Properties

Label 7623.2.a.cy.1.9
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 1.9
Root \(2.63994\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.63994 q^{2} +4.96928 q^{4} -3.08369 q^{5} +1.00000 q^{7} +7.83871 q^{8} +O(q^{10})\) \(q+2.63994 q^{2} +4.96928 q^{4} -3.08369 q^{5} +1.00000 q^{7} +7.83871 q^{8} -8.14075 q^{10} +5.64097 q^{13} +2.63994 q^{14} +10.7552 q^{16} -5.60085 q^{17} -0.122652 q^{19} -15.3237 q^{20} -1.67325 q^{23} +4.50913 q^{25} +14.8918 q^{26} +4.96928 q^{28} +8.85038 q^{29} +1.59773 q^{31} +12.7156 q^{32} -14.7859 q^{34} -3.08369 q^{35} +4.17268 q^{37} -0.323795 q^{38} -24.1721 q^{40} +3.48859 q^{41} +5.10698 q^{43} -4.41727 q^{46} +1.59400 q^{47} +1.00000 q^{49} +11.9038 q^{50} +28.0316 q^{52} +11.8564 q^{53} +7.83871 q^{56} +23.3645 q^{58} -6.61445 q^{59} +8.48918 q^{61} +4.21790 q^{62} +12.0580 q^{64} -17.3950 q^{65} -8.04949 q^{67} -27.8322 q^{68} -8.14075 q^{70} -6.24379 q^{71} -3.51005 q^{73} +11.0156 q^{74} -0.609494 q^{76} +9.39769 q^{79} -33.1656 q^{80} +9.20967 q^{82} -9.43386 q^{83} +17.2713 q^{85} +13.4821 q^{86} +8.45556 q^{89} +5.64097 q^{91} -8.31482 q^{92} +4.20807 q^{94} +0.378222 q^{95} -5.68478 q^{97} +2.63994 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} + O(q^{10}) \) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} - 6q^{10} + 6q^{13} + 38q^{16} - 8q^{17} - 7q^{20} + 31q^{25} - q^{26} + 18q^{28} + 14q^{29} + 26q^{31} + 41q^{32} + 21q^{34} - 5q^{35} + 24q^{37} - 8q^{38} - 5q^{40} - 19q^{41} - 6q^{43} - q^{46} - 15q^{47} + 10q^{49} + q^{50} - 25q^{52} + q^{53} + 3q^{56} + 11q^{58} - 23q^{59} - 11q^{62} + 53q^{64} + 29q^{65} + 38q^{67} - 87q^{68} - 6q^{70} - 26q^{71} - q^{73} + 39q^{74} - 2q^{76} + 5q^{79} - 6q^{80} + 5q^{82} - 6q^{83} - q^{85} + 41q^{86} + 9q^{89} + 6q^{91} + 48q^{92} + 42q^{95} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.63994 1.86672 0.933359 0.358943i \(-0.116863\pi\)
0.933359 + 0.358943i \(0.116863\pi\)
\(3\) 0 0
\(4\) 4.96928 2.48464
\(5\) −3.08369 −1.37907 −0.689534 0.724254i \(-0.742184\pi\)
−0.689534 + 0.724254i \(0.742184\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 7.83871 2.77140
\(9\) 0 0
\(10\) −8.14075 −2.57433
\(11\) 0 0
\(12\) 0 0
\(13\) 5.64097 1.56452 0.782262 0.622949i \(-0.214066\pi\)
0.782262 + 0.622949i \(0.214066\pi\)
\(14\) 2.63994 0.705553
\(15\) 0 0
\(16\) 10.7552 2.68879
\(17\) −5.60085 −1.35841 −0.679203 0.733951i \(-0.737674\pi\)
−0.679203 + 0.733951i \(0.737674\pi\)
\(18\) 0 0
\(19\) −0.122652 −0.0281384 −0.0140692 0.999901i \(-0.504479\pi\)
−0.0140692 + 0.999901i \(0.504479\pi\)
\(20\) −15.3237 −3.42648
\(21\) 0 0
\(22\) 0 0
\(23\) −1.67325 −0.348896 −0.174448 0.984666i \(-0.555814\pi\)
−0.174448 + 0.984666i \(0.555814\pi\)
\(24\) 0 0
\(25\) 4.50913 0.901826
\(26\) 14.8918 2.92053
\(27\) 0 0
\(28\) 4.96928 0.939105
\(29\) 8.85038 1.64347 0.821737 0.569867i \(-0.193005\pi\)
0.821737 + 0.569867i \(0.193005\pi\)
\(30\) 0 0
\(31\) 1.59773 0.286960 0.143480 0.989653i \(-0.454171\pi\)
0.143480 + 0.989653i \(0.454171\pi\)
\(32\) 12.7156 2.24782
\(33\) 0 0
\(34\) −14.7859 −2.53576
\(35\) −3.08369 −0.521238
\(36\) 0 0
\(37\) 4.17268 0.685984 0.342992 0.939338i \(-0.388560\pi\)
0.342992 + 0.939338i \(0.388560\pi\)
\(38\) −0.323795 −0.0525265
\(39\) 0 0
\(40\) −24.1721 −3.82195
\(41\) 3.48859 0.544827 0.272413 0.962180i \(-0.412178\pi\)
0.272413 + 0.962180i \(0.412178\pi\)
\(42\) 0 0
\(43\) 5.10698 0.778807 0.389403 0.921067i \(-0.372681\pi\)
0.389403 + 0.921067i \(0.372681\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −4.41727 −0.651290
\(47\) 1.59400 0.232509 0.116255 0.993219i \(-0.462911\pi\)
0.116255 + 0.993219i \(0.462911\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 11.9038 1.68346
\(51\) 0 0
\(52\) 28.0316 3.88728
\(53\) 11.8564 1.62861 0.814303 0.580440i \(-0.197119\pi\)
0.814303 + 0.580440i \(0.197119\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 7.83871 1.04749
\(57\) 0 0
\(58\) 23.3645 3.06790
\(59\) −6.61445 −0.861128 −0.430564 0.902560i \(-0.641685\pi\)
−0.430564 + 0.902560i \(0.641685\pi\)
\(60\) 0 0
\(61\) 8.48918 1.08693 0.543464 0.839432i \(-0.317112\pi\)
0.543464 + 0.839432i \(0.317112\pi\)
\(62\) 4.21790 0.535674
\(63\) 0 0
\(64\) 12.0580 1.50725
\(65\) −17.3950 −2.15758
\(66\) 0 0
\(67\) −8.04949 −0.983402 −0.491701 0.870764i \(-0.663625\pi\)
−0.491701 + 0.870764i \(0.663625\pi\)
\(68\) −27.8322 −3.37515
\(69\) 0 0
\(70\) −8.14075 −0.973006
