Properties

Label 1045.6.a.h.1.4
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(167.601091705\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.1541 q^{2} -26.5431 q^{3} +71.1059 q^{4} +25.0000 q^{5} +269.522 q^{6} +225.388 q^{7} -397.085 q^{8} +461.539 q^{9} +O(q^{10})\) \(q-10.1541 q^{2} -26.5431 q^{3} +71.1059 q^{4} +25.0000 q^{5} +269.522 q^{6} +225.388 q^{7} -397.085 q^{8} +461.539 q^{9} -253.853 q^{10} +121.000 q^{11} -1887.37 q^{12} +301.560 q^{13} -2288.62 q^{14} -663.579 q^{15} +1756.66 q^{16} +2040.38 q^{17} -4686.51 q^{18} +361.000 q^{19} +1777.65 q^{20} -5982.51 q^{21} -1228.65 q^{22} -4324.44 q^{23} +10539.9 q^{24} +625.000 q^{25} -3062.07 q^{26} -5800.70 q^{27} +16026.4 q^{28} -3919.47 q^{29} +6738.05 q^{30} -6975.87 q^{31} -5130.56 q^{32} -3211.72 q^{33} -20718.3 q^{34} +5634.70 q^{35} +32818.1 q^{36} -5293.41 q^{37} -3665.63 q^{38} -8004.34 q^{39} -9927.13 q^{40} +9357.37 q^{41} +60747.0 q^{42} -2266.87 q^{43} +8603.81 q^{44} +11538.5 q^{45} +43910.8 q^{46} +20194.6 q^{47} -46627.2 q^{48} +33992.8 q^{49} -6346.32 q^{50} -54158.2 q^{51} +21442.7 q^{52} +9539.74 q^{53} +58900.9 q^{54} +3025.00 q^{55} -89498.3 q^{56} -9582.08 q^{57} +39798.7 q^{58} +49102.9 q^{59} -47184.3 q^{60} -53831.1 q^{61} +70833.7 q^{62} +104025. q^{63} -4116.81 q^{64} +7538.99 q^{65} +32612.2 q^{66} +67595.6 q^{67} +145083. q^{68} +114784. q^{69} -57215.4 q^{70} +37673.0 q^{71} -183270. q^{72} +10208.0 q^{73} +53749.8 q^{74} -16589.5 q^{75} +25669.2 q^{76} +27272.0 q^{77} +81276.9 q^{78} -86791.0 q^{79} +43916.4 q^{80} +41814.9 q^{81} -95015.7 q^{82} +52744.8 q^{83} -425392. q^{84} +51009.6 q^{85} +23018.0 q^{86} +104035. q^{87} -48047.3 q^{88} -33484.9 q^{89} -117163. q^{90} +67968.0 q^{91} -307493. q^{92} +185161. q^{93} -205058. q^{94} +9025.00 q^{95} +136181. q^{96} -125580. q^{97} -345167. q^{98} +55846.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + O(q^{10}) \) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.1541 −1.79501 −0.897505 0.441005i \(-0.854622\pi\)
−0.897505 + 0.441005i \(0.854622\pi\)
\(3\) −26.5431 −1.70274 −0.851372 0.524563i \(-0.824229\pi\)
−0.851372 + 0.524563i \(0.824229\pi\)
\(4\) 71.1059 2.22206
\(5\) 25.0000 0.447214
\(6\) 269.522 3.05644
\(7\) 225.388 1.73855 0.869273 0.494333i \(-0.164588\pi\)
0.869273 + 0.494333i \(0.164588\pi\)
\(8\) −397.085 −2.19361
\(9\) 461.539 1.89934
\(10\) −253.853 −0.802753
\(11\) 121.000 0.301511
\(12\) −1887.37 −3.78360
\(13\) 301.560 0.494897 0.247448 0.968901i \(-0.420408\pi\)
0.247448 + 0.968901i \(0.420408\pi\)
\(14\) −2288.62 −3.12070
\(15\) −663.579 −0.761490
\(16\) 1756.66 1.71549
\(17\) 2040.38 1.71234 0.856169 0.516696i \(-0.172838\pi\)
0.856169 + 0.516696i \(0.172838\pi\)
\(18\) −4686.51 −3.40932
\(19\) 361.000 0.229416
\(20\) 1777.65 0.993735
\(21\) −5982.51 −2.96030
\(22\) −1228.65 −0.541216
\(23\) −4324.44 −1.70455 −0.852276 0.523093i \(-0.824778\pi\)
−0.852276 + 0.523093i \(0.824778\pi\)
\(24\) 10539.9 3.73515
\(25\) 625.000 0.200000
\(26\) −3062.07 −0.888345
\(27\) −5800.70 −1.53134
\(28\) 16026.4 3.86315
\(29\) −3919.47 −0.865430 −0.432715 0.901531i \(-0.642444\pi\)
−0.432715 + 0.901531i \(0.642444\pi\)
\(30\) 6738.05 1.36688
\(31\) −6975.87 −1.30375 −0.651874 0.758327i \(-0.726017\pi\)
−0.651874 + 0.758327i \(0.726017\pi\)
\(32\) −5130.56 −0.885706
\(33\) −3211.72 −0.513396
\(34\) −20718.3 −3.07366
\(35\) 5634.70 0.777501
\(36\) 32818.1 4.22043
\(37\) −5293.41 −0.635669 −0.317834 0.948146i \(-0.602956\pi\)
−0.317834 + 0.948146i \(0.602956\pi\)
\(38\) −3665.63 −0.411803
\(39\) −8004.34 −0.842683
\(40\) −9927.13 −0.981011
\(41\) 9357.37 0.869349 0.434675 0.900588i \(-0.356863\pi\)
0.434675 + 0.900588i \(0.356863\pi\)
\(42\) 60747.0 5.31376
\(43\) −2266.87 −0.186963 −0.0934814 0.995621i \(-0.529800\pi\)
−0.0934814 + 0.995621i \(0.529800\pi\)
\(44\) 8603.81 0.669976
\(45\) 11538.5 0.849409
\(46\) 43910.8 3.05969
\(47\) 20194.6 1.33349 0.666746 0.745285i \(-0.267687\pi\)
0.666746 + 0.745285i \(0.267687\pi\)
\(48\) −46627.2 −2.92103
\(49\) 33992.8 2.02254
\(50\) −6346.32 −0.359002
\(51\) −54158.2 −2.91567
\(52\) 21442.7 1.09969
\(53\) 9539.74 0.466495 0.233247 0.972417i \(-0.425065\pi\)
0.233247 + 0.972417i \(0.425065\pi\)
\(54\) 58900.9 2.74877
\(55\) 3025.00 0.134840
\(56\) −89498.3 −3.81368
\(57\) −9582.08 −0.390636
\(58\) 39798.7 1.55346
\(59\) 49102.9 1.83644 0.918221 0.396069i \(-0.129626\pi\)
0.918221 + 0.396069i \(0.129626\pi\)
\(60\) −47184.3 −1.69208
\(61\) −53831.1 −1.85229 −0.926144 0.377170i \(-0.876897\pi\)
−0.926144 + 0.377170i \(0.876897\pi\)
\(62\) 70833.7 2.34024
\(63\) 104025. 3.30208
\(64\) −4116.81 −0.125635
\(65\) 7538.99 0.221325
\(66\) 32612.2 0.921551
\(67\) 67595.6 1.83964 0.919818 0.392346i \(-0.128337\pi\)
0.919818 + 0.392346i \(0.128337\pi\)
\(68\) 145083. 3.80492
\(69\) 114784. 2.90241
\(70\) −57215.4 −1.39562
\(71\) 37673.0 0.886919 0.443459 0.896294i \(-0.353751\pi\)
0.443459 + 0.896294i \(0.353751\pi\)
\(72\) −183270. −4.16639
\(73\) 10208.0 0.224199 0.112099 0.993697i \(-0.464242\pi\)
0.112099 + 0.993697i \(0.464242\pi\)
\(74\) 53749.8 1.14103
\(75\) −16589.5 −0.340549
\(76\) 25669.2 0.509775
\(77\) 27272.0 0.524191
\(78\) 81276.9 1.51262
