Properties

Label 35.10.a.b.1.1
Level $35$
Weight $10$
Character 35.1
Self dual yes
Analytic conductor $18.026$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.0262542657\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 35.1

$q$-expansion

\(f(q)\) \(=\) \(q-14.8284 q^{2} -239.735 q^{3} -292.118 q^{4} +625.000 q^{5} +3554.89 q^{6} +2401.00 q^{7} +11923.8 q^{8} +37789.9 q^{9} +O(q^{10})\) \(q-14.8284 q^{2} -239.735 q^{3} -292.118 q^{4} +625.000 q^{5} +3554.89 q^{6} +2401.00 q^{7} +11923.8 q^{8} +37789.9 q^{9} -9267.77 q^{10} -16523.6 q^{11} +70030.9 q^{12} +26311.4 q^{13} -35603.1 q^{14} -149834. q^{15} -27246.9 q^{16} -144003. q^{17} -560365. q^{18} -159710. q^{19} -182574. q^{20} -575604. q^{21} +245019. q^{22} +2.07393e6 q^{23} -2.85855e6 q^{24} +390625. q^{25} -390156. q^{26} -4.34086e6 q^{27} -701375. q^{28} -4.94938e6 q^{29} +2.22181e6 q^{30} +4.22040e6 q^{31} -5.70096e6 q^{32} +3.96128e6 q^{33} +2.13533e6 q^{34} +1.50062e6 q^{35} -1.10391e7 q^{36} -1.29081e7 q^{37} +2.36824e6 q^{38} -6.30776e6 q^{39} +7.45238e6 q^{40} -2.87518e7 q^{41} +8.53530e6 q^{42} +3.54825e7 q^{43} +4.82683e6 q^{44} +2.36187e7 q^{45} -3.07532e7 q^{46} +5.95633e7 q^{47} +6.53205e6 q^{48} +5.76480e6 q^{49} -5.79235e6 q^{50} +3.45225e7 q^{51} -7.68602e6 q^{52} +2.31161e6 q^{53} +6.43681e7 q^{54} -1.03272e7 q^{55} +2.86290e7 q^{56} +3.82880e7 q^{57} +7.33915e7 q^{58} -1.68651e8 q^{59} +4.37693e7 q^{60} -6.70167e7 q^{61} -6.25819e7 q^{62} +9.07336e7 q^{63} +9.84867e7 q^{64} +1.64446e7 q^{65} -5.87395e7 q^{66} -1.56259e8 q^{67} +4.20657e7 q^{68} -4.97195e8 q^{69} -2.22519e7 q^{70} +6.95067e7 q^{71} +4.50599e8 q^{72} -7.83438e7 q^{73} +1.91407e8 q^{74} -9.36465e7 q^{75} +4.66540e7 q^{76} -3.96731e7 q^{77} +9.35342e7 q^{78} -4.26957e8 q^{79} -1.70293e7 q^{80} +2.96838e8 q^{81} +4.26344e8 q^{82} -5.31242e8 q^{83} +1.68144e8 q^{84} -9.00016e7 q^{85} -5.26149e8 q^{86} +1.18654e9 q^{87} -1.97024e8 q^{88} -1.14168e8 q^{89} -3.50228e8 q^{90} +6.31736e7 q^{91} -6.05833e8 q^{92} -1.01178e9 q^{93} -8.83231e8 q^{94} -9.98185e7 q^{95} +1.36672e9 q^{96} -1.46573e9 q^{97} -8.54829e7 q^{98} -6.24424e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 24 q^{2} - 174 q^{3} - 720 q^{4} + 1250 q^{5} + 2952 q^{6} + 4802 q^{7} + 20544 q^{8} + 22428 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 24 q^{2} - 174 q^{3} - 720 q^{4} + 1250 q^{5} + 2952 q^{6} + 4802 q^{7} + 20544 q^{8} + 22428 q^{9} - 15000 q^{10} + 18566 q^{11} + 41904 q^{12} - 51090 q^{13} - 57624 q^{14} - 108750 q^{15} + 112768 q^{16} - 373910 q^{17} - 419472 q^{18} - 143276 q^{19} - 450000 q^{20} - 417774 q^{21} - 76808 q^{22} - 498908 q^{23} - 2291904 q^{24} + 781250 q^{25} + 319736 q^{26} - 6644538 q^{27} - 1728720 q^{28} - 11577554 q^{29} + 1845000 q^{30} - 3953760 q^{31} - 11398656 q^{32} + 6267894 q^{33} + 4243944 q^{34} + 3001250 q^{35} - 4466016 q^{36} - 3205412 q^{37} + 2217520 q^{38} - 11395746 q^{39} + 12840000 q^{40} + 1058992 q^{41} + 7087752 q^{42} + 15948180 q^{43} - 10187376 q^{44} + 14017500 q^{45} - 7156176 q^{46} + 65501290 q^{47} + 15735936 q^{48} + 11529602 q^{49} - 9375000 q^{50} + 19409466 q^{51} + 25432656 q^{52} - 25114688 q^{53} + 85496472 q^{54} + 11603750 q^{55} + 49326144 q^{56} + 39368244 q^{57} + 134182296 q^{58} - 116159208 q^{59} + 26190000 q^{60} - 44688544 q^{61} + 12388000 q^{62} + 53849628 q^{63} + 79055872 q^{64} - 31931250 q^{65} - 79894824 q^{66} + 118092496 q^{67} + 140439024 q^{68} - 666320892 q^{69} - 36015000 q^{70} - 294165824 q^{71} + 318176640 q^{72} - 57419332 q^{73} + 102418064 q^{74} - 67968750 q^{75} + 39622368 q^{76} + 44576966 q^{77} + 140199000 q^{78} - 692852854 q^{79} + 70480000 q^{80} + 447773346 q^{81} + 152932128 q^{82} - 540679928 q^{83} + 100611504 q^{84} - 233693750 q^{85} - 346989008 q^{86} + 750836190 q^{87} + 105455296 q^{88} - 779043704 q^{89} - 262170000 q^{90} - 122667090 q^{91} + 495040608 q^{92} - 1549107360 q^{93} - 937691032 q^{94} - 89547500 q^{95} + 992180736 q^{96} - 2673039406 q^{97} - 138355224 q^{98} - 1163466540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.8284 −0.655330 −0.327665 0.944794i \(-0.606262\pi\)
−0.327665 + 0.944794i \(0.606262\pi\)
\(3\) −239.735 −1.70878 −0.854390 0.519633i \(-0.826069\pi\)
−0.854390 + 0.519633i \(0.826069\pi\)
\(4\) −292.118 −0.570542
\(5\) 625.000 0.447214
\(6\) 3554.89 1.11981
\(7\) 2401.00 0.377964
\(8\) 11923.8 1.02922
\(9\) 37789.9 1.91993
\(10\) −9267.77 −0.293073
\(11\) −16523.6 −0.340280 −0.170140 0.985420i \(-0.554422\pi\)
−0.170140 + 0.985420i \(0.554422\pi\)
\(12\) 70030.9 0.974931
\(13\) 26311.4 0.255505 0.127752 0.991806i \(-0.459224\pi\)
0.127752 + 0.991806i \(0.459224\pi\)
\(14\) −35603.1 −0.247691
\(15\) −149834. −0.764189
\(16\) −27246.9 −0.103939
\(17\) −144003. −0.418167 −0.209084 0.977898i \(-0.567048\pi\)
−0.209084 + 0.977898i \(0.567048\pi\)
\(18\) −560365. −1.25819
\(19\) −159710. −0.281151 −0.140576 0.990070i \(-0.544895\pi\)
−0.140576 + 0.990070i \(0.544895\pi\)
\(20\) −182574. −0.255154
\(21\) −575604. −0.645858
\(22\) 245019. 0.222996
\(23\) 2.07393e6 1.54533 0.772663 0.634817i \(-0.218925\pi\)
0.772663 + 0.634817i \(0.218925\pi\)
\(24\) −2.85855e6 −1.75872
\(25\) 390625. 0.200000
\(26\) −390156. −0.167440
\(27\) −4.34086e6 −1.57195
\(28\) −701375. −0.215645
\(29\) −4.94938e6 −1.29945 −0.649725 0.760169i \(-0.725116\pi\)
−0.649725 + 0.760169i \(0.725116\pi\)
\(30\) 2.22181e6 0.500796
\(31\) 4.22040e6 0.820779 0.410389 0.911910i \(-0.365393\pi\)
0.410389 + 0.911910i \(0.365393\pi\)
\(32\) −5.70096e6 −0.961110
\(33\) 3.96128e6 0.581464
\(34\) 2.13533e6 0.274038
\(35\) 1.50062e6 0.169031
\(36\) −1.10391e7 −1.09540
\(37\) −1.29081e7 −1.13228 −0.566142 0.824308i \(-0.691565\pi\)
