Properties

Label 177.6.a.c.1.9
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 1.9
Root \(-5.43261\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.43261 q^{2} +9.00000 q^{3} +23.2437 q^{4} +48.3022 q^{5} +66.8935 q^{6} +120.542 q^{7} -65.0821 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+7.43261 q^{2} +9.00000 q^{3} +23.2437 q^{4} +48.3022 q^{5} +66.8935 q^{6} +120.542 q^{7} -65.0821 q^{8} +81.0000 q^{9} +359.012 q^{10} -192.015 q^{11} +209.193 q^{12} +600.307 q^{13} +895.942 q^{14} +434.720 q^{15} -1227.53 q^{16} +2195.23 q^{17} +602.041 q^{18} -393.685 q^{19} +1122.72 q^{20} +1084.88 q^{21} -1427.17 q^{22} -212.558 q^{23} -585.739 q^{24} -791.894 q^{25} +4461.85 q^{26} +729.000 q^{27} +2801.84 q^{28} -320.477 q^{29} +3231.11 q^{30} -1196.80 q^{31} -7041.12 q^{32} -1728.13 q^{33} +16316.3 q^{34} +5822.45 q^{35} +1882.74 q^{36} +1866.98 q^{37} -2926.10 q^{38} +5402.76 q^{39} -3143.61 q^{40} -10116.5 q^{41} +8063.48 q^{42} +18212.6 q^{43} -4463.14 q^{44} +3912.48 q^{45} -1579.86 q^{46} +19027.8 q^{47} -11047.8 q^{48} -2276.61 q^{49} -5885.84 q^{50} +19757.1 q^{51} +13953.4 q^{52} -18428.0 q^{53} +5418.37 q^{54} -9274.74 q^{55} -7845.13 q^{56} -3543.16 q^{57} -2381.98 q^{58} -3481.00 q^{59} +10104.5 q^{60} -16435.9 q^{61} -8895.35 q^{62} +9763.91 q^{63} -13053.0 q^{64} +28996.2 q^{65} -12844.5 q^{66} +10398.4 q^{67} +51025.3 q^{68} -1913.02 q^{69} +43276.0 q^{70} -16382.6 q^{71} -5271.65 q^{72} -68804.3 q^{73} +13876.6 q^{74} -7127.05 q^{75} -9150.69 q^{76} -23145.9 q^{77} +40156.6 q^{78} -3498.36 q^{79} -59292.4 q^{80} +6561.00 q^{81} -75192.2 q^{82} -95365.4 q^{83} +25216.6 q^{84} +106035. q^{85} +135367. q^{86} -2884.29 q^{87} +12496.7 q^{88} -19992.9 q^{89} +29080.0 q^{90} +72362.2 q^{91} -4940.64 q^{92} -10771.2 q^{93} +141426. q^{94} -19015.8 q^{95} -63370.0 q^{96} -99691.0 q^{97} -16921.2 q^{98} -15553.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + O(q^{10}) \) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + 601q^{10} + 1480q^{11} + 1782q^{12} + 472q^{13} + 1065q^{14} + 1422q^{15} + 6370q^{16} + 1565q^{17} + 1782q^{18} + 3939q^{19} + 8033q^{20} + 3717q^{21} - 1738q^{22} + 7245q^{23} + 6507q^{24} + 9690q^{25} + 3764q^{26} + 8748q^{27} + 12154q^{28} + 10003q^{29} + 5409q^{30} + 7295q^{31} + 11628q^{32} + 13320q^{33} - 16344q^{34} + 11015q^{35} + 16038q^{36} + 6741q^{37} + 3035q^{38} + 4248q^{39} + 5572q^{40} + 34025q^{41} + 9585q^{42} - 6336q^{43} + 41168q^{44} + 12798q^{45} + 2345q^{46} + 66167q^{47} + 57330q^{48} + 28319q^{49} + 31173q^{50} + 14085q^{51} + 16440q^{52} + 62290q^{53} + 16038q^{54} + 55764q^{55} + 107306q^{56} + 35451q^{57} + 37952q^{58} - 41772q^{59} + 72297q^{60} + 68469q^{61} + 99190q^{62} + 33453q^{63} + 68525q^{64} + 80156q^{65} - 15642q^{66} + 113310q^{67} + 33887q^{68} + 65205q^{69} + 32034q^{70} + 84520q^{71} + 58563q^{72} + 135895q^{73} - 31962q^{74} + 87210q^{75} - 61848q^{76} - 3799q^{77} + 33876q^{78} + 14122q^{79} + 77609q^{80} + 78732q^{81} - 1501q^{82} + 114463q^{83} + 109386q^{84} - 101097q^{85} - 203536q^{86} + 90027q^{87} - 244967q^{88} + 189109q^{89} + 48681q^{90} - 168249q^{91} - 71946q^{92} + 65655q^{93} - 472284q^{94} + 21923q^{95} + 104652q^{96} - 76192q^{97} - 17544q^{98} + 119880q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.43261 1.31391 0.656956 0.753929i \(-0.271844\pi\)
0.656956 + 0.753929i \(0.271844\pi\)
\(3\) 9.00000 0.577350
\(4\) 23.2437 0.726366
\(5\) 48.3022 0.864057 0.432028 0.901860i \(-0.357798\pi\)
0.432028 + 0.901860i \(0.357798\pi\)
\(6\) 66.8935 0.758588
\(7\) 120.542 0.929808 0.464904 0.885361i \(-0.346089\pi\)
0.464904 + 0.885361i \(0.346089\pi\)
\(8\) −65.0821 −0.359531
\(9\) 81.0000 0.333333
\(10\) 359.012 1.13529
\(11\) −192.015 −0.478468 −0.239234 0.970962i \(-0.576896\pi\)
−0.239234 + 0.970962i \(0.576896\pi\)
\(12\) 209.193 0.419368
\(13\) 600.307 0.985178 0.492589 0.870262i \(-0.336051\pi\)
0.492589 + 0.870262i \(0.336051\pi\)
\(14\) 895.942 1.22169
\(15\) 434.720 0.498863
\(16\) −1227.53 −1.19876
\(17\) 2195.23 1.84229 0.921146 0.389218i \(-0.127255\pi\)
0.921146 + 0.389218i \(0.127255\pi\)
\(18\) 602.041 0.437971
\(19\) −393.685 −0.250187 −0.125093 0.992145i \(-0.539923\pi\)
−0.125093 + 0.992145i \(0.539923\pi\)
\(20\) 1122.72 0.627621
\(21\) 1084.88 0.536825
\(22\) −1427.17 −0.628665
\(23\) −212.558 −0.0837834 −0.0418917 0.999122i \(-0.513338\pi\)
−0.0418917 + 0.999122i \(0.513338\pi\)
\(24\) −585.739 −0.207575
\(25\) −791.894 −0.253406
\(26\) 4461.85 1.29444
\(27\) 729.000 0.192450
\(28\) 2801.84 0.675381
\(29\) −320.477 −0.0707623 −0.0353812 0.999374i \(-0.511265\pi\)
−0.0353812 + 0.999374i \(0.511265\pi\)
\(30\) 3231.11 0.655463
\(31\) −1196.80 −0.223675 −0.111837 0.993727i \(-0.535674\pi\)
−0.111837 + 0.993727i \(0.535674\pi\)
\(32\) −7041.12 −1.21553
\(33\) −1728.13 −0.276244
\(34\) 16316.3 2.42061
\(35\) 5822.45 0.803407
\(36\) 1882.74 0.242122
\(37\) 1866.98 0.224200 0.112100 0.993697i \(-0.464242\pi\)
0.112100 + 0.993697i \(0.464242\pi\)
\(38\) −2926.10 −0.328724
\(39\) 5402.76 0.568793
\(40\) −3143.61 −0.310655
\(41\) −10116.5 −0.939879 −0.469939 0.882699i \(-0.655724\pi\)
−0.469939 + 0.882699i \(0.655724\pi\)
\(42\) 8063.48 0.705341
\(43\) 18212.6 1.50211 0.751053 0.660242i \(-0.229546\pi\)
0.751053 + 0.660242i \(0.229546\pi\)
\(44\) −4463.14 −0.347543
\(45\) 3912.48 0.288019
\(46\) −1579.86 −0.110084
