0.333778\pi\)
\(380\) −5.18959e6 −1.84363
\(381\) 0 0
\(382\) 1.58351e6 0.555216
\(383\) −3.28779e6 −1.14527 −0.572634 0.819811i \(-0.694078\pi\)
−0.572634 + 0.819811i \(0.694078\pi\)
\(384\) 0 0
\(385\) −3.02649e6 −1.04061
\(386\) −1.95676e6 −0.668450
\(387\) 0 0
\(388\) 3.31964e6 1.11947
\(389\) 2.17987e6 0.730392 0.365196 0.930931i \(-0.381002\pi\)
0.365196 + 0.930931i \(0.381002\pi\)
\(390\) 0 0
\(391\) 226672. 0.0749819
\(392\) −1.46251e6 −0.480710
\(393\) 0 0
\(394\) −3.97939e6 −1.29144
\(395\) 1.40106e6 0.451818
\(396\) 0 0
\(397\) −3.30454e6 −1.05229 −0.526144 0.850396i \(-0.676363\pi\)
−0.526144 + 0.850396i \(0.676363\pi\)
\(398\) 5.99839e6 1.89814
\(399\) 0 0
\(400\) −280836. −0.0877613
\(401\) −3.56153e6 −1.10605 −0.553026 0.833164i \(-0.686527\pi\)
−0.553026 + 0.833164i \(0.686527\pi\)
\(402\) 0 0
\(403\) 61458.9 0.0188505
\(404\) 4.81758e6 1.46851
\(405\) 0 0
\(406\) −3.44788e6 −1.03809
\(407\) −1.90353e6 −0.569605
\(408\) 0 0
\(409\) −2.96716e6 −0.877066 −0.438533 0.898715i \(-0.644502\pi\)
−0.438533 + 0.898715i \(0.644502\pi\)
\(410\) 5.63166e6 1.65454
\(411\) 0 0
\(412\) 4.11603e6 1.19464
\(413\) 2.83366e6 0.817472
\(414\) 0 0
\(415\) −2.88325e6 −0.821792
\(416\) −144574. −0.0409596
\(417\) 0 0
\(418\) −1.23928e7 −3.46918
\(419\) 1.51390e6 0.421272 0.210636 0.977565i \(-0.432447\pi\)
0.210636 + 0.977565i \(0.432447\pi\)
\(420\) 0 0
\(421\) 746530. 0.205278 0.102639 0.994719i \(-0.467271\pi\)
0.102639 + 0.994719i \(0.467271\pi\)
\(422\) −2.61975e6 −0.716109
\(423\) 0 0
\(424\) 7.01386e6 1.89471
\(425\) −736703. −0.197843
\(426\) 0 0
\(427\) −4.10506e6 −1.08956
\(428\) 5.33206e6 1.40697
\(429\) 0 0
\(430\) −2.26116e6 −0.589738
\(431\) −2.15954e6 −0.559976 −0.279988 0.960004i \(-0.590330\pi\)
−0.279988 + 0.960004i \(0.590330\pi\)
\(432\) 0 0
\(433\) 5.74239e6 1.47188 0.735941 0.677045i \(-0.236740\pi\)
0.735941 + 0.677045i \(0.236740\pi\)
\(434\) 3.05888e6 0.779538
\(435\) 0 0
\(436\) 1.30818e7 3.29574
\(437\) −1.35618e6 −0.339714
\(438\) 0 0
\(439\) 3.04352e6 0.753728 0.376864 0.926269i \(-0.377002\pi\)
0.376864 + 0.926269i \(0.377002\pi\)
\(440\) 3.98571e6 0.981464
\(441\) 0 0
\(442\) 114639. 0.0279111
\(443\) 2.95192e6 0.714652 0.357326 0.933980i \(-0.383689\pi\)
0.357326 + 0.933980i \(0.383689\pi\)
\(444\) 0 0
\(445\) −2.36172e6 −0.565365
\(446\) 5.91108e6 1.40711
\(447\) 0 0
\(448\) −8.00499e6 −1.88437
\(449\) −3.29085e6 −0.770356 −0.385178 0.922842i \(-0.625860\pi\)
−0.385178 + 0.922842i \(0.625860\pi\)
\(450\) 0 0
\(451\) 8.44384e6 1.95478
\(452\) −1.17950e7 −2.71551
\(453\) 0 0
\(454\) 6.37726e6 1.45209
\(455\) −167503. −0.0379309
\(456\) 0 0
