Properties

Label 7623.2.a.cy.1.4
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 231)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.33330\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.33330 q^{2} -0.222305 q^{4} +0.873210 q^{5} +1.00000 q^{7} +2.96300 q^{8} +O(q^{10})\) \(q-1.33330 q^{2} -0.222305 q^{4} +0.873210 q^{5} +1.00000 q^{7} +2.96300 q^{8} -1.16425 q^{10} -0.0395440 q^{13} -1.33330 q^{14} -3.50597 q^{16} +2.04633 q^{17} +5.69421 q^{19} -0.194119 q^{20} -5.97870 q^{23} -4.23750 q^{25} +0.0527241 q^{26} -0.222305 q^{28} -4.67254 q^{29} +7.47891 q^{31} -1.25149 q^{32} -2.72838 q^{34} +0.873210 q^{35} +11.5704 q^{37} -7.59210 q^{38} +2.58733 q^{40} -6.14882 q^{41} +1.79689 q^{43} +7.97142 q^{46} -6.04773 q^{47} +1.00000 q^{49} +5.64987 q^{50} +0.00879083 q^{52} +0.124401 q^{53} +2.96300 q^{56} +6.22991 q^{58} +14.3460 q^{59} -7.55944 q^{61} -9.97165 q^{62} +8.68056 q^{64} -0.0345302 q^{65} +4.85938 q^{67} -0.454910 q^{68} -1.16425 q^{70} +11.2503 q^{71} -0.612954 q^{73} -15.4269 q^{74} -1.26585 q^{76} +0.155227 q^{79} -3.06145 q^{80} +8.19824 q^{82} +8.91599 q^{83} +1.78688 q^{85} -2.39580 q^{86} -5.17689 q^{89} -0.0395440 q^{91} +1.32910 q^{92} +8.06345 q^{94} +4.97224 q^{95} +7.94222 q^{97} -1.33330 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} + O(q^{10}) \) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} - 6q^{10} + 6q^{13} + 38q^{16} - 8q^{17} - 7q^{20} + 31q^{25} - q^{26} + 18q^{28} + 14q^{29} + 26q^{31} + 41q^{32} + 21q^{34} - 5q^{35} + 24q^{37} - 8q^{38} - 5q^{40} - 19q^{41} - 6q^{43} - q^{46} - 15q^{47} + 10q^{49} + q^{50} - 25q^{52} + q^{53} + 3q^{56} + 11q^{58} - 23q^{59} - 11q^{62} + 53q^{64} + 29q^{65} + 38q^{67} - 87q^{68} - 6q^{70} - 26q^{71} - q^{73} + 39q^{74} - 2q^{76} + 5q^{79} - 6q^{80} + 5q^{82} - 6q^{83} - q^{85} + 41q^{86} + 9q^{89} + 6q^{91} + 48q^{92} + 42q^{95} + 24q^{97} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33330 −0.942787 −0.471394 0.881923i \(-0.656249\pi\)
−0.471394 + 0.881923i \(0.656249\pi\)
\(3\) 0 0
\(4\) −0.222305 −0.111152
\(5\) 0.873210 0.390512 0.195256 0.980752i \(-0.437446\pi\)
0.195256 + 0.980752i \(0.437446\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.96300 1.04758
\(9\) 0 0
\(10\) −1.16425 −0.368169
\(11\) 0 0
\(12\) 0 0
\(13\) −0.0395440 −0.0109675 −0.00548377 0.999985i \(-0.501746\pi\)
−0.00548377 + 0.999985i \(0.501746\pi\)
\(14\) −1.33330 −0.356340
\(15\) 0 0
\(16\) −3.50597 −0.876493
\(17\) 2.04633 0.496308 0.248154 0.968721i \(-0.420176\pi\)
0.248154 + 0.968721i \(0.420176\pi\)
\(18\) 0 0
\(19\) 5.69421 1.30634 0.653170 0.757211i \(-0.273439\pi\)
0.653170 + 0.757211i \(0.273439\pi\)
\(20\) −0.194119 −0.0434063
\(21\) 0 0
\(22\) 0 0
\(23\) −5.97870 −1.24665 −0.623323 0.781965i \(-0.714218\pi\)
−0.623323 + 0.781965i \(0.714218\pi\)
\(24\) 0 0
\(25\) −4.23750 −0.847501
\(26\) 0.0527241 0.0103401
\(27\) 0 0
\(28\) −0.222305 −0.0420117
\(29\) −4.67254 −0.867669 −0.433834 0.900993i \(-0.642840\pi\)
−0.433834 + 0.900993i \(0.642840\pi\)
\(30\) 0 0
\(31\) 7.47891 1.34325 0.671626 0.740890i \(-0.265596\pi\)
0.671626 + 0.740890i \(0.265596\pi\)
\(32\) −1.25149 −0.221234
\(33\) 0 0
\(34\) −2.72838 −0.467913
\(35\) 0.873210 0.147600
\(36\) 0 0
\(37\) 11.5704 1.90217 0.951085 0.308930i \(-0.0999708\pi\)
0.951085 + 0.308930i \(0.0999708\pi\)
\(38\) −7.59210 −1.23160
\(39\) 0 0
\(40\) 2.58733 0.409092
\(41\) −6.14882 −0.960285 −0.480142 0.877191i \(-0.659415\pi\)
−0.480142 + 0.877191i \(0.659415\pi\)
\(42\) 0 0
\(43\) 1.79689 0.274024 0.137012 0.990569i \(-0.456250\pi\)
0.137012 + 0.990569i \(0.456250\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 7.97142 1.17532
\(47\) −6.04773 −0.882152 −0.441076 0.897470i \(-0.645403\pi\)
−0.441076 + 0.897470i \(0.645403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.64987 0.799013
\(51\) 0 0
\(52\) 0.00879083 0.00121907
\(53\) 0.124401 0.0170878 0.00854390 0.999964i \(-0.497280\pi\)
0.00854390 + 0.999964i \(0.497280\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.96300 0.395948
\(57\) 0 0
\(58\) 6.22991 0.818027
\(59\) 14.3460 1.86769 0.933845 0.357679i \(-0.116432\pi\)
0.933845 + 0.357679i \(0.116432\pi\)
\(60\) 0 0
\(61\) −7.55944 −0.967887 −0.483944 0.875099i \(-0.660796\pi\)
−0.483944 + 0.875099i \(0.660796\pi\)
\(62\) −9.97165 −1.26640
\(63\) 0 0
\(64\) 8.68056 1.08507
\(65\) −0.0345302 −0.00428295
\(66\) 0 0
\(67\) 4.85938 0.593668 0.296834 0.954929i \(-0.404069\pi\)
0.296834 + 0.954929i \(0.404069\pi\)
