Properties

Label 6025.2.a.p.1.16
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 1.16
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.930197 q^{2} +1.32621 q^{3} -1.13473 q^{4} -1.23364 q^{6} -4.33497 q^{7} +2.91592 q^{8} -1.24116 q^{9} +O(q^{10})\) \(q-0.930197 q^{2} +1.32621 q^{3} -1.13473 q^{4} -1.23364 q^{6} -4.33497 q^{7} +2.91592 q^{8} -1.24116 q^{9} +0.882357 q^{11} -1.50490 q^{12} +2.68232 q^{13} +4.03238 q^{14} -0.442916 q^{16} +0.304406 q^{17} +1.15452 q^{18} -4.13564 q^{19} -5.74909 q^{21} -0.820766 q^{22} -2.19664 q^{23} +3.86713 q^{24} -2.49509 q^{26} -5.62468 q^{27} +4.91903 q^{28} +8.97537 q^{29} +5.91415 q^{31} -5.41984 q^{32} +1.17019 q^{33} -0.283158 q^{34} +1.40839 q^{36} +10.9828 q^{37} +3.84696 q^{38} +3.55733 q^{39} -6.07092 q^{41} +5.34779 q^{42} -2.71940 q^{43} -1.00124 q^{44} +2.04331 q^{46} +9.50435 q^{47} -0.587400 q^{48} +11.7920 q^{49} +0.403707 q^{51} -3.04372 q^{52} +11.0767 q^{53} +5.23206 q^{54} -12.6404 q^{56} -5.48474 q^{57} -8.34887 q^{58} -7.93694 q^{59} -1.60387 q^{61} -5.50133 q^{62} +5.38040 q^{63} +5.92735 q^{64} -1.08851 q^{66} -15.5753 q^{67} -0.345420 q^{68} -2.91321 q^{69} -9.40214 q^{71} -3.61913 q^{72} -4.11094 q^{73} -10.2162 q^{74} +4.69285 q^{76} -3.82499 q^{77} -3.30902 q^{78} +9.90696 q^{79} -3.73604 q^{81} +5.64716 q^{82} -10.7285 q^{83} +6.52368 q^{84} +2.52958 q^{86} +11.9033 q^{87} +2.57288 q^{88} -9.48120 q^{89} -11.6278 q^{91} +2.49260 q^{92} +7.84342 q^{93} -8.84092 q^{94} -7.18786 q^{96} -1.41584 q^{97} -10.9689 q^{98} -1.09515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.930197 −0.657749 −0.328874 0.944374i \(-0.606669\pi\)
−0.328874 + 0.944374i \(0.606669\pi\)
\(3\) 1.32621 0.765689 0.382845 0.923813i \(-0.374944\pi\)
0.382845 + 0.923813i \(0.374944\pi\)
\(4\) −1.13473 −0.567366
\(5\) 0 0
\(6\) −1.23364 −0.503631
\(7\) −4.33497 −1.63847 −0.819233 0.573461i \(-0.805600\pi\)
−0.819233 + 0.573461i \(0.805600\pi\)
\(8\) 2.91592 1.03093
\(9\) −1.24116 −0.413720
\(10\) 0 0
\(11\) 0.882357 0.266041 0.133020 0.991113i \(-0.457532\pi\)
0.133020 + 0.991113i \(0.457532\pi\)
\(12\) −1.50490 −0.434426
\(13\) 2.68232 0.743943 0.371971 0.928244i \(-0.378682\pi\)
0.371971 + 0.928244i \(0.378682\pi\)
\(14\) 4.03238 1.07770
\(15\) 0 0
\(16\) −0.442916 −0.110729
\(17\) 0.304406 0.0738294 0.0369147 0.999318i \(-0.488247\pi\)
0.0369147 + 0.999318i \(0.488247\pi\)
\(18\) 1.15452 0.272124
\(19\) −4.13564 −0.948781 −0.474390 0.880315i \(-0.657331\pi\)
−0.474390 + 0.880315i \(0.657331\pi\)
\(20\) 0 0
\(21\) −5.74909 −1.25455
\(22\) −0.820766 −0.174988
\(23\) −2.19664 −0.458031 −0.229015 0.973423i \(-0.573551\pi\)
−0.229015 + 0.973423i \(0.573551\pi\)
\(24\) 3.86713 0.789375
\(25\) 0 0
\(26\) −2.49509 −0.489328
\(27\) −5.62468 −1.08247
\(28\) 4.91903 0.929610
\(29\) 8.97537 1.66669 0.833343 0.552757i \(-0.186424\pi\)
0.833343 + 0.552757i \(0.186424\pi\)
\(30\) 0 0
\(31\) 5.91415 1.06221 0.531107 0.847305i \(-0.321776\pi\)
0.531107 + 0.847305i \(0.321776\pi\)
\(32\) −5.41984 −0.958102
\(33\) 1.17019 0.203704
\(34\) −0.283158 −0.0485612
\(35\) 0 0
\(36\) 1.40839 0.234731
\(37\) 10.9828 1.80556 0.902779 0.430105i \(-0.141523\pi\)
0.902779 + 0.430105i \(0.141523\pi\)
\(38\) 3.84696 0.624059
\(39\) 3.55733 0.569629
\(40\) 0 0
\(41\) −6.07092 −0.948119 −0.474059 0.880493i \(-0.657212\pi\)
−0.474059 + 0.880493i \(0.657212\pi\)
\(42\) 5.34779 0.825182
\(43\) −2.71940 −0.414705 −0.207352 0.978266i \(-0.566485\pi\)
−0.207352 + 0.978266i \(0.566485\pi\)
\(44\) −1.00124 −0.150943
\(45\) 0 0
\(46\) 2.04331 0.301269
\(47\) 9.50435 1.38635 0.693176 0.720769i \(-0.256211\pi\)
0.693176 + 0.720769i \(0.256211\pi\)
\(48\) −0.587400 −0.0847839
\(49\) 11.7920 1.68457
\(50\) 0 0
\(51\) 0.403707 0.0565303
\(52\) −3.04372 −0.422088
\(53\) 11.0767 1.52150 0.760748 0.649048i \(-0.224832\pi\)
0.760748 + 0.649048i \(0.224832\pi\)
\(54\) 5.23206 0.711994
\(55\) 0 0
\(56\) −12.6404 −1.68915
\(57\) −5.48474 −0.726471
\(58\) −8.34887 −1.09626
\(59\) −7.93694 −1.03330 −0.516651 0.856196i \(-0.672821\pi\)
−0.516651 + 0.856196i \(0.672821\pi\)
\(60\) 0 0
\(61\) −1.60387 −0.205355 −0.102678 0.994715i \(-0.532741\pi\)
−0.102678 + 0.994715i \(0.532741\pi\)
\(62\) −5.50133 −0.698670
\(63\) 5.38040 0.677866
\(64\) 5.92735 0.740919
\(65\) 0 0
\(66\) −1.08851 −0.133986
\(67\) −15.5753 −1.90282 −0.951410 0.307926i \(-0.900365\pi\)
−0.951410 + 0.307926i \(0.900365\pi\)
\(68\) −0.345420 −0.0418883
\(69\) −2.91321 −0.350709
\(70\) 0 0
\(71\) −9.40214 −1.11583 −0.557915 0.829898i \(-0.688398\pi\)
−0.557915 + 0.829898i \(0.688398\pi\)
\(72\) −3.61913 −0.426518
\(73\) −4.11094 −0.481150 −0.240575 0.970631i \(-0.577336\pi\)
−0.240575 + 0.970631i \(0.577336\pi\)
