Properties

Label 4598.2.a.cb.1.7
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 16 x^{6} - 4 x^{5} + 75 x^{4} + 32 x^{3} - 90 x^{2} - 28 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.182716\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} +3.30349 q^{6} +2.41197 q^{7} +1.00000 q^{8} +7.91304 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} +3.30349 q^{6} +2.41197 q^{7} +1.00000 q^{8} +7.91304 q^{9} +1.88260 q^{10} +3.30349 q^{12} -3.16592 q^{13} +2.41197 q^{14} +6.21916 q^{15} +1.00000 q^{16} -0.0684367 q^{17} +7.91304 q^{18} -1.00000 q^{19} +1.88260 q^{20} +7.96793 q^{21} -7.39138 q^{23} +3.30349 q^{24} -1.45580 q^{25} -3.16592 q^{26} +16.2302 q^{27} +2.41197 q^{28} -7.11637 q^{29} +6.21916 q^{30} -5.53983 q^{31} +1.00000 q^{32} -0.0684367 q^{34} +4.54079 q^{35} +7.91304 q^{36} +8.71254 q^{37} -1.00000 q^{38} -10.4586 q^{39} +1.88260 q^{40} +2.36137 q^{41} +7.96793 q^{42} -1.76442 q^{43} +14.8971 q^{45} -7.39138 q^{46} +9.11437 q^{47} +3.30349 q^{48} -1.18238 q^{49} -1.45580 q^{50} -0.226080 q^{51} -3.16592 q^{52} +8.63343 q^{53} +16.2302 q^{54} +2.41197 q^{56} -3.30349 q^{57} -7.11637 q^{58} +5.32542 q^{59} +6.21916 q^{60} -14.3424 q^{61} -5.53983 q^{62} +19.0860 q^{63} +1.00000 q^{64} -5.96017 q^{65} +11.3594 q^{67} -0.0684367 q^{68} -24.4173 q^{69} +4.54079 q^{70} -13.1580 q^{71} +7.91304 q^{72} +5.34443 q^{73} +8.71254 q^{74} -4.80922 q^{75} -1.00000 q^{76} -10.4586 q^{78} -3.95165 q^{79} +1.88260 q^{80} +29.8770 q^{81} +2.36137 q^{82} -5.25612 q^{83} +7.96793 q^{84} -0.128839 q^{85} -1.76442 q^{86} -23.5089 q^{87} +6.41191 q^{89} +14.8971 q^{90} -7.63611 q^{91} -7.39138 q^{92} -18.3008 q^{93} +9.11437 q^{94} -1.88260 q^{95} +3.30349 q^{96} -2.67951 q^{97} -1.18238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 3.30349 1.90727 0.953635 0.300966i \(-0.0973089\pi\)
0.953635 + 0.300966i \(0.0973089\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.88260 0.841926 0.420963 0.907078i \(-0.361692\pi\)
0.420963 + 0.907078i \(0.361692\pi\)
\(6\) 3.30349 1.34864
\(7\) 2.41197 0.911640 0.455820 0.890072i \(-0.349346\pi\)
0.455820 + 0.890072i \(0.349346\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.91304 2.63768
\(10\) 1.88260 0.595332
\(11\) 0 0
\(12\) 3.30349 0.953635
\(13\) −3.16592 −0.878068 −0.439034 0.898470i \(-0.644679\pi\)
−0.439034 + 0.898470i \(0.644679\pi\)
\(14\) 2.41197 0.644627
\(15\) 6.21916 1.60578
\(16\) 1.00000 0.250000
\(17\) −0.0684367 −0.0165983 −0.00829916 0.999966i \(-0.502642\pi\)
−0.00829916 + 0.999966i \(0.502642\pi\)
\(18\) 7.91304 1.86512
\(19\) −1.00000 −0.229416
\(20\) 1.88260 0.420963
\(21\) 7.96793 1.73874
\(22\) 0 0
\(23\) −7.39138 −1.54121 −0.770605 0.637313i \(-0.780046\pi\)
−0.770605 + 0.637313i \(0.780046\pi\)
\(24\) 3.30349 0.674322
\(25\) −1.45580 −0.291160
\(26\) −3.16592 −0.620888
\(27\) 16.2302 3.12350
\(28\) 2.41197 0.455820
\(29\) −7.11637 −1.32148 −0.660738 0.750616i \(-0.729757\pi\)
−0.660738 + 0.750616i \(0.729757\pi\)
\(30\) 6.21916 1.13546
\(31\) −5.53983 −0.994982 −0.497491 0.867469i \(-0.665745\pi\)
−0.497491 + 0.867469i \(0.665745\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −0.0684367 −0.0117368
\(35\) 4.54079 0.767534
\(36\) 7.91304 1.31884
\(37\) 8.71254 1.43233 0.716166 0.697930i \(-0.245895\pi\)
0.716166 + 0.697930i \(0.245895\pi\)
\(38\) −1.00000 −0.162221
\(39\) −10.4586 −1.67471
\(40\) 1.88260 0.297666
\(41\) 2.36137 0.368783 0.184392 0.982853i \(-0.440969\pi\)
0.184392 + 0.982853i \(0.440969\pi\)
\(42\) 7.96793 1.22948
\(43\) −1.76442 −0.269072 −0.134536 0.990909i \(-0.542954\pi\)
−0.134536 + 0.990909i \(0.542954\pi\)
\(44\) 0 0
\(45\) 14.8971 2.22073
\(46\) −7.39138 −1.08980
\(47\) 9.11437 1.32947 0.664734 0.747080i \(-0.268545\pi\)
0.664734 + 0.747080i \(0.268545\pi\)
\(48\) 3.30349 0.476818
\(49\) −1.18238 −0.168912
\(50\) −1.45580 −0.205881
\(51\) −0.226080 −0.0316575
\(52\) −3.16592 −0.439034
\(53\) 8.63343 1.18589 0.592947 0.805242i \(-0.297964\pi\)
0.592947 + 0.805242i \(0.297964\pi\)
\(54\) 16.2302 2.20865
\(55\) 0 0
\(56\) 2.41197 0.322314
\(57\) −3.30349 −0.437558
\(58\) −7.11637 −0.934425
\(59\) 5.32542 0.693311 0.346655 0.937993i \(-0.387317\pi\)
0.346655 + 0.937993i \(0.387317\pi\)
\(60\) 6.21916 0.802891
\(61\) −14.3424 −1.83636 −0.918179 0.396165i \(-0.870341\pi\)
−0.918179 + 0.396165i \(0.870341\pi\)
\(62\) −5.53983 −0.703559
\(63\) 19.0860 2.40461
\(64\) 1.00000 0.125000
\(65\) −5.96017 −0.739269
\(66\) 0 0
\(67\) 11.3594 1.38777 0.693883 0.720088i \(-0.255898\pi\)
0.693883 + 0.720088i \(0.255898\pi\)
\(68\) −0.0684367 −0.00829916
\(69\) −24.4173 −2.93950
\(70\) 4.54079 0.542729
\(71\) −13.1580 −1.56156 −0.780782 0.624803i \(-0.785179\pi\)
−0.780782 + 0.624803i \(0.785179\pi\)
\(72\) 7.91304 0.932560
\(73\) 5.34443 0.625519 0.312759 0.949832i \(-0.398747\pi\)
0.312759 + 0.949832i \(0.398747\pi\)
\(74\) 8.71254 1.01281
\(75\) −4.80922 −0.555320
