Properties

Label 6025.2.a.p.1.1
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 1.1
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68673 q^{2} +2.58072 q^{3} +5.21850 q^{4} -6.93370 q^{6} +1.24945 q^{7} -8.64724 q^{8} +3.66013 q^{9} +O(q^{10})\) \(q-2.68673 q^{2} +2.58072 q^{3} +5.21850 q^{4} -6.93370 q^{6} +1.24945 q^{7} -8.64724 q^{8} +3.66013 q^{9} -5.71181 q^{11} +13.4675 q^{12} -3.28322 q^{13} -3.35693 q^{14} +12.7958 q^{16} +5.29090 q^{17} -9.83378 q^{18} +6.14996 q^{19} +3.22448 q^{21} +15.3461 q^{22} +2.22338 q^{23} -22.3161 q^{24} +8.82111 q^{26} +1.70362 q^{27} +6.52026 q^{28} -5.09304 q^{29} -4.50984 q^{31} -17.0842 q^{32} -14.7406 q^{33} -14.2152 q^{34} +19.1004 q^{36} -4.88794 q^{37} -16.5233 q^{38} -8.47308 q^{39} -4.77605 q^{41} -8.66331 q^{42} +2.72100 q^{43} -29.8071 q^{44} -5.97362 q^{46} -2.52165 q^{47} +33.0223 q^{48} -5.43887 q^{49} +13.6544 q^{51} -17.1335 q^{52} -7.67961 q^{53} -4.57716 q^{54} -10.8043 q^{56} +15.8714 q^{57} +13.6836 q^{58} -8.39323 q^{59} -12.2037 q^{61} +12.1167 q^{62} +4.57315 q^{63} +20.3092 q^{64} +39.6039 q^{66} +15.2352 q^{67} +27.6106 q^{68} +5.73793 q^{69} -6.27039 q^{71} -31.6500 q^{72} -5.27275 q^{73} +13.1325 q^{74} +32.0936 q^{76} -7.13662 q^{77} +22.7648 q^{78} +9.38460 q^{79} -6.58383 q^{81} +12.8319 q^{82} -2.13252 q^{83} +16.8270 q^{84} -7.31059 q^{86} -13.1437 q^{87} +49.3913 q^{88} +8.11125 q^{89} -4.10222 q^{91} +11.6027 q^{92} -11.6386 q^{93} +6.77498 q^{94} -44.0897 q^{96} -10.0464 q^{97} +14.6128 q^{98} -20.9060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68673 −1.89980 −0.949901 0.312550i \(-0.898817\pi\)
−0.949901 + 0.312550i \(0.898817\pi\)
\(3\) 2.58072 1.48998 0.744991 0.667075i \(-0.232454\pi\)
0.744991 + 0.667075i \(0.232454\pi\)
\(4\) 5.21850 2.60925
\(5\) 0 0
\(6\) −6.93370 −2.83067
\(7\) 1.24945 0.472248 0.236124 0.971723i \(-0.424123\pi\)
0.236124 + 0.971723i \(0.424123\pi\)
\(8\) −8.64724 −3.05726
\(9\) 3.66013 1.22004
\(10\) 0 0
\(11\) −5.71181 −1.72217 −0.861087 0.508457i \(-0.830216\pi\)
−0.861087 + 0.508457i \(0.830216\pi\)
\(12\) 13.4675 3.88774
\(13\) −3.28322 −0.910601 −0.455300 0.890338i \(-0.650468\pi\)
−0.455300 + 0.890338i \(0.650468\pi\)
\(14\) −3.35693 −0.897178
\(15\) 0 0
\(16\) 12.7958 3.19894
\(17\) 5.29090 1.28323 0.641616 0.767026i \(-0.278264\pi\)
0.641616 + 0.767026i \(0.278264\pi\)
\(18\) −9.83378 −2.31784
\(19\) 6.14996 1.41090 0.705449 0.708760i \(-0.250745\pi\)
0.705449 + 0.708760i \(0.250745\pi\)
\(20\) 0 0
\(21\) 3.22448 0.703640
\(22\) 15.3461 3.27179
\(23\) 2.22338 0.463607 0.231804 0.972763i \(-0.425537\pi\)
0.231804 + 0.972763i \(0.425537\pi\)
\(24\) −22.3161 −4.55526
\(25\) 0 0
\(26\) 8.82111 1.72996
\(27\) 1.70362 0.327862
\(28\) 6.52026 1.23221
\(29\) −5.09304 −0.945753 −0.472877 0.881129i \(-0.656784\pi\)
−0.472877 + 0.881129i \(0.656784\pi\)
\(30\) 0 0
\(31\) −4.50984 −0.809991 −0.404996 0.914319i \(-0.632727\pi\)
−0.404996 + 0.914319i \(0.632727\pi\)
\(32\) −17.0842 −3.02010
\(33\) −14.7406 −2.56601
\(34\) −14.2152 −2.43789
\(35\) 0 0
\(36\) 19.1004 3.18340
\(37\) −4.88794 −0.803572 −0.401786 0.915734i \(-0.631610\pi\)
−0.401786 + 0.915734i \(0.631610\pi\)
\(38\) −16.5233 −2.68043
\(39\) −8.47308 −1.35678
\(40\) 0 0
\(41\) −4.77605 −0.745894 −0.372947 0.927853i \(-0.621653\pi\)
−0.372947 + 0.927853i \(0.621653\pi\)
\(42\) −8.66331 −1.33678
\(43\) 2.72100 0.414949 0.207474 0.978240i \(-0.433476\pi\)
0.207474 + 0.978240i \(0.433476\pi\)
\(44\) −29.8071 −4.49359
\(45\) 0 0
\(46\) −5.97362 −0.880762
\(47\) −2.52165 −0.367820 −0.183910 0.982943i \(-0.558876\pi\)
−0.183910 + 0.982943i \(0.558876\pi\)
\(48\) 33.0223 4.76636
\(49\) −5.43887 −0.776982
\(50\) 0 0
\(51\) 13.6544 1.91199
\(52\) −17.1335 −2.37599
\(53\) −7.67961 −1.05488 −0.527438 0.849594i \(-0.676847\pi\)
−0.527438 + 0.849594i \(0.676847\pi\)
\(54\) −4.57716 −0.622873
\(55\) 0 0
\(56\) −10.8043 −1.44378
\(57\) 15.8714 2.10221
\(58\) 13.6836 1.79675
\(59\) −8.39323 −1.09271 −0.546353 0.837555i \(-0.683984\pi\)
−0.546353 + 0.837555i \(0.683984\pi\)
\(60\) 0 0
\(61\) −12.2037 −1.56252 −0.781260 0.624205i \(-0.785423\pi\)
−0.781260 + 0.624205i \(0.785423\pi\)
\(62\) 12.1167 1.53882
\(63\) 4.57315 0.576163
\(64\) 20.3092 2.53865
\(65\) 0 0
\(66\) 39.6039 4.87491
\(67\) 15.2352 1.86128 0.930641 0.365934i \(-0.119250\pi\)
0.930641 + 0.365934i \(0.119250\pi\)
\(68\) 27.6106 3.34828
\(69\) 5.73793 0.690766
\(70\) 0 0
\(71\) −6.27039 −0.744159 −0.372079 0.928201i \(-0.621355\pi\)
−0.372079 + 0.928201i \(0.621355\pi\)
\(72\) −31.6500 −3.72999
\(73\) −5.27275 −0.617129 −0.308564 0.951203i \(-0.599849\pi\)
−0.308564 + 0.951203i \(0.599849\pi\)
