Properties

Label 2667.2.a.j.1.4
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
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 1.4
Root \(-1.52532\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.246202 q^{2} +1.00000 q^{3} -1.93938 q^{4} -0.318209 q^{5} +0.246202 q^{6} +1.00000 q^{7} -0.969884 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.246202 q^{2} +1.00000 q^{3} -1.93938 q^{4} -0.318209 q^{5} +0.246202 q^{6} +1.00000 q^{7} -0.969884 q^{8} +1.00000 q^{9} -0.0783436 q^{10} +2.79943 q^{11} -1.93938 q^{12} -6.49995 q^{13} +0.246202 q^{14} -0.318209 q^{15} +3.63998 q^{16} -1.33136 q^{17} +0.246202 q^{18} +4.36328 q^{19} +0.617130 q^{20} +1.00000 q^{21} +0.689226 q^{22} -5.29356 q^{23} -0.969884 q^{24} -4.89874 q^{25} -1.60030 q^{26} +1.00000 q^{27} -1.93938 q^{28} -2.35110 q^{29} -0.0783436 q^{30} -4.76449 q^{31} +2.83594 q^{32} +2.79943 q^{33} -0.327782 q^{34} -0.318209 q^{35} -1.93938 q^{36} +1.06889 q^{37} +1.07425 q^{38} -6.49995 q^{39} +0.308626 q^{40} -1.46345 q^{41} +0.246202 q^{42} +8.04774 q^{43} -5.42918 q^{44} -0.318209 q^{45} -1.30329 q^{46} -7.16642 q^{47} +3.63998 q^{48} +1.00000 q^{49} -1.20608 q^{50} -1.33136 q^{51} +12.6059 q^{52} +9.12591 q^{53} +0.246202 q^{54} -0.890805 q^{55} -0.969884 q^{56} +4.36328 q^{57} -0.578846 q^{58} -5.02542 q^{59} +0.617130 q^{60} -2.48901 q^{61} -1.17303 q^{62} +1.00000 q^{63} -6.58175 q^{64} +2.06834 q^{65} +0.689226 q^{66} +0.549822 q^{67} +2.58201 q^{68} -5.29356 q^{69} -0.0783436 q^{70} -11.9210 q^{71} -0.969884 q^{72} -13.8588 q^{73} +0.263163 q^{74} -4.89874 q^{75} -8.46208 q^{76} +2.79943 q^{77} -1.60030 q^{78} -1.49518 q^{79} -1.15827 q^{80} +1.00000 q^{81} -0.360305 q^{82} -17.1283 q^{83} -1.93938 q^{84} +0.423650 q^{85} +1.98137 q^{86} -2.35110 q^{87} -2.71513 q^{88} +12.8927 q^{89} -0.0783436 q^{90} -6.49995 q^{91} +10.2663 q^{92} -4.76449 q^{93} -1.76439 q^{94} -1.38844 q^{95} +2.83594 q^{96} -7.20075 q^{97} +0.246202 q^{98} +2.79943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.246202 0.174091 0.0870455 0.996204i \(-0.472257\pi\)
0.0870455 + 0.996204i \(0.472257\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.93938 −0.969692
\(5\) −0.318209 −0.142307 −0.0711537 0.997465i \(-0.522668\pi\)
−0.0711537 + 0.997465i \(0.522668\pi\)
\(6\) 0.246202 0.100511
\(7\) 1.00000 0.377964
\(8\) −0.969884 −0.342906
\(9\) 1.00000 0.333333
\(10\) −0.0783436 −0.0247744
\(11\) 2.79943 0.844061 0.422031 0.906582i \(-0.361317\pi\)
0.422031 + 0.906582i \(0.361317\pi\)
\(12\) −1.93938 −0.559852
\(13\) −6.49995 −1.80276 −0.901381 0.433027i \(-0.857445\pi\)
−0.901381 + 0.433027i \(0.857445\pi\)
\(14\) 0.246202 0.0658002
\(15\) −0.318209 −0.0821612
\(16\) 3.63998 0.909996
\(17\) −1.33136 −0.322901 −0.161451 0.986881i \(-0.551617\pi\)
−0.161451 + 0.986881i \(0.551617\pi\)
\(18\) 0.246202 0.0580303
\(19\) 4.36328 1.00101 0.500503 0.865735i \(-0.333149\pi\)
0.500503 + 0.865735i \(0.333149\pi\)
\(20\) 0.617130 0.137994
\(21\) 1.00000 0.218218
\(22\) 0.689226 0.146943
\(23\) −5.29356 −1.10378 −0.551892 0.833915i \(-0.686094\pi\)
−0.551892 + 0.833915i \(0.686094\pi\)
\(24\) −0.969884 −0.197977
\(25\) −4.89874 −0.979749
\(26\) −1.60030 −0.313845
\(27\) 1.00000 0.192450
\(28\) −1.93938 −0.366509
\(29\) −2.35110 −0.436589 −0.218295 0.975883i \(-0.570049\pi\)
−0.218295 + 0.975883i \(0.570049\pi\)
\(30\) −0.0783436 −0.0143035
\(31\) −4.76449 −0.855729 −0.427864 0.903843i \(-0.640734\pi\)
−0.427864 + 0.903843i \(0.640734\pi\)
\(32\) 2.83594 0.501328
\(33\) 2.79943 0.487319
\(34\) −0.327782 −0.0562142
\(35\) −0.318209 −0.0537871
\(36\) −1.93938 −0.323231
\(37\) 1.06889 0.175725 0.0878624 0.996133i \(-0.471996\pi\)
0.0878624 + 0.996133i \(0.471996\pi\)
\(38\) 1.07425 0.174266
\(39\) −6.49995 −1.04082
\(40\) 0.308626 0.0487980
\(41\) −1.46345 −0.228553 −0.114277 0.993449i \(-0.536455\pi\)
−0.114277 + 0.993449i \(0.536455\pi\)
\(42\) 0.246202 0.0379898
\(43\) 8.04774 1.22727 0.613635 0.789590i \(-0.289707\pi\)
0.613635 + 0.789590i \(0.289707\pi\)
\(44\) −5.42918 −0.818480
\(45\) −0.318209 −0.0474358
\(46\) −1.30329 −0.192159
\(47\) −7.16642 −1.04533 −0.522665 0.852538i \(-0.675062\pi\)
−0.522665 + 0.852538i \(0.675062\pi\)
\(48\) 3.63998 0.525386
\(49\) 1.00000 0.142857
\(50\) −1.20608 −0.170565
\(51\) −1.33136 −0.186427
\(52\) 12.6059 1.74812
\(53\) 9.12591 1.25354 0.626770 0.779204i \(-0.284377\pi\)
0.626770 + 0.779204i \(0.284377\pi\)
\(54\) 0.246202 0.0335038
\(55\) −0.890805 −0.120116
\(56\) −0.969884 −0.129606
\(57\) 4.36328 0.577931
\(58\) −0.578846 −0.0760063
\(59\) −5.02542 −0.654255 −0.327127 0.944980i \(-0.606081\pi\)
−0.327127 + 0.944980i \(0.606081\pi\)
\(60\) 0.617130 0.0796711
\(61\) −2.48901 −0.318685 −0.159343 0.987223i \(-0.550937\pi\)
−0.159343 + 0.987223i \(0.550937\pi\)
\(62\) −1.17303 −0.148975
\(63\) 1.00000 0.125988
\(64\) −6.58175 −0.822719
\(65\) 2.06834 0.256546
\(66\) 0.689226 0.0848378
\(67\) 0.549822 0.0671714 0.0335857 0.999436i \(-0.489307\pi\)
0.0335857 + 0.999436i \(0.489307\pi\)
\(68\) 2.58201 0.313115
\(69\) −5.29356 −0.637270
\(70\) −0.0783436 −0.00936386
\(71\) −11.9210 −1.41476 −0.707380 0.706833i \(-0.750123\pi\)