−0.566142 + 0.824308i \(0.691565\pi\)
\(38\) 2.36824e6 0.184247
\(39\) −6.30776e6 −0.436601
\(40\) 7.45238e6 0.460283
\(41\) −2.87518e7 −1.58905 −0.794525 0.607231i \(-0.792280\pi\)
−0.794525 + 0.607231i \(0.792280\pi\)
\(42\) 8.53530e6 0.423250
\(43\) 3.54825e7 1.58273 0.791363 0.611347i \(-0.209372\pi\)
0.791363 + 0.611347i \(0.209372\pi\)
\(44\) 4.82683e6 0.194144
\(45\) 2.36187e7 0.858617
\(46\) −3.07532e7 −1.01270
\(47\) 5.95633e7 1.78049 0.890243 0.455485i \(-0.150534\pi\)
0.890243 + 0.455485i \(0.150534\pi\)
\(48\) 6.53205e6 0.177608
\(49\) 5.76480e6 0.142857
\(50\) −5.79235e6 −0.131066
\(51\) 3.45225e7 0.714555
\(52\) −7.68602e6 −0.145776
\(53\) 2.31161e6 0.0402414 0.0201207 0.999798i \(-0.493595\pi\)
0.0201207 + 0.999798i \(0.493595\pi\)
\(54\) 6.43681e7 1.03015
\(55\) −1.03272e7 −0.152178
\(56\) 2.86290e7 0.389010
\(57\) 3.82880e7 0.480425
\(58\) 7.33915e7 0.851569
\(59\) −1.68651e8 −1.81198 −0.905992 0.423296i \(-0.860873\pi\)
−0.905992 + 0.423296i \(0.860873\pi\)
\(60\) 4.37693e7 0.436002
\(61\) −6.70167e7 −0.619725 −0.309863 0.950781i \(-0.600283\pi\)
−0.309863 + 0.950781i \(0.600283\pi\)
\(62\) −6.25819e7 −0.537881
\(63\) 9.07336e7 0.725664
\(64\) 9.84867e7 0.733783
\(65\) 1.64446e7 0.114265
\(66\) −5.87395e7 −0.381051
\(67\) −1.56259e8 −0.947343 −0.473671 0.880702i \(-0.657072\pi\)
−0.473671 + 0.880702i \(0.657072\pi\)
\(68\) 4.20657e7 0.238582
\(69\) −4.97195e8 −2.64062
\(70\) −2.22519e7 −0.110771
\(71\) 6.95067e7 0.324612 0.162306 0.986740i \(-0.448107\pi\)
0.162306 + 0.986740i \(0.448107\pi\)
\(72\) 4.50599e8 1.97603
\(73\) −7.83438e7 −0.322888 −0.161444 0.986882i \(-0.551615\pi\)
−0.161444 + 0.986882i \(0.551615\pi\)
\(74\) 1.91407e8 0.742020
\(75\) −9.36465e7 −0.341756
\(76\) 4.66540e7 0.160409
\(77\) −3.96731e7 −0.128614
\(78\) 9.35342e7 0.286118
\(79\) −4.26957e8 −1.23328 −0.616641 0.787245i \(-0.711507\pi\)
−0.616641 + 0.787245i \(0.711507\pi\)
\(80\) −1.70293e7 −0.0464828
\(81\) 2.96838e8 0.766190
\(82\) 4.26344e8 1.04135
\(83\) −5.31242e8 −1.22869 −0.614343 0.789039i \(-0.710579\pi\)
−0.614343 + 0.789039i \(0.710579\pi\)
\(84\) 1.68144e8 0.368489
\(85\) −9.00016e7 −0.187010
\(86\) −5.26149e8 −1.03721
\(87\) 1.18654e9 2.22047
\(88\) −1.97024e8 −0.350225
\(89\) −1.14168e8 −0.192881 −0.0964404 0.995339i \(-0.530746\pi\)
−0.0964404 + 0.995339i \(0.530746\pi\)
\(90\) −3.50228e8 −0.562678
\(91\) 6.31736e7 0.0965716
\(92\) −6.05833e8 −0.881674
\(93\) −1.01178e9 −1.40253
\(94\) −8.83231e8 −1.16681
\(95\) −9.98185e7 −0.125735
\(96\) 1.36672e9 1.64232
\(97\) −1.46573e9 −1.68105 −0.840524 0.541774i \(-0.817753\pi\)
−0.840524 + 0.541774i \(0.817753\pi\)
\(98\) −8.54829e7 −0.0936186
\(99\) −6.24424e8 −0.653313
\(100\) −1.14108e8 −0.114108
\(101\) 7.53733e8 0.720728 0.360364 0.932812i \(-0.382652\pi\)
0.360364 + 0.932812i \(0.382652\pi\)
\(102\) −5.11914e8 −0.468270
\(103\) −1.32143e9 −1.15685 −0.578425 0.815736i \(-0.696332\pi\)
−0.578425 + 0.815736i \(0.696332\pi\)
\(104\) 3.13732e8 0.262971
\(105\) −3.59752e8 −0.288836
\(106\) −3.42775e7 −0.0263714
\(107\) 1.07364e9 0.791831 0.395915 0.918287i \(-0.370427\pi\)
0.395915 + 0.918287i \(0.370427\pi\)
\(108\) 1.26804e9 0.896864
\(109\) 1.08650e9 0.737245 0.368623 0.929579i \(-0.379830\pi\)
0.368623 + 0.929579i \(0.379830\pi\)
\(110\) 1.53137e8 0.0997268
\(111\) 3.09453e9 1.93482
\(112\) −6.54199e7 −0.0392852
\(113\) 2.85559e9 1.64757 0.823783 0.566906i \(-0.191860\pi\)
0.823783 + 0.566906i \(0.191860\pi\)
\(114\) −5.67751e8 −0.314837
\(115\) 1.29621e9 0.691090
\(116\) 1.44580e9 0.741392
\(117\) 9.94305e8 0.490550
\(118\) 2.50083e9 1.18745
\(119\) −3.45750e8 −0.158052
\(120\) −1.78660e9 −0.786522
\(121\) −2.08492e9 −0.884209
\(122\) 9.93753e8 0.406125
\(123\) 6.89281e9 2.71534
\(124\) −1.23285e9 −0.468289
\(125\) 2.44141e8 0.0894427
\(126\) −1.34544e9 −0.475549
\(127\) −3.86082e9 −1.31693 −0.658465 0.752611i \(-0.728794\pi\)
−0.658465 + 0.752611i \(0.728794\pi\)
\(128\) 1.45849e9 0.480240
\(129\) −8.50639e9 −2.70453
\(130\) −2.43848e8 −0.0748814
\(131\) 4.01900e8 0.119233 0.0596166 0.998221i \(-0.481012\pi\)
0.0596166 + 0.998221i \(0.481012\pi\)
\(132\) −1.15716e9 −0.331750
\(133\) −3.83463e8 −0.106265
\(134\) 2.31707e9 0.620822
\(135\) −2.71304e9 −0.702997
\(136\) −1.71706e9 −0.430388
\(137\) 3.04172e9 0.737695 0.368847 0.929490i \(-0.379753\pi\)
0.368847 + 0.929490i \(0.379753\pi\)
\(138\) 7.37262e9 1.73048
\(139\) 8.36421e8 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(140\) −4.38359e8 −0.0964393
\(141\) −1.42794e10 −3.04246
\(142\) −1.03068e9 −0.212728
\(143\) −4.34758e8 −0.0869431
\(144\) −1.02966e9 −0.199555
\(145\) −3.09336e9 −0.581132
\(146\) 1.16172e9 0.211598
\(147\) −1.38202e9 −0.244111
\(148\) 3.77069e9 0.646016
\(149\) −7.76217e9 −1.29016 −0.645082 0.764114i \(-0.723177\pi\)
−0.645082 + 0.764114i \(0.723177\pi\)
\(150\) 1.38863e9 0.223963
\(151\) 8.38042e9 1.31181 0.655903 0.754846i \(-0.272288\pi\)
0.655903 + 0.754846i \(0.272288\pi\)
\(152\) −1.90435e9 −0.289367
\(153\) −5.44184e9 −0.802850
\(154\) 5.88290e8 0.0842845
\(155\) 2.63775e9 0.367063
\(156\) 1.84261e9 0.249099
\(157\) −8.49699e9 −1.11613 −0.558067 0.829796i \(-0.688457\pi\)
−0.558067 + 0.829796i \(0.688457\pi\)
\(158\) 6.33110e9 0.808206
\(159\) −5.54173e8 −0.0687636
\(160\) −3.56310e9 −0.429821
\(161\) 4.97952e9 0.584078
\(162\) −4.40163e9 −0.502107
\(163\) 4.25863e9 0.472526 0.236263 0.971689i \(-0.424077\pi\)
0.236263 + 0.971689i \(0.424077\pi\)
\(164\) 8.39891e9 0.906621
\(165\) 2.47580e9 0.260039
\(166\) 7.87749e9 0.805195
\(167\) 9.23536e8 0.0918818 0.0459409 0.998944i \(-0.485371\pi\)
0.0459409 + 0.998944i \(0.485371\pi\)
\(168\) −6.86339e9 −0.664732
\(169\) −9.91221e9 −0.934717
\(170\) 1.33458e9 0.122553
