Properties

Label 177.6.a.a.1.1
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-9.21944\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.2194 q^{2} +9.00000 q^{3} +72.4370 q^{4} -99.2561 q^{5} -91.9750 q^{6} +109.985 q^{7} -413.244 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-10.2194 q^{2} +9.00000 q^{3} +72.4370 q^{4} -99.2561 q^{5} -91.9750 q^{6} +109.985 q^{7} -413.244 q^{8} +81.0000 q^{9} +1014.34 q^{10} -193.795 q^{11} +651.933 q^{12} +577.502 q^{13} -1123.98 q^{14} -893.304 q^{15} +1905.14 q^{16} -332.271 q^{17} -827.775 q^{18} -2111.75 q^{19} -7189.82 q^{20} +989.862 q^{21} +1980.48 q^{22} +3186.50 q^{23} -3719.20 q^{24} +6726.76 q^{25} -5901.75 q^{26} +729.000 q^{27} +7966.96 q^{28} +6111.58 q^{29} +9129.08 q^{30} -2024.27 q^{31} -6245.66 q^{32} -1744.16 q^{33} +3395.63 q^{34} -10916.6 q^{35} +5867.40 q^{36} +3581.82 q^{37} +21580.9 q^{38} +5197.52 q^{39} +41017.0 q^{40} +4115.68 q^{41} -10115.8 q^{42} -23103.3 q^{43} -14038.0 q^{44} -8039.74 q^{45} -32564.3 q^{46} -6685.33 q^{47} +17146.3 q^{48} -4710.38 q^{49} -68743.8 q^{50} -2990.44 q^{51} +41832.5 q^{52} +18280.2 q^{53} -7449.98 q^{54} +19235.4 q^{55} -45450.5 q^{56} -19005.8 q^{57} -62457.0 q^{58} +3481.00 q^{59} -64708.3 q^{60} -14865.7 q^{61} +20686.9 q^{62} +8908.76 q^{63} +2862.70 q^{64} -57320.5 q^{65} +17824.3 q^{66} -10836.8 q^{67} -24068.8 q^{68} +28678.5 q^{69} +111562. q^{70} -80021.9 q^{71} -33472.8 q^{72} -22189.8 q^{73} -36604.2 q^{74} +60540.9 q^{75} -152969. q^{76} -21314.5 q^{77} -53115.7 q^{78} -57520.3 q^{79} -189097. q^{80} +6561.00 q^{81} -42060.0 q^{82} -98908.2 q^{83} +71702.7 q^{84} +32979.9 q^{85} +236103. q^{86} +55004.2 q^{87} +80084.8 q^{88} -91785.6 q^{89} +82161.7 q^{90} +63516.3 q^{91} +230821. q^{92} -18218.4 q^{93} +68320.4 q^{94} +209604. q^{95} -56211.0 q^{96} +49151.1 q^{97} +48137.5 q^{98} -15697.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.2194 −1.80656 −0.903280 0.429052i \(-0.858848\pi\)
−0.903280 + 0.429052i \(0.858848\pi\)
\(3\) 9.00000 0.577350
\(4\) 72.4370 2.26366
\(5\) −99.2561 −1.77555 −0.887773 0.460281i \(-0.847749\pi\)
−0.887773 + 0.460281i \(0.847749\pi\)
\(6\) −91.9750 −1.04302
\(7\) 109.985 0.848373 0.424187 0.905575i \(-0.360560\pi\)
0.424187 + 0.905575i \(0.360560\pi\)
\(8\) −413.244 −2.28287
\(9\) 81.0000 0.333333
\(10\) 1014.34 3.20763
\(11\) −193.795 −0.482905 −0.241453 0.970413i \(-0.577624\pi\)
−0.241453 + 0.970413i \(0.577624\pi\)
\(12\) 651.933 1.30692
\(13\) 577.502 0.947752 0.473876 0.880591i \(-0.342854\pi\)
0.473876 + 0.880591i \(0.342854\pi\)
\(14\) −1123.98 −1.53264
\(15\) −893.304 −1.02511
\(16\) 1905.14 1.86049
\(17\) −332.271 −0.278850 −0.139425 0.990233i \(-0.544525\pi\)
−0.139425 + 0.990233i \(0.544525\pi\)
\(18\) −827.775 −0.602187
\(19\) −2111.75 −1.34202 −0.671010 0.741448i \(-0.734139\pi\)
−0.671010 + 0.741448i \(0.734139\pi\)
\(20\) −7189.82 −4.01923
\(21\) 989.862 0.489808
\(22\) 1980.48 0.872397
\(23\) 3186.50 1.25601 0.628007 0.778208i \(-0.283871\pi\)
0.628007 + 0.778208i \(0.283871\pi\)
\(24\) −3719.20 −1.31802
\(25\) 6726.76 2.15256
\(26\) −5901.75 −1.71217
\(27\) 729.000 0.192450
\(28\) 7966.96 1.92043
\(29\) 6111.58 1.34946 0.674728 0.738067i \(-0.264261\pi\)
0.674728 + 0.738067i \(0.264261\pi\)
\(30\) 9129.08 1.85193
\(31\) −2024.27 −0.378324 −0.189162 0.981946i \(-0.560577\pi\)
−0.189162 + 0.981946i \(0.560577\pi\)
\(32\) −6245.66 −1.07821
\(33\) −1744.16 −0.278805
\(34\) 3395.63 0.503759
\(35\) −10916.6 −1.50633
\(36\) 5867.40 0.754553
\(37\) 3581.82 0.430129 0.215065 0.976600i \(-0.431004\pi\)
0.215065 + 0.976600i \(0.431004\pi\)
\(38\) 21580.9 2.42444
\(39\) 5197.52 0.547185
\(40\) 41017.0 4.05335
\(41\) 4115.68 0.382369 0.191184 0.981554i \(-0.438767\pi\)
0.191184 + 0.981554i \(0.438767\pi\)
\(42\) −10115.8 −0.884868
\(43\) −23103.3 −1.90547 −0.952737 0.303795i \(-0.901746\pi\)
−0.952737 + 0.303795i \(0.901746\pi\)
\(44\) −14038.0 −1.09313
\(45\) −8039.74 −0.591849
\(46\) −32564.3 −2.26906
\(47\) −6685.33 −0.441447 −0.220723 0.975336i \(-0.570842\pi\)
−0.220723 + 0.975336i \(0.570842\pi\)
\(48\) 17146.3 1.07415
\(49\) −4710.38 −0.280263
\(50\) −68743.8 −3.88874
\(51\) −2990.44 −0.160994
\(52\) 41832.5 2.14539
\(53\) 18280.2 0.893904 0.446952 0.894558i \(-0.352509\pi\)
0.446952 + 0.894558i \(0.352509\pi\)
\(54\) −7449.98 −0.347673
\(55\) 19235.4 0.857420
\(56\) −45450.5 −1.93673
\(57\) −19005.8 −0.774815
\(58\) −62457.0 −2.43787
\(59\) 3481.00 0.130189
\(60\) −64708.3 −2.32050
\(61\) −14865.7 −0.511516 −0.255758 0.966741i \(-0.582325\pi\)
−0.255758 + 0.966741i \(0.582325\pi\)
\(62\) 20686.9 0.683465
\(63\) 8908.76 0.282791
\(64\) 2862.70 0.0873628
\(65\) −57320.5 −1.68278
\(66\) 17824.3 0.503679
\(67\) −10836.8 −0.294926 −0.147463 0.989068i \(-0.547111\pi\)
−0.147463 + 0.989068i \(0.547111\pi\)
\(68\) −24068.8 −0.631221
\(69\) 28678.5 0.725160
\(70\) 111562. 2.72127
\(71\) −80021.9 −1.88392 −0.941961 0.335722i \(-0.891020\pi\)
−0.941961 + 0.335722i \(0.891020\pi\)
\(72\) −33472.8 −0.760958
\(73\) −22189.8 −0.487357 −0.243678 0.969856i \(-0.578354\pi\)
−0.243678 + 0.969856i \(0.578354\pi\)
\(74\) −36604.2 −0.777054
\(75\) 60540.9 1.24278
\(76\) −152969. −3.03787
\(77\) −21314.5 −0.409684
