Properties

Label 1859.2.a.t.1.1
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 1.1
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} -1.06756 q^{5} +0.230476 q^{6} -3.59787 q^{7} -10.1571 q^{8} -2.99307 q^{9} +O(q^{10})\) \(q-2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} -1.06756 q^{5} +0.230476 q^{6} -3.59787 q^{7} -10.1571 q^{8} -2.99307 q^{9} +2.95619 q^{10} +1.00000 q^{11} -0.471752 q^{12} +9.96293 q^{14} +0.0888538 q^{15} +16.7902 q^{16} -7.39916 q^{17} +8.28816 q^{18} -4.02839 q^{19} -6.05092 q^{20} +0.299454 q^{21} -2.76912 q^{22} +0.0759617 q^{23} +0.845385 q^{24} -3.86032 q^{25} +0.498808 q^{27} -20.3928 q^{28} -4.74746 q^{29} -0.246046 q^{30} -0.177026 q^{31} -26.1799 q^{32} -0.0832308 q^{33} +20.4891 q^{34} +3.84094 q^{35} -16.9647 q^{36} +4.15643 q^{37} +11.1551 q^{38} +10.8433 q^{40} +3.24661 q^{41} -0.829223 q^{42} -1.63410 q^{43} +5.66800 q^{44} +3.19528 q^{45} -0.210347 q^{46} -7.85313 q^{47} -1.39747 q^{48} +5.94470 q^{49} +10.6897 q^{50} +0.615838 q^{51} -4.66525 q^{53} -1.38126 q^{54} -1.06756 q^{55} +36.5440 q^{56} +0.335287 q^{57} +13.1463 q^{58} +6.77125 q^{59} +0.503623 q^{60} +2.93743 q^{61} +0.490206 q^{62} +10.7687 q^{63} +38.9146 q^{64} +0.230476 q^{66} +6.14511 q^{67} -41.9385 q^{68} -0.00632236 q^{69} -10.6360 q^{70} -7.85704 q^{71} +30.4010 q^{72} +12.3455 q^{73} -11.5096 q^{74} +0.321298 q^{75} -22.8329 q^{76} -3.59787 q^{77} +13.7084 q^{79} -17.9246 q^{80} +8.93770 q^{81} -8.99024 q^{82} -13.3856 q^{83} +1.69731 q^{84} +7.89904 q^{85} +4.52500 q^{86} +0.395135 q^{87} -10.1571 q^{88} -3.95646 q^{89} -8.84810 q^{90} +0.430551 q^{92} +0.0147340 q^{93} +21.7462 q^{94} +4.30055 q^{95} +2.17897 q^{96} -9.04232 q^{97} -16.4616 q^{98} -2.99307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76912 −1.95806 −0.979030 0.203715i \(-0.934698\pi\)
−0.979030 + 0.203715i \(0.934698\pi\)
\(3\) −0.0832308 −0.0480533 −0.0240267 0.999711i \(-0.507649\pi\)
−0.0240267 + 0.999711i \(0.507649\pi\)
\(4\) 5.66800 2.83400
\(5\) −1.06756 −0.477427 −0.238713 0.971090i \(-0.576726\pi\)
−0.238713 + 0.971090i \(0.576726\pi\)
\(6\) 0.230476 0.0940913
\(7\) −3.59787 −1.35987 −0.679934 0.733273i \(-0.737992\pi\)
−0.679934 + 0.733273i \(0.737992\pi\)
\(8\) −10.1571 −3.59108
\(9\) −2.99307 −0.997691
\(10\) 2.95619 0.934830
\(11\) 1.00000 0.301511
\(12\) −0.471752 −0.136183
\(13\) 0 0
\(14\) 9.96293 2.66271
\(15\) 0.0888538 0.0229419
\(16\) 16.7902 4.19756
\(17\) −7.39916 −1.79456 −0.897280 0.441461i \(-0.854460\pi\)
−0.897280 + 0.441461i \(0.854460\pi\)
\(18\) 8.28816 1.95354
\(19\) −4.02839 −0.924177 −0.462088 0.886834i \(-0.652900\pi\)
−0.462088 + 0.886834i \(0.652900\pi\)
\(20\) −6.05092 −1.35303
\(21\) 0.299454 0.0653462
\(22\) −2.76912 −0.590377
\(23\) 0.0759617 0.0158391 0.00791956 0.999969i \(-0.497479\pi\)
0.00791956 + 0.999969i \(0.497479\pi\)
\(24\) 0.845385 0.172564
\(25\) −3.86032 −0.772064
\(26\) 0 0
\(27\) 0.498808 0.0959957
\(28\) −20.3928 −3.85387
\(29\) −4.74746 −0.881581 −0.440791 0.897610i \(-0.645302\pi\)
−0.440791 + 0.897610i \(0.645302\pi\)
\(30\) −0.246046 −0.0449217
\(31\) −0.177026 −0.0317948 −0.0158974 0.999874i \(-0.505061\pi\)
−0.0158974 + 0.999874i \(0.505061\pi\)
\(32\) −26.1799 −4.62799
\(33\) −0.0832308 −0.0144886
\(34\) 20.4891 3.51386
\(35\) 3.84094 0.649237
\(36\) −16.9647 −2.82746
\(37\) 4.15643 0.683312 0.341656 0.939825i \(-0.389012\pi\)
0.341656 + 0.939825i \(0.389012\pi\)
\(38\) 11.1551 1.80959
\(39\) 0 0
\(40\) 10.8433 1.71448
\(41\) 3.24661 0.507035 0.253518 0.967331i \(-0.418412\pi\)
0.253518 + 0.967331i \(0.418412\pi\)
\(42\) −0.829223 −0.127952
\(43\) −1.63410 −0.249197 −0.124599 0.992207i \(-0.539764\pi\)
−0.124599 + 0.992207i \(0.539764\pi\)
\(44\) 5.66800 0.854483
\(45\) 3.19528 0.476324
\(46\) −0.210347 −0.0310139
\(47\) −7.85313 −1.14550 −0.572748 0.819731i \(-0.694123\pi\)
−0.572748 + 0.819731i \(0.694123\pi\)
\(48\) −1.39747 −0.201707
\(49\) 5.94470 0.849243
\(50\) 10.6897 1.51175
\(51\) 0.615838 0.0862346
\(52\) 0 0
\(53\) −4.66525 −0.640821 −0.320411 0.947279i \(-0.603821\pi\)
−0.320411 + 0.947279i \(0.603821\pi\)
\(54\) −1.38126 −0.187965
\(55\) −1.06756 −0.143950
\(56\) 36.5440 4.88340
\(57\) 0.335287 0.0444098
\(58\) 13.1463 1.72619
\(59\) 6.77125 0.881542 0.440771 0.897620i \(-0.354705\pi\)
0.440771 + 0.897620i \(0.354705\pi\)
\(60\) 0.503623 0.0650175
\(61\) 2.93743 0.376099 0.188050 0.982160i \(-0.439783\pi\)
0.188050 + 0.982160i \(0.439783\pi\)
\(62\) 0.490206 0.0622562
\(63\) 10.7687 1.35673
\(64\) 38.9146 4.86433
\(65\) 0 0
\(66\) 0.230476 0.0283696
\(67\) 6.14511 0.750745 0.375372 0.926874i \(-0.377515\pi\)
0.375372 + 0.926874i \(0.377515\pi\)
\(68\) −41.9385 −5.08579
\(69\) −0.00632236 −0.000761122 0
\(70\) −10.6360 −1.27125
\(71\) −7.85704 −0.932459 −0.466230 0.884664i \(-0.654388\pi\)
−0.466230 + 0.884664i \(0.654388\pi\)
\(72\) 30.4010 3.58279
\(73\) 12.3455 1.44493 0.722464 0.691409i \(-0.243010\pi\)
0.722464 + 0.691409i \(0.243010\pi\)