\(74\) −10.2162 −1.18760
\(75\) 0 0
\(76\) 4.69285 0.538306
\(77\) −3.82499 −0.435898
\(78\) −3.30902 −0.374673
\(79\) 9.90696 1.11462 0.557310 0.830304i \(-0.311833\pi\)
0.557310 + 0.830304i \(0.311833\pi\)
\(80\) 0 0
\(81\) −3.73604 −0.415115
\(82\) 5.64716 0.623624
\(83\) −10.7285 −1.17761 −0.588803 0.808277i \(-0.700401\pi\)
−0.588803 + 0.808277i \(0.700401\pi\)
\(84\) 6.52368 0.711792
\(85\) 0 0
\(86\) 2.52958 0.272772
\(87\) 11.9033 1.27616
\(88\) 2.57288 0.274270
\(89\) −9.48120 −1.00501 −0.502503 0.864576i \(-0.667587\pi\)
−0.502503 + 0.864576i \(0.667587\pi\)
\(90\) 0 0
\(91\) −11.6278 −1.21892
\(92\) 2.49260 0.259871
\(93\) 7.84342 0.813325
\(94\) −8.84092 −0.911871
\(95\) 0 0
\(96\) −7.18786 −0.733608
\(97\) −1.41584 −0.143757 −0.0718784 0.997413i \(-0.522899\pi\)
−0.0718784 + 0.997413i \(0.522899\pi\)
\(98\) −10.9689 −1.10802
\(99\) −1.09515 −0.110066
\(100\) 0 0
\(101\) 16.9462 1.68621 0.843104 0.537750i \(-0.180726\pi\)
0.843104 + 0.537750i \(0.180726\pi\)
\(102\) −0.375528 −0.0371828
\(103\) −1.90525 −0.187729 −0.0938647 0.995585i \(-0.529922\pi\)
−0.0938647 + 0.995585i \(0.529922\pi\)
\(104\) 7.82144 0.766956
\(105\) 0 0
\(106\) −10.3035 −1.00076
\(107\) 8.61469 0.832814 0.416407 0.909178i \(-0.363289\pi\)
0.416407 + 0.909178i \(0.363289\pi\)
\(108\) 6.38251 0.614157
\(109\) −8.16711 −0.782267 −0.391134 0.920334i \(-0.627917\pi\)
−0.391134 + 0.920334i \(0.627917\pi\)
\(110\) 0 0
\(111\) 14.5655 1.38250
\(112\) 1.92003 0.181426
\(113\) 4.19717 0.394837 0.197418 0.980319i \(-0.436744\pi\)
0.197418 + 0.980319i \(0.436744\pi\)
\(114\) 5.10189 0.477835
\(115\) 0 0
\(116\) −10.1847 −0.945621
\(117\) −3.32920 −0.307784
\(118\) 7.38292 0.679653
\(119\) −1.31959 −0.120967
\(120\) 0 0
\(121\) −10.2214 −0.929222
\(122\) 1.49192 0.135072
\(123\) −8.05133 −0.725964
\(124\) −6.71098 −0.602664
\(125\) 0 0
\(126\) −5.00483 −0.445866
\(127\) −4.94642 −0.438924 −0.219462 0.975621i \(-0.570430\pi\)
−0.219462 + 0.975621i \(0.570430\pi\)
\(128\) 5.32607 0.470763
\(129\) −3.60650 −0.317535
\(130\) 0 0
\(131\) 13.6851 1.19567 0.597836 0.801618i \(-0.296027\pi\)
0.597836 + 0.801618i \(0.296027\pi\)
\(132\) −1.32786 −0.115575
\(133\) 17.9279 1.55454
\(134\) 14.4881 1.25158
\(135\) 0 0
\(136\) 0.887624 0.0761132
\(137\) 19.0577 1.62821 0.814105 0.580717i \(-0.197228\pi\)
0.814105 + 0.580717i \(0.197228\pi\)
\(138\) 2.70986 0.230678
\(139\) −21.7352 −1.84356 −0.921778 0.387717i \(-0.873264\pi\)
−0.921778 + 0.387717i \(0.873264\pi\)
\(140\) 0 0
\(141\) 12.6048 1.06151
\(142\) 8.74585 0.733935
\(143\) 2.36677 0.197919
\(144\) 0.549730 0.0458108
\(145\) 0 0
\(146\) 3.82399 0.316476
\(147\) 15.6387 1.28986
\(148\) −12.4625 −1.02441
\(149\) −6.03822 −0.494671 −0.247335 0.968930i \(-0.579555\pi\)
−0.247335 + 0.968930i \(0.579555\pi\)
\(150\) 0 0
\(151\) −15.0115 −1.22162 −0.610808 0.791779i \(-0.709155\pi\)
−0.610808 + 0.791779i \(0.709155\pi\)
\(152\) −12.0592 −0.978130
\(153\) −0.377817 −0.0305447
\(154\) 3.55800 0.286712
\(155\) 0 0
\(156\) −4.03662 −0.323188
\(157\) 4.38682 0.350107 0.175053 0.984559i \(-0.443990\pi\)
0.175053 + 0.984559i \(0.443990\pi\)
\(158\) −9.21543 −0.733140
\(159\) 14.6900 1.16499
\(160\) 0 0
\(161\) 9.52236 0.750467
\(162\) 3.47525 0.273042
\(163\) −5.32658 −0.417210 −0.208605 0.978000i \(-0.566892\pi\)
−0.208605 + 0.978000i \(0.566892\pi\)
\(164\) 6.88888 0.537931
\(165\) 0 0
\(166\) 9.97963 0.774569
\(167\) −8.59533 −0.665127 −0.332563 0.943081i \(-0.607914\pi\)
−0.332563 + 0.943081i \(0.607914\pi\)
\(168\) −16.7639 −1.29336
\(169\) −5.80514 −0.446549
\(170\) 0 0
\(171\) 5.13299 0.392530
\(172\) 3.08579 0.235290
\(173\) 3.91350 0.297538 0.148769 0.988872i \(-0.452469\pi\)
0.148769 + 0.988872i \(0.452469\pi\)
\(174\) −11.0724 −0.839395
\(175\) 0 0
\(176\) −0.390810 −0.0294584
\(177\) −10.5261 −0.791187
\(178\) 8.81939 0.661041
\(179\) −2.52352 −0.188617 −0.0943084 0.995543i \(-0.530064\pi\)
−0.0943084 + 0.995543i \(0.530064\pi\)
\(180\) 0 0
\(181\) −16.5056 −1.22685 −0.613426 0.789752i \(-0.710209\pi\)
−0.613426 + 0.789752i \(0.710209\pi\)
\(182\) 10.8161 0.801746
\(183\) −2.12708 −0.157238
\(184\) −6.40522 −0.472199
\(185\) 0 0
\(186\) −7.29593 −0.534964
\(187\) 0.268595 0.0196416
\(188\) −10.7849 −0.786569
\(189\) 24.3828 1.77359
\(190\) 0 0
\(191\) −22.6006 −1.63532 −0.817660 0.575701i \(-0.804729\pi\)
−0.817660 + 0.575701i \(0.804729\pi\)
\(192\) 7.86093 0.567314
\(193\) 6.58611 0.474079 0.237039 0.971500i \(-0.423823\pi\)
0.237039 + 0.971500i \(0.423823\pi\)
\(194\) 1.31701 0.0945559
\(195\) 0 0
\(196\) −13.3807 −0.955767
\(197\) −3.59184 −0.255908 −0.127954 0.991780i \(-0.540841\pi\)
−0.127954 + 0.991780i \(0.540841\pi\)
\(198\) 1.01870 0.0723961
