Properties

Label 7605.2.a.bx.1.1
Level $7605$
Weight $2$
Character 7605.1
Self dual yes
Analytic conductor $60.726$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.7262307372\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.34292\) of defining polynomial
Character \(\chi\) \(=\) 7605.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48929 q^{2} +4.19656 q^{4} -1.00000 q^{5} +1.19656 q^{7} -5.46787 q^{8} +O(q^{10})\) \(q-2.48929 q^{2} +4.19656 q^{4} -1.00000 q^{5} +1.19656 q^{7} -5.46787 q^{8} +2.48929 q^{10} -1.19656 q^{11} -2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} -6.97858 q^{19} -4.19656 q^{20} +2.97858 q^{22} -4.17513 q^{23} +1.00000 q^{25} +5.02142 q^{28} -6.00000 q^{29} +2.97858 q^{31} -2.05333 q^{32} +15.3717 q^{34} -1.19656 q^{35} -7.78202 q^{37} +17.3717 q^{38} +5.46787 q^{40} -6.17513 q^{41} -9.95715 q^{43} -5.02142 q^{44} +10.3931 q^{46} -1.02142 q^{47} -5.56825 q^{49} -2.48929 q^{50} -10.1751 q^{53} +1.19656 q^{55} -6.54262 q^{56} +14.9357 q^{58} +5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} -5.32464 q^{64} -9.37169 q^{67} -25.9143 q^{68} +2.97858 q^{70} -5.19656 q^{71} +11.9572 q^{73} +19.3717 q^{74} -29.2860 q^{76} -1.43175 q^{77} -1.78202 q^{79} -5.21798 q^{80} +15.3717 q^{82} -5.37169 q^{83} +6.17513 q^{85} +24.7862 q^{86} +6.54262 q^{88} +10.1751 q^{89} -17.5212 q^{92} +2.54262 q^{94} +6.97858 q^{95} +1.82487 q^{97} +13.8610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 8 q^{4} - 3 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 8 q^{4} - 3 q^{5} - q^{7} + 6 q^{8} + q^{11} + 6 q^{14} + 26 q^{16} + q^{17} - 6 q^{19} - 8 q^{20} - 6 q^{22} + 7 q^{23} + 3 q^{25} + 30 q^{28} - 18 q^{29} - 6 q^{31} + 22 q^{32} + 22 q^{34} + q^{35} - 13 q^{37} + 28 q^{38} - 6 q^{40} + q^{41} - 30 q^{44} + 22 q^{46} - 18 q^{47} + 12 q^{49} - 11 q^{53} - q^{55} + 16 q^{56} - 8 q^{59} + 9 q^{61} - 28 q^{62} + 30 q^{64} - 4 q^{67} - 18 q^{68} - 6 q^{70} - 11 q^{71} + 6 q^{73} + 34 q^{74} - 4 q^{76} - 33 q^{77} + 5 q^{79} - 26 q^{80} + 22 q^{82} + 8 q^{83} - q^{85} + 56 q^{86} - 16 q^{88} + 11 q^{89} - 2 q^{92} - 28 q^{94} + 6 q^{95} + 25 q^{97} + 10 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48929 −1.76019 −0.880096 0.474795i \(-0.842522\pi\)
−0.880096 + 0.474795i \(0.842522\pi\)
\(3\) 0 0
\(4\) 4.19656 2.09828
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.19656 0.452256 0.226128 0.974098i \(-0.427393\pi\)
0.226128 + 0.974098i \(0.427393\pi\)
\(8\) −5.46787 −1.93318
\(9\) 0 0
