Properties

Label 177.6.a.c.1.11
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + 15565376 x^{4} + 6775664 x^{3} - 75006848 x^{2} + 21512960 x + 49172480\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-8.49197\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.4920 q^{2} +9.00000 q^{3} +78.0815 q^{4} +46.0665 q^{5} +94.4278 q^{6} +183.145 q^{7} +483.486 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+10.4920 q^{2} +9.00000 q^{3} +78.0815 q^{4} +46.0665 q^{5} +94.4278 q^{6} +183.145 q^{7} +483.486 q^{8} +81.0000 q^{9} +483.328 q^{10} -536.597 q^{11} +702.734 q^{12} -601.772 q^{13} +1921.55 q^{14} +414.598 q^{15} +2574.11 q^{16} -1948.89 q^{17} +849.850 q^{18} -1829.58 q^{19} +3596.94 q^{20} +1648.31 q^{21} -5629.96 q^{22} -143.630 q^{23} +4351.37 q^{24} -1002.88 q^{25} -6313.78 q^{26} +729.000 q^{27} +14300.3 q^{28} +4181.48 q^{29} +4349.96 q^{30} +6331.93 q^{31} +11536.0 q^{32} -4829.37 q^{33} -20447.7 q^{34} +8436.86 q^{35} +6324.60 q^{36} -1983.22 q^{37} -19195.9 q^{38} -5415.95 q^{39} +22272.5 q^{40} +18079.8 q^{41} +17294.0 q^{42} -16207.9 q^{43} -41898.3 q^{44} +3731.39 q^{45} -1506.96 q^{46} +10082.4 q^{47} +23167.0 q^{48} +16735.2 q^{49} -10522.2 q^{50} -17540.0 q^{51} -46987.3 q^{52} +17087.2 q^{53} +7648.65 q^{54} -24719.1 q^{55} +88548.1 q^{56} -16466.2 q^{57} +43872.0 q^{58} -3481.00 q^{59} +32372.5 q^{60} -10827.9 q^{61} +66434.5 q^{62} +14834.8 q^{63} +38663.6 q^{64} -27721.5 q^{65} -50669.6 q^{66} +53212.3 q^{67} -152172. q^{68} -1292.67 q^{69} +88519.3 q^{70} -82455.8 q^{71} +39162.4 q^{72} -25989.7 q^{73} -20807.9 q^{74} -9025.91 q^{75} -142856. q^{76} -98275.1 q^{77} -56824.0 q^{78} +18631.5 q^{79} +118580. q^{80} +6561.00 q^{81} +189692. q^{82} +105042. q^{83} +128702. q^{84} -89778.4 q^{85} -170053. q^{86} +37633.3 q^{87} -259437. q^{88} -61443.6 q^{89} +39149.6 q^{90} -110212. q^{91} -11214.9 q^{92} +56987.4 q^{93} +105784. q^{94} -84282.2 q^{95} +103824. q^{96} +170505. q^{97} +175585. q^{98} -43464.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + O(q^{10}) \) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + 601q^{10} + 1480q^{11} + 1782q^{12} + 472q^{13} + 1065q^{14} + 1422q^{15} + 6370q^{16} + 1565q^{17} + 1782q^{18} + 3939q^{19} + 8033q^{20} + 3717q^{21} - 1738q^{22} + 7245q^{23} + 6507q^{24} + 9690q^{25} + 3764q^{26} + 8748q^{27} + 12154q^{28} + 10003q^{29} + 5409q^{30} + 7295q^{31} + 11628q^{32} + 13320q^{33} - 16344q^{34} + 11015q^{35} + 16038q^{36} + 6741q^{37} + 3035q^{38} + 4248q^{39} + 5572q^{40} + 34025q^{41} + 9585q^{42} - 6336q^{43} + 41168q^{44} + 12798q^{45} + 2345q^{46} + 66167q^{47} + 57330q^{48} + 28319q^{49} + 31173q^{50} + 14085q^{51} + 16440q^{52} + 62290q^{53} + 16038q^{54} + 55764q^{55} + 107306q^{56} + 35451q^{57} + 37952q^{58} - 41772q^{59} + 72297q^{60} + 68469q^{61} + 99190q^{62} + 33453q^{63} + 68525q^{64} + 80156q^{65} - 15642q^{66} + 113310q^{67} + 33887q^{68} + 65205q^{69} + 32034q^{70} + 84520q^{71} + 58563q^{72} + 135895q^{73} - 31962q^{74} + 87210q^{75} - 61848q^{76} - 3799q^{77} + 33876q^{78} + 14122q^{79} + 77609q^{80} + 78732q^{81} - 1501q^{82} + 114463q^{83} + 109386q^{84} - 101097q^{85} - 203536q^{86} + 90027q^{87} - 244967q^{88} + 189109q^{89} + 48681q^{90} - 168249q^{91} - 71946q^{92} + 65655q^{93} - 472284q^{94} + 21923q^{95} + 104652q^{96} - 76192q^{97} - 17544q^{98} + 119880q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.4920 1.85474 0.927368 0.374150i \(-0.122065\pi\)
0.927368 + 0.374150i \(0.122065\pi\)
\(3\) 9.00000 0.577350
\(4\) 78.0815 2.44005
\(5\) 46.0665 0.824062 0.412031 0.911170i \(-0.364819\pi\)
0.412031 + 0.911170i \(0.364819\pi\)
\(6\) 94.4278 1.07083
\(7\) 183.145 1.41270 0.706351 0.707862i \(-0.250340\pi\)
0.706351 + 0.707862i \(0.250340\pi\)
\(8\) 483.486 2.67091
\(9\) 81.0000 0.333333
\(10\) 483.328 1.52842
\(11\) −536.597 −1.33711 −0.668554 0.743664i \(-0.733086\pi\)
−0.668554 + 0.743664i \(0.733086\pi\)
\(12\) 702.734 1.40876
\(13\) −601.772 −0.987583 −0.493792 0.869580i \(-0.664389\pi\)
−0.493792 + 0.869580i \(0.664389\pi\)
\(14\) 1921.55 2.62019
\(15\) 414.598 0.475773
\(16\) 2574.11 2.51378
\(17\) −1948.89 −1.63555 −0.817776 0.575536i \(-0.804793\pi\)
−0.817776 + 0.575536i \(0.804793\pi\)
\(18\) 849.850 0.618245
\(19\) −1829.58 −1.16270 −0.581349 0.813654i \(-0.697475\pi\)
−0.581349 + 0.813654i \(0.697475\pi\)
\(20\) 3596.94 2.01075
\(21\) 1648.31 0.815624
\(22\) −5629.96 −2.47998
\(23\) −143.630 −0.0566143 −0.0283071 0.999599i \(-0.509012\pi\)
−0.0283071 + 0.999599i \(0.509012\pi\)
\(24\) 4351.37 1.54205
\(25\) −1002.88 −0.320921
\(26\) −6313.78 −1.83171
\(27\) 729.000 0.192450
\(28\) 14300.3 3.44706
\(29\) 4181.48 0.923284 0.461642 0.887066i \(-0.347261\pi\)
0.461642 + 0.887066i \(0.347261\pi\)
\(30\) 4349.96 0.882433
\(31\) 6331.93 1.18340 0.591701 0.806158i \(-0.298457\pi\)
0.591701 + 0.806158i \(0.298457\pi\)
\(32\) 11536.0 1.99150
\(33\) −4829.37 −0.771980
\(34\) −20447.7 −3.03352
\(35\) 8436.86 1.16415
\(36\) 6324.60 0.813349
\(37\) −1983.22 −0.238159 −0.119079 0.992885i \(-0.537994\pi\)
−0.119079 + 0.992885i \(0.537994\pi\)
\(38\) −19195.9 −2.15650
\(39\) −5415.95 −0.570181
\(40\) 22272.5 2.20099
\(41\) 18079.8 1.67970 0.839852 0.542815i \(-0.182641\pi\)
0.839852 + 0.542815i \(0.182641\pi\)
\(42\) 17294.0 1.51277
\(43\) −16207.9 −1.33677 −0.668383 0.743817i \(-0.733013\pi\)
−0.668383 + 0.743817i \(0.733013\pi\)
