Properties

Label 177.8.a.c.1.15
Level $177$
Weight $8$
Character 177.1
Self dual yes
Analytic conductor $55.292$
Analytic rank $0$
Dimension $17$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(55.2921495107\)
Analytic rank: \(0\)
Dimension: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
Defining polynomial: \(x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{31}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{5} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(16.5905\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+16.5905 q^{2} -27.0000 q^{3} +147.246 q^{4} +174.998 q^{5} -447.945 q^{6} +1111.07 q^{7} +319.307 q^{8} +729.000 q^{9} +O(q^{10})\) \(q+16.5905 q^{2} -27.0000 q^{3} +147.246 q^{4} +174.998 q^{5} -447.945 q^{6} +1111.07 q^{7} +319.307 q^{8} +729.000 q^{9} +2903.31 q^{10} +3459.76 q^{11} -3975.65 q^{12} -368.734 q^{13} +18433.2 q^{14} -4724.94 q^{15} -13550.0 q^{16} +12018.6 q^{17} +12094.5 q^{18} -20398.0 q^{19} +25767.8 q^{20} -29998.9 q^{21} +57399.3 q^{22} +27686.4 q^{23} -8621.30 q^{24} -47500.8 q^{25} -6117.50 q^{26} -19683.0 q^{27} +163601. q^{28} +141983. q^{29} -78389.3 q^{30} +224521. q^{31} -265674. q^{32} -93413.4 q^{33} +199395. q^{34} +194434. q^{35} +107343. q^{36} +433168. q^{37} -338413. q^{38} +9955.82 q^{39} +55878.1 q^{40} +286012. q^{41} -497698. q^{42} -152357. q^{43} +509436. q^{44} +127573. q^{45} +459333. q^{46} +449388. q^{47} +365851. q^{48} +410931. q^{49} -788065. q^{50} -324502. q^{51} -54294.7 q^{52} +141405. q^{53} -326552. q^{54} +605449. q^{55} +354773. q^{56} +550745. q^{57} +2.35558e6 q^{58} -205379. q^{59} -695730. q^{60} -522147. q^{61} +3.72492e6 q^{62} +809969. q^{63} -2.67327e6 q^{64} -64527.6 q^{65} -1.54978e6 q^{66} +1.89319e6 q^{67} +1.76969e6 q^{68} -747533. q^{69} +3.22578e6 q^{70} +3.16299e6 q^{71} +232775. q^{72} +3.37201e6 q^{73} +7.18650e6 q^{74} +1.28252e6 q^{75} -3.00352e6 q^{76} +3.84403e6 q^{77} +165172. q^{78} -1.64311e6 q^{79} -2.37123e6 q^{80} +531441. q^{81} +4.74509e6 q^{82} -6.36325e6 q^{83} -4.41722e6 q^{84} +2.10322e6 q^{85} -2.52769e6 q^{86} -3.83355e6 q^{87} +1.10473e6 q^{88} +5.43034e6 q^{89} +2.11651e6 q^{90} -409689. q^{91} +4.07672e6 q^{92} -6.06206e6 q^{93} +7.45560e6 q^{94} -3.56959e6 q^{95} +7.17320e6 q^{96} -2.91053e6 q^{97} +6.81757e6 q^{98} +2.52216e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) \) \( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.5905 1.46641 0.733206 0.680007i \(-0.238023\pi\)
0.733206 + 0.680007i \(0.238023\pi\)
\(3\) −27.0000 −0.577350
\(4\) 147.246 1.15036
\(5\) 174.998 0.626091 0.313045 0.949738i \(-0.398651\pi\)
0.313045 + 0.949738i \(0.398651\pi\)
\(6\) −447.945 −0.846633
\(7\) 1111.07 1.22433 0.612164 0.790731i \(-0.290299\pi\)
0.612164 + 0.790731i \(0.290299\pi\)
\(8\) 319.307 0.220493
\(9\) 729.000 0.333333
\(10\) 2903.31 0.918107
\(11\) 3459.76 0.783738 0.391869 0.920021i \(-0.371829\pi\)
0.391869 + 0.920021i \(0.371829\pi\)
\(12\) −3975.65 −0.664162
\(13\) −368.734 −0.0465491 −0.0232746 0.999729i \(-0.507409\pi\)
−0.0232746 + 0.999729i \(0.507409\pi\)
\(14\) 18433.2 1.79537
\(15\) −4724.94 −0.361474
\(16\) −13550.0 −0.827029
\(17\) 12018.6 0.593310 0.296655 0.954985i \(-0.404129\pi\)
0.296655 + 0.954985i \(0.404129\pi\)
\(18\) 12094.5 0.488804
\(19\) −20398.0 −0.682259 −0.341129 0.940016i \(-0.610809\pi\)
−0.341129 + 0.940016i \(0.610809\pi\)
\(20\) 25767.8 0.720231
\(21\) −29998.9 −0.706866
\(22\) 57399.3 1.14928
\(23\) 27686.4 0.474481 0.237241 0.971451i \(-0.423757\pi\)
0.237241 + 0.971451i \(0.423757\pi\)
\(24\) −8621.30 −0.127301
\(25\) −47500.8 −0.608010
\(26\) −6117.50 −0.0682602
\(27\) −19683.0 −0.192450
\(28\) 163601. 1.40842
\(29\) 141983. 1.08105 0.540523 0.841329i \(-0.318227\pi\)
0.540523 + 0.841329i \(0.318227\pi\)
\(30\) −78389.3 −0.530069
\(31\) 224521. 1.35360 0.676801 0.736166i \(-0.263366\pi\)
0.676801 + 0.736166i \(0.263366\pi\)
\(32\) −265674. −1.43326
\(33\) −93413.4 −0.452492
\(34\) 199395. 0.870037
\(35\) 194434. 0.766541
\(36\) 107343. 0.383454
\(37\) 433168. 1.40589 0.702944 0.711246i \(-0.251869\pi\)
0.702944 + 0.711246i \(0.251869\pi\)
\(38\) −338413. −1.00047
\(39\) 9955.82 0.0268751
\(40\) 55878.1 0.138048
\(41\) 286012. 0.648097 0.324049 0.946040i \(-0.394956\pi\)
0.324049 + 0.946040i \(0.394956\pi\)
\(42\) −497698. −1.03656
\(43\) −152357. −0.292229 −0.146115 0.989268i \(-0.546677\pi\)
−0.146115 + 0.989268i \(0.546677\pi\)
\(44\) 509436. 0.901583
\(45\) 127573. 0.208697
\(46\) 459333. 0.695785
\(47\) 449388. 0.631363 0.315682 0.948865i \(-0.397767\pi\)
0.315682 + 0.948865i \(0.397767\pi\)
\(48\) 365851. 0.477486
\(49\) 410931. 0.498980
\(50\) −788065. −0.891593
\(51\) −324502. −0.342548
\(52\) −54294.7 −0.0535483
\(53\) 141405. 0.130467 0.0652335 0.997870i \(-0.479221\pi\)
0.0652335 + 0.997870i \(0.479221\pi\)
\(54\) −326552. −0.282211
\(55\) 605449. 0.490691
\(56\) 354773. 0.269955
\(57\) 550745. 0.393902
\(58\) 2.35558e6 1.58526
\(59\) −205379. −0.130189
\(60\) −695730. −0.415826
\(61\) −522147. −0.294536 −0.147268 0.989097i \(-0.547048\pi\)
−0.147268 + 0.989097i \(0.547048\pi\)
\(62\) 3.72492e6 1.98494
\(63\) 809969. 0.408109
\(64\) −2.67327e6 −1.27472
\(65\) −64527.6 −0.0291440
\(66\) −1.54978e6 −0.663539
\(67\) 1.89319e6 0.769010 0.384505 0.923123i \(-0.374372\pi\)
0.384505 + 0.923123i \(0.374372\pi\)
\(68\) 1.76969e6 0.682522
\(69\) −747533. −0.273942
