Properties

Label 177.10.a.b.1.1
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +31900.3 q^{10} -16906.1 q^{11} -120085. q^{12} -19313.4 q^{13} +450296. q^{14} +57857.4 q^{15} +1.17670e6 q^{16} +336949. q^{17} -293016. q^{18} -788177. q^{19} -1.05896e6 q^{20} +816700. q^{21} +755028. q^{22} +124126. q^{23} +3.51088e6 q^{24} -1.44292e6 q^{25} +862542. q^{26} -531441. q^{27} -1.49480e7 q^{28} +4.52185e6 q^{29} -2.58392e6 q^{30} -5.79823e6 q^{31} -3.03596e7 q^{32} +1.36939e6 q^{33} -1.50482e7 q^{34} +7.20198e6 q^{35} +9.72690e6 q^{36} +3.64731e6 q^{37} +3.52001e7 q^{38} +1.56439e6 q^{39} +3.09603e7 q^{40} +1.96043e7 q^{41} -3.64740e7 q^{42} -3.00271e6 q^{43} -2.50638e7 q^{44} -4.68645e6 q^{45} -5.54351e6 q^{46} -3.78665e7 q^{47} -9.53129e7 q^{48} +6.13075e7 q^{49} +6.44409e7 q^{50} -2.72929e7 q^{51} -2.86328e7 q^{52} +8.32101e7 q^{53} +2.37343e7 q^{54} +1.20758e7 q^{55} +4.37027e8 q^{56} +6.38424e7 q^{57} -2.01947e8 q^{58} -1.21174e7 q^{59} +8.57756e7 q^{60} +1.36610e8 q^{61} +2.58950e8 q^{62} -6.61527e7 q^{63} +7.53392e8 q^{64} +1.37954e7 q^{65} -6.11572e7 q^{66} -4.31228e7 q^{67} +4.99539e8 q^{68} -1.00542e7 q^{69} -3.21642e8 q^{70} +2.79479e8 q^{71} -2.84381e8 q^{72} -1.26714e8 q^{73} -1.62890e8 q^{74} +1.16876e8 q^{75} -1.16850e9 q^{76} +1.70459e8 q^{77} -6.98659e7 q^{78} +5.15802e8 q^{79} -8.40506e8 q^{80} +4.30467e7 q^{81} -8.75532e8 q^{82} -4.95727e8 q^{83} +1.21078e9 q^{84} -2.40679e8 q^{85} +1.34102e8 q^{86} -3.66270e8 q^{87} +7.32779e8 q^{88} +3.38658e8 q^{89} +2.09298e8 q^{90} +1.94732e8 q^{91} +1.84021e8 q^{92} +4.69656e8 q^{93} +1.69112e9 q^{94} +5.62987e8 q^{95} +2.45912e9 q^{96} +1.18214e9 q^{97} -2.73801e9 q^{98} -1.10921e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −44.6602 −1.97372 −0.986860 0.161577i \(-0.948342\pi\)
−0.986860 + 0.161577i \(0.948342\pi\)
\(3\) −81.0000 −0.577350
\(4\) 1482.53 2.89557
\(5\) −714.289 −0.511104 −0.255552 0.966795i \(-0.582257\pi\)
−0.255552 + 0.966795i \(0.582257\pi\)
\(6\) 3617.48 1.13953
\(7\) −10082.7 −1.58722 −0.793609 0.608429i \(-0.791800\pi\)
−0.793609 + 0.608429i \(0.791800\pi\)
\(8\) −43344.2 −3.74133
\(9\) 6561.00 0.333333
\(10\) 31900.3 1.00878
\(11\) −16906.1 −0.348157 −0.174078 0.984732i \(-0.555695\pi\)
−0.174078 + 0.984732i \(0.555695\pi\)
\(12\) −120085. −1.67176
\(13\) −19313.4 −0.187549 −0.0937745 0.995593i \(-0.529893\pi\)
−0.0937745 + 0.995593i \(0.529893\pi\)
\(14\) 450296. 3.13272
\(15\) 57857.4 0.295086
\(16\) 1.17670e6 4.48877
\(17\) 336949. 0.978463 0.489232 0.872154i \(-0.337277\pi\)
0.489232 + 0.872154i \(0.337277\pi\)
\(18\) −293016. −0.657907
\(19\) −788177. −1.38750 −0.693750 0.720216i \(-0.744043\pi\)
−0.693750 + 0.720216i \(0.744043\pi\)
\(20\) −1.05896e6 −1.47994
\(21\) 816700. 0.916380
\(22\) 755028. 0.687164
\(23\) 124126. 0.0924887 0.0462444 0.998930i \(-0.485275\pi\)
0.0462444 + 0.998930i \(0.485275\pi\)
\(24\) 3.51088e6 2.16006
\(25\) −1.44292e6 −0.738773
\(26\) 862542. 0.370169
\(27\) −531441. −0.192450
\(28\) −1.49480e7 −4.59590
\(29\) 4.52185e6 1.18720 0.593602 0.804759i \(-0.297706\pi\)
0.593602 + 0.804759i \(0.297706\pi\)
\(30\) −2.58392e6 −0.582417
\(31\) −5.79823e6 −1.12763 −0.563816 0.825900i \(-0.690667\pi\)
−0.563816 + 0.825900i \(0.690667\pi\)
\(32\) −3.03596e7 −5.11824
\(33\) 1.36939e6 0.201009
\(34\) −1.50482e7 −1.93121
\(35\) 7.20198e6 0.811233
\(36\) 9.72690e6 0.965191
\(37\) 3.64731e6 0.319937 0.159969 0.987122i \(-0.448861\pi\)
0.159969 + 0.987122i \(0.448861\pi\)
\(38\) 3.52001e7 2.73854
\(39\) 1.56439e6 0.108281
\(40\) 3.09603e7 1.91221
\(41\) 1.96043e7 1.08349 0.541744 0.840544i \(-0.317764\pi\)
0.541744 + 0.840544i \(0.317764\pi\)
\(42\) −3.64740e7 −1.80868
\(43\) −3.00271e6 −0.133938 −0.0669692 0.997755i \(-0.521333\pi\)
−0.0669692 + 0.997755i \(0.521333\pi\)
\(44\) −2.50638e7 −1.00811
\(45\) −4.68645e6 −0.170368
\(46\) −5.54351e6 −0.182547
\(47\) −3.78665e7 −1.13192 −0.565958 0.824434i \(-0.691494\pi\)
−0.565958 + 0.824434i \(0.691494\pi\)
\(48\) −9.53129e7 −2.59159
\(49\) 6.13075e7 1.51926
\(50\) 6.44409e7 1.45813
\(51\) −2.72929e7 −0.564916
\(52\) −2.86328e7 −0.543062
\(53\) 8.32101e7 1.44855 0.724277 0.689509i \(-0.242174\pi\)
0.724277 + 0.689509i \(0.242174\pi\)
\(54\) 2.37343e7 0.379843
\(55\) 1.20758e7 0.177944
\(56\) 4.37027e8 5.93830
\(57\) 6.38424e7 0.801073
\(58\) −2.01947e8 −2.34321
\(59\) −1.21174e7 −0.130189
\(60\) 8.57756e7 0.854443
\(61\) 1.36610e8 1.26328 0.631639 0.775263i \(-0.282383\pi\)
0.631639 + 0.775263i \(0.282383\pi\)
\(62\) 2.58950e8 2.22563
\(63\) −6.61527e7 −0.529072
\(64\) 7.53392e8 5.61321
\(65\) 1.37954e7 0.0958570
\(66\) −6.11572e7 −0.396735
\(67\) −4.31228e7 −0.261439 −0.130720 0.991419i \(-0.541729\pi\)
−0.130720 + 0.991419i \(0.541729\pi\)
\(68\) 4.99539e8 2.83321
\(69\) −1.00542e7 −0.0533984
\(70\) −3.21642e8 −1.60115
\(71\) 2.79479e8 1.30523 0.652613 0.757691i \(-0.273673\pi\)
0.652613 + 0.757691i \(0.273673\pi\)
\(72\) −2.84381e8 −1.24711
\(73\) −1.26714e8 −0.522241 −0.261120 0.965306i \(-0.584092\pi\)
−0.261120 + 0.965306i \(0.584092\pi\)
\(74\) −1.62890e8 −0.631467
\(75\) 1.16876e8 0.426531
\(76\) −1.16850e9 −4.01760
\(77\) 1.70459e8 0.552601
\(78\) −6.98659e7 −0.213717
\(79\) 5.15802e8 1.48991 0.744957 0.667112i \(-0.232470\pi\)
0.744957 + 0.667112i \(0.232470\pi\)
\(80\) −8.40506e8 −2.29423
\(81\) 4.30467e7 0.111111
\(82\) −8.75532e8 −2.13850