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −10.4586 −1.18420
\(79\) −3.95165 −0.444595 −0.222298 0.974979i \(-0.571356\pi\)
−0.222298 + 0.974979i \(0.571356\pi\)
\(80\) 1.88260 0.210482
\(81\) 29.8770 3.31967
\(82\) 2.36137 0.260769
\(83\) −5.25612 −0.576934 −0.288467 0.957490i \(-0.593146\pi\)
−0.288467 + 0.957490i \(0.593146\pi\)
\(84\) 7.96793 0.869372
\(85\) −0.128839 −0.0139746
\(86\) −1.76442 −0.190262
\(87\) −23.5089 −2.52041
\(88\) 0 0
\(89\) 6.41191 0.679661 0.339831 0.940487i \(-0.389630\pi\)
0.339831 + 0.940487i \(0.389630\pi\)
\(90\) 14.8971 1.57029
\(91\) −7.63611 −0.800482
\(92\) −7.39138 −0.770605
\(93\) −18.3008 −1.89770
\(94\) 9.11437 0.940075
\(95\) −1.88260 −0.193151
\(96\) 3.30349 0.337161
\(97\) −2.67951 −0.272063 −0.136032 0.990704i \(-0.543435\pi\)
−0.136032 + 0.990704i \(0.543435\pi\)
\(98\) −1.18238 −0.119439
\(99\) 0 0
\(100\) −1.45580 −0.145580
\(101\) −11.8482 −1.17894 −0.589471 0.807789i \(-0.700664\pi\)
−0.589471 + 0.807789i \(0.700664\pi\)
\(102\) −0.226080 −0.0223852
\(103\) −11.8327 −1.16591 −0.582957 0.812503i \(-0.698104\pi\)
−0.582957 + 0.812503i \(0.698104\pi\)
\(104\) −3.16592 −0.310444
\(105\) 15.0005 1.46389
\(106\) 8.63343 0.838553
\(107\) 8.26216 0.798733 0.399367 0.916791i \(-0.369230\pi\)
0.399367 + 0.916791i \(0.369230\pi\)
\(108\) 16.2302 1.56175
\(109\) 4.92876 0.472090 0.236045 0.971742i \(-0.424149\pi\)
0.236045 + 0.971742i \(0.424149\pi\)
\(110\) 0 0
\(111\) 28.7818 2.73184
\(112\) 2.41197 0.227910
\(113\) −19.1454 −1.80105 −0.900524 0.434807i \(-0.856817\pi\)
−0.900524 + 0.434807i \(0.856817\pi\)
\(114\) −3.30349 −0.309400
\(115\) −13.9151 −1.29759
\(116\) −7.11637 −0.660738
\(117\) −25.0520 −2.31606
\(118\) 5.32542 0.490245
\(119\) −0.165067 −0.0151317
\(120\) 6.21916 0.567729
\(121\) 0 0
\(122\) −14.3424 −1.29850
\(123\) 7.80074 0.703369
\(124\) −5.53983 −0.497491
\(125\) −12.1537 −1.08706
\(126\) 19.0860 1.70032
\(127\) −1.25227 −0.111121 −0.0555606 0.998455i \(-0.517695\pi\)
−0.0555606 + 0.998455i \(0.517695\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.82874 −0.513192
\(130\) −5.96017 −0.522742
\(131\) 13.7739 1.20343 0.601714 0.798711i \(-0.294485\pi\)
0.601714 + 0.798711i \(0.294485\pi\)
\(132\) 0 0
\(133\) −2.41197 −0.209145
\(134\) 11.3594 0.981299
\(135\) 30.5550 2.62975
\(136\) −0.0684367 −0.00586839
\(137\) 1.83597 0.156858 0.0784289 0.996920i \(-0.475010\pi\)
0.0784289 + 0.996920i \(0.475010\pi\)
\(138\) −24.4173 −2.07854
\(139\) −15.9172 −1.35008 −0.675039 0.737782i \(-0.735873\pi\)
−0.675039 + 0.737782i \(0.735873\pi\)
\(140\) 4.54079 0.383767
\(141\) 30.1092 2.53565
\(142\) −13.1580 −1.10419
\(143\) 0 0
\(144\) 7.91304 0.659420
\(145\) −13.3973 −1.11259
\(146\) 5.34443 0.442308
\(147\) −3.90598 −0.322160
\(148\) 8.71254 0.716166
\(149\) −3.08074 −0.252384 −0.126192 0.992006i \(-0.540276\pi\)
−0.126192 + 0.992006i \(0.540276\pi\)
\(150\) −4.80922 −0.392671
\(151\) 17.4026 1.41620 0.708101 0.706112i \(-0.249552\pi\)
0.708101 + 0.706112i \(0.249552\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −0.541542 −0.0437811
\(154\) 0 0
\(155\) −10.4293 −0.837702
\(156\) −10.4586 −0.837356
\(157\) 8.92808 0.712538 0.356269 0.934383i \(-0.384049\pi\)
0.356269 + 0.934383i \(0.384049\pi\)
\(158\) −3.95165 −0.314376
\(159\) 28.5205 2.26182
\(160\) 1.88260 0.148833
\(161\) −17.8278 −1.40503
\(162\) 29.8770 2.34736
\(163\) −3.61306 −0.282997 −0.141498 0.989938i \(-0.545192\pi\)
−0.141498 + 0.989938i \(0.545192\pi\)
\(164\) 2.36137 0.184392
\(165\) 0 0
\(166\) −5.25612 −0.407954
\(167\) −24.7026 −1.91154 −0.955771 0.294112i \(-0.904976\pi\)
−0.955771 + 0.294112i \(0.904976\pi\)
\(168\) 7.96793 0.614739
\(169\) −2.97696 −0.228997
\(170\) −0.128839 −0.00988151
\(171\) −7.91304 −0.605125
\(172\) −1.76442 −0.134536
\(173\) 14.2517 1.08354 0.541770 0.840527i \(-0.317754\pi\)
0.541770 + 0.840527i \(0.317754\pi\)
\(174\) −23.5089 −1.78220
\(175\) −3.51135 −0.265433
\(176\) 0 0
\(177\) 17.5925 1.32233
\(178\) 6.41191 0.480593
\(179\) −12.3954 −0.926475 −0.463237 0.886234i \(-0.653312\pi\)
−0.463237 + 0.886234i \(0.653312\pi\)
\(180\) 14.8971 1.11037
\(181\) 9.78871 0.727589 0.363795 0.931479i \(-0.381481\pi\)
0.363795 + 0.931479i \(0.381481\pi\)
\(182\) −7.63611 −0.566026
\(183\) −47.3800 −3.50243
\(184\) −7.39138 −0.544900
\(185\) 16.4023 1.20592
\(186\) −18.3008 −1.34188
\(187\) 0 0
\(188\) 9.11437 0.664734
\(189\) 39.1467 2.84751
\(190\) −1.88260 −0.136579
\(191\) 4.26597 0.308674 0.154337 0.988018i \(-0.450676\pi\)
0.154337 + 0.988018i \(0.450676\pi\)
\(192\) 3.30349 0.238409
\(193\) −10.3339 −0.743854 −0.371927 0.928262i \(-0.621303\pi\)
−0.371927 + 0.928262i \(0.621303\pi\)
\(194\) −2.67951 −0.192378
\(195\) −19.6894 −1.40998
\(196\) −1.18238 −0.0844558
\(197\) 12.8943 0.918683 0.459342 0.888260i \(-0.348085\pi\)
0.459342 + 0.888260i \(0.348085\pi\)
\(198\) 0 0
