Properties

Label 6025.2.a.p.1.2
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 1.2
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.67602 q^{2} -0.199289 q^{3} +5.16108 q^{4} +0.533301 q^{6} +2.87374 q^{7} -8.45912 q^{8} -2.96028 q^{9} +O(q^{10})\) \(q-2.67602 q^{2} -0.199289 q^{3} +5.16108 q^{4} +0.533301 q^{6} +2.87374 q^{7} -8.45912 q^{8} -2.96028 q^{9} -0.806904 q^{11} -1.02855 q^{12} +5.09752 q^{13} -7.69018 q^{14} +12.3146 q^{16} +0.390647 q^{17} +7.92178 q^{18} +0.489734 q^{19} -0.572704 q^{21} +2.15929 q^{22} +1.83958 q^{23} +1.68581 q^{24} -13.6411 q^{26} +1.18782 q^{27} +14.8316 q^{28} -8.05368 q^{29} -5.55127 q^{31} -16.0359 q^{32} +0.160807 q^{33} -1.04538 q^{34} -15.2783 q^{36} +2.20153 q^{37} -1.31054 q^{38} -1.01588 q^{39} -3.59719 q^{41} +1.53257 q^{42} +9.27459 q^{43} -4.16450 q^{44} -4.92275 q^{46} -10.9779 q^{47} -2.45416 q^{48} +1.25837 q^{49} -0.0778515 q^{51} +26.3087 q^{52} +1.68955 q^{53} -3.17863 q^{54} -24.3093 q^{56} -0.0975985 q^{57} +21.5518 q^{58} -5.02546 q^{59} +3.39923 q^{61} +14.8553 q^{62} -8.50708 q^{63} +18.2832 q^{64} -0.430323 q^{66} -12.9814 q^{67} +2.01616 q^{68} -0.366608 q^{69} +8.48671 q^{71} +25.0414 q^{72} -13.1818 q^{73} -5.89135 q^{74} +2.52756 q^{76} -2.31883 q^{77} +2.71851 q^{78} +8.08502 q^{79} +8.64413 q^{81} +9.62615 q^{82} -0.366678 q^{83} -2.95577 q^{84} -24.8190 q^{86} +1.60501 q^{87} +6.82569 q^{88} -2.24259 q^{89} +14.6489 q^{91} +9.49422 q^{92} +1.10631 q^{93} +29.3772 q^{94} +3.19578 q^{96} -7.32434 q^{97} -3.36741 q^{98} +2.38866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67602 −1.89223 −0.946116 0.323828i \(-0.895030\pi\)
−0.946116 + 0.323828i \(0.895030\pi\)
\(3\) −0.199289 −0.115060 −0.0575298 0.998344i \(-0.518322\pi\)
−0.0575298 + 0.998344i \(0.518322\pi\)
\(4\) 5.16108 2.58054
\(5\) 0 0
\(6\) 0.533301 0.217719
\(7\) 2.87374 1.08617 0.543085 0.839678i \(-0.317256\pi\)
0.543085 + 0.839678i \(0.317256\pi\)
\(8\) −8.45912 −2.99075
\(9\) −2.96028 −0.986761
\(10\) 0 0
\(11\) −0.806904 −0.243291 −0.121645 0.992574i \(-0.538817\pi\)
−0.121645 + 0.992574i \(0.538817\pi\)
\(12\) −1.02855 −0.296916
\(13\) 5.09752 1.41380 0.706899 0.707315i \(-0.250094\pi\)
0.706899 + 0.707315i \(0.250094\pi\)
\(14\) −7.69018 −2.05529
\(15\) 0 0
\(16\) 12.3146 3.07865
\(17\) 0.390647 0.0947457 0.0473729 0.998877i \(-0.484915\pi\)
0.0473729 + 0.998877i \(0.484915\pi\)
\(18\) 7.92178 1.86718
\(19\) 0.489734 0.112353 0.0561763 0.998421i \(-0.482109\pi\)
0.0561763 + 0.998421i \(0.482109\pi\)
\(20\) 0 0
\(21\) −0.572704 −0.124974
\(22\) 2.15929 0.460362
\(23\) 1.83958 0.383579 0.191789 0.981436i \(-0.438571\pi\)
0.191789 + 0.981436i \(0.438571\pi\)
\(24\) 1.68581 0.344114
\(25\) 0 0
\(26\) −13.6411 −2.67523
\(27\) 1.18782 0.228596
\(28\) 14.8316 2.80291
\(29\) −8.05368 −1.49553 −0.747765 0.663963i \(-0.768873\pi\)
−0.747765 + 0.663963i \(0.768873\pi\)
\(30\) 0 0
\(31\) −5.55127 −0.997038 −0.498519 0.866879i \(-0.666123\pi\)
−0.498519 + 0.866879i \(0.666123\pi\)
\(32\) −16.0359 −2.83477
\(33\) 0.160807 0.0279929
\(34\) −1.04538 −0.179281
\(35\) 0 0
\(36\) −15.2783 −2.54638
\(37\) 2.20153 0.361930 0.180965 0.983490i \(-0.442078\pi\)
0.180965 + 0.983490i \(0.442078\pi\)
\(38\) −1.31054 −0.212597
\(39\) −1.01588 −0.162671
\(40\) 0 0
\(41\) −3.59719 −0.561787 −0.280893 0.959739i \(-0.590631\pi\)
−0.280893 + 0.959739i \(0.590631\pi\)
\(42\) 1.53257 0.236480
\(43\) 9.27459 1.41436 0.707181 0.707033i \(-0.249967\pi\)
0.707181 + 0.707033i \(0.249967\pi\)
\(44\) −4.16450 −0.627821
\(45\) 0 0
\(46\) −4.92275 −0.725820
\(47\) −10.9779 −1.60130 −0.800649 0.599134i \(-0.795512\pi\)
−0.800649 + 0.599134i \(0.795512\pi\)
\(48\) −2.45416 −0.354228
\(49\) 1.25837 0.179767
\(50\) 0 0
\(51\) −0.0778515 −0.0109014
\(52\) 26.3087 3.64836
\(53\) 1.68955 0.232077 0.116039 0.993245i \(-0.462980\pi\)
0.116039 + 0.993245i \(0.462980\pi\)
\(54\) −3.17863 −0.432556
\(55\) 0 0
\(56\) −24.3093 −3.24847
\(57\) −0.0975985 −0.0129272
\(58\) 21.5518 2.82989
\(59\) −5.02546 −0.654259 −0.327130 0.944979i \(-0.606081\pi\)
−0.327130 + 0.944979i \(0.606081\pi\)
\(60\) 0 0
\(61\) 3.39923 0.435227 0.217613 0.976035i \(-0.430173\pi\)
0.217613 + 0.976035i \(0.430173\pi\)
\(62\) 14.8553 1.88663
\(63\) −8.50708 −1.07179
\(64\) 18.2832 2.28539
\(65\) 0 0
\(66\) −0.430323 −0.0529690
\(67\) −12.9814 −1.58594 −0.792968 0.609263i \(-0.791465\pi\)
−0.792968 + 0.609263i \(0.791465\pi\)
\(68\) 2.01616 0.244495
\(69\) −0.366608 −0.0441344
\(70\) 0 0
\(71\) 8.48671 1.00719 0.503594 0.863941i \(-0.332011\pi\)
0.503594 + 0.863941i \(0.332011\pi\)
\(72\) 25.0414 2.95116
\(73\) −13.1818 −1.54281 −0.771404 0.636346i \(-0.780445\pi\)
−0.771404 + 0.636346i \(0.780445\pi\)
\(74\) −5.89135 −0.684855
