Properties

Label 207.6.a.f.1.3
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 1.3
Root \(-7.90234\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24792 q^{2} -26.9469 q^{4} -53.3906 q^{5} +89.8688 q^{7} +132.508 q^{8} +O(q^{10})\) \(q-2.24792 q^{2} -26.9469 q^{4} -53.3906 q^{5} +89.8688 q^{7} +132.508 q^{8} +120.018 q^{10} -225.013 q^{11} +725.747 q^{13} -202.018 q^{14} +564.433 q^{16} -44.9540 q^{17} +1212.50 q^{19} +1438.71 q^{20} +505.810 q^{22} +529.000 q^{23} -274.446 q^{25} -1631.42 q^{26} -2421.68 q^{28} -2592.49 q^{29} +585.421 q^{31} -5509.05 q^{32} +101.053 q^{34} -4798.15 q^{35} -3849.04 q^{37} -2725.59 q^{38} -7074.66 q^{40} +4299.92 q^{41} -20567.4 q^{43} +6063.39 q^{44} -1189.15 q^{46} +5221.50 q^{47} -8730.61 q^{49} +616.931 q^{50} -19556.6 q^{52} +15753.7 q^{53} +12013.6 q^{55} +11908.3 q^{56} +5827.70 q^{58} +13780.6 q^{59} -18988.5 q^{61} -1315.98 q^{62} -5677.98 q^{64} -38748.1 q^{65} +1951.43 q^{67} +1211.37 q^{68} +10785.8 q^{70} -75281.4 q^{71} -4177.11 q^{73} +8652.32 q^{74} -32673.0 q^{76} -20221.6 q^{77} -95896.7 q^{79} -30135.4 q^{80} -9665.87 q^{82} -13366.7 q^{83} +2400.12 q^{85} +46233.9 q^{86} -29815.9 q^{88} -50932.1 q^{89} +65222.0 q^{91} -14254.9 q^{92} -11737.5 q^{94} -64735.9 q^{95} +44280.7 q^{97} +19625.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24792 −0.397380 −0.198690 0.980062i \(-0.563669\pi\)
−0.198690 + 0.980062i \(0.563669\pi\)
\(3\) 0 0
\(4\) −26.9469 −0.842090
\(5\) −53.3906 −0.955080 −0.477540 0.878610i \(-0.658471\pi\)
−0.477540 + 0.878610i \(0.658471\pi\)
\(6\) 0 0
\(7\) 89.8688 0.693208 0.346604 0.938012i \(-0.387335\pi\)
0.346604 + 0.938012i \(0.387335\pi\)
\(8\) 132.508 0.732009
\(9\) 0 0
\(10\) 120.018 0.379529
\(11\) −225.013 −0.560693 −0.280347 0.959899i \(-0.590449\pi\)
−0.280347 + 0.959899i \(0.590449\pi\)
\(12\) 0 0
\(13\) 725.747 1.19104 0.595521 0.803340i \(-0.296946\pi\)
0.595521 + 0.803340i \(0.296946\pi\)
\(14\) −202.018 −0.275467
\(15\) 0 0
\(16\) 564.433 0.551204
\(17\) −44.9540 −0.0377265 −0.0188632 0.999822i \(-0.506005\pi\)
−0.0188632 + 0.999822i \(0.506005\pi\)
\(18\) 0 0
\(19\) 1212.50 0.770542 0.385271 0.922803i \(-0.374108\pi\)
0.385271 + 0.922803i \(0.374108\pi\)
\(20\) 1438.71 0.804263
\(21\) 0 0
\(22\) 505.810 0.222808
\(23\) 529.000 0.208514
\(24\) 0 0
\(25\) −274.446 −0.0878226
\(26\) −1631.42 −0.473296
\(27\) 0 0
\(28\) −2421.68 −0.583743
\(29\) −2592.49 −0.572430 −0.286215 0.958165i \(-0.592397\pi\)
−0.286215 + 0.958165i \(0.592397\pi\)
\(30\) 0 0
\(31\) 585.421 0.109412 0.0547059 0.998503i \(-0.482578\pi\)
0.0547059 + 0.998503i \(0.482578\pi\)
\(32\) −5509.05 −0.951046
\(33\) 0 0
\(34\) 101.053 0.0149917
\(35\) −4798.15 −0.662069
\(36\) 0 0
\(37\) −3849.04 −0.462219 −0.231109 0.972928i \(-0.574236\pi\)
−0.231109 + 0.972928i \(0.574236\pi\)
\(38\) −2725.59 −0.306198
\(39\) 0 0
\(40\) −7074.66 −0.699127
\(41\) 4299.92 0.399485 0.199743 0.979848i \(-0.435989\pi\)
0.199743 + 0.979848i \(0.435989\pi\)
\(42\) 0 0
\(43\) −20567.4 −1.69632 −0.848162 0.529737i \(-0.822291\pi\)
−0.848162 + 0.529737i \(0.822291\pi\)
\(44\) 6063.39 0.472154
\(45\) 0 0
\(46\) −1189.15 −0.0828594
\(47\) 5221.50 0.344787 0.172393 0.985028i \(-0.444850\pi\)
0.172393 + 0.985028i \(0.444850\pi\)
\(48\) 0 0
\(49\) −8730.61 −0.519462
\(50\) 616.931 0.0348989
\(51\) 0 0
\(52\) −19556.6 −1.00296
\(53\) 15753.7 0.770360 0.385180 0.922841i \(-0.374139\pi\)
0.385180 + 0.922841i \(0.374139\pi\)
\(54\) 0 0
\(55\) 12013.6 0.535507
\(56\) 11908.3 0.507434
\(57\) 0 0
\(58\) 5827.70 0.227472
\(59\) 13780.6 0.515392 0.257696 0.966226i \(-0.417037\pi\)
0.257696 + 0.966226i \(0.417037\pi\)
\(60\) 0 0
\(61\) −18988.5 −0.653380 −0.326690 0.945131i \(-0.605933\pi\)
−0.326690 + 0.945131i \(0.605933\pi\)
\(62\) −1315.98 −0.0434780
\(63\) 0 0
\(64\) −5677.98 −0.173278
\(65\) −38748.1 −1.13754
\(66\) 0 0
\(67\) 1951.43 0.0531088 0.0265544 0.999647i \(-0.491546\pi\)
0.0265544 + 0.999647i \(0.491546\pi\)
\(68\) 1211.37 0.0317691
\(69\) 0 0
\(70\) 10785.8 0.263093
\(71\) −75281.4 −1.77232 −0.886160 0.463380i \(-0.846637\pi\)
−0.886160 + 0.463380i \(0.846637\pi\)
\(72\) 0 0
\(73\) −4177.11 −0.0917422 −0.0458711 0.998947i \(-0.514606\pi\)
−0.0458711 + 0.998947i \(0.514606\pi\)
\(74\) 8652.32 0.183676
\(75\) 0 0
\(76\) −32673.0 −0.648865
\(77\) −20221.6 −0.388677
\(78\) 0 0
\(79\) −95896.7 −1.72877 −0.864383 0.502835i \(-0.832290\pi\)
−0.864383 + 0.502835i \(0.832290\pi\)
\(80\) −30135.4 −0.526444
\(81\) 0 0
\(82\) −9665.87 −0.158747
