Properties

Label 570.6.a.j.1.3
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.4187772934\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 25872 x^{2} - 1407374 x - 6356280\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(183.641\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -323.562 q^{11} -144.000 q^{12} +197.723 q^{13} -222.886 q^{14} -225.000 q^{15} +256.000 q^{16} +1232.08 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -501.494 q^{21} +1294.25 q^{22} -3776.19 q^{23} +576.000 q^{24} +625.000 q^{25} -790.890 q^{26} -729.000 q^{27} +891.544 q^{28} -4736.64 q^{29} +900.000 q^{30} +4826.60 q^{31} -1024.00 q^{32} +2912.06 q^{33} -4928.34 q^{34} +1393.04 q^{35} +1296.00 q^{36} -11273.5 q^{37} -1444.00 q^{38} -1779.50 q^{39} -1600.00 q^{40} -2353.15 q^{41} +2005.97 q^{42} -1920.53 q^{43} -5176.99 q^{44} +2025.00 q^{45} +15104.8 q^{46} -3445.61 q^{47} -2304.00 q^{48} -13702.1 q^{49} -2500.00 q^{50} -11088.8 q^{51} +3163.56 q^{52} +28779.8 q^{53} +2916.00 q^{54} -8089.05 q^{55} -3566.18 q^{56} -3249.00 q^{57} +18946.6 q^{58} +23431.7 q^{59} -3600.00 q^{60} +22487.3 q^{61} -19306.4 q^{62} +4513.44 q^{63} +4096.00 q^{64} +4943.06 q^{65} -11648.2 q^{66} +33101.9 q^{67} +19713.4 q^{68} +33985.7 q^{69} -5572.15 q^{70} +9436.16 q^{71} -5184.00 q^{72} +76218.4 q^{73} +45093.8 q^{74} -5625.00 q^{75} +5776.00 q^{76} -18029.4 q^{77} +7118.01 q^{78} -58507.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +9412.61 q^{82} -99966.1 q^{83} -8023.90 q^{84} +30802.1 q^{85} +7682.11 q^{86} +42629.8 q^{87} +20708.0 q^{88} -35586.1 q^{89} -8100.00 q^{90} +11017.4 q^{91} -60419.1 q^{92} -43439.4 q^{93} +13782.4 q^{94} +9025.00 q^{95} +9216.00 q^{96} +76052.9 q^{97} +54808.5 q^{98} -26208.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} - 400q^{10} - 246q^{11} - 576q^{12} + 640q^{13} + 432q^{14} - 900q^{15} + 1024q^{16} - 612q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 972q^{21} + 984q^{22} - 1242q^{23} + 2304q^{24} + 2500q^{25} - 2560q^{26} - 2916q^{27} - 1728q^{28} - 6230q^{29} + 3600q^{30} - 11360q^{31} - 4096q^{32} + 2214q^{33} + 2448q^{34} - 2700q^{35} + 5184q^{36} - 4792q^{37} - 5776q^{38} - 5760q^{39} - 6400q^{40} + 9170q^{41} - 3888q^{42} - 11412q^{43} - 3936q^{44} + 8100q^{45} + 4968q^{46} - 29858q^{47} - 9216q^{48} + 31092q^{49} - 10000q^{50} + 5508q^{51} + 10240q^{52} + 27498q^{53} + 11664q^{54} - 6150q^{55} + 6912q^{56} - 12996q^{57} + 24920q^{58} + 54984q^{59} - 14400q^{60} + 20868q^{61} + 45440q^{62} - 8748q^{63} + 16384q^{64} + 16000q^{65} - 8856q^{66} - 20244q^{67} - 9792q^{68} + 11178q^{69} + 10800q^{70} + 86864q^{71} - 20736q^{72} - 3728q^{73} + 19168q^{74} - 22500q^{75} + 23104q^{76} + 18796q^{77} + 23040q^{78} + 164192q^{79} + 25600q^{80} + 26244q^{81} - 36680q^{82} - 60506q^{83} + 15552q^{84} - 15300q^{85} + 45648q^{86} + 56070q^{87} + 15744q^{88} + 113798q^{89} - 32400q^{90} + 159528q^{91} - 19872q^{92} + 102240q^{93} + 119432q^{94} + 36100q^{95} + 36864q^{96} + 79440q^{97} - 124368q^{98} - 19926q^{99} + O(q^{100}) \)

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
\(7\) 55.7215 0.429811 0.214906 0.976635i \(-0.431056\pi\)
0.214906 + 0.976635i \(0.431056\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) −323.562 −0.806261 −0.403131 0.915142i \(-0.632078\pi\)
−0.403131 + 0.915142i \(0.632078\pi\)
\(12\) −144.000 −0.288675
\(13\) 197.723 0.324487 0.162244 0.986751i \(-0.448127\pi\)
0.162244 + 0.986751i \(0.448127\pi\)
\(14\) −222.886 −0.303922
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) 1232.08 1.03399 0.516997 0.855987i \(-0.327050\pi\)
0.516997 + 0.855987i \(0.327050\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) −501.494 −0.248152
\(22\) 1294.25 0.570113
\(23\) −3776.19 −1.48845 −0.744226 0.667928i \(-0.767181\pi\)
−0.744226 + 0.667928i \(0.767181\pi\)
\(24\) 576.000 0.204124
\(25\) 625.000 0.200000
\(26\) −790.890 −0.229447
\(27\) −729.000 −0.192450
\(28\) 891.544 0.214906
\(29\) −4736.64 −1.04587 −0.522933 0.852374i \(-0.675162\pi\)
−0.522933 + 0.852374i \(0.675162\pi\)
\(30\) 900.000 0.182574
\(31\) 4826.60 0.902064 0.451032 0.892508i \(-0.351056\pi\)
0.451032 + 0.892508i \(0.351056\pi\)
\(32\) −1024.00 −0.176777
\(33\) 2912.06 0.465495
\(34\) −4928.34 −0.731144
\(35\) 1393.04 0.192217
\(36\) 1296.00 0.166667
\(37\) −11273.5 −1.35379 −0.676897 0.736078i \(-0.736676\pi\)
−0.676897 + 0.736078i \(0.736676\pi\)
\(38\) −1444.00 −0.162221
\(39\) −1779.50 −0.187343
\(40\) −1600.00 −0.158114
\(41\) −2353.15 −0.218620 −0.109310 0.994008i \(-0.534864\pi\)
−0.109310 + 0.994008i \(0.534864\pi\)
\(42\) 2005.97 0.175470
\(43\) −1920.53 −0.158398 −0.0791990 0.996859i \(-0.525236\pi\)
−0.0791990 + 0.996859i \(0.525236\pi\)
\(44\) −5176.99 −0.403131
\(45\) 2025.00 0.149071
\(46\) 15104.8 1.05249
\(47\) −3445.61 −0.227521 −0.113760 0.993508i \(-0.536290\pi\)
−0.113760 + 0.993508i \(0.536290\pi\)
\(48\) −2304.00 −0.144338
\(49\) −13702.1 −0.815262
\(50\) −2500.00 −0.141421
\(51\) −11088.8 −0.596977
\(52\) 3163.56 0.162244
\(53\) 28779.8 1.40733 0.703667 0.710530i \(-0.251545\pi\)
0.703667 + 0.710530i \(0.251545\pi\)
\(54\) 2916.00 0.136083
\(55\) −8089.05 −0.360571
\(56\) −3566.18 −0.151961
\(57\) −3249.00 −0.132453
\(58\) 18946.6 0.739538
\(59\) 23431.7 0.876342 0.438171 0.898892i \(-0.355626\pi\)
0.438171 + 0.898892i \(0.355626\pi\)