\(79\) −86791.0 −1.56461 −0.782306 0.622894i \(-0.785957\pi\)
−0.782306 + 0.622894i \(0.785957\pi\)
\(80\) 43916.4 0.767188
\(81\) 41814.9 0.708140
\(82\) −95015.7 −1.56049
\(83\) 52744.8 0.840397 0.420199 0.907432i \(-0.361960\pi\)
0.420199 + 0.907432i \(0.361960\pi\)
\(84\) −425392. −6.57795
\(85\) 51009.6 0.765781
\(86\) 23018.0 0.335600
\(87\) 104035. 1.47361
\(88\) −48047.3 −0.661397
\(89\) −33484.9 −0.448099 −0.224049 0.974578i \(-0.571928\pi\)
−0.224049 + 0.974578i \(0.571928\pi\)
\(90\) −117163. −1.52470
\(91\) 67968.0 0.860401
\(92\) −307493. −3.78761
\(93\) 185161. 2.21995
\(94\) −205058. −2.39363
\(95\) 9025.00 0.102598
\(96\) 136181. 1.50813
\(97\) −125580. −1.35516 −0.677580 0.735449i \(-0.736971\pi\)
−0.677580 + 0.735449i \(0.736971\pi\)
\(98\) −345167. −3.63048
\(99\) 55846.2 0.572671
\(100\) 44441.2 0.444412
\(101\) −65113.3 −0.635135 −0.317568 0.948236i \(-0.602866\pi\)
−0.317568 + 0.948236i \(0.602866\pi\)
\(102\) 549928. 5.23366
\(103\) −2943.09 −0.0273345 −0.0136672 0.999907i \(-0.504351\pi\)
−0.0136672 + 0.999907i \(0.504351\pi\)
\(104\) −119745. −1.08561
\(105\) −149563. −1.32388
\(106\) −96867.5 −0.837363
\(107\) −133233. −1.12500 −0.562501 0.826796i \(-0.690161\pi\)
−0.562501 + 0.826796i \(0.690161\pi\)
\(108\) −412464. −3.40272
\(109\) −172712. −1.39238 −0.696189 0.717858i \(-0.745123\pi\)
−0.696189 + 0.717858i \(0.745123\pi\)
\(110\) −30716.2 −0.242039
\(111\) 140504. 1.08238
\(112\) 395930. 2.98245
\(113\) 222419. 1.63861 0.819303 0.573360i \(-0.194360\pi\)
0.819303 + 0.573360i \(0.194360\pi\)
\(114\) 97297.4 0.701196
\(115\) −108111. −0.762299
\(116\) −278697. −1.92304
\(117\) 139181. 0.939975
\(118\) −498596. −3.29643
\(119\) 459878. 2.97698
\(120\) 263497. 1.67041
\(121\) 14641.0 0.0909091
\(122\) 546607. 3.32487
\(123\) −248374. −1.48028
\(124\) −496025. −2.89701
\(125\) 15625.0 0.0894427
\(126\) −1.05628e6 −5.92727
\(127\) 79680.3 0.438371 0.219185 0.975683i \(-0.429660\pi\)
0.219185 + 0.975683i \(0.429660\pi\)
\(128\) 205980. 1.11122
\(129\) 60169.8 0.318350
\(130\) −76551.7 −0.397280
\(131\) −28314.1 −0.144153 −0.0720767 0.997399i \(-0.522963\pi\)
−0.0720767 + 0.997399i \(0.522963\pi\)
\(132\) −228372. −1.14080
\(133\) 81365.1 0.398850
\(134\) −686373. −3.30216
\(135\) −145017. −0.684835
\(136\) −810206. −3.75620
\(137\) −32655.6 −0.148647 −0.0743235 0.997234i \(-0.523680\pi\)
−0.0743235 + 0.997234i \(0.523680\pi\)
\(138\) −1.16553e6 −5.20986
\(139\) 370256. 1.62542 0.812709 0.582670i \(-0.197992\pi\)
0.812709 + 0.582670i \(0.197992\pi\)
\(140\) 400661. 1.72765
\(141\) −536028. −2.27059
\(142\) −382535. −1.59203
\(143\) 36488.7 0.149217
\(144\) 810765. 3.25828
\(145\) −97986.7 −0.387032
\(146\) −103653. −0.402439
\(147\) −902276. −3.44387
\(148\) −376392. −1.41249
\(149\) 86222.3 0.318166 0.159083 0.987265i \(-0.449146\pi\)
0.159083 + 0.987265i \(0.449146\pi\)
\(150\) 168451. 0.611288
\(151\) −11798.8 −0.0421111 −0.0210555 0.999778i \(-0.506703\pi\)
−0.0210555 + 0.999778i \(0.506703\pi\)
\(152\) −143348. −0.503248
\(153\) 941716. 3.25230
\(154\) −276922. −0.940928
\(155\) −174397. −0.583054
\(156\) −569156. −1.87249
\(157\) 460605. 1.49135 0.745675 0.666310i \(-0.232127\pi\)
0.745675 + 0.666310i \(0.232127\pi\)
\(158\) 881285. 2.80849
\(159\) −253215. −0.794321
\(160\) −128264. −0.396100
\(161\) −974677. −2.96344
\(162\) −424593. −1.27112
\(163\) 487602. 1.43746 0.718732 0.695287i \(-0.244723\pi\)
0.718732 + 0.695287i \(0.244723\pi\)
\(164\) 665364. 1.93174
\(165\) −80293.0 −0.229598
\(166\) −535576. −1.50852
\(167\) 363771. 1.00934 0.504670 0.863313i \(-0.331614\pi\)
0.504670 + 0.863313i \(0.331614\pi\)
\(168\) 2.37557e6 6.49373
\(169\) −280355. −0.755077
\(170\) −517957. −1.37458
\(171\) 166615. 0.435737
\(172\) −161188. −0.415442
\(173\) −163994. −0.416595 −0.208297 0.978066i \(-0.566792\pi\)
−0.208297 + 0.978066i \(0.566792\pi\)
\(174\) −1.05638e6 −2.64514
\(175\) 140868. 0.347709
\(176\) 212555. 0.517238
\(177\) −1.30335e6 −3.12699
\(178\) 340009. 0.804342
\(179\) 673625. 1.57140 0.785698 0.618611i \(-0.212304\pi\)
0.785698 + 0.618611i \(0.212304\pi\)
\(180\) 820452. 1.88744
\(181\) −100232. −0.227411 −0.113705 0.993515i \(-0.536272\pi\)
−0.113705 + 0.993515i \(0.536272\pi\)
\(182\) −690154. −1.54443
\(183\) 1.42885e6 3.15397
\(184\) 1.71717e6 3.73911
\(185\) −132335. −0.284280
\(186\) −1.88015e6 −3.98483
\(187\) 246886. 0.516289
\(188\) 1.43595e6 2.96310
\(189\) −1.30741e6 −2.66230
\(190\) −91640.8 −0.184164
\(191\) −486687. −0.965309 −0.482655 0.875811i \(-0.660327\pi\)
−0.482655 + 0.875811i \(0.660327\pi\)
\(192\) 109273. 0.213925
\(193\) −27158.2 −0.0524817 −0.0262408 0.999656i \(-0.508354\pi\)
−0.0262408 + 0.999656i \(0.508354\pi\)
\(194\) 1.27515e6 2.43252
\(195\) −200109. −0.376859
\(196\) 2.41709e6 4.49420
\(197\) 1.03646e6 1.90277 0.951386 0.308000i \(-0.0996598\pi\)
0.951386 + 0.308000i \(0.0996598\pi\)
\(198\) −567068. −1.02795
\(199\) 92983.3 0.166446 0.0832228 0.996531i \(-0.473479\pi\)
0.0832228 + 0.996531i \(0.473479\pi\)
\(200\) −248178. −0.438721
\(201\) −1.79420e6 −3.13243
\(202\) 661167. 1.14007
\(203\) −883402. −1.50459
\(204\) −3.85097e6 −6.47879
\(205\) 233934. 0.388785
\(206\) 29884.4 0.0490656
