Properties

Label 1110.6.a.a.1.1
Level $1110$
Weight $6$
Character 1110.1
Self dual yes
Analytic conductor $178.026$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(178.026039992\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1110.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +33.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +33.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +39.0000 q^{11} -144.000 q^{12} -314.000 q^{13} +132.000 q^{14} -225.000 q^{15} +256.000 q^{16} -1949.00 q^{17} +324.000 q^{18} +922.000 q^{19} +400.000 q^{20} -297.000 q^{21} +156.000 q^{22} +3844.00 q^{23} -576.000 q^{24} +625.000 q^{25} -1256.00 q^{26} -729.000 q^{27} +528.000 q^{28} -8313.00 q^{29} -900.000 q^{30} +5985.00 q^{31} +1024.00 q^{32} -351.000 q^{33} -7796.00 q^{34} +825.000 q^{35} +1296.00 q^{36} -1369.00 q^{37} +3688.00 q^{38} +2826.00 q^{39} +1600.00 q^{40} -13607.0 q^{41} -1188.00 q^{42} +847.000 q^{43} +624.000 q^{44} +2025.00 q^{45} +15376.0 q^{46} +2904.00 q^{47} -2304.00 q^{48} -15718.0 q^{49} +2500.00 q^{50} +17541.0 q^{51} -5024.00 q^{52} -33851.0 q^{53} -2916.00 q^{54} +975.000 q^{55} +2112.00 q^{56} -8298.00 q^{57} -33252.0 q^{58} -2186.00 q^{59} -3600.00 q^{60} +19893.0 q^{61} +23940.0 q^{62} +2673.00 q^{63} +4096.00 q^{64} -7850.00 q^{65} -1404.00 q^{66} -18596.0 q^{67} -31184.0 q^{68} -34596.0 q^{69} +3300.00 q^{70} -17740.0 q^{71} +5184.00 q^{72} -44536.0 q^{73} -5476.00 q^{74} -5625.00 q^{75} +14752.0 q^{76} +1287.00 q^{77} +11304.0 q^{78} +79732.0 q^{79} +6400.00 q^{80} +6561.00 q^{81} -54428.0 q^{82} +36254.0 q^{83} -4752.00 q^{84} -48725.0 q^{85} +3388.00 q^{86} +74817.0 q^{87} +2496.00 q^{88} -57970.0 q^{89} +8100.00 q^{90} -10362.0 q^{91} +61504.0 q^{92} -53865.0 q^{93} +11616.0 q^{94} +23050.0 q^{95} -9216.00 q^{96} +85531.0 q^{97} -62872.0 q^{98} +3159.00 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −9.00000 −0.577350
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −36.0000 −0.408248
\(7\) 33.0000 0.254548 0.127274 0.991868i \(-0.459377\pi\)
0.127274 + 0.991868i \(0.459377\pi\)
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 100.000 0.316228
\(11\) 39.0000 0.0971813 0.0485907 0.998819i \(-0.484527\pi\)
0.0485907 + 0.998819i \(0.484527\pi\)
\(12\) −144.000 −0.288675
\(13\) −314.000 −0.515313 −0.257657 0.966237i \(-0.582950\pi\)
−0.257657 + 0.966237i \(0.582950\pi\)
\(14\) 132.000 0.179992
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) −1949.00 −1.63565 −0.817823 0.575469i \(-0.804819\pi\)
−0.817823 + 0.575469i \(0.804819\pi\)
\(18\) 324.000 0.235702
\(19\) 922.000 0.585932 0.292966 0.956123i \(-0.405358\pi\)
0.292966 + 0.956123i \(0.405358\pi\)
\(20\) 400.000 0.223607
\(21\) −297.000 −0.146963
\(22\) 156.000 0.0687176
\(23\) 3844.00 1.51518 0.757589 0.652732i \(-0.226377\pi\)
0.757589 + 0.652732i \(0.226377\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) −1256.00 −0.364381
\(27\) −729.000 −0.192450
\(28\) 528.000 0.127274
\(29\) −8313.00 −1.83554 −0.917768 0.397118i \(-0.870011\pi\)
−0.917768 + 0.397118i \(0.870011\pi\)
\(30\) −900.000 −0.182574
\(31\) 5985.00 1.11856 0.559281 0.828978i \(-0.311077\pi\)
0.559281 + 0.828978i \(0.311077\pi\)
\(32\) 1024.00 0.176777
\(33\) −351.000 −0.0561077
\(34\) −7796.00 −1.15658
\(35\) 825.000 0.113837
\(36\) 1296.00 0.166667
\(37\) −1369.00 −0.164399
\(38\) 3688.00 0.414316
\(39\) 2826.00 0.297516
\(40\) 1600.00 0.158114
\(41\) −13607.0 −1.26416 −0.632081 0.774902i \(-0.717799\pi\)
−0.632081 + 0.774902i \(0.717799\pi\)
\(42\) −1188.00 −0.103919
\(43\) 847.000 0.0698574 0.0349287 0.999390i \(-0.488880\pi\)
0.0349287 + 0.999390i \(0.488880\pi\)
\(44\) 624.000 0.0485907
\(45\) 2025.00 0.149071
\(46\) 15376.0 1.07139
\(47\) 2904.00 0.191757 0.0958787 0.995393i \(-0.469434\pi\)
0.0958787 + 0.995393i \(0.469434\pi\)
\(48\) −2304.00 −0.144338
\(49\) −15718.0 −0.935206
\(50\) 2500.00 0.141421
\(51\) 17541.0 0.944341
\(52\) −5024.00 −0.257657
\(53\) −33851.0 −1.65532 −0.827660 0.561230i \(-0.810328\pi\)
−0.827660 + 0.561230i \(0.810328\pi\)
\(54\) −2916.00 −0.136083
\(55\) 975.000 0.0434608
\(56\) 2112.00 0.0899961
\(57\) −8298.00 −0.338288
\(58\) −33252.0 −1.29792
\(59\) −2186.00 −0.0817561 −0.0408780 0.999164i \(-0.513016\pi\)
−0.0408780 + 0.999164i \(0.513016\pi\)
\(60\) −3600.00 −0.129099
\(61\) 19893.0 0.684504 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(62\) 23940.0 0.790943
\(63\) 2673.00 0.0848492
\(64\) 4096.00 0.125000
\(65\) −7850.00 −0.230455
\(66\) −1404.00 −0.0396741
\(67\) −18596.0 −0.506096 −0.253048 0.967454i \(-0.581433\pi\)
−0.253048 + 0.967454i \(0.581433\pi\)
\(68\) −31184.0 −0.817823
\(69\) −34596.0 −0.874789
\(70\) 3300.00 0.0804950
\(71\) −17740.0 −0.417645 −0.208823 0.977954i \(-0.566963\pi\)
−0.208823 + 0.977954i \(0.566963\pi\)
\(72\) 5184.00 0.117851
\(73\) −44536.0 −0.978147 −0.489073 0.872243i \(-0.662665\pi\)
−0.489073 + 0.872243i \(0.662665\pi\)
\(74\) −5476.00 −0.116248
\(75\) −5625.00 −0.115470
\(76\) 14752.0 0.292966
\(77\) 1287.00 0.0247373
\(78\) 11304.0 0.210376
\(79\) 79732.0 1.43736 0.718679 0.695342i \(-0.244747\pi\)
0.718679 + 0.695342i \(0.244747\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) −54428.0 −0.893898
