Properties

Label 17.10.a.b.1.1
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 2986 x^{5} + 8252 x^{4} + 2252056 x^{3} - 10388768 x^{2} - 243559296 x - 675998208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(42.3973\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +O(q^{10})\) \(q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +105924. q^{10} +36573.4 q^{11} +141074. q^{12} +69902.2 q^{13} -121791. q^{14} -274171. q^{15} +732260. q^{16} +83521.0 q^{17} +323924. q^{18} +640587. q^{19} -3.21175e6 q^{20} +315239. q^{21} -1.55061e6 q^{22} +2.09284e6 q^{23} -3.59900e6 q^{24} +4.28875e6 q^{25} -2.96367e6 q^{26} -2.99844e6 q^{27} +3.69283e6 q^{28} +4.99200e6 q^{29} +1.16241e7 q^{30} -5.61791e6 q^{31} -1.42544e7 q^{32} +4.01355e6 q^{33} -3.54107e6 q^{34} -7.17685e6 q^{35} -9.82174e6 q^{36} +3.47843e6 q^{37} -2.71592e7 q^{38} +7.67105e6 q^{39} +8.19361e7 q^{40} +469632. q^{41} -1.33653e7 q^{42} +3.50525e6 q^{43} +4.70163e7 q^{44} +1.90881e7 q^{45} -8.87310e7 q^{46} +1.55290e6 q^{47} +8.03580e7 q^{48} -3.21017e7 q^{49} -1.81832e8 q^{50} +9.16557e6 q^{51} +8.98617e7 q^{52} +1.03903e8 q^{53} +1.27126e8 q^{54} -9.13740e7 q^{55} -9.42094e7 q^{56} +7.02978e7 q^{57} -2.11648e8 q^{58} -7.79169e7 q^{59} -3.52456e8 q^{60} +1.79259e7 q^{61} +2.38185e8 q^{62} -2.19473e7 q^{63} +2.29433e8 q^{64} -1.74642e8 q^{65} -1.70164e8 q^{66} +8.26939e7 q^{67} +1.07369e8 q^{68} +2.29668e8 q^{69} +3.04279e8 q^{70} -1.03521e8 q^{71} +2.50566e8 q^{72} +1.43348e7 q^{73} -1.47476e8 q^{74} +4.70646e8 q^{75} +8.23496e8 q^{76} +1.05061e8 q^{77} -3.25232e8 q^{78} +3.90455e8 q^{79} -1.82946e9 q^{80} -1.78666e8 q^{81} -1.99111e7 q^{82} -3.47368e8 q^{83} +4.05250e8 q^{84} -2.08667e8 q^{85} -1.48613e8 q^{86} +5.47821e8 q^{87} -1.19945e9 q^{88} -4.95430e7 q^{89} -8.09284e8 q^{90} +2.00802e8 q^{91} +2.69042e9 q^{92} -6.16508e8 q^{93} -6.58387e7 q^{94} -1.60043e9 q^{95} -1.56428e9 q^{96} +6.49870e8 q^{97} +1.36103e9 q^{98} -2.79428e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.3973 −1.87372 −0.936858 0.349711i \(-0.886280\pi\)
−0.936858 + 0.349711i \(0.886280\pi\)
\(3\) 109.740 0.782200 0.391100 0.920348i \(-0.372095\pi\)
0.391100 + 0.920348i \(0.372095\pi\)
\(4\) 1285.53 2.51081
\(5\) −2498.37 −1.78769 −0.893846 0.448375i \(-0.852003\pi\)
−0.893846 + 0.448375i \(0.852003\pi\)
\(6\) −4652.67 −1.46562
\(7\) 2872.61 0.452205 0.226102 0.974104i \(-0.427402\pi\)
0.226102 + 0.974104i \(0.427402\pi\)
\(8\) −32795.8 −2.83082
\(9\) −7640.20 −0.388163
\(10\) 105924. 3.34962
\(11\) 36573.4 0.753178 0.376589 0.926380i \(-0.377097\pi\)
0.376589 + 0.926380i \(0.377097\pi\)
\(12\) 141074. 1.96396
\(13\) 69902.2 0.678806 0.339403 0.940641i \(-0.389775\pi\)
0.339403 + 0.940641i \(0.389775\pi\)
\(14\) −121791. −0.847303
\(15\) −274171. −1.39833
\(16\) 732260. 2.79335
\(17\) 83521.0 0.242536
\(18\) 323924. 0.727306
\(19\) 640587. 1.12768 0.563841 0.825883i \(-0.309323\pi\)
0.563841 + 0.825883i \(0.309323\pi\)
\(20\) −3.21175e6 −4.48855
\(21\) 315239. 0.353715
\(22\) −1.55061e6 −1.41124
\(23\) 2.09284e6 1.55941 0.779707 0.626144i \(-0.215368\pi\)
0.779707 + 0.626144i \(0.215368\pi\)
\(24\) −3.59900e6 −2.21427
\(25\) 4.28875e6 2.19584
\(26\) −2.96367e6 −1.27189
\(27\) −2.99844e6 −1.08582
\(28\) 3.69283e6 1.13540
\(29\) 4.99200e6 1.31064 0.655321 0.755351i \(-0.272534\pi\)
0.655321 + 0.755351i \(0.272534\pi\)
\(30\) 1.16241e7 2.62008
\(31\) −5.61791e6 −1.09257 −0.546283 0.837601i \(-0.683958\pi\)
−0.546283 + 0.837601i \(0.683958\pi\)
\(32\) −1.42544e7 −2.40312
\(33\) 4.01355e6 0.589136
\(34\) −3.54107e6 −0.454443
\(35\) −7.17685e6 −0.808402
\(36\) −9.82174e6 −0.974602
\(37\) 3.47843e6 0.305123 0.152562 0.988294i \(-0.451248\pi\)
0.152562 + 0.988294i \(0.451248\pi\)
\(38\) −2.71592e7 −2.11296
\(39\) 7.67105e6 0.530963
\(40\) 8.19361e7 5.06064
\(41\) 469632. 0.0259555 0.0129778 0.999916i \(-0.495869\pi\)
0.0129778 + 0.999916i \(0.495869\pi\)
\(42\) −1.33653e7 −0.662760
\(43\) 3.50525e6 0.156355 0.0781773 0.996939i \(-0.475090\pi\)
0.0781773 + 0.996939i \(0.475090\pi\)
\(44\) 4.70163e7 1.89109
\(45\) 1.90881e7 0.693915
\(46\) −8.87310e7 −2.92190
\(47\) 1.55290e6 0.0464197 0.0232098 0.999731i \(-0.492611\pi\)
0.0232098 + 0.999731i \(0.492611\pi\)
\(48\) 8.03580e7 2.18496
\(49\) −3.21017e7 −0.795511
\(50\) −1.81832e8 −4.11438
\(51\) 9.16557e6 0.189711
\(52\) 8.98617e7 1.70435
\(53\) 1.03903e8 1.80878 0.904390 0.426706i \(-0.140326\pi\)
0.904390 + 0.426706i \(0.140326\pi\)
\(54\) 1.27126e8 2.03452
\(55\) −9.13740e7 −1.34645
\(56\) −9.42094e7 −1.28011
\(57\) 7.02978e7 0.882074
\(58\) −2.11648e8 −2.45577
\(59\) −7.79169e7 −0.837139 −0.418569 0.908185i \(-0.637468\pi\)
−0.418569 + 0.908185i \(0.637468\pi\)
\(60\) −3.52456e8 −3.51095
\(61\) 1.79259e7 0.165766 0.0828831 0.996559i \(-0.473587\pi\)
0.0828831 + 0.996559i \(0.473587\pi\)
\(62\) 2.38185e8 2.04716
\(63\) −2.19473e7 −0.175529
\(64\) 2.29433e8 1.70941
\(65\) −1.74642e8 −1.21350
\(66\) −1.70164e8 −1.10387
\(67\) 8.26939e7 0.501345 0.250673 0.968072i \(-0.419348\pi\)
0.250673 + 0.968072i \(0.419348\pi\)
\(68\) 1.07369e8 0.608960
\(69\) 2.29668e8 1.21977
\(70\) 3.04279e8 1.51472
\(71\) −1.03521e8 −0.483465 −0.241732 0.970343i \(-0.577716\pi\)
−0.241732 + 0.970343i \(0.577716\pi\)
\(72\) 2.50566e8 1.09882
\(73\) 1.43348e7 0.0590797 0.0295399 0.999564i \(-0.490596\pi\)
0.0295399 + 0.999564i \(0.490596\pi\)
\(74\) −1.47476e8 −0.571714
\(75\) 4.70646e8 1.71759
