Properties

Label 3549.2.a.bf.1.5
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.146218\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +0.152606 q^{10} -3.53195 q^{11} +1.97862 q^{12} -0.146218 q^{14} -1.04369 q^{15} +3.87218 q^{16} +6.85108 q^{17} +0.146218 q^{18} +3.55174 q^{19} -2.06507 q^{20} +1.00000 q^{21} -0.516433 q^{22} +0.0937939 q^{23} +0.581745 q^{24} -3.91070 q^{25} -1.00000 q^{27} +1.97862 q^{28} -10.5871 q^{29} -0.152606 q^{30} -4.44756 q^{31} +1.72967 q^{32} +3.53195 q^{33} +1.00175 q^{34} -1.04369 q^{35} -1.97862 q^{36} -12.0790 q^{37} +0.519327 q^{38} -0.607163 q^{40} -1.37186 q^{41} +0.146218 q^{42} +6.68018 q^{43} +6.98839 q^{44} +1.04369 q^{45} +0.0137143 q^{46} +9.55298 q^{47} -3.87218 q^{48} +1.00000 q^{49} -0.571814 q^{50} -6.85108 q^{51} -3.01527 q^{53} -0.146218 q^{54} -3.68627 q^{55} +0.581745 q^{56} -3.55174 q^{57} -1.54803 q^{58} -0.747537 q^{59} +2.06507 q^{60} +5.72344 q^{61} -0.650312 q^{62} -1.00000 q^{63} -7.49145 q^{64} +0.516433 q^{66} +9.38048 q^{67} -13.5557 q^{68} -0.0937939 q^{69} -0.152606 q^{70} -4.41098 q^{71} -0.581745 q^{72} +10.4079 q^{73} -1.76616 q^{74} +3.91070 q^{75} -7.02754 q^{76} +3.53195 q^{77} -11.4527 q^{79} +4.04137 q^{80} +1.00000 q^{81} -0.200591 q^{82} +0.520292 q^{83} -1.97862 q^{84} +7.15043 q^{85} +0.976761 q^{86} +10.5871 q^{87} +2.05469 q^{88} +4.78217 q^{89} +0.152606 q^{90} -0.185582 q^{92} +4.44756 q^{93} +1.39681 q^{94} +3.70692 q^{95} -1.72967 q^{96} -5.89081 q^{97} +0.146218 q^{98} -3.53195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.146218 0.103392 0.0516958 0.998663i \(-0.483537\pi\)
0.0516958 + 0.998663i \(0.483537\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.97862 −0.989310
\(5\) 1.04369 0.466754 0.233377 0.972386i \(-0.425022\pi\)
0.233377 + 0.972386i \(0.425022\pi\)
\(6\) −0.146218 −0.0596931
\(7\) −1.00000 −0.377964
\(8\) −0.581745 −0.205678
\(9\) 1.00000 0.333333
\(10\) 0.152606 0.0482584
\(11\) −3.53195 −1.06492 −0.532461 0.846454i \(-0.678733\pi\)
−0.532461 + 0.846454i \(0.678733\pi\)
\(12\) 1.97862 0.571179
\(13\) 0 0
\(14\) −0.146218 −0.0390783
\(15\) −1.04369 −0.269480
\(16\) 3.87218 0.968045
\(17\) 6.85108 1.66163 0.830816 0.556547i \(-0.187874\pi\)
0.830816 + 0.556547i \(0.187874\pi\)
\(18\) 0.146218 0.0344638
\(19\) 3.55174 0.814824 0.407412 0.913244i \(-0.366431\pi\)
0.407412 + 0.913244i \(0.366431\pi\)
\(20\) −2.06507 −0.461764
\(21\) 1.00000 0.218218
\(22\) −0.516433 −0.110104
\(23\) 0.0937939 0.0195574 0.00977869 0.999952i \(-0.496887\pi\)
0.00977869 + 0.999952i \(0.496887\pi\)
\(24\) 0.581745 0.118748
\(25\) −3.91070 −0.782141
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.97862 0.373924
\(29\) −10.5871 −1.96598 −0.982991 0.183653i \(-0.941208\pi\)
−0.982991 + 0.183653i \(0.941208\pi\)
\(30\) −0.152606 −0.0278620
\(31\) −4.44756 −0.798805 −0.399402 0.916776i \(-0.630782\pi\)
−0.399402 + 0.916776i \(0.630782\pi\)
\(32\) 1.72967 0.305765
\(33\) 3.53195 0.614833
\(34\) 1.00175 0.171799
\(35\) −1.04369 −0.176416
\(36\) −1.97862 −0.329770
\(37\) −12.0790 −1.98577 −0.992885 0.119075i \(-0.962007\pi\)
−0.992885 + 0.119075i \(0.962007\pi\)
\(38\) 0.519327 0.0842459
\(39\) 0 0
\(40\) −0.607163 −0.0960009
\(41\) −1.37186 −0.214249 −0.107125 0.994246i \(-0.534164\pi\)
−0.107125 + 0.994246i \(0.534164\pi\)
\(42\) 0.146218 0.0225619
\(43\) 6.68018 1.01872 0.509359 0.860554i \(-0.329883\pi\)
0.509359 + 0.860554i \(0.329883\pi\)
\(44\) 6.98839 1.05354
\(45\) 1.04369 0.155585
\(46\) 0.0137143 0.00202207
\(47\) 9.55298 1.39345 0.696723 0.717341i \(-0.254641\pi\)
0.696723 + 0.717341i \(0.254641\pi\)
\(48\) −3.87218 −0.558901
\(49\) 1.00000 0.142857
\(50\) −0.571814 −0.0808667
\(51\) −6.85108 −0.959344
\(52\) 0 0
\(53\) −3.01527 −0.414179 −0.207090 0.978322i \(-0.566399\pi\)
−0.207090 + 0.978322i \(0.566399\pi\)
\(54\) −0.146218 −0.0198977
\(55\) −3.68627 −0.497057
\(56\) 0.581745 0.0777389
\(57\) −3.55174 −0.470439
\(58\) −1.54803 −0.203266
\(59\) −0.747537 −0.0973210 −0.0486605 0.998815i \(-0.515495\pi\)
−0.0486605 + 0.998815i \(0.515495\pi\)
\(60\) 2.06507 0.266600
\(61\) 5.72344 0.732812 0.366406 0.930455i \(-0.380588\pi\)
0.366406 + 0.930455i \(0.380588\pi\)
\(62\) −0.650312 −0.0825896
\(63\) −1.00000 −0.125988
\(64\) −7.49145 −0.936431
\(65\) 0 0
\(66\) 0.516433 0.0635686
\(67\) 9.38048 1.14601 0.573004 0.819553i \(-0.305778\pi\)
0.573004 + 0.819553i \(0.305778\pi\)
\(68\) −13.5557 −1.64387
\(69\) −0.0937939 −0.0112915
\(70\) −0.152606 −0.0182400
\(71\) −4.41098 −0.523487 −0.261744 0.965137i \(-0.584297\pi\)
−0.261744 + 0.965137i \(0.584297\pi\)
\(72\) −0.581745 −0.0685593
\(73\) 10.4079 1.21816 0.609078 0.793110i \(-0.291540\pi\)
0.609078 + 0.793110i \(0.291540\pi\)
\(74\) −1.76616 −0.205312
\(75\) 3.91070 0.451569
\(76\) −7.02754 −0.806114
\(77\) 3.53195 0.402503
\(78\) 0 0
\(79\) −11.4527 −1.28853 −0.644267 0.764801i \(-0.722837\pi\)
−0.644267 + 0.764801i \(0.722837\pi\)
\(80\) 4.04137 0.451839
