Properties

Label 1900.2.a.k.1.2
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.56310016.1
Defining polynomial: \( x^{6} - 9x^{4} + 14x^{2} - 4 \) 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 380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.23277\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.62236 q^{3} -4.74397 q^{7} -0.367938 q^{9} +O(q^{10})\) \(q-1.62236 q^{3} -4.74397 q^{7} -0.367938 q^{9} +4.48028 q^{11} -0.843176 q^{13} -5.52315 q^{17} +1.00000 q^{19} +7.69643 q^{21} +0.779187 q^{23} +5.46402 q^{27} -10.6570 q^{29} -8.65699 q^{31} -7.26864 q^{33} -1.62236 q^{37} +1.36794 q^{39} +4.73588 q^{41} +9.67504 q^{43} -3.18559 q^{47} +15.5052 q^{49} +8.96056 q^{51} +6.17922 q^{53} -1.62236 q^{57} +11.6964 q^{59} +6.48028 q^{61} +1.74549 q^{63} +14.8880 q^{67} -1.26412 q^{69} +0.303566 q^{71} -10.0800 q^{73} -21.2543 q^{77} +4.00000 q^{79} -7.76081 q^{81} -0.779187 q^{83} +17.2895 q^{87} -5.69643 q^{89} +4.00000 q^{91} +14.0448 q^{93} +6.17922 q^{97} -1.64847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 10 q^{9} + 18 q^{11} + 6 q^{19} + 4 q^{21} - 4 q^{29} + 8 q^{31} - 4 q^{39} + 4 q^{41} + 12 q^{49} + 36 q^{51} + 28 q^{59} + 30 q^{61} - 32 q^{69} + 44 q^{71} + 24 q^{79} + 50 q^{81} + 8 q^{89} + 24 q^{91} + 90 q^{99}+O(q^{100}) \) 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
\(3\) −1.62236 −0.936672 −0.468336 0.883551i \(-0.655146\pi\)
−0.468336 + 0.883551i \(0.655146\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.74397 −1.79305 −0.896525 0.442993i \(-0.853917\pi\)
−0.896525 + 0.442993i \(0.853917\pi\)
\(8\) 0 0
\(9\) −0.367938 −0.122646
\(10\) 0 0
\(11\) 4.48028 1.35085 0.675427 0.737426i \(-0.263959\pi\)
0.675427 + 0.737426i \(0.263959\pi\)
\(12\) 0 0
\(13\) −0.843176 −0.233855 −0.116928 0.993140i \(-0.537305\pi\)
−0.116928 + 0.993140i \(0.537305\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.52315 −1.33956 −0.669781 0.742559i \(-0.733612\pi\)
−0.669781 + 0.742559i \(0.733612\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 7.69643 1.67950
\(22\) 0 0
\(23\) 0.779187 0.162472 0.0812358 0.996695i \(-0.474113\pi\)
0.0812358 + 0.996695i \(0.474113\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.46402 1.05155
\(28\) 0 0
\(29\) −10.6570 −1.97895 −0.989477 0.144691i \(-0.953781\pi\)
−0.989477 + 0.144691i \(0.953781\pi\)
\(30\) 0 0
\(31\) −8.65699 −1.55484 −0.777421 0.628981i \(-0.783472\pi\)
−0.777421 + 0.628981i \(0.783472\pi\)
\(32\) 0 0
\(33\) −7.26864 −1.26531
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.62236 −0.266715 −0.133357 0.991068i \(-0.542576\pi\)
−0.133357 + 0.991068i \(0.542576\pi\)
\(38\) 0 0
\(39\) 1.36794 0.219045
\(40\) 0 0
\(41\) 4.73588 0.739620 0.369810 0.929107i \(-0.379423\pi\)
0.369810 + 0.929107i \(0.379423\pi\)
\(42\) 0 0
\(43\) 9.67504 1.47543 0.737715 0.675112i \(-0.235905\pi\)
0.737715 + 0.675112i \(0.235905\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.18559 −0.464666 −0.232333 0.972636i \(-0.574636\pi\)
−0.232333 + 0.972636i \(0.574636\pi\)
\(48\) 0 0
\(49\) 15.5052 2.21503
\(50\) 0 0
\(51\) 8.96056 1.25473
\(52\) 0 0
\(53\) 6.17922 0.848780 0.424390 0.905479i \(-0.360488\pi\)
0.424390 + 0.905479i \(0.360488\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.62236 −0.214887
\(58\) 0 0
\(59\) 11.6964 1.52275 0.761373 0.648314i \(-0.224526\pi\)
0.761373 + 0.648314i \(0.224526\pi\)
\(60\) 0 0
\(61\) 6.48028 0.829715 0.414857 0.909886i \(-0.363831\pi\)
0.414857 + 0.909886i \(0.363831\pi\)
\(62\) 0 0
\(63\) 1.74549 0.219911
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.8880 1.81885 0.909427 0.415864i \(-0.136521\pi\)
0.909427 + 0.415864i \(0.136521\pi\)
\(68\) 0 0
\(69\) −1.26412 −0.152183
\(70\) 0 0
\(71\) 0.303566 0.0360266 0.0180133 0.999838i \(-0.494266\pi\)
0.0180133 + 0.999838i \(0.494266\pi\)
\(72\) 0 0
\(73\) −10.0800 −1.17978 −0.589888 0.807485i \(-0.700828\pi\)
−0.589888 + 0.807485i \(0.700828\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −21.2543 −2.42215
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) −7.76081 −0.862312