\(10\) 2.48929 0.787182
\(11\) −1.19656 −0.360776 −0.180388 0.983596i \(-0.557735\pi\)
−0.180388 + 0.983596i \(0.557735\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −2.97858 −0.796058
\(15\) 0 0
\(16\) 5.21798 1.30450
\(17\) −6.17513 −1.49769 −0.748845 0.662745i \(-0.769391\pi\)
−0.748845 + 0.662745i \(0.769391\pi\)
\(18\) 0 0
\(19\) −6.97858 −1.60100 −0.800498 0.599336i \(-0.795431\pi\)
−0.800498 + 0.599336i \(0.795431\pi\)
\(20\) −4.19656 −0.938379
\(21\) 0 0
\(22\) 2.97858 0.635035
\(23\) −4.17513 −0.870576 −0.435288 0.900291i \(-0.643353\pi\)
−0.435288 + 0.900291i \(0.643353\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 5.02142 0.948960
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 2.97858 0.534968 0.267484 0.963562i \(-0.413808\pi\)
0.267484 + 0.963562i \(0.413808\pi\)
\(32\) −2.05333 −0.362980
\(33\) 0 0
\(34\) 15.3717 2.63622
\(35\) −1.19656 −0.202255
\(36\) 0 0
\(37\) −7.78202 −1.27936 −0.639678 0.768643i \(-0.720932\pi\)
−0.639678 + 0.768643i \(0.720932\pi\)
\(38\) 17.3717 2.81806
\(39\) 0 0
\(40\) 5.46787 0.864545
\(41\) −6.17513 −0.964394 −0.482197 0.876063i \(-0.660161\pi\)
−0.482197 + 0.876063i \(0.660161\pi\)
\(42\) 0 0
\(43\) −9.95715 −1.51845 −0.759226 0.650827i \(-0.774422\pi\)
−0.759226 + 0.650827i \(0.774422\pi\)
\(44\) −5.02142 −0.757008
\(45\) 0 0
\(46\) 10.3931 1.53238
\(47\) −1.02142 −0.148990 −0.0744949 0.997221i \(-0.523734\pi\)
−0.0744949 + 0.997221i \(0.523734\pi\)
\(48\) 0 0
\(49\) −5.56825 −0.795464
\(50\) −2.48929 −0.352039
\(51\) 0 0
\(52\) 0 0
\(53\) −10.1751 −1.39766 −0.698831 0.715287i \(-0.746296\pi\)
−0.698831 + 0.715287i \(0.746296\pi\)
\(54\) 0 0
\(55\) 1.19656 0.161344
\(56\) −6.54262 −0.874294
\(57\) 0 0
\(58\) 14.9357 1.96116
\(59\) 5.37169 0.699335 0.349667 0.936874i \(-0.386295\pi\)
0.349667 + 0.936874i \(0.386295\pi\)
\(60\) 0 0
\(61\) 12.5682 1.60920 0.804600 0.593818i \(-0.202380\pi\)
0.804600 + 0.593818i \(0.202380\pi\)
\(62\) −7.41454 −0.941647
\(63\) 0 0
\(64\) −5.32464 −0.665579
\(65\) 0 0
\(66\) 0 0
\(67\) −9.37169 −1.14493 −0.572467 0.819928i \(-0.694014\pi\)
−0.572467 + 0.819928i \(0.694014\pi\)
\(68\) −25.9143 −3.14257
\(69\) 0 0
\(70\) 2.97858 0.356008
\(71\) −5.19656 −0.616718 −0.308359 0.951270i \(-0.599780\pi\)
−0.308359 + 0.951270i \(0.599780\pi\)
\(72\) 0 0
\(73\) 11.9572 1.39948 0.699740 0.714398i \(-0.253299\pi\)
0.699740 + 0.714398i \(0.253299\pi\)
\(74\) 19.3717 2.25191
\(75\) 0 0
\(76\) −29.2860 −3.35933
\(77\) −1.43175 −0.163163
\(78\) 0 0