\(83\) −13366.7 −0.212976 −0.106488 0.994314i \(-0.533961\pi\)
−0.106488 + 0.994314i \(0.533961\pi\)
\(84\) 0 0
\(85\) 2400.12 0.0360318
\(86\) 46233.9 0.674084
\(87\) 0 0
\(88\) −29815.9 −0.410432
\(89\) −50932.1 −0.681580 −0.340790 0.940139i \(-0.610695\pi\)
−0.340790 + 0.940139i \(0.610695\pi\)
\(90\) 0 0
\(91\) 65222.0 0.825640
\(92\) −14254.9 −0.175588
\(93\) 0 0
\(94\) −11737.5 −0.137011
\(95\) −64735.9 −0.735929
\(96\) 0 0
\(97\) 44280.7 0.477843 0.238921 0.971039i \(-0.423206\pi\)
0.238921 + 0.971039i \(0.423206\pi\)
\(98\) 19625.7 0.206424
\(99\) 0 0
\(100\) 7395.45 0.0739545
\(101\) −198402. −1.93527 −0.967637 0.252346i \(-0.918798\pi\)
−0.967637 + 0.252346i \(0.918798\pi\)
\(102\) 0 0
\(103\) 201915. 1.87532 0.937658 0.347559i \(-0.112989\pi\)
0.937658 + 0.347559i \(0.112989\pi\)
\(104\) 96167.1 0.871853
\(105\) 0 0
\(106\) −35413.1 −0.306125
\(107\) −37688.4 −0.318235 −0.159117 0.987260i \(-0.550865\pi\)
−0.159117 + 0.987260i \(0.550865\pi\)
\(108\) 0 0
\(109\) −86493.8 −0.697298 −0.348649 0.937253i \(-0.613360\pi\)
−0.348649 + 0.937253i \(0.613360\pi\)
\(110\) −27005.5 −0.212799
\(111\) 0 0
\(112\) 50724.9 0.382099
\(113\) 150822. 1.11114 0.555571 0.831469i \(-0.312500\pi\)
0.555571 + 0.831469i \(0.312500\pi\)
\(114\) 0 0
\(115\) −28243.6 −0.199148
\(116\) 69859.5 0.482037
\(117\) 0 0
\(118\) −30977.6 −0.204806
\(119\) −4039.96 −0.0261523
\(120\) 0 0
\(121\) −110420. −0.685623
\(122\) 42684.6 0.259640
\(123\) 0 0
\(124\) −15775.3 −0.0921346
\(125\) 181498. 1.03896
\(126\) 0 0
\(127\) −47605.4 −0.261907 −0.130953 0.991389i \(-0.541804\pi\)
−0.130953 + 0.991389i \(0.541804\pi\)
\(128\) 189053. 1.01990
\(129\) 0 0
\(130\) 87102.5 0.452035
\(131\) 260443. 1.32597 0.662985 0.748632i \(-0.269289\pi\)
0.662985 + 0.748632i \(0.269289\pi\)
\(132\) 0 0
\(133\) 108966. 0.534146
\(134\) −4386.66 −0.0211043
\(135\) 0 0
\(136\) −5956.75 −0.0276161
\(137\) −121613. −0.553580 −0.276790 0.960930i \(-0.589271\pi\)
−0.276790 + 0.960930i \(0.589271\pi\)
\(138\) 0 0
\(139\) 61341.2 0.269287 0.134643 0.990894i \(-0.457011\pi\)
0.134643 + 0.990894i \(0.457011\pi\)
\(140\) 129295. 0.557521
\(141\) 0 0
\(142\) 169227. 0.704284
\(143\) −163302. −0.667809
\(144\) 0 0
\(145\) 138415. 0.546716
\(146\) 9389.81 0.0364565
\(147\) 0 0
\(148\) 103719. 0.389230
\(149\) 171257. 0.631950 0.315975 0.948767i \(-0.397668\pi\)
0.315975 + 0.948767i \(0.397668\pi\)
\(150\) 0 0
\(151\) −459607. −1.64038 −0.820189 0.572092i \(-0.806132\pi\)
−0.820189 + 0.572092i \(0.806132\pi\)
\(152\) 160665. 0.564043
\(153\) 0 0
\(154\) 45456.5 0.154452
\(155\) −31256.0 −0.104497
\(156\) 0 0
\(157\) 387631. 1.25508 0.627538 0.778586i \(-0.284063\pi\)
0.627538 + 0.778586i \(0.284063\pi\)
\(158\) 215568. 0.686976
\(159\) 0 0
\(160\) 294131. 0.908325
\(161\) 47540.6 0.144544
\(162\) 0 0
\(163\) −286971. −0.845998 −0.422999 0.906130i \(-0.639023\pi\)
−0.422999 + 0.906130i \(0.639023\pi\)
\(164\) −115869. −0.336402
\(165\) 0 0
\(166\) 30047.3 0.0846322
\(167\) −580711. −1.61127 −0.805636 0.592411i \(-0.798176\pi\)
−0.805636 + 0.592411i \(0.798176\pi\)
\(168\) 0 0
\(169\) 155416. 0.418581
\(170\) −5395.27 −0.0143183
\(171\) 0 0
\(172\) 554228. 1.42846
\(173\) 191878. 0.487427 0.243714 0.969847i \(-0.421634\pi\)
0.243714 + 0.969847i \(0.421634\pi\)
\(174\) 0 0
\(175\) −24664.1 −0.0608793
\(176\) −127005. −0.309056
\(177\) 0 0
\(178\) 114491. 0.270846
\(179\) −18757.8 −0.0437571 −0.0218785 0.999761i \(-0.506965\pi\)
−0.0218785 + 0.999761i \(0.506965\pi\)
\(180\) 0 0
\(181\) 47967.6 0.108831 0.0544154 0.998518i \(-0.482670\pi\)
0.0544154 + 0.998518i \(0.482670\pi\)
\(182\) −146614. −0.328092
\(183\) 0 0
\(184\) 70096.6 0.152634
\(185\) 205502. 0.441456
\(186\) 0 0
\(187\) 10115.2 0.0211530
\(188\) −140703. −0.290341
\(189\) 0 0
\(190\) 145521. 0.292443
\(191\) 14294.3 0.0283518 0.0141759 0.999900i \(-0.495488\pi\)
0.0141759 + 0.999900i \(0.495488\pi\)
\(192\) 0 0
\(193\) −422764. −0.816968 −0.408484 0.912765i \(-0.633942\pi\)
−0.408484 + 0.912765i \(0.633942\pi\)
\(194\) −99539.3 −0.189885
\(195\) 0 0
\(196\) 235262. 0.437434
\(197\) 311005. 0.570955 0.285477 0.958385i \(-0.407848\pi\)
0.285477 + 0.958385i \(0.407848\pi\)
\(198\) 0 0
\(199\) 60066.4 0.107522 0.0537612 0.998554i \(-0.482879\pi\)
0.0537612 + 0.998554i \(0.482879\pi\)
\(200\) −36366.2 −0.0642869
\(201\) 0 0
\(202\) 445991. 0.769038
\(203\) −232984. −0.396813
\(204\) 0 0
\(205\) −229575. −0.381540
\(206\) −453887. −0.745212
\(207\) 0 0
\(208\) 409636. 0.656507
\(209\) −272827. −0.432038
\(210\) 0 0