\(78\) −53115.7 −0.988522
\(79\) −57520.3 −1.03694 −0.518470 0.855096i \(-0.673498\pi\)
−0.518470 + 0.855096i \(0.673498\pi\)
\(80\) −189097. −3.30338
\(81\) 6561.00 0.111111
\(82\) −42060.0 −0.690772
\(83\) −98908.2 −1.57593 −0.787966 0.615719i \(-0.788866\pi\)
−0.787966 + 0.615719i \(0.788866\pi\)
\(84\) 71702.7 1.10876
\(85\) 32979.9 0.495111
\(86\) 236103. 3.44235
\(87\) 55004.2 0.779109
\(88\) 80084.8 1.10241
\(89\) −91785.6 −1.22829 −0.614143 0.789195i \(-0.710498\pi\)
−0.614143 + 0.789195i \(0.710498\pi\)
\(90\) 82161.7 1.06921
\(91\) 63516.3 0.804048
\(92\) 230821. 2.84319
\(93\) −18218.4 −0.218426
\(94\) 68320.4 0.797500
\(95\) 209604. 2.38282
\(96\) −56211.0 −0.622505
\(97\) 49151.1 0.530400 0.265200 0.964193i \(-0.414562\pi\)
0.265200 + 0.964193i \(0.414562\pi\)
\(98\) 48137.5 0.506312
\(99\) −15697.4 −0.160968
\(100\) 487267. 4.87267
\(101\) −24936.4 −0.243237 −0.121619 0.992577i \(-0.538809\pi\)
−0.121619 + 0.992577i \(0.538809\pi\)
\(102\) 30560.7 0.290845
\(103\) −134019. −1.24472 −0.622361 0.782731i \(-0.713826\pi\)
−0.622361 + 0.782731i \(0.713826\pi\)
\(104\) −238649. −2.16360
\(105\) −98249.8 −0.869678
\(106\) −186813. −1.61489
\(107\) 106814. 0.901924 0.450962 0.892543i \(-0.351081\pi\)
0.450962 + 0.892543i \(0.351081\pi\)
\(108\) 52806.6 0.435641
\(109\) 186806. 1.50600 0.752998 0.658023i \(-0.228607\pi\)
0.752998 + 0.658023i \(0.228607\pi\)
\(110\) −196575. −1.54898
\(111\) 32236.4 0.248335
\(112\) 209536. 1.57839
\(113\) −129207. −0.951900 −0.475950 0.879472i \(-0.657896\pi\)
−0.475950 + 0.879472i \(0.657896\pi\)
\(114\) 194228. 1.39975
\(115\) −316279. −2.23011
\(116\) 442705. 3.05471
\(117\) 46777.6 0.315917
\(118\) −35573.9 −0.235194
\(119\) −36544.7 −0.236569
\(120\) 369153. 2.34020
\(121\) −123494. −0.766803
\(122\) 151919. 0.924085
\(123\) 37041.2 0.220761
\(124\) −146632. −0.856396
\(125\) −357497. −2.04643
\(126\) −91042.5 −0.510879
\(127\) −221537. −1.21881 −0.609406 0.792858i \(-0.708592\pi\)
−0.609406 + 0.792858i \(0.708592\pi\)
\(128\) 170606. 0.920384
\(129\) −207930. −1.10013
\(130\) 585784. 3.04004
\(131\) 103256. 0.525700 0.262850 0.964837i \(-0.415338\pi\)
0.262850 + 0.964837i \(0.415338\pi\)
\(132\) −126342. −0.631120
\(133\) −232260. −1.13853
\(134\) 110746. 0.532801
\(135\) −72357.7 −0.341704
\(136\) 137309. 0.636579
\(137\) −395523. −1.80041 −0.900204 0.435469i \(-0.856582\pi\)
−0.900204 + 0.435469i \(0.856582\pi\)
\(138\) −293078. −1.31004
\(139\) 239860. 1.05298 0.526492 0.850180i \(-0.323507\pi\)
0.526492 + 0.850180i \(0.323507\pi\)
\(140\) −790769. −3.40981
\(141\) −60168.0 −0.254869
\(142\) 817779. 3.40342
\(143\) −111917. −0.457674
\(144\) 154316. 0.620163
\(145\) −606611. −2.39602
\(146\) 226768. 0.880439
\(147\) −42393.4 −0.161810
\(148\) 259456. 0.973666
\(149\) −265499. −0.979708 −0.489854 0.871804i \(-0.662950\pi\)
−0.489854 + 0.871804i \(0.662950\pi\)
\(150\) −618694. −2.24516
\(151\) 481345. 1.71796 0.858982 0.512005i \(-0.171097\pi\)
0.858982 + 0.512005i \(0.171097\pi\)
\(152\) 872669. 3.06366
\(153\) −26914.0 −0.0929500
\(154\) 217823. 0.740118
\(155\) 200921. 0.671732
\(156\) 376493. 1.23864
\(157\) 108460. 0.351173 0.175587 0.984464i \(-0.443818\pi\)
0.175587 + 0.984464i \(0.443818\pi\)
\(158\) 587826. 1.87329
\(159\) 164522. 0.516096
\(160\) 619920. 1.91441
\(161\) 350466. 1.06557
\(162\) −67049.8 −0.200729
\(163\) 167294. 0.493187 0.246594 0.969119i \(-0.420689\pi\)
0.246594 + 0.969119i \(0.420689\pi\)
\(164\) 298128. 0.865552
\(165\) 173118. 0.495032
\(166\) 1.01079e6 2.84701
\(167\) −700984. −1.94499 −0.972494 0.232930i \(-0.925169\pi\)
−0.972494 + 0.232930i \(0.925169\pi\)
\(168\) −409055. −1.11817
\(169\) −37784.8 −0.101765
\(170\) −337037. −0.894448
\(171\) −171052. −0.447340
\(172\) −1.67354e6 −4.31334
\(173\) −375116. −0.952906 −0.476453 0.879200i \(-0.658078\pi\)
−0.476453 + 0.879200i \(0.658078\pi\)
\(174\) −562113. −1.40751
\(175\) 739841. 1.82618
\(176\) −369207. −0.898439
\(177\) 31329.0 0.0751646
\(178\) 937998. 2.21897
\(179\) 252271. 0.588485 0.294242 0.955731i \(-0.404933\pi\)
0.294242 + 0.955731i \(0.404933\pi\)
\(180\) −582375. −1.33974
\(181\) 737343. 1.67291 0.836456 0.548033i \(-0.184623\pi\)
0.836456 + 0.548033i \(0.184623\pi\)
\(182\) −649101. −1.45256
\(183\) −133791. −0.295324
\(184\) −1.31680e6 −2.86732
\(185\) −355517. −0.763715
\(186\) 186182. 0.394599
\(187\) 64392.7 0.134658
\(188\) −484266. −0.999285
\(189\) 80178.8 0.163269
\(190\) −2.14204e6 −4.30470
\(191\) 984468. 1.95262 0.976311 0.216370i \(-0.0694217\pi\)
0.976311 + 0.216370i \(0.0694217\pi\)
\(192\) 25764.3 0.0504389
\(193\) 3026.14 0.00584785 0.00292392 0.999996i \(-0.499069\pi\)
0.00292392 + 0.999996i \(0.499069\pi\)
\(194\) −502297. −0.958200
\(195\) −515885. −0.971552
\(196\) −341206. −0.634419
\(197\) −416621. −0.764848 −0.382424 0.923987i \(-0.624911\pi\)
−0.382424 + 0.923987i \(0.624911\pi\)
\(198\) 160419. 0.290799
\(199\) −1.00316e6 −1.79572 −0.897861 0.440280i \(-0.854879\pi\)
−0.897861 + 0.440280i \(0.854879\pi\)
\(200\) −2.77980e6 −4.91403
\(201\) −97530.8 −0.170275
\(202\) 254836. 0.439423
\(203\) 672180. 1.14484
\(204\) −216619. −0.364436
\(205\) −408506. −0.678913
\(206\) 1.36960e6 2.24866