\(75\) 0 0
\(76\) 2.52756 0.289931
\(77\) −2.31883 −0.264255
\(78\) 2.71851 0.307811
\(79\) 8.08502 0.909636 0.454818 0.890584i \(-0.349704\pi\)
0.454818 + 0.890584i \(0.349704\pi\)
\(80\) 0 0
\(81\) 8.64413 0.960459
\(82\) 9.62615 1.06303
\(83\) −0.366678 −0.0402481 −0.0201240 0.999797i \(-0.506406\pi\)
−0.0201240 + 0.999797i \(0.506406\pi\)
\(84\) −2.95577 −0.322501
\(85\) 0 0
\(86\) −24.8190 −2.67630
\(87\) 1.60501 0.172075
\(88\) 6.82569 0.727621
\(89\) −2.24259 −0.237715 −0.118857 0.992911i \(-0.537923\pi\)
−0.118857 + 0.992911i \(0.537923\pi\)
\(90\) 0 0
\(91\) 14.6489 1.53563
\(92\) 9.49422 0.989841
\(93\) 1.10631 0.114719
\(94\) 29.3772 3.03003
\(95\) 0 0
\(96\) 3.19578 0.326168
\(97\) −7.32434 −0.743674 −0.371837 0.928298i \(-0.621272\pi\)
−0.371837 + 0.928298i \(0.621272\pi\)
\(98\) −3.36741 −0.340160
\(99\) 2.38866 0.240070
\(100\) 0 0
\(101\) 3.65598 0.363783 0.181892 0.983319i \(-0.441778\pi\)
0.181892 + 0.983319i \(0.441778\pi\)
\(102\) 0.208332 0.0206280
\(103\) 19.1218 1.88413 0.942064 0.335434i \(-0.108883\pi\)
0.942064 + 0.335434i \(0.108883\pi\)
\(104\) −43.1205 −4.22832
\(105\) 0 0
\(106\) −4.52127 −0.439144
\(107\) −6.56240 −0.634411 −0.317205 0.948357i \(-0.602744\pi\)
−0.317205 + 0.948357i \(0.602744\pi\)
\(108\) 6.13043 0.589901
\(109\) −15.2722 −1.46282 −0.731408 0.681940i \(-0.761136\pi\)
−0.731408 + 0.681940i \(0.761136\pi\)
\(110\) 0 0
\(111\) −0.438741 −0.0416435
\(112\) 35.3889 3.34394
\(113\) −0.183036 −0.0172186 −0.00860929 0.999963i \(-0.502740\pi\)
−0.00860929 + 0.999963i \(0.502740\pi\)
\(114\) 0.261176 0.0244613
\(115\) 0 0
\(116\) −41.5657 −3.85928
\(117\) −15.0901 −1.39508
\(118\) 13.4482 1.23801
\(119\) 1.12262 0.102910
\(120\) 0 0
\(121\) −10.3489 −0.940810
\(122\) −9.09640 −0.823550
\(123\) 0.716880 0.0646389
\(124\) −28.6506 −2.57290
\(125\) 0 0
\(126\) 22.7651 2.02808
\(127\) −15.1585 −1.34510 −0.672551 0.740051i \(-0.734801\pi\)
−0.672551 + 0.740051i \(0.734801\pi\)
\(128\) −16.8543 −1.48972
\(129\) −1.84832 −0.162736
\(130\) 0 0
\(131\) 7.10114 0.620430 0.310215 0.950667i \(-0.399599\pi\)
0.310215 + 0.950667i \(0.399599\pi\)
\(132\) 0.829938 0.0722368
\(133\) 1.40737 0.122034
\(134\) 34.7386 3.00096
\(135\) 0 0
\(136\) −3.30453 −0.283361
\(137\) 7.60403 0.649656 0.324828 0.945773i \(-0.394694\pi\)
0.324828 + 0.945773i \(0.394694\pi\)
\(138\) 0.981050 0.0835125
\(139\) −21.2414 −1.80167 −0.900835 0.434161i \(-0.857045\pi\)
−0.900835 + 0.434161i \(0.857045\pi\)
\(140\) 0 0
\(141\) 2.18778 0.184245
\(142\) −22.7106 −1.90583
\(143\) −4.11321 −0.343964
\(144\) −36.4547 −3.03789
\(145\) 0 0
\(146\) 35.2746 2.91935
\(147\) −0.250778 −0.0206839
\(148\) 11.3623 0.933975
\(149\) −16.0916 −1.31827 −0.659137 0.752023i \(-0.729078\pi\)
−0.659137 + 0.752023i \(0.729078\pi\)
\(150\) 0 0
\(151\) −10.5518 −0.858695 −0.429348 0.903139i \(-0.641256\pi\)
−0.429348 + 0.903139i \(0.641256\pi\)
\(152\) −4.14272 −0.336019
\(153\) −1.15642 −0.0934914
\(154\) 6.20523 0.500032
\(155\) 0 0
\(156\) −5.24304 −0.419779
\(157\) −0.254366 −0.0203006 −0.0101503 0.999948i \(-0.503231\pi\)
−0.0101503 + 0.999948i \(0.503231\pi\)
\(158\) −21.6357 −1.72124
\(159\) −0.336708 −0.0267027
\(160\) 0 0
\(161\) 5.28647 0.416632
\(162\) −23.1319 −1.81741
\(163\) −8.82845 −0.691497 −0.345749 0.938327i \(-0.612375\pi\)
−0.345749 + 0.938327i \(0.612375\pi\)
\(164\) −18.5654 −1.44971
\(165\) 0 0
\(166\) 0.981236 0.0761587
\(167\) 3.04162 0.235367 0.117684 0.993051i \(-0.462453\pi\)
0.117684 + 0.993051i \(0.462453\pi\)
\(168\) 4.84457 0.373767
\(169\) 12.9847 0.998824
\(170\) 0 0
\(171\) −1.44975 −0.110865
\(172\) 47.8669 3.64982
\(173\) −6.02560 −0.458118 −0.229059 0.973413i \(-0.573565\pi\)
−0.229059 + 0.973413i \(0.573565\pi\)
\(174\) −4.29504 −0.325606
\(175\) 0 0
\(176\) −9.93670 −0.749007
\(177\) 1.00152 0.0752787
\(178\) 6.00123 0.449811
\(179\) 7.72419 0.577333 0.288667 0.957430i \(-0.406788\pi\)
0.288667 + 0.957430i \(0.406788\pi\)
\(180\) 0 0
\(181\) −10.3144 −0.766662 −0.383331 0.923611i \(-0.625223\pi\)
−0.383331 + 0.923611i \(0.625223\pi\)
\(182\) −39.2008 −2.90576
\(183\) −0.677429 −0.0500770
\(184\) −15.5612 −1.14719
\(185\) 0 0
\(186\) −2.96050 −0.217074
\(187\) −0.315214 −0.0230507
\(188\) −56.6581 −4.13221
\(189\) 3.41348 0.248294
\(190\) 0 0
\(191\) −16.6263 −1.20304 −0.601519 0.798858i \(-0.705438\pi\)
−0.601519 + 0.798858i \(0.705438\pi\)
\(192\) −3.64363 −0.262956
\(193\) 26.5699 1.91254 0.956271 0.292481i \(-0.0944810\pi\)
0.956271 + 0.292481i \(0.0944810\pi\)
\(194\) 19.6001 1.40720
\(195\) 0 0
\(196\) 6.49453 0.463895
\(197\) 4.42875 0.315536 0.157768 0.987476i \(-0.449570\pi\)
0.157768 + 0.987476i \(0.449570\pi\)
\(198\) −6.39211 −0.454268