\(83\) −4.95727e8 −1.14655 −0.573273 0.819365i \(-0.694326\pi\)
−0.573273 + 0.819365i \(0.694326\pi\)
\(84\) 1.21078e9 2.65344
\(85\) −2.40679e8 −0.500096
\(86\) 1.34102e8 0.264357
\(87\) −3.66270e8 −0.685432
\(88\) 7.32779e8 1.30257
\(89\) 3.38658e8 0.572145 0.286073 0.958208i \(-0.407650\pi\)
0.286073 + 0.958208i \(0.407650\pi\)
\(90\) 2.09298e8 0.336259
\(91\) 1.94732e8 0.297681
\(92\) 1.84021e8 0.267808
\(93\) 4.69656e8 0.651039
\(94\) 1.69112e9 2.23409
\(95\) 5.62987e8 0.709156
\(96\) 2.45912e9 2.95502
\(97\) 1.18214e9 1.35580 0.677898 0.735156i \(-0.262891\pi\)
0.677898 + 0.735156i \(0.262891\pi\)
\(98\) −2.73801e9 −2.99859
\(99\) −1.10921e8 −0.116052
\(100\) −2.13917e9 −2.13917
\(101\) −1.65119e9 −1.57889 −0.789444 0.613823i \(-0.789631\pi\)
−0.789444 + 0.613823i \(0.789631\pi\)
\(102\) 1.21891e9 1.11499
\(103\) −1.01347e9 −0.887243 −0.443621 0.896214i \(-0.646307\pi\)
−0.443621 + 0.896214i \(0.646307\pi\)
\(104\) 8.37126e8 0.701683
\(105\) −5.83360e8 −0.468365
\(106\) −3.71618e9 −2.85904
\(107\) 1.81281e9 1.33698 0.668491 0.743721i \(-0.266941\pi\)
0.668491 + 0.743721i \(0.266941\pi\)
\(108\) −7.87879e8 −0.557253
\(109\) 2.21832e9 1.50523 0.752617 0.658458i \(-0.228791\pi\)
0.752617 + 0.658458i \(0.228791\pi\)
\(110\) −5.39308e8 −0.351212
\(111\) −2.95432e8 −0.184716
\(112\) −1.18644e10 −7.12464
\(113\) 3.03819e9 1.75292 0.876459 0.481477i \(-0.159899\pi\)
0.876459 + 0.481477i \(0.159899\pi\)
\(114\) −2.85121e9 −1.58109
\(115\) −8.86621e7 −0.0472713
\(116\) 6.70379e9 3.43763
\(117\) −1.26716e8 −0.0625163
\(118\) 5.41164e8 0.256957
\(119\) −3.39736e9 −1.55303
\(120\) −2.50778e9 −1.10401
\(121\) −2.07213e9 −0.878787
\(122\) −6.10103e9 −2.49336
\(123\) −1.58795e9 −0.625552
\(124\) −8.59606e9 −3.26514
\(125\) 2.42576e9 0.888694
\(126\) 2.95439e9 1.04424
\(127\) −3.83014e8 −0.130647 −0.0653233 0.997864i \(-0.520808\pi\)
−0.0653233 + 0.997864i \(0.520808\pi\)
\(128\) −1.81025e10 −5.96066
\(129\) 2.43219e8 0.0773294
\(130\) −6.16105e8 −0.189195
\(131\) 4.36924e9 1.29624 0.648120 0.761539i \(-0.275556\pi\)
0.648120 + 0.761539i \(0.275556\pi\)
\(132\) 2.03017e9 0.582035
\(133\) 7.94697e9 2.20226
\(134\) 1.92587e9 0.516008
\(135\) 3.79603e8 0.0983620
\(136\) −1.46048e10 −3.66075
\(137\) 3.55561e8 0.0862327 0.0431163 0.999070i \(-0.486271\pi\)
0.0431163 + 0.999070i \(0.486271\pi\)
\(138\) 4.49024e8 0.105393
\(139\) −4.32519e9 −0.982739 −0.491369 0.870951i \(-0.663504\pi\)
−0.491369 + 0.870951i \(0.663504\pi\)
\(140\) 1.06772e10 2.34898
\(141\) 3.06718e9 0.653512
\(142\) −1.24816e10 −2.57615
\(143\) 3.26514e8 0.0652965
\(144\) 7.72035e9 1.49626
\(145\) −3.22991e9 −0.606784
\(146\) 5.65906e9 1.03076
\(147\) −4.96591e9 −0.877144
\(148\) 5.40726e9 0.926402
\(149\) 6.02336e9 1.00115 0.500577 0.865692i \(-0.333121\pi\)
0.500577 + 0.865692i \(0.333121\pi\)
\(150\) −5.21971e9 −0.841852
\(151\) 4.61177e9 0.721890 0.360945 0.932587i \(-0.382454\pi\)
0.360945 + 0.932587i \(0.382454\pi\)
\(152\) 3.41629e10 5.19109
\(153\) 2.21073e9 0.326154
\(154\) −7.61273e9 −1.09068
\(155\) 4.14161e9 0.576337
\(156\) 2.31926e9 0.313537
\(157\) −1.23953e10 −1.62821 −0.814103 0.580721i \(-0.802771\pi\)
−0.814103 + 0.580721i \(0.802771\pi\)
\(158\) −2.30358e10 −2.94067
\(159\) −6.74002e9 −0.836323
\(160\) 2.16855e10 2.61595
\(161\) −1.25153e9 −0.146800
\(162\) −1.92247e9 −0.219302
\(163\) −6.68175e9 −0.741389 −0.370694 0.928755i \(-0.620880\pi\)
−0.370694 + 0.928755i \(0.620880\pi\)
\(164\) 2.90640e10 3.13732
\(165\) −9.78141e8 −0.102736
\(166\) 2.21393e10 2.26296
\(167\) −7.15932e9 −0.712275 −0.356138 0.934434i \(-0.615907\pi\)
−0.356138 + 0.934434i \(0.615907\pi\)
\(168\) −3.53992e10 −3.42848
\(169\) −1.02315e10 −0.964825
\(170\) 1.07488e10 0.987050
\(171\) −5.17123e9 −0.462500
\(172\) −4.45161e9 −0.387828
\(173\) −1.96798e10 −1.67037 −0.835184 0.549970i \(-0.814639\pi\)
−0.835184 + 0.549970i \(0.814639\pi\)
\(174\) 1.63577e10 1.35285
\(175\) 1.45485e10 1.17259
\(176\) −1.98934e10 −1.56279
\(177\) 9.81506e8 0.0751646
\(178\) −1.51245e10 −1.12925
\(179\) 7.58491e9 0.552220 0.276110 0.961126i \(-0.410955\pi\)
0.276110 + 0.961126i \(0.410955\pi\)
\(180\) −6.94782e9 −0.493313
\(181\) 6.65611e9 0.460964 0.230482 0.973077i \(-0.425970\pi\)
0.230482 + 0.973077i \(0.425970\pi\)
\(182\) −8.69677e9 −0.587539
\(183\) −1.10654e10 −0.729353
\(184\) −5.38016e9 −0.346031
\(185\) −2.60524e9 −0.163521
\(186\) −2.09749e10 −1.28497
\(187\) −5.69648e9 −0.340659
\(188\) −5.61383e10 −3.27755
\(189\) 5.35837e9 0.305460
\(190\) −2.51431e10 −1.39968
\(191\) −3.30386e9 −0.179627 −0.0898136 0.995959i \(-0.528627\pi\)
−0.0898136 + 0.995959i \(0.528627\pi\)
\(192\) −6.10247e10 −3.24079
\(193\) −6.10928e8 −0.0316944 −0.0158472 0.999874i \(-0.505045\pi\)
−0.0158472 + 0.999874i \(0.505045\pi\)
\(194\) −5.27944e10 −2.67596
\(195\) −1.11743e9 −0.0553431
\(196\) 9.08904e10 4.39912
\(197\) −1.35254e10 −0.639812 −0.319906 0.947449i \(-0.603651\pi\)
−0.319906 + 0.947449i \(0.603651\pi\)
\(198\) 4.95374e9 0.229055
\(199\) 2.83709e10 1.28243 0.641217 0.767360i \(-0.278430\pi\)
0.641217 + 0.767360i \(0.278430\pi\)
\(200\) 6.25420e10 2.76399
\(201\) 3.49295e9 0.150942
\(202\) 7.37425e10 3.11628
\(203\) −4.55925e10 −1.88435
\(204\) −4.04626e10 −1.63576
\(205\) −1.40031e10 −0.553775
\(206\) 4.52617e10 1.75117
\(207\) 8.14393e8 0.0308296
\(208\) −2.27262e10 −0.841863
\(209\) 1.33250e10 0.483067