\(76\) 8.23496e8 2.83140
\(77\) 1.05061e8 0.340591
\(78\) −3.25232e8 −0.994873
\(79\) 3.90455e8 1.12784 0.563922 0.825828i \(-0.309292\pi\)
0.563922 + 0.825828i \(0.309292\pi\)
\(80\) −1.82946e9 −4.99365
\(81\) −1.78666e8 −0.461167
\(82\) −1.99111e7 −0.0486333
\(83\) −3.47368e8 −0.803411 −0.401706 0.915769i \(-0.631582\pi\)
−0.401706 + 0.915769i \(0.631582\pi\)
\(84\) 4.05250e8 0.888110
\(85\) −2.08667e8 −0.433579
\(86\) −1.48613e8 −0.292964
\(87\) 5.47821e8 1.02518
\(88\) −1.19945e9 −2.13212
\(89\) −4.95430e7 −0.0837004 −0.0418502 0.999124i \(-0.513325\pi\)
−0.0418502 + 0.999124i \(0.513325\pi\)
\(90\) −8.09284e8 −1.30020
\(91\) 2.00802e8 0.306959
\(92\) 2.69042e9 3.91539
\(93\) −6.16508e8 −0.854605
\(94\) −6.58387e7 −0.0869772
\(95\) −1.60043e9 −2.01595
\(96\) −1.56428e9 −1.87972
\(97\) 6.49870e8 0.745338 0.372669 0.927964i \(-0.378443\pi\)
0.372669 + 0.927964i \(0.378443\pi\)
\(98\) 1.36103e9 1.49056
\(99\) −2.79428e8 −0.292356
\(100\) 5.51334e9 5.51334
\(101\) −5.41669e8 −0.517950 −0.258975 0.965884i \(-0.583385\pi\)
−0.258975 + 0.965884i \(0.583385\pi\)
\(102\) −3.88596e8 −0.355465
\(103\) 1.38535e9 1.21281 0.606403 0.795157i \(-0.292612\pi\)
0.606403 + 0.795157i \(0.292612\pi\)
\(104\) −2.29250e9 −1.92158
\(105\) −7.87585e8 −0.632333
\(106\) −4.40520e9 −3.38914
\(107\) 3.51366e8 0.259139 0.129569 0.991570i \(-0.458641\pi\)
0.129569 + 0.991570i \(0.458641\pi\)
\(108\) −3.85460e9 −2.72629
\(109\) −8.82255e8 −0.598652 −0.299326 0.954151i \(-0.596762\pi\)
−0.299326 + 0.954151i \(0.596762\pi\)
\(110\) 3.87401e9 2.52286
\(111\) 3.81722e8 0.238668
\(112\) 2.10349e9 1.26317
\(113\) 1.98816e9 1.14709 0.573545 0.819174i \(-0.305568\pi\)
0.573545 + 0.819174i \(0.305568\pi\)
\(114\) −2.98044e9 −1.65276
\(115\) −5.22871e9 −2.78775
\(116\) 6.41739e9 3.29077
\(117\) −5.34067e8 −0.263487
\(118\) 3.30347e9 1.56856
\(119\) 2.39923e8 0.109676
\(120\) 8.99164e9 3.95844
\(121\) −1.02034e9 −0.432723
\(122\) −7.60009e8 −0.310598
\(123\) 5.15372e7 0.0203024
\(124\) −7.22202e9 −2.74322
\(125\) −5.83527e9 −2.13780
\(126\) 9.30507e8 0.328891
\(127\) −3.59412e8 −0.122596 −0.0612980 0.998120i \(-0.519524\pi\)
−0.0612980 + 0.998120i \(0.519524\pi\)
\(128\) −2.42907e9 −0.799826
\(129\) 3.84665e8 0.122301
\(130\) 7.40435e9 2.27375
\(131\) 2.17687e8 0.0645820 0.0322910 0.999479i \(-0.489720\pi\)
0.0322910 + 0.999479i \(0.489720\pi\)
\(132\) 5.15955e9 1.47921
\(133\) 1.84015e9 0.509943
\(134\) −3.50600e9 −0.939378
\(135\) 7.49123e9 1.94111
\(136\) −2.73914e9 −0.686576
\(137\) 3.81268e9 0.924671 0.462336 0.886705i \(-0.347011\pi\)
0.462336 + 0.886705i \(0.347011\pi\)
\(138\) −9.73731e9 −2.28551
\(139\) 1.05651e9 0.240054 0.120027 0.992771i \(-0.461702\pi\)
0.120027 + 0.992771i \(0.461702\pi\)
\(140\) −9.22608e9 −2.02974
\(141\) 1.70414e8 0.0363095
\(142\) 4.38900e9 0.905875
\(143\) 2.55656e9 0.511262
\(144\) −5.59461e9 −1.08427
\(145\) −1.24719e10 −2.34302
\(146\) −6.07757e8 −0.110699
\(147\) −3.52283e9 −0.622249
\(148\) 4.47164e9 0.766106
\(149\) 1.11231e10 1.84879 0.924394 0.381439i \(-0.124571\pi\)
0.924394 + 0.381439i \(0.124571\pi\)
\(150\) −1.99541e10 −3.21827
\(151\) −4.54386e8 −0.0711261 −0.0355630 0.999367i \(-0.511322\pi\)
−0.0355630 + 0.999367i \(0.511322\pi\)
\(152\) −2.10085e10 −3.19227
\(153\) −6.38117e8 −0.0941432
\(154\) −4.45430e9 −0.638170
\(155\) 1.40357e10 1.95317
\(156\) 9.86139e9 1.33315
\(157\) 1.18078e10 1.55102 0.775512 0.631332i \(-0.217492\pi\)
0.775512 + 0.631332i \(0.217492\pi\)
\(158\) −1.65542e10 −2.11326
\(159\) 1.14023e10 1.41483
\(160\) 3.56129e10 4.29603
\(161\) 6.01192e9 0.705175
\(162\) 7.57495e9 0.864096
\(163\) 9.05833e8 0.100509 0.0502544 0.998736i \(-0.483997\pi\)
0.0502544 + 0.998736i \(0.483997\pi\)
\(164\) 6.03728e8 0.0651694
\(165\) −1.00273e10 −1.05319
\(166\) 1.47275e10 1.50536
\(167\) 1.08715e10 1.08159 0.540797 0.841153i \(-0.318123\pi\)
0.540797 + 0.841153i \(0.318123\pi\)
\(168\) −1.03385e10 −1.00130
\(169\) −5.71818e9 −0.539222
\(170\) 8.84691e9 0.812403
\(171\) −4.89422e9 −0.437724
\(172\) 4.50611e9 0.392576
\(173\) −2.10914e10 −1.79019 −0.895093 0.445880i \(-0.852891\pi\)
−0.895093 + 0.445880i \(0.852891\pi\)
\(174\) −2.32261e10 −1.92090
\(175\) 1.23199e10 0.992970
\(176\) 2.67812e10 2.10389
\(177\) −8.55057e9 −0.654810
\(178\) 2.10049e9 0.156831
\(179\) −2.13633e10 −1.55535 −0.777676 0.628665i \(-0.783602\pi\)
−0.777676 + 0.628665i \(0.783602\pi\)
\(180\) 2.45384e10 1.74229
\(181\) −1.23594e10 −0.855937 −0.427969 0.903794i \(-0.640771\pi\)
−0.427969 + 0.903794i \(0.640771\pi\)
\(182\) −8.51345e9 −0.575154
\(183\) 1.96718e9 0.129662
\(184\) −6.86364e10 −4.41443
\(185\) −8.69042e9 −0.545466
\(186\) 2.61383e10 1.60129
\(187\) 3.05464e9 0.182673
\(188\) 1.99630e9 0.116551
\(189\) −8.61334e9 −0.491013
\(190\) 6.78538e10 3.77731
\(191\) 2.02521e10 1.10108 0.550540 0.834809i \(-0.314422\pi\)
0.550540 + 0.834809i \(0.314422\pi\)
\(192\) 2.51779e10 1.33710
\(193\) −2.75114e10 −1.42727 −0.713633 0.700520i \(-0.752952\pi\)
−0.713633 + 0.700520i \(0.752952\pi\)
\(194\) −2.75527e10 −1.39655
\(195\) −1.91652e10 −0.949197
\(196\) −4.12679e10 −1.99738
\(197\) 1.58792e10 0.751156 0.375578 0.926791i \(-0.377444\pi\)
0.375578 + 0.926791i \(0.377444\pi\)
\(198\) 1.18470e10 0.547791
\(199\) 3.50786e10 1.58563 0.792817 0.609460i \(-0.208614\pi\)
0.792817 + 0.609460i \(0.208614\pi\)
\(200\) −1.40653e11 −6.21604
\(201\) 9.07480e9 0.392152
