Properties

Label 1045.6.a.h.1.1
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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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1045,6,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 1.1
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.7623 q^{2} -11.3539 q^{3} +83.8277 q^{4} +25.0000 q^{5} +122.194 q^{6} -59.3342 q^{7} -557.787 q^{8} -114.090 q^{9} +O(q^{10})\) \(q-10.7623 q^{2} -11.3539 q^{3} +83.8277 q^{4} +25.0000 q^{5} +122.194 q^{6} -59.3342 q^{7} -557.787 q^{8} -114.090 q^{9} -269.058 q^{10} +121.000 q^{11} -951.769 q^{12} +781.069 q^{13} +638.574 q^{14} -283.847 q^{15} +3320.60 q^{16} +774.166 q^{17} +1227.87 q^{18} +361.000 q^{19} +2095.69 q^{20} +673.673 q^{21} -1302.24 q^{22} +2900.65 q^{23} +6333.04 q^{24} +625.000 q^{25} -8406.12 q^{26} +4054.35 q^{27} -4973.85 q^{28} -2591.30 q^{29} +3054.85 q^{30} +2389.59 q^{31} -17888.2 q^{32} -1373.82 q^{33} -8331.83 q^{34} -1483.35 q^{35} -9563.87 q^{36} +1235.84 q^{37} -3885.20 q^{38} -8868.16 q^{39} -13944.7 q^{40} +8939.92 q^{41} -7250.29 q^{42} -2987.40 q^{43} +10143.2 q^{44} -2852.24 q^{45} -31217.8 q^{46} +23106.3 q^{47} -37701.7 q^{48} -13286.5 q^{49} -6726.46 q^{50} -8789.79 q^{51} +65475.2 q^{52} +17689.3 q^{53} -43634.2 q^{54} +3025.00 q^{55} +33095.8 q^{56} -4098.75 q^{57} +27888.4 q^{58} -15720.2 q^{59} -23794.2 q^{60} +46680.1 q^{61} -25717.5 q^{62} +6769.41 q^{63} +86259.6 q^{64} +19526.7 q^{65} +14785.5 q^{66} -24948.4 q^{67} +64896.6 q^{68} -32933.6 q^{69} +15964.4 q^{70} +6610.43 q^{71} +63637.7 q^{72} +66614.6 q^{73} -13300.5 q^{74} -7096.17 q^{75} +30261.8 q^{76} -7179.44 q^{77} +95442.0 q^{78} +54873.9 q^{79} +83015.0 q^{80} -18308.8 q^{81} -96214.4 q^{82} +52528.5 q^{83} +56472.5 q^{84} +19354.2 q^{85} +32151.4 q^{86} +29421.3 q^{87} -67492.2 q^{88} -27702.4 q^{89} +30696.7 q^{90} -46344.1 q^{91} +243155. q^{92} -27131.1 q^{93} -248677. q^{94} +9025.00 q^{95} +203100. q^{96} +19556.4 q^{97} +142993. q^{98} -13804.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.7623 −1.90253 −0.951264 0.308376i \(-0.900214\pi\)
−0.951264 + 0.308376i \(0.900214\pi\)
\(3\) −11.3539 −0.728351 −0.364176 0.931330i \(-0.618649\pi\)
−0.364176 + 0.931330i \(0.618649\pi\)
\(4\) 83.8277 2.61962
\(5\) 25.0000 0.447214
\(6\) 122.194 1.38571
\(7\) −59.3342 −0.457678 −0.228839 0.973464i \(-0.573493\pi\)
−0.228839 + 0.973464i \(0.573493\pi\)
\(8\) −557.787 −3.08137
\(9\) −114.090 −0.469505
\(10\) −269.058 −0.850837
\(11\) 121.000 0.301511
\(12\) −951.769 −1.90800
\(13\) 781.069 1.28183 0.640916 0.767611i \(-0.278555\pi\)
0.640916 + 0.767611i \(0.278555\pi\)
\(14\) 638.574 0.870745
\(15\) −283.847 −0.325729
\(16\) 3320.60 3.24277
\(17\) 774.166 0.649699 0.324849 0.945766i \(-0.394686\pi\)
0.324849 + 0.945766i \(0.394686\pi\)
\(18\) 1227.87 0.893246
\(19\) 361.000 0.229416
\(20\) 2095.69 1.17153
\(21\) 673.673 0.333350
\(22\) −1302.24 −0.573634
\(23\) 2900.65 1.14334 0.571671 0.820483i \(-0.306295\pi\)
0.571671 + 0.820483i \(0.306295\pi\)
\(24\) 6333.04 2.24432
\(25\) 625.000 0.200000
\(26\) −8406.12 −2.43872
\(27\) 4054.35 1.07032
\(28\) −4973.85 −1.19894
\(29\) −2591.30 −0.572167 −0.286083 0.958205i \(-0.592353\pi\)
−0.286083 + 0.958205i \(0.592353\pi\)
\(30\) 3054.85 0.619708
\(31\) 2389.59 0.446600 0.223300 0.974750i \(-0.428317\pi\)
0.223300 + 0.974750i \(0.428317\pi\)
\(32\) −17888.2 −3.08810
\(33\) −1373.82 −0.219606
\(34\) −8331.83 −1.23607
\(35\) −1483.35 −0.204680
\(36\) −9563.87 −1.22992
\(37\) 1235.84 0.148408 0.0742039 0.997243i \(-0.476358\pi\)
0.0742039 + 0.997243i \(0.476358\pi\)
\(38\) −3885.20 −0.436470
\(39\) −8868.16 −0.933624
\(40\) −13944.7 −1.37803
\(41\) 8939.92 0.830566 0.415283 0.909692i \(-0.363683\pi\)
0.415283 + 0.909692i \(0.363683\pi\)
\(42\) −7250.29 −0.634208
\(43\) −2987.40 −0.246389 −0.123195 0.992383i \(-0.539314\pi\)
−0.123195 + 0.992383i \(0.539314\pi\)
\(44\) 10143.2 0.789844
\(45\) −2852.24 −0.209969
\(46\) −31217.8 −2.17524
\(47\) 23106.3 1.52576 0.762879 0.646542i \(-0.223785\pi\)
0.762879 + 0.646542i \(0.223785\pi\)
\(48\) −37701.7 −2.36188
\(49\) −13286.5 −0.790531
\(50\) −6726.46 −0.380506
\(51\) −8789.79 −0.473209
\(52\) 65475.2 3.35791
\(53\) 17689.3 0.865008 0.432504 0.901632i \(-0.357630\pi\)
0.432504 + 0.901632i \(0.357630\pi\)
\(54\) −43634.2 −2.03631
\(55\) 3025.00 0.134840
\(56\) 33095.8 1.41027
\(57\) −4098.75 −0.167095
\(58\) 27888.4 1.08856
\(59\) −15720.2 −0.587934 −0.293967 0.955816i \(-0.594976\pi\)
−0.293967 + 0.955816i \(0.594976\pi\)
\(60\) −23794.2 −0.853284
\(61\) 46680.1 1.60623 0.803115 0.595824i \(-0.203175\pi\)
0.803115 + 0.595824i \(0.203175\pi\)
\(62\) −25717.5 −0.849670
\(63\) 6769.41 0.214882
\(64\) 86259.6 2.63243
\(65\) 19526.7 0.573253
\(66\) 14785.5 0.417807
\(67\) −24948.4 −0.678978 −0.339489 0.940610i \(-0.610254\pi\)
−0.339489 + 0.940610i \(0.610254\pi\)
\(68\) 64896.6 1.70196
\(69\) −32933.6 −0.832754
\(70\) 15964.4 0.389409
\(71\) 6610.43 0.155627 0.0778133 0.996968i \(-0.475206\pi\)
0.0778133 + 0.996968i \(0.475206\pi\)
\(72\) 63637.7 1.44672
\(73\) 66614.6 1.46306 0.731530 0.681809i \(-0.238806\pi\)
0.731530 + 0.681809i \(0.238806\pi\)
\(74\) −13300.5 −0.282350