\(211\) −1.08896e6 −1.68385 −0.841926 0.539593i \(-0.818578\pi\)
−0.841926 + 0.539593i \(0.818578\pi\)
\(212\) −424514. −0.648712
\(213\) 0 0
\(214\) 84720.3 0.126460
\(215\) 1.09811e6 1.62012
\(216\) 0 0
\(217\) 52611.1 0.0758452
\(218\) 194431. 0.277092
\(219\) 0 0
\(220\) −323728. −0.450945
\(221\) −32625.2 −0.0449338
\(222\) 0 0
\(223\) 365915. 0.492741 0.246370 0.969176i \(-0.420762\pi\)
0.246370 + 0.969176i \(0.420762\pi\)
\(224\) −495091. −0.659273
\(225\) 0 0
\(226\) −339036. −0.441545
\(227\) −1.08830e6 −1.40179 −0.700894 0.713265i \(-0.747216\pi\)
−0.700894 + 0.713265i \(0.747216\pi\)
\(228\) 0 0
\(229\) −1.45107e6 −1.82853 −0.914263 0.405121i \(-0.867229\pi\)
−0.914263 + 0.405121i \(0.867229\pi\)
\(230\) 63489.3 0.0791373
\(231\) 0 0
\(232\) −343525. −0.419023
\(233\) 1.27334e6 1.53657 0.768286 0.640106i \(-0.221110\pi\)
0.768286 + 0.640106i \(0.221110\pi\)
\(234\) 0 0
\(235\) −278779. −0.329299
\(236\) −371344. −0.434006
\(237\) 0 0
\(238\) 9081.50 0.0103924
\(239\) −799348. −0.905193 −0.452596 0.891715i \(-0.649502\pi\)
−0.452596 + 0.891715i \(0.649502\pi\)
\(240\) 0 0
\(241\) 727560. 0.806913 0.403456 0.914999i \(-0.367809\pi\)
0.403456 + 0.914999i \(0.367809\pi\)
\(242\) 248216. 0.272453
\(243\) 0 0
\(244\) 511681. 0.550205
\(245\) 466132. 0.496128
\(246\) 0 0
\(247\) 879966. 0.917748
\(248\) 77572.9 0.0800904
\(249\) 0 0
\(250\) −407993. −0.412860
\(251\) −960924. −0.962730 −0.481365 0.876520i \(-0.659859\pi\)
−0.481365 + 0.876520i \(0.659859\pi\)
\(252\) 0 0
\(253\) −119032. −0.116913
\(254\) 107013. 0.104076
\(255\) 0 0
\(256\) −243281. −0.232010
\(257\) 1.57691e6 1.48927 0.744637 0.667470i \(-0.232623\pi\)
0.744637 + 0.667470i \(0.232623\pi\)
\(258\) 0 0
\(259\) −345908. −0.320414
\(260\) 1.04414e6 0.957911
\(261\) 0 0
\(262\) −585454. −0.526914
\(263\) −1.42682e6 −1.27198 −0.635991 0.771696i \(-0.719409\pi\)
−0.635991 + 0.771696i \(0.719409\pi\)
\(264\) 0 0
\(265\) −841101. −0.735755
\(266\) −244946. −0.212259
\(267\) 0 0
\(268\) −52585.0 −0.0447224
\(269\) 341906. 0.288089 0.144044 0.989571i \(-0.453989\pi\)
0.144044 + 0.989571i \(0.453989\pi\)
\(270\) 0 0
\(271\) 723709. 0.598605 0.299303 0.954158i \(-0.403246\pi\)
0.299303 + 0.954158i \(0.403246\pi\)
\(272\) −25373.5 −0.0207950
\(273\) 0 0
\(274\) 273377. 0.219981
\(275\) 61753.7 0.0492415
\(276\) 0 0
\(277\) −1.82928e6 −1.43245 −0.716226 0.697868i \(-0.754132\pi\)
−0.716226 + 0.697868i \(0.754132\pi\)
\(278\) −137890. −0.107009
\(279\) 0 0
\(280\) −635791. −0.484640
\(281\) −1.14935e6 −0.868337 −0.434169 0.900832i \(-0.642958\pi\)
−0.434169 + 0.900832i \(0.642958\pi\)
\(282\) 0 0
\(283\) −1.83262e6 −1.36021 −0.680105 0.733115i \(-0.738066\pi\)
−0.680105 + 0.733115i \(0.738066\pi\)
\(284\) 2.02860e6 1.49245
\(285\) 0 0
\(286\) 367090. 0.265374
\(287\) 386429. 0.276926
\(288\) 0 0
\(289\) −1.41784e6 −0.998577
\(290\) −311145. −0.217254
\(291\) 0 0
\(292\) 112560. 0.0772552
\(293\) −1.33169e6 −0.906221 −0.453111 0.891454i \(-0.649686\pi\)
−0.453111 + 0.891454i \(0.649686\pi\)
\(294\) 0 0
\(295\) −735754. −0.492241
\(296\) −510027. −0.338348
\(297\) 0 0
\(298\) −384972. −0.251124
\(299\) 383920. 0.248349
\(300\) 0 0
\(301\) −1.84837e6 −1.17591
\(302\) 1.03316e6 0.651853
\(303\) 0 0
\(304\) 684373. 0.424726
\(305\) 1.01381e6 0.624031
\(306\) 0 0
\(307\) 3.00299e6 1.81848 0.909239 0.416275i \(-0.136665\pi\)
0.909239 + 0.416275i \(0.136665\pi\)
\(308\) 544909. 0.327301
\(309\) 0 0
\(310\) 70260.9 0.0415250
\(311\) −2.75093e6 −1.61279 −0.806397 0.591374i \(-0.798586\pi\)
−0.806397 + 0.591374i \(0.798586\pi\)
\(312\) 0 0
\(313\) −119894. −0.0691727 −0.0345864 0.999402i \(-0.511011\pi\)
−0.0345864 + 0.999402i \(0.511011\pi\)
\(314\) −871364. −0.498741
\(315\) 0 0
\(316\) 2.58412e6 1.45578
\(317\) −514254. −0.287428 −0.143714 0.989619i \(-0.545905\pi\)
−0.143714 + 0.989619i \(0.545905\pi\)
\(318\) 0 0
\(319\) 583343. 0.320957
\(320\) 303151. 0.165494
\(321\) 0 0
\(322\) −106867. −0.0574388
\(323\) −54506.6 −0.0290698
\(324\) 0 0
\(325\) −199178. −0.104600
\(326\) 645088. 0.336182
\(327\) 0 0
\(328\) 569773. 0.292427
\(329\) 469250. 0.239009
\(330\) 0 0
\(331\) 2.46021e6 1.23425 0.617124 0.786866i \(-0.288298\pi\)
0.617124 + 0.786866i \(0.288298\pi\)
\(332\) 360192. 0.179345
\(333\) 0 0
\(334\) 1.30539e6 0.640286
\(335\) −104188. −0.0507231
\(336\) 0 0
\(337\) −1.42694e6 −0.684432 −0.342216 0.939621i \(-0.611177\pi\)
−0.342216 + 0.939621i \(0.611177\pi\)
\(338\) −349363. −0.166335
\(339\) 0 0
\(340\) −64675.7 −0.0303420
\(341\) −131727. −0.0613465
