Properties

Label 22.10.a.d.1.2
Level $22$
Weight $10$
Character 22.1
Self dual yes
Analytic conductor $11.331$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.3307883956\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{889}) \)
Defining polynomial: \( x^{2} - x - 222 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-14.4081\) of defining polynomial
Character \(\chi\) \(=\) 22.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} +O(q^{10})\) \(q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} -18969.3 q^{10} +14641.0 q^{11} +31660.2 q^{12} +82461.9 q^{13} -18794.5 q^{14} +146624. q^{15} +65536.0 q^{16} +440826. q^{17} +70209.9 q^{18} +804401. q^{19} +303509. q^{20} +145273. q^{21} -234256. q^{22} -228403. q^{23} -506562. q^{24} -547523. q^{25} -1.31939e6 q^{26} -2.97693e6 q^{27} +300712. q^{28} +2.28497e6 q^{29} -2.34598e6 q^{30} +2.56508e6 q^{31} -1.04858e6 q^{32} +1.81069e6 q^{33} -7.05322e6 q^{34} +1.39265e6 q^{35} -1.12336e6 q^{36} -4.68709e6 q^{37} -1.28704e7 q^{38} +1.01983e7 q^{39} -4.85614e6 q^{40} +3.30235e6 q^{41} -2.32436e6 q^{42} +7.81398e6 q^{43} +3.74810e6 q^{44} -5.20247e6 q^{45} +3.65445e6 q^{46} -2.85515e6 q^{47} +8.10500e6 q^{48} -3.89738e7 q^{49} +8.76036e6 q^{50} +5.45181e7 q^{51} +2.11103e7 q^{52} +9.97047e6 q^{53} +4.76310e7 q^{54} +1.73581e7 q^{55} -4.81140e6 q^{56} +9.94823e7 q^{57} -3.65595e7 q^{58} +6.31658e7 q^{59} +3.75357e7 q^{60} -2.12529e8 q^{61} -4.10412e7 q^{62} -5.15454e6 q^{63} +1.67772e7 q^{64} +9.77653e7 q^{65} -2.89710e7 q^{66} -2.27892e8 q^{67} +1.12852e8 q^{68} -2.82472e7 q^{69} -2.22824e7 q^{70} -1.55605e8 q^{71} +1.79737e7 q^{72} -1.04177e8 q^{73} +7.49935e7 q^{74} -6.77135e7 q^{75} +2.05927e8 q^{76} +1.71982e7 q^{77} -1.63172e8 q^{78} -2.96624e8 q^{79} +7.76982e7 q^{80} -2.81793e8 q^{81} -5.28376e7 q^{82} -7.38793e8 q^{83} +3.71898e7 q^{84} +5.22635e8 q^{85} -1.25024e8 q^{86} +2.82588e8 q^{87} -5.99695e7 q^{88} +9.00049e8 q^{89} +8.32396e7 q^{90} +9.68645e7 q^{91} -5.84712e7 q^{92} +3.17229e8 q^{93} +4.56823e7 q^{94} +9.53683e8 q^{95} -1.29680e8 q^{96} +1.29157e9 q^{97} +6.23581e8 q^{98} -6.42465e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9} + 8336 q^{10} + 29282 q^{11} - 5376 q^{12} + 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} + 690472 q^{17} + 50256 q^{18} + 511212 q^{19} - 133376 q^{20} + 1398810 q^{21} - 468512 q^{22} + 874751 q^{23} + 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} - 1917440 q^{28} - 2951058 q^{29} - 6296304 q^{30} - 5818705 q^{31} - 2097152 q^{32} - 307461 q^{33} - 11047552 q^{34} + 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} + 381948 q^{39} + 2134016 q^{40} + 13427994 q^{41} - 22380960 q^{42} - 17820762 q^{43} + 7496192 q^{44} - 7330788 q^{45} - 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} - 6588336 q^{50} + 18401250 q^{51} + 38480384 q^{52} + 96842752 q^{53} + 4956336 q^{54} - 7627961 q^{55} + 30679040 q^{56} + 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} - 90424326 q^{61} + 93099280 q^{62} - 15960420 q^{63} + 33554432 q^{64} - 18029712 q^{65} + 4919376 q^{66} - 295944891 q^{67} + 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} + 12865536 q^{72} - 255975514 q^{73} - 42542480 q^{74} - 206496864 q^{75} + 130870272 q^{76} - 109661090 q^{77} - 6111168 q^{78} - 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} - 277699042 q^{83} + 358095360 q^{84} + 96595042 q^{85} + 285132192 q^{86} + 1040096232 q^{87} - 119939072 q^{88} + 1363672217 q^{89} + 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} - 896705664 q^{94} + 1454033872 q^{95} + 22020096 q^{96} + 1398434043 q^{97} + 68017824 q^{98} - 45987381 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 −0.707107
\(3\) 123.672 0.881510 0.440755 0.897627i \(-0.354711\pi\)
0.440755 + 0.897627i \(0.354711\pi\)
\(4\) 256.000 0.500000
\(5\) 1185.58 0.848333 0.424166 0.905584i \(-0.360567\pi\)
0.424166 + 0.905584i \(0.360567\pi\)
\(6\) −1978.76 −0.623322
\(7\) 1174.66 0.184914 0.0924570 0.995717i \(-0.470528\pi\)
0.0924570 + 0.995717i \(0.470528\pi\)
\(8\) −4096.00 −0.353553
\(9\) −4388.12 −0.222940
\(10\) −18969.3 −0.599862
\(11\) 14641.0 0.301511
\(12\) 31660.2 0.440755
\(13\) 82461.9 0.800771 0.400386 0.916347i \(-0.368876\pi\)
0.400386 + 0.916347i \(0.368876\pi\)
\(14\) −18794.5 −0.130754
\(15\) 146624. 0.747814
\(16\) 65536.0 0.250000
\(17\) 440826. 1.28011 0.640055 0.768329i \(-0.278911\pi\)
0.640055 + 0.768329i \(0.278911\pi\)
\(18\) 70209.9 0.157642
\(19\) 804401. 1.41606 0.708030 0.706183i \(-0.249584\pi\)
0.708030 + 0.706183i \(0.249584\pi\)
\(20\) 303509. 0.424166
\(21\) 145273. 0.163004
\(22\) −234256. −0.213201
\(23\) −228403. −0.170187 −0.0850936 0.996373i \(-0.527119\pi\)
−0.0850936 + 0.996373i \(0.527119\pi\)
\(24\) −506562. −0.311661
\(25\) −547523. −0.280332
\(26\) −1.31939e6 −0.566231
\(27\) −2.97693e6 −1.07803
\(28\) 300712. 0.0924570
\(29\) 2.28497e6 0.599914 0.299957 0.953953i \(-0.403028\pi\)
0.299957 + 0.953953i \(0.403028\pi\)
\(30\) −2.34598e6 −0.528784
\(31\) 2.56508e6 0.498853 0.249427 0.968394i \(-0.419758\pi\)
0.249427 + 0.968394i \(0.419758\pi\)
\(32\) −1.04858e6 −0.176777
\(33\) 1.81069e6 0.265785
\(34\) −7.05322e6 −0.905175
\(35\) 1.39265e6 0.156869
\(36\) −1.12336e6 −0.111470
\(37\) −4.68709e6 −0.411146 −0.205573 0.978642i \(-0.565906\pi\)
−0.205573 + 0.978642i \(0.565906\pi\)
\(38\) −1.28704e7 −1.00131
\(39\) 1.01983e7 0.705888
\(40\) −4.85614e6 −0.299931
\(41\) 3.30235e6 0.182514 0.0912569 0.995827i \(-0.470912\pi\)
0.0912569 + 0.995827i \(0.470912\pi\)
\(42\) −2.32436e6 −0.115261
\(43\) 7.81398e6 0.348549 0.174275 0.984697i \(-0.444242\pi\)
0.174275 + 0.984697i \(0.444242\pi\)