\(74\) 13.1325 1.52663
\(75\) 0 0
\(76\) 32.0936 3.68139
\(77\) −7.13662 −0.813293
\(78\) 22.7648 2.57761
\(79\) 9.38460 1.05585 0.527925 0.849291i \(-0.322970\pi\)
0.527925 + 0.849291i \(0.322970\pi\)
\(80\) 0 0
\(81\) −6.58383 −0.731536
\(82\) 12.8319 1.41705
\(83\) −2.13252 −0.234074 −0.117037 0.993128i \(-0.537340\pi\)
−0.117037 + 0.993128i \(0.537340\pi\)
\(84\) 16.8270 1.83597
\(85\) 0 0
\(86\) −7.31059 −0.788321
\(87\) −13.1437 −1.40915
\(88\) 49.3913 5.26514
\(89\) 8.11125 0.859791 0.429895 0.902879i \(-0.358550\pi\)
0.429895 + 0.902879i \(0.358550\pi\)
\(90\) 0 0
\(91\) −4.10222 −0.430029
\(92\) 11.6027 1.20967
\(93\) −11.6386 −1.20687
\(94\) 6.77498 0.698786
\(95\) 0 0
\(96\) −44.0897 −4.49989
\(97\) −10.0464 −1.02006 −0.510031 0.860156i \(-0.670366\pi\)
−0.510031 + 0.860156i \(0.670366\pi\)
\(98\) 14.6128 1.47611
\(99\) −20.9060 −2.10113
\(100\) 0 0
\(101\) −16.4859 −1.64041 −0.820207 0.572067i \(-0.806142\pi\)
−0.820207 + 0.572067i \(0.806142\pi\)
\(102\) −36.6855 −3.63241
\(103\) 8.12695 0.800772 0.400386 0.916347i \(-0.368876\pi\)
0.400386 + 0.916347i \(0.368876\pi\)
\(104\) 28.3908 2.78394
\(105\) 0 0
\(106\) 20.6330 2.00406
\(107\) 15.5719 1.50539 0.752697 0.658368i \(-0.228753\pi\)
0.752697 + 0.658368i \(0.228753\pi\)
\(108\) 8.89035 0.855474
\(109\) −17.5584 −1.68179 −0.840893 0.541202i \(-0.817970\pi\)
−0.840893 + 0.541202i \(0.817970\pi\)
\(110\) 0 0
\(111\) −12.6144 −1.19731
\(112\) 15.9877 1.51069
\(113\) −4.82918 −0.454291 −0.227146 0.973861i \(-0.572939\pi\)
−0.227146 + 0.973861i \(0.572939\pi\)
\(114\) −42.6420 −3.99379
\(115\) 0 0
\(116\) −26.5780 −2.46771
\(117\) −12.0170 −1.11097
\(118\) 22.5503 2.07592
\(119\) 6.61072 0.606004
\(120\) 0 0
\(121\) 21.6247 1.96588
\(122\) 32.7880 2.96848
\(123\) −12.3257 −1.11137
\(124\) −23.5346 −2.11347
\(125\) 0 0
\(126\) −12.2868 −1.09460
\(127\) 12.2103 1.08349 0.541746 0.840542i \(-0.317763\pi\)
0.541746 + 0.840542i \(0.317763\pi\)
\(128\) −20.3967 −1.80283
\(129\) 7.02215 0.618266
\(130\) 0 0
\(131\) −10.1109 −0.883392 −0.441696 0.897165i \(-0.645623\pi\)
−0.441696 + 0.897165i \(0.645623\pi\)
\(132\) −76.9238 −6.69536
\(133\) 7.68407 0.666294
\(134\) −40.9330 −3.53607
\(135\) 0 0
\(136\) −45.7517 −3.92318
\(137\) −13.2155 −1.12908 −0.564539 0.825406i \(-0.690946\pi\)
−0.564539 + 0.825406i \(0.690946\pi\)
\(138\) −15.4163 −1.31232
\(139\) 15.9583 1.35357 0.676784 0.736182i \(-0.263373\pi\)
0.676784 + 0.736182i \(0.263373\pi\)
\(140\) 0 0
\(141\) −6.50768 −0.548045
\(142\) 16.8468 1.41375
\(143\) 18.7531 1.56821
\(144\) 46.8342 3.90285
\(145\) 0 0
\(146\) 14.1664 1.17242
\(147\) −14.0362 −1.15769
\(148\) −25.5077 −2.09672
\(149\) 4.94740 0.405307 0.202653 0.979251i \(-0.435044\pi\)
0.202653 + 0.979251i \(0.435044\pi\)
\(150\) 0 0
\(151\) −9.19121 −0.747970 −0.373985 0.927435i \(-0.622009\pi\)
−0.373985 + 0.927435i \(0.622009\pi\)
\(152\) −53.1802 −4.31348
\(153\) 19.3654 1.56560
\(154\) 19.1741 1.54510
\(155\) 0 0
\(156\) −44.2168 −3.54017
\(157\) 7.17472 0.572605 0.286302 0.958139i \(-0.407574\pi\)
0.286302 + 0.958139i \(0.407574\pi\)
\(158\) −25.2138 −2.00591
\(159\) −19.8190 −1.57174
\(160\) 0 0
\(161\) 2.77801 0.218937
\(162\) 17.6889 1.38977
\(163\) 14.9501 1.17098 0.585490 0.810680i \(-0.300902\pi\)
0.585490 + 0.810680i \(0.300902\pi\)
\(164\) −24.9238 −1.94622
\(165\) 0 0
\(166\) 5.72950 0.444695
\(167\) 4.27656 0.330930 0.165465 0.986216i \(-0.447088\pi\)
0.165465 + 0.986216i \(0.447088\pi\)
\(168\) −27.8829 −2.15121
\(169\) −2.22048 −0.170807
\(170\) 0 0
\(171\) 22.5097 1.72136
\(172\) 14.1996 1.08271
\(173\) −8.86646 −0.674105 −0.337052 0.941486i \(-0.609430\pi\)
−0.337052 + 0.941486i \(0.609430\pi\)
\(174\) 35.3136 2.67712
\(175\) 0 0
\(176\) −73.0869 −5.50913
\(177\) −21.6606 −1.62811
\(178\) −21.7927 −1.63343
\(179\) 19.6157 1.46615 0.733075 0.680148i \(-0.238084\pi\)
0.733075 + 0.680148i \(0.238084\pi\)
\(180\) 0 0
\(181\) 15.9326 1.18426 0.592132 0.805841i \(-0.298286\pi\)
0.592132 + 0.805841i \(0.298286\pi\)
\(182\) 11.0215 0.816971
\(183\) −31.4943 −2.32813
\(184\) −19.2261 −1.41737
\(185\) 0 0
\(186\) 31.2699 2.29282
\(187\) −30.2206 −2.20995
\(188\) −13.1592 −0.959735
\(189\) 2.12859 0.154832
\(190\) 0 0
\(191\) −13.9904 −1.01231 −0.506157 0.862442i \(-0.668934\pi\)
−0.506157 + 0.862442i \(0.668934\pi\)
\(192\) 52.4124 3.78254
\(193\) 5.85035 0.421117 0.210559 0.977581i \(-0.432472\pi\)
0.210559 + 0.977581i \(0.432472\pi\)
\(194\) 26.9920 1.93792
\(195\) 0 0
\(196\) −28.3828 −2.02734
\(197\) 0.760772 0.0542028 0.0271014 0.999633i \(-0.491372\pi\)
0.0271014 + 0.999633i \(0.491372\pi\)
\(198\) 56.1686 3.99173