\(83\) 36254.0 0.577645 0.288822 0.957383i \(-0.406736\pi\)
0.288822 + 0.957383i \(0.406736\pi\)
\(84\) −4752.00 −0.0734815
\(85\) −48725.0 −0.731483
\(86\) 3388.00 0.0493966
\(87\) 74817.0 1.05975
\(88\) 2496.00 0.0343588
\(89\) −57970.0 −0.775762 −0.387881 0.921710i \(-0.626793\pi\)
−0.387881 + 0.921710i \(0.626793\pi\)
\(90\) 8100.00 0.105409
\(91\) −10362.0 −0.131172
\(92\) 61504.0 0.757589
\(93\) −53865.0 −0.645802
\(94\) 11616.0 0.135593
\(95\) 23050.0 0.262037
\(96\) −9216.00 −0.102062
\(97\) 85531.0 0.922984 0.461492 0.887144i \(-0.347314\pi\)
0.461492 + 0.887144i \(0.347314\pi\)
\(98\) −62872.0 −0.661290
\(99\) 3159.00 0.0323938
\(100\) 10000.0 0.100000
\(101\) 102124. 0.996149 0.498075 0.867134i \(-0.334041\pi\)
0.498075 + 0.867134i \(0.334041\pi\)
\(102\) 70164.0 0.667750
\(103\) 107864. 1.00181 0.500903 0.865504i \(-0.333001\pi\)
0.500903 + 0.865504i \(0.333001\pi\)
\(104\) −20096.0 −0.182191
\(105\) −7425.00 −0.0657239
\(106\) −135404. −1.17049
\(107\) 110946. 0.936811 0.468406 0.883513i \(-0.344829\pi\)
0.468406 + 0.883513i \(0.344829\pi\)
\(108\) −11664.0 −0.0962250
\(109\) −50987.0 −0.411049 −0.205524 0.978652i \(-0.565890\pi\)
−0.205524 + 0.978652i \(0.565890\pi\)
\(110\) 3900.00 0.0307314
\(111\) 12321.0 0.0949158
\(112\) 8448.00 0.0636369
\(113\) −15919.0 −0.117279 −0.0586394 0.998279i \(-0.518676\pi\)
−0.0586394 + 0.998279i \(0.518676\pi\)
\(114\) −33192.0 −0.239206
\(115\) 96100.0 0.677608
\(116\) −133008. −0.917768
\(117\) −25434.0 −0.171771
\(118\) −8744.00 −0.0578103
\(119\) −64317.0 −0.416350
\(120\) −14400.0 −0.0912871
\(121\) −159530. −0.990556
\(122\) 79572.0 0.484017
\(123\) 122463. 0.729864
\(124\) 95760.0 0.559281
\(125\) 15625.0 0.0894427
\(126\) 10692.0 0.0599974
\(127\) −217920. −1.19891 −0.599457 0.800407i \(-0.704617\pi\)
−0.599457 + 0.800407i \(0.704617\pi\)
\(128\) 16384.0 0.0883883
\(129\) −7623.00 −0.0403322
\(130\) −31400.0 −0.162956
\(131\) −229662. −1.16926 −0.584630 0.811300i \(-0.698760\pi\)
−0.584630 + 0.811300i \(0.698760\pi\)
\(132\) −5616.00 −0.0280538
\(133\) 30426.0 0.149147
\(134\) −74384.0 −0.357864
\(135\) −18225.0 −0.0860663
\(136\) −124736. −0.578288
\(137\) 112422. 0.511741 0.255870 0.966711i \(-0.417638\pi\)
0.255870 + 0.966711i \(0.417638\pi\)
\(138\) −138384. −0.618569
\(139\) 151281. 0.664121 0.332061 0.943258i \(-0.392256\pi\)
0.332061 + 0.943258i \(0.392256\pi\)
\(140\) 13200.0 0.0569186
\(141\) −26136.0 −0.110711
\(142\) −70960.0 −0.295320
\(143\) −12246.0 −0.0500788
\(144\) 20736.0 0.0833333
\(145\) −207825. −0.820876
\(146\) −178144. −0.691654
\(147\) 141462. 0.539941
\(148\) −21904.0 −0.0821995
\(149\) −488610. −1.80300 −0.901502 0.432775i \(-0.857534\pi\)
−0.901502 + 0.432775i \(0.857534\pi\)
\(150\) −22500.0 −0.0816497
\(151\) −268862. −0.959593 −0.479796 0.877380i \(-0.659290\pi\)
−0.479796 + 0.877380i \(0.659290\pi\)
\(152\) 59008.0 0.207158
\(153\) −157869. −0.545216
\(154\) 5148.00 0.0174919
\(155\) 149625. 0.500236
\(156\) 45216.0 0.148758
\(157\) −222005. −0.718809 −0.359405 0.933182i \(-0.617020\pi\)
−0.359405 + 0.933182i \(0.617020\pi\)
\(158\) 318928. 1.01637
\(159\) 304659. 0.955699
\(160\) 25600.0 0.0790569
\(161\) 126852. 0.385685
\(162\) 26244.0 0.0785674
\(163\) 24951.0 0.0735561 0.0367781 0.999323i \(-0.488291\pi\)
0.0367781 + 0.999323i \(0.488291\pi\)
\(164\) −217712. −0.632081
\(165\) −8775.00 −0.0250921
\(166\) 145016. 0.408456
\(167\) −333728. −0.925980 −0.462990 0.886364i \(-0.653223\pi\)
−0.462990 + 0.886364i \(0.653223\pi\)
\(168\) −19008.0 −0.0519593
\(169\) −272697. −0.734452
\(170\) −194900. −0.517237
\(171\) 74682.0 0.195311
\(172\) 13552.0 0.0349287
\(173\) 210781. 0.535447 0.267723 0.963496i \(-0.413729\pi\)
0.267723 + 0.963496i \(0.413729\pi\)
\(174\) 299268. 0.749354
\(175\) 20625.0 0.0509095
\(176\) 9984.00 0.0242953
\(177\) 19674.0 0.0472019
\(178\) −231880. −0.548546
\(179\) −90788.0 −0.211785 −0.105893 0.994378i \(-0.533770\pi\)
−0.105893 + 0.994378i \(0.533770\pi\)
\(180\) 32400.0 0.0745356
\(181\) −238526. −0.541177 −0.270588 0.962695i \(-0.587218\pi\)
−0.270588 + 0.962695i \(0.587218\pi\)
\(182\) −41448.0 −0.0927524
\(183\) −179037. −0.395198
\(184\) 246016. 0.535696
\(185\) −34225.0 −0.0735215
\(186\) −215460. −0.456651
\(187\) −76011.0 −0.158954
\(188\) 46464.0 0.0958787
\(189\) −24057.0 −0.0489877
\(190\) 92200.0 0.185288
\(191\) −684575. −1.35781 −0.678903 0.734228i \(-0.737544\pi\)
−0.678903 + 0.734228i \(0.737544\pi\)
\(192\) −36864.0 −0.0721688
\(193\) 108706. 0.210068 0.105034 0.994469i \(-0.466505\pi\)
0.105034 + 0.994469i \(0.466505\pi\)
\(194\) 342124. 0.652648
\(195\) 70650.0 0.133053
\(196\) −251488. −0.467603
\(197\) 75198.0 0.138051 0.0690257 0.997615i \(-0.478011\pi\)
0.0690257 + 0.997615i \(0.478011\pi\)
\(198\) 12636.0 0.0229059
\(199\) −280268. −0.501696 −0.250848 0.968026i \(-0.580709\pi\)
−0.250848 + 0.968026i \(0.580709\pi\)
\(200\) 40000.0 0.0707107
\(201\) 167364. 0.292194
\(202\) 408496. 0.704384
\(203\) −274329. −0.467231
\(204\) 280656. 0.472171
\(205\) −340175. −0.565350
\(206\) 431456. 0.708384
\(207\) 311364. 0.505059
\(208\) −80384.0 −0.128828
\(209\) 35958.0 0.0569416
\(210\) −29700.0 −0.0464738
