Properties

Label 43.6.a.b.1.5
Level 43
Weight 6
Character 43.1
Self dual yes
Analytic conductor 6.897
Analytic rank 0
Dimension 10
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.86024\) of \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +O(q^{10})\) \(q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +78.5700 q^{10} +436.853 q^{11} +424.428 q^{12} -617.704 q^{13} -377.575 q^{14} +628.124 q^{15} +703.768 q^{16} +833.458 q^{17} +40.6196 q^{18} +1356.52 q^{19} +1205.41 q^{20} -3018.51 q^{21} -812.652 q^{22} -904.822 q^{23} -1674.81 q^{24} -1341.08 q^{25} +1149.08 q^{26} +3938.53 q^{27} -5792.70 q^{28} +5326.52 q^{29} -1168.46 q^{30} +919.124 q^{31} -4912.95 q^{32} -6496.71 q^{33} -1550.43 q^{34} -8572.80 q^{35} +623.180 q^{36} +4962.82 q^{37} -2523.46 q^{38} +9186.24 q^{39} -4756.59 q^{40} -5931.38 q^{41} +5615.15 q^{42} +1849.00 q^{43} -12467.6 q^{44} +922.264 q^{45} +1683.19 q^{46} +17815.9 q^{47} -10466.2 q^{48} +24390.4 q^{49} +2494.73 q^{50} -12394.9 q^{51} +17629.0 q^{52} +24713.3 q^{53} -7326.61 q^{54} -18451.2 q^{55} +22858.2 q^{56} -20173.7 q^{57} -9908.61 q^{58} +33834.6 q^{59} -17926.4 q^{60} +45948.5 q^{61} -1709.79 q^{62} -4432.02 q^{63} -13381.3 q^{64} +26089.6 q^{65} +12085.4 q^{66} -58523.0 q^{67} -23786.5 q^{68} +13456.1 q^{69} +15947.5 q^{70} +1792.64 q^{71} -2459.09 q^{72} -46710.3 q^{73} -9232.03 q^{74} +19944.0 q^{75} -38714.5 q^{76} +88668.8 q^{77} -17088.6 q^{78} -79459.7 q^{79} -29724.7 q^{80} -53266.1 q^{81} +11033.8 q^{82} +91200.9 q^{83} +86146.8 q^{84} -35202.4 q^{85} -3439.58 q^{86} -79213.9 q^{87} +49197.6 q^{88} -16470.2 q^{89} -1715.63 q^{90} -125376. q^{91} +25823.2 q^{92} -13668.8 q^{93} -33141.8 q^{94} -57294.8 q^{95} +73063.4 q^{96} +145639. q^{97} -45372.0 q^{98} -9539.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86024 −0.328847 −0.164423 0.986390i \(-0.552576\pi\)
−0.164423 + 0.986390i \(0.552576\pi\)
\(3\) −14.8716 −0.954013 −0.477007 0.878900i \(-0.658278\pi\)
−0.477007 + 0.878900i \(0.658278\pi\)
\(4\) −28.5395 −0.891860
\(5\) −42.2365 −0.755550 −0.377775 0.925898i \(-0.623311\pi\)
−0.377775 + 0.925898i \(0.623311\pi\)
\(6\) 27.6647 0.313724
\(7\) 202.971 1.56563 0.782816 0.622253i \(-0.213782\pi\)
0.782816 + 0.622253i \(0.213782\pi\)
\(8\) 112.618 0.622132
\(9\) −21.8357 −0.0898588
\(10\) 78.5700 0.248460
\(11\) 436.853 1.08856 0.544282 0.838902i \(-0.316802\pi\)
0.544282 + 0.838902i \(0.316802\pi\)
\(12\) 424.428 0.850846
\(13\) −617.704 −1.01373 −0.506864 0.862026i \(-0.669196\pi\)
−0.506864 + 0.862026i \(0.669196\pi\)
\(14\) −377.575 −0.514853
\(15\) 628.124 0.720804
\(16\) 703.768 0.687273
\(17\) 833.458 0.699458 0.349729 0.936851i \(-0.386274\pi\)
0.349729 + 0.936851i \(0.386274\pi\)
\(18\) 40.6196 0.0295498
\(19\) 1356.52 0.862071 0.431036 0.902335i \(-0.358148\pi\)
0.431036 + 0.902335i \(0.358148\pi\)
\(20\) 1205.41 0.673844
\(21\) −3018.51 −1.49363
\(22\) −812.652 −0.357971
\(23\) −904.822 −0.356651 −0.178326 0.983972i \(-0.557068\pi\)
−0.178326 + 0.983972i \(0.557068\pi\)
\(24\) −1674.81 −0.593522
\(25\) −1341.08 −0.429145
\(26\) 1149.08 0.333362
\(27\) 3938.53 1.03974
\(28\) −5792.70 −1.39632
\(29\) 5326.52 1.17611 0.588056 0.808820i \(-0.299893\pi\)
0.588056 + 0.808820i \(0.299893\pi\)
\(30\) −1168.46 −0.237034
\(31\) 919.124 0.171779 0.0858895 0.996305i \(-0.472627\pi\)
0.0858895 + 0.996305i \(0.472627\pi\)
\(32\) −4912.95 −0.848140
\(33\) −6496.71 −1.03850
\(34\) −1550.43 −0.230015
\(35\) −8572.80 −1.18291
\(36\) 623.180 0.0801415
\(37\) 4962.82 0.595969 0.297985 0.954571i \(-0.403686\pi\)
0.297985 + 0.954571i \(0.403686\pi\)
\(38\) −2523.46 −0.283490
\(39\) 9186.24 0.967111
\(40\) −4756.59 −0.470052
\(41\) −5931.38 −0.551057 −0.275528 0.961293i \(-0.588853\pi\)
−0.275528 + 0.961293i \(0.588853\pi\)
\(42\) 5615.15 0.491177
\(43\) 1849.00 0.152499
\(44\) −12467.6 −0.970847
\(45\) 922.264 0.0678928
\(46\) 1683.19 0.117284
\(47\) 17815.9 1.17642 0.588210 0.808708i \(-0.299833\pi\)
0.588210 + 0.808708i \(0.299833\pi\)
\(48\) −10466.2 −0.655668
\(49\) 24390.4 1.45120
\(50\) 2494.73 0.141123
\(51\) −12394.9 −0.667292
\(52\) 17629.0 0.904104
\(53\) 24713.3 1.20848 0.604241 0.796801i \(-0.293476\pi\)
0.604241 + 0.796801i \(0.293476\pi\)
\(54\) −7326.61 −0.341915
\(55\) −18451.2 −0.822464
\(56\) 22858.2 0.974030
\(57\) −20173.7 −0.822428
\(58\) −9908.61 −0.386761
\(59\) 33834.6 1.26541 0.632706 0.774392i \(-0.281944\pi\)
0.632706 + 0.774392i \(0.281944\pi\)
\(60\) −17926.4 −0.642856
\(61\) 45948.5 1.58105 0.790527 0.612427i \(-0.209807\pi\)
0.790527 + 0.612427i \(0.209807\pi\)
\(62\) −1709.79 −0.0564890
\(63\) −4432.02 −0.140686
\(64\) −13381.3 −0.408365
\(65\) 26089.6 0.765922
\(66\) 12085.4 0.341509
\(67\) −58523.0 −1.59272 −0.796361 0.604822i \(-0.793244\pi\)
−0.796361 + 0.604822i \(0.793244\pi\)
\(68\) −23786.5 −0.623818
\(69\) 13456.1 0.340250
\(70\) 15947.5 0.388997
\(71\) 1792.64 0.0422034 0.0211017 0.999777i \(-0.493283\pi\)
0.0211017 + 0.999777i \(0.493283\pi\)
\(72\) −2459.09 −0.0559041
\(73\) −46710.3 −1.02590 −0.512951 0.858418i \(-0.671448\pi\)
−0.512951 + 0.858418i \(0.671448\pi\)
\(74\) −9232.03 −0.195983
\(75\) 19944.0 0.409410
\(76\) −38714.5 −0.768847
\(77\) 88668.8 1.70429
\(78\) −17088.6 −0.318031