\(79\) −1.78202 −0.200493 −0.100246 0.994963i \(-0.531963\pi\)
−0.100246 + 0.994963i \(0.531963\pi\)
\(80\) −5.21798 −0.583388
\(81\) 0 0
\(82\) 15.3717 1.69752
\(83\) −5.37169 −0.589620 −0.294810 0.955556i \(-0.595256\pi\)
−0.294810 + 0.955556i \(0.595256\pi\)
\(84\) 0 0
\(85\) 6.17513 0.669787
\(86\) 24.7862 2.67277
\(87\) 0 0
\(88\) 6.54262 0.697445
\(89\) 10.1751 1.07856 0.539281 0.842126i \(-0.318696\pi\)
0.539281 + 0.842126i \(0.318696\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −17.5212 −1.82671
\(93\) 0 0
\(94\) 2.54262 0.262251
\(95\) 6.97858 0.715987
\(96\) 0 0
\(97\) 1.82487 0.185287 0.0926435 0.995699i \(-0.470468\pi\)
0.0926435 + 0.995699i \(0.470468\pi\)
\(98\) 13.8610 1.40017
\(99\) 0 0
\(100\) 4.19656 0.419656
\(101\) 10.3503 1.02989 0.514945 0.857223i \(-0.327812\pi\)
0.514945 + 0.857223i \(0.327812\pi\)
\(102\) 0 0
\(103\) 18.7434 1.84684 0.923420 0.383790i \(-0.125381\pi\)
0.923420 + 0.383790i \(0.125381\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 25.3288 2.46016
\(107\) 18.5682 1.79506 0.897530 0.440953i \(-0.145359\pi\)
0.897530 + 0.440953i \(0.145359\pi\)
\(108\) 0 0
\(109\) −8.39312 −0.803915 −0.401957 0.915658i \(-0.631670\pi\)
−0.401957 + 0.915658i \(0.631670\pi\)
\(110\) −2.97858 −0.283996
\(111\) 0 0
\(112\) 6.24361 0.589966
\(113\) −7.95715 −0.748546 −0.374273 0.927319i \(-0.622108\pi\)
−0.374273 + 0.927319i \(0.622108\pi\)
\(114\) 0 0
\(115\) 4.17513 0.389333
\(116\) −25.1793 −2.33784
\(117\) 0 0
\(118\) −13.3717 −1.23096
\(119\) −7.38890 −0.677340
\(120\) 0 0
\(121\) −9.56825 −0.869841
\(122\) −31.2860 −2.83250
\(123\) 0 0
\(124\) 12.4998 1.12251
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.3931 −0.922240 −0.461120 0.887338i \(-0.652552\pi\)
−0.461120 + 0.887338i \(0.652552\pi\)
\(128\) 17.3612 1.53453
\(129\) 0 0
\(130\) 0 0
\(131\) 6.39312 0.558569 0.279285 0.960208i \(-0.409903\pi\)
0.279285 + 0.960208i \(0.409903\pi\)
\(132\) 0 0
\(133\) −8.35027 −0.724060
\(134\) 23.3288 2.01531
\(135\) 0 0
\(136\) 33.7648 2.89531
\(137\) 16.7434 1.43048 0.715242 0.698877i \(-0.246316\pi\)
0.715242 + 0.698877i \(0.246316\pi\)
\(138\) 0 0
\(139\) 5.78202 0.490424 0.245212 0.969469i \(-0.421142\pi\)
0.245212 + 0.969469i \(0.421142\pi\)
\(140\) −5.02142 −0.424388
\(141\) 0 0
\(142\) 12.9357 1.08554
\(143\) 0 0
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) −29.7648 −2.46335
\(147\) 0 0
\(148\) −32.6577 −2.68445
\(149\) 15.3461 1.25720 0.628599 0.777730i \(-0.283629\pi\)
0.628599 + 0.777730i \(0.283629\pi\)
\(150\) 0 0
