Properties

Label 29.6.a.b.1.5
Level $29$
Weight $6$
Character 29.1
Self dual yes
Analytic conductor $4.651$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.65113077458\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-4.83960\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.83960 q^{2} +15.9679 q^{3} +2.10095 q^{4} +31.5616 q^{5} +93.2461 q^{6} +106.304 q^{7} -174.599 q^{8} +11.9736 q^{9} +O(q^{10})\) \(q+5.83960 q^{2} +15.9679 q^{3} +2.10095 q^{4} +31.5616 q^{5} +93.2461 q^{6} +106.304 q^{7} -174.599 q^{8} +11.9736 q^{9} +184.307 q^{10} -152.796 q^{11} +33.5477 q^{12} +325.745 q^{13} +620.776 q^{14} +503.972 q^{15} -1086.82 q^{16} -664.939 q^{17} +69.9212 q^{18} -1595.33 q^{19} +66.3091 q^{20} +1697.46 q^{21} -892.268 q^{22} +719.327 q^{23} -2787.97 q^{24} -2128.87 q^{25} +1902.22 q^{26} -3689.00 q^{27} +223.340 q^{28} +841.000 q^{29} +2942.99 q^{30} +2059.61 q^{31} -759.420 q^{32} -2439.83 q^{33} -3882.98 q^{34} +3355.13 q^{35} +25.1559 q^{36} +14948.4 q^{37} -9316.11 q^{38} +5201.47 q^{39} -5510.60 q^{40} +14673.9 q^{41} +9912.48 q^{42} +10298.3 q^{43} -321.016 q^{44} +377.906 q^{45} +4200.58 q^{46} +4588.36 q^{47} -17354.2 q^{48} -5506.36 q^{49} -12431.7 q^{50} -10617.7 q^{51} +684.373 q^{52} +8952.75 q^{53} -21542.3 q^{54} -4822.48 q^{55} -18560.6 q^{56} -25474.1 q^{57} +4911.10 q^{58} -13734.5 q^{59} +1058.82 q^{60} -33480.9 q^{61} +12027.3 q^{62} +1272.85 q^{63} +30343.4 q^{64} +10281.0 q^{65} -14247.6 q^{66} +37519.2 q^{67} -1397.00 q^{68} +11486.1 q^{69} +19592.6 q^{70} -14763.7 q^{71} -2090.58 q^{72} +63298.3 q^{73} +87292.9 q^{74} -33993.5 q^{75} -3351.71 q^{76} -16242.9 q^{77} +30374.5 q^{78} -27148.9 q^{79} -34301.6 q^{80} -61815.2 q^{81} +85689.7 q^{82} -54499.5 q^{83} +3566.27 q^{84} -20986.5 q^{85} +60138.1 q^{86} +13429.0 q^{87} +26678.0 q^{88} -139829. q^{89} +2206.82 q^{90} +34628.2 q^{91} +1511.27 q^{92} +32887.6 q^{93} +26794.2 q^{94} -50351.2 q^{95} -12126.3 q^{96} +89845.2 q^{97} -32154.9 q^{98} -1829.52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.83960 1.03231 0.516153 0.856497i \(-0.327364\pi\)
0.516153 + 0.856497i \(0.327364\pi\)
\(3\) 15.9679 1.02434 0.512170 0.858884i \(-0.328842\pi\)
0.512170 + 0.858884i \(0.328842\pi\)
\(4\) 2.10095 0.0656545
\(5\) 31.5616 0.564590 0.282295 0.959328i \(-0.408904\pi\)
0.282295 + 0.959328i \(0.408904\pi\)
\(6\) 93.2461 1.05743
\(7\) 106.304 0.819986 0.409993 0.912089i \(-0.365531\pi\)
0.409993 + 0.912089i \(0.365531\pi\)
\(8\) −174.599 −0.964530
\(9\) 11.9736 0.0492742
\(10\) 184.307 0.582830
\(11\) −152.796 −0.380741 −0.190371 0.981712i \(-0.560969\pi\)
−0.190371 + 0.981712i \(0.560969\pi\)
\(12\) 33.5477 0.0672526
\(13\) 325.745 0.534589 0.267294 0.963615i \(-0.413870\pi\)
0.267294 + 0.963615i \(0.413870\pi\)
\(14\) 620.776 0.846476
\(15\) 503.972 0.578333
\(16\) −1086.82 −1.06134
\(17\) −664.939 −0.558033 −0.279016 0.960286i \(-0.590008\pi\)
−0.279016 + 0.960286i \(0.590008\pi\)
\(18\) 69.9212 0.0508660
\(19\) −1595.33 −1.01383 −0.506917 0.861995i \(-0.669215\pi\)
−0.506917 + 0.861995i \(0.669215\pi\)
\(20\) 66.3091 0.0370679
\(21\) 1697.46 0.839945
\(22\) −892.268 −0.393041
\(23\) 719.327 0.283535 0.141768 0.989900i \(-0.454721\pi\)
0.141768 + 0.989900i \(0.454721\pi\)
\(24\) −2787.97 −0.988007
\(25\) −2128.87 −0.681238
\(26\) 1902.22 0.551859
\(27\) −3689.00 −0.973867
\(28\) 223.340 0.0538358
\(29\) 841.000 0.185695
\(30\) 2942.99 0.597016
\(31\) 2059.61 0.384929 0.192464 0.981304i \(-0.438352\pi\)
0.192464 + 0.981304i \(0.438352\pi\)
\(32\) −759.420 −0.131101
\(33\) −2439.83 −0.390009
\(34\) −3882.98 −0.576060
\(35\) 3355.13 0.462956
\(36\) 25.1559 0.00323508
\(37\) 14948.4 1.79511 0.897556 0.440901i \(-0.145341\pi\)
0.897556 + 0.440901i \(0.145341\pi\)
\(38\) −9316.11 −1.04659
\(39\) 5201.47 0.547601
\(40\) −5510.60 −0.544564
\(41\) 14673.9 1.36328 0.681641 0.731687i \(-0.261267\pi\)
0.681641 + 0.731687i \(0.261267\pi\)
\(42\) 9912.48 0.867080
\(43\) 10298.3 0.849367 0.424683 0.905342i \(-0.360385\pi\)
0.424683 + 0.905342i \(0.360385\pi\)
\(44\) −321.016 −0.0249974
\(45\) 377.906 0.0278197
\(46\) 4200.58 0.292695
\(47\) 4588.36 0.302979 0.151490 0.988459i \(-0.451593\pi\)
0.151490 + 0.988459i \(0.451593\pi\)
\(48\) −17354.2 −1.08718
\(49\) −5506.36 −0.327623
\(50\) −12431.7 −0.703246
\(51\) −10617.7 −0.571616
\(52\) 684.373 0.0350982
\(53\) 8952.75 0.437791 0.218896 0.975748i \(-0.429755\pi\)
0.218896 + 0.975748i \(0.429755\pi\)
\(54\) −21542.3 −1.00533
\(55\) −4822.48 −0.214963
\(56\) −18560.6 −0.790901
\(57\) −25474.1 −1.03851
\(58\) 4911.10 0.191694
\(59\) −13734.5 −0.513670 −0.256835 0.966455i \(-0.582680\pi\)
−0.256835 + 0.966455i \(0.582680\pi\)
\(60\) 1058.82 0.0379702
\(61\) −33480.9 −1.15205 −0.576026 0.817431i \(-0.695397\pi\)
−0.576026 + 0.817431i \(0.695397\pi\)
\(62\) 12027.3 0.397364
\(63\) 1272.85 0.0404042
\(64\) 30343.4 0.926007
\(65\) 10281.0 0.301824
\(66\) −14247.6 −0.402608
\(67\) 37519.2 1.02110 0.510548 0.859849i \(-0.329442\pi\)
0.510548 + 0.859849i \(0.329442\pi\)
\(68\) −1397.00 −0.0366374
\(69\) 11486.1 0.290437
\(70\) 19592.6 0.477912
\(71\) −14763.7 −0.347576 −0.173788 0.984783i \(-0.555601\pi\)
−0.173788 + 0.984783i \(0.555601\pi\)
\(72\) −2090.58 −0.0475264
\(73\) 63298.3 1.39022 0.695112 0.718901i \(-0.255355\pi\)
