Properties

Label 6025.2.a.p.1.20
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.434323 q^{2} -1.75836 q^{3} -1.81136 q^{4} +0.763695 q^{6} +2.56007 q^{7} +1.65536 q^{8} +0.0918227 q^{9} +O(q^{10})\) \(q-0.434323 q^{2} -1.75836 q^{3} -1.81136 q^{4} +0.763695 q^{6} +2.56007 q^{7} +1.65536 q^{8} +0.0918227 q^{9} -2.96950 q^{11} +3.18503 q^{12} -5.29169 q^{13} -1.11190 q^{14} +2.90377 q^{16} +2.85851 q^{17} -0.0398807 q^{18} +6.43901 q^{19} -4.50152 q^{21} +1.28972 q^{22} -7.60122 q^{23} -2.91072 q^{24} +2.29830 q^{26} +5.11362 q^{27} -4.63722 q^{28} -7.01151 q^{29} +3.60166 q^{31} -4.57190 q^{32} +5.22144 q^{33} -1.24152 q^{34} -0.166324 q^{36} +0.899709 q^{37} -2.79661 q^{38} +9.30468 q^{39} +9.31833 q^{41} +1.95511 q^{42} +12.1683 q^{43} +5.37884 q^{44} +3.30138 q^{46} -3.09637 q^{47} -5.10586 q^{48} -0.446048 q^{49} -5.02629 q^{51} +9.58517 q^{52} -3.14521 q^{53} -2.22096 q^{54} +4.23784 q^{56} -11.3221 q^{57} +3.04526 q^{58} -12.8277 q^{59} -6.41135 q^{61} -1.56428 q^{62} +0.235072 q^{63} -3.82185 q^{64} -2.26779 q^{66} +4.29165 q^{67} -5.17781 q^{68} +13.3657 q^{69} -9.51025 q^{71} +0.152000 q^{72} +7.02430 q^{73} -0.390764 q^{74} -11.6634 q^{76} -7.60212 q^{77} -4.04124 q^{78} +10.5199 q^{79} -9.26704 q^{81} -4.04716 q^{82} +16.8677 q^{83} +8.15388 q^{84} -5.28496 q^{86} +12.3288 q^{87} -4.91559 q^{88} -13.4750 q^{89} -13.5471 q^{91} +13.7686 q^{92} -6.33301 q^{93} +1.34483 q^{94} +8.03903 q^{96} -8.44994 q^{97} +0.193729 q^{98} -0.272667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.434323 −0.307113 −0.153556 0.988140i \(-0.549073\pi\)
−0.153556 + 0.988140i \(0.549073\pi\)
\(3\) −1.75836 −1.01519 −0.507594 0.861596i \(-0.669465\pi\)
−0.507594 + 0.861596i \(0.669465\pi\)
\(4\) −1.81136 −0.905682
\(5\) 0 0
\(6\) 0.763695 0.311777
\(7\) 2.56007 0.967615 0.483808 0.875174i \(-0.339253\pi\)
0.483808 + 0.875174i \(0.339253\pi\)
\(8\) 1.65536 0.585259
\(9\) 0.0918227 0.0306076
\(10\) 0 0
\(11\) −2.96950 −0.895337 −0.447668 0.894200i \(-0.647746\pi\)
−0.447668 + 0.894200i \(0.647746\pi\)
\(12\) 3.18503 0.919438
\(13\) −5.29169 −1.46765 −0.733825 0.679338i \(-0.762267\pi\)
−0.733825 + 0.679338i \(0.762267\pi\)
\(14\) −1.11190 −0.297167
\(15\) 0 0
\(16\) 2.90377 0.725942
\(17\) 2.85851 0.693291 0.346646 0.937996i \(-0.387321\pi\)
0.346646 + 0.937996i \(0.387321\pi\)
\(18\) −0.0398807 −0.00939996
\(19\) 6.43901 1.47721 0.738606 0.674138i \(-0.235485\pi\)
0.738606 + 0.674138i \(0.235485\pi\)
\(20\) 0 0
\(21\) −4.50152 −0.982312
\(22\) 1.28972 0.274969
\(23\) −7.60122 −1.58496 −0.792482 0.609896i \(-0.791211\pi\)
−0.792482 + 0.609896i \(0.791211\pi\)
\(24\) −2.91072 −0.594148
\(25\) 0 0
\(26\) 2.29830 0.450734
\(27\) 5.11362 0.984116
\(28\) −4.63722 −0.876351
\(29\) −7.01151 −1.30201 −0.651003 0.759075i \(-0.725651\pi\)
−0.651003 + 0.759075i \(0.725651\pi\)
\(30\) 0 0
\(31\) 3.60166 0.646878 0.323439 0.946249i \(-0.395161\pi\)
0.323439 + 0.946249i \(0.395161\pi\)
\(32\) −4.57190 −0.808205
\(33\) 5.22144 0.908936
\(34\) −1.24152 −0.212918
\(35\) 0 0
\(36\) −0.166324 −0.0277207
\(37\) 0.899709 0.147911 0.0739557 0.997262i \(-0.476438\pi\)
0.0739557 + 0.997262i \(0.476438\pi\)
\(38\) −2.79661 −0.453670
\(39\) 9.30468 1.48994
\(40\) 0 0
\(41\) 9.31833 1.45528 0.727640 0.685960i \(-0.240617\pi\)
0.727640 + 0.685960i \(0.240617\pi\)
\(42\) 1.95511 0.301680
\(43\) 12.1683 1.85565 0.927823 0.373020i \(-0.121678\pi\)
0.927823 + 0.373020i \(0.121678\pi\)
\(44\) 5.37884 0.810890
\(45\) 0 0
\(46\) 3.30138 0.486762
\(47\) −3.09637 −0.451653 −0.225826 0.974168i \(-0.572508\pi\)
−0.225826 + 0.974168i \(0.572508\pi\)
\(48\) −5.10586 −0.736967
\(49\) −0.446048 −0.0637212
\(50\) 0 0
\(51\) −5.02629 −0.703821
\(52\) 9.58517 1.32922
\(53\) −3.14521 −0.432028 −0.216014 0.976390i \(-0.569306\pi\)
−0.216014 + 0.976390i \(0.569306\pi\)
\(54\) −2.22096 −0.302234
\(55\) 0 0
\(56\) 4.23784 0.566305
\(57\) −11.3221 −1.49965
\(58\) 3.04526 0.399862
\(59\) −12.8277 −1.67002 −0.835010 0.550235i \(-0.814538\pi\)
−0.835010 + 0.550235i \(0.814538\pi\)
\(60\) 0 0
\(61\) −6.41135 −0.820889 −0.410445 0.911886i \(-0.634627\pi\)
−0.410445 + 0.911886i \(0.634627\pi\)
\(62\) −1.56428 −0.198664
\(63\) 0.235072 0.0296163
\(64\) −3.82185 −0.477732
\(65\) 0 0
\(66\) −2.26779 −0.279146
\(67\) 4.29165 0.524309 0.262154 0.965026i \(-0.415567\pi\)
0.262154 + 0.965026i \(0.415567\pi\)
\(68\) −5.17781 −0.627901
\(69\) 13.3657 1.60904
\(70\) 0 0
\(71\) −9.51025 −1.12866 −0.564329 0.825550i \(-0.690865\pi\)
−0.564329 + 0.825550i \(0.690865\pi\)
\(72\) 0.152000 0.0179133
\(73\) 7.02430 0.822132 0.411066 0.911606i \(-0.365157\pi\)
0.411066 + 0.911606i \(0.365157\pi\)
\(74\) −0.390764 −0.0454254
\(75\) 0 0