\(199\) 13.1491 0.932117 0.466059 0.884754i \(-0.345674\pi\)
0.466059 + 0.884754i \(0.345674\pi\)
\(200\) −1.45580 −0.102941
\(201\) 37.5255 2.64684
\(202\) −11.8482 −0.833638
\(203\) −17.1645 −1.20471
\(204\) −0.226080 −0.0158287
\(205\) 4.44552 0.310488
\(206\) −11.8327 −0.824426
\(207\) −58.4883 −4.06522
\(208\) −3.16592 −0.219517
\(209\) 0 0
\(210\) 15.0005 1.03513
\(211\) 26.5013 1.82442 0.912212 0.409719i \(-0.134373\pi\)
0.912212 + 0.409719i \(0.134373\pi\)
\(212\) 8.63343 0.592947
\(213\) −43.4672 −2.97833
\(214\) 8.26216 0.564790
\(215\) −3.32171 −0.226539
\(216\) 16.2302 1.10432
\(217\) −13.3619 −0.907066
\(218\) 4.92876 0.333818
\(219\) 17.6553 1.19303
\(220\) 0 0
\(221\) 0.216665 0.0145745
\(222\) 28.7818 1.93171
\(223\) −29.7656 −1.99325 −0.996625 0.0820854i \(-0.973842\pi\)
−0.996625 + 0.0820854i \(0.973842\pi\)
\(224\) 2.41197 0.161157
\(225\) −11.5198 −0.767986
\(226\) −19.1454 −1.27353
\(227\) 24.0754 1.59794 0.798969 0.601372i \(-0.205379\pi\)
0.798969 + 0.601372i \(0.205379\pi\)
\(228\) −3.30349 −0.218779
\(229\) 7.85068 0.518787 0.259394 0.965772i \(-0.416477\pi\)
0.259394 + 0.965772i \(0.416477\pi\)
\(230\) −13.9151 −0.917531
\(231\) 0 0
\(232\) −7.11637 −0.467213
\(233\) −22.1903 −1.45374 −0.726869 0.686776i \(-0.759025\pi\)
−0.726869 + 0.686776i \(0.759025\pi\)
\(234\) −25.0520 −1.63770
\(235\) 17.1588 1.11931
\(236\) 5.32542 0.346655
\(237\) −13.0542 −0.847963
\(238\) −0.165067 −0.0106997
\(239\) −2.33473 −0.151021 −0.0755107 0.997145i \(-0.524059\pi\)
−0.0755107 + 0.997145i \(0.524059\pi\)
\(240\) 6.21916 0.401445
\(241\) 28.6284 1.84412 0.922060 0.387046i \(-0.126505\pi\)
0.922060 + 0.387046i \(0.126505\pi\)
\(242\) 0 0
\(243\) 50.0080 3.20801
\(244\) −14.3424 −0.918179
\(245\) −2.22596 −0.142211
\(246\) 7.80074 0.497357
\(247\) 3.16592 0.201443
\(248\) −5.53983 −0.351779
\(249\) −17.3635 −1.10037
\(250\) −12.1537 −0.768669
\(251\) 5.69434 0.359424 0.179712 0.983719i \(-0.442483\pi\)
0.179712 + 0.983719i \(0.442483\pi\)
\(252\) 19.0860 1.20231
\(253\) 0 0
\(254\) −1.25227 −0.0785746
\(255\) −0.425619 −0.0266533
\(256\) 1.00000 0.0625000
\(257\) −14.4196 −0.899473 −0.449737 0.893161i \(-0.648482\pi\)
−0.449737 + 0.893161i \(0.648482\pi\)
\(258\) −5.82874 −0.362882
\(259\) 21.0144 1.30577
\(260\) −5.96017 −0.369634
\(261\) −56.3121 −3.48563
\(262\) 13.7739 0.850953
\(263\) −6.25442 −0.385664 −0.192832 0.981232i \(-0.561767\pi\)
−0.192832 + 0.981232i \(0.561767\pi\)
\(264\) 0 0
\(265\) 16.2533 0.998435
\(266\) −2.41197 −0.147888
\(267\) 21.1817 1.29630
\(268\) 11.3594 0.693883
\(269\) 16.9603 1.03409 0.517043 0.855960i \(-0.327033\pi\)
0.517043 + 0.855960i \(0.327033\pi\)
\(270\) 30.5550 1.85952
\(271\) 10.9294 0.663912 0.331956 0.943295i \(-0.392291\pi\)
0.331956 + 0.943295i \(0.392291\pi\)
\(272\) −0.0684367 −0.00414958
\(273\) −25.2258 −1.52674
\(274\) 1.83597 0.110915
\(275\) 0 0
\(276\) −24.4173 −1.46975
\(277\) 17.4179 1.04654 0.523271 0.852166i \(-0.324711\pi\)
0.523271 + 0.852166i \(0.324711\pi\)
\(278\) −15.9172 −0.954649
\(279\) −43.8368 −2.62444
\(280\) 4.54079 0.271364
\(281\) 11.8423 0.706451 0.353225 0.935538i \(-0.385085\pi\)
0.353225 + 0.935538i \(0.385085\pi\)
\(282\) 30.1092 1.79298
\(283\) 3.87917 0.230593 0.115296 0.993331i \(-0.463218\pi\)
0.115296 + 0.993331i \(0.463218\pi\)
\(284\) −13.1580 −0.780782
\(285\) −6.21916 −0.368391
\(286\) 0 0
\(287\) 5.69555 0.336198
\(288\) 7.91304 0.466280
\(289\) −16.9953 −0.999724
\(290\) −13.3973 −0.786717
\(291\) −8.85174 −0.518898
\(292\) 5.34443 0.312759
\(293\) −0.882661 −0.0515656 −0.0257828 0.999668i \(-0.508208\pi\)
−0.0257828 + 0.999668i \(0.508208\pi\)
\(294\) −3.90598 −0.227802
\(295\) 10.0257 0.583717
\(296\) 8.71254 0.506406
\(297\) 0 0
\(298\) −3.08074 −0.178462
\(299\) 23.4005 1.35329
\(300\) −4.80922 −0.277660
\(301\) −4.25574 −0.245297
\(302\) 17.4026 1.00141
\(303\) −39.1405 −2.24856
\(304\) −1.00000 −0.0573539
\(305\) −27.0011 −1.54608
\(306\) −0.541542 −0.0309579
\(307\) 21.8100 1.24476 0.622380 0.782715i \(-0.286166\pi\)
0.622380 + 0.782715i \(0.286166\pi\)
\(308\) 0 0
\(309\) −39.0893 −2.22371
\(310\) −10.4293 −0.592345
\(311\) 7.08973 0.402022 0.201011 0.979589i \(-0.435577\pi\)
0.201011 + 0.979589i \(0.435577\pi\)
\(312\) −10.4586 −0.592100
\(313\) 7.51385 0.424708 0.212354 0.977193i \(-0.431887\pi\)
0.212354 + 0.977193i \(0.431887\pi\)
\(314\) 8.92808 0.503841
\(315\) 35.9315 2.02451
\(316\) −3.95165 −0.222298
\(317\) 15.4744 0.869131 0.434566 0.900640i \(-0.356902\pi\)
0.434566 + 0.900640i \(0.356902\pi\)
\(318\) 28.5205 1.59935
\(319\) 0 0
\(320\) 1.88260 0.105241
\(321\) 27.2940 1.52340
\(322\) −17.8278 −0.993506
\(323\) 0.0684367 0.00380792
\(324\) 29.8770 1.65984
\(325\) 4.60894 0.255658
\(326\) −3.61306 −0.200109
\(327\) 16.2821 0.900402
\(328\) 2.36137 0.130385
\(329\) 21.9836 1.21200
\(330\) 0 0
\(331\) 10.4405 0.573864 0.286932 0.957951i \(-0.407365\pi\)
