Properties

Label 177.6.a.c.1.10
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 1.10
Root \(-7.23155\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +826.983 q^{10} +542.050 q^{11} +478.994 q^{12} -202.326 q^{13} -1120.58 q^{14} +806.240 q^{15} +105.442 q^{16} -431.232 q^{17} +747.756 q^{18} +362.462 q^{19} +4767.70 q^{20} -1092.47 q^{21} +5003.96 q^{22} +1693.68 q^{23} +1763.17 q^{24} +4899.97 q^{25} -1867.79 q^{26} +729.000 q^{27} -6460.34 q^{28} -7671.32 q^{29} +7442.84 q^{30} -2429.08 q^{31} -5295.65 q^{32} +4878.45 q^{33} -3980.94 q^{34} -10874.0 q^{35} +4310.94 q^{36} +2539.77 q^{37} +3346.09 q^{38} -1820.94 q^{39} +17549.8 q^{40} +6567.27 q^{41} -10085.2 q^{42} +779.187 q^{43} +28848.7 q^{44} +7256.16 q^{45} +15635.3 q^{46} -13880.3 q^{47} +948.975 q^{48} -2072.46 q^{49} +45234.3 q^{50} -3881.09 q^{51} -10768.1 q^{52} +14568.1 q^{53} +6729.80 q^{54} +48558.0 q^{55} -23780.4 q^{56} +3262.16 q^{57} -70818.2 q^{58} -3481.00 q^{59} +42909.3 q^{60} +19600.2 q^{61} -22424.2 q^{62} -9832.26 q^{63} -52261.2 q^{64} -18124.8 q^{65} +45035.7 q^{66} -56140.8 q^{67} -22950.8 q^{68} +15243.2 q^{69} -100384. q^{70} -37168.2 q^{71} +15868.5 q^{72} +82040.6 q^{73} +23446.1 q^{74} +44099.7 q^{75} +19290.8 q^{76} -65797.3 q^{77} -16810.1 q^{78} +77491.2 q^{79} +9445.69 q^{80} +6561.00 q^{81} +60626.0 q^{82} -63660.2 q^{83} -58143.1 q^{84} -38630.7 q^{85} +7193.11 q^{86} -69041.9 q^{87} +106192. q^{88} -15534.4 q^{89} +66985.6 q^{90} +24559.6 q^{91} +90140.5 q^{92} -21861.7 q^{93} -128137. q^{94} +32470.2 q^{95} -47660.9 q^{96} -93095.6 q^{97} -19132.0 q^{98} +43906.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + O(q^{10}) \) \( 12q + 22q^{2} + 108q^{3} + 198q^{4} + 158q^{5} + 198q^{6} + 413q^{7} + 723q^{8} + 972q^{9} + 601q^{10} + 1480q^{11} + 1782q^{12} + 472q^{13} + 1065q^{14} + 1422q^{15} + 6370q^{16} + 1565q^{17} + 1782q^{18} + 3939q^{19} + 8033q^{20} + 3717q^{21} - 1738q^{22} + 7245q^{23} + 6507q^{24} + 9690q^{25} + 3764q^{26} + 8748q^{27} + 12154q^{28} + 10003q^{29} + 5409q^{30} + 7295q^{31} + 11628q^{32} + 13320q^{33} - 16344q^{34} + 11015q^{35} + 16038q^{36} + 6741q^{37} + 3035q^{38} + 4248q^{39} + 5572q^{40} + 34025q^{41} + 9585q^{42} - 6336q^{43} + 41168q^{44} + 12798q^{45} + 2345q^{46} + 66167q^{47} + 57330q^{48} + 28319q^{49} + 31173q^{50} + 14085q^{51} + 16440q^{52} + 62290q^{53} + 16038q^{54} + 55764q^{55} + 107306q^{56} + 35451q^{57} + 37952q^{58} - 41772q^{59} + 72297q^{60} + 68469q^{61} + 99190q^{62} + 33453q^{63} + 68525q^{64} + 80156q^{65} - 15642q^{66} + 113310q^{67} + 33887q^{68} + 65205q^{69} + 32034q^{70} + 84520q^{71} + 58563q^{72} + 135895q^{73} - 31962q^{74} + 87210q^{75} - 61848q^{76} - 3799q^{77} + 33876q^{78} + 14122q^{79} + 77609q^{80} + 78732q^{81} - 1501q^{82} + 114463q^{83} + 109386q^{84} - 101097q^{85} - 203536q^{86} + 90027q^{87} - 244967q^{88} + 189109q^{89} + 48681q^{90} - 168249q^{91} - 71946q^{92} + 65655q^{93} - 472284q^{94} + 21923q^{95} + 104652q^{96} - 76192q^{97} - 17544q^{98} + 119880q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.23155 1.63192 0.815961 0.578106i \(-0.196208\pi\)
0.815961 + 0.578106i \(0.196208\pi\)
\(3\) 9.00000 0.577350
\(4\) 53.2215 1.66317
\(5\) 89.5822 1.60249 0.801247 0.598333i \(-0.204170\pi\)
0.801247 + 0.598333i \(0.204170\pi\)
\(6\) 83.0840 0.942191
\(7\) −121.386 −0.936318 −0.468159 0.883644i \(-0.655083\pi\)
−0.468159 + 0.883644i \(0.655083\pi\)
\(8\) 195.908 1.08225
\(9\) 81.0000 0.333333
\(10\) 826.983 2.61515
\(11\) 542.050 1.35070 0.675348 0.737499i \(-0.263993\pi\)
0.675348 + 0.737499i \(0.263993\pi\)
\(12\) 478.994 0.960233
\(13\) −202.326 −0.332043 −0.166021 0.986122i \(-0.553092\pi\)
−0.166021 + 0.986122i \(0.553092\pi\)
\(14\) −1120.58 −1.52800
\(15\) 806.240 0.925201
\(16\) 105.442 0.102970
\(17\) −431.232 −0.361900 −0.180950 0.983492i \(-0.557917\pi\)
−0.180950 + 0.983492i \(0.557917\pi\)
\(18\) 747.756 0.543974
\(19\) 362.462 0.230345 0.115173 0.993346i \(-0.463258\pi\)
0.115173 + 0.993346i \(0.463258\pi\)
\(20\) 4767.70 2.66523
\(21\) −1092.47 −0.540583
\(22\) 5003.96 2.20423
\(23\) 1693.68 0.667595 0.333797 0.942645i \(-0.391670\pi\)
0.333797 + 0.942645i \(0.391670\pi\)
\(24\) 1763.17 0.624835
\(25\) 4899.97 1.56799
\(26\) −1867.79 −0.541868
\(27\) 729.000 0.192450
\(28\) −6460.34 −1.55726
\(29\) −7671.32 −1.69385 −0.846925 0.531712i \(-0.821549\pi\)
−0.846925 + 0.531712i \(0.821549\pi\)
\(30\) 7442.84 1.50986
\(31\) −2429.08 −0.453980 −0.226990 0.973897i \(-0.572889\pi\)
−0.226990 + 0.973897i \(0.572889\pi\)
\(32\) −5295.65 −0.914207
\(33\) 4878.45 0.779825
\(34\) −3980.94 −0.590593
\(35\) −10874.0 −1.50044
\(36\) 4310.94 0.554391
\(37\) 2539.77 0.304994 0.152497 0.988304i \(-0.451269\pi\)
0.152497 + 0.988304i \(0.451269\pi\)
\(38\) 3346.09 0.375905
\(39\) −1820.94 −0.191705
\(40\) 17549.8 1.73429
\(41\) 6567.27 0.610134 0.305067 0.952331i \(-0.401321\pi\)
0.305067 + 0.952331i \(0.401321\pi\)
\(42\) −10085.2 −0.882190
\(43\) 779.187 0.0642645 0.0321322 0.999484i \(-0.489770\pi\)
0.0321322 + 0.999484i \(0.489770\pi\)
\(44\) 28848.7 2.24644
\(45\) 7256.16 0.534165
\(46\) 15635.3 1.08946
\(47\) −13880.3 −0.916549 −0.458275 0.888811i \(-0.651532\pi\)
−0.458275 + 0.888811i \(0.651532\pi\)
\(48\) 948.975 0.0594500
\(49\) −2072.46 −0.123309
\(50\) 45234.3 2.55884
\(51\) −3881.09 −0.208943