\(82\) 0 0
\(83\) −0.779187 −0.0855268 −0.0427634 0.999085i \(-0.513616\pi\)
−0.0427634 + 0.999085i \(0.513616\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 17.2895 1.85363
\(88\) 0 0
\(89\) −5.69643 −0.603821 −0.301910 0.953336i \(-0.597624\pi\)
−0.301910 + 0.953336i \(0.597624\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 14.0448 1.45638
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.17922 0.627404 0.313702 0.949521i \(-0.398431\pi\)
0.313702 + 0.949521i \(0.398431\pi\)
\(98\) 0 0
\(99\) −1.64847 −0.165677
\(100\) 0 0
\(101\) 3.36794 0.335122 0.167561 0.985862i \(-0.446411\pi\)
0.167561 + 0.985862i \(0.446411\pi\)
\(102\) 0 0
\(103\) −3.71368 −0.365919 −0.182960 0.983120i \(-0.558568\pi\)
−0.182960 + 0.983120i \(0.558568\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.2031 0.986374 0.493187 0.869923i \(-0.335832\pi\)
0.493187 + 0.869923i \(0.335832\pi\)
\(108\) 0 0
\(109\) 2.96056 0.283570 0.141785 0.989897i \(-0.454716\pi\)
0.141785 + 0.989897i \(0.454716\pi\)
\(110\) 0 0
\(111\) 2.63206 0.249824
\(112\) 0 0
\(113\) −7.08638 −0.666631 −0.333315 0.942815i \(-0.608167\pi\)
−0.333315 + 0.942815i \(0.608167\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.310237 0.0286814
\(118\) 0 0
\(119\) 26.2016 2.40190
\(120\) 0 0
\(121\) 9.07290 0.824809
\(122\) 0 0
\(123\) −7.68331 −0.692781
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.79817 0.869447 0.434723 0.900564i \(-0.356846\pi\)
0.434723 + 0.900564i \(0.356846\pi\)
\(128\) 0 0
\(129\) −15.6964 −1.38199
\(130\) 0 0
\(131\) 12.5841 1.09948 0.549739 0.835337i \(-0.314727\pi\)
0.549739 + 0.835337i \(0.314727\pi\)
\(132\) 0 0
\(133\) −4.74397 −0.411354
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.89586 0.760024 0.380012 0.924981i \(-0.375920\pi\)
0.380012 + 0.924981i \(0.375920\pi\)
\(138\) 0 0
\(139\) 6.25560 0.530593 0.265296 0.964167i \(-0.414530\pi\)
0.265296 + 0.964167i \(0.414530\pi\)
\(140\) 0 0
\(141\) 5.16819 0.435240
\(142\) 0 0
\(143\) −3.77767 −0.315904
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −25.1551 −2.07476
\(148\) 0 0
\(149\) 2.48028 0.203192 0.101596 0.994826i \(-0.467605\pi\)
0.101596 + 0.994826i \(0.467605\pi\)
\(150\) 0 0
\(151\) 3.69643 0.300812 0.150406 0.988624i \(-0.451942\pi\)
0.150406 + 0.988624i \(0.451942\pi\)
\(152\) 0 0
\(153\) 2.03218 0.164292
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.8479 1.50422 0.752112 0.659035i \(-0.229035\pi\)
0.752112 + 0.659035i \(0.229035\pi\)
\(158\) 0 0
\(159\) −10.0249 −0.795029
\(160\) 0 0
\(161\) −3.69643 −0.291320
\(162\) 0 0
\(163\) 2.46554 0.193116 0.0965580 0.995327i \(-0.469217\pi\)
0.0965580 + 0.995327i \(0.469217\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.49134 −0.579697 −0.289849 0.957072i \(-0.593605\pi\)
−0.289849 + 0.957072i \(0.593605\pi\)
\(168\) 0 0
\(169\) −12.2891 −0.945312
\(170\) 0 0
\(171\) −0.367938 −0.0281369
\(172\) 0 0
\(173\) −20.0653 −1.52554 −0.762768 0.646673i \(-0.776160\pi\)
−0.762768 + 0.646673i \(0.776160\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.9759 −1.42631
\(178\) 0 0
\(179\) −3.69643 −0.276284 −0.138142 0.990412i \(-0.544113\pi\)
−0.138142 + 0.990412i \(0.544113\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −10.5134 −0.777170
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −24.7453 −1.80955
\(188\) 0 0
\(189\) −25.9211 −1.88548
\(190\) 0 0
\(191\) 0.887659 0.0642288 0.0321144 0.999484i \(-0.489776\pi\)
0.0321144 + 0.999484i \(0.489776\pi\)
\(192\) 0 0
\(193\) 19.1581 1.37903 0.689516 0.724271i \(-0.257823\pi\)
0.689516 + 0.724271i \(0.257823\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.37271 0.240295 0.120148 0.992756i \(-0.461663\pi\)
0.120148 + 0.992756i \(0.461663\pi\)
\(198\) 0 0
\(199\) 4.58409 0.324958 0.162479 0.986712i \(-0.448051\pi\)
0.162479 + 0.986712i \(0.448051\pi\)
\(200\) 0 0
\(201\) −24.1537 −1.70367
\(202\) 0 0
\(203\) 50.5564 3.54836
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.286693 −0.0199265
\(208\) 0 0
\(209\) 4.48028 0.309907