\(74\) −11.5096 −1.33797
\(75\) 0.321298 0.0371002
\(76\) −22.8329 −2.61912
\(77\) −3.59787 −0.410016
\(78\) 0 0
\(79\) 13.7084 1.54232 0.771158 0.636644i \(-0.219678\pi\)
0.771158 + 0.636644i \(0.219678\pi\)
\(80\) −17.9246 −2.00403
\(81\) 8.93770 0.993078
\(82\) −8.99024 −0.992806
\(83\) −13.3856 −1.46926 −0.734632 0.678466i \(-0.762645\pi\)
−0.734632 + 0.678466i \(0.762645\pi\)
\(84\) 1.69731 0.185191
\(85\) 7.89904 0.856771
\(86\) 4.52500 0.487943
\(87\) 0.395135 0.0423629
\(88\) −10.1571 −1.08275
\(89\) −3.95646 −0.419384 −0.209692 0.977768i \(-0.567246\pi\)
−0.209692 + 0.977768i \(0.567246\pi\)
\(90\) −8.84810 −0.932672
\(91\) 0 0
\(92\) 0.430551 0.0448881
\(93\) 0.0147340 0.00152785
\(94\) 21.7462 2.24295
\(95\) 4.30055 0.441227
\(96\) 2.17897 0.222390
\(97\) −9.04232 −0.918108 −0.459054 0.888408i \(-0.651812\pi\)
−0.459054 + 0.888408i \(0.651812\pi\)
\(98\) −16.4616 −1.66287
\(99\) −2.99307 −0.300815
\(100\) −21.8803 −2.18803
\(101\) −14.7658 −1.46925 −0.734624 0.678475i \(-0.762641\pi\)
−0.734624 + 0.678475i \(0.762641\pi\)
\(102\) −1.70533 −0.168853
\(103\) 4.61089 0.454325 0.227162 0.973857i \(-0.427055\pi\)
0.227162 + 0.973857i \(0.427055\pi\)
\(104\) 0 0
\(105\) −0.319685 −0.0311980
\(106\) 12.9186 1.25477
\(107\) −5.71764 −0.552745 −0.276373 0.961051i \(-0.589132\pi\)
−0.276373 + 0.961051i \(0.589132\pi\)
\(108\) 2.82725 0.272052
\(109\) −15.4449 −1.47935 −0.739676 0.672963i \(-0.765021\pi\)
−0.739676 + 0.672963i \(0.765021\pi\)
\(110\) 2.95619 0.281862
\(111\) −0.345943 −0.0328354
\(112\) −60.4092 −5.70813
\(113\) −14.1429 −1.33045 −0.665227 0.746641i \(-0.731665\pi\)
−0.665227 + 0.746641i \(0.731665\pi\)
\(114\) −0.928447 −0.0869570
\(115\) −0.0810936 −0.00756202
\(116\) −26.9086 −2.49840
\(117\) 0 0
\(118\) −18.7504 −1.72611
\(119\) 26.6213 2.44037
\(120\) −0.902498 −0.0823864
\(121\) 1.00000 0.0909091
\(122\) −8.13408 −0.736425
\(123\) −0.270218 −0.0243647
\(124\) −1.00338 −0.0901065
\(125\) 9.45891 0.846030
\(126\) −29.8198 −2.65656
\(127\) −10.3241 −0.916116 −0.458058 0.888922i \(-0.651455\pi\)
−0.458058 + 0.888922i \(0.651455\pi\)
\(128\) −55.3993 −4.89665
\(129\) 0.136007 0.0119748
\(130\) 0 0
\(131\) 16.5969 1.45008 0.725039 0.688707i \(-0.241822\pi\)
0.725039 + 0.688707i \(0.241822\pi\)
\(132\) −0.471752 −0.0410608
\(133\) 14.4937 1.25676
\(134\) −17.0165 −1.47000
\(135\) −0.532507 −0.0458309
\(136\) 75.1542 6.44442
\(137\) 11.6276 0.993412 0.496706 0.867919i \(-0.334543\pi\)
0.496706 + 0.867919i \(0.334543\pi\)
\(138\) 0.0175073 0.00149032
\(139\) 16.1863 1.37291 0.686454 0.727173i \(-0.259166\pi\)
0.686454 + 0.727173i \(0.259166\pi\)
\(140\) 21.7705 1.83994
\(141\) 0.653622 0.0550449
\(142\) 21.7571 1.82581
\(143\) 0 0
\(144\) −50.2544 −4.18787
\(145\) 5.06819 0.420890
\(146\) −34.1860 −2.82926
\(147\) −0.494782 −0.0408089
\(148\) 23.5586 1.93651
\(149\) 6.28767 0.515106 0.257553 0.966264i \(-0.417084\pi\)
0.257553 + 0.966264i \(0.417084\pi\)
\(150\) −0.889710 −0.0726445
\(151\) 0.938333 0.0763605 0.0381802 0.999271i \(-0.487844\pi\)
0.0381802 + 0.999271i \(0.487844\pi\)
\(152\) 40.9169 3.31880
\(153\) 22.1462 1.79042
\(154\) 9.96293 0.802836
\(155\) 0.188986 0.0151797
\(156\) 0 0
\(157\) 18.5627 1.48146 0.740732 0.671800i \(-0.234479\pi\)
0.740732 + 0.671800i \(0.234479\pi\)
\(158\) −37.9601 −3.01995
\(159\) 0.388293 0.0307936
\(160\) 27.9485 2.20953
\(161\) −0.273301 −0.0215391
\(162\) −24.7495 −1.94451
\(163\) −8.94537 −0.700655 −0.350328 0.936627i \(-0.613930\pi\)
−0.350328 + 0.936627i \(0.613930\pi\)
\(164\) 18.4018 1.43694
\(165\) 0.0888538 0.00691726
\(166\) 37.0663 2.87691
\(167\) 1.59550 0.123464 0.0617319 0.998093i \(-0.480338\pi\)
0.0617319 + 0.998093i \(0.480338\pi\)
\(168\) −3.04159 −0.234664
\(169\) 0 0
\(170\) −21.8733 −1.67761
\(171\) 12.0573 0.922043
\(172\) −9.26206 −0.706225
\(173\) 4.86380 0.369788 0.184894 0.982758i \(-0.440806\pi\)
0.184894 + 0.982758i \(0.440806\pi\)
\(174\) −1.09417 −0.0829492
\(175\) 13.8889 1.04991
\(176\) 16.7902 1.26561
\(177\) −0.563577 −0.0423610
\(178\) 10.9559 0.821179
\(179\) 7.69662 0.575272 0.287636 0.957740i \(-0.407131\pi\)
0.287636 + 0.957740i \(0.407131\pi\)
\(180\) 18.1108 1.34990
\(181\) −14.4747 −1.07589 −0.537946 0.842979i \(-0.680800\pi\)
−0.537946 + 0.842979i \(0.680800\pi\)
\(182\) 0 0
\(183\) −0.244485 −0.0180728
\(184\) −0.771552 −0.0568796
\(185\) −4.43723 −0.326231
\(186\) −0.0408002 −0.00299162
\(187\) −7.39916 −0.541080
\(188\) −44.5115 −3.24634
\(189\) −1.79465 −0.130542
\(190\) −11.9087 −0.863949
\(191\) 11.7232 0.848263 0.424132 0.905601i \(-0.360579\pi\)
0.424132 + 0.905601i \(0.360579\pi\)
\(192\) −3.23889 −0.233747
\(193\) 9.03444 0.650313 0.325157 0.945660i \(-0.394583\pi\)
0.325157 + 0.945660i \(0.394583\pi\)
\(194\) 25.0392 1.79771
\(195\) 0 0
\(196\) 33.6946 2.40675
\(197\) 12.5092 0.891241 0.445621 0.895222i \(-0.352983\pi\)
0.445621 + 0.895222i \(0.352983\pi\)
\(198\) 8.28816 0.589014