\(79\) −79459.7 −1.43245 −0.716225 0.697870i \(-0.754131\pi\)
−0.716225 + 0.697870i \(0.754131\pi\)
\(80\) −29724.7 −0.519269
\(81\) −53266.1 −0.902067
\(82\) 11033.8 0.181213
\(83\) 91200.9 1.45313 0.726564 0.687099i \(-0.241116\pi\)
0.726564 + 0.687099i \(0.241116\pi\)
\(84\) 86146.8 1.33211
\(85\) −35202.4 −0.528475
\(86\) −3439.58 −0.0501487
\(87\) −79213.9 −1.12203
\(88\) 49197.6 0.677231
\(89\) −16470.2 −0.220406 −0.110203 0.993909i \(-0.535150\pi\)
−0.110203 + 0.993909i \(0.535150\pi\)
\(90\) −1715.63 −0.0223263
\(91\) −125376. −1.58713
\(92\) 25823.2 0.318083
\(93\) −13668.8 −0.163879
\(94\) −33141.8 −0.386862
\(95\) −57294.8 −0.651338
\(96\) 73063.4 0.809137
\(97\) 145639. 1.57163 0.785813 0.618464i \(-0.212245\pi\)
0.785813 + 0.618464i \(0.212245\pi\)
\(98\) −45372.0 −0.477224
\(99\) −9539.00 −0.0978171
\(100\) 38273.7 0.382737
\(101\) −59937.9 −0.584653 −0.292327 0.956319i \(-0.594429\pi\)
−0.292327 + 0.956319i \(0.594429\pi\)
\(102\) 23057.4 0.219437
\(103\) −176381. −1.63817 −0.819083 0.573675i \(-0.805517\pi\)
−0.819083 + 0.573675i \(0.805517\pi\)
\(104\) −69564.5 −0.630674
\(105\) 127491. 1.12851
\(106\) −45972.6 −0.397406
\(107\) 145711. 1.23036 0.615180 0.788387i \(-0.289083\pi\)
0.615180 + 0.788387i \(0.289083\pi\)
\(108\) −112404. −0.927302
\(109\) −74113.8 −0.597493 −0.298746 0.954333i \(-0.596568\pi\)
−0.298746 + 0.954333i \(0.596568\pi\)
\(110\) 34323.6 0.270465
\(111\) −73805.0 −0.568563
\(112\) 142845. 1.07602
\(113\) 170870. 1.25884 0.629419 0.777066i \(-0.283293\pi\)
0.629419 + 0.777066i \(0.283293\pi\)
\(114\) 37527.8 0.270453
\(115\) 38216.5 0.269468
\(116\) −152016. −1.04893
\(117\) 13488.0 0.0910925
\(118\) −62940.5 −0.416127
\(119\) 169168. 1.09509
\(120\) 70738.1 0.448436
\(121\) 29789.9 0.184972
\(122\) −85475.2 −0.519925
\(123\) 88209.1 0.525716
\(124\) −26231.3 −0.153203
\(125\) 188632. 1.07979
\(126\) 8244.62 0.0462641
\(127\) 117267. 0.645156 0.322578 0.946543i \(-0.395451\pi\)
0.322578 + 0.946543i \(0.395451\pi\)
\(128\) 182107. 0.982430
\(129\) −27497.6 −0.145486
\(130\) −48533.0 −0.251871
\(131\) −64361.8 −0.327680 −0.163840 0.986487i \(-0.552388\pi\)
−0.163840 + 0.986487i \(0.552388\pi\)
\(132\) 185413. 0.926200
\(133\) 275335. 1.34969
\(134\) 108867. 0.523762
\(135\) −166350. −0.785575
\(136\) 93862.4 0.435155
\(137\) −219763. −1.00035 −0.500176 0.865924i \(-0.666731\pi\)
−0.500176 + 0.865924i \(0.666731\pi\)
\(138\) −25031.7 −0.111890
\(139\) 14710.6 0.0645793 0.0322896 0.999479i \(-0.489720\pi\)
0.0322896 + 0.999479i \(0.489720\pi\)
\(140\) 244664. 1.05499
\(141\) −264950. −1.12232
\(142\) −3334.74 −0.0138785
\(143\) −269846. −1.10351
\(144\) −15367.3 −0.0617576
\(145\) −224974. −0.888611
\(146\) 86892.4 0.337365
\(147\) −362724. −1.38447
\(148\) −141636. −0.531521
\(149\) −396393. −1.46272 −0.731359 0.681993i \(-0.761113\pi\)
−0.731359 + 0.681993i \(0.761113\pi\)
\(150\) −37100.5 −0.134633
\(151\) 70722.8 0.252416 0.126208 0.992004i \(-0.459719\pi\)
0.126208 + 0.992004i \(0.459719\pi\)
\(152\) 152769. 0.536323
\(153\) −18199.1 −0.0628525
\(154\) −164945. −0.560451
\(155\) −38820.6 −0.129787
\(156\) −262171. −0.862527
\(157\) −469441. −1.51996 −0.759980 0.649946i \(-0.774791\pi\)
−0.759980 + 0.649946i \(0.774791\pi\)
\(158\) 147814. 0.471057
\(159\) −367526. −1.15291
\(160\) 207506. 0.640812
\(161\) −183653. −0.558385
\(162\) 99087.7 0.296642
\(163\) 660494. 1.94715 0.973576 0.228362i \(-0.0733370\pi\)
0.973576 + 0.228362i \(0.0733370\pi\)
\(164\) 169279. 0.491465
\(165\) 274398. 0.784642
\(166\) −169655. −0.477857
\(167\) 488059. 1.35419 0.677097 0.735894i \(-0.263238\pi\)
0.677097 + 0.735894i \(0.263238\pi\)
\(168\) −339938. −0.929238
\(169\) 10264.9 0.0276464
\(170\) 65484.8 0.173787
\(171\) −29620.6 −0.0774647
\(172\) −52769.6 −0.136007
\(173\) 648829. 1.64822 0.824109 0.566431i \(-0.191676\pi\)
0.824109 + 0.566431i \(0.191676\pi\)
\(174\) 147357. 0.368975
\(175\) −272200. −0.671883
\(176\) 307443. 0.748141
\(177\) −503175. −1.20722
\(178\) 30638.4 0.0724797
\(179\) −203377. −0.474428 −0.237214 0.971457i \(-0.576234\pi\)
−0.237214 + 0.971457i \(0.576234\pi\)
\(180\) −26321.0 −0.0605509
\(181\) 174043. 0.394875 0.197438 0.980315i \(-0.436738\pi\)
0.197438 + 0.980315i \(0.436738\pi\)
\(182\) 233230. 0.521922
\(183\) −683327. −1.50835
\(184\) −101899. −0.221884
\(185\) −209612. −0.450284
\(186\) 25427.3 0.0538912
\(187\) 364099. 0.761405
\(188\) −508456. −1.04920
\(189\) 799409. 1.62785
\(190\) 106582. 0.214190
\(191\) −529048. −1.04933 −0.524664 0.851309i \(-0.675809\pi\)
−0.524664 + 0.851309i \(0.675809\pi\)
\(192\) 199001. 0.389586
\(193\) −74996.7 −0.144927 −0.0724634 0.997371i \(-0.523086\pi\)
−0.0724634 + 0.997371i \(0.523086\pi\)
\(194\) −270924. −0.516824
\(195\) −387995. −0.730700
\(196\) −696090. −1.29427
\(197\) 741584. 1.36143 0.680714 0.732549i \(-0.261669\pi\)
0.680714 + 0.732549i \(0.261669\pi\)
\(198\) 17744.8 0.0321669
\(199\) −46763.5 −0.0837093 −0.0418547 0.999124i \(-0.513327\pi\)
−0.0418547 + 0.999124i \(0.513327\pi\)
\(200\) −151029. −0.266985
\(201\) 870331. 1.51948
\(202\) 111499. 0.192261
\(203\) 1.08113e6 1.84136
\(204\) 353743. 0.595131
\(205\) 250521. 0.416351
\(206\) 328110. 0.538706
