Properties

Label 1859.2.a.t.1.11
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +O(q^{10})\) \(q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +1.08548 q^{10} +1.00000 q^{11} +2.28586 q^{12} -1.38048 q^{14} +3.86754 q^{15} +3.31771 q^{16} -2.34667 q^{17} +0.520307 q^{18} -6.23610 q^{19} +6.00575 q^{20} -4.91864 q^{21} -0.340522 q^{22} -8.20474 q^{23} -1.60468 q^{24} +5.16137 q^{25} +5.49366 q^{27} -7.63796 q^{28} -4.01420 q^{29} -1.31698 q^{30} +0.723646 q^{31} -3.77496 q^{32} -1.21327 q^{33} +0.799091 q^{34} -12.9230 q^{35} +2.87876 q^{36} -10.0577 q^{37} +2.12353 q^{38} -4.21605 q^{40} -4.40518 q^{41} +1.67490 q^{42} +9.58073 q^{43} -1.88404 q^{44} +4.87069 q^{45} +2.79390 q^{46} +4.76081 q^{47} -4.02529 q^{48} +9.43510 q^{49} -1.75756 q^{50} +2.84714 q^{51} +5.18522 q^{53} -1.87071 q^{54} -3.18769 q^{55} +5.36186 q^{56} +7.56609 q^{57} +1.36692 q^{58} -0.694630 q^{59} -7.28661 q^{60} +10.3413 q^{61} -0.246418 q^{62} -6.19442 q^{63} -5.34997 q^{64} +0.413146 q^{66} +7.17195 q^{67} +4.42122 q^{68} +9.95459 q^{69} +4.40056 q^{70} +2.32931 q^{71} -2.02090 q^{72} -2.44069 q^{73} +3.42485 q^{74} -6.26215 q^{75} +11.7491 q^{76} +4.05402 q^{77} -2.59565 q^{79} -10.5758 q^{80} -2.08140 q^{81} +1.50006 q^{82} +13.6065 q^{83} +9.26693 q^{84} +7.48044 q^{85} -3.26245 q^{86} +4.87032 q^{87} +1.32260 q^{88} -15.3302 q^{89} -1.65858 q^{90} +15.4581 q^{92} -0.877980 q^{93} -1.62116 q^{94} +19.8788 q^{95} +4.58006 q^{96} -12.7385 q^{97} -3.21286 q^{98} -1.52797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.340522 −0.240786 −0.120393 0.992726i \(-0.538415\pi\)
−0.120393 + 0.992726i \(0.538415\pi\)
\(3\) −1.21327 −0.700483 −0.350242 0.936659i \(-0.613901\pi\)
−0.350242 + 0.936659i \(0.613901\pi\)
\(4\) −1.88404 −0.942022
\(5\) −3.18769 −1.42558 −0.712789 0.701378i \(-0.752568\pi\)
−0.712789 + 0.701378i \(0.752568\pi\)
\(6\) 0.413146 0.168666
\(7\) 4.05402 1.53228 0.766138 0.642676i \(-0.222176\pi\)
0.766138 + 0.642676i \(0.222176\pi\)
\(8\) 1.32260 0.467611
\(9\) −1.52797 −0.509323
\(10\) 1.08548 0.343259
\(11\) 1.00000 0.301511
\(12\) 2.28586 0.659871
\(13\) 0 0
\(14\) −1.38048 −0.368950
\(15\) 3.86754 0.998594
\(16\) 3.31771 0.829428
\(17\) −2.34667 −0.569150 −0.284575 0.958654i \(-0.591852\pi\)
−0.284575 + 0.958654i \(0.591852\pi\)
\(18\) 0.520307 0.122638
\(19\) −6.23610 −1.43066 −0.715330 0.698787i \(-0.753723\pi\)
−0.715330 + 0.698787i \(0.753723\pi\)
\(20\) 6.00575 1.34293
\(21\) −4.91864 −1.07333
\(22\) −0.340522 −0.0725996
\(23\) −8.20474 −1.71081 −0.855403 0.517963i \(-0.826691\pi\)
−0.855403 + 0.517963i \(0.826691\pi\)
\(24\) −1.60468 −0.327554
\(25\) 5.16137 1.03227
\(26\) 0 0
\(27\) 5.49366 1.05726
\(28\) −7.63796 −1.44344
\(29\) −4.01420 −0.745419 −0.372709 0.927948i \(-0.621571\pi\)
−0.372709 + 0.927948i \(0.621571\pi\)
\(30\) −1.31698 −0.240447
\(31\) 0.723646 0.129971 0.0649854 0.997886i \(-0.479300\pi\)
0.0649854 + 0.997886i \(0.479300\pi\)
\(32\) −3.77496 −0.667325
\(33\) −1.21327 −0.211204
\(34\) 0.799091 0.137043
\(35\) −12.9230 −2.18438
\(36\) 2.87876 0.479794
\(37\) −10.0577 −1.65347 −0.826734 0.562593i \(-0.809804\pi\)
−0.826734 + 0.562593i \(0.809804\pi\)
\(38\) 2.12353 0.344482
\(39\) 0 0
\(40\) −4.21605 −0.666616
\(41\) −4.40518 −0.687974 −0.343987 0.938974i \(-0.611778\pi\)
−0.343987 + 0.938974i \(0.611778\pi\)
\(42\) 1.67490 0.258443
\(43\) 9.58073 1.46105 0.730524 0.682887i \(-0.239276\pi\)
0.730524 + 0.682887i \(0.239276\pi\)
\(44\) −1.88404 −0.284030
\(45\) 4.87069 0.726080
\(46\) 2.79390 0.411937
\(47\) 4.76081 0.694435 0.347217 0.937785i \(-0.387127\pi\)
0.347217 + 0.937785i \(0.387127\pi\)
\(48\) −4.02529 −0.581001
\(49\) 9.43510 1.34787
\(50\) −1.75756 −0.248557
\(51\) 2.84714 0.398680
\(52\) 0 0
\(53\) 5.18522 0.712245 0.356122 0.934439i \(-0.384099\pi\)
0.356122 + 0.934439i \(0.384099\pi\)
\(54\) −1.87071 −0.254572
\(55\) −3.18769 −0.429828
\(56\) 5.36186 0.716509
\(57\) 7.56609 1.00215
\(58\) 1.36692 0.179486
\(59\) −0.694630 −0.0904331 −0.0452166 0.998977i \(-0.514398\pi\)
−0.0452166 + 0.998977i \(0.514398\pi\)
\(60\) −7.28661 −0.940698
\(61\) 10.3413 1.32407 0.662033 0.749475i \(-0.269694\pi\)
0.662033 + 0.749475i \(0.269694\pi\)
\(62\) −0.246418 −0.0312951
\(63\) −6.19442 −0.780424
\(64\) −5.34997 −0.668746
\(65\) 0 0
\(66\) 0.413146 0.0508548
\(67\) 7.17195 0.876193 0.438097 0.898928i \(-0.355653\pi\)
0.438097 + 0.898928i \(0.355653\pi\)
\(68\) 4.42122 0.536152
\(69\) 9.95459 1.19839
\(70\) 4.40056 0.525967
\(71\) 2.32931 0.276438 0.138219 0.990402i \(-0.455862\pi\)
0.138219 + 0.990402i \(0.455862\pi\)
\(72\) −2.02090 −0.238165
\(73\) −2.44069 −0.285662 −0.142831 0.989747i \(-0.545620\pi\)
−0.142831 + 0.989747i \(0.545620\pi\)
\(74\) 3.42485 0.398131
\(75\) −6.26215 −0.723091
\(76\) 11.7491 1.34771
\(77\) 4.05402 0.461999
\(78\) 0 0
\(79\) −2.59565 −0.292034 −0.146017 0.989282i \(-0.546645\pi\)
−0.146017 + 0.989282i \(0.546645\pi\)
