Properties

Label 7600.2.a.ck.1.3
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.66064384.1
Defining polynomial: \( x^{6} - 9x^{4} + 13x^{2} - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.30397\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.537080 q^{3} +3.18676 q^{7} -2.71155 q^{9} +O(q^{10})\) \(q-0.537080 q^{3} +3.18676 q^{7} -2.71155 q^{9} -4.15544 q^{11} +2.07086 q^{13} +5.79470 q^{17} +1.00000 q^{19} -1.71155 q^{21} +2.60794 q^{23} +3.06756 q^{27} +6.00000 q^{29} -2.59933 q^{31} +2.23180 q^{33} +4.30266 q^{37} -1.11222 q^{39} -0.599328 q^{41} -3.18676 q^{43} -11.7086 q^{47} +3.15544 q^{49} -3.11222 q^{51} +11.7503 q^{53} -0.537080 q^{57} +1.71155 q^{59} -8.75476 q^{61} -8.64104 q^{63} -4.76228 q^{67} -1.40067 q^{69} -13.7115 q^{71} -2.72714 q^{73} -13.2424 q^{77} +1.40067 q^{79} +6.48711 q^{81} +7.07154 q^{83} -3.22248 q^{87} +16.5353 q^{89} +6.59933 q^{91} +1.39605 q^{93} +2.07086 q^{97} +11.2677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 14 q^{9} - 2 q^{11} + 6 q^{19} + 20 q^{21} + 36 q^{29} + 8 q^{39} + 12 q^{41} - 4 q^{49} - 4 q^{51} - 20 q^{59} - 14 q^{61} - 24 q^{69} - 52 q^{71} + 24 q^{79} + 38 q^{81} + 24 q^{89} + 24 q^{91} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −0.537080 −0.310083 −0.155042 0.987908i \(-0.549551\pi\)
−0.155042 + 0.987908i \(0.549551\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.18676 1.20448 0.602241 0.798314i \(-0.294275\pi\)
0.602241 + 0.798314i \(0.294275\pi\)
\(8\) 0 0
\(9\) −2.71155 −0.903848
\(10\) 0 0
\(11\) −4.15544 −1.25291 −0.626456 0.779457i \(-0.715495\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(12\) 0 0
\(13\) 2.07086 0.574353 0.287176 0.957878i \(-0.407283\pi\)
0.287176 + 0.957878i \(0.407283\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.79470 1.40542 0.702710 0.711476i \(-0.251973\pi\)
0.702710 + 0.711476i \(0.251973\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.71155 −0.373490
\(22\) 0 0
\(23\) 2.60794 0.543793 0.271896 0.962327i \(-0.412349\pi\)
0.271896 + 0.962327i \(0.412349\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.06756 0.590352
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.59933 −0.466853 −0.233427 0.972374i \(-0.574994\pi\)
−0.233427 + 0.972374i \(0.574994\pi\)
\(32\) 0 0
\(33\) 2.23180 0.388507
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.30266 0.707353 0.353677 0.935368i \(-0.384931\pi\)
0.353677 + 0.935368i \(0.384931\pi\)
\(38\) 0 0
\(39\) −1.11222 −0.178097
\(40\) 0 0
\(41\) −0.599328 −0.0935993 −0.0467997 0.998904i \(-0.514902\pi\)
−0.0467997 + 0.998904i \(0.514902\pi\)
\(42\) 0 0
\(43\) −3.18676 −0.485976 −0.242988 0.970029i \(-0.578128\pi\)
−0.242988 + 0.970029i \(0.578128\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.7086 −1.70787 −0.853937 0.520376i \(-0.825792\pi\)
−0.853937 + 0.520376i \(0.825792\pi\)
\(48\) 0 0
\(49\) 3.15544 0.450777
\(50\) 0 0
\(51\) −3.11222 −0.435798
\(52\) 0 0
\(53\) 11.7503 1.61403 0.807017 0.590529i \(-0.201081\pi\)
0.807017 + 0.590529i \(0.201081\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.537080 −0.0711380
\(58\) 0 0
\(59\) 1.71155 0.222824 0.111412 0.993774i \(-0.464463\pi\)
0.111412 + 0.993774i \(0.464463\pi\)
\(60\) 0 0
\(61\) −8.75476 −1.12093 −0.560466 0.828177i \(-0.689378\pi\)
−0.560466 + 0.828177i \(0.689378\pi\)
\(62\) 0 0
\(63\) −8.64104 −1.08867
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.76228 −0.581805 −0.290902 0.956753i \(-0.593956\pi\)
−0.290902 + 0.956753i \(0.593956\pi\)
\(68\) 0 0
\(69\) −1.40067 −0.168621
\(70\) 0 0
\(71\) −13.7115 −1.62726 −0.813631 0.581382i \(-0.802512\pi\)
−0.813631 + 0.581382i \(0.802512\pi\)
\(72\) 0 0
\(73\) −2.72714 −0.319188 −0.159594 0.987183i \(-0.551018\pi\)
−0.159594 + 0.987183i \(0.551018\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13.2424 −1.50911
\(78\) 0 0
\(79\) 1.40067 0.157588 0.0787939 0.996891i \(-0.474893\pi\)
0.0787939 + 0.996891i \(0.474893\pi\)
\(80\) 0 0
\(81\) 6.48711 0.720790
\(82\) 0 0
\(83\) 7.07154 0.776203 0.388101 0.921617i \(-0.373131\pi\)