\(81\) 1.00000 0.111111
\(82\) −0.200591 −0.0221515
\(83\) 0.520292 0.0571094 0.0285547 0.999592i \(-0.490910\pi\)
0.0285547 + 0.999592i \(0.490910\pi\)
\(84\) −1.97862 −0.215885
\(85\) 7.15043 0.775573
\(86\) 0.976761 0.105327
\(87\) 10.5871 1.13506
\(88\) 2.05469 0.219031
\(89\) 4.78217 0.506909 0.253455 0.967347i \(-0.418433\pi\)
0.253455 + 0.967347i \(0.418433\pi\)
\(90\) 0.152606 0.0160861
\(91\) 0 0
\(92\) −0.185582 −0.0193483
\(93\) 4.44756 0.461190
\(94\) 1.39681 0.144070
\(95\) 3.70692 0.380322
\(96\) −1.72967 −0.176534
\(97\) −5.89081 −0.598121 −0.299060 0.954234i \(-0.596673\pi\)
−0.299060 + 0.954234i \(0.596673\pi\)
\(98\) 0.146218 0.0147702
\(99\) −3.53195 −0.354974
\(100\) 7.73780 0.773780
\(101\) 6.24161 0.621063 0.310532 0.950563i \(-0.399493\pi\)
0.310532 + 0.950563i \(0.399493\pi\)
\(102\) −1.00175 −0.0991880
\(103\) 16.3514 1.61115 0.805575 0.592494i \(-0.201857\pi\)
0.805575 + 0.592494i \(0.201857\pi\)
\(104\) 0 0
\(105\) 1.04369 0.101854
\(106\) −0.440886 −0.0428226
\(107\) 12.5824 1.21639 0.608194 0.793789i \(-0.291894\pi\)
0.608194 + 0.793789i \(0.291894\pi\)
\(108\) 1.97862 0.190393
\(109\) 16.5546 1.58564 0.792820 0.609456i \(-0.208612\pi\)
0.792820 + 0.609456i \(0.208612\pi\)
\(110\) −0.538998 −0.0513915
\(111\) 12.0790 1.14649
\(112\) −3.87218 −0.365887
\(113\) 4.24986 0.399793 0.199897 0.979817i \(-0.435939\pi\)
0.199897 + 0.979817i \(0.435939\pi\)
\(114\) −0.519327 −0.0486394
\(115\) 0.0978920 0.00912848
\(116\) 20.9479 1.94497
\(117\) 0 0
\(118\) −0.109303 −0.0100622
\(119\) −6.85108 −0.628038
\(120\) 0.607163 0.0554262
\(121\) 1.47466 0.134060
\(122\) 0.836869 0.0757665
\(123\) 1.37186 0.123697
\(124\) 8.80003 0.790266
\(125\) −9.30004 −0.831821
\(126\) −0.146218 −0.0130261
\(127\) 13.1132 1.16361 0.581803 0.813330i \(-0.302347\pi\)
0.581803 + 0.813330i \(0.302347\pi\)
\(128\) −4.55472 −0.402585
\(129\) −6.68018 −0.588157
\(130\) 0 0
\(131\) 16.3145 1.42541 0.712704 0.701465i \(-0.247470\pi\)
0.712704 + 0.701465i \(0.247470\pi\)
\(132\) −6.98839 −0.608261
\(133\) −3.55174 −0.307975
\(134\) 1.37159 0.118487
\(135\) −1.04369 −0.0898268
\(136\) −3.98558 −0.341761
\(137\) −13.8001 −1.17902 −0.589511 0.807760i \(-0.700680\pi\)
−0.589511 + 0.807760i \(0.700680\pi\)
\(138\) −0.0137143 −0.00116744
\(139\) 10.6210 0.900863 0.450432 0.892811i \(-0.351270\pi\)
0.450432 + 0.892811i \(0.351270\pi\)
\(140\) 2.06507 0.174531
\(141\) −9.55298 −0.804506
\(142\) −0.644964 −0.0541242
\(143\) 0 0
\(144\) 3.87218 0.322682
\(145\) −11.0497 −0.917630
\(146\) 1.52182 0.125947
\(147\) −1.00000 −0.0824786
\(148\) 23.8997 1.96454
\(149\) −17.4093 −1.42622 −0.713112 0.701050i \(-0.752715\pi\)
−0.713112 + 0.701050i \(0.752715\pi\)
\(150\) 0.571814 0.0466884
\(151\) 8.14197 0.662584 0.331292 0.943528i \(-0.392515\pi\)
0.331292 + 0.943528i \(0.392515\pi\)
\(152\) −2.06620 −0.167591
\(153\) 6.85108 0.553877
\(154\) 0.516433 0.0416154
\(155\) −4.64189 −0.372845
\(156\) 0 0
\(157\) 6.68582 0.533587 0.266793 0.963754i \(-0.414036\pi\)
0.266793 + 0.963754i \(0.414036\pi\)
\(158\) −1.67459 −0.133223
\(159\) 3.01527 0.239127
\(160\) 1.80525 0.142717
\(161\) −0.0937939 −0.00739199
\(162\) 0.146218 0.0114879
\(163\) −1.38383 −0.108390 −0.0541951 0.998530i \(-0.517259\pi\)
−0.0541951 + 0.998530i \(0.517259\pi\)
\(164\) 2.71440 0.211959
\(165\) 3.68627 0.286976
\(166\) 0.0760759 0.00590463
\(167\) −9.73351 −0.753201 −0.376601 0.926376i \(-0.622907\pi\)
−0.376601 + 0.926376i \(0.622907\pi\)
\(168\) −0.581745 −0.0448826
\(169\) 0 0
\(170\) 1.04552 0.0801877
\(171\) 3.55174 0.271608
\(172\) −13.2175 −1.00783
\(173\) 21.8671 1.66253 0.831263 0.555880i \(-0.187619\pi\)
0.831263 + 0.555880i \(0.187619\pi\)
\(174\) 1.54803 0.117356
\(175\) 3.91070 0.295621
\(176\) −13.6763 −1.03089
\(177\) 0.747537 0.0561883
\(178\) 0.699238 0.0524101
\(179\) 9.76241 0.729677 0.364838 0.931071i \(-0.381124\pi\)
0.364838 + 0.931071i \(0.381124\pi\)
\(180\) −2.06507 −0.153921
\(181\) −6.12994 −0.455635 −0.227818 0.973704i \(-0.573159\pi\)
−0.227818 + 0.973704i \(0.573159\pi\)
\(182\) 0 0
\(183\) −5.72344 −0.423089
\(184\) −0.0545641 −0.00402252
\(185\) −12.6067 −0.926866
\(186\) 0.650312 0.0476832
\(187\) −24.1977 −1.76951
\(188\) −18.9017 −1.37855
\(189\) 1.00000 0.0727393
\(190\) 0.542018 0.0393221
\(191\) −6.99754 −0.506324 −0.253162 0.967424i \(-0.581471\pi\)
−0.253162 + 0.967424i \(0.581471\pi\)
\(192\) 7.49145 0.540649
\(193\) −0.616731 −0.0443933 −0.0221966 0.999754i \(-0.507066\pi\)
−0.0221966 + 0.999754i \(0.507066\pi\)
\(194\) −0.861340 −0.0618406
\(195\) 0 0
\(196\) −1.97862 −0.141330
\(197\) 16.1657 1.15176 0.575881 0.817534i \(-0.304659\pi\)
0.575881 + 0.817534i \(0.304659\pi\)
\(198\) −0.516433 −0.0367013
\(199\) −12.2086 −0.865444 −0.432722 0.901527i \(-0.642447\pi\)
−0.432722 + 0.901527i \(0.642447\pi\)
\(200\) 2.27503 0.160869
\(201\) −9.38048 −0.661648
\(202\) 0.912634 0.0642127
\(203\) 10.5871 0.743071
\(204\) 13.5557 0.949088
\(205\) −1.43181 −0.100002