\(80\) −10.5758 −1.18242
\(81\) −2.08140 −0.231267
\(82\) 1.50006 0.165654
\(83\) 13.6065 1.49351 0.746756 0.665098i \(-0.231610\pi\)
0.746756 + 0.665098i \(0.231610\pi\)
\(84\) 9.26693 1.01110
\(85\) 7.48044 0.811368
\(86\) −3.26245 −0.351799
\(87\) 4.87032 0.522153
\(88\) 1.32260 0.140990
\(89\) −15.3302 −1.62500 −0.812498 0.582964i \(-0.801893\pi\)
−0.812498 + 0.582964i \(0.801893\pi\)
\(90\) −1.65858 −0.174830
\(91\) 0 0
\(92\) 15.4581 1.61162
\(93\) −0.877980 −0.0910423
\(94\) −1.62116 −0.167210
\(95\) 19.8788 2.03952
\(96\) 4.58006 0.467450
\(97\) −12.7385 −1.29340 −0.646700 0.762744i \(-0.723852\pi\)
−0.646700 + 0.762744i \(0.723852\pi\)
\(98\) −3.21286 −0.324548
\(99\) −1.52797 −0.153567
\(100\) −9.72425 −0.972425
\(101\) 0.398607 0.0396629 0.0198315 0.999803i \(-0.493687\pi\)
0.0198315 + 0.999803i \(0.493687\pi\)
\(102\) −0.969516 −0.0959964
\(103\) 13.6068 1.34072 0.670360 0.742036i \(-0.266140\pi\)
0.670360 + 0.742036i \(0.266140\pi\)
\(104\) 0 0
\(105\) 15.6791 1.53012
\(106\) −1.76568 −0.171498
\(107\) 7.75320 0.749530 0.374765 0.927120i \(-0.377723\pi\)
0.374765 + 0.927120i \(0.377723\pi\)
\(108\) −10.3503 −0.995958
\(109\) 9.30888 0.891629 0.445815 0.895125i \(-0.352914\pi\)
0.445815 + 0.895125i \(0.352914\pi\)
\(110\) 1.08548 0.103496
\(111\) 12.2027 1.15823
\(112\) 13.4501 1.27091
\(113\) −8.75929 −0.824005 −0.412003 0.911183i \(-0.635171\pi\)
−0.412003 + 0.911183i \(0.635171\pi\)
\(114\) −2.57642 −0.241304
\(115\) 26.1542 2.43889
\(116\) 7.56294 0.702201
\(117\) 0 0
\(118\) 0.236537 0.0217750
\(119\) −9.51343 −0.872095
\(120\) 5.11522 0.466953
\(121\) 1.00000 0.0909091
\(122\) −3.52144 −0.318816
\(123\) 5.34469 0.481914
\(124\) −1.36338 −0.122435
\(125\) −0.514399 −0.0460093
\(126\) 2.10934 0.187915
\(127\) 16.8374 1.49408 0.747040 0.664779i \(-0.231474\pi\)
0.747040 + 0.664779i \(0.231474\pi\)
\(128\) 9.37171 0.828350
\(129\) −11.6240 −1.02344
\(130\) 0 0
\(131\) 14.5768 1.27358 0.636792 0.771035i \(-0.280261\pi\)
0.636792 + 0.771035i \(0.280261\pi\)
\(132\) 2.28586 0.198959
\(133\) −25.2813 −2.19217
\(134\) −2.44221 −0.210975
\(135\) −17.5121 −1.50720
\(136\) −3.10371 −0.266141
\(137\) −2.47456 −0.211416 −0.105708 0.994397i \(-0.533711\pi\)
−0.105708 + 0.994397i \(0.533711\pi\)
\(138\) −3.38976 −0.288555
\(139\) 8.57679 0.727474 0.363737 0.931502i \(-0.381501\pi\)
0.363737 + 0.931502i \(0.381501\pi\)
\(140\) 24.3475 2.05774
\(141\) −5.77616 −0.486440
\(142\) −0.793180 −0.0665622
\(143\) 0 0
\(144\) −5.06937 −0.422447
\(145\) 12.7960 1.06265
\(146\) 0.831110 0.0687832
\(147\) −11.4474 −0.944162
\(148\) 18.9491 1.55760
\(149\) −18.2363 −1.49398 −0.746989 0.664837i \(-0.768501\pi\)
−0.746989 + 0.664837i \(0.768501\pi\)
\(150\) 2.13240 0.174110
\(151\) −16.5757 −1.34891 −0.674455 0.738316i \(-0.735621\pi\)
−0.674455 + 0.738316i \(0.735621\pi\)
\(152\) −8.24789 −0.668992
\(153\) 3.58563 0.289881
\(154\) −1.38048 −0.111243
\(155\) −2.30676 −0.185283
\(156\) 0 0
\(157\) −3.20959 −0.256153 −0.128077 0.991764i \(-0.540880\pi\)
−0.128077 + 0.991764i \(0.540880\pi\)
\(158\) 0.883878 0.0703176
\(159\) −6.29109 −0.498916
\(160\) 12.0334 0.951324
\(161\) −33.2622 −2.62143
\(162\) 0.708763 0.0556857
\(163\) 11.8715 0.929850 0.464925 0.885350i \(-0.346081\pi\)
0.464925 + 0.885350i \(0.346081\pi\)
\(164\) 8.29956 0.648087
\(165\) 3.86754 0.301087
\(166\) −4.63333 −0.359616
\(167\) 12.1933 0.943545 0.471773 0.881720i \(-0.343614\pi\)
0.471773 + 0.881720i \(0.343614\pi\)
\(168\) −6.50540 −0.501903
\(169\) 0 0
\(170\) −2.54726 −0.195366
\(171\) 9.52857 0.728668
\(172\) −18.0505 −1.37634
\(173\) −0.995436 −0.0756816 −0.0378408 0.999284i \(-0.512048\pi\)
−0.0378408 + 0.999284i \(0.512048\pi\)
\(174\) −1.65845 −0.125727
\(175\) 20.9243 1.58173
\(176\) 3.31771 0.250082
\(177\) 0.842776 0.0633469
\(178\) 5.22027 0.391276
\(179\) −13.8360 −1.03415 −0.517077 0.855939i \(-0.672980\pi\)
−0.517077 + 0.855939i \(0.672980\pi\)
\(180\) −9.17660 −0.683984
\(181\) 19.6335 1.45935 0.729673 0.683796i \(-0.239672\pi\)
0.729673 + 0.683796i \(0.239672\pi\)
\(182\) 0 0
\(183\) −12.5468 −0.927486
\(184\) −10.8516 −0.799992
\(185\) 32.0607 2.35715
\(186\) 0.298972 0.0219217
\(187\) −2.34667 −0.171605
\(188\) −8.96957 −0.654173
\(189\) 22.2714 1.62001
\(190\) −6.76916 −0.491086
\(191\) 9.98283 0.722332 0.361166 0.932501i \(-0.382379\pi\)
0.361166 + 0.932501i \(0.382379\pi\)
\(192\) 6.49097 0.468446
\(193\) −2.95160 −0.212461 −0.106230 0.994342i \(-0.533878\pi\)
−0.106230 + 0.994342i \(0.533878\pi\)
\(194\) 4.33775 0.311432
\(195\) 0 0
\(196\) −17.7762 −1.26973
\(197\) −1.96116 −0.139727 −0.0698635 0.997557i \(-0.522256\pi\)
−0.0698635 + 0.997557i \(0.522256\pi\)
\(198\) 0.520307 0.0369766
\(199\) −8.54240 −0.605555 −0.302777 0.953061i \(-0.597914\pi\)
−0.302777 + 0.953061i \(0.597914\pi\)
\(200\) 6.82645 0.482703
\(201\) −8.70153 −0.613759
\(202\) −0.135735 −0.00955025
