Properties

Label 6025.2.a.p.1.12
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 1.12
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.49203 q^{2} +3.12646 q^{3} +0.226139 q^{4} -4.66475 q^{6} +4.66024 q^{7} +2.64665 q^{8} +6.77474 q^{9} +O(q^{10})\) \(q-1.49203 q^{2} +3.12646 q^{3} +0.226139 q^{4} -4.66475 q^{6} +4.66024 q^{7} +2.64665 q^{8} +6.77474 q^{9} -5.92431 q^{11} +0.707014 q^{12} -4.29102 q^{13} -6.95319 q^{14} -4.40114 q^{16} -5.72527 q^{17} -10.1081 q^{18} -1.23168 q^{19} +14.5700 q^{21} +8.83922 q^{22} -3.63376 q^{23} +8.27462 q^{24} +6.40231 q^{26} +11.8016 q^{27} +1.05386 q^{28} +1.81182 q^{29} -1.11419 q^{31} +1.27332 q^{32} -18.5221 q^{33} +8.54225 q^{34} +1.53203 q^{36} -7.32690 q^{37} +1.83770 q^{38} -13.4157 q^{39} -6.45271 q^{41} -21.7389 q^{42} -4.57155 q^{43} -1.33972 q^{44} +5.42167 q^{46} -7.71296 q^{47} -13.7600 q^{48} +14.7178 q^{49} -17.8998 q^{51} -0.970368 q^{52} +10.1745 q^{53} -17.6082 q^{54} +12.3340 q^{56} -3.85081 q^{57} -2.70329 q^{58} -5.66965 q^{59} +4.76640 q^{61} +1.66239 q^{62} +31.5719 q^{63} +6.90245 q^{64} +27.6354 q^{66} -14.0103 q^{67} -1.29471 q^{68} -11.3608 q^{69} -3.96855 q^{71} +17.9303 q^{72} +8.92040 q^{73} +10.9319 q^{74} -0.278532 q^{76} -27.6087 q^{77} +20.0166 q^{78} +1.77420 q^{79} +16.5729 q^{81} +9.62761 q^{82} -9.93218 q^{83} +3.29485 q^{84} +6.82087 q^{86} +5.66459 q^{87} -15.6795 q^{88} -7.03898 q^{89} -19.9972 q^{91} -0.821736 q^{92} -3.48346 q^{93} +11.5079 q^{94} +3.98098 q^{96} +5.03884 q^{97} -21.9594 q^{98} -40.1356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49203 −1.05502 −0.527511 0.849548i \(-0.676874\pi\)
−0.527511 + 0.849548i \(0.676874\pi\)
\(3\) 3.12646 1.80506 0.902531 0.430626i \(-0.141707\pi\)
0.902531 + 0.430626i \(0.141707\pi\)
\(4\) 0.226139 0.113070
\(5\) 0 0
\(6\) −4.66475 −1.90438
\(7\) 4.66024 1.76140 0.880702 0.473670i \(-0.157071\pi\)
0.880702 + 0.473670i \(0.157071\pi\)
\(8\) 2.64665 0.935730
\(9\) 6.77474 2.25825
\(10\) 0 0
\(11\) −5.92431 −1.78625 −0.893123 0.449812i \(-0.851491\pi\)
−0.893123 + 0.449812i \(0.851491\pi\)
\(12\) 0.707014 0.204097
\(13\) −4.29102 −1.19012 −0.595058 0.803683i \(-0.702871\pi\)
−0.595058 + 0.803683i \(0.702871\pi\)
\(14\) −6.95319 −1.85832
\(15\) 0 0
\(16\) −4.40114 −1.10028
\(17\) −5.72527 −1.38858 −0.694291 0.719694i \(-0.744282\pi\)
−0.694291 + 0.719694i \(0.744282\pi\)
\(18\) −10.1081 −2.38250
\(19\) −1.23168 −0.282568 −0.141284 0.989969i \(-0.545123\pi\)
−0.141284 + 0.989969i \(0.545123\pi\)
\(20\) 0 0
\(21\) 14.5700 3.17944
\(22\) 8.83922 1.88453
\(23\) −3.63376 −0.757692 −0.378846 0.925460i \(-0.623679\pi\)
−0.378846 + 0.925460i \(0.623679\pi\)
\(24\) 8.27462 1.68905
\(25\) 0 0
\(26\) 6.40231 1.25560
\(27\) 11.8016 2.27121
\(28\) 1.05386 0.199161
\(29\) 1.81182 0.336447 0.168224 0.985749i \(-0.446197\pi\)
0.168224 + 0.985749i \(0.446197\pi\)
\(30\) 0 0
\(31\) −1.11419 −0.200114 −0.100057 0.994982i \(-0.531902\pi\)
−0.100057 + 0.994982i \(0.531902\pi\)
\(32\) 1.27332 0.225093
\(33\) −18.5221 −3.22428
\(34\) 8.54225 1.46498
\(35\) 0 0
\(36\) 1.53203 0.255339
\(37\) −7.32690 −1.20454 −0.602268 0.798294i \(-0.705736\pi\)
−0.602268 + 0.798294i \(0.705736\pi\)
\(38\) 1.83770 0.298115
\(39\) −13.4157 −2.14823
\(40\) 0 0
\(41\) −6.45271 −1.00774 −0.503872 0.863778i \(-0.668092\pi\)
−0.503872 + 0.863778i \(0.668092\pi\)
\(42\) −21.7389 −3.35438
\(43\) −4.57155 −0.697155 −0.348578 0.937280i \(-0.613335\pi\)
−0.348578 + 0.937280i \(0.613335\pi\)
\(44\) −1.33972 −0.201970
\(45\) 0 0
\(46\) 5.42167 0.799381
\(47\) −7.71296 −1.12505 −0.562525 0.826780i \(-0.690170\pi\)
−0.562525 + 0.826780i \(0.690170\pi\)
\(48\) −13.7600 −1.98608
\(49\) 14.7178 2.10255
\(50\) 0 0
\(51\) −17.8998 −2.50648
\(52\) −0.970368 −0.134566
\(53\) 10.1745 1.39758 0.698788 0.715329i \(-0.253723\pi\)
0.698788 + 0.715329i \(0.253723\pi\)
\(54\) −17.6082 −2.39618
\(55\) 0 0
\(56\) 12.3340 1.64820
\(57\) −3.85081 −0.510052
\(58\) −2.70329 −0.354959
\(59\) −5.66965 −0.738126 −0.369063 0.929404i \(-0.620321\pi\)
−0.369063 + 0.929404i \(0.620321\pi\)
\(60\) 0 0
\(61\) 4.76640 0.610275 0.305138 0.952308i \(-0.401298\pi\)
0.305138 + 0.952308i \(0.401298\pi\)
\(62\) 1.66239 0.211124
\(63\) 31.5719 3.97768
\(64\) 6.90245 0.862807
\(65\) 0 0
\(66\) 27.6354 3.40169
\(67\) −14.0103 −1.71163 −0.855814 0.517283i \(-0.826943\pi\)
−0.855814 + 0.517283i \(0.826943\pi\)
\(68\) −1.29471 −0.157006
\(69\) −11.3608 −1.36768
\(70\) 0 0
\(71\) −3.96855 −0.470980 −0.235490 0.971877i \(-0.575669\pi\)
−0.235490 + 0.971877i \(0.575669\pi\)
\(72\) 17.9303 2.11311
\(73\) 8.92040 1.04405 0.522027 0.852929i \(-0.325176\pi\)
0.522027 + 0.852929i \(0.325176\pi\)