\(199\) −21.0736 −1.49387 −0.746934 0.664899i \(-0.768475\pi\)
−0.746934 + 0.664899i \(0.768475\pi\)
\(200\) 0 0
\(201\) −20.6561 −1.45697
\(202\) −15.7633 −1.10910
\(203\) −38.9080 −2.73081
\(204\) −0.458100 −0.0320734
\(205\) 0 0
\(206\) 1.77225 0.123479
\(207\) 2.72638 0.189496
\(208\) −1.18804 −0.0823760
\(209\) −3.64911 −0.252414
\(210\) 0 0
\(211\) 28.9947 1.99607 0.998037 0.0626191i \(-0.0199453\pi\)
0.998037 + 0.0626191i \(0.0199453\pi\)
\(212\) −12.5690 −0.863245
\(213\) −12.4692 −0.854378
\(214\) −8.01336 −0.547782
\(215\) 0 0
\(216\) −16.4011 −1.11595
\(217\) −25.6377 −1.74040
\(218\) 7.59702 0.514535
\(219\) −5.45199 −0.368411
\(220\) 0 0
\(221\) 0.816516 0.0549248
\(222\) −13.5488 −0.909335
\(223\) −7.57709 −0.507399 −0.253700 0.967283i \(-0.581647\pi\)
−0.253700 + 0.967283i \(0.581647\pi\)
\(224\) 23.4949 1.56982
\(225\) 0 0
\(226\) −3.90420 −0.259704
\(227\) −9.73925 −0.646416 −0.323208 0.946328i \(-0.604761\pi\)
−0.323208 + 0.946328i \(0.604761\pi\)
\(228\) 6.22371 0.412175
\(229\) −24.7729 −1.63704 −0.818520 0.574478i \(-0.805205\pi\)
−0.818520 + 0.574478i \(0.805205\pi\)
\(230\) 0 0
\(231\) −5.07275 −0.333763
\(232\) 26.1715 1.71824
\(233\) 20.9912 1.37518 0.687589 0.726100i \(-0.258669\pi\)
0.687589 + 0.726100i \(0.258669\pi\)
\(234\) 3.09681 0.202445
\(235\) 0 0
\(236\) 9.00630 0.586260
\(237\) 13.1387 0.853453
\(238\) 1.22748 0.0795658
\(239\) −0.936020 −0.0605461 −0.0302730 0.999542i \(-0.509638\pi\)
−0.0302730 + 0.999542i \(0.509638\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 9.50796 0.611195
\(243\) 11.9193 0.764621
\(244\) 1.81997 0.116512
\(245\) 0 0
\(246\) 7.48933 0.477502
\(247\) −11.0931 −0.705839
\(248\) 17.2452 1.09507
\(249\) −14.2283 −0.901680
\(250\) 0 0
\(251\) 11.8204 0.746099 0.373050 0.927811i \(-0.378312\pi\)
0.373050 + 0.927811i \(0.378312\pi\)
\(252\) −6.10531 −0.384598
\(253\) −1.93822 −0.121855
\(254\) 4.60115 0.288702
\(255\) 0 0
\(256\) −16.8090 −1.05056
\(257\) −14.9566 −0.932964 −0.466482 0.884531i \(-0.654479\pi\)
−0.466482 + 0.884531i \(0.654479\pi\)
\(258\) 3.35476 0.208858
\(259\) −47.6100 −2.95834
\(260\) 0 0
\(261\) −11.1399 −0.689541
\(262\) −12.7298 −0.786453
\(263\) −12.3331 −0.760494 −0.380247 0.924885i \(-0.624161\pi\)
−0.380247 + 0.924885i \(0.624161\pi\)
\(264\) 3.41219 0.210006
\(265\) 0 0
\(266\) −16.6765 −1.02250
\(267\) −12.5741 −0.769522
\(268\) 17.6738 1.07960
\(269\) −2.61251 −0.159287 −0.0796437 0.996823i \(-0.525378\pi\)
−0.0796437 + 0.996823i \(0.525378\pi\)
\(270\) 0 0
\(271\) −9.75632 −0.592654 −0.296327 0.955086i \(-0.595762\pi\)
−0.296327 + 0.955086i \(0.595762\pi\)
\(272\) −0.134826 −0.00817505
\(273\) −15.4209 −0.933317
\(274\) −17.7274 −1.07095
\(275\) 0 0
\(276\) 3.30571 0.198980
\(277\) 0.508682 0.0305637 0.0152819 0.999883i \(-0.495135\pi\)
0.0152819 + 0.999883i \(0.495135\pi\)
\(278\) 20.2180 1.21260
\(279\) −7.34042 −0.439459
\(280\) 0 0
\(281\) −25.0618 −1.49506 −0.747530 0.664228i \(-0.768760\pi\)
−0.747530 + 0.664228i \(0.768760\pi\)
\(282\) −11.7249 −0.698210
\(283\) 1.51258 0.0899134 0.0449567 0.998989i \(-0.485685\pi\)
0.0449567 + 0.998989i \(0.485685\pi\)
\(284\) 10.6689 0.633084
\(285\) 0 0
\(286\) −2.20156 −0.130181
\(287\) 26.3173 1.55346
\(288\) 6.72689 0.396386
\(289\) −16.9073 −0.994549
\(290\) 0 0
\(291\) −1.87771 −0.110073
\(292\) 4.66482 0.272988
\(293\) 27.7625 1.62190 0.810950 0.585115i \(-0.198951\pi\)
0.810950 + 0.585115i \(0.198951\pi\)
\(294\) −14.5470 −0.848401
\(295\) 0 0
\(296\) 32.0249 1.86141
\(297\) −4.96298 −0.287981
\(298\) 5.61674 0.325369
\(299\) −5.89209 −0.340749
\(300\) 0 0
\(301\) 11.7885 0.679479
\(302\) 13.9636 0.803516
\(303\) 22.4742 1.29111
\(304\) 1.83174 0.105057
\(305\) 0 0
\(306\) 0.351444 0.0200907
\(307\) −19.1572 −1.09336 −0.546679 0.837342i \(-0.684108\pi\)
−0.546679 + 0.837342i \(0.684108\pi\)
\(308\) 4.34034 0.247314
\(309\) −2.52676 −0.143742
\(310\) 0 0
\(311\) −4.09651 −0.232292 −0.116146 0.993232i \(-0.537054\pi\)
−0.116146 + 0.993232i \(0.537054\pi\)
\(312\) 10.3729 0.587250
\(313\) 27.8074 1.57177 0.785883 0.618375i \(-0.212209\pi\)
0.785883 + 0.618375i \(0.212209\pi\)
\(314\) −4.08061 −0.230282
\(315\) 0 0
\(316\) −11.2418 −0.632398
\(317\) 14.6718 0.824048 0.412024 0.911173i \(-0.364822\pi\)
0.412024 + 0.911173i \(0.364822\pi\)
\(318\) −13.6646 −0.766273
\(319\) 7.91949 0.443406
\(320\) 0 0
\(321\) 11.4249 0.637676
\(322\) −8.85767 −0.493619
\(323\) −1.25891 −0.0700479
\(324\) 4.23941 0.235523
\(325\) 0 0
\(326\) 4.95477 0.274420
\(327\) −10.8313 −0.598974
\(328\) −17.7023 −0.977448
\(329\) −41.2011 −2.27149
\(330\) 0 0
\(331\) −14.8331 −0.815303 −0.407651 0.913138i \(-0.633652\pi\)
−0.407651 + 0.913138i \(0.633652\pi\)