\(44\) 3.74810e6 0.150756
\(45\) −5.20247e6 −0.189127
\(46\) 3.65445e6 0.120341
\(47\) −2.85515e6 −0.0853470 −0.0426735 0.999089i \(-0.513588\pi\)
−0.0426735 + 0.999089i \(0.513588\pi\)
\(48\) 8.10500e6 0.220378
\(49\) −3.89738e7 −0.965807
\(50\) 8.76036e6 0.198224
\(51\) 5.45181e7 1.12843
\(52\) 2.11103e7 0.400386
\(53\) 9.97047e6 0.173570 0.0867849 0.996227i \(-0.472341\pi\)
0.0867849 + 0.996227i \(0.472341\pi\)
\(54\) 4.76310e7 0.762285
\(55\) 1.73581e7 0.255782
\(56\) −4.81140e6 −0.0653770
\(57\) 9.94823e7 1.24827
\(58\) −3.65595e7 −0.424203
\(59\) 6.31658e7 0.678653 0.339326 0.940669i \(-0.389801\pi\)
0.339326 + 0.940669i \(0.389801\pi\)
\(60\) 3.75357e7 0.373907
\(61\) −2.12529e8 −1.96532 −0.982660 0.185414i \(-0.940637\pi\)
−0.982660 + 0.185414i \(0.940637\pi\)
\(62\) −4.10412e7 −0.352743
\(63\) −5.15454e6 −0.0412247
\(64\) 1.67772e7 0.125000
\(65\) 9.77653e7 0.679320
\(66\) −2.89710e7 −0.187939
\(67\) −2.27892e8 −1.38163 −0.690815 0.723031i \(-0.742748\pi\)
−0.690815 + 0.723031i \(0.742748\pi\)
\(68\) 1.12852e8 0.640055
\(69\) −2.82472e7 −0.150022
\(70\) −2.22824e7 −0.110923
\(71\) −1.55605e8 −0.726708 −0.363354 0.931651i \(-0.618368\pi\)
−0.363354 + 0.931651i \(0.618368\pi\)
\(72\) 1.79737e7 0.0788211
\(73\) −1.04177e8 −0.429357 −0.214679 0.976685i \(-0.568870\pi\)
−0.214679 + 0.976685i \(0.568870\pi\)
\(74\) 7.49935e7 0.290724
\(75\) −6.77135e7 −0.247115
\(76\) 2.05927e8 0.708030
\(77\) 1.71982e7 0.0557537
\(78\) −1.63172e8 −0.499138
\(79\) −2.96624e8 −0.856811 −0.428405 0.903587i \(-0.640924\pi\)
−0.428405 + 0.903587i \(0.640924\pi\)
\(80\) 7.76982e7 0.212083
\(81\) −2.81793e8 −0.727358
\(82\) −5.28376e7 −0.129057
\(83\) −7.38793e8 −1.70872 −0.854361 0.519680i \(-0.826051\pi\)
−0.854361 + 0.519680i \(0.826051\pi\)
\(84\) 3.71898e7 0.0815018
\(85\) 5.22635e8 1.08596
\(86\) −1.25024e8 −0.246462
\(87\) 2.82588e8 0.528830
\(88\) −5.99695e7 −0.106600
\(89\) 9.00049e8 1.52059 0.760293 0.649580i \(-0.225055\pi\)
0.760293 + 0.649580i \(0.225055\pi\)
\(90\) 8.32396e7 0.133733
\(91\) 9.68645e7 0.148074
\(92\) −5.84712e7 −0.0850936
\(93\) 3.17229e8 0.439744
\(94\) 4.56823e7 0.0603494
\(95\) 9.53683e8 1.20129
\(96\) −1.29680e8 −0.155830
\(97\) 1.29157e9 1.48131 0.740653 0.671888i \(-0.234516\pi\)
0.740653 + 0.671888i \(0.234516\pi\)
\(98\) 6.23581e8 0.682929
\(99\) −6.42465e7 −0.0672188
\(100\) −1.40166e8 −0.140166
\(101\) 1.45652e9 1.39275 0.696373 0.717681i \(-0.254796\pi\)
0.696373 + 0.717681i \(0.254796\pi\)
\(102\) −8.72289e8 −0.797921
\(103\) −1.95971e9 −1.71563 −0.857814 0.513960i \(-0.828178\pi\)
−0.857814 + 0.513960i \(0.828178\pi\)
\(104\) −3.37764e8 −0.283115
\(105\) 1.72233e8 0.138281
\(106\) −1.59528e8 −0.122732
\(107\) 6.07627e8 0.448136 0.224068 0.974573i \(-0.428066\pi\)
0.224068 + 0.974573i \(0.428066\pi\)
\(108\) −7.62095e8 −0.539017
\(109\) −1.14761e9 −0.778708 −0.389354 0.921088i \(-0.627302\pi\)
−0.389354 + 0.921088i \(0.627302\pi\)
\(110\) −2.77729e8 −0.180865
\(111\) −5.79664e8 −0.362429
\(112\) 7.69823e7 0.0462285
\(113\) −2.54053e8 −0.146579 −0.0732895 0.997311i \(-0.523350\pi\)
−0.0732895 + 0.997311i \(0.523350\pi\)
\(114\) −1.59172e9 −0.882661
\(115\) −2.70790e8 −0.144375
\(116\) 5.84952e8 0.299957
\(117\) −3.61853e8 −0.178524
\(118\) −1.01065e9 −0.479880
\(119\) 5.17820e8 0.236710
\(120\) −6.00571e8 −0.264392
\(121\) 2.14359e8 0.0909091
\(122\) 3.40046e9 1.38969
\(123\) 4.08410e8 0.160888
\(124\) 6.56660e8 0.249427
\(125\) −2.96472e9 −1.08615
\(126\) 8.24726e7 0.0291502
\(127\) −1.26227e8 −0.0430561 −0.0215280 0.999768i \(-0.506853\pi\)
−0.0215280 + 0.999768i \(0.506853\pi\)
\(128\) −2.68435e8 −0.0883883
\(129\) 9.66374e8 0.307250
\(130\) −1.56425e9 −0.480352
\(131\) −1.87859e9 −0.557328 −0.278664 0.960389i \(-0.589892\pi\)
−0.278664 + 0.960389i \(0.589892\pi\)
\(132\) 4.63536e8 0.132893
\(133\) 9.44895e8 0.261849
\(134\) 3.64627e9 0.976960
\(135\) −3.52940e9 −0.914531
\(136\) −1.80563e9 −0.452587
\(137\) 6.32338e9 1.53358 0.766791 0.641897i \(-0.221852\pi\)
0.766791 + 0.641897i \(0.221852\pi\)
\(138\) 4.51955e8 0.106081
\(139\) −7.82379e9 −1.77767 −0.888833 0.458230i \(-0.848483\pi\)
−0.888833 + 0.458230i \(0.848483\pi\)
\(140\) 3.56519e8 0.0784343
\(141\) −3.53103e8 −0.0752342
\(142\) 2.48967e9 0.513860
\(143\) 1.20733e9 0.241442
\(144\) −2.87580e8 −0.0557349
\(145\) 2.70901e9 0.508927
\(146\) 1.66683e9 0.303602
\(147\) −4.81998e9 −0.851369
\(148\) −1.19990e9 −0.205573
\(149\) −2.69524e8 −0.0447981 −0.0223991 0.999749i \(-0.507130\pi\)
−0.0223991 + 0.999749i \(0.507130\pi\)
\(150\) 1.08342e9 0.174737
\(151\) 1.18223e10 1.85057 0.925286 0.379270i \(-0.123825\pi\)
0.925286 + 0.379270i \(0.123825\pi\)
\(152\) −3.29483e9 −0.500653
\(153\) −1.93440e9 −0.285387
\(154\) −2.75170e8 −0.0394238
\(155\) 3.04111e9 0.423194
\(156\) 2.61076e9 0.352944
\(157\) 3.66990e9 0.482065 0.241032 0.970517i \(-0.422514\pi\)
0.241032 + 0.970517i \(0.422514\pi\)
\(158\) 4.74599e9 0.605857
\(159\) 1.23307e9 0.153004
\(160\) −1.24317e9 −0.149965
\(161\) −2.68295e8 −0.0314700
\(162\) 4.50870e9 0.514320
\(163\) −1.30610e10 −1.44921 −0.724605 0.689165i \(-0.757978\pi\)
−0.724605 + 0.689165i \(0.757978\pi\)
\(164\) 8.45401e8 0.0912569
\(165\) 2.14672e9 0.225474
\(166\) 1.18207e10 1.20825
\(167\) −1.16911e9 −0.116314 −0.0581571 0.998307i \(-0.518522\pi\)
−0.0581571 + 0.998307i \(0.518522\pi\)
\(168\) −5.95037e8 −0.0576305
\(169\) −3.80453e9 −0.358765
\(170\) −8.36217e9 −0.767889
\(171\) −3.52981e9 −0.315696
\(172\) 2.00038e9 0.174275
\(173\) 1.90893e10 1.62025 0.810124 0.586258i \(-0.199399\pi\)
0.810124 + 0.586258i \(0.199399\pi\)
\(174\) −4.52140e9 −0.373940
\(175\) −6.43151e8 −0.0518373
\(176\) 9.59513e8 0.0753778