\(74\) 10.9319 1.27081
\(75\) 0 0
\(76\) −0.278532 −0.0319498
\(77\) −27.6087 −3.14630
\(78\) 20.0166 2.26643
\(79\) 1.77420 0.199614 0.0998068 0.995007i \(-0.468178\pi\)
0.0998068 + 0.995007i \(0.468178\pi\)
\(80\) 0 0
\(81\) 16.5729 1.84143
\(82\) 9.62761 1.06319
\(83\) −9.93218 −1.09020 −0.545099 0.838372i \(-0.683508\pi\)
−0.545099 + 0.838372i \(0.683508\pi\)
\(84\) 3.29485 0.359498
\(85\) 0 0
\(86\) 6.82087 0.735514
\(87\) 5.66459 0.607308
\(88\) −15.6795 −1.67144
\(89\) −7.03898 −0.746131 −0.373065 0.927805i \(-0.621693\pi\)
−0.373065 + 0.927805i \(0.621693\pi\)
\(90\) 0 0
\(91\) −19.9972 −2.09627
\(92\) −0.821736 −0.0856719
\(93\) −3.48346 −0.361217
\(94\) 11.5079 1.18695
\(95\) 0 0
\(96\) 3.98098 0.406307
\(97\) 5.03884 0.511617 0.255808 0.966727i \(-0.417658\pi\)
0.255808 + 0.966727i \(0.417658\pi\)
\(98\) −21.9594 −2.21823
\(99\) −40.1356 −4.03378
\(100\) 0 0
\(101\) −8.87959 −0.883552 −0.441776 0.897125i \(-0.645651\pi\)
−0.441776 + 0.897125i \(0.645651\pi\)
\(102\) 26.7070 2.64438
\(103\) 3.12126 0.307547 0.153774 0.988106i \(-0.450857\pi\)
0.153774 + 0.988106i \(0.450857\pi\)
\(104\) −11.3568 −1.11363
\(105\) 0 0
\(106\) −15.1806 −1.47447
\(107\) −2.37926 −0.230012 −0.115006 0.993365i \(-0.536689\pi\)
−0.115006 + 0.993365i \(0.536689\pi\)
\(108\) 2.66879 0.256805
\(109\) −10.9286 −1.04677 −0.523386 0.852096i \(-0.675331\pi\)
−0.523386 + 0.852096i \(0.675331\pi\)
\(110\) 0 0
\(111\) −22.9072 −2.17426
\(112\) −20.5104 −1.93805
\(113\) 12.3477 1.16157 0.580787 0.814055i \(-0.302745\pi\)
0.580787 + 0.814055i \(0.302745\pi\)
\(114\) 5.74550 0.538116
\(115\) 0 0
\(116\) 0.409724 0.0380419
\(117\) −29.0706 −2.68757
\(118\) 8.45926 0.778738
\(119\) −26.6811 −2.44585
\(120\) 0 0
\(121\) 24.0974 2.19068
\(122\) −7.11159 −0.643853
\(123\) −20.1741 −1.81904
\(124\) −0.251961 −0.0226268
\(125\) 0 0
\(126\) −47.1061 −4.19654
\(127\) −8.83493 −0.783974 −0.391987 0.919971i \(-0.628212\pi\)
−0.391987 + 0.919971i \(0.628212\pi\)
\(128\) −12.8453 −1.13537
\(129\) −14.2928 −1.25841
\(130\) 0 0
\(131\) 10.6930 0.934252 0.467126 0.884191i \(-0.345289\pi\)
0.467126 + 0.884191i \(0.345289\pi\)
\(132\) −4.18857 −0.364568
\(133\) −5.73994 −0.497716
\(134\) 20.9037 1.80580
\(135\) 0 0
\(136\) −15.1528 −1.29934
\(137\) −6.53145 −0.558020 −0.279010 0.960288i \(-0.590006\pi\)
−0.279010 + 0.960288i \(0.590006\pi\)
\(138\) 16.9506 1.44293
\(139\) −9.68333 −0.821329 −0.410664 0.911787i \(-0.634703\pi\)
−0.410664 + 0.911787i \(0.634703\pi\)
\(140\) 0 0
\(141\) −24.1142 −2.03079
\(142\) 5.92117 0.496893
\(143\) 25.4213 2.12584
\(144\) −29.8166 −2.48471
\(145\) 0 0
\(146\) −13.3095 −1.10150
\(147\) 46.0147 3.79522
\(148\) −1.65690 −0.136196
\(149\) 14.7898 1.21163 0.605814 0.795606i \(-0.292847\pi\)
0.605814 + 0.795606i \(0.292847\pi\)
\(150\) 0 0
\(151\) −1.21804 −0.0991228 −0.0495614 0.998771i \(-0.515782\pi\)
−0.0495614 + 0.998771i \(0.515782\pi\)
\(152\) −3.25983 −0.264407
\(153\) −38.7872 −3.13576
\(154\) 41.1929 3.31942
\(155\) 0 0
\(156\) −3.03381 −0.242899
\(157\) 9.48425 0.756926 0.378463 0.925616i \(-0.376453\pi\)
0.378463 + 0.925616i \(0.376453\pi\)
\(158\) −2.64716 −0.210597
\(159\) 31.8101 2.52271
\(160\) 0 0
\(161\) −16.9342 −1.33460
\(162\) −24.7271 −1.94275
\(163\) 2.02231 0.158400 0.0791999 0.996859i \(-0.474763\pi\)
0.0791999 + 0.996859i \(0.474763\pi\)
\(164\) −1.45921 −0.113945
\(165\) 0 0
\(166\) 14.8191 1.15018
\(167\) −12.0440 −0.931992 −0.465996 0.884787i \(-0.654304\pi\)
−0.465996 + 0.884787i \(0.654304\pi\)
\(168\) 38.5617 2.97510
\(169\) 5.41287 0.416375
\(170\) 0 0
\(171\) −8.34434 −0.638107
\(172\) −1.03381 −0.0788270
\(173\) 10.6055 0.806322 0.403161 0.915129i \(-0.367911\pi\)
0.403161 + 0.915129i \(0.367911\pi\)
\(174\) −8.45171 −0.640723
\(175\) 0 0
\(176\) 26.0737 1.96538
\(177\) −17.7259 −1.33236
\(178\) 10.5023 0.787184
\(179\) −15.6670 −1.17101 −0.585505 0.810669i \(-0.699104\pi\)
−0.585505 + 0.810669i \(0.699104\pi\)
\(180\) 0 0
\(181\) 6.00433 0.446298 0.223149 0.974784i \(-0.428366\pi\)
0.223149 + 0.974784i \(0.428366\pi\)
\(182\) 29.8363 2.21161
\(183\) 14.9020 1.10158
\(184\) −9.61728 −0.708995
\(185\) 0 0
\(186\) 5.19740 0.381092
\(187\) 33.9183 2.48035
\(188\) −1.74420 −0.127209
\(189\) 54.9981 4.00052
\(190\) 0 0
\(191\) −14.5050 −1.04954 −0.524772 0.851243i \(-0.675849\pi\)
−0.524772 + 0.851243i \(0.675849\pi\)
\(192\) 21.5802 1.55742
\(193\) 3.41996 0.246174 0.123087 0.992396i \(-0.460721\pi\)
0.123087 + 0.992396i \(0.460721\pi\)
\(194\) −7.51808 −0.539767
\(195\) 0 0
\(196\) 3.32827 0.237734
\(197\) 20.5076 1.46111 0.730554 0.682855i \(-0.239262\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(198\) 59.8834 4.25573
