Properties

Label 177.10.a.c.1.8
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 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +17651.6 q^{10} -58323.1 q^{11} +26254.4 q^{12} +142785. q^{13} -44121.2 q^{14} +104313. q^{15} +8868.30 q^{16} -634613. q^{17} -89929.3 q^{18} +1.07010e6 q^{19} +417417. q^{20} -260736. q^{21} +799414. q^{22} -325370. q^{23} -928301. q^{24} -294653. q^{25} -1.95710e6 q^{26} -531441. q^{27} -1.04336e6 q^{28} -4.66165e6 q^{29} -1.42978e6 q^{30} -5.51199e6 q^{31} -5.98934e6 q^{32} +4.72417e6 q^{33} +8.69841e6 q^{34} -4.14543e6 q^{35} -2.12660e6 q^{36} +1.62950e7 q^{37} -1.46674e7 q^{38} -1.15656e7 q^{39} -1.47590e7 q^{40} -2.02347e7 q^{41} +3.57382e6 q^{42} -3.84725e7 q^{43} +1.89041e7 q^{44} -8.44936e6 q^{45} +4.45974e6 q^{46} -3.59866e6 q^{47} -718332. q^{48} -2.99919e7 q^{49} +4.03871e6 q^{50} +5.14036e7 q^{51} -4.62805e7 q^{52} +5.97566e7 q^{53} +7.28427e6 q^{54} +7.51094e7 q^{55} +3.68910e7 q^{56} -8.66778e7 q^{57} +6.38956e7 q^{58} +1.21174e7 q^{59} -3.38108e7 q^{60} +5.83430e7 q^{61} +7.55509e7 q^{62} +2.11196e7 q^{63} +7.75531e7 q^{64} -1.83881e8 q^{65} -6.47525e7 q^{66} +1.77772e7 q^{67} +2.05696e8 q^{68} +2.63550e7 q^{69} +5.68200e7 q^{70} -1.90982e8 q^{71} +7.51924e7 q^{72} -4.70490e8 q^{73} -2.23350e8 q^{74} +2.38669e7 q^{75} -3.46848e8 q^{76} -1.87740e8 q^{77} +1.58525e8 q^{78} -1.31253e8 q^{79} -1.14207e7 q^{80} +4.30467e7 q^{81} +2.77350e8 q^{82} -5.84868e7 q^{83} +8.45118e7 q^{84} +8.17265e8 q^{85} +5.27329e8 q^{86} +3.77594e8 q^{87} -6.68412e8 q^{88} +5.00612e8 q^{89} +1.15812e8 q^{90} +4.59619e8 q^{91} +1.05462e8 q^{92} +4.46471e8 q^{93} +4.93255e7 q^{94} -1.37809e9 q^{95} +4.85136e8 q^{96} +5.11624e8 q^{97} +4.11088e8 q^{98} -3.82658e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.7066 −0.605754 −0.302877 0.953030i \(-0.597947\pi\)
−0.302877 + 0.953030i \(0.597947\pi\)
\(3\) −81.0000 −0.577350
\(4\) −324.128 −0.633062
\(5\) −1287.82 −0.921487 −0.460743 0.887533i \(-0.652417\pi\)
−0.460743 + 0.887533i \(0.652417\pi\)
\(6\) 1110.24 0.349732
\(7\) 3218.96 0.506728 0.253364 0.967371i \(-0.418463\pi\)
0.253364 + 0.967371i \(0.418463\pi\)
\(8\) 11460.5 0.989234
\(9\) 6561.00 0.333333
\(10\) 17651.6 0.558194
\(11\) −58323.1 −1.20108 −0.600542 0.799593i \(-0.705049\pi\)
−0.600542 + 0.799593i \(0.705049\pi\)
\(12\) 26254.4 0.365499
\(13\) 142785. 1.38655 0.693277 0.720671i \(-0.256166\pi\)
0.693277 + 0.720671i \(0.256166\pi\)
\(14\) −44121.2 −0.306952
\(15\) 104313. 0.532021
\(16\) 8868.30 0.0338299
\(17\) −634613. −1.84284 −0.921422 0.388563i \(-0.872972\pi\)
−0.921422 + 0.388563i \(0.872972\pi\)
\(18\) −89929.3 −0.201918
\(19\) 1.07010e6 1.88379 0.941894 0.335911i \(-0.109044\pi\)
0.941894 + 0.335911i \(0.109044\pi\)
\(20\) 417417. 0.583358
\(21\) −260736. −0.292560
\(22\) 799414. 0.727561
\(23\) −325370. −0.242439 −0.121220 0.992626i \(-0.538681\pi\)
−0.121220 + 0.992626i \(0.538681\pi\)
\(24\) −928301. −0.571134
\(25\) −294653. −0.150863
\(26\) −1.95710e6 −0.839911
\(27\) −531441. −0.192450
\(28\) −1.04336e6 −0.320790
\(29\) −4.66165e6 −1.22391 −0.611954 0.790893i \(-0.709616\pi\)
−0.611954 + 0.790893i \(0.709616\pi\)
\(30\) −1.42978e6 −0.322274
\(31\) −5.51199e6 −1.07197 −0.535983 0.844229i \(-0.680059\pi\)
−0.535983 + 0.844229i \(0.680059\pi\)
\(32\) −5.98934e6 −1.00973
\(33\) 4.72417e6 0.693446
\(34\) 8.69841e6 1.11631
\(35\) −4.14543e6 −0.466943
\(36\) −2.12660e6 −0.211021
\(37\) 1.62950e7 1.42938 0.714690 0.699442i \(-0.246568\pi\)
0.714690 + 0.699442i \(0.246568\pi\)
\(38\) −1.46674e7 −1.14111
\(39\) −1.15656e7 −0.800528
\(40\) −1.47590e7 −0.911566
\(41\) −2.02347e7 −1.11833 −0.559164 0.829057i \(-0.688878\pi\)
−0.559164 + 0.829057i \(0.688878\pi\)
\(42\) 3.57382e6 0.177219
\(43\) −3.84725e7 −1.71610 −0.858050 0.513566i \(-0.828324\pi\)
−0.858050 + 0.513566i \(0.828324\pi\)
\(44\) 1.89041e7 0.760361
\(45\) −8.44936e6 −0.307162
\(46\) 4.45974e6 0.146859
\(47\) −3.59866e6 −0.107572 −0.0537861 0.998552i \(-0.517129\pi\)
−0.0537861 + 0.998552i \(0.517129\pi\)
\(48\) −718332. −0.0195317
\(49\) −2.99919e7 −0.743227
\(50\) 4.03871e6 0.0913856
\(51\) 5.14036e7 1.06397
\(52\) −4.62805e7 −0.877775
\(53\) 5.97566e7 1.04027 0.520133 0.854085i \(-0.325882\pi\)
0.520133 + 0.854085i \(0.325882\pi\)
\(54\) 7.28427e6 0.116577
\(55\) 7.51094e7 1.10678
\(56\) 3.68910e7 0.501272
\(57\) −8.66778e7 −1.08761
\(58\) 6.38956e7 0.741388
\(59\) 1.21174e7 0.130189
\(60\) −3.38108e7 −0.336802
\(61\) 5.83430e7 0.539516 0.269758 0.962928i \(-0.413056\pi\)
0.269758 + 0.962928i \(0.413056\pi\)
\(62\) 7.55509e7 0.649347
\(63\) 2.11196e7 0.168909
\(64\) 7.75531e7 0.577816
\(65\) −1.83881e8 −1.27769
\(66\) −6.47525e7 −0.420058
\(67\) 1.77772e7 0.107777 0.0538884 0.998547i \(-0.482838\pi\)
0.0538884 + 0.998547i \(0.482838\pi\)
\(68\) 2.05696e8 1.16664
\(69\) 2.63550e7 0.139972
\(70\) 5.68200e7 0.282853
\(71\) −1.90982e8 −0.891926 −0.445963 0.895051i \(-0.647139\pi\)
−0.445963 + 0.895051i \(0.647139\pi\)
\(72\) 7.51924e7 0.329745
\(73\) −4.70490e8 −1.93909 −0.969544 0.244916i \(-0.921240\pi\)
−0.969544 + 0.244916i \(0.921240\pi\)
\(74\) −2.23350e8 −0.865852
\(75\) 2.38669e7 0.0871005
\(76\) −3.46848e8 −1.19255
\(77\) −1.87740e8 −0.608623
\(78\) 1.58525e8 0.484923
\(79\) −1.31253e8 −0.379131 −0.189565 0.981868i \(-0.560708\pi\)
−0.189565 + 0.981868i \(0.560708\pi\)
\(80\) −1.14207e7 −0.0311738
\(81\) 4.30467e7 0.111111
