Properties

Label 177.10.a.c.1.13
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
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: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+13.0004 q^{2} -81.0000 q^{3} -342.991 q^{4} -5.38377 q^{5} -1053.03 q^{6} -6261.56 q^{7} -11115.2 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+13.0004 q^{2} -81.0000 q^{3} -342.991 q^{4} -5.38377 q^{5} -1053.03 q^{6} -6261.56 q^{7} -11115.2 q^{8} +6561.00 q^{9} -69.9909 q^{10} -43612.2 q^{11} +27782.3 q^{12} -69107.7 q^{13} -81402.5 q^{14} +436.085 q^{15} +31109.9 q^{16} -325669. q^{17} +85295.3 q^{18} -628064. q^{19} +1846.58 q^{20} +507186. q^{21} -566974. q^{22} -408662. q^{23} +900330. q^{24} -1.95310e6 q^{25} -898425. q^{26} -531441. q^{27} +2.14766e6 q^{28} -7.39061e6 q^{29} +5669.26 q^{30} +685788. q^{31} +6.09541e6 q^{32} +3.53259e6 q^{33} -4.23382e6 q^{34} +33710.8 q^{35} -2.25036e6 q^{36} +4.07607e6 q^{37} -8.16506e6 q^{38} +5.59772e6 q^{39} +59841.6 q^{40} -2.00366e6 q^{41} +6.59360e6 q^{42} +5.29965e6 q^{43} +1.49586e7 q^{44} -35322.9 q^{45} -5.31275e6 q^{46} -4.79365e7 q^{47} -2.51990e6 q^{48} -1.14649e6 q^{49} -2.53909e7 q^{50} +2.63792e7 q^{51} +2.37033e7 q^{52} +2.75368e7 q^{53} -6.90892e6 q^{54} +234798. q^{55} +6.95984e7 q^{56} +5.08732e7 q^{57} -9.60806e7 q^{58} +1.21174e7 q^{59} -149573. q^{60} -1.32205e8 q^{61} +8.91549e6 q^{62} -4.10821e7 q^{63} +6.33143e7 q^{64} +372060. q^{65} +4.59249e7 q^{66} -8.56509e7 q^{67} +1.11702e8 q^{68} +3.31016e7 q^{69} +438252. q^{70} +1.57797e8 q^{71} -7.29267e7 q^{72} +3.62252e8 q^{73} +5.29903e7 q^{74} +1.58201e8 q^{75} +2.15420e8 q^{76} +2.73080e8 q^{77} +7.27724e7 q^{78} +1.14795e7 q^{79} -167489. q^{80} +4.30467e7 q^{81} -2.60482e7 q^{82} -4.93368e7 q^{83} -1.73960e8 q^{84} +1.75333e6 q^{85} +6.88973e7 q^{86} +5.98639e8 q^{87} +4.84757e8 q^{88} +8.84760e8 q^{89} -459210. q^{90} +4.32722e8 q^{91} +1.40167e8 q^{92} -5.55488e7 q^{93} -6.23191e8 q^{94} +3.38135e6 q^{95} -4.93729e8 q^{96} -7.61382e8 q^{97} -1.49048e7 q^{98} -2.86139e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.0004 0.574540 0.287270 0.957850i \(-0.407252\pi\)
0.287270 + 0.957850i \(0.407252\pi\)
\(3\) −81.0000 −0.577350
\(4\) −342.991 −0.669904
\(5\) −5.38377 −0.00385231 −0.00192615 0.999998i \(-0.500613\pi\)
−0.00192615 + 0.999998i \(0.500613\pi\)
\(6\) −1053.03 −0.331711
\(7\) −6261.56 −0.985692 −0.492846 0.870117i \(-0.664043\pi\)
−0.492846 + 0.870117i \(0.664043\pi\)
\(8\) −11115.2 −0.959427
\(9\) 6561.00 0.333333
\(10\) −69.9909 −0.00221331
\(11\) −43612.2 −0.898133 −0.449066 0.893498i \(-0.648243\pi\)
−0.449066 + 0.893498i \(0.648243\pi\)
\(12\) 27782.3 0.386769
\(13\) −69107.7 −0.671091 −0.335545 0.942024i \(-0.608921\pi\)
−0.335545 + 0.942024i \(0.608921\pi\)
\(14\) −81402.5 −0.566319
\(15\) 436.085 0.00222413
\(16\) 31109.9 0.118675
\(17\) −325669. −0.945707 −0.472853 0.881141i \(-0.656776\pi\)
−0.472853 + 0.881141i \(0.656776\pi\)
\(18\) 85295.3 0.191513
\(19\) −628064. −1.10564 −0.552819 0.833302i \(-0.686448\pi\)
−0.552819 + 0.833302i \(0.686448\pi\)
\(20\) 1846.58 0.00258068
\(21\) 507186. 0.569090
\(22\) −566974. −0.516013
\(23\) −408662. −0.304501 −0.152250 0.988342i \(-0.548652\pi\)
−0.152250 + 0.988342i \(0.548652\pi\)
\(24\) 900330. 0.553925
\(25\) −1.95310e6 −0.999985
\(26\) −898425. −0.385569
\(27\) −531441. −0.192450
\(28\) 2.14766e6 0.660319
\(29\) −7.39061e6 −1.94039 −0.970196 0.242323i \(-0.922091\pi\)
−0.970196 + 0.242323i \(0.922091\pi\)
\(30\) 5669.26 0.00127785
\(31\) 685788. 0.133371 0.0666856 0.997774i \(-0.478758\pi\)
0.0666856 + 0.997774i \(0.478758\pi\)
\(32\) 6.09541e6 1.02761
\(33\) 3.53259e6 0.518537
\(34\) −4.23382e6 −0.543346
\(35\) 33710.8 0.00379719
\(36\) −2.25036e6 −0.223301
\(37\) 4.07607e6 0.357547 0.178774 0.983890i \(-0.442787\pi\)
0.178774 + 0.983890i \(0.442787\pi\)
\(38\) −8.16506e6 −0.635233
\(39\) 5.59772e6 0.387455
\(40\) 59841.6 0.00369601
\(41\) −2.00366e6 −0.110738 −0.0553689 0.998466i \(-0.517633\pi\)
−0.0553689 + 0.998466i \(0.517633\pi\)
\(42\) 6.59360e6 0.326965
\(43\) 5.29965e6 0.236395 0.118198 0.992990i \(-0.462288\pi\)
0.118198 + 0.992990i \(0.462288\pi\)
\(44\) 1.49586e7 0.601663
\(45\) −35322.9 −0.00128410
\(46\) −5.31275e6 −0.174948
\(47\) −4.79365e7 −1.43293 −0.716467 0.697621i \(-0.754242\pi\)
−0.716467 + 0.697621i \(0.754242\pi\)
\(48\) −2.51990e6 −0.0685170
\(49\) −1.14649e6 −0.0284112
\(50\) −2.53909e7 −0.574531
\(51\) 2.63792e7 0.546004
\(52\) 2.37033e7 0.449566
\(53\) 2.75368e7 0.479372 0.239686 0.970850i \(-0.422956\pi\)
0.239686 + 0.970850i \(0.422956\pi\)
\(54\) −6.90892e6 −0.110570
\(55\) 234798. 0.00345989
\(56\) 6.95984e7 0.945699
\(57\) 5.08732e7 0.638340
\(58\) −9.60806e7 −1.11483
\(59\) 1.21174e7 0.130189
\(60\) −149573. −0.00148995
\(61\) −1.32205e8 −1.22254 −0.611271 0.791421i \(-0.709342\pi\)
−0.611271 + 0.791421i \(0.709342\pi\)
\(62\) 8.91549e6 0.0766271
\(63\) −4.10821e7 −0.328564
\(64\) 6.33143e7 0.471728
\(65\) 372060. 0.00258525
\(66\) 4.59249e7 0.297920
\(67\) −8.56509e7 −0.519272 −0.259636 0.965706i \(-0.583603\pi\)
−0.259636 + 0.965706i \(0.583603\pi\)
\(68\) 1.11702e8 0.633533
\(69\) 3.31016e7 0.175804
\(70\) 438252. 0.00218164
\(71\) 1.57797e8 0.736949 0.368475 0.929638i \(-0.379880\pi\)
0.368475 + 0.929638i \(0.379880\pi\)
\(72\) −7.29267e7 −0.319809
\(73\) 3.62252e8 1.49299 0.746497 0.665389i \(-0.231734\pi\)
0.746497 + 0.665389i \(0.231734\pi\)
\(74\) 5.29903e7 0.205425
\(75\) 1.58201e8 0.577342
\(76\) 2.15420e8 0.740671