\(70\) 3.22578e6 1.12406
\(71\) 3.16299e6 1.04880 0.524400 0.851472i \(-0.324289\pi\)
0.524400 + 0.851472i \(0.324289\pi\)
\(72\) 232775. 0.0734975
\(73\) 3.37201e6 1.01452 0.507258 0.861794i \(-0.330659\pi\)
0.507258 + 0.861794i \(0.330659\pi\)
\(74\) 7.18650e6 2.06161
\(75\) 1.28252e6 0.351035
\(76\) −3.00352e6 −0.784844
\(77\) 3.84403e6 0.959553
\(78\) 165172. 0.0394100
\(79\) −1.64311e6 −0.374949 −0.187475 0.982269i \(-0.560030\pi\)
−0.187475 + 0.982269i \(0.560030\pi\)
\(80\) −2.37123e6 −0.517795
\(81\) 531441. 0.111111
\(82\) 4.74509e6 0.950377
\(83\) −6.36325e6 −1.22153 −0.610767 0.791810i \(-0.709139\pi\)
−0.610767 + 0.791810i \(0.709139\pi\)
\(84\) −4.41722e6 −0.813152
\(85\) 2.10322e6 0.371466
\(86\) −2.52769e6 −0.428528
\(87\) −3.83355e6 −0.624142
\(88\) 1.10473e6 0.172809
\(89\) 5.43034e6 0.816511 0.408256 0.912868i \(-0.366137\pi\)
0.408256 + 0.912868i \(0.366137\pi\)
\(90\) 2.11651e6 0.306036
\(91\) −409689. −0.0569914
\(92\) 4.07672e6 0.545825
\(93\) −6.06206e6 −0.781502
\(94\) 7.45560e6 0.925838
\(95\) −3.56959e6 −0.427156
\(96\) 7.17320e6 0.827492
\(97\) −2.91053e6 −0.323796 −0.161898 0.986807i \(-0.551762\pi\)
−0.161898 + 0.986807i \(0.551762\pi\)
\(98\) 6.81757e6 0.731709
\(99\) 2.52216e6 0.261246
\(100\) −6.99432e6 −0.699432
\(101\) −1.20381e7 −1.16261 −0.581305 0.813686i \(-0.697458\pi\)
−0.581305 + 0.813686i \(0.697458\pi\)
\(102\) −5.38366e6 −0.502316
\(103\) −4.50334e6 −0.406074 −0.203037 0.979171i \(-0.565081\pi\)
−0.203037 + 0.979171i \(0.565081\pi\)
\(104\) −117739. −0.0102637
\(105\) −5.24973e6 −0.442562
\(106\) 2.34599e6 0.191318
\(107\) −1.38674e6 −0.109434 −0.0547171 0.998502i \(-0.517426\pi\)
−0.0547171 + 0.998502i \(0.517426\pi\)
\(108\) −2.89825e6 −0.221387
\(109\) −1.51322e7 −1.11920 −0.559602 0.828761i \(-0.689046\pi\)
−0.559602 + 0.828761i \(0.689046\pi\)
\(110\) 1.00447e7 0.719555
\(111\) −1.16955e7 −0.811689
\(112\) −1.50550e7 −1.01256
\(113\) −1.74988e7 −1.14086 −0.570432 0.821345i \(-0.693224\pi\)
−0.570432 + 0.821345i \(0.693224\pi\)
\(114\) 9.13716e6 0.577623
\(115\) 4.84506e6 0.297068
\(116\) 2.09065e7 1.24359
\(117\) −268807. −0.0155164
\(118\) −3.40735e6 −0.190910
\(119\) 1.33535e7 0.726407
\(120\) −1.50871e6 −0.0797023
\(121\) −7.51726e6 −0.385754
\(122\) −8.66270e6 −0.431911
\(123\) −7.72232e6 −0.374179
\(124\) 3.30599e7 1.55713
\(125\) −2.19842e7 −1.00676
\(126\) 1.34378e7 0.598456
\(127\) −2.00254e7 −0.867495 −0.433748 0.901034i \(-0.642809\pi\)
−0.433748 + 0.901034i \(0.642809\pi\)
\(128\) −1.03448e7 −0.436000
\(129\) 4.11365e6 0.168719
\(130\) −1.07055e6 −0.0427370
\(131\) 1.77758e7 0.690845 0.345422 0.938447i \(-0.387736\pi\)
0.345422 + 0.938447i \(0.387736\pi\)
\(132\) −1.37548e7 −0.520529
\(133\) −2.26635e7 −0.835308
\(134\) 3.14090e7 1.12769
\(135\) −3.44448e6 −0.120491
\(136\) 3.83762e6 0.130821
\(137\) 4.37881e7 1.45490 0.727451 0.686159i \(-0.240705\pi\)
0.727451 + 0.686159i \(0.240705\pi\)
\(138\) −1.24020e7 −0.401712
\(139\) −2.03284e7 −0.642024 −0.321012 0.947075i \(-0.604023\pi\)
−0.321012 + 0.947075i \(0.604023\pi\)
\(140\) 2.86298e7 0.881799
\(141\) −1.21335e7 −0.364518
\(142\) 5.24757e7 1.53797
\(143\) −1.27573e6 −0.0364823
\(144\) −9.87798e6 −0.275676
\(145\) 2.48467e7 0.676832
\(146\) 5.59435e7 1.48770
\(147\) −1.10951e7 −0.288086
\(148\) 6.37824e7 1.61728
\(149\) 6.14768e7 1.52251 0.761254 0.648454i \(-0.224584\pi\)
0.761254 + 0.648454i \(0.224584\pi\)
\(150\) 2.12777e7 0.514762
\(151\) 6.11417e6 0.144517 0.0722583 0.997386i \(-0.476979\pi\)
0.0722583 + 0.997386i \(0.476979\pi\)
\(152\) −6.51322e6 −0.150433
\(153\) 8.76155e6 0.197770
\(154\) 6.37745e7 1.40710
\(155\) 3.92906e7 0.847477
\(156\) 1.46596e6 0.0309161
\(157\) 3.59609e7 0.741621 0.370810 0.928709i \(-0.379080\pi\)
0.370810 + 0.928709i \(0.379080\pi\)
\(158\) −2.72601e7 −0.549830
\(159\) −3.81795e6 −0.0753251
\(160\) −4.64923e7 −0.897349
\(161\) 3.07615e7 0.580921
\(162\) 8.81690e6 0.162935
\(163\) −3.88451e7 −0.702553 −0.351277 0.936272i \(-0.614252\pi\)
−0.351277 + 0.936272i \(0.614252\pi\)
\(164\) 4.21142e7 0.745547
\(165\) −1.63471e7 −0.283301
\(166\) −1.05570e8 −1.79127
\(167\) −8.48288e7 −1.40940 −0.704702 0.709503i \(-0.748919\pi\)
−0.704702 + 0.709503i \(0.748919\pi\)
\(168\) −9.57886e6 −0.155859
\(169\) −6.26126e7 −0.997833
\(170\) 3.48936e7 0.544722
\(171\) −1.48701e7 −0.227420
\(172\) −2.24341e7 −0.336169
\(173\) −2.04205e7 −0.299850 −0.149925 0.988697i \(-0.547903\pi\)
−0.149925 + 0.988697i \(0.547903\pi\)
\(174\) −6.36006e7 −0.915249
\(175\) −5.27767e7 −0.744404
\(176\) −4.68799e7 −0.648175
\(177\) 5.54523e6 0.0751646
\(178\) 9.00924e7 1.19734
\(179\) −2.15476e7 −0.280811 −0.140405 0.990094i \(-0.544841\pi\)
−0.140405 + 0.990094i \(0.544841\pi\)
\(180\) 1.87847e7 0.240077
\(181\) −6.19200e7 −0.776168 −0.388084 0.921624i \(-0.626863\pi\)
−0.388084 + 0.921624i \(0.626863\pi\)
\(182\) −6.79696e6 −0.0835728
\(183\) 1.40980e7 0.170050
\(184\) 8.84047e6 0.104620
\(185\) 7.58034e7 0.880213
\(186\) −1.00573e8 −1.14600
\(187\) 4.15814e7 0.465000
\(188\) 6.61708e7 0.726296
\(189\) −2.18692e7 −0.235622
\(190\) −5.92215e7 −0.626386
\(191\) −1.83254e8 −1.90300 −0.951498 0.307656i \(-0.900456\pi\)
−0.951498 + 0.307656i \(0.900456\pi\)
\(192\) 7.21784e7 0.735958
\(193\) −2.51674e7 −0.251993 −0.125996 0.992031i \(-0.540213\pi\)
−0.125996 + 0.992031i \(0.540213\pi\)
\(194\) −4.82873e7 −0.474818
\(195\) 1.74225e6 0.0168263