−0.707380 + 0.706833i \(0.750123\pi\)
\(72\) −0.969884 −0.114302
\(73\) −13.8588 −1.62205 −0.811027 0.585008i \(-0.801091\pi\)
−0.811027 + 0.585008i \(0.801091\pi\)
\(74\) 0.263163 0.0305921
\(75\) −4.89874 −0.565658
\(76\) −8.46208 −0.970667
\(77\) 2.79943 0.319025
\(78\) −1.60030 −0.181198
\(79\) −1.49518 −0.168221 −0.0841106 0.996456i \(-0.526805\pi\)
−0.0841106 + 0.996456i \(0.526805\pi\)
\(80\) −1.15827 −0.129499
\(81\) 1.00000 0.111111
\(82\) −0.360305 −0.0397891
\(83\) −17.1283 −1.88008 −0.940039 0.341067i \(-0.889212\pi\)
−0.940039 + 0.341067i \(0.889212\pi\)
\(84\) −1.93938 −0.211604
\(85\) 0.423650 0.0459512
\(86\) 1.98137 0.213657
\(87\) −2.35110 −0.252065
\(88\) −2.71513 −0.289433
\(89\) 12.8927 1.36662 0.683309 0.730129i \(-0.260540\pi\)
0.683309 + 0.730129i \(0.260540\pi\)
\(90\) −0.0783436 −0.00825814
\(91\) −6.49995 −0.681380
\(92\) 10.2663 1.07033
\(93\) −4.76449 −0.494055
\(94\) −1.76439 −0.181983
\(95\) −1.38844 −0.142450
\(96\) 2.83594 0.289442
\(97\) −7.20075 −0.731125 −0.365563 0.930787i \(-0.619123\pi\)
−0.365563 + 0.930787i \(0.619123\pi\)
\(98\) 0.246202 0.0248701
\(99\) 2.79943 0.281354
\(100\) 9.50055 0.950055
\(101\) −0.894063 −0.0889625 −0.0444813 0.999010i \(-0.514164\pi\)
−0.0444813 + 0.999010i \(0.514164\pi\)
\(102\) −0.327782 −0.0324553
\(103\) 10.2130 1.00631 0.503157 0.864195i \(-0.332172\pi\)
0.503157 + 0.864195i \(0.332172\pi\)
\(104\) 6.30420 0.618177
\(105\) −0.318209 −0.0310540
\(106\) 2.24682 0.218230
\(107\) 1.98724 0.192114 0.0960569 0.995376i \(-0.469377\pi\)
0.0960569 + 0.995376i \(0.469377\pi\)
\(108\) −1.93938 −0.186617
\(109\) −18.2252 −1.74566 −0.872831 0.488022i \(-0.837718\pi\)
−0.872831 + 0.488022i \(0.837718\pi\)
\(110\) −0.219318 −0.0209111
\(111\) 1.06889 0.101455
\(112\) 3.63998 0.343946
\(113\) −6.23590 −0.586624 −0.293312 0.956017i \(-0.594757\pi\)
−0.293312 + 0.956017i \(0.594757\pi\)
\(114\) 1.07425 0.100613
\(115\) 1.68446 0.157077
\(116\) 4.55970 0.423357
\(117\) −6.49995 −0.600921
\(118\) −1.23727 −0.113900
\(119\) −1.33136 −0.122045
\(120\) 0.308626 0.0281735
\(121\) −3.16317 −0.287561
\(122\) −0.612799 −0.0554802
\(123\) −1.46345 −0.131955
\(124\) 9.24019 0.829793
\(125\) 3.14987 0.281733
\(126\) 0.246202 0.0219334
\(127\) −1.00000 −0.0887357
\(128\) −7.29232 −0.644556
\(129\) 8.04774 0.708564
\(130\) 0.509230 0.0446624
\(131\) −18.7890 −1.64160 −0.820800 0.571215i \(-0.806472\pi\)
−0.820800 + 0.571215i \(0.806472\pi\)
\(132\) −5.42918 −0.472549
\(133\) 4.36328 0.378344
\(134\) 0.135367 0.0116939
\(135\) −0.318209 −0.0273871
\(136\) 1.29126 0.110725
\(137\) 20.9329 1.78842 0.894209 0.447649i \(-0.147739\pi\)
0.894209 + 0.447649i \(0.147739\pi\)
\(138\) −1.30329 −0.110943
\(139\) −5.77630 −0.489940 −0.244970 0.969531i \(-0.578778\pi\)
−0.244970 + 0.969531i \(0.578778\pi\)
\(140\) 0.617130 0.0521570
\(141\) −7.16642 −0.603522
\(142\) −2.93497 −0.246297
\(143\) −18.1962 −1.52164
\(144\) 3.63998 0.303332
\(145\) 0.748143 0.0621299
\(146\) −3.41207 −0.282385
\(147\) 1.00000 0.0824786
\(148\) −2.07299 −0.170399
\(149\) −5.65638 −0.463389 −0.231694 0.972789i \(-0.574427\pi\)
−0.231694 + 0.972789i \(0.574427\pi\)
\(150\) −1.20608 −0.0984760
\(151\) −2.50255 −0.203655 −0.101827 0.994802i \(-0.532469\pi\)
−0.101827 + 0.994802i \(0.532469\pi\)
\(152\) −4.23188 −0.343250
\(153\) −1.33136 −0.107634
\(154\) 0.689226 0.0555394
\(155\) 1.51610 0.121776
\(156\) 12.6059 1.00928
\(157\) −14.3393 −1.14440 −0.572201 0.820113i \(-0.693910\pi\)
−0.572201 + 0.820113i \(0.693910\pi\)
\(158\) −0.368117 −0.0292858
\(159\) 9.12591 0.723731
\(160\) −0.902421 −0.0713426
\(161\) −5.29356 −0.417191
\(162\) 0.246202 0.0193434
\(163\) −16.7787 −1.31421 −0.657105 0.753799i \(-0.728219\pi\)
−0.657105 + 0.753799i \(0.728219\pi\)
\(164\) 2.83820 0.221626
\(165\) −0.890805 −0.0693491
\(166\) −4.21703 −0.327305
\(167\) −10.9980 −0.851048 −0.425524 0.904947i \(-0.639910\pi\)
−0.425524 + 0.904947i \(0.639910\pi\)
\(168\) −0.969884 −0.0748282
\(169\) 29.2493 2.24995
\(170\) 0.104303 0.00799970
\(171\) 4.36328 0.333668
\(172\) −15.6077 −1.19007
\(173\) 14.9307 1.13516 0.567579 0.823319i \(-0.307880\pi\)
0.567579 + 0.823319i \(0.307880\pi\)
\(174\) −0.578846 −0.0438822
\(175\) −4.89874 −0.370310
\(176\) 10.1899 0.768092
\(177\) −5.02542 −0.377734
\(178\) 3.17419 0.237916
\(179\) 10.5989 0.792200 0.396100 0.918207i \(-0.370363\pi\)
0.396100 + 0.918207i \(0.370363\pi\)
\(180\) 0.617130 0.0459981
\(181\) 14.6508 1.08898 0.544491 0.838766i \(-0.316723\pi\)
0.544491 + 0.838766i \(0.316723\pi\)
\(182\) −1.60030 −0.118622
\(183\) −2.48901 −0.183993
\(184\) 5.13414 0.378494
\(185\) −0.340131 −0.0250069
\(186\) −1.17303 −0.0860105
\(187\) −3.72704 −0.272548
\(188\) 13.8985 1.01365
\(189\) 1.00000 0.0727393
\(190\) −0.341835 −0.0247993
\(191\) −17.6738 −1.27883 −0.639415 0.768862i \(-0.720823\pi\)
−0.639415 + 0.768862i \(0.720823\pi\)
\(192\) −6.58175 −0.474997
\(193\) −13.3112 −0.958158 −0.479079 0.877772i \(-0.659029\pi\)
−0.479079 + 0.877772i \(0.659029\pi\)
\(194\) −1.77284 −0.127282
\(195\) 2.06834 0.148117
\(196\) −1.93938 −0.138527
\(197\) 3.10847 0.221469 0.110735 0.993850i \(-0.464680\pi\)