0.286932 + 0.957951i \(0.407365\pi\)
\(332\) −5.25612 −0.288467
\(333\) 68.9426 3.77803
\(334\) −24.7026 −1.35166
\(335\) 21.3852 1.16840
\(336\) 7.96793 0.434686
\(337\) −26.5055 −1.44385 −0.721924 0.691972i \(-0.756742\pi\)
−0.721924 + 0.691972i \(0.756742\pi\)
\(338\) −2.97696 −0.161925
\(339\) −63.2466 −3.43508
\(340\) −0.128839 −0.00698729
\(341\) 0 0
\(342\) −7.91304 −0.427888
\(343\) −19.7357 −1.06563
\(344\) −1.76442 −0.0951312
\(345\) −45.9682 −2.47485
\(346\) 14.2517 0.766179
\(347\) 23.8096 1.27817 0.639084 0.769137i \(-0.279314\pi\)
0.639084 + 0.769137i \(0.279314\pi\)
\(348\) −23.5089 −1.26021
\(349\) −21.0247 −1.12543 −0.562714 0.826652i \(-0.690243\pi\)
−0.562714 + 0.826652i \(0.690243\pi\)
\(350\) −3.51135 −0.187690
\(351\) −51.3834 −2.74264
\(352\) 0 0
\(353\) 18.4736 0.983253 0.491626 0.870806i \(-0.336403\pi\)
0.491626 + 0.870806i \(0.336403\pi\)
\(354\) 17.5925 0.935029
\(355\) −24.7713 −1.31472
\(356\) 6.41191 0.339831
\(357\) −0.545298 −0.0288603
\(358\) −12.3954 −0.655117
\(359\) 34.8001 1.83668 0.918341 0.395791i \(-0.129529\pi\)
0.918341 + 0.395791i \(0.129529\pi\)
\(360\) 14.8971 0.785147
\(361\) 1.00000 0.0526316
\(362\) 9.78871 0.514483
\(363\) 0 0
\(364\) −7.63611 −0.400241
\(365\) 10.0615 0.526641
\(366\) −47.3800 −2.47659
\(367\) −10.0520 −0.524713 −0.262356 0.964971i \(-0.584500\pi\)
−0.262356 + 0.964971i \(0.584500\pi\)
\(368\) −7.39138 −0.385302
\(369\) 18.6856 0.972732
\(370\) 16.4023 0.852713
\(371\) 20.8236 1.08111
\(372\) −18.3008 −0.948850
\(373\) −20.6591 −1.06969 −0.534843 0.844951i \(-0.679629\pi\)
−0.534843 + 0.844951i \(0.679629\pi\)
\(374\) 0 0
\(375\) −40.1497 −2.07332
\(376\) 9.11437 0.470038
\(377\) 22.5299 1.16035
\(378\) 39.1467 2.01349
\(379\) 11.5387 0.592704 0.296352 0.955079i \(-0.404230\pi\)
0.296352 + 0.955079i \(0.404230\pi\)
\(380\) −1.88260 −0.0965756
\(381\) −4.13687 −0.211938
\(382\) 4.26597 0.218266
\(383\) 5.30452 0.271048 0.135524 0.990774i \(-0.456728\pi\)
0.135524 + 0.990774i \(0.456728\pi\)
\(384\) 3.30349 0.168580
\(385\) 0 0
\(386\) −10.3339 −0.525984
\(387\) −13.9619 −0.709725
\(388\) −2.67951 −0.136032
\(389\) −22.9500 −1.16361 −0.581805 0.813328i \(-0.697653\pi\)
−0.581805 + 0.813328i \(0.697653\pi\)
\(390\) −19.6894 −0.997010
\(391\) 0.505842 0.0255815
\(392\) −1.18238 −0.0597193
\(393\) 45.5018 2.29526
\(394\) 12.8943 0.649607
\(395\) −7.43939 −0.374316
\(396\) 0 0
\(397\) 0.483759 0.0242792 0.0121396 0.999926i \(-0.496136\pi\)
0.0121396 + 0.999926i \(0.496136\pi\)
\(398\) 13.1491 0.659106
\(399\) −7.96793 −0.398895
\(400\) −1.45580 −0.0727900
\(401\) −36.1672 −1.80610 −0.903051 0.429532i \(-0.858678\pi\)
−0.903051 + 0.429532i \(0.858678\pi\)
\(402\) 37.5255 1.87160
\(403\) 17.5386 0.873662
\(404\) −11.8482 −0.589471
\(405\) 56.2467 2.79492
\(406\) −17.1645 −0.851860
\(407\) 0 0
\(408\) −0.226080 −0.0111926
\(409\) 12.0788 0.597256 0.298628 0.954370i \(-0.403471\pi\)
0.298628 + 0.954370i \(0.403471\pi\)
\(410\) 4.44552 0.219548
\(411\) 6.06512 0.299170
\(412\) −11.8327 −0.582957
\(413\) 12.8448 0.632050
\(414\) −58.4883 −2.87454
\(415\) −9.89520 −0.485736
\(416\) −3.16592 −0.155222
\(417\) −52.5822 −2.57496
\(418\) 0 0
\(419\) −14.4844 −0.707611 −0.353806 0.935319i \(-0.615113\pi\)
−0.353806 + 0.935319i \(0.615113\pi\)
\(420\) 15.0005 0.731947
\(421\) 8.74595 0.426252 0.213126 0.977025i \(-0.431636\pi\)
0.213126 + 0.977025i \(0.431636\pi\)
\(422\) 26.5013 1.29006
\(423\) 72.1223 3.50671
\(424\) 8.63343 0.419277
\(425\) 0.0996300 0.00483277
\(426\) −43.4672 −2.10599
\(427\) −34.5935 −1.67410
\(428\) 8.26216 0.399367
\(429\) 0 0
\(430\) −3.32171 −0.160187
\(431\) 18.0983 0.871763 0.435881 0.900004i \(-0.356437\pi\)
0.435881 + 0.900004i \(0.356437\pi\)
\(432\) 16.2302 0.780874
\(433\) 19.3031 0.927648 0.463824 0.885927i \(-0.346477\pi\)
0.463824 + 0.885927i \(0.346477\pi\)
\(434\) −13.3619 −0.641392
\(435\) −44.2579 −2.12200
\(436\) 4.92876 0.236045
\(437\) 7.39138 0.353578
\(438\) 17.6553 0.843602
\(439\) −0.543248 −0.0259278 −0.0129639 0.999916i \(-0.504127\pi\)
−0.0129639 + 0.999916i \(0.504127\pi\)
\(440\) 0 0
\(441\) −9.35623 −0.445535
\(442\) 0.216665 0.0103057
\(443\) −24.5763 −1.16765 −0.583827 0.811878i \(-0.698445\pi\)
−0.583827 + 0.811878i \(0.698445\pi\)
\(444\) 28.7818 1.36592
\(445\) 12.0711 0.572225
\(446\) −29.7656 −1.40944
\(447\) −10.1772 −0.481365
\(448\) 2.41197 0.113955
\(449\) 30.2173 1.42604 0.713022 0.701141i \(-0.247326\pi\)
0.713022 + 0.701141i \(0.247326\pi\)
\(450\) −11.5198 −0.543048
\(451\) 0 0
\(452\) −19.1454 −0.900524
\(453\) 57.4892 2.70108
\(454\) 24.0754 1.12991
\(455\) −14.3758 −0.673947
\(456\) −3.30349 −0.154700
\(457\) 34.7631 1.62615 0.813073 0.582161i \(-0.197793\pi\)
0.813073 + 0.582161i \(0.197793\pi\)
\(458\) 7.85068 0.366838
\(459\) −1.11074 −0.0518448
\(460\) −13.9151 −0.648793
\(461\) 10.2206 0.476019 0.238010 0.971263i \(-0.423505\pi\)