0.695112 + 0.718901i \(0.255355\pi\)
\(74\) 87292.9 1.85310
\(75\) −33993.5 −0.697820
\(76\) −3351.71 −0.0665629
\(77\) −16242.9 −0.312203
\(78\) 30374.5 0.565292
\(79\) −27148.9 −0.489423 −0.244711 0.969596i \(-0.578693\pi\)
−0.244711 + 0.969596i \(0.578693\pi\)
\(80\) −34301.6 −0.599224
\(81\) −61815.2 −1.04685
\(82\) 85689.7 1.40732
\(83\) −54499.5 −0.868356 −0.434178 0.900827i \(-0.642961\pi\)
−0.434178 + 0.900827i \(0.642961\pi\)
\(84\) 3566.27 0.0551462
\(85\) −20986.5 −0.315060
\(86\) 60138.1 0.876806
\(87\) 13429.0 0.190215
\(88\) 26678.0 0.367237
\(89\) −139829. −1.87120 −0.935602 0.353057i \(-0.885142\pi\)
−0.935602 + 0.353057i \(0.885142\pi\)
\(90\) 2206.82 0.0287185
\(91\) 34628.2 0.438355
\(92\) 1511.27 0.0186154
\(93\) 32887.6 0.394298
\(94\) 26794.2 0.312767
\(95\) −50351.2 −0.572401
\(96\) −12126.3 −0.134292
\(97\) 89845.2 0.969539 0.484770 0.874642i \(-0.338903\pi\)
0.484770 + 0.874642i \(0.338903\pi\)
\(98\) −32154.9 −0.338207
\(99\) −1829.52 −0.0187607
\(100\) −4472.64 −0.0447264
\(101\) −107293. −1.04657 −0.523285 0.852158i \(-0.675294\pi\)
−0.523285 + 0.852158i \(0.675294\pi\)
\(102\) −62003.0 −0.590082
\(103\) 160302. 1.48884 0.744419 0.667713i \(-0.232727\pi\)
0.744419 + 0.667713i \(0.232727\pi\)
\(104\) −56874.7 −0.515627
\(105\) 53574.4 0.474225
\(106\) 52280.5 0.451934
\(107\) 79970.2 0.675256 0.337628 0.941280i \(-0.390375\pi\)
0.337628 + 0.941280i \(0.390375\pi\)
\(108\) −7750.40 −0.0639388
\(109\) −97964.0 −0.789769 −0.394885 0.918731i \(-0.629215\pi\)
−0.394885 + 0.918731i \(0.629215\pi\)
\(110\) −28161.3 −0.221907
\(111\) 238695. 1.83881
\(112\) −115533. −0.870287
\(113\) −237682. −1.75105 −0.875527 0.483170i \(-0.839485\pi\)
−0.875527 + 0.483170i \(0.839485\pi\)
\(114\) −148759. −1.07206
\(115\) 22703.1 0.160081
\(116\) 1766.90 0.0121917
\(117\) 3900.36 0.0263414
\(118\) −80204.2 −0.530264
\(119\) −70686.0 −0.457579
\(120\) −87992.7 −0.557819
\(121\) −137704. −0.855036
\(122\) −195515. −1.18927
\(123\) 234311. 1.39647
\(124\) 4327.12 0.0252723
\(125\) −165820. −0.949210
\(126\) 7432.94 0.0417094
\(127\) 194961. 1.07260 0.536299 0.844028i \(-0.319822\pi\)
0.536299 + 0.844028i \(0.319822\pi\)
\(128\) 201495. 1.08702
\(129\) 164442. 0.870041
\(130\) 60037.1 0.311574
\(131\) 350750. 1.78575 0.892873 0.450309i \(-0.148686\pi\)
0.892873 + 0.450309i \(0.148686\pi\)
\(132\) −5125.95 −0.0256059
\(133\) −169591. −0.831330
\(134\) 219097. 1.05408
\(135\) −116431. −0.549836
\(136\) 116097. 0.538239
\(137\) 185712. 0.845356 0.422678 0.906280i \(-0.361090\pi\)
0.422678 + 0.906280i \(0.361090\pi\)
\(138\) 67074.5 0.299819
\(139\) −316673. −1.39019 −0.695095 0.718918i \(-0.744638\pi\)
−0.695095 + 0.718918i \(0.744638\pi\)
\(140\) 7048.95 0.0303952
\(141\) 73266.4 0.310354
\(142\) −86214.2 −0.358804
\(143\) −49772.6 −0.203540
\(144\) −13013.1 −0.0522969
\(145\) 26543.3 0.104842
\(146\) 369637. 1.43514
\(147\) −87925.0 −0.335598
\(148\) 31405.8 0.117857
\(149\) −326686. −1.20549 −0.602747 0.797932i \(-0.705927\pi\)
−0.602747 + 0.797932i \(0.705927\pi\)
\(150\) −198509. −0.720363
\(151\) 427072. 1.52426 0.762130 0.647424i \(-0.224154\pi\)
0.762130 + 0.647424i \(0.224154\pi\)
\(152\) 278543. 0.977874
\(153\) −7961.74 −0.0274966
\(154\) −94852.0 −0.322289
\(155\) 65004.4 0.217327
\(156\) 10928.0 0.0359525
\(157\) 48668.5 0.157579 0.0787896 0.996891i \(-0.474894\pi\)
0.0787896 + 0.996891i \(0.474894\pi\)
\(158\) −158539. −0.505234
\(159\) 142957. 0.448447
\(160\) −23968.5 −0.0740185
\(161\) 76467.7 0.232495
\(162\) −360976. −1.08067
\(163\) −149764. −0.441509 −0.220755 0.975329i \(-0.570852\pi\)
−0.220755 + 0.975329i \(0.570852\pi\)
\(164\) 30829.0 0.0895056
\(165\) −77004.8 −0.220195
\(166\) −318256. −0.896408
\(167\) 371818. 1.03167 0.515833 0.856689i \(-0.327482\pi\)
0.515833 + 0.856689i \(0.327482\pi\)
\(168\) −296374. −0.810152
\(169\) −265183. −0.714215
\(170\) −122553. −0.325238
\(171\) −19101.9 −0.0499559
\(172\) 21636.2 0.0557648
\(173\) −434068. −1.10266 −0.551331 0.834287i \(-0.685880\pi\)
−0.551331 + 0.834287i \(0.685880\pi\)
\(174\) 78420.0 0.196360
\(175\) −226308. −0.558606
\(176\) 166061. 0.404098
\(177\) −219312. −0.526173
\(178\) −816543. −1.93165
\(179\) 341482. 0.796590 0.398295 0.917257i \(-0.369602\pi\)
0.398295 + 0.917257i \(0.369602\pi\)
\(180\) 793.961 0.00182649
\(181\) 542203. 1.23017 0.615086 0.788460i \(-0.289121\pi\)
0.615086 + 0.788460i \(0.289121\pi\)
\(182\) 202215. 0.452517
\(183\) −534619. −1.18009
\(184\) −125593. −0.273478
\(185\) 471796. 1.01350
\(186\) 192050. 0.407036
\(187\) 101600. 0.212466
\(188\) 9639.89 0.0198920
\(189\) −392158. −0.798558
\(190\) −294031. −0.590893
\(191\) −454420. −0.901310 −0.450655 0.892698i \(-0.648810\pi\)
−0.450655 + 0.892698i \(0.648810\pi\)
\(192\) 484520. 0.948547
\(193\) 791182. 1.52891 0.764457 0.644674i \(-0.223007\pi\)
0.764457 + 0.644674i \(0.223007\pi\)
\(194\) 524660. 1.00086
\(195\) 164166. 0.309170
\(196\) −11568.6 −0.0215099
\(197\) −519219. −0.953201 −0.476601 0.879120i \(-0.658131\pi\)
−0.476601 + 0.879120i \(0.658131\pi\)
\(198\) −10683.7 −0.0193668
\(199\) −301548. −0.539789 −0.269895 0.962890i \(-0.586989\pi\)
−0.269895 + 0.962890i \(0.586989\pi\)
\(200\) 371697. 0.657074
\(201\) 599103. 1.04595