\(52\) −10768.1 −0.552244
\(53\) 14568.1 0.712382 0.356191 0.934413i \(-0.384075\pi\)
0.356191 + 0.934413i \(0.384075\pi\)
\(54\) 6729.80 0.314064
\(55\) 48558.0 2.16448
\(56\) −23780.4 −1.01333
\(57\) 3262.16 0.132990
\(58\) −70818.2 −2.76423
\(59\) −3481.00 −0.130189
\(60\) 42909.3 1.53877
\(61\) 19600.2 0.674429 0.337214 0.941428i \(-0.390515\pi\)
0.337214 + 0.941428i \(0.390515\pi\)
\(62\) −22424.2 −0.740861
\(63\) −9832.26 −0.312106
\(64\) −52261.2 −1.59489
\(65\) −18124.8 −0.532097
\(66\) 45035.7 1.27261
\(67\) −56140.8 −1.52789 −0.763944 0.645283i \(-0.776740\pi\)
−0.763944 + 0.645283i \(0.776740\pi\)
\(68\) −22950.8 −0.601903
\(69\) 15243.2 0.385436
\(70\) −100384. −2.44861
\(71\) −37168.2 −0.875036 −0.437518 0.899210i \(-0.644142\pi\)
−0.437518 + 0.899210i \(0.644142\pi\)
\(72\) 15868.5 0.360749
\(73\) 82040.6 1.80186 0.900931 0.433962i \(-0.142885\pi\)
0.900931 + 0.433962i \(0.142885\pi\)
\(74\) 23446.1 0.497726
\(75\) 44099.7 0.905280
\(76\) 19290.8 0.383104
\(77\) −65797.3 −1.26468
\(78\) −16810.1 −0.312848
\(79\) 77491.2 1.39696 0.698481 0.715629i \(-0.253860\pi\)
0.698481 + 0.715629i \(0.253860\pi\)
\(80\) 9445.69 0.165009
\(81\) 6561.00 0.111111
\(82\) 60626.0 0.995691
\(83\) −63660.2 −1.01432 −0.507158 0.861853i \(-0.669304\pi\)
−0.507158 + 0.861853i \(0.669304\pi\)
\(84\) −58143.1 −0.899083
\(85\) −38630.7 −0.579943
\(86\) 7193.11 0.104875
\(87\) −69041.9 −0.977945
\(88\) 106192. 1.46179
\(89\) −15534.4 −0.207883 −0.103941 0.994583i \(-0.533145\pi\)
−0.103941 + 0.994583i \(0.533145\pi\)
\(90\) 66985.6 0.871716
\(91\) 24559.6 0.310897
\(92\) 90140.5 1.11033
\(93\) −21861.7 −0.262106
\(94\) −128137. −1.49574
\(95\) 32470.2 0.369127
\(96\) −47660.9 −0.527818
\(97\) −93095.6 −1.00461 −0.502307 0.864689i \(-0.667515\pi\)
−0.502307 + 0.864689i \(0.667515\pi\)
\(98\) −19132.0 −0.201231
\(99\) 43906.1 0.450232
\(100\) 260784. 2.60784
\(101\) −77938.5 −0.760236 −0.380118 0.924938i \(-0.624117\pi\)
−0.380118 + 0.924938i \(0.624117\pi\)
\(102\) −35828.5 −0.340979
\(103\) 75407.0 0.700356 0.350178 0.936683i \(-0.386121\pi\)
0.350178 + 0.936683i \(0.386121\pi\)
\(104\) −39637.2 −0.359352
\(105\) −97866.2 −0.866282
\(106\) 134486. 1.16255
\(107\) −154511. −1.30467 −0.652333 0.757933i \(-0.726210\pi\)
−0.652333 + 0.757933i \(0.726210\pi\)
\(108\) 38798.5 0.320078
\(109\) −186965. −1.50728 −0.753641 0.657286i \(-0.771704\pi\)
−0.753641 + 0.657286i \(0.771704\pi\)
\(110\) 448266. 3.53227
\(111\) 22858.0 0.176088
\(112\) −12799.1 −0.0964130
\(113\) −160142. −1.17980 −0.589901 0.807476i \(-0.700833\pi\)
−0.589901 + 0.807476i \(0.700833\pi\)
\(114\) 30114.8 0.217029
\(115\) 151724. 1.06982
\(116\) −408279. −2.81717
\(117\) −16388.4 −0.110681
\(118\) −32135.0 −0.212458
\(119\) 52345.5 0.338854
\(120\) 157948. 1.00130
\(121\) 132767. 0.824380
\(122\) 180940. 1.10062
\(123\) 59105.4 0.352261
\(124\) −129279. −0.755048
\(125\) 159006. 0.910201
\(126\) −90767.0 −0.509333
\(127\) 277139. 1.52472 0.762358 0.647156i \(-0.224042\pi\)
0.762358 + 0.647156i \(0.224042\pi\)
\(128\) −312991. −1.68852
\(129\) 7012.69 0.0371031
\(130\) −167320. −0.868341
\(131\) 36895.9 0.187845 0.0939226 0.995580i \(-0.470059\pi\)
0.0939226 + 0.995580i \(0.470059\pi\)
\(132\) 259639. 1.29698
\(133\) −43997.8 −0.215676
\(134\) −518266. −2.49340
\(135\) 65305.4 0.308400
\(136\) −84481.7 −0.391665
\(137\) 289045. 1.31572 0.657860 0.753140i \(-0.271462\pi\)
0.657860 + 0.753140i \(0.271462\pi\)
\(138\) 140718. 0.629002
\(139\) −303040. −1.33034 −0.665170 0.746692i \(-0.731641\pi\)
−0.665170 + 0.746692i \(0.731641\pi\)
\(140\) −578732. −2.49550
\(141\) −124923. −0.529170
\(142\) −343120. −1.42799
\(143\) −109671. −0.448489
\(144\) 8540.77 0.0343235
\(145\) −687214. −2.71439
\(146\) 757362. 2.94050
\(147\) −18652.1 −0.0711925
\(148\) 135171. 0.507257
\(149\) 246895. 0.911059 0.455530 0.890221i \(-0.349450\pi\)
0.455530 + 0.890221i \(0.349450\pi\)
\(150\) 407109. 1.47735
\(151\) 528032. 1.88459 0.942297 0.334777i \(-0.108661\pi\)
0.942297 + 0.334777i \(0.108661\pi\)
\(152\) 71009.1 0.249290
\(153\) −34929.8 −0.120633
\(154\) −607411. −2.06386
\(155\) −217602. −0.727501
\(156\) −96913.0 −0.318838
\(157\) −289375. −0.936940 −0.468470 0.883479i \(-0.655195\pi\)
−0.468470 + 0.883479i \(0.655195\pi\)
\(158\) 715364. 2.27973
\(159\) 131113. 0.411294
\(160\) −474396. −1.46501
\(161\) −205589. −0.625081
\(162\) 60568.2 0.181325
\(163\) −282099. −0.831634 −0.415817 0.909448i \(-0.636504\pi\)
−0.415817 + 0.909448i \(0.636504\pi\)
\(164\) 349520. 1.01476
\(165\) 437022. 1.24967
\(166\) −587683. −1.65528
\(167\) 616710. 1.71116 0.855578 0.517674i \(-0.173202\pi\)
0.855578 + 0.517674i \(0.173202\pi\)
\(168\) −214024. −0.585044
\(169\) −330357. −0.889748
\(170\) −356622. −0.946423
\(171\) 29359.5 0.0767817
\(172\) 41469.5 0.106883
\(173\) −332590. −0.844877 −0.422438 0.906392i \(-0.638826\pi\)
−0.422438 + 0.906392i \(0.638826\pi\)
\(174\) −637364. −1.59593
\(175\) −594787. −1.46814
\(176\) 57154.7 0.139082
\(177\) −31329.0 −0.0751646
\(178\) −143406. −0.339249
\(179\) 220129. 0.513506 0.256753 0.966477i \(-0.417347\pi\)
0.256753 + 0.966477i \(0.417347\pi\)
\(180\) 386184. 0.888409
\(181\) −610281. −1.38463 −0.692314 0.721596i \(-0.743409\pi\)
−0.692314 + 0.721596i \(0.743409\pi\)
\(182\) 226723. 0.507361
\(183\) 176402. 0.389382
\(184\) 331806. 0.722502