0.238010 + 0.971263i \(0.423505\pi\)
\(462\) 0 0
\(463\) −5.73645 −0.266596 −0.133298 0.991076i \(-0.542557\pi\)
−0.133298 + 0.991076i \(0.542557\pi\)
\(464\) −7.11637 −0.330369
\(465\) −34.4531 −1.59772
\(466\) −22.1903 −1.02795
\(467\) −25.2965 −1.17058 −0.585292 0.810823i \(-0.699020\pi\)
−0.585292 + 0.810823i \(0.699020\pi\)
\(468\) −25.0520 −1.15803
\(469\) 27.3985 1.26514
\(470\) 17.1588 0.791474
\(471\) 29.4938 1.35900
\(472\) 5.32542 0.245122
\(473\) 0 0
\(474\) −13.0542 −0.599600
\(475\) 1.45580 0.0667966
\(476\) −0.165067 −0.00756585
\(477\) 68.3167 3.12801
\(478\) −2.33473 −0.106788
\(479\) −6.51483 −0.297670 −0.148835 0.988862i \(-0.547552\pi\)
−0.148835 + 0.988862i \(0.547552\pi\)
\(480\) 6.21916 0.283865
\(481\) −27.5832 −1.25769
\(482\) 28.6284 1.30399
\(483\) −58.8940 −2.67977
\(484\) 0 0
\(485\) −5.04446 −0.229057
\(486\) 50.0080 2.26841
\(487\) −26.5992 −1.20532 −0.602662 0.797997i \(-0.705893\pi\)
−0.602662 + 0.797997i \(0.705893\pi\)
\(488\) −14.3424 −0.649251
\(489\) −11.9357 −0.539751
\(490\) −2.22596 −0.100559
\(491\) −16.5430 −0.746576 −0.373288 0.927715i \(-0.621770\pi\)
−0.373288 + 0.927715i \(0.621770\pi\)
\(492\) 7.80074 0.351685
\(493\) 0.487021 0.0219343
\(494\) 3.16592 0.142441
\(495\) 0 0
\(496\) −5.53983 −0.248746
\(497\) −31.7367 −1.42359
\(498\) −17.3635 −0.778079
\(499\) 8.60654 0.385282 0.192641 0.981269i \(-0.438295\pi\)
0.192641 + 0.981269i \(0.438295\pi\)
\(500\) −12.1537 −0.543531
\(501\) −81.6047 −3.64583
\(502\) 5.69434 0.254151
\(503\) −10.3371 −0.460906 −0.230453 0.973083i \(-0.574021\pi\)
−0.230453 + 0.973083i \(0.574021\pi\)
\(504\) 19.0860 0.850160
\(505\) −22.3055 −0.992583
\(506\) 0 0
\(507\) −9.83434 −0.436758
\(508\) −1.25227 −0.0555606
\(509\) −35.1873 −1.55965 −0.779825 0.625997i \(-0.784692\pi\)
−0.779825 + 0.625997i \(0.784692\pi\)
\(510\) −0.425619 −0.0188467
\(511\) 12.8906 0.570248
\(512\) 1.00000 0.0441942
\(513\) −16.2302 −0.716579
\(514\) −14.4196 −0.636023
\(515\) −22.2764 −0.981614
\(516\) −5.82874 −0.256596
\(517\) 0 0
\(518\) 21.0144 0.923320
\(519\) 47.0805 2.06660
\(520\) −5.96017 −0.261371
\(521\) 9.17004 0.401747 0.200873 0.979617i \(-0.435622\pi\)
0.200873 + 0.979617i \(0.435622\pi\)
\(522\) −56.3121 −2.46471
\(523\) −40.4012 −1.76662 −0.883311 0.468788i \(-0.844691\pi\)
−0.883311 + 0.468788i \(0.844691\pi\)
\(524\) 13.7739 0.601714
\(525\) −11.5997 −0.506253
\(526\) −6.25442 −0.272706
\(527\) 0.379127 0.0165150
\(528\) 0 0
\(529\) 31.6325 1.37533
\(530\) 16.2533 0.706000
\(531\) 42.1402 1.82873
\(532\) −2.41197 −0.104572
\(533\) −7.47589 −0.323817
\(534\) 21.1817 0.916620
\(535\) 15.5544 0.672475
\(536\) 11.3594 0.490649
\(537\) −40.9480 −1.76704
\(538\) 16.9603 0.731209
\(539\) 0 0
\(540\) 30.5550 1.31488
\(541\) −22.9546 −0.986895 −0.493447 0.869776i \(-0.664263\pi\)
−0.493447 + 0.869776i \(0.664263\pi\)
\(542\) 10.9294 0.469456
\(543\) 32.3369 1.38771
\(544\) −0.0684367 −0.00293420
\(545\) 9.27891 0.397465
\(546\) −25.2258 −1.07957
\(547\) −22.0926 −0.944611 −0.472306 0.881435i \(-0.656578\pi\)
−0.472306 + 0.881435i \(0.656578\pi\)
\(548\) 1.83597 0.0784289
\(549\) −113.492 −4.84373
\(550\) 0 0
\(551\) 7.11637 0.303168
\(552\) −24.4173 −1.03927
\(553\) −9.53127 −0.405311
\(554\) 17.4179 0.740017
\(555\) 54.1847 2.30001
\(556\) −15.9172 −0.675039
\(557\) −1.14809 −0.0486463 −0.0243232 0.999704i \(-0.507743\pi\)
−0.0243232 + 0.999704i \(0.507743\pi\)
\(558\) −43.8368 −1.85576
\(559\) 5.58601 0.236263
\(560\) 4.54079 0.191884
\(561\) 0 0
\(562\) 11.8423 0.499536
\(563\) −40.9190 −1.72453 −0.862265 0.506458i \(-0.830954\pi\)
−0.862265 + 0.506458i \(0.830954\pi\)
\(564\) 30.1092 1.26783
\(565\) −36.0432 −1.51635
\(566\) 3.87917 0.163054
\(567\) 72.0626 3.02635
\(568\) −13.1580 −0.552097
\(569\) 7.10111 0.297694 0.148847 0.988860i \(-0.452444\pi\)
0.148847 + 0.988860i \(0.452444\pi\)
\(570\) −6.21916 −0.260492
\(571\) 21.1001 0.883012 0.441506 0.897258i \(-0.354444\pi\)
0.441506 + 0.897258i \(0.354444\pi\)
\(572\) 0 0
\(573\) 14.0926 0.588725
\(574\) 5.69555 0.237728
\(575\) 10.7604 0.448738
\(576\) 7.91304 0.329710
\(577\) −24.3512 −1.01375 −0.506877 0.862018i \(-0.669200\pi\)
−0.506877 + 0.862018i \(0.669200\pi\)
\(578\) −16.9953 −0.706912
\(579\) −34.1381 −1.41873
\(580\) −13.3973 −0.556293
\(581\) −12.6776 −0.525957
\(582\) −8.85174 −0.366916
\(583\) 0 0
\(584\) 5.34443 0.221154
\(585\) −47.1631 −1.94995
\(586\) −0.882661 −0.0364624
\(587\) 10.9498 0.451946 0.225973 0.974134i \(-0.427444\pi\)
0.225973 + 0.974134i \(0.427444\pi\)
\(588\) −3.90598 −0.161080
\(589\) 5.53983 0.228265
\(590\) 10.0257 0.412750
\(591\) 42.5963 1.75218
\(592\) 8.71254 0.358083
\(593\) 34.8544 1.43130 0.715649 0.698461i \(-0.246131\pi\)
0.715649 + 0.698461i \(0.246131\pi\)
\(594\) 0 0
\(595\) −0.310757 −0.0127398
\(596\) −3.08074 −0.126192
\(597\) 43.4380 1.77780
\(598\) 23.4005 0.956918
