Properties

Label 4016.2.a.g.1.3
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 7
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.358013\)
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.358013 q^{3} +2.25358 q^{5} +4.66949 q^{7} -2.87183 q^{9} +O(q^{10})\) \(q-0.358013 q^{3} +2.25358 q^{5} +4.66949 q^{7} -2.87183 q^{9} +0.681867 q^{11} +0.464791 q^{13} -0.806810 q^{15} -0.986388 q^{17} +2.32972 q^{19} -1.67174 q^{21} +5.37412 q^{23} +0.0786287 q^{25} +2.10219 q^{27} -4.75253 q^{29} +1.57250 q^{31} -0.244117 q^{33} +10.5231 q^{35} +3.55119 q^{37} -0.166401 q^{39} +0.278393 q^{41} +1.78076 q^{43} -6.47190 q^{45} -2.22141 q^{47} +14.8042 q^{49} +0.353139 q^{51} +2.88544 q^{53} +1.53664 q^{55} -0.834068 q^{57} +6.32720 q^{59} +0.0560602 q^{61} -13.4100 q^{63} +1.04744 q^{65} +5.83951 q^{67} -1.92400 q^{69} +2.74305 q^{71} +9.63680 q^{73} -0.0281501 q^{75} +3.18397 q^{77} -3.00611 q^{79} +7.86287 q^{81} +2.32667 q^{83} -2.22291 q^{85} +1.70147 q^{87} -10.3727 q^{89} +2.17034 q^{91} -0.562976 q^{93} +5.25021 q^{95} -4.01956 q^{97} -1.95820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + 5q^{11} - q^{13} + 6q^{15} - 8q^{17} + 15q^{19} - 3q^{21} + 5q^{23} - 9q^{25} + 9q^{27} + 21q^{31} + 7q^{35} - q^{37} + 23q^{39} - 10q^{41} + 23q^{43} - 4q^{45} + 10q^{47} - 13q^{49} + 20q^{51} - q^{53} + 23q^{55} - 6q^{57} + 4q^{59} + 3q^{61} + 4q^{63} + 4q^{65} + 28q^{67} + 18q^{69} + 18q^{71} - 7q^{73} - 11q^{75} + 6q^{77} + 30q^{79} - 5q^{81} - 13q^{83} + q^{85} + 7q^{87} + 18q^{91} + 36q^{93} - 2q^{97} + 10q^{99} + O(q^{100}) \)

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 0
\(3\) −0.358013 −0.206699 −0.103349 0.994645i \(-0.532956\pi\)
−0.103349 + 0.994645i \(0.532956\pi\)
\(4\) 0 0
\(5\) 2.25358 1.00783 0.503916 0.863753i \(-0.331892\pi\)
0.503916 + 0.863753i \(0.331892\pi\)
\(6\) 0 0
\(7\) 4.66949 1.76490 0.882451 0.470404i \(-0.155892\pi\)
0.882451 + 0.470404i \(0.155892\pi\)
\(8\) 0 0
\(9\) −2.87183 −0.957276
\(10\) 0 0
\(11\) 0.681867 0.205591 0.102795 0.994703i \(-0.467221\pi\)
0.102795 + 0.994703i \(0.467221\pi\)
\(12\) 0 0
\(13\) 0.464791 0.128910 0.0644550 0.997921i \(-0.479469\pi\)
0.0644550 + 0.997921i \(0.479469\pi\)
\(14\) 0 0
\(15\) −0.806810 −0.208318
\(16\) 0 0
\(17\) −0.986388 −0.239234 −0.119617 0.992820i \(-0.538167\pi\)
−0.119617 + 0.992820i \(0.538167\pi\)
\(18\) 0 0
\(19\) 2.32972 0.534474 0.267237 0.963631i \(-0.413889\pi\)
0.267237 + 0.963631i \(0.413889\pi\)
\(20\) 0 0
\(21\) −1.67174 −0.364803
\(22\) 0 0
\(23\) 5.37412 1.12058 0.560290 0.828296i \(-0.310690\pi\)
0.560290 + 0.828296i \(0.310690\pi\)
\(24\) 0 0
\(25\) 0.0786287 0.0157257
\(26\) 0 0
\(27\) 2.10219 0.404566
\(28\) 0 0
\(29\) −4.75253 −0.882523 −0.441261 0.897379i \(-0.645469\pi\)
−0.441261 + 0.897379i \(0.645469\pi\)
\(30\) 0 0
\(31\) 1.57250 0.282430 0.141215 0.989979i \(-0.454899\pi\)
0.141215 + 0.989979i \(0.454899\pi\)
\(32\) 0 0
\(33\) −0.244117 −0.0424953
\(34\) 0 0
\(35\) 10.5231 1.77873
\(36\) 0 0
\(37\) 3.55119 0.583812 0.291906 0.956447i \(-0.405711\pi\)
0.291906 + 0.956447i \(0.405711\pi\)
\(38\) 0 0
\(39\) −0.166401 −0.0266455
\(40\) 0 0
\(41\) 0.278393 0.0434777 0.0217389 0.999764i \(-0.493080\pi\)
0.0217389 + 0.999764i \(0.493080\pi\)
\(42\) 0 0
\(43\) 1.78076 0.271563 0.135782 0.990739i \(-0.456645\pi\)
0.135782 + 0.990739i \(0.456645\pi\)
\(44\) 0 0
\(45\) −6.47190 −0.964773
\(46\) 0 0
\(47\) −2.22141 −0.324026 −0.162013 0.986789i \(-0.551799\pi\)
−0.162013 + 0.986789i \(0.551799\pi\)
\(48\) 0 0
\(49\) 14.8042 2.11488
\(50\) 0 0
\(51\) 0.353139 0.0494494
\(52\) 0 0
\(53\) 2.88544 0.396346 0.198173 0.980167i \(-0.436499\pi\)
0.198173 + 0.980167i \(0.436499\pi\)
\(54\) 0 0
\(55\) 1.53664 0.207201
\(56\) 0 0
\(57\) −0.834068 −0.110475
\(58\) 0 0
\(59\) 6.32720 0.823731 0.411866 0.911245i \(-0.364877\pi\)
0.411866 + 0.911245i \(0.364877\pi\)
\(60\) 0 0
\(61\) 0.0560602 0.00717778 0.00358889 0.999994i \(-0.498858\pi\)
0.00358889 + 0.999994i \(0.498858\pi\)
\(62\) 0 0
\(63\) −13.4100 −1.68950
\(64\) 0 0
\(65\) 1.04744 0.129920
\(66\) 0 0
\(67\) 5.83951 0.713410 0.356705 0.934217i \(-0.383900\pi\)
0.356705 + 0.934217i \(0.383900\pi\)
\(68\) 0 0
\(69\) −1.92400 −0.231623