\(207\) 19757.4 0.0320483
\(208\) −434720. −0.696709
\(209\) 592602. 0.938420
\(210\) −237164. −0.371109
\(211\) 360269. 0.557084 0.278542 0.960424i \(-0.410149\pi\)
0.278542 + 0.960424i \(0.410149\pi\)
\(212\) −705304. −1.07780
\(213\) −26659.4 −0.0402626
\(214\) −271057. −0.404600
\(215\) −78095.3 −0.115220
\(216\) 443549. 0.646856
\(217\) 186556. 0.268943
\(218\) 137869. 0.196484
\(219\) 694657. 0.978723
\(220\) 526587. 0.733523
\(221\) −514830. −0.709061
\(222\) 137295. 0.186970
\(223\) −184494. −0.248440 −0.124220 0.992255i \(-0.539643\pi\)
−0.124220 + 0.992255i \(0.539643\pi\)
\(224\) −997189. −1.32788
\(225\) 29283.4 0.0385625
\(226\) −317859. −0.413965
\(227\) −404674. −0.521243 −0.260621 0.965441i \(-0.583927\pi\)
−0.260621 + 0.965441i \(0.583927\pi\)
\(228\) 575746. 0.733490
\(229\) 605861. 0.763456 0.381728 0.924275i \(-0.375329\pi\)
0.381728 + 0.924275i \(0.375329\pi\)
\(230\) −71091.9 −0.0886136
\(231\) −1.31865e6 −1.62592
\(232\) 599862. 0.731698
\(233\) −126192. −0.152280 −0.0761400 0.997097i \(-0.524260\pi\)
−0.0761400 + 0.997097i \(0.524260\pi\)
\(234\) −25090.9 −0.0299555
\(235\) −752480. −0.888844
\(236\) −965624. −1.12857
\(237\) 1.18169e6 1.36658
\(238\) −314693. −0.360118
\(239\) 1.31948e6 1.49420 0.747098 0.664714i \(-0.231446\pi\)
0.747098 + 0.664714i \(0.231446\pi\)
\(240\) 442054. 0.495390
\(241\) 1.51669e6 1.68211 0.841055 0.540949i \(-0.181935\pi\)
0.841055 + 0.540949i \(0.181935\pi\)
\(242\) −55416.4 −0.0608275
\(243\) −164910. −0.179156
\(244\) −1.31135e6 −1.41008
\(245\) −1.03017e6 −1.09646
\(246\) −164090. −0.172880
\(247\) −837930. −0.873907
\(248\) 103510. 0.106869
\(249\) −1.35630e6 −1.38630
\(250\) −350900. −0.355086
\(251\) −1.30092e6 −1.30337 −0.651685 0.758490i \(-0.725938\pi\)
−0.651685 + 0.758490i \(0.725938\pi\)
\(252\) 126488. 0.125472
\(253\) −395275. −0.388238
\(254\) −218144. −0.212158
\(255\) 523515. 0.504172
\(256\) 89439.4 0.0852960
\(257\) −223343. −0.210930 −0.105465 0.994423i \(-0.533633\pi\)
−0.105465 + 0.994423i \(0.533633\pi\)
\(258\) 51152.1 0.0478425
\(259\) 1.00731e6 0.933069
\(260\) −744586. −0.683095
\(261\) −116308. −0.105684
\(262\) 119728. 0.107757
\(263\) 216725. 0.193206 0.0966028 0.995323i \(-0.469202\pi\)
0.0966028 + 0.995323i \(0.469202\pi\)
\(264\) −731646. −0.646087
\(265\) −1.04380e6 −0.913068
\(266\) −512190. −0.443840
\(267\) 244938. 0.210270
\(268\) 1.67022e6 1.42048
\(269\) 1.12157e6 0.945029 0.472515 0.881323i \(-0.343346\pi\)
0.472515 + 0.881323i \(0.343346\pi\)
\(270\) 309450. 0.258334
\(271\) −318880. −0.263757 −0.131878 0.991266i \(-0.542101\pi\)
−0.131878 + 0.991266i \(0.542101\pi\)
\(272\) 586561. 0.480719
\(273\) 1.86454e6 1.51414
\(274\) 408812. 0.328963
\(275\) −585854. −0.467152
\(276\) −384032. −0.303455
\(277\) −353813. −0.277061 −0.138530 0.990358i \(-0.544238\pi\)
−0.138530 + 0.990358i \(0.544238\pi\)
\(278\) −27365.2 −0.0212367
\(279\) −20069.7 −0.0154359
\(280\) −965452. −0.735928
\(281\) −248237. −0.187543 −0.0937717 0.995594i \(-0.529892\pi\)
−0.0937717 + 0.995594i \(0.529892\pi\)
\(282\) 492871. 0.369072
\(283\) −420812. −0.312336 −0.156168 0.987730i \(-0.549914\pi\)
−0.156168 + 0.987730i \(0.549914\pi\)
\(284\) −51161.1 −0.0376395
\(285\) 852065. 0.621385
\(286\) 501978. 0.362886
\(287\) −1.20390e6 −0.862753
\(288\) 107278. 0.0762129
\(289\) −725205. −0.510759
\(290\) 418505. 0.292217
\(291\) −2.16589e6 −1.49935
\(292\) 1.33309e6 0.914960
\(293\) −59022.2 −0.0401649 −0.0200824 0.999798i \(-0.506393\pi\)
−0.0200824 + 0.999798i \(0.506393\pi\)
\(294\) 674754. 0.455278
\(295\) −1.42906e6 −0.956081
\(296\) 558903. 0.370772
\(297\) 1.72056e6 1.13182
\(298\) 737386. 0.481010
\(299\) 558912. 0.361548
\(300\) −569191. −0.365136
\(301\) 375294. 0.238757
\(302\) −131561. −0.0830063
\(303\) 891373. 0.557767
\(304\) 954678. 0.592479
\(305\) −1.94070e6 −1.19456
\(306\) 33854.8 0.0206688
\(307\) 969345. 0.586993 0.293496 0.955960i \(-0.405181\pi\)
0.293496 + 0.955960i \(0.405181\pi\)
\(308\) −2.53056e6 −1.51999
\(309\) 2.62306e6 1.56283
\(310\) 72215.6 0.0426802
\(311\) −3.12666e6 −1.83307 −0.916537 0.399950i \(-0.869028\pi\)
−0.916537 + 0.399950i \(0.869028\pi\)
\(312\) 1.03454e6 0.601671
\(313\) 230443. 0.132955 0.0664773 0.997788i \(-0.478824\pi\)
0.0664773 + 0.997788i \(0.478824\pi\)
\(314\) 873274. 0.499834
\(315\) 187193. 0.106295
\(316\) 2.26774e6 1.27754
\(317\) −580982. −0.324724 −0.162362 0.986731i \(-0.551911\pi\)
−0.162362 + 0.986731i \(0.551911\pi\)
\(318\) 683686. 0.379130
\(319\) 2.32691e6 1.28027
\(320\) 565180. 0.308540
\(321\) −2.16695e6 −1.17378
\(322\) 341639. 0.183623
\(323\) 1.13061e6 0.602983
\(324\) 1.52019e6 0.804517
\(325\) 828389. 0.435037
\(326\) −1.22868e6 −0.640315
\(327\) 1.10219e6 0.570016
\(328\) −667981. −0.342830
\(329\) 3.61611e6 1.84184
\(330\) −510446. −0.258027
\(331\) −2.54254e6 −1.27555 −0.637776 0.770222i \(-0.720145\pi\)
−0.637776 + 0.770222i \(0.720145\pi\)
\(332\) −2.60283e6 −1.29599
\(333\) −108367. −0.0535531
\(334\) −907906. −0.445323
\(335\) 2.47181e6 1.20338
\(336\) −2.12433e6 −1.02653
\(337\) 2.09346e6 1.00413 0.502066 0.864829i \(-0.332573\pi\)
0.502066 + 0.864829i \(0.332573\pi\)
\(338\) −19095.2 −0.00909143
\(339\) −2.54111e6 −1.20095
\(340\) 1.00466e6 0.471326