\(60\) −3600.00 −0.129099
\(61\) 22487.3 0.773771 0.386886 0.922128i \(-0.373551\pi\)
0.386886 + 0.922128i \(0.373551\pi\)
\(62\) −19306.4 −0.637855
\(63\) 4513.44 0.143270
\(64\) 4096.00 0.125000
\(65\) 4943.06 0.145115
\(66\) −11648.2 −0.329155
\(67\) 33101.9 0.900879 0.450440 0.892807i \(-0.351267\pi\)
0.450440 + 0.892807i \(0.351267\pi\)
\(68\) 19713.4 0.516997
\(69\) 33985.7 0.859358
\(70\) −5572.15 −0.135918
\(71\) 9436.16 0.222152 0.111076 0.993812i \(-0.464570\pi\)
0.111076 + 0.993812i \(0.464570\pi\)
\(72\) −5184.00 −0.117851
\(73\) 76218.4 1.67399 0.836995 0.547211i \(-0.184310\pi\)
0.836995 + 0.547211i \(0.184310\pi\)
\(74\) 45093.8 0.957277
\(75\) −5625.00 −0.115470
\(76\) 5776.00 0.114708
\(77\) −18029.4 −0.346540
\(78\) 7118.01 0.132471
\(79\) −58507.4 −1.05473 −0.527367 0.849637i \(-0.676821\pi\)
−0.527367 + 0.849637i \(0.676821\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 9412.61 0.154588
\(83\) −99966.1 −1.59279 −0.796393 0.604780i \(-0.793261\pi\)
−0.796393 + 0.604780i \(0.793261\pi\)
\(84\) −8023.90 −0.124076
\(85\) 30802.1 0.462416
\(86\) 7682.11 0.112004
\(87\) 42629.8 0.603831
\(88\) 20708.0 0.285056
\(89\) −35586.1 −0.476218 −0.238109 0.971238i \(-0.576528\pi\)
−0.238109 + 0.971238i \(0.576528\pi\)
\(90\) −8100.00 −0.105409
\(91\) 11017.4 0.139468
\(92\) −60419.1 −0.744226
\(93\) −43439.4 −0.520807
\(94\) 13782.4 0.160881
\(95\) 9025.00 0.102598
\(96\) 9216.00 0.102062
\(97\) 76052.9 0.820704 0.410352 0.911927i \(-0.365406\pi\)
0.410352 + 0.911927i \(0.365406\pi\)
\(98\) 54808.5 0.576478
\(99\) −26208.5 −0.268754
\(100\) 10000.0 0.100000
\(101\) −28533.7 −0.278326 −0.139163 0.990269i \(-0.544441\pi\)
−0.139163 + 0.990269i \(0.544441\pi\)
\(102\) 44355.0 0.422126
\(103\) −164583. −1.52859 −0.764295 0.644867i \(-0.776913\pi\)
−0.764295 + 0.644867i \(0.776913\pi\)
\(104\) −12654.2 −0.114724
\(105\) −12537.3 −0.110977
\(106\) −115119. −0.995136
\(107\) −99871.8 −0.843303 −0.421651 0.906758i \(-0.638549\pi\)
−0.421651 + 0.906758i \(0.638549\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 187471. 1.51136 0.755682 0.654939i \(-0.227306\pi\)
0.755682 + 0.654939i \(0.227306\pi\)
\(110\) 32356.2 0.254962
\(111\) 101461. 0.781613
\(112\) 14264.7 0.107453
\(113\) 68254.9 0.502849 0.251425 0.967877i \(-0.419101\pi\)
0.251425 + 0.967877i \(0.419101\pi\)
\(114\) 12996.0 0.0936586
\(115\) −94404.8 −0.665656
\(116\) −75786.3 −0.522933
\(117\) 16015.5 0.108162
\(118\) −93726.8 −0.619667
\(119\) 68653.6 0.444422
\(120\) 14400.0 0.0912871
\(121\) −56358.7 −0.349943
\(122\) −89949.2 −0.547139
\(123\) 21178.4 0.126221
\(124\) 77225.6 0.451032
\(125\) 15625.0 0.0894427
\(126\) −18053.8 −0.101307
\(127\) −172249. −0.947649 −0.473825 0.880619i \(-0.657127\pi\)
−0.473825 + 0.880619i \(0.657127\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 17284.8 0.0914511
\(130\) −19772.3 −0.102612
\(131\) 140517. 0.715404 0.357702 0.933836i \(-0.383560\pi\)
0.357702 + 0.933836i \(0.383560\pi\)
\(132\) 46592.9 0.232748
\(133\) 20115.5 0.0986055
\(134\) −132408. −0.637018
\(135\) −18225.0 −0.0860663
\(136\) −78853.4 −0.365572
\(137\) −222742. −1.01391 −0.506955 0.861972i \(-0.669229\pi\)
−0.506955 + 0.861972i \(0.669229\pi\)
\(138\) −135943. −0.607658
\(139\) −397260. −1.74397 −0.871983 0.489536i \(-0.837166\pi\)
−0.871983 + 0.489536i \(0.837166\pi\)
\(140\) 22288.6 0.0961087
\(141\) 31010.4 0.131359
\(142\) −37744.6 −0.157085
\(143\) −63975.5 −0.261621
\(144\) 20736.0 0.0833333
\(145\) −118416. −0.467725
\(146\) −304874. −1.18369
\(147\) 123319. 0.470692
\(148\) −180375. −0.676897
\(149\) 64763.5 0.238982 0.119491 0.992835i \(-0.461874\pi\)
0.119491 + 0.992835i \(0.461874\pi\)
\(150\) 22500.0 0.0816497
\(151\) 496084. 1.77057 0.885285 0.465049i \(-0.153963\pi\)
0.885285 + 0.465049i \(0.153963\pi\)
\(152\) −23104.0 −0.0811107
\(153\) 99798.8 0.344665
\(154\) 72117.4 0.245041
\(155\) 120665. 0.403415
\(156\) −28472.0 −0.0936714
\(157\) −306681. −0.992974 −0.496487 0.868044i \(-0.665377\pi\)
−0.496487 + 0.868044i \(0.665377\pi\)
\(158\) 234030. 0.745810
\(159\) −259018. −0.812525
\(160\) −25600.0 −0.0790569
\(161\) −210415. −0.639753
\(162\) −26244.0 −0.0785674
\(163\) −304398. −0.897373 −0.448687 0.893689i \(-0.648108\pi\)
−0.448687 + 0.893689i \(0.648108\pi\)
\(164\) −37650.5 −0.109310
\(165\) 72801.4 0.208176
\(166\) 399864. 1.12627
\(167\) −508435. −1.41073 −0.705366 0.708844i \(-0.749217\pi\)
−0.705366 + 0.708844i \(0.749217\pi\)
\(168\) 32095.6 0.0877348
\(169\) −332199. −0.894708
\(170\) −123208. −0.326978
\(171\) 29241.0 0.0764719
\(172\) −30728.4 −0.0791990
\(173\) −605576. −1.53834 −0.769172 0.639042i \(-0.779331\pi\)
−0.769172 + 0.639042i \(0.779331\pi\)
\(174\) −170519. −0.426973
\(175\) 34825.9 0.0859622
\(176\) −82831.8 −0.201565
\(177\) −210885. −0.505956
\(178\) 142344. 0.336737
\(179\) −302750. −0.706240 −0.353120 0.935578i \(-0.614879\pi\)
−0.353120 + 0.935578i \(0.614879\pi\)
\(180\) 32400.0 0.0745356
\(181\) 228082. 0.517481 0.258740 0.965947i \(-0.416693\pi\)
0.258740 + 0.965947i \(0.416693\pi\)
\(182\) −44069.6 −0.0986190
\(183\) −202386. −0.446737
\(184\) 241676. 0.526247
\(185\) −281836. −0.605435
\(186\) 173758. 0.368266
\(187\) −398656. −0.833669
\(188\) −55129.7 −0.113760
\(189\) −40621.0 −0.0827172
\(190\) −36100.0 −0.0725476
