Properties

Label 354.6.a.a.1.1
Level 354
Weight 6
Character 354.1
Self dual yes
Analytic conductor 56.776
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 354.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.7758722138\)
Analytic rank: \(0\)
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
Root \(0\)
Character \(\chi\) = 354.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +10.0000 q^{5} -36.0000 q^{6} +144.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +10.0000 q^{5} -36.0000 q^{6} +144.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +40.0000 q^{10} +668.000 q^{11} -144.000 q^{12} -270.000 q^{13} +576.000 q^{14} -90.0000 q^{15} +256.000 q^{16} -758.000 q^{17} +324.000 q^{18} +868.000 q^{19} +160.000 q^{20} -1296.00 q^{21} +2672.00 q^{22} +784.000 q^{23} -576.000 q^{24} -3025.00 q^{25} -1080.00 q^{26} -729.000 q^{27} +2304.00 q^{28} -4574.00 q^{29} -360.000 q^{30} +8948.00 q^{31} +1024.00 q^{32} -6012.00 q^{33} -3032.00 q^{34} +1440.00 q^{35} +1296.00 q^{36} -670.000 q^{37} +3472.00 q^{38} +2430.00 q^{39} +640.000 q^{40} -7934.00 q^{41} -5184.00 q^{42} +4884.00 q^{43} +10688.0 q^{44} +810.000 q^{45} +3136.00 q^{46} +24280.0 q^{47} -2304.00 q^{48} +3929.00 q^{49} -12100.0 q^{50} +6822.00 q^{51} -4320.00 q^{52} +28962.0 q^{53} -2916.00 q^{54} +6680.00 q^{55} +9216.00 q^{56} -7812.00 q^{57} -18296.0 q^{58} -3481.00 q^{59} -1440.00 q^{60} +30490.0 q^{61} +35792.0 q^{62} +11664.0 q^{63} +4096.00 q^{64} -2700.00 q^{65} -24048.0 q^{66} -30764.0 q^{67} -12128.0 q^{68} -7056.00 q^{69} +5760.00 q^{70} +22452.0 q^{71} +5184.00 q^{72} -20966.0 q^{73} -2680.00 q^{74} +27225.0 q^{75} +13888.0 q^{76} +96192.0 q^{77} +9720.00 q^{78} +70520.0 q^{79} +2560.00 q^{80} +6561.00 q^{81} -31736.0 q^{82} +29756.0 q^{83} -20736.0 q^{84} -7580.00 q^{85} +19536.0 q^{86} +41166.0 q^{87} +42752.0 q^{88} -16470.0 q^{89} +3240.00 q^{90} -38880.0 q^{91} +12544.0 q^{92} -80532.0 q^{93} +97120.0 q^{94} +8680.00 q^{95} -9216.00 q^{96} +18506.0 q^{97} +15716.0 q^{98} +54108.0 q^{99} +O(q^{100})\)

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
\(5\) 10.0000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) −36.0000 −0.408248
\(7\) 144.000 1.11075 0.555376 0.831599i \(-0.312574\pi\)
0.555376 + 0.831599i \(0.312574\pi\)
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 40.0000 0.126491
\(11\) 668.000 1.66454 0.832271 0.554369i \(-0.187040\pi\)
0.832271 + 0.554369i \(0.187040\pi\)
\(12\) −144.000 −0.288675
\(13\) −270.000 −0.443104 −0.221552 0.975149i \(-0.571112\pi\)
−0.221552 + 0.975149i \(0.571112\pi\)
\(14\) 576.000 0.785421
\(15\) −90.0000 −0.103280
\(16\) 256.000 0.250000
\(17\) −758.000 −0.636132 −0.318066 0.948069i \(-0.603033\pi\)
−0.318066 + 0.948069i \(0.603033\pi\)
\(18\) 324.000 0.235702
\(19\) 868.000 0.551615 0.275807 0.961213i \(-0.411055\pi\)
0.275807 + 0.961213i \(0.411055\pi\)
\(20\) 160.000 0.0894427
\(21\) −1296.00 −0.641293
\(22\) 2672.00 1.17701
\(23\) 784.000 0.309027 0.154514 0.987991i \(-0.450619\pi\)
0.154514 + 0.987991i \(0.450619\pi\)
\(24\) −576.000 −0.204124
\(25\) −3025.00 −0.968000
\(26\) −1080.00 −0.313322
\(27\) −729.000 −0.192450
\(28\) 2304.00 0.555376
\(29\) −4574.00 −1.00995 −0.504977 0.863133i \(-0.668499\pi\)
−0.504977 + 0.863133i \(0.668499\pi\)
\(30\) −360.000 −0.0730297
\(31\) 8948.00 1.67233 0.836165 0.548479i \(-0.184793\pi\)
0.836165 + 0.548479i \(0.184793\pi\)
\(32\) 1024.00 0.176777
\(33\) −6012.00 −0.961024
\(34\) −3032.00 −0.449813
\(35\) 1440.00 0.198697
\(36\) 1296.00 0.166667
\(37\) −670.000 −0.0804582 −0.0402291 0.999190i \(-0.512809\pi\)
−0.0402291 + 0.999190i \(0.512809\pi\)
\(38\) 3472.00 0.390050
\(39\) 2430.00 0.255826
\(40\) 640.000 0.0632456
\(41\) −7934.00 −0.737110 −0.368555 0.929606i \(-0.620147\pi\)
−0.368555 + 0.929606i \(0.620147\pi\)
\(42\) −5184.00 −0.453463
\(43\) 4884.00 0.402814 0.201407 0.979508i \(-0.435449\pi\)
0.201407 + 0.979508i \(0.435449\pi\)
\(44\) 10688.0 0.832271
\(45\) 810.000 0.0596285
\(46\) 3136.00 0.218515
\(47\) 24280.0 1.60326 0.801630 0.597820i \(-0.203966\pi\)
0.801630 + 0.597820i \(0.203966\pi\)
\(48\) −2304.00 −0.144338
\(49\) 3929.00 0.233772
\(50\) −12100.0 −0.684479
\(51\) 6822.00 0.367271
\(52\) −4320.00 −0.221552
\(53\) 28962.0 1.41625 0.708123 0.706089i \(-0.249542\pi\)
0.708123 + 0.706089i \(0.249542\pi\)
\(54\) −2916.00 −0.136083
\(55\) 6680.00 0.297762
\(56\) 9216.00 0.392710
\(57\) −7812.00 −0.318475
\(58\) −18296.0 −0.714145
\(59\) −3481.00 −0.130189
\(60\) −1440.00 −0.0516398
\(61\) 30490.0 1.04914 0.524569 0.851368i \(-0.324226\pi\)
0.524569 + 0.851368i \(0.324226\pi\)
\(62\) 35792.0 1.18252
\(63\) 11664.0 0.370251
\(64\) 4096.00 0.125000
\(65\) −2700.00 −0.0792648
\(66\) −24048.0 −0.679546
\(67\) −30764.0 −0.837251 −0.418626 0.908159i \(-0.637488\pi\)
−0.418626 + 0.908159i \(0.637488\pi\)
\(68\) −12128.0 −0.318066
\(69\) −7056.00 −0.178417
\(70\) 5760.00 0.140500
\(71\) 22452.0 0.528578 0.264289 0.964444i \(-0.414863\pi\)
0.264289 + 0.964444i \(0.414863\pi\)
\(72\) 5184.00 0.117851
\(73\) −20966.0 −0.460478 −0.230239 0.973134i \(-0.573951\pi\)
−0.230239 + 0.973134i \(0.573951\pi\)
\(74\) −2680.00 −0.0568926
\(75\) 27225.0 0.558875
\(76\) 13888.0 0.275807
\(77\) 96192.0 1.84889
