Properties

Label 731.2.a.c.1.6
Level 731
Weight 2
Character 731.1
Self dual yes
Analytic conductor 5.837
Analytic rank 1
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.83706438776\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.2460365.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.178849\)
Character \(\chi\) = 731.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +O(q^{10})\) \(q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +0.571360 q^{10} -1.62328 q^{11} -3.27827 q^{12} -2.15615 q^{13} -4.01269 q^{14} -0.508127 q^{15} -4.23774 q^{16} -1.00000 q^{17} +0.124444 q^{18} -3.82998 q^{19} +0.543797 q^{20} +3.56860 q^{21} -3.19464 q^{22} +4.47568 q^{23} +0.437186 q^{24} -4.91571 q^{25} -4.24333 q^{26} +5.13996 q^{27} -3.81911 q^{28} -3.55839 q^{29} -1.00000 q^{30} +9.03159 q^{31} -7.84035 q^{32} +2.84109 q^{33} -1.96801 q^{34} -0.591956 q^{35} +0.118441 q^{36} +4.37329 q^{37} -7.53745 q^{38} +3.77371 q^{39} -0.0725200 q^{40} -10.4363 q^{41} +7.02304 q^{42} -1.00000 q^{43} -3.04053 q^{44} +0.0183581 q^{45} +8.80820 q^{46} -10.5387 q^{47} +7.41693 q^{48} -2.84267 q^{49} -9.67419 q^{50} +1.75021 q^{51} -4.03863 q^{52} -2.68238 q^{53} +10.1155 q^{54} -0.471277 q^{55} +0.509311 q^{56} +6.70327 q^{57} -7.00296 q^{58} +8.62164 q^{59} -0.951759 q^{60} -4.69008 q^{61} +17.7743 q^{62} -0.128930 q^{63} -6.95442 q^{64} -0.625980 q^{65} +5.59130 q^{66} -11.1335 q^{67} -1.87307 q^{68} -7.83338 q^{69} -1.16498 q^{70} +9.13386 q^{71} -0.0157951 q^{72} +16.6916 q^{73} +8.60670 q^{74} +8.60353 q^{75} -7.17384 q^{76} +3.30980 q^{77} +7.42671 q^{78} +12.6668 q^{79} -1.23032 q^{80} -9.18570 q^{81} -20.5389 q^{82} +11.1971 q^{83} +6.68425 q^{84} -0.290323 q^{85} -1.96801 q^{86} +6.22793 q^{87} +0.405481 q^{88} +7.63942 q^{89} +0.0361291 q^{90} +4.39629 q^{91} +8.38329 q^{92} -15.8072 q^{93} -20.7403 q^{94} -1.11193 q^{95} +13.7222 q^{96} -13.1442 q^{97} -5.59440 q^{98} -0.102646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} - 4q^{10} + 4q^{11} + 11q^{12} - 10q^{13} - 7q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} - 20q^{19} + q^{20} - 8q^{21} + 2q^{22} - 3q^{23} - 9q^{24} - 7q^{25} - 3q^{26} - 6q^{27} - 11q^{28} - 15q^{29} - 6q^{30} + 12q^{31} + q^{32} - 2q^{33} + q^{34} - 9q^{35} - 16q^{36} - 14q^{37} + 27q^{38} + 5q^{39} - 7q^{40} - 2q^{41} + 19q^{42} - 6q^{43} - 12q^{44} - 18q^{45} + 14q^{46} - 11q^{47} - 6q^{48} + 3q^{49} + 7q^{50} + 3q^{51} - 5q^{52} + 3q^{53} + 25q^{54} + 6q^{55} + 22q^{56} + 11q^{57} - 21q^{58} + 2q^{59} - q^{60} - 20q^{61} + 3q^{62} + 23q^{63} - 39q^{64} - 34q^{65} + 7q^{66} - 2q^{67} - 5q^{68} - 17q^{69} - q^{70} + q^{71} + 21q^{72} + 13q^{73} + 28q^{74} - 5q^{75} - 29q^{76} - 11q^{77} - 26q^{79} + 12q^{80} + 2q^{81} - 9q^{82} + 10q^{83} - 3q^{84} - 3q^{85} + q^{86} + 12q^{87} - 6q^{88} - 15q^{89} + 15q^{90} + 8q^{91} - 9q^{92} - 11q^{93} - 33q^{94} - 21q^{95} + 25q^{96} - 22q^{97} - 3q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96801 1.39160 0.695798 0.718238i \(-0.255051\pi\)
0.695798 + 0.718238i \(0.255051\pi\)
\(3\) −1.75021 −1.01048 −0.505242 0.862978i \(-0.668597\pi\)
−0.505242 + 0.862978i \(0.668597\pi\)
\(4\) 1.87307 0.936537
\(5\) 0.290323 0.129837 0.0649183 0.997891i \(-0.479321\pi\)
0.0649183 + 0.997891i \(0.479321\pi\)
\(6\) −3.44443 −1.40618
\(7\) −2.03895 −0.770652 −0.385326 0.922780i \(-0.625911\pi\)
−0.385326 + 0.922780i \(0.625911\pi\)
\(8\) −0.249790 −0.0883143
\(9\) 0.0632334 0.0210778
\(10\) 0.571360 0.180680
\(11\) −1.62328 −0.489439 −0.244719 0.969594i \(-0.578696\pi\)
−0.244719 + 0.969594i \(0.578696\pi\)
\(12\) −3.27827 −0.946356
\(13\) −2.15615 −0.598008 −0.299004 0.954252i \(-0.596654\pi\)
−0.299004 + 0.954252i \(0.596654\pi\)
\(14\) −4.01269 −1.07244
\(15\) −0.508127 −0.131198
\(16\) −4.23774 −1.05944
\(17\) −1.00000 −0.242536
\(18\) 0.124444 0.0293318
\(19\) −3.82998 −0.878657 −0.439329 0.898326i \(-0.644784\pi\)
−0.439329 + 0.898326i \(0.644784\pi\)
\(20\) 0.543797 0.121597
\(21\) 3.56860 0.778732
\(22\) −3.19464 −0.681100
\(23\) 4.47568 0.933244 0.466622 0.884457i \(-0.345471\pi\)
0.466622 + 0.884457i \(0.345471\pi\)
\(24\) 0.437186 0.0892401
\(25\) −4.91571 −0.983142
\(26\) −4.24333 −0.832185
\(27\) 5.13996 0.989185
\(28\) −3.81911 −0.721745
\(29\) −3.55839 −0.660776 −0.330388 0.943845i \(-0.607180\pi\)
−0.330388 + 0.943845i \(0.607180\pi\)
\(30\) −1.00000 −0.182574
\(31\) 9.03159 1.62212 0.811061 0.584962i \(-0.198891\pi\)
0.811061 + 0.584962i \(0.198891\pi\)
\(32\) −7.84035 −1.38599
\(33\) 2.84109 0.494570
\(34\) −1.96801 −0.337511
\(35\) −0.591956 −0.100059
\(36\) 0.118441 0.0197402
\(37\) 4.37329 0.718965 0.359483 0.933152i \(-0.382953\pi\)
0.359483 + 0.933152i \(0.382953\pi\)
\(38\) −7.53745 −1.22274
\(39\) 3.77371 0.604278
\(40\) −0.0725200 −0.0114664
\(41\) −10.4363 −1.62988 −0.814942 0.579543i \(-0.803231\pi\)
−0.814942 + 0.579543i \(0.803231\pi\)
\(42\) 7.02304 1.08368
\(43\) −1.00000 −0.152499
\(44\) −3.04053 −0.458378
\(45\) 0.0183581 0.00273667
\(46\) 8.80820 1.29870
\(47\) −10.5387 −1.53723 −0.768615 0.639712i \(-0.779054\pi\)
−0.768615 + 0.639712i \(0.779054\pi\)
\(48\) 7.41693 1.07054
\(49\) −2.84267 −0.406095
\(50\) −9.67419 −1.36814
\(51\) 1.75021 0.245078
\(52\) −4.03863 −0.560057
