Properties

Label 5445.2.a.bz.1.6
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.4785439006\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.437199552.1
Defining polynomial: \(x^{6} - 13 x^{4} + 49 x^{2} - 48\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1815)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.63162\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.63162 q^{2} +4.92542 q^{4} -1.00000 q^{5} +4.16741 q^{7} +7.69860 q^{8} +O(q^{10})\) \(q+2.63162 q^{2} +4.92542 q^{4} -1.00000 q^{5} +4.16741 q^{7} +7.69860 q^{8} -2.63162 q^{10} -5.26324 q^{13} +10.9670 q^{14} +10.4089 q^{16} +4.23450 q^{17} +2.50245 q^{19} -4.92542 q^{20} -5.48352 q^{23} +1.00000 q^{25} -13.8508 q^{26} +20.5263 q^{28} +5.26324 q^{29} +10.1162 q^{31} +11.9952 q^{32} +11.1436 q^{34} -4.16741 q^{35} -4.48352 q^{37} +6.58549 q^{38} -7.69860 q^{40} -3.46410 q^{41} +6.66986 q^{43} -14.4305 q^{46} -4.21817 q^{47} +10.3673 q^{49} +2.63162 q^{50} -25.9237 q^{52} +3.63268 q^{53} +32.0832 q^{56} +13.8508 q^{58} +6.58549 q^{59} +12.2585 q^{61} +26.6220 q^{62} +10.7489 q^{64} +5.26324 q^{65} -4.48352 q^{67} +20.8567 q^{68} -10.9670 q^{70} -1.26535 q^{71} -4.55993 q^{73} -11.7989 q^{74} +12.3256 q^{76} +6.86112 q^{79} -10.4089 q^{80} -9.11620 q^{82} -4.87072 q^{83} -4.23450 q^{85} +17.5525 q^{86} -15.1162 q^{89} -21.9341 q^{91} -27.0087 q^{92} -11.1006 q^{94} -2.50245 q^{95} -16.1852 q^{97} +27.2829 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 14q^{4} - 6q^{5} + O(q^{10}) \) \( 6q + 14q^{4} - 6q^{5} - 8q^{14} + 10q^{16} - 14q^{20} + 4q^{23} + 6q^{25} - 52q^{26} + 18q^{31} + 26q^{34} + 10q^{37} + 20q^{38} + 68q^{49} + 16q^{53} + 76q^{56} + 52q^{58} + 20q^{59} + 16q^{64} + 10q^{67} + 8q^{70} + 4q^{71} - 10q^{80} - 12q^{82} + 12q^{86} - 48q^{89} + 16q^{91} - 30q^{92} + 2q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.63162 1.86084 0.930418 0.366500i \(-0.119444\pi\)
0.930418 + 0.366500i \(0.119444\pi\)
\(3\) 0 0
\(4\) 4.92542 2.46271
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.16741 1.57513 0.787567 0.616229i \(-0.211341\pi\)
0.787567 + 0.616229i \(0.211341\pi\)
\(8\) 7.69860 2.72187
\(9\) 0 0
\(10\) −2.63162 −0.832191
\(11\) 0 0
\(12\) 0 0
\(13\) −5.26324 −1.45976 −0.729880 0.683575i \(-0.760424\pi\)
−0.729880 + 0.683575i \(0.760424\pi\)
\(14\) 10.9670 2.93107
\(15\) 0 0
\(16\) 10.4089 2.60224
\(17\) 4.23450 1.02702 0.513508 0.858085i \(-0.328345\pi\)
0.513508 + 0.858085i \(0.328345\pi\)
\(18\) 0 0
\(19\) 2.50245 0.574101 0.287051 0.957915i \(-0.407325\pi\)
0.287051 + 0.957915i \(0.407325\pi\)
\(20\) −4.92542 −1.10136
\(21\) 0 0
\(22\) 0 0
\(23\) −5.48352 −1.14339 −0.571697 0.820465i \(-0.693715\pi\)
−0.571697 + 0.820465i \(0.693715\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −13.8508 −2.71637
\(27\) 0 0
\(28\) 20.5263 3.87910
\(29\) 5.26324 0.977359 0.488680 0.872463i \(-0.337479\pi\)
0.488680 + 0.872463i \(0.337479\pi\)
\(30\) 0 0
\(31\) 10.1162 1.81692 0.908461 0.417969i \(-0.137258\pi\)
0.908461 + 0.417969i \(0.137258\pi\)
\(32\) 11.9952 2.12047
\(33\) 0 0
\(34\) 11.1436 1.91111
\(35\) −4.16741 −0.704421
\(36\) 0 0
\(37\) −4.48352 −0.737087 −0.368543 0.929611i \(-0.620143\pi\)
−0.368543 + 0.929611i \(0.620143\pi\)
\(38\) 6.58549 1.06831
\(39\) 0 0
\(40\) −7.69860 −1.21726
\(41\) −3.46410 −0.541002 −0.270501 0.962720i \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(42\) 0 0
\(43\) 6.66986 1.01714 0.508572 0.861019i \(-0.330174\pi\)
0.508572 + 0.861019i \(0.330174\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −14.4305 −2.12767
\(47\) −4.21817 −0.615283 −0.307642 0.951502i \(-0.599540\pi\)
−0.307642 + 0.951502i \(0.599540\pi\)
\(48\) 0 0
\(49\) 10.3673 1.48105
\(50\) 2.63162 0.372167
\(51\) 0 0
\(52\) −25.9237 −3.59497
\(53\) 3.63268 0.498986 0.249493 0.968377i \(-0.419736\pi\)
0.249493 + 0.968377i \(0.419736\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 32.0832 4.28730
\(57\) 0 0
\(58\) 13.8508 1.81871
\(59\) 6.58549 0.857358 0.428679 0.903457i \(-0.358979\pi\)
0.428679 + 0.903457i \(0.358979\pi\)
\(60\) 0 0
\(61\) 12.2585 1.56954 0.784772 0.619785i \(-0.212780\pi\)
0.784772 + 0.619785i \(0.212780\pi\)
\(62\) 26.6220 3.38100
\(63\) 0 0
\(64\) 10.7489 1.34361
\(65\) 5.26324 0.652825
\(66\) 0 0
\(67\) −4.48352 −0.547749 −0.273875 0.961765i \(-0.588305\pi\)
−0.273875 + 0.961765i \(0.588305\pi\)
\(68\) 20.8567 2.52925
\(69\) 0 0