\(44\) −41898.3 −3.26261
\(45\) 3731.39 0.274687
\(46\) −1506.96 −0.105005
\(47\) 10082.4 0.665763 0.332881 0.942969i \(-0.391979\pi\)
0.332881 + 0.942969i \(0.391979\pi\)
\(48\) 23167.0 1.45133
\(49\) 16735.2 0.995726
\(50\) −10522.2 −0.595224
\(51\) −17540.0 −0.944287
\(52\) −46987.3 −2.40975
\(53\) 17087.2 0.835565 0.417783 0.908547i \(-0.362807\pi\)
0.417783 + 0.908547i \(0.362807\pi\)
\(54\) 7648.65 0.356944
\(55\) −24719.1 −1.10186
\(56\) 88548.1 3.77320
\(57\) −16466.2 −0.671284
\(58\) 43872.0 1.71245
\(59\) −3481.00 −0.130189
\(60\) 32372.5 1.16091
\(61\) −10827.9 −0.372582 −0.186291 0.982495i \(-0.559647\pi\)
−0.186291 + 0.982495i \(0.559647\pi\)
\(62\) 66434.5 2.19490
\(63\) 14834.8 0.470901
\(64\) 38663.6 1.17992
\(65\) −27721.5 −0.813830
\(66\) −50669.6 −1.43182
\(67\) 53212.3 1.44819 0.724094 0.689701i \(-0.242258\pi\)
0.724094 + 0.689701i \(0.242258\pi\)
\(68\) −152172. −3.99082
\(69\) −1292.67 −0.0326863
\(70\) 88519.3 2.15920
\(71\) −82455.8 −1.94122 −0.970611 0.240653i \(-0.922638\pi\)
−0.970611 + 0.240653i \(0.922638\pi\)
\(72\) 39162.4 0.890303
\(73\) −25989.7 −0.570813 −0.285406 0.958407i \(-0.592129\pi\)
−0.285406 + 0.958407i \(0.592129\pi\)
\(74\) −20807.9 −0.441722
\(75\) −9025.91 −0.185284
\(76\) −142856. −2.83704
\(77\) −98275.1 −1.88893
\(78\) −56824.0 −1.05754
\(79\) 18631.5 0.335877 0.167938 0.985798i \(-0.446289\pi\)
0.167938 + 0.985798i \(0.446289\pi\)
\(80\) 118580. 2.07151
\(81\) 6561.00 0.111111
\(82\) 189692. 3.11541
\(83\) 105042. 1.67367 0.836833 0.547458i \(-0.184404\pi\)
0.836833 + 0.547458i \(0.184404\pi\)
\(84\) 128702. 1.99016
\(85\) −89778.4 −1.34780
\(86\) −170053. −2.47935
\(87\) 37633.3 0.533058
\(88\) −259437. −3.57129
\(89\) −61443.6 −0.822246 −0.411123 0.911580i \(-0.634863\pi\)
−0.411123 + 0.911580i \(0.634863\pi\)
\(90\) 39149.6 0.509473
\(91\) −110212. −1.39516
\(92\) −11214.9 −0.138142
\(93\) 56987.4 0.683237
\(94\) 105784. 1.23481
\(95\) −84282.2 −0.958136
\(96\) 103824. 1.14979
\(97\) 170505. 1.83996 0.919980 0.391966i \(-0.128205\pi\)
0.919980 + 0.391966i \(0.128205\pi\)
\(98\) 175585. 1.84681
\(99\) −43464.3 −0.445703
\(100\) −78306.3 −0.783063
\(101\) 38589.6 0.376415 0.188208 0.982129i \(-0.439732\pi\)
0.188208 + 0.982129i \(0.439732\pi\)
\(102\) −184029. −1.75140
\(103\) −8597.79 −0.0798534 −0.0399267 0.999203i \(-0.512712\pi\)
−0.0399267 + 0.999203i \(0.512712\pi\)
\(104\) −290948. −2.63774
\(105\) 75931.7 0.672125
\(106\) 179278. 1.54975
\(107\) −45162.4 −0.381345 −0.190672 0.981654i \(-0.561067\pi\)
−0.190672 + 0.981654i \(0.561067\pi\)
\(108\) 56921.4 0.469587
\(109\) 74420.5 0.599966 0.299983 0.953945i \(-0.403019\pi\)
0.299983 + 0.953945i \(0.403019\pi\)
\(110\) −259352. −2.04366
\(111\) −17849.0 −0.137501
\(112\) 471437. 3.55123
\(113\) 119180. 0.878026 0.439013 0.898481i \(-0.355328\pi\)
0.439013 + 0.898481i \(0.355328\pi\)
\(114\) −172763. −1.24506
\(115\) −6616.54 −0.0466537
\(116\) 326496. 2.25286
\(117\) −48743.5 −0.329194
\(118\) −36522.6 −0.241466
\(119\) −356929. −2.31055
\(120\) 200453. 1.27074
\(121\) 126885. 0.787857
\(122\) −113607. −0.691041
\(123\) 162718. 0.969778
\(124\) 494407. 2.88756
\(125\) −190157. −1.08852
\(126\) 155646. 0.873396
\(127\) 187431. 1.03118 0.515588 0.856837i \(-0.327574\pi\)
0.515588 + 0.856837i \(0.327574\pi\)
\(128\) 36506.0 0.196942
\(129\) −145871. −0.771783
\(130\) −290854. −1.50944
\(131\) 200431. 1.02044 0.510220 0.860044i \(-0.329564\pi\)
0.510220 + 0.860044i \(0.329564\pi\)
\(132\) −377085. −1.88367
\(133\) −335078. −1.64255
\(134\) 558302. 2.68601
\(135\) 33582.5 0.158591
\(136\) −942260. −4.36841
\(137\) 65393.6 0.297669 0.148834 0.988862i \(-0.452448\pi\)
0.148834 + 0.988862i \(0.452448\pi\)
\(138\) −13562.7 −0.0606244
\(139\) −102562. −0.450245 −0.225123 0.974330i \(-0.572278\pi\)
−0.225123 + 0.974330i \(0.572278\pi\)
\(140\) 658762. 2.84059
\(141\) 90741.7 0.384378
\(142\) −865124. −3.60046
\(143\) 322909. 1.32051
\(144\) 208503. 0.837928
\(145\) 192626. 0.760843
\(146\) −272683. −1.05871
\(147\) 150617. 0.574883
\(148\) −154853. −0.581119
\(149\) 412586. 1.52247 0.761235 0.648476i \(-0.224593\pi\)
0.761235 + 0.648476i \(0.224593\pi\)
\(150\) −94699.6 −0.343653
\(151\) −344222. −1.22856 −0.614280 0.789088i \(-0.710553\pi\)
−0.614280 + 0.789088i \(0.710553\pi\)
\(152\) −884575. −3.10546
\(153\) −157860. −0.545184
\(154\) −1.03110e6 −3.50348
\(155\) 291690. 0.975197
\(156\) −422885. −1.39127
\(157\) −69151.6 −0.223900 −0.111950 0.993714i \(-0.535710\pi\)
−0.111950 + 0.993714i \(0.535710\pi\)
\(158\) 195481. 0.622963
\(159\) 153784. 0.482414
\(160\) 531422. 1.64112
\(161\) −26305.2 −0.0799791
\(162\) 68837.8 0.206082
\(163\) −435248. −1.28312 −0.641561 0.767072i \(-0.721713\pi\)
−0.641561 + 0.767072i \(0.721713\pi\)
\(164\) 1.41169e6 4.09856
\(165\) −222472. −0.636159
\(166\) 1.10210e6 3.10421
\(167\) −282385. −0.783521 −0.391761 0.920067i \(-0.628134\pi\)
−0.391761 + 0.920067i \(0.628134\pi\)
\(168\) 796933. 2.17846
\(169\) −9163.31 −0.0246795
\(170\) −941952. −2.49981
\(171\) −148196. −0.387566
\(172\) −1.26554e6 −3.26177
\(173\) −542664. −1.37853 −0.689265 0.724510i \(-0.742066\pi\)
−0.689265 + 0.724510i \(0.742066\pi\)
\(174\) 394848. 0.988682
\(175\) −183672. −0.453366
\(176\) −1.38126e6 −3.36120
\(177\) −31329.0 −0.0751646
\(178\) −644665. −1.52505
\(179\) −36141.3 −0.0843084 −0.0421542 0.999111i \(-0.513422\pi\)