\(82\) 2.77350e8 0.677431
\(83\) −5.84868e7 −0.135271 −0.0676357 0.997710i \(-0.521546\pi\)
−0.0676357 + 0.997710i \(0.521546\pi\)
\(84\) 8.45118e7 0.185208
\(85\) 8.17265e8 1.69816
\(86\) 5.27329e8 1.03953
\(87\) 3.77594e8 0.706624
\(88\) −6.68412e8 −1.18815
\(89\) 5.00612e8 0.845759 0.422879 0.906186i \(-0.361019\pi\)
0.422879 + 0.906186i \(0.361019\pi\)
\(90\) 1.15812e8 0.186065
\(91\) 4.59619e8 0.702606
\(92\) 1.05462e8 0.153479
\(93\) 4.46471e8 0.618899
\(94\) 4.93255e7 0.0651623
\(95\) −1.37809e9 −1.73588
\(96\) 4.85136e8 0.582966
\(97\) 5.11624e8 0.586784 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(98\) 4.11088e8 0.450213
\(99\) −3.82658e8 −0.400361
\(100\) 9.55053e7 0.0955053
\(101\) −1.61259e9 −1.54198 −0.770989 0.636848i \(-0.780238\pi\)
−0.770989 + 0.636848i \(0.780238\pi\)
\(102\) −7.04572e8 −0.644502
\(103\) −1.90647e8 −0.166903 −0.0834514 0.996512i \(-0.526594\pi\)
−0.0834514 + 0.996512i \(0.526594\pi\)
\(104\) 1.63639e9 1.37163
\(105\) 3.35780e8 0.269590
\(106\) −8.19063e8 −0.630146
\(107\) 8.83809e7 0.0651826 0.0325913 0.999469i \(-0.489624\pi\)
0.0325913 + 0.999469i \(0.489624\pi\)
\(108\) 1.72255e8 0.121833
\(109\) 2.73851e9 1.85821 0.929107 0.369812i \(-0.120578\pi\)
0.929107 + 0.369812i \(0.120578\pi\)
\(110\) −1.02950e9 −0.670438
\(111\) −1.31990e9 −0.825253
\(112\) 2.85467e7 0.0171425
\(113\) 1.25793e9 0.725779 0.362890 0.931832i \(-0.381790\pi\)
0.362890 + 0.931832i \(0.381790\pi\)
\(114\) 1.18806e9 0.658821
\(115\) 4.19018e8 0.223404
\(116\) 1.51097e9 0.774810
\(117\) 9.36811e8 0.462185
\(118\) −1.66088e8 −0.0788624
\(119\) −2.04280e9 −0.933821
\(120\) 1.19548e9 0.526293
\(121\) 1.04364e9 0.442603
\(122\) −7.99687e8 −0.326814
\(123\) 1.63901e9 0.645666
\(124\) 1.78659e9 0.678621
\(125\) 2.89473e9 1.06050
\(126\) −2.89479e8 −0.102317
\(127\) −2.31195e9 −0.788608 −0.394304 0.918980i \(-0.629014\pi\)
−0.394304 + 0.918980i \(0.629014\pi\)
\(128\) 2.00355e9 0.659712
\(129\) 3.11627e9 0.990791
\(130\) 2.52039e9 0.773967
\(131\) 3.61228e9 1.07167 0.535834 0.844323i \(-0.319997\pi\)
0.535834 + 0.844323i \(0.319997\pi\)
\(132\) −1.53124e9 −0.438995
\(133\) 3.44460e9 0.954568
\(134\) −2.43665e8 −0.0652863
\(135\) 6.84399e8 0.177340
\(136\) −7.27299e9 −1.82300
\(137\) 7.85703e7 0.0190553 0.00952765 0.999955i \(-0.496967\pi\)
0.00952765 + 0.999955i \(0.496967\pi\)
\(138\) −3.61239e8 −0.0847888
\(139\) 5.49642e9 1.24886 0.624430 0.781081i \(-0.285331\pi\)
0.624430 + 0.781081i \(0.285331\pi\)
\(140\) 1.34365e9 0.295604
\(141\) 2.91491e8 0.0621069
\(142\) 2.61772e9 0.540288
\(143\) −8.32765e9 −1.66537
\(144\) 5.81849e7 0.0112766
\(145\) 6.00336e9 1.12782
\(146\) 6.44884e9 1.17461
\(147\) 2.42934e9 0.429102
\(148\) −5.28167e9 −0.904886
\(149\) −5.68911e9 −0.945596 −0.472798 0.881171i \(-0.656756\pi\)
−0.472798 + 0.881171i \(0.656756\pi\)
\(150\) −3.27135e8 −0.0527615
\(151\) −5.62546e8 −0.0880565 −0.0440283 0.999030i \(-0.514019\pi\)
−0.0440283 + 0.999030i \(0.514019\pi\)
\(152\) 1.22639e10 1.86351
\(153\) −4.16369e9 −0.614282
\(154\) 2.57328e9 0.368676
\(155\) 7.09843e9 0.987802
\(156\) 3.74872e9 0.506784
\(157\) −7.75677e9 −1.01890 −0.509451 0.860500i \(-0.670151\pi\)
−0.509451 + 0.860500i \(0.670151\pi\)
\(158\) 1.79905e9 0.229660
\(159\) −4.84029e9 −0.600598
\(160\) 7.71317e9 0.930449
\(161\) −1.04736e9 −0.122851
\(162\) −5.90026e8 −0.0673060
\(163\) −1.46466e10 −1.62515 −0.812573 0.582859i \(-0.801934\pi\)
−0.812573 + 0.582859i \(0.801934\pi\)
\(164\) 6.55862e9 0.707971
\(165\) −6.08387e9 −0.639001
\(166\) 8.01657e8 0.0819412
\(167\) 1.83446e10 1.82509 0.912547 0.408972i \(-0.134113\pi\)
0.912547 + 0.408972i \(0.134113\pi\)
\(168\) −2.98817e9 −0.289410
\(169\) 9.78301e9 0.922534
\(170\) −1.12020e10 −1.02867
\(171\) 7.02091e9 0.627929
\(172\) 1.24700e10 1.08640
\(173\) 3.91756e9 0.332513 0.166256 0.986083i \(-0.446832\pi\)
0.166256 + 0.986083i \(0.446832\pi\)
\(174\) −5.17555e9 −0.428040
\(175\) −9.48478e8 −0.0764462
\(176\) −5.17227e8 −0.0406325
\(177\) −9.81506e8 −0.0751646
\(178\) −6.86172e9 −0.512322
\(179\) 6.82016e9 0.496542 0.248271 0.968691i \(-0.420138\pi\)
0.248271 + 0.968691i \(0.420138\pi\)
\(180\) 2.73867e9 0.194453
\(181\) −6.85477e9 −0.474722 −0.237361 0.971422i \(-0.576282\pi\)
−0.237361 + 0.971422i \(0.576282\pi\)
\(182\) −6.29984e9 −0.425606
\(183\) −4.72578e9 −0.311490
\(184\) −3.72891e9 −0.239829
\(185\) −2.09850e10 −1.31715
\(186\) −6.11962e9 −0.374901
\(187\) 3.70126e10 2.21341
\(188\) 1.16643e9 0.0680999
\(189\) −1.71069e9 −0.0975198
\(190\) 1.88890e10 1.05152
\(191\) 3.27100e9 0.177840 0.0889201 0.996039i \(-0.471658\pi\)
0.0889201 + 0.996039i \(0.471658\pi\)
\(192\) −6.28180e9 −0.333602
\(193\) 1.06930e10 0.554743 0.277371 0.960763i \(-0.410537\pi\)
0.277371 + 0.960763i \(0.410537\pi\)
\(194\) −7.01265e9 −0.355446
\(195\) 1.48943e10 0.737676
\(196\) 9.72120e9 0.470509
\(197\) 6.60109e9 0.312261 0.156131 0.987736i \(-0.450098\pi\)
0.156131 + 0.987736i \(0.450098\pi\)
\(198\) 5.24496e9 0.242520
\(199\) −3.54383e9 −0.160190 −0.0800949 0.996787i \(-0.525522\pi\)
−0.0800949 + 0.996787i \(0.525522\pi\)
\(200\) −3.37688e9 −0.149238
\(201\) −1.43995e9 −0.0622250
\(202\) 2.21032e10 0.934059
\(203\) −1.50057e10 −0.620189
\(204\) −1.66614e10 −0.673557
\(205\) 2.60585e10 1.03052
\(206\) 2.61314e9 0.101102
\(207\) −2.13476e9 −0.0808131
\(208\) 1.26626e9 0.0469070
\(209\) −6.24114e10 −2.26259