\(76\) −11.6634 −1.33788
\(77\) −7.60212 −0.866341
\(78\) −4.04124 −0.457580
\(79\) 10.5199 1.18359 0.591793 0.806090i \(-0.298420\pi\)
0.591793 + 0.806090i \(0.298420\pi\)
\(80\) 0 0
\(81\) −9.26704 −1.02967
\(82\) −4.04716 −0.446935
\(83\) 16.8677 1.85147 0.925737 0.378167i \(-0.123445\pi\)
0.925737 + 0.378167i \(0.123445\pi\)
\(84\) 8.15388 0.889662
\(85\) 0 0
\(86\) −5.28496 −0.569892
\(87\) 12.3288 1.32178
\(88\) −4.91559 −0.524004
\(89\) −13.4750 −1.42835 −0.714174 0.699968i \(-0.753197\pi\)
−0.714174 + 0.699968i \(0.753197\pi\)
\(90\) 0 0
\(91\) −13.5471 −1.42012
\(92\) 13.7686 1.43547
\(93\) −6.33301 −0.656703
\(94\) 1.34483 0.138708
\(95\) 0 0
\(96\) 8.03903 0.820480
\(97\) −8.44994 −0.857961 −0.428981 0.903314i \(-0.641127\pi\)
−0.428981 + 0.903314i \(0.641127\pi\)
\(98\) 0.193729 0.0195696
\(99\) −0.272667 −0.0274041
\(100\) 0 0
\(101\) 6.34736 0.631586 0.315793 0.948828i \(-0.397730\pi\)
0.315793 + 0.948828i \(0.397730\pi\)
\(102\) 2.18303 0.216152
\(103\) 4.71869 0.464946 0.232473 0.972603i \(-0.425318\pi\)
0.232473 + 0.972603i \(0.425318\pi\)
\(104\) −8.75966 −0.858955
\(105\) 0 0
\(106\) 1.36604 0.132681
\(107\) 10.6747 1.03197 0.515983 0.856599i \(-0.327427\pi\)
0.515983 + 0.856599i \(0.327427\pi\)
\(108\) −9.26262 −0.891296
\(109\) 9.16193 0.877553 0.438777 0.898596i \(-0.355412\pi\)
0.438777 + 0.898596i \(0.355412\pi\)
\(110\) 0 0
\(111\) −1.58201 −0.150158
\(112\) 7.43384 0.702432
\(113\) −2.64944 −0.249238 −0.124619 0.992205i \(-0.539771\pi\)
−0.124619 + 0.992205i \(0.539771\pi\)
\(114\) 4.91744 0.460561
\(115\) 0 0
\(116\) 12.7004 1.17920
\(117\) −0.485897 −0.0449212
\(118\) 5.57135 0.512884
\(119\) 7.31799 0.670839
\(120\) 0 0
\(121\) −2.18209 −0.198372
\(122\) 2.78460 0.252105
\(123\) −16.3850 −1.47738
\(124\) −6.52392 −0.585865
\(125\) 0 0
\(126\) −0.102097 −0.00909555
\(127\) 18.9576 1.68221 0.841106 0.540870i \(-0.181905\pi\)
0.841106 + 0.540870i \(0.181905\pi\)
\(128\) 10.8037 0.954922
\(129\) −21.3962 −1.88383
\(130\) 0 0
\(131\) 2.15948 0.188674 0.0943371 0.995540i \(-0.469927\pi\)
0.0943371 + 0.995540i \(0.469927\pi\)
\(132\) −9.45792 −0.823207
\(133\) 16.4843 1.42937
\(134\) −1.86396 −0.161022
\(135\) 0 0
\(136\) 4.73187 0.405755
\(137\) 14.4702 1.23627 0.618136 0.786072i \(-0.287888\pi\)
0.618136 + 0.786072i \(0.287888\pi\)
\(138\) −5.80501 −0.494155
\(139\) 14.1665 1.20159 0.600796 0.799403i \(-0.294851\pi\)
0.600796 + 0.799403i \(0.294851\pi\)
\(140\) 0 0
\(141\) 5.44453 0.458512
\(142\) 4.13052 0.346625
\(143\) 15.7137 1.31404
\(144\) 0.266632 0.0222193
\(145\) 0 0
\(146\) −3.05081 −0.252487
\(147\) 0.784313 0.0646890
\(148\) −1.62970 −0.133961
\(149\) −7.67393 −0.628673 −0.314336 0.949312i \(-0.601782\pi\)
−0.314336 + 0.949312i \(0.601782\pi\)
\(150\) 0 0
\(151\) 12.4626 1.01419 0.507096 0.861890i \(-0.330719\pi\)
0.507096 + 0.861890i \(0.330719\pi\)
\(152\) 10.6589 0.864551
\(153\) 0.262476 0.0212199
\(154\) 3.30177 0.266064
\(155\) 0 0
\(156\) −16.8542 −1.34941
\(157\) −1.13132 −0.0902890 −0.0451445 0.998980i \(-0.514375\pi\)
−0.0451445 + 0.998980i \(0.514375\pi\)
\(158\) −4.56905 −0.363494
\(159\) 5.53041 0.438590
\(160\) 0 0
\(161\) −19.4596 −1.53363
\(162\) 4.02488 0.316225
\(163\) 13.0961 1.02577 0.512885 0.858458i \(-0.328577\pi\)
0.512885 + 0.858458i \(0.328577\pi\)
\(164\) −16.8789 −1.31802
\(165\) 0 0
\(166\) −7.32604 −0.568611
\(167\) −20.9567 −1.62168 −0.810840 0.585268i \(-0.800989\pi\)
−0.810840 + 0.585268i \(0.800989\pi\)
\(168\) −7.45164 −0.574907
\(169\) 15.0020 1.15400
\(170\) 0 0
\(171\) 0.591247 0.0452138
\(172\) −22.0412 −1.68063
\(173\) 21.8599 1.66198 0.830989 0.556288i \(-0.187775\pi\)
0.830989 + 0.556288i \(0.187775\pi\)
\(174\) −5.35466 −0.405935
\(175\) 0 0
\(176\) −8.62272 −0.649962
\(177\) 22.5556 1.69539
\(178\) 5.85250 0.438664
\(179\) −3.67446 −0.274642 −0.137321 0.990527i \(-0.543849\pi\)
−0.137321 + 0.990527i \(0.543849\pi\)
\(180\) 0 0
\(181\) 5.78781 0.430205 0.215102 0.976592i \(-0.430991\pi\)
0.215102 + 0.976592i \(0.430991\pi\)
\(182\) 5.88381 0.436137
\(183\) 11.2734 0.833357
\(184\) −12.5828 −0.927614
\(185\) 0 0
\(186\) 2.75057 0.201682
\(187\) −8.48834 −0.620729
\(188\) 5.60866 0.409054
\(189\) 13.0912 0.952245
\(190\) 0 0
\(191\) −22.1639 −1.60372 −0.801862 0.597509i \(-0.796157\pi\)
−0.801862 + 0.597509i \(0.796157\pi\)
\(192\) 6.72019 0.484988
\(193\) 2.47506 0.178159 0.0890795 0.996025i \(-0.471607\pi\)
0.0890795 + 0.996025i \(0.471607\pi\)
\(194\) 3.67000 0.263491
\(195\) 0 0
\(196\) 0.807956 0.0577111
\(197\) −15.5601 −1.10861 −0.554306 0.832313i \(-0.687016\pi\)
−0.554306 + 0.832313i \(0.687016\pi\)
\(198\) 0.118426 0.00841613
\(199\) −7.37484 −0.522788 −0.261394 0.965232i \(-0.584182\pi\)