0.388101 + 0.921617i \(0.373131\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.22248 −0.345486
\(88\) 0 0
\(89\) 16.5353 1.75274 0.876370 0.481639i \(-0.159958\pi\)
0.876370 + 0.481639i \(0.159958\pi\)
\(90\) 0 0
\(91\) 6.59933 0.691798
\(92\) 0 0
\(93\) 1.39605 0.144763
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.07086 0.210264 0.105132 0.994458i \(-0.466474\pi\)
0.105132 + 0.994458i \(0.466474\pi\)
\(98\) 0 0
\(99\) 11.2677 1.13244
\(100\) 0 0
\(101\) −1.71155 −0.170305 −0.0851525 0.996368i \(-0.527138\pi\)
−0.0851525 + 0.996368i \(0.527138\pi\)
\(102\) 0 0
\(103\) −5.75296 −0.566856 −0.283428 0.958994i \(-0.591472\pi\)
−0.283428 + 0.958994i \(0.591472\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.4324 1.49191 0.745955 0.665996i \(-0.231993\pi\)
0.745955 + 0.665996i \(0.231993\pi\)
\(108\) 0 0
\(109\) 11.7115 1.12176 0.560881 0.827896i \(-0.310462\pi\)
0.560881 + 0.827896i \(0.310462\pi\)
\(110\) 0 0
\(111\) −2.31087 −0.219338
\(112\) 0 0
\(113\) −10.5927 −0.996477 −0.498239 0.867040i \(-0.666020\pi\)
−0.498239 + 0.867040i \(0.666020\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.61523 −0.519128
\(118\) 0 0
\(119\) 18.4663 1.69280
\(120\) 0 0
\(121\) 6.26765 0.569787
\(122\) 0 0
\(123\) 0.321887 0.0290236
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.07484 0.539055 0.269528 0.962993i \(-0.413132\pi\)
0.269528 + 0.962993i \(0.413132\pi\)
\(128\) 0 0
\(129\) 1.71155 0.150693
\(130\) 0 0
\(131\) 13.5785 1.18636 0.593181 0.805069i \(-0.297872\pi\)
0.593181 + 0.805069i \(0.297872\pi\)
\(132\) 0 0
\(133\) 3.18676 0.276327
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.94302 −0.678618 −0.339309 0.940675i \(-0.610193\pi\)
−0.339309 + 0.940675i \(0.610193\pi\)
\(138\) 0 0
\(139\) −3.26765 −0.277159 −0.138579 0.990351i \(-0.544254\pi\)
−0.138579 + 0.990351i \(0.544254\pi\)
\(140\) 0 0
\(141\) 6.28845 0.529583
\(142\) 0 0
\(143\) −8.60532 −0.719613
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.69472 −0.139778
\(148\) 0 0
\(149\) 8.44389 0.691751 0.345875 0.938280i \(-0.387582\pi\)
0.345875 + 0.938280i \(0.387582\pi\)
\(150\) 0 0
\(151\) −0.887783 −0.0722468 −0.0361234 0.999347i \(-0.511501\pi\)
−0.0361234 + 0.999347i \(0.511501\pi\)
\(152\) 0 0
\(153\) −15.7126 −1.27029
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.14172 0.330545 0.165273 0.986248i \(-0.447150\pi\)
0.165273 + 0.986248i \(0.447150\pi\)
\(158\) 0 0
\(159\) −6.31087 −0.500485
\(160\) 0 0
\(161\) 8.31087 0.654989
\(162\) 0 0
\(163\) 24.7126 1.93564 0.967819 0.251647i \(-0.0809723\pi\)
0.967819 + 0.251647i \(0.0809723\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.60464 0.278935 0.139468 0.990227i \(-0.455461\pi\)
0.139468 + 0.990227i \(0.455461\pi\)
\(168\) 0 0
\(169\) −8.71155 −0.670119
\(170\) 0 0
\(171\) −2.71155 −0.207357
\(172\) 0 0
\(173\) −22.4205 −1.70460 −0.852300 0.523054i \(-0.824793\pi\)
−0.852300 + 0.523054i \(0.824793\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.919237 −0.0690941
\(178\) 0 0
\(179\) 5.13464 0.383781 0.191890 0.981416i \(-0.438538\pi\)
0.191890 + 0.981416i \(0.438538\pi\)
\(180\) 0 0
\(181\) 20.8462 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(182\) 0 0
\(183\) 4.70201 0.347583
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −24.0795 −1.76087
\(188\) 0 0
\(189\) 9.77557 0.711068
\(190\) 0 0
\(191\) 5.26765 0.381154 0.190577 0.981672i \(-0.438964\pi\)
0.190577 + 0.981672i \(0.438964\pi\)
\(192\) 0 0
\(193\) 2.07086 0.149064 0.0745318 0.997219i \(-0.476254\pi\)
0.0745318 + 0.997219i \(0.476254\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.4318 0.743232 0.371616 0.928387i \(-0.378804\pi\)
0.371616 + 0.928387i \(0.378804\pi\)
\(198\) 0 0
\(199\) 2.73235 0.193691 0.0968455 0.995299i \(-0.469125\pi\)
0.0968455 + 0.995299i \(0.469125\pi\)
\(200\) 0 0
\(201\) 2.55773 0.180408
\(202\) 0 0
\(203\) 19.1206 1.34200
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.07154 −0.491506
\(208\) 0 0
\(209\) −4.15544 −0.287438
\(210\) 0 0
\(211\) 15.7340 1.08317 0.541585 0.840646i \(-0.317824\pi\)
0.541585 + 0.840646i \(0.317824\pi\)