0.110735 + 0.993850i \(0.464680\pi\)
\(198\) 0.689226 0.0489812
\(199\) −21.0921 −1.49518 −0.747590 0.664160i \(-0.768789\pi\)
−0.747590 + 0.664160i \(0.768789\pi\)
\(200\) 4.75121 0.335961
\(201\) 0.549822 0.0387814
\(202\) −0.220120 −0.0154876
\(203\) −2.35110 −0.165015
\(204\) 2.58201 0.180777
\(205\) 0.465684 0.0325248
\(206\) 2.51445 0.175190
\(207\) −5.29356 −0.367928
\(208\) −23.6597 −1.64051
\(209\) 12.2147 0.844910
\(210\) −0.0783436 −0.00540622
\(211\) 3.11651 0.214549 0.107275 0.994229i \(-0.465788\pi\)
0.107275 + 0.994229i \(0.465788\pi\)
\(212\) −17.6986 −1.21555
\(213\) −11.9210 −0.816812
\(214\) 0.489262 0.0334453
\(215\) −2.56086 −0.174649
\(216\) −0.969884 −0.0659922
\(217\) −4.76449 −0.323435
\(218\) −4.48709 −0.303904
\(219\) −13.8588 −0.936494
\(220\) 1.72761 0.116476
\(221\) 8.65375 0.582114
\(222\) 0.263163 0.0176624
\(223\) −14.2513 −0.954337 −0.477169 0.878812i \(-0.658337\pi\)
−0.477169 + 0.878812i \(0.658337\pi\)
\(224\) 2.83594 0.189484
\(225\) −4.89874 −0.326583
\(226\) −1.53529 −0.102126
\(227\) 14.3103 0.949808 0.474904 0.880038i \(-0.342483\pi\)
0.474904 + 0.880038i \(0.342483\pi\)
\(228\) −8.46208 −0.560415
\(229\) 19.1899 1.26810 0.634051 0.773291i \(-0.281391\pi\)
0.634051 + 0.773291i \(0.281391\pi\)
\(230\) 0.414717 0.0273456
\(231\) 2.79943 0.184189
\(232\) 2.28030 0.149709
\(233\) −11.6209 −0.761310 −0.380655 0.924717i \(-0.624301\pi\)
−0.380655 + 0.924717i \(0.624301\pi\)
\(234\) −1.60030 −0.104615
\(235\) 2.28042 0.148758
\(236\) 9.74623 0.634426
\(237\) −1.49518 −0.0971226
\(238\) −0.327782 −0.0212470
\(239\) 0.298510 0.0193090 0.00965449 0.999953i \(-0.496927\pi\)
0.00965449 + 0.999953i \(0.496927\pi\)
\(240\) −1.15827 −0.0747663
\(241\) 18.4344 1.18747 0.593734 0.804662i \(-0.297653\pi\)
0.593734 + 0.804662i \(0.297653\pi\)
\(242\) −0.778778 −0.0500617
\(243\) 1.00000 0.0641500
\(244\) 4.82715 0.309027
\(245\) −0.318209 −0.0203296
\(246\) −0.360305 −0.0229722
\(247\) −28.3611 −1.80457
\(248\) 4.62101 0.293434
\(249\) −17.1283 −1.08546
\(250\) 0.775504 0.0490472
\(251\) 27.6399 1.74462 0.872308 0.488956i \(-0.162622\pi\)
0.872308 + 0.488956i \(0.162622\pi\)
\(252\) −1.93938 −0.122170
\(253\) −14.8190 −0.931662
\(254\) −0.246202 −0.0154481
\(255\) 0.423650 0.0265300
\(256\) 11.3681 0.710508
\(257\) 2.39616 0.149469 0.0747343 0.997203i \(-0.476189\pi\)
0.0747343 + 0.997203i \(0.476189\pi\)
\(258\) 1.98137 0.123355
\(259\) 1.06889 0.0664177
\(260\) −4.01131 −0.248771
\(261\) −2.35110 −0.145530
\(262\) −4.62588 −0.285788
\(263\) 19.2268 1.18558 0.592789 0.805358i \(-0.298027\pi\)
0.592789 + 0.805358i \(0.298027\pi\)
\(264\) −2.71513 −0.167104
\(265\) −2.90395 −0.178388
\(266\) 1.07425 0.0658664
\(267\) 12.8927 0.789017
\(268\) −1.06632 −0.0651356
\(269\) 16.0800 0.980414 0.490207 0.871606i \(-0.336921\pi\)
0.490207 + 0.871606i \(0.336921\pi\)
\(270\) −0.0783436 −0.00476784
\(271\) −24.7242 −1.50189 −0.750945 0.660365i \(-0.770402\pi\)
−0.750945 + 0.660365i \(0.770402\pi\)
\(272\) −4.84611 −0.293839
\(273\) −6.49995 −0.393395
\(274\) 5.15372 0.311348
\(275\) −13.7137 −0.826968
\(276\) 10.2663 0.617956
\(277\) 27.1986 1.63421 0.817103 0.576492i \(-0.195579\pi\)
0.817103 + 0.576492i \(0.195579\pi\)
\(278\) −1.42214 −0.0852941
\(279\) −4.76449 −0.285243
\(280\) 0.308626 0.0184439
\(281\) 21.1941 1.26433 0.632167 0.774832i \(-0.282166\pi\)
0.632167 + 0.774832i \(0.282166\pi\)
\(282\) −1.76439 −0.105068
\(283\) 31.0745 1.84719 0.923593 0.383374i \(-0.125238\pi\)
0.923593 + 0.383374i \(0.125238\pi\)
\(284\) 23.1194 1.37188
\(285\) −1.38844 −0.0822438
\(286\) −4.47993 −0.264904
\(287\) −1.46345 −0.0863850
\(288\) 2.83594 0.167109
\(289\) −15.2275 −0.895735
\(290\) 0.184194 0.0108163
\(291\) −7.20075 −0.422115
\(292\) 26.8776 1.57289
\(293\) −18.9325 −1.10605 −0.553024 0.833165i \(-0.686526\pi\)
−0.553024 + 0.833165i \(0.686526\pi\)
\(294\) 0.246202 0.0143588
\(295\) 1.59914 0.0931052
\(296\) −1.03670 −0.0602570
\(297\) 2.79943 0.162440
\(298\) −1.39261 −0.0806718
\(299\) 34.4079 1.98986
\(300\) 9.50055 0.548514
\(301\) 8.04774 0.463864
\(302\) −0.616133 −0.0354545
\(303\) −0.894063 −0.0513626
\(304\) 15.8823 0.910910
\(305\) 0.792026 0.0453513
\(306\) −0.327782 −0.0187381
\(307\) −4.25979 −0.243119 −0.121559 0.992584i \(-0.538790\pi\)
−0.121559 + 0.992584i \(0.538790\pi\)
\(308\) −5.42918 −0.309356
\(309\) 10.2130 0.580996
\(310\) 0.373268 0.0212002
\(311\) 21.6483 1.22757 0.613783 0.789475i \(-0.289647\pi\)
0.613783 + 0.789475i \(0.289647\pi\)
\(312\) 6.30420 0.356905
\(313\) −0.443304 −0.0250570 −0.0125285 0.999922i \(-0.503988\pi\)
−0.0125285 + 0.999922i \(0.503988\pi\)
\(314\) −3.53037 −0.199230
\(315\) −0.318209 −0.0179290
\(316\) 2.89974 0.163123
\(317\) 9.20138 0.516801 0.258401 0.966038i \(-0.416805\pi\)
0.258401 + 0.966038i \(0.416805\pi\)
\(318\) 2.24682 0.125995
\(319\) −6.58176 −0.368508
\(320\) 2.09437 0.117079
\(321\) 1.98724 0.110917
\(322\) −1.30329 −0.0726293
\(323\) −5.80908 −0.323226
\(324\) −1.93938 −0.107744
\(325\) 31.8416 1.76625
\(326\) −4.13095 −0.228792
\(327\) −18.2252 −1.00786
\(328\) 1.41938 0.0783722