\(70\) −10.9670 −1.31081
\(71\) −1.26535 −0.150170 −0.0750849 0.997177i \(-0.523923\pi\)
−0.0750849 + 0.997177i \(0.523923\pi\)
\(72\) 0 0
\(73\) −4.55993 −0.533699 −0.266850 0.963738i \(-0.585983\pi\)
−0.266850 + 0.963738i \(0.585983\pi\)
\(74\) −11.7989 −1.37160
\(75\) 0 0
\(76\) 12.3256 1.41385
\(77\) 0 0
\(78\) 0 0
\(79\) 6.86112 0.771936 0.385968 0.922512i \(-0.373868\pi\)
0.385968 + 0.922512i \(0.373868\pi\)
\(80\) −10.4089 −1.16376
\(81\) 0 0
\(82\) −9.11620 −1.00672
\(83\) −4.87072 −0.534631 −0.267316 0.963609i \(-0.586137\pi\)
−0.267316 + 0.963609i \(0.586137\pi\)
\(84\) 0 0
\(85\) −4.23450 −0.459296
\(86\) 17.5525 1.89274
\(87\) 0 0
\(88\) 0 0
\(89\) −15.1162 −1.60231 −0.801157 0.598454i \(-0.795782\pi\)
−0.801157 + 0.598454i \(0.795782\pi\)
\(90\) 0 0
\(91\) −21.9341 −2.29932
\(92\) −27.0087 −2.81585
\(93\) 0 0
\(94\) −11.1006 −1.14494
\(95\) −2.50245 −0.256746
\(96\) 0 0
\(97\) −16.1852 −1.64336 −0.821680 0.569949i \(-0.806963\pi\)
−0.821680 + 0.569949i \(0.806963\pi\)
\(98\) 27.2829 2.75598
\(99\) 0 0
\(100\) 4.92542 0.492542
\(101\) −3.59828 −0.358042 −0.179021 0.983845i \(-0.557293\pi\)
−0.179021 + 0.983845i \(0.557293\pi\)
\(102\) 0 0
\(103\) 1.36732 0.134726 0.0673632 0.997729i \(-0.478541\pi\)
0.0673632 + 0.997729i \(0.478541\pi\)
\(104\) −40.5196 −3.97327
\(105\) 0 0
\(106\) 9.55982 0.928532
\(107\) −12.9618 −1.25307 −0.626534 0.779394i \(-0.715527\pi\)
−0.626534 + 0.779394i \(0.715527\pi\)
\(108\) 0 0
\(109\) 5.96655 0.571492 0.285746 0.958305i \(-0.407759\pi\)
0.285746 + 0.958305i \(0.407759\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 43.3784 4.09887
\(113\) 6.06902 0.570925 0.285462 0.958390i \(-0.407853\pi\)
0.285462 + 0.958390i \(0.407853\pi\)
\(114\) 0 0
\(115\) 5.48352 0.511341
\(116\) 25.9237 2.40695
\(117\) 0 0
\(118\) 17.3305 1.59540
\(119\) 17.6469 1.61769
\(120\) 0 0
\(121\) 0 0
\(122\) 32.2598 2.92066
\(123\) 0 0
\(124\) 49.8266 4.47456
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 9.82317 0.871665 0.435833 0.900028i \(-0.356454\pi\)
0.435833 + 0.900028i \(0.356454\pi\)
\(128\) 4.29658 0.379768
\(129\) 0 0
\(130\) 13.8508 1.21480
\(131\) −3.46410 −0.302660 −0.151330 0.988483i \(-0.548356\pi\)
−0.151330 + 0.988483i \(0.548356\pi\)
\(132\) 0 0
\(133\) 10.4287 0.904286
\(134\) −11.7989 −1.01927
\(135\) 0 0
\(136\) 32.5997 2.79540
\(137\) −20.5997 −1.75995 −0.879976 0.475017i \(-0.842442\pi\)
−0.879976 + 0.475017i \(0.842442\pi\)
\(138\) 0 0
\(139\) −17.6984 −1.50116 −0.750579 0.660781i \(-0.770225\pi\)
−0.750579 + 0.660781i \(0.770225\pi\)
\(140\) −20.5263 −1.73479
\(141\) 0 0
\(142\) −3.32993 −0.279441
\(143\) 0 0
\(144\) 0 0
\(145\) −5.26324 −0.437088
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) −22.0832 −1.81523
\(149\) 20.5263 1.68158 0.840789 0.541363i \(-0.182092\pi\)
0.840789 + 0.541363i \(0.182092\pi\)
\(150\) 0 0
\(151\) −3.84198 −0.312656 −0.156328 0.987705i \(-0.549966\pi\)
−0.156328 + 0.987705i \(0.549966\pi\)
\(152\) 19.2654 1.56263
\(153\) 0 0
\(154\) 0 0
\(155\) −10.1162 −0.812553
\(156\) 0 0
\(157\) −0.781830 −0.0623969 −0.0311984 0.999513i \(-0.509932\pi\)
−0.0311984 + 0.999513i \(0.509932\pi\)
\(158\) 18.0558 1.43645
\(159\) 0 0
\(160\) −11.9952 −0.948303
\(161\) −22.8521 −1.80100
\(162\) 0 0
\(163\) −7.74887 −0.606939 −0.303469 0.952841i \(-0.598145\pi\)
−0.303469 + 0.952841i \(0.598145\pi\)
\(164\) −17.0622 −1.33233
\(165\) 0 0
\(166\) −12.8179 −0.994861
\(167\) −14.8851 −1.15185 −0.575924 0.817504i \(-0.695357\pi\)
−0.575924 + 0.817504i \(0.695357\pi\)
\(168\) 0 0
\(169\) 14.7017 1.13090
\(170\) −11.1436 −0.854675
\(171\) 0 0
\(172\) 32.8519 2.50493
\(173\) −2.19166 −0.166628 −0.0833142 0.996523i \(-0.526551\pi\)
−0.0833142 + 0.996523i \(0.526551\pi\)
\(174\) 0 0
\(175\) 4.16741 0.315027
\(176\) 0 0
\(177\) 0 0
\(178\) −39.7801 −2.98164
\(179\) 13.8508 1.03526 0.517630 0.855604i \(-0.326814\pi\)
0.517630 + 0.855604i \(0.326814\pi\)
\(180\) 0 0
\(181\) 7.36732 0.547609 0.273804 0.961785i \(-0.411718\pi\)
0.273804 + 0.961785i \(0.411718\pi\)
\(182\) −57.7222 −4.27865
\(183\) 0 0
\(184\) −42.2154 −3.11216
\(185\) 4.48352 0.329635
\(186\) 0 0
\(187\) 0 0
\(188\) −20.7763 −1.51527
\(189\) 0 0
\(190\) −6.58549 −0.477762
\(191\) −0.679859 −0.0491929 −0.0245965 0.999697i \(-0.507830\pi\)
−0.0245965 + 0.999697i \(0.507830\pi\)
\(192\) 0 0
\(193\) 4.95245 0.356485 0.178242 0.983987i \(-0.442959\pi\)