\(71\) −6.24379 −0.741001 −0.370501 0.928832i \(-0.620814\pi\)
−0.370501 + 0.928832i \(0.620814\pi\)
\(72\) 0 0
\(73\) −3.51005 −0.410820 −0.205410 0.978676i \(-0.565853\pi\)
−0.205410 + 0.978676i \(0.565853\pi\)
\(74\) 11.0156 1.28054
\(75\) 0 0
\(76\) −0.609494 −0.0699138
\(77\) 0 0
\(78\) 0 0
\(79\) 9.39769 1.05732 0.528661 0.848833i \(-0.322694\pi\)
0.528661 + 0.848833i \(0.322694\pi\)
\(80\) −33.1656 −3.70803
\(81\) 0 0
\(82\) 9.20967 1.01704
\(83\) −9.43386 −1.03550 −0.517750 0.855532i \(-0.673230\pi\)
−0.517750 + 0.855532i \(0.673230\pi\)
\(84\) 0 0
\(85\) 17.2713 1.87333
\(86\) 13.4821 1.45381
\(87\) 0 0
\(88\) 0 0
\(89\) 8.45556 0.896288 0.448144 0.893961i \(-0.352085\pi\)
0.448144 + 0.893961i \(0.352085\pi\)
\(90\) 0 0
\(91\) 5.64097 0.591335
\(92\) −8.31482 −0.866880
\(93\) 0 0
\(94\) 4.20807 0.434030
\(95\) 0.378222 0.0388047
\(96\) 0 0
\(97\) −5.68478 −0.577202 −0.288601 0.957449i \(-0.593190\pi\)
−0.288601 + 0.957449i \(0.593190\pi\)
\(98\) 2.63994 0.266674
\(99\) 0 0
\(100\) 22.4071 2.24071
\(101\) 16.8776 1.67938 0.839690 0.543066i \(-0.182737\pi\)
0.839690 + 0.543066i \(0.182737\pi\)
\(102\) 0 0
\(103\) −13.2172 −1.30233 −0.651163 0.758938i \(-0.725719\pi\)
−0.651163 + 0.758938i \(0.725719\pi\)
\(104\) 44.2180 4.33593
\(105\) 0 0
\(106\) 31.3003 3.04015
\(107\) 11.0745 1.07061 0.535307 0.844658i \(-0.320196\pi\)
0.535307 + 0.844658i \(0.320196\pi\)
\(108\) 0 0
\(109\) 4.87369 0.466815 0.233407 0.972379i \(-0.425012\pi\)
0.233407 + 0.972379i \(0.425012\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 10.7552 1.01627
\(113\) 5.28263 0.496948 0.248474 0.968639i \(-0.420071\pi\)
0.248474 + 0.968639i \(0.420071\pi\)
\(114\) 0 0
\(115\) 5.15977 0.481151
\(116\) 43.9800 4.08344
\(117\) 0 0
\(118\) −17.4617 −1.60748
\(119\) −5.60085 −0.513429
\(120\) 0 0
\(121\) 0 0
\(122\) 22.4109 2.02899
\(123\) 0 0
\(124\) 7.93955 0.712992
\(125\) 1.51368 0.135388
\(126\) 0 0
\(127\) 11.3400 1.00627 0.503133 0.864209i \(-0.332181\pi\)
0.503133 + 0.864209i \(0.332181\pi\)
\(128\) 6.40120 0.565792
\(129\) 0 0
\(130\) −45.9217 −4.02760
\(131\) −0.970284 −0.0847741 −0.0423870 0.999101i \(-0.513496\pi\)
−0.0423870 + 0.999101i \(0.513496\pi\)
\(132\) 0 0
\(133\) −0.122652 −0.0106353
\(134\) −21.2502 −1.83574
\(135\) 0 0
\(136\) −43.9035 −3.76469
\(137\) 0.125101 0.0106881 0.00534403 0.999986i \(-0.498299\pi\)
0.00534403 + 0.999986i \(0.498299\pi\)
\(138\) 0 0
\(139\) 1.67835 0.142355 0.0711777 0.997464i \(-0.477324\pi\)
0.0711777 + 0.997464i \(0.477324\pi\)
\(140\) −15.3237 −1.29509
\(141\) 0 0
\(142\) −16.4832 −1.38324
\(143\) 0 0
\(144\) 0 0
\(145\) −27.2918 −2.26646
\(146\) −9.26631 −0.766885
\(147\) 0 0
\(148\) 20.7352 1.70442
\(149\) 14.1791 1.16160 0.580800 0.814046i \(-0.302740\pi\)
0.580800 + 0.814046i \(0.302740\pi\)
\(150\) 0 0
\(151\) −15.8823 −1.29249 −0.646243 0.763132i \(-0.723661\pi\)
−0.646243 + 0.763132i \(0.723661\pi\)
\(152\) −0.961437 −0.0779829
\(153\) 0 0
\(154\) 0 0
\(155\) −4.92689 −0.395737
\(156\) 0 0
\(157\) −9.19854 −0.734124 −0.367062 0.930197i \(-0.619636\pi\)
−0.367062 + 0.930197i \(0.619636\pi\)
\(158\) 24.8093 1.97372
\(159\) 0 0
\(160\) −39.2108 −3.09989
\(161\) −1.67325 −0.131870
\(162\) 0 0
\(163\) 9.76942 0.765200 0.382600 0.923914i \(-0.375029\pi\)
0.382600 + 0.923914i \(0.375029\pi\)
\(164\) 17.3358 1.35370
\(165\) 0 0
\(166\) −24.9048 −1.93299
\(167\) 6.10236 0.472215 0.236107 0.971727i \(-0.424128\pi\)
0.236107 + 0.971727i \(0.424128\pi\)
\(168\) 0 0
\(169\) 18.8206 1.44774
\(170\) 45.5951 3.49699
\(171\) 0 0
\(172\) 25.3780 1.93505
\(173\) 6.73818 0.512294 0.256147 0.966638i \(-0.417547\pi\)
0.256147 + 0.966638i \(0.417547\pi\)
\(174\) 0 0
\(175\) 4.50913 0.340858
\(176\) 0 0
\(177\) 0 0
\(178\) 22.3222 1.67312
\(179\) −12.9936 −0.971184 −0.485592 0.874186i \(-0.661396\pi\)
−0.485592 + 0.874186i \(0.661396\pi\)
\(180\) 0 0
\(181\) −4.09819 −0.304616 −0.152308 0.988333i \(-0.548671\pi\)
−0.152308 + 0.988333i \(0.548671\pi\)
\(182\) 14.8918 1.10386
\(183\) 0 0
\(184\) −13.1161 −0.966931
\(185\) −12.8672 −0.946018
\(186\) 0 0
\(187\) 0 0
\(188\) 7.92105 0.577702
\(189\) 0 0
\(190\) 0.998483 0.0724375
\(191\) −21.5036 −1.55595 −0.777973 0.628297i \(-0.783752\pi\)
−0.777973 + 0.628297i \(0.783752\pi\)
\(192\) 0 0
\(193\) −17.7964 −1.28101 −0.640506 0.767953i \(-0.721275\pi\)
−0.640506 + 0.767953i \(0.721275\pi\)
\(194\) −15.0075 −1.07747
\(195\) 0 0
\(196\) 4.96928 0.354948