\(53\) −2.68238 −0.368453 −0.184226 0.982884i \(-0.558978\pi\)
−0.184226 + 0.982884i \(0.558978\pi\)
\(54\) 10.1155 1.37655
\(55\) −0.471277 −0.0635470
\(56\) 0.509311 0.0680596
\(57\) 6.70327 0.887869
\(58\) −7.00296 −0.919533
\(59\) 8.62164 1.12244 0.561221 0.827666i \(-0.310332\pi\)
0.561221 + 0.827666i \(0.310332\pi\)
\(60\) −0.951759 −0.122872
\(61\) −4.69008 −0.600504 −0.300252 0.953860i \(-0.597071\pi\)
−0.300252 + 0.953860i \(0.597071\pi\)
\(62\) 17.7743 2.25734
\(63\) −0.128930 −0.0162437
\(64\) −6.95442 −0.869303
\(65\) −0.625980 −0.0776433
\(66\) 5.59130 0.688241
\(67\) −11.1335 −1.36017 −0.680084 0.733134i \(-0.738057\pi\)
−0.680084 + 0.733134i \(0.738057\pi\)
\(68\) −1.87307 −0.227144
\(69\) −7.83338 −0.943028
\(70\) −1.16498 −0.139241
\(71\) 9.13386 1.08399 0.541995 0.840382i \(-0.317669\pi\)
0.541995 + 0.840382i \(0.317669\pi\)
\(72\) −0.0157951 −0.00186147
\(73\) 16.6916 1.95360 0.976800 0.214155i \(-0.0686999\pi\)
0.976800 + 0.214155i \(0.0686999\pi\)
\(74\) 8.60670 1.00051
\(75\) 8.60353 0.993450
\(76\) −7.17384 −0.822896
\(77\) 3.30980 0.377187
\(78\) 7.42671 0.840910
\(79\) 12.6668 1.42513 0.712564 0.701607i \(-0.247534\pi\)
0.712564 + 0.701607i \(0.247534\pi\)
\(80\) −1.23032 −0.137553
\(81\) −9.18570 −1.02063
\(82\) −20.5389 −2.26814
\(83\) 11.1971 1.22904 0.614520 0.788901i \(-0.289350\pi\)
0.614520 + 0.788901i \(0.289350\pi\)
\(84\) 6.68425 0.729311
\(85\) −0.290323 −0.0314900
\(86\) −1.96801 −0.212216
\(87\) 6.22793 0.667704
\(88\) 0.405481 0.0432244
\(89\) 7.63942 0.809777 0.404889 0.914366i \(-0.367310\pi\)
0.404889 + 0.914366i \(0.367310\pi\)
\(90\) 0.0361291 0.00380834
\(91\) 4.39629 0.460856
\(92\) 8.38329 0.874018
\(93\) −15.8072 −1.63913
\(94\) −20.7403 −2.13920
\(95\) −1.11193 −0.114082
\(96\) 13.7222 1.40052
\(97\) −13.1442 −1.33459 −0.667294 0.744794i \(-0.732548\pi\)
−0.667294 + 0.744794i \(0.732548\pi\)
\(98\) −5.59440 −0.565120
\(99\) −0.102646 −0.0103163
\(100\) −9.20750 −0.920750
\(101\) 13.2118 1.31462 0.657309 0.753621i \(-0.271695\pi\)
0.657309 + 0.753621i \(0.271695\pi\)
\(102\) 3.44443 0.341050
\(103\) 12.9351 1.27454 0.637268 0.770642i \(-0.280065\pi\)
0.637268 + 0.770642i \(0.280065\pi\)
\(104\) 0.538585 0.0528126
\(105\) 1.03605 0.101108
\(106\) −5.27895 −0.512737
\(107\) −9.52343 −0.920665 −0.460332 0.887747i \(-0.652270\pi\)
−0.460332 + 0.887747i \(0.652270\pi\)
\(108\) 9.62752 0.926409
\(109\) −13.9100 −1.33234 −0.666170 0.745800i \(-0.732068\pi\)
−0.666170 + 0.745800i \(0.732068\pi\)
\(110\) −0.927480 −0.0884317
\(111\) −7.65418 −0.726503
\(112\) 8.64056 0.816456
\(113\) −16.5162 −1.55371 −0.776856 0.629678i \(-0.783187\pi\)
−0.776856 + 0.629678i \(0.783187\pi\)
\(114\) 13.1921 1.23555
\(115\) 1.29939 0.121169
\(116\) −6.66513 −0.618842
\(117\) −0.136341 −0.0126047
\(118\) 16.9675 1.56199
\(119\) 2.03895 0.186911
\(120\) 0.126925 0.0115866
\(121\) −8.36495 −0.760450
\(122\) −9.23014 −0.835658
\(123\) 18.2658 1.64697
\(124\) 16.9168 1.51918
\(125\) −2.87876 −0.257484
\(126\) −0.253736 −0.0226046
\(127\) 12.9951 1.15313 0.576564 0.817052i \(-0.304393\pi\)
0.576564 + 0.817052i \(0.304393\pi\)
\(128\) 1.99430 0.176273
\(129\) 1.75021 0.154097
\(130\) −1.23194 −0.108048
\(131\) −22.2129 −1.94075 −0.970375 0.241602i \(-0.922327\pi\)
−0.970375 + 0.241602i \(0.922327\pi\)
\(132\) 5.32157 0.463183
\(133\) 7.80915 0.677139
\(134\) −21.9108 −1.89280
\(135\) 1.49225 0.128432
\(136\) 0.249790 0.0214194
\(137\) −8.64720 −0.738780 −0.369390 0.929274i \(-0.620433\pi\)
−0.369390 + 0.929274i \(0.620433\pi\)
\(138\) −15.4162 −1.31231
\(139\) 3.98915 0.338355 0.169178 0.985586i \(-0.445889\pi\)
0.169178 + 0.985586i \(0.445889\pi\)
\(140\) −1.10878 −0.0937088
\(141\) 18.4450 1.55335
\(142\) 17.9756 1.50847
\(143\) 3.50004 0.292688
\(144\) −0.267967 −0.0223306
\(145\) −1.03308 −0.0857929
\(146\) 32.8492 2.71862
\(147\) 4.97526 0.410353
\(148\) 8.19151 0.673338
\(149\) 6.38854 0.523370 0.261685 0.965153i \(-0.415722\pi\)
0.261685 + 0.965153i \(0.415722\pi\)
\(150\) 16.9319 1.38248
\(151\) −9.92516 −0.807698 −0.403849 0.914826i \(-0.632328\pi\)
−0.403849 + 0.914826i \(0.632328\pi\)
\(152\) 0.956692 0.0775980
\(153\) −0.0632334 −0.00511212
\(154\) 6.51373 0.524892
\(155\) 2.62208 0.210611
\(156\) 7.06845 0.565929
\(157\) −20.7619 −1.65698 −0.828491 0.560002i \(-0.810800\pi\)
−0.828491 + 0.560002i \(0.810800\pi\)
\(158\) 24.9285 1.98320
\(159\) 4.69472 0.372315
\(160\) −2.27624 −0.179952
\(161\) −9.12571 −0.719207
\(162\) −18.0776 −1.42031
\(163\) −10.0984 −0.790965 −0.395483 0.918473i \(-0.629423\pi\)
−0.395483 + 0.918473i \(0.629423\pi\)
\(164\) −19.5481 −1.52645
\(165\) 0.824834 0.0642133
\(166\) 22.0360 1.71033
\(167\) −7.23726 −0.560036 −0.280018 0.959995i \(-0.590340\pi\)
−0.280018 + 0.959995i \(0.590340\pi\)
\(168\) −0.891401 −0.0687731
\(169\) −8.35102 −0.642386
\(170\) −0.571360 −0.0438213
\(171\) −0.242183 −0.0185202
\(172\) −1.87307 −0.142821
\(173\) 12.3178 0.936501 0.468251 0.883596i \(-0.344884\pi\)
0.468251 + 0.883596i \(0.344884\pi\)
\(174\) 12.2566 0.929174
\(175\) 10.0229 0.757661
\(176\) 6.87906 0.518528
\(177\) −15.0897 −1.13421
\(178\) 15.0345 1.12688
\(179\) 0.130015 0.00971775 0.00485888 0.999988i \(-0.498453\pi\)