\(70\) 0 0
\(71\) 2.74305 0.325540 0.162770 0.986664i \(-0.447957\pi\)
0.162770 + 0.986664i \(0.447957\pi\)
\(72\) 0 0
\(73\) 9.63680 1.12790 0.563951 0.825808i \(-0.309281\pi\)
0.563951 + 0.825808i \(0.309281\pi\)
\(74\) 0 0
\(75\) −0.0281501 −0.00325049
\(76\) 0 0
\(77\) 3.18397 0.362847
\(78\) 0 0
\(79\) −3.00611 −0.338214 −0.169107 0.985598i \(-0.554088\pi\)
−0.169107 + 0.985598i \(0.554088\pi\)
\(80\) 0 0
\(81\) 7.86287 0.873652
\(82\) 0 0
\(83\) 2.32667 0.255385 0.127693 0.991814i \(-0.459243\pi\)
0.127693 + 0.991814i \(0.459243\pi\)
\(84\) 0 0
\(85\) −2.22291 −0.241108
\(86\) 0 0
\(87\) 1.70147 0.182416
\(88\) 0 0
\(89\) −10.3727 −1.09950 −0.549750 0.835329i \(-0.685277\pi\)
−0.549750 + 0.835329i \(0.685277\pi\)
\(90\) 0 0
\(91\) 2.17034 0.227513
\(92\) 0 0
\(93\) −0.562976 −0.0583778
\(94\) 0 0
\(95\) 5.25021 0.538660
\(96\) 0 0
\(97\) −4.01956 −0.408124 −0.204062 0.978958i \(-0.565414\pi\)
−0.204062 + 0.978958i \(0.565414\pi\)
\(98\) 0 0
\(99\) −1.95820 −0.196807
\(100\) 0 0
\(101\) −11.3006 −1.12445 −0.562226 0.826983i \(-0.690055\pi\)
−0.562226 + 0.826983i \(0.690055\pi\)
\(102\) 0 0
\(103\) −1.11246 −0.109614 −0.0548071 0.998497i \(-0.517454\pi\)
−0.0548071 + 0.998497i \(0.517454\pi\)
\(104\) 0 0
\(105\) −3.76740 −0.367660
\(106\) 0 0
\(107\) 9.37893 0.906696 0.453348 0.891334i \(-0.350230\pi\)
0.453348 + 0.891334i \(0.350230\pi\)
\(108\) 0 0
\(109\) −3.44018 −0.329510 −0.164755 0.986335i \(-0.552683\pi\)
−0.164755 + 0.986335i \(0.552683\pi\)
\(110\) 0 0
\(111\) −1.27137 −0.120673
\(112\) 0 0
\(113\) 14.3670 1.35153 0.675767 0.737115i \(-0.263813\pi\)
0.675767 + 0.737115i \(0.263813\pi\)
\(114\) 0 0
\(115\) 12.1110 1.12936
\(116\) 0 0
\(117\) −1.33480 −0.123402
\(118\) 0 0
\(119\) −4.60593 −0.422225
\(120\) 0 0
\(121\) −10.5351 −0.957732
\(122\) 0 0
\(123\) −0.0996683 −0.00898679
\(124\) 0 0
\(125\) −11.0907 −0.991983
\(126\) 0 0
\(127\) −0.360627 −0.0320005 −0.0160002 0.999872i \(-0.505093\pi\)
−0.0160002 + 0.999872i \(0.505093\pi\)
\(128\) 0 0
\(129\) −0.637534 −0.0561318
\(130\) 0 0
\(131\) −17.6353 −1.54080 −0.770402 0.637558i \(-0.779945\pi\)
−0.770402 + 0.637558i \(0.779945\pi\)
\(132\) 0 0
\(133\) 10.8786 0.943295
\(134\) 0 0
\(135\) 4.73745 0.407735
\(136\) 0 0
\(137\) −0.948673 −0.0810506 −0.0405253 0.999179i \(-0.512903\pi\)
−0.0405253 + 0.999179i \(0.512903\pi\)
\(138\) 0 0
\(139\) 13.1604 1.11625 0.558126 0.829756i \(-0.311520\pi\)
0.558126 + 0.829756i \(0.311520\pi\)
\(140\) 0 0
\(141\) 0.795293 0.0669758
\(142\) 0 0
\(143\) 0.316926 0.0265027
\(144\) 0 0
\(145\) −10.7102 −0.889435
\(146\) 0 0
\(147\) −5.30008 −0.437143
\(148\) 0 0
\(149\) 9.21002 0.754515 0.377257 0.926108i \(-0.376867\pi\)
0.377257 + 0.926108i \(0.376867\pi\)
\(150\) 0 0
\(151\) −15.1103 −1.22966 −0.614828 0.788661i \(-0.710774\pi\)
−0.614828 + 0.788661i \(0.710774\pi\)
\(152\) 0 0
\(153\) 2.83274 0.229013
\(154\) 0 0
\(155\) 3.54376 0.284642
\(156\) 0 0
\(157\) 3.02040 0.241054 0.120527 0.992710i \(-0.461542\pi\)
0.120527 + 0.992710i \(0.461542\pi\)
\(158\) 0 0
\(159\) −1.03302 −0.0819241
\(160\) 0 0
\(161\) 25.0944 1.97772
\(162\) 0 0
\(163\) −6.10519 −0.478195 −0.239098 0.970996i \(-0.576852\pi\)
−0.239098 + 0.970996i \(0.576852\pi\)
\(164\) 0 0
\(165\) −0.550137 −0.0428281
\(166\) 0 0
\(167\) −0.604730 −0.0467954 −0.0233977 0.999726i \(-0.507448\pi\)
−0.0233977 + 0.999726i \(0.507448\pi\)
\(168\) 0 0
\(169\) −12.7840 −0.983382
\(170\) 0 0
\(171\) −6.69055 −0.511639
\(172\) 0 0
\(173\) 2.88294 0.219186 0.109593 0.993977i \(-0.465045\pi\)
0.109593 + 0.993977i \(0.465045\pi\)
\(174\) 0 0
\(175\) 0.367156 0.0277544
\(176\) 0 0
\(177\) −2.26522 −0.170264
\(178\) 0 0
\(179\) −9.12375 −0.681941 −0.340971 0.940074i \(-0.610756\pi\)
−0.340971 + 0.940074i \(0.610756\pi\)
\(180\) 0 0
\(181\) 12.1054 0.899788 0.449894 0.893082i \(-0.351462\pi\)
0.449894 + 0.893082i \(0.351462\pi\)
\(182\) 0 0
\(183\) −0.0200703 −0.00148364
\(184\) 0 0
\(185\) 8.00289 0.588385
\(186\) 0 0
\(187\) −0.672585 −0.0491843
\(188\) 0 0
\(189\) 9.81615 0.714020
\(190\) 0 0
\(191\) −21.7332 −1.57256 −0.786279 0.617872i \(-0.787995\pi\)
−0.786279 + 0.617872i \(0.787995\pi\)
\(192\) 0 0