\(207\) 258107. 0.418671
\(208\) 1.10022e6 1.76328
\(209\) 409248. 0.648068
\(210\) 1.00406e6 1.57112
\(211\) 241371. 0.373231 0.186616 0.982433i \(-0.440248\pi\)
0.186616 + 0.982433i \(0.440248\pi\)
\(212\) 1.32416e6 2.02349
\(213\) −720197. −1.08768
\(214\) −1.09158e6 −1.62938
\(215\) 2.29314e6 3.38326
\(216\) −301255. −0.439339
\(217\) −222639. −0.320960
\(218\) −1.90905e6 −2.72067
\(219\) −199708. −0.281375
\(220\) 1.39335e6 1.94091
\(221\) −191887. −0.264281
\(222\) −329438. −0.448633
\(223\) 227725. 0.306654 0.153327 0.988176i \(-0.451001\pi\)
0.153327 + 0.988176i \(0.451001\pi\)
\(224\) −686927. −0.914725
\(225\) 544868. 0.717522
\(226\) 1.32043e6 1.71966
\(227\) 1.00306e6 1.29200 0.645998 0.763339i \(-0.276442\pi\)
0.645998 + 0.763339i \(0.276442\pi\)
\(228\) −1.37672e6 −1.75392
\(229\) −682918. −0.860558 −0.430279 0.902696i \(-0.641585\pi\)
−0.430279 + 0.902696i \(0.641585\pi\)
\(230\) 3.23220e6 4.02883
\(231\) −191831. −0.236531
\(232\) −2.52558e6 −3.08064
\(233\) 1.32745e6 1.60187 0.800935 0.598752i \(-0.204336\pi\)
0.800935 + 0.598752i \(0.204336\pi\)
\(234\) −478041. −0.570724
\(235\) 663560. 0.783809
\(236\) 252153. 0.294703
\(237\) −517683. −0.598677
\(238\) 373467. 0.427376
\(239\) −1.27290e6 −1.44145 −0.720727 0.693220i \(-0.756192\pi\)
−0.720727 + 0.693220i \(0.756192\pi\)
\(240\) −1.70187e6 −1.90721
\(241\) 641199. 0.711132 0.355566 0.934651i \(-0.384288\pi\)
0.355566 + 0.934651i \(0.384288\pi\)
\(242\) 1.26204e6 1.38527
\(243\) 59049.0 0.0641500
\(244\) −1.07682e6 −1.15790
\(245\) 467534. 0.497620
\(246\) −378540. −0.398817
\(247\) −1.21954e6 −1.27190
\(248\) 836518. 0.863666
\(249\) −890174. −0.909864
\(250\) 3.65342e6 3.69700
\(251\) −1.79177e6 −1.79514 −0.897571 0.440870i \(-0.854670\pi\)
−0.897571 + 0.440870i \(0.854670\pi\)
\(252\) 645324. 0.640142
\(253\) −617529. −0.606536
\(254\) 2.26398e6 2.20186
\(255\) 296820. 0.285853
\(256\) −1.83510e6 −1.75009
\(257\) −511016. −0.482616 −0.241308 0.970449i \(-0.577576\pi\)
−0.241308 + 0.970449i \(0.577576\pi\)
\(258\) 2.12493e6 1.98744
\(259\) 393945. 0.364910
\(260\) −4.15213e6 −3.80923
\(261\) 495038. 0.449819
\(262\) −1.05522e6 −0.949708
\(263\) 453523. 0.404306 0.202153 0.979354i \(-0.435206\pi\)
0.202153 + 0.979354i \(0.435206\pi\)
\(264\) 720763. 0.636477
\(265\) −1.81442e6 −1.58717
\(266\) 2.37357e6 2.05683
\(267\) −826070. −0.709151
\(268\) −784983. −0.667611
\(269\) 1.74732e6 1.47229 0.736144 0.676825i \(-0.236645\pi\)
0.736144 + 0.676825i \(0.236645\pi\)
\(270\) 739455. 0.617309
\(271\) −223578. −0.184929 −0.0924647 0.995716i \(-0.529475\pi\)
−0.0924647 + 0.995716i \(0.529475\pi\)
\(272\) −633024. −0.518797
\(273\) 571647. 0.464217
\(274\) 4.04203e6 3.25254
\(275\) −1.30362e6 −1.03948
\(276\) 2.07739e6 1.64151
\(277\) 588786. 0.461061 0.230530 0.973065i \(-0.425954\pi\)
0.230530 + 0.973065i \(0.425954\pi\)
\(278\) −2.45124e6 −1.90228
\(279\) −163966. −0.126108
\(280\) 4.51124e6 3.43875
\(281\) 815660. 0.616231 0.308115 0.951349i \(-0.400302\pi\)
0.308115 + 0.951349i \(0.400302\pi\)
\(282\) 614884. 0.460437
\(283\) −1.08887e6 −0.808186 −0.404093 0.914718i \(-0.632413\pi\)
−0.404093 + 0.914718i \(0.632413\pi\)
\(284\) −5.79655e6 −4.26455
\(285\) 1.88644e6 1.37572
\(286\) 1.14373e6 0.826816
\(287\) 452662. 0.324391
\(288\) −505899. −0.359403
\(289\) −1.30945e6 −0.922243
\(290\) 6.19923e6 4.32855
\(291\) 442360. 0.306227
\(292\) −1.60737e6 −1.10321
\(293\) −1.13966e6 −0.775541 −0.387770 0.921756i \(-0.626755\pi\)
−0.387770 + 0.921756i \(0.626755\pi\)
\(294\) 433237. 0.292319
\(295\) −345510. −0.231156
\(296\) −1.48017e6 −0.981931
\(297\) −141277. −0.0929351
\(298\) 2.71325e6 1.76990
\(299\) 1.84021e6 1.19039
\(300\) 4.38540e6 2.81324
\(301\) −2.54101e6 −1.61655
\(302\) −4.91908e6 −3.10361
\(303\) −224428. −0.140433
\(304\) −4.02318e6 −2.49681
\(305\) 1.47551e6 0.908221
\(306\) 275046. 0.167920
\(307\) −1.27600e6 −0.772688 −0.386344 0.922355i \(-0.626262\pi\)
−0.386344 + 0.922355i \(0.626262\pi\)
\(308\) −1.54396e6 −0.927384
\(309\) −1.20617e6 −0.718640
\(310\) −2.05330e6 −1.21352
\(311\) −1.30216e6 −0.763422 −0.381711 0.924282i \(-0.624665\pi\)
−0.381711 + 0.924282i \(0.624665\pi\)
\(312\) −2.14784e6 −1.24915
\(313\) −2.37612e6 −1.37090 −0.685452 0.728118i \(-0.740395\pi\)
−0.685452 + 0.728118i \(0.740395\pi\)
\(314\) −1.10840e6 −0.634416
\(315\) −884248. −0.502109
\(316\) −4.16660e6 −2.34728
\(317\) 2.63675e6 1.47374 0.736869 0.676035i \(-0.236303\pi\)
0.736869 + 0.676035i \(0.236303\pi\)
\(318\) −1.68132e6 −0.932358
\(319\) −1.18440e6 −0.651659
\(320\) −284141. −0.155117
\(321\) 961328. 0.520726
\(322\) −3.58157e6 −1.92501
\(323\) 701675. 0.374222
\(324\) 475259. 0.251518
\(325\) 3.88472e6 2.04010
\(326\) −1.70965e6 −0.890972
\(327\) 1.68125e6 0.869487
\(328\) −1.70078e6 −0.872899
\(329\) −735284. −0.374512
\(330\) −1.76917e6 −0.894305
\(331\) 345030. 0.173096 0.0865480 0.996248i \(-0.472416\pi\)
0.0865480 + 0.996248i \(0.472416\pi\)
\(332\) −7.16462e6 −3.56737
\(333\) 290127. 0.143376
\(334\) 7.16366e6 3.51374
\(335\) 1.07561e6 0.523654
\(336\) 1.88583e6 0.911283
\(337\) 1.21026e6 0.580503 0.290251 0.956950i \(-0.406261\pi\)
0.290251 + 0.956950i \(0.406261\pi\)
\(338\) 386140. 0.183845
\(339\) −1.16287e6 −0.549580