\(210\) 0 0
\(211\) −14.8817 −1.02450 −0.512248 0.858837i \(-0.671187\pi\)
−0.512248 + 0.858837i \(0.671187\pi\)
\(212\) 0 0
\(213\) −0.492494 −0.0337451
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 41.0685 2.78791
\(218\) 0 0
\(219\) 16.3534 1.10506
\(220\) 0 0
\(221\) 4.65699 0.313263
\(222\) 0 0
\(223\) 18.7839 1.25786 0.628931 0.777461i \(-0.283493\pi\)
0.628931 + 0.777461i \(0.283493\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.843176 −0.0559636 −0.0279818 0.999608i \(-0.508908\pi\)
−0.0279818 + 0.999608i \(0.508908\pi\)
\(228\) 0 0
\(229\) −4.86273 −0.321338 −0.160669 0.987008i \(-0.551365\pi\)
−0.160669 + 0.987008i \(0.551365\pi\)
\(230\) 0 0
\(231\) 34.4822 2.26876
\(232\) 0 0
\(233\) −4.90268 −0.321185 −0.160593 0.987021i \(-0.551341\pi\)
−0.160593 + 0.987021i \(0.551341\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.48945 −0.421535
\(238\) 0 0
\(239\) −6.20164 −0.401151 −0.200575 0.979678i \(-0.564281\pi\)
−0.200575 + 0.979678i \(0.564281\pi\)
\(240\) 0 0
\(241\) −3.26412 −0.210261 −0.105130 0.994458i \(-0.533526\pi\)
−0.105130 + 0.994458i \(0.533526\pi\)
\(242\) 0 0
\(243\) −3.80121 −0.243848
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.843176 −0.0536500
\(248\) 0 0
\(249\) 1.26412 0.0801106
\(250\) 0 0
\(251\) 28.4263 1.79425 0.897127 0.441773i \(-0.145650\pi\)
0.897127 + 0.441773i \(0.145650\pi\)
\(252\) 0 0
\(253\) 3.49097 0.219476
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.55192 −0.595832 −0.297916 0.954592i \(-0.596292\pi\)
−0.297916 + 0.954592i \(0.596292\pi\)
\(258\) 0 0
\(259\) 7.69643 0.478233
\(260\) 0 0
\(261\) 3.92112 0.242711
\(262\) 0 0
\(263\) −9.54706 −0.588697 −0.294349 0.955698i \(-0.595103\pi\)
−0.294349 + 0.955698i \(0.595103\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.24168 0.565582
\(268\) 0 0
\(269\) −14.3534 −0.875144 −0.437572 0.899183i \(-0.644161\pi\)
−0.437572 + 0.899183i \(0.644161\pi\)
\(270\) 0 0
\(271\) −12.1038 −0.735254 −0.367627 0.929973i \(-0.619830\pi\)
−0.367627 + 0.929973i \(0.619830\pi\)
\(272\) 0 0
\(273\) −6.48945 −0.392760
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3.59055 0.215735 0.107868 0.994165i \(-0.465598\pi\)
0.107868 + 0.994165i \(0.465598\pi\)
\(278\) 0 0
\(279\) 3.18524 0.190695
\(280\) 0 0
\(281\) 26.7069 1.59320 0.796599 0.604509i \(-0.206631\pi\)
0.796599 + 0.604509i \(0.206631\pi\)
\(282\) 0 0
\(283\) −20.4751 −1.21712 −0.608559 0.793508i \(-0.708252\pi\)
−0.608559 + 0.793508i \(0.708252\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.4668 −1.32618
\(288\) 0 0
\(289\) 13.5052 0.794424
\(290\) 0 0
\(291\) −10.0249 −0.587672
\(292\) 0 0
\(293\) 19.1581 1.11923 0.559615 0.828753i \(-0.310949\pi\)
0.559615 + 0.828753i \(0.310949\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 24.4803 1.42049
\(298\) 0 0
\(299\) −0.656992 −0.0379948
\(300\) 0 0
\(301\) −45.8981 −2.64552
\(302\) 0 0
\(303\) −5.46402 −0.313900
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −32.0495 −1.82916 −0.914580 0.404404i \(-0.867479\pi\)
−0.914580 + 0.404404i \(0.867479\pi\)
\(308\) 0 0
\(309\) 6.02493 0.342746
\(310\) 0 0
\(311\) −20.5301 −1.16416 −0.582079 0.813132i \(-0.697760\pi\)
−0.582079 + 0.813132i \(0.697760\pi\)
\(312\) 0 0
\(313\) 14.7932 0.836163 0.418082 0.908409i \(-0.362703\pi\)
0.418082 + 0.908409i \(0.362703\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.9485 0.951925 0.475962 0.879466i \(-0.342100\pi\)
0.475962 + 0.879466i \(0.342100\pi\)
\(318\) 0 0
\(319\) −47.7463 −2.67328
\(320\) 0 0
\(321\) −16.5532 −0.923908
\(322\) 0 0
\(323\) −5.52315 −0.307316
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.80310 −0.265612
\(328\) 0 0
\(329\) 15.1123 0.833170
\(330\) 0 0
\(331\) −22.1287 −1.21631 −0.608153 0.793820i \(-0.708089\pi\)
−0.608153 + 0.793820i \(0.708089\pi\)
\(332\) 0 0
\(333\) 0.596929 0.0327115
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −27.9948 −1.52498 −0.762488 0.647002i \(-0.776022\pi\)
−0.762488 + 0.647002i \(0.776022\pi\)
\(338\) 0 0
\(339\) 11.4967 0.624414
\(340\) 0 0