\(332\) 12.1740 0.668134
\(333\) −13.6314 −0.746996
\(334\) 7.99536 0.437486
\(335\) 0 0
\(336\) 2.54636 0.138916
\(337\) −3.92047 −0.213562 −0.106781 0.994283i \(-0.534054\pi\)
−0.106781 + 0.994283i \(0.534054\pi\)
\(338\) 5.39992 0.293717
\(339\) 5.56634 0.302322
\(340\) 0 0
\(341\) 5.21840 0.282592
\(342\) −4.77470 −0.258186
\(343\) −20.7731 −1.12164
\(344\) −7.92956 −0.427533
\(345\) 0 0
\(346\) −3.64033 −0.195705
\(347\) −1.88740 −0.101321 −0.0506606 0.998716i \(-0.516133\pi\)
−0.0506606 + 0.998716i \(0.516133\pi\)
\(348\) −13.5070 −0.724052
\(349\) −5.79692 −0.310302 −0.155151 0.987891i \(-0.549586\pi\)
−0.155151 + 0.987891i \(0.549586\pi\)
\(350\) 0 0
\(351\) −15.0872 −0.805296
\(352\) −4.78224 −0.254894
\(353\) −20.8216 −1.10822 −0.554111 0.832443i \(-0.686942\pi\)
−0.554111 + 0.832443i \(0.686942\pi\)
\(354\) 9.79132 0.520403
\(355\) 0 0
\(356\) 10.7586 0.570206
\(357\) −1.75006 −0.0926230
\(358\) 2.34737 0.124062
\(359\) −15.4514 −0.815492 −0.407746 0.913095i \(-0.633685\pi\)
−0.407746 + 0.913095i \(0.633685\pi\)
\(360\) 0 0
\(361\) −1.89649 −0.0998153
\(362\) 15.3535 0.806961
\(363\) −13.5558 −0.711495
\(364\) 13.1944 0.691577
\(365\) 0 0
\(366\) 1.97860 0.103423
\(367\) 38.0380 1.98557 0.992785 0.119912i \(-0.0382613\pi\)
0.992785 + 0.119912i \(0.0382613\pi\)
\(368\) 0.972925 0.0507172
\(369\) 7.53499 0.392256
\(370\) 0 0
\(371\) −48.0170 −2.49292
\(372\) −8.90019 −0.461453
\(373\) 15.6921 0.812505 0.406253 0.913761i \(-0.366835\pi\)
0.406253 + 0.913761i \(0.366835\pi\)
\(374\) −0.249846 −0.0129192
\(375\) 0 0
\(376\) 27.7139 1.42924
\(377\) 24.0749 1.23992
\(378\) −22.6808 −1.16658
\(379\) −4.85553 −0.249412 −0.124706 0.992194i \(-0.539799\pi\)
−0.124706 + 0.992194i \(0.539799\pi\)
\(380\) 0 0
\(381\) −6.56001 −0.336079
\(382\) 21.0230 1.07563
\(383\) −18.3938 −0.939878 −0.469939 0.882699i \(-0.655724\pi\)
−0.469939 + 0.882699i \(0.655724\pi\)
\(384\) 7.06351 0.360458
\(385\) 0 0
\(386\) −6.12638 −0.311825
\(387\) 3.37521 0.171572
\(388\) 1.60660 0.0815628
\(389\) −30.6318 −1.55310 −0.776548 0.630058i \(-0.783031\pi\)
−0.776548 + 0.630058i \(0.783031\pi\)
\(390\) 0 0
\(391\) −0.668670 −0.0338161
\(392\) 34.3845 1.73668
\(393\) 18.1494 0.915514
\(394\) 3.34112 0.168323
\(395\) 0 0
\(396\) 1.24270 0.0624480
\(397\) −4.67514 −0.234639 −0.117319 0.993094i \(-0.537430\pi\)
−0.117319 + 0.993094i \(0.537430\pi\)
\(398\) 19.6026 0.982590
\(399\) 23.7762 1.19030
\(400\) 0 0
\(401\) −7.50388 −0.374726 −0.187363 0.982291i \(-0.559994\pi\)
−0.187363 + 0.982291i \(0.559994\pi\)
\(402\) 19.2143 0.958320
\(403\) 15.8637 0.790226
\(404\) −19.2294 −0.956698
\(405\) 0 0
\(406\) 36.1921 1.79618
\(407\) 9.69073 0.480352
\(408\) 1.17718 0.0582790
\(409\) −7.22831 −0.357417 −0.178709 0.983902i \(-0.557192\pi\)
−0.178709 + 0.983902i \(0.557192\pi\)
\(410\) 0 0
\(411\) 25.2746 1.24670
\(412\) 2.16195 0.106511
\(413\) 34.4064 1.69303
\(414\) −2.53607 −0.124641
\(415\) 0 0
\(416\) −14.5378 −0.712773
\(417\) −28.8255 −1.41159
\(418\) 3.39439 0.166025
\(419\) 12.9158 0.630979 0.315490 0.948929i \(-0.397831\pi\)
0.315490 + 0.948929i \(0.397831\pi\)
\(420\) 0 0
\(421\) 25.6611 1.25064 0.625322 0.780367i \(-0.284967\pi\)
0.625322 + 0.780367i \(0.284967\pi\)
\(422\) −26.9708 −1.31292
\(423\) −11.7964 −0.573562
\(424\) 32.2986 1.56856
\(425\) 0 0
\(426\) 11.5989 0.561966
\(427\) 6.95275 0.336467
\(428\) −9.77537 −0.472510
\(429\) 3.13884 0.151544
\(430\) 0 0
\(431\) −4.38626 −0.211279 −0.105639 0.994404i \(-0.533689\pi\)
−0.105639 + 0.994404i \(0.533689\pi\)
\(432\) 2.49126 0.119861
\(433\) −10.6818 −0.513335 −0.256667 0.966500i \(-0.582624\pi\)
−0.256667 + 0.966500i \(0.582624\pi\)
\(434\) 23.8481 1.14475
\(435\) 0 0
\(436\) 9.26749 0.443832
\(437\) 9.08450 0.434571
\(438\) 5.07142 0.242322
\(439\) 6.07260 0.289829 0.144915 0.989444i \(-0.453709\pi\)
0.144915 + 0.989444i \(0.453709\pi\)
\(440\) 0 0
\(441\) −14.6357 −0.696940
\(442\) −0.759521 −0.0361267
\(443\) −23.3422 −1.10902 −0.554512 0.832176i \(-0.687095\pi\)
−0.554512 + 0.832176i \(0.687095\pi\)
\(444\) −16.5280 −0.784382
\(445\) 0 0
\(446\) 7.04819 0.333741
\(447\) −8.00797 −0.378764
\(448\) −25.6949 −1.21397
\(449\) 14.5863 0.688371 0.344185 0.938902i \(-0.388155\pi\)
0.344185 + 0.938902i \(0.388155\pi\)
\(450\) 0 0
\(451\) −5.35672 −0.252238
\(452\) −4.76267 −0.224017
\(453\) −19.9084 −0.935378
\(454\) 9.05942 0.425180
\(455\) 0 0
\(456\) −15.9931 −0.748943
\(457\) −21.6065 −1.01071 −0.505355 0.862912i \(-0.668638\pi\)
−0.505355 + 0.862912i \(0.668638\pi\)
\(458\) 23.0437 1.07676
\(459\) −1.71219 −0.0799181
\(460\) 0 0
\(461\) −8.71776 −0.406026 −0.203013 0.979176i \(-0.565073\pi\)
−0.203013 + 0.979176i \(0.565073\pi\)
\(462\) 4.71866 0.219532