\(199\) −2.77785 −0.196917 −0.0984583 0.995141i \(-0.531391\pi\)
−0.0984583 + 0.995141i \(0.531391\pi\)
\(200\) 0 0
\(201\) −43.8026 −3.08959
\(202\) 13.2486 0.932166
\(203\) 8.44353 0.592620
\(204\) −4.04785 −0.283406
\(205\) 0 0
\(206\) −4.65700 −0.324469
\(207\) −24.6178 −1.71105
\(208\) 18.8854 1.30947
\(209\) 7.29688 0.504735
\(210\) 0 0
\(211\) 22.9148 1.57752 0.788760 0.614701i \(-0.210723\pi\)
0.788760 + 0.614701i \(0.210723\pi\)
\(212\) 2.30085 0.158023
\(213\) −12.4075 −0.850147
\(214\) 3.54991 0.242667
\(215\) 0 0
\(216\) 31.2345 2.12524
\(217\) −5.19237 −0.352481
\(218\) 16.3058 1.10437
\(219\) 27.8893 1.88458
\(220\) 0 0
\(221\) 24.5673 1.65257
\(222\) 34.1782 2.29389
\(223\) 7.52468 0.503890 0.251945 0.967742i \(-0.418930\pi\)
0.251945 + 0.967742i \(0.418930\pi\)
\(224\) 5.93397 0.396480
\(225\) 0 0
\(226\) −18.4231 −1.22549
\(227\) 0.950254 0.0630706 0.0315353 0.999503i \(-0.489960\pi\)
0.0315353 + 0.999503i \(0.489960\pi\)
\(228\) −0.870818 −0.0576713
\(229\) 14.6545 0.968396 0.484198 0.874958i \(-0.339111\pi\)
0.484198 + 0.874958i \(0.339111\pi\)
\(230\) 0 0
\(231\) −86.3174 −5.67927
\(232\) 4.79526 0.314824
\(233\) −19.1614 −1.25530 −0.627651 0.778495i \(-0.715984\pi\)
−0.627651 + 0.778495i \(0.715984\pi\)
\(234\) 43.3740 2.83545
\(235\) 0 0
\(236\) −1.28213 −0.0834595
\(237\) 5.54697 0.360315
\(238\) 39.8089 2.58043
\(239\) −3.88636 −0.251388 −0.125694 0.992069i \(-0.540116\pi\)
−0.125694 + 0.992069i \(0.540116\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −35.9540 −2.31121
\(243\) 16.4097 1.05268
\(244\) 1.07787 0.0690035
\(245\) 0 0
\(246\) 30.1003 1.91913
\(247\) 5.28518 0.336288
\(248\) −2.94885 −0.187252
\(249\) −31.0525 −1.96787
\(250\) 0 0
\(251\) −13.8452 −0.873904 −0.436952 0.899485i \(-0.643942\pi\)
−0.436952 + 0.899485i \(0.643942\pi\)
\(252\) 7.13964 0.449755
\(253\) 21.5275 1.35342
\(254\) 13.1819 0.827109
\(255\) 0 0
\(256\) 5.36056 0.335035
\(257\) 6.17221 0.385012 0.192506 0.981296i \(-0.438338\pi\)
0.192506 + 0.981296i \(0.438338\pi\)
\(258\) 21.3252 1.32765
\(259\) −34.1451 −2.12167
\(260\) 0 0
\(261\) 12.2746 0.759781
\(262\) −15.9542 −0.985656
\(263\) 14.8523 0.915835 0.457917 0.888995i \(-0.348596\pi\)
0.457917 + 0.888995i \(0.348596\pi\)
\(264\) −49.0214 −3.01706
\(265\) 0 0
\(266\) 8.56414 0.525101
\(267\) −22.0071 −1.34681
\(268\) −3.16827 −0.193533
\(269\) 24.7594 1.50960 0.754802 0.655952i \(-0.227733\pi\)
0.754802 + 0.655952i \(0.227733\pi\)
\(270\) 0 0
\(271\) 21.9399 1.33275 0.666376 0.745616i \(-0.267845\pi\)
0.666376 + 0.745616i \(0.267845\pi\)
\(272\) 25.1977 1.52784
\(273\) −62.5204 −3.78390
\(274\) 9.74509 0.588723
\(275\) 0 0
\(276\) −2.56912 −0.154643
\(277\) 17.9537 1.07873 0.539367 0.842071i \(-0.318664\pi\)
0.539367 + 0.842071i \(0.318664\pi\)
\(278\) 14.4478 0.866519
\(279\) −7.54832 −0.451906
\(280\) 0 0
\(281\) 14.9520 0.891960 0.445980 0.895043i \(-0.352855\pi\)
0.445980 + 0.895043i \(0.352855\pi\)
\(282\) 35.9791 2.14252
\(283\) −16.8819 −1.00352 −0.501761 0.865006i \(-0.667314\pi\)
−0.501761 + 0.865006i \(0.667314\pi\)
\(284\) −0.897443 −0.0532534
\(285\) 0 0
\(286\) −37.9293 −2.24281
\(287\) −30.0712 −1.77505
\(288\) 8.62641 0.508316
\(289\) 15.7787 0.928160
\(290\) 0 0
\(291\) 15.7537 0.923500
\(292\) 2.01725 0.118051
\(293\) −16.3651 −0.956061 −0.478030 0.878343i \(-0.658649\pi\)
−0.478030 + 0.878343i \(0.658649\pi\)
\(294\) −68.6550 −4.00404
\(295\) 0 0
\(296\) −19.3917 −1.12712
\(297\) −69.9161 −4.05694
\(298\) −22.0668 −1.27829
\(299\) 15.5926 0.901741
\(300\) 0 0
\(301\) −21.3045 −1.22797
\(302\) 1.81735 0.104577
\(303\) −27.7617 −1.59487
\(304\) 5.42081 0.310905
\(305\) 0 0
\(306\) 57.8715 3.30829
\(307\) 19.0297 1.08608 0.543041 0.839706i \(-0.317273\pi\)
0.543041 + 0.839706i \(0.317273\pi\)
\(308\) −6.24340 −0.355751
\(309\) 9.75850 0.555142
\(310\) 0 0
\(311\) −16.3005 −0.924318 −0.462159 0.886797i \(-0.652925\pi\)
−0.462159 + 0.886797i \(0.652925\pi\)
\(312\) −35.5066 −2.01017
\(313\) 1.71271 0.0968084 0.0484042 0.998828i \(-0.484586\pi\)
0.0484042 + 0.998828i \(0.484586\pi\)
\(314\) −14.1507 −0.798573
\(315\) 0 0
\(316\) 0.401217 0.0225702
\(317\) 9.33229 0.524154 0.262077 0.965047i \(-0.415593\pi\)
0.262077 + 0.965047i \(0.415593\pi\)
\(318\) −47.4615 −2.66151
\(319\) −10.7338 −0.600978
\(320\) 0 0
\(321\) −7.43865 −0.415185
\(322\) 25.2663 1.40803
\(323\) 7.05172 0.392368
\(324\) 3.74777 0.208209
\(325\) 0 0
\(326\) −3.01734 −0.167115
\(327\) −34.1678 −1.88949
\(328\) −17.0780 −0.942977
\(329\) −35.9442 −1.98167
\(330\) 0 0
\(331\) 12.2007 0.670613 0.335306 0.942109i \(-0.391160\pi\)
0.335306 + 0.942109i \(0.391160\pi\)
\(332\) −2.24605 −0.123268