\(47\) 19027.8 1.25645 0.628224 0.778033i \(-0.283782\pi\)
0.628224 + 0.778033i \(0.283782\pi\)
\(48\) −11047.8 −0.692104
\(49\) −2276.61 −0.135456
\(50\) −5885.84 −0.332953
\(51\) 19757.1 1.06365
\(52\) 13953.4 0.715600
\(53\) −18428.0 −0.901131 −0.450566 0.892743i \(-0.648778\pi\)
−0.450566 + 0.892743i \(0.648778\pi\)
\(54\) 5418.37 0.252863
\(55\) −9274.74 −0.413424
\(56\) −7845.13 −0.334295
\(57\) −3543.16 −0.144445
\(58\) −2381.98 −0.0929755
\(59\) −3481.00 −0.130189
\(60\) 10104.5 0.362357
\(61\) −16435.9 −0.565547 −0.282773 0.959187i \(-0.591254\pi\)
−0.282773 + 0.959187i \(0.591254\pi\)
\(62\) −8895.35 −0.293889
\(63\) 9763.91 0.309936
\(64\) −13053.0 −0.398345
\(65\) 28996.2 0.851250
\(66\) −12844.5 −0.362960
\(67\) 10398.4 0.282995 0.141497 0.989939i \(-0.454808\pi\)
0.141497 + 0.989939i \(0.454808\pi\)
\(68\) 51025.3 1.33818
\(69\) −1913.02 −0.0483724
\(70\) 43276.0 1.05561
\(71\) −16382.6 −0.385688 −0.192844 0.981229i \(-0.561771\pi\)
−0.192844 + 0.981229i \(0.561771\pi\)
\(72\) −5271.65 −0.119844
\(73\) −68804.3 −1.51115 −0.755577 0.655060i \(-0.772643\pi\)
−0.755577 + 0.655060i \(0.772643\pi\)
\(74\) 13876.6 0.294580
\(75\) −7127.05 −0.146304
\(76\) −9150.69 −0.181727
\(77\) −23145.9 −0.444884
\(78\) 40156.6 0.747344
\(79\) −3498.36 −0.0630662 −0.0315331 0.999503i \(-0.510039\pi\)
−0.0315331 + 0.999503i \(0.510039\pi\)
\(80\) −59292.4 −1.03580
\(81\) 6561.00 0.111111
\(82\) −75192.2 −1.23492
\(83\) −95365.4 −1.51948 −0.759741 0.650226i \(-0.774674\pi\)
−0.759741 + 0.650226i \(0.774674\pi\)
\(84\) 25216.6 0.389931
\(85\) 106035. 1.59184
\(86\) 135367. 1.97364
\(87\) −2884.29 −0.0408546
\(88\) 12496.7 0.172024
\(89\) −19992.9 −0.267548 −0.133774 0.991012i \(-0.542710\pi\)
−0.133774 + 0.991012i \(0.542710\pi\)
\(90\) 29080.0 0.378432
\(91\) 72362.2 0.916027
\(92\) −4940.64 −0.0608574
\(93\) −10771.2 −0.129139
\(94\) 141426. 1.65086
\(95\) −19015.8 −0.216176
\(96\) −63370.0 −0.701788
\(97\) −99691.0 −1.07579 −0.537894 0.843012i \(-0.680780\pi\)
−0.537894 + 0.843012i \(0.680780\pi\)
\(98\) −16921.2 −0.177978
\(99\) −15553.2 −0.159489
\(100\) −18406.6 −0.184066
\(101\) −77792.2 −0.758809 −0.379405 0.925231i \(-0.623871\pi\)
−0.379405 + 0.925231i \(0.623871\pi\)
\(102\) 146847. 1.39754
\(103\) −53809.1 −0.499761 −0.249880 0.968277i \(-0.580391\pi\)
−0.249880 + 0.968277i \(0.580391\pi\)
\(104\) −39069.2 −0.354202
\(105\) 52402.1 0.463847
\(106\) −136968. −1.18401
\(107\) −90583.1 −0.764870 −0.382435 0.923982i \(-0.624914\pi\)
−0.382435 + 0.923982i \(0.624914\pi\)
\(108\) 16944.7 0.139789
\(109\) 206631. 1.66583 0.832913 0.553405i \(-0.186672\pi\)
0.832913 + 0.553405i \(0.186672\pi\)
\(110\) −68935.6 −0.543202
\(111\) 16802.9 0.129442
\(112\) −147969. −1.11462
\(113\) 83781.9 0.617240 0.308620 0.951185i \(-0.400133\pi\)
0.308620 + 0.951185i \(0.400133\pi\)
\(114\) −26334.9 −0.189789
\(115\) −10267.0 −0.0723936
\(116\) −7449.08 −0.0513993
\(117\) 48624.8 0.328393
\(118\) −25872.9 −0.171057
\(119\) 264618. 1.71298
\(120\) −28292.5 −0.179357
\(121\) −124181. −0.771068
\(122\) −122162. −0.743079
\(123\) −91048.7 −0.542639
\(124\) −27818.1 −0.162470
\(125\) −189195. −1.08301
\(126\) 72571.3 0.407229
\(127\) −230499. −1.26812 −0.634059 0.773285i \(-0.718612\pi\)
−0.634059 + 0.773285i \(0.718612\pi\)
\(128\) 128298. 0.692142
\(129\) 163913. 0.867241
\(130\) 215517. 1.11847
\(131\) 186771. 0.950892 0.475446 0.879745i \(-0.342287\pi\)
0.475446 + 0.879745i \(0.342287\pi\)
\(132\) −40168.2 −0.200654
\(133\) −47455.6 −0.232626
\(134\) 77287.0 0.371830
\(135\) 35212.3 0.166288
\(136\) −142870. −0.662361
\(137\) 111807. 0.508941 0.254471 0.967081i \(-0.418099\pi\)
0.254471 + 0.967081i \(0.418099\pi\)
\(138\) −14218.8 −0.0635571
\(139\) 195432. 0.857942 0.428971 0.903318i \(-0.358876\pi\)
0.428971 + 0.903318i \(0.358876\pi\)
\(140\) 135335. 0.583568
\(141\) 171250. 0.725410
\(142\) −121765. −0.506760
\(143\) −115268. −0.471376
\(144\) −99429.8 −0.399586
\(145\) −15479.8 −0.0611427
\(146\) −511396. −1.98552
\(147\) −20489.5 −0.0782057
\(148\) 43395.6 0.162851
\(149\) −371327. −1.37022 −0.685111 0.728438i \(-0.740246\pi\)
−0.685111 + 0.728438i \(0.740246\pi\)
\(150\) −52972.6 −0.192231
\(151\) −405248. −1.44637 −0.723184 0.690655i \(-0.757322\pi\)
−0.723184 + 0.690655i \(0.757322\pi\)
\(152\) 25621.8 0.0899500
\(153\) 177814. 0.614097
\(154\) −172034. −0.584538
\(155\) −57808.1 −0.193268
\(156\) 125580. 0.413152
\(157\) 93561.5 0.302934 0.151467 0.988462i \(-0.451600\pi\)
0.151467 + 0.988462i \(0.451600\pi\)
\(158\) −26001.9 −0.0828634
\(159\) −165852. −0.520268
\(160\) −340102. −1.05029
\(161\) −25622.2 −0.0779026
\(162\) 48765.4 0.145990
\(163\) −314860. −0.928216 −0.464108 0.885779i \(-0.653625\pi\)
−0.464108 + 0.885779i \(0.653625\pi\)
\(164\) −235146. −0.682696
\(165\) −83472.7 −0.238690
\(166\) −708814. −1.99647
\(167\) 82055.5 0.227676 0.113838 0.993499i \(-0.463686\pi\)
0.113838 + 0.993499i \(0.463686\pi\)
\(168\) −70606.2 −0.193005
\(169\) −10924.8 −0.0294238
\(170\) 788114. 2.09154
\(171\) −31888.5 −0.0833956
\(172\) 423328. 1.09108
\(173\) −138981. −0.353053 −0.176527 0.984296i \(-0.556486\pi\)
−0.176527 + 0.984296i \(0.556486\pi\)
\(174\) −21437.8 −0.0536794
\(175\) −95456.5 −0.235619
\(176\) 235704. 0.573568
\(177\) −31329.0 −0.0751646
\(178\) −148600. −0.351535
\(179\) 377160. 0.879819 0.439909 0.898042i \(-0.355011\pi\)
0.439909 + 0.898042i \(0.355011\pi\)