\(342\) 0 0
\(343\) −2.29503e6 −1.05330
\(344\) −2.72534e6 −1.24172
\(345\) 0 0
\(346\) −431326. −0.193694
\(347\) −1.63440e6 −0.728676 −0.364338 0.931267i \(-0.618705\pi\)
−0.364338 + 0.931267i \(0.618705\pi\)
\(348\) 0 0
\(349\) −2.65498e6 −1.16680 −0.583402 0.812184i \(-0.698279\pi\)
−0.583402 + 0.812184i \(0.698279\pi\)
\(350\) 55442.8 0.0241922
\(351\) 0 0
\(352\) 1.23961e6 0.533245
\(353\) −934019. −0.398950 −0.199475 0.979903i \(-0.563924\pi\)
−0.199475 + 0.979903i \(0.563924\pi\)
\(354\) 0 0
\(355\) 4.01932e6 1.69271
\(356\) 1.37246e6 0.573952
\(357\) 0 0
\(358\) 42165.9 0.0173882
\(359\) −2.98227e6 −1.22127 −0.610634 0.791913i \(-0.709085\pi\)
−0.610634 + 0.791913i \(0.709085\pi\)
\(360\) 0 0
\(361\) −1.00595e6 −0.406265
\(362\) −107827. −0.0432471
\(363\) 0 0
\(364\) −1.75753e6 −0.695263
\(365\) 223019. 0.0876211
\(366\) 0 0
\(367\) 4.17728e6 1.61893 0.809466 0.587167i \(-0.199757\pi\)
0.809466 + 0.587167i \(0.199757\pi\)
\(368\) 298585. 0.114934
\(369\) 0 0
\(370\) −461952. −0.175426
\(371\) 1.41577e6 0.534020
\(372\) 0 0
\(373\) −1.12351e6 −0.418124 −0.209062 0.977902i \(-0.567041\pi\)
−0.209062 + 0.977902i \(0.567041\pi\)
\(374\) −22738.2 −0.00840576
\(375\) 0 0
\(376\) 691889. 0.252387
\(377\) −1.88149e6 −0.681788
\(378\) 0 0
\(379\) 3.45021e6 1.23381 0.616904 0.787039i \(-0.288387\pi\)
0.616904 + 0.787039i \(0.288387\pi\)
\(380\) 1.74443e6 0.619718
\(381\) 0 0
\(382\) −32132.5 −0.0112664
\(383\) 573250. 0.199686 0.0998430 0.995003i \(-0.468166\pi\)
0.0998430 + 0.995003i \(0.468166\pi\)
\(384\) 0 0
\(385\) 1.07964e6 0.371218
\(386\) 950339. 0.324646
\(387\) 0 0
\(388\) −1.19323e6 −0.402386
\(389\) 5.10842e6 1.71164 0.855820 0.517274i \(-0.173053\pi\)
0.855820 + 0.517274i \(0.173053\pi\)
\(390\) 0 0
\(391\) −23780.7 −0.00786651
\(392\) −1.15687e6 −0.380251
\(393\) 0 0
\(394\) −699114. −0.226886
\(395\) 5.11998e6 1.65111
\(396\) 0 0
\(397\) −417826. −0.133051 −0.0665256 0.997785i \(-0.521191\pi\)
−0.0665256 + 0.997785i \(0.521191\pi\)
\(398\) −135024. −0.0427272
\(399\) 0 0
\(400\) −154906. −0.0484082
\(401\) −3.79619e6 −1.17893 −0.589463 0.807795i \(-0.700661\pi\)
−0.589463 + 0.807795i \(0.700661\pi\)
\(402\) 0 0
\(403\) 424868. 0.130314
\(404\) 5.34631e6 1.62967
\(405\) 0 0
\(406\) 523729. 0.157685
\(407\) 866082. 0.259163
\(408\) 0 0
\(409\) 4.95389e6 1.46433 0.732164 0.681129i \(-0.238511\pi\)
0.732164 + 0.681129i \(0.238511\pi\)
\(410\) 516066. 0.151616
\(411\) 0 0
\(412\) −5.44096e6 −1.57918
\(413\) 1.23844e6 0.357274
\(414\) 0 0
\(415\) 713658. 0.203409
\(416\) −3.99818e6 −1.13274
\(417\) 0 0
\(418\) 613293. 0.171683
\(419\) 2.38845e6 0.664631 0.332316 0.943168i \(-0.392170\pi\)
0.332316 + 0.943168i \(0.392170\pi\)
\(420\) 0 0
\(421\) −582907. −0.160285 −0.0801427 0.996783i \(-0.525538\pi\)
−0.0801427 + 0.996783i \(0.525538\pi\)
\(422\) 2.44788e6 0.669128
\(423\) 0 0
\(424\) 2.08749e6 0.563910
\(425\) 12337.4 0.00331324
\(426\) 0 0
\(427\) −1.70647e6 −0.452929
\(428\) 1.01558e6 0.267982
\(429\) 0 0
\(430\) −2.46845e6 −0.643804
\(431\) 1.17212e6 0.303935 0.151967 0.988386i \(-0.451439\pi\)
0.151967 + 0.988386i \(0.451439\pi\)
\(432\) 0 0
\(433\) −5.34133e6 −1.36908 −0.684542 0.728974i \(-0.739998\pi\)
−0.684542 + 0.728974i \(0.739998\pi\)
\(434\) −118265. −0.0301393
\(435\) 0 0
\(436\) 2.33074e6 0.587188
\(437\) 641410. 0.160669
\(438\) 0 0
\(439\) 3.68652e6 0.912967 0.456483 0.889732i \(-0.349109\pi\)
0.456483 + 0.889732i \(0.349109\pi\)
\(440\) 1.59189e6 0.391996
\(441\) 0 0
\(442\) 73338.9 0.0178558
\(443\) 705619. 0.170829 0.0854143 0.996346i \(-0.472779\pi\)
0.0854143 + 0.996346i \(0.472779\pi\)
\(444\) 0 0
\(445\) 2.71930e6 0.650963
\(446\) −822548. −0.195805
\(447\) 0 0
\(448\) −510273. −0.120118
\(449\) −442688. −0.103629 −0.0518146 0.998657i \(-0.516500\pi\)
−0.0518146 + 0.998657i \(0.516500\pi\)
\(450\) 0 0
\(451\) −967537. −0.223989
\(452\) −4.06419e6 −0.935682
\(453\) 0 0
\(454\) 2.44640e6 0.557042
\(455\) −3.48224e6 −0.788552
\(456\) 0 0
\(457\) 4.85276e6 1.08692 0.543461 0.839434i \(-0.317113\pi\)
0.543461 + 0.839434i \(0.317113\pi\)
\(458\) 3.26190e6 0.726619
\(459\) 0 0
\(460\) 761077. 0.167700
\(461\) −8.87833e6 −1.94571 −0.972857 0.231408i \(-0.925667\pi\)
−0.972857 + 0.231408i \(0.925667\pi\)
\(462\) 0 0
\(463\) −3.58364e6 −0.776911 −0.388456 0.921467i \(-0.626991\pi\)
−0.388456 + 0.921467i \(0.626991\pi\)
\(464\) −1.46329e6 −0.315526
\(465\) 0 0
\(466\) −2.86235e6 −0.610603
\(467\) 6.13857e6 1.30249 0.651246 0.758867i \(-0.274247\pi\)
0.651246 + 0.758867i \(0.274247\pi\)