\(199\) 3.44630 0.244302 0.122151 0.992512i \(-0.461021\pi\)
0.122151 + 0.992512i \(0.461021\pi\)
\(200\) 0 0
\(201\) 2.58706 0.182477
\(202\) −9.78347 −0.688362
\(203\) −23.1442 −1.62440
\(204\) −0.401798 −0.0281315
\(205\) 0 0
\(206\) −51.1703 −3.56521
\(207\) −5.44568 −0.378501
\(208\) 62.7740 4.35259
\(209\) −0.395168 −0.0273343
\(210\) 0 0
\(211\) −0.758471 −0.0522153 −0.0261076 0.999659i \(-0.508311\pi\)
−0.0261076 + 0.999659i \(0.508311\pi\)
\(212\) 8.71990 0.598885
\(213\) −1.69131 −0.115886
\(214\) 17.5611 1.20045
\(215\) 0 0
\(216\) −10.0479 −0.683673
\(217\) −15.9529 −1.08295
\(218\) 40.8688 2.76799
\(219\) 2.62698 0.177515
\(220\) 0 0
\(221\) 1.99133 0.133951
\(222\) 1.17408 0.0787991
\(223\) 0.994567 0.0666011 0.0333006 0.999445i \(-0.489398\pi\)
0.0333006 + 0.999445i \(0.489398\pi\)
\(224\) −46.0830 −3.07905
\(225\) 0 0
\(226\) 0.489808 0.0325815
\(227\) 9.15012 0.607315 0.303657 0.952781i \(-0.401792\pi\)
0.303657 + 0.952781i \(0.401792\pi\)
\(228\) −0.503714 −0.0333593
\(229\) 24.8061 1.63924 0.819618 0.572910i \(-0.194186\pi\)
0.819618 + 0.572910i \(0.194186\pi\)
\(230\) 0 0
\(231\) 0.462117 0.0304051
\(232\) 68.1270 4.47276
\(233\) −20.8307 −1.36466 −0.682332 0.731042i \(-0.739034\pi\)
−0.682332 + 0.731042i \(0.739034\pi\)
\(234\) 40.3814 2.63982
\(235\) 0 0
\(236\) −25.9368 −1.68834
\(237\) −1.61126 −0.104662
\(238\) −3.00414 −0.194730
\(239\) −27.2186 −1.76062 −0.880311 0.474397i \(-0.842666\pi\)
−0.880311 + 0.474397i \(0.842666\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 27.6939 1.78023
\(243\) −5.28614 −0.339106
\(244\) 17.5437 1.12312
\(245\) 0 0
\(246\) −1.91839 −0.122312
\(247\) 2.49643 0.158844
\(248\) 46.9589 2.98189
\(249\) 0.0730748 0.00463093
\(250\) 0 0
\(251\) 17.6839 1.11620 0.558100 0.829774i \(-0.311531\pi\)
0.558100 + 0.829774i \(0.311531\pi\)
\(252\) −43.9057 −2.76580
\(253\) −1.48436 −0.0933211
\(254\) 40.5645 2.54524
\(255\) 0 0
\(256\) 8.53615 0.533509
\(257\) 24.6433 1.53721 0.768604 0.639725i \(-0.220952\pi\)
0.768604 + 0.639725i \(0.220952\pi\)
\(258\) 4.94615 0.307934
\(259\) 6.32663 0.393118
\(260\) 0 0
\(261\) 23.8412 1.47573
\(262\) −19.0028 −1.17400
\(263\) 21.3217 1.31475 0.657376 0.753563i \(-0.271666\pi\)
0.657376 + 0.753563i \(0.271666\pi\)
\(264\) −1.36029 −0.0837198
\(265\) 0 0
\(266\) −3.76614 −0.230917
\(267\) 0.446924 0.0273513
\(268\) −66.9983 −4.09257
\(269\) 21.8448 1.33190 0.665951 0.745996i \(-0.268026\pi\)
0.665951 + 0.745996i \(0.268026\pi\)
\(270\) 0 0
\(271\) 1.65986 0.100830 0.0504148 0.998728i \(-0.483946\pi\)
0.0504148 + 0.998728i \(0.483946\pi\)
\(272\) 4.81066 0.291689
\(273\) −2.91937 −0.176688
\(274\) −20.3485 −1.22930
\(275\) 0 0
\(276\) −1.89209 −0.113891
\(277\) −17.1120 −1.02816 −0.514080 0.857742i \(-0.671866\pi\)
−0.514080 + 0.857742i \(0.671866\pi\)
\(278\) 56.8424 3.40918
\(279\) 16.4333 0.983839
\(280\) 0 0
\(281\) 26.8613 1.60241 0.801205 0.598390i \(-0.204193\pi\)
0.801205 + 0.598390i \(0.204193\pi\)
\(282\) −5.85455 −0.348633
\(283\) 4.41536 0.262466 0.131233 0.991352i \(-0.458106\pi\)
0.131233 + 0.991352i \(0.458106\pi\)
\(284\) 43.8006 2.59909
\(285\) 0 0
\(286\) 11.0070 0.650859
\(287\) −10.3374 −0.610196
\(288\) 47.4708 2.79724
\(289\) −16.8474 −0.991023
\(290\) 0 0
\(291\) 1.45966 0.0855668
\(292\) −68.0321 −3.98128
\(293\) −27.4208 −1.60194 −0.800971 0.598703i \(-0.795683\pi\)
−0.800971 + 0.598703i \(0.795683\pi\)
\(294\) 0.671088 0.0391387
\(295\) 0 0
\(296\) −18.6230 −1.08244
\(297\) −0.958455 −0.0556152
\(298\) 43.0614 2.49448
\(299\) 9.37730 0.542303
\(300\) 0 0
\(301\) 26.6527 1.53624
\(302\) 28.2369 1.62485
\(303\) −0.728596 −0.0418567
\(304\) 6.03088 0.345895
\(305\) 0 0
\(306\) 3.09462 0.176907
\(307\) −22.4558 −1.28162 −0.640809 0.767700i \(-0.721401\pi\)
−0.640809 + 0.767700i \(0.721401\pi\)
\(308\) −11.9677 −0.681921
\(309\) −3.81076 −0.216787
\(310\) 0 0
\(311\) −17.0158 −0.964880 −0.482440 0.875929i \(-0.660249\pi\)
−0.482440 + 0.875929i \(0.660249\pi\)
\(312\) 8.59344 0.486508
\(313\) 30.6076 1.73004 0.865022 0.501734i \(-0.167304\pi\)
0.865022 + 0.501734i \(0.167304\pi\)
\(314\) 0.680689 0.0384135
\(315\) 0 0
\(316\) 41.7275 2.34735
\(317\) 13.1196 0.736869 0.368434 0.929654i \(-0.379894\pi\)
0.368434 + 0.929654i \(0.379894\pi\)
\(318\) 0.901039 0.0505277
\(319\) 6.49854 0.363848
\(320\) 0 0
\(321\) 1.30781 0.0729950
\(322\) −14.1467 −0.788365
\(323\) 0.191313 0.0106449
\(324\) 44.6131 2.47850
\(325\) 0 0
\(326\) 23.6251 1.30847
\(327\) 3.04359 0.168311
\(328\) 30.4291 1.68016
\(329\) −31.5477 −1.73928
\(330\) 0 0
\(331\) 20.2977 1.11566 0.557832 0.829954i \(-0.311633\pi\)
0.557832 + 0.829954i \(0.311633\pi\)
\(332\) −1.89245 −0.103862
\(333\) −6.51716 −0.357138
