Properties

Label 8034.2.a.z.1.6
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} - 6316 x + 1552\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.937159\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.937159 q^{10} -4.70314 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.792704 q^{14} +0.937159 q^{15} +1.00000 q^{16} -3.60442 q^{17} -1.00000 q^{18} -0.803399 q^{19} -0.937159 q^{20} +0.792704 q^{21} +4.70314 q^{22} -4.68922 q^{23} +1.00000 q^{24} -4.12173 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.792704 q^{28} -3.11482 q^{29} -0.937159 q^{30} -3.57843 q^{31} -1.00000 q^{32} +4.70314 q^{33} +3.60442 q^{34} +0.742890 q^{35} +1.00000 q^{36} +1.63083 q^{37} +0.803399 q^{38} -1.00000 q^{39} +0.937159 q^{40} -7.48219 q^{41} -0.792704 q^{42} +3.98449 q^{43} -4.70314 q^{44} -0.937159 q^{45} +4.68922 q^{46} +0.579710 q^{47} -1.00000 q^{48} -6.37162 q^{49} +4.12173 q^{50} +3.60442 q^{51} +1.00000 q^{52} +5.61866 q^{53} +1.00000 q^{54} +4.40759 q^{55} +0.792704 q^{56} +0.803399 q^{57} +3.11482 q^{58} -1.93187 q^{59} +0.937159 q^{60} -14.8337 q^{61} +3.57843 q^{62} -0.792704 q^{63} +1.00000 q^{64} -0.937159 q^{65} -4.70314 q^{66} +5.77582 q^{67} -3.60442 q^{68} +4.68922 q^{69} -0.742890 q^{70} -5.96557 q^{71} -1.00000 q^{72} +0.810762 q^{73} -1.63083 q^{74} +4.12173 q^{75} -0.803399 q^{76} +3.72820 q^{77} +1.00000 q^{78} +6.43093 q^{79} -0.937159 q^{80} +1.00000 q^{81} +7.48219 q^{82} -5.41646 q^{83} +0.792704 q^{84} +3.37791 q^{85} -3.98449 q^{86} +3.11482 q^{87} +4.70314 q^{88} -18.2668 q^{89} +0.937159 q^{90} -0.792704 q^{91} -4.68922 q^{92} +3.57843 q^{93} -0.579710 q^{94} +0.752913 q^{95} +1.00000 q^{96} +10.4350 q^{97} +6.37162 q^{98} -4.70314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −0.937159 −0.419110 −0.209555 0.977797i \(-0.567202\pi\)
−0.209555 + 0.977797i \(0.567202\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.792704 −0.299614 −0.149807 0.988715i \(-0.547865\pi\)
−0.149807 + 0.988715i \(0.547865\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.937159 0.296356
\(11\) −4.70314 −1.41805 −0.709025 0.705183i \(-0.750865\pi\)
−0.709025 + 0.705183i \(0.750865\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 0.792704 0.211859
\(15\) 0.937159 0.241973
\(16\) 1.00000 0.250000
\(17\) −3.60442 −0.874199 −0.437100 0.899413i \(-0.643994\pi\)
−0.437100 + 0.899413i \(0.643994\pi\)
\(18\) −1.00000 −0.235702
\(19\) −0.803399 −0.184312 −0.0921562 0.995745i \(-0.529376\pi\)
−0.0921562 + 0.995745i \(0.529376\pi\)
\(20\) −0.937159 −0.209555
\(21\) 0.792704 0.172982
\(22\) 4.70314 1.00271
\(23\) −4.68922 −0.977770 −0.488885 0.872348i \(-0.662596\pi\)
−0.488885 + 0.872348i \(0.662596\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.12173 −0.824347
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −0.792704 −0.149807
\(29\) −3.11482 −0.578408 −0.289204 0.957268i \(-0.593391\pi\)
−0.289204 + 0.957268i \(0.593391\pi\)
\(30\) −0.937159 −0.171101
\(31\) −3.57843 −0.642704 −0.321352 0.946960i \(-0.604137\pi\)
−0.321352 + 0.946960i \(0.604137\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.70314 0.818712
\(34\) 3.60442 0.618152
\(35\) 0.742890 0.125571
\(36\) 1.00000 0.166667
\(37\) 1.63083 0.268107 0.134054 0.990974i \(-0.457201\pi\)
0.134054 + 0.990974i \(0.457201\pi\)
\(38\) 0.803399 0.130329
\(39\) −1.00000 −0.160128
\(40\) 0.937159 0.148178
\(41\) −7.48219 −1.16852 −0.584261 0.811566i \(-0.698616\pi\)
−0.584261 + 0.811566i \(0.698616\pi\)
\(42\) −0.792704 −0.122317
\(43\) 3.98449 0.607629 0.303815 0.952731i \(-0.401740\pi\)
0.303815 + 0.952731i \(0.401740\pi\)
\(44\) −4.70314 −0.709025
\(45\) −0.937159 −0.139703
\(46\) 4.68922 0.691387
\(47\) 0.579710 0.0845593 0.0422797 0.999106i \(-0.486538\pi\)
0.0422797 + 0.999106i \(0.486538\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.37162 −0.910231
\(50\) 4.12173 0.582901
\(51\) 3.60442 0.504719
\(52\) 1.00000 0.138675
\(53\) 5.61866 0.771782 0.385891 0.922544i \(-0.373894\pi\)
0.385891 + 0.922544i \(0.373894\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.40759 0.594320
\(56\) 0.792704 0.105930
\(57\) 0.803399 0.106413
\(58\) 3.11482 0.408996
\(59\) −1.93187 −0.251508 −0.125754 0.992061i \(-0.540135\pi\)
−0.125754 + 0.992061i \(0.540135\pi\)
\(60\) 0.937159 0.120987
\(61\) −14.8337 −1.89926 −0.949628 0.313380i \(-0.898539\pi\)
−0.949628 + 0.313380i \(0.898539\pi\)
\(62\) 3.57843 0.454461
\(63\) −0.792704 −0.0998713
\(64\) 1.00000 0.125000
\(65\) −0.937159 −0.116240
\(66\) −4.70314 −0.578917
\(67\) 5.77582 0.705629 0.352815 0.935693i \(-0.385225\pi\)
0.352815 + 0.935693i \(0.385225\pi\)
\(68\) −3.60442 −0.437100
\(69\) 4.68922 0.564516
\(70\) −0.742890 −0.0887923
\(71\) −5.96557 −0.707983 −0.353991 0.935249i \(-0.615176\pi\)
−0.353991 + 0.935249i \(0.615176\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.810762 0.0948925 0.0474462 0.998874i \(-0.484892\pi\)
0.0474462 + 0.998874i \(0.484892\pi\)
\(74\) −1.63083 −0.189580
\(75\) 4.12173 0.475937
\(76\) −0.803399 −0.0921562
\(77\) 3.72820 0.424868
\(78\) 1.00000 0.113228