−0.261394 + 0.965232i \(0.584182\pi\)
\(200\) 0 0
\(201\) −7.54626 −0.532272
\(202\) −2.75680 −0.193968
\(203\) −17.9500 −1.25984
\(204\) 9.10444 0.637438
\(205\) 0 0
\(206\) −2.04943 −0.142791
\(207\) −0.697964 −0.0485118
\(208\) −15.3658 −1.06543
\(209\) −19.1206 −1.32260
\(210\) 0 0
\(211\) −22.7501 −1.56618 −0.783092 0.621905i \(-0.786359\pi\)
−0.783092 + 0.621905i \(0.786359\pi\)
\(212\) 5.69712 0.391280
\(213\) 16.7224 1.14580
\(214\) −4.63628 −0.316929
\(215\) 0 0
\(216\) 8.46489 0.575963
\(217\) 9.22050 0.625929
\(218\) −3.97923 −0.269508
\(219\) −12.3512 −0.834619
\(220\) 0 0
\(221\) −15.1264 −1.01751
\(222\) 0.687103 0.0461154
\(223\) −27.9178 −1.86952 −0.934759 0.355284i \(-0.884384\pi\)
−0.934759 + 0.355284i \(0.884384\pi\)
\(224\) −11.7044 −0.782031
\(225\) 0 0
\(226\) 1.15071 0.0765441
\(227\) −13.5560 −0.899742 −0.449871 0.893094i \(-0.648530\pi\)
−0.449871 + 0.893094i \(0.648530\pi\)
\(228\) 20.5084 1.35820
\(229\) −19.7523 −1.30527 −0.652633 0.757674i \(-0.726336\pi\)
−0.652633 + 0.757674i \(0.726336\pi\)
\(230\) 0 0
\(231\) 13.3672 0.879500
\(232\) −11.6066 −0.762010
\(233\) 15.8232 1.03661 0.518306 0.855195i \(-0.326563\pi\)
0.518306 + 0.855195i \(0.326563\pi\)
\(234\) 0.211036 0.0137959
\(235\) 0 0
\(236\) 23.2356 1.51251
\(237\) −18.4978 −1.20156
\(238\) −3.17837 −0.206023
\(239\) −18.9691 −1.22701 −0.613505 0.789691i \(-0.710241\pi\)
−0.613505 + 0.789691i \(0.710241\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 0.947731 0.0609225
\(243\) 0.953917 0.0611938
\(244\) 11.6133 0.743465
\(245\) 0 0
\(246\) 7.11636 0.453723
\(247\) −34.0733 −2.16803
\(248\) 5.96206 0.378591
\(249\) −29.6595 −1.87960
\(250\) 0 0
\(251\) −4.53587 −0.286302 −0.143151 0.989701i \(-0.545723\pi\)
−0.143151 + 0.989701i \(0.545723\pi\)
\(252\) −0.425801 −0.0268230
\(253\) 22.5718 1.41908
\(254\) −8.23371 −0.516629
\(255\) 0 0
\(256\) 2.95141 0.184463
\(257\) 0.317324 0.0197941 0.00989706 0.999951i \(-0.496850\pi\)
0.00989706 + 0.999951i \(0.496850\pi\)
\(258\) 9.29286 0.578548
\(259\) 2.30332 0.143121
\(260\) 0 0
\(261\) −0.643816 −0.0398512
\(262\) −0.937909 −0.0579442
\(263\) −1.08643 −0.0669920 −0.0334960 0.999439i \(-0.510664\pi\)
−0.0334960 + 0.999439i \(0.510664\pi\)
\(264\) 8.64337 0.531963
\(265\) 0 0
\(266\) −7.15951 −0.438978
\(267\) 23.6939 1.45004
\(268\) −7.77374 −0.474857
\(269\) 26.1591 1.59495 0.797475 0.603352i \(-0.206169\pi\)
0.797475 + 0.603352i \(0.206169\pi\)
\(270\) 0 0
\(271\) −21.8047 −1.32454 −0.662271 0.749264i \(-0.730407\pi\)
−0.662271 + 0.749264i \(0.730407\pi\)
\(272\) 8.30045 0.503289
\(273\) 23.8206 1.44169
\(274\) −6.28473 −0.379674
\(275\) 0 0
\(276\) −24.2101 −1.45727
\(277\) −10.6259 −0.638447 −0.319224 0.947679i \(-0.603422\pi\)
−0.319224 + 0.947679i \(0.603422\pi\)
\(278\) −6.15285 −0.369024
\(279\) 0.330714 0.0197993
\(280\) 0 0
\(281\) −11.0206 −0.657431 −0.328716 0.944429i \(-0.606616\pi\)
−0.328716 + 0.944429i \(0.606616\pi\)
\(282\) −2.36468 −0.140815
\(283\) −13.0006 −0.772805 −0.386403 0.922330i \(-0.626282\pi\)
−0.386403 + 0.922330i \(0.626282\pi\)
\(284\) 17.2265 1.02221
\(285\) 0 0
\(286\) −6.82480 −0.403559
\(287\) 23.8556 1.40815
\(288\) −0.419804 −0.0247372
\(289\) −8.82891 −0.519347
\(290\) 0 0
\(291\) 14.8580 0.870992
\(292\) −12.7236 −0.744590
\(293\) 10.5751 0.617801 0.308901 0.951094i \(-0.400039\pi\)
0.308901 + 0.951094i \(0.400039\pi\)
\(294\) −0.340645 −0.0198668
\(295\) 0 0
\(296\) 1.48934 0.0865664
\(297\) −15.1849 −0.881115
\(298\) 3.33296 0.193073
\(299\) 40.2233 2.32617
\(300\) 0 0
\(301\) 31.1517 1.79555
\(302\) −5.41279 −0.311471
\(303\) −11.1609 −0.641179
\(304\) 18.6974 1.07237
\(305\) 0 0
\(306\) −0.113999 −0.00651691
\(307\) −16.6124 −0.948122 −0.474061 0.880492i \(-0.657212\pi\)
−0.474061 + 0.880492i \(0.657212\pi\)
\(308\) 13.7702 0.784630
\(309\) −8.29714 −0.472008
\(310\) 0 0
\(311\) 12.2930 0.697072 0.348536 0.937295i \(-0.386679\pi\)
0.348536 + 0.937295i \(0.386679\pi\)
\(312\) 15.4026 0.872002
\(313\) −7.49184 −0.423464 −0.211732 0.977328i \(-0.567910\pi\)
−0.211732 + 0.977328i \(0.567910\pi\)
\(314\) 0.491357 0.0277289
\(315\) 0 0
\(316\) −19.0554 −1.07195
\(317\) −6.91570 −0.388425 −0.194212 0.980960i \(-0.562215\pi\)
−0.194212 + 0.980960i \(0.562215\pi\)
\(318\) −2.40198 −0.134696
\(319\) 20.8207 1.16573
\(320\) 0 0
\(321\) −18.7700 −1.04764
\(322\) 8.45176 0.470998
\(323\) 18.4060 1.02414
\(324\) 16.7860 0.932554
\(325\) 0 0
\(326\) −5.68795 −0.315027
\(327\) −16.1099 −0.890882
\(328\) 15.4252 0.851715
\(329\) −7.92693 −0.437026
\(330\) 0 0
\(331\) 8.37109 0.460117 0.230058 0.973177i \(-0.426108\pi\)
0.230058 + 0.973177i \(0.426108\pi\)
\(332\) −30.5536 −1.67685
\(333\) 0.0826137 0.00452720