0.178242 + 0.983987i \(0.442959\pi\)
\(194\) −42.5933 −3.05802
\(195\) 0 0
\(196\) 51.0635 3.64739
\(197\) −3.59828 −0.256367 −0.128183 0.991750i \(-0.540915\pi\)
−0.128183 + 0.991750i \(0.540915\pi\)
\(198\) 0 0
\(199\) 3.88380 0.275315 0.137658 0.990480i \(-0.456043\pi\)
0.137658 + 0.990480i \(0.456043\pi\)
\(200\) 7.69860 0.544373
\(201\) 0 0
\(202\) −9.46929 −0.666257
\(203\) 21.9341 1.53947
\(204\) 0 0
\(205\) 3.46410 0.241943
\(206\) 3.59828 0.250704
\(207\) 0 0
\(208\) −54.7848 −3.79864
\(209\) 0 0
\(210\) 0 0
\(211\) 24.4500 1.68321 0.841603 0.540097i \(-0.181612\pi\)
0.841603 + 0.540097i \(0.181612\pi\)
\(212\) 17.8925 1.22886
\(213\) 0 0
\(214\) −34.1106 −2.33176
\(215\) −6.66986 −0.454881
\(216\) 0 0
\(217\) 42.1584 2.86190
\(218\) 15.7017 1.06345
\(219\) 0 0
\(220\) 0 0
\(221\) −22.2872 −1.49920
\(222\) 0 0
\(223\) 1.59972 0.107125 0.0535626 0.998564i \(-0.482942\pi\)
0.0535626 + 0.998564i \(0.482942\pi\)
\(224\) 49.9889 3.34002
\(225\) 0 0
\(226\) 15.9713 1.06240
\(227\) −18.6176 −1.23569 −0.617847 0.786299i \(-0.711995\pi\)
−0.617847 + 0.786299i \(0.711995\pi\)
\(228\) 0 0
\(229\) 23.3344 1.54198 0.770989 0.636848i \(-0.219762\pi\)
0.770989 + 0.636848i \(0.219762\pi\)
\(230\) 14.4305 0.951522
\(231\) 0 0
\(232\) 40.5196 2.66024
\(233\) −9.75608 −0.639142 −0.319571 0.947562i \(-0.603539\pi\)
−0.319571 + 0.947562i \(0.603539\pi\)
\(234\) 0 0
\(235\) 4.21817 0.275163
\(236\) 32.4363 2.11143
\(237\) 0 0
\(238\) 46.4399 3.01025
\(239\) 8.59317 0.555846 0.277923 0.960603i \(-0.410354\pi\)
0.277923 + 0.960603i \(0.410354\pi\)
\(240\) 0 0
\(241\) −8.97105 −0.577876 −0.288938 0.957348i \(-0.593302\pi\)
−0.288938 + 0.957348i \(0.593302\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 60.3784 3.86533
\(245\) −10.3673 −0.662344
\(246\) 0 0
\(247\) −13.1710 −0.838050
\(248\) 77.8806 4.94542
\(249\) 0 0
\(250\) −2.63162 −0.166438
\(251\) −5.32014 −0.335804 −0.167902 0.985804i \(-0.553699\pi\)
−0.167902 + 0.985804i \(0.553699\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 25.8508 1.62203
\(255\) 0 0
\(256\) −10.1908 −0.636923
\(257\) −27.7707 −1.73229 −0.866145 0.499794i \(-0.833409\pi\)
−0.866145 + 0.499794i \(0.833409\pi\)
\(258\) 0 0
\(259\) −18.6847 −1.16101
\(260\) 25.9237 1.60772
\(261\) 0 0
\(262\) −9.11620 −0.563201
\(263\) −5.89946 −0.363776 −0.181888 0.983319i \(-0.558221\pi\)
−0.181888 + 0.983319i \(0.558221\pi\)
\(264\) 0 0
\(265\) −3.63268 −0.223154
\(266\) 27.4445 1.68273
\(267\) 0 0
\(268\) −22.0832 −1.34895
\(269\) 6.23240 0.379996 0.189998 0.981784i \(-0.439152\pi\)
0.189998 + 0.981784i \(0.439152\pi\)
\(270\) 0 0
\(271\) −29.7657 −1.80814 −0.904068 0.427389i \(-0.859433\pi\)
−0.904068 + 0.427389i \(0.859433\pi\)
\(272\) 44.0767 2.67254
\(273\) 0 0
\(274\) −54.2106 −3.27498
\(275\) 0 0
\(276\) 0 0
\(277\) 9.29648 0.558571 0.279286 0.960208i \(-0.409902\pi\)
0.279286 + 0.960208i \(0.409902\pi\)
\(278\) −46.5754 −2.79341
\(279\) 0 0
\(280\) −32.0832 −1.91734
\(281\) −11.5406 −0.688453 −0.344227 0.938887i \(-0.611859\pi\)
−0.344227 + 0.938887i \(0.611859\pi\)
\(282\) 0 0
\(283\) −7.50735 −0.446265 −0.223133 0.974788i \(-0.571628\pi\)
−0.223133 + 0.974788i \(0.571628\pi\)
\(284\) −6.23240 −0.369825
\(285\) 0 0
\(286\) 0 0
\(287\) −14.4363 −0.852150
\(288\) 0 0
\(289\) 0.930985 0.0547638
\(290\) −13.8508 −0.813350
\(291\) 0 0
\(292\) −22.4596 −1.31435
\(293\) 18.0909 1.05688 0.528441 0.848970i \(-0.322777\pi\)
0.528441 + 0.848970i \(0.322777\pi\)
\(294\) 0 0
\(295\) −6.58549 −0.383422
\(296\) −34.5168 −2.00625
\(297\) 0 0
\(298\) 54.0173 3.12914
\(299\) 28.8611 1.66908
\(300\) 0 0
\(301\) 27.7961 1.60214
\(302\) −10.1106 −0.581802
\(303\) 0 0
\(304\) 26.0478 1.49395
\(305\) −12.2585 −0.701921
\(306\) 0 0
\(307\) 3.90907 0.223102 0.111551 0.993759i \(-0.464418\pi\)
0.111551 + 0.993759i \(0.464418\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −26.6220 −1.51203
\(311\) −22.5196 −1.27697 −0.638484 0.769635i \(-0.720438\pi\)
−0.638484 + 0.769635i \(0.720438\pi\)
\(312\) 0 0
\(313\) 19.2542 1.08831 0.544157 0.838984i \(-0.316850\pi\)
0.544157 + 0.838984i \(0.316850\pi\)
\(314\) −2.05748 −0.116110
\(315\) 0 0
\(316\) 33.7939 1.90106
\(317\) 8.36732 0.469956 0.234978 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −10.7489 −0.600880
\(321\) 0 0
\(322\) −60.1380 −3.35136
\(323\) 10.5966 0.589612
\(324\) 0 0
\(325\) −5.26324 −0.291952
\(326\) −20.3921 −1.12941