\(77\) 2.73080e8 0.885282
\(78\) 7.27724e7 0.222608
\(79\) 1.14795e7 0.0331590 0.0165795 0.999863i \(-0.494722\pi\)
0.0165795 + 0.999863i \(0.494722\pi\)
\(80\) −167489. −0.000457172 0
\(81\) 4.30467e7 0.111111
\(82\) −2.60482e7 −0.0636233
\(83\) −4.93368e7 −0.114109 −0.0570545 0.998371i \(-0.518171\pi\)
−0.0570545 + 0.998371i \(0.518171\pi\)
\(84\) −1.73960e8 −0.381235
\(85\) 1.75333e6 0.00364316
\(86\) 6.88973e7 0.135819
\(87\) 5.98639e8 1.12029
\(88\) 4.84757e8 0.861692
\(89\) 8.84760e8 1.49476 0.747378 0.664399i \(-0.231312\pi\)
0.747378 + 0.664399i \(0.231312\pi\)
\(90\) −459210. −0.000737769 0
\(91\) 4.32722e8 0.661489
\(92\) 1.40167e8 0.203986
\(93\) −5.55488e7 −0.0770019
\(94\) −6.23191e8 −0.823277
\(95\) 3.38135e6 0.00425926
\(96\) −4.93729e8 −0.593291
\(97\) −7.61382e8 −0.873232 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(98\) −1.49048e7 −0.0163234
\(99\) −2.86139e8 −0.299378
\(100\) 6.69894e8 0.669894
\(101\) 9.88097e8 0.944830 0.472415 0.881376i \(-0.343382\pi\)
0.472415 + 0.881376i \(0.343382\pi\)
\(102\) 3.42939e8 0.313701
\(103\) −8.31308e8 −0.727770 −0.363885 0.931444i \(-0.618550\pi\)
−0.363885 + 0.931444i \(0.618550\pi\)
\(104\) 7.68145e8 0.643862
\(105\) −2.73057e6 −0.00219231
\(106\) 3.57989e8 0.275418
\(107\) −9.36999e8 −0.691054 −0.345527 0.938409i \(-0.612300\pi\)
−0.345527 + 0.938409i \(0.612300\pi\)
\(108\) 1.82279e8 0.128923
\(109\) −5.10879e8 −0.346656 −0.173328 0.984864i \(-0.555452\pi\)
−0.173328 + 0.984864i \(0.555452\pi\)
\(110\) 3.05245e6 0.00198784
\(111\) −3.30161e8 −0.206430
\(112\) −1.94797e8 −0.116977
\(113\) −4.27921e8 −0.246894 −0.123447 0.992351i \(-0.539395\pi\)
−0.123447 + 0.992351i \(0.539395\pi\)
\(114\) 6.61369e8 0.366752
\(115\) 2.20014e6 0.00117303
\(116\) 2.53491e9 1.29988
\(117\) −4.53416e8 −0.223697
\(118\) 1.57530e8 0.0747987
\(119\) 2.03920e9 0.932176
\(120\) −4.84717e6 −0.00213389
\(121\) −4.55927e8 −0.193357
\(122\) −1.71871e9 −0.702400
\(123\) 1.62296e8 0.0639345
\(124\) −2.35219e8 −0.0893459
\(125\) 2.10302e7 0.00770456
\(126\) −5.34082e8 −0.188773
\(127\) 2.84159e9 0.969270 0.484635 0.874716i \(-0.338952\pi\)
0.484635 + 0.874716i \(0.338952\pi\)
\(128\) −2.29774e9 −0.756583
\(129\) −4.29271e8 −0.136483
\(130\) 4.83691e6 0.00148533
\(131\) 2.87084e9 0.851704 0.425852 0.904793i \(-0.359974\pi\)
0.425852 + 0.904793i \(0.359974\pi\)
\(132\) −1.21164e9 −0.347370
\(133\) 3.93266e9 1.08982
\(134\) −1.11349e9 −0.298343
\(135\) 2.86115e6 0.000741377 0
\(136\) 3.61987e9 0.907336
\(137\) −2.90047e9 −0.703438 −0.351719 0.936106i \(-0.614403\pi\)
−0.351719 + 0.936106i \(0.614403\pi\)
\(138\) 4.30332e8 0.101006
\(139\) −1.76889e9 −0.401916 −0.200958 0.979600i \(-0.564405\pi\)
−0.200958 + 0.979600i \(0.564405\pi\)
\(140\) −1.15625e7 −0.00254375
\(141\) 3.88286e9 0.827304
\(142\) 2.05142e9 0.423407
\(143\) 3.01394e9 0.602729
\(144\) 2.04112e8 0.0395583
\(145\) 3.97893e7 0.00747499
\(146\) 4.70940e9 0.857784
\(147\) 9.28660e7 0.0164032
\(148\) −1.39805e9 −0.239522
\(149\) −3.34952e9 −0.556730 −0.278365 0.960475i \(-0.589793\pi\)
−0.278365 + 0.960475i \(0.589793\pi\)
\(150\) 2.05667e9 0.331706
\(151\) 4.36665e9 0.683521 0.341760 0.939787i \(-0.388977\pi\)
0.341760 + 0.939787i \(0.388977\pi\)
\(152\) 6.98105e9 1.06078
\(153\) −2.13672e9 −0.315236
\(154\) 3.55014e9 0.508630
\(155\) −3.69212e6 −0.000513787 0
\(156\) −1.91997e9 −0.259557
\(157\) −6.73348e9 −0.884486 −0.442243 0.896895i \(-0.645817\pi\)
−0.442243 + 0.896895i \(0.645817\pi\)
\(158\) 1.49238e8 0.0190512
\(159\) −2.23048e9 −0.276766
\(160\) −3.28163e7 −0.00395867
\(161\) 2.55886e9 0.300144
\(162\) 5.59623e8 0.0638378
\(163\) −9.26677e9 −1.02822 −0.514108 0.857726i \(-0.671877\pi\)
−0.514108 + 0.857726i \(0.671877\pi\)
\(164\) 6.87235e8 0.0741837
\(165\) −1.90186e7 −0.00199757
\(166\) −6.41396e8 −0.0655602
\(167\) 1.00723e10 1.00209 0.501043 0.865422i \(-0.332950\pi\)
0.501043 + 0.865422i \(0.332950\pi\)
\(168\) −5.63747e9 −0.546000
\(169\) −5.82862e9 −0.549637
\(170\) 2.27939e7 0.00209314
\(171\) −4.12073e9 −0.368546
\(172\) −1.81773e9 −0.158362
\(173\) 1.80552e9 0.153248 0.0766240 0.997060i \(-0.475586\pi\)
0.0766240 + 0.997060i \(0.475586\pi\)
\(174\) 7.78253e9 0.643649
\(175\) 1.22294e10 0.985677
\(176\) −1.35677e9 −0.106586
\(177\) −9.81506e8 −0.0751646
\(178\) 1.15022e10 0.858797
\(179\) −2.22042e9 −0.161658 −0.0808289 0.996728i \(-0.525757\pi\)
−0.0808289 + 0.996728i \(0.525757\pi\)
\(180\) 1.21154e7 0.000860226 0
\(181\) −3.48123e8 −0.0241090 −0.0120545 0.999927i \(-0.503837\pi\)
−0.0120545 + 0.999927i \(0.503837\pi\)
\(182\) 5.62554e9 0.380052
\(183\) 1.07086e10 0.705835
\(184\) 4.54235e9 0.292146
\(185\) −2.19446e7 −0.00137738
\(186\) −7.22155e8 −0.0442407
\(187\) 1.42031e10 0.849370
\(188\) 1.64418e10 0.959927
\(189\) 3.32765e9 0.189697
\(190\) 4.39587e7 0.00244711
\(191\) −1.65843e10 −0.901671 −0.450835 0.892607i \(-0.648874\pi\)
−0.450835 + 0.892607i \(0.648874\pi\)
\(192\) −5.12846e9 −0.272352
\(193\) 3.25642e9 0.168940 0.0844701 0.996426i \(-0.473080\pi\)
0.0844701 + 0.996426i \(0.473080\pi\)
\(194\) −9.89824e9 −0.501707
\(195\) −3.01368e7 −0.00149259
\(196\) 3.93237e8 0.0190328
\(197\) 9.55814e8 0.0452143 0.0226071 0.999744i \(-0.492803\pi\)
0.0226071 + 0.999744i \(0.492803\pi\)
\(198\) −3.71991e9 −0.172004
\(199\) −2.28494e10 −1.03285 −0.516423 0.856333i \(-0.672737\pi\)
−0.516423 + 0.856333i \(0.672737\pi\)
\(200\) 2.17090e10 0.959412
\(201\) 6.93772e9 0.299802
\(202\) 1.28456e10 0.542842
\(203\) 4.62767e10 1.91263