\(79\) 6.43093 0.723536 0.361768 0.932268i \(-0.382173\pi\)
0.361768 + 0.932268i \(0.382173\pi\)
\(80\) −0.937159 −0.104778
\(81\) 1.00000 0.111111
\(82\) 7.48219 0.826270
\(83\) −5.41646 −0.594534 −0.297267 0.954794i \(-0.596075\pi\)
−0.297267 + 0.954794i \(0.596075\pi\)
\(84\) 0.792704 0.0864911
\(85\) 3.37791 0.366386
\(86\) −3.98449 −0.429659
\(87\) 3.11482 0.333944
\(88\) 4.70314 0.501357
\(89\) −18.2668 −1.93628 −0.968141 0.250406i \(-0.919436\pi\)
−0.968141 + 0.250406i \(0.919436\pi\)
\(90\) 0.937159 0.0987852
\(91\) −0.792704 −0.0830979
\(92\) −4.68922 −0.488885
\(93\) 3.57843 0.371066
\(94\) −0.579710 −0.0597925
\(95\) 0.752913 0.0772472
\(96\) 1.00000 0.102062
\(97\) 10.4350 1.05951 0.529755 0.848151i \(-0.322284\pi\)
0.529755 + 0.848151i \(0.322284\pi\)
\(98\) 6.37162 0.643631
\(99\) −4.70314 −0.472684
\(100\) −4.12173 −0.412173
\(101\) −1.41189 −0.140488 −0.0702441 0.997530i \(-0.522378\pi\)
−0.0702441 + 0.997530i \(0.522378\pi\)
\(102\) −3.60442 −0.356890
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −0.742890 −0.0724986
\(106\) −5.61866 −0.545732
\(107\) 0.502970 0.0486240 0.0243120 0.999704i \(-0.492260\pi\)
0.0243120 + 0.999704i \(0.492260\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 17.7539 1.70052 0.850259 0.526365i \(-0.176445\pi\)
0.850259 + 0.526365i \(0.176445\pi\)
\(110\) −4.40759 −0.420247
\(111\) −1.63083 −0.154792
\(112\) −0.792704 −0.0749035
\(113\) 8.02786 0.755198 0.377599 0.925969i \(-0.376750\pi\)
0.377599 + 0.925969i \(0.376750\pi\)
\(114\) −0.803399 −0.0752453
\(115\) 4.39454 0.409793
\(116\) −3.11482 −0.289204
\(117\) 1.00000 0.0924500
\(118\) 1.93187 0.177843
\(119\) 2.85724 0.261922
\(120\) −0.937159 −0.0855505
\(121\) 11.1196 1.01087
\(122\) 14.8337 1.34298
\(123\) 7.48219 0.674646
\(124\) −3.57843 −0.321352
\(125\) 8.54851 0.764602
\(126\) 0.792704 0.0706197
\(127\) −8.03716 −0.713183 −0.356591 0.934260i \(-0.616061\pi\)
−0.356591 + 0.934260i \(0.616061\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.98449 −0.350815
\(130\) 0.937159 0.0821943
\(131\) 4.13397 0.361186 0.180593 0.983558i \(-0.442198\pi\)
0.180593 + 0.983558i \(0.442198\pi\)
\(132\) 4.70314 0.409356
\(133\) 0.636858 0.0552226
\(134\) −5.77582 −0.498955
\(135\) 0.937159 0.0806578
\(136\) 3.60442 0.309076
\(137\) −17.8896 −1.52842 −0.764208 0.644970i \(-0.776870\pi\)
−0.764208 + 0.644970i \(0.776870\pi\)
\(138\) −4.68922 −0.399173
\(139\) −17.3454 −1.47122 −0.735608 0.677407i \(-0.763104\pi\)
−0.735608 + 0.677407i \(0.763104\pi\)
\(140\) 0.742890 0.0627856
\(141\) −0.579710 −0.0488204
\(142\) 5.96557 0.500619
\(143\) −4.70314 −0.393297
\(144\) 1.00000 0.0833333
\(145\) 2.91908 0.242417
\(146\) −0.810762 −0.0670991
\(147\) 6.37162 0.525522
\(148\) 1.63083 0.134054
\(149\) −9.59017 −0.785657 −0.392829 0.919612i \(-0.628503\pi\)
−0.392829 + 0.919612i \(0.628503\pi\)
\(150\) −4.12173 −0.336538
\(151\) 8.93579 0.727184 0.363592 0.931558i \(-0.381550\pi\)
0.363592 + 0.931558i \(0.381550\pi\)
\(152\) 0.803399 0.0651643
\(153\) −3.60442 −0.291400
\(154\) −3.72820 −0.300427
\(155\) 3.35355 0.269364
\(156\) −1.00000 −0.0800641
\(157\) −18.9333 −1.51104 −0.755521 0.655125i \(-0.772616\pi\)
−0.755521 + 0.655125i \(0.772616\pi\)
\(158\) −6.43093 −0.511617
\(159\) −5.61866 −0.445588
\(160\) 0.937159 0.0740889
\(161\) 3.71716 0.292953
\(162\) −1.00000 −0.0785674
\(163\) −9.61838 −0.753370 −0.376685 0.926341i \(-0.622936\pi\)
−0.376685 + 0.926341i \(0.622936\pi\)
\(164\) −7.48219 −0.584261
\(165\) −4.40759 −0.343131
\(166\) 5.41646 0.420399
\(167\) −25.2414 −1.95324 −0.976621 0.214970i \(-0.931035\pi\)
−0.976621 + 0.214970i \(0.931035\pi\)
\(168\) −0.792704 −0.0611584
\(169\) 1.00000 0.0769231
\(170\) −3.37791 −0.259074
\(171\) −0.803399 −0.0614375
\(172\) 3.98449 0.303815
\(173\) 0.222644 0.0169273 0.00846364 0.999964i \(-0.497306\pi\)
0.00846364 + 0.999964i \(0.497306\pi\)
\(174\) −3.11482 −0.236134
\(175\) 3.26731 0.246986
\(176\) −4.70314 −0.354513
\(177\) 1.93187 0.145208
\(178\) 18.2668 1.36916
\(179\) 25.3993 1.89843 0.949217 0.314623i \(-0.101878\pi\)
0.949217 + 0.314623i \(0.101878\pi\)
\(180\) −0.937159 −0.0698517
\(181\) −6.58007 −0.489093 −0.244546 0.969638i \(-0.578639\pi\)
−0.244546 + 0.969638i \(0.578639\pi\)
\(182\) 0.792704 0.0587591
\(183\) 14.8337 1.09654
\(184\) 4.68922 0.345694
\(185\) −1.52835 −0.112366
\(186\) −3.57843 −0.262383
\(187\) 16.9521 1.23966
\(188\) 0.579710 0.0422797
\(189\) 0.792704 0.0576607
\(190\) −0.752913 −0.0546220
\(191\) 11.0853 0.802105 0.401052 0.916055i \(-0.368644\pi\)
0.401052 + 0.916055i \(0.368644\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.80068 0.489524 0.244762 0.969583i \(-0.421290\pi\)
0.244762 + 0.969583i \(0.421290\pi\)
\(194\) −10.4350 −0.749186
\(195\) 0.937159 0.0671113
\(196\) −6.37162 −0.455116
\(197\) −5.08227 −0.362096 −0.181048 0.983474i \(-0.557949\pi\)
−0.181048 + 0.983474i \(0.557949\pi\)
\(198\) 4.70314 0.334238
\(199\) 15.9413 1.13005 0.565024 0.825074i \(-0.308867\pi\)
0.565024 + 0.825074i \(0.308867\pi\)
\(200\) 4.12173 0.291451
\(201\) −5.77582 −0.407395
\(202\) 1.41189 0.0993401