\(199\) −13.2393 −0.938511 −0.469255 0.883063i \(-0.655478\pi\)
−0.469255 + 0.883063i \(0.655478\pi\)
\(200\) 0 0
\(201\) 39.3180 2.77328
\(202\) 44.2932 3.11646
\(203\) −6.36350 −0.446630
\(204\) 71.2553 4.98887
\(205\) 0 0
\(206\) −21.8349 −1.52131
\(207\) 8.13787 0.565621
\(208\) −42.0113 −2.91296
\(209\) −35.1274 −2.42981
\(210\) 0 0
\(211\) 10.5091 0.723480 0.361740 0.932279i \(-0.382183\pi\)
0.361740 + 0.932279i \(0.382183\pi\)
\(212\) −40.0761 −2.75244
\(213\) −16.1821 −1.10878
\(214\) −41.8375 −2.85995
\(215\) 0 0
\(216\) −14.7316 −1.00236
\(217\) −5.63482 −0.382516
\(218\) 47.1745 3.19506
\(219\) −13.6075 −0.919510
\(220\) 0 0
\(221\) −17.3712 −1.16851
\(222\) 33.8915 2.27465
\(223\) −11.7804 −0.788876 −0.394438 0.918923i \(-0.629061\pi\)
−0.394438 + 0.918923i \(0.629061\pi\)
\(224\) −21.3459 −1.42623
\(225\) 0 0
\(226\) 12.9747 0.863063
\(227\) −9.33932 −0.619873 −0.309936 0.950757i \(-0.600308\pi\)
−0.309936 + 0.950757i \(0.600308\pi\)
\(228\) 82.8247 5.48520
\(229\) −16.5911 −1.09637 −0.548186 0.836357i \(-0.684681\pi\)
−0.548186 + 0.836357i \(0.684681\pi\)
\(230\) 0 0
\(231\) −18.4176 −1.21179
\(232\) 44.0407 2.89141
\(233\) 2.57802 0.168892 0.0844460 0.996428i \(-0.473088\pi\)
0.0844460 + 0.996428i \(0.473088\pi\)
\(234\) 32.2864 2.11063
\(235\) 0 0
\(236\) −43.8001 −2.85114
\(237\) 24.2190 1.57320
\(238\) −17.7612 −1.15129
\(239\) −26.0214 −1.68318 −0.841592 0.540113i \(-0.818381\pi\)
−0.841592 + 0.540113i \(0.818381\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −58.0998 −3.73479
\(243\) −22.1019 −1.41784
\(244\) −63.6849 −4.07701
\(245\) 0 0
\(246\) 33.1157 2.11138
\(247\) −20.1917 −1.28477
\(248\) 38.9977 2.47635
\(249\) −5.50344 −0.348767
\(250\) 0 0
\(251\) 27.0049 1.70453 0.852267 0.523107i \(-0.175227\pi\)
0.852267 + 0.523107i \(0.175227\pi\)
\(252\) 23.8650 1.50335
\(253\) −12.6995 −0.798413
\(254\) −32.8059 −2.05842
\(255\) 0 0
\(256\) 14.1821 0.886381
\(257\) −27.5253 −1.71698 −0.858490 0.512830i \(-0.828597\pi\)
−0.858490 + 0.512830i \(0.828597\pi\)
\(258\) −18.8666 −1.17458
\(259\) −6.10723 −0.379485
\(260\) 0 0
\(261\) −18.6412 −1.15386
\(262\) 27.1652 1.67827
\(263\) 7.57437 0.467056 0.233528 0.972350i \(-0.424973\pi\)
0.233528 + 0.972350i \(0.424973\pi\)
\(264\) 127.465 7.84495
\(265\) 0 0
\(266\) −20.6450 −1.26583
\(267\) 20.9329 1.28107
\(268\) 79.5052 4.85655
\(269\) −8.18678 −0.499157 −0.249578 0.968355i \(-0.580292\pi\)
−0.249578 + 0.968355i \(0.580292\pi\)
\(270\) 0 0
\(271\) −3.63408 −0.220755 −0.110377 0.993890i \(-0.535206\pi\)
−0.110377 + 0.993890i \(0.535206\pi\)
\(272\) 67.7012 4.10499
\(273\) −10.5867 −0.640735
\(274\) 35.5065 2.14503
\(275\) 0 0
\(276\) 29.9434 1.80238
\(277\) −2.42885 −0.145935 −0.0729677 0.997334i \(-0.523247\pi\)
−0.0729677 + 0.997334i \(0.523247\pi\)
\(278\) −42.8757 −2.57151
\(279\) −16.5066 −0.988225
\(280\) 0 0
\(281\) −16.3717 −0.976655 −0.488328 0.872660i \(-0.662393\pi\)
−0.488328 + 0.872660i \(0.662393\pi\)
\(282\) 17.4844 1.04118
\(283\) 6.08266 0.361576 0.180788 0.983522i \(-0.442135\pi\)
0.180788 + 0.983522i \(0.442135\pi\)
\(284\) −32.7221 −1.94170
\(285\) 0 0
\(286\) −50.3845 −2.97930
\(287\) −5.96744 −0.352247
\(288\) −62.5306 −3.68465
\(289\) 10.9937 0.646686
\(290\) 0 0
\(291\) −25.9271 −1.51987
\(292\) −27.5159 −1.61024
\(293\) 10.4470 0.610322 0.305161 0.952301i \(-0.401290\pi\)
0.305161 + 0.952301i \(0.401290\pi\)
\(294\) 37.7115 2.19938
\(295\) 0 0
\(296\) 42.2671 2.45673
\(297\) −9.73075 −0.564635
\(298\) −13.2923 −0.770003
\(299\) −7.29985 −0.422161
\(300\) 0 0
\(301\) 3.39976 0.195959
\(302\) 24.6943 1.42100
\(303\) −42.5457 −2.44418
\(304\) 78.6935 4.51338
\(305\) 0 0
\(306\) −52.0296 −2.97433
\(307\) 17.7832 1.01494 0.507470 0.861669i \(-0.330581\pi\)
0.507470 + 0.861669i \(0.330581\pi\)
\(308\) −37.2425 −2.12209
\(309\) 20.9734 1.19314
\(310\) 0 0
\(311\) −5.30634 −0.300895 −0.150447 0.988618i \(-0.548071\pi\)
−0.150447 + 0.988618i \(0.548071\pi\)
\(312\) 73.2687 4.14802
\(313\) −25.9853 −1.46878 −0.734389 0.678729i \(-0.762531\pi\)
−0.734389 + 0.678729i \(0.762531\pi\)
\(314\) −19.2765 −1.08784
\(315\) 0 0
\(316\) 48.9735 2.75498
\(317\) 0.511802 0.0287457 0.0143728 0.999897i \(-0.495425\pi\)
0.0143728 + 0.999897i \(0.495425\pi\)
\(318\) 53.2481 2.98601
\(319\) 29.0904 1.62875
\(320\) 0 0
\(321\) 40.1868 2.24301
\(322\) −7.46374 −0.415938
\(323\) 32.5389 1.81051
\(324\) −34.3577 −1.90876
\(325\) 0 0
\(326\) −40.1668 −2.22463
\(327\) −45.3133 −2.50583
\(328\) 41.2997 2.28039
\(329\) −3.15067 −0.173702
\(330\) 0 0
\(331\) −4.37953 −0.240721 −0.120360 0.992730i \(-0.538405\pi\)
−0.120360 + 0.992730i \(0.538405\pi\)
\(332\) −11.1286 −0.610759