0.00485888 + 0.999988i \(0.498453\pi\)
\(180\) 0.0343862 0.00256299
\(181\) 11.3606 0.844426 0.422213 0.906497i \(-0.361253\pi\)
0.422213 + 0.906497i \(0.361253\pi\)
\(182\) 8.65195 0.641325
\(183\) 8.20863 0.606799
\(184\) −1.11798 −0.0824188
\(185\) 1.26967 0.0933479
\(186\) −31.1087 −2.28100
\(187\) 1.62328 0.118706
\(188\) −19.7398 −1.43967
\(189\) −10.4801 −0.762318
\(190\) −2.18830 −0.158756
\(191\) −13.7029 −0.991508 −0.495754 0.868463i \(-0.665108\pi\)
−0.495754 + 0.868463i \(0.665108\pi\)
\(192\) 12.1717 0.878417
\(193\) 25.2883 1.82029 0.910146 0.414288i \(-0.135970\pi\)
0.910146 + 0.414288i \(0.135970\pi\)
\(194\) −25.8679 −1.85721
\(195\) 1.09560 0.0784573
\(196\) −5.32453 −0.380323
\(197\) 0.863989 0.0615566 0.0307783 0.999526i \(-0.490201\pi\)
0.0307783 + 0.999526i \(0.490201\pi\)
\(198\) −0.202008 −0.0143561
\(199\) 0.708054 0.0501926 0.0250963 0.999685i \(-0.492011\pi\)
0.0250963 + 0.999685i \(0.492011\pi\)
\(200\) 1.22790 0.0868255
\(201\) 19.4859 1.37443
\(202\) 26.0009 1.82942
\(203\) 7.25539 0.509229
\(204\) 3.27827 0.229525
\(205\) −3.02991 −0.211618
\(206\) 25.4565 1.77364
\(207\) 0.283013 0.0196707
\(208\) 9.13720 0.633551
\(209\) 6.21714 0.430049
\(210\) 2.03895 0.140701
\(211\) −23.4681 −1.61561 −0.807805 0.589450i \(-0.799344\pi\)
−0.807805 + 0.589450i \(0.799344\pi\)
\(212\) −5.02429 −0.345070
\(213\) −15.9862 −1.09535
\(214\) −18.7422 −1.28119
\(215\) −0.290323 −0.0197999
\(216\) −1.28391 −0.0873592
\(217\) −18.4150 −1.25009
\(218\) −27.3751 −1.85408
\(219\) −29.2137 −1.97408
\(220\) −0.882738 −0.0595142
\(221\) 2.15615 0.145038
\(222\) −15.0635 −1.01100
\(223\) 6.07464 0.406788 0.203394 0.979097i \(-0.434803\pi\)
0.203394 + 0.979097i \(0.434803\pi\)
\(224\) 15.9861 1.06812
\(225\) −0.310837 −0.0207225
\(226\) −32.5041 −2.16214
\(227\) 2.33319 0.154859 0.0774297 0.996998i \(-0.475329\pi\)
0.0774297 + 0.996998i \(0.475329\pi\)
\(228\) 12.5557 0.831523
\(229\) −13.0781 −0.864222 −0.432111 0.901820i \(-0.642231\pi\)
−0.432111 + 0.901820i \(0.642231\pi\)
\(230\) 2.55723 0.168618
\(231\) −5.79285 −0.381141
\(232\) 0.888852 0.0583560
\(233\) 3.89356 0.255075 0.127538 0.991834i \(-0.459293\pi\)
0.127538 + 0.991834i \(0.459293\pi\)
\(234\) −0.268320 −0.0175406
\(235\) −3.05964 −0.199589
\(236\) 16.1490 1.05121
\(237\) −22.1696 −1.44007
\(238\) 4.01269 0.260104
\(239\) −26.4426 −1.71043 −0.855215 0.518273i \(-0.826575\pi\)
−0.855215 + 0.518273i \(0.826575\pi\)
\(240\) 2.15331 0.138996
\(241\) −12.0233 −0.774489 −0.387244 0.921977i \(-0.626573\pi\)
−0.387244 + 0.921977i \(0.626573\pi\)
\(242\) −16.4623 −1.05824
\(243\) 0.657032 0.0421486
\(244\) −8.78488 −0.562394
\(245\) −0.825293 −0.0527260
\(246\) 35.9473 2.29192
\(247\) 8.25800 0.525444
\(248\) −2.25601 −0.143256
\(249\) −19.5973 −1.24193
\(250\) −5.66544 −0.358314
\(251\) 9.23449 0.582876 0.291438 0.956590i \(-0.405866\pi\)
0.291438 + 0.956590i \(0.405866\pi\)
\(252\) −0.241496 −0.0152128
\(253\) −7.26530 −0.456766
\(254\) 25.5745 1.60469
\(255\) 0.508127 0.0318201
\(256\) 17.8337 1.11460
\(257\) 3.17529 0.198069 0.0990347 0.995084i \(-0.468425\pi\)
0.0990347 + 0.995084i \(0.468425\pi\)
\(258\) 3.44443 0.214441
\(259\) −8.91694 −0.554072
\(260\) −1.17251 −0.0727159
\(261\) −0.225009 −0.0139277
\(262\) −43.7153 −2.70074
\(263\) 6.52724 0.402487 0.201244 0.979541i \(-0.435502\pi\)
0.201244 + 0.979541i \(0.435502\pi\)
\(264\) −0.709677 −0.0436776
\(265\) −0.778756 −0.0478386
\(266\) 15.3685 0.942304
\(267\) −13.3706 −0.818267
\(268\) −20.8538 −1.27385
\(269\) −6.08823 −0.371206 −0.185603 0.982625i \(-0.559424\pi\)
−0.185603 + 0.982625i \(0.559424\pi\)
\(270\) 2.93677 0.178726
\(271\) −29.2935 −1.77945 −0.889726 0.456494i \(-0.849105\pi\)
−0.889726 + 0.456494i \(0.849105\pi\)
\(272\) 4.23774 0.256951
\(273\) −7.69443 −0.465688
\(274\) −17.0178 −1.02808
\(275\) 7.97960 0.481188
\(276\) −14.6725 −0.883181
\(277\) −22.1385 −1.33018 −0.665088 0.746765i \(-0.731606\pi\)
−0.665088 + 0.746765i \(0.731606\pi\)
\(278\) 7.85070 0.470854
\(279\) 0.571098 0.0341908
\(280\) 0.147865 0.00883662
\(281\) −6.17797 −0.368547 −0.184273 0.982875i \(-0.558993\pi\)
−0.184273 + 0.982875i \(0.558993\pi\)
\(282\) 36.2999 2.16163
\(283\) −8.74612 −0.519903 −0.259952 0.965622i \(-0.583707\pi\)
−0.259952 + 0.965622i \(0.583707\pi\)
\(284\) 17.1084 1.01520
\(285\) 1.94611 0.115278
\(286\) 6.88813 0.407304
\(287\) 21.2792 1.25607
\(288\) −0.495772 −0.0292136
\(289\) 1.00000 0.0588235
\(290\) −2.03312 −0.119389
\(291\) 23.0050 1.34858
\(292\) 31.2645 1.82962
\(293\) −5.00471 −0.292378 −0.146189 0.989257i \(-0.546701\pi\)
−0.146189 + 0.989257i \(0.546701\pi\)
\(294\) 9.79138 0.571045
\(295\) 2.50306 0.145734
\(296\) −1.09241 −0.0634949
\(297\) −8.34361 −0.484145
\(298\) 12.5727 0.728319
\(299\) −9.65024 −0.558088
\(300\) 16.1150 0.930403
\(301\) 2.03895 0.117523
\(302\) −19.5328 −1.12399
\(303\) −23.1233 −1.32840
\(304\) 16.2305 0.930881
\(305\) −1.36164 −0.0779673
\(306\) −0.124444 −0.00711400
\(307\) 30.6932 1.75175 0.875877 0.482534i \(-0.160284\pi\)
0.875877 + 0.482534i \(0.160284\pi\)
\(308\) 6.19951 0.353250
\(309\) −22.6392 −1.28790
\(310\) 5.16029 0.293085
\(311\) 10.8925 0.617657 0.308828 0.951118i \(-0.400063\pi\)
0.308828 + 0.951118i \(0.400063\pi\)