\(191\) −4471.26 −0.00886843 −0.00443421 0.999990i \(-0.501411\pi\)
−0.00443421 + 0.999990i \(0.501411\pi\)
\(192\) −36864.0 −0.0721688
\(193\) 424454. 0.820233 0.410117 0.912033i \(-0.365488\pi\)
0.410117 + 0.912033i \(0.365488\pi\)
\(194\) −304212. −0.580325
\(195\) −44487.6 −0.0837823
\(196\) −219234. −0.407631
\(197\) −866220. −1.59024 −0.795120 0.606453i \(-0.792592\pi\)
−0.795120 + 0.606453i \(0.792592\pi\)
\(198\) 104834. 0.190038
\(199\) 887988. 1.58955 0.794776 0.606903i \(-0.207588\pi\)
0.794776 + 0.606903i \(0.207588\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −297917. −0.520123
\(202\) 114135. 0.196806
\(203\) −263933. −0.449525
\(204\) −177420. −0.298488
\(205\) −58828.8 −0.0977700
\(206\) 658331. 1.08088
\(207\) −305872. −0.496151
\(208\) 50617.0 0.0811218
\(209\) −116806. −0.184969
\(210\) 50149.4 0.0784724
\(211\) −233988. −0.361816 −0.180908 0.983500i \(-0.557904\pi\)
−0.180908 + 0.983500i \(0.557904\pi\)
\(212\) 460476. 0.703667
\(213\) −84925.4 −0.128259
\(214\) 399487. 0.596305
\(215\) −48013.2 −0.0708377
\(216\) 46656.0 0.0680414
\(217\) 268946. 0.387717
\(218\) −749886. −1.06870
\(219\) −685966. −0.966478
\(220\) −129425. −0.180285
\(221\) 243611. 0.335518
\(222\) −405844. −0.552684
\(223\) −429226. −0.577994 −0.288997 0.957330i \(-0.593322\pi\)
−0.288997 + 0.957330i \(0.593322\pi\)
\(224\) −57058.8 −0.0759806
\(225\) 50625.0 0.0666667
\(226\) −273020. −0.355568
\(227\) −269561. −0.347210 −0.173605 0.984815i \(-0.555542\pi\)
−0.173605 + 0.984815i \(0.555542\pi\)
\(228\) −51984.0 −0.0662266
\(229\) −1.08241e6 −1.36396 −0.681981 0.731370i \(-0.738881\pi\)
−0.681981 + 0.731370i \(0.738881\pi\)
\(230\) 377619. 0.470690
\(231\) 162264. 0.200075
\(232\) 303145. 0.369769
\(233\) −1.05017e6 −1.26727 −0.633636 0.773632i \(-0.718438\pi\)
−0.633636 + 0.773632i \(0.718438\pi\)
\(234\) −64062.1 −0.0764824
\(235\) −86140.1 −0.101750
\(236\) 374907. 0.438171
\(237\) 526567. 0.608951
\(238\) −274614. −0.314254
\(239\) 1.45536e6 1.64806 0.824032 0.566543i \(-0.191719\pi\)
0.824032 + 0.566543i \(0.191719\pi\)
\(240\) −57600.0 −0.0645497
\(241\) −436561. −0.484175 −0.242087 0.970254i \(-0.577832\pi\)
−0.242087 + 0.970254i \(0.577832\pi\)
\(242\) 225435. 0.247447
\(243\) −59049.0 −0.0641500
\(244\) 359797. 0.386886
\(245\) −342553. −0.364596
\(246\) −84713.5 −0.0892514
\(247\) 71377.8 0.0744425
\(248\) −308903. −0.318928
\(249\) 899695. 0.919595
\(250\) −62500.0 −0.0632456
\(251\) −1.58899e6 −1.59197 −0.795987 0.605313i \(-0.793048\pi\)
−0.795987 + 0.605313i \(0.793048\pi\)
\(252\) 72215.1 0.0716352
\(253\) 1.22183e6 1.20008
\(254\) 688996. 0.670089
\(255\) −277219. −0.266976
\(256\) 65536.0 0.0625000
\(257\) 259559. 0.245134 0.122567 0.992460i \(-0.460887\pi\)
0.122567 + 0.992460i \(0.460887\pi\)
\(258\) −69139.0 −0.0646657
\(259\) −628174. −0.581876
\(260\) 79089.0 0.0725576
\(261\) −383668. −0.348622
\(262\) −562069. −0.505867
\(263\) −1.65796e6 −1.47804 −0.739018 0.673686i \(-0.764710\pi\)
−0.739018 + 0.673686i \(0.764710\pi\)
\(264\) −186372. −0.164577
\(265\) 719494. 0.629379
\(266\) −80461.9 −0.0697246
\(267\) 320275. 0.274944
\(268\) 529631. 0.450440
\(269\) −953680. −0.803567 −0.401783 0.915735i \(-0.631610\pi\)
−0.401783 + 0.915735i \(0.631610\pi\)
\(270\) 72900.0 0.0608581
\(271\) 1.51102e6 1.24982 0.624908 0.780698i \(-0.285136\pi\)
0.624908 + 0.780698i \(0.285136\pi\)
\(272\) 315414. 0.258499
\(273\) −99156.6 −0.0805221
\(274\) 890966. 0.716943
\(275\) −202226. −0.161252
\(276\) 543772. 0.429679
\(277\) 1.60914e6 1.26007 0.630036 0.776566i \(-0.283040\pi\)
0.630036 + 0.776566i \(0.283040\pi\)
\(278\) 1.58904e6 1.23317
\(279\) 390955. 0.300688
\(280\) −89154.4 −0.0679591
\(281\) −1.10334e6 −0.833572 −0.416786 0.909005i \(-0.636844\pi\)
−0.416786 + 0.909005i \(0.636844\pi\)
\(282\) −124042. −0.0928849
\(283\) −1.73551e6 −1.28813 −0.644067 0.764969i \(-0.722754\pi\)
−0.644067 + 0.764969i \(0.722754\pi\)
\(284\) 150979. 0.111076
\(285\) −81225.0 −0.0592349
\(286\) 255902. 0.184994
\(287\) −131121. −0.0939655
\(288\) −82944.0 −0.0589256
\(289\) 98175.2 0.0691444
\(290\) 473664. 0.330732
\(291\) −684476. −0.473834
\(292\) 1.21949e6 0.836995
\(293\) −811028. −0.551908 −0.275954 0.961171i \(-0.588994\pi\)
−0.275954 + 0.961171i \(0.588994\pi\)
\(294\) −493276. −0.332829
\(295\) 585792. 0.391912
\(296\) 721501. 0.478639
\(297\) 235877. 0.155165
\(298\) −259054. −0.168985
\(299\) −746639. −0.482984
\(300\) −90000.0 −0.0577350
\(301\) −107015. −0.0680812
\(302\) −1.98434e6 −1.25198
\(303\) 256803. 0.160692
\(304\) 92416.0 0.0573539
\(305\) 562182. 0.346041
\(306\) −399195. −0.243715
\(307\) −1.77216e6 −1.07314 −0.536572 0.843855i \(-0.680281\pi\)
−0.536572 + 0.843855i \(0.680281\pi\)
\(308\) −288470. −0.173270
\(309\) 1.48124e6 0.882532
\(310\) −482660. −0.285258
\(311\) −772132. −0.452679 −0.226339 0.974048i \(-0.572676\pi\)
−0.226339 + 0.974048i \(0.572676\pi\)
\(312\) 113888. 0.0662357
\(313\) −306148. −0.176632 −0.0883162 0.996092i \(-0.528149\pi\)
−0.0883162 + 0.996092i \(0.528149\pi\)
\(314\) 1.22672e6 0.702139
\(315\) 112836. 0.0640725
\(316\) −936119. −0.527367
\(317\) 120173. 0.0671675 0.0335838 0.999436i \(-0.489308\pi\)
0.0335838 + 0.999436i \(0.489308\pi\)
\(318\) 1.03607e6 0.574542
\(319\) 1.53260e6 0.843240
\(320\) 102400. 0.0559017
\(321\) 898846. 0.486881
\(322\) 841661. 0.452374