\(193\) 13.9952 1.00739 0.503697 0.863880i \(-0.331973\pi\)
0.503697 + 0.863880i \(0.331973\pi\)
\(194\) 0 0
\(195\) −0.374998 −0.0268542
\(196\) 0 0
\(197\) −8.06139 −0.574350 −0.287175 0.957878i \(-0.592716\pi\)
−0.287175 + 0.957878i \(0.592716\pi\)
\(198\) 0 0
\(199\) 19.9548 1.41456 0.707281 0.706933i \(-0.249922\pi\)
0.707281 + 0.706933i \(0.249922\pi\)
\(200\) 0 0
\(201\) −2.09062 −0.147461
\(202\) 0 0
\(203\) −22.1919 −1.55757
\(204\) 0 0
\(205\) 0.627382 0.0438183
\(206\) 0 0
\(207\) −15.4335 −1.07270
\(208\) 0 0
\(209\) 1.58856 0.109883
\(210\) 0 0
\(211\) 21.5982 1.48688 0.743439 0.668803i \(-0.233193\pi\)
0.743439 + 0.668803i \(0.233193\pi\)
\(212\) 0 0
\(213\) −0.982045 −0.0672886
\(214\) 0 0
\(215\) 4.01309 0.273690
\(216\) 0 0
\(217\) 7.34279 0.498461
\(218\) 0 0
\(219\) −3.45009 −0.233136
\(220\) 0 0
\(221\) −0.458465 −0.0308397
\(222\) 0 0
\(223\) −23.1367 −1.54935 −0.774674 0.632361i \(-0.782086\pi\)
−0.774674 + 0.632361i \(0.782086\pi\)
\(224\) 0 0
\(225\) −0.225808 −0.0150539
\(226\) 0 0
\(227\) 5.98118 0.396985 0.198492 0.980102i \(-0.436396\pi\)
0.198492 + 0.980102i \(0.436396\pi\)
\(228\) 0 0
\(229\) 24.9844 1.65101 0.825506 0.564393i \(-0.190890\pi\)
0.825506 + 0.564393i \(0.190890\pi\)
\(230\) 0 0
\(231\) −1.13990 −0.0750001
\(232\) 0 0
\(233\) 8.09995 0.530646 0.265323 0.964160i \(-0.414521\pi\)
0.265323 + 0.964160i \(0.414521\pi\)
\(234\) 0 0
\(235\) −5.00613 −0.326564
\(236\) 0 0
\(237\) 1.07623 0.0699084
\(238\) 0 0
\(239\) 14.5792 0.943052 0.471526 0.881852i \(-0.343703\pi\)
0.471526 + 0.881852i \(0.343703\pi\)
\(240\) 0 0
\(241\) −30.4446 −1.96111 −0.980553 0.196254i \(-0.937122\pi\)
−0.980553 + 0.196254i \(0.937122\pi\)
\(242\) 0 0
\(243\) −9.12157 −0.585149
\(244\) 0 0
\(245\) 33.3624 2.13145
\(246\) 0 0
\(247\) 1.08283 0.0688990
\(248\) 0 0
\(249\) −0.832978 −0.0527878
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) 3.66443 0.230381
\(254\) 0 0
\(255\) 0.795828 0.0498367
\(256\) 0 0
\(257\) 7.48685 0.467017 0.233508 0.972355i \(-0.424979\pi\)
0.233508 + 0.972355i \(0.424979\pi\)
\(258\) 0 0
\(259\) 16.5823 1.03037
\(260\) 0 0
\(261\) 13.6484 0.844818
\(262\) 0 0
\(263\) −1.11608 −0.0688202 −0.0344101 0.999408i \(-0.510955\pi\)
−0.0344101 + 0.999408i \(0.510955\pi\)
\(264\) 0 0
\(265\) 6.50257 0.399450
\(266\) 0 0
\(267\) 3.71354 0.227265
\(268\) 0 0
\(269\) −8.28310 −0.505029 −0.252515 0.967593i \(-0.581258\pi\)
−0.252515 + 0.967593i \(0.581258\pi\)
\(270\) 0 0
\(271\) 22.2358 1.35073 0.675364 0.737484i \(-0.263986\pi\)
0.675364 + 0.737484i \(0.263986\pi\)
\(272\) 0 0
\(273\) −0.777009 −0.0470267
\(274\) 0 0
\(275\) 0.0536143 0.00323306
\(276\) 0 0
\(277\) −10.6054 −0.637219 −0.318609 0.947886i \(-0.603216\pi\)
−0.318609 + 0.947886i \(0.603216\pi\)
\(278\) 0 0
\(279\) −4.51596 −0.270363
\(280\) 0 0
\(281\) 8.18734 0.488416 0.244208 0.969723i \(-0.421472\pi\)
0.244208 + 0.969723i \(0.421472\pi\)
\(282\) 0 0
\(283\) 27.4202 1.62996 0.814980 0.579490i \(-0.196748\pi\)
0.814980 + 0.579490i \(0.196748\pi\)
\(284\) 0 0
\(285\) −1.87964 −0.111340
\(286\) 0 0
\(287\) 1.29996 0.0767340
\(288\) 0 0
\(289\) −16.0270 −0.942767
\(290\) 0 0
\(291\) 1.43905 0.0843587
\(292\) 0 0
\(293\) −3.15462 −0.184295 −0.0921475 0.995745i \(-0.529373\pi\)
−0.0921475 + 0.995745i \(0.529373\pi\)
\(294\) 0 0
\(295\) 14.2589 0.830183
\(296\) 0 0
\(297\) 1.43341 0.0831750
\(298\) 0 0
\(299\) 2.49784 0.144454
\(300\) 0 0
\(301\) 8.31525 0.479283
\(302\) 0 0
\(303\) 4.04576 0.232423
\(304\) 0 0
\(305\) 0.126336 0.00723400
\(306\) 0 0
\(307\) 18.4553 1.05330 0.526650 0.850082i \(-0.323448\pi\)
0.526650 + 0.850082i \(0.323448\pi\)
\(308\) 0 0
\(309\) 0.398275 0.0226571
\(310\) 0 0
\(311\) −25.0171 −1.41859 −0.709296 0.704911i \(-0.750987\pi\)
−0.709296 + 0.704911i \(0.750987\pi\)
\(312\) 0 0
\(313\) 10.0867 0.570132 0.285066 0.958508i \(-0.407984\pi\)
0.285066 + 0.958508i \(0.407984\pi\)
\(314\) 0 0
\(315\) −30.2205 −1.70273
\(316\) 0 0
\(317\) 22.3677 1.25629 0.628147 0.778095i \(-0.283814\pi\)
0.628147 + 0.778095i \(0.283814\pi\)
\(318\) 0 0
\(319\) −3.24059 −0.181438
\(320\) 0 0
\(321\) −3.35777 −0.187413
\(322\) 0 0
\(323\) −2.29801 −0.127864
\(324\) 0 0
\(325\) 0.0365459 0.00202720