\(312\) −0.942637 −0.0533663
\(313\) 13.8368 0.782104 0.391052 0.920369i \(-0.372111\pi\)
0.391052 + 0.920369i \(0.372111\pi\)
\(314\) −40.8597 −2.30585
\(315\) −0.0374314 −0.00210902
\(316\) 23.7259 1.33469
\(317\) −10.4203 −0.585261 −0.292630 0.956226i \(-0.594531\pi\)
−0.292630 + 0.956226i \(0.594531\pi\)
\(318\) 9.23927 0.518112
\(319\) 5.77628 0.323410
\(320\) −2.01903 −0.112867
\(321\) 16.6680 0.930317
\(322\) −17.9595 −1.00084
\(323\) 3.82998 0.213106
\(324\) −17.2055 −0.955861
\(325\) 10.5990 0.587927
\(326\) −19.8737 −1.10070
\(327\) 24.3455 1.34631
\(328\) 2.60690 0.143942
\(329\) 21.4880 1.18467
\(330\) 1.62328 0.0893589
\(331\) −29.7774 −1.63671 −0.818356 0.574711i \(-0.805114\pi\)
−0.818356 + 0.574711i \(0.805114\pi\)
\(332\) 20.9730 1.15104
\(333\) 0.276538 0.0151542
\(334\) −14.2430 −0.779344
\(335\) −3.23230 −0.176599
\(336\) −15.1228 −0.825016
\(337\) 26.0579 1.41946 0.709732 0.704472i \(-0.248816\pi\)
0.709732 + 0.704472i \(0.248816\pi\)
\(338\) −16.4349 −0.893942
\(339\) 28.9068 1.57000
\(340\) −0.543797 −0.0294916
\(341\) −14.6608 −0.793929
\(342\) −0.476619 −0.0257726
\(343\) 20.0687 1.08361
\(344\) 0.249790 0.0134678
\(345\) −2.27421 −0.122440
\(346\) 24.2415 1.30323
\(347\) −0.450411 −0.0241793 −0.0120897 0.999927i \(-0.503848\pi\)
−0.0120897 + 0.999927i \(0.503848\pi\)
\(348\) 11.6654 0.625330
\(349\) −3.89246 −0.208359 −0.104179 0.994559i \(-0.533222\pi\)
−0.104179 + 0.994559i \(0.533222\pi\)
\(350\) 19.7252 1.05436
\(351\) −11.0825 −0.591541
\(352\) 12.7271 0.678357
\(353\) 9.88564 0.526159 0.263080 0.964774i \(-0.415262\pi\)
0.263080 + 0.964774i \(0.415262\pi\)
\(354\) −29.6967 −1.57836
\(355\) 2.65177 0.140741
\(356\) 14.3092 0.758387
\(357\) −3.56860 −0.188870
\(358\) 0.255871 0.0135232
\(359\) −6.99527 −0.369196 −0.184598 0.982814i \(-0.559098\pi\)
−0.184598 + 0.982814i \(0.559098\pi\)
\(360\) −0.00458569 −0.000241687 0
\(361\) −4.33126 −0.227961
\(362\) 22.3578 1.17510
\(363\) 14.6404 0.768422
\(364\) 8.23458 0.431609
\(365\) 4.84595 0.253649
\(366\) 16.1547 0.844419
\(367\) 6.14611 0.320824 0.160412 0.987050i \(-0.448718\pi\)
0.160412 + 0.987050i \(0.448718\pi\)
\(368\) −18.9668 −0.988712
\(369\) −0.659926 −0.0343544
\(370\) 2.49873 0.129903
\(371\) 5.46924 0.283949
\(372\) −29.6080 −1.53510
\(373\) −36.5968 −1.89491 −0.947456 0.319886i \(-0.896356\pi\)
−0.947456 + 0.319886i \(0.896356\pi\)
\(374\) 3.19464 0.165191
\(375\) 5.03844 0.260184
\(376\) 2.63247 0.135759
\(377\) 7.67242 0.395150
\(378\) −20.6250 −1.06084
\(379\) −3.10751 −0.159622 −0.0798110 0.996810i \(-0.525432\pi\)
−0.0798110 + 0.996810i \(0.525432\pi\)
\(380\) −2.08273 −0.106842
\(381\) −22.7441 −1.16522
\(382\) −26.9675 −1.37978
\(383\) 24.4575 1.24972 0.624860 0.780737i \(-0.285156\pi\)
0.624860 + 0.780737i \(0.285156\pi\)
\(384\) −3.49044 −0.178121
\(385\) 0.960913 0.0489727
\(386\) 49.7677 2.53311
\(387\) −0.0632334 −0.00321433
\(388\) −24.6200 −1.24989
\(389\) 9.09194 0.460980 0.230490 0.973075i \(-0.425967\pi\)
0.230490 + 0.973075i \(0.425967\pi\)
\(390\) 2.15615 0.109181
\(391\) −4.47568 −0.226345
\(392\) 0.710071 0.0358640
\(393\) 38.8772 1.96110
\(394\) 1.70034 0.0856619
\(395\) 3.67747 0.185034
\(396\) −0.192263 −0.00966159
\(397\) −2.48190 −0.124563 −0.0622814 0.998059i \(-0.519838\pi\)
−0.0622814 + 0.998059i \(0.519838\pi\)
\(398\) 1.39346 0.0698478
\(399\) −13.6676 −0.684238
\(400\) 20.8315 1.04158
\(401\) −13.1073 −0.654550 −0.327275 0.944929i \(-0.606130\pi\)
−0.327275 + 0.944929i \(0.606130\pi\)
\(402\) 38.3485 1.91265
\(403\) −19.4735 −0.970042
\(404\) 24.7466 1.23119
\(405\) −2.66682 −0.132516
\(406\) 14.2787 0.708640
\(407\) −7.09910 −0.351889
\(408\) −0.437186 −0.0216439
\(409\) −18.8328 −0.931220 −0.465610 0.884990i \(-0.654165\pi\)
−0.465610 + 0.884990i \(0.654165\pi\)
\(410\) −5.96291 −0.294487
\(411\) 15.1344 0.746525
\(412\) 24.2285 1.19365
\(413\) −17.5791 −0.865012
\(414\) 0.556972 0.0273737
\(415\) 3.25078 0.159574
\(416\) 16.9050 0.828834
\(417\) −6.98185 −0.341903
\(418\) 12.2354 0.598454
\(419\) 17.6002 0.859824 0.429912 0.902871i \(-0.358545\pi\)
0.429912 + 0.902871i \(0.358545\pi\)
\(420\) 1.94059 0.0946913
\(421\) 8.05613 0.392632 0.196316 0.980541i \(-0.437102\pi\)
0.196316 + 0.980541i \(0.437102\pi\)
\(422\) −46.1855 −2.24827
\(423\) −0.666399 −0.0324014
\(424\) 0.670032 0.0325396
\(425\) 4.91571 0.238447
\(426\) −31.4610 −1.52429
\(427\) 9.56286 0.462779
\(428\) −17.8381 −0.862237
\(429\) −6.12581 −0.295757
\(430\) −0.571360 −0.0275534
\(431\) 22.7136 1.09407 0.547037 0.837109i \(-0.315756\pi\)
0.547037 + 0.837109i \(0.315756\pi\)
\(432\) −21.7818 −1.04798
\(433\) 23.4488 1.12688 0.563439 0.826158i \(-0.309478\pi\)
0.563439 + 0.826158i \(0.309478\pi\)
\(434\) −36.2410 −1.73962
\(435\) 1.80811 0.0866924
\(436\) −26.0545 −1.24779
\(437\) −17.1418 −0.820002
\(438\) −57.4930 −2.74712
\(439\) −27.1168 −1.29421 −0.647106 0.762400i \(-0.724021\pi\)
−0.647106 + 0.762400i \(0.724021\pi\)
\(440\) 0.117721 0.00561211
\(441\) −0.179752 −0.00855960
\(442\) 4.24333 0.201835
\(443\) 15.9713 0.758820 0.379410 0.925229i \(-0.376127\pi\)
0.379410 + 0.925229i \(0.376127\pi\)
\(444\) −14.3369 −0.680397
\(445\) 2.21790 0.105139
\(446\) 11.9550 0.566085