\(210\) 2.60530e10 0.924422
\(211\) −7.15753e9 −0.248595 −0.124297 0.992245i \(-0.539668\pi\)
−0.124297 + 0.992245i \(0.539668\pi\)
\(212\) 1.23362e11 4.19439
\(213\) −2.26378e10 −0.753573
\(214\) −8.09604e10 −2.63883
\(215\) 2.14480e9 0.0684564
\(216\) 2.30349e10 0.720019
\(217\) 5.84619e10 1.78980
\(218\) −9.90704e10 −2.97091
\(219\) 1.02638e10 0.301516
\(220\) 1.79028e10 0.515251
\(221\) −6.50766e9 −0.183510
\(222\) 1.31941e10 0.364578
\(223\) −3.19386e10 −0.864856 −0.432428 0.901668i \(-0.642343\pi\)
−0.432428 + 0.901668i \(0.642343\pi\)
\(224\) 3.06107e11 8.12376
\(225\) −9.46697e9 −0.246258
\(226\) −1.35686e11 −3.45977
\(227\) −2.57665e10 −0.644080 −0.322040 0.946726i \(-0.604369\pi\)
−0.322040 + 0.946726i \(0.604369\pi\)
\(228\) 9.46484e10 2.31956
\(229\) 5.02517e10 1.20751 0.603756 0.797169i \(-0.293670\pi\)
0.603756 + 0.797169i \(0.293670\pi\)
\(230\) 3.95967e9 0.0933004
\(231\) −1.38072e10 −0.319044
\(232\) −1.95996e11 −4.44172
\(233\) 7.38541e9 0.164162 0.0820811 0.996626i \(-0.473843\pi\)
0.0820811 + 0.996626i \(0.473843\pi\)
\(234\) 5.65914e9 0.123390
\(235\) 2.70476e10 0.578527
\(236\) −1.79644e10 −0.376971
\(237\) −4.17800e10 −0.860203
\(238\) 1.51727e11 3.06525
\(239\) −6.16374e10 −1.22195 −0.610976 0.791649i \(-0.709223\pi\)
−0.610976 + 0.791649i \(0.709223\pi\)
\(240\) 6.80810e10 1.32457
\(241\) 9.05914e9 0.172986 0.0864929 0.996252i \(-0.472434\pi\)
0.0864929 + 0.996252i \(0.472434\pi\)
\(242\) 9.25419e10 1.73448
\(243\) −3.48678e9 −0.0641500
\(244\) 2.02529e11 3.65791
\(245\) −4.37913e10 −0.776499
\(246\) 7.09181e10 1.23466
\(247\) 1.52224e10 0.260224
\(248\) 2.51319e11 4.21884
\(249\) 4.01539e10 0.661958
\(250\) −1.08335e11 −1.75403
\(251\) 2.81470e10 0.447611 0.223806 0.974634i \(-0.428152\pi\)
0.223806 + 0.974634i \(0.428152\pi\)
\(252\) −9.80735e10 −1.53197
\(253\) −2.09849e9 −0.0322006
\(254\) 1.71055e10 0.257860
\(255\) 1.94950e10 0.288731
\(256\) 4.22726e11 6.15147
\(257\) −1.40914e9 −0.0201491 −0.0100745 0.999949i \(-0.503207\pi\)
−0.0100745 + 0.999949i \(0.503207\pi\)
\(258\) −1.08622e10 −0.152627
\(259\) −3.67748e10 −0.507810
\(260\) 2.04521e10 0.277561
\(261\) 2.96679e10 0.395734
\(262\) −1.95131e11 −2.55841
\(263\) 7.83402e9 0.100968 0.0504840 0.998725i \(-0.483924\pi\)
0.0504840 + 0.998725i \(0.483924\pi\)
\(264\) −5.93551e10 −0.752039
\(265\) −5.94361e10 −0.740362
\(266\) −3.54913e11 −4.34665
\(267\) −2.74313e10 −0.330328
\(268\) −6.39310e10 −0.757016
\(269\) −1.12060e11 −1.30486 −0.652431 0.757848i \(-0.726251\pi\)
−0.652431 + 0.757848i \(0.726251\pi\)
\(270\) −1.69531e10 −0.194139
\(271\) −1.03942e11 −1.17066 −0.585330 0.810795i \(-0.699035\pi\)
−0.585330 + 0.810795i \(0.699035\pi\)
\(272\) 3.96489e11 4.39209
\(273\) −1.57733e10 −0.171866
\(274\) −1.58794e10 −0.170199
\(275\) 2.43940e10 0.257209
\(276\) −1.49057e10 −0.154619
\(277\) 8.37465e9 0.0854688 0.0427344 0.999086i \(-0.486393\pi\)
0.0427344 + 0.999086i \(0.486393\pi\)
\(278\) 1.93164e11 1.93965
\(279\) −3.80422e10 −0.375878
\(280\) −3.12164e11 −3.03509
\(281\) 2.73924e10 0.262091 0.131045 0.991376i \(-0.458167\pi\)
0.131045 + 0.991376i \(0.458167\pi\)
\(282\) −1.36981e11 −1.28985
\(283\) 4.96575e10 0.460199 0.230100 0.973167i \(-0.426095\pi\)
0.230100 + 0.973167i \(0.426095\pi\)
\(284\) 4.14336e11 3.77938
\(285\) −4.56019e10 −0.409431
\(286\) −1.45822e10 −0.128877
\(287\) −1.97665e11 −1.71973
\(288\) −1.99189e11 −1.70608
\(289\) −5.05298e9 −0.0426095
\(290\) 1.44248e11 1.19762
\(291\) −9.57530e10 −0.782769
\(292\) −1.87857e11 −1.51219
\(293\) −2.07884e11 −1.64785 −0.823924 0.566700i \(-0.808220\pi\)
−0.823924 + 0.566700i \(0.808220\pi\)
\(294\) 2.21779e11 1.73124
\(295\) 8.65530e9 0.0665401
\(296\) −1.58090e11 −1.19699
\(297\) 8.98457e9 0.0670028
\(298\) −2.69004e11 −1.97600
\(299\) −2.39731e9 −0.0173462
\(300\) 1.73273e11 1.23505
\(301\) 3.02754e10 0.212589
\(302\) −2.05962e11 −1.42481
\(303\) 1.33747e11 0.911571
\(304\) −9.27450e11 −6.22816
\(305\) −9.75792e10 −0.645666
\(306\) −9.87314e10 −0.643738
\(307\) −1.03771e11 −0.666735 −0.333368 0.942797i \(-0.608185\pi\)
−0.333368 + 0.942797i \(0.608185\pi\)
\(308\) 2.52711e11 1.60010
\(309\) 8.20909e10 0.512250
\(310\) −1.84965e11 −1.13753
\(311\) −3.62366e10 −0.219647 −0.109824 0.993951i \(-0.535029\pi\)
−0.109824 + 0.993951i \(0.535029\pi\)
\(312\) −6.78072e10 −0.405117
\(313\) −3.00938e10 −0.177226 −0.0886131 0.996066i \(-0.528243\pi\)
−0.0886131 + 0.996066i \(0.528243\pi\)
\(314\) 5.53577e11 3.21362
\(315\) 4.72522e10 0.270411
\(316\) 7.64694e11 4.31415
\(317\) 2.82988e11 1.57399 0.786993 0.616962i \(-0.211637\pi\)
0.786993 + 0.616962i \(0.211637\pi\)
\(318\) 3.01011e11 1.65067
\(319\) −7.64466e10 −0.413333
\(320\) −5.38140e11 −2.86893
\(321\) −1.46838e11 −0.771906
\(322\) 5.58936e10 0.289741
\(323\) −2.65576e11 −1.35762
\(324\) 6.38182e10 0.321730
\(325\) 2.78677e10 0.138556
\(326\) 2.98408e11 1.46329
\(327\) −1.79684e11 −0.869047
\(328\) −8.49733e11 −4.05368
\(329\) 3.81797e11 1.79660
\(330\) 4.36840e10 0.202773
\(331\) −1.25712e11 −0.575638 −0.287819 0.957685i \(-0.592930\pi\)
−0.287819 + 0.957685i \(0.592930\pi\)
\(332\) −7.34932e11 −3.31990
\(333\) 2.39300e10 0.106646
\(334\) 3.19737e11 1.40583
\(335\) 3.08022e10 0.133623
\(336\) 9.61013e11 4.11342
\(337\) −4.20323e11 −1.77520 −0.887602 0.460612i \(-0.847630\pi\)
−0.887602 + 0.460612i \(0.847630\pi\)