\(203\) 2.46913 0.173299
\(204\) 3.60442 0.252360
\(205\) 7.01200 0.489740
\(206\) 1.00000 0.0696733
\(207\) −4.68922 −0.325923
\(208\) 1.00000 0.0693375
\(209\) 3.77850 0.261364
\(210\) 0.742890 0.0512643
\(211\) 10.7284 0.738571 0.369285 0.929316i \(-0.379603\pi\)
0.369285 + 0.929316i \(0.379603\pi\)
\(212\) 5.61866 0.385891
\(213\) 5.96557 0.408754
\(214\) −0.502970 −0.0343824
\(215\) −3.73410 −0.254664
\(216\) 1.00000 0.0680414
\(217\) 2.83663 0.192563
\(218\) −17.7539 −1.20245
\(219\) −0.810762 −0.0547862
\(220\) 4.40759 0.297160
\(221\) −3.60442 −0.242459
\(222\) 1.63083 0.109454
\(223\) −19.7800 −1.32457 −0.662284 0.749253i \(-0.730413\pi\)
−0.662284 + 0.749253i \(0.730413\pi\)
\(224\) 0.792704 0.0529648
\(225\) −4.12173 −0.274782
\(226\) −8.02786 −0.534006
\(227\) 13.3566 0.886507 0.443254 0.896396i \(-0.353824\pi\)
0.443254 + 0.896396i \(0.353824\pi\)
\(228\) 0.803399 0.0532064
\(229\) −1.87870 −0.124148 −0.0620741 0.998072i \(-0.519772\pi\)
−0.0620741 + 0.998072i \(0.519772\pi\)
\(230\) −4.39454 −0.289768
\(231\) −3.72820 −0.245298
\(232\) 3.11482 0.204498
\(233\) 16.0079 1.04871 0.524356 0.851499i \(-0.324306\pi\)
0.524356 + 0.851499i \(0.324306\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −0.543280 −0.0354397
\(236\) −1.93187 −0.125754
\(237\) −6.43093 −0.417734
\(238\) −2.85724 −0.185207
\(239\) 17.4394 1.12806 0.564031 0.825754i \(-0.309250\pi\)
0.564031 + 0.825754i \(0.309250\pi\)
\(240\) 0.937159 0.0604933
\(241\) −6.56601 −0.422954 −0.211477 0.977383i \(-0.567827\pi\)
−0.211477 + 0.977383i \(0.567827\pi\)
\(242\) −11.1196 −0.714792
\(243\) −1.00000 −0.0641500
\(244\) −14.8337 −0.949628
\(245\) 5.97122 0.381487
\(246\) −7.48219 −0.477047
\(247\) −0.803399 −0.0511191
\(248\) 3.57843 0.227230
\(249\) 5.41646 0.343254
\(250\) −8.54851 −0.540655
\(251\) 18.8493 1.18976 0.594878 0.803816i \(-0.297200\pi\)
0.594878 + 0.803816i \(0.297200\pi\)
\(252\) −0.792704 −0.0499357
\(253\) 22.0541 1.38653
\(254\) 8.03716 0.504296
\(255\) −3.37791 −0.211533
\(256\) 1.00000 0.0625000
\(257\) −15.0916 −0.941389 −0.470694 0.882296i \(-0.655997\pi\)
−0.470694 + 0.882296i \(0.655997\pi\)
\(258\) 3.98449 0.248064
\(259\) −1.29277 −0.0803287
\(260\) −0.937159 −0.0581201
\(261\) −3.11482 −0.192803
\(262\) −4.13397 −0.255397
\(263\) 2.51843 0.155293 0.0776465 0.996981i \(-0.475259\pi\)
0.0776465 + 0.996981i \(0.475259\pi\)
\(264\) −4.70314 −0.289458
\(265\) −5.26557 −0.323462
\(266\) −0.636858 −0.0390483
\(267\) 18.2668 1.11791
\(268\) 5.77582 0.352815
\(269\) −26.3178 −1.60462 −0.802312 0.596905i \(-0.796397\pi\)
−0.802312 + 0.596905i \(0.796397\pi\)
\(270\) −0.937159 −0.0570337
\(271\) 6.11955 0.371736 0.185868 0.982575i \(-0.440490\pi\)
0.185868 + 0.982575i \(0.440490\pi\)
\(272\) −3.60442 −0.218550
\(273\) 0.792704 0.0479766
\(274\) 17.8896 1.08075
\(275\) 19.3851 1.16897
\(276\) 4.68922 0.282258
\(277\) −31.2379 −1.87690 −0.938451 0.345413i \(-0.887739\pi\)
−0.938451 + 0.345413i \(0.887739\pi\)
\(278\) 17.3454 1.04031
\(279\) −3.57843 −0.214235
\(280\) −0.742890 −0.0443961
\(281\) −18.1874 −1.08497 −0.542484 0.840066i \(-0.682516\pi\)
−0.542484 + 0.840066i \(0.682516\pi\)
\(282\) 0.579710 0.0345212
\(283\) 1.52975 0.0909343 0.0454671 0.998966i \(-0.485522\pi\)
0.0454671 + 0.998966i \(0.485522\pi\)
\(284\) −5.96557 −0.353991
\(285\) −0.752913 −0.0445987
\(286\) 4.70314 0.278103
\(287\) 5.93116 0.350105
\(288\) −1.00000 −0.0589256
\(289\) −4.00818 −0.235775
\(290\) −2.91908 −0.171414
\(291\) −10.4350 −0.611708
\(292\) 0.810762 0.0474462
\(293\) −9.77976 −0.571340 −0.285670 0.958328i \(-0.592216\pi\)
−0.285670 + 0.958328i \(0.592216\pi\)
\(294\) −6.37162 −0.371600
\(295\) 1.81047 0.105409
\(296\) −1.63083 −0.0947902
\(297\) 4.70314 0.272904
\(298\) 9.59017 0.555543
\(299\) −4.68922 −0.271184
\(300\) 4.12173 0.237968
\(301\) −3.15852 −0.182054
\(302\) −8.93579 −0.514197
\(303\) 1.41189 0.0811108
\(304\) −0.803399 −0.0460781
\(305\) 13.9015 0.795997
\(306\) 3.60442 0.206051
\(307\) −17.1789 −0.980451 −0.490225 0.871596i \(-0.663086\pi\)
−0.490225 + 0.871596i \(0.663086\pi\)
\(308\) 3.72820 0.212434
\(309\) 1.00000 0.0568880
\(310\) −3.35355 −0.190469
\(311\) 28.7706 1.63143 0.815715 0.578454i \(-0.196344\pi\)
0.815715 + 0.578454i \(0.196344\pi\)
\(312\) 1.00000 0.0566139
\(313\) 26.0073 1.47002 0.735010 0.678057i \(-0.237178\pi\)
0.735010 + 0.678057i \(0.237178\pi\)
\(314\) 18.9333 1.06847
\(315\) 0.742890 0.0418571
\(316\) 6.43093 0.361768
\(317\) −0.494041 −0.0277481 −0.0138741 0.999904i \(-0.504416\pi\)
−0.0138741 + 0.999904i \(0.504416\pi\)
\(318\) 5.61866 0.315079
\(319\) 14.6494 0.820212
\(320\) −0.937159 −0.0523888
\(321\) −0.502970 −0.0280731
\(322\) −3.71716 −0.207149
\(323\) 2.89579 0.161126
\(324\) 1.00000 0.0555556
\(325\) −4.12173 −0.228633
\(326\) 9.61838 0.532713
\(327\) −17.7539 −0.981794
\(328\) 7.48219 0.413135
\(329\) −0.459538 −0.0253352
\(330\) 4.40759 0.242630
\(331\) 13.2952 0.730768 0.365384 0.930857i \(-0.380938\pi\)
0.365384 + 0.930857i \(0.380938\pi\)
\(332\) −5.41646 −0.297267
\(333\) 1.63083 0.0893691