\(180\) 90940.6 0.209207
\(181\) −395990. −0.898438 −0.449219 0.893422i \(-0.648298\pi\)
−0.449219 + 0.893422i \(0.648298\pi\)
\(182\) 537840. 1.20358
\(183\) −147923. −0.326519
\(184\) 13833.7 0.0301228
\(185\) 90179.5 0.193722
\(186\) −80058.2 −0.169677
\(187\) −421517. −0.881478
\(188\) 442277. 0.912640
\(189\) 87875.2 0.178942
\(190\) −141337. −0.284036
\(191\) 611684. 1.21323 0.606616 0.794995i \(-0.292527\pi\)
0.606616 + 0.794995i \(0.292527\pi\)
\(192\) −117477. −0.229984
\(193\) 374856. 0.724388 0.362194 0.932103i \(-0.382028\pi\)
0.362194 + 0.932103i \(0.382028\pi\)
\(194\) −740965. −1.41349
\(195\) 260965. 0.491469
\(196\) −52916.9 −0.0983908
\(197\) 527822. 0.968997 0.484498 0.874792i \(-0.339002\pi\)
0.484498 + 0.874792i \(0.339002\pi\)
\(198\) −115601. −0.209555
\(199\) 167623. 0.300055 0.150028 0.988682i \(-0.452064\pi\)
0.150028 + 0.988682i \(0.452064\pi\)
\(200\) 51538.1 0.0911074
\(201\) 93585.3 0.163387
\(202\) −578199. −0.997009
\(203\) −38631.0 −0.0657954
\(204\) 459228. 0.772597
\(205\) −488651. −0.812108
\(206\) −399942. −0.656642
\(207\) −17217.2 −0.0279278
\(208\) −736894. −1.18099
\(209\) 75593.3 0.119706
\(210\) 389484. 0.609455
\(211\) −256097. −0.396003 −0.198001 0.980202i \(-0.563445\pi\)
−0.198001 + 0.980202i \(0.563445\pi\)
\(212\) −428335. −0.654551
\(213\) −147443. −0.222677
\(214\) −673269. −1.00497
\(215\) 879709. 1.29790
\(216\) −47444.9 −0.0691918
\(217\) −144265. −0.207975
\(218\) 1.53581e6 2.18875
\(219\) −619239. −0.872465
\(220\) −215579. −0.300297
\(221\) 1.31781e6 1.81499
\(222\) 124889. 0.170076
\(223\) 615040. 0.828212 0.414106 0.910229i \(-0.364094\pi\)
0.414106 + 0.910229i \(0.364094\pi\)
\(224\) −848751. −1.13021
\(225\) −64143.4 −0.0844687
\(226\) 622718. 0.810999
\(227\) 1.04368e6 1.34432 0.672161 0.740405i \(-0.265366\pi\)
0.672161 + 0.740405i \(0.265366\pi\)
\(228\) −82356.2 −0.104920
\(229\) −608125. −0.766309 −0.383154 0.923684i \(-0.625162\pi\)
−0.383154 + 0.923684i \(0.625162\pi\)
\(230\) −76310.9 −0.0951189
\(231\) −208313. −0.256854
\(232\) 20857.3 0.0254413
\(233\) 1.00513e6 1.21292 0.606462 0.795113i \(-0.292588\pi\)
0.606462 + 0.795113i \(0.292588\pi\)
\(234\) 361410. 0.431479
\(235\) 919086. 1.08564
\(236\) −80911.3 −0.0945648
\(237\) −31485.2 −0.0364113
\(238\) 1.96680e6 2.25070
\(239\) 1.22727e6 1.38978 0.694891 0.719115i \(-0.255453\pi\)
0.694891 + 0.719115i \(0.255453\pi\)
\(240\) −533631. −0.598017
\(241\) 1.34998e6 1.49721 0.748607 0.663014i \(-0.230723\pi\)
0.748607 + 0.663014i \(0.230723\pi\)
\(242\) −922991. −1.01312
\(243\) 59049.0 0.0641500
\(244\) −382031. −0.410794
\(245\) −109965. −0.117042
\(246\) −676730. −0.712980
\(247\) −236332. −0.246479
\(248\) 77890.3 0.0804182
\(249\) −858289. −0.877273
\(250\) −1.40621e6 −1.42299
\(251\) 448506. 0.449350 0.224675 0.974434i \(-0.427868\pi\)
0.224675 + 0.974434i \(0.427868\pi\)
\(252\) 226949. 0.225127
\(253\) 40814.3 0.0400877
\(254\) −1.71321e6 −1.66620
\(255\) 954312. 0.919052
\(256\) 1.37128e6 1.30776
\(257\) 656292. 0.619818 0.309909 0.950766i \(-0.399701\pi\)
0.309909 + 0.950766i \(0.399701\pi\)
\(258\) 1.21830e6 1.13948
\(259\) 225050. 0.208463
\(260\) 673978. 0.618319
\(261\) −25958.6 −0.0235874
\(262\) 1.38820e6 1.24939
\(263\) 1.25395e6 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(264\) 112471. 0.0993183
\(265\) −890113. −0.778628
\(266\) −352719. −0.305650
\(267\) −179936. −0.154469
\(268\) 241697. 0.205558
\(269\) 295417. 0.248917 0.124459 0.992225i \(-0.460281\pi\)
0.124459 + 0.992225i \(0.460281\pi\)
\(270\) 261720. 0.218488
\(271\) 1.36641e6 1.13021 0.565103 0.825020i \(-0.308836\pi\)
0.565103 + 0.825020i \(0.308836\pi\)
\(272\) −2.69471e6 −2.20846
\(273\) 651260. 0.528868
\(274\) 831018. 0.668704
\(275\) 152055. 0.121247
\(276\) −44465.8 −0.0351361
\(277\) −180534. −0.141371 −0.0706853 0.997499i \(-0.522519\pi\)
−0.0706853 + 0.997499i \(0.522519\pi\)
\(278\) 1.45257e6 1.12726
\(279\) −96940.8 −0.0745583
\(280\) −378937. −0.288850
\(281\) 748821. 0.565734 0.282867 0.959159i \(-0.408715\pi\)
0.282867 + 0.959159i \(0.408715\pi\)
\(282\) 1.27284e6 0.953125
\(283\) −1.43420e6 −1.06450 −0.532248 0.846589i \(-0.678652\pi\)
−0.532248 + 0.846589i \(0.678652\pi\)
\(284\) −380792. −0.280151
\(285\) −171143. −0.124809
\(286\) −856741. −0.619347
\(287\) −1.21947e6 −0.873907
\(288\) −570330. −0.405177
\(289\) 3.39919e6 2.39404
\(290\) −115055. −0.0803361
\(291\) −897219. −0.621107
\(292\) −1.59927e6 −1.09765
\(293\) −1.99988e6 −1.36093 −0.680465 0.732781i \(-0.738222\pi\)
−0.680465 + 0.732781i \(0.738222\pi\)
\(294\) −152291. −0.102755
\(295\) −168140. −0.112491
\(296\) −121507. −0.0806070
\(297\) −139979. −0.0920812
\(298\) −2.75993e6 −1.80035
\(299\) −127600. −0.0825416
\(300\) −165659. −0.106270
\(301\) 2.19538e6 1.39667
\(302\) −3.01205e6 −1.90040
\(303\) −700130. −0.438099
\(304\) 483259. 0.299914
\(305\) −793890. −0.488665
\(306\) 1.32162e6 0.806870
\(307\) 2.66083e6 1.61128 0.805639 0.592407i \(-0.201822\pi\)
0.805639 + 0.592407i \(0.201822\pi\)
\(308\) −537996. −0.323148
\(309\) −484282. −0.288537
\(310\) −429665. −0.253937
\(311\) −2.11645e6 −1.24082 −0.620408 0.784279i \(-0.713033\pi\)
−0.620408 + 0.784279i \(0.713033\pi\)
\(312\) −351623. −0.204499
\(313\) 725870. 0.418792 0.209396 0.977831i \(-0.432850\pi\)
0.209396 + 0.977831i \(0.432850\pi\)
\(314\) 695407. 0.398029
\(315\) 471619. 0.267802