\(207\) −1.99589e6 −3.23751
\(208\) 529737. 0.848988
\(209\) 43681.0 0.0691714
\(210\) 1.51868e6 2.37639
\(211\) 774246. 1.19722 0.598608 0.801042i \(-0.295721\pi\)
0.598608 + 0.801042i \(0.295721\pi\)
\(212\) 678332. 1.03658
\(213\) −999959. −1.51020
\(214\) 1.35287e6 2.01939
\(215\) −56671.7 −0.0836123
\(216\) 2.30337e6 3.35915
\(217\) −1.57228e6 −2.26663
\(218\) 1.75374e6 2.49933
\(219\) −270952. −0.381753
\(220\) 215095. 0.299622
\(221\) 615297. 0.847431
\(222\) −1.42669e6 −1.94288
\(223\) −1.31638e6 −1.77263 −0.886317 0.463079i \(-0.846744\pi\)
−0.886317 + 0.463079i \(0.846744\pi\)
\(224\) −1.15637e6 −1.53984
\(225\) 288462. 0.379867
\(226\) −2.25846e6 −2.94131
\(227\) −297690. −0.383441 −0.191721 0.981450i \(-0.561407\pi\)
−0.191721 + 0.981450i \(0.561407\pi\)
\(228\) −681342. −0.868016
\(229\) 188631. 0.237697 0.118849 0.992912i \(-0.462080\pi\)
0.118849 + 0.992912i \(0.462080\pi\)
\(230\) 1.09777e6 1.36833
\(231\) −723884. −0.892563
\(232\) 1.55636e6 1.89841
\(233\) 1.13612e6 1.37100 0.685498 0.728074i \(-0.259584\pi\)
0.685498 + 0.728074i \(0.259584\pi\)
\(234\) −1.41326e6 −1.68726
\(235\) 504865. 0.596356
\(236\) 3.49150e6 4.08068
\(237\) 2.30371e6 2.66413
\(238\) −4.66965e6 −5.34370
\(239\) 1.07740e6 1.22006 0.610032 0.792377i \(-0.291157\pi\)
0.610032 + 0.792377i \(0.291157\pi\)
\(240\) −1.16568e6 −1.30632
\(241\) −377432. −0.418597 −0.209299 0.977852i \(-0.567118\pi\)
−0.209299 + 0.977852i \(0.567118\pi\)
\(242\) −148666. −0.163183
\(243\) 299670. 0.325557
\(244\) −3.82771e6 −4.11589
\(245\) 849821. 0.904507
\(246\) 2.52202e6 2.65711
\(247\) 108863. 0.113537
\(248\) 2.77001e6 2.85991
\(249\) −1.40001e6 −1.43098
\(250\) −158658. −0.160551
\(251\) −902541. −0.904238 −0.452119 0.891958i \(-0.649332\pi\)
−0.452119 + 0.891958i \(0.649332\pi\)
\(252\) 7.39681e6 7.33742
\(253\) −523257. −0.513942
\(254\) −809082. −0.786880
\(255\) −1.35395e6 −1.30393
\(256\) −1.95981e6 −1.86902
\(257\) −677407. −0.639759 −0.319880 0.947458i \(-0.603643\pi\)
−0.319880 + 0.947458i \(0.603643\pi\)
\(258\) −610971. −0.571441
\(259\) −1.19307e6 −1.10514
\(260\) 536066. 0.491796
\(261\) −1.80899e6 −1.64374
\(262\) 287505. 0.258757
\(263\) −1.24926e6 −1.11369 −0.556845 0.830617i \(-0.687988\pi\)
−0.556845 + 0.830617i \(0.687988\pi\)
\(264\) 1.27533e6 1.12619
\(265\) 238494. 0.208623
\(266\) −826190. −0.715939
\(267\) 888794. 0.762997
\(268\) 4.80645e6 4.08778
\(269\) 197672. 0.166558 0.0832788 0.996526i \(-0.473461\pi\)
0.0832788 + 0.996526i \(0.473461\pi\)
\(270\) 1.47252e6 1.22929
\(271\) −2.29425e6 −1.89765 −0.948826 0.315799i \(-0.897728\pi\)
−0.948826 + 0.315799i \(0.897728\pi\)
\(272\) 3.58425e6 2.93749
\(273\) −1.80408e6 −1.46504
\(274\) 331588. 0.266823
\(275\) 75625.0 0.0603023
\(276\) 8.16183e6 6.44933
\(277\) 1.80573e6 1.41401 0.707005 0.707208i \(-0.250046\pi\)
0.707005 + 0.707208i \(0.250046\pi\)
\(278\) −3.75962e6 −2.91764
\(279\) −3.21963e6 −2.47626
\(280\) −2.23746e6 −1.70553
\(281\) −397475. −0.300292 −0.150146 0.988664i \(-0.547974\pi\)
−0.150146 + 0.988664i \(0.547974\pi\)
\(282\) 5.44288e6 4.07574
\(283\) 404247. 0.300041 0.150020 0.988683i \(-0.452066\pi\)
0.150020 + 0.988683i \(0.452066\pi\)
\(284\) 2.67877e6 1.97079
\(285\) −239552. −0.174698
\(286\) −370510. −0.267846
\(287\) 2.10904e6 1.51140
\(288\) −2.36795e6 −1.68225
\(289\) 2.74331e6 1.93210
\(290\) 994967. 0.694726
\(291\) 3.33328e6 2.30749
\(292\) 725848. 0.498183
\(293\) 40076.3 0.0272721 0.0136361 0.999907i \(-0.495659\pi\)
0.0136361 + 0.999907i \(0.495659\pi\)
\(294\) 9.16181e6 6.18177
\(295\) 1.22757e6 0.821282
\(296\) 2.10193e6 1.39441
\(297\) −701885. −0.461716
\(298\) −875510. −0.571111
\(299\) −1.30408e6 −0.843577
\(300\) −1.17961e6 −0.756719
\(301\) −510926. −0.325043
\(302\) 119806. 0.0755897
\(303\) 1.72831e6 1.08147
\(304\) 634153. 0.393559
\(305\) −1.34578e6 −0.828368
\(306\) −9.56228e6 −5.83792
\(307\) 264356. 0.160082 0.0800411 0.996792i \(-0.474495\pi\)
0.0800411 + 0.996792i \(0.474495\pi\)
\(308\) 1.93920e6 1.16478
\(309\) 78118.8 0.0465436
\(310\) 1.77084e6 1.04659
\(311\) 796081. 0.466720 0.233360 0.972390i \(-0.425028\pi\)
0.233360 + 0.972390i \(0.425028\pi\)
\(312\) 3.17840e6 1.84851
\(313\) −1.51951e6 −0.876685 −0.438342 0.898808i \(-0.644434\pi\)
−0.438342 + 0.898808i \(0.644434\pi\)
\(314\) −4.67703e6 −2.67699
\(315\) 2.60063e6 1.47674
\(316\) −6.17135e6 −3.47666
\(317\) 1.15691e6 0.646626 0.323313 0.946292i \(-0.395203\pi\)
0.323313 + 0.946292i \(0.395203\pi\)
\(318\) 2.57117e6 1.42581
\(319\) −474256. −0.260937
\(320\) −102920. −0.0561858
\(321\) 3.53643e6 1.91559
\(322\) 9.89698e6 5.31940
\(323\) 736578. 0.392837
\(324\) 2.97329e6 1.57353
\(325\) 188475. 0.0989794
\(326\) −4.95117e6 −2.58026
\(327\) 4.58433e6 2.37086
\(328\) −3.71567e6 −1.90701
\(329\) 4.55162e6 2.31834
\(330\) 815304. 0.412130
\(331\) 1.74505e6 0.875464 0.437732 0.899106i \(-0.355782\pi\)
0.437732 + 0.899106i \(0.355782\pi\)
\(332\) 3.75047e6 1.86741
\(333\) −2.44311e6 −1.20735
\(334\) −3.69377e6 −1.81177
\(335\) 1.68989e6 0.822710
\(336\) −1.05092e7 −5.07835
\(337\) −450377. −0.216024 −0.108012 0.994150i \(-0.534448\pi\)
−0.108012 + 0.994150i \(0.534448\pi\)
\(338\) 2.84675e6 1.35537