\(197\) 18.1083 1.29016 0.645080 0.764115i \(-0.276824\pi\)
0.645080 + 0.764115i \(0.276824\pi\)
\(198\) 0 0
\(199\) 2.67139 0.189370 0.0946848 0.995507i \(-0.469816\pi\)
0.0946848 + 0.995507i \(0.469816\pi\)
\(200\) 35.3458 2.49933
\(201\) 0 0
\(202\) 44.5557 3.13493
\(203\) 8.85038 0.621175
\(204\) 0 0
\(205\) −10.7577 −0.751352
\(206\) −34.8925 −2.43108
\(207\) 0 0
\(208\) 60.6696 4.20668
\(209\) 0 0
\(210\) 0 0
\(211\) 8.15447 0.561377 0.280688 0.959799i \(-0.409437\pi\)
0.280688 + 0.959799i \(0.409437\pi\)
\(212\) 58.9179 4.04650
\(213\) 0 0
\(214\) 29.2360 1.99853
\(215\) −15.7483 −1.07403
\(216\) 0 0
\(217\) 1.59773 0.108461
\(218\) 12.8662 0.871412
\(219\) 0 0
\(220\) 0 0
\(221\) −31.5942 −2.12526
\(222\) 0 0
\(223\) 8.48763 0.568374 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(224\) 12.7156 0.849595
\(225\) 0 0
\(226\) 13.9458 0.927662
\(227\) −22.1524 −1.47031 −0.735154 0.677900i \(-0.762890\pi\)
−0.735154 + 0.677900i \(0.762890\pi\)
\(228\) 0 0
\(229\) −8.98014 −0.593424 −0.296712 0.954967i \(-0.595890\pi\)
−0.296712 + 0.954967i \(0.595890\pi\)
\(230\) 13.6215 0.898173
\(231\) 0 0
\(232\) 69.3756 4.55473
\(233\) 19.8909 1.30309 0.651547 0.758608i \(-0.274120\pi\)
0.651547 + 0.758608i \(0.274120\pi\)
\(234\) 0 0
\(235\) −4.91541 −0.320646
\(236\) −32.8690 −2.13959
\(237\) 0 0
\(238\) −14.7859 −0.958428
\(239\) −9.21976 −0.596377 −0.298188 0.954507i \(-0.596382\pi\)
−0.298188 + 0.954507i \(0.596382\pi\)
\(240\) 0 0
\(241\) 0.802919 0.0517206 0.0258603 0.999666i \(-0.491767\pi\)
0.0258603 + 0.999666i \(0.491767\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 42.1851 2.70062
\(245\) −3.08369 −0.197010
\(246\) 0 0
\(247\) −0.691879 −0.0440232
\(248\) 12.5241 0.795282
\(249\) 0 0
\(250\) 3.99603 0.252731
\(251\) −0.459277 −0.0289893 −0.0144947 0.999895i \(-0.504614\pi\)
−0.0144947 + 0.999895i \(0.504614\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 29.9370 1.87842
\(255\) 0 0
\(256\) −7.21718 −0.451073
\(257\) 23.3574 1.45699 0.728496 0.685050i \(-0.240220\pi\)
0.728496 + 0.685050i \(0.240220\pi\)
\(258\) 0 0
\(259\) 4.17268 0.259277
\(260\) −86.4406 −5.36082
\(261\) 0 0
\(262\) −2.56149 −0.158249
\(263\) −4.96169 −0.305951 −0.152975 0.988230i \(-0.548886\pi\)
−0.152975 + 0.988230i \(0.548886\pi\)
\(264\) 0 0
\(265\) −36.5615 −2.24596
\(266\) −0.323795 −0.0198531
\(267\) 0 0
\(268\) −40.0002 −2.44340
\(269\) −1.03203 −0.0629239 −0.0314620 0.999505i \(-0.510016\pi\)
−0.0314620 + 0.999505i \(0.510016\pi\)
\(270\) 0 0
\(271\) −15.1427 −0.919856 −0.459928 0.887956i \(-0.652125\pi\)
−0.459928 + 0.887956i \(0.652125\pi\)
\(272\) −60.2381 −3.65247
\(273\) 0 0
\(274\) 0.330258 0.0199516
\(275\) 0 0
\(276\) 0 0
\(277\) 1.07001 0.0642909 0.0321455 0.999483i \(-0.489766\pi\)
0.0321455 + 0.999483i \(0.489766\pi\)
\(278\) 4.43073 0.265737
\(279\) 0 0
\(280\) −24.1721 −1.44456
\(281\) −31.3090 −1.86774 −0.933868 0.357617i \(-0.883589\pi\)
−0.933868 + 0.357617i \(0.883589\pi\)
\(282\) 0 0
\(283\) −31.9651 −1.90013 −0.950063 0.312059i \(-0.898981\pi\)
−0.950063 + 0.312059i \(0.898981\pi\)
\(284\) −31.0271 −1.84112
\(285\) 0 0
\(286\) 0 0
\(287\) 3.48859 0.205925
\(288\) 0 0
\(289\) 14.3695 0.845266
\(290\) −72.0487 −4.23085
\(291\) 0 0
\(292\) −17.4424 −1.02074
\(293\) −0.472963 −0.0276308 −0.0138154 0.999905i \(-0.504398\pi\)
−0.0138154 + 0.999905i \(0.504398\pi\)
\(294\) 0 0
\(295\) 20.3969 1.18755
\(296\) 32.7084 1.90114
\(297\) 0 0
\(298\) 37.4321 2.16838
\(299\) −9.43873 −0.545856
\(300\) 0 0
\(301\) 5.10698 0.294361
\(302\) −41.9284 −2.41271
\(303\) 0 0
\(304\) −1.31915 −0.0756583
\(305\) −26.1780 −1.49895
\(306\) 0 0
\(307\) 22.3522 1.27571 0.637854 0.770158i \(-0.279823\pi\)
0.637854 + 0.770158i \(0.279823\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −13.0067 −0.738730
\(311\) −21.9838 −1.24659 −0.623293 0.781988i \(-0.714206\pi\)
−0.623293 + 0.781988i \(0.714206\pi\)
\(312\) 0 0
\(313\) −7.95027 −0.449376 −0.224688 0.974431i \(-0.572136\pi\)
−0.224688 + 0.974431i \(0.572136\pi\)
\(314\) −24.2836 −1.37040
\(315\) 0 0
\(316\) 46.6997 2.62707
\(317\) 15.1227 0.849374 0.424687 0.905340i \(-0.360384\pi\)
0.424687 + 0.905340i \(0.360384\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −37.1831 −2.07860
\(321\) 0 0
\(322\) −4.41727 −0.246165
\(323\) 0.686958 0.0382234
\(324\) 0 0
\(325\) 25.4359 1.41093
\(326\) 25.7907 1.42841
\(327\) 0 0
\(328\) 27.3461 1.50993
