Properties

Label 17.10.a.b.1.2
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 1.2
Root \(28.6400\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +O(q^{10})\) \(q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} -50887.2 q^{10} +18658.0 q^{11} +75204.0 q^{12} +118081. q^{13} +274904. q^{14} +433484. q^{15} -324950. q^{16} +83521.0 q^{17} -1.14098e6 q^{18} +365652. q^{19} +547695. q^{20} -2.34178e6 q^{21} -534365. q^{22} +1.22678e6 q^{23} +1.42367e6 q^{24} +1.20385e6 q^{25} -3.38183e6 q^{26} +4.91741e6 q^{27} -2.95877e6 q^{28} -2.55483e6 q^{29} -1.24150e7 q^{30} +8.56431e6 q^{31} +6.31884e6 q^{32} +4.55201e6 q^{33} -2.39204e6 q^{34} -1.70547e7 q^{35} +1.22803e7 q^{36} -7.97315e6 q^{37} -1.04723e7 q^{38} +2.88083e7 q^{39} +1.03683e7 q^{40} -3.21617e7 q^{41} +6.70686e7 q^{42} -2.38617e7 q^{43} +5.75133e6 q^{44} +7.07850e7 q^{45} -3.51351e7 q^{46} -1.94506e7 q^{47} -7.92783e7 q^{48} +5.17797e7 q^{49} -3.44784e7 q^{50} +2.03767e7 q^{51} +3.63984e7 q^{52} -1.96101e7 q^{53} -1.40835e8 q^{54} +3.31513e7 q^{55} -5.60118e7 q^{56} +8.92083e7 q^{57} +7.31702e7 q^{58} +1.58423e7 q^{59} +1.33622e8 q^{60} -1.09913e8 q^{61} -2.45282e8 q^{62} -3.82396e8 q^{63} -1.45973e7 q^{64} +2.09805e8 q^{65} -1.30370e8 q^{66} -8.19198e7 q^{67} +2.57453e7 q^{68} +2.99299e8 q^{69} +4.88447e8 q^{70} +1.93682e8 q^{71} +2.32475e8 q^{72} -1.53405e7 q^{73} +2.28351e8 q^{74} +2.93705e8 q^{75} +1.12712e8 q^{76} -1.79091e8 q^{77} -8.25069e8 q^{78} +1.36544e8 q^{79} -5.77367e8 q^{80} +4.15558e8 q^{81} +9.21111e8 q^{82} -6.51497e8 q^{83} -7.21854e8 q^{84} +1.48399e8 q^{85} +6.83399e8 q^{86} -6.23303e8 q^{87} +1.08877e8 q^{88} -6.97006e8 q^{89} -2.02728e9 q^{90} -1.13341e9 q^{91} +3.78156e8 q^{92} +2.08944e9 q^{93} +5.57064e8 q^{94} +6.49686e8 q^{95} +1.54161e9 q^{96} -4.50260e8 q^{97} -1.48297e9 q^{98} +7.43311e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −28.6400 −1.26572 −0.632861 0.774266i \(-0.718119\pi\)
−0.632861 + 0.774266i \(0.718119\pi\)
\(3\) 243.971 1.73897 0.869485 0.493959i \(-0.164451\pi\)
0.869485 + 0.493959i \(0.164451\pi\)
\(4\) 308.250 0.602051
\(5\) 1776.79 1.27137 0.635683 0.771950i \(-0.280718\pi\)
0.635683 + 0.771950i \(0.280718\pi\)
\(6\) −6987.32 −2.20105
\(7\) −9598.61 −1.51101 −0.755505 0.655143i \(-0.772608\pi\)
−0.755505 + 0.655143i \(0.772608\pi\)
\(8\) 5835.40 0.503693
\(9\) 39838.7 2.02402
\(10\) −50887.2 −1.60920
\(11\) 18658.0 0.384236 0.192118 0.981372i \(-0.438464\pi\)
0.192118 + 0.981372i \(0.438464\pi\)
\(12\) 75204.0 1.04695
\(13\) 118081. 1.14666 0.573329 0.819325i \(-0.305652\pi\)
0.573329 + 0.819325i \(0.305652\pi\)
\(14\) 274904. 1.91252
\(15\) 433484. 2.21087
\(16\) −324950. −1.23959
\(17\) 83521.0 0.242536
\(18\) −1.14098e6 −2.56184
\(19\) 365652. 0.643690 0.321845 0.946792i \(-0.395697\pi\)
0.321845 + 0.946792i \(0.395697\pi\)
\(20\) 547695. 0.765427
\(21\) −2.34178e6 −2.62760
\(22\) −534365. −0.486336
\(23\) 1.22678e6 0.914098 0.457049 0.889441i \(-0.348906\pi\)
0.457049 + 0.889441i \(0.348906\pi\)
\(24\) 1.42367e6 0.875907
\(25\) 1.20385e6 0.616373
\(26\) −3.38183e6 −1.45135
\(27\) 4.91741e6 1.78073
\(28\) −2.95877e6 −0.909704
\(29\) −2.55483e6 −0.670765 −0.335382 0.942082i \(-0.608866\pi\)
−0.335382 + 0.942082i \(0.608866\pi\)
\(30\) −1.24150e7 −2.79834
\(31\) 8.56431e6 1.66558 0.832789 0.553591i \(-0.186743\pi\)
0.832789 + 0.553591i \(0.186743\pi\)
\(32\) 6.31884e6 1.06528
\(33\) 4.55201e6 0.668175
\(34\) −2.39204e6 −0.306983
\(35\) −1.70547e7 −1.92105
\(36\) 1.22803e7 1.21856
\(37\) −7.97315e6 −0.699394 −0.349697 0.936863i \(-0.613715\pi\)
−0.349697 + 0.936863i \(0.613715\pi\)
\(38\) −1.04723e7 −0.814732
\(39\) 2.88083e7 1.99400
\(40\) 1.03683e7 0.640378
\(41\) −3.21617e7 −1.77751 −0.888754 0.458384i \(-0.848428\pi\)
−0.888754 + 0.458384i \(0.848428\pi\)
\(42\) 6.70686e7 3.32581
\(43\) −2.38617e7 −1.06437 −0.532186 0.846628i \(-0.678629\pi\)
−0.532186 + 0.846628i \(0.678629\pi\)
\(44\) 5.75133e6 0.231330
\(45\) 7.07850e7 2.57327
\(46\) −3.51351e7 −1.15699
\(47\) −1.94506e7 −0.581423 −0.290711 0.956811i \(-0.593892\pi\)
−0.290711 + 0.956811i \(0.593892\pi\)
\(48\) −7.92783e7 −2.15560
\(49\) 5.17797e7 1.28315
\(50\) −3.44784e7 −0.780156
\(51\) 2.03767e7 0.421762
\(52\) 3.63984e7 0.690347
\(53\) −1.96101e7 −0.341380 −0.170690 0.985325i \(-0.554600\pi\)
−0.170690 + 0.985325i \(0.554600\pi\)
\(54\) −1.40835e8 −2.25391
\(55\) 3.31513e7 0.488505
\(56\) −5.60118e7 −0.761085
\(57\) 8.92083e7 1.11936
\(58\) 7.31702e7 0.849002
\(59\) 1.58423e7 0.170210 0.0851051 0.996372i \(-0.472877\pi\)
0.0851051 + 0.996372i \(0.472877\pi\)
\(60\) 1.33622e8 1.33105
\(61\) −1.09913e8 −1.01640 −0.508201 0.861238i \(-0.669689\pi\)
−0.508201 + 0.861238i \(0.669689\pi\)
\(62\) −2.45282e8 −2.10816
\(63\) −3.82396e8 −3.05831
\(64\) −1.45973e7 −0.108759
\(65\) 2.09805e8 1.45782
\(66\) −1.30370e8 −0.845723
\(67\) −8.19198e7 −0.496652 −0.248326 0.968677i \(-0.579880\pi\)
−0.248326 + 0.968677i \(0.579880\pi\)
\(68\) 2.57453e7 0.146019
\(69\) 2.99299e8 1.58959
\(70\) 4.88447e8 2.43151
\(71\) 1.93682e8 0.904537 0.452268 0.891882i \(-0.350615\pi\)
0.452268 + 0.891882i \(0.350615\pi\)
\(72\) 2.32475e8 1.01948
\(73\) −1.53405e7 −0.0632245 −0.0316123 0.999500i \(-0.510064\pi\)
−0.0316123 + 0.999500i \(0.510064\pi\)
\(74\) 2.28351e8 0.885238
\(75\) 2.93705e8 1.07185
\(76\) 1.12712e8 0.387534
\(77\) −1.79091e8 −0.580584
\(78\) −8.25069e8 −2.52385