\(199\) −9.29242 −0.658722 −0.329361 0.944204i \(-0.606833\pi\)
−0.329361 + 0.944204i \(0.606833\pi\)
\(200\) 39.2097 2.77255
\(201\) −0.511463 −0.0360758
\(202\) 40.8881 2.87687
\(203\) 17.0808 1.19884
\(204\) 3.49057 0.244389
\(205\) −3.46595 −0.242072
\(206\) −12.7681 −0.889595
\(207\) −0.227359 −0.0158025
\(208\) 0 0
\(209\) −4.02839 −0.278650
\(210\) 0.885244 0.0610876
\(211\) −17.5910 −1.21101 −0.605506 0.795841i \(-0.707029\pi\)
−0.605506 + 0.795841i \(0.707029\pi\)
\(212\) −26.4426 −1.81609
\(213\) 0.653948 0.0448078
\(214\) 15.8328 1.08231
\(215\) 1.74449 0.118973
\(216\) −5.06646 −0.344729
\(217\) 0.636917 0.0432368
\(218\) 42.7687 2.89666
\(219\) −1.02752 −0.0694336
\(220\) −6.05092 −0.407953
\(221\) 0 0
\(222\) 0.957955 0.0642938
\(223\) −3.52807 −0.236257 −0.118128 0.992998i \(-0.537689\pi\)
−0.118128 + 0.992998i \(0.537689\pi\)
\(224\) 94.1919 6.29346
\(225\) 11.5542 0.770281
\(226\) 39.1634 2.60511
\(227\) −11.9612 −0.793894 −0.396947 0.917841i \(-0.629930\pi\)
−0.396947 + 0.917841i \(0.629930\pi\)
\(228\) 1.90040 0.125857
\(229\) 2.51261 0.166038 0.0830189 0.996548i \(-0.473544\pi\)
0.0830189 + 0.996548i \(0.473544\pi\)
\(230\) 0.224558 0.0148069
\(231\) 0.299454 0.0197026
\(232\) 48.2205 3.16583
\(233\) 5.75858 0.377257 0.188629 0.982049i \(-0.439596\pi\)
0.188629 + 0.982049i \(0.439596\pi\)
\(234\) 0 0
\(235\) 8.38367 0.546890
\(236\) 38.3795 2.49829
\(237\) −1.14096 −0.0741134
\(238\) −73.7173 −4.77839
\(239\) 21.8495 1.41332 0.706662 0.707551i \(-0.250200\pi\)
0.706662 + 0.707551i \(0.250200\pi\)
\(240\) 1.49188 0.0963002
\(241\) −11.9547 −0.770073 −0.385036 0.922901i \(-0.625811\pi\)
−0.385036 + 0.922901i \(0.625811\pi\)
\(242\) −2.76912 −0.178005
\(243\) −2.24032 −0.143716
\(244\) 16.6493 1.06587
\(245\) −6.34631 −0.405451
\(246\) 0.748265 0.0477076
\(247\) 0 0
\(248\) 1.79807 0.114178
\(249\) 1.11410 0.0706030
\(250\) −26.1928 −1.65658
\(251\) −9.13942 −0.576875 −0.288437 0.957499i \(-0.593136\pi\)
−0.288437 + 0.957499i \(0.593136\pi\)
\(252\) 61.0370 3.84497
\(253\) 0.0759617 0.00477567
\(254\) 28.5886 1.79381
\(255\) −0.657443 −0.0411707
\(256\) 75.5779 4.72362
\(257\) 5.49334 0.342665 0.171333 0.985213i \(-0.445193\pi\)
0.171333 + 0.985213i \(0.445193\pi\)
\(258\) −0.376620 −0.0234473
\(259\) −14.9543 −0.929215
\(260\) 0 0
\(261\) 14.2095 0.879546
\(262\) −45.9588 −2.83934
\(263\) −4.72227 −0.291188 −0.145594 0.989344i \(-0.546509\pi\)
−0.145594 + 0.989344i \(0.546509\pi\)
\(264\) 0.845385 0.0520299
\(265\) 4.98043 0.305945
\(266\) −40.1346 −2.46081
\(267\) 0.329299 0.0201528
\(268\) 34.8305 2.12761
\(269\) 7.18076 0.437818 0.218909 0.975745i \(-0.429750\pi\)
0.218909 + 0.975745i \(0.429750\pi\)
\(270\) 1.47457 0.0897397
\(271\) −0.0615331 −0.00373787 −0.00186893 0.999998i \(-0.500595\pi\)
−0.00186893 + 0.999998i \(0.500595\pi\)
\(272\) −124.234 −7.53277
\(273\) 0 0
\(274\) −32.1981 −1.94516
\(275\) −3.86032 −0.232786
\(276\) −0.0358351 −0.00215702
\(277\) −10.2546 −0.616141 −0.308070 0.951364i \(-0.599683\pi\)
−0.308070 + 0.951364i \(0.599683\pi\)
\(278\) −44.8219 −2.68824
\(279\) 0.529852 0.0317214
\(280\) −39.0129 −2.33147
\(281\) 27.5362 1.64267 0.821336 0.570444i \(-0.193229\pi\)
0.821336 + 0.570444i \(0.193229\pi\)
\(282\) −1.80996 −0.107781
\(283\) −8.61317 −0.512000 −0.256000 0.966677i \(-0.582405\pi\)
−0.256000 + 0.966677i \(0.582405\pi\)
\(284\) −44.5337 −2.64259
\(285\) −0.357938 −0.0212024
\(286\) 0 0
\(287\) −11.6809 −0.689502
\(288\) 78.3582 4.61730
\(289\) 37.7476 2.22045
\(290\) −14.0344 −0.824129
\(291\) 0.752600 0.0441182
\(292\) 69.9741 4.09493
\(293\) 20.8257 1.21665 0.608325 0.793688i \(-0.291842\pi\)
0.608325 + 0.793688i \(0.291842\pi\)
\(294\) 1.37011 0.0799064
\(295\) −7.22871 −0.420872
\(296\) −42.2173 −2.45383
\(297\) 0.498808 0.0289438
\(298\) −17.4113 −1.00861
\(299\) 0 0
\(300\) 1.82111 0.105142
\(301\) 5.87927 0.338876
\(302\) −2.59835 −0.149518
\(303\) 1.22897 0.0706022
\(304\) −67.6377 −3.87929
\(305\) −3.13588 −0.179560
\(306\) −61.3255 −3.50574
\(307\) −23.2876 −1.32909 −0.664546 0.747247i \(-0.731375\pi\)
−0.664546 + 0.747247i \(0.731375\pi\)
\(308\) −20.3928 −1.16199
\(309\) −0.383768 −0.0218318
\(310\) −0.523323 −0.0297228
\(311\) 10.1504 0.575579 0.287789 0.957694i \(-0.407080\pi\)
0.287789 + 0.957694i \(0.407080\pi\)
\(312\) 0 0
\(313\) 26.8824 1.51948 0.759741 0.650226i \(-0.225326\pi\)
0.759741 + 0.650226i \(0.225326\pi\)
\(314\) −51.4023 −2.90080
\(315\) −11.4962 −0.647738
\(316\) 77.6992 4.37092
\(317\) −12.6709 −0.711667 −0.355834 0.934549i \(-0.615803\pi\)
−0.355834 + 0.934549i \(0.615803\pi\)
\(318\) −1.07523 −0.0602957
\(319\) −4.74746 −0.265807
\(320\) −41.5436 −2.32236
\(321\) 0.475884 0.0265612
\(322\) 0.756801 0.0421749
\(323\) 29.8067 1.65849
\(324\) 50.6589 2.81438
\(325\) 0 0
\(326\) 24.7708 1.37193
\(327\) 1.28549 0.0710878
\(328\) −32.9762 −1.82081
\(329\) 28.2546 1.55772
\(330\) −0.246046 −0.0135444
\(331\) 1.82373 0.100241 0.0501205 0.998743i \(-0.484039\pi\)
