Properties

Label 177.12.a.a.1.15
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +89491.8 q^{10} -483868. q^{11} +468984. q^{12} +396263. q^{13} +933890. q^{14} -2.00171e6 q^{15} +3.48309e6 q^{16} -1.10618e7 q^{17} +641505. q^{18} +2.99198e6 q^{19} -1.58982e7 q^{20} -2.08888e7 q^{21} -5.25672e6 q^{22} +1.83605e7 q^{23} +1.05016e7 q^{24} +1.90283e7 q^{25} +4.30498e6 q^{26} -1.43489e7 q^{27} -1.65905e8 q^{28} +2.21124e7 q^{29} -2.17465e7 q^{30} -2.01984e8 q^{31} +1.26347e8 q^{32} +1.17580e8 q^{33} -1.20175e8 q^{34} +7.08115e8 q^{35} -1.13963e8 q^{36} -8.11946e8 q^{37} +3.25047e7 q^{38} -9.62920e7 q^{39} -3.55996e8 q^{40} -1.31207e9 q^{41} -2.26935e8 q^{42} +1.05670e8 q^{43} +9.33854e8 q^{44} +4.86416e8 q^{45} +1.99467e8 q^{46} +2.23379e9 q^{47} -8.46390e8 q^{48} +5.41220e9 q^{49} +2.06722e8 q^{50} +2.68803e9 q^{51} -7.64778e8 q^{52} +3.80575e9 q^{53} -1.55886e8 q^{54} -3.98587e9 q^{55} -3.71499e9 q^{56} -7.27050e8 q^{57} +2.40228e8 q^{58} +7.14924e8 q^{59} +3.86326e9 q^{60} +7.57915e9 q^{61} -2.19434e9 q^{62} +5.07599e9 q^{63} -5.76073e9 q^{64} +3.26422e9 q^{65} +1.27738e9 q^{66} -9.14960e9 q^{67} +2.13491e10 q^{68} -4.46159e9 q^{69} +7.69292e9 q^{70} +1.16988e10 q^{71} -2.55189e9 q^{72} -9.76078e9 q^{73} -8.82094e9 q^{74} -4.62388e9 q^{75} -5.77444e9 q^{76} -4.15945e10 q^{77} -1.04611e9 q^{78} +8.26975e9 q^{79} +2.86919e10 q^{80} +3.48678e9 q^{81} -1.42543e10 q^{82} -1.53345e10 q^{83} +4.03150e10 q^{84} -9.11220e10 q^{85} +1.14799e9 q^{86} -5.37331e9 q^{87} +2.09111e10 q^{88} +1.16326e9 q^{89} +5.28440e9 q^{90} +3.40637e10 q^{91} -3.54352e10 q^{92} +4.90821e10 q^{93} +2.42677e10 q^{94} +2.46464e10 q^{95} -3.07024e10 q^{96} -8.72582e10 q^{97} +5.87978e10 q^{98} -2.85719e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.8639 0.240062 0.120031 0.992770i \(-0.461701\pi\)
0.120031 + 0.992770i \(0.461701\pi\)
\(3\) −243.000 −0.577350
\(4\) −1929.97 −0.942370
\(5\) 8237.50 1.17886 0.589428 0.807821i \(-0.299353\pi\)
0.589428 + 0.807821i \(0.299353\pi\)
\(6\) −2639.94 −0.138600
\(7\) 85962.3 1.93317 0.966583 0.256355i \(-0.0825216\pi\)
0.966583 + 0.256355i \(0.0825216\pi\)
\(8\) −43216.5 −0.466288
\(9\) 59049.0 0.333333
\(10\) 89491.8 0.282998
\(11\) −483868. −0.905873 −0.452937 0.891543i \(-0.649624\pi\)
−0.452937 + 0.891543i \(0.649624\pi\)
\(12\) 468984. 0.544078
\(13\) 396263. 0.296002 0.148001 0.988987i \(-0.452716\pi\)
0.148001 + 0.988987i \(0.452716\pi\)
\(14\) 933890. 0.464079
\(15\) −2.00171e6 −0.680612
\(16\) 3.48309e6 0.830432
\(17\) −1.10618e7 −1.88955 −0.944775 0.327719i \(-0.893720\pi\)
−0.944775 + 0.327719i \(0.893720\pi\)
\(18\) 641505. 0.0800205
\(19\) 2.99198e6 0.277213 0.138606 0.990348i \(-0.455738\pi\)
0.138606 + 0.990348i \(0.455738\pi\)
\(20\) −1.58982e7 −1.11092
\(21\) −2.08888e7 −1.11611
\(22\) −5.25672e6 −0.217465
\(23\) 1.83605e7 0.594813 0.297406 0.954751i \(-0.403878\pi\)
0.297406 + 0.954751i \(0.403878\pi\)
\(24\) 1.05016e7 0.269212
\(25\) 1.90283e7 0.389700
\(26\) 4.30498e6 0.0710588
\(27\) −1.43489e7 −0.192450
\(28\) −1.65905e8 −1.82176
\(29\) 2.21124e7 0.200192 0.100096 0.994978i \(-0.468085\pi\)
0.100096 + 0.994978i \(0.468085\pi\)
\(30\) −2.17465e7 −0.163389
\(31\) −2.01984e8 −1.26715 −0.633574 0.773682i \(-0.718413\pi\)
−0.633574 + 0.773682i \(0.718413\pi\)
\(32\) 1.26347e8 0.665643
\(33\) 1.17580e8 0.523006
\(34\) −1.20175e8 −0.453608
\(35\) 7.08115e8 2.27892
\(36\) −1.13963e8 −0.314123
\(37\) −8.11946e8 −1.92494 −0.962471 0.271385i \(-0.912518\pi\)
−0.962471 + 0.271385i \(0.912518\pi\)
\(38\) 3.25047e7 0.0665482
\(39\) −9.62920e7 −0.170897
\(40\) −3.55996e8 −0.549687
\(41\) −1.31207e9 −1.76867 −0.884335 0.466853i \(-0.845388\pi\)
−0.884335 + 0.466853i \(0.845388\pi\)
\(42\) −2.26935e8 −0.267936
\(43\) 1.05670e8 0.109616 0.0548080 0.998497i \(-0.482545\pi\)
0.0548080 + 0.998497i \(0.482545\pi\)
\(44\) 9.33854e8 0.853668
\(45\) 4.86416e8 0.392952
\(46\) 1.99467e8 0.142792
\(47\) 2.23379e9 1.42070 0.710351 0.703847i \(-0.248536\pi\)
0.710351 + 0.703847i \(0.248536\pi\)
\(48\) −8.46390e8 −0.479450
\(49\) 5.41220e9 2.73713
\(50\) 2.06722e8 0.0935519
\(51\) 2.68803e9 1.09093
\(52\) −7.64778e8 −0.278944
\(53\) 3.80575e9 1.25004 0.625019 0.780610i \(-0.285091\pi\)
0.625019 + 0.780610i \(0.285091\pi\)
\(54\) −1.55886e8 −0.0461999
\(55\) −3.98587e9 −1.06789
\(56\) −3.71499e9 −0.901413
\(57\) −7.27050e8 −0.160049
\(58\) 2.40228e8 0.0480584
\(59\) 7.14924e8 0.130189
\(60\) 3.86326e9 0.641389
\(61\) 7.57915e9 1.14896 0.574482 0.818517i \(-0.305204\pi\)
0.574482 + 0.818517i \(0.305204\pi\)
\(62\) −2.19434e9 −0.304193
\(63\) 5.07599e9 0.644388
\(64\) −5.76073e9 −0.670637
\(65\) 3.26422e9 0.348944
\(66\) 1.27738e9 0.125554
\(67\) −9.14960e9 −0.827925 −0.413962 0.910294i \(-0.635856\pi\)
−0.413962 + 0.910294i \(0.635856\pi\)
\(68\) 2.13491e10 1.78066
\(69\) −4.46159e9 −0.343415
\(70\) 7.69292e9 0.547082
\(71\) 1.16988e10 0.769518 0.384759 0.923017i \(-0.374285\pi\)
0.384759 + 0.923017i \(0.374285\pi\)
\(72\) −2.55189e9 −0.155429
\(73\) −9.76078e9 −0.551073 −0.275536 0.961291i \(-0.588855\pi\)
−0.275536 + 0.961291i \(0.588855\pi\)
\(74\) −8.82094e9 −0.462105
\(75\) −4.62388e9 −0.224993
\(76\) −5.77444e9 −0.261237
\(77\) −4.15945e10 −1.75120
\(78\) −1.04611e9 −0.0410258
\(79\) 8.26975e9 0.302373 0.151187 0.988505i \(-0.451691\pi\)
0.151187 + 0.988505i \(0.451691\pi\)
\(80\) 2.86919e10 0.978960
\(81\) 3.48678e9 0.111111
\(82\) −1.42543e10 −0.424590