\(212\) 0 0
\(213\) 7.36420 0.504586
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.28343 −0.562316
\(218\) 0 0
\(219\) 1.46469 0.0989748
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −18.8219 −1.26041 −0.630203 0.776430i \(-0.717028\pi\)
−0.630203 + 0.776430i \(0.717028\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.4418 0.958533 0.479267 0.877669i \(-0.340903\pi\)
0.479267 + 0.877669i \(0.340903\pi\)
\(228\) 0 0
\(229\) −4.17785 −0.276080 −0.138040 0.990427i \(-0.544080\pi\)
−0.138040 + 0.990427i \(0.544080\pi\)
\(230\) 0 0
\(231\) 7.11222 0.467950
\(232\) 0 0
\(233\) 12.0847 0.791697 0.395849 0.918316i \(-0.370450\pi\)
0.395849 + 0.918316i \(0.370450\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.752273 −0.0488654
\(238\) 0 0
\(239\) 11.3541 0.734435 0.367218 0.930135i \(-0.380310\pi\)
0.367218 + 0.930135i \(0.380310\pi\)
\(240\) 0 0
\(241\) −3.40067 −0.219057 −0.109528 0.993984i \(-0.534934\pi\)
−0.109528 + 0.993984i \(0.534934\pi\)
\(242\) 0 0
\(243\) −12.6868 −0.813857
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.07086 0.131766
\(248\) 0 0
\(249\) −3.79798 −0.240687
\(250\) 0 0
\(251\) −3.04322 −0.192086 −0.0960432 0.995377i \(-0.530619\pi\)
−0.0960432 + 0.995377i \(0.530619\pi\)
\(252\) 0 0
\(253\) −10.8371 −0.681324
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.2881 1.07840 0.539201 0.842177i \(-0.318726\pi\)
0.539201 + 0.842177i \(0.318726\pi\)
\(258\) 0 0
\(259\) 13.7115 0.851994
\(260\) 0 0
\(261\) −16.2693 −1.00704
\(262\) 0 0
\(263\) 1.19336 0.0735859 0.0367930 0.999323i \(-0.488286\pi\)
0.0367930 + 0.999323i \(0.488286\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −8.88078 −0.543495
\(268\) 0 0
\(269\) 22.1089 1.34800 0.674000 0.738731i \(-0.264575\pi\)
0.674000 + 0.738731i \(0.264575\pi\)
\(270\) 0 0
\(271\) 4.08644 0.248234 0.124117 0.992268i \(-0.460390\pi\)
0.124117 + 0.992268i \(0.460390\pi\)
\(272\) 0 0
\(273\) −3.54437 −0.214515
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.0199 −0.602037 −0.301019 0.953618i \(-0.597327\pi\)
−0.301019 + 0.953618i \(0.597327\pi\)
\(278\) 0 0
\(279\) 7.04820 0.421964
\(280\) 0 0
\(281\) 0.599328 0.0357529 0.0178765 0.999840i \(-0.494309\pi\)
0.0178765 + 0.999840i \(0.494309\pi\)
\(282\) 0 0
\(283\) −5.41856 −0.322100 −0.161050 0.986946i \(-0.551488\pi\)
−0.161050 + 0.986946i \(0.551488\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.90991 −0.112739
\(288\) 0 0
\(289\) 16.5785 0.975207
\(290\) 0 0
\(291\) −1.11222 −0.0651993
\(292\) 0 0
\(293\) 3.46691 0.202539 0.101269 0.994859i \(-0.467710\pi\)
0.101269 + 0.994859i \(0.467710\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −12.7470 −0.739658
\(298\) 0 0
\(299\) 5.40067 0.312329
\(300\) 0 0
\(301\) −10.1554 −0.585350
\(302\) 0 0
\(303\) 0.919237 0.0528088
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.5901 0.946846 0.473423 0.880835i \(-0.343018\pi\)
0.473423 + 0.880835i \(0.343018\pi\)
\(308\) 0 0
\(309\) 3.08980 0.175772
\(310\) 0 0
\(311\) 4.15544 0.235633 0.117817 0.993035i \(-0.462411\pi\)
0.117817 + 0.993035i \(0.462411\pi\)
\(312\) 0 0
\(313\) −0.919237 −0.0519583 −0.0259792 0.999662i \(-0.508270\pi\)
−0.0259792 + 0.999662i \(0.508270\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.7292 −1.50126 −0.750630 0.660723i \(-0.770250\pi\)
−0.750630 + 0.660723i \(0.770250\pi\)
\(318\) 0 0
\(319\) −24.9326 −1.39596
\(320\) 0 0
\(321\) −8.28845 −0.462616
\(322\) 0 0
\(323\) 5.79470 0.322426
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.29004 −0.347840
\(328\) 0 0
\(329\) −37.3125 −2.05710
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) −11.6669 −0.639340
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.5040 1.22587 0.612935 0.790133i \(-0.289989\pi\)
0.612935 + 0.790133i \(0.289989\pi\)
\(338\) 0 0
\(339\) 5.68913 0.308991
\(340\) 0 0
\(341\) 10.8013 0.584926
\(342\) 0 0
\(343\) −12.2517 −0.661530
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.4543 0.775946 0.387973 0.921671i \(-0.373175\pi\)
0.387973 + 0.921671i \(0.373175\pi\)
\(348\) 0 0