\(75\) −7096.17 −0.145670
\(76\) 30261.8 0.600981
\(77\) −7179.44 −0.137995
\(78\) 95442.0 1.77625
\(79\) 54873.9 0.989232 0.494616 0.869112i \(-0.335309\pi\)
0.494616 + 0.869112i \(0.335309\pi\)
\(80\) 83015.0 1.45021
\(81\) −18308.8 −0.310061
\(82\) −96214.4 −1.58018
\(83\) 52528.5 0.836950 0.418475 0.908228i \(-0.362565\pi\)
0.418475 + 0.908228i \(0.362565\pi\)
\(84\) 56472.5 0.873250
\(85\) 19354.2 0.290554
\(86\) 32151.4 0.468763
\(87\) 29421.3 0.416738
\(88\) −67492.2 −0.929067
\(89\) −27702.4 −0.370716 −0.185358 0.982671i \(-0.559345\pi\)
−0.185358 + 0.982671i \(0.559345\pi\)
\(90\) 30696.7 0.399472
\(91\) −46344.1 −0.586666
\(92\) 243155. 2.99512
\(93\) −27131.1 −0.325282
\(94\) −248677. −2.90280
\(95\) 9025.00 0.102598
\(96\) 203100. 2.24922
\(97\) 19556.4 0.211038 0.105519 0.994417i \(-0.466350\pi\)
0.105519 + 0.994417i \(0.466350\pi\)
\(98\) 142993. 1.50401
\(99\) −13804.8 −0.141561
\(100\) 52392.3 0.523923
\(101\) −77117.1 −0.752224 −0.376112 0.926574i \(-0.622739\pi\)
−0.376112 + 0.926574i \(0.622739\pi\)
\(102\) 94598.6 0.900294
\(103\) −26847.9 −0.249354 −0.124677 0.992197i \(-0.539790\pi\)
−0.124677 + 0.992197i \(0.539790\pi\)
\(104\) −435670. −3.94979
\(105\) 16841.8 0.149079
\(106\) −190378. −1.64570
\(107\) 224022. 1.89161 0.945806 0.324731i \(-0.105274\pi\)
0.945806 + 0.324731i \(0.105274\pi\)
\(108\) 339867. 2.80382
\(109\) −41787.6 −0.336884 −0.168442 0.985712i \(-0.553874\pi\)
−0.168442 + 0.985712i \(0.553874\pi\)
\(110\) −32556.0 −0.256537
\(111\) −14031.5 −0.108093
\(112\) −197025. −1.48415
\(113\) −35286.6 −0.259964 −0.129982 0.991516i \(-0.541492\pi\)
−0.129982 + 0.991516i \(0.541492\pi\)
\(114\) 44112.1 0.317904
\(115\) 72516.3 0.511318
\(116\) −217223. −1.49886
\(117\) −89111.8 −0.601826
\(118\) 169186. 1.11856
\(119\) −45934.5 −0.297353
\(120\) 158326. 1.00369
\(121\) 14641.0 0.0909091
\(122\) −502387. −3.05590
\(123\) −101503. −0.604944
\(124\) 200314. 1.16992
\(125\) 15625.0 0.0894427
\(126\) −72854.7 −0.408819
\(127\) −177287. −0.975367 −0.487683 0.873021i \(-0.662158\pi\)
−0.487683 + 0.873021i \(0.662158\pi\)
\(128\) −355931. −1.92018
\(129\) 33918.5 0.179458
\(130\) −210153. −1.09063
\(131\) 103759. 0.528260 0.264130 0.964487i \(-0.414915\pi\)
0.264130 + 0.964487i \(0.414915\pi\)
\(132\) −115164. −0.575284
\(133\) −21419.6 −0.104998
\(134\) 268503. 1.29177
\(135\) 101359. 0.478660
\(136\) −431820. −2.00196
\(137\) −116243. −0.529132 −0.264566 0.964368i \(-0.585229\pi\)
−0.264566 + 0.964368i \(0.585229\pi\)
\(138\) 354443. 1.58434
\(139\) −250320. −1.09890 −0.549451 0.835526i \(-0.685163\pi\)
−0.549451 + 0.835526i \(0.685163\pi\)
\(140\) −124346. −0.536182
\(141\) −262346. −1.11129
\(142\) −71143.6 −0.296084
\(143\) 94509.3 0.386487
\(144\) −378846. −1.52250
\(145\) −64782.5 −0.255881
\(146\) −716928. −2.78352
\(147\) 150853. 0.575784
\(148\) 103597. 0.388772
\(149\) −7538.50 −0.0278176 −0.0139088 0.999903i \(-0.504427\pi\)
−0.0139088 + 0.999903i \(0.504427\pi\)
\(150\) 76371.3 0.277142
\(151\) −439881. −1.56998 −0.784988 0.619511i \(-0.787331\pi\)
−0.784988 + 0.619511i \(0.787331\pi\)
\(152\) −201361. −0.706914
\(153\) −88324.3 −0.305036
\(154\) 77267.5 0.262540
\(155\) 59739.7 0.199726
\(156\) −743397. −2.44574
\(157\) 313502. 1.01506 0.507529 0.861635i \(-0.330559\pi\)
0.507529 + 0.861635i \(0.330559\pi\)
\(158\) −590571. −1.88204
\(159\) −200842. −0.630030
\(160\) −447205. −1.38104
\(161\) −172108. −0.523282
\(162\) 197045. 0.589900
\(163\) −134307. −0.395941 −0.197970 0.980208i \(-0.563435\pi\)
−0.197970 + 0.980208i \(0.563435\pi\)
\(164\) 749413. 2.17576
\(165\) −34345.5 −0.0982109
\(166\) −565329. −1.59232
\(167\) −235267. −0.652785 −0.326393 0.945234i \(-0.605833\pi\)
−0.326393 + 0.945234i \(0.605833\pi\)
\(168\) −375766. −1.02717
\(169\) 238776. 0.643093
\(170\) −208296. −0.552788
\(171\) −41186.3 −0.107712
\(172\) −250427. −0.645446
\(173\) −267094. −0.678499 −0.339250 0.940696i \(-0.610173\pi\)
−0.339250 + 0.940696i \(0.610173\pi\)
\(174\) −316641. −0.792857
\(175\) −37083.9 −0.0915356
\(176\) 401793. 0.977733
\(177\) 178485. 0.428223
\(178\) 298142. 0.705299
\(179\) −166988. −0.389540 −0.194770 0.980849i \(-0.562396\pi\)
−0.194770 + 0.980849i \(0.562396\pi\)
\(180\) −239097. −0.550038
\(181\) −113407. −0.257302 −0.128651 0.991690i \(-0.541065\pi\)
−0.128651 + 0.991690i \(0.541065\pi\)
\(182\) 498770. 1.11615
\(183\) −530000. −1.16990
\(184\) −1.61795e6 −3.52306
\(185\) 30895.9 0.0663700
\(186\) 291994. 0.618858
\(187\) 93674.1 0.195892
\(188\) 1.93695e6 3.99690
\(189\) −240562. −0.489860
\(190\) −97130.0 −0.195195
\(191\) 915845. 1.81651 0.908257 0.418414i \(-0.137414\pi\)
0.908257 + 0.418414i \(0.137414\pi\)
\(192\) −979381. −1.91734
\(193\) −284642. −0.550055 −0.275027 0.961436i \(-0.588687\pi\)
−0.275027 + 0.961436i \(0.588687\pi\)
\(194\) −210473. −0.401506
\(195\) −221704. −0.417529
\(196\) −1.11377e6 −2.07089
\(197\) 1.06139e6 1.94854 0.974269 0.225387i \(-0.0723648\pi\)
0.974269 + 0.225387i \(0.0723648\pi\)
\(198\) 148572. 0.269324
\(199\) −316683. −0.566881 −0.283441 0.958990i \(-0.591476\pi\)
−0.283441 + 0.958990i \(0.591476\pi\)
\(200\) −348617. −0.616273
\(201\) 283261. 0.494534
\(202\) 829960. 1.43113
\(203\) 153753. 0.261868