\(599\) 12.0037 0.490460 0.245230 0.969465i \(-0.421137\pi\)
0.245230 + 0.969465i \(0.421137\pi\)
\(600\) −4.80922 −0.196335
\(601\) −15.7288 −0.641591 −0.320795 0.947148i \(-0.603950\pi\)
−0.320795 + 0.947148i \(0.603950\pi\)
\(602\) −4.25574 −0.173451
\(603\) 89.8870 3.66048
\(604\) 17.4026 0.708101
\(605\) 0 0
\(606\) −39.1405 −1.58997
\(607\) −25.9881 −1.05482 −0.527412 0.849610i \(-0.676837\pi\)
−0.527412 + 0.849610i \(0.676837\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −56.7027 −2.29771
\(610\) −27.0011 −1.09324
\(611\) −28.8554 −1.16736
\(612\) −0.541542 −0.0218905
\(613\) 38.5286 1.55616 0.778078 0.628168i \(-0.216195\pi\)
0.778078 + 0.628168i \(0.216195\pi\)
\(614\) 21.8100 0.880178
\(615\) 14.6857 0.592185
\(616\) 0 0
\(617\) 1.01409 0.0408255 0.0204128 0.999792i \(-0.493502\pi\)
0.0204128 + 0.999792i \(0.493502\pi\)
\(618\) −39.0893 −1.57240
\(619\) 23.3860 0.939964 0.469982 0.882676i \(-0.344260\pi\)
0.469982 + 0.882676i \(0.344260\pi\)
\(620\) −10.4293 −0.418851
\(621\) −119.963 −4.81396
\(622\) 7.08973 0.284272
\(623\) 15.4654 0.619606
\(624\) −10.4586 −0.418678
\(625\) −15.6017 −0.624066
\(626\) 7.51385 0.300314
\(627\) 0 0
\(628\) 8.92808 0.356269
\(629\) −0.596257 −0.0237743
\(630\) 35.9315 1.43154
\(631\) 11.2632 0.448382 0.224191 0.974545i \(-0.428026\pi\)
0.224191 + 0.974545i \(0.428026\pi\)
\(632\) −3.95165 −0.157188
\(633\) 87.5467 3.47967
\(634\) 15.4744 0.614569
\(635\) −2.35753 −0.0935559
\(636\) 28.5205 1.13091
\(637\) 3.74333 0.148316
\(638\) 0 0
\(639\) −104.120 −4.11891
\(640\) 1.88260 0.0744165
\(641\) −12.1252 −0.478918 −0.239459 0.970906i \(-0.576970\pi\)
−0.239459 + 0.970906i \(0.576970\pi\)
\(642\) 27.2940 1.07721
\(643\) 9.15192 0.360916 0.180458 0.983583i \(-0.442242\pi\)
0.180458 + 0.983583i \(0.442242\pi\)
\(644\) −17.8278 −0.702515
\(645\) −10.9732 −0.432070
\(646\) 0.0684367 0.00269260
\(647\) 24.1081 0.947788 0.473894 0.880582i \(-0.342848\pi\)
0.473894 + 0.880582i \(0.342848\pi\)
\(648\) 29.8770 1.17368
\(649\) 0 0
\(650\) 4.60894 0.180778
\(651\) −44.1409 −1.73002
\(652\) −3.61306 −0.141498
\(653\) −14.8121 −0.579642 −0.289821 0.957081i \(-0.593596\pi\)
−0.289821 + 0.957081i \(0.593596\pi\)
\(654\) 16.2821 0.636681
\(655\) 25.9308 1.01320
\(656\) 2.36137 0.0921958
\(657\) 42.2907 1.64992
\(658\) 21.9836 0.857011
\(659\) 21.6275 0.842489 0.421244 0.906947i \(-0.361593\pi\)
0.421244 + 0.906947i \(0.361593\pi\)
\(660\) 0 0
\(661\) 7.88808 0.306811 0.153405 0.988163i \(-0.450976\pi\)
0.153405 + 0.988163i \(0.450976\pi\)
\(662\) 10.4405 0.405783
\(663\) 0.715750 0.0277974
\(664\) −5.25612 −0.203977
\(665\) −4.54079 −0.176084
\(666\) 68.9426 2.67147
\(667\) 52.5998 2.03667
\(668\) −24.7026 −0.955771
\(669\) −98.3302 −3.80167
\(670\) 21.3852 0.826181
\(671\) 0 0
\(672\) 7.96793 0.307370
\(673\) −29.4014 −1.13334 −0.566669 0.823945i \(-0.691768\pi\)
−0.566669 + 0.823945i \(0.691768\pi\)
\(674\) −26.5055 −1.02095
\(675\) −23.6279 −0.909437
\(676\) −2.97696 −0.114498
\(677\) −27.6599 −1.06306 −0.531528 0.847041i \(-0.678382\pi\)
−0.531528 + 0.847041i \(0.678382\pi\)
\(678\) −63.2466 −2.42897
\(679\) −6.46291 −0.248024
\(680\) −0.128839 −0.00494076
\(681\) 79.5327 3.04770
\(682\) 0 0
\(683\) −43.0143 −1.64589 −0.822947 0.568117i \(-0.807672\pi\)
−0.822947 + 0.568117i \(0.807672\pi\)
\(684\) −7.91304 −0.302563
\(685\) 3.45641 0.132063
\(686\) −19.7357 −0.753512
\(687\) 25.9346 0.989468
\(688\) −1.76442 −0.0672679
\(689\) −27.3328 −1.04129
\(690\) −45.9682 −1.74998
\(691\) −22.3751 −0.851190 −0.425595 0.904914i \(-0.639935\pi\)
−0.425595 + 0.904914i \(0.639935\pi\)
\(692\) 14.2517 0.541770
\(693\) 0 0
\(694\) 23.8096 0.903801
\(695\) −29.9658 −1.13667
\(696\) −23.5089 −0.891101
\(697\) −0.161604 −0.00612119
\(698\) −21.0247 −0.795798
\(699\) −73.3055 −2.77267
\(700\) −3.51135 −0.132717
\(701\) 16.8504 0.636430 0.318215 0.948019i \(-0.396917\pi\)
0.318215 + 0.948019i \(0.396917\pi\)
\(702\) −51.3834 −1.93934
\(703\) −8.71254 −0.328600
\(704\) 0 0
\(705\) 56.6838 2.13483
\(706\) 18.4736 0.695265
\(707\) −28.5776 −1.07477
\(708\) 17.5925 0.661165
\(709\) 1.44052 0.0541000 0.0270500 0.999634i \(-0.491389\pi\)
0.0270500 + 0.999634i \(0.491389\pi\)
\(710\) −24.7713 −0.929649
\(711\) −31.2695 −1.17270
\(712\) 6.41191 0.240296
\(713\) 40.9470 1.53348
\(714\) −0.545298 −0.0204073
\(715\) 0 0
\(716\) −12.3954 −0.463237
\(717\) −7.71277 −0.288039
\(718\) 34.8001 1.29873
\(719\) −20.5362 −0.765870 −0.382935 0.923775i \(-0.625087\pi\)
−0.382935 + 0.923775i \(0.625087\pi\)
\(720\) 14.8971 0.555183
\(721\) −28.5403 −1.06289
\(722\) 1.00000 0.0372161
\(723\) 94.5738 3.51724
\(724\) 9.78871 0.363795
\(725\) 10.3600 0.384761
\(726\) 0 0
\(727\) 14.6689 0.544041 0.272021 0.962291i \(-0.412308\pi\)
0.272021 + 0.962291i \(0.412308\pi\)
\(728\) −7.63611 −0.283013
\(729\) 75.5697 2.79888
\(730\) 10.0615 0.372391
\(731\) 0.120751 0.00446614
\(732\) −47.3800 −1.75122