\(333\) −49.6378 −2.72014
\(334\) 17.9699 0.983271
\(335\) 0 0
\(336\) −64.1248 −3.49829
\(337\) 1.32894 0.0723920 0.0361960 0.999345i \(-0.488476\pi\)
0.0361960 + 0.999345i \(0.488476\pi\)
\(338\) −8.07614 −0.439284
\(339\) 38.6046 2.09671
\(340\) 0 0
\(341\) 6.60078 0.357452
\(342\) 12.4500 0.673217
\(343\) 35.9669 1.94203
\(344\) −12.0993 −0.652350
\(345\) 0 0
\(346\) −15.8237 −0.850687
\(347\) −2.21075 −0.118679 −0.0593396 0.998238i \(-0.518899\pi\)
−0.0593396 + 0.998238i \(0.518899\pi\)
\(348\) 1.28099 0.0686680
\(349\) 17.8704 0.956580 0.478290 0.878202i \(-0.341257\pi\)
0.478290 + 0.878202i \(0.341257\pi\)
\(350\) 0 0
\(351\) −50.6407 −2.70300
\(352\) −7.54354 −0.402072
\(353\) 9.10115 0.484405 0.242203 0.970226i \(-0.422130\pi\)
0.242203 + 0.970226i \(0.422130\pi\)
\(354\) 26.4475 1.40567
\(355\) 0 0
\(356\) −1.59179 −0.0843647
\(357\) −83.4174 −4.41492
\(358\) 23.3756 1.23544
\(359\) −23.0382 −1.21591 −0.607956 0.793971i \(-0.708010\pi\)
−0.607956 + 0.793971i \(0.708010\pi\)
\(360\) 0 0
\(361\) −17.4830 −0.920155
\(362\) −8.95861 −0.470854
\(363\) 75.3396 3.95430
\(364\) −4.52214 −0.237025
\(365\) 0 0
\(366\) −22.2341 −1.16219
\(367\) 32.4970 1.69633 0.848164 0.529734i \(-0.177708\pi\)
0.848164 + 0.529734i \(0.177708\pi\)
\(368\) 15.9927 0.833677
\(369\) −43.7154 −2.27573
\(370\) 0 0
\(371\) 47.4156 2.46170
\(372\) −0.787745 −0.0408427
\(373\) 35.2363 1.82447 0.912234 0.409671i \(-0.134356\pi\)
0.912234 + 0.409671i \(0.134356\pi\)
\(374\) −50.6069 −2.61682
\(375\) 0 0
\(376\) −20.4135 −1.05274
\(377\) −7.77458 −0.400411
\(378\) −82.0585 −4.22063
\(379\) −5.18922 −0.266553 −0.133276 0.991079i \(-0.542550\pi\)
−0.133276 + 0.991079i \(0.542550\pi\)
\(380\) 0 0
\(381\) −27.6221 −1.41512
\(382\) 21.6418 1.10729
\(383\) −5.72356 −0.292460 −0.146230 0.989251i \(-0.546714\pi\)
−0.146230 + 0.989251i \(0.546714\pi\)
\(384\) −40.1602 −2.04942
\(385\) 0 0
\(386\) −5.10267 −0.259719
\(387\) −30.9711 −1.57435
\(388\) 1.13948 0.0578483
\(389\) 24.8562 1.26026 0.630130 0.776490i \(-0.283002\pi\)
0.630130 + 0.776490i \(0.283002\pi\)
\(390\) 0 0
\(391\) 20.8043 1.05212
\(392\) 38.9529 1.96742
\(393\) 33.4312 1.68638
\(394\) −30.5979 −1.54150
\(395\) 0 0
\(396\) −9.07623 −0.456098
\(397\) −34.8213 −1.74763 −0.873815 0.486259i \(-0.838361\pi\)
−0.873815 + 0.486259i \(0.838361\pi\)
\(398\) 4.14462 0.207751
\(399\) −17.9457 −0.898408
\(400\) 0 0
\(401\) −32.1370 −1.60484 −0.802422 0.596757i \(-0.796456\pi\)
−0.802422 + 0.596757i \(0.796456\pi\)
\(402\) 65.3545 3.25959
\(403\) 4.78100 0.238158
\(404\) −2.00802 −0.0999028
\(405\) 0 0
\(406\) −12.5980 −0.625227
\(407\) 43.4068 2.15160
\(408\) −47.3745 −2.34539
\(409\) −30.4791 −1.50709 −0.753547 0.657395i \(-0.771659\pi\)
−0.753547 + 0.657395i \(0.771659\pi\)
\(410\) 0 0
\(411\) −20.4203 −1.00726
\(412\) 0.705839 0.0347742
\(413\) −26.4219 −1.30014
\(414\) 36.7304 1.80520
\(415\) 0 0
\(416\) −5.46384 −0.267887
\(417\) −30.2745 −1.48255
\(418\) −10.8871 −0.532507
\(419\) −14.0542 −0.686592 −0.343296 0.939227i \(-0.611543\pi\)
−0.343296 + 0.939227i \(0.611543\pi\)
\(420\) 0 0
\(421\) 7.96690 0.388283 0.194141 0.980974i \(-0.437808\pi\)
0.194141 + 0.980974i \(0.437808\pi\)
\(422\) −34.1895 −1.66432
\(423\) −52.2533 −2.54064
\(424\) 26.9283 1.30775
\(425\) 0 0
\(426\) 18.5123 0.896923
\(427\) 22.2126 1.07494
\(428\) −0.538043 −0.0260073
\(429\) 79.4787 3.83727
\(430\) 0 0
\(431\) −39.6560 −1.91016 −0.955080 0.296348i \(-0.904231\pi\)
−0.955080 + 0.296348i \(0.904231\pi\)
\(432\) −51.9403 −2.49898
\(433\) 3.27667 0.157467 0.0787333 0.996896i \(-0.474912\pi\)
0.0787333 + 0.996896i \(0.474912\pi\)
\(434\) 7.74715 0.371875
\(435\) 0 0
\(436\) −2.47139 −0.118358
\(437\) 4.47565 0.214099
\(438\) −41.6115 −1.98827
\(439\) −14.5064 −0.692355 −0.346177 0.938169i \(-0.612520\pi\)
−0.346177 + 0.938169i \(0.612520\pi\)
\(440\) 0 0
\(441\) 99.7094 4.74807
\(442\) −36.6550 −1.74350
\(443\) −19.5267 −0.927742 −0.463871 0.885903i \(-0.653540\pi\)
−0.463871 + 0.885903i \(0.653540\pi\)
\(444\) −5.18022 −0.245842
\(445\) 0 0
\(446\) −11.2270 −0.531614
\(447\) 46.2397 2.18706
\(448\) 32.1671 1.51975
\(449\) −2.85475 −0.134724 −0.0673621 0.997729i \(-0.521458\pi\)
−0.0673621 + 0.997729i \(0.521458\pi\)
\(450\) 0 0
\(451\) 38.2279 1.80008
\(452\) 2.79230 0.131339
\(453\) −3.80815 −0.178923
\(454\) −1.41780 −0.0665408
\(455\) 0 0
\(456\) −10.1917 −0.477271
\(457\) −11.7309 −0.548749 −0.274375 0.961623i \(-0.588471\pi\)
−0.274375 + 0.961623i \(0.588471\pi\)
\(458\) −21.8649 −1.02168
\(459\) −67.5671 −3.15376
\(460\) 0 0
\(461\) 1.41285 0.0658028 0.0329014 0.999459i \(-0.489525\pi\)
0.0329014 + 0.999459i \(0.489525\pi\)
\(462\) 128.788 5.99175