\(83\) −1.53345e10 −0.427308 −0.213654 0.976909i \(-0.568537\pi\)
−0.213654 + 0.976909i \(0.568537\pi\)
\(84\) 4.03150e10 1.05179
\(85\) −9.11220e10 −2.22751
\(86\) 1.14799e9 0.0263146
\(87\) −5.37331e9 −0.115581
\(88\) 2.09111e10 0.422398
\(89\) 1.16326e9 0.0220816 0.0110408 0.999939i \(-0.496486\pi\)
0.0110408 + 0.999939i \(0.496486\pi\)
\(90\) 5.28440e9 0.0943326
\(91\) 3.40637e10 0.572222
\(92\) −3.54352e10 −0.560534
\(93\) 4.90821e10 0.731588
\(94\) 2.42677e10 0.341056
\(95\) 2.46464e10 0.326794
\(96\) −3.07024e10 −0.384309
\(97\) −8.72582e10 −1.03172 −0.515860 0.856673i \(-0.672527\pi\)
−0.515860 + 0.856673i \(0.672527\pi\)
\(98\) 5.87978e10 0.657079
\(99\) −2.85719e10 −0.301958
\(100\) −3.67241e10 −0.367241
\(101\) −1.13741e11 −1.07683 −0.538417 0.842678i \(-0.680978\pi\)
−0.538417 + 0.842678i \(0.680978\pi\)
\(102\) 2.92026e10 0.261891
\(103\) −1.22475e11 −1.04098 −0.520489 0.853869i \(-0.674250\pi\)
−0.520489 + 0.853869i \(0.674250\pi\)
\(104\) −1.71251e10 −0.138023
\(105\) −1.72072e11 −1.31574
\(106\) 4.13455e10 0.300086
\(107\) −7.70211e10 −0.530883 −0.265441 0.964127i \(-0.585518\pi\)
−0.265441 + 0.964127i \(0.585518\pi\)
\(108\) 2.76930e10 0.181359
\(109\) −2.18663e11 −1.36123 −0.680613 0.732643i \(-0.738287\pi\)
−0.680613 + 0.732643i \(0.738287\pi\)
\(110\) −4.33022e10 −0.256360
\(111\) 1.97303e11 1.11137
\(112\) 2.99414e11 1.60536
\(113\) −1.83692e11 −0.937907 −0.468953 0.883223i \(-0.655369\pi\)
−0.468953 + 0.883223i \(0.655369\pi\)
\(114\) −7.89864e9 −0.0384216
\(115\) 1.51244e11 0.701198
\(116\) −4.26764e10 −0.188655
\(117\) 2.33989e10 0.0986675
\(118\) 7.76690e9 0.0312534
\(119\) −9.50902e11 −3.65281
\(120\) 8.65070e10 0.317362
\(121\) −5.11831e10 −0.179394
\(122\) 8.23395e10 0.275822
\(123\) 3.18834e11 1.02114
\(124\) 3.89824e11 1.19412
\(125\) −2.45476e11 −0.719456
\(126\) 5.51453e10 0.154693
\(127\) 2.26605e10 0.0608624 0.0304312 0.999537i \(-0.490312\pi\)
0.0304312 + 0.999537i \(0.490312\pi\)
\(128\) −3.21344e11 −0.826638
\(129\) −2.56777e10 −0.0632868
\(130\) 3.54623e10 0.0837681
\(131\) 6.04141e11 1.36819 0.684095 0.729393i \(-0.260197\pi\)
0.684095 + 0.729393i \(0.260197\pi\)
\(132\) −2.26926e11 −0.492866
\(133\) 2.57197e11 0.535898
\(134\) −9.94008e10 −0.198753
\(135\) −1.18199e11 −0.226871
\(136\) 4.78054e11 0.881076
\(137\) 6.09570e10 0.107910 0.0539548 0.998543i \(-0.482817\pi\)
0.0539548 + 0.998543i \(0.482817\pi\)
\(138\) −4.84705e10 −0.0824408
\(139\) −1.08597e12 −1.77515 −0.887575 0.460664i \(-0.847611\pi\)
−0.887575 + 0.460664i \(0.847611\pi\)
\(140\) −1.36664e12 −2.14759
\(141\) −5.42810e11 −0.820243
\(142\) 1.27095e11 0.184732
\(143\) −1.91739e11 −0.268141
\(144\) 2.05673e11 0.276811
\(145\) 1.82151e11 0.235998
\(146\) −1.06041e11 −0.132291
\(147\) −1.31516e12 −1.58028
\(148\) 1.56704e12 1.81401
\(149\) 1.17467e12 1.31036 0.655179 0.755474i \(-0.272593\pi\)
0.655179 + 0.755474i \(0.272593\pi\)
\(150\) −5.02336e10 −0.0540122
\(151\) 1.70016e12 1.76244 0.881222 0.472702i \(-0.156721\pi\)
0.881222 + 0.472702i \(0.156721\pi\)
\(152\) −1.29303e11 −0.129261
\(153\) −6.53191e11 −0.629850
\(154\) −4.51880e11 −0.420396
\(155\) −1.66384e12 −1.49378
\(156\) 1.85841e11 0.161048
\(157\) −1.21187e12 −1.01393 −0.506965 0.861967i \(-0.669233\pi\)
−0.506965 + 0.861967i \(0.669233\pi\)
\(158\) 8.98422e10 0.0725882
\(159\) −9.24798e11 −0.721710
\(160\) 1.04079e12 0.784697
\(161\) 1.57831e12 1.14987
\(162\) 3.78802e10 0.0266735
\(163\) 5.80190e11 0.394947 0.197473 0.980308i \(-0.436726\pi\)
0.197473 + 0.980308i \(0.436726\pi\)
\(164\) 2.53227e12 1.66674
\(165\) 9.68565e11 0.616549
\(166\) −1.66594e11 −0.102580
\(167\) −2.85780e12 −1.70252 −0.851258 0.524747i \(-0.824160\pi\)
−0.851258 + 0.524747i \(0.824160\pi\)
\(168\) 9.02743e11 0.520431
\(169\) −1.63514e12 −0.912383
\(170\) −9.89944e11 −0.534739
\(171\) 1.76673e11 0.0924043
\(172\) −2.03940e11 −0.103299
\(173\) −2.29060e11 −0.112381 −0.0561907 0.998420i \(-0.517895\pi\)
−0.0561907 + 0.998420i \(0.517895\pi\)
\(174\) −5.83754e10 −0.0277465
\(175\) 1.63572e12 0.753354
\(176\) −1.68536e12 −0.752267
\(177\) −1.73727e11 −0.0751646
\(178\) 1.26376e10 0.00530096
\(179\) 1.96341e12 0.798581 0.399290 0.916824i \(-0.369257\pi\)
0.399290 + 0.916824i \(0.369257\pi\)
\(180\) −9.38771e11 −0.370306
\(181\) −3.39509e12 −1.29903 −0.649514 0.760349i \(-0.725028\pi\)
−0.649514 + 0.760349i \(0.725028\pi\)
\(182\) 3.70066e11 0.137368
\(183\) −1.84173e12 −0.663355
\(184\) −7.93475e11 −0.277354
\(185\) −6.68841e12 −2.26923
\(186\) 5.33225e11 0.175626
\(187\) 5.35248e12 1.71169
\(188\) −4.31115e12 −1.33883
\(189\) −1.23347e12 −0.372038
\(190\) 2.67757e11 0.0784506
\(191\) −1.17412e12 −0.334218 −0.167109 0.985938i \(-0.553443\pi\)
−0.167109 + 0.985938i \(0.553443\pi\)
\(192\) 1.39986e12 0.387193
\(193\) 1.88890e12 0.507744 0.253872 0.967238i \(-0.418296\pi\)
0.253872 + 0.967238i \(0.418296\pi\)
\(194\) −9.47968e11 −0.247676
\(195\) −7.93205e11 −0.201463
\(196\) −1.04454e13 −2.57939
\(197\) 6.29932e12 1.51262 0.756310 0.654214i \(-0.227000\pi\)
0.756310 + 0.654214i \(0.227000\pi\)
\(198\) −3.10404e11 −0.0724884
\(199\) −9.06904e11 −0.206001 −0.103001 0.994681i \(-0.532844\pi\)
−0.103001 + 0.994681i \(0.532844\pi\)
\(200\) −8.22337e11 −0.181712
\(201\) 2.22335e12 0.478003
\(202\) −1.23567e12 −0.258507
\(203\) 1.90083e12 0.387004
\(204\) −5.18783e12 −1.02806
\(205\) −1.08082e13 −2.08501
\(206\) −1.33056e12 −0.249899