\(185\) 227519. 0.488751
\(186\) −201817. −0.427736
\(187\) −233749. −0.488817
\(188\) −738733. −1.52438
\(189\) −88490.3 −0.180194
\(190\) 299750. 0.602387
\(191\) 348513. 0.691250 0.345625 0.938373i \(-0.387667\pi\)
0.345625 + 0.938373i \(0.387667\pi\)
\(192\) −470351. −0.920808
\(193\) 126850. 0.245131 0.122566 0.992460i \(-0.460888\pi\)
0.122566 + 0.992460i \(0.460888\pi\)
\(194\) −859416. −1.63945
\(195\) −163123. −0.307206
\(196\) −110299. −0.205084
\(197\) 344780. 0.632961 0.316481 0.948599i \(-0.397499\pi\)
0.316481 + 0.948599i \(0.397499\pi\)
\(198\) 405321. 0.734744
\(199\) 508413. 0.910089 0.455045 0.890469i \(-0.349623\pi\)
0.455045 + 0.890469i \(0.349623\pi\)
\(200\) 959941. 1.69695
\(201\) −505267. −0.882126
\(202\) −719493. −1.24065
\(203\) 931190. 1.58598
\(204\) −206558. −0.347509
\(205\) 588310. 0.977736
\(206\) 696124. 1.14293
\(207\) 137188. 0.222532
\(208\) −21333.6 −0.0341906
\(209\) 196473. 0.311126
\(210\) −903456. −1.41371
\(211\) 798353. 1.23449 0.617247 0.786770i \(-0.288248\pi\)
0.617247 + 0.786770i \(0.288248\pi\)
\(212\) 775336. 1.18481
\(213\) −334514. −0.505202
\(214\) −1.42637e6 −2.12911
\(215\) 69801.3 0.102983
\(216\) 142817. 0.208278
\(217\) 294856. 0.425070
\(218\) −1.72598e6 −2.45977
\(219\) 738365. 1.04031
\(220\) 2.58433e6 3.59991
\(221\) 87249.6 0.120166
\(222\) 211015. 0.287362
\(223\) 633080. 0.852504 0.426252 0.904604i \(-0.359834\pi\)
0.426252 + 0.904604i \(0.359834\pi\)
\(224\) 642818. 0.855988
\(225\) 396897. 0.522663
\(226\) −1.47836e6 −1.92535
\(227\) 1.05889e6 1.36392 0.681958 0.731392i \(-0.261129\pi\)
0.681958 + 0.731392i \(0.261129\pi\)
\(228\) 173617. 0.221185
\(229\) 327031. 0.412097 0.206049 0.978542i \(-0.433939\pi\)
0.206049 + 0.978542i \(0.433939\pi\)
\(230\) 1.40065e6 1.74586
\(231\) −592175. −0.730164
\(232\) −1.50287e6 −1.83316
\(233\) 1.17104e6 1.41313 0.706564 0.707649i \(-0.250244\pi\)
0.706564 + 0.707649i \(0.250244\pi\)
\(234\) −151291. −0.180623
\(235\) −1.24343e6 −1.46877
\(236\) −185264. −0.216527
\(237\) 697421. 0.806536
\(238\) 483230. 0.552983
\(239\) 571554. 0.647235 0.323618 0.946188i \(-0.395101\pi\)
0.323618 + 0.946188i \(0.395101\pi\)
\(240\) 85011.2 0.0952683
\(241\) 482157. 0.534744 0.267372 0.963593i \(-0.413845\pi\)
0.267372 + 0.963593i \(0.413845\pi\)
\(242\) 1.22565e6 1.34533
\(243\) 59049.0 0.0641500
\(244\) 1.04315e6 1.12169
\(245\) −185655. −0.197602
\(246\) 545634. 0.574863
\(247\) −73335.7 −0.0764844
\(248\) −475875. −0.491319
\(249\) −572942. −0.585615
\(250\) 1.46787e6 1.48538
\(251\) −526100. −0.527089 −0.263545 0.964647i \(-0.584892\pi\)
−0.263545 + 0.964647i \(0.584892\pi\)
\(252\) −523288. −0.519086
\(253\) 918062. 0.901718
\(254\) 2.55843e6 2.48822
\(255\) −347677. −0.334830
\(256\) −1.21703e6 −1.16065
\(257\) −214918. −0.202974 −0.101487 0.994837i \(-0.532360\pi\)
−0.101487 + 0.994837i \(0.532360\pi\)
\(258\) 64738.0 0.0605494
\(259\) −308293. −0.285571
\(260\) −964631. −0.884969
\(261\) −621377. −0.564617
\(262\) 340607. 0.306549
\(263\) −439795. −0.392068 −0.196034 0.980597i \(-0.562806\pi\)
−0.196034 + 0.980597i \(0.562806\pi\)
\(264\) 955725. 0.843963
\(265\) 1.30504e6 1.14159
\(266\) −406168. −0.351967
\(267\) −139809. −0.120021
\(268\) −2.98790e6 −2.54114
\(269\) 860184. 0.724788 0.362394 0.932025i \(-0.381960\pi\)
0.362394 + 0.932025i \(0.381960\pi\)
\(270\) 602870. 0.503286
\(271\) −2.12669e6 −1.75906 −0.879532 0.475840i \(-0.842144\pi\)
−0.879532 + 0.475840i \(0.842144\pi\)
\(272\) −45469.8 −0.0372650
\(273\) 221036. 0.179497
\(274\) 2.66833e6 2.14715
\(275\) 2.65603e6 2.11788
\(276\) 811264. 0.641047
\(277\) 2.44085e6 1.91136 0.955680 0.294409i \(-0.0951226\pi\)
0.955680 + 0.294409i \(0.0951226\pi\)
\(278\) −2.79753e6 −2.17101
\(279\) −196755. −0.151327
\(280\) −2.13030e6 −1.62385
\(281\) −1.75576e6 −1.32647 −0.663237 0.748409i \(-0.730818\pi\)
−0.663237 + 0.748409i \(0.730818\pi\)
\(282\) −1.15323e6 −0.863564
\(283\) 1.52824e6 1.13429 0.567145 0.823618i \(-0.308048\pi\)
0.567145 + 0.823618i \(0.308048\pi\)
\(284\) −1.97815e6 −1.45534
\(285\) 292232. 0.213115
\(286\) −1.01243e6 −0.731899
\(287\) −797174. −0.571279
\(288\) −428948. −0.304736
\(289\) −1.23390e6 −0.869028
\(290\) −6.34405e6 −4.42967
\(291\) −837860. −0.580015
\(292\) 4.36632e6 2.99681
\(293\) 2.08785e6 1.42079 0.710397 0.703802i \(-0.248516\pi\)
0.710397 + 0.703802i \(0.248516\pi\)
\(294\) −172188. −0.116181
\(295\) −311836. −0.208627
\(296\) 497561. 0.330078
\(297\) 395155. 0.259942
\(298\) 2.27922e6 1.48678
\(299\) −342677. −0.221670
\(300\) 2.34705e6 1.50564
\(301\) −94582.4 −0.0601719
\(302\) 4.87455e6 3.07551
\(303\) −701447. −0.438923
\(304\) 38218.6 0.0237187
\(305\) 1.75583e6 1.08077
\(306\) −322456. −0.196864
\(307\) 3.15846e6 1.91262 0.956311 0.292352i \(-0.0944380\pi\)
0.956311 + 0.292352i \(0.0944380\pi\)
\(308\) −3.50183e6 −2.10338
\(309\) 678663. 0.404350
\(310\) −2.00880e6 −1.18723
\(311\) 3.00584e6 1.76224 0.881120 0.472892i \(-0.156790\pi\)
0.881120 + 0.472892i \(0.156790\pi\)
\(312\) −356735. −0.207472
\(313\) −1.02498e6 −0.591365 −0.295683 0.955286i \(-0.595547\pi\)
−0.295683 + 0.955286i \(0.595547\pi\)
\(314\) −2.67138e6 −1.52901
\(315\) −880795. −0.500148
\(316\) 4.12420e6 2.32339
\(317\) −1.16894e6 −0.653345 −0.326673 0.945138i \(-0.605927\pi\)
−0.326673 + 0.945138i \(0.605927\pi\)
\(318\) 1.21037e6 0.671200