\(203\) −16.2737 −1.14219
\(204\) −5.36415 −0.375565
\(205\) 14.0424 0.980761
\(206\) −4.63342 −0.322826
\(207\) 12.5366 0.871353
\(208\) 0 0
\(209\) −6.23610 −0.431360
\(210\) −5.33908 −0.368431
\(211\) 23.0336 1.58570 0.792848 0.609420i \(-0.208598\pi\)
0.792848 + 0.609420i \(0.208598\pi\)
\(212\) −9.76919 −0.670950
\(213\) −2.82608 −0.193640
\(214\) −2.64014 −0.180476
\(215\) −30.5404 −2.08284
\(216\) 7.26593 0.494384
\(217\) 2.93368 0.199151
\(218\) −3.16988 −0.214691
\(219\) 2.96123 0.200101
\(220\) 6.00575 0.404908
\(221\) 0 0
\(222\) −4.15528 −0.278884
\(223\) 8.80848 0.589860 0.294930 0.955519i \(-0.404704\pi\)
0.294930 + 0.955519i \(0.404704\pi\)
\(224\) −15.3038 −1.02253
\(225\) −7.88642 −0.525761
\(226\) 2.98273 0.198408
\(227\) 20.6166 1.36837 0.684185 0.729309i \(-0.260158\pi\)
0.684185 + 0.729309i \(0.260158\pi\)
\(228\) −14.2549 −0.944051
\(229\) 6.88948 0.455269 0.227635 0.973747i \(-0.426901\pi\)
0.227635 + 0.973747i \(0.426901\pi\)
\(230\) −8.90607 −0.587249
\(231\) −4.91864 −0.323622
\(232\) −5.30920 −0.348566
\(233\) 10.1842 0.667186 0.333593 0.942717i \(-0.391739\pi\)
0.333593 + 0.942717i \(0.391739\pi\)
\(234\) 0 0
\(235\) −15.1760 −0.989971
\(236\) 1.30871 0.0851900
\(237\) 3.14924 0.204565
\(238\) 3.23954 0.209988
\(239\) −18.7944 −1.21571 −0.607854 0.794049i \(-0.707969\pi\)
−0.607854 + 0.794049i \(0.707969\pi\)
\(240\) 12.8314 0.828262
\(241\) 1.23448 0.0795200 0.0397600 0.999209i \(-0.487341\pi\)
0.0397600 + 0.999209i \(0.487341\pi\)
\(242\) −0.340522 −0.0218896
\(243\) −13.9557 −0.895257
\(244\) −19.4834 −1.24730
\(245\) −30.0762 −1.92150
\(246\) −1.81998 −0.116038
\(247\) 0 0
\(248\) 0.957097 0.0607757
\(249\) −16.5084 −1.04618
\(250\) 0.175164 0.0110784
\(251\) −24.5319 −1.54844 −0.774220 0.632916i \(-0.781858\pi\)
−0.774220 + 0.632916i \(0.781858\pi\)
\(252\) 11.6706 0.735177
\(253\) −8.20474 −0.515828
\(254\) −5.73352 −0.359753
\(255\) −9.07582 −0.568350
\(256\) 7.50867 0.469292
\(257\) −12.8523 −0.801706 −0.400853 0.916142i \(-0.631286\pi\)
−0.400853 + 0.916142i \(0.631286\pi\)
\(258\) 3.95824 0.246429
\(259\) −40.7739 −2.53357
\(260\) 0 0
\(261\) 6.13358 0.379659
\(262\) −4.96374 −0.306661
\(263\) 7.20748 0.444432 0.222216 0.974997i \(-0.428671\pi\)
0.222216 + 0.974997i \(0.428671\pi\)
\(264\) −1.60468 −0.0987611
\(265\) −16.5289 −1.01536
\(266\) 8.60884 0.527842
\(267\) 18.5997 1.13828
\(268\) −13.5123 −0.825394
\(269\) 12.9503 0.789592 0.394796 0.918769i \(-0.370815\pi\)
0.394796 + 0.918769i \(0.370815\pi\)
\(270\) 5.96326 0.362912
\(271\) −6.05682 −0.367926 −0.183963 0.982933i \(-0.558893\pi\)
−0.183963 + 0.982933i \(0.558893\pi\)
\(272\) −7.78556 −0.472069
\(273\) 0 0
\(274\) 0.842642 0.0509059
\(275\) 5.16137 0.311242
\(276\) −18.7549 −1.12891
\(277\) 26.3488 1.58314 0.791572 0.611076i \(-0.209263\pi\)
0.791572 + 0.611076i \(0.209263\pi\)
\(278\) −2.92059 −0.175165
\(279\) −1.10571 −0.0661971
\(280\) −17.0920 −1.02144
\(281\) 14.3133 0.853863 0.426931 0.904284i \(-0.359595\pi\)
0.426931 + 0.904284i \(0.359595\pi\)
\(282\) 1.96691 0.117128
\(283\) −13.4251 −0.798040 −0.399020 0.916942i \(-0.630650\pi\)
−0.399020 + 0.916942i \(0.630650\pi\)
\(284\) −4.38852 −0.260410
\(285\) −24.1184 −1.42865
\(286\) 0 0
\(287\) −17.8587 −1.05417
\(288\) 5.76803 0.339884
\(289\) −11.4932 −0.676068
\(290\) −4.35733 −0.255871
\(291\) 15.4553 0.906005
\(292\) 4.59838 0.269100
\(293\) 19.2112 1.12233 0.561165 0.827704i \(-0.310353\pi\)
0.561165 + 0.827704i \(0.310353\pi\)
\(294\) 3.89808 0.227340
\(295\) 2.21427 0.128920
\(296\) −13.3023 −0.773179
\(297\) 5.49366 0.318775
\(298\) 6.20987 0.359728
\(299\) 0 0
\(300\) 11.7982 0.681168
\(301\) 38.8405 2.23873
\(302\) 5.64439 0.324798
\(303\) −0.483619 −0.0277832
\(304\) −20.6896 −1.18663
\(305\) −32.9648 −1.88756
\(306\) −1.22099 −0.0697992
\(307\) 17.1911 0.981146 0.490573 0.871400i \(-0.336788\pi\)
0.490573 + 0.871400i \(0.336788\pi\)
\(308\) −7.63796 −0.435213
\(309\) −16.5088 −0.939151
\(310\) 0.785503 0.0446136
\(311\) −13.4197 −0.760960 −0.380480 0.924789i \(-0.624241\pi\)
−0.380480 + 0.924789i \(0.624241\pi\)
\(312\) 0 0
\(313\) −13.0687 −0.738684 −0.369342 0.929293i \(-0.620417\pi\)
−0.369342 + 0.929293i \(0.620417\pi\)
\(314\) 1.09294 0.0616780
\(315\) 19.7459 1.11256
\(316\) 4.89033 0.275103
\(317\) 11.3044 0.634918 0.317459 0.948272i \(-0.397170\pi\)
0.317459 + 0.948272i \(0.397170\pi\)
\(318\) 2.14225 0.120132
\(319\) −4.01420 −0.224752
\(320\) 17.0540 0.953350
\(321\) −9.40675 −0.525034
\(322\) 11.3265 0.631202
\(323\) 14.6340 0.814260
\(324\) 3.92145 0.217858
\(325\) 0 0
\(326\) −4.04252 −0.223894
\(327\) −11.2942 −0.624571
\(328\) −5.82631 −0.321704
\(329\) 19.3004 1.06407
\(330\) −1.31698 −0.0724975
\(331\) 5.18040 0.284740 0.142370 0.989813i \(-0.454528\pi\)
0.142370 + 0.989813i \(0.454528\pi\)
\(332\) −25.6353 −1.40692
\(333\) 15.3678 0.842149
\(334\) −4.15209 −0.227192
\(335\) −22.8620 −1.24908