\(327\) 0 0
\(328\) −26.6687 −1.47253
\(329\) −17.5789 −0.969153
\(330\) 0 0
\(331\) −12.5525 −0.689950 −0.344975 0.938612i \(-0.612113\pi\)
−0.344975 + 0.938612i \(0.612113\pi\)
\(332\) −23.9904 −1.31664
\(333\) 0 0
\(334\) −39.1720 −2.14340
\(335\) 4.48352 0.244961
\(336\) 0 0
\(337\) 21.3638 1.16376 0.581879 0.813275i \(-0.302318\pi\)
0.581879 + 0.813275i \(0.302318\pi\)
\(338\) 38.6893 2.10442
\(339\) 0 0
\(340\) −20.8567 −1.13111
\(341\) 0 0
\(342\) 0 0
\(343\) 14.0330 0.757712
\(344\) 51.3486 2.76853
\(345\) 0 0
\(346\) −5.76760 −0.310068
\(347\) −8.22529 −0.441557 −0.220778 0.975324i \(-0.570860\pi\)
−0.220778 + 0.975324i \(0.570860\pi\)
\(348\) 0 0
\(349\) −6.11536 −0.327348 −0.163674 0.986515i \(-0.552334\pi\)
−0.163674 + 0.986515i \(0.552334\pi\)
\(350\) 10.9670 0.586213
\(351\) 0 0
\(352\) 0 0
\(353\) 23.0361 1.22609 0.613043 0.790050i \(-0.289945\pi\)
0.613043 + 0.790050i \(0.289945\pi\)
\(354\) 0 0
\(355\) 1.26535 0.0671579
\(356\) −74.4537 −3.94604
\(357\) 0 0
\(358\) 36.4502 1.92645
\(359\) −15.2630 −0.805552 −0.402776 0.915299i \(-0.631955\pi\)
−0.402776 + 0.915299i \(0.631955\pi\)
\(360\) 0 0
\(361\) −12.7378 −0.670408
\(362\) 19.3880 1.01901
\(363\) 0 0
\(364\) −108.035 −5.66255
\(365\) 4.55993 0.238678
\(366\) 0 0
\(367\) −32.3816 −1.69030 −0.845152 0.534527i \(-0.820490\pi\)
−0.845152 + 0.534527i \(0.820490\pi\)
\(368\) −57.0777 −2.97538
\(369\) 0 0
\(370\) 11.7989 0.613397
\(371\) 15.1389 0.785970
\(372\) 0 0
\(373\) 8.15821 0.422416 0.211208 0.977441i \(-0.432260\pi\)
0.211208 + 0.977441i \(0.432260\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −32.4740 −1.67472
\(377\) −27.7017 −1.42671
\(378\) 0 0
\(379\) 7.48352 0.384403 0.192201 0.981356i \(-0.438437\pi\)
0.192201 + 0.981356i \(0.438437\pi\)
\(380\) −12.3256 −0.632291
\(381\) 0 0
\(382\) −1.78913 −0.0915399
\(383\) 18.1380 0.926810 0.463405 0.886147i \(-0.346628\pi\)
0.463405 + 0.886147i \(0.346628\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.0330 0.663360
\(387\) 0 0
\(388\) −79.7190 −4.04712
\(389\) −17.7849 −0.901732 −0.450866 0.892592i \(-0.648885\pi\)
−0.450866 + 0.892592i \(0.648885\pi\)
\(390\) 0 0
\(391\) −23.2200 −1.17428
\(392\) 79.8139 4.03121
\(393\) 0 0
\(394\) −9.46929 −0.477056
\(395\) −6.86112 −0.345220
\(396\) 0 0
\(397\) −8.33437 −0.418290 −0.209145 0.977885i \(-0.567068\pi\)
−0.209145 + 0.977885i \(0.567068\pi\)
\(398\) 10.2207 0.512317
\(399\) 0 0
\(400\) 10.4089 0.520447
\(401\) 13.2654 0.662440 0.331220 0.943554i \(-0.392540\pi\)
0.331220 + 0.943554i \(0.392540\pi\)
\(402\) 0 0
\(403\) −53.2440 −2.65227
\(404\) −17.7230 −0.881754
\(405\) 0 0
\(406\) 57.7222 2.86470
\(407\) 0 0
\(408\) 0 0
\(409\) −16.8609 −0.833718 −0.416859 0.908971i \(-0.636869\pi\)
−0.416859 + 0.908971i \(0.636869\pi\)
\(410\) 9.11620 0.450217
\(411\) 0 0
\(412\) 6.73465 0.331792
\(413\) 27.4445 1.35045
\(414\) 0 0
\(415\) 4.87072 0.239094
\(416\) −63.1335 −3.09538
\(417\) 0 0
\(418\) 0 0
\(419\) −9.79606 −0.478569 −0.239284 0.970950i \(-0.576913\pi\)
−0.239284 + 0.970950i \(0.576913\pi\)
\(420\) 0 0
\(421\) −17.8651 −0.870690 −0.435345 0.900264i \(-0.643374\pi\)
−0.435345 + 0.900264i \(0.643374\pi\)
\(422\) 64.3430 3.13217
\(423\) 0 0
\(424\) 27.9665 1.35817
\(425\) 4.23450 0.205403
\(426\) 0 0
\(427\) 51.0863 2.47224
\(428\) −63.8425 −3.08595
\(429\) 0 0
\(430\) −17.5525 −0.846459
\(431\) −37.1959 −1.79166 −0.895832 0.444393i \(-0.853420\pi\)
−0.895832 + 0.444393i \(0.853420\pi\)
\(432\) 0 0
\(433\) −10.1852 −0.489470 −0.244735 0.969590i \(-0.578701\pi\)
−0.244735 + 0.969590i \(0.578701\pi\)
\(434\) 110.945 5.32552
\(435\) 0 0
\(436\) 29.3878 1.40742
\(437\) −13.7222 −0.656423
\(438\) 0 0
\(439\) −19.7134 −0.940870 −0.470435 0.882435i \(-0.655903\pi\)
−0.470435 + 0.882435i \(0.655903\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −58.6514 −2.78976
\(443\) 26.4363 1.25603 0.628014 0.778202i \(-0.283868\pi\)
0.628014 + 0.778202i \(0.283868\pi\)
\(444\) 0 0
\(445\) 15.1162 0.716577
\(446\) 4.20986 0.199342
\(447\) 0 0
\(448\) 44.7950 2.11636
\(449\) 21.7017 1.02417 0.512083 0.858936i \(-0.328874\pi\)
0.512083 + 0.858936i \(0.328874\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 29.8925 1.40602
\(453\) 0 0
\(454\) −48.9944 −2.29942
\(455\) 21.9341 1.02829
\(456\) 0 0
\(457\) 11.7989 0.551930 0.275965 0.961168i \(-0.411003\pi\)
0.275965 + 0.961168i \(0.411003\pi\)
\(458\) 61.4072 2.86937