\(447\) −11.1813 −0.528857
\(448\) 14.1797 0.669930
\(449\) 2.09305 0.0987773 0.0493887 0.998780i \(-0.484273\pi\)
0.0493887 + 0.998780i \(0.484273\pi\)
\(450\) −0.611732 −0.0288373
\(451\) 16.9412 0.797728
\(452\) −30.9361 −1.45511
\(453\) 17.3711 0.816166
\(454\) 4.59175 0.215502
\(455\) 1.27635 0.0598360
\(456\) −1.67441 −0.0784115
\(457\) −31.6882 −1.48231 −0.741155 0.671334i \(-0.765722\pi\)
−0.741155 + 0.671334i \(0.765722\pi\)
\(458\) −25.7378 −1.20265
\(459\) −5.13996 −0.239913
\(460\) 2.43386 0.113479
\(461\) 37.8519 1.76294 0.881470 0.472240i \(-0.156554\pi\)
0.881470 + 0.472240i \(0.156554\pi\)
\(462\) −11.4004 −0.530395
\(463\) −6.58466 −0.306015 −0.153007 0.988225i \(-0.548896\pi\)
−0.153007 + 0.988225i \(0.548896\pi\)
\(464\) 15.0795 0.700050
\(465\) −4.58919 −0.212819
\(466\) 7.66257 0.354962
\(467\) 1.76387 0.0816223 0.0408112 0.999167i \(-0.487006\pi\)
0.0408112 + 0.999167i \(0.487006\pi\)
\(468\) −0.255376 −0.0118048
\(469\) 22.7006 1.04822
\(470\) −6.02140 −0.277747
\(471\) 36.3377 1.67435
\(472\) −2.15360 −0.0991277
\(473\) 1.62328 0.0746387
\(474\) −43.6300 −2.00399
\(475\) 18.8271 0.863845
\(476\) 3.81911 0.175049
\(477\) −0.169616 −0.00776617
\(478\) −52.0394 −2.38023
\(479\) −19.7593 −0.902824 −0.451412 0.892316i \(-0.649080\pi\)
−0.451412 + 0.892316i \(0.649080\pi\)
\(480\) 3.98389 0.181839
\(481\) −9.42947 −0.429947
\(482\) −23.6620 −1.07777
\(483\) 15.9719 0.726747
\(484\) −15.6682 −0.712190
\(485\) −3.81606 −0.173278
\(486\) 1.29305 0.0586538
\(487\) 3.87891 0.175770 0.0878851 0.996131i \(-0.471989\pi\)
0.0878851 + 0.996131i \(0.471989\pi\)
\(488\) 1.17154 0.0530330
\(489\) 17.6743 0.799258
\(490\) −1.62419 −0.0733733
\(491\) −33.7516 −1.52319 −0.761595 0.648053i \(-0.775583\pi\)
−0.761595 + 0.648053i \(0.775583\pi\)
\(492\) 34.2132 1.54245
\(493\) 3.55839 0.160262
\(494\) 16.2519 0.731206
\(495\) −0.0298005 −0.00133943
\(496\) −38.2735 −1.71853
\(497\) −18.6235 −0.835379
\(498\) −38.5677 −1.72826
\(499\) −24.2088 −1.08373 −0.541867 0.840464i \(-0.682282\pi\)
−0.541867 + 0.840464i \(0.682282\pi\)
\(500\) −5.39214 −0.241144
\(501\) 12.6667 0.565908
\(502\) 18.1736 0.811127
\(503\) 37.7657 1.68389 0.841944 0.539565i \(-0.181411\pi\)
0.841944 + 0.539565i \(0.181411\pi\)
\(504\) 0.0322055 0.00143455
\(505\) 3.83568 0.170686
\(506\) −14.2982 −0.635633
\(507\) 14.6160 0.649121
\(508\) 24.3408 1.07995
\(509\) −28.6665 −1.27062 −0.635311 0.772256i \(-0.719128\pi\)
−0.635311 + 0.772256i \(0.719128\pi\)
\(510\) 1.00000 0.0442807
\(511\) −34.0333 −1.50555
\(512\) 31.1083 1.37480
\(513\) −19.6859 −0.869155
\(514\) 6.24902 0.275632
\(515\) 3.75537 0.165481
\(516\) 3.27827 0.144318
\(517\) 17.1073 0.752379
\(518\) −17.5487 −0.771044
\(519\) −21.5586 −0.946320
\(520\) 0.156364 0.00685701
\(521\) 13.7677 0.603175 0.301588 0.953438i \(-0.402483\pi\)
0.301588 + 0.953438i \(0.402483\pi\)
\(522\) −0.442821 −0.0193817
\(523\) −28.5582 −1.24876 −0.624381 0.781120i \(-0.714649\pi\)
−0.624381 + 0.781120i \(0.714649\pi\)
\(524\) −41.6064 −1.81759
\(525\) −17.5422 −0.765604
\(526\) 12.8457 0.560099
\(527\) −9.03159 −0.393422
\(528\) −12.0398 −0.523965
\(529\) −2.96828 −0.129056
\(530\) −1.53260 −0.0665720
\(531\) 0.545176 0.0236586
\(532\) 14.6271 0.634166
\(533\) 22.5023 0.974683
\(534\) −26.3135 −1.13870
\(535\) −2.76487 −0.119536
\(536\) 2.78103 0.120122
\(537\) −0.227553 −0.00981963
\(538\) −11.9817 −0.516569
\(539\) 4.61446 0.198759
\(540\) 2.79510 0.120282
\(541\) 26.6222 1.14458 0.572290 0.820052i \(-0.306055\pi\)
0.572290 + 0.820052i \(0.306055\pi\)
\(542\) −57.6500 −2.47628
\(543\) −19.8834 −0.853279
\(544\) 7.84035 0.336152
\(545\) −4.03841 −0.172986
\(546\) −15.1427 −0.648049
\(547\) 41.2606 1.76417 0.882087 0.471086i \(-0.156138\pi\)
0.882087 + 0.471086i \(0.156138\pi\)
\(548\) −16.1969 −0.691895
\(549\) −0.296570 −0.0126573
\(550\) 15.7040 0.669619
\(551\) 13.6286 0.580596
\(552\) 1.95670 0.0832828
\(553\) −25.8271 −1.09828
\(554\) −43.5689 −1.85107
\(555\) −2.22219 −0.0943266
\(556\) 7.47197 0.316882
\(557\) 26.7375 1.13290 0.566451 0.824095i \(-0.308316\pi\)
0.566451 + 0.824095i \(0.308316\pi\)
\(558\) 1.12393 0.0475797
\(559\) 2.15615 0.0911954
\(560\) 2.50856 0.106006
\(561\) −2.84109 −0.119951
\(562\) −12.1583 −0.512868
\(563\) 9.49245 0.400059 0.200029 0.979790i \(-0.435896\pi\)
0.200029 + 0.979790i \(0.435896\pi\)
\(564\) 34.5488 1.45477
\(565\) −4.79504 −0.201729
\(566\) −17.2125 −0.723495
\(567\) 18.7292 0.786553
\(568\) −2.28155 −0.0957318
\(569\) 30.1917 1.26570 0.632851 0.774274i \(-0.281885\pi\)
0.632851 + 0.774274i \(0.281885\pi\)
\(570\) 3.82998 0.160420
\(571\) −15.9145 −0.666003 −0.333001 0.942926i \(-0.608061\pi\)
−0.333001 + 0.942926i \(0.608061\pi\)
\(572\) 6.55584 0.274114
\(573\) 23.9830 1.00190
\(574\) 41.8778 1.74795
\(575\) −22.0012 −0.917512
\(576\) −0.439752 −0.0183230
\(577\) −14.1386 −0.588599 −0.294299 0.955713i \(-0.595086\pi\)
−0.294299 + 0.955713i \(0.595086\pi\)
\(578\) 1.96801 0.0818585
\(579\) −44.2598 −1.83938
\(580\) −1.93504 −0.0803483
\(581\) −22.8304 −0.947163
\(582\) 45.2742 1.87668
\(583\) 4.35426 0.180335
\(584\) −4.16939 −0.172531
\(585\) −0.0395829 −0.00163655
\(586\) −9.84934 −0.406872
\(587\) 39.1949 1.61775 0.808873 0.587983i \(-0.200078\pi\)