\(171\) −6.03541e9 −0.539789
\(172\) −1.03651e10 −0.903012
\(173\) −4.76006e9 −0.404022 −0.202011 0.979383i \(-0.564748\pi\)
−0.202011 + 0.979383i \(0.564748\pi\)
\(174\) −1.75945e10 −1.45514
\(175\) 9.37891e8 0.0755929
\(176\) 4.50217e8 0.0353683
\(177\) 4.04315e10 3.09628
\(178\) 1.69293e9 0.126401
\(179\) −9.47187e9 −0.689599 −0.344800 0.938676i \(-0.612053\pi\)
−0.344800 + 0.938676i \(0.612053\pi\)
\(180\) −6.89944e9 −0.489877
\(181\) −7.85395e9 −0.543919 −0.271960 0.962309i \(-0.587672\pi\)
−0.271960 + 0.962309i \(0.587672\pi\)
\(182\) −9.36766e8 −0.0632863
\(183\) 1.60663e10 1.05897
\(184\) 2.47292e10 1.59049
\(185\) −8.06758e9 −0.506373
\(186\) 1.50031e10 0.919120
\(187\) 2.37944e9 0.142294
\(188\) −1.73995e10 −1.01584
\(189\) −1.04224e10 −0.594141
\(190\) 1.48015e9 0.0823976
\(191\) 1.78210e10 0.968909 0.484454 0.874817i \(-0.339018\pi\)
0.484454 + 0.874817i \(0.339018\pi\)
\(192\) −2.36107e10 −1.25387
\(193\) −1.93101e9 −0.100179 −0.0500894 0.998745i \(-0.515951\pi\)
−0.0500894 + 0.998745i \(0.515951\pi\)
\(194\) 2.17344e10 1.10164
\(195\) −3.94235e9 −0.195254
\(196\) −1.68400e9 −0.0815061
\(197\) 3.24598e10 1.53549 0.767746 0.640755i \(-0.221378\pi\)
0.767746 + 0.640755i \(0.221378\pi\)
\(198\) 9.25923e9 0.428136
\(199\) −2.75463e10 −1.24516 −0.622578 0.782558i \(-0.713915\pi\)
−0.622578 + 0.782558i \(0.713915\pi\)
\(200\) 4.65773e9 0.205845
\(201\) 3.74606e10 1.61880
\(202\) −1.11767e10 −0.472315
\(203\) −1.18835e10 −0.491146
\(204\) −1.00846e10 −0.407684
\(205\) −1.79699e10 −0.710645
\(206\) 1.95947e10 0.758118
\(207\) 7.83738e10 2.96691
\(208\) −7.16904e8 −0.0265568
\(209\) 2.63897e9 0.0956702
\(210\) 5.33456e9 0.189283
\(211\) 1.94450e10 0.675362 0.337681 0.941261i \(-0.390357\pi\)
0.337681 + 0.941261i \(0.390357\pi\)
\(212\) −6.75261e8 −0.0229594
\(213\) −1.66632e10 −0.554690
\(214\) −1.59204e10 −0.518911
\(215\) 2.21765e10 0.707817
\(216\) −5.17595e10 −1.61789
\(217\) 1.01332e10 0.310225
\(218\) −1.61111e10 −0.483139
\(219\) 1.87818e10 0.551744
\(220\) 3.01677e9 0.0868240
\(221\) −3.78891e9 −0.106844
\(222\) −4.58870e10 −1.26795
\(223\) −4.90459e10 −1.32810 −0.664050 0.747688i \(-0.731164\pi\)
−0.664050 + 0.747688i \(0.731164\pi\)
\(224\) −1.36880e10 −0.363265
\(225\) 1.47617e10 0.383985
\(226\) −4.23439e10 −1.07970
\(227\) −6.87990e10 −1.71975 −0.859876 0.510503i \(-0.829459\pi\)
−0.859876 + 0.510503i \(0.829459\pi\)
\(228\) −1.11846e10 −0.274103
\(229\) −3.08456e9 −0.0741198 −0.0370599 0.999313i \(-0.511799\pi\)
−0.0370599 + 0.999313i \(0.511799\pi\)
\(230\) −1.92207e10 −0.452892
\(231\) 9.51103e9 0.219773
\(232\) −5.90154e10 −1.33743
\(233\) −1.48643e10 −0.330402 −0.165201 0.986260i \(-0.552827\pi\)
−0.165201 + 0.986260i \(0.552827\pi\)
\(234\) −1.47440e10 −0.321472
\(235\) 3.72271e10 0.796258
\(236\) 4.92659e10 1.03381
\(237\) 1.02357e11 2.10741
\(238\) 5.12693e9 0.103576
\(239\) 4.06416e10 0.805713 0.402857 0.915263i \(-0.368017\pi\)
0.402857 + 0.915263i \(0.368017\pi\)
\(240\) 4.08253e9 0.0794289
\(241\) −2.09799e10 −0.400615 −0.200308 0.979733i \(-0.564194\pi\)
−0.200308 + 0.979733i \(0.564194\pi\)
\(242\) 3.09161e10 0.579449
\(243\) 1.42788e10 0.262701
\(244\) 1.95768e10 0.353580
\(245\) 3.60300e9 0.0638877
\(246\) −1.02210e11 −1.77944
\(247\) −4.20218e9 −0.0718354
\(248\) 5.03232e10 0.844765
\(249\) 1.27357e11 2.09955
\(250\) −3.62022e9 −0.0586145
\(251\) −9.95566e10 −1.58321 −0.791605 0.611034i \(-0.790754\pi\)
−0.791605 + 0.611034i \(0.790754\pi\)
\(252\) −2.65049e10 −0.414022
\(253\) −3.42688e10 −0.525844
\(254\) 5.72499e10 0.863024
\(255\) 2.15765e10 0.319559
\(256\) −7.20522e10 −1.04850
\(257\) −1.30781e11 −1.87002 −0.935009 0.354624i \(-0.884609\pi\)
−0.935009 + 0.354624i \(0.884609\pi\)
\(258\) 1.26136e11 1.77236
\(259\) −3.09924e10 −0.427963
\(260\) −4.80376e9 −0.0651931
\(261\) −1.87037e11 −2.49485
\(262\) −5.95954e9 −0.0781371
\(263\) −3.27938e10 −0.422660 −0.211330 0.977415i \(-0.567779\pi\)
−0.211330 + 0.977415i \(0.567779\pi\)
\(264\) 4.72335e10 0.598456
\(265\) 1.44475e9 0.0179965
\(266\) 5.68615e9 0.0696387
\(267\) 2.73700e10 0.329591
\(268\) 4.56459e10 0.540499
\(269\) 7.47690e9 0.0870636 0.0435318 0.999052i \(-0.486139\pi\)
0.0435318 + 0.999052i \(0.486139\pi\)
\(270\) 4.02301e10 0.460695
\(271\) 6.72735e9 0.0757674 0.0378837 0.999282i \(-0.487938\pi\)
0.0378837 + 0.999282i \(0.487938\pi\)
\(272\) 3.92363e9 0.0434638
\(273\) −1.51449e10 −0.165020
\(274\) −4.51039e10 −0.483434
\(275\) −6.45452e9 −0.0680561
\(276\) 1.45239e11 1.50659
\(277\) −1.52676e11 −1.55815 −0.779077 0.626928i \(-0.784312\pi\)
−0.779077 + 0.626928i \(0.784312\pi\)
\(278\) −1.24028e10 −0.124543
\(279\) 1.59489e11 1.57583
\(280\) 1.78932e10 0.173971
\(281\) 3.09796e10 0.296413 0.148206 0.988956i \(-0.452650\pi\)
0.148206 + 0.988956i \(0.452650\pi\)
\(282\) 2.11741e11 1.99381
\(283\) −8.92078e10 −0.826731 −0.413365 0.910565i \(-0.635647\pi\)
−0.413365 + 0.910565i \(0.635647\pi\)
\(284\) −2.03041e10 −0.185205
\(285\) 2.39300e10 0.214853
\(286\) 6.44678e9 0.0569765
\(287\) −6.90331e10 −0.600605
\(288\) −2.15439e11 −1.84526
\(289\) −9.78512e10 −0.825136
\(290\) 4.58697e10 0.380833
\(291\) 3.51386e11 2.87254
\(292\) 2.28856e10 0.184221
\(293\) 6.30090e10 0.499457 0.249728 0.968316i \(-0.419659\pi\)
0.249728 + 0.968316i \(0.419659\pi\)
\(294\) 2.04933e10 0.159973
\(295\) −1.05407e11 −0.810344
\(296\) −1.53914e11 −1.16537
\(297\) 7.17265e10 0.534904
\(298\) 1.15101e11 0.845483
\(299\) 5.45681e10 0.394838
\(300\) 2.73558e10 0.194986
\(301\) 8.51934e10 0.598214
\(302\) −1.24268e11 −0.859665
\(303\) −1.80696e11 −1.23157
\(304\) 4.35160e9 0.0292225
\(305\) −4.18855e10 −0.277150
\(306\) 8.06939e10 0.526132
\(307\) −1.22461e11 −0.786821 −0.393411 0.919363i \(-0.628705\pi\)