\(333\) −17.8905 −0.980393
\(334\) −11.4899 −0.628702
\(335\) 0 0
\(336\) 41.2597 2.25090
\(337\) −9.09028 −0.495179 −0.247589 0.968865i \(-0.579638\pi\)
−0.247589 + 0.968865i \(0.579638\pi\)
\(338\) 5.96584 0.324499
\(339\) −12.4628 −0.676885
\(340\) 0 0
\(341\) 25.7593 1.39495
\(342\) −60.4774 −3.27024
\(343\) −15.5418 −0.839176
\(344\) −23.5291 −1.26861
\(345\) 0 0
\(346\) 23.8218 1.28067
\(347\) 0.771121 0.0413959 0.0206980 0.999786i \(-0.493411\pi\)
0.0206980 + 0.999786i \(0.493411\pi\)
\(348\) −68.5905 −3.67684
\(349\) 30.0795 1.61012 0.805060 0.593194i \(-0.202133\pi\)
0.805060 + 0.593194i \(0.202133\pi\)
\(350\) 0 0
\(351\) −5.59336 −0.298551
\(352\) 97.5819 5.20113
\(353\) 27.7365 1.47627 0.738133 0.674655i \(-0.235707\pi\)
0.738133 + 0.674655i \(0.235707\pi\)
\(354\) 58.1961 3.09309
\(355\) 0 0
\(356\) 42.3286 2.24341
\(357\) 17.0604 0.902934
\(358\) −52.7022 −2.78540
\(359\) 6.19082 0.326739 0.163370 0.986565i \(-0.447764\pi\)
0.163370 + 0.986565i \(0.447764\pi\)
\(360\) 0 0
\(361\) 18.8221 0.990635
\(362\) −42.8067 −2.24987
\(363\) 55.8075 2.92913
\(364\) −21.4074 −1.12205
\(365\) 0 0
\(366\) 84.6166 4.42298
\(367\) −14.6701 −0.765772 −0.382886 0.923796i \(-0.625070\pi\)
−0.382886 + 0.923796i \(0.625070\pi\)
\(368\) 28.4499 1.48305
\(369\) −17.4810 −0.910024
\(370\) 0 0
\(371\) −9.59529 −0.498163
\(372\) −60.7363 −3.14903
\(373\) −7.45878 −0.386201 −0.193100 0.981179i \(-0.561854\pi\)
−0.193100 + 0.981179i \(0.561854\pi\)
\(374\) 81.1946 4.19847
\(375\) 0 0
\(376\) 21.8053 1.12452
\(377\) 16.7216 0.861204
\(378\) −5.71894 −0.294150
\(379\) −32.3225 −1.66030 −0.830148 0.557543i \(-0.811744\pi\)
−0.830148 + 0.557543i \(0.811744\pi\)
\(380\) 0 0
\(381\) 31.5115 1.61438
\(382\) 37.5885 1.92320
\(383\) 4.30576 0.220014 0.110007 0.993931i \(-0.464913\pi\)
0.110007 + 0.993931i \(0.464913\pi\)
\(384\) −52.6383 −2.68619
\(385\) 0 0
\(386\) −15.7183 −0.800040
\(387\) 9.95923 0.506256
\(388\) −52.4274 −2.66160
\(389\) 16.1415 0.818404 0.409202 0.912444i \(-0.365807\pi\)
0.409202 + 0.912444i \(0.365807\pi\)
\(390\) 0 0
\(391\) 11.7637 0.594916
\(392\) 47.0312 2.37544
\(393\) −26.0934 −1.31624
\(394\) −2.04399 −0.102975
\(395\) 0 0
\(396\) −109.098 −5.48237
\(397\) −31.3345 −1.57263 −0.786316 0.617825i \(-0.788014\pi\)
−0.786316 + 0.617825i \(0.788014\pi\)
\(398\) 35.5704 1.78299
\(399\) 19.8305 0.992765
\(400\) 0 0
\(401\) −27.1821 −1.35741 −0.678705 0.734411i \(-0.737458\pi\)
−0.678705 + 0.734411i \(0.737458\pi\)
\(402\) −105.637 −5.26868
\(403\) 14.8068 0.737578
\(404\) −86.0320 −4.28025
\(405\) 0 0
\(406\) 17.0970 0.848509
\(407\) 27.9189 1.38389
\(408\) −118.072 −5.84546
\(409\) 36.8301 1.82113 0.910566 0.413363i \(-0.135646\pi\)
0.910566 + 0.413363i \(0.135646\pi\)
\(410\) 0 0
\(411\) −34.1056 −1.68230
\(412\) 42.4105 2.08942
\(413\) −10.4869 −0.516028
\(414\) −21.8642 −1.07457
\(415\) 0 0
\(416\) 56.0913 2.75010
\(417\) 41.1840 2.01679
\(418\) 94.3778 4.61617
\(419\) −13.5764 −0.663249 −0.331624 0.943411i \(-0.607597\pi\)
−0.331624 + 0.943411i \(0.607597\pi\)
\(420\) 0 0
\(421\) −12.1607 −0.592678 −0.296339 0.955083i \(-0.595766\pi\)
−0.296339 + 0.955083i \(0.595766\pi\)
\(422\) −28.2352 −1.37447
\(423\) −9.22957 −0.448757
\(424\) 66.4074 3.22503
\(425\) 0 0
\(426\) 43.4770 2.10647
\(427\) −15.2479 −0.737897
\(428\) 81.2620 3.92795
\(429\) 48.3966 2.33661
\(430\) 0 0
\(431\) −15.1822 −0.731301 −0.365650 0.930752i \(-0.619153\pi\)
−0.365650 + 0.930752i \(0.619153\pi\)
\(432\) 21.7991 1.04881
\(433\) −28.7849 −1.38331 −0.691657 0.722226i \(-0.743119\pi\)
−0.691657 + 0.722226i \(0.743119\pi\)
\(434\) 15.1392 0.726706
\(435\) 0 0
\(436\) −91.6283 −4.38820
\(437\) 13.6737 0.654103
\(438\) 36.5597 1.74689
\(439\) 39.1528 1.86866 0.934331 0.356406i \(-0.115998\pi\)
0.934331 + 0.356406i \(0.115998\pi\)
\(440\) 0 0
\(441\) −19.9070 −0.947953
\(442\) 46.6716 2.21994
\(443\) −26.4163 −1.25508 −0.627538 0.778586i \(-0.715937\pi\)
−0.627538 + 0.778586i \(0.715937\pi\)
\(444\) −65.8283 −3.12407
\(445\) 0 0
\(446\) 31.6508 1.49871
\(447\) 12.7679 0.603899
\(448\) 25.3753 1.19887
\(449\) −9.28281 −0.438083 −0.219041 0.975716i \(-0.570293\pi\)
−0.219041 + 0.975716i \(0.570293\pi\)
\(450\) 0 0
\(451\) 27.2799 1.28456
\(452\) −25.2011 −1.18536
\(453\) −23.7200 −1.11446
\(454\) 25.0922 1.17764
\(455\) 0 0
\(456\) −137.243 −6.42701
\(457\) 8.44046 0.394828 0.197414 0.980320i \(-0.436746\pi\)
0.197414 + 0.980320i \(0.436746\pi\)
\(458\) 44.5758 2.08289
\(459\) 9.01369 0.420723
\(460\) 0 0
\(461\) −2.99442 −0.139464 −0.0697319 0.997566i \(-0.522214\pi\)
−0.0697319 + 0.997566i \(0.522214\pi\)
\(462\) 49.4832 2.30216