\(341\) 401522. 0.186992
\(342\) 55101.5 0.0254740
\(343\) 1.53921e6 0.706421
\(344\) 208231. 0.0948743
\(345\) −568341. −0.257076
\(346\) −1.20698e6 −0.542012
\(347\) −4.07369e6 −1.81620 −0.908100 0.418753i \(-0.862467\pi\)
−0.908100 + 0.418753i \(0.862467\pi\)
\(348\) 2.26073e6 1.00069
\(349\) −1.01046e6 −0.444073 −0.222037 0.975038i \(-0.571270\pi\)
−0.222037 + 0.975038i \(0.571270\pi\)
\(350\) 506358. 0.220947
\(351\) −2.43284e6 −1.05401
\(352\) −2.14624e6 −0.923255
\(353\) −655684. −0.280064 −0.140032 0.990147i \(-0.544721\pi\)
−0.140032 + 0.990147i \(0.544721\pi\)
\(354\) 936026. 0.396990
\(355\) −75714.9 −0.0318868
\(356\) 470050. 0.196571
\(357\) −2.51580e6 −1.04473
\(358\) 378330. 0.156014
\(359\) 1.78546e6 0.731162 0.365581 0.930780i \(-0.380870\pi\)
0.365581 + 0.930780i \(0.380870\pi\)
\(360\) 103863. 0.0422383
\(361\) −635943. −0.256833
\(362\) −323762. −0.129854
\(363\) −443024. −0.176466
\(364\) 3.57818e6 1.41549
\(365\) 1.97288e6 0.775119
\(366\) 1.27115e6 0.496015
\(367\) 2.96896e6 1.15064 0.575320 0.817928i \(-0.304878\pi\)
0.575320 + 0.817928i \(0.304878\pi\)
\(368\) −636785. −0.245117
\(369\) 129516. 0.0495173
\(370\) 389929. 0.148075
\(371\) 5.01609e6 1.89204
\(372\) 390102. 0.146157
\(373\) −3.94005e6 −1.46632 −0.733162 0.680055i \(-0.761956\pi\)
−0.733162 + 0.680055i \(0.761956\pi\)
\(374\) −677311. −0.250386
\(375\) −2.80525e6 −1.03013
\(376\) 2.00639e6 0.731889
\(377\) −3.29021e6 −1.19226
\(378\) −1.48709e6 −0.535314
\(379\) −4.36353e6 −1.56042 −0.780208 0.625520i \(-0.784887\pi\)
−0.780208 + 0.625520i \(0.784887\pi\)
\(380\) 1.63517e6 0.580902
\(381\) −1.74394e6 −0.615487
\(382\) 984155. 0.345068
\(383\) −3.53079e6 −1.22991 −0.614957 0.788561i \(-0.710827\pi\)
−0.614957 + 0.788561i \(0.710827\pi\)
\(384\) −2.70822e6 −0.937251
\(385\) −3.74506e6 −1.28768
\(386\) 139512. 0.0476587
\(387\) −40374.2 −0.0137033
\(388\) −4.15647e6 −1.40167
\(389\) −5.57419e6 −1.86770 −0.933851 0.357663i \(-0.883574\pi\)
−0.933851 + 0.357663i \(0.883574\pi\)
\(390\) 721763. 0.240289
\(391\) −754131. −0.249462
\(392\) 2.74680e6 0.902841
\(393\) 957163. 0.312611
\(394\) −1.37952e6 −0.447702
\(395\) 3.35610e6 1.08229
\(396\) 272238. 0.0872391
\(397\) 5.87343e6 1.87032 0.935159 0.354229i \(-0.115257\pi\)
0.935159 + 0.354229i \(0.115257\pi\)
\(398\) 86991.2 0.0275276
\(399\) −4.09468e6 −1.28762
\(400\) −943807. −0.294940
\(401\) −46354.8 −0.0143957 −0.00719786 0.999974i \(-0.502291\pi\)
−0.00719786 + 0.999974i \(0.502291\pi\)
\(402\) −1.61902e6 −0.499676
\(403\) −567746. −0.174137
\(404\) 1.71060e6 0.521429
\(405\) 2.24978e6 0.681556
\(406\) −2.01116e6 −0.605526
\(407\) 2.16802e6 0.648751
\(408\) −1.39588e6 −0.415144
\(409\) 2.92397e6 0.864301 0.432150 0.901802i \(-0.357755\pi\)
0.432150 + 0.901802i \(0.357755\pi\)
\(410\) −466029. −0.136916
\(411\) 3.26822e6 0.954349
\(412\) 5.03382e6 1.46101
\(413\) 6.86747e6 1.98117
\(414\) −36753.5 −0.0105390
\(415\) −3.85201e6 −1.09791
\(416\) 3.03475e6 0.859784
\(417\) −218770. −0.0616095
\(418\) −1.10238e6 −0.308597
\(419\) 3.23273e6 0.899569 0.449785 0.893137i \(-0.351501\pi\)
0.449785 + 0.893137i \(0.351501\pi\)
\(420\) −3.63854e6 −1.00648
\(421\) −4.62842e6 −1.27271 −0.636353 0.771398i \(-0.719558\pi\)
−0.636353 + 0.771398i \(0.719558\pi\)
\(422\) −670186. −0.183195
\(423\) −389022. −0.105712
\(424\) 2.78316e6 0.751836
\(425\) −1.11773e6 −0.300169
\(426\) 49592.9 0.0132402
\(427\) 9.32623e6 2.47535
\(428\) −4.15851e6 −1.09731
\(429\) 4.01304e6 1.05276
\(430\) 145276. 0.0378898
\(431\) 1.87590e6 0.486425 0.243213 0.969973i \(-0.421799\pi\)
0.243213 + 0.969973i \(0.421799\pi\)
\(432\) 2.77181e6 0.714585
\(433\) −3.80994e6 −0.976559 −0.488280 0.872687i \(-0.662375\pi\)
−0.488280 + 0.872687i \(0.662375\pi\)
\(434\) −347039. −0.0884410
\(435\) 3.34572e6 0.847747
\(436\) 2.11517e6 0.532880
\(437\) −1.22741e6 −0.307459
\(438\) −1.29223e6 −0.321850
\(439\) 2.35939e6 0.584304 0.292152 0.956372i \(-0.405629\pi\)
0.292152 + 0.956372i \(0.405629\pi\)
\(440\) −2.07793e6 −0.511682
\(441\) −532581. −0.130404
\(442\) 957707. 0.233172
\(443\) −2.55633e6 −0.618881 −0.309440 0.950919i \(-0.600142\pi\)
−0.309440 + 0.950919i \(0.600142\pi\)
\(444\) 2.10636e6 0.507078
\(445\) 695642. 0.166527
\(446\) 343204. 0.0816987
\(447\) 5.89500e6 1.39545
\(448\) −2.71602e6 −0.639350
\(449\) 3.71934e6 0.870662 0.435331 0.900270i \(-0.356631\pi\)
0.435331 + 0.900270i \(0.356631\pi\)
\(450\) −54474.1 −0.0126811
\(451\) −2.59115e6 −0.599861
\(452\) −4.87655e6 −1.12271
\(453\) −1.05176e6 −0.240808
\(454\) 752790. 0.171409
\(455\) 5.29545e6 1.19915
\(456\) −2.27192e6 −0.511659
\(457\) −2.59594e6 −0.581438 −0.290719 0.956808i \(-0.593895\pi\)
−0.290719 + 0.956808i \(0.593895\pi\)
\(458\) −1.12705e6 −0.251060
\(459\) 3.28260e6 0.727254
\(460\) −1.09068e6 −0.240327
\(461\) −6.62260e6 −1.45136 −0.725682 0.688031i \(-0.758475\pi\)
−0.725682 + 0.688031i \(0.758475\pi\)
\(462\) 2.45300e6 0.534678
\(463\) 5.09992e6 1.10563 0.552817 0.833303i \(-0.313553\pi\)
0.552817 + 0.833303i \(0.313553\pi\)
\(464\) 3.74864e6 0.808311
\(465\) 577324. 0.123819
\(466\) 234748. 0.0500768
\(467\) 3.91009e6 0.829649 0.414825 0.909901i \(-0.363843\pi\)
0.414825 + 0.909901i \(0.363843\pi\)