\(196\) 6.05081e7 0.574007
\(197\) 4.11501e7 0.383477 0.191738 0.981446i \(-0.438588\pi\)
0.191738 + 0.981446i \(0.438588\pi\)
\(198\) 4.18441e7 0.383094
\(199\) 1.20872e8 1.08728 0.543638 0.839320i \(-0.317047\pi\)
0.543638 + 0.839320i \(0.317047\pi\)
\(200\) −1.51674e7 −0.134062
\(201\) −5.11161e7 −0.443988
\(202\) −1.99719e8 −1.70486
\(203\) 1.57753e8 1.32355
\(204\) −4.77817e7 −0.394054
\(205\) 5.00514e7 0.405768
\(206\) −7.47129e7 −0.595471
\(207\) 2.01834e7 0.158160
\(208\) 4.99636e6 0.0384975
\(209\) −7.05720e7 −0.534712
\(210\) −8.70959e7 −0.648978
\(211\) −1.24225e8 −0.910379 −0.455189 0.890395i \(-0.650428\pi\)
−0.455189 + 0.890395i \(0.650428\pi\)
\(212\) 2.08214e7 0.150084
\(213\) −8.54006e7 −0.605525
\(214\) −2.30068e7 −0.160475
\(215\) −2.66622e7 −0.182962
\(216\) −6.28493e6 −0.0424338
\(217\) 2.49458e8 1.65725
\(218\) −2.51052e8 −1.64121
\(219\) −9.10443e7 −0.585731
\(220\) 8.91502e7 0.564473
\(221\) −4.43166e6 −0.0276181
\(222\) −1.94035e8 −1.19027
\(223\) −4.32331e6 −0.0261065 −0.0130533 0.999915i \(-0.504155\pi\)
−0.0130533 + 0.999915i \(0.504155\pi\)
\(224\) −2.95182e8 −1.75478
\(225\) −3.46281e7 −0.202670
\(226\) −2.90315e8 −1.67298
\(227\) −1.29928e8 −0.737244 −0.368622 0.929579i \(-0.620170\pi\)
−0.368622 + 0.929579i \(0.620170\pi\)
\(228\) 8.10952e7 0.453130
\(229\) −6.03820e7 −0.332264 −0.166132 0.986103i \(-0.553128\pi\)
−0.166132 + 0.986103i \(0.553128\pi\)
\(230\) 8.03821e7 0.435624
\(231\) −1.03789e8 −0.553998
\(232\) 4.53363e7 0.238362
\(233\) −2.38228e8 −1.23381 −0.616904 0.787038i \(-0.711613\pi\)
−0.616904 + 0.787038i \(0.711613\pi\)
\(234\) −4.45966e6 −0.0227534
\(235\) 7.86419e7 0.395291
\(236\) −3.02413e7 −0.149764
\(237\) 4.43640e7 0.216477
\(238\) 2.21541e8 1.06521
\(239\) −3.08535e7 −0.146188 −0.0730940 0.997325i \(-0.523287\pi\)
−0.0730940 + 0.997325i \(0.523287\pi\)
\(240\) 6.40231e7 0.298949
\(241\) 9.76207e6 0.0449244 0.0224622 0.999748i \(-0.492849\pi\)
0.0224622 + 0.999748i \(0.492849\pi\)
\(242\) −1.24715e8 −0.565674
\(243\) −1.43489e7 −0.0641500
\(244\) −7.68842e7 −0.338823
\(245\) 7.19120e7 0.312407
\(246\) −1.28117e8 −0.548701
\(247\) 7.52142e6 0.0317585
\(248\) 7.16912e7 0.298459
\(249\) 1.71808e8 0.705253
\(250\) −3.64730e8 −1.47632
\(251\) 2.04882e8 0.817798 0.408899 0.912580i \(-0.365913\pi\)
0.408899 + 0.912580i \(0.365913\pi\)
\(252\) 1.19265e8 0.469474
\(253\) 9.57882e7 0.371869
\(254\) −3.32232e8 −1.27211
\(255\) −5.67870e7 −0.214466
\(256\) 1.70553e8 0.635360
\(257\) −7.58629e7 −0.278781 −0.139391 0.990237i \(-0.544514\pi\)
−0.139391 + 0.990237i \(0.544514\pi\)
\(258\) 6.82477e7 0.247411
\(259\) 4.81280e8 1.72127
\(260\) −9.50145e6 −0.0335261
\(261\) 1.03506e8 0.360348
\(262\) 2.94911e8 1.01306
\(263\) −3.76186e8 −1.27514 −0.637569 0.770393i \(-0.720060\pi\)
−0.637569 + 0.770393i \(0.720060\pi\)
\(264\) −2.98276e7 −0.0997710
\(265\) 2.47456e7 0.0816842
\(266\) −3.76000e8 −1.22491
\(267\) −1.46619e8 −0.471413
\(268\) 2.78765e8 0.884640
\(269\) −5.43241e8 −1.70161 −0.850804 0.525483i \(-0.823885\pi\)
−0.850804 + 0.525483i \(0.823885\pi\)
\(270\) −5.71458e7 −0.176690
\(271\) 5.59119e8 1.70652 0.853261 0.521484i \(-0.174621\pi\)
0.853261 + 0.521484i \(0.174621\pi\)
\(272\) −1.62852e8 −0.490685
\(273\) 1.10616e7 0.0329040
\(274\) 7.26468e8 2.13349
\(275\) −1.64341e8 −0.476521
\(276\) −1.10071e8 −0.315132
\(277\) 4.08022e8 1.15346 0.576732 0.816933i \(-0.304328\pi\)
0.576732 + 0.816933i \(0.304328\pi\)
\(278\) −3.37259e8 −0.941472
\(279\) 1.63676e8 0.451200
\(280\) 6.20844e7 0.169017
\(281\) 3.46395e8 0.931321 0.465660 0.884964i \(-0.345817\pi\)
0.465660 + 0.884964i \(0.345817\pi\)
\(282\) −2.01301e8 −0.534533
\(283\) 1.32435e8 0.347337 0.173669 0.984804i \(-0.444438\pi\)
0.173669 + 0.984804i \(0.444438\pi\)
\(284\) 4.65738e8 1.20650
\(285\) 9.63791e7 0.246619
\(286\) −2.11651e7 −0.0534981
\(287\) 3.17779e8 0.793484
\(288\) −1.93676e8 −0.477753
\(289\) −2.65892e8 −0.647983
\(290\) 4.12221e8 0.992515
\(291\) 7.85844e7 0.186944
\(292\) 4.96516e8 1.16706
\(293\) −6.11894e8 −1.42115 −0.710574 0.703622i \(-0.751565\pi\)
−0.710574 + 0.703622i \(0.751565\pi\)
\(294\) −1.84075e8 −0.422453
\(295\) −3.59408e7 −0.0815101
\(296\) 1.38314e8 0.309988
\(297\) −6.80984e7 −0.150831
\(298\) 1.01993e9 2.23262
\(299\) −1.02089e7 −0.0220867
\(300\) 1.88847e8 0.403817
\(301\) −1.69279e8 −0.357785
\(302\) 1.01437e8 0.211921
\(303\) 3.25029e8 0.671233
\(304\) 2.76393e8 0.564248
\(305\) −9.13745e7 −0.184406
\(306\) 1.45359e8 0.290012
\(307\) 1.61294e8 0.318151 0.159075 0.987266i \(-0.449149\pi\)
0.159075 + 0.987266i \(0.449149\pi\)
\(308\) 5.66019e8 1.10383
\(309\) 1.21590e8 0.234447
\(310\) 6.51853e8 1.24275
\(311\) 5.52921e8 1.04232 0.521160 0.853459i \(-0.325499\pi\)
0.521160 + 0.853459i \(0.325499\pi\)
\(312\) 3.17897e6 0.00592577
\(313\) 3.45307e8 0.636503 0.318252 0.948006i \(-0.396904\pi\)
0.318252 + 0.948006i \(0.396904\pi\)
\(314\) 5.96611e8 1.08752
\(315\) 1.41743e8 0.255514
\(316\) −2.41942e8 −0.431327
\(317\) −5.61715e8 −0.990395 −0.495198 0.868780i \(-0.664904\pi\)
−0.495198 + 0.868780i \(0.664904\pi\)
\(318\) −6.33418e7 −0.110458
\(319\) 4.91227e8 0.847257
\(320\) −4.67817e8 −0.798088
\(321\) 3.74421e7 0.0631818
\(322\) 5.10350e8 0.851869
\(323\) −2.45154e8 −0.404791
\(324\) 7.82527e7 0.127818
\(325\) 1.75152e7 0.0283023
\(326\) −6.44461e8 −1.03023
\(327\) 4.08570e8 0.646173
\(328\) 9.13256e7 0.142901