\(78\) 9720.00 0.180896
\(79\) 70520.0 1.27129 0.635645 0.771982i \(-0.280734\pi\)
0.635645 + 0.771982i \(0.280734\pi\)
\(80\) 2560.00 0.0447214
\(81\) 6561.00 0.111111
\(82\) −31736.0 −0.521216
\(83\) 29756.0 0.474110 0.237055 0.971496i \(-0.423818\pi\)
0.237055 + 0.971496i \(0.423818\pi\)
\(84\) −20736.0 −0.320647
\(85\) −7580.00 −0.113795
\(86\) 19536.0 0.284832
\(87\) 41166.0 0.583097
\(88\) 42752.0 0.588504
\(89\) −16470.0 −0.220404 −0.110202 0.993909i \(-0.535150\pi\)
−0.110202 + 0.993909i \(0.535150\pi\)
\(90\) 3240.00 0.0421637
\(91\) −38880.0 −0.492179
\(92\) 12544.0 0.154514
\(93\) −80532.0 −0.965520
\(94\) 97120.0 1.13368
\(95\) 8680.00 0.0986758
\(96\) −9216.00 −0.102062
\(97\) 18506.0 0.199702 0.0998512 0.995002i \(-0.468163\pi\)
0.0998512 + 0.995002i \(0.468163\pi\)
\(98\) 15716.0 0.165302
\(99\) 54108.0 0.554847
\(100\) −48400.0 −0.484000
\(101\) −17370.0 −0.169432 −0.0847162 0.996405i \(-0.526998\pi\)
−0.0847162 + 0.996405i \(0.526998\pi\)
\(102\) 27288.0 0.259700
\(103\) 86156.0 0.800189 0.400094 0.916474i \(-0.368977\pi\)
0.400094 + 0.916474i \(0.368977\pi\)
\(104\) −17280.0 −0.156661
\(105\) −12960.0 −0.114718
\(106\) 115848. 1.00144
\(107\) 12924.0 0.109128 0.0545642 0.998510i \(-0.482623\pi\)
0.0545642 + 0.998510i \(0.482623\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 2530.00 0.0203964 0.0101982 0.999948i \(-0.496754\pi\)
0.0101982 + 0.999948i \(0.496754\pi\)
\(110\) 26720.0 0.210550
\(111\) 6030.00 0.0464526
\(112\) 36864.0 0.277688
\(113\) 7826.00 0.0576559 0.0288279 0.999584i \(-0.490823\pi\)
0.0288279 + 0.999584i \(0.490823\pi\)
\(114\) −31248.0 −0.225196
\(115\) 7840.00 0.0552804
\(116\) −73184.0 −0.504977
\(117\) −21870.0 −0.147701
\(118\) −13924.0 −0.0920575
\(119\) −109152. −0.706585
\(120\) −5760.00 −0.0365148
\(121\) 285173. 1.77070
\(122\) 121960. 0.741853
\(123\) 71406.0 0.425571
\(124\) 143168. 0.836165
\(125\) −61500.0 −0.352047
\(126\) 46656.0 0.261807
\(127\) −60752.0 −0.334235 −0.167117 0.985937i \(-0.553446\pi\)
−0.167117 + 0.985937i \(0.553446\pi\)
\(128\) 16384.0 0.0883883
\(129\) −43956.0 −0.232565
\(130\) −10800.0 −0.0560487
\(131\) 151572. 0.771686 0.385843 0.922564i \(-0.373911\pi\)
0.385843 + 0.922564i \(0.373911\pi\)
\(132\) −96192.0 −0.480512
\(133\) 124992. 0.612707
\(134\) −123056. −0.592026
\(135\) −7290.00 −0.0344265
\(136\) −48512.0 −0.224906
\(137\) −164334. −0.748042 −0.374021 0.927420i \(-0.622021\pi\)
−0.374021 + 0.927420i \(0.622021\pi\)
\(138\) −28224.0 −0.126160
\(139\) 72620.0 0.318801 0.159400 0.987214i \(-0.449044\pi\)
0.159400 + 0.987214i \(0.449044\pi\)
\(140\) 23040.0 0.0993487
\(141\) −218520. −0.925643
\(142\) 89808.0 0.373761
\(143\) −180360. −0.737565
\(144\) 20736.0 0.0833333
\(145\) −45740.0 −0.180666
\(146\) −83864.0 −0.325607
\(147\) −35361.0 −0.134968
\(148\) −10720.0 −0.0402291
\(149\) 238702. 0.880827 0.440413 0.897795i \(-0.354832\pi\)
0.440413 + 0.897795i \(0.354832\pi\)
\(150\) 108900. 0.395184
\(151\) −154540. −0.551567 −0.275784 0.961220i \(-0.588937\pi\)
−0.275784 + 0.961220i \(0.588937\pi\)
\(152\) 55552.0 0.195025
\(153\) −61398.0 −0.212044
\(154\) 384768. 1.30737
\(155\) 89480.0 0.299155
\(156\) 38880.0 0.127913
\(157\) −318462. −1.03112 −0.515559 0.856854i \(-0.672416\pi\)
−0.515559 + 0.856854i \(0.672416\pi\)
\(158\) 282080. 0.898938
\(159\) −260658. −0.817670
\(160\) 10240.0 0.0316228
\(161\) 112896. 0.343253
\(162\) 26244.0 0.0785674
\(163\) −285260. −0.840953 −0.420477 0.907303i \(-0.638137\pi\)
−0.420477 + 0.907303i \(0.638137\pi\)
\(164\) −126944. −0.368555
\(165\) −60120.0 −0.171913
\(166\) 119024. 0.335247
\(167\) 187644. 0.520647 0.260324 0.965521i \(-0.416171\pi\)
0.260324 + 0.965521i \(0.416171\pi\)
\(168\) −82944.0 −0.226731
\(169\) −298393. −0.803659
\(170\) −30320.0 −0.0804650
\(171\) 70308.0 0.183872
\(172\) 78144.0 0.201407
\(173\) 382126. 0.970714 0.485357 0.874316i \(-0.338690\pi\)
0.485357 + 0.874316i \(0.338690\pi\)
\(174\) 164664. 0.412312
\(175\) −435600. −1.07521
\(176\) 171008. 0.416135
\(177\) 31329.0 0.0751646
\(178\) −65880.0 −0.155849
\(179\) −366964. −0.856034 −0.428017 0.903771i \(-0.640788\pi\)
−0.428017 + 0.903771i \(0.640788\pi\)
\(180\) 12960.0 0.0298142
\(181\) 62006.0 0.140682 0.0703408 0.997523i \(-0.477591\pi\)
0.0703408 + 0.997523i \(0.477591\pi\)
\(182\) −155520. −0.348023
\(183\) −274410. −0.605720
\(184\) 50176.0 0.109258
\(185\) −6700.00 −0.0143928
\(186\) −322128. −0.682725
\(187\) −506344. −1.05887
\(188\) 388480. 0.801630
\(189\) −104976. −0.213764
\(190\) 34720.0 0.0697743
\(191\) −123288. −0.244533 −0.122266 0.992497i \(-0.539016\pi\)
−0.122266 + 0.992497i \(0.539016\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −661310. −1.27794 −0.638972 0.769230i \(-0.720640\pi\)
−0.638972 + 0.769230i \(0.720640\pi\)
\(194\) 74024.0 0.141211
\(195\) 24300.0 0.0457636
\(196\) 62864.0 0.116886
\(197\) −590550. −1.08415 −0.542077 0.840329i \(-0.682362\pi\)
−0.542077 + 0.840329i \(0.682362\pi\)
\(198\) 216432. 0.392336
\(199\) 483256. 0.865057 0.432528 0.901620i \(-0.357622\pi\)
0.432528 + 0.901620i \(0.357622\pi\)
\(200\) −193600. −0.342240
\(201\) 276876. 0.483387
\(202\) −69480.0 −0.119807
\(203\) −658656. −1.12181
\(204\) 109152. 0.183635