\(323\) 444783. 0.237215
\(324\) 104976. 0.0555556
\(325\) 123577. 0.0648975
\(326\) 1.21759e6 0.634539
\(327\) −1.68724e6 −0.872586
\(328\) 150602. 0.0772940
\(329\) −191994. −0.0977909
\(330\) −291206. −0.147202
\(331\) 2.29067e6 1.14919 0.574597 0.818437i \(-0.305159\pi\)
0.574597 + 0.818437i \(0.305159\pi\)
\(332\) −1.59946e6 −0.796393
\(333\) −913150. −0.451265
\(334\) 2.03374e6 0.997538
\(335\) 827549. 0.402885
\(336\) −128382. −0.0620379
\(337\) −2.00112e6 −0.959840 −0.479920 0.877312i \(-0.659334\pi\)
−0.479920 + 0.877312i \(0.659334\pi\)
\(338\) 1.32880e6 0.632654
\(339\) −614294. −0.290320
\(340\) 492834. 0.231208
\(341\) −1.56170e6 −0.727299
\(342\) −116964. −0.0540738
\(343\) −1.70001e6 −0.780220
\(344\) 122914. 0.0560021
\(345\) 849644. 0.384317
\(346\) 2.42230e6 1.08777
\(347\) 422685. 0.188449 0.0942243 0.995551i \(-0.469963\pi\)
0.0942243 + 0.995551i \(0.469963\pi\)
\(348\) 682077. 0.301915
\(349\) −99505.8 −0.0437305 −0.0218653 0.999761i \(-0.506960\pi\)
−0.0218653 + 0.999761i \(0.506960\pi\)
\(350\) −139304. −0.0607845
\(351\) −144140. −0.0624476
\(352\) 331327. 0.142528
\(353\) −1.81758e6 −0.776350 −0.388175 0.921586i \(-0.626894\pi\)
−0.388175 + 0.921586i \(0.626894\pi\)
\(354\) 843541. 0.357765
\(355\) 235904. 0.0993492
\(356\) −569378. −0.238109
\(357\) −617882. −0.256587
\(358\) 1.21100e6 0.499387
\(359\) 1.34275e6 0.549871 0.274935 0.961463i \(-0.411344\pi\)
0.274935 + 0.961463i \(0.411344\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −912327. −0.365914
\(363\) 507228. 0.202040
\(364\) 176278. 0.0697341
\(365\) 1.90546e6 0.748631
\(366\) 809543. 0.315891
\(367\) 904456. 0.350528 0.175264 0.984522i \(-0.443922\pi\)
0.175264 + 0.984522i \(0.443922\pi\)
\(368\) −966706. −0.372113
\(369\) −190605. −0.0728735
\(370\) 1.12735e6 0.428107
\(371\) 1.60365e6 0.604888
\(372\) −695031. −0.260403
\(373\) 4.63728e6 1.72580 0.862901 0.505373i \(-0.168645\pi\)
0.862901 + 0.505373i \(0.168645\pi\)
\(374\) 1.59462e6 0.589493
\(375\) −140625. −0.0516398
\(376\) 220519. 0.0804407
\(377\) −936541. −0.339370
\(378\) 162484. 0.0584899
\(379\) 3.96309e6 1.41722 0.708608 0.705602i \(-0.249323\pi\)
0.708608 + 0.705602i \(0.249323\pi\)
\(380\) 144400. 0.0512989
\(381\) 1.55024e6 0.547126
\(382\) 17885.0 0.00627092
\(383\) −2.03540e6 −0.709010 −0.354505 0.935054i \(-0.615351\pi\)
−0.354505 + 0.935054i \(0.615351\pi\)
\(384\) 147456. 0.0510310
\(385\) −450734. −0.154977
\(386\) −1.69782e6 −0.579993
\(387\) −155563. −0.0527993
\(388\) 1.21685e6 0.410352
\(389\) −2.59927e6 −0.870917 −0.435459 0.900209i \(-0.643414\pi\)
−0.435459 + 0.900209i \(0.643414\pi\)
\(390\) 177950. 0.0592430
\(391\) −4.65259e6 −1.53905
\(392\) 876935. 0.288239
\(393\) −1.26465e6 −0.413038
\(394\) 3.46488e6 1.12447
\(395\) −1.46269e6 −0.471692
\(396\) −419336. −0.134377
\(397\) −98354.5 −0.0313197 −0.0156599 0.999877i \(-0.504985\pi\)
−0.0156599 + 0.999877i \(0.504985\pi\)
\(398\) −3.55195e6 −1.12398
\(399\) −181039. −0.0569299
\(400\) 160000. 0.0500000
\(401\) 247336. 0.0768116 0.0384058 0.999262i \(-0.487772\pi\)
0.0384058 + 0.999262i \(0.487772\pi\)
\(402\) 1.19167e6 0.367782
\(403\) 954328. 0.292708
\(404\) −456539. −0.139163
\(405\) 164025. 0.0496904
\(406\) 1.05573e6 0.317862
\(407\) 3.64766e6 1.09151
\(408\) 709681. 0.211063
\(409\) 4.43935e6 1.31223 0.656117 0.754659i \(-0.272198\pi\)
0.656117 + 0.754659i \(0.272198\pi\)
\(410\) 235315. 0.0691338
\(411\) 2.00467e6 0.585382
\(412\) −2.63332e6 −0.764295
\(413\) 1.30565e6 0.376662
\(414\) 1.22349e6 0.350831
\(415\) −2.49915e6 −0.712315
\(416\) −202468. −0.0573618
\(417\) 3.57534e6 1.00688
\(418\) 467223. 0.130793
\(419\) −2.66341e6 −0.741146 −0.370573 0.928803i \(-0.620839\pi\)
−0.370573 + 0.928803i \(0.620839\pi\)
\(420\) −200597. −0.0554884
\(421\) 1.50786e6 0.414626 0.207313 0.978275i \(-0.433528\pi\)
0.207313 + 0.978275i \(0.433528\pi\)
\(422\) 935952. 0.255842
\(423\) −279094. −0.0758402
\(424\) −1.84190e6 −0.497568
\(425\) 770053. 0.206799
\(426\) 339702. 0.0906930
\(427\) 1.25303e6 0.332576
\(428\) −1.59795e6 −0.421651
\(429\) 575779. 0.151047
\(430\) 192053. 0.0500898
\(431\) 2.72245e6 0.705937 0.352969 0.935635i \(-0.385172\pi\)
0.352969 + 0.935635i \(0.385172\pi\)
\(432\) −186624. −0.0481125
\(433\) 527935. 0.135320 0.0676598 0.997708i \(-0.478447\pi\)
0.0676598 + 0.997708i \(0.478447\pi\)
\(434\) −1.07578e6 −0.274157
\(435\) 1.06574e6 0.270041
\(436\) 2.99954e6 0.755682
\(437\) −1.36321e6 −0.341474
\(438\) 2.74386e6 0.683403
\(439\) −5.25839e6 −1.30224 −0.651121 0.758974i \(-0.725701\pi\)
−0.651121 + 0.758974i \(0.725701\pi\)
\(440\) 517699. 0.127481
\(441\) −1.10987e6 −0.271754
\(442\) −974443. −0.237247
\(443\) −4.05256e6 −0.981116 −0.490558 0.871408i \(-0.663207\pi\)
−0.490558 + 0.871408i \(0.663207\pi\)
\(444\) 1.62338e6 0.390807
\(445\) −889653. −0.212971
\(446\) 1.71690e6 0.408704
\(447\) −582871. −0.137976
\(448\) 228235. 0.0537264
\(449\) 2.18810e6 0.512214 0.256107 0.966648i \(-0.417560\pi\)
0.256107 + 0.966648i \(0.417560\pi\)
\(450\) −202500. −0.0471405
\(451\) 761391. 0.176265
\(452\) 1.09208e6 0.251425
\(453\) −4.46476e6 −1.02224
\(454\) 1.07824e6 0.245514
\(455\) 275435. 0.0623721
\(456\) 207936. 0.0468293
\(457\) 5.70254e6 1.27726 0.638628 0.769516i \(-0.279502\pi\)
0.638628 + 0.769516i \(0.279502\pi\)
\(458\) 4.32963e6 0.964467