\(334\) 25.2414 1.38115
\(335\) −5.41287 −0.295736
\(336\) 0.792704 0.0432455
\(337\) −1.04274 −0.0568015 −0.0284007 0.999597i \(-0.509041\pi\)
−0.0284007 + 0.999597i \(0.509041\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −8.02786 −0.436014
\(340\) 3.37791 0.183193
\(341\) 16.8299 0.911388
\(342\) 0.803399 0.0434429
\(343\) 10.5997 0.572332
\(344\) −3.98449 −0.214829
\(345\) −4.39454 −0.236594
\(346\) −0.222644 −0.0119694
\(347\) 25.2951 1.35791 0.678956 0.734179i \(-0.262433\pi\)
0.678956 + 0.734179i \(0.262433\pi\)
\(348\) 3.11482 0.166972
\(349\) 17.3267 0.927475 0.463737 0.885973i \(-0.346508\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(350\) −3.26731 −0.174645
\(351\) −1.00000 −0.0533761
\(352\) 4.70314 0.250678
\(353\) −16.7368 −0.890811 −0.445406 0.895329i \(-0.646941\pi\)
−0.445406 + 0.895329i \(0.646941\pi\)
\(354\) −1.93187 −0.102678
\(355\) 5.59068 0.296723
\(356\) −18.2668 −0.968141
\(357\) −2.85724 −0.151221
\(358\) −25.3993 −1.34240
\(359\) 6.34619 0.334939 0.167470 0.985877i \(-0.446440\pi\)
0.167470 + 0.985877i \(0.446440\pi\)
\(360\) 0.937159 0.0493926
\(361\) −18.3545 −0.966029
\(362\) 6.58007 0.345841
\(363\) −11.1196 −0.583625
\(364\) −0.792704 −0.0415490
\(365\) −0.759812 −0.0397704
\(366\) −14.8337 −0.775368
\(367\) 30.8119 1.60837 0.804185 0.594379i \(-0.202602\pi\)
0.804185 + 0.594379i \(0.202602\pi\)
\(368\) −4.68922 −0.244442
\(369\) −7.48219 −0.389507
\(370\) 1.52835 0.0794551
\(371\) −4.45393 −0.231237
\(372\) 3.57843 0.185533
\(373\) −26.3688 −1.36533 −0.682663 0.730734i \(-0.739178\pi\)
−0.682663 + 0.730734i \(0.739178\pi\)
\(374\) −16.9521 −0.876571
\(375\) −8.54851 −0.441443
\(376\) −0.579710 −0.0298962
\(377\) −3.11482 −0.160421
\(378\) −0.792704 −0.0407723
\(379\) 9.77930 0.502329 0.251165 0.967944i \(-0.419186\pi\)
0.251165 + 0.967944i \(0.419186\pi\)
\(380\) 0.752913 0.0386236
\(381\) 8.03716 0.411756
\(382\) −11.0853 −0.567174
\(383\) −32.4570 −1.65847 −0.829237 0.558897i \(-0.811225\pi\)
−0.829237 + 0.558897i \(0.811225\pi\)
\(384\) 1.00000 0.0510310
\(385\) −3.49392 −0.178066
\(386\) −6.80068 −0.346146
\(387\) 3.98449 0.202543
\(388\) 10.4350 0.529755
\(389\) 7.67508 0.389142 0.194571 0.980888i \(-0.437669\pi\)
0.194571 + 0.980888i \(0.437669\pi\)
\(390\) −0.937159 −0.0474549
\(391\) 16.9019 0.854766
\(392\) 6.37162 0.321815
\(393\) −4.13397 −0.208531
\(394\) 5.08227 0.256041
\(395\) −6.02680 −0.303241
\(396\) −4.70314 −0.236342
\(397\) −7.64131 −0.383506 −0.191753 0.981443i \(-0.561417\pi\)
−0.191753 + 0.981443i \(0.561417\pi\)
\(398\) −15.9413 −0.799065
\(399\) −0.636858 −0.0318828
\(400\) −4.12173 −0.206087
\(401\) −12.6513 −0.631777 −0.315888 0.948796i \(-0.602303\pi\)
−0.315888 + 0.948796i \(0.602303\pi\)
\(402\) 5.77582 0.288072
\(403\) −3.57843 −0.178254
\(404\) −1.41189 −0.0702441
\(405\) −0.937159 −0.0465678
\(406\) −2.46913 −0.122541
\(407\) −7.67004 −0.380190
\(408\) −3.60442 −0.178445
\(409\) 24.4350 1.20823 0.604115 0.796897i \(-0.293527\pi\)
0.604115 + 0.796897i \(0.293527\pi\)
\(410\) −7.01200 −0.346298
\(411\) 17.8896 0.882431
\(412\) −1.00000 −0.0492665
\(413\) 1.53140 0.0753552
\(414\) 4.68922 0.230462
\(415\) 5.07609 0.249175
\(416\) −1.00000 −0.0490290
\(417\) 17.3454 0.849407
\(418\) −3.77850 −0.184813
\(419\) −23.6809 −1.15689 −0.578444 0.815722i \(-0.696340\pi\)
−0.578444 + 0.815722i \(0.696340\pi\)
\(420\) −0.742890 −0.0362493
\(421\) −12.5451 −0.611411 −0.305705 0.952126i \(-0.598892\pi\)
−0.305705 + 0.952126i \(0.598892\pi\)
\(422\) −10.7284 −0.522248
\(423\) 0.579710 0.0281864
\(424\) −5.61866 −0.272866
\(425\) 14.8564 0.720643
\(426\) −5.96557 −0.289033
\(427\) 11.7587 0.569043
\(428\) 0.502970 0.0243120
\(429\) 4.70314 0.227070
\(430\) 3.73410 0.180074
\(431\) −18.7049 −0.900984 −0.450492 0.892780i \(-0.648751\pi\)
−0.450492 + 0.892780i \(0.648751\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 32.1566 1.54535 0.772673 0.634805i \(-0.218919\pi\)
0.772673 + 0.634805i \(0.218919\pi\)
\(434\) −2.83663 −0.136163
\(435\) −2.91908 −0.139959
\(436\) 17.7539 0.850259
\(437\) 3.76732 0.180215
\(438\) 0.810762 0.0387397
\(439\) 31.5854 1.50749 0.753745 0.657167i \(-0.228245\pi\)
0.753745 + 0.657167i \(0.228245\pi\)
\(440\) −4.40759 −0.210124
\(441\) −6.37162 −0.303410
\(442\) 3.60442 0.171445
\(443\) 26.8464 1.27551 0.637756 0.770238i \(-0.279863\pi\)
0.637756 + 0.770238i \(0.279863\pi\)
\(444\) −1.63083 −0.0773959
\(445\) 17.1189 0.811515
\(446\) 19.7800 0.936611
\(447\) 9.59017 0.453599
\(448\) −0.792704 −0.0374517
\(449\) −1.58098 −0.0746108 −0.0373054 0.999304i \(-0.511877\pi\)
−0.0373054 + 0.999304i \(0.511877\pi\)
\(450\) 4.12173 0.194300
\(451\) 35.1898 1.65702
\(452\) 8.02786 0.377599
\(453\) −8.93579 −0.419840
\(454\) −13.3566 −0.626855
\(455\) 0.742890 0.0348272
\(456\) −0.803399 −0.0376226
\(457\) −13.8693 −0.648777 −0.324389 0.945924i \(-0.605159\pi\)
−0.324389 + 0.945924i \(0.605159\pi\)
\(458\) 1.87870 0.0877861
\(459\) 3.60442 0.168240
\(460\) 4.39454 0.204897
\(461\) 2.70162 0.125827 0.0629136 0.998019i \(-0.479961\pi\)
0.0629136 + 0.998019i \(0.479961\pi\)