\(329\) −7.16642 −0.395098
\(330\) −0.219318 −0.0120731
\(331\) 20.2676 1.11401 0.557005 0.830509i \(-0.311951\pi\)
0.557005 + 0.830509i \(0.311951\pi\)
\(332\) 33.2184 1.82310
\(333\) 1.06889 0.0585749
\(334\) −2.70772 −0.148160
\(335\) −0.174958 −0.00955899
\(336\) 3.63998 0.198577
\(337\) 4.22202 0.229988 0.114994 0.993366i \(-0.463315\pi\)
0.114994 + 0.993366i \(0.463315\pi\)
\(338\) 7.20124 0.391696
\(339\) −6.23590 −0.338687
\(340\) −0.821619 −0.0445586
\(341\) −13.3379 −0.722287
\(342\) 1.07425 0.0580887
\(343\) 1.00000 0.0539949
\(344\) −7.80538 −0.420838
\(345\) 1.68446 0.0906883
\(346\) 3.67596 0.197621
\(347\) 23.1846 1.24462 0.622308 0.782773i \(-0.286195\pi\)
0.622308 + 0.782773i \(0.286195\pi\)
\(348\) 4.55970 0.244425
\(349\) 10.0741 0.539255 0.269628 0.962965i \(-0.413099\pi\)
0.269628 + 0.962965i \(0.413099\pi\)
\(350\) −1.20608 −0.0644677
\(351\) −6.49995 −0.346942
\(352\) 7.93902 0.423151
\(353\) −26.1314 −1.39084 −0.695418 0.718606i \(-0.744781\pi\)
−0.695418 + 0.718606i \(0.744781\pi\)
\(354\) −1.23727 −0.0657601
\(355\) 3.79336 0.201331
\(356\) −25.0038 −1.32520
\(357\) −1.33136 −0.0704629
\(358\) 2.60947 0.137915
\(359\) 12.9795 0.685033 0.342517 0.939512i \(-0.388721\pi\)
0.342517 + 0.939512i \(0.388721\pi\)
\(360\) 0.308626 0.0162660
\(361\) 0.0382221 0.00201169
\(362\) 3.60704 0.189582
\(363\) −3.16317 −0.166023
\(364\) 12.6059 0.660729
\(365\) 4.41001 0.230830
\(366\) −0.612799 −0.0320315
\(367\) −10.0344 −0.523792 −0.261896 0.965096i \(-0.584348\pi\)
−0.261896 + 0.965096i \(0.584348\pi\)
\(368\) −19.2685 −1.00444
\(369\) −1.46345 −0.0761844
\(370\) −0.0837409 −0.00435348
\(371\) 9.12591 0.473793
\(372\) 9.24019 0.479081
\(373\) −35.1339 −1.81916 −0.909581 0.415527i \(-0.863597\pi\)
−0.909581 + 0.415527i \(0.863597\pi\)
\(374\) −0.917605 −0.0474482
\(375\) 3.14987 0.162659
\(376\) 6.95060 0.358450
\(377\) 15.2821 0.787066
\(378\) 0.246202 0.0126633
\(379\) 13.4078 0.688710 0.344355 0.938840i \(-0.388098\pi\)
0.344355 + 0.938840i \(0.388098\pi\)
\(380\) 2.69271 0.138133
\(381\) −1.00000 −0.0512316
\(382\) −4.35132 −0.222633
\(383\) −30.0733 −1.53667 −0.768337 0.640046i \(-0.778915\pi\)
−0.768337 + 0.640046i \(0.778915\pi\)
\(384\) −7.29232 −0.372134
\(385\) −0.890805 −0.0453996
\(386\) −3.27723 −0.166807
\(387\) 8.04774 0.409090
\(388\) 13.9650 0.708967
\(389\) −16.7975 −0.851667 −0.425833 0.904802i \(-0.640019\pi\)
−0.425833 + 0.904802i \(0.640019\pi\)
\(390\) 0.509230 0.0257858
\(391\) 7.04762 0.356414
\(392\) −0.969884 −0.0489865
\(393\) −18.7890 −0.947778
\(394\) 0.765310 0.0385558
\(395\) 0.475781 0.0239391
\(396\) −5.42918 −0.272827
\(397\) −21.2921 −1.06862 −0.534309 0.845289i \(-0.679428\pi\)
−0.534309 + 0.845289i \(0.679428\pi\)
\(398\) −5.19292 −0.260297
\(399\) 4.36328 0.218437
\(400\) −17.8313 −0.891567
\(401\) −6.43709 −0.321453 −0.160727 0.986999i \(-0.551384\pi\)
−0.160727 + 0.986999i \(0.551384\pi\)
\(402\) 0.135367 0.00675150
\(403\) 30.9690 1.54267
\(404\) 1.73393 0.0862663
\(405\) −0.318209 −0.0158119
\(406\) −0.578846 −0.0287277
\(407\) 2.99229 0.148322
\(408\) 1.29126 0.0639269
\(409\) 8.28563 0.409698 0.204849 0.978794i \(-0.434330\pi\)
0.204849 + 0.978794i \(0.434330\pi\)
\(410\) 0.114652 0.00566228
\(411\) 20.9329 1.03254
\(412\) −19.8069 −0.975816
\(413\) −5.02542 −0.247285
\(414\) −1.30329 −0.0640530
\(415\) 5.45039 0.267549
\(416\) −18.4335 −0.903774
\(417\) −5.77630 −0.282867
\(418\) 3.00729 0.147091
\(419\) 27.2585 1.33167 0.665833 0.746101i \(-0.268076\pi\)
0.665833 + 0.746101i \(0.268076\pi\)
\(420\) 0.617130 0.0301128
\(421\) −21.3651 −1.04127 −0.520635 0.853780i \(-0.674305\pi\)
−0.520635 + 0.853780i \(0.674305\pi\)
\(422\) 0.767290 0.0373511
\(423\) −7.16642 −0.348443
\(424\) −8.85107 −0.429846
\(425\) 6.52197 0.316362
\(426\) −2.93497 −0.142200
\(427\) −2.48901 −0.120452
\(428\) −3.85402 −0.186291
\(429\) −18.1962 −0.878520
\(430\) −0.630490 −0.0304049
\(431\) −11.7546 −0.566197 −0.283099 0.959091i \(-0.591362\pi\)
−0.283099 + 0.959091i \(0.591362\pi\)
\(432\) 3.63998 0.175129
\(433\) 5.70487 0.274159 0.137079 0.990560i \(-0.456228\pi\)
0.137079 + 0.990560i \(0.456228\pi\)
\(434\) −1.17303 −0.0563071
\(435\) 0.748143 0.0358707
\(436\) 35.3458 1.69276
\(437\) −23.0973 −1.10489
\(438\) −3.41207 −0.163035
\(439\) 2.94845 0.140722 0.0703609 0.997522i \(-0.477585\pi\)
0.0703609 + 0.997522i \(0.477585\pi\)
\(440\) 0.863977 0.0411885
\(441\) 1.00000 0.0476190
\(442\) 2.13057 0.101341
\(443\) −4.63594 −0.220260 −0.110130 0.993917i \(-0.535127\pi\)
−0.110130 + 0.993917i \(0.535127\pi\)
\(444\) −2.07299 −0.0983799
\(445\) −4.10256 −0.194480
\(446\) −3.50869 −0.166141
\(447\) −5.65638 −0.267538
\(448\) −6.58175 −0.310959
\(449\) 39.5232 1.86522 0.932608 0.360890i \(-0.117527\pi\)
0.932608 + 0.360890i \(0.117527\pi\)
\(450\) −1.20608 −0.0568551
\(451\) −4.09685 −0.192913
\(452\) 12.0938 0.568845
\(453\) −2.50255 −0.117580
\(454\) 3.52322 0.165353
\(455\) 2.06834 0.0969654
\(456\) −4.23188 −0.198176
\(457\) −28.2011 −1.31919 −0.659597 0.751620i \(-0.729273\pi\)
−0.659597 + 0.751620i \(0.729273\pi\)
\(458\) 4.72458 0.220765
\(459\) −1.33136 −0.0621424