\(326\) 0 0
\(327\) 1.23163 0.0681092
\(328\) 0 0
\(329\) −10.3729 −0.571875
\(330\) 0 0
\(331\) 19.0247 1.04569 0.522846 0.852427i \(-0.324870\pi\)
0.522846 + 0.852427i \(0.324870\pi\)
\(332\) 0 0
\(333\) −10.1984 −0.558869
\(334\) 0 0
\(335\) 13.1598 0.718998
\(336\) 0 0
\(337\) 16.3647 0.891445 0.445722 0.895171i \(-0.352947\pi\)
0.445722 + 0.895171i \(0.352947\pi\)
\(338\) 0 0
\(339\) −5.14357 −0.279360
\(340\) 0 0
\(341\) 1.07224 0.0580649
\(342\) 0 0
\(343\) 36.4415 1.96766
\(344\) 0 0
\(345\) −4.33589 −0.233437
\(346\) 0 0
\(347\) −0.559753 −0.0300491 −0.0150246 0.999887i \(-0.504783\pi\)
−0.0150246 + 0.999887i \(0.504783\pi\)
\(348\) 0 0
\(349\) −11.4850 −0.614777 −0.307389 0.951584i \(-0.599455\pi\)
−0.307389 + 0.951584i \(0.599455\pi\)
\(350\) 0 0
\(351\) 0.977079 0.0521526
\(352\) 0 0
\(353\) −0.0283464 −0.00150872 −0.000754362 1.00000i \(-0.500240\pi\)
−0.000754362 1.00000i \(0.500240\pi\)
\(354\) 0 0
\(355\) 6.18168 0.328089
\(356\) 0 0
\(357\) 1.64898 0.0872734
\(358\) 0 0
\(359\) 6.12611 0.323324 0.161662 0.986846i \(-0.448315\pi\)
0.161662 + 0.986846i \(0.448315\pi\)
\(360\) 0 0
\(361\) −13.5724 −0.714338
\(362\) 0 0
\(363\) 3.77168 0.197962
\(364\) 0 0
\(365\) 21.7173 1.13674
\(366\) 0 0
\(367\) 5.29169 0.276224 0.138112 0.990417i \(-0.455897\pi\)
0.138112 + 0.990417i \(0.455897\pi\)
\(368\) 0 0
\(369\) −0.799498 −0.0416202
\(370\) 0 0
\(371\) 13.4735 0.699511
\(372\) 0 0
\(373\) 27.7468 1.43668 0.718338 0.695694i \(-0.244903\pi\)
0.718338 + 0.695694i \(0.244903\pi\)
\(374\) 0 0
\(375\) 3.97061 0.205042
\(376\) 0 0
\(377\) −2.20893 −0.113766
\(378\) 0 0
\(379\) −4.91895 −0.252669 −0.126335 0.991988i \(-0.540321\pi\)
−0.126335 + 0.991988i \(0.540321\pi\)
\(380\) 0 0
\(381\) 0.129109 0.00661446
\(382\) 0 0
\(383\) 5.62298 0.287321 0.143661 0.989627i \(-0.454113\pi\)
0.143661 + 0.989627i \(0.454113\pi\)
\(384\) 0 0
\(385\) 7.17534 0.365689
\(386\) 0 0
\(387\) −5.11403 −0.259961
\(388\) 0 0
\(389\) 32.4279 1.64416 0.822080 0.569372i \(-0.192813\pi\)
0.822080 + 0.569372i \(0.192813\pi\)
\(390\) 0 0
\(391\) −5.30096 −0.268081
\(392\) 0 0
\(393\) 6.31366 0.318482
\(394\) 0 0
\(395\) −6.77452 −0.340863
\(396\) 0 0
\(397\) −4.65060 −0.233407 −0.116704 0.993167i \(-0.537233\pi\)
−0.116704 + 0.993167i \(0.537233\pi\)
\(398\) 0 0
\(399\) −3.89468 −0.194978
\(400\) 0 0
\(401\) −19.4879 −0.973180 −0.486590 0.873630i \(-0.661759\pi\)
−0.486590 + 0.873630i \(0.661759\pi\)
\(402\) 0 0
\(403\) 0.730885 0.0364080
\(404\) 0 0
\(405\) 17.7196 0.880495
\(406\) 0 0
\(407\) 2.42144 0.120026
\(408\) 0 0
\(409\) −20.7056 −1.02383 −0.511913 0.859037i \(-0.671063\pi\)
−0.511913 + 0.859037i \(0.671063\pi\)
\(410\) 0 0
\(411\) 0.339637 0.0167531
\(412\) 0 0
\(413\) 29.5448 1.45381
\(414\) 0 0
\(415\) 5.24334 0.257386
\(416\) 0 0
\(417\) −4.71160 −0.230728
\(418\) 0 0
\(419\) −30.0719 −1.46911 −0.734555 0.678549i \(-0.762609\pi\)
−0.734555 + 0.678549i \(0.762609\pi\)
\(420\) 0 0
\(421\) −24.2237 −1.18059 −0.590295 0.807188i \(-0.700988\pi\)
−0.590295 + 0.807188i \(0.700988\pi\)
\(422\) 0 0
\(423\) 6.37951 0.310182
\(424\) 0 0
\(425\) −0.0775584 −0.00376214
\(426\) 0 0
\(427\) 0.261773 0.0126681
\(428\) 0 0
\(429\) −0.113463 −0.00547807
\(430\) 0 0
\(431\) −12.0779 −0.581774 −0.290887 0.956757i \(-0.593950\pi\)
−0.290887 + 0.956757i \(0.593950\pi\)
\(432\) 0 0
\(433\) 19.5412 0.939089 0.469544 0.882909i \(-0.344418\pi\)
0.469544 + 0.882909i \(0.344418\pi\)
\(434\) 0 0
\(435\) 3.83439 0.183845
\(436\) 0 0
\(437\) 12.5202 0.598921
\(438\) 0 0
\(439\) 12.2606 0.585168 0.292584 0.956240i \(-0.405485\pi\)
0.292584 + 0.956240i \(0.405485\pi\)
\(440\) 0 0
\(441\) −42.5150 −2.02452
\(442\) 0 0
\(443\) −24.8669 −1.18146 −0.590731 0.806869i \(-0.701160\pi\)
−0.590731 + 0.806869i \(0.701160\pi\)
\(444\) 0 0
\(445\) −23.3756 −1.10811
\(446\) 0 0
\(447\) −3.29730 −0.155957
\(448\) 0 0
\(449\) −20.3163 −0.958785 −0.479393 0.877601i \(-0.659143\pi\)
−0.479393 + 0.877601i \(0.659143\pi\)
\(450\) 0 0
\(451\) 0.189827 0.00893862
\(452\) 0 0
\(453\) 5.40966 0.254168
\(454\) 0 0
\(455\) 4.89104 0.229295
\(456\) 0 0
\(457\) −26.0262 −1.21746 −0.608728 0.793379i \(-0.708320\pi\)
−0.608728 + 0.793379i \(0.708320\pi\)