\(68\) −0.454910 −0.0551659
\(69\) 0 0
\(70\) −1.16425 −0.139155
\(71\) 11.2503 1.33516 0.667582 0.744536i \(-0.267329\pi\)
0.667582 + 0.744536i \(0.267329\pi\)
\(72\) 0 0
\(73\) −0.612954 −0.0717409 −0.0358704 0.999356i \(-0.511420\pi\)
−0.0358704 + 0.999356i \(0.511420\pi\)
\(74\) −15.4269 −1.79334
\(75\) 0 0
\(76\) −1.26585 −0.145203
\(77\) 0 0
\(78\) 0 0
\(79\) 0.155227 0.0174644 0.00873220 0.999962i \(-0.497220\pi\)
0.00873220 + 0.999962i \(0.497220\pi\)
\(80\) −3.06145 −0.342281
\(81\) 0 0
\(82\) 8.19824 0.905344
\(83\) 8.91599 0.978657 0.489328 0.872100i \(-0.337242\pi\)
0.489328 + 0.872100i \(0.337242\pi\)
\(84\) 0 0
\(85\) 1.78688 0.193814
\(86\) −2.39580 −0.258346
\(87\) 0 0
\(88\) 0 0
\(89\) −5.17689 −0.548749 −0.274374 0.961623i \(-0.588471\pi\)
−0.274374 + 0.961623i \(0.588471\pi\)
\(90\) 0 0
\(91\) −0.0395440 −0.00414534
\(92\) 1.32910 0.138568
\(93\) 0 0
\(94\) 8.06345 0.831682
\(95\) 4.97224 0.510141
\(96\) 0 0
\(97\) 7.94222 0.806410 0.403205 0.915110i \(-0.367896\pi\)
0.403205 + 0.915110i \(0.367896\pi\)
\(98\) −1.33330 −0.134684
\(99\) 0 0
\(100\) 0.942018 0.0942018
\(101\) −9.09560 −0.905046 −0.452523 0.891753i \(-0.649476\pi\)
−0.452523 + 0.891753i \(0.649476\pi\)
\(102\) 0 0
\(103\) 3.43750 0.338707 0.169354 0.985555i \(-0.445832\pi\)
0.169354 + 0.985555i \(0.445832\pi\)
\(104\) −0.117169 −0.0114894
\(105\) 0 0
\(106\) −0.165864 −0.0161102
\(107\) 3.29161 0.318212 0.159106 0.987262i \(-0.449139\pi\)
0.159106 + 0.987262i \(0.449139\pi\)
\(108\) 0 0
\(109\) −9.99510 −0.957357 −0.478678 0.877990i \(-0.658884\pi\)
−0.478678 + 0.877990i \(0.658884\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −3.50597 −0.331283
\(113\) −4.40261 −0.414163 −0.207081 0.978324i \(-0.566397\pi\)
−0.207081 + 0.978324i \(0.566397\pi\)
\(114\) 0 0
\(115\) −5.22067 −0.486830
\(116\) 1.03873 0.0964435
\(117\) 0 0
\(118\) −19.1275 −1.76083
\(119\) 2.04633 0.187587
\(120\) 0 0
\(121\) 0 0
\(122\) 10.0790 0.912512
\(123\) 0 0
\(124\) −1.66260 −0.149306
\(125\) −8.06628 −0.721470
\(126\) 0 0
\(127\) −12.9823 −1.15200 −0.575998 0.817451i \(-0.695386\pi\)
−0.575998 + 0.817451i \(0.695386\pi\)
\(128\) −9.07082 −0.801755
\(129\) 0 0
\(130\) 0.0460393 0.00403791
\(131\) 18.1255 1.58363 0.791817 0.610758i \(-0.209135\pi\)
0.791817 + 0.610758i \(0.209135\pi\)
\(132\) 0 0
\(133\) 5.69421 0.493750
\(134\) −6.47902 −0.559702
\(135\) 0 0
\(136\) 6.06329 0.519923
\(137\) −5.20699 −0.444863 −0.222431 0.974948i \(-0.571399\pi\)
−0.222431 + 0.974948i \(0.571399\pi\)
\(138\) 0 0
\(139\) 18.1482 1.53931 0.769657 0.638458i \(-0.220427\pi\)
0.769657 + 0.638458i \(0.220427\pi\)
\(140\) −0.194119 −0.0164061
\(141\) 0 0
\(142\) −15.0000 −1.25878
\(143\) 0 0
\(144\) 0 0
\(145\) −4.08011 −0.338835
\(146\) 0.817253 0.0676364
\(147\) 0 0
\(148\) −2.57217 −0.211431
\(149\) 11.0495 0.905212 0.452606 0.891711i \(-0.350494\pi\)
0.452606 + 0.891711i \(0.350494\pi\)
\(150\) 0 0
\(151\) −15.9314 −1.29648 −0.648240 0.761436i \(-0.724495\pi\)
−0.648240 + 0.761436i \(0.724495\pi\)
\(152\) 16.8720 1.36850
\(153\) 0 0
\(154\) 0 0
\(155\) 6.53066 0.524555
\(156\) 0 0
\(157\) 16.0035 1.27722 0.638610 0.769531i \(-0.279510\pi\)
0.638610 + 0.769531i \(0.279510\pi\)
\(158\) −0.206964 −0.0164652
\(159\) 0 0
\(160\) −1.09281 −0.0863945
\(161\) −5.97870 −0.471188
\(162\) 0 0
\(163\) 22.0034 1.72344 0.861721 0.507383i \(-0.169387\pi\)
0.861721 + 0.507383i \(0.169387\pi\)
\(164\) 1.36691 0.106738
\(165\) 0 0
\(166\) −11.8877 −0.922665
\(167\) −4.72101 −0.365323 −0.182661 0.983176i \(-0.558471\pi\)
−0.182661 + 0.983176i \(0.558471\pi\)
\(168\) 0 0
\(169\) −12.9984 −0.999880
\(170\) −2.38245 −0.182725
\(171\) 0 0
\(172\) −0.399458 −0.0304584
\(173\) −9.47572 −0.720426 −0.360213 0.932870i \(-0.617296\pi\)
−0.360213 + 0.932870i \(0.617296\pi\)
\(174\) 0 0
\(175\) −4.23750 −0.320325
\(176\) 0 0
\(177\) 0 0
\(178\) 6.90235 0.517353
\(179\) −17.7185 −1.32434 −0.662170 0.749353i \(-0.730364\pi\)
−0.662170 + 0.749353i \(0.730364\pi\)
\(180\) 0 0
\(181\) 16.2742 1.20965 0.604826 0.796358i \(-0.293243\pi\)
0.604826 + 0.796358i \(0.293243\pi\)
\(182\) 0.0527241 0.00390817
\(183\) 0 0
\(184\) −17.7149 −1.30596
\(185\) 10.1034 0.742819
\(186\) 0 0
\(187\) 0 0
\(188\) 1.34444 0.0980534
\(189\) 0 0
\(190\) −6.62950 −0.480954
\(191\) −6.44604 −0.466419 −0.233210 0.972426i \(-0.574923\pi\)
−0.233210 + 0.972426i \(0.574923\pi\)
\(192\) 0 0
\(193\) 1.81074 0.130340 0.0651701 0.997874i \(-0.479241\pi\)