\(79\) 1.36544e8 0.394413 0.197206 0.980362i \(-0.436813\pi\)
0.197206 + 0.980362i \(0.436813\pi\)
\(80\) −5.77367e8 −1.57597
\(81\) 4.15558e8 1.07263
\(82\) 9.21111e8 2.24983
\(83\) −6.51497e8 −1.50682 −0.753409 0.657552i \(-0.771592\pi\)
−0.753409 + 0.657552i \(0.771592\pi\)
\(84\) −7.21854e8 −1.58195
\(85\) 1.48399e8 0.308352
\(86\) 6.83399e8 1.34720
\(87\) −6.23303e8 −1.16644
\(88\) 1.08877e8 0.193537
\(89\) −6.97006e8 −1.17756 −0.588778 0.808295i \(-0.700391\pi\)
−0.588778 + 0.808295i \(0.700391\pi\)
\(90\) −2.02728e9 −3.25704
\(91\) −1.13341e9 −1.73261
\(92\) 3.78156e8 0.550334
\(93\) 2.08944e9 2.89639
\(94\) 5.57064e8 0.735919
\(95\) 6.49686e8 0.818365
\(96\) 1.54161e9 1.85249
\(97\) −4.50260e8 −0.516405 −0.258203 0.966091i \(-0.583130\pi\)
−0.258203 + 0.966091i \(0.583130\pi\)
\(98\) −1.48297e9 −1.62411
\(99\) 7.43311e8 0.777700
\(100\) 3.71088e8 0.371088
\(101\) 5.43766e8 0.519955 0.259978 0.965615i \(-0.416285\pi\)
0.259978 + 0.965615i \(0.416285\pi\)
\(102\) −5.83588e8 −0.533833
\(103\) 9.99479e8 0.874996 0.437498 0.899219i \(-0.355865\pi\)
0.437498 + 0.899219i \(0.355865\pi\)
\(104\) 6.89049e8 0.577564
\(105\) −4.16085e9 −3.34064
\(106\) 5.61633e8 0.432092
\(107\) 2.11598e7 0.0156058 0.00780289 0.999970i \(-0.497516\pi\)
0.00780289 + 0.999970i \(0.497516\pi\)
\(108\) 1.51579e9 1.07209
\(109\) −2.38161e9 −1.61604 −0.808019 0.589156i \(-0.799460\pi\)
−0.808019 + 0.589156i \(0.799460\pi\)
\(110\) −9.49454e8 −0.618311
\(111\) −1.94521e9 −1.21623
\(112\) 3.11907e9 1.87303
\(113\) 1.14225e9 0.659035 0.329517 0.944150i \(-0.393114\pi\)
0.329517 + 0.944150i \(0.393114\pi\)
\(114\) −2.55493e9 −1.41679
\(115\) 2.17974e9 1.16215
\(116\) −7.87525e8 −0.403835
\(117\) 4.70419e9 2.32086
\(118\) −4.53725e8 −0.215439
\(119\) −8.01686e8 −0.366474
\(120\) 2.52956e9 1.11360
\(121\) −2.00983e9 −0.852363
\(122\) 3.14792e9 1.28648
\(123\) −7.84651e9 −3.09103
\(124\) 2.63995e9 1.00276
\(125\) −1.33130e9 −0.487731
\(126\) 1.09518e10 3.87097
\(127\) 5.42933e9 1.85195 0.925975 0.377584i \(-0.123245\pi\)
0.925975 + 0.377584i \(0.123245\pi\)
\(128\) −2.81718e9 −0.927619
\(129\) −5.82156e9 −1.85091
\(130\) −6.00881e9 −1.84520
\(131\) 2.35819e9 0.699613 0.349806 0.936822i \(-0.386247\pi\)
0.349806 + 0.936822i \(0.386247\pi\)
\(132\) 1.40316e9 0.402275
\(133\) −3.50975e9 −0.972621
\(134\) 2.34618e9 0.628623
\(135\) 8.73719e9 2.26397
\(136\) 4.87379e8 0.122163
\(137\) −9.19603e8 −0.223027 −0.111514 0.993763i \(-0.535570\pi\)
−0.111514 + 0.993763i \(0.535570\pi\)
\(138\) −8.57194e9 −2.01198
\(139\) 1.27752e9 0.290269 0.145135 0.989412i \(-0.453638\pi\)
0.145135 + 0.989412i \(0.453638\pi\)
\(140\) −5.25711e9 −1.15657
\(141\) −4.74537e9 −1.01108
\(142\) −5.54705e9 −1.14489
\(143\) 2.20315e9 0.440588
\(144\) −1.29456e10 −2.50894
\(145\) −4.53939e9 −0.852788
\(146\) 4.39351e8 0.0800246
\(147\) 1.26327e10 2.23136
\(148\) −2.45772e9 −0.421071
\(149\) −1.13853e9 −0.189237 −0.0946183 0.995514i \(-0.530163\pi\)
−0.0946183 + 0.995514i \(0.530163\pi\)
\(150\) −8.41171e9 −1.35667
\(151\) 1.89477e9 0.296593 0.148296 0.988943i \(-0.452621\pi\)
0.148296 + 0.988943i \(0.452621\pi\)
\(152\) 2.13373e9 0.324222
\(153\) 3.32737e9 0.490896
\(154\) 5.12917e9 0.734858
\(155\) 1.52170e10 2.11756
\(156\) 8.88014e9 1.20049
\(157\) 6.87991e9 0.903721 0.451860 0.892089i \(-0.350760\pi\)
0.451860 + 0.892089i \(0.350760\pi\)
\(158\) −3.91062e9 −0.499217
\(159\) −4.78429e9 −0.593650
\(160\) 1.12272e10 1.35436
\(161\) −1.17754e10 −1.38121
\(162\) −1.19016e10 −1.35765
\(163\) 1.18995e10 1.32034 0.660171 0.751116i \(-0.270484\pi\)
0.660171 + 0.751116i \(0.270484\pi\)
\(164\) −9.91384e9 −1.07015
\(165\) 8.08795e9 0.849495
\(166\) 1.86589e10 1.90721
\(167\) −1.62243e10 −1.61415 −0.807073 0.590451i \(-0.798950\pi\)
−0.807073 + 0.590451i \(0.798950\pi\)
\(168\) −1.36652e10 −1.32350
\(169\) 3.33857e9 0.314826
\(170\) −4.25015e9 −0.390287
\(171\) 1.45671e10 1.30284
\(172\) −7.35537e9 −0.640806
\(173\) 9.77316e9 0.829521 0.414761 0.909931i \(-0.363865\pi\)
0.414761 + 0.909931i \(0.363865\pi\)
\(174\) 1.78514e10 1.47639
\(175\) −1.15553e10 −0.931345
\(176\) −6.06292e9 −0.476293
\(177\) 3.86507e9 0.295990
\(178\) 1.99623e10 1.49046
\(179\) −1.22507e10 −0.891915 −0.445958 0.895054i \(-0.647137\pi\)
−0.445958 + 0.895054i \(0.647137\pi\)
\(180\) 2.18195e10 1.54924
\(181\) 1.21812e10 0.843597 0.421798 0.906690i \(-0.361399\pi\)
0.421798 + 0.906690i \(0.361399\pi\)
\(182\) 3.24609e10 2.19300
\(183\) −2.68156e10 −1.76749
\(184\) 7.15878e9 0.460425
\(185\) −1.41666e10 −0.889186
\(186\) −5.98416e10 −3.66602
\(187\) 1.55834e9 0.0931909
\(188\) −5.99564e9 −0.350046
\(189\) −4.72003e10 −2.69071
\(190\) −1.86070e10 −1.03582
\(191\) −1.62713e10 −0.884651 −0.442325 0.896855i \(-0.645846\pi\)
−0.442325 + 0.896855i \(0.645846\pi\)
\(192\) −3.56132e9 −0.189128
\(193\) 1.78626e10 0.926696 0.463348 0.886176i \(-0.346648\pi\)
0.463348 + 0.886176i \(0.346648\pi\)
\(194\) 1.28954e10 0.653625
\(195\) 5.11862e10 2.53511
\(196\) 1.59611e10 0.772522
\(197\) 1.24709e10 0.589927 0.294963 0.955509i \(-0.404693\pi\)
0.294963 + 0.955509i \(0.404693\pi\)
\(198\) −2.12884e10 −0.984352
\(199\) −1.76972e10 −0.799957 −0.399978 0.916525i \(-0.630982\pi\)
−0.399978 + 0.916525i \(0.630982\pi\)
\(200\) 7.02497e9 0.310463
\(201\) −1.99860e10 −0.863663
\(202\) −1.55735e10 −0.658119
\(203\) 2.45228e10 1.01353
\(204\) 6.28111e9 0.253922
\(205\) −5.71445e10 −2.25986