\(206\) 2.39086 0.166579
\(207\) 0.0937939 0.00651912
\(208\) 0 0
\(209\) −12.5445 −0.867725
\(210\) 0.152606 0.0105308
\(211\) 3.69598 0.254442 0.127221 0.991874i \(-0.459394\pi\)
0.127221 + 0.991874i \(0.459394\pi\)
\(212\) 5.96608 0.409752
\(213\) 4.41098 0.302236
\(214\) 1.83977 0.125764
\(215\) 6.97206 0.475491
\(216\) 0.581745 0.0395827
\(217\) 4.44756 0.301920
\(218\) 2.42057 0.163942
\(219\) −10.4079 −0.703303
\(220\) 7.29373 0.491743
\(221\) 0 0
\(222\) 1.76616 0.118537
\(223\) 2.45236 0.164222 0.0821112 0.996623i \(-0.473834\pi\)
0.0821112 + 0.996623i \(0.473834\pi\)
\(224\) −1.72967 −0.115568
\(225\) −3.91070 −0.260714
\(226\) 0.621405 0.0413352
\(227\) 26.2329 1.74114 0.870568 0.492048i \(-0.163752\pi\)
0.870568 + 0.492048i \(0.163752\pi\)
\(228\) 7.02754 0.465410
\(229\) −17.0027 −1.12357 −0.561786 0.827282i \(-0.689886\pi\)
−0.561786 + 0.827282i \(0.689886\pi\)
\(230\) 0.0143135 0.000943807 0
\(231\) −3.53195 −0.232385
\(232\) 6.15901 0.404359
\(233\) 17.2121 1.12760 0.563802 0.825910i \(-0.309338\pi\)
0.563802 + 0.825910i \(0.309338\pi\)
\(234\) 0 0
\(235\) 9.97038 0.650396
\(236\) 1.47909 0.0962807
\(237\) 11.4527 0.743935
\(238\) −1.00175 −0.0649338
\(239\) 9.39453 0.607681 0.303841 0.952723i \(-0.401731\pi\)
0.303841 + 0.952723i \(0.401731\pi\)
\(240\) −4.04137 −0.260869
\(241\) 17.6662 1.13798 0.568991 0.822344i \(-0.307334\pi\)
0.568991 + 0.822344i \(0.307334\pi\)
\(242\) 0.215621 0.0138607
\(243\) −1.00000 −0.0641500
\(244\) −11.3245 −0.724978
\(245\) 1.04369 0.0666791
\(246\) 0.200591 0.0127892
\(247\) 0 0
\(248\) 2.58734 0.164296
\(249\) −0.520292 −0.0329721
\(250\) −1.35983 −0.0860033
\(251\) 21.3529 1.34778 0.673892 0.738830i \(-0.264621\pi\)
0.673892 + 0.738830i \(0.264621\pi\)
\(252\) 1.97862 0.124641
\(253\) −0.331275 −0.0208271
\(254\) 1.91738 0.120307
\(255\) −7.15043 −0.447777
\(256\) 14.3169 0.894807
\(257\) 6.07035 0.378658 0.189329 0.981914i \(-0.439369\pi\)
0.189329 + 0.981914i \(0.439369\pi\)
\(258\) −0.976761 −0.0608105
\(259\) 12.0790 0.750551
\(260\) 0 0
\(261\) −10.5871 −0.655327
\(262\) 2.38548 0.147375
\(263\) −11.3627 −0.700652 −0.350326 0.936628i \(-0.613929\pi\)
−0.350326 + 0.936628i \(0.613929\pi\)
\(264\) −2.05469 −0.126458
\(265\) −3.14702 −0.193320
\(266\) −0.519327 −0.0318420
\(267\) −4.78217 −0.292664
\(268\) −18.5604 −1.13376
\(269\) 12.4693 0.760266 0.380133 0.924932i \(-0.375878\pi\)
0.380133 + 0.924932i \(0.375878\pi\)
\(270\) −0.152606 −0.00928733
\(271\) −23.4805 −1.42634 −0.713170 0.700991i \(-0.752741\pi\)
−0.713170 + 0.700991i \(0.752741\pi\)
\(272\) 26.5286 1.60853
\(273\) 0 0
\(274\) −2.01782 −0.121901
\(275\) 13.8124 0.832919
\(276\) 0.185582 0.0111707
\(277\) −4.47714 −0.269005 −0.134503 0.990913i \(-0.542944\pi\)
−0.134503 + 0.990913i \(0.542944\pi\)
\(278\) 1.55298 0.0931416
\(279\) −4.44756 −0.266268
\(280\) 0.607163 0.0362849
\(281\) −3.45840 −0.206311 −0.103156 0.994665i \(-0.532894\pi\)
−0.103156 + 0.994665i \(0.532894\pi\)
\(282\) −1.39681 −0.0831791
\(283\) 28.4306 1.69002 0.845011 0.534748i \(-0.179594\pi\)
0.845011 + 0.534748i \(0.179594\pi\)
\(284\) 8.72766 0.517891
\(285\) −3.70692 −0.219579
\(286\) 0 0
\(287\) 1.37186 0.0809786
\(288\) 1.72967 0.101922
\(289\) 29.9373 1.76102
\(290\) −1.61567 −0.0948752
\(291\) 5.89081 0.345325
\(292\) −20.5933 −1.20513
\(293\) −27.7150 −1.61913 −0.809563 0.587033i \(-0.800296\pi\)
−0.809563 + 0.587033i \(0.800296\pi\)
\(294\) −0.146218 −0.00852759
\(295\) −0.780199 −0.0454250
\(296\) 7.02688 0.408429
\(297\) 3.53195 0.204944
\(298\) −2.54555 −0.147459
\(299\) 0 0
\(300\) −7.73780 −0.446742
\(301\) −6.68018 −0.385039
\(302\) 1.19050 0.0685056
\(303\) −6.24161 −0.358571
\(304\) 13.7530 0.788786
\(305\) 5.97352 0.342043
\(306\) 1.00175 0.0572662
\(307\) 18.9470 1.08136 0.540681 0.841227i \(-0.318166\pi\)
0.540681 + 0.841227i \(0.318166\pi\)
\(308\) −6.98839 −0.398200
\(309\) −16.3514 −0.930198
\(310\) −0.678726 −0.0385490
\(311\) 19.1810 1.08766 0.543828 0.839197i \(-0.316974\pi\)
0.543828 + 0.839197i \(0.316974\pi\)
\(312\) 0 0
\(313\) −8.34389 −0.471624 −0.235812 0.971799i \(-0.575775\pi\)
−0.235812 + 0.971799i \(0.575775\pi\)
\(314\) 0.977585 0.0551683
\(315\) −1.04369 −0.0588055
\(316\) 22.6606 1.27476
\(317\) −10.5961 −0.595136 −0.297568 0.954701i \(-0.596175\pi\)
−0.297568 + 0.954701i \(0.596175\pi\)
\(318\) 0.440886 0.0247237
\(319\) 37.3932 2.09362
\(320\) −7.81878 −0.437083
\(321\) −12.5824 −0.702282
\(322\) −0.0137143 −0.000764269 0
\(323\) 24.3332 1.35394
\(324\) −1.97862 −0.109923
\(325\) 0 0
\(326\) −0.202341 −0.0112066
\(327\) −16.5546 −0.915469
\(328\) 0.798075 0.0440663
\(329\) −9.55298 −0.526673
\(330\) 0.538998 0.0296709
\(331\) 14.6461 0.805023 0.402512 0.915415i \(-0.368137\pi\)
0.402512 + 0.915415i \(0.368137\pi\)
\(332\) −1.02946 −0.0564989
\(333\) −12.0790 −0.661923
\(334\) −1.42321 −0.0778747
\(335\) 9.79034 0.534904
\(336\) 3.87218 0.211245
\(337\) −16.4037 −0.893567 −0.446783 0.894642i \(-0.647431\pi\)