\(349\) −13.3541 −0.714828 −0.357414 0.933946i \(-0.616342\pi\)
−0.357414 + 0.933946i \(0.616342\pi\)
\(350\) 0 0
\(351\) 6.35248 0.339070
\(352\) 0 0
\(353\) 17.6410 0.938937 0.469469 0.882949i \(-0.344446\pi\)
0.469469 + 0.882949i \(0.344446\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.91789 −0.524910
\(358\) 0 0
\(359\) −12.4663 −0.657947 −0.328973 0.944339i \(-0.606703\pi\)
−0.328973 + 0.944339i \(0.606703\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −3.36623 −0.176681
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 16.4291 0.857594 0.428797 0.903401i \(-0.358938\pi\)
0.428797 + 0.903401i \(0.358938\pi\)
\(368\) 0 0
\(369\) 1.62511 0.0845996
\(370\) 0 0
\(371\) 37.4455 1.94407
\(372\) 0 0
\(373\) −5.29334 −0.274079 −0.137039 0.990566i \(-0.543759\pi\)
−0.137039 + 0.990566i \(0.543759\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.4252 0.639928
\(378\) 0 0
\(379\) −14.5353 −0.746629 −0.373314 0.927705i \(-0.621779\pi\)
−0.373314 + 0.927705i \(0.621779\pi\)
\(380\) 0 0
\(381\) −3.26268 −0.167152
\(382\) 0 0
\(383\) −0.453598 −0.0231778 −0.0115889 0.999933i \(-0.503689\pi\)
−0.0115889 + 0.999933i \(0.503689\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.64104 0.439249
\(388\) 0 0
\(389\) 16.1554 0.819113 0.409557 0.912285i \(-0.365683\pi\)
0.409557 + 0.912285i \(0.365683\pi\)
\(390\) 0 0
\(391\) 15.1122 0.764258
\(392\) 0 0
\(393\) −7.29276 −0.367871
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 32.7563 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(398\) 0 0
\(399\) −1.71155 −0.0856844
\(400\) 0 0
\(401\) 12.0864 0.603568 0.301784 0.953376i \(-0.402418\pi\)
0.301784 + 0.953376i \(0.402418\pi\)
\(402\) 0 0
\(403\) −5.38284 −0.268138
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17.8794 −0.886251
\(408\) 0 0
\(409\) −19.1346 −0.946147 −0.473073 0.881023i \(-0.656855\pi\)
−0.473073 + 0.881023i \(0.656855\pi\)
\(410\) 0 0
\(411\) 4.26604 0.210428
\(412\) 0 0
\(413\) 5.45428 0.268388
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.75499 0.0859423
\(418\) 0 0
\(419\) −8.04484 −0.393016 −0.196508 0.980502i \(-0.562960\pi\)
−0.196508 + 0.980502i \(0.562960\pi\)
\(420\) 0 0
\(421\) −29.3591 −1.43087 −0.715437 0.698678i \(-0.753772\pi\)
−0.715437 + 0.698678i \(0.753772\pi\)
\(422\) 0 0
\(423\) 31.7484 1.54366
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −27.8993 −1.35014
\(428\) 0 0
\(429\) 4.62175 0.223140
\(430\) 0 0
\(431\) 32.0448 1.54355 0.771773 0.635898i \(-0.219370\pi\)
0.771773 + 0.635898i \(0.219370\pi\)
\(432\) 0 0
\(433\) 0.482831 0.0232034 0.0116017 0.999933i \(-0.496307\pi\)
0.0116017 + 0.999933i \(0.496307\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.60794 0.124755
\(438\) 0 0
\(439\) 27.3591 1.30578 0.652889 0.757454i \(-0.273557\pi\)
0.652889 + 0.757454i \(0.273557\pi\)
\(440\) 0 0
\(441\) −8.55611 −0.407434
\(442\) 0 0
\(443\) −23.3815 −1.11089 −0.555444 0.831554i \(-0.687452\pi\)
−0.555444 + 0.831554i \(0.687452\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.53505 −0.214500
\(448\) 0 0
\(449\) 23.1346 1.09179 0.545895 0.837853i \(-0.316190\pi\)
0.545895 + 0.837853i \(0.316190\pi\)
\(450\) 0 0
\(451\) 2.49047 0.117272
\(452\) 0 0
\(453\) 0.476811 0.0224025
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 21.2503 0.994049 0.497025 0.867736i \(-0.334426\pi\)
0.497025 + 0.867736i \(0.334426\pi\)
\(458\) 0 0
\(459\) 17.7756 0.829692
\(460\) 0 0
\(461\) 31.5785 1.47076 0.735379 0.677656i \(-0.237004\pi\)
0.735379 + 0.677656i \(0.237004\pi\)
\(462\) 0 0
\(463\) 15.6119 0.725547 0.362774 0.931877i \(-0.381830\pi\)
0.362774 + 0.931877i \(0.381830\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.8264 1.38020 0.690101 0.723713i \(-0.257566\pi\)
0.690101 + 0.723713i \(0.257566\pi\)
\(468\) 0 0
\(469\) −15.1762 −0.700774
\(470\) 0 0
\(471\) −2.22443 −0.102496
\(472\) 0 0
\(473\) 13.2424 0.608885
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −31.8616 −1.45884
\(478\) 0 0
\(479\) −4.53531 −0.207223 −0.103612 0.994618i \(-0.533040\pi\)
−0.103612 + 0.994618i \(0.533040\pi\)
\(480\) 0 0