\(339\) −5.90369e6 −2.79013
\(340\) 3.62708e6 1.70161
\(341\) −844080. −0.393095
\(342\) −1.69183e6 −0.782153
\(343\) 3.87348e6 1.77773
\(344\) 900140. 0.410123
\(345\) 2.86960e6 1.29800
\(346\) 1.66522e6 0.747792
\(347\) −1.95861e6 −0.873221 −0.436611 0.899651i \(-0.643821\pi\)
−0.436611 + 0.899651i \(0.643821\pi\)
\(348\) 7.39750e6 3.27444
\(349\) 2.25042e6 0.989009 0.494505 0.869175i \(-0.335349\pi\)
0.494505 + 0.869175i \(0.335349\pi\)
\(350\) −1.43038e6 −0.624141
\(351\) −1.74926e6 −0.757854
\(352\) −620797. −0.267050
\(353\) −1.17412e6 −0.501506 −0.250753 0.968051i \(-0.580678\pi\)
−0.250753 + 0.968051i \(0.580678\pi\)
\(354\) 1.32343e7 5.61298
\(355\) 941824. 0.396642
\(356\) −2.38097e6 −0.995702
\(357\) −1.22066e7 −5.06903
\(358\) −6.84006e6 −2.82067
\(359\) −96972.8 −0.0397113 −0.0198556 0.999803i \(-0.506321\pi\)
−0.0198556 + 0.999803i \(0.506321\pi\)
\(360\) −4.58175e6 −1.86327
\(361\) 130321. 0.0526316
\(362\) 1.01777e6 0.408205
\(363\) −388618. −0.154795
\(364\) 4.83292e6 1.91186
\(365\) 255200. 0.100265
\(366\) −1.45087e7 −5.66141
\(367\) 2.28277e6 0.884702 0.442351 0.896842i \(-0.354145\pi\)
0.442351 + 0.896842i \(0.354145\pi\)
\(368\) −7.59655e6 −2.92413
\(369\) 4.31879e6 1.65119
\(370\) 1.34375e6 0.510285
\(371\) 2.15014e6 0.811023
\(372\) 1.31661e7 4.93286
\(373\) 1.40204e6 0.521782 0.260891 0.965368i \(-0.415984\pi\)
0.260891 + 0.965368i \(0.415984\pi\)
\(374\) −2.50691e6 −0.926744
\(375\) −414737. −0.152298
\(376\) −8.01897e6 −2.92516
\(377\) −1.18195e6 −0.428299
\(378\) 1.32756e7 4.77885
\(379\) 3.98577e6 1.42532 0.712662 0.701507i \(-0.247489\pi\)
0.712662 + 0.701507i \(0.247489\pi\)
\(380\) 641730. 0.227978
\(381\) −2.11497e6 −0.746433
\(382\) 4.94187e6 1.73274
\(383\) −394403. −0.137386 −0.0686931 0.997638i \(-0.521883\pi\)
−0.0686931 + 0.997638i \(0.521883\pi\)
\(384\) −5.46737e6 −1.89213
\(385\) 681799. 0.234425
\(386\) 275767. 0.0942051
\(387\) −1.04625e6 −0.355105
\(388\) −8.92946e6 −3.01124
\(389\) −4.68652e6 −1.57028 −0.785138 0.619320i \(-0.787408\pi\)
−0.785138 + 0.619320i \(0.787408\pi\)
\(390\) 2.03192e6 0.676466
\(391\) −8.82351e6 −2.91877
\(392\) −1.34980e7 −4.43666
\(393\) 751546. 0.245456
\(394\) −1.05243e7 −3.41549
\(395\) −2.16977e6 −0.699716
\(396\) 3.97099e6 1.27251
\(397\) −3.86740e6 −1.23152 −0.615762 0.787932i \(-0.711152\pi\)
−0.615762 + 0.787932i \(0.711152\pi\)
\(398\) −944163. −0.298771
\(399\) −2.15969e6 −0.679139
\(400\) 1.09791e6 0.343097
\(401\) 245850. 0.0763499 0.0381750 0.999271i \(-0.487846\pi\)
0.0381750 + 0.999271i \(0.487846\pi\)
\(402\) 1.82185e7 5.62274
\(403\) −2.10364e6 −0.645221
\(404\) −4.62994e6 −1.41131
\(405\) 1.04537e6 0.316690
\(406\) 8.97015e6 2.70075
\(407\) −640502. −0.191661
\(408\) 2.15054e7 6.39584
\(409\) 904301. 0.267304 0.133652 0.991028i \(-0.457330\pi\)
0.133652 + 0.991028i \(0.457330\pi\)
\(410\) −2.37539e6 −0.697872
\(411\) 866782. 0.253108
\(412\) −209271. −0.0607388
\(413\) 1.10672e7 3.19274
\(414\) 2.02665e7 5.81137
\(415\) 1.31862e6 0.375837
\(416\) −1.54717e6 −0.438333
\(417\) −9.82776e6 −2.76767
\(418\) −443542. −0.124163
\(419\) 1.74051e6 0.484331 0.242165 0.970235i \(-0.422142\pi\)
0.242165 + 0.970235i \(0.422142\pi\)
\(420\) −1.06348e7 −2.94175
\(421\) 4.53648e6 1.24742 0.623712 0.781654i \(-0.285624\pi\)
0.623712 + 0.781654i \(0.285624\pi\)
\(422\) −7.86177e6 −2.14901
\(423\) 9.32058e6 2.53275
\(424\) −3.78809e6 −1.02331
\(425\) 1.27524e6 0.342468
\(426\) 1.01537e7 2.71081
\(427\) −1.21329e7 −3.22029
\(428\) −9.47367e6 −2.49982
\(429\) −968525. −0.254078
\(430\) 575451. 0.150085
\(431\) 1.60114e6 0.415181 0.207590 0.978216i \(-0.433438\pi\)
0.207590 + 0.978216i \(0.433438\pi\)
\(432\) −1.01898e7 −2.62699
\(433\) −2.28982e6 −0.586923 −0.293461 0.955971i \(-0.594807\pi\)
−0.293461 + 0.955971i \(0.594807\pi\)
\(434\) 1.59651e7 4.06862
\(435\) 2.60088e6 0.659017
\(436\) −1.22809e7 −3.09395
\(437\) −1.56112e6 −0.391051
\(438\) 2.75128e6 0.685250
\(439\) 2.58669e6 0.640594 0.320297 0.947317i \(-0.396217\pi\)
0.320297 + 0.947317i \(0.396217\pi\)
\(440\) −1.20118e6 −0.295786
\(441\) 1.56890e7 3.84148
\(442\) −6.24779e6 −1.52115
\(443\) −925017. −0.223945 −0.111972 0.993711i \(-0.535717\pi\)
−0.111972 + 0.993711i \(0.535717\pi\)
\(444\) 9.99064e6 2.40511
\(445\) −837122. −0.200396
\(446\) 1.33667e7 3.18189
\(447\) −2.28861e6 −0.541755
\(448\) −927881. −0.218422
\(449\) −2.43364e6 −0.569693 −0.284847 0.958573i \(-0.591943\pi\)
−0.284847 + 0.958573i \(0.591943\pi\)
\(450\) −2.92907e6 −0.681865
\(451\) 1.13224e6 0.262119
\(452\) 1.58153e7 3.64108
\(453\) 313178. 0.0717043
\(454\) 3.02277e6 0.688281
\(455\) 1.69920e6 0.384783
\(456\) 3.80490e6 0.856902
\(457\) −4.44298e6 −0.995139 −0.497570 0.867424i \(-0.665774\pi\)
−0.497570 + 0.867424i \(0.665774\pi\)
\(458\) −1.91538e6 −0.426669
\(459\) −1.18357e7 −2.62217
\(460\) −7.68732e6 −1.69387
\(461\) −2.88800e6 −0.632914 −0.316457 0.948607i \(-0.602493\pi\)
−0.316457 + 0.948607i \(0.602493\pi\)
\(462\) 7.35039e6 1.60216
\(463\) −5.76578e6 −1.24999 −0.624994 0.780630i \(-0.714899\pi\)
−0.624994 + 0.780630i \(0.714899\pi\)
\(464\) −6.88516e6 −1.48463
\(465\) 4.62904e6 0.992792
\(466\) −1.15363e7 −2.46095
\(467\) 9.08207e6 1.92705 0.963524 0.267622i \(-0.0862380\pi\)