0.0651701 + 0.997874i \(0.479241\pi\)
\(194\) −10.5894 −0.760273
\(195\) 0 0
\(196\) −0.222305 −0.0158789
\(197\) −6.85772 −0.488592 −0.244296 0.969701i \(-0.578557\pi\)
−0.244296 + 0.969701i \(0.578557\pi\)
\(198\) 0 0
\(199\) −5.07400 −0.359687 −0.179843 0.983695i \(-0.557559\pi\)
−0.179843 + 0.983695i \(0.557559\pi\)
\(200\) −12.5557 −0.887825
\(201\) 0 0
\(202\) 12.1272 0.853266
\(203\) −4.67254 −0.327948
\(204\) 0 0
\(205\) −5.36922 −0.375002
\(206\) −4.58323 −0.319329
\(207\) 0 0
\(208\) 0.138640 0.00961296
\(209\) 0 0
\(210\) 0 0
\(211\) −8.10688 −0.558101 −0.279050 0.960276i \(-0.590020\pi\)
−0.279050 + 0.960276i \(0.590020\pi\)
\(212\) −0.0276550 −0.00189935
\(213\) 0 0
\(214\) −4.38871 −0.300006
\(215\) 1.56907 0.107009
\(216\) 0 0
\(217\) 7.47891 0.507702
\(218\) 13.3265 0.902583
\(219\) 0 0
\(220\) 0 0
\(221\) −0.0809201 −0.00544328
\(222\) 0 0
\(223\) −16.2050 −1.08517 −0.542583 0.840002i \(-0.682554\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(224\) −1.25149 −0.0836187
\(225\) 0 0
\(226\) 5.87001 0.390467
\(227\) 23.6742 1.57131 0.785655 0.618665i \(-0.212326\pi\)
0.785655 + 0.618665i \(0.212326\pi\)
\(228\) 0 0
\(229\) 10.1567 0.671176 0.335588 0.942009i \(-0.391065\pi\)
0.335588 + 0.942009i \(0.391065\pi\)
\(230\) 6.96073 0.458977
\(231\) 0 0
\(232\) −13.8448 −0.908952
\(233\) 23.5158 1.54057 0.770287 0.637697i \(-0.220113\pi\)
0.770287 + 0.637697i \(0.220113\pi\)
\(234\) 0 0
\(235\) −5.28094 −0.344491
\(236\) −3.18919 −0.207598
\(237\) 0 0
\(238\) −2.72838 −0.176854
\(239\) 7.82554 0.506192 0.253096 0.967441i \(-0.418551\pi\)
0.253096 + 0.967441i \(0.418551\pi\)
\(240\) 0 0
\(241\) 6.86139 0.441981 0.220991 0.975276i \(-0.429071\pi\)
0.220991 + 0.975276i \(0.429071\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.68050 0.107583
\(245\) 0.873210 0.0557874
\(246\) 0 0
\(247\) −0.225172 −0.0143273
\(248\) 22.1600 1.40716
\(249\) 0 0
\(250\) 10.7548 0.680193
\(251\) 2.56709 0.162033 0.0810166 0.996713i \(-0.474183\pi\)
0.0810166 + 0.996713i \(0.474183\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 17.3094 1.08609
\(255\) 0 0
\(256\) −5.26696 −0.329185
\(257\) 19.5915 1.22208 0.611042 0.791598i \(-0.290750\pi\)
0.611042 + 0.791598i \(0.290750\pi\)
\(258\) 0 0
\(259\) 11.5704 0.718953
\(260\) 0.00767624 0.000476060 0
\(261\) 0 0
\(262\) −24.1668 −1.49303
\(263\) −26.5306 −1.63595 −0.817974 0.575255i \(-0.804903\pi\)
−0.817974 + 0.575255i \(0.804903\pi\)
\(264\) 0 0
\(265\) 0.108628 0.00667298
\(266\) −7.59210 −0.465501
\(267\) 0 0
\(268\) −1.08026 −0.0659876
\(269\) 17.1248 1.04412 0.522058 0.852910i \(-0.325164\pi\)
0.522058 + 0.852910i \(0.325164\pi\)
\(270\) 0 0
\(271\) −5.29554 −0.321681 −0.160840 0.986980i \(-0.551420\pi\)
−0.160840 + 0.986980i \(0.551420\pi\)
\(272\) −7.17438 −0.435010
\(273\) 0 0
\(274\) 6.94249 0.419411
\(275\) 0 0
\(276\) 0 0
\(277\) −2.45004 −0.147209 −0.0736044 0.997288i \(-0.523450\pi\)
−0.0736044 + 0.997288i \(0.523450\pi\)
\(278\) −24.1971 −1.45125
\(279\) 0 0
\(280\) 2.58733 0.154622
\(281\) 0.301746 0.0180006 0.00900031 0.999959i \(-0.497135\pi\)
0.00900031 + 0.999959i \(0.497135\pi\)
\(282\) 0 0
\(283\) −24.0094 −1.42721 −0.713605 0.700548i \(-0.752939\pi\)
−0.713605 + 0.700548i \(0.752939\pi\)
\(284\) −2.50100 −0.148407
\(285\) 0 0
\(286\) 0 0
\(287\) −6.14882 −0.362954
\(288\) 0 0
\(289\) −12.8125 −0.753678
\(290\) 5.44002 0.319449
\(291\) 0 0
\(292\) 0.136263 0.00797418
\(293\) −1.96403 −0.114740 −0.0573700 0.998353i \(-0.518271\pi\)
−0.0573700 + 0.998353i \(0.518271\pi\)
\(294\) 0 0
\(295\) 12.5271 0.729354
\(296\) 34.2833 1.99268
\(297\) 0 0
\(298\) −14.7324 −0.853422
\(299\) 0.236422 0.0136726
\(300\) 0 0
\(301\) 1.79689 0.103571
\(302\) 21.2414 1.22230
\(303\) 0 0
\(304\) −19.9637 −1.14500
\(305\) −6.60098 −0.377971
\(306\) 0 0
\(307\) −20.0180 −1.14249 −0.571243 0.820781i \(-0.693538\pi\)
−0.571243 + 0.820781i \(0.693538\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.70735 −0.494544
\(311\) −17.7041 −1.00391 −0.501954 0.864894i \(-0.667385\pi\)
−0.501954 + 0.864894i \(0.667385\pi\)
\(312\) 0 0
\(313\) 28.3315 1.60139 0.800697 0.599070i \(-0.204463\pi\)
0.800697 + 0.599070i \(0.204463\pi\)
\(314\) −21.3375 −1.20415
\(315\) 0 0
\(316\) −0.0345077 −0.00194121
\(317\) 21.9554 1.23314 0.616570 0.787300i \(-0.288522\pi\)
0.616570 + 0.787300i \(0.288522\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 7.57995 0.423732
\(321\) 0 0
\(322\) 7.97142 0.444230
\(323\) 11.6522 0.648347
\(324\) 0 0