\(316\) −81314.8 −0.0458091
\(317\) −1.20622e6 −0.674186 −0.337093 0.941471i \(-0.609444\pi\)
−0.337093 + 0.941471i \(0.609444\pi\)
\(318\) −1.23271e6 −0.683587
\(319\) 61536.4 0.0338575
\(320\) −630487. −0.344192
\(321\) −815248. −0.441598
\(322\) −190440. −0.102357
\(323\) −864229. −0.460917
\(324\) 152502. 0.0807073
\(325\) −475379. −0.249650
\(326\) −2.34023e6 −1.21959
\(327\) 1.85968e6 0.961765
\(328\) 658405. 0.337916
\(329\) 2.29365e6 1.16826
\(330\) −620420. −0.313618
\(331\) −1.12789e6 −0.565845 −0.282923 0.959143i \(-0.591304\pi\)
−0.282923 + 0.959143i \(0.591304\pi\)
\(332\) −2.21665e6 −1.10370
\(333\) 151226. 0.0747334
\(334\) 609887. 0.299146
\(335\) 502264. 0.244523
\(336\) −1.33172e6 −0.643524
\(337\) −2.51669e6 −1.20713 −0.603567 0.797312i \(-0.706255\pi\)
−0.603567 + 0.797312i \(0.706255\pi\)
\(338\) −81200.1 −0.0386603
\(339\) 754037. 0.356364
\(340\) 2.46464e6 1.15626
\(341\) 229803. 0.107021
\(342\) −237014. −0.109575
\(343\) −2.30038e6 −1.05576
\(344\) −1.18531e6 −0.540054
\(345\) −92403.3 −0.0417965
\(346\) −1.03299e6 −0.463881
\(347\) 3.97910e6 1.77403 0.887015 0.461741i \(-0.152775\pi\)
0.887015 + 0.461741i \(0.152775\pi\)
\(348\) −67041.7 −0.0296754
\(349\) −1.16212e6 −0.510726 −0.255363 0.966845i \(-0.582195\pi\)
−0.255363 + 0.966845i \(0.582195\pi\)
\(350\) −709491. −0.309583
\(351\) 437624. 0.189598
\(352\) 1.35200e6 0.581593
\(353\) −2.71947e6 −1.16158 −0.580788 0.814055i \(-0.697256\pi\)
−0.580788 + 0.814055i \(0.697256\pi\)
\(354\) −232856. −0.0987597
\(355\) −791315. −0.333256
\(356\) −464710. −0.194338
\(357\) 2.38156e6 0.988988
\(358\) 2.80329e6 1.15601
\(359\) −2.66436e6 −1.09108 −0.545540 0.838085i \(-0.683675\pi\)
−0.545540 + 0.838085i \(0.683675\pi\)
\(360\) −254633. −0.103552
\(361\) −2.32111e6 −0.937407
\(362\) −2.94324e6 −1.18047
\(363\) −1.11763e6 −0.445176
\(364\) 1.68197e6 0.665371
\(365\) −3.32340e6 −1.30572
\(366\) −1.09945e6 −0.429017
\(367\) −4.17455e6 −1.61787 −0.808936 0.587897i \(-0.799956\pi\)
−0.808936 + 0.587897i \(0.799956\pi\)
\(368\) 260921. 0.100436
\(369\) −819439. −0.313293
\(370\) 670269. 0.254533
\(371\) −2.22135e6 −0.837879
\(372\) −250363. −0.0938020
\(373\) −2.61953e6 −0.974879 −0.487440 0.873157i \(-0.662069\pi\)
−0.487440 + 0.873157i \(0.662069\pi\)
\(374\) −3.13297e6 −1.15818
\(375\) −1.70275e6 −0.625278
\(376\) −1.23837e6 −0.451732
\(377\) −192385. −0.0697135
\(378\) 653142. 0.235114
\(379\) 1.25240e6 0.447864 0.223932 0.974605i \(-0.428111\pi\)
0.223932 + 0.974605i \(0.428111\pi\)
\(380\) −441999. −0.157023
\(381\) −2.07449e6 −0.732148
\(382\) 4.54641e6 1.59408
\(383\) 5.09439e6 1.77458 0.887289 0.461214i \(-0.152586\pi\)
0.887289 + 0.461214i \(0.152586\pi\)
\(384\) 1.15468e6 0.399609
\(385\) −1.11800e6 −0.384405
\(386\) 2.78616e6 0.951783
\(387\) 1.47522e6 0.500702
\(388\) −2.31719e6 −0.781416
\(389\) 2.50585e6 0.839615 0.419808 0.907613i \(-0.362098\pi\)
0.419808 + 0.907613i \(0.362098\pi\)
\(390\) 1.93965e6 0.645748
\(391\) −466615. −0.154353
\(392\) 148167. 0.0487008
\(393\) 1.68094e6 0.548998
\(394\) 3.92310e6 1.27318
\(395\) −168978. −0.0544927
\(396\) −361514. −0.115848
\(397\) 3.27595e6 1.04318 0.521592 0.853195i \(-0.325338\pi\)
0.521592 + 0.853195i \(0.325338\pi\)
\(398\) 1.24588e6 0.394246
\(399\) −427100. −0.134307
\(400\) 972073. 0.303773
\(401\) 6.06788e6 1.88441 0.942206 0.335033i \(-0.108748\pi\)
0.942206 + 0.335033i \(0.108748\pi\)
\(402\) 695583. 0.214676
\(403\) −718447. −0.220360
\(404\) −1.80818e6 −0.551173
\(405\) 316911. 0.0960063
\(406\) −287129. −0.0864494
\(407\) −358488. −0.107273
\(408\) −1.28583e6 −0.382414
\(409\) −325513. −0.0962189 −0.0481095 0.998842i \(-0.515320\pi\)
−0.0481095 + 0.998842i \(0.515320\pi\)
\(410\) −3.63195e6 −1.06704
\(411\) 1.00626e6 0.293837
\(412\) −1.25072e6 −0.363009
\(413\) −419607. −0.121051
\(414\) −127969. −0.0366947
\(415\) −4.60636e6 −1.31292
\(416\) −4.22683e6 −1.19752
\(417\) 1.75888e6 0.495333
\(418\) 561855. 0.157284
\(419\) 5.62708e6 1.56584 0.782921 0.622121i \(-0.213729\pi\)
0.782921 + 0.622121i \(0.213729\pi\)
\(420\) 1.21802e6 0.336923
\(421\) 1.40296e6 0.385780 0.192890 0.981220i \(-0.438214\pi\)
0.192890 + 0.981220i \(0.438214\pi\)
\(422\) −1.90347e6 −0.520313
\(423\) 1.54125e6 0.418816
\(424\) 1.19933e6 0.323985
\(425\) −1.73839e6 −0.466848
\(426\) −1.09589e6 −0.292578
\(427\) −1.98122e6 −0.525850
\(428\) −2.10549e6 −0.555576
\(429\) −1.03741e6 −0.272149
\(430\) 6.53853e6 1.70533
\(431\) −1.55865e6 −0.404163 −0.202082 0.979369i \(-0.564771\pi\)
−0.202082 + 0.979369i \(0.564771\pi\)
\(432\) −894868. −0.230701
\(433\) 2.65215e6 0.679795 0.339898 0.940462i \(-0.389608\pi\)
0.339898 + 0.940462i \(0.389608\pi\)
\(434\) −1.07226e6 −0.273261
\(435\) −139318. −0.0353007
\(436\) 4.80287e6 1.21000
\(437\) 83680.9 0.0209615
\(438\) −4.60256e6 −1.14634
\(439\) 2.58237e6 0.639525 0.319763 0.947498i \(-0.396397\pi\)
0.319763 + 0.947498i \(0.396397\pi\)
\(440\) 603620. 0.148639
\(441\) −184406. −0.0451521
\(442\) 9.79479e6 2.38473
\(443\) 4.79743e6 1.16145 0.580723 0.814101i \(-0.302770\pi\)
0.580723 + 0.814101i \(0.302770\pi\)
\(444\) 390561. 0.0940223
\(445\) −965704. −0.231177
\(446\) 4.57136e6 1.08820
\(447\) −3.34194e6 −0.791098
\(448\) −1.57343e6 −0.370384
\(449\) 4.66201e6 1.09133 0.545667 0.838002i \(-0.316276\pi\)
0.545667 + 0.838002i \(0.316276\pi\)
\(450\) −476753. −0.110984
\(451\) 1.94252e6 0.449702