\(207\) 1.08417e12 0.198271
\(208\) 1.38022e12 0.245810
\(209\) −1.44772e12 −0.251120
\(210\) −1.86938e12 −0.315858
\(211\) 3.90505e12 0.642796 0.321398 0.946944i \(-0.395847\pi\)
0.321398 + 0.946944i \(0.395847\pi\)
\(212\) −7.34500e12 −1.17800
\(213\) −2.84280e12 −0.444281
\(214\) −8.36753e11 −0.127445
\(215\) 8.70454e11 0.129221
\(216\) 6.20110e11 0.0897373
\(217\) −1.73630e13 −2.44961
\(218\) −2.37555e12 −0.326778
\(219\) 2.37187e12 0.318162
\(220\) 7.69262e12 1.00635
\(221\) −4.38340e12 −0.559312
\(222\) 2.14349e12 0.266796
\(223\) −7.60771e12 −0.923798 −0.461899 0.886933i \(-0.652832\pi\)
−0.461899 + 0.886933i \(0.652832\pi\)
\(224\) 1.08611e13 1.28680
\(225\) 1.12360e12 0.129900
\(226\) −1.99562e12 −0.225155
\(227\) −1.20683e13 −1.32894 −0.664468 0.747317i \(-0.731342\pi\)
−0.664468 + 0.747317i \(0.731342\pi\)
\(228\) 1.40319e12 0.150825
\(229\) 7.78483e12 0.816872 0.408436 0.912787i \(-0.366074\pi\)
0.408436 + 0.912787i \(0.366074\pi\)
\(230\) 1.64311e12 0.168331
\(231\) 1.01075e13 1.01106
\(232\) −9.55621e11 −0.0933473
\(233\) 1.58706e13 1.51403 0.757016 0.653396i \(-0.226656\pi\)
0.757016 + 0.653396i \(0.226656\pi\)
\(234\) 2.54205e11 0.0236863
\(235\) 1.84008e13 1.67480
\(236\) −1.37979e12 −0.122686
\(237\) −2.00955e12 −0.174575
\(238\) −1.03305e13 −0.876900
\(239\) 1.46660e13 1.21653 0.608264 0.793735i \(-0.291866\pi\)
0.608264 + 0.793735i \(0.291866\pi\)
\(240\) −6.97214e12 −0.565203
\(241\) −1.66704e13 −1.32085 −0.660423 0.750894i \(-0.729623\pi\)
−0.660423 + 0.750894i \(0.729623\pi\)
\(242\) −5.56051e11 −0.0430655
\(243\) −8.47289e11 −0.0641500
\(244\) −1.46276e13 −1.08275
\(245\) 4.45830e13 3.22668
\(246\) 3.46379e12 0.245137
\(247\) 1.18561e12 0.0820557
\(248\) 8.72903e12 0.590856
\(249\) 3.72629e12 0.246707
\(250\) −2.66684e12 −0.172714
\(251\) 9.30603e12 0.589602 0.294801 0.955559i \(-0.404747\pi\)
0.294801 + 0.955559i \(0.404747\pi\)
\(252\) −9.79653e12 −0.607253
\(253\) −8.88404e12 −0.538825
\(254\) 2.46182e11 0.0146107
\(255\) 2.21426e13 1.28605
\(256\) 8.30691e12 0.472193
\(257\) 6.33866e12 0.352667 0.176334 0.984330i \(-0.443576\pi\)
0.176334 + 0.984330i \(0.443576\pi\)
\(258\) −2.78962e11 −0.0151927
\(259\) −6.97968e13 −3.72123
\(260\) −6.29986e12 −0.328835
\(261\) 1.30572e12 0.0667307
\(262\) 6.56336e12 0.328450
\(263\) −2.79755e13 −1.37095 −0.685474 0.728097i \(-0.740405\pi\)
−0.685474 + 0.728097i \(0.740405\pi\)
\(264\) −5.08140e12 −0.243872
\(265\) 3.13499e13 1.47361
\(266\) 2.79418e12 0.128649
\(267\) −2.82672e11 −0.0127488
\(268\) 1.76585e13 0.780212
\(269\) −2.54120e13 −1.10002 −0.550011 0.835157i \(-0.685377\pi\)
−0.550011 + 0.835157i \(0.685377\pi\)
\(270\) −1.28411e12 −0.0544630
\(271\) −1.78642e13 −0.742426 −0.371213 0.928548i \(-0.621058\pi\)
−0.371213 + 0.928548i \(0.621058\pi\)
\(272\) −3.85294e13 −1.56914
\(273\) −8.27748e12 −0.330372
\(274\) 6.62234e11 0.0259050
\(275\) −9.20719e12 −0.353019
\(276\) 8.61076e12 0.323624
\(277\) −3.46602e13 −1.27700 −0.638501 0.769621i \(-0.720445\pi\)
−0.638501 + 0.769621i \(0.720445\pi\)
\(278\) −1.17979e13 −0.426145
\(279\) −1.19269e13 −0.422383
\(280\) −3.06023e13 −1.06264
\(281\) 6.87979e12 0.234256 0.117128 0.993117i \(-0.462631\pi\)
0.117128 + 0.993117i \(0.462631\pi\)
\(282\) −5.89706e12 −0.196909
\(283\) −3.44800e13 −1.12913 −0.564563 0.825390i \(-0.690955\pi\)
−0.564563 + 0.825390i \(0.690955\pi\)
\(284\) −2.25783e13 −0.725171
\(285\) −5.98908e12 −0.188675
\(286\) −2.08304e12 −0.0643703
\(287\) −1.12789e14 −3.41913
\(288\) 7.46069e12 0.221881
\(289\) 8.80925e13 2.57040
\(290\) 1.97888e12 0.0566539
\(291\) 2.12037e13 0.595663
\(292\) 1.88381e13 0.519314
\(293\) −5.73101e13 −1.55046 −0.775228 0.631681i \(-0.782365\pi\)
−0.775228 + 0.631681i \(0.782365\pi\)
\(294\) −1.42879e13 −0.379365
\(295\) 5.88919e12 0.153474
\(296\) 3.50895e13 0.897578
\(297\) 6.94298e12 0.174335
\(298\) 1.27615e13 0.314566
\(299\) 7.27557e12 0.176066
\(300\) 8.92397e12 0.212027
\(301\) 9.08361e12 0.211906
\(302\) 1.84704e13 0.423095
\(303\) 2.76390e13 0.621711
\(304\) 1.04213e13 0.230207
\(305\) 6.24333e13 1.35446
\(306\) −7.09623e12 −0.151203
\(307\) 1.85741e13 0.388728 0.194364 0.980929i \(-0.437736\pi\)
0.194364 + 0.980929i \(0.437736\pi\)
\(308\) 8.02762e13 1.65028
\(309\) 2.97613e13 0.601008
\(310\) −1.80759e13 −0.358600
\(311\) 6.17250e12 0.120304 0.0601519 0.998189i \(-0.480841\pi\)
0.0601519 + 0.998189i \(0.480841\pi\)
\(312\) 4.16140e12 0.0796874
\(313\) 4.47637e13 0.842233 0.421117 0.907006i \(-0.361638\pi\)
0.421117 + 0.907006i \(0.361638\pi\)
\(314\) −1.31657e13 −0.243406
\(315\) 4.18135e13 0.759641
\(316\) −1.59604e13 −0.284948
\(317\) −5.36595e13 −0.941500 −0.470750 0.882267i \(-0.656017\pi\)
−0.470750 + 0.882267i \(0.656017\pi\)
\(318\) −1.00470e13 −0.173255
\(319\) −1.06995e13 −0.181349
\(320\) −4.74540e13 −0.790584
\(321\) 1.87161e13 0.306505
\(322\) 1.71466e13 0.276040
\(323\) −3.30968e13 −0.523808
\(324\) −6.72941e12 −0.104708
\(325\) 7.54022e12 0.115352
\(326\) 6.30315e12 0.0948115
\(327\) 5.31352e13 0.785905
\(328\) 5.67032e13 0.824710
\(329\) 1.92021e14 2.74645
\(330\) 1.05224e13 0.148010
\(331\) −4.04640e13 −0.559777 −0.279888 0.960033i \(-0.590297\pi\)
−0.279888 + 0.960033i \(0.590297\pi\)
\(332\) 2.95953e13 0.402683
\(333\) −4.79446e13 −0.641647
\(334\) −3.10470e13 −0.408709
\(335\) −7.53699e13 −0.976004
\(336\) −7.27577e13 −0.926857
\(337\) 1.42628e14 1.78748 0.893741 0.448583i \(-0.148071\pi\)