\(340\) 2.38897e6 1.12076
\(341\) 392294. 0.182695
\(342\) 1.74806e6 0.808146
\(343\) −2.36658e6 −1.08614
\(344\) 9.54731e6 4.34996
\(345\) −2.84652e6 −1.28756
\(346\) 3.83348e6 1.72148
\(347\) −3.75698e6 −1.67500 −0.837500 0.546437i \(-0.815984\pi\)
−0.837500 + 0.546437i \(0.815984\pi\)
\(348\) 3.98434e6 1.76364
\(349\) 402933. 0.177080 0.0885399 0.996073i \(-0.471780\pi\)
0.0885399 + 0.996073i \(0.471780\pi\)
\(350\) −7.56076e6 −3.29910
\(351\) 420999. 0.182395
\(352\) 1.21038e6 0.520673
\(353\) −2.57154e6 −1.09839 −0.549196 0.835694i \(-0.685066\pi\)
−0.549196 + 0.835694i \(0.685066\pi\)
\(354\) −320165. −0.135789
\(355\) 7.94266e6 3.34499
\(356\) −6.64868e6 −2.78042
\(357\) −328903. −0.136583
\(358\) −2.57807e6 −1.06313
\(359\) 181007. 0.0741241 0.0370620 0.999313i \(-0.488200\pi\)
0.0370620 + 0.999313i \(0.488200\pi\)
\(360\) 3.32238e6 1.35112
\(361\) 1.98340e6 0.801017
\(362\) −7.53524e6 −3.02222
\(363\) −1.11145e6 −0.442714
\(364\) 4.60093e6 1.82009
\(365\) 2.20248e6 0.865324
\(366\) 1.36727e6 0.533521
\(367\) −395859. −0.153418 −0.0767089 0.997054i \(-0.524441\pi\)
−0.0767089 + 0.997054i \(0.524441\pi\)
\(368\) 6.07073e6 2.33680
\(369\) 333370. 0.127456
\(370\) 3.63319e6 1.37970
\(371\) 2.01054e6 0.758365
\(372\) −1.31969e6 −0.494441
\(373\) −1.17285e6 −0.436486 −0.218243 0.975894i \(-0.570033\pi\)
−0.218243 + 0.975894i \(0.570033\pi\)
\(374\) −658057. −0.243268
\(375\) −3.21747e6 −1.18151
\(376\) 2.76267e6 1.00777
\(377\) 3.52945e6 1.27895
\(378\) −819383. −0.294956
\(379\) −1.54397e6 −0.552130 −0.276065 0.961139i \(-0.589030\pi\)
−0.276065 + 0.961139i \(0.589030\pi\)
\(380\) 1.51831e7 5.39388
\(381\) −1.99383e6 −0.703681
\(382\) −1.00607e7 −3.52753
\(383\) −5.57141e6 −1.94074 −0.970371 0.241619i \(-0.922322\pi\)
−0.970371 + 0.241619i \(0.922322\pi\)
\(384\) 1.53545e6 0.531384
\(385\) 2.11560e6 0.727412
\(386\) −30925.5 −0.0105645
\(387\) −1.87137e6 −0.635158
\(388\) 3.56036e6 1.20064
\(389\) −1.44734e6 −0.484949 −0.242474 0.970158i \(-0.577959\pi\)
−0.242474 + 0.970158i \(0.577959\pi\)
\(390\) 5.27206e6 1.75517
\(391\) −1.05878e6 −0.350239
\(392\) 1.94654e6 0.639805
\(393\) 929306. 0.303513
\(394\) 4.25763e6 1.38174
\(395\) 5.70924e6 1.84113
\(396\) −1.13708e6 −0.364377
\(397\) 5.20211e6 1.65654 0.828272 0.560326i \(-0.189324\pi\)
0.828272 + 0.560326i \(0.189324\pi\)
\(398\) 1.02518e7 3.24408
\(399\) −2.09034e6 −0.657333
\(400\) 1.28154e7 4.00482
\(401\) 1.93344e6 0.600439 0.300220 0.953870i \(-0.402940\pi\)
0.300220 + 0.953870i \(0.402940\pi\)
\(402\) 996711. 0.307613
\(403\) −1.16902e6 −0.358558
\(404\) −1.80632e6 −0.550606
\(405\) −651219. −0.197283
\(406\) −6.86931e6 −2.06823
\(407\) −694140. −0.207712
\(408\) 1.23578e6 0.367529
\(409\) −4.68677e6 −1.38537 −0.692684 0.721241i \(-0.743572\pi\)
−0.692684 + 0.721241i \(0.743572\pi\)
\(410\) 4.17471e6 1.22650
\(411\) −3.55971e6 −1.03947
\(412\) −9.70791e6 −2.81762
\(413\) 382857. 0.110449
\(414\) −2.63771e6 −0.756355
\(415\) 9.81724e6 2.79814
\(416\) −3.60688e6 −1.02188
\(417\) 2.15874e6 0.607940
\(418\) −4.18229e6 −1.17077
\(419\) 5.57751e6 1.55205 0.776025 0.630703i \(-0.217233\pi\)
0.776025 + 0.630703i \(0.217233\pi\)
\(420\) −7.11692e6 −1.96865
\(421\) −1.52289e6 −0.418759 −0.209379 0.977834i \(-0.567144\pi\)
−0.209379 + 0.977834i \(0.567144\pi\)
\(422\) −2.46667e6 −0.674265
\(423\) −541512. −0.147149
\(424\) −7.55418e6 −2.04067
\(425\) −2.23511e6 −0.600243
\(426\) 7.36001e6 1.96496
\(427\) −1.63499e6 −0.433957
\(428\) 7.73731e6 2.04165
\(429\) −1.00725e6 −0.264238
\(430\) −2.34347e7 −6.11206
\(431\) −1.32186e6 −0.342761 −0.171380 0.985205i \(-0.554823\pi\)
−0.171380 + 0.985205i \(0.554823\pi\)
\(432\) 1.38885e6 0.358051
\(433\) 4.13752e6 1.06052 0.530262 0.847834i \(-0.322094\pi\)
0.530262 + 0.847834i \(0.322094\pi\)
\(434\) 2.27524e6 0.579834
\(435\) −5.45950e6 −1.38334
\(436\) 1.35316e7 3.40906
\(437\) −6.72910e6 −1.68560
\(438\) 2.04091e6 0.508322
\(439\) −916784. −0.227042 −0.113521 0.993536i \(-0.536213\pi\)
−0.113521 + 0.993536i \(0.536213\pi\)
\(440\) −7.94890e6 −1.95738
\(441\) −381541. −0.0934210
\(442\) 1.96098e6 0.477439
\(443\) 1.86032e6 0.450378 0.225189 0.974315i \(-0.427700\pi\)
0.225189 + 0.974315i \(0.427700\pi\)
\(444\) 2.33511e6 0.562146
\(445\) 9.11027e6 2.18088
\(446\) −2.32722e6 −0.553989
\(447\) −2.38949e6 −0.565635
\(448\) 314854. 0.0741163
\(449\) 2.38131e6 0.557442 0.278721 0.960372i \(-0.410090\pi\)
0.278721 + 0.960372i \(0.410090\pi\)
\(450\) −5.56825e6 −1.29625
\(451\) −797601. −0.184648
\(452\) −9.35940e6 −2.15478
\(453\) 4.33211e6 0.991867
\(454\) −1.02507e7 −2.33407
\(455\) −6.30438e6 −1.42762
\(456\) 7.85402e6 1.76881
\(457\) 679422. 0.152177 0.0760885 0.997101i \(-0.475757\pi\)
0.0760885 + 0.997101i \(0.475757\pi\)
\(458\) 6.97905e6 1.55465
\(459\) −242226. −0.0536647
\(460\) −2.29104e7 −5.04821
\(461\) −278818. −0.0611039 −0.0305520 0.999533i \(-0.509727\pi\)
−0.0305520 + 0.999533i \(0.509727\pi\)
\(462\) 1.96040e6 0.427307
\(463\) 5.43255e6 1.17774 0.588872 0.808226i \(-0.299572\pi\)
0.588872 + 0.808226i \(0.299572\pi\)
\(464\) 1.16434e7 2.51065
\(465\) 1.80829e6 0.387825
\(466\) −1.35658e7 −2.89387
\(467\) −373892. −0.0793330 −0.0396665 0.999213i \(-0.512630\pi\)