\(206\) −2.86251e10 −1.10750
\(207\) 4.88735e10 1.85015
\(208\) −3.83703e10 −1.42138
\(209\) 6.82233e9 0.247329
\(210\) 1.19167e11 4.22832
\(211\) −3.49985e10 −1.21556 −0.607782 0.794104i \(-0.707941\pi\)
−0.607782 + 0.794104i \(0.707941\pi\)
\(212\) −6.04481e9 −0.205528
\(213\) 4.72527e10 1.57296
\(214\) −6.06018e8 −0.0197526
\(215\) −4.23972e10 −1.35321
\(216\) 2.86950e10 0.896943
\(217\) −8.22055e10 −2.51670
\(218\) 6.82094e10 2.04545
\(219\) −3.74262e9 −0.109946
\(220\) 1.02189e10 0.294105
\(221\) 9.86223e9 0.278106
\(222\) 5.57110e10 1.53940
\(223\) 4.75965e10 1.28885 0.644426 0.764667i \(-0.277096\pi\)
0.644426 + 0.764667i \(0.277096\pi\)
\(224\) −6.06521e10 −1.60964
\(225\) 4.79600e10 1.24755
\(226\) −3.27141e10 −0.834154
\(227\) 1.17164e10 0.292873 0.146436 0.989220i \(-0.453220\pi\)
0.146436 + 0.989220i \(0.453220\pi\)
\(228\) 2.74985e10 0.673910
\(229\) 2.48997e10 0.598321 0.299161 0.954203i \(-0.403293\pi\)
0.299161 + 0.954203i \(0.403293\pi\)
\(230\) −6.24277e10 −1.47096
\(231\) −4.36929e10 −1.00962
\(232\) −1.49084e10 −0.337860
\(233\) 6.50866e10 1.44674 0.723369 0.690462i \(-0.242593\pi\)
0.723369 + 0.690462i \(0.242593\pi\)
\(234\) −1.34728e11 −2.93756
\(235\) −3.45596e10 −0.739201
\(236\) 4.88340e9 0.102475
\(237\) 3.33128e10 0.685872
\(238\) 2.29603e10 0.463854
\(239\) 4.29823e10 0.852117 0.426058 0.904696i \(-0.359902\pi\)
0.426058 + 0.904696i \(0.359902\pi\)
\(240\) −1.40861e11 −2.74056
\(241\) −7.83992e10 −1.49705 −0.748523 0.663109i \(-0.769236\pi\)
−0.748523 + 0.663109i \(0.769236\pi\)
\(242\) 5.75614e10 1.07885
\(243\) 4.59462e9 0.0845320
\(244\) −3.38807e10 −0.611926
\(245\) 9.20017e10 1.63135
\(246\) 2.24724e11 3.91239
\(247\) 4.31764e10 0.738092
\(248\) 4.99762e10 0.838940
\(249\) −1.58946e11 −2.62031
\(250\) 3.81284e10 0.617331
\(251\) 2.92884e10 0.465762 0.232881 0.972505i \(-0.425185\pi\)
0.232881 + 0.972505i \(0.425185\pi\)
\(252\) −1.17874e11 −1.84126
\(253\) 2.28893e10 0.351230
\(254\) −1.55496e11 −2.34405
\(255\) 3.62051e10 0.536214
\(256\) 8.81579e10 1.28287
\(257\) 3.01696e10 0.431390 0.215695 0.976461i \(-0.430798\pi\)
0.215695 + 0.976461i \(0.430798\pi\)
\(258\) 1.66729e11 2.34274
\(259\) 7.65311e10 1.05679
\(260\) 6.46723e10 0.877684
\(261\) −1.01781e11 −1.35764
\(262\) −6.75385e10 −0.885515
\(263\) −9.10348e10 −1.17329 −0.586647 0.809843i \(-0.699552\pi\)
−0.586647 + 0.809843i \(0.699552\pi\)
\(264\) 2.65628e10 0.336555
\(265\) −3.48430e10 −0.434019
\(266\) 1.00519e11 1.23107
\(267\) −1.70049e11 −2.04774
\(268\) −2.52518e10 −0.299010
\(269\) −6.95622e10 −0.810005 −0.405003 0.914316i \(-0.632729\pi\)
−0.405003 + 0.914316i \(0.632729\pi\)
\(270\) −2.50233e11 −2.86555
\(271\) −9.57591e10 −1.07849 −0.539247 0.842147i \(-0.681291\pi\)
−0.539247 + 0.842147i \(0.681291\pi\)
\(272\) −2.71401e10 −0.300644
\(273\) −2.76519e11 −3.01296
\(274\) 2.63374e10 0.282290
\(275\) 2.24615e10 0.236833
\(276\) 9.22591e10 0.957014
\(277\) −8.55452e10 −0.873045 −0.436523 0.899693i \(-0.643790\pi\)
−0.436523 + 0.899693i \(0.643790\pi\)
\(278\) −3.65882e10 −0.367400
\(279\) 3.41191e11 3.37116
\(280\) −9.95211e10 −0.967618
\(281\) −4.39159e10 −0.420188 −0.210094 0.977681i \(-0.567377\pi\)
−0.210094 + 0.977681i \(0.567377\pi\)
\(282\) 1.35907e11 1.27974
\(283\) 8.04249e10 0.745335 0.372668 0.927965i \(-0.378443\pi\)
0.372668 + 0.927965i \(0.378443\pi\)
\(284\) 5.97024e10 0.544577
\(285\) 1.58504e11 1.42311
\(286\) −6.30983e10 −0.557661
\(287\) 3.08708e11 2.68583
\(288\) 2.51735e11 2.15614
\(289\) 6.97576e9 0.0588235
\(290\) 1.30008e11 1.07939
\(291\) −1.09850e11 −0.898013
\(292\) −4.72870e9 −0.0380644
\(293\) −2.21747e10 −0.175774 −0.0878869 0.996130i \(-0.528011\pi\)
−0.0878869 + 0.996130i \(0.528011\pi\)
\(294\) −3.61802e11 −2.82428
\(295\) 2.81485e10 0.216399
\(296\) −4.65265e10 −0.352280
\(297\) 9.17490e10 0.684222
\(298\) 3.26074e10 0.239521
\(299\) 1.44860e11 1.04816
\(300\) 9.05345e10 0.645310
\(301\) 2.29039e11 1.60828
\(302\) −5.42663e10 −0.375404
\(303\) 1.32663e11 0.904187
\(304\) −1.18819e11 −0.797908
\(305\) −1.95293e11 −1.29222
\(306\) −9.52959e10 −0.621338
\(307\) 1.36198e11 0.875081 0.437540 0.899199i \(-0.355850\pi\)
0.437540 + 0.899199i \(0.355850\pi\)
\(308\) −5.52048e10 −0.349541
\(309\) 2.43844e11 1.52159
\(310\) −4.35814e11 −2.68024
\(311\) 2.63133e11 1.59497 0.797486 0.603337i \(-0.206163\pi\)
0.797486 + 0.603337i \(0.206163\pi\)
\(312\) 1.68108e11 1.00437
\(313\) 1.85944e11 1.09504 0.547522 0.836791i \(-0.315571\pi\)
0.547522 + 0.836791i \(0.315571\pi\)
\(314\) −1.97041e11 −1.14386
\(315\) −6.79438e11 −3.88823
\(316\) 4.20897e10 0.237456
\(317\) −3.15409e11 −1.75431 −0.877157 0.480203i \(-0.840563\pi\)
−0.877157 + 0.480203i \(0.840563\pi\)
\(318\) 1.37022e11 0.751395
\(319\) −4.76680e10 −0.257732
\(320\) −2.59364e10 −0.138272
\(321\) 5.16238e9 0.0271380
\(322\) 3.37248e11 1.74823
\(323\) 3.05396e10 0.156118
\(324\) 1.28096e11 0.645776
\(325\) 1.42152e11 0.706769
\(326\) −3.40803e11 −1.67118
\(327\) −5.81043e11 −2.81024
\(328\) −1.87676e11 −0.895318
\(329\) 1.86698e11 0.878535
\(330\) −2.31639e11 −1.07522
\(331\) −1.33188e10 −0.0609871 −0.0304936 0.999535i \(-0.509708\pi\)
−0.0304936 + 0.999535i \(0.509708\pi\)
\(332\) −2.00824e11 −0.907181
\(333\) −3.17640e11 −1.41559
\(334\) 4.64665e11 2.04306
\(335\) −1.45554e11 −0.631426
\(336\) 7.60961e11 3.25714
\(337\) −8.96864e10 −0.378785 −0.189392 0.981902i \(-0.560652\pi\)