\(463\) 10.3910 0.482910 0.241455 0.970412i \(-0.422375\pi\)
0.241455 + 0.970412i \(0.422375\pi\)
\(464\) −65.1693 −3.02541
\(465\) 0 0
\(466\) −6.92645 −0.320861
\(467\) 23.5923 1.09172 0.545861 0.837876i \(-0.316203\pi\)
0.545861 + 0.837876i \(0.316203\pi\)
\(468\) −62.7108 −2.89881
\(469\) 19.0357 0.878986
\(470\) 0 0
\(471\) 18.5160 0.853170
\(472\) 72.5782 3.34068
\(473\) −15.5418 −0.714614
\(474\) −65.0700 −2.98876
\(475\) 0 0
\(476\) 34.4981 1.58122
\(477\) −28.1084 −1.28700
\(478\) 69.9124 3.19772
\(479\) −5.49906 −0.251259 −0.125629 0.992077i \(-0.540095\pi\)
−0.125629 + 0.992077i \(0.540095\pi\)
\(480\) 0 0
\(481\) 16.0482 0.731733
\(482\) −2.68673 −0.122377
\(483\) 7.16926 0.326213
\(484\) 112.849 5.12949
\(485\) 0 0
\(486\) 59.3818 2.69361
\(487\) −9.89752 −0.448499 −0.224250 0.974532i \(-0.571993\pi\)
−0.224250 + 0.974532i \(0.571993\pi\)
\(488\) 105.528 4.77703
\(489\) 38.5820 1.74474
\(490\) 0 0
\(491\) −22.6134 −1.02053 −0.510265 0.860017i \(-0.670453\pi\)
−0.510265 + 0.860017i \(0.670453\pi\)
\(492\) −64.3215 −2.89984
\(493\) −26.9468 −1.21362
\(494\) 54.2495 2.44080
\(495\) 0 0
\(496\) −57.7068 −2.59111
\(497\) −7.83454 −0.351427
\(498\) 14.7863 0.662588
\(499\) −25.9120 −1.15998 −0.579990 0.814624i \(-0.696944\pi\)
−0.579990 + 0.814624i \(0.696944\pi\)
\(500\) 0 0
\(501\) 11.0366 0.493080
\(502\) −72.5548 −3.23828
\(503\) 1.28878 0.0574637 0.0287319 0.999587i \(-0.490853\pi\)
0.0287319 + 0.999587i \(0.490853\pi\)
\(504\) −39.5451 −1.76148
\(505\) 0 0
\(506\) 34.1202 1.51683
\(507\) −5.73046 −0.254499
\(508\) 63.7197 2.82710
\(509\) 8.97659 0.397880 0.198940 0.980012i \(-0.436250\pi\)
0.198940 + 0.980012i \(0.436250\pi\)
\(510\) 0 0
\(511\) −6.58804 −0.291438
\(512\) 2.69004 0.118884
\(513\) 10.4772 0.462580
\(514\) 73.9530 3.26192
\(515\) 0 0
\(516\) 36.6451 1.61321
\(517\) 14.4032 0.633451
\(518\) 16.4085 0.720947
\(519\) −22.8819 −1.00440
\(520\) 0 0
\(521\) −8.94427 −0.391856 −0.195928 0.980618i \(-0.562772\pi\)
−0.195928 + 0.980618i \(0.562772\pi\)
\(522\) 50.0838 2.19211
\(523\) −29.1659 −1.27534 −0.637669 0.770311i \(-0.720101\pi\)
−0.637669 + 0.770311i \(0.720101\pi\)
\(524\) −52.7636 −2.30499
\(525\) 0 0
\(526\) −20.3503 −0.887313
\(527\) −23.8611 −1.03941
\(528\) −188.617 −8.20851
\(529\) −18.0566 −0.785068
\(530\) 0 0
\(531\) −30.7203 −1.33315
\(532\) 40.0994 1.73853
\(533\) 15.6808 0.679212
\(534\) −56.2410 −2.43378
\(535\) 0 0
\(536\) −131.743 −5.69042
\(537\) 50.6228 2.18454
\(538\) 21.9956 0.948300
\(539\) 31.0658 1.33810
\(540\) 0 0
\(541\) 33.3854 1.43535 0.717676 0.696378i \(-0.245206\pi\)
0.717676 + 0.696378i \(0.245206\pi\)
\(542\) 9.76379 0.419391
\(543\) 41.1177 1.76453
\(544\) −90.3911 −3.87549
\(545\) 0 0
\(546\) 28.4435 1.21727
\(547\) −2.45635 −0.105026 −0.0525129 0.998620i \(-0.516723\pi\)
−0.0525129 + 0.998620i \(0.516723\pi\)
\(548\) −68.9652 −2.94605
\(549\) −44.6671 −1.90634
\(550\) 0 0
\(551\) −31.3220 −1.33436
\(552\) −49.6173 −2.11185
\(553\) 11.7256 0.498623
\(554\) 6.52565 0.277248
\(555\) 0 0
\(556\) 83.2785 3.53180
\(557\) −24.1979 −1.02530 −0.512649 0.858598i \(-0.671336\pi\)
−0.512649 + 0.858598i \(0.671336\pi\)
\(558\) 44.3488 1.87743
\(559\) −8.93364 −0.377853
\(560\) 0 0
\(561\) −77.9911 −3.29279
\(562\) 43.9864 1.85545
\(563\) 16.2348 0.684214 0.342107 0.939661i \(-0.388859\pi\)
0.342107 + 0.939661i \(0.388859\pi\)
\(564\) −33.9603 −1.42999
\(565\) 0 0
\(566\) −16.3424 −0.686924
\(567\) −8.22616 −0.345466
\(568\) 54.2216 2.27509
\(569\) 21.7141 0.910303 0.455152 0.890414i \(-0.349585\pi\)
0.455152 + 0.890414i \(0.349585\pi\)
\(570\) 0 0
\(571\) −12.1684 −0.509232 −0.254616 0.967042i \(-0.581949\pi\)
−0.254616 + 0.967042i \(0.581949\pi\)
\(572\) 97.8631 4.09186
\(573\) −36.1055 −1.50833
\(574\) 16.0329 0.669199
\(575\) 0 0
\(576\) 74.3343 3.09726
\(577\) −37.8843 −1.57714 −0.788572 0.614942i \(-0.789179\pi\)
−0.788572 + 0.614942i \(0.789179\pi\)
\(578\) −29.5370 −1.22858
\(579\) 15.0981 0.627457
\(580\) 0 0
\(581\) −2.66448 −0.110541
\(582\) 69.6590 2.88746
\(583\) 43.8644 1.81668
\(584\) 45.5947 1.88672
\(585\) 0 0
\(586\) −28.0683 −1.15949
\(587\) 1.81908 0.0750813 0.0375406 0.999295i \(-0.488048\pi\)
0.0375406 + 0.999295i \(0.488048\pi\)
\(588\) −73.2481 −3.02070
\(589\) −27.7354 −1.14282
\(590\) 0 0
\(591\) 1.96334 0.0807612
\(592\) −62.5449 −2.57058
\(593\) 43.3283 1.77928 0.889640 0.456663i \(-0.150955\pi\)
0.889640 + 0.456663i \(0.150955\pi\)
\(594\) 26.1439 1.07270
\(595\) 0 0
\(596\) 25.8180 1.05755
\(597\) −34.1670 −1.39836
\(598\) 19.6127 0.802023
\(599\) −17.5241 −0.716017 −0.358008 0.933718i \(-0.616544\pi\)
−0.358008 + 0.933718i \(0.616544\pi\)
\(600\) 0 0