−0.0396665 + 0.999213i \(0.512630\pi\)
\(468\) 3.38843e6 0.715129
\(469\) −1.19188e6 −0.250207
\(470\) −6.78121e6 −1.41600
\(471\) 976143. 0.202750
\(472\) −1.43850e6 −0.297205
\(473\) 4.47732e6 0.920164
\(474\) 5.29043e6 1.08155
\(475\) −1.42053e7 −2.88878
\(476\) −2.64719e6 −0.535511
\(477\) 1.48070e6 0.297968
\(478\) 1.30084e7 2.60407
\(479\) −526098. −0.104768 −0.0523839 0.998627i \(-0.516682\pi\)
−0.0523839 + 0.998627i \(0.516682\pi\)
\(480\) 5.57928e6 1.10529
\(481\) 2.06851e6 0.407656
\(482\) −6.55270e6 −1.28470
\(483\) 3.15420e6 0.615206
\(484\) −8.94556e6 −1.73578
\(485\) −4.87854e6 −0.941750
\(486\) −603448. −0.115891
\(487\) −5.03131e6 −0.961299 −0.480650 0.876913i \(-0.659599\pi\)
−0.480650 + 0.876913i \(0.659599\pi\)
\(488\) 6.14315e6 1.16773
\(489\) 1.50565e6 0.284742
\(490\) −4.77793e6 −0.898980
\(491\) 4.50265e6 0.842878 0.421439 0.906857i \(-0.361525\pi\)
0.421439 + 0.906857i \(0.361525\pi\)
\(492\) 2.68315e6 0.499727
\(493\) −2.03070e6 −0.376296
\(494\) 1.24630e7 2.29777
\(495\) 1.55806e6 0.285807
\(496\) −3.85652e6 −0.703868
\(497\) −8.80118e6 −1.59827
\(498\) 9.09709e6 1.64372
\(499\) 4.33681e6 0.779685 0.389842 0.920882i \(-0.372529\pi\)
0.389842 + 0.920882i \(0.372529\pi\)
\(500\) −2.58960e7 −4.63242
\(501\) −6.30885e6 −1.12294
\(502\) 1.83109e7 3.24303
\(503\) −4.73584e6 −0.834597 −0.417299 0.908769i \(-0.637023\pi\)
−0.417299 + 0.908769i \(0.637023\pi\)
\(504\) −3.68149e6 −0.645576
\(505\) 2.47509e6 0.431879
\(506\) 6.31081e6 1.09574
\(507\) −340063. −0.0587543
\(508\) −1.60475e7 −2.75897
\(509\) 5.24411e6 0.897175 0.448587 0.893739i \(-0.351927\pi\)
0.448587 + 0.893739i \(0.351927\pi\)
\(510\) −3.03333e6 −0.516410
\(511\) −2.44054e6 −0.413460
\(512\) 1.32944e7 2.24126
\(513\) −1.53947e6 −0.258272
\(514\) 5.22230e6 0.871875
\(515\) 1.33022e7 2.21006
\(516\) −1.50618e7 −2.49031
\(517\) 1.29559e6 0.213177
\(518\) −4.02590e6 −0.659232
\(519\) −3.37604e6 −0.550161
\(520\) 2.36874e7 3.84157
\(521\) 1.11744e7 1.80356 0.901781 0.432194i \(-0.142261\pi\)
0.901781 + 0.432194i \(0.142261\pi\)
\(522\) −5.05901e6 −0.812624
\(523\) 7.05297e6 1.12750 0.563752 0.825944i \(-0.309357\pi\)
0.563752 + 0.825944i \(0.309357\pi\)
\(524\) 7.47957e6 1.19000
\(525\) 6.65857e6 1.05434
\(526\) −4.63476e6 −0.730403
\(527\) 672607. 0.105496
\(528\) −3.32287e6 −0.518714
\(529\) 3.71744e6 0.577571
\(530\) 1.85424e7 2.86731
\(531\) 281961. 0.0433963
\(532\) −1.68242e7 −2.57725
\(533\) 2.37681e6 0.362391
\(534\) 8.44198e6 1.28112
\(535\) −1.06020e7 −1.60141
\(536\) 4.47823e6 0.673278
\(537\) 2.27044e6 0.339762
\(538\) −1.78567e7 −2.65978
\(539\) 912850. 0.135340
\(540\) −5.24138e6 −0.773501
\(541\) −734520. −0.107897 −0.0539486 0.998544i \(-0.517181\pi\)
−0.0539486 + 0.998544i \(0.517181\pi\)
\(542\) 2.28484e6 0.334086
\(543\) 6.63609e6 0.965857
\(544\) 2.07525e6 0.300659
\(545\) −1.85416e7 −2.67397
\(546\) −5.84191e6 −0.838636
\(547\) −5.09324e6 −0.727824 −0.363912 0.931433i \(-0.618559\pi\)
−0.363912 + 0.931433i \(0.618559\pi\)
\(548\) −2.86505e7 −4.07551
\(549\) −1.20412e6 −0.170505
\(550\) 1.33222e7 1.87789
\(551\) −1.29061e7 −1.81100
\(552\) −1.18512e7 −1.65545
\(553\) −6.32635e6 −0.879712
\(554\) −6.01707e6 −0.832934
\(555\) −3.19965e6 −0.440931
\(556\) 1.73748e7 2.38359
\(557\) −3.78806e6 −0.517343 −0.258672 0.965965i \(-0.583285\pi\)
−0.258672 + 0.965965i \(0.583285\pi\)
\(558\) 1.67564e6 0.227822
\(559\) −1.33422e7 −1.80592
\(560\) −2.07977e7 −2.80250
\(561\) 579534. 0.0777449
\(562\) −8.33559e6 −1.11326
\(563\) −8.41523e6 −1.11891 −0.559455 0.828861i \(-0.688989\pi\)
−0.559455 + 0.828861i \(0.688989\pi\)
\(564\) −4.35839e6 −0.576937
\(565\) 1.28246e7 1.69014
\(566\) 1.11277e7 1.46004
\(567\) 721609. 0.0942637
\(568\) 3.30686e7 4.30075
\(569\) −4.34598e6 −0.562739 −0.281370 0.959599i \(-0.590789\pi\)
−0.281370 + 0.959599i \(0.590789\pi\)
\(570\) −1.92783e7 −2.48532
\(571\) 766497. 0.0983830 0.0491915 0.998789i \(-0.484336\pi\)
0.0491915 + 0.998789i \(0.484336\pi\)
\(572\) −8.10695e6 −1.03602
\(573\) 8.86022e6 1.12735
\(574\) −4.62595e6 −0.586032
\(575\) 2.14348e7 2.70365
\(576\) 231879. 0.0291209
\(577\) 460709. 0.0576086 0.0288043 0.999585i \(-0.490830\pi\)
0.0288043 + 0.999585i \(0.490830\pi\)
\(578\) 1.33819e7 1.66609
\(579\) 27235.3 0.00337626
\(580\) −4.39411e7 −5.42377
\(581\) −1.08784e7 −1.33698
\(582\) −4.52067e6 −0.553217
\(583\) −3.54262e6 −0.431671
\(584\) 9.16982e6 1.11257
\(585\) −4.64296e6 −0.560926
\(586\) 1.16467e7 1.40106
\(587\) 279534. 0.0334841 0.0167421 0.999860i \(-0.494671\pi\)
0.0167421 + 0.999860i \(0.494671\pi\)
\(588\) −3.07085e6 −0.366282
\(589\) 4.27475e6 0.507718
\(590\) 3.53092e6 0.417598
\(591\) −3.74959e6 −0.441585
\(592\) 6.82386e6 0.800251
\(593\) 4.02162e6 0.469639 0.234819 0.972039i \(-0.424550\pi\)
0.234819 + 0.972039i \(0.424550\pi\)
\(594\) 1.44377e6 0.167893
\(595\) 3.62729e6 0.420039
\(596\) −1.92319e7 −2.21772
\(597\) −9.02847e6 −1.03676
\(598\) −1.88059e7 −2.15051
\(599\) −60227.1 −0.00685843 −0.00342922 0.999994i \(-0.501092\pi\)
−0.00342922 + 0.999994i \(0.501092\pi\)
\(600\) −2.50182e7 −2.83712
\(601\) 4.60932e6 0.520536 0.260268 0.965536i \(-0.416189\pi\)
0.260268 + 0.965536i \(0.416189\pi\)
\(602\) 2.59677e7 2.92040