0.0501205 + 0.998743i \(0.484039\pi\)
\(332\) −75.8697 −4.16389
\(333\) −12.4405 −0.681734
\(334\) −4.41813 −0.241750
\(335\) −6.56027 −0.358426
\(336\) 5.02790 0.274295
\(337\) 3.80255 0.207138 0.103569 0.994622i \(-0.466974\pi\)
0.103569 + 0.994622i \(0.466974\pi\)
\(338\) 0 0
\(339\) 1.17713 0.0639327
\(340\) 44.7718 2.42809
\(341\) −0.177026 −0.00958650
\(342\) −33.3880 −1.80542
\(343\) 3.79684 0.205010
\(344\) 16.5977 0.894889
\(345\) 0.00674949 0.000363380 0
\(346\) −13.4684 −0.724067
\(347\) −32.1531 −1.72607 −0.863034 0.505146i \(-0.831439\pi\)
−0.863034 + 0.505146i \(0.831439\pi\)
\(348\) 2.23963 0.120057
\(349\) 19.6322 1.05089 0.525444 0.850828i \(-0.323899\pi\)
0.525444 + 0.850828i \(0.323899\pi\)
\(350\) −38.4601 −2.05578
\(351\) 0 0
\(352\) −26.1799 −1.39539
\(353\) −1.45809 −0.0776064 −0.0388032 0.999247i \(-0.512355\pi\)
−0.0388032 + 0.999247i \(0.512355\pi\)
\(354\) 1.56061 0.0829455
\(355\) 8.38785 0.445181
\(356\) −22.4252 −1.18853
\(357\) −2.21571 −0.117268
\(358\) −21.3128 −1.12642
\(359\) −16.4893 −0.870273 −0.435136 0.900365i \(-0.643300\pi\)
−0.435136 + 0.900365i \(0.643300\pi\)
\(360\) −32.4548 −1.71052
\(361\) −2.77204 −0.145897
\(362\) 40.0820 2.10666
\(363\) −0.0832308 −0.00436849
\(364\) 0 0
\(365\) −13.1795 −0.689847
\(366\) 0.677006 0.0353877
\(367\) 0.508181 0.0265269 0.0132634 0.999912i \(-0.495778\pi\)
0.0132634 + 0.999912i \(0.495778\pi\)
\(368\) 1.27542 0.0664856
\(369\) −9.71734 −0.505865
\(370\) 12.2872 0.638781
\(371\) 16.7850 0.871433
\(372\) 0.0835125 0.00432992
\(373\) −10.6038 −0.549044 −0.274522 0.961581i \(-0.588520\pi\)
−0.274522 + 0.961581i \(0.588520\pi\)
\(374\) 20.4891 1.05947
\(375\) −0.787273 −0.0406546
\(376\) 79.7652 4.11357
\(377\) 0 0
\(378\) 4.96959 0.255608
\(379\) 0.217213 0.0111575 0.00557873 0.999984i \(-0.498224\pi\)
0.00557873 + 0.999984i \(0.498224\pi\)
\(380\) 24.3755 1.25044
\(381\) 0.859284 0.0440225
\(382\) −32.4630 −1.66095
\(383\) 32.6070 1.66614 0.833070 0.553168i \(-0.186581\pi\)
0.833070 + 0.553168i \(0.186581\pi\)
\(384\) 4.61093 0.235300
\(385\) 3.84094 0.195752
\(386\) −25.0174 −1.27335
\(387\) 4.89097 0.248622
\(388\) −51.2519 −2.60192
\(389\) −0.457808 −0.0232118 −0.0116059 0.999933i \(-0.503694\pi\)
−0.0116059 + 0.999933i \(0.503694\pi\)
\(390\) 0 0
\(391\) −0.562053 −0.0284243
\(392\) −60.3810 −3.04970
\(393\) −1.38137 −0.0696811
\(394\) −34.6393 −1.74510
\(395\) −14.6345 −0.736342
\(396\) −16.9647 −0.852510
\(397\) 16.8626 0.846309 0.423155 0.906057i \(-0.360923\pi\)
0.423155 + 0.906057i \(0.360923\pi\)
\(398\) 25.7318 1.28982
\(399\) −1.20632 −0.0603915
\(400\) −64.8157 −3.24078
\(401\) −31.2746 −1.56178 −0.780889 0.624670i \(-0.785233\pi\)
−0.780889 + 0.624670i \(0.785233\pi\)
\(402\) 1.41630 0.0706386
\(403\) 0 0
\(404\) −83.6923 −4.16385
\(405\) −9.54152 −0.474122
\(406\) −47.2986 −2.34739
\(407\) 4.15643 0.206026
\(408\) −6.25514 −0.309676
\(409\) −32.4052 −1.60233 −0.801166 0.598442i \(-0.795787\pi\)
−0.801166 + 0.598442i \(0.795787\pi\)
\(410\) 9.59761 0.473992
\(411\) −0.967774 −0.0477368
\(412\) 26.1345 1.28756
\(413\) −24.3621 −1.19878
\(414\) 0.629583 0.0309423
\(415\) 14.2899 0.701465
\(416\) 0 0
\(417\) −1.34720 −0.0659728
\(418\) 11.1551 0.545613
\(419\) −2.47724 −0.121021 −0.0605105 0.998168i \(-0.519273\pi\)
−0.0605105 + 0.998168i \(0.519273\pi\)
\(420\) −1.81197 −0.0884152
\(421\) −0.302840 −0.0147595 −0.00737975 0.999973i \(-0.502349\pi\)
−0.00737975 + 0.999973i \(0.502349\pi\)
\(422\) 48.7114 2.37123
\(423\) 23.5050 1.14285
\(424\) 47.3855 2.30124
\(425\) 28.5631 1.38552
\(426\) −1.81086 −0.0877363
\(427\) −10.5685 −0.511445
\(428\) −32.4076 −1.56648
\(429\) 0 0
\(430\) −4.83070 −0.232957
\(431\) −8.14677 −0.392416 −0.196208 0.980562i \(-0.562863\pi\)
−0.196208 + 0.980562i \(0.562863\pi\)
\(432\) 8.37511 0.402948
\(433\) 38.5372 1.85198 0.925989 0.377549i \(-0.123233\pi\)
0.925989 + 0.377549i \(0.123233\pi\)
\(434\) −1.76370 −0.0846602
\(435\) −0.421830 −0.0202252
\(436\) −87.5416 −4.19248
\(437\) −0.306004 −0.0146381
\(438\) 2.84533 0.135955
\(439\) 11.9879 0.572151 0.286075 0.958207i \(-0.407649\pi\)
0.286075 + 0.958207i \(0.407649\pi\)
\(440\) 10.8433 0.516935
\(441\) −17.7929 −0.847282
\(442\) 0 0
\(443\) 19.4876 0.925885 0.462942 0.886388i \(-0.346794\pi\)
0.462942 + 0.886388i \(0.346794\pi\)
\(444\) −1.96080 −0.0930556
\(445\) 4.22375 0.200225
\(446\) 9.76962 0.462605
\(447\) −0.523328 −0.0247525
\(448\) −140.010 −6.61484
\(449\) 30.0643 1.41882 0.709412 0.704794i \(-0.248961\pi\)
0.709412 + 0.704794i \(0.248961\pi\)
\(450\) −31.9950 −1.50826
\(451\) 3.24661 0.152877
\(452\) −80.1621 −3.77051
\(453\) −0.0780982 −0.00366938
\(454\) 33.1220 1.55449
\(455\) 0 0
\(456\) −3.40555 −0.159479
\(457\) 32.6615 1.52784 0.763919 0.645312i \(-0.223273\pi\)
0.763919 + 0.645312i \(0.223273\pi\)
\(458\) −6.95770 −0.325112
\(459\) −3.69076 −0.172270
\(460\) −0.459639 −0.0214308
\(461\) −19.8261 −0.923394 −0.461697 0.887038i \(-0.652759\pi\)