\(601\) 25.6494 1.04626 0.523129 0.852253i \(-0.324764\pi\)
0.523129 + 0.852253i \(0.324764\pi\)
\(602\) −9.13421 −0.372283
\(603\) 55.7630 2.27085
\(604\) −47.9644 −1.95164
\(605\) 0 0
\(606\) 114.309 4.64347
\(607\) 7.39927 0.300327 0.150163 0.988661i \(-0.452020\pi\)
0.150163 + 0.988661i \(0.452020\pi\)
\(608\) −105.068 −4.26105
\(609\) −16.4224 −0.665470
\(610\) 0 0
\(611\) 8.27912 0.334937
\(612\) 101.058 4.08505
\(613\) −22.5538 −0.910938 −0.455469 0.890252i \(-0.650528\pi\)
−0.455469 + 0.890252i \(0.650528\pi\)
\(614\) −47.7786 −1.92819
\(615\) 0 0
\(616\) 61.7120 2.48645
\(617\) 27.0999 1.09100 0.545500 0.838111i \(-0.316340\pi\)
0.545500 + 0.838111i \(0.316340\pi\)
\(618\) −56.3498 −2.26672
\(619\) −23.3911 −0.940168 −0.470084 0.882622i \(-0.655776\pi\)
−0.470084 + 0.882622i \(0.655776\pi\)
\(620\) 0 0
\(621\) 3.78780 0.151999
\(622\) 14.2567 0.571641
\(623\) 10.1346 0.406034
\(624\) −108.419 −4.34025
\(625\) 0 0
\(626\) 69.8155 2.79039
\(627\) −90.6541 −3.62038
\(628\) 37.4413 1.49407
\(629\) −25.8616 −1.03117
\(630\) 0 0
\(631\) −14.0498 −0.559314 −0.279657 0.960100i \(-0.590221\pi\)
−0.279657 + 0.960100i \(0.590221\pi\)
\(632\) −81.1508 −3.22801
\(633\) 27.1212 1.07797
\(634\) −1.37507 −0.0546111
\(635\) 0 0
\(636\) −103.425 −4.10108
\(637\) 17.8570 0.707520
\(638\) −78.1581 −3.09431
\(639\) −22.9505 −0.907906
\(640\) 0 0
\(641\) 15.4541 0.610400 0.305200 0.952288i \(-0.401277\pi\)
0.305200 + 0.952288i \(0.401277\pi\)
\(642\) −107.971 −4.26127
\(643\) −41.9982 −1.65625 −0.828124 0.560545i \(-0.810592\pi\)
−0.828124 + 0.560545i \(0.810592\pi\)
\(644\) 14.4970 0.571263
\(645\) 0 0
\(646\) −87.4231 −3.43961
\(647\) 11.2851 0.443664 0.221832 0.975085i \(-0.428796\pi\)
0.221832 + 0.975085i \(0.428796\pi\)
\(648\) 56.9319 2.23650
\(649\) 47.9405 1.88183
\(650\) 0 0
\(651\) −14.5419 −0.569942
\(652\) 78.0170 3.05538
\(653\) −27.4812 −1.07542 −0.537711 0.843129i \(-0.680711\pi\)
−0.537711 + 0.843129i \(0.680711\pi\)
\(654\) 121.744 4.76058
\(655\) 0 0
\(656\) −61.1132 −2.38607
\(657\) −19.2990 −0.752924
\(658\) 8.46500 0.330000
\(659\) 40.0611 1.56056 0.780279 0.625431i \(-0.215077\pi\)
0.780279 + 0.625431i \(0.215077\pi\)
\(660\) 0 0
\(661\) 49.2805 1.91679 0.958394 0.285449i \(-0.0921426\pi\)
0.958394 + 0.285449i \(0.0921426\pi\)
\(662\) 11.7666 0.457322
\(663\) −44.8302 −1.74106
\(664\) 18.4404 0.715627
\(665\) 0 0
\(666\) 48.0669 1.86255
\(667\) −11.3238 −0.438458
\(668\) 22.3172 0.863480
\(669\) −30.4020 −1.17541
\(670\) 0 0
\(671\) 69.7050 2.69093
\(672\) −55.0879 −2.12506
\(673\) −4.32553 −0.166737 −0.0833685 0.996519i \(-0.526568\pi\)
−0.0833685 + 0.996519i \(0.526568\pi\)
\(674\) 24.4231 0.940742
\(675\) 0 0
\(676\) −11.5876 −0.445677
\(677\) −38.0959 −1.46415 −0.732073 0.681226i \(-0.761447\pi\)
−0.732073 + 0.681226i \(0.761447\pi\)
\(678\) 33.4841 1.28595
\(679\) −12.5525 −0.481722
\(680\) 0 0
\(681\) −24.1022 −0.923599
\(682\) −69.2083 −2.65012
\(683\) −35.9542 −1.37575 −0.687874 0.725830i \(-0.741456\pi\)
−0.687874 + 0.725830i \(0.741456\pi\)
\(684\) 117.467 4.49146
\(685\) 0 0
\(686\) 41.7564 1.59427
\(687\) −42.8171 −1.63357
\(688\) 34.8173 1.32740
\(689\) 25.2138 0.960570
\(690\) 0 0
\(691\) 20.7606 0.789772 0.394886 0.918730i \(-0.370784\pi\)
0.394886 + 0.918730i \(0.370784\pi\)
\(692\) −46.2697 −1.75891
\(693\) −26.1210 −0.992253
\(694\) −2.07179 −0.0786441
\(695\) 0 0
\(696\) 113.657 4.30815
\(697\) −25.2696 −0.957156
\(698\) −80.8155 −3.05891
\(699\) 6.65317 0.251646
\(700\) 0 0
\(701\) 3.55693 0.134343 0.0671716 0.997741i \(-0.478602\pi\)
0.0671716 + 0.997741i \(0.478602\pi\)
\(702\) 15.0278 0.567189
\(703\) −30.0606 −1.13376
\(704\) −116.002 −4.37199
\(705\) 0 0
\(706\) −74.5205 −2.80462
\(707\) −20.5984 −0.774681
\(708\) −113.036 −4.24815
\(709\) 19.1731 0.720060 0.360030 0.932941i \(-0.382766\pi\)
0.360030 + 0.932941i \(0.382766\pi\)
\(710\) 0 0
\(711\) 34.3489 1.28818
\(712\) −70.1399 −2.62860
\(713\) −10.0271 −0.375518
\(714\) −45.8367 −1.71540
\(715\) 0 0
\(716\) 102.365 3.82555
\(717\) −67.1541 −2.50791
\(718\) −16.6330 −0.620740
\(719\) −17.5165 −0.653256 −0.326628 0.945153i \(-0.605912\pi\)
−0.326628 + 0.945153i \(0.605912\pi\)
\(720\) 0 0
\(721\) 10.1542 0.378163
\(722\) −50.5697 −1.88201
\(723\) 2.58072 0.0959781
\(724\) 83.1445 3.09004
\(725\) 0 0
\(726\) −149.939 −5.56477
\(727\) −28.7088 −1.06475 −0.532376 0.846508i \(-0.678701\pi\)
−0.532376 + 0.846508i \(0.678701\pi\)
\(728\) 35.4728 1.31471
\(729\) −37.2874 −1.38101
\(730\) 0 0
\(731\) 14.3966 0.532476
\(732\) −164.353 −6.07467
\(733\) −42.4695 −1.56865 −0.784323 0.620352i \(-0.786990\pi\)
−0.784323 + 0.620352i \(0.786990\pi\)