−0.393411 + 0.919363i \(0.628705\pi\)
\(308\) 1.15892e10 0.0733797
\(309\) 3.16793e11 1.97680
\(310\) −3.91137e10 −0.240548
\(311\) 2.77926e11 1.68464 0.842321 0.538975i \(-0.181188\pi\)
0.842321 + 0.538975i \(0.181188\pi\)
\(312\) −7.52125e10 −0.449360
\(313\) 1.22493e11 0.721374 0.360687 0.932687i \(-0.382542\pi\)
0.360687 + 0.932687i \(0.382542\pi\)
\(314\) 1.25997e11 0.731436
\(315\) 5.67085e10 0.324527
\(316\) 1.24722e11 0.703639
\(317\) 2.32000e11 1.29039 0.645197 0.764016i \(-0.276775\pi\)
0.645197 + 0.764016i \(0.276775\pi\)
\(318\) 8.21752e9 0.0450628
\(319\) 8.17814e10 0.442177
\(320\) 6.15542e10 0.328158
\(321\) −2.57390e11 −1.35306
\(322\) −7.38384e10 −0.382764
\(323\) 2.29986e10 0.117568
\(324\) −8.67115e10 −0.437144
\(325\) 1.02779e10 0.0511009
\(326\) −6.31487e10 −0.309660
\(327\) −2.60473e11 −1.25979
\(328\) −3.42831e11 −1.63549
\(329\) 1.43012e11 0.672961
\(330\) −3.67122e10 −0.170411
\(331\) −3.74253e11 −1.71372 −0.856859 0.515551i \(-0.827587\pi\)
−0.856859 + 0.515551i \(0.827587\pi\)
\(332\) 1.55185e11 0.701018
\(333\) −4.87797e11 −2.17390
\(334\) −1.36946e10 −0.0602129
\(335\) −9.76616e10 −0.423665
\(336\) 1.56834e10 0.0671297
\(337\) 3.35878e11 1.41856 0.709280 0.704927i \(-0.249020\pi\)
0.709280 + 0.704927i \(0.249020\pi\)
\(338\) 1.46982e11 0.612548
\(339\) −6.84585e11 −2.81533
\(340\) 2.62911e10 0.106697
\(341\) −6.97361e10 −0.279295
\(342\) 8.94956e10 0.353740
\(343\) 1.38413e10 0.0539949
\(344\) 4.23086e11 1.62898
\(345\) −3.10747e11 −1.18092
\(346\) 7.05842e10 0.264768
\(347\) −3.63698e11 −1.34666 −0.673331 0.739341i \(-0.735137\pi\)
−0.673331 + 0.739341i \(0.735137\pi\)
\(348\) −3.46609e11 −1.26687
\(349\) 1.08740e11 0.392350 0.196175 0.980569i \(-0.437148\pi\)
0.196175 + 0.980569i \(0.437148\pi\)
\(350\) −1.39074e10 −0.0495383
\(351\) −1.14214e11 −0.401640
\(352\) 9.42002e10 0.327047
\(353\) −3.36249e11 −1.15259 −0.576296 0.817241i \(-0.695502\pi\)
−0.576296 + 0.817241i \(0.695502\pi\)
\(354\) −5.99535e11 −2.02908
\(355\) 4.34417e10 0.145171
\(356\) 3.33505e10 0.110047
\(357\) 8.28884e10 0.270077
\(358\) 1.40453e11 0.451915
\(359\) 5.49944e11 1.74741 0.873703 0.486460i \(-0.161712\pi\)
0.873703 + 0.486460i \(0.161712\pi\)
\(360\) 2.81625e11 0.883709
\(361\) −2.97181e11 −0.920954
\(362\) 1.16462e11 0.356447
\(363\) 4.99828e11 1.51092
\(364\) −1.84541e10 −0.0550982
\(365\) −4.89649e10 −0.144400
\(366\) −2.38237e11 −0.693977
\(367\) −1.32204e11 −0.380405 −0.190203 0.981745i \(-0.560914\pi\)
−0.190203 + 0.981745i \(0.560914\pi\)
\(368\) −5.65084e10 −0.160619
\(369\) −1.08653e12 −3.05086
\(370\) 1.19630e11 0.331841
\(371\) 5.55017e9 0.0152098
\(372\) 2.95558e11 0.800203
\(373\) 4.88064e11 1.30553 0.652765 0.757560i \(-0.273609\pi\)
0.652765 + 0.757560i \(0.273609\pi\)
\(374\) −3.52833e10 −0.0932496
\(375\) −5.85291e10 −0.152838
\(376\) 7.10222e11 1.83252
\(377\) −1.30225e11 −0.332015
\(378\) 1.54548e11 0.389359
\(379\) 3.00162e11 0.747274 0.373637 0.927575i \(-0.378111\pi\)
0.373637 + 0.927575i \(0.378111\pi\)
\(380\) 2.91587e10 0.0717369
\(381\) 9.25574e11 2.25034
\(382\) −2.64258e11 −0.634955
\(383\) 7.74202e11 1.83848 0.919241 0.393694i \(-0.128803\pi\)
0.919241 + 0.393694i \(0.128803\pi\)
\(384\) −3.49651e11 −0.820623
\(385\) −2.47957e10 −0.0575179
\(386\) 2.86338e10 0.0656501
\(387\) 1.34088e12 3.03872
\(388\) 4.28165e11 0.959109
\(389\) −1.70127e11 −0.376703 −0.188352 0.982102i \(-0.560314\pi\)
−0.188352 + 0.982102i \(0.560314\pi\)
\(390\) 5.84589e10 0.127956
\(391\) −2.98652e11 −0.646204
\(392\) 6.87383e10 0.147032
\(393\) −9.63495e10 −0.203743
\(394\) −4.81327e11 −1.00625
\(395\) −2.66848e11 −0.551540
\(396\) 1.82405e11 0.372743
\(397\) −5.47242e11 −1.10566 −0.552831 0.833293i \(-0.686452\pi\)
−0.552831 + 0.833293i \(0.686452\pi\)
\(398\) 4.08468e11 0.815988
\(399\) 9.19294e10 0.181584
\(400\) −1.06433e10 −0.0207878
\(401\) −4.57174e11 −0.882941 −0.441471 0.897276i \(-0.645543\pi\)
−0.441471 + 0.897276i \(0.645543\pi\)
\(402\) −5.55483e11 −1.06085
\(403\) 1.11045e11 0.209713
\(404\) −2.20179e11 −0.411206
\(405\) 1.85523e11 0.342650
\(406\) 1.76213e11 0.321863
\(407\) 2.13288e11 0.385294
\(408\) 4.11639e11 0.735437
\(409\) 9.42996e10 0.166631 0.0833153 0.996523i \(-0.473449\pi\)
0.0833153 + 0.996523i \(0.473449\pi\)
\(410\) 2.66465e11 0.465707
\(411\) −7.29207e11 −1.26056
\(412\) 3.86013e11 0.660032
\(413\) −4.04930e11 −0.684865
\(414\) −1.16216e12 −1.94431
\(415\) −3.32026e11 −0.549485
\(416\) −1.50000e11 −0.245568
\(417\) −2.00519e11 −0.324746
\(418\) −3.91318e10 −0.0626955
\(419\) 1.66874e11 0.264500 0.132250 0.991216i \(-0.457780\pi\)
0.132250 + 0.991216i \(0.457780\pi\)
\(420\) 1.05090e11 0.164793
\(421\) −5.52779e11 −0.857594 −0.428797 0.903401i \(-0.641062\pi\)
−0.428797 + 0.903401i \(0.641062\pi\)
\(422\) −2.88339e11 −0.442585
\(423\) 2.25089e12 3.41840
\(424\) 2.75631e10 0.0414174
\(425\) −5.62510e10 −0.0836334
\(426\) 2.47089e11 0.363505
\(427\) −1.60907e11 −0.234234
\(428\) −3.13630e11 −0.451773
\(429\) 1.04227e11 0.148567
\(430\) −3.28843e11 −0.463853
\(431\) −4.37408e11 −0.610575 −0.305288 0.952260i \(-0.598753\pi\)
−0.305288 + 0.952260i \(0.598753\pi\)
\(432\) 1.18275e11 0.163387
\(433\) 2.79837e11 0.382569 0.191285 0.981535i \(-0.438735\pi\)
0.191285 + 0.981535i \(0.438735\pi\)
\(434\) −1.50259e11 −0.203300
\(435\) 7.41587e11 0.993026
\(436\) −3.17387e11 −0.420630
\(437\) −3.31227e11 −0.434470
\(438\) −2.78504e11 −0.361575
\(439\) 8.87150e11 1.14000 0.570002 0.821643i \(-0.306942\pi\)
0.570002 + 0.821643i \(0.306942\pi\)
\(440\) −1.23140e11 −0.156625
\(441\) 2.17851e11 0.274275
\(442\) 5.61835e10 0.0700178
\(443\) −5.87852e11 −0.725189 −0.362594 0.931947i \(-0.618109\pi\)