\(151\) 8.58546 0.698675 0.349337 0.936997i \(-0.386407\pi\)
0.349337 + 0.936997i \(0.386407\pi\)
\(152\) 38.1579 3.09502
\(153\) 0 0
\(154\) 3.56404 0.287198
\(155\) −2.97858 −0.239245
\(156\) 0 0
\(157\) 2.78623 0.222365 0.111183 0.993800i \(-0.464536\pi\)
0.111183 + 0.993800i \(0.464536\pi\)
\(158\) 4.43596 0.352906
\(159\) 0 0
\(160\) 2.05333 0.162330
\(161\) −4.99579 −0.393723
\(162\) 0 0
\(163\) −8.76060 −0.686183 −0.343091 0.939302i \(-0.611474\pi\)
−0.343091 + 0.939302i \(0.611474\pi\)
\(164\) −25.9143 −2.02357
\(165\) 0 0
\(166\) 13.3717 1.03784
\(167\) −17.3717 −1.34426 −0.672131 0.740432i \(-0.734621\pi\)
−0.672131 + 0.740432i \(0.734621\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −15.3717 −1.17895
\(171\) 0 0
\(172\) −41.7858 −3.18614
\(173\) 7.95715 0.604971 0.302486 0.953154i \(-0.402184\pi\)
0.302486 + 0.953154i \(0.402184\pi\)
\(174\) 0 0
\(175\) 1.19656 0.0904513
\(176\) −6.24361 −0.470630
\(177\) 0 0
\(178\) −25.3288 −1.89848
\(179\) 15.5640 1.16331 0.581655 0.813435i \(-0.302405\pi\)
0.581655 + 0.813435i \(0.302405\pi\)
\(180\) 0 0
\(181\) 15.7820 1.17307 0.586534 0.809925i \(-0.300492\pi\)
0.586534 + 0.809925i \(0.300492\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 22.8291 1.68298
\(185\) 7.78202 0.572145
\(186\) 0 0
\(187\) 7.38890 0.540330
\(188\) −4.28646 −0.312622
\(189\) 0 0
\(190\) −17.3717 −1.26028
\(191\) −10.7434 −0.777364 −0.388682 0.921372i \(-0.627070\pi\)
−0.388682 + 0.921372i \(0.627070\pi\)
\(192\) 0 0
\(193\) −9.73917 −0.701041 −0.350521 0.936555i \(-0.613995\pi\)
−0.350521 + 0.936555i \(0.613995\pi\)
\(194\) −4.54262 −0.326141
\(195\) 0 0
\(196\) −23.3675 −1.66911
\(197\) −9.56404 −0.681410 −0.340705 0.940170i \(-0.610666\pi\)
−0.340705 + 0.940170i \(0.610666\pi\)
\(198\) 0 0
\(199\) 5.95715 0.422291 0.211146 0.977455i \(-0.432281\pi\)
0.211146 + 0.977455i \(0.432281\pi\)
\(200\) −5.46787 −0.386636
\(201\) 0 0
\(202\) −25.7648 −1.81281
\(203\) −7.17935 −0.503891
\(204\) 0 0
\(205\) 6.17513 0.431290
\(206\) −46.6577 −3.25080
\(207\) 0 0
\(208\) 0 0
\(209\) 8.35027 0.577600
\(210\) 0 0
\(211\) 23.9143 1.64633 0.823164 0.567803i \(-0.192206\pi\)
0.823164 + 0.567803i \(0.192206\pi\)
\(212\) −42.7005 −2.93269
\(213\) 0 0
\(214\) −46.2217 −3.15965
\(215\) 9.95715 0.679072
\(216\) 0 0
\(217\) 3.56404 0.241943
\(218\) 20.8929 1.41504
\(219\) 0 0
\(220\) 5.02142 0.338544
\(221\) 0 0
\(222\) 0 0
\(223\) −2.62831 −0.176004 −0.0880022 0.996120i \(-0.528048\pi\)
−0.0880022 + 0.996120i \(0.528048\pi\)