\(460\) −3.26682 −0.152316
\(461\) 25.8036 1.20179 0.600897 0.799327i \(-0.294810\pi\)
0.600897 + 0.799327i \(0.294810\pi\)
\(462\) 0.689226 0.0320657
\(463\) −11.7873 −0.547801 −0.273900 0.961758i \(-0.588314\pi\)
−0.273900 + 0.961758i \(0.588314\pi\)
\(464\) −8.55798 −0.397294
\(465\) 1.51610 0.0703077
\(466\) −2.86108 −0.132537
\(467\) −21.0242 −0.972884 −0.486442 0.873713i \(-0.661706\pi\)
−0.486442 + 0.873713i \(0.661706\pi\)
\(468\) 12.6059 0.582708
\(469\) 0.549822 0.0253884
\(470\) 0.561444 0.0258975
\(471\) −14.3393 −0.660721
\(472\) 4.87408 0.224348
\(473\) 22.5291 1.03589
\(474\) −0.368117 −0.0169082
\(475\) −21.3746 −0.980734
\(476\) 2.58201 0.118346
\(477\) 9.12591 0.417847
\(478\) 0.0734936 0.00336152
\(479\) 29.9975 1.37062 0.685311 0.728251i \(-0.259666\pi\)
0.685311 + 0.728251i \(0.259666\pi\)
\(480\) −0.902421 −0.0411897
\(481\) −6.94774 −0.316790
\(482\) 4.53860 0.206727
\(483\) −5.29356 −0.240866
\(484\) 6.13460 0.278845
\(485\) 2.29134 0.104045
\(486\) 0.246202 0.0111679
\(487\) 12.1673 0.551354 0.275677 0.961250i \(-0.411098\pi\)
0.275677 + 0.961250i \(0.411098\pi\)
\(488\) 2.41405 0.109279
\(489\) −16.7787 −0.758760
\(490\) −0.0783436 −0.00353920
\(491\) 16.0438 0.724048 0.362024 0.932169i \(-0.382086\pi\)
0.362024 + 0.932169i \(0.382086\pi\)
\(492\) 2.83820 0.127956
\(493\) 3.13016 0.140975
\(494\) −6.98256 −0.314160
\(495\) −0.890805 −0.0400387
\(496\) −17.3427 −0.778709
\(497\) −11.9210 −0.534729
\(498\) −4.21703 −0.188969
\(499\) −26.3857 −1.18119 −0.590593 0.806970i \(-0.701106\pi\)
−0.590593 + 0.806970i \(0.701106\pi\)
\(500\) −6.10881 −0.273194
\(501\) −10.9980 −0.491353
\(502\) 6.80500 0.303722
\(503\) 18.3203 0.816862 0.408431 0.912789i \(-0.366076\pi\)
0.408431 + 0.912789i \(0.366076\pi\)
\(504\) −0.969884 −0.0432021
\(505\) 0.284499 0.0126600
\(506\) −3.64846 −0.162194
\(507\) 29.2493 1.29901
\(508\) 1.93938 0.0860463
\(509\) 36.9703 1.63868 0.819339 0.573309i \(-0.194340\pi\)
0.819339 + 0.573309i \(0.194340\pi\)
\(510\) 0.104303 0.00461863
\(511\) −13.8588 −0.613079
\(512\) 17.3835 0.768249
\(513\) 4.36328 0.192644
\(514\) 0.589940 0.0260211
\(515\) −3.24986 −0.143206
\(516\) −15.6077 −0.687089
\(517\) −20.0619 −0.882323
\(518\) 0.263163 0.0115627
\(519\) 14.9307 0.655384
\(520\) −2.00605 −0.0879712
\(521\) −2.13160 −0.0933871 −0.0466936 0.998909i \(-0.514868\pi\)
−0.0466936 + 0.998909i \(0.514868\pi\)
\(522\) −0.578846 −0.0253354
\(523\) −24.4693 −1.06997 −0.534983 0.844863i \(-0.679682\pi\)
−0.534983 + 0.844863i \(0.679682\pi\)
\(524\) 36.4390 1.59185
\(525\) −4.89874 −0.213799
\(526\) 4.73368 0.206398
\(527\) 6.34324 0.276316
\(528\) 10.1899 0.443458
\(529\) 5.02182 0.218340
\(530\) −0.714957 −0.0310557
\(531\) −5.02542 −0.218085
\(532\) −8.46208 −0.366878
\(533\) 9.51238 0.412027
\(534\) 3.17419 0.137361
\(535\) −0.632358 −0.0273392
\(536\) −0.533263 −0.0230335
\(537\) 10.5989 0.457377
\(538\) 3.95892 0.170681
\(539\) 2.79943 0.120580
\(540\) 0.617130 0.0265570
\(541\) −3.07605 −0.132250 −0.0661250 0.997811i \(-0.521064\pi\)
−0.0661250 + 0.997811i \(0.521064\pi\)
\(542\) −6.08715 −0.261466
\(543\) 14.6508 0.628724
\(544\) −3.77564 −0.161879
\(545\) 5.79944 0.248421
\(546\) −1.60030 −0.0684865
\(547\) 38.7810 1.65816 0.829078 0.559133i \(-0.188866\pi\)
0.829078 + 0.559133i \(0.188866\pi\)
\(548\) −40.5969 −1.73422
\(549\) −2.48901 −0.106228
\(550\) −3.37634 −0.143968
\(551\) −10.2585 −0.437028
\(552\) 5.13414 0.218524
\(553\) −1.49518 −0.0635817
\(554\) 6.69635 0.284500
\(555\) −0.340131 −0.0144378
\(556\) 11.2025 0.475091
\(557\) 15.3795 0.651651 0.325825 0.945430i \(-0.394358\pi\)
0.325825 + 0.945430i \(0.394358\pi\)
\(558\) −1.17303 −0.0496582
\(559\) −52.3099 −2.21247
\(560\) −1.15827 −0.0489461
\(561\) −3.72704 −0.157356
\(562\) 5.21803 0.220109
\(563\) 17.9471 0.756380 0.378190 0.925728i \(-0.376547\pi\)
0.378190 + 0.925728i \(0.376547\pi\)
\(564\) 13.8985 0.585230
\(565\) 1.98432 0.0834809
\(566\) 7.65060 0.321579
\(567\) 1.00000 0.0419961
\(568\) 11.5620 0.485129
\(569\) 10.7314 0.449884 0.224942 0.974372i \(-0.427781\pi\)
0.224942 + 0.974372i \(0.427781\pi\)
\(570\) −0.341835 −0.0143179
\(571\) −18.4705 −0.772966 −0.386483 0.922296i \(-0.626310\pi\)
−0.386483 + 0.922296i \(0.626310\pi\)
\(572\) 35.2894 1.47552
\(573\) −17.6738 −0.738333
\(574\) −0.360305 −0.0150389
\(575\) 25.9318 1.08143
\(576\) −6.58175 −0.274240
\(577\) −0.892310 −0.0371473 −0.0185737 0.999827i \(-0.505913\pi\)
−0.0185737 + 0.999827i \(0.505913\pi\)
\(578\) −3.74904 −0.155939
\(579\) −13.3112 −0.553193
\(580\) −1.45094 −0.0602469
\(581\) −17.1283 −0.710603
\(582\) −1.77284 −0.0734865
\(583\) 25.5474 1.05806
\(584\) 13.4415 0.556212
\(585\) 2.06834 0.0855154
\(586\) −4.66121 −0.192553
\(587\) −30.5797 −1.26216 −0.631080 0.775718i \(-0.717388\pi\)
−0.631080 + 0.775718i \(0.717388\pi\)
\(588\) −1.93938 −0.0799789
\(589\) −20.7888 −0.856589
\(590\) 0.393710 0.0162088
\(591\) 3.10847 0.127865
\(592\) 3.89075 0.159909
\(593\) 33.7801 1.38718 0.693590 0.720370i \(-0.256028\pi\)
0.693590 + 0.720370i \(0.256028\pi\)
\(594\) 0.689226 0.0282793
\(595\) 0.423650 0.0173679
\(596\) 10.9699 0.449344