\(463\) −30.3025 −1.40827 −0.704137 0.710064i \(-0.748666\pi\)
−0.704137 + 0.710064i \(0.748666\pi\)
\(464\) −7.97409 −0.370188
\(465\) 0 0
\(466\) 28.5892 1.32437
\(467\) 10.2416 0.473927 0.236963 0.971519i \(-0.423848\pi\)
0.236963 + 0.971519i \(0.423848\pi\)
\(468\) −6.57399 −0.303883
\(469\) −65.2913 −3.01487
\(470\) 0 0
\(471\) 29.6521 1.36630
\(472\) −15.0056 −0.690687
\(473\) 27.0833 1.24529
\(474\) −8.27623 −0.380140
\(475\) 0 0
\(476\) −6.03364 −0.276552
\(477\) 68.9296 3.15607
\(478\) 5.79855 0.265219
\(479\) −16.8364 −0.769275 −0.384638 0.923068i \(-0.625674\pi\)
−0.384638 + 0.923068i \(0.625674\pi\)
\(480\) 0 0
\(481\) 31.4399 1.43354
\(482\) −1.49203 −0.0679599
\(483\) −52.9441 −2.40904
\(484\) 5.44937 0.247699
\(485\) 0 0
\(486\) −24.4836 −1.11060
\(487\) −19.1209 −0.866452 −0.433226 0.901285i \(-0.642625\pi\)
−0.433226 + 0.901285i \(0.642625\pi\)
\(488\) 12.6150 0.571053
\(489\) 6.32268 0.285921
\(490\) 0 0
\(491\) 13.6920 0.617910 0.308955 0.951077i \(-0.400021\pi\)
0.308955 + 0.951077i \(0.400021\pi\)
\(492\) −4.56216 −0.205678
\(493\) −10.3732 −0.467185
\(494\) −7.88563 −0.354791
\(495\) 0 0
\(496\) 4.90369 0.220182
\(497\) −18.4944 −0.829586
\(498\) 46.3312 2.07615
\(499\) 41.2184 1.84519 0.922595 0.385770i \(-0.126064\pi\)
0.922595 + 0.385770i \(0.126064\pi\)
\(500\) 0 0
\(501\) −37.6550 −1.68230
\(502\) 20.6575 0.921988
\(503\) 23.7713 1.05991 0.529956 0.848025i \(-0.322209\pi\)
0.529956 + 0.848025i \(0.322209\pi\)
\(504\) 83.5596 3.72204
\(505\) 0 0
\(506\) −32.1196 −1.42789
\(507\) 16.9231 0.751582
\(508\) −1.99792 −0.0886435
\(509\) 0.527203 0.0233679 0.0116839 0.999932i \(-0.496281\pi\)
0.0116839 + 0.999932i \(0.496281\pi\)
\(510\) 0 0
\(511\) 41.5712 1.83900
\(512\) 17.6924 0.781903
\(513\) −14.5358 −0.641771
\(514\) −9.20910 −0.406196
\(515\) 0 0
\(516\) −3.23215 −0.142288
\(517\) 45.6939 2.00962
\(518\) 50.9454 2.23841
\(519\) 33.1577 1.45546
\(520\) 0 0
\(521\) 19.7412 0.864876 0.432438 0.901664i \(-0.357654\pi\)
0.432438 + 0.901664i \(0.357654\pi\)
\(522\) −18.3141 −0.801585
\(523\) 22.0882 0.965849 0.482925 0.875662i \(-0.339574\pi\)
0.482925 + 0.875662i \(0.339574\pi\)
\(524\) 2.41811 0.105635
\(525\) 0 0
\(526\) −22.1601 −0.966225
\(527\) 6.37902 0.277874
\(528\) 81.5183 3.54763
\(529\) −9.79577 −0.425903
\(530\) 0 0
\(531\) −38.4104 −1.66687
\(532\) −1.29802 −0.0562765
\(533\) 27.6887 1.19933
\(534\) 32.8351 1.42091
\(535\) 0 0
\(536\) −37.0802 −1.60162
\(537\) −48.9823 −2.11374
\(538\) −36.9416 −1.59267
\(539\) −87.1929 −3.75567
\(540\) 0 0
\(541\) −7.32264 −0.314825 −0.157412 0.987533i \(-0.550315\pi\)
−0.157412 + 0.987533i \(0.550315\pi\)
\(542\) −32.7348 −1.40608
\(543\) 18.7723 0.805596
\(544\) −7.29010 −0.312561
\(545\) 0 0
\(546\) 93.2820 3.99210
\(547\) −27.9274 −1.19409 −0.597045 0.802208i \(-0.703658\pi\)
−0.597045 + 0.802208i \(0.703658\pi\)
\(548\) −1.47702 −0.0630950
\(549\) 32.2911 1.37815
\(550\) 0 0
\(551\) −2.23160 −0.0950692
\(552\) −30.0680 −1.27978
\(553\) 8.26821 0.351600
\(554\) −26.7874 −1.13809
\(555\) 0 0
\(556\) −2.18978 −0.0928673
\(557\) 13.5066 0.572293 0.286146 0.958186i \(-0.407626\pi\)
0.286146 + 0.958186i \(0.407626\pi\)
\(558\) 11.2623 0.476770
\(559\) 19.6166 0.829696
\(560\) 0 0
\(561\) 106.044 4.47718
\(562\) −22.3087 −0.941037
\(563\) 4.30396 0.181390 0.0906951 0.995879i \(-0.471091\pi\)
0.0906951 + 0.995879i \(0.471091\pi\)
\(564\) −5.45317 −0.229620
\(565\) 0 0
\(566\) 25.1882 1.05874
\(567\) 77.2335 3.24350
\(568\) −10.5033 −0.440710
\(569\) 10.2392 0.429248 0.214624 0.976697i \(-0.431147\pi\)
0.214624 + 0.976697i \(0.431147\pi\)
\(570\) 0 0
\(571\) −25.4305 −1.06423 −0.532117 0.846671i \(-0.678603\pi\)
−0.532117 + 0.846671i \(0.678603\pi\)
\(572\) 5.74876 0.240368
\(573\) −45.3492 −1.89449
\(574\) 44.8670 1.87271
\(575\) 0 0
\(576\) 46.7623 1.94843
\(577\) −12.6994 −0.528684 −0.264342 0.964429i \(-0.585155\pi\)
−0.264342 + 0.964429i \(0.585155\pi\)
\(578\) −23.5423 −0.979229
\(579\) 10.6924 0.444360
\(580\) 0 0
\(581\) −46.2863 −1.92028
\(582\) −23.5050 −0.974312
\(583\) −60.2769 −2.49641
\(584\) 23.6091 0.976953
\(585\) 0 0
\(586\) 24.4172 1.00866
\(587\) 37.3627 1.54212 0.771061 0.636761i \(-0.219726\pi\)
0.771061 + 0.636761i \(0.219726\pi\)
\(588\) 10.4057 0.429124
\(589\) 1.37233 0.0565457
\(590\) 0 0
\(591\) 64.1162 2.63739
\(592\) 32.2467 1.32533
\(593\) −20.9359 −0.859736 −0.429868 0.902892i \(-0.641440\pi\)
−0.429868 + 0.902892i \(0.641440\pi\)
\(594\) 104.317 4.28016
\(595\) 0 0
\(596\) 3.34455 0.136998
\(597\) −8.68483 −0.355447
\(598\) −23.2645 −0.951356
\(599\) −40.5567 −1.65710 −0.828551 0.559914i \(-0.810834\pi\)
−0.828551 + 0.559914i \(0.810834\pi\)