\(459\) −898190. −0.198992
\(460\) −1.51048e6 −0.332828
\(461\) 5.34460e6 1.17129 0.585643 0.810569i \(-0.300842\pi\)
0.585643 + 0.810569i \(0.300842\pi\)
\(462\) −649057. −0.141474
\(463\) −7.83396e6 −1.69836 −0.849179 0.528106i \(-0.822902\pi\)
−0.849179 + 0.528106i \(0.822902\pi\)
\(464\) −1.21258e6 −0.261466
\(465\) −1.08599e6 −0.232912
\(466\) 4.20068e6 0.896096
\(467\) 1.90391e6 0.403974 0.201987 0.979388i \(-0.435260\pi\)
0.201987 + 0.979388i \(0.435260\pi\)
\(468\) 256248. 0.0540812
\(469\) 1.84449e6 0.387208
\(470\) 344561. 0.0719484
\(471\) 2.76013e6 0.573294
\(472\) −1.49963e6 −0.309834
\(473\) 621410. 0.127710
\(474\) −2.10627e6 −0.430594
\(475\) 225625. 0.0458831
\(476\) 1.09846e6 0.222211
\(477\) 2.33116e6 0.469112
\(478\) −5.82142e6 −1.16536
\(479\) −4.60771e6 −0.917585 −0.458792 0.888544i \(-0.651718\pi\)
−0.458792 + 0.888544i \(0.651718\pi\)
\(480\) 230400. 0.0456435
\(481\) −2.22902e6 −0.439289
\(482\) 1.74624e6 0.342363
\(483\) 1.89374e6 0.369362
\(484\) −901739. −0.174972
\(485\) 1.90132e6 0.367030
\(486\) 236196. 0.0453609
\(487\) −6.14863e6 −1.17478 −0.587389 0.809305i \(-0.699844\pi\)
−0.587389 + 0.809305i \(0.699844\pi\)
\(488\) −1.43919e6 −0.273569
\(489\) 2.73958e6 0.518099
\(490\) 1.37021e6 0.257809
\(491\) −4.44651e6 −0.832369 −0.416184 0.909280i \(-0.636633\pi\)
−0.416184 + 0.909280i \(0.636633\pi\)
\(492\) 338854. 0.0631103
\(493\) −5.83595e6 −1.08142
\(494\) −285511. −0.0526388
\(495\) −655213. −0.120190
\(496\) 1.23561e6 0.225516
\(497\) 525797. 0.0954832
\(498\) −3.59878e6 −0.650252
\(499\) 7.39955e6 1.33031 0.665156 0.746704i \(-0.268365\pi\)
0.665156 + 0.746704i \(0.268365\pi\)
\(500\) 250000. 0.0447214
\(501\) 4.57592e6 0.814486
\(502\) 6.35595e6 1.12570
\(503\) 2.46864e6 0.435048 0.217524 0.976055i \(-0.430202\pi\)
0.217524 + 0.976055i \(0.430202\pi\)
\(504\) −288860. −0.0506537
\(505\) −713342. −0.124471
\(506\) −4.88733e6 −0.848585
\(507\) 2.98979e6 0.516560
\(508\) −2.75599e6 −0.473825
\(509\) −2.12404e6 −0.363386 −0.181693 0.983355i \(-0.558158\pi\)
−0.181693 + 0.983355i \(0.558158\pi\)
\(510\) 1.10888e6 0.188781
\(511\) 4.24701e6 0.719500
\(512\) −262144. −0.0441942
\(513\) −263169. −0.0441511
\(514\) −1.03824e6 −0.173336
\(515\) −4.11457e6 −0.683606
\(516\) 276556. 0.0457255
\(517\) 1.11487e6 0.183441
\(518\) 2.51270e6 0.411448
\(519\) 5.45019e6 0.888163
\(520\) −316356. −0.0513060
\(521\) 2.05370e6 0.331469 0.165735 0.986170i \(-0.447000\pi\)
0.165735 + 0.986170i \(0.447000\pi\)
\(522\) 1.53467e6 0.246513
\(523\) 1.21833e7 1.94765 0.973827 0.227289i \(-0.0729863\pi\)
0.973827 + 0.227289i \(0.0729863\pi\)
\(524\) 2.24827e6 0.357702
\(525\) −313433. −0.0496303
\(526\) 6.63184e6 1.04513
\(527\) 5.94678e6 0.932729
\(528\) 745487. 0.116374
\(529\) 7.82330e6 1.21549
\(530\) −2.87798e6 −0.445038
\(531\) 1.89797e6 0.292114
\(532\) 321847. 0.0493027
\(533\) −465271. −0.0709395
\(534\) −1.28110e6 −0.194415
\(535\) −2.49680e6 −0.377136
\(536\) −2.11852e6 −0.318509
\(537\) 2.72475e6 0.407748
\(538\) 3.81472e6 0.568208
\(539\) 4.43348e6 0.657314
\(540\) −291600. −0.0430331
\(541\) −2.20773e6 −0.324304 −0.162152 0.986766i \(-0.551843\pi\)
−0.162152 + 0.986766i \(0.551843\pi\)
\(542\) −6.04407e6 −0.883753
\(543\) −2.05274e6 −0.298768
\(544\) −1.26165e6 −0.182786
\(545\) 4.68679e6 0.675902
\(546\) 396626. 0.0569377
\(547\) 387887. 0.0554290 0.0277145 0.999616i \(-0.491177\pi\)
0.0277145 + 0.999616i \(0.491177\pi\)
\(548\) −3.56386e6 −0.506955
\(549\) 1.82147e6 0.257924
\(550\) 808905. 0.114023
\(551\) −1.70993e6 −0.239938
\(552\) −2.17509e6 −0.303829
\(553\) −3.26012e6 −0.453337
\(554\) −6.43657e6 −0.891005
\(555\) 2.53653e6 0.349548
\(556\) −6.35616e6 −0.871983
\(557\) 5.31812e6 0.726307 0.363154 0.931729i \(-0.381700\pi\)
0.363154 + 0.931729i \(0.381700\pi\)
\(558\) −1.56382e6 −0.212618
\(559\) −379732. −0.0513981
\(560\) 356618. 0.0480544
\(561\) 3.58790e6 0.481319
\(562\) 4.41336e6 0.589424
\(563\) −1.31055e7 −1.74254 −0.871271 0.490802i \(-0.836704\pi\)
−0.871271 + 0.490802i \(0.836704\pi\)
\(564\) 496167. 0.0656796
\(565\) 1.70637e6 0.224881
\(566\) 6.94204e6 0.910848
\(567\) 365589. 0.0477568
\(568\) −603914. −0.0785424
\(569\) 7.43591e6 0.962839 0.481419 0.876490i \(-0.340121\pi\)
0.481419 + 0.876490i \(0.340121\pi\)
\(570\) 324900. 0.0418854
\(571\) −1.06829e7 −1.37119 −0.685595 0.727983i \(-0.740458\pi\)
−0.685595 + 0.727983i \(0.740458\pi\)
\(572\) −1.02361e6 −0.130811
\(573\) 40241.3 0.00512019
\(574\) 524485. 0.0664436
\(575\) −2.36012e6 −0.297690
\(576\) 331776. 0.0416667
\(577\) 1.56085e7 1.95174 0.975868 0.218361i \(-0.0700709\pi\)
0.975868 + 0.218361i \(0.0700709\pi\)
\(578\) −392701. −0.0488925
\(579\) −3.82009e6 −0.473562
\(580\) −1.89466e6 −0.233863
\(581\) −5.57026e6 −0.684597
\(582\) 2.73790e6 0.335051
\(583\) −9.31203e6 −1.13468
\(584\) −4.87798e6 −0.591845
\(585\) 400388. 0.0483717
\(586\) 3.24411e6 0.390258
\(587\) −1.29739e7 −1.55408 −0.777041 0.629450i \(-0.783280\pi\)
−0.777041 + 0.629450i \(0.783280\pi\)
\(588\) 1.97310e6 0.235346
\(589\) 1.74240e6 0.206948
\(590\) −2.34317e6 −0.277124
\(591\) 7.79598e6 0.918125
\(592\) −2.88600e6 −0.338449
\(593\) −1.28984e7 −1.50626 −0.753130 0.657871i \(-0.771457\pi\)
−0.753130 + 0.657871i \(0.771457\pi\)
\(594\) −943507. −0.109718
\(595\) 1.71634e6 0.198752
\(596\) 1.03622e6 0.119491