\(457\) 5.82436e6 1.30454 0.652271 0.757986i \(-0.273816\pi\)
0.652271 + 0.757986i \(0.273816\pi\)
\(458\) 5.62371e6 1.25273
\(459\) 0 0
\(460\) 1.07085e6 0.235957
\(461\) 1.73714e6 0.380700 0.190350 0.981716i \(-0.439038\pi\)
0.190350 + 0.981716i \(0.439038\pi\)
\(462\) 0 0
\(463\) 3.08948e6 0.669780 0.334890 0.942257i \(-0.391301\pi\)
0.334890 + 0.942257i \(0.391301\pi\)
\(464\) 392207. 0.0845708
\(465\) 0 0
\(466\) 1.34399e7 2.86702
\(467\) 1.75231e6 0.371808 0.185904 0.982568i \(-0.440479\pi\)
0.185904 + 0.982568i \(0.440479\pi\)
\(468\) 0 0
\(469\) −4.07469e6 −0.855387
\(470\) −7.20117e6 −1.50369
\(471\) 0 0
\(472\) −3.73178e6 −0.771011
\(473\) −3.39027e6 −0.696757
\(474\) 0 0
\(475\) 4.40769e6 0.896349
\(476\) 3.58244e6 0.724706
\(477\) 0 0
\(478\) 1.02624e7 2.05438
\(479\) 5.38341e6 1.07206 0.536030 0.844199i \(-0.319924\pi\)
0.536030 + 0.844199i \(0.319924\pi\)
\(480\) 0 0
\(481\) −105352. −0.0207625
\(482\) 9.51372e6 1.86523
\(483\) 0 0
\(484\) 5.97639e6 1.15965
\(485\) 2.30523e6 0.445000
\(486\) 0 0
\(487\) −6.11771e6 −1.16887 −0.584436 0.811440i \(-0.698684\pi\)
−0.584436 + 0.811440i \(0.698684\pi\)
\(488\) 5.40613e6 1.02763
\(489\) 0 0
\(490\) −2.49341e6 −0.469141
\(491\) −5.22411e6 −0.977932 −0.488966 0.872303i \(-0.662626\pi\)
−0.488966 + 0.872303i \(0.662626\pi\)
\(492\) 0 0
\(493\) 1.02886e6 0.190650
\(494\) −685885. −0.126454
\(495\) 0 0
\(496\) −347957. −0.0635070
\(497\) −6.11027e6 −1.10961
\(498\) 0 0
\(499\) 8.89404e6 1.59900 0.799498 0.600668i \(-0.205099\pi\)
0.799498 + 0.600668i \(0.205099\pi\)
\(500\) −9.80623e6 −1.75419
\(501\) 0 0
\(502\) −1.00097e7 −1.77281
\(503\) 3.62219e6 0.638339 0.319170 0.947698i \(-0.396596\pi\)
0.319170 + 0.947698i \(0.396596\pi\)
\(504\) 0 0
\(505\) 3.34543e6 0.583746
\(506\) 2.55718e6 0.444003
\(507\) 0 0
\(508\) −1.07499e7 −1.84819
\(509\) −454923. −0.0778294 −0.0389147 0.999243i \(-0.512390\pi\)
−0.0389147 + 0.999243i \(0.512390\pi\)
\(510\) 0 0
\(511\) −5.80448e6 −0.983357
\(512\) 1.88446e6 0.317696
\(513\) 0 0
\(514\) 1.15790e7 1.93314
\(515\) 2.85826e6 0.474879
\(516\) 0 0
\(517\) −1.07971e7 −1.77656
\(518\) −5.24349e6 −0.858610
\(519\) 0 0
\(520\) 220592. 0.0357751
\(521\) −4.46566e6 −0.720761 −0.360380 0.932805i \(-0.617353\pi\)
−0.360380 + 0.932805i \(0.617353\pi\)
\(522\) 0 0
\(523\) −2.91793e6 −0.466467 −0.233234 0.972421i \(-0.574931\pi\)
−0.233234 + 0.972421i \(0.574931\pi\)
\(524\) −1.27803e7 −2.03336
\(525\) 0 0
\(526\) 495743. 0.0781254
\(527\) −912777. −0.143165
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) 1.19578e7 1.84911
\(531\) 0 0
\(532\) −2.14337e7 −3.28336
\(533\) 467330. 0.0712534
\(534\) 0 0
\(535\) 3.70270e6 0.559286