−0.461697 + 0.887038i \(0.652759\pi\)
\(462\) −0.829223 −0.0385789
\(463\) −34.1267 −1.58600 −0.793002 0.609219i \(-0.791483\pi\)
−0.793002 + 0.609219i \(0.791483\pi\)
\(464\) −79.7110 −3.70049
\(465\) −0.0157294 −0.000729435 0
\(466\) −15.9462 −0.738692
\(467\) −25.7139 −1.18990 −0.594950 0.803763i \(-0.702828\pi\)
−0.594950 + 0.803763i \(0.702828\pi\)
\(468\) 0 0
\(469\) −22.1093 −1.02091
\(470\) −23.2154 −1.07084
\(471\) −1.54499 −0.0711893
\(472\) −68.7764 −3.16569
\(473\) −1.63410 −0.0751358
\(474\) 3.15945 0.145118
\(475\) 15.5509 0.713524
\(476\) 150.889 6.91600
\(477\) 13.9634 0.639342
\(478\) −60.5037 −2.76738
\(479\) −11.4684 −0.524006 −0.262003 0.965067i \(-0.584383\pi\)
−0.262003 + 0.965067i \(0.584383\pi\)
\(480\) −2.32618 −0.106175
\(481\) 0 0
\(482\) 33.1041 1.50785
\(483\) 0.0227470 0.00103503
\(484\) 5.66800 0.257636
\(485\) 9.65320 0.438329
\(486\) 6.20370 0.281405
\(487\) −20.0757 −0.909716 −0.454858 0.890564i \(-0.650310\pi\)
−0.454858 + 0.890564i \(0.650310\pi\)
\(488\) −29.8358 −1.35060
\(489\) 0.744530 0.0336688
\(490\) 17.5737 0.793898
\(491\) −15.9592 −0.720229 −0.360115 0.932908i \(-0.617262\pi\)
−0.360115 + 0.932908i \(0.617262\pi\)
\(492\) −1.53160 −0.0690497
\(493\) 35.1272 1.58205
\(494\) 0 0
\(495\) 3.19528 0.143617
\(496\) −2.97231 −0.133461
\(497\) 28.2686 1.26802
\(498\) −3.08506 −0.138245
\(499\) 8.09336 0.362308 0.181154 0.983455i \(-0.442017\pi\)
0.181154 + 0.983455i \(0.442017\pi\)
\(500\) 53.6131 2.39765
\(501\) −0.132795 −0.00593285
\(502\) 25.3081 1.12956
\(503\) 42.9784 1.91631 0.958156 0.286246i \(-0.0924076\pi\)
0.958156 + 0.286246i \(0.0924076\pi\)
\(504\) −109.379 −4.87213
\(505\) 15.7633 0.701458
\(506\) −0.210347 −0.00935106
\(507\) 0 0
\(508\) −58.5171 −2.59627
\(509\) 8.50105 0.376802 0.188401 0.982092i \(-0.439670\pi\)
0.188401 + 0.982092i \(0.439670\pi\)
\(510\) 1.82054 0.0806147
\(511\) −44.4174 −1.96491
\(512\) −98.4852 −4.35247
\(513\) −2.00940 −0.0887170
\(514\) −15.2117 −0.670959
\(515\) −4.92240 −0.216907
\(516\) 0.770889 0.0339365
\(517\) −7.85313 −0.345380
\(518\) 41.4102 1.81946
\(519\) −0.404818 −0.0177695
\(520\) 0 0
\(521\) −24.8637 −1.08930 −0.544650 0.838664i \(-0.683337\pi\)
−0.544650 + 0.838664i \(0.683337\pi\)
\(522\) −39.3477 −1.72220
\(523\) 23.2138 1.01507 0.507534 0.861631i \(-0.330557\pi\)
0.507534 + 0.861631i \(0.330557\pi\)
\(524\) 94.0713 4.10952
\(525\) −1.15599 −0.0504515
\(526\) 13.0765 0.570163
\(527\) 1.30984 0.0570577
\(528\) −1.39747 −0.0608169
\(529\) −22.9942 −0.999749
\(530\) −13.7914 −0.599059
\(531\) −20.2669 −0.879507
\(532\) 82.1501 3.56166
\(533\) 0 0
\(534\) −0.911868 −0.0394604
\(535\) 6.10391 0.263895
\(536\) −62.4166 −2.69599
\(537\) −0.640596 −0.0276437
\(538\) −19.8843 −0.857275
\(539\) 5.94470 0.256056
\(540\) −3.01825 −0.129885
\(541\) 5.86746 0.252262 0.126131 0.992014i \(-0.459744\pi\)
0.126131 + 0.992014i \(0.459744\pi\)
\(542\) 0.170392 0.00731897
\(543\) 1.20474 0.0517002
\(544\) 193.709 8.30521
\(545\) 16.4883 0.706282
\(546\) 0 0
\(547\) 1.40934 0.0602590 0.0301295 0.999546i \(-0.490408\pi\)
0.0301295 + 0.999546i \(0.490408\pi\)
\(548\) 65.9052 2.81533
\(549\) −8.79194 −0.375231
\(550\) 10.6897 0.455809
\(551\) 19.1246 0.814737
\(552\) 0.0642169 0.00273325
\(553\) −49.3211 −2.09735
\(554\) 28.3963 1.20644
\(555\) 0.369314 0.0156765
\(556\) 91.7442 3.89082
\(557\) −14.5323 −0.615752 −0.307876 0.951426i \(-0.599618\pi\)
−0.307876 + 0.951426i \(0.599618\pi\)
\(558\) −1.46722 −0.0621124
\(559\) 0 0
\(560\) 64.4903 2.72521
\(561\) 0.615838 0.0260007
\(562\) −76.2510 −3.21645
\(563\) 43.1530 1.81868 0.909340 0.416053i \(-0.136587\pi\)
0.909340 + 0.416053i \(0.136587\pi\)
\(564\) 3.70473 0.155997
\(565\) 15.0984 0.635194
\(566\) 23.8509 1.00253
\(567\) −32.1567 −1.35046
\(568\) 79.8049 3.34854
\(569\) 21.1516 0.886723 0.443361 0.896343i \(-0.353786\pi\)
0.443361 + 0.896343i \(0.353786\pi\)
\(570\) 0.991172 0.0415156
\(571\) −17.8433 −0.746718 −0.373359 0.927687i \(-0.621794\pi\)
−0.373359 + 0.927687i \(0.621794\pi\)
\(572\) 0 0
\(573\) −0.975734 −0.0407619
\(574\) 32.3458 1.35009
\(575\) −0.293237 −0.0122288
\(576\) −116.474 −4.85309
\(577\) 12.9238 0.538025 0.269013 0.963137i \(-0.413303\pi\)
0.269013 + 0.963137i \(0.413303\pi\)
\(578\) −104.527 −4.34777
\(579\) −0.751944 −0.0312497
\(580\) 28.7265 1.19280
\(581\) 48.1598 1.99800
\(582\) −2.08404 −0.0863860
\(583\) −4.66525 −0.193215
\(584\) −125.394 −5.18886
\(585\) 0 0
\(586\) −57.6688 −2.38228
\(587\) −35.4448 −1.46296 −0.731482 0.681861i \(-0.761171\pi\)
−0.731482 + 0.681861i \(0.761171\pi\)
\(588\) −2.80443 −0.115653
\(589\) 0.713131 0.0293840
\(590\) 20.0171 0.824092
\(591\) −1.04115 −0.0428271
\(592\) 69.7874 2.86824
\(593\) −32.1072 −1.31848 −0.659242 0.751931i \(-0.729123\pi\)
−0.659242 + 0.751931i \(0.729123\pi\)
\(594\) −1.38126 −0.0566737
\(595\) −28.4197 −1.16510
\(596\) 35.6385 1.45981
\(597\) 0.773416 0.0316538
\(598\) 0 0