−0.189392 + 0.981902i \(0.560652\pi\)
\(338\) −9.56167e10 −0.398482
\(339\) 2.78676e11 1.14604
\(340\) 4.57440e10 0.185643
\(341\) 1.59793e11 0.639975
\(342\) −4.17202e11 −1.64903
\(343\) −1.09675e11 −0.427843
\(344\) −1.39243e11 −0.536117
\(345\) 5.31792e11 2.02095
\(346\) −2.79903e11 −1.04994
\(347\) −3.71901e11 −1.37703 −0.688516 0.725221i \(-0.741738\pi\)
−0.688516 + 0.725221i \(0.741738\pi\)
\(348\) −1.92133e11 −0.702256
\(349\) 2.40556e11 0.867963 0.433982 0.900922i \(-0.357108\pi\)
0.433982 + 0.900922i \(0.357108\pi\)
\(350\) 3.30944e11 1.17882
\(351\) 5.80651e11 2.04189
\(352\) 1.17897e11 0.409318
\(353\) −2.31047e11 −0.791980 −0.395990 0.918255i \(-0.629599\pi\)
−0.395990 + 0.918255i \(0.629599\pi\)
\(354\) −1.10696e11 −0.374641
\(355\) 3.44132e11 1.15000
\(356\) −2.14852e11 −0.708949
\(357\) −1.95588e11 −0.637287
\(358\) 3.50861e11 1.12892
\(359\) 2.17507e11 0.691110 0.345555 0.938398i \(-0.387691\pi\)
0.345555 + 0.938398i \(0.387691\pi\)
\(360\) 4.13059e11 1.29614
\(361\) −1.88986e11 −0.585664
\(362\) −3.48868e11 −1.06776
\(363\) −4.90339e11 −1.48223
\(364\) −3.49374e11 −1.04312
\(365\) −2.72568e10 −0.0803815
\(366\) 7.67999e11 2.23715
\(367\) 1.24703e11 0.358823 0.179412 0.983774i \(-0.442581\pi\)
0.179412 + 0.983774i \(0.442581\pi\)
\(368\) −3.98644e11 −1.13310
\(369\) −1.28128e12 −3.59771
\(370\) 4.05731e11 1.12546
\(371\) 1.88230e11 0.515829
\(372\) 6.44070e11 1.74377
\(373\) 6.71444e11 1.79606 0.898028 0.439938i \(-0.144999\pi\)
0.898028 + 0.439938i \(0.144999\pi\)
\(374\) −4.46307e10 −0.117954
\(375\) −3.24798e11 −0.848149
\(376\) −1.13502e11 −0.292858
\(377\) −3.01676e11 −0.769138
\(378\) 1.35182e12 3.40569
\(379\) −2.57132e11 −0.640147 −0.320073 0.947393i \(-0.603708\pi\)
−0.320073 + 0.947393i \(0.603708\pi\)
\(380\) 2.00266e11 0.492697
\(381\) 1.32460e12 3.22049
\(382\) 4.66010e11 1.11972
\(383\) −1.54303e11 −0.366420 −0.183210 0.983074i \(-0.558649\pi\)
−0.183210 + 0.983074i \(0.558649\pi\)
\(384\) −6.87309e11 −1.61310
\(385\) −3.18207e11 −0.738135
\(386\) −5.11586e11 −1.17294
\(387\) −9.50620e11 −2.15431
\(388\) −1.38793e11 −0.310902
\(389\) 1.53781e11 0.340510 0.170255 0.985400i \(-0.445541\pi\)
0.170255 + 0.985400i \(0.445541\pi\)
\(390\) −1.46597e12 −3.20874
\(391\) 1.02462e11 0.221701
\(392\) 3.02156e11 0.646314
\(393\) 5.75329e11 1.21661
\(394\) −3.57165e11 −0.746683
\(395\) 2.42610e11 0.501443
\(396\) 2.29126e11 0.468215
\(397\) −5.53284e10 −0.111787 −0.0558934 0.998437i \(-0.517801\pi\)
−0.0558934 + 0.998437i \(0.517801\pi\)
\(398\) 5.06849e11 1.01252
\(399\) −8.56276e11 −1.69136
\(400\) −3.91192e11 −0.764047
\(401\) −5.98775e11 −1.15642 −0.578208 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(402\) 5.72400e11 1.09316
\(403\) 1.01128e12 1.90985
\(404\) 1.67616e11 0.313039
\(405\) 7.38358e11 1.36370
\(406\) −7.02333e11 −1.28285
\(407\) −1.48763e11 −0.268732
\(408\) 1.18906e11 0.212439
\(409\) −8.67423e11 −1.53277 −0.766384 0.642383i \(-0.777946\pi\)
−0.766384 + 0.642383i \(0.777946\pi\)
\(410\) 1.63662e12 2.86036
\(411\) −2.24356e11 −0.387838
\(412\) 3.08089e11 0.526792
\(413\) −1.52065e11 −0.257189
\(414\) −1.39974e12 −2.34178
\(415\) −1.15757e12 −1.91572
\(416\) 7.46134e11 1.22151
\(417\) 3.11678e11 0.504770
\(418\) −1.95392e11 −0.313049
\(419\) −6.41732e11 −1.01716 −0.508581 0.861014i \(-0.669830\pi\)
−0.508581 + 0.861014i \(0.669830\pi\)
\(420\) −1.28258e12 −2.01124
\(421\) 4.57623e11 0.709967 0.354983 0.934873i \(-0.384487\pi\)
0.354983 + 0.934873i \(0.384487\pi\)
\(422\) 1.00236e12 1.53857
\(423\) −7.74886e11 −1.17681
\(424\) −1.14433e11 −0.171951
\(425\) 1.00547e11 0.149492
\(426\) −1.35332e12 −1.99093
\(427\) 1.05501e12 1.53579
\(428\) 6.52252e9 0.00939547
\(429\) 5.37505e11 0.766169
\(430\) 1.21426e12 1.71278
\(431\) 7.38734e10 0.103119 0.0515597 0.998670i \(-0.483581\pi\)
0.0515597 + 0.998670i \(0.483581\pi\)
\(432\) −1.59791e12 −2.20737
\(433\) 1.03868e12 1.41999 0.709995 0.704206i \(-0.248697\pi\)
0.709995 + 0.704206i \(0.248697\pi\)
\(434\) 2.35437e12 3.18545
\(435\) −1.10748e12 −1.48297
\(436\) −7.34132e11 −0.972937
\(437\) 4.48576e11 0.588396
\(438\) 1.07189e11 0.139160
\(439\) 9.61297e11 1.23529 0.617643 0.786459i \(-0.288088\pi\)
0.617643 + 0.786459i \(0.288088\pi\)
\(440\) 1.93451e11 0.246056
\(441\) 2.06284e12 2.59712
\(442\) −2.82454e11 −0.352004
\(443\) 2.39240e11 0.295132 0.147566 0.989052i \(-0.452856\pi\)
0.147566 + 0.989052i \(0.452856\pi\)
\(444\) −5.99612e11 −0.732229
\(445\) −1.23843e12 −1.49711
\(446\) −1.36316e12 −1.63133
\(447\) −2.77767e11 −0.329077
\(448\) 1.40114e11 0.164335
\(449\) −5.56831e11 −0.646569 −0.323285 0.946302i \(-0.604787\pi\)
−0.323285 + 0.946302i \(0.604787\pi\)
\(450\) −1.37357e12 −1.57905
\(451\) −6.00073e11 −0.682983
\(452\) 3.52099e11 0.396772
\(453\) 4.62269e11 0.515766
\(454\) −3.35558e11 −0.370695
\(455\) −2.01383e12 −2.20279
\(456\) 5.20566e11 0.563812
\(457\) 6.83226e11 0.732726 0.366363 0.930472i \(-0.380603\pi\)
0.366363 + 0.930472i \(0.380603\pi\)
\(458\) −7.13128e11 −0.757308
\(459\) 4.10707e11 0.431892
\(460\) 6.71904e11 0.699676
\(461\) −9.09123e11 −0.937494 −0.468747 0.883333i \(-0.655294\pi\)
−0.468747 + 0.883333i \(0.655294\pi\)
\(462\) 1.25137e12 1.27790
\(463\) 3.46507e11 0.350427 0.175213 0.984530i \(-0.443938\pi\)
0.175213 + 0.984530i \(0.443938\pi\)
\(464\) 8.30191e11 0.831471
\(465\) 3.71250e12 3.68237