\(224\) −2.45692 −0.164160
\(225\) 0 0
\(226\) 19.8077 1.31759
\(227\) 15.7648 1.04635 0.523174 0.852226i \(-0.324748\pi\)
0.523174 + 0.852226i \(0.324748\pi\)
\(228\) 0 0
\(229\) −8.74338 −0.577779 −0.288890 0.957362i \(-0.593286\pi\)
−0.288890 + 0.957362i \(0.593286\pi\)
\(230\) −10.3931 −0.685302
\(231\) 0 0
\(232\) 32.8072 2.15390
\(233\) 2.17513 0.142498 0.0712489 0.997459i \(-0.477302\pi\)
0.0712489 + 0.997459i \(0.477302\pi\)
\(234\) 0 0
\(235\) 1.02142 0.0666303
\(236\) 22.5426 1.46740
\(237\) 0 0
\(238\) 18.3931 1.19225
\(239\) 2.80344 0.181340 0.0906698 0.995881i \(-0.471099\pi\)
0.0906698 + 0.995881i \(0.471099\pi\)
\(240\) 0 0
\(241\) 6.00000 0.386494 0.193247 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) 23.8181 1.53109
\(243\) 0 0
\(244\) 52.7434 3.37655
\(245\) 5.56825 0.355742
\(246\) 0 0
\(247\) 0 0
\(248\) −16.2865 −1.03419
\(249\) 0 0
\(250\) 2.48929 0.157436
\(251\) 23.9143 1.50946 0.754729 0.656037i \(-0.227768\pi\)
0.754729 + 0.656037i \(0.227768\pi\)
\(252\) 0 0
\(253\) 4.99579 0.314083
\(254\) 25.8715 1.62332
\(255\) 0 0
\(256\) −32.5678 −2.03549
\(257\) 19.9572 1.24489 0.622447 0.782662i \(-0.286139\pi\)
0.622447 + 0.782662i \(0.286139\pi\)
\(258\) 0 0
\(259\) −9.31163 −0.578597
\(260\) 0 0
\(261\) 0 0
\(262\) −15.9143 −0.983189
\(263\) −8.00000 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 0 0
\(265\) 10.1751 0.625054
\(266\) 20.7862 1.27449
\(267\) 0 0
\(268\) −39.3288 −2.40239
\(269\) 2.35027 0.143298 0.0716492 0.997430i \(-0.477174\pi\)
0.0716492 + 0.997430i \(0.477174\pi\)
\(270\) 0 0
\(271\) −10.9786 −0.666901 −0.333451 0.942768i \(-0.608213\pi\)
−0.333451 + 0.942768i \(0.608213\pi\)
\(272\) −32.2217 −1.95373
\(273\) 0 0
\(274\) −41.6791 −2.51793
\(275\) −1.19656 −0.0721551
\(276\) 0 0
\(277\) 1.21377 0.0729283 0.0364642 0.999335i \(-0.488391\pi\)
0.0364642 + 0.999335i \(0.488391\pi\)
\(278\) −14.3931 −0.863242
\(279\) 0 0
\(280\) 6.54262 0.390996
\(281\) 11.9572 0.713304 0.356652 0.934237i \(-0.383918\pi\)
0.356652 + 0.934237i \(0.383918\pi\)
\(282\) 0 0
\(283\) −29.8715 −1.77567 −0.887837 0.460158i \(-0.847793\pi\)
−0.887837 + 0.460158i \(0.847793\pi\)
\(284\) −21.8077 −1.29405
\(285\) 0 0
\(286\) 0 0
\(287\) −7.38890 −0.436153
\(288\) 0 0
\(289\) 21.1323 1.24308
\(290\) −14.9357 −0.877056
\(291\) 0 0
\(292\) 50.1789 2.93650
\(293\) 0.777809 0.0454401 0.0227200 0.999742i \(-0.492767\pi\)
0.0227200 + 0.999742i \(0.492767\pi\)
\(294\) 0 0
\(295\) −5.37169 −0.312752
\(296\) 42.5510 2.47323
\(297\) 0 0