\(202\) −626548. −1.08038
\(203\) 89402.1 0.152268
\(204\) −22307.2 −0.0375292
\(205\) 463131. 0.769696
\(206\) 936103. 1.53693
\(207\) 8612.96 0.0139710
\(208\) −354025. −0.567383
\(209\) 243760. 0.386009
\(210\) 312853. 0.489545
\(211\) −473908. −0.732804 −0.366402 0.930457i \(-0.619410\pi\)
−0.366402 + 0.930457i \(0.619410\pi\)
\(212\) 18809.2 0.0287430
\(213\) −235745. −0.356036
\(214\) 466994. 0.697071
\(215\) 325031. 0.479544
\(216\) 644095. 0.939324
\(217\) 218945. 0.315636
\(218\) −572071. −0.815283
\(219\) 1.01074e6 1.42406
\(220\) −10131.8 −0.0141133
\(221\) −216601. −0.298318
\(222\) 1.39388e6 1.89821
\(223\) −135893. −0.182993 −0.0914963 0.995805i \(-0.529165\pi\)
−0.0914963 + 0.995805i \(0.529165\pi\)
\(224\) −80729.7 −0.107501
\(225\) −25490.3 −0.0335675
\(226\) −1.38797e6 −1.80762
\(227\) −1.21029e6 −1.55893 −0.779464 0.626448i \(-0.784508\pi\)
−0.779464 + 0.626448i \(0.784508\pi\)
\(228\) −53519.7 −0.0681831
\(229\) −577029. −0.727125 −0.363563 0.931570i \(-0.618440\pi\)
−0.363563 + 0.931570i \(0.618440\pi\)
\(230\) 132577. 0.165253
\(231\) −259365. −0.319802
\(232\) −146837. −0.179109
\(233\) −966231. −1.16598 −0.582990 0.812479i \(-0.698117\pi\)
−0.582990 + 0.812479i \(0.698117\pi\)
\(234\) 22776.5 0.0271924
\(235\) 144816. 0.171059
\(236\) −28855.5 −0.0337248
\(237\) −433510. −0.501336
\(238\) −412778. −0.472361
\(239\) 592337. 0.670771 0.335386 0.942081i \(-0.391133\pi\)
0.335386 + 0.942081i \(0.391133\pi\)
\(240\) −547724. −0.613810
\(241\) 405276. 0.449478 0.224739 0.974419i \(-0.427847\pi\)
0.224739 + 0.974419i \(0.427847\pi\)
\(242\) −804139. −0.882658
\(243\) −90630.9 −0.0984601
\(244\) −70341.5 −0.0756374
\(245\) −173789. −0.184973
\(246\) 1.36828e6 1.44158
\(247\) −519672. −0.541985
\(248\) −359605. −0.371275
\(249\) −870243. −0.889492
\(250\) −968324. −0.979875
\(251\) 922052. 0.923785 0.461893 0.886936i \(-0.347171\pi\)
0.461893 + 0.886936i \(0.347171\pi\)
\(252\) 2674.19 0.00265272
\(253\) −109910. −0.107954
\(254\) 1.13849e6 1.10725
\(255\) −335110. −0.322729
\(256\) 205661. 0.196133
\(257\) 461687. 0.436028 0.218014 0.975946i \(-0.430042\pi\)
0.218014 + 0.975946i \(0.430042\pi\)
\(258\) 960279. 0.898148
\(259\) 1.58909e6 1.47197
\(260\) 21599.9 0.0198161
\(261\) 10069.8 0.00914999
\(262\) 2.04824e6 1.84344
\(263\) −1.78425e6 −1.59062 −0.795311 0.606202i \(-0.792692\pi\)
−0.795311 + 0.606202i \(0.792692\pi\)
\(264\) 425991. 0.376175
\(265\) 282563. 0.247173
\(266\) −990344. −0.858187
\(267\) −2.23277e6 −1.91675
\(268\) 78825.9 0.0670396
\(269\) −1.43033e6 −1.20519 −0.602596 0.798046i \(-0.705867\pi\)
−0.602596 + 0.798046i \(0.705867\pi\)
\(270\) −679909. −0.567599
\(271\) 418695. 0.346318 0.173159 0.984894i \(-0.444603\pi\)
0.173159 + 0.984894i \(0.444603\pi\)
\(272\) 722667. 0.592265
\(273\) 552939. 0.449025
\(274\) 1.08449e6 0.872666
\(275\) 325282. 0.259375
\(276\) 24131.7 0.0190685
\(277\) 319476. 0.250172 0.125086 0.992146i \(-0.460079\pi\)
0.125086 + 0.992146i \(0.460079\pi\)
\(278\) −1.84925e6 −1.43510
\(279\) 24661.0 0.0189671
\(280\) −585802. −0.446535
\(281\) 421076. 0.318123 0.159061 0.987269i \(-0.449153\pi\)
0.159061 + 0.987269i \(0.449153\pi\)
\(282\) 427847. 0.320380
\(283\) −129444. −0.0960759 −0.0480380 0.998846i \(-0.515297\pi\)
−0.0480380 + 0.998846i \(0.515297\pi\)
\(284\) −31017.7 −0.0228199
\(285\) −804002. −0.586334
\(286\) −290652. −0.210116
\(287\) 1.55990e6 1.11787
\(288\) −9093.02 −0.00645991
\(289\) −977713. −0.688600
\(290\) 155002. 0.108229
\(291\) 1.43464e6 0.993139
\(292\) 132986. 0.0912746
\(293\) 1.71643e6 1.16804 0.584020 0.811740i \(-0.301479\pi\)
0.584020 + 0.811740i \(0.301479\pi\)
\(294\) −513447. −0.346439
\(295\) −433483. −0.290013
\(296\) −2.60998e6 −1.73144
\(297\) 563665. 0.370792
\(298\) −1.90772e6 −1.24444
\(299\) 234317. 0.151575
\(300\) −71418.6 −0.0458150
\(301\) 1.09476e6 0.696469
\(302\) 2.49393e6 1.57350
\(303\) −1.71324e6 −1.07204
\(304\) 1.73383e6 1.07603
\(305\) −1.05671e6 −0.650437
\(306\) −46493.4 −0.0283849
\(307\) 2.88448e6 1.74671 0.873356 0.487083i \(-0.161939\pi\)
0.873356 + 0.487083i \(0.161939\pi\)
\(308\) −34125.4 −0.0204975
\(309\) 2.55969e6 1.52508
\(310\) 379600. 0.224348
\(311\) −2.59382e6 −1.52069 −0.760343 0.649522i \(-0.774969\pi\)
−0.760343 + 0.649522i \(0.774969\pi\)
\(312\) −908169. −0.528178
\(313\) 1.47281e6 0.849742 0.424871 0.905254i \(-0.360319\pi\)
0.424871 + 0.905254i \(0.360319\pi\)
\(314\) 284205. 0.162670
\(315\) 40173.1 0.0228118
\(316\) −57038.3 −0.0321328
\(317\) 661940. 0.369973 0.184987 0.982741i \(-0.440776\pi\)
0.184987 + 0.982741i \(0.440776\pi\)
\(318\) 834809. 0.462935
\(319\) −128501. −0.0707019
\(320\) 957685. 0.522815
\(321\) 1.27696e6 0.691693
\(322\) 446541. 0.240006
\(323\) 1.06080e6 0.565753
\(324\) −129870. −0.0687302
\(325\) −693469. −0.364182
\(326\) −874564. −0.455772
\(327\) −1.56428e6 −0.808993
\(328\) −2.56204e6 −1.31493
\(329\) 487763. 0.248439
\(330\) −449677. −0.227309
\(331\) 3.40774e6 1.70961 0.854805 0.518949i \(-0.173677\pi\)
0.854805 + 0.518949i \(0.173677\pi\)
\(332\) −114501. −0.0570115
\(333\) 178987. 0.0884527
\(334\) 2.17127e6 1.06499
\(335\) 1.18417e6 0.576501
\(336\) −1.84483e6 −0.891471
\(337\) −2.52588e6 −1.21154 −0.605771 0.795639i \(-0.707135\pi\)