\(336\) −16.3186 −0.890254
\(337\) −7.41964 −0.404174 −0.202087 0.979368i \(-0.564772\pi\)
−0.202087 + 0.979368i \(0.564772\pi\)
\(338\) 0 0
\(339\) 10.6274 0.577202
\(340\) −14.0935 −0.764327
\(341\) 0.723646 0.0391876
\(342\) −3.24469 −0.175453
\(343\) 9.87196 0.533036
\(344\) 12.6715 0.683202
\(345\) −31.7321 −1.70840
\(346\) 0.338968 0.0182230
\(347\) 23.8714 1.28149 0.640743 0.767755i \(-0.278626\pi\)
0.640743 + 0.767755i \(0.278626\pi\)
\(348\) −9.17590 −0.491880
\(349\) 22.7399 1.21724 0.608620 0.793462i \(-0.291724\pi\)
0.608620 + 0.793462i \(0.291724\pi\)
\(350\) −7.12519 −0.380858
\(351\) 0 0
\(352\) −3.77496 −0.201206
\(353\) 19.7394 1.05062 0.525312 0.850910i \(-0.323949\pi\)
0.525312 + 0.850910i \(0.323949\pi\)
\(354\) −0.286984 −0.0152530
\(355\) −7.42510 −0.394084
\(356\) 28.8828 1.53078
\(357\) 11.5424 0.610888
\(358\) 4.71148 0.249009
\(359\) 10.7299 0.566302 0.283151 0.959075i \(-0.408620\pi\)
0.283151 + 0.959075i \(0.408620\pi\)
\(360\) 6.44200 0.339523
\(361\) 19.8889 1.04679
\(362\) −6.68564 −0.351390
\(363\) −1.21327 −0.0636803
\(364\) 0 0
\(365\) 7.78018 0.407233
\(366\) 4.27246 0.223325
\(367\) 4.36648 0.227928 0.113964 0.993485i \(-0.463645\pi\)
0.113964 + 0.993485i \(0.463645\pi\)
\(368\) −27.2210 −1.41899
\(369\) 6.73098 0.350401
\(370\) −10.9174 −0.567567
\(371\) 21.0210 1.09136
\(372\) 1.65415 0.0857639
\(373\) 1.64386 0.0851161 0.0425580 0.999094i \(-0.486449\pi\)
0.0425580 + 0.999094i \(0.486449\pi\)
\(374\) 0.799091 0.0413200
\(375\) 0.624107 0.0322287
\(376\) 6.29666 0.324725
\(377\) 0 0
\(378\) −7.58392 −0.390075
\(379\) 27.3618 1.40548 0.702741 0.711446i \(-0.251959\pi\)
0.702741 + 0.711446i \(0.251959\pi\)
\(380\) −37.4525 −1.92127
\(381\) −20.4284 −1.04658
\(382\) −3.39938 −0.173927
\(383\) 8.65412 0.442205 0.221102 0.975251i \(-0.429034\pi\)
0.221102 + 0.975251i \(0.429034\pi\)
\(384\) −11.3704 −0.580245
\(385\) −12.9230 −0.658616
\(386\) 1.00508 0.0511575
\(387\) −14.6391 −0.744145
\(388\) 23.9999 1.21841
\(389\) −3.91452 −0.198474 −0.0992369 0.995064i \(-0.531640\pi\)
−0.0992369 + 0.995064i \(0.531640\pi\)
\(390\) 0 0
\(391\) 19.2538 0.973705
\(392\) 12.4789 0.630279
\(393\) −17.6857 −0.892125
\(394\) 0.667819 0.0336442
\(395\) 8.27414 0.416317
\(396\) 2.87876 0.144663
\(397\) −33.0114 −1.65680 −0.828398 0.560140i \(-0.810747\pi\)
−0.828398 + 0.560140i \(0.810747\pi\)
\(398\) 2.90888 0.145809
\(399\) 30.6731 1.53558
\(400\) 17.1239 0.856197
\(401\) −3.51309 −0.175435 −0.0877177 0.996145i \(-0.527957\pi\)
−0.0877177 + 0.996145i \(0.527957\pi\)
\(402\) 2.96306 0.147784
\(403\) 0 0
\(404\) −0.750994 −0.0373633
\(405\) 6.63486 0.329689
\(406\) 5.54154 0.275022
\(407\) −10.0577 −0.498539
\(408\) 3.76564 0.186427
\(409\) 34.1687 1.68953 0.844766 0.535136i \(-0.179740\pi\)
0.844766 + 0.535136i \(0.179740\pi\)
\(410\) −4.78173 −0.236153
\(411\) 3.00232 0.148093
\(412\) −25.6358 −1.26299
\(413\) −2.81605 −0.138569
\(414\) −4.26899 −0.209809
\(415\) −43.3734 −2.12912
\(416\) 0 0
\(417\) −10.4060 −0.509583
\(418\) 2.12353 0.103865
\(419\) 19.2903 0.942391 0.471196 0.882029i \(-0.343823\pi\)
0.471196 + 0.882029i \(0.343823\pi\)
\(420\) −29.5401 −1.44141
\(421\) −19.0828 −0.930038 −0.465019 0.885301i \(-0.653952\pi\)
−0.465019 + 0.885301i \(0.653952\pi\)
\(422\) −7.84343 −0.381812
\(423\) −7.27437 −0.353692
\(424\) 6.85799 0.333053
\(425\) −12.1120 −0.587519
\(426\) 0.962344 0.0466257
\(427\) 41.9238 2.02883
\(428\) −14.6074 −0.706074
\(429\) 0 0
\(430\) 10.3997 0.501517
\(431\) −1.54727 −0.0745295 −0.0372647 0.999305i \(-0.511864\pi\)
−0.0372647 + 0.999305i \(0.511864\pi\)
\(432\) 18.2264 0.876918
\(433\) 7.28913 0.350293 0.175147 0.984542i \(-0.443960\pi\)
0.175147 + 0.984542i \(0.443960\pi\)
\(434\) −0.998983 −0.0479527
\(435\) −15.5251 −0.744371
\(436\) −17.5384 −0.839935
\(437\) 51.1656 2.44758
\(438\) −1.00836 −0.0481815
\(439\) 14.1267 0.674229 0.337114 0.941464i \(-0.390549\pi\)
0.337114 + 0.941464i \(0.390549\pi\)
\(440\) −4.21605 −0.200992
\(441\) −14.4165 −0.686502
\(442\) 0 0
\(443\) −13.3152 −0.632624 −0.316312 0.948655i \(-0.602445\pi\)
−0.316312 + 0.948655i \(0.602445\pi\)
\(444\) −22.9904 −1.09108
\(445\) 48.8679 2.31656
\(446\) −2.99948 −0.142030
\(447\) 22.1256 1.04651
\(448\) −21.6889 −1.02470
\(449\) −3.03021 −0.143004 −0.0715022 0.997440i \(-0.522779\pi\)
−0.0715022 + 0.997440i \(0.522779\pi\)
\(450\) 2.68550 0.126596
\(451\) −4.40518 −0.207432
\(452\) 16.5029 0.776231
\(453\) 20.1108 0.944889
\(454\) −7.02040 −0.329484
\(455\) 0 0
\(456\) 10.0069 0.468618
\(457\) −23.8096 −1.11376 −0.556882 0.830592i \(-0.688002\pi\)
−0.556882 + 0.830592i \(0.688002\pi\)
\(458\) −2.34602 −0.109622
\(459\) −12.8918 −0.601737
\(460\) −49.2756 −2.29749
\(461\) −15.5141 −0.722565 −0.361283 0.932456i \(-0.617661\pi\)
−0.361283 + 0.932456i \(0.617661\pi\)
\(462\) 1.67490 0.0779236
\(463\) −18.3059 −0.850748 −0.425374 0.905018i \(-0.639857\pi\)