\(329\) 1.59400 0.0878803
\(330\) 0 0
\(331\) −6.02542 −0.331187 −0.165594 0.986194i \(-0.552954\pi\)
−0.165594 + 0.986194i \(0.552954\pi\)
\(332\) −46.8795 −2.57285
\(333\) 0 0
\(334\) 16.1099 0.881492
\(335\) 24.8221 1.35618
\(336\) 0 0
\(337\) −20.8494 −1.13574 −0.567869 0.823119i \(-0.692232\pi\)
−0.567869 + 0.823119i \(0.692232\pi\)
\(338\) 49.6851 2.70252
\(339\) 0 0
\(340\) 85.8258 4.65456
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 40.0321 2.15839
\(345\) 0 0
\(346\) 17.7884 0.956309
\(347\) 1.49329 0.0801643 0.0400821 0.999196i \(-0.487238\pi\)
0.0400821 + 0.999196i \(0.487238\pi\)
\(348\) 0 0
\(349\) 21.4795 1.14977 0.574886 0.818234i \(-0.305046\pi\)
0.574886 + 0.818234i \(0.305046\pi\)
\(350\) 11.9038 0.636287
\(351\) 0 0
\(352\) 0 0
\(353\) −11.4760 −0.610808 −0.305404 0.952223i \(-0.598792\pi\)
−0.305404 + 0.952223i \(0.598792\pi\)
\(354\) 0 0
\(355\) 19.2539 1.02189
\(356\) 42.0180 2.22695
\(357\) 0 0
\(358\) −34.3022 −1.81293
\(359\) −5.72481 −0.302144 −0.151072 0.988523i \(-0.548273\pi\)
−0.151072 + 0.988523i \(0.548273\pi\)
\(360\) 0 0
\(361\) −18.9850 −0.999208
\(362\) −10.8190 −0.568632
\(363\) 0 0
\(364\) 28.0316 1.46925
\(365\) 10.8239 0.566548
\(366\) 0 0
\(367\) 17.4991 0.913445 0.456723 0.889609i \(-0.349023\pi\)
0.456723 + 0.889609i \(0.349023\pi\)
\(368\) −17.9960 −0.938109
\(369\) 0 0
\(370\) −33.9687 −1.76595
\(371\) 11.8564 0.615555
\(372\) 0 0
\(373\) 9.54362 0.494150 0.247075 0.968996i \(-0.420531\pi\)
0.247075 + 0.968996i \(0.420531\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 12.4949 0.644377
\(377\) 49.9247 2.57126
\(378\) 0 0
\(379\) 31.9605 1.64170 0.820850 0.571144i \(-0.193500\pi\)
0.820850 + 0.571144i \(0.193500\pi\)
\(380\) 1.87949 0.0964158
\(381\) 0 0
\(382\) −56.7682 −2.90452
\(383\) 9.82236 0.501899 0.250950 0.968000i \(-0.419257\pi\)
0.250950 + 0.968000i \(0.419257\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −46.9814 −2.39129
\(387\) 0 0
\(388\) −28.2493 −1.43414
\(389\) −33.1998 −1.68330 −0.841648 0.540027i \(-0.818414\pi\)
−0.841648 + 0.540027i \(0.818414\pi\)
\(390\) 0 0
\(391\) 9.37160 0.473942
\(392\) 7.83871 0.395915
\(393\) 0 0
\(394\) 47.8047 2.40837
\(395\) −28.9795 −1.45812
\(396\) 0 0
\(397\) 23.6535 1.18713 0.593566 0.804785i \(-0.297719\pi\)
0.593566 + 0.804785i \(0.297719\pi\)
\(398\) 7.05230 0.353500
\(399\) 0 0
\(400\) 48.4965 2.42482
\(401\) −25.2737 −1.26211 −0.631054 0.775739i \(-0.717377\pi\)
−0.631054 + 0.775739i \(0.717377\pi\)
\(402\) 0 0
\(403\) 9.01273 0.448956
\(404\) 83.8693 4.17265
\(405\) 0 0
\(406\) 23.3645 1.15956
\(407\) 0 0
\(408\) 0 0
\(409\) −13.9735 −0.690947 −0.345474 0.938428i \(-0.612282\pi\)
−0.345474 + 0.938428i \(0.612282\pi\)
\(410\) −28.3998 −1.40256
\(411\) 0 0
\(412\) −65.6798 −3.23581
\(413\) −6.61445 −0.325476
\(414\) 0 0
\(415\) 29.0911 1.42803
\(416\) 71.7282 3.51676
\(417\) 0 0
\(418\) 0 0
\(419\) −29.7445 −1.45311 −0.726556 0.687107i \(-0.758880\pi\)
−0.726556 + 0.687107i \(0.758880\pi\)
\(420\) 0 0
\(421\) 36.2675 1.76757 0.883786 0.467892i \(-0.154986\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(422\) 21.5273 1.04793
\(423\) 0 0
\(424\) 92.9392 4.51353
\(425\) −25.2550 −1.22505
\(426\) 0 0
\(427\) 8.48918 0.410820
\(428\) 55.0323 2.66009
\(429\) 0 0
\(430\) −41.5746 −2.00491
\(431\) 35.8066 1.72474 0.862372 0.506275i \(-0.168978\pi\)
0.862372 + 0.506275i \(0.168978\pi\)
\(432\) 0 0
\(433\) −23.0958 −1.10992 −0.554958 0.831879i \(-0.687266\pi\)
−0.554958 + 0.831879i \(0.687266\pi\)
\(434\) 4.21790 0.202466
\(435\) 0 0
\(436\) 24.2187 1.15987
\(437\) 0.205228 0.00981737
\(438\) 0 0
\(439\) −24.7837 −1.18286 −0.591431 0.806356i \(-0.701437\pi\)
−0.591431 + 0.806356i \(0.701437\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −83.4069 −3.96726
\(443\) −13.2945 −0.631642 −0.315821 0.948819i \(-0.602280\pi\)
−0.315821 + 0.948819i \(0.602280\pi\)
\(444\) 0 0
\(445\) −26.0743 −1.23604
\(446\) 22.4068 1.06099
\(447\) 0 0
\(448\) 12.0580 0.569686
\(449\) −20.8714 −0.984981 −0.492490 0.870318i \(-0.663913\pi\)
−0.492490 + 0.870318i \(0.663913\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 26.2509 1.23474
\(453\) 0 0
\(454\) −58.4810 −2.74465
\(455\) −17.3950 −0.815490
\(456\) 0 0
\(457\) 28.2344 1.32075 0.660375 0.750936i \(-0.270397\pi\)
0.660375 + 0.750936i \(0.270397\pi\)
\(458\) −23.7070 −1.10776
\(459\) 0 0
\(460\) 25.6403 1.19549
\(461\) −13.5432 −0.630770 −0.315385 0.948964i \(-0.602134\pi\)