\(468\) 0 0
\(469\) 175373. 0.0368155
\(470\) 626672. 0.130857
\(471\) 0 0
\(472\) 1.82603e6 0.377271
\(473\) 4.62793e6 0.951117
\(474\) 0 0
\(475\) −332764. −0.0676710
\(476\) 108864. 0.0220226
\(477\) 0 0
\(478\) 1.79687e6 0.359705
\(479\) −505577. −0.100681 −0.0503406 0.998732i \(-0.516031\pi\)
−0.0503406 + 0.998732i \(0.516031\pi\)
\(480\) 0 0
\(481\) −2.79343e6 −0.550522
\(482\) −1.63550e6 −0.320651
\(483\) 0 0
\(484\) 2.97548e6 0.577356
\(485\) −2.36417e6 −0.456378
\(486\) 0 0
\(487\) −751626. −0.143608 −0.0718041 0.997419i \(-0.522876\pi\)
−0.0718041 + 0.997419i \(0.522876\pi\)
\(488\) −2.51612e6 −0.478280
\(489\) 0 0
\(490\) −1.04783e6 −0.197151
\(491\) 2.19083e6 0.410115 0.205057 0.978750i \(-0.434262\pi\)
0.205057 + 0.978750i \(0.434262\pi\)
\(492\) 0 0
\(493\) 116543. 0.0215957
\(494\) −1.97809e6 −0.364694
\(495\) 0 0
\(496\) 330431. 0.0603083
\(497\) −6.76545e6 −1.22859
\(498\) 0 0
\(499\) 2.21183e6 0.397649 0.198824 0.980035i \(-0.436288\pi\)
0.198824 + 0.980035i \(0.436288\pi\)
\(500\) −4.89081e6 −0.874895
\(501\) 0 0
\(502\) 2.16008e6 0.382569
\(503\) 1.05756e7 1.86373 0.931866 0.362803i \(-0.118180\pi\)
0.931866 + 0.362803i \(0.118180\pi\)
\(504\) 0 0
\(505\) 1.05928e7 1.84834
\(506\) 267573. 0.0464587
\(507\) 0 0
\(508\) 1.28282e6 0.220549
\(509\) 1.00676e7 1.72239 0.861195 0.508275i \(-0.169717\pi\)
0.861195 + 0.508275i \(0.169717\pi\)
\(510\) 0 0
\(511\) −375392. −0.0635964
\(512\) −5.50282e6 −0.927707
\(513\) 0 0
\(514\) −3.54477e6 −0.591807
\(515\) −1.07803e7 −1.79108
\(516\) 0 0
\(517\) −1.17490e6 −0.193320
\(518\) 777573. 0.127326
\(519\) 0 0
\(520\) −5.13442e6 −0.832689
\(521\) −7.71005e6 −1.24441 −0.622204 0.782855i \(-0.713763\pi\)
−0.622204 + 0.782855i \(0.713763\pi\)
\(522\) 0 0
\(523\) 153540. 0.0245453 0.0122726 0.999925i \(-0.496093\pi\)
0.0122726 + 0.999925i \(0.496093\pi\)
\(524\) −7.01811e6 −1.11659
\(525\) 0 0
\(526\) 3.20738e6 0.505460
\(527\) −26317.0 −0.00412772
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) 1.89073e6 0.292374
\(531\) 0 0
\(532\) −2.93628e6 −0.449799
\(533\) 3.12066e6 0.475804
\(534\) 0 0
\(535\) 2.01220e6 0.303940
\(536\) 258580. 0.0388761
\(537\) 0 0
\(538\) −768577. −0.114481
\(539\) 1.96450e6 0.291259
\(540\) 0 0
\(541\) 267983. 0.0393653 0.0196827 0.999806i \(-0.493734\pi\)
0.0196827 + 0.999806i \(0.493734\pi\)
\(542\) −1.62684e6 −0.237873
\(543\) 0 0
\(544\) 247654. 0.0358796
\(545\) 4.61795e6 0.665976
\(546\) 0 0
\(547\) 6.44942e6 0.921621 0.460810 0.887499i \(-0.347559\pi\)
0.460810 + 0.887499i \(0.347559\pi\)
\(548\) 3.27710e6 0.466164
\(549\) 0 0
\(550\) −138817. −0.0195676
\(551\) −3.14338e6 −0.441081
\(552\) 0 0
\(553\) −8.61812e6 −1.19839
\(554\) 4.11207e6 0.569227
\(555\) 0 0
\(556\) −1.65295e6 −0.226764
\(557\) 1.36650e7 1.86626 0.933132 0.359534i \(-0.117064\pi\)
0.933132 + 0.359534i \(0.117064\pi\)
\(558\) 0 0
\(559\) −1.49268e7 −2.02039
\(560\) −2.70823e6 −0.364935
\(561\) 0 0
\(562\) 2.58366e6 0.345059
\(563\) −564712. −0.0750855 −0.0375427 0.999295i \(-0.511953\pi\)
−0.0375427 + 0.999295i \(0.511953\pi\)
\(564\) 0 0
\(565\) −8.05250e6 −1.06123
\(566\) 4.11957e6 0.540519
\(567\) 0 0
\(568\) −9.97537e6 −1.29735
\(569\) −5.68519e6 −0.736147 −0.368074 0.929797i \(-0.619983\pi\)
−0.368074 + 0.929797i \(0.619983\pi\)
\(570\) 0 0
\(571\) 5.94914e6 0.763597 0.381798 0.924246i \(-0.375305\pi\)
0.381798 + 0.924246i \(0.375305\pi\)
\(572\) 4.40049e6 0.562355
\(573\) 0 0
\(574\) −868660. −0.110045
\(575\) −145182. −0.0183123
\(576\) 0 0
\(577\) −7.28162e6 −0.910518 −0.455259 0.890359i \(-0.650453\pi\)
−0.455259 + 0.890359i \(0.650453\pi\)
\(578\) 3.18718e6 0.396814
\(579\) 0 0
\(580\) −3.72984e6 −0.460384
\(581\) −1.20125e6 −0.147637
\(582\) 0 0
\(583\) −3.54479e6 −0.431935
\(584\) −553500. −0.0671561
\(585\) 0 0
\(586\) 2.99353e6 0.360114
\(587\) −9.14151e6 −1.09502 −0.547511 0.836799i \(-0.684425\pi\)
−0.547511 + 0.836799i \(0.684425\pi\)
\(588\) 0 0
\(589\) 709821. 0.0843064
\(590\) 1.65391e6 0.195606
\(591\) 0 0
\(592\) −2.17252e6 −0.254777
\(593\) −6.14133e6 −0.717176 −0.358588 0.933496i \(-0.616742\pi\)
−0.358588 + 0.933496i \(0.616742\pi\)
\(594\) 0 0
\(595\) 215696. 0.0249775
\(596\) −4.61484e6 −0.532159
\(597\) 0 0
\(598\) −863021. −0.0986890
\(599\) 6.53791e6 0.744512 0.372256 0.928130i \(-0.378584\pi\)
0.372256 + 0.928130i \(0.378584\pi\)
\(600\) 0 0
\(601\) −9.92849e6 −1.12124 −0.560618 0.828075i \(-0.689436\pi\)
−0.560618 + 0.828075i \(0.689436\pi\)
\(602\) 4.15498e6 0.467281
\(603\) 0 0
\(604\) 1.23850e7 1.38135