\(466\) −1.86408e12 −1.83117
\(467\) 3.54586e11 0.344982 0.172491 0.985011i \(-0.444818\pi\)
0.172491 + 0.985011i \(0.444818\pi\)
\(468\) 1.45007e12 1.39727
\(469\) 7.86316e11 0.750446
\(470\) 9.89786e11 0.935623
\(471\) 1.67850e12 1.57154
\(472\) 9.24465e10 0.0857336
\(473\) −4.45212e11 −0.408970
\(474\) −9.54078e11 −0.868123
\(475\) 4.40191e11 0.396753
\(476\) −2.47120e11 −0.220636
\(477\) −7.81241e11 −0.690959
\(478\) −1.23101e12 −1.07854
\(479\) 1.13858e12 0.988222 0.494111 0.869399i \(-0.335494\pi\)
0.494111 + 0.869399i \(0.335494\pi\)
\(480\) 2.73912e12 2.35519
\(481\) −9.41475e11 −0.801966
\(482\) 2.24535e12 1.89484
\(483\) −2.87286e12 −2.40189
\(484\) −6.19529e11 −0.513166
\(485\) −8.00017e11 −0.656540
\(486\) −1.31590e11 −0.106994
\(487\) 1.19842e10 0.00965450 0.00482725 0.999988i \(-0.498463\pi\)
0.00482725 + 0.999988i \(0.498463\pi\)
\(488\) −6.41388e11 −0.511955
\(489\) 2.90314e12 2.29603
\(490\) −2.63493e12 −2.06484
\(491\) −1.60620e11 −0.124719 −0.0623597 0.998054i \(-0.519863\pi\)
−0.0623597 + 0.998054i \(0.519863\pi\)
\(492\) −2.41869e12 −1.86096
\(493\) −2.13382e11 −0.162684
\(494\) −1.23657e12 −0.934219
\(495\) 1.32071e12 0.988742
\(496\) −2.78297e12 −2.06463
\(497\) −1.85908e12 −1.36676
\(498\) 4.55222e12 3.31658
\(499\) −1.44413e12 −1.04269 −0.521345 0.853346i \(-0.674569\pi\)
−0.521345 + 0.853346i \(0.674569\pi\)
\(500\) −4.10373e11 −0.293639
\(501\) −3.95826e12 −2.80695
\(502\) −8.38820e11 −0.589525
\(503\) 1.19095e12 0.829539 0.414769 0.909927i \(-0.363862\pi\)
0.414769 + 0.909927i \(0.363862\pi\)
\(504\) −2.23144e12 −1.54045
\(505\) 9.66158e11 0.661054
\(506\) −6.55551e11 −0.444559
\(507\) 8.14514e11 0.547473
\(508\) 1.67359e12 1.11497
\(509\) −2.34412e12 −1.54793 −0.773963 0.633231i \(-0.781728\pi\)
−0.773963 + 0.633231i \(0.781728\pi\)
\(510\) −1.03691e12 −0.678698
\(511\) 1.47247e11 0.0955328
\(512\) −1.08245e12 −0.696132
\(513\) 1.79806e12 1.14624
\(514\) −8.64056e11 −0.546019
\(515\) 1.77586e12 1.11244
\(516\) −1.79449e12 −1.11434
\(517\) −3.62909e11 −0.223404
\(518\) −2.19185e12 −1.33760
\(519\) 2.38437e12 1.44251
\(520\) 1.22429e12 0.734295
\(521\) 1.55789e12 0.926333 0.463166 0.886271i \(-0.346713\pi\)
0.463166 + 0.886271i \(0.346713\pi\)
\(522\) 2.91501e12 1.71839
\(523\) 5.98253e10 0.0349645 0.0174823 0.999847i \(-0.494435\pi\)
0.0174823 + 0.999847i \(0.494435\pi\)
\(524\) 7.26912e11 0.421202
\(525\) −2.81916e12 −1.61958
\(526\) 2.60724e12 1.48506
\(527\) 7.15300e11 0.403962
\(528\) −1.47917e12 −0.828260
\(529\) −2.96153e11 −0.164424
\(530\) 9.97904e11 0.549348
\(531\) 6.31139e11 0.344508
\(532\) −1.08188e12 −0.585567
\(533\) −3.79768e12 −2.03820
\(534\) 4.87021e12 2.59186
\(535\) 3.75966e10 0.0198407
\(536\) −4.78035e11 −0.250160
\(537\) −2.98882e12 −1.55101
\(538\) 1.99226e12 1.02524
\(539\) 9.66107e11 0.493033
\(540\) 2.69324e12 1.36302
\(541\) 2.35116e12 1.18004 0.590018 0.807390i \(-0.299121\pi\)
0.590018 + 0.807390i \(0.299121\pi\)
\(542\) 2.74254e12 1.36507
\(543\) 2.97185e12 1.46699
\(544\) 5.27756e11 0.258368
\(545\) −4.23162e12 −2.05458
\(546\) 7.91951e12 3.81357
\(547\) 3.16333e12 1.51078 0.755391 0.655274i \(-0.227447\pi\)
0.755391 + 0.655274i \(0.227447\pi\)
\(548\) −2.83468e11 −0.134274
\(549\) −4.37880e12 −2.05722
\(550\) −6.43297e11 −0.299764
\(551\) −9.34177e11 −0.431764
\(552\) 1.74653e12 0.800665
\(553\) −1.31063e12 −0.595961
\(554\) 2.45002e12 1.10503
\(555\) −3.45624e12 −1.54627
\(556\) 3.93796e11 0.174757
\(557\) 3.53542e12 1.55630 0.778148 0.628081i \(-0.216159\pi\)
0.778148 + 0.628081i \(0.216159\pi\)
\(558\) −9.77172e12 −4.26695
\(559\) −2.81761e12 −1.22047
\(560\) 5.54193e12 2.38130
\(561\) 3.80188e11 0.162056
\(562\) 1.25775e12 0.531841
\(563\) −1.75567e12 −0.736472 −0.368236 0.929732i \(-0.620038\pi\)
−0.368236 + 0.929732i \(0.620038\pi\)
\(564\) −1.46276e12 −0.608719
\(565\) 2.02954e12 0.837875
\(566\) −2.30337e12 −0.943387
\(567\) −3.98878e12 −1.62075
\(568\) 1.13021e12 0.455609
\(569\) −2.32211e9 −0.000928706 0 −0.000464353 1.00000i \(-0.500148\pi\)
−0.000464353 1.00000i \(0.500148\pi\)
\(570\) −4.53957e12 −1.80126
\(571\) −2.57323e12 −1.01302 −0.506509 0.862235i \(-0.669064\pi\)
−0.506509 + 0.862235i \(0.669064\pi\)
\(572\) 6.79121e11 0.265256
\(573\) −3.96972e12 −1.53838
\(574\) −8.84139e12 −3.39952
\(575\) 1.47687e12 0.563425
\(576\) −5.81539e11 −0.220129
\(577\) −1.59532e12 −0.599178 −0.299589 0.954068i \(-0.596850\pi\)
−0.299589 + 0.954068i \(0.596850\pi\)
\(578\) −1.99786e11 −0.0744542
\(579\) 4.35796e12 1.61150
\(580\) −1.39927e12 −0.513422
\(581\) 6.25346e12 2.27682
\(582\) 3.14611e12 1.13663
\(583\) −3.65885e11 −0.131171
\(584\) −8.95177e10 −0.0318457
\(585\) 8.35835e12 2.95066
\(586\) 6.35085e11 0.222481
\(587\) −2.68434e12 −0.933182 −0.466591 0.884473i \(-0.654518\pi\)
−0.466591 + 0.884473i \(0.654518\pi\)
\(588\) 3.89404e12 1.34339
\(589\) 3.13156e12 1.07212
\(590\) −8.06173e11 −0.273901
\(591\) 3.04252e12 1.02586
\(592\) 2.59087e12 0.866959
\(593\) 4.50719e12 1.49679 0.748393 0.663256i \(-0.230826\pi\)
0.748393 + 0.663256i \(0.230826\pi\)
\(594\) −2.62769e12 −0.866035
\(595\) −1.42443e12 −0.465922
\(596\) −3.50951e11 −0.113930
\(597\) −4.31761e12 −1.39110
\(598\) −4.14878e12 −1.32668
\(599\) −4.19976e12 −1.33292 −0.666459 0.745542i \(-0.732191\pi\)
−0.666459 + 0.745542i \(0.732191\pi\)
\(600\) 1.71389e12 0.539885
\(601\) 4.96222e12 1.55146 0.775730 0.631065i \(-0.217382\pi\)