−0.425374 + 0.905018i \(0.639857\pi\)
\(464\) −13.3180 −0.618271
\(465\) 2.79873 0.129788
\(466\) −3.46793 −0.160649
\(467\) 27.5553 1.27511 0.637553 0.770407i \(-0.279947\pi\)
0.637553 + 0.770407i \(0.279947\pi\)
\(468\) 0 0
\(469\) 29.0753 1.34257
\(470\) 5.16776 0.238371
\(471\) 3.89411 0.179431
\(472\) −0.918720 −0.0422875
\(473\) 9.58073 0.440522
\(474\) −1.07238 −0.0492563
\(475\) −32.1868 −1.47683
\(476\) 17.9237 0.821533
\(477\) −7.92286 −0.362763
\(478\) 6.39990 0.292725
\(479\) −8.86209 −0.404919 −0.202460 0.979291i \(-0.564893\pi\)
−0.202460 + 0.979291i \(0.564893\pi\)
\(480\) −14.5998 −0.666387
\(481\) 0 0
\(482\) −0.420368 −0.0191473
\(483\) 40.3561 1.83627
\(484\) −1.88404 −0.0856384
\(485\) 40.6064 1.84384
\(486\) 4.75222 0.215565
\(487\) −1.95588 −0.0886296 −0.0443148 0.999018i \(-0.514110\pi\)
−0.0443148 + 0.999018i \(0.514110\pi\)
\(488\) 13.6774 0.619147
\(489\) −14.4034 −0.651344
\(490\) 10.2416 0.462669
\(491\) −41.7444 −1.88390 −0.941949 0.335755i \(-0.891008\pi\)
−0.941949 + 0.335755i \(0.891008\pi\)
\(492\) −10.0696 −0.453974
\(493\) 9.41999 0.424255
\(494\) 0 0
\(495\) 4.87069 0.218921
\(496\) 2.40085 0.107801
\(497\) 9.44306 0.423579
\(498\) 5.62149 0.251905
\(499\) −27.7777 −1.24350 −0.621749 0.783216i \(-0.713578\pi\)
−0.621749 + 0.783216i \(0.713578\pi\)
\(500\) 0.969151 0.0433418
\(501\) −14.7938 −0.660938
\(502\) 8.35366 0.372842
\(503\) 24.6062 1.09714 0.548569 0.836106i \(-0.315173\pi\)
0.548569 + 0.836106i \(0.315173\pi\)
\(504\) −8.19276 −0.364935
\(505\) −1.27064 −0.0565426
\(506\) 2.79390 0.124204
\(507\) 0 0
\(508\) −31.7225 −1.40746
\(509\) −40.3334 −1.78775 −0.893874 0.448318i \(-0.852023\pi\)
−0.893874 + 0.448318i \(0.852023\pi\)
\(510\) 3.09052 0.136850
\(511\) −9.89463 −0.437713
\(512\) −21.3003 −0.941348
\(513\) −34.2590 −1.51257
\(514\) 4.37650 0.193039
\(515\) −43.3743 −1.91130
\(516\) 21.9002 0.964103
\(517\) 4.76081 0.209380
\(518\) 13.8844 0.610047
\(519\) 1.20773 0.0530137
\(520\) 0 0
\(521\) 16.8953 0.740198 0.370099 0.928992i \(-0.379324\pi\)
0.370099 + 0.928992i \(0.379324\pi\)
\(522\) −2.08862 −0.0914164
\(523\) 4.22744 0.184853 0.0924265 0.995720i \(-0.470538\pi\)
0.0924265 + 0.995720i \(0.470538\pi\)
\(524\) −27.4634 −1.19975
\(525\) −25.3869 −1.10798
\(526\) −2.45431 −0.107013
\(527\) −1.69816 −0.0739728
\(528\) −4.02529 −0.175178
\(529\) 44.3177 1.92686
\(530\) 5.62845 0.244484
\(531\) 1.06137 0.0460597
\(532\) 47.6311 2.06507
\(533\) 0 0
\(534\) −6.33361 −0.274082
\(535\) −24.7148 −1.06851
\(536\) 9.48564 0.409717
\(537\) 16.7869 0.724408
\(538\) −4.40985 −0.190122
\(539\) 9.43510 0.406399
\(540\) 32.9936 1.41982
\(541\) −34.1415 −1.46786 −0.733929 0.679227i \(-0.762315\pi\)
−0.733929 + 0.679227i \(0.762315\pi\)
\(542\) 2.06248 0.0885912
\(543\) −23.8208 −1.02225
\(544\) 8.85857 0.379808
\(545\) −29.6738 −1.27109
\(546\) 0 0
\(547\) −26.3451 −1.12644 −0.563218 0.826309i \(-0.690437\pi\)
−0.563218 + 0.826309i \(0.690437\pi\)
\(548\) 4.66218 0.199159
\(549\) −15.8012 −0.674377
\(550\) −1.75756 −0.0749427
\(551\) 25.0330 1.06644
\(552\) 13.1660 0.560381
\(553\) −10.5228 −0.447477
\(554\) −8.97234 −0.381198
\(555\) −38.8983 −1.65114
\(556\) −16.1591 −0.685297
\(557\) −30.8796 −1.30841 −0.654205 0.756317i \(-0.726997\pi\)
−0.654205 + 0.756317i \(0.726997\pi\)
\(558\) 0.376519 0.0159393
\(559\) 0 0
\(560\) −42.8747 −1.81179
\(561\) 2.84714 0.120207
\(562\) −4.87401 −0.205598
\(563\) 2.54576 0.107291 0.0536456 0.998560i \(-0.482916\pi\)
0.0536456 + 0.998560i \(0.482916\pi\)
\(564\) 10.8825 0.458237
\(565\) 27.9219 1.17468
\(566\) 4.57155 0.192156
\(567\) −8.43805 −0.354365
\(568\) 3.08075 0.129265
\(569\) 45.7155 1.91649 0.958247 0.285942i \(-0.0923063\pi\)
0.958247 + 0.285942i \(0.0923063\pi\)
\(570\) 8.21283 0.343998
\(571\) 33.6349 1.40758 0.703788 0.710410i \(-0.251491\pi\)
0.703788 + 0.710410i \(0.251491\pi\)
\(572\) 0 0
\(573\) −12.1119 −0.505982
\(574\) 6.08129 0.253828
\(575\) −42.3477 −1.76602
\(576\) 8.17459 0.340608
\(577\) 6.91915 0.288048 0.144024 0.989574i \(-0.453996\pi\)
0.144024 + 0.989574i \(0.453996\pi\)
\(578\) 3.91368 0.162787
\(579\) 3.58109 0.148825
\(580\) −24.1083 −1.00104
\(581\) 55.1612 2.28847
\(582\) −5.26287 −0.218153
\(583\) 5.18522 0.214750
\(584\) −3.22807 −0.133578
\(585\) 0 0
\(586\) −6.54184 −0.270241
\(587\) −7.84590 −0.323835 −0.161917 0.986804i \(-0.551768\pi\)
−0.161917 + 0.986804i \(0.551768\pi\)
\(588\) 21.5673 0.889421
\(589\) −4.51273 −0.185944
\(590\) −0.754007 −0.0310420
\(591\) 2.37942 0.0978764
\(592\) −33.3684 −1.37143
\(593\) −20.0657 −0.823999 −0.411999 0.911184i \(-0.635169\pi\)
−0.411999 + 0.911184i \(0.635169\pi\)
\(594\) −1.87071 −0.0767563
\(595\) 30.3259 1.24324
\(596\) 34.3580 1.40736
\(597\) 10.3643 0.424181
\(598\) 0 0
\(599\) −27.3966 −1.11940 −0.559698 0.828697i \(-0.689083\pi\)
−0.559698 + 0.828697i \(0.689083\pi\)
\(600\) −8.28234 −0.338125