\(462\) 3.72820 0.173452
\(463\) −30.6401 −1.42396 −0.711982 0.702198i \(-0.752202\pi\)
−0.711982 + 0.702198i \(0.752202\pi\)
\(464\) −3.11482 −0.144602
\(465\) −3.35355 −0.155517
\(466\) −16.0079 −0.741551
\(467\) −20.2536 −0.937223 −0.468612 0.883404i \(-0.655246\pi\)
−0.468612 + 0.883404i \(0.655246\pi\)
\(468\) 1.00000 0.0462250
\(469\) −4.57852 −0.211416
\(470\) 0.543280 0.0250596
\(471\) 18.9333 0.872400
\(472\) 1.93187 0.0889214
\(473\) −18.7396 −0.861649
\(474\) 6.43093 0.295382
\(475\) 3.31140 0.151937
\(476\) 2.85724 0.130961
\(477\) 5.61866 0.257261
\(478\) −17.4394 −0.797660
\(479\) 20.6640 0.944162 0.472081 0.881555i \(-0.343503\pi\)
0.472081 + 0.881555i \(0.343503\pi\)
\(480\) −0.937159 −0.0427753
\(481\) 1.63083 0.0743596
\(482\) 6.56601 0.299074
\(483\) −3.71716 −0.169137
\(484\) 11.1196 0.505434
\(485\) −9.77921 −0.444051
\(486\) 1.00000 0.0453609
\(487\) −21.3896 −0.969257 −0.484628 0.874720i \(-0.661045\pi\)
−0.484628 + 0.874720i \(0.661045\pi\)
\(488\) 14.8337 0.671488
\(489\) 9.61838 0.434958
\(490\) −5.97122 −0.269752
\(491\) −42.5182 −1.91882 −0.959409 0.282017i \(-0.908996\pi\)
−0.959409 + 0.282017i \(0.908996\pi\)
\(492\) 7.48219 0.337323
\(493\) 11.2271 0.505644
\(494\) 0.803399 0.0361466
\(495\) 4.40759 0.198107
\(496\) −3.57843 −0.160676
\(497\) 4.72893 0.212121
\(498\) −5.41646 −0.242718
\(499\) 10.6374 0.476196 0.238098 0.971241i \(-0.423476\pi\)
0.238098 + 0.971241i \(0.423476\pi\)
\(500\) 8.54851 0.382301
\(501\) 25.2414 1.12770
\(502\) −18.8493 −0.841285
\(503\) 5.29457 0.236073 0.118037 0.993009i \(-0.462340\pi\)
0.118037 + 0.993009i \(0.462340\pi\)
\(504\) 0.792704 0.0353098
\(505\) 1.32316 0.0588800
\(506\) −22.0541 −0.980423
\(507\) −1.00000 −0.0444116
\(508\) −8.03716 −0.356591
\(509\) 26.7767 1.18686 0.593428 0.804887i \(-0.297774\pi\)
0.593428 + 0.804887i \(0.297774\pi\)
\(510\) 3.37791 0.149576
\(511\) −0.642694 −0.0284311
\(512\) −1.00000 −0.0441942
\(513\) 0.803399 0.0354710
\(514\) 15.0916 0.665662
\(515\) 0.937159 0.0412962
\(516\) −3.98449 −0.175407
\(517\) −2.72646 −0.119909
\(518\) 1.29277 0.0568009
\(519\) −0.222644 −0.00977297
\(520\) 0.937159 0.0410971
\(521\) 29.6848 1.30052 0.650258 0.759714i \(-0.274661\pi\)
0.650258 + 0.759714i \(0.274661\pi\)
\(522\) 3.11482 0.136332
\(523\) −1.23849 −0.0541553 −0.0270777 0.999633i \(-0.508620\pi\)
−0.0270777 + 0.999633i \(0.508620\pi\)
\(524\) 4.13397 0.180593
\(525\) −3.26731 −0.142597
\(526\) −2.51843 −0.109809
\(527\) 12.8981 0.561852
\(528\) 4.70314 0.204678
\(529\) −1.01123 −0.0439667
\(530\) 5.26557 0.228722
\(531\) −1.93187 −0.0838359
\(532\) 0.636858 0.0276113
\(533\) −7.48219 −0.324090
\(534\) −18.2668 −0.790484
\(535\) −0.471363 −0.0203788
\(536\) −5.77582 −0.249478
\(537\) −25.3993 −1.09606
\(538\) 26.3178 1.13464
\(539\) 29.9666 1.29075
\(540\) 0.937159 0.0403289
\(541\) 24.2953 1.04454 0.522268 0.852781i \(-0.325086\pi\)
0.522268 + 0.852781i \(0.325086\pi\)
\(542\) −6.11955 −0.262857
\(543\) 6.58007 0.282378
\(544\) 3.60442 0.154538
\(545\) −16.6383 −0.712704
\(546\) −0.792704 −0.0339246
\(547\) −21.1912 −0.906069 −0.453035 0.891493i \(-0.649659\pi\)
−0.453035 + 0.891493i \(0.649659\pi\)
\(548\) −17.8896 −0.764208
\(549\) −14.8337 −0.633085
\(550\) −19.3851 −0.826583
\(551\) 2.50244 0.106608
\(552\) −4.68922 −0.199586
\(553\) −5.09782 −0.216781
\(554\) 31.2379 1.32717
\(555\) 1.52835 0.0648748
\(556\) −17.3454 −0.735608
\(557\) 21.2459 0.900217 0.450108 0.892974i \(-0.351385\pi\)
0.450108 + 0.892974i \(0.351385\pi\)
\(558\) 3.57843 0.151487
\(559\) 3.98449 0.168526
\(560\) 0.742890 0.0313928
\(561\) −16.9521 −0.715718
\(562\) 18.1874 0.767188
\(563\) −29.5654 −1.24603 −0.623017 0.782209i \(-0.714093\pi\)
−0.623017 + 0.782209i \(0.714093\pi\)
\(564\) −0.579710 −0.0244102
\(565\) −7.52339 −0.316511
\(566\) −1.52975 −0.0643002
\(567\) −0.792704 −0.0332904
\(568\) 5.96557 0.250310
\(569\) 24.0452 1.00803 0.504013 0.863696i \(-0.331856\pi\)
0.504013 + 0.863696i \(0.331856\pi\)
\(570\) 0.752913 0.0315361
\(571\) 20.1068 0.841443 0.420721 0.907190i \(-0.361777\pi\)
0.420721 + 0.907190i \(0.361777\pi\)
\(572\) −4.70314 −0.196648
\(573\) −11.0853 −0.463096
\(574\) −5.93116 −0.247562
\(575\) 19.3277 0.806021
\(576\) 1.00000 0.0416667
\(577\) 9.84511 0.409857 0.204929 0.978777i \(-0.434304\pi\)
0.204929 + 0.978777i \(0.434304\pi\)
\(578\) 4.00818 0.166718
\(579\) −6.80068 −0.282627
\(580\) 2.91908 0.121208
\(581\) 4.29365 0.178131
\(582\) 10.4350 0.432543
\(583\) −26.4253 −1.09443
\(584\) −0.810762 −0.0335496
\(585\) −0.937159 −0.0387468
\(586\) 9.77976 0.403998
\(587\) −31.2144 −1.28836 −0.644179 0.764875i \(-0.722801\pi\)
−0.644179 + 0.764875i \(0.722801\pi\)
\(588\) 6.37162 0.262761
\(589\) 2.87491 0.118458
\(590\) −1.81047 −0.0745358
\(591\) 5.08227 0.209056
\(592\) 1.63083 0.0670268
\(593\) 31.3049 1.28554 0.642769 0.766060i \(-0.277785\pi\)
0.642769 + 0.766060i \(0.277785\pi\)
\(594\) −4.70314 −0.192972
\(595\) −2.67768 −0.109774
\(596\) −9.59017 −0.392829
\(597\) −15.9413 −0.652434
\(598\) 4.68922 0.191756
\(599\) 8.02028 0.327700 0.163850 0.986485i \(-0.447609\pi\)