\(597\) −21.0921 −0.863243
\(598\) 8.47129 0.346417
\(599\) −8.67399 −0.354410 −0.177205 0.984174i \(-0.556706\pi\)
−0.177205 + 0.984174i \(0.556706\pi\)
\(600\) 4.75121 0.193967
\(601\) −19.4904 −0.795031 −0.397516 0.917595i \(-0.630128\pi\)
−0.397516 + 0.917595i \(0.630128\pi\)
\(602\) 1.98137 0.0807546
\(603\) 0.549822 0.0223905
\(604\) 4.85341 0.197483
\(605\) 1.00655 0.0409220
\(606\) −0.220120 −0.00894176
\(607\) −32.4809 −1.31836 −0.659179 0.751986i \(-0.729096\pi\)
−0.659179 + 0.751986i \(0.729096\pi\)
\(608\) 12.3740 0.501832
\(609\) −2.35110 −0.0952716
\(610\) 0.194998 0.00789524
\(611\) 46.5814 1.88448
\(612\) 2.58201 0.104372
\(613\) −7.74253 −0.312718 −0.156359 0.987700i \(-0.549976\pi\)
−0.156359 + 0.987700i \(0.549976\pi\)
\(614\) −1.04877 −0.0423248
\(615\) 0.465684 0.0187782
\(616\) −2.71513 −0.109396
\(617\) 36.9258 1.48658 0.743288 0.668971i \(-0.233265\pi\)
0.743288 + 0.668971i \(0.233265\pi\)
\(618\) 2.51445 0.101146
\(619\) 5.50391 0.221221 0.110610 0.993864i \(-0.464719\pi\)
0.110610 + 0.993864i \(0.464719\pi\)
\(620\) −2.94031 −0.118086
\(621\) −5.29356 −0.212423
\(622\) 5.32986 0.213708
\(623\) 12.8927 0.516533
\(624\) −23.6597 −0.947146
\(625\) 23.4914 0.939656
\(626\) −0.109142 −0.00436221
\(627\) 12.2147 0.487809
\(628\) 27.8095 1.10972
\(629\) −1.42308 −0.0567417
\(630\) −0.0783436 −0.00312129
\(631\) 30.7518 1.22421 0.612105 0.790777i \(-0.290323\pi\)
0.612105 + 0.790777i \(0.290323\pi\)
\(632\) 1.45015 0.0576840
\(633\) 3.11651 0.123870
\(634\) 2.26540 0.0899704
\(635\) 0.318209 0.0126277
\(636\) −17.6986 −0.701797
\(637\) −6.49995 −0.257537
\(638\) −1.62044 −0.0641539
\(639\) −11.9210 −0.471587
\(640\) 2.32048 0.0917250
\(641\) 11.7811 0.465324 0.232662 0.972558i \(-0.425256\pi\)
0.232662 + 0.972558i \(0.425256\pi\)
\(642\) 0.489262 0.0193096
\(643\) −34.3871 −1.35609 −0.678047 0.735019i \(-0.737173\pi\)
−0.678047 + 0.735019i \(0.737173\pi\)
\(644\) 10.2663 0.404547
\(645\) −2.56086 −0.100834
\(646\) −1.43021 −0.0562707
\(647\) −6.03048 −0.237083 −0.118541 0.992949i \(-0.537822\pi\)
−0.118541 + 0.992949i \(0.537822\pi\)
\(648\) −0.969884 −0.0381006
\(649\) −14.0683 −0.552231
\(650\) 7.83946 0.307489
\(651\) −4.76449 −0.186735
\(652\) 32.5404 1.27438
\(653\) 6.35698 0.248768 0.124384 0.992234i \(-0.460305\pi\)
0.124384 + 0.992234i \(0.460305\pi\)
\(654\) −4.48709 −0.175459
\(655\) 5.97882 0.233612
\(656\) −5.32695 −0.207982
\(657\) −13.8588 −0.540685
\(658\) −1.76439 −0.0687830
\(659\) 22.5576 0.878720 0.439360 0.898311i \(-0.355205\pi\)
0.439360 + 0.898311i \(0.355205\pi\)
\(660\) 1.72761 0.0672473
\(661\) −44.8294 −1.74366 −0.871830 0.489809i \(-0.837067\pi\)
−0.871830 + 0.489809i \(0.837067\pi\)
\(662\) 4.98993 0.193939
\(663\) 8.65375 0.336084
\(664\) 16.6125 0.644690
\(665\) −1.38844 −0.0538412
\(666\) 0.263163 0.0101974
\(667\) 12.4457 0.481900
\(668\) 21.3293 0.825255
\(669\) −14.2513 −0.550987
\(670\) −0.0430750 −0.00166413
\(671\) −6.96782 −0.268990
\(672\) 2.83594 0.109399
\(673\) 25.0877 0.967059 0.483529 0.875328i \(-0.339355\pi\)
0.483529 + 0.875328i \(0.339355\pi\)
\(674\) 1.03947 0.0400388
\(675\) −4.89874 −0.188553
\(676\) −56.7257 −2.18176
\(677\) −34.4793 −1.32515 −0.662573 0.748997i \(-0.730536\pi\)
−0.662573 + 0.748997i \(0.730536\pi\)
\(678\) −1.53529 −0.0589624
\(679\) −7.20075 −0.276339
\(680\) −0.410891 −0.0157569
\(681\) 14.3103 0.548372
\(682\) −3.28381 −0.125744
\(683\) 12.6147 0.482690 0.241345 0.970439i \(-0.422411\pi\)
0.241345 + 0.970439i \(0.422411\pi\)
\(684\) −8.46208 −0.323556
\(685\) −6.66104 −0.254505
\(686\) 0.246202 0.00940003
\(687\) 19.1899 0.732139
\(688\) 29.2936 1.11681
\(689\) −59.3179 −2.25983
\(690\) 0.414717 0.0157880
\(691\) −41.2619 −1.56968 −0.784839 0.619700i \(-0.787254\pi\)
−0.784839 + 0.619700i \(0.787254\pi\)
\(692\) −28.9563 −1.10075
\(693\) 2.79943 0.106342
\(694\) 5.70810 0.216676
\(695\) 1.83807 0.0697220
\(696\) 2.28030 0.0864345
\(697\) 1.94838 0.0738002
\(698\) 2.48027 0.0938795
\(699\) −11.6209 −0.439542
\(700\) 9.50055 0.359087
\(701\) −34.9290 −1.31925 −0.659624 0.751595i \(-0.729285\pi\)
−0.659624 + 0.751595i \(0.729285\pi\)
\(702\) −1.60030 −0.0603994
\(703\) 4.66387 0.175901
\(704\) −18.4252 −0.694425
\(705\) 2.28042 0.0858856
\(706\) −6.43361 −0.242132
\(707\) −0.894063 −0.0336247
\(708\) 9.74623 0.366286
\(709\) 26.8327 1.00772 0.503861 0.863785i \(-0.331912\pi\)
0.503861 + 0.863785i \(0.331912\pi\)
\(710\) 0.933933 0.0350499
\(711\) −1.49518 −0.0560738
\(712\) −12.5044 −0.468621
\(713\) 25.2212 0.944540
\(714\) −0.327782 −0.0122669
\(715\) 5.79019 0.216541
\(716\) −20.5554 −0.768191
\(717\) 0.298510 0.0111480
\(718\) 3.19558 0.119258
\(719\) 20.7889 0.775296 0.387648 0.921808i \(-0.373288\pi\)
0.387648 + 0.921808i \(0.373288\pi\)
\(720\) −1.15827 −0.0431664
\(721\) 10.2130 0.380351
\(722\) 0.00941036 0.000350217 0
\(723\) 18.4344 0.685585
\(724\) −28.4135 −1.05598
\(725\) 11.5175 0.427748
\(726\) −0.778778 −0.0289032
\(727\) 22.0538 0.817928 0.408964 0.912550i \(-0.365890\pi\)
0.408964 + 0.912550i \(0.365890\pi\)
\(728\) 6.30420 0.233649
\(729\) 1.00000 0.0370370
\(730\) 1.08575 0.0401855