\(177\) 7.81187e9 0.598240
\(178\) −1.44008e10 −1.07522
\(179\) −1.99470e10 −1.45224 −0.726122 0.687566i \(-0.758679\pi\)
−0.726122 + 0.687566i \(0.758679\pi\)
\(180\) −1.33183e9 −0.0945635
\(181\) −8.20947e9 −0.568541 −0.284270 0.958744i \(-0.591751\pi\)
−0.284270 + 0.958744i \(0.591751\pi\)
\(182\) −1.54983e9 −0.104704
\(183\) −2.62840e10 −1.73245
\(184\) 9.35539e8 0.0601703
\(185\) −5.55693e9 −0.348788
\(186\) −5.07567e9 −0.310946
\(187\) 6.45414e9 0.385968
\(188\) −7.30918e8 −0.0426735
\(189\) −3.49688e9 −0.199344
\(190\) −1.52589e10 −0.849440
\(191\) 1.24525e10 0.677027 0.338513 0.940962i \(-0.390076\pi\)
0.338513 + 0.940962i \(0.390076\pi\)
\(192\) 2.07488e9 0.110189
\(193\) 1.60846e9 0.0834456 0.0417228 0.999129i \(-0.486715\pi\)
0.0417228 + 0.999129i \(0.486715\pi\)
\(194\) −2.06651e10 −1.04744
\(195\) 1.20909e10 0.598828
\(196\) −9.97729e9 −0.482903
\(197\) 4.02780e10 1.90533 0.952664 0.304024i \(-0.0983304\pi\)
0.952664 + 0.304024i \(0.0983304\pi\)
\(198\) 1.02794e9 0.0475309
\(199\) 3.22083e10 1.45589 0.727945 0.685636i \(-0.240476\pi\)
0.727945 + 0.685636i \(0.240476\pi\)
\(200\) 2.24265e9 0.0991122
\(201\) −2.81839e10 −1.21792
\(202\) −2.33044e10 −0.984819
\(203\) 2.68405e9 0.110933
\(204\) 1.39566e10 0.564215
\(205\) 3.91520e9 0.154832
\(206\) 3.13553e10 1.21313
\(207\) 1.00226e9 0.0379415
\(208\) 5.40423e9 0.200193
\(209\) 1.17772e10 0.426958
\(210\) −2.75572e9 −0.0977796
\(211\) 1.06111e10 0.368544 0.184272 0.982875i \(-0.441007\pi\)
0.184272 + 0.982875i \(0.441007\pi\)
\(212\) 2.55244e9 0.0867849
\(213\) −1.92440e10 −0.640601
\(214\) −9.72203e9 −0.316880
\(215\) 9.26410e9 0.295686
\(216\) 1.21935e10 0.381143
\(217\) 3.01309e9 0.0922450
\(218\) 1.83618e10 0.550630
\(219\) −1.28838e10 −0.378483
\(220\) 4.44367e9 0.127891
\(221\) 3.63514e10 1.02508
\(222\) 9.27463e9 0.256276
\(223\) −2.11175e10 −0.571835 −0.285918 0.958254i \(-0.592298\pi\)
−0.285918 + 0.958254i \(0.592298\pi\)
\(224\) −1.23172e9 −0.0326885
\(225\) 2.40260e9 0.0624970
\(226\) 4.06485e9 0.103647
\(227\) −5.33286e9 −0.133304 −0.0666521 0.997776i \(-0.521232\pi\)
−0.0666521 + 0.997776i \(0.521232\pi\)
\(228\) 2.54675e10 0.624135
\(229\) −2.62407e10 −0.630545 −0.315272 0.949001i \(-0.602096\pi\)
−0.315272 + 0.949001i \(0.602096\pi\)
\(230\) 4.33265e9 0.102089
\(231\) 2.12694e9 0.0491474
\(232\) −9.35923e9 −0.212102
\(233\) 4.77174e10 1.06066 0.530329 0.847792i \(-0.322068\pi\)
0.530329 + 0.847792i \(0.322068\pi\)
\(234\) 5.78965e9 0.126235
\(235\) −3.38501e9 −0.0724026
\(236\) 1.61704e10 0.339326
\(237\) −3.66843e10 −0.755287
\(238\) −8.28512e9 −0.167380
\(239\) −2.64340e10 −0.524050 −0.262025 0.965061i \(-0.584390\pi\)
−0.262025 + 0.965061i \(0.584390\pi\)
\(240\) 9.60913e9 0.186953
\(241\) −4.95287e10 −0.945758 −0.472879 0.881127i \(-0.656785\pi\)
−0.472879 + 0.881127i \(0.656785\pi\)
\(242\) −3.42974e9 −0.0642824
\(243\) 2.37449e10 0.436860
\(244\) −5.44074e10 −0.982660
\(245\) −4.62066e10 −0.819325
\(246\) −6.53455e9 −0.113765
\(247\) 6.63325e10 1.13394
\(248\) −1.05066e10 −0.176371
\(249\) −9.13683e10 −1.50626
\(250\) 4.74355e10 0.768022
\(251\) −8.76978e10 −1.39462 −0.697311 0.716768i \(-0.745620\pi\)
−0.697311 + 0.716768i \(0.745620\pi\)
\(252\) −1.31956e9 −0.0206123
\(253\) −3.34405e9 −0.0513134
\(254\) 2.01963e9 0.0304453
\(255\) 6.46356e10 0.957285
\(256\) 4.29497e9 0.0625000
\(257\) −1.09539e11 −1.56628 −0.783140 0.621846i \(-0.786383\pi\)
−0.783140 + 0.621846i \(0.786383\pi\)
\(258\) −1.54620e10 −0.217258
\(259\) −5.50573e9 −0.0760266
\(260\) 2.50279e10 0.339660
\(261\) −1.00267e10 −0.133745
\(262\) 3.00574e10 0.394091
\(263\) 4.08592e9 0.0526610 0.0263305 0.999653i \(-0.491618\pi\)
0.0263305 + 0.999653i \(0.491618\pi\)
\(264\) −7.41658e9 −0.0939693
\(265\) 1.18208e10 0.147245
\(266\) −1.51183e10 −0.185155
\(267\) 1.11311e11 1.34041
\(268\) −5.83403e10 −0.690815
\(269\) −8.48247e10 −0.987727 −0.493864 0.869539i \(-0.664416\pi\)
−0.493864 + 0.869539i \(0.664416\pi\)
\(270\) 5.64704e10 0.646671
\(271\) 6.76455e10 0.761864 0.380932 0.924603i \(-0.375603\pi\)
0.380932 + 0.924603i \(0.375603\pi\)
\(272\) 2.88900e10 0.320028
\(273\) 1.19795e10 0.130529
\(274\) −1.01174e11 −1.08441
\(275\) −8.01628e9 −0.0845232
\(276\) −7.23128e9 −0.0750109
\(277\) 1.22944e11 1.25472 0.627361 0.778728i \(-0.284135\pi\)
0.627361 + 0.778728i \(0.284135\pi\)
\(278\) 1.25181e11 1.25700
\(279\) −1.12559e10 −0.111214
\(280\) −5.70430e9 −0.0554614
\(281\) −1.28901e11 −1.23333 −0.616664 0.787226i \(-0.711516\pi\)
−0.616664 + 0.787226i \(0.711516\pi\)
\(282\) 5.64965e9 0.0531986
\(283\) 2.08828e10 0.193530 0.0967651 0.995307i \(-0.469150\pi\)
0.0967651 + 0.995307i \(0.469150\pi\)
\(284\) −3.98348e10 −0.363354
\(285\) 1.17944e11 1.05895
\(286\) −1.93172e10 −0.170725
\(287\) 3.87913e9 0.0337494
\(288\) 4.60128e9 0.0394105
\(289\) 7.57401e10 0.638683
\(290\) −4.33442e10 −0.359866
\(291\) 1.59731e11 1.30579
\(292\) −2.66693e10 −0.214679
\(293\) 3.85968e9 0.0305948 0.0152974 0.999883i \(-0.495131\pi\)
0.0152974 + 0.999883i \(0.495131\pi\)
\(294\) 7.71197e10 0.602009
\(295\) 7.48881e10 0.575723
\(296\) 1.91983e10 0.145362
\(297\) −4.35853e10 −0.325039
\(298\) 4.31239e9 0.0316770
\(299\) −1.88346e10 −0.136281
\(300\) −1.73347e10 −0.123558
\(301\) 9.17874e9 0.0644516
\(302\) −1.89157e11 −1.30855
\(303\) 1.80132e11 1.22772
\(304\) 5.27172e10 0.354015
\(305\) −2.51970e11 −1.66725
\(306\) 3.09504e10 0.201799
\(307\) 4.11326e10 0.264279 0.132140 0.991231i \(-0.457815\pi\)
0.132140 + 0.991231i \(0.457815\pi\)
\(308\) 4.40273e9 0.0278768
\(309\) −2.42362e11 −1.51234
\(310\) −4.86577e10 −0.299243
\(311\) −2.75638e11 −1.67078 −0.835388 0.549661i \(-0.814757\pi\)