\(211\) −25865.0 −0.0399951 −0.0199975 0.999800i \(-0.506366\pi\)
−0.0199975 + 0.999800i \(0.506366\pi\)
\(212\) −541616. −0.827660
\(213\) 159660. 0.241128
\(214\) 443784. 0.662426
\(215\) 21175.0 0.0312412
\(216\) −46656.0 −0.0680414
\(217\) 197505. 0.284727
\(218\) −203948. −0.290655
\(219\) 400824. 0.564733
\(220\) 15600.0 0.0217304
\(221\) 611986. 0.842870
\(222\) 49284.0 0.0671156
\(223\) −853541. −1.14938 −0.574688 0.818372i \(-0.694877\pi\)
−0.574688 + 0.818372i \(0.694877\pi\)
\(224\) 33792.0 0.0449981
\(225\) 50625.0 0.0666667
\(226\) −63676.0 −0.0829287
\(227\) −1.06611e6 −1.37322 −0.686608 0.727028i \(-0.740901\pi\)
−0.686608 + 0.727028i \(0.740901\pi\)
\(228\) −132768. −0.169144
\(229\) −262972. −0.331376 −0.165688 0.986178i \(-0.552984\pi\)
−0.165688 + 0.986178i \(0.552984\pi\)
\(230\) 384400. 0.479142
\(231\) −11583.0 −0.0142821
\(232\) −532032. −0.648960
\(233\) −134608. −0.162436 −0.0812178 0.996696i \(-0.525881\pi\)
−0.0812178 + 0.996696i \(0.525881\pi\)
\(234\) −101736. −0.121460
\(235\) 72600.0 0.0857565
\(236\) −34976.0 −0.0408780
\(237\) −717588. −0.829859
\(238\) −257268. −0.294404
\(239\) −1.39927e6 −1.58455 −0.792277 0.610161i \(-0.791105\pi\)
−0.792277 + 0.610161i \(0.791105\pi\)
\(240\) −57600.0 −0.0645497
\(241\) −933458. −1.03527 −0.517633 0.855603i \(-0.673187\pi\)
−0.517633 + 0.855603i \(0.673187\pi\)
\(242\) −638120. −0.700429
\(243\) −59049.0 −0.0641500
\(244\) 318288. 0.342252
\(245\) −392950. −0.418237
\(246\) 489852. 0.516092
\(247\) −289508. −0.301938
\(248\) 383040. 0.395471
\(249\) −326286. −0.333503
\(250\) 62500.0 0.0632456
\(251\) −123680. −0.123913 −0.0619563 0.998079i \(-0.519734\pi\)
−0.0619563 + 0.998079i \(0.519734\pi\)
\(252\) 42768.0 0.0424246
\(253\) 149916. 0.147247
\(254\) −871680. −0.847760
\(255\) 438525. 0.422322
\(256\) 65536.0 0.0625000
\(257\) −1.48420e6 −1.40171 −0.700856 0.713302i \(-0.747199\pi\)
−0.700856 + 0.713302i \(0.747199\pi\)
\(258\) −30492.0 −0.0285192
\(259\) −45177.0 −0.0418474
\(260\) −125600. −0.115228
\(261\) −673353. −0.611845
\(262\) −918648. −0.826791
\(263\) 1.47930e6 1.31876 0.659380 0.751810i \(-0.270819\pi\)
0.659380 + 0.751810i \(0.270819\pi\)
\(264\) −22464.0 −0.0198371
\(265\) −846275. −0.740281
\(266\) 121704. 0.105463
\(267\) 521730. 0.447886
\(268\) −297536. −0.253048
\(269\) 784136. 0.660710 0.330355 0.943857i \(-0.392832\pi\)
0.330355 + 0.943857i \(0.392832\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 998872. 0.826203 0.413101 0.910685i \(-0.364446\pi\)
0.413101 + 0.910685i \(0.364446\pi\)
\(272\) −498944. −0.408912
\(273\) 93258.0 0.0757320
\(274\) 449688. 0.361855
\(275\) 24375.0 0.0194363
\(276\) −553536. −0.437394
\(277\) 54376.0 0.0425802 0.0212901 0.999773i \(-0.493223\pi\)
0.0212901 + 0.999773i \(0.493223\pi\)
\(278\) 605124. 0.469605
\(279\) 484785. 0.372854
\(280\) 52800.0 0.0402475
\(281\) 1.65057e6 1.24700 0.623502 0.781821i \(-0.285709\pi\)
0.623502 + 0.781821i \(0.285709\pi\)
\(282\) −104544. −0.0782846
\(283\) 234044. 0.173713 0.0868563 0.996221i \(-0.472318\pi\)
0.0868563 + 0.996221i \(0.472318\pi\)
\(284\) −283840. −0.208823
\(285\) −207450. −0.151287
\(286\) −48984.0 −0.0354111
\(287\) −449031. −0.321789
\(288\) 82944.0 0.0589256
\(289\) 2.37874e6 1.67534
\(290\) −831300. −0.580447
\(291\) −769779. −0.532885
\(292\) −712576. −0.489073
\(293\) 953967. 0.649179 0.324589 0.945855i \(-0.394774\pi\)
0.324589 + 0.945855i \(0.394774\pi\)
\(294\) 565848. 0.381796
\(295\) −54650.0 −0.0365624
\(296\) −87616.0 −0.0581238
\(297\) −28431.0 −0.0187026
\(298\) −1.95444e6 −1.27492
\(299\) −1.20702e6 −0.780791
\(300\) −90000.0 −0.0577350
\(301\) 27951.0 0.0177820
\(302\) −1.07545e6 −0.678535
\(303\) −919116. −0.575127
\(304\) 236032. 0.146483
\(305\) 497325. 0.306119
\(306\) −631476. −0.385526
\(307\) 255702. 0.154842 0.0774209 0.996998i \(-0.475331\pi\)
0.0774209 + 0.996998i \(0.475331\pi\)
\(308\) 20592.0 0.0123686
\(309\) −970776. −0.578393
\(310\) 598500. 0.353720
\(311\) −2.81516e6 −1.65045 −0.825225 0.564804i \(-0.808952\pi\)
−0.825225 + 0.564804i \(0.808952\pi\)
\(312\) 180864. 0.105188
\(313\) −2.65446e6 −1.53150 −0.765748 0.643141i \(-0.777631\pi\)
−0.765748 + 0.643141i \(0.777631\pi\)
\(314\) −888020. −0.508275
\(315\) 66825.0 0.0379457
\(316\) 1.27571e6 0.718679
\(317\) −401267. −0.224277 −0.112139 0.993693i \(-0.535770\pi\)
−0.112139 + 0.993693i \(0.535770\pi\)
\(318\) 1.21864e6 0.675781
\(319\) −324207. −0.178380
\(320\) 102400. 0.0559017
\(321\) −998514. −0.540868
\(322\) 507408. 0.272720
\(323\) −1.79698e6 −0.958377
\(324\) 104976. 0.0555556
\(325\) −196250. −0.103063
\(326\) 99804.0 0.0520120
\(327\) 458883. 0.237319
\(328\) −870848. −0.446949
\(329\) 95832.0 0.0488113
\(330\) −35100.0 −0.0177428
\(331\) −3.11456e6 −1.56252 −0.781261 0.624204i \(-0.785423\pi\)
−0.781261 + 0.624204i \(0.785423\pi\)
\(332\) 580064. 0.288822
\(333\) −110889. −0.0547997
\(334\) −1.33491e6 −0.654767
\(335\) −464900. −0.226333
\(336\) −76032.0 −0.0367408
\(337\) 2.82311e6 1.35411 0.677053 0.735935i \(-0.263257\pi\)
0.677053 + 0.735935i \(0.263257\pi\)
\(338\) −1.09079e6 −0.519336
\(339\) 143271. 0.0677110
\(340\) −779600. −0.365742
\(341\) 233415. 0.108703