\(202\) 2.29653e10 0.970491
\(203\) 1.43401e10 0.592678
\(204\) 1.17826e10 0.476329
\(205\) −1.17332e9 −0.0464005
\(206\) −5.87351e10 −2.27245
\(207\) −1.59898e10 −0.605306
\(208\) 5.11866e10 1.89614
\(209\) 2.34284e10 0.849346
\(210\) 3.33915e10 1.18481
\(211\) −2.22358e10 −0.772293 −0.386146 0.922438i \(-0.626194\pi\)
−0.386146 + 0.922438i \(0.626194\pi\)
\(212\) 1.33571e11 4.54150
\(213\) −1.13603e10 −0.378166
\(214\) −1.48970e10 −0.485552
\(215\) −8.75742e9 −0.279514
\(216\) 9.83361e10 3.07377
\(217\) −1.61381e10 −0.494063
\(218\) 3.74052e10 1.12170
\(219\) 1.57310e9 0.0462122
\(220\) −1.17464e11 −3.38068
\(221\) 5.83830e9 0.164635
\(222\) −1.61840e10 −0.447195
\(223\) 4.29725e9 0.116364 0.0581821 0.998306i \(-0.481470\pi\)
0.0581821 + 0.998306i \(0.481470\pi\)
\(224\) −4.09474e10 −1.08670
\(225\) −3.27669e10 −0.852343
\(226\) −8.42925e10 −2.14932
\(227\) 2.64486e10 0.661129 0.330565 0.943783i \(-0.392761\pi\)
0.330565 + 0.943783i \(0.392761\pi\)
\(228\) 9.03702e10 2.21472
\(229\) −1.98494e10 −0.476966 −0.238483 0.971147i \(-0.576650\pi\)
−0.238483 + 0.971147i \(0.576650\pi\)
\(230\) 2.21683e11 5.22345
\(231\) 1.15293e10 0.266410
\(232\) −1.63717e11 −3.71019
\(233\) −2.09016e10 −0.464598 −0.232299 0.972644i \(-0.574625\pi\)
−0.232299 + 0.972644i \(0.574625\pi\)
\(234\) 2.26430e10 0.493700
\(235\) −3.87972e9 −0.0829841
\(236\) −1.00165e11 −2.10190
\(237\) 4.28484e10 0.882200
\(238\) −1.01721e10 −0.205501
\(239\) −3.88402e10 −0.769999 −0.385000 0.922917i \(-0.625798\pi\)
−0.385000 + 0.922917i \(0.625798\pi\)
\(240\) −2.00764e11 −3.90603
\(241\) −1.37408e10 −0.262383 −0.131192 0.991357i \(-0.541880\pi\)
−0.131192 + 0.991357i \(0.541880\pi\)
\(242\) 4.32596e10 0.810799
\(243\) 3.94116e10 0.725096
\(244\) 2.30443e10 0.416207
\(245\) 8.02022e10 1.42213
\(246\) −2.18504e9 −0.0380410
\(247\) 4.47785e10 0.765478
\(248\) 1.84244e11 3.09286
\(249\) −3.81200e10 −0.628428
\(250\) 2.47400e11 4.00562
\(251\) −7.04853e10 −1.12090 −0.560450 0.828188i \(-0.689372\pi\)
−0.560450 + 0.828188i \(0.689372\pi\)
\(252\) −2.82140e10 −0.440719
\(253\) 7.65423e10 1.17452
\(254\) 1.52381e10 0.229710
\(255\) −2.28990e10 −0.339146
\(256\) −1.44835e10 −0.210762
\(257\) 6.32271e10 0.904075 0.452038 0.891999i \(-0.350697\pi\)
0.452038 + 0.891999i \(0.350697\pi\)
\(258\) −1.63088e10 −0.229156
\(259\) 9.99216e9 0.137978
\(260\) −2.24508e11 −3.04686
\(261\) −3.81399e10 −0.508742
\(262\) −9.22934e9 −0.121008
\(263\) −7.65063e9 −0.0986044 −0.0493022 0.998784i \(-0.515700\pi\)
−0.0493022 + 0.998784i \(0.515700\pi\)
\(264\) −1.31627e11 −1.66774
\(265\) −2.59588e11 −3.23354
\(266\) −7.80177e10 −0.955489
\(267\) −5.43684e9 −0.0654705
\(268\) 1.06306e11 1.25878
\(269\) 5.99383e10 0.697942 0.348971 0.937134i \(-0.386531\pi\)
0.348971 + 0.937134i \(0.386531\pi\)
\(270\) −3.17608e11 −3.63709
\(271\) −4.61140e10 −0.519363 −0.259681 0.965694i \(-0.583618\pi\)
−0.259681 + 0.965694i \(0.583618\pi\)
\(272\) 6.11591e10 0.677487
\(273\) 2.20359e10 0.240104
\(274\) −1.61647e11 −1.73257
\(275\) 1.56854e11 1.65386
\(276\) 2.95246e11 3.06262
\(277\) 3.74719e9 0.0382426 0.0191213 0.999817i \(-0.493913\pi\)
0.0191213 + 0.999817i \(0.493913\pi\)
\(278\) −4.47934e10 −0.449792
\(279\) 4.29220e10 0.424093
\(280\) 2.35370e11 2.28845
\(281\) −1.09177e10 −0.104461 −0.0522305 0.998635i \(-0.516633\pi\)
−0.0522305 + 0.998635i \(0.516633\pi\)
\(282\) −7.22511e9 −0.0680336
\(283\) 2.09684e10 0.194324 0.0971620 0.995269i \(-0.469024\pi\)
0.0971620 + 0.995269i \(0.469024\pi\)
\(284\) −1.33079e11 −1.21389
\(285\) −1.75630e11 −1.57688
\(286\) −1.08391e11 −0.957960
\(287\) 1.34907e9 0.0117372
\(288\) 1.08907e11 0.932800
\(289\) 6.97576e9 0.0588235
\(290\) 5.28775e11 4.39016
\(291\) 7.13165e10 0.583004
\(292\) 1.84279e10 0.148338
\(293\) −2.40168e11 −1.90375 −0.951875 0.306485i \(-0.900847\pi\)
−0.951875 + 0.306485i \(0.900847\pi\)
\(294\) 1.49359e11 1.16592
\(295\) 1.94666e11 1.49655
\(296\) −1.14078e11 −0.863750
\(297\) −1.09663e11 −0.817817
\(298\) −4.71589e11 −3.46410
\(299\) 1.46294e11 1.05854
\(300\) 6.05032e11 4.31253
\(301\) 1.00692e10 0.0707042
\(302\) 1.92648e10 0.133270
\(303\) −5.94426e10 −0.405141
\(304\) 4.69076e11 3.15001
\(305\) −4.47855e10 −0.296339
\(306\) 2.70545e10 0.176398
\(307\) −2.30483e11 −1.48087 −0.740435 0.672128i \(-0.765380\pi\)
−0.740435 + 0.672128i \(0.765380\pi\)
\(308\) 1.35059e11 0.855158
\(309\) 1.52028e11 0.948658
\(310\) −5.95074e11 −3.65968
\(311\) 1.47492e11 0.894016 0.447008 0.894530i \(-0.352490\pi\)
0.447008 + 0.894530i \(0.352490\pi\)
\(312\) −2.51578e11 −1.50306
\(313\) 1.79761e11 1.05863 0.529317 0.848424i \(-0.322448\pi\)
0.529317 + 0.848424i \(0.322448\pi\)
\(314\) −5.00617e11 −2.90618
\(315\) 5.48326e10 0.313792
\(316\) 5.01943e11 2.83180
\(317\) 4.91432e10 0.273336 0.136668 0.990617i \(-0.456361\pi\)
0.136668 + 0.990617i \(0.456361\pi\)
\(318\) −4.83425e11 −2.65099
\(319\) 1.82574e11 0.987146
\(320\) −5.73209e11 −3.05589
\(321\) 3.85588e10 0.202698
\(322\) −2.54889e11 −1.32130
\(323\) 5.35025e10 0.273503
\(324\) −2.29681e11 −1.15790
\(325\) 2.99793e11 1.49055
\(326\) −3.84049e10 −0.188325
\(327\) −9.68183e10 −0.468266
\(328\) −1.54019e10 −0.0734756
\(329\) 4.46086e9 0.0209912
\(330\) 4.25133e11 1.97339
\(331\) 2.45275e11 1.12312 0.561562 0.827434i \(-0.310200\pi\)
0.561562 + 0.827434i \(0.310200\pi\)
\(332\) −4.46553e11 −2.01721
\(333\) −2.65759e10 −0.118437
\(334\) −4.60922e11 −2.02660