\(334\) −8.13942 −0.445369
\(335\) 0 0
\(336\) −7.05262 −0.384752
\(337\) 10.6212 0.578575 0.289287 0.957242i \(-0.406582\pi\)
0.289287 + 0.957242i \(0.406582\pi\)
\(338\) −34.7473 −1.89001
\(339\) 0.0364771 0.00198116
\(340\) 0 0
\(341\) 4.47934 0.242570
\(342\) 3.87956 0.209783
\(343\) −16.4999 −0.890913
\(344\) −78.4549 −4.23000
\(345\) 0 0
\(346\) 16.1246 0.866865
\(347\) −1.73240 −0.0930001 −0.0465001 0.998918i \(-0.514807\pi\)
−0.0465001 + 0.998918i \(0.514807\pi\)
\(348\) 8.28358 0.444047
\(349\) −31.0836 −1.66387 −0.831933 0.554876i \(-0.812766\pi\)
−0.831933 + 0.554876i \(0.812766\pi\)
\(350\) 0 0
\(351\) 6.05493 0.323188
\(352\) 12.9394 0.689673
\(353\) −33.0003 −1.75643 −0.878214 0.478268i \(-0.841265\pi\)
−0.878214 + 0.478268i \(0.841265\pi\)
\(354\) −2.68008 −0.142445
\(355\) 0 0
\(356\) −11.5742 −0.613432
\(357\) −0.223725 −0.0118408
\(358\) −20.6701 −1.09245
\(359\) 32.1190 1.69518 0.847589 0.530654i \(-0.178054\pi\)
0.847589 + 0.530654i \(0.178054\pi\)
\(360\) 0 0
\(361\) −18.7602 −0.987377
\(362\) 27.6015 1.45070
\(363\) 2.06242 0.108249
\(364\) 75.6044 3.96275
\(365\) 0 0
\(366\) 1.81281 0.0947572
\(367\) −1.93764 −0.101144 −0.0505719 0.998720i \(-0.516104\pi\)
−0.0505719 + 0.998720i \(0.516104\pi\)
\(368\) 22.6537 1.18091
\(369\) 10.6487 0.554349
\(370\) 0 0
\(371\) 4.85532 0.252076
\(372\) 5.70974 0.296036
\(373\) 8.78738 0.454993 0.227497 0.973779i \(-0.426946\pi\)
0.227497 + 0.973779i \(0.426946\pi\)
\(374\) 0.843519 0.0436173
\(375\) 0 0
\(376\) 92.8637 4.78908
\(377\) −41.0538 −2.11438
\(378\) −9.13454 −0.469830
\(379\) 15.6012 0.801378 0.400689 0.916214i \(-0.368771\pi\)
0.400689 + 0.916214i \(0.368771\pi\)
\(380\) 0 0
\(381\) 3.02093 0.154767
\(382\) 44.4924 2.27643
\(383\) 3.43332 0.175435 0.0877173 0.996145i \(-0.472043\pi\)
0.0877173 + 0.996145i \(0.472043\pi\)
\(384\) 3.35888 0.171407
\(385\) 0 0
\(386\) −71.1016 −3.61897
\(387\) −27.4554 −1.39564
\(388\) −37.8015 −1.91908
\(389\) −16.1302 −0.817836 −0.408918 0.912571i \(-0.634094\pi\)
−0.408918 + 0.912571i \(0.634094\pi\)
\(390\) 0 0
\(391\) 0.718626 0.0363425
\(392\) −10.6447 −0.537637
\(393\) −1.41518 −0.0713863
\(394\) −11.8514 −0.597067
\(395\) 0 0
\(396\) 12.3281 0.619510
\(397\) 4.27325 0.214468 0.107234 0.994234i \(-0.465801\pi\)
0.107234 + 0.994234i \(0.465801\pi\)
\(398\) −9.22236 −0.462275
\(399\) −0.280472 −0.0140412
\(400\) 0 0
\(401\) −0.0337541 −0.00168560 −0.000842800 1.00000i \(-0.500268\pi\)
−0.000842800 1.00000i \(0.500268\pi\)
\(402\) −6.92302 −0.345289
\(403\) −28.2977 −1.40961
\(404\) 18.8688 0.938758
\(405\) 0 0
\(406\) 61.9342 3.07374
\(407\) −1.77642 −0.0880541
\(408\) 0.658555 0.0326034
\(409\) 12.7748 0.631672 0.315836 0.948814i \(-0.397715\pi\)
0.315836 + 0.948814i \(0.397715\pi\)
\(410\) 0 0
\(411\) −1.51540 −0.0747491
\(412\) 98.6892 4.86207
\(413\) −14.4419 −0.710637
\(414\) 14.5727 0.716211
\(415\) 0 0
\(416\) −81.7433 −4.00780
\(417\) 4.23317 0.207299
\(418\) 1.05748 0.0517229
\(419\) −37.5266 −1.83329 −0.916646 0.399699i \(-0.869115\pi\)
−0.916646 + 0.399699i \(0.869115\pi\)
\(420\) 0 0
\(421\) −9.23835 −0.450250 −0.225125 0.974330i \(-0.572279\pi\)
−0.225125 + 0.974330i \(0.572279\pi\)
\(422\) 2.02968 0.0988034
\(423\) 32.4978 1.58010
\(424\) −14.2921 −0.694086
\(425\) 0 0
\(426\) 4.52597 0.219284
\(427\) 9.76849 0.472730
\(428\) −33.8691 −1.63712
\(429\) 0.819717 0.0395763
\(430\) 0 0
\(431\) −28.2694 −1.36169 −0.680845 0.732427i \(-0.738387\pi\)
−0.680845 + 0.732427i \(0.738387\pi\)
\(432\) 14.6275 0.703767
\(433\) 2.19007 0.105248 0.0526239 0.998614i \(-0.483242\pi\)
0.0526239 + 0.998614i \(0.483242\pi\)
\(434\) 42.6903 2.04920
\(435\) 0 0
\(436\) −78.8213 −3.77486
\(437\) 0.900904 0.0430961
\(438\) −7.02984 −0.335899
\(439\) 16.6956 0.796839 0.398419 0.917203i \(-0.369559\pi\)
0.398419 + 0.917203i \(0.369559\pi\)
\(440\) 0 0
\(441\) −3.72512 −0.177387
\(442\) −5.32884 −0.253467
\(443\) 10.7664 0.511529 0.255764 0.966739i \(-0.417673\pi\)
0.255764 + 0.966739i \(0.417673\pi\)
\(444\) −2.26438 −0.107463
\(445\) 0 0
\(446\) −2.66148 −0.126025
\(447\) 3.20688 0.151680
\(448\) 52.5410 2.48233
\(449\) −32.2748 −1.52314 −0.761571 0.648082i \(-0.775571\pi\)
−0.761571 + 0.648082i \(0.775571\pi\)
\(450\) 0 0
\(451\) 2.90259 0.136677
\(452\) −0.944664 −0.0444333
\(453\) 2.10286 0.0988011
\(454\) −24.4859 −1.14918
\(455\) 0 0
\(456\) 0.825597 0.0386621
\(457\) −19.5040 −0.912358 −0.456179 0.889888i \(-0.650782\pi\)
−0.456179 + 0.889888i \(0.650782\pi\)
\(458\) −66.3817 −3.10181
\(459\) 0.464017 0.0216585
\(460\) 0 0
\(461\) −7.59585 −0.353774 −0.176887 0.984231i \(-0.556603\pi\)
−0.176887 + 0.984231i \(0.556603\pi\)
\(462\) −1.23663 −0.0575334
\(463\) −12.5155 −0.581644 −0.290822 0.956777i \(-0.593929\pi\)
