Properties

Label 4598.2.a.cb.1.6
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 1.6
Root \(1.24609\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.79123 q^{3} +1.00000 q^{4} +4.02325 q^{5} +2.79123 q^{6} +0.274917 q^{7} +1.00000 q^{8} +4.79095 q^{9} +4.02325 q^{10} +2.79123 q^{12} +0.597016 q^{13} +0.274917 q^{14} +11.2298 q^{15} +1.00000 q^{16} -2.62721 q^{17} +4.79095 q^{18} -1.00000 q^{19} +4.02325 q^{20} +0.767355 q^{21} +4.04740 q^{23} +2.79123 q^{24} +11.1866 q^{25} +0.597016 q^{26} +4.99894 q^{27} +0.274917 q^{28} -7.29532 q^{29} +11.2298 q^{30} -1.48056 q^{31} +1.00000 q^{32} -2.62721 q^{34} +1.10606 q^{35} +4.79095 q^{36} -8.31155 q^{37} -1.00000 q^{38} +1.66641 q^{39} +4.02325 q^{40} -12.3427 q^{41} +0.767355 q^{42} +5.58432 q^{43} +19.2752 q^{45} +4.04740 q^{46} -9.10733 q^{47} +2.79123 q^{48} -6.92442 q^{49} +11.1866 q^{50} -7.33314 q^{51} +0.597016 q^{52} +7.30127 q^{53} +4.99894 q^{54} +0.274917 q^{56} -2.79123 q^{57} -7.29532 q^{58} -7.53037 q^{59} +11.2298 q^{60} +4.83533 q^{61} -1.48056 q^{62} +1.31711 q^{63} +1.00000 q^{64} +2.40195 q^{65} -14.0217 q^{67} -2.62721 q^{68} +11.2972 q^{69} +1.10606 q^{70} -9.61823 q^{71} +4.79095 q^{72} -3.15625 q^{73} -8.31155 q^{74} +31.2242 q^{75} -1.00000 q^{76} +1.66641 q^{78} -2.42106 q^{79} +4.02325 q^{80} -0.419665 q^{81} -12.3427 q^{82} +15.7948 q^{83} +0.767355 q^{84} -10.5699 q^{85} +5.58432 q^{86} -20.3629 q^{87} +1.49871 q^{89} +19.2752 q^{90} +0.164130 q^{91} +4.04740 q^{92} -4.13259 q^{93} -9.10733 q^{94} -4.02325 q^{95} +2.79123 q^{96} +9.00939 q^{97} -6.92442 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} + 8q^{3} + 8q^{4} + 8q^{6} + 4q^{7} + 8q^{8} + 22q^{9} + O(q^{10}) \) \( 8q + 8q^{2} + 8q^{3} + 8q^{4} + 8q^{6} + 4q^{7} + 8q^{8} + 22q^{9} + 8q^{12} - 12q^{13} + 4q^{14} + 4q^{15} + 8q^{16} - 4q^{17} + 22q^{18} - 8q^{19} - 20q^{21} + 14q^{23} + 8q^{24} + 36q^{25} - 12q^{26} + 32q^{27} + 4q^{28} - 2q^{29} + 4q^{30} + 8q^{32} - 4q^{34} + 36q^{35} + 22q^{36} + 24q^{37} - 8q^{38} + 16q^{39} + 8q^{41} - 20q^{42} + 8q^{43} + 16q^{45} + 14q^{46} - 16q^{47} + 8q^{48} + 34q^{49} + 36q^{50} + 18q^{51} - 12q^{52} + 36q^{53} + 32q^{54} + 4q^{56} - 8q^{57} - 2q^{58} - 24q^{59} + 4q^{60} + 12q^{61} + 24q^{63} + 8q^{64} + 16q^{65} + 16q^{67} - 4q^{68} + 4q^{69} + 36q^{70} + 4q^{71} + 22q^{72} - 20q^{73} + 24q^{74} + 40q^{75} - 8q^{76} + 16q^{78} - 12q^{79} + 40q^{81} + 8q^{82} + 20q^{83} - 20q^{84} + 12q^{85} + 8q^{86} - 36q^{87} + 8q^{89} + 16q^{90} - 24q^{91} + 14q^{92} + 12q^{93} - 16q^{94} + 8q^{96} + 4q^{97} + 34q^{98} + O(q^{100}) \)

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
\(3\) 2.79123 1.61152 0.805758 0.592245i \(-0.201758\pi\)
0.805758 + 0.592245i \(0.201758\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.02325 1.79925 0.899627 0.436660i \(-0.143839\pi\)
0.899627 + 0.436660i \(0.143839\pi\)
\(6\) 2.79123 1.13951
\(7\) 0.274917 0.103909 0.0519544 0.998649i \(-0.483455\pi\)
0.0519544 + 0.998649i \(0.483455\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.79095 1.59698
\(10\) 4.02325 1.27226
\(11\) 0 0
\(12\) 2.79123 0.805758
\(13\) 0.597016 0.165583 0.0827913 0.996567i \(-0.473617\pi\)
0.0827913 + 0.996567i \(0.473617\pi\)
\(14\) 0.274917 0.0734746
\(15\) 11.2298 2.89952
\(16\) 1.00000 0.250000
\(17\) −2.62721 −0.637192 −0.318596 0.947891i \(-0.603211\pi\)
−0.318596 + 0.947891i \(0.603211\pi\)
\(18\) 4.79095 1.12924
\(19\) −1.00000 −0.229416
\(20\) 4.02325 0.899627
\(21\) 0.767355 0.167451
\(22\) 0 0
\(23\) 4.04740 0.843942 0.421971 0.906609i \(-0.361338\pi\)
0.421971 + 0.906609i \(0.361338\pi\)
\(24\) 2.79123 0.569757
\(25\) 11.1866 2.23731
\(26\) 0.597016 0.117085
\(27\) 4.99894 0.962047
\(28\) 0.274917 0.0519544
\(29\) −7.29532 −1.35471 −0.677354 0.735657i \(-0.736873\pi\)
−0.677354 + 0.735657i \(0.736873\pi\)
\(30\) 11.2298 2.05027
\(31\) −1.48056 −0.265917 −0.132959 0.991122i \(-0.542448\pi\)
−0.132959 + 0.991122i \(0.542448\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.62721 −0.450563
\(35\) 1.10606 0.186958
\(36\) 4.79095 0.798491
\(37\) −8.31155 −1.36641 −0.683205 0.730227i \(-0.739414\pi\)
−0.683205 + 0.730227i \(0.739414\pi\)
\(38\) −1.00000 −0.162221
\(39\) 1.66641 0.266839
\(40\) 4.02325 0.636132
\(41\) −12.3427 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(42\) 0.767355 0.118405
\(43\) 5.58432 0.851601 0.425800 0.904817i \(-0.359993\pi\)
0.425800 + 0.904817i \(0.359993\pi\)
\(44\) 0 0
\(45\) 19.2752 2.87338
\(46\) 4.04740 0.596757
\(47\) −9.10733 −1.32844 −0.664221 0.747537i \(-0.731236\pi\)
−0.664221 + 0.747537i \(0.731236\pi\)
\(48\) 2.79123 0.402879
\(49\) −6.92442 −0.989203
\(50\) 11.1866 1.58202
\(51\) −7.33314 −1.02684
\(52\) 0.597016 0.0827913
\(53\) 7.30127 1.00291 0.501454 0.865185i \(-0.332799\pi\)
0.501454 + 0.865185i \(0.332799\pi\)
\(54\) 4.99894 0.680270
\(55\) 0 0
\(56\) 0.274917 0.0367373
\(57\) −2.79123 −0.369707
\(58\) −7.29532 −0.957923
\(59\) −7.53037 −0.980370 −0.490185 0.871618i \(-0.663071\pi\)