\(298\) −38.2008 −2.21291
\(299\) 0 0
\(300\) 0 0
\(301\) −11.9143 −0.686729
\(302\) −21.3717 −1.22980
\(303\) 0 0
\(304\) −36.4141 −2.08849
\(305\) −12.5682 −0.719656
\(306\) 0 0
\(307\) −0.760597 −0.0434095 −0.0217048 0.999764i \(-0.506909\pi\)
−0.0217048 + 0.999764i \(0.506909\pi\)
\(308\) −6.00842 −0.342362
\(309\) 0 0
\(310\) 7.41454 0.421117
\(311\) 23.1281 1.31147 0.655736 0.754990i \(-0.272358\pi\)
0.655736 + 0.754990i \(0.272358\pi\)
\(312\) 0 0
\(313\) −33.9143 −1.91695 −0.958475 0.285176i \(-0.907948\pi\)
−0.958475 + 0.285176i \(0.907948\pi\)
\(314\) −6.93573 −0.391406
\(315\) 0 0
\(316\) −7.47835 −0.420690
\(317\) 9.64973 0.541983 0.270991 0.962582i \(-0.412648\pi\)
0.270991 + 0.962582i \(0.412648\pi\)
\(318\) 0 0
\(319\) 7.17935 0.401966
\(320\) 5.32464 0.297656
\(321\) 0 0
\(322\) 12.4360 0.693029
\(323\) 43.0937 2.39780
\(324\) 0 0
\(325\) 0 0
\(326\) 21.8077 1.20781
\(327\) 0 0
\(328\) 33.7648 1.86435
\(329\) −1.22219 −0.0673816
\(330\) 0 0
\(331\) −15.3288 −0.842550 −0.421275 0.906933i \(-0.638417\pi\)
−0.421275 + 0.906933i \(0.638417\pi\)
\(332\) −22.5426 −1.23719
\(333\) 0 0
\(334\) 43.2432 2.36616
\(335\) 9.37169 0.512030
\(336\) 0 0
\(337\) −22.3503 −1.21750 −0.608748 0.793363i \(-0.708328\pi\)
−0.608748 + 0.793363i \(0.708328\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 25.9143 1.40540
\(341\) −3.56404 −0.193004
\(342\) 0 0
\(343\) −15.0386 −0.812010
\(344\) 54.4444 2.93544
\(345\) 0 0
\(346\) −19.8077 −1.06487
\(347\) 5.78202 0.310395 0.155198 0.987883i \(-0.450399\pi\)
0.155198 + 0.987883i \(0.450399\pi\)
\(348\) 0 0
\(349\) 27.5212 1.47318 0.736588 0.676342i \(-0.236436\pi\)
0.736588 + 0.676342i \(0.236436\pi\)
\(350\) −2.97858 −0.159212
\(351\) 0 0
\(352\) 2.45692 0.130955
\(353\) −28.7434 −1.52986 −0.764928 0.644116i \(-0.777225\pi\)
−0.764928 + 0.644116i \(0.777225\pi\)
\(354\) 0 0
\(355\) 5.19656 0.275805
\(356\) 42.7005 2.26312
\(357\) 0 0
\(358\) −38.7434 −2.04765
\(359\) −12.5855 −0.664235 −0.332118 0.943238i \(-0.607763\pi\)
−0.332118 + 0.943238i \(0.607763\pi\)
\(360\) 0 0
\(361\) 29.7005 1.56319
\(362\) −39.2860 −2.06483
\(363\) 0 0
\(364\) 0 0
\(365\) −11.9572 −0.625866
\(366\) 0 0
\(367\) −27.9143 −1.45712 −0.728558 0.684985i \(-0.759809\pi\)
−0.728558 + 0.684985i \(0.759809\pi\)
\(368\) −21.7858 −1.13566
\(369\) 0 0
\(370\) −19.3717 −1.00709
\(371\) −12.1751 −0.632102
\(372\) 0 0
\(373\) −2.35027 −0.121692 −0.0608462 0.998147i \(-0.519380\pi\)
−0.0608462 + 0.998147i \(0.519380\pi\)
\(374\) −18.3931 −0.951085