\(600\) 0 0
\(601\) −21.1739 −0.863700 −0.431850 0.901946i \(-0.642139\pi\)
−0.431850 + 0.901946i \(0.642139\pi\)
\(602\) 31.7869 1.29554
\(603\) −94.9160 −3.86528
\(604\) −0.275447 −0.0112078
\(605\) 0 0
\(606\) 41.4211 1.68262
\(607\) −27.6387 −1.12182 −0.560910 0.827877i \(-0.689549\pi\)
−0.560910 + 0.827877i \(0.689549\pi\)
\(608\) −1.56833 −0.0636041
\(609\) 26.3984 1.06972
\(610\) 0 0
\(611\) 33.0965 1.33894
\(612\) −8.77130 −0.354559
\(613\) 36.9421 1.49208 0.746039 0.665902i \(-0.231953\pi\)
0.746039 + 0.665902i \(0.231953\pi\)
\(614\) −28.3928 −1.14584
\(615\) 0 0
\(616\) −73.0704 −2.94409
\(617\) 40.1279 1.61549 0.807744 0.589533i \(-0.200688\pi\)
0.807744 + 0.589533i \(0.200688\pi\)
\(618\) −14.5599 −0.585686
\(619\) −30.3391 −1.21943 −0.609716 0.792620i \(-0.708716\pi\)
−0.609716 + 0.792620i \(0.708716\pi\)
\(620\) 0 0
\(621\) −42.8841 −1.72088
\(622\) 24.3208 0.975175
\(623\) −32.8033 −1.31424
\(624\) 59.0444 2.36367
\(625\) 0 0
\(626\) −2.55541 −0.102135
\(627\) 22.8134 0.911078
\(628\) 2.14476 0.0855852
\(629\) 41.9485 1.67260
\(630\) 0 0
\(631\) −36.0636 −1.43567 −0.717835 0.696213i \(-0.754867\pi\)
−0.717835 + 0.696213i \(0.754867\pi\)
\(632\) 4.69569 0.186784
\(633\) 71.6422 2.84752
\(634\) −13.9240 −0.552993
\(635\) 0 0
\(636\) 7.19352 0.285241
\(637\) −63.1545 −2.50227
\(638\) 16.0151 0.634044
\(639\) −26.8859 −1.06359
\(640\) 0 0
\(641\) 40.0078 1.58021 0.790106 0.612970i \(-0.210025\pi\)
0.790106 + 0.612970i \(0.210025\pi\)
\(642\) 11.0987 0.438029
\(643\) −23.3695 −0.921604 −0.460802 0.887503i \(-0.652438\pi\)
−0.460802 + 0.887503i \(0.652438\pi\)
\(644\) −3.82948 −0.150903
\(645\) 0 0
\(646\) −10.5214 −0.413957
\(647\) −43.5626 −1.71262 −0.856312 0.516459i \(-0.827250\pi\)
−0.856312 + 0.516459i \(0.827250\pi\)
\(648\) 43.8625 1.72308
\(649\) 33.5888 1.31847
\(650\) 0 0
\(651\) −16.2337 −0.636250
\(652\) 0.457324 0.0179102
\(653\) 11.8810 0.464939 0.232469 0.972604i \(-0.425319\pi\)
0.232469 + 0.972604i \(0.425319\pi\)
\(654\) 50.9793 1.99345
\(655\) 0 0
\(656\) 28.3993 1.10881
\(657\) 60.4334 2.35773
\(658\) 53.6297 2.09070
\(659\) 22.2402 0.866357 0.433178 0.901308i \(-0.357392\pi\)
0.433178 + 0.901308i \(0.357392\pi\)
\(660\) 0 0
\(661\) 20.7001 0.805140 0.402570 0.915389i \(-0.368117\pi\)
0.402570 + 0.915389i \(0.368117\pi\)
\(662\) −18.2038 −0.707511
\(663\) 76.8085 2.98300
\(664\) −26.2870 −1.02013
\(665\) 0 0
\(666\) 74.0609 2.86980
\(667\) −6.58374 −0.254923
\(668\) −2.72362 −0.105380
\(669\) 23.5256 0.909551
\(670\) 0 0
\(671\) −28.2376 −1.09010
\(672\) 18.5523 0.715671
\(673\) −4.14046 −0.159603 −0.0798016 0.996811i \(-0.525429\pi\)
−0.0798016 + 0.996811i \(0.525429\pi\)
\(674\) −1.98281 −0.0763751
\(675\) 0 0
\(676\) 1.22406 0.0470793
\(677\) −38.9911 −1.49855 −0.749275 0.662259i \(-0.769598\pi\)
−0.749275 + 0.662259i \(0.769598\pi\)
\(678\) −57.5990 −2.21208
\(679\) 23.4822 0.901164
\(680\) 0 0
\(681\) 2.97093 0.113846
\(682\) −9.84853 −0.377120
\(683\) −20.2200 −0.773696 −0.386848 0.922144i \(-0.626436\pi\)
−0.386848 + 0.922144i \(0.626436\pi\)
\(684\) −1.88698 −0.0721505
\(685\) 0 0
\(686\) −53.6635 −2.04888
\(687\) 45.8166 1.74801
\(688\) 20.1200 0.767070
\(689\) −43.6590 −1.66328
\(690\) 0 0
\(691\) −10.4772 −0.398570 −0.199285 0.979942i \(-0.563862\pi\)
−0.199285 + 0.979942i \(0.563862\pi\)
\(692\) 2.39832 0.0911705
\(693\) −187.042 −7.10512
\(694\) 3.29849 0.125209
\(695\) 0 0
\(696\) 14.9922 0.568277
\(697\) 36.9435 1.39934
\(698\) −26.6631 −1.00921
\(699\) −59.9072 −2.26590
\(700\) 0 0
\(701\) 23.2337 0.877524 0.438762 0.898603i \(-0.355417\pi\)
0.438762 + 0.898603i \(0.355417\pi\)
\(702\) 75.5573 2.85173
\(703\) 9.02443 0.340363
\(704\) −40.8923 −1.54118
\(705\) 0 0
\(706\) −13.5791 −0.511058
\(707\) −41.3810 −1.55629
\(708\) −4.00852 −0.150650
\(709\) −28.6569 −1.07623 −0.538116 0.842871i \(-0.680864\pi\)
−0.538116 + 0.842871i \(0.680864\pi\)
\(710\) 0 0
\(711\) 12.0198 0.450777
\(712\) −18.6297 −0.698177
\(713\) 4.04869 0.151625
\(714\) 124.461 4.65783
\(715\) 0 0
\(716\) −3.54293 −0.132405
\(717\) −12.1505 −0.453770
\(718\) 34.3736 1.28281
\(719\) −5.87954 −0.219270 −0.109635 0.993972i \(-0.534968\pi\)
−0.109635 + 0.993972i \(0.534968\pi\)
\(720\) 0 0
\(721\) 14.5458 0.541715
\(722\) 26.0850 0.970783
\(723\) 3.12646 0.116274
\(724\) 1.35781 0.0504627
\(725\) 0 0
\(726\) −112.409 −4.17187
\(727\) −49.0096 −1.81767 −0.908833 0.417161i \(-0.863025\pi\)
−0.908833 + 0.417161i \(0.863025\pi\)
\(728\) −52.9255 −1.96155
\(729\) 1.58556 0.0587245
\(730\) 0 0
\(731\) 26.1734 0.968058
\(732\) 3.36991 0.124556
\(733\) 15.4332 0.570040 0.285020 0.958522i \(-0.408000\pi\)
0.285020 + 0.958522i \(0.408000\pi\)