0.963524 + 0.267622i \(0.0862380\pi\)
\(468\) 9.89661e6 2.08868
\(469\) 1.52353e7 3.19829
\(470\) −5.12645e6 −1.07046
\(471\) −1.22259e7 −2.53939
\(472\) −1.94980e7 −4.02843
\(473\) −274291. −0.0563714
\(474\) −2.33921e7 −4.78215
\(475\) 225625. 0.0458831
\(476\) 3.27000e7 6.61502
\(477\) 4.40296e6 0.886030
\(478\) −1.09400e7 −2.19003
\(479\) 4.72261e6 0.940466 0.470233 0.882542i \(-0.344170\pi\)
0.470233 + 0.882542i \(0.344170\pi\)
\(480\) 3.40453e6 0.674456
\(481\) −1.59628e6 −0.314591
\(482\) 3.83249e6 0.751386
\(483\) 2.58710e7 5.04598
\(484\) 1.04106e6 0.202005
\(485\) −3.13950e6 −0.606046
\(486\) −3.04288e6 −0.584379
\(487\) 6.38443e6 1.21983 0.609916 0.792466i \(-0.291203\pi\)
0.609916 + 0.792466i \(0.291203\pi\)
\(488\) 2.13755e7 4.06319
\(489\) −1.29425e7 −2.44763
\(490\) −8.62917e6 −1.62360
\(491\) 8.35168e6 1.56340 0.781700 0.623655i \(-0.214353\pi\)
0.781700 + 0.623655i \(0.214353\pi\)
\(492\) −1.76609e7 −3.28927
\(493\) −7.99722e6 −1.48191
\(494\) −1.10541e6 −0.203800
\(495\) 1.39615e6 0.256106
\(496\) −1.22542e7 −2.23656
\(497\) 8.49104e6 1.54195
\(498\) 1.42159e7 2.56862
\(499\) −1.29797e6 −0.233352 −0.116676 0.993170i \(-0.537224\pi\)
−0.116676 + 0.993170i \(0.537224\pi\)
\(500\) 1.11103e6 0.198747
\(501\) −9.65563e6 −1.71865
\(502\) 9.16450e6 1.62312
\(503\) −7.57590e6 −1.33510 −0.667551 0.744564i \(-0.732657\pi\)
−0.667551 + 0.744564i \(0.732657\pi\)
\(504\) −4.13069e7 −7.24346
\(505\) −1.62783e6 −0.284041
\(506\) 5.31321e6 0.922530
\(507\) 7.44150e6 1.28570
\(508\) 5.66574e6 0.974085
\(509\) 237682. 0.0406632 0.0203316 0.999793i \(-0.493528\pi\)
0.0203316 + 0.999793i \(0.493528\pi\)
\(510\) 1.37482e7 2.34056
\(511\) 2.30076e6 0.389780
\(512\) 1.33087e7 2.24368
\(513\) −2.09405e6 −0.351313
\(514\) 6.87846e6 1.14837
\(515\) −73577.2 −0.0122243
\(516\) 4.27843e6 0.707392
\(517\) 2.44355e6 0.402063
\(518\) 1.21146e7 1.98374
\(519\) 4.35293e6 0.709354
\(520\) −2.99362e6 −0.485499
\(521\) 3.23968e6 0.522887 0.261443 0.965219i \(-0.415802\pi\)
0.261443 + 0.965219i \(0.415802\pi\)
\(522\) 1.83686e7 2.95053
\(523\) −115473. −0.0184597 −0.00922987 0.999957i \(-0.502938\pi\)
−0.00922987 + 0.999957i \(0.502938\pi\)
\(524\) −2.01330e6 −0.320317
\(525\) −3.73907e6 −0.592059
\(526\) 1.26851e7 1.99908
\(527\) −1.42334e7 −2.23246
\(528\) −5.64189e6 −0.880724
\(529\) 1.22644e7 1.90550
\(530\) −2.42169e6 −0.374480
\(531\) 2.26629e7 3.48802
\(532\) 5.78554e6 0.886267
\(533\) 2.82181e6 0.430238
\(534\) −9.02491e6 −1.36959
\(535\) −3.33083e6 −0.503116
\(536\) −2.68412e7 −4.03544
\(537\) −1.78801e7 −2.67568
\(538\) −2.00718e6 −0.298973
\(539\) 4.11313e6 0.609819
\(540\) −1.03116e7 −1.52174
\(541\) −949774. −0.139517 −0.0697585 0.997564i \(-0.522223\pi\)
−0.0697585 + 0.997564i \(0.522223\pi\)
\(542\) 2.32960e7 3.40630
\(543\) 2.66048e6 0.387222
\(544\) −1.04683e7 −1.51663
\(545\) −4.31781e6 −0.622691
\(546\) 1.83189e7 2.62976
\(547\) 4.07296e6 0.582025 0.291012 0.956719i \(-0.406008\pi\)
0.291012 + 0.956719i \(0.406008\pi\)
\(548\) −2.32200e6 −0.330302
\(549\) −2.48451e7 −3.51812
\(550\) −767904. −0.108243
\(551\) −1.41493e6 −0.198543
\(552\) −4.55791e7 −6.36675
\(553\) −1.95617e7 −2.72015
\(554\) −1.83355e7 −2.53816
\(555\) 3.51259e6 0.484056
\(556\) 2.63274e7 3.61177
\(557\) −1.12551e7 −1.53714 −0.768570 0.639766i \(-0.779031\pi\)
−0.768570 + 0.639766i \(0.779031\pi\)
\(558\) 3.26925e7 4.44490
\(559\) −683596. −0.0925274
\(560\) 9.89824e6 1.33379
\(561\) −6.55314e6 −0.879108
\(562\) 4.03600e6 0.539027
\(563\) −751057. −0.0998624 −0.0499312 0.998753i \(-0.515900\pi\)
−0.0499312 + 0.998753i \(0.515900\pi\)
\(564\) −3.81147e7 −5.04539
\(565\) 5.56046e6 0.732807
\(566\) −4.10476e6 −0.538576
\(567\) 9.42459e6 1.23113
\(568\) −1.49594e7 −1.94555
\(569\) −6.45997e6 −0.836470 −0.418235 0.908339i \(-0.637351\pi\)
−0.418235 + 0.908339i \(0.637351\pi\)
\(570\) 2.43244e6 0.313584
\(571\) −7.99521e6 −1.02622 −0.513109 0.858323i \(-0.671506\pi\)
−0.513109 + 0.858323i \(0.671506\pi\)
\(572\) 2.59456e6 0.331569
\(573\) 1.29182e7 1.64367
\(574\) −2.14154e7 −2.71298
\(575\) −2.70277e6 −0.340910
\(576\) −1.90007e6 −0.238623
\(577\) −2.43992e6 −0.305096 −0.152548 0.988296i \(-0.548748\pi\)
−0.152548 + 0.988296i \(0.548748\pi\)
\(578\) −2.78558e7 −3.46814
\(579\) 720864. 0.0893629
\(580\) −6.96743e6 −0.860008
\(581\) 1.18881e7 1.46107
\(582\) −3.38465e7 −4.14197
\(583\) 1.15431e6 0.140654
\(584\) −4.05344e6 −0.491804
\(585\) 3.47953e6 0.420370
\(586\) −406939. −0.0489537
\(587\) −1.64377e6 −0.196900 −0.0984500 0.995142i \(-0.531388\pi\)
−0.0984500 + 0.995142i \(0.531388\pi\)
\(588\) −6.41572e7 −7.65247
\(589\) −2.51829e6 −0.299101
\(590\) −1.24649e7 −1.47421
\(591\) −2.75109e7 −3.23993
\(592\) −9.29870e6 −1.09048
\(593\) 1.22812e7 1.43419 0.717093 0.696977i \(-0.245472\pi\)
0.717093 + 0.696977i \(0.245472\pi\)
\(594\) 7.12701e6 0.828784
\(595\) 1.14970e7 1.33134
\(596\) 6.13091e6 0.706983
\(597\) −2.46807e6 −0.283414
\(598\) 1.32417e7 1.51423
\(599\) 1.47273e7 1.67709 0.838547 0.544829i \(-0.183405\pi\)
0.838547 + 0.544829i \(0.183405\pi\)
\(600\) 6.58743e6 0.747030
\(601\) 6.79536e6 0.767408 0.383704 0.923456i \(-0.374648\pi\)
0.383704 + 0.923456i \(0.374648\pi\)