\(463\) 16.2752 0.756375 0.378187 0.925729i \(-0.376548\pi\)
0.378187 + 0.925729i \(0.376548\pi\)
\(464\) −3.97534 −0.184550
\(465\) 0 0
\(466\) −19.5260 −0.904522
\(467\) −6.86128 −0.317502 −0.158751 0.987319i \(-0.550747\pi\)
−0.158751 + 0.987319i \(0.550747\pi\)
\(468\) 3.77775 0.174626
\(469\) 67.5183 3.11771
\(470\) 0 0
\(471\) 5.81786 0.268073
\(472\) −23.1435 −1.06526
\(473\) −2.39948 −0.110328
\(474\) −12.2216 −0.561358
\(475\) 0 0
\(476\) 1.49738 0.0686325
\(477\) −13.7479 −0.629473
\(478\) 0.870683 0.0398241
\(479\) 17.6985 0.808664 0.404332 0.914612i \(-0.367504\pi\)
0.404332 + 0.914612i \(0.367504\pi\)
\(480\) 0 0
\(481\) 29.4594 1.34323
\(482\) −0.930197 −0.0423693
\(483\) 12.6287 0.574624
\(484\) 11.5986 0.527210
\(485\) 0 0
\(486\) −11.0873 −0.502928
\(487\) −9.06661 −0.410847 −0.205424 0.978673i \(-0.565857\pi\)
−0.205424 + 0.978673i \(0.565857\pi\)
\(488\) −4.67677 −0.211707
\(489\) −7.06418 −0.319453
\(490\) 0 0
\(491\) −16.2481 −0.733269 −0.366634 0.930365i \(-0.619490\pi\)
−0.366634 + 0.930365i \(0.619490\pi\)
\(492\) 9.13611 0.411888
\(493\) 2.73216 0.123050
\(494\) 10.3188 0.464265
\(495\) 0 0
\(496\) −2.61947 −0.117618
\(497\) 40.7580 1.82825
\(498\) 13.2351 0.593079
\(499\) 31.2373 1.39837 0.699186 0.714940i \(-0.253546\pi\)
0.699186 + 0.714940i \(0.253546\pi\)
\(500\) 0 0
\(501\) −11.3992 −0.509280
\(502\) −10.9953 −0.490746
\(503\) 36.0521 1.60749 0.803743 0.594977i \(-0.202839\pi\)
0.803743 + 0.594977i \(0.202839\pi\)
\(504\) 15.6888 0.698835
\(505\) 0 0
\(506\) 1.80293 0.0801498
\(507\) −7.69884 −0.341918
\(508\) 5.61287 0.249031
\(509\) 6.06492 0.268823 0.134412 0.990926i \(-0.457086\pi\)
0.134412 + 0.990926i \(0.457086\pi\)
\(510\) 0 0
\(511\) 17.8208 0.788347
\(512\) 4.98355 0.220244
\(513\) 23.2616 1.02703
\(514\) 13.9125 0.613656
\(515\) 0 0
\(516\) 4.09242 0.180159
\(517\) 8.38623 0.368826
\(518\) 44.2867 1.94585
\(519\) 5.19013 0.227822
\(520\) 0 0
\(521\) −33.8087 −1.48119 −0.740593 0.671954i \(-0.765455\pi\)
−0.740593 + 0.671954i \(0.765455\pi\)
\(522\) 10.3623 0.453545
\(523\) −23.5838 −1.03125 −0.515625 0.856815i \(-0.672440\pi\)
−0.515625 + 0.856815i \(0.672440\pi\)
\(524\) −15.5289 −0.678385
\(525\) 0 0
\(526\) 11.4723 0.500214
\(527\) 1.80031 0.0784225
\(528\) −0.518297 −0.0225560
\(529\) −18.1748 −0.790208
\(530\) 0 0
\(531\) 9.85101 0.427498
\(532\) −20.3433 −0.881996
\(533\) −16.2842 −0.705346
\(534\) 11.6964 0.506152
\(535\) 0 0
\(536\) −45.4162 −1.96168
\(537\) −3.34672 −0.144422
\(538\) 2.43015 0.104771
\(539\) 10.4047 0.448164
\(540\) 0 0
\(541\) −12.4241 −0.534152 −0.267076 0.963675i \(-0.586058\pi\)
−0.267076 + 0.963675i \(0.586058\pi\)
\(542\) 9.07531 0.389818
\(543\) −21.8899 −0.939388
\(544\) −1.64983 −0.0707360
\(545\) 0 0
\(546\) 14.3445 0.613888
\(547\) −12.3673 −0.528786 −0.264393 0.964415i \(-0.585172\pi\)
−0.264393 + 0.964415i \(0.585172\pi\)
\(548\) −21.6254 −0.923792
\(549\) 1.99067 0.0849596
\(550\) 0 0
\(551\) −37.1189 −1.58132
\(552\) −8.49468 −0.361558
\(553\) −42.9464 −1.82627
\(554\) −0.473174 −0.0201033
\(555\) 0 0
\(556\) 24.6637 1.04597
\(557\) 14.4719 0.613195 0.306598 0.951839i \(-0.400809\pi\)
0.306598 + 0.951839i \(0.400809\pi\)
\(558\) 6.82804 0.289054
\(559\) −7.29432 −0.308517
\(560\) 0 0
\(561\) 0.356214 0.0150394
\(562\) 23.3124 0.983374
\(563\) 2.71732 0.114521 0.0572607 0.998359i \(-0.481763\pi\)
0.0572607 + 0.998359i \(0.481763\pi\)
\(564\) −14.3031 −0.602268
\(565\) 0 0
\(566\) −1.40700 −0.0591404
\(567\) 16.1956 0.680152
\(568\) −27.4159 −1.15035
\(569\) −35.2838 −1.47917 −0.739586 0.673062i \(-0.764979\pi\)
−0.739586 + 0.673062i \(0.764979\pi\)
\(570\) 0 0
\(571\) −34.4873 −1.44325 −0.721625 0.692285i \(-0.756604\pi\)
−0.721625 + 0.692285i \(0.756604\pi\)
\(572\) −2.68565 −0.112293
\(573\) −29.9732 −1.25215
\(574\) −24.4803 −1.02179
\(575\) 0 0
\(576\) −7.35680 −0.306533
\(577\) −6.57108 −0.273558 −0.136779 0.990602i \(-0.543675\pi\)
−0.136779 + 0.990602i \(0.543675\pi\)
\(578\) 15.7272 0.654164
\(579\) 8.73458 0.362997
\(580\) 0 0
\(581\) 46.5078 1.92947
\(582\) 1.74664 0.0724004
\(583\) 9.77357 0.404780
\(584\) −11.9872 −0.496033
\(585\) 0 0
\(586\) −25.8246 −1.06680
\(587\) 3.17806 0.131173 0.0655863 0.997847i \(-0.479108\pi\)
0.0655863 + 0.997847i \(0.479108\pi\)
\(588\) −17.7457 −0.731821
\(589\) −24.4588 −1.00781
\(590\) 0 0
\(591\) −4.76354 −0.195946
\(592\) −4.86445 −0.199928
\(593\) −35.0450 −1.43913 −0.719563 0.694428i \(-0.755658\pi\)
−0.719563 + 0.694428i \(0.755658\pi\)
\(594\) 4.61655 0.189419
\(595\) 0 0
\(596\) 6.85177 0.280660
\(597\) −27.9481 −1.14384
\(598\) 5.48081 0.224127
\(599\) −18.6149 −0.760583 −0.380292 0.924867i \(-0.624176\pi\)
−0.380292 + 0.924867i \(0.624176\pi\)