−0.605771 + 0.795639i \(0.707135\pi\)
\(338\) −1.54856e6 −0.737288
\(339\) −3.79527e6 −1.79368
\(340\) −44091.5 −0.0206851
\(341\) −314700. −0.146558
\(342\) −111548. −0.0515698
\(343\) −2.37201e6 −1.08863
\(344\) −1.79807e6 −0.819240
\(345\) 362520. 0.163978
\(346\) −2.53478e6 −1.13828
\(347\) −2.09340e6 −0.933317 −0.466658 0.884438i \(-0.654542\pi\)
−0.466658 + 0.884438i \(0.654542\pi\)
\(348\) 28213.6 0.0124885
\(349\) 2.90749e6 1.27777 0.638887 0.769300i \(-0.279395\pi\)
0.638887 + 0.769300i \(0.279395\pi\)
\(350\) −1.32155e6 −0.576652
\(351\) −1.20168e6 −0.520619
\(352\) 116036. 0.0499157
\(353\) −8176.61 −0.00349250 −0.00174625 0.999998i \(-0.500556\pi\)
−0.00174625 + 0.999998i \(0.500556\pi\)
\(354\) −1.28069e6 −0.543171
\(355\) −465966. −0.196238
\(356\) −293772. −0.122853
\(357\) −1.12871e6 −0.468717
\(358\) 1.99412e6 0.822324
\(359\) 457001. 0.187146 0.0935732 0.995612i \(-0.470171\pi\)
0.0935732 + 0.995612i \(0.470171\pi\)
\(360\) −65981.9 −0.0268330
\(361\) 68986.9 0.0278611
\(362\) 3.16625e6 1.26991
\(363\) −2.19885e6 −0.875848
\(364\) 72752.0 0.0287800
\(365\) 1.99779e6 0.784907
\(366\) −3.12196e6 −1.21822
\(367\) 3.50049e6 1.35664 0.678318 0.734768i \(-0.262709\pi\)
0.678318 + 0.734768i \(0.262709\pi\)
\(368\) −781776. −0.300928
\(369\) 175700. 0.0671746
\(370\) 2.75510e6 1.04624
\(371\) 951717. 0.358983
\(372\) 69095.0 0.0258875
\(373\) −2.17554e6 −0.809645 −0.404822 0.914395i \(-0.632667\pi\)
−0.404822 + 0.914395i \(0.632667\pi\)
\(374\) 593304. 0.219330
\(375\) −2.64780e6 −0.972315
\(376\) −801121. −0.292232
\(377\) 273952. 0.0992707
\(378\) −2.29004e6 −0.824355
\(379\) 1.97581e6 0.706557 0.353278 0.935518i \(-0.385067\pi\)
0.353278 + 0.935518i \(0.385067\pi\)
\(380\) −105785. −0.0375807
\(381\) 3.11311e6 1.09871
\(382\) −2.65363e6 −0.930428
\(383\) 2.77434e6 0.966412 0.483206 0.875507i \(-0.339472\pi\)
0.483206 + 0.875507i \(0.339472\pi\)
\(384\) 3.21745e6 1.11348
\(385\) −512651. −0.176267
\(386\) 4.62019e6 1.57831
\(387\) 123308. 0.0418519
\(388\) 188760. 0.0636547
\(389\) 2.12869e6 0.713245 0.356622 0.934249i \(-0.383928\pi\)
0.356622 + 0.934249i \(0.383928\pi\)
\(390\) 958667. 0.319158
\(391\) −478309. −0.158222
\(392\) 961402. 0.316002
\(393\) 5.60074e6 1.82921
\(394\) −3.03203e6 −0.983995
\(395\) −856861. −0.276323
\(396\) −3843.73 −0.00123173
\(397\) 2.73423e6 0.870680 0.435340 0.900266i \(-0.356628\pi\)
0.435340 + 0.900266i \(0.356628\pi\)
\(398\) −1.76092e6 −0.557228
\(399\) −2.70801e6 −0.851566
\(400\) 2.31369e6 0.723028
\(401\) −1.29206e6 −0.401257 −0.200628 0.979667i \(-0.564298\pi\)
−0.200628 + 0.979667i \(0.564298\pi\)
\(402\) 3.49852e6 1.07974
\(403\) 670908. 0.205779
\(404\) −225417. −0.0687120
\(405\) −1.95098e6 −0.591039
\(406\) 522072. 0.157187
\(407\) −2.28406e6 −0.683473
\(408\) 1.85383e6 0.551340
\(409\) −2.78691e6 −0.823787 −0.411894 0.911232i \(-0.635132\pi\)
−0.411894 + 0.911232i \(0.635132\pi\)
\(410\) 2.70450e6 0.794561
\(411\) 2.96544e6 0.865933
\(412\) 336787. 0.0977489
\(413\) −1.46004e6 −0.421202
\(414\) 50296.2 0.0144223
\(415\) −1.72009e6 −0.490265
\(416\) −247378. −0.0700853
\(417\) −5.05660e6 −1.42403
\(418\) 1.42346e6 0.398479
\(419\) −1.51265e6 −0.420924 −0.210462 0.977602i \(-0.567497\pi\)
−0.210462 + 0.977602i \(0.567497\pi\)
\(420\) 112557. 0.0311350
\(421\) 2.55990e6 0.703911 0.351955 0.936017i \(-0.385517\pi\)
0.351955 + 0.936017i \(0.385517\pi\)
\(422\) −2.76743e6 −0.756477
\(423\) 54939.3 0.0149291
\(424\) −1.56314e6 −0.422263
\(425\) 1.41557e6 0.380153
\(426\) −1.37666e6 −0.367538
\(427\) −3.55917e6 −0.944666
\(428\) 168013. 0.0443336
\(429\) −794763. −0.208495
\(430\) 1.89805e6 0.495036
\(431\) −5.38406e6 −1.39610 −0.698051 0.716048i \(-0.745949\pi\)
−0.698051 + 0.716048i \(0.745949\pi\)
\(432\) 4.00927e6 1.03361
\(433\) 1.90699e6 0.488797 0.244398 0.969675i \(-0.421410\pi\)
0.244398 + 0.969675i \(0.421410\pi\)
\(434\) 1.27855e6 0.325833
\(435\) 423840. 0.107394
\(436\) −205817. −0.0518520
\(437\) −1.14757e6 −0.287458
\(438\) 5.90232e6 1.47007
\(439\) −3.84641e6 −0.952565 −0.476283 0.879292i \(-0.658016\pi\)
−0.476283 + 0.879292i \(0.658016\pi\)
\(440\) 841998. 0.207338
\(441\) −65931.1 −0.0161434
\(442\) −1.26486e6 −0.307955
\(443\) 1.43911e6 0.348406 0.174203 0.984710i \(-0.444265\pi\)
0.174203 + 0.984710i \(0.444265\pi\)
\(444\) 501485. 0.120726
\(445\) −4.41321e6 −1.05646
\(446\) −793558. −0.188904
\(447\) −5.21649e6 −1.23484
\(448\) 3.22564e6 0.759313
\(449\) −5.05146e6 −1.18250 −0.591249 0.806489i \(-0.701365\pi\)
−0.591249 + 0.806489i \(0.701365\pi\)
\(450\) −148853. −0.0346519
\(451\) −2.24211e6 −0.519058
\(452\) −499356. −0.114965
\(453\) 6.81945e6 1.56136
\(454\) −7.06763e6 −1.60929
\(455\) 1.09292e6 0.247491
\(456\) 4.44774e6 1.00168
\(457\) −3.02849e6 −0.678323 −0.339161 0.940728i \(-0.610143\pi\)
−0.339161 + 0.940728i \(0.610143\pi\)
\(458\) −3.36962e6 −0.750615
\(459\) 2.45296e6 0.543450
\(460\) 47697.9 0.0105101
\(461\) −3.54068e6 −0.775951 −0.387976 0.921670i \(-0.626826\pi\)
−0.387976 + 0.921670i \(0.626826\pi\)
\(462\) −1.51459e6 −0.330133
\(463\) 3.78475e6 0.820512 0.410256 0.911970i \(-0.365439\pi\)
0.410256 + 0.911970i \(0.365439\pi\)
\(464\) −914012. −0.197087
\(465\) 1.03798e6 0.222617
\(466\) −5.64240e6 −1.20365