\(342\) 298728. 0.138105
\(343\) −1.07332e6 −0.492602
\(344\) 54208.0 0.0246983
\(345\) −864900. −0.391217
\(346\) 843124. 0.378618
\(347\) −265980. −0.118584 −0.0592919 0.998241i \(-0.518884\pi\)
−0.0592919 + 0.998241i \(0.518884\pi\)
\(348\) 1.19707e6 0.529873
\(349\) 1.33488e6 0.586648 0.293324 0.956013i \(-0.405239\pi\)
0.293324 + 0.956013i \(0.405239\pi\)
\(350\) 82500.0 0.0359985
\(351\) 228906. 0.0991721
\(352\) 39936.0 0.0171794
\(353\) −2.92493e6 −1.24934 −0.624668 0.780891i \(-0.714766\pi\)
−0.624668 + 0.780891i \(0.714766\pi\)
\(354\) 78696.0 0.0333768
\(355\) −443500. −0.186777
\(356\) −927520. −0.387881
\(357\) 578853. 0.240380
\(358\) −363152. −0.149755
\(359\) 461730. 0.189083 0.0945414 0.995521i \(-0.469862\pi\)
0.0945414 + 0.995521i \(0.469862\pi\)
\(360\) 129600. 0.0527046
\(361\) −1.62602e6 −0.656684
\(362\) −954104. −0.382670
\(363\) 1.43577e6 0.571898
\(364\) −165792. −0.0655858
\(365\) −1.11340e6 −0.437441
\(366\) −716148. −0.279447
\(367\) −224343. −0.0869456 −0.0434728 0.999055i \(-0.513842\pi\)
−0.0434728 + 0.999055i \(0.513842\pi\)
\(368\) 984064. 0.378795
\(369\) −1.10217e6 −0.421387
\(370\) −136900. −0.0519875
\(371\) −1.11708e6 −0.421357
\(372\) −861840. −0.322901
\(373\) −2.42261e6 −0.901596 −0.450798 0.892626i \(-0.648861\pi\)
−0.450798 + 0.892626i \(0.648861\pi\)
\(374\) −304044. −0.112398
\(375\) −140625. −0.0516398
\(376\) 185856. 0.0677965
\(377\) 2.61028e6 0.945876
\(378\) −96228.0 −0.0346395
\(379\) 1.39673e6 0.499475 0.249738 0.968314i \(-0.419656\pi\)
0.249738 + 0.968314i \(0.419656\pi\)
\(380\) 368800. 0.131018
\(381\) 1.96128e6 0.692193
\(382\) −2.73830e6 −0.960114
\(383\) −3.82780e6 −1.33337 −0.666687 0.745338i \(-0.732288\pi\)
−0.666687 + 0.745338i \(0.732288\pi\)
\(384\) −147456. −0.0510310
\(385\) 32175.0 0.0110628
\(386\) 434824. 0.148541
\(387\) 68607.0 0.0232858
\(388\) 1.36850e6 0.461492
\(389\) 5.08828e6 1.70489 0.852447 0.522814i \(-0.175118\pi\)
0.852447 + 0.522814i \(0.175118\pi\)
\(390\) 282600. 0.0940829
\(391\) −7.49196e6 −2.47830
\(392\) −1.00595e6 −0.330645
\(393\) 2.06696e6 0.675072
\(394\) 300792. 0.0976171
\(395\) 1.99330e6 0.642806
\(396\) 50544.0 0.0161969
\(397\) −2.26217e6 −0.720360 −0.360180 0.932883i \(-0.617285\pi\)
−0.360180 + 0.932883i \(0.617285\pi\)
\(398\) −1.12107e6 −0.354753
\(399\) −273834. −0.0861103
\(400\) 160000. 0.0500000
\(401\) 1.18719e6 0.368688 0.184344 0.982862i \(-0.440984\pi\)
0.184344 + 0.982862i \(0.440984\pi\)
\(402\) 669456. 0.206613
\(403\) −1.87929e6 −0.576410
\(404\) 1.63398e6 0.498075
\(405\) 164025. 0.0496904
\(406\) −1.09732e6 −0.330382
\(407\) −53391.0 −0.0159765
\(408\) 1.12262e6 0.333875
\(409\) −466906. −0.138013 −0.0690067 0.997616i \(-0.521983\pi\)
−0.0690067 + 0.997616i \(0.521983\pi\)
\(410\) −1.36070e6 −0.399763
\(411\) −1.01180e6 −0.295454
\(412\) 1.72582e6 0.500903
\(413\) −72138.0 −0.0208108
\(414\) 1.24546e6 0.357131
\(415\) 906350. 0.258331
\(416\) −321536. −0.0910954
\(417\) −1.36153e6 −0.383431
\(418\) 143832. 0.0402638
\(419\) −1.49434e6 −0.415829 −0.207914 0.978147i \(-0.566668\pi\)
−0.207914 + 0.978147i \(0.566668\pi\)
\(420\) −118800. −0.0328619
\(421\) −3.25272e6 −0.894419 −0.447210 0.894429i \(-0.647582\pi\)
−0.447210 + 0.894429i \(0.647582\pi\)
\(422\) −103460. −0.0282808
\(423\) 235224. 0.0639191
\(424\) −2.16646e6 −0.585244
\(425\) −1.21812e6 −0.327129
\(426\) 638640. 0.170503
\(427\) 656469. 0.174239
\(428\) 1.77514e6 0.468406
\(429\) 110214. 0.0289130
\(430\) 84700.0 0.0220908
\(431\) 5.68679e6 1.47460 0.737300 0.675566i \(-0.236101\pi\)
0.737300 + 0.675566i \(0.236101\pi\)
\(432\) −186624. −0.0481125
\(433\) 6.82025e6 1.74816 0.874078 0.485785i \(-0.161466\pi\)
0.874078 + 0.485785i \(0.161466\pi\)
\(434\) 790020. 0.201332
\(435\) 1.87042e6 0.473933
\(436\) −815792. −0.205524
\(437\) 3.54417e6 0.887791
\(438\) 1.60330e6 0.399327
\(439\) −2.25054e6 −0.557346 −0.278673 0.960386i \(-0.589895\pi\)
−0.278673 + 0.960386i \(0.589895\pi\)
\(440\) 62400.0 0.0153657
\(441\) −1.27316e6 −0.311735
\(442\) 2.44794e6 0.595999
\(443\) 4.16289e6 1.00783 0.503914 0.863754i \(-0.331893\pi\)
0.503914 + 0.863754i \(0.331893\pi\)
\(444\) 197136. 0.0474579
\(445\) −1.44925e6 −0.346931
\(446\) −3.41416e6 −0.812732
\(447\) 4.39749e6 1.04096
\(448\) 135168. 0.0318184
\(449\) 3.84574e6 0.900252 0.450126 0.892965i \(-0.351379\pi\)
0.450126 + 0.892965i \(0.351379\pi\)
\(450\) 202500. 0.0471405
\(451\) −530673. −0.122853
\(452\) −254704. −0.0586394
\(453\) 2.41976e6 0.554021
\(454\) −4.26445e6 −0.971010
\(455\) −259050. −0.0586618
\(456\) −531072. −0.119603
\(457\) −1.00536e6 −0.225182 −0.112591 0.993641i \(-0.535915\pi\)
−0.112591 + 0.993641i \(0.535915\pi\)
\(458\) −1.05189e6 −0.234318
\(459\) 1.42082e6 0.314780
\(460\) 1.53760e6 0.338804
\(461\) 1.70673e6 0.374034 0.187017 0.982357i \(-0.440118\pi\)
0.187017 + 0.982357i \(0.440118\pi\)
\(462\) −46332.0 −0.0100989
\(463\) 5.72391e6 1.24091 0.620455 0.784242i \(-0.286948\pi\)
0.620455 + 0.784242i \(0.286948\pi\)
\(464\) −2.12813e6 −0.458884
\(465\) −1.34662e6 −0.288811
\(466\) −538432. −0.114859
\(467\) −669435. −0.142042 −0.0710209 0.997475i \(-0.522626\pi\)
−0.0710209 + 0.997475i \(0.522626\pi\)