0.808873 + 0.587983i \(0.200078\pi\)
\(588\) 9.31904 0.384311
\(589\) −34.5908 −1.42529
\(590\) 4.92606 0.202803
\(591\) −1.51216 −0.0622020
\(592\) −18.5329 −0.761697
\(593\) −2.62039 −0.107607 −0.0538033 0.998552i \(-0.517134\pi\)
−0.0538033 + 0.998552i \(0.517134\pi\)
\(594\) −16.4203 −0.673735
\(595\) 0.591956 0.0242678
\(596\) 11.9662 0.490155
\(597\) −1.23924 −0.0507188
\(598\) −18.9918 −0.776632
\(599\) 25.3129 1.03426 0.517128 0.855908i \(-0.327001\pi\)
0.517128 + 0.855908i \(0.327001\pi\)
\(600\) −2.14908 −0.0877358
\(601\) 10.5933 0.432109 0.216055 0.976381i \(-0.430681\pi\)
0.216055 + 0.976381i \(0.430681\pi\)
\(602\) 4.01269 0.163545
\(603\) −0.704006 −0.0286693
\(604\) −18.5906 −0.756439
\(605\) −2.42854 −0.0987342
\(606\) −45.5070 −1.84860
\(607\) 11.3511 0.460729 0.230364 0.973104i \(-0.426008\pi\)
0.230364 + 0.973104i \(0.426008\pi\)
\(608\) 30.0284 1.21781
\(609\) −12.6985 −0.514568
\(610\) −2.67973 −0.108499
\(611\) 22.7230 0.919276
\(612\) −0.118441 −0.00478769
\(613\) −37.0120 −1.49490 −0.747449 0.664319i \(-0.768722\pi\)
−0.747449 + 0.664319i \(0.768722\pi\)
\(614\) 60.4046 2.43773
\(615\) 5.30299 0.213837
\(616\) −0.826757 −0.0333110
\(617\) 35.6001 1.43321 0.716603 0.697482i \(-0.245696\pi\)
0.716603 + 0.697482i \(0.245696\pi\)
\(618\) −44.5542 −1.79223
\(619\) −36.8760 −1.48217 −0.741086 0.671410i \(-0.765689\pi\)
−0.741086 + 0.671410i \(0.765689\pi\)
\(620\) 4.91136 0.197245
\(621\) 23.0048 0.923151
\(622\) 21.4366 0.859528
\(623\) −15.5764 −0.624057
\(624\) −15.9920 −0.640193
\(625\) 23.7428 0.949712
\(626\) 27.2311 1.08837
\(627\) −10.8813 −0.434557
\(628\) −38.8886 −1.55183
\(629\) −4.37329 −0.174375
\(630\) −0.0736655 −0.00293490
\(631\) 37.7041 1.50098 0.750489 0.660883i \(-0.229818\pi\)
0.750489 + 0.660883i \(0.229818\pi\)
\(632\) −3.16405 −0.125859
\(633\) 41.0741 1.63255
\(634\) −20.5072 −0.814446
\(635\) 3.77278 0.149718
\(636\) 8.79356 0.348687
\(637\) 6.12921 0.242848
\(638\) 11.3678 0.450055
\(639\) 0.577565 0.0228481
\(640\) 0.578992 0.0228867
\(641\) −22.5274 −0.889777 −0.444888 0.895586i \(-0.646757\pi\)
−0.444888 + 0.895586i \(0.646757\pi\)
\(642\) 32.8028 1.29462
\(643\) 34.1041 1.34493 0.672467 0.740127i \(-0.265235\pi\)
0.672467 + 0.740127i \(0.265235\pi\)
\(644\) −17.0931 −0.673564
\(645\) 0.508127 0.0200075
\(646\) 7.53745 0.296557
\(647\) −7.44519 −0.292700 −0.146350 0.989233i \(-0.546753\pi\)
−0.146350 + 0.989233i \(0.546753\pi\)
\(648\) 2.29450 0.0901365
\(649\) −13.9954 −0.549367
\(650\) 20.8590 0.818157
\(651\) 32.2301 1.26320
\(652\) −18.9150 −0.740769
\(653\) 8.06440 0.315584 0.157792 0.987472i \(-0.449562\pi\)
0.157792 + 0.987472i \(0.449562\pi\)
\(654\) 47.9122 1.87352
\(655\) −6.44893 −0.251980
\(656\) 44.2265 1.72676
\(657\) 1.05546 0.0411776
\(658\) 42.2886 1.64858
\(659\) −11.4301 −0.445254 −0.222627 0.974904i \(-0.571463\pi\)
−0.222627 + 0.974904i \(0.571463\pi\)
\(660\) 1.54498 0.0601381
\(661\) 23.6134 0.918457 0.459228 0.888318i \(-0.348126\pi\)
0.459228 + 0.888318i \(0.348126\pi\)
\(662\) −58.6023 −2.27764
\(663\) −3.77371 −0.146559
\(664\) −2.79693 −0.108542
\(665\) 2.26718 0.0879174
\(666\) 0.544231 0.0210885
\(667\) −15.9262 −0.616666
\(668\) −13.5559 −0.524495
\(669\) −10.6319 −0.411053
\(670\) −6.36121 −0.245755
\(671\) 7.61334 0.293910
\(672\) −27.9790 −1.07931
\(673\) 3.41852 0.131774 0.0658872 0.997827i \(-0.479012\pi\)
0.0658872 + 0.997827i \(0.479012\pi\)
\(674\) 51.2823 1.97532
\(675\) −25.2665 −0.972510
\(676\) −15.6421 −0.601619
\(677\) 41.1771 1.58257 0.791283 0.611450i \(-0.209414\pi\)
0.791283 + 0.611450i \(0.209414\pi\)
\(678\) 56.8890 2.18481
\(679\) 26.8004 1.02850
\(680\) 0.0725200 0.00278102
\(681\) −4.08358 −0.156483
\(682\) −28.8527 −1.10483
\(683\) −3.65574 −0.139883 −0.0699415 0.997551i \(-0.522281\pi\)
−0.0699415 + 0.997551i \(0.522281\pi\)
\(684\) −0.453626 −0.0173448
\(685\) −2.51048 −0.0959207
\(686\) 39.4955 1.50795
\(687\) 22.8893 0.873283
\(688\) 4.23774 0.161562
\(689\) 5.78360 0.220338
\(690\) −4.47568 −0.170386
\(691\) −29.8410 −1.13520 −0.567602 0.823303i \(-0.692129\pi\)
−0.567602 + 0.823303i \(0.692129\pi\)
\(692\) 23.0721 0.877069
\(693\) 0.209290 0.00795027
\(694\) −0.886415 −0.0336479
\(695\) 1.15814 0.0439309
\(696\) −1.55568 −0.0589678
\(697\) 10.4363 0.395305
\(698\) −7.66041 −0.289951
\(699\) −6.81454 −0.257750
\(700\) 18.7737 0.709578
\(701\) 15.0041 0.566697 0.283348 0.959017i \(-0.408555\pi\)
0.283348 + 0.959017i \(0.408555\pi\)
\(702\) −21.8105 −0.823185
\(703\) −16.7496 −0.631724
\(704\) 11.2890 0.425470
\(705\) 5.35500 0.201681
\(706\) 19.4551 0.732201
\(707\) −26.9382 −1.01311
\(708\) −28.2641 −1.06223
\(709\) −20.2740 −0.761407 −0.380703 0.924697i \(-0.624318\pi\)
−0.380703 + 0.924697i \(0.624318\pi\)
\(710\) 5.21872 0.195855
\(711\) 0.800966 0.0300386
\(712\) −1.90826 −0.0715149
\(713\) 40.4225 1.51384
\(714\) −7.02304 −0.262831
\(715\) 1.01614 0.0380016
\(716\) 0.243527 0.00910104
\(717\) 46.2801 1.72836
\(718\) −13.7668 −0.513772
\(719\) 45.0527 1.68018 0.840091 0.542446i \(-0.182502\pi\)
0.840091 + 0.542446i \(0.182502\pi\)
\(720\) −0.0777970 −0.00289932
\(721\) −26.3741 −0.982224
\(722\) −8.52398 −0.317230
\(723\) 21.0433 0.782608