\(204\) −9.04782e9 −0.365770
\(205\) 1.07872e7 0.000426596 0
\(206\) −1.08073e10 −0.418133
\(207\) −2.68123e9 −0.101500
\(208\) −2.14993e9 −0.0796417
\(209\) 2.73912e10 0.993009
\(210\) −3.54984e7 −0.00125957
\(211\) 2.10406e10 0.730781 0.365390 0.930854i \(-0.380936\pi\)
0.365390 + 0.930854i \(0.380936\pi\)
\(212\) −9.44488e9 −0.321133
\(213\) −1.27816e10 −0.425478
\(214\) −1.21813e10 −0.397038
\(215\) −2.85321e7 −0.000910668 0
\(216\) 5.90706e9 0.184642
\(217\) −4.29410e9 −0.131463
\(218\) −6.64161e9 −0.199168
\(219\) −2.93424e10 −0.861980
\(220\) −8.05334e7 −0.00231779
\(221\) 2.25063e10 0.634655
\(222\) −4.29222e9 −0.118602
\(223\) −2.84613e10 −0.770696 −0.385348 0.922771i \(-0.625919\pi\)
−0.385348 + 0.922771i \(0.625919\pi\)
\(224\) −3.81668e10 −1.01291
\(225\) −1.28143e10 −0.333328
\(226\) −5.56313e9 −0.141851
\(227\) −2.93030e10 −0.732479 −0.366240 0.930521i \(-0.619355\pi\)
−0.366240 + 0.930521i \(0.619355\pi\)
\(228\) −1.74490e10 −0.427626
\(229\) 2.53540e10 0.609238 0.304619 0.952474i \(-0.401471\pi\)
0.304619 + 0.952474i \(0.401471\pi\)
\(230\) 2.86026e7 0.000673954 0
\(231\) −2.21195e10 −0.511118
\(232\) 8.21480e10 1.86166
\(233\) −5.06606e10 −1.12608 −0.563039 0.826430i \(-0.690368\pi\)
−0.563039 + 0.826430i \(0.690368\pi\)
\(234\) −5.89457e9 −0.128523
\(235\) 2.58079e8 0.00552010
\(236\) −4.15614e9 −0.0872140
\(237\) −9.29840e8 −0.0191444
\(238\) 2.65103e10 0.535572
\(239\) 2.41312e10 0.478397 0.239198 0.970971i \(-0.423115\pi\)
0.239198 + 0.970971i \(0.423115\pi\)
\(240\) 1.35666e7 0.000263949 0
\(241\) −5.41759e10 −1.03450 −0.517249 0.855835i \(-0.673044\pi\)
−0.517249 + 0.855835i \(0.673044\pi\)
\(242\) −5.92721e9 −0.111092
\(243\) −3.48678e9 −0.0641500
\(244\) 4.53451e10 0.818986
\(245\) 6.17246e6 0.000109449 0
\(246\) 2.10991e9 0.0367329
\(247\) 4.34041e10 0.741983
\(248\) −7.62266e9 −0.127960
\(249\) 3.99628e9 0.0658808
\(250\) 2.73400e8 0.00442658
\(251\) −2.51631e10 −0.400158 −0.200079 0.979780i \(-0.564120\pi\)
−0.200079 + 0.979780i \(0.564120\pi\)
\(252\) 1.40908e10 0.220106
\(253\) 1.78226e10 0.273482
\(254\) 3.69417e10 0.556884
\(255\) −1.42019e8 −0.00210338
\(256\) −6.22884e10 −0.906415
\(257\) −9.81242e10 −1.40306 −0.701531 0.712639i \(-0.747500\pi\)
−0.701531 + 0.712639i \(0.747500\pi\)
\(258\) −5.58068e9 −0.0784149
\(259\) −2.55225e10 −0.352432
\(260\) −1.27613e8 −0.00173187
\(261\) −4.84898e10 −0.646797
\(262\) 3.73220e10 0.489338
\(263\) 6.22591e10 0.802420 0.401210 0.915986i \(-0.368590\pi\)
0.401210 + 0.915986i \(0.368590\pi\)
\(264\) −3.92653e10 −0.497498
\(265\) −1.48252e8 −0.00184669
\(266\) 5.11260e10 0.626144
\(267\) −7.16655e10 −0.862998
\(268\) 2.93775e10 0.347863
\(269\) −8.07261e10 −0.940002 −0.470001 0.882666i \(-0.655746\pi\)
−0.470001 + 0.882666i \(0.655746\pi\)
\(270\) 3.71960e7 0.000425951 0
\(271\) −1.34610e11 −1.51605 −0.758026 0.652224i \(-0.773836\pi\)
−0.758026 + 0.652224i \(0.773836\pi\)
\(272\) −1.01315e10 −0.112232
\(273\) −3.50505e10 −0.381911
\(274\) −3.77072e10 −0.404153
\(275\) 8.51787e10 0.898119
\(276\) −1.13535e10 −0.117772
\(277\) −1.24234e11 −1.26789 −0.633944 0.773379i \(-0.718565\pi\)
−0.633944 + 0.773379i \(0.718565\pi\)
\(278\) −2.29962e10 −0.230917
\(279\) 4.49946e9 0.0444571
\(280\) −3.74701e8 −0.00364313
\(281\) −9.46201e10 −0.905326 −0.452663 0.891682i \(-0.649526\pi\)
−0.452663 + 0.891682i \(0.649526\pi\)
\(282\) 5.04785e10 0.475319
\(283\) −5.75537e10 −0.533377 −0.266689 0.963783i \(-0.585930\pi\)
−0.266689 + 0.963783i \(0.585930\pi\)
\(284\) −5.41231e10 −0.493685
\(285\) −2.73889e8 −0.00245908
\(286\) 3.91823e10 0.346292
\(287\) 1.25460e10 0.109153
\(288\) 3.99920e10 0.342537
\(289\) −1.25275e10 −0.105639
\(290\) 5.17275e8 0.00429468
\(291\) 6.16719e10 0.504161
\(292\) −1.24249e11 −1.00016
\(293\) −2.37210e11 −1.88030 −0.940152 0.340754i \(-0.889318\pi\)
−0.940152 + 0.340754i \(0.889318\pi\)
\(294\) 1.20729e9 0.00942430
\(295\) −6.52370e7 −0.000501528 0
\(296\) −4.53062e10 −0.343040
\(297\) 2.31773e10 0.172846
\(298\) −4.35450e10 −0.319864
\(299\) 2.82417e10 0.204348
\(300\) −5.42614e10 −0.386763
\(301\) −3.31840e10 −0.233013
\(302\) 5.67680e10 0.392710
\(303\) −8.00359e10 −0.545498
\(304\) −1.95390e10 −0.131211
\(305\) 7.11762e8 0.00470961
\(306\) −2.77781e10 −0.181115
\(307\) −8.86156e10 −0.569360 −0.284680 0.958623i \(-0.591887\pi\)
−0.284680 + 0.958623i \(0.591887\pi\)
\(308\) −9.36640e10 −0.593054
\(309\) 6.73359e10 0.420178
\(310\) −4.79989e7 −0.000295191 0
\(311\) −1.52131e11 −0.922137 −0.461068 0.887365i \(-0.652534\pi\)
−0.461068 + 0.887365i \(0.652534\pi\)
\(312\) −6.22197e10 −0.371734
\(313\) 2.58244e11 1.52083 0.760415 0.649438i \(-0.224996\pi\)
0.760415 + 0.649438i \(0.224996\pi\)
\(314\) −8.75376e10 −0.508172
\(315\) 2.21176e8 0.00126573
\(316\) −3.93736e9 −0.0222133
\(317\) −3.16618e11 −1.76104 −0.880521 0.474008i \(-0.842807\pi\)
−0.880521 + 0.474008i \(0.842807\pi\)
\(318\) −2.89971e10 −0.159013
\(319\) 3.22321e11 1.74273
\(320\) −3.40869e8 −0.00181724
\(321\) 7.58969e10 0.398980
\(322\) 3.32661e10 0.172445
\(323\) 2.04541e11 1.04561
\(324\) −1.47646e10 −0.0744338
\(325\) 1.34974e11 0.671081
\(326\) −1.20471e11 −0.590751
\(327\) 4.13812e10 0.200142
\(328\) 2.22710e10 0.106245
\(329\) 3.00157e11 1.41243
\(330\) −2.47249e8 −0.00114768
\(331\) 1.66007e11 0.760153 0.380077 0.924955i \(-0.375898\pi\)
0.380077 + 0.924955i \(0.375898\pi\)
\(332\) 1.69221e10 0.0764420
\(333\) 2.67431e10 0.119182
\(334\) 1.30944e11 0.575739
\(335\) 4.61124e8 0.00200040