\(334\) 9.10198 0.498038
\(335\) 0 0
\(336\) −13.0714 −0.713101
\(337\) −20.3399 −1.10798 −0.553992 0.832522i \(-0.686896\pi\)
−0.553992 + 0.832522i \(0.686896\pi\)
\(338\) −6.51570 −0.354407
\(339\) 4.65866 0.253023
\(340\) 0 0
\(341\) −10.6951 −0.579174
\(342\) −0.256792 −0.0138857
\(343\) −19.0624 −1.02927
\(344\) 20.1429 1.08603
\(345\) 0 0
\(346\) −9.49426 −0.510415
\(347\) 17.5249 0.940787 0.470393 0.882457i \(-0.344112\pi\)
0.470393 + 0.882457i \(0.344112\pi\)
\(348\) −22.3319 −1.19711
\(349\) −17.0839 −0.914481 −0.457241 0.889343i \(-0.651162\pi\)
−0.457241 + 0.889343i \(0.651162\pi\)
\(350\) 0 0
\(351\) −27.0597 −1.44434
\(352\) 13.5762 0.723615
\(353\) −9.69646 −0.516091 −0.258045 0.966133i \(-0.583078\pi\)
−0.258045 + 0.966133i \(0.583078\pi\)
\(354\) −9.79642 −0.520674
\(355\) 0 0
\(356\) 24.4081 1.29363
\(357\) −12.8676 −0.681028
\(358\) 1.59590 0.0843460
\(359\) −5.89623 −0.311191 −0.155596 0.987821i \(-0.549730\pi\)
−0.155596 + 0.987821i \(0.549730\pi\)
\(360\) 0 0
\(361\) 22.4609 1.18215
\(362\) −2.51378 −0.132121
\(363\) 3.83690 0.201385
\(364\) 24.5387 1.28618
\(365\) 0 0
\(366\) −4.89632 −0.255934
\(367\) −5.35529 −0.279544 −0.139772 0.990184i \(-0.544637\pi\)
−0.139772 + 0.990184i \(0.544637\pi\)
\(368\) −22.0722 −1.15059
\(369\) 0.855634 0.0445425
\(370\) 0 0
\(371\) −8.05195 −0.418037
\(372\) 11.4714 0.594764
\(373\) −13.5963 −0.703989 −0.351995 0.936002i \(-0.614496\pi\)
−0.351995 + 0.936002i \(0.614496\pi\)
\(374\) 3.68668 0.190634
\(375\) 0 0
\(376\) −5.12562 −0.264334
\(377\) 37.1028 1.91089
\(378\) −5.68581 −0.292447
\(379\) 16.3033 0.837445 0.418723 0.908114i \(-0.362478\pi\)
0.418723 + 0.908114i \(0.362478\pi\)
\(380\) 0 0
\(381\) −33.3342 −1.70776
\(382\) 9.62629 0.492524
\(383\) −28.5533 −1.45901 −0.729503 0.683978i \(-0.760248\pi\)
−0.729503 + 0.683978i \(0.760248\pi\)
\(384\) −18.9968 −0.969426
\(385\) 0 0
\(386\) −1.07498 −0.0547149
\(387\) 1.11732 0.0567968
\(388\) 15.3059 0.777040
\(389\) 3.86930 0.196181 0.0980906 0.995177i \(-0.468727\pi\)
0.0980906 + 0.995177i \(0.468727\pi\)
\(390\) 0 0
\(391\) −21.7282 −1.09884
\(392\) −0.738372 −0.0372934
\(393\) −3.79713 −0.191540
\(394\) 6.75811 0.340469
\(395\) 0 0
\(396\) 0.493899 0.0248194
\(397\) 3.78760 0.190094 0.0950470 0.995473i \(-0.469700\pi\)
0.0950470 + 0.995473i \(0.469700\pi\)
\(398\) 3.20306 0.160555
\(399\) −28.9853 −1.45108
\(400\) 0 0
\(401\) 6.33566 0.316388 0.158194 0.987408i \(-0.449433\pi\)
0.158194 + 0.987408i \(0.449433\pi\)
\(402\) 3.27751 0.163467
\(403\) −19.0589 −0.949391
\(404\) −11.4974 −0.572016
\(405\) 0 0
\(406\) 7.79607 0.386913
\(407\) −2.67168 −0.132430
\(408\) −8.32033 −0.411917
\(409\) −28.3807 −1.40334 −0.701668 0.712504i \(-0.747561\pi\)
−0.701668 + 0.712504i \(0.747561\pi\)
\(410\) 0 0
\(411\) −25.4438 −1.25505
\(412\) −8.54726 −0.421093
\(413\) −32.8397 −1.61594
\(414\) 0.303142 0.0148986
\(415\) 0 0
\(416\) 24.1931 1.18616
\(417\) −24.9099 −1.21984
\(418\) 8.30453 0.406188
\(419\) −14.4457 −0.705717 −0.352859 0.935677i \(-0.614790\pi\)
−0.352859 + 0.935677i \(0.614790\pi\)
\(420\) 0 0
\(421\) 12.0873 0.589097 0.294548 0.955637i \(-0.404831\pi\)
0.294548 + 0.955637i \(0.404831\pi\)
\(422\) 9.88091 0.480995
\(423\) −0.284317 −0.0138240
\(424\) −5.20646 −0.252848
\(425\) 0 0
\(426\) −7.26293 −0.351890
\(427\) −16.4135 −0.794305
\(428\) −19.3358 −0.934632
\(429\) −27.6302 −1.33400
\(430\) 0 0
\(431\) −14.7881 −0.712316 −0.356158 0.934426i \(-0.615913\pi\)
−0.356158 + 0.934426i \(0.615913\pi\)
\(432\) 14.8487 0.714411
\(433\) 22.3991 1.07643 0.538216 0.842807i \(-0.319098\pi\)
0.538216 + 0.842807i \(0.319098\pi\)
\(434\) −4.00467 −0.192231
\(435\) 0 0
\(436\) −16.5956 −0.794784
\(437\) −48.9443 −2.34133
\(438\) 5.36442 0.256322
\(439\) −34.0058 −1.62301 −0.811504 0.584346i \(-0.801351\pi\)
−0.811504 + 0.584346i \(0.801351\pi\)
\(440\) 0 0
\(441\) −0.0409574 −0.00195035
\(442\) 6.56972 0.312490
\(443\) 11.4103 0.542120 0.271060 0.962562i \(-0.412626\pi\)
0.271060 + 0.962562i \(0.412626\pi\)
\(444\) 2.86560 0.135995
\(445\) 0 0
\(446\) 12.1254 0.574152
\(447\) 13.4935 0.638221
\(448\) −9.78421 −0.462260
\(449\) −38.0727 −1.79676 −0.898381 0.439216i \(-0.855256\pi\)
−0.898381 + 0.439216i \(0.855256\pi\)
\(450\) 0 0
\(451\) −27.6708 −1.30297
\(452\) 4.79909 0.225730
\(453\) −21.9137 −1.02960
\(454\) 5.88767 0.276322
\(455\) 0 0
\(456\) −18.7422 −0.877682
\(457\) −12.1182 −0.566865 −0.283433 0.958992i \(-0.591473\pi\)
−0.283433 + 0.958992i \(0.591473\pi\)
\(458\) 8.57885 0.400863
\(459\) 14.6173 0.682279
\(460\) 0 0
\(461\) −14.6145 −0.680667 −0.340334 0.940305i \(-0.610540\pi\)
−0.340334 + 0.940305i \(0.610540\pi\)
\(462\) −5.80570 −0.270105