0.893741 + 0.448583i \(0.148071\pi\)
\(338\) −1.77640e13 −0.219028
\(339\) 4.46373e13 0.541501
\(340\) 1.75863e14 2.09914
\(341\) 9.77336e13 1.14788
\(342\) 1.91937e12 0.0221827
\(343\) 2.95270e14 3.35816
\(344\) −4.56667e12 −0.0511127
\(345\) −3.67524e13 −0.404837
\(346\) −2.48849e12 −0.0269785
\(347\) −7.80059e12 −0.0832368 −0.0416184 0.999134i \(-0.513251\pi\)
−0.0416184 + 0.999134i \(0.513251\pi\)
\(348\) 1.03704e13 0.108920
\(349\) 7.69940e12 0.0796007 0.0398004 0.999208i \(-0.487328\pi\)
0.0398004 + 0.999208i \(0.487328\pi\)
\(350\) 1.77703e13 0.180851
\(351\) −5.68594e12 −0.0569657
\(352\) −6.11355e13 −0.602989
\(353\) 7.78335e13 0.755797 0.377899 0.925847i \(-0.376647\pi\)
0.377899 + 0.925847i \(0.376647\pi\)
\(354\) −1.88736e12 −0.0180441
\(355\) 9.63685e13 0.907150
\(356\) −2.24506e12 −0.0208091
\(357\) 2.31069e14 2.10895
\(358\) 2.13304e13 0.191709
\(359\) −2.86817e13 −0.253855 −0.126928 0.991912i \(-0.540512\pi\)
−0.126928 + 0.991912i \(0.540512\pi\)
\(360\) −2.10212e13 −0.183229
\(361\) −1.07538e14 −0.923153
\(362\) −3.68840e13 −0.311847
\(363\) 1.24375e13 0.103573
\(364\) −6.57421e13 −0.539245
\(365\) −8.04044e13 −0.649635
\(366\) −2.00085e13 −0.159246
\(367\) −1.54421e14 −1.21072 −0.605361 0.795951i \(-0.706971\pi\)
−0.605361 + 0.795951i \(0.706971\pi\)
\(368\) 6.39510e13 0.493952
\(369\) −7.74766e13 −0.589556
\(370\) −7.26625e13 −0.544754
\(371\) 3.27151e14 2.41653
\(372\) −9.47272e13 −0.689427
\(373\) −1.03292e14 −0.740747 −0.370374 0.928883i \(-0.620770\pi\)
−0.370374 + 0.928883i \(0.620770\pi\)
\(374\) 5.81490e13 0.410912
\(375\) 5.96507e13 0.415378
\(376\) −9.65364e13 −0.662457
\(377\) 8.76233e12 0.0592574
\(378\) −1.34003e13 −0.0893120
\(379\) 5.20020e13 0.341589 0.170795 0.985307i \(-0.445367\pi\)
0.170795 + 0.985307i \(0.445367\pi\)
\(380\) −4.75669e13 −0.307961
\(381\) −5.50650e12 −0.0351389
\(382\) −1.27556e13 −0.0802329
\(383\) 1.46641e14 0.909204 0.454602 0.890695i \(-0.349782\pi\)
0.454602 + 0.890695i \(0.349782\pi\)
\(384\) 7.80866e13 0.477259
\(385\) −3.42634e14 −2.06441
\(386\) 2.05210e13 0.121890
\(387\) 6.23969e12 0.0365387
\(388\) 1.68406e14 0.972262
\(389\) −7.06368e13 −0.402076 −0.201038 0.979583i \(-0.564432\pi\)
−0.201038 + 0.979583i \(0.564432\pi\)
\(390\) −8.61734e12 −0.0483635
\(391\) −2.03100e14 −1.12393
\(392\) −2.33896e14 −1.27629
\(393\) −1.46806e14 −0.789925
\(394\) 6.84355e13 0.363122
\(395\) 6.81221e13 0.356454
\(396\) 5.51431e13 0.284556
\(397\) −2.55213e14 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(398\) −9.85256e12 −0.0494529
\(399\) −6.24989e13 −0.309401
\(400\) 6.62772e13 0.323619
\(401\) −2.40852e14 −1.16000 −0.579998 0.814618i \(-0.696947\pi\)
−0.579998 + 0.814618i \(0.696947\pi\)
\(402\) 2.41544e13 0.114750
\(403\) −8.00388e13 −0.375079
\(404\) 2.19517e14 1.01478
\(405\) 2.87224e13 0.130984
\(406\) 2.06506e13 0.0929049
\(407\) 3.92875e14 1.74375
\(408\) −1.16167e14 −0.508689
\(409\) −6.22186e11 −0.00268808 −0.00134404 0.999999i \(-0.500428\pi\)
−0.00134404 + 0.999999i \(0.500428\pi\)
\(410\) −1.17420e14 −0.500530
\(411\) −1.48126e13 −0.0623017
\(412\) 2.36373e14 0.980986
\(413\) 6.14566e13 0.251677
\(414\) 1.17783e13 0.0475972
\(415\) −1.26318e14 −0.503735
\(416\) 5.00669e13 0.197032
\(417\) 2.63890e14 1.02488
\(418\) −1.57280e13 −0.0602842
\(419\) 1.06449e12 0.00402686 0.00201343 0.999998i \(-0.499359\pi\)
0.00201343 + 0.999998i \(0.499359\pi\)
\(420\) 3.32094e14 1.23991
\(421\) −8.27486e13 −0.304936 −0.152468 0.988308i \(-0.548722\pi\)
−0.152468 + 0.988308i \(0.548722\pi\)
\(422\) 4.24243e13 0.154311
\(423\) 1.31903e14 0.473568
\(424\) −1.64471e14 −0.582878
\(425\) −2.10488e14 −0.736357
\(426\) −3.08840e13 −0.106655
\(427\) 6.51522e14 2.22114
\(428\) 1.48649e14 0.500288
\(429\) 4.65926e13 0.154811
\(430\) 9.45657e12 0.0310211
\(431\) −4.78272e13 −0.154900 −0.0774498 0.996996i \(-0.524678\pi\)
−0.0774498 + 0.996996i \(0.524678\pi\)
\(432\) −4.99785e13 −0.159817
\(433\) −5.79214e14 −1.82876 −0.914378 0.404862i \(-0.867319\pi\)
−0.914378 + 0.404862i \(0.867319\pi\)
\(434\) −1.88631e14 −0.588056
\(435\) −4.42627e13 −0.136253
\(436\) 4.22015e14 1.28278
\(437\) 5.49340e13 0.164890
\(438\) 2.57679e13 0.0763784
\(439\) −4.41293e14 −1.29173 −0.645865 0.763452i \(-0.723503\pi\)
−0.645865 + 0.763452i \(0.723503\pi\)
\(440\) 1.72255e14 0.497946
\(441\) 3.19585e14 0.912376
\(442\) −4.76210e13 −0.134269
\(443\) 7.49085e13 0.208598 0.104299 0.994546i \(-0.466740\pi\)
0.104299 + 0.994546i \(0.466740\pi\)
\(444\) −3.80790e14 −1.04732
\(445\) 9.58235e12 0.0260311
\(446\) −8.26497e13 −0.221768
\(447\) −2.85444e14 −0.756535
\(448\) −4.95206e14 −1.29645
\(449\) −7.10060e13 −0.183628 −0.0918142 0.995776i \(-0.529267\pi\)
−0.0918142 + 0.995776i \(0.529267\pi\)
\(450\) 1.22068e13 0.0311840
\(451\) 6.34870e14 1.60219
\(452\) 3.54522e14 0.883856
\(453\) −4.13138e14 −1.01755
\(454\) −1.31109e14 −0.319027
\(455\) 2.80600e14 0.674567
\(456\) 3.14206e13 0.0746290
\(457\) 6.60526e14 1.55007 0.775034 0.631920i \(-0.217733\pi\)
0.775034 + 0.631920i \(0.217733\pi\)
\(458\) 8.45740e13 0.196100
\(459\) 1.58725e14 0.363644
\(460\) −2.91898e14 −0.660788
\(461\) −3.75432e14 −0.839800 −0.419900 0.907570i \(-0.637935\pi\)
−0.419900 + 0.907570i \(0.637935\pi\)
\(462\) 1.09807e14 0.242716
\(463\) −4.33108e14 −0.946021 −0.473011 0.881057i \(-0.656833\pi\)
−0.473011 + 0.881057i \(0.656833\pi\)
\(464\) 7.70194e13 0.166246