\(335\) −2.06600e11 −0.896251
\(336\) 2.30837e11 0.988049
\(337\) 6.51138e10 0.275004 0.137502 0.990502i \(-0.456093\pi\)
0.137502 + 0.990502i \(0.456093\pi\)
\(338\) 2.42435e11 1.01035
\(339\) 2.18180e11 0.897254
\(340\) −2.68248e11 −1.08863
\(341\) −2.05466e11 −0.822896
\(342\) 2.07502e11 0.820170
\(343\) −2.08136e11 −0.811938
\(344\) −1.14957e11 −0.442612
\(345\) −5.73797e11 −2.18058
\(346\) 8.94219e11 3.35430
\(347\) −7.31021e10 −0.270675 −0.135337 0.990800i \(-0.543212\pi\)
−0.135337 + 0.990800i \(0.543212\pi\)
\(348\) 7.04242e11 2.57404
\(349\) 1.43103e11 0.516337 0.258169 0.966100i \(-0.416881\pi\)
0.258169 + 0.966100i \(0.416881\pi\)
\(350\) −5.22331e11 −1.86054
\(351\) −2.09598e11 −0.737062
\(352\) −5.21332e11 −1.80998
\(353\) 3.76830e11 1.29169 0.645846 0.763467i \(-0.276505\pi\)
0.645846 + 0.763467i \(0.276505\pi\)
\(354\) 3.62521e11 1.22693
\(355\) 2.58634e11 0.864286
\(356\) −6.36892e10 −0.210156
\(357\) 2.63291e10 0.0857884
\(358\) 9.05745e11 2.91429
\(359\) −3.51198e11 −1.11590 −0.557952 0.829873i \(-0.688413\pi\)
−0.557952 + 0.829873i \(0.688413\pi\)
\(360\) −6.26009e11 −1.96435
\(361\) 8.76640e10 0.271668
\(362\) 5.24003e11 1.60378
\(363\) −1.11971e11 −0.338476
\(364\) 2.58137e11 0.770716
\(365\) −3.58137e10 −0.105616
\(366\) −8.34031e10 −0.242950
\(367\) −4.78044e11 −1.37553 −0.687766 0.725933i \(-0.741408\pi\)
−0.687766 + 0.725933i \(0.741408\pi\)
\(368\) 1.53251e12 4.35599
\(369\) −3.58808e9 −0.0100750
\(370\) 3.68451e11 1.02205
\(371\) 2.98472e11 0.817939
\(372\) −7.92542e11 −2.14575
\(373\) 6.76181e11 1.80873 0.904364 0.426762i \(-0.140346\pi\)
0.904364 + 0.426762i \(0.140346\pi\)
\(374\) −1.29509e11 −0.342276
\(375\) −6.40361e11 −1.67218
\(376\) −5.09284e10 −0.131406
\(377\) 3.48952e11 0.889672
\(378\) 3.65183e11 0.920019
\(379\) −5.13122e11 −1.27745 −0.638725 0.769435i \(-0.720538\pi\)
−0.638725 + 0.769435i \(0.720538\pi\)
\(380\) −2.05740e12 −5.06166
\(381\) −3.94418e10 −0.0958946
\(382\) −8.58633e11 −2.06311
\(383\) −7.63819e11 −1.81383 −0.906914 0.421316i \(-0.861568\pi\)
−0.906914 + 0.421316i \(0.861568\pi\)
\(384\) −2.66566e11 −0.625624
\(385\) −2.62481e11 −0.608871
\(386\) 1.16641e12 2.67429
\(387\) −2.67808e10 −0.0606910
\(388\) 8.35429e11 1.87140
\(389\) 3.33397e11 0.738224 0.369112 0.929385i \(-0.379662\pi\)
0.369112 + 0.929385i \(0.379662\pi\)
\(390\) 8.12551e11 1.77853
\(391\) 1.74796e11 0.378214
\(392\) 1.05280e12 2.25195
\(393\) 2.38889e10 0.0505160
\(394\) −6.73235e11 −1.40745
\(395\) −9.75503e11 −2.01624
\(396\) −3.59214e11 −0.734049
\(397\) −6.95415e11 −1.40503 −0.702517 0.711667i \(-0.747941\pi\)
−0.702517 + 0.711667i \(0.747941\pi\)
\(398\) −1.48724e12 −2.97103
\(399\) 2.01938e11 0.398878
\(400\) 3.14048e12 6.13375
\(401\) 5.82880e11 1.12572 0.562859 0.826553i \(-0.309701\pi\)
0.562859 + 0.826553i \(0.309701\pi\)
\(402\) −3.84747e11 −0.734782
\(403\) −3.92705e11 −0.741640
\(404\) −6.96334e11 −1.30047
\(405\) 4.46374e11 0.824425
\(406\) −6.07980e11 −1.11051
\(407\) 1.27218e11 0.229812
\(408\) −3.00592e11 −0.537040
\(409\) 2.34282e11 0.413985 0.206993 0.978343i \(-0.433632\pi\)
0.206993 + 0.978343i \(0.433632\pi\)
\(410\) 4.97455e10 0.0869413
\(411\) 4.18402e11 0.723278
\(412\) 1.78091e12 3.04512
\(413\) −2.23825e11 −0.378558
\(414\) 6.77923e11 1.13417
\(415\) 8.67854e11 1.43625
\(416\) −9.96417e11 −1.63125
\(417\) 1.15941e11 0.187770
\(418\) −9.93302e11 −1.59143
\(419\) −6.51621e11 −1.03284 −0.516419 0.856336i \(-0.672735\pi\)
−0.516419 + 0.856336i \(0.672735\pi\)
\(420\) −1.01247e12 −1.58767
\(421\) −5.97500e11 −0.926976 −0.463488 0.886103i \(-0.653402\pi\)
−0.463488 + 0.886103i \(0.653402\pi\)
\(422\) 9.42739e11 1.44706
\(423\) −1.18644e10 −0.0180184
\(424\) −3.40757e12 −5.12034
\(425\) 3.58201e11 0.532570
\(426\) 4.81648e11 0.708576
\(427\) 5.14939e10 0.0749602
\(428\) 4.51692e11 0.650648
\(429\) 2.80556e11 0.399909
\(430\) 3.71291e11 0.523729
\(431\) −1.45053e11 −0.202478 −0.101239 0.994862i \(-0.532281\pi\)
−0.101239 + 0.994862i \(0.532281\pi\)
\(432\) −2.19564e12 −3.03308
\(433\) −2.07018e11 −0.283017 −0.141509 0.989937i \(-0.545195\pi\)
−0.141509 + 0.989937i \(0.545195\pi\)
\(434\) 6.84211e11 0.925734
\(435\) −1.36866e12 −1.83271
\(436\) −1.13417e12 −1.50310
\(437\) 1.34065e12 1.75853
\(438\) −6.66951e10 −0.0865885
\(439\) 1.27742e12 1.64151 0.820757 0.571278i \(-0.193552\pi\)
0.820757 + 0.571278i \(0.193552\pi\)
\(440\) 2.99668e12 3.81156
\(441\) 2.45264e11 0.308788
\(442\) −2.47529e11 −0.308479
\(443\) 2.56214e10 0.0316072 0.0158036 0.999875i \(-0.494969\pi\)
0.0158036 + 0.999875i \(0.494969\pi\)
\(444\) 4.90716e11 0.599248
\(445\) 1.23777e11 0.149630
\(446\) −1.82192e11 −0.218033
\(447\) 1.22064e12 1.44612
\(448\) 6.59070e11 0.773002
\(449\) −6.93244e11 −0.804967 −0.402483 0.915427i \(-0.631853\pi\)
−0.402483 + 0.915427i \(0.631853\pi\)
\(450\) 1.38923e12 1.59705
\(451\) 1.71760e10 0.0195491
\(452\) 2.55584e12 2.88012
\(453\) −4.98642e10 −0.0556348
\(454\) −1.12135e12 −1.23877
\(455\) −5.01678e11 −0.548749
\(456\) −2.30547e12 −2.49700
\(457\) −1.01211e12 −1.08544 −0.542721 0.839913i \(-0.682606\pi\)
−0.542721 + 0.839913i \(0.682606\pi\)
\(458\) 8.41560e11 0.893698
\(459\) −2.50433e11 −0.263350
\(460\) −6.72168e12 −6.99951
\(461\) 4.59728e11 0.474075 0.237037 0.971501i \(-0.423824\pi\)
0.237037 + 0.971501i \(0.423824\pi\)
\(462\) −4.88814e11 −0.499177
\(463\) −7.53078e11 −0.761598 −0.380799 0.924658i \(-0.624351\pi\)