\(205\) −79340.0 −0.131858
\(206\) 344624. 0.565819
\(207\) 63504.0 0.103009
\(208\) −69120.0 −0.110776
\(209\) 579824. 0.918186
\(210\) −51840.0 −0.0811179
\(211\) 347908. 0.537970 0.268985 0.963144i \(-0.413312\pi\)
0.268985 + 0.963144i \(0.413312\pi\)
\(212\) 463392. 0.708123
\(213\) −202068. −0.305175
\(214\) 51696.0 0.0771654
\(215\) 48840.0 0.0720576
\(216\) −46656.0 −0.0680414
\(217\) 1.28851e6 1.85754
\(218\) 10120.0 0.0144225
\(219\) 188694. 0.265857
\(220\) 106880. 0.148881
\(221\) 204660. 0.281872
\(222\) 24120.0 0.0328469
\(223\) 295704. 0.398194 0.199097 0.979980i \(-0.436199\pi\)
0.199097 + 0.979980i \(0.436199\pi\)
\(224\) 147456. 0.196355
\(225\) −245025. −0.322667
\(226\) 31304.0 0.0407689
\(227\) −1.21872e6 −1.56979 −0.784893 0.619631i \(-0.787282\pi\)
−0.784893 + 0.619631i \(0.787282\pi\)
\(228\) −124992. −0.159237
\(229\) 272066. 0.342835 0.171418 0.985198i \(-0.445165\pi\)
0.171418 + 0.985198i \(0.445165\pi\)
\(230\) 31360.0 0.0390892
\(231\) −865728. −1.06746
\(232\) −292736. −0.357072
\(233\) 1.27718e6 1.54121 0.770605 0.637313i \(-0.219954\pi\)
0.770605 + 0.637313i \(0.219954\pi\)
\(234\) −87480.0 −0.104441
\(235\) 242800. 0.286800
\(236\) −55696.0 −0.0650945
\(237\) −634680. −0.733980
\(238\) −436608. −0.499631
\(239\) −23500.0 −0.0266117 −0.0133059 0.999911i \(-0.504236\pi\)
−0.0133059 + 0.999911i \(0.504236\pi\)
\(240\) −23040.0 −0.0258199
\(241\) 245090. 0.271821 0.135910 0.990721i \(-0.456604\pi\)
0.135910 + 0.990721i \(0.456604\pi\)
\(242\) 1.14069e6 1.25207
\(243\) −59049.0 −0.0641500
\(244\) 487840. 0.524569
\(245\) 39290.0 0.0418183
\(246\) 285624. 0.300924
\(247\) −234360. −0.244422
\(248\) 572672. 0.591258
\(249\) −267804. −0.273728
\(250\) −246000. −0.248934
\(251\) 1.90925e6 1.91284 0.956421 0.291992i \(-0.0943182\pi\)
0.956421 + 0.291992i \(0.0943182\pi\)
\(252\) 186624. 0.185125
\(253\) 523712. 0.514388
\(254\) −243008. −0.236339
\(255\) 68220.0 0.0656994
\(256\) 65536.0 0.0625000
\(257\) −372510. −0.351808 −0.175904 0.984407i \(-0.556285\pi\)
−0.175904 + 0.984407i \(0.556285\pi\)
\(258\) −175824. −0.164448
\(259\) −96480.0 −0.0893692
\(260\) −43200.0 −0.0396324
\(261\) −370494. −0.336651
\(262\) 606288. 0.545665
\(263\) −585324. −0.521803 −0.260902 0.965365i \(-0.584020\pi\)
−0.260902 + 0.965365i \(0.584020\pi\)
\(264\) −384768. −0.339773
\(265\) 289620. 0.253346
\(266\) 499968. 0.433250
\(267\) 148230. 0.127250
\(268\) −492224. −0.418626
\(269\) 655622. 0.552424 0.276212 0.961097i \(-0.410921\pi\)
0.276212 + 0.961097i \(0.410921\pi\)
\(270\) −29160.0 −0.0243432
\(271\) −1.77119e6 −1.46502 −0.732508 0.680758i \(-0.761650\pi\)
−0.732508 + 0.680758i \(0.761650\pi\)
\(272\) −194048. −0.159033
\(273\) 349920. 0.284159
\(274\) −657336. −0.528946
\(275\) −2.02070e6 −1.61128
\(276\) −112896. −0.0892084
\(277\) −2.36205e6 −1.84965 −0.924825 0.380392i \(-0.875789\pi\)
−0.924825 + 0.380392i \(0.875789\pi\)
\(278\) 290480. 0.225426
\(279\) 724788. 0.557443
\(280\) 92160.0 0.0702502
\(281\) −906022. −0.684499 −0.342250 0.939609i \(-0.611189\pi\)
−0.342250 + 0.939609i \(0.611189\pi\)
\(282\) −874080. −0.654528
\(283\) −1.20084e6 −0.891293 −0.445647 0.895209i \(-0.647026\pi\)
−0.445647 + 0.895209i \(0.647026\pi\)
\(284\) 359232. 0.264289
\(285\) −78120.0 −0.0569705
\(286\) −721440. −0.521537
\(287\) −1.14250e6 −0.818747
\(288\) 82944.0 0.0589256
\(289\) −845293. −0.595337
\(290\) −182960. −0.127750
\(291\) −166554. −0.115298
\(292\) −335456. −0.230239
\(293\) −951158. −0.647267 −0.323634 0.946182i \(-0.604905\pi\)
−0.323634 + 0.946182i \(0.604905\pi\)
\(294\) −141444. −0.0954369
\(295\) −34810.0 −0.0232889
\(296\) −42880.0 −0.0284463
\(297\) −486972. −0.320341
\(298\) 954808. 0.622838
\(299\) −211680. −0.136931
\(300\) 435600. 0.279438
\(301\) 703296. 0.447427
\(302\) −618160. −0.390017
\(303\) 156330. 0.0978218
\(304\) 222208. 0.137904
\(305\) 304900. 0.187676
\(306\) −245592. −0.149938
\(307\) −1.02955e6 −0.623449 −0.311724 0.950173i \(-0.600907\pi\)
−0.311724 + 0.950173i \(0.600907\pi\)
\(308\) 1.53907e6 0.924447
\(309\) −775404. −0.461989
\(310\) 357920. 0.211535
\(311\) 848428. 0.497409 0.248705 0.968579i \(-0.419995\pi\)
0.248705 + 0.968579i \(0.419995\pi\)
\(312\) 155520. 0.0904482
\(313\) −2.03667e6 −1.17506 −0.587530 0.809203i \(-0.699899\pi\)
−0.587530 + 0.809203i \(0.699899\pi\)
\(314\) −1.27385e6 −0.729111
\(315\) 116640. 0.0662325
\(316\) 1.12832e6 0.635645
\(317\) −2.92485e6 −1.63476 −0.817382 0.576097i \(-0.804575\pi\)
−0.817382 + 0.576097i \(0.804575\pi\)
\(318\) −1.04263e6 −0.578180
\(319\) −3.05543e6 −1.68111
\(320\) 40960.0 0.0223607
\(321\) −116316. −0.0630053
\(322\) 451584. 0.242716
\(323\) −657944. −0.350899
\(324\) 104976. 0.0555556
\(325\) 816750. 0.428924
\(326\) −1.14104e6 −0.594644
\(327\) −22770.0 −0.0117759
\(328\) −507776. −0.260608
\(329\) 3.49632e6 1.78083
\(330\) −240480. −0.121561
\(331\) −1.78040e6 −0.893200 −0.446600 0.894734i \(-0.647365\pi\)
−0.446600 + 0.894734i \(0.647365\pi\)
\(332\) 476096. 0.237055
\(333\) −54270.0 −0.0268194
\(334\) 750576. 0.368153
\(335\) −307640. −0.149772
\(336\) −331776. −0.160323
\(337\) 2.05064e6 0.983592 0.491796 0.870710i \(-0.336341\pi\)
0.491796 + 0.870710i \(0.336341\pi\)