\(536\) 5.36614e6 0.806771
\(537\) 0 0
\(538\) −1.11194e7 −1.65625
\(539\) −3.73850e6 −0.554275
\(540\) 0 0
\(541\) −2.73195e6 −0.401310 −0.200655 0.979662i \(-0.564307\pi\)
−0.200655 + 0.979662i \(0.564307\pi\)
\(542\) −5.52323e6 −0.807597
\(543\) 0 0
\(544\) 2.14718e6 0.311080
\(545\) 9.08432e6 1.31009
\(546\) 0 0
\(547\) −5.55388e6 −0.793648 −0.396824 0.917895i \(-0.629888\pi\)
−0.396824 + 0.917895i \(0.629888\pi\)
\(548\) 1.66513e7 2.36863
\(549\) 0 0
\(550\) −8.31105e6 −1.17152
\(551\) −6.15564e6 −0.863763
\(552\) 0 0
\(553\) 5.78657e6 0.804652
\(554\) −1.98875e7 −2.75300
\(555\) 0 0
\(556\) −5.35588e6 −0.734757
\(557\) 1.69772e6 0.231862 0.115931 0.993257i \(-0.463015\pi\)
0.115931 + 0.993257i \(0.463015\pi\)
\(558\) 0 0
\(559\) −187637. −0.0253974
\(560\) 948338. 0.127789
\(561\) 0 0
\(562\) −1.18191e7 −1.57849
\(563\) −4.59153e6 −0.610501 −0.305250 0.952272i \(-0.598740\pi\)
−0.305250 + 0.952272i \(0.598740\pi\)
\(564\) 0 0
\(565\) −8.19068e6 −1.07944
\(566\) −1.23440e7 −1.61963
\(567\) 0 0
\(568\) 8.04689e6 1.04654
\(569\) 1.10517e7 1.43103 0.715517 0.698595i \(-0.246191\pi\)
0.715517 + 0.698595i \(0.246191\pi\)
\(570\) 0 0
\(571\) −1.35952e7 −1.74500 −0.872500 0.488613i \(-0.837503\pi\)
−0.872500 + 0.488613i \(0.837503\pi\)
\(572\) 812018. 0.103771
\(573\) 0 0
\(574\) 2.32595e7 2.94660
\(575\) −909506. −0.114719
\(576\) 0 0
\(577\) 4.14819e6 0.518703 0.259351 0.965783i \(-0.416491\pi\)
0.259351 + 0.965783i \(0.416491\pi\)
\(578\) 1.14640e7 1.42730
\(579\) 0 0
\(580\) 4.86053e6 0.599948
\(581\) −1.19082e7 −1.46355
\(582\) 0 0
\(583\) 1.79290e7 2.18467
\(584\) 7.64418e6 0.927468
\(585\) 0 0
\(586\) −5.04200e6 −0.606539
\(587\) 55407.2 0.00663699 0.00331849 0.999994i \(-0.498944\pi\)
0.00331849 + 0.999994i \(0.498944\pi\)
\(588\) 0 0
\(589\) 5.46114e6 0.648628
\(590\) −6.36225e6 −0.752455
\(591\) 0 0
\(592\) 596464. 0.0699487
\(593\) 1.44004e7 1.68166 0.840829 0.541300i \(-0.182068\pi\)
0.840829 + 0.541300i \(0.182068\pi\)
\(594\) 0 0
\(595\) 2.48773e6 0.288078
\(596\) 589856. 0.0680190
\(597\) 0 0
\(598\) 141529. 0.0161842
\(599\) −1.33225e6 −0.151712 −0.0758559 0.997119i \(-0.524169\pi\)
−0.0758559 + 0.997119i \(0.524169\pi\)
\(600\) 0 0
\(601\) −4.11211e6 −0.464386 −0.232193 0.972670i \(-0.574590\pi\)
−0.232193 + 0.972670i \(0.574590\pi\)
\(602\) −9.33889e6 −1.05028
\(603\) 0 0
\(604\) −2.63848e7 −2.94280
\(605\) 4.15013e6 0.460971
\(606\) 0 0
\(607\) −5.38575e6 −0.593300 −0.296650 0.954986i \(-0.595869\pi\)
−0.296650 + 0.954986i \(0.595869\pi\)
\(608\) −1.28466e7 −1.40938
\(609\) 0 0
\(610\) 9.21683e6 1.00290
\(611\) −597572. −0.0647571
\(612\) 0 0