\(468\) −406944. −0.0858855
\(469\) −613668. −0.128825
\(470\) 290400. 0.0606390
\(471\) 1.99804e6 0.415005
\(472\) −139904. −0.0289051
\(473\) 33033.0 0.00678883
\(474\) −2.87035e6 −0.586799
\(475\) 576250. 0.117186
\(476\) −1.02907e6 −0.208175
\(477\) −2.74193e6 −0.551773
\(478\) −5.59708e6 −1.12045
\(479\) −3.52900e6 −0.702769 −0.351385 0.936231i \(-0.614289\pi\)
−0.351385 + 0.936231i \(0.614289\pi\)
\(480\) −230400. −0.0456435
\(481\) 429866. 0.0847170
\(482\) −3.73383e6 −0.732044
\(483\) −1.14167e6 −0.222675
\(484\) −2.55248e6 −0.495278
\(485\) 2.13828e6 0.412771
\(486\) −236196. −0.0453609
\(487\) 577114. 0.110265 0.0551327 0.998479i \(-0.482442\pi\)
0.0551327 + 0.998479i \(0.482442\pi\)
\(488\) 1.27315e6 0.242009
\(489\) −224559. −0.0424677
\(490\) −1.57180e6 −0.295738
\(491\) 318012. 0.0595305 0.0297653 0.999557i \(-0.490524\pi\)
0.0297653 + 0.999557i \(0.490524\pi\)
\(492\) 1.95941e6 0.364932
\(493\) 1.62020e7 3.00229
\(494\) −1.15803e6 −0.213503
\(495\) 78975.0 0.0144869
\(496\) 1.53216e6 0.279640
\(497\) −585420. −0.106311
\(498\) −1.30514e6 −0.235822
\(499\) 6.13994e6 1.10386 0.551928 0.833892i \(-0.313892\pi\)
0.551928 + 0.833892i \(0.313892\pi\)
\(500\) 250000. 0.0447214
\(501\) 3.00355e6 0.534615
\(502\) −494720. −0.0876194
\(503\) 3.15074e6 0.555255 0.277628 0.960689i \(-0.410452\pi\)
0.277628 + 0.960689i \(0.410452\pi\)
\(504\) 171072. 0.0299987
\(505\) 2.55310e6 0.445491
\(506\) 599664. 0.104119
\(507\) 2.45427e6 0.424036
\(508\) −3.48672e6 −0.599457
\(509\) −4.25165e6 −0.727382 −0.363691 0.931520i \(-0.618484\pi\)
−0.363691 + 0.931520i \(0.618484\pi\)
\(510\) 1.75410e6 0.298627
\(511\) −1.46969e6 −0.248985
\(512\) 262144. 0.0441942
\(513\) −672138. −0.112763
\(514\) −5.93679e6 −0.991161
\(515\) 2.69660e6 0.448021
\(516\) −121968. −0.0201661
\(517\) 113256. 0.0186352
\(518\) −180708. −0.0295905
\(519\) −1.89703e6 −0.309140
\(520\) −502400. −0.0814782
\(521\) −601477. −0.0970789 −0.0485394 0.998821i \(-0.515457\pi\)
−0.0485394 + 0.998821i \(0.515457\pi\)
\(522\) −2.69341e6 −0.432640
\(523\) 8.90864e6 1.42415 0.712077 0.702101i \(-0.247755\pi\)
0.712077 + 0.702101i \(0.247755\pi\)
\(524\) −3.67459e6 −0.584630
\(525\) −185625. −0.0293926
\(526\) 5.91719e6 0.932505
\(527\) −1.16648e7 −1.82957
\(528\) −89856.0 −0.0140269
\(529\) 8.33999e6 1.29577
\(530\) −3.38510e6 −0.523458
\(531\) −177066. −0.0272520
\(532\) 486816. 0.0745737
\(533\) 4.27260e6 0.651439
\(534\) 2.08692e6 0.316703
\(535\) 2.77365e6 0.418955
\(536\) −1.19014e6 −0.178932
\(537\) 817092. 0.122274
\(538\) 3.13654e6 0.467192
\(539\) −613002. −0.0908845
\(540\) −291600. −0.0430331
\(541\) −1.13061e7 −1.66081 −0.830406 0.557158i \(-0.811892\pi\)
−0.830406 + 0.557158i \(0.811892\pi\)
\(542\) 3.99549e6 0.584214
\(543\) 2.14673e6 0.312449
\(544\) −1.99578e6 −0.289144
\(545\) −1.27468e6 −0.183827
\(546\) 373032. 0.0535506
\(547\) −697065. −0.0996105 −0.0498052 0.998759i \(-0.515860\pi\)
−0.0498052 + 0.998759i \(0.515860\pi\)
\(548\) 1.79875e6 0.255870
\(549\) 1.61133e6 0.228168
\(550\) 97500.0 0.0137435
\(551\) −7.66459e6 −1.07550
\(552\) −2.21414e6 −0.309285
\(553\) 2.63116e6 0.365876
\(554\) 217504. 0.0301088
\(555\) 308025. 0.0424476
\(556\) 2.42050e6 0.332061
\(557\) −3.60869e6 −0.492846 −0.246423 0.969162i \(-0.579255\pi\)
−0.246423 + 0.969162i \(0.579255\pi\)
\(558\) 1.93914e6 0.263648
\(559\) −265958. −0.0359984
\(560\) 211200. 0.0284593
\(561\) 684099. 0.0917723
\(562\) 6.60228e6 0.881766
\(563\) 2.19924e6 0.292417 0.146208 0.989254i \(-0.453293\pi\)
0.146208 + 0.989254i \(0.453293\pi\)
\(564\) −418176. −0.0553556
\(565\) −397975. −0.0524487
\(566\) 936176. 0.122833
\(567\) 216513. 0.0282831
\(568\) −1.13536e6 −0.147660
\(569\) −5.91609e6 −0.766045 −0.383022 0.923739i \(-0.625117\pi\)
−0.383022 + 0.923739i \(0.625117\pi\)
\(570\) −829800. −0.106976
\(571\) 1.20739e7 1.54974 0.774868 0.632123i \(-0.217816\pi\)
0.774868 + 0.632123i \(0.217816\pi\)
\(572\) −195936. −0.0250394
\(573\) 6.16118e6 0.783929
\(574\) −1.79612e6 −0.227539
\(575\) 2.40250e6 0.303036
\(576\) 331776. 0.0416667
\(577\) −1.08768e7 −1.36007 −0.680037 0.733178i \(-0.738036\pi\)
−0.680037 + 0.733178i \(0.738036\pi\)
\(578\) 9.51498e6 1.18464
\(579\) −978354. −0.121283
\(580\) −3.32520e6 −0.410438
\(581\) 1.19638e6 0.147038
\(582\) −3.07912e6 −0.376807
\(583\) −1.32019e6 −0.160866
\(584\) −2.85030e6 −0.345827
\(585\) −635850. −0.0768184
\(586\) 3.81587e6 0.459039
\(587\) −2.08187e6 −0.249378 −0.124689 0.992196i \(-0.539793\pi\)
−0.124689 + 0.992196i \(0.539793\pi\)
\(588\) 2.26339e6 0.269971
\(589\) 5.51817e6 0.655401
\(590\) −218600. −0.0258535
\(591\) −676782. −0.0797040
\(592\) −350464. −0.0410997
\(593\) −1.16666e7 −1.36240 −0.681202 0.732095i \(-0.738543\pi\)
−0.681202 + 0.732095i \(0.738543\pi\)
\(594\) −113724. −0.0132247
\(595\) −1.60792e6 −0.186197
\(596\) −7.81776e6 −0.901502
\(597\) 2.52241e6 0.289654
\(598\) −4.82806e6 −0.552103
\(599\) 1.29817e6 0.147830 0.0739152 0.997265i \(-0.476451\pi\)
0.0739152 + 0.997265i \(0.476451\pi\)
\(600\) −360000. −0.0408248
\(601\) 9.83205e6 1.11034 0.555172 0.831735i \(-0.312652\pi\)
0.555172 + 0.831735i \(0.312652\pi\)
\(602\) 111804. 0.0125738