\(467\) −3.93030e6 −0.833938 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(468\) 8194.44 0.00172944
\(469\) 3.98846e6 0.837285
\(470\) 845666. 0.176585
\(471\) 777134. 0.161415
\(472\) 2.39803e6 0.495450
\(473\) −1.57354e6 −0.323389
\(474\) −2.53153e6 −0.517531
\(475\) 3.39625e6 0.690663
\(476\) −148507. −0.0300421
\(477\) 107197. 0.0215718
\(478\) 3.45901e6 0.692441
\(479\) −3.65493e6 −0.727848 −0.363924 0.931429i \(-0.618563\pi\)
−0.363924 + 0.931429i \(0.618563\pi\)
\(480\) −382726. −0.0758202
\(481\) 4.86938e6 0.959647
\(482\) 2.36665e6 0.463999
\(483\) 1.22103e6 0.238154
\(484\) −289309. −0.0561370
\(485\) 2.83565e6 0.547392
\(486\) −529248. −0.101641
\(487\) −3.90232e6 −0.745591 −0.372796 0.927913i \(-0.621601\pi\)
−0.372796 + 0.927913i \(0.621601\pi\)
\(488\) 5.84571e6 1.11119
\(489\) −2.39142e6 −0.452256
\(490\) −1.01486e6 −0.190948
\(491\) 8.22645e6 1.53996 0.769979 0.638069i \(-0.220267\pi\)
0.769979 + 0.638069i \(0.220267\pi\)
\(492\) 492275. 0.0916843
\(493\) −559214. −0.103624
\(494\) −3.03468e6 −0.559494
\(495\) −57742.6 −0.0105921
\(496\) −2.23841e6 −0.408542
\(497\) −1.56945e6 −0.285007
\(498\) −5.08187e6 −0.918228
\(499\) 1.95126e6 0.350803 0.175401 0.984497i \(-0.443878\pi\)
0.175401 + 0.984497i \(0.443878\pi\)
\(500\) −348379. −0.0623200
\(501\) 5.93715e6 1.05678
\(502\) 5.38442e6 0.953629
\(503\) 6.74097e6 1.18796 0.593981 0.804479i \(-0.297555\pi\)
0.593981 + 0.804479i \(0.297555\pi\)
\(504\) −222238. −0.0389710
\(505\) −3.38633e6 −0.590883
\(506\) −641832. −0.111441
\(507\) −4.23441e6 −0.731599
\(508\) 409601. 0.0704210
\(509\) 2.57165e6 0.439964 0.219982 0.975504i \(-0.429400\pi\)
0.219982 + 0.975504i \(0.429400\pi\)
\(510\) −1.95691e6 −0.333155
\(511\) 6.72889e6 1.13996
\(512\) −5.24686e6 −0.884554
\(513\) 5.88519e6 0.987341
\(514\) 2.69607e6 0.450114
\(515\) 5.05940e6 0.840583
\(516\) 345485. 0.0571221
\(517\) −701083. −0.115357
\(518\) 9.27963e6 1.51952
\(519\) −6.93115e6 −1.12950
\(520\) −1.79505e6 −0.291118
\(521\) 1.25025e6 0.201791 0.100896 0.994897i \(-0.467829\pi\)
0.100896 + 0.994897i \(0.467829\pi\)
\(522\) 58803.8 0.00944559
\(523\) −188395. −0.0301172 −0.0150586 0.999887i \(-0.504793\pi\)
−0.0150586 + 0.999887i \(0.504793\pi\)
\(524\) 736907. 0.117242
\(525\) −3.61367e6 −0.572202
\(526\) −1.04193e7 −1.64201
\(527\) −1.36951e6 −0.214803
\(528\) 2.65165e6 0.413934
\(529\) −5.91891e6 −0.919608
\(530\) 1.65005e6 0.255158
\(531\) −164452. −0.0253107
\(532\) −356301. −0.0545806
\(533\) 4.77995e6 0.728795
\(534\) −1.30385e7 −1.97867
\(535\) 2.52398e6 0.381243
\(536\) −6.55080e6 −0.984878
\(537\) 5.45274e6 0.815980
\(538\) −8.35258e6 −1.24413
\(539\) 841349. 0.124740
\(540\) −244615. −0.0360992
\(541\) −7.69990e6 −1.13108 −0.565538 0.824722i \(-0.691331\pi\)
−0.565538 + 0.824722i \(0.691331\pi\)
\(542\) 2.44501e6 0.357506
\(543\) 8.65785e6 1.26012
\(544\) 504968. 0.0731588
\(545\) −3.09190e6 −0.445896
\(546\) 3.22895e6 0.463531
\(547\) 1.21820e7 1.74081 0.870406 0.492334i \(-0.163856\pi\)
0.870406 + 0.492334i \(0.163856\pi\)
\(548\) 390172. 0.0555015
\(549\) −400888. −0.0567664
\(550\) 1.89952e6 0.267755
\(551\) −1.34167e6 −0.188264
\(552\) −2.00546e6 −0.280135
\(553\) −2.88605e6 −0.401320
\(554\) 1.86561e6 0.258254
\(555\) 7.53359e6 1.03817
\(556\) −665313. −0.0912723
\(557\) 5.21687e6 0.712479 0.356239 0.934395i \(-0.384059\pi\)
0.356239 + 0.934395i \(0.384059\pi\)
\(558\) 144010. 0.0195798
\(559\) 3.35463e6 0.454062
\(560\) −3.64641e6 −0.491356
\(561\) 1.62234e6 0.217638
\(562\) 2.45892e6 0.328400
\(563\) −782547. −0.104049 −0.0520247 0.998646i \(-0.516567\pi\)
−0.0520247 + 0.998646i \(0.516567\pi\)
\(564\) 153929. 0.0203761
\(565\) −7.50160e6 −0.988627
\(566\) −755899. −0.0991797
\(567\) −6.57123e6 −0.858399
\(568\) 2.57772e6 0.335247
\(569\) 1.01820e7 1.31841 0.659206 0.751962i \(-0.270893\pi\)
0.659206 + 0.751962i \(0.270893\pi\)
\(570\) −4.69505e6 −0.605276
\(571\) −1.56900e6 −0.201388 −0.100694 0.994917i \(-0.532106\pi\)
−0.100694 + 0.994917i \(0.532106\pi\)
\(572\) −104569. −0.0133633
\(573\) −7.25614e6 −0.923249
\(574\) 9.10919e6 1.15399
\(575\) −1.53135e6 −0.193155
\(576\) 363321. 0.0456283
\(577\) −1.53116e7 −1.91462 −0.957308 0.289069i \(-0.906654\pi\)
−0.957308 + 0.289069i \(0.906654\pi\)
\(578\) −5.70945e6 −0.710845
\(579\) 1.26335e7 1.56613
\(580\) 55766.0 0.00688334
\(581\) −5.79355e6 −0.712040
\(582\) 8.37771e6 1.02522
\(583\) −1.36794e6 −0.166685
\(584\) −1.10518e7 −1.34091
\(585\) 123101. 0.0148721
\(586\) 1.00233e7 1.20577
\(587\) 3.65745e6 0.438110 0.219055 0.975712i \(-0.429703\pi\)
0.219055 + 0.975712i \(0.429703\pi\)
\(588\) −184726. −0.0220335
\(589\) −3.28576e6 −0.390254
\(590\) −2.53137e6 −0.299382
\(591\) −8.29083e6 −0.976403
\(592\) −1.62462e7 −1.90523
\(593\) −7.18479e6 −0.839029 −0.419515 0.907749i \(-0.637800\pi\)
−0.419515 + 0.907749i \(0.637800\pi\)
\(594\) 3.29158e6 0.382770
\(595\) −2.23096e6 −0.258345
\(596\) −686350. −0.0791462
\(597\) −4.81509e6 −0.552928
\(598\) 1.36832e6 0.156471
\(599\) 2.35482e6 0.268158 0.134079 0.990971i \(-0.457192\pi\)
0.134079 + 0.990971i \(0.457192\pi\)
\(600\) 5.93522e6 0.673068
\(601\) −7.49135e6 −0.846007 −0.423003 0.906128i \(-0.639024\pi\)
−0.423003 + 0.906128i \(0.639024\pi\)
\(602\) 6.39295e6 0.718969
\(603\) 449241. 0.0503137