\(601\) 22.6514 0.923970 0.461985 0.886888i \(-0.347137\pi\)
0.461985 + 0.886888i \(0.347137\pi\)
\(602\) −13.2261 −0.539054
\(603\) −10.9585 −0.446265
\(604\) 31.2293 1.27070
\(605\) −3.18769 −0.129598
\(606\) 0.164683 0.00668979
\(607\) −11.6319 −0.472124 −0.236062 0.971738i \(-0.575857\pi\)
−0.236062 + 0.971738i \(0.575857\pi\)
\(608\) 23.5410 0.954715
\(609\) 19.7444 0.800083
\(610\) 11.2252 0.454497
\(611\) 0 0
\(612\) −6.75549 −0.273075
\(613\) −27.6162 −1.11541 −0.557704 0.830040i \(-0.688318\pi\)
−0.557704 + 0.830040i \(0.688318\pi\)
\(614\) −5.85394 −0.236246
\(615\) −17.0372 −0.687006
\(616\) 5.36186 0.216036
\(617\) −13.4667 −0.542150 −0.271075 0.962558i \(-0.587379\pi\)
−0.271075 + 0.962558i \(0.587379\pi\)
\(618\) 5.62160 0.226134
\(619\) 1.79201 0.0720271 0.0360136 0.999351i \(-0.488534\pi\)
0.0360136 + 0.999351i \(0.488534\pi\)
\(620\) 4.34604 0.174541
\(621\) −45.0741 −1.80876
\(622\) 4.56970 0.183228
\(623\) −62.1489 −2.48994
\(624\) 0 0
\(625\) −24.1671 −0.966684
\(626\) 4.45017 0.177865
\(627\) 7.56609 0.302160
\(628\) 6.04702 0.241302
\(629\) 23.6019 0.941071
\(630\) −6.72392 −0.267887
\(631\) −34.8888 −1.38890 −0.694451 0.719540i \(-0.744353\pi\)
−0.694451 + 0.719540i \(0.744353\pi\)
\(632\) −3.43302 −0.136558
\(633\) −27.9460 −1.11075
\(634\) −3.84940 −0.152879
\(635\) −53.6725 −2.12993
\(636\) 11.8527 0.469990
\(637\) 0 0
\(638\) 1.36692 0.0541171
\(639\) −3.55911 −0.140796
\(640\) −29.8741 −1.18088
\(641\) 3.84384 0.151823 0.0759114 0.997115i \(-0.475813\pi\)
0.0759114 + 0.997115i \(0.475813\pi\)
\(642\) 3.20321 0.126420
\(643\) −7.25080 −0.285944 −0.142972 0.989727i \(-0.545666\pi\)
−0.142972 + 0.989727i \(0.545666\pi\)
\(644\) 62.6675 2.46944
\(645\) 37.0538 1.45899
\(646\) −4.98321 −0.196062
\(647\) 27.5012 1.08118 0.540592 0.841285i \(-0.318200\pi\)
0.540592 + 0.841285i \(0.318200\pi\)
\(648\) −2.75287 −0.108143
\(649\) −0.694630 −0.0272666
\(650\) 0 0
\(651\) −3.55935 −0.139502
\(652\) −22.3665 −0.875940
\(653\) 9.21600 0.360650 0.180325 0.983607i \(-0.442285\pi\)
0.180325 + 0.983607i \(0.442285\pi\)
\(654\) 3.84593 0.150388
\(655\) −46.4665 −1.81559
\(656\) −14.6151 −0.570625
\(657\) 3.72931 0.145494
\(658\) −6.57222 −0.256212
\(659\) −29.7952 −1.16066 −0.580328 0.814383i \(-0.697075\pi\)
−0.580328 + 0.814383i \(0.697075\pi\)
\(660\) −7.28661 −0.283631
\(661\) 15.5749 0.605793 0.302896 0.953024i \(-0.402046\pi\)
0.302896 + 0.953024i \(0.402046\pi\)
\(662\) −1.76404 −0.0685614
\(663\) 0 0
\(664\) 17.9961 0.698382
\(665\) 80.5889 3.12510
\(666\) −5.23307 −0.202777
\(667\) 32.9355 1.27527
\(668\) −22.9727 −0.888841
\(669\) −10.6871 −0.413187
\(670\) 7.78500 0.300761
\(671\) 10.3413 0.399221
\(672\) 18.5677 0.716263
\(673\) 0.147971 0.00570386 0.00285193 0.999996i \(-0.499092\pi\)
0.00285193 + 0.999996i \(0.499092\pi\)
\(674\) 2.52655 0.0973192
\(675\) 28.3548 1.09138
\(676\) 0 0
\(677\) −13.5263 −0.519857 −0.259928 0.965628i \(-0.583699\pi\)
−0.259928 + 0.965628i \(0.583699\pi\)
\(678\) −3.61887 −0.138982
\(679\) −51.6422 −1.98185
\(680\) 9.89366 0.379404
\(681\) −25.0135 −0.958520
\(682\) −0.246418 −0.00943582
\(683\) −28.2401 −1.08058 −0.540289 0.841480i \(-0.681685\pi\)
−0.540289 + 0.841480i \(0.681685\pi\)
\(684\) −17.9523 −0.686422
\(685\) 7.88813 0.301390
\(686\) −3.36162 −0.128347
\(687\) −8.35881 −0.318909
\(688\) 31.7861 1.21183
\(689\) 0 0
\(690\) 10.8055 0.411358
\(691\) 4.75615 0.180932 0.0904662 0.995900i \(-0.471164\pi\)
0.0904662 + 0.995900i \(0.471164\pi\)
\(692\) 1.87545 0.0712937
\(693\) −6.19442 −0.235307
\(694\) −8.12875 −0.308563
\(695\) −27.3402 −1.03707
\(696\) 6.44150 0.244165
\(697\) 10.3375 0.391560
\(698\) −7.74344 −0.293094
\(699\) −12.3562 −0.467353
\(700\) −39.4223 −1.49002
\(701\) 13.5172 0.510536 0.255268 0.966870i \(-0.417836\pi\)
0.255268 + 0.966870i \(0.417836\pi\)
\(702\) 0 0
\(703\) 62.7205 2.36555
\(704\) −5.34997 −0.201635
\(705\) 18.4126 0.693458
\(706\) −6.72171 −0.252975
\(707\) 1.61596 0.0607745
\(708\) −1.58783 −0.0596742
\(709\) 37.1430 1.39493 0.697466 0.716617i \(-0.254311\pi\)
0.697466 + 0.716617i \(0.254311\pi\)
\(710\) 2.52841 0.0948896
\(711\) 3.96608 0.148740
\(712\) −20.2758 −0.759866
\(713\) −5.93733 −0.222355
\(714\) −3.93044 −0.147093
\(715\) 0 0
\(716\) 26.0677 0.974196
\(717\) 22.8027 0.851583
\(718\) −3.65377 −0.136357
\(719\) −33.2422 −1.23973 −0.619863 0.784710i \(-0.712812\pi\)
−0.619863 + 0.784710i \(0.712812\pi\)
\(720\) 16.1596 0.602232
\(721\) 55.1623 2.05435
\(722\) −6.77262 −0.252051
\(723\) −1.49776 −0.0557024
\(724\) −36.9904 −1.37474
\(725\) −20.7188 −0.769476
\(726\) 0.413146 0.0153333
\(727\) −23.9978 −0.890029 −0.445015 0.895523i \(-0.646802\pi\)
−0.445015 + 0.895523i \(0.646802\pi\)
\(728\) 0 0
\(729\) 23.1762 0.858379
\(730\) −2.64932 −0.0980558
\(731\) −22.4828 −0.831555
\(732\) 23.6387 0.873712
\(733\) 46.2211 1.70721 0.853607 0.520918i \(-0.174410\pi\)