\(204\) −736828. −1.23963
\(205\) 223498. 0.371440
\(206\) 288946. 0.474404
\(207\) −330934. −0.536804
\(208\) 2.59362e6 4.15669
\(209\) 43681.0 0.0691714
\(210\) −181257. −0.283627
\(211\) −779443. −1.20525 −0.602626 0.798024i \(-0.705879\pi\)
−0.602626 + 0.798024i \(0.705879\pi\)
\(212\) 1.48285e6 2.26599
\(213\) −75054.0 −0.113351
\(214\) −2.41100e6 −3.59885
\(215\) −74684.9 −0.110189
\(216\) −2.26146e6 −3.29803
\(217\) −141784. −0.204399
\(218\) 449731. 0.640932
\(219\) −756334. −1.06562
\(220\) 253579. 0.353229
\(221\) 604677. 0.832804
\(222\) 151012. 0.205650
\(223\) −217590. −0.293006 −0.146503 0.989210i \(-0.546802\pi\)
−0.146503 + 0.989210i \(0.546802\pi\)
\(224\) 1.06138e6 1.41336
\(225\) −71306.0 −0.0939009
\(226\) 379766. 0.494590
\(227\) 1.11249e6 1.43295 0.716476 0.697611i \(-0.245754\pi\)
0.716476 + 0.697611i \(0.245754\pi\)
\(228\) −343589. −0.437725
\(229\) −333227. −0.419906 −0.209953 0.977712i \(-0.567331\pi\)
−0.209953 + 0.977712i \(0.567331\pi\)
\(230\) −780444. −0.972797
\(231\) 81514.4 0.100509
\(232\) 1.44539e6 1.76306
\(233\) −808064. −0.975115 −0.487558 0.873091i \(-0.662112\pi\)
−0.487558 + 0.873091i \(0.662112\pi\)
\(234\) 959051. 1.14499
\(235\) 577657. 0.682340
\(236\) −1.31779e6 −1.54016
\(237\) −623031. −0.720508
\(238\) 494363. 0.565722
\(239\) −395232. −0.447567 −0.223783 0.974639i \(-0.571841\pi\)
−0.223783 + 0.974639i \(0.571841\pi\)
\(240\) −942542. −1.05626
\(241\) 899860. 0.998004 0.499002 0.866601i \(-0.333700\pi\)
0.499002 + 0.866601i \(0.333700\pi\)
\(242\) −157571. −0.172957
\(243\) −777331. −0.844482
\(244\) 3.91309e6 4.20771
\(245\) −332161. −0.353536
\(246\) 1.09241e6 1.15092
\(247\) 281966. 0.294072
\(248\) −1.33288e6 −1.37614
\(249\) −596402. −0.609594
\(250\) −168161. −0.170167
\(251\) −185739. −0.186088 −0.0930442 0.995662i \(-0.529660\pi\)
−0.0930442 + 0.995662i \(0.529660\pi\)
\(252\) 567465. 0.562908
\(253\) 350979. 0.344730
\(254\) 1.90802e6 1.85566
\(255\) −219745. −0.211625
\(256\) 1.07034e6 1.02076
\(257\) −98722.1 −0.0932356 −0.0466178 0.998913i \(-0.514844\pi\)
−0.0466178 + 0.998913i \(0.514844\pi\)
\(258\) −365042. −0.341424
\(259\) −73327.4 −0.0679230
\(260\) 1.63688e6 1.50170
\(261\) 295640. 0.268635
\(262\) −1.11669e6 −1.00503
\(263\) 43322.8 0.0386213 0.0193107 0.999814i \(-0.493853\pi\)
0.0193107 + 0.999814i \(0.493853\pi\)
\(264\) 766298. 0.676687
\(265\) 442232. 0.386843
\(266\) 230525. 0.199763
\(267\) 314529. 0.270012
\(268\) −2.09137e6 −1.77866
\(269\) 890980. 0.750736 0.375368 0.926876i \(-0.377516\pi\)
0.375368 + 0.926876i \(0.377516\pi\)
\(270\) −1.09086e6 −0.910664
\(271\) 960136. 0.794163 0.397081 0.917783i \(-0.370023\pi\)
0.397081 + 0.917783i \(0.370023\pi\)
\(272\) 2.57070e6 2.10683
\(273\) 526185. 0.427299
\(274\) 1.25104e6 1.00669
\(275\) 75625.0 0.0603023
\(276\) −2.76075e6 −2.18150
\(277\) 931543. 0.729463 0.364732 0.931113i \(-0.381161\pi\)
0.364732 + 0.931113i \(0.381161\pi\)
\(278\) 2.69403e6 2.09069
\(279\) −272627. −0.209681
\(280\) 827396. 0.630694
\(281\) −2.41833e6 −1.82705 −0.913524 0.406785i \(-0.866650\pi\)
−0.913524 + 0.406785i \(0.866650\pi\)
\(282\) 2.82345e6 2.11426
\(283\) 373999. 0.277590 0.138795 0.990321i \(-0.455677\pi\)
0.138795 + 0.990321i \(0.455677\pi\)
\(284\) 554137. 0.407682
\(285\) −102469. −0.0747273
\(286\) −1.01714e6 −0.735302
\(287\) −530443. −0.380132
\(288\) 2.04086e6 1.44988
\(289\) −820523. −0.577892
\(290\) 697210. 0.486820
\(291\) −222041. −0.153710
\(292\) 5.58415e6 3.83266
\(293\) −1.04044e6 −0.708027 −0.354013 0.935240i \(-0.615183\pi\)
−0.354013 + 0.935240i \(0.615183\pi\)
\(294\) −1.62353e6 −1.09545
\(295\) −393006. −0.262932
\(296\) −689334. −0.457299
\(297\) 490576. 0.322712
\(298\) 81131.9 0.0529238
\(299\) 2.26561e6 1.46557
\(300\) −594856. −0.381600
\(301\) 177255. 0.112767
\(302\) 4.73415e6 2.98693
\(303\) 875578. 0.547883
\(304\) 1.19874e6 0.743943
\(305\) 1.16700e6 0.718328
\(306\) 950576. 0.580341
\(307\) −1.38126e6 −0.836430 −0.418215 0.908348i \(-0.637344\pi\)
−0.418215 + 0.908348i \(0.637344\pi\)
\(308\) −601836. −0.361494
\(309\) 304827. 0.181618
\(310\) −642938. −0.379984
\(311\) −1.83175e6 −1.07390 −0.536952 0.843613i \(-0.680424\pi\)
−0.536952 + 0.843613i \(0.680424\pi\)
\(312\) 4.94654e6 2.87684
\(313\) −1.95172e6 −1.12605 −0.563024 0.826440i \(-0.690362\pi\)
−0.563024 + 0.826440i \(0.690362\pi\)
\(314\) −3.37401e6 −1.93118
\(315\) 169235. 0.0960981
\(316\) 4.59996e6 2.59141
\(317\) −1.82443e6 −1.01971 −0.509857 0.860259i \(-0.670302\pi\)
−0.509857 + 0.860259i \(0.670302\pi\)
\(318\) 2.16152e6 1.19865
\(319\) −313547. −0.172515
\(320\) 2.15649e6 1.17726
\(321\) −2.54352e6 −1.37776
\(322\) 1.85228e6 0.995559
\(323\) 279474. 0.149051
\(324\) −1.53478e6 −0.812241
\(325\) 488168. 0.256366
\(326\) 1.44546e6 0.753289
\(327\) 474451. 0.245370
\(328\) −4.98657e6 −2.55928
\(329\) −1.37099e6 −0.698305
\(330\) 369637. 0.186849
\(331\) 464579. 0.233072 0.116536 0.993186i \(-0.462821\pi\)
0.116536 + 0.993186i \(0.462821\pi\)
\(332\) 4.40334e6 2.19249
\(333\) −140996. −0.0696781
\(334\) 2.53202e6 1.24194
\(335\) −623710. −0.303648
\(336\) 2.23700e6 1.08098
\(337\) 2.97214e6 1.42559 0.712795 0.701372i \(-0.247429\pi\)