−0.0421542 + 0.999111i \(0.513422\pi\)
\(180\) 291352. 0.670250
\(181\) −597328. −1.35524 −0.677620 0.735412i \(-0.736989\pi\)
−0.677620 + 0.735412i \(0.736989\pi\)
\(182\) −1.15634e6 −2.58765
\(183\) −97451.5 −0.215110
\(184\) −69443.2 −0.151212
\(185\) −91360.0 −0.196258
\(186\) 597910. 1.26723
\(187\) 1.04577e6 2.18691
\(188\) 787250. 1.62449
\(189\) 133513. 0.271875
\(190\) −884287. −1.77709
\(191\) 653350. 1.29587 0.647936 0.761695i \(-0.275632\pi\)
0.647936 + 0.761695i \(0.275632\pi\)
\(192\) 347972. 0.681227
\(193\) −339340. −0.655755 −0.327878 0.944720i \(-0.606333\pi\)
−0.327878 + 0.944720i \(0.606333\pi\)
\(194\) 1.78894e6 3.41264
\(195\) −249494. −0.469865
\(196\) 1.30671e6 2.42962
\(197\) −375530. −0.689411 −0.344706 0.938711i \(-0.612021\pi\)
−0.344706 + 0.938711i \(0.612021\pi\)
\(198\) −456027. −0.826661
\(199\) −314088. −0.562235 −0.281118 0.959673i \(-0.590705\pi\)
−0.281118 + 0.959673i \(0.590705\pi\)
\(200\) −484878. −0.857151
\(201\) 478911. 0.836112
\(202\) 404882. 0.698151
\(203\) 765818. 1.30432
\(204\) −1.36955e6 −2.30410
\(205\) 832871. 1.38418
\(206\) −90207.8 −0.148107
\(207\) −11634.0 −0.0188714
\(208\) −1.54903e6 −2.48257
\(209\) 981746. 1.55465
\(210\) 796673. 1.24661
\(211\) −383881. −0.593595 −0.296797 0.954941i \(-0.595919\pi\)
−0.296797 + 0.954941i \(0.595919\pi\)
\(212\) 1.33419e6 2.03882
\(213\) −742102. −1.12077
\(214\) −473843. −0.707294
\(215\) −746641. −1.10158
\(216\) 352461. 0.514017
\(217\) 1.15966e6 1.67179
\(218\) 780818. 1.11278
\(219\) −233907. −0.329559
\(220\) −1.93011e6 −2.68859
\(221\) 1.17279e6 1.61524
\(222\) −187271. −0.255028
\(223\) −507820. −0.683829 −0.341915 0.939731i \(-0.611075\pi\)
−0.341915 + 0.939731i \(0.611075\pi\)
\(224\) 2.11276e6 2.81339
\(225\) −81233.2 −0.106974
\(226\) 1.25043e6 1.62851
\(227\) 1.23528e6 1.59111 0.795554 0.605882i \(-0.207180\pi\)
0.795554 + 0.605882i \(0.207180\pi\)
\(228\) −1.28571e6 −1.63796
\(229\) 941944. 1.18696 0.593481 0.804848i \(-0.297753\pi\)
0.593481 + 0.804848i \(0.297753\pi\)
\(230\) −69420.5 −0.0865303
\(231\) −884476. −1.09058
\(232\) 2.02169e6 2.46601
\(233\) 249966. 0.301641 0.150821 0.988561i \(-0.451808\pi\)
0.150821 + 0.988561i \(0.451808\pi\)
\(234\) −511416. −0.610569
\(235\) 464461. 0.548630
\(236\) −271802. −0.317667
\(237\) 167683. 0.193918
\(238\) −3.74489e6 −4.28546
\(239\) 1.41078e6 1.59759 0.798794 0.601604i \(-0.205472\pi\)
0.798794 + 0.601604i \(0.205472\pi\)
\(240\) 1.06722e6 1.19599
\(241\) 25730.6 0.0285369 0.0142685 0.999898i \(-0.495458\pi\)
0.0142685 + 0.999898i \(0.495458\pi\)
\(242\) 1.33128e6 1.46127
\(243\) 59049.0 0.0641500
\(244\) −845462. −0.909117
\(245\) 770930. 0.820540
\(246\) 1.70723e6 1.79868
\(247\) 1.10099e6 1.14826
\(248\) 3.06140e6 3.16076
\(249\) 945381. 0.966292
\(250\) −1.99512e6 −2.01892
\(251\) −1.03590e6 −1.03785 −0.518925 0.854820i \(-0.673668\pi\)
−0.518925 + 0.854820i \(0.673668\pi\)
\(252\) 1.15832e6 1.14902
\(253\) 77071.5 0.0756994
\(254\) 1.96652e6 1.91256
\(255\) −808005. −0.778151
\(256\) −854215. −0.814643
\(257\) 1.04974e6 0.991403 0.495702 0.868493i \(-0.334911\pi\)
0.495702 + 0.868493i \(0.334911\pi\)
\(258\) −1.53048e6 −1.43145
\(259\) −363217. −0.336447
\(260\) −2.16454e6 −1.98578
\(261\) 338700. 0.307761
\(262\) 2.10292e6 1.89265
\(263\) −1.38970e6 −1.23889 −0.619445 0.785040i \(-0.712642\pi\)
−0.619445 + 0.785040i \(0.712642\pi\)
\(264\) −2.33493e6 −2.06189
\(265\) 787146. 0.688558
\(266\) −3.51563e6 −3.04649
\(267\) −552993. −0.474724
\(268\) 4.15490e6 3.53365
\(269\) −1.65552e6 −1.39494 −0.697469 0.716615i \(-0.745690\pi\)
−0.697469 + 0.716615i \(0.745690\pi\)
\(270\) 352346. 0.294144
\(271\) 890523. 0.736583 0.368292 0.929710i \(-0.379943\pi\)
0.368292 + 0.929710i \(0.379943\pi\)
\(272\) −5.01666e6 −4.11142
\(273\) −991905. −0.805496
\(274\) 686107. 0.552097
\(275\) 538142. 0.429106
\(276\) −100934. −0.0797561
\(277\) −748295. −0.585967 −0.292984 0.956117i \(-0.594648\pi\)
−0.292984 + 0.956117i \(0.594648\pi\)
\(278\) −1.07608e6 −0.835087
\(279\) 512887. 0.394467
\(280\) 4.07910e6 3.10935
\(281\) 110769. 0.0836861 0.0418430 0.999124i \(-0.486677\pi\)
0.0418430 + 0.999124i \(0.486677\pi\)
\(282\) 952059. 0.712921
\(283\) −220603. −0.163736 −0.0818682 0.996643i \(-0.526089\pi\)
−0.0818682 + 0.996643i \(0.526089\pi\)
\(284\) −6.43827e6 −4.73667
\(285\) −758540. −0.553180
\(286\) 3.38795e6 2.44919
\(287\) 3.31122e6 2.37292
\(288\) 934415. 0.663833
\(289\) 2.37830e6 1.67503
\(290\) 2.02103e6 1.41116
\(291\) 1.53455e6 1.06230
\(292\) −2.02931e6 −1.39281
\(293\) 1.55524e6 1.05835 0.529173 0.848514i \(-0.322502\pi\)
0.529173 + 0.848514i \(0.322502\pi\)
\(294\) 1.58026e6 1.06626
\(295\) −160357. −0.107284
\(296\) −958859. −0.636100
\(297\) −391179. −0.257327
\(298\) 4.32884e6 2.82378
\(299\) 86432.6 0.0559113
\(300\) −704757. −0.452102
\(301\) −2.96840e6 −1.88845
\(302\) −3.61157e6 −2.27865
\(303\) 347307. 0.217324
\(304\) −4.70954e6 −2.92277
\(305\) −498805. −0.307031
\(306\) −1.65626e6 −1.01117
\(307\) −1.00187e6 −0.606686 −0.303343 0.952881i \(-0.598103\pi\)
−0.303343 + 0.952881i \(0.598103\pi\)
\(308\) −7.67347e6 −4.60909
\(309\) −77380.1 −0.0461034
\(310\) 3.06040e6 1.80873
\(311\) 2.66702e6 1.56360 0.781800 0.623529i \(-0.214302\pi\)
0.781800 + 0.623529i \(0.214302\pi\)
\(312\) −2.61854e6 −1.52290
\(313\) 1.88511e6 1.08762 0.543808 0.839210i \(-0.316982\pi\)
0.543808 + 0.839210i \(0.316982\pi\)