−0.446783 + 0.894642i \(0.647431\pi\)
\(338\) 0 0
\(339\) −4.24986 −0.230821
\(340\) −14.1480 −0.767282
\(341\) 15.7085 0.850665
\(342\) 0.519327 0.0280820
\(343\) −1.00000 −0.0539949
\(344\) −3.88616 −0.209528
\(345\) −0.0978920 −0.00527033
\(346\) 3.19736 0.171891
\(347\) 16.6360 0.893068 0.446534 0.894767i \(-0.352658\pi\)
0.446534 + 0.894767i \(0.352658\pi\)
\(348\) −20.9479 −1.12293
\(349\) −22.3603 −1.19692 −0.598459 0.801154i \(-0.704220\pi\)
−0.598459 + 0.801154i \(0.704220\pi\)
\(350\) 0.571814 0.0305648
\(351\) 0 0
\(352\) −6.10911 −0.325617
\(353\) 16.2683 0.865874 0.432937 0.901424i \(-0.357477\pi\)
0.432937 + 0.901424i \(0.357477\pi\)
\(354\) 0.109303 0.00580940
\(355\) −4.60371 −0.244340
\(356\) −9.46210 −0.501490
\(357\) 6.85108 0.362598
\(358\) 1.42744 0.0754424
\(359\) 30.0297 1.58491 0.792454 0.609931i \(-0.208803\pi\)
0.792454 + 0.609931i \(0.208803\pi\)
\(360\) −0.607163 −0.0320003
\(361\) −6.38517 −0.336062
\(362\) −0.896306 −0.0471088
\(363\) −1.47466 −0.0773995
\(364\) 0 0
\(365\) 10.8627 0.568579
\(366\) −0.836869 −0.0437438
\(367\) −20.6436 −1.07758 −0.538792 0.842439i \(-0.681119\pi\)
−0.538792 + 0.842439i \(0.681119\pi\)
\(368\) 0.363187 0.0189324
\(369\) −1.37186 −0.0714164
\(370\) −1.84333 −0.0958301
\(371\) 3.01527 0.156545
\(372\) −8.80003 −0.456260
\(373\) 1.02353 0.0529966 0.0264983 0.999649i \(-0.491564\pi\)
0.0264983 + 0.999649i \(0.491564\pi\)
\(374\) −3.53813 −0.182952
\(375\) 9.30004 0.480252
\(376\) −5.55740 −0.286601
\(377\) 0 0
\(378\) 0.146218 0.00752063
\(379\) 16.0762 0.825779 0.412890 0.910781i \(-0.364519\pi\)
0.412890 + 0.910781i \(0.364519\pi\)
\(380\) −7.33459 −0.376257
\(381\) −13.1132 −0.671809
\(382\) −1.02316 −0.0523496
\(383\) −3.72843 −0.190514 −0.0952571 0.995453i \(-0.530367\pi\)
−0.0952571 + 0.995453i \(0.530367\pi\)
\(384\) 4.55472 0.232432
\(385\) 3.68627 0.187870
\(386\) −0.0901770 −0.00458989
\(387\) 6.68018 0.339573
\(388\) 11.6557 0.591727
\(389\) −13.9725 −0.708435 −0.354218 0.935163i \(-0.615253\pi\)
−0.354218 + 0.935163i \(0.615253\pi\)
\(390\) 0 0
\(391\) 0.642589 0.0324971
\(392\) −0.581745 −0.0293825
\(393\) −16.3145 −0.822960
\(394\) 2.36372 0.119082
\(395\) −11.9531 −0.601428
\(396\) 6.98839 0.351180
\(397\) 15.6076 0.783321 0.391660 0.920110i \(-0.371901\pi\)
0.391660 + 0.920110i \(0.371901\pi\)
\(398\) −1.78511 −0.0894796
\(399\) 3.55174 0.177809
\(400\) −15.1429 −0.757147
\(401\) −20.6443 −1.03093 −0.515463 0.856912i \(-0.672380\pi\)
−0.515463 + 0.856912i \(0.672380\pi\)
\(402\) −1.37159 −0.0684088
\(403\) 0 0
\(404\) −12.3498 −0.614424
\(405\) 1.04369 0.0518615
\(406\) 1.54803 0.0768273
\(407\) 42.6623 2.11469
\(408\) 3.98558 0.197316
\(409\) 12.4181 0.614034 0.307017 0.951704i \(-0.400669\pi\)
0.307017 + 0.951704i \(0.400669\pi\)
\(410\) −0.209355 −0.0103393
\(411\) 13.8001 0.680709
\(412\) −32.3532 −1.59393
\(413\) 0.747537 0.0367839
\(414\) 0.0137143 0.000674022 0
\(415\) 0.543025 0.0266560
\(416\) 0 0
\(417\) −10.6210 −0.520114
\(418\) −1.83424 −0.0897154
\(419\) 14.0864 0.688165 0.344082 0.938939i \(-0.388190\pi\)
0.344082 + 0.938939i \(0.388190\pi\)
\(420\) −2.06507 −0.100765
\(421\) −8.37137 −0.407995 −0.203998 0.978971i \(-0.565394\pi\)
−0.203998 + 0.978971i \(0.565394\pi\)
\(422\) 0.540418 0.0263072
\(423\) 9.55298 0.464482
\(424\) 1.75412 0.0851875
\(425\) −26.7926 −1.29963
\(426\) 0.644964 0.0312486
\(427\) −5.72344 −0.276977
\(428\) −24.8958 −1.20338
\(429\) 0 0
\(430\) 1.01944 0.0491617
\(431\) 0.617158 0.0297274 0.0148637 0.999890i \(-0.495269\pi\)
0.0148637 + 0.999890i \(0.495269\pi\)
\(432\) −3.87218 −0.186300
\(433\) −5.24759 −0.252183 −0.126092 0.992019i \(-0.540243\pi\)
−0.126092 + 0.992019i \(0.540243\pi\)
\(434\) 0.650312 0.0312160
\(435\) 11.0497 0.529794
\(436\) −32.7552 −1.56869
\(437\) 0.333131 0.0159358
\(438\) −1.52182 −0.0727155
\(439\) −15.2408 −0.727405 −0.363702 0.931515i \(-0.618488\pi\)
−0.363702 + 0.931515i \(0.618488\pi\)
\(440\) 2.14447 0.102234
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 31.8306 1.51232 0.756159 0.654388i \(-0.227074\pi\)
0.756159 + 0.654388i \(0.227074\pi\)
\(444\) −23.8997 −1.13423
\(445\) 4.99112 0.236602
\(446\) 0.358579 0.0169792
\(447\) 17.4093 0.823431
\(448\) 7.49145 0.353938
\(449\) −11.8827 −0.560778 −0.280389 0.959886i \(-0.590463\pi\)
−0.280389 + 0.959886i \(0.590463\pi\)
\(450\) −0.571814 −0.0269556
\(451\) 4.84535 0.228159
\(452\) −8.40886 −0.395520
\(453\) −8.14197 −0.382543
\(454\) 3.83571 0.180019
\(455\) 0 0
\(456\) 2.06620 0.0967589
\(457\) −29.8436 −1.39602 −0.698012 0.716086i \(-0.745932\pi\)
−0.698012 + 0.716086i \(0.745932\pi\)
\(458\) −2.48610 −0.116168
\(459\) −6.85108 −0.319781
\(460\) −0.193691 −0.00903090
\(461\) 37.9731 1.76858 0.884291 0.466936i \(-0.154642\pi\)
0.884291 + 0.466936i \(0.154642\pi\)
\(462\) −0.516433 −0.0240267
\(463\) −40.1068 −1.86392 −0.931961 0.362559i \(-0.881903\pi\)
−0.931961 + 0.362559i \(0.881903\pi\)