\(341\) −38.7857 −2.10037
\(342\) 0 0
\(343\) −40.3484 −2.17861
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.1024 0.918105 0.459052 0.888409i \(-0.348189\pi\)
0.459052 + 0.888409i \(0.348189\pi\)
\(348\) 0 0
\(349\) −19.2411 −1.02995 −0.514976 0.857205i \(-0.672199\pi\)
−0.514976 + 0.857205i \(0.672199\pi\)
\(350\) 0 0
\(351\) −4.60713 −0.245910
\(352\) 0 0
\(353\) −7.42735 −0.395318 −0.197659 0.980271i \(-0.563334\pi\)
−0.197659 + 0.980271i \(0.563334\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −42.5086 −2.24979
\(358\) 0 0
\(359\) 28.1767 1.48711 0.743555 0.668675i \(-0.233138\pi\)
0.743555 + 0.668675i \(0.233138\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −14.7195 −0.772575
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 26.1165 1.36327 0.681636 0.731692i \(-0.261269\pi\)
0.681636 + 0.731692i \(0.261269\pi\)
\(368\) 0 0
\(369\) −1.74251 −0.0907115
\(370\) 0 0
\(371\) −29.3140 −1.52191
\(372\) 0 0
\(373\) 0.438217 0.0226900 0.0113450 0.999936i \(-0.496389\pi\)
0.0113450 + 0.999936i \(0.496389\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.98572 0.462788
\(378\) 0 0
\(379\) −13.7753 −0.707591 −0.353795 0.935323i \(-0.615109\pi\)
−0.353795 + 0.935323i \(0.615109\pi\)
\(380\) 0 0
\(381\) −15.8962 −0.814386
\(382\) 0 0
\(383\) 22.3153 1.14026 0.570130 0.821555i \(-0.306893\pi\)
0.570130 + 0.821555i \(0.306893\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.55982 −0.180956
\(388\) 0 0
\(389\) 14.4263 0.731444 0.365722 0.930724i \(-0.380822\pi\)
0.365722 + 0.930724i \(0.380822\pi\)
\(390\) 0 0
\(391\) −4.30357 −0.217641
\(392\) 0 0
\(393\) −20.4160 −1.02985
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 16.4512 0.825662 0.412831 0.910808i \(-0.364540\pi\)
0.412831 + 0.910808i \(0.364540\pi\)
\(398\) 0 0
\(399\) 7.69643 0.385304
\(400\) 0 0
\(401\) 2.96056 0.147843 0.0739216 0.997264i \(-0.476449\pi\)
0.0739216 + 0.997264i \(0.476449\pi\)
\(402\) 0 0
\(403\) 7.29937 0.363608
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.26864 −0.360293
\(408\) 0 0
\(409\) 17.0893 0.845012 0.422506 0.906360i \(-0.361151\pi\)
0.422506 + 0.906360i \(0.361151\pi\)
\(410\) 0 0
\(411\) −14.4323 −0.711893
\(412\) 0 0
\(413\) −55.4875 −2.73036
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.1489 −0.496991
\(418\) 0 0
\(419\) −15.3929 −0.751991 −0.375995 0.926622i \(-0.622699\pi\)
−0.375995 + 0.926622i \(0.622699\pi\)
\(420\) 0 0
\(421\) −16.4323 −0.800862 −0.400431 0.916327i \(-0.631140\pi\)
−0.400431 + 0.916327i \(0.631140\pi\)
\(422\) 0 0
\(423\) 1.17210 0.0569895
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −30.7422 −1.48772
\(428\) 0 0
\(429\) 6.12874 0.295899
\(430\) 0 0
\(431\) 15.1852 0.731447 0.365724 0.930724i \(-0.380822\pi\)
0.365724 + 0.930724i \(0.380822\pi\)
\(432\) 0 0
\(433\) −23.4380 −1.12636 −0.563179 0.826335i \(-0.690422\pi\)
−0.563179 + 0.826335i \(0.690422\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.779187 0.0372735
\(438\) 0 0
\(439\) 0.511196 0.0243980 0.0121990 0.999926i \(-0.496117\pi\)
0.0121990 + 0.999926i \(0.496117\pi\)
\(440\) 0 0
\(441\) −5.70496 −0.271665
\(442\) 0 0
\(443\) 19.7834 0.939940 0.469970 0.882682i \(-0.344265\pi\)
0.469970 + 0.882682i \(0.344265\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.02391 −0.190325
\(448\) 0 0
\(449\) 31.1682 1.47092 0.735459 0.677569i \(-0.236967\pi\)
0.735459 + 0.677569i \(0.236967\pi\)
\(450\) 0 0
\(451\) 21.2180 0.999119
\(452\) 0 0
\(453\) −5.99696 −0.281762
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.20950 0.337246 0.168623 0.985681i \(-0.446068\pi\)
0.168623 + 0.985681i \(0.446068\pi\)
\(458\) 0 0
\(459\) −30.1786 −1.40862
\(460\) 0 0
\(461\) −5.41591 −0.252244 −0.126122 0.992015i \(-0.540253\pi\)
−0.126122 + 0.992015i \(0.540253\pi\)
\(462\) 0 0
\(463\) −8.73715 −0.406050 −0.203025 0.979174i \(-0.565077\pi\)
−0.203025 + 0.979174i \(0.565077\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.3584 0.803249 0.401624 0.915804i \(-0.368446\pi\)
0.401624 + 0.915804i \(0.368446\pi\)
\(468\) 0 0