−0.315385 + 0.948964i \(0.602134\pi\)
\(462\) 0 0
\(463\) −33.9584 −1.57818 −0.789090 0.614277i \(-0.789448\pi\)
−0.789090 + 0.614277i \(0.789448\pi\)
\(464\) 95.1873 4.41896
\(465\) 0 0
\(466\) 52.5107 2.43251
\(467\) −12.5809 −0.582172 −0.291086 0.956697i \(-0.594017\pi\)
−0.291086 + 0.956697i \(0.594017\pi\)
\(468\) 0 0
\(469\) −8.04949 −0.371691
\(470\) −12.9764 −0.598556
\(471\) 0 0
\(472\) −51.8488 −2.38653
\(473\) 0 0
\(474\) 0 0
\(475\) −0.553056 −0.0253759
\(476\) −27.8322 −1.27569
\(477\) 0 0
\(478\) −24.3396 −1.11327
\(479\) 28.8916 1.32009 0.660046 0.751225i \(-0.270537\pi\)
0.660046 + 0.751225i \(0.270537\pi\)
\(480\) 0 0
\(481\) 23.5380 1.07324
\(482\) 2.11966 0.0965478
\(483\) 0 0
\(484\) 0 0
\(485\) 17.5301 0.796001
\(486\) 0 0
\(487\) 25.5077 1.15586 0.577932 0.816085i \(-0.303860\pi\)
0.577932 + 0.816085i \(0.303860\pi\)
\(488\) 66.5443 3.01232
\(489\) 0 0
\(490\) −8.14075 −0.367762
\(491\) 4.66598 0.210573 0.105286 0.994442i \(-0.466424\pi\)
0.105286 + 0.994442i \(0.466424\pi\)
\(492\) 0 0
\(493\) −49.5697 −2.23250
\(494\) −1.82652 −0.0821789
\(495\) 0 0
\(496\) 17.1838 0.771576
\(497\) −6.24379 −0.280072
\(498\) 0 0
\(499\) −18.4958 −0.827987 −0.413994 0.910280i \(-0.635866\pi\)
−0.413994 + 0.910280i \(0.635866\pi\)
\(500\) 7.52191 0.336390
\(501\) 0 0
\(502\) −1.21246 −0.0541149
\(503\) −23.1076 −1.03032 −0.515159 0.857094i \(-0.672267\pi\)
−0.515159 + 0.857094i \(0.672267\pi\)
\(504\) 0 0
\(505\) −52.0451 −2.31598
\(506\) 0 0
\(507\) 0 0
\(508\) 56.3518 2.50021
\(509\) 28.6541 1.27007 0.635036 0.772483i \(-0.280985\pi\)
0.635036 + 0.772483i \(0.280985\pi\)
\(510\) 0 0
\(511\) −3.51005 −0.155275
\(512\) −31.8553 −1.40782
\(513\) 0 0
\(514\) 61.6620 2.71979
\(515\) 40.7576 1.79600
\(516\) 0 0
\(517\) 0 0
\(518\) 11.0156 0.483998
\(519\) 0 0
\(520\) −136.354 −5.97954
\(521\) 7.99220 0.350144 0.175072 0.984556i \(-0.443984\pi\)
0.175072 + 0.984556i \(0.443984\pi\)
\(522\) 0 0
\(523\) −37.2399 −1.62839 −0.814194 0.580592i \(-0.802821\pi\)
−0.814194 + 0.580592i \(0.802821\pi\)
\(524\) −4.82161 −0.210633
\(525\) 0 0
\(526\) −13.0986 −0.571124
\(527\) −8.94863 −0.389808
\(528\) 0 0
\(529\) −20.2002 −0.878272
\(530\) −96.5202 −4.19257
\(531\) 0 0
\(532\) −0.609494 −0.0264249
\(533\) 19.6791 0.852394
\(534\) 0 0
\(535\) −34.1503 −1.47645
\(536\) −63.0977 −2.72541
\(537\) 0 0
\(538\) −2.72449 −0.117461
\(539\) 0 0
\(540\) 0 0
\(541\) 22.9890 0.988376 0.494188 0.869355i \(-0.335465\pi\)
0.494188 + 0.869355i \(0.335465\pi\)
\(542\) −39.9759 −1.71711
\(543\) 0 0
\(544\) −71.2180 −3.05345
\(545\) −15.0289 −0.643769
\(546\) 0 0
\(547\) −30.4285 −1.30103 −0.650515 0.759493i \(-0.725447\pi\)
−0.650515 + 0.759493i \(0.725447\pi\)
\(548\) 0.621660 0.0265560
\(549\) 0 0
\(550\) 0 0
\(551\) −1.08552 −0.0462447
\(552\) 0 0
\(553\) 9.39769 0.399630
\(554\) 2.82477 0.120013
\(555\) 0 0
\(556\) 8.34016 0.353702
\(557\) −42.4812 −1.79998 −0.899992 0.435906i \(-0.856428\pi\)
−0.899992 + 0.435906i \(0.856428\pi\)
\(558\) 0 0
\(559\) 28.8083 1.21846
\(560\) −33.1656 −1.40150
\(561\) 0 0
\(562\) −82.6538 −3.48654
\(563\) 12.0958 0.509777 0.254888 0.966971i \(-0.417961\pi\)
0.254888 + 0.966971i \(0.417961\pi\)
\(564\) 0 0
\(565\) −16.2900 −0.685325
\(566\) −84.3858 −3.54700
\(567\) 0 0
\(568\) −48.9433 −2.05361
\(569\) −34.0054 −1.42558 −0.712789 0.701378i \(-0.752568\pi\)
−0.712789 + 0.701378i \(0.752568\pi\)
\(570\) 0 0
\(571\) −16.0762 −0.672767 −0.336383 0.941725i \(-0.609204\pi\)
−0.336383 + 0.941725i \(0.609204\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 9.20967 0.384404
\(575\) −7.54489 −0.314643
\(576\) 0 0
\(577\) 3.94068 0.164053 0.0820264 0.996630i \(-0.473861\pi\)
0.0820264 + 0.996630i \(0.473861\pi\)
\(578\) 37.9347 1.57787
\(579\) 0 0
\(580\) −135.621 −5.63134
\(581\) −9.43386 −0.391383
\(582\) 0 0
\(583\) 0 0
\(584\) −27.5142 −1.13855
\(585\) 0 0
\(586\) −1.24859 −0.0515789
\(587\) −9.92820 −0.409781 −0.204890 0.978785i \(-0.565684\pi\)
−0.204890 + 0.978785i \(0.565684\pi\)
\(588\) 0 0
\(589\) −0.195965 −0.00807460
\(590\) 53.8466 2.21683
\(591\) 0 0
\(592\) 44.8778 1.84447
\(593\) 1.35512 0.0556480 0.0278240 0.999613i \(-0.491142\pi\)
0.0278240 + 0.999613i \(0.491142\pi\)
\(594\) 0 0
\(595\) 17.2713 0.708053
\(596\) 70.4601 2.88616
\(597\) 0 0
\(598\) −24.9177 −1.01896
\(599\) 30.7682 1.25716 0.628578 0.777747i \(-0.283637\pi\)
0.628578 + 0.777747i \(0.283637\pi\)
\(600\) 0 0