\(338\) 4.56940e11 1.90430
\(339\) −2.46093e11 −1.01205
\(340\) −3.56815e11 −1.44807
\(341\) 9.80251e10 0.392593
\(342\) 2.30948e11 0.912845
\(343\) −2.11273e11 −0.824175
\(344\) 1.30150e11 0.501108
\(345\) 7.18163e9 0.0272921
\(346\) 8.78902e11 3.29684
\(347\) −1.58534e11 −0.587001 −0.293500 0.955959i \(-0.594820\pi\)
−0.293500 + 0.955959i \(0.594820\pi\)
\(348\) −5.43007e11 −1.98472
\(349\) −4.32565e10 −0.156076 −0.0780382 0.996950i \(-0.524866\pi\)
−0.0780382 + 0.996950i \(0.524866\pi\)
\(350\) −6.49739e11 −2.31437
\(351\) 1.02640e10 0.0360938
\(352\) 5.13260e11 1.78195
\(353\) −5.07910e11 −1.74101 −0.870504 0.492161i \(-0.836207\pi\)
−0.870504 + 0.492161i \(0.836207\pi\)
\(354\) −4.38343e10 −0.148354
\(355\) −1.99629e11 −0.667107
\(356\) 5.02071e11 1.65669
\(357\) 2.75187e11 0.896644
\(358\) −3.38744e11 −1.08993
\(359\) 5.31759e11 1.68962 0.844811 0.535065i \(-0.179713\pi\)
0.844811 + 0.535065i \(0.179713\pi\)
\(360\) 2.03130e11 0.637403
\(361\) 2.98536e11 0.925154
\(362\) −2.97263e11 −0.909814
\(363\) 1.67843e11 0.507368
\(364\) 2.88697e11 0.861957
\(365\) 9.05103e10 0.266919
\(366\) 4.94184e11 1.43954
\(367\) 2.26219e11 0.650928 0.325464 0.945555i \(-0.394480\pi\)
0.325464 + 0.945555i \(0.394480\pi\)
\(368\) 1.46060e11 0.415160
\(369\) 1.28624e11 0.361163
\(370\) 1.16350e11 0.322745
\(371\) −8.38984e11 −2.29917
\(372\) 6.96281e11 1.88513
\(373\) −4.91064e11 −1.31356 −0.656778 0.754084i \(-0.728081\pi\)
−0.656778 + 0.754084i \(0.728081\pi\)
\(374\) 2.54406e11 0.672365
\(375\) −1.96486e11 −0.513087
\(376\) 1.64129e12 4.23487
\(377\) −8.73325e10 −0.222659
\(378\) −2.39306e11 −0.602893
\(379\) −1.07690e11 −0.268101 −0.134050 0.990975i \(-0.542798\pi\)
−0.134050 + 0.990975i \(0.542798\pi\)
\(380\) 8.34646e11 2.05341
\(381\) 3.10241e10 0.0754288
\(382\) 1.47551e11 0.354534
\(383\) 4.65577e11 1.10560 0.552799 0.833315i \(-0.313560\pi\)
0.552799 + 0.833315i \(0.313560\pi\)
\(384\) 1.46630e12 3.44139
\(385\) −1.21757e11 −0.282436
\(386\) 2.72842e10 0.0625558
\(387\) −1.97008e10 −0.0446461
\(388\) 1.75255e12 3.92581
\(389\) 6.17970e11 1.36834 0.684171 0.729322i \(-0.260164\pi\)
0.684171 + 0.729322i \(0.260164\pi\)
\(390\) 4.99045e10 0.109232
\(391\) 4.18243e10 0.0904968
\(392\) −2.65733e12 −5.68404
\(393\) −3.53908e11 −0.748384
\(394\) 6.04047e11 1.26281
\(395\) −3.68432e11 −0.761501
\(396\) −1.64443e11 −0.336038
\(397\) 7.25731e11 1.46628 0.733142 0.680075i \(-0.238053\pi\)
0.733142 + 0.680075i \(0.238053\pi\)
\(398\) −1.26705e12 −2.53117
\(399\) −6.43704e11 −1.27148
\(400\) −1.69788e12 −3.31618
\(401\) −3.42697e11 −0.661852 −0.330926 0.943657i \(-0.607361\pi\)
−0.330926 + 0.943657i \(0.607361\pi\)
\(402\) −1.55996e11 −0.297917
\(403\) 1.11984e11 0.211486
\(404\) −2.44795e12 −4.57178
\(405\) −3.07478e10 −0.0567893
\(406\) 2.03617e12 3.71918
\(407\) −6.16616e10 −0.111388
\(408\) 1.18299e12 2.11354
\(409\) 3.28076e11 0.579721 0.289860 0.957069i \(-0.406391\pi\)
0.289860 + 0.957069i \(0.406391\pi\)
\(410\) 6.25383e11 1.09300
\(411\) −2.88005e10 −0.0497865
\(412\) −1.50250e12 −2.56908
\(413\) 1.22176e11 0.206638
\(414\) −3.63710e10 −0.0608490
\(415\) 3.54093e11 0.586004
\(416\) 5.86348e11 0.959921
\(417\) 3.50340e11 0.567385
\(418\) −5.95096e11 −0.953440
\(419\) −9.17573e11 −1.45438 −0.727189 0.686437i \(-0.759174\pi\)
−0.727189 + 0.686437i \(0.759174\pi\)
\(420\) −8.64851e11 −1.35619
\(421\) −6.07549e11 −0.942566 −0.471283 0.881982i \(-0.656209\pi\)
−0.471283 + 0.881982i \(0.656209\pi\)
\(422\) 3.19657e11 0.490656
\(423\) −2.48442e11 −0.377306
\(424\) −3.60668e12 −5.41952
\(425\) −4.86190e11 −0.722862
\(426\) 1.01101e12 1.48734
\(427\) −1.37740e12 −2.00510
\(428\) 2.68755e12 3.87132
\(429\) −2.64476e10 −0.0376989
\(430\) −9.57873e10 −0.135114
\(431\) 7.76828e11 1.08437 0.542185 0.840259i \(-0.317597\pi\)
0.542185 + 0.840259i \(0.317597\pi\)
\(432\) −6.25348e11 −0.863863
\(433\) −3.38772e11 −0.463140 −0.231570 0.972818i \(-0.574386\pi\)
−0.231570 + 0.972818i \(0.574386\pi\)
\(434\) −2.61092e12 −3.53256
\(435\) 2.61623e11 0.350327
\(436\) 3.28873e12 4.35851
\(437\) −9.78336e10 −0.128328
\(438\) −4.58384e11 −0.595108
\(439\) −1.32693e12 −1.70513 −0.852566 0.522619i \(-0.824955\pi\)
−0.852566 + 0.522619i \(0.824955\pi\)
\(440\) −5.23416e11 −0.665748
\(441\) 4.02239e11 0.506419
\(442\) 2.90633e11 0.362197
\(443\) 5.39539e11 0.665589 0.332795 0.942999i \(-0.392008\pi\)
0.332795 + 0.942999i \(0.392008\pi\)
\(444\) −4.37988e11 −0.534858
\(445\) −2.41900e11 −0.292426
\(446\) 1.42638e12 1.70698
\(447\) −4.87892e11 −0.578016
\(448\) −7.59623e12 −8.90938
\(449\) −4.12062e11 −0.478470 −0.239235 0.970962i \(-0.576897\pi\)
−0.239235 + 0.970962i \(0.576897\pi\)
\(450\) 4.22797e11 0.486044
\(451\) −3.31431e11 −0.377224
\(452\) 4.50421e12 5.07570
\(453\) −3.73553e11 −0.416783
\(454\) 1.15074e12 1.27123
\(455\) −1.39095e11 −0.152146
\(456\) −2.76719e12 −2.99708
\(457\) 1.04050e12 1.11589 0.557944 0.829879i \(-0.311590\pi\)
0.557944 + 0.829879i \(0.311590\pi\)
\(458\) −2.24425e12 −2.38329
\(459\) −1.79069e11 −0.188305
\(460\) −1.31445e11 −0.136878
\(461\) −3.43691e11 −0.354417 −0.177208 0.984173i \(-0.556707\pi\)
−0.177208 + 0.984173i \(0.556707\pi\)
\(462\) 6.16631e11 0.629704
\(463\) 1.60518e12 1.62334 0.811668 0.584119i \(-0.198560\pi\)
0.811668 + 0.584119i \(0.198560\pi\)
\(464\) 5.32087e12 5.32908
\(465\) −3.35471e11 −0.332749