\(613\) −2.17889e6 −0.234199 −0.117100 0.993120i \(-0.537360\pi\)
−0.117100 + 0.993120i \(0.537360\pi\)
\(614\) −2.00430e7 −2.14557
\(615\) 0 0
\(616\) 1.64616e7 1.74791
\(617\) −1.40873e7 −1.48976 −0.744880 0.667199i \(-0.767493\pi\)
−0.744880 + 0.667199i \(0.767493\pi\)
\(618\) 0 0
\(619\) −5.63132e6 −0.590722 −0.295361 0.955386i \(-0.595440\pi\)
−0.295361 + 0.955386i \(0.595440\pi\)
\(620\) −4.31215e6 −0.450521
\(621\) 0 0
\(622\) −2.11268e7 −2.18956
\(623\) −9.75425e6 −1.00687
\(624\) 0 0
\(625\) −1.43687e6 −0.147135
\(626\) 2.17150e7 2.21474
\(627\) 0 0
\(628\) −3.18100e7 −3.21858
\(629\) 1.56467e6 0.157687
\(630\) 0 0
\(631\) −1.47000e7 −1.46976 −0.734878 0.678200i \(-0.762760\pi\)
−0.734878 + 0.678200i \(0.762760\pi\)
\(632\) −7.62059e6 −0.758919
\(633\) 0 0
\(634\) 1.58503e7 1.56608
\(635\) −7.46499e6 −0.734675
\(636\) 0 0
\(637\) −206910. −0.0202038
\(638\) 1.16070e7 1.12893
\(639\) 0 0
\(640\) 1.19610e7 1.15430
\(641\) 1.20465e7 1.15802 0.579012 0.815319i \(-0.303439\pi\)
0.579012 + 0.815319i \(0.303439\pi\)
\(642\) 0 0
\(643\) 4.72652e6 0.450831 0.225416 0.974263i \(-0.427626\pi\)
0.225416 + 0.974263i \(0.427626\pi\)
\(644\) 4.42275e6 0.420221
\(645\) 0 0
\(646\) 1.01867e7 0.960396
\(647\) 1.24621e7 1.17039 0.585196 0.810892i \(-0.301018\pi\)
0.585196 + 0.810892i \(0.301018\pi\)
\(648\) 0 0
\(649\) −9.53926e6 −0.889002
\(650\) −459981. −0.0427028
\(651\) 0 0
\(652\) 3.23232e7 2.97780
\(653\) 7.75118e6 0.711353 0.355676 0.934609i \(-0.384251\pi\)
0.355676 + 0.934609i \(0.384251\pi\)
\(654\) 0 0
\(655\) −8.87493e6 −0.808280
\(656\) −2.64585e6 −0.240052
\(657\) 0 0
\(658\) −2.97418e7 −2.67795
\(659\) −1.52713e7 −1.36981 −0.684907 0.728630i \(-0.740157\pi\)
−0.684907 + 0.728630i \(0.740157\pi\)
\(660\) 0 0
\(661\) 2.21977e7 1.97608 0.988041 0.154190i \(-0.0492767\pi\)
0.988041 + 0.154190i \(0.0492767\pi\)
\(662\) −2.86814e7 −2.54363
\(663\) 0 0
\(664\) 1.56825e7 1.38037
\(665\) −1.48841e7 −1.30517
\(666\) 0 0
\(667\) 1.27019e6 0.110549
\(668\) −1.20172e7 −1.04198
\(669\) 0 0
\(670\) 9.14866e6 0.787355
\(671\) 1.38193e7 1.18489
\(672\) 0 0
\(673\) 6.38649e6 0.543531 0.271766 0.962363i \(-0.412392\pi\)
0.271766 + 0.962363i \(0.412392\pi\)
\(674\) 6.41261e6 0.543732
\(675\) 0 0
\(676\) −2.00017e7 −1.68345
\(677\) −6.89077e6 −0.577825 −0.288913 0.957356i \(-0.593294\pi\)
−0.288913 + 0.957356i \(0.593294\pi\)
\(678\) 0 0
\(679\) 9.52093e6 0.792510
\(680\) −3.27620e6 −0.271705
\(681\) 0 0
\(682\) −1.02974e7 −0.847749
\(683\) 2.36161e7 1.93712 0.968558 0.248788i \(-0.0800321\pi\)
0.968558 + 0.248788i \(0.0800321\pi\)
\(684\) 0 0
\(685\) 1.15630e7 0.941555
\(686\) 1.38359e7 1.12253
\(687\) 0 0