−0.490185 + 0.871618i \(0.663071\pi\)
\(60\) 11.2298 1.44976
\(61\) 4.83533 0.619100 0.309550 0.950883i \(-0.399822\pi\)
0.309550 + 0.950883i \(0.399822\pi\)
\(62\) −1.48056 −0.188032
\(63\) 1.31711 0.165940
\(64\) 1.00000 0.125000
\(65\) 2.40195 0.297925
\(66\) 0 0
\(67\) −14.0217 −1.71303 −0.856514 0.516124i \(-0.827374\pi\)
−0.856514 + 0.516124i \(0.827374\pi\)
\(68\) −2.62721 −0.318596
\(69\) 11.2972 1.36003
\(70\) 1.10606 0.132199
\(71\) −9.61823 −1.14147 −0.570737 0.821133i \(-0.693342\pi\)
−0.570737 + 0.821133i \(0.693342\pi\)
\(72\) 4.79095 0.564619
\(73\) −3.15625 −0.369411 −0.184705 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(74\) −8.31155 −0.966198
\(75\) 31.2242 3.60546
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 1.66641 0.188684
\(79\) −2.42106 −0.272391 −0.136195 0.990682i \(-0.543487\pi\)
−0.136195 + 0.990682i \(0.543487\pi\)
\(80\) 4.02325 0.449813
\(81\) −0.419665 −0.0466294
\(82\) −12.3427 −1.36302
\(83\) 15.7948 1.73370 0.866852 0.498566i \(-0.166140\pi\)
0.866852 + 0.498566i \(0.166140\pi\)
\(84\) 0.767355 0.0837253
\(85\) −10.5699 −1.14647
\(86\) 5.58432 0.602173
\(87\) −20.3629 −2.18313
\(88\) 0 0
\(89\) 1.49871 0.158863 0.0794315 0.996840i \(-0.474689\pi\)
0.0794315 + 0.996840i \(0.474689\pi\)
\(90\) 19.2752 2.03178
\(91\) 0.164130 0.0172055
\(92\) 4.04740 0.421971
\(93\) −4.13259 −0.428530
\(94\) −9.10733 −0.939350
\(95\) −4.02325 −0.412777
\(96\) 2.79123 0.284878
\(97\) 9.00939 0.914765 0.457382 0.889270i \(-0.348787\pi\)
0.457382 + 0.889270i \(0.348787\pi\)
\(98\) −6.92442 −0.699472
\(99\) 0 0
\(100\) 11.1866 1.11866
\(101\) 2.30943 0.229797 0.114898 0.993377i \(-0.463346\pi\)
0.114898 + 0.993377i \(0.463346\pi\)
\(102\) −7.33314 −0.726089
\(103\) 10.3403 1.01886 0.509428 0.860513i \(-0.329857\pi\)
0.509428 + 0.860513i \(0.329857\pi\)
\(104\) 0.597016 0.0585423
\(105\) 3.08726 0.301286
\(106\) 7.30127 0.709162
\(107\) −9.00544 −0.870589 −0.435294 0.900288i \(-0.643356\pi\)
−0.435294 + 0.900288i \(0.643356\pi\)
\(108\) 4.99894 0.481023
\(109\) 16.8995 1.61867 0.809337 0.587344i \(-0.199827\pi\)
0.809337 + 0.587344i \(0.199827\pi\)
\(110\) 0 0
\(111\) −23.1994 −2.20199
\(112\) 0.274917 0.0259772
\(113\) 2.84546 0.267678 0.133839 0.991003i \(-0.457269\pi\)
0.133839 + 0.991003i \(0.457269\pi\)
\(114\) −2.79123 −0.261422
\(115\) 16.2837 1.51847
\(116\) −7.29532 −0.677354
\(117\) 2.86027 0.264432
\(118\) −7.53037 −0.693227
\(119\) −0.722264 −0.0662098
\(120\) 11.2298 1.02514
\(121\) 0 0
\(122\) 4.83533 0.437770
\(123\) −34.4512 −3.10636
\(124\) −1.48056 −0.132959
\(125\) 24.8901 2.22624
\(126\) 1.31711 0.117338
\(127\) 5.59695 0.496649 0.248324 0.968677i \(-0.420120\pi\)
0.248324 + 0.968677i \(0.420120\pi\)
\(128\) 1.00000 0.0883883
\(129\) 15.5871 1.37237
\(130\) 2.40195 0.210665
\(131\) −7.73690 −0.675976 −0.337988 0.941150i \(-0.609746\pi\)
−0.337988 + 0.941150i \(0.609746\pi\)
\(132\) 0 0
\(133\) −0.274917 −0.0238383
\(134\) −14.0217 −1.21129
\(135\) 20.1120 1.73097
\(136\) −2.62721 −0.225281
\(137\) −1.10706 −0.0945829 −0.0472914 0.998881i \(-0.515059\pi\)
−0.0472914 + 0.998881i \(0.515059\pi\)
\(138\) 11.2972 0.961683
\(139\) 14.8792 1.26204 0.631020 0.775767i \(-0.282637\pi\)
0.631020 + 0.775767i \(0.282637\pi\)
\(140\) 1.10606 0.0934791
\(141\) −25.4206 −2.14080
\(142\) −9.61823 −0.807144
\(143\) 0 0
\(144\) 4.79095 0.399246
\(145\) −29.3509 −2.43746
\(146\) −3.15625 −0.261213
\(147\) −19.3276 −1.59412
\(148\) −8.31155 −0.683205
\(149\) 20.9576 1.71691 0.858457 0.512885i \(-0.171423\pi\)
0.858457 + 0.512885i \(0.171423\pi\)
\(150\) 31.2242 2.54945
\(151\) −4.07961 −0.331994 −0.165997 0.986126i \(-0.553084\pi\)
−0.165997 + 0.986126i \(0.553084\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −12.5868 −1.01758
\(154\) 0 0
\(155\) −5.95669 −0.478453
\(156\) 1.66641 0.133419
\(157\) 19.7161 1.57352 0.786758 0.617262i \(-0.211758\pi\)
0.786758 + 0.617262i \(0.211758\pi\)
\(158\) −2.42106 −0.192609
\(159\) 20.3795 1.61620
\(160\) 4.02325 0.318066
\(161\) 1.11270 0.0876929
\(162\) −0.419665 −0.0329720
\(163\) 16.9154 1.32492 0.662460 0.749098i \(-0.269513\pi\)
0.662460 + 0.749098i \(0.269513\pi\)
\(164\) −12.3427 −0.963800
\(165\) 0 0
\(166\) 15.7948 1.22591
\(167\) −23.1451 −1.79102 −0.895512 0.445038i \(-0.853190\pi\)
−0.895512 + 0.445038i \(0.853190\pi\)
\(168\) 0.767355 0.0592027
\(169\) −12.6436 −0.972582
\(170\) −10.5699 −0.810676
\(171\) −4.79095 −0.366373
\(172\) 5.58432 0.425800
\(173\) −23.5008 −1.78673 −0.893366 0.449330i \(-0.851663\pi\)
−0.893366 + 0.449330i \(0.851663\pi\)
\(174\) −20.3629 −1.54371
\(175\) 3.07537 0.232476
\(176\) 0 0
\(177\) −21.0190 −1.57988
\(178\) 1.49871 0.112333
\(179\) 7.52415 0.562381 0.281191 0.959652i \(-0.409271\pi\)
0.281191 + 0.959652i \(0.409271\pi\)
\(180\) 19.2752 1.43669
\(181\) 19.6253 1.45874 0.729370 0.684120i \(-0.239813\pi\)
0.729370 + 0.684120i \(0.239813\pi\)
\(182\) 0.164130 0.0121661
\(183\) 13.4965 0.997690
\(184\) 4.04740 0.298379