\(603\) −1.50628e6 −0.168699
\(604\) −4.30179e6 −0.479796
\(605\) −3.98825e6 −0.442990
\(606\) −3.67646e6 −0.406676
\(607\) −5.97191e6 −0.657872 −0.328936 0.944352i \(-0.606690\pi\)
−0.328936 + 0.944352i \(0.606690\pi\)
\(608\) 944128. 0.103579
\(609\) 2.46896e6 0.269756
\(610\) 1.98930e6 0.216459
\(611\) −911856. −0.0988151
\(612\) −2.52590e6 −0.272608
\(613\) 8.52197e6 0.915986 0.457993 0.888956i \(-0.348568\pi\)
0.457993 + 0.888956i \(0.348568\pi\)
\(614\) 1.02281e6 0.109490
\(615\) 3.06158e6 0.326405
\(616\) 82368.0 0.00874594
\(617\) 6.24075e6 0.659970 0.329985 0.943986i \(-0.392956\pi\)
0.329985 + 0.943986i \(0.392956\pi\)
\(618\) −3.88310e6 −0.408985
\(619\) 1.66424e7 1.74578 0.872891 0.487916i \(-0.162243\pi\)
0.872891 + 0.487916i \(0.162243\pi\)
\(620\) 2.39400e6 0.250118
\(621\) −2.80228e6 −0.291596
\(622\) −1.12607e7 −1.16704
\(623\) −1.91301e6 −0.197468
\(624\) 723456. 0.0743791
\(625\) 390625. 0.0400000
\(626\) −1.06178e7 −1.08293
\(627\) −323622. −0.0328753
\(628\) −3.55208e6 −0.359405
\(629\) 2.66818e6 0.268899
\(630\) 267300. 0.0268317
\(631\) −4.06681e6 −0.406612 −0.203306 0.979115i \(-0.565169\pi\)
−0.203306 + 0.979115i \(0.565169\pi\)
\(632\) 5.10285e6 0.508183
\(633\) 232785. 0.0230912
\(634\) −1.60507e6 −0.158588
\(635\) −5.44800e6 −0.536170
\(636\) 4.87454e6 0.477850
\(637\) 4.93545e6 0.481924
\(638\) −1.29683e6 −0.126134
\(639\) −1.43694e6 −0.139215
\(640\) 409600. 0.0395285
\(641\) 1.07901e7 1.03724 0.518619 0.855005i \(-0.326446\pi\)
0.518619 + 0.855005i \(0.326446\pi\)
\(642\) −3.99406e6 −0.382452
\(643\) −5.25226e6 −0.500978 −0.250489 0.968119i \(-0.580591\pi\)
−0.250489 + 0.968119i \(0.580591\pi\)
\(644\) 2.02963e6 0.192842
\(645\) −190575. −0.0180371
\(646\) −7.18791e6 −0.677675
\(647\) 1.04141e7 0.978049 0.489025 0.872270i \(-0.337353\pi\)
0.489025 + 0.872270i \(0.337353\pi\)
\(648\) 419904. 0.0392837
\(649\) −85254.0 −0.00794517
\(650\) −785000. −0.0728763
\(651\) −1.77754e6 −0.164387
\(652\) 399216. 0.0367781
\(653\) 848008. 0.0778246 0.0389123 0.999243i \(-0.487611\pi\)
0.0389123 + 0.999243i \(0.487611\pi\)
\(654\) 1.83553e6 0.167810
\(655\) −5.74155e6 −0.522909
\(656\) −3.48339e6 −0.316041
\(657\) −3.60742e6 −0.326049
\(658\) 383328. 0.0345148
\(659\) −2.09114e6 −0.187573 −0.0937865 0.995592i \(-0.529897\pi\)
−0.0937865 + 0.995592i \(0.529897\pi\)
\(660\) −140400. −0.0125461
\(661\) −5.74771e6 −0.511671 −0.255836 0.966720i \(-0.582351\pi\)
−0.255836 + 0.966720i \(0.582351\pi\)
\(662\) −1.24582e7 −1.10487
\(663\) −5.50787e6 −0.486631
\(664\) 2.32026e6 0.204228
\(665\) 760650. 0.0667008
\(666\) −443556. −0.0387492
\(667\) −3.19552e7 −2.78116
\(668\) −5.33965e6 −0.462990
\(669\) 7.68187e6 0.663593
\(670\) −1.85960e6 −0.160041
\(671\) 775827. 0.0665210
\(672\) −304128. −0.0259796
\(673\) −1.11962e7 −0.952866 −0.476433 0.879211i \(-0.658070\pi\)
−0.476433 + 0.879211i \(0.658070\pi\)
\(674\) 1.12924e7 0.957497
\(675\) −455625. −0.0384900
\(676\) −4.36315e6 −0.367226
\(677\) 1.39483e7 1.16964 0.584818 0.811165i \(-0.301166\pi\)
0.584818 + 0.811165i \(0.301166\pi\)
\(678\) 573084. 0.0478789
\(679\) 2.82252e6 0.234943
\(680\) −3.11840e6 −0.258618
\(681\) 9.59502e6 0.792826
\(682\) 933660. 0.0768649
\(683\) 1.28224e7 1.05176 0.525879 0.850559i \(-0.323736\pi\)
0.525879 + 0.850559i \(0.323736\pi\)
\(684\) 1.19491e6 0.0976553
\(685\) 2.81055e6 0.228857
\(686\) −4.29330e6 −0.348322
\(687\) 2.36675e6 0.191320
\(688\) 216832. 0.0174643
\(689\) 1.06292e7 0.853008
\(690\) −3.45960e6 −0.276632
\(691\) −1.33622e7 −1.06459 −0.532295 0.846559i \(-0.678670\pi\)
−0.532295 + 0.846559i \(0.678670\pi\)
\(692\) 3.37250e6 0.267723
\(693\) 104247. 0.00824576
\(694\) −1.06392e6 −0.0838514
\(695\) 3.78202e6 0.297004
\(696\) 4.78829e6 0.374677
\(697\) 2.65200e7 2.06772
\(698\) 5.33950e6 0.414823
\(699\) 1.21147e6 0.0937822
\(700\) 330000. 0.0254548
\(701\) −968218. −0.0744180 −0.0372090 0.999308i \(-0.511847\pi\)
−0.0372090 + 0.999308i \(0.511847\pi\)
\(702\) 915624. 0.0701252
\(703\) −1.26222e6 −0.0963266
\(704\) 159744. 0.0121477
\(705\) −653400. −0.0495115
\(706\) −1.16997e7 −0.883414
\(707\) 3.37009e6 0.253567
\(708\) 314784. 0.0236010
\(709\) −1.81516e7 −1.35613 −0.678063 0.735003i \(-0.737181\pi\)
−0.678063 + 0.735003i \(0.737181\pi\)
\(710\) −1.77400e6 −0.132071
\(711\) 6.45829e6 0.479119
\(712\) −3.71008e6 −0.274273
\(713\) 2.30063e7 1.69482
\(714\) 2.31541e6 0.169974
\(715\) −306150. −0.0223959
\(716\) −1.45261e6 −0.105893
\(717\) 1.25934e7 0.914843
\(718\) 1.84692e6 0.133702
\(719\) 6.74731e6 0.486753 0.243376 0.969932i \(-0.421745\pi\)
0.243376 + 0.969932i \(0.421745\pi\)
\(720\) 518400. 0.0372678
\(721\) 3.55951e6 0.255007
\(722\) −6.50406e6 −0.464346
\(723\) 8.40112e6 0.597711
\(724\) −3.81642e6 −0.270588
\(725\) −5.19562e6 −0.367107
\(726\) 5.74308e6 0.404393
\(727\) −8.47793e6 −0.594914 −0.297457 0.954735i \(-0.596138\pi\)
−0.297457 + 0.954735i \(0.596138\pi\)
\(728\) −663168. −0.0463762
\(729\) 531441. 0.0370370
\(730\) −4.45360e6 −0.309317
\(731\) −1.65080e6 −0.114262
\(732\) −2.86459e6 −0.197599
\(733\) −5.48169e6 −0.376838 −0.188419 0.982089i \(-0.560336\pi\)
−0.188419 + 0.982089i \(0.560336\pi\)
\(734\) −897372. −0.0614798