\(469\) −70.6280 −3.26130
\(470\) 0 0
\(471\) −30.5781 −1.40896
\(472\) 0 0
\(473\) 43.3469 1.99309
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −2.27357 −0.104100
\(478\) 0 0
\(479\) 7.44682 0.340254 0.170127 0.985422i \(-0.445582\pi\)
0.170127 + 0.985422i \(0.445582\pi\)
\(480\) 0 0
\(481\) 1.36794 0.0623726
\(482\) 0 0
\(483\) 5.99696 0.272871
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −2.15530 −0.0976661 −0.0488330 0.998807i \(-0.515550\pi\)
−0.0488330 + 0.998807i \(0.515550\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 29.3140 1.32292 0.661461 0.749980i \(-0.269937\pi\)
0.661461 + 0.749980i \(0.269937\pi\)
\(492\) 0 0
\(493\) 58.8602 2.65093
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.44011 −0.0645976
\(498\) 0 0
\(499\) −23.5696 −1.05512 −0.527560 0.849518i \(-0.676893\pi\)
−0.527560 + 0.849518i \(0.676893\pi\)
\(500\) 0 0
\(501\) 12.1537 0.542986
\(502\) 0 0
\(503\) 9.08297 0.404990 0.202495 0.979283i \(-0.435095\pi\)
0.202495 + 0.979283i \(0.435095\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 19.9373 0.885447
\(508\) 0 0
\(509\) −18.5112 −0.820494 −0.410247 0.911974i \(-0.634558\pi\)
−0.410247 + 0.911974i \(0.634558\pi\)
\(510\) 0 0
\(511\) 47.8192 2.11540
\(512\) 0 0
\(513\) 5.46402 0.241242
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −14.2723 −0.627697
\(518\) 0 0
\(519\) 32.5532 1.42893
\(520\) 0 0
\(521\) −25.0893 −1.09918 −0.549591 0.835434i \(-0.685216\pi\)
−0.549591 + 0.835434i \(0.685216\pi\)
\(522\) 0 0
\(523\) −28.5181 −1.24701 −0.623504 0.781820i \(-0.714292\pi\)
−0.623504 + 0.781820i \(0.714292\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 47.8139 2.08281
\(528\) 0 0
\(529\) −22.3929 −0.973603
\(530\) 0 0
\(531\) −4.30357 −0.186759
\(532\) 0 0
\(533\) −3.99318 −0.172964
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 5.99696 0.258788
\(538\) 0 0
\(539\) 69.4677 2.99218
\(540\) 0 0
\(541\) −15.6485 −0.672780 −0.336390 0.941723i \(-0.609206\pi\)
−0.336390 + 0.941723i \(0.609206\pi\)
\(542\) 0 0
\(543\) 3.24473 0.139245
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −10.8543 −0.464098 −0.232049 0.972704i \(-0.574543\pi\)
−0.232049 + 0.972704i \(0.574543\pi\)
\(548\) 0 0
\(549\) −2.38434 −0.101761
\(550\) 0 0
\(551\) −10.6570 −0.454003
\(552\) 0 0
\(553\) −18.9759 −0.806936
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.8763 0.799814 0.399907 0.916556i \(-0.369042\pi\)
0.399907 + 0.916556i \(0.369042\pi\)
\(558\) 0 0
\(559\) −8.15777 −0.345037
\(560\) 0 0
\(561\) 40.1458 1.69496
\(562\) 0 0
\(563\) −22.2846 −0.939183 −0.469591 0.882884i \(-0.655599\pi\)
−0.469591 + 0.882884i \(0.655599\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 36.8170 1.54617
\(568\) 0 0
\(569\) −7.11833 −0.298416 −0.149208 0.988806i \(-0.547672\pi\)
−0.149208 + 0.988806i \(0.547672\pi\)
\(570\) 0 0
\(571\) 1.21017 0.0506440 0.0253220 0.999679i \(-0.491939\pi\)
0.0253220 + 0.999679i \(0.491939\pi\)
\(572\) 0 0
\(573\) −1.44011 −0.0601613
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −41.4143 −1.72410 −0.862050 0.506823i \(-0.830820\pi\)
−0.862050 + 0.506823i \(0.830820\pi\)
\(578\) 0 0
\(579\) −31.0814 −1.29170
\(580\) 0 0
\(581\) 3.69643 0.153354
\(582\) 0 0
\(583\) 27.6846 1.14658
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.0591336 −0.00244071 −0.00122035 0.999999i \(-0.500388\pi\)
−0.00122035 + 0.999999i \(0.500388\pi\)
\(588\) 0 0
\(589\) −8.65699 −0.356705
\(590\) 0 0
\(591\) −5.47175 −0.225078
\(592\) 0 0
\(593\) 42.8828 1.76099 0.880493 0.474059i \(-0.157212\pi\)
0.880493 + 0.474059i \(0.157212\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.43706 −0.304379
\(598\) 0 0
\(599\) 15.3430 0.626898 0.313449 0.949605i \(-0.398515\pi\)
0.313449 + 0.949605i \(0.398515\pi\)
\(600\) 0 0
\(601\) −12.5781 −0.513072 −0.256536 0.966535i \(-0.582581\pi\)
−0.256536 + 0.966535i \(0.582581\pi\)
\(602\) 0 0
\(603\) −5.47785 −0.223075
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2.65751 0.107865 0.0539325 0.998545i \(-0.482824\pi\)
0.0539325 + 0.998545i \(0.482824\pi\)