\(329\) 4.99302e8 0.772996
\(330\) −2.71208e8 −0.415435
\(331\) −7.48834e8 −1.13498 −0.567489 0.823381i \(-0.692085\pi\)
−0.567489 + 0.823381i \(0.692085\pi\)
\(332\) −9.36965e8 −1.40521
\(333\) 3.15780e8 0.468629
\(334\) −1.40736e9 −2.06677
\(335\) 3.31304e8 0.481470
\(336\) 4.06486e8 0.584599
\(337\) 3.77520e8 0.537322 0.268661 0.963235i \(-0.413419\pi\)
0.268661 + 0.963235i \(0.413419\pi\)
\(338\) −1.03878e9 −1.46323
\(339\) 4.72468e8 0.658678
\(340\) 3.09692e8 0.427321
\(341\) 7.76787e8 1.06087
\(342\) −2.46703e8 −0.333491
\(343\) −4.58440e8 −0.613413
\(344\) −4.86488e7 −0.0644344
\(345\) −1.30817e8 −0.171512
\(346\) −3.38787e8 −0.439703
\(347\) 2.25075e8 0.289185 0.144592 0.989491i \(-0.453813\pi\)
0.144592 + 0.989491i \(0.453813\pi\)
\(348\) −5.64476e8 −0.717989
\(349\) 2.00272e8 0.252192 0.126096 0.992018i \(-0.459755\pi\)
0.126096 + 0.992018i \(0.459755\pi\)
\(350\) −8.75594e8 −1.09160
\(351\) 7.25779e6 0.00895838
\(352\) −9.19168e8 −1.12330
\(353\) −9.69527e6 −0.0117314 −0.00586568 0.999983i \(-0.501867\pi\)
−0.00586568 + 0.999983i \(0.501867\pi\)
\(354\) 9.19985e7 0.110222
\(355\) 5.53515e8 0.656645
\(356\) 7.99598e8 0.939284
\(357\) −3.60544e8 −0.419391
\(358\) −3.57487e8 −0.411784
\(359\) 1.59435e9 1.81867 0.909334 0.416067i \(-0.136592\pi\)
0.909334 + 0.416067i \(0.136592\pi\)
\(360\) 4.07351e7 0.0460161
\(361\) −4.77795e8 −0.534523
\(362\) −1.02729e9 −1.13818
\(363\) 2.02966e8 0.222715
\(364\) −6.03252e7 −0.0655607
\(365\) 5.90094e8 0.635179
\(366\) 2.33893e8 0.249364
\(367\) 4.36226e8 0.460660 0.230330 0.973113i \(-0.426019\pi\)
0.230330 + 0.973113i \(0.426019\pi\)
\(368\) −3.75152e8 −0.392410
\(369\) 2.08503e8 0.216032
\(370\) 1.25762e9 1.29075
\(371\) 1.57111e8 0.159734
\(372\) −8.92616e8 −0.899010
\(373\) 8.71065e8 0.869100 0.434550 0.900648i \(-0.356907\pi\)
0.434550 + 0.900648i \(0.356907\pi\)
\(374\) 6.89858e8 0.681882
\(375\) 5.93574e8 0.581253
\(376\) 1.43493e8 0.139211
\(377\) −5.23540e7 −0.0503217
\(378\) −3.62822e8 −0.345519
\(379\) 1.10371e9 1.04140 0.520702 0.853739i \(-0.325670\pi\)
0.520702 + 0.853739i \(0.325670\pi\)
\(380\) −5.25610e8 −0.491384
\(381\) 5.40685e8 0.500849
\(382\) −3.04029e9 −2.79057
\(383\) 3.23348e8 0.294086 0.147043 0.989130i \(-0.453024\pi\)
0.147043 + 0.989130i \(0.453024\pi\)
\(384\) 2.79309e8 0.251725
\(385\) 6.72696e8 0.600767
\(386\) −4.17541e8 −0.369525
\(387\) −1.11068e8 −0.0974098
\(388\) −4.28565e8 −0.372483
\(389\) 1.09065e9 0.939423 0.469711 0.882820i \(-0.344358\pi\)
0.469711 + 0.882820i \(0.344358\pi\)
\(390\) 2.89048e7 0.0246742
\(391\) 3.32751e8 0.281515
\(392\) 1.31213e8 0.110021
\(393\) −4.79948e8 −0.398859
\(394\) 6.82702e8 0.562334
\(395\) −2.87541e8 −0.234752
\(396\) 3.71379e8 0.300528
\(397\) −2.19755e9 −1.76268 −0.881338 0.472487i \(-0.843356\pi\)
−0.881338 + 0.472487i \(0.843356\pi\)
\(398\) 2.00533e9 1.59439
\(399\) 6.11915e8 0.482266
\(400\) 6.43638e8 0.502842
\(401\) −2.55403e9 −1.97797 −0.988987 0.148004i \(-0.952715\pi\)
−0.988987 + 0.148004i \(0.952715\pi\)
\(402\) −8.48044e8 −0.651069
\(403\) −8.27885e7 −0.0630089
\(404\) −1.77257e9 −1.33742
\(405\) 9.30009e7 0.0695656
\(406\) 2.61721e9 1.94087
\(407\) 1.49866e9 1.10185
\(408\) −1.03616e8 −0.0755293
\(409\) −2.88636e8 −0.208602 −0.104301 0.994546i \(-0.533261\pi\)
−0.104301 + 0.994546i \(0.533261\pi\)
\(410\) 8.30380e8 0.595022
\(411\) −1.18228e9 −0.839989
\(412\) −6.63101e8 −0.467132
\(413\) −2.28190e8 −0.159394
\(414\) 3.34854e8 0.231928
\(415\) −1.11355e9 −0.764791
\(416\) 9.79631e7 0.0667169
\(417\) 5.48867e8 0.370673
\(418\) −1.17083e9 −0.784108
\(419\) −5.30993e8 −0.352647 −0.176323 0.984332i \(-0.556420\pi\)
−0.176323 + 0.984332i \(0.556420\pi\)
\(420\) −7.73004e8 −0.509107
\(421\) −2.15095e9 −1.40489 −0.702445 0.711738i \(-0.747908\pi\)
−0.702445 + 0.711738i \(0.747908\pi\)
\(422\) −2.06097e9 −1.33499
\(423\) 3.27604e8 0.210454
\(424\) 4.51518e7 0.0287670
\(425\) −5.70892e8 −0.360739
\(426\) −1.41684e9 −0.887949
\(427\) −5.80141e8 −0.360609
\(428\) −2.04193e8 −0.125889
\(429\) 3.44447e7 0.0210631
\(430\) −4.42340e8 −0.268298
\(431\) −3.30976e8 −0.199125 −0.0995624 0.995031i \(-0.531744\pi\)
−0.0995624 + 0.995031i \(0.531744\pi\)
\(432\) 2.66706e8 0.159162
\(433\) 2.05100e9 1.21411 0.607056 0.794659i \(-0.292350\pi\)
0.607056 + 0.794659i \(0.292350\pi\)
\(434\) 4.13865e9 2.43021
\(435\) −6.70862e8 −0.390769
\(436\) −2.22816e9 −1.28749
\(437\) −5.64746e8 −0.323719
\(438\) −1.51047e9 −0.858922
\(439\) 1.57643e9 0.889299 0.444649 0.895705i \(-0.353328\pi\)
0.444649 + 0.895705i \(0.353328\pi\)
\(440\) 1.93324e8 0.108194
\(441\) 2.99569e8 0.166327
\(442\) −7.35237e7 −0.0404995
\(443\) 3.27614e8 0.179040 0.0895199 0.995985i \(-0.471467\pi\)
0.0895199 + 0.995985i \(0.471467\pi\)
\(444\) −1.72213e9 −0.933737
\(445\) 9.50297e8 0.511210
\(446\) −7.17261e7 −0.0382829
\(447\) −1.65987e9 −0.879020
\(448\) −2.97019e9 −1.56067
\(449\) −3.76746e7 −0.0196420 −0.00982101 0.999952i \(-0.503126\pi\)
−0.00982101 + 0.999952i \(0.503126\pi\)
\(450\) −5.74499e8 −0.297198
\(451\) 9.89531e8 0.507939
\(452\) −2.57664e9 −1.31241
\(453\) −1.65082e8 −0.0834367
\(454\) −2.15557e9 −1.08110
\(455\) −7.16946e7 −0.0356818
\(456\) 1.75857e8 0.0868525
\(457\) 1.95746e8 0.0959372 0.0479686 0.998849i \(-0.484725\pi\)
0.0479686 + 0.998849i \(0.484725\pi\)
\(458\) −1.00177e9 −0.487236
\(459\) −2.36562e8 −0.114183
\(460\) 7.13417e8 0.341736