\(210\) −4.60242e9 −0.163305
\(211\) 1.86373e10 0.647308 0.323654 0.946176i \(-0.395089\pi\)
0.323654 + 0.946176i \(0.395089\pi\)
\(212\) −1.93688e10 −0.658553
\(213\) 1.54695e10 0.514954
\(214\) −1.21141e9 −0.0394846
\(215\) 4.95456e10 1.58136
\(216\) −6.09058e9 −0.190378
\(217\) −1.77429e10 −0.543195
\(218\) −3.75358e10 −1.12562
\(219\) 3.81097e10 1.11953
\(220\) −2.43451e10 −0.700662
\(221\) −9.06131e10 −2.55520
\(222\) 1.80914e10 0.499900
\(223\) −4.63375e10 −1.25476 −0.627380 0.778713i \(-0.715873\pi\)
−0.627380 + 0.778713i \(0.715873\pi\)
\(224\) −1.92795e10 −0.511657
\(225\) −1.93322e9 −0.0502875
\(226\) −1.72420e10 −0.439643
\(227\) −1.44421e10 −0.361005 −0.180503 0.983575i \(-0.557772\pi\)
−0.180503 + 0.983575i \(0.557772\pi\)
\(228\) 2.80947e10 0.688522
\(229\) −9.47681e9 −0.227721 −0.113860 0.993497i \(-0.536322\pi\)
−0.113860 + 0.993497i \(0.536322\pi\)
\(230\) −5.74332e9 −0.135328
\(231\) 1.52069e10 0.351389
\(232\) −5.34249e10 −1.21073
\(233\) 6.67568e9 0.148386 0.0741931 0.997244i \(-0.476362\pi\)
0.0741931 + 0.997244i \(0.476362\pi\)
\(234\) −1.28405e10 −0.279970
\(235\) 4.63441e9 0.0991264
\(236\) −3.92757e9 −0.0824177
\(237\) 1.06315e10 0.218891
\(238\) 2.79999e10 0.565666
\(239\) −1.54044e10 −0.305389 −0.152695 0.988273i \(-0.548795\pi\)
−0.152695 + 0.988273i \(0.548795\pi\)
\(240\) 9.25080e8 0.0179982
\(241\) 8.37352e10 1.59894 0.799469 0.600707i \(-0.205114\pi\)
0.799469 + 0.600707i \(0.205114\pi\)
\(242\) −1.43047e10 −0.268109
\(243\) −3.48678e9 −0.0641500
\(244\) −1.89106e10 −0.341547
\(245\) 3.86240e10 0.684874
\(246\) −2.24653e10 −0.391115
\(247\) 1.52794e11 2.61197
\(248\) −6.31702e10 −1.06042
\(249\) 4.73743e9 0.0780990
\(250\) −3.96770e10 −0.642405
\(251\) −1.74665e10 −0.277763 −0.138881 0.990309i \(-0.544351\pi\)
−0.138881 + 0.990309i \(0.544351\pi\)
\(252\) −6.84546e9 −0.106930
\(253\) 1.89766e10 0.291190
\(254\) 3.16891e10 0.477703
\(255\) −6.61985e10 −0.980431
\(256\) −6.71691e10 −0.977439
\(257\) −7.76557e10 −1.11039 −0.555194 0.831721i \(-0.687356\pi\)
−0.555194 + 0.831721i \(0.687356\pi\)
\(258\) −4.27137e10 −0.600176
\(259\) 5.24531e10 0.724307
\(260\) 5.96008e10 0.808858
\(261\) −3.05851e10 −0.407970
\(262\) −4.95122e10 −0.649167
\(263\) −1.93846e10 −0.249837 −0.124918 0.992167i \(-0.539867\pi\)
−0.124918 + 0.992167i \(0.539867\pi\)
\(264\) 5.41414e10 0.685981
\(265\) −7.69556e10 −0.958592
\(266\) −4.72140e10 −0.578233
\(267\) −4.05496e10 −0.488299
\(268\) −5.76207e9 −0.0682295
\(269\) 2.06615e10 0.240589 0.120294 0.992738i \(-0.461616\pi\)
0.120294 + 0.992738i \(0.461616\pi\)
\(270\) −9.38081e9 −0.107425
\(271\) −4.67978e10 −0.527064 −0.263532 0.964651i \(-0.584887\pi\)
−0.263532 + 0.964651i \(0.584887\pi\)
\(272\) −5.62794e9 −0.0623432
\(273\) −3.72292e10 −0.405650
\(274\) −1.07694e9 −0.0115428
\(275\) 1.71851e10 0.181199
\(276\) −8.54239e9 −0.0886112
\(277\) −9.14024e10 −0.932821 −0.466411 0.884568i \(-0.654453\pi\)
−0.466411 + 0.884568i \(0.654453\pi\)
\(278\) −7.53375e10 −0.756502
\(279\) −3.61642e10 −0.357322
\(280\) −4.75088e10 −0.461916
\(281\) −1.31051e11 −1.25390 −0.626951 0.779059i \(-0.715697\pi\)
−0.626951 + 0.779059i \(0.715697\pi\)
\(282\) −3.99537e9 −0.0376215
\(283\) −1.84063e11 −1.70580 −0.852901 0.522073i \(-0.825159\pi\)
−0.852901 + 0.522073i \(0.825159\pi\)
\(284\) 6.19025e10 0.564645
\(285\) 1.11625e11 1.00221
\(286\) 1.14144e11 1.00880
\(287\) −6.51347e10 −0.566688
\(288\) −3.92960e10 −0.336575
\(289\) 2.84146e11 2.39608
\(290\) −8.22859e10 −0.683179
\(291\) −4.14415e10 −0.338780
\(292\) 1.52499e11 1.22756
\(293\) 3.58566e10 0.284227 0.142113 0.989850i \(-0.454610\pi\)
0.142113 + 0.989850i \(0.454610\pi\)
\(294\) −3.32981e10 −0.259930
\(295\) −1.56049e10 −0.119967
\(296\) 1.86749e11 1.41399
\(297\) 3.09953e10 0.231149
\(298\) 7.79786e10 0.572799
\(299\) −4.64580e10 −0.336155
\(300\) −7.73593e9 −0.0551400
\(301\) −1.23842e11 −0.869596
\(302\) 7.71062e9 0.0533406
\(303\) 1.30620e11 0.890262
\(304\) 9.48994e9 0.0637283
\(305\) −7.51351e10 −0.497157
\(306\) 5.70703e10 0.372103
\(307\) 2.81321e11 1.80750 0.903751 0.428059i \(-0.140802\pi\)
0.903751 + 0.428059i \(0.140802\pi\)
\(308\) 6.08517e10 0.385296
\(309\) 1.54424e10 0.0963614
\(310\) −9.72957e10 −0.598365
\(311\) 2.77783e11 1.68377 0.841886 0.539655i \(-0.181445\pi\)
0.841886 + 0.539655i \(0.181445\pi\)
\(312\) −1.32547e11 −0.791909
\(313\) −1.15722e11 −0.681500 −0.340750 0.940154i \(-0.610681\pi\)
−0.340750 + 0.940154i \(0.610681\pi\)
\(314\) 1.06319e11 0.617204
\(315\) −2.71982e10 −0.155648
\(316\) 4.25429e10 0.240013
\(317\) 2.98400e10 0.165971 0.0829855 0.996551i \(-0.473554\pi\)
0.0829855 + 0.996551i \(0.473554\pi\)
\(318\) 6.63441e10 0.363815
\(319\) 2.71882e11 1.47002
\(320\) −9.98742e10 −0.532450
\(321\) −7.15885e9 −0.0376332
\(322\) 1.43557e10 0.0744173
\(323\) −6.79097e11 −3.47153
\(324\) −1.39526e10 −0.0703402
\(325\) −4.20720e10 −0.209179
\(326\) 2.00756e11 0.984439
\(327\) −2.21820e11 −1.07284
\(328\) −2.31900e11 −1.10629
\(329\) −1.15840e10 −0.0545099
\(330\) 8.33894e10 0.387078
\(331\) −2.79768e10 −0.128107 −0.0640534 0.997946i \(-0.520403\pi\)
−0.0640534 + 0.997946i \(0.520403\pi\)
\(332\) 1.89572e10 0.0856352
\(333\) 1.06912e11 0.476460
\(334\) −2.51444e11 −1.10556
\(335\) −2.28937e10 −0.0993149
\(336\) −2.31229e9 −0.00989725
\(337\) 1.18707e10 0.0501350 0.0250675 0.999686i \(-0.492020\pi\)
0.0250675 + 0.999686i \(0.492020\pi\)