\(468\) −384941. −0.0812417
\(469\) −1.18785e7 −2.49362
\(470\) 1.39979e6 0.292294
\(471\) 6.98134e6 1.45006
\(472\) 3.81039e6 0.787253
\(473\) 807742. 0.166004
\(474\) −2.19823e6 −0.449394
\(475\) −1.81920e6 −0.369954
\(476\) −4.82798e6 −0.976670
\(477\) −539631. −0.108593
\(478\) −2.45455e6 −0.491362
\(479\) −8.49397e6 −1.69150 −0.845750 0.533580i \(-0.820846\pi\)
−0.845750 + 0.533580i \(0.820846\pi\)
\(480\) −3.08594e6 −0.611343
\(481\) −3.06555e6 −0.604152
\(482\) −2.82141e6 −0.553157
\(483\) 2.73121e6 0.532706
\(484\) −850190. −0.164969
\(485\) −6.15129e6 −1.18744
\(486\) 306773. 0.0589150
\(487\) 7.46234e6 1.42578 0.712890 0.701276i \(-0.247386\pi\)
0.712890 + 0.701276i \(0.247386\pi\)
\(488\) 5.17463e6 0.983625
\(489\) −9.82260e6 −1.85761
\(490\) 1.91635e6 0.360567
\(491\) 2.46640e6 0.461700 0.230850 0.972989i \(-0.425849\pi\)
0.230850 + 0.972989i \(0.425849\pi\)
\(492\) −2.51745e6 −0.468864
\(493\) 4.43943e6 0.822641
\(494\) 1.55875e6 0.287382
\(495\) 402894. 0.0739057
\(496\) 646850. 0.118059
\(497\) 363855. 0.0660750
\(498\) 2.52305e6 0.455882
\(499\) −2.03466e6 −0.365798 −0.182899 0.983132i \(-0.558548\pi\)
−0.182899 + 0.983132i \(0.558548\pi\)
\(500\) −5.38345e6 −0.963021
\(501\) −7.25821e6 −1.29192
\(502\) 2.42003e6 0.428609
\(503\) −5.11148e6 −0.900797 −0.450398 0.892828i \(-0.648718\pi\)
−0.450398 + 0.892828i \(0.648718\pi\)
\(504\) −499125. −0.0875253
\(505\) 2.53157e6 0.441734
\(506\) 735305. 0.127671
\(507\) −152656. −0.0263750
\(508\) −3.34673e6 −0.575389
\(509\) 5.43324e6 0.929532 0.464766 0.885433i \(-0.346138\pi\)
0.464766 + 0.885433i \(0.346138\pi\)
\(510\) −973864. −0.165795
\(511\) −9.48086e6 −1.60618
\(512\) −5.99380e6 −1.01048
\(513\) 5.34271e6 0.896330
\(514\) 415471. 0.0693638
\(515\) 7.44970e6 1.23772
\(516\) 784767. 0.129753
\(517\) 7.78292e6 1.28061
\(518\) −1.87384e6 −0.306837
\(519\) −9.64911e6 −1.57242
\(520\) 2.93816e6 0.476505
\(521\) 8.89569e6 1.43577 0.717886 0.696161i \(-0.245110\pi\)
0.717886 + 0.696161i \(0.245110\pi\)
\(522\) 216361. 0.0347539
\(523\) 5.98910e6 0.957430 0.478715 0.877970i \(-0.341103\pi\)
0.478715 + 0.877970i \(0.341103\pi\)
\(524\) 1.83686e6 0.292245
\(525\) 4.04805e6 0.640985
\(526\) −403160. −0.0635351
\(527\) 766051. 0.120152
\(528\) −4.57217e6 −0.713737
\(529\) −5.61764e6 −0.872800
\(530\) 1.94172e6 0.300260
\(531\) −738803. −0.113708
\(532\) −7.85794e6 −1.20373
\(533\) 3.66384e6 0.558622
\(534\) −455642. −0.0691466
\(535\) −6.15431e6 −0.929598
\(536\) −6.59075e6 −0.990884
\(537\) 3.02454e6 0.452610
\(538\) −2.08639e6 −0.310770
\(539\) 1.06550e7 1.57973
\(540\) 4.74754e6 0.700623
\(541\) 3.07873e6 0.452249 0.226125 0.974098i \(-0.427394\pi\)
0.226125 + 0.974098i \(0.427394\pi\)
\(542\) 593193. 0.0867356
\(543\) −2.58830e6 −0.376716
\(544\) −4.09474e6 −0.593238
\(545\) 3.13031e6 0.451435
\(546\) −3.46850e6 −0.497920
\(547\) −1.37829e7 −1.96958 −0.984789 0.173755i \(-0.944410\pi\)
−0.984789 + 0.173755i \(0.944410\pi\)
\(548\) 6.27192e6 0.892174
\(549\) −1.00332e6 −0.142072
\(550\) 1.08983e6 0.153621
\(551\) 7.22555e6 1.01389
\(552\) 1.51540e6 0.211680
\(553\) −1.61280e7 −2.24269
\(554\) 658177. 0.0911105
\(555\) 3.11727e6 0.429577
\(556\) −419833. −0.0575956
\(557\) 3.17087e6 0.433053 0.216526 0.976277i \(-0.430527\pi\)
0.216526 + 0.976277i \(0.430527\pi\)
\(558\) 37334.5 0.00507603
\(559\) −1.14213e6 −0.154592
\(560\) −6.03326e6 −0.812984
\(561\) −5.41473e6 −0.726390
\(562\) 461781. 0.0616730
\(563\) 1.15175e7 1.53139 0.765697 0.643201i \(-0.222394\pi\)
0.765697 + 0.643201i \(0.222394\pi\)
\(564\) 7.56155e6 1.00095
\(565\) −7.21696e6 −0.951115
\(566\) 782812. 0.102711
\(567\) −1.08115e7 −1.41230
\(568\) 201884. 0.0262561
\(569\) −1.09971e7 −1.42397 −0.711983 0.702197i \(-0.752203\pi\)
−0.711983 + 0.702197i \(0.752203\pi\)
\(570\) −1.58505e6 −0.204341
\(571\) −2.17295e6 −0.278907 −0.139454 0.990229i \(-0.544535\pi\)
−0.139454 + 0.990229i \(0.544535\pi\)
\(572\) 7.70127e6 0.984175
\(573\) 7.86778e6 1.00107
\(574\) 2.23955e6 0.283714
\(575\) 1.21344e6 0.153055
\(576\) 292190. 0.0366952
\(577\) −1.05167e7 −1.31505 −0.657524 0.753434i \(-0.728396\pi\)
−0.657524 + 0.753434i \(0.728396\pi\)
\(578\) 1.34905e6 0.167962
\(579\) 1.11532e6 0.138262
\(580\) 6.42064e6 0.792517
\(581\) 1.85112e7 2.27506
\(582\) 4.02907e6 0.493057
\(583\) 1.07961e7 1.31551
\(584\) −5.26042e6 −0.638246
\(585\) −569686. −0.0688249
\(586\) 109795. 0.0132081
\(587\) 2.96292e6 0.354915 0.177457 0.984128i \(-0.443213\pi\)
0.177457 + 0.984128i \(0.443213\pi\)
\(588\) 1.03520e7 1.23475
\(589\) 1.24681e6 0.148086
\(590\) 2.65839e6 0.314404
\(591\) −1.10285e7 −1.29882
\(592\) 3.49267e6 0.409594
\(593\) 7.54824e6 0.881473 0.440737 0.897636i \(-0.354717\pi\)
0.440737 + 0.897636i \(0.354717\pi\)
\(594\) −3.20065e6 −0.372197
\(595\) −7.14507e6 −0.827398
\(596\) 1.13129e7 1.30454
\(597\) 695447. 0.0798598
\(598\) −1.03971e6 −0.118894
\(599\) 7.70971e6 0.877953 0.438976 0.898499i \(-0.355341\pi\)
0.438976 + 0.898499i \(0.355341\pi\)
\(600\) 2.24605e6 0.254707
\(601\) 3.40171e6 0.384159 0.192079 0.981379i \(-0.438477\pi\)
0.192079 + 0.981379i \(0.438477\pi\)
\(602\) −698137. −0.0785144
\(603\) 1.27789e6 0.143120
\(604\) −2.01839e6 −0.225120
\(605\) −1.25822e6 −0.139756