\(597\) −7.99190e6 −0.917728
\(598\) 2.98655e6 0.341521
\(599\) −1.65848e7 −1.88862 −0.944308 0.329063i \(-0.893267\pi\)
−0.944308 + 0.329063i \(0.893267\pi\)
\(600\) 360000. 0.0408248
\(601\) −103666. −0.0117071 −0.00585357 0.999983i \(-0.501863\pi\)
−0.00585357 + 0.999983i \(0.501863\pi\)
\(602\) 428059. 0.0481407
\(603\) 2.68126e6 0.300293
\(604\) 7.93735e6 0.885285
\(605\) −1.40897e6 −0.156499
\(606\) −1.02721e6 −0.113626
\(607\) −6.89646e6 −0.759721 −0.379861 0.925044i \(-0.624028\pi\)
−0.379861 + 0.925044i \(0.624028\pi\)
\(608\) −369664. −0.0405554
\(609\) 2.37540e6 0.259533
\(610\) −2.24873e6 −0.244688
\(611\) −681274. −0.0738276
\(612\) 1.59678e6 0.172332
\(613\) −1.09253e7 −1.17431 −0.587154 0.809475i \(-0.699752\pi\)
−0.587154 + 0.809475i \(0.699752\pi\)
\(614\) 7.08866e6 0.758827
\(615\) 529460. 0.0564475
\(616\) 1.15388e6 0.122520
\(617\) 1.55281e6 0.164212 0.0821060 0.996624i \(-0.473835\pi\)
0.0821060 + 0.996624i \(0.473835\pi\)
\(618\) −5.92498e6 −0.624044
\(619\) −1.08260e7 −1.13565 −0.567823 0.823150i \(-0.692214\pi\)
−0.567823 + 0.823150i \(0.692214\pi\)
\(620\) 1.93064e6 0.201708
\(621\) 2.75285e6 0.286453
\(622\) 3.08853e6 0.320092
\(623\) −1.98291e6 −0.204684
\(624\) −455553. −0.0468357
\(625\) 390625. 0.0400000
\(626\) 1.22459e6 0.124898
\(627\) 1.05125e6 0.106792
\(628\) −4.90690e6 −0.496487
\(629\) −1.38898e7 −1.39982
\(630\) −451344. −0.0453061
\(631\) 9.72446e6 0.972282 0.486141 0.873880i \(-0.338404\pi\)
0.486141 + 0.873880i \(0.338404\pi\)
\(632\) 3.74448e6 0.372905
\(633\) 2.10589e6 0.208894
\(634\) −480693. −0.0474946
\(635\) −4.30623e6 −0.423802
\(636\) −4.14428e6 −0.406263
\(637\) −2.70922e6 −0.264542
\(638\) −6.13039e6 −0.596261
\(639\) 764329. 0.0740505
\(640\) −409600. −0.0395285
\(641\) −1.50759e6 −0.144923 −0.0724615 0.997371i \(-0.523085\pi\)
−0.0724615 + 0.997371i \(0.523085\pi\)
\(642\) −3.59538e6 −0.344277
\(643\) −1.91979e7 −1.83116 −0.915582 0.402132i \(-0.868269\pi\)
−0.915582 + 0.402132i \(0.868269\pi\)
\(644\) −3.36664e6 −0.319877
\(645\) 432119. 0.0408982
\(646\) −1.77913e6 −0.167736
\(647\) 6.64303e6 0.623886 0.311943 0.950101i \(-0.399020\pi\)
0.311943 + 0.950101i \(0.399020\pi\)
\(648\) −419904. −0.0392837
\(649\) −7.58160e6 −0.706560
\(650\) −494306. −0.0458894
\(651\) −2.42051e6 −0.223849
\(652\) −4.87037e6 −0.448687
\(653\) −1.85251e7 −1.70011 −0.850055 0.526694i \(-0.823431\pi\)
−0.850055 + 0.526694i \(0.823431\pi\)
\(654\) 6.74897e6 0.617012
\(655\) 3.51293e6 0.319938
\(656\) −602407. −0.0546551
\(657\) 6.17369e6 0.557997
\(658\) 767977. 0.0691486
\(659\) 1.15464e6 0.103570 0.0517848 0.998658i \(-0.483509\pi\)
0.0517848 + 0.998658i \(0.483509\pi\)
\(660\) 1.16482e6 0.104088
\(661\) −7.84013e6 −0.697943 −0.348971 0.937133i \(-0.613469\pi\)
−0.348971 + 0.937133i \(0.613469\pi\)
\(662\) −9.16270e6 −0.812603
\(663\) −2.19250e6 −0.193711
\(664\) 6.39783e6 0.563135
\(665\) 502887. 0.0440977
\(666\) 3.65260e6 0.319092
\(667\) 1.78865e7 1.55672
\(668\) −8.13496e6 −0.705366
\(669\) 3.86303e6 0.333705
\(670\) −3.31019e6 −0.284883
\(671\) −7.27603e6 −0.623862
\(672\) 513529. 0.0438674
\(673\) 1.33341e7 1.13482 0.567410 0.823435i \(-0.307945\pi\)
0.567410 + 0.823435i \(0.307945\pi\)
\(674\) 8.00449e6 0.678709
\(675\) −455625. −0.0384900
\(676\) −5.31518e6 −0.447354
\(677\) 1.75174e7 1.46892 0.734458 0.678654i \(-0.237437\pi\)
0.734458 + 0.678654i \(0.237437\pi\)
\(678\) 2.45718e6 0.205287
\(679\) 4.23778e6 0.352748
\(680\) −1.97134e6 −0.163489
\(681\) 2.42605e6 0.200462
\(682\) 6.24682e6 0.514278
\(683\) 1.67243e7 1.37182 0.685910 0.727687i \(-0.259404\pi\)
0.685910 + 0.727687i \(0.259404\pi\)
\(684\) 467856. 0.0382360
\(685\) −5.56854e6 −0.453435
\(686\) 6.80006e6 0.551699
\(687\) 9.74167e6 0.787484
\(688\) −491655. −0.0395995
\(689\) 5.69041e6 0.456662
\(690\) −3.39857e6 −0.271753
\(691\) −2.04176e7 −1.62671 −0.813354 0.581769i \(-0.802361\pi\)
−0.813354 + 0.581769i \(0.802361\pi\)
\(692\) −9.68922e6 −0.769172
\(693\) −1.46038e6 −0.115513
\(694\) −1.69074e6 −0.133253
\(695\) −9.93151e6 −0.779925
\(696\) −2.72831e6 −0.213486
\(697\) −2.89928e6 −0.226052
\(698\) 398023. 0.0309222
\(699\) 9.45152e6 0.731659
\(700\) 557215. 0.0429811
\(701\) 5.75032e6 0.441975 0.220987 0.975277i \(-0.429072\pi\)
0.220987 + 0.975277i \(0.429072\pi\)
\(702\) 576559. 0.0441571
\(703\) −4.06972e6 −0.310582
\(704\) −1.32531e6 −0.100783
\(705\) 775261. 0.0587456
\(706\) 7.27033e6 0.548962
\(707\) −1.58994e6 −0.119628
\(708\) −3.37416e6 −0.252978
\(709\) −2.56404e6 −0.191562 −0.0957811 0.995402i \(-0.530535\pi\)
−0.0957811 + 0.995402i \(0.530535\pi\)
\(710\) −943616. −0.0702505
\(711\) −4.73910e6 −0.351578
\(712\) 2.27751e6 0.168368
\(713\) −1.82262e7 −1.34268
\(714\) 2.47153e6 0.181435
\(715\) −1.59939e6 −0.117001
\(716\) −4.84401e6 −0.353120
\(717\) −1.30982e7 −0.951511
\(718\) −5.37102e6 −0.388817
\(719\) 5.85540e6 0.422410 0.211205 0.977442i \(-0.432261\pi\)
0.211205 + 0.977442i \(0.432261\pi\)
\(720\) 518400. 0.0372678
\(721\) −9.17079e6 −0.657005
\(722\) −521284. −0.0372161
\(723\) 3.92905e6 0.279538
\(724\) 3.64931e6 0.258740
\(725\) −2.96040e6 −0.209173
\(726\) −2.02891e6 −0.142864
\(727\) 1.97861e7 1.38843 0.694214 0.719768i \(-0.255752\pi\)
0.694214 + 0.719768i \(0.255752\pi\)
\(728\) −705113. −0.0493095
\(729\) 531441. 0.0370370
\(730\) −7.62184e6 −0.529362