\(688\) 1.06233e6 0.0855634
\(689\) 992293. 0.0796328
\(690\) 0 0
\(691\) 1.22060e7 0.972472 0.486236 0.873828i \(-0.338370\pi\)
0.486236 + 0.873828i \(0.338370\pi\)
\(692\) −2.36877e7 −1.88043
\(693\) 0 0
\(694\) −3.85699e7 −3.03983
\(695\) −3.71924e6 −0.292073
\(696\) 0 0
\(697\) −6.94071e6 −0.541155
\(698\) 3.19489e7 2.48209
\(699\) 0 0
\(700\) −1.43743e7 −1.10877
\(701\) −6.09955e6 −0.468816 −0.234408 0.972138i \(-0.575315\pi\)
−0.234408 + 0.972138i \(0.575315\pi\)
\(702\) 0 0
\(703\) −9.36143e6 −0.714420
\(704\) 2.69481e7 2.04925
\(705\) 0 0
\(706\) −2.11104e7 −1.59399
\(707\) 1.38171e7 1.03961
\(708\) 0 0
\(709\) 2.32369e7 1.73605 0.868026 0.496518i \(-0.165388\pi\)
0.868026 + 0.496518i \(0.165388\pi\)
\(710\) 1.37190e7 1.02136
\(711\) 0 0
\(712\) 1.28458e7 0.949645
\(713\) −1.12688e6 −0.0830145
\(714\) 0 0
\(715\) 563883. 0.0412500
\(716\) −8.61493e6 −0.628014
\(717\) 0 0
\(718\) −5.58815e6 −0.404536
\(719\) 1.64452e7 1.18636 0.593179 0.805071i \(-0.297873\pi\)
0.593179 + 0.805071i \(0.297873\pi\)
\(720\) 0 0
\(721\) 1.18050e7 0.845723
\(722\) −3.79855e7 −2.71191
\(723\) 0 0
\(724\) 2.42399e7 1.71863
\(725\) −4.12821e6 −0.291687
\(726\) 0 0
\(727\) −3.66575e6 −0.257233 −0.128617 0.991694i \(-0.541054\pi\)
−0.128617 + 0.991694i \(0.541054\pi\)
\(728\) 911076. 0.0637127
\(729\) 0 0
\(730\) 1.30324e7 0.905146
\(731\) 2.78675e6 0.192888
\(732\) 0 0
\(733\) −2.15654e7 −1.48251 −0.741256 0.671223i \(-0.765769\pi\)
−0.741256 + 0.671223i \(0.765769\pi\)
\(734\) −2.49571e7 −1.70984
\(735\) 0 0
\(736\) 2.65083e6 0.180380
\(737\) 1.37171e7 0.930235
\(738\) 0 0
\(739\) 2.21913e7 1.49476 0.747380 0.664397i \(-0.231311\pi\)
0.747380 + 0.664397i \(0.231311\pi\)
\(740\) 7.39184e6 0.496219
\(741\) 0 0
\(742\) 4.93875e7 3.29312
\(743\) 6.61440e6 0.439560 0.219780 0.975549i \(-0.429466\pi\)
0.219780 + 0.975549i \(0.429466\pi\)
\(744\) 0 0
\(745\) 409609. 0.0270382
\(746\) 2.72448e7 1.79241
\(747\) 0 0
\(748\) −1.20600e7 −0.788119
\(749\) 1.52927e7 0.996044
\(750\) 0 0
\(751\) −8.17370e6 −0.528834 −0.264417 0.964409i \(-0.585179\pi\)
−0.264417 + 0.964409i \(0.585179\pi\)
\(752\) 3.38323e6 0.218166
\(753\) 0 0
\(754\) 642394. 0.0411503
\(755\) −1.83222e7 −1.16979
\(756\) 0 0
\(757\) −6.07796e6 −0.385495 −0.192747 0.981248i \(-0.561740\pi\)
−0.192747 + 0.981248i \(0.561740\pi\)
\(758\) −2.58686e7 −1.63531
\(759\) 0 0
\(760\) 1.96015e7 1.23099
\(761\) −2.93696e6 −0.183838 −0.0919192 0.995766i \(-0.529300\pi\)
−0.0919192 + 0.995766i \(0.529300\pi\)
\(762\) 0 0
\(763\) 3.75195e7 2.33317
\(764\) −9.21971e6 −0.571457
\(765\) 0 0
\(766\) 3.04882e7 1.87741
\(767\) −527957. −0.0324048
\(768\) 0 0