\(601\) 13.2165 0.539113 0.269557 0.962985i \(-0.413123\pi\)
0.269557 + 0.962985i \(0.413123\pi\)
\(602\) 13.4821 0.549490
\(603\) 0 0
\(604\) −78.9237 −3.21136
\(605\) 0 0
\(606\) 0 0
\(607\) 5.83308 0.236757 0.118379 0.992969i \(-0.462230\pi\)
0.118379 + 0.992969i \(0.462230\pi\)
\(608\) −1.55960 −0.0632499
\(609\) 0 0
\(610\) −69.1083 −2.79811
\(611\) 8.99173 0.363767
\(612\) 0 0
\(613\) −6.67731 −0.269694 −0.134847 0.990866i \(-0.543054\pi\)
−0.134847 + 0.990866i \(0.543054\pi\)
\(614\) 59.0084 2.38139
\(615\) 0 0
\(616\) 0 0
\(617\) −15.1716 −0.610785 −0.305392 0.952227i \(-0.598788\pi\)
−0.305392 + 0.952227i \(0.598788\pi\)
\(618\) 0 0
\(619\) 27.9902 1.12502 0.562510 0.826790i \(-0.309836\pi\)
0.562510 + 0.826790i \(0.309836\pi\)
\(620\) −24.4831 −0.983264
\(621\) 0 0
\(622\) −58.0359 −2.32703
\(623\) 8.45556 0.338765
\(624\) 0 0
\(625\) −27.2134 −1.08854
\(626\) −20.9882 −0.838858
\(627\) 0 0
\(628\) −45.7101 −1.82403
\(629\) −23.3705 −0.931844
\(630\) 0 0
\(631\) −5.58035 −0.222150 −0.111075 0.993812i \(-0.535429\pi\)
−0.111075 + 0.993812i \(0.535429\pi\)
\(632\) 73.6658 2.93027
\(633\) 0 0
\(634\) 39.9230 1.58554
\(635\) −34.9692 −1.38771
\(636\) 0 0
\(637\) 5.64097 0.223503
\(638\) 0 0
\(639\) 0 0
\(640\) −19.7393 −0.780265
\(641\) −10.9667 −0.433158 −0.216579 0.976265i \(-0.569490\pi\)
−0.216579 + 0.976265i \(0.569490\pi\)
\(642\) 0 0
\(643\) 0.399143 0.0157406 0.00787032 0.999969i \(-0.497495\pi\)
0.00787032 + 0.999969i \(0.497495\pi\)
\(644\) −8.31482 −0.327650
\(645\) 0 0
\(646\) 1.81353 0.0713523
\(647\) −31.2956 −1.23036 −0.615178 0.788389i \(-0.710916\pi\)
−0.615178 + 0.788389i \(0.710916\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 67.1492 2.63381
\(651\) 0 0
\(652\) 48.5470 1.90125
\(653\) 26.1788 1.02446 0.512228 0.858849i \(-0.328820\pi\)
0.512228 + 0.858849i \(0.328820\pi\)
\(654\) 0 0
\(655\) 2.99205 0.116909
\(656\) 37.5204 1.46493
\(657\) 0 0
\(658\) 4.20807 0.164048
\(659\) −5.84482 −0.227682 −0.113841 0.993499i \(-0.536315\pi\)
−0.113841 + 0.993499i \(0.536315\pi\)
\(660\) 0 0
\(661\) −6.32811 −0.246135 −0.123067 0.992398i \(-0.539273\pi\)
−0.123067 + 0.992398i \(0.539273\pi\)
\(662\) −15.9067 −0.618233
\(663\) 0 0
\(664\) −73.9494 −2.86979
\(665\) 0.378222 0.0146668
\(666\) 0 0
\(667\) −14.8089 −0.573401
\(668\) 30.3243 1.17328
\(669\) 0 0
\(670\) 65.5289 2.53160
\(671\) 0 0
\(672\) 0 0
\(673\) −4.21912 −0.162635 −0.0813176 0.996688i \(-0.525913\pi\)
−0.0813176 + 0.996688i \(0.525913\pi\)
\(674\) −55.0411 −2.12010
\(675\) 0 0
\(676\) 93.5246 3.59710
\(677\) 17.9247 0.688902 0.344451 0.938804i \(-0.388065\pi\)
0.344451 + 0.938804i \(0.388065\pi\)
\(678\) 0 0
\(679\) −5.68478 −0.218162
\(680\) 135.385 5.19176
\(681\) 0 0
\(682\) 0 0
\(683\) 5.96513 0.228249 0.114125 0.993466i \(-0.463594\pi\)
0.114125 + 0.993466i \(0.463594\pi\)
\(684\) 0 0
\(685\) −0.385771 −0.0147396
\(686\) 2.63994 0.100793
\(687\) 0 0
\(688\) 54.9264 2.09405
\(689\) 66.8818 2.54799
\(690\) 0 0
\(691\) −39.4084 −1.49917 −0.749583 0.661910i \(-0.769746\pi\)
−0.749583 + 0.661910i \(0.769746\pi\)
\(692\) 33.4839 1.27287
\(693\) 0 0
\(694\) 3.94221 0.149644
\(695\) −5.17549 −0.196318
\(696\) 0 0
\(697\) −19.5391 −0.740096
\(698\) 56.7046 2.14630
\(699\) 0 0
\(700\) 22.4071 0.846910
\(701\) −25.4284 −0.960417 −0.480208 0.877154i \(-0.659439\pi\)
−0.480208 + 0.877154i \(0.659439\pi\)
\(702\) 0 0
\(703\) −0.511789 −0.0193025
\(704\) 0 0
\(705\) 0 0
\(706\) −30.2961 −1.14021
\(707\) 16.8776 0.634746
\(708\) 0 0
\(709\) 7.08068 0.265921 0.132960 0.991121i \(-0.457552\pi\)
0.132960 + 0.991121i \(0.457552\pi\)
\(710\) 50.8291 1.90758
\(711\) 0 0
\(712\) 66.2807 2.48398
\(713\) −2.67339 −0.100119
\(714\) 0 0
\(715\) 0 0
\(716\) −64.5686 −2.41304
\(717\) 0 0
\(718\) −15.1132 −0.564018
\(719\) 21.5811 0.804840 0.402420 0.915455i \(-0.368169\pi\)
0.402420 + 0.915455i \(0.368169\pi\)
\(720\) 0 0
\(721\) −13.2172 −0.492233
\(722\) −50.1191 −1.86524
\(723\) 0 0
\(724\) −20.3650 −0.756861
\(725\) 39.9075 1.48213
\(726\) 0 0
\(727\) 35.7114 1.32446 0.662231 0.749300i \(-0.269610\pi\)
0.662231 + 0.749300i \(0.269610\pi\)
\(728\) 44.2180 1.63883
\(729\) 0 0
\(730\) 28.5744 1.05759
\(731\) −28.6034 −1.05794
\(732\) 0 0
\(733\) −6.34501 −0.234358 −0.117179 0.993111i \(-0.537385\pi\)
−0.117179 + 0.993111i \(0.537385\pi\)
\(734\) 46.1965 1.70515
\(735\) 0 0
\(736\) −21.2763 −0.784254
\(737\) 0 0
\(738\) 0 0