\(735\) 3.53655e6 0.241469
\(736\) 3.93626e6 0.267848
\(737\) −725244. −0.0491830
\(738\) −4.40867e6 −0.297966
\(739\) −6.20108e6 −0.417692 −0.208846 0.977949i \(-0.566971\pi\)
−0.208846 + 0.977949i \(0.566971\pi\)
\(740\) −547600. −0.0367607
\(741\) 2.60557e6 0.174324
\(742\) −4.46833e6 −0.297945
\(743\) 2.80639e6 0.186499 0.0932495 0.995643i \(-0.470275\pi\)
0.0932495 + 0.995643i \(0.470275\pi\)
\(744\) −3.44736e6 −0.228325
\(745\) −1.22152e7 −0.806328
\(746\) −9.69046e6 −0.637525
\(747\) 2.93657e6 0.192548
\(748\) −1.21618e6 −0.0794772
\(749\) 3.66122e6 0.238463
\(750\) −562500. −0.0365148
\(751\) 1.53333e7 0.992056 0.496028 0.868307i \(-0.334791\pi\)
0.496028 + 0.868307i \(0.334791\pi\)
\(752\) 743424. 0.0479393
\(753\) 1.11312e6 0.0715409
\(754\) 1.04411e7 0.668835
\(755\) −6.72155e6 −0.429143
\(756\) −384912. −0.0244938
\(757\) −7.76521e6 −0.492508 −0.246254 0.969205i \(-0.579200\pi\)
−0.246254 + 0.969205i \(0.579200\pi\)
\(758\) 5.58691e6 0.353182
\(759\) −1.34924e6 −0.0850131
\(760\) 1.47520e6 0.0926439
\(761\) −2.21402e7 −1.38586 −0.692931 0.721004i \(-0.743681\pi\)
−0.692931 + 0.721004i \(0.743681\pi\)
\(762\) 7.84512e6 0.489454
\(763\) −1.68257e6 −0.104631
\(764\) −1.09532e7 −0.678903
\(765\) −3.94672e6 −0.243828
\(766\) −1.53112e7 −0.942838
\(767\) 686404. 0.0421300
\(768\) −589824. −0.0360844
\(769\) −7.73520e6 −0.471689 −0.235845 0.971791i \(-0.575786\pi\)
−0.235845 + 0.971791i \(0.575786\pi\)
\(770\) 128700. 0.00782261
\(771\) 1.33578e7 0.809279
\(772\) 1.73930e6 0.105034
\(773\) −4.80564e6 −0.289269 −0.144635 0.989485i \(-0.546201\pi\)
−0.144635 + 0.989485i \(0.546201\pi\)
\(774\) 274428. 0.0164655
\(775\) 3.74062e6 0.223712
\(776\) 5.47398e6 0.326324
\(777\) 406593. 0.0241606
\(778\) 2.03531e7 1.20554
\(779\) −1.25457e7 −0.740712
\(780\) 1.13040e6 0.0665266
\(781\) −691860. −0.0405873
\(782\) −2.99678e7 −1.75242
\(783\) 6.06018e6 0.353249
\(784\) −4.02381e6 −0.233801
\(785\) −5.55012e6 −0.321461
\(786\) 8.26783e6 0.477348
\(787\) 6.16670e6 0.354908 0.177454 0.984129i \(-0.443214\pi\)
0.177454 + 0.984129i \(0.443214\pi\)
\(788\) 1.20317e6 0.0690257
\(789\) −1.33137e7 −0.761387
\(790\) 7.97320e6 0.454532
\(791\) −525327. −0.0298530
\(792\) 202176. 0.0114529
\(793\) −6.24640e6 −0.352734
\(794\) −9.04870e6 −0.509372
\(795\) 7.61648e6 0.427402
\(796\) −4.48429e6 −0.250848
\(797\) −1.64535e7 −0.917516 −0.458758 0.888561i \(-0.651705\pi\)
−0.458758 + 0.888561i \(0.651705\pi\)
\(798\) −1.09534e6 −0.0608892
\(799\) −5.65990e6 −0.313647
\(800\) 640000. 0.0353553
\(801\) −4.69557e6 −0.258587
\(802\) 4.74876e6 0.260702
\(803\) −1.73690e6 −0.0950576
\(804\) 2.67782e6 0.146097
\(805\) 3.17130e6 0.172484
\(806\) −7.51716e6 −0.407583
\(807\) −7.05722e6 −0.381461
\(808\) 6.53594e6 0.352192
\(809\) −1.92853e7 −1.03599 −0.517994 0.855384i \(-0.673321\pi\)
−0.517994 + 0.855384i \(0.673321\pi\)
\(810\) 656100. 0.0351364
\(811\) 2.03924e7 1.08872 0.544361 0.838851i \(-0.316772\pi\)
0.544361 + 0.838851i \(0.316772\pi\)
\(812\) −4.38926e6 −0.233615
\(813\) −8.98985e6 −0.477008
\(814\) −213564. −0.0112971
\(815\) 623775. 0.0328953
\(816\) 4.49050e6 0.236085
\(817\) 780934. 0.0409316
\(818\) −1.86762e6 −0.0975902
\(819\) −839322. −0.0437239
\(820\) −5.44280e6 −0.282675
\(821\) −1.77357e7 −0.918312 −0.459156 0.888356i \(-0.651848\pi\)
−0.459156 + 0.888356i \(0.651848\pi\)
\(822\) −4.04719e6 −0.208917
\(823\) 2.12567e7 1.09395 0.546974 0.837150i \(-0.315780\pi\)
0.546974 + 0.837150i \(0.315780\pi\)
\(824\) 6.90330e6 0.354192
\(825\) −219375. −0.0112215
\(826\) −288552. −0.0147155
\(827\) −1.80840e7 −0.919457 −0.459728 0.888060i \(-0.652053\pi\)
−0.459728 + 0.888060i \(0.652053\pi\)
\(828\) 4.98182e6 0.252530
\(829\) −7.22698e6 −0.365233 −0.182617 0.983184i \(-0.558457\pi\)
−0.182617 + 0.983184i \(0.558457\pi\)
\(830\) 3.62540e6 0.182667
\(831\) −489384. −0.0245837
\(832\) −1.28614e6 −0.0644142
\(833\) 3.06344e7 1.52967
\(834\) −5.44612e6 −0.271126
\(835\) −8.34320e6 −0.414111
\(836\) 575328. 0.0284708
\(837\) −4.36306e6 −0.215267
\(838\) −5.97736e6 −0.294035
\(839\) 2.07234e7 1.01638 0.508191 0.861245i \(-0.330314\pi\)
0.508191 + 0.861245i \(0.330314\pi\)
\(840\) −475200. −0.0232369
\(841\) 4.85948e7 2.36919
\(842\) −1.30109e7 −0.632450
\(843\) −1.48551e7 −0.719959
\(844\) −413840. −0.0199975
\(845\) −6.81742e6 −0.328457
\(846\) 940896. 0.0451976
\(847\) −5.26449e6 −0.252144
\(848\) −8.66586e6 −0.413830
\(849\) −2.10640e6 −0.100293
\(850\) −4.87250e6 −0.231315
\(851\) −5.26244e6 −0.249094
\(852\) 2.55456e6 0.120564
\(853\) 3.18129e7 1.49703 0.748516 0.663117i \(-0.230767\pi\)
0.748516 + 0.663117i \(0.230767\pi\)
\(854\) 2.62588e6 0.123205
\(855\) 1.86705e6 0.0873455
\(856\) 7.10054e6 0.331213
\(857\) 2.10862e7 0.980723 0.490362 0.871519i \(-0.336865\pi\)
0.490362 + 0.871519i \(0.336865\pi\)
\(858\) 440856. 0.0204446
\(859\) 1.17976e7 0.545521 0.272760 0.962082i \(-0.412063\pi\)
0.272760 + 0.962082i \(0.412063\pi\)
\(860\) 338800. 0.0156206
\(861\) 4.04128e6 0.185785
\(862\) 2.27472e7 1.04270
\(863\) 2.96415e7 1.35479 0.677397 0.735617i \(-0.263108\pi\)
0.677397 + 0.735617i \(0.263108\pi\)
\(864\) −746496. −0.0340207
\(865\) 5.26952e6 0.239459
\(866\) 2.72810e7 1.23613