\(319\) −4.15824e6 −2.28788
\(320\) −4.68167e6 −2.55580
\(321\) −1.39060e6 −0.753249
\(322\) −1.89791e6 −1.02008
\(323\) −156305. −0.0833620
\(324\) 349186. 0.184797
\(325\) −991393. −0.520640
\(326\) −2.60421e6 −1.35716
\(327\) −1.68269e6 −0.870230
\(328\) 1.28658e6 0.660315
\(329\) 1.68488e6 0.858181
\(330\) 4.03439e6 2.03936
\(331\) 3.00630e6 1.50821 0.754105 0.656754i \(-0.228071\pi\)
0.754105 + 0.656754i \(0.228071\pi\)
\(332\) −3.38809e6 −1.68698
\(333\) 205722. 0.101665
\(334\) 5.69319e6 2.79247
\(335\) −5.02921e6 −2.44843
\(336\) −115192. −0.0556641
\(337\) −969092. −0.464826 −0.232413 0.972617i \(-0.574662\pi\)
−0.232413 + 0.972617i \(0.574662\pi\)
\(338\) −3.04971e6 −1.45200
\(339\) −1.44128e6 −0.681159
\(340\) −2.05599e6 −0.964546
\(341\) −1.31668e6 −0.613190
\(342\) 271033. 0.125302
\(343\) 2.29170e6 1.05177
\(344\) 152649. 0.0695500
\(345\) 1.36552e6 0.617659
\(346\) −3.07032e6 −1.37877
\(347\) −2.01845e6 −0.899902 −0.449951 0.893053i \(-0.648559\pi\)
−0.449951 + 0.893053i \(0.648559\pi\)
\(348\) −3.67451e6 −1.62649
\(349\) −2.28363e6 −1.00360 −0.501802 0.864983i \(-0.667329\pi\)
−0.501802 + 0.864983i \(0.667329\pi\)
\(350\) −5.49081e6 −2.39589
\(351\) −147496. −0.0639016
\(352\) −2.87051e6 −1.23482
\(353\) 483424. 0.206486 0.103243 0.994656i \(-0.467078\pi\)
0.103243 + 0.994656i \(0.467078\pi\)
\(354\) −289215. −0.122663
\(355\) −3.32961e6 −1.40224
\(356\) −826763. −0.345745
\(357\) 471110. 0.195637
\(358\) 2.03214e6 0.838002
\(359\) 2.19256e6 0.897875 0.448938 0.893563i \(-0.351803\pi\)
0.448938 + 0.893563i \(0.351803\pi\)
\(360\) 1.42154e6 0.578098
\(361\) −2.34472e6 −0.946941
\(362\) −5.63384e6 −2.25961
\(363\) 1.19491e6 0.475956
\(364\) 1.30710e6 0.517076
\(365\) 7.34937e6 2.88747
\(366\) 1.62846e6 0.635441
\(367\) −2.55829e6 −0.991482 −0.495741 0.868470i \(-0.665103\pi\)
−0.495741 + 0.868470i \(0.665103\pi\)
\(368\) 178585. 0.0687425
\(369\) 531949. 0.203378
\(370\) 2.10035e6 0.797604
\(371\) −1.76836e6 −0.667016
\(372\) −1.16351e6 −0.435927
\(373\) 1.33933e6 0.498444 0.249222 0.968446i \(-0.419825\pi\)
0.249222 + 0.968446i \(0.419825\pi\)
\(374\) −2.15787e6 −0.797712
\(375\) 1.43105e6 0.525505
\(376\) −2.71927e6 −0.991932
\(377\) 1.55211e6 0.562431
\(378\) −816903. −0.294063
\(379\) −124784. −0.0446234 −0.0223117 0.999751i \(-0.507103\pi\)
−0.0223117 + 0.999751i \(0.507103\pi\)
\(380\) 1.72811e6 0.613922
\(381\) 2.49425e6 0.880295
\(382\) 3.21731e6 1.12807
\(383\) 2.20676e6 0.768703 0.384351 0.923187i \(-0.374425\pi\)
0.384351 + 0.923187i \(0.374425\pi\)
\(384\) −2.81692e6 −0.974869
\(385\) −5.89426e6 −2.02664
\(386\) 1.17102e6 0.400035
\(387\) 63114.2 0.0214215
\(388\) −4.95469e6 −1.67085
\(389\) 3.70241e6 1.24054 0.620269 0.784389i \(-0.287023\pi\)
0.620269 + 0.784389i \(0.287023\pi\)
\(390\) −1.50588e6 −0.501337
\(391\) −730371. −0.241603
\(392\) −406010. −0.133451
\(393\) 332063. 0.108452
\(394\) 3.18286e6 1.03294
\(395\) 6.94183e6 2.23862
\(396\) 2.33675e6 0.748814
\(397\) 2.11382e6 0.673118 0.336559 0.941662i \(-0.390737\pi\)
0.336559 + 0.941662i \(0.390737\pi\)
\(398\) 4.69344e6 1.48520
\(399\) −395980. −0.124521
\(400\) 516661. 0.161456
\(401\) −2.67664e6 −0.831245 −0.415623 0.909537i \(-0.636436\pi\)
−0.415623 + 0.909537i \(0.636436\pi\)
\(402\) −4.66440e6 −1.43956
\(403\) 491466. 0.150741
\(404\) −4.14801e6 −1.26440
\(405\) 587749. 0.178055
\(406\) 8.59633e6 2.58820
\(407\) 1.37669e6 0.411954
\(408\) −760335. −0.226128
\(409\) 3.98828e6 1.17890 0.589451 0.807804i \(-0.299344\pi\)
0.589451 + 0.807804i \(0.299344\pi\)
\(410\) 5.43101e6 1.59559
\(411\) 2.60140e6 0.759632
\(412\) 4.01328e6 1.16481
\(413\) 422544. 0.121898
\(414\) 1.26646e6 0.363154
\(415\) −5.70282e6 −1.62543
\(416\) 1.07145e6 0.303556
\(417\) −2.72736e6 −0.768072
\(418\) 1.81375e6 0.507734
\(419\) −3.00819e6 −0.837087 −0.418543 0.908197i \(-0.637459\pi\)
−0.418543 + 0.908197i \(0.637459\pi\)
\(420\) −5.20859e6 −1.44078
\(421\) −7.18527e6 −1.97578 −0.987888 0.155170i \(-0.950407\pi\)
−0.987888 + 0.155170i \(0.950407\pi\)
\(422\) 7.37003e6 2.01460
\(423\) −1.12431e6 −0.305516
\(424\) 2.85400e6 0.770973
\(425\) −2.11302e6 −0.567456
\(426\) −3.08808e6 −0.824451
\(427\) −2.37919e6 −0.631480
\(428\) −8.22330e6 −2.16988
\(429\) −987039. −0.258935
\(430\) 644374. 0.168061
\(431\) 3.00434e6 0.779032 0.389516 0.921020i \(-0.372642\pi\)
0.389516 + 0.921020i \(0.372642\pi\)
\(432\) 76867.0 0.0198167
\(433\) 1.50180e6 0.384938 0.192469 0.981303i \(-0.438350\pi\)
0.192469 + 0.981303i \(0.438350\pi\)
\(434\) 2.72198e6 0.693681
\(435\) −6.18492e6 −1.56715
\(436\) −9.95057e6 −2.50687
\(437\) 613897. 0.153777
\(438\) 6.81626e6 1.69770
\(439\) 1.12031e6 0.277445 0.138722 0.990331i \(-0.455700\pi\)
0.138722 + 0.990331i \(0.455700\pi\)
\(440\) 9.51289e6 2.34251
\(441\) −167869. −0.0411030
\(442\) 805449. 0.196102
\(443\) −312245. −0.0755937 −0.0377969 0.999285i \(-0.512034\pi\)
−0.0377969 + 0.999285i \(0.512034\pi\)
\(444\) 1.21654e6 0.292865
\(445\) −1.39160e6 −0.333131
\(446\) 5.84431e6 1.39122
\(447\) 2.22205e6 0.526000
\(448\) 6.34378e6 1.49332
\(449\) −7.57161e6 −1.77244 −0.886222 0.463261i \(-0.846679\pi\)
−0.886222 + 0.463261i \(0.846679\pi\)
\(450\) 3.66398e6 0.852946
\(451\) 3.55979e6 0.824105
\(452\) −8.52300e6 −1.96221
\(453\) 4.75229e6 1.08807
\(454\) 9.77522e6 2.22580
\(455\) 2.20010e6 0.498212
\(456\) 639082. 0.143928