\(599\) −1.44295 −0.0589574 −0.0294787 0.999565i \(-0.509385\pi\)
−0.0294787 + 0.999565i \(0.509385\pi\)
\(600\) −3.26346 −0.133230
\(601\) 20.1961 0.823817 0.411909 0.911225i \(-0.364862\pi\)
0.411909 + 0.911225i \(0.364862\pi\)
\(602\) −16.2804 −0.663539
\(603\) −18.3928 −0.749011
\(604\) 5.31847 0.216406
\(605\) −1.06756 −0.0434024
\(606\) −3.40315 −0.138243
\(607\) −27.8276 −1.12949 −0.564744 0.825266i \(-0.691025\pi\)
−0.564744 + 0.825266i \(0.691025\pi\)
\(608\) 105.463 4.27708
\(609\) −1.42165 −0.0576080
\(610\) 8.68360 0.351589
\(611\) 0 0
\(612\) 125.525 5.07404
\(613\) 9.69450 0.391557 0.195779 0.980648i \(-0.437277\pi\)
0.195779 + 0.980648i \(0.437277\pi\)
\(614\) 64.4860 2.60244
\(615\) 0.288474 0.0116324
\(616\) 36.5440 1.47240
\(617\) −3.06092 −0.123228 −0.0616141 0.998100i \(-0.519625\pi\)
−0.0616141 + 0.998100i \(0.519625\pi\)
\(618\) 1.06270 0.0427480
\(619\) 11.9387 0.479858 0.239929 0.970790i \(-0.422876\pi\)
0.239929 + 0.970790i \(0.422876\pi\)
\(620\) 1.07117 0.0430193
\(621\) 0.0378903 0.00152049
\(622\) −28.1077 −1.12702
\(623\) 14.2348 0.570307
\(624\) 0 0
\(625\) 9.20366 0.368146
\(626\) −74.4404 −2.97524
\(627\) 0.335287 0.0133901
\(628\) 105.213 4.19847
\(629\) −30.7541 −1.22625
\(630\) 31.8343 1.26831
\(631\) −26.8571 −1.06917 −0.534583 0.845116i \(-0.679531\pi\)
−0.534583 + 0.845116i \(0.679531\pi\)
\(632\) −139.238 −5.53858
\(633\) 1.46411 0.0581931
\(634\) 35.0871 1.39349
\(635\) 11.0216 0.437378
\(636\) 2.20084 0.0872691
\(637\) 0 0
\(638\) 13.1463 0.520466
\(639\) 23.5167 0.930306
\(640\) 59.1420 2.33779
\(641\) −17.7268 −0.700166 −0.350083 0.936719i \(-0.613847\pi\)
−0.350083 + 0.936719i \(0.613847\pi\)
\(642\) −1.31778 −0.0520085
\(643\) −26.3650 −1.03974 −0.519868 0.854247i \(-0.674019\pi\)
−0.519868 + 0.854247i \(0.674019\pi\)
\(644\) −1.54907 −0.0610419
\(645\) −0.145196 −0.00571707
\(646\) −82.5383 −3.24743
\(647\) −19.9925 −0.785986 −0.392993 0.919542i \(-0.628560\pi\)
−0.392993 + 0.919542i \(0.628560\pi\)
\(648\) −90.7813 −3.56623
\(649\) 6.77125 0.265795
\(650\) 0 0
\(651\) −0.0530112 −0.00207767
\(652\) −50.7024 −1.98566
\(653\) −17.9579 −0.702747 −0.351373 0.936235i \(-0.614285\pi\)
−0.351373 + 0.936235i \(0.614285\pi\)
\(654\) −3.55967 −0.139194
\(655\) −17.7182 −0.692306
\(656\) 54.5114 2.12831
\(657\) −36.9509 −1.44159
\(658\) −78.2402 −3.05012
\(659\) 21.1859 0.825284 0.412642 0.910893i \(-0.364606\pi\)
0.412642 + 0.910893i \(0.364606\pi\)
\(660\) 0.503623 0.0196035
\(661\) −44.2078 −1.71949 −0.859743 0.510727i \(-0.829376\pi\)
−0.859743 + 0.510727i \(0.829376\pi\)
\(662\) −5.05011 −0.196278
\(663\) 0 0
\(664\) 135.959 5.27625
\(665\) −15.4728 −0.600010
\(666\) 34.4491 1.33488
\(667\) −0.360625 −0.0139635
\(668\) 9.04332 0.349896
\(669\) 0.293644 0.0113529
\(670\) 18.1661 0.701819
\(671\) 2.93743 0.113398
\(672\) −7.83967 −0.302422
\(673\) 40.0351 1.54324 0.771620 0.636084i \(-0.219447\pi\)
0.771620 + 0.636084i \(0.219447\pi\)
\(674\) −10.5297 −0.405589
\(675\) −1.92556 −0.0741148
\(676\) 0 0
\(677\) −18.3099 −0.703706 −0.351853 0.936055i \(-0.614448\pi\)
−0.351853 + 0.936055i \(0.614448\pi\)
\(678\) −3.25960 −0.125184
\(679\) 32.5331 1.24851
\(680\) −80.2315 −3.07674
\(681\) 0.995542 0.0381493
\(682\) 0.490206 0.0187709
\(683\) −28.7058 −1.09840 −0.549199 0.835692i \(-0.685067\pi\)
−0.549199 + 0.835692i \(0.685067\pi\)
\(684\) 68.3407 2.61307
\(685\) −12.4131 −0.474281
\(686\) −10.5139 −0.401422
\(687\) −0.209126 −0.00797867
\(688\) −27.4369 −1.04602
\(689\) 0 0
\(690\) −0.0186901 −0.000711520 0
\(691\) −36.8448 −1.40164 −0.700822 0.713336i \(-0.747183\pi\)
−0.700822 + 0.713336i \(0.747183\pi\)
\(692\) 27.5680 1.04798
\(693\) 10.7687 0.409069
\(694\) 89.0356 3.37975
\(695\) −17.2799 −0.655463
\(696\) −4.01343 −0.152129
\(697\) −24.0222 −0.909906
\(698\) −54.3639 −2.05770
\(699\) −0.479291 −0.0181285
\(700\) 78.7225 2.97543
\(701\) 27.8483 1.05182 0.525908 0.850542i \(-0.323726\pi\)
0.525908 + 0.850542i \(0.323726\pi\)
\(702\) 0 0
\(703\) −16.7437 −0.631501
\(704\) 38.9146 1.46665
\(705\) −0.697780 −0.0262799
\(706\) 4.03762 0.151958
\(707\) 53.1253 1.99798
\(708\) −3.19436 −0.120051
\(709\) −24.0443 −0.903004 −0.451502 0.892270i \(-0.649112\pi\)
−0.451502 + 0.892270i \(0.649112\pi\)
\(710\) −23.2269 −0.871691
\(711\) −41.0302 −1.53875
\(712\) 40.1862 1.50604
\(713\) −0.0134472 −0.000503602 0
\(714\) 6.13555 0.229617
\(715\) 0 0
\(716\) 43.6244 1.63032
\(717\) −1.81855 −0.0679150
\(718\) 45.6608 1.70405
\(719\) −13.0734 −0.487557 −0.243778 0.969831i \(-0.578387\pi\)
−0.243778 + 0.969831i \(0.578387\pi\)
\(720\) 53.6495 1.99940
\(721\) −16.5894 −0.617822
\(722\) 7.67610 0.285675
\(723\) 0.995003 0.0370046
\(724\) −82.0423 −3.04908
\(725\) 18.3267 0.680637
\(726\) 0.230476 0.00855376
\(727\) −35.0957 −1.30163 −0.650814 0.759238i \(-0.725572\pi\)
−0.650814 + 0.759238i \(0.725572\pi\)
\(728\) 0 0
\(729\) −26.6266 −0.986172
\(730\) 36.4956 1.35076
\(731\) 12.0909 0.447200