\(461\) −1.06215e9 −0.504931 −0.252465 0.967606i \(-0.581241\pi\)
−0.252465 + 0.967606i \(0.581241\pi\)
\(462\) −1.72191e9 −0.812389
\(463\) 1.12424e9 0.526412 0.263206 0.964740i \(-0.415220\pi\)
0.263206 + 0.964740i \(0.415220\pi\)
\(464\) −1.92388e9 −0.894056
\(465\) −1.06085e9 −0.489291
\(466\) −3.95234e9 −1.80927
\(467\) −1.93669e9 −0.879936 −0.439968 0.898013i \(-0.645010\pi\)
−0.439968 + 0.898013i \(0.645010\pi\)
\(468\) −3.95809e7 −0.0178494
\(469\) 2.10346e9 0.941521
\(470\) 1.30471e9 0.579659
\(471\) −9.70945e8 −0.428175
\(472\) −6.55790e7 −0.0287057
\(473\) −5.27119e8 −0.229031
\(474\) 7.36024e8 0.317444
\(475\) 9.68919e8 0.414820
\(476\) 1.96625e9 0.835631
\(477\) 1.03085e8 0.0434890
\(478\) −5.11877e8 −0.214372
\(479\) 2.67237e9 1.11102 0.555510 0.831510i \(-0.312523\pi\)
0.555510 + 0.831510i \(0.312523\pi\)
\(480\) 1.25529e9 0.518085
\(481\) −1.59724e8 −0.0654428
\(482\) 1.61958e8 0.0658777
\(483\) −8.30561e8 −0.335395
\(484\) −1.10689e9 −0.443757
\(485\) −5.09337e8 −0.202726
\(486\) −2.38056e8 −0.0940703
\(487\) 9.86225e8 0.386923 0.193462 0.981108i \(-0.438029\pi\)
0.193462 + 0.981108i \(0.438029\pi\)
\(488\) −1.66725e8 −0.0649430
\(489\) 1.04882e9 0.405619
\(490\) 1.19306e9 0.458116
\(491\) −3.33799e9 −1.27262 −0.636312 0.771431i \(-0.719541\pi\)
−0.636312 + 0.771431i \(0.719541\pi\)
\(492\) −1.13708e9 −0.430442
\(493\) 1.70644e9 0.641395
\(494\) 1.24784e8 0.0465711
\(495\) 4.41373e8 0.163564
\(496\) −3.04227e9 −1.11947
\(497\) 3.51430e9 1.28408
\(498\) 2.85039e9 1.03419
\(499\) 4.31622e9 1.55508 0.777539 0.628835i \(-0.216468\pi\)
0.777539 + 0.628835i \(0.216468\pi\)
\(500\) −3.23710e9 −1.15814
\(501\) 2.29038e9 0.813720
\(502\) 3.39911e9 1.19923
\(503\) −3.79261e9 −1.32877 −0.664386 0.747389i \(-0.731307\pi\)
−0.664386 + 0.747389i \(0.731307\pi\)
\(504\) 2.58629e8 0.0899851
\(505\) −2.10664e9 −0.727899
\(506\) 1.58918e9 0.545313
\(507\) 1.69054e9 0.576099
\(508\) −2.94866e9 −0.997934
\(509\) 1.85516e9 0.623548 0.311774 0.950156i \(-0.399077\pi\)
0.311774 + 0.950156i \(0.399077\pi\)
\(510\) −9.42128e8 −0.314496
\(511\) 3.74653e9 1.24210
\(512\) 4.15370e9 1.36770
\(513\) 4.01493e8 0.131301
\(514\) −1.25861e9 −0.408808
\(515\) −7.88075e8 −0.254239
\(516\) 6.05720e8 0.194088
\(517\) 1.55477e9 0.494824
\(518\) 7.98470e9 2.52409
\(519\) 5.51352e8 0.173118
\(520\) −2.06041e7 −0.00642603
\(521\) −2.97325e8 −0.0921083 −0.0460542 0.998939i \(-0.514665\pi\)
−0.0460542 + 0.998939i \(0.514665\pi\)
\(522\) 1.71722e9 0.528419
\(523\) 2.48461e9 0.759456 0.379728 0.925098i \(-0.376018\pi\)
0.379728 + 0.925098i \(0.376018\pi\)
\(524\) 2.61743e9 0.794722
\(525\) 1.42497e9 0.429782
\(526\) −6.24113e9 −1.86988
\(527\) 2.69842e9 0.803106
\(528\) 1.26576e9 0.374224
\(529\) −2.63829e9 −0.774867
\(530\) 4.10544e8 0.119783
\(531\) −1.49721e8 −0.0433963
\(532\) −3.33712e9 −0.960907
\(533\) −1.05462e8 −0.0301684
\(534\) −2.43249e9 −0.691285
\(535\) −2.42677e8 −0.0685157
\(536\) 6.04509e8 0.169561
\(537\) 5.81786e8 0.162126
\(538\) −9.01267e9 −2.49526
\(539\) 1.42172e9 0.391070
\(540\) −5.07187e8 −0.138609
\(541\) −4.16187e9 −1.13005 −0.565026 0.825073i \(-0.691134\pi\)
−0.565026 + 0.825073i \(0.691134\pi\)
\(542\) 9.27610e9 2.50246
\(543\) 1.67184e9 0.448121
\(544\) −3.19303e9 −0.850367
\(545\) −2.64810e9 −0.700724
\(546\) 1.83518e8 0.0482508
\(547\) 6.75557e9 1.76484 0.882422 0.470459i \(-0.155912\pi\)
0.882422 + 0.470459i \(0.155912\pi\)
\(548\) 6.44764e9 1.67367
\(549\) −3.80645e8 −0.0981786
\(550\) −2.72651e9 −0.698776
\(551\) −2.89617e9 −0.737552
\(552\) −2.38693e8 −0.0604022
\(553\) −1.82561e9 −0.459061
\(554\) 6.76931e9 1.69145
\(555\) −2.04669e9 −0.508191
\(556\) −2.99328e9 −0.738560
\(557\) 3.44498e9 0.844681 0.422341 0.906437i \(-0.361209\pi\)
0.422341 + 0.906437i \(0.361209\pi\)
\(558\) 2.71547e9 0.661645
\(559\) 5.61793e7 0.0136030
\(560\) −2.63460e9 −0.633951
\(561\) −1.12270e9 −0.268468
\(562\) 5.74688e9 1.36570
\(563\) −2.05492e9 −0.485306 −0.242653 0.970113i \(-0.578018\pi\)
−0.242653 + 0.970113i \(0.578018\pi\)
\(564\) −1.78661e9 −0.419327
\(565\) −3.06225e9 −0.714284
\(566\) 2.19717e9 0.509339
\(567\) 5.90468e8 0.136036
\(568\) 1.00996e9 0.231253
\(569\) 7.09854e8 0.161538 0.0807692 0.996733i \(-0.474262\pi\)
0.0807692 + 0.996733i \(0.474262\pi\)
\(570\) 1.59898e9 0.361644
\(571\) −3.56358e7 −0.00801051 −0.00400525 0.999992i \(-0.501275\pi\)
−0.00400525 + 0.999992i \(0.501275\pi\)
\(572\) −1.87847e8 −0.0419679
\(573\) 4.94787e9 1.09869
\(574\) 5.27212e9 1.16357
\(575\) −1.31513e9 −0.288490
\(576\) −1.94882e9 −0.424905
\(577\) −1.37806e9 −0.298644 −0.149322 0.988789i \(-0.547709\pi\)
−0.149322 + 0.988789i \(0.547709\pi\)
\(578\) −4.41130e9 −0.950209
\(579\) 6.79520e8 0.145488
\(580\) 3.65859e9 0.778602
\(581\) −7.07001e9 −1.49556
\(582\) 1.30376e9 0.274136
\(583\) 4.89228e8 0.102252
\(584\) 1.07671e9 0.223693
\(585\) −4.70406e7 −0.00971466
\(586\) −1.01517e10 −2.08399
\(587\) 2.82850e9 0.577195 0.288597 0.957451i \(-0.406811\pi\)
0.288597 + 0.957451i \(0.406811\pi\)
\(588\) −1.63372e9 −0.331403
\(589\) −4.57977e9 −0.923506
\(590\) −5.96278e8 −0.119527
\(591\) −1.11105e9 −0.221400
\(592\) −5.86945e9 −1.16271
\(593\) −4.23981e9 −0.834940 −0.417470 0.908691i \(-0.637083\pi\)
−0.417470 + 0.908691i \(0.637083\pi\)
\(594\) −1.12979e9 −0.221180
\(595\) 2.33683e9 0.454797
\(596\) 9.05224e9 1.75143
\(597\) −3.26354e9 −0.627739
\(598\) −1.69372e8 −0.0323882