0.775730 + 0.631065i \(0.217382\pi\)
\(602\) −6.55968e12 −2.03563
\(603\) −3.26358e12 −1.00523
\(604\) 5.84063e11 0.178564
\(605\) −3.57104e12 −1.08367
\(606\) −3.79947e12 −1.14445
\(607\) 4.06493e12 1.21536 0.607679 0.794183i \(-0.292101\pi\)
0.607679 + 0.794183i \(0.292101\pi\)
\(608\) 2.31050e12 0.685708
\(609\) 5.98284e12 1.76250
\(610\) 5.59318e12 1.63559
\(611\) −2.29674e12 −0.666693
\(612\) 1.02566e12 0.295544
\(613\) −3.12747e12 −0.894583 −0.447291 0.894388i \(-0.647611\pi\)
−0.447291 + 0.894388i \(0.647611\pi\)
\(614\) −3.90071e12 −1.10761
\(615\) −1.39416e13 −3.92984
\(616\) −1.04507e12 −0.292436
\(617\) 1.99199e12 0.553354 0.276677 0.960963i \(-0.410767\pi\)
0.276677 + 0.960963i \(0.410767\pi\)
\(618\) −6.98368e12 −1.92591
\(619\) 5.76812e12 1.57916 0.789581 0.613647i \(-0.210298\pi\)
0.789581 + 0.613647i \(0.210298\pi\)
\(620\) 4.69063e12 1.27488
\(621\) 6.03260e12 1.62777
\(622\) −7.53613e12 −2.01879
\(623\) 6.69029e12 1.77930
\(624\) −9.36124e12 −2.47174
\(625\) −4.71671e12 −1.23646
\(626\) −5.32543e12 −1.38602
\(627\) 1.66445e12 0.430097
\(628\) 2.12073e12 0.544086
\(629\) −6.65925e11 −0.169628
\(630\) 1.94591e13 4.92142
\(631\) −2.73184e12 −0.685999 −0.342999 0.939336i \(-0.611443\pi\)
−0.342999 + 0.939336i \(0.611443\pi\)
\(632\) 7.96789e11 0.198663
\(633\) −8.53860e12 −2.11383
\(634\) 9.03332e12 2.22047
\(635\) 9.64677e12 2.35451
\(636\) −1.47476e12 −0.357407
\(637\) 6.11419e12 1.47134
\(638\) 1.36521e12 0.326217
\(639\) 7.71604e12 1.83080
\(640\) −5.00553e12 −1.17934
\(641\) −3.77475e12 −0.883135 −0.441567 0.897228i \(-0.645577\pi\)
−0.441567 + 0.897228i \(0.645577\pi\)
\(642\) −1.47851e11 −0.0343491
\(643\) 1.26222e12 0.291197 0.145598 0.989344i \(-0.453489\pi\)
0.145598 + 0.989344i \(0.453489\pi\)
\(644\) −3.62978e12 −0.831559
\(645\) −1.03437e13 −2.35319
\(646\) −8.74654e11 −0.197601
\(647\) 5.94830e12 1.33451 0.667257 0.744827i \(-0.267468\pi\)
0.667257 + 0.744827i \(0.267468\pi\)
\(648\) 2.42495e12 0.540275
\(649\) 2.95587e11 0.0654009
\(650\) −4.07123e12 −0.894573
\(651\) −2.00557e13 −4.37647
\(652\) 3.66804e12 0.794913
\(653\) −1.12364e12 −0.241835 −0.120918 0.992663i \(-0.538584\pi\)
−0.120918 + 0.992663i \(0.538584\pi\)
\(654\) 1.66411e13 3.55698
\(655\) 4.19000e12 0.889464
\(656\) 1.04509e13 2.20337
\(657\) −6.11144e11 −0.127967
\(658\) −5.34705e12 −1.11198
\(659\) −8.58385e11 −0.177296 −0.0886478 0.996063i \(-0.528255\pi\)
−0.0886478 + 0.996063i \(0.528255\pi\)
\(660\) 2.49311e12 0.511439
\(661\) −2.45857e12 −0.500929 −0.250465 0.968126i \(-0.580583\pi\)
−0.250465 + 0.968126i \(0.580583\pi\)
\(662\) 3.81450e11 0.0771927
\(663\) 2.40609e12 0.483617
\(664\) −3.80174e12 −0.758973
\(665\) −6.23608e12 −1.23656
\(666\) 9.09721e12 1.79174
\(667\) −3.13422e12 −0.613145
\(668\) −5.00115e12 −0.971798
\(669\) 1.16121e13 2.24127
\(670\) 4.16867e12 0.799210
\(671\) −2.05076e12 −0.390538
\(672\) −1.47973e13 −2.79912
\(673\) 2.80053e12 0.526225 0.263113 0.964765i \(-0.415251\pi\)
0.263113 + 0.964765i \(0.415251\pi\)
\(674\) 2.56862e12 0.479436
\(675\) 5.91984e12 1.09760
\(676\) 1.02911e12 0.189541
\(677\) −3.74996e12 −0.686085 −0.343042 0.939320i \(-0.611457\pi\)
−0.343042 + 0.939320i \(0.611457\pi\)
\(678\) −7.98127e12 −1.45057
\(679\) 4.32187e12 0.780293
\(680\) 8.65969e11 0.155315
\(681\) 2.85846e12 0.509297
\(682\) −4.57647e12 −0.810030
\(683\) −4.38021e12 −0.770197 −0.385099 0.922875i \(-0.625833\pi\)
−0.385099 + 0.922875i \(0.625833\pi\)
\(684\) 4.49031e12 0.784375
\(685\) −1.63394e12 −0.283549
\(686\) 3.14109e12 0.541530
\(687\) 6.07480e12 1.04046
\(688\) 7.75386e12 1.31938
\(689\) −2.31558e12 −0.391447
\(690\) −1.52305e13 −2.55796
\(691\) 1.91905e11 0.0320211 0.0160105 0.999872i \(-0.494903\pi\)
0.0160105 + 0.999872i \(0.494903\pi\)
\(692\) 3.01258e12 0.499414
\(693\) −7.13475e12 −1.17511
\(694\) 1.06512e13 1.74294
\(695\) 2.26988e12 0.369039
\(696\) −3.63722e12 −0.587528
\(697\) −2.68618e12 −0.431109
\(698\) −6.88952e12 −1.09860
\(699\) 1.58792e13 2.51583
\(700\) −3.56193e12 −0.560717
\(701\) 4.79909e12 0.750633 0.375316 0.926897i \(-0.377534\pi\)
0.375316 + 0.926897i \(0.377534\pi\)
\(702\) −1.66299e13 −2.58447
\(703\) −2.91540e12 −0.450193
\(704\) −2.72357e11 −0.0417890
\(705\) −8.43152e12 −1.28545
\(706\) 6.61719e12 1.00243
\(707\) −5.21940e12 −0.785658
\(708\) 1.19141e12 0.178201
\(709\) −7.09288e12 −1.05418 −0.527090 0.849810i \(-0.676717\pi\)
−0.527090 + 0.849810i \(0.676717\pi\)
\(710\) −9.85593e12 −1.45558
\(711\) 5.43974e12 0.798298
\(712\) −4.06731e12 −0.593127
\(713\) 1.05066e13 1.52250
\(714\) 5.60164e12 0.806627
\(715\) 3.91454e12 0.560148
\(716\) −3.77629e12 −0.536978
\(717\) 1.04864e13 1.48181
\(718\) −6.22939e12 −0.874753
\(719\) 8.16373e12 1.13922 0.569611 0.821914i \(-0.307094\pi\)
0.569611 + 0.821914i \(0.307094\pi\)
\(720\) −2.30016e13 −3.18979
\(721\) −9.59361e12 −1.32213
\(722\) 5.41257e12 0.741287
\(723\) −1.91271e13 −2.60332
\(724\) 3.75484e12 0.507888
\(725\) −3.07564e12 −0.413441
\(726\) 1.40433e13 1.87609
\(727\) 1.27003e13 1.68619 0.843097 0.537762i \(-0.180730\pi\)
0.843097 + 0.537762i \(0.180730\pi\)
\(728\) −6.61391e12 −0.872705
\(729\) −7.05847e12 −0.925629
\(730\) 7.80634e11 0.101741
\(731\) −1.99295e12 −0.258148
\(732\) −8.26591e12 −1.06412
\(733\) −9.65924e12 −1.23588 −0.617938 0.786227i \(-0.712032\pi\)
−0.617938 + 0.786227i \(0.712032\pi\)
\(734\) −3.57150e12 −0.454170