\(734\) −48.4863 −1.78966
\(735\) 0 0
\(736\) −4.62694 −0.170551
\(737\) 83.0012 3.05739
\(738\) 65.2245 2.40095
\(739\) −19.0798 −0.701863 −0.350931 0.936401i \(-0.614135\pi\)
−0.350931 + 0.936401i \(0.614135\pi\)
\(740\) 0 0
\(741\) 16.5239 0.607021
\(742\) −70.7453 −2.59714
\(743\) −28.2323 −1.03574 −0.517871 0.855459i \(-0.673275\pi\)
−0.517871 + 0.855459i \(0.673275\pi\)
\(744\) −9.21947 −0.338002
\(745\) 0 0
\(746\) −52.5735 −1.92485
\(747\) −67.2879 −2.46194
\(748\) 7.67024 0.280452
\(749\) −11.0879 −0.405143
\(750\) 0 0
\(751\) 10.2127 0.372667 0.186333 0.982487i \(-0.440340\pi\)
0.186333 + 0.982487i \(0.440340\pi\)
\(752\) 33.9458 1.23788
\(753\) −43.2866 −1.57745
\(754\) 11.5999 0.422442
\(755\) 0 0
\(756\) 12.4372 0.452337
\(757\) −42.5055 −1.54489 −0.772445 0.635082i \(-0.780966\pi\)
−0.772445 + 0.635082i \(0.780966\pi\)
\(758\) 7.74245 0.281219
\(759\) 67.3049 2.44301
\(760\) 0 0
\(761\) −33.2390 −1.20491 −0.602456 0.798152i \(-0.705811\pi\)
−0.602456 + 0.798152i \(0.705811\pi\)
\(762\) 41.2128 1.49298
\(763\) −50.9299 −1.84379
\(764\) −3.28014 −0.118671
\(765\) 0 0
\(766\) 8.53970 0.308552
\(767\) 24.3286 0.878455
\(768\) 16.7596 0.604759
\(769\) 24.0517 0.867328 0.433664 0.901075i \(-0.357221\pi\)
0.433664 + 0.901075i \(0.357221\pi\)
\(770\) 0 0
\(771\) 19.2972 0.694971
\(772\) 0.773387 0.0278348
\(773\) −19.5958 −0.704813 −0.352407 0.935847i \(-0.614637\pi\)
−0.352407 + 0.935847i \(0.614637\pi\)
\(774\) 46.2096 1.66097
\(775\) 0 0
\(776\) 13.3360 0.478735
\(777\) −106.753 −3.82975
\(778\) −37.0861 −1.32960
\(779\) 7.94770 0.284756
\(780\) 0 0
\(781\) 23.5109 0.841286
\(782\) −31.0405 −1.11001
\(783\) 21.3824 0.764143
\(784\) −64.7752 −2.31340
\(785\) 0 0
\(786\) −49.8802 −1.77917
\(787\) 14.4340 0.514515 0.257257 0.966343i \(-0.417181\pi\)
0.257257 + 0.966343i \(0.417181\pi\)
\(788\) 4.63757 0.165207
\(789\) 46.4352 1.65314
\(790\) 0 0
\(791\) 57.5432 2.04600
\(792\) −106.225 −3.77453
\(793\) −20.4527 −0.726298
\(794\) 51.9542 1.84379
\(795\) 0 0
\(796\) −0.628181 −0.0222653
\(797\) −36.2235 −1.28310 −0.641551 0.767081i \(-0.721709\pi\)
−0.641551 + 0.767081i \(0.721709\pi\)
\(798\) 26.7754 0.947839
\(799\) 44.1588 1.56223
\(800\) 0 0
\(801\) −47.6873 −1.68495
\(802\) 47.9492 1.69314
\(803\) −52.8472 −1.86494
\(804\) −9.90547 −0.349339
\(805\) 0 0
\(806\) −7.13337 −0.251262
\(807\) 77.4091 2.72493
\(808\) −23.5011 −0.826766
\(809\) −33.5485 −1.17950 −0.589751 0.807585i \(-0.700774\pi\)
−0.589751 + 0.807585i \(0.700774\pi\)
\(810\) 0 0
\(811\) −41.8458 −1.46941 −0.734703 0.678389i \(-0.762678\pi\)
−0.734703 + 0.678389i \(0.762678\pi\)
\(812\) 1.90941 0.0670072
\(813\) 68.5940 2.40570
\(814\) −64.7641 −2.26998
\(815\) 0 0
\(816\) 78.7796 2.75784
\(817\) 5.63071 0.196994
\(818\) 45.4755 1.59002
\(819\) −135.476 −4.73390
\(820\) 0 0
\(821\) −29.6138 −1.03353 −0.516765 0.856127i \(-0.672864\pi\)
−0.516765 + 0.856127i \(0.672864\pi\)
\(822\) 30.4676 1.06268
\(823\) 5.60965 0.195540 0.0977701 0.995209i \(-0.468829\pi\)
0.0977701 + 0.995209i \(0.468829\pi\)
\(824\) 8.26088 0.287781
\(825\) 0 0
\(826\) 39.4222 1.37167
\(827\) 13.9106 0.483720 0.241860 0.970311i \(-0.422242\pi\)
0.241860 + 0.970311i \(0.422242\pi\)
\(828\) −5.56704 −0.193468
\(829\) 22.9062 0.795567 0.397783 0.917479i \(-0.369780\pi\)
0.397783 + 0.917479i \(0.369780\pi\)
\(830\) 0 0
\(831\) 56.1315 1.94718
\(832\) −29.6186 −1.02684
\(833\) −84.2635 −2.91956
\(834\) 45.1703 1.56412
\(835\) 0 0
\(836\) 1.65011 0.0570702
\(837\) −13.1491 −0.454500
\(838\) 20.9692 0.724369
\(839\) −5.57070 −0.192322 −0.0961609 0.995366i \(-0.530656\pi\)
−0.0961609 + 0.995366i \(0.530656\pi\)
\(840\) 0 0
\(841\) −25.7173 −0.886803
\(842\) −11.8868 −0.409647
\(843\) 46.7467 1.61004
\(844\) 5.18193 0.178369
\(845\) 0 0
\(846\) 77.9632 2.68043
\(847\) 112.300 3.85867
\(848\) −44.7794 −1.53773
\(849\) −52.7804 −1.81142
\(850\) 0 0
\(851\) 26.6242 0.912667
\(852\) −2.80582 −0.0961257
\(853\) 35.8612 1.22786 0.613931 0.789359i \(-0.289587\pi\)
0.613931 + 0.789359i \(0.289587\pi\)
\(854\) −33.1417 −1.13409
\(855\) 0 0
\(856\) −6.29705 −0.215229
\(857\) −0.654119 −0.0223443 −0.0111721 0.999938i \(-0.503556\pi\)
−0.0111721 + 0.999938i \(0.503556\pi\)
\(858\) −118.584 −4.04840
\(859\) 2.58305 0.0881324 0.0440662 0.999029i \(-0.485969\pi\)
0.0440662 + 0.999029i \(0.485969\pi\)
\(860\) 0 0
\(861\) −94.0163 −3.20407
\(862\) 59.1677 2.01526
\(863\) 52.4627 1.78585 0.892925 0.450206i \(-0.148649\pi\)
0.892925 + 0.450206i \(0.148649\pi\)
\(864\) 15.0272 0.511234
\(865\) 0 0
\(866\) −4.88887 −0.166130
\(867\) 49.3315 1.67539
\(868\) −1.17420 −0.0398549
\(869\) −10.5109 −0.356559
\(870\) 0 0
\(871\) 60.1184 2.03704