\(464\) −40.9953 −1.90316
\(465\) 4.64189 0.215262
\(466\) 2.51672 0.116585
\(467\) 21.2918 0.985268 0.492634 0.870236i \(-0.336034\pi\)
0.492634 + 0.870236i \(0.336034\pi\)
\(468\) 0 0
\(469\) −9.38048 −0.433150
\(470\) 1.45785 0.0672454
\(471\) −6.68582 −0.308066
\(472\) 0.434876 0.0200168
\(473\) −23.5941 −1.08486
\(474\) 1.67459 0.0769166
\(475\) −13.8898 −0.637307
\(476\) 13.5557 0.621324
\(477\) −3.01527 −0.138060
\(478\) 1.37365 0.0628291
\(479\) −22.7366 −1.03886 −0.519430 0.854513i \(-0.673856\pi\)
−0.519430 + 0.854513i \(0.673856\pi\)
\(480\) −1.80525 −0.0823978
\(481\) 0 0
\(482\) 2.58311 0.117658
\(483\) 0.0937939 0.00426777
\(484\) −2.91779 −0.132627
\(485\) −6.14820 −0.279175
\(486\) −0.146218 −0.00663257
\(487\) −7.35639 −0.333350 −0.166675 0.986012i \(-0.553303\pi\)
−0.166675 + 0.986012i \(0.553303\pi\)
\(488\) −3.32958 −0.150723
\(489\) 1.38383 0.0625791
\(490\) 0.152606 0.00689406
\(491\) 40.6568 1.83482 0.917408 0.397948i \(-0.130278\pi\)
0.917408 + 0.397948i \(0.130278\pi\)
\(492\) −2.71440 −0.122374
\(493\) −72.5334 −3.26674
\(494\) 0 0
\(495\) −3.68627 −0.165686
\(496\) −17.2217 −0.773279
\(497\) 4.41098 0.197860
\(498\) −0.0760759 −0.00340904
\(499\) 0.0721207 0.00322856 0.00161428 0.999999i \(-0.499486\pi\)
0.00161428 + 0.999999i \(0.499486\pi\)
\(500\) 18.4013 0.822929
\(501\) 9.73351 0.434861
\(502\) 3.12217 0.139349
\(503\) 5.61475 0.250349 0.125175 0.992135i \(-0.460051\pi\)
0.125175 + 0.992135i \(0.460051\pi\)
\(504\) 0.581745 0.0259130
\(505\) 6.51432 0.289884
\(506\) −0.0484383 −0.00215334
\(507\) 0 0
\(508\) −25.9460 −1.15117
\(509\) −29.8050 −1.32108 −0.660541 0.750790i \(-0.729673\pi\)
−0.660541 + 0.750790i \(0.729673\pi\)
\(510\) −1.04552 −0.0462964
\(511\) −10.4079 −0.460420
\(512\) 11.2028 0.495100
\(513\) −3.55174 −0.156813
\(514\) 0.887592 0.0391500
\(515\) 17.0658 0.752010
\(516\) 13.2175 0.581870
\(517\) −33.7406 −1.48391
\(518\) 1.76616 0.0776006
\(519\) −21.8671 −0.959860
\(520\) 0 0
\(521\) 35.8915 1.57243 0.786217 0.617951i \(-0.212037\pi\)
0.786217 + 0.617951i \(0.212037\pi\)
\(522\) −1.54803 −0.0677553
\(523\) −21.9498 −0.959800 −0.479900 0.877323i \(-0.659327\pi\)
−0.479900 + 0.877323i \(0.659327\pi\)
\(524\) −32.2803 −1.41017
\(525\) −3.91070 −0.170677
\(526\) −1.66142 −0.0724415
\(527\) −30.4706 −1.32732
\(528\) 13.6763 0.595186
\(529\) −22.9912 −0.999618
\(530\) −0.460150 −0.0199876
\(531\) −0.747537 −0.0324403
\(532\) 7.02754 0.304682
\(533\) 0 0
\(534\) −0.699238 −0.0302590
\(535\) 13.1322 0.567754
\(536\) −5.45704 −0.235708
\(537\) −9.76241 −0.421279
\(538\) 1.82323 0.0786051
\(539\) −3.53195 −0.152132
\(540\) 2.06507 0.0888666
\(541\) 8.34399 0.358736 0.179368 0.983782i \(-0.442595\pi\)
0.179368 + 0.983782i \(0.442595\pi\)
\(542\) −3.43327 −0.147472
\(543\) 6.12994 0.263061
\(544\) 11.8501 0.508070
\(545\) 17.2779 0.740103
\(546\) 0 0
\(547\) −2.88177 −0.123216 −0.0616078 0.998100i \(-0.519623\pi\)
−0.0616078 + 0.998100i \(0.519623\pi\)
\(548\) 27.3052 1.16642
\(549\) 5.72344 0.244271
\(550\) 2.01962 0.0861168
\(551\) −37.6027 −1.60193
\(552\) 0.0545641 0.00232240
\(553\) 11.4527 0.487020
\(554\) −0.654637 −0.0278129
\(555\) 12.6067 0.535126
\(556\) −21.0150 −0.891233
\(557\) 27.3118 1.15724 0.578620 0.815597i \(-0.303592\pi\)
0.578620 + 0.815597i \(0.303592\pi\)
\(558\) −0.650312 −0.0275299
\(559\) 0 0
\(560\) −4.04137 −0.170779
\(561\) 24.1977 1.02163
\(562\) −0.505680 −0.0213308
\(563\) 7.36528 0.310410 0.155205 0.987882i \(-0.450396\pi\)
0.155205 + 0.987882i \(0.450396\pi\)
\(564\) 18.9017 0.795906
\(565\) 4.43555 0.186605
\(566\) 4.15705 0.174734
\(567\) −1.00000 −0.0419961
\(568\) 2.56607 0.107670
\(569\) −8.04377 −0.337212 −0.168606 0.985683i \(-0.553927\pi\)
−0.168606 + 0.985683i \(0.553927\pi\)
\(570\) −0.542018 −0.0227026
\(571\) −0.677399 −0.0283482 −0.0141741 0.999900i \(-0.504512\pi\)
−0.0141741 + 0.999900i \(0.504512\pi\)
\(572\) 0 0
\(573\) 6.99754 0.292326
\(574\) 0.200591 0.00837250
\(575\) −0.366800 −0.0152966
\(576\) −7.49145 −0.312144
\(577\) 19.9767 0.831642 0.415821 0.909446i \(-0.363494\pi\)
0.415821 + 0.909446i \(0.363494\pi\)
\(578\) 4.37737 0.182075
\(579\) 0.616731 0.0256305
\(580\) 21.8632 0.907821
\(581\) −0.520292 −0.0215853
\(582\) 0.861340 0.0357037
\(583\) 10.6498 0.441069
\(584\) −6.05476 −0.250548
\(585\) 0 0
\(586\) −4.05242 −0.167404
\(587\) 3.89654 0.160828 0.0804138 0.996762i \(-0.474376\pi\)
0.0804138 + 0.996762i \(0.474376\pi\)
\(588\) 1.97862 0.0815969
\(589\) −15.7965 −0.650885
\(590\) −0.114079 −0.00469656
\(591\) −16.1657 −0.664970
\(592\) −46.7719 −1.92231
\(593\) 19.7898 0.812668 0.406334 0.913725i \(-0.366807\pi\)
0.406334 + 0.913725i \(0.366807\pi\)
\(594\) 0.516433 0.0211895
\(595\) −7.15043 −0.293139
\(596\) 34.4464 1.41098
\(597\) 12.2086 0.499664
\(598\) 0 0
\(599\) 18.1661 0.742247 0.371123 0.928584i \(-0.378973\pi\)
0.371123 + 0.928584i \(0.378973\pi\)
\(600\) −2.27503 −0.0928778
\(601\) 28.3757 1.15747 0.578735 0.815516i \(-0.303547\pi\)