\(769\) 6.47116e6 0.394608 0.197304 0.980342i \(-0.436781\pi\)
0.197304 + 0.980342i \(0.436781\pi\)
\(770\) 2.80651e7 1.70584
\(771\) 0 0
\(772\) 1.13929e7 0.688003
\(773\) −2.52231e7 −1.51827 −0.759136 0.650932i \(-0.774378\pi\)
−0.759136 + 0.650932i \(0.774378\pi\)
\(774\) 0 0
\(775\) 3.66245e6 0.219037
\(776\) −1.25385e7 −0.747468
\(777\) 0 0
\(778\) −2.02143e7 −1.19732
\(779\) 4.15263e7 2.45177
\(780\) 0 0
\(781\) 2.05697e7 1.20670
\(782\) −2.10197e6 −0.122916
\(783\) 0 0
\(784\) 1.17145e6 0.0680663
\(785\) −2.20895e7 −1.27942
\(786\) 0 0
\(787\) −1.74674e7 −1.00529 −0.502644 0.864493i \(-0.667639\pi\)
−0.502644 + 0.864493i \(0.667639\pi\)
\(788\) 2.31693e7 1.32922
\(789\) 0 0
\(790\) −1.29922e7 −0.740655
\(791\) −3.38287e7 −1.92240
\(792\) 0 0
\(793\) 764838. 0.0431903
\(794\) 3.06435e7 1.72499
\(795\) 0 0
\(796\) −3.49246e7 −1.95366
\(797\) −2.12790e6 −0.118660 −0.0593302 0.998238i \(-0.518896\pi\)
−0.0593302 + 0.998238i \(0.518896\pi\)
\(798\) 0 0
\(799\) 8.87505e6 0.491817
\(800\) −8.61542e6 −0.475939
\(801\) 0 0
\(802\) 3.30266e7 1.81312
\(803\) 1.95402e7 1.06940
\(804\) 0 0
\(805\) 3.07125e6 0.167042
\(806\) −569917. −0.0309011
\(807\) 0 0
\(808\) −1.81964e7 −0.980519
\(809\) 5.17917e6 0.278220 0.139110 0.990277i \(-0.455576\pi\)
0.139110 + 0.990277i \(0.455576\pi\)
\(810\) 0 0
\(811\) 2.72737e7 1.45610 0.728050 0.685524i \(-0.240427\pi\)
0.728050 + 0.685524i \(0.240427\pi\)
\(812\) 2.00747e7 1.06846
\(813\) 0 0
\(814\) 1.76517e7 0.933740
\(815\) 2.24459e7 1.18371
\(816\) 0 0
\(817\) −1.66731e7 −0.873900
\(818\) 2.75149e7 1.43775
\(819\) 0 0
\(820\) −3.27894e7 −1.70294
\(821\) −2.28417e7 −1.18269 −0.591346 0.806418i \(-0.701403\pi\)
−0.591346 + 0.806418i \(0.701403\pi\)
\(822\) 0 0
\(823\) 1.38673e7 0.713664 0.356832 0.934169i \(-0.383857\pi\)
0.356832 + 0.934169i \(0.383857\pi\)
\(824\) −1.55465e7 −0.797656
\(825\) 0 0
\(826\) −2.62770e7 −1.34006
\(827\) 7.98777e6 0.406127 0.203064 0.979166i \(-0.434910\pi\)
0.203064 + 0.979166i \(0.434910\pi\)
\(828\) 0 0
\(829\) −8.88714e6 −0.449134 −0.224567 0.974459i \(-0.572097\pi\)
−0.224567 + 0.974459i \(0.572097\pi\)
\(830\) 2.67368e7 1.34715
\(831\) 0 0
\(832\) 1.49146e6 0.0746969
\(833\) 3.07299e6 0.153444
\(834\) 0 0
\(835\) −8.34498e6 −0.414199
\(836\) 7.21547e7 3.57066
\(837\) 0 0
\(838\) −1.40386e7 −0.690581
\(839\) 2.25661e7 1.10676 0.553379 0.832930i \(-0.313338\pi\)
0.553379 + 0.832930i \(0.313338\pi\)
\(840\) 0 0
\(841\) −1.47458e7 −0.718917
\(842\) −6.92268e6 −0.336507
\(843\) 0 0
\(844\) 1.52531e7 0.737057
\(845\) −1.38896e7 −0.669187
\(846\) 0 0
\(847\) 1.71406e7 0.820953
\(848\) −5.61799e6 −0.268282
\(849\) 0 0