\(452\) 1.94740e6 0.448342
\(453\) −3.64724e6 −0.835061
\(454\) 7.75728e6 1.76632
\(455\) 3.49526e6 0.791499
\(456\) 230596. 0.0519327
\(457\) −3.52146e6 −0.788738 −0.394369 0.918952i \(-0.629037\pi\)
−0.394369 + 0.918952i \(0.629037\pi\)
\(458\) −4.51995e6 −1.00686
\(459\) 1.60032e6 0.354549
\(460\) −238644. −0.0525843
\(461\) −3.24447e6 −0.711037 −0.355518 0.934669i \(-0.615696\pi\)
−0.355518 + 0.934669i \(0.615696\pi\)
\(462\) −1.54831e6 −0.337483
\(463\) 3.08362e6 0.668511 0.334255 0.942483i \(-0.391515\pi\)
0.334255 + 0.942483i \(0.391515\pi\)
\(464\) 393395. 0.0848269
\(465\) −520273. −0.111583
\(466\) 7.47076e6 1.59367
\(467\) −4.71258e6 −0.999923 −0.499962 0.866048i \(-0.666653\pi\)
−0.499962 + 0.866048i \(0.666653\pi\)
\(468\) 1.13022e6 0.238533
\(469\) 1.25344e6 0.263131
\(470\) 6.83121e6 1.42644
\(471\) 842054. 0.174899
\(472\) 226551. 0.0468070
\(473\) −3.49709e6 −0.718710
\(474\) −234017. −0.0478412
\(475\) 311756. 0.0633989
\(476\) 6.15070e6 1.24425
\(477\) −1.49267e6 −0.300377
\(478\) 9.12184e6 1.82605
\(479\) −1.95384e6 −0.389089 −0.194545 0.980894i \(-0.562323\pi\)
−0.194545 + 0.980894i \(0.562323\pi\)
\(480\) −3.06091e6 −0.606385
\(481\) 1.12076e6 0.220877
\(482\) 1.00339e7 1.96721
\(483\) −230600. −0.0449771
\(484\) −2.88643e6 −0.560078
\(485\) −4.81530e6 −0.929542
\(486\) 438888. 0.0842875
\(487\) −3.00669e6 −0.574468 −0.287234 0.957860i \(-0.592736\pi\)
−0.287234 + 0.957860i \(0.592736\pi\)
\(488\) 1.06968e6 0.203332
\(489\) −2.83374e6 −0.535906
\(490\) −817331. −0.153783
\(491\) 600072. 0.112331 0.0561655 0.998421i \(-0.482113\pi\)
0.0561655 + 0.998421i \(0.482113\pi\)
\(492\) −2.11631e6 −0.394155
\(493\) −703522. −0.130365
\(494\) −1.75656e6 −0.323851
\(495\) −751254. −0.137808
\(496\) 1.46911e6 0.268132
\(497\) −1.97479e6 −0.358616
\(498\) −6.37933e6 −1.15266
\(499\) −9.20598e6 −1.65508 −0.827540 0.561407i \(-0.810260\pi\)
−0.827540 + 0.561407i \(0.810260\pi\)
\(500\) −4.39759e6 −0.786664
\(501\) 738500. 0.131449
\(502\) 3.33357e6 0.590406
\(503\) −5.84921e6 −1.03081 −0.515403 0.856948i \(-0.672358\pi\)
−0.515403 + 0.856948i \(0.672358\pi\)
\(504\) −635456. −0.111432
\(505\) −3.75754e6 −0.655654
\(506\) 303357. 0.0526717
\(507\) −98323.6 −0.0169878
\(508\) −5.35765e6 −0.921118
\(509\) 7.98607e6 1.36628 0.683139 0.730289i \(-0.260614\pi\)
0.683139 + 0.730289i \(0.260614\pi\)
\(510\) 7.09303e6 1.20755
\(511\) −8.29381e6 −1.40508
\(512\) 6.08669e6 1.02614
\(513\) −286996. −0.0481485
\(514\) 4.87796e6 0.814387
\(515\) −2.59910e6 −0.431822
\(516\) 3.80995e6 0.629935
\(517\) −3.65362e6 −0.601170
\(518\) 1.67271e6 0.273903
\(519\) −1.25083e6 −0.203835
\(520\) −1.88713e6 −0.306051
\(521\) −2.58297e6 −0.416893 −0.208446 0.978034i \(-0.566841\pi\)
−0.208446 + 0.978034i \(0.566841\pi\)
\(522\) −192941. −0.0309918
\(523\) −4.44025e6 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(524\) 4.34125e6 0.690695
\(525\) −859109. −0.136035
\(526\) 9.32011e6 1.46878
\(527\) −2.62725e6 −0.412074
\(528\) 2.12133e6 0.331149
\(529\) −6.39116e6 −0.992980
\(530\) −6.61586e6 −1.02305
\(531\) −281961. −0.0433963
\(532\) −1.10304e6 −0.168971
\(533\) −6.07302e6 −0.925948
\(534\) −1.33740e6 −0.202959
\(535\) −4.37537e6 −0.660891
\(536\) −676748. −0.101745
\(537\) 3.39444e6 0.507964
\(538\) 2.19572e6 0.327056
\(539\) 437143. 0.0648115
\(540\) 818465. 0.120786
\(541\) 4.63492e6 0.680846 0.340423 0.940272i \(-0.389430\pi\)
0.340423 + 0.940272i \(0.389430\pi\)
\(542\) 1.01560e7 1.48499
\(543\) −3.56391e6 −0.518713
\(544\) −1.54569e7 −2.23936
\(545\) 9.98074e6 1.43937
\(546\) 4.84056e6 0.694887
\(547\) −1.30458e7 −1.86425 −0.932124 0.362138i \(-0.882047\pi\)
−0.932124 + 0.362138i \(0.882047\pi\)
\(548\) 2.59881e6 0.369677
\(549\) −1.33131e6 −0.188516
\(550\) 1.13017e6 0.159308
\(551\) 126167. 0.0177038
\(552\) 124504. 0.0173914
\(553\) −421699. −0.0586395
\(554\) −1.34184e6 −0.185749
\(555\) 811615. 0.111845
\(556\) 4.54256e6 0.623180
\(557\) −5.71867e6 −0.781011 −0.390506 0.920600i \(-0.627700\pi\)
−0.390506 + 0.920600i \(0.627700\pi\)
\(558\) −720523. −0.0979631
\(559\) 1.09331e7 1.47984
\(560\) −7.14723e6 −0.963091
\(561\) −3.79365e6 −0.508921
\(562\) 5.56570e6 0.743325
\(563\) 5.22161e6 0.694278 0.347139 0.937814i \(-0.387153\pi\)
0.347139 + 0.937814i \(0.387153\pi\)
\(564\) 3.98049e6 0.526913
\(565\) 4.04685e6 0.533330
\(566\) −1.06599e7 −1.39865
\(567\) 790876. 0.103312
\(568\) 1.06621e6 0.138667
\(569\) −845736. −0.109510 −0.0547550 0.998500i \(-0.517438\pi\)
−0.0547550 + 0.998500i \(0.517438\pi\)
\(570\) −1.27204e6 −0.163988
\(571\) −4.22254e6 −0.541981 −0.270990 0.962582i \(-0.587351\pi\)
−0.270990 + 0.962582i \(0.587351\pi\)
\(572\) −2.67925e6 −0.342392
\(573\) 5.50516e6 0.700460
\(574\) −9.06382e6 −1.14824
\(575\) 168324. 0.0212312
\(576\) −1.05729e6 −0.132782
\(577\) −8.12269e6 −1.01569 −0.507844 0.861449i \(-0.669557\pi\)
−0.507844 + 0.861449i \(0.669557\pi\)
\(578\) 2.52649e7 3.14555
\(579\) 3.37371e6 0.418226
\(580\) −359807. −0.0444119
\(581\) −1.14955e7 −1.41283
\(582\) −6.66868e6 −0.816080
\(583\) 3.53844e6 0.431163
\(584\) 4.47793e6 0.543307
\(585\) 2.34869e6 0.283750
\(586\) −1.48644e7 −1.78814
\(587\) 1.23310e7 1.47708 0.738539 0.674210i \(-0.235516\pi\)
0.738539 + 0.674210i \(0.235516\pi\)
\(588\) −476252. −0.0568059
\(589\) 471162. 0.0559605
\(590\) −1.24972e6 −0.147803
\(591\) 4.75040e6 0.559450
\(592\) −2.29178e6 −0.268762