\(600\) 0 0
\(601\) 8.79674 0.358827 0.179413 0.983774i \(-0.442580\pi\)
0.179413 + 0.983774i \(0.442580\pi\)
\(602\) −10.9657 −0.446927
\(603\) 19.3314 0.787235
\(604\) 17.0340 0.693104
\(605\) 0 0
\(606\) −20.9055 −0.849227
\(607\) 44.5048 1.80639 0.903197 0.429226i \(-0.141213\pi\)
0.903197 + 0.429226i \(0.141213\pi\)
\(608\) 22.4145 0.909028
\(609\) −51.6003 −2.09095
\(610\) 0 0
\(611\) 25.4937 1.03137
\(612\) 0.428721 0.0173300
\(613\) −47.1882 −1.90591 −0.952956 0.303109i \(-0.901975\pi\)
−0.952956 + 0.303109i \(0.901975\pi\)
\(614\) 17.8200 0.719155
\(615\) 0 0
\(616\) −11.1534 −0.449382
\(617\) 3.11780 0.125518 0.0627590 0.998029i \(-0.480010\pi\)
0.0627590 + 0.998029i \(0.480010\pi\)
\(618\) 2.35039 0.0945464
\(619\) 23.7548 0.954787 0.477393 0.878690i \(-0.341582\pi\)
0.477393 + 0.878690i \(0.341582\pi\)
\(620\) 0 0
\(621\) 12.3554 0.495804
\(622\) 3.81056 0.152789
\(623\) 41.1007 1.64667
\(624\) −1.57560 −0.0630744
\(625\) 0 0
\(626\) −25.8664 −1.03383
\(627\) −4.83950 −0.193271
\(628\) −4.97787 −0.198639
\(629\) 3.34323 0.133303
\(630\) 0 0
\(631\) −47.0576 −1.87334 −0.936668 0.350220i \(-0.886107\pi\)
−0.936668 + 0.350220i \(0.886107\pi\)
\(632\) 28.8879 1.14910
\(633\) 38.4531 1.52837
\(634\) −13.6476 −0.542016
\(635\) 0 0
\(636\) −16.6692 −0.660978
\(637\) 31.6299 1.25322
\(638\) −7.36668 −0.291650
\(639\) 11.6696 0.461641
\(640\) 0 0
\(641\) 25.2677 0.998015 0.499007 0.866598i \(-0.333698\pi\)
0.499007 + 0.866598i \(0.333698\pi\)
\(642\) −10.6274 −0.419431
\(643\) −1.36761 −0.0539332 −0.0269666 0.999636i \(-0.508585\pi\)
−0.0269666 + 0.999636i \(0.508585\pi\)
\(644\) −10.8053 −0.425790
\(645\) 0 0
\(646\) 1.17104 0.0460739
\(647\) −47.9634 −1.88563 −0.942817 0.333310i \(-0.891834\pi\)
−0.942817 + 0.333310i \(0.891834\pi\)
\(648\) −10.8940 −0.427956
\(649\) −7.00321 −0.274900
\(650\) 0 0
\(651\) −34.0010 −1.33261
\(652\) 6.04425 0.236711
\(653\) −18.9603 −0.741975 −0.370987 0.928638i \(-0.620981\pi\)
−0.370987 + 0.928638i \(0.620981\pi\)
\(654\) 10.0753 0.393974
\(655\) 0 0
\(656\) 2.68891 0.104984
\(657\) 5.10234 0.199061
\(658\) 38.3251 1.49407
\(659\) −8.62976 −0.336168 −0.168084 0.985773i \(-0.553758\pi\)
−0.168084 + 0.985773i \(0.553758\pi\)
\(660\) 0 0
\(661\) −16.6323 −0.646920 −0.323460 0.946242i \(-0.604846\pi\)
−0.323460 + 0.946242i \(0.604846\pi\)
\(662\) 13.7977 0.536265
\(663\) 1.08287 0.0420553
\(664\) −31.2835 −1.21403
\(665\) 0 0
\(666\) 12.6799 0.491336
\(667\) −19.7156 −0.763393
\(668\) 9.75341 0.377371
\(669\) −10.0488 −0.388510
\(670\) 0 0
\(671\) −1.41519 −0.0546328
\(672\) 31.1592 1.20199
\(673\) −10.4577 −0.403113 −0.201557 0.979477i \(-0.564600\pi\)
−0.201557 + 0.979477i \(0.564600\pi\)
\(674\) 3.64681 0.140470
\(675\) 0 0
\(676\) 6.58728 0.253357
\(677\) 41.7207 1.60346 0.801728 0.597689i \(-0.203914\pi\)
0.801728 + 0.597689i \(0.203914\pi\)
\(678\) −5.17780 −0.198852
\(679\) 6.13763 0.235541
\(680\) 0 0
\(681\) −12.9163 −0.494954
\(682\) −4.85414 −0.185875
\(683\) −32.9092 −1.25924 −0.629618 0.776905i \(-0.716789\pi\)
−0.629618 + 0.776905i \(0.716789\pi\)
\(684\) −5.82457 −0.222708
\(685\) 0 0
\(686\) 19.3231 0.737758
\(687\) −32.8541 −1.25346
\(688\) 1.20447 0.0459198
\(689\) 29.7112 1.13191
\(690\) 0 0
\(691\) 23.1023 0.878855 0.439427 0.898278i \(-0.355181\pi\)
0.439427 + 0.898278i \(0.355181\pi\)
\(692\) −4.44078 −0.168813
\(693\) 4.74743 0.180340
\(694\) 1.75566 0.0666438
\(695\) 0 0
\(696\) 34.7089 1.31564
\(697\) −1.84803 −0.0699990
\(698\) 5.39228 0.204101
\(699\) 27.8388 1.05296
\(700\) 0 0
\(701\) 16.5438 0.624852 0.312426 0.949942i \(-0.398858\pi\)
0.312426 + 0.949942i \(0.398858\pi\)
\(702\) 14.0341 0.529683
\(703\) −45.4208 −1.71308
\(704\) 5.23004 0.197115
\(705\) 0 0
\(706\) 19.3682 0.728932
\(707\) −73.4612 −2.76279
\(708\) 11.9443 0.448893
\(709\) 31.5902 1.18639 0.593197 0.805058i \(-0.297866\pi\)
0.593197 + 0.805058i \(0.297866\pi\)
\(710\) 0 0
\(711\) −12.2961 −0.461141
\(712\) −27.6464 −1.03609
\(713\) −12.9913 −0.486526
\(714\) 1.62790 0.0609227
\(715\) 0 0
\(716\) 2.86352 0.107015
\(717\) −1.24136 −0.0463595
\(718\) 14.3728 0.536389
\(719\) −17.6028 −0.656474 −0.328237 0.944595i \(-0.606454\pi\)
−0.328237 + 0.944595i \(0.606454\pi\)
\(720\) 0 0
\(721\) 8.25919 0.307588
\(722\) 1.76411 0.0656534
\(723\) 1.32621 0.0493224
\(724\) 18.7295 0.696075
\(725\) 0 0
\(726\) 12.6096 0.467985
\(727\) 34.7819 1.28999 0.644995 0.764187i \(-0.276859\pi\)
0.644995 + 0.764187i \(0.276859\pi\)
\(728\) −33.9057 −1.25663
\(729\) 27.0156 1.00058
\(730\) 0 0
\(731\) −0.827803 −0.0306174
\(732\) 2.41367 0.0892117
\(733\) −35.3016 −1.30389 −0.651947 0.758265i \(-0.726048\pi\)
−0.651947 + 0.758265i \(0.726048\pi\)