\(463\) −8.87604 −0.412504 −0.206252 0.978499i \(-0.566127\pi\)
−0.206252 + 0.978499i \(0.566127\pi\)
\(464\) −20.3598 −0.945180
\(465\) 0 0
\(466\) −6.87238 −0.318357
\(467\) −39.0070 −1.80503 −0.902515 0.430658i \(-0.858282\pi\)
−0.902515 + 0.430658i \(0.858282\pi\)
\(468\) 0.880136 0.0406843
\(469\) 10.9869 0.507329
\(470\) 0 0
\(471\) 1.98926 0.0916604
\(472\) −21.2344 −0.977394
\(473\) −36.1337 −1.66143
\(474\) 8.03403 0.369015
\(475\) 0 0
\(476\) −13.2555 −0.607567
\(477\) −0.288802 −0.0132233
\(478\) 8.23871 0.376830
\(479\) 14.0416 0.641578 0.320789 0.947151i \(-0.396052\pi\)
0.320789 + 0.947151i \(0.396052\pi\)
\(480\) 0 0
\(481\) −4.76098 −0.217082
\(482\) −0.434323 −0.0197829
\(483\) 34.2170 1.55693
\(484\) 3.95256 0.179662
\(485\) 0 0
\(486\) −0.414308 −0.0187934
\(487\) 7.89889 0.357933 0.178966 0.983855i \(-0.442725\pi\)
0.178966 + 0.983855i \(0.442725\pi\)
\(488\) −10.6131 −0.480433
\(489\) −23.0277 −1.04135
\(490\) 0 0
\(491\) 41.5169 1.87363 0.936817 0.349821i \(-0.113758\pi\)
0.936817 + 0.349821i \(0.113758\pi\)
\(492\) 29.6791 1.33804
\(493\) −20.0425 −0.902669
\(494\) 14.7988 0.665829
\(495\) 0 0
\(496\) 10.4584 0.469595
\(497\) −24.3469 −1.09211
\(498\) 12.8818 0.577247
\(499\) 28.3650 1.26979 0.634896 0.772597i \(-0.281043\pi\)
0.634896 + 0.772597i \(0.281043\pi\)
\(500\) 0 0
\(501\) 36.8494 1.64631
\(502\) 1.97003 0.0879269
\(503\) 12.1673 0.542513 0.271257 0.962507i \(-0.412561\pi\)
0.271257 + 0.962507i \(0.412561\pi\)
\(504\) 0.389130 0.0173332
\(505\) 0 0
\(506\) −9.80344 −0.435816
\(507\) −26.3788 −1.17153
\(508\) −34.3391 −1.52355
\(509\) −32.1405 −1.42460 −0.712301 0.701875i \(-0.752347\pi\)
−0.712301 + 0.701875i \(0.752347\pi\)
\(510\) 0 0
\(511\) 17.9827 0.795507
\(512\) −22.8893 −1.01157
\(513\) 32.9267 1.45375
\(514\) −0.137821 −0.00607902
\(515\) 0 0
\(516\) 38.7563 1.70615
\(517\) 9.19467 0.404381
\(518\) −1.00038 −0.0439543
\(519\) −38.4376 −1.68722
\(520\) 0 0
\(521\) 16.4370 0.720119 0.360059 0.932929i \(-0.382756\pi\)
0.360059 + 0.932929i \(0.382756\pi\)
\(522\) 0.279624 0.0122388
\(523\) 30.7325 1.34384 0.671918 0.740625i \(-0.265471\pi\)
0.671918 + 0.740625i \(0.265471\pi\)
\(524\) −3.91160 −0.170879
\(525\) 0 0
\(526\) 0.471860 0.0205741
\(527\) 10.2954 0.448475
\(528\) 15.1618 0.659834
\(529\) 34.7785 1.51211
\(530\) 0 0
\(531\) −1.17787 −0.0511152
\(532\) −29.8591 −1.29456
\(533\) −49.3097 −2.13584
\(534\) −10.2908 −0.445326
\(535\) 0 0
\(536\) 7.10424 0.306856
\(537\) 6.46102 0.278813
\(538\) −11.3615 −0.489829
\(539\) 1.32454 0.0570520
\(540\) 0 0
\(541\) −39.9511 −1.71763 −0.858816 0.512284i \(-0.828800\pi\)
−0.858816 + 0.512284i \(0.828800\pi\)
\(542\) 9.47029 0.406784
\(543\) −10.1770 −0.436739
\(544\) −13.0688 −0.560321
\(545\) 0 0
\(546\) −10.3458 −0.442761
\(547\) 28.4899 1.21814 0.609071 0.793116i \(-0.291543\pi\)
0.609071 + 0.793116i \(0.291543\pi\)
\(548\) −26.2108 −1.11967
\(549\) −0.588707 −0.0251254
\(550\) 0 0
\(551\) −45.1472 −1.92334
\(552\) 22.1250 0.941703
\(553\) 26.9318 1.14526
\(554\) 4.61506 0.196075
\(555\) 0 0
\(556\) −25.6608 −1.08826
\(557\) −4.95855 −0.210100 −0.105050 0.994467i \(-0.533500\pi\)
−0.105050 + 0.994467i \(0.533500\pi\)
\(558\) −0.143637 −0.00608063
\(559\) −64.3908 −2.72344
\(560\) 0 0
\(561\) 14.9255 0.630157
\(562\) 4.78648 0.201905
\(563\) 27.7731 1.17050 0.585249 0.810853i \(-0.300997\pi\)
0.585249 + 0.810853i \(0.300997\pi\)
\(564\) −9.86203 −0.415266
\(565\) 0 0
\(566\) 5.64645 0.237338
\(567\) −23.7242 −0.996325
\(568\) −15.7429 −0.660558
\(569\) 25.8478 1.08359 0.541797 0.840509i \(-0.317744\pi\)
0.541797 + 0.840509i \(0.317744\pi\)
\(570\) 0 0
\(571\) 29.8843 1.25062 0.625309 0.780378i \(-0.284973\pi\)
0.625309 + 0.780378i \(0.284973\pi\)
\(572\) −28.4631 −1.19010
\(573\) 38.9721 1.62808
\(574\) −10.3610 −0.432461
\(575\) 0 0
\(576\) −0.350933 −0.0146222
\(577\) 25.0417 1.04250 0.521250 0.853404i \(-0.325466\pi\)
0.521250 + 0.853404i \(0.325466\pi\)
\(578\) 3.83460 0.159498
\(579\) −4.35205 −0.180865
\(580\) 0 0
\(581\) 43.1826 1.79151
\(582\) −6.45317 −0.267493
\(583\) 9.33969 0.386811
\(584\) 11.6278 0.481160
\(585\) 0 0
\(586\) −4.59299 −0.189735
\(587\) −0.613835 −0.0253357 −0.0126678 0.999920i \(-0.504032\pi\)
−0.0126678 + 0.999920i \(0.504032\pi\)
\(588\) −1.42068 −0.0585877
\(589\) 23.1912 0.955575
\(590\) 0 0
\(591\) 27.3602 1.12545
\(592\) 2.61255 0.107375
\(593\) −23.7785 −0.976467 −0.488233 0.872713i \(-0.662358\pi\)
−0.488233 + 0.872713i \(0.662358\pi\)
\(594\) 6.59513 0.270602
\(595\) 0 0
\(596\) 13.9003 0.569377
\(597\) 12.9676 0.530729
\(598\) −17.4699 −0.714397
\(599\) −36.9243 −1.50869 −0.754343 0.656480i \(-0.772044\pi\)
−0.754343 + 0.656480i \(0.772044\pi\)
\(600\) 0 0