−0.290822 + 0.956777i \(0.593929\pi\)
\(464\) −99.1779 −4.60422
\(465\) 0 0
\(466\) 55.7433 2.58226
\(467\) −11.4282 −0.528833 −0.264416 0.964409i \(-0.585179\pi\)
−0.264416 + 0.964409i \(0.585179\pi\)
\(468\) −77.8813 −3.60006
\(469\) −37.3053 −1.72260
\(470\) 0 0
\(471\) 0.0506924 0.00233578
\(472\) 42.5110 1.95673
\(473\) −7.48370 −0.344101
\(474\) 4.31175 0.198045
\(475\) 0 0
\(476\) 5.79391 0.265564
\(477\) −5.00155 −0.229005
\(478\) 72.8374 3.33150
\(479\) 24.3966 1.11471 0.557354 0.830275i \(-0.311817\pi\)
0.557354 + 0.830275i \(0.311817\pi\)
\(480\) 0 0
\(481\) 11.2224 0.511696
\(482\) −2.67602 −0.121889
\(483\) −1.05353 −0.0479375
\(484\) −53.4116 −2.42780
\(485\) 0 0
\(486\) 14.1458 0.641667
\(487\) 32.5012 1.47277 0.736385 0.676563i \(-0.236531\pi\)
0.736385 + 0.676563i \(0.236531\pi\)
\(488\) −28.7545 −1.30165
\(489\) 1.75941 0.0795633
\(490\) 0 0
\(491\) 15.3890 0.694498 0.347249 0.937773i \(-0.387116\pi\)
0.347249 + 0.937773i \(0.387116\pi\)
\(492\) 3.69988 0.166803
\(493\) −3.14614 −0.141695
\(494\) −6.68049 −0.300569
\(495\) 0 0
\(496\) −68.3618 −3.06953
\(497\) 24.3886 1.09398
\(498\) −0.195550 −0.00876278
\(499\) −33.4862 −1.49905 −0.749525 0.661976i \(-0.769718\pi\)
−0.749525 + 0.661976i \(0.769718\pi\)
\(500\) 0 0
\(501\) −0.606160 −0.0270812
\(502\) −47.3225 −2.11211
\(503\) 38.0060 1.69460 0.847302 0.531111i \(-0.178225\pi\)
0.847302 + 0.531111i \(0.178225\pi\)
\(504\) 71.9624 3.20546
\(505\) 0 0
\(506\) 3.97219 0.176585
\(507\) −2.58771 −0.114924
\(508\) −78.2344 −3.47109
\(509\) 28.9990 1.28536 0.642679 0.766136i \(-0.277823\pi\)
0.642679 + 0.766136i \(0.277823\pi\)
\(510\) 0 0
\(511\) −37.8809 −1.67575
\(512\) 10.8657 0.480202
\(513\) 0.581715 0.0256833
\(514\) −65.9460 −2.90875
\(515\) 0 0
\(516\) −9.53935 −0.419946
\(517\) 8.85814 0.389581
\(518\) −16.9302 −0.743870
\(519\) 1.20083 0.0527108
\(520\) 0 0
\(521\) −8.52198 −0.373355 −0.186677 0.982421i \(-0.559772\pi\)
−0.186677 + 0.982421i \(0.559772\pi\)
\(522\) −63.7995 −2.79243
\(523\) 6.18981 0.270662 0.135331 0.990800i \(-0.456790\pi\)
0.135331 + 0.990800i \(0.456790\pi\)
\(524\) 36.6496 1.60104
\(525\) 0 0
\(526\) −57.0573 −2.48782
\(527\) −2.16859 −0.0944651
\(528\) 1.98027 0.0861804
\(529\) −19.6159 −0.852867
\(530\) 0 0
\(531\) 14.8768 0.645598
\(532\) 7.26353 0.314914
\(533\) −18.3367 −0.794253
\(534\) −1.19598 −0.0517550
\(535\) 0 0
\(536\) 109.812 4.74314
\(537\) −1.53935 −0.0664277
\(538\) −58.4572 −2.52027
\(539\) −1.01538 −0.0437355
\(540\) 0 0
\(541\) 23.0092 0.989244 0.494622 0.869108i \(-0.335306\pi\)
0.494622 + 0.869108i \(0.335306\pi\)
\(542\) −4.44183 −0.190793
\(543\) 2.05554 0.0882117
\(544\) −6.26437 −0.268583
\(545\) 0 0
\(546\) 7.81229 0.334335
\(547\) 34.2241 1.46332 0.731658 0.681672i \(-0.238747\pi\)
0.731658 + 0.681672i \(0.238747\pi\)
\(548\) 39.2450 1.67646
\(549\) −10.0627 −0.429465
\(550\) 0 0
\(551\) −3.94416 −0.168027
\(552\) 3.10118 0.131995
\(553\) 23.2342 0.988020
\(554\) 45.7920 1.94552
\(555\) 0 0
\(556\) −109.629 −4.64929
\(557\) −8.34480 −0.353580 −0.176790 0.984249i \(-0.556571\pi\)
−0.176790 + 0.984249i \(0.556571\pi\)
\(558\) −43.9760 −1.86165
\(559\) 47.2774 1.99962
\(560\) 0 0
\(561\) 0.0628187 0.00265221
\(562\) −71.8813 −3.03213
\(563\) −21.1210 −0.890146 −0.445073 0.895494i \(-0.646822\pi\)
−0.445073 + 0.895494i \(0.646822\pi\)
\(564\) 11.2913 0.475451
\(565\) 0 0
\(566\) −11.8156 −0.496647
\(567\) 24.8410 1.04322
\(568\) −71.7901 −3.01225
\(569\) 38.2880 1.60512 0.802559 0.596573i \(-0.203471\pi\)
0.802559 + 0.596573i \(0.203471\pi\)
\(570\) 0 0
\(571\) 4.36826 0.182806 0.0914031 0.995814i \(-0.470865\pi\)
0.0914031 + 0.995814i \(0.470865\pi\)
\(572\) −21.2286 −0.887612
\(573\) 3.31344 0.138421
\(574\) 27.6630 1.15463
\(575\) 0 0
\(576\) −54.1233 −2.25514
\(577\) 9.27981 0.386324 0.193162 0.981167i \(-0.438126\pi\)
0.193162 + 0.981167i \(0.438126\pi\)
\(578\) 45.0840 1.87525
\(579\) −5.29508 −0.220056
\(580\) 0 0
\(581\) −1.05373 −0.0437163
\(582\) −3.90608 −0.161912
\(583\) −1.36330 −0.0564623
\(584\) 111.506 4.61415
\(585\) 0 0
\(586\) 73.3787 3.03125
\(587\) −12.4373 −0.513342 −0.256671 0.966499i \(-0.582626\pi\)
−0.256671 + 0.966499i \(0.582626\pi\)
\(588\) −1.29429 −0.0533755
\(589\) −2.71865 −0.112020
\(590\) 0 0
\(591\) −0.882602 −0.0363054
\(592\) 27.1110 1.11426
\(593\) −37.5611 −1.54245 −0.771225 0.636563i \(-0.780356\pi\)
−0.771225 + 0.636563i \(0.780356\pi\)
\(594\) 2.56484 0.105237
\(595\) 0 0
\(596\) −83.0500 −3.40186
\(597\) −0.686809 −0.0281092
\(598\) −25.0938 −1.02616
\(599\) −22.2278 −0.908204 −0.454102 0.890950i \(-0.650040\pi\)
−0.454102 + 0.890950i \(0.650040\pi\)
\(600\) 0 0
\(601\) −46.9863 −1.91661 −0.958305 0.285747i \(-0.907758\pi\)