\(375\) 0 0
\(376\) 5.58500 0.288025
\(377\) 0 0
\(378\) 0 0
\(379\) −24.5510 −1.26110 −0.630551 0.776148i \(-0.717171\pi\)
−0.630551 + 0.776148i \(0.717171\pi\)
\(380\) 29.2860 1.50234
\(381\) 0 0
\(382\) 26.7434 1.36831
\(383\) 5.80765 0.296757 0.148379 0.988931i \(-0.452595\pi\)
0.148379 + 0.988931i \(0.452595\pi\)
\(384\) 0 0
\(385\) 1.43175 0.0729687
\(386\) 24.2436 1.23397
\(387\) 0 0
\(388\) 7.65815 0.388784
\(389\) −13.6497 −0.692069 −0.346034 0.938222i \(-0.612472\pi\)
−0.346034 + 0.938222i \(0.612472\pi\)
\(390\) 0 0
\(391\) 25.7820 1.30385
\(392\) 30.4464 1.53778
\(393\) 0 0
\(394\) 23.8077 1.19941
\(395\) 1.78202 0.0896631
\(396\) 0 0
\(397\) 12.1323 0.608902 0.304451 0.952528i \(-0.401527\pi\)
0.304451 + 0.952528i \(0.401527\pi\)
\(398\) −14.8291 −0.743314
\(399\) 0 0
\(400\) 5.21798 0.260899
\(401\) −37.4439 −1.86986 −0.934930 0.354832i \(-0.884538\pi\)
−0.934930 + 0.354832i \(0.884538\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 43.4355 2.16100
\(405\) 0 0
\(406\) 17.8715 0.886946
\(407\) 9.31163 0.461561
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −15.3717 −0.759154
\(411\) 0 0
\(412\) 78.6577 3.87519
\(413\) 6.42754 0.316279
\(414\) 0 0
\(415\) 5.37169 0.263686
\(416\) 0 0
\(417\) 0 0
\(418\) −20.7862 −1.01669
\(419\) −3.17935 −0.155321 −0.0776606 0.996980i \(-0.524745\pi\)
−0.0776606 + 0.996980i \(0.524745\pi\)
\(420\) 0 0
\(421\) 16.3074 0.794775 0.397388 0.917651i \(-0.369917\pi\)
0.397388 + 0.917651i \(0.369917\pi\)
\(422\) −59.5296 −2.89786
\(423\) 0 0
\(424\) 55.6363 2.70194
\(425\) −6.17513 −0.299538
\(426\) 0 0
\(427\) 15.0386 0.727771
\(428\) 77.9227 3.76654
\(429\) 0 0
\(430\) −24.7862 −1.19530
\(431\) 4.58546 0.220874 0.110437 0.993883i \(-0.464775\pi\)
0.110437 + 0.993883i \(0.464775\pi\)
\(432\) 0 0
\(433\) −38.3503 −1.84300 −0.921498 0.388383i \(-0.873034\pi\)
−0.921498 + 0.388383i \(0.873034\pi\)
\(434\) −8.87192 −0.425866
\(435\) 0 0
\(436\) −35.2222 −1.68684
\(437\) 29.1365 1.39379
\(438\) 0 0
\(439\) 7.73917 0.369371 0.184685 0.982798i \(-0.440873\pi\)
0.184685 + 0.982798i \(0.440873\pi\)
\(440\) −6.54262 −0.311907
\(441\) 0 0
\(442\) 0 0
\(443\) −34.9185 −1.65903 −0.829514 0.558485i \(-0.811383\pi\)
−0.829514 + 0.558485i \(0.811383\pi\)
\(444\) 0 0
\(445\) −10.1751 −0.482348
\(446\) 6.54262 0.309802
\(447\) 0 0
\(448\) −6.37123 −0.301012
\(449\) −6.17513 −0.291423 −0.145711 0.989327i \(-0.546547\pi\)
−0.145711 + 0.989327i \(0.546547\pi\)
\(450\) 0 0
\(451\) 7.38890 0.347930