0.712795 + 0.701372i \(0.247429\pi\)
\(338\) −2.56978e6 −1.22350
\(339\) 400640. 0.189345
\(340\) 1.62242e6 0.761140
\(341\) 289140. 0.134655
\(342\) 443261. 0.204925
\(343\) 1.78557e6 0.819486
\(344\) 1.66633e6 0.759216
\(345\) −823341. −0.372419
\(346\) 2.87456e6 1.29086
\(347\) 343604. 0.153191 0.0765957 0.997062i \(-0.475595\pi\)
0.0765957 + 0.997062i \(0.475595\pi\)
\(348\) 2.46632e6 1.09169
\(349\) 1.04465e6 0.459099 0.229549 0.973297i \(-0.426275\pi\)
0.229549 + 0.973297i \(0.426275\pi\)
\(350\) 399109. 0.174149
\(351\) 3.16673e6 1.37196
\(352\) −2.16447e6 −0.931099
\(353\) −2.06027e6 −0.880009 −0.440004 0.897996i \(-0.645023\pi\)
−0.440004 + 0.897996i \(0.645023\pi\)
\(354\) −1.92092e6 −0.814706
\(355\) 165261. 0.0695983
\(356\) −2.32223e6 −0.971135
\(357\) 521535. 0.216577
\(358\) 1.79718e6 0.741112
\(359\) 2.51980e6 1.03188 0.515941 0.856624i \(-0.327442\pi\)
0.515941 + 0.856624i \(0.327442\pi\)
\(360\) 1.59094e6 0.646991
\(361\) 130321. 0.0526316
\(362\) 1.22052e6 0.489525
\(363\) −166232. −0.0662137
\(364\) −3.88492e6 −1.53684
\(365\) 1.66537e6 0.654301
\(366\) 5.70404e6 2.22577
\(367\) −1.58811e6 −0.615481 −0.307740 0.951470i \(-0.599573\pi\)
−0.307740 + 0.951470i \(0.599573\pi\)
\(368\) 9.63191e6 3.70760
\(369\) −1.01995e6 −0.389954
\(370\) −332512. −0.126271
\(371\) −1.04958e6 −0.395895
\(372\) −2.27434e6 −0.852113
\(373\) −3.49518e6 −1.30076 −0.650380 0.759609i \(-0.725390\pi\)
−0.650380 + 0.759609i \(0.725390\pi\)
\(374\) −1.00815e6 −0.372689
\(375\) −177404. −0.0651457
\(376\) −1.28884e7 −4.70142
\(377\) −2.02398e6 −0.733421
\(378\) 2.58900e6 0.931972
\(379\) −4.78062e6 −1.70957 −0.854783 0.518985i \(-0.826310\pi\)
−0.854783 + 0.518985i \(0.826310\pi\)
\(380\) 756545. 0.268767
\(381\) 2.01290e6 0.710410
\(382\) −9.85663e6 −3.45597
\(383\) 2.32447e6 0.809705 0.404853 0.914382i \(-0.367323\pi\)
0.404853 + 0.914382i \(0.367323\pi\)
\(384\) 4.04120e6 1.39856
\(385\) −179486. −0.0617133
\(386\) 3.06341e6 1.04650
\(387\) 340831. 0.115681
\(388\) 1.63937e6 0.552839
\(389\) 1.27764e6 0.428089 0.214044 0.976824i \(-0.431336\pi\)
0.214044 + 0.976824i \(0.431336\pi\)
\(390\) 2.38605e6 0.794361
\(391\) 2.24559e6 0.742828
\(392\) 7.41101e6 2.43592
\(393\) −1.17807e6 −0.384759
\(394\) −1.14230e7 −3.70715
\(395\) 1.37185e6 0.442398
\(396\) −1.15723e6 −0.370835
\(397\) −1.95724e6 −0.623257 −0.311629 0.950204i \(-0.600874\pi\)
−0.311629 + 0.950204i \(0.600874\pi\)
\(398\) 3.40825e6 1.07851
\(399\) 243196. 0.0764758
\(400\) 2.07538e6 0.648555
\(401\) −4.33926e6 −1.34758 −0.673790 0.738923i \(-0.735335\pi\)
−0.673790 + 0.738923i \(0.735335\pi\)
\(402\) −3.04855e6 −0.940866
\(403\) 1.86643e6 0.572466
\(404\) −6.46455e6 −1.97054
\(405\) −457720. −0.138663
\(406\) −1.65474e6 −0.498211
\(407\) 149536. 0.0447466
\(408\) 4.90283e6 1.45813
\(409\) 2.22731e6 0.658375 0.329187 0.944265i \(-0.393225\pi\)
0.329187 + 0.944265i \(0.393225\pi\)
\(410\) −2.40536e6 −0.706676
\(411\) 1.31980e6 0.385394
\(412\) −2.25060e6 −0.653213
\(413\) 932747. 0.269084
\(414\) 3.56162e6 1.02129
\(415\) 1.31321e6 0.374295
\(416\) −1.39719e7 −3.95843
\(417\) 2.84210e6 0.800386
\(418\) −470109. −0.131601
\(419\) 5.15801e6 1.43531 0.717657 0.696396i \(-0.245214\pi\)
0.717657 + 0.696396i \(0.245214\pi\)
\(420\) 1.41181e6 0.390529
\(421\) 3.77198e6 1.03720 0.518602 0.855016i \(-0.326453\pi\)
0.518602 + 0.855016i \(0.326453\pi\)
\(422\) 8.38862e6 2.29303
\(423\) −2.63619e6 −0.716350
\(424\) −9.86684e6 −2.66541
\(425\) 483854. 0.129940
\(426\) 807756. 0.215653
\(427\) −2.76973e6 −0.735136
\(428\) 1.87793e7 4.95530
\(429\) −1.07305e6 −0.281498
\(430\) 803784. 0.209637
\(431\) 5.46460e6 1.41699 0.708493 0.705718i \(-0.249375\pi\)
0.708493 + 0.705718i \(0.249375\pi\)
\(432\) 1.34629e7 3.47079
\(433\) −5.62184e6 −1.44098 −0.720491 0.693464i \(-0.756083\pi\)
−0.720491 + 0.693464i \(0.756083\pi\)
\(434\) 1.52593e6 0.388875
\(435\) 735532. 0.186371
\(436\) −3.50296e6 −0.882508
\(437\) 1.04714e6 0.262301
\(438\) 8.13991e6 2.02738
\(439\) −3.02707e6 −0.749655 −0.374827 0.927095i \(-0.622298\pi\)
−0.374827 + 0.927095i \(0.622298\pi\)
\(440\) −1.68731e6 −0.415491
\(441\) 1.51585e6 0.371158
\(442\) −6.50774e6 −1.58443
\(443\) 5.67545e6 1.37401 0.687007 0.726650i \(-0.258924\pi\)
0.687007 + 0.726650i \(0.258924\pi\)
\(444\) −1.17623e6 −0.283162
\(445\) −692559. −0.165789
\(446\) 2.34177e6 0.557452
\(447\) 85591.2 0.0202610
\(448\) −5.11814e6 −1.20481
\(449\) −2.85299e6 −0.667859 −0.333930 0.942598i \(-0.608375\pi\)
−0.333930 + 0.942598i \(0.608375\pi\)
\(450\) 767419. 0.178649
\(451\) 1.08173e6 0.250425
\(452\) −2.95800e6 −0.681007
\(453\) 4.99436e6 1.14349
\(454\) −1.19730e7 −2.72623
\(455\) −1.15860e6 −0.262365
\(456\) 2.28623e6 0.514882
\(457\) 6.86476e6 1.53757 0.768785 0.639508i \(-0.220862\pi\)
0.768785 + 0.639508i \(0.220862\pi\)
\(458\) 3.58630e6 0.798883
\(459\) 3.13874e6 0.695383
\(460\) 6.07888e6 1.33946
\(461\) 4.26147e6 0.933914 0.466957 0.884280i \(-0.345350\pi\)
0.466957 + 0.884280i \(0.345350\pi\)
\(462\) −877285. −0.191221
\(463\) 5.89172e6 1.27729 0.638645 0.769502i \(-0.279495\pi\)
0.638645 + 0.769502i \(0.279495\pi\)
\(464\) −8.60467e6 −1.85541
\(465\) −678277. −0.145470
\(466\) 8.69665e6 1.85518