\(735\) 2.24457e13 2.83688
\(736\) 7.75186e12 0.973768
\(737\) −1.52846e12 −0.190832
\(738\) 3.66959e13 4.55369
\(739\) 5.87320e11 0.0724394 0.0362197 0.999344i \(-0.488468\pi\)
0.0362197 + 0.999344i \(0.488468\pi\)
\(740\) −4.36685e12 −0.535335
\(741\) 1.05338e13 1.28352
\(742\) −5.39090e12 −0.652895
\(743\) −6.32905e12 −0.761884 −0.380942 0.924599i \(-0.624400\pi\)
−0.380942 + 0.924599i \(0.624400\pi\)
\(744\) 1.21927e13 1.45889
\(745\) −2.02292e12 −0.240589
\(746\) −1.92302e13 −2.27331
\(747\) −2.59548e13 −3.04982
\(748\) 4.80357e11 0.0561057
\(749\) −2.03105e11 −0.0235805
\(750\) 9.30221e12 1.07352
\(751\) −5.48219e12 −0.628889 −0.314445 0.949276i \(-0.601818\pi\)
−0.314445 + 0.949276i \(0.601818\pi\)
\(752\) 6.32046e12 0.720723
\(753\) 7.14551e12 0.809946
\(754\) 8.64000e12 0.973515
\(755\) 3.36661e12 0.377078
\(756\) −1.45495e13 −1.61994
\(757\) 6.94071e12 0.768197 0.384099 0.923292i \(-0.374512\pi\)
0.384099 + 0.923292i \(0.374512\pi\)
\(758\) 7.36426e12 0.810247
\(759\) 5.58433e12 0.610778
\(760\) 3.79118e12 0.412205
\(761\) −1.18446e13 −1.28023 −0.640117 0.768277i \(-0.721114\pi\)
−0.640117 + 0.768277i \(0.721114\pi\)
\(762\) −3.79365e13 −4.07624
\(763\) 2.28602e13 2.44185
\(764\) −5.01562e12 −0.532605
\(765\) 5.91203e12 0.624109
\(766\) 4.41923e12 0.463786
\(767\) 1.87068e12 0.195173
\(768\) 2.15079e13 2.23087
\(769\) −1.22311e12 −0.126123 −0.0630617 0.998010i \(-0.520086\pi\)
−0.0630617 + 0.998010i \(0.520086\pi\)
\(770\) 9.11344e12 0.934274
\(771\) 7.36049e12 0.750174
\(772\) 5.50615e12 0.557918
\(773\) 2.56478e12 0.258370 0.129185 0.991621i \(-0.458764\pi\)
0.129185 + 0.991621i \(0.458764\pi\)
\(774\) 2.72258e13 2.72675
\(775\) 1.03102e13 1.02662
\(776\) −2.62745e12 −0.260110
\(777\) 1.86714e13 1.83773
\(778\) −4.40429e12 −0.430991
\(779\) −1.17600e13 −1.14416
\(780\) 1.57781e13 1.52627
\(781\) 3.61372e12 0.347556
\(782\) −2.93452e12 −0.280612
\(783\) −1.25631e13 −1.19445
\(784\) −1.68258e13 −1.59057
\(785\) 1.22241e13 1.14896
\(786\) −1.64774e13 −1.53988
\(787\) −7.44338e12 −0.691646 −0.345823 0.938300i \(-0.612400\pi\)
−0.345823 + 0.938300i \(0.612400\pi\)
\(788\) 3.84414e12 0.355166
\(789\) −2.22098e13 −2.04032
\(790\) −6.94835e12 −0.634687
\(791\) −1.09640e13 −0.995808
\(792\) 4.33752e12 0.391722
\(793\) −1.29786e13 −1.16547
\(794\) 1.58460e12 0.141491
\(795\) −8.50067e12 −0.754747
\(796\) −5.45517e12 −0.481615
\(797\) 1.00963e13 0.886337 0.443168 0.896438i \(-0.353854\pi\)
0.443168 + 0.896438i \(0.353854\pi\)
\(798\) 2.45238e13 2.14079
\(799\) −1.62453e12 −0.141016
\(800\) 7.60696e12 0.656608
\(801\) −2.77678e13 −2.38339
\(802\) 1.71489e13 1.46370
\(803\) −2.86222e11 −0.0242931
\(804\) −6.16069e12 −0.519969
\(805\) −2.09224e13 −1.75603
\(806\) −2.89631e13 −2.41734
\(807\) −1.69711e13 −1.40857
\(808\) 3.17309e12 0.261898
\(809\) −8.02349e12 −0.658560 −0.329280 0.944232i \(-0.606806\pi\)
−0.329280 + 0.944232i \(0.606806\pi\)
\(810\) −2.11466e13 −1.72607
\(811\) 2.03065e13 1.64832 0.824160 0.566357i \(-0.191648\pi\)
0.824160 + 0.566357i \(0.191648\pi\)
\(812\) 7.55915e12 0.610198
\(813\) −2.33624e13 −1.87547
\(814\) 4.26057e12 0.340140
\(815\) 2.11430e13 1.67864
\(816\) −6.62140e12 −0.522810
\(817\) −8.72507e12 −0.685125
\(818\) 2.48430e13 1.94006
\(819\) −4.51537e13 −3.50684
\(820\) −1.76148e13 −1.36055
\(821\) 2.20512e13 1.69390 0.846951 0.531671i \(-0.178436\pi\)
0.846951 + 0.531671i \(0.178436\pi\)
\(822\) 6.42557e12 0.490894
\(823\) 8.31984e12 0.632143 0.316072 0.948735i \(-0.397636\pi\)
0.316072 + 0.948735i \(0.397636\pi\)
\(824\) 5.83236e12 0.440729
\(825\) 5.47995e12 0.411845
\(826\) 4.35513e12 0.325530
\(827\) 6.70382e12 0.498365 0.249182 0.968457i \(-0.419838\pi\)
0.249182 + 0.968457i \(0.419838\pi\)
\(828\) 1.50653e13 1.11388
\(829\) −1.86852e13 −1.37405 −0.687025 0.726634i \(-0.741084\pi\)
−0.687025 + 0.726634i \(0.741084\pi\)
\(830\) 3.31529e13 2.42476
\(831\) −2.08705e13 −1.51820
\(832\) −1.72366e12 −0.124709
\(833\) 4.32470e12 0.311210
\(834\) −8.92645e12 −0.638898
\(835\) −2.88272e13 −2.05217
\(836\) 2.10298e12 0.148904
\(837\) 4.21142e13 2.96595
\(838\) 1.83792e13 1.28744
\(839\) 2.31979e13 1.61629 0.808147 0.588980i \(-0.200470\pi\)
0.808147 + 0.588980i \(0.200470\pi\)
\(840\) −2.42802e13 −1.68266
\(841\) −7.98001e12 −0.550074
\(842\) −1.31063e13 −0.898620
\(843\) −1.07142e13 −0.730694
\(844\) −1.07883e13 −0.731831
\(845\) 5.93194e12 0.400259
\(846\) 2.21927e13 1.48951
\(847\) 1.92915e13 1.28793
\(848\) 6.37230e12 0.423170
\(849\) 1.96213e13 1.29612
\(850\) −2.87967e12 −0.189216
\(851\) −9.78133e12 −0.639315
\(852\) 1.45656e13 0.947003
\(853\) −6.15810e12 −0.398269 −0.199134 0.979972i \(-0.563813\pi\)
−0.199134 + 0.979972i \(0.563813\pi\)
\(854\) −3.02156e13 −1.94389
\(855\) 2.58827e13 1.65639
\(856\) 1.23476e11 0.00786052
\(857\) 8.90805e12 0.564117 0.282058 0.959397i \(-0.408983\pi\)
0.282058 + 0.959397i \(0.408983\pi\)
\(858\) −1.53941e13 −0.969756
\(859\) −1.06938e13 −0.670135 −0.335068 0.942194i \(-0.608759\pi\)
−0.335068 + 0.942194i \(0.608759\pi\)
\(860\) −1.30689e13 −0.814699
\(861\) 7.53156e13 4.67058
\(862\) −2.11574e12 −0.130520
\(863\) −6.21448e12 −0.381379 −0.190689 0.981650i \(-0.561072\pi\)
−0.190689 + 0.981650i \(0.561072\pi\)
\(864\) 3.10723e13 1.89698
\(865\) 1.73648e13 1.05463
\(866\) −2.97478e13 −1.79731
\(867\) 1.70188e12 0.102292
\(868\) −2.53399e13 −1.51518
\(869\) 2.54764e12 0.151548
\(870\) 3.17182e13 1.87703