0.578735 + 0.815516i \(0.303547\pi\)
\(602\) −0.976761 −0.0398098
\(603\) 9.38048 0.382003
\(604\) −16.1099 −0.655501
\(605\) 1.53909 0.0625730
\(606\) −0.912634 −0.0370732
\(607\) −3.81922 −0.155017 −0.0775087 0.996992i \(-0.524697\pi\)
−0.0775087 + 0.996992i \(0.524697\pi\)
\(608\) 6.14333 0.249145
\(609\) −10.5871 −0.429012
\(610\) 0.873434 0.0353643
\(611\) 0 0
\(612\) −13.5557 −0.547956
\(613\) 25.9181 1.04682 0.523411 0.852080i \(-0.324659\pi\)
0.523411 + 0.852080i \(0.324659\pi\)
\(614\) 2.77039 0.111804
\(615\) 1.43181 0.0577360
\(616\) −2.05469 −0.0827859
\(617\) 10.8734 0.437747 0.218873 0.975753i \(-0.429762\pi\)
0.218873 + 0.975753i \(0.429762\pi\)
\(618\) −2.39086 −0.0961746
\(619\) −46.0428 −1.85062 −0.925308 0.379216i \(-0.876194\pi\)
−0.925308 + 0.379216i \(0.876194\pi\)
\(620\) 9.18453 0.368860
\(621\) −0.0937939 −0.00376382
\(622\) 2.80461 0.112454
\(623\) −4.78217 −0.191594
\(624\) 0 0
\(625\) 9.84713 0.393885
\(626\) −1.22002 −0.0487620
\(627\) 12.5445 0.500981
\(628\) −13.2287 −0.527883
\(629\) −82.7540 −3.29962
\(630\) −0.152606 −0.00607999
\(631\) 0.673777 0.0268226 0.0134113 0.999910i \(-0.495731\pi\)
0.0134113 + 0.999910i \(0.495731\pi\)
\(632\) 6.66257 0.265023
\(633\) −3.69598 −0.146902
\(634\) −1.54934 −0.0615320
\(635\) 13.6861 0.543118
\(636\) −5.96608 −0.236570
\(637\) 0 0
\(638\) 5.46755 0.216462
\(639\) −4.41098 −0.174496
\(640\) −4.75374 −0.187908
\(641\) −25.8132 −1.01956 −0.509780 0.860305i \(-0.670273\pi\)
−0.509780 + 0.860305i \(0.670273\pi\)
\(642\) −1.83977 −0.0726100
\(643\) −45.2454 −1.78430 −0.892152 0.451736i \(-0.850805\pi\)
−0.892152 + 0.451736i \(0.850805\pi\)
\(644\) 0.185582 0.00731297
\(645\) −6.97206 −0.274525
\(646\) 3.55795 0.139986
\(647\) −35.7822 −1.40674 −0.703372 0.710821i \(-0.748323\pi\)
−0.703372 + 0.710821i \(0.748323\pi\)
\(648\) −0.581745 −0.0228531
\(649\) 2.64026 0.103639
\(650\) 0 0
\(651\) −4.44756 −0.174313
\(652\) 2.73808 0.107231
\(653\) 42.0570 1.64582 0.822908 0.568174i \(-0.192350\pi\)
0.822908 + 0.568174i \(0.192350\pi\)
\(654\) −2.42057 −0.0946518
\(655\) 17.0274 0.665315
\(656\) −5.31210 −0.207403
\(657\) 10.4079 0.406052
\(658\) −1.39681 −0.0544535
\(659\) −4.31664 −0.168152 −0.0840761 0.996459i \(-0.526794\pi\)
−0.0840761 + 0.996459i \(0.526794\pi\)
\(660\) −7.29373 −0.283908
\(661\) 38.3032 1.48982 0.744910 0.667165i \(-0.232492\pi\)
0.744910 + 0.667165i \(0.232492\pi\)
\(662\) 2.14152 0.0832326
\(663\) 0 0
\(664\) −0.302677 −0.0117461
\(665\) −3.70692 −0.143748
\(666\) −1.76616 −0.0684373
\(667\) −0.993008 −0.0384494
\(668\) 19.2589 0.745150
\(669\) −2.45236 −0.0948138
\(670\) 1.43152 0.0553045
\(671\) −20.2149 −0.780388
\(672\) 1.72967 0.0667235
\(673\) −6.22782 −0.240065 −0.120032 0.992770i \(-0.538300\pi\)
−0.120032 + 0.992770i \(0.538300\pi\)
\(674\) −2.39851 −0.0923872
\(675\) 3.91070 0.150523
\(676\) 0 0
\(677\) 42.5387 1.63489 0.817447 0.576004i \(-0.195389\pi\)
0.817447 + 0.576004i \(0.195389\pi\)
\(678\) −0.621405 −0.0238649
\(679\) 5.89081 0.226068
\(680\) −4.15973 −0.159518
\(681\) −26.2329 −1.00525
\(682\) 2.29687 0.0879516
\(683\) −42.7618 −1.63624 −0.818118 0.575051i \(-0.804982\pi\)
−0.818118 + 0.575051i \(0.804982\pi\)
\(684\) −7.02754 −0.268705
\(685\) −14.4031 −0.550313
\(686\) −0.146218 −0.00558262
\(687\) 17.0027 0.648695
\(688\) 25.8669 0.986165
\(689\) 0 0
\(690\) −0.0143135 −0.000544907 0
\(691\) −19.5828 −0.744967 −0.372483 0.928039i \(-0.621494\pi\)
−0.372483 + 0.928039i \(0.621494\pi\)
\(692\) −43.2667 −1.64475
\(693\) 3.53195 0.134168
\(694\) 2.43248 0.0923356
\(695\) 11.0851 0.420481
\(696\) −6.15901 −0.233457
\(697\) −9.39875 −0.356003
\(698\) −3.26947 −0.123751
\(699\) −17.2121 −0.651023
\(700\) −7.73780 −0.292461
\(701\) −49.5279 −1.87064 −0.935322 0.353799i \(-0.884890\pi\)
−0.935322 + 0.353799i \(0.884890\pi\)
\(702\) 0 0
\(703\) −42.9013 −1.61805
\(704\) 26.4594 0.997227
\(705\) −9.97038 −0.375506
\(706\) 2.37871 0.0895241
\(707\) −6.24161 −0.234740
\(708\) −1.47909 −0.0555877
\(709\) 12.7801 0.479968 0.239984 0.970777i \(-0.422858\pi\)
0.239984 + 0.970777i \(0.422858\pi\)
\(710\) −0.673144 −0.0252627
\(711\) −11.4527 −0.429511
\(712\) −2.78200 −0.104260
\(713\) −0.417153 −0.0156225
\(714\) 1.00175 0.0374895
\(715\) 0 0
\(716\) −19.3161 −0.721877
\(717\) −9.39453 −0.350845
\(718\) 4.39088 0.163866
\(719\) −21.8912 −0.816405 −0.408203 0.912891i \(-0.633844\pi\)
−0.408203 + 0.912891i \(0.633844\pi\)
\(720\) 4.04137 0.150613
\(721\) −16.3514 −0.608957
\(722\) −0.933625 −0.0347459
\(723\) −17.6662 −0.657014
\(724\) 12.1288 0.450764
\(725\) 41.4032 1.53767
\(726\) −0.215621 −0.00800246
\(727\) −2.99931 −0.111238 −0.0556191 0.998452i \(-0.517713\pi\)
−0.0556191 + 0.998452i \(0.517713\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.58832 0.0587863
\(731\) 45.7665 1.69273
\(732\) 11.3245 0.418566
\(733\) −24.7708 −0.914931 −0.457465 0.889227i \(-0.651243\pi\)
−0.457465 + 0.889227i \(0.651243\pi\)