−0.380799 + 0.924658i \(0.624351\pi\)
\(464\) 3.65544e12 3.66108
\(465\) 1.54027e12 1.52777
\(466\) 8.86170e11 0.870523
\(467\) −1.22063e12 −1.18757 −0.593783 0.804625i \(-0.702366\pi\)
−0.593783 + 0.804625i \(0.702366\pi\)
\(468\) −6.86562e11 −0.661566
\(469\) 2.37547e11 0.226711
\(470\) 1.64490e11 0.155488
\(471\) 1.29578e12 1.21321
\(472\) 2.55534e12 2.36979
\(473\) 1.28199e11 0.117763
\(474\) −1.81666e12 −1.65299
\(475\) 2.74732e12 2.47621
\(476\) 3.08429e11 0.275375
\(477\) −7.93839e11 −0.702101
\(478\) 1.64672e12 1.44276
\(479\) 1.22689e12 1.06487 0.532436 0.846470i \(-0.321277\pi\)
0.532436 + 0.846470i \(0.321277\pi\)
\(480\) 3.90815e12 3.36036
\(481\) 2.43150e11 0.207120
\(482\) 5.82574e11 0.491631
\(483\) 6.59746e11 0.551588
\(484\) −1.31168e12 −1.08648
\(485\) −1.62362e12 −1.33243
\(486\) −1.67095e12 −1.35862
\(487\) 1.96428e12 1.58242 0.791211 0.611543i \(-0.209451\pi\)
0.791211 + 0.611543i \(0.209451\pi\)
\(488\) −5.87892e11 −0.469255
\(489\) 9.94058e10 0.0786180
\(490\) −3.40036e12 −2.66466
\(491\) −2.27273e12 −1.76474 −0.882371 0.470554i \(-0.844054\pi\)
−0.882371 + 0.470554i \(0.844054\pi\)
\(492\) 6.62529e10 0.0509755
\(493\) 4.16937e11 0.317877
\(494\) −1.89849e12 −1.43429
\(495\) 6.98116e11 0.522642
\(496\) −4.11377e12 −3.05192
\(497\) −2.97374e11 −0.218625
\(498\) 1.61619e12 1.17750
\(499\) 2.31148e12 1.66893 0.834464 0.551063i \(-0.185778\pi\)
0.834464 + 0.551063i \(0.185778\pi\)
\(500\) −7.50144e12 −5.36759
\(501\) 1.19303e12 0.846024
\(502\) 2.98839e12 2.10025
\(503\) −2.10646e12 −1.46723 −0.733615 0.679565i \(-0.762168\pi\)
−0.733615 + 0.679565i \(0.762168\pi\)
\(504\) 7.19779e11 0.496891
\(505\) 1.35329e12 0.925935
\(506\) −3.24519e12 −2.20071
\(507\) −6.27511e11 −0.421780
\(508\) −4.62037e11 −0.307815
\(509\) −1.57634e12 −1.04093 −0.520464 0.853884i \(-0.674241\pi\)
−0.520464 + 0.853884i \(0.674241\pi\)
\(510\) 9.70858e11 0.635462
\(511\) 4.11782e10 0.0267161
\(512\) 1.85774e12 1.19473
\(513\) −1.92076e12 −1.22446
\(514\) −2.68066e12 −1.69398
\(515\) −3.46112e12 −2.16812
\(516\) 4.94499e11 0.307073
\(517\) 5.67946e10 0.0349623
\(518\) −4.23641e11 −0.258532
\(519\) −2.31456e12 −1.40028
\(520\) 5.72752e12 3.43520
\(521\) −3.90823e11 −0.232386 −0.116193 0.993227i \(-0.537069\pi\)
−0.116193 + 0.993227i \(0.537069\pi\)
\(522\) 1.61703e12 0.953237
\(523\) −2.52838e12 −1.47770 −0.738849 0.673871i \(-0.764630\pi\)
−0.738849 + 0.673871i \(0.764630\pi\)
\(524\) 2.79844e11 0.162153
\(525\) 1.35198e12 0.776701
\(526\) 3.24366e11 0.184757
\(527\) −4.69214e11 −0.264986
\(528\) 2.93896e12 1.64566
\(529\) 2.57884e12 1.43177
\(530\) 1.10058e13 6.05874
\(531\) 5.95301e11 0.324946
\(532\) 2.36558e12 1.28037
\(533\) 3.28283e10 0.0176188
\(534\) 2.30507e11 0.122673
\(535\) −8.77843e11 −0.463260
\(536\) −2.71201e12 −1.41922
\(537\) −2.34440e12 −1.21660
\(538\) −2.54123e12 −1.30774
\(539\) −1.17407e12 −0.599161
\(540\) 9.63022e12 4.87376
\(541\) 1.45109e12 0.728296 0.364148 0.931341i \(-0.381360\pi\)
0.364148 + 0.931341i \(0.381360\pi\)
\(542\) 1.95511e12 0.973138
\(543\) −1.35631e12 −0.669515
\(544\) −1.19054e12 −0.582842
\(545\) 2.20420e12 1.07021
\(546\) −9.34264e11 −0.449886
\(547\) −2.60966e10 −0.0124635 −0.00623177 0.999981i \(-0.501984\pi\)
−0.00623177 + 0.999981i \(0.501984\pi\)
\(548\) 4.90133e12 2.32167
\(549\) −1.36957e11 −0.0643442
\(550\) −6.65019e12 −3.09886
\(551\) 3.19781e12 1.47799
\(552\) −7.53214e12 −3.45297
\(553\) 1.12162e12 0.510016
\(554\) −1.58871e11 −0.0716557
\(555\) −9.53684e11 −0.426664
\(556\) 1.35818e12 0.602729
\(557\) −2.42622e12 −1.06803 −0.534013 0.845477i \(-0.679317\pi\)
−0.534013 + 0.845477i \(0.679317\pi\)
\(558\) −1.81978e12 −0.794629
\(559\) 2.45025e11 0.106134
\(560\) −5.25532e12 −2.25815
\(561\) 3.35216e11 0.142887
\(562\) 4.62883e11 0.195730
\(563\) −3.14392e12 −1.31881 −0.659406 0.751787i \(-0.729192\pi\)
−0.659406 + 0.751787i \(0.729192\pi\)
\(564\) 2.19073e11 0.0911662
\(565\) −4.96716e12 −2.05064
\(566\) −8.89004e11 −0.364108
\(567\) −5.13236e11 −0.208542
\(568\) 3.39504e12 1.36860
\(569\) −4.68855e12 −1.87514 −0.937570 0.347798i \(-0.886930\pi\)
−0.937570 + 0.347798i \(0.886930\pi\)
\(570\) 7.44626e12 2.95462
\(571\) 2.51532e12 0.990216 0.495108 0.868831i \(-0.335128\pi\)
0.495108 + 0.868831i \(0.335128\pi\)
\(572\) 3.28654e12 1.28368
\(573\) 2.22245e12 0.861265
\(574\) −5.71969e10 −0.0219922
\(575\) 8.97569e12 3.42423
\(576\) −1.75291e12 −0.663528
\(577\) 1.66387e12 0.624924 0.312462 0.949930i \(-0.398846\pi\)
0.312462 + 0.949930i \(0.398846\pi\)
\(578\) −2.95754e11 −0.110219
\(579\) −3.01909e12 −1.11641
\(580\) −1.60330e13 −5.88288
\(581\) −9.97850e11 −0.363306
\(582\) −3.02363e12 −1.09238
\(583\) 3.80007e12 1.36233
\(584\) −4.70121e11 −0.167244
\(585\) 1.33430e12 0.471034
\(586\) 1.01825e13 3.56709
\(587\) 1.10214e12 0.383147 0.191573 0.981478i \(-0.438641\pi\)
0.191573 + 0.981478i \(0.438641\pi\)
\(588\) −4.52872e12 −1.56235
\(589\) −3.59876e12 −1.23207
\(590\) −8.25330e12 −2.80410
\(591\) 1.74258e12 0.587555
\(592\) 2.54711e12 0.852316
\(593\) −1.47081e12 −0.488438 −0.244219 0.969720i \(-0.578532\pi\)
−0.244219 + 0.969720i \(0.578532\pi\)
\(594\) 4.64942e12 1.53236
\(595\) −5.99418e11 −0.196066
\(596\) 1.42991e13 4.64195
\(597\) 3.84951e12 1.24028
\(598\) −6.20250e12 −1.98340
\(599\) 3.93181e12 1.24788 0.623938 0.781473i \(-0.285532\pi\)
0.623938 + 0.781473i \(0.285532\pi\)
\(600\) −1.54352e13 −4.86219