\(734\) −35.3829 −1.30601
\(735\) 0 0
\(736\) 11.9054 0.438840
\(737\) −13.7429 −0.506228
\(738\) −7.00903 −0.258006
\(739\) −14.8693 −0.546975 −0.273487 0.961876i \(-0.588177\pi\)
−0.273487 + 0.961876i \(0.588177\pi\)
\(740\) 0 0
\(741\) −14.7118 −0.540453
\(742\) 44.6653 1.63971
\(743\) 28.8502 1.05841 0.529206 0.848494i \(-0.322490\pi\)
0.529206 + 0.848494i \(0.322490\pi\)
\(744\) 22.8708 0.838484
\(745\) 0 0
\(746\) −14.5967 −0.534424
\(747\) 13.3158 0.487199
\(748\) −0.304784 −0.0111440
\(749\) −37.3444 −1.36454
\(750\) 0 0
\(751\) 26.4978 0.966918 0.483459 0.875367i \(-0.339380\pi\)
0.483459 + 0.875367i \(0.339380\pi\)
\(752\) −4.20963 −0.153509
\(753\) 15.6764 0.571280
\(754\) −22.3944 −0.815555
\(755\) 0 0
\(756\) −27.6680 −1.00628
\(757\) −34.8758 −1.26758 −0.633790 0.773505i \(-0.718502\pi\)
−0.633790 + 0.773505i \(0.718502\pi\)
\(758\) 4.51660 0.164050
\(759\) −2.57049 −0.0933029
\(760\) 0 0
\(761\) 43.4881 1.57644 0.788221 0.615392i \(-0.211002\pi\)
0.788221 + 0.615392i \(0.211002\pi\)
\(762\) 6.10210 0.221056
\(763\) 35.4042 1.28172
\(764\) 25.6456 0.927826
\(765\) 0 0
\(766\) 17.1098 0.618203
\(767\) −21.2894 −0.768717
\(768\) −22.2923 −0.804405
\(769\) 49.0482 1.76872 0.884362 0.466801i \(-0.154594\pi\)
0.884362 + 0.466801i \(0.154594\pi\)
\(770\) 0 0
\(771\) −19.8356 −0.714361
\(772\) −7.47348 −0.268976
\(773\) −28.0305 −1.00819 −0.504093 0.863649i \(-0.668173\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(774\) −3.13962 −0.112851
\(775\) 0 0
\(776\) −4.12848 −0.148204
\(777\) −63.1410 −2.26517
\(778\) 28.4937 1.02155
\(779\) 25.1071 0.899557
\(780\) 0 0
\(781\) −8.29605 −0.296856
\(782\) 0.621995 0.0222425
\(783\) −50.4836 −1.80414
\(784\) −5.22285 −0.186530
\(785\) 0 0
\(786\) −16.8825 −0.602178
\(787\) 14.4420 0.514801 0.257400 0.966305i \(-0.417134\pi\)
0.257400 + 0.966305i \(0.417134\pi\)
\(788\) 4.07578 0.145194
\(789\) −16.3564 −0.582302
\(790\) 0 0
\(791\) −18.1946 −0.646926
\(792\) −3.19336 −0.113471
\(793\) −4.30211 −0.152772
\(794\) 4.34880 0.154333
\(795\) 0 0
\(796\) 23.9129 0.847570
\(797\) −10.9710 −0.388612 −0.194306 0.980941i \(-0.562245\pi\)
−0.194306 + 0.980941i \(0.562245\pi\)
\(798\) −22.1165 −0.782917
\(799\) 2.89318 0.102353
\(800\) 0 0
\(801\) 11.7677 0.415791
\(802\) 6.98009 0.246475
\(803\) −3.62732 −0.128005
\(804\) 23.4392 0.826635
\(805\) 0 0
\(806\) −14.7564 −0.519770
\(807\) −3.46474 −0.121965
\(808\) 49.4137 1.73837
\(809\) −39.0394 −1.37255 −0.686276 0.727342i \(-0.740756\pi\)
−0.686276 + 0.727342i \(0.740756\pi\)
\(810\) 0 0
\(811\) −22.6660 −0.795912 −0.397956 0.917405i \(-0.630280\pi\)
−0.397956 + 0.917405i \(0.630280\pi\)
\(812\) 44.1502 1.54937
\(813\) −12.9390 −0.453789
\(814\) −9.01430 −0.315951
\(815\) 0 0
\(816\) −0.178808 −0.00625954
\(817\) 11.2465 0.393464
\(818\) 6.72376 0.235091
\(819\) 14.4320 0.504294
\(820\) 0 0
\(821\) 24.9834 0.871926 0.435963 0.899965i \(-0.356408\pi\)
0.435963 + 0.899965i \(0.356408\pi\)
\(822\) −23.5104 −0.820018
\(823\) −35.0663 −1.22233 −0.611167 0.791502i \(-0.709300\pi\)
−0.611167 + 0.791502i \(0.709300\pi\)
\(824\) −5.55555 −0.193537
\(825\) 0 0
\(826\) −32.0047 −1.11359
\(827\) 5.28536 0.183790 0.0918949 0.995769i \(-0.470708\pi\)
0.0918949 + 0.995769i \(0.470708\pi\)
\(828\) −3.09371 −0.107514
\(829\) 0.699646 0.0242997 0.0121499 0.999926i \(-0.496132\pi\)
0.0121499 + 0.999926i \(0.496132\pi\)
\(830\) 0 0
\(831\) 0.674620 0.0234023
\(832\) 15.8991 0.551202
\(833\) 3.58955 0.124371
\(834\) 26.8134 0.928473
\(835\) 0 0
\(836\) 4.14077 0.143211
\(837\) −33.2652 −1.14981
\(838\) −12.0143 −0.415026
\(839\) 44.8426 1.54814 0.774069 0.633101i \(-0.218218\pi\)
0.774069 + 0.633101i \(0.218218\pi\)
\(840\) 0 0
\(841\) 51.5573 1.77784
\(842\) −23.8699 −0.822610
\(843\) −33.2372 −1.14475
\(844\) −32.9012 −1.13251
\(845\) 0 0
\(846\) 10.9730 0.377260
\(847\) 44.3097 1.52250
\(848\) −4.90603 −0.168474
\(849\) 2.00600 0.0688457
\(850\) 0 0
\(851\) −24.1252 −0.827001
\(852\) 14.1493 0.484746
\(853\) 10.7624 0.368497 0.184249 0.982880i \(-0.441015\pi\)
0.184249 + 0.982880i \(0.441015\pi\)
\(854\) −6.46743 −0.221311
\(855\) 0 0
\(856\) 25.1197 0.858575
\(857\) −21.5155 −0.734956 −0.367478 0.930032i \(-0.619779\pi\)
−0.367478 + 0.930032i \(0.619779\pi\)
\(858\) −2.91974 −0.0996782
\(859\) 2.12944 0.0726556 0.0363278 0.999340i \(-0.488434\pi\)
0.0363278 + 0.999340i \(0.488434\pi\)
\(860\) 0 0
\(861\) 34.9023 1.18947
\(862\) 4.08009 0.138968
\(863\) −10.2693 −0.349571 −0.174785 0.984607i \(-0.555923\pi\)
−0.174785 + 0.984607i \(0.555923\pi\)
\(864\) 30.4849 1.03712
\(865\) 0 0
\(866\) 9.93618 0.337645
\(867\) −22.4227 −0.761515
\(868\) 29.0919 0.987444
\(869\) 8.74148 0.296534
\(870\) 0 0