\(458\) 0 0
\(459\) −2.07357 −0.0967861
\(460\) 0 0
\(461\) −10.3380 −0.481490 −0.240745 0.970588i \(-0.577392\pi\)
−0.240745 + 0.970588i \(0.577392\pi\)
\(462\) 0 0
\(463\) −1.96910 −0.0915117 −0.0457559 0.998953i \(-0.514570\pi\)
−0.0457559 + 0.998953i \(0.514570\pi\)
\(464\) 0 0
\(465\) −1.26871 −0.0588351
\(466\) 0 0
\(467\) 34.7843 1.60963 0.804814 0.593528i \(-0.202265\pi\)
0.804814 + 0.593528i \(0.202265\pi\)
\(468\) 0 0
\(469\) 27.2676 1.25910
\(470\) 0 0
\(471\) −1.08134 −0.0498256
\(472\) 0 0
\(473\) 1.21424 0.0558309
\(474\) 0 0
\(475\) 0.183183 0.00840500
\(476\) 0 0
\(477\) −8.28648 −0.379412
\(478\) 0 0
\(479\) −10.7833 −0.492701 −0.246351 0.969181i \(-0.579232\pi\)
−0.246351 + 0.969181i \(0.579232\pi\)
\(480\) 0 0
\(481\) 1.65056 0.0752592
\(482\) 0 0
\(483\) −8.98411 −0.408791
\(484\) 0 0
\(485\) −9.05840 −0.411321
\(486\) 0 0
\(487\) −21.7901 −0.987402 −0.493701 0.869632i \(-0.664356\pi\)
−0.493701 + 0.869632i \(0.664356\pi\)
\(488\) 0 0
\(489\) 2.18573 0.0988423
\(490\) 0 0
\(491\) −23.6974 −1.06945 −0.534725 0.845026i \(-0.679585\pi\)
−0.534725 + 0.845026i \(0.679585\pi\)
\(492\) 0 0
\(493\) 4.68784 0.211130
\(494\) 0 0
\(495\) −4.41297 −0.198348
\(496\) 0 0
\(497\) 12.8086 0.574546
\(498\) 0 0
\(499\) 5.33650 0.238895 0.119447 0.992841i \(-0.461888\pi\)
0.119447 + 0.992841i \(0.461888\pi\)
\(500\) 0 0
\(501\) 0.216501 0.00967255
\(502\) 0 0
\(503\) 21.7718 0.970755 0.485378 0.874305i \(-0.338682\pi\)
0.485378 + 0.874305i \(0.338682\pi\)
\(504\) 0 0
\(505\) −25.4668 −1.13326
\(506\) 0 0
\(507\) 4.57682 0.203264
\(508\) 0 0
\(509\) 4.15914 0.184351 0.0921753 0.995743i \(-0.470618\pi\)
0.0921753 + 0.995743i \(0.470618\pi\)
\(510\) 0 0
\(511\) 44.9990 1.99064
\(512\) 0 0
\(513\) 4.89750 0.216230
\(514\) 0 0
\(515\) −2.50702 −0.110473
\(516\) 0 0
\(517\) −1.51471 −0.0666167
\(518\) 0 0
\(519\) −1.03213 −0.0453055
\(520\) 0 0
\(521\) −37.9596 −1.66304 −0.831520 0.555494i \(-0.812529\pi\)
−0.831520 + 0.555494i \(0.812529\pi\)
\(522\) 0 0
\(523\) 27.9866 1.22377 0.611884 0.790947i \(-0.290412\pi\)
0.611884 + 0.790947i \(0.290412\pi\)
\(524\) 0 0
\(525\) −0.131447 −0.00573680
\(526\) 0 0
\(527\) −1.55110 −0.0675669
\(528\) 0 0
\(529\) 5.88113 0.255701
\(530\) 0 0
\(531\) −18.1706 −0.788538
\(532\) 0 0
\(533\) 0.129395 0.00560471
\(534\) 0 0
\(535\) 21.1362 0.913797
\(536\) 0 0
\(537\) 3.26642 0.140956
\(538\) 0 0
\(539\) 10.0945 0.434800
\(540\) 0 0
\(541\) −25.0936 −1.07886 −0.539429 0.842031i \(-0.681360\pi\)
−0.539429 + 0.842031i \(0.681360\pi\)
\(542\) 0 0
\(543\) −4.33389 −0.185985
\(544\) 0 0
\(545\) −7.75273 −0.332091
\(546\) 0 0
\(547\) 12.9856 0.555225 0.277613 0.960693i \(-0.410457\pi\)
0.277613 + 0.960693i \(0.410457\pi\)
\(548\) 0 0
\(549\) −0.160995 −0.00687111
\(550\) 0 0
\(551\) −11.0721 −0.471685
\(552\) 0 0
\(553\) −14.0370 −0.596915
\(554\) 0 0
\(555\) −2.86514 −0.121618
\(556\) 0 0
\(557\) −43.4396 −1.84060 −0.920298 0.391219i \(-0.872054\pi\)
−0.920298 + 0.391219i \(0.872054\pi\)
\(558\) 0 0
\(559\) 0.827682 0.0350072
\(560\) 0 0
\(561\) 0.240794 0.0101663
\(562\) 0 0
\(563\) 31.9340 1.34586 0.672929 0.739707i \(-0.265036\pi\)
0.672929 + 0.739707i \(0.265036\pi\)
\(564\) 0 0
\(565\) 32.3772 1.36212
\(566\) 0 0
\(567\) 36.7156 1.54191
\(568\) 0 0
\(569\) −22.4340 −0.940480 −0.470240 0.882539i \(-0.655833\pi\)
−0.470240 + 0.882539i \(0.655833\pi\)
\(570\) 0 0
\(571\) −15.4435 −0.646291 −0.323146 0.946349i \(-0.604740\pi\)
−0.323146 + 0.946349i \(0.604740\pi\)
\(572\) 0 0
\(573\) 7.78075 0.325045
\(574\) 0 0
\(575\) 0.422560 0.0176220
\(576\) 0 0
\(577\) −34.0505 −1.41754 −0.708771 0.705439i \(-0.750750\pi\)
−0.708771 + 0.705439i \(0.750750\pi\)
\(578\) 0 0
\(579\) −5.01044 −0.208227
\(580\) 0 0
\(581\) 10.8644 0.450730
\(582\) 0 0
\(583\) 1.96749 0.0814849
\(584\) 0 0
\(585\) −3.00808 −0.124369
\(586\) 0 0
\(587\) −21.8100 −0.900195 −0.450098 0.892979i \(-0.648611\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(588\) 0 0
\(589\) 3.66349 0.150951
\(590\) 0 0
\(591\) 2.88608 0.118717
\(592\) 0 0
\(593\) −25.9000 −1.06359 −0.531794 0.846874i \(-0.678482\pi\)
−0.531794 + 0.846874i \(0.678482\pi\)
\(594\) 0 0
\(595\) −10.3798 −0.425532