\(465\) 4.04314e14 0.862437
\(466\) 1.72417e14 0.363461
\(467\) −2.65554e14 −0.553235 −0.276618 0.960980i \(-0.589214\pi\)
−0.276618 + 0.960980i \(0.589214\pi\)
\(468\) −4.51594e13 −0.0929813
\(469\) −7.86521e14 −1.60052
\(470\) 1.99905e14 0.402056
\(471\) 2.94485e14 0.585393
\(472\) −3.08965e13 −0.0607056
\(473\) −5.11302e13 −0.0992982
\(474\) −2.18316e13 −0.0419088
\(475\) 5.69322e13 0.108030
\(476\) 1.83522e15 3.44230
\(477\) 2.24726e14 0.416679
\(478\) 1.59330e14 0.292042
\(479\) −6.60593e14 −1.19699 −0.598493 0.801128i \(-0.704233\pi\)
−0.598493 + 0.801128i \(0.704233\pi\)
\(480\) −2.52911e14 −0.453045
\(481\) −3.21744e14 −0.569788
\(482\) −1.81106e14 −0.317084
\(483\) −3.83529e14 −0.663879
\(484\) 9.87822e13 0.169055
\(485\) −7.18789e14 −1.21625
\(486\) −9.20490e12 −0.0154000
\(487\) 5.52491e14 0.913936 0.456968 0.889483i \(-0.348935\pi\)
0.456968 + 0.889483i \(0.348935\pi\)
\(488\) −3.27544e14 −0.535749
\(489\) −1.40986e14 −0.228023
\(490\) 4.84347e14 0.774602
\(491\) −5.75971e14 −0.910862 −0.455431 0.890271i \(-0.650515\pi\)
−0.455431 + 0.890271i \(0.650515\pi\)
\(492\) −6.15341e14 −0.962294
\(493\) −2.44604e14 −0.378273
\(494\) 1.28804e13 0.0196984
\(495\) −2.35361e14 −0.355964
\(496\) −7.03527e14 −1.05228
\(497\) 1.00565e15 1.48761
\(498\) 4.04823e13 0.0592248
\(499\) −4.91363e14 −0.710967 −0.355484 0.934683i \(-0.615684\pi\)
−0.355484 + 0.934683i \(0.615684\pi\)
\(500\) 4.73763e14 0.677994
\(501\) 6.94445e14 0.982948
\(502\) 1.01100e14 0.141541
\(503\) −7.40782e13 −0.102581 −0.0512905 0.998684i \(-0.516333\pi\)
−0.0512905 + 0.998684i \(0.516333\pi\)
\(504\) −2.19367e14 −0.300471
\(505\) −9.36940e14 −1.26943
\(506\) −9.65157e13 −0.129351
\(507\) 3.97338e14 0.526764
\(508\) −4.37342e13 −0.0573549
\(509\) 5.93005e14 0.769327 0.384663 0.923057i \(-0.374318\pi\)
0.384663 + 0.923057i \(0.374318\pi\)
\(510\) 2.40556e14 0.308731
\(511\) −8.39059e14 −1.06531
\(512\) 7.48358e14 0.939993
\(513\) −4.29316e13 −0.0533496
\(514\) 6.88628e13 0.0846618
\(515\) −1.00888e15 −1.22716
\(516\) 4.95574e13 0.0596396
\(517\) −1.08086e15 −1.28698
\(518\) −7.58268e14 −0.893325
\(519\) 5.56615e13 0.0648835
\(520\) −1.41068e14 −0.162709
\(521\) −8.94351e13 −0.102071 −0.0510353 0.998697i \(-0.516252\pi\)
−0.0510353 + 0.998697i \(0.516252\pi\)
\(522\) 1.41852e13 0.0160195
\(523\) 5.03702e14 0.562878 0.281439 0.959579i \(-0.409188\pi\)
0.281439 + 0.959579i \(0.409188\pi\)
\(524\) −1.16598e15 −1.28934
\(525\) −3.97479e14 −0.434949
\(526\) −3.03924e14 −0.329112
\(527\) 2.23431e15 2.39434
\(528\) 4.09541e14 0.434321
\(529\) −6.15704e14 −0.646198
\(530\) 3.40583e14 0.353758
\(531\) 4.22156e13 0.0433963
\(532\) −4.96384e14 −0.505015
\(533\) −5.19926e14 −0.523530
\(534\) −3.07093e12 −0.00306051
\(535\) −6.34461e14 −0.625834
\(536\) 3.95414e14 0.386052
\(537\) −4.77108e14 −0.461061
\(538\) −2.76075e14 −0.264073
\(539\) −2.61879e15 −2.47949
\(540\) 2.28121e14 0.213796
\(541\) 1.23010e14 0.114118 0.0570591 0.998371i \(-0.481828\pi\)
0.0570591 + 0.998371i \(0.481828\pi\)
\(542\) −1.94076e14 −0.178228
\(543\) 8.25006e14 0.749995
\(544\) −1.39764e15 −1.25777
\(545\) −1.80124e15 −1.60469
\(546\) −8.99261e13 −0.0793097
\(547\) −1.02482e15 −0.894779 −0.447389 0.894339i \(-0.647646\pi\)
−0.447389 + 0.894339i \(0.647646\pi\)
\(548\) −1.17645e14 −0.101691
\(549\) 4.47541e14 0.382988
\(550\) −1.00026e14 −0.0847462
\(551\) 6.61598e13 0.0554958
\(552\) 1.92814e14 0.160131
\(553\) 7.10887e14 0.584538
\(554\) −3.76546e14 −0.306559
\(555\) 1.62528e15 1.31014
\(556\) 2.09589e15 1.67285
\(557\) 1.43675e15 1.13547 0.567736 0.823211i \(-0.307819\pi\)
0.567736 + 0.823211i \(0.307819\pi\)
\(558\) −1.29574e14 −0.101398
\(559\) 4.18730e13 0.0324466
\(560\) 2.46643e15 1.89249
\(561\) −1.30065e15 −0.988246
\(562\) 7.47417e13 0.0562358
\(563\) −1.26652e15 −0.943658 −0.471829 0.881690i \(-0.656406\pi\)
−0.471829 + 0.881690i \(0.656406\pi\)
\(564\) 1.04761e15 0.772973
\(565\) −1.51317e15 −1.10566
\(566\) −3.74589e14 −0.271060
\(567\) 2.99732e14 0.214796
\(568\) −5.05579e14 −0.358817
\(569\) 1.80928e14 0.127171 0.0635855 0.997976i \(-0.479746\pi\)
0.0635855 + 0.997976i \(0.479746\pi\)
\(570\) −6.50650e13 −0.0452935
\(571\) 1.54365e15 1.06427 0.532133 0.846661i \(-0.321391\pi\)
0.532133 + 0.846661i \(0.321391\pi\)
\(572\) 3.70052e14 0.252688
\(573\) 2.85312e14 0.192961
\(574\) −1.22533e15 −0.820802
\(575\) 3.49368e14 0.231798
\(576\) −3.40165e14 −0.223546
\(577\) 2.99098e15 1.94691 0.973455 0.228877i \(-0.0735053\pi\)
0.973455 + 0.228877i \(0.0735053\pi\)
\(578\) 9.57032e14 0.617054
\(579\) −4.59004e14 −0.293146
\(580\) −3.51547e14 −0.222397
\(581\) −1.31819e15 −0.826058
\(582\) 2.30356e14 0.142996
\(583\) −1.84148e15 −1.13238
\(584\) 4.21827e14 0.256959
\(585\) 1.92749e14 0.116315
\(586\) −6.22614e14 −0.372205
\(587\) 2.47994e15 1.46869 0.734346 0.678775i \(-0.237489\pi\)
0.734346 + 0.678775i \(0.237489\pi\)
\(588\) 2.53823e15 1.48921
\(589\) −6.04331e14 −0.351270
\(590\) 6.39798e13 0.0368432
\(591\) −1.53074e15 −0.873311
\(592\) −2.82808e15 −1.59853
\(593\) −5.82093e14 −0.325980 −0.162990 0.986628i \(-0.552114\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(594\) 7.54282e13 0.0418512
\(595\) −7.83306e15 −4.30614
\(596\) −2.26708e15 −1.23484
\(597\) 2.20378e14 0.118935
\(598\) 7.90414e13 0.0422667
\(599\) −2.52906e15 −1.34002 −0.670010 0.742352i \(-0.733710\pi\)
−0.670010 + 0.742352i \(0.733710\pi\)