\(599\) −7.47951e9 −1.42193 −0.710967 0.703225i \(-0.751742\pi\)
−0.710967 + 0.703225i \(0.751742\pi\)
\(600\) 4.09519e8 0.0774006
\(601\) 2.42694e9 0.456034 0.228017 0.973657i \(-0.426776\pi\)
0.228017 + 0.973657i \(0.426776\pi\)
\(602\) −2.80844e9 −0.524659
\(603\) 1.38013e9 0.256337
\(604\) 9.00288e8 0.166246
\(605\) −1.31550e9 −0.241517
\(606\) 5.39241e9 0.984304
\(607\) −6.09411e9 −1.10599 −0.552993 0.833186i \(-0.686514\pi\)
−0.552993 + 0.833186i \(0.686514\pi\)
\(608\) 5.41921e9 0.977852
\(609\) −4.25933e9 −0.764154
\(610\) −1.51595e9 −0.270415
\(611\) −1.65705e8 −0.0293894
\(612\) 1.29011e9 0.227507
\(613\) −6.89396e9 −1.20881 −0.604403 0.796678i \(-0.706588\pi\)
−0.604403 + 0.796678i \(0.706588\pi\)
\(614\) 2.67595e9 0.466540
\(615\) −1.35139e9 −0.234270
\(616\) 1.22743e9 0.211574
\(617\) −1.05989e10 −1.81661 −0.908304 0.418311i \(-0.862622\pi\)
−0.908304 + 0.418311i \(0.862622\pi\)
\(618\) 2.01725e9 0.343795
\(619\) 7.11095e9 1.20507 0.602533 0.798094i \(-0.294158\pi\)
0.602533 + 0.798094i \(0.294158\pi\)
\(620\) 5.78540e9 0.974905
\(621\) −5.44951e8 −0.0913140
\(622\) 9.17326e9 1.52847
\(623\) 6.03349e9 0.999678
\(624\) −1.34902e8 −0.0222265
\(625\) −1.36187e8 −0.0223130
\(626\) 5.72884e9 0.933375
\(627\) 1.90544e9 0.308716
\(628\) 5.29511e9 0.853133
\(629\) 5.20607e9 0.834128
\(630\) 2.35159e9 0.374688
\(631\) −3.97705e9 −0.630170 −0.315085 0.949063i \(-0.602033\pi\)
−0.315085 + 0.949063i \(0.602033\pi\)
\(632\) −5.24658e8 −0.0826735
\(633\) 3.35409e9 0.525607
\(634\) −9.31916e9 −1.45233
\(635\) −3.50439e9 −0.543131
\(636\) −5.62179e8 −0.0866512
\(637\) −1.51524e8 −0.0232271
\(638\) 8.14973e9 1.24243
\(639\) 2.30582e9 0.349600
\(640\) −1.81031e9 −0.272976
\(641\) 5.39534e8 0.0809125 0.0404563 0.999181i \(-0.487119\pi\)
0.0404563 + 0.999181i \(0.487119\pi\)
\(642\) 6.21185e8 0.0926506
\(643\) 6.57420e8 0.0975225 0.0487612 0.998810i \(-0.484473\pi\)
0.0487612 + 0.998810i \(0.484473\pi\)
\(644\) 4.52952e9 0.668269
\(645\) 7.19879e8 0.105633
\(646\) −4.06725e9 −0.593590
\(647\) −2.49688e9 −0.362437 −0.181219 0.983443i \(-0.558004\pi\)
−0.181219 + 0.983443i \(0.558004\pi\)
\(648\) 1.69693e8 0.0244992
\(649\) −7.10561e8 −0.102034
\(650\) 2.90586e8 0.0415029
\(651\) −6.73537e9 −0.956815
\(652\) −5.71979e9 −0.808191
\(653\) −9.29237e9 −1.30596 −0.652981 0.757374i \(-0.726482\pi\)
−0.652981 + 0.757374i \(0.726482\pi\)
\(654\) 6.77840e9 0.947556
\(655\) 3.11073e9 0.432532
\(656\) −3.87547e9 −0.535995
\(657\) 2.45819e9 0.338172
\(658\) 8.28369e9 1.13353
\(659\) −6.58505e9 −0.896315 −0.448157 0.893955i \(-0.647920\pi\)
−0.448157 + 0.893955i \(0.647920\pi\)
\(660\) −2.40706e9 −0.325898
\(661\) −3.64989e9 −0.491558 −0.245779 0.969326i \(-0.579044\pi\)
−0.245779 + 0.969326i \(0.579044\pi\)
\(662\) −1.24236e10 −1.66434
\(663\) 1.19655e8 0.0159453
\(664\) −2.03183e9 −0.269339
\(665\) −3.96607e9 −0.522979
\(666\) 5.23896e9 0.687203
\(667\) 3.93100e9 0.512936
\(668\) −1.24907e10 −1.62132
\(669\) 1.16729e8 0.0150726
\(670\) 5.49651e9 0.706033
\(671\) −1.80650e9 −0.230839
\(672\) 7.96992e9 1.01312
\(673\) 7.02119e9 0.887887 0.443944 0.896055i \(-0.353579\pi\)
0.443944 + 0.896055i \(0.353579\pi\)
\(674\) 6.26326e9 0.787936
\(675\) 9.34958e8 0.117012
\(676\) −9.21947e9 −1.14787
\(677\) 8.84175e9 1.09516 0.547580 0.836753i \(-0.315549\pi\)
0.547580 + 0.836753i \(0.315549\pi\)
\(678\) 7.83850e9 0.965893
\(679\) −3.23380e9 −0.396433
\(680\) 6.71575e8 0.0819055
\(681\) 3.50805e9 0.425648
\(682\) 1.28873e10 1.55567
\(683\) 3.28325e9 0.394304 0.197152 0.980373i \(-0.436831\pi\)
0.197152 + 0.980373i \(0.436831\pi\)
\(684\) −2.18957e9 −0.261615
\(685\) 7.66281e9 0.910901
\(686\) −7.60577e9 −0.899516
\(687\) 1.63032e9 0.191833
\(688\) 2.06445e9 0.241682
\(689\) −5.21410e7 −0.00607312
\(690\) −2.17032e9 −0.251508
\(691\) 3.72206e9 0.429151 0.214576 0.976707i \(-0.431163\pi\)
0.214576 + 0.976707i \(0.431163\pi\)
\(692\) −3.00684e9 −0.344936
\(693\) 2.80230e9 0.319851
\(694\) 3.73413e9 0.424063
\(695\) −3.55742e9 −0.401965
\(696\) −1.22408e9 −0.137619
\(697\) 3.43745e9 0.384523
\(698\) 3.32263e9 0.369818
\(699\) 6.43216e9 0.712339
\(700\) −7.77117e9 −0.856334
\(701\) 2.70122e9 0.296174 0.148087 0.988974i \(-0.452688\pi\)
0.148087 + 0.988974i \(0.452688\pi\)
\(702\) 1.20411e8 0.0131367
\(703\) −8.83575e9 −0.959179
\(704\) −9.24887e9 −0.999044
\(705\) −2.12333e9 −0.228221
\(706\) −1.60850e8 −0.0172030
\(707\) −1.33752e10 −1.42342
\(708\) 8.16515e8 0.0864665
\(709\) 4.56678e8 0.0481225 0.0240613 0.999710i \(-0.492340\pi\)
0.0240613 + 0.999710i \(0.492340\pi\)
\(710\) 9.18312e9 0.962911
\(711\) −1.19783e9 −0.124983
\(712\) 1.73395e9 0.180035
\(713\) 6.21617e9 0.642258
\(714\) −5.98162e9 −0.615000
\(715\) −2.23250e8 −0.0228412
\(716\) −3.17281e9 −0.323034
\(717\) 8.33045e8 0.0844017
\(718\) 2.64512e10 2.66692
\(719\) 4.28395e9 0.429827 0.214913 0.976633i \(-0.431053\pi\)
0.214913 + 0.976633i \(0.431053\pi\)
\(720\) −1.72862e9 −0.172598
\(721\) −5.00352e9 −0.497167
\(722\) −7.92689e9 −0.783831
\(723\) −2.63576e8 −0.0259371
\(724\) −9.11749e9 −0.892874
\(725\) −6.74432e9 −0.657287
\(726\) 3.36732e9 0.326592
\(727\) 9.46884e9 0.913958 0.456979 0.889477i \(-0.348931\pi\)
0.456979 + 0.889477i \(0.348931\pi\)
\(728\) −1.30817e8 −0.0125662
\(729\) 3.87420e8 0.0370370
\(730\) 9.78998e9 0.931433
\(731\) −1.83112e9 −0.173383
\(732\) 2.07587e9 0.195619