\(596\) 0 0
\(597\) −7.14409 −0.292388
\(598\) 0 0
\(599\) 48.0636 1.96383 0.981913 0.189331i \(-0.0606319\pi\)
0.981913 + 0.189331i \(0.0606319\pi\)
\(600\) 0 0
\(601\) 3.37140 0.137522 0.0687611 0.997633i \(-0.478095\pi\)
0.0687611 + 0.997633i \(0.478095\pi\)
\(602\) 0 0
\(603\) −16.7701 −0.682930
\(604\) 0 0
\(605\) −23.7416 −0.965234
\(606\) 0 0
\(607\) −13.6598 −0.554433 −0.277216 0.960808i \(-0.589412\pi\)
−0.277216 + 0.960808i \(0.589412\pi\)
\(608\) 0 0
\(609\) 7.94498 0.321947
\(610\) 0 0
\(611\) −1.03249 −0.0417702
\(612\) 0 0
\(613\) −10.0736 −0.406870 −0.203435 0.979088i \(-0.565211\pi\)
−0.203435 + 0.979088i \(0.565211\pi\)
\(614\) 0 0
\(615\) −0.224611 −0.00905717
\(616\) 0 0
\(617\) 22.2686 0.896500 0.448250 0.893908i \(-0.352048\pi\)
0.448250 + 0.893908i \(0.352048\pi\)
\(618\) 0 0
\(619\) −2.92761 −0.117671 −0.0588354 0.998268i \(-0.518739\pi\)
−0.0588354 + 0.998268i \(0.518739\pi\)
\(620\) 0 0
\(621\) 11.2974 0.453349
\(622\) 0 0
\(623\) −48.4351 −1.94051
\(624\) 0 0
\(625\) −25.3870 −1.01548
\(626\) 0 0
\(627\) −0.568724 −0.0227126
\(628\) 0 0
\(629\) −3.50285 −0.139668
\(630\) 0 0
\(631\) 1.95941 0.0780027 0.0390014 0.999239i \(-0.487582\pi\)
0.0390014 + 0.999239i \(0.487582\pi\)
\(632\) 0 0
\(633\) −7.73241 −0.307336
\(634\) 0 0
\(635\) −0.812703 −0.0322511
\(636\) 0 0
\(637\) 6.88085 0.272629
\(638\) 0 0
\(639\) −7.87756 −0.311631
\(640\) 0 0
\(641\) −43.3664 −1.71287 −0.856435 0.516255i \(-0.827326\pi\)
−0.856435 + 0.516255i \(0.827326\pi\)
\(642\) 0 0
\(643\) −20.0953 −0.792480 −0.396240 0.918147i \(-0.629685\pi\)
−0.396240 + 0.918147i \(0.629685\pi\)
\(644\) 0 0
\(645\) −1.43674 −0.0565714
\(646\) 0 0
\(647\) 9.18944 0.361274 0.180637 0.983550i \(-0.442184\pi\)
0.180637 + 0.983550i \(0.442184\pi\)
\(648\) 0 0
\(649\) 4.31431 0.169351
\(650\) 0 0
\(651\) −2.62881 −0.103031
\(652\) 0 0
\(653\) 7.73955 0.302872 0.151436 0.988467i \(-0.451610\pi\)
0.151436 + 0.988467i \(0.451610\pi\)
\(654\) 0 0
\(655\) −39.7426 −1.55287
\(656\) 0 0
\(657\) −27.6752 −1.07971
\(658\) 0 0
\(659\) 10.9678 0.427243 0.213622 0.976916i \(-0.431474\pi\)
0.213622 + 0.976916i \(0.431474\pi\)
\(660\) 0 0
\(661\) −22.9753 −0.893636 −0.446818 0.894625i \(-0.647443\pi\)
−0.446818 + 0.894625i \(0.647443\pi\)
\(662\) 0 0
\(663\) 0.164136 0.00637452
\(664\) 0 0
\(665\) 24.5158 0.950683
\(666\) 0 0
\(667\) −25.5407 −0.988938
\(668\) 0 0
\(669\) 8.28323 0.320248
\(670\) 0 0
\(671\) 0.0382256 0.00147568
\(672\) 0 0
\(673\) −40.6928 −1.56859 −0.784296 0.620387i \(-0.786976\pi\)
−0.784296 + 0.620387i \(0.786976\pi\)
\(674\) 0 0
\(675\) 0.165292 0.00636210
\(676\) 0 0
\(677\) −3.47467 −0.133543 −0.0667713 0.997768i \(-0.521270\pi\)
−0.0667713 + 0.997768i \(0.521270\pi\)
\(678\) 0 0
\(679\) −18.7693 −0.720299
\(680\) 0 0
\(681\) −2.14134 −0.0820562
\(682\) 0 0
\(683\) −13.6429 −0.522033 −0.261016 0.965334i \(-0.584058\pi\)
−0.261016 + 0.965334i \(0.584058\pi\)
\(684\) 0 0
\(685\) −2.13791 −0.0816854
\(686\) 0 0
\(687\) −8.94471 −0.341262
\(688\) 0 0
\(689\) 1.34113 0.0510929
\(690\) 0 0
\(691\) −51.5022 −1.95924 −0.979619 0.200867i \(-0.935624\pi\)
−0.979619 + 0.200867i \(0.935624\pi\)
\(692\) 0 0
\(693\) −9.14382 −0.347345
\(694\) 0 0
\(695\) 29.6581 1.12500
\(696\) 0 0
\(697\) −0.274604 −0.0104014
\(698\) 0 0
\(699\) −2.89988 −0.109684
\(700\) 0 0
\(701\) −29.0166 −1.09594 −0.547971 0.836497i \(-0.684600\pi\)
−0.547971 + 0.836497i \(0.684600\pi\)
\(702\) 0 0
\(703\) 8.27327 0.312032
\(704\) 0 0
\(705\) 1.79226 0.0675003
\(706\) 0 0
\(707\) −52.7681 −1.98455
\(708\) 0 0
\(709\) −18.5227 −0.695634 −0.347817 0.937563i \(-0.613077\pi\)
−0.347817 + 0.937563i \(0.613077\pi\)
\(710\) 0 0
\(711\) 8.63303 0.323764
\(712\) 0 0
\(713\) 8.45081 0.316485
\(714\) 0 0
\(715\) 0.714218 0.0267102
\(716\) 0 0
\(717\) −5.21955 −0.194927
\(718\) 0 0
\(719\) 16.7133 0.623300 0.311650 0.950197i \(-0.399118\pi\)
0.311650 + 0.950197i \(0.399118\pi\)
\(720\) 0 0
\(721\) −5.19463 −0.193458
\(722\) 0 0
\(723\) 10.8995 0.405358
\(724\) 0 0
\(725\) −0.373685 −0.0138783
\(726\) 0 0
\(727\) −5.88214 −0.218156 −0.109078 0.994033i \(-0.534790\pi\)
−0.109078 + 0.994033i \(0.534790\pi\)
\(728\) 0 0
\(729\) −20.3230 −0.752703