\(604\) 897256. 0.100075
\(605\) −4.34616e6 −0.482745
\(606\) −1.00047e7 −1.10668
\(607\) 248110. 0.0273320 0.0136660 0.999907i \(-0.495650\pi\)
0.0136660 + 0.999907i \(0.495650\pi\)
\(608\) 1.21153e6 0.132915
\(609\) 1.42756e6 0.155974
\(610\) −6.17075e6 −0.671450
\(611\) 1.49464e6 0.161969
\(612\) −16727.2 −0.00180528
\(613\) −1.97712e6 −0.212511 −0.106256 0.994339i \(-0.533886\pi\)
−0.106256 + 0.994339i \(0.533886\pi\)
\(614\) 1.68442e7 1.80314
\(615\) 7.39522e6 0.788431
\(616\) 2.83599e6 0.301129
\(617\) 1.43605e7 1.51865 0.759323 0.650714i \(-0.225530\pi\)
0.759323 + 0.650714i \(0.225530\pi\)
\(618\) 1.49476e7 1.57435
\(619\) −3.63487e6 −0.381297 −0.190648 0.981658i \(-0.561059\pi\)
−0.190648 + 0.981658i \(0.561059\pi\)
\(620\) 136571. 0.0142685
\(621\) −2.65360e6 −0.276126
\(622\) −1.51469e7 −1.56981
\(623\) −1.48644e7 −1.53436
\(624\) −5.65304e6 −0.581193
\(625\) 1.41917e6 0.145323
\(626\) 8.60065e6 0.877193
\(627\) 3.89234e6 0.395405
\(628\) 102250. 0.0103458
\(629\) −9.93980e6 −1.00173
\(630\) 234595. 0.0235487
\(631\) −1.71093e6 −0.171065 −0.0855323 0.996335i \(-0.527259\pi\)
−0.0855323 + 0.996335i \(0.527259\pi\)
\(632\) 4.74015e6 0.472063
\(633\) −7.56731e6 −0.750641
\(634\) 3.86547e6 0.381926
\(635\) 6.15326e6 0.605579
\(636\) 300344. 0.0294426
\(637\) −1.79367e6 −0.175144
\(638\) −750397. −0.0729860
\(639\) −176775. −0.0171265
\(640\) 6.35949e6 0.613723
\(641\) −7.33888e6 −0.705480 −0.352740 0.935721i \(-0.614750\pi\)
−0.352740 + 0.935721i \(0.614750\pi\)
\(642\) 7.45691e6 0.714038
\(643\) 1.65108e7 1.57485 0.787426 0.616409i \(-0.211413\pi\)
0.787426 + 0.616409i \(0.211413\pi\)
\(644\) 160654. 0.0152643
\(645\) 5.19006e6 0.491217
\(646\) 6.19464e6 0.584030
\(647\) −4.75302e6 −0.446384 −0.223192 0.974774i \(-0.571648\pi\)
−0.223192 + 0.974774i \(0.571648\pi\)
\(648\) 1.07928e7 1.00971
\(649\) 2.09858e6 0.195575
\(650\) −4.04958e6 −0.375947
\(651\) 3.49610e6 0.323319
\(652\) −314647. −0.0289871
\(653\) 2.06957e7 1.89932 0.949658 0.313290i \(-0.101431\pi\)
0.949658 + 0.313290i \(0.101431\pi\)
\(654\) −9.13477e6 −0.835128
\(655\) 1.10702e7 1.00821
\(656\) −1.59478e7 −1.44691
\(657\) 757911. 0.0685022
\(658\) 2.84834e6 0.256465
\(659\) 1.75250e7 1.57197 0.785987 0.618244i \(-0.212155\pi\)
0.785987 + 0.618244i \(0.212155\pi\)
\(660\) −161783. −0.0144568
\(661\) 5.06876e6 0.451230 0.225615 0.974217i \(-0.427561\pi\)
0.225615 + 0.974217i \(0.427561\pi\)
\(662\) 1.98999e7 1.76484
\(663\) −3.45866e6 −0.305579
\(664\) 9.51554e6 0.837555
\(665\) −5.35256e6 −0.469361
\(666\) 1.04521e6 0.0913102
\(667\) 604954. 0.0526511
\(668\) 781170. 0.0677336
\(669\) −2.16992e6 −0.187447
\(670\) 6.91505e6 0.595125
\(671\) 5.11574e6 0.438634
\(672\) −1.28908e6 −0.110118
\(673\) 1.07503e7 0.914922 0.457461 0.889230i \(-0.348759\pi\)
0.457461 + 0.889230i \(0.348759\pi\)
\(674\) −1.47501e7 −1.25068
\(675\) 7.85340e6 0.663435
\(676\) −557135. −0.0468914
\(677\) −6.95239e6 −0.582992 −0.291496 0.956572i \(-0.594153\pi\)
−0.291496 + 0.956572i \(0.594153\pi\)
\(678\) −2.21629e7 −1.85162
\(679\) 9.55094e6 0.795009
\(680\) 3.66422e6 0.303885
\(681\) −1.93258e7 −1.59687
\(682\) −1.83772e6 −0.151293
\(683\) −1.26571e7 −1.03821 −0.519103 0.854711i \(-0.673734\pi\)
−0.519103 + 0.854711i \(0.673734\pi\)
\(684\) −40132.1 −0.00327983
\(685\) 5.86137e6 0.477280
\(686\) −1.38516e7 −1.12380
\(687\) −9.21394e6 −0.744824
\(688\) −1.11924e7 −0.901470
\(689\) 2.91632e6 0.234038
\(690\) 2.11697e6 0.169275
\(691\) −7.61067e6 −0.606356 −0.303178 0.952934i \(-0.598048\pi\)
−0.303178 + 0.952934i \(0.598048\pi\)
\(692\) −911952. −0.0723947
\(693\) −194486. −0.0153835
\(694\) −1.22246e7 −0.963468
\(695\) −9.99470e6 −0.784888
\(696\) −2.34468e6 −0.183468
\(697\) −9.75724e6 −0.760756
\(698\) 1.69786e7 1.31905
\(699\) −1.54287e7 −1.19436
\(700\) −475461. −0.0366750
\(701\) −1.63413e7 −1.25600 −0.628002 0.778211i \(-0.716127\pi\)
−0.628002 + 0.778211i \(0.716127\pi\)
\(702\) −7.01731e6 −0.537437
\(703\) −2.38477e7 −1.81995
\(704\) −4.63635e6 −0.352569
\(705\) 2.31240e6 0.175223
\(706\) −47748.1 −0.00360533
\(707\) −1.14057e7 −0.858172
\(708\) −460762. −0.0345456
\(709\) 1.11269e7 0.831300 0.415650 0.909525i \(-0.363554\pi\)
0.415650 + 0.909525i \(0.363554\pi\)
\(710\) −2.72105e6 −0.202577
\(711\) −325071. −0.0241159
\(712\) 2.44139e7 1.80483
\(713\) 1.48153e6 0.109141
\(714\) −6.59120e6 −0.483859
\(715\) −1.57090e6 −0.114917
\(716\) 717434. 0.0522997
\(717\) 9.45838e6 0.687098
\(718\) 2.66871e6 0.193192
\(719\) 1.28895e7 0.929849 0.464924 0.885350i \(-0.346081\pi\)
0.464924 + 0.885350i \(0.346081\pi\)
\(720\) −410715. −0.0295263
\(721\) 1.70409e7 1.22083
\(722\) 402856. 0.0287612
\(723\) 6.47141e6 0.460419
\(724\) 1.13914e6 0.0807664
\(725\) −1.79038e6 −0.126503
\(726\) −1.28404e7 −0.904143
\(727\) −2.32214e7 −1.62949 −0.814745 0.579820i \(-0.803123\pi\)
−0.814745 + 0.579820i \(0.803123\pi\)
\(728\) −6.04603e6 −0.422807
\(729\) 1.35739e7 0.945990
\(730\) 1.16663e7 0.810264
\(731\) −6.84776e6 −0.473974
\(732\) −1.12321e6 −0.0774785
\(733\) −8.72009e6 −0.599461 −0.299731 0.954024i \(-0.596897\pi\)
−0.299731 + 0.954024i \(0.596897\pi\)
\(734\) 2.04415e7 1.40046
\(735\) −2.77505e6 −0.189475
\(736\) −546271. −0.0371718
\(737\) −5.73279e6 −0.388774
\(738\) 1.02602e6 0.0693447