\(466\) −3.29834e11 −0.324010
\(467\) 1.49305e12 1.45261 0.726305 0.687373i \(-0.241236\pi\)
0.726305 + 0.687373i \(0.241236\pi\)
\(468\) −1.87860e11 −0.181021
\(469\) 4.34795e11 0.414961
\(470\) −1.20795e12 −1.14185
\(471\) 1.00402e12 0.940045
\(472\) 5.25217e11 0.487080
\(473\) 5.07639e10 0.0466316
\(474\) 1.86590e12 1.69780
\(475\) 1.13727e12 1.02505
\(476\) −5.03671e12 −4.49692
\(477\) 5.45942e11 0.482852
\(478\) 2.75274e12 2.41179
\(479\) −4.99884e11 −0.433870 −0.216935 0.976186i \(-0.569606\pi\)
−0.216935 + 0.976186i \(0.569606\pi\)
\(480\) −1.75653e12 −1.51032
\(481\) −7.04422e10 −0.0600040
\(482\) −4.04583e11 −0.341426
\(483\) 1.01374e11 0.0847548
\(484\) −3.07201e12 −2.54459
\(485\) −8.44387e11 −0.692953
\(486\) 1.55720e11 0.126614
\(487\) 1.80213e12 1.45180 0.725899 0.687802i \(-0.241424\pi\)
0.725899 + 0.687802i \(0.241424\pi\)
\(488\) −5.92125e12 −4.72634
\(489\) 5.41222e11 0.428041
\(490\) 1.95573e12 1.53259
\(491\) 2.17553e12 1.68926 0.844632 0.535347i \(-0.179819\pi\)
0.844632 + 0.535347i \(0.179819\pi\)
\(492\) −2.35419e12 −1.81133
\(493\) 1.52363e12 1.16163
\(494\) −6.79836e11 −0.513610
\(495\) 7.92294e10 0.0593148
\(496\) −6.82279e12 −5.06168
\(497\) −2.81790e12 −2.07168
\(498\) −1.79328e12 −1.30652
\(499\) 2.29747e12 1.65882 0.829408 0.558643i \(-0.188678\pi\)
0.829408 + 0.558643i \(0.188678\pi\)
\(500\) 3.59626e12 2.57328
\(501\) 5.79905e11 0.411232
\(502\) −1.25705e12 −0.883459
\(503\) −7.81795e11 −0.544549 −0.272275 0.962220i \(-0.587776\pi\)
−0.272275 + 0.962220i \(0.587776\pi\)
\(504\) 2.86733e12 1.97943
\(505\) 1.17943e12 0.806976
\(506\) 9.37188e10 0.0635550
\(507\) 8.28751e11 0.557042
\(508\) −5.67831e11 −0.378297
\(509\) −3.00641e11 −0.198526 −0.0992631 0.995061i \(-0.531649\pi\)
−0.0992631 + 0.995061i \(0.531649\pi\)
\(510\) −8.70652e11 −0.569874
\(511\) 1.27762e12 0.828910
\(512\) −9.61052e12 −6.18062
\(513\) 4.18870e11 0.267024
\(514\) 6.29325e10 0.0397687
\(515\) 7.23909e11 0.453473
\(516\) 3.60581e11 0.223913
\(517\) 6.40172e11 0.394085
\(518\) 1.64237e12 1.00228
\(519\) 1.59406e12 0.964388
\(520\) −5.97950e11 −0.358633
\(521\) −2.82772e11 −0.168138 −0.0840690 0.996460i \(-0.526792\pi\)
−0.0840690 + 0.996460i \(0.526792\pi\)
\(522\) −1.32497e12 −0.781069
\(523\) 2.40276e12 1.40428 0.702139 0.712040i \(-0.252229\pi\)
0.702139 + 0.712040i \(0.252229\pi\)
\(524\) 6.47754e12 3.75335
\(525\) −1.17843e12 −0.676997
\(526\) −3.49869e11 −0.199283
\(527\) −1.95371e12 −1.10335
\(528\) 1.61137e12 0.902280
\(529\) −1.78575e12 −0.991446
\(530\) 2.65443e12 1.46127
\(531\) −7.95020e10 −0.0433963
\(532\) 1.17816e13 6.37681
\(533\) −3.78627e11 −0.203207
\(534\) 1.22509e12 0.651975
\(535\) −1.29487e12 −0.683336
\(536\) 1.86912e12 0.978130
\(537\) −6.14378e11 −0.318824
\(538\) 5.00461e12 2.57543
\(539\) −1.03647e12 −0.528940
\(540\) 5.62773e11 0.284814
\(541\) −1.63631e12 −0.821253 −0.410627 0.911804i \(-0.634690\pi\)
−0.410627 + 0.911804i \(0.634690\pi\)
\(542\) 4.64208e12 2.31055
\(543\) −5.39145e11 −0.266138
\(544\) −1.02296e13 −5.00801
\(545\) −1.58452e12 −0.769331
\(546\) 7.04438e11 0.339216
\(547\) −2.05554e12 −0.981709 −0.490854 0.871242i \(-0.663315\pi\)
−0.490854 + 0.871242i \(0.663315\pi\)
\(548\) 5.27131e11 0.249693
\(549\) 8.96299e11 0.421092
\(550\) −1.08944e12 −0.507658
\(551\) −3.56402e12 −1.64724
\(552\) 4.35793e11 0.199781
\(553\) −5.20069e12 −2.36482
\(554\) −3.74014e11 −0.168692
\(555\) 2.11024e11 0.0944091
\(556\) −6.41223e12 −2.84559
\(557\) 1.75217e12 0.771309 0.385654 0.922643i \(-0.373976\pi\)
0.385654 + 0.922643i \(0.373976\pi\)
\(558\) 1.69897e12 0.741877
\(559\) 5.79926e10 0.0251200
\(560\) 8.47459e12 3.64143
\(561\) 4.61415e11 0.196679
\(562\) −1.22335e12 −0.517294
\(563\) 1.47516e12 0.618802 0.309401 0.950932i \(-0.399872\pi\)
0.309401 + 0.950932i \(0.399872\pi\)
\(564\) 4.54720e12 1.89229
\(565\) −2.17014e12 −0.895923
\(566\) −2.21771e12 −0.908304
\(567\) −4.34028e11 −0.176357
\(568\) −1.21138e13 −4.88328
\(569\) −2.61095e12 −1.04422 −0.522111 0.852878i \(-0.674855\pi\)
−0.522111 + 0.852878i \(0.674855\pi\)
\(570\) 2.03659e12 0.808103
\(571\) −1.13826e12 −0.448104 −0.224052 0.974577i \(-0.571928\pi\)
−0.224052 + 0.974577i \(0.571928\pi\)
\(572\) 4.84068e11 0.189071
\(573\) 2.67613e11 0.103708
\(574\) 8.82774e12 3.39427
\(575\) −1.79104e11 −0.0683282
\(576\) 4.94300e12 1.87107
\(577\) 5.82770e11 0.218880 0.109440 0.993993i \(-0.465094\pi\)
0.109440 + 0.993993i \(0.465094\pi\)
\(578\) 2.25667e11 0.0840993
\(579\) 4.94851e10 0.0182987
\(580\) −4.78845e12 −1.75699
\(581\) 4.99827e12 1.81982
\(582\) 4.27635e12 1.54497
\(583\) −1.40675e12 −0.504324
\(584\) 5.49231e12 1.95388
\(585\) 9.05116e10 0.0319523
\(586\) 9.28415e12 3.25239
\(587\) −5.08815e11 −0.176884 −0.0884420 0.996081i \(-0.528189\pi\)
−0.0884420 + 0.996081i \(0.528189\pi\)
\(588\) −7.36213e12 −2.53983
\(589\) 4.57003e12 1.56459
\(590\) −3.86547e11 −0.131331
\(591\) 1.09556e12 0.369395
\(592\) 4.29180e12 1.43612
\(593\) 8.59531e11 0.285440 0.142720 0.989763i \(-0.454415\pi\)
0.142720 + 0.989763i \(0.454415\pi\)
\(594\) −4.01253e11 −0.132245
\(595\) 2.42670e12 0.793762
\(596\) 8.92983e12 2.89891
\(597\) −2.29805e12 −0.740414
\(598\) 1.07064e11 0.0342365
\(599\) −3.76859e12 −1.19607 −0.598037 0.801469i \(-0.704052\pi\)
−0.598037 + 0.801469i \(0.704052\pi\)
\(600\) −5.06590e12 −1.59579
\(601\) −4.46763e12 −1.39683 −0.698413 0.715695i \(-0.746110\pi\)