\(593\) −1.45287e7 −1.69664 −0.848320 0.529484i \(-0.822386\pi\)
−0.848320 + 0.529484i \(0.822386\pi\)
\(594\) −1.04041e6 −0.120987
\(595\) 1.27816e7 1.48011
\(596\) −8.63102e6 −0.995283
\(597\) 1.50861e6 0.173237
\(598\) −948402. −0.108452
\(599\) 8.46504e6 0.963967 0.481983 0.876180i \(-0.339917\pi\)
0.481983 + 0.876180i \(0.339917\pi\)
\(600\) 463843. 0.0526009
\(601\) 4.80633e6 0.542785 0.271392 0.962469i \(-0.412516\pi\)
0.271392 + 0.962469i \(0.412516\pi\)
\(602\) 1.63174e7 1.83510
\(603\) 842268. 0.0943315
\(604\) −9.41948e6 −1.05059
\(605\) −5.99824e6 −0.666247
\(606\) −5.20379e6 −0.575623
\(607\) −7.55460e6 −0.832223 −0.416111 0.909314i \(-0.636607\pi\)
−0.416111 + 0.909314i \(0.636607\pi\)
\(608\) 2.77198e6 0.304110
\(609\) −347679. −0.0379870
\(610\) −5.90068e6 −0.642062
\(611\) 1.14225e7 1.23782
\(612\) 4.13305e6 0.446059
\(613\) 1.78145e7 1.91480 0.957399 0.288768i \(-0.0932456\pi\)
0.957399 + 0.288768i \(0.0932456\pi\)
\(614\) 1.97769e7 2.11708
\(615\) −4.39786e6 −0.468871
\(616\) 1.50638e6 0.159950
\(617\) 1.13067e6 0.119570 0.0597851 0.998211i \(-0.480958\pi\)
0.0597851 + 0.998211i \(0.480958\pi\)
\(618\) −3.59948e6 −0.379113
\(619\) 39879.3 0.00418332 0.00209166 0.999998i \(-0.499334\pi\)
0.00209166 + 0.999998i \(0.499334\pi\)
\(620\) −1.34368e6 −0.140383
\(621\) −154955. −0.0161241
\(622\) −1.57308e7 −1.63032
\(623\) −2.40999e6 −0.248768
\(624\) −6.63204e6 −0.681845
\(625\) −6.66386e6 −0.682379
\(626\) 5.39511e6 0.550256
\(627\) 680339. 0.0691125
\(628\) 2.17472e6 0.220041
\(629\) 4.09846e6 0.413042
\(630\) 3.50536e6 0.351869
\(631\) 7.70574e6 0.770443 0.385222 0.922824i \(-0.374125\pi\)
0.385222 + 0.922824i \(0.374125\pi\)
\(632\) 227681. 0.0226743
\(633\) −2.30487e6 −0.228632
\(634\) −8.96539e6 −0.885821
\(635\) −1.11336e7 −1.09573
\(636\) −3.85501e6 −0.377905
\(637\) −1.36667e6 −0.133449
\(638\) 457376. 0.0444858
\(639\) −1.32699e6 −0.128563
\(640\) 6.19709e6 0.598050
\(641\) 1.60378e7 1.54170 0.770848 0.637019i \(-0.219833\pi\)
0.770848 + 0.637019i \(0.219833\pi\)
\(642\) −6.05942e6 −0.580221
\(643\) 2.62458e6 0.250341 0.125170 0.992135i \(-0.460052\pi\)
0.125170 + 0.992135i \(0.460052\pi\)
\(644\) −595555. −0.0565858
\(645\) 7.91738e6 0.749346
\(646\) −6.42348e6 −0.605605
\(647\) 1.06120e6 0.0996634 0.0498317 0.998758i \(-0.484132\pi\)
0.0498317 + 0.998758i \(0.484132\pi\)
\(648\) −427004. −0.0399479
\(649\) 668404. 0.0622912
\(650\) −3.53331e6 −0.328018
\(651\) −1.29838e6 −0.120074
\(652\) −7.31852e6 −0.674224
\(653\) −1.18303e7 −1.08571 −0.542854 0.839827i \(-0.682656\pi\)
−0.542854 + 0.839827i \(0.682656\pi\)
\(654\) 1.38223e7 1.26367
\(655\) 9.02145e6 0.821624
\(656\) 1.24183e7 1.12669
\(657\) −5.57315e6 −0.503718
\(658\) 1.70478e7 1.53499
\(659\) 3.08114e6 0.276375 0.138187 0.990406i \(-0.455872\pi\)
0.138187 + 0.990406i \(0.455872\pi\)
\(660\) −1.94022e6 −0.173376
\(661\) −1.52738e7 −1.35970 −0.679850 0.733351i \(-0.737955\pi\)
−0.679850 + 0.733351i \(0.737955\pi\)
\(662\) −8.38318e6 −0.743471
\(663\) 1.18603e7 1.04788
\(664\) 6.20658e6 0.546301
\(665\) −2.29221e6 −0.201002
\(666\) 1.12400e6 0.0981932
\(667\) 68120.0 0.00592871
\(668\) 1.90727e6 0.165376
\(669\) 5.53536e6 0.478168
\(670\) 3.73314e6 0.321282
\(671\) 3.15593e6 0.270596
\(672\) −7.63876e6 −0.652528
\(673\) 1.59289e6 0.135565 0.0677824 0.997700i \(-0.478408\pi\)
0.0677824 + 0.997700i \(0.478408\pi\)
\(674\) −1.87056e7 −1.58607
\(675\) −577291. −0.0487680
\(676\) −253934. −0.0213724
\(677\) −1.45086e7 −1.21662 −0.608308 0.793701i \(-0.708151\pi\)
−0.608308 + 0.793701i \(0.708151\pi\)
\(678\) 5.60446e6 0.468231
\(679\) −1.20170e7 −1.00028
\(680\) −6.90096e6 −0.572318
\(681\) 9.39313e6 0.776145
\(682\) 1.70804e6 0.140617
\(683\) 1.08149e7 0.887094 0.443547 0.896251i \(-0.353720\pi\)
0.443547 + 0.896251i \(0.353720\pi\)
\(684\) −741206. −0.0605757
\(685\) 5.40053e6 0.439754
\(686\) −1.70978e7 −1.38717
\(687\) −5.47312e6 −0.442429
\(688\) −2.23565e7 −1.80066
\(689\) −1.10624e7 −0.887775
\(690\) −686798. −0.0549169
\(691\) 1.24968e7 0.995639 0.497820 0.867281i \(-0.334134\pi\)
0.497820 + 0.867281i \(0.334134\pi\)
\(692\) −3.23043e6 −0.256446
\(693\) −1.87481e6 −0.148295
\(694\) 2.95751e7 2.33092
\(695\) 9.43978e6 0.741310
\(696\) 187716. 0.0146885
\(697\) −2.22081e7 −1.73153
\(698\) −8.63759e6 −0.671049
\(699\) 9.04619e6 0.700282
\(700\) −2.21876e6 −0.171146
\(701\) −4.63586e6 −0.356316 −0.178158 0.984002i \(-0.557014\pi\)
−0.178158 + 0.984002i \(0.557014\pi\)
\(702\) 3.25269e6 0.249115
\(703\) −735003. −0.0560920
\(704\) 2.50636e6 0.190595
\(705\) 8.27177e6 0.626796
\(706\) −2.02128e7 −1.52621
\(707\) −9.37723e6 −0.705547
\(708\) −728202. −0.0545970
\(709\) −1.99355e7 −1.48940 −0.744699 0.667401i \(-0.767407\pi\)
−0.744699 + 0.667401i \(0.767407\pi\)
\(710\) −5.88153e6 −0.437870
\(711\) −283367. −0.0210221
\(712\) 1.30118e6 0.0961919
\(713\) 254390. 0.0187403
\(714\) 1.77012e7 1.29944
\(715\) −5.56769e6 −0.407296
\(716\) 8.76660e6 0.639070
\(717\) 1.10455e7 0.802391
\(718\) −1.98031e7 −1.43358
\(719\) 4.81963e6 0.347689 0.173845 0.984773i \(-0.444381\pi\)
0.173845 + 0.984773i \(0.444381\pi\)
\(720\) −4.80268e6 −0.345265
\(721\) −6.48625e6 −0.464682
\(722\) −1.72519e7 −1.23167
\(723\) 1.21498e7 0.864417
\(724\) −9.20428e6 −0.652595
\(725\) 253784. 0.0179316
\(726\) −8.30692e6 −0.584923
\(727\) 3.77212e6 0.264697 0.132349 0.991203i \(-0.457748\pi\)