\(600\) 1.99828e14 0.104912
\(601\) −2.26350e15 −1.17753 −0.588764 0.808305i \(-0.700385\pi\)
−0.588764 + 0.808305i \(0.700385\pi\)
\(602\) 9.86839e13 0.0508704
\(603\) −5.40275e14 −0.275975
\(604\) −3.28126e15 −1.66088
\(605\) −4.21621e14 −0.211479
\(606\) 3.00269e14 0.149249
\(607\) −1.26647e15 −0.623816 −0.311908 0.950112i \(-0.600968\pi\)
−0.311908 + 0.950112i \(0.600968\pi\)
\(608\) 3.78029e14 0.184525
\(609\) −4.61903e14 −0.223437
\(610\) 6.78272e14 0.325154
\(611\) 8.85167e14 0.420532
\(612\) 1.26064e15 0.593552
\(613\) −9.03727e14 −0.421701 −0.210850 0.977518i \(-0.567623\pi\)
−0.210850 + 0.977518i \(0.567623\pi\)
\(614\) 2.01788e14 0.0933188
\(615\) 2.62639e15 1.20378
\(616\) 1.79757e15 0.816566
\(617\) −5.84125e14 −0.262989 −0.131494 0.991317i \(-0.541978\pi\)
−0.131494 + 0.991317i \(0.541978\pi\)
\(618\) 3.23325e14 0.144279
\(619\) −1.25676e15 −0.555846 −0.277923 0.960603i \(-0.589646\pi\)
−0.277923 + 0.960603i \(0.589646\pi\)
\(620\) 3.21117e15 1.40770
\(621\) −2.63452e14 −0.114472
\(622\) 6.70577e13 0.0288803
\(623\) 9.99965e13 0.0426875
\(624\) −3.35393e14 −0.141919
\(625\) −2.95123e15 −1.23783
\(626\) 4.86311e14 0.202188
\(627\) 3.51797e14 0.144984
\(628\) 2.33888e15 0.955498
\(629\) 8.98162e15 3.63727
\(630\) 4.54259e14 0.182361
\(631\) 4.09495e15 1.62962 0.814811 0.579727i \(-0.196841\pi\)
0.814811 + 0.579727i \(0.196841\pi\)
\(632\) −3.57390e14 −0.140993
\(633\) −9.48928e14 −0.371119
\(634\) −5.82954e14 −0.226018
\(635\) 1.86666e14 0.0717479
\(636\) 1.78484e15 0.680118
\(637\) 2.14466e15 0.810197
\(638\) −1.16239e14 −0.0435348
\(639\) 6.90800e14 0.256506
\(640\) −2.64707e15 −0.974486
\(641\) −1.76266e15 −0.643353 −0.321677 0.946850i \(-0.604246\pi\)
−0.321677 + 0.946850i \(0.604246\pi\)
\(642\) 2.03331e14 0.0735802
\(643\) 6.57445e14 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(644\) −3.04609e15 −1.08360
\(645\) −2.11520e14 −0.0746060
\(646\) −3.59562e14 −0.125746
\(647\) 4.34672e15 1.50726 0.753630 0.657299i \(-0.228301\pi\)
0.753630 + 0.657299i \(0.228301\pi\)
\(648\) −1.50687e14 −0.0518098
\(649\) −3.45929e14 −0.117935
\(650\) 8.19165e13 0.0276916
\(651\) 4.21921e15 1.41428
\(652\) −1.11975e15 −0.372186
\(653\) 2.44494e15 0.805833 0.402917 0.915237i \(-0.367996\pi\)
0.402917 + 0.915237i \(0.367996\pi\)
\(654\) 5.77258e14 0.188665
\(655\) 4.97662e15 1.61290
\(656\) −4.57006e15 −1.46876
\(657\) −5.76364e14 −0.183691
\(658\) 2.08611e15 0.659318
\(659\) 2.36423e15 0.741001 0.370501 0.928832i \(-0.379186\pi\)
0.370501 + 0.928832i \(0.379186\pi\)
\(660\) −1.86931e15 −0.581017
\(661\) 1.16589e15 0.359377 0.179689 0.983724i \(-0.442491\pi\)
0.179689 + 0.983724i \(0.442491\pi\)
\(662\) −4.39599e14 −0.134381
\(663\) 1.06517e15 0.322919
\(664\) 6.62705e14 0.199249
\(665\) 2.11866e15 0.631747
\(666\) −5.20868e14 −0.154035
\(667\) 4.05994e14 0.119077
\(668\) 5.51548e15 1.60440
\(669\) 1.84867e15 0.533355
\(670\) −8.18814e14 −0.234301
\(671\) −3.66731e15 −1.04082
\(672\) −2.63925e15 −0.742934
\(673\) 5.29220e15 1.47759 0.738794 0.673932i \(-0.235396\pi\)
0.738794 + 0.673932i \(0.235396\pi\)
\(674\) 1.54951e15 0.429106
\(675\) −2.73035e14 −0.0749977
\(676\) 3.15577e15 0.859802
\(677\) 6.24406e15 1.68744 0.843722 0.536780i \(-0.180360\pi\)
0.843722 + 0.536780i \(0.180360\pi\)
\(678\) 4.84937e14 0.129994
\(679\) −7.50092e15 −1.99448
\(680\) 3.93797e15 1.03866
\(681\) 2.93260e15 0.767262
\(682\) 1.06177e15 0.275561
\(683\) −6.47234e15 −1.66628 −0.833139 0.553063i \(-0.813459\pi\)
−0.833139 + 0.553063i \(0.813459\pi\)
\(684\) −3.40975e14 −0.0870791
\(685\) 5.02133e14 0.127210
\(686\) 3.20779e15 0.806165
\(687\) −1.89171e15 −0.471621
\(688\) 3.68057e14 0.0910287
\(689\) 1.50808e15 0.370014
\(690\) −3.99276e14 −0.0971858
\(691\) −8.56379e14 −0.206793 −0.103397 0.994640i \(-0.532971\pi\)
−0.103397 + 0.994640i \(0.532971\pi\)
\(692\) 4.42079e14 0.105905
\(693\) −2.45611e15 −0.583734
\(694\) −8.47452e13 −0.0199819
\(695\) −8.94565e15 −2.09264
\(696\) 2.32216e14 0.0538941
\(697\) 1.45139e16 3.34199
\(698\) 8.36459e13 0.0191091
\(699\) −3.85655e15 −0.874127
\(700\) −3.15689e15 −0.709939
\(701\) 5.92029e13 0.0132097 0.00660486 0.999978i \(-0.497898\pi\)
0.00660486 + 0.999978i \(0.497898\pi\)
\(702\) −6.17718e13 −0.0136753
\(703\) −2.42932e15 −0.533619
\(704\) 2.78743e15 0.607512
\(705\) −4.47140e15 −0.966948
\(706\) 8.45578e14 0.181438
\(707\) −9.77743e15 −2.08170
\(708\) 3.35288e14 0.0708329
\(709\) −3.72819e15 −0.781528 −0.390764 0.920491i \(-0.627789\pi\)
−0.390764 + 0.920491i \(0.627789\pi\)
\(710\) 1.04694e15 0.217772
\(711\) 4.88321e14 0.100791
\(712\) −5.02720e13 −0.0102964
\(713\) −3.70851e15 −0.753716
\(714\) 2.51032e15 0.506278
\(715\) −1.57945e15 −0.316099
\(716\) −3.78933e15 −0.752559
\(717\) −3.56383e15 −0.702363
\(718\) −3.11597e14 −0.0609409
\(719\) 4.38046e15 0.850180 0.425090 0.905151i \(-0.360242\pi\)
0.425090 + 0.905151i \(0.360242\pi\)
\(720\) 1.69423e15 0.326320
\(721\) −1.05282e16 −2.01238
\(722\) −1.16829e15 −0.221614
\(723\) 4.05090e15 0.762590
\(724\) 6.55243e15 1.22417
\(725\) 4.20762e14 0.0780148
\(726\) 1.35120e14 0.0248639
\(727\) 1.21393e15 0.221694 0.110847 0.993837i \(-0.464644\pi\)
0.110847 + 0.993837i \(0.464644\pi\)
\(728\) −1.47211e15 −0.266820
\(729\) 2.05891e14 0.0370370
\(730\) −8.73509e14 −0.155952
\(731\) −1.16890e15 −0.207125
\(732\) 3.55450e15 0.625126
\(733\) 2.96462e15 0.517485 0.258742 0.965946i \(-0.416692\pi\)