\(338\) −1.19357e6 −0.568273
\(339\) −70434.0 −0.0332876
\(340\) −121280. −0.0568973
\(341\) 5.97726e6 2.78366
\(342\) 281232. 0.130017
\(343\) −1.85443e6 −0.851090
\(344\) 312576. 0.142416
\(345\) −70560.0 −0.0319162
\(346\) 1.52850e6 0.686399
\(347\) 4.14393e6 1.84752 0.923760 0.382973i \(-0.125100\pi\)
0.923760 + 0.382973i \(0.125100\pi\)
\(348\) 658656. 0.291548
\(349\) −4.06117e6 −1.78479 −0.892397 0.451251i \(-0.850978\pi\)
−0.892397 + 0.451251i \(0.850978\pi\)
\(350\) −1.74240e6 −0.760287
\(351\) 196830. 0.0852753
\(352\) 684032. 0.294252
\(353\) 1.74215e6 0.744128 0.372064 0.928207i \(-0.378650\pi\)
0.372064 + 0.928207i \(0.378650\pi\)
\(354\) 125316. 0.0531494
\(355\) 224520. 0.0945549
\(356\) −263520. −0.110202
\(357\) 982368. 0.407947
\(358\) −1.46786e6 −0.605307
\(359\) 51396.0 0.0210471 0.0105236 0.999945i \(-0.496650\pi\)
0.0105236 + 0.999945i \(0.496650\pi\)
\(360\) 51840.0 0.0210819
\(361\) −1.72268e6 −0.695721
\(362\) 248024. 0.0994769
\(363\) −2.56656e6 −1.02231
\(364\) −622080. −0.246089
\(365\) −209660. −0.0823727
\(366\) −1.09764e6 −0.428309
\(367\) −1.11117e6 −0.430642 −0.215321 0.976543i \(-0.569080\pi\)
−0.215321 + 0.976543i \(0.569080\pi\)
\(368\) 200704. 0.0772568
\(369\) −642654. −0.245703
\(370\) −26800.0 −0.0101773
\(371\) 4.17053e6 1.57310
\(372\) −1.28851e6 −0.482760
\(373\) −1.62915e6 −0.606301 −0.303150 0.952943i \(-0.598038\pi\)
−0.303150 + 0.952943i \(0.598038\pi\)
\(374\) −2.02538e6 −0.748732
\(375\) 553500. 0.203254
\(376\) 1.55392e6 0.566838
\(377\) 1.23498e6 0.447514
\(378\) −419904. −0.151154
\(379\) −4.04878e6 −1.44786 −0.723929 0.689874i \(-0.757666\pi\)
−0.723929 + 0.689874i \(0.757666\pi\)
\(380\) 138880. 0.0493379
\(381\) 546768. 0.192970
\(382\) −493152. −0.172911
\(383\) 3.00009e6 1.04505 0.522526 0.852624i \(-0.324990\pi\)
0.522526 + 0.852624i \(0.324990\pi\)
\(384\) −147456. −0.0510310
\(385\) 961920. 0.330740
\(386\) −2.64524e6 −0.903643
\(387\) 395604. 0.134271
\(388\) 296096. 0.0998512
\(389\) 2.25118e6 0.754286 0.377143 0.926155i \(-0.376907\pi\)
0.377143 + 0.926155i \(0.376907\pi\)
\(390\) 97200.0 0.0323597
\(391\) −594272. −0.196582
\(392\) 251456. 0.0826508
\(393\) −1.36415e6 −0.445533
\(394\) −2.36220e6 −0.766613
\(395\) 705200. 0.227415
\(396\) 865728. 0.277424
\(397\) 2.20847e6 0.703258 0.351629 0.936140i \(-0.385628\pi\)
0.351629 + 0.936140i \(0.385628\pi\)
\(398\) 1.93302e6 0.611687
\(399\) −1.12493e6 −0.353747
\(400\) −774400. −0.242000
\(401\) −1.84577e6 −0.573215 −0.286608 0.958048i \(-0.592528\pi\)
−0.286608 + 0.958048i \(0.592528\pi\)
\(402\) 1.10750e6 0.341806
\(403\) −2.41596e6 −0.741015
\(404\) −277920. −0.0847162
\(405\) 65610.0 0.0198762
\(406\) −2.63462e6 −0.793238
\(407\) −447560. −0.133926
\(408\) 436608. 0.129850
\(409\) −1.46560e6 −0.433218 −0.216609 0.976258i \(-0.569500\pi\)
−0.216609 + 0.976258i \(0.569500\pi\)
\(410\) −317360. −0.0932379
\(411\) 1.47901e6 0.431882
\(412\) 1.37850e6 0.400094
\(413\) −501264. −0.144608
\(414\) 254016. 0.0728384
\(415\) 297560. 0.0848114
\(416\) −276480. −0.0783304
\(417\) −653580. −0.184060
\(418\) 2.31930e6 0.649255
\(419\) 574716. 0.159926 0.0799628 0.996798i \(-0.474520\pi\)
0.0799628 + 0.996798i \(0.474520\pi\)
\(420\) −207360. −0.0573590
\(421\) 6.54649e6 1.80013 0.900064 0.435758i \(-0.143520\pi\)
0.900064 + 0.435758i \(0.143520\pi\)
\(422\) 1.39163e6 0.380402
\(423\) 1.96668e6 0.534420
\(424\) 1.85357e6 0.500719
\(425\) 2.29295e6 0.615775
\(426\) −808272. −0.215791
\(427\) 4.39056e6 1.16533
\(428\) 206784. 0.0545642
\(429\) 1.62324e6 0.425833
\(430\) 195360. 0.0509524
\(431\) 2.89068e6 0.749561 0.374780 0.927114i \(-0.377718\pi\)
0.374780 + 0.927114i \(0.377718\pi\)
\(432\) −186624. −0.0481125
\(433\) 5.76752e6 1.47832 0.739162 0.673528i \(-0.235222\pi\)
0.739162 + 0.673528i \(0.235222\pi\)
\(434\) 5.15405e6 1.31348
\(435\) 411660. 0.104307
\(436\) 40480.0 0.0101982
\(437\) 680512. 0.170464
\(438\) 754776. 0.187989
\(439\) −556504. −0.137818 −0.0689092 0.997623i \(-0.521952\pi\)
−0.0689092 + 0.997623i \(0.521952\pi\)
\(440\) 427520. 0.105275
\(441\) 318249. 0.0779239
\(442\) 818640. 0.199314
\(443\) 4.61716e6 1.11780 0.558901 0.829234i \(-0.311223\pi\)
0.558901 + 0.829234i \(0.311223\pi\)
\(444\) 96480.0 0.0232263
\(445\) −164700. −0.0394270
\(446\) 1.18282e6 0.281566
\(447\) −2.14832e6 −0.508545
\(448\) 589824. 0.138844
\(449\) 2.68851e6 0.629354 0.314677 0.949199i \(-0.398104\pi\)
0.314677 + 0.949199i \(0.398104\pi\)
\(450\) −980100. −0.228160
\(451\) −5.29991e6 −1.22695
\(452\) 125216. 0.0288279
\(453\) 1.39086e6 0.318448
\(454\) −4.87490e6 −1.11001
\(455\) −388800. −0.0880436
\(456\) −499968. −0.112598
\(457\) −7.30747e6 −1.63673 −0.818364 0.574700i \(-0.805119\pi\)
−0.818364 + 0.574700i \(0.805119\pi\)
\(458\) 1.08826e6 0.242421
\(459\) 552582. 0.122424
\(460\) 125440. 0.0276402
\(461\) −94014.0 −0.0206035 −0.0103017 0.999947i \(-0.503279\pi\)
−0.0103017 + 0.999947i \(0.503279\pi\)
\(462\) −3.46291e6 −0.754808
\(463\) 7.21852e6 1.56493 0.782466 0.622693i \(-0.213962\pi\)
0.782466 + 0.622693i \(0.213962\pi\)
\(464\) −1.17094e6 −0.252488
\(465\) −805320. −0.172717
\(466\) 5.10871e6 1.08980
\(467\) 6.60437e6 1.40133 0.700663 0.713492i \(-0.252888\pi\)