−0.362594 + 0.931947i \(0.618109\pi\)
\(444\) −9.03967e11 −1.10390
\(445\) −7.13549e10 −0.0862589
\(446\) 7.27274e11 0.870344
\(447\) 1.86086e12 2.20460
\(448\) 2.36466e11 0.277344
\(449\) −5.19918e11 −0.603707 −0.301854 0.953354i \(-0.597605\pi\)
−0.301854 + 0.953354i \(0.597605\pi\)
\(450\) −2.18892e11 −0.251637
\(451\) 4.75082e11 0.540723
\(452\) −8.34168e11 −0.940006
\(453\) −2.00908e12 −2.24159
\(454\) 1.02018e12 1.12701
\(455\) 3.94835e10 0.0431881
\(456\) 4.56538e11 0.494465
\(457\) −1.03055e12 −1.10521 −0.552607 0.833442i \(-0.686367\pi\)
−0.552607 + 0.833442i \(0.686367\pi\)
\(458\) 4.57392e10 0.0485729
\(459\) 6.25095e11 0.657338
\(460\) −3.78646e11 −0.394296
\(461\) 9.37018e11 0.966259 0.483130 0.875549i \(-0.339500\pi\)
0.483130 + 0.875549i \(0.339500\pi\)
\(462\) −1.41034e11 −0.144024
\(463\) 1.08281e12 1.09506 0.547529 0.836787i \(-0.315569\pi\)
0.547529 + 0.836787i \(0.315569\pi\)
\(464\) 1.34855e11 0.135063
\(465\) −6.32361e11 −0.627230
\(466\) 2.20414e11 0.216522
\(467\) 1.52419e11 0.148290 0.0741451 0.997247i \(-0.476377\pi\)
0.0741451 + 0.997247i \(0.476377\pi\)
\(468\) −2.90454e11 −0.279879
\(469\) −3.75177e11 −0.358062
\(470\) −5.52019e11 −0.521812
\(471\) 2.03703e12 1.90723
\(472\) −2.01096e12 −1.86494
\(473\) −5.86297e11 −0.538570
\(474\) −1.51779e12 −1.38105
\(475\) −6.23865e10 −0.0562302
\(476\) 1.01000e11 0.0901756
\(477\) 8.73554e10 0.0772604
\(478\) −6.02652e11 −0.528008
\(479\) −2.02244e11 −0.175535 −0.0877677 0.996141i \(-0.527973\pi\)
−0.0877677 + 0.996141i \(0.527973\pi\)
\(480\) 8.54200e11 0.734470
\(481\) −3.39631e11 −0.289304
\(482\) 3.11099e11 0.262535
\(483\) −1.19376e12 −0.998060
\(484\) 6.09042e11 0.504479
\(485\) −9.16079e11 −0.751788
\(486\) −2.11732e11 −0.172156
\(487\) 8.35572e11 0.673137 0.336568 0.941659i \(-0.390734\pi\)
0.336568 + 0.941659i \(0.390734\pi\)
\(488\) −7.99094e11 −0.637836
\(489\) −1.02094e12 −0.807442
\(490\) −5.34268e10 −0.0418675
\(491\) −1.06242e12 −0.824953 −0.412476 0.910968i \(-0.635336\pi\)
−0.412476 + 0.910968i \(0.635336\pi\)
\(492\) −2.01351e12 −1.54921
\(493\) 7.12723e11 0.543387
\(494\) 6.23117e10 0.0470759
\(495\) −3.90265e11 −0.292170
\(496\) −1.14993e11 −0.0853108
\(497\) 1.66886e11 0.122692
\(498\) −1.88851e12 −1.37590
\(499\) −3.33938e11 −0.241109 −0.120554 0.992707i \(-0.538467\pi\)
−0.120554 + 0.992707i \(0.538467\pi\)
\(500\) −7.13178e10 −0.0510309
\(501\) −2.21404e11 −0.157006
\(502\) 1.47627e12 1.03752
\(503\) −3.60934e11 −0.251404 −0.125702 0.992068i \(-0.540118\pi\)
−0.125702 + 0.992068i \(0.540118\pi\)
\(504\) 1.08189e12 0.746870
\(505\) 4.71083e11 0.322319
\(506\) 5.08152e11 0.344601
\(507\) 2.37630e12 1.59723
\(508\) 1.12781e12 0.751365
\(509\) 4.09926e11 0.270692 0.135346 0.990798i \(-0.456785\pi\)
0.135346 + 0.990798i \(0.456785\pi\)
\(510\) −3.19946e11 −0.209417
\(511\) −1.88104e11 −0.122040
\(512\) 3.21676e11 0.206873
\(513\) 6.93277e11 0.441955
\(514\) 1.93928e12 1.22548
\(515\) −8.25894e11 −0.517359
\(516\) 2.48487e12 1.54305
\(517\) −9.84199e11 −0.605865
\(518\) 4.59569e11 0.280457
\(519\) 1.14115e12 0.690384
\(520\) 1.96082e11 0.117604
\(521\) −1.09884e12 −0.653377 −0.326688 0.945132i \(-0.605933\pi\)
−0.326688 + 0.945132i \(0.605933\pi\)
\(522\) 2.77346e12 1.63495
\(523\) 2.97552e12 1.73902 0.869511 0.493914i \(-0.164434\pi\)
0.869511 + 0.493914i \(0.164434\pi\)
\(524\) −1.17402e11 −0.0680276
\(525\) −2.24845e11 −0.129172
\(526\) 4.86280e11 0.276982
\(527\) −6.07748e11 −0.343223
\(528\) −1.07933e11 −0.0604367
\(529\) 2.50005e12 1.38803
\(530\) −2.14234e10 −0.0117936
\(531\) −6.37329e12 −3.47887
\(532\) 1.12016e11 0.0606288
\(533\) −7.56500e11 −0.406010
\(534\) −4.05855e11 −0.215991
\(535\) 6.71026e11 0.354118
\(536\) −1.86320e12 −0.975028
\(537\) 2.27074e12 1.17837
\(538\) −1.10871e11 −0.0570554
\(539\) −9.52551e10 −0.0486115
\(540\) 7.92526e11 0.401090
\(541\) 2.97095e12 1.49110 0.745551 0.666449i \(-0.232187\pi\)
0.745551 + 0.666449i \(0.232187\pi\)
\(542\) −9.97561e10 −0.0496527
\(543\) 1.88287e12 0.929438
\(544\) 8.20952e11 0.401904
\(545\) 6.79065e11 0.329706
\(546\) 2.24576e11 0.108142
\(547\) −1.50514e12 −0.718842 −0.359421 0.933176i \(-0.617026\pi\)
−0.359421 + 0.933176i \(0.617026\pi\)
\(548\) −8.88540e11 −0.420886
\(549\) −2.53256e12 −1.18983
\(550\) 9.57104e10 0.0445992
\(551\) 7.90463e11 0.365342
\(552\) −5.92845e12 −2.71779
\(553\) −1.02512e12 −0.466136
\(554\) 2.26394e12 1.02111
\(555\) 1.93408e12 0.865279
\(556\) −2.44333e11 −0.108429
\(557\) −2.17354e12 −0.956797 −0.478399 0.878143i \(-0.658783\pi\)
−0.478399 + 0.878143i \(0.658783\pi\)
\(558\) −2.36496e12 −1.03269
\(559\) 9.33593e11 0.404394
\(560\) −4.08874e10 −0.0175689
\(561\) −5.70434e11 −0.243149
\(562\) −4.59379e11 −0.194248
\(563\) 1.40104e12 0.587710 0.293855 0.955850i \(-0.405062\pi\)
0.293855 + 0.955850i \(0.405062\pi\)
\(564\) 4.17127e12 1.73585
\(565\) 1.78474e12 0.736814
\(566\) 1.32281e12 0.541781
\(567\) 7.12707e11 0.289592
\(568\) 8.28784e11 0.334098
\(569\) −1.81226e12 −0.724795 −0.362397 0.932024i \(-0.618042\pi\)
−0.362397 + 0.932024i \(0.618042\pi\)
\(570\) −3.54844e11 −0.140799
\(571\) −3.38885e12 −1.33410 −0.667052 0.745012i \(-0.732444\pi\)
−0.667052 + 0.745012i \(0.732444\pi\)
\(572\) 1.27001e11 0.0496048
\(573\) −4.27233e12 −1.65565
\(574\) 1.02365e12 0.393594
\(575\) 8.10131e11 0.309065
\(576\) 3.72180e12 1.40881
\(577\) 2.86129e12 1.07466 0.537329 0.843373i \(-0.319433\pi\)
0.537329 + 0.843373i \(0.319433\pi\)
\(578\) 1.45098e12 0.540737
\(579\) 4.62930e11 0.171183
\(580\) 9.03626e11 0.331560
\(581\) −1.27551e12 −0.464400
\(582\) −5.21050e12 −1.88246
\(583\) −3.81960e10 −0.0136933
\(584\) −9.34156e11 −0.332324
\(585\) 6.21440e11 0.219381
\(586\) −9.34324e11 −0.327309