\(730\) 0 0
\(731\) −1.75652 −0.0649672
\(732\) 0 0
\(733\) 0.631585 0.0233281 0.0116641 0.999932i \(-0.496287\pi\)
0.0116641 + 0.999932i \(0.496287\pi\)
\(734\) 0 0
\(735\) −11.9442 −0.440567
\(736\) 0 0
\(737\) 3.98177 0.146670
\(738\) 0 0
\(739\) −24.4246 −0.898473 −0.449236 0.893413i \(-0.648304\pi\)
−0.449236 + 0.893413i \(0.648304\pi\)
\(740\) 0 0
\(741\) −0.387668 −0.0142413
\(742\) 0 0
\(743\) −42.5291 −1.56024 −0.780120 0.625629i \(-0.784842\pi\)
−0.780120 + 0.625629i \(0.784842\pi\)
\(744\) 0 0
\(745\) 20.7555 0.760424
\(746\) 0 0
\(747\) −6.68180 −0.244474
\(748\) 0 0
\(749\) 43.7949 1.60023
\(750\) 0 0
\(751\) −28.3865 −1.03584 −0.517919 0.855429i \(-0.673293\pi\)
−0.517919 + 0.855429i \(0.673293\pi\)
\(752\) 0 0
\(753\) 0.358013 0.0130467
\(754\) 0 0
\(755\) −34.0522 −1.23929
\(756\) 0 0
\(757\) 23.1842 0.842645 0.421323 0.906911i \(-0.361566\pi\)
0.421323 + 0.906911i \(0.361566\pi\)
\(758\) 0 0
\(759\) −1.31191 −0.0476194
\(760\) 0 0
\(761\) −29.7476 −1.07835 −0.539174 0.842194i \(-0.681264\pi\)
−0.539174 + 0.842194i \(0.681264\pi\)
\(762\) 0 0
\(763\) −16.0639 −0.581553
\(764\) 0 0
\(765\) 6.38380 0.230807
\(766\) 0 0
\(767\) 2.94083 0.106187
\(768\) 0 0
\(769\) 30.6145 1.10399 0.551993 0.833849i \(-0.313867\pi\)
0.551993 + 0.833849i \(0.313867\pi\)
\(770\) 0 0
\(771\) −2.68038 −0.0965317
\(772\) 0 0
\(773\) 24.8766 0.894748 0.447374 0.894347i \(-0.352359\pi\)
0.447374 + 0.894347i \(0.352359\pi\)
\(774\) 0 0
\(775\) 0.123644 0.00444142
\(776\) 0 0
\(777\) −5.93666 −0.212976
\(778\) 0 0
\(779\) 0.648578 0.0232377
\(780\) 0 0
\(781\) 1.87039 0.0669279
\(782\) 0 0
\(783\) −9.99071 −0.357039
\(784\) 0 0
\(785\) 6.80672 0.242942
\(786\) 0 0
\(787\) −32.1374 −1.14557 −0.572787 0.819704i \(-0.694138\pi\)
−0.572787 + 0.819704i \(0.694138\pi\)
\(788\) 0 0
\(789\) 0.399569 0.0142250
\(790\) 0 0
\(791\) 67.0866 2.38533
\(792\) 0 0
\(793\) 0.0260563 0.000925287 0
\(794\) 0 0
\(795\) −2.32800 −0.0825657
\(796\) 0 0
\(797\) 1.16154 0.0411440 0.0205720 0.999788i \(-0.493451\pi\)
0.0205720 + 0.999788i \(0.493451\pi\)
\(798\) 0 0
\(799\) 2.19117 0.0775182
\(800\) 0 0
\(801\) 29.7885 1.05252
\(802\) 0 0
\(803\) 6.57101 0.231886
\(804\) 0 0
\(805\) 56.5523 1.99321
\(806\) 0 0
\(807\) 2.96545 0.104389
\(808\) 0 0
\(809\) 27.8304 0.978465 0.489232 0.872153i \(-0.337277\pi\)
0.489232 + 0.872153i \(0.337277\pi\)
\(810\) 0 0
\(811\) 28.3598 0.995847 0.497924 0.867221i \(-0.334096\pi\)
0.497924 + 0.867221i \(0.334096\pi\)
\(812\) 0 0
\(813\) −7.96069 −0.279194
\(814\) 0 0
\(815\) −13.7585 −0.481941
\(816\) 0 0
\(817\) 4.14867 0.145144
\(818\) 0 0
\(819\) −6.23284 −0.217793
\(820\) 0 0
\(821\) 7.07414 0.246889 0.123445 0.992351i \(-0.460606\pi\)
0.123445 + 0.992351i \(0.460606\pi\)
\(822\) 0 0
\(823\) 32.8771 1.14602 0.573011 0.819548i \(-0.305775\pi\)
0.573011 + 0.819548i \(0.305775\pi\)
\(824\) 0 0
\(825\) −0.0191946 −0.000668270 0
\(826\) 0 0
\(827\) 35.8898 1.24801 0.624006 0.781420i \(-0.285504\pi\)
0.624006 + 0.781420i \(0.285504\pi\)
\(828\) 0 0
\(829\) 32.7648 1.13797 0.568984 0.822349i \(-0.307337\pi\)
0.568984 + 0.822349i \(0.307337\pi\)
\(830\) 0 0
\(831\) 3.79688 0.131712
\(832\) 0 0
\(833\) −14.6027 −0.505952
\(834\) 0 0
\(835\) −1.36281 −0.0471619
\(836\) 0 0
\(837\) 3.30570 0.114262
\(838\) 0 0
\(839\) 8.55189 0.295244 0.147622 0.989044i \(-0.452838\pi\)
0.147622 + 0.989044i \(0.452838\pi\)
\(840\) 0 0
\(841\) −6.41345 −0.221154
\(842\) 0 0
\(843\) −2.93117 −0.100955
\(844\) 0 0
\(845\) −28.8097 −0.991084
\(846\) 0 0
\(847\) −49.1934 −1.69030
\(848\) 0 0
\(849\) −9.81676 −0.336910
\(850\) 0 0
\(851\) 19.0845 0.654208
\(852\) 0 0
\(853\) −40.7800 −1.39628 −0.698140 0.715961i \(-0.745989\pi\)
−0.698140 + 0.715961i \(0.745989\pi\)
\(854\) 0 0
\(855\) −15.0777 −0.515646
\(856\) 0 0
\(857\) −22.2800 −0.761069 −0.380535 0.924767i \(-0.624260\pi\)
−0.380535 + 0.924767i \(0.624260\pi\)
\(858\) 0 0
\(859\) 44.1604 1.50673 0.753367 0.657600i \(-0.228428\pi\)
0.753367 + 0.657600i \(0.228428\pi\)
\(860\) 0 0
\(861\) −0.465401 −0.0158608
\(862\) 0 0
\(863\) −54.9486 −1.87047 −0.935236 0.354024i \(-0.884813\pi\)
−0.935236 + 0.354024i \(0.884813\pi\)
\(864\) 0 0
\(865\) 6.49695 0.220903