\(457\) 529334. 0.118560 0.0592801 0.998241i \(-0.481119\pi\)
0.0592801 + 0.998241i \(0.481119\pi\)
\(458\) 3.01900e6 0.672511
\(459\) −314368. −0.0696477
\(460\) 8.07498e6 1.77929
\(461\) −2.93740e6 −0.643740 −0.321870 0.946784i \(-0.604311\pi\)
−0.321870 + 0.946784i \(0.604311\pi\)
\(462\) −5.46670e6 −1.19157
\(463\) 5.29725e6 1.14841 0.574206 0.818711i \(-0.305311\pi\)
0.574206 + 0.818711i \(0.305311\pi\)
\(464\) −808877. −0.174416
\(465\) −1.95842e6 −0.420023
\(466\) 1.08105e7 2.30612
\(467\) −6.50929e6 −1.38115 −0.690576 0.723260i \(-0.742643\pi\)
−0.690576 + 0.723260i \(0.742643\pi\)
\(468\) −872217. −0.184081
\(469\) 6.81470e6 1.43059
\(470\) −1.14788e7 −2.39691
\(471\) −2.60437e6 −0.540942
\(472\) −681954. −0.140896
\(473\) 422359. 0.0868018
\(474\) 6.43827e6 1.31621
\(475\) 1.77605e6 0.361179
\(476\) 2.78591e6 0.563572
\(477\) 1.18001e6 0.237461
\(478\) 5.27633e6 1.05624
\(479\) 4.95192e6 0.986131 0.493065 0.869992i \(-0.335876\pi\)
0.493065 + 0.869992i \(0.335876\pi\)
\(480\) −4.26956e6 −0.845825
\(481\) −513863. −0.101271
\(482\) 4.45106e6 0.872661
\(483\) −1.85030e6 −0.360891
\(484\) 7.06608e6 1.37109
\(485\) −8.33970e6 −1.60989
\(486\) 545114. 0.104688
\(487\) −5.32846e6 −1.01807 −0.509037 0.860745i \(-0.669998\pi\)
−0.509037 + 0.860745i \(0.669998\pi\)
\(488\) 3.83983e6 0.729898
\(489\) −2.53889e6 −0.480144
\(490\) −1.71388e6 −0.322472
\(491\) −7.43544e6 −1.39188 −0.695942 0.718098i \(-0.745013\pi\)
−0.695942 + 0.718098i \(0.745013\pi\)
\(492\) 3.14568e6 0.585871
\(493\) 3.30812e6 0.613005
\(494\) −677002. −0.124817
\(495\) 3.93320e6 0.721495
\(496\) −256126. −0.0467465
\(497\) 4.51170e6 0.819312
\(498\) −5.28914e6 −0.955679
\(499\) 2.82668e6 0.508188 0.254094 0.967179i \(-0.418223\pi\)
0.254094 + 0.967179i \(0.418223\pi\)
\(500\) 8.46252e6 1.51382
\(501\) 5.55039e6 0.987936
\(502\) −4.85672e6 −0.860169
\(503\) −7.04752e6 −1.24199 −0.620993 0.783816i \(-0.713270\pi\)
−0.620993 + 0.783816i \(0.713270\pi\)
\(504\) −1.92621e6 −0.337776
\(505\) −6.98190e6 −1.21828
\(506\) 8.47513e6 1.47153
\(507\) −2.97321e6 −0.513696
\(508\) 1.47498e7 2.53587
\(509\) −3.11157e6 −0.532334 −0.266167 0.963927i \(-0.585757\pi\)
−0.266167 + 0.963927i \(0.585757\pi\)
\(510\) −3.20959e6 −0.546418
\(511\) −9.95857e6 −1.68712
\(512\) −1.21940e6 −0.205576
\(513\) 264235. 0.0443299
\(514\) −1.98402e6 −0.331237
\(515\) 6.75512e6 1.12232
\(516\) 373226. 0.0617089
\(517\) −7.52384e6 −1.23798
\(518\) −2.84602e6 −0.466030
\(519\) −2.99331e6 −0.487790
\(520\) −3.55079e6 −0.575860
\(521\) −1.27221e6 −0.205336 −0.102668 0.994716i \(-0.532738\pi\)
−0.102668 + 0.994716i \(0.532738\pi\)
\(522\) −5.73627e6 −0.921411
\(523\) −2.80084e6 −0.447748 −0.223874 0.974618i \(-0.571870\pi\)
−0.223874 + 0.974618i \(0.571870\pi\)
\(524\) 1.96366e6 0.312419
\(525\) −5.35309e6 −0.847629
\(526\) −4.05999e6 −0.639824
\(527\) 1.04750e6 0.164296
\(528\) 514392. 0.0802988
\(529\) −3.56778e6 −0.554317
\(530\) 1.20476e7 1.86298
\(531\) −281961. −0.0433963
\(532\) −2.34163e6 −0.358707
\(533\) −1.32873e6 −0.202590
\(534\) −1.29066e6 −0.195865
\(535\) −1.38414e7 −2.09072
\(536\) −1.09984e7 −1.65355
\(537\) 1.98117e6 0.296473
\(538\) 7.94083e6 1.18280
\(539\) −1.12337e6 −0.166553
\(540\) 3.47565e6 0.512923
\(541\) −9.35654e6 −1.37443 −0.687214 0.726455i \(-0.741167\pi\)
−0.687214 + 0.726455i \(0.741167\pi\)
\(542\) −1.96327e7 −2.87066
\(543\) −5.49253e6 −0.799415
\(544\) 2.28366e6 0.330852
\(545\) −1.67488e7 −2.41541
\(546\) 2.04051e6 0.292925
\(547\) 5.63105e6 0.804676 0.402338 0.915491i \(-0.368198\pi\)
0.402338 + 0.915491i \(0.368198\pi\)
\(548\) 1.53834e7 2.18827
\(549\) 1.58762e6 0.224810
\(550\) 2.45193e7 3.45621
\(551\) −2.78057e6 −0.390170
\(552\) 2.98625e6 0.417137
\(553\) −9.40634e6 −1.30800
\(554\) 2.25329e7 3.11919
\(555\) 2.04767e6 0.282180
\(556\) −1.61282e7 −2.21259
\(557\) −1.18592e7 −1.61964 −0.809818 0.586681i \(-0.800434\pi\)
−0.809818 + 0.586681i \(0.800434\pi\)
\(558\) −1.81636e6 −0.246954
\(559\) −157650. −0.0213385
\(560\) −1.14657e6 −0.154501
\(561\) −2.10375e6 −0.282219
\(562\) −1.62084e7 −2.16470
\(563\) 1.16587e7 1.55017 0.775085 0.631856i \(-0.217707\pi\)
0.775085 + 0.631856i \(0.217707\pi\)
\(564\) −6.64860e6 −0.880101
\(565\) −1.43459e7 −1.89063
\(566\) 1.41080e7 1.85107
\(567\) −796413. −0.104035
\(568\) −7.28153e6 −0.947005
\(569\) −6.42402e6 −0.831814 −0.415907 0.909407i \(-0.636536\pi\)
−0.415907 + 0.909407i \(0.636536\pi\)
\(570\) 2.69775e6 0.347788
\(571\) 1.91324e6 0.245573 0.122786 0.992433i \(-0.460817\pi\)
0.122786 + 0.992433i \(0.460817\pi\)
\(572\) −5.83686e6 −0.745914
\(573\) 3.13662e6 0.399094
\(574\) −7.35915e6 −0.932283
\(575\) 8.29900e6 1.04678
\(576\) −4.23316e6 −0.531628
\(577\) 3.05466e6 0.381965 0.190983 0.981593i \(-0.438833\pi\)
0.190983 + 0.981593i \(0.438833\pi\)
\(578\) −1.13908e7 −1.41819
\(579\) 1.14165e6 0.141526
\(580\) −3.65746e7 −4.51449
\(581\) 7.72746e6 0.949721
\(582\) −7.73475e6 −0.946539
\(583\) 7.89663e6 0.962211
\(584\) 1.60724e7 1.95006
\(585\) −1.46811e6 −0.177366
\(586\) 1.92741e7 2.31862
\(587\) 1.06077e7 1.27065 0.635325 0.772245i \(-0.280866\pi\)
0.635325 + 0.772245i \(0.280866\pi\)
\(588\) −992693. −0.118405
\(589\) −880449. −0.104572
\(590\) −2.87873e6 −0.340463
\(591\) 3.10302e6 0.365440
\(592\) 267798. 0.0314053
\(593\) −8.48186e6 −0.990500 −0.495250 0.868751i \(-0.664923\pi\)