\(459\) 0 0
\(460\) 27.0087 1.25929
\(461\) −31.0527 −1.44627 −0.723135 0.690706i \(-0.757300\pi\)
−0.723135 + 0.690706i \(0.757300\pi\)
\(462\) 0 0
\(463\) 38.3704 1.78323 0.891613 0.452799i \(-0.149575\pi\)
0.891613 + 0.452799i \(0.149575\pi\)
\(464\) 54.7848 2.54332
\(465\) 0 0
\(466\) −25.6743 −1.18934
\(467\) −14.9528 −0.691934 −0.345967 0.938247i \(-0.612449\pi\)
−0.345967 + 0.938247i \(0.612449\pi\)
\(468\) 0 0
\(469\) −18.6847 −0.862779
\(470\) 11.1006 0.512033
\(471\) 0 0
\(472\) 50.6991 2.33361
\(473\) 0 0
\(474\) 0 0
\(475\) 2.50245 0.114820
\(476\) 86.9185 3.98390
\(477\) 0 0
\(478\) 22.6139 1.03434
\(479\) −12.1914 −0.557041 −0.278521 0.960430i \(-0.589844\pi\)
−0.278521 + 0.960430i \(0.589844\pi\)
\(480\) 0 0
\(481\) 23.5979 1.07597
\(482\) −23.6084 −1.07533
\(483\) 0 0
\(484\) 0 0
\(485\) 16.1852 0.734933
\(486\) 0 0
\(487\) 14.2872 0.647414 0.323707 0.946157i \(-0.395071\pi\)
0.323707 + 0.946157i \(0.395071\pi\)
\(488\) 94.3735 4.27209
\(489\) 0 0
\(490\) −27.2829 −1.23251
\(491\) 26.0579 1.17597 0.587987 0.808870i \(-0.299921\pi\)
0.587987 + 0.808870i \(0.299921\pi\)
\(492\) 0 0
\(493\) 22.2872 1.00376
\(494\) −34.6610 −1.55947
\(495\) 0 0
\(496\) 105.299 4.72806
\(497\) −5.27325 −0.236537
\(498\) 0 0
\(499\) 28.8651 1.29218 0.646089 0.763262i \(-0.276403\pi\)
0.646089 + 0.763262i \(0.276403\pi\)
\(500\) −4.92542 −0.220272
\(501\) 0 0
\(502\) −14.0006 −0.624877
\(503\) −39.3729 −1.75555 −0.877776 0.479071i \(-0.840974\pi\)
−0.877776 + 0.479071i \(0.840974\pi\)
\(504\) 0 0
\(505\) 3.59828 0.160121
\(506\) 0 0
\(507\) 0 0
\(508\) 48.3833 2.14666
\(509\) −20.0832 −0.890174 −0.445087 0.895487i \(-0.646827\pi\)
−0.445087 + 0.895487i \(0.646827\pi\)
\(510\) 0 0
\(511\) −19.0031 −0.840648
\(512\) −35.4114 −1.56498
\(513\) 0 0
\(514\) −73.0819 −3.22351
\(515\) −1.36732 −0.0602515
\(516\) 0 0
\(517\) 0 0
\(518\) −49.1710 −2.16045
\(519\) 0 0
\(520\) 40.5196 1.77690
\(521\) 34.7520 1.52251 0.761256 0.648452i \(-0.224583\pi\)
0.761256 + 0.648452i \(0.224583\pi\)
\(522\) 0 0
\(523\) 14.6939 0.642519 0.321260 0.946991i \(-0.395894\pi\)
0.321260 + 0.946991i \(0.395894\pi\)
\(524\) −17.0622 −0.745364
\(525\) 0 0
\(526\) −15.5251 −0.676928
\(527\) 42.8370 1.86601
\(528\) 0 0
\(529\) 7.06902 0.307348
\(530\) −9.55982 −0.415252
\(531\) 0 0
\(532\) 51.3659 2.22700
\(533\) 18.2324 0.789733
\(534\) 0 0
\(535\) 12.9618 0.560389
\(536\) −34.5168 −1.49090
\(537\) 0 0
\(538\) 16.4013 0.707110
\(539\) 0 0
\(540\) 0 0
\(541\) −3.32993 −0.143165 −0.0715824 0.997435i \(-0.522805\pi\)
−0.0715824 + 0.997435i \(0.522805\pi\)
\(542\) −78.3319 −3.36464
\(543\) 0 0
\(544\) 50.7936 2.17776
\(545\) −5.96655 −0.255579
\(546\) 0 0
\(547\) −27.4545 −1.17387 −0.586934 0.809635i \(-0.699665\pi\)
−0.586934 + 0.809635i \(0.699665\pi\)
\(548\) −101.462 −4.33426
\(549\) 0 0
\(550\) 0 0
\(551\) 13.1710 0.561103
\(552\) 0 0
\(553\) 28.5931 1.21590
\(554\) 24.4648 1.03941
\(555\) 0 0
\(556\) −87.1720 −3.69692
\(557\) −26.8283 −1.13675 −0.568375 0.822770i \(-0.692428\pi\)
−0.568375 + 0.822770i \(0.692428\pi\)
\(558\) 0 0
\(559\) −35.1051 −1.48479
\(560\) −43.3784 −1.83307
\(561\) 0 0
\(562\) −30.3704 −1.28110
\(563\) −36.9668 −1.55797 −0.778983 0.627045i \(-0.784264\pi\)
−0.778983 + 0.627045i \(0.784264\pi\)
\(564\) 0 0
\(565\) −6.06902 −0.255325
\(566\) −19.7565 −0.830427
\(567\) 0 0
\(568\) −9.74145 −0.408742
\(569\) 32.4594 1.36077 0.680384 0.732856i \(-0.261813\pi\)
0.680384 + 0.732856i \(0.261813\pi\)
\(570\) 0 0
\(571\) −18.0092 −0.753661 −0.376830 0.926282i \(-0.622986\pi\)
−0.376830 + 0.926282i \(0.622986\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −37.9910 −1.58571
\(575\) −5.48352 −0.228679
\(576\) 0 0
\(577\) 39.5997 1.64856 0.824279 0.566184i \(-0.191581\pi\)
0.824279 + 0.566184i \(0.191581\pi\)
\(578\) 2.45000 0.101906
\(579\) 0 0
\(580\) −25.9237 −1.07642
\(581\) −20.2983 −0.842116
\(582\) 0 0
\(583\) 0 0
\(584\) −35.1051 −1.45266
\(585\) 0 0
\(586\) 47.6084 1.96668
\(587\) 24.9813 1.03109 0.515544 0.856863i \(-0.327590\pi\)
0.515544 + 0.856863i \(0.327590\pi\)
\(588\) 0 0
\(589\) 25.3153 1.04310
\(590\) −17.3305 −0.713486
\(591\) 0 0
\(592\) −46.6687 −1.91807
\(593\) −1.92331 −0.0789807 −0.0394904 0.999220i \(-0.512573\pi\)
−0.0394904 + 0.999220i \(0.512573\pi\)
\(594\) 0 0
\(595\) −17.6469 −0.723453
\(596\) 101.101 4.14124
\(597\) 0 0
\(598\) 75.9514 3.10588