\(587\) −7.85729e11 −0.273150 −0.136575 0.990630i \(-0.543609\pi\)
−0.136575 + 0.990630i \(0.543609\pi\)
\(588\) 4.03714e11 0.139276
\(589\) −6.74039e11 −0.230763
\(590\) 1.56302e12 0.531043
\(591\) −7.78174e12 −2.62382
\(592\) 3.51707e11 0.117688
\(593\) 8.24271e11 0.273731 0.136865 0.990590i \(-0.456297\pi\)
0.136865 + 0.990590i \(0.456297\pi\)
\(594\) −1.06359e12 −0.350538
\(595\) −2.16094e11 −0.0706831
\(596\) 2.26747e12 0.736093
\(597\) 6.60380e12 2.12770
\(598\) −8.09159e11 −0.258749
\(599\) −2.60594e10 −0.00827073 −0.00413537 0.999991i \(-0.501316\pi\)
−0.00413537 + 0.999991i \(0.501316\pi\)
\(600\) −1.11662e12 −0.351743
\(601\) 1.90372e11 0.0595207 0.0297603 0.999557i \(-0.490526\pi\)
0.0297603 + 0.999557i \(0.490526\pi\)
\(602\) −1.26328e12 −0.392028
\(603\) −5.90499e12 −1.81883
\(604\) −2.44807e12 −0.748441
\(605\) −1.30307e12 −0.395430
\(606\) 2.67944e12 0.807082
\(607\) 1.77675e12 0.531222 0.265611 0.964080i \(-0.414426\pi\)
0.265611 + 0.964080i \(0.414426\pi\)
\(608\) 9.10497e11 0.270217
\(609\) 2.84888e12 0.839260
\(610\) 6.21096e11 0.181624
\(611\) 1.56719e12 0.454922
\(612\) 1.58966e12 0.458060
\(613\) −2.48518e11 −0.0710863 −0.0355431 0.999368i \(-0.511316\pi\)
−0.0355431 + 0.999368i \(0.511316\pi\)
\(614\) 1.81591e12 0.515628
\(615\) 4.30801e12 1.21434
\(616\) −4.73054e11 −0.132372
\(617\) 3.52347e12 0.978786 0.489393 0.872063i \(-0.337218\pi\)
0.489393 + 0.872063i \(0.337218\pi\)
\(618\) −4.69755e12 −1.29546
\(619\) −6.69712e12 −1.83350 −0.916748 0.399466i \(-0.869196\pi\)
−0.916748 + 0.399466i \(0.869196\pi\)
\(620\) −7.70534e11 −0.209425
\(621\) −9.00266e12 −2.42917
\(622\) −4.12121e12 −1.10400
\(623\) −2.74117e11 −0.0729021
\(624\) 1.71867e11 0.0453798
\(625\) 1.52588e11 0.0400000
\(626\) −1.81637e12 −0.472738
\(627\) −6.32654e11 −0.163479
\(628\) 2.48212e12 0.636802
\(629\) 1.85880e12 0.473484
\(630\) −8.40897e11 −0.212672
\(631\) 6.29917e11 0.158180 0.0790900 0.996867i \(-0.474799\pi\)
0.0790900 + 0.996867i \(0.474799\pi\)
\(632\) −5.09095e12 −1.26932
\(633\) −4.66165e12 −1.15404
\(634\) −3.44020e12 −0.845634
\(635\) −2.41301e12 −0.588949
\(636\) 1.61884e11 0.0392325
\(637\) 1.51680e11 0.0365006
\(638\) −1.21269e12 −0.289772
\(639\) 2.62665e12 0.623231
\(640\) 9.11555e11 0.214770
\(641\) 2.82049e12 0.659877 0.329938 0.944002i \(-0.392972\pi\)
0.329938 + 0.944002i \(0.392972\pi\)
\(642\) 3.81668e12 0.886704
\(643\) 7.19804e12 1.66060 0.830300 0.557317i \(-0.188169\pi\)
0.830300 + 0.557317i \(0.188169\pi\)
\(644\) −1.45461e12 −0.333241
\(645\) −5.31649e12 −1.20950
\(646\) −3.41033e11 −0.0770459
\(647\) 7.17803e12 1.61041 0.805204 0.592998i \(-0.202056\pi\)
0.805204 + 0.592998i \(0.202056\pi\)
\(648\) 3.53943e12 0.788580
\(649\) 2.78671e12 0.616582
\(650\) −1.52405e11 −0.0334880
\(651\) −2.42928e12 −0.530106
\(652\) −1.24402e12 −0.269596
\(653\) −1.54599e12 −0.332734 −0.166367 0.986064i \(-0.553204\pi\)
−0.166367 + 0.986064i \(0.553204\pi\)
\(654\) 3.86240e12 0.825578
\(655\) 2.51187e11 0.0533227
\(656\) 7.83398e11 0.165164
\(657\) −2.96061e12 −0.619921
\(658\) −2.12064e12 −0.441011
\(659\) 2.38624e12 0.492868 0.246434 0.969160i \(-0.420741\pi\)
0.246434 + 0.969160i \(0.420741\pi\)
\(660\) −7.23225e11 −0.148363
\(661\) −2.35488e12 −0.479802 −0.239901 0.970797i \(-0.577115\pi\)
−0.239901 + 0.970797i \(0.577115\pi\)
\(662\) 5.54958e12 1.12305
\(663\) 9.08333e11 0.182572
\(664\) −6.33443e12 −1.26459
\(665\) −2.39664e11 −0.0475232
\(666\) 7.23326e12 1.42462
\(667\) −1.02647e13 −2.00807
\(668\) −2.69781e11 −0.0524225
\(669\) 1.17580e13 2.26943
\(670\) 1.44817e12 0.277640
\(671\) 1.10736e12 0.210880
\(672\) 3.28149e12 0.620740
\(673\) −6.32709e12 −1.18887 −0.594437 0.804142i \(-0.702625\pi\)
−0.594437 + 0.804142i \(0.702625\pi\)
\(674\) −4.98055e12 −0.929625
\(675\) −1.69565e12 −0.314390
\(676\) 2.89553e12 0.533296
\(677\) 3.16670e12 0.579372 0.289686 0.957122i \(-0.406449\pi\)
0.289686 + 0.957122i \(0.406449\pi\)
\(678\) 1.01513e13 1.84497
\(679\) −3.51921e12 −0.635376
\(680\) −1.07316e12 −0.192475
\(681\) 1.64935e13 2.93868
\(682\) 1.03408e12 0.183030
\(683\) −6.06916e12 −1.06717 −0.533587 0.845745i \(-0.679156\pi\)
−0.533587 + 0.845745i \(0.679156\pi\)
\(684\) 1.76305e12 0.307973
\(685\) 1.90107e12 0.329907
\(686\) −2.05245e11 −0.0353845
\(687\) 7.39478e11 0.126654
\(688\) −9.66788e11 −0.164507
\(689\) 6.08216e10 0.0102818
\(690\) 4.60789e12 0.773893
\(691\) −1.36410e12 −0.227611 −0.113806 0.993503i \(-0.536304\pi\)
−0.113806 + 0.993503i \(0.536304\pi\)
\(692\) 1.39050e12 0.230512
\(693\) −1.49924e12 −0.246929
\(694\) 5.39307e12 0.882508
\(695\) 5.22763e11 0.0849911
\(696\) 1.41481e13 2.28536
\(697\) 4.14033e12 0.664489
\(698\) −1.61244e12 −0.257119
\(699\) 3.56349e12 0.564584
\(700\) −2.73974e11 −0.0431290
\(701\) 4.27032e12 0.667927 0.333964 0.942586i \(-0.391614\pi\)
0.333964 + 0.942586i \(0.391614\pi\)
\(702\) 1.69361e12 0.263207
\(703\) 2.06155e12 0.318343
\(704\) −1.62735e12 −0.249692
\(705\) −8.92464e12 −1.36063
\(706\) 4.98605e12 0.755328
\(707\) 1.80971e12 0.272410
\(708\) −1.18108e13 −1.76656
\(709\) 4.76449e12 0.708122 0.354061 0.935222i \(-0.384800\pi\)
0.354061 + 0.935222i \(0.384800\pi\)
\(710\) −6.44172e11 −0.0951348
\(711\) −1.61347e13 −2.36781
\(712\) −1.36132e12 −0.198517
\(713\) 8.75284e12 1.26837
\(714\) −1.22910e12 −0.176989
\(715\) −2.71724e11 −0.0388822
\(716\) 2.76690e12 0.393446
\(717\) −9.74323e12 −1.37679
\(718\) −8.15481e12 −1.14513
\(719\) −2.64192e12 −0.368671 −0.184336 0.982863i \(-0.559013\pi\)
−0.184336 + 0.982863i \(0.559013\pi\)
\(720\) −6.43537e11 −0.0892436
\(721\) −3.17276e12 −0.437248
\(722\) 4.40672e12 0.603529
\(723\) 5.02963e12 0.684563
\(724\) 2.29428e12 0.310329
\(725\) −1.93335e12 −0.259890