\(314\) −725537. −0.415275
\(315\) 683385. 0.388051
\(316\) 1.45477e6 0.819555
\(317\) −2.77185e6 −1.54925 −0.774624 0.632422i \(-0.782061\pi\)
−0.774624 + 0.632422i \(0.782061\pi\)
\(318\) 1.61350e6 0.894750
\(319\) −2.24377e6 −1.23453
\(320\) 1.78110e6 0.972327
\(321\) −406462. −0.220169
\(322\) −275993. −0.148340
\(323\) 3.56564e6 1.90165
\(324\) 512293. 0.271116
\(325\) 603505. 0.316936
\(326\) −4.56661e6 −2.37985
\(327\) 669785. 0.346390
\(328\) 8.74131e6 4.48634
\(329\) 1.84654e6 0.940524
\(330\) −2.33417e6 −1.17991
\(331\) −3.55141e6 −1.78168 −0.890842 0.454312i \(-0.849885\pi\)
−0.890842 + 0.454312i \(0.849885\pi\)
\(332\) 8.20186e6 4.08383
\(333\) −160641. −0.0793863
\(334\) −2.96278e6 −1.45323
\(335\) 2.45130e6 1.19340
\(336\) 4.24293e6 2.05030
\(337\) 3.41206e6 1.63660 0.818298 0.574794i \(-0.194918\pi\)
0.818298 + 0.574794i \(0.194918\pi\)
\(338\) −96141.2 −0.0457739
\(339\) 1.07262e6 0.506928
\(340\) −7.01003e6 −3.28869
\(341\) −3.39770e6 −1.58234
\(342\) −1.55487e6 −0.718833
\(343\) −13155.6 −0.00603774
\(344\) −7.83629e6 −3.57038
\(345\) −59548.8 −0.0269355
\(346\) −5.69362e6 −2.55681
\(347\) −111495. −0.0497088 −0.0248544 0.999691i \(-0.507912\pi\)
−0.0248544 + 0.999691i \(0.507912\pi\)
\(348\) 2.93847e6 1.30069
\(349\) −691993. −0.304115 −0.152058 0.988372i \(-0.548590\pi\)
−0.152058 + 0.988372i \(0.548590\pi\)
\(350\) −1.92709e6 −0.840875
\(351\) −438692. −0.190060
\(352\) −6.19017e6 −2.66285
\(353\) −2.81613e6 −1.20286 −0.601432 0.798924i \(-0.705403\pi\)
−0.601432 + 0.798924i \(0.705403\pi\)
\(354\) −328703. −0.139411
\(355\) −3.79845e6 −1.59969
\(356\) −4.79761e6 −2.00632
\(357\) −3.21236e6 −1.33400
\(358\) −379193. −0.156370
\(359\) 2.09260e6 0.856940 0.428470 0.903556i \(-0.359053\pi\)
0.428470 + 0.903556i \(0.359053\pi\)
\(360\) 1.80407e6 0.733665
\(361\) 871258. 0.351867
\(362\) −6.26715e6 −2.51361
\(363\) 1.14197e6 0.454870
\(364\) −8.60549e6 −3.40426
\(365\) −1.19725e6 −0.470385
\(366\) −1.02246e6 −0.398973
\(367\) 3.12044e6 1.20935 0.604674 0.796473i \(-0.293304\pi\)
0.604674 + 0.796473i \(0.293304\pi\)
\(368\) −369720. −0.142316
\(369\) 1.46446e6 0.559902
\(370\) −958547. −0.364006
\(371\) 3.12943e6 1.18040
\(372\) 4.44966e6 1.66713
\(373\) −696892. −0.259354 −0.129677 0.991556i \(-0.541394\pi\)
−0.129677 + 0.991556i \(0.541394\pi\)
\(374\) 1.09722e7 4.05614
\(375\) −1.71141e6 −0.628458
\(376\) 4.87470e6 1.77819
\(377\) −2.51630e6 −0.911820
\(378\) 1.40081e6 0.504256
\(379\) −5.00770e6 −1.79077 −0.895386 0.445291i \(-0.853100\pi\)
−0.895386 + 0.445291i \(0.853100\pi\)
\(380\) −6.58088e6 −2.33790
\(381\) 1.68688e6 0.595349
\(382\) 6.85493e6 2.40350
\(383\) 359356. 0.125178 0.0625890 0.998039i \(-0.480064\pi\)
0.0625890 + 0.998039i \(0.480064\pi\)
\(384\) 328554. 0.113705
\(385\) −4.52719e6 −1.55660
\(386\) −3.56035e6 −1.21625
\(387\) −1.31284e6 −0.445589
\(388\) 1.33133e7 4.48959
\(389\) 2.58030e6 0.864561 0.432280 0.901739i \(-0.357709\pi\)
0.432280 + 0.901739i \(0.357709\pi\)
\(390\) −2.61768e6 −0.871476
\(391\) 279919. 0.0925956
\(392\) 8.09122e6 2.65949
\(393\) 1.80388e6 0.589152
\(394\) −3.94005e6 −1.27868
\(395\) 858287. 0.276783
\(396\) −3.39376e6 −1.08754
\(397\) −2.84643e6 −0.906409 −0.453204 0.891407i \(-0.649719\pi\)
−0.453204 + 0.891407i \(0.649719\pi\)
\(398\) −3.29540e6 −1.04280
\(399\) −3.01571e6 −0.948324
\(400\) −2.58153e6 −0.806727
\(401\) −2.13470e6 −0.662944 −0.331472 0.943465i \(-0.607545\pi\)
−0.331472 + 0.943465i \(0.607545\pi\)
\(402\) 5.02472e6 1.55077
\(403\) −3.81038e6 −1.16871
\(404\) 3.01314e6 0.918471
\(405\) 302242. 0.0915625
\(406\) 8.03495e6 2.41918
\(407\) 1.06419e6 0.318444
\(408\) −8.48034e6 −2.52210
\(409\) 1.68398e6 0.497771 0.248885 0.968533i \(-0.419936\pi\)
0.248885 + 0.968533i \(0.419936\pi\)
\(410\) 8.73846e6 2.56729
\(411\) 588542. 0.171859
\(412\) −671328. −0.194846
\(413\) −637528. −0.183918
\(414\) −122064. −0.0350015
\(415\) 4.83893e6 1.37921
\(416\) −6.94203e6 −1.96677
\(417\) −923058. −0.259949
\(418\) 1.03005e7 2.88347
\(419\) 6.14268e6 1.70932 0.854659 0.519190i \(-0.173766\pi\)
0.854659 + 0.519190i \(0.173766\pi\)
\(420\) 5.92886e6 1.64002
\(421\) −1.00451e6 −0.276217 −0.138108 0.990417i \(-0.544102\pi\)
−0.138108 + 0.990417i \(0.544102\pi\)
\(422\) −4.02766e6 −1.10096
\(423\) 816675. 0.221921
\(424\) 8.26141e6 2.23172
\(425\) 1.95450e6 0.524884
\(426\) −7.78612e6 −2.07872
\(427\) −1.98309e6 −0.526347
\(428\) −3.52635e6 −0.930499
\(429\) 2.90618e6 0.762394
\(430\) −7.83374e6 −2.04314
\(431\) 2.54886e6 0.660927 0.330464 0.943819i \(-0.392795\pi\)
0.330464 + 0.943819i \(0.392795\pi\)
\(432\) 1.87653e6 0.483778
\(433\) −4.98914e6 −1.27881 −0.639404 0.768871i \(-0.720819\pi\)
−0.639404 + 0.768871i \(0.720819\pi\)
\(434\) 1.21672e7 3.10074
\(435\) 1.73364e6 0.439273
\(436\) 5.81087e6 1.46395
\(437\) 262783. 0.0658253
\(438\) −2.45415e6 −0.611245
\(439\) −996560. −0.246798 −0.123399 0.992357i \(-0.539380\pi\)
−0.123399 + 0.992357i \(0.539380\pi\)
\(440\) −1.19514e7 −2.94297
\(441\) 1.35555e6 0.331909
\(442\) 1.23048e7 2.99585
\(443\) −6.09227e6 −1.47493 −0.737463 0.675388i \(-0.763976\pi\)
−0.737463 + 0.675388i \(0.763976\pi\)
\(444\) −1.39368e6 −0.335509
\(445\) −2.83049e6 −0.677582
\(446\) −5.32804e6 −1.26832
\(447\) 3.71327e6 0.878999
\(448\) 7.08105e6 1.66687
\(449\) 1.80157e6 0.421732 0.210866 0.977515i \(-0.432372\pi\)
0.210866 + 0.977515i \(0.432372\pi\)