\(731\) −10.7144 −0.396287
\(732\) 4.82715 0.178417
\(733\) −31.0700 −1.14760 −0.573798 0.818997i \(-0.694531\pi\)
−0.573798 + 0.818997i \(0.694531\pi\)
\(734\) −2.47049 −0.0911875
\(735\) −0.318209 −0.0117373
\(736\) −15.0122 −0.553358
\(737\) 1.53919 0.0566968
\(738\) −0.360305 −0.0132630
\(739\) 47.8405 1.75984 0.879921 0.475120i \(-0.157595\pi\)
0.879921 + 0.475120i \(0.157595\pi\)
\(740\) 0.659645 0.0242490
\(741\) −28.3611 −1.04187
\(742\) 2.24682 0.0824832
\(743\) 17.0228 0.624507 0.312254 0.949999i \(-0.398916\pi\)
0.312254 + 0.949999i \(0.398916\pi\)
\(744\) 4.62101 0.169414
\(745\) 1.79991 0.0659436
\(746\) −8.65002 −0.316700
\(747\) −17.1283 −0.626693
\(748\) 7.22817 0.264288
\(749\) 1.98724 0.0726122
\(750\) 0.775504 0.0283174
\(751\) −24.1639 −0.881754 −0.440877 0.897568i \(-0.645332\pi\)
−0.440877 + 0.897568i \(0.645332\pi\)
\(752\) −26.0857 −0.951246
\(753\) 27.6399 1.00725
\(754\) 3.76247 0.137021
\(755\) 0.796335 0.0289816
\(756\) −1.93938 −0.0705347
\(757\) −35.9690 −1.30732 −0.653658 0.756790i \(-0.726767\pi\)
−0.653658 + 0.756790i \(0.726767\pi\)
\(758\) 3.30101 0.119898
\(759\) −14.8190 −0.537895
\(760\) 1.34662 0.0488471
\(761\) −28.0258 −1.01593 −0.507967 0.861376i \(-0.669603\pi\)
−0.507967 + 0.861376i \(0.669603\pi\)
\(762\) −0.246202 −0.00891895
\(763\) −18.2252 −0.659798
\(764\) 34.2763 1.24007
\(765\) 0.423650 0.0153171
\(766\) −7.40410 −0.267521
\(767\) 32.6650 1.17946
\(768\) 11.3681 0.410212
\(769\) −15.0578 −0.542997 −0.271498 0.962439i \(-0.587519\pi\)
−0.271498 + 0.962439i \(0.587519\pi\)
\(770\) −0.219318 −0.00790367
\(771\) 2.39616 0.0862957
\(772\) 25.8155 0.929119
\(773\) 29.8191 1.07252 0.536260 0.844053i \(-0.319837\pi\)
0.536260 + 0.844053i \(0.319837\pi\)
\(774\) 1.98137 0.0712189
\(775\) 23.3400 0.838399
\(776\) 6.98389 0.250707
\(777\) 1.06889 0.0383463
\(778\) −4.13557 −0.148268
\(779\) −6.38546 −0.228783
\(780\) −4.01131 −0.143628
\(781\) −33.3720 −1.19414
\(782\) 1.73514 0.0620484
\(783\) −2.35110 −0.0840216
\(784\) 3.63998 0.129999
\(785\) 4.56290 0.162857
\(786\) −4.62588 −0.165000
\(787\) 22.2169 0.791947 0.395974 0.918262i \(-0.370407\pi\)
0.395974 + 0.918262i \(0.370407\pi\)
\(788\) −6.02851 −0.214757
\(789\) 19.2268 0.684494
\(790\) 0.117138 0.00416759
\(791\) −6.23590 −0.221723
\(792\) −2.71513 −0.0964778
\(793\) 16.1784 0.574513
\(794\) −5.24215 −0.186037
\(795\) −2.90395 −0.102992
\(796\) 40.9057 1.44987
\(797\) 10.9848 0.389102 0.194551 0.980892i \(-0.437675\pi\)
0.194551 + 0.980892i \(0.437675\pi\)
\(798\) 1.07425 0.0380280
\(799\) 9.54106 0.337539
\(800\) −13.8925 −0.491175
\(801\) 12.8927 0.455539
\(802\) −1.58482 −0.0559621
\(803\) −38.7969 −1.36911
\(804\) −1.06632 −0.0376061
\(805\) 1.68446 0.0593694
\(806\) 7.62462 0.268566
\(807\) 16.0800 0.566042
\(808\) 0.867137 0.0305058
\(809\) 15.6198 0.549162 0.274581 0.961564i \(-0.411461\pi\)
0.274581 + 0.961564i \(0.411461\pi\)
\(810\) −0.0783436 −0.00275271
\(811\) −33.9143 −1.19089 −0.595447 0.803395i \(-0.703025\pi\)
−0.595447 + 0.803395i \(0.703025\pi\)
\(812\) 4.55970 0.160014
\(813\) −24.7242 −0.867117
\(814\) 0.736708 0.0258216
\(815\) 5.33914 0.187022
\(816\) −4.84611 −0.169648
\(817\) 35.1146 1.22850
\(818\) 2.03994 0.0713247
\(819\) −6.49995 −0.227127
\(820\) −0.903141 −0.0315391
\(821\) 15.7908 0.551102 0.275551 0.961286i \(-0.411140\pi\)
0.275551 + 0.961286i \(0.411140\pi\)
\(822\) 5.15372 0.179757
\(823\) 21.7601 0.758509 0.379254 0.925292i \(-0.376181\pi\)
0.379254 + 0.925292i \(0.376181\pi\)
\(824\) −9.90540 −0.345071
\(825\) −13.7137 −0.477450
\(826\) −1.23727 −0.0430501
\(827\) −35.0663 −1.21937 −0.609687 0.792642i \(-0.708705\pi\)
−0.609687 + 0.792642i \(0.708705\pi\)
\(828\) 10.2663 0.356777
\(829\) 9.47354 0.329030 0.164515 0.986375i \(-0.447394\pi\)
0.164515 + 0.986375i \(0.447394\pi\)
\(830\) 1.34190 0.0465779
\(831\) 27.1986 0.943509
\(832\) 42.7811 1.48317
\(833\) −1.33136 −0.0461288
\(834\) −1.42214 −0.0492446
\(835\) 3.49965 0.121110
\(836\) −23.6890 −0.819302
\(837\) −4.76449 −0.164685
\(838\) 6.71109 0.231831
\(839\) 0.187162 0.00646157 0.00323078 0.999995i \(-0.498972\pi\)
0.00323078 + 0.999995i \(0.498972\pi\)
\(840\) 0.308626 0.0106486
\(841\) −23.4723 −0.809390
\(842\) −5.26012 −0.181276
\(843\) 21.1941 0.729963
\(844\) −6.04411 −0.208047
\(845\) −9.30740 −0.320184
\(846\) −1.76439 −0.0606609
\(847\) −3.16317 −0.108688
\(848\) 33.2181 1.14072
\(849\) 31.0745 1.06647
\(850\) 1.60572 0.0550758
\(851\) −5.65825 −0.193962
\(852\) 23.1194 0.792056
\(853\) −17.7583 −0.608034 −0.304017 0.952667i \(-0.598328\pi\)
−0.304017 + 0.952667i \(0.598328\pi\)
\(854\) −0.612799 −0.0209696
\(855\) −1.38844 −0.0474835
\(856\) −1.92739 −0.0658769
\(857\) −24.4576 −0.835455 −0.417727 0.908572i \(-0.637173\pi\)
−0.417727 + 0.908572i \(0.637173\pi\)
\(858\) −4.47993 −0.152942
\(859\) 6.32700 0.215874 0.107937 0.994158i \(-0.465575\pi\)
0.107937 + 0.994158i \(0.465575\pi\)
\(860\) 4.96650 0.169356
\(861\) −1.46345 −0.0498744
\(862\) −2.89399 −0.0985698
\(863\) −0.857036 −0.0291738 −0.0145869 0.999894i \(-0.504643\pi\)
−0.0145869 + 0.999894i \(0.504643\pi\)
\(864\) 2.83594 0.0964806