\(726\) −7.41167e12 −0.990150
\(727\) −3.54861e12 −0.471144 −0.235572 0.971857i \(-0.575696\pi\)
−0.235572 + 0.971857i \(0.575696\pi\)
\(728\) 7.53270e11 0.0993938
\(729\) −9.26577e12 −1.21509
\(730\) 7.26072e11 0.0946296
\(731\) −5.10956e12 −0.661844
\(732\) −4.69324e12 −0.604189
\(733\) −1.34909e13 −1.72613 −0.863063 0.505095i \(-0.831457\pi\)
−0.863063 + 0.505095i \(0.831457\pi\)
\(734\) 1.96037e12 0.249291
\(735\) −8.63766e11 −0.109170
\(736\) −1.18234e13 −1.48523
\(737\) 2.58195e12 0.322362
\(738\) 1.61115e13 1.99932
\(739\) −1.33151e13 −1.64227 −0.821133 0.570736i \(-0.806658\pi\)
−0.821133 + 0.570736i \(0.806658\pi\)
\(740\) 2.35668e12 0.288907
\(741\) 1.00741e12 0.122751
\(742\) −8.23003e10 −0.00996744
\(743\) 1.37811e13 1.65896 0.829479 0.558538i \(-0.188637\pi\)
0.829479 + 0.558538i \(0.188637\pi\)
\(744\) −1.20642e13 −1.44352
\(745\) −4.85135e12 −0.576979
\(746\) −7.23722e12 −0.855553
\(747\) −2.00756e13 −2.35899
\(748\) −6.95075e11 −0.0811848
\(749\) 2.57781e12 0.299284
\(750\) 8.67894e11 0.100159
\(751\) −1.31166e12 −0.150467 −0.0752334 0.997166i \(-0.523970\pi\)
−0.0752334 + 0.997166i \(0.523970\pi\)
\(752\) −1.62292e12 −0.185062
\(753\) 2.38672e13 2.70535
\(754\) 1.93103e12 0.217580
\(755\) 5.23776e12 0.586657
\(756\) 3.04457e12 0.338983
\(757\) 1.31405e13 1.45439 0.727196 0.686430i \(-0.240823\pi\)
0.727196 + 0.686430i \(0.240823\pi\)
\(758\) −4.45093e12 −0.489711
\(759\) 8.21543e12 0.898551
\(760\) −1.19022e12 −0.129409
\(761\) 4.85816e12 0.525099 0.262549 0.964919i \(-0.415437\pi\)
0.262549 + 0.964919i \(0.415437\pi\)
\(762\) −1.37248e13 −1.47472
\(763\) 2.60869e12 0.278652
\(764\) −5.20584e12 −0.552804
\(765\) −3.40115e12 −0.359045
\(766\) −1.14802e13 −1.20481
\(767\) −4.43743e12 −0.462970
\(768\) 1.72735e13 1.79165
\(769\) −1.57384e13 −1.62290 −0.811452 0.584420i \(-0.801322\pi\)
−0.811452 + 0.584420i \(0.801322\pi\)
\(770\) 3.67681e11 0.0376932
\(771\) 3.13528e13 3.19545
\(772\) 5.64081e11 0.0571562
\(773\) 1.97088e12 0.198542 0.0992710 0.995060i \(-0.468349\pi\)
0.0992710 + 0.995060i \(0.468349\pi\)
\(774\) −1.98831e13 −1.99136
\(775\) 1.64859e12 0.164156
\(776\) −1.74770e13 −1.73017
\(777\) 7.42997e12 0.731295
\(778\) 2.52271e12 0.246865
\(779\) 4.59194e12 0.446763
\(780\) 1.15163e12 0.111401
\(781\) −1.14850e12 −0.110459
\(782\) 4.42854e12 0.423477
\(783\) 2.14846e13 2.04267
\(784\) −1.57073e11 −0.0148484
\(785\) −5.31062e12 −0.499150
\(786\) 1.42871e12 0.133519
\(787\) −1.29627e13 −1.20451 −0.602253 0.798306i \(-0.705730\pi\)
−0.602253 + 0.798306i \(0.705730\pi\)
\(788\) −9.48207e12 −0.876063
\(789\) 7.86182e12 0.722232
\(790\) 3.95694e12 0.361441
\(791\) 6.85627e12 0.622721
\(792\) −7.44551e12 −0.672405
\(793\) −1.76330e12 −0.158343
\(794\) 8.11474e12 0.724573
\(795\) −3.46358e11 −0.0307520
\(796\) 8.04675e12 0.710414
\(797\) 1.04429e13 0.916762 0.458381 0.888756i \(-0.348429\pi\)
0.458381 + 0.888756i \(0.348429\pi\)
\(798\) −1.36317e12 −0.118997
\(799\) −8.57727e12 −0.744541
\(800\) −2.22694e12 −0.192222
\(801\) −4.31439e12 −0.370317
\(802\) 6.77917e12 0.578618
\(803\) 1.29452e12 0.109872
\(804\) −1.09429e13 −0.923594
\(805\) 3.11220e12 0.261208
\(806\) −1.64662e12 −0.137431
\(807\) −1.79248e12 −0.148772
\(808\) 8.98737e12 0.741791
\(809\) −6.99142e12 −0.573848 −0.286924 0.957953i \(-0.592633\pi\)
−0.286924 + 0.957953i \(0.592633\pi\)
\(810\) −2.75102e12 −0.224549
\(811\) −1.14380e13 −0.928442 −0.464221 0.885719i \(-0.653666\pi\)
−0.464221 + 0.885719i \(0.653666\pi\)
\(812\) 3.47137e12 0.280220
\(813\) −1.61278e12 −0.129470
\(814\) −3.16273e12 −0.252495
\(815\) 2.66164e12 0.211320
\(816\) −9.40631e11 −0.0742700
\(817\) −5.66689e12 −0.444985
\(818\) −1.39831e12 −0.109198
\(819\) 2.38733e12 0.185410
\(820\) 5.24932e12 0.405453
\(821\) −4.42435e12 −0.339864 −0.169932 0.985456i \(-0.554355\pi\)
−0.169932 + 0.985456i \(0.554355\pi\)
\(822\) 1.08130e13 0.826081
\(823\) 1.71948e13 1.30647 0.653234 0.757156i \(-0.273412\pi\)
0.653234 + 0.757156i \(0.273412\pi\)
\(824\) −1.57565e13 −1.19066
\(825\) 1.54737e12 0.116293
\(826\) 6.00448e12 0.448813
\(827\) 3.04498e12 0.226365 0.113182 0.993574i \(-0.463896\pi\)
0.113182 + 0.993574i \(0.463896\pi\)
\(828\) −2.28944e13 −1.69275
\(829\) −8.03416e12 −0.590806 −0.295403 0.955373i \(-0.595454\pi\)
−0.295403 + 0.955373i \(0.595454\pi\)
\(830\) 4.92343e12 0.360094
\(831\) 3.66017e13 2.66254
\(832\) 2.59132e12 0.187485
\(833\) −8.30146e11 −0.0597382
\(834\) 2.97339e12 0.212816
\(835\) 5.77210e11 0.0410908
\(836\) −7.70891e11 −0.0545839
\(837\) −1.83202e13 −1.29022
\(838\) −2.47448e12 −0.173335
\(839\) 1.36209e13 0.949020 0.474510 0.880250i \(-0.342625\pi\)
0.474510 + 0.880250i \(0.342625\pi\)
\(840\) −4.28962e12 −0.297277
\(841\) 9.98921e12 0.688571
\(842\) 8.19684e12 0.562007
\(843\) −7.42689e12 −0.506504
\(844\) −5.68023e12 −0.385323
\(845\) −6.19513e12 −0.418018
\(846\) −3.33772e13 −2.24018
\(847\) −5.00589e12 −0.334200
\(848\) −6.29842e10 −0.00418264
\(849\) 2.13862e13 1.41270
\(850\) 8.34114e11 0.0548075
\(851\) −2.67706e13 −1.74975
\(852\) 4.86762e12 0.316474
\(853\) 3.64211e12 0.235549 0.117775 0.993040i \(-0.462424\pi\)
0.117775 + 0.993040i \(0.462424\pi\)
\(854\) 2.38600e12 0.153501
\(855\) −3.77213e12 −0.241401
\(856\) 1.28019e13 0.814971
\(857\) 1.62518e13 1.02917 0.514587 0.857438i \(-0.327945\pi\)
0.514587 + 0.857438i \(0.327945\pi\)
\(858\) −1.54552e12 −0.0973602
\(859\) 1.69063e13 1.05944 0.529722 0.848171i \(-0.322296\pi\)
0.529722 + 0.848171i \(0.322296\pi\)
\(860\) −6.47816e12 −0.403839
\(861\) 1.65496e13 1.02630
\(862\) 6.48608e12 0.400128
\(863\) −1.56857e13 −0.962619 −0.481310 0.876551i \(-0.659839\pi\)
−0.481310 + 0.876551i \(0.659839\pi\)
\(864\) 2.47471e13 1.51082