\(731\) −2.36625e6 −0.163783
\(732\) −3.23817e6 −0.223369
\(733\) −1.19040e6 −0.0818337 −0.0409168 0.999163i \(-0.513028\pi\)
−0.0409168 + 0.999163i \(0.513028\pi\)
\(734\) −3.61782e6 −0.247860
\(735\) 3.08298e6 0.210500
\(736\) 3.86682e6 0.263124
\(737\) −1.07105e7 −0.726344
\(738\) 762422. 0.0515293
\(739\) −2.38479e7 −1.60634 −0.803172 0.595747i \(-0.796856\pi\)
−0.803172 + 0.595747i \(0.796856\pi\)
\(740\) −4.50938e6 −0.302718
\(741\) −642400. −0.0429794
\(742\) −6.41461e6 −0.427721
\(743\) 7.43500e6 0.494093 0.247047 0.969004i \(-0.420540\pi\)
0.247047 + 0.969004i \(0.420540\pi\)
\(744\) 2.78012e6 0.184133
\(745\) 1.61909e6 0.106876
\(746\) −1.85491e7 −1.22033
\(747\) −8.09725e6 −0.530929
\(748\) −6.37849e6 −0.416835
\(749\) −5.56501e6 −0.362461
\(750\) 562500. 0.0365148
\(751\) −3.11090e6 −0.201273 −0.100637 0.994923i \(-0.532088\pi\)
−0.100637 + 0.994923i \(0.532088\pi\)
\(752\) −882075. −0.0568802
\(753\) 1.43009e7 0.919127
\(754\) 3.74616e6 0.239971
\(755\) 1.24021e7 0.791823
\(756\) −649936. −0.0413586
\(757\) −5.43869e6 −0.344948 −0.172474 0.985014i \(-0.555176\pi\)
−0.172474 + 0.985014i \(0.555176\pi\)
\(758\) −1.58524e7 −1.00212
\(759\) −1.09965e7 −0.692867
\(760\) −577600. −0.0362738
\(761\) 1.55660e7 0.974354 0.487177 0.873303i \(-0.338027\pi\)
0.487177 + 0.873303i \(0.338027\pi\)
\(762\) −6.20097e6 −0.386876
\(763\) 1.04462e7 0.649601
\(764\) −71540.2 −0.00443421
\(765\) 2.49497e6 0.154139
\(766\) 8.14160e6 0.501346
\(767\) 4.63297e6 0.284362
\(768\) −589824. −0.0360844
\(769\) 7.42681e6 0.452884 0.226442 0.974025i \(-0.427291\pi\)
0.226442 + 0.974025i \(0.427291\pi\)
\(770\) 1.80294e6 0.109586
\(771\) −2.33604e6 −0.141528
\(772\) 6.79126e6 0.410117
\(773\) 1.01626e7 0.611724 0.305862 0.952076i \(-0.401055\pi\)
0.305862 + 0.952076i \(0.401055\pi\)
\(774\) 622251. 0.0373347
\(775\) 3.01663e6 0.180413
\(776\) −4.86739e6 −0.290163
\(777\) 5.65356e6 0.335946
\(778\) 1.03971e7 0.615831
\(779\) −849488. −0.0501549
\(780\) −711801. −0.0418911
\(781\) −3.05318e6 −0.179112
\(782\) 1.86104e7 1.08827
\(783\) 3.45301e6 0.201277
\(784\) −3.50774e6 −0.203816
\(785\) −7.66703e6 −0.444072
\(786\) 5.05862e6 0.292062
\(787\) −1.03062e6 −0.0593148 −0.0296574 0.999560i \(-0.509442\pi\)
−0.0296574 + 0.999560i \(0.509442\pi\)
\(788\) −1.38595e7 −0.795120
\(789\) 1.49216e7 0.853344
\(790\) 5.85074e6 0.333536
\(791\) 3.80327e6 0.216130
\(792\) 1.67734e6 0.0950188
\(793\) 4.44624e6 0.251079
\(794\) 393418. 0.0221464
\(795\) −6.47544e6 −0.363372
\(796\) 1.42078e7 0.794776
\(797\) −1.61275e7 −0.899332 −0.449666 0.893197i \(-0.648457\pi\)
−0.449666 + 0.893197i \(0.648457\pi\)
\(798\) 724157. 0.0402555
\(799\) −4.24528e6 −0.235255
\(800\) −640000. −0.0353553
\(801\) −2.88248e6 −0.158739
\(802\) −989345. −0.0543140
\(803\) −2.46614e7 −1.34967
\(804\) −4.76668e6 −0.260061
\(805\) −5.26038e6 −0.286106
\(806\) −3.81731e6 −0.206976
\(807\) 8.58312e6 0.463940
\(808\) 1.82615e6 0.0984032
\(809\) 6.31826e6 0.339411 0.169706 0.985495i \(-0.445718\pi\)
0.169706 + 0.985495i \(0.445718\pi\)
\(810\) −656100. −0.0351364
\(811\) −2.13453e6 −0.113959 −0.0569796 0.998375i \(-0.518147\pi\)
−0.0569796 + 0.998375i \(0.518147\pi\)
\(812\) −4.22293e6 −0.224762
\(813\) −1.35992e7 −0.721582
\(814\) −1.45906e7 −0.771815
\(815\) −7.60995e6 −0.401317
\(816\) −2.83872e6 −0.149244
\(817\) −693311. −0.0363390
\(818\) −1.77574e7 −0.927890
\(819\) 892409. 0.0464894
\(820\) −941261. −0.0488850
\(821\) 3.60470e7 1.86643 0.933214 0.359322i \(-0.116992\pi\)
0.933214 + 0.359322i \(0.116992\pi\)
\(822\) −8.01869e6 −0.413927
\(823\) −3.39430e7 −1.74683 −0.873416 0.486975i \(-0.838100\pi\)
−0.873416 + 0.486975i \(0.838100\pi\)
\(824\) 1.05333e7 0.540438
\(825\) 1.82004e6 0.0930990
\(826\) −5.22260e6 −0.266340
\(827\) 2.54773e7 1.29536 0.647680 0.761913i \(-0.275740\pi\)
0.647680 + 0.761913i \(0.275740\pi\)
\(828\) −4.89395e6 −0.248075
\(829\) 1.13108e7 0.571622 0.285811 0.958286i \(-0.407737\pi\)
0.285811 + 0.958286i \(0.407737\pi\)
\(830\) 9.99661e6 0.503683
\(831\) −1.44823e7 −0.727503
\(832\) 809871. 0.0405609
\(833\) −1.68822e7 −0.842977
\(834\) −1.43014e7 −0.711971
\(835\) −1.27109e7 −0.630898
\(836\) −1.86889e6 −0.0924845
\(837\) −3.51859e6 −0.173602
\(838\) 1.06537e7 0.524069
\(839\) 3.41934e6 0.167702 0.0838509 0.996478i \(-0.473278\pi\)
0.0838509 + 0.996478i \(0.473278\pi\)
\(840\) 802390. 0.0392362
\(841\) 1.92465e6 0.0938342
\(842\) −6.03146e6 −0.293185
\(843\) 9.93005e6 0.481263
\(844\) −3.74381e6 −0.180908
\(845\) −8.30497e6 −0.400126
\(846\) 1.11638e6 0.0536271
\(847\) −3.14039e6 −0.150409
\(848\) 7.36762e6 0.351834
\(849\) 1.56196e7 0.743704
\(850\) −3.08021e6 −0.146229
\(851\) 4.25707e7 2.01506
\(852\) −1.35881e6 −0.0641296
\(853\) 3.52352e6 0.165807 0.0829037 0.996558i \(-0.473581\pi\)
0.0829037 + 0.996558i \(0.473581\pi\)
\(854\) −5.01210e6 −0.235166
\(855\) 731025. 0.0341993
\(856\) 6.39180e6 0.298152
\(857\) 1.07382e7 0.499434 0.249717 0.968319i \(-0.419662\pi\)
0.249717 + 0.968319i \(0.419662\pi\)
\(858\) −2.30312e6 −0.106807
\(859\) 3.74704e7 1.73263 0.866313 0.499501i \(-0.166483\pi\)
0.866313 + 0.499501i \(0.166483\pi\)
\(860\) −768211. −0.0354189
\(861\) 1.18009e6 0.0542510
\(862\) −1.08898e7 −0.499173
\(863\) 7.80040e6 0.356525 0.178262 0.983983i \(-0.442952\pi\)
0.178262 + 0.983983i \(0.442952\pi\)
\(864\) 746496. 0.0340207