\(450\) −852297. −0.198408
\(451\) −9.70154e6 −2.24595
\(452\) 9.30576e6 2.14242
\(453\) −3.09800e6 −0.709309
\(454\) 1.29605e7 2.95109
\(455\) −5.07706e6 −1.14970
\(456\) −7.96118e6 −1.79294
\(457\) −3.51589e6 −0.787489 −0.393744 0.919220i \(-0.628820\pi\)
−0.393744 + 0.919220i \(0.628820\pi\)
\(458\) 9.88286e6 2.20150
\(459\) −1.42074e6 −0.314762
\(460\) −516629. −0.113837
\(461\) 6.94554e6 1.52214 0.761068 0.648672i \(-0.224675\pi\)
0.761068 + 0.648672i \(0.224675\pi\)
\(462\) −9.27990e6 −2.02273
\(463\) −4.78918e6 −1.03827 −0.519133 0.854693i \(-0.673745\pi\)
−0.519133 + 0.854693i \(0.673745\pi\)
\(464\) 1.07636e7 2.32094
\(465\) 2.62521e6 0.563030
\(466\) 2.62264e6 0.559465
\(467\) 2.62555e6 0.557094 0.278547 0.960423i \(-0.410147\pi\)
0.278547 + 0.960423i \(0.410147\pi\)
\(468\) −3.80597e6 −0.803250
\(469\) 9.74557e6 2.04586
\(470\) 4.87311e6 1.01756
\(471\) −622365. −0.129269
\(472\) −1.68301e6 −0.347723
\(473\) 8.69711e6 1.78740
\(474\) 1.75933e6 0.359668
\(475\) 1.83485e6 0.373135
\(476\) −2.78696e7 −5.63784
\(477\) 1.38406e6 0.278522
\(478\) 1.48019e7 2.96311
\(479\) −2.10029e6 −0.418255 −0.209128 0.977888i \(-0.567062\pi\)
−0.209128 + 0.977888i \(0.567062\pi\)
\(480\) 4.78280e6 0.947500
\(481\) 1.19345e6 0.235202
\(482\) 269965. 0.0529285
\(483\) −236747. −0.0461760
\(484\) 9.90739e6 1.92241
\(485\) 7.85458e6 1.51624
\(486\) 619541. 0.118981
\(487\) −3.94358e6 −0.753474 −0.376737 0.926320i \(-0.622954\pi\)
−0.376737 + 0.926320i \(0.622954\pi\)
\(488\) −5.23516e6 −0.995131
\(489\) −3.91723e6 −0.740811
\(490\) 8.08858e6 1.52189
\(491\) 377373. 0.0706427 0.0353213 0.999376i \(-0.488755\pi\)
0.0353213 + 0.999376i \(0.488755\pi\)
\(492\) 1.27053e7 2.36630
\(493\) −8.14924e6 −1.51008
\(494\) 1.15515e7 2.12972
\(495\) −2.00225e6 −0.367287
\(496\) 1.62991e7 2.97482
\(497\) −1.51014e7 −2.74237
\(498\) 9.91891e6 1.79222
\(499\) −2.96483e6 −0.533026 −0.266513 0.963831i \(-0.585872\pi\)
−0.266513 + 0.963831i \(0.585872\pi\)
\(500\) −1.48477e7 −2.65604
\(501\) −2.54147e6 −0.452366
\(502\) −1.08687e7 −1.92494
\(503\) −3.33200e6 −0.587198 −0.293599 0.955929i \(-0.594853\pi\)
−0.293599 + 0.955929i \(0.594853\pi\)
\(504\) 7.17240e6 1.25773
\(505\) 1.77769e6 0.310190
\(506\) 808632. 0.140402
\(507\) −82469.8 −0.0142487
\(508\) 1.46349e7 2.51612
\(509\) −3.15713e6 −0.540129 −0.270065 0.962842i \(-0.587045\pi\)
−0.270065 + 0.962842i \(0.587045\pi\)
\(510\) −8.47757e6 −1.44326
\(511\) −4.75988e6 −0.806388
\(512\) −1.01306e7 −1.70789
\(513\) −1.33376e6 −0.223761
\(514\) 1.10139e7 1.83879
\(515\) −396070. −0.0658042
\(516\) −1.13898e7 −1.88319
\(517\) −5.41019e6 −0.890197
\(518\) −3.81087e6 −0.624021
\(519\) −4.88398e6 −0.795894
\(520\) −1.34030e7 −2.17367
\(521\) −9.78221e6 −1.57886 −0.789429 0.613842i \(-0.789623\pi\)
−0.789429 + 0.613842i \(0.789623\pi\)
\(522\) 3.55363e6 0.570816
\(523\) 1.09469e7 1.75000 0.874999 0.484124i \(-0.160862\pi\)
0.874999 + 0.484124i \(0.160862\pi\)
\(524\) 1.56500e7 2.48992
\(525\) −1.65305e6 −0.261751
\(526\) −1.45807e7 −2.29781
\(527\) −1.23402e7 −1.93552
\(528\) −1.24314e7 −1.94059
\(529\) −6.41571e6 −0.996795
\(530\) 8.25871e6 1.27709
\(531\) −281961. −0.0433963
\(532\) −2.61634e7 −4.00789
\(533\) −1.08799e7 −1.65885
\(534\) −5.80198e6 −0.880488
\(535\) −2.08047e6 −0.314252
\(536\) 2.57274e7 3.86798
\(537\) −325271. −0.0486755
\(538\) −1.73697e7 −2.58724
\(539\) −8.98004e6 −1.33139
\(540\) 2.62217e6 0.386969
\(541\) −9.12573e6 −1.34052 −0.670262 0.742125i \(-0.733818\pi\)
−0.670262 + 0.742125i \(0.733818\pi\)
\(542\) 9.34334e6 1.36617
\(543\) −5.37595e6 −0.782449
\(544\) −2.24823e7 −3.25720
\(545\) 3.42829e6 0.494409
\(546\) −1.04070e7 −1.49398
\(547\) 6.24984e6 0.893100 0.446550 0.894759i \(-0.352652\pi\)
0.446550 + 0.894759i \(0.352652\pi\)
\(548\) 5.10603e6 0.726326
\(549\) −877064. −0.124194
\(550\) 5.64617e6 0.795879
\(551\) −7.65035e6 −1.07350
\(552\) −624989. −0.0873020
\(553\) 3.41227e6 0.474493
\(554\) −7.85109e6 −1.08681
\(555\) −822240. −0.113309
\(556\) −8.00819e6 −1.09862
\(557\) −8.18033e6 −1.11721 −0.558603 0.829435i \(-0.688662\pi\)
−0.558603 + 0.829435i \(0.688662\pi\)
\(558\) 5.38119e6 0.731633
\(559\) 9.75346e6 1.32017
\(560\) 2.17174e7 2.92643
\(561\) 9.41190e6 1.26261
\(562\) 1.16219e6 0.155216
\(563\) 6.48080e6 0.861704 0.430852 0.902423i \(-0.358213\pi\)
0.430852 + 0.902423i \(0.358213\pi\)
\(564\) 7.08525e6 0.937901
\(565\) 5.49020e6 0.723548
\(566\) −2.31456e6 −0.303688
\(567\) 1.20162e6 0.156967
\(568\) −3.98662e7 −5.18483
\(569\) −708193. −0.0917004 −0.0458502 0.998948i \(-0.514600\pi\)
−0.0458502 + 0.998948i \(0.514600\pi\)
\(570\) −7.95858e6 −1.02600
\(571\) 4.84800e6 0.622260 0.311130 0.950367i \(-0.399292\pi\)
0.311130 + 0.950367i \(0.399292\pi\)
\(572\) 2.52132e7 3.22209
\(573\) 5.88015e6 0.748172
\(574\) 3.47412e7 4.40114
\(575\) 144044. 0.0181687
\(576\) 3.13175e6 0.393307
\(577\) 5.03751e6 0.629907 0.314954 0.949107i \(-0.398011\pi\)
0.314954 + 0.949107i \(0.398011\pi\)
\(578\) 2.49531e7 3.10674
\(579\) −3.05406e6 −0.378600
\(580\) 1.50405e7 1.85649
\(581\) 1.92380e7 2.36439
\(582\) 1.61004e7 1.97029
\(583\) −9.16892e6 −1.11724
\(584\) −1.25656e7 −1.52459
\(585\) −2.24544e6 −0.271277
\(586\) 1.63175e7 1.96295
\(587\) −714405. −0.0855755 −0.0427878 0.999084i \(-0.513624\pi\)
−0.0427878 + 0.999084i \(0.513624\pi\)
\(588\) 1.17604e7 1.40274
\(589\) −1.15848e7 −1.37594
\(590\) −1.68247e6 −0.198983