0.258742 + 0.965946i \(0.416692\pi\)
\(734\) −1.67763e15 −0.290648
\(735\) −1.08337e16 −1.86292
\(736\) 2.31980e15 0.395933
\(737\) 4.42720e15 0.749995
\(738\) −8.41701e14 −0.141530
\(739\) −2.03703e15 −0.339980 −0.169990 0.985446i \(-0.554374\pi\)
−0.169990 + 0.985446i \(0.554374\pi\)
\(740\) 1.29085e16 2.13845
\(741\) −2.88103e14 −0.0473749
\(742\) 3.55415e15 0.580116
\(743\) 6.69761e15 1.08513 0.542564 0.840014i \(-0.317454\pi\)
0.542564 + 0.840014i \(0.317454\pi\)
\(744\) −2.12116e15 −0.341131
\(745\) 9.67631e15 1.54472
\(746\) −1.12216e15 −0.177825
\(747\) −9.05490e14 −0.142436
\(748\) −1.03301e16 −1.61305
\(749\) −6.62091e15 −1.02628
\(750\) 6.48042e14 0.0997163
\(751\) 7.35730e15 1.12383 0.561913 0.827197i \(-0.310066\pi\)
0.561913 + 0.827197i \(0.310066\pi\)
\(752\) 7.78047e15 1.17980
\(753\) −2.26137e15 −0.340407
\(754\) 9.51935e13 0.0142254
\(755\) 1.40050e16 2.07767
\(756\) 2.38056e15 0.350597
\(757\) 1.95976e15 0.286534 0.143267 0.989684i \(-0.454239\pi\)
0.143267 + 0.989684i \(0.454239\pi\)
\(758\) 5.64947e14 0.0820025
\(759\) 2.15882e15 0.311091
\(760\) −1.06513e15 −0.152380
\(761\) 6.64037e15 0.943141 0.471571 0.881828i \(-0.343687\pi\)
0.471571 + 0.881828i \(0.343687\pi\)
\(762\) −5.98223e13 −0.00843550
\(763\) −1.87968e16 −2.63148
\(764\) 2.26603e15 0.314957
\(765\) −5.38066e15 −0.742502
\(766\) 1.59310e15 0.218265
\(767\) 2.83298e14 0.0385362
\(768\) −2.01858e15 −0.272621
\(769\) −1.22042e15 −0.163649 −0.0818245 0.996647i \(-0.526075\pi\)
−0.0818245 + 0.996647i \(0.526075\pi\)
\(770\) −3.72236e15 −0.495587
\(771\) −1.54029e15 −0.203612
\(772\) −3.64554e15 −0.478483
\(773\) 4.40427e15 0.573967 0.286984 0.957936i \(-0.407347\pi\)
0.286984 + 0.957936i \(0.407347\pi\)
\(774\) 6.77876e13 0.00877153
\(775\) −3.84341e15 −0.493807
\(776\) 3.77099e15 0.481079
\(777\) 1.69606e16 2.14845
\(778\) −7.67395e14 −0.0965231
\(779\) −3.92569e15 −0.490298
\(780\) 1.53087e15 0.189853
\(781\) −5.66066e15 −0.697086
\(782\) −2.20647e15 −0.269812
\(783\) −3.17289e14 −0.0385270
\(784\) 1.88512e16 2.27300
\(785\) −9.98279e15 −1.19528
\(786\) −1.59490e15 −0.189631
\(787\) 6.50230e14 0.0767725 0.0383863 0.999263i \(-0.487778\pi\)
0.0383863 + 0.999263i \(0.487778\pi\)
\(788\) −1.21575e16 −1.42545
\(789\) 6.79804e15 0.791517
\(790\) 7.40075e14 0.0855710
\(791\) −1.57906e16 −1.81313
\(792\) 1.23478e15 0.140799
\(793\) 3.00334e15 0.340096
\(794\) −2.77262e15 −0.311802
\(795\) −7.61802e15 −0.850791
\(796\) 1.75030e15 0.194129
\(797\) 6.73756e15 0.742133 0.371066 0.928606i \(-0.378992\pi\)
0.371066 + 0.928606i \(0.378992\pi\)
\(798\) −6.78985e14 −0.0742753
\(799\) −2.47098e16 −2.68449
\(800\) 2.40418e15 0.259401
\(801\) 6.86893e13 0.00736055
\(802\) −2.61661e15 −0.278471
\(803\) 4.72293e15 0.499202
\(804\) −4.29102e15 −0.450456
\(805\) 1.30013e16 1.35553
\(806\) −8.69537e14 −0.0900420
\(807\) 6.17512e15 0.635098
\(808\) 4.91548e15 0.502116
\(809\) 3.23155e15 0.327864 0.163932 0.986472i \(-0.447582\pi\)
0.163932 + 0.986472i \(0.447582\pi\)
\(810\) 3.12039e14 0.0314442
\(811\) 1.00420e16 1.00509 0.502545 0.864551i \(-0.332397\pi\)
0.502545 + 0.864551i \(0.332397\pi\)
\(812\) −3.66856e15 −0.364702
\(813\) 4.34101e15 0.428640
\(814\) 4.26817e15 0.418608
\(815\) 4.77932e15 0.465585
\(816\) 9.36263e15 0.905946
\(817\) 3.16161e14 0.0303870
\(818\) −6.75939e12 −0.000645304 0
\(819\) 2.01143e15 0.190741
\(820\) 2.08596e16 1.96485
\(821\) 1.93004e16 1.80584 0.902921 0.429807i \(-0.141418\pi\)
0.902921 + 0.429807i \(0.141418\pi\)
\(822\) −1.60923e14 −0.0149562
\(823\) −1.83195e16 −1.69128 −0.845639 0.533756i \(-0.820780\pi\)
−0.845639 + 0.533756i \(0.820780\pi\)
\(824\) 5.29292e15 0.485396
\(825\) 2.23735e15 0.203815
\(826\) 6.67661e14 0.0604179
\(827\) 1.21826e16 1.09512 0.547558 0.836768i \(-0.315558\pi\)
0.547558 + 0.836768i \(0.315558\pi\)
\(828\) −2.09241e15 −0.186845
\(829\) 1.91421e16 1.69801 0.849004 0.528386i \(-0.177203\pi\)
0.849004 + 0.528386i \(0.177203\pi\)
\(830\) −1.37232e15 −0.120927
\(831\) 8.42242e15 0.737278
\(832\) −2.28276e15 −0.198510
\(833\) −5.98689e16 −5.17194
\(834\) 2.86688e15 0.246035
\(835\) −2.35411e16 −2.00702
\(836\) 2.79407e15 0.236648
\(837\) 2.89825e15 0.243863
\(838\) 1.15646e13 0.000966693 0
\(839\) 4.48286e15 0.372276 0.186138 0.982524i \(-0.440403\pi\)
0.186138 + 0.982524i \(0.440403\pi\)
\(840\) 7.43635e15 0.613513
\(841\) −1.17116e16 −0.959923
\(842\) −8.98976e14 −0.0732034
\(843\) −1.67179e15 −0.135248
\(844\) −7.53665e15 −0.605752
\(845\) −1.34694e16 −1.07557
\(846\) 1.43298e15 0.113685
\(847\) −4.39982e15 −0.346798
\(848\) 1.32558e16 1.03807
\(849\) 8.37864e15 0.651901
\(850\) −2.28673e15 −0.176771
\(851\) −1.49077e16 −1.14498
\(852\) 5.48653e15 0.418678
\(853\) −6.72216e15 −0.509670 −0.254835 0.966984i \(-0.582021\pi\)
−0.254835 + 0.966984i \(0.582021\pi\)
\(854\) 7.07809e15 0.533210
\(855\) 1.45535e15 0.108931
\(856\) 3.32858e15 0.247545
\(857\) −7.04888e15 −0.520865 −0.260433 0.965492i \(-0.583865\pi\)
−0.260433 + 0.965492i \(0.583865\pi\)
\(858\) 5.06180e14 0.0371642
\(859\) −2.45330e16 −1.78973 −0.894865 0.446337i \(-0.852728\pi\)
−0.894865 + 0.446337i \(0.852728\pi\)
\(860\) −1.67995e15 −0.121774
\(861\) 2.74077e16 1.97404
\(862\) −5.19593e14 −0.0371854
\(863\) 1.06121e16 0.754642 0.377321 0.926083i \(-0.376845\pi\)
0.377321 + 0.926083i \(0.376845\pi\)
\(864\) −1.81295e15 −0.128103
\(865\) −1.88688e15 −0.132482
\(866\) −6.29255e15 −0.439014