\(325\) 0.167568 0.00929499
\(326\) −29.3372 −1.62484
\(327\) 0 0
\(328\) −18.2190 −1.00598
\(329\) −6.04773 −0.333422
\(330\) 0 0
\(331\) 23.1465 1.27225 0.636123 0.771587i \(-0.280537\pi\)
0.636123 + 0.771587i \(0.280537\pi\)
\(332\) −1.98207 −0.108780
\(333\) 0 0
\(334\) 6.29454 0.344422
\(335\) 4.24326 0.231834
\(336\) 0 0
\(337\) −35.0111 −1.90717 −0.953587 0.301117i \(-0.902640\pi\)
−0.953587 + 0.301117i \(0.902640\pi\)
\(338\) 17.3308 0.942674
\(339\) 0 0
\(340\) −0.397232 −0.0215429
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 5.32420 0.287062
\(345\) 0 0
\(346\) 12.6340 0.679208
\(347\) −3.75958 −0.201825 −0.100912 0.994895i \(-0.532176\pi\)
−0.100912 + 0.994895i \(0.532176\pi\)
\(348\) 0 0
\(349\) 12.1740 0.651658 0.325829 0.945429i \(-0.394357\pi\)
0.325829 + 0.945429i \(0.394357\pi\)
\(350\) 5.64987 0.301998
\(351\) 0 0
\(352\) 0 0
\(353\) 5.79059 0.308202 0.154101 0.988055i \(-0.450752\pi\)
0.154101 + 0.988055i \(0.450752\pi\)
\(354\) 0 0
\(355\) 9.82387 0.521397
\(356\) 1.15085 0.0609948
\(357\) 0 0
\(358\) 23.6241 1.24857
\(359\) 5.76086 0.304046 0.152023 0.988377i \(-0.451421\pi\)
0.152023 + 0.988377i \(0.451421\pi\)
\(360\) 0 0
\(361\) 13.4240 0.706525
\(362\) −21.6984 −1.14044
\(363\) 0 0
\(364\) 0.00879083 0.000460765 0
\(365\) −0.535238 −0.0280156
\(366\) 0 0
\(367\) 14.2580 0.744263 0.372132 0.928180i \(-0.378627\pi\)
0.372132 + 0.928180i \(0.378627\pi\)
\(368\) 20.9612 1.09268
\(369\) 0 0
\(370\) −13.4709 −0.700320
\(371\) 0.124401 0.00645858
\(372\) 0 0
\(373\) −32.2223 −1.66841 −0.834203 0.551458i \(-0.814072\pi\)
−0.834203 + 0.551458i \(0.814072\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −17.9195 −0.924125
\(377\) 0.184771 0.00951619
\(378\) 0 0
\(379\) −28.5774 −1.46792 −0.733960 0.679193i \(-0.762330\pi\)
−0.733960 + 0.679193i \(0.762330\pi\)
\(380\) −1.10535 −0.0567035
\(381\) 0 0
\(382\) 8.59452 0.439734
\(383\) 20.1613 1.03019 0.515097 0.857132i \(-0.327756\pi\)
0.515097 + 0.857132i \(0.327756\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.41427 −0.122883
\(387\) 0 0
\(388\) −1.76559 −0.0896345
\(389\) 16.5608 0.839663 0.419832 0.907602i \(-0.362089\pi\)
0.419832 + 0.907602i \(0.362089\pi\)
\(390\) 0 0
\(391\) −12.2344 −0.618721
\(392\) 2.96300 0.149654
\(393\) 0 0
\(394\) 9.14342 0.460639
\(395\) 0.135546 0.00682005
\(396\) 0 0
\(397\) 30.9920 1.55545 0.777723 0.628607i \(-0.216375\pi\)
0.777723 + 0.628607i \(0.216375\pi\)
\(398\) 6.76518 0.339108
\(399\) 0 0
\(400\) 14.8566 0.742828
\(401\) −3.48264 −0.173915 −0.0869574 0.996212i \(-0.527714\pi\)
−0.0869574 + 0.996212i \(0.527714\pi\)
\(402\) 0 0
\(403\) −0.295746 −0.0147322
\(404\) 2.02200 0.100598
\(405\) 0 0
\(406\) 6.22991 0.309185
\(407\) 0 0
\(408\) 0 0
\(409\) 26.5883 1.31471 0.657353 0.753583i \(-0.271676\pi\)
0.657353 + 0.753583i \(0.271676\pi\)
\(410\) 7.15879 0.353547
\(411\) 0 0
\(412\) −0.764174 −0.0376481
\(413\) 14.3460 0.705920
\(414\) 0 0
\(415\) 7.78553 0.382177
\(416\) 0.0494889 0.00242639
\(417\) 0 0
\(418\) 0 0
\(419\) −29.1491 −1.42402 −0.712012 0.702167i \(-0.752216\pi\)
−0.712012 + 0.702167i \(0.752216\pi\)
\(420\) 0 0
\(421\) −19.9909 −0.974297 −0.487148 0.873319i \(-0.661963\pi\)
−0.487148 + 0.873319i \(0.661963\pi\)
\(422\) 10.8089 0.526170
\(423\) 0 0
\(424\) 0.368601 0.0179008
\(425\) −8.67134 −0.420622
\(426\) 0 0
\(427\) −7.55944 −0.365827
\(428\) −0.731740 −0.0353700
\(429\) 0 0
\(430\) −2.09204 −0.100887
\(431\) 16.9285 0.815417 0.407709 0.913112i \(-0.366328\pi\)
0.407709 + 0.913112i \(0.366328\pi\)
\(432\) 0 0
\(433\) −8.55148 −0.410958 −0.205479 0.978662i \(-0.565875\pi\)
−0.205479 + 0.978662i \(0.565875\pi\)
\(434\) −9.97165 −0.478654
\(435\) 0 0
\(436\) 2.22196 0.106413
\(437\) −34.0440 −1.62854
\(438\) 0 0
\(439\) 33.9408 1.61990 0.809952 0.586496i \(-0.199493\pi\)
0.809952 + 0.586496i \(0.199493\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.107891 0.00513185
\(443\) 35.1601 1.67051 0.835254 0.549864i \(-0.185320\pi\)
0.835254 + 0.549864i \(0.185320\pi\)
\(444\) 0 0
\(445\) −4.52051 −0.214293
\(446\) 21.6061 1.02308
\(447\) 0 0
\(448\) 8.68056 0.410118
\(449\) 1.92800 0.0909879 0.0454939 0.998965i \(-0.485514\pi\)
0.0454939 + 0.998965i \(0.485514\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.978723 0.0460352
\(453\) 0 0
\(454\) −31.5648 −1.48141
\(455\) −0.0345302 −0.00161880
\(456\) 0 0
\(457\) 7.65166 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(458\) −13.5420 −0.632776
\(459\) 0 0