0.163850 + 0.986485i \(0.447609\pi\)
\(600\) −4.12173 −0.168269
\(601\) 24.6819 1.00680 0.503398 0.864055i \(-0.332083\pi\)
0.503398 + 0.864055i \(0.332083\pi\)
\(602\) 3.15852 0.128732
\(603\) 5.77582 0.235210
\(604\) 8.93579 0.363592
\(605\) −10.4208 −0.423665
\(606\) −1.41189 −0.0573540
\(607\) 35.6610 1.44744 0.723718 0.690095i \(-0.242431\pi\)
0.723718 + 0.690095i \(0.242431\pi\)
\(608\) 0.803399 0.0325821
\(609\) −2.46913 −0.100054
\(610\) −13.9015 −0.562855
\(611\) 0.579710 0.0234525
\(612\) −3.60442 −0.145700
\(613\) 26.1783 1.05733 0.528665 0.848830i \(-0.322693\pi\)
0.528665 + 0.848830i \(0.322693\pi\)
\(614\) 17.1789 0.693283
\(615\) −7.01200 −0.282751
\(616\) −3.72820 −0.150213
\(617\) −11.4978 −0.462884 −0.231442 0.972849i \(-0.574344\pi\)
−0.231442 + 0.972849i \(0.574344\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 2.45533 0.0986879 0.0493440 0.998782i \(-0.484287\pi\)
0.0493440 + 0.998782i \(0.484287\pi\)
\(620\) 3.35355 0.134682
\(621\) 4.68922 0.188172
\(622\) −28.7706 −1.15360
\(623\) 14.4802 0.580137
\(624\) −1.00000 −0.0400320
\(625\) 12.5973 0.503894
\(626\) −26.0073 −1.03946
\(627\) −3.77850 −0.150899
\(628\) −18.9333 −0.755521
\(629\) −5.87820 −0.234379
\(630\) −0.742890 −0.0295974
\(631\) −18.3325 −0.729807 −0.364904 0.931045i \(-0.618898\pi\)
−0.364904 + 0.931045i \(0.618898\pi\)
\(632\) −6.43093 −0.255809
\(633\) −10.7284 −0.426414
\(634\) 0.494041 0.0196209
\(635\) 7.53210 0.298902
\(636\) −5.61866 −0.222794
\(637\) −6.37162 −0.252453
\(638\) −14.6494 −0.579977
\(639\) −5.96557 −0.235994
\(640\) 0.937159 0.0370445
\(641\) 42.7020 1.68663 0.843313 0.537423i \(-0.180602\pi\)
0.843313 + 0.537423i \(0.180602\pi\)
\(642\) 0.502970 0.0198507
\(643\) 32.3813 1.27699 0.638496 0.769625i \(-0.279557\pi\)
0.638496 + 0.769625i \(0.279557\pi\)
\(644\) 3.71716 0.146477
\(645\) 3.73410 0.147030
\(646\) −2.89579 −0.113933
\(647\) −33.6185 −1.32168 −0.660839 0.750527i \(-0.729800\pi\)
−0.660839 + 0.750527i \(0.729800\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 9.08585 0.356651
\(650\) 4.12173 0.161668
\(651\) −2.83663 −0.111176
\(652\) −9.61838 −0.376685
\(653\) 7.01542 0.274535 0.137267 0.990534i \(-0.456168\pi\)
0.137267 + 0.990534i \(0.456168\pi\)
\(654\) 17.7539 0.694233
\(655\) −3.87418 −0.151377
\(656\) −7.48219 −0.292131
\(657\) 0.810762 0.0316308
\(658\) 0.459538 0.0179147
\(659\) 19.1360 0.745433 0.372716 0.927945i \(-0.378426\pi\)
0.372716 + 0.927945i \(0.378426\pi\)
\(660\) −4.40759 −0.171565
\(661\) −24.9601 −0.970836 −0.485418 0.874282i \(-0.661333\pi\)
−0.485418 + 0.874282i \(0.661333\pi\)
\(662\) −13.2952 −0.516731
\(663\) 3.60442 0.139984
\(664\) 5.41646 0.210200
\(665\) −0.596837 −0.0231443
\(666\) −1.63083 −0.0631935
\(667\) 14.6061 0.565549
\(668\) −25.2414 −0.976621
\(669\) 19.7800 0.764739
\(670\) 5.41287 0.209117
\(671\) 69.7648 2.69324
\(672\) −0.792704 −0.0305792
\(673\) 30.0790 1.15946 0.579731 0.814808i \(-0.303158\pi\)
0.579731 + 0.814808i \(0.303158\pi\)
\(674\) 1.04274 0.0401647
\(675\) 4.12173 0.158646
\(676\) 1.00000 0.0384615
\(677\) 15.5954 0.599378 0.299689 0.954037i \(-0.403117\pi\)
0.299689 + 0.954037i \(0.403117\pi\)
\(678\) 8.02786 0.308308
\(679\) −8.27183 −0.317444
\(680\) −3.37791 −0.129537
\(681\) −13.3566 −0.511825
\(682\) −16.8299 −0.644448
\(683\) −29.5061 −1.12902 −0.564509 0.825427i \(-0.690935\pi\)
−0.564509 + 0.825427i \(0.690935\pi\)
\(684\) −0.803399 −0.0307187
\(685\) 16.7654 0.640575
\(686\) −10.5997 −0.404700
\(687\) 1.87870 0.0716770
\(688\) 3.98449 0.151907
\(689\) 5.61866 0.214054
\(690\) 4.39454 0.167297
\(691\) 40.5561 1.54283 0.771414 0.636333i \(-0.219550\pi\)
0.771414 + 0.636333i \(0.219550\pi\)
\(692\) 0.222644 0.00846364
\(693\) 3.72820 0.141623
\(694\) −25.2951 −0.960189
\(695\) 16.2554 0.616602
\(696\) −3.11482 −0.118067
\(697\) 26.9689 1.02152
\(698\) −17.3267 −0.655824
\(699\) −16.0079 −0.605474
\(700\) 3.26731 0.123493
\(701\) 24.4791 0.924564 0.462282 0.886733i \(-0.347031\pi\)
0.462282 + 0.886733i \(0.347031\pi\)
\(702\) 1.00000 0.0377426
\(703\) −1.31021 −0.0494155
\(704\) −4.70314 −0.177256
\(705\) 0.543280 0.0204611
\(706\) 16.7368 0.629899
\(707\) 1.11921 0.0420922
\(708\) 1.93187 0.0726041
\(709\) 29.0564 1.09124 0.545618 0.838034i \(-0.316295\pi\)
0.545618 + 0.838034i \(0.316295\pi\)
\(710\) −5.59068 −0.209815
\(711\) 6.43093 0.241179
\(712\) 18.2668 0.684579
\(713\) 16.7800 0.628417
\(714\) 2.85724 0.106929
\(715\) 4.40759 0.164835
\(716\) 25.3993 0.949217
\(717\) −17.4394 −0.651286
\(718\) −6.34619 −0.236838
\(719\) 38.6846 1.44269 0.721347 0.692574i \(-0.243523\pi\)
0.721347 + 0.692574i \(0.243523\pi\)
\(720\) −0.937159 −0.0349259
\(721\) 0.792704 0.0295218
\(722\) 18.3545 0.683086
\(723\) 6.56601 0.244193
\(724\) −6.58007 −0.244546
\(725\) 12.8385 0.476808
\(726\) 11.1196 0.412685
\(727\) 21.4901 0.797024 0.398512 0.917163i \(-0.369527\pi\)
0.398512 + 0.917163i \(0.369527\pi\)
\(728\) 0.792704 0.0293796
\(729\) 1.00000 0.0370370
\(730\) 0.759812 0.0281219
\(731\) −14.3618 −0.531189
\(732\) 14.8337 0.548268