\(602\) 5.18799e6 0.583456
\(603\) 3.11980e7 3.49408
\(604\) −838965. −0.0935732
\(605\) 366025. 0.0406558
\(606\) −1.75495e7 −1.94125
\(607\) −8.18047e6 −0.901170 −0.450585 0.892734i \(-0.648784\pi\)
−0.450585 + 0.892734i \(0.648784\pi\)
\(608\) −1.85213e6 −0.203195
\(609\) 2.34483e7 2.56193
\(610\) 1.36652e7 1.48693
\(611\) 6.08987e6 0.659941
\(612\) 6.69615e7 7.22681
\(613\) −3.67643e6 −0.395162 −0.197581 0.980287i \(-0.563308\pi\)
−0.197581 + 0.980287i \(0.563308\pi\)
\(614\) −2.68430e6 −0.287349
\(615\) −6.20935e6 −0.662001
\(616\) −1.08293e7 −1.14987
\(617\) −2.73263e6 −0.288980 −0.144490 0.989506i \(-0.546154\pi\)
−0.144490 + 0.989506i \(0.546154\pi\)
\(618\) −793227. −0.0835461
\(619\) −5.52095e6 −0.579145 −0.289572 0.957156i \(-0.593513\pi\)
−0.289572 + 0.957156i \(0.593513\pi\)
\(620\) −1.24006e7 −1.29558
\(621\) 2.50848e7 2.61024
\(622\) −8.08349e6 −0.837767
\(623\) −7.54710e6 −0.779040
\(624\) −1.40609e7 −1.44561
\(625\) 390625. 0.0400000
\(626\) 1.54293e7 1.57366
\(627\) −1.15943e6 −0.117781
\(628\) 3.27517e7 3.31387
\(629\) −1.08006e7 −1.08848
\(630\) −2.64071e7 −2.65075
\(631\) 6.65025e6 0.664912 0.332456 0.943119i \(-0.392123\pi\)
0.332456 + 0.943119i \(0.392123\pi\)
\(632\) 3.44634e7 3.43214
\(633\) −2.05509e7 −2.03855
\(634\) −1.17474e7 −1.16070
\(635\) 1.99201e6 0.196045
\(636\) −1.80051e7 −1.76503
\(637\) 1.02509e7 1.00095
\(638\) 4.81564e6 0.468384
\(639\) 1.73875e7 1.68456
\(640\) 5.14951e6 0.496954
\(641\) −7.19051e6 −0.691217 −0.345608 0.938379i \(-0.612327\pi\)
−0.345608 + 0.938379i \(0.612327\pi\)
\(642\) −3.59093e7 −3.43850
\(643\) −6.58045e6 −0.627665 −0.313833 0.949478i \(-0.601613\pi\)
−0.313833 + 0.949478i \(0.601613\pi\)
\(644\) −6.93053e7 −6.58494
\(645\) 1.50425e6 0.142370
\(646\) −7.47930e6 −0.705147
\(647\) 3.88918e6 0.365256 0.182628 0.983182i \(-0.441540\pi\)
0.182628 + 0.983182i \(0.441540\pi\)
\(648\) −1.66041e7 −1.55338
\(649\) 5.94145e6 0.553708
\(650\) −1.91379e6 −0.177669
\(651\) 4.17332e7 3.85948
\(652\) 3.46714e7 3.19413
\(653\) −1.59534e6 −0.146410 −0.0732048 0.997317i \(-0.523323\pi\)
−0.0732048 + 0.997317i \(0.523323\pi\)
\(654\) −4.65498e7 −4.25572
\(655\) −707854. −0.0644674
\(656\) 1.64377e7 1.49136
\(657\) 4.71138e6 0.425829
\(658\) −4.62177e7 −4.16144
\(659\) −120758. −0.0108318 −0.00541591 0.999985i \(-0.501724\pi\)
−0.00541591 + 0.999985i \(0.501724\pi\)
\(660\) −5.70930e6 −0.510180
\(661\) −2.37243e6 −0.211198 −0.105599 0.994409i \(-0.533676\pi\)
−0.105599 + 0.994409i \(0.533676\pi\)
\(662\) −1.77194e7 −1.57147
\(663\) −1.63319e7 −1.44296
\(664\) −2.09442e7 −1.84350
\(665\) 2.03413e6 0.178371
\(666\) 2.48076e7 2.16720
\(667\) 1.69495e7 1.47517
\(668\) 2.58663e7 2.24281
\(669\) 3.49409e7 3.01834
\(670\) −1.71593e7 −1.47677
\(671\) −6.51356e6 −0.558486
\(672\) 3.06936e7 2.62195
\(673\) 1.50066e7 1.27716 0.638581 0.769555i \(-0.279522\pi\)
0.638581 + 0.769555i \(0.279522\pi\)
\(674\) 4.57318e6 0.387765
\(675\) −3.62544e6 −0.306267
\(676\) −1.99349e7 −1.67783
\(677\) 1.05509e7 0.884743 0.442372 0.896832i \(-0.354137\pi\)
0.442372 + 0.896832i \(0.354137\pi\)
\(678\) 5.99467e7 5.00830
\(679\) −2.83042e7 −2.35601
\(680\) −2.02551e7 −1.67982
\(681\) 7.90162e6 0.652902
\(682\) 8.57088e6 0.705609
\(683\) 1.42631e7 1.16993 0.584967 0.811057i \(-0.301108\pi\)
0.584967 + 0.811057i \(0.301108\pi\)
\(684\) 1.18473e7 0.968234
\(685\) −816390. −0.0664769
\(686\) −3.93317e7 −3.19104
\(687\) −5.00686e6 −0.404738
\(688\) −3.98211e6 −0.320732
\(689\) 2.87680e6 0.230867
\(690\) −2.91383e7 −2.32992
\(691\) −8.18051e6 −0.651756 −0.325878 0.945412i \(-0.605660\pi\)
−0.325878 + 0.945412i \(0.605660\pi\)
\(692\) −1.16610e7 −0.925698
\(693\) 1.25871e7 0.995615
\(694\) 1.98879e7 1.56744
\(695\) 9.25640e6 0.726909
\(696\) −4.13108e7 −3.23251
\(697\) 1.90926e7 1.48862
\(698\) −2.28510e7 −1.77528
\(699\) −3.01563e7 −2.33446
\(700\) 1.00165e7 0.772630
\(701\) −2.26151e6 −0.173821 −0.0869107 0.996216i \(-0.527699\pi\)
−0.0869107 + 0.996216i \(0.527699\pi\)
\(702\) 1.77621e7 1.36036
\(703\) −1.91092e6 −0.145832
\(704\) −498135. −0.0378804
\(705\) −1.34007e7 −1.01544
\(706\) 1.19222e7 0.900209
\(707\) −1.46758e7 −1.10421
\(708\) −9.26755e7 −6.94835
\(709\) −7.90604e6 −0.590668 −0.295334 0.955394i \(-0.595431\pi\)
−0.295334 + 0.955394i \(0.595431\pi\)
\(710\) −9.56338e6 −0.711976
\(711\) −4.00574e7 −2.97172
\(712\) 1.32964e7 0.982952
\(713\) 3.01667e7 2.22231
\(714\) 1.23947e8 9.09895
\(715\) 912218. 0.0667319
\(716\) 4.78987e7 3.49173
\(717\) −2.85976e7 −2.07746
\(718\) 984672. 0.0712821
\(719\) −1.43546e7 −1.03554 −0.517772 0.855519i \(-0.673238\pi\)
−0.517772 + 0.855519i \(0.673238\pi\)
\(720\) 2.02691e7 1.45715
\(721\) −663337. −0.0475222
\(722\) −1.32329e6 −0.0944742
\(723\) 1.00182e7 0.712763
\(724\) −7.12711e6 −0.505320
\(725\) −2.44967e6 −0.173086
\(726\) 3.94607e6 0.277858
\(727\) −5.73300e6 −0.402296 −0.201148 0.979561i \(-0.564467\pi\)
−0.201148 + 0.979561i \(0.564467\pi\)
\(728\) −2.69891e7 −1.88738
\(729\) −1.81152e7 −1.26248
\(730\) −2.59133e6 −0.179976
\(731\) −4.62528e6 −0.320144
\(732\) 1.01599e8 7.00831
\(733\) 1.61841e7 1.11258 0.556288 0.830990i \(-0.312225\pi\)
0.556288 + 0.830990i \(0.312225\pi\)