\(460\) 1.16058 0.0541123
\(461\) 40.7525 1.89803 0.949017 0.315224i \(-0.102080\pi\)
0.949017 + 0.315224i \(0.102080\pi\)
\(462\) 0 0
\(463\) −8.37407 −0.389176 −0.194588 0.980885i \(-0.562337\pi\)
−0.194588 + 0.980885i \(0.562337\pi\)
\(464\) 16.3818 0.760505
\(465\) 0 0
\(466\) −31.3537 −1.45243
\(467\) −9.49614 −0.439429 −0.219714 0.975564i \(-0.570513\pi\)
−0.219714 + 0.975564i \(0.570513\pi\)
\(468\) 0 0
\(469\) 4.85938 0.224385
\(470\) 7.04109 0.324781
\(471\) 0 0
\(472\) 42.5072 1.95655
\(473\) 0 0
\(474\) 0 0
\(475\) −24.1292 −1.10712
\(476\) −0.454910 −0.0208507
\(477\) 0 0
\(478\) −10.4338 −0.477232
\(479\) −36.2983 −1.65851 −0.829256 0.558869i \(-0.811235\pi\)
−0.829256 + 0.558869i \(0.811235\pi\)
\(480\) 0 0
\(481\) −0.457542 −0.0208621
\(482\) −9.14831 −0.416694
\(483\) 0 0
\(484\) 0 0
\(485\) 6.93523 0.314912
\(486\) 0 0
\(487\) 5.36736 0.243218 0.121609 0.992578i \(-0.461195\pi\)
0.121609 + 0.992578i \(0.461195\pi\)
\(488\) −22.3987 −1.01394
\(489\) 0 0
\(490\) −1.16425 −0.0525956
\(491\) 23.0614 1.04075 0.520373 0.853939i \(-0.325793\pi\)
0.520373 + 0.853939i \(0.325793\pi\)
\(492\) 0 0
\(493\) −9.56156 −0.430631
\(494\) 0.300222 0.0135076
\(495\) 0 0
\(496\) −26.2208 −1.17735
\(497\) 11.2503 0.504644
\(498\) 0 0
\(499\) 33.1392 1.48351 0.741756 0.670670i \(-0.233993\pi\)
0.741756 + 0.670670i \(0.233993\pi\)
\(500\) 1.79318 0.0801932
\(501\) 0 0
\(502\) −3.42270 −0.152763
\(503\) −18.1118 −0.807563 −0.403782 0.914855i \(-0.632304\pi\)
−0.403782 + 0.914855i \(0.632304\pi\)
\(504\) 0 0
\(505\) −7.94237 −0.353431
\(506\) 0 0
\(507\) 0 0
\(508\) 2.88604 0.128047
\(509\) 15.5919 0.691100 0.345550 0.938400i \(-0.387692\pi\)
0.345550 + 0.938400i \(0.387692\pi\)
\(510\) 0 0
\(511\) −0.612954 −0.0271155
\(512\) 25.1641 1.11211
\(513\) 0 0
\(514\) −26.1214 −1.15217
\(515\) 3.00166 0.132269
\(516\) 0 0
\(517\) 0 0
\(518\) −15.4269 −0.677819
\(519\) 0 0
\(520\) −0.102313 −0.00448673
\(521\) 15.4692 0.677716 0.338858 0.940838i \(-0.389959\pi\)
0.338858 + 0.940838i \(0.389959\pi\)
\(522\) 0 0
\(523\) 17.3464 0.758504 0.379252 0.925293i \(-0.376181\pi\)
0.379252 + 0.925293i \(0.376181\pi\)
\(524\) −4.02940 −0.176025
\(525\) 0 0
\(526\) 35.3733 1.54235
\(527\) 15.3043 0.666667
\(528\) 0 0
\(529\) 12.7449 0.554126
\(530\) −0.144834 −0.00629120
\(531\) 0 0
\(532\) −1.26585 −0.0548816
\(533\) 0.243149 0.0105320
\(534\) 0 0
\(535\) 2.87427 0.124265
\(536\) 14.3984 0.621914
\(537\) 0 0
\(538\) −22.8325 −0.984380
\(539\) 0 0
\(540\) 0 0
\(541\) −30.2945 −1.30246 −0.651232 0.758879i \(-0.725748\pi\)
−0.651232 + 0.758879i \(0.725748\pi\)
\(542\) 7.06055 0.303277
\(543\) 0 0
\(544\) −2.56096 −0.109800
\(545\) −8.72782 −0.373859
\(546\) 0 0
\(547\) 30.4490 1.30191 0.650954 0.759118i \(-0.274369\pi\)
0.650954 + 0.759118i \(0.274369\pi\)
\(548\) 1.15754 0.0494476
\(549\) 0 0
\(550\) 0 0
\(551\) −26.6064 −1.13347
\(552\) 0 0
\(553\) 0.155227 0.00660092
\(554\) 3.26665 0.138787
\(555\) 0 0
\(556\) −4.03445 −0.171099
\(557\) 7.17456 0.303996 0.151998 0.988381i \(-0.451429\pi\)
0.151998 + 0.988381i \(0.451429\pi\)
\(558\) 0 0
\(559\) −0.0710563 −0.00300536
\(560\) −3.06145 −0.129370
\(561\) 0 0
\(562\) −0.402318 −0.0169708
\(563\) 9.01364 0.379880 0.189940 0.981796i \(-0.439171\pi\)
0.189940 + 0.981796i \(0.439171\pi\)
\(564\) 0 0
\(565\) −3.84441 −0.161735
\(566\) 32.0118 1.34556
\(567\) 0 0
\(568\) 33.3347 1.39869
\(569\) 7.45999 0.312739 0.156370 0.987699i \(-0.450021\pi\)
0.156370 + 0.987699i \(0.450021\pi\)
\(570\) 0 0
\(571\) 37.5921 1.57318 0.786590 0.617475i \(-0.211844\pi\)
0.786590 + 0.617475i \(0.211844\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 8.19824 0.342188
\(575\) 25.3348 1.05653
\(576\) 0 0
\(577\) −12.1230 −0.504688 −0.252344 0.967638i \(-0.581201\pi\)
−0.252344 + 0.967638i \(0.581201\pi\)
\(578\) 17.0830 0.710558
\(579\) 0 0
\(580\) 0.907029 0.0376623
\(581\) 8.91599 0.369897
\(582\) 0 0
\(583\) 0 0
\(584\) −1.81619 −0.0751543
\(585\) 0 0
\(586\) 2.61865 0.108175
\(587\) 1.28073 0.0528615 0.0264307 0.999651i \(-0.491586\pi\)
0.0264307 + 0.999651i \(0.491586\pi\)
\(588\) 0 0
\(589\) 42.5865 1.75474
\(590\) −16.7024 −0.687626
\(591\) 0 0
\(592\) −40.5656 −1.66724
\(593\) −24.7324 −1.01564 −0.507819 0.861464i \(-0.669548\pi\)
−0.507819 + 0.861464i \(0.669548\pi\)
\(594\) 0 0
\(595\) 1.78688 0.0732548
\(596\) −2.45636 −0.100617
\(597\) 0 0
\(598\) −0.315222 −0.0128904
\(599\) 27.9003 1.13998 0.569988 0.821653i \(-0.306948\pi\)
0.569988 + 0.821653i \(0.306948\pi\)