0.700663 + 0.713492i \(0.252888\pi\)
\(468\) −349920. −0.0738506
\(469\) −4.43002e6 −0.929979
\(470\) 971200. 0.202798
\(471\) 2.86616e6 0.595316
\(472\) −222784. −0.0460287
\(473\) 3.26251e6 0.670501
\(474\) −2.53872e6 −0.519002
\(475\) −2.62570e6 −0.533963
\(476\) −1.74643e6 −0.353292
\(477\) 2.34592e6 0.472082
\(478\) −94000.0 −0.0188173
\(479\) −2.49691e6 −0.497237 −0.248619 0.968601i \(-0.579977\pi\)
−0.248619 + 0.968601i \(0.579977\pi\)
\(480\) −92160.0 −0.0182574
\(481\) 180900. 0.0356513
\(482\) 980360. 0.192206
\(483\) −1.01606e6 −0.198177
\(484\) 4.56277e6 0.885350
\(485\) 185060. 0.0357238
\(486\) −236196. −0.0453609
\(487\) −5.19649e6 −0.992859 −0.496429 0.868077i \(-0.665356\pi\)
−0.496429 + 0.868077i \(0.665356\pi\)
\(488\) 1.95136e6 0.370926
\(489\) 2.56734e6 0.485525
\(490\) 157160. 0.0295700
\(491\) −4.40080e6 −0.823812 −0.411906 0.911226i \(-0.635137\pi\)
−0.411906 + 0.911226i \(0.635137\pi\)
\(492\) 1.14250e6 0.212785
\(493\) 3.46709e6 0.642463
\(494\) −937440. −0.172833
\(495\) 541080. 0.0992541
\(496\) 2.29069e6 0.418082
\(497\) 3.23309e6 0.587120
\(498\) −1.07122e6 −0.193555
\(499\) −5.37090e6 −0.965597 −0.482798 0.875732i \(-0.660380\pi\)
−0.482798 + 0.875732i \(0.660380\pi\)
\(500\) −984000. −0.176023
\(501\) −1.68880e6 −0.300596
\(502\) 7.63701e6 1.35258
\(503\) 8.18554e6 1.44254 0.721269 0.692655i \(-0.243559\pi\)
0.721269 + 0.692655i \(0.243559\pi\)
\(504\) 746496. 0.130903
\(505\) −173700. −0.0303090
\(506\) 2.09485e6 0.363728
\(507\) 2.68554e6 0.463993
\(508\) −972032. −0.167117
\(509\) 1.00295e7 1.71587 0.857935 0.513759i \(-0.171747\pi\)
0.857935 + 0.513759i \(0.171747\pi\)
\(510\) 272880. 0.0464565
\(511\) −3.01910e6 −0.511477
\(512\) 262144. 0.0441942
\(513\) −632772. −0.106158
\(514\) −1.49004e6 −0.248765
\(515\) 861560. 0.143142
\(516\) −703296. −0.116282
\(517\) 1.62190e7 2.66869
\(518\) −385920. −0.0631936
\(519\) −3.43913e6 −0.560442
\(520\) −172800. −0.0280243
\(521\) −1.00780e7 −1.62659 −0.813295 0.581852i \(-0.802328\pi\)
−0.813295 + 0.581852i \(0.802328\pi\)
\(522\) −1.48198e6 −0.238048
\(523\) 8.07562e6 1.29099 0.645493 0.763766i \(-0.276652\pi\)
0.645493 + 0.763766i \(0.276652\pi\)
\(524\) 2.42515e6 0.385843
\(525\) 3.92040e6 0.620772
\(526\) −2.34130e6 −0.368971
\(527\) −6.78258e6 −1.06382
\(528\) −1.53907e6 −0.240256
\(529\) −5.82169e6 −0.904502
\(530\) 1.15848e6 0.179143
\(531\) −281961. −0.0433963
\(532\) 1.99987e6 0.306354
\(533\) 2.14218e6 0.326616
\(534\) 592920. 0.0899794
\(535\) 129240. 0.0195215
\(536\) −1.96890e6 −0.296013
\(537\) 3.30268e6 0.494231
\(538\) 2.62249e6 0.390623
\(539\) 2.62457e6 0.389123
\(540\) −116640. −0.0172133
\(541\) 5.84779e6 0.859011 0.429506 0.903064i \(-0.358688\pi\)
0.429506 + 0.903064i \(0.358688\pi\)
\(542\) −7.08477e6 −1.03592
\(543\) −558054. −0.0812226
\(544\) −776192. −0.112453
\(545\) 25300.0 0.00364863
\(546\) 1.39968e6 0.200931
\(547\) −6.65004e6 −0.950289 −0.475144 0.879908i \(-0.657604\pi\)
−0.475144 + 0.879908i \(0.657604\pi\)
\(548\) −2.62934e6 −0.374021
\(549\) 2.46969e6 0.349713
\(550\) −8.08280e6 −1.13934
\(551\) −3.97023e6 −0.557105
\(552\) −451584. −0.0630799
\(553\) 1.01549e7 1.41209
\(554\) −9.44820e6 −1.30790
\(555\) 60300.0 0.00830969
\(556\) 1.16192e6 0.159400
\(557\) −7.90510e6 −1.07962 −0.539808 0.841788i \(-0.681503\pi\)
−0.539808 + 0.841788i \(0.681503\pi\)
\(558\) 2.89915e6 0.394172
\(559\) −1.31868e6 −0.178488
\(560\) 368640. 0.0496744
\(561\) 4.55710e6 0.611337
\(562\) −3.62409e6 −0.484014
\(563\) 1.17640e7 1.56418 0.782088 0.623169i \(-0.214155\pi\)
0.782088 + 0.623169i \(0.214155\pi\)
\(564\) −3.49632e6 −0.462821
\(565\) 78260.0 0.0103138
\(566\) −4.80338e6 −0.630239
\(567\) 944784. 0.123417
\(568\) 1.43693e6 0.186881
\(569\) −7.06042e6 −0.914218 −0.457109 0.889411i \(-0.651115\pi\)
−0.457109 + 0.889411i \(0.651115\pi\)
\(570\) −312480. −0.0402842
\(571\) −1.15454e6 −0.148190 −0.0740950 0.997251i \(-0.523607\pi\)
−0.0740950 + 0.997251i \(0.523607\pi\)
\(572\) −2.88576e6 −0.368782
\(573\) 1.10959e6 0.141181
\(574\) −4.56998e6 −0.578942
\(575\) −2.37160e6 −0.299138
\(576\) 331776. 0.0416667
\(577\) −3.23390e6 −0.404378 −0.202189 0.979347i \(-0.564805\pi\)
−0.202189 + 0.979347i \(0.564805\pi\)
\(578\) −3.38117e6 −0.420967
\(579\) 5.95179e6 0.737821
\(580\) −731840. −0.0903329
\(581\) 4.28486e6 0.526619
\(582\) −666216. −0.0815282
\(583\) 1.93466e7 2.35740
\(584\) −1.34182e6 −0.162803
\(585\) −218700. −0.0264216
\(586\) −3.80463e6 −0.457687
\(587\) −1.10814e7 −1.32739 −0.663697 0.748002i \(-0.731014\pi\)
−0.663697 + 0.748002i \(0.731014\pi\)
\(588\) −565776. −0.0674841
\(589\) 7.76686e6 0.922481
\(590\) −139240. −0.0164677
\(591\) 5.31495e6 0.625937
\(592\) −171520. −0.0201146
\(593\) 8.45888e6 0.987816 0.493908 0.869514i \(-0.335568\pi\)
0.493908 + 0.869514i \(0.335568\pi\)
\(594\) −1.94789e6 −0.226515
\(595\) −1.09152e6 −0.126398
\(596\) 3.81923e6 0.440413
\(597\) −4.34930e6 −0.499441
\(598\) −846720. −0.0968249
\(599\) −3.20524e6 −0.365000 −0.182500 0.983206i \(-0.558419\pi\)
−0.182500 + 0.983206i \(0.558419\pi\)
\(600\) 1.74240e6 0.197592
\(601\) −1.21283e7 −1.36967 −0.684834 0.728699i \(-0.740125\pi\)
−0.684834 + 0.728699i \(0.740125\pi\)
\(602\) 2.81318e6 0.316378
\(603\) −2.49188e6 −0.279084