−0.495250 + 0.868751i \(0.664923\pi\)
\(594\) 3.64789e6 0.424205
\(595\) 4.68923e6 0.543011
\(596\) 1.31401e7 1.51525
\(597\) 4.57572e6 0.525440
\(598\) −3.16344e6 −0.361748
\(599\) 1.50366e7 1.71231 0.856155 0.516718i \(-0.172847\pi\)
0.856155 + 0.516718i \(0.172847\pi\)
\(600\) 8.63947e6 0.979736
\(601\) 1.00070e7 1.13010 0.565050 0.825057i \(-0.308857\pi\)
0.565050 + 0.825057i \(0.308857\pi\)
\(602\) −873142. −0.0981960
\(603\) −4.54740e6 −0.509296
\(604\) 2.81027e7 3.13441
\(605\) 1.18936e7 1.32107
\(606\) −6.47544e6 −0.716288
\(607\) 9.84700e6 1.08476 0.542378 0.840134i \(-0.317524\pi\)
0.542378 + 0.840134i \(0.317524\pi\)
\(608\) −1.91947e6 −0.210583
\(609\) 8.38071e6 0.915667
\(610\) 1.62090e7 1.76373
\(611\) 2.80836e6 0.304333
\(612\) −1.85902e6 −0.200634
\(613\) 5.23546e6 0.562735 0.281368 0.959600i \(-0.409212\pi\)
0.281368 + 0.959600i \(0.409212\pi\)
\(614\) 2.91575e7 3.12125
\(615\) 5.29479e6 0.564496
\(616\) −1.28902e7 −1.36870
\(617\) −1.58209e7 −1.67308 −0.836542 0.547902i \(-0.815427\pi\)
−0.836542 + 0.547902i \(0.815427\pi\)
\(618\) 6.26511e6 0.659869
\(619\) −1.50849e7 −1.58240 −0.791198 0.611560i \(-0.790542\pi\)
−0.791198 + 0.611560i \(0.790542\pi\)
\(620\) −1.15811e7 −1.20996
\(621\) 1.23470e6 0.128479
\(622\) 2.77486e7 2.87584
\(623\) 1.88565e6 0.194644
\(624\) −192003. −0.0197399
\(625\) −1.06833e6 −0.109397
\(626\) −9.46218e6 −0.965062
\(627\) 1.76825e6 0.179629
\(628\) −1.54010e7 −1.55829
\(629\) −1.09523e6 −0.110377
\(630\) −8.13111e6 −0.816203
\(631\) 7.96398e6 0.796264 0.398132 0.917328i \(-0.369659\pi\)
0.398132 + 0.917328i \(0.369659\pi\)
\(632\) 1.51811e7 1.51186
\(633\) 7.18517e6 0.712735
\(634\) −1.07911e7 −1.06621
\(635\) 2.48268e7 2.44335
\(636\) 6.97802e6 0.684053
\(637\) 419312. 0.0409439
\(638\) −3.83870e7 −3.73364
\(639\) −3.01063e6 −0.291679
\(640\) −2.80384e7 −2.70585
\(641\) 9.73869e6 0.936172 0.468086 0.883683i \(-0.344944\pi\)
0.468086 + 0.883683i \(0.344944\pi\)
\(642\) −1.28374e7 −1.22924
\(643\) 2.84747e6 0.271601 0.135801 0.990736i \(-0.456639\pi\)
0.135801 + 0.990736i \(0.456639\pi\)
\(644\) −1.09418e7 −1.03962
\(645\) 628212. 0.0594575
\(646\) −1.44294e6 −0.136040
\(647\) −1.48035e7 −1.39028 −0.695140 0.718874i \(-0.744658\pi\)
−0.695140 + 0.718874i \(0.744658\pi\)
\(648\) 1.28535e6 0.120250
\(649\) −1.88688e6 −0.175846
\(650\) −9.15209e6 −0.849644
\(651\) 2.65370e6 0.245414
\(652\) −1.50137e7 −1.38315
\(653\) −4.55203e6 −0.417755 −0.208878 0.977942i \(-0.566981\pi\)
−0.208878 + 0.977942i \(0.566981\pi\)
\(654\) −1.55338e7 −1.42015
\(655\) 3.30522e6 0.301021
\(656\) 692463. 0.0628257
\(657\) 6.64529e6 0.600621
\(658\) 1.55540e7 1.40049
\(659\) 1.78757e7 1.60343 0.801714 0.597708i \(-0.203922\pi\)
0.801714 + 0.597708i \(0.203922\pi\)
\(660\) 2.32590e7 2.07841
\(661\) 3.89590e6 0.346820 0.173410 0.984850i \(-0.444521\pi\)
0.173410 + 0.984850i \(0.444521\pi\)
\(662\) 2.77528e7 2.46128
\(663\) 785247. 0.0693781
\(664\) −1.24715e7 −1.09774
\(665\) −3.94142e6 −0.345620
\(666\) 1.89913e6 0.165909
\(667\) −1.29928e7 −1.13081
\(668\) 3.28222e7 2.84595
\(669\) 5.69772e6 0.492193
\(670\) −4.64274e7 −3.99565
\(671\) 1.06243e7 0.910949
\(672\) 5.78536e6 0.494205
\(673\) −2.23886e6 −0.190541 −0.0952706 0.995451i \(-0.530372\pi\)
−0.0952706 + 0.995451i \(0.530372\pi\)
\(674\) −8.94622e6 −0.758560
\(675\) 3.57208e6 0.301760
\(676\) −1.75821e7 −1.47980
\(677\) 8.27181e6 0.693631 0.346816 0.937933i \(-0.387263\pi\)
0.346816 + 0.937933i \(0.387263\pi\)
\(678\) −1.33052e7 −1.11160
\(679\) 1.13005e7 0.940639
\(680\) −7.56805e6 −0.627642
\(681\) 9.53004e6 0.787457
\(682\) −1.21550e7 −1.00068
\(683\) −1.20134e7 −0.985403 −0.492702 0.870198i \(-0.663991\pi\)
−0.492702 + 0.870198i \(0.663991\pi\)
\(684\) 1.56255e6 0.127701
\(685\) 2.58933e7 2.10844
\(686\) 2.11559e7 1.71641
\(687\) 2.94328e6 0.237925
\(688\) 82158.8 0.00661733
\(689\) −2.94751e6 −0.236541
\(690\) 1.26058e7 1.00797
\(691\) 6.53362e6 0.520545 0.260273 0.965535i \(-0.416188\pi\)
0.260273 + 0.965535i \(0.416188\pi\)
\(692\) −1.77009e7 −1.40518
\(693\) −5.32958e6 −0.421560
\(694\) −1.86335e7 −1.46857
\(695\) −2.71470e7 −2.13186
\(696\) −1.35258e7 −1.05838
\(697\) −2.83202e6 −0.220808
\(698\) −2.10814e7 −1.63780
\(699\) 1.05393e7 0.815870
\(700\) −3.16555e7 −2.44177
\(701\) −7.08221e6 −0.544344 −0.272172 0.962249i \(-0.587742\pi\)
−0.272172 + 0.962249i \(0.587742\pi\)
\(702\) −1.36162e6 −0.104283
\(703\) 920573. 0.0702538
\(704\) −2.83282e7 −2.15421
\(705\) −1.11909e7 −0.847992
\(706\) 4.46275e6 0.336970
\(707\) 9.46064e6 0.711823
\(708\) −1.66738e6 −0.125012
\(709\) −7.79243e6 −0.582180 −0.291090 0.956696i \(-0.594018\pi\)
−0.291090 + 0.956696i \(0.594018\pi\)
\(710\) −3.07375e7 −2.28835
\(711\) 6.27679e6 0.465654
\(712\) −3.04330e6 −0.224980
\(713\) −4.11409e6 −0.303075
\(714\) 4.34907e6 0.319265
\(715\) −9.82457e6 −0.718701
\(716\) 1.17156e7 0.854049
\(717\) 5.14398e6 0.373682
\(718\) 2.02408e7 1.46526
\(719\) −8.35425e6 −0.602678 −0.301339 0.953517i \(-0.597434\pi\)
−0.301339 + 0.953517i \(0.597434\pi\)
\(720\) 765101. 0.0550032
\(721\) −9.15335e6 −0.655755
\(722\) −2.16454e7 −1.54533
\(723\) 4.33942e6 0.308735
\(724\) −3.24801e7 −2.30288
\(725\) −3.75892e7 −2.65594
\(726\) 1.10308e7 0.776724
\(727\) 1.48925e7 1.04503 0.522517 0.852629i \(-0.324993\pi\)
0.522517 + 0.852629i \(0.324993\pi\)