\(733\) −33.9224 −1.25295 −0.626475 0.779441i \(-0.715503\pi\)
−0.626475 + 0.779441i \(0.715503\pi\)
\(734\) −30.8119 −1.13729
\(735\) −5.97122 −0.220252
\(736\) 4.68922 0.172847
\(737\) −27.1645 −1.00062
\(738\) 7.48219 0.275423
\(739\) 3.01425 0.110881 0.0554406 0.998462i \(-0.482344\pi\)
0.0554406 + 0.998462i \(0.482344\pi\)
\(740\) −1.52835 −0.0561832
\(741\) 0.803399 0.0295136
\(742\) 4.45393 0.163509
\(743\) −6.72363 −0.246666 −0.123333 0.992365i \(-0.539358\pi\)
−0.123333 + 0.992365i \(0.539358\pi\)
\(744\) −3.57843 −0.131191
\(745\) 8.98751 0.329277
\(746\) 26.3688 0.965431
\(747\) −5.41646 −0.198178
\(748\) 16.9521 0.619830
\(749\) −0.398707 −0.0145684
\(750\) 8.54851 0.312148
\(751\) 45.2545 1.65136 0.825679 0.564140i \(-0.190792\pi\)
0.825679 + 0.564140i \(0.190792\pi\)
\(752\) 0.579710 0.0211398
\(753\) −18.8493 −0.686906
\(754\) 3.11482 0.113435
\(755\) −8.37425 −0.304770
\(756\) 0.792704 0.0288304
\(757\) 8.39311 0.305053 0.152526 0.988299i \(-0.451259\pi\)
0.152526 + 0.988299i \(0.451259\pi\)
\(758\) −9.77930 −0.355200
\(759\) −22.0541 −0.800512
\(760\) −0.752913 −0.0273110
\(761\) 14.2758 0.517496 0.258748 0.965945i \(-0.416690\pi\)
0.258748 + 0.965945i \(0.416690\pi\)
\(762\) −8.03716 −0.291156
\(763\) −14.0736 −0.509499
\(764\) 11.0853 0.401052
\(765\) 3.37791 0.122129
\(766\) 32.4570 1.17272
\(767\) −1.93187 −0.0697557
\(768\) −1.00000 −0.0360844
\(769\) −29.7150 −1.07155 −0.535776 0.844360i \(-0.679981\pi\)
−0.535776 + 0.844360i \(0.679981\pi\)
\(770\) 3.49392 0.125912
\(771\) 15.0916 0.543511
\(772\) 6.80068 0.244762
\(773\) −32.4335 −1.16655 −0.583277 0.812274i \(-0.698230\pi\)
−0.583277 + 0.812274i \(0.698230\pi\)
\(774\) −3.98449 −0.143220
\(775\) 14.7493 0.529811
\(776\) −10.4350 −0.374593
\(777\) 1.29277 0.0463778
\(778\) −7.67508 −0.275165
\(779\) 6.01119 0.215373
\(780\) 0.937159 0.0335557
\(781\) 28.0569 1.00396
\(782\) −16.9019 −0.604411
\(783\) 3.11482 0.111315
\(784\) −6.37162 −0.227558
\(785\) 17.7435 0.633293
\(786\) 4.13397 0.147454
\(787\) 7.44005 0.265209 0.132605 0.991169i \(-0.457666\pi\)
0.132605 + 0.991169i \(0.457666\pi\)
\(788\) −5.08227 −0.181048
\(789\) −2.51843 −0.0896584
\(790\) 6.02680 0.214424
\(791\) −6.36372 −0.226268
\(792\) 4.70314 0.167119
\(793\) −14.8337 −0.526759
\(794\) 7.64131 0.271180
\(795\) 5.26557 0.186751
\(796\) 15.9413 0.565024
\(797\) 23.0552 0.816658 0.408329 0.912835i \(-0.366112\pi\)
0.408329 + 0.912835i \(0.366112\pi\)
\(798\) 0.636858 0.0225445
\(799\) −2.08951 −0.0739217
\(800\) 4.12173 0.145725
\(801\) −18.2668 −0.645427
\(802\) 12.6513 0.446734
\(803\) −3.81313 −0.134562
\(804\) −5.77582 −0.203698
\(805\) −3.48357 −0.122780
\(806\) 3.57843 0.126045
\(807\) 26.3178 0.926430
\(808\) 1.41189 0.0496700
\(809\) −24.4161 −0.858423 −0.429211 0.903204i \(-0.641208\pi\)
−0.429211 + 0.903204i \(0.641208\pi\)
\(810\) 0.937159 0.0329284
\(811\) 1.52704 0.0536217 0.0268108 0.999641i \(-0.491465\pi\)
0.0268108 + 0.999641i \(0.491465\pi\)
\(812\) 2.46913 0.0866495
\(813\) −6.11955 −0.214622
\(814\) 7.67004 0.268835
\(815\) 9.01395 0.315745
\(816\) 3.60442 0.126180
\(817\) −3.20114 −0.111994
\(818\) −24.4350 −0.854348
\(819\) −0.792704 −0.0276993
\(820\) 7.01200 0.244870
\(821\) 8.57849 0.299392 0.149696 0.988732i \(-0.452171\pi\)
0.149696 + 0.988732i \(0.452171\pi\)
\(822\) −17.8896 −0.623973
\(823\) −2.61365 −0.0911059 −0.0455530 0.998962i \(-0.514505\pi\)
−0.0455530 + 0.998962i \(0.514505\pi\)
\(824\) 1.00000 0.0348367
\(825\) −19.3851 −0.674903
\(826\) −1.53140 −0.0532842
\(827\) −17.7252 −0.616366 −0.308183 0.951327i \(-0.599721\pi\)
−0.308183 + 0.951327i \(0.599721\pi\)
\(828\) −4.68922 −0.162962
\(829\) 45.1815 1.56922 0.784610 0.619990i \(-0.212863\pi\)
0.784610 + 0.619990i \(0.212863\pi\)
\(830\) −5.07609 −0.176194
\(831\) 31.2379 1.08363
\(832\) 1.00000 0.0346688
\(833\) 22.9660 0.795724
\(834\) −17.3454 −0.600622
\(835\) 23.6552 0.818623
\(836\) 3.77850 0.130682
\(837\) 3.57843 0.123689
\(838\) 23.6809 0.818043
\(839\) −52.4895 −1.81214 −0.906069 0.423129i \(-0.860932\pi\)
−0.906069 + 0.423129i \(0.860932\pi\)
\(840\) 0.742890 0.0256321
\(841\) −19.2979 −0.665445
\(842\) 12.5451 0.432333
\(843\) 18.1874 0.626406
\(844\) 10.7284 0.369285
\(845\) −0.937159 −0.0322392
\(846\) −0.579710 −0.0199308
\(847\) −8.81451 −0.302870
\(848\) 5.61866 0.192945
\(849\) −1.52975 −0.0525009
\(850\) −14.8564 −0.509572
\(851\) −7.64733 −0.262147
\(852\) 5.96557 0.204377
\(853\) −41.2017 −1.41072 −0.705359 0.708850i \(-0.749214\pi\)
−0.705359 + 0.708850i \(0.749214\pi\)
\(854\) −11.7587 −0.402374
\(855\) 0.752913 0.0257491
\(856\) −0.502970 −0.0171912
\(857\) −35.6191 −1.21673 −0.608363 0.793659i \(-0.708173\pi\)
−0.608363 + 0.793659i \(0.708173\pi\)
\(858\) −4.70314 −0.160563
\(859\) 7.62712 0.260234 0.130117 0.991499i \(-0.458465\pi\)
0.130117 + 0.991499i \(0.458465\pi\)
\(860\) −3.73410 −0.127332
\(861\) −5.93116 −0.202133
\(862\) 18.7049 0.637092
\(863\) −4.07478 −0.138707 −0.0693536 0.997592i \(-0.522094\pi\)
−0.0693536 + 0.997592i \(0.522094\pi\)
\(864\) 1.00000 0.0340207
\(865\) −0.208653 −0.00709440