\(604\) −2.47264e6 −0.275784
\(605\) 2.85173e6 0.316752
\(606\) 625320. 0.0691705
\(607\) −9.77040e6 −1.07632 −0.538159 0.842843i \(-0.680880\pi\)
−0.538159 + 0.842843i \(0.680880\pi\)
\(608\) 888832. 0.0975126
\(609\) 5.92790e6 0.647676
\(610\) 1.21960e6 0.132707
\(611\) −6.55560e6 −0.710411
\(612\) −982368. −0.106022
\(613\) −8.06750e6 −0.867137 −0.433569 0.901121i \(-0.642746\pi\)
−0.433569 + 0.901121i \(0.642746\pi\)
\(614\) −4.11819e6 −0.440845
\(615\) 714060. 0.0761284
\(616\) 6.15629e6 0.653683
\(617\) −1.87807e7 −1.98609 −0.993045 0.117739i \(-0.962435\pi\)
−0.993045 + 0.117739i \(0.962435\pi\)
\(618\) −3.10162e6 −0.326676
\(619\) 341924. 0.0358677 0.0179338 0.999839i \(-0.494291\pi\)
0.0179338 + 0.999839i \(0.494291\pi\)
\(620\) 1.43168e6 0.149578
\(621\) −571536. −0.0594723
\(622\) 3.39371e6 0.351722
\(623\) −2.37168e6 −0.244814
\(624\) 622080. 0.0639565
\(625\) 8.83812e6 0.905024
\(626\) −8.14668e6 −0.830892
\(627\) −5.21842e6 −0.530115
\(628\) −5.09539e6 −0.515559
\(629\) 507860. 0.0511820
\(630\) 466560. 0.0468334
\(631\) 5.27552e6 0.527463 0.263731 0.964596i \(-0.415047\pi\)
0.263731 + 0.964596i \(0.415047\pi\)
\(632\) 4.51328e6 0.449469
\(633\) −3.13117e6 −0.310597
\(634\) −1.16994e7 −1.15595
\(635\) −607520. −0.0597897
\(636\) −4.17053e6 −0.408835
\(637\) −1.06083e6 −0.103585
\(638\) −1.22217e7 −1.18872
\(639\) 1.81861e6 0.176193
\(640\) 163840. 0.0158114
\(641\) −1.63359e7 −1.57036 −0.785180 0.619268i \(-0.787429\pi\)
−0.785180 + 0.619268i \(0.787429\pi\)
\(642\) −465264. −0.0445515
\(643\) 2.91785e6 0.278314 0.139157 0.990270i \(-0.455561\pi\)
0.139157 + 0.990270i \(0.455561\pi\)
\(644\) 1.80634e6 0.171626
\(645\) −439560. −0.0416024
\(646\) −2.63178e6 −0.248123
\(647\) −2.05355e7 −1.92861 −0.964306 0.264791i \(-0.914697\pi\)
−0.964306 + 0.264791i \(0.914697\pi\)
\(648\) 419904. 0.0392837
\(649\) −2.32531e6 −0.216705
\(650\) 3.26700e6 0.303295
\(651\) −1.15966e7 −1.07245
\(652\) −4.56416e6 −0.420477
\(653\) 6.24731e6 0.573338 0.286669 0.958030i \(-0.407452\pi\)
0.286669 + 0.958030i \(0.407452\pi\)
\(654\) −91080.0 −0.00832681
\(655\) 1.51572e6 0.138043
\(656\) −2.03110e6 −0.184278
\(657\) −1.69825e6 −0.153493
\(658\) 1.39853e7 1.25923
\(659\) 9.89587e6 0.887647 0.443824 0.896114i \(-0.353622\pi\)
0.443824 + 0.896114i \(0.353622\pi\)
\(660\) −961920. −0.0859566
\(661\) −7.91732e6 −0.704814 −0.352407 0.935847i \(-0.614637\pi\)
−0.352407 + 0.935847i \(0.614637\pi\)
\(662\) −7.12162e6 −0.631588
\(663\) −1.84194e6 −0.162739
\(664\) 1.90438e6 0.167623
\(665\) 1.24992e6 0.109604
\(666\) −217080. −0.0189642
\(667\) −3.58602e6 −0.312103
\(668\) 3.00230e6 0.260324
\(669\) −2.66134e6 −0.229898
\(670\) −1.23056e6 −0.105905
\(671\) 2.03673e7 1.74634
\(672\) −1.32710e6 −0.113366
\(673\) −2.00843e7 −1.70930 −0.854652 0.519201i \(-0.826229\pi\)
−0.854652 + 0.519201i \(0.826229\pi\)
\(674\) 8.20257e6 0.695505
\(675\) 2.20522e6 0.186292
\(676\) −4.77429e6 −0.401830
\(677\) −2.59145e6 −0.217306 −0.108653 0.994080i \(-0.534654\pi\)
−0.108653 + 0.994080i \(0.534654\pi\)
\(678\) −281736. −0.0235379
\(679\) 2.66486e6 0.221820
\(680\) −485120. −0.0402325
\(681\) 1.09685e7 0.906317
\(682\) 2.39091e7 1.96835
\(683\) 1.07639e7 0.882912 0.441456 0.897283i \(-0.354462\pi\)
0.441456 + 0.897283i \(0.354462\pi\)
\(684\) 1.12493e6 0.0919358
\(685\) −1.64334e6 −0.133814
\(686\) −7.41773e6 −0.601812
\(687\) −2.44859e6 −0.197936
\(688\) 1.25030e6 0.100703
\(689\) −7.81974e6 −0.627544
\(690\) −282240. −0.0225681
\(691\) 9.50333e6 0.757148 0.378574 0.925571i \(-0.376415\pi\)
0.378574 + 0.925571i \(0.376415\pi\)
\(692\) 6.11402e6 0.485357
\(693\) 7.79155e6 0.616298
\(694\) 1.65757e7 1.30639
\(695\) 726200. 0.0570288
\(696\) 2.63462e6 0.206156
\(697\) 6.01397e6 0.468899
\(698\) −1.62447e7 −1.26204
\(699\) −1.14946e7 −0.889818
\(700\) −6.96960e6 −0.537604
\(701\) 9.14537e6 0.702921 0.351460 0.936203i \(-0.385685\pi\)
0.351460 + 0.936203i \(0.385685\pi\)
\(702\) 787320. 0.0602988
\(703\) −581560. −0.0443819
\(704\) 2.73613e6 0.208068
\(705\) −2.18520e6 −0.165584
\(706\) 6.96858e6 0.526178
\(707\) −2.50128e6 −0.188197
\(708\) 501264. 0.0375823
\(709\) 816646. 0.0610124 0.0305062 0.999535i \(-0.490288\pi\)
0.0305062 + 0.999535i \(0.490288\pi\)
\(710\) 898080. 0.0668604
\(711\) 5.71212e6 0.423763
\(712\) −1.05408e6 −0.0779244
\(713\) 7.01523e6 0.516795
\(714\) 3.92947e6 0.288462
\(715\) −1.80360e6 −0.131940
\(716\) −5.87142e6 −0.428017
\(717\) 211500. 0.0153643
\(718\) 205584. 0.0148826
\(719\) −8.50306e6 −0.613413 −0.306707 0.951804i \(-0.599227\pi\)
−0.306707 + 0.951804i \(0.599227\pi\)
\(720\) 207360. 0.0149071
\(721\) 1.24065e7 0.888812
\(722\) −6.89070e6 −0.491949
\(723\) −2.20581e6 −0.156936
\(724\) 992096. 0.0703408
\(725\) 1.38363e7 0.977635
\(726\) −1.02662e7 −0.722885
\(727\) −1.08352e7 −0.760327 −0.380164 0.924919i \(-0.624132\pi\)
−0.380164 + 0.924919i \(0.624132\pi\)
\(728\) −2.48832e6 −0.174011
\(729\) 531441. 0.0370370
\(730\) −838640. −0.0582463
\(731\) −3.70207e6 −0.256243
\(732\) −4.39056e6 −0.302860
\(733\) −5.30468e6 −0.364669 −0.182335 0.983237i \(-0.558365\pi\)
−0.182335 + 0.983237i \(0.558365\pi\)
\(734\) −4.44469e6 −0.304510
\(735\) −353610. −0.0241438
\(736\) 802816. 0.0546288