−0.835388 + 0.549661i \(0.814757\pi\)
\(312\) −4.17721e10 −0.249569
\(313\) 3.14160e11 1.85013 0.925064 0.379810i \(-0.124011\pi\)
0.925064 + 0.379810i \(0.124011\pi\)
\(314\) −5.87183e10 −0.340871
\(315\) −6.11112e9 −0.0349722
\(316\) −7.59358e10 −0.428405
\(317\) 2.58171e11 1.43595 0.717977 0.696067i \(-0.245068\pi\)
0.717977 + 0.696067i \(0.245068\pi\)
\(318\) −1.97292e10 −0.108190
\(319\) 3.34542e10 0.180881
\(320\) 1.98907e10 0.106042
\(321\) 7.51467e10 0.395037
\(322\) 4.29273e9 0.0222527
\(323\) 3.54601e11 1.81271
\(324\) −7.21391e10 −0.363679
\(325\) −4.51498e10 −0.224482
\(326\) 2.08975e11 1.02475
\(327\) −1.41928e11 −0.686440
\(328\) −1.35264e10 −0.0645284
\(329\) −3.35382e9 −0.0157819
\(330\) −3.43475e10 −0.159434
\(331\) −5.94811e10 −0.272366 −0.136183 0.990684i \(-0.543484\pi\)
−0.136183 + 0.990684i \(0.543484\pi\)
\(332\) −1.89131e11 −0.854361
\(333\) 2.05675e10 0.0916607
\(334\) 1.87058e10 0.0822466
\(335\) −2.70184e11 −1.17208
\(336\) 9.52059e9 0.0407509
\(337\) 9.61669e10 0.406154 0.203077 0.979163i \(-0.434906\pi\)
0.203077 + 0.979163i \(0.434906\pi\)
\(338\) 6.08724e10 0.253685
\(339\) −3.14194e10 −0.129211
\(340\) 1.33795e11 0.542980
\(341\) 3.75553e10 0.150410
\(342\) 5.64770e10 0.223231
\(343\) −9.31825e10 −0.363505
\(344\) −3.20061e10 −0.123231
\(345\) −3.34893e10 −0.127268
\(346\) −3.05428e11 −1.14569
\(347\) −3.65974e11 −1.35509 −0.677543 0.735483i \(-0.736955\pi\)
−0.677543 + 0.735483i \(0.736955\pi\)
\(348\) 7.23424e10 0.264415
\(349\) −4.32258e11 −1.55966 −0.779828 0.625993i \(-0.784694\pi\)
−0.779828 + 0.625993i \(0.784694\pi\)
\(350\) 1.02904e10 0.0366545
\(351\) −2.45484e11 −0.863259
\(352\) −1.53522e10 −0.0533002
\(353\) −3.67882e11 −1.26102 −0.630511 0.776180i \(-0.717155\pi\)
−0.630511 + 0.776180i \(0.717155\pi\)
\(354\) −1.24990e11 −0.423019
\(355\) −1.84482e11 −0.616490
\(356\) 2.30413e11 0.760293
\(357\) 6.40401e10 0.208663
\(358\) 3.19152e11 1.02689
\(359\) −1.25751e11 −0.399564 −0.199782 0.979840i \(-0.564023\pi\)
−0.199782 + 0.979840i \(0.564023\pi\)
\(360\) 2.13093e10 0.0668665
\(361\) 3.24374e11 1.00522
\(362\) 1.31352e11 0.402019
\(363\) 2.65103e10 0.0801373
\(364\) 2.47973e10 0.0740369
\(365\) −1.23510e11 −0.364238
\(366\) 4.20543e11 1.22503
\(367\) 5.19603e11 1.49511 0.747557 0.664197i \(-0.231227\pi\)
0.747557 + 0.664197i \(0.231227\pi\)
\(368\) −1.49686e10 −0.0425468
\(369\) −1.44911e10 −0.0406896
\(370\) 8.89109e10 0.246631
\(371\) 1.17119e10 0.0320955
\(372\) 8.12108e10 0.219872
\(373\) 4.65238e11 1.24447 0.622237 0.782829i \(-0.286224\pi\)
0.622237 + 0.782829i \(0.286224\pi\)
\(374\) −1.03266e11 −0.272920
\(375\) −3.66654e11 −0.957450
\(376\) 1.16947e10 0.0301747
\(377\) 1.88423e11 0.480394
\(378\) 5.59500e10 0.140957
\(379\) 4.48793e11 1.11730 0.558650 0.829404i \(-0.311320\pi\)
0.558650 + 0.829404i \(0.311320\pi\)
\(380\) 2.44143e11 0.600645
\(381\) −1.56108e10 −0.0379544
\(382\) −1.99240e11 −0.478730
\(383\) 2.75704e11 0.654710 0.327355 0.944901i \(-0.393843\pi\)
0.327355 + 0.944901i \(0.393843\pi\)
\(384\) −3.31981e10 −0.0779152
\(385\) 2.03898e10 0.0472977
\(386\) −2.57354e10 −0.0590049
\(387\) −3.42887e10 −0.0777055
\(388\) 3.30641e11 0.740653
\(389\) 8.29663e11 1.83708 0.918540 0.395327i \(-0.129369\pi\)
0.918540 + 0.395327i \(0.129369\pi\)
\(390\) −1.93454e11 −0.423435
\(391\) −1.00686e11 −0.217858
\(392\) 1.59637e11 0.341464
\(393\) −2.32330e11 −0.491290
\(394\) −6.44448e11 −1.34727
\(395\) −3.51672e11 −0.726861
\(396\) −1.64471e10 −0.0336094
\(397\) 1.53152e11 0.309432 0.154716 0.987959i \(-0.450554\pi\)
0.154716 + 0.987959i \(0.450554\pi\)
\(398\) −5.15332e11 −1.02947
\(399\) 1.16858e11 0.230823
\(400\) −3.58824e10 −0.0700829
\(401\) 2.05461e11 0.396807 0.198404 0.980120i \(-0.436424\pi\)
0.198404 + 0.980120i \(0.436424\pi\)
\(402\) 4.50943e11 0.861200
\(403\) 2.11521e11 0.399467
\(404\) 3.72870e11 0.696373
\(405\) −3.34089e11 −0.617042
\(406\) −4.29448e10 −0.0784411
\(407\) −6.86237e10 −0.123965
\(408\) −2.23306e11 −0.398960
\(409\) −6.57635e11 −1.16206 −0.581032 0.813880i \(-0.697351\pi\)
−0.581032 + 0.813880i \(0.697351\pi\)
\(410\) −6.26432e10 −0.109483
\(411\) 7.82029e11 1.35187
\(412\) −5.01685e11 −0.857814
\(413\) 7.41981e10 0.125492
\(414\) −1.60362e10 −0.0268287
\(415\) −8.75899e11 −1.44956
\(416\) −8.64676e10 −0.141558
\(417\) −9.67587e11 −1.56703
\(418\) −1.88436e11 −0.301905
\(419\) −3.79470e11 −0.601471 −0.300735 0.953708i \(-0.597232\pi\)
−0.300735 + 0.953708i \(0.597232\pi\)
\(420\) 4.40915e10 0.0691407
\(421\) 9.15367e11 1.42012 0.710061 0.704140i \(-0.248667\pi\)
0.710061 + 0.704140i \(0.248667\pi\)
\(422\) −1.69778e11 −0.260600
\(423\) 1.25287e10 0.0190272
\(424\) −4.08390e10 −0.0613662
\(425\) −2.41362e11 −0.358855
\(426\) 3.07904e11 0.452973
\(427\) −2.49648e11 −0.363415
\(428\) 1.55553e11 0.224068
\(429\) 1.49313e11 0.212833
\(430\) −1.48226e11 −0.209081
\(431\) 4.90485e11 0.684664 0.342332 0.939579i \(-0.388783\pi\)
0.342332 + 0.939579i \(0.388783\pi\)
\(432\) −1.95096e11 −0.269508
\(433\) −5.67227e11 −0.775464 −0.387732 0.921772i \(-0.626741\pi\)
−0.387732 + 0.921772i \(0.626741\pi\)
\(434\) −4.82094e10 −0.0652271
\(435\) 3.35030e11 0.448624
\(436\) −2.93788e11 −0.389354
\(437\) −1.83728e11 −0.240995
\(438\) 2.06141e11 0.267628
\(439\) −1.15068e12 −1.47865 −0.739323 0.673351i \(-0.764854\pi\)
−0.739323 + 0.673351i \(0.764854\pi\)
\(440\) −7.10987e10 −0.0904326
\(441\) 1.71022e11 0.215317
\(442\) −5.81622e11 −0.724838
\(443\) −4.44419e11 −0.548247 −0.274123 0.961695i \(-0.588388\pi\)
−0.274123 + 0.961695i \(0.588388\pi\)
\(444\) −1.48394e11 −0.181215
\(445\) 1.06708e12 1.28996
\(446\) 3.37880e11 0.404349
\(447\) −3.33327e10 −0.0394900