\(865\) −4.75108 −0.161541
\(866\) 1.40455 0.0477286
\(867\) −15.2275 −0.517153
\(868\) 9.24019 0.313632
\(869\) −4.18567 −0.141989
\(870\) 0.184194 0.00624477
\(871\) −3.57381 −0.121094
\(872\) 17.6764 0.598598
\(873\) −7.20075 −0.243708
\(874\) −5.68660 −0.192352
\(875\) 3.14987 0.106485
\(876\) 26.8776 0.908111
\(877\) 6.88110 0.232358 0.116179 0.993228i \(-0.462935\pi\)
0.116179 + 0.993228i \(0.462935\pi\)
\(878\) 0.725913 0.0244984
\(879\) −18.9325 −0.638577
\(880\) −3.24251 −0.109305
\(881\) −51.7694 −1.74416 −0.872078 0.489367i \(-0.837228\pi\)
−0.872078 + 0.489367i \(0.837228\pi\)
\(882\) 0.246202 0.00829005
\(883\) −18.4022 −0.619283 −0.309641 0.950853i \(-0.600209\pi\)
−0.309641 + 0.950853i \(0.600209\pi\)
\(884\) −16.7829 −0.564472
\(885\) 1.59914 0.0537543
\(886\) −1.14138 −0.0383453
\(887\) −54.6988 −1.83661 −0.918303 0.395878i \(-0.870440\pi\)
−0.918303 + 0.395878i \(0.870440\pi\)
\(888\) −1.03670 −0.0347894
\(889\) −1.00000 −0.0335389
\(890\) −1.01006 −0.0338572
\(891\) 2.79943 0.0937846
\(892\) 27.6387 0.925413
\(893\) −31.2691 −1.04638
\(894\) −1.39261 −0.0465759
\(895\) −3.37267 −0.112736
\(896\) −7.29232 −0.243619
\(897\) 34.4079 1.14885
\(898\) 9.73069 0.324717
\(899\) 11.2018 0.373602
\(900\) 9.50055 0.316685
\(901\) −12.1498 −0.404770
\(902\) −1.00865 −0.0335844
\(903\) 8.04774 0.267812
\(904\) 6.04810 0.201157
\(905\) −4.66200 −0.154970
\(906\) −0.616133 −0.0204696
\(907\) 39.2425 1.30303 0.651514 0.758637i \(-0.274134\pi\)
0.651514 + 0.758637i \(0.274134\pi\)
\(908\) −27.7532 −0.921021
\(909\) −0.894063 −0.0296542
\(910\) 0.509230 0.0168808
\(911\) 7.34578 0.243377 0.121688 0.992568i \(-0.461169\pi\)
0.121688 + 0.992568i \(0.461169\pi\)
\(912\) 15.8823 0.525914
\(913\) −47.9496 −1.58690
\(914\) −6.94317 −0.229660
\(915\) 0.792026 0.0261836
\(916\) −37.2165 −1.22967
\(917\) −18.7890 −0.620467
\(918\) −0.327782 −0.0108184
\(919\) 58.3954 1.92629 0.963144 0.268986i \(-0.0866887\pi\)
0.963144 + 0.268986i \(0.0866887\pi\)
\(920\) −1.63373 −0.0538625
\(921\) −4.25979 −0.140365
\(922\) 6.35289 0.209221
\(923\) 77.4858 2.55048
\(924\) −5.42918 −0.178607
\(925\) −5.23623 −0.172166
\(926\) −2.90205 −0.0953672
\(927\) 10.2130 0.335438
\(928\) −6.66759 −0.218874
\(929\) −43.5784 −1.42976 −0.714880 0.699247i \(-0.753519\pi\)
−0.714880 + 0.699247i \(0.753519\pi\)
\(930\) 0.373268 0.0122399
\(931\) 4.36328 0.143001
\(932\) 22.5374 0.738236
\(933\) 21.6483 0.708735
\(934\) −5.17620 −0.169370
\(935\) 1.18598 0.0387857
\(936\) 6.30420 0.206059
\(937\) 19.8795 0.649435 0.324718 0.945811i \(-0.394731\pi\)
0.324718 + 0.945811i \(0.394731\pi\)
\(938\) 0.135367 0.00441989
\(939\) −0.443304 −0.0144667
\(940\) −4.42261 −0.144250
\(941\) 8.08530 0.263573 0.131787 0.991278i \(-0.457929\pi\)
0.131787 + 0.991278i \(0.457929\pi\)
\(942\) −3.53037 −0.115026
\(943\) 7.74689 0.252274
\(944\) −18.2925 −0.595369
\(945\) −0.318209 −0.0103513
\(946\) 5.54671 0.180339
\(947\) 40.1421 1.30444 0.652221 0.758028i \(-0.273837\pi\)
0.652221 + 0.758028i \(0.273837\pi\)
\(948\) 2.89974 0.0941790
\(949\) 90.0818 2.92418
\(950\) −5.26246 −0.170737
\(951\) 9.20138 0.298375
\(952\) 1.29126 0.0418500
\(953\) 29.1867 0.945449 0.472725 0.881210i \(-0.343271\pi\)
0.472725 + 0.881210i \(0.343271\pi\)
\(954\) 2.24682 0.0727433
\(955\) 5.62396 0.181987
\(956\) −0.578925 −0.0187238
\(957\) −6.58176 −0.212758
\(958\) 7.38544 0.238613
\(959\) 20.9329 0.675959
\(960\) 2.09437 0.0675956
\(961\) −8.29959 −0.267729
\(962\) −1.71055 −0.0551502
\(963\) 1.98724 0.0640379
\(964\) −35.7515 −1.15148
\(965\) 4.23573 0.136353
\(966\) −1.30329 −0.0419325
\(967\) −15.3154 −0.492511 −0.246256 0.969205i \(-0.579200\pi\)
−0.246256 + 0.969205i \(0.579200\pi\)
\(968\) 3.06791 0.0986062
\(969\) −5.80908 −0.186615
\(970\) 0.564133 0.0181132
\(971\) −50.0150 −1.60506 −0.802529 0.596613i \(-0.796513\pi\)
−0.802529 + 0.596613i \(0.796513\pi\)
\(972\) −1.93938 −0.0622058
\(973\) −5.77630 −0.185180
\(974\) 2.99562 0.0959858
\(975\) 31.8416 1.01975
\(976\) −9.05995 −0.290002
\(977\) 11.7653 0.376406 0.188203 0.982130i \(-0.439734\pi\)
0.188203 + 0.982130i \(0.439734\pi\)
\(978\) −4.13095 −0.132093
\(979\) 36.0921 1.15351
\(980\) 0.617130 0.0197135
\(981\) −18.2252 −0.581887
\(982\) 3.95002 0.126050
\(983\) −10.5544 −0.336633 −0.168316 0.985733i \(-0.553833\pi\)
−0.168316 + 0.985733i \(0.553833\pi\)
\(984\) 1.41938 0.0452482
\(985\) −0.989142 −0.0315167
\(986\) 0.770651 0.0245425
\(987\) −7.16642 −0.228110
\(988\) 55.0031 1.74988
\(989\) −42.6013 −1.35464
\(990\) −0.219318 −0.00697038
\(991\) 2.89587 0.0919905 0.0459952 0.998942i \(-0.485354\pi\)
0.0459952 + 0.998942i \(0.485354\pi\)
\(992\) −13.5118 −0.429000
\(993\) 20.2676 0.643174
\(994\) −2.93497 −0.0930915
\(995\) 6.71170 0.212775
\(996\) 33.2184 1.05257
\(997\) −13.5622 −0.429518 −0.214759 0.976667i \(-0.568897\pi\)
−0.214759 + 0.976667i \(0.568897\pi\)
\(998\) −6.49621 −0.205634
\(999\) 1.06889 0.0338182
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 2667.2.a.j.1.4 7
3.2 odd 2 8001.2.a.l.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.4 7 1.1 even 1 trivial
8001.2.a.l.1.4 7 3.2 odd 2