\(734\) 39.4145 1.45482
\(735\) 0 0
\(736\) −37.9848 −1.40014
\(737\) −87.0208 −3.20545
\(738\) 46.9666 1.72887
\(739\) −38.8874 −1.43050 −0.715249 0.698870i \(-0.753687\pi\)
−0.715249 + 0.698870i \(0.753687\pi\)
\(740\) 0 0
\(741\) −52.1091 −1.91428
\(742\) 25.7799 0.946411
\(743\) 1.03128 0.0378339 0.0189170 0.999821i \(-0.493978\pi\)
0.0189170 + 0.999821i \(0.493978\pi\)
\(744\) 100.642 3.68972
\(745\) 0 0
\(746\) 20.0397 0.733706
\(747\) −7.80531 −0.285581
\(748\) −157.706 −5.76632
\(749\) 19.4563 0.710918
\(750\) 0 0
\(751\) 14.0086 0.511181 0.255590 0.966785i \(-0.417730\pi\)
0.255590 + 0.966785i \(0.417730\pi\)
\(752\) −32.2664 −1.17664
\(753\) 69.6922 2.53972
\(754\) −44.9262 −1.63612
\(755\) 0 0
\(756\) 11.1080 0.403996
\(757\) 38.1157 1.38534 0.692670 0.721255i \(-0.256434\pi\)
0.692670 + 0.721255i \(0.256434\pi\)
\(758\) 86.8418 3.15424
\(759\) −32.7740 −1.18962
\(760\) 0 0
\(761\) 3.59136 0.130187 0.0650933 0.997879i \(-0.479266\pi\)
0.0650933 + 0.997879i \(0.479266\pi\)
\(762\) −84.6628 −3.06701
\(763\) −21.9383 −0.794219
\(764\) −73.0092 −2.64138
\(765\) 0 0
\(766\) −11.5684 −0.417984
\(767\) 27.5568 0.995018
\(768\) 36.6001 1.32069
\(769\) −39.3482 −1.41893 −0.709466 0.704740i \(-0.751064\pi\)
−0.709466 + 0.704740i \(0.751064\pi\)
\(770\) 0 0
\(771\) −71.0352 −2.55827
\(772\) 30.5301 1.09880
\(773\) 25.6925 0.924094 0.462047 0.886856i \(-0.347115\pi\)
0.462047 + 0.886856i \(0.347115\pi\)
\(774\) −26.7577 −0.961786
\(775\) 0 0
\(776\) 86.8740 3.11859
\(777\) −15.7611 −0.565425
\(778\) −43.3677 −1.55481
\(779\) −29.3726 −1.05238
\(780\) 0 0
\(781\) 35.8153 1.28157
\(782\) −31.6059 −1.13022
\(783\) −8.67660 −0.310077
\(784\) −69.5945 −2.48552
\(785\) 0 0
\(786\) 70.1058 2.50059
\(787\) 3.98083 0.141901 0.0709506 0.997480i \(-0.477397\pi\)
0.0709506 + 0.997480i \(0.477397\pi\)
\(788\) 3.97009 0.141429
\(789\) 19.5473 0.695904
\(790\) 0 0
\(791\) −6.03382 −0.214538
\(792\) 180.779 6.42370
\(793\) 40.0673 1.42283
\(794\) 84.1871 2.98769
\(795\) 0 0
\(796\) −69.0894 −2.44881
\(797\) 39.8549 1.41173 0.705866 0.708345i \(-0.250558\pi\)
0.705866 + 0.708345i \(0.250558\pi\)
\(798\) −53.2791 −1.88606
\(799\) −13.3418 −0.471999
\(800\) 0 0
\(801\) 29.6882 1.04898
\(802\) 73.0309 2.57881
\(803\) 30.1169 1.06280
\(804\) 205.181 7.23617
\(805\) 0 0
\(806\) −39.7818 −1.40125
\(807\) −21.1278 −0.743734
\(808\) 142.558 5.01517
\(809\) 14.3004 0.502774 0.251387 0.967887i \(-0.419113\pi\)
0.251387 + 0.967887i \(0.419113\pi\)
\(810\) 0 0
\(811\) 52.5174 1.84414 0.922068 0.387028i \(-0.126498\pi\)
0.922068 + 0.387028i \(0.126498\pi\)
\(812\) −33.2079 −1.16537
\(813\) −9.37857 −0.328921
\(814\) −75.0106 −2.62912
\(815\) 0 0
\(816\) 174.718 6.11635
\(817\) 16.7341 0.585451
\(818\) −98.9525 −3.45979
\(819\) −15.0147 −0.524655
\(820\) 0 0
\(821\) −18.4325 −0.643300 −0.321650 0.946859i \(-0.604237\pi\)
−0.321650 + 0.946859i \(0.604237\pi\)
\(822\) 91.6324 3.19605
\(823\) −38.9994 −1.35944 −0.679718 0.733474i \(-0.737898\pi\)
−0.679718 + 0.733474i \(0.737898\pi\)
\(824\) −70.2757 −2.44817
\(825\) 0 0
\(826\) 28.1755 0.980351
\(827\) 18.2963 0.636226 0.318113 0.948053i \(-0.396951\pi\)
0.318113 + 0.948053i \(0.396951\pi\)
\(828\) 42.4675 1.47585
\(829\) 2.36565 0.0821624 0.0410812 0.999156i \(-0.486920\pi\)
0.0410812 + 0.999156i \(0.486920\pi\)
\(830\) 0 0
\(831\) −6.26818 −0.217441
\(832\) −66.6795 −2.31169
\(833\) −28.7766 −0.997049
\(834\) −110.650 −3.83150
\(835\) 0 0
\(836\) −183.312 −6.33999
\(837\) −7.68306 −0.265565
\(838\) 36.4760 1.26004
\(839\) −19.8535 −0.685420 −0.342710 0.939441i \(-0.611345\pi\)
−0.342710 + 0.939441i \(0.611345\pi\)
\(840\) 0 0
\(841\) −3.06096 −0.105550
\(842\) 32.6726 1.12597
\(843\) −42.2509 −1.45520
\(844\) 54.8420 1.88774
\(845\) 0 0
\(846\) 24.7973 0.852550
\(847\) 27.0190 0.928385
\(848\) −98.2665 −3.37448
\(849\) 15.6977 0.538742
\(850\) 0 0
\(851\) −10.8677 −0.372542
\(852\) −84.4466 −2.89309
\(853\) 17.5358 0.600415 0.300208 0.953874i \(-0.402944\pi\)
0.300208 + 0.953874i \(0.402944\pi\)
\(854\) 40.9669 1.40186
\(855\) 0 0
\(856\) −134.654 −4.60238
\(857\) −42.6899 −1.45826 −0.729130 0.684375i \(-0.760075\pi\)
−0.729130 + 0.684375i \(0.760075\pi\)
\(858\) −130.028 −4.43910
\(859\) −19.1579 −0.653659 −0.326830 0.945083i \(-0.605980\pi\)
−0.326830 + 0.945083i \(0.605980\pi\)
\(860\) 0 0
\(861\) −15.4003 −0.524841
\(862\) 40.7904 1.38933
\(863\) 12.8156 0.436248 0.218124 0.975921i \(-0.430006\pi\)
0.218124 + 0.975921i \(0.430006\pi\)
\(864\) −29.1051 −0.990175
\(865\) 0 0
\(866\) 77.3372 2.62803
\(867\) 28.3716 0.963550
\(868\) −29.4053 −0.998082
\(869\) −53.6030 −1.81836
\(870\) 0 0