\(606\) −1.65817e6 −0.183420
\(607\) 5.29342e6 0.583129 0.291564 0.956551i \(-0.405824\pi\)
0.291564 + 0.956551i \(0.405824\pi\)
\(608\) −6.66453e6 −0.731157
\(609\) −1.60782e7 −1.75668
\(610\) 3.61017e6 0.392829
\(611\) −1.10049e7 −1.19257
\(612\) 519395. 0.0560556
\(613\) 1.51319e7 1.62646 0.813229 0.581944i \(-0.197708\pi\)
0.813229 + 0.581944i \(0.197708\pi\)
\(614\) −1.80321e6 −0.193031
\(615\) −3.72565e6 −0.397204
\(616\) 9.98570e6 1.06029
\(617\) 2.54291e6 0.268917 0.134458 0.990919i \(-0.457071\pi\)
0.134458 + 0.990919i \(0.457071\pi\)
\(618\) −4.87952e6 −0.513932
\(619\) 8.70953e6 0.913626 0.456813 0.889563i \(-0.348991\pi\)
0.456813 + 0.889563i \(0.348991\pi\)
\(620\) 1.10792e6 0.115752
\(621\) −3.56367e6 −0.370824
\(622\) 5.81634e6 0.602801
\(623\) −3.34297e6 −0.345074
\(624\) 6.46498e6 0.664669
\(625\) −3.77627e6 −0.386690
\(626\) −428680. −0.0437217
\(627\) −8.81293e6 −0.895265
\(628\) 1.33976e7 1.35559
\(629\) 4.13630e6 0.416855
\(630\) −348224. −0.0349548
\(631\) 1.28039e7 1.28018 0.640089 0.768301i \(-0.278898\pi\)
0.640089 + 0.768301i \(0.278898\pi\)
\(632\) −8.94859e6 −0.891173
\(633\) −5.35777e6 −0.531465
\(634\) 1.08077e6 0.106785
\(635\) −4.95293e6 −0.487447
\(636\) 1.04890e7 1.02823
\(637\) −1.50660e7 −1.47113
\(638\) −4.32861e6 −0.421014
\(639\) −39143.6 −0.00379235
\(640\) −7.69156e6 −0.742274
\(641\) −1.14881e7 −1.10434 −0.552170 0.833732i \(-0.686200\pi\)
−0.552170 + 0.833732i \(0.686200\pi\)
\(642\) 4.03105e6 0.385994
\(643\) −1.13485e7 −1.08246 −0.541230 0.840875i \(-0.682041\pi\)
−0.541230 + 0.840875i \(0.682041\pi\)
\(644\) 5.24137e6 0.498001
\(645\) 1.16140e6 0.109922
\(646\) −2.10320e6 −0.198289
\(647\) −6.22456e6 −0.584585 −0.292293 0.956329i \(-0.594418\pi\)
−0.292293 + 0.956329i \(0.594418\pi\)
\(648\) −5.99872e6 −0.561205
\(649\) 1.47808e7 1.37748
\(650\) −1.54100e6 −0.143060
\(651\) −2.77438e6 −0.256575
\(652\) −1.88502e7 −1.73659
\(653\) −382501. −0.0351034 −0.0175517 0.999846i \(-0.505587\pi\)
−0.0175517 + 0.999846i \(0.505587\pi\)
\(654\) −2.05034e6 −0.187448
\(655\) 2.71842e6 0.247579
\(656\) −4.17432e6 −0.378727
\(657\) 1.01995e6 0.0921863
\(658\) −6.72683e6 −0.605684
\(659\) −2.06346e7 −1.85090 −0.925449 0.378872i \(-0.876312\pi\)
−0.925449 + 0.378872i \(0.876312\pi\)
\(660\) −7.83119e6 −0.699790
\(661\) −3.78028e6 −0.336527 −0.168264 0.985742i \(-0.553816\pi\)
−0.168264 + 0.985742i \(0.553816\pi\)
\(662\) 4.72973e6 0.419461
\(663\) 7.65635e6 0.676453
\(664\) 1.02709e7 0.904038
\(665\) −1.16292e7 −1.01976
\(666\) 201588. 0.0176108
\(667\) −4.81956e6 −0.419462
\(668\) −1.39290e7 −1.20775
\(669\) 2.74373e6 0.237015
\(670\) −4.59816e6 −0.395728
\(671\) 2.00728e7 1.72108
\(672\) 1.48298e7 1.26681
\(673\) −7.82427e6 −0.665895 −0.332948 0.942945i \(-0.608043\pi\)
−0.332948 + 0.942945i \(0.608043\pi\)
\(674\) −3.89435e6 −0.330206
\(675\) −5.28187e6 −0.446199
\(676\) −292955. −0.0246567
\(677\) 5.22258e6 0.437939 0.218969 0.975732i \(-0.429730\pi\)
0.218969 + 0.975732i \(0.429730\pi\)
\(678\) 4.72707e6 0.394928
\(679\) 2.95606e7 2.46059
\(680\) −3.96442e6 −0.328781
\(681\) 6.01814e6 0.497273
\(682\) −746928. −0.0614919
\(683\) −1.18085e7 −0.968598 −0.484299 0.874902i \(-0.660925\pi\)
−0.484299 + 0.874902i \(0.660925\pi\)
\(684\) 845358. 0.0690877
\(685\) 9.28202e6 0.755816
\(686\) −2.86330e6 −0.232304
\(687\) −9.01012e6 −0.728348
\(688\) 1.30127e6 0.104808
\(689\) −1.52655e7 −1.22507
\(690\) 1.05725e6 0.0845386
\(691\) 1.90341e7 1.51648 0.758241 0.651974i \(-0.226059\pi\)
0.758241 + 0.651974i \(0.226059\pi\)
\(692\) −1.85172e7 −1.46998
\(693\) −1.93614e6 −0.153146
\(694\) 7.57803e6 0.597252
\(695\) −621324. −0.0487928
\(696\) −8.92091e6 −0.698049
\(697\) −4.94356e6 −0.385441
\(698\) 1.87969e6 0.146032
\(699\) 1.87668e6 0.145277
\(700\) 7.76847e6 0.599225
\(701\) 2.48342e7 1.90878 0.954390 0.298564i \(-0.0965075\pi\)
0.954390 + 0.298564i \(0.0965075\pi\)
\(702\) 4.52567e6 0.346609
\(703\) 6.73218e6 0.513768
\(704\) −5.84567e6 −0.444532
\(705\) 1.11906e7 0.847969
\(706\) 1.21973e6 0.0920983
\(707\) −1.21657e7 −0.915352
\(708\) 1.43604e7 1.07667
\(709\) −1.83486e7 −1.37084 −0.685422 0.728146i \(-0.740382\pi\)
−0.685422 + 0.728146i \(0.740382\pi\)
\(710\) 140848. 0.0104859
\(711\) 1.73506e6 0.128718
\(712\) −1.85484e6 −0.137122
\(713\) −831644. −0.0612651
\(714\) 4.67999e6 0.343558
\(715\) 1.13974e7 0.833756
\(716\) 5.80429e6 0.423123
\(717\) −1.96228e7 −1.42548
\(718\) −3.32138e6 −0.240440
\(719\) −387175. −0.0279309 −0.0139655 0.999902i \(-0.504445\pi\)
−0.0139655 + 0.999902i \(0.504445\pi\)
\(720\) 649060. 0.0466609
\(721\) −3.58002e7 −2.56476
\(722\) 1.18301e6 0.0844587
\(723\) −2.25556e7 −1.60476
\(724\) −4.96710e6 −0.352173
\(725\) −7.14328e6 −0.504723
\(726\) 824130. 0.0580302
\(727\) 5.28478e6 0.370843 0.185422 0.982659i \(-0.440635\pi\)
0.185422 + 0.982659i \(0.440635\pi\)
\(728\) −1.41196e7 −0.987403
\(729\) 1.53961e7 1.07298
\(730\) −3.67003e6 −0.254896
\(731\) 1.54106e6 0.106666
\(732\) 1.95018e7 1.34523
\(733\) 2.20879e7 1.51843 0.759215 0.650840i \(-0.225583\pi\)
0.759215 + 0.650840i \(0.225583\pi\)
\(734\) −5.52298e6 −0.378385
\(735\) 1.53202e7 1.04603
\(736\) 4.44535e6 0.302490
\(737\) −2.55660e7 −1.73378
\(738\) −240931. −0.0162836