\(338\) −1.34092e11 −0.558828
\(339\) −1.01893e11 −0.419029
\(340\) −2.64898e11 −1.07504
\(341\) 3.21476e11 1.28752
\(342\) −9.62331e10 −0.380371
\(343\) −2.26440e11 −0.883342
\(344\) −4.40915e11 −1.69762
\(345\) −3.39404e10 −0.128983
\(346\) −5.36966e10 −0.201421
\(347\) 1.23258e11 0.456385 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(348\) −1.22389e11 −0.447337
\(349\) 1.27299e11 0.459314 0.229657 0.973272i \(-0.426239\pi\)
0.229657 + 0.973272i \(0.426239\pi\)
\(350\) 1.30005e10 0.0463076
\(351\) −7.58817e10 −0.266843
\(352\) 3.49317e11 1.21277
\(353\) 3.18952e11 1.09330 0.546649 0.837362i \(-0.315903\pi\)
0.546649 + 0.837362i \(0.315903\pi\)
\(354\) 1.34532e10 0.0455313
\(355\) 2.45949e11 0.821898
\(356\) −1.62262e11 −0.535418
\(357\) 1.65466e11 0.539142
\(358\) −9.34815e10 −0.300782
\(359\) 8.68092e9 0.0275829 0.0137915 0.999905i \(-0.495610\pi\)
0.0137915 + 0.999905i \(0.495610\pi\)
\(360\) −9.68340e10 −0.303855
\(361\) 8.22420e11 2.54866
\(362\) 9.39559e10 0.287565
\(363\) −8.45345e10 −0.255537
\(364\) −1.48975e11 −0.444793
\(365\) 6.05905e11 1.78684
\(366\) 6.47746e10 0.188686
\(367\) −2.06720e11 −0.594819 −0.297410 0.954750i \(-0.596123\pi\)
−0.297410 + 0.954750i \(0.596123\pi\)
\(368\) −2.88548e9 −0.00820169
\(369\) −1.32760e11 −0.372776
\(370\) 2.87634e11 0.797871
\(371\) 1.92354e11 0.527132
\(372\) −1.44714e11 −0.391802
\(373\) 2.25859e11 0.604154 0.302077 0.953284i \(-0.402320\pi\)
0.302077 + 0.953284i \(0.402320\pi\)
\(374\) −5.07318e11 −1.34078
\(375\) −2.34473e11 −0.612282
\(376\) −4.12425e10 −0.106414
\(377\) −6.65613e11 −1.69702
\(378\) 2.34478e10 0.0590730
\(379\) 5.35540e11 1.33326 0.666630 0.745388i \(-0.267736\pi\)
0.666630 + 0.745388i \(0.267736\pi\)
\(380\) 4.46677e11 1.09892
\(381\) 1.87268e11 0.455303
\(382\) −4.48344e10 −0.107727
\(383\) −1.30230e11 −0.309256 −0.154628 0.987973i \(-0.549418\pi\)
−0.154628 + 0.987973i \(0.549418\pi\)
\(384\) −1.62287e11 −0.380885
\(385\) 2.41775e11 0.560838
\(386\) −1.46565e11 −0.336038
\(387\) −2.52418e11 −0.572033
\(388\) −1.65831e11 −0.371470
\(389\) 7.18519e11 1.59098 0.795491 0.605965i \(-0.207213\pi\)
0.795491 + 0.605965i \(0.207213\pi\)
\(390\) −2.04151e11 −0.446850
\(391\) 2.06484e11 0.446778
\(392\) −3.43722e11 −0.735225
\(393\) −2.92594e11 −0.618728
\(394\) −9.04789e10 −0.189153
\(395\) 1.69030e11 0.349364
\(396\) 1.24030e11 0.253454
\(397\) 6.32135e11 1.27718 0.638591 0.769546i \(-0.279518\pi\)
0.638591 + 0.769546i \(0.279518\pi\)
\(398\) 4.85741e10 0.0970356
\(399\) −2.79013e11 −0.551120
\(400\) −2.61307e9 −0.00510366
\(401\) 9.05543e11 1.74888 0.874438 0.485137i \(-0.161230\pi\)
0.874438 + 0.485137i \(0.161230\pi\)
\(402\) 1.97369e10 0.0376930
\(403\) −7.87028e11 −1.48634
\(404\) 5.22686e11 0.976168
\(405\) −5.54363e10 −0.102387
\(406\) 2.05678e11 0.375682
\(407\) −9.50377e11 −1.71681
\(408\) 5.89112e11 1.05251
\(409\) 4.28566e11 0.757290 0.378645 0.925542i \(-0.376390\pi\)
0.378645 + 0.925542i \(0.376390\pi\)
\(410\) −3.57175e11 −0.624244
\(411\) −6.36420e9 −0.0110016
\(412\) 6.17941e10 0.105660
\(413\) 3.90053e10 0.0659704
\(414\) 2.92603e10 0.0489528
\(415\) 7.53202e10 0.124651
\(416\) −8.55186e11 −1.40004
\(417\) −4.45210e11 −0.721029
\(418\) 8.55450e11 1.37057
\(419\) 2.10147e11 0.333088 0.166544 0.986034i \(-0.446739\pi\)
0.166544 + 0.986034i \(0.446739\pi\)
\(420\) −1.08836e11 −0.170667
\(421\) 5.69267e11 0.883174 0.441587 0.897218i \(-0.354416\pi\)
0.441587 + 0.897218i \(0.354416\pi\)
\(422\) −2.55454e11 −0.392109
\(423\) −2.36108e10 −0.0358574
\(424\) 6.84841e11 1.02907
\(425\) 1.86991e11 0.278016
\(426\) −2.12035e11 −0.311935
\(427\) 1.87804e11 0.273388
\(428\) −2.86467e10 −0.0412646
\(429\) 6.74540e11 0.961501
\(430\) −6.79104e11 −0.957917
\(431\) −1.13091e12 −1.57864 −0.789318 0.613985i \(-0.789566\pi\)
−0.789318 + 0.613985i \(0.789566\pi\)
\(432\) −4.71298e9 −0.00651056
\(433\) −7.03103e11 −0.961222 −0.480611 0.876934i \(-0.659585\pi\)
−0.480611 + 0.876934i \(0.659585\pi\)
\(434\) 2.43196e11 0.329042
\(435\) −4.86272e11 −0.651145
\(436\) −8.87628e11 −1.17636
\(437\) −3.48178e11 −0.456704
\(438\) −5.22356e11 −0.678162
\(439\) 1.82759e11 0.234849 0.117424 0.993082i \(-0.462536\pi\)
0.117424 + 0.993082i \(0.462536\pi\)
\(440\) 8.60793e11 1.09487
\(441\) −1.96777e11 −0.247742
\(442\) 1.24200e12 1.54783
\(443\) 1.37003e12 1.69010 0.845050 0.534687i \(-0.179571\pi\)
0.845050 + 0.534687i \(0.179571\pi\)
\(444\) 4.27816e11 0.522436
\(445\) −6.44697e11 −0.779356
\(446\) 6.35132e11 0.760076
\(447\) 4.60818e11 0.545940
\(448\) 2.49641e11 0.292795
\(449\) 5.34788e11 0.620973 0.310487 0.950578i \(-0.399508\pi\)
0.310487 + 0.950578i \(0.399508\pi\)
\(450\) 2.64980e10 0.0304619
\(451\) 1.18015e12 1.34320
\(452\) −4.07731e11 −0.459463
\(453\) 4.55662e10 0.0508395
\(454\) 1.97953e11 0.218680
\(455\) −5.91905e11 −0.647442
\(456\) −9.93372e11 −1.07590
\(457\) −5.62934e11 −0.603719 −0.301859 0.953352i \(-0.597607\pi\)
−0.301859 + 0.953352i \(0.597607\pi\)
\(458\) 1.29895e11 0.137943
\(459\) 3.37259e11 0.354656
\(460\) −1.35815e11 −0.141429
\(461\) −1.56743e11 −0.161635 −0.0808175 0.996729i \(-0.525753\pi\)
−0.0808175 + 0.996729i \(0.525753\pi\)
\(462\) −2.08436e11 −0.212855
\(463\) −2.23867e11 −0.226400 −0.113200 0.993572i \(-0.536110\pi\)
−0.113200 + 0.993572i \(0.536110\pi\)
\(464\) −4.13409e10 −0.0414047
\(465\) −5.74973e11 −0.570307