\(467\) 184209. 0.0390858 0.0195429 0.999809i \(-0.493779\pi\)
0.0195429 + 0.999809i \(0.493779\pi\)
\(468\) −7.47004e6 −1.57655
\(469\) 1.48029e6 0.310753
\(470\) −6.21694e6 −1.29817
\(471\) −3.55946e6 −0.739318
\(472\) 8.76854e6 1.81164
\(473\) −361475. −0.0742892
\(474\) 6.70527e6 1.37079
\(475\) 225625. 0.0458831
\(476\) −3.85059e6 −0.778950
\(477\) −2.01816e6 −0.406125
\(478\) 4.25362e6 0.851509
\(479\) 6.60969e6 1.31626 0.658131 0.752903i \(-0.271347\pi\)
0.658131 + 0.752903i \(0.271347\pi\)
\(480\) 5.07751e6 1.00588
\(481\) 965274. 0.190234
\(482\) −9.68459e6 −1.89873
\(483\) 1.95409e6 0.381133
\(484\) 1.22732e6 0.238147
\(485\) 488911. 0.0943791
\(486\) 8.36589e6 1.60665
\(487\) 6.87622e6 1.31379 0.656897 0.753980i \(-0.271869\pi\)
0.656897 + 0.753980i \(0.271869\pi\)
\(488\) −2.60376e7 −4.94938
\(489\) 1.52491e6 0.288384
\(490\) 3.57483e6 0.672613
\(491\) 7.29840e6 1.36623 0.683116 0.730310i \(-0.260624\pi\)
0.683116 + 0.730310i \(0.260624\pi\)
\(492\) −8.50874e6 −1.58472
\(493\) −2.00610e6 −0.371736
\(494\) −3.03461e6 −0.559481
\(495\) −345121. −0.0633080
\(496\) 7.93487e6 1.44822
\(497\) −392225. −0.0712269
\(498\) 6.41867e6 1.15977
\(499\) −1.01937e7 −1.83265 −0.916327 0.400431i \(-0.868860\pi\)
−0.916327 + 0.400431i \(0.868860\pi\)
\(500\) 1.30981e6 0.234306
\(501\) 2.67119e6 0.475457
\(502\) 1.99899e6 0.354039
\(503\) 6.25337e6 1.10203 0.551016 0.834495i \(-0.314240\pi\)
0.551016 + 0.834495i \(0.314240\pi\)
\(504\) −3.77589e6 −0.662130
\(505\) −1.92793e6 −0.336405
\(506\) −3.77735e6 −0.655860
\(507\) −2.71103e6 −0.468397
\(508\) −1.48616e7 −2.55509
\(509\) 4.29252e6 0.734374 0.367187 0.930147i \(-0.380321\pi\)
0.367187 + 0.930147i \(0.380321\pi\)
\(510\) 2.36496e6 0.402624
\(511\) −3.95252e6 −0.669611
\(512\) −129590. −0.0218473
\(513\) 1.46362e6 0.245547
\(514\) 1.06248e6 0.177383
\(515\) −671197. −0.111515
\(516\) 2.84331e6 0.470111
\(517\) 2.79586e6 0.460033
\(518\) 789173. 0.129225
\(519\) 3.03255e6 0.494186
\(520\) −1.08918e7 −1.76640
\(521\) 1.38612e6 0.223722 0.111861 0.993724i \(-0.464319\pi\)
0.111861 + 0.993724i \(0.464319\pi\)
\(522\) −3.18178e6 −0.511085
\(523\) 3.93347e6 0.628814 0.314407 0.949288i \(-0.398194\pi\)
0.314407 + 0.949288i \(0.398194\pi\)
\(524\) 8.69789e6 1.38384
\(525\) 421045. 0.0666700
\(526\) −466254. −0.0734782
\(527\) 1.84994e6 0.290155
\(528\) −4.56190e6 −0.712133
\(529\) 1.97744e6 0.307230
\(530\) −4.75944e6 −0.735981
\(531\) 1.79351e6 0.276038
\(532\) −1.79556e6 −0.275056
\(533\) 6.98270e6 1.06465
\(534\) −3.38507e6 −0.513705
\(535\) 5.60056e6 0.845955
\(536\) 1.39159e7 2.09218
\(537\) 1.89596e6 0.283722
\(538\) −9.58902e6 −1.42830
\(539\) −1.60766e6 −0.238354
\(540\) 8.49667e6 1.25390
\(541\) 2.27386e6 0.334019 0.167010 0.985955i \(-0.446589\pi\)
0.167010 + 0.985955i \(0.446589\pi\)
\(542\) −1.03333e7 −1.51092
\(543\) 1.28761e6 0.187406
\(544\) −1.38485e7 −2.00634
\(545\) −1.04469e6 −0.150659
\(546\) −5.66297e6 −0.812948
\(547\) −801558. −0.114543 −0.0572713 0.998359i \(-0.518240\pi\)
−0.0572713 + 0.998359i \(0.518240\pi\)
\(548\) −9.74435e6 −1.38612
\(549\) −5.32572e6 −0.754132
\(550\) −813901. −0.114727
\(551\) −935459. −0.131264
\(552\) 1.83700e7 2.56602
\(553\) −3.25590e6 −0.452750
\(554\) −1.00256e7 −1.38782
\(555\) −350788. −0.0483407
\(556\) −2.09838e7 −2.87870
\(557\) −3.90669e6 −0.533545 −0.266772 0.963760i \(-0.585957\pi\)
−0.266772 + 0.963760i \(0.585957\pi\)
\(558\) 2.93410e6 0.398924
\(559\) −2.33336e6 −0.315830
\(560\) −4.92563e6 −0.663730
\(561\) −1.06356e6 −0.142678
\(562\) 2.60269e7 3.47601
\(563\) −1.35944e7 −1.80755 −0.903774 0.428010i \(-0.859215\pi\)
−0.903774 + 0.428010i \(0.859215\pi\)
\(564\) −2.19919e7 −2.91115
\(565\) −882165. −0.116260
\(566\) −4.02510e6 −0.528123
\(567\) 1.08634e6 0.141908
\(568\) −3.68721e6 −0.479543
\(569\) −4.90008e6 −0.634487 −0.317244 0.948344i \(-0.602757\pi\)
−0.317244 + 0.948344i \(0.602757\pi\)
\(570\) 1.10280e6 0.142171
\(571\) 8.27029e6 1.06153 0.530763 0.847520i \(-0.321906\pi\)
0.530763 + 0.847520i \(0.321906\pi\)
\(572\) 7.92250e6 1.01245
\(573\) −1.03984e7 −1.32306
\(574\) 5.70880e6 0.723211
\(575\) 1.81291e6 0.228668
\(576\) −9.84132e6 −1.23594
\(577\) 7.05888e6 0.882666 0.441333 0.897343i \(-0.354506\pi\)
0.441333 + 0.897343i \(0.354506\pi\)
\(578\) 8.83074e6 1.09946
\(579\) 3.23179e6 0.400633
\(580\) −5.43057e6 −0.670309
\(581\) −3.11673e6 −0.383053
\(582\) 2.38968e6 0.292437
\(583\) 2.14040e6 0.260810
\(584\) −3.71568e7 −4.50823
\(585\) −2.22780e6 −0.269145
\(586\) 1.11976e7 1.34704
\(587\) 2.47297e6 0.296226 0.148113 0.988970i \(-0.452680\pi\)
0.148113 + 0.988970i \(0.452680\pi\)
\(588\) 1.26456e7 1.50833
\(589\) 862641. 0.102457
\(590\) 4.22966e6 0.500236
\(591\) −1.20509e7 −1.41922
\(592\) 4.10372e6 0.481253
\(593\) 64423.8 0.00752332 0.00376166 0.999993i \(-0.498803\pi\)
0.00376166 + 0.999993i \(0.498803\pi\)
\(594\) −5.27974e6 −0.613969
\(595\) −1.14836e6 −0.132980
\(596\) −631936. −0.0728714
\(597\) 3.59558e6 0.412889
\(598\) −2.43832e7 −2.78829
\(599\) 1.57792e6 0.179688 0.0898440 0.995956i \(-0.471363\pi\)
0.0898440 + 0.995956i \(0.471363\pi\)
\(600\) 3.95815e6 0.448864
\(601\) −821710. −0.0927967 −0.0463984 0.998923i \(-0.514774\pi\)
−0.0463984 + 0.998923i \(0.514774\pi\)