\(867\) −2.14065e16 −1.48402
\(868\) 3.35102e16 2.30844
\(869\) −4.00147e15 −0.273912
\(870\) −4.80867e14 −0.0327092
\(871\) −3.62565e15 −0.245068
\(872\) 9.44987e15 0.634724
\(873\) −5.15251e15 −0.343906
\(874\) 5.96800e14 0.0395837
\(875\) −2.11017e16 −1.39083
\(876\) −4.57765e15 −0.299826
\(877\) −2.63364e16 −1.71419 −0.857095 0.515158i \(-0.827733\pi\)
−0.857095 + 0.515158i \(0.827733\pi\)
\(878\) −4.79418e15 −0.310095
\(879\) 1.39264e16 0.895157
\(880\) −1.38831e16 −0.886813
\(881\) 1.09544e16 0.695376 0.347688 0.937610i \(-0.386967\pi\)
0.347688 + 0.937610i \(0.386967\pi\)
\(882\) 3.47195e15 0.219026
\(883\) 1.44671e16 0.906977 0.453489 0.891262i \(-0.350179\pi\)
0.453489 + 0.891262i \(0.350179\pi\)
\(884\) 8.45985e15 0.527079
\(885\) −1.43107e15 −0.0886082
\(886\) 8.13802e14 0.0500764
\(887\) 2.79787e15 0.171099 0.0855494 0.996334i \(-0.472735\pi\)
0.0855494 + 0.996334i \(0.472735\pi\)
\(888\) −8.52674e15 −0.518217
\(889\) 1.94795e15 0.117657
\(890\) 1.04102e14 0.00624906
\(891\) −1.68714e15 −0.100653
\(892\) 1.46827e16 0.870560
\(893\) 6.68343e15 0.393837
\(894\) −3.10105e15 −0.181615
\(895\) 1.61736e16 0.941411
\(896\) −2.76235e16 −1.59803
\(897\) −1.76796e15 −0.101652
\(898\) −7.71405e14 −0.0440821
\(899\) −4.46635e15 −0.253673
\(900\) −2.16852e15 −0.122414
\(901\) −4.20986e16 −2.36201
\(902\) 6.89720e15 0.384624
\(903\) −2.20732e15 −0.122344
\(904\) 7.93854e15 0.437335
\(905\) −2.79670e16 −1.53137
\(906\) −4.48831e15 −0.244274
\(907\) −8.75436e14 −0.0473570 −0.0236785 0.999720i \(-0.507538\pi\)
−0.0236785 + 0.999720i \(0.507538\pi\)
\(908\) 2.32915e16 1.25235
\(909\) −6.71628e15 −0.358945
\(910\) 3.04842e15 0.161938
\(911\) −2.34424e16 −1.23780 −0.618902 0.785468i \(-0.712422\pi\)
−0.618902 + 0.785468i \(0.712422\pi\)
\(912\) −2.53238e15 −0.132910
\(913\) 7.41990e15 0.387087
\(914\) 7.17592e15 0.372112
\(915\) −1.51713e16 −0.781999
\(916\) −1.50245e16 −0.769796
\(917\) 5.19334e16 2.64494
\(918\) 1.72438e15 0.0872970
\(919\) 3.60450e16 1.81388 0.906942 0.421255i \(-0.138410\pi\)
0.906942 + 0.421255i \(0.138410\pi\)
\(920\) −6.53625e15 −0.326961
\(921\) −4.51350e15 −0.224433
\(922\) −4.07867e15 −0.201604
\(923\) 4.63579e15 0.227779
\(924\) −1.95071e16 −0.952791
\(925\) −1.54500e16 −0.750149
\(926\) −4.70526e15 −0.227103
\(927\) −7.23200e15 −0.346992
\(928\) 2.79385e15 0.133257
\(929\) 9.70256e15 0.460045 0.230022 0.973185i \(-0.426120\pi\)
0.230022 + 0.973185i \(0.426120\pi\)
\(930\) 4.39244e15 0.207038
\(931\) 1.61932e16 0.758767
\(932\) −3.06298e16 −1.42678
\(933\) −1.49992e15 −0.0694574
\(934\) −2.88496e15 −0.132811
\(935\) 4.40910e16 2.01784
\(936\) −1.01122e15 −0.0460075
\(937\) 3.90978e16 1.76842 0.884209 0.467092i \(-0.154698\pi\)
0.884209 + 0.467092i \(0.154698\pi\)
\(938\) −8.54473e15 −0.384222
\(939\) −1.08776e16 −0.486264
\(940\) −3.55131e16 −1.57828
\(941\) 1.82589e15 0.0806735 0.0403367 0.999186i \(-0.487157\pi\)
0.0403367 + 0.999186i \(0.487157\pi\)
\(942\) 3.19926e15 0.140530
\(943\) −2.40902e16 −1.05203
\(944\) 2.49014e15 0.108113
\(945\) −1.01607e16 −0.438579
\(946\) −5.55476e14 −0.0238377
\(947\) −2.15121e16 −0.917819 −0.458910 0.888483i \(-0.651760\pi\)
−0.458910 + 0.888483i \(0.651760\pi\)
\(948\) 3.87838e15 0.164515
\(949\) −3.86784e15 −0.163119
\(950\) 6.18509e14 0.0259338
\(951\) 1.30393e16 0.543575
\(952\) 4.10947e16 1.70326
\(953\) 7.52149e14 0.0309951 0.0154975 0.999880i \(-0.495067\pi\)
0.0154975 + 0.999880i \(0.495067\pi\)
\(954\) 2.44141e15 0.100029
\(955\) −9.67183e15 −0.393994
\(956\) −2.83049e16 −1.14642
\(957\) 2.59998e15 0.104702
\(958\) −7.17665e15 −0.287350
\(959\) 5.24001e15 0.208607
\(960\) 1.15313e16 0.456444
\(961\) 1.53890e16 0.605664
\(962\) −3.49541e15 −0.136784
\(963\) −4.54802e15 −0.176961
\(964\) 3.21734e16 1.24473
\(965\) 1.55599e16 0.598557
\(966\) −4.16664e15 −0.159372
\(967\) −2.01815e16 −0.767552 −0.383776 0.923426i \(-0.625376\pi\)
−0.383776 + 0.923426i \(0.625376\pi\)
\(968\) 2.21196e15 0.0836492
\(969\) 8.04252e15 0.302420
\(970\) −7.80889e15 −0.291974
\(971\) −9.72014e15 −0.361382 −0.180691 0.983540i \(-0.557833\pi\)
−0.180691 + 0.983540i \(0.557833\pi\)
\(972\) 1.63525e15 0.0604531
\(973\) −9.33522e16 −3.43166
\(974\) 6.00223e15 0.219401
\(975\) −1.83227e15 −0.0665985
\(976\) 2.63988e16 0.954137
\(977\) −1.22870e15 −0.0441595 −0.0220797 0.999756i \(-0.507029\pi\)
−0.0220797 + 0.999756i \(0.507029\pi\)
\(978\) −1.53167e15 −0.0547394
\(979\) −5.62864e14 −0.0200032
\(980\) −8.60440e16 −3.04073
\(981\) −1.29119e16 −0.453742
\(982\) −6.25732e15 −0.218663
\(983\) 6.19993e15 0.215448 0.107724 0.994181i \(-0.465644\pi\)
0.107724 + 0.994181i \(0.465644\pi\)
\(984\) −1.37789e16 −0.476147
\(985\) 5.18907e16 1.78316
\(986\) −2.65736e15 −0.0908088
\(987\) −4.66612e16 −1.58567
\(988\) −2.28820e15 −0.0773269
\(989\) 1.94014e15 0.0652010
\(990\) −2.55695e15 −0.0854534
\(991\) −4.86156e16 −1.61574 −0.807868 0.589363i \(-0.799379\pi\)
−0.807868 + 0.589363i \(0.799379\pi\)
\(992\) −2.55201e16 −0.843469
\(993\) 9.83275e15 0.323187
\(994\) 1.09254e16 0.357117
\(995\) −7.47063e15 −0.242845
\(996\) −7.19165e15 −0.232489
\(997\) 2.26942e16 0.729610 0.364805 0.931084i \(-0.381136\pi\)
0.364805 + 0.931084i \(0.381136\pi\)
\(998\) −5.33814e15 −0.170676
\(999\) 1.16505e16 0.370455
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 177.12.a.a.1.15 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.15 26 1.1 even 1 trivial