\(481\) 8.91020 0.406270
\(482\) 0 0
\(483\) −4.46360 −0.203101
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −39.2550 −1.77881 −0.889407 0.457116i \(-0.848882\pi\)
−0.889407 + 0.457116i \(0.848882\pi\)
\(488\) 0 0
\(489\) −13.2726 −0.600209
\(490\) 0 0
\(491\) −38.8910 −1.75513 −0.877564 0.479460i \(-0.840832\pi\)
−0.877564 + 0.479460i \(0.840832\pi\)
\(492\) 0 0
\(493\) 34.7682 1.56588
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −43.6954 −1.96001
\(498\) 0 0
\(499\) −4.73235 −0.211849 −0.105924 0.994374i \(-0.533780\pi\)
−0.105924 + 0.994374i \(0.533780\pi\)
\(500\) 0 0
\(501\) −1.93598 −0.0864931
\(502\) 0 0
\(503\) −1.85567 −0.0827400 −0.0413700 0.999144i \(-0.513172\pi\)
−0.0413700 + 0.999144i \(0.513172\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.67880 0.207793
\(508\) 0 0
\(509\) 22.8878 1.01448 0.507242 0.861804i \(-0.330665\pi\)
0.507242 + 0.861804i \(0.330665\pi\)
\(510\) 0 0
\(511\) −8.69074 −0.384456
\(512\) 0 0
\(513\) 3.06756 0.135436
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 48.6543 2.13982
\(518\) 0 0
\(519\) 12.0416 0.528568
\(520\) 0 0
\(521\) −29.7340 −1.30267 −0.651334 0.758791i \(-0.725790\pi\)
−0.651334 + 0.758791i \(0.725790\pi\)
\(522\) 0 0
\(523\) −30.6497 −1.34022 −0.670109 0.742263i \(-0.733752\pi\)
−0.670109 + 0.742263i \(0.733752\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.0623 −0.656125
\(528\) 0 0
\(529\) −16.1987 −0.704289
\(530\) 0 0
\(531\) −4.64093 −0.201399
\(532\) 0 0
\(533\) −1.24112 −0.0537590
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.75771 −0.119004
\(538\) 0 0
\(539\) −13.1122 −0.564783
\(540\) 0 0
\(541\) 2.21946 0.0954220 0.0477110 0.998861i \(-0.484807\pi\)
0.0477110 + 0.998861i \(0.484807\pi\)
\(542\) 0 0
\(543\) −11.1961 −0.480469
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14.4297 0.616970 0.308485 0.951229i \(-0.400178\pi\)
0.308485 + 0.951229i \(0.400178\pi\)
\(548\) 0 0
\(549\) 23.7389 1.01315
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 4.46360 0.189812
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.4610 0.824588 0.412294 0.911051i \(-0.364728\pi\)
0.412294 + 0.911051i \(0.364728\pi\)
\(558\) 0 0
\(559\) −6.59933 −0.279122
\(560\) 0 0
\(561\) 12.9326 0.546016
\(562\) 0 0
\(563\) 12.3649 0.521118 0.260559 0.965458i \(-0.416093\pi\)
0.260559 + 0.965458i \(0.416093\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 20.6729 0.868179
\(568\) 0 0
\(569\) 15.0898 0.632597 0.316299 0.948660i \(-0.397560\pi\)
0.316299 + 0.948660i \(0.397560\pi\)
\(570\) 0 0
\(571\) −17.1571 −0.718000 −0.359000 0.933337i \(-0.616882\pi\)
−0.359000 + 0.933337i \(0.616882\pi\)
\(572\) 0 0
\(573\) −2.82915 −0.118190
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.5165 −0.937374 −0.468687 0.883364i \(-0.655273\pi\)
−0.468687 + 0.883364i \(0.655273\pi\)
\(578\) 0 0
\(579\) −1.11222 −0.0462222
\(580\) 0 0
\(581\) 22.5353 0.934922
\(582\) 0 0
\(583\) −48.8278 −2.02224
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.49544 −0.309370 −0.154685 0.987964i \(-0.549436\pi\)
−0.154685 + 0.987964i \(0.549436\pi\)
\(588\) 0 0
\(589\) −2.59933 −0.107103
\(590\) 0 0
\(591\) −5.60269 −0.230464
\(592\) 0 0
\(593\) 27.8094 1.14199 0.570997 0.820952i \(-0.306557\pi\)
0.570997 + 0.820952i \(0.306557\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.46749 −0.0600603
\(598\) 0 0
\(599\) 45.4903 1.85869 0.929343 0.369219i \(-0.120375\pi\)
0.929343 + 0.369219i \(0.120375\pi\)
\(600\) 0 0
\(601\) −16.5993 −0.677101 −0.338550 0.940948i \(-0.609937\pi\)
−0.338550 + 0.940948i \(0.609937\pi\)
\(602\) 0 0
\(603\) 12.9131 0.525863
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 5.08417 0.206360 0.103180 0.994663i \(-0.467098\pi\)
0.103180 + 0.994663i \(0.467098\pi\)
\(608\) 0 0
\(609\) −10.2693 −0.416132
\(610\) 0 0
\(611\) −24.2469 −0.980923
\(612\) 0 0
\(613\) 4.63706 0.187289 0.0936445 0.995606i \(-0.470148\pi\)
0.0936445 + 0.995606i \(0.470148\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 40.2874 1.62191 0.810955 0.585108i \(-0.198948\pi\)
0.810955 + 0.585108i \(0.198948\pi\)