\(728\) 4.81140e6 0.336468
\(729\) 531441. 0.0370370
\(730\) 6.78461e7 4.71214
\(731\) −336011. −0.0232573
\(732\) 9.38838e6 0.647609
\(733\) −495642. −0.0340728 −0.0170364 0.999855i \(-0.505423\pi\)
−0.0170364 + 0.999855i \(0.505423\pi\)
\(734\) −2.36170e7 −1.61802
\(735\) −1.67090e6 −0.114086
\(736\) −8.96916e6 −0.610320
\(737\) −3.04311e7 −2.06371
\(738\) 4.91071e6 0.331897
\(739\) −1.10697e7 −0.745633 −0.372816 0.927905i \(-0.621608\pi\)
−0.372816 + 0.927905i \(0.621608\pi\)
\(740\) 1.21089e7 0.812877
\(741\) −660021. −0.0441583
\(742\) −1.63247e7 −1.08852
\(743\) −8.05234e6 −0.535119 −0.267559 0.963541i \(-0.586217\pi\)
−0.267559 + 0.963541i \(0.586217\pi\)
\(744\) −4.28287e6 −0.283663
\(745\) 2.21174e7 1.45997
\(746\) 1.23641e7 0.813423
\(747\) −5.15648e6 −0.338105
\(748\) −1.24405e7 −0.812988
\(749\) 1.87554e7 1.22158
\(750\) 1.32108e7 0.857584
\(751\) −2.48039e7 −1.60480 −0.802399 0.596788i \(-0.796443\pi\)
−0.802399 + 0.596788i \(0.796443\pi\)
\(752\) −1.46357e6 −0.0943774
\(753\) −4.73490e6 −0.304315
\(754\) 1.43284e7 0.917844
\(755\) 4.73023e7 3.02005
\(756\) −4.70959e6 −0.299694
\(757\) 4.14819e6 0.263099 0.131549 0.991310i \(-0.458005\pi\)
0.131549 + 0.991310i \(0.458005\pi\)
\(758\) −1.15195e6 −0.0728219
\(759\) 8.26256e6 0.520607
\(760\) 6.36115e6 0.399486
\(761\) −4.38843e6 −0.274693 −0.137346 0.990523i \(-0.543857\pi\)
−0.137346 + 0.990523i \(0.543857\pi\)
\(762\) 2.30258e7 1.43657
\(763\) 2.26950e7 1.41130
\(764\) 1.85484e7 1.14967
\(765\) −3.12909e6 −0.193314
\(766\) 2.03718e7 1.25446
\(767\) 704298. 0.0432283
\(768\) −1.09533e7 −0.670104
\(769\) 6.58376e6 0.401475 0.200737 0.979645i \(-0.435666\pi\)
0.200737 + 0.979645i \(0.435666\pi\)
\(770\) −5.44132e7 −3.30733
\(771\) −1.93426e6 −0.117187
\(772\) 6.75117e6 0.407695
\(773\) 1.53957e7 0.926723 0.463361 0.886169i \(-0.346643\pi\)
0.463361 + 0.886169i \(0.346643\pi\)
\(774\) 582642. 0.0349582
\(775\) −1.19024e7 −0.711837
\(776\) −1.82381e7 −1.08724
\(777\) −2.77464e6 −0.164875
\(778\) 3.41789e7 2.02446
\(779\) 2.38039e6 0.140541
\(780\) −8.68168e6 −0.510937
\(781\) −2.01470e7 −1.18191
\(782\) −6.74246e6 −0.394277
\(783\) −5.59239e6 −0.325982
\(784\) −218523. −0.0126972
\(785\) −2.59228e7 −1.50144
\(786\) 3.06546e6 0.176986
\(787\) −3.16211e7 −1.81987 −0.909935 0.414750i \(-0.863869\pi\)
−0.909935 + 0.414750i \(0.863869\pi\)
\(788\) 1.83497e7 1.05272
\(789\) −3.95816e6 −0.226360
\(790\) 6.40839e7 3.65326
\(791\) 1.94390e7 1.10467
\(792\) 8.60153e6 0.487262
\(793\) −3.96564e6 −0.223939
\(794\) 1.95138e7 1.09848
\(795\) 1.17454e7 0.659096
\(796\) 2.70585e7 1.51364
\(797\) 2.35875e6 0.131534 0.0657668 0.997835i \(-0.479051\pi\)
0.0657668 + 0.997835i \(0.479051\pi\)
\(798\) −3.65551e6 −0.203208
\(799\) 5.98565e6 0.331699
\(800\) −2.59485e7 −1.43347
\(801\) −1.25828e6 −0.0692943
\(802\) −2.47095e7 −1.35653
\(803\) 4.44701e7 2.43377
\(804\) −2.68911e7 −1.46713
\(805\) −1.84172e7 −1.00169
\(806\) 4.53700e6 0.245998
\(807\) 7.74166e6 0.418456
\(808\) −1.52687e7 −0.822763
\(809\) −101171. −0.00543479 −0.00271740 0.999996i \(-0.500865\pi\)
−0.00271740 + 0.999996i \(0.500865\pi\)
\(810\) 5.42583e6 0.290572
\(811\) 2.38375e7 1.27265 0.636324 0.771422i \(-0.280454\pi\)
0.636324 + 0.771422i \(0.280454\pi\)
\(812\) 4.95594e7 2.63776
\(813\) −1.91402e7 −1.01560
\(814\) 1.27089e7 0.672277
\(815\) −2.52710e7 −1.33269
\(816\) −409229. −0.0215150
\(817\) 282426. 0.0148030
\(818\) 3.68180e7 1.92388
\(819\) 1.98932e6 0.103632
\(820\) 3.13108e7 1.62614
\(821\) 8.77488e6 0.454343 0.227171 0.973855i \(-0.427052\pi\)
0.227171 + 0.973855i \(0.427052\pi\)
\(822\) 2.40150e7 1.23966
\(823\) −2.52557e6 −0.129975 −0.0649875 0.997886i \(-0.520701\pi\)
−0.0649875 + 0.997886i \(0.520701\pi\)
\(824\) 1.47728e7 0.757957
\(825\) 2.39043e7 1.22276
\(826\) 3.90074e6 0.198928
\(827\) −653924. −0.0332478 −0.0166239 0.999862i \(-0.505292\pi\)
−0.0166239 + 0.999862i \(0.505292\pi\)
\(828\) 7.30138e6 0.370108
\(829\) −2.14350e7 −1.08327 −0.541636 0.840613i \(-0.682195\pi\)
−0.541636 + 0.840613i \(0.682195\pi\)
\(830\) −5.26459e7 −2.65258
\(831\) 2.19677e7 1.10352
\(832\) 1.05738e7 0.529570
\(833\) 893710. 0.0446256
\(834\) −2.51777e7 −1.25343
\(835\) 5.52462e7 2.74212
\(836\) 1.04566e7 0.517457
\(837\) −1.77080e6 −0.0873686
\(838\) −2.77703e7 −1.36606
\(839\) −6.47262e6 −0.317450 −0.158725 0.987323i \(-0.550738\pi\)
−0.158725 + 0.987323i \(0.550738\pi\)
\(840\) −1.91727e7 −0.937531
\(841\) 3.83380e7 1.86913
\(842\) −6.63311e7 −3.22431
\(843\) −1.58018e7 −0.765841
\(844\) 4.24895e7 2.05318
\(845\) −2.95941e7 −1.42582
\(846\) −1.03791e7 −0.498579
\(847\) −1.61161e7 −0.771882
\(848\) 1.53608e6 0.0733542
\(849\) 1.37541e7 0.654883
\(850\) −1.95065e7 −0.926045
\(851\) 4.30158e6 0.203612
\(852\) −1.78033e7 −0.840238
\(853\) −9.71818e6 −0.457312 −0.228656 0.973507i \(-0.573433\pi\)
−0.228656 + 0.973507i \(0.573433\pi\)
\(854\) −2.19636e7 −1.03053
\(855\) 2.63008e6 0.123042
\(856\) −3.02698e7 −1.41197
\(857\) 6.76227e6 0.314514 0.157257 0.987558i \(-0.449735\pi\)
0.157257 + 0.987558i \(0.449735\pi\)
\(858\) −9.11190e6 −0.422562
\(859\) 2.19326e7 1.01416 0.507080 0.861899i \(-0.330725\pi\)
0.507080 + 0.861899i \(0.330725\pi\)
\(860\) 3.71493e6 0.171279
\(861\) −7.17456e6 −0.329828
\(862\) 2.77347e7 1.27132
\(863\) 8.93392e6 0.408333 0.204167 0.978936i \(-0.434552\pi\)
0.204167 + 0.978936i \(0.434552\pi\)