\(336\) 1.57785e10 0.0675367
\(337\) −3.96343e11 −1.67393 −0.836963 0.547259i \(-0.815671\pi\)
−0.836963 + 0.547259i \(0.815671\pi\)
\(338\) −7.57742e10 −0.315788
\(339\) 3.46616e10 0.142544
\(340\) −6.01375e8 −0.00244056
\(341\) −2.99087e10 −0.119785
\(342\) −5.35709e10 −0.211744
\(343\) 2.59855e11 1.01370
\(344\) −5.89066e10 −0.226804
\(345\) −1.78211e8 −0.000677250 0
\(346\) 2.34724e10 0.0880472
\(347\) 2.17182e11 0.804158 0.402079 0.915605i \(-0.368288\pi\)
0.402079 + 0.915605i \(0.368288\pi\)
\(348\) −2.05328e11 −0.750484
\(349\) −2.10061e11 −0.757933 −0.378966 0.925410i \(-0.623720\pi\)
−0.378966 + 0.925410i \(0.623720\pi\)
\(350\) 1.58987e11 0.566311
\(351\) 3.67267e10 0.129152
\(352\) −2.65834e11 −0.922930
\(353\) 6.15837e10 0.211096 0.105548 0.994414i \(-0.466340\pi\)
0.105548 + 0.994414i \(0.466340\pi\)
\(354\) −1.27599e10 −0.0431851
\(355\) −8.49545e8 −0.00283896
\(356\) −3.03464e11 −1.00134
\(357\) −1.65175e11 −0.538192
\(358\) −2.88663e10 −0.0928789
\(359\) 2.41244e11 0.766535 0.383268 0.923637i \(-0.374799\pi\)
0.383268 + 0.923637i \(0.374799\pi\)
\(360\) 3.92620e8 0.00123200
\(361\) 7.17766e10 0.222434
\(362\) −4.52572e9 −0.0138516
\(363\) 3.69301e10 0.111635
\(364\) −1.48420e11 −0.443134
\(365\) −1.95028e9 −0.00575147
\(366\) 1.39216e11 0.405531
\(367\) 4.54037e11 1.30645 0.653227 0.757162i \(-0.273415\pi\)
0.653227 + 0.757162i \(0.273415\pi\)
\(368\) −1.27134e10 −0.0361366
\(369\) −1.31460e10 −0.0369126
\(370\) −2.85288e8 −0.000791362 0
\(371\) −1.72424e11 −0.472513
\(372\) 1.90527e10 0.0515839
\(373\) 3.76935e11 1.00827 0.504134 0.863625i \(-0.331812\pi\)
0.504134 + 0.863625i \(0.331812\pi\)
\(374\) 1.84646e11 0.487997
\(375\) −1.70344e9 −0.00444823
\(376\) 5.32823e11 1.37479
\(377\) 5.10748e11 1.30218
\(378\) 4.32606e10 0.108988
\(379\) 5.70349e11 1.41992 0.709961 0.704241i \(-0.248712\pi\)
0.709961 + 0.704241i \(0.248712\pi\)
\(380\) −1.15977e9 −0.00285329
\(381\) −2.30169e11 −0.559608
\(382\) −2.15602e11 −0.518046
\(383\) 1.35501e11 0.321772 0.160886 0.986973i \(-0.448565\pi\)
0.160886 + 0.986973i \(0.448565\pi\)
\(384\) 1.86117e11 0.436814
\(385\) −1.47020e9 −0.00341038
\(386\) 4.23347e10 0.0970629
\(387\) 3.47710e10 0.0787984
\(388\) 2.61147e11 0.584982
\(389\) 2.72102e11 0.602503 0.301251 0.953545i \(-0.402596\pi\)
0.301251 + 0.953545i \(0.402596\pi\)
\(390\) −3.91790e8 −0.000857555 0
\(391\) 1.33088e11 0.287969
\(392\) 1.27435e10 0.0272584
\(393\) −2.32538e11 −0.491731
\(394\) 1.24259e10 0.0259774
\(395\) −6.18030e7 −0.000127739 0
\(396\) 9.81432e10 0.200554
\(397\) 3.58106e11 0.723526 0.361763 0.932270i \(-0.382175\pi\)
0.361763 + 0.932270i \(0.382175\pi\)
\(398\) −2.97050e11 −0.593412
\(399\) −3.18545e11 −0.629207
\(400\) −6.07607e10 −0.118673
\(401\) −6.62237e11 −1.27898 −0.639490 0.768799i \(-0.720854\pi\)
−0.639490 + 0.768799i \(0.720854\pi\)
\(402\) 9.01929e10 0.172248
\(403\) −4.73932e10 −0.0895043
\(404\) −3.38908e11 −0.632945
\(405\) −2.31753e8 −0.000428034 0
\(406\) 6.01614e11 1.09888
\(407\) −1.77766e11 −0.321125
\(408\) −2.93210e11 −0.523851
\(409\) 3.42205e11 0.604688 0.302344 0.953199i \(-0.402231\pi\)
0.302344 + 0.953199i \(0.402231\pi\)
\(410\) 1.40238e8 0.000245097 0
\(411\) 2.34938e11 0.406130
\(412\) 2.85131e11 0.487536
\(413\) −7.58736e10 −0.128326
\(414\) −3.48569e10 −0.0583160
\(415\) 2.65618e8 0.000439583 0
\(416\) −4.21240e11 −0.689620
\(417\) 1.43280e11 0.232046
\(418\) 3.56096e11 0.570523
\(419\) −9.70797e11 −1.53874 −0.769370 0.638803i \(-0.779430\pi\)
−0.769370 + 0.638803i \(0.779430\pi\)
\(420\) 9.36561e8 0.00146864
\(421\) 2.64923e11 0.411008 0.205504 0.978656i \(-0.434117\pi\)
0.205504 + 0.978656i \(0.434117\pi\)
\(422\) 2.73535e11 0.419863
\(423\) −3.14511e11 −0.477644
\(424\) −3.06077e11 −0.459922
\(425\) 6.36063e11 0.945693
\(426\) −1.66165e11 −0.244454
\(427\) 8.27810e11 1.20505
\(428\) 3.21382e11 0.462940
\(429\) −2.44129e11 −0.347986
\(430\) −3.70927e8 −0.000523215 0
\(431\) −5.88050e11 −0.820855 −0.410427 0.911893i \(-0.634620\pi\)
−0.410427 + 0.911893i \(0.634620\pi\)
\(432\) −1.65331e10 −0.0228390
\(433\) 1.45666e12 1.99142 0.995711 0.0925180i \(-0.0294916\pi\)
0.995711 + 0.0925180i \(0.0294916\pi\)
\(434\) −5.58249e10 −0.0755308
\(435\) −3.22294e9 −0.00431569
\(436\) 1.75227e11 0.232226
\(437\) 2.56666e11 0.336668
\(438\) −3.81462e11 −0.495242
\(439\) 6.78683e11 0.872121 0.436060 0.899917i \(-0.356373\pi\)
0.436060 + 0.899917i \(0.356373\pi\)
\(440\) −2.60982e9 −0.00331951
\(441\) −7.52215e9 −0.00947040
\(442\) 2.92589e11 0.364635
\(443\) −9.72292e11 −1.19944 −0.599722 0.800208i \(-0.704722\pi\)
−0.599722 + 0.800208i \(0.704722\pi\)
\(444\) 1.13242e11 0.138288
\(445\) −4.76334e9 −0.00575826
\(446\) −3.70007e11 −0.442795
\(447\) 2.71311e11 0.321428
\(448\) −3.96446e11 −0.464979
\(449\) 5.40504e11 0.627611 0.313806 0.949487i \(-0.398396\pi\)
0.313806 + 0.949487i \(0.398396\pi\)
\(450\) −1.66590e11 −0.191510
\(451\) 8.73838e10 0.0994572
\(452\) 1.46773e11 0.165395
\(453\) −3.53698e11 −0.394631
\(454\) −3.80949e11 −0.420839
\(455\) −2.32967e9 −0.00254826
\(456\) −5.65465e11 −0.612440
\(457\) 1.70451e12 1.82801 0.914003 0.405708i \(-0.132975\pi\)
0.914003 + 0.405708i \(0.132975\pi\)
\(458\) 3.29611e11 0.350032
\(459\) 1.73074e11 0.182001
\(460\) −7.54627e8 −0.000785818 0
\(461\) −9.89439e11 −1.02032 −0.510158 0.860081i \(-0.670413\pi\)
−0.510158 + 0.860081i \(0.670413\pi\)
\(462\) −2.87561e11 −0.293658
\(463\) −4.94694e11 −0.500290 −0.250145 0.968208i \(-0.580478\pi\)