\(600\) 0 0
\(601\) 34.4256 1.40425 0.702124 0.712055i \(-0.252235\pi\)
0.702124 + 0.712055i \(0.252235\pi\)
\(602\) −2.39580 −0.0976456
\(603\) 0 0
\(604\) 3.54163 0.144107
\(605\) 0 0
\(606\) 0 0
\(607\) 26.4243 1.07253 0.536264 0.844050i \(-0.319835\pi\)
0.536264 + 0.844050i \(0.319835\pi\)
\(608\) −7.12624 −0.289007
\(609\) 0 0
\(610\) 8.80111 0.356346
\(611\) 0.239152 0.00967503
\(612\) 0 0
\(613\) 39.6007 1.59946 0.799729 0.600361i \(-0.204976\pi\)
0.799729 + 0.600361i \(0.204976\pi\)
\(614\) 26.6900 1.07712
\(615\) 0 0
\(616\) 0 0
\(617\) −17.0640 −0.686971 −0.343486 0.939158i \(-0.611608\pi\)
−0.343486 + 0.939158i \(0.611608\pi\)
\(618\) 0 0
\(619\) 29.2807 1.17689 0.588445 0.808538i \(-0.299741\pi\)
0.588445 + 0.808538i \(0.299741\pi\)
\(620\) −1.45180 −0.0583056
\(621\) 0 0
\(622\) 23.6049 0.946471
\(623\) −5.17689 −0.207408
\(624\) 0 0
\(625\) 14.1440 0.565758
\(626\) −37.7745 −1.50977
\(627\) 0 0
\(628\) −3.55766 −0.141966
\(629\) 23.6770 0.944062
\(630\) 0 0
\(631\) −40.2944 −1.60410 −0.802048 0.597260i \(-0.796256\pi\)
−0.802048 + 0.597260i \(0.796256\pi\)
\(632\) 0.459938 0.0182954
\(633\) 0 0
\(634\) −29.2732 −1.16259
\(635\) −11.3363 −0.449867
\(636\) 0 0
\(637\) −0.0395440 −0.00156679
\(638\) 0 0
\(639\) 0 0
\(640\) −7.92074 −0.313095
\(641\) 12.5572 0.495980 0.247990 0.968763i \(-0.420230\pi\)
0.247990 + 0.968763i \(0.420230\pi\)
\(642\) 0 0
\(643\) −4.13705 −0.163149 −0.0815747 0.996667i \(-0.525995\pi\)
−0.0815747 + 0.996667i \(0.525995\pi\)
\(644\) 1.32910 0.0523737
\(645\) 0 0
\(646\) −15.5359 −0.611254
\(647\) 37.6088 1.47856 0.739278 0.673400i \(-0.235167\pi\)
0.739278 + 0.673400i \(0.235167\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −0.223419 −0.00876320
\(651\) 0 0
\(652\) −4.89147 −0.191565
\(653\) −6.02137 −0.235634 −0.117817 0.993035i \(-0.537590\pi\)
−0.117817 + 0.993035i \(0.537590\pi\)
\(654\) 0 0
\(655\) 15.8274 0.618428
\(656\) 21.5576 0.841682
\(657\) 0 0
\(658\) 8.06345 0.314346
\(659\) −38.6192 −1.50439 −0.752195 0.658940i \(-0.771005\pi\)
−0.752195 + 0.658940i \(0.771005\pi\)
\(660\) 0 0
\(661\) 43.0833 1.67575 0.837874 0.545864i \(-0.183798\pi\)
0.837874 + 0.545864i \(0.183798\pi\)
\(662\) −30.8613 −1.19946
\(663\) 0 0
\(664\) 26.4181 1.02522
\(665\) 4.97224 0.192815
\(666\) 0 0
\(667\) 27.9357 1.08168
\(668\) 1.04950 0.0406066
\(669\) 0 0
\(670\) −5.65755 −0.218570
\(671\) 0 0
\(672\) 0 0
\(673\) 21.0171 0.810149 0.405075 0.914284i \(-0.367246\pi\)
0.405075 + 0.914284i \(0.367246\pi\)
\(674\) 46.6803 1.79806
\(675\) 0 0
\(676\) 2.88962 0.111139
\(677\) −23.8886 −0.918115 −0.459057 0.888407i \(-0.651813\pi\)
−0.459057 + 0.888407i \(0.651813\pi\)
\(678\) 0 0
\(679\) 7.94222 0.304794
\(680\) 5.29453 0.203036
\(681\) 0 0
\(682\) 0 0
\(683\) 13.5672 0.519134 0.259567 0.965725i \(-0.416420\pi\)
0.259567 + 0.965725i \(0.416420\pi\)
\(684\) 0 0
\(685\) −4.54679 −0.173724
\(686\) −1.33330 −0.0509057
\(687\) 0 0
\(688\) −6.29985 −0.240180
\(689\) −0.00491932 −0.000187411 0
\(690\) 0 0
\(691\) −4.91171 −0.186850 −0.0934251 0.995626i \(-0.529782\pi\)
−0.0934251 + 0.995626i \(0.529782\pi\)
\(692\) 2.10650 0.0800771
\(693\) 0 0
\(694\) 5.01266 0.190278
\(695\) 15.8472 0.601120
\(696\) 0 0
\(697\) −12.5825 −0.476597
\(698\) −16.2316 −0.614375
\(699\) 0 0
\(700\) 0.942018 0.0356049
\(701\) 36.9242 1.39461 0.697304 0.716775i \(-0.254383\pi\)
0.697304 + 0.716775i \(0.254383\pi\)
\(702\) 0 0
\(703\) 65.8845 2.48488
\(704\) 0 0
\(705\) 0 0
\(706\) −7.72061 −0.290569
\(707\) −9.09560 −0.342075
\(708\) 0 0
\(709\) 0.489376 0.0183789 0.00918945 0.999958i \(-0.497075\pi\)
0.00918945 + 0.999958i \(0.497075\pi\)
\(710\) −13.0982 −0.491566
\(711\) 0 0
\(712\) −15.3391 −0.574858
\(713\) −44.7142 −1.67456
\(714\) 0 0
\(715\) 0 0
\(716\) 3.93890 0.147204
\(717\) 0 0
\(718\) −7.68096 −0.286651
\(719\) −10.1392 −0.378127 −0.189064 0.981965i \(-0.560545\pi\)
−0.189064 + 0.981965i \(0.560545\pi\)
\(720\) 0 0
\(721\) 3.43750 0.128019
\(722\) −17.8982 −0.666103
\(723\) 0 0
\(724\) −3.61784 −0.134456
\(725\) 19.7999 0.735350
\(726\) 0 0
\(727\) −10.5834 −0.392516 −0.196258 0.980552i \(-0.562879\pi\)
−0.196258 + 0.980552i \(0.562879\pi\)
\(728\) −0.117169 −0.00434257
\(729\) 0 0
\(730\) 0.713634 0.0264128
\(731\) 3.67704 0.136000
\(732\) 0 0
\(733\) −12.5752 −0.464475 −0.232238 0.972659i \(-0.574605\pi\)
−0.232238 + 0.972659i \(0.574605\pi\)
\(734\) −19.0103 −0.701682
\(735\) 0 0
\(736\) 7.48229 0.275801
\(737\) 0 0
\(738\) 0 0