\(618\) 0 0
\(619\) 43.3815 1.74365 0.871825 0.489818i \(-0.162937\pi\)
0.871825 + 0.489818i \(0.162937\pi\)
\(620\) 0 0
\(621\) 8.00000 0.321029
\(622\) 0 0
\(623\) 52.6940 2.11114
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.23180 0.0891296
\(628\) 0 0
\(629\) 24.9326 0.994129
\(630\) 0 0
\(631\) −7.53369 −0.299911 −0.149956 0.988693i \(-0.547913\pi\)
−0.149956 + 0.988693i \(0.547913\pi\)
\(632\) 0 0
\(633\) −8.45040 −0.335873
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.53446 0.258905
\(638\) 0 0
\(639\) 37.1795 1.47080
\(640\) 0 0
\(641\) −23.3075 −0.920591 −0.460296 0.887766i \(-0.652257\pi\)
−0.460296 + 0.887766i \(0.652257\pi\)
\(642\) 0 0
\(643\) −1.87419 −0.0739110 −0.0369555 0.999317i \(-0.511766\pi\)
−0.0369555 + 0.999317i \(0.511766\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 47.0371 1.84922 0.924609 0.380917i \(-0.124392\pi\)
0.924609 + 0.380917i \(0.124392\pi\)
\(648\) 0 0
\(649\) −7.11222 −0.279179
\(650\) 0 0
\(651\) 4.44887 0.174365
\(652\) 0 0
\(653\) 24.1630 0.945571 0.472785 0.881178i \(-0.343249\pi\)
0.472785 + 0.881178i \(0.343249\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 7.39477 0.288497
\(658\) 0 0
\(659\) −10.2885 −0.400781 −0.200391 0.979716i \(-0.564221\pi\)
−0.200391 + 0.979716i \(0.564221\pi\)
\(660\) 0 0
\(661\) 5.93598 0.230883 0.115441 0.993314i \(-0.463172\pi\)
0.115441 + 0.993314i \(0.463172\pi\)
\(662\) 0 0
\(663\) −6.44496 −0.250302
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 15.6476 0.605879
\(668\) 0 0
\(669\) 10.1089 0.390831
\(670\) 0 0
\(671\) 36.3799 1.40443
\(672\) 0 0
\(673\) −40.7053 −1.56907 −0.784537 0.620082i \(-0.787099\pi\)
−0.784537 + 0.620082i \(0.787099\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.8761 0.725469 0.362734 0.931893i \(-0.381843\pi\)
0.362734 + 0.931893i \(0.381843\pi\)
\(678\) 0 0
\(679\) 6.59933 0.253259
\(680\) 0 0
\(681\) −7.75638 −0.297225
\(682\) 0 0
\(683\) 19.6576 0.752179 0.376089 0.926583i \(-0.377269\pi\)
0.376089 + 0.926583i \(0.377269\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.24384 0.0856079
\(688\) 0 0
\(689\) 24.3333 0.927025
\(690\) 0 0
\(691\) 48.2451 1.83533 0.917665 0.397354i \(-0.130072\pi\)
0.917665 + 0.397354i \(0.130072\pi\)
\(692\) 0 0
\(693\) 35.9073 1.36401
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.47293 −0.131546
\(698\) 0 0
\(699\) −6.49047 −0.245492
\(700\) 0 0
\(701\) 0.512889 0.0193715 0.00968577 0.999953i \(-0.496917\pi\)
0.00968577 + 0.999953i \(0.496917\pi\)
\(702\) 0 0
\(703\) 4.30266 0.162278
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.45428 −0.205129
\(708\) 0 0
\(709\) −8.84618 −0.332225 −0.166113 0.986107i \(-0.553122\pi\)
−0.166113 + 0.986107i \(0.553122\pi\)
\(710\) 0 0
\(711\) −3.79798 −0.142436
\(712\) 0 0
\(713\) −6.77889 −0.253871
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.09806 −0.227736
\(718\) 0 0
\(719\) −7.84456 −0.292553 −0.146276 0.989244i \(-0.546729\pi\)
−0.146276 + 0.989244i \(0.546729\pi\)
\(720\) 0 0
\(721\) −18.3333 −0.682767
\(722\) 0 0
\(723\) 1.82643 0.0679258
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.91130 0.107974 0.0539870 0.998542i \(-0.482807\pi\)
0.0539870 + 0.998542i \(0.482807\pi\)
\(728\) 0 0
\(729\) −12.6475 −0.468427
\(730\) 0 0
\(731\) −18.4663 −0.683001
\(732\) 0 0
\(733\) −33.7775 −1.24760 −0.623800 0.781584i \(-0.714412\pi\)
−0.623800 + 0.781584i \(0.714412\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.7893 0.728950
\(738\) 0 0
\(739\) 35.8030 1.31703 0.658517 0.752566i \(-0.271184\pi\)
0.658517 + 0.752566i \(0.271184\pi\)
\(740\) 0 0
\(741\) −1.11222 −0.0408583
\(742\) 0 0
\(743\) 5.66948 0.207993 0.103996 0.994578i \(-0.466837\pi\)
0.103996 + 0.994578i \(0.466837\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −19.1748 −0.701569
\(748\) 0 0
\(749\) 49.1795 1.79698
\(750\) 0 0
\(751\) 27.4679 1.00232 0.501159 0.865355i \(-0.332907\pi\)
0.501159 + 0.865355i \(0.332907\pi\)
\(752\) 0 0
\(753\) 1.63445 0.0595628
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −41.6370 −1.51332 −0.756662 0.653806i \(-0.773171\pi\)