0.853607 + 0.520918i \(0.174410\pi\)
\(734\) −1.48688 −0.0548818
\(735\) 36.4906 1.34598
\(736\) 30.9726 1.14166
\(737\) 7.17195 0.264182
\(738\) −2.29205 −0.0843715
\(739\) 38.6098 1.42028 0.710142 0.704058i \(-0.248631\pi\)
0.710142 + 0.704058i \(0.248631\pi\)
\(740\) −60.4037 −2.22049
\(741\) 0 0
\(742\) −7.15812 −0.262783
\(743\) −4.54400 −0.166703 −0.0833517 0.996520i \(-0.526562\pi\)
−0.0833517 + 0.996520i \(0.526562\pi\)
\(744\) −1.16122 −0.0425724
\(745\) 58.1317 2.12978
\(746\) −0.559772 −0.0204947
\(747\) −20.7904 −0.760680
\(748\) 4.42122 0.161656
\(749\) 31.4317 1.14849
\(750\) −0.212522 −0.00776021
\(751\) 15.0106 0.547744 0.273872 0.961766i \(-0.411696\pi\)
0.273872 + 0.961766i \(0.411696\pi\)
\(752\) 15.7950 0.575984
\(753\) 29.7639 1.08466
\(754\) 0 0
\(755\) 52.8381 1.92298
\(756\) −41.9604 −1.52608
\(757\) −24.8517 −0.903251 −0.451625 0.892208i \(-0.649156\pi\)
−0.451625 + 0.892208i \(0.649156\pi\)
\(758\) −9.31730 −0.338420
\(759\) 9.95459 0.361329
\(760\) 26.2917 0.953700
\(761\) 34.4446 1.24862 0.624308 0.781178i \(-0.285381\pi\)
0.624308 + 0.781178i \(0.285381\pi\)
\(762\) 6.95632 0.252001
\(763\) 37.7384 1.36622
\(764\) −18.8081 −0.680453
\(765\) −11.4299 −0.413248
\(766\) −2.94692 −0.106477
\(767\) 0 0
\(768\) −9.11006 −0.328731
\(769\) −1.69417 −0.0610935 −0.0305467 0.999533i \(-0.509725\pi\)
−0.0305467 + 0.999533i \(0.509725\pi\)
\(770\) 4.40056 0.158585
\(771\) 15.5934 0.561582
\(772\) 5.56094 0.200143
\(773\) −3.09763 −0.111414 −0.0557071 0.998447i \(-0.517741\pi\)
−0.0557071 + 0.998447i \(0.517741\pi\)
\(774\) 4.98493 0.179179
\(775\) 3.73501 0.134165
\(776\) −16.8480 −0.604808
\(777\) 49.4699 1.77472
\(778\) 1.33298 0.0477896
\(779\) 27.4712 0.984256
\(780\) 0 0
\(781\) 2.32931 0.0833491
\(782\) −6.55634 −0.234454
\(783\) −22.0527 −0.788098
\(784\) 31.3030 1.11796
\(785\) 10.2312 0.365167
\(786\) 6.02237 0.214811
\(787\) 1.37743 0.0491000 0.0245500 0.999699i \(-0.492185\pi\)
0.0245500 + 0.999699i \(0.492185\pi\)
\(788\) 3.69492 0.131626
\(789\) −8.74463 −0.311317
\(790\) −2.81753 −0.100243
\(791\) −35.5104 −1.26260
\(792\) −2.02090 −0.0718095
\(793\) 0 0
\(794\) 11.2411 0.398932
\(795\) 20.0540 0.711243
\(796\) 16.0943 0.570446
\(797\) −50.0186 −1.77175 −0.885875 0.463925i \(-0.846441\pi\)
−0.885875 + 0.463925i \(0.846441\pi\)
\(798\) −10.4449 −0.369744
\(799\) −11.1720 −0.395238
\(800\) −19.4840 −0.688863
\(801\) 23.4241 0.827648
\(802\) 1.19629 0.0422423
\(803\) −2.44069 −0.0861302
\(804\) 16.3941 0.578174
\(805\) 106.030 3.73705
\(806\) 0 0
\(807\) −15.7122 −0.553096
\(808\) 0.527199 0.0185468
\(809\) 20.9847 0.737784 0.368892 0.929472i \(-0.379737\pi\)
0.368892 + 0.929472i \(0.379737\pi\)
\(810\) −2.25932 −0.0793843
\(811\) −36.4314 −1.27928 −0.639641 0.768674i \(-0.720917\pi\)
−0.639641 + 0.768674i \(0.720917\pi\)
\(812\) 30.6603 1.07597
\(813\) 7.34858 0.257726
\(814\) 3.42485 0.120041
\(815\) −37.8428 −1.32557
\(816\) 9.44601 0.330677
\(817\) −59.7464 −2.09026
\(818\) −11.6352 −0.406815
\(819\) 0 0
\(820\) −26.4564 −0.923898
\(821\) −18.3895 −0.641799 −0.320899 0.947113i \(-0.603985\pi\)
−0.320899 + 0.947113i \(0.603985\pi\)
\(822\) −1.02235 −0.0356587
\(823\) 30.3408 1.05761 0.528807 0.848742i \(-0.322640\pi\)
0.528807 + 0.848742i \(0.322640\pi\)
\(824\) 17.9964 0.626935
\(825\) −6.26215 −0.218020
\(826\) 0.958926 0.0333653
\(827\) −3.11611 −0.108358 −0.0541788 0.998531i \(-0.517254\pi\)
−0.0541788 + 0.998531i \(0.517254\pi\)
\(828\) −23.6195 −0.820834
\(829\) 23.6630 0.821850 0.410925 0.911669i \(-0.365206\pi\)
0.410925 + 0.911669i \(0.365206\pi\)
\(830\) 14.7696 0.512661
\(831\) −31.9682 −1.10897
\(832\) 0 0
\(833\) −22.1410 −0.767141
\(834\) 3.54347 0.122700
\(835\) −38.8684 −1.34510
\(836\) 11.7491 0.406351
\(837\) 3.97547 0.137412
\(838\) −6.56876 −0.226914
\(839\) −1.11574 −0.0385195 −0.0192598 0.999815i \(-0.506131\pi\)
−0.0192598 + 0.999815i \(0.506131\pi\)
\(840\) 20.7372 0.715502
\(841\) −12.8862 −0.444351
\(842\) 6.49811 0.223940
\(843\) −17.3660 −0.598116
\(844\) −43.3962 −1.49376
\(845\) 0 0
\(846\) 2.47708 0.0851639
\(847\) 4.05402 0.139298
\(848\) 17.2031 0.590756
\(849\) 16.2883 0.559014
\(850\) 4.12441 0.141466
\(851\) 82.5204 2.82876
\(852\) 5.32447 0.182413
\(853\) 31.0297 1.06244 0.531219 0.847235i \(-0.321734\pi\)
0.531219 + 0.847235i \(0.321734\pi\)
\(854\) −14.2760 −0.488514
\(855\) −30.3741 −1.03877
\(856\) 10.2544 0.350489
\(857\) 42.0441 1.43620 0.718099 0.695941i \(-0.245012\pi\)
0.718099 + 0.695941i \(0.245012\pi\)
\(858\) 0 0
\(859\) 44.7236 1.52595 0.762975 0.646428i \(-0.223738\pi\)
0.762975 + 0.646428i \(0.223738\pi\)
\(860\) 57.5395 1.96208
\(861\) 21.6675 0.738426
\(862\) 0.526880 0.0179456
\(863\) 41.5738 1.41519 0.707594 0.706619i \(-0.249781\pi\)
0.707594 + 0.706619i \(0.249781\pi\)
\(864\) −20.7384 −0.705533
\(865\) 3.17314 0.107890
\(866\) −2.48211 −0.0843456
\(867\) 13.9443 0.473575