\(466\) −9.15011e10 −0.0898856
\(467\) −1.11895e12 −1.08865 −0.544323 0.838876i \(-0.683213\pi\)
−0.544323 + 0.838876i \(0.683213\pi\)
\(468\) −3.03647e11 −0.292592
\(469\) 5.72240e10 0.0546136
\(470\) −6.35223e10 −0.0600462
\(471\) 6.28298e11 0.588263
\(472\) 1.38871e11 0.128787
\(473\) 2.24384e12 2.06118
\(474\) −1.45723e11 −0.132594
\(475\) −3.15308e11 −0.284193
\(476\) 6.62127e11 0.591167
\(477\) 3.92063e11 0.346756
\(478\) 2.11142e11 0.184991
\(479\) 8.89411e11 0.771956 0.385978 0.922508i \(-0.373864\pi\)
0.385978 + 0.922508i \(0.373864\pi\)
\(480\) −6.24766e11 −0.537195
\(481\) 2.32668e12 1.98191
\(482\) −1.14773e12 −0.968563
\(483\) 8.48358e10 0.0709279
\(484\) −3.38271e11 −0.280195
\(485\) −6.58878e11 −0.540713
\(486\) 4.77921e10 0.0388591
\(487\) 9.69722e11 0.781209 0.390604 0.920559i \(-0.372266\pi\)
0.390604 + 0.920559i \(0.372266\pi\)
\(488\) 6.68640e11 0.533708
\(489\) 1.18637e12 0.938279
\(490\) −5.29406e11 −0.414865
\(491\) 7.10876e11 0.551985 0.275992 0.961160i \(-0.410994\pi\)
0.275992 + 0.961160i \(0.410994\pi\)
\(492\) −5.31248e11 −0.408747
\(493\) 2.95835e12 2.25547
\(494\) −2.09429e12 −1.58221
\(495\) 4.92793e11 0.368928
\(496\) −4.88820e10 −0.0362644
\(497\) −6.14763e11 −0.451964
\(498\) −6.49342e10 −0.0473088
\(499\) 1.54484e12 1.11540 0.557702 0.830041i \(-0.311683\pi\)
0.557702 + 0.830041i \(0.311683\pi\)
\(500\) −9.38261e11 −0.671365
\(501\) −1.48592e12 −1.05372
\(502\) 2.39407e11 0.168256
\(503\) 1.95247e12 1.35997 0.679983 0.733228i \(-0.261987\pi\)
0.679983 + 0.733228i \(0.261987\pi\)
\(504\) 2.42042e11 0.167091
\(505\) 2.07672e12 1.42091
\(506\) −2.60106e11 −0.176389
\(507\) −7.92424e11 −0.532625
\(508\) 7.49367e11 0.499238
\(509\) −2.22432e12 −1.46882 −0.734409 0.678707i \(-0.762541\pi\)
−0.734409 + 0.678707i \(0.762541\pi\)
\(510\) 9.07359e11 0.593900
\(511\) −1.51449e12 −0.982590
\(512\) −1.05152e11 −0.0676246
\(513\) −5.68693e11 −0.362535
\(514\) 1.06440e12 0.672621
\(515\) 2.45519e11 0.153799
\(516\) −1.01007e12 −0.627232
\(517\) 2.09885e11 0.129203
\(518\) −7.18957e11 −0.438752
\(519\) −3.17322e11 −0.191976
\(520\) −2.10737e12 −1.26394
\(521\) −1.81361e12 −1.07839 −0.539193 0.842182i \(-0.681271\pi\)
−0.539193 + 0.842182i \(0.681271\pi\)
\(522\) 4.19219e11 0.247129
\(523\) 1.81150e12 1.05872 0.529361 0.848397i \(-0.322432\pi\)
0.529361 + 0.848397i \(0.322432\pi\)
\(524\) −1.17084e12 −0.678432
\(525\) 7.68267e10 0.0441363
\(526\) 2.65698e11 0.151340
\(527\) 3.49798e12 1.97547
\(528\) 4.18954e10 0.0234592
\(529\) −1.69529e12 −0.941223
\(530\) 1.05480e12 0.580671
\(531\) 7.95020e10 0.0433963
\(532\) −1.11649e12 −0.604301
\(533\) −2.88920e12 −1.55062
\(534\) 5.55799e11 0.295789
\(535\) −1.13818e11 −0.0600649
\(536\) 2.03735e11 0.106617
\(537\) −5.52433e11 −0.286678
\(538\) −2.83199e11 −0.145738
\(539\) 1.74922e12 0.892678
\(540\) −2.21833e11 −0.112267
\(541\) 1.59726e12 0.801657 0.400828 0.916153i \(-0.368722\pi\)
0.400828 + 0.916153i \(0.368722\pi\)
\(542\) 6.41440e11 0.319271
\(543\) 5.55236e11 0.274081
\(544\) 3.80091e12 1.86077
\(545\) −3.52670e12 −1.71232
\(546\) 5.10287e11 0.245724
\(547\) 2.14748e12 1.02562 0.512810 0.858502i \(-0.328605\pi\)
0.512810 + 0.858502i \(0.328605\pi\)
\(548\) −2.54668e10 −0.0120632
\(549\) 3.82788e11 0.179839
\(550\) −2.35550e11 −0.109762
\(551\) −4.98842e12 −2.30558
\(552\) 3.02042e11 0.138465
\(553\) −4.22500e11 −0.192116
\(554\) 1.25282e12 0.565060
\(555\) 1.69979e12 0.760459
\(556\) −1.78154e12 −0.790606
\(557\) 7.75058e11 0.341182 0.170591 0.985342i \(-0.445432\pi\)
0.170591 + 0.985342i \(0.445432\pi\)
\(558\) 4.95689e11 0.216449
\(559\) −5.49329e12 −2.37947
\(560\) −3.67630e10 −0.0157966
\(561\) −2.99802e12 −1.27791
\(562\) 1.79628e12 0.759556
\(563\) 1.27236e12 0.533729 0.266865 0.963734i \(-0.414012\pi\)
0.266865 + 0.963734i \(0.414012\pi\)
\(564\) −9.44805e10 −0.0393175
\(565\) −1.61999e12 −0.668796
\(566\) 2.52289e12 1.03330
\(567\) 1.38566e11 0.0563031
\(568\) −2.18875e12 −0.882324
\(569\) −2.12273e12 −0.848963 −0.424482 0.905437i \(-0.639544\pi\)
−0.424482 + 0.905437i \(0.639544\pi\)
\(570\) −1.53001e12 −0.607095
\(571\) 2.38084e12 0.937277 0.468639 0.883390i \(-0.344745\pi\)
0.468639 + 0.883390i \(0.344745\pi\)
\(572\) 2.69922e12 1.05428
\(573\) −2.64951e11 −0.102676
\(574\) 8.92778e11 0.343273
\(575\) 9.58715e10 0.0365750
\(576\) 5.08826e11 0.192605
\(577\) −4.36889e12 −1.64089 −0.820446 0.571724i \(-0.806275\pi\)
−0.820446 + 0.571724i \(0.806275\pi\)
\(578\) −3.89468e12 −1.45143
\(579\) −8.66133e11 −0.320281
\(580\) −1.94585e12 −0.713977
\(581\) −1.88267e11 −0.0685458
\(582\) 5.68024e11 0.205217
\(583\) −3.48519e12 −1.24945
\(584\) −5.39206e12 −1.91821
\(585\) −1.20644e12 −0.425897
\(586\) −4.91474e11 −0.172171
\(587\) −2.04674e12 −0.711525 −0.355763 0.934576i \(-0.615779\pi\)
−0.355763 + 0.934576i \(0.615779\pi\)
\(588\) −7.87417e11 −0.271648
\(589\) −5.89836e12 −2.01935
\(590\) 2.13891e11 0.0726707
\(591\) −5.34689e11 −0.180284
\(592\) 1.44509e11 0.0483557
\(593\) 4.09546e12 1.36005 0.680027 0.733187i \(-0.261968\pi\)
0.680027 + 0.733187i \(0.261968\pi\)
\(594\) −4.24841e11 −0.140019
\(595\) 2.63075e12 0.860503
\(596\) 1.84400e12 0.598621
\(597\) 2.87051e11 0.0924856
\(598\) 6.36783e11 0.203627
\(599\) 2.90714e12 0.922666 0.461333 0.887227i \(-0.347371\pi\)
0.461333 + 0.887227i \(0.347371\pi\)
\(600\) 2.73527e11 0.0861628
\(601\) 1.56733e12 0.490034 0.245017 0.969519i \(-0.421207\pi\)