−0.698413 + 0.715695i \(0.746110\pi\)
\(602\) −1.35211e12 −0.419592
\(603\) −2.82929e11 −0.0871464
\(604\) 6.83709e12 2.09028
\(605\) 1.48010e12 0.449151
\(606\) −5.97315e12 −1.79919
\(607\) 5.11907e12 1.53053 0.765265 0.643715i \(-0.222608\pi\)
0.765265 + 0.643715i \(0.222608\pi\)
\(608\) 2.39287e13 7.10155
\(609\) 3.69299e12 1.08793
\(610\) 4.35790e12 1.27436
\(611\) 7.31332e11 0.212290
\(612\) 3.27747e12 0.944404
\(613\) −4.88066e12 −1.39607 −0.698034 0.716065i \(-0.745941\pi\)
−0.698034 + 0.716065i \(0.745941\pi\)
\(614\) 4.63444e12 1.31595
\(615\) 1.13425e12 0.319722
\(616\) −7.38840e12 −2.06746
\(617\) 7.01368e11 0.194833 0.0974165 0.995244i \(-0.468942\pi\)
0.0974165 + 0.995244i \(0.468942\pi\)
\(618\) −3.66620e12 −1.01104
\(619\) −2.21391e12 −0.606111 −0.303055 0.952973i \(-0.598007\pi\)
−0.303055 + 0.952973i \(0.598007\pi\)
\(620\) 6.14008e12 1.66883
\(621\) −6.59658e10 −0.0177995
\(622\) 1.61834e12 0.433523
\(623\) −3.41459e12 −0.908118
\(624\) 1.84082e12 0.486050
\(625\) 1.08550e12 0.284558
\(626\) 1.34400e12 0.349795
\(627\) −1.07932e12 −0.278899
\(628\) −1.83765e13 −4.71459
\(629\) 1.22896e12 0.313047
\(630\) −2.11029e12 −0.533716
\(631\) −1.22716e12 −0.308155 −0.154078 0.988059i \(-0.549241\pi\)
−0.154078 + 0.988059i \(0.549241\pi\)
\(632\) −2.23570e13 −5.57426
\(633\) 5.79760e11 0.143526
\(634\) −1.26383e13 −3.10661
\(635\) 2.73583e11 0.0667740
\(636\) −9.99230e12 −2.42163
\(637\) −1.18406e12 −0.284935
\(638\) 3.41412e12 0.815804
\(639\) 1.83366e12 0.435076
\(640\) 1.29304e13 3.04652
\(641\) 6.87504e12 1.60847 0.804237 0.594309i \(-0.202574\pi\)
0.804237 + 0.594309i \(0.202574\pi\)
\(642\) 6.55780e12 1.52353
\(643\) 6.49891e12 1.49931 0.749655 0.661829i \(-0.230220\pi\)
0.749655 + 0.661829i \(0.230220\pi\)
\(644\) −1.85544e12 −0.425069
\(645\) −1.73729e11 −0.0395233
\(646\) 1.18607e13 2.67956
\(647\) −3.42884e12 −0.769268 −0.384634 0.923069i \(-0.625672\pi\)
−0.384634 + 0.923069i \(0.625672\pi\)
\(648\) −1.86583e12 −0.415703
\(649\) 2.04857e11 0.0453262
\(650\) −1.24458e12 −0.273471
\(651\) −4.73541e12 −1.03334
\(652\) −9.90591e12 −2.14674
\(653\) −3.38071e12 −0.727609 −0.363805 0.931475i \(-0.618522\pi\)
−0.363805 + 0.931475i \(0.618522\pi\)
\(654\) 8.02470e12 1.71526
\(655\) −3.12090e12 −0.662513
\(656\) 2.30684e13 4.86352
\(657\) −8.31369e11 −0.174080
\(658\) −1.70511e13 −3.54598
\(659\) −7.25128e12 −1.49772 −0.748859 0.662729i \(-0.769398\pi\)
−0.748859 + 0.662729i \(0.769398\pi\)
\(660\) −1.45013e12 −0.297480
\(661\) 9.13436e12 1.86111 0.930554 0.366154i \(-0.119326\pi\)
0.930554 + 0.366154i \(0.119326\pi\)
\(662\) 5.61430e12 1.13615
\(663\) 5.27120e11 0.105949
\(664\) 2.14869e13 4.28960
\(665\) −5.67643e12 −1.12558
\(666\) −1.06872e12 −0.210489
\(667\) 5.61281e11 0.109803
\(668\) −1.06139e13 −2.06244
\(669\) 2.58703e12 0.499325
\(670\) −1.37563e12 −0.263734
\(671\) −2.30954e12 −0.439819
\(672\) −2.47946e13 −4.69025
\(673\) 5.01704e12 0.942713 0.471357 0.881943i \(-0.343764\pi\)
0.471357 + 0.881943i \(0.343764\pi\)
\(674\) 1.87717e13 3.50376
\(675\) 7.66825e11 0.142177
\(676\) −1.51685e13 −2.79372
\(677\) 1.26871e12 0.232120 0.116060 0.993242i \(-0.462973\pi\)
0.116060 + 0.993242i \(0.462973\pi\)
\(678\) 1.09906e13 1.99750
\(679\) −1.19191e13 −2.15194
\(680\) 1.04321e13 1.87103
\(681\) 2.08709e12 0.371860
\(682\) −4.37782e12 −0.774869
\(683\) 7.93026e12 1.39442 0.697211 0.716866i \(-0.254424\pi\)
0.697211 + 0.716866i \(0.254424\pi\)
\(684\) −7.66652e12 −1.33920
\(685\) −2.53974e11 −0.0440739
\(686\) 9.43547e12 1.62669
\(687\) −4.07039e12 −0.697157
\(688\) −3.53330e12 −0.601218
\(689\) −1.60707e12 −0.271675
\(690\) −3.20733e11 −0.0538670
\(691\) 1.01252e13 1.68947 0.844736 0.535183i \(-0.179757\pi\)
0.844736 + 0.535183i \(0.179757\pi\)
\(692\) −2.91759e13 −4.83667
\(693\) 1.11838e12 0.184200
\(694\) 7.08014e12 1.15858
\(695\) 3.08943e12 0.502282
\(696\) 1.58757e13 2.56443
\(697\) 6.60566e12 1.06015
\(698\) 1.93184e12 0.308051
\(699\) −5.98219e11 −0.0947791
\(700\) 2.15686e13 3.39533
\(701\) −7.69928e12 −1.20426 −0.602128 0.798399i \(-0.705680\pi\)
−0.602128 + 0.798399i \(0.705680\pi\)
\(702\) −4.58390e11 −0.0712391
\(703\) −2.87473e12 −0.443913
\(704\) −1.27369e13 −1.95428
\(705\) −2.19086e12 −0.334013
\(706\) 2.26834e13 3.43626
\(707\) 1.66485e13 2.50604
\(708\) 1.45512e12 0.217645
\(709\) 3.84430e12 0.571359 0.285679 0.958325i \(-0.407781\pi\)
0.285679 + 0.958325i \(0.407781\pi\)
\(710\) 8.91545e12 1.31668
\(711\) 3.38418e12 0.496638
\(712\) −1.46789e13 −2.14058
\(713\) −7.19713e11 −0.104293
\(714\) −1.22899e13 −1.76973
\(715\) −2.33226e11 −0.0333733
\(716\) 1.12449e13 1.59899
\(717\) 4.99263e12 0.705494
\(718\) −2.37484e13 −3.33484
\(719\) −4.05595e12 −0.565995 −0.282997 0.959121i \(-0.591329\pi\)
−0.282997 + 0.959121i \(0.591329\pi\)
\(720\) −5.51456e12 −0.764742
\(721\) 1.02185e13 1.40825
\(722\) −1.33327e13 −1.82599
\(723\) −7.33790e11 −0.0998734
\(724\) 9.86790e12 1.33475
\(725\) −6.52465e12 −0.877073
\(726\) −7.49589e12 −1.00140
\(727\) −6.97886e12 −0.926573 −0.463287 0.886209i \(-0.653330\pi\)
−0.463287 + 0.886209i \(0.653330\pi\)
\(728\) −8.44050e12 −1.11372
\(729\) 2.82430e11 0.0370370
\(730\) −4.04221e12 −0.526824
\(731\) −1.01176e12 −0.131054
\(732\) −1.64048e13 −2.11190
\(733\) −2.31364e12 −0.296024 −0.148012 0.988986i \(-0.547287\pi\)