\(734\) −2.31795e7 −1.58805
\(735\) −2.25569e7 −1.54014
\(736\) 2.21868e7 1.50973
\(737\) 8.17907e6 0.554671
\(738\) −4.38534e7 −2.96389
\(739\) 3.88947e6 0.261987 0.130994 0.991383i \(-0.458183\pi\)
0.130994 + 0.991383i \(0.458183\pi\)
\(740\) −9.40981e6 −0.631686
\(741\) −2.88957e6 −0.193325
\(742\) −2.18328e7 −1.45579
\(743\) 1.66895e7 1.10910 0.554550 0.832150i \(-0.312890\pi\)
0.554550 + 0.832150i \(0.312890\pi\)
\(744\) −7.35249e7 −4.86970
\(745\) 2.15556e6 0.142288
\(746\) −1.42365e7 −0.936603
\(747\) 2.43438e7 1.59620
\(748\) 1.75551e7 1.14723
\(749\) −3.00292e7 −1.95587
\(750\) 4.21128e6 0.273376
\(751\) −5.75777e6 −0.372524 −0.186262 0.982500i \(-0.559637\pi\)
−0.186262 + 0.982500i \(0.559637\pi\)
\(752\) 3.54750e7 2.28759
\(753\) 2.39563e7 1.53968
\(754\) 1.20017e7 0.768800
\(755\) −294970. −0.0188326
\(756\) −9.29644e7 −5.91579
\(757\) −6.78603e6 −0.430404 −0.215202 0.976570i \(-0.569041\pi\)
−0.215202 + 0.976570i \(0.569041\pi\)
\(758\) −4.04719e7 −2.55847
\(759\) 1.38889e7 0.875111
\(760\) −3.58369e6 −0.225059
\(761\) 2.97107e7 1.85974 0.929869 0.367892i \(-0.119920\pi\)
0.929869 + 0.367892i \(0.119920\pi\)
\(762\) 2.14756e7 1.33985
\(763\) −3.89273e7 −2.42071
\(764\) −3.46063e7 −2.14497
\(765\) 2.35429e7 1.45447
\(766\) 4.00481e6 0.246609
\(767\) 1.48075e7 0.908850
\(768\) 5.20195e7 3.18246
\(769\) −2.52714e7 −1.54104 −0.770518 0.637418i \(-0.780002\pi\)
−0.770518 + 0.637418i \(0.780002\pi\)
\(770\) −6.92306e6 −0.420796
\(771\) 1.79805e7 1.08935
\(772\) −1.93111e6 −0.116617
\(773\) −7.62260e6 −0.458833 −0.229416 0.973328i \(-0.573682\pi\)
−0.229416 + 0.973328i \(0.573682\pi\)
\(774\) 1.06237e7 0.637417
\(775\) −4.35992e6 −0.260750
\(776\) 4.98659e7 2.97269
\(777\) 3.16679e7 1.88177
\(778\) 4.75874e7 2.81866
\(779\) 3.37801e6 0.199442
\(780\) −1.42289e7 −0.837403
\(781\) 4.55843e6 0.267416
\(782\) 8.95949e7 5.23922
\(783\) 2.27357e7 1.32527
\(784\) 5.97137e7 3.46964
\(785\) 1.15151e7 0.666952
\(786\) −7.63128e6 −0.440597
\(787\) −1.75761e6 −0.101155 −0.0505774 0.998720i \(-0.516106\pi\)
−0.0505774 + 0.998720i \(0.516106\pi\)
\(788\) 7.36984e7 4.22807
\(789\) 3.31593e7 1.89633
\(790\) 2.20321e7 1.25600
\(791\) 5.01305e7 2.84879
\(792\) −2.21757e7 −1.25622
\(793\) −1.62333e7 −0.916692
\(794\) 3.92700e7 2.21060
\(795\) −6.33037e6 −0.355231
\(796\) 6.61166e6 0.369852
\(797\) −8.32497e6 −0.464234 −0.232117 0.972688i \(-0.574565\pi\)
−0.232117 + 0.972688i \(0.574565\pi\)
\(798\) 2.19297e7 1.21906
\(799\) 4.12047e7 2.28339
\(800\) −3.20660e6 −0.177141
\(801\) −1.54546e7 −0.851090
\(802\) −2.49638e6 −0.137049
\(803\) 1.23517e6 0.0675985
\(804\) −1.27578e8 −6.96044
\(805\) −2.43669e7 −1.32529
\(806\) 2.13606e7 1.15818
\(807\) −5.24684e6 −0.283605
\(808\) 2.58555e7 1.39324
\(809\) 1.72803e6 0.0928282 0.0464141 0.998922i \(-0.485221\pi\)
0.0464141 + 0.998922i \(0.485221\pi\)
\(810\) −1.06148e7 −0.568461
\(811\) 1.89604e7 1.01227 0.506133 0.862455i \(-0.331074\pi\)
0.506133 + 0.862455i \(0.331074\pi\)
\(812\) −6.28150e7 −3.34329
\(813\) 6.08965e7 3.23122
\(814\) 6.50373e6 0.344034
\(815\) 1.21901e7 0.642853
\(816\) −9.51374e7 −5.00179
\(817\) −818340. −0.0428922
\(818\) −9.18237e6 −0.479812
\(819\) 3.13698e7 1.63419
\(820\) 1.66341e7 0.863902
\(821\) −1.85913e7 −0.962611 −0.481305 0.876553i \(-0.659837\pi\)
−0.481305 + 0.876553i \(0.659837\pi\)
\(822\) −8.80140e6 −0.454331
\(823\) −4.19372e6 −0.215824 −0.107912 0.994160i \(-0.534417\pi\)
−0.107912 + 0.994160i \(0.534417\pi\)
\(824\) 1.16866e6 0.0599610
\(825\) −2.00733e6 −0.102679
\(826\) −1.12378e8 −5.73099
\(827\) −1.68892e6 −0.0858710 −0.0429355 0.999078i \(-0.513671\pi\)
−0.0429355 + 0.999078i \(0.513671\pi\)
\(828\) −1.41920e8 −7.19395
\(829\) 1.40877e7 0.711957 0.355979 0.934494i \(-0.384148\pi\)
0.355979 + 0.934494i \(0.384148\pi\)
\(830\) −1.33894e7 −0.674631
\(831\) −4.79297e7 −2.40770
\(832\) −1.24146e6 −0.0621765
\(833\) 6.93584e7 3.46327
\(834\) 9.97921e7 4.96799
\(835\) 9.09428e6 0.451390
\(836\) 3.10598e6 0.153703
\(837\) 4.04649e7 1.99648
\(838\) −1.76733e7 −0.869378
\(839\) −2.67640e7 −1.31264 −0.656320 0.754483i \(-0.727888\pi\)
−0.656320 + 0.754483i \(0.727888\pi\)
\(840\) 5.93892e7 2.90408
\(841\) −5.14892e6 −0.251030
\(842\) −4.60639e7 −2.23914
\(843\) 1.05502e7 0.511321
\(844\) 5.50534e7 2.66028
\(845\) −7.00887e6 −0.337681
\(846\) −9.46422e7 −4.54631
\(847\) 3.29991e6 0.158050
\(848\) 1.67581e7 0.800265
\(849\) −1.07300e7 −0.510892
\(850\) −1.29489e7 −0.614733
\(851\) 2.28910e7 1.08353
\(852\) −7.11029e7 −3.35574
\(853\) −9.99904e6 −0.470528 −0.235264 0.971931i \(-0.575596\pi\)
−0.235264 + 0.971931i \(0.575596\pi\)
\(854\) 1.23199e8 5.78044
\(855\) 4.16538e6 0.194868
\(856\) 5.29050e7 2.46781
\(857\) −1.58990e7 −0.739466 −0.369733 0.929138i \(-0.620551\pi\)
−0.369733 + 0.929138i \(0.620551\pi\)
\(858\) 9.83451e6 0.456073
\(859\) 1.35325e7 0.625740 0.312870 0.949796i \(-0.398710\pi\)
0.312870 + 0.949796i \(0.398710\pi\)
\(860\) −4.02969e6 −0.185792
\(861\) −5.59806e7 −2.57353
\(862\) −1.62582e7 −0.745253
\(863\) −3.24042e7 −1.48107 −0.740533 0.672021i \(-0.765427\pi\)
−0.740533 + 0.672021i \(0.765427\pi\)
\(864\) 2.97608e7 1.35631
\(865\) −4.09986e6 −0.186307
\(866\) 2.32510e7 1.05353