\(608\) 0 0
\(609\) −82.0208 −3.32365
\(610\) 0 0
\(611\) 2.68602 0.108665
\(612\) 0 0
\(613\) 34.1052 1.37750 0.688748 0.725001i \(-0.258161\pi\)
0.688748 + 0.725001i \(0.258161\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29.9226 1.20464 0.602319 0.798255i \(-0.294244\pi\)
0.602319 + 0.798255i \(0.294244\pi\)
\(618\) 0 0
\(619\) 17.2102 0.691735 0.345868 0.938283i \(-0.387585\pi\)
0.345868 + 0.938283i \(0.387585\pi\)
\(620\) 0 0
\(621\) 4.25749 0.170847
\(622\) 0 0
\(623\) 27.0237 1.08268
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −7.26864 −0.290281
\(628\) 0 0
\(629\) 8.96056 0.357281
\(630\) 0 0
\(631\) −3.36195 −0.133837 −0.0669186 0.997758i \(-0.521317\pi\)
−0.0669186 + 0.997758i \(0.521317\pi\)
\(632\) 0 0
\(633\) 24.1435 0.959617
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.0736 −0.517996
\(638\) 0 0
\(639\) −0.111693 −0.00441853
\(640\) 0 0
\(641\) −16.2745 −0.642806 −0.321403 0.946943i \(-0.604154\pi\)
−0.321403 + 0.946943i \(0.604154\pi\)
\(642\) 0 0
\(643\) 35.7040 1.40803 0.704015 0.710185i \(-0.251389\pi\)
0.704015 + 0.710185i \(0.251389\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.2881 0.601036 0.300518 0.953776i \(-0.402840\pi\)
0.300518 + 0.953776i \(0.402840\pi\)
\(648\) 0 0
\(649\) 52.4033 2.05701
\(650\) 0 0
\(651\) −66.6280 −2.61136
\(652\) 0 0
\(653\) 16.4512 0.643785 0.321892 0.946776i \(-0.395681\pi\)
0.321892 + 0.946776i \(0.395681\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.70882 0.144695
\(658\) 0 0
\(659\) 7.03944 0.274218 0.137109 0.990556i \(-0.456219\pi\)
0.137109 + 0.990556i \(0.456219\pi\)
\(660\) 0 0
\(661\) 6.35343 0.247120 0.123560 0.992337i \(-0.460569\pi\)
0.123560 + 0.992337i \(0.460569\pi\)
\(662\) 0 0
\(663\) −7.55533 −0.293425
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.30378 −0.321524
\(668\) 0 0
\(669\) −30.4743 −1.17820
\(670\) 0 0
\(671\) 29.0335 1.12082
\(672\) 0 0
\(673\) 7.08638 0.273160 0.136580 0.990629i \(-0.456389\pi\)
0.136580 + 0.990629i \(0.456389\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.6095 −0.676786 −0.338393 0.941005i \(-0.609883\pi\)
−0.338393 + 0.941005i \(0.609883\pi\)
\(678\) 0 0
\(679\) −29.3140 −1.12497
\(680\) 0 0
\(681\) 1.36794 0.0524195
\(682\) 0 0
\(683\) −26.5855 −1.01726 −0.508632 0.860984i \(-0.669849\pi\)
−0.508632 + 0.860984i \(0.669849\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.88911 0.300988
\(688\) 0 0
\(689\) −5.21017 −0.198492
\(690\) 0 0
\(691\) 49.4907 1.88271 0.941357 0.337411i \(-0.109551\pi\)
0.941357 + 0.337411i \(0.109551\pi\)
\(692\) 0 0
\(693\) 7.82027 0.297067
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −26.1570 −0.990766
\(698\) 0 0
\(699\) 7.95392 0.300845
\(700\) 0 0
\(701\) 29.3389 1.10812 0.554058 0.832478i \(-0.313079\pi\)
0.554058 + 0.832478i \(0.313079\pi\)
\(702\) 0 0
\(703\) −1.62236 −0.0611886
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.9774 −0.600891
\(708\) 0 0
\(709\) 24.7359 0.928975 0.464488 0.885580i \(-0.346238\pi\)
0.464488 + 0.885580i \(0.346238\pi\)
\(710\) 0 0
\(711\) −1.47175 −0.0551951
\(712\) 0 0
\(713\) −6.74541 −0.252618
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.0613 0.375747
\(718\) 0 0
\(719\) 26.7548 0.997786 0.498893 0.866663i \(-0.333740\pi\)
0.498893 + 0.866663i \(0.333740\pi\)
\(720\) 0 0
\(721\) 17.6175 0.656112
\(722\) 0 0
\(723\) 5.29559 0.196945
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 27.2108 1.00919 0.504596 0.863355i \(-0.331641\pi\)
0.504596 + 0.863355i \(0.331641\pi\)
\(728\) 0 0
\(729\) 29.4494 1.09072
\(730\) 0 0
\(731\) −53.4367 −1.97643
\(732\) 0 0
\(733\) −40.0026 −1.47753 −0.738765 0.673963i \(-0.764591\pi\)
−0.738765 + 0.673963i \(0.764591\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 66.7022 2.45701
\(738\) 0 0
\(739\) 35.1123 1.29163 0.645814 0.763495i \(-0.276518\pi\)
0.645814 + 0.763495i \(0.276518\pi\)
\(740\) 0 0
\(741\) 1.36794 0.0502525
\(742\) 0 0
\(743\) −25.6476 −0.940918 −0.470459 0.882422i \(-0.655912\pi\)