\(185\) −33.4395 −2.45852
\(186\) −4.13259 −0.303016
\(187\) 0 0
\(188\) −9.10733 −0.664221
\(189\) 1.37429 0.0999650
\(190\) −4.02325 −0.291877
\(191\) 20.9322 1.51460 0.757300 0.653067i \(-0.226518\pi\)
0.757300 + 0.653067i \(0.226518\pi\)
\(192\) 2.79123 0.201439
\(193\) 1.89921 0.136708 0.0683542 0.997661i \(-0.478225\pi\)
0.0683542 + 0.997661i \(0.478225\pi\)
\(194\) 9.00939 0.646836
\(195\) 6.70438 0.480111
\(196\) −6.92442 −0.494601
\(197\) −1.40362 −0.100004 −0.0500020 0.998749i \(-0.515923\pi\)
−0.0500020 + 0.998749i \(0.515923\pi\)
\(198\) 0 0
\(199\) −3.60404 −0.255483 −0.127742 0.991807i \(-0.540773\pi\)
−0.127742 + 0.991807i \(0.540773\pi\)
\(200\) 11.1866 0.791009
\(201\) −39.1379 −2.76057
\(202\) 2.30943 0.162491
\(203\) −2.00561 −0.140766
\(204\) −7.33314 −0.513422
\(205\) −49.6576 −3.46824
\(206\) 10.3403 0.720441
\(207\) 19.3909 1.34776
\(208\) 0.597016 0.0413956
\(209\) 0 0
\(210\) 3.08726 0.213041
\(211\) 18.7715 1.29228 0.646141 0.763218i \(-0.276382\pi\)
0.646141 + 0.763218i \(0.276382\pi\)
\(212\) 7.30127 0.501454
\(213\) −26.8467 −1.83950
\(214\) −9.00544 −0.615599
\(215\) 22.4671 1.53225
\(216\) 4.99894 0.340135
\(217\) −0.407032 −0.0276311
\(218\) 16.8995 1.14458
\(219\) −8.80980 −0.595311
\(220\) 0 0
\(221\) −1.56849 −0.105508
\(222\) −23.1994 −1.55704
\(223\) −14.6688 −0.982298 −0.491149 0.871075i \(-0.663423\pi\)
−0.491149 + 0.871075i \(0.663423\pi\)
\(224\) 0.274917 0.0183686
\(225\) 53.5942 3.57295
\(226\) 2.84546 0.189277
\(227\) 3.54422 0.235238 0.117619 0.993059i \(-0.462474\pi\)
0.117619 + 0.993059i \(0.462474\pi\)
\(228\) −2.79123 −0.184854
\(229\) −16.7749 −1.10852 −0.554259 0.832344i \(-0.686998\pi\)
−0.554259 + 0.832344i \(0.686998\pi\)
\(230\) 16.2837 1.07372
\(231\) 0 0
\(232\) −7.29532 −0.478961
\(233\) 25.7392 1.68623 0.843115 0.537734i \(-0.180719\pi\)
0.843115 + 0.537734i \(0.180719\pi\)
\(234\) 2.86027 0.186982
\(235\) −36.6411 −2.39020
\(236\) −7.53037 −0.490185
\(237\) −6.75773 −0.438962
\(238\) −0.722264 −0.0468174
\(239\) 3.83627 0.248148 0.124074 0.992273i \(-0.460404\pi\)
0.124074 + 0.992273i \(0.460404\pi\)
\(240\) 11.2298 0.724881
\(241\) −10.9064 −0.702540 −0.351270 0.936274i \(-0.614250\pi\)
−0.351270 + 0.936274i \(0.614250\pi\)
\(242\) 0 0
\(243\) −16.1682 −1.03719
\(244\) 4.83533 0.309550
\(245\) −27.8587 −1.77983
\(246\) −34.4512 −2.19653
\(247\) −0.597016 −0.0379872
\(248\) −1.48056 −0.0940160
\(249\) 44.0868 2.79389
\(250\) 24.8901 1.57419
\(251\) 13.9463 0.880283 0.440141 0.897928i \(-0.354928\pi\)
0.440141 + 0.897928i \(0.354928\pi\)
\(252\) 1.31711 0.0829702
\(253\) 0 0
\(254\) 5.59695 0.351184
\(255\) −29.5031 −1.84755
\(256\) 1.00000 0.0625000
\(257\) 16.8311 1.04989 0.524947 0.851135i \(-0.324085\pi\)
0.524947 + 0.851135i \(0.324085\pi\)
\(258\) 15.5871 0.970410
\(259\) −2.28498 −0.141982
\(260\) 2.40195 0.148962
\(261\) −34.9515 −2.16344
\(262\) −7.73690 −0.477987
\(263\) −1.71132 −0.105525 −0.0527623 0.998607i \(-0.516803\pi\)
−0.0527623 + 0.998607i \(0.516803\pi\)
\(264\) 0 0
\(265\) 29.3749 1.80448
\(266\) −0.274917 −0.0168562
\(267\) 4.18324 0.256010
\(268\) −14.0217 −0.856514
\(269\) 22.3017 1.35976 0.679880 0.733323i \(-0.262032\pi\)
0.679880 + 0.733323i \(0.262032\pi\)
\(270\) 20.1120 1.22398
\(271\) −2.26292 −0.137463 −0.0687314 0.997635i \(-0.521895\pi\)
−0.0687314 + 0.997635i \(0.521895\pi\)
\(272\) −2.62721 −0.159298
\(273\) 0.458123 0.0277269
\(274\) −1.10706 −0.0668802
\(275\) 0 0
\(276\) 11.2972 0.680013
\(277\) 9.83937 0.591190 0.295595 0.955313i \(-0.404482\pi\)
0.295595 + 0.955313i \(0.404482\pi\)
\(278\) 14.8792 0.892397
\(279\) −7.09331 −0.424665
\(280\) 1.10606 0.0660997
\(281\) 17.9598 1.07139 0.535697 0.844410i \(-0.320049\pi\)
0.535697 + 0.844410i \(0.320049\pi\)
\(282\) −25.4206 −1.51378
\(283\) 26.5193 1.57641 0.788206 0.615412i \(-0.211010\pi\)
0.788206 + 0.615412i \(0.211010\pi\)
\(284\) −9.61823 −0.570737
\(285\) −11.2298 −0.665197
\(286\) 0 0
\(287\) −3.39320 −0.200294
\(288\) 4.79095 0.282309
\(289\) −10.0978 −0.593986
\(290\) −29.3509 −1.72355
\(291\) 25.1472 1.47416
\(292\) −3.15625 −0.184705
\(293\) −12.3885 −0.723745 −0.361872 0.932228i \(-0.617862\pi\)
−0.361872 + 0.932228i \(0.617862\pi\)
\(294\) −19.3276 −1.12721
\(295\) −30.2966 −1.76393
\(296\) −8.31155 −0.483099
\(297\) 0 0
\(298\) 20.9576 1.21404
\(299\) 2.41637 0.139742
\(300\) 31.2242 1.80273
\(301\) 1.53522 0.0884887
\(302\) −4.07961 −0.234755
\(303\) 6.44614 0.370321
\(304\) −1.00000 −0.0573539
\(305\) 19.4537 1.11392
\(306\) −12.5868 −0.719541
\(307\) −29.2289 −1.66818 −0.834090 0.551628i \(-0.814007\pi\)
−0.834090 + 0.551628i \(0.814007\pi\)
\(308\) 0 0
\(309\) 28.8620 1.64190
\(310\) −5.95669 −0.338317
\(311\) 10.9986 0.623675 0.311837 0.950136i \(-0.399056\pi\)
0.311837 + 0.950136i \(0.399056\pi\)
\(312\) 1.66641 0.0943418
\(313\) 15.5213 0.877314 0.438657 0.898654i \(-0.355454\pi\)
0.438657 + 0.898654i \(0.355454\pi\)
\(314\) 19.7161 1.11264
\(315\) 5.29907 0.298569
\(316\) −2.42106 −0.136195