\(739\) 2.49740e7 1.68220 0.841098 0.540882i \(-0.181910\pi\)
0.841098 + 0.540882i \(0.181910\pi\)
\(740\) 991217. 0.0665410
\(741\) −8.29807e6 −0.555177
\(742\) 5.55765e6 0.370580
\(743\) −288063. −0.0191433 −0.00957164 0.999954i \(-0.503047\pi\)
−0.00957164 + 0.999954i \(0.503047\pi\)
\(744\) −5.74213e6 −0.380312
\(745\) −1.03107e7 −0.680611
\(746\) −1.27043e7 −0.835801
\(747\) −652558. −0.0427875
\(748\) 213456. 0.0139494
\(749\) 8.50119e6 0.553701
\(750\) −1.54621e7 −1.00373
\(751\) 2.19870e7 1.42255 0.711274 0.702915i \(-0.248119\pi\)
0.711274 + 0.702915i \(0.248119\pi\)
\(752\) −4.98670e6 −0.321565
\(753\) 1.47232e7 0.946271
\(754\) 1.59977e6 0.102478
\(755\) 1.34791e7 0.860582
\(756\) −823902. −0.0524289
\(757\) −6.72062e6 −0.426255 −0.213128 0.977024i \(-0.568365\pi\)
−0.213128 + 0.977024i \(0.568365\pi\)
\(758\) 1.15379e7 0.729382
\(759\) −1.75504e6 −0.110581
\(760\) 8.79124e6 0.552098
\(761\) −1.10936e7 −0.694400 −0.347200 0.937791i \(-0.612868\pi\)
−0.347200 + 0.937791i \(0.612868\pi\)
\(762\) 1.81793e7 1.13420
\(763\) −1.04140e7 −0.647600
\(764\) −954712. −0.0591751
\(765\) −251285. −0.0155243
\(766\) 1.62010e7 0.997632
\(767\) −4.47396e6 −0.274602
\(768\) 3.28397e6 0.200907
\(769\) 6.42928e6 0.392054 0.196027 0.980598i \(-0.437196\pi\)
0.196027 + 0.980598i \(0.437196\pi\)
\(770\) −2.99368e6 −0.181961
\(771\) 7.37217e6 0.446642
\(772\) 1.66223e6 0.100380
\(773\) −1.38614e7 −0.834371 −0.417185 0.908821i \(-0.636983\pi\)
−0.417185 + 0.908821i \(0.636983\pi\)
\(774\) 720071. 0.0432039
\(775\) −4.38463e6 −0.262228
\(776\) −1.56868e7 −0.935150
\(777\) 2.53743e7 1.50780
\(778\) 1.24307e7 0.736287
\(779\) −2.34097e7 −1.38214
\(780\) 344905. 0.0202984
\(781\) 2.25584e6 0.132337
\(782\) −2.79313e6 −0.163333
\(783\) −3.10245e6 −0.180843
\(784\) 5.98440e6 0.347721
\(785\) 1.53605e6 0.0889677
\(786\) 3.27061e7 1.88831
\(787\) 2.48798e7 1.43189 0.715945 0.698157i \(-0.245996\pi\)
0.715945 + 0.698157i \(0.245996\pi\)
\(788\) −1.09085e6 −0.0625820
\(789\) −2.84907e7 −1.62934
\(790\) −5.00372e6 −0.285250
\(791\) −2.52666e7 −1.43584
\(792\) 319432. 0.0180953
\(793\) −1.09062e7 −0.615874
\(794\) 1.59668e7 0.898808
\(795\) 4.51193e6 0.253189
\(796\) −633537. −0.0354396
\(797\) 2.80418e7 1.56372 0.781861 0.623453i \(-0.214271\pi\)
0.781861 + 0.623453i \(0.214271\pi\)
\(798\) −1.58137e7 −0.879076
\(799\) −3.05098e6 −0.169072
\(800\) 1.61671e6 0.0893112
\(801\) −1.67426e6 −0.0922021
\(802\) −7.54513e6 −0.414220
\(803\) −9.67173e6 −0.529316
\(804\) 1.25868e6 0.0686714
\(805\) 2.41344e6 0.131264
\(806\) 3.91783e6 0.212426
\(807\) −2.28394e7 −1.23453
\(808\) 1.87332e7 1.00945
\(809\) 2.45320e7 1.31784 0.658919 0.752214i \(-0.271014\pi\)
0.658919 + 0.752214i \(0.271014\pi\)
\(810\) −1.13930e7 −0.610133
\(811\) 2.44306e7 1.30431 0.652156 0.758084i \(-0.273865\pi\)
0.652156 + 0.758084i \(0.273865\pi\)
\(812\) 187829. 0.00999706
\(813\) 6.68568e6 0.354748
\(814\) −1.33380e7 −0.705553
\(815\) −4.72680e6 −0.249272
\(816\) 1.15395e7 0.606681
\(817\) −1.64292e7 −0.861118
\(818\) −1.62745e7 −0.850400
\(819\) 414625. 0.0215996
\(820\) 973012. 0.0505340
\(821\) −4.22220e6 −0.218615 −0.109308 0.994008i \(-0.534863\pi\)
−0.109308 + 0.994008i \(0.534863\pi\)
\(822\) 1.73170e7 0.893907
\(823\) −2.11475e7 −1.08833 −0.544165 0.838979i \(-0.683153\pi\)
−0.544165 + 0.838979i \(0.683153\pi\)
\(824\) −2.79886e7 −1.43603
\(825\) 5.19408e6 0.265689
\(826\) −8.52607e6 −0.434809
\(827\) 2.31990e6 0.117952 0.0589761 0.998259i \(-0.481216\pi\)
0.0589761 + 0.998259i \(0.481216\pi\)
\(828\) 18095.4 0.000917257 0
\(829\) 2.89837e7 1.46476 0.732381 0.680895i \(-0.238409\pi\)
0.732381 + 0.680895i \(0.238409\pi\)
\(830\) −1.00446e7 −0.506103
\(831\) 5.10137e6 0.256262
\(832\) 9.88423e6 0.495033
\(833\) 3.66139e6 0.182824
\(834\) −2.95286e7 −1.47003
\(835\) 1.17352e7 0.582469
\(836\) 512127. 0.0253432
\(837\) −7.59790e6 −0.374869
\(838\) −8.83328e6 −0.434522
\(839\) 3.32541e7 1.63095 0.815473 0.578795i \(-0.196477\pi\)
0.815473 + 0.578795i \(0.196477\pi\)
\(840\) −9.35402e6 −0.457404
\(841\) 707281. 0.0344828
\(842\) 1.49488e7 0.726651
\(843\) 6.72370e6 0.325866
\(844\) −995655. −0.0481119
\(845\) −8.36958e6 −0.403239
\(846\) 320824. 0.0154113
\(847\) −1.46386e7 −0.701118
\(848\) −9.73000e6 −0.464647
\(849\) −2.06694e6 −0.0984145
\(850\) 8.26635e6 0.392434
\(851\) 1.07528e7 0.508977
\(852\) −495288. −0.0233754
\(853\) 1.48503e7 0.698816 0.349408 0.936971i \(-0.386383\pi\)
0.349408 + 0.936971i \(0.386383\pi\)
\(854\) −2.07841e7 −0.975184
\(855\) −602886. −0.0282046
\(856\) −1.39627e7 −0.651305
\(857\) 2.15523e7 1.00240 0.501201 0.865331i \(-0.332892\pi\)
0.501201 + 0.865331i \(0.332892\pi\)
\(858\) −4.64110e6 −0.215230
\(859\) −1.84444e7 −0.852867 −0.426434 0.904519i \(-0.640230\pi\)
−0.426434 + 0.904519i \(0.640230\pi\)
\(860\) 682872. 0.0314843
\(861\) 2.49083e7 1.14508
\(862\) −3.14408e7 −1.44120
\(863\) −2.12674e7 −0.972046 −0.486023 0.873946i \(-0.661553\pi\)
−0.486023 + 0.873946i \(0.661553\pi\)
\(864\) 2.80150e6 0.127675
\(865\) −1.36999e7 −0.622552
\(866\) 1.11360e7 0.504587
\(867\) −1.56120e7 −0.705361
\(868\) 459993. 0.0207229
\(869\) 4.14824e6 0.186343
\(870\) 2.47506e6 0.110863
\(871\) 1.22217e7 0.545867
\(872\) 1.71044e7 0.761756
\(873\) 1.07577e6 0.0477733