\(601\) −28.8902 −1.17846 −0.589228 0.807967i \(-0.700568\pi\)
−0.589228 + 0.807967i \(0.700568\pi\)
\(602\) −13.5299 −0.551436
\(603\) 0.394071 0.0160478
\(604\) −22.5743 −0.918535
\(605\) 0 0
\(606\) 4.84745 0.196914
\(607\) −7.38525 −0.299758 −0.149879 0.988704i \(-0.547888\pi\)
−0.149879 + 0.988704i \(0.547888\pi\)
\(608\) −29.4385 −1.19389
\(609\) 31.5624 1.27897
\(610\) 0 0
\(611\) 16.3850 0.662868
\(612\) −0.475440 −0.0192185
\(613\) −28.1453 −1.13678 −0.568388 0.822760i \(-0.692433\pi\)
−0.568388 + 0.822760i \(0.692433\pi\)
\(614\) 7.21516 0.291180
\(615\) 0 0
\(616\) −12.5843 −0.507034
\(617\) 1.73238 0.0697430 0.0348715 0.999392i \(-0.488898\pi\)
0.0348715 + 0.999392i \(0.488898\pi\)
\(618\) 3.60364 0.144960
\(619\) −17.2161 −0.691972 −0.345986 0.938240i \(-0.612456\pi\)
−0.345986 + 0.938240i \(0.612456\pi\)
\(620\) 0 0
\(621\) −38.8697 −1.55979
\(622\) −5.33913 −0.214080
\(623\) −34.4969 −1.38209
\(624\) 27.0186 1.08161
\(625\) 0 0
\(626\) 3.25388 0.130051
\(627\) 33.6209 1.34269
\(628\) 2.04923 0.0817731
\(629\) 2.57183 0.102546
\(630\) 0 0
\(631\) 3.04591 0.121256 0.0606279 0.998160i \(-0.480690\pi\)
0.0606279 + 0.998160i \(0.480690\pi\)
\(632\) 17.4143 0.692704
\(633\) 40.0029 1.58997
\(634\) 3.00365 0.119290
\(635\) 0 0
\(636\) −10.0176 −0.397223
\(637\) 2.36035 0.0935205
\(638\) −9.04289 −0.358011
\(639\) −0.873256 −0.0345455
\(640\) 0 0
\(641\) −8.46426 −0.334318 −0.167159 0.985930i \(-0.553459\pi\)
−0.167159 + 0.985930i \(0.553459\pi\)
\(642\) 8.15224 0.321743
\(643\) −3.99210 −0.157433 −0.0787165 0.996897i \(-0.525082\pi\)
−0.0787165 + 0.996897i \(0.525082\pi\)
\(644\) 35.2485 1.38898
\(645\) 0 0
\(646\) −7.99415 −0.314525
\(647\) 14.5637 0.572559 0.286279 0.958146i \(-0.407581\pi\)
0.286279 + 0.958146i \(0.407581\pi\)
\(648\) −15.3403 −0.602624
\(649\) 38.0917 1.49523
\(650\) 0 0
\(651\) −16.2129 −0.635436
\(652\) −23.7219 −0.929020
\(653\) −7.40618 −0.289826 −0.144913 0.989444i \(-0.546290\pi\)
−0.144913 + 0.989444i \(0.546290\pi\)
\(654\) 6.99691 0.273601
\(655\) 0 0
\(656\) 27.0583 1.05645
\(657\) 0.644990 0.0251634
\(658\) 3.44285 0.134216
\(659\) −21.7644 −0.847822 −0.423911 0.905704i \(-0.639343\pi\)
−0.423911 + 0.905704i \(0.639343\pi\)
\(660\) 0 0
\(661\) −3.19111 −0.124120 −0.0620598 0.998072i \(-0.519767\pi\)
−0.0620598 + 0.998072i \(0.519767\pi\)
\(662\) −3.63575 −0.141308
\(663\) 26.5976 1.03296
\(664\) 27.9222 1.08359
\(665\) 0 0
\(666\) −0.0358810 −0.00139036
\(667\) 53.2960 2.06363
\(668\) 37.9602 1.46873
\(669\) 49.0896 1.89791
\(670\) 0 0
\(671\) 19.0385 0.734973
\(672\) 20.5805 0.793909
\(673\) 7.45989 0.287558 0.143779 0.989610i \(-0.454075\pi\)
0.143779 + 0.989610i \(0.454075\pi\)
\(674\) 8.83407 0.340276
\(675\) 0 0
\(676\) −27.1740 −1.04516
\(677\) −1.15471 −0.0443790 −0.0221895 0.999754i \(-0.507064\pi\)
−0.0221895 + 0.999754i \(0.507064\pi\)
\(678\) −2.02336 −0.0777067
\(679\) −21.6324 −0.830176
\(680\) 0 0
\(681\) 23.8363 0.913407
\(682\) 4.64514 0.177871
\(683\) −36.9117 −1.41239 −0.706193 0.708020i \(-0.749589\pi\)
−0.706193 + 0.708020i \(0.749589\pi\)
\(684\) −1.07096 −0.0409493
\(685\) 0 0
\(686\) 8.27923 0.316103
\(687\) 34.7315 1.32509
\(688\) 35.3339 1.34709
\(689\) 16.6435 0.634066
\(690\) 0 0
\(691\) −42.2188 −1.60608 −0.803039 0.595926i \(-0.796785\pi\)
−0.803039 + 0.595926i \(0.796785\pi\)
\(692\) −39.5963 −1.50522
\(693\) −0.698046 −0.0265166
\(694\) −7.61147 −0.288927
\(695\) 0 0
\(696\) 20.4085 0.773584
\(697\) 26.6366 1.00893
\(698\) 7.41994 0.280849
\(699\) −27.8229 −1.05236
\(700\) 0 0
\(701\) −1.45850 −0.0550869 −0.0275434 0.999621i \(-0.508768\pi\)
−0.0275434 + 0.999621i \(0.508768\pi\)
\(702\) 11.7526 0.443574
\(703\) 5.79324 0.218496
\(704\) 11.3490 0.427731
\(705\) 0 0
\(706\) 4.21139 0.158498
\(707\) 16.2497 0.611132
\(708\) −40.8565 −1.53548
\(709\) 38.9217 1.46174 0.730868 0.682519i \(-0.239115\pi\)
0.730868 + 0.682519i \(0.239115\pi\)
\(710\) 0 0
\(711\) 0.965969 0.0362267
\(712\) −22.3060 −0.835953
\(713\) −27.3770 −1.02528
\(714\) 5.58871 0.209152
\(715\) 0 0
\(716\) 6.65578 0.248738
\(717\) 33.3545 1.24565
\(718\) 2.56087 0.0955707
\(719\) −32.6261 −1.21675 −0.608375 0.793650i \(-0.708178\pi\)
−0.608375 + 0.793650i \(0.708178\pi\)
\(720\) 0 0
\(721\) 12.0802 0.449889
\(722\) −9.75528 −0.363054
\(723\) −1.75836 −0.0653940
\(724\) −10.4838 −0.389629
\(725\) 0 0
\(726\) −1.66645 −0.0618478
\(727\) −6.49756 −0.240981 −0.120491 0.992714i \(-0.538447\pi\)
−0.120491 + 0.992714i \(0.538447\pi\)
\(728\) −22.4253 −0.831138
\(729\) 26.1238 0.967547
\(730\) 0 0
\(731\) 34.7832 1.28650
\(732\) −20.4203 −0.754757
\(733\) −36.8654 −1.36165 −0.680827 0.732444i \(-0.738379\pi\)
−0.680827 + 0.732444i \(0.738379\pi\)