\(317\) −23.9485 −1.34508 −0.672541 0.740060i \(-0.734797\pi\)
−0.672541 + 0.740060i \(0.734797\pi\)
\(318\) 20.3795 1.14283
\(319\) 0 0
\(320\) 4.02325 0.224907
\(321\) −25.1362 −1.40297
\(322\) 1.11270 0.0620083
\(323\) 2.62721 0.146182
\(324\) −0.419665 −0.0233147
\(325\) 6.67856 0.370460
\(326\) 16.9154 0.936859
\(327\) 47.1702 2.60852
\(328\) −12.3427 −0.681509
\(329\) −2.50376 −0.138037
\(330\) 0 0
\(331\) 25.6584 1.41031 0.705156 0.709052i \(-0.250877\pi\)
0.705156 + 0.709052i \(0.250877\pi\)
\(332\) 15.7948 0.866852
\(333\) −39.8202 −2.18213
\(334\) −23.1451 −1.26644
\(335\) −56.4130 −3.08217
\(336\) 0.767355 0.0418626
\(337\) −2.94204 −0.160263 −0.0801314 0.996784i \(-0.525534\pi\)
−0.0801314 + 0.996784i \(0.525534\pi\)
\(338\) −12.6436 −0.687720
\(339\) 7.94233 0.431368
\(340\) −10.5699 −0.573235
\(341\) 0 0
\(342\) −4.79095 −0.259065
\(343\) −3.82806 −0.206696
\(344\) 5.58432 0.301086
\(345\) 45.4516 2.44703
\(346\) −23.5008 −1.26341
\(347\) −6.33884 −0.340287 −0.170144 0.985419i \(-0.554423\pi\)
−0.170144 + 0.985419i \(0.554423\pi\)
\(348\) −20.3629 −1.09157
\(349\) −10.5789 −0.566276 −0.283138 0.959079i \(-0.591375\pi\)
−0.283138 + 0.959079i \(0.591375\pi\)
\(350\) 3.07537 0.164386
\(351\) 2.98445 0.159298
\(352\) 0 0
\(353\) −35.1642 −1.87160 −0.935800 0.352532i \(-0.885321\pi\)
−0.935800 + 0.352532i \(0.885321\pi\)
\(354\) −21.0190 −1.11715
\(355\) −38.6966 −2.05380
\(356\) 1.49871 0.0794315
\(357\) −2.01600 −0.106698
\(358\) 7.52415 0.397664
\(359\) 24.1939 1.27691 0.638453 0.769661i \(-0.279575\pi\)
0.638453 + 0.769661i \(0.279575\pi\)
\(360\) 19.2752 1.01589
\(361\) 1.00000 0.0526316
\(362\) 19.6253 1.03148
\(363\) 0 0
\(364\) 0.164130 0.00860273
\(365\) −12.6984 −0.664664
\(366\) 13.4965 0.705473
\(367\) −23.2519 −1.21374 −0.606869 0.794802i \(-0.707575\pi\)
−0.606869 + 0.794802i \(0.707575\pi\)
\(368\) 4.04740 0.210986
\(369\) −59.1330 −3.07834
\(370\) −33.4395 −1.73843
\(371\) 2.00724 0.104211
\(372\) −4.13259 −0.214265
\(373\) 8.15845 0.422429 0.211214 0.977440i \(-0.432258\pi\)
0.211214 + 0.977440i \(0.432258\pi\)
\(374\) 0 0
\(375\) 69.4739 3.58762
\(376\) −9.10733 −0.469675
\(377\) −4.35543 −0.224316
\(378\) 1.37429 0.0706860
\(379\) −18.9997 −0.975951 −0.487976 0.872857i \(-0.662265\pi\)
−0.487976 + 0.872857i \(0.662265\pi\)
\(380\) −4.02325 −0.206388
\(381\) 15.6224 0.800357
\(382\) 20.9322 1.07098
\(383\) 12.1817 0.622456 0.311228 0.950335i \(-0.399260\pi\)
0.311228 + 0.950335i \(0.399260\pi\)
\(384\) 2.79123 0.142439
\(385\) 0 0
\(386\) 1.89921 0.0966674
\(387\) 26.7542 1.35999
\(388\) 9.00939 0.457382
\(389\) −24.1433 −1.22411 −0.612057 0.790814i \(-0.709658\pi\)
−0.612057 + 0.790814i \(0.709658\pi\)
\(390\) 6.70438 0.339489
\(391\) −10.6334 −0.537753
\(392\) −6.92442 −0.349736
\(393\) −21.5954 −1.08935
\(394\) −1.40362 −0.0707135
\(395\) −9.74054 −0.490100
\(396\) 0 0
\(397\) −10.1918 −0.511510 −0.255755 0.966742i \(-0.582324\pi\)
−0.255755 + 0.966742i \(0.582324\pi\)
\(398\) −3.60404 −0.180654
\(399\) −0.767355 −0.0384158
\(400\) 11.1866 0.559328
\(401\) 12.2313 0.610800 0.305400 0.952224i \(-0.401210\pi\)
0.305400 + 0.952224i \(0.401210\pi\)
\(402\) −39.1379 −1.95202
\(403\) −0.883921 −0.0440313
\(404\) 2.30943 0.114898
\(405\) −1.68842 −0.0838981
\(406\) −2.00561 −0.0995365
\(407\) 0 0
\(408\) −7.33314 −0.363044
\(409\) −27.8419 −1.37669 −0.688347 0.725381i \(-0.741663\pi\)
−0.688347 + 0.725381i \(0.741663\pi\)
\(410\) −49.6576 −2.45242
\(411\) −3.09007 −0.152422
\(412\) 10.3403 0.509428
\(413\) −2.07022 −0.101869
\(414\) 19.3909 0.953011
\(415\) 63.5464 3.11937
\(416\) 0.597016 0.0292711
\(417\) 41.5313 2.03380
\(418\) 0 0
\(419\) 2.74637 0.134169 0.0670846 0.997747i \(-0.478630\pi\)
0.0670846 + 0.997747i \(0.478630\pi\)
\(420\) 3.08726 0.150643
\(421\) 3.45765 0.168516 0.0842579 0.996444i \(-0.473148\pi\)
0.0842579 + 0.996444i \(0.473148\pi\)
\(422\) 18.7715 0.913782
\(423\) −43.6328 −2.12150
\(424\) 7.30127 0.354581
\(425\) −29.3894 −1.42560
\(426\) −26.8467 −1.30073
\(427\) 1.32931 0.0643299
\(428\) −9.00544 −0.435294
\(429\) 0 0
\(430\) 22.4671 1.08346
\(431\) 33.1455 1.59656 0.798281 0.602285i \(-0.205743\pi\)
0.798281 + 0.602285i \(0.205743\pi\)
\(432\) 4.99894 0.240512
\(433\) −17.0841 −0.821008 −0.410504 0.911859i \(-0.634647\pi\)
−0.410504 + 0.911859i \(0.634647\pi\)
\(434\) −0.407032 −0.0195382
\(435\) −81.9251 −3.92801
\(436\) 16.8995 0.809337
\(437\) −4.04740 −0.193614
\(438\) −8.80980 −0.420949
\(439\) 36.1437 1.72505 0.862523 0.506018i \(-0.168883\pi\)
0.862523 + 0.506018i \(0.168883\pi\)
\(440\) 0 0
\(441\) −33.1745 −1.57974
\(442\) −1.56849 −0.0746053
\(443\) 19.4900 0.925996 0.462998 0.886359i \(-0.346774\pi\)
0.462998 + 0.886359i \(0.346774\pi\)
\(444\) −23.1994 −1.10100
\(445\) 6.02969 0.285835
\(446\) −14.6688 −0.694590
\(447\) 58.4974 2.76683
\(448\) 0.274917 0.0129886
\(449\) −12.8197 −0.604998 −0.302499 0.953150i \(-0.597821\pi\)
−0.302499 + 0.953150i \(0.597821\pi\)