\(605\) 5.89540e6 0.654825
\(606\) 0 0
\(607\) −2.59619e6 −0.285999 −0.143000 0.989723i \(-0.545675\pi\)
−0.143000 + 0.989723i \(0.545675\pi\)
\(608\) −6.67970e6 −0.732821
\(609\) 0 0
\(610\) −2.27896e6 −0.247977
\(611\) 3.78949e6 0.410656
\(612\) 0 0
\(613\) −4.12434e6 −0.443306 −0.221653 0.975126i \(-0.571145\pi\)
−0.221653 + 0.975126i \(0.571145\pi\)
\(614\) −6.75047e6 −0.722626
\(615\) 0 0
\(616\) −2.67952e6 −0.284515
\(617\) −1.17375e7 −1.24126 −0.620631 0.784103i \(-0.713124\pi\)
−0.620631 + 0.784103i \(0.713124\pi\)
\(618\) 0 0
\(619\) 6.90815e6 0.724662 0.362331 0.932050i \(-0.381981\pi\)
0.362331 + 0.932050i \(0.381981\pi\)
\(620\) 842251. 0.0879959
\(621\) 0 0
\(622\) 6.18387e6 0.640892
\(623\) −4.57721e6 −0.472477
\(624\) 0 0
\(625\) −8.83266e6 −0.904465
\(626\) 269511. 0.0274878
\(627\) 0 0
\(628\) −1.04455e7 −1.05689
\(629\) 173030. 0.0174379
\(630\) 0 0
\(631\) 793455. 0.0793321 0.0396660 0.999213i \(-0.487371\pi\)
0.0396660 + 0.999213i \(0.487371\pi\)
\(632\) −1.27071e7 −1.26547
\(633\) 0 0
\(634\) 1.15600e6 0.114218
\(635\) 2.54168e6 0.250142
\(636\) 0 0
\(637\) −6.33621e6 −0.618702
\(638\) −1.31131e6 −0.127542
\(639\) 0 0
\(640\) −1.00937e7 −0.974089
\(641\) −3.78009e6 −0.363377 −0.181689 0.983356i \(-0.558156\pi\)
−0.181689 + 0.983356i \(0.558156\pi\)
\(642\) 0 0
\(643\) 1.21266e7 1.15667 0.578336 0.815799i \(-0.303702\pi\)
0.578336 + 0.815799i \(0.303702\pi\)
\(644\) −1.28107e6 −0.121719
\(645\) 0 0
\(646\) 122526. 0.0115518
\(647\) 6.56812e6 0.616851 0.308425 0.951249i \(-0.400198\pi\)
0.308425 + 0.951249i \(0.400198\pi\)
\(648\) 0 0
\(649\) −3.10081e6 −0.288977
\(650\) 447736. 0.0415660
\(651\) 0 0
\(652\) 7.73297e6 0.712406
\(653\) 9.97904e6 0.915811 0.457905 0.889001i \(-0.348600\pi\)
0.457905 + 0.889001i \(0.348600\pi\)
\(654\) 0 0
\(655\) −1.39052e7 −1.26641
\(656\) 2.42702e6 0.220198
\(657\) 0 0
\(658\) −1.05484e6 −0.0949773
\(659\) −1.22411e7 −1.09801 −0.549006 0.835818i \(-0.684994\pi\)
−0.549006 + 0.835818i \(0.684994\pi\)
\(660\) 0 0
\(661\) −7.26433e6 −0.646684 −0.323342 0.946282i \(-0.604806\pi\)
−0.323342 + 0.946282i \(0.604806\pi\)
\(662\) −5.53035e6 −0.490465
\(663\) 0 0
\(664\) −1.77120e6 −0.155900
\(665\) −5.81773e6 −0.510152
\(666\) 0 0
\(667\) −1.37143e6 −0.119360
\(668\) 1.56483e7 1.35683
\(669\) 0 0
\(670\) 234206. 0.0201563
\(671\) 4.27265e6 0.366346
\(672\) 0 0
\(673\) 1.76906e7 1.50558 0.752791 0.658260i \(-0.228707\pi\)
0.752791 + 0.658260i \(0.228707\pi\)
\(674\) 3.20764e6 0.271979
\(675\) 0 0
\(676\) −4.18798e6 −0.352482
\(677\) −8.88669e6 −0.745193 −0.372596 0.927994i \(-0.621532\pi\)
−0.372596 + 0.927994i \(0.621532\pi\)
\(678\) 0 0
\(679\) 3.97945e6 0.331244
\(680\) 318035. 0.0263756
\(681\) 0 0
\(682\) 296112. 0.0243778
\(683\) 3.93961e6 0.323148 0.161574 0.986861i \(-0.448343\pi\)
0.161574 + 0.986861i \(0.448343\pi\)
\(684\) 0 0
\(685\) 6.49301e6 0.528713
\(686\) 5.15905e6 0.418561
\(687\) 0 0
\(688\) −1.16089e7 −0.935021
\(689\) 1.14332e7 0.917531
\(690\) 0 0
\(691\) 2.19400e7 1.74800 0.873999 0.485927i \(-0.161518\pi\)
0.873999 + 0.485927i \(0.161518\pi\)
\(692\) −5.17051e6 −0.410457
\(693\) 0 0
\(694\) 3.67399e6 0.289561
\(695\) −3.27504e6 −0.257190
\(696\) 0 0
\(697\) −193299. −0.0150712
\(698\) 5.96818e6 0.463664
\(699\) 0 0
\(700\) 664620. 0.0512658
\(701\) −1.20994e7 −0.929969 −0.464984 0.885319i \(-0.653940\pi\)
−0.464984 + 0.885319i \(0.653940\pi\)
\(702\) 0 0
\(703\) −4.66694e6 −0.356159
\(704\) 1.27762e6 0.0971559
\(705\) 0 0
\(706\) 2.09960e6 0.158535
\(707\) −1.78301e7 −1.34155
\(708\) 0 0
\(709\) 1.95715e7 1.46221 0.731103 0.682267i \(-0.239006\pi\)
0.731103 + 0.682267i \(0.239006\pi\)
\(710\) −9.03510e6 −0.672647
\(711\) 0 0
\(712\) −6.74890e6 −0.498923
\(713\) 309688. 0.0228139
\(714\) 0 0
\(715\) 8.71881e6 0.637811
\(716\) 505463. 0.0368474
\(717\) 0 0
\(718\) 6.70390e6 0.485307
\(719\) 1.98434e7 1.43151 0.715753 0.698354i \(-0.246084\pi\)
0.715753 + 0.698354i \(0.246084\pi\)
\(720\) 0 0
\(721\) 1.81458e7 1.29998
\(722\) 2.26130e6 0.161441
\(723\) 0 0
\(724\) −1.29258e6 −0.0916452
\(725\) 711497. 0.0502722
\(726\) 0 0
\(727\) 2.50056e7 1.75469 0.877345 0.479860i \(-0.159312\pi\)
0.877345 + 0.479860i \(0.159312\pi\)
\(728\) 8.64242e6 0.604376
\(729\) 0 0
\(730\) −501327. −0.0348188
\(731\) 924588. 0.0639963
\(732\) 0 0
\(733\) 2.53798e7 1.74473 0.872365 0.488855i \(-0.162585\pi\)
0.872365 + 0.488855i \(0.162585\pi\)
\(734\) −9.39018e6 −0.643330
\(735\) 0 0
\(736\) −2.91429e6 −0.198307
\(737\) −439097. −0.0297777
\(738\) 0 0