\(739\) −10.9804 −0.403922 −0.201961 0.979394i \(-0.564731\pi\)
−0.201961 + 0.979394i \(0.564731\pi\)
\(740\) −63.9409 −2.35051
\(741\) 0 0
\(742\) 31.3003 1.14907
\(743\) −18.4186 −0.675711 −0.337856 0.941198i \(-0.609702\pi\)
−0.337856 + 0.941198i \(0.609702\pi\)
\(744\) 0 0
\(745\) −43.7240 −1.60192
\(746\) 25.1946 0.922438
\(747\) 0 0
\(748\) 0 0
\(749\) 11.0745 0.404654
\(750\) 0 0
\(751\) 4.96566 0.181200 0.0905998 0.995887i \(-0.471122\pi\)
0.0905998 + 0.995887i \(0.471122\pi\)
\(752\) 17.1438 0.625170
\(753\) 0 0
\(754\) 131.798 4.79981
\(755\) 48.9761 1.78242
\(756\) 0 0
\(757\) −1.04107 −0.0378384 −0.0189192 0.999821i \(-0.506023\pi\)
−0.0189192 + 0.999821i \(0.506023\pi\)
\(758\) 84.3737 3.06459
\(759\) 0 0
\(760\) 2.96477 0.107544
\(761\) −42.0282 −1.52352 −0.761760 0.647860i \(-0.775664\pi\)
−0.761760 + 0.647860i \(0.775664\pi\)
\(762\) 0 0
\(763\) 4.87369 0.176439
\(764\) −106.857 −3.86597
\(765\) 0 0
\(766\) 25.9304 0.936905
\(767\) −37.3119 −1.34726
\(768\) 0 0
\(769\) −44.1300 −1.59137 −0.795684 0.605712i \(-0.792888\pi\)
−0.795684 + 0.605712i \(0.792888\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −88.4352 −3.18285
\(773\) 37.3027 1.34168 0.670842 0.741600i \(-0.265933\pi\)
0.670842 + 0.741600i \(0.265933\pi\)
\(774\) 0 0
\(775\) 7.20436 0.258788
\(776\) −44.5614 −1.59966
\(777\) 0 0
\(778\) −87.6454 −3.14224
\(779\) −0.427884 −0.0153305
\(780\) 0 0
\(781\) 0 0
\(782\) 24.7404 0.884717
\(783\) 0 0
\(784\) 10.7552 0.384113
\(785\) 28.3654 1.01241
\(786\) 0 0
\(787\) −7.35809 −0.262288 −0.131144 0.991363i \(-0.541865\pi\)
−0.131144 + 0.991363i \(0.541865\pi\)
\(788\) 89.9850 3.20558
\(789\) 0 0
\(790\) −76.5042 −2.72190
\(791\) 5.28263 0.187829
\(792\) 0 0
\(793\) 47.8872 1.70053
\(794\) 62.4437 2.21604
\(795\) 0 0
\(796\) 13.2749 0.470515
\(797\) −6.00177 −0.212594 −0.106297 0.994334i \(-0.533899\pi\)
−0.106297 + 0.994334i \(0.533899\pi\)
\(798\) 0 0
\(799\) −8.92778 −0.315842
\(800\) 57.3362 2.02714
\(801\) 0 0
\(802\) −66.7210 −2.35600
\(803\) 0 0
\(804\) 0 0
\(805\) 5.15977 0.181858
\(806\) 23.7931 0.838075
\(807\) 0 0
\(808\) 132.298 4.65424
\(809\) −28.3939 −0.998278 −0.499139 0.866522i \(-0.666350\pi\)
−0.499139 + 0.866522i \(0.666350\pi\)
\(810\) 0 0
\(811\) −31.9066 −1.12039 −0.560196 0.828360i \(-0.689274\pi\)
−0.560196 + 0.828360i \(0.689274\pi\)
\(812\) 43.9800 1.54340
\(813\) 0 0
\(814\) 0 0
\(815\) −30.1259 −1.05526
\(816\) 0 0
\(817\) −0.626383 −0.0219144
\(818\) −36.8893 −1.28980
\(819\) 0 0
\(820\) −53.4582 −1.86684
\(821\) −4.55941 −0.159125 −0.0795623 0.996830i \(-0.525352\pi\)
−0.0795623 + 0.996830i \(0.525352\pi\)
\(822\) 0 0
\(823\) 46.5932 1.62414 0.812069 0.583562i \(-0.198341\pi\)
0.812069 + 0.583562i \(0.198341\pi\)
\(824\) −103.606 −3.60927
\(825\) 0 0
\(826\) −17.4617 −0.607572
\(827\) −1.00246 −0.0348589 −0.0174294 0.999848i \(-0.505548\pi\)
−0.0174294 + 0.999848i \(0.505548\pi\)
\(828\) 0 0
\(829\) −50.4845 −1.75340 −0.876699 0.481039i \(-0.840260\pi\)
−0.876699 + 0.481039i \(0.840260\pi\)
\(830\) 76.7987 2.66572
\(831\) 0 0
\(832\) 68.0187 2.35813
\(833\) −5.60085 −0.194058
\(834\) 0 0
\(835\) −18.8178 −0.651216
\(836\) 0 0
\(837\) 0 0
\(838\) −78.5236 −2.71255
\(839\) 26.0614 0.899739 0.449869 0.893094i \(-0.351471\pi\)
0.449869 + 0.893094i \(0.351471\pi\)
\(840\) 0 0
\(841\) 49.3292 1.70101
\(842\) 95.7441 3.29956
\(843\) 0 0
\(844\) 40.5218 1.39482
\(845\) −58.0368 −1.99652
\(846\) 0 0
\(847\) 0 0
\(848\) 127.518 4.37898
\(849\) 0 0
\(850\) −66.6716 −2.28682
\(851\) −6.98191 −0.239337
\(852\) 0 0
\(853\) 30.1888 1.03364 0.516822 0.856093i \(-0.327115\pi\)
0.516822 + 0.856093i \(0.327115\pi\)
\(854\) 22.4109 0.766886
\(855\) 0 0
\(856\) 86.8099 2.96710
\(857\) −25.3151 −0.864748 −0.432374 0.901694i \(-0.642324\pi\)
−0.432374 + 0.901694i \(0.642324\pi\)
\(858\) 0 0
\(859\) −10.7680 −0.367399 −0.183699 0.982982i \(-0.558807\pi\)
−0.183699 + 0.982982i \(0.558807\pi\)
\(860\) −78.2578 −2.66857
\(861\) 0 0
\(862\) 94.5273 3.21961
\(863\) 35.3003 1.20163 0.600817 0.799386i \(-0.294842\pi\)
0.600817 + 0.799386i \(0.294842\pi\)
\(864\) 0 0
\(865\) −20.7784 −0.706488
\(866\) −60.9716 −2.07190
\(867\) 0 0
\(868\) 7.93955 0.269486
\(869\) 0 0
\(870\) 0 0
\(871\) −45.4070 −1.53856
\(872\) 38.2035 1.29373
\(873\) 0 0
\(874\) 0.541788 0.0183263
\(875\) 1.51368 0.0511718
\(876\) 0 0
\(877\) 4.16706 0.140712 0.0703558 0.997522i \(-0.477587\pi\)
0.0703558 + 0.997522i \(0.477587\pi\)