\(448\) 1.97075e10 0.0231143
\(449\) 6.03886e11 0.701208 0.350604 0.936524i \(-0.385976\pi\)
0.350604 + 0.936524i \(0.385976\pi\)
\(450\) −3.84415e10 −0.0441921
\(451\) 4.83497e10 0.0550300
\(452\) −6.50377e10 −0.0732895
\(453\) 1.46209e12 1.63130
\(454\) 8.53258e10 0.0942603
\(455\) 1.14841e11 0.125616
\(456\) −4.07479e11 −0.441330
\(457\) −2.80219e11 −0.300521 −0.150260 0.988646i \(-0.548011\pi\)
−0.150260 + 0.988646i \(0.548011\pi\)
\(458\) 4.19851e11 0.445862
\(459\) −1.31231e12 −1.38000
\(460\) −6.93224e10 −0.0721877
\(461\) 1.25259e12 1.29168 0.645838 0.763475i \(-0.276508\pi\)
0.645838 + 0.763475i \(0.276508\pi\)
\(462\) −3.40310e10 −0.0347525
\(463\) 1.46886e11 0.148548 0.0742739 0.997238i \(-0.476336\pi\)
0.0742739 + 0.997238i \(0.476336\pi\)
\(464\) 1.49748e11 0.149979
\(465\) 3.76101e11 0.373050
\(466\) −7.63479e11 −0.749999
\(467\) 1.49431e12 1.45383 0.726916 0.686726i \(-0.240953\pi\)
0.726916 + 0.686726i \(0.240953\pi\)
\(468\) −9.26344e10 −0.0892618
\(469\) −2.67695e11 −0.255483
\(470\) 5.41601e10 0.0511964
\(471\) 4.53865e11 0.424945
\(472\) −2.58727e11 −0.239940
\(473\) 1.14404e11 0.105092
\(474\) 5.86948e11 0.534069
\(475\) −4.40428e11 −0.396966
\(476\) 1.32562e11 0.118355
\(477\) −4.37516e10 −0.0386956
\(478\) 4.22944e11 0.370559
\(479\) −1.58007e11 −0.137140 −0.0685702 0.997646i \(-0.521844\pi\)
−0.0685702 + 0.997646i \(0.521844\pi\)
\(480\) −1.53746e11 −0.132196
\(481\) −3.86507e11 −0.329234
\(482\) 7.92459e11 0.668752
\(483\) −3.31808e10 −0.0277411
\(484\) 5.48759e10 0.0454545
\(485\) 1.53126e12 1.25664
\(486\) −3.79919e11 −0.308907
\(487\) −1.99896e12 −1.61036 −0.805181 0.593029i \(-0.797932\pi\)
−0.805181 + 0.593029i \(0.797932\pi\)
\(488\) 8.70518e11 0.694846
\(489\) −1.61528e12 −1.27749
\(490\) 7.39305e11 0.579351
\(491\) 9.33204e11 0.724619 0.362310 0.932058i \(-0.381988\pi\)
0.362310 + 0.932058i \(0.381988\pi\)
\(492\) 1.04553e11 0.0804439
\(493\) 1.00727e12 0.767956
\(494\) −1.06132e12 −0.801817
\(495\) −7.61694e10 −0.0570239
\(496\) 1.68105e11 0.124713
\(497\) −1.82782e11 −0.134379
\(498\) 1.46189e12 1.06508
\(499\) −1.93508e12 −1.39716 −0.698580 0.715532i \(-0.746184\pi\)
−0.698580 + 0.715532i \(0.746184\pi\)
\(500\) −7.58968e11 −0.543074
\(501\) −1.44587e11 −0.102532
\(502\) 1.40316e12 0.986147
\(503\) 1.50533e12 1.04852 0.524260 0.851558i \(-0.324342\pi\)
0.524260 + 0.851558i \(0.324342\pi\)
\(504\) 2.11130e10 0.0145751
\(505\) 1.72683e12 1.18151
\(506\) 5.35048e10 0.0362840
\(507\) −4.70515e11 −0.316255
\(508\) −3.23140e10 −0.0215280
\(509\) −1.56888e12 −1.03600 −0.518001 0.855380i \(-0.673324\pi\)
−0.518001 + 0.855380i \(0.673324\pi\)
\(510\) −1.03417e12 −0.676902
\(511\) −1.22372e11 −0.0793942
\(512\) −6.87195e10 −0.0441942
\(513\) −2.39465e12 −1.52656
\(514\) 1.75262e12 1.10753
\(515\) −2.32339e12 −1.45542
\(516\) 2.47392e11 0.153625
\(517\) −4.18022e10 −0.0257331
\(518\) 8.80916e10 0.0537590
\(519\) 2.36082e12 1.42827
\(520\) −4.00447e11 −0.240176
\(521\) −8.36119e11 −0.497163 −0.248581 0.968611i \(-0.579964\pi\)
−0.248581 + 0.968611i \(0.579964\pi\)
\(522\) 1.60427e11 0.0945717
\(523\) −1.04380e12 −0.610043 −0.305021 0.952345i \(-0.598664\pi\)
−0.305021 + 0.952345i \(0.598664\pi\)
\(524\) −4.80919e11 −0.278664
\(525\) −7.95401e10 −0.0456951
\(526\) −6.53748e10 −0.0372370
\(527\) 1.13075e12 0.638587
\(528\) 1.18665e11 0.0664463
\(529\) −1.74898e12 −0.971036
\(530\) −1.89133e11 −0.104118
\(531\) −2.77179e11 −0.151299
\(532\) 2.41893e11 0.130925
\(533\) 2.72318e11 0.146152
\(534\) −1.78098e12 −0.947815
\(535\) 7.20391e11 0.380169
\(536\) 9.33444e11 0.488480
\(537\) −2.46690e12 −1.28017
\(538\) 1.35719e12 0.698428
\(539\) −5.70615e11 −0.291202
\(540\) −9.03526e11 −0.457266
\(541\) −2.61498e11 −0.131245 −0.0656223 0.997845i \(-0.520903\pi\)
−0.0656223 + 0.997845i \(0.520903\pi\)
\(542\) −1.08233e12 −0.538719
\(543\) −1.01529e12 −0.501175
\(544\) −4.62240e11 −0.226294
\(545\) −1.36058e12 −0.660604
\(546\) −1.91672e11 −0.0922977
\(547\) 3.97347e12 1.89770 0.948848 0.315734i \(-0.102251\pi\)
0.948848 + 0.315734i \(0.102251\pi\)
\(548\) 1.61879e12 0.766791
\(549\) 9.32602e11 0.438148
\(550\) 1.28260e11 0.0597669
\(551\) 1.83803e12 0.849514
\(552\) 1.15700e11 0.0530407
\(553\) −3.48432e11 −0.158436
\(554\) −1.96710e12 −0.887223
\(555\) −6.87239e11 −0.307461
\(556\) −2.00289e12 −0.888833
\(557\) −1.26345e12 −0.556175 −0.278087 0.960556i \(-0.589700\pi\)
−0.278087 + 0.960556i \(0.589700\pi\)
\(558\) 1.80094e11 0.0786403
\(559\) 6.44356e11 0.279108
\(560\) 9.12688e10 0.0392172
\(561\) 7.98199e11 0.340235
\(562\) 2.06242e12 0.872095
\(563\) 2.98705e12 1.25301 0.626505 0.779417i \(-0.284485\pi\)
0.626505 + 0.779417i \(0.284485\pi\)
\(564\) −9.03944e10 −0.0376171
\(565\) −3.01201e11 −0.124348
\(566\) −3.34124e11 −0.136847
\(567\) −3.31011e11 −0.134499
\(568\) 6.37357e11 0.256930
\(569\) −4.48345e11 −0.179311 −0.0896555 0.995973i \(-0.528577\pi\)
−0.0896555 + 0.995973i \(0.528577\pi\)
\(570\) −1.88711e12 −0.748790
\(571\) 1.93797e12 0.762931 0.381466 0.924383i \(-0.375420\pi\)
0.381466 + 0.924383i \(0.375420\pi\)
\(572\) 3.09075e11 0.120721
\(573\) 1.54003e12 0.596806
\(574\) −6.20660e10 −0.0238644
\(575\) 1.25056e11 0.0477089
\(576\) −7.36205e10 −0.0278675
\(577\) −1.54518e12 −0.580347 −0.290174 0.956974i \(-0.593713\pi\)
−0.290174 + 0.956974i \(0.593713\pi\)
\(578\) −1.21184e12 −0.451617
\(579\) 1.98923e11 0.0735581
\(580\) 6.93508e11 0.254463
\(581\) −8.67828e11 −0.315967
\(582\) −2.55570e12 −0.923330
\(583\) 1.45978e11 0.0523333
\(584\) 4.26709e11 0.151801
\(585\) −4.29006e11 −0.151447
\(586\) −6.17549e10 −0.0216338
\(587\) −1.73985e10 −0.00604841 −0.00302421 0.999995i \(-0.500963\pi\)