\(599\) −19.9889 −0.816723 −0.408362 0.912820i \(-0.633900\pi\)
−0.408362 + 0.912820i \(0.633900\pi\)
\(600\) 0 0
\(601\) 0.176619 0.00720444 0.00360222 0.999994i \(-0.498853\pi\)
0.00360222 + 0.999994i \(0.498853\pi\)
\(602\) 73.1487 2.98132
\(603\) 0 0
\(604\) −18.9234 −0.769982
\(605\) 0 0
\(606\) 0 0
\(607\) −11.8089 −0.479310 −0.239655 0.970858i \(-0.577034\pi\)
−0.239655 + 0.970858i \(0.577034\pi\)
\(608\) 30.0173 1.21736
\(609\) 0 0
\(610\) −32.2598 −1.30616
\(611\) 22.2012 0.898166
\(612\) 0 0
\(613\) 13.4114 0.541683 0.270841 0.962624i \(-0.412698\pi\)
0.270841 + 0.962624i \(0.412698\pi\)
\(614\) 10.2872 0.415157
\(615\) 0 0
\(616\) 0 0
\(617\) 27.9341 1.12458 0.562292 0.826939i \(-0.309920\pi\)
0.562292 + 0.826939i \(0.309920\pi\)
\(618\) 0 0
\(619\) 38.2324 1.53669 0.768345 0.640036i \(-0.221081\pi\)
0.768345 + 0.640036i \(0.221081\pi\)
\(620\) −49.8266 −2.00108
\(621\) 0 0
\(622\) −59.2630 −2.37623
\(623\) −62.9954 −2.52386
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 50.6698 2.02517
\(627\) 0 0
\(628\) −3.85085 −0.153665
\(629\) −18.9855 −0.757000
\(630\) 0 0
\(631\) 0.952817 0.0379310 0.0189655 0.999820i \(-0.493963\pi\)
0.0189655 + 0.999820i \(0.493963\pi\)
\(632\) 52.8210 2.10111
\(633\) 0 0
\(634\) 22.0196 0.874511
\(635\) −9.82317 −0.389821
\(636\) 0 0
\(637\) −54.5657 −2.16197
\(638\) 0 0
\(639\) 0 0
\(640\) −4.29658 −0.169837
\(641\) −4.47592 −0.176788 −0.0883941 0.996086i \(-0.528173\pi\)
−0.0883941 + 0.996086i \(0.528173\pi\)
\(642\) 0 0
\(643\) 21.8980 0.863574 0.431787 0.901976i \(-0.357883\pi\)
0.431787 + 0.901976i \(0.357883\pi\)
\(644\) −112.556 −4.43534
\(645\) 0 0
\(646\) 27.8863 1.09717
\(647\) −21.2796 −0.836587 −0.418293 0.908312i \(-0.637372\pi\)
−0.418293 + 0.908312i \(0.637372\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −13.8508 −0.543275
\(651\) 0 0
\(652\) −38.1665 −1.49471
\(653\) −20.5307 −0.803429 −0.401714 0.915765i \(-0.631586\pi\)
−0.401714 + 0.915765i \(0.631586\pi\)
\(654\) 0 0
\(655\) 3.46410 0.135354
\(656\) −36.0576 −1.40781
\(657\) 0 0
\(658\) −46.2609 −1.80344
\(659\) 18.9855 0.739569 0.369784 0.929118i \(-0.379432\pi\)
0.369784 + 0.929118i \(0.379432\pi\)
\(660\) 0 0
\(661\) −2.86507 −0.111438 −0.0557192 0.998446i \(-0.517745\pi\)
−0.0557192 + 0.998446i \(0.517745\pi\)
\(662\) −33.0335 −1.28388
\(663\) 0 0
\(664\) −37.4977 −1.45519
\(665\) −10.4287 −0.404409
\(666\) 0 0
\(667\) −28.8611 −1.11751
\(668\) −73.3156 −2.83667
\(669\) 0 0
\(670\) 11.7989 0.455832
\(671\) 0 0
\(672\) 0 0
\(673\) −49.6033 −1.91207 −0.956033 0.293261i \(-0.905260\pi\)
−0.956033 + 0.293261i \(0.905260\pi\)
\(674\) 56.2213 2.16556
\(675\) 0 0
\(676\) 72.4120 2.78508
\(677\) 34.3927 1.32182 0.660909 0.750466i \(-0.270171\pi\)
0.660909 + 0.750466i \(0.270171\pi\)
\(678\) 0 0
\(679\) −67.4505 −2.58851
\(680\) −32.5997 −1.25014
\(681\) 0 0
\(682\) 0 0
\(683\) −8.20394 −0.313915 −0.156958 0.987605i \(-0.550169\pi\)
−0.156958 + 0.987605i \(0.550169\pi\)
\(684\) 0 0
\(685\) 20.5997 0.787075
\(686\) 36.9296 1.40998
\(687\) 0 0
\(688\) 69.4262 2.64685
\(689\) −19.1196 −0.728401
\(690\) 0 0
\(691\) −21.0832 −0.802044 −0.401022 0.916068i \(-0.631345\pi\)
−0.401022 + 0.916068i \(0.631345\pi\)
\(692\) −10.7948 −0.410358
\(693\) 0 0
\(694\) −21.6458 −0.821665
\(695\) 17.6984 0.671338
\(696\) 0 0
\(697\) −14.6687 −0.555618
\(698\) −16.0933 −0.609141
\(699\) 0 0
\(700\) 20.5263 0.775820
\(701\) −22.0671 −0.833461 −0.416731 0.909030i \(-0.636824\pi\)
−0.416731 + 0.909030i \(0.636824\pi\)
\(702\) 0 0
\(703\) −11.2198 −0.423162
\(704\) 0 0
\(705\) 0 0
\(706\) 60.6222 2.28154
\(707\) −14.9955 −0.563964
\(708\) 0 0
\(709\) −39.7992 −1.49469 −0.747344 0.664437i \(-0.768671\pi\)
−0.747344 + 0.664437i \(0.768671\pi\)
\(710\) 3.32993 0.124970
\(711\) 0 0
\(712\) −116.374 −4.36128
\(713\) −55.4724 −2.07746
\(714\) 0 0
\(715\) 0 0
\(716\) 68.2213 2.54955
\(717\) 0 0
\(718\) −40.1665 −1.49900
\(719\) −12.1380 −0.452672 −0.226336 0.974049i \(-0.572675\pi\)
−0.226336 + 0.974049i \(0.572675\pi\)
\(720\) 0 0
\(721\) 5.69820 0.212212
\(722\) −33.5209 −1.24752
\(723\) 0 0
\(724\) 36.2872 1.34860
\(725\) 5.26324 0.195472
\(726\) 0 0
\(727\) 38.9670 1.44521 0.722604 0.691262i \(-0.242945\pi\)
0.722604 + 0.691262i \(0.242945\pi\)
\(728\) −168.862 −6.25843
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) 28.2435 1.04462
\(732\) 0 0
\(733\) 5.65576 0.208900 0.104450 0.994530i \(-0.466692\pi\)