\(734\) 2.32593 0.0858515
\(735\) 0 0
\(736\) 34.7520 1.28097
\(737\) −12.7440 −0.469433
\(738\) −0.371621 −0.0136796
\(739\) −49.1741 −1.80890 −0.904450 0.426580i \(-0.859718\pi\)
−0.904450 + 0.426580i \(0.859718\pi\)
\(740\) 0 0
\(741\) 59.9130 2.20096
\(742\) 3.49715 0.128384
\(743\) 22.5144 0.825974 0.412987 0.910737i \(-0.364486\pi\)
0.412987 + 0.910737i \(0.364486\pi\)
\(744\) −10.4834 −0.384341
\(745\) 0 0
\(746\) 5.90518 0.216204
\(747\) 1.54884 0.0566691
\(748\) 15.3755 0.562183
\(749\) 27.3280 0.998545
\(750\) 0 0
\(751\) −12.5774 −0.458957 −0.229479 0.973314i \(-0.573702\pi\)
−0.229479 + 0.973314i \(0.573702\pi\)
\(752\) −8.99115 −0.327873
\(753\) 7.97569 0.290650
\(754\) −16.1146 −0.586858
\(755\) 0 0
\(756\) −23.7129 −0.862431
\(757\) 2.31525 0.0841491 0.0420745 0.999114i \(-0.486603\pi\)
0.0420745 + 0.999114i \(0.486603\pi\)
\(758\) −7.08090 −0.257190
\(759\) −39.6893 −1.44063
\(760\) 0 0
\(761\) −47.6708 −1.72807 −0.864033 0.503435i \(-0.832069\pi\)
−0.864033 + 0.503435i \(0.832069\pi\)
\(762\) 14.4778 0.524475
\(763\) 23.4552 0.849134
\(764\) 40.1469 1.45246
\(765\) 0 0
\(766\) 12.4013 0.448079
\(767\) 67.8800 2.45101
\(768\) −5.18964 −0.187265
\(769\) −12.2319 −0.441094 −0.220547 0.975376i \(-0.570784\pi\)
−0.220547 + 0.975376i \(0.570784\pi\)
\(770\) 0 0
\(771\) −0.557969 −0.0200948
\(772\) −4.48324 −0.161355
\(773\) 9.31386 0.334996 0.167498 0.985872i \(-0.446431\pi\)
0.167498 + 0.985872i \(0.446431\pi\)
\(774\) −0.485279 −0.0174430
\(775\) 0 0
\(776\) −13.9877 −0.502129
\(777\) −4.05006 −0.145295
\(778\) −1.68052 −0.0602497
\(779\) 60.0009 2.14976
\(780\) 0 0
\(781\) 28.2407 1.01053
\(782\) 9.43704 0.337468
\(783\) −35.8542 −1.28132
\(784\) −1.29522 −0.0462579
\(785\) 0 0
\(786\) 1.64918 0.0588243
\(787\) 3.90661 0.139255 0.0696277 0.997573i \(-0.477819\pi\)
0.0696277 + 0.997573i \(0.477819\pi\)
\(788\) 28.1850 1.00405
\(789\) 1.91033 0.0680095
\(790\) 0 0
\(791\) −6.78274 −0.241166
\(792\) −0.451363 −0.0160385
\(793\) 33.9269 1.20478
\(794\) −1.64504 −0.0583802
\(795\) 0 0
\(796\) 13.3585 0.473480
\(797\) 8.80375 0.311845 0.155922 0.987769i \(-0.450165\pi\)
0.155922 + 0.987769i \(0.450165\pi\)
\(798\) 12.5890 0.445645
\(799\) −8.85102 −0.313127
\(800\) 0 0
\(801\) −1.23731 −0.0437182
\(802\) −2.75172 −0.0971667
\(803\) −20.8586 −0.736085
\(804\) 13.6690 0.482069
\(805\) 0 0
\(806\) 8.27771 0.291570
\(807\) −45.9971 −1.61917
\(808\) 10.5072 0.369641
\(809\) 31.2057 1.09713 0.548567 0.836107i \(-0.315174\pi\)
0.548567 + 0.836107i \(0.315174\pi\)
\(810\) 0 0
\(811\) 21.8358 0.766759 0.383380 0.923591i \(-0.374760\pi\)
0.383380 + 0.923591i \(0.374760\pi\)
\(812\) 32.5139 1.14101
\(813\) 38.3405 1.34466
\(814\) 1.16037 0.0406711
\(815\) 0 0
\(816\) −14.5952 −0.510933
\(817\) 78.3518 2.74118
\(818\) 12.3264 0.430982
\(819\) −1.24393 −0.0434664
\(820\) 0 0
\(821\) 4.07821 0.142331 0.0711653 0.997465i \(-0.477328\pi\)
0.0711653 + 0.997465i \(0.477328\pi\)
\(822\) 11.0508 0.385441
\(823\) −22.9341 −0.799432 −0.399716 0.916639i \(-0.630891\pi\)
−0.399716 + 0.916639i \(0.630891\pi\)
\(824\) 7.81114 0.272114
\(825\) 0 0
\(826\) 14.2630 0.496274
\(827\) −31.1806 −1.08425 −0.542127 0.840296i \(-0.682381\pi\)
−0.542127 + 0.840296i \(0.682381\pi\)
\(828\) 1.26427 0.0439363
\(829\) 36.9740 1.28416 0.642080 0.766638i \(-0.278072\pi\)
0.642080 + 0.766638i \(0.278072\pi\)
\(830\) 0 0
\(831\) 18.6841 0.648144
\(832\) 20.2241 0.701143
\(833\) −1.27504 −0.0441773
\(834\) 10.8189 0.374629
\(835\) 0 0
\(836\) 34.6344 1.19786
\(837\) 18.4175 0.636603
\(838\) 6.27408 0.216735
\(839\) −1.70060 −0.0587112 −0.0293556 0.999569i \(-0.509346\pi\)
−0.0293556 + 0.999569i \(0.509346\pi\)
\(840\) 0 0
\(841\) 20.1613 0.695218
\(842\) −5.24977 −0.180919
\(843\) 19.3781 0.667417
\(844\) 41.2088 1.41847
\(845\) 0 0
\(846\) 0.123485 0.00424552
\(847\) −5.58630 −0.191948
\(848\) −9.13296 −0.313627
\(849\) 22.8597 0.784543
\(850\) 0 0
\(851\) −6.83889 −0.234434
\(852\) −30.2904 −1.03773
\(853\) −29.5900 −1.01314 −0.506571 0.862198i \(-0.669087\pi\)
−0.506571 + 0.862198i \(0.669087\pi\)
\(854\) 7.12876 0.243941
\(855\) 0 0
\(856\) 17.6705 0.603967
\(857\) 39.2074 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(858\) 12.0004 0.409688
\(859\) 4.86252 0.165907 0.0829535 0.996553i \(-0.473565\pi\)
0.0829535 + 0.996553i \(0.473565\pi\)
\(860\) 0 0
\(861\) −41.9466 −1.42954
\(862\) 6.42279 0.218761
\(863\) 32.0662 1.09155 0.545774 0.837933i \(-0.316236\pi\)
0.545774 + 0.837933i \(0.316236\pi\)
\(864\) −23.3789 −0.795367
\(865\) 0 0
\(866\) −9.72845 −0.330586
\(867\) 15.5244 0.527236
\(868\) −16.7017 −0.566892
\(869\) −31.2389 −1.05971
\(870\) 0 0
\(871\) −22.7101 −0.769502
\(872\) 15.1663 0.513596