\(450\) 53.5942 2.52646
\(451\) 0 0
\(452\) 2.84546 0.133839
\(453\) −11.3871 −0.535014
\(454\) 3.54422 0.166338
\(455\) 0.660335 0.0309570
\(456\) −2.79123 −0.130711
\(457\) 2.20055 0.102937 0.0514687 0.998675i \(-0.483610\pi\)
0.0514687 + 0.998675i \(0.483610\pi\)
\(458\) −16.7749 −0.783841
\(459\) −13.1333 −0.613008
\(460\) 16.2837 0.759233
\(461\) −3.39457 −0.158101 −0.0790505 0.996871i \(-0.525189\pi\)
−0.0790505 + 0.996871i \(0.525189\pi\)
\(462\) 0 0
\(463\) 18.5198 0.860690 0.430345 0.902665i \(-0.358392\pi\)
0.430345 + 0.902665i \(0.358392\pi\)
\(464\) −7.29532 −0.338677
\(465\) −16.6265 −0.771034
\(466\) 25.7392 1.19234
\(467\) 29.7909 1.37856 0.689280 0.724495i \(-0.257927\pi\)
0.689280 + 0.724495i \(0.257927\pi\)
\(468\) 2.86027 0.132216
\(469\) −3.85481 −0.177999
\(470\) −36.6411 −1.69013
\(471\) 55.0321 2.53574
\(472\) −7.53037 −0.346613
\(473\) 0 0
\(474\) −6.75773 −0.310393
\(475\) −11.1866 −0.513275
\(476\) −0.722264 −0.0331049
\(477\) 34.9800 1.60163
\(478\) 3.83627 0.175467
\(479\) 25.3380 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(480\) 11.2298 0.512568
\(481\) −4.96213 −0.226254
\(482\) −10.9064 −0.496771
\(483\) 3.10579 0.141319
\(484\) 0 0
\(485\) 36.2470 1.64589
\(486\) −16.1682 −0.733405
\(487\) −1.08718 −0.0492650 −0.0246325 0.999697i \(-0.507842\pi\)
−0.0246325 + 0.999697i \(0.507842\pi\)
\(488\) 4.83533 0.218885
\(489\) 47.2148 2.13513
\(490\) −27.8587 −1.25853
\(491\) 17.1850 0.775550 0.387775 0.921754i \(-0.373244\pi\)
0.387775 + 0.921754i \(0.373244\pi\)
\(492\) −34.4512 −1.55318
\(493\) 19.1663 0.863209
\(494\) −0.597016 −0.0268610
\(495\) 0 0
\(496\) −1.48056 −0.0664793
\(497\) −2.64421 −0.118609
\(498\) 44.0868 1.97558
\(499\) −8.60896 −0.385390 −0.192695 0.981259i \(-0.561723\pi\)
−0.192695 + 0.981259i \(0.561723\pi\)
\(500\) 24.8901 1.11312
\(501\) −64.6033 −2.88626
\(502\) 13.9463 0.622454
\(503\) −7.29741 −0.325376 −0.162688 0.986678i \(-0.552016\pi\)
−0.162688 + 0.986678i \(0.552016\pi\)
\(504\) 1.31711 0.0586688
\(505\) 9.29141 0.413462
\(506\) 0 0
\(507\) −35.2911 −1.56733
\(508\) 5.59695 0.248324
\(509\) 3.57411 0.158420 0.0792098 0.996858i \(-0.474760\pi\)
0.0792098 + 0.996858i \(0.474760\pi\)
\(510\) −29.5031 −1.30642
\(511\) −0.867705 −0.0383850
\(512\) 1.00000 0.0441942
\(513\) −4.99894 −0.220709
\(514\) 16.8311 0.742388
\(515\) 41.6015 1.83318
\(516\) 15.5871 0.686184
\(517\) 0 0
\(518\) −2.28498 −0.100396
\(519\) −65.5960 −2.87935
\(520\) 2.40195 0.105332
\(521\) 20.7089 0.907275 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(522\) −34.9515 −1.52979
\(523\) 9.17755 0.401306 0.200653 0.979662i \(-0.435694\pi\)
0.200653 + 0.979662i \(0.435694\pi\)
\(524\) −7.73690 −0.337988
\(525\) 8.58406 0.374639
\(526\) −1.71132 −0.0746171
\(527\) 3.88975 0.169440
\(528\) 0 0
\(529\) −6.61852 −0.287762
\(530\) 29.3749 1.27596
\(531\) −36.0776 −1.56563
\(532\) −0.274917 −0.0119191
\(533\) −7.36877 −0.319177
\(534\) 4.18324 0.181027
\(535\) −36.2312 −1.56641
\(536\) −14.0217 −0.605647
\(537\) 21.0016 0.906286
\(538\) 22.3017 0.961495
\(539\) 0 0
\(540\) 20.1120 0.865483
\(541\) −18.0117 −0.774383 −0.387191 0.921999i \(-0.626555\pi\)
−0.387191 + 0.921999i \(0.626555\pi\)
\(542\) −2.26292 −0.0972008
\(543\) 54.7788 2.35078
\(544\) −2.62721 −0.112641
\(545\) 67.9908 2.91240
\(546\) 0.458123 0.0196059
\(547\) −18.2006 −0.778200 −0.389100 0.921196i \(-0.627214\pi\)
−0.389100 + 0.921196i \(0.627214\pi\)
\(548\) −1.10706 −0.0472914
\(549\) 23.1658 0.988692
\(550\) 0 0
\(551\) 7.29532 0.310791
\(552\) 11.2972 0.480842
\(553\) −0.665590 −0.0283038
\(554\) 9.83937 0.418035
\(555\) −93.3371 −3.96194
\(556\) 14.8792 0.631020
\(557\) −31.3931 −1.33017 −0.665083 0.746769i \(-0.731604\pi\)
−0.665083 + 0.746769i \(0.731604\pi\)
\(558\) −7.09331 −0.300284
\(559\) 3.33393 0.141010
\(560\) 1.10606 0.0467395
\(561\) 0 0
\(562\) 17.9598 0.757590
\(563\) −11.9362 −0.503051 −0.251526 0.967851i \(-0.580932\pi\)
−0.251526 + 0.967851i \(0.580932\pi\)
\(564\) −25.4206 −1.07040
\(565\) 11.4480 0.481621
\(566\) 26.5193 1.11469
\(567\) −0.115373 −0.00484520
\(568\) −9.61823 −0.403572
\(569\) −4.74045 −0.198730 −0.0993649 0.995051i \(-0.531681\pi\)
−0.0993649 + 0.995051i \(0.531681\pi\)
\(570\) −11.2298 −0.470365
\(571\) 10.4663 0.438001 0.219001 0.975725i \(-0.429720\pi\)
0.219001 + 0.975725i \(0.429720\pi\)
\(572\) 0 0
\(573\) 58.4265 2.44080
\(574\) −3.39320 −0.141630
\(575\) 45.2765 1.88816
\(576\) 4.79095 0.199623
\(577\) −27.8884 −1.16101 −0.580504 0.814258i \(-0.697144\pi\)
−0.580504 + 0.814258i \(0.697144\pi\)
\(578\) −10.0978 −0.420012
\(579\) 5.30113 0.220308
\(580\) −29.3509 −1.21873
\(581\) 4.34225 0.180147
\(582\) 25.1472 1.04239
\(583\) 0 0
\(584\) −3.15625 −0.130606
\(585\) 11.5076 0.475781
\(586\) −12.3885 −0.511765
\(587\) −0.355712 −0.0146818 −0.00734089 0.999973i \(-0.502337\pi\)
−0.00734089 + 0.999973i \(0.502337\pi\)
\(588\) −19.3276 −0.797058
\(589\) 1.48056 0.0610056
\(590\) −30.2966 −1.24729
\(591\) −3.91783 −0.161158