−0.756662 + 0.653806i \(0.773171\pi\)
\(758\) 0 0
\(759\) 5.82040 0.211267
\(760\) 0 0
\(761\) −9.46967 −0.343275 −0.171638 0.985160i \(-0.554906\pi\)
−0.171638 + 0.985160i \(0.554906\pi\)
\(762\) 0 0
\(763\) 37.3219 1.35114
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.54437 0.127980
\(768\) 0 0
\(769\) 1.90858 0.0688253 0.0344127 0.999408i \(-0.489044\pi\)
0.0344127 + 0.999408i \(0.489044\pi\)
\(770\) 0 0
\(771\) −9.28510 −0.334395
\(772\) 0 0
\(773\) −28.4007 −1.02150 −0.510751 0.859729i \(-0.670633\pi\)
−0.510751 + 0.859729i \(0.670633\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −7.36420 −0.264189
\(778\) 0 0
\(779\) −0.599328 −0.0214732
\(780\) 0 0
\(781\) 56.9775 2.03881
\(782\) 0 0
\(783\) 18.4053 0.657753
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15.6708 −0.558605 −0.279303 0.960203i \(-0.590103\pi\)
−0.279303 + 0.960203i \(0.590103\pi\)
\(788\) 0 0
\(789\) −0.640931 −0.0228178
\(790\) 0 0
\(791\) −33.7564 −1.20024
\(792\) 0 0
\(793\) −18.1299 −0.643811
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.9225 −1.30786 −0.653932 0.756554i \(-0.726882\pi\)
−0.653932 + 0.756554i \(0.726882\pi\)
\(798\) 0 0
\(799\) −67.8478 −2.40028
\(800\) 0 0
\(801\) −44.8362 −1.58421
\(802\) 0 0
\(803\) 11.3325 0.399914
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −11.8742 −0.417993
\(808\) 0 0
\(809\) 43.0465 1.51343 0.756716 0.653743i \(-0.226802\pi\)
0.756716 + 0.653743i \(0.226802\pi\)
\(810\) 0 0
\(811\) −32.2469 −1.13234 −0.566170 0.824288i \(-0.691575\pi\)
−0.566170 + 0.824288i \(0.691575\pi\)
\(812\) 0 0
\(813\) −2.19475 −0.0769731
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −3.18676 −0.111491
\(818\) 0 0
\(819\) −17.8944 −0.625280
\(820\) 0 0
\(821\) 5.18121 0.180826 0.0904128 0.995904i \(-0.471181\pi\)
0.0904128 + 0.995904i \(0.471181\pi\)
\(822\) 0 0
\(823\) 25.8517 0.901133 0.450567 0.892743i \(-0.351222\pi\)
0.450567 + 0.892743i \(0.351222\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.97816 0.346974 0.173487 0.984836i \(-0.444496\pi\)
0.173487 + 0.984836i \(0.444496\pi\)
\(828\) 0 0
\(829\) 21.9808 0.763425 0.381713 0.924281i \(-0.375334\pi\)
0.381713 + 0.924281i \(0.375334\pi\)
\(830\) 0 0
\(831\) 5.38149 0.186682
\(832\) 0 0
\(833\) 18.2848 0.633531
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −7.97359 −0.275607
\(838\) 0 0
\(839\) 16.1089 0.556140 0.278070 0.960561i \(-0.410305\pi\)
0.278070 + 0.960561i \(0.410305\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) −0.321887 −0.0110864
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 19.9735 0.686298
\(848\) 0 0
\(849\) 2.91020 0.0998779
\(850\) 0 0
\(851\) 11.2211 0.384653
\(852\) 0 0
\(853\) 44.9615 1.53945 0.769727 0.638373i \(-0.220392\pi\)
0.769727 + 0.638373i \(0.220392\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −46.2431 −1.57963 −0.789817 0.613343i \(-0.789824\pi\)
−0.789817 + 0.613343i \(0.789824\pi\)
\(858\) 0 0
\(859\) 10.7772 0.367713 0.183856 0.982953i \(-0.441142\pi\)
0.183856 + 0.982953i \(0.441142\pi\)
\(860\) 0 0
\(861\) 1.02578 0.0349584
\(862\) 0 0
\(863\) −22.7966 −0.776007 −0.388003 0.921658i \(-0.626835\pi\)
−0.388003 + 0.921658i \(0.626835\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.90400 −0.302396
\(868\) 0 0
\(869\) −5.82040 −0.197444
\(870\) 0 0
\(871\) −9.86201 −0.334161
\(872\) 0 0
\(873\) −5.61523 −0.190047
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −4.94644 −0.167029 −0.0835146 0.996507i \(-0.526615\pi\)
−0.0835146 + 0.996507i \(0.526615\pi\)
\(878\) 0 0
\(879\) −1.86201 −0.0628039
\(880\) 0 0
\(881\) 2.53033 0.0852490 0.0426245 0.999091i \(-0.486428\pi\)
0.0426245 + 0.999091i \(0.486428\pi\)
\(882\) 0 0
\(883\) −29.7430 −1.00093 −0.500465 0.865757i \(-0.666838\pi\)
−0.500465 + 0.865757i \(0.666838\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −45.5450 −1.52925 −0.764626 0.644474i \(-0.777076\pi\)
−0.764626 + 0.644474i \(0.777076\pi\)
\(888\) 0 0
\(889\) 19.3591 0.649282
\(890\) 0 0
\(891\) −26.9568 −0.903086
\(892\) 0 0
\(893\) −11.7086 −0.391813