−0.470459 + 0.882422i \(0.655912\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.286693 0.0104895
\(748\) 0 0
\(749\) −48.4033 −1.76862
\(750\) 0 0
\(751\) −13.2641 −0.484015 −0.242007 0.970274i \(-0.577806\pi\)
−0.242007 + 0.970274i \(0.577806\pi\)
\(752\) 0 0
\(753\) −46.1178 −1.68063
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.77092 −0.100711 −0.0503554 0.998731i \(-0.516035\pi\)
−0.0503554 + 0.998731i \(0.516035\pi\)
\(758\) 0 0
\(759\) −5.66363 −0.205577
\(760\) 0 0
\(761\) 10.7838 0.390914 0.195457 0.980712i \(-0.437381\pi\)
0.195457 + 0.980712i \(0.437381\pi\)
\(762\) 0 0
\(763\) −14.0448 −0.508455
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.86216 −0.356102
\(768\) 0 0
\(769\) −40.6090 −1.46440 −0.732199 0.681090i \(-0.761506\pi\)
−0.732199 + 0.681090i \(0.761506\pi\)
\(770\) 0 0
\(771\) 15.4967 0.558099
\(772\) 0 0
\(773\) 17.4410 0.627310 0.313655 0.949537i \(-0.398446\pi\)
0.313655 + 0.949537i \(0.398446\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −12.4864 −0.447947
\(778\) 0 0
\(779\) 4.73588 0.169680
\(780\) 0 0
\(781\) 1.36006 0.0486668
\(782\) 0 0
\(783\) −58.2300 −2.08097
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −30.8346 −1.09914 −0.549568 0.835449i \(-0.685208\pi\)
−0.549568 + 0.835449i \(0.685208\pi\)
\(788\) 0 0
\(789\) 15.4888 0.551416
\(790\) 0 0
\(791\) 33.6175 1.19530
\(792\) 0 0
\(793\) −5.46402 −0.194033
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 38.1340 1.35077 0.675387 0.737463i \(-0.263976\pi\)
0.675387 + 0.737463i \(0.263976\pi\)
\(798\) 0 0
\(799\) 17.5945 0.622449
\(800\) 0 0
\(801\) 2.09594 0.0740563
\(802\) 0 0
\(803\) −45.1612 −1.59371
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 23.2865 0.819722
\(808\) 0 0
\(809\) 30.7917 1.08258 0.541290 0.840836i \(-0.317936\pi\)
0.541290 + 0.840836i \(0.317936\pi\)
\(810\) 0 0
\(811\) −19.0275 −0.668145 −0.334072 0.942547i \(-0.608423\pi\)
−0.334072 + 0.942547i \(0.608423\pi\)
\(812\) 0 0
\(813\) 19.6368 0.688692
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.67504 0.338487
\(818\) 0 0
\(819\) −1.47175 −0.0514272
\(820\) 0 0
\(821\) −42.1228 −1.47009 −0.735047 0.678016i \(-0.762840\pi\)
−0.735047 + 0.678016i \(0.762840\pi\)
\(822\) 0 0
\(823\) 41.6298 1.45112 0.725562 0.688157i \(-0.241580\pi\)
0.725562 + 0.688157i \(0.241580\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −7.54814 −0.262475 −0.131237 0.991351i \(-0.541895\pi\)
−0.131237 + 0.991351i \(0.541895\pi\)
\(828\) 0 0
\(829\) 51.6674 1.79448 0.897242 0.441540i \(-0.145568\pi\)
0.897242 + 0.441540i \(0.145568\pi\)
\(830\) 0 0
\(831\) −5.82518 −0.202073
\(832\) 0 0
\(833\) −85.6376 −2.96717
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −47.3020 −1.63500
\(838\) 0 0
\(839\) 45.1682 1.55938 0.779689 0.626166i \(-0.215377\pi\)
0.779689 + 0.626166i \(0.215377\pi\)
\(840\) 0 0
\(841\) 84.5715 2.91626
\(842\) 0 0
\(843\) −43.3282 −1.49230
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −43.0415 −1.47892
\(848\) 0 0
\(849\) 33.2180 1.14004
\(850\) 0 0
\(851\) −1.26412 −0.0433336
\(852\) 0 0
\(853\) −10.6721 −0.365405 −0.182702 0.983168i \(-0.558485\pi\)
−0.182702 + 0.983168i \(0.558485\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −29.7119 −1.01494 −0.507470 0.861669i \(-0.669419\pi\)
−0.507470 + 0.861669i \(0.669419\pi\)
\(858\) 0 0
\(859\) −15.6734 −0.534769 −0.267385 0.963590i \(-0.586159\pi\)
−0.267385 + 0.963590i \(0.586159\pi\)
\(860\) 0 0
\(861\) 36.4494 1.24219
\(862\) 0 0
\(863\) −39.5741 −1.34712 −0.673559 0.739134i \(-0.735235\pi\)
−0.673559 + 0.739134i \(0.735235\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −21.9104 −0.744115
\(868\) 0 0
\(869\) 17.9211 0.607932
\(870\) 0 0
\(871\) −12.5532 −0.425348
\(872\) 0 0
\(873\) −2.27357 −0.0769487
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 47.9393 1.61880 0.809398 0.587260i \(-0.199793\pi\)
0.809398 + 0.587260i \(0.199793\pi\)
\(878\) 0 0
\(879\) −31.0814 −1.04835
\(880\) 0 0
\(881\) −2.32251 −0.0782473 −0.0391237 0.999234i \(-0.512457\pi\)
−0.0391237 + 0.999234i \(0.512457\pi\)
\(882\) 0 0