\(724\) 21.2792 0.790836
\(725\) 17.4920 0.649637
\(726\) 28.8125 1.06933
\(727\) −27.5550 −1.02196 −0.510979 0.859593i \(-0.670717\pi\)
−0.510979 + 0.859593i \(0.670717\pi\)
\(728\) −1.09815 −0.0407002
\(729\) 26.4072 0.978043
\(730\) 9.53689 0.352976
\(731\) 1.00000 0.0369863
\(732\) 15.3754 0.568290
\(733\) −19.7851 −0.730780 −0.365390 0.930854i \(-0.619064\pi\)
−0.365390 + 0.930854i \(0.619064\pi\)
\(734\) 12.0956 0.446457
\(735\) 1.44443 0.0532788
\(736\) −35.0909 −1.29347
\(737\) 18.0728 0.665719
\(738\) −1.29874 −0.0478074
\(739\) −3.05594 −0.112415 −0.0562073 0.998419i \(-0.517901\pi\)
−0.0562073 + 0.998419i \(0.517901\pi\)
\(740\) 2.37819 0.0874238
\(741\) −14.4532 −0.530953
\(742\) 10.7635 0.395142
\(743\) 20.2997 0.744723 0.372362 0.928088i \(-0.378548\pi\)
0.372362 + 0.928088i \(0.378548\pi\)
\(744\) 3.94848 0.144758
\(745\) 1.85474 0.0679525
\(746\) −72.0230 −2.63695
\(747\) 0.708030 0.0259055
\(748\) 3.04053 0.111173
\(749\) 19.4178 0.709512
\(750\) 9.91571 0.362071
\(751\) 47.6061 1.73717 0.868586 0.495538i \(-0.165029\pi\)
0.868586 + 0.495538i \(0.165029\pi\)
\(752\) 44.6603 1.62859
\(753\) −16.1623 −0.588986
\(754\) 15.0994 0.549888
\(755\) −2.88151 −0.104869
\(756\) −19.6301 −0.713939
\(757\) 34.0339 1.23698 0.618491 0.785792i \(-0.287744\pi\)
0.618491 + 0.785792i \(0.287744\pi\)
\(758\) −6.11561 −0.222129
\(759\) 12.7158 0.461554
\(760\) 0.277750 0.0100751
\(761\) 13.9303 0.504973 0.252486 0.967600i \(-0.418752\pi\)
0.252486 + 0.967600i \(0.418752\pi\)
\(762\) −44.7607 −1.62151
\(763\) 28.3619 1.02677
\(764\) −25.6666 −0.928584
\(765\) −0.0183581 −0.000663740 0
\(766\) 48.1327 1.73910
\(767\) −18.5895 −0.671229
\(768\) −31.2126 −1.12629
\(769\) −30.3307 −1.09375 −0.546877 0.837213i \(-0.684183\pi\)
−0.546877 + 0.837213i \(0.684183\pi\)
\(770\) 1.89109 0.0681501
\(771\) −5.55743 −0.200146
\(772\) 47.3669 1.70477
\(773\) −46.9073 −1.68714 −0.843570 0.537019i \(-0.819550\pi\)
−0.843570 + 0.537019i \(0.819550\pi\)
\(774\) −0.124444 −0.00447305
\(775\) −44.3967 −1.59478
\(776\) 3.28329 0.117863
\(777\) 15.6065 0.559881
\(778\) 17.8931 0.641497
\(779\) 39.9710 1.43211
\(780\) 2.05213 0.0734782
\(781\) −14.8269 −0.530546
\(782\) −8.80820 −0.314981
\(783\) −18.2900 −0.653630
\(784\) 12.0465 0.430232
\(785\) −6.02767 −0.215137
\(786\) 76.5109 2.72905
\(787\) 11.9255 0.425097 0.212548 0.977151i \(-0.431824\pi\)
0.212548 + 0.977151i \(0.431824\pi\)
\(788\) 1.61832 0.0576501
\(789\) −11.4240 −0.406707
\(790\) 7.23732 0.257492
\(791\) 33.6758 1.19737
\(792\) 0.0256399 0.000911076 0
\(793\) 10.1125 0.359106
\(794\) −4.88440 −0.173341
\(795\) 1.36299 0.0483402
\(796\) 1.32624 0.0470073
\(797\) −27.9547 −0.990207 −0.495103 0.868834i \(-0.664870\pi\)
−0.495103 + 0.868834i \(0.664870\pi\)
\(798\) −26.8981 −0.952183
\(799\) 10.5387 0.372833
\(800\) 38.5409 1.36263
\(801\) 0.483067 0.0170683
\(802\) −25.7954 −0.910868
\(803\) −27.0951 −0.956167
\(804\) 36.4985 1.28720
\(805\) −2.64941 −0.0933793
\(806\) −38.3240 −1.34991
\(807\) 10.6557 0.375098
\(808\) −3.30017 −0.116100
\(809\) −16.3735 −0.575662 −0.287831 0.957681i \(-0.592934\pi\)
−0.287831 + 0.957681i \(0.592934\pi\)
\(810\) −5.24834 −0.184408
\(811\) 28.0230 0.984021 0.492011 0.870589i \(-0.336262\pi\)
0.492011 + 0.870589i \(0.336262\pi\)
\(812\) 13.5899 0.476912
\(813\) 51.2697 1.79811
\(814\) −13.9711 −0.489687
\(815\) −2.93179 −0.102696
\(816\) −7.41693 −0.259645
\(817\) 3.82998 0.133994
\(818\) −37.0631 −1.29588
\(819\) 0.277992 0.00971384
\(820\) −5.67526 −0.198189
\(821\) −16.2972 −0.568778 −0.284389 0.958709i \(-0.591791\pi\)
−0.284389 + 0.958709i \(0.591791\pi\)
\(822\) 29.7847 1.03886
\(823\) 32.8529 1.14518 0.572590 0.819842i \(-0.305939\pi\)
0.572590 + 0.819842i \(0.305939\pi\)
\(824\) −3.23107 −0.112560
\(825\) −13.9660 −0.486233
\(826\) −34.5960 −1.20375
\(827\) 8.61783 0.299671 0.149836 0.988711i \(-0.452126\pi\)
0.149836 + 0.988711i \(0.452126\pi\)
\(828\) 0.530104 0.0184224
\(829\) −8.83234 −0.306760 −0.153380 0.988167i \(-0.549016\pi\)
−0.153380 + 0.988167i \(0.549016\pi\)
\(830\) 6.39757 0.222063
\(831\) 38.7471 1.34412
\(832\) 14.9948 0.519850
\(833\) 2.84267 0.0984926
\(834\) −13.7404 −0.475790
\(835\) −2.10115 −0.0727132
\(836\) 11.6452 0.402757
\(837\) 46.4220 1.60458
\(838\) 34.6374 1.19653
\(839\) 16.3682 0.565092 0.282546 0.959254i \(-0.408821\pi\)
0.282546 + 0.959254i \(0.408821\pi\)
\(840\) −0.258795 −0.00892926
\(841\) −16.3379 −0.563375
\(842\) 15.8546 0.546384
\(843\) 10.8127 0.372410
\(844\) −43.9575 −1.51308
\(845\) −2.42450 −0.0834052
\(846\) −1.31148 −0.0450897
\(847\) 17.0557 0.586042
\(848\) 11.3672 0.390352
\(849\) 15.3076 0.525354
\(850\) 9.67419 0.331822
\(851\) 19.5735 0.670970
\(852\) −29.9433 −1.02584
\(853\) −35.2003 −1.20523 −0.602617 0.798030i \(-0.705875\pi\)
−0.602617 + 0.798030i \(0.705875\pi\)
\(854\) 18.8198 0.644002
\(855\) −0.0703113 −0.00240459
\(856\) 2.37886 0.0813078
\(857\) 40.1336 1.37094 0.685469 0.728101i \(-0.259597\pi\)
0.685469 + 0.728101i \(0.259597\pi\)
\(858\) −12.0557 −0.411574
\(859\) −19.4321 −0.663016 −0.331508 0.943452i \(-0.607557\pi\)
−0.331508 + 0.943452i \(0.607557\pi\)
\(860\) −0.543797 −0.0185433
\(861\) −37.2431 −1.26924
\(862\) 44.7006 1.52251