\(603\) −877778. −0.0983085
\(604\) 3.48672e7 3.88888
\(605\) 1.22576e7 1.36149
\(606\) 2.29353e6 0.253701
\(607\) −6.23116e6 −0.686431 −0.343216 0.939257i \(-0.611516\pi\)
−0.343216 + 0.939257i \(0.611516\pi\)
\(608\) 1.31893e7 1.44698
\(609\) 6.04962e6 0.660975
\(610\) −1.50789e7 −1.64076
\(611\) −3.86079e6 −0.418382
\(612\) −1.94957e6 −0.210407
\(613\) 5.27500e6 0.566984 0.283492 0.958975i \(-0.408507\pi\)
0.283492 + 0.958975i \(0.408507\pi\)
\(614\) 1.30400e7 1.39591
\(615\) −3.67656e6 −0.391971
\(616\) 8.80810e6 0.935256
\(617\) −1.43161e7 −1.51395 −0.756975 0.653444i \(-0.773323\pi\)
−0.756975 + 0.653444i \(0.773323\pi\)
\(618\) 1.23264e7 1.29827
\(619\) 1.67507e7 1.75714 0.878569 0.477615i \(-0.158499\pi\)
0.878569 + 0.477615i \(0.158499\pi\)
\(620\) 1.45541e7 1.52057
\(621\) 2.32296e6 0.241720
\(622\) 1.33074e7 1.37917
\(623\) −1.00950e7 −1.04204
\(624\) 9.90199e6 1.01803
\(625\) 1.44626e7 1.48097
\(626\) 2.42826e7 2.47662
\(627\) 3.68323e6 0.374162
\(628\) 7.85654e6 0.794936
\(629\) −1.19014e6 −0.119942
\(630\) 9.03652e6 0.907089
\(631\) 7.91210e6 0.791076 0.395538 0.918450i \(-0.370558\pi\)
0.395538 + 0.918450i \(0.370558\pi\)
\(632\) 2.37699e7 2.36720
\(633\) 2.17233e6 0.215485
\(634\) −2.69461e7 −2.66240
\(635\) 2.19889e7 2.16406
\(636\) 1.19175e7 1.16826
\(637\) −2.72025e6 −0.265620
\(638\) 1.21039e7 1.17726
\(639\) −6.48177e6 −0.627974
\(640\) −1.69337e7 −1.63418
\(641\) −1.24774e7 −1.19945 −0.599723 0.800208i \(-0.704722\pi\)
−0.599723 + 0.800208i \(0.704722\pi\)
\(642\) −9.82424e6 −0.940722
\(643\) 1.49984e6 0.143060 0.0715299 0.997438i \(-0.477212\pi\)
0.0715299 + 0.997438i \(0.477212\pi\)
\(644\) 2.53867e7 2.41208
\(645\) 2.06383e7 1.95333
\(646\) −7.17073e6 −0.676055
\(647\) −6.33662e6 −0.595109 −0.297555 0.954705i \(-0.596171\pi\)
−0.297555 + 0.954705i \(0.596171\pi\)
\(648\) −2.71129e6 −0.253653
\(649\) −674602. −0.0628689
\(650\) −3.96997e7 −3.68556
\(651\) −2.00375e6 −0.185306
\(652\) 1.21183e7 1.11641
\(653\) −6.01496e6 −0.552014 −0.276007 0.961156i \(-0.589011\pi\)
−0.276007 + 0.961156i \(0.589011\pi\)
\(654\) −1.71814e7 −1.57078
\(655\) −1.02488e7 −0.933404
\(656\) 7.84095e6 0.711393
\(657\) −1.79738e6 −0.162452
\(658\) 7.51419e6 0.676578
\(659\) 9.61791e6 0.862714 0.431357 0.902181i \(-0.358035\pi\)
0.431357 + 0.902181i \(0.358035\pi\)
\(660\) 1.25402e7 1.12058
\(661\) −8.42469e6 −0.749981 −0.374990 0.927029i \(-0.622354\pi\)
−0.374990 + 0.927029i \(0.622354\pi\)
\(662\) −3.52601e6 −0.312708
\(663\) −1.72699e6 −0.152583
\(664\) 4.08733e7 3.59765
\(665\) 2.30532e7 2.02152
\(666\) −2.96494e6 −0.259018
\(667\) 1.94746e7 1.69494
\(668\) −5.07772e7 −4.40278
\(669\) 2.04952e6 0.177047
\(670\) −1.09922e7 −0.946012
\(671\) 2.88090e6 0.247014
\(672\) −6.18234e6 −0.528117
\(673\) 4.81831e6 0.410069 0.205035 0.978755i \(-0.434269\pi\)
0.205035 + 0.978755i \(0.434269\pi\)
\(674\) −1.23682e7 −1.04871
\(675\) 4.90381e6 0.414261
\(676\) −2.73702e6 −0.230362
\(677\) −1.49503e7 −1.25365 −0.626826 0.779159i \(-0.715647\pi\)
−0.626826 + 0.779159i \(0.715647\pi\)
\(678\) 1.18839e7 0.992849
\(679\) 5.40586e6 0.449977
\(680\) −1.36288e7 −1.13028
\(681\) 9.02751e6 0.745934
\(682\) −4.00903e6 −0.330049
\(683\) 1.14545e6 0.0939559 0.0469780 0.998896i \(-0.485041\pi\)
0.0469780 + 0.998896i \(0.485041\pi\)
\(684\) −1.23905e7 −1.01262
\(685\) 3.92581e7 3.19671
\(686\) 2.41851e7 1.96218
\(687\) −6.14627e6 −0.496843
\(688\) −4.40151e7 −3.54511
\(689\) 1.05568e7 0.847200
\(690\) 2.90898e7 2.32604
\(691\) 1.14659e7 0.913511 0.456755 0.889592i \(-0.349011\pi\)
0.456755 + 0.889592i \(0.349011\pi\)
\(692\) −2.71723e7 −2.15705
\(693\) −1.72648e6 −0.136561
\(694\) 3.83942e7 3.02599
\(695\) −2.38076e7 −1.86962
\(696\) −2.27302e7 −1.77861
\(697\) −1.36752e6 −0.106624
\(698\) −4.11775e6 −0.319905
\(699\) 1.19470e7 0.924840
\(700\) 5.35919e7 4.13384
\(701\) −5.89914e6 −0.453413 −0.226706 0.973963i \(-0.572796\pi\)
−0.226706 + 0.973963i \(0.572796\pi\)
\(702\) −4.30237e6 −0.329507
\(703\) −7.56391e6 −0.577242
\(704\) −554779. −0.0421880
\(705\) 5.97204e6 0.452532
\(706\) 2.62798e7 1.98431
\(707\) −2.74262e6 −0.206356
\(708\) 2.26938e6 0.170147
\(709\) 1.68552e6 0.125927 0.0629636 0.998016i \(-0.479945\pi\)
0.0629636 + 0.998016i \(0.479945\pi\)
\(710\) −8.11695e7 −6.04293
\(711\) −4.65914e6 −0.345647
\(712\) 3.79299e7 2.80402
\(713\) −6.45034e6 −0.475180
\(714\) 3.36120e6 0.246746
\(715\) 1.11085e7 0.812622
\(716\) 1.82738e7 1.33213
\(717\) −1.14561e7 −0.832223
\(718\) −1.84979e6 −0.133910
\(719\) 1.79183e7 1.29263 0.646314 0.763072i \(-0.276310\pi\)
0.646314 + 0.763072i \(0.276310\pi\)
\(720\) −1.53168e7 −1.10113
\(721\) −1.47400e7 −1.05599
\(722\) −2.02692e7 −1.44708
\(723\) 5.77079e6 0.410573
\(724\) 5.34110e7 3.78690
\(725\) 4.11112e7 2.90479
\(726\) 1.13584e7 0.799789
\(727\) −8.60696e6 −0.603968 −0.301984 0.953313i \(-0.597649\pi\)
−0.301984 + 0.953313i \(0.597649\pi\)
\(728\) −2.62477e7 −1.83554
\(729\) 531441. 0.0370370
\(730\) −2.25081e7 −1.56326
\(731\) 7.67657e6 0.531342
\(732\) −9.69142e6 −0.668513
\(733\) −4.93390e6 −0.339180 −0.169590 0.985515i \(-0.554244\pi\)
−0.169590 + 0.985515i \(0.554244\pi\)
\(734\) 4.04546e6 0.277158
\(735\) 4.20780e6 0.287301