\(733\) 49.7416 1.83725 0.918623 0.395135i \(-0.129302\pi\)
0.918623 + 0.395135i \(0.129302\pi\)
\(734\) −10.0520 −0.371028
\(735\) −7.35343 −0.271235
\(736\) −7.39138 −0.272450
\(737\) 0 0
\(738\) 18.6856 0.687825
\(739\) 42.1810 1.55165 0.775826 0.630947i \(-0.217333\pi\)
0.775826 + 0.630947i \(0.217333\pi\)
\(740\) 16.4023 0.602959
\(741\) 10.4586 0.384205
\(742\) 20.8236 0.764459
\(743\) 4.83219 0.177276 0.0886380 0.996064i \(-0.471749\pi\)
0.0886380 + 0.996064i \(0.471749\pi\)
\(744\) −18.3008 −0.670938
\(745\) −5.79982 −0.212489
\(746\) −20.6591 −0.756383
\(747\) −41.5919 −1.52177
\(748\) 0 0
\(749\) 19.9281 0.728158
\(750\) −40.1497 −1.46606
\(751\) 28.9857 1.05770 0.528851 0.848714i \(-0.322623\pi\)
0.528851 + 0.848714i \(0.322623\pi\)
\(752\) 9.11437 0.332367
\(753\) 18.8112 0.685518
\(754\) 22.5299 0.820489
\(755\) 32.7622 1.19234
\(756\) 39.1467 1.42375
\(757\) 32.3975 1.17751 0.588753 0.808313i \(-0.299619\pi\)
0.588753 + 0.808313i \(0.299619\pi\)
\(758\) 11.5387 0.419105
\(759\) 0 0
\(760\) −1.88260 −0.0682893
\(761\) 20.0438 0.726587 0.363293 0.931675i \(-0.381652\pi\)
0.363293 + 0.931675i \(0.381652\pi\)
\(762\) −4.13687 −0.149863
\(763\) 11.8880 0.430376
\(764\) 4.26597 0.154337
\(765\) −1.01951 −0.0368604
\(766\) 5.30452 0.191660
\(767\) −16.8598 −0.608774
\(768\) 3.30349 0.119204
\(769\) 25.6006 0.923182 0.461591 0.887093i \(-0.347279\pi\)
0.461591 + 0.887093i \(0.347279\pi\)
\(770\) 0 0
\(771\) −47.6351 −1.71554
\(772\) −10.3339 −0.371927
\(773\) 33.8041 1.21585 0.607925 0.793995i \(-0.292002\pi\)
0.607925 + 0.793995i \(0.292002\pi\)
\(774\) −13.9619 −0.501851
\(775\) 8.06487 0.289699
\(776\) −2.67951 −0.0961889
\(777\) 69.4209 2.49046
\(778\) −22.9500 −0.822796
\(779\) −2.36137 −0.0846047
\(780\) −19.6894 −0.704992
\(781\) 0 0
\(782\) 0.505842 0.0180889
\(783\) −115.500 −4.12763
\(784\) −1.18238 −0.0422279
\(785\) 16.8080 0.599905
\(786\) 45.5018 1.62300
\(787\) 18.3654 0.654656 0.327328 0.944911i \(-0.393852\pi\)
0.327328 + 0.944911i \(0.393852\pi\)
\(788\) 12.8943 0.459342
\(789\) −20.6614 −0.735566
\(790\) −7.43939 −0.264682
\(791\) −46.1782 −1.64191
\(792\) 0 0
\(793\) 45.4069 1.61245
\(794\) 0.483759 0.0171680
\(795\) 53.6927 1.90429
\(796\) 13.1491 0.466059
\(797\) −32.4974 −1.15112 −0.575559 0.817760i \(-0.695215\pi\)
−0.575559 + 0.817760i \(0.695215\pi\)
\(798\) −7.96793 −0.282062
\(799\) −0.623757 −0.0220669
\(800\) −1.45580 −0.0514703
\(801\) 50.7377 1.79273
\(802\) −36.1672 −1.27711
\(803\) 0 0
\(804\) 37.5255 1.32342
\(805\) −33.5627 −1.18293
\(806\) 17.5386 0.617772
\(807\) 56.0280 1.97228
\(808\) −11.8482 −0.416819
\(809\) 36.7995 1.29380 0.646901 0.762574i \(-0.276065\pi\)
0.646901 + 0.762574i \(0.276065\pi\)
\(810\) 56.2467 1.97631
\(811\) −27.2780 −0.957862 −0.478931 0.877853i \(-0.658976\pi\)
−0.478931 + 0.877853i \(0.658976\pi\)
\(812\) −17.1645 −0.602356
\(813\) 36.1050 1.26626
\(814\) 0 0
\(815\) −6.80196 −0.238262
\(816\) −0.226080 −0.00791437
\(817\) 1.76442 0.0617293
\(818\) 12.0788 0.422324
\(819\) −60.4249 −2.11142
\(820\) 4.44552 0.155244
\(821\) 1.63228 0.0569669 0.0284835 0.999594i \(-0.490932\pi\)
0.0284835 + 0.999594i \(0.490932\pi\)
\(822\) 6.06512 0.211545
\(823\) 53.4082 1.86169 0.930846 0.365412i \(-0.119072\pi\)
0.930846 + 0.365412i \(0.119072\pi\)
\(824\) −11.8327 −0.412213
\(825\) 0 0
\(826\) 12.8448 0.446927
\(827\) 4.12284 0.143365 0.0716825 0.997427i \(-0.477163\pi\)
0.0716825 + 0.997427i \(0.477163\pi\)
\(828\) −58.4883 −2.03261
\(829\) 12.8328 0.445702 0.222851 0.974853i \(-0.428464\pi\)
0.222851 + 0.974853i \(0.428464\pi\)
\(830\) −9.89520 −0.343467
\(831\) 57.5400 1.99604
\(832\) −3.16592 −0.109758
\(833\) 0.0809183 0.00280365
\(834\) −52.5822 −1.82077
\(835\) −46.5052 −1.60938
\(836\) 0 0
\(837\) −89.9123 −3.10782
\(838\) −14.4844 −0.500357
\(839\) −16.9755 −0.586058 −0.293029 0.956104i \(-0.594663\pi\)
−0.293029 + 0.956104i \(0.594663\pi\)
\(840\) 15.0005 0.517565
\(841\) 21.6427 0.746301
\(842\) 8.74595 0.301405
\(843\) 39.1208 1.34739
\(844\) 26.5013 0.912212
\(845\) −5.60443 −0.192798
\(846\) 72.1223 2.47962
\(847\) 0 0
\(848\) 8.63343 0.296473
\(849\) 12.8148 0.439803
\(850\) 0.0996300 0.00341728
\(851\) −64.3977 −2.20752
\(852\) −43.4672 −1.48916
\(853\) −18.3348 −0.627771 −0.313886 0.949461i \(-0.601631\pi\)
−0.313886 + 0.949461i \(0.601631\pi\)
\(854\) −34.5935 −1.18377
\(855\) −14.8971 −0.509471
\(856\) 8.26216 0.282395
\(857\) 9.14446 0.312369 0.156184 0.987728i \(-0.450081\pi\)
0.156184 + 0.987728i \(0.450081\pi\)
\(858\) 0 0
\(859\) 56.1013 1.91415 0.957076 0.289836i \(-0.0936007\pi\)
0.957076 + 0.289836i \(0.0936007\pi\)
\(860\) −3.32171 −0.113269
\(861\) 18.8152 0.641220
\(862\) 18.0983 0.616429
\(863\) 9.49783 0.323310 0.161655 0.986847i \(-0.448317\pi\)
0.161655 + 0.986847i \(0.448317\pi\)
\(864\) 16.2302 0.552161
\(865\) 26.8304 0.912261
\(866\) 19.3031 0.655946