\(601\) 8.77198e11 0.274260 0.137130 0.990553i \(-0.456212\pi\)
0.137130 + 0.990553i \(0.456212\pi\)
\(602\) −4.26907e11 −0.132480
\(603\) −6.31798e11 −0.194603
\(604\) −5.84129e11 −0.178584
\(605\) 2.54919e12 0.773575
\(606\) 2.52021e12 0.759119
\(607\) −1.09458e12 −0.327265 −0.163632 0.986521i \(-0.552321\pi\)
−0.163632 + 0.986521i \(0.552321\pi\)
\(608\) −9.13121e12 −2.70995
\(609\) 1.57367e12 0.463593
\(610\) 1.89879e12 0.555254
\(611\) 1.08551e11 0.0315100
\(612\) −8.20322e11 −0.236376
\(613\) −4.47212e12 −1.27921 −0.639605 0.768704i \(-0.720902\pi\)
−0.639605 + 0.768704i \(0.720902\pi\)
\(614\) 9.77188e12 2.77473
\(615\) −1.28759e11 −0.0362945
\(616\) −3.44555e12 −0.964152
\(617\) −2.92442e12 −0.812376 −0.406188 0.913790i \(-0.633142\pi\)
−0.406188 + 0.913790i \(0.633142\pi\)
\(618\) −6.44557e12 −1.77751
\(619\) 1.52167e12 0.416593 0.208296 0.978066i \(-0.433208\pi\)
0.208296 + 0.978066i \(0.433208\pi\)
\(620\) 1.80433e13 4.90404
\(621\) −6.27527e12 −1.69325
\(622\) −6.25325e12 −1.67513
\(623\) −1.42318e11 −0.0378497
\(624\) 5.61720e12 1.48316
\(625\) 6.20223e12 1.62588
\(626\) −7.62139e12 −1.98358
\(627\) 2.57103e12 0.664359
\(628\) 1.51793e13 3.89433
\(629\) 2.90522e11 0.0740033
\(630\) −2.32476e12 −0.587956
\(631\) −6.61053e12 −1.65998 −0.829992 0.557775i \(-0.811655\pi\)
−0.829992 + 0.557775i \(0.811655\pi\)
\(632\) −1.28053e13 −3.19273
\(633\) −2.44015e12 −0.604088
\(634\) −2.08354e12 −0.512154
\(635\) 8.97946e11 0.219164
\(636\) 1.46580e13 3.55236
\(637\) −2.24398e12 −0.539998
\(638\) −7.74066e12 −1.84963
\(639\) 7.90919e11 0.187663
\(640\) 6.06873e12 1.42984
\(641\) 3.36551e12 0.787389 0.393694 0.919241i \(-0.371197\pi\)
0.393694 + 0.919241i \(0.371197\pi\)
\(642\) −1.63479e12 −0.379799
\(643\) −1.05715e12 −0.243887 −0.121943 0.992537i \(-0.538913\pi\)
−0.121943 + 0.992537i \(0.538913\pi\)
\(644\) 7.72852e12 1.77056
\(645\) −9.61036e11 −0.218636
\(646\) −2.26836e12 −0.512467
\(647\) 3.32786e12 0.746613 0.373307 0.927708i \(-0.378224\pi\)
0.373307 + 0.927708i \(0.378224\pi\)
\(648\) 5.85948e12 1.30548
\(649\) −2.84968e12 −0.630515
\(650\) −1.27104e13 −2.79287
\(651\) −1.77099e12 −0.386456
\(652\) 1.16448e12 0.252358
\(653\) −6.30246e12 −1.35644 −0.678220 0.734859i \(-0.737249\pi\)
−0.678220 + 0.734859i \(0.737249\pi\)
\(654\) 4.10484e12 0.877397
\(655\) −5.43863e11 −0.115453
\(656\) 3.43893e11 0.0725029
\(657\) −1.09521e11 −0.0229325
\(658\) −1.89129e11 −0.0393315
\(659\) 2.83854e12 0.586287 0.293143 0.956069i \(-0.405299\pi\)
0.293143 + 0.956069i \(0.405299\pi\)
\(660\) −1.28905e13 −2.64437
\(661\) 6.58551e12 1.34178 0.670892 0.741555i \(-0.265911\pi\)
0.670892 + 0.741555i \(0.265911\pi\)
\(662\) −1.03990e13 −2.10442
\(663\) 6.40694e11 0.128777
\(664\) 1.13922e13 2.27432
\(665\) −4.59740e12 −0.911621
\(666\) 1.12675e12 0.221918
\(667\) 1.04475e13 2.04383
\(668\) 1.39757e13 2.71568
\(669\) 4.71579e11 0.0910201
\(670\) 8.75931e12 1.67932
\(671\) 6.55609e11 0.124851
\(672\) −4.49355e12 −0.850018
\(673\) −2.50086e12 −0.469918 −0.234959 0.972005i \(-0.575496\pi\)
−0.234959 + 0.972005i \(0.575496\pi\)
\(674\) −2.76065e12 −0.515279
\(675\) −1.28596e13 −2.38429
\(676\) −7.35091e12 −1.35388
\(677\) 1.03159e13 1.88737 0.943687 0.330839i \(-0.107332\pi\)
0.943687 + 0.330839i \(0.107332\pi\)
\(678\) −9.25023e12 −1.68120
\(679\) 1.86682e12 0.337045
\(680\) 6.84339e12 1.22739
\(681\) 2.90246e12 0.517136
\(682\) 8.71121e12 1.54187
\(683\) 9.27753e12 1.63132 0.815660 0.578531i \(-0.196374\pi\)
0.815660 + 0.578531i \(0.196374\pi\)
\(684\) −6.29168e12 −1.09904
\(685\) −9.52550e12 −1.65303
\(686\) 8.82440e12 1.52134
\(687\) −2.17826e12 −0.373083
\(688\) 2.56675e12 0.436753
\(689\) 7.26304e12 1.22781
\(690\) 2.43275e13 4.08579
\(691\) 1.58767e12 0.264917 0.132458 0.991189i \(-0.457713\pi\)
0.132458 + 0.991189i \(0.457713\pi\)
\(692\) −2.71137e13 −4.49481
\(693\) −8.02686e11 −0.132205
\(694\) 3.09934e12 0.507167
\(695\) −2.63957e12 −0.429142
\(696\) −1.79662e13 −2.90212
\(697\) 3.92241e10 0.00629514
\(698\) −6.06717e12 −0.967469
\(699\) −2.29373e12 −0.363408
\(700\) 1.58376e13 2.49316
\(701\) −1.15310e13 −1.80358 −0.901791 0.432172i \(-0.857747\pi\)
−0.901791 + 0.432172i \(0.857747\pi\)
\(702\) 8.88638e12 1.38105
\(703\) 2.22824e12 0.344082
\(704\) 8.39113e12 1.28749
\(705\) −4.25759e11 −0.0649102
\(706\) −1.59766e13 −2.42026
\(707\) −1.55600e12 −0.234220
\(708\) −1.09921e13 −1.64410
\(709\) −1.03429e12 −0.153722 −0.0768609 0.997042i \(-0.524490\pi\)
−0.0768609 + 0.997042i \(0.524490\pi\)
\(710\) −1.09654e13 −1.61943
\(711\) −2.98315e12 −0.437787
\(712\) 1.62480e12 0.236941
\(713\) −1.17574e13 −1.70376
\(714\) −1.11628e12 −0.160743
\(715\) −6.38724e12 −0.913979
\(716\) −2.74632e13 −3.90519
\(717\) −4.26231e12 −0.602294
\(718\) 1.48899e13 2.09089
\(719\) 8.27525e12 1.15478 0.577392 0.816467i \(-0.304070\pi\)
0.577392 + 0.816467i \(0.304070\pi\)
\(720\) 1.39774e13 1.93835
\(721\) 3.97956e12 0.548437
\(722\) −3.71672e12 −0.509029
\(723\) −1.50791e12 −0.205236
\(724\) −1.58884e13 −2.14909
\(725\) 2.14095e13 2.87796
\(726\) 4.74729e12 0.634207
\(727\) 5.25612e12 0.697848 0.348924 0.937151i \(-0.386547\pi\)
0.348924 + 0.937151i \(0.386547\pi\)
\(728\) −6.58544e12 −0.868948
\(729\) 7.84169e12 1.02834
\(730\) 1.51841e12 0.197895
\(731\) 2.92762e11 0.0379215
\(732\) 2.52887e12 0.325557
\(733\) 7.86667e12 1.00652 0.503261 0.864134i \(-0.332133\pi\)
0.503261 + 0.864134i \(0.332133\pi\)