\(734\) −3.01845 −0.111413
\(735\) −1.04369 −0.0384972
\(736\) 0.162232 0.00597997
\(737\) −33.1314 −1.22041
\(738\) −0.200591 −0.00738385
\(739\) 3.77938 0.139027 0.0695133 0.997581i \(-0.477855\pi\)
0.0695133 + 0.997581i \(0.477855\pi\)
\(740\) 24.9440 0.916958
\(741\) 0 0
\(742\) 0.440886 0.0161854
\(743\) 28.1339 1.03213 0.516066 0.856549i \(-0.327396\pi\)
0.516066 + 0.856549i \(0.327396\pi\)
\(744\) −2.58734 −0.0948566
\(745\) −18.1700 −0.665695
\(746\) 0.149659 0.00547940
\(747\) 0.520292 0.0190365
\(748\) 47.8780 1.75059
\(749\) −12.5824 −0.459751
\(750\) 1.35983 0.0496540
\(751\) −16.3083 −0.595097 −0.297548 0.954707i \(-0.596169\pi\)
−0.297548 + 0.954707i \(0.596169\pi\)
\(752\) 36.9909 1.34892
\(753\) −21.3529 −0.778144
\(754\) 0 0
\(755\) 8.49772 0.309264
\(756\) −1.97862 −0.0719617
\(757\) −33.3205 −1.21105 −0.605526 0.795825i \(-0.707037\pi\)
−0.605526 + 0.795825i \(0.707037\pi\)
\(758\) 2.35063 0.0853786
\(759\) 0.331275 0.0120245
\(760\) −2.15648 −0.0782239
\(761\) 21.2851 0.771586 0.385793 0.922585i \(-0.373928\pi\)
0.385793 + 0.922585i \(0.373928\pi\)
\(762\) −1.91738 −0.0694593
\(763\) −16.5546 −0.599315
\(764\) 13.8455 0.500911
\(765\) 7.15043 0.258524
\(766\) −0.545163 −0.0196975
\(767\) 0 0
\(768\) −14.3169 −0.516617
\(769\) −35.2935 −1.27272 −0.636358 0.771394i \(-0.719560\pi\)
−0.636358 + 0.771394i \(0.719560\pi\)
\(770\) 0.538998 0.0194241
\(771\) −6.07035 −0.218618
\(772\) 1.22028 0.0439187
\(773\) 19.4548 0.699741 0.349871 0.936798i \(-0.386226\pi\)
0.349871 + 0.936798i \(0.386226\pi\)
\(774\) 0.976761 0.0351089
\(775\) 17.3931 0.624778
\(776\) 3.42695 0.123020
\(777\) −12.0790 −0.433331
\(778\) −2.04303 −0.0732462
\(779\) −4.87250 −0.174575
\(780\) 0 0
\(781\) 15.5794 0.557473
\(782\) 0.0939580 0.00335993
\(783\) 10.5871 0.378353
\(784\) 3.87218 0.138292
\(785\) 6.97795 0.249054
\(786\) −2.38548 −0.0850871
\(787\) −49.1398 −1.75164 −0.875822 0.482635i \(-0.839680\pi\)
−0.875822 + 0.482635i \(0.839680\pi\)
\(788\) −31.9859 −1.13945
\(789\) 11.3627 0.404522
\(790\) −1.74776 −0.0621826
\(791\) −4.24986 −0.151108
\(792\) 2.05469 0.0730103
\(793\) 0 0
\(794\) 2.28210 0.0809887
\(795\) 3.14702 0.111613
\(796\) 24.1562 0.856193
\(797\) −2.13400 −0.0755902 −0.0377951 0.999286i \(-0.512033\pi\)
−0.0377951 + 0.999286i \(0.512033\pi\)
\(798\) 0.519327 0.0183840
\(799\) 65.4483 2.31539
\(800\) −6.76423 −0.239152
\(801\) 4.78217 0.168970
\(802\) −3.01856 −0.106589
\(803\) −36.7603 −1.29724
\(804\) 18.5604 0.654575
\(805\) −0.0978920 −0.00345024
\(806\) 0 0
\(807\) −12.4693 −0.438940
\(808\) −3.63102 −0.127739
\(809\) 25.4023 0.893096 0.446548 0.894760i \(-0.352653\pi\)
0.446548 + 0.894760i \(0.352653\pi\)
\(810\) 0.152606 0.00536204
\(811\) −15.6885 −0.550899 −0.275450 0.961316i \(-0.588827\pi\)
−0.275450 + 0.961316i \(0.588827\pi\)
\(812\) −20.9479 −0.735128
\(813\) 23.4805 0.823498
\(814\) 6.23798 0.218641
\(815\) −1.44430 −0.0505915
\(816\) −26.5286 −0.928688
\(817\) 23.7262 0.830076
\(818\) 1.81574 0.0634859
\(819\) 0 0
\(820\) 2.83300 0.0989326
\(821\) −29.7835 −1.03945 −0.519725 0.854334i \(-0.673966\pi\)
−0.519725 + 0.854334i \(0.673966\pi\)
\(822\) 2.01782 0.0703795
\(823\) −38.8845 −1.35543 −0.677714 0.735326i \(-0.737029\pi\)
−0.677714 + 0.735326i \(0.737029\pi\)
\(824\) −9.51233 −0.331378
\(825\) −13.8124 −0.480886
\(826\) 0.109303 0.00380314
\(827\) 18.0200 0.626615 0.313308 0.949652i \(-0.398563\pi\)
0.313308 + 0.949652i \(0.398563\pi\)
\(828\) −0.185582 −0.00644944
\(829\) 16.6753 0.579158 0.289579 0.957154i \(-0.406485\pi\)
0.289579 + 0.957154i \(0.406485\pi\)
\(830\) 0.0793999 0.00275601
\(831\) 4.47714 0.155310
\(832\) 0 0
\(833\) 6.85108 0.237376
\(834\) −1.55298 −0.0537753
\(835\) −10.1588 −0.351560
\(836\) 24.8209 0.858449
\(837\) 4.44756 0.153730
\(838\) 2.05968 0.0711504
\(839\) −47.1236 −1.62689 −0.813444 0.581643i \(-0.802410\pi\)
−0.813444 + 0.581643i \(0.802410\pi\)
\(840\) −0.607163 −0.0209491
\(841\) 83.0875 2.86509
\(842\) −1.22404 −0.0421833
\(843\) 3.45840 0.119114
\(844\) −7.31295 −0.251722
\(845\) 0 0
\(846\) 1.39681 0.0480235
\(847\) −1.47466 −0.0506699
\(848\) −11.6757 −0.400944
\(849\) −28.4306 −0.975735
\(850\) −3.91755 −0.134371
\(851\) −1.13293 −0.0388364
\(852\) −8.72766 −0.299005
\(853\) 4.30839 0.147517 0.0737583 0.997276i \(-0.476501\pi\)
0.0737583 + 0.997276i \(0.476501\pi\)
\(854\) −0.836869 −0.0286371
\(855\) 3.70692 0.126774
\(856\) −7.31975 −0.250184
\(857\) −6.11232 −0.208793 −0.104396 0.994536i \(-0.533291\pi\)
−0.104396 + 0.994536i \(0.533291\pi\)
\(858\) 0 0
\(859\) 34.4693 1.17608 0.588039 0.808832i \(-0.299900\pi\)
0.588039 + 0.808832i \(0.299900\pi\)
\(860\) −13.7951 −0.470408
\(861\) −1.37186 −0.0467530
\(862\) 0.0902394 0.00307357
\(863\) 6.39934 0.217836 0.108918 0.994051i \(-0.465261\pi\)
0.108918 + 0.994051i \(0.465261\pi\)
\(864\) −1.72967 −0.0588446
\(865\) 22.8226 0.775990
\(866\) −0.767291 −0.0260736
\(867\) −29.9373 −1.01673