−0.958305 + 0.285747i \(0.907758\pi\)
\(602\) −71.3233 −2.90692
\(603\) 38.4288 1.56494
\(604\) −54.4588 −2.21590
\(605\) 0 0
\(606\) 1.94974 0.0792026
\(607\) 0.527341 0.0214041 0.0107021 0.999943i \(-0.496593\pi\)
0.0107021 + 0.999943i \(0.496593\pi\)
\(608\) −7.85332 −0.318494
\(609\) 4.61237 0.186903
\(610\) 0 0
\(611\) −55.9603 −2.26391
\(612\) −5.96840 −0.241258
\(613\) 9.71818 0.392514 0.196257 0.980553i \(-0.437121\pi\)
0.196257 + 0.980553i \(0.437121\pi\)
\(614\) 60.0921 2.42512
\(615\) 0 0
\(616\) 19.6153 0.790321
\(617\) −2.81867 −0.113476 −0.0567378 0.998389i \(-0.518070\pi\)
−0.0567378 + 0.998389i \(0.518070\pi\)
\(618\) 10.1977 0.410211
\(619\) −2.75560 −0.110757 −0.0553785 0.998465i \(-0.517637\pi\)
−0.0553785 + 0.998465i \(0.517637\pi\)
\(620\) 0 0
\(621\) 2.18509 0.0876845
\(622\) 45.5347 1.82578
\(623\) −6.44463 −0.258199
\(624\) −12.5102 −0.500807
\(625\) 0 0
\(626\) −81.9065 −3.27364
\(627\) 0.0787526 0.00314507
\(628\) −1.31281 −0.0523866
\(629\) 0.860022 0.0342913
\(630\) 0 0
\(631\) −21.5819 −0.859161 −0.429580 0.903029i \(-0.641338\pi\)
−0.429580 + 0.903029i \(0.641338\pi\)
\(632\) −68.3922 −2.72050
\(633\) 0.151155 0.00600787
\(634\) −35.1083 −1.39433
\(635\) 0 0
\(636\) −1.73778 −0.0689075
\(637\) 6.41455 0.254154
\(638\) −17.3902 −0.688486
\(639\) −25.1231 −0.993853
\(640\) 0 0
\(641\) −21.4224 −0.846135 −0.423068 0.906098i \(-0.639047\pi\)
−0.423068 + 0.906098i \(0.639047\pi\)
\(642\) −3.49973 −0.138123
\(643\) −29.1001 −1.14760 −0.573798 0.818997i \(-0.694531\pi\)
−0.573798 + 0.818997i \(0.694531\pi\)
\(644\) 27.2839 1.07514
\(645\) 0 0
\(646\) −0.511957 −0.0201427
\(647\) 8.60753 0.338397 0.169198 0.985582i \(-0.445882\pi\)
0.169198 + 0.985582i \(0.445882\pi\)
\(648\) −73.1218 −2.87249
\(649\) 4.05506 0.159175
\(650\) 0 0
\(651\) 3.17924 0.124604
\(652\) −45.5643 −1.78444
\(653\) 10.3765 0.406062 0.203031 0.979172i \(-0.434921\pi\)
0.203031 + 0.979172i \(0.434921\pi\)
\(654\) −8.14470 −0.318483
\(655\) 0 0
\(656\) −44.2980 −1.72955
\(657\) 39.0217 1.52238
\(658\) 84.4223 3.29113
\(659\) −39.6868 −1.54598 −0.772990 0.634418i \(-0.781240\pi\)
−0.772990 + 0.634418i \(0.781240\pi\)
\(660\) 0 0
\(661\) −37.6874 −1.46587 −0.732934 0.680300i \(-0.761850\pi\)
−0.732934 + 0.680300i \(0.761850\pi\)
\(662\) −54.3171 −2.11109
\(663\) −0.396850 −0.0154124
\(664\) 3.10177 0.120372
\(665\) 0 0
\(666\) 17.4401 0.675789
\(667\) −14.8154 −0.573654
\(668\) 15.6980 0.607375
\(669\) −0.198206 −0.00766309
\(670\) 0 0
\(671\) −2.74285 −0.105887
\(672\) 9.18382 0.354274
\(673\) −31.7217 −1.22278 −0.611390 0.791329i \(-0.709390\pi\)
−0.611390 + 0.791329i \(0.709390\pi\)
\(674\) −28.4226 −1.09480
\(675\) 0 0
\(676\) 67.0152 2.57751
\(677\) −45.3409 −1.74259 −0.871297 0.490757i \(-0.836720\pi\)
−0.871297 + 0.490757i \(0.836720\pi\)
\(678\) −0.0976133 −0.00374882
\(679\) −21.0482 −0.807757
\(680\) 0 0
\(681\) −1.82352 −0.0698773
\(682\) −11.9868 −0.458999
\(683\) −7.82593 −0.299451 −0.149726 0.988728i \(-0.547839\pi\)
−0.149726 + 0.988728i \(0.547839\pi\)
\(684\) −7.48228 −0.286092
\(685\) 0 0
\(686\) 44.1542 1.68581
\(687\) −4.94359 −0.188610
\(688\) 114.213 4.35433
\(689\) 8.61251 0.328111
\(690\) 0 0
\(691\) −35.0023 −1.33155 −0.665775 0.746152i \(-0.731899\pi\)
−0.665775 + 0.746152i \(0.731899\pi\)
\(692\) −31.0986 −1.18219
\(693\) 6.86439 0.260757
\(694\) 4.63594 0.175978
\(695\) 0 0
\(696\) −13.5770 −0.514633
\(697\) −1.40523 −0.0532269
\(698\) 83.1803 3.14842
\(699\) 4.15133 0.157018
\(700\) 0 0
\(701\) −8.28122 −0.312778 −0.156389 0.987696i \(-0.549985\pi\)
−0.156389 + 0.987696i \(0.549985\pi\)
\(702\) −16.2031 −0.611547
\(703\) 1.07816 0.0406638
\(704\) −14.7527 −0.556015
\(705\) 0 0
\(706\) 88.3094 3.32357
\(707\) 10.5063 0.395131
\(708\) 5.16892 0.194260
\(709\) −23.7901 −0.893458 −0.446729 0.894669i \(-0.647411\pi\)
−0.446729 + 0.894669i \(0.647411\pi\)
\(710\) 0 0
\(711\) −23.9340 −0.897594
\(712\) 18.9704 0.710945
\(713\) −10.2120 −0.382443
\(714\) 0.598692 0.0224055
\(715\) 0 0
\(716\) 39.8652 1.48983
\(717\) 5.42436 0.202576
\(718\) −85.9512 −3.20767
\(719\) 33.8950 1.26407 0.632035 0.774940i \(-0.282220\pi\)
0.632035 + 0.774940i \(0.282220\pi\)
\(720\) 0 0
\(721\) 54.9510 2.04648
\(722\) 50.2026 1.86835
\(723\) −0.199289 −0.00741163
\(724\) −53.2334 −1.97840
\(725\) 0 0
\(726\) −5.51908 −0.204832
\(727\) −26.5707 −0.985451 −0.492725 0.870185i \(-0.663999\pi\)
−0.492725 + 0.870185i \(0.663999\pi\)
\(728\) −123.917 −4.59267
\(729\) −24.8789 −0.921442
\(730\) 0 0
\(731\) 3.62309 0.134005
\(732\) −3.49627 −0.129226
\(733\) −50.9266 −1.88102 −0.940509 0.339768i \(-0.889651\pi\)
−0.940509 + 0.339768i \(0.889651\pi\)
\(734\) 5.18516 0.191388