\(873\) −0.775896 −0.0262601
\(874\) 21.2576 0.719050
\(875\) 0 0
\(876\) 22.3726 0.755899
\(877\) −14.5057 −0.489823 −0.244912 0.969545i \(-0.578759\pi\)
−0.244912 + 0.969545i \(0.578759\pi\)
\(878\) 14.7695 0.498446
\(879\) −18.5947 −0.627185
\(880\) 0 0
\(881\) −23.9591 −0.807202 −0.403601 0.914935i \(-0.632242\pi\)
−0.403601 + 0.914935i \(0.632242\pi\)
\(882\) 0.0177887 0.000598977 0
\(883\) 27.8892 0.938546 0.469273 0.883053i \(-0.344516\pi\)
0.469273 + 0.883053i \(0.344516\pi\)
\(884\) 27.3993 0.921540
\(885\) 0 0
\(886\) −4.95576 −0.166492
\(887\) −7.79600 −0.261764 −0.130882 0.991398i \(-0.541781\pi\)
−0.130882 + 0.991398i \(0.541781\pi\)
\(888\) −2.61880 −0.0878812
\(889\) 48.5327 1.62773
\(890\) 0 0
\(891\) 27.5184 0.921902
\(892\) 50.5694 1.69319
\(893\) −19.9376 −0.667186
\(894\) −5.86054 −0.196006
\(895\) 0 0
\(896\) 27.6582 0.923997
\(897\) −70.7269 −2.36150
\(898\) 16.5358 0.551808
\(899\) −25.2531 −0.842238
\(900\) 0 0
\(901\) −8.99062 −0.299521
\(902\) 12.0180 0.400157
\(903\) −54.7758 −1.82282
\(904\) −4.38577 −0.145869
\(905\) 0 0
\(906\) 9.51762 0.316202
\(907\) −10.2519 −0.340408 −0.170204 0.985409i \(-0.554443\pi\)
−0.170204 + 0.985409i \(0.554443\pi\)
\(908\) 24.5548 0.814880
\(909\) 0.582831 0.0193313
\(910\) 0 0
\(911\) −5.42341 −0.179686 −0.0898428 0.995956i \(-0.528636\pi\)
−0.0898428 + 0.995956i \(0.528636\pi\)
\(912\) −32.8767 −1.08866
\(913\) −50.0887 −1.65769
\(914\) 5.26321 0.174091
\(915\) 0 0
\(916\) 35.7785 1.18216
\(917\) 5.52841 0.182564
\(918\) −6.34864 −0.209536
\(919\) −33.2008 −1.09519 −0.547596 0.836743i \(-0.684457\pi\)
−0.547596 + 0.836743i \(0.684457\pi\)
\(920\) 0 0
\(921\) 29.2106 0.962522
\(922\) 6.34743 0.209041
\(923\) 50.3253 1.65648
\(924\) −24.2129 −0.796547
\(925\) 0 0
\(926\) 3.85506 0.126685
\(927\) 0.433282 0.0142309
\(928\) 32.0559 1.05229
\(929\) −15.0877 −0.495012 −0.247506 0.968886i \(-0.579611\pi\)
−0.247506 + 0.968886i \(0.579611\pi\)
\(930\) 0 0
\(931\) −2.87211 −0.0941297
\(932\) −28.6616 −0.938842
\(933\) −21.6155 −0.707660
\(934\) 16.9416 0.554348
\(935\) 0 0
\(936\) −0.804335 −0.0262905
\(937\) −20.5706 −0.672011 −0.336005 0.941860i \(-0.609076\pi\)
−0.336005 + 0.941860i \(0.609076\pi\)
\(938\) −4.77187 −0.155807
\(939\) 13.1733 0.429896
\(940\) 0 0
\(941\) 55.0850 1.79572 0.897860 0.440281i \(-0.145121\pi\)
0.897860 + 0.440281i \(0.145121\pi\)
\(942\) −0.863982 −0.0281500
\(943\) −70.8307 −2.30656
\(944\) −37.2485 −1.21234
\(945\) 0 0
\(946\) 15.6937 0.510246
\(947\) 43.4046 1.41046 0.705230 0.708978i \(-0.250844\pi\)
0.705230 + 0.708978i \(0.250844\pi\)
\(948\) 33.5063 1.08823
\(949\) −37.1704 −1.20660
\(950\) 0 0
\(951\) 12.1603 0.394324
\(952\) 12.1139 0.392614
\(953\) −1.58717 −0.0514134 −0.0257067 0.999670i \(-0.508184\pi\)
−0.0257067 + 0.999670i \(0.508184\pi\)
\(954\) 0.125433 0.00406105
\(955\) 0 0
\(956\) 34.3600 1.11128
\(957\) −36.6102 −1.18344
\(958\) −6.09859 −0.197037
\(959\) 37.0447 1.19623
\(960\) 0 0
\(961\) −18.0280 −0.581549
\(962\) 2.06780 0.0666686
\(963\) 0.980182 0.0315859
\(964\) −1.81136 −0.0583401
\(965\) 0 0
\(966\) −14.8612 −0.478152
\(967\) 27.9141 0.897657 0.448829 0.893618i \(-0.351841\pi\)
0.448829 + 0.893618i \(0.351841\pi\)
\(968\) −3.61215 −0.116099
\(969\) −32.3643 −1.03969
\(970\) 0 0
\(971\) −48.4758 −1.55566 −0.777832 0.628473i \(-0.783680\pi\)
−0.777832 + 0.628473i \(0.783680\pi\)
\(972\) −1.72789 −0.0554221
\(973\) 36.2673 1.16268
\(974\) −3.43067 −0.109926
\(975\) 0 0
\(976\) −18.6171 −0.595918
\(977\) −3.82977 −0.122525 −0.0612626 0.998122i \(-0.519513\pi\)
−0.0612626 + 0.998122i \(0.519513\pi\)
\(978\) 10.0015 0.319811
\(979\) 40.0140 1.27885
\(980\) 0 0
\(981\) 0.841272 0.0268598
\(982\) −18.0317 −0.575416
\(983\) 4.09982 0.130764 0.0653820 0.997860i \(-0.479173\pi\)
0.0653820 + 0.997860i \(0.479173\pi\)
\(984\) −27.1231 −0.864651
\(985\) 0 0
\(986\) 8.70491 0.277221
\(987\) 13.9384 0.443664
\(988\) 61.7191 1.96355
\(989\) −92.4938 −2.94113
\(990\) 0 0
\(991\) −43.7654 −1.39025 −0.695126 0.718888i \(-0.744652\pi\)
−0.695126 + 0.718888i \(0.744652\pi\)
\(992\) −16.4664 −0.522810
\(993\) −14.7194 −0.467105
\(994\) 10.5744 0.335400
\(995\) 0 0
\(996\) 53.7242 1.70232
\(997\) −16.2468 −0.514542 −0.257271 0.966339i \(-0.582823\pi\)
−0.257271 + 0.966339i \(0.582823\pi\)
\(998\) −12.3196 −0.389969
\(999\) 4.60077 0.145562
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 6025.2.a.p.1.20 46
5.2 odd 4 1205.2.b.c.724.20 46
5.3 odd 4 1205.2.b.c.724.27 yes 46
5.4 even 2 inner 6025.2.a.p.1.27 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.20 46 5.2 odd 4
1205.2.b.c.724.27 yes 46 5.3 odd 4
6025.2.a.p.1.20 46 1.1 even 1 trivial
6025.2.a.p.1.27 46 5.4 even 2 inner