\(733\) −7.31501e9 −0.686043 −0.343021 0.939328i \(-0.611450\pi\)
−0.343021 + 0.939328i \(0.611450\pi\)
\(734\) 7.23723e9 0.675517
\(735\) −1.94162e9 −0.180368
\(736\) −7.35556e9 −0.680054
\(737\) 6.54997e9 0.602703
\(738\) 3.45917e9 0.316792
\(739\) −9.28262e9 −0.846087 −0.423043 0.906109i \(-0.639038\pi\)
−0.423043 + 0.906109i \(0.639038\pi\)
\(740\) 1.11618e10 1.01256
\(741\) −2.03078e8 −0.0183358
\(742\) 2.60656e9 0.234236
\(743\) −8.15117e9 −0.729053 −0.364526 0.931193i \(-0.618769\pi\)
−0.364526 + 0.931193i \(0.618769\pi\)
\(744\) −1.93566e9 −0.172315
\(745\) 1.07583e10 0.953228
\(746\) 1.44515e10 1.27446
\(747\) −4.63881e9 −0.407178
\(748\) 6.12270e9 0.534919
\(749\) −1.54077e9 −0.133983
\(750\) 9.84772e9 0.852357
\(751\) −1.21007e10 −1.04248 −0.521242 0.853409i \(-0.674531\pi\)
−0.521242 + 0.853409i \(0.674531\pi\)
\(752\) −6.08923e9 −0.522156
\(753\) −5.53182e9 −0.472156
\(754\) −8.68582e8 −0.0737923
\(755\) 1.06996e9 0.0904805
\(756\) −3.22016e9 −0.271051
\(757\) −2.15810e10 −1.80816 −0.904078 0.427367i \(-0.859441\pi\)
−0.904078 + 0.427367i \(0.859441\pi\)
\(758\) 1.83112e10 1.52713
\(759\) −2.58628e9 −0.214699
\(760\) −1.13980e9 −0.0941847
\(761\) 2.06853e9 0.170144 0.0850719 0.996375i \(-0.472888\pi\)
0.0850719 + 0.996375i \(0.472888\pi\)
\(762\) 8.97025e9 0.734450
\(763\) −1.68129e10 −1.37027
\(764\) −2.69835e10 −2.18913
\(765\) 1.53325e9 0.123822
\(766\) 5.36452e9 0.431251
\(767\) 7.57302e7 0.00606018
\(768\) −4.60494e9 −0.366825
\(769\) 1.90437e10 1.51011 0.755055 0.655662i \(-0.227610\pi\)
0.755055 + 0.655662i \(0.227610\pi\)
\(770\) 1.11604e10 0.880972
\(771\) 2.04830e9 0.160954
\(772\) −3.70581e9 −0.289883
\(773\) 7.43503e9 0.578968 0.289484 0.957183i \(-0.406516\pi\)
0.289484 + 0.957183i \(0.406516\pi\)
\(774\) −1.84269e9 −0.142843
\(775\) −1.06649e10 −0.823003
\(776\) −9.29355e8 −0.0713946
\(777\) −1.29946e10 −0.993774
\(778\) 1.80945e10 1.37758
\(779\) −5.83405e9 −0.442170
\(780\) 2.56539e8 0.0193563
\(781\) 1.09432e10 0.821986
\(782\) 5.52053e9 0.412816
\(783\) −2.79465e9 −0.208047
\(784\) −5.56814e9 −0.412671
\(785\) 6.29308e9 0.464322
\(786\) −7.96259e9 −0.584892
\(787\) 9.17424e9 0.670901 0.335451 0.942058i \(-0.391111\pi\)
0.335451 + 0.942058i \(0.391111\pi\)
\(788\) 6.05920e9 0.441137
\(789\) 1.01570e10 0.736201
\(790\) −4.77046e9 −0.344243
\(791\) −1.94424e10 −1.39679
\(792\) 8.05345e8 0.0576028
\(793\) 1.92533e8 0.0137104
\(794\) −3.64586e10 −2.58481
\(795\) −6.68132e8 −0.0471604
\(796\) 1.77979e10 1.25076
\(797\) −2.11317e10 −1.47853 −0.739265 0.673415i \(-0.764827\pi\)
−0.739265 + 0.673415i \(0.764827\pi\)
\(798\) 1.01520e10 0.707200
\(799\) 5.40101e9 0.374594
\(800\) 1.26197e10 0.871436
\(801\) 3.95872e9 0.272170
\(802\) −4.23727e10 −2.90052
\(803\) 1.16663e10 0.795115
\(804\) −7.52666e9 −0.510747
\(805\) 5.38319e9 0.363709
\(806\) −1.37351e9 −0.0923970
\(807\) 1.46675e10 0.982424
\(808\) −3.84386e9 −0.256347
\(809\) −2.83173e9 −0.188032 −0.0940161 0.995571i \(-0.529971\pi\)
−0.0940161 + 0.995571i \(0.529971\pi\)
\(810\) 1.54294e9 0.102012
\(811\) 2.43178e10 1.60085 0.800427 0.599430i \(-0.204606\pi\)
0.800427 + 0.599430i \(0.204606\pi\)
\(812\) 2.32286e10 1.52257
\(813\) −1.50962e10 −0.985261
\(814\) 2.48635e10 1.61576
\(815\) −6.79780e9 −0.439862
\(816\) 4.39701e9 0.283297
\(817\) 3.10778e9 0.199376
\(818\) −4.78863e9 −0.305897
\(819\) −2.98663e8 −0.0189971
\(820\) 7.36988e9 0.466780
\(821\) −2.00983e10 −1.26753 −0.633765 0.773525i \(-0.718491\pi\)
−0.633765 + 0.773525i \(0.718491\pi\)
\(822\) −1.96146e10 −1.23177
\(823\) 1.63406e10 1.02180 0.510902 0.859639i \(-0.329312\pi\)
0.510902 + 0.859639i \(0.329312\pi\)
\(824\) −1.43795e9 −0.0895362
\(825\) 4.43721e9 0.275120
\(826\) −3.78580e9 −0.233737
\(827\) −9.17251e9 −0.563922 −0.281961 0.959426i \(-0.590985\pi\)
−0.281961 + 0.959426i \(0.590985\pi\)
\(828\) 2.97193e9 0.181942
\(829\) −2.43239e10 −1.48283 −0.741417 0.671045i \(-0.765846\pi\)
−0.741417 + 0.671045i \(0.765846\pi\)
\(830\) −1.84745e10 −1.12150
\(831\) −1.10166e10 −0.665953
\(832\) 9.85727e8 0.0593369
\(833\) 4.93881e9 0.296050
\(834\) 9.10600e9 0.543559
\(835\) −1.48448e10 −0.882415
\(836\) −1.03915e10 −0.615113
\(837\) −4.41924e9 −0.260501
\(838\) −8.80946e9 −0.517125
\(839\) 1.35860e9 0.0794193 0.0397096 0.999211i \(-0.487357\pi\)
0.0397096 + 0.999211i \(0.487357\pi\)
\(840\) −1.67628e9 −0.0975817
\(841\) 2.90934e9 0.168659
\(842\) −3.56854e10 −2.06015
\(843\) −9.35266e9 −0.537698
\(844\) −1.82917e10 −1.04726
\(845\) −1.09571e10 −0.624734
\(846\) 5.43513e9 0.308613
\(847\) −8.35219e9 −0.472290
\(848\) −1.91605e9 −0.107900
\(849\) −3.57575e9 −0.200535
\(850\) −9.47142e9 −0.528992
\(851\) 1.19929e10 0.667067
\(852\) −1.25749e10 −0.696574
\(853\) −1.40851e10 −0.777031 −0.388516 0.921442i \(-0.627012\pi\)
−0.388516 + 0.921442i \(0.627012\pi\)
\(854\) −9.62486e9 −0.528800
\(855\) −2.60223e9 −0.142385
\(856\) −4.42797e8 −0.0241294
\(857\) 2.25854e10 1.22573 0.612865 0.790188i \(-0.290017\pi\)
0.612865 + 0.790188i \(0.290017\pi\)
\(858\) 5.71457e8 0.0308871
\(859\) 3.28621e10 1.76897 0.884483 0.466572i \(-0.154511\pi\)
0.884483 + 0.466572i \(0.154511\pi\)
\(860\) −3.92591e9 −0.210473
\(861\) −8.58002e9 −0.458118
\(862\) −5.49107e9 −0.291999
\(863\) −7.68268e9 −0.406888 −0.203444 0.979087i \(-0.565213\pi\)
−0.203444 + 0.979087i \(0.565213\pi\)
\(864\) 5.22926e9 0.275831
\(865\) −3.57353e9 −0.187733
\(866\) 3.40273e10 1.78039