\(867\) −7.28160e7 −3.28987
\(868\) −1.11798e8 −5.03658
\(869\) −1.05017e7 −0.471749
\(870\) −2.64096e7 −1.18294
\(871\) 2.03841e7 0.910430
\(872\) 6.85815e7 3.05433
\(873\) −5.79599e7 −2.57390
\(874\) 1.58518e7 0.701940
\(875\) 3.52169e6 0.155500
\(876\) −1.92663e7 −0.848278
\(877\) 2.57415e6 0.113015 0.0565073 0.998402i \(-0.482004\pi\)
0.0565073 + 0.998402i \(0.482004\pi\)
\(878\) −2.62655e7 −1.14987
\(879\) −1.06375e6 −0.0464374
\(880\) 5.31389e6 0.231316
\(881\) 3.70931e7 1.61010 0.805052 0.593205i \(-0.202137\pi\)
0.805052 + 0.593205i \(0.202137\pi\)
\(882\) −1.59308e8 −6.89549
\(883\) 3.19800e7 1.38031 0.690154 0.723662i \(-0.257543\pi\)
0.690154 + 0.723662i \(0.257543\pi\)
\(884\) 4.37512e7 1.88304
\(885\) −3.25836e7 −1.39843
\(886\) 9.39272e6 0.401982
\(887\) −3.08947e7 −1.31849 −0.659243 0.751930i \(-0.729123\pi\)
−0.659243 + 0.751930i \(0.729123\pi\)
\(888\) −5.57919e7 −2.37432
\(889\) 1.79590e7 0.762127
\(890\) 8.50023e6 0.359712
\(891\) 5.05961e6 0.213512
\(892\) −9.36023e7 −3.93890
\(893\) 7.29025e6 0.305924
\(894\) 2.32388e7 0.972455
\(895\) 1.68406e7 0.702749
\(896\) 4.64255e7 1.93191
\(897\) 3.46143e7 1.43640
\(898\) 2.47115e7 1.02260
\(899\) 2.73417e7 1.12830
\(900\) 2.05113e7 0.844087
\(901\) 1.94647e7 0.798797
\(902\) −1.14969e7 −0.470505
\(903\) 1.35616e7 0.553466
\(904\) −8.83191e7 −3.59446
\(905\) −2.50581e6 −0.101701
\(906\) −3.18004e6 −0.128710
\(907\) 3.07938e7 1.24293 0.621463 0.783444i \(-0.286539\pi\)
0.621463 + 0.783444i \(0.286539\pi\)
\(908\) −2.11675e7 −0.852029
\(909\) −3.00523e7 −1.20633
\(910\) −1.72538e7 −0.690689
\(911\) −1.65169e7 −0.659374 −0.329687 0.944090i \(-0.606943\pi\)
−0.329687 + 0.944090i \(0.606943\pi\)
\(912\) −1.68324e7 −0.670131
\(913\) 6.38212e6 0.253389
\(914\) 4.51145e7 1.78628
\(915\) 3.57212e7 1.41050
\(916\) 1.34128e7 0.528178
\(917\) −6.38167e6 −0.250617
\(918\) 1.20180e8 4.70681
\(919\) −2.27468e7 −0.888447 −0.444224 0.895916i \(-0.646520\pi\)
−0.444224 + 0.895916i \(0.646520\pi\)
\(920\) 4.29293e7 1.67218
\(921\) −7.01683e6 −0.272579
\(922\) 2.93250e7 1.13609
\(923\) 1.13606e7 0.438933
\(924\) −5.14724e7 −1.98333
\(925\) −3.30838e6 −0.127134
\(926\) 5.85464e7 2.24374
\(927\) −1.35835e6 −0.0519173
\(928\) 2.01090e7 0.766517
\(929\) −1.11615e7 −0.424309 −0.212154 0.977236i \(-0.568048\pi\)
−0.212154 + 0.977236i \(0.568048\pi\)
\(930\) −4.70037e7 −1.78207
\(931\) 1.22714e7 0.464002
\(932\) 8.07852e7 3.04643
\(933\) −2.11305e7 −0.794704
\(934\) −9.22203e7 −3.45907
\(935\) 6.17216e6 0.230892
\(936\) −5.52669e7 −2.06194
\(937\) −1.11028e7 −0.413126 −0.206563 0.978433i \(-0.566228\pi\)
−0.206563 + 0.978433i \(0.566228\pi\)
\(938\) −1.54700e8 −5.74096
\(939\) 4.03326e7 1.49277
\(940\) 3.58988e7 1.32514
\(941\) −3.17630e7 −1.16936 −0.584679 0.811265i \(-0.698780\pi\)
−0.584679 + 0.811265i \(0.698780\pi\)
\(942\) 1.24143e8 4.55822
\(943\) −4.04654e7 −1.48185
\(944\) 8.62570e7 3.15039
\(945\) −3.26852e7 −1.19062
\(946\) 2.78518e6 0.101187
\(947\) −3.37175e7 −1.22174 −0.610872 0.791730i \(-0.709181\pi\)
−0.610872 + 0.791730i \(0.709181\pi\)
\(948\) 1.63807e8 5.91986
\(949\) 3.07832e6 0.110955
\(950\) −2.29102e6 −0.0823607
\(951\) −3.07081e7 −1.10104
\(952\) −1.82611e8 −6.53032
\(953\) 2.14313e7 0.764393 0.382197 0.924081i \(-0.375168\pi\)
0.382197 + 0.924081i \(0.375168\pi\)
\(954\) −4.47081e7 −1.59043
\(955\) −1.21672e7 −0.431700
\(956\) 7.66095e7 2.71105
\(957\) 1.25882e7 0.444309
\(958\) −4.79539e7 −1.68814
\(959\) −7.36018e6 −0.258429
\(960\) 2.73183e6 0.0956700
\(961\) 2.00336e7 0.699761
\(962\) 1.62088e7 0.564693
\(963\) −6.14923e7 −2.13676
\(964\) −2.68376e7 −0.930147
\(965\) −678955. −0.0234705
\(966\) −2.62697e8 −9.05758
\(967\) −1.15995e7 −0.398909 −0.199455 0.979907i \(-0.563917\pi\)
−0.199455 + 0.979907i \(0.563917\pi\)
\(968\) −5.81372e6 −0.199419
\(969\) −1.95511e7 −0.668901
\(970\) 3.18788e7 1.08786
\(971\) 3.45146e7 1.17478 0.587388 0.809305i \(-0.300156\pi\)
0.587388 + 0.809305i \(0.300156\pi\)
\(972\) 2.13083e7 0.723408
\(973\) 8.34513e7 2.82586
\(974\) −6.48282e7 −2.18961
\(975\) −5.00271e6 −0.168537
\(976\) −9.45627e7 −3.17757
\(977\) −6.74177e6 −0.225963 −0.112982 0.993597i \(-0.536040\pi\)
−0.112982 + 0.993597i \(0.536040\pi\)
\(978\) 1.31420e8 4.39352
\(979\) −4.05167e6 −0.135107
\(980\) 6.04272e7 2.00987
\(981\) −7.97134e7 −2.64459
\(982\) −8.48038e7 −2.80632
\(983\) −2.18941e6 −0.0722676 −0.0361338 0.999347i \(-0.511504\pi\)
−0.0361338 + 0.999347i \(0.511504\pi\)
\(984\) 9.86256e7 3.24715
\(985\) 2.59115e7 0.850946
\(986\) 8.12046e7 2.66004
\(987\) −1.20814e8 −3.94753
\(988\) 7.74080e6 0.252286
\(989\) 9.80294e6 0.318688
\(990\) −1.41767e7 −0.459713
\(991\) 2.33318e7 0.754682 0.377341 0.926074i \(-0.376838\pi\)
0.377341 + 0.926074i \(0.376838\pi\)
\(992\) 3.57901e7 1.15474
\(993\) −4.63191e7 −1.49069
\(994\) −8.62189e7 −2.76781
\(995\) 2.32458e6 0.0744368
\(996\) −9.95492e7 −3.17972
\(997\) 3.02337e7 0.963282 0.481641 0.876369i \(-0.340041\pi\)
0.481641 + 0.876369i \(0.340041\pi\)
\(998\) 1.31797e7 0.418870
\(999\) 3.07055e7 0.973424
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 1045.6.a.h.1.4 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.4 40 1.1 even 1 trivial