\(602\) −1.90767e6 −0.214542
\(603\) 2.84635e6 0.318783
\(604\) −3.68743e7 −4.11274
\(605\) 366025. 0.0406558
\(606\) −9.42326e6 −1.04236
\(607\) −798319. −0.0879437 −0.0439719 0.999033i \(-0.514001\pi\)
−0.0439719 + 0.999033i \(0.514001\pi\)
\(608\) −6.45764e6 −0.708460
\(609\) −1.74569e6 −0.190732
\(610\) −1.25597e7 −1.36664
\(611\) 1.80476e7 1.95576
\(612\) −7.40403e6 −0.799079
\(613\) −1.54064e7 −1.65597 −0.827983 0.560754i \(-0.810511\pi\)
−0.827983 + 0.560754i \(0.810511\pi\)
\(614\) 1.48656e7 1.59133
\(615\) −2.53757e6 −0.270539
\(616\) 4.00460e6 0.425213
\(617\) −1.90156e6 −0.201094 −0.100547 0.994932i \(-0.532059\pi\)
−0.100547 + 0.994932i \(0.532059\pi\)
\(618\) −3.28065e6 −0.345533
\(619\) −8.77685e6 −0.920687 −0.460344 0.887741i \(-0.652274\pi\)
−0.460344 + 0.887741i \(0.652274\pi\)
\(620\) 5.00784e6 0.523205
\(621\) 1.17603e7 1.22374
\(622\) 1.97139e7 2.04313
\(623\) 1.64370e6 0.169669
\(624\) −2.94476e7 −3.02753
\(625\) 390625. 0.0400000
\(626\) 2.10051e7 2.14234
\(627\) −495948. −0.0503811
\(628\) 2.62801e7 2.65906
\(629\) 956743. 0.0964204
\(630\) −1.82137e6 −0.182829
\(631\) 2.07418e6 0.207383 0.103692 0.994609i \(-0.466934\pi\)
0.103692 + 0.994609i \(0.466934\pi\)
\(632\) −3.06080e7 −3.04819
\(633\) 8.84969e6 0.877847
\(634\) 1.96351e7 1.94003
\(635\) −4.43218e6 −0.436197
\(636\) −1.68361e7 −1.65044
\(637\) −1.03776e7 −1.01333
\(638\) 3.37450e6 0.328214
\(639\) −754181. −0.0730674
\(640\) −8.89829e6 −0.858730
\(641\) 1.58592e7 1.52453 0.762267 0.647263i \(-0.224086\pi\)
0.762267 + 0.647263i \(0.224086\pi\)
\(642\) 2.73742e7 2.62123
\(643\) −8.24222e6 −0.786171 −0.393085 0.919502i \(-0.628592\pi\)
−0.393085 + 0.919502i \(0.628592\pi\)
\(644\) −1.44274e7 −1.37080
\(645\) 847963. 0.0802560
\(646\) −3.00779e6 −0.283574
\(647\) 3.71842e6 0.349219 0.174609 0.984638i \(-0.444134\pi\)
0.174609 + 0.984638i \(0.444134\pi\)
\(648\) 1.02124e7 0.955412
\(649\) −1.90215e6 −0.177269
\(650\) −5.25383e6 −0.487744
\(651\) 1.60980e6 0.148874
\(652\) −1.12587e7 −1.03721
\(653\) 264259. 0.0242519 0.0121260 0.999926i \(-0.496140\pi\)
0.0121260 + 0.999926i \(0.496140\pi\)
\(654\) −5.10619e6 −0.466824
\(655\) 2.59398e6 0.236245
\(656\) 2.96859e7 2.69334
\(657\) −7.60004e6 −0.686914
\(658\) 1.47551e7 1.32855
\(659\) 1.85292e7 1.66205 0.831023 0.556237i \(-0.187755\pi\)
0.831023 + 0.556237i \(0.187755\pi\)
\(660\) −2.87910e6 −0.257275
\(661\) −6.74709e6 −0.600638 −0.300319 0.953839i \(-0.597093\pi\)
−0.300319 + 0.953839i \(0.597093\pi\)
\(662\) −4.99996e6 −0.443426
\(663\) −6.86543e6 −0.606574
\(664\) −2.92997e7 −2.57895
\(665\) −535491. −0.0469568
\(666\) 1.51745e6 0.132565
\(667\) −7.51646e6 −0.654182
\(668\) −1.97219e7 −1.71005
\(669\) 2.47048e6 0.213411
\(670\) 6.71257e6 0.577699
\(671\) 5.64830e6 0.484296
\(672\) −1.20508e7 −1.02942
\(673\) 1.54373e6 0.131382 0.0656908 0.997840i \(-0.479075\pi\)
0.0656908 + 0.997840i \(0.479075\pi\)
\(674\) −3.19872e7 −2.71223
\(675\) 2.53397e6 0.214063
\(676\) 2.00160e7 1.68466
\(677\) −1.23313e7 −1.03404 −0.517020 0.855973i \(-0.672959\pi\)
−0.517020 + 0.855973i \(0.672959\pi\)
\(678\) −4.31181e6 −0.360235
\(679\) −1.16037e6 −0.0965874
\(680\) −1.07955e7 −0.895304
\(681\) −1.26311e7 −1.04369
\(682\) −3.11182e6 −0.256185
\(683\) 1.65020e7 1.35359 0.676793 0.736174i \(-0.263369\pi\)
0.676793 + 0.736174i \(0.263369\pi\)
\(684\) −3.45256e6 −0.282163
\(685\) −2.90606e6 −0.236635
\(686\) −1.92169e7 −1.55910
\(687\) 3.78342e6 0.305839
\(688\) −9.91996e6 −0.798985
\(689\) 1.38165e7 1.10879
\(690\) 8.86106e6 0.708538
\(691\) −1.82638e7 −1.45511 −0.727557 0.686047i \(-0.759344\pi\)
−0.727557 + 0.686047i \(0.759344\pi\)
\(692\) −2.23899e7 −1.77741
\(693\) 819099. 0.0647893
\(694\) −3.69798e6 −0.291451
\(695\) −6.25800e6 −0.491444
\(696\) −1.64108e7 −1.28412
\(697\) 6.92099e6 0.539618
\(698\) −1.12428e7 −0.873448
\(699\) 9.17465e6 0.710226
\(700\) −3.10866e6 −0.239788
\(701\) 1.06232e7 0.816508 0.408254 0.912868i \(-0.366138\pi\)
0.408254 + 0.912868i \(0.366138\pi\)
\(702\) −3.40814e7 −2.61020
\(703\) 446137. 0.0340471
\(704\) 1.04374e7 0.793709
\(705\) −6.55865e6 −0.496983
\(706\) 2.21733e7 1.67424
\(707\) 4.57568e6 0.344276
\(708\) 1.49620e7 1.12178
\(709\) 5.50436e6 0.411236 0.205618 0.978632i \(-0.434080\pi\)
0.205618 + 0.978632i \(0.434080\pi\)
\(710\) −1.77859e6 −0.132413
\(711\) −6.26054e6 −0.464449
\(712\) 1.54520e7 1.14231
\(713\) 6.93136e6 0.510616
\(714\) −5.61293e6 −0.412044
\(715\) 2.36273e6 0.172842
\(716\) −1.39982e7 −1.02045
\(717\) 4.48742e6 0.325986
\(718\) −2.71189e7 −1.96319
\(719\) 7.09249e6 0.511654 0.255827 0.966723i \(-0.417652\pi\)
0.255827 + 0.966723i \(0.417652\pi\)
\(720\) −9.47115e6 −0.680881
\(721\) 1.59300e6 0.114124
\(722\) −1.40256e6 −0.100133
\(723\) −1.02169e7 −0.726898
\(724\) −9.50665e6 −0.674033
\(725\) −1.61956e6 −0.114433
\(726\) 1.78904e6 0.125974
\(727\) 2.70960e7 1.90138 0.950692 0.310137i \(-0.100375\pi\)
0.950692 + 0.310137i \(0.100375\pi\)
\(728\) 2.58501e7 1.80773
\(729\) 1.32748e7 0.925141
\(730\) −1.79232e7 −1.24483
\(731\) −2.31274e6 −0.160079
\(732\) −4.44287e7 −3.06469
\(733\) 2.83368e7 1.94801 0.974004 0.226531i \(-0.0727385\pi\)
0.974004 + 0.226531i \(0.0727385\pi\)