\(737\) −2.05504e7 −1.39364
\(738\) −2.57062e6 −0.173739
\(739\) −8.40620e6 −0.566224 −0.283112 0.959087i \(-0.591367\pi\)
−0.283112 + 0.959087i \(0.591367\pi\)
\(740\) −107200. −0.00719640
\(741\) 2.10924e6 0.141117
\(742\) 1.66821e7 1.11235
\(743\) −1.37732e7 −0.915297 −0.457649 0.889133i \(-0.651308\pi\)
−0.457649 + 0.889133i \(0.651308\pi\)
\(744\) −5.15405e6 −0.341363
\(745\) 2.38702e6 0.157567
\(746\) −6.51658e6 −0.428719
\(747\) 2.41024e6 0.158037
\(748\) −8.10150e6 −0.529434
\(749\) 1.86106e6 0.121215
\(750\) 2.21400e6 0.143722
\(751\) 1.52343e7 0.985653 0.492826 0.870128i \(-0.335964\pi\)
0.492826 + 0.870128i \(0.335964\pi\)
\(752\) 6.21568e6 0.400815
\(753\) −1.71833e7 −1.10438
\(754\) 4.93992e6 0.316440
\(755\) −1.54540e6 −0.0986674
\(756\) −1.67962e6 −0.106882
\(757\) 1.37267e7 0.870615 0.435308 0.900282i \(-0.356640\pi\)
0.435308 + 0.900282i \(0.356640\pi\)
\(758\) −1.61951e7 −1.02379
\(759\) −4.71341e6 −0.296982
\(760\) 555520. 0.0348872
\(761\) 1.43391e7 0.897553 0.448776 0.893644i \(-0.351860\pi\)
0.448776 + 0.893644i \(0.351860\pi\)
\(762\) 2.18707e6 0.136451
\(763\) 364320. 0.0226554
\(764\) −1.97261e6 −0.122266
\(765\) −613980. −0.0379316
\(766\) 1.20004e7 0.738963
\(767\) 939870. 0.0576872
\(768\) −589824. −0.0360844
\(769\) −7.24143e6 −0.441579 −0.220790 0.975321i \(-0.570863\pi\)
−0.220790 + 0.975321i \(0.570863\pi\)
\(770\) 3.84768e6 0.233869
\(771\) 3.35259e6 0.203116
\(772\) −1.05810e7 −0.638972
\(773\) −3.09402e7 −1.86241 −0.931204 0.364499i \(-0.881240\pi\)
−0.931204 + 0.364499i \(0.881240\pi\)
\(774\) 1.58242e6 0.0949442
\(775\) −2.70677e7 −1.61881
\(776\) 1.18438e6 0.0706055
\(777\) 868320. 0.0515973
\(778\) 9.00471e6 0.533360
\(779\) −6.88671e6 −0.406601
\(780\) 388800. 0.0228818
\(781\) 1.49979e7 0.879840
\(782\) −2.37709e6 −0.139004
\(783\) 3.33445e6 0.194366
\(784\) 1.00582e6 0.0584429
\(785\) −3.18462e6 −0.184452
\(786\) −5.45659e6 −0.315040
\(787\) −2.90146e7 −1.66986 −0.834929 0.550358i \(-0.814491\pi\)
−0.834929 + 0.550358i \(0.814491\pi\)
\(788\) −9.44880e6 −0.542077
\(789\) 5.26792e6 0.301263
\(790\) 2.82080e6 0.160807
\(791\) 1.12694e6 0.0640414
\(792\) 3.46291e6 0.196168
\(793\) −8.23230e6 −0.464877
\(794\) 8.83386e6 0.497278
\(795\) −2.60658e6 −0.146269
\(796\) 7.73210e6 0.432528
\(797\) 7.73735e6 0.431466 0.215733 0.976452i \(-0.430786\pi\)
0.215733 + 0.976452i \(0.430786\pi\)
\(798\) −4.49971e6 −0.250137
\(799\) −1.84042e7 −1.01988
\(800\) −3.09760e6 −0.171120
\(801\) −1.33407e6 −0.0734678
\(802\) −7.38310e6 −0.405324
\(803\) −1.40053e7 −0.766484
\(804\) 4.43002e6 0.241694
\(805\) 1.12896e6 0.0614029
\(806\) −9.66384e6 −0.523977
\(807\) −5.90060e6 −0.318942
\(808\) −1.11168e6 −0.0599034
\(809\) 9.58319e6 0.514801 0.257400 0.966305i \(-0.417134\pi\)
0.257400 + 0.966305i \(0.417134\pi\)
\(810\) 262440. 0.0140546
\(811\) −1.96672e7 −1.05000 −0.525002 0.851101i \(-0.675935\pi\)
−0.525002 + 0.851101i \(0.675935\pi\)
\(812\) −1.05385e7 −0.560904
\(813\) 1.59407e7 0.845827
\(814\) −1.79024e6 −0.0947001
\(815\) −2.85260e6 −0.150434
\(816\) 1.74643e6 0.0918177
\(817\) 4.23931e6 0.222198
\(818\) −5.86239e6 −0.306331
\(819\) −3.14928e6 −0.164060
\(820\) −1.26944e6 −0.0659292
\(821\) −2.89008e6 −0.149642 −0.0748208 0.997197i \(-0.523838\pi\)
−0.0748208 + 0.997197i \(0.523838\pi\)
\(822\) 5.91602e6 0.305387
\(823\) −2.68337e7 −1.38096 −0.690480 0.723351i \(-0.742601\pi\)
−0.690480 + 0.723351i \(0.742601\pi\)
\(824\) 5.51398e6 0.282909
\(825\) 1.81863e7 0.930271
\(826\) −2.00506e6 −0.102253
\(827\) −1.51559e7 −0.770579 −0.385289 0.922796i \(-0.625898\pi\)
−0.385289 + 0.922796i \(0.625898\pi\)
\(828\) 1.01606e6 0.0515045
\(829\) −7.80067e6 −0.394226 −0.197113 0.980381i \(-0.563157\pi\)
−0.197113 + 0.980381i \(0.563157\pi\)
\(830\) 1.19024e6 0.0599707
\(831\) 2.12585e7 1.06790
\(832\) −1.10592e6 −0.0553880
\(833\) −2.97818e6 −0.148710
\(834\) −2.61432e6 −0.130150
\(835\) 1.87644e6 0.0931362
\(836\) 9.27718e6 0.459093
\(837\) −6.52309e6 −0.321840
\(838\) 2.29886e6 0.113085
\(839\) −1.62610e6 −0.0797519 −0.0398760 0.999205i \(-0.512696\pi\)
−0.0398760 + 0.999205i \(0.512696\pi\)
\(840\) −829440. −0.0405590
\(841\) 410327. 0.0200051
\(842\) 2.61860e7 1.27288
\(843\) 8.15420e6 0.395196
\(844\) 5.56653e6 0.268985
\(845\) −2.98393e6 −0.143763
\(846\) 7.86672e6 0.377892
\(847\) 4.10649e7 1.96681
\(848\) 7.41427e6 0.354062
\(849\) 1.08076e7 0.514588
\(850\) 9.17180e6 0.435419
\(851\) −525280. −0.0248638
\(852\) −3.23309e6 −0.152587
\(853\) 1.07577e7 0.506229 0.253114 0.967436i \(-0.418545\pi\)
0.253114 + 0.967436i \(0.418545\pi\)
\(854\) 1.75622e7 0.824015
\(855\) 703080. 0.0328919
\(856\) 827136. 0.0385827
\(857\) −2.11452e7 −0.983468 −0.491734 0.870745i \(-0.663637\pi\)
−0.491734 + 0.870745i \(0.663637\pi\)
\(858\) 6.49296e6 0.301110
\(859\) 288860. 0.0133569 0.00667843 0.999978i \(-0.497874\pi\)
0.00667843 + 0.999978i \(0.497874\pi\)
\(860\) 781440. 0.0360288
\(861\) 1.02825e7 0.472704
\(862\) 1.15627e7 0.530019
\(863\) −5.88884e6 −0.269155 −0.134578 0.990903i \(-0.542968\pi\)
−0.134578 + 0.990903i \(0.542968\pi\)
\(864\) −746496. −0.0340207
\(865\) 3.82126e6 0.173647
\(866\) 2.30701e7 1.04533
\(867\) 7.60764e6 0.343718
\(868\) 2.06162e7 0.928772