−0.148012 + 0.988986i \(0.547287\pi\)
\(734\) −1.01030e13 −1.28475
\(735\) 3.54710e12 0.448312
\(736\) −3.76842e12 −0.473379
\(737\) 7.29037e11 0.0910219
\(738\) −5.74437e12 −0.712834
\(739\) −8.89103e12 −1.09661 −0.548305 0.836278i \(-0.684727\pi\)
−0.548305 + 0.836278i \(0.684727\pi\)
\(740\) −3.86235e12 −0.473488
\(741\) −1.23302e12 −0.150240
\(742\) 3.74692e13 4.53792
\(743\) −6.42980e12 −0.774012 −0.387006 0.922077i \(-0.626491\pi\)
−0.387006 + 0.922077i \(0.626491\pi\)
\(744\) −2.03569e13 −2.43575
\(745\) −4.30242e12 −0.511693
\(746\) 2.19310e13 2.59259
\(747\) −3.25247e12 −0.382182
\(748\) −8.44522e12 −0.986402
\(749\) −1.82780e13 −2.12208
\(750\) 8.77511e12 1.01269
\(751\) 5.87435e12 0.673877 0.336938 0.941527i \(-0.390609\pi\)
0.336938 + 0.941527i \(0.390609\pi\)
\(752\) −4.45576e13 −5.08091
\(753\) −2.27991e12 −0.258428
\(754\) 3.90029e12 0.439466
\(755\) −3.29413e12 −0.368961
\(756\) 7.94396e12 0.884482
\(757\) 2.51325e12 0.278167 0.139083 0.990281i \(-0.455584\pi\)
0.139083 + 0.990281i \(0.455584\pi\)
\(758\) 4.80945e12 0.529156
\(759\) 1.69977e11 0.0185910
\(760\) −2.44022e13 −2.65319
\(761\) −4.65254e12 −0.502874 −0.251437 0.967874i \(-0.580903\pi\)
−0.251437 + 0.967874i \(0.580903\pi\)
\(762\) −1.38554e12 −0.148875
\(763\) −2.23666e13 −2.38913
\(764\) −4.89809e12 −0.520124
\(765\) −1.57910e12 −0.166699
\(766\) −2.07928e13 −2.18214
\(767\) 2.34028e11 0.0244168
\(768\) −3.42408e13 −3.55155
\(769\) −1.90426e13 −1.96362 −0.981812 0.189857i \(-0.939198\pi\)
−0.981812 + 0.189857i \(0.939198\pi\)
\(770\) 5.43769e12 0.557450
\(771\) 1.14140e11 0.0116331
\(772\) −9.05720e11 −0.0917733
\(773\) 1.38070e13 1.39089 0.695445 0.718579i \(-0.255207\pi\)
0.695445 + 0.718579i \(0.255207\pi\)
\(774\) 8.79840e11 0.0881190
\(775\) 8.36635e12 0.833064
\(776\) −5.12387e13 −5.07248
\(777\) 2.97876e12 0.293184
\(778\) −2.75987e13 −2.70072
\(779\) −1.54517e13 −1.50334
\(780\) −1.65662e12 −0.160250
\(781\) −4.72488e12 −0.454424
\(782\) −1.86788e12 −0.178615
\(783\) −2.40310e12 −0.228477
\(784\) 7.21408e13 6.81959
\(785\) 8.85384e12 0.832182
\(786\) 1.58056e13 1.47710
\(787\) 1.23088e13 1.14375 0.571874 0.820342i \(-0.306217\pi\)
0.571874 + 0.820342i \(0.306217\pi\)
\(788\) −2.00518e13 −1.85262
\(789\) −6.34556e11 −0.0582939
\(790\) 1.64542e13 1.50299
\(791\) −3.06332e13 −2.78226
\(792\) 4.80776e12 0.434190
\(793\) −2.63841e12 −0.236926
\(794\) −3.24113e13 −2.89403
\(795\) 4.81433e12 0.427448
\(796\) 4.20609e13 3.71338
\(797\) −1.82300e13 −1.60038 −0.800191 0.599745i \(-0.795269\pi\)
−0.800191 + 0.599745i \(0.795269\pi\)
\(798\) 2.87480e13 2.50954
\(799\) −1.27591e13 −1.10754
\(800\) 4.38063e13 3.78122
\(801\) 2.22193e12 0.190715
\(802\) 1.53049e13 1.30631
\(803\) 2.14223e12 0.181822
\(804\) 5.17841e12 0.437064
\(805\) 8.93955e11 0.0750299
\(806\) −5.00122e12 −0.417415
\(807\) 9.07685e12 0.753363
\(808\) 7.15696e13 5.90714
\(809\) −7.40819e12 −0.608056 −0.304028 0.952663i \(-0.598332\pi\)
−0.304028 + 0.952663i \(0.598332\pi\)
\(810\) 1.37320e12 0.112086
\(811\) 1.07341e13 0.871310 0.435655 0.900114i \(-0.356517\pi\)
0.435655 + 0.900114i \(0.356517\pi\)
\(812\) −6.75924e13 −5.45627
\(813\) 8.41933e12 0.675880
\(814\) 2.75382e12 0.219850
\(815\) 4.77270e12 0.378927
\(816\) −3.21156e13 −2.53578
\(817\) 2.36667e12 0.185839
\(818\) −1.46519e13 −1.14421
\(819\) 1.27764e12 0.0992270
\(820\) −2.07601e13 −1.60349
\(821\) −1.58404e13 −1.21680 −0.608402 0.793629i \(-0.708189\pi\)
−0.608402 + 0.793629i \(0.708189\pi\)
\(822\) 1.28623e12 0.0982646
\(823\) 1.15449e13 0.877181 0.438591 0.898687i \(-0.355478\pi\)
0.438591 + 0.898687i \(0.355478\pi\)
\(824\) 4.39279e13 3.31947
\(825\) −1.97591e12 −0.148500
\(826\) −5.45640e12 −0.407846
\(827\) −2.22688e13 −1.65547 −0.827737 0.561116i \(-0.810372\pi\)
−0.827737 + 0.561116i \(0.810372\pi\)
\(828\) 1.20736e12 0.0892692
\(829\) −2.43527e13 −1.79082 −0.895410 0.445243i \(-0.853117\pi\)
−0.895410 + 0.445243i \(0.853117\pi\)
\(830\) −1.58138e13 −1.15661
\(831\) −6.78347e11 −0.0493455
\(832\) −1.45506e13 −1.05275
\(833\) 2.06575e13 1.48654
\(834\) −1.56463e13 −1.11986
\(835\) 5.11383e12 0.364047
\(836\) 1.97547e13 1.39876
\(837\) 3.08142e12 0.217013
\(838\) 4.09790e13 2.87054
\(839\) −1.29695e13 −0.903638 −0.451819 0.892110i \(-0.649225\pi\)
−0.451819 + 0.892110i \(0.649225\pi\)
\(840\) 2.52853e13 1.75231
\(841\) 5.93997e12 0.409451
\(842\) 2.71332e13 1.86036
\(843\) −2.21878e12 −0.151318
\(844\) −1.06113e13 −0.719824
\(845\) 7.30824e12 0.493126
\(846\) 1.10955e13 0.744696
\(847\) 2.08927e13 1.39483
\(848\) 9.79136e13 6.50222
\(849\) −4.02226e12 −0.265696
\(850\) 2.17133e13 1.42673
\(851\) 4.52728e11 0.0295906
\(852\) −3.35612e13 −2.18203
\(853\) −1.28073e13 −0.828298 −0.414149 0.910209i \(-0.635921\pi\)
−0.414149 + 0.910209i \(0.635921\pi\)
\(854\) 6.15150e13 3.95750
\(855\) 3.69376e12 0.236385
\(856\) −7.85748e13 −5.00209
\(857\) 4.05538e12 0.256814 0.128407 0.991722i \(-0.459014\pi\)
0.128407 + 0.991722i \(0.459014\pi\)
\(858\) 1.18116e12 0.0744072
\(859\) 2.20178e13 1.37976 0.689881 0.723923i \(-0.257663\pi\)
0.689881 + 0.723923i \(0.257663\pi\)
\(860\) 3.17974e12 0.198221
\(861\) 1.60108e13 0.992887
\(862\) −3.46933e13 −2.14024
\(863\) 4.04656e12 0.248334 0.124167 0.992261i \(-0.460374\pi\)
0.124167 + 0.992261i \(0.460374\pi\)
\(864\) 1.61343e13 0.985005
\(865\) 1.40570e13 0.853732
\(866\) 1.51296e13 0.914108