\(734\) 2.02678e13 2.57735
\(735\) 8.80136e12 1.11239
\(736\) −2.98323e13 −3.74746
\(737\) 3.02439e12 0.377602
\(738\) 1.52125e11 0.0188776
\(739\) −8.65193e12 −1.06712 −0.533560 0.845762i \(-0.679146\pi\)
−0.533560 + 0.845762i \(0.679146\pi\)
\(740\) −1.11718e13 −1.36956
\(741\) 4.91397e12 0.598757
\(742\) −1.26544e13 −1.53258
\(743\) 9.67486e12 1.16465 0.582325 0.812956i \(-0.302143\pi\)
0.582325 + 0.812956i \(0.302143\pi\)
\(744\) 2.02189e13 2.41924
\(745\) −2.77896e13 −3.30506
\(746\) −2.86683e13 −3.38904
\(747\) 2.65396e12 0.311854
\(748\) 3.92685e12 0.458656
\(749\) 1.00934e12 0.117184
\(750\) 2.71496e13 3.13320
\(751\) 5.48720e12 0.629464 0.314732 0.949181i \(-0.398085\pi\)
0.314732 + 0.949181i \(0.398085\pi\)
\(752\) 1.13712e12 0.129666
\(753\) −7.73503e12 −0.876768
\(754\) −1.47946e13 −1.66699
\(755\) 1.13523e12 0.127151
\(756\) −1.10727e13 −1.23284
\(757\) 1.33117e13 1.47333 0.736667 0.676255i \(-0.236398\pi\)
0.736667 + 0.676255i \(0.236398\pi\)
\(758\) 2.17550e13 2.39358
\(759\) 8.39973e12 0.918708
\(760\) 5.24872e13 5.70680
\(761\) 9.94914e12 1.07536 0.537681 0.843148i \(-0.319301\pi\)
0.537681 + 0.843148i \(0.319301\pi\)
\(762\) 1.67223e12 0.179679
\(763\) −2.53437e12 −0.270713
\(764\) 2.60347e13 2.76460
\(765\) 1.59426e12 0.168299
\(766\) 3.23839e13 3.39860
\(767\) −5.44656e12 −0.568255
\(768\) −1.58941e12 −0.164858
\(769\) 5.14283e12 0.530315 0.265157 0.964205i \(-0.414576\pi\)
0.265157 + 0.964205i \(0.414576\pi\)
\(770\) 1.11285e13 1.14085
\(771\) 6.93853e12 0.707168
\(772\) −3.53668e13 −3.58359
\(773\) −3.51233e12 −0.353824 −0.176912 0.984227i \(-0.556611\pi\)
−0.176912 + 0.984227i \(0.556611\pi\)
\(774\) 1.13543e12 0.113718
\(775\) −2.40938e13 −2.39910
\(776\) −2.13130e13 −2.10992
\(777\) 1.09654e12 0.107927
\(778\) −1.41351e13 −1.38322
\(779\) 3.00840e11 0.0292696
\(780\) −2.46375e13 −2.38325
\(781\) −3.78610e12 −0.364135
\(782\) −7.41090e12 −0.708665
\(783\) −1.49682e13 −1.42312
\(784\) −2.35068e13 −2.22214
\(785\) −2.95002e13 −2.77275
\(786\) −1.01282e12 −0.0946527
\(787\) 6.67867e12 0.620589 0.310294 0.950641i \(-0.399572\pi\)
0.310294 + 0.950641i \(0.399572\pi\)
\(788\) 2.04132e13 1.88601
\(789\) −8.39577e11 −0.0771284
\(790\) 4.13587e13 3.77785
\(791\) 5.71119e12 0.518719
\(792\) 9.16405e12 0.827607
\(793\) 1.25306e12 0.112523
\(794\) 2.94838e13 2.63263
\(795\) −2.84871e13 −2.52928
\(796\) 4.50947e13 3.98122
\(797\) −4.54726e12 −0.399197 −0.199599 0.979878i \(-0.563964\pi\)
−0.199599 + 0.979878i \(0.563964\pi\)
\(798\) −8.56163e12 −0.747384
\(799\) 1.29699e11 0.0112584
\(800\) −6.11337e13 −5.27687
\(801\) 3.78519e11 0.0324894
\(802\) −2.47126e13 −2.10927
\(803\) 5.24272e11 0.0444976
\(804\) 1.16660e13 0.984620
\(805\) −1.50200e13 −1.26063
\(806\) 1.66496e13 1.38962
\(807\) 6.57761e12 0.545931
\(808\) 1.77645e13 1.46623
\(809\) 6.56062e12 0.538488 0.269244 0.963072i \(-0.413226\pi\)
0.269244 + 0.963072i \(0.413226\pi\)
\(810\) −1.89251e13 −1.54474
\(811\) 1.03164e13 0.837403 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(812\) 1.84346e13 1.48810
\(813\) −5.06053e12 −0.406246
\(814\) −5.39370e12 −0.430603
\(815\) −2.26311e12 −0.179679
\(816\) 6.71158e12 0.529931
\(817\) 2.24542e12 0.176318
\(818\) −9.93295e12 −0.775690
\(819\) −1.53417e12 −0.119150
\(820\) −1.50834e12 −0.116503
\(821\) −2.30549e13 −1.77100 −0.885500 0.464639i \(-0.846184\pi\)
−0.885500 + 0.464639i \(0.846184\pi\)
\(822\) −1.77391e13 −1.35522
\(823\) −1.48191e12 −0.112596 −0.0562979 0.998414i \(-0.517930\pi\)
−0.0562979 + 0.998414i \(0.517930\pi\)
\(824\) −4.54336e13 −3.43324
\(825\) 1.72131e13 1.29365
\(826\) 9.48956e12 0.709310
\(827\) 1.73025e13 1.28627 0.643137 0.765751i \(-0.277632\pi\)
0.643137 + 0.765751i \(0.277632\pi\)
\(828\) −2.05554e13 −1.51981
\(829\) −2.31346e13 −1.70124 −0.850622 0.525778i \(-0.823774\pi\)
−0.850622 + 0.525778i \(0.823774\pi\)
\(830\) −3.67947e13 −2.69113
\(831\) 4.11216e11 0.0299134
\(832\) 1.60379e13 1.16036
\(833\) −2.68117e12 −0.192940
\(834\) −4.91561e12 −0.351828
\(835\) −2.71610e13 −1.93356
\(836\) 3.01180e13 2.13255
\(837\) 1.68450e13 1.18633
\(838\) 2.76270e13 1.93524
\(839\) 4.17604e12 0.290962 0.145481 0.989361i \(-0.453527\pi\)
0.145481 + 0.989361i \(0.453527\pi\)
\(840\) 2.58295e13 1.79002
\(841\) 1.04129e13 0.717780
\(842\) 2.53324e13 1.73689
\(843\) −1.19811e12 −0.0817095
\(844\) −2.85849e13 −1.93908
\(845\) 1.42862e13 0.963962
\(846\) 5.03021e11 0.0337613
\(847\) −2.93103e12 −0.195679
\(848\) 7.60839e13 5.05256
\(849\) 2.30107e12 0.152000
\(850\) −1.51868e13 −0.997884
\(851\) 7.27981e12 0.475814
\(852\) −1.46041e13 −0.949503
\(853\) 6.57843e12 0.425453 0.212727 0.977112i \(-0.431766\pi\)
0.212727 + 0.977112i \(0.431766\pi\)
\(854\) −2.18321e12 −0.140454
\(855\) 1.22276e13 0.782516
\(856\) −1.15233e13 −0.733576
\(857\) −2.26445e13 −1.43400 −0.716999 0.697074i \(-0.754485\pi\)
−0.716999 + 0.697074i \(0.754485\pi\)
\(858\) −1.18948e13 −0.749316
\(859\) −1.95924e13 −1.22777 −0.613886 0.789395i \(-0.710395\pi\)
−0.613886 + 0.789395i \(0.710395\pi\)
\(860\) −1.12580e13 −0.701805
\(861\) 1.48046e11 0.00918086
\(862\) 6.14986e12 0.379387
\(863\) 8.76018e12 0.537606 0.268803 0.963195i \(-0.413372\pi\)
0.268803 + 0.963195i \(0.413372\pi\)
\(864\) 4.27411e13 2.60936
\(865\) 5.26942e13 3.20030
\(866\) 8.77703e12 0.530294
\(867\) 7.65517e11 0.0460118
\(868\) −2.07460e13 −1.24050
\(869\) 1.42802e13 0.849467
\(870\) 5.80276e13 3.43398