\(871\) −41.7779 −1.41559
\(872\) −23.8146 −0.806466
\(873\) 1.75729 0.0594751
\(874\) −8.45038 −0.285838
\(875\) 0 0
\(876\) 6.18655 0.209024
\(877\) −5.83603 −0.197069 −0.0985343 0.995134i \(-0.531415\pi\)
−0.0985343 + 0.995134i \(0.531415\pi\)
\(878\) −5.64871 −0.190635
\(879\) 36.8189 1.24187
\(880\) 0 0
\(881\) 23.6510 0.796823 0.398412 0.917207i \(-0.369562\pi\)
0.398412 + 0.917207i \(0.369562\pi\)
\(882\) 13.6141 0.458411
\(883\) 21.4740 0.722658 0.361329 0.932438i \(-0.382323\pi\)
0.361329 + 0.932438i \(0.382323\pi\)
\(884\) −0.926528 −0.0311625
\(885\) 0 0
\(886\) 21.7129 0.729459
\(887\) 19.7851 0.664320 0.332160 0.943223i \(-0.392223\pi\)
0.332160 + 0.943223i \(0.392223\pi\)
\(888\) 42.4718 1.42526
\(889\) 21.4426 0.719162
\(890\) 0 0
\(891\) −3.29652 −0.110438
\(892\) 8.59797 0.287881
\(893\) −39.3066 −1.31534
\(894\) 7.44899 0.249132
\(895\) 0 0
\(896\) −23.0884 −0.771329
\(897\) −7.81417 −0.260907
\(898\) −13.5681 −0.452775
\(899\) 53.0817 1.77038
\(900\) 0 0
\(901\) 3.37180 0.112331
\(902\) 4.98281 0.165909
\(903\) 15.6341 0.520270
\(904\) 12.2386 0.407051
\(905\) 0 0
\(906\) 18.5187 0.615244
\(907\) −0.445947 −0.0148074 −0.00740371 0.999973i \(-0.502357\pi\)
−0.00740371 + 0.999973i \(0.502357\pi\)
\(908\) 11.0514 0.366755
\(909\) −21.0329 −0.697619
\(910\) 0 0
\(911\) 3.07240 0.101793 0.0508965 0.998704i \(-0.483792\pi\)
0.0508965 + 0.998704i \(0.483792\pi\)
\(912\) 2.42928 0.0804414
\(913\) −9.46637 −0.313291
\(914\) 20.0983 0.664793
\(915\) 0 0
\(916\) 28.1106 0.928802
\(917\) −59.3245 −1.95907
\(918\) 1.59267 0.0525660
\(919\) 9.98217 0.329281 0.164641 0.986354i \(-0.447354\pi\)
0.164641 + 0.986354i \(0.447354\pi\)
\(920\) 0 0
\(921\) −25.4065 −0.837172
\(922\) 8.10924 0.267063
\(923\) −25.2196 −0.830113
\(924\) 5.75622 0.189366
\(925\) 0 0
\(926\) −15.1392 −0.497505
\(927\) 2.36472 0.0776675
\(928\) −48.6451 −1.59685
\(929\) 2.23534 0.0733392 0.0366696 0.999327i \(-0.488325\pi\)
0.0366696 + 0.999327i \(0.488325\pi\)
\(930\) 0 0
\(931\) −48.7674 −1.59829
\(932\) −23.8194 −0.780230
\(933\) −5.43284 −0.177863
\(934\) 6.38235 0.208837
\(935\) 0 0
\(936\) −9.70767 −0.317305
\(937\) 46.5278 1.52000 0.759999 0.649924i \(-0.225199\pi\)
0.759999 + 0.649924i \(0.225199\pi\)
\(938\) −62.8053 −2.05067
\(939\) 36.8785 1.20348
\(940\) 0 0
\(941\) 37.9006 1.23552 0.617761 0.786366i \(-0.288040\pi\)
0.617761 + 0.786366i \(0.288040\pi\)
\(942\) −5.41176 −0.176325
\(943\) 13.3356 0.434267
\(944\) 3.51539 0.114416
\(945\) 0 0
\(946\) 2.23199 0.0725684
\(947\) 22.0207 0.715576 0.357788 0.933803i \(-0.383531\pi\)
0.357788 + 0.933803i \(0.383531\pi\)
\(948\) −14.9090 −0.484220
\(949\) −11.0269 −0.357948
\(950\) 0 0
\(951\) 19.4579 0.630964
\(952\) −3.84783 −0.124709
\(953\) 49.8117 1.61356 0.806779 0.590853i \(-0.201209\pi\)
0.806779 + 0.590853i \(0.201209\pi\)
\(954\) 12.7883 0.414035
\(955\) 0 0
\(956\) 1.06213 0.0343518
\(957\) 10.5029 0.339511
\(958\) −16.4631 −0.531898
\(959\) −82.6147 −2.66777
\(960\) 0 0
\(961\) 3.97722 0.128297
\(962\) −27.4030 −0.883509
\(963\) −10.6922 −0.344552
\(964\) −1.13473 −0.0365473
\(965\) 0 0
\(966\) −11.7472 −0.377959
\(967\) −12.7604 −0.410348 −0.205174 0.978726i \(-0.565776\pi\)
−0.205174 + 0.978726i \(0.565776\pi\)
\(968\) −29.8049 −0.957966
\(969\) −1.66959 −0.0536349
\(970\) 0 0
\(971\) 6.51886 0.209200 0.104600 0.994514i \(-0.466644\pi\)
0.104600 + 0.994514i \(0.466644\pi\)
\(972\) −13.5252 −0.433820
\(973\) 94.2215 3.02060
\(974\) 8.43374 0.270234
\(975\) 0 0
\(976\) 0.710381 0.0227388
\(977\) 21.9764 0.703089 0.351544 0.936171i \(-0.385657\pi\)
0.351544 + 0.936171i \(0.385657\pi\)
\(978\) 6.57108 0.210120
\(979\) −8.36580 −0.267372
\(980\) 0 0
\(981\) 10.1367 0.323640
\(982\) 15.1140 0.482307
\(983\) −9.07592 −0.289477 −0.144738 0.989470i \(-0.546234\pi\)
−0.144738 + 0.989470i \(0.546234\pi\)
\(984\) −23.4770 −0.748421
\(985\) 0 0
\(986\) −2.54145 −0.0809362
\(987\) −54.6414 −1.73925
\(988\) 12.5877 0.400469
\(989\) 5.97354 0.189947
\(990\) 0 0
\(991\) 19.4358 0.617400 0.308700 0.951159i \(-0.400106\pi\)
0.308700 + 0.951159i \(0.400106\pi\)
\(992\) −32.0538 −1.01771
\(993\) −19.6719 −0.624269
\(994\) −37.9130 −1.20253
\(995\) 0 0
\(996\) 16.1453 0.511583
\(997\) −35.1276 −1.11250 −0.556250 0.831015i \(-0.687760\pi\)
−0.556250 + 0.831015i \(0.687760\pi\)
\(998\) −29.0568 −0.919777
\(999\) −61.7746 −1.95446
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.1.16 46
5.2 odd 4 1205.2.b.c.724.16 46
5.3 odd 4 1205.2.b.c.724.31 yes 46
5.4 even 2 inner 6025.2.a.p.1.31 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.16 46 5.2 odd 4
1205.2.b.c.724.31 yes 46 5.3 odd 4
6025.2.a.p.1.16 46 1.1 even 1 trivial
6025.2.a.p.1.31 46 5.4 even 2 inner