\(591\) −3.37977e6 −0.398032
\(592\) −5.10504e6 −0.598680
\(593\) 1.42859e7 1.66829 0.834145 0.551545i \(-0.185962\pi\)
0.834145 + 0.551545i \(0.185962\pi\)
\(594\) −4.10424e6 −0.477273
\(595\) −1.64425e7 −1.90404
\(596\) 3.22153e7 3.71490
\(597\) −2.82679e6 −0.324607
\(598\) 906849. 0.103701
\(599\) 1.22307e7 1.39279 0.696395 0.717659i \(-0.254786\pi\)
0.696395 + 0.717659i \(0.254786\pi\)
\(600\) −4.36390e6 −0.494877
\(601\) 1.62678e7 1.83714 0.918571 0.395257i \(-0.129344\pi\)
0.918571 + 0.395257i \(0.129344\pi\)
\(602\) −3.11444e7 −3.50258
\(603\) 4.31019e6 0.482729
\(604\) −2.68774e7 −2.99774
\(605\) 5.84515e6 0.649243
\(606\) 3.64393e6 0.403078
\(607\) −4.79971e6 −0.528741 −0.264371 0.964421i \(-0.585164\pi\)
−0.264371 + 0.964421i \(0.585164\pi\)
\(608\) −2.11060e7 −2.31551
\(609\) 6.89237e6 0.753052
\(610\) −5.23345e6 −0.569461
\(611\) −6.06731e6 −0.657496
\(612\) −1.23259e7 −1.33027
\(613\) 7.16201e6 0.769810 0.384905 0.922956i \(-0.374234\pi\)
0.384905 + 0.922956i \(0.374234\pi\)
\(614\) −1.05116e7 −1.12524
\(615\) 7.49584e6 0.799157
\(616\) −4.75147e7 −5.04517
\(617\) −1.31807e6 −0.139388 −0.0696942 0.997568i \(-0.522202\pi\)
−0.0696942 + 0.997568i \(0.522202\pi\)
\(618\) −811870. −0.0855097
\(619\) 8.49355e6 0.890969 0.445485 0.895290i \(-0.353031\pi\)
0.445485 + 0.895290i \(0.353031\pi\)
\(620\) 2.27756e7 2.37953
\(621\) −104706. −0.0108954
\(622\) 2.79823e7 2.90007
\(623\) −1.12531e7 −1.16159
\(624\) −1.39413e7 −1.43331
\(625\) −5.62586e6 −0.576088
\(626\) 1.97785e7 2.01724
\(627\) 8.83571e6 0.897579
\(628\) −5.39947e6 −0.546326
\(629\) 3.86507e6 0.389521
\(630\) 7.17006e6 0.719733
\(631\) 2.71872e6 0.271826 0.135913 0.990721i \(-0.456603\pi\)
0.135913 + 0.990721i \(0.456603\pi\)
\(632\) 9.00806e6 0.897096
\(633\) −3.45492e6 −0.342712
\(634\) −2.90821e7 −2.87345
\(635\) 8.63430e6 0.849753
\(636\) 1.20077e7 1.17711
\(637\) −1.00708e7 −0.983362
\(638\) −2.35416e7 −2.28973
\(639\) −6.67892e6 −0.647074
\(640\) 1.68170e6 0.162293
\(641\) −9.82087e6 −0.944071 −0.472036 0.881579i \(-0.656481\pi\)
−0.472036 + 0.881579i \(0.656481\pi\)
\(642\) −4.26458e6 −0.408356
\(643\) 1.88105e7 1.79421 0.897103 0.441822i \(-0.145668\pi\)
0.897103 + 0.441822i \(0.145668\pi\)
\(644\) −2.05395e6 −0.195153
\(645\) −6.71977e6 −0.635997
\(646\) 3.74106e7 3.52707
\(647\) 1.01896e7 0.956964 0.478482 0.878097i \(-0.341187\pi\)
0.478482 + 0.878097i \(0.341187\pi\)
\(648\) 3.17215e6 0.296768
\(649\) 1.86789e6 0.174077
\(650\) 6.33195e6 0.587834
\(651\) 1.04370e7 0.965210
\(652\) −3.39848e7 −3.13088
\(653\) −7.39824e6 −0.678962 −0.339481 0.940613i \(-0.610251\pi\)
−0.339481 + 0.940613i \(0.610251\pi\)
\(654\) 7.02737e6 0.642463
\(655\) 9.23317e6 0.840907
\(656\) 4.65394e7 4.22241
\(657\) −2.10516e6 −0.190271
\(658\) 1.93739e7 1.74442
\(659\) 2.69270e6 0.241532 0.120766 0.992681i \(-0.461465\pi\)
0.120766 + 0.992681i \(0.461465\pi\)
\(660\) −1.73710e7 −1.55226
\(661\) −1.86231e7 −1.65786 −0.828930 0.559352i \(-0.811050\pi\)
−0.828930 + 0.559352i \(0.811050\pi\)
\(662\) −3.72613e7 −3.30456
\(663\) 1.05551e7 0.932561
\(664\) 5.07865e7 4.47021
\(665\) −1.54359e7 −1.35356
\(666\) −1.68544e6 −0.147241
\(667\) −600587. −0.0522711
\(668\) −2.20491e7 −1.91183
\(669\) −4.57038e6 −0.394809
\(670\) 2.57190e7 2.21344
\(671\) 5.81024e6 0.498182
\(672\) 1.90148e7 1.62431
\(673\) −4.21307e6 −0.358559 −0.179280 0.983798i \(-0.557377\pi\)
−0.179280 + 0.983798i \(0.557377\pi\)
\(674\) 3.57992e7 3.03546
\(675\) −731099. −0.0617613
\(676\) −715485. −0.0602191
\(677\) −208397. −0.0174751 −0.00873756 0.999962i \(-0.502781\pi\)
−0.00873756 + 0.999962i \(0.502781\pi\)
\(678\) 1.12539e7 0.940219
\(679\) 3.12272e7 2.59931
\(680\) −4.34066e7 −3.59984
\(681\) 1.11175e7 0.918627
\(682\) −3.56485e7 −2.93482
\(683\) −4.15227e6 −0.340591 −0.170296 0.985393i \(-0.554472\pi\)
−0.170296 + 0.985393i \(0.554472\pi\)
\(684\) −1.15714e7 −0.945679
\(685\) 3.01245e6 0.245298
\(686\) −138028. −0.0111984
\(687\) 8.47750e6 0.685292
\(688\) −4.17210e7 −3.36034
\(689\) −1.02826e7 −0.825190
\(690\) −624785. −0.0499583
\(691\) 8.97043e6 0.714691 0.357345 0.933972i \(-0.383682\pi\)
0.357345 + 0.933972i \(0.383682\pi\)
\(692\) −4.23720e7 −3.36368
\(693\) −7.96029e6 −0.629645
\(694\) −1.16981e6 −0.0921967
\(695\) −4.72467e6 −0.371030
\(696\) 1.81952e7 1.42375
\(697\) −3.52354e7 −2.74724
\(698\) −7.26037e6 −0.564053
\(699\) 2.24969e6 0.174153
\(700\) −1.43414e7 −1.10623
\(701\) 1.23886e7 0.952195 0.476097 0.879393i \(-0.342051\pi\)
0.476097 + 0.879393i \(0.342051\pi\)
\(702\) −4.60274e6 −0.352512
\(703\) 3.62846e6 0.276907
\(704\) −2.07468e7 −1.57768
\(705\) 4.18015e6 0.316752
\(706\) −2.95468e7 −2.23100
\(707\) 7.06751e6 0.531763
\(708\) −2.44622e6 −0.183405
\(709\) −7.98264e6 −0.596391 −0.298195 0.954505i \(-0.596385\pi\)
−0.298195 + 0.954505i \(0.596385\pi\)
\(710\) −3.98532e7 −2.96700
\(711\) 1.50915e6 0.111959
\(712\) −2.97071e7 −2.19614
\(713\) −909457. −0.0669974
\(714\) −3.37040e7 −2.47421
\(715\) 1.48753e7 1.08818
\(716\) −2.82197e6 −0.205717
\(717\) 1.26970e7 0.922368
\(718\) 2.19555e7 1.58940
\(719\) 1.40569e7 1.01407 0.507035 0.861926i \(-0.330742\pi\)
0.507035 + 0.861926i \(0.330742\pi\)
\(720\) 9.60501e6 0.690505
\(721\) −1.57464e6 −0.112809
\(722\) 9.14121e6 0.652621
\(723\) 231575. 0.0164758
\(724\) −4.66403e7 −3.30685
\(725\) −4.19352e6 −0.296301
\(726\) 1.19815e7 0.843663