\(866\) 0 0
\(867\) 5.73788 0.194869
\(868\) 0 0
\(869\) −2.04977 −0.0695336
\(870\) 0 0
\(871\) 2.71415 0.0919656
\(872\) 0 0
\(873\) 11.5435 0.390687
\(874\) 0 0
\(875\) −51.7880 −1.75075
\(876\) 0 0
\(877\) 52.8730 1.78540 0.892698 0.450656i \(-0.148810\pi\)
0.892698 + 0.450656i \(0.148810\pi\)
\(878\) 0 0
\(879\) 1.12939 0.0380935
\(880\) 0 0
\(881\) −36.9873 −1.24613 −0.623067 0.782168i \(-0.714114\pi\)
−0.623067 + 0.782168i \(0.714114\pi\)
\(882\) 0 0
\(883\) 55.4842 1.86719 0.933597 0.358326i \(-0.116652\pi\)
0.933597 + 0.358326i \(0.116652\pi\)
\(884\) 0 0
\(885\) −5.10485 −0.171598
\(886\) 0 0
\(887\) −27.5877 −0.926306 −0.463153 0.886278i \(-0.653282\pi\)
−0.463153 + 0.886278i \(0.653282\pi\)
\(888\) 0 0
\(889\) −1.68395 −0.0564777
\(890\) 0 0
\(891\) 5.36143 0.179615
\(892\) 0 0
\(893\) −5.17526 −0.173184
\(894\) 0 0
\(895\) −20.5611 −0.687282
\(896\) 0 0
\(897\) −0.894259 −0.0298584
\(898\) 0 0
\(899\) −7.47337 −0.249251
\(900\) 0 0
\(901\) −2.84616 −0.0948194
\(902\) 0 0
\(903\) −2.97696 −0.0990671
\(904\) 0 0
\(905\) 27.2805 0.906836
\(906\) 0 0
\(907\) 31.2818 1.03870 0.519348 0.854563i \(-0.326175\pi\)
0.519348 + 0.854563i \(0.326175\pi\)
\(908\) 0 0
\(909\) 32.4534 1.07641
\(910\) 0 0
\(911\) −41.7288 −1.38254 −0.691268 0.722598i \(-0.742948\pi\)
−0.691268 + 0.722598i \(0.742948\pi\)
\(912\) 0 0
\(913\) 1.58648 0.0525048
\(914\) 0 0
\(915\) −0.0452300 −0.00149526
\(916\) 0 0
\(917\) −82.3480 −2.71937
\(918\) 0 0
\(919\) 34.8630 1.15002 0.575012 0.818145i \(-0.304997\pi\)
0.575012 + 0.818145i \(0.304997\pi\)
\(920\) 0 0
\(921\) −6.60723 −0.217716
\(922\) 0 0
\(923\) 1.27494 0.0419653
\(924\) 0 0
\(925\) 0.279225 0.00918088
\(926\) 0 0
\(927\) 3.19480 0.104931
\(928\) 0 0
\(929\) 38.2158 1.25382 0.626910 0.779092i \(-0.284320\pi\)
0.626910 + 0.779092i \(0.284320\pi\)
\(930\) 0 0
\(931\) 34.4895 1.13035
\(932\) 0 0
\(933\) 8.95645 0.293221
\(934\) 0 0
\(935\) −1.51573 −0.0495695
\(936\) 0 0
\(937\) −23.1614 −0.756651 −0.378326 0.925673i \(-0.623500\pi\)
−0.378326 + 0.925673i \(0.623500\pi\)
\(938\) 0 0
\(939\) −3.61115 −0.117846
\(940\) 0 0
\(941\) −53.5932 −1.74709 −0.873544 0.486744i \(-0.838184\pi\)
−0.873544 + 0.486744i \(0.838184\pi\)
\(942\) 0 0
\(943\) 1.49612 0.0487203
\(944\) 0 0
\(945\) 22.1215 0.719612
\(946\) 0 0
\(947\) 52.7975 1.71569 0.857844 0.513911i \(-0.171804\pi\)
0.857844 + 0.513911i \(0.171804\pi\)
\(948\) 0 0
\(949\) 4.47910 0.145398
\(950\) 0 0
\(951\) −8.00791 −0.259674
\(952\) 0 0
\(953\) −5.49662 −0.178053 −0.0890264 0.996029i \(-0.528376\pi\)
−0.0890264 + 0.996029i \(0.528376\pi\)
\(954\) 0 0
\(955\) −48.9775 −1.58487
\(956\) 0 0
\(957\) 1.16017 0.0375031
\(958\) 0 0
\(959\) −4.42982 −0.143046
\(960\) 0 0
\(961\) −28.5272 −0.920233
\(962\) 0 0
\(963\) −26.9347 −0.867958
\(964\) 0 0
\(965\) 31.5392 1.01528
\(966\) 0 0
\(967\) −18.1431 −0.583442 −0.291721 0.956503i \(-0.594228\pi\)
−0.291721 + 0.956503i \(0.594228\pi\)
\(968\) 0 0
\(969\) 0.822715 0.0264294
\(970\) 0 0
\(971\) 15.9803 0.512832 0.256416 0.966567i \(-0.417458\pi\)
0.256416 + 0.966567i \(0.417458\pi\)
\(972\) 0 0
\(973\) 61.4525 1.97008
\(974\) 0 0
\(975\) −0.0130839 −0.000419020 0
\(976\) 0 0
\(977\) 34.0089 1.08804 0.544020 0.839072i \(-0.316901\pi\)
0.544020 + 0.839072i \(0.316901\pi\)
\(978\) 0 0
\(979\) −7.07278 −0.226047
\(980\) 0 0
\(981\) 9.87961 0.315432
\(982\) 0 0
\(983\) −2.66699 −0.0850637 −0.0425318 0.999095i \(-0.513542\pi\)
−0.0425318 + 0.999095i \(0.513542\pi\)
\(984\) 0 0
\(985\) −18.1670 −0.578849
\(986\) 0 0
\(987\) 3.71362 0.118206
\(988\) 0 0
\(989\) 9.57001 0.304309
\(990\) 0 0
\(991\) 23.2217 0.737660 0.368830 0.929497i \(-0.379758\pi\)
0.368830 + 0.929497i \(0.379758\pi\)
\(992\) 0 0
\(993\) −6.81107 −0.216143
\(994\) 0 0
\(995\) 44.9699 1.42564
\(996\) 0 0
\(997\) 25.3804 0.803805 0.401903 0.915682i \(-0.368349\pi\)
0.401903 + 0.915682i \(0.368349\pi\)
\(998\) 0 0
\(999\) 7.46527 0.236191
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 4016.2.a.g.1.3 7
4.3 odd 2 1004.2.a.a.1.5 7
12.11 even 2 9036.2.a.i.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.5 7 4.3 odd 2
4016.2.a.g.1.3 7 1.1 even 1 trivial
9036.2.a.i.1.2 7 12.11 even 2