\(874\) −6.70133e6 −0.296744
\(875\) −1.76274e7 −0.778339
\(876\) 2.12351e6 0.0934963
\(877\) −2.51615e7 −1.10468 −0.552342 0.833618i \(-0.686266\pi\)
−0.552342 + 0.833618i \(0.686266\pi\)
\(878\) −2.24615e7 −0.983338
\(879\) 2.74078e7 1.19647
\(880\) 5.24115e6 0.228150
\(881\) 1.60794e7 0.697961 0.348980 0.937130i \(-0.386528\pi\)
0.348980 + 0.937130i \(0.386528\pi\)
\(882\) −385011. −0.0166649
\(883\) −7.09137e6 −0.306075 −0.153038 0.988220i \(-0.548906\pi\)
−0.153038 + 0.988220i \(0.548906\pi\)
\(884\) −455067. −0.0195859
\(885\) −6.92182e6 −0.297072
\(886\) 8.40384e6 0.359661
\(887\) −1.00313e7 −0.428103 −0.214051 0.976822i \(-0.568666\pi\)
−0.214051 + 0.976822i \(0.568666\pi\)
\(888\) −4.16758e7 −1.77358
\(889\) 2.07252e7 0.879516
\(890\) −2.57714e7 −1.09059
\(891\) 9.44512e6 0.398578
\(892\) −285503. −0.0120143
\(893\) −7.31996e6 −0.307171
\(894\) −3.04622e7 −1.27473
\(895\) 1.07777e7 0.449747
\(896\) 2.14198e7 0.891344
\(897\) 3.74156e6 0.155264
\(898\) −2.94985e7 −1.22070
\(899\) 1.73213e6 0.0714795
\(900\) −53553.7 −0.00220386
\(901\) −5.95304e6 −0.244302
\(902\) −1.30930e7 −0.535826
\(903\) 1.74810e7 0.713421
\(904\) 4.14989e7 1.68894
\(905\) 1.71128e7 0.694543
\(906\) 3.98228e7 1.61180
\(907\) −2.99381e7 −1.20839 −0.604193 0.796838i \(-0.706505\pi\)
−0.604193 + 0.796838i \(0.706505\pi\)
\(908\) −2.54276e6 −0.102351
\(909\) −1.28469e6 −0.0515689
\(910\) 6.38222e6 0.255487
\(911\) 2.83738e7 1.13272 0.566360 0.824158i \(-0.308351\pi\)
0.566360 + 0.824158i \(0.308351\pi\)
\(912\) 2.76857e7 1.10222
\(913\) 8.32731e6 0.330619
\(914\) −1.76852e7 −0.700236
\(915\) −1.68734e7 −0.666269
\(916\) −1.21231e6 −0.0477391
\(917\) 3.72863e7 1.46429
\(918\) 1.43243e7 0.561006
\(919\) −3.91491e7 −1.52909 −0.764545 0.644570i \(-0.777036\pi\)
−0.764545 + 0.644570i \(0.777036\pi\)
\(920\) −3.96392e6 −0.154403
\(921\) 4.60590e7 1.78923
\(922\) −2.06762e7 −0.801019
\(923\) −4.80921e6 −0.185810
\(924\) −544911. −0.0209965
\(925\) −3.18233e7 −1.22290
\(926\) 2.21014e7 0.847019
\(927\) 1.91940e6 0.0733613
\(928\) −638672. −0.0243449
\(929\) 3.44851e6 0.131097 0.0655484 0.997849i \(-0.479120\pi\)
0.0655484 + 0.997849i \(0.479120\pi\)
\(930\) 6.06141e6 0.229809
\(931\) 8.78447e6 0.332156
\(932\) −2.03000e6 −0.0765519
\(933\) −4.14179e7 −1.55770
\(934\) −2.29514e7 −0.860879
\(935\) 3.20665e6 0.119956
\(936\) −680997. −0.0254071
\(937\) −3.55183e7 −1.32161 −0.660805 0.750558i \(-0.729785\pi\)
−0.660805 + 0.750558i \(0.729785\pi\)
\(938\) 2.32910e7 0.864334
\(939\) 2.35177e7 0.870425
\(940\) 304250. 0.0112308
\(941\) −8.10962e6 −0.298557 −0.149278 0.988795i \(-0.547695\pi\)
−0.149278 + 0.988795i \(0.547695\pi\)
\(942\) 4.53815e6 0.166629
\(943\) 1.05553e7 0.386538
\(944\) 1.49269e7 0.545180
\(945\) −1.23771e7 −0.450858
\(946\) −9.18886e6 −0.333836
\(947\) 1.58835e7 0.575535 0.287767 0.957700i \(-0.407087\pi\)
0.287767 + 0.957700i \(0.407087\pi\)
\(948\) −910781. −0.0329150
\(949\) 2.06191e7 0.743199
\(950\) 1.98328e7 0.712975
\(951\) 1.05698e7 0.378979
\(952\) 1.23417e7 0.441349
\(953\) −1.76043e7 −0.627893 −0.313946 0.949441i \(-0.601651\pi\)
−0.313946 + 0.949441i \(0.601651\pi\)
\(954\) 625988. 0.0222687
\(955\) −1.43422e7 −0.508871
\(956\) 1.24447e6 0.0440392
\(957\) −2.05190e6 −0.0724229
\(958\) −2.13433e7 −0.751361
\(959\) 1.97421e7 0.693180
\(960\) 1.52922e7 0.535541
\(961\) −2.43872e7 −0.851830
\(962\) 2.84353e7 0.990649
\(963\) 957534. 0.0332727
\(964\) 851464. 0.0295103
\(965\) 2.49709e7 0.863210
\(966\) 7.13032e6 0.245848
\(967\) −5.37843e7 −1.84965 −0.924825 0.380393i \(-0.875789\pi\)
−0.924825 + 0.380393i \(0.875789\pi\)
\(968\) 2.40430e7 0.824708
\(969\) 1.69387e7 0.579524
\(970\) 1.65591e7 0.565076
\(971\) 1.22227e7 0.416026 0.208013 0.978126i \(-0.433300\pi\)
0.208013 + 0.978126i \(0.433300\pi\)
\(972\) −190410. −0.00646435
\(973\) −3.36638e7 −1.13994
\(974\) −2.27880e7 −0.769678
\(975\) −1.10732e7 −0.373047
\(976\) 3.63875e7 1.22272
\(977\) 4.33000e6 0.145128 0.0725640 0.997364i \(-0.476882\pi\)
0.0725640 + 0.997364i \(0.476882\pi\)
\(978\) −1.39650e7 −0.466866
\(979\) 2.13652e7 0.712445
\(980\) −365122. −0.0121443
\(981\) −1.17299e6 −0.0389153
\(982\) 4.80392e7 1.58971
\(983\) 4.71098e7 1.55499 0.777494 0.628890i \(-0.216490\pi\)
0.777494 + 0.628890i \(0.216490\pi\)
\(984\) −4.09104e7 −1.34693
\(985\) −1.63873e7 −0.538168
\(986\) −3.26559e6 −0.106972
\(987\) 7.78855e6 0.254486
\(988\) −1.09180e6 −0.0355838
\(989\) 7.40786e6 0.240825
\(990\) −337194. −0.0109343
\(991\) −2.09978e7 −0.679187 −0.339594 0.940572i \(-0.610290\pi\)
−0.339594 + 0.940572i \(0.610290\pi\)
\(992\) −1.56411e6 −0.0504647
\(993\) 5.44145e7 1.75122
\(994\) −9.16495e6 −0.294215
\(995\) −9.51734e6 −0.304760
\(996\) −1.82833e6 −0.0583992
\(997\) −4.51805e7 −1.43951 −0.719753 0.694231i \(-0.755745\pi\)
−0.719753 + 0.694231i \(0.755745\pi\)
\(998\) 1.13946e7 0.362136
\(999\) −5.51448e7 −1.74820
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 29.6.a.b.1.5 7
3.2 odd 2 261.6.a.e.1.3 7
4.3 odd 2 464.6.a.k.1.3 7
5.4 even 2 725.6.a.b.1.3 7
29.28 even 2 841.6.a.b.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.a.b.1.5 7 1.1 even 1 trivial
261.6.a.e.1.3 7 3.2 odd 2
464.6.a.k.1.3 7 4.3 odd 2
725.6.a.b.1.3 7 5.4 even 2
841.6.a.b.1.3 7 29.28 even 2