−0.250145 + 0.968208i \(0.580478\pi\)
\(464\) −2.29921e11 −0.230276
\(465\) 2.99062e8 0.000296635 0
\(466\) −6.58606e11 −0.646977
\(467\) 8.03745e11 0.781974 0.390987 0.920396i \(-0.372134\pi\)
0.390987 + 0.920396i \(0.372134\pi\)
\(468\) 1.55517e11 0.149855
\(469\) 5.36308e11 0.511843
\(470\) 3.35512e9 0.00317152
\(471\) 5.45412e11 0.510658
\(472\) −1.34687e11 −0.124907
\(473\) −2.31129e11 −0.212314
\(474\) −1.20883e10 −0.0109992
\(475\) 1.22667e12 1.10562
\(476\) −6.99426e11 −0.624468
\(477\) 1.80669e11 0.159791
\(478\) 3.13714e11 0.274858
\(479\) −1.44136e12 −1.25101 −0.625507 0.780219i \(-0.715108\pi\)
−0.625507 + 0.780219i \(0.715108\pi\)
\(480\) 2.65812e9 0.00228554
\(481\) −2.81688e11 −0.239947
\(482\) −7.04306e11 −0.594360
\(483\) −2.07268e11 −0.173288
\(484\) 1.56379e11 0.129531
\(485\) 4.09910e9 0.00336396
\(486\) −4.53294e10 −0.0368568
\(487\) 3.24854e10 0.0261703 0.0130851 0.999914i \(-0.495835\pi\)
0.0130851 + 0.999914i \(0.495835\pi\)
\(488\) 1.46948e12 1.17294
\(489\) 7.50608e11 0.593640
\(490\) 8.02441e7 6.28827e−5 0
\(491\) −1.66719e12 −1.29455 −0.647276 0.762256i \(-0.724092\pi\)
−0.647276 + 0.762256i \(0.724092\pi\)
\(492\) −5.56661e10 −0.0428300
\(493\) 2.40689e12 1.83504
\(494\) 5.64268e11 0.426299
\(495\) 1.54051e9 0.00115330
\(496\) 2.13348e10 0.0158278
\(497\) −9.88058e11 −0.726405
\(498\) 5.19531e10 0.0378512
\(499\) 2.24713e12 1.62247 0.811235 0.584720i \(-0.198796\pi\)
0.811235 + 0.584720i \(0.198796\pi\)
\(500\) −7.21316e9 −0.00516132
\(501\) −8.15858e11 −0.578555
\(502\) −3.27129e11 −0.229907
\(503\) 7.88688e11 0.549350 0.274675 0.961537i \(-0.411430\pi\)
0.274675 + 0.961537i \(0.411430\pi\)
\(504\) 4.56635e11 0.315233
\(505\) −5.31969e9 −0.00363978
\(506\) 2.31700e11 0.157126
\(507\) 4.72119e11 0.317333
\(508\) −9.74639e11 −0.649318
\(509\) 8.56844e11 0.565811 0.282906 0.959148i \(-0.408702\pi\)
0.282906 + 0.959148i \(0.408702\pi\)
\(510\) −1.84630e9 −0.00120847
\(511\) −2.26826e12 −1.47163
\(512\) 3.66674e11 0.235811
\(513\) 3.33779e11 0.212780
\(514\) −1.27565e12 −0.806115
\(515\) 4.47557e9 0.00280360
\(516\) 1.47236e11 0.0914304
\(517\) 2.09061e12 1.28696
\(518\) −3.31802e11 −0.202486
\(519\) −1.46247e11 −0.0884778
\(520\) −4.13551e9 −0.00248036
\(521\) 5.21995e10 0.0310382 0.0155191 0.999880i \(-0.495060\pi\)
0.0155191 + 0.999880i \(0.495060\pi\)
\(522\) −6.30385e11 −0.371611
\(523\) −1.08408e12 −0.633585 −0.316793 0.948495i \(-0.602606\pi\)
−0.316793 + 0.948495i \(0.602606\pi\)
\(524\) −9.84673e11 −0.570560
\(525\) −9.90583e11 −0.569081
\(526\) 8.09390e11 0.461022
\(527\) −2.23340e11 −0.126130
\(528\) 1.09898e11 0.0615374
\(529\) −1.63415e12 −0.907279
\(530\) −1.92733e9 −0.00106100
\(531\) 7.95020e10 0.0433963
\(532\) −1.34887e12 −0.730073
\(533\) 1.38468e11 0.0743151
\(534\) −9.31677e11 −0.495827
\(535\) 5.04458e9 0.00266216
\(536\) 9.52025e11 0.498204
\(537\) 1.79854e11 0.0933332
\(538\) −1.04947e12 −0.540069
\(539\) 5.00011e10 0.0255170
\(540\) −9.81349e8 −0.000496651 0
\(541\) −1.26617e12 −0.635482 −0.317741 0.948178i \(-0.602924\pi\)
−0.317741 + 0.948178i \(0.602924\pi\)
\(542\) −1.74997e12 −0.871033
\(543\) 2.81979e10 0.0139193
\(544\) −1.98509e12 −0.971818
\(545\) 2.75045e9 0.00133543
\(546\) −4.55669e11 −0.219423
\(547\) 1.17605e12 0.561673 0.280836 0.959756i \(-0.409388\pi\)
0.280836 + 0.959756i \(0.409388\pi\)
\(548\) 9.94835e11 0.471236
\(549\) −8.67398e11 −0.407514
\(550\) 1.10735e12 0.516006
\(551\) 4.64178e12 2.14537
\(552\) −3.67930e11 −0.168671
\(553\) −7.18796e10 −0.0326846
\(554\) −1.61508e12 −0.728452
\(555\) 1.77751e9 0.000795233 0
\(556\) 6.06714e11 0.269245
\(557\) −1.12035e12 −0.493178 −0.246589 0.969120i \(-0.579310\pi\)
−0.246589 + 0.969120i \(0.579310\pi\)
\(558\) 5.84945e10 0.0255424
\(559\) −3.66246e11 −0.158643
\(560\) 1.04874e9 0.000450631 0
\(561\) −1.15045e12 −0.490384
\(562\) −1.23010e12 −0.520146
\(563\) 1.73855e12 0.729290 0.364645 0.931147i \(-0.381190\pi\)
0.364645 + 0.931147i \(0.381190\pi\)
\(564\) −1.33178e12 −0.554214
\(565\) 2.30383e9 0.000951113 0
\(566\) −7.48219e11 −0.306447
\(567\) −2.69540e11 −0.109521
\(568\) −1.75395e12 −0.707048
\(569\) −1.86209e11 −0.0744723 −0.0372361 0.999306i \(-0.511855\pi\)
−0.0372361 + 0.999306i \(0.511855\pi\)
\(570\) −3.56066e9 −0.00141284
\(571\) 1.86548e12 0.734391 0.367195 0.930144i \(-0.380318\pi\)
0.367195 + 0.930144i \(0.380318\pi\)
\(572\) −1.03375e12 −0.403770
\(573\) 1.34333e12 0.520580
\(574\) 1.63103e11 0.0627130
\(575\) 7.98155e11 0.304496
\(576\) 4.15405e11 0.157243
\(577\) −4.30621e12 −1.61735 −0.808675 0.588256i \(-0.799815\pi\)
−0.808675 + 0.588256i \(0.799815\pi\)
\(578\) −1.62861e11 −0.0606936
\(579\) −2.63770e11 −0.0975376
\(580\) −1.36474e10 −0.00500752
\(581\) 3.08925e11 0.112476
\(582\) 8.01757e11 0.289661
\(583\) −1.20094e12 −0.430540
\(584\) −4.02650e12 −1.43242
\(585\) 2.44108e9 0.000861750 0
\(586\) −3.08381e12 −1.08031
\(587\) 2.77522e12 0.964775 0.482387 0.875958i \(-0.339770\pi\)
0.482387 + 0.875958i \(0.339770\pi\)
\(588\) −3.18522e10 −0.0109886
\(589\) −4.30719e11 −0.147460
\(590\) −8.48105e8 −0.000288148 0
\(591\) −7.74209e10 −0.0261045
\(592\) 1.26806e11 0.0424319
\(593\) −2.32710e11 −0.0772802 −0.0386401 0.999253i \(-0.512303\pi\)
−0.0386401 + 0.999253i \(0.512303\pi\)
\(594\) 3.01313e11 0.0993068
\(595\) −1.09786e10 −0.00359103
\(596\) 1.14886e12 0.372956
\(597\) 1.85080e12 0.596314
\(598\) 3.67152e11 0.117406
\(599\) −3.06957e12 −0.974220 −0.487110 0.873341i \(-0.661949\pi\)
−0.487110 + 0.873341i \(0.661949\pi\)