\(739\) 1.50131e7 1.01125 0.505625 0.862753i \(-0.331262\pi\)
0.505625 + 0.862753i \(0.331262\pi\)
\(740\) −5.53764e6 −0.371745
\(741\) 0 0
\(742\) −3.18253e6 −0.212209
\(743\) 2.53859e7 1.68702 0.843512 0.537111i \(-0.180484\pi\)
0.843512 + 0.537111i \(0.180484\pi\)
\(744\) 0 0
\(745\) −9.14351e6 −0.603563
\(746\) 2.52556e6 0.166154
\(747\) 0 0
\(748\) −272573. −0.0178127
\(749\) −3.38701e6 −0.220603
\(750\) 0 0
\(751\) 1.25539e7 0.812230 0.406115 0.913822i \(-0.366883\pi\)
0.406115 + 0.913822i \(0.366883\pi\)
\(752\) 2.94719e6 0.190048
\(753\) 0 0
\(754\) 4.22944e6 0.270928
\(755\) 2.45387e7 1.56669
\(756\) 0 0
\(757\) 6.15033e6 0.390085 0.195042 0.980795i \(-0.437516\pi\)
0.195042 + 0.980795i \(0.437516\pi\)
\(758\) −7.75579e6 −0.490290
\(759\) 0 0
\(760\) −8.57800e6 −0.538706
\(761\) 6.22830e6 0.389859 0.194930 0.980817i \(-0.437552\pi\)
0.194930 + 0.980817i \(0.437552\pi\)
\(762\) 0 0
\(763\) −7.77309e6 −0.483373
\(764\) −385187. −0.0238747
\(765\) 0 0
\(766\) −1.28862e6 −0.0793511
\(767\) 1.00012e7 0.613853
\(768\) 0 0
\(769\) 8.72415e6 0.531995 0.265997 0.963974i \(-0.414299\pi\)
0.265997 + 0.963974i \(0.414299\pi\)
\(770\) −2.42695e6 −0.147514
\(771\) 0 0
\(772\) 1.13922e7 0.687960
\(773\) 7.23571e6 0.435545 0.217772 0.976000i \(-0.430121\pi\)
0.217772 + 0.976000i \(0.430121\pi\)
\(774\) 0 0
\(775\) −160666. −0.00960883
\(776\) 5.86753e6 0.349785
\(777\) 0 0
\(778\) −1.14833e7 −0.680171
\(779\) 5.21364e6 0.307820
\(780\) 0 0
\(781\) 1.69393e7 0.993728
\(782\) 53457.0 0.00312599
\(783\) 0 0
\(784\) −4.92784e6 −0.286330
\(785\) −2.06959e7 −1.19870
\(786\) 0 0
\(787\) −1.35431e7 −0.779440 −0.389720 0.920933i \(-0.627428\pi\)
−0.389720 + 0.920933i \(0.627428\pi\)
\(788\) −8.38061e6 −0.480795
\(789\) 0 0
\(790\) −1.15093e7 −0.656117
\(791\) 1.35542e7 0.770253
\(792\) 0 0
\(793\) −1.37809e7 −0.778203
\(794\) 939238. 0.0528718
\(795\) 0 0
\(796\) −1.61860e6 −0.0905435
\(797\) −1.01044e7 −0.563461 −0.281731 0.959494i \(-0.590908\pi\)
−0.281731 + 0.959494i \(0.590908\pi\)
\(798\) 0 0
\(799\) −234727. −0.0130076
\(800\) 1.51193e6 0.0835233
\(801\) 0 0
\(802\) 8.53352e6 0.468481
\(803\) 939904. 0.0514392
\(804\) 0 0
\(805\) −2.53822e6 −0.138051
\(806\) −955068. −0.0517841
\(807\) 0 0
\(808\) −2.62898e7 −1.41664
\(809\) 3.23912e6 0.174003 0.0870013 0.996208i \(-0.472272\pi\)
0.0870013 + 0.996208i \(0.472272\pi\)
\(810\) 0 0
\(811\) 6.20038e6 0.331029 0.165515 0.986207i \(-0.447072\pi\)
0.165515 + 0.986207i \(0.447072\pi\)
\(812\) 6.27818e6 0.334152
\(813\) 0 0
\(814\) −1.94688e6 −0.102986
\(815\) 1.53216e7 0.807995
\(816\) 0 0
\(817\) −2.49379e7 −1.30709
\(818\) −1.11359e7 −0.581894
\(819\) 0 0
\(820\) 6.18633e6 0.321291
\(821\) −1.75836e7 −0.910439 −0.455219 0.890379i \(-0.650439\pi\)
−0.455219 + 0.890379i \(0.650439\pi\)
\(822\) 0 0
\(823\) −3.80649e7 −1.95896 −0.979478 0.201549i \(-0.935402\pi\)
−0.979478 + 0.201549i \(0.935402\pi\)
\(824\) 2.67552e7 1.37275
\(825\) 0 0
\(826\) −2.78392e6 −0.141973
\(827\) −8.39081e6 −0.426619 −0.213310 0.976985i \(-0.568424\pi\)
−0.213310 + 0.976985i \(0.568424\pi\)
\(828\) 0 0
\(829\) 394283. 0.0199261 0.00996305 0.999950i \(-0.496829\pi\)
0.00996305 + 0.999950i \(0.496829\pi\)
\(830\) −1.60424e6 −0.0808305
\(831\) 0 0
\(832\) −4.12078e6 −0.206382
\(833\) 392476. 0.0195975
\(834\) 0 0
\(835\) 3.10045e7 1.53889
\(836\) 7.35183e6 0.363814
\(837\) 0 0
\(838\) −5.36904e6 −0.264111
\(839\) −1.63376e7 −0.801276 −0.400638 0.916236i \(-0.631212\pi\)
−0.400638 + 0.916236i \(0.631212\pi\)
\(840\) 0 0
\(841\) −1.37901e7 −0.672324
\(842\) 1.31033e6 0.0636941
\(843\) 0 0
\(844\) 2.93439e7 1.41795
\(845\) −8.29775e6 −0.399778
\(846\) 0 0
\(847\) −9.92334e6 −0.475280
\(848\) 8.89193e6 0.424626
\(849\) 0 0
\(850\) −27733.5 −0.00131661
\(851\) −2.03614e6 −0.0963793
\(852\) 0 0
\(853\) 2.38816e6 0.112380 0.0561901 0.998420i \(-0.482105\pi\)
0.0561901 + 0.998420i \(0.482105\pi\)
\(854\) 3.83601e6 0.179985
\(855\) 0 0
\(856\) −4.99400e6 −0.232951
\(857\) 1.41990e7 0.660398 0.330199 0.943911i \(-0.392884\pi\)
0.330199 + 0.943911i \(0.392884\pi\)
\(858\) 0 0
\(859\) 1.13234e7 0.523595 0.261797 0.965123i \(-0.415685\pi\)
0.261797 + 0.965123i \(0.415685\pi\)
\(860\) −2.95905e7 −1.36429
\(861\) 0 0
\(862\) −2.63484e6 −0.120777
\(863\) −2.55589e7 −1.16819 −0.584097 0.811684i \(-0.698551\pi\)
−0.584097 + 0.811684i \(0.698551\pi\)
\(864\) 0 0
\(865\) −1.02445e7 −0.465532
\(866\) 1.20069e7 0.544046
\(867\) 0 0
\(868\) −1.41770e6 −0.0638684
\(869\) 2.15780e7 0.969307
\(870\) 0 0
\(871\) 1.41625e6 0.0632548