\(732\) −1.38574 −0.0512184
\(733\) 16.9099 0.624580 0.312290 0.949987i \(-0.398904\pi\)
0.312290 + 0.949987i \(0.398904\pi\)
\(734\) −1.40721 −0.0519412
\(735\) 0.528209 0.0194833
\(736\) −1.98867 −0.0733033
\(737\) 6.14511 0.226358
\(738\) 26.9084 0.990513
\(739\) −40.1331 −1.47632 −0.738159 0.674626i \(-0.764305\pi\)
−0.738159 + 0.674626i \(0.764305\pi\)
\(740\) −25.1502 −0.924540
\(741\) 0 0
\(742\) −46.4796 −1.70632
\(743\) −16.1379 −0.592043 −0.296022 0.955181i \(-0.595660\pi\)
−0.296022 + 0.955181i \(0.595660\pi\)
\(744\) −0.149655 −0.00548663
\(745\) −6.71245 −0.245925
\(746\) 29.3632 1.07506
\(747\) 40.0641 1.46587
\(748\) −41.9385 −1.53342
\(749\) 20.5713 0.751661
\(750\) 2.18005 0.0796041
\(751\) −42.9030 −1.56555 −0.782777 0.622303i \(-0.786197\pi\)
−0.782777 + 0.622303i \(0.786197\pi\)
\(752\) −131.856 −4.80829
\(753\) 0.760681 0.0277208
\(754\) 0 0
\(755\) −1.00173 −0.0364565
\(756\) −10.1721 −0.369955
\(757\) −16.5187 −0.600383 −0.300191 0.953879i \(-0.597051\pi\)
−0.300191 + 0.953879i \(0.597051\pi\)
\(758\) −0.601487 −0.0218470
\(759\) −0.00632236 −0.000229487 0
\(760\) −43.6812 −1.58448
\(761\) −16.8904 −0.612276 −0.306138 0.951987i \(-0.599037\pi\)
−0.306138 + 0.951987i \(0.599037\pi\)
\(762\) −2.37946 −0.0861986
\(763\) 55.5688 2.01172
\(764\) 66.4473 2.40398
\(765\) −23.6424 −0.854793
\(766\) −90.2925 −3.26240
\(767\) 0 0
\(768\) −6.29041 −0.226986
\(769\) −27.1130 −0.977721 −0.488861 0.872362i \(-0.662587\pi\)
−0.488861 + 0.872362i \(0.662587\pi\)
\(770\) −10.6360 −0.383295
\(771\) −0.457215 −0.0164662
\(772\) 51.2072 1.84299
\(773\) 5.18388 0.186451 0.0932255 0.995645i \(-0.470282\pi\)
0.0932255 + 0.995645i \(0.470282\pi\)
\(774\) −13.5437 −0.486817
\(775\) 0.683377 0.0245476
\(776\) 91.8439 3.29700
\(777\) 1.24466 0.0446519
\(778\) 1.26772 0.0454500
\(779\) −13.0786 −0.468590
\(780\) 0 0
\(781\) −7.85704 −0.281147
\(782\) 1.55639 0.0556564
\(783\) −2.36807 −0.0846280
\(784\) 99.8129 3.56475
\(785\) −19.8168 −0.707291
\(786\) 3.82519 0.136440
\(787\) 27.2338 0.970780 0.485390 0.874298i \(-0.338678\pi\)
0.485390 + 0.874298i \(0.338678\pi\)
\(788\) 70.9020 2.52578
\(789\) 0.393038 0.0139925
\(790\) 40.5247 1.44180
\(791\) 50.8844 1.80924
\(792\) 30.4010 1.08025
\(793\) 0 0
\(794\) −46.6945 −1.65713
\(795\) −0.414525 −0.0147017
\(796\) −52.6695 −1.86682
\(797\) −24.5981 −0.871308 −0.435654 0.900114i \(-0.643483\pi\)
−0.435654 + 0.900114i \(0.643483\pi\)
\(798\) 3.34044 0.118250
\(799\) 58.1066 2.05566
\(800\) 101.063 3.57310
\(801\) 11.8420 0.418415
\(802\) 86.6029 3.05805
\(803\) 12.3455 0.435662
\(804\) −2.89897 −0.102239
\(805\) 0.291765 0.0102833
\(806\) 0 0
\(807\) −0.597660 −0.0210386
\(808\) 149.978 5.27619
\(809\) −25.7953 −0.906914 −0.453457 0.891278i \(-0.649809\pi\)
−0.453457 + 0.891278i \(0.649809\pi\)
\(810\) 26.4216 0.928359
\(811\) −14.3539 −0.504035 −0.252017 0.967723i \(-0.581094\pi\)
−0.252017 + 0.967723i \(0.581094\pi\)
\(812\) 96.8138 3.39750
\(813\) 0.00512145 0.000179617 0
\(814\) −11.5096 −0.403412
\(815\) 9.54970 0.334511
\(816\) 10.3401 0.361975
\(817\) 6.58278 0.230302
\(818\) 89.7336 3.13746
\(819\) 0 0
\(820\) −19.6450 −0.686033
\(821\) −18.0028 −0.628302 −0.314151 0.949373i \(-0.601720\pi\)
−0.314151 + 0.949373i \(0.601720\pi\)
\(822\) 2.67988 0.0934715
\(823\) 36.4575 1.27083 0.635415 0.772171i \(-0.280829\pi\)
0.635415 + 0.772171i \(0.280829\pi\)
\(824\) −46.8334 −1.63152
\(825\) 0.321298 0.0111861
\(826\) 67.4615 2.34729
\(827\) −3.73303 −0.129810 −0.0649051 0.997891i \(-0.520674\pi\)
−0.0649051 + 0.997891i \(0.520674\pi\)
\(828\) −1.28867 −0.0447844
\(829\) 48.5365 1.68574 0.842872 0.538115i \(-0.180863\pi\)
0.842872 + 0.538115i \(0.180863\pi\)
\(830\) −39.5705 −1.37351
\(831\) 0.853501 0.0296076
\(832\) 0 0
\(833\) −43.9858 −1.52402
\(834\) 3.73056 0.129179
\(835\) −1.70329 −0.0589449
\(836\) −22.8329 −0.789694
\(837\) −0.0883021 −0.00305217
\(838\) 6.85976 0.236966
\(839\) 45.6319 1.57539 0.787694 0.616067i \(-0.211275\pi\)
0.787694 + 0.616067i \(0.211275\pi\)
\(840\) 3.24708 0.112035
\(841\) −6.46161 −0.222814
\(842\) 0.838598 0.0289000
\(843\) −2.29186 −0.0789359
\(844\) −99.7056 −3.43201
\(845\) 0 0
\(846\) −65.0880 −2.23777
\(847\) −3.59787 −0.123624
\(848\) −78.3306 −2.68989
\(849\) 0.716881 0.0246033
\(850\) −79.0946 −2.71292
\(851\) 0.315729 0.0108231
\(852\) 3.70658 0.126985
\(853\) 26.8405 0.919000 0.459500 0.888178i \(-0.348029\pi\)
0.459500 + 0.888178i \(0.348029\pi\)
\(854\) 29.2654 1.00144
\(855\) −12.8718 −0.440208
\(856\) 58.0748 1.98495
\(857\) 25.5969 0.874375 0.437187 0.899370i \(-0.355975\pi\)
0.437187 + 0.899370i \(0.355975\pi\)
\(858\) 0 0
\(859\) −10.7407 −0.366468 −0.183234 0.983069i \(-0.558657\pi\)
−0.183234 + 0.983069i \(0.558657\pi\)
\(860\) 9.88779 0.337171
\(861\) 0.972211 0.0331328
\(862\) 22.5593 0.768374
\(863\) 39.9441 1.35971 0.679857 0.733345i \(-0.262042\pi\)
0.679857 + 0.733345i \(0.262042\pi\)
\(864\) −13.0587 −0.444267