\(600\) −1.75843e12 −0.553917
\(601\) 4.30421e12 1.34573 0.672866 0.739764i \(-0.265063\pi\)
0.672866 + 0.739764i \(0.265063\pi\)
\(602\) −4.31404e11 −0.133875
\(603\) −5.61956e11 −0.173091
\(604\) −1.49772e12 −0.457893
\(605\) 2.45460e9 0.000744873 0
\(606\) −1.04049e12 −0.313410
\(607\) −1.31155e12 −0.392134 −0.196067 0.980590i \(-0.562817\pi\)
−0.196067 + 0.980590i \(0.562817\pi\)
\(608\) −3.82831e12 −1.13616
\(609\) −3.74842e12 −1.10426
\(610\) 9.25315e9 0.00270586
\(611\) 3.31278e12 0.961628
\(612\) 7.32874e11 0.211178
\(613\) −5.03412e12 −1.43996 −0.719982 0.693993i \(-0.755850\pi\)
−0.719982 + 0.693993i \(0.755850\pi\)
\(614\) −1.15203e12 −0.327120
\(615\) −8.73765e8 −0.000246295 0
\(616\) −3.03534e12 −0.849363
\(617\) −1.09480e11 −0.0304125 −0.0152062 0.999884i \(-0.504840\pi\)
−0.0152062 + 0.999884i \(0.504840\pi\)
\(618\) 8.75391e11 0.241409
\(619\) 4.84630e12 1.32679 0.663395 0.748270i \(-0.269115\pi\)
0.663395 + 0.748270i \(0.269115\pi\)
\(620\) 1.26636e9 0.000344188 0
\(621\) 2.17180e11 0.0586012
\(622\) −1.97775e12 −0.529805
\(623\) −5.53997e12 −1.47337
\(624\) 1.74145e11 0.0459811
\(625\) 3.81453e12 0.999955
\(626\) 3.35726e12 0.873777
\(627\) −2.21869e12 −0.573314
\(628\) 2.30952e12 0.592520
\(629\) −1.32745e12 −0.338135
\(630\) 2.87537e9 0.000727213 0
\(631\) 4.13465e12 1.03826 0.519130 0.854695i \(-0.326256\pi\)
0.519130 + 0.854695i \(0.326256\pi\)
\(632\) −1.27597e11 −0.0318136
\(633\) −1.70429e12 −0.421916
\(634\) −4.11615e12 −1.01179
\(635\) −1.52985e10 −0.00373393
\(636\) 7.65035e11 0.185406
\(637\) 7.92316e10 0.0190665
\(638\) 4.19028e12 1.00127
\(639\) 1.03531e12 0.245650
\(640\) 1.23705e10 0.00291459
\(641\) 4.53660e12 1.06138 0.530688 0.847567i \(-0.321934\pi\)
0.530688 + 0.847567i \(0.321934\pi\)
\(642\) 9.86687e11 0.229230
\(643\) 6.06625e11 0.139949 0.0699747 0.997549i \(-0.477708\pi\)
0.0699747 + 0.997549i \(0.477708\pi\)
\(644\) −8.77665e11 −0.201068
\(645\) 2.31110e9 0.000525774 0
\(646\) 2.65911e12 0.600744
\(647\) 1.16298e12 0.260917 0.130459 0.991454i \(-0.458355\pi\)
0.130459 + 0.991454i \(0.458355\pi\)
\(648\) −4.78472e11 −0.106603
\(649\) −5.28464e11 −0.116927
\(650\) 1.75471e12 0.385563
\(651\) 3.47822e11 0.0759002
\(652\) 3.17842e12 0.688805
\(653\) −2.30996e12 −0.497159 −0.248579 0.968612i \(-0.579964\pi\)
−0.248579 + 0.968612i \(0.579964\pi\)
\(654\) 5.37971e11 0.114990
\(655\) −1.54559e10 −0.00328103
\(656\) −6.23336e10 −0.0131418
\(657\) 2.37674e12 0.497664
\(658\) 3.90215e12 0.811498
\(659\) −1.47955e12 −0.305594 −0.152797 0.988258i \(-0.548828\pi\)
−0.152797 + 0.988258i \(0.548828\pi\)
\(660\) 6.52321e9 0.00133818
\(661\) −7.87237e12 −1.60398 −0.801990 0.597337i \(-0.796225\pi\)
−0.801990 + 0.597337i \(0.796225\pi\)
\(662\) 2.15815e12 0.436738
\(663\) −1.82301e12 −0.366418
\(664\) 5.48388e11 0.109479
\(665\) −2.11725e10 −0.00419832
\(666\) 3.47670e11 0.0684751
\(667\) 3.02026e12 0.590851
\(668\) −3.45471e12 −0.671302
\(669\) 2.30537e12 0.444961
\(670\) 5.99478e9 0.00114931
\(671\) 5.76575e12 1.09801
\(672\) 3.09151e12 0.584802
\(673\) 3.54705e12 0.666499 0.333249 0.942839i \(-0.391855\pi\)
0.333249 + 0.942839i \(0.391855\pi\)
\(674\) −5.15260e12 −0.961738
\(675\) 1.03796e12 0.192447
\(676\) 1.99916e12 0.368204
\(677\) 7.97527e11 0.145914 0.0729569 0.997335i \(-0.476756\pi\)
0.0729569 + 0.997335i \(0.476756\pi\)
\(678\) 4.50613e11 0.0818975
\(679\) 4.76744e12 0.860738
\(680\) −1.94885e10 −0.00349534
\(681\) 2.37354e12 0.422897
\(682\) −3.88824e11 −0.0688213
\(683\) −4.33649e12 −0.762509 −0.381254 0.924470i \(-0.624508\pi\)
−0.381254 + 0.924470i \(0.624508\pi\)
\(684\) 1.41337e12 0.246890
\(685\) 1.56155e10 0.00270986
\(686\) 3.37821e12 0.582409
\(687\) −2.05368e12 −0.351744
\(688\) 1.64872e11 0.0280542
\(689\) −1.90301e12 −0.321702
\(690\) −2.31681e9 −0.000389107 0
\(691\) −1.10521e13 −1.84414 −0.922070 0.387023i \(-0.873503\pi\)
−0.922070 + 0.387023i \(0.873503\pi\)
\(692\) −6.19277e11 −0.102661
\(693\) 1.79168e12 0.295094
\(694\) 2.82344e12 0.462021
\(695\) 9.52330e9 0.00154830
\(696\) −6.65399e12 −1.07483
\(697\) 6.52529e11 0.104725
\(698\) −2.73087e12 −0.435463
\(699\) 4.10351e12 0.650142
\(700\) −4.19458e12 −0.660309
\(701\) 5.98491e12 0.936109 0.468055 0.883700i \(-0.344955\pi\)
0.468055 + 0.883700i \(0.344955\pi\)
\(702\) 4.77460e11 0.0742027
\(703\) −2.56003e12 −0.395318
\(704\) −2.76127e12 −0.423675
\(705\) −2.09044e10 −0.00318703
\(706\) 8.00609e11 0.121283
\(707\) −6.18703e12 −0.931311
\(708\) 3.36648e11 0.0503531
\(709\) −1.03720e13 −1.54154 −0.770769 0.637114i \(-0.780128\pi\)
−0.770769 + 0.637114i \(0.780128\pi\)
\(710\) −1.10444e10 −0.00163109
\(711\) 7.53170e10 0.0110530
\(712\) −9.83427e12 −1.43411
\(713\) −2.80255e11 −0.0406117
\(714\) −2.14733e12 −0.309213
\(715\) −1.62263e10 −0.00232190
\(716\) 7.61584e11 0.108295
\(717\) −1.95463e12 −0.276202
\(718\) 3.13626e12 0.440405
\(719\) 1.20078e13 1.67565 0.837823 0.545942i \(-0.183828\pi\)
0.837823 + 0.545942i \(0.183828\pi\)
\(720\) −1.09889e9 −0.000152391 0
\(721\) 5.20528e12 0.717358
\(722\) 9.33122e11 0.127797
\(723\) 4.38825e12 0.597267
\(724\) 1.19403e11 0.0161507
\(725\) 1.44346e13 1.94036
\(726\) 4.80104e11 0.0641388
\(727\) 1.07636e12 0.142907 0.0714536 0.997444i \(-0.477236\pi\)
0.0714536 + 0.997444i \(0.477236\pi\)
\(728\) −4.80978e12 −0.634650
\(729\) 2.82430e11 0.0370370
\(730\) −2.53543e10 −0.00330445
\(731\) −1.72593e12 −0.223561
\(732\) −3.67296e12 −0.472842
\(733\) 2.05646e12 0.263118 0.131559 0.991308i \(-0.458002\pi\)