\(871\) −50.0206 −1.69488
\(872\) 151.831 5.14166
\(873\) −36.7713 −1.24452
\(874\) −36.7376 −1.24267
\(875\) 0 0
\(876\) −71.0108 −2.39923
\(877\) 29.6224 1.00028 0.500139 0.865945i \(-0.333282\pi\)
0.500139 + 0.865945i \(0.333282\pi\)
\(878\) −105.193 −3.55009
\(879\) 26.9609 0.909368
\(880\) 0 0
\(881\) 27.5400 0.927845 0.463922 0.885876i \(-0.346442\pi\)
0.463922 + 0.885876i \(0.346442\pi\)
\(882\) 53.4847 1.80092
\(883\) 9.69519 0.326269 0.163134 0.986604i \(-0.447840\pi\)
0.163134 + 0.986604i \(0.447840\pi\)
\(884\) −90.6516 −3.04894
\(885\) 0 0
\(886\) 70.9733 2.38440
\(887\) 6.60583 0.221802 0.110901 0.993831i \(-0.464626\pi\)
0.110901 + 0.993831i \(0.464626\pi\)
\(888\) 109.080 3.66048
\(889\) 15.2562 0.511677
\(890\) 0 0
\(891\) 37.6055 1.25983
\(892\) −61.4762 −2.05838
\(893\) −15.5080 −0.518957
\(894\) −34.3038 −1.14729
\(895\) 0 0
\(896\) −25.4847 −0.851384
\(897\) −18.8389 −0.629012
\(898\) 24.9404 0.832271
\(899\) 22.9688 0.766052
\(900\) 0 0
\(901\) −40.6321 −1.35365
\(902\) −73.2936 −2.44041
\(903\) 8.77383 0.291975
\(904\) 41.7591 1.38889
\(905\) 0 0
\(906\) 63.7291 2.11726
\(907\) 18.6330 0.618700 0.309350 0.950948i \(-0.399888\pi\)
0.309350 + 0.950948i \(0.399888\pi\)
\(908\) −48.7373 −1.61740
\(909\) −60.3408 −2.00138
\(910\) 0 0
\(911\) −10.4778 −0.347146 −0.173573 0.984821i \(-0.555531\pi\)
−0.173573 + 0.984821i \(0.555531\pi\)
\(912\) 203.086 6.72485
\(913\) 12.1805 0.403117
\(914\) −22.6772 −0.750096
\(915\) 0 0
\(916\) −86.5807 −2.86071
\(917\) −12.6330 −0.417180
\(918\) −24.2173 −0.799291
\(919\) 33.4620 1.10381 0.551905 0.833907i \(-0.313901\pi\)
0.551905 + 0.833907i \(0.313901\pi\)
\(920\) 0 0
\(921\) 45.8935 1.51224
\(922\) 8.04518 0.264954
\(923\) 20.5871 0.677631
\(924\) −96.1125 −3.16187
\(925\) 0 0
\(926\) −27.9177 −0.917433
\(927\) 29.7457 0.976978
\(928\) 87.0107 2.85627
\(929\) 38.0410 1.24809 0.624043 0.781390i \(-0.285489\pi\)
0.624043 + 0.781390i \(0.285489\pi\)
\(930\) 0 0
\(931\) −33.4489 −1.09624
\(932\) 13.4534 0.440681
\(933\) −13.6942 −0.448328
\(934\) −63.3861 −2.07406
\(935\) 0 0
\(936\) 103.914 3.39653
\(937\) 27.2333 0.889673 0.444836 0.895612i \(-0.353262\pi\)
0.444836 + 0.895612i \(0.353262\pi\)
\(938\) −51.1437 −1.66990
\(939\) −67.0609 −2.18845
\(940\) 0 0
\(941\) −39.6482 −1.29249 −0.646247 0.763129i \(-0.723662\pi\)
−0.646247 + 0.763129i \(0.723662\pi\)
\(942\) −49.7473 −1.62086
\(943\) −10.6190 −0.345802
\(944\) −107.398 −3.49550
\(945\) 0 0
\(946\) 41.7567 1.35763
\(947\) −3.86951 −0.125742 −0.0628711 0.998022i \(-0.520026\pi\)
−0.0628711 + 0.998022i \(0.520026\pi\)
\(948\) 126.387 4.10486
\(949\) 17.3116 0.561958
\(950\) 0 0
\(951\) 1.32082 0.0428305
\(952\) −57.1645 −1.85271
\(953\) 20.5864 0.666859 0.333430 0.942775i \(-0.391794\pi\)
0.333430 + 0.942775i \(0.391794\pi\)
\(954\) 75.5196 2.44504
\(955\) 0 0
\(956\) −135.793 −4.39185
\(957\) 75.0744 2.42681
\(958\) 14.7745 0.477342
\(959\) −16.5121 −0.533204
\(960\) 0 0
\(961\) −10.6613 −0.343914
\(962\) −43.1170 −1.39015
\(963\) 56.9952 1.83665
\(964\) 5.21850 0.168077
\(965\) 0 0
\(966\) −19.2619 −0.619740
\(967\) −52.3145 −1.68232 −0.841161 0.540785i \(-0.818127\pi\)
−0.841161 + 0.540785i \(0.818127\pi\)
\(968\) −186.994 −6.01022
\(969\) 83.9738 2.69763
\(970\) 0 0
\(971\) 29.3275 0.941165 0.470582 0.882356i \(-0.344044\pi\)
0.470582 + 0.882356i \(0.344044\pi\)
\(972\) −115.339 −3.69949
\(973\) 19.9391 0.639219
\(974\) 26.5919 0.852061
\(975\) 0 0
\(976\) −156.155 −4.99841
\(977\) −43.0111 −1.37605 −0.688024 0.725688i \(-0.741522\pi\)
−0.688024 + 0.725688i \(0.741522\pi\)
\(978\) −103.659 −3.31466
\(979\) −46.3299 −1.48071
\(980\) 0 0
\(981\) −64.2659 −2.05185
\(982\) 60.7561 1.93880
\(983\) 47.7953 1.52443 0.762216 0.647322i \(-0.224111\pi\)
0.762216 + 0.647322i \(0.224111\pi\)
\(984\) 106.583 3.39774
\(985\) 0 0
\(986\) 72.3986 2.30564
\(987\) −8.13102 −0.258813
\(988\) −105.370 −3.35228
\(989\) 6.04983 0.192373
\(990\) 0 0
\(991\) −8.79367 −0.279340 −0.139670 0.990198i \(-0.544604\pi\)
−0.139670 + 0.990198i \(0.544604\pi\)
\(992\) 77.0472 2.44625
\(993\) −11.3023 −0.358669
\(994\) 21.0493 0.667642
\(995\) 0 0
\(996\) −28.7197 −0.910020
\(997\) 25.3984 0.804375 0.402188 0.915557i \(-0.368250\pi\)
0.402188 + 0.915557i \(0.368250\pi\)
\(998\) 69.6185 2.20373
\(999\) −8.32719 −0.263461
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.1.1 46
5.2 odd 4 1205.2.b.c.724.1 46
5.3 odd 4 1205.2.b.c.724.46 yes 46
5.4 even 2 inner 6025.2.a.p.1.46 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.1 46 5.2 odd 4
1205.2.b.c.724.46 yes 46 5.3 odd 4
6025.2.a.p.1.1 46 1.1 even 1 trivial
6025.2.a.p.1.46 46 5.4 even 2 inner