\(739\) 1.39740 0.0514043 0.0257022 0.999670i \(-0.491818\pi\)
0.0257022 + 0.999670i \(0.491818\pi\)
\(740\) −2.24604 −0.0825662
\(741\) 0 0
\(742\) −0.165864 −0.00608907
\(743\) 24.1170 0.884767 0.442383 0.896826i \(-0.354133\pi\)
0.442383 + 0.896826i \(0.354133\pi\)
\(744\) 0 0
\(745\) 9.64856 0.353496
\(746\) 42.9620 1.57295
\(747\) 0 0
\(748\) 0 0
\(749\) 3.29161 0.120273
\(750\) 0 0
\(751\) −19.2248 −0.701523 −0.350762 0.936465i \(-0.614077\pi\)
−0.350762 + 0.936465i \(0.614077\pi\)
\(752\) 21.2032 0.773200
\(753\) 0 0
\(754\) −0.246355 −0.00897174
\(755\) −13.9115 −0.506290
\(756\) 0 0
\(757\) −42.4814 −1.54401 −0.772006 0.635615i \(-0.780747\pi\)
−0.772006 + 0.635615i \(0.780747\pi\)
\(758\) 38.1023 1.38394
\(759\) 0 0
\(760\) 14.7328 0.534414
\(761\) 14.7018 0.532939 0.266470 0.963843i \(-0.414143\pi\)
0.266470 + 0.963843i \(0.414143\pi\)
\(762\) 0 0
\(763\) −9.99510 −0.361847
\(764\) 1.43299 0.0518437
\(765\) 0 0
\(766\) −26.8811 −0.971254
\(767\) −0.567298 −0.0204839
\(768\) 0 0
\(769\) 45.4931 1.64052 0.820262 0.571988i \(-0.193828\pi\)
0.820262 + 0.571988i \(0.193828\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.402537 −0.0144876
\(773\) −6.05381 −0.217741 −0.108870 0.994056i \(-0.534723\pi\)
−0.108870 + 0.994056i \(0.534723\pi\)
\(774\) 0 0
\(775\) −31.6919 −1.13841
\(776\) 23.5328 0.844779
\(777\) 0 0
\(778\) −22.0805 −0.791624
\(779\) −35.0127 −1.25446
\(780\) 0 0
\(781\) 0 0
\(782\) 16.3122 0.583322
\(783\) 0 0
\(784\) −3.50597 −0.125213
\(785\) 13.9744 0.498769
\(786\) 0 0
\(787\) −54.7630 −1.95209 −0.976046 0.217566i \(-0.930188\pi\)
−0.976046 + 0.217566i \(0.930188\pi\)
\(788\) 1.52451 0.0543083
\(789\) 0 0
\(790\) −0.180723 −0.00642985
\(791\) −4.40261 −0.156539
\(792\) 0 0
\(793\) 0.298931 0.0106153
\(794\) −41.3218 −1.46645
\(795\) 0 0
\(796\) 1.12798 0.0399801
\(797\) 43.2922 1.53349 0.766744 0.641953i \(-0.221876\pi\)
0.766744 + 0.641953i \(0.221876\pi\)
\(798\) 0 0
\(799\) −12.3757 −0.437819
\(800\) 5.30319 0.187496
\(801\) 0 0
\(802\) 4.64342 0.163965
\(803\) 0 0
\(804\) 0 0
\(805\) −5.22067 −0.184004
\(806\) 0.394319 0.0138893
\(807\) 0 0
\(808\) −26.9503 −0.948108
\(809\) −15.5173 −0.545559 −0.272779 0.962077i \(-0.587943\pi\)
−0.272779 + 0.962077i \(0.587943\pi\)
\(810\) 0 0
\(811\) −41.4421 −1.45523 −0.727615 0.685986i \(-0.759371\pi\)
−0.727615 + 0.685986i \(0.759371\pi\)
\(812\) 1.03873 0.0364522
\(813\) 0 0
\(814\) 0 0
\(815\) 19.2136 0.673024
\(816\) 0 0
\(817\) 10.2319 0.357968
\(818\) −35.4502 −1.23949
\(819\) 0 0
\(820\) 1.19360 0.0416824
\(821\) −40.0922 −1.39923 −0.699613 0.714522i \(-0.746644\pi\)
−0.699613 + 0.714522i \(0.746644\pi\)
\(822\) 0 0
\(823\) 4.23033 0.147460 0.0737301 0.997278i \(-0.476510\pi\)
0.0737301 + 0.997278i \(0.476510\pi\)
\(824\) 10.1853 0.354823
\(825\) 0 0
\(826\) −19.1275 −0.665532
\(827\) 47.6889 1.65830 0.829152 0.559023i \(-0.188824\pi\)
0.829152 + 0.559023i \(0.188824\pi\)
\(828\) 0 0
\(829\) 4.68523 0.162725 0.0813624 0.996685i \(-0.474073\pi\)
0.0813624 + 0.996685i \(0.474073\pi\)
\(830\) −10.3805 −0.360311
\(831\) 0 0
\(832\) −0.343264 −0.0119005
\(833\) 2.04633 0.0709012
\(834\) 0 0
\(835\) −4.12244 −0.142663
\(836\) 0 0
\(837\) 0 0
\(838\) 38.8645 1.34255
\(839\) 6.93707 0.239494 0.119747 0.992804i \(-0.461792\pi\)
0.119747 + 0.992804i \(0.461792\pi\)
\(840\) 0 0
\(841\) −7.16738 −0.247151
\(842\) 26.6539 0.918555
\(843\) 0 0
\(844\) 1.80220 0.0620343
\(845\) −11.3504 −0.390465
\(846\) 0 0
\(847\) 0 0
\(848\) −0.436146 −0.0149773
\(849\) 0 0
\(850\) 11.5615 0.396557
\(851\) −69.1763 −2.37133
\(852\) 0 0
\(853\) 6.23883 0.213613 0.106807 0.994280i \(-0.465937\pi\)
0.106807 + 0.994280i \(0.465937\pi\)
\(854\) 10.0790 0.344897
\(855\) 0 0
\(856\) 9.75304 0.333352
\(857\) 26.5684 0.907559 0.453779 0.891114i \(-0.350075\pi\)
0.453779 + 0.891114i \(0.350075\pi\)
\(858\) 0 0
\(859\) 44.6475 1.52335 0.761677 0.647957i \(-0.224377\pi\)
0.761677 + 0.647957i \(0.224377\pi\)
\(860\) −0.348811 −0.0118944
\(861\) 0 0
\(862\) −22.5708 −0.768765
\(863\) 21.2309 0.722707 0.361353 0.932429i \(-0.382315\pi\)
0.361353 + 0.932429i \(0.382315\pi\)
\(864\) 0 0
\(865\) −8.27430 −0.281335
\(866\) 11.4017 0.387446
\(867\) 0 0
\(868\) −1.66260 −0.0564323
\(869\) 0 0
\(870\) 0 0
\(871\) −0.192159 −0.00651107
\(872\) −29.6155 −1.00291
\(873\) 0 0
\(874\) 45.3909 1.53537
\(875\) −8.06628 −0.272690
\(876\) 0 0
\(877\) −9.63512 −0.325355 −0.162677 0.986679i \(-0.552013\pi\)
−0.162677 + 0.986679i \(0.552013\pi\)