\(872\) −1.14611e7 −0.510428
\(873\) 0 0
\(874\) −1.44184e6 −0.0638466
\(875\) 1.63110e7 0.720214
\(876\) 0 0
\(877\) 1.94757e7 0.855056 0.427528 0.904002i \(-0.359385\pi\)
0.427528 + 0.904002i \(0.359385\pi\)
\(878\) −8.28699e6 −0.362794
\(879\) 0 0
\(880\) 6.78085e6 0.295174
\(881\) −9.76547e6 −0.423890 −0.211945 0.977282i \(-0.567980\pi\)
−0.211945 + 0.977282i \(0.567980\pi\)
\(882\) 0 0
\(883\) 4.86226e6 0.209863 0.104932 0.994479i \(-0.466538\pi\)
0.104932 + 0.994479i \(0.466538\pi\)
\(884\) 879148. 0.0378383
\(885\) 0 0
\(886\) −1.58617e6 −0.0678838
\(887\) 3.00831e7 1.28385 0.641925 0.766767i \(-0.278136\pi\)
0.641925 + 0.766767i \(0.278136\pi\)
\(888\) 0 0
\(889\) −4.27824e6 −0.181556
\(890\) −6.11276e6 −0.258680
\(891\) 0 0
\(892\) −9.86027e6 −0.414932
\(893\) 6.33105e6 0.265673
\(894\) 0 0
\(895\) 1.00149e6 0.0417915
\(896\) 1.69900e7 0.707005
\(897\) 0 0
\(898\) 995127. 0.0411801
\(899\) −1.51770e6 −0.0626306
\(900\) 0 0
\(901\) −708193. −0.0290630
\(902\) 2.17494e6 0.0890085
\(903\) 0 0
\(904\) 1.99851e7 0.813366
\(905\) −2.56102e6 −0.103942
\(906\) 0 0
\(907\) −3.27277e7 −1.32098 −0.660491 0.750834i \(-0.729652\pi\)
−0.660491 + 0.750834i \(0.729652\pi\)
\(908\) 2.93262e7 1.18043
\(909\) 0 0
\(910\) 7.82779e6 0.313354
\(911\) 1.44550e6 0.0577062 0.0288531 0.999584i \(-0.490814\pi\)
0.0288531 + 0.999584i \(0.490814\pi\)
\(912\) 0 0
\(913\) 3.00769e6 0.119414
\(914\) −1.09086e7 −0.431921
\(915\) 0 0
\(916\) 3.91019e7 1.53978
\(917\) 2.34057e7 0.919174
\(918\) 0 0
\(919\) 1.02478e7 0.400258 0.200129 0.979770i \(-0.435864\pi\)
0.200129 + 0.979770i \(0.435864\pi\)
\(920\) −3.74250e6 −0.145778
\(921\) 0 0
\(922\) 1.99578e7 0.773187
\(923\) −5.46353e7 −2.11091
\(924\) 0 0
\(925\) 1.05635e6 0.0405933
\(926\) 8.05572e6 0.308729
\(927\) 0 0
\(928\) 1.42821e7 0.544407
\(929\) −4.79655e7 −1.82343 −0.911716 0.410821i \(-0.865242\pi\)
−0.911716 + 0.410821i \(0.865242\pi\)
\(930\) 0 0
\(931\) −1.05858e7 −0.400268
\(932\) −3.43124e7 −1.29393
\(933\) 0 0
\(934\) −1.37990e7 −0.517583
\(935\) −540058. −0.0202028
\(936\) 0 0
\(937\) −1.18919e7 −0.442489 −0.221244 0.975218i \(-0.571012\pi\)
−0.221244 + 0.975218i \(0.571012\pi\)
\(938\) −394224. −0.0146297
\(939\) 0 0
\(940\) 7.51222e6 0.277299
\(941\) −3.72086e7 −1.36984 −0.684919 0.728619i \(-0.740162\pi\)
−0.684919 + 0.728619i \(0.740162\pi\)
\(942\) 0 0
\(943\) 2.27466e6 0.0832985
\(944\) 7.77822e6 0.284086
\(945\) 0 0
\(946\) −1.04032e7 −0.377954
\(947\) −2.24159e7 −0.812235 −0.406118 0.913821i \(-0.633118\pi\)
−0.406118 + 0.913821i \(0.633118\pi\)
\(948\) 0 0
\(949\) −3.03153e6 −0.109269
\(950\) 748027. 0.0268911
\(951\) 0 0
\(952\) −535326. −0.0191437
\(953\) −1.19242e7 −0.425302 −0.212651 0.977128i \(-0.568210\pi\)
−0.212651 + 0.977128i \(0.568210\pi\)
\(954\) 0 0
\(955\) −763182. −0.0270782
\(956\) 2.15399e7 0.762253
\(957\) 0 0
\(958\) 1.13649e6 0.0400086
\(959\) −1.09292e7 −0.383746
\(960\) 0 0
\(961\) −2.82864e7 −0.988029
\(962\) 6.27940e6 0.218766
\(963\) 0 0
\(964\) −1.96055e7 −0.679493
\(965\) 2.25716e7 0.780270
\(966\) 0 0
\(967\) 1.40918e7 0.484619 0.242309 0.970199i \(-0.422095\pi\)
0.242309 + 0.970199i \(0.422095\pi\)
\(968\) −1.46315e7 −0.501882
\(969\) 0 0
\(970\) 5.31446e6 0.181355
\(971\) 2.06293e7 0.702160 0.351080 0.936346i \(-0.385815\pi\)
0.351080 + 0.936346i \(0.385815\pi\)
\(972\) 0 0
\(973\) 5.51265e6 0.186672
\(974\) 1.68959e6 0.0570669
\(975\) 0 0
\(976\) −1.07177e7 −0.360146
\(977\) −2.77805e7 −0.931116 −0.465558 0.885017i \(-0.654146\pi\)
−0.465558 + 0.885017i \(0.654146\pi\)
\(978\) 0 0
\(979\) 1.14604e7 0.382157
\(980\) −1.25608e7 −0.417784
\(981\) 0 0
\(982\) −4.92481e6 −0.162971
\(983\) 8.68777e6 0.286764 0.143382 0.989667i \(-0.454202\pi\)
0.143382 + 0.989667i \(0.454202\pi\)
\(984\) 0 0
\(985\) −1.66047e7 −0.545307
\(986\) −261979. −0.00858171
\(987\) 0 0
\(988\) −2.37123e7 −0.772826
\(989\) −1.08802e7 −0.353708
\(990\) 0 0
\(991\) −5.74667e7 −1.85880 −0.929399 0.369077i \(-0.879674\pi\)
−0.929399 + 0.369077i \(0.879674\pi\)
\(992\) −3.22511e6 −0.104056
\(993\) 0 0
\(994\) 1.52082e7 0.488215
\(995\) −3.20698e6 −0.102692
\(996\) 0 0
\(997\) −3.52375e7 −1.12271 −0.561354 0.827576i \(-0.689719\pi\)
−0.561354 + 0.827576i \(0.689719\pi\)
\(998\) −4.97200e6 −0.158017
\(999\) 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.1.3 5
3.2 odd 2 69.6.a.e.1.3 5
12.11 even 2 1104.6.a.r.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.e.1.3 5 3.2 odd 2
207.6.a.f.1.3 5 1.1 even 1 trivial
1104.6.a.r.1.3 5 12.11 even 2