\(739\) −1.90903e7 −1.28588 −0.642941 0.765916i \(-0.722286\pi\)
−0.642941 + 0.765916i \(0.722286\pi\)
\(740\) 5.98223e6 0.401591
\(741\) 1.24613e7 0.833719
\(742\) −9.33112e6 −0.622191
\(743\) −8.08984e6 −0.537610 −0.268805 0.963195i \(-0.586629\pi\)
−0.268805 + 0.963195i \(0.586629\pi\)
\(744\) −1.53936e6 −0.101955
\(745\) 1.67423e7 1.10516
\(746\) 7.32944e6 0.482196
\(747\) −1.99144e6 −0.130576
\(748\) −1.03912e7 −0.679066
\(749\) 2.95751e7 1.92629
\(750\) 5.21844e6 0.338756
\(751\) 3.66332e6 0.237015 0.118507 0.992953i \(-0.462189\pi\)
0.118507 + 0.992953i \(0.462189\pi\)
\(752\) 1.25382e7 0.808522
\(753\) 1.93468e7 1.24343
\(754\) 6.12059e6 0.392071
\(755\) −2.98708e6 −0.190713
\(756\) −2.28147e7 −1.45181
\(757\) 3.20177e6 0.203072 0.101536 0.994832i \(-0.467624\pi\)
0.101536 + 0.994832i \(0.467624\pi\)
\(758\) 8.11722e6 0.513138
\(759\) 5.87836e6 0.370384
\(760\) −6.45243e6 −0.405218
\(761\) −1.65236e7 −1.03429 −0.517147 0.855897i \(-0.673006\pi\)
−0.517147 + 0.855897i \(0.673006\pi\)
\(762\) 3.24415e6 0.202401
\(763\) −1.50430e7 −0.935454
\(764\) 1.50988e7 0.935854
\(765\) 768668. 0.0474882
\(766\) 6.56811e6 0.404453
\(767\) −2.08998e7 −1.28278
\(768\) −1.33011e6 −0.0813735
\(769\) 1.98289e7 1.20916 0.604579 0.796545i \(-0.293342\pi\)
0.604579 + 0.796545i \(0.293342\pi\)
\(770\) 6.96671e6 0.423449
\(771\) 3.32146e6 0.201230
\(772\) 2.14037e6 0.129254
\(773\) 2.13192e7 1.28329 0.641643 0.767004i \(-0.278253\pi\)
0.641643 + 0.767004i \(0.278253\pi\)
\(774\) 75105.7 0.00450630
\(775\) −1.23262e6 −0.0737180
\(776\) 1.64016e7 0.977759
\(777\) −1.49803e7 −0.890160
\(778\) 1.03693e7 0.614188
\(779\) −8.04606e6 −0.475050
\(780\) 1.10732e7 0.651682
\(781\) 783122. 0.0459411
\(782\) 1.40286e6 0.0820350
\(783\) 2.09787e7 1.22285
\(784\) 1.71652e7 0.997374
\(785\) 1.98276e7 1.14841
\(786\) −1.78055e6 −0.102801
\(787\) 2.08248e7 1.19852 0.599258 0.800556i \(-0.295462\pi\)
0.599258 + 0.800556i \(0.295462\pi\)
\(788\) −2.11645e7 −1.21420
\(789\) −3.22305e6 −0.184321
\(790\) −6.24315e6 −0.355907
\(791\) 3.46817e7 1.97088
\(792\) −1.07426e6 −0.0608552
\(793\) −2.83826e7 −1.60276
\(794\) −1.09260e7 −0.615048
\(795\) 1.55230e7 0.871079
\(796\) 1.33461e6 0.0746570
\(797\) −1.52522e7 −0.850527 −0.425263 0.905070i \(-0.639819\pi\)
−0.425263 + 0.905070i \(0.639819\pi\)
\(798\) 7.61708e6 0.423430
\(799\) 1.48488e7 0.822856
\(800\) 6.58865e6 0.363975
\(801\) 359637. 0.0198054
\(802\) 86231.0 0.00473399
\(803\) −2.04056e7 −1.11676
\(804\) −2.48388e7 −1.35516
\(805\) 7.75686e6 0.421887
\(806\) 1.05614e6 0.0572645
\(807\) −1.66795e7 −0.901571
\(808\) −6.75009e6 −0.363732
\(809\) 1.69851e6 0.0912426 0.0456213 0.998959i \(-0.485473\pi\)
0.0456213 + 0.998959i \(0.485473\pi\)
\(810\) −4.18512e6 −0.224128
\(811\) −8.51667e6 −0.454693 −0.227346 0.973814i \(-0.573005\pi\)
−0.227346 + 0.973814i \(0.573005\pi\)
\(812\) −3.08550e7 −1.64223
\(813\) 4.74225e6 0.251627
\(814\) −4.03304e6 −0.213340
\(815\) −2.78970e7 −1.47117
\(816\) −8.72310e6 −0.458612
\(817\) 2.50821e6 0.131465
\(818\) −5.43929e6 −0.284223
\(819\) 2.73768e6 0.142617
\(820\) −7.14975e6 −0.371326
\(821\) 1.11108e7 0.575293 0.287647 0.957737i \(-0.407127\pi\)
0.287647 + 0.957737i \(0.407127\pi\)
\(822\) −6.07968e6 −0.313835
\(823\) −1.20698e7 −0.621157 −0.310578 0.950548i \(-0.600523\pi\)
−0.310578 + 0.950548i \(0.600523\pi\)
\(824\) −1.98636e7 −1.01916
\(825\) 8.71259e6 0.445669
\(826\) −1.27751e7 −0.651501
\(827\) 1.25034e7 0.635719 0.317859 0.948138i \(-0.397036\pi\)
0.317859 + 0.948138i \(0.397036\pi\)
\(828\) −563867. −0.0285825
\(829\) −4.43044e6 −0.223903 −0.111952 0.993714i \(-0.535710\pi\)
−0.111952 + 0.993714i \(0.535710\pi\)
\(830\) 7.16565e6 0.361044
\(831\) 5.26177e6 0.264319
\(832\) 8.26568e6 0.413971
\(833\) 2.03284e7 1.01506
\(834\) 406964. 0.0202601
\(835\) −2.06139e7 −1.02316
\(836\) −1.69126e7 −0.836939
\(837\) 3.62000e6 0.178605
\(838\) −6.01365e6 −0.295821
\(839\) −2.49502e7 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(840\) 1.43578e7 0.702085
\(841\) 7.86071e6 0.383241
\(842\) 8.60998e6 0.418525
\(843\) 3.69169e6 0.178919
\(844\) −1.02819e7 −0.496840
\(845\) −433554. −0.0208882
\(846\) 723674. 0.0347630
\(847\) 6.04651e6 0.289598
\(848\) 1.73924e7 0.830558
\(849\) 6.25815e6 0.297973
\(850\) 2.07925e6 0.0987096
\(851\) −4.49047e6 −0.212553
\(852\) 760847. 0.0359086
\(853\) 1.87125e7 0.880561 0.440280 0.897860i \(-0.354879\pi\)
0.440280 + 0.897860i \(0.354879\pi\)
\(854\) −1.73490e7 −0.814011
\(855\) 1.25107e6 0.0585285
\(856\) 1.64096e7 0.765446
\(857\) −9.57836e6 −0.445491 −0.222746 0.974877i \(-0.571502\pi\)
−0.222746 + 0.974877i \(0.571502\pi\)
\(858\) −7.46522e6 −0.346198
\(859\) −2.56964e7 −1.18820 −0.594100 0.804391i \(-0.702492\pi\)
−0.594100 + 0.804391i \(0.702492\pi\)
\(860\) 2.22880e6 0.102760
\(861\) 1.79039e7 0.823077
\(862\) −3.48962e6 −0.159959
\(863\) −3.20924e7 −1.46681 −0.733406 0.679791i \(-0.762071\pi\)
−0.733406 + 0.679791i \(0.762071\pi\)
\(864\) −1.93498e7 −0.881845
\(865\) −2.74043e7 −1.24531
\(866\) 7.08740e6 0.321139
\(867\) 1.07849e7 0.487271
\(868\) −5.32421e6 −0.239859
\(869\) −3.47122e7 −1.55931
\(870\) −6.22384e6 −0.278779
\(871\) 3.61499e7 1.61459
\(872\) −8.34654e6 −0.371720