0.132349 + 0.991203i \(0.457748\pi\)
\(728\) −4.70949e6 −0.329340
\(729\) 531441. 0.0370370
\(730\) −2.47016e7 −1.71560
\(731\) 3.99809e7 2.76732
\(732\) −3.43828e6 −0.237172
\(733\) −8.67096e6 −0.596084 −0.298042 0.954553i \(-0.596333\pi\)
−0.298042 + 0.954553i \(0.596333\pi\)
\(734\) −3.10278e7 −2.12574
\(735\) −989689. −0.0675742
\(736\) 1.49665e6 0.101841
\(737\) −1.99664e6 −0.135404
\(738\) −6.09057e6 −0.411639
\(739\) 2.67260e7 1.80021 0.900103 0.435678i \(-0.143491\pi\)
0.900103 + 0.435678i \(0.143491\pi\)
\(740\) 2.09611e6 0.140713
\(741\) −2.12698e6 −0.142305
\(742\) −1.65104e7 −1.10090
\(743\) 882576. 0.0586516 0.0293258 0.999570i \(-0.490664\pi\)
0.0293258 + 0.999570i \(0.490664\pi\)
\(744\) 701013. 0.0464294
\(745\) −1.79359e7 −1.18395
\(746\) −1.94699e7 −1.28091
\(747\) −7.72460e6 −0.506494
\(748\) −9.79762e6 −0.640275
\(749\) −1.09191e7 −0.711183
\(750\) −1.26559e7 −0.821561
\(751\) 1.50079e7 0.971005 0.485502 0.874235i \(-0.338637\pi\)
0.485502 + 0.874235i \(0.338637\pi\)
\(752\) −2.33572e7 −1.50618
\(753\) 4.03656e6 0.259432
\(754\) −1.42992e6 −0.0915974
\(755\) −1.95744e7 −1.24974
\(756\) 2.04254e6 0.129977
\(757\) −2.73466e7 −1.73446 −0.867228 0.497910i \(-0.834101\pi\)
−0.867228 + 0.497910i \(0.834101\pi\)
\(758\) 9.30862e6 0.588454
\(759\) 367329. 0.0231446
\(760\) 1.23759e6 0.0777219
\(761\) 1.85952e7 1.16397 0.581983 0.813201i \(-0.302277\pi\)
0.581983 + 0.813201i \(0.302277\pi\)
\(762\) −1.54189e7 −0.961979
\(763\) 2.49077e7 1.54890
\(764\) 1.42178e7 0.881250
\(765\) 8.58881e6 0.530615
\(766\) 3.78646e7 2.33164
\(767\) −2.08967e6 −0.128259
\(768\) 1.23416e7 0.755035
\(769\) 1.69589e6 0.103414 0.0517072 0.998662i \(-0.483534\pi\)
0.0517072 + 0.998662i \(0.483534\pi\)
\(770\) −8.30964e6 −0.505074
\(771\) 5.90663e6 0.357852
\(772\) 8.71305e6 0.526171
\(773\) −8.47019e6 −0.509853 −0.254926 0.966960i \(-0.582051\pi\)
−0.254926 + 0.966960i \(0.582051\pi\)
\(774\) 1.09647e7 0.657879
\(775\) 947739. 0.0566806
\(776\) 6.48810e6 0.386780
\(777\) 2.02545e6 0.120356
\(778\) 1.86250e7 1.10318
\(779\) 3.98272e6 0.235145
\(780\) 6.06580e6 0.356987
\(781\) 3.14570e6 0.184539
\(782\) −3.46817e6 −0.202807
\(783\) −233628. −0.0136182
\(784\) 2.79461e6 0.162379
\(785\) 4.51923e6 0.261752
\(786\) 1.24938e7 0.721335
\(787\) −7.45024e6 −0.428779 −0.214389 0.976748i \(-0.568776\pi\)
−0.214389 + 0.976748i \(0.568776\pi\)
\(788\) 1.22686e7 0.703846
\(789\) 1.12855e7 0.645401
\(790\) −1.25595e6 −0.0715987
\(791\) 1.00992e7 0.573915
\(792\) 1.01224e6 0.0573414
\(793\) −9.86658e6 −0.557165
\(794\) 2.43489e7 1.37065
\(795\) −8.01101e6 −0.449541
\(796\) 3.89618e6 0.217950
\(797\) 1.44140e7 0.803783 0.401892 0.915687i \(-0.368353\pi\)
0.401892 + 0.915687i \(0.368353\pi\)
\(798\) −3.17447e6 −0.176467
\(799\) 4.17705e7 2.31474
\(800\) 5.57582e6 0.308023
\(801\) −1.61943e6 −0.0891827
\(802\) 4.51002e7 2.47595
\(803\) 1.32114e7 0.723039
\(804\) 2.17527e6 0.118679
\(805\) −1.23761e6 −0.0673122
\(806\) −5.33994e6 −0.289533
\(807\) 2.65875e6 0.143712
\(808\) 5.06288e6 0.272816
\(809\) −2.19181e7 −1.17742 −0.588710 0.808344i \(-0.700364\pi\)
−0.588710 + 0.808344i \(0.700364\pi\)
\(810\) 2.35548e6 0.126144
\(811\) −1.90616e6 −0.101767 −0.0508836 0.998705i \(-0.516204\pi\)
−0.0508836 + 0.998705i \(0.516204\pi\)
\(812\) −897927. −0.0477915
\(813\) 1.22977e7 0.652525
\(814\) −2.66451e6 −0.140947
\(815\) −1.52085e7 −0.802031
\(816\) −2.42524e7 −1.27506
\(817\) −7.17002e6 −0.375807
\(818\) −2.41941e6 −0.126423
\(819\) 5.86134e6 0.305342
\(820\) −1.13581e7 −0.589888
\(821\) −5.58709e6 −0.289286 −0.144643 0.989484i \(-0.546203\pi\)
−0.144643 + 0.989484i \(0.546203\pi\)
\(822\) 7.47916e6 0.386077
\(823\) 7.03605e6 0.362101 0.181050 0.983474i \(-0.442050\pi\)
0.181050 + 0.983474i \(0.442050\pi\)
\(824\) 3.50201e6 0.179680
\(825\) 1.36850e6 0.0700018
\(826\) −3.11877e6 −0.159050
\(827\) −1.36355e7 −0.693276 −0.346638 0.937999i \(-0.612677\pi\)
−0.346638 + 0.937999i \(0.612677\pi\)
\(828\) −400192. −0.0202858
\(829\) 8.78197e6 0.443819 0.221909 0.975067i \(-0.428771\pi\)
0.221909 + 0.975067i \(0.428771\pi\)
\(830\) −3.42373e7 −1.72506
\(831\) −1.62481e6 −0.0816204
\(832\) −7.83578e6 −0.392440
\(833\) −4.99770e6 −0.249550
\(834\) 1.30731e7 0.650824
\(835\) 3.96346e6 0.196725
\(836\) 1.75707e6 0.0869507
\(837\) −872467. −0.0430463
\(838\) 4.18239e7 2.05738
\(839\) 2.47541e7 1.21407 0.607034 0.794676i \(-0.292359\pi\)
0.607034 + 0.794676i \(0.292359\pi\)
\(840\) −3.41044e6 −0.166768
\(841\) −2.04084e7 −0.994993
\(842\) 1.04277e7 0.506882
\(843\) 6.73939e6 0.326627
\(844\) −5.95264e6 −0.287643
\(845\) −527694. −0.0254238
\(846\) 1.14555e7 0.550287
\(847\) −1.49691e7 −0.716946
\(848\) 2.26209e7 1.08024
\(849\) −1.29078e7 −0.614587
\(850\) −1.29208e7 −0.613397
\(851\) −396843. −0.0187843
\(852\) −3.42712e6 −0.161745
\(853\) 3.15345e7 1.48393 0.741964 0.670439i \(-0.233894\pi\)
0.741964 + 0.670439i \(0.233894\pi\)
\(854\) −1.47256e7 −0.690921
\(855\) −1.54028e6 −0.0720585
\(856\) 5.89534e6 0.274995
\(857\) −3.48098e7 −1.61901 −0.809505 0.587113i \(-0.800265\pi\)
−0.809505 + 0.587113i \(0.800265\pi\)
\(858\) −7.71067e6 −0.357580
\(859\) −3.28394e7 −1.51849 −0.759246 0.650803i \(-0.774432\pi\)
−0.759246 + 0.650803i \(0.774432\pi\)
\(860\) 2.04477e7 0.942754
\(861\) −1.09752e7 −0.504550
\(862\) −1.15849e7 −0.531035
\(863\) 2.13743e7 0.976935 0.488468 0.872582i \(-0.337556\pi\)