\(878\) −65.4275 −2.20807
\(879\) 0 0
\(880\) 0 0
\(881\) 40.6561 1.36974 0.684870 0.728665i \(-0.259859\pi\)
0.684870 + 0.728665i \(0.259859\pi\)
\(882\) 0 0
\(883\) −19.1697 −0.645113 −0.322556 0.946550i \(-0.604542\pi\)
−0.322556 + 0.946550i \(0.604542\pi\)
\(884\) −157.001 −5.28050
\(885\) 0 0
\(886\) −35.0967 −1.17910
\(887\) −37.0380 −1.24362 −0.621808 0.783170i \(-0.713602\pi\)
−0.621808 + 0.783170i \(0.713602\pi\)
\(888\) 0 0
\(889\) 11.3400 0.380333
\(890\) −68.8346 −2.30734
\(891\) 0 0
\(892\) 42.1774 1.41220
\(893\) −0.195508 −0.00654244
\(894\) 0 0
\(895\) 40.0681 1.33933
\(896\) 6.40120 0.213849
\(897\) 0 0
\(898\) −55.0992 −1.83868
\(899\) 14.1405 0.471612
\(900\) 0 0
\(901\) −66.4061 −2.21231
\(902\) 0 0
\(903\) 0 0
\(904\) 41.4090 1.37724
\(905\) 12.6375 0.420086
\(906\) 0 0
\(907\) −28.7583 −0.954905 −0.477452 0.878658i \(-0.658440\pi\)
−0.477452 + 0.878658i \(0.658440\pi\)
\(908\) −110.082 −3.65318
\(909\) 0 0
\(910\) −45.9217 −1.52229
\(911\) −44.7716 −1.48335 −0.741675 0.670759i \(-0.765968\pi\)
−0.741675 + 0.670759i \(0.765968\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 74.5371 2.46547
\(915\) 0 0
\(916\) −44.6248 −1.47445
\(917\) −0.970284 −0.0320416
\(918\) 0 0
\(919\) −19.3392 −0.637943 −0.318971 0.947764i \(-0.603337\pi\)
−0.318971 + 0.947764i \(0.603337\pi\)
\(920\) 40.4459 1.33346
\(921\) 0 0
\(922\) −35.7533 −1.17747
\(923\) −35.2210 −1.15931
\(924\) 0 0
\(925\) 18.8152 0.618638
\(926\) −89.6481 −2.94602
\(927\) 0 0
\(928\) 112.538 3.69423
\(929\) 26.9129 0.882985 0.441493 0.897265i \(-0.354449\pi\)
0.441493 + 0.897265i \(0.354449\pi\)
\(930\) 0 0
\(931\) −0.122652 −0.00401977
\(932\) 98.8433 3.23772
\(933\) 0 0
\(934\) −33.2127 −1.08675
\(935\) 0 0
\(936\) 0 0
\(937\) −42.5349 −1.38956 −0.694778 0.719224i \(-0.744497\pi\)
−0.694778 + 0.719224i \(0.744497\pi\)
\(938\) −21.2502 −0.693843
\(939\) 0 0
\(940\) −24.4260 −0.796690
\(941\) −48.7704 −1.58987 −0.794934 0.606695i \(-0.792495\pi\)
−0.794934 + 0.606695i \(0.792495\pi\)
\(942\) 0 0
\(943\) −5.83727 −0.190088
\(944\) −71.1395 −2.31540
\(945\) 0 0
\(946\) 0 0
\(947\) −0.641845 −0.0208572 −0.0104286 0.999946i \(-0.503320\pi\)
−0.0104286 + 0.999946i \(0.503320\pi\)
\(948\) 0 0
\(949\) −19.8001 −0.642738
\(950\) −1.46003 −0.0473698
\(951\) 0 0
\(952\) −43.9035 −1.42292
\(953\) 7.65944 0.248114 0.124057 0.992275i \(-0.460409\pi\)
0.124057 + 0.992275i \(0.460409\pi\)
\(954\) 0 0
\(955\) 66.3104 2.14576
\(956\) −45.8156 −1.48178
\(957\) 0 0
\(958\) 76.2721 2.46424
\(959\) 0.125101 0.00403971
\(960\) 0 0
\(961\) −28.4473 −0.917654
\(962\) 62.1388 2.00343
\(963\) 0 0
\(964\) 3.98993 0.128507
\(965\) 54.8785 1.76660
\(966\) 0 0
\(967\) 29.7387 0.956333 0.478166 0.878269i \(-0.341302\pi\)
0.478166 + 0.878269i \(0.341302\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 46.2784 1.48591
\(971\) 34.9188 1.12060 0.560299 0.828291i \(-0.310686\pi\)
0.560299 + 0.828291i \(0.310686\pi\)
\(972\) 0 0
\(973\) 1.67835 0.0538053
\(974\) 67.3388 2.15767
\(975\) 0 0
\(976\) 91.3026 2.92253
\(977\) −31.9341 −1.02166 −0.510832 0.859681i \(-0.670662\pi\)
−0.510832 + 0.859681i \(0.670662\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −15.3237 −0.489498
\(981\) 0 0
\(982\) 12.3179 0.393080
\(983\) 33.9111 1.08159 0.540797 0.841153i \(-0.318123\pi\)
0.540797 + 0.841153i \(0.318123\pi\)
\(984\) 0 0
\(985\) −55.8402 −1.77922
\(986\) −130.861 −4.16746
\(987\) 0 0
\(988\) −3.43814 −0.109382
\(989\) −8.54523 −0.271722
\(990\) 0 0
\(991\) −13.3101 −0.422809 −0.211404 0.977399i \(-0.567804\pi\)
−0.211404 + 0.977399i \(0.567804\pi\)
\(992\) 20.3160 0.645034
\(993\) 0 0
\(994\) −16.4832 −0.522816
\(995\) −8.23772 −0.261153
\(996\) 0 0
\(997\) 2.95257 0.0935088 0.0467544 0.998906i \(-0.485112\pi\)
0.0467544 + 0.998906i \(0.485112\pi\)
\(998\) −48.8279 −1.54562
\(999\) 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.1.9 10
3.2 odd 2 2541.2.a.br.1.2 10
11.2 odd 10 693.2.m.j.631.5 20
11.6 odd 10 693.2.m.j.190.5 20
11.10 odd 2 7623.2.a.cx.1.2 10
33.2 even 10 231.2.j.g.169.1 20
33.17 even 10 231.2.j.g.190.1 yes 20
33.32 even 2 2541.2.a.bq.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.169.1 20 33.2 even 10
231.2.j.g.190.1 yes 20 33.17 even 10
693.2.m.j.190.5 20 11.6 odd 10
693.2.m.j.631.5 20 11.2 odd 10
2541.2.a.bq.1.9 10 33.32 even 2
2541.2.a.br.1.2 10 3.2 odd 2
7623.2.a.cx.1.2 10 11.10 odd 2
7623.2.a.cy.1.9 10 1.1 even 1 trivial