\(871\) 5.78049e12 0.340316
\(872\) 2.89342e13 1.69468
\(873\) −4.96514e12 −0.289312
\(874\) −5.68399e13 −3.29497
\(875\) −1.67624e13 −0.966721
\(876\) 2.02227e12 0.116030
\(877\) 1.76925e13 1.00993 0.504965 0.863140i \(-0.331505\pi\)
0.504965 + 0.863140i \(0.331505\pi\)
\(878\) −5.41593e13 −3.07573
\(879\) −2.63559e13 −1.48911
\(880\) −6.69095e13 −3.76111
\(881\) −1.40172e13 −0.783919 −0.391959 0.919983i \(-0.628203\pi\)
−0.391959 + 0.919983i \(0.628203\pi\)
\(882\) −1.03985e13 −0.578580
\(883\) −7.52196e12 −0.416397 −0.208199 0.978087i \(-0.566760\pi\)
−0.208199 + 0.978087i \(0.566760\pi\)
\(884\) 7.50534e12 0.413366
\(885\) 2.13625e13 1.17060
\(886\) −1.08628e12 −0.0592229
\(887\) −4.64548e12 −0.251985 −0.125992 0.992031i \(-0.540211\pi\)
−0.125992 + 0.992031i \(0.540211\pi\)
\(888\) −1.25189e13 −0.675626
\(889\) −1.03245e12 −0.0554384
\(890\) −5.24782e12 −0.280365
\(891\) −6.53440e12 −0.347341
\(892\) 5.52427e12 0.292168
\(893\) 9.94765e11 0.0523467
\(894\) −5.17520e13 −2.70962
\(895\) 5.33734e13 2.78049
\(896\) −6.97777e12 −0.361685
\(897\) 1.60543e13 0.827991
\(898\) 2.93917e13 1.50828
\(899\) −2.80446e13 −1.43196
\(900\) −4.21230e13 −2.14007
\(901\) 8.67807e12 0.438694
\(902\) −7.28217e11 −0.0366295
\(903\) 1.10499e12 0.0553049
\(904\) −6.52031e13 −3.24721
\(905\) 3.08783e13 1.53015
\(906\) 2.11411e12 0.104244
\(907\) −2.57831e13 −1.26503 −0.632517 0.774546i \(-0.717978\pi\)
−0.632517 + 0.774546i \(0.717978\pi\)
\(908\) 3.40006e13 1.65997
\(909\) 4.13846e12 0.201049
\(910\) 2.12698e13 1.02820
\(911\) 3.74022e13 1.79914 0.899568 0.436781i \(-0.143882\pi\)
0.899568 + 0.436781i \(0.143882\pi\)
\(912\) 5.14763e13 2.46394
\(913\) −1.27044e13 −0.605112
\(914\) 4.29110e13 2.03381
\(915\) −4.91475e12 −0.231796
\(916\) −2.55170e13 −1.19757
\(917\) 6.25329e11 0.0292043
\(918\) 1.06177e13 0.493444
\(919\) 9.74612e12 0.450726 0.225363 0.974275i \(-0.427643\pi\)
0.225363 + 0.974275i \(0.427643\pi\)
\(920\) 1.71480e14 7.89164
\(921\) −2.52932e13 −1.15834
\(922\) −1.94912e13 −0.888281
\(923\) −7.23633e12 −0.328179
\(924\) 1.48214e13 0.668905
\(925\) 1.49181e13 0.670002
\(926\) 3.19285e13 1.42702
\(927\) −1.05843e13 −0.470766
\(928\) −7.11582e13 −3.14963
\(929\) 6.34542e12 0.279505 0.139752 0.990186i \(-0.455369\pi\)
0.139752 + 0.990186i \(0.455369\pi\)
\(930\) −6.53033e13 −2.86261
\(931\) −2.05640e13 −0.897084
\(932\) −2.68697e13 −1.16652
\(933\) 1.61857e13 0.699300
\(934\) 5.17514e13 2.22516
\(935\) −7.63164e12 −0.326562
\(936\) 1.75151e13 0.745886
\(937\) −2.80091e13 −1.18706 −0.593528 0.804813i \(-0.702265\pi\)
−0.593528 + 0.804813i \(0.702265\pi\)
\(938\) −1.00714e13 −0.424791
\(939\) 1.97269e13 0.828064
\(940\) −4.98751e12 −0.208357
\(941\) 2.68353e13 1.11571 0.557857 0.829937i \(-0.311624\pi\)
0.557857 + 0.829937i \(0.311624\pi\)
\(942\) −5.49376e13 −2.27321
\(943\) 9.82866e11 0.0404755
\(944\) −5.70554e13 −2.33842
\(945\) 2.15193e13 0.877781
\(946\) −5.43528e12 −0.220654
\(947\) −1.27250e13 −0.514140 −0.257070 0.966393i \(-0.582757\pi\)
−0.257070 + 0.966393i \(0.582757\pi\)
\(948\) 5.50831e13 2.21503
\(949\) 1.00203e12 0.0401037
\(950\) −1.16479e14 −4.63972
\(951\) 5.39296e12 0.213804
\(952\) −7.86846e12 −0.310473
\(953\) −2.88311e13 −1.13225 −0.566125 0.824319i \(-0.691558\pi\)
−0.566125 + 0.824319i \(0.691558\pi\)
\(954\) 3.36566e13 1.31554
\(955\) −5.05972e13 −1.96839
\(956\) −4.99303e13 −1.93332
\(957\) 2.00356e13 0.772146
\(958\) −5.20170e13 −1.99527
\(959\) 1.09523e13 0.418141
\(960\) −6.29038e13 −2.39032
\(961\) 5.12133e12 0.193699
\(962\) −1.03089e13 −0.388083
\(963\) −2.68451e12 −0.100588
\(964\) −1.76643e13 −0.658794
\(965\) 6.87338e13 2.55151
\(966\) −2.79715e13 −1.03352
\(967\) 3.76299e13 1.38393 0.691964 0.721932i \(-0.256745\pi\)
0.691964 + 0.721932i \(0.256745\pi\)
\(968\) 3.34628e13 1.22496
\(969\) 5.87134e12 0.213934
\(970\) 6.88371e13 2.49660
\(971\) −5.14050e13 −1.85575 −0.927873 0.372895i \(-0.878365\pi\)
−0.927873 + 0.372895i \(0.878365\pi\)
\(972\) 5.06649e13 1.82058
\(973\) 3.03495e12 0.108553
\(974\) −8.32801e13 −2.96501
\(975\) 3.28992e13 1.16591
\(976\) 1.31264e13 0.463043
\(977\) −2.18727e13 −0.768027 −0.384013 0.923328i \(-0.625458\pi\)
−0.384013 + 0.923328i \(0.625458\pi\)
\(978\) −4.21454e12 −0.147308
\(979\) −1.81195e12 −0.0630413
\(980\) 1.03103e14 3.57069
\(981\) 6.74060e12 0.232374
\(982\) 9.63577e13 3.30663
\(983\) −1.94063e13 −0.662906 −0.331453 0.943472i \(-0.607539\pi\)
−0.331453 + 0.943472i \(0.607539\pi\)
\(984\) −1.69020e12 −0.0574726
\(985\) −3.96722e13 −1.34284
\(986\) −1.76770e13 −0.595611
\(987\) 4.89533e11 0.0164193
\(988\) 5.75642e13 1.92197
\(989\) 7.33593e12 0.243822
\(990\) −2.95982e13 −0.979281
\(991\) 3.18629e12 0.104943 0.0524716 0.998622i \(-0.483290\pi\)
0.0524716 + 0.998622i \(0.483290\pi\)
\(992\) 8.00802e13 2.62556
\(993\) 2.69164e13 0.878509
\(994\) 1.26079e13 0.409641
\(995\) −8.76394e13 −2.83462
\(996\) −4.90046e13 −1.57786
\(997\) −2.11989e13 −0.679492 −0.339746 0.940517i \(-0.610341\pi\)
−0.339746 + 0.940517i \(0.610341\pi\)
\(998\) −9.80005e13 −3.12709
\(999\) −1.04299e13 −0.331309
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 17.10.a.b.1.1 7
3.2 odd 2 153.10.a.f.1.7 7
4.3 odd 2 272.10.a.g.1.3 7
17.16 even 2 289.10.a.b.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.1 7 1.1 even 1 trivial
153.10.a.f.1.7 7 3.2 odd 2
272.10.a.g.1.3 7 4.3 odd 2
289.10.a.b.1.1 7 17.16 even 2