\(867\) −56.1438 −1.90674
\(868\) −13.3619 −0.453533
\(869\) 0 0
\(870\) −44.2579 −1.50048
\(871\) −35.9628 −1.21855
\(872\) 4.92876 0.166909
\(873\) −21.2031 −0.717616
\(874\) 7.39138 0.250017
\(875\) −29.3145 −0.991009
\(876\) 17.6553 0.596516
\(877\) −49.0925 −1.65773 −0.828867 0.559445i \(-0.811014\pi\)
−0.828867 + 0.559445i \(0.811014\pi\)
\(878\) −0.543248 −0.0183337
\(879\) −2.91586 −0.0983495
\(880\) 0 0
\(881\) −37.3645 −1.25884 −0.629422 0.777064i \(-0.716708\pi\)
−0.629422 + 0.777064i \(0.716708\pi\)
\(882\) −9.35623 −0.315041
\(883\) 22.6572 0.762476 0.381238 0.924477i \(-0.375498\pi\)
0.381238 + 0.924477i \(0.375498\pi\)
\(884\) 0.216665 0.00728723
\(885\) 33.1197 1.11330
\(886\) −24.5763 −0.825656
\(887\) −31.0484 −1.04250 −0.521251 0.853403i \(-0.674535\pi\)
−0.521251 + 0.853403i \(0.674535\pi\)
\(888\) 28.7818 0.965853
\(889\) −3.02045 −0.101303
\(890\) 12.0711 0.404624
\(891\) 0 0
\(892\) −29.7656 −0.996625
\(893\) −9.11437 −0.305001
\(894\) −10.1772 −0.340376
\(895\) −23.3356 −0.780024
\(896\) 2.41197 0.0805784
\(897\) 77.3034 2.58108
\(898\) 30.2173 1.00837
\(899\) 39.4235 1.31485
\(900\) −11.5198 −0.383993
\(901\) −0.590843 −0.0196838
\(902\) 0 0
\(903\) −14.0588 −0.467847
\(904\) −19.1454 −0.636767
\(905\) 18.4283 0.612577
\(906\) 57.4892 1.90995
\(907\) −11.8840 −0.394603 −0.197301 0.980343i \(-0.563218\pi\)
−0.197301 + 0.980343i \(0.563218\pi\)
\(908\) 24.0754 0.798969
\(909\) −93.7554 −3.10967
\(910\) −14.3758 −0.476553
\(911\) −33.5828 −1.11265 −0.556324 0.830966i \(-0.687788\pi\)
−0.556324 + 0.830966i \(0.687788\pi\)
\(912\) −3.30349 −0.109389
\(913\) 0 0
\(914\) 34.7631 1.14986
\(915\) −89.1979 −2.94879
\(916\) 7.85068 0.259394
\(917\) 33.2222 1.09709
\(918\) −1.11074 −0.0366598
\(919\) −3.27575 −0.108057 −0.0540285 0.998539i \(-0.517206\pi\)
−0.0540285 + 0.998539i \(0.517206\pi\)
\(920\) −13.9151 −0.458766
\(921\) 72.0489 2.37409
\(922\) 10.2206 0.336597
\(923\) 41.6571 1.37116
\(924\) 0 0
\(925\) −12.6837 −0.417038
\(926\) −5.73645 −0.188512
\(927\) −93.6329 −3.07531
\(928\) −7.11637 −0.233606
\(929\) −0.192133 −0.00630369 −0.00315185 0.999995i \(-0.501003\pi\)
−0.00315185 + 0.999995i \(0.501003\pi\)
\(930\) −34.4531 −1.12976
\(931\) 1.18238 0.0387510
\(932\) −22.1903 −0.726869
\(933\) 23.4208 0.766764
\(934\) −25.2965 −0.827728
\(935\) 0 0
\(936\) −25.0520 −0.818851
\(937\) 8.33878 0.272416 0.136208 0.990680i \(-0.456508\pi\)
0.136208 + 0.990680i \(0.456508\pi\)
\(938\) 27.3985 0.894592
\(939\) 24.8219 0.810032
\(940\) 17.1588 0.559657
\(941\) 32.4537 1.05796 0.528980 0.848634i \(-0.322575\pi\)
0.528980 + 0.848634i \(0.322575\pi\)
\(942\) 29.4938 0.960960
\(943\) −17.4538 −0.568373
\(944\) 5.32542 0.173328
\(945\) 73.6978 2.39739
\(946\) 0 0
\(947\) 39.7033 1.29018 0.645092 0.764105i \(-0.276819\pi\)
0.645092 + 0.764105i \(0.276819\pi\)
\(948\) −13.0542 −0.423982
\(949\) −16.9200 −0.549248
\(950\) 1.45580 0.0472324
\(951\) 51.1196 1.65767
\(952\) −0.165067 −0.00534987
\(953\) 28.2036 0.913604 0.456802 0.889568i \(-0.348995\pi\)
0.456802 + 0.889568i \(0.348995\pi\)
\(954\) 68.3167 2.21183
\(955\) 8.03113 0.259881
\(956\) −2.33473 −0.0755107
\(957\) 0 0
\(958\) −6.51483 −0.210485
\(959\) 4.42832 0.142998
\(960\) 6.21916 0.200723
\(961\) −0.310330 −0.0100106
\(962\) −27.5832 −0.889318
\(963\) 65.3788 2.10680
\(964\) 28.6284 0.922060
\(965\) −19.4547 −0.626270
\(966\) −58.8940 −1.89488
\(967\) −50.9270 −1.63770 −0.818851 0.574006i \(-0.805389\pi\)
−0.818851 + 0.574006i \(0.805389\pi\)
\(968\) 0 0
\(969\) 0.226080 0.00726273
\(970\) −5.04446 −0.161968
\(971\) −25.2762 −0.811151 −0.405576 0.914062i \(-0.632929\pi\)
−0.405576 + 0.914062i \(0.632929\pi\)
\(972\) 50.0080 1.60401
\(973\) −38.3918 −1.23079
\(974\) −26.5992 −0.852293
\(975\) 15.2256 0.487609
\(976\) −14.3424 −0.459090
\(977\) −51.5477 −1.64916 −0.824579 0.565747i \(-0.808588\pi\)
−0.824579 + 0.565747i \(0.808588\pi\)
\(978\) −11.9357 −0.381662
\(979\) 0 0
\(980\) −2.22596 −0.0711056
\(981\) 39.0015 1.24522
\(982\) −16.5430 −0.527909
\(983\) −8.63287 −0.275346 −0.137673 0.990478i \(-0.543962\pi\)
−0.137673 + 0.990478i \(0.543962\pi\)
\(984\) 7.80074 0.248679
\(985\) 24.2749 0.773464
\(986\) 0.487021 0.0155099
\(987\) 72.6226 2.31160
\(988\) 3.16592 0.100721
\(989\) 13.0415 0.414696
\(990\) 0 0
\(991\) −23.8596 −0.757925 −0.378962 0.925412i \(-0.623719\pi\)
−0.378962 + 0.925412i \(0.623719\pi\)
\(992\) −5.53983 −0.175890
\(993\) 34.4902 1.09451
\(994\) −31.7367 −1.00663
\(995\) 24.7546 0.784774
\(996\) −17.3635 −0.550185
\(997\) −15.9135 −0.503987 −0.251993 0.967729i \(-0.581086\pi\)
−0.251993 + 0.967729i \(0.581086\pi\)
\(998\) 8.60654 0.272435
\(999\) 141.406 4.47388
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 4598.2.a.cb.1.7 yes 8
11.10 odd 2 4598.2.a.by.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.by.1.7 8 11.10 odd 2
4598.2.a.cb.1.7 yes 8 1.1 even 1 trivial