\(867\) 4.09291e11 0.0246006
\(868\) 8.66717e13 5.18249
\(869\) −8.72018e12 −0.518724
\(870\) −1.16841e13 −0.691448
\(871\) 8.32851e11 0.0490327
\(872\) −9.61511e13 −5.63158
\(873\) 7.75599e12 0.451932
\(874\) 4.36927e12 0.253284
\(875\) −2.44582e13 −1.41055
\(876\) 1.52164e13 0.873061
\(877\) −3.26723e13 −1.86501 −0.932504 0.361158i \(-0.882381\pi\)
−0.932504 + 0.361158i \(0.882381\pi\)
\(878\) 5.92610e13 3.36545
\(879\) 1.68386e13 0.951386
\(880\) 1.42096e13 0.798751
\(881\) 1.87901e13 1.05084 0.525421 0.850842i \(-0.323908\pi\)
0.525421 + 0.850842i \(0.323908\pi\)
\(882\) −1.79641e13 −0.999530
\(883\) 1.77166e13 0.980746 0.490373 0.871513i \(-0.336861\pi\)
0.490373 + 0.871513i \(0.336861\pi\)
\(884\) −9.64781e12 −0.531366
\(885\) −7.01079e11 −0.0384169
\(886\) −2.40959e13 −1.31369
\(887\) 7.96820e11 0.0432219 0.0216110 0.999766i \(-0.493120\pi\)
0.0216110 + 0.999766i \(0.493120\pi\)
\(888\) 1.28053e13 0.691083
\(889\) 3.86182e12 0.207364
\(890\) 1.08033e13 0.577166
\(891\) −7.27750e11 −0.0386841
\(892\) −4.73500e13 −2.50425
\(893\) 2.98455e13 1.57053
\(894\) 2.17894e13 1.14084
\(895\) −5.41782e12 −0.282242
\(896\) 1.82523e14 9.46086
\(897\) 1.94182e11 0.0100148
\(898\) 1.84028e13 0.944365
\(899\) −2.62187e13 −1.33873
\(900\) −1.40351e13 −0.713057
\(901\) 2.80376e13 1.41736
\(902\) 1.48018e13 0.744534
\(903\) −2.45231e12 −0.122738
\(904\) −1.31688e14 −6.55824
\(905\) −4.75439e12 −0.235600
\(906\) 1.66829e13 0.822614
\(907\) −3.02533e13 −1.48436 −0.742180 0.670200i \(-0.766208\pi\)
−0.742180 + 0.670200i \(0.766208\pi\)
\(908\) −3.81997e13 −1.86498
\(909\) −1.08335e13 −0.526296
\(910\) 6.21201e12 0.300293
\(911\) −2.80501e13 −1.34928 −0.674639 0.738148i \(-0.735701\pi\)
−0.674639 + 0.738148i \(0.735701\pi\)
\(912\) 7.51235e13 3.59583
\(913\) 8.38079e12 0.399178
\(914\) −4.64691e13 −2.20245
\(915\) 7.90391e12 0.372775
\(916\) 7.44998e13 3.49644
\(917\) −4.40538e13 −2.05741
\(918\) 7.99724e12 0.371662
\(919\) −3.79031e13 −1.75289 −0.876445 0.481503i \(-0.840091\pi\)
−0.876445 + 0.481503i \(0.840091\pi\)
\(920\) 3.84299e12 0.176858
\(921\) 8.40545e12 0.384940
\(922\) 1.53493e13 0.699519
\(923\) −5.39770e12 −0.244794
\(924\) −2.04696e13 −0.923815
\(925\) −5.26276e12 −0.236361
\(926\) −7.16875e13 −3.20401
\(927\) −6.64936e12 −0.295748
\(928\) −1.37281e14 −6.07639
\(929\) 1.77369e12 0.0781281 0.0390640 0.999237i \(-0.487562\pi\)
0.0390640 + 0.999237i \(0.487562\pi\)
\(930\) 1.49822e13 0.656753
\(931\) −4.83212e13 −2.10797
\(932\) 1.09491e13 0.475344
\(933\) 2.93517e12 0.126814
\(934\) −6.66800e13 −2.86704
\(935\) 4.06894e12 0.174112
\(936\) 5.49238e12 0.233894
\(937\) 8.40273e11 0.0356117 0.0178058 0.999841i \(-0.494332\pi\)
0.0178058 + 0.999841i \(0.494332\pi\)
\(938\) −1.94180e13 −0.819017
\(939\) 2.43760e12 0.102322
\(940\) 4.00990e13 1.67517
\(941\) 2.44547e13 1.01674 0.508370 0.861139i \(-0.330248\pi\)
0.508370 + 0.861139i \(0.330248\pi\)
\(942\) −4.48398e13 −1.85539
\(943\) 2.43341e12 0.100210
\(944\) −1.42585e13 −0.584387
\(945\) −3.82743e12 −0.156122
\(946\) −2.26713e12 −0.0920377
\(947\) 2.87343e13 1.16098 0.580491 0.814266i \(-0.302861\pi\)
0.580491 + 0.814266i \(0.302861\pi\)
\(948\) −6.19402e13 −2.49078
\(949\) 2.44728e12 0.0979458
\(950\) −5.07908e13 −2.02316
\(951\) −2.29220e13 −0.908742
\(952\) 1.47256e14 5.81041
\(953\) 4.58606e13 1.80103 0.900516 0.434822i \(-0.143189\pi\)
0.900516 + 0.434822i \(0.143189\pi\)
\(954\) −2.43819e13 −0.953014
\(955\) 2.35992e12 0.0918082
\(956\) −9.13795e13 −3.53825
\(957\) 6.19218e12 0.238638
\(958\) 2.23249e13 0.856338
\(959\) −3.58502e12 −0.136870
\(960\) 4.35893e13 1.65638
\(961\) 7.17982e12 0.271555
\(962\) 3.14596e12 0.118431
\(963\) 1.18938e13 0.445660
\(964\) 1.34305e13 0.500893
\(965\) 4.36379e11 0.0161991
\(966\) −4.52738e12 −0.167282
\(967\) −6.54729e12 −0.240792 −0.120396 0.992726i \(-0.538416\pi\)
−0.120396 + 0.992726i \(0.538416\pi\)
\(968\) 8.98149e13 3.28783
\(969\) 2.15116e13 0.783820
\(970\) 3.77105e13 1.36770
\(971\) −7.61211e12 −0.274801 −0.137401 0.990516i \(-0.543875\pi\)
−0.137401 + 0.990516i \(0.543875\pi\)
\(972\) −5.16927e12 −0.185751
\(973\) 4.36096e13 1.55982
\(974\) −8.04835e13 −2.86544
\(975\) −2.25728e12 −0.0799954
\(976\) 1.60750e14 5.67055
\(977\) −8.95339e12 −0.314385 −0.157192 0.987568i \(-0.550244\pi\)
−0.157192 + 0.987568i \(0.550244\pi\)
\(978\) −2.41711e13 −0.844833
\(979\) −5.72537e12 −0.199196
\(980\) −6.49221e13 −2.24841
\(981\) 1.45544e13 0.501745
\(982\) −9.71594e13 −3.33414
\(983\) 4.12416e13 1.40878 0.704392 0.709811i \(-0.251220\pi\)
0.704392 + 0.709811i \(0.251220\pi\)
\(984\) 6.88283e13 2.34040
\(985\) 9.66105e12 0.327010
\(986\) −6.80458e13 −2.29274
\(987\) −3.09255e13 −1.03727
\(988\) 2.25677e13 0.753498
\(989\) −3.72715e11 −0.0123878
\(990\) −3.53840e12 −0.117071
\(991\) −1.53502e13 −0.505572 −0.252786 0.967522i \(-0.581347\pi\)
−0.252786 + 0.967522i \(0.581347\pi\)
\(992\) 1.76032e14 5.77149
\(993\) 1.01826e13 0.332345
\(994\) 1.25848e14 4.08891
\(995\) −2.02651e13 −0.655457
\(996\) 5.95295e13 1.91675
\(997\) −3.08890e13 −0.990092 −0.495046 0.868867i \(-0.664849\pi\)
−0.495046 + 0.868867i \(0.664849\pi\)
\(998\) −1.02606e14 −3.27404
\(999\) −1.93833e12 −0.0615720
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 177.10.a.b.1.1 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.1 21 1.1 even 1 trivial