0.245017 + 0.969519i \(0.421207\pi\)
\(602\) 1.69745e12 0.526761
\(603\) 1.16636e11 0.0359256
\(604\) 1.82337e11 0.0557453
\(605\) −1.34401e12 −0.407853
\(606\) −1.79036e12 −0.539279
\(607\) 1.13643e12 0.339777 0.169889 0.985463i \(-0.445659\pi\)
0.169889 + 0.985463i \(0.445659\pi\)
\(608\) −6.40917e12 −1.90211
\(609\) 1.21546e12 0.358066
\(610\) 1.02985e12 0.301155
\(611\) −5.13834e11 −0.149155
\(612\) 1.34957e12 0.388878
\(613\) −9.45096e11 −0.270336 −0.135168 0.990823i \(-0.543157\pi\)
−0.135168 + 0.990823i \(0.543157\pi\)
\(614\) −3.85596e12 −1.09490
\(615\) −2.11074e12 −0.594973
\(616\) −2.15159e12 −0.602070
\(617\) 6.31900e12 1.75535 0.877677 0.479252i \(-0.159092\pi\)
0.877677 + 0.479252i \(0.159092\pi\)
\(618\) −2.11664e11 −0.0583713
\(619\) −6.28762e12 −1.72139 −0.860693 0.509125i \(-0.829969\pi\)
−0.860693 + 0.509125i \(0.829969\pi\)
\(620\) −2.30080e12 −0.625340
\(621\) 1.72915e11 0.0466574
\(622\) −3.80747e12 −1.01995
\(623\) 1.61145e12 0.428570
\(624\) −1.02567e11 −0.0270818
\(625\) −3.15238e12 −0.826378
\(626\) 1.58616e12 0.412821
\(627\) 5.05532e12 1.30631
\(628\) 2.51418e12 0.645028
\(629\) −1.03410e13 −2.63412
\(630\) 3.72796e11 0.0942842
\(631\) −7.30194e12 −1.83361 −0.916803 0.399340i \(-0.869239\pi\)
−0.916803 + 0.399340i \(0.869239\pi\)
\(632\) −1.50423e12 −0.375049
\(633\) −1.50962e12 −0.373723
\(634\) −4.09007e11 −0.100538
\(635\) 2.97737e12 0.726692
\(636\) 1.56887e12 0.380216
\(637\) −4.28239e12 −1.03052
\(638\) −3.72659e12 −0.890469
\(639\) −1.25303e12 −0.297309
\(640\) −2.58020e12 −0.607916
\(641\) 2.82813e12 0.661665 0.330833 0.943689i \(-0.392670\pi\)
0.330833 + 0.943689i \(0.392670\pi\)
\(642\) 9.81239e10 0.0227964
\(643\) 1.81353e12 0.418384 0.209192 0.977875i \(-0.432917\pi\)
0.209192 + 0.977875i \(0.432917\pi\)
\(644\) 3.39477e11 0.0777721
\(645\) −4.01319e12 −0.913001
\(646\) 9.30815e12 2.10289
\(647\) −3.84912e12 −0.863560 −0.431780 0.901979i \(-0.642114\pi\)
−0.431780 + 0.901979i \(0.642114\pi\)
\(648\) 4.93337e11 0.109915
\(649\) −7.06722e11 −0.156368
\(650\) 5.76666e11 0.126711
\(651\) 1.43717e12 0.313614
\(652\) 4.74737e12 1.02882
\(653\) 6.98077e12 1.50243 0.751214 0.660058i \(-0.229469\pi\)
0.751214 + 0.660058i \(0.229469\pi\)
\(654\) 3.04040e12 0.649877
\(655\) −4.65195e12 −0.987528
\(656\) −1.79447e11 −0.0378329
\(657\) −3.08689e12 −0.646363
\(658\) 1.58777e11 0.0330196
\(659\) 5.02751e12 1.03841 0.519205 0.854650i \(-0.326228\pi\)
0.519205 + 0.854650i \(0.326228\pi\)
\(660\) 1.97195e12 0.404528
\(661\) 7.25536e12 1.47827 0.739133 0.673560i \(-0.235236\pi\)
0.739133 + 0.673560i \(0.235236\pi\)
\(662\) 3.83468e11 0.0776012
\(663\) 7.33966e12 1.47525
\(664\) −6.70288e11 −0.133815
\(665\) −4.43602e12 −0.879621
\(666\) −1.46540e12 −0.288617
\(667\) 1.51676e12 0.296723
\(668\) −5.94601e12 −1.15540
\(669\) 3.75334e12 0.724436
\(670\) 3.13796e11 0.0601604
\(671\) −3.40274e12 −0.648004
\(672\) 1.56164e12 0.295405
\(673\) 1.04093e13 1.95593 0.977964 0.208774i \(-0.0669473\pi\)
0.977964 + 0.208774i \(0.0669473\pi\)
\(674\) −1.62707e11 −0.0303695
\(675\) 1.56591e11 0.0290335
\(676\) −3.17095e12 −0.584021
\(677\) −1.06163e11 −0.0194234 −0.00971171 0.999953i \(-0.503091\pi\)
−0.00971171 + 0.999953i \(0.503091\pi\)
\(678\) 1.39661e12 0.253828
\(679\) 1.64690e12 0.297340
\(680\) 9.36627e12 1.67987
\(681\) 1.16981e12 0.208426
\(682\) −4.40636e12 −0.779921
\(683\) 5.27750e12 0.927973 0.463986 0.885842i \(-0.346419\pi\)
0.463986 + 0.885842i \(0.346419\pi\)
\(684\) −2.27567e12 −0.397518
\(685\) −1.01184e11 −0.0175592
\(686\) 3.10373e12 0.535088
\(687\) 7.67621e11 0.131475
\(688\) −3.41186e11 −0.0580555
\(689\) 8.53234e12 1.44239
\(690\) 4.65209e11 0.0781317
\(691\) −6.28768e12 −1.04915 −0.524577 0.851363i \(-0.675777\pi\)
−0.524577 + 0.851363i \(0.675777\pi\)
\(692\) −1.26979e12 −0.210501
\(693\) −1.23176e12 −0.202874
\(694\) −1.68945e12 −0.276457
\(695\) −7.07839e12 −1.15081
\(696\) 4.32742e12 0.699016
\(697\) 1.28412e13 2.06090
\(698\) −1.74484e12 −0.278232
\(699\) −5.40730e11 −0.0856708
\(700\) 3.07428e11 0.0483952
\(701\) 1.18219e13 1.84908 0.924540 0.381086i \(-0.124450\pi\)
0.924540 + 0.381086i \(0.124450\pi\)
\(702\) 1.04008e12 0.161641
\(703\) 1.74373e13 2.69265
\(704\) −4.52314e12 −0.694006
\(705\) −3.75387e11 −0.0572307
\(706\) −4.37176e12 −0.662270
\(707\) −5.19087e12 −0.781363
\(708\) 3.18133e11 0.0475839
\(709\) −4.92112e12 −0.731402 −0.365701 0.930732i \(-0.619171\pi\)
−0.365701 + 0.930732i \(0.619171\pi\)
\(710\) −3.37114e12 −0.497868
\(711\) −8.61154e11 −0.126377
\(712\) 5.73727e12 0.836653
\(713\) 1.79344e12 0.259886
\(714\) −2.26799e12 −0.326587
\(715\) 1.07245e13 1.53462
\(716\) −2.21060e12 −0.314342
\(717\) 1.24775e12 0.176316
\(718\) −1.18986e11 −0.0167085
\(719\) −3.96463e12 −0.553251 −0.276626 0.960978i \(-0.589216\pi\)
−0.276626 + 0.960978i \(0.589216\pi\)
\(720\) −7.49315e10 −0.0103913
\(721\) −6.13687e11 −0.0845743
\(722\) −1.12726e13 −1.54386
\(723\) −6.78255e12 −0.923147
\(724\) 2.22182e12 0.300529
\(725\) 1.37357e12 0.184642
\(726\) 1.15868e12 0.154793
\(727\) 3.63519e12 0.482638 0.241319 0.970446i \(-0.422420\pi\)
0.241319 + 0.970446i \(0.422420\pi\)
\(728\) 5.26747e12 0.695042
\(729\) 2.82430e11 0.0370370
\(730\) −8.30493e12 −1.08239
\(731\) 2.44152e13 3.16251
\(732\) 1.53176e12 0.197192
\(733\) −6.02702e12 −0.771143 −0.385572 0.922678i \(-0.625996\pi\)