\(850\) 6.83156e6 0.324319
\(851\) 1.93169e6 0.0914350
\(852\) 0 0
\(853\) −3.35094e7 −1.57686 −0.788431 0.615124i \(-0.789106\pi\)
−0.788431 + 0.615124i \(0.789106\pi\)
\(854\) 3.80668e7 1.78608
\(855\) 0 0
\(856\) −2.01396e7 −0.939433
\(857\) 1.84965e7 0.860276 0.430138 0.902763i \(-0.358465\pi\)
0.430138 + 0.902763i \(0.358465\pi\)
\(858\) 0 0
\(859\) 3.55324e7 1.64302 0.821508 0.570198i \(-0.193133\pi\)
0.821508 + 0.570198i \(0.193133\pi\)
\(860\) 1.31652e7 0.606989
\(861\) 0 0
\(862\) 2.00258e7 0.917955
\(863\) 1.37196e7 0.627067 0.313534 0.949577i \(-0.398487\pi\)
0.313534 + 0.949577i \(0.398487\pi\)
\(864\) 0 0
\(865\) −1.64492e7 −0.747489
\(866\) −5.32501e7 −2.41282
\(867\) 0 0
\(868\) −1.78098e7 −0.802342
\(869\) −1.94799e7 −0.875060
\(870\) 0 0
\(871\) 759180. 0.0339078
\(872\) −4.94111e7 −2.20056
\(873\) 0 0
\(874\) 1.25761e7 0.556886
\(875\) −2.81248e7 −1.24185
\(876\) 0 0
\(877\) −1.74346e7 −0.765443 −0.382721 0.923864i \(-0.625013\pi\)
−0.382721 + 0.923864i \(0.625013\pi\)
\(878\) −2.82230e7 −1.23557
\(879\) 0 0
\(880\) −3.19249e6 −0.138971
\(881\) −3.33087e7 −1.44583 −0.722916 0.690936i \(-0.757199\pi\)
−0.722916 + 0.690936i \(0.757199\pi\)
\(882\) 0 0
\(883\) 3.36375e6 0.145185 0.0725925 0.997362i \(-0.476873\pi\)
0.0725925 + 0.997362i \(0.476873\pi\)
\(884\) −667466. −0.0287276
\(885\) 0 0
\(886\) −2.73736e7 −1.17151
\(887\) 1.07106e7 0.457095 0.228547 0.973533i \(-0.426602\pi\)
0.228547 + 0.973533i \(0.426602\pi\)
\(888\) 0 0
\(889\) −3.08315e7 −1.30840
\(890\) 2.19006e7 0.926790
\(891\) 0 0
\(892\) −3.44162e7 −1.44828
\(893\) −5.30994e7 −2.22824
\(894\) 0 0
\(895\) −5.98239e6 −0.249642
\(896\) 4.94008e7 2.05572
\(897\) 0 0
\(898\) 3.05165e7 1.26283
\(899\) −5.11486e6 −0.211074
\(900\) 0 0
\(901\) −1.47374e7 −0.604795
\(902\) −7.83010e7 −3.20443
\(903\) 0 0
\(904\) 4.45505e7 1.81314
\(905\) 1.68327e7 0.683174
\(906\) 0 0
\(907\) 1.90456e7 0.768735 0.384367 0.923180i \(-0.374420\pi\)
0.384367 + 0.923180i \(0.374420\pi\)
\(908\) −3.71305e7 −1.49457
\(909\) 0 0
\(910\) 1.55328e6 0.0621793
\(911\) −1.05019e6 −0.0419249 −0.0209624 0.999780i \(-0.506673\pi\)
−0.0209624 + 0.999780i \(0.506673\pi\)
\(912\) 0 0
\(913\) 4.00879e7 1.59161
\(914\) −5.40102e7 −2.13851
\(915\) 0 0
\(916\) −3.27431e7 −1.28938
\(917\) −3.66547e7 −1.43948
\(918\) 0 0
\(919\) −1.19851e7 −0.468114 −0.234057 0.972223i \(-0.575200\pi\)
−0.234057 + 0.972223i \(0.575200\pi\)
\(920\) −4.04467e6 −0.157548
\(921\) 0 0
\(922\) −1.61088e7 −0.624073
\(923\) 1.13844e6 0.0439852
\(924\) 0 0
\(925\) −6.27813e6 −0.241255
\(926\) −2.86492e7 −1.09796
\(927\) 0 0
\(928\) 1.20320e7 0.458636