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2.90059 −0.0968480
\(898\) 0 0
\(899\) −15.5960 −0.520155
\(900\) 0 0
\(901\) 68.0897 2.26840
\(902\) 0 0
\(903\) 5.45428 0.181507
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −33.2034 −1.10250 −0.551250 0.834340i \(-0.685849\pi\)
−0.551250 + 0.834340i \(0.685849\pi\)
\(908\) 0 0
\(909\) 4.64093 0.153930
\(910\) 0 0
\(911\) −55.7788 −1.84803 −0.924017 0.382351i \(-0.875114\pi\)
−0.924017 + 0.382351i \(0.875114\pi\)
\(912\) 0 0
\(913\) −29.3853 −0.972513
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 43.2715 1.42895
\(918\) 0 0
\(919\) 28.5769 0.942665 0.471333 0.881956i \(-0.343773\pi\)
0.471333 + 0.881956i \(0.343773\pi\)
\(920\) 0 0
\(921\) −8.91020 −0.293601
\(922\) 0 0
\(923\) −28.3947 −0.934622
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 15.5994 0.512352
\(928\) 0 0
\(929\) −54.4937 −1.78788 −0.893940 0.448186i \(-0.852070\pi\)
−0.893940 + 0.448186i \(0.852070\pi\)
\(930\) 0 0
\(931\) 3.15544 0.103415
\(932\) 0 0
\(933\) −2.23180 −0.0730659
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −37.1484 −1.21359 −0.606793 0.794860i \(-0.707544\pi\)
−0.606793 + 0.794860i \(0.707544\pi\)
\(938\) 0 0
\(939\) 0.493704 0.0161114
\(940\) 0 0
\(941\) 32.3973 1.05612 0.528061 0.849206i \(-0.322919\pi\)
0.528061 + 0.849206i \(0.322919\pi\)
\(942\) 0 0
\(943\) −1.56301 −0.0508986
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −35.4662 −1.15250 −0.576249 0.817275i \(-0.695484\pi\)
−0.576249 + 0.817275i \(0.695484\pi\)
\(948\) 0 0
\(949\) −5.64752 −0.183326
\(950\) 0 0
\(951\) 14.3557 0.465516
\(952\) 0 0
\(953\) −14.3411 −0.464553 −0.232277 0.972650i \(-0.574617\pi\)
−0.232277 + 0.972650i \(0.574617\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 13.3908 0.432864
\(958\) 0 0
\(959\) −25.3125 −0.817383
\(960\) 0 0
\(961\) −24.2435 −0.782048
\(962\) 0 0
\(963\) −41.8458 −1.34846
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 27.9351 0.898331 0.449165 0.893449i \(-0.351721\pi\)
0.449165 + 0.893449i \(0.351721\pi\)
\(968\) 0 0
\(969\) −3.11222 −0.0999788
\(970\) 0 0
\(971\) 42.5993 1.36708 0.683539 0.729914i \(-0.260440\pi\)
0.683539 + 0.729914i \(0.260440\pi\)
\(972\) 0 0
\(973\) −10.4132 −0.333833
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 39.5597 1.26563 0.632813 0.774304i \(-0.281900\pi\)
0.632813 + 0.774304i \(0.281900\pi\)
\(978\) 0 0
\(979\) −68.7114 −2.19603
\(980\) 0 0
\(981\) −31.7564 −1.01390
\(982\) 0 0
\(983\) 39.7689 1.26843 0.634215 0.773157i \(-0.281323\pi\)
0.634215 + 0.773157i \(0.281323\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 20.0398 0.637874
\(988\) 0 0
\(989\) −8.31087 −0.264270
\(990\) 0 0
\(991\) −55.2019 −1.75355 −0.876773 0.480905i \(-0.840308\pi\)
−0.876773 + 0.480905i \(0.840308\pi\)
\(992\) 0 0
\(993\) 4.29664 0.136350
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −11.6543 −0.369097 −0.184548 0.982823i \(-0.559082\pi\)
−0.184548 + 0.982823i \(0.559082\pi\)
\(998\) 0 0
\(999\) 13.1987 0.417587
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 7600.2.a.ck.1.3 6
4.3 odd 2 475.2.a.j.1.1 6
5.2 odd 4 1520.2.d.h.609.4 6
5.3 odd 4 1520.2.d.h.609.3 6
5.4 even 2 inner 7600.2.a.ck.1.4 6
12.11 even 2 4275.2.a.br.1.6 6
20.3 even 4 95.2.b.b.39.6 yes 6
20.7 even 4 95.2.b.b.39.1 6
20.19 odd 2 475.2.a.j.1.6 6
60.23 odd 4 855.2.c.d.514.1 6
60.47 odd 4 855.2.c.d.514.6 6
60.59 even 2 4275.2.a.br.1.1 6
76.75 even 2 9025.2.a.bx.1.6 6
380.227 odd 4 1805.2.b.e.1084.6 6
380.303 odd 4 1805.2.b.e.1084.1 6
380.379 even 2 9025.2.a.bx.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.b.b.39.1 6 20.7 even 4
95.2.b.b.39.6 yes 6 20.3 even 4
475.2.a.j.1.1 6 4.3 odd 2
475.2.a.j.1.6 6 20.19 odd 2
855.2.c.d.514.1 6 60.23 odd 4
855.2.c.d.514.6 6 60.47 odd 4
1520.2.d.h.609.3 6 5.3 odd 4
1520.2.d.h.609.4 6 5.2 odd 4
1805.2.b.e.1084.1 6 380.303 odd 4
1805.2.b.e.1084.6 6 380.227 odd 4
4275.2.a.br.1.1 6 60.59 even 2
4275.2.a.br.1.6 6 12.11 even 2
7600.2.a.ck.1.3 6 1.1 even 1 trivial
7600.2.a.ck.1.4 6 5.4 even 2 inner
9025.2.a.bx.1.1 6 380.379 even 2
9025.2.a.bx.1.6 6 76.75 even 2