\(734\) 1.70917e7 1.17097
\(735\) 3.77132e6 0.257499
\(736\) −5.18875e7 −3.53076
\(737\) −3.01875e6 −0.204719
\(738\) 1.09771e7 0.741900
\(739\) 3.55006e6 0.239125 0.119563 0.992827i \(-0.461851\pi\)
0.119563 + 0.992827i \(0.461851\pi\)
\(740\) 2.58993e6 0.173864
\(741\) −3.20140e6 −0.214188
\(742\) 1.12959e7 0.753202
\(743\) 634499. 0.0421656 0.0210828 0.999778i \(-0.493289\pi\)
0.0210828 + 0.999778i \(0.493289\pi\)
\(744\) 1.51334e7 1.00231
\(745\) −188463. −0.0124404
\(746\) 3.76163e7 2.47473
\(747\) −5.99295e6 −0.392952
\(748\) 7.85249e6 0.513161
\(749\) −1.32922e7 −0.865749
\(750\) 1.90928e6 0.123942
\(751\) 1.57078e7 1.01628 0.508141 0.861274i \(-0.330333\pi\)
0.508141 + 0.861274i \(0.330333\pi\)
\(752\) 7.67268e7 4.94769
\(753\) 2.10886e6 0.135538
\(754\) 2.17828e7 1.39536
\(755\) −1.09970e7 −0.702115
\(756\) −2.01657e7 −1.28324
\(757\) −1.38932e7 −0.881176 −0.440588 0.897709i \(-0.645230\pi\)
−0.440588 + 0.897709i \(0.645230\pi\)
\(758\) 5.14506e7 3.25250
\(759\) −3.98497e6 −0.251085
\(760\) −5.03403e6 −0.316142
\(761\) 1.18702e7 0.743014 0.371507 0.928430i \(-0.378841\pi\)
0.371507 + 0.928430i \(0.378841\pi\)
\(762\) −2.16634e7 −1.35158
\(763\) 2.47943e6 0.154184
\(764\) 7.67732e7 4.75857
\(765\) −2.20811e6 −0.136416
\(766\) −2.50167e7 −1.54049
\(767\) −1.22786e7 −0.753633
\(768\) −1.21526e7 −0.743472
\(769\) 2.38420e6 0.145387 0.0726936 0.997354i \(-0.476840\pi\)
0.0726936 + 0.997354i \(0.476840\pi\)
\(770\) 1.93169e6 0.117411
\(771\) 1.12088e6 0.0679083
\(772\) −2.38609e7 −1.44093
\(773\) −2.25242e7 −1.35582 −0.677909 0.735146i \(-0.737114\pi\)
−0.677909 + 0.735146i \(0.737114\pi\)
\(774\) −3.66814e6 −0.220086
\(775\) 1.49349e6 0.0893200
\(776\) −1.09083e7 −0.650286
\(777\) 832549. 0.0494718
\(778\) −1.37504e7 −0.814451
\(779\) 3.22731e6 0.190545
\(780\) −1.85849e7 −1.09377
\(781\) 799862. 0.0469232
\(782\) −2.41677e7 −1.41325
\(783\) −1.05060e7 −0.612399
\(784\) −4.41190e7 −2.56351
\(785\) 7.83754e6 0.453947
\(786\) 1.26788e7 0.732015
\(787\) 1.10526e7 0.636105 0.318052 0.948073i \(-0.396971\pi\)
0.318052 + 0.948073i \(0.396971\pi\)
\(788\) 8.89738e7 5.10442
\(789\) −491882. −0.0281299
\(790\) −1.47643e7 −0.841675
\(791\) 2.09370e6 0.118980
\(792\) 7.70016e6 0.436201
\(793\) 3.64604e7 2.05892
\(794\) 2.10644e7 1.18576
\(795\) −5.02104e6 −0.281758
\(796\) −2.65468e7 −1.48501
\(797\) 1.18016e7 0.658107 0.329053 0.944311i \(-0.393270\pi\)
0.329053 + 0.944311i \(0.393270\pi\)
\(798\) −2.61735e6 −0.145497
\(799\) 1.78881e7 0.991283
\(800\) −1.11801e7 −0.617621
\(801\) 3.16055e6 0.174053
\(802\) 4.67005e7 2.56381
\(803\) 8.06037e6 0.441129
\(804\) 2.37451e7 1.29549
\(805\) −4.30270e6 −0.234019
\(806\) −2.00872e7 −1.08913
\(807\) −1.01161e7 −0.546800
\(808\) 4.30149e7 2.31788
\(809\) 3.28789e7 1.76622 0.883112 0.469162i \(-0.155444\pi\)
0.883112 + 0.469162i \(0.155444\pi\)
\(810\) 4.92613e6 0.263811
\(811\) 3.21795e7 1.71802 0.859008 0.511963i \(-0.171081\pi\)
0.859008 + 0.511963i \(0.171081\pi\)
\(812\) 1.28887e7 0.685994
\(813\) −1.09013e7 −0.578430
\(814\) −1.60936e6 −0.0851318
\(815\) −3.35768e6 −0.177070
\(816\) −2.91874e7 −1.53451
\(817\) −1.07845e6 −0.0565256
\(818\) −2.39711e7 −1.25258
\(819\) 5.28738e6 0.275442
\(820\) 1.87353e7 0.973031
\(821\) 1.16127e7 0.601278 0.300639 0.953738i \(-0.402800\pi\)
0.300639 + 0.953738i \(0.402800\pi\)
\(822\) −1.42042e7 −0.733223
\(823\) 8.87616e6 0.456799 0.228400 0.973567i \(-0.426651\pi\)
0.228400 + 0.973567i \(0.426651\pi\)
\(824\) 1.49754e7 0.768353
\(825\) −858637. −0.0439212
\(826\) −1.00385e7 −0.511941
\(827\) −7.58442e6 −0.385619 −0.192810 0.981236i \(-0.561760\pi\)
−0.192810 + 0.981236i \(0.561760\pi\)
\(828\) −2.77415e7 −1.40622
\(829\) −1.00226e7 −0.506519 −0.253260 0.967398i \(-0.581503\pi\)
−0.253260 + 0.967398i \(0.581503\pi\)
\(830\) −1.41332e7 −0.712108
\(831\) −1.05766e7 −0.531305
\(832\) 6.73747e7 3.37434
\(833\) −1.02859e7 −0.513607
\(834\) −3.05876e7 −1.52276
\(835\) −5.88168e6 −0.291934
\(836\) 3.66168e6 0.181203
\(837\) 9.68822e6 0.478003
\(838\) −5.55122e7 −2.73073
\(839\) −2.77359e7 −1.36031 −0.680153 0.733070i \(-0.738087\pi\)
−0.680153 + 0.733070i \(0.738087\pi\)
\(840\) −9.39415e6 −0.459366
\(841\) −1.37963e7 −0.672625
\(842\) −4.05953e7 −1.97331
\(843\) 2.74574e7 1.33073
\(844\) −6.53389e7 −3.15730
\(845\) 5.96939e6 0.287600
\(846\) 2.83715e7 1.36288
\(847\) −868712. −0.0416071
\(848\) 5.87390e7 2.80503
\(849\) −4.24633e6 −0.202183
\(850\) −5.20740e6 −0.247214
\(851\) 3.58473e6 0.169681
\(852\) −6.29160e6 −0.296936
\(853\) −2.03117e7 −0.955814 −0.477907 0.878410i \(-0.658604\pi\)
−0.477907 + 0.878410i \(0.658604\pi\)
\(854\) 2.98087e7 1.39862
\(855\) −1.02966e6 −0.0481701
\(856\) −1.24957e8 −5.82875
\(857\) 2.27983e7 1.06035 0.530176 0.847888i \(-0.322126\pi\)
0.530176 + 0.847888i \(0.322126\pi\)
\(858\) 1.15485e7 0.535558
\(859\) −2.14205e7 −0.990484 −0.495242 0.868755i \(-0.664921\pi\)
−0.495242 + 0.868755i \(0.664921\pi\)
\(860\) −6.26067e6 −0.288652
\(861\) 6.02258e6 0.276869
\(862\) −5.88119e7 −2.69586
\(863\) −9.24837e6 −0.422706 −0.211353 0.977410i \(-0.567787\pi\)
−0.211353 + 0.977410i \(0.567787\pi\)
\(864\) −7.25251e7 −3.30525
\(865\) −6.67736e6 −0.303434
\(866\) 6.05041e7 2.74151