−0.00302421 + 0.999995i \(0.500963\pi\)
\(588\) −1.23392e12 −0.425684
\(589\) 2.06335e12 0.706406
\(590\) −1.19821e12 −0.407098
\(591\) 4.98128e12 1.67957
\(592\) −3.07173e11 −0.102786
\(593\) 8.05756e10 0.0267582 0.0133791 0.999910i \(-0.495741\pi\)
0.0133791 + 0.999910i \(0.495741\pi\)
\(594\) 6.97365e11 0.229838
\(595\) 6.13917e11 0.200809
\(596\) −6.89982e10 −0.0223991
\(597\) 3.98327e12 1.28338
\(598\) 3.01353e11 0.0963652
\(599\) 4.11009e11 0.130446 0.0652229 0.997871i \(-0.479224\pi\)
0.0652229 + 0.997871i \(0.479224\pi\)
\(600\) 2.77354e11 0.0873684
\(601\) −3.07127e12 −0.960246 −0.480123 0.877201i \(-0.659408\pi\)
−0.480123 + 0.877201i \(0.659408\pi\)
\(602\) −1.46860e11 −0.0455742
\(603\) 1.00002e12 0.308020
\(604\) 3.02651e12 0.925286
\(605\) 2.54140e11 0.0771212
\(606\) −2.88211e12 −0.868128
\(607\) 1.67239e12 0.500021 0.250010 0.968243i \(-0.419566\pi\)
0.250010 + 0.968243i \(0.419566\pi\)
\(608\) −8.43476e11 −0.250326
\(609\) 3.31943e11 0.0977882
\(610\) 4.03152e12 1.17892
\(611\) −2.35441e11 −0.0683434
\(612\) −4.95206e11 −0.142694
\(613\) −2.38637e11 −0.0682598 −0.0341299 0.999417i \(-0.510866\pi\)
−0.0341299 + 0.999417i \(0.510866\pi\)
\(614\) −6.58121e11 −0.186874
\(615\) 4.84203e11 0.136486
\(616\) −7.04436e10 −0.0197119
\(617\) 2.55970e12 0.711060 0.355530 0.934665i \(-0.384300\pi\)
0.355530 + 0.934665i \(0.384300\pi\)
\(618\) 3.87779e12 1.06939
\(619\) −4.65350e12 −1.27401 −0.637004 0.770860i \(-0.719827\pi\)
−0.637004 + 0.770860i \(0.719827\pi\)
\(620\) 7.78524e11 0.211597
\(621\) 6.79941e11 0.183468
\(622\) 4.41022e12 1.18142
\(623\) 1.05725e12 0.281178
\(624\) 6.68354e11 0.176472
\(625\) −2.44554e12 −0.641083
\(626\) −5.02657e12 −1.30824
\(627\) 1.45652e12 0.376368
\(628\) 9.39493e11 0.241032
\(629\) −2.06619e12 −0.526312
\(630\) 9.77780e10 0.0247291
\(631\) −2.86910e12 −0.720466 −0.360233 0.932862i \(-0.617303\pi\)
−0.360233 + 0.932862i \(0.617303\pi\)
\(632\) 1.21497e12 0.302928
\(633\) 1.31230e12 0.324875
\(634\) −4.13073e12 −1.01537
\(635\) −1.49652e11 −0.0365259
\(636\) 3.15667e11 0.0765018
\(637\) −3.21385e12 −0.773390
\(638\) −5.35267e11 −0.127902
\(639\) 6.82812e11 0.162012
\(640\) −3.18252e11 −0.0749827
\(641\) −6.45940e12 −1.51123 −0.755615 0.655016i \(-0.772662\pi\)
−0.755615 + 0.655016i \(0.772662\pi\)
\(642\) −1.20235e12 −0.279333
\(643\) −2.55823e12 −0.590188 −0.295094 0.955468i \(-0.595351\pi\)
−0.295094 + 0.955468i \(0.595351\pi\)
\(644\) −6.86836e10 −0.0157350
\(645\) 1.14571e12 0.260650
\(646\) −5.67362e12 −1.28178
\(647\) −9.97781e11 −0.223855 −0.111927 0.993716i \(-0.535702\pi\)
−0.111927 + 0.993716i \(0.535702\pi\)
\(648\) 1.15423e12 0.257160
\(649\) 9.24810e11 0.204622
\(650\) 7.22397e11 0.158732
\(651\) 3.72636e11 0.0813149
\(652\) −3.34361e12 −0.724605
\(653\) −7.53538e12 −1.62179 −0.810897 0.585188i \(-0.801021\pi\)
−0.810897 + 0.585188i \(0.801021\pi\)
\(654\) 2.27084e12 0.485386
\(655\) −2.22722e12 −0.472800
\(656\) 2.16423e11 0.0456284
\(657\) 4.57141e11 0.0957208
\(658\) 5.36611e10 0.0111595
\(659\) −8.67293e12 −1.79135 −0.895677 0.444706i \(-0.853308\pi\)
−0.895677 + 0.444706i \(0.853308\pi\)
\(660\) 5.49560e11 0.112737
\(661\) 4.77055e12 0.971991 0.485995 0.873961i \(-0.338457\pi\)
0.485995 + 0.873961i \(0.338457\pi\)
\(662\) 9.51697e11 0.192592
\(663\) 4.49567e12 0.903615
\(664\) 3.02610e12 0.604124
\(665\) 1.12025e12 0.222135
\(666\) −3.29081e11 −0.0648139
\(667\) −5.21894e11 −0.102098
\(668\) −2.99293e11 −0.0581571
\(669\) −2.61166e12 −0.504079
\(670\) 4.32294e12 0.828787
\(671\) −3.11163e12 −0.592567
\(672\) −1.52329e11 −0.0288152
\(673\) −7.71533e12 −1.44973 −0.724864 0.688892i \(-0.758098\pi\)
−0.724864 + 0.688892i \(0.758098\pi\)
\(674\) −1.53867e12 −0.287194
\(675\) 1.62994e12 0.302207
\(676\) −9.73959e11 −0.179383
\(677\) 9.14395e12 1.67296 0.836479 0.548000i \(-0.184611\pi\)
0.836479 + 0.548000i \(0.184611\pi\)
\(678\) 5.02711e11 0.0913659
\(679\) 1.51715e12 0.273914
\(680\) −2.14071e12 −0.383945
\(681\) −6.59528e11 −0.117509
\(682\) −6.00885e11 −0.106356
\(683\) 8.83407e11 0.155334 0.0776672 0.996979i \(-0.475253\pi\)
0.0776672 + 0.996979i \(0.475253\pi\)
\(684\) −9.03631e11 −0.157848
\(685\) 7.49688e12 1.30099
\(686\) 1.49092e12 0.257037
\(687\) −3.24525e12 −0.555832
\(688\) 5.12097e11 0.0871373
\(689\) 8.22184e11 0.138990
\(690\) 5.35829e11 0.0899923
\(691\) 6.58731e12 1.09915 0.549575 0.835445i \(-0.314790\pi\)
0.549575 + 0.835445i \(0.314790\pi\)
\(692\) 4.88685e12 0.810124
\(693\) −7.54676e10 −0.0124297
\(694\) 5.85558e12 0.958191
\(695\) −9.27573e12 −1.50805
\(696\) −1.15748e12 −0.186970
\(697\) 1.45576e12 0.233638
\(698\) 6.91613e12 1.10284
\(699\) 5.90133e12 0.934981
\(700\) −1.64647e11 −0.0259186
\(701\) 6.57894e12 1.02902 0.514512 0.857483i \(-0.327973\pi\)
0.514512 + 0.857483i \(0.327973\pi\)
\(702\) 3.92774e12 0.610416
\(703\) −3.77030e12 −0.582207
\(704\) 2.45635e11 0.0376889
\(705\) −4.18632e11 −0.0638236
\(706\) 5.88612e12 0.891678
\(707\) 1.71092e12 0.257538
\(708\) 1.99984e12 0.299120
\(709\) 8.74938e11 0.130038 0.0650188 0.997884i \(-0.479289\pi\)
0.0650188 + 0.997884i \(0.479289\pi\)
\(710\) 2.95171e12 0.435924
\(711\) 1.30162e12 0.191017
\(712\) −3.68660e12 −0.537609
\(713\) −5.85872e11 −0.0848985
\(714\) −1.02464e12 −0.147547
\(715\) 1.43138e12 0.204823
\(716\) −5.10644e12 −0.726122
\(717\) −3.26916e12 −0.461955
\(718\) 2.01202e12 0.282535
\(719\) 8.46541e12 1.18132 0.590660 0.806920i \(-0.298867\pi\)
0.590660 + 0.806920i \(0.298867\pi\)
\(720\) −3.40949e11 −0.0472818
\(721\) −2.30198e12 −0.317244
\(722\) −5.18998e12 −0.710801
\(723\) −6.12534e12 −0.833696
\(724\) −2.10163e12 −0.284270
\(725\) −1.25107e12 −0.168175
\(726\) −4.24165e11 −0.0566656