\(736\) −1.99018e7 −1.35425
\(737\) 2.10011e6 0.142421
\(738\) −3.40686e6 −0.230257
\(739\) −6.04050e6 −0.406876 −0.203438 0.979088i \(-0.565212\pi\)
−0.203438 + 0.979088i \(0.565212\pi\)
\(740\) −2.57526e7 −1.72879
\(741\) −1.09759e7 −0.734333
\(742\) −2.05466e7 −1.37003
\(743\) −7.90866e6 −0.525570 −0.262785 0.964854i \(-0.584641\pi\)
−0.262785 + 0.964854i \(0.584641\pi\)
\(744\) 7.52866e6 0.498638
\(745\) 2.63524e7 1.73952
\(746\) 1.19859e7 0.788539
\(747\) −8.01157e6 −0.525310
\(748\) 4.66442e6 0.304820
\(749\) 1.17479e7 0.765168
\(750\) 3.28808e7 2.13446
\(751\) −6.20100e6 −0.401201 −0.200601 0.979673i \(-0.564289\pi\)
−0.200601 + 0.979673i \(0.564289\pi\)
\(752\) −1.27365e7 −0.821307
\(753\) −1.61260e7 −1.03643
\(754\) −3.60690e7 −2.31050
\(755\) −4.77764e7 −3.05033
\(756\) 5.80792e6 0.369586
\(757\) 6.28292e6 0.398494 0.199247 0.979949i \(-0.436150\pi\)
0.199247 + 0.979949i \(0.436150\pi\)
\(758\) 1.57785e7 0.997455
\(759\) −5.55776e6 −0.350183
\(760\) −8.66177e7 −5.43967
\(761\) −4.81278e6 −0.301255 −0.150627 0.988591i \(-0.548129\pi\)
−0.150627 + 0.988591i \(0.548129\pi\)
\(762\) 2.03758e7 1.27124
\(763\) 2.05458e7 1.27765
\(764\) 7.13120e7 4.42007
\(765\) 2.67138e6 0.165037
\(766\) 5.69367e7 3.50607
\(767\) 2.01028e6 0.123387
\(768\) −1.65159e7 −1.01042
\(769\) −7.75895e6 −0.473137 −0.236569 0.971615i \(-0.576023\pi\)
−0.236569 + 0.971615i \(0.576023\pi\)
\(770\) −2.16202e7 −1.31411
\(771\) −4.59915e6 −0.278639
\(772\) 219205. 0.0132375
\(773\) 1.00740e7 0.606389 0.303195 0.952929i \(-0.401947\pi\)
0.303195 + 0.952929i \(0.401947\pi\)
\(774\) 1.91243e7 1.14745
\(775\) −1.36168e7 −0.814367
\(776\) −2.03114e7 −1.21084
\(777\) 3.54550e6 0.210681
\(778\) 1.47910e7 0.876089
\(779\) −8.69130e6 −0.513146
\(780\) −3.73692e7 −2.19926
\(781\) 1.55079e7 0.909756
\(782\) 1.08202e7 0.632728
\(783\) 4.45534e6 0.259703
\(784\) −8.97393e6 −0.521426
\(785\) −1.07653e7 −0.623525
\(786\) −9.49699e6 −0.548314
\(787\) −8.19431e6 −0.471602 −0.235801 0.971801i \(-0.575771\pi\)
−0.235801 + 0.971801i \(0.575771\pi\)
\(788\) −3.01788e7 −1.73136
\(789\) 4.08171e6 0.233426
\(790\) −5.83452e7 −3.32612
\(791\) −1.42108e7 −0.807567
\(792\) 6.48687e6 0.367470
\(793\) −8.58494e6 −0.484791
\(794\) −5.31626e7 −2.99265
\(795\) −1.63298e7 −0.916352
\(796\) −7.26662e7 −4.06490
\(797\) −1.92457e7 −1.07322 −0.536610 0.843830i \(-0.680295\pi\)
−0.536610 + 0.843830i \(0.680295\pi\)
\(798\) 2.13621e7 1.18751
\(799\) 2.22134e6 0.123097
\(800\) −4.20131e7 −2.32092
\(801\) −7.43463e6 −0.409429
\(802\) −1.97587e7 −1.08473
\(803\) 4.30029e6 0.235347
\(804\) −7.06485e6 −0.385445
\(805\) −3.47859e7 −1.89197
\(806\) 1.19467e7 0.647756
\(807\) 1.57259e7 0.850026
\(808\) 1.03048e7 0.555280
\(809\) −3.71300e6 −0.199459 −0.0997296 0.995015i \(-0.531798\pi\)
−0.0997296 + 0.995015i \(0.531798\pi\)
\(810\) 6.65510e6 0.356403
\(811\) −2.16439e7 −1.15553 −0.577767 0.816201i \(-0.696076\pi\)
−0.577767 + 0.816201i \(0.696076\pi\)
\(812\) 4.86907e7 2.59153
\(813\) −2.01220e6 −0.106769
\(814\) 7.09372e6 0.375244
\(815\) −1.66050e7 −0.875677
\(816\) −5.69721e6 −0.299528
\(817\) 4.87885e7 2.55718
\(818\) 4.78962e7 2.50275
\(819\) 5.14482e6 0.268016
\(820\) −2.95910e7 −1.53683
\(821\) −2.51582e7 −1.30263 −0.651316 0.758807i \(-0.725783\pi\)
−0.651316 + 0.758807i \(0.725783\pi\)
\(822\) 3.63783e7 1.87786
\(823\) −1.27945e7 −0.658451 −0.329225 0.944251i \(-0.606788\pi\)
−0.329225 + 0.944251i \(0.606788\pi\)
\(824\) 5.53824e7 2.84154
\(825\) −1.17325e7 −0.600147
\(826\) −3.91258e6 −0.199532
\(827\) −4.64226e6 −0.236029 −0.118015 0.993012i \(-0.537653\pi\)
−0.118015 + 0.993012i \(0.537653\pi\)
\(828\) 1.86965e7 0.947728
\(829\) −1.53561e7 −0.776059 −0.388029 0.921647i \(-0.626844\pi\)
−0.388029 + 0.921647i \(0.626844\pi\)
\(830\) −1.00327e8 −5.05500
\(831\) 5.29908e6 0.266194
\(832\) 1.65322e6 0.0827983
\(833\) 1.56512e6 0.0781513
\(834\) −2.20612e7 −1.09828
\(835\) 6.95769e7 3.45341
\(836\) 2.96447e7 1.46700
\(837\) −1.47569e6 −0.0728085
\(838\) −5.69991e7 −2.80387
\(839\) −1.78634e6 −0.0876112 −0.0438056 0.999040i \(-0.513948\pi\)
−0.0438056 + 0.999040i \(0.513948\pi\)
\(840\) 4.06011e7 1.98536
\(841\) 1.68403e7 0.821031
\(842\) 1.55631e7 0.756513
\(843\) 7.34094e6 0.355781
\(844\) 1.74842e7 0.844868
\(845\) 3.75037e6 0.180689
\(846\) 5.53395e6 0.265833
\(847\) −1.35825e7 −0.650535
\(848\) 3.48263e7 1.66310
\(849\) −9.79986e6 −0.466606
\(850\) 2.28416e7 1.08437
\(851\) 1.14135e7 0.540248
\(852\) −5.21689e7 −2.46214
\(853\) −2.41934e7 −1.13848 −0.569239 0.822172i \(-0.692762\pi\)
−0.569239 + 0.822172i \(0.692762\pi\)
\(854\) 1.67087e7 0.783969
\(855\) 1.69779e7 0.794273
\(856\) −4.41404e7 −2.05898
\(857\) −2.04166e6 −0.0949578 −0.0474789 0.998872i \(-0.515119\pi\)
−0.0474789 + 0.998872i \(0.515119\pi\)
\(858\) 1.02936e7 0.477363
\(859\) 4.39878e6 0.203399 0.101700 0.994815i \(-0.467572\pi\)
0.101700 + 0.994815i \(0.467572\pi\)
\(860\) 1.66109e8 7.65854
\(861\) 4.07396e6 0.187287
\(862\) 1.35086e7 0.619217
\(863\) 2.14857e7 0.982023 0.491012 0.871153i \(-0.336627\pi\)
0.491012 + 0.871153i \(0.336627\pi\)
\(864\) −4.55309e6 −0.207502
\(865\) 3.72325e7 1.69193
\(866\) −4.22832e7 −1.91590
\(867\) −1.17851e7 −0.532457
\(868\) −1.61273e7 −0.726544