\(735\) 0 0
\(736\) −29.4993 −1.08736
\(737\) 10.4748 0.385843
\(738\) −28.4961 −1.04896
\(739\) 37.8448 1.39214 0.696071 0.717973i \(-0.254930\pi\)
0.696071 + 0.717973i \(0.254930\pi\)
\(740\) 0 0
\(741\) −0.497510 −0.0182765
\(742\) −12.9929 −0.476986
\(743\) −18.8351 −0.690992 −0.345496 0.938420i \(-0.612289\pi\)
−0.345496 + 0.938420i \(0.612289\pi\)
\(744\) −9.35839 −0.343095
\(745\) 0 0
\(746\) −23.5152 −0.860953
\(747\) 1.08547 0.0397153
\(748\) −1.62685 −0.0594834
\(749\) −18.8586 −0.689079
\(750\) 0 0
\(751\) 40.1498 1.46509 0.732544 0.680720i \(-0.238333\pi\)
0.732544 + 0.680720i \(0.238333\pi\)
\(752\) −135.189 −4.92984
\(753\) −3.52421 −0.128429
\(754\) 109.861 4.00089
\(755\) 0 0
\(756\) 17.6172 0.640733
\(757\) −11.3231 −0.411546 −0.205773 0.978600i \(-0.565971\pi\)
−0.205773 + 0.978600i \(0.565971\pi\)
\(758\) −41.7490 −1.51639
\(759\) 0.295817 0.0107375
\(760\) 0 0
\(761\) 27.9931 1.01475 0.507374 0.861726i \(-0.330616\pi\)
0.507374 + 0.861726i \(0.330616\pi\)
\(762\) −8.08406 −0.292855
\(763\) −43.8884 −1.58887
\(764\) −85.8098 −3.10449
\(765\) 0 0
\(766\) −9.18764 −0.331963
\(767\) −25.6174 −0.924990
\(768\) −1.70116 −0.0613853
\(769\) −8.32041 −0.300042 −0.150021 0.988683i \(-0.547934\pi\)
−0.150021 + 0.988683i \(0.547934\pi\)
\(770\) 0 0
\(771\) −4.91114 −0.176870
\(772\) 137.129 4.93539
\(773\) 11.4321 0.411183 0.205591 0.978638i \(-0.434088\pi\)
0.205591 + 0.978638i \(0.434088\pi\)
\(774\) 73.4713 2.64087
\(775\) 0 0
\(776\) 61.9575 2.22414
\(777\) −1.26083 −0.0452319
\(778\) 43.1649 1.54754
\(779\) −1.76167 −0.0631182
\(780\) 0 0
\(781\) −6.84796 −0.245039
\(782\) −1.92306 −0.0687684
\(783\) −9.56631 −0.341872
\(784\) 15.4963 0.553439
\(785\) 0 0
\(786\) 3.78705 0.135079
\(787\) −11.5127 −0.410384 −0.205192 0.978722i \(-0.565782\pi\)
−0.205192 + 0.978722i \(0.565782\pi\)
\(788\) 22.8572 0.814253
\(789\) −4.24918 −0.151275
\(790\) 0 0
\(791\) −0.525997 −0.0187023
\(792\) −20.2060 −0.717989
\(793\) 17.3276 0.615323
\(794\) −11.4353 −0.405824
\(795\) 0 0
\(796\) 17.7866 0.630430
\(797\) −8.19431 −0.290257 −0.145129 0.989413i \(-0.546360\pi\)
−0.145129 + 0.989413i \(0.546360\pi\)
\(798\) 0.750550 0.0265692
\(799\) −4.28850 −0.151716
\(800\) 0 0
\(801\) 6.63872 0.234568
\(802\) 0.0903266 0.00318954
\(803\) 10.6364 0.375351
\(804\) 13.3520 0.470889
\(805\) 0 0
\(806\) 75.7253 2.66731
\(807\) −4.35343 −0.153248
\(808\) −30.9263 −1.08799
\(809\) 9.19094 0.323136 0.161568 0.986862i \(-0.448345\pi\)
0.161568 + 0.986862i \(0.448345\pi\)
\(810\) 0 0
\(811\) −23.9711 −0.841740 −0.420870 0.907121i \(-0.638275\pi\)
−0.420870 + 0.907121i \(0.638275\pi\)
\(812\) −119.449 −4.19183
\(813\) −0.330793 −0.0116014
\(814\) 4.75375 0.166619
\(815\) 0 0
\(816\) −0.958711 −0.0335616
\(817\) 4.54208 0.158907
\(818\) −34.1856 −1.19527
\(819\) −43.3650 −1.51530
\(820\) 0 0
\(821\) −5.58377 −0.194875 −0.0974375 0.995242i \(-0.531065\pi\)
−0.0974375 + 0.995242i \(0.531065\pi\)
\(822\) 4.05524 0.141443
\(823\) −2.02001 −0.0704131 −0.0352066 0.999380i \(-0.511209\pi\)
−0.0352066 + 0.999380i \(0.511209\pi\)
\(824\) −161.754 −5.63495
\(825\) 0 0
\(826\) 38.6467 1.34469
\(827\) −24.2638 −0.843735 −0.421867 0.906658i \(-0.638625\pi\)
−0.421867 + 0.906658i \(0.638625\pi\)
\(828\) −28.1056 −0.976737
\(829\) 0.464596 0.0161361 0.00806805 0.999967i \(-0.497432\pi\)
0.00806805 + 0.999967i \(0.497432\pi\)
\(830\) 0 0
\(831\) 3.41023 0.118299
\(832\) 93.1988 3.23109
\(833\) 0.491577 0.0170321
\(834\) −11.3281 −0.392258
\(835\) 0 0
\(836\) −2.03949 −0.0705374
\(837\) −6.59391 −0.227919
\(838\) 100.422 3.46901
\(839\) 11.0915 0.382921 0.191461 0.981500i \(-0.438678\pi\)
0.191461 + 0.981500i \(0.438678\pi\)
\(840\) 0 0
\(841\) 35.8617 1.23661
\(842\) 24.7220 0.851977
\(843\) −5.35316 −0.184372
\(844\) −3.91453 −0.134744
\(845\) 0 0
\(846\) −86.9648 −2.98991
\(847\) −29.7400 −1.02188
\(848\) 20.8061 0.714486
\(849\) −0.879933 −0.0301992
\(850\) 0 0
\(851\) 4.04990 0.138829
\(852\) −8.72897 −0.299050
\(853\) 38.1172 1.30511 0.652553 0.757743i \(-0.273698\pi\)
0.652553 + 0.757743i \(0.273698\pi\)
\(854\) −26.1407 −0.894516
\(855\) 0 0
\(856\) 55.5121 1.89736
\(857\) 17.6418 0.602634 0.301317 0.953524i \(-0.402574\pi\)
0.301317 + 0.953524i \(0.402574\pi\)
\(858\) −2.19358 −0.0748875
\(859\) −27.4875 −0.937862 −0.468931 0.883235i \(-0.655361\pi\)
−0.468931 + 0.883235i \(0.655361\pi\)
\(860\) 0 0
\(861\) 2.06013 0.0702089
\(862\) 75.6495 2.57663
\(863\) 19.2496 0.655263 0.327632 0.944806i \(-0.393750\pi\)
0.327632 + 0.944806i \(0.393750\pi\)
\(864\) −19.0477 −0.648017
\(865\) 0 0
\(866\) −5.86066 −0.199153
\(867\) 3.35750 0.114027
\(868\) −82.3342 −2.79461
\(869\) −6.52383 −0.221306
\(870\) 0 0