\(872\) −28.9242 −0.979496
\(873\) 34.1368 1.15536
\(874\) −6.67778 −0.225879
\(875\) 0 0
\(876\) 6.30685 0.213089
\(877\) 19.1481 0.646586 0.323293 0.946299i \(-0.395210\pi\)
0.323293 + 0.946299i \(0.395210\pi\)
\(878\) 21.6440 0.730449
\(879\) −51.1649 −1.72575
\(880\) 0 0
\(881\) −38.6243 −1.30129 −0.650643 0.759384i \(-0.725501\pi\)
−0.650643 + 0.759384i \(0.725501\pi\)
\(882\) −148.769 −5.00931
\(883\) 40.7541 1.37149 0.685743 0.727844i \(-0.259477\pi\)
0.685743 + 0.727844i \(0.259477\pi\)
\(884\) 5.55562 0.186856
\(885\) 0 0
\(886\) 29.1344 0.978788
\(887\) −44.2838 −1.48690 −0.743452 0.668789i \(-0.766813\pi\)
−0.743452 + 0.668789i \(0.766813\pi\)
\(888\) −60.6274 −2.03452
\(889\) −41.1729 −1.38089
\(890\) 0 0
\(891\) −98.1827 −3.28925
\(892\) 1.70162 0.0569745
\(893\) 9.49993 0.317903
\(894\) −68.9908 −2.30740
\(895\) 0 0
\(896\) −59.8620 −1.99985
\(897\) 48.7495 1.62770
\(898\) 4.25936 0.142137
\(899\) −2.01871 −0.0673277
\(900\) 0 0
\(901\) −58.2518 −1.94065
\(902\) −57.0369 −1.89912
\(903\) −66.6077 −2.21657
\(904\) 32.6800 1.08692
\(905\) 0 0
\(906\) 5.68186 0.188767
\(907\) −0.773290 −0.0256767 −0.0128383 0.999918i \(-0.504087\pi\)
−0.0128383 + 0.999918i \(0.504087\pi\)
\(908\) 0.214889 0.00713136
\(909\) −60.1569 −1.99528
\(910\) 0 0
\(911\) 39.1307 1.29646 0.648228 0.761446i \(-0.275510\pi\)
0.648228 + 0.761446i \(0.275510\pi\)
\(912\) 16.9479 0.561202
\(913\) 58.8413 1.94736
\(914\) 17.5028 0.578942
\(915\) 0 0
\(916\) 3.31395 0.109496
\(917\) 49.8319 1.64560
\(918\) 100.812 3.32729
\(919\) 24.2527 0.800023 0.400011 0.916510i \(-0.369006\pi\)
0.400011 + 0.916510i \(0.369006\pi\)
\(920\) 0 0
\(921\) 59.4955 1.96044
\(922\) −2.10800 −0.0694233
\(923\) 17.0291 0.560520
\(924\) −19.5197 −0.642152
\(925\) 0 0
\(926\) 45.2120 1.48576
\(927\) 21.1457 0.694517
\(928\) 2.30703 0.0757320
\(929\) 4.12264 0.135260 0.0676298 0.997710i \(-0.478456\pi\)
0.0676298 + 0.997710i \(0.478456\pi\)
\(930\) 0 0
\(931\) −18.1277 −0.594112
\(932\) −4.33313 −0.141936
\(933\) −50.9629 −1.66845
\(934\) −15.2808 −0.500003
\(935\) 0 0
\(936\) −76.9394 −2.51484
\(937\) −8.27592 −0.270362 −0.135181 0.990821i \(-0.543162\pi\)
−0.135181 + 0.990821i \(0.543162\pi\)
\(938\) 97.4162 3.18075
\(939\) 5.35473 0.174745
\(940\) 0 0
\(941\) 11.2610 0.367100 0.183550 0.983010i \(-0.441241\pi\)
0.183550 + 0.983010i \(0.441241\pi\)
\(942\) −44.2417 −1.44147
\(943\) 23.4476 0.763560
\(944\) 24.9529 0.812148
\(945\) 0 0
\(946\) −40.4090 −1.31381
\(947\) 28.2529 0.918096 0.459048 0.888411i \(-0.348191\pi\)
0.459048 + 0.888411i \(0.348191\pi\)
\(948\) 1.25439 0.0407406
\(949\) −38.2776 −1.24254
\(950\) 0 0
\(951\) 29.1770 0.946130
\(952\) −70.6155 −2.28866
\(953\) 39.0186 1.26394 0.631968 0.774995i \(-0.282248\pi\)
0.631968 + 0.774995i \(0.282248\pi\)
\(954\) −102.845 −3.32972
\(955\) 0 0
\(956\) −0.878858 −0.0284243
\(957\) −33.5588 −1.08480
\(958\) 25.1203 0.811602
\(959\) −30.4381 −0.982899
\(960\) 0 0
\(961\) −29.7586 −0.959955
\(962\) −46.9091 −1.51241
\(963\) −16.1188 −0.519423
\(964\) 0.226139 0.00728345
\(965\) 0 0
\(966\) 78.9939 2.54159
\(967\) 39.9098 1.28341 0.641707 0.766950i \(-0.278227\pi\)
0.641707 + 0.766950i \(0.278227\pi\)
\(968\) 63.7773 2.04988
\(969\) 22.0469 0.708249
\(970\) 0 0
\(971\) 50.1082 1.60805 0.804024 0.594597i \(-0.202688\pi\)
0.804024 + 0.594597i \(0.202688\pi\)
\(972\) 3.71087 0.119026
\(973\) −45.1266 −1.44669
\(974\) 28.5289 0.914126
\(975\) 0 0
\(976\) −20.9776 −0.671477
\(977\) −42.4558 −1.35828 −0.679141 0.734008i \(-0.737648\pi\)
−0.679141 + 0.734008i \(0.737648\pi\)
\(978\) −9.43359 −0.301653
\(979\) 41.7011 1.33277
\(980\) 0 0
\(981\) −74.0385 −2.36387
\(982\) −20.4288 −0.651908
\(983\) 18.7770 0.598895 0.299447 0.954113i \(-0.403198\pi\)
0.299447 + 0.954113i \(0.403198\pi\)
\(984\) −53.3938 −1.70213
\(985\) 0 0
\(986\) 15.4771 0.492890
\(987\) −112.378 −3.57703
\(988\) 1.19519 0.0380239
\(989\) 16.6119 0.528229
\(990\) 0 0
\(991\) −7.86345 −0.249791 −0.124895 0.992170i \(-0.539860\pi\)
−0.124895 + 0.992170i \(0.539860\pi\)
\(992\) −1.41872 −0.0450443
\(993\) 38.1451 1.21050
\(994\) 27.5941 0.875230
\(995\) 0 0
\(996\) −7.02219 −0.222507
\(997\) 4.32111 0.136851 0.0684255 0.997656i \(-0.478202\pi\)
0.0684255 + 0.997656i \(0.478202\pi\)
\(998\) −61.4989 −1.94671
\(999\) −86.4688 −2.73575
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.1.12 46
5.2 odd 4 1205.2.b.c.724.12 46
5.3 odd 4 1205.2.b.c.724.35 yes 46
5.4 even 2 inner 6025.2.a.p.1.35 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.12 46 5.2 odd 4
1205.2.b.c.724.35 yes 46 5.3 odd 4
6025.2.a.p.1.12 46 1.1 even 1 trivial
6025.2.a.p.1.35 46 5.4 even 2 inner