\(592\) −8.31155 −0.341603
\(593\) −34.4326 −1.41398 −0.706990 0.707224i \(-0.749947\pi\)
−0.706990 + 0.707224i \(0.749947\pi\)
\(594\) 0 0
\(595\) −2.90585 −0.119128
\(596\) 20.9576 0.858457
\(597\) −10.0597 −0.411716
\(598\) 2.41637 0.0988126
\(599\) 9.20766 0.376215 0.188107 0.982148i \(-0.439765\pi\)
0.188107 + 0.982148i \(0.439765\pi\)
\(600\) 31.2242 1.27472
\(601\) −40.2925 −1.64357 −0.821783 0.569801i \(-0.807020\pi\)
−0.821783 + 0.569801i \(0.807020\pi\)
\(602\) 1.53522 0.0625710
\(603\) −67.1774 −2.73568
\(604\) −4.07961 −0.165997
\(605\) 0 0
\(606\) 6.44614 0.261856
\(607\) 21.8513 0.886916 0.443458 0.896295i \(-0.353751\pi\)
0.443458 + 0.896295i \(0.353751\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −5.59810 −0.226847
\(610\) 19.4537 0.787659
\(611\) −5.43723 −0.219967
\(612\) −12.5868 −0.508792
\(613\) 18.0805 0.730264 0.365132 0.930956i \(-0.381024\pi\)
0.365132 + 0.930956i \(0.381024\pi\)
\(614\) −29.2289 −1.17958
\(615\) −138.606 −5.58912
\(616\) 0 0
\(617\) −45.2047 −1.81987 −0.909936 0.414749i \(-0.863870\pi\)
−0.909936 + 0.414749i \(0.863870\pi\)
\(618\) 28.8620 1.16100
\(619\) 18.8902 0.759263 0.379631 0.925138i \(-0.376051\pi\)
0.379631 + 0.925138i \(0.376051\pi\)
\(620\) −5.95669 −0.239226
\(621\) 20.2327 0.811912
\(622\) 10.9986 0.441004
\(623\) 0.412021 0.0165073
\(624\) 1.66641 0.0667097
\(625\) 44.2063 1.76825
\(626\) 15.5213 0.620355
\(627\) 0 0
\(628\) 19.7161 0.786758
\(629\) 21.8362 0.870666
\(630\) 5.29907 0.211120
\(631\) −6.89416 −0.274452 −0.137226 0.990540i \(-0.543819\pi\)
−0.137226 + 0.990540i \(0.543819\pi\)
\(632\) −2.42106 −0.0963046
\(633\) 52.3955 2.08253
\(634\) −23.9485 −0.951116
\(635\) 22.5179 0.893597
\(636\) 20.3795 0.808100
\(637\) −4.13399 −0.163795
\(638\) 0 0
\(639\) −46.0804 −1.82291
\(640\) 4.02325 0.159033
\(641\) −15.7499 −0.622085 −0.311043 0.950396i \(-0.600678\pi\)
−0.311043 + 0.950396i \(0.600678\pi\)
\(642\) −25.1362 −0.992048
\(643\) 40.9900 1.61649 0.808245 0.588847i \(-0.200418\pi\)
0.808245 + 0.588847i \(0.200418\pi\)
\(644\) 1.11270 0.0438465
\(645\) 62.7108 2.46924
\(646\) 2.62721 0.103366
\(647\) −5.82684 −0.229077 −0.114538 0.993419i \(-0.536539\pi\)
−0.114538 + 0.993419i \(0.536539\pi\)
\(648\) −0.419665 −0.0164860
\(649\) 0 0
\(650\) 6.67856 0.261955
\(651\) −1.13612 −0.0445280
\(652\) 16.9154 0.662460
\(653\) 18.8227 0.736591 0.368295 0.929709i \(-0.379942\pi\)
0.368295 + 0.929709i \(0.379942\pi\)
\(654\) 47.1702 1.84450
\(655\) −31.1275 −1.21625
\(656\) −12.3427 −0.481900
\(657\) −15.1214 −0.589943
\(658\) −2.50376 −0.0976066
\(659\) 29.6469 1.15488 0.577440 0.816433i \(-0.304052\pi\)
0.577440 + 0.816433i \(0.304052\pi\)
\(660\) 0 0
\(661\) 26.1657 1.01773 0.508864 0.860847i \(-0.330066\pi\)
0.508864 + 0.860847i \(0.330066\pi\)
\(662\) 25.6584 0.997241
\(663\) −4.37800 −0.170028
\(664\) 15.7948 0.612957
\(665\) −1.10606 −0.0428911
\(666\) −39.8202 −1.54300
\(667\) −29.5271 −1.14329
\(668\) −23.1451 −0.895512
\(669\) −40.9441 −1.58299
\(670\) −56.4130 −2.17942
\(671\) 0 0
\(672\) 0.767355 0.0296014
\(673\) 30.9303 1.19228 0.596138 0.802882i \(-0.296701\pi\)
0.596138 + 0.802882i \(0.296701\pi\)
\(674\) −2.94204 −0.113323
\(675\) 55.9210 2.15240
\(676\) −12.6436 −0.486291
\(677\) −21.2288 −0.815888 −0.407944 0.913007i \(-0.633754\pi\)
−0.407944 + 0.913007i \(0.633754\pi\)
\(678\) 7.94233 0.305023
\(679\) 2.47683 0.0950520
\(680\) −10.5699 −0.405338
\(681\) 9.89271 0.379090
\(682\) 0 0
\(683\) −8.46842 −0.324035 −0.162017 0.986788i \(-0.551800\pi\)
−0.162017 + 0.986788i \(0.551800\pi\)
\(684\) −4.79095 −0.183186
\(685\) −4.45400 −0.170179
\(686\) −3.82806 −0.146156
\(687\) −46.8226 −1.78639
\(688\) 5.58432 0.212900
\(689\) 4.35898 0.166064
\(690\) 45.4516 1.73031
\(691\) 0.920788 0.0350284 0.0175142 0.999847i \(-0.494425\pi\)
0.0175142 + 0.999847i \(0.494425\pi\)
\(692\) −23.5008 −0.893366
\(693\) 0 0
\(694\) −6.33884 −0.240619
\(695\) 59.8629 2.27073
\(696\) −20.3629 −0.771854
\(697\) 32.4268 1.22825
\(698\) −10.5789 −0.400418
\(699\) 71.8439 2.71738
\(700\) 3.07537 0.116238
\(701\) −10.4383 −0.394249 −0.197124 0.980379i \(-0.563160\pi\)
−0.197124 + 0.980379i \(0.563160\pi\)
\(702\) 2.98445 0.112641
\(703\) 8.31155 0.313476
\(704\) 0 0
\(705\) −102.274 −3.85185
\(706\) −35.1642 −1.32342
\(707\) 0.634900 0.0238779
\(708\) −21.0190 −0.789941
\(709\) −13.2648 −0.498170 −0.249085 0.968482i \(-0.580130\pi\)
−0.249085 + 0.968482i \(0.580130\pi\)
\(710\) −38.6966 −1.45226
\(711\) −11.5992 −0.435003
\(712\) 1.49871 0.0561666
\(713\) −5.99244 −0.224419
\(714\) −2.01600 −0.0754470
\(715\) 0 0
\(716\) 7.52415 0.281191
\(717\) 10.7079 0.399894
\(718\) 24.1939 0.902909
\(719\) −44.0301 −1.64205 −0.821023 0.570895i \(-0.806596\pi\)
−0.821023 + 0.570895i \(0.806596\pi\)
\(720\) 19.2752 0.718344
\(721\) 2.84271 0.105868
\(722\) 1.00000 0.0372161
\(723\) −30.4421 −1.13215
\(724\) 19.6253 0.729370
\(725\) −81.6096 −3.03090
\(726\) 0 0
\(727\) −14.8909 −0.552271 −0.276136 0.961119i \(-0.589054\pi\)