\(727\) −4.57971e12 −0.608042 −0.304021 0.952665i \(-0.598329\pi\)
−0.304021 + 0.952665i \(0.598329\pi\)
\(728\) −3.96757e11 −0.0523520
\(729\) 8.48313e12 1.11245
\(730\) 1.97616e12 0.257555
\(731\) 3.44461e12 0.446182
\(732\) −6.72869e12 −0.866225
\(733\) 2.48940e12 0.318512 0.159256 0.987237i \(-0.449090\pi\)
0.159256 + 0.987237i \(0.449090\pi\)
\(734\) −8.31365e12 −1.05721
\(735\) −5.71448e12 −0.722244
\(736\) 2.39498e11 0.0300851
\(737\) −3.33656e12 −0.416577
\(738\) 2.31858e11 0.0287719
\(739\) −8.85822e12 −1.09256 −0.546282 0.837602i \(-0.683957\pi\)
−0.546282 + 0.837602i \(0.683957\pi\)
\(740\) −1.42257e12 −0.174394
\(741\) 8.20350e12 0.999580
\(742\) −1.87390e11 −0.0226949
\(743\) −1.02362e13 −1.23222 −0.616112 0.787659i \(-0.711293\pi\)
−0.616112 + 0.787659i \(0.711293\pi\)
\(744\) −1.29937e12 −0.155473
\(745\) −3.19543e11 −0.0380037
\(746\) −7.44381e12 −0.879975
\(747\) 3.24191e12 0.380942
\(748\) 1.65226e12 0.192984
\(749\) 7.13753e11 0.0828667
\(750\) 5.86647e12 0.677019
\(751\) 3.19150e12 0.366113 0.183056 0.983102i \(-0.441401\pi\)
0.183056 + 0.983102i \(0.441401\pi\)
\(752\) −1.87115e11 −0.0213367
\(753\) −1.08458e13 −1.22937
\(754\) −3.01477e12 −0.339690
\(755\) 1.40163e13 1.56990
\(756\) −8.95201e11 −0.0996718
\(757\) 1.65793e13 1.83499 0.917496 0.397746i \(-0.130207\pi\)
0.917496 + 0.397746i \(0.130207\pi\)
\(758\) −7.18069e12 −0.790050
\(759\) −4.13567e11 −0.0452333
\(760\) −3.90628e12 −0.424720
\(761\) 8.76788e12 0.947685 0.473842 0.880610i \(-0.342867\pi\)
0.473842 + 0.880610i \(0.342867\pi\)
\(762\) 2.49772e11 0.0268378
\(763\) −1.34805e12 −0.143994
\(764\) 3.18784e12 0.338513
\(765\) −2.29339e12 −0.242103
\(766\) −4.41127e12 −0.462950
\(767\) 5.20877e12 0.543446
\(768\) 5.31169e11 0.0550944
\(769\) 1.02168e13 1.05353 0.526764 0.850011i \(-0.323405\pi\)
0.526764 + 0.850011i \(0.323405\pi\)
\(770\) −3.26237e11 −0.0334445
\(771\) −1.35469e13 −1.38069
\(772\) 4.11767e11 0.0417228
\(773\) −4.77737e12 −0.481262 −0.240631 0.970617i \(-0.577354\pi\)
−0.240631 + 0.970617i \(0.577354\pi\)
\(774\) 5.48619e11 0.0549461
\(775\) −1.40444e12 −0.139844
\(776\) −5.29026e12 −0.523720
\(777\) −6.80907e11 −0.0670183
\(778\) −1.32746e13 −1.29901
\(779\) 2.65641e12 0.258450
\(780\) 3.09526e12 0.299414
\(781\) −2.27821e12 −0.219111
\(782\) 1.61098e12 0.154049
\(783\) −6.80220e12 −0.646728
\(784\) −2.55419e12 −0.241452
\(785\) 4.35096e12 0.408951
\(786\) 3.71728e12 0.347395
\(787\) −1.03319e11 −0.00960053 −0.00480026 0.999988i \(-0.501528\pi\)
−0.00480026 + 0.999988i \(0.501528\pi\)
\(788\) 1.03112e13 0.952664
\(789\) 5.05316e11 0.0464212
\(790\) 5.62676e12 0.513968
\(791\) −2.98426e11 −0.0271045
\(792\) 2.63154e11 0.0237654
\(793\) −1.75255e13 −1.57377
\(794\) −2.45043e12 −0.218801
\(795\) 1.46191e12 0.129798
\(796\) 8.24531e12 0.727945
\(797\) −1.18659e13 −1.04169 −0.520844 0.853652i \(-0.674383\pi\)
−0.520844 + 0.853652i \(0.674383\pi\)
\(798\) −1.86972e12 −0.163216
\(799\) −1.25862e12 −0.109254
\(800\) 5.74119e11 0.0495561
\(801\) −3.94953e12 −0.338999
\(802\) −3.28738e12 −0.280585
\(803\) −1.52526e12 −0.129456
\(804\) −7.21508e12 −0.608961
\(805\) −3.18086e11 −0.0266970
\(806\) −3.38434e12 −0.282466
\(807\) −1.04905e13 −0.870691
\(808\) −5.96592e12 −0.492410
\(809\) 1.31694e13 1.08093 0.540465 0.841367i \(-0.318249\pi\)
0.540465 + 0.841367i \(0.318249\pi\)
\(810\) 5.34542e12 0.436314
\(811\) −3.03385e12 −0.246263 −0.123132 0.992390i \(-0.539294\pi\)
−0.123132 + 0.992390i \(0.539294\pi\)
\(812\) 6.87118e11 0.0554663
\(813\) 8.36589e12 0.671591
\(814\) 1.09798e12 0.0876566
\(815\) −1.54848e13 −1.22941
\(816\) 3.57290e12 0.282108
\(817\) 6.28557e12 0.493566
\(818\) 1.05222e13 0.821704
\(819\) −4.25053e11 −0.0330115
\(820\) 1.00229e12 0.0774162
\(821\) 1.60816e13 1.23534 0.617670 0.786438i \(-0.288077\pi\)
0.617670 + 0.786438i \(0.288077\pi\)
\(822\) −1.25125e13 −0.955915
\(823\) 9.77833e12 0.742960 0.371480 0.928441i \(-0.378850\pi\)
0.371480 + 0.928441i \(0.378850\pi\)
\(824\) 8.02695e12 0.606566
\(825\) −9.91393e11 −0.0745080
\(826\) −1.18717e12 −0.0887366
\(827\) 1.19955e13 0.891749 0.445874 0.895096i \(-0.352893\pi\)
0.445874 + 0.895096i \(0.352893\pi\)
\(828\) 2.56579e11 0.0189707
\(829\) 1.25391e13 0.922085 0.461043 0.887378i \(-0.347475\pi\)
0.461043 + 0.887378i \(0.347475\pi\)
\(830\) 1.40144e13 1.02500
\(831\) 1.52048e13 1.10605
\(832\) 1.38348e12 0.100096
\(833\) −1.71807e13 −1.23634
\(834\) 1.54814e13 1.10806
\(835\) −1.38608e12 −0.0986732
\(836\) 3.01497e12 0.213479
\(837\) −7.63607e12 −0.537781
\(838\) 6.07152e12 0.425304
\(839\) 1.36095e13 0.948233 0.474116 0.880462i \(-0.342768\pi\)
0.474116 + 0.880462i \(0.342768\pi\)
\(840\) −7.05465e11 −0.0488898
\(841\) −9.28607e12 −0.640103
\(842\) −1.46459e13 −1.00418
\(843\) −1.59415e13 −1.08719
\(844\) 2.71644e12 0.184272
\(845\) −4.51057e12 −0.304352
\(846\) −2.00460e11 −0.0134543
\(847\) 2.51798e11 0.0168104
\(848\) 6.53425e11 0.0433925
\(849\) 2.58262e12 0.170599
\(850\) 3.86180e12 0.253749
\(851\) 1.07055e12 0.0699718
\(852\) −4.92647e12 −0.320300
\(853\) −5.86443e12 −0.379276 −0.189638 0.981854i \(-0.560731\pi\)
−0.189638 + 0.981854i \(0.560731\pi\)
\(854\) 3.99437e12 0.256974
\(855\) −4.18488e12 −0.267815
\(856\) −2.48884e12 −0.158440
\(857\) −1.19243e12 −0.0755128 −0.0377564 0.999287i \(-0.512021\pi\)
−0.0377564 + 0.999287i \(0.512021\pi\)
\(858\) −2.38901e12 −0.150496
\(859\) 1.96633e13 1.23222 0.616108 0.787662i \(-0.288709\pi\)
0.616108 + 0.787662i \(0.288709\pi\)
\(860\) 2.37161e12 0.147843
\(861\) 4.79741e11 0.0297504
\(862\) −7.84775e12 −0.484131
\(863\) −1.56800e13 −0.962271 −0.481135 0.876646i \(-0.659775\pi\)
−0.481135 + 0.876646i \(0.659775\pi\)