\(883\) 34.3919 1.15738 0.578690 0.815548i \(-0.303564\pi\)
0.578690 + 0.815548i \(0.303564\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −44.1002 −1.48074 −0.740370 0.672200i \(-0.765350\pi\)
−0.740370 + 0.672200i \(0.765350\pi\)
\(888\) 0 0
\(889\) −46.4822 −1.55896
\(890\) 0 0
\(891\) −34.7706 −1.16486
\(892\) 0 0
\(893\) −3.18559 −0.106602
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.06588 0.0355887
\(898\) 0 0
\(899\) 92.2575 3.07696
\(900\) 0 0
\(901\) −34.1287 −1.13699
\(902\) 0 0
\(903\) 74.4633 2.47798
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 25.3706 0.842417 0.421208 0.906964i \(-0.361606\pi\)
0.421208 + 0.906964i \(0.361606\pi\)
\(908\) 0 0
\(909\) −1.23919 −0.0411015
\(910\) 0 0
\(911\) 29.8252 0.988152 0.494076 0.869419i \(-0.335506\pi\)
0.494076 + 0.869419i \(0.335506\pi\)
\(912\) 0 0
\(913\) −3.49097 −0.115534
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −59.6985 −1.97142
\(918\) 0 0
\(919\) −15.8422 −0.522587 −0.261293 0.965259i \(-0.584149\pi\)
−0.261293 + 0.965259i \(0.584149\pi\)
\(920\) 0 0
\(921\) 51.9959 1.71332
\(922\) 0 0
\(923\) −0.255960 −0.00842501
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.36640 0.0448786
\(928\) 0 0
\(929\) −7.97098 −0.261519 −0.130760 0.991414i \(-0.541742\pi\)
−0.130760 + 0.991414i \(0.541742\pi\)
\(930\) 0 0
\(931\) 15.5052 0.508163
\(932\) 0 0
\(933\) 33.3073 1.09043
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0.848033 0.0277040 0.0138520 0.999904i \(-0.495591\pi\)
0.0138520 + 0.999904i \(0.495591\pi\)
\(938\) 0 0
\(939\) −24.0000 −0.783210
\(940\) 0 0
\(941\) 31.3140 1.02081 0.510403 0.859935i \(-0.329496\pi\)
0.510403 + 0.859935i \(0.329496\pi\)
\(942\) 0 0
\(943\) 3.69013 0.120167
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −25.9885 −0.844514 −0.422257 0.906476i \(-0.638762\pi\)
−0.422257 + 0.906476i \(0.638762\pi\)
\(948\) 0 0
\(949\) 8.49922 0.275896
\(950\) 0 0
\(951\) −27.4967 −0.891641
\(952\) 0 0
\(953\) 41.6347 1.34868 0.674340 0.738421i \(-0.264428\pi\)
0.674340 + 0.738421i \(0.264428\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 77.4618 2.50399
\(958\) 0 0
\(959\) −42.2016 −1.36276
\(960\) 0 0
\(961\) 43.9435 1.41753
\(962\) 0 0
\(963\) −3.75412 −0.120975
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 13.2656 0.426593 0.213296 0.976988i \(-0.431580\pi\)
0.213296 + 0.976988i \(0.431580\pi\)
\(968\) 0 0
\(969\) 8.96056 0.287855
\(970\) 0 0
\(971\) 25.3140 0.812364 0.406182 0.913792i \(-0.366860\pi\)
0.406182 + 0.913792i \(0.366860\pi\)
\(972\) 0 0
\(973\) −29.6763 −0.951380
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −50.7694 −1.62426 −0.812128 0.583479i \(-0.801691\pi\)
−0.812128 + 0.583479i \(0.801691\pi\)
\(978\) 0 0
\(979\) −25.5216 −0.815674
\(980\) 0 0
\(981\) −1.08930 −0.0347788
\(982\) 0 0
\(983\) 45.4123 1.44843 0.724214 0.689575i \(-0.242203\pi\)
0.724214 + 0.689575i \(0.242203\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −24.5177 −0.780407
\(988\) 0 0
\(989\) 7.53866 0.239716
\(990\) 0 0
\(991\) 45.6175 1.44909 0.724545 0.689228i \(-0.242050\pi\)
0.724545 + 0.689228i \(0.242050\pi\)
\(992\) 0 0
\(993\) 35.9009 1.13928
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 59.5705 1.88662 0.943309 0.331917i \(-0.107695\pi\)
0.943309 + 0.331917i \(0.107695\pi\)
\(998\) 0 0
\(999\) −8.86462 −0.280464
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 1900.2.a.k.1.2 6
4.3 odd 2 7600.2.a.cj.1.5 6
5.2 odd 4 380.2.c.b.229.5 yes 6
5.3 odd 4 380.2.c.b.229.2 6
5.4 even 2 inner 1900.2.a.k.1.5 6
15.2 even 4 3420.2.f.c.1369.6 6
15.8 even 4 3420.2.f.c.1369.5 6
20.3 even 4 1520.2.d.i.609.5 6
20.7 even 4 1520.2.d.i.609.2 6
20.19 odd 2 7600.2.a.cj.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.c.b.229.2 6 5.3 odd 4
380.2.c.b.229.5 yes 6 5.2 odd 4
1520.2.d.i.609.2 6 20.7 even 4
1520.2.d.i.609.5 6 20.3 even 4
1900.2.a.k.1.2 6 1.1 even 1 trivial
1900.2.a.k.1.5 6 5.4 even 2 inner
3420.2.f.c.1369.5 6 15.8 even 4
3420.2.f.c.1369.6 6 15.2 even 4
7600.2.a.cj.1.2 6 20.19 odd 2
7600.2.a.cj.1.5 6 4.3 odd 2