\(866\) −32.1566 −1.09272
\(867\) 4.00818 0.136125
\(868\) 2.83663 0.0962816
\(869\) −30.2456 −1.02601
\(870\) 2.91908 0.0989661
\(871\) 5.77582 0.195706
\(872\) −17.7539 −0.601224
\(873\) 10.4350 0.353170
\(874\) −3.76732 −0.127431
\(875\) −6.77644 −0.229085
\(876\) −0.810762 −0.0273931
\(877\) −1.87904 −0.0634506 −0.0317253 0.999497i \(-0.510100\pi\)
−0.0317253 + 0.999497i \(0.510100\pi\)
\(878\) −31.5854 −1.06596
\(879\) 9.77976 0.329863
\(880\) 4.40759 0.148580
\(881\) −14.0026 −0.471759 −0.235879 0.971782i \(-0.575797\pi\)
−0.235879 + 0.971782i \(0.575797\pi\)
\(882\) 6.37162 0.214544
\(883\) −17.2474 −0.580422 −0.290211 0.956963i \(-0.593726\pi\)
−0.290211 + 0.956963i \(0.593726\pi\)
\(884\) −3.60442 −0.121230
\(885\) −1.81047 −0.0608582
\(886\) −26.8464 −0.901923
\(887\) 1.85975 0.0624443 0.0312222 0.999512i \(-0.490060\pi\)
0.0312222 + 0.999512i \(0.490060\pi\)
\(888\) 1.63083 0.0547272
\(889\) 6.37109 0.213679
\(890\) −17.1189 −0.573828
\(891\) −4.70314 −0.157561
\(892\) −19.7800 −0.662284
\(893\) −0.465738 −0.0155853
\(894\) −9.59017 −0.320743
\(895\) −23.8032 −0.795653
\(896\) 0.792704 0.0264824
\(897\) 4.68922 0.156568
\(898\) 1.58098 0.0527578
\(899\) 11.1462 0.371745
\(900\) −4.12173 −0.137391
\(901\) −20.2520 −0.674691
\(902\) −35.1898 −1.17169
\(903\) 3.15852 0.105109
\(904\) −8.02786 −0.267003
\(905\) 6.16657 0.204984
\(906\) 8.93579 0.296872
\(907\) 31.3348 1.04046 0.520228 0.854028i \(-0.325847\pi\)
0.520228 + 0.854028i \(0.325847\pi\)
\(908\) 13.3566 0.443254
\(909\) −1.41189 −0.0468294
\(910\) −0.742890 −0.0246265
\(911\) −5.22797 −0.173210 −0.0866051 0.996243i \(-0.527602\pi\)
−0.0866051 + 0.996243i \(0.527602\pi\)
\(912\) 0.803399 0.0266032
\(913\) 25.4744 0.843080
\(914\) 13.8693 0.458755
\(915\) −13.9015 −0.459569
\(916\) −1.87870 −0.0620741
\(917\) −3.27701 −0.108216
\(918\) −3.60442 −0.118963
\(919\) 39.1606 1.29179 0.645894 0.763427i \(-0.276485\pi\)
0.645894 + 0.763427i \(0.276485\pi\)
\(920\) −4.39454 −0.144884
\(921\) 17.1789 0.566064
\(922\) −2.70162 −0.0889732
\(923\) −5.96557 −0.196359
\(924\) −3.72820 −0.122649
\(925\) −6.72186 −0.221013
\(926\) 30.6401 1.00689
\(927\) −1.00000 −0.0328443
\(928\) 3.11482 0.102249
\(929\) 27.1936 0.892194 0.446097 0.894985i \(-0.352814\pi\)
0.446097 + 0.894985i \(0.352814\pi\)
\(930\) 3.35355 0.109967
\(931\) 5.11896 0.167767
\(932\) 16.0079 0.524356
\(933\) −28.7706 −0.941907
\(934\) 20.2536 0.662717
\(935\) −15.8868 −0.519554
\(936\) −1.00000 −0.0326860
\(937\) 30.3989 0.993089 0.496545 0.868011i \(-0.334602\pi\)
0.496545 + 0.868011i \(0.334602\pi\)
\(938\) 4.57852 0.149494
\(939\) −26.0073 −0.848716
\(940\) −0.543280 −0.0177198
\(941\) −38.1436 −1.24345 −0.621723 0.783237i \(-0.713567\pi\)
−0.621723 + 0.783237i \(0.713567\pi\)
\(942\) −18.9333 −0.616880
\(943\) 35.0856 1.14255
\(944\) −1.93187 −0.0628770
\(945\) −0.742890 −0.0241662
\(946\) 18.7396 0.609278
\(947\) −18.8645 −0.613014 −0.306507 0.951868i \(-0.599160\pi\)
−0.306507 + 0.951868i \(0.599160\pi\)
\(948\) −6.43093 −0.208867
\(949\) 0.810762 0.0263184
\(950\) −3.31140 −0.107436
\(951\) 0.494041 0.0160204
\(952\) −2.85724 −0.0926035
\(953\) −22.5227 −0.729582 −0.364791 0.931089i \(-0.618860\pi\)
−0.364791 + 0.931089i \(0.618860\pi\)
\(954\) −5.61866 −0.181911
\(955\) −10.3887 −0.336170
\(956\) 17.4394 0.564031
\(957\) −14.6494 −0.473549
\(958\) −20.6640 −0.667623
\(959\) 14.1812 0.457935
\(960\) 0.937159 0.0302467
\(961\) −18.1949 −0.586931
\(962\) −1.63083 −0.0525801
\(963\) 0.502970 0.0162080
\(964\) −6.56601 −0.211477
\(965\) −6.37332 −0.205164
\(966\) 3.71716 0.119598
\(967\) −38.8121 −1.24811 −0.624057 0.781379i \(-0.714517\pi\)
−0.624057 + 0.781379i \(0.714517\pi\)
\(968\) −11.1196 −0.357396
\(969\) −2.89579 −0.0930261
\(970\) 9.77921 0.313992
\(971\) 30.7021 0.985276 0.492638 0.870234i \(-0.336033\pi\)
0.492638 + 0.870234i \(0.336033\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 13.7498 0.440797
\(974\) 21.3896 0.685368
\(975\) 4.12173 0.132001
\(976\) −14.8337 −0.474814
\(977\) −28.5714 −0.914081 −0.457040 0.889446i \(-0.651091\pi\)
−0.457040 + 0.889446i \(0.651091\pi\)
\(978\) −9.61838 −0.307562
\(979\) 85.9116 2.74575
\(980\) 5.97122 0.190744
\(981\) 17.7539 0.566839
\(982\) 42.5182 1.35681
\(983\) 32.6252 1.04058 0.520291 0.853989i \(-0.325823\pi\)
0.520291 + 0.853989i \(0.325823\pi\)
\(984\) −7.48219 −0.238524
\(985\) 4.76289 0.151758
\(986\) −11.2271 −0.357544
\(987\) 0.459538 0.0146273
\(988\) −0.803399 −0.0255595
\(989\) −18.6842 −0.594121
\(990\) −4.40759 −0.140082
\(991\) −13.3840 −0.425156 −0.212578 0.977144i \(-0.568186\pi\)
−0.212578 + 0.977144i \(0.568186\pi\)
\(992\) 3.57843 0.113615
\(993\) −13.2952 −0.421909
\(994\) −4.72893 −0.149993
\(995\) −14.9395 −0.473615
\(996\) 5.41646 0.171627
\(997\) −47.8225 −1.51455 −0.757276 0.653094i \(-0.773470\pi\)
−0.757276 + 0.653094i \(0.773470\pi\)
\(998\) −10.6374 −0.336722
\(999\) −1.63083 −0.0515973
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 8034.2.a.z.1.6 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.6 14 1.1 even 1 trivial