\(727\) −1.08044e7 −0.758166 −0.379083 0.925363i \(-0.623760\pi\)
−0.379083 + 0.925363i \(0.623760\pi\)
\(728\) −5.32858e7 −3.72635
\(729\) 531441. 0.0370370
\(730\) −1.25615e7 −0.872440
\(731\) 3.15874e7 2.18635
\(732\) −7.60916e6 −0.524879
\(733\) −1.13233e7 −0.778419 −0.389210 0.921149i \(-0.627252\pi\)
−0.389210 + 0.921149i \(0.627252\pi\)
\(734\) 3.27396e7 2.24302
\(735\) 6.93837e6 0.473739
\(736\) −1.65692e6 −0.112747
\(737\) −2.85535e7 −1.93638
\(738\) 1.53651e7 1.03847
\(739\) 7.10841e6 0.478808 0.239404 0.970920i \(-0.423048\pi\)
0.239404 + 0.970920i \(0.423048\pi\)
\(740\) −7.13353e6 −0.478878
\(741\) 9.90890e6 0.662949
\(742\) 3.28339e7 2.18934
\(743\) 2.17570e7 1.44586 0.722932 0.690919i \(-0.242794\pi\)
0.722932 + 0.690919i \(0.242794\pi\)
\(744\) 2.75526e7 1.82486
\(745\) 1.90064e7 1.25461
\(746\) −7.31178e6 −0.481034
\(747\) 8.50843e6 0.557889
\(748\) 8.16551e7 5.33616
\(749\) −8.27128e6 −0.538726
\(750\) −1.79561e7 −1.16562
\(751\) 1.14558e7 0.741180 0.370590 0.928797i \(-0.379155\pi\)
0.370590 + 0.928797i \(0.379155\pi\)
\(752\) 2.59533e7 1.67358
\(753\) −9.32313e6 −0.599203
\(754\) −2.64009e7 −1.69118
\(755\) −1.58571e7 −1.01241
\(756\) 1.04249e7 0.663387
\(757\) −2.26799e7 −1.43847 −0.719236 0.694766i \(-0.755508\pi\)
−0.719236 + 0.694766i \(0.755508\pi\)
\(758\) −5.25407e7 −3.32141
\(759\) 693643. 0.0437051
\(760\) −4.07493e7 −2.55909
\(761\) 1.63222e7 1.02169 0.510844 0.859673i \(-0.329333\pi\)
0.510844 + 0.859673i \(0.329333\pi\)
\(762\) 1.76987e7 1.10422
\(763\) 1.36298e7 0.847573
\(764\) 5.10145e7 3.16199
\(765\) −7.27205e6 −0.449266
\(766\) 3.77035e6 0.232172
\(767\) 2.09477e6 0.128572
\(768\) −7.68794e6 −0.470335
\(769\) −2.90386e7 −1.77076 −0.885379 0.464870i \(-0.846101\pi\)
−0.885379 + 0.464870i \(0.846101\pi\)
\(770\) −4.74992e7 −2.88708
\(771\) 9.44769e6 0.572387
\(772\) −2.64962e7 −1.60007
\(773\) 7.51073e6 0.452099 0.226050 0.974116i \(-0.427419\pi\)
0.226050 + 0.974116i \(0.427419\pi\)
\(774\) −1.37743e7 −0.826450
\(775\) −6.35016e6 −0.379779
\(776\) 8.24369e7 4.91436
\(777\) −3.26896e6 −0.194248
\(778\) 2.70724e7 1.60353
\(779\) −3.30783e7 −1.95299
\(780\) −1.94808e7 −1.14649
\(781\) 4.42455e7 2.59562
\(782\) 2.93690e6 0.171740
\(783\) 3.04830e6 0.177686
\(784\) 4.30782e7 2.50304
\(785\) −3.18557e6 −0.184507
\(786\) 1.89263e7 1.09272
\(787\) 2.97607e7 1.71280 0.856399 0.516315i \(-0.172697\pi\)
0.856399 + 0.516315i \(0.172697\pi\)
\(788\) −2.93219e7 −1.68220
\(789\) −1.25073e7 −0.715273
\(790\) 9.00513e6 0.513360
\(791\) 2.18272e7 1.24039
\(792\) −2.10144e7 −1.19043
\(793\) 6.51596e6 0.367955
\(794\) −2.98647e7 −1.68115
\(795\) 7.08431e6 0.397539
\(796\) −2.45244e7 −1.37188
\(797\) 1.18682e7 0.661817 0.330909 0.943663i \(-0.392645\pi\)
0.330909 + 0.943663i \(0.392645\pi\)
\(798\) −3.16407e7 −1.75889
\(799\) −1.96495e7 −1.08889
\(800\) −1.15692e7 −0.639114
\(801\) −4.97693e6 −0.274082
\(802\) −2.23973e7 −1.22959
\(803\) 1.39460e7 0.763238
\(804\) 3.73941e7 2.04015
\(805\) −1.21179e6 −0.0659078
\(806\) −3.99784e7 −2.16764
\(807\) −1.48997e7 −0.805368
\(808\) 1.86576e7 1.00537
\(809\) −1.20080e7 −0.645057 −0.322528 0.946560i \(-0.604533\pi\)
−0.322528 + 0.946560i \(0.604533\pi\)
\(810\) 3.17112e6 0.169824
\(811\) 3.34804e7 1.78747 0.893734 0.448597i \(-0.148076\pi\)
0.893734 + 0.448597i \(0.148076\pi\)
\(812\) 5.97963e7 3.18261
\(813\) 8.01470e6 0.425266
\(814\) 1.11655e7 0.590630
\(815\) −2.00503e7 −1.05737
\(816\) −4.51499e7 −2.37373
\(817\) 2.96536e7 1.55426
\(818\) 1.76683e7 0.923233
\(819\) −8.92715e6 −0.465053
\(820\) 6.50318e7 3.37747
\(821\) −2.19093e7 −1.13441 −0.567207 0.823575i \(-0.691976\pi\)
−0.567207 + 0.823575i \(0.691976\pi\)
\(822\) 6.17497e6 0.318754
\(823\) −1.77211e7 −0.911994 −0.455997 0.889981i \(-0.650717\pi\)
−0.455997 + 0.889981i \(0.650717\pi\)
\(824\) −4.15691e6 −0.213281
\(825\) 4.84328e6 0.247745
\(826\) −6.68893e6 −0.341120
\(827\) 1.64575e7 0.836759 0.418380 0.908272i \(-0.362598\pi\)
0.418380 + 0.908272i \(0.362598\pi\)
\(828\) −908404. −0.0460472
\(829\) −7.42705e6 −0.375345 −0.187672 0.982232i \(-0.560094\pi\)
−0.187672 + 0.982232i \(0.560094\pi\)
\(830\) 5.07699e7 2.55806
\(831\) −6.73465e6 −0.338308
\(832\) −2.32667e7 −1.16527
\(833\) −3.26150e7 −1.62856
\(834\) −9.68470e6 −0.482138
\(835\) −1.30085e7 −0.645670
\(836\) 7.66562e7 3.79343
\(837\) 4.61598e6 0.227746
\(838\) 6.44488e7 3.17033
\(839\) 728562. 0.0357324 0.0178662 0.999840i \(-0.494313\pi\)
0.0178662 + 0.999840i \(0.494313\pi\)
\(840\) 3.67119e7 1.79518
\(841\) −3.02636e6 −0.147547
\(842\) −1.05393e7 −0.512309
\(843\) 996923. 0.0483162
\(844\) −2.99740e7 −1.44840
\(845\) −422122. −0.0203374
\(846\) 8.56853e6 0.411605
\(847\) 2.32384e7 1.11301
\(848\) 4.39843e7 2.10043
\(849\) −1.98543e6 −0.0945332
\(850\) 2.05065e7 0.973521
\(851\) 284850. 0.0134832
\(852\) −5.79445e7 −2.73472
\(853\) 325772. 0.0153300 0.00766499 0.999971i \(-0.497560\pi\)
0.00766499 + 0.999971i \(0.497560\pi\)
\(854\) −2.08065e7 −0.976235
\(855\) −6.82686e6 −0.319379
\(856\) −2.18354e7 −1.01854
\(857\) 6.77652e6 0.315177 0.157589 0.987505i \(-0.449628\pi\)
0.157589 + 0.987505i \(0.449628\pi\)
\(858\) 3.04916e7 1.41404
\(859\) −1.74661e7 −0.807631 −0.403815 0.914840i \(-0.632316\pi\)
−0.403815 + 0.914840i \(0.632316\pi\)
\(860\) −5.82989e7 −2.68790
\(861\) 2.98010e7 1.37001
\(862\) 2.67426e7 1.22585
\(863\) −1.22281e7 −0.558897 −0.279449 0.960161i \(-0.590152\pi\)