\(868\) −8.80003 −0.298692
\(869\) 40.4505 1.37219
\(870\) 1.61567 0.0547762
\(871\) 0 0
\(872\) −9.63053 −0.326131
\(873\) −5.89081 −0.199374
\(874\) 0.0487097 0.00164763
\(875\) 9.30004 0.314399
\(876\) 20.5933 0.695784
\(877\) −14.7519 −0.498137 −0.249069 0.968486i \(-0.580124\pi\)
−0.249069 + 0.968486i \(0.580124\pi\)
\(878\) −2.22848 −0.0752075
\(879\) 27.7150 0.934803
\(880\) −14.2739 −0.481173
\(881\) −51.9538 −1.75037 −0.875184 0.483791i \(-0.839260\pi\)
−0.875184 + 0.483791i \(0.839260\pi\)
\(882\) 0.146218 0.00492341
\(883\) −22.7151 −0.764426 −0.382213 0.924074i \(-0.624838\pi\)
−0.382213 + 0.924074i \(0.624838\pi\)
\(884\) 0 0
\(885\) 0.780199 0.0262261
\(886\) 4.65420 0.156361
\(887\) 14.6854 0.493089 0.246544 0.969132i \(-0.420705\pi\)
0.246544 + 0.969132i \(0.420705\pi\)
\(888\) −7.02688 −0.235807
\(889\) −13.1132 −0.439802
\(890\) 0.729790 0.0244626
\(891\) −3.53195 −0.118325
\(892\) −4.85229 −0.162467
\(893\) 33.9297 1.13541
\(894\) 2.54555 0.0851358
\(895\) 10.1890 0.340580
\(896\) 4.55472 0.152163
\(897\) 0 0
\(898\) −1.73746 −0.0579797
\(899\) 47.0869 1.57044
\(900\) 7.73780 0.257927
\(901\) −20.6579 −0.688214
\(902\) 0.708476 0.0235897
\(903\) 6.68018 0.222303
\(904\) −2.47233 −0.0822286
\(905\) −6.39778 −0.212669
\(906\) −1.19050 −0.0395517
\(907\) −3.21863 −0.106873 −0.0534364 0.998571i \(-0.517017\pi\)
−0.0534364 + 0.998571i \(0.517017\pi\)
\(908\) −51.9049 −1.72252
\(909\) 6.24161 0.207021
\(910\) 0 0
\(911\) 30.7915 1.02017 0.510083 0.860125i \(-0.329615\pi\)
0.510083 + 0.860125i \(0.329615\pi\)
\(912\) −13.7530 −0.455406
\(913\) −1.83764 −0.0608171
\(914\) −4.36366 −0.144337
\(915\) −5.97352 −0.197478
\(916\) 33.6420 1.11156
\(917\) −16.3145 −0.538754
\(918\) −1.00175 −0.0330627
\(919\) 17.5053 0.577446 0.288723 0.957413i \(-0.406769\pi\)
0.288723 + 0.957413i \(0.406769\pi\)
\(920\) −0.0569482 −0.00187753
\(921\) −18.9470 −0.624325
\(922\) 5.55233 0.182856
\(923\) 0 0
\(924\) 6.98839 0.229901
\(925\) 47.2373 1.55315
\(926\) −5.86433 −0.192714
\(927\) 16.3514 0.537050
\(928\) −18.3123 −0.601129
\(929\) −33.3753 −1.09501 −0.547505 0.836803i \(-0.684422\pi\)
−0.547505 + 0.836803i \(0.684422\pi\)
\(930\) 0.678726 0.0222563
\(931\) 3.55174 0.116403
\(932\) −34.0563 −1.11555
\(933\) −19.1810 −0.627959
\(934\) 3.11324 0.101868
\(935\) −25.2550 −0.825925
\(936\) 0 0
\(937\) 28.0519 0.916416 0.458208 0.888845i \(-0.348491\pi\)
0.458208 + 0.888845i \(0.348491\pi\)
\(938\) −1.37159 −0.0447841
\(939\) 8.34389 0.272292
\(940\) −19.7276 −0.643443
\(941\) 54.9687 1.79193 0.895965 0.444125i \(-0.146485\pi\)
0.895965 + 0.444125i \(0.146485\pi\)
\(942\) −0.977585 −0.0318515
\(943\) −0.128672 −0.00419015
\(944\) −2.89460 −0.0942111
\(945\) 1.04369 0.0339513
\(946\) −3.44987 −0.112165
\(947\) 42.8342 1.39192 0.695962 0.718079i \(-0.254978\pi\)
0.695962 + 0.718079i \(0.254978\pi\)
\(948\) −22.6606 −0.735983
\(949\) 0 0
\(950\) −2.03093 −0.0658922
\(951\) 10.5961 0.343602
\(952\) 3.98558 0.129173
\(953\) −24.9354 −0.807736 −0.403868 0.914817i \(-0.632335\pi\)
−0.403868 + 0.914817i \(0.632335\pi\)
\(954\) −0.440886 −0.0142742
\(955\) −7.30328 −0.236329
\(956\) −18.5882 −0.601185
\(957\) −37.3932 −1.20875
\(958\) −3.32449 −0.107409
\(959\) 13.8001 0.445629
\(960\) 7.81878 0.252350
\(961\) −11.2192 −0.361911
\(962\) 0 0
\(963\) 12.5824 0.405462
\(964\) −34.9547 −1.12582
\(965\) −0.643678 −0.0207207
\(966\) 0.0137143 0.000441251 0
\(967\) 20.0431 0.644543 0.322272 0.946647i \(-0.395554\pi\)
0.322272 + 0.946647i \(0.395554\pi\)
\(968\) −0.857875 −0.0275732
\(969\) −24.3332 −0.781696
\(970\) −0.898975 −0.0288643
\(971\) −19.2927 −0.619134 −0.309567 0.950878i \(-0.600184\pi\)
−0.309567 + 0.950878i \(0.600184\pi\)
\(972\) 1.97862 0.0634643
\(973\) −10.6210 −0.340494
\(974\) −1.07563 −0.0344655
\(975\) 0 0
\(976\) 22.1622 0.709395
\(977\) −23.6469 −0.756533 −0.378266 0.925697i \(-0.623480\pi\)
−0.378266 + 0.925697i \(0.623480\pi\)
\(978\) 0.202341 0.00647015
\(979\) −16.8904 −0.539819
\(980\) −2.06507 −0.0659663
\(981\) 16.5546 0.528547
\(982\) 5.94474 0.189704
\(983\) −42.0050 −1.33975 −0.669876 0.742473i \(-0.733653\pi\)
−0.669876 + 0.742473i \(0.733653\pi\)
\(984\) −0.798075 −0.0254417
\(985\) 16.8721 0.537589
\(986\) −10.6057 −0.337753
\(987\) 9.55298 0.304075
\(988\) 0 0
\(989\) 0.626560 0.0199234
\(990\) −0.538998 −0.0171305
\(991\) 28.0000 0.889450 0.444725 0.895667i \(-0.353301\pi\)
0.444725 + 0.895667i \(0.353301\pi\)
\(992\) −7.69281 −0.244247
\(993\) −14.6461 −0.464780
\(994\) 0.644964 0.0204570
\(995\) −12.7420 −0.403949
\(996\) 1.02946 0.0326197
\(997\) −15.9033 −0.503664 −0.251832 0.967771i \(-0.581033\pi\)
−0.251832 + 0.967771i \(0.581033\pi\)
\(998\) 0.0105453 0.000333806 0
\(999\) 12.0790 0.382162
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 3549.2.a.bf.1.5 yes 9
13.12 even 2 3549.2.a.be.1.5 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.5 9 13.12 even 2
3549.2.a.bf.1.5 yes 9 1.1 even 1 trivial