\(864\) 3.12154e12 0.190571
\(865\) 2.26319e13 1.37451
\(866\) 9.07564e12 0.548336
\(867\) 9.36696e12 0.563006
\(868\) 7.71350e11 0.0461225
\(869\) −4.34288e12 −0.258338
\(870\) −5.36049e12 −0.317225
\(871\) −1.87924e13 −1.10637
\(872\) 4.70061e12 0.275315
\(873\) −5.66756e12 −0.330242
\(874\) 2.93964e12 0.170409
\(875\) −3.48253e12 −0.200844
\(876\) −3.29826e12 −0.189241
\(877\) −1.56274e13 −0.892047 −0.446023 0.895021i \(-0.647160\pi\)
−0.446023 + 0.895021i \(0.647160\pi\)
\(878\) 1.84109e13 1.04556
\(879\) 4.77336e11 0.0269696
\(880\) 1.13758e12 0.0639455
\(881\) 7.19215e12 0.402223 0.201112 0.979568i \(-0.435545\pi\)
0.201112 + 0.979568i \(0.435545\pi\)
\(882\) −2.73635e12 −0.152252
\(883\) 8.94240e11 0.0495029 0.0247515 0.999694i \(-0.492121\pi\)
0.0247515 + 0.999694i \(0.492121\pi\)
\(884\) 9.30596e12 0.512538
\(885\) 9.26160e12 0.507506
\(886\) 7.11071e12 0.387669
\(887\) 1.98339e13 1.07585 0.537926 0.842992i \(-0.319208\pi\)
0.537926 + 0.842992i \(0.319208\pi\)
\(888\) 2.37431e12 0.128138
\(889\) −1.48273e11 −0.00796168
\(890\) −1.70733e13 −0.912142
\(891\) −4.12574e12 −0.219307
\(892\) −5.40609e12 −0.285918
\(893\) −2.29668e12 −0.120856
\(894\) 5.33324e11 0.0279236
\(895\) −2.36488e13 −1.23199
\(896\) −3.15320e11 −0.0163442
\(897\) −2.32932e12 −0.120133
\(898\) −9.66218e12 −0.495829
\(899\) 5.86112e12 0.299269
\(900\) 6.15065e11 0.0312485
\(901\) 4.39525e12 0.222189
\(902\) −7.73595e11 −0.0389121
\(903\) 1.13516e12 0.0568148
\(904\) 1.04060e12 0.0518235
\(905\) −9.73300e12 −0.482312
\(906\) −2.33935e13 −1.15350
\(907\) −1.02442e13 −0.502625 −0.251313 0.967906i \(-0.580862\pi\)
−0.251313 + 0.967906i \(0.580862\pi\)
\(908\) −1.36521e12 −0.0666521
\(909\) −6.39141e12 −0.310498
\(910\) −1.83745e12 −0.0888239
\(911\) −7.68070e12 −0.369461 −0.184730 0.982789i \(-0.559141\pi\)
−0.184730 + 0.982789i \(0.559141\pi\)
\(912\) 6.51967e12 0.312068
\(913\) −1.08167e13 −0.515199
\(914\) 4.48350e12 0.212500
\(915\) −3.11618e13 −1.46969
\(916\) −6.71762e12 −0.315272
\(917\) −2.20670e12 −0.103058
\(918\) 2.09970e13 0.975809
\(919\) 1.89989e13 0.878633 0.439317 0.898332i \(-0.355221\pi\)
0.439317 + 0.898332i \(0.355221\pi\)
\(920\) 1.10916e12 0.0510444
\(921\) 5.08697e12 0.232965
\(922\) −2.00414e13 −0.913352
\(923\) −1.28315e13 −0.581927
\(924\) 5.44496e11 0.0245737
\(925\) 2.56629e12 0.115257
\(926\) −2.35018e12 −0.105039
\(927\) 8.59943e12 0.382482
\(928\) −2.39596e12 −0.106051
\(929\) 2.17473e13 0.957931 0.478966 0.877834i \(-0.341012\pi\)
0.478966 + 0.877834i \(0.341012\pi\)
\(930\) −6.01762e12 −0.263786
\(931\) −3.13506e13 −1.36764
\(932\) 1.22157e13 0.530329
\(933\) −3.40889e13 −1.47281
\(934\) −2.39089e13 −1.02802
\(935\) 7.65191e12 0.327429
\(936\) 1.48215e12 0.0631177
\(937\) 3.95881e13 1.67779 0.838893 0.544297i \(-0.183203\pi\)
0.838893 + 0.544297i \(0.183203\pi\)
\(938\) 4.28311e12 0.180654
\(939\) 3.88530e13 1.63091
\(940\) −8.66562e11 −0.0362013
\(941\) −4.13659e13 −1.71985 −0.859923 0.510424i \(-0.829488\pi\)
−0.859923 + 0.510424i \(0.829488\pi\)
\(942\) −7.26184e12 −0.300481
\(943\) −7.54267e11 −0.0310615
\(944\) 4.13963e12 0.169663
\(945\) −4.14583e12 −0.169110
\(946\) −1.83047e12 −0.0743109
\(947\) 7.78696e12 0.314625 0.157313 0.987549i \(-0.449717\pi\)
0.157313 + 0.987549i \(0.449717\pi\)
\(948\) −9.39117e12 −0.377644
\(949\) −8.59064e12 −0.343817
\(950\) 7.04685e12 0.280698
\(951\) 3.19286e13 1.26581
\(952\) −2.12099e12 −0.0836898
\(953\) 1.26501e13 0.496794 0.248397 0.968658i \(-0.420096\pi\)
0.248397 + 0.968658i \(0.420096\pi\)
\(954\) 7.00026e11 0.0273619
\(955\) 1.47634e13 0.574344
\(956\) −6.76710e12 −0.262025
\(957\) 4.13736e12 0.159448
\(958\) 2.52810e12 0.0969729
\(959\) 7.42781e12 0.283581
\(960\) 2.45994e12 0.0934767
\(961\) −1.98600e13 −0.751145
\(962\) 6.18411e12 0.232803
\(963\) −2.66634e12 −0.0999074
\(964\) −1.26793e13 −0.472879
\(965\) 1.90696e12 0.0707896
\(966\) 5.30892e11 0.0196159
\(967\) −6.51628e12 −0.239652 −0.119826 0.992795i \(-0.538234\pi\)
−0.119826 + 0.992795i \(0.538234\pi\)
\(968\) −8.78014e11 −0.0321412
\(969\) 4.38544e13 1.59792
\(970\) −2.45001e13 −0.888578
\(971\) 2.06099e13 0.744028 0.372014 0.928227i \(-0.378667\pi\)
0.372014 + 0.928227i \(0.378667\pi\)
\(972\) 6.07870e12 0.218430
\(973\) −9.19027e12 −0.328716
\(974\) 3.19833e13 1.13870
\(975\) −5.58379e12 −0.197883
\(976\) −1.39283e13 −0.491330
\(977\) −3.23219e13 −1.13494 −0.567468 0.823395i \(-0.692077\pi\)
−0.567468 + 0.823395i \(0.692077\pi\)
\(978\) 2.58445e13 0.903324
\(979\) 1.31776e13 0.458474
\(980\) −1.18289e13 −0.409663
\(981\) 5.03585e12 0.173605
\(982\) −1.49313e13 −0.512383
\(983\) 2.94079e13 1.00455 0.502277 0.864707i \(-0.332496\pi\)
0.502277 + 0.864707i \(0.332496\pi\)
\(984\) −1.67285e12 −0.0568824
\(985\) 4.77528e13 1.61635
\(986\) −1.61164e13 −0.543027
\(987\) −4.14775e11 −0.0139119
\(988\) 1.69811e13 0.566970
\(989\) −1.78474e12 −0.0593186
\(990\) 1.21871e12 0.0403220
\(991\) 3.67690e13 1.21102 0.605508 0.795839i \(-0.292970\pi\)
0.605508 + 0.795839i \(0.292970\pi\)
\(992\) −2.68968e12 −0.0881857
\(993\) −7.35617e12 −0.240093
\(994\) 2.92451e12 0.0950200
\(995\) 3.81855e13 1.23508
\(996\) −2.33903e13 −0.753128
\(997\) −7.67620e12 −0.246047 −0.123024 0.992404i \(-0.539259\pi\)
−0.123024 + 0.992404i \(0.539259\pi\)
\(998\) 3.09613e13 0.987941
\(999\) 1.39532e13 0.443229
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 22.10.a.d.1.2 2
3.2 odd 2 198.10.a.n.1.1 2
4.3 odd 2 176.10.a.e.1.1 2
11.10 odd 2 242.10.a.e.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.10.a.d.1.2 2 1.1 even 1 trivial
176.10.a.e.1.1 2 4.3 odd 2
198.10.a.n.1.1 2 3.2 odd 2
242.10.a.e.1.2 2 11.10 odd 2