\(869\) 1.11472e7 0.500743
\(870\) 5.57931e7 2.49909
\(871\) −6.25825e6 −0.279516
\(872\) −7.71963e7 −3.43800
\(873\) 3.98124e6 0.176800
\(874\) 6.87676e7 3.04513
\(875\) −3.93192e7 −1.73614
\(876\) −1.44663e7 −0.636938
\(877\) 3.80492e7 1.67050 0.835251 0.549869i \(-0.185322\pi\)
0.835251 + 0.549869i \(0.185322\pi\)
\(878\) 9.36902e6 0.410164
\(879\) −1.02569e7 −0.447759
\(880\) 3.66461e7 1.59522
\(881\) −2.79654e7 −1.21390 −0.606949 0.794741i \(-0.707607\pi\)
−0.606949 + 0.794741i \(0.707607\pi\)
\(882\) 3.89913e6 0.168771
\(883\) −4.11323e7 −1.77534 −0.887669 0.460481i \(-0.847677\pi\)
−0.887669 + 0.460481i \(0.847677\pi\)
\(884\) −1.38997e7 −0.598241
\(885\) −3.10959e6 −0.133458
\(886\) −1.90114e7 −0.813635
\(887\) −2.45600e7 −1.04814 −0.524070 0.851675i \(-0.675587\pi\)
−0.524070 + 0.851675i \(0.675587\pi\)
\(888\) −1.33215e7 −0.566918
\(889\) −2.43656e7 −1.03401
\(890\) −9.31019e7 −3.93989
\(891\) −1.27149e6 −0.0536561
\(892\) 1.64957e7 0.694159
\(893\) 1.41178e7 0.592430
\(894\) 2.44192e7 1.02185
\(895\) −2.50394e7 −1.04488
\(896\) 1.87640e7 0.780829
\(897\) 1.65619e7 0.687272
\(898\) −2.43356e7 −1.00705
\(899\) −1.23715e7 −0.510532
\(900\) 3.94686e7 1.62422
\(901\) −6.07399e6 −0.249265
\(902\) 8.15104e6 0.333577
\(903\) −2.28691e7 −0.933318
\(904\) 5.33942e7 2.17307
\(905\) −7.31858e7 −2.97033
\(906\) −4.42717e7 −1.79187
\(907\) 2.64205e7 1.06640 0.533202 0.845988i \(-0.320988\pi\)
0.533202 + 0.845988i \(0.320988\pi\)
\(908\) 7.26585e7 2.92463
\(909\) −2.01985e6 −0.0810792
\(910\) 6.44272e7 2.57909
\(911\) 4.37194e7 1.74533 0.872666 0.488317i \(-0.162389\pi\)
0.872666 + 0.488317i \(0.162389\pi\)
\(912\) −3.62086e7 −1.44154
\(913\) 1.91680e7 0.761025
\(914\) −6.94331e6 −0.274917
\(915\) 1.32796e7 0.524362
\(916\) −4.94686e7 −1.94801
\(917\) 1.13566e7 0.445990
\(918\) 2.47541e6 0.0969485
\(919\) −3.62009e7 −1.41394 −0.706969 0.707245i \(-0.749938\pi\)
−0.706969 + 0.707245i \(0.749938\pi\)
\(920\) 1.30701e8 5.09106
\(921\) −1.14840e7 −0.446112
\(922\) 2.84937e6 0.110388
\(923\) −4.62128e7 −1.78549
\(924\) −1.38956e7 −0.535425
\(925\) 2.40940e7 0.925881
\(926\) −5.55176e7 −2.12767
\(927\) −1.08555e7 −0.414907
\(928\) −3.81709e7 −1.45500
\(929\) 2.73689e7 1.04044 0.520221 0.854032i \(-0.325850\pi\)
0.520221 + 0.854032i \(0.325850\pi\)
\(930\) −1.84797e7 −0.700628
\(931\) 9.94715e6 0.376118
\(932\) 9.61563e7 3.62608
\(933\) −1.17195e7 −0.440762
\(934\) 3.82097e6 0.143320
\(935\) −6.39136e6 −0.239092
\(936\) −1.93306e7 −0.721199
\(937\) 4.36536e7 1.62432 0.812158 0.583437i \(-0.198292\pi\)
0.812158 + 0.583437i \(0.198292\pi\)
\(938\) 1.21803e7 0.452014
\(939\) −2.13850e7 −0.791491
\(940\) 4.80663e7 1.77428
\(941\) 9.38560e6 0.345532 0.172766 0.984963i \(-0.444730\pi\)
0.172766 + 0.984963i \(0.444730\pi\)
\(942\) −9.97564e6 −0.366280
\(943\) 1.31146e7 0.480260
\(944\) 6.63179e6 0.242215
\(945\) −7.95823e6 −0.289893
\(946\) −4.57557e7 −1.66233
\(947\) 1.33282e7 0.482942 0.241471 0.970408i \(-0.422370\pi\)
0.241471 + 0.970408i \(0.422370\pi\)
\(948\) −3.74994e7 −1.35520
\(949\) −1.28147e7 −0.461893
\(950\) 1.45170e8 5.21876
\(951\) 2.37307e7 0.850864
\(952\) 1.51019e7 0.540057
\(953\) 3.84674e7 1.37202 0.686010 0.727592i \(-0.259361\pi\)
0.686010 + 0.727592i \(0.259361\pi\)
\(954\) −1.51319e7 −0.538297
\(955\) −9.77145e7 −3.46697
\(956\) −9.22053e7 −3.26296
\(957\) −1.06596e7 −0.376236
\(958\) 5.37643e6 0.189269
\(959\) −4.35015e7 −1.52742
\(960\) −2.55727e6 −0.0895567
\(961\) −2.45315e7 −0.856871
\(962\) −2.11390e7 −0.736455
\(963\) 8.65195e6 0.300641
\(964\) 4.64466e7 1.60976
\(965\) −300363. −0.0103831
\(966\) −3.22341e7 −1.11141
\(967\) −4.34724e7 −1.49502 −0.747511 0.664249i \(-0.768751\pi\)
−0.747511 + 0.664249i \(0.768751\pi\)
\(968\) 5.10333e7 1.75051
\(969\) 6.31507e6 0.216057
\(970\) 4.98560e7 1.70133
\(971\) −1.32711e6 −0.0451710 −0.0225855 0.999745i \(-0.507190\pi\)
−0.0225855 + 0.999745i \(0.507190\pi\)
\(972\) 4.27734e6 0.145214
\(973\) 2.63810e7 0.893323
\(974\) 5.14172e7 1.73664
\(975\) 3.49625e7 1.17785
\(976\) −2.83212e7 −0.951670
\(977\) −2.29185e7 −0.768158 −0.384079 0.923300i \(-0.625481\pi\)
−0.384079 + 0.923300i \(0.625481\pi\)
\(978\) −1.53869e7 −0.514403
\(979\) 1.77876e7 0.593146
\(980\) 3.38668e7 1.12644
\(981\) 1.51313e7 0.501999
\(982\) −4.60146e7 −1.52271
\(983\) 5.50750e7 1.81790 0.908952 0.416900i \(-0.136884\pi\)
0.908952 + 0.416900i \(0.136884\pi\)
\(984\) −1.53070e7 −0.503969
\(985\) 4.13521e7 1.35802
\(986\) 2.07527e7 0.679801
\(987\) −6.61756e6 −0.216224
\(988\) −8.83399e7 −2.87915
\(989\) −7.36187e7 −2.39330
\(990\) −1.59226e7 −0.516327
\(991\) 5.09544e7 1.64815 0.824077 0.566478i \(-0.191694\pi\)
0.824077 + 0.566478i \(0.191694\pi\)
\(992\) 1.26429e7 0.407913
\(993\) 3.10527e6 0.0999370
\(994\) 8.99432e7 2.88737
\(995\) 9.95700e7 3.18839
\(996\) −6.44816e7 −2.05962
\(997\) −3.69215e7 −1.17636 −0.588181 0.808729i \(-0.700156\pi\)
−0.588181 + 0.808729i \(0.700156\pi\)
\(998\) −4.43198e7 −1.40855
\(999\) 2.61114e6 0.0827784
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 177.6.a.a.1.1 11
3.2 odd 2 531.6.a.b.1.11 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.1 11 1.1 even 1 trivial
531.6.a.b.1.11 11 3.2 odd 2