\(871\) −66.1732 −2.24219
\(872\) 129.190 4.37492
\(873\) 21.6821 0.733829
\(874\) −2.41084 −0.0815478
\(875\) 0 0
\(876\) 13.5580 0.458084
\(877\) 41.2611 1.39329 0.696644 0.717417i \(-0.254676\pi\)
0.696644 + 0.717417i \(0.254676\pi\)
\(878\) −44.6778 −1.50780
\(879\) 5.46467 0.184319
\(880\) 0 0
\(881\) 32.1377 1.08275 0.541373 0.840783i \(-0.317905\pi\)
0.541373 + 0.840783i \(0.317905\pi\)
\(882\) 9.96850 0.335657
\(883\) −9.13498 −0.307416 −0.153708 0.988116i \(-0.549122\pi\)
−0.153708 + 0.988116i \(0.549122\pi\)
\(884\) 10.2774 0.345667
\(885\) 0 0
\(886\) −28.8112 −0.967931
\(887\) −13.8765 −0.465928 −0.232964 0.972485i \(-0.574842\pi\)
−0.232964 + 0.972485i \(0.574842\pi\)
\(888\) 3.71136 0.124545
\(889\) −43.5616 −1.46101
\(890\) 0 0
\(891\) −6.97498 −0.233671
\(892\) 5.13304 0.171867
\(893\) −5.37627 −0.179910
\(894\) −8.58167 −0.287014
\(895\) 0 0
\(896\) −48.4349 −1.61809
\(897\) −1.86879 −0.0623971
\(898\) 86.3680 2.88214
\(899\) 44.7082 1.49110
\(900\) 0 0
\(901\) 0.660017 0.0219883
\(902\) −7.76738 −0.258625
\(903\) −5.31160 −0.176759
\(904\) 1.54832 0.0514965
\(905\) 0 0
\(906\) −5.62730 −0.186954
\(907\) 20.5930 0.683778 0.341889 0.939740i \(-0.388933\pi\)
0.341889 + 0.939740i \(0.388933\pi\)
\(908\) 47.2245 1.56720
\(909\) −10.8227 −0.358967
\(910\) 0 0
\(911\) −29.8513 −0.989018 −0.494509 0.869173i \(-0.664652\pi\)
−0.494509 + 0.869173i \(0.664652\pi\)
\(912\) −1.20189 −0.0397985
\(913\) 0.295873 0.00979198
\(914\) 52.1931 1.72639
\(915\) 0 0
\(916\) 128.027 4.23012
\(917\) 20.4068 0.673892
\(918\) −1.24172 −0.0409828
\(919\) −44.8288 −1.47877 −0.739383 0.673285i \(-0.764883\pi\)
−0.739383 + 0.673285i \(0.764883\pi\)
\(920\) 0 0
\(921\) 4.47519 0.147462
\(922\) 20.3266 0.669422
\(923\) 43.2612 1.42396
\(924\) 2.38502 0.0784615
\(925\) 0 0
\(926\) 33.4917 1.10061
\(927\) −56.6060 −1.85918
\(928\) 129.148 4.23949
\(929\) −53.9902 −1.77136 −0.885681 0.464294i \(-0.846308\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(930\) 0 0
\(931\) 0.616264 0.0201972
\(932\) −107.509 −3.52157
\(933\) 3.39107 0.111019
\(934\) 30.5820 1.00067
\(935\) 0 0
\(936\) 127.649 4.17234
\(937\) −41.8090 −1.36584 −0.682920 0.730493i \(-0.739290\pi\)
−0.682920 + 0.730493i \(0.739290\pi\)
\(938\) 99.8296 3.25955
\(939\) −6.09975 −0.199058
\(940\) 0 0
\(941\) 17.5326 0.571548 0.285774 0.958297i \(-0.407749\pi\)
0.285774 + 0.958297i \(0.407749\pi\)
\(942\) −0.135654 −0.00441984
\(943\) −6.61732 −0.215490
\(944\) −61.8866 −2.01424
\(945\) 0 0
\(946\) 20.0265 0.651119
\(947\) −60.8556 −1.97754 −0.988770 0.149444i \(-0.952252\pi\)
−0.988770 + 0.149444i \(0.952252\pi\)
\(948\) −8.31582 −0.270085
\(949\) −67.1943 −2.18122
\(950\) 0 0
\(951\) −2.61459 −0.0847838
\(952\) −9.49634 −0.307778
\(953\) −47.7538 −1.54690 −0.773449 0.633859i \(-0.781470\pi\)
−0.773449 + 0.633859i \(0.781470\pi\)
\(954\) 13.3842 0.433331
\(955\) 0 0
\(956\) −140.477 −4.54336
\(957\) −1.29509 −0.0418642
\(958\) −65.2857 −2.10928
\(959\) 21.8520 0.705637
\(960\) 0 0
\(961\) −0.183358 −0.00591476
\(962\) −30.0313 −0.968247
\(963\) 19.4266 0.626012
\(964\) 5.16108 0.166227
\(965\) 0 0
\(966\) 2.81928 0.0907088
\(967\) −10.5625 −0.339666 −0.169833 0.985473i \(-0.554323\pi\)
−0.169833 + 0.985473i \(0.554323\pi\)
\(968\) 87.5426 2.81373
\(969\) −0.0381265 −0.00122480
\(970\) 0 0
\(971\) −42.2601 −1.35619 −0.678096 0.734973i \(-0.737195\pi\)
−0.678096 + 0.734973i \(0.737195\pi\)
\(972\) −27.2822 −0.875076
\(973\) −61.0422 −1.95692
\(974\) −86.9739 −2.78682
\(975\) 0 0
\(976\) 41.8602 1.33991
\(977\) 0.878630 0.0281099 0.0140549 0.999901i \(-0.495526\pi\)
0.0140549 + 0.999901i \(0.495526\pi\)
\(978\) −4.70822 −0.150552
\(979\) 1.80956 0.0578337
\(980\) 0 0
\(981\) 45.2102 1.44345
\(982\) −41.1814 −1.31415
\(983\) 20.9666 0.668731 0.334365 0.942444i \(-0.391478\pi\)
0.334365 + 0.942444i \(0.391478\pi\)
\(984\) −6.06417 −0.193319
\(985\) 0 0
\(986\) 8.41914 0.268120
\(987\) 6.28711 0.200121
\(988\) 12.8843 0.409903
\(989\) 17.0614 0.542519
\(990\) 0 0
\(991\) 3.56254 0.113168 0.0565840 0.998398i \(-0.481979\pi\)
0.0565840 + 0.998398i \(0.481979\pi\)
\(992\) 89.0196 2.82638
\(993\) −4.04511 −0.128368
\(994\) −65.2643 −2.07006
\(995\) 0 0
\(996\) 0.377145 0.0119503
\(997\) 5.26746 0.166822 0.0834111 0.996515i \(-0.473419\pi\)
0.0834111 + 0.996515i \(0.473419\pi\)
\(998\) 89.6098 2.83655
\(999\) 2.61502 0.0827356
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.1.2 46
5.2 odd 4 1205.2.b.c.724.2 46
5.3 odd 4 1205.2.b.c.724.45 yes 46
5.4 even 2 inner 6025.2.a.p.1.45 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.2 46 5.2 odd 4
1205.2.b.c.724.45 yes 46 5.3 odd 4
6025.2.a.p.1.2 46 1.1 even 1 trivial
6025.2.a.p.1.45 46 5.4 even 2 inner