\(868\) −5.52718 −0.187605
\(869\) −2.59565 −0.0880516
\(870\) 5.28663 0.179234
\(871\) 0 0
\(872\) 12.3120 0.416936
\(873\) 19.4641 0.658759
\(874\) −17.4230 −0.589342
\(875\) −2.08539 −0.0704989
\(876\) −5.57908 −0.188500
\(877\) −2.69580 −0.0910306 −0.0455153 0.998964i \(-0.514493\pi\)
−0.0455153 + 0.998964i \(0.514493\pi\)
\(878\) −4.81044 −0.162345
\(879\) −23.3084 −0.786174
\(880\) −10.5758 −0.356512
\(881\) 45.7371 1.54092 0.770461 0.637487i \(-0.220026\pi\)
0.770461 + 0.637487i \(0.220026\pi\)
\(882\) 4.90915 0.165300
\(883\) −43.7239 −1.47143 −0.735713 0.677293i \(-0.763153\pi\)
−0.735713 + 0.677293i \(0.763153\pi\)
\(884\) 0 0
\(885\) −2.68651 −0.0903060
\(886\) 4.53412 0.152327
\(887\) −13.1632 −0.441977 −0.220989 0.975276i \(-0.570928\pi\)
−0.220989 + 0.975276i \(0.570928\pi\)
\(888\) 16.1393 0.541599
\(889\) 68.2593 2.28934
\(890\) −16.6406 −0.557794
\(891\) −2.08140 −0.0697295
\(892\) −16.5956 −0.555661
\(893\) −29.6889 −0.993500
\(894\) −7.53427 −0.251984
\(895\) 44.1050 1.47427
\(896\) 37.9931 1.26926
\(897\) 0 0
\(898\) 1.03185 0.0344334
\(899\) −2.90486 −0.0968826
\(900\) 14.8584 0.495279
\(901\) −12.1680 −0.405374
\(902\) 1.50006 0.0499466
\(903\) −47.1241 −1.56819
\(904\) −11.5851 −0.385314
\(905\) −62.5855 −2.08041
\(906\) −6.84818 −0.227516
\(907\) −31.6975 −1.05250 −0.526250 0.850330i \(-0.676402\pi\)
−0.526250 + 0.850330i \(0.676402\pi\)
\(908\) −38.8425 −1.28903
\(909\) −0.609060 −0.0202012
\(910\) 0 0
\(911\) 23.6450 0.783393 0.391696 0.920094i \(-0.371888\pi\)
0.391696 + 0.920094i \(0.371888\pi\)
\(912\) 25.1021 0.831214
\(913\) 13.6065 0.450311
\(914\) 8.10768 0.268178
\(915\) 39.9953 1.32220
\(916\) −12.9801 −0.428874
\(917\) 59.0949 1.95148
\(918\) 4.38994 0.144890
\(919\) 27.0043 0.890788 0.445394 0.895335i \(-0.353064\pi\)
0.445394 + 0.895335i \(0.353064\pi\)
\(920\) 34.5916 1.14045
\(921\) −20.8574 −0.687276
\(922\) 5.28290 0.173983
\(923\) 0 0
\(924\) 9.26693 0.304860
\(925\) −51.9113 −1.70683
\(926\) 6.23357 0.204848
\(927\) −20.7908 −0.682859
\(928\) 15.1535 0.497437
\(929\) 30.8019 1.01058 0.505288 0.862951i \(-0.331386\pi\)
0.505288 + 0.862951i \(0.331386\pi\)
\(930\) −0.953029 −0.0312511
\(931\) −58.8382 −1.92835
\(932\) −19.1874 −0.628505
\(933\) 16.2817 0.533040
\(934\) −9.38318 −0.307027
\(935\) 7.48044 0.244637
\(936\) 0 0
\(937\) 51.5301 1.68342 0.841708 0.539933i \(-0.181550\pi\)
0.841708 + 0.539933i \(0.181550\pi\)
\(938\) −9.90077 −0.323272
\(939\) 15.8559 0.517436
\(940\) 28.5922 0.932575
\(941\) −43.8944 −1.43092 −0.715459 0.698655i \(-0.753782\pi\)
−0.715459 + 0.698655i \(0.753782\pi\)
\(942\) −1.32603 −0.0432044
\(943\) 36.1434 1.17699
\(944\) −2.30458 −0.0750078
\(945\) −70.9944 −2.30945
\(946\) −3.26245 −0.106071
\(947\) −0.525148 −0.0170650 −0.00853251 0.999964i \(-0.502716\pi\)
−0.00853251 + 0.999964i \(0.502716\pi\)
\(948\) −5.93330 −0.192705
\(949\) 0 0
\(950\) 10.9603 0.355600
\(951\) −13.7153 −0.444749
\(952\) −12.5825 −0.407801
\(953\) −6.98333 −0.226212 −0.113106 0.993583i \(-0.536080\pi\)
−0.113106 + 0.993583i \(0.536080\pi\)
\(954\) 2.69791 0.0873480
\(955\) −31.8222 −1.02974
\(956\) 35.4095 1.14522
\(957\) 4.87032 0.157435
\(958\) 3.01774 0.0974987
\(959\) −10.0319 −0.323948
\(960\) −20.6912 −0.667806
\(961\) −30.4763 −0.983108
\(962\) 0 0
\(963\) −11.8467 −0.381753
\(964\) −2.32582 −0.0749096
\(965\) 9.40878 0.302879
\(966\) −13.7422 −0.442146
\(967\) −12.2724 −0.394652 −0.197326 0.980338i \(-0.563226\pi\)
−0.197326 + 0.980338i \(0.563226\pi\)
\(968\) 1.32260 0.0425101
\(969\) −17.7551 −0.570375
\(970\) −13.8274 −0.443971
\(971\) 39.1865 1.25755 0.628777 0.777586i \(-0.283556\pi\)
0.628777 + 0.777586i \(0.283556\pi\)
\(972\) 26.2931 0.843352
\(973\) 34.7705 1.11469
\(974\) 0.666022 0.0213407
\(975\) 0 0
\(976\) 34.3094 1.09822
\(977\) −32.7362 −1.04733 −0.523663 0.851926i \(-0.675435\pi\)
−0.523663 + 0.851926i \(0.675435\pi\)
\(978\) 4.90468 0.156834
\(979\) −15.3302 −0.489955
\(980\) 56.6649 1.81009
\(981\) −14.2237 −0.454127
\(982\) 14.2149 0.453615
\(983\) −47.8968 −1.52767 −0.763836 0.645411i \(-0.776686\pi\)
−0.763836 + 0.645411i \(0.776686\pi\)
\(984\) 7.06890 0.225348
\(985\) 6.25158 0.199192
\(986\) −3.20771 −0.102154
\(987\) −23.4167 −0.745361
\(988\) 0 0
\(989\) −78.6074 −2.49957
\(990\) −1.65858 −0.0527131
\(991\) 39.8530 1.26597 0.632986 0.774163i \(-0.281829\pi\)
0.632986 + 0.774163i \(0.281829\pi\)
\(992\) −2.73174 −0.0867327
\(993\) −6.28523 −0.199456
\(994\) −3.21557 −0.101992
\(995\) 27.2305 0.863266
\(996\) 31.1026 0.985525
\(997\) 35.4976 1.12422 0.562110 0.827062i \(-0.309990\pi\)
0.562110 + 0.827062i \(0.309990\pi\)
\(998\) 9.45891 0.299416
\(999\) −55.2533 −1.74814
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 1859.2.a.t.1.11 yes 21
13.12 even 2 1859.2.a.s.1.11 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.11 21 13.12 even 2
1859.2.a.t.1.11 yes 21 1.1 even 1 trivial