0.131559 + 0.991308i \(0.458002\pi\)
\(734\) 5.90264e12 0.750610
\(735\) −4.99969e8 −6.31902e−5 0
\(736\) −2.49096e12 −0.312908
\(737\) 3.73542e12 0.466376
\(738\) −1.70903e11 −0.0212078
\(739\) 2.23059e12 0.275118 0.137559 0.990494i \(-0.456074\pi\)
0.137559 + 0.990494i \(0.456074\pi\)
\(740\) 7.52679e9 0.000922714 0
\(741\) −3.51573e12 −0.428384
\(742\) −2.24157e12 −0.271478
\(743\) 9.80053e12 1.17978 0.589888 0.807485i \(-0.299172\pi\)
0.589888 + 0.807485i \(0.299172\pi\)
\(744\) 6.17436e11 0.0738777
\(745\) 1.80330e10 0.00214470
\(746\) 4.90028e12 0.579291
\(747\) −3.23699e11 −0.0380363
\(748\) −4.87154e12 −0.568996
\(749\) 5.86707e12 0.681167
\(750\) −2.21454e10 −0.00255569
\(751\) −7.83593e12 −0.898899 −0.449450 0.893306i \(-0.648380\pi\)
−0.449450 + 0.893306i \(0.648380\pi\)
\(752\) −1.49130e12 −0.170053
\(753\) 2.03821e12 0.231032
\(754\) 6.63991e12 0.748154
\(755\) −2.35090e10 −0.00263313
\(756\) −1.14135e12 −0.127078
\(757\) −1.40537e12 −0.155547 −0.0777733 0.996971i \(-0.524781\pi\)
−0.0777733 + 0.996971i \(0.524781\pi\)
\(758\) 7.41475e12 0.815802
\(759\) −1.44363e12 −0.157895
\(760\) −3.75843e10 −0.00408644
\(761\) −5.80533e12 −0.627475 −0.313737 0.949510i \(-0.601581\pi\)
−0.313737 + 0.949510i \(0.601581\pi\)
\(762\) −2.99228e12 −0.321517
\(763\) 3.19890e12 0.341696
\(764\) 5.68827e12 0.604033
\(765\) 1.15036e10 0.00121439
\(766\) 1.76156e12 0.184871
\(767\) −8.37403e11 −0.0873686
\(768\) 5.04536e12 0.523319
\(769\) −1.55106e13 −1.59942 −0.799708 0.600390i \(-0.795012\pi\)
−0.799708 + 0.600390i \(0.795012\pi\)
\(770\) −1.91131e10 −0.00195940
\(771\) 7.94806e12 0.810058
\(772\) −1.11692e12 −0.113174
\(773\) −5.80456e11 −0.0584738 −0.0292369 0.999573i \(-0.509308\pi\)
−0.0292369 + 0.999573i \(0.509308\pi\)
\(774\) 4.52035e11 0.0452729
\(775\) −1.33941e12 −0.133369
\(776\) 8.46290e12 0.837802
\(777\) 2.06733e12 0.203476
\(778\) 3.53743e12 0.346162
\(779\) 1.25842e12 0.122436
\(780\) 1.03367e10 0.000999895 0
\(781\) −6.88189e12 −0.661878
\(782\) 1.73020e12 0.165449
\(783\) 3.92767e12 0.373428
\(784\) −3.56673e10 −0.00337170
\(785\) 3.62515e10 0.00340731
\(786\) −3.02308e12 −0.282519
\(787\) −1.09674e13 −1.01910 −0.509550 0.860441i \(-0.670188\pi\)
−0.509550 + 0.860441i \(0.670188\pi\)
\(788\) −3.27835e11 −0.0302892
\(789\) −5.04299e12 −0.463277
\(790\) −8.03461e8 −7.33910e−5 0
\(791\) 2.67945e12 0.243362
\(792\) 3.18049e12 0.287231
\(793\) 9.13639e12 0.820437
\(794\) 4.65551e12 0.415695
\(795\) 1.20084e10 0.00106619
\(796\) 7.83713e12 0.691908
\(797\) 7.83453e12 0.687781 0.343891 0.939010i \(-0.388255\pi\)
0.343891 + 0.939010i \(0.388255\pi\)
\(798\) −4.14120e12 −0.361504
\(799\) 1.56114e13 1.35513
\(800\) −1.19049e13 −1.02759
\(801\) 5.80491e12 0.498252
\(802\) −8.60932e12 −0.734825
\(803\) −1.57986e13 −1.34091
\(804\) −2.37957e12 −0.200839
\(805\) −1.37763e10 −0.00115625
\(806\) −6.16129e11 −0.0514238
\(807\) 6.53882e12 0.542711
\(808\) −1.09829e13 −0.906495
\(809\) −1.37396e12 −0.112773 −0.0563867 0.998409i \(-0.517958\pi\)
−0.0563867 + 0.998409i \(0.517958\pi\)
\(810\) −3.01288e9 −0.000245923 0
\(811\) −1.75453e13 −1.42419 −0.712095 0.702083i \(-0.752254\pi\)
−0.712095 + 0.702083i \(0.752254\pi\)
\(812\) −1.58725e13 −1.28128
\(813\) 1.09034e13 0.875293
\(814\) −2.31102e12 −0.184499
\(815\) 4.98901e10 0.00396100
\(816\) 8.20655e11 0.0647970
\(817\) −3.32852e12 −0.261367
\(818\) 4.44878e12 0.347417
\(819\) 2.83909e12 0.220496
\(820\) −3.69992e9 −0.000285778 0
\(821\) −2.09757e13 −1.61128 −0.805641 0.592405i \(-0.798179\pi\)
−0.805641 + 0.592405i \(0.798179\pi\)
\(822\) 3.05428e12 0.233338
\(823\) 1.73596e13 1.31898 0.659492 0.751712i \(-0.270771\pi\)
0.659492 + 0.751712i \(0.270771\pi\)
\(824\) 9.24014e12 0.698242
\(825\) −6.89948e12 −0.518530
\(826\) −9.86383e11 −0.0737285
\(827\) 1.37776e13 1.02423 0.512117 0.858916i \(-0.328861\pi\)
0.512117 + 0.858916i \(0.328861\pi\)
\(828\) 9.19637e11 0.0679954
\(829\) 5.24467e12 0.385676 0.192838 0.981231i \(-0.438231\pi\)
0.192838 + 0.981231i \(0.438231\pi\)
\(830\) 3.45313e9 0.000252558 0
\(831\) 1.00629e13 0.732015
\(832\) −4.37550e12 −0.316572
\(833\) 3.73378e11 0.0268687
\(834\) 1.86269e12 0.133320
\(835\) −5.42270e10 −0.00386035
\(836\) −9.39494e12 −0.665221
\(837\) −3.64456e11 −0.0256673
\(838\) −1.26207e13 −0.884068
\(839\) −2.45026e13 −1.70720 −0.853599 0.520931i \(-0.825585\pi\)
−0.853599 + 0.520931i \(0.825585\pi\)
\(840\) 3.03508e10 0.00210336
\(841\) 4.01140e13 2.76512
\(842\) 3.44409e12 0.236140
\(843\) 7.66423e12 0.522690
\(844\) −7.21673e12 −0.489553
\(845\) 3.13799e10 0.00211737
\(846\) −4.08876e12 −0.274426
\(847\) 2.85481e12 0.190591
\(848\) 8.56669e11 0.0568894
\(849\) 4.66185e12 0.307945
\(850\) 8.26905e12 0.543338
\(851\) −1.66573e12 −0.108873
\(852\) 4.38397e12 0.285029
\(853\) −1.15100e13 −0.744396 −0.372198 0.928153i \(-0.621396\pi\)
−0.372198 + 0.928153i \(0.621396\pi\)
\(854\) 1.07618e13 0.692350
\(855\) 2.21850e10 0.00141975
\(856\) 1.04149e13 0.663016
\(857\) −1.59723e13 −1.01147 −0.505737 0.862688i \(-0.668779\pi\)
−0.505737 + 0.862688i \(0.668779\pi\)
\(858\) −3.17376e12 −0.199932
\(859\) 2.59977e13 1.62917 0.814583 0.580046i \(-0.196966\pi\)
0.814583 + 0.580046i \(0.196966\pi\)
\(860\) 9.78623e9 0.000610060 0
\(861\) −1.01623e12 −0.0630197
\(862\) −7.64485e12 −0.471614
\(863\) 1.59640e13 0.979698 0.489849 0.871807i \(-0.337052\pi\)
0.489849 + 0.871807i \(0.337052\pi\)
\(864\) −3.23935e12 −0.197764
\(865\) −9.72050e9 −0.000590359 0