\(871\) −9.67315e12 −0.569490
\(872\) −1.38977e13 −0.813987
\(873\) −1.79378e13 −1.04521
\(874\) −1.28472e13 −0.744745
\(875\) 1.27786e13 0.736966
\(876\) −1.15366e12 −0.0661928
\(877\) 1.74120e13 0.993916 0.496958 0.867775i \(-0.334450\pi\)
0.496958 + 0.867775i \(0.334450\pi\)
\(878\) −2.75316e13 −1.56353
\(879\) −5.40999e12 −0.305665
\(880\) −1.07725e13 −0.605544
\(881\) 1.85361e13 1.03664 0.518318 0.855188i \(-0.326558\pi\)
0.518318 + 0.855188i \(0.326558\pi\)
\(882\) −5.90797e13 −3.28723
\(883\) −5.46626e12 −0.302599 −0.151299 0.988488i \(-0.548346\pi\)
−0.151299 + 0.988488i \(0.548346\pi\)
\(884\) 3.04003e12 0.167434
\(885\) 6.86741e12 0.376312
\(886\) −6.85183e12 −0.373555
\(887\) −3.61417e13 −1.96043 −0.980216 0.197930i \(-0.936578\pi\)
−0.980216 + 0.197930i \(0.936578\pi\)
\(888\) −1.13511e13 −0.612604
\(889\) −5.21140e13 −2.79832
\(890\) 3.54687e13 1.89492
\(891\) 7.75348e12 0.412142
\(892\) 1.46716e13 0.775954
\(893\) −7.11214e12 −0.374256
\(894\) 7.95525e12 0.416519
\(895\) −2.17670e13 −1.13395
\(896\) 2.70410e13 1.40164
\(897\) 3.53415e13 1.82272
\(898\) 1.59476e13 0.818376
\(899\) −2.18803e13 −1.11721
\(900\) 1.47837e13 0.751088
\(901\) −1.63785e12 −0.0827968
\(902\) 1.71861e13 0.864466
\(903\) 5.58789e13 2.79674
\(904\) 6.66549e12 0.331951
\(905\) 2.16433e13 1.07252
\(906\) −1.32394e13 −0.652816
\(907\) −3.39738e13 −1.66691 −0.833454 0.552589i \(-0.813640\pi\)
−0.833454 + 0.552589i \(0.813640\pi\)
\(908\) 3.61159e12 0.176324
\(909\) 2.16630e13 1.05240
\(910\) 5.76762e13 2.78811
\(911\) 2.01195e12 0.0967797 0.0483898 0.998829i \(-0.484591\pi\)
0.0483898 + 0.998829i \(0.484591\pi\)
\(912\) −2.89882e13 −1.38754
\(913\) −1.21556e13 −0.578974
\(914\) −1.95676e13 −0.927427
\(915\) −4.76457e13 −2.24713
\(916\) 7.67533e12 0.360220
\(917\) −2.26353e13 −1.05712
\(918\) −1.17626e13 −0.546654
\(919\) 1.59408e11 0.00737207 0.00368604 0.999993i \(-0.498827\pi\)
0.00368604 + 0.999993i \(0.498827\pi\)
\(920\) 1.27196e13 0.585369
\(921\) 3.32283e13 1.52174
\(922\) 2.60373e13 1.18661
\(923\) 2.28701e13 1.03720
\(924\) −1.34683e13 −0.607842
\(925\) −9.59850e12 −0.431088
\(926\) −9.92396e12 −0.443543
\(927\) 3.98180e13 1.77101
\(928\) −1.61435e13 −0.714551
\(929\) 4.18504e13 1.84344 0.921721 0.387854i \(-0.126784\pi\)
0.921721 + 0.387854i \(0.126784\pi\)
\(930\) −1.06326e14 −4.66086
\(931\) 1.89334e13 0.825950
\(932\) 2.00629e13 0.871009
\(933\) 6.41967e13 2.77361
\(934\) −1.01554e13 −0.436651
\(935\) 2.76883e12 0.118480
\(936\) 2.74508e13 1.16900
\(937\) 1.52091e13 0.644576 0.322288 0.946642i \(-0.395548\pi\)
0.322288 + 0.946642i \(0.395548\pi\)
\(938\) −2.25201e13 −0.949855
\(939\) 4.53648e13 1.90425
\(940\) −1.06530e13 −0.445037
\(941\) −1.93636e13 −0.805067 −0.402534 0.915405i \(-0.631870\pi\)
−0.402534 + 0.915405i \(0.631870\pi\)
\(942\) −4.80722e13 −1.98914
\(943\) −3.94555e13 −1.62482
\(944\) −5.14797e12 −0.210990
\(945\) −8.38649e13 −3.42087
\(946\) 1.27509e13 0.517642
\(947\) −3.99237e13 −1.61308 −0.806540 0.591179i \(-0.798663\pi\)
−0.806540 + 0.591179i \(0.798663\pi\)
\(948\) 1.02687e13 0.412930
\(949\) −1.81141e12 −0.0724969
\(950\) −1.26071e13 −0.502178
\(951\) −7.69506e13 −3.05070
\(952\) −4.67816e12 −0.184590
\(953\) −3.60339e13 −1.41512 −0.707559 0.706654i \(-0.750204\pi\)
−0.707559 + 0.706654i \(0.750204\pi\)
\(954\) 2.23748e13 0.874562
\(955\) −2.89106e13 −1.12472
\(956\) 1.32493e13 0.513018
\(957\) −1.16296e13 −0.448188
\(958\) −3.26090e13 −1.25081
\(959\) 8.82691e12 0.336996
\(960\) −6.32771e12 −0.240451
\(961\) 4.69079e13 1.77415
\(962\) 2.69639e13 1.01507
\(963\) 8.42981e11 0.0315864
\(964\) −2.41666e13 −0.901297
\(965\) 3.17381e13 1.17817
\(966\) 8.22787e13 3.04012
\(967\) 2.93298e13 1.07867 0.539337 0.842090i \(-0.318675\pi\)
0.539337 + 0.842090i \(0.318675\pi\)
\(968\) −1.17281e13 −0.429329
\(969\) 7.45077e12 0.271484
\(970\) 2.29125e13 0.830997
\(971\) 4.26932e13 1.54125 0.770623 0.637291i \(-0.219945\pi\)
0.770623 + 0.637291i \(0.219945\pi\)
\(972\) 1.41629e12 0.0508925
\(973\) −1.22624e13 −0.438600
\(974\) −3.43228e11 −0.0122199
\(975\) 3.46809e13 1.22905
\(976\) 3.57163e13 1.25992
\(977\) −3.65451e12 −0.128323 −0.0641613 0.997940i \(-0.520437\pi\)
−0.0641613 + 0.997940i \(0.520437\pi\)
\(978\) −8.31460e13 −2.90614
\(979\) −1.30047e13 −0.452460
\(980\) 2.83595e13 0.982158
\(981\) −9.48803e13 −3.27089
\(982\) 4.60017e12 0.157860
\(983\) −5.51397e13 −1.88353 −0.941767 0.336265i \(-0.890836\pi\)
−0.941767 + 0.336265i \(0.890836\pi\)
\(984\) −4.57876e13 −1.55693
\(985\) 2.21581e13 0.750013
\(986\) 6.11125e12 0.205913
\(987\) 4.55490e13 1.52775
\(988\) 1.33091e13 0.444369
\(989\) −2.92732e13 −0.972941
\(990\) −3.78250e13 −1.25147
\(991\) 4.65397e13 1.53282 0.766412 0.642350i \(-0.222040\pi\)
0.766412 + 0.642350i \(0.222040\pi\)
\(992\) 5.41166e13 1.77430
\(993\) −3.24939e12 −0.106055
\(994\) 5.32440e13 1.72994
\(995\) −3.14442e13 −1.01704
\(996\) −4.89951e13 −1.57756
\(997\) 4.29398e13 1.37636 0.688179 0.725541i \(-0.258410\pi\)
0.688179 + 0.725541i \(0.258410\pi\)
\(998\) 4.13600e13 1.31975
\(999\) −3.92072e13 −1.24544
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.1.2 7
3.2 odd 2 153.10.a.f.1.6 7
4.3 odd 2 272.10.a.g.1.1 7
17.16 even 2 289.10.a.b.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.2 7 1.1 even 1 trivial
153.10.a.f.1.6 7 3.2 odd 2
272.10.a.g.1.1 7 4.3 odd 2
289.10.a.b.1.2 7 17.16 even 2