−0.276136 + 0.961119i \(0.589054\pi\)
\(728\) 0.164130 0.00608305
\(729\) −43.8701 −1.62482
\(730\) −12.6984 −0.469988
\(731\) −14.6712 −0.542633
\(732\) 13.4965 0.498845
\(733\) 19.1078 0.705763 0.352882 0.935668i \(-0.385202\pi\)
0.352882 + 0.935668i \(0.385202\pi\)
\(734\) −23.2519 −0.858242
\(735\) −77.7599 −2.86822
\(736\) 4.04740 0.149189
\(737\) 0 0
\(738\) −59.1330 −2.17672
\(739\) −18.8804 −0.694527 −0.347264 0.937768i \(-0.612889\pi\)
−0.347264 + 0.937768i \(0.612889\pi\)
\(740\) −33.4395 −1.22926
\(741\) −1.66641 −0.0612170
\(742\) 2.00724 0.0736882
\(743\) 27.1802 0.997147 0.498573 0.866848i \(-0.333857\pi\)
0.498573 + 0.866848i \(0.333857\pi\)
\(744\) −4.13259 −0.151508
\(745\) 84.3178 3.08916
\(746\) 8.15845 0.298702
\(747\) 75.6720 2.76869
\(748\) 0 0
\(749\) −2.47575 −0.0904618
\(750\) 69.4739 2.53683
\(751\) 12.7321 0.464601 0.232300 0.972644i \(-0.425375\pi\)
0.232300 + 0.972644i \(0.425375\pi\)
\(752\) −9.10733 −0.332110
\(753\) 38.9273 1.41859
\(754\) −4.35543 −0.158615
\(755\) −16.4133 −0.597341
\(756\) 1.37429 0.0499825
\(757\) 36.4140 1.32349 0.661745 0.749729i \(-0.269816\pi\)
0.661745 + 0.749729i \(0.269816\pi\)
\(758\) −18.9997 −0.690102
\(759\) 0 0
\(760\) −4.02325 −0.145939
\(761\) 19.2127 0.696461 0.348230 0.937409i \(-0.386783\pi\)
0.348230 + 0.937409i \(0.386783\pi\)
\(762\) 15.6224 0.565938
\(763\) 4.64594 0.168194
\(764\) 20.9322 0.757300
\(765\) −50.6400 −1.83089
\(766\) 12.1817 0.440143
\(767\) −4.49575 −0.162332
\(768\) 2.79123 0.100720
\(769\) −15.0316 −0.542052 −0.271026 0.962572i \(-0.587363\pi\)
−0.271026 + 0.962572i \(0.587363\pi\)
\(770\) 0 0
\(771\) 46.9794 1.69192
\(772\) 1.89921 0.0683542
\(773\) −25.2426 −0.907914 −0.453957 0.891023i \(-0.649988\pi\)
−0.453957 + 0.891023i \(0.649988\pi\)
\(774\) 26.7542 0.961659
\(775\) −16.5624 −0.594940
\(776\) 9.00939 0.323418
\(777\) −6.37791 −0.228806
\(778\) −24.1433 −0.865579
\(779\) 12.3427 0.442222
\(780\) 6.70438 0.240055
\(781\) 0 0
\(782\) −10.6334 −0.380249
\(783\) −36.4689 −1.30329
\(784\) −6.92442 −0.247301
\(785\) 79.3228 2.83115
\(786\) −21.5954 −0.770284
\(787\) −32.2538 −1.14972 −0.574862 0.818250i \(-0.694944\pi\)
−0.574862 + 0.818250i \(0.694944\pi\)
\(788\) −1.40362 −0.0500020
\(789\) −4.77668 −0.170054
\(790\) −9.74054 −0.346553
\(791\) 0.782265 0.0278141
\(792\) 0 0
\(793\) 2.88677 0.102512
\(794\) −10.1918 −0.361692
\(795\) 81.9919 2.90795
\(796\) −3.60404 −0.127742
\(797\) −17.7608 −0.629121 −0.314561 0.949237i \(-0.601857\pi\)
−0.314561 + 0.949237i \(0.601857\pi\)
\(798\) −0.767355 −0.0271641
\(799\) 23.9269 0.846472
\(800\) 11.1866 0.395505
\(801\) 7.18025 0.253701
\(802\) 12.2313 0.431901
\(803\) 0 0
\(804\) −39.1379 −1.38029
\(805\) 4.47667 0.157782
\(806\) −0.883921 −0.0311348
\(807\) 62.2492 2.19127
\(808\) 2.30943 0.0812454
\(809\) 21.3809 0.751714 0.375857 0.926678i \(-0.377348\pi\)
0.375857 + 0.926678i \(0.377348\pi\)
\(810\) −1.68842 −0.0593249
\(811\) −9.48316 −0.332999 −0.166499 0.986042i \(-0.553246\pi\)
−0.166499 + 0.986042i \(0.553246\pi\)
\(812\) −2.00561 −0.0703830
\(813\) −6.31633 −0.221523
\(814\) 0 0
\(815\) 68.0551 2.38387
\(816\) −7.33314 −0.256711
\(817\) −5.58432 −0.195371
\(818\) −27.8419 −0.973470
\(819\) 0.786337 0.0274768
\(820\) −49.6576 −1.73412
\(821\) −3.84674 −0.134252 −0.0671261 0.997744i \(-0.521383\pi\)
−0.0671261 + 0.997744i \(0.521383\pi\)
\(822\) −3.09007 −0.107778
\(823\) −15.9227 −0.555031 −0.277516 0.960721i \(-0.589511\pi\)
−0.277516 + 0.960721i \(0.589511\pi\)
\(824\) 10.3403 0.360220
\(825\) 0 0
\(826\) −2.07022 −0.0720323
\(827\) 21.3561 0.742624 0.371312 0.928508i \(-0.378908\pi\)
0.371312 + 0.928508i \(0.378908\pi\)
\(828\) 19.3909 0.673880
\(829\) 22.3416 0.775957 0.387978 0.921668i \(-0.373174\pi\)
0.387978 + 0.921668i \(0.373174\pi\)
\(830\) 63.5464 2.20573
\(831\) 27.4639 0.952712
\(832\) 0.597016 0.0206978
\(833\) 18.1919 0.630312
\(834\) 41.5313 1.43811
\(835\) −93.1187 −3.22250
\(836\) 0 0
\(837\) −7.40126 −0.255825
\(838\) 2.74637 0.0948719
\(839\) 0.807131 0.0278653 0.0139326 0.999903i \(-0.495565\pi\)
0.0139326 + 0.999903i \(0.495565\pi\)
\(840\) 3.08726 0.106521
\(841\) 24.2217 0.835233
\(842\) 3.45765 0.119159
\(843\) 50.1300 1.72657
\(844\) 18.7715 0.646141
\(845\) −50.8683 −1.74992
\(846\) −43.6328 −1.50013
\(847\) 0 0
\(848\) 7.30127 0.250727
\(849\) 74.0215 2.54041
\(850\) −29.3894 −1.00805
\(851\) −33.6402 −1.15317
\(852\) −26.8467 −0.919752
\(853\) −35.6981 −1.22228 −0.611139 0.791523i \(-0.709289\pi\)
−0.611139 + 0.791523i \(0.709289\pi\)
\(854\) 1.32931 0.0454881
\(855\) −19.2752 −0.659198
\(856\) −9.00544 −0.307800
\(857\) 53.2489 1.81895 0.909474 0.415760i \(-0.136484\pi\)
0.909474 + 0.415760i \(0.136484\pi\)
\(858\) 0 0
\(859\) −57.5833 −1.96472 −0.982358 0.187009i \(-0.940121\pi\)
−0.982358 + 0.187009i \(0.940121\pi\)
\(860\) 22.4671 0.766123
\(861\) −9.47120 −0.322778
\(862\) 33.1455 1.12894
\(863\) −41.2077 −1.40273 −0.701364 0.712804i \(-0.747425\pi\)