\(865\) −5.19239 −0.176547
\(866\) −106.714 −3.62629
\(867\) −3.14176 −0.106700
\(868\) 3.61005 0.122533
\(869\) 13.7084 0.465026
\(870\) 1.16810 0.0396021
\(871\) 0 0
\(872\) 156.876 5.31248
\(873\) 27.0643 0.915988
\(874\) 0.847360 0.0286624
\(875\) −34.0320 −1.15049
\(876\) −5.82400 −0.196775
\(877\) 7.22726 0.244047 0.122024 0.992527i \(-0.461062\pi\)
0.122024 + 0.992527i \(0.461062\pi\)
\(878\) −33.1959 −1.12031
\(879\) −1.73334 −0.0584641
\(880\) −17.9246 −0.604237
\(881\) 8.06588 0.271747 0.135873 0.990726i \(-0.456616\pi\)
0.135873 + 0.990726i \(0.456616\pi\)
\(882\) 49.2706 1.65903
\(883\) −23.9866 −0.807214 −0.403607 0.914932i \(-0.632244\pi\)
−0.403607 + 0.914932i \(0.632244\pi\)
\(884\) 0 0
\(885\) 0.601651 0.0202243
\(886\) −53.9635 −1.81294
\(887\) 8.68123 0.291487 0.145744 0.989322i \(-0.453443\pi\)
0.145744 + 0.989322i \(0.453443\pi\)
\(888\) 3.51378 0.117915
\(889\) 37.1448 1.24580
\(890\) −11.6961 −0.392053
\(891\) 8.93770 0.299424
\(892\) −19.9971 −0.669552
\(893\) 31.6355 1.05864
\(894\) 1.44915 0.0484670
\(895\) −8.21659 −0.274650
\(896\) 199.320 6.65880
\(897\) 0 0
\(898\) −83.2516 −2.77814
\(899\) 0.840424 0.0280297
\(900\) 65.4893 2.18298
\(901\) 34.5189 1.14999
\(902\) −8.99024 −0.299342
\(903\) −0.489337 −0.0162841
\(904\) 143.651 4.77777
\(905\) 15.4525 0.513660
\(906\) 0.216263 0.00718486
\(907\) −42.2401 −1.40256 −0.701279 0.712887i \(-0.747387\pi\)
−0.701279 + 0.712887i \(0.747387\pi\)
\(908\) −67.7962 −2.24990
\(909\) 44.1950 1.46585
\(910\) 0 0
\(911\) −21.4429 −0.710434 −0.355217 0.934784i \(-0.615593\pi\)
−0.355217 + 0.934784i \(0.615593\pi\)
\(912\) 5.62954 0.186413
\(913\) −13.3856 −0.442999
\(914\) −90.4433 −2.99160
\(915\) 0.261002 0.00862844
\(916\) 14.2415 0.470551
\(917\) −59.7136 −1.97192
\(918\) 10.2202 0.337315
\(919\) −50.6078 −1.66940 −0.834699 0.550706i \(-0.814358\pi\)
−0.834699 + 0.550706i \(0.814358\pi\)
\(920\) 0.823677 0.0271558
\(921\) 1.93824 0.0638673
\(922\) 54.9008 1.80806
\(923\) 0 0
\(924\) 1.69731 0.0558373
\(925\) −16.0451 −0.527561
\(926\) 94.5009 3.10549
\(927\) −13.8007 −0.453275
\(928\) 124.288 4.07995
\(929\) −5.98422 −0.196336 −0.0981679 0.995170i \(-0.531298\pi\)
−0.0981679 + 0.995170i \(0.531298\pi\)
\(930\) 0.0435566 0.00142828
\(931\) −23.9476 −0.784851
\(932\) 32.6396 1.06915
\(933\) −0.844829 −0.0276585
\(934\) 71.2049 2.32989
\(935\) 7.89904 0.258326
\(936\) 0 0
\(937\) −12.3851 −0.404605 −0.202302 0.979323i \(-0.564842\pi\)
−0.202302 + 0.979323i \(0.564842\pi\)
\(938\) 61.2233 1.99901
\(939\) −2.23744 −0.0730162
\(940\) 47.5187 1.54989
\(941\) 50.8259 1.65688 0.828439 0.560079i \(-0.189229\pi\)
0.828439 + 0.560079i \(0.189229\pi\)
\(942\) 4.27825 0.139393
\(943\) 0.246618 0.00803099
\(944\) 113.691 3.70033
\(945\) 1.91589 0.0623240
\(946\) 4.52500 0.147120
\(947\) −16.6969 −0.542575 −0.271288 0.962498i \(-0.587449\pi\)
−0.271288 + 0.962498i \(0.587449\pi\)
\(948\) −6.46697 −0.210037
\(949\) 0 0
\(950\) −43.0622 −1.39712
\(951\) 1.05461 0.0341980
\(952\) −270.395 −8.76356
\(953\) 10.5606 0.342092 0.171046 0.985263i \(-0.445285\pi\)
0.171046 + 0.985263i \(0.445285\pi\)
\(954\) −38.6664 −1.25187
\(955\) −12.5152 −0.404983
\(956\) 123.843 4.00536
\(957\) 0.395135 0.0127729
\(958\) 31.7574 1.02604
\(959\) −41.8346 −1.35091
\(960\) 3.45771 0.111597
\(961\) −30.9687 −0.998989
\(962\) 0 0
\(963\) 17.1133 0.551469
\(964\) −67.7595 −2.18239
\(965\) −9.64479 −0.310477
\(966\) −0.0629892 −0.00202664
\(967\) 10.8624 0.349310 0.174655 0.984630i \(-0.444119\pi\)
0.174655 + 0.984630i \(0.444119\pi\)
\(968\) −10.1571 −0.326462
\(969\) −2.48084 −0.0796961
\(970\) −26.7308 −0.858275
\(971\) 50.5037 1.62074 0.810371 0.585918i \(-0.199266\pi\)
0.810371 + 0.585918i \(0.199266\pi\)
\(972\) −12.6981 −0.407292
\(973\) −58.2364 −1.86697
\(974\) 55.5919 1.78128
\(975\) 0 0
\(976\) 49.3201 1.57870
\(977\) 8.04995 0.257541 0.128770 0.991674i \(-0.458897\pi\)
0.128770 + 0.991674i \(0.458897\pi\)
\(978\) −2.06169 −0.0659256
\(979\) −3.95646 −0.126449
\(980\) −35.9709 −1.14905
\(981\) 46.2277 1.47594
\(982\) 44.1929 1.41025
\(983\) −29.9305 −0.954636 −0.477318 0.878731i \(-0.658391\pi\)
−0.477318 + 0.878731i \(0.658391\pi\)
\(984\) 2.74464 0.0874958
\(985\) −13.3543 −0.425502
\(986\) −97.2714 −3.09775
\(987\) −2.35165 −0.0748539
\(988\) 0 0
\(989\) −0.124129 −0.00394707
\(990\) −8.84810 −0.281211
\(991\) 14.9437 0.474701 0.237351 0.971424i \(-0.423721\pi\)
0.237351 + 0.971424i \(0.423721\pi\)
\(992\) 4.63452 0.147146
\(993\) −0.151790 −0.00481692
\(994\) −78.2791 −2.48286
\(995\) 9.92020 0.314492
\(996\) 6.31470 0.200089
\(997\) −52.1103 −1.65035 −0.825174 0.564878i \(-0.808923\pi\)
−0.825174 + 0.564878i \(0.808923\pi\)
\(998\) −22.4114 −0.709422
\(999\) 2.07326 0.0655950
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.1.1 yes 21
13.12 even 2 1859.2.a.s.1.21 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.21 21 13.12 even 2
1859.2.a.t.1.1 yes 21 1.1 even 1 trivial