\(866\) 1.89371e13 1.14415
\(867\) 1.01472e12 0.0609905
\(868\) 1.47284e12 0.0880676
\(869\) −5.00646e11 −0.0297812
\(870\) −4.18993e10 −0.00247953
\(871\) 5.91914e12 0.348479
\(872\) 5.67852e12 0.332591
\(873\) −4.99543e12 −0.291077
\(874\) 3.33674e12 0.193429
\(875\) −1.31682e11 −0.00759433
\(876\) 1.00642e13 0.577444
\(877\) 6.66416e11 0.0380406 0.0190203 0.999819i \(-0.493945\pi\)
0.0190203 + 0.999819i \(0.493945\pi\)
\(878\) 8.82312e12 0.501068
\(879\) 1.92140e13 1.08559
\(880\) 7.30454e9 0.000410602 0
\(881\) −4.71400e12 −0.263632 −0.131816 0.991274i \(-0.542081\pi\)
−0.131816 + 0.991274i \(0.542081\pi\)
\(882\) −9.77906e10 −0.00544112
\(883\) −3.24260e12 −0.179503 −0.0897513 0.995964i \(-0.528607\pi\)
−0.0897513 + 0.995964i \(0.528607\pi\)
\(884\) −7.71944e12 −0.425158
\(885\) 5.28420e9 0.000289557 0
\(886\) −1.26401e13 −0.689129
\(887\) 1.15928e13 0.628829 0.314414 0.949286i \(-0.398192\pi\)
0.314414 + 0.949286i \(0.398192\pi\)
\(888\) 3.66981e12 0.198054
\(889\) −1.77928e13 −0.955402
\(890\) −6.19251e10 −0.00330835
\(891\) −1.87736e12 −0.0997925
\(892\) 9.76196e12 0.516292
\(893\) 3.01072e13 1.58430
\(894\) 3.52714e12 0.184673
\(895\) 1.19542e10 0.000622756 0
\(896\) 1.43875e13 0.745758
\(897\) −2.28758e12 −0.117980
\(898\) 7.02675e12 0.360588
\(899\) −5.06839e12 −0.258792
\(900\) 4.39517e12 0.223298
\(901\) −8.96790e12 −0.453345
\(902\) 1.13602e12 0.0571422
\(903\) 2.68791e12 0.134530
\(904\) 4.75642e12 0.236877
\(905\) 1.87421e9 9.28752e−5 0
\(906\) −4.59821e12 −0.226731
\(907\) −3.56853e13 −1.75088 −0.875441 0.483325i \(-0.839429\pi\)
−0.875441 + 0.483325i \(0.839429\pi\)
\(908\) 1.00506e13 0.490691
\(909\) 6.48291e12 0.314943
\(910\) −3.02866e10 −0.00146408
\(911\) −3.47841e12 −0.167320 −0.0836602 0.996494i \(-0.526661\pi\)
−0.0836602 + 0.996494i \(0.526661\pi\)
\(912\) 1.58266e12 0.0757549
\(913\) 2.15169e12 0.102485
\(914\) 2.21593e13 1.05026
\(915\) −5.76527e10 −0.00271910
\(916\) −8.69620e12 −0.408131
\(917\) −1.79760e13 −0.839518
\(918\) 2.25002e12 0.104567
\(919\) 1.60113e13 0.740471 0.370235 0.928938i \(-0.379277\pi\)
0.370235 + 0.928938i \(0.379277\pi\)
\(920\) −2.44549e10 −0.00112544
\(921\) 7.17786e12 0.328720
\(922\) −1.28631e13 −0.586213
\(923\) −1.09050e13 −0.494560
\(924\) 7.58678e12 0.342400
\(925\) −7.96095e12 −0.357542
\(926\) −6.43119e12 −0.287437
\(927\) −5.45421e12 −0.242590
\(928\) −4.50488e13 −1.99397
\(929\) −1.18366e13 −0.521384 −0.260692 0.965422i \(-0.583951\pi\)
−0.260692 + 0.965422i \(0.583951\pi\)
\(930\) 3.88791e9 0.000170429 0
\(931\) 7.20072e11 0.0314125
\(932\) 1.73761e13 0.754365
\(933\) 1.23226e13 0.532396
\(934\) 1.04490e13 0.449275
\(935\) −7.64664e10 −0.00327204
\(936\) 5.03980e12 0.214621
\(937\) 1.91151e13 0.810118 0.405059 0.914291i \(-0.367251\pi\)
0.405059 + 0.914291i \(0.367251\pi\)
\(938\) 6.97220e12 0.294074
\(939\) −2.09178e13 −0.878051
\(940\) −8.85187e10 −0.00369794
\(941\) −1.05459e13 −0.438462 −0.219231 0.975673i \(-0.570355\pi\)
−0.219231 + 0.975673i \(0.570355\pi\)
\(942\) 7.09054e12 0.293393
\(943\) 8.18817e11 0.0337198
\(944\) 3.76970e11 0.0154502
\(945\) −1.79153e10 −0.000730770 0
\(946\) −3.00476e12 −0.121983
\(947\) −2.96110e13 −1.19641 −0.598203 0.801345i \(-0.704118\pi\)
−0.598203 + 0.801345i \(0.704118\pi\)
\(948\) 3.18927e11 0.0128249
\(949\) −2.50344e13 −1.00193
\(950\) 1.59471e13 0.635223
\(951\) 2.56461e13 1.01674
\(952\) −2.26660e13 −0.894354
\(953\) −4.92564e13 −1.93439 −0.967196 0.254031i \(-0.918244\pi\)
−0.967196 + 0.254031i \(0.918244\pi\)
\(954\) 2.34876e12 0.0918061
\(955\) 8.92862e10 0.00347352
\(956\) −8.27677e12 −0.320480
\(957\) −2.61080e13 −1.00617
\(958\) −1.87382e13 −0.718757
\(959\) 1.81615e13 0.693374
\(960\) 2.76104e10 0.00104919
\(961\) −2.59693e13 −0.982212
\(962\) −3.66204e12 −0.137859
\(963\) −6.14765e12 −0.230351
\(964\) 1.85818e13 0.693014
\(965\) −1.75318e10 −0.000650810 0
\(966\) −2.69455e12 −0.0995611
\(967\) −4.25456e13 −1.56472 −0.782359 0.622828i \(-0.785984\pi\)
−0.782359 + 0.622828i \(0.785984\pi\)
\(968\) 5.06771e12 0.185512
\(969\) −1.65678e13 −0.603682
\(970\) 5.32898e10 0.00193273
\(971\) −5.03139e13 −1.81636 −0.908179 0.418582i \(-0.862527\pi\)
−0.908179 + 0.418582i \(0.862527\pi\)
\(972\) 1.19593e12 0.0429743
\(973\) 1.10760e13 0.396165
\(974\) 4.22322e11 0.0150359
\(975\) −1.09329e13 −0.387449
\(976\) −4.11289e12 −0.145085
\(977\) −3.70742e13 −1.30181 −0.650903 0.759161i \(-0.725610\pi\)
−0.650903 + 0.759161i \(0.725610\pi\)
\(978\) 9.75817e12 0.341070
\(979\) −3.85863e13 −1.34249
\(980\) −2.11710e9 −7.33201e−5 0
\(981\) −3.35188e12 −0.115552
\(982\) −2.16741e13 −0.743772
\(983\) −3.04886e13 −1.04147 −0.520734 0.853719i \(-0.674342\pi\)
−0.520734 + 0.853719i \(0.674342\pi\)
\(984\) −1.80395e12 −0.0613404
\(985\) −5.14588e9 −0.000174179 0
\(986\) 3.12905e13 1.05430
\(987\) −2.43127e13 −0.815467
\(988\) −1.48872e13 −0.497057
\(989\) −2.16576e12 −0.0719826
\(990\) 2.00271e10 0.000662614 0
\(991\) 3.56051e13 1.17268 0.586341 0.810064i \(-0.300568\pi\)
0.586341 + 0.810064i \(0.300568\pi\)
\(992\) 4.18016e12 0.137054
\(993\) −1.34466e13 −0.438875
\(994\) −1.28451e13 −0.417349
\(995\) 1.23016e11 0.00397884
\(996\) −1.37069e12 −0.0441338
\(997\) −1.70884e13 −0.547738 −0.273869 0.961767i \(-0.588304\pi\)
−0.273869 + 0.961767i \(0.588304\pi\)
\(998\) 2.92135e13 0.932174
\(999\) −2.16619e12 −0.0688100
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.c.1.13 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.13 22 1.1 even 1 trivial