\(865\) −2.97504e12 −0.180684
\(866\) −4.14955e12 −0.250709
\(867\) 2.34584e13 1.40998
\(868\) −2.96008e12 −0.176997
\(869\) 7.05485e12 0.419661
\(870\) −1.09966e13 −0.650760
\(871\) −4.11138e12 −0.242050
\(872\) 1.29553e13 0.758790
\(873\) −5.53897e13 −3.22749
\(874\) 4.91158e12 0.284721
\(875\) 5.86182e11 0.0338062
\(876\) −5.48649e12 −0.314794
\(877\) 2.37521e13 1.35583 0.677914 0.735141i \(-0.262884\pi\)
0.677914 + 0.735141i \(0.262884\pi\)
\(878\) −1.31550e13 −0.747079
\(879\) −1.51055e13 −0.853462
\(880\) 2.81385e11 0.0158172
\(881\) 1.13698e13 0.635858 0.317929 0.948115i \(-0.397013\pi\)
0.317929 + 0.948115i \(0.397013\pi\)
\(882\) −3.23039e12 −0.179741
\(883\) −1.21711e12 −0.0673762 −0.0336881 0.999432i \(-0.510725\pi\)
−0.0336881 + 0.999432i \(0.510725\pi\)
\(884\) 1.10681e12 0.0609588
\(885\) 2.52697e13 1.38470
\(886\) 8.71692e12 0.475238
\(887\) 3.43743e13 1.86457 0.932283 0.361730i \(-0.117814\pi\)
0.932283 + 0.361730i \(0.117814\pi\)
\(888\) 3.68986e13 1.99137
\(889\) −9.26983e12 −0.497753
\(890\) 1.05808e12 0.0565281
\(891\) −4.90482e12 −0.260719
\(892\) 1.43272e13 0.757738
\(893\) −9.51284e12 −0.500586
\(894\) −2.75937e13 −1.44474
\(895\) −5.91992e12 −0.308398
\(896\) 3.50183e12 0.181513
\(897\) −1.30819e13 −0.674690
\(898\) 7.70957e12 0.395627
\(899\) −2.08884e13 −1.06656
\(900\) −4.31215e12 −0.219080
\(901\) −3.32877e11 −0.0168276
\(902\) −7.04472e12 −0.354352
\(903\) −2.04238e13 −1.02222
\(904\) 3.40495e13 1.69571
\(905\) −4.90872e12 −0.243248
\(906\) 2.97915e13 1.46898
\(907\) −3.08586e13 −1.51406 −0.757030 0.653381i \(-0.773350\pi\)
−0.757030 + 0.653381i \(0.773350\pi\)
\(908\) 2.00974e13 0.981192
\(909\) 2.84835e13 1.38374
\(910\) −5.85478e11 −0.0283025
\(911\) −3.36006e13 −1.61627 −0.808136 0.588996i \(-0.799523\pi\)
−0.808136 + 0.588996i \(0.799523\pi\)
\(912\) −1.04323e12 −0.0499348
\(913\) 8.77802e12 0.418098
\(914\) 1.52814e13 0.724280
\(915\) 1.00414e13 0.473587
\(916\) 9.01056e11 0.0422885
\(917\) 9.64961e11 0.0450659
\(918\) −9.26917e12 −0.430773
\(919\) −1.46200e13 −0.676127 −0.338063 0.941123i \(-0.609772\pi\)
−0.338063 + 0.941123i \(0.609772\pi\)
\(920\) 1.54557e13 0.711287
\(921\) 2.93583e13 1.34450
\(922\) −1.38945e13 −0.633219
\(923\) 1.82882e12 0.0829398
\(924\) −2.77834e12 −0.125390
\(925\) −5.04224e12 −0.226457
\(926\) −1.60563e13 −0.717625
\(927\) −4.99367e13 −2.22107
\(928\) 2.82162e13 1.24891
\(929\) −1.36244e13 −0.600130 −0.300065 0.953919i \(-0.597008\pi\)
−0.300065 + 0.953919i \(0.597008\pi\)
\(930\) 9.37693e12 0.411043
\(931\) −9.20694e11 −0.0401644
\(932\) 4.34213e12 0.188508
\(933\) −6.66287e13 −2.87868
\(934\) −2.26013e12 −0.0971790
\(935\) 1.48715e12 0.0636358
\(936\) 1.18559e13 0.504885
\(937\) −1.06580e13 −0.451697 −0.225848 0.974162i \(-0.572515\pi\)
−0.225848 + 0.974162i \(0.572515\pi\)
\(938\) 5.56328e12 0.234649
\(939\) −2.93658e13 −1.23267
\(940\) −1.08747e13 −0.454299
\(941\) 1.54253e13 0.641328 0.320664 0.947193i \(-0.396094\pi\)
0.320664 + 0.947193i \(0.396094\pi\)
\(942\) −3.02059e13 −1.24986
\(943\) −5.96294e13 −2.45560
\(944\) 4.59522e12 0.188335
\(945\) −6.51400e12 −0.265708
\(946\) 8.69386e12 0.352941
\(947\) 1.97267e13 0.797039 0.398519 0.917160i \(-0.369524\pi\)
0.398519 + 0.917160i \(0.369524\pi\)
\(948\) −2.99002e13 −1.20236
\(949\) −2.06133e12 −0.0824993
\(950\) 9.25094e11 0.0368493
\(951\) −5.56186e13 −2.20500
\(952\) −4.12265e12 −0.162671
\(953\) −1.39214e12 −0.0546721 −0.0273361 0.999626i \(-0.508702\pi\)
−0.0273361 + 0.999626i \(0.508702\pi\)
\(954\) −1.29534e12 −0.0506311
\(955\) 1.11381e13 0.433309
\(956\) −1.18721e13 −0.459694
\(957\) −1.96059e13 −0.755583
\(958\) 2.99895e12 0.115034
\(959\) 7.30317e12 0.278822
\(960\) −1.47567e13 −0.560749
\(961\) −8.62783e12 −0.326322
\(962\) 5.03619e12 0.189589
\(963\) 4.05728e13 1.52026
\(964\) 6.12861e12 0.228568
\(965\) −1.20688e12 −0.0448013
\(966\) 1.77017e13 0.654059
\(967\) 5.29760e12 0.194832 0.0974160 0.995244i \(-0.468942\pi\)
0.0974160 + 0.995244i \(0.468942\pi\)
\(968\) −2.48602e13 −0.910049
\(969\) −5.51357e12 −0.200898
\(970\) 1.35840e13 0.492669
\(971\) −7.97890e12 −0.288042 −0.144021 0.989575i \(-0.546003\pi\)
−0.144021 + 0.989575i \(0.546003\pi\)
\(972\) −4.17108e12 −0.149882
\(973\) 2.00825e12 0.0718306
\(974\) −1.23902e13 −0.441127
\(975\) −2.46397e12 −0.0873202
\(976\) 1.82600e12 0.0644135
\(977\) −6.27831e12 −0.220454 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(978\) 1.51390e13 0.529141
\(979\) 1.88646e12 0.0656335
\(980\) −1.05250e12 −0.0364506
\(981\) 4.10589e13 1.41546
\(982\) 1.57540e13 0.540616
\(983\) 1.25053e12 0.0427173 0.0213586 0.999772i \(-0.493201\pi\)
0.0213586 + 0.999772i \(0.493201\pi\)
\(984\) 8.21886e13 2.79469
\(985\) 2.02874e13 0.686692
\(986\) −1.05686e13 −0.356098
\(987\) −3.42849e13 −1.14994
\(988\) 1.22753e12 0.0409851
\(989\) 7.35883e13 2.44583
\(990\) 5.78702e12 0.191468
\(991\) 1.89095e13 0.622801 0.311400 0.950279i \(-0.399202\pi\)
0.311400 + 0.950279i \(0.399202\pi\)
\(992\) −2.40603e13 −0.788858
\(993\) 8.97216e13 2.92836
\(994\) −2.47465e12 −0.0804036
\(995\) −1.72164e13 −0.556851
\(996\) −3.72034e13 −1.19788
\(997\) −7.17482e12 −0.229976 −0.114988 0.993367i \(-0.536683\pi\)
−0.114988 + 0.993367i \(0.536683\pi\)
\(998\) 4.95178e12 0.158006
\(999\) 5.60324e13 1.77989
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 35.10.a.b.1.1 2
3.2 odd 2 315.10.a.b.1.2 2
5.2 odd 4 175.10.b.c.99.1 4
5.3 odd 4 175.10.b.c.99.4 4
5.4 even 2 175.10.a.c.1.2 2
7.6 odd 2 245.10.a.c.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.a.b.1.1 2 1.1 even 1 trivial
175.10.a.c.1.2 2 5.4 even 2
175.10.b.c.99.1 4 5.2 odd 4
175.10.b.c.99.4 4 5.3 odd 4
245.10.a.c.1.1 2 7.6 odd 2
315.10.a.b.1.2 2 3.2 odd 2