\(867\) −2.14087e7 −0.967258
\(868\) 3.16008e6 0.142364
\(869\) 3.10955e6 0.139684
\(870\) 7.48170e6 0.335121
\(871\) 5.83914e6 0.260798
\(872\) −3.26317e6 −0.145328
\(873\) 6.92801e6 0.307661
\(874\) 1.41767e7 0.627763
\(875\) 515625. 0.0227674
\(876\) 6.41318e6 0.282367
\(877\) 2.78687e7 1.22354 0.611769 0.791036i \(-0.290458\pi\)
0.611769 + 0.791036i \(0.290458\pi\)
\(878\) −9.00215e6 −0.394103
\(879\) −8.58570e6 −0.374804
\(880\) 249600. 0.0108652
\(881\) 6.85755e6 0.297666 0.148833 0.988862i \(-0.452448\pi\)
0.148833 + 0.988862i \(0.452448\pi\)
\(882\) −5.09263e6 −0.220430
\(883\) 3.20274e7 1.38235 0.691177 0.722685i \(-0.257092\pi\)
0.691177 + 0.722685i \(0.257092\pi\)
\(884\) 9.79178e6 0.421435
\(885\) 491850. 0.0211093
\(886\) 1.66516e7 0.712641
\(887\) 1.72295e7 0.735297 0.367649 0.929965i \(-0.380163\pi\)
0.367649 + 0.929965i \(0.380163\pi\)
\(888\) 788544. 0.0335578
\(889\) −7.19136e6 −0.305180
\(890\) −5.79700e6 −0.245317
\(891\) 255879. 0.0107979
\(892\) −1.36567e7 −0.574688
\(893\) 2.67749e6 0.112357
\(894\) 1.75900e7 0.736073
\(895\) −2.26970e6 −0.0947133
\(896\) 540672. 0.0224990
\(897\) 1.08631e7 0.450790
\(898\) 1.53830e7 0.636574
\(899\) −4.97533e7 −2.05316
\(900\) 810000. 0.0333333
\(901\) 6.59756e7 2.70752
\(902\) −2.12269e6 −0.0868702
\(903\) −251559. −0.0102665
\(904\) −1.01882e6 −0.0414643
\(905\) −5.96315e6 −0.242022
\(906\) 9.67903e6 0.391752
\(907\) 5.48652e6 0.221452 0.110726 0.993851i \(-0.464682\pi\)
0.110726 + 0.993851i \(0.464682\pi\)
\(908\) −1.70578e7 −0.686608
\(909\) 8.27204e6 0.332050
\(910\) −1.03620e6 −0.0414801
\(911\) 4.96866e6 0.198355 0.0991776 0.995070i \(-0.468379\pi\)
0.0991776 + 0.995070i \(0.468379\pi\)
\(912\) −2.12429e6 −0.0845719
\(913\) 1.41391e6 0.0561363
\(914\) −4.02146e6 −0.159228
\(915\) −4.47592e6 −0.176738
\(916\) −4.20755e6 −0.165688
\(917\) −7.57885e6 −0.297632
\(918\) 5.68328e6 0.222583
\(919\) 3.54149e7 1.38324 0.691619 0.722262i \(-0.256898\pi\)
0.691619 + 0.722262i \(0.256898\pi\)
\(920\) 6.15040e6 0.239571
\(921\) −2.30132e6 −0.0893979
\(922\) 6.82690e6 0.264482
\(923\) 5.57036e6 0.215218
\(924\) −185328. −0.00714103
\(925\) −855625. −0.0328798
\(926\) 2.28957e7 0.877457
\(927\) 8.73698e6 0.333935
\(928\) −8.51251e6 −0.324480
\(929\) −2.56797e7 −0.976228 −0.488114 0.872780i \(-0.662315\pi\)
−0.488114 + 0.872780i \(0.662315\pi\)
\(930\) −5.38650e6 −0.204220
\(931\) −1.44920e7 −0.547966
\(932\) −2.15373e6 −0.0812178
\(933\) 2.53365e7 0.952888
\(934\) −2.67774e6 −0.100439
\(935\) −1.90028e6 −0.0710865
\(936\) −1.62778e6 −0.0607302
\(937\) 2.44479e7 0.909687 0.454843 0.890571i \(-0.349695\pi\)
0.454843 + 0.890571i \(0.349695\pi\)
\(938\) −2.45467e6 −0.0910933
\(939\) 2.38902e7 0.884209
\(940\) 1.16160e6 0.0428782
\(941\) −5.02352e7 −1.84941 −0.924707 0.380679i \(-0.875690\pi\)
−0.924707 + 0.380679i \(0.875690\pi\)
\(942\) 7.99218e6 0.293453
\(943\) −5.23053e7 −1.91543
\(944\) −559616. −0.0204390
\(945\) −601425. −0.0219080
\(946\) 132132. 0.00480043
\(947\) 2.01510e7 0.730165 0.365083 0.930975i \(-0.381041\pi\)
0.365083 + 0.930975i \(0.381041\pi\)
\(948\) −1.14814e7 −0.414929
\(949\) 1.39843e7 0.504052
\(950\) 2.30500e6 0.0828632
\(951\) 3.61140e6 0.129487
\(952\) −4.11629e6 −0.147202
\(953\) 8.29606e6 0.295896 0.147948 0.988995i \(-0.452733\pi\)
0.147948 + 0.988995i \(0.452733\pi\)
\(954\) −1.09677e7 −0.390163
\(955\) −1.71144e7 −0.607229
\(956\) −2.23883e7 −0.792277
\(957\) 2.91786e6 0.102988
\(958\) −1.41160e7 −0.496933
\(959\) 3.70993e6 0.130262
\(960\) −921600. −0.0322749
\(961\) 7.19107e6 0.251180
\(962\) 1.71946e6 0.0599039
\(963\) 8.98663e6 0.312270
\(964\) −1.49353e7 −0.517633
\(965\) 2.71765e6 0.0939453
\(966\) −4.56667e6 −0.157455
\(967\) −1.08855e7 −0.374355 −0.187178 0.982326i \(-0.559934\pi\)
−0.187178 + 0.982326i \(0.559934\pi\)
\(968\) −1.02099e7 −0.350214
\(969\) 1.61728e7 0.553319
\(970\) 8.55310e6 0.291873
\(971\) −2.54160e7 −0.865087 −0.432544 0.901613i \(-0.642384\pi\)
−0.432544 + 0.901613i \(0.642384\pi\)
\(972\) −944784. −0.0320750
\(973\) 4.99227e6 0.169050
\(974\) 2.30846e6 0.0779694
\(975\) 1.76625e6 0.0595032
\(976\) 5.09261e6 0.171126
\(977\) 4.03548e7 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(978\) −898236. −0.0300292
\(979\) −2.26083e6 −0.0753896
\(980\) −6.28720e6 −0.209118
\(981\) −4.12995e6 −0.137016
\(982\) 1.27205e6 0.0420944
\(983\) 8.20067e6 0.270686 0.135343 0.990799i \(-0.456786\pi\)
0.135343 + 0.990799i \(0.456786\pi\)
\(984\) 7.83763e6 0.258046
\(985\) 1.87995e6 0.0617385
\(986\) 6.48081e7 2.12294
\(987\) −862488. −0.0281812
\(988\) −4.63213e6 −0.150969
\(989\) 3.25587e6 0.105846
\(990\) 315900. 0.0102438
\(991\) 2.13917e7 0.691928 0.345964 0.938248i \(-0.387552\pi\)
0.345964 + 0.938248i \(0.387552\pi\)
\(992\) 6.12864e6 0.197736
\(993\) 2.80310e7 0.902123
\(994\) −2.34168e6 −0.0751729
\(995\) −7.00670e6 −0.224365
\(996\) −5.22058e6 −0.166752
\(997\) 9.54605e6 0.304149 0.152074 0.988369i \(-0.451405\pi\)
0.152074 + 0.988369i \(0.451405\pi\)
\(998\) 2.45597e7 0.780544
\(999\) 998001. 0.0316386
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 1110.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.6.a.a.1.1 1 1.1 even 1 trivial