\(873\) −3.18014e6 −0.141225
\(874\) 2.28328e6 0.101107
\(875\) 3.82868e7 1.69055
\(876\) −1.98252e7 −0.872884
\(877\) 5.49507e6 0.241254 0.120627 0.992698i \(-0.461510\pi\)
0.120627 + 0.992698i \(0.461510\pi\)
\(878\) −4.38903e6 −0.192147
\(879\) 877754. 0.0383178
\(880\) −1.29853e7 −0.565258
\(881\) −2.28313e7 −0.991038 −0.495519 0.868597i \(-0.665022\pi\)
−0.495519 + 0.868597i \(0.665022\pi\)
\(882\) 990729. 0.0428828
\(883\) −2.80025e7 −1.20864 −0.604318 0.796743i \(-0.706554\pi\)
−0.604318 + 0.796743i \(0.706554\pi\)
\(884\) 1.46930e7 0.632383
\(885\) 2.12524e7 0.912114
\(886\) 4.75538e6 0.203517
\(887\) −4.93689e6 −0.210690 −0.105345 0.994436i \(-0.533595\pi\)
−0.105345 + 0.994436i \(0.533595\pi\)
\(888\) −8.31177e6 −0.353721
\(889\) 2.38018e7 1.01008
\(890\) −1.29406e6 −0.0547620
\(891\) −2.32695e7 −0.981957
\(892\) 5.26538e6 0.221573
\(893\) 2.41676e7 1.01416
\(894\) −1.09661e7 −0.458890
\(895\) 8.58995e6 0.358454
\(896\) 3.69625e7 1.53812
\(897\) −8.31191e6 −0.344921
\(898\) −6.91886e6 −0.286315
\(899\) 4.89574e6 0.202031
\(900\) −835733. −0.0343923
\(901\) 2.05975e7 0.845282
\(902\) 4.82015e6 0.197262
\(903\) −5.58122e6 −0.227777
\(904\) 1.92430e7 0.783164
\(905\) −7.35097e6 −0.298348
\(906\) 1.95653e6 0.0791891
\(907\) −1.84794e7 −0.745880 −0.372940 0.927856i \(-0.621650\pi\)
−0.372940 + 0.927856i \(0.621650\pi\)
\(908\) 1.15492e7 0.464876
\(909\) 1.30879e6 0.0525363
\(910\) −9.85081e6 −0.394338
\(911\) 1.37578e6 0.0549229 0.0274615 0.999623i \(-0.491258\pi\)
0.0274615 + 0.999623i \(0.491258\pi\)
\(912\) −1.41976e7 −0.565233
\(913\) 3.98414e7 1.58182
\(914\) 4.82906e6 0.191204
\(915\) 2.88614e7 1.13963
\(916\) −1.72910e7 −0.680896
\(917\) −1.30636e7 −0.513027
\(918\) −6.10642e6 −0.239155
\(919\) −2.38412e7 −0.931192 −0.465596 0.884997i \(-0.654160\pi\)
−0.465596 + 0.884997i \(0.654160\pi\)
\(920\) 4.30387e6 0.167645
\(921\) −1.44157e7 −0.559999
\(922\) 1.23196e7 0.477276
\(923\) −1.10732e6 −0.0427828
\(924\) 3.76335e7 1.45009
\(925\) −6.65552e6 −0.255757
\(926\) −9.48708e6 −0.363584
\(927\) 3.85139e6 0.147204
\(928\) −2.61690e7 −0.997508
\(929\) 4.74191e6 0.180266 0.0901331 0.995930i \(-0.471271\pi\)
0.0901331 + 0.995930i \(0.471271\pi\)
\(930\) −1.07396e6 −0.0407175
\(931\) 3.30861e7 1.25104
\(932\) 3.60147e6 0.135812
\(933\) 4.64985e7 1.74878
\(934\) −7.27370e6 −0.272828
\(935\) −1.53783e7 −0.575279
\(936\) 1.51899e6 0.0566716
\(937\) −1.07340e7 −0.399404 −0.199702 0.979857i \(-0.563997\pi\)
−0.199702 + 0.979857i \(0.563997\pi\)
\(938\) 2.20969e7 0.820018
\(939\) −3.42706e6 −0.126840
\(940\) 2.14754e7 0.792724
\(941\) 2.93932e7 1.08211 0.541057 0.840986i \(-0.318024\pi\)
0.541057 + 0.840986i \(0.318024\pi\)
\(942\) −1.29870e7 −0.476849
\(943\) 5.36685e6 0.196535
\(944\) 2.38117e7 0.869683
\(945\) −3.37642e7 −1.22992
\(946\) −1.50259e6 −0.0545901
\(947\) 4.42575e7 1.60366 0.801830 0.597552i \(-0.203860\pi\)
0.801830 + 0.597552i \(0.203860\pi\)
\(948\) −3.37249e7 −1.21879
\(949\) 2.88531e7 1.03999
\(950\) 3.38415e6 0.121658
\(951\) 8.64013e6 0.309791
\(952\) 1.90514e7 0.681293
\(953\) 2.46336e7 0.878609 0.439304 0.898338i \(-0.355225\pi\)
0.439304 + 0.898338i \(0.355225\pi\)
\(954\) 1.00384e6 0.0357104
\(955\) 2.23451e7 0.792820
\(956\) −3.76573e7 −1.33261
\(957\) −3.46049e7 −1.22140
\(958\) 1.58008e7 0.556244
\(959\) −4.46056e7 −1.56618
\(960\) −8.40512e6 −0.294351
\(961\) −2.77844e7 −0.970492
\(962\) 5.70266e6 0.198673
\(963\) −3.18170e6 −0.110559
\(964\) −4.32856e7 −1.50021
\(965\) 3.16760e6 0.109499
\(966\) −5.08071e6 −0.175179
\(967\) −1.51031e7 −0.519397 −0.259698 0.965690i \(-0.583623\pi\)
−0.259698 + 0.965690i \(0.583623\pi\)
\(968\) 3.35488e6 0.115077
\(969\) −1.68139e7 −0.575253
\(970\) 1.14429e7 0.390487
\(971\) 2.95351e7 1.00529 0.502643 0.864494i \(-0.332361\pi\)
0.502643 + 0.864494i \(0.332361\pi\)
\(972\) 4.70646e6 0.159782
\(973\) 2.98583e6 0.101107
\(974\) −1.38817e7 −0.468863
\(975\) −1.23195e7 −0.415031
\(976\) 3.23371e7 1.08662
\(977\) 2.11745e7 0.709705 0.354852 0.934922i \(-0.384531\pi\)
0.354852 + 0.934922i \(0.384531\pi\)
\(978\) 1.82724e7 0.610869
\(979\) −7.19505e6 −0.239926
\(980\) 2.94004e7 0.977886
\(981\) 1.61833e6 0.0536900
\(982\) −4.58810e6 −0.151829
\(983\) −1.08531e7 −0.358236 −0.179118 0.983828i \(-0.557324\pi\)
−0.179118 + 0.983828i \(0.557324\pi\)
\(984\) 9.93394e6 0.327065
\(985\) −3.13219e7 −1.02863
\(986\) −8.25841e6 −0.270523
\(987\) −5.37774e7 −1.75714
\(988\) 2.39141e7 0.779402
\(989\) −1.67302e6 −0.0543888
\(990\) −749479. −0.0243037
\(991\) −1.68782e7 −0.545936 −0.272968 0.962023i \(-0.588005\pi\)
−0.272968 + 0.962023i \(0.588005\pi\)
\(992\) −4.51561e6 −0.145693
\(993\) 3.78116e7 1.21689
\(994\) −676857. −0.0217286
\(995\) 1.97513e6 0.0632466
\(996\) 3.87082e7 1.23639
\(997\) −1.21396e7 −0.386783 −0.193392 0.981122i \(-0.561949\pi\)
−0.193392 + 0.981122i \(0.561949\pi\)
\(998\) 3.78496e6 0.120291
\(999\) 1.95462e7 0.619653
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 43.6.a.b.1.5 10
3.2 odd 2 387.6.a.e.1.6 10
4.3 odd 2 688.6.a.h.1.8 10
5.4 even 2 1075.6.a.b.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.5 10 1.1 even 1 trivial
387.6.a.e.1.6 10 3.2 odd 2
688.6.a.h.1.8 10 4.3 odd 2
1075.6.a.b.1.6 10 5.4 even 2