−0.385572 + 0.922678i \(0.625996\pi\)
\(734\) 2.83344e12 0.360314
\(735\) −3.12855e12 −0.395412
\(736\) 1.94875e12 0.244797
\(737\) −1.03682e12 −0.129449
\(738\) 1.81969e12 0.225810
\(739\) 2.88139e12 0.355387 0.177694 0.984086i \(-0.443136\pi\)
0.177694 + 0.984086i \(0.443136\pi\)
\(740\) 6.80183e12 0.833840
\(741\) −1.23763e13 −1.50802
\(742\) −2.63653e12 −0.319312
\(743\) −1.09604e13 −1.31940 −0.659700 0.751529i \(-0.729317\pi\)
−0.659700 + 0.751529i \(0.729317\pi\)
\(744\) 5.11679e12 0.612236
\(745\) 7.32653e12 0.871354
\(746\) −3.09577e12 −0.365969
\(747\) −3.83732e11 −0.0450905
\(748\) −1.19968e13 −1.40123
\(749\) 2.84495e11 0.0330298
\(750\) 3.21384e12 0.370893
\(751\) 1.56238e12 0.179228 0.0896141 0.995977i \(-0.471437\pi\)
0.0896141 + 0.995977i \(0.471437\pi\)
\(752\) −3.19140e10 −0.00363916
\(753\) 1.41479e12 0.160366
\(754\) 9.12333e12 1.02797
\(755\) 7.24456e11 0.0811429
\(756\) 5.54482e11 0.0617361
\(757\) −1.08454e13 −1.20037 −0.600186 0.799860i \(-0.704907\pi\)
−0.600186 + 0.799860i \(0.704907\pi\)
\(758\) −7.34045e12 −0.807628
\(759\) −1.53711e12 −0.168119
\(760\) −1.57936e13 −1.71720
\(761\) 1.50904e12 0.163106 0.0815530 0.996669i \(-0.474012\pi\)
0.0815530 + 0.996669i \(0.474012\pi\)
\(762\) −2.56681e12 −0.275802
\(763\) 8.81517e12 0.941609
\(764\) −1.06022e12 −0.112584
\(765\) 5.36208e12 0.566052
\(766\) 1.78502e12 0.187333
\(767\) 1.73018e12 0.180514
\(768\) 5.44070e12 0.564325
\(769\) 5.47095e12 0.564149 0.282075 0.959392i \(-0.408977\pi\)
0.282075 + 0.959392i \(0.408977\pi\)
\(770\) −3.31392e12 −0.339730
\(771\) 6.29011e12 0.641082
\(772\) −3.46590e12 −0.351187
\(773\) 9.29631e12 0.936489 0.468245 0.883599i \(-0.344887\pi\)
0.468245 + 0.883599i \(0.344887\pi\)
\(774\) 3.45981e12 0.346512
\(775\) 1.62413e12 0.161719
\(776\) 5.86347e12 0.580466
\(777\) −4.24870e12 −0.418179
\(778\) −9.84849e12 −0.963744
\(779\) −2.16531e13 −2.10669
\(780\) −4.82767e12 −0.466994
\(781\) 1.11386e13 1.07128
\(782\) −2.83021e12 −0.270637
\(783\) 2.47739e12 0.235541
\(784\) −2.65977e11 −0.0251433
\(785\) 9.98929e12 0.938904
\(786\) 4.01049e12 0.374797
\(787\) −8.64096e12 −0.802926 −0.401463 0.915875i \(-0.631498\pi\)
−0.401463 + 0.915875i \(0.631498\pi\)
\(788\) −2.13960e12 −0.197681
\(789\) 1.57015e12 0.144243
\(790\) −2.31684e12 −0.211629
\(791\) 4.04924e12 0.367773
\(792\) −4.38545e12 −0.396051
\(793\) 8.33049e12 0.748068
\(794\) −8.66446e12 −0.773658
\(795\) 6.23340e12 0.553443
\(796\) 1.14866e12 0.101410
\(797\) 7.53539e12 0.661521 0.330760 0.943715i \(-0.392695\pi\)
0.330760 + 0.943715i \(0.392695\pi\)
\(798\) 3.82433e12 0.333843
\(799\) 2.28376e12 0.198239
\(800\) 1.76478e12 0.152330
\(801\) 3.28452e12 0.281920
\(802\) −1.24120e13 −1.05939
\(803\) 2.74404e13 2.32901
\(804\) 4.66728e11 0.0393923
\(805\) 1.34880e12 0.113205
\(806\) 1.07875e13 0.900355
\(807\) −1.67358e12 −0.138904
\(808\) −1.84811e13 −1.52538
\(809\) −4.53883e12 −0.372542 −0.186271 0.982498i \(-0.559640\pi\)
−0.186271 + 0.982498i \(0.559640\pi\)
\(810\) 7.59846e11 0.0620216
\(811\) 1.70530e13 1.38422 0.692112 0.721790i \(-0.256680\pi\)
0.692112 + 0.721790i \(0.256680\pi\)
\(812\) 4.86376e12 0.392618
\(813\) 3.79062e12 0.304300
\(814\) 1.30265e13 1.03996
\(815\) 1.88621e13 1.49755
\(816\) 4.55863e11 0.0359939
\(817\) −4.11693e13 −3.23277
\(818\) −5.87420e12 −0.458732
\(819\) 3.01556e12 0.234202
\(820\) −8.44630e12 −0.652385
\(821\) −2.05429e13 −1.57804 −0.789021 0.614367i \(-0.789412\pi\)
−0.789021 + 0.614367i \(0.789412\pi\)
\(822\) 8.72318e10 0.00666425
\(823\) 1.59691e13 1.21334 0.606670 0.794954i \(-0.292505\pi\)
0.606670 + 0.794954i \(0.292505\pi\)
\(824\) −2.18492e12 −0.165106
\(825\) −1.39199e12 −0.104615
\(826\) −5.34632e11 −0.0399618
\(827\) −1.00485e13 −0.747009 −0.373504 0.927628i \(-0.621844\pi\)
−0.373504 + 0.927628i \(0.621844\pi\)
\(828\) 6.91934e11 0.0511597
\(829\) −1.76339e13 −1.29674 −0.648369 0.761326i \(-0.724549\pi\)
−0.648369 + 0.761326i \(0.724549\pi\)
\(830\) −1.03239e12 −0.0755077
\(831\) 7.40359e12 0.538565
\(832\) 1.10734e13 0.801173
\(833\) 1.90332e13 1.36965
\(834\) 6.10234e12 0.436766
\(835\) −2.36245e13 −1.68180
\(836\) 2.02293e13 1.43236
\(837\) 2.92930e12 0.206300
\(838\) −2.88041e12 −0.201770
\(839\) 1.66900e13 1.16286 0.581429 0.813597i \(-0.302494\pi\)
0.581429 + 0.813597i \(0.302494\pi\)
\(840\) 3.84821e12 0.266687
\(841\) 7.22387e12 0.497953
\(842\) −7.80274e12 −0.534986
\(843\) 1.06152e13 0.723941
\(844\) −6.04085e12 −0.409786
\(845\) −1.25987e13 −0.850102
\(846\) 3.23625e11 0.0217208
\(847\) 3.35942e12 0.224279
\(848\) 5.29940e11 0.0351921
\(849\) 1.49091e13 0.984845
\(850\) −2.56302e12 −0.168409
\(851\) −5.30192e12 −0.346538
\(852\) −5.01410e12 −0.325998
\(853\) −7.73139e12 −0.500019 −0.250010 0.968243i \(-0.580434\pi\)
−0.250010 + 0.968243i \(0.580434\pi\)
\(854\) −2.57416e12 −0.165606
\(855\) −9.04164e12 −0.578628
\(856\) 1.01289e12 0.0644808
\(857\) 2.47110e12 0.156486 0.0782432 0.996934i \(-0.475069\pi\)
0.0782432 + 0.996934i \(0.475069\pi\)
\(858\) −9.24568e12 −0.582433
\(859\) 9.11844e11 0.0571415 0.0285707 0.999592i \(-0.490904\pi\)
0.0285707 + 0.999592i \(0.490904\pi\)
\(860\) −1.60591e13 −1.00110
\(861\) 5.27591e12 0.327177
\(862\) 1.55010e13 0.956265
\(863\) 1.90816e11 0.0117103 0.00585513 0.999983i \(-0.498136\pi\)
0.00585513 + 0.999983i \(0.498136\pi\)
\(864\) 3.18298e12 0.194322
\(865\) −5.04510e12 −0.306406