\(867\) 7.17909e9 0.374113
\(868\) 3.67318e10 1.90644
\(869\) −5.68477e9 −0.293862
\(870\) −1.11300e10 −0.573029
\(871\) −6.98083e8 −0.0357967
\(872\) −4.83183e9 −0.246776
\(873\) −2.12178e9 −0.107932
\(874\) −9.36945e9 −0.474705
\(875\) −2.44260e10 −1.23261
\(876\) −1.34059e10 −0.673803
\(877\) 3.95364e10 1.97924 0.989621 0.143702i \(-0.0459008\pi\)
0.989621 + 0.143702i \(0.0459008\pi\)
\(878\) 2.61538e10 1.30408
\(879\) 1.65211e10 0.820500
\(880\) −8.20387e9 −0.405816
\(881\) 1.90800e10 0.940074 0.470037 0.882647i \(-0.344241\pi\)
0.470037 + 0.882647i \(0.344241\pi\)
\(882\) 4.97001e9 0.243903
\(883\) −4.60772e9 −0.225228 −0.112614 0.993639i \(-0.535922\pi\)
−0.112614 + 0.993639i \(0.535922\pi\)
\(884\) −6.52546e8 −0.0317708
\(885\) 9.70403e8 0.0470599
\(886\) 5.43530e9 0.262546
\(887\) −1.44107e10 −0.693349 −0.346674 0.937986i \(-0.612689\pi\)
−0.346674 + 0.937986i \(0.612689\pi\)
\(888\) −3.73447e9 −0.178972
\(889\) −2.22495e10 −1.06210
\(890\) 1.57660e10 0.749644
\(891\) 1.83866e9 0.0870820
\(892\) −6.36591e8 −0.0300320
\(893\) −9.16660e9 −0.430753
\(894\) −2.75382e10 −1.28901
\(895\) −3.77078e9 −0.175813
\(896\) −1.14938e10 −0.533807
\(897\) 2.75641e8 0.0127518
\(898\) −6.25042e8 −0.0288033
\(899\) 3.18782e10 1.46330
\(900\) −5.09886e9 −0.233144
\(901\) 1.69949e9 0.0774074
\(902\) 1.64169e10 0.744847
\(903\) 4.57055e9 0.206567
\(904\) −5.58750e9 −0.251552
\(905\) −1.08358e10 −0.485951
\(906\) −2.73881e9 −0.122353
\(907\) 3.03408e10 1.35021 0.675105 0.737721i \(-0.264098\pi\)
0.675105 + 0.737721i \(0.264098\pi\)
\(908\) −1.91314e10 −0.848098
\(909\) −8.77579e9 −0.387537
\(910\) −1.18945e9 −0.0523242
\(911\) −3.82951e9 −0.167814 −0.0839072 0.996474i \(-0.526740\pi\)
−0.0839072 + 0.996474i \(0.526740\pi\)
\(912\) −7.46262e9 −0.325769
\(913\) −2.20153e10 −0.957363
\(914\) 3.24754e9 0.140683
\(915\) 2.46711e9 0.106467
\(916\) −8.89104e9 −0.382224
\(917\) 1.97502e10 0.845821
\(918\) −3.92469e9 −0.167439
\(919\) 2.78817e10 1.18499 0.592495 0.805574i \(-0.298143\pi\)
0.592495 + 0.805574i \(0.298143\pi\)
\(920\) 1.54706e9 0.0655014
\(921\) −4.35493e9 −0.183684
\(922\) −1.76216e10 −0.740436
\(923\) −1.16630e9 −0.0488208
\(924\) −1.52825e10 −0.637299
\(925\) −2.05758e10 −0.854794
\(926\) 1.86518e10 0.771936
\(927\) −3.28294e9 −0.135358
\(928\) −3.77212e10 −1.54942
\(929\) 1.44369e10 0.590770 0.295385 0.955378i \(-0.404552\pi\)
0.295385 + 0.955378i \(0.404552\pi\)
\(930\) −1.76000e10 −0.717502
\(931\) −8.38216e9 −0.340433
\(932\) −3.50782e10 −1.41933
\(933\) −1.49289e10 −0.601784
\(934\) −3.21308e10 −1.29035
\(935\) 7.27664e9 0.291132
\(936\) −8.58321e7 −0.00342125
\(937\) −3.25299e10 −1.29180 −0.645898 0.763424i \(-0.723517\pi\)
−0.645898 + 0.763424i \(0.723517\pi\)
\(938\) 3.48976e10 1.38066
\(939\) −9.32330e9 −0.367485
\(940\) 1.15797e10 0.454727
\(941\) −1.74946e9 −0.0684448 −0.0342224 0.999414i \(-0.510895\pi\)
−0.0342224 + 0.999414i \(0.510895\pi\)
\(942\) −1.61085e10 −0.627881
\(943\) 7.91863e9 0.307510
\(944\) 2.78290e9 0.107670
\(945\) −3.82705e9 −0.147521
\(946\) −8.74520e9 −0.335854
\(947\) −2.65135e10 −1.01448 −0.507239 0.861805i \(-0.669334\pi\)
−0.507239 + 0.861805i \(0.669334\pi\)
\(948\) 6.53244e9 0.249027
\(949\) −1.24337e9 −0.0472248
\(950\) 1.60749e10 0.608297
\(951\) 1.51663e10 0.571805
\(952\) 4.26386e9 0.160167
\(953\) 3.31597e10 1.24104 0.620519 0.784191i \(-0.286922\pi\)
0.620519 + 0.784191i \(0.286922\pi\)
\(954\) 1.71023e9 0.0637727
\(955\) −3.20691e10 −1.19145
\(956\) −4.54307e9 −0.168169
\(957\) −1.32631e10 −0.489164
\(958\) 4.43361e10 1.62921
\(959\) 4.86516e10 1.78128
\(960\) 1.26310e10 0.460776
\(961\) 2.28970e10 0.832236
\(962\) −2.64991e9 −0.0959661
\(963\) −1.01094e9 −0.0364780
\(964\) 1.43743e9 0.0516793
\(965\) −4.40424e9 −0.157770
\(966\) −1.37795e10 −0.491827
\(967\) 1.58334e9 0.0563095 0.0281547 0.999604i \(-0.491037\pi\)
0.0281547 + 0.999604i \(0.491037\pi\)
\(968\) −2.40032e9 −0.0850559
\(969\) 6.61917e9 0.233706
\(970\) −8.45017e9 −0.297279
\(971\) −7.55884e9 −0.264965 −0.132482 0.991185i \(-0.542295\pi\)
−0.132482 + 0.991185i \(0.542295\pi\)
\(972\) −2.11282e9 −0.0737958
\(973\) −2.25863e10 −0.786048
\(974\) 1.63620e10 0.567388
\(975\) −4.72909e8 −0.0163404
\(976\) 7.07511e9 0.243590
\(977\) 1.24479e9 0.0427036 0.0213518 0.999772i \(-0.493203\pi\)
0.0213518 + 0.999772i \(0.493203\pi\)
\(978\) 1.74004e10 0.594805
\(979\) 1.87877e10 0.639931
\(980\) 1.05888e10 0.359381
\(981\) −1.10314e10 −0.373068
\(982\) −5.53792e10 −1.86619
\(983\) 1.03091e10 0.346166 0.173083 0.984907i \(-0.444627\pi\)
0.173083 + 0.984907i \(0.444627\pi\)
\(984\) −2.46579e9 −0.0825037
\(985\) 7.20117e9 0.240091
\(986\) 2.83107e10 0.940550
\(987\) −1.34811e10 −0.446289
\(988\) 1.10750e9 0.0365338
\(989\) −4.21823e9 −0.138657
\(990\) 7.32261e9 0.239852
\(991\) −1.42062e10 −0.463683 −0.231842 0.972754i \(-0.574475\pi\)
−0.231842 + 0.972754i \(0.574475\pi\)
\(992\) −5.96494e10 −1.94006
\(993\) 2.02185e10 0.655280
\(994\) 5.83041e10 1.88298
\(995\) 2.11523e10 0.680733
\(996\) 2.52981e10 0.811296
\(997\) 8.79297e9 0.280998 0.140499 0.990081i \(-0.455129\pi\)
0.140499 + 0.990081i \(0.455129\pi\)
\(998\) 7.16085e10 2.28038
\(999\) −8.52605e9 −0.270563
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.8.a.c.1.15 17
3.2 odd 2 531.8.a.c.1.3 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.8.a.c.1.15 17 1.1 even 1 trivial
531.8.a.c.1.3 17 3.2 odd 2