\(878\) −45.2533 −1.52722
\(879\) 0 0
\(880\) 0 0
\(881\) 38.9952 1.31378 0.656891 0.753985i \(-0.271871\pi\)
0.656891 + 0.753985i \(0.271871\pi\)
\(882\) 0 0
\(883\) 14.8304 0.499081 0.249541 0.968364i \(-0.419720\pi\)
0.249541 + 0.968364i \(0.419720\pi\)
\(884\) 0.0179889 0.000605034 0
\(885\) 0 0
\(886\) −46.8791 −1.57493
\(887\) −17.6091 −0.591254 −0.295627 0.955303i \(-0.595529\pi\)
−0.295627 + 0.955303i \(0.595529\pi\)
\(888\) 0 0
\(889\) −12.9823 −0.435413
\(890\) 6.02721 0.202032
\(891\) 0 0
\(892\) 3.60245 0.120619
\(893\) −34.4370 −1.15239
\(894\) 0 0
\(895\) −15.4720 −0.517170
\(896\) −9.07082 −0.303035
\(897\) 0 0
\(898\) −2.57060 −0.0857822
\(899\) −34.9455 −1.16550
\(900\) 0 0
\(901\) 0.254566 0.00848081
\(902\) 0 0
\(903\) 0 0
\(904\) −13.0450 −0.433869
\(905\) 14.2108 0.472383
\(906\) 0 0
\(907\) 46.0126 1.52782 0.763911 0.645322i \(-0.223277\pi\)
0.763911 + 0.645322i \(0.223277\pi\)
\(908\) −5.26289 −0.174655
\(909\) 0 0
\(910\) 0.0460393 0.00152619
\(911\) −19.5000 −0.646064 −0.323032 0.946388i \(-0.604702\pi\)
−0.323032 + 0.946388i \(0.604702\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −10.2020 −0.337451
\(915\) 0 0
\(916\) −2.25789 −0.0746029
\(917\) 18.1255 0.598558
\(918\) 0 0
\(919\) −11.7377 −0.387191 −0.193596 0.981081i \(-0.562015\pi\)
−0.193596 + 0.981081i \(0.562015\pi\)
\(920\) −15.4689 −0.509993
\(921\) 0 0
\(922\) −54.3354 −1.78944
\(923\) −0.444882 −0.0146435
\(924\) 0 0
\(925\) −49.0298 −1.61209
\(926\) 11.1652 0.366910
\(927\) 0 0
\(928\) 5.84764 0.191958
\(929\) −35.6903 −1.17096 −0.585480 0.810687i \(-0.699094\pi\)
−0.585480 + 0.810687i \(0.699094\pi\)
\(930\) 0 0
\(931\) 5.69421 0.186620
\(932\) −5.22769 −0.171239
\(933\) 0 0
\(934\) 12.6612 0.414288
\(935\) 0 0
\(936\) 0 0
\(937\) −35.3541 −1.15497 −0.577485 0.816402i \(-0.695966\pi\)
−0.577485 + 0.816402i \(0.695966\pi\)
\(938\) −6.47902 −0.211548
\(939\) 0 0
\(940\) 1.17398 0.0382910
\(941\) −30.5431 −0.995678 −0.497839 0.867270i \(-0.665873\pi\)
−0.497839 + 0.867270i \(0.665873\pi\)
\(942\) 0 0
\(943\) 36.7620 1.19713
\(944\) −50.2966 −1.63702
\(945\) 0 0
\(946\) 0 0
\(947\) −38.9527 −1.26579 −0.632897 0.774236i \(-0.718134\pi\)
−0.632897 + 0.774236i \(0.718134\pi\)
\(948\) 0 0
\(949\) 0.0242387 0.000786821 0
\(950\) 32.1715 1.04378
\(951\) 0 0
\(952\) 6.06329 0.196512
\(953\) 35.2846 1.14298 0.571490 0.820609i \(-0.306366\pi\)
0.571490 + 0.820609i \(0.306366\pi\)
\(954\) 0 0
\(955\) −5.62875 −0.182142
\(956\) −1.73966 −0.0562645
\(957\) 0 0
\(958\) 48.3966 1.56362
\(959\) −5.20699 −0.168142
\(960\) 0 0
\(961\) 24.9341 0.804326
\(962\) 0.610042 0.0196685
\(963\) 0 0
\(964\) −1.52532 −0.0491273
\(965\) 1.58116 0.0508993
\(966\) 0 0
\(967\) −31.4791 −1.01230 −0.506150 0.862445i \(-0.668932\pi\)
−0.506150 + 0.862445i \(0.668932\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −9.24675 −0.296895
\(971\) 34.4771 1.10642 0.553211 0.833041i \(-0.313402\pi\)
0.553211 + 0.833041i \(0.313402\pi\)
\(972\) 0 0
\(973\) 18.1482 0.581806
\(974\) −7.15631 −0.229303
\(975\) 0 0
\(976\) 26.5032 0.848346
\(977\) −5.51932 −0.176579 −0.0882894 0.996095i \(-0.528140\pi\)
−0.0882894 + 0.996095i \(0.528140\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.194119 −0.00620090
\(981\) 0 0
\(982\) −30.7478 −0.981202
\(983\) 33.0076 1.05278 0.526390 0.850243i \(-0.323545\pi\)
0.526390 + 0.850243i \(0.323545\pi\)
\(984\) 0 0
\(985\) −5.98823 −0.190801
\(986\) 12.7485 0.405993
\(987\) 0 0
\(988\) 0.0500568 0.00159252
\(989\) −10.7431 −0.341610
\(990\) 0 0
\(991\) −40.9399 −1.30050 −0.650249 0.759721i \(-0.725335\pi\)
−0.650249 + 0.759721i \(0.725335\pi\)
\(992\) −9.35978 −0.297173
\(993\) 0 0
\(994\) −15.0000 −0.475772
\(995\) −4.43067 −0.140462
\(996\) 0 0
\(997\) 37.8795 1.19966 0.599828 0.800129i \(-0.295236\pi\)
0.599828 + 0.800129i \(0.295236\pi\)
\(998\) −44.1845 −1.39864
\(999\) 0 0
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 7623.2.a.cy.1.4 10
3.2 odd 2 2541.2.a.br.1.7 10
11.2 odd 10 693.2.m.j.631.2 20
11.6 odd 10 693.2.m.j.190.2 20
11.10 odd 2 7623.2.a.cx.1.7 10
33.2 even 10 231.2.j.g.169.4 20
33.17 even 10 231.2.j.g.190.4 yes 20
33.32 even 2 2541.2.a.bq.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.169.4 20 33.2 even 10
231.2.j.g.190.4 yes 20 33.17 even 10
693.2.m.j.190.2 20 11.6 odd 10
693.2.m.j.631.2 20 11.2 odd 10
2541.2.a.bq.1.4 10 33.32 even 2
2541.2.a.br.1.7 10 3.2 odd 2
7623.2.a.cx.1.7 10 11.10 odd 2
7623.2.a.cy.1.4 10 1.1 even 1 trivial