0.488468 + 0.872582i \(0.337556\pi\)
\(864\) −5.13297e6 −0.233929
\(865\) −6.71309e6 −0.305058
\(866\) 1.97124e7 0.893191
\(867\) 3.05927e7 1.38220
\(868\) −3.35325e6 −0.151066
\(869\) 671736. 0.0301752
\(870\) −1.03550e6 −0.0463821
\(871\) 6.24221e6 0.278800
\(872\) −1.34480e7 −0.598916
\(873\) −8.07497e6 −0.358596
\(874\) 621967. 0.0275416
\(875\) −2.28059e7 −1.00700
\(876\) −1.43934e7 −0.633729
\(877\) 1.54465e7 0.678158 0.339079 0.940758i \(-0.389885\pi\)
0.339079 + 0.940758i \(0.389885\pi\)
\(878\) 1.91938e7 0.840280
\(879\) −1.79990e7 −0.785733
\(880\) 1.13850e7 0.495595
\(881\) 4.43148e6 0.192357 0.0961787 0.995364i \(-0.469338\pi\)
0.0961787 + 0.995364i \(0.469338\pi\)
\(882\) −1.37062e6 −0.0593259
\(883\) 6.63288e6 0.286286 0.143143 0.989702i \(-0.454279\pi\)
0.143143 + 0.989702i \(0.454279\pi\)
\(884\) 3.06309e7 1.31834
\(885\) −1.51326e6 −0.0649465
\(886\) 3.56574e7 1.52604
\(887\) −1.88116e7 −0.802818 −0.401409 0.915899i \(-0.631479\pi\)
−0.401409 + 0.915899i \(0.631479\pi\)
\(888\) −1.09357e6 −0.0465385
\(889\) −2.77848e7 −1.17911
\(890\) −7.17770e6 −0.303746
\(891\) −1.25981e6 −0.0531631
\(892\) 1.42958e7 0.601585
\(893\) −7.49096e6 −0.314347
\(894\) −2.48394e7 −1.03943
\(895\) 1.82177e7 0.760213
\(896\) 1.54653e7 0.643560
\(897\) −1.14840e6 −0.0476554
\(898\) 3.46509e7 1.43392
\(899\) 383547. 0.0158278
\(900\) −1.49093e6 −0.0613552
\(901\) −4.04537e7 −1.66015
\(902\) 1.44380e7 0.590869
\(903\) 1.97584e7 0.806368
\(904\) −5.45270e6 −0.221917
\(905\) −1.91272e7 −0.776301
\(906\) −2.71085e7 −1.09720
\(907\) 8.97079e6 0.362087 0.181043 0.983475i \(-0.442053\pi\)
0.181043 + 0.983475i \(0.442053\pi\)
\(908\) 2.42590e7 0.976470
\(909\) −6.30117e6 −0.252936
\(910\) 2.59789e7 1.03996
\(911\) 4.68204e7 1.86913 0.934564 0.355794i \(-0.115789\pi\)
0.934564 + 0.355794i \(0.115789\pi\)
\(912\) 4.34933e6 0.173155
\(913\) 1.83116e7 0.727024
\(914\) −2.61737e7 −1.03633
\(915\) −7.14501e6 −0.282131
\(916\) −1.41351e7 −0.556621
\(917\) 2.25138e7 0.884147
\(918\) 1.18946e7 0.465846
\(919\) −2.58264e7 −1.00873 −0.504366 0.863490i \(-0.668274\pi\)
−0.504366 + 0.863490i \(0.668274\pi\)
\(920\) 668200. 0.0260278
\(921\) 2.39474e7 0.930272
\(922\) −2.41149e7 −0.934240
\(923\) −9.83457e6 −0.379971
\(924\) −4.84196e6 −0.186570
\(925\) −1.47845e6 −0.0568137
\(926\) 2.29193e7 0.878364
\(927\) −4.35853e6 −0.166587
\(928\) 2.25652e6 0.0860139
\(929\) 4.55842e7 1.73291 0.866453 0.499259i \(-0.166394\pi\)
0.866453 + 0.499259i \(0.166394\pi\)
\(930\) −3.86699e6 −0.146611
\(931\) 896268. 0.0338894
\(932\) 2.33630e7 0.881026
\(933\) −1.90481e7 −0.716386
\(934\) −3.50268e7 −1.31381
\(935\) −2.03602e7 −0.761647
\(936\) −3.16461e6 −0.118067
\(937\) 1.83075e6 0.0681208 0.0340604 0.999420i \(-0.489156\pi\)
0.0340604 + 0.999420i \(0.489156\pi\)
\(938\) 9.31634e6 0.345731
\(939\) 6.53283e6 0.241790
\(940\) 2.13630e7 0.788573
\(941\) 6.42585e6 0.236568 0.118284 0.992980i \(-0.462261\pi\)
0.118284 + 0.992980i \(0.462261\pi\)
\(942\) 6.25866e6 0.229802
\(943\) 2.15035e6 0.0787463
\(944\) 4.27303e6 0.156065
\(945\) 4.24457e6 0.154616
\(946\) −2.59925e7 −0.944322
\(947\) −2.39260e7 −0.866953 −0.433477 0.901165i \(-0.642713\pi\)
−0.433477 + 0.901165i \(0.642713\pi\)
\(948\) −731833. −0.0264479
\(949\) −4.13037e7 −1.48876
\(950\) 2.31716e6 0.0833006
\(951\) −1.08560e7 −0.389241
\(952\) −1.72219e7 −0.615869
\(953\) 3.98437e7 1.42111 0.710554 0.703643i \(-0.248445\pi\)
0.710554 + 0.703643i \(0.248445\pi\)
\(954\) −1.10944e7 −0.394669
\(955\) 2.95457e7 1.04830
\(956\) 2.85264e7 1.00949
\(957\) 553827. 0.0195476
\(958\) −1.45221e7 −0.511230
\(959\) 1.34774e7 0.473218
\(960\) −5.67438e6 −0.198720
\(961\) −2.71968e7 −0.949970
\(962\) 8.33019e6 0.290213
\(963\) −7.33723e6 −0.254957
\(964\) 3.13785e7 1.08752
\(965\) 1.81064e7 0.625913
\(966\) −1.71396e6 −0.0590959
\(967\) 4.45202e7 1.53105 0.765527 0.643403i \(-0.222478\pi\)
0.765527 + 0.643403i \(0.222478\pi\)
\(968\) 8.08198e6 0.277223
\(969\) −7.77806e6 −0.266111
\(970\) −3.57903e7 −1.22134
\(971\) 4.02063e7 1.36850 0.684252 0.729245i \(-0.260129\pi\)
0.684252 + 0.729245i \(0.260129\pi\)
\(972\) 1.37252e6 0.0465964
\(973\) 2.35577e7 0.797722
\(974\) −2.23475e7 −0.754801
\(975\) −4.27841e6 −0.144136
\(976\) 2.01755e7 0.677954
\(977\) −1.46923e7 −0.492440 −0.246220 0.969214i \(-0.579189\pi\)
−0.246220 + 0.969214i \(0.579189\pi\)
\(978\) −2.10621e7 −0.704133
\(979\) 3.83894e6 0.128013
\(980\) −2.55601e6 −0.0850152
\(981\) 1.67371e7 0.555275
\(982\) 4.46010e6 0.147593
\(983\) −550436. −0.0181687 −0.00908433 0.999959i \(-0.502892\pi\)
−0.00908433 + 0.999959i \(0.502892\pi\)
\(984\) 5.92564e6 0.195096
\(985\) 2.54950e7 0.837268
\(986\) −5.22900e6 −0.171288
\(987\) 2.06429e7 0.674493
\(988\) −5.49322e6 −0.179034
\(989\) −3.87124e6 −0.125852
\(990\) −5.58378e6 −0.181067
\(991\) −3.24918e7 −1.05097 −0.525485 0.850803i \(-0.676116\pi\)
−0.525485 + 0.850803i \(0.676116\pi\)
\(992\) 8.42681e6 0.271884
\(993\) −1.01510e7 −0.326691
\(994\) −1.46778e7 −0.471190
\(995\) 8.09657e6 0.259265
\(996\) −1.99498e7 −0.637221
\(997\) 619302. 0.0197317 0.00986586 0.999951i \(-0.496860\pi\)
0.00986586 + 0.999951i \(0.496860\pi\)
\(998\) −6.84245e7 −2.17463
\(999\) 1.36103e6 0.0431474
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.1.9 12
3.2 odd 2 531.6.a.c.1.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.c.1.9 12 1.1 even 1 trivial
531.6.a.c.1.4 12 3.2 odd 2