\(869\) 4.71074e7 2.11612
\(870\) 1.64664e6 0.0737565
\(871\) 8.30628e6 0.370989
\(872\) 161920. 0.00721123
\(873\) 1.49899e6 0.0665675
\(874\) 2.72205e6 0.120536
\(875\) −8.85600e6 −0.391037
\(876\) 3.01910e6 0.132928
\(877\) −2.11673e7 −0.929322 −0.464661 0.885489i \(-0.653824\pi\)
−0.464661 + 0.885489i \(0.653824\pi\)
\(878\) −2.22602e6 −0.0974523
\(879\) 8.56042e6 0.373700
\(880\) 1.71008e6 0.0744406
\(881\) 8.90400e6 0.386496 0.193248 0.981150i \(-0.438098\pi\)
0.193248 + 0.981150i \(0.438098\pi\)
\(882\) 1.27300e6 0.0551005
\(883\) −5.14056e6 −0.221875 −0.110938 0.993827i \(-0.535385\pi\)
−0.110938 + 0.993827i \(0.535385\pi\)
\(884\) 3.27456e6 0.140936
\(885\) 313290. 0.0134459
\(886\) 1.84686e7 0.790406
\(887\) −3.23951e7 −1.38252 −0.691259 0.722607i \(-0.742944\pi\)
−0.691259 + 0.722607i \(0.742944\pi\)
\(888\) 385920. 0.0164235
\(889\) −8.74829e6 −0.371252
\(890\) −658800. −0.0278791
\(891\) 4.38275e6 0.184949
\(892\) 4.73126e6 0.199097
\(893\) 2.10750e7 0.884382
\(894\) −8.59327e6 −0.359596
\(895\) −3.66964e6 −0.153132
\(896\) 2.35930e6 0.0981776
\(897\) 1.90512e6 0.0790572
\(898\) 1.07540e7 0.445021
\(899\) −4.09282e7 −1.68897
\(900\) −3.92040e6 −0.161333
\(901\) −2.19532e7 −0.900919
\(902\) −2.11996e7 −0.867586
\(903\) −6.32966e6 −0.258322
\(904\) 500864. 0.0203844
\(905\) 620060. 0.0251659
\(906\) 5.56344e6 0.225176
\(907\) 4.57769e7 1.84769 0.923843 0.382773i \(-0.125031\pi\)
0.923843 + 0.382773i \(0.125031\pi\)
\(908\) −1.94996e7 −0.784893
\(909\) −1.40697e6 −0.0564775
\(910\) −1.55520e6 −0.0622562
\(911\) −2.69585e7 −1.07622 −0.538108 0.842876i \(-0.680861\pi\)
−0.538108 + 0.842876i \(0.680861\pi\)
\(912\) −1.99987e6 −0.0796187
\(913\) 1.98770e7 0.789176
\(914\) −2.92299e7 −1.15734
\(915\) −2.74410e6 −0.108355
\(916\) 4.35306e6 0.171418
\(917\) 2.18264e7 0.857153
\(918\) 2.21033e6 0.0865665
\(919\) 7.83943e6 0.306193 0.153097 0.988211i \(-0.451075\pi\)
0.153097 + 0.988211i \(0.451075\pi\)
\(920\) 501760. 0.0195446
\(921\) 9.26593e6 0.359948
\(922\) −376056. −0.0145688
\(923\) −6.06204e6 −0.234215
\(924\) −1.38516e7 −0.533730
\(925\) 2.02675e6 0.0778836
\(926\) 2.88741e7 1.10657
\(927\) 6.97864e6 0.266730
\(928\) −4.68378e6 −0.178536
\(929\) 3.18869e7 1.21220 0.606099 0.795389i \(-0.292734\pi\)
0.606099 + 0.795389i \(0.292734\pi\)
\(930\) −3.22128e6 −0.122130
\(931\) 3.41037e6 0.128952
\(932\) 2.04348e7 0.770605
\(933\) −7.63585e6 −0.287179
\(934\) 2.64175e7 0.990887
\(935\) −5.06344e6 −0.189416
\(936\) −1.39968e6 −0.0522203
\(937\) −1.96004e7 −0.729316 −0.364658 0.931142i \(-0.618814\pi\)
−0.364658 + 0.931142i \(0.618814\pi\)
\(938\) −1.77201e7 −0.657595
\(939\) 1.83300e7 0.678421
\(940\) 3.88480e6 0.143400
\(941\) 3.41351e7 1.25669 0.628344 0.777936i \(-0.283733\pi\)
0.628344 + 0.777936i \(0.283733\pi\)
\(942\) 1.14646e7 0.420952
\(943\) −6.22026e6 −0.227787
\(944\) −891136. −0.0325472
\(945\) −1.04976e6 −0.0382393
\(946\) 1.30500e7 0.474116
\(947\) 3.87207e6 0.140303 0.0701517 0.997536i \(-0.477652\pi\)
0.0701517 + 0.997536i \(0.477652\pi\)
\(948\) −1.01549e7 −0.366990
\(949\) 5.66082e6 0.204039
\(950\) −1.05028e7 −0.377569
\(951\) 2.63236e7 0.943831
\(952\) −6.98573e6 −0.249815
\(953\) −1.01832e7 −0.363204 −0.181602 0.983372i \(-0.558128\pi\)
−0.181602 + 0.983372i \(0.558128\pi\)
\(954\) 9.38369e6 0.333813
\(955\) −1.23288e6 −0.0437434
\(956\) −376000. −0.0133059
\(957\) 2.74989e7 0.970589
\(958\) −9.98763e6 −0.351600
\(959\) −2.36641e7 −0.830890
\(960\) −368640. −0.0129099
\(961\) 5.14376e7 1.79668
\(962\) 723600. 0.0252093
\(963\) 1.04684e6 0.0363761
\(964\) 3.92144e6 0.135910
\(965\) −6.61310e6 −0.228606
\(966\) −4.06426e6 −0.140132
\(967\) 8.52484e6 0.293170 0.146585 0.989198i \(-0.453172\pi\)
0.146585 + 0.989198i \(0.453172\pi\)
\(968\) 1.82511e7 0.626037
\(969\) 5.92150e6 0.202592
\(970\) 740240. 0.0252606
\(971\) −1.76365e6 −0.0600295 −0.0300148 0.999549i \(-0.509555\pi\)
−0.0300148 + 0.999549i \(0.509555\pi\)
\(972\) −944784. −0.0320750
\(973\) 1.04573e7 0.354109
\(974\) −2.07860e7 −0.702057
\(975\) −7.35075e6 −0.247640
\(976\) 7.80544e6 0.262285
\(977\) −1.32884e7 −0.445387 −0.222694 0.974888i \(-0.571485\pi\)
−0.222694 + 0.974888i \(0.571485\pi\)
\(978\) 1.02694e7 0.343318
\(979\) −1.10020e7 −0.366871
\(980\) 628640. 0.0209092
\(981\) 204930. 0.00679881
\(982\) −1.76032e7 −0.582523
\(983\) −3.59079e7 −1.18524 −0.592620 0.805482i \(-0.701906\pi\)
−0.592620 + 0.805482i \(0.701906\pi\)
\(984\) 4.56998e6 0.150462
\(985\) −5.90550e6 −0.193939
\(986\) 1.38684e7 0.454290
\(987\) −3.14669e7 −1.02816
\(988\) −3.74976e6 −0.122211
\(989\) 3.82906e6 0.124480
\(990\) 2.16432e6 0.0701833
\(991\) 2.41676e7 0.781716 0.390858 0.920451i \(-0.372178\pi\)
0.390858 + 0.920451i \(0.372178\pi\)
\(992\) 9.16275e6 0.295629
\(993\) 1.60236e7 0.515689
\(994\) 1.29324e7 0.415156
\(995\) 4.83256e6 0.154746
\(996\) −4.28486e6 −0.136864
\(997\) −1.89753e7 −0.604576 −0.302288 0.953217i \(-0.597750\pi\)
−0.302288 + 0.953217i \(0.597750\pi\)
\(998\) −2.14836e7 −0.682780
\(999\) 488430. 0.0154842
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 354.6.a.a.1.1 1
3.2 odd 2 1062.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.6.a.a.1.1 1 1.1 even 1 trivial
1062.6.a.a.1.1 1 3.2 odd 2