0.104450 + 0.994530i \(0.466692\pi\)
\(734\) −85.2159 −3.14538
\(735\) 0 0
\(736\) −65.7759 −2.42453
\(737\) 0 0
\(738\) 0 0
\(739\) −28.8040 −1.05957 −0.529786 0.848131i \(-0.677728\pi\)
−0.529786 + 0.848131i \(0.677728\pi\)
\(740\) 22.0832 0.811796
\(741\) 0 0
\(742\) 39.8397 1.46256
\(743\) 43.2688 1.58738 0.793690 0.608323i \(-0.208157\pi\)
0.793690 + 0.608323i \(0.208157\pi\)
\(744\) 0 0
\(745\) −20.5263 −0.752024
\(746\) 21.4693 0.786047
\(747\) 0 0
\(748\) 0 0
\(749\) −54.0173 −1.97375
\(750\) 0 0
\(751\) 7.58549 0.276799 0.138399 0.990377i \(-0.455804\pi\)
0.138399 + 0.990377i \(0.455804\pi\)
\(752\) −43.9067 −1.60111
\(753\) 0 0
\(754\) −72.9003 −2.65487
\(755\) 3.84198 0.139824
\(756\) 0 0
\(757\) 42.1741 1.53284 0.766422 0.642338i \(-0.222035\pi\)
0.766422 + 0.642338i \(0.222035\pi\)
\(758\) 19.6938 0.715310
\(759\) 0 0
\(760\) −19.2654 −0.698828
\(761\) −6.15318 −0.223052 −0.111526 0.993761i \(-0.535574\pi\)
−0.111526 + 0.993761i \(0.535574\pi\)
\(762\) 0 0
\(763\) 24.8651 0.900176
\(764\) −3.34860 −0.121148
\(765\) 0 0
\(766\) 47.7324 1.72464
\(767\) −34.6610 −1.25154
\(768\) 0 0
\(769\) 20.4592 0.737777 0.368888 0.929474i \(-0.379738\pi\)
0.368888 + 0.929474i \(0.379738\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 24.3929 0.877919
\(773\) −34.2355 −1.23137 −0.615683 0.787994i \(-0.711120\pi\)
−0.615683 + 0.787994i \(0.711120\pi\)
\(774\) 0 0
\(775\) 10.1162 0.363385
\(776\) −124.604 −4.47301
\(777\) 0 0
\(778\) −46.8032 −1.67798
\(779\) −8.66874 −0.310590
\(780\) 0 0
\(781\) 0 0
\(782\) −61.1061 −2.18515
\(783\) 0 0
\(784\) 107.913 3.85403
\(785\) 0.781830 0.0279047
\(786\) 0 0
\(787\) −4.73655 −0.168840 −0.0844199 0.996430i \(-0.526904\pi\)
−0.0844199 + 0.996430i \(0.526904\pi\)
\(788\) −17.7230 −0.631357
\(789\) 0 0
\(790\) −18.0558 −0.642398
\(791\) 25.2921 0.899283
\(792\) 0 0
\(793\) −64.5196 −2.29116
\(794\) −21.9329 −0.778369
\(795\) 0 0
\(796\) 19.1294 0.678022
\(797\) 20.5307 0.727235 0.363617 0.931548i \(-0.381542\pi\)
0.363617 + 0.931548i \(0.381542\pi\)
\(798\) 0 0
\(799\) −17.8618 −0.631906
\(800\) 11.9952 0.424094
\(801\) 0 0
\(802\) 34.9094 1.23269
\(803\) 0 0
\(804\) 0 0
\(805\) 22.8521 0.805431
\(806\) −140.118 −4.93544
\(807\) 0 0
\(808\) −27.7017 −0.974542
\(809\) 48.8707 1.71820 0.859101 0.511807i \(-0.171024\pi\)
0.859101 + 0.511807i \(0.171024\pi\)
\(810\) 0 0
\(811\) −10.9468 −0.384394 −0.192197 0.981356i \(-0.561561\pi\)
−0.192197 + 0.981356i \(0.561561\pi\)
\(812\) 108.035 3.79127
\(813\) 0 0
\(814\) 0 0
\(815\) 7.74887 0.271431
\(816\) 0 0
\(817\) 16.6910 0.583944
\(818\) −44.3715 −1.55141
\(819\) 0 0
\(820\) 17.0622 0.595837
\(821\) 26.8136 0.935802 0.467901 0.883781i \(-0.345010\pi\)
0.467901 + 0.883781i \(0.345010\pi\)
\(822\) 0 0
\(823\) −20.1020 −0.700711 −0.350355 0.936617i \(-0.613939\pi\)
−0.350355 + 0.936617i \(0.613939\pi\)
\(824\) 10.5265 0.366707
\(825\) 0 0
\(826\) 72.2234 2.51297
\(827\) −23.1104 −0.803629 −0.401814 0.915721i \(-0.631620\pi\)
−0.401814 + 0.915721i \(0.631620\pi\)
\(828\) 0 0
\(829\) −41.0721 −1.42649 −0.713247 0.700913i \(-0.752776\pi\)
−0.713247 + 0.700913i \(0.752776\pi\)
\(830\) 12.8179 0.444915
\(831\) 0 0
\(832\) −56.5739 −1.96135
\(833\) 43.9004 1.52106
\(834\) 0 0
\(835\) 14.8851 0.515122
\(836\) 0 0
\(837\) 0 0
\(838\) −25.7795 −0.890538
\(839\) 7.40338 0.255593 0.127797 0.991800i \(-0.459210\pi\)
0.127797 + 0.991800i \(0.459210\pi\)
\(840\) 0 0
\(841\) −1.29831 −0.0447693
\(842\) −47.0141 −1.62021
\(843\) 0 0
\(844\) 120.426 4.14525
\(845\) −14.7017 −0.505754
\(846\) 0 0
\(847\) 0 0
\(848\) 37.8123 1.29848
\(849\) 0 0
\(850\) 11.1436 0.382222
\(851\) 24.5855 0.842780
\(852\) 0 0
\(853\) −26.3686 −0.902845 −0.451423 0.892310i \(-0.649083\pi\)
−0.451423 + 0.892310i \(0.649083\pi\)
\(854\) 134.440 4.60044
\(855\) 0 0
\(856\) −99.7880 −3.41068
\(857\) −38.3588 −1.31031 −0.655156 0.755493i \(-0.727397\pi\)
−0.655156 + 0.755493i \(0.727397\pi\)
\(858\) 0 0
\(859\) 2.53831 0.0866060 0.0433030 0.999062i \(-0.486212\pi\)
0.0433030 + 0.999062i \(0.486212\pi\)
\(860\) −32.8519 −1.12024
\(861\) 0 0
\(862\) −97.8855 −3.33399
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 0 0
\(865\) 2.19166 0.0745185
\(866\) −26.8036 −0.910824
\(867\) 0 0
\(868\) 207.648 7.04803
\(869\) 0 0
\(870\) 0 0
\(871\) 23.5979 0.799583
\(872\) 45.9341 1.55552
\(873\) 0 0
\(874\) −36.1117 −1.22150