\(863\) 7.90822 0.269199 0.134600 0.990900i \(-0.457025\pi\)
0.134600 + 0.990900i \(0.457025\pi\)
\(864\) −40.2990 −1.37100
\(865\) 3.57613 0.121592
\(866\) 46.1475 1.56816
\(867\) −1.75021 −0.0594402
\(868\) −34.4927 −1.17076
\(869\) −20.5619 −0.697513
\(870\) 3.55839 0.120641
\(871\) 24.0054 0.813391
\(872\) 3.47460 0.117665
\(873\) −0.831150 −0.0281302
\(874\) −33.7352 −1.14111
\(875\) 5.86967 0.198431
\(876\) −54.7195 −1.84880
\(877\) −27.2520 −0.920235 −0.460117 0.887858i \(-0.652193\pi\)
−0.460117 + 0.887858i \(0.652193\pi\)
\(878\) −53.3661 −1.80102
\(879\) 8.75929 0.295444
\(880\) 1.99715 0.0673240
\(881\) −24.4933 −0.825200 −0.412600 0.910912i \(-0.635379\pi\)
−0.412600 + 0.910912i \(0.635379\pi\)
\(882\) −0.353753 −0.0119115
\(883\) 10.5544 0.355182 0.177591 0.984104i \(-0.443170\pi\)
0.177591 + 0.984104i \(0.443170\pi\)
\(884\) 4.03863 0.135834
\(885\) −4.38089 −0.147262
\(886\) 31.4318 1.05597
\(887\) −48.7310 −1.63623 −0.818113 0.575057i \(-0.804980\pi\)
−0.818113 + 0.575057i \(0.804980\pi\)
\(888\) 1.91194 0.0641605
\(889\) −26.4964 −0.888660
\(890\) 4.36486 0.146311
\(891\) 14.9110 0.499537
\(892\) 11.3783 0.380972
\(893\) 40.3631 1.35070
\(894\) −22.0049 −0.735955
\(895\) 0.0377463 0.00126172
\(896\) −4.06629 −0.135845
\(897\) 16.8899 0.563938
\(898\) 4.11916 0.137458
\(899\) −32.1379 −1.07186
\(900\) −0.582221 −0.0194074
\(901\) 2.68238 0.0893629
\(902\) 33.3404 1.11011
\(903\) −3.56860 −0.118755
\(904\) 4.12559 0.137215
\(905\) 3.29824 0.109637
\(906\) 34.1866 1.13577
\(907\) −36.9873 −1.22814 −0.614072 0.789250i \(-0.710469\pi\)
−0.614072 + 0.789250i \(0.710469\pi\)
\(908\) 4.37025 0.145032
\(909\) 0.835424 0.0277093
\(910\) 2.51186 0.0832675
\(911\) 24.6253 0.815872 0.407936 0.913010i \(-0.366249\pi\)
0.407936 + 0.913010i \(0.366249\pi\)
\(912\) −28.4067 −0.940640
\(913\) −18.1761 −0.601540
\(914\) −62.3627 −2.06278
\(915\) 2.38316 0.0787847
\(916\) −24.4962 −0.809376
\(917\) 45.2911 1.49564
\(918\) −10.1155 −0.333861
\(919\) −29.2801 −0.965860 −0.482930 0.875659i \(-0.660428\pi\)
−0.482930 + 0.875659i \(0.660428\pi\)
\(920\) −0.324576 −0.0107010
\(921\) −53.7196 −1.77012
\(922\) 74.4931 2.45330
\(923\) −19.6940 −0.648235
\(924\) −10.8504 −0.356953
\(925\) −21.4979 −0.706845
\(926\) −12.9587 −0.425849
\(927\) 0.817932 0.0268644
\(928\) 27.8990 0.915830
\(929\) 18.5784 0.609537 0.304768 0.952426i \(-0.401421\pi\)
0.304768 + 0.952426i \(0.401421\pi\)
\(930\) −9.03159 −0.296158
\(931\) 10.8874 0.356819
\(932\) 7.29292 0.238888
\(933\) −19.0642 −0.624132
\(934\) 3.47133 0.113585
\(935\) 0.471277 0.0154124
\(936\) 0.0340566 0.00111317
\(937\) −47.0951 −1.53853 −0.769265 0.638930i \(-0.779377\pi\)
−0.769265 + 0.638930i \(0.779377\pi\)
\(938\) 44.6751 1.45869
\(939\) −24.2174 −0.790304
\(940\) −5.73093 −0.186922
\(941\) −16.6518 −0.542834 −0.271417 0.962462i \(-0.587492\pi\)
−0.271417 + 0.962462i \(0.587492\pi\)
\(942\) 71.5131 2.33002
\(943\) −46.7098 −1.52108
\(944\) −36.5363 −1.18915
\(945\) −3.04263 −0.0989767
\(946\) 3.19464 0.103867
\(947\) −4.33979 −0.141024 −0.0705121 0.997511i \(-0.522463\pi\)
−0.0705121 + 0.997511i \(0.522463\pi\)
\(948\) −41.5253 −1.34868
\(949\) −35.9895 −1.16827
\(950\) 37.0519 1.20212
\(951\) 18.2377 0.591396
\(952\) −0.509311 −0.0165069
\(953\) −40.9878 −1.32773 −0.663863 0.747854i \(-0.731084\pi\)
−0.663863 + 0.747854i \(0.731084\pi\)
\(954\) −0.333806 −0.0108074
\(955\) −3.97828 −0.128734
\(956\) −49.5290 −1.60188
\(957\) −10.1097 −0.326800
\(958\) −38.8865 −1.25637
\(959\) 17.6312 0.569342
\(960\) 3.53373 0.114051
\(961\) 50.5696 1.63128
\(962\) −18.5573 −0.598312
\(963\) −0.602199 −0.0194056
\(964\) −22.5205 −0.725337
\(965\) 7.34178 0.236340
\(966\) 31.4329 1.01134
\(967\) 57.1108 1.83656 0.918279 0.395934i \(-0.129579\pi\)
0.918279 + 0.395934i \(0.129579\pi\)
\(968\) 2.08948 0.0671586
\(969\) −6.70327 −0.215340
\(970\) −7.51005 −0.241133
\(971\) 6.52691 0.209459 0.104729 0.994501i \(-0.466602\pi\)
0.104729 + 0.994501i \(0.466602\pi\)
\(972\) 1.23067 0.0394738
\(973\) −8.13369 −0.260754
\(974\) 7.63375 0.244601
\(975\) −18.5505 −0.594091
\(976\) 19.8754 0.636195
\(977\) 21.7372 0.695435 0.347718 0.937599i \(-0.386957\pi\)
0.347718 + 0.937599i \(0.386957\pi\)
\(978\) 34.7832 1.11224
\(979\) −12.4010 −0.396336
\(980\) −1.54583 −0.0493799
\(981\) −0.879579 −0.0280828
\(982\) −66.4236 −2.11966
\(983\) −10.4438 −0.333106 −0.166553 0.986033i \(-0.553264\pi\)
−0.166553 + 0.986033i \(0.553264\pi\)
\(984\) −4.56262 −0.145451
\(985\) 0.250836 0.00799230
\(986\) 7.00296 0.223020
\(987\) −37.6084 −1.19709
\(988\) 15.4679 0.492098
\(989\) −4.47568 −0.142318
\(990\) −0.0586477 −0.00186395
\(991\) 20.2566 0.643471 0.321735 0.946830i \(-0.395734\pi\)
0.321735 + 0.946830i \(0.395734\pi\)
\(992\) −70.8108 −2.24825
\(993\) 52.1167 1.65387
\(994\) −36.6513 −1.16251
\(995\) 0.205565 0.00651684
\(996\) −36.7071 −1.16311
\(997\) −53.5272 −1.69522 −0.847611 0.530618i \(-0.821960\pi\)
−0.847611 + 0.530618i \(0.821960\pi\)
\(998\) −47.6432 −1.50812
\(999\) 22.4785 0.711190
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 731.2.a.c.1.6 6
3.2 odd 2 6579.2.a.j.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.6 6 1.1 even 1 trivial
6579.2.a.j.1.1 6 3.2 odd 2