−0.701364 + 0.712804i \(0.747425\pi\)
\(864\) 4.99894 0.170067
\(865\) −94.5496 −3.21478
\(866\) −17.0841 −0.580540
\(867\) −28.1852 −0.957218
\(868\) −0.407032 −0.0138156
\(869\) 0 0
\(870\) −81.9251 −2.77752
\(871\) −8.37121 −0.283647
\(872\) 16.8995 0.572288
\(873\) 43.1635 1.46086
\(874\) −4.04740 −0.136905
\(875\) 6.84270 0.231326
\(876\) −8.80980 −0.297656
\(877\) −29.3504 −0.991092 −0.495546 0.868582i \(-0.665032\pi\)
−0.495546 + 0.868582i \(0.665032\pi\)
\(878\) 36.1437 1.21979
\(879\) −34.5792 −1.16633
\(880\) 0 0
\(881\) 1.36463 0.0459757 0.0229878 0.999736i \(-0.492682\pi\)
0.0229878 + 0.999736i \(0.492682\pi\)
\(882\) −33.1745 −1.11704
\(883\) 11.8574 0.399034 0.199517 0.979894i \(-0.436063\pi\)
0.199517 + 0.979894i \(0.436063\pi\)
\(884\) −1.56849 −0.0527539
\(885\) −84.5646 −2.84261
\(886\) 19.4900 0.654778
\(887\) −28.7149 −0.964152 −0.482076 0.876129i \(-0.660117\pi\)
−0.482076 + 0.876129i \(0.660117\pi\)
\(888\) −23.1994 −0.778521
\(889\) 1.53869 0.0516061
\(890\) 6.02969 0.202116
\(891\) 0 0
\(892\) −14.6688 −0.491149
\(893\) 9.10733 0.304765
\(894\) 58.4974 1.95645
\(895\) 30.2716 1.01187
\(896\) 0.274917 0.00918432
\(897\) 6.74463 0.225196
\(898\) −12.8197 −0.427798
\(899\) 10.8012 0.360240
\(900\) 53.5942 1.78647
\(901\) −19.1820 −0.639044
\(902\) 0 0
\(903\) 4.28515 0.142601
\(904\) 2.84546 0.0946386
\(905\) 78.9577 2.62464
\(906\) −11.3871 −0.378312
\(907\) 20.8425 0.692063 0.346031 0.938223i \(-0.387529\pi\)
0.346031 + 0.938223i \(0.387529\pi\)
\(908\) 3.54422 0.117619
\(909\) 11.0644 0.366981
\(910\) 0.660335 0.0218899
\(911\) −33.3467 −1.10483 −0.552413 0.833571i \(-0.686293\pi\)
−0.552413 + 0.833571i \(0.686293\pi\)
\(912\) −2.79123 −0.0924268
\(913\) 0 0
\(914\) 2.20055 0.0727877
\(915\) 54.2998 1.79510
\(916\) −16.7749 −0.554259
\(917\) −2.12700 −0.0702398
\(918\) −13.1333 −0.433462
\(919\) −15.9480 −0.526076 −0.263038 0.964786i \(-0.584724\pi\)
−0.263038 + 0.964786i \(0.584724\pi\)
\(920\) 16.2837 0.536859
\(921\) −81.5845 −2.68830
\(922\) −3.39457 −0.111794
\(923\) −5.74224 −0.189008
\(924\) 0 0
\(925\) −92.9776 −3.05709
\(926\) 18.5198 0.608600
\(927\) 49.5397 1.62710
\(928\) −7.29532 −0.239481
\(929\) −34.2521 −1.12377 −0.561887 0.827214i \(-0.689924\pi\)
−0.561887 + 0.827214i \(0.689924\pi\)
\(930\) −16.6265 −0.545203
\(931\) 6.92442 0.226939
\(932\) 25.7392 0.843115
\(933\) 30.6996 1.00506
\(934\) 29.7909 0.974789
\(935\) 0 0
\(936\) 2.86027 0.0934910
\(937\) 32.5123 1.06213 0.531065 0.847331i \(-0.321792\pi\)
0.531065 + 0.847331i \(0.321792\pi\)
\(938\) −3.85481 −0.125864
\(939\) 43.3234 1.41381
\(940\) −36.6411 −1.19510
\(941\) 12.8788 0.419838 0.209919 0.977719i \(-0.432680\pi\)
0.209919 + 0.977719i \(0.432680\pi\)
\(942\) 55.0321 1.79304
\(943\) −49.9557 −1.62678
\(944\) −7.53037 −0.245093
\(945\) 5.52912 0.179862
\(946\) 0 0
\(947\) −27.4064 −0.890589 −0.445295 0.895384i \(-0.646901\pi\)
−0.445295 + 0.895384i \(0.646901\pi\)
\(948\) −6.75773 −0.219481
\(949\) −1.88433 −0.0611680
\(950\) −11.1866 −0.362940
\(951\) −66.8457 −2.16762
\(952\) −0.722264 −0.0234087
\(953\) 13.5962 0.440423 0.220212 0.975452i \(-0.429325\pi\)
0.220212 + 0.975452i \(0.429325\pi\)
\(954\) 34.9800 1.13252
\(955\) 84.2155 2.72515
\(956\) 3.83627 0.124074
\(957\) 0 0
\(958\) 25.3380 0.818632
\(959\) −0.304350 −0.00982798
\(960\) 11.2298 0.362441
\(961\) −28.8079 −0.929288
\(962\) −4.96213 −0.159985
\(963\) −43.1446 −1.39031
\(964\) −10.9064 −0.351270
\(965\) 7.64101 0.245973
\(966\) 3.10579 0.0999273
\(967\) −19.4593 −0.625768 −0.312884 0.949791i \(-0.601295\pi\)
−0.312884 + 0.949791i \(0.601295\pi\)
\(968\) 0 0
\(969\) 7.33314 0.235574
\(970\) 36.2470 1.16382
\(971\) −54.0585 −1.73482 −0.867410 0.497594i \(-0.834217\pi\)
−0.867410 + 0.497594i \(0.834217\pi\)
\(972\) −16.1682 −0.518595
\(973\) 4.09055 0.131137
\(974\) −1.08718 −0.0348356
\(975\) 18.6414 0.597002
\(976\) 4.83533 0.154775
\(977\) −34.0503 −1.08937 −0.544684 0.838642i \(-0.683350\pi\)
−0.544684 + 0.838642i \(0.683350\pi\)
\(978\) 47.2148 1.50976
\(979\) 0 0
\(980\) −27.8587 −0.889913
\(981\) 80.9644 2.58499
\(982\) 17.1850 0.548397
\(983\) 51.6148 1.64626 0.823129 0.567855i \(-0.192226\pi\)
0.823129 + 0.567855i \(0.192226\pi\)
\(984\) −34.4512 −1.09826
\(985\) −5.64713 −0.179932
\(986\) 19.1663 0.610381
\(987\) −6.98856 −0.222448
\(988\) −0.597016 −0.0189936
\(989\) 22.6020 0.718702
\(990\) 0 0
\(991\) 7.22913 0.229641 0.114820 0.993386i \(-0.463371\pi\)
0.114820 + 0.993386i \(0.463371\pi\)
\(992\) −1.48056 −0.0470080
\(993\) 71.6183 2.27274
\(994\) −2.64421 −0.0838693
\(995\) −14.5000 −0.459679
\(996\) 44.0868 1.39695
\(997\) 40.4932 1.28243 0.641216 0.767360i \(-0.278430\pi\)
0.641216 + 0.767360i \(0.278430\pi\)
\(998\) −8.60896 −0.272512
\(999\) −41.5489 −1.31455
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.1.6 yes 8
11.10 odd 2 4598.2.a.by.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.by.1.6 8 11.10 odd 2
4598.2.a.cb.1.6 yes 8 1.1 even 1 trivial