\(929\) −1.29362e7 −0.491777 −0.245888 0.969298i \(-0.579080\pi\)
−0.245888 + 0.969298i \(0.579080\pi\)
\(930\) 0 0
\(931\) −1.83857e7 −0.695194
\(932\) −7.82513e7 −2.95088
\(933\) 0 0
\(934\) −1.62494e7 −0.609496
\(935\) −8.37469e6 −0.313285
\(936\) 0 0
\(937\) −1.25390e7 −0.466567 −0.233283 0.972409i \(-0.574947\pi\)
−0.233283 + 0.972409i \(0.574947\pi\)
\(938\) 3.77852e7 1.40222
\(939\) 0 0
\(940\) 4.19276e7 1.54768
\(941\) 2.45328e7 0.903178 0.451589 0.892226i \(-0.350857\pi\)
0.451589 + 0.892226i \(0.350857\pi\)
\(942\) 0 0
\(943\) −8.56874e6 −0.313789
\(944\) 2.98909e6 0.109171
\(945\) 0 0
\(946\) 3.14385e7 1.14218
\(947\) 2.08008e7 0.753713 0.376856 0.926272i \(-0.377005\pi\)
0.376856 + 0.926272i \(0.377005\pi\)
\(948\) 0 0
\(949\) 1.08147e6 0.0389806
\(950\) −4.08732e7 −1.46937
\(951\) 0 0
\(952\) −1.35311e7 −0.483885
\(953\) 9.76608e6 0.348328 0.174164 0.984717i \(-0.444278\pi\)
0.174164 + 0.984717i \(0.444278\pi\)
\(954\) 0 0
\(955\) −6.40236e6 −0.227160
\(956\) −5.97512e7 −2.11447
\(957\) 0 0
\(958\) −4.99212e7 −1.75740
\(959\) 4.77570e7 1.67684
\(960\) 0 0
\(961\) −2.40914e7 −0.841498
\(962\) 976946. 0.0340356
\(963\) 0 0
\(964\) −5.53920e7 −1.91979
\(965\) 7.91147e6 0.273488
\(966\) 0 0
\(967\) −2.35516e7 −0.809942 −0.404971 0.914329i \(-0.632718\pi\)
−0.404971 + 0.914329i \(0.632718\pi\)
\(968\) −2.25733e7 −0.774294
\(969\) 0 0
\(970\) −2.13768e7 −0.729479
\(971\) −2.32199e7 −0.790336 −0.395168 0.918609i \(-0.629314\pi\)
−0.395168 + 0.918609i \(0.629314\pi\)
\(972\) 0 0
\(973\) −1.53610e7 −0.520160
\(974\) 5.67305e7 1.91610
\(975\) 0 0
\(976\) −4.33022e6 −0.145508
\(977\) 3.29920e7 1.10579 0.552895 0.833251i \(-0.313523\pi\)
0.552895 + 0.833251i \(0.313523\pi\)
\(978\) 0 0
\(979\) 3.28368e7 1.09497
\(980\) 1.45175e7 0.482864
\(981\) 0 0
\(982\) 4.84440e7 1.60310
\(983\) 2.82144e7 0.931294 0.465647 0.884970i \(-0.345822\pi\)
0.465647 + 0.884970i \(0.345822\pi\)
\(984\) 0 0
\(985\) 1.60893e7 0.528379
\(986\) −9.54074e6 −0.312529
\(987\) 0 0
\(988\) 3.99345e6 0.130153
\(989\) 3.44042e6 0.111846
\(990\) 0 0
\(991\) −3.77541e7 −1.22118 −0.610590 0.791947i \(-0.709068\pi\)
−0.610590 + 0.791947i \(0.709068\pi\)
\(992\) −1.06745e7 −0.344405
\(993\) 0 0
\(994\) 5.66615e7 1.81896
\(995\) −2.42524e7 −0.776600
\(996\) 0 0
\(997\) 3.33776e7 1.06345 0.531726 0.846917i \(-0.321544\pi\)
0.531726 + 0.846917i \(0.321544\pi\)
\(998\) −8.24758e7 −2.62120
\(999\) 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 207.6.a.f.1.2 5
3.2 odd 2 69.6.a.e.1.4 5
12.11 even 2 1104.6.a.r.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.e.1.4 5 3.2 odd 2
207.6.a.f.1.2 5 1.1 even 1 trivial
1104.6.a.r.1.2 5 12.11 even 2