\(865\) −1.51394e7 −0.687968
\(866\) −2.11174e6 −0.0956854
\(867\) −883577. −0.0399206
\(868\) 4.30313e6 0.193859
\(869\) 1.89308e7 0.850392
\(870\) −4.26298e6 −0.190948
\(871\) 6.54500e6 0.292324
\(872\) −1.19982e7 −0.534348
\(873\) 6.16029e6 0.273568
\(874\) 5.45282e6 0.241459
\(875\) 870649. 0.0384435
\(876\) −1.09755e7 −0.483239
\(877\) −3.39330e7 −1.48978 −0.744891 0.667186i \(-0.767499\pi\)
−0.744891 + 0.667186i \(0.767499\pi\)
\(878\) 2.10336e7 0.920824
\(879\) 7.29925e6 0.318644
\(880\) −2.07080e6 −0.0901427
\(881\) 3.75147e6 0.162840 0.0814202 0.996680i \(-0.474054\pi\)
0.0814202 + 0.996680i \(0.474054\pi\)
\(882\) 4.43948e6 0.192159
\(883\) −3.16434e7 −1.36578 −0.682891 0.730520i \(-0.739278\pi\)
−0.682891 + 0.730520i \(0.739278\pi\)
\(884\) 3.89777e6 0.167759
\(885\) −5.27213e6 −0.226271
\(886\) 1.62103e7 0.693754
\(887\) 2.22713e7 0.950468 0.475234 0.879860i \(-0.342363\pi\)
0.475234 + 0.879860i \(0.342363\pi\)
\(888\) −6.49351e6 −0.276342
\(889\) −9.59798e6 −0.407310
\(890\) 3.55861e6 0.150593
\(891\) −2.12289e6 −0.0895846
\(892\) −6.86761e6 −0.288997
\(893\) −1.24386e6 −0.0521968
\(894\) 2.33148e6 0.0975638
\(895\) −7.56876e6 −0.315840
\(896\) −912941. −0.0379903
\(897\) 6.71975e6 0.278851
\(898\) −8.75239e6 −0.362190
\(899\) −2.28619e7 −0.943437
\(900\) 810000. 0.0333333
\(901\) 3.54591e7 1.45518
\(902\) −3.04556e6 −0.124638
\(903\) 963132. 0.0393067
\(904\) −4.36832e6 −0.177784
\(905\) 5.70204e6 0.231424
\(906\) 1.78590e7 0.722832
\(907\) 1.96192e7 0.791886 0.395943 0.918275i \(-0.370418\pi\)
0.395943 + 0.918275i \(0.370418\pi\)
\(908\) −4.31297e6 −0.173605
\(909\) −2.31123e6 −0.0927754
\(910\) −1.10174e6 −0.0441037
\(911\) 1.51503e7 0.604818 0.302409 0.953178i \(-0.402209\pi\)
0.302409 + 0.953178i \(0.402209\pi\)
\(912\) −831744. −0.0331133
\(913\) 3.23452e7 1.28420
\(914\) −2.28102e7 −0.903156
\(915\) −5.05964e6 −0.199787
\(916\) −1.73185e7 −0.681981
\(917\) 7.82983e6 0.307488
\(918\) 3.59276e6 0.140709
\(919\) −4.82506e7 −1.88458 −0.942289 0.334800i \(-0.891331\pi\)
−0.942289 + 0.334800i \(0.891331\pi\)
\(920\) 6.04191e6 0.235345
\(921\) 1.59495e7 0.619580
\(922\) −2.13784e7 −0.828224
\(923\) 1.86574e6 0.0720854
\(924\) 2.59623e6 0.100037
\(925\) −7.04591e6 −0.270759
\(926\) 3.13359e7 1.20092
\(927\) −1.33312e7 −0.509530
\(928\) 4.85032e6 0.184885
\(929\) −1.93067e7 −0.733956 −0.366978 0.930230i \(-0.619608\pi\)
−0.366978 + 0.930230i \(0.619608\pi\)
\(930\) 4.34394e6 0.164694
\(931\) −4.94646e6 −0.187034
\(932\) −1.68027e7 −0.633636
\(933\) 6.94918e6 0.261354
\(934\) −7.61562e6 −0.285653
\(935\) −9.96639e6 −0.372828
\(936\) −1.02499e6 −0.0382412
\(937\) 4.97419e7 1.85086 0.925430 0.378919i \(-0.123704\pi\)
0.925430 + 0.378919i \(0.123704\pi\)
\(938\) −7.37796e6 −0.273797
\(939\) 2.75533e6 0.101979
\(940\) −1.37824e6 −0.0508752
\(941\) 2.66909e6 0.0982630 0.0491315 0.998792i \(-0.484355\pi\)
0.0491315 + 0.998792i \(0.484355\pi\)
\(942\) −1.10405e7 −0.405380
\(943\) 8.88596e6 0.325406
\(944\) 5.99851e6 0.219086
\(945\) −1.01552e6 −0.0369923
\(946\) −2.48564e6 −0.0903047
\(947\) 2.16503e7 0.784493 0.392247 0.919860i \(-0.371698\pi\)
0.392247 + 0.919860i \(0.371698\pi\)
\(948\) 8.42507e6 0.304476
\(949\) 1.50701e7 0.543188
\(950\) −902500. −0.0324443
\(951\) −1.08156e6 −0.0387792
\(952\) −4.39383e6 −0.157127
\(953\) −2.37305e6 −0.0846398 −0.0423199 0.999104i \(-0.513475\pi\)
−0.0423199 + 0.999104i \(0.513475\pi\)
\(954\) −9.32464e6 −0.331712
\(955\) −111782. −0.00396608
\(956\) 2.32857e7 0.824032
\(957\) −1.37934e7 −0.486845
\(958\) 1.84308e7 0.648830
\(959\) −1.24115e7 −0.435790
\(960\) −921600. −0.0322749
\(961\) −5.33306e6 −0.186281
\(962\) 8.91606e6 0.310624
\(963\) −8.08962e6 −0.281101
\(964\) −6.98497e6 −0.242087
\(965\) 1.06114e7 0.366819
\(966\) −7.57495e6 −0.261178
\(967\) 1.12757e7 0.387774 0.193887 0.981024i \(-0.437890\pi\)
0.193887 + 0.981024i \(0.437890\pi\)
\(968\) 3.60696e6 0.123724
\(969\) −4.00304e6 −0.136956
\(970\) −7.60529e6 −0.259529
\(971\) −4.25830e7 −1.44940 −0.724699 0.689065i \(-0.758021\pi\)
−0.724699 + 0.689065i \(0.758021\pi\)
\(972\) −944784. −0.0320750
\(973\) −2.21359e7 −0.749576
\(974\) 2.45945e7 0.830693
\(975\) −1.11219e6 −0.0374686
\(976\) 5.75675e6 0.193443
\(977\) 2.96822e7 0.994855 0.497427 0.867506i \(-0.334278\pi\)
0.497427 + 0.867506i \(0.334278\pi\)
\(978\) −1.09583e7 −0.366351
\(979\) 1.15143e7 0.383956
\(980\) −5.48085e6 −0.182298
\(981\) 1.51852e7 0.503788
\(982\) 1.77861e7 0.588574
\(983\) −2.44497e7 −0.807029 −0.403515 0.914973i \(-0.632212\pi\)
−0.403515 + 0.914973i \(0.632212\pi\)
\(984\) −1.35542e6 −0.0446257
\(985\) −2.16555e7 −0.711177
\(986\) 2.33438e7 0.764679
\(987\) 1.72795e6 0.0564596
\(988\) 1.14205e6 0.0372212
\(989\) 7.25229e6 0.235768
\(990\) 2.62085e6 0.0849874
\(991\) 2.05824e7 0.665752 0.332876 0.942971i \(-0.391981\pi\)
0.332876 + 0.942971i \(0.391981\pi\)
\(992\) −4.94244e6 −0.159464
\(993\) −2.06161e7 −0.663487
\(994\) −2.10319e6 −0.0675168
\(995\) 2.21997e7 0.710869
\(996\) 1.43951e7 0.459798
\(997\) −1.80814e7 −0.576094 −0.288047 0.957616i \(-0.593006\pi\)
−0.288047 + 0.957616i \(0.593006\pi\)
\(998\) −2.95982e7 −0.940673
\(999\) 8.21835e6 0.260538
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 570.6.a.j.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.j.1.3 4 1.1 even 1 trivial