\(875\) −4.16741 −0.140884
\(876\) 0 0
\(877\) 32.1386 1.08524 0.542621 0.839978i \(-0.317432\pi\)
0.542621 + 0.839978i \(0.317432\pi\)
\(878\) −51.8782 −1.75081
\(879\) 0 0
\(880\) 0 0
\(881\) −47.1051 −1.58701 −0.793505 0.608564i \(-0.791746\pi\)
−0.793505 + 0.608564i \(0.791746\pi\)
\(882\) 0 0
\(883\) −19.9528 −0.671466 −0.335733 0.941957i \(-0.608984\pi\)
−0.335733 + 0.941957i \(0.608984\pi\)
\(884\) −109.774 −3.69209
\(885\) 0 0
\(886\) 69.5704 2.33726
\(887\) −48.6316 −1.63289 −0.816445 0.577424i \(-0.804058\pi\)
−0.816445 + 0.577424i \(0.804058\pi\)
\(888\) 0 0
\(889\) 40.9372 1.37299
\(890\) 39.7801 1.33343
\(891\) 0 0
\(892\) 7.87930 0.263819
\(893\) −10.5558 −0.353235
\(894\) 0 0
\(895\) −13.8508 −0.462983
\(896\) 17.9056 0.598185
\(897\) 0 0
\(898\) 57.1106 1.90581
\(899\) 53.2440 1.77579
\(900\) 0 0
\(901\) 15.3826 0.512468
\(902\) 0 0
\(903\) 0 0
\(904\) 46.7229 1.55398
\(905\) −7.36732 −0.244898
\(906\) 0 0
\(907\) 40.0361 1.32938 0.664688 0.747121i \(-0.268565\pi\)
0.664688 + 0.747121i \(0.268565\pi\)
\(908\) −91.6995 −3.04316
\(909\) 0 0
\(910\) 57.7222 1.91347
\(911\) 22.1492 0.733834 0.366917 0.930254i \(-0.380413\pi\)
0.366917 + 0.930254i \(0.380413\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 31.0503 1.02705
\(915\) 0 0
\(916\) 114.932 3.79745
\(917\) −14.4363 −0.476730
\(918\) 0 0
\(919\) −24.4453 −0.806377 −0.403189 0.915117i \(-0.632098\pi\)
−0.403189 + 0.915117i \(0.632098\pi\)
\(920\) 42.2154 1.39180
\(921\) 0 0
\(922\) −81.7190 −2.69127
\(923\) 6.65985 0.219212
\(924\) 0 0
\(925\) −4.48352 −0.147417
\(926\) 100.976 3.31829
\(927\) 0 0
\(928\) 63.1335 2.07246
\(929\) 57.2716 1.87902 0.939509 0.342523i \(-0.111281\pi\)
0.939509 + 0.342523i \(0.111281\pi\)
\(930\) 0 0
\(931\) 25.9437 0.850270
\(932\) −48.0528 −1.57402
\(933\) 0 0
\(934\) −39.3501 −1.28758
\(935\) 0 0
\(936\) 0 0
\(937\) −51.0099 −1.66642 −0.833210 0.552957i \(-0.813500\pi\)
−0.833210 + 0.552957i \(0.813500\pi\)
\(938\) −49.1710 −1.60549
\(939\) 0 0
\(940\) 20.7763 0.677647
\(941\) 15.1681 0.494467 0.247233 0.968956i \(-0.420479\pi\)
0.247233 + 0.968956i \(0.420479\pi\)
\(942\) 0 0
\(943\) 18.9955 0.618578
\(944\) 68.5480 2.23105
\(945\) 0 0
\(946\) 0 0
\(947\) 55.9199 1.81715 0.908576 0.417720i \(-0.137171\pi\)
0.908576 + 0.417720i \(0.137171\pi\)
\(948\) 0 0
\(949\) 24.0000 0.779073
\(950\) 6.58549 0.213662
\(951\) 0 0
\(952\) 135.856 4.40313
\(953\) 32.7177 1.05983 0.529915 0.848051i \(-0.322224\pi\)
0.529915 + 0.848051i \(0.322224\pi\)
\(954\) 0 0
\(955\) 0.679859 0.0219997
\(956\) 42.3250 1.36889
\(957\) 0 0
\(958\) −32.0832 −1.03656
\(959\) −85.8475 −2.77216
\(960\) 0 0
\(961\) 71.3375 2.30121
\(962\) 62.1006 2.00220
\(963\) 0 0
\(964\) −44.1862 −1.42314
\(965\) −4.95245 −0.159425
\(966\) 0 0
\(967\) −53.9473 −1.73483 −0.867414 0.497587i \(-0.834219\pi\)
−0.867414 + 0.497587i \(0.834219\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 42.5933 1.36759
\(971\) −4.14915 −0.133153 −0.0665763 0.997781i \(-0.521208\pi\)
−0.0665763 + 0.997781i \(0.521208\pi\)
\(972\) 0 0
\(973\) −73.7565 −2.36452
\(974\) 37.5984 1.20473
\(975\) 0 0
\(976\) 127.598 4.08432
\(977\) 13.5668 0.434039 0.217020 0.976167i \(-0.430366\pi\)
0.217020 + 0.976167i \(0.430366\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −51.0635 −1.63116
\(981\) 0 0
\(982\) 68.5744 2.18830
\(983\) −36.7489 −1.17211 −0.586054 0.810272i \(-0.699319\pi\)
−0.586054 + 0.810272i \(0.699319\pi\)
\(984\) 0 0
\(985\) 3.59828 0.114651
\(986\) 58.6514 1.86784
\(987\) 0 0
\(988\) −64.8727 −2.06387
\(989\) −36.5743 −1.16300
\(990\) 0 0
\(991\) −48.6830 −1.54647 −0.773233 0.634122i \(-0.781362\pi\)
−0.773233 + 0.634122i \(0.781362\pi\)
\(992\) 121.346 3.85273
\(993\) 0 0
\(994\) −13.8772 −0.440157
\(995\) −3.88380 −0.123125
\(996\) 0 0
\(997\) −41.7558 −1.32242 −0.661210 0.750200i \(-0.729957\pi\)
−0.661210 + 0.750200i \(0.729957\pi\)
\(998\) 75.9619 2.40453
\(999\) 0 0
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 5445.2.a.bz.1.6 6
3.2 odd 2 1815.2.a.y.1.1 6
11.10 odd 2 inner 5445.2.a.bz.1.1 6
15.14 odd 2 9075.2.a.dq.1.6 6
33.32 even 2 1815.2.a.y.1.6 yes 6
165.164 even 2 9075.2.a.dq.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1815.2.a.y.1.1 6 3.2 odd 2
1815.2.a.y.1.6 yes 6 33.32 even 2
5445.2.a.bz.1.1 6 11.10 odd 2 inner
5445.2.a.bz.1.6 6 1.1 even 1 trivial
9075.2.a.dq.1.1 6 165.164 even 2
9075.2.a.dq.1.6 6 15.14 odd 2