\(864\) −3.86053e6 −0.175939
\(865\) −2.97941e7 −1.35391
\(866\) 1.38639e7 0.628190
\(867\) −1.11051e7 −0.501734
\(868\) 1.56927e7 0.706965
\(869\) 4.20041e7 1.88687
\(870\) −5.70964e7 −2.55747
\(871\) 1.13588e7 0.507324
\(872\) −3.66279e7 −1.63125
\(873\) −7.54074e6 −0.334872
\(874\) 5.66722e6 0.250952
\(875\) −1.93010e7 −0.852238
\(876\) 3.92969e7 1.73021
\(877\) −4.03113e7 −1.76981 −0.884907 0.465767i \(-0.845778\pi\)
−0.884907 + 0.465767i \(0.845778\pi\)
\(878\) 1.03422e7 0.452769
\(879\) 1.87907e7 0.820295
\(880\) 5.12004e6 0.222878
\(881\) 5.96563e6 0.258950 0.129475 0.991583i \(-0.458671\pi\)
0.129475 + 0.991583i \(0.458671\pi\)
\(882\) −1.54969e6 −0.0670770
\(883\) 3.38326e7 1.46027 0.730136 0.683302i \(-0.239457\pi\)
0.730136 + 0.683302i \(0.239457\pi\)
\(884\) 4.64356e6 0.199857
\(885\) −2.80652e6 −0.120451
\(886\) −2.88250e6 −0.123363
\(887\) −3.81525e7 −1.62822 −0.814112 0.580708i \(-0.802776\pi\)
−0.814112 + 0.580708i \(0.802776\pi\)
\(888\) 4.47805e6 0.190571
\(889\) −3.36408e7 −1.42762
\(890\) −1.28467e7 −0.543644
\(891\) 3.55639e6 0.150077
\(892\) 3.36935e7 1.41786
\(893\) −5.03110e6 −0.211123
\(894\) 2.05130e7 0.858392
\(895\) 1.97197e7 0.822891
\(896\) 3.79927e7 1.58099
\(897\) −3.08409e6 −0.127981
\(898\) −6.98977e7 −2.89249
\(899\) 1.86342e7 0.768975
\(900\) 2.11235e7 0.869279
\(901\) −6.28223e6 −0.257811
\(902\) 3.28624e7 1.34488
\(903\) −851242. −0.0347403
\(904\) −3.13730e7 −1.27684
\(905\) −5.46703e7 −2.21886
\(906\) 4.38710e7 1.77565
\(907\) −9.47966e6 −0.382626 −0.191313 0.981529i \(-0.561275\pi\)
−0.191313 + 0.981529i \(0.561275\pi\)
\(908\) 5.63559e7 2.26843
\(909\) −6.31302e6 −0.253412
\(910\) 2.03103e7 0.813043
\(911\) 1.83383e7 0.732087 0.366043 0.930598i \(-0.380712\pi\)
0.366043 + 0.930598i \(0.380712\pi\)
\(912\) 343968. 0.0136940
\(913\) −3.45070e7 −1.37003
\(914\) 4.88657e6 0.193481
\(915\) 1.58025e7 0.623982
\(916\) 1.74051e7 0.685389
\(917\) −4.47865e6 −0.175883
\(918\) −2.90211e6 −0.113660
\(919\) −1.14654e7 −0.447816 −0.223908 0.974610i \(-0.571882\pi\)
−0.223908 + 0.974610i \(0.571882\pi\)
\(920\) 2.97239e7 1.15781
\(921\) 2.84261e7 1.10425
\(922\) −2.71168e7 −1.05053
\(923\) 7.52011e6 0.290549
\(924\) −3.15165e7 −1.21439
\(925\) 1.24448e7 0.478227
\(926\) 4.89018e7 1.87412
\(927\) 6.10797e6 0.233452
\(928\) 4.06246e7 1.54853
\(929\) 3.21954e7 1.22392 0.611962 0.790887i \(-0.290380\pi\)
0.611962 + 0.790887i \(0.290380\pi\)
\(930\) −1.80792e7 −0.685445
\(931\) −751187. −0.0284036
\(932\) 6.23244e7 2.35027
\(933\) 2.70526e7 1.01743
\(934\) −6.00908e7 −2.25393
\(935\) −2.09398e7 −0.783327
\(936\) −3.21062e6 −0.119784
\(937\) 1.18294e7 0.440165 0.220082 0.975481i \(-0.429367\pi\)
0.220082 + 0.975481i \(0.429367\pi\)
\(938\) 6.29103e7 2.33461
\(939\) −9.22484e6 −0.341425
\(940\) −6.61773e7 −2.44281
\(941\) 3.64458e7 1.34176 0.670878 0.741568i \(-0.265917\pi\)
0.670878 + 0.741568i \(0.265917\pi\)
\(942\) −2.40424e7 −0.882776
\(943\) 1.11229e7 0.407322
\(944\) −367042. −0.0134056
\(945\) −7.92716e6 −0.288761
\(946\) 3.89903e6 0.141654
\(947\) −2.71277e7 −0.982965 −0.491483 0.870887i \(-0.663545\pi\)
−0.491483 + 0.870887i \(0.663545\pi\)
\(948\) 3.71178e7 1.34141
\(949\) −1.65990e7 −0.598295
\(950\) 1.63957e7 0.589416
\(951\) −1.05204e7 −0.377209
\(952\) 1.02549e7 0.366723
\(953\) 2.81557e7 1.00423 0.502117 0.864800i \(-0.332555\pi\)
0.502117 + 0.864800i \(0.332555\pi\)
\(954\) 1.08934e7 0.387517
\(955\) 3.12205e7 1.10773
\(956\) 3.04190e7 1.07646
\(957\) −3.74242e7 −1.32091
\(958\) 4.57139e7 1.60929
\(959\) −3.50860e7 −1.23193
\(960\) −4.21351e7 −1.47559
\(961\) −2.27287e7 −0.793902
\(962\) −4.74375e6 −0.165266
\(963\) −1.25154e7 −0.434889
\(964\) 2.56611e7 0.889372
\(965\) 1.13635e7 0.392821
\(966\) −1.70812e7 −0.588946
\(967\) −5.11650e7 −1.75957 −0.879785 0.475372i \(-0.842313\pi\)
−0.879785 + 0.475372i \(0.842313\pi\)
\(968\) 2.60101e7 0.892183
\(969\) −1.40675e6 −0.0481290
\(970\) −7.69884e7 −2.62722
\(971\) −6.44355e6 −0.219319 −0.109660 0.993969i \(-0.534976\pi\)
−0.109660 + 0.993969i \(0.534976\pi\)
\(972\) 3.14268e6 0.106693
\(973\) 3.67848e7 1.24562
\(974\) −4.91899e7 −1.66142
\(975\) −8.92253e6 −0.300591
\(976\) 2.06668e6 0.0694462
\(977\) 3.15126e7 1.05620 0.528102 0.849181i \(-0.322904\pi\)
0.528102 + 0.849181i \(0.322904\pi\)
\(978\) −2.34379e7 −0.783558
\(979\) −8.42041e6 −0.280787
\(980\) −9.88085e6 −0.328647
\(981\) −1.51442e7 −0.502427
\(982\) −6.86407e7 −2.27145
\(983\) 1.64341e6 0.0542454 0.0271227 0.999632i \(-0.491366\pi\)
0.0271227 + 0.999632i \(0.491366\pi\)
\(984\) 1.15792e7 0.381233
\(985\) 3.08862e7 1.01432
\(986\) 3.05391e7 1.00038
\(987\) 1.51639e7 0.495471
\(988\) −3.90304e6 −0.127207
\(989\) 1.31970e6 0.0429026
\(990\) 3.63095e7 1.17742
\(991\) −4.16969e7 −1.34871 −0.674357 0.738405i \(-0.735579\pi\)
−0.674357 + 0.738405i \(0.735579\pi\)
\(992\) 1.28635e7 0.415032
\(993\) 2.70567e7 0.870765
\(994\) 4.16500e7 1.33705
\(995\) 4.55448e7 1.45841
\(996\) −3.04928e7 −0.973979
\(997\) −4.32397e6 −0.137767 −0.0688835 0.997625i \(-0.521944\pi\)
−0.0688835 + 0.997625i \(0.521944\pi\)
\(998\) 2.60946e7 0.829324
\(999\) 1.85150e6 0.0586961
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.1.10 12
3.2 odd 2 531.6.a.c.1.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.c.1.10 12 1.1 even 1 trivial
531.6.a.c.1.3 12 3.2 odd 2