\(866\) 9.63719e12 0.582264
\(867\) −2.30158e13 −1.38338
\(868\) 5.75096e12 0.343876
\(869\) 7.65511e12 0.455368
\(870\) 6.66516e12 0.394433
\(871\) 2.53831e12 0.149439
\(872\) 3.13848e13 1.83821
\(873\) 3.35676e12 0.195595
\(874\) 4.77235e12 0.276650
\(875\) 9.31802e12 0.537387
\(876\) −1.23524e13 −0.708734
\(877\) −2.11889e13 −1.20951 −0.604757 0.796410i \(-0.706730\pi\)
−0.604757 + 0.796410i \(0.706730\pi\)
\(878\) −2.50501e12 −0.142261
\(879\) −2.90438e12 −0.164098
\(880\) 6.66093e11 0.0374423
\(881\) −1.88415e13 −1.05371 −0.526857 0.849954i \(-0.676630\pi\)
−0.526857 + 0.849954i \(0.676630\pi\)
\(882\) 2.69715e12 0.150071
\(883\) −1.58998e13 −0.880175 −0.440088 0.897955i \(-0.645053\pi\)
−0.440088 + 0.897955i \(0.645053\pi\)
\(884\) 2.93702e13 1.61760
\(885\) 1.26400e12 0.0692632
\(886\) −1.87785e13 −1.02378
\(887\) 1.82433e13 0.989570 0.494785 0.869016i \(-0.335247\pi\)
0.494785 + 0.869016i \(0.335247\pi\)
\(888\) −1.51267e13 −0.816368
\(889\) −7.44208e12 −0.399610
\(890\) 8.83663e12 0.472098
\(891\) −2.51062e12 −0.133454
\(892\) 1.50193e13 0.794342
\(893\) −3.85091e12 −0.202643
\(894\) −6.31626e12 −0.330706
\(895\) −8.78311e12 −0.457556
\(896\) 6.44934e12 0.334295
\(897\) 3.76310e12 0.194079
\(898\) −7.33014e12 −0.376157
\(899\) 2.56950e13 1.31199
\(900\) 6.26611e11 0.0318351
\(901\) −3.79223e13 −1.91705
\(902\) −1.61759e13 −0.813652
\(903\) 1.00312e13 0.502061
\(904\) 1.44165e13 0.717965
\(905\) 8.82769e12 0.437450
\(906\) −6.24560e11 −0.0307962
\(907\) 4.33489e12 0.212689 0.106345 0.994329i \(-0.466085\pi\)
0.106345 + 0.994329i \(0.466085\pi\)
\(908\) 4.68108e12 0.228539
\(909\) −1.05802e13 −0.513993
\(910\) 8.11304e12 0.392191
\(911\) 2.18451e13 1.05080 0.525401 0.850854i \(-0.323915\pi\)
0.525401 + 0.850854i \(0.323915\pi\)
\(912\) −7.68685e11 −0.0367935
\(913\) 3.41113e12 0.162472
\(914\) 7.71594e12 0.365705
\(915\) 6.08594e12 0.287034
\(916\) 3.07170e12 0.144161
\(917\) 1.16278e13 0.543044
\(918\) −4.62269e12 −0.214834
\(919\) −2.52060e13 −1.16569 −0.582845 0.812583i \(-0.698061\pi\)
−0.582845 + 0.812583i \(0.698061\pi\)
\(920\) 4.80215e12 0.220999
\(921\) −2.27870e13 −1.04356
\(922\) 2.14843e12 0.0979110
\(923\) −2.72693e13 −1.23670
\(924\) −4.92899e12 −0.222451
\(925\) −4.80139e12 −0.215640
\(926\) 3.06847e12 0.137143
\(927\) −1.25084e12 −0.0556343
\(928\) 2.79202e13 1.23581
\(929\) −6.09574e12 −0.268507 −0.134254 0.990947i \(-0.542864\pi\)
−0.134254 + 0.990947i \(0.542864\pi\)
\(930\) 7.88095e12 0.345466
\(931\) −3.20942e13 −1.40008
\(932\) −2.16377e12 −0.0939377
\(933\) −2.25004e13 −0.972127
\(934\) 1.53371e13 0.659451
\(935\) −4.76654e13 −2.03963
\(936\) 1.07363e13 0.457209
\(937\) 8.28034e12 0.350930 0.175465 0.984486i \(-0.443857\pi\)
0.175465 + 0.984486i \(0.443857\pi\)
\(938\) −7.84349e11 −0.0330824
\(939\) 9.37347e12 0.393464
\(940\) −1.50214e12 −0.0627532
\(941\) −1.28286e13 −0.533368 −0.266684 0.963784i \(-0.585928\pi\)
−0.266684 + 0.963784i \(0.585928\pi\)
\(942\) −8.61186e12 −0.356343
\(943\) 6.58376e12 0.271126
\(944\) 1.07460e11 0.00440427
\(945\) 2.20305e12 0.0898632
\(946\) −3.07555e13 −1.24857
\(947\) −4.37117e12 −0.176613 −0.0883066 0.996093i \(-0.528146\pi\)
−0.0883066 + 0.996093i \(0.528146\pi\)
\(948\) −3.44598e12 −0.138572
\(949\) −6.71789e13 −2.68865
\(950\) 4.32181e12 0.172151
\(951\) −2.41704e12 −0.0958235
\(952\) −2.34115e13 −0.923767
\(953\) 1.81879e13 0.714272 0.357136 0.934052i \(-0.383753\pi\)
0.357136 + 0.934052i \(0.383753\pi\)
\(954\) −5.37387e12 −0.210049
\(955\) −4.21244e12 −0.163877
\(956\) 4.99299e12 0.193330
\(957\) −2.20224e13 −0.848715
\(958\) −1.21908e13 −0.467616
\(959\) 2.52915e11 0.00965586
\(960\) 8.08981e12 0.307410
\(961\) 3.94240e12 0.149109
\(962\) −3.18910e13 −1.20055
\(963\) 5.79867e11 0.0217275
\(964\) −2.71409e13 −1.01223
\(965\) −1.37706e13 −0.511188
\(966\) −1.16281e12 −0.0429649
\(967\) 2.69067e13 0.989558 0.494779 0.869019i \(-0.335249\pi\)
0.494779 + 0.869019i \(0.335249\pi\)
\(968\) 1.19606e13 0.437838
\(969\) 5.50069e13 2.00429
\(970\) 9.03100e12 0.327539
\(971\) 2.98718e13 1.07839 0.539193 0.842182i \(-0.318729\pi\)
0.539193 + 0.842182i \(0.318729\pi\)
\(972\) 1.13016e12 0.0406110
\(973\) 1.76928e13 0.632832
\(974\) −1.32916e13 −0.473220
\(975\) 3.40783e12 0.120770
\(976\) 5.17403e11 0.0182518
\(977\) −1.14354e13 −0.401536 −0.200768 0.979639i \(-0.564344\pi\)
−0.200768 + 0.979639i \(0.564344\pi\)
\(978\) −1.62612e13 −0.568366
\(979\) −2.91973e13 −1.01583
\(980\) −1.25191e13 −0.433568
\(981\) 1.79674e13 0.619404
\(982\) −9.74372e12 −0.334367
\(983\) −1.66845e13 −0.569932 −0.284966 0.958538i \(-0.591982\pi\)
−0.284966 + 0.958538i \(0.591982\pi\)
\(984\) 1.87839e13 0.638715
\(985\) −8.50100e12 −0.287744
\(986\) −4.05490e13 −1.36626
\(987\) 9.38300e11 0.0314713
\(988\) −4.95247e13 −1.65354
\(989\) 1.25178e13 0.416050
\(990\) −6.75454e12 −0.223479
\(991\) 4.04049e13 1.33077 0.665384 0.746501i \(-0.268268\pi\)
0.665384 + 0.746501i \(0.268268\pi\)
\(992\) 3.30131e13 1.08239
\(993\) 2.26612e12 0.0739625
\(994\) 8.42634e12 0.273779
\(995\) 4.56381e12 0.147613
\(996\) −1.53553e12 −0.0494415
\(997\) −3.04999e13 −0.977620 −0.488810 0.872390i \(-0.662569\pi\)
−0.488810 + 0.872390i \(0.662569\pi\)
\(998\) −2.11746e13 −0.675660
\(999\) −8.65985e12 −0.275084
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.1.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.8 22 1.1 even 1 trivial