\(867\) 9.31612e6 0.420908
\(868\) −1.18855e7 −0.535447
\(869\) 6.63974e6 0.298265
\(870\) −7.91604e6 −0.354576
\(871\) −1.94864e7 −0.870335
\(872\) 2.33086e7 1.03806
\(873\) −2.23119e6 −0.0990833
\(874\) −1.12696e7 −0.499034
\(875\) −927097. −0.0409360
\(876\) −6.34018e7 −2.79152
\(877\) 3.63817e7 1.59729 0.798646 0.601802i \(-0.205550\pi\)
0.798646 + 0.601802i \(0.205550\pi\)
\(878\) 3.25783e7 1.42624
\(879\) 1.18131e7 0.515692
\(880\) 1.00448e7 0.437256
\(881\) −2.16771e7 −0.940937 −0.470469 0.882417i \(-0.655915\pi\)
−0.470469 + 0.882417i \(0.655915\pi\)
\(882\) −1.63140e7 −0.706139
\(883\) 9.31432e6 0.402021 0.201011 0.979589i \(-0.435577\pi\)
0.201011 + 0.979589i \(0.435577\pi\)
\(884\) 5.06887e7 2.18163
\(885\) 4.46213e6 0.191507
\(886\) −6.10811e7 −2.61410
\(887\) 3.26365e7 1.39282 0.696410 0.717644i \(-0.254780\pi\)
0.696410 + 0.717644i \(0.254780\pi\)
\(888\) 7.82661e6 0.333074
\(889\) 1.05192e7 0.446404
\(890\) 7.45355e6 0.315419
\(891\) −2.21536e6 −0.0934869
\(892\) −1.82400e7 −0.767562
\(893\) 8.34137e6 0.350033
\(894\) −921161. −0.0385471
\(895\) −4.17470e6 −0.174208
\(896\) 2.11189e7 0.878823
\(897\) −2.57234e7 −1.06745
\(898\) 3.07049e7 1.27062
\(899\) −6.19214e6 −0.255530
\(900\) −5.97742e6 −0.245984
\(901\) 1.36944e7 0.561995
\(902\) −1.16419e7 −0.476441
\(903\) −2.01253e6 −0.0821339
\(904\) 1.96824e7 0.801046
\(905\) −2.83517e6 −0.115069
\(906\) −5.37509e7 −2.17553
\(907\) 7.02589e6 0.283585 0.141792 0.989896i \(-0.454713\pi\)
0.141792 + 0.989896i \(0.454713\pi\)
\(908\) 9.32576e7 3.75379
\(909\) 8.79826e6 0.353173
\(910\) 1.24693e7 0.499157
\(911\) −461521. −0.0184245 −0.00921225 0.999958i \(-0.502932\pi\)
−0.00921225 + 0.999958i \(0.502932\pi\)
\(912\) −1.36103e7 −0.541852
\(913\) 6.35594e6 0.252350
\(914\) −7.38808e7 −2.92527
\(915\) −1.32500e7 −0.523195
\(916\) −2.79337e7 −1.09999
\(917\) −6.15646e6 −0.241773
\(918\) −3.37802e7 −1.32299
\(919\) −2.34434e7 −0.915655 −0.457827 0.889041i \(-0.651372\pi\)
−0.457827 + 0.889041i \(0.651372\pi\)
\(920\) −4.04487e7 −1.57556
\(921\) 1.56827e7 0.609215
\(922\) −4.58633e7 −1.77680
\(923\) 5.16320e6 0.199487
\(924\) 6.83317e6 0.263295
\(925\) 772398. 0.0296816
\(926\) −6.34086e7 −2.43008
\(927\) 3.06306e6 0.117073
\(928\) 4.63537e7 1.76691
\(929\) 4.22693e7 1.60689 0.803444 0.595380i \(-0.202998\pi\)
0.803444 + 0.595380i \(0.202998\pi\)
\(930\) 7.29984e6 0.276762
\(931\) −4.79641e6 −0.181360
\(932\) −6.77382e7 −2.55443
\(933\) 2.07974e7 0.782179
\(934\) −1.98252e6 −0.0743619
\(935\) 2.34185e6 0.0876054
\(936\) 4.97054e7 1.85445
\(937\) −1.99938e7 −0.743954 −0.371977 0.928242i \(-0.621320\pi\)
−0.371977 + 0.928242i \(0.621320\pi\)
\(938\) −1.59314e7 −0.591217
\(939\) 2.21596e7 0.820159
\(940\) 4.84237e7 1.78747
\(941\) −2.22235e6 −0.0818161 −0.0409081 0.999163i \(-0.513025\pi\)
−0.0409081 + 0.999163i \(0.513025\pi\)
\(942\) 3.83080e7 1.40657
\(943\) 2.59316e7 0.949621
\(944\) −5.22006e7 −1.90654
\(945\) −6.01404e6 −0.219072
\(946\) 3.89031e6 0.141337
\(947\) −3.46033e7 −1.25384 −0.626921 0.779083i \(-0.715685\pi\)
−0.626921 + 0.779083i \(0.715685\pi\)
\(948\) −5.22273e7 −1.88746
\(949\) 5.20306e7 1.87540
\(950\) −2.42825e6 −0.0872940
\(951\) 2.07143e7 0.742709
\(952\) 2.56217e7 0.916253
\(953\) 3.96218e7 1.41320 0.706598 0.707615i \(-0.250229\pi\)
0.706598 + 0.707615i \(0.250229\pi\)
\(954\) 2.17201e7 0.772665
\(955\) 2.28961e7 0.812369
\(956\) −3.31314e7 −1.17245
\(957\) 3.55997e6 0.125651
\(958\) −7.11357e7 −2.50423
\(959\) 6.89716e6 0.242172
\(960\) −2.44845e7 −0.857459
\(961\) −2.29190e7 −0.800548
\(962\) −1.03886e7 −0.361925
\(963\) −2.55586e7 −0.888121
\(964\) 7.54332e7 2.61439
\(965\) −7.11605e6 −0.245992
\(966\) −2.10306e7 −0.725117
\(967\) −4.44968e7 −1.53025 −0.765126 0.643881i \(-0.777323\pi\)
−0.765126 + 0.643881i \(0.777323\pi\)
\(968\) −8.16656e6 −0.280124
\(969\) −3.17311e6 −0.108562
\(970\) −5.26182e6 −0.179559
\(971\) −2.71793e7 −0.925104 −0.462552 0.886592i \(-0.653066\pi\)
−0.462552 + 0.886592i \(0.653066\pi\)
\(972\) −6.51619e7 −2.21222
\(973\) 1.48525e7 0.502943
\(974\) −7.40041e7 −2.49953
\(975\) −5.54260e6 −0.186725
\(976\) 1.55006e8 5.20864
\(977\) −1.83806e7 −0.616060 −0.308030 0.951377i \(-0.599670\pi\)
−0.308030 + 0.951377i \(0.599670\pi\)
\(978\) −1.64115e7 −0.548659
\(979\) −3.35199e6 −0.111775
\(980\) −2.78443e7 −0.926129
\(981\) 4.76753e6 0.158169
\(982\) −7.85478e7 −2.59929
\(983\) 3.36412e7 1.11042 0.555211 0.831709i \(-0.312637\pi\)
0.555211 + 0.831709i \(0.312637\pi\)
\(984\) 5.66169e7 1.86405
\(985\) 2.65347e7 0.871413
\(986\) 2.15903e7 0.707238
\(987\) 1.55661e7 0.508612
\(988\) 2.36366e7 0.770357
\(989\) −8.66540e6 −0.281707
\(990\) 3.71431e6 0.120445
\(991\) −4.62718e7 −1.49669 −0.748346 0.663308i \(-0.769152\pi\)
−0.748346 + 0.663308i \(0.769152\pi\)
\(992\) −4.27455e7 −1.37915
\(993\) −5.27477e6 −0.169758
\(994\) 4.22125e6 0.135511
\(995\) −7.91707e6 −0.253517
\(996\) −4.99950e7 −1.59690
\(997\) −2.98971e7 −0.952556 −0.476278 0.879295i \(-0.658014\pi\)
−0.476278 + 0.879295i \(0.658014\pi\)
\(998\) 1.09708e8 3.48668
\(999\) 5.01051e6 0.158843
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.1.1 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.1 40 1.1 even 1 trivial