−0.279449 + 0.960161i \(0.590152\pi\)
\(864\) 8.40973e6 0.383264
\(865\) −2.49986e7 −1.13599
\(866\) −5.23459e7 −2.37185
\(867\) 2.14047e7 0.967080
\(868\) 9.05483e7 4.07926
\(869\) −9.99760e6 −0.449103
\(870\) 1.81893e7 0.814736
\(871\) −3.20217e7 −1.43021
\(872\) 3.59813e7 1.60245
\(873\) 1.38109e7 0.613320
\(874\) 2.75711e6 0.122089
\(875\) −3.48263e7 −1.53776
\(876\) −1.82638e7 −0.804139
\(877\) −2.26822e7 −0.995834 −0.497917 0.867225i \(-0.665902\pi\)
−0.497917 + 0.867225i \(0.665902\pi\)
\(878\) −1.04559e7 −0.457746
\(879\) 1.39971e7 0.611037
\(880\) −6.36299e7 −2.76984
\(881\) −1.07389e7 −0.466145 −0.233073 0.972459i \(-0.574878\pi\)
−0.233073 + 0.972459i \(0.574878\pi\)
\(882\) 1.42224e7 0.615603
\(883\) 1.63107e7 0.703997 0.351999 0.936001i \(-0.385502\pi\)
0.351999 + 0.936001i \(0.385502\pi\)
\(884\) 9.15729e7 3.94127
\(885\) −1.44322e6 −0.0619403
\(886\) −6.39200e7 −2.73560
\(887\) 1.28289e6 0.0547493 0.0273747 0.999625i \(-0.491285\pi\)
0.0273747 + 0.999625i \(0.491285\pi\)
\(888\) −8.62973e6 −0.367253
\(889\) 3.43271e7 1.45674
\(890\) −2.96974e7 −1.25674
\(891\) −3.52061e6 −0.148568
\(892\) −3.96514e7 −1.66858
\(893\) −1.84466e7 −0.774081
\(894\) 3.89596e7 1.63031
\(895\) −1.66490e6 −0.0694754
\(896\) 6.68590e6 0.278221
\(897\) 777894. 0.0322804
\(898\) 1.89021e7 0.782201
\(899\) 2.64769e7 1.09262
\(900\) −6.34281e6 −0.261021
\(901\) −3.33010e7 −1.36661
\(902\) −1.01788e8 −4.16564
\(903\) −2.67156e7 −1.09030
\(904\) 5.76219e7 2.34513
\(905\) −2.75168e7 −1.11680
\(906\) −3.25041e7 −1.31558
\(907\) −2.80898e7 −1.13379 −0.566893 0.823791i \(-0.691855\pi\)
−0.566893 + 0.823791i \(0.691855\pi\)
\(908\) 9.64523e7 3.88238
\(909\) 3.12576e6 0.125472
\(910\) −5.32684e7 −2.13239
\(911\) 3.24554e7 1.29566 0.647829 0.761785i \(-0.275677\pi\)
0.647829 + 0.761785i \(0.275677\pi\)
\(912\) −4.23859e7 −1.68746
\(913\) −5.63654e7 −2.23787
\(914\) −3.68886e7 −1.46058
\(915\) −4.48925e6 −0.177264
\(916\) 7.35484e7 2.89624
\(917\) 3.67081e7 1.44158
\(918\) −1.49064e7 −0.583801
\(919\) −2.73570e7 −1.06851 −0.534256 0.845323i \(-0.679408\pi\)
−0.534256 + 0.845323i \(0.679408\pi\)
\(920\) −3.19900e6 −0.124608
\(921\) −9.01680e6 −0.350270
\(922\) 7.28724e7 2.82316
\(923\) 4.96196e7 1.91712
\(924\) −6.90612e7 −2.66106
\(925\) 1.98893e6 0.0764302
\(926\) −5.02480e7 −1.92571
\(927\) −696421. −0.0266178
\(928\) 4.82375e7 1.83872
\(929\) −2.68916e7 −1.02230 −0.511148 0.859493i \(-0.670780\pi\)
−0.511148 + 0.859493i \(0.670780\pi\)
\(930\) 2.75436e7 1.04427
\(931\) −3.06183e7 −1.15773
\(932\) 1.95177e7 0.736019
\(933\) 2.40032e7 0.902745
\(934\) 2.75472e7 1.03326
\(935\) 4.81748e7 1.80215
\(936\) −2.35668e7 −0.879248
\(937\) −3.27080e7 −1.21704 −0.608520 0.793538i \(-0.708237\pi\)
−0.608520 + 0.793538i \(0.708237\pi\)
\(938\) 1.02250e8 3.79453
\(939\) 1.69660e7 0.627935
\(940\) 3.62658e7 1.33868
\(941\) 2.24893e7 0.827947 0.413973 0.910289i \(-0.364141\pi\)
0.413973 + 0.910289i \(0.364141\pi\)
\(942\) −6.52984e6 −0.239759
\(943\) −2.59680e6 −0.0950953
\(944\) −8.96049e6 −0.327267
\(945\) 6.15047e6 0.224042
\(946\) 9.12498e7 3.31516
\(947\) −2.60237e7 −0.942963 −0.471482 0.881876i \(-0.656281\pi\)
−0.471482 + 0.881876i \(0.656281\pi\)
\(948\) 1.30930e7 0.473170
\(949\) 1.56399e7 0.563725
\(950\) 1.92512e7 0.692066
\(951\) −2.49466e7 −0.894459
\(952\) −1.72570e8 −6.17126
\(953\) −4.54892e7 −1.62247 −0.811233 0.584722i \(-0.801203\pi\)
−0.811233 + 0.584722i \(0.801203\pi\)
\(954\) 1.45215e7 0.516584
\(955\) 3.00975e7 1.06788
\(956\) 1.10156e8 3.89819
\(957\) −2.01939e7 −0.712756
\(958\) −2.20362e7 −0.775753
\(959\) 1.19765e7 0.420517
\(960\) 1.60299e7 0.561373
\(961\) 1.14642e7 0.400439
\(962\) 1.25216e7 0.436237
\(963\) −3.65815e6 −0.127115
\(964\) 2.00908e6 0.0696315
\(965\) −1.56322e7 −0.540383
\(966\) −2.48394e6 −0.0856442
\(967\) 3.16445e7 1.08826 0.544129 0.839002i \(-0.316860\pi\)
0.544129 + 0.839002i \(0.316860\pi\)
\(968\) 6.13472e7 2.10429
\(969\) 3.20908e7 1.09792
\(970\) 8.24100e7 2.81223
\(971\) −2.31685e7 −0.788587 −0.394293 0.918985i \(-0.629011\pi\)
−0.394293 + 0.918985i \(0.629011\pi\)
\(972\) 4.61064e6 0.156529
\(973\) −1.87837e7 −0.636063
\(974\) −4.13760e7 −1.39750
\(975\) 5.43154e6 0.182983
\(976\) −2.78724e7 −0.936590
\(977\) −1.39480e7 −0.467492 −0.233746 0.972298i \(-0.575098\pi\)
−0.233746 + 0.972298i \(0.575098\pi\)
\(978\) −4.10995e7 −1.37401
\(979\) 3.29704e7 1.09943
\(980\) 6.01954e7 2.00216
\(981\) 6.02806e6 0.199989
\(982\) 3.95939e6 0.131024
\(983\) −9.57136e6 −0.315929 −0.157965 0.987445i \(-0.550493\pi\)
−0.157965 + 0.987445i \(0.550493\pi\)
\(984\) 7.86718e7 2.59019
\(985\) −1.72993e7 −0.568118
\(986\) −8.55016e7 −2.80080
\(987\) 1.66189e7 0.543012
\(988\) 8.59669e7 2.80181
\(989\) 2.32794e6 0.0756801
\(990\) −2.10075e7 −0.681220
\(991\) −3.03725e7 −0.982417 −0.491209 0.871042i \(-0.663445\pi\)
−0.491209 + 0.871042i \(0.663445\pi\)
\(992\) 7.30451e7 2.35674
\(993\) −3.19627e7 −1.02866
\(994\) −1.58443e8 −5.08637
\(995\) −1.44689e7 −0.463317
\(996\) 7.38167e7 2.35780
\(997\) −2.69504e7 −0.858671 −0.429336 0.903145i \(-0.641252\pi\)
−0.429336 + 0.903145i \(0.641252\pi\)
\(998\) −3.11069e7 −0.988623
\(999\) −1.44577e6 −0.0458337
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 177.6.a.c.1.11 12
3.2 odd 2 531.6.a.c.1.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.c.1.11 12 1.1 even 1 trivial
531.6.a.c.1.2 12 3.2 odd 2