\(452\) −33.3927 −1.57066
\(453\) 0 0
\(454\) −39.2432 −1.84177
\(455\) 0 0
\(456\) 0 0
\(457\) −1.38890 −0.0649702 −0.0324851 0.999472i \(-0.510342\pi\)
−0.0324851 + 0.999472i \(0.510342\pi\)
\(458\) 21.7648 1.01700
\(459\) 0 0
\(460\) 17.5212 0.816930
\(461\) 28.4826 1.32657 0.663283 0.748369i \(-0.269163\pi\)
0.663283 + 0.748369i \(0.269163\pi\)
\(462\) 0 0
\(463\) −16.3759 −0.761053 −0.380526 0.924770i \(-0.624257\pi\)
−0.380526 + 0.924770i \(0.624257\pi\)
\(464\) −31.3079 −1.45343
\(465\) 0 0
\(466\) −5.41454 −0.250824
\(467\) −25.7476 −1.19146 −0.595728 0.803186i \(-0.703136\pi\)
−0.595728 + 0.803186i \(0.703136\pi\)
\(468\) 0 0
\(469\) −11.2138 −0.517804
\(470\) −2.54262 −0.117282
\(471\) 0 0
\(472\) −29.3717 −1.35194
\(473\) 11.9143 0.547820
\(474\) 0 0
\(475\) −6.97858 −0.320199
\(476\) −31.0080 −1.42125
\(477\) 0 0
\(478\) −6.97858 −0.319193
\(479\) −7.58967 −0.346781 −0.173391 0.984853i \(-0.555472\pi\)
−0.173391 + 0.984853i \(0.555472\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −14.9357 −0.680304
\(483\) 0 0
\(484\) −40.1537 −1.82517
\(485\) −1.82487 −0.0828629
\(486\) 0 0
\(487\) −4.41033 −0.199851 −0.0999255 0.994995i \(-0.531860\pi\)
−0.0999255 + 0.994995i \(0.531860\pi\)
\(488\) −68.7215 −3.11088
\(489\) 0 0
\(490\) −13.8610 −0.626175
\(491\) 0.0856914 0.00386720 0.00193360 0.999998i \(-0.499385\pi\)
0.00193360 + 0.999998i \(0.499385\pi\)
\(492\) 0 0
\(493\) 37.0508 1.66868
\(494\) 0 0
\(495\) 0 0
\(496\) 15.5422 0.697863
\(497\) −6.21798 −0.278915
\(498\) 0 0
\(499\) 17.7220 0.793344 0.396672 0.917960i \(-0.370165\pi\)
0.396672 + 0.917960i \(0.370165\pi\)
\(500\) −4.19656 −0.187676
\(501\) 0 0
\(502\) −59.5296 −2.65694
\(503\) 8.70054 0.387938 0.193969 0.981008i \(-0.437864\pi\)
0.193969 + 0.981008i \(0.437864\pi\)
\(504\) 0 0
\(505\) −10.3503 −0.460581
\(506\) −12.4360 −0.552846
\(507\) 0 0
\(508\) −43.6153 −1.93512
\(509\) −33.3545 −1.47841 −0.739206 0.673480i \(-0.764799\pi\)
−0.739206 + 0.673480i \(0.764799\pi\)
\(510\) 0 0
\(511\) 14.3074 0.632923
\(512\) 46.3482 2.04832
\(513\) 0 0
\(514\) −49.6791 −2.19125
\(515\) −18.7434 −0.825932
\(516\) 0 0
\(517\) 1.22219 0.0537519
\(518\) 23.1793 1.01844
\(519\) 0 0
\(520\) 0 0
\(521\) −18.7005 −0.819285 −0.409643 0.912246i \(-0.634347\pi\)
−0.409643 + 0.912246i \(0.634347\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 26.8291 1.17203
\(525\) 0 0
\(526\) 19.9143 0.868305
\(527\) −18.3931 −0.801217
\(528\) 0 0
\(529\) −5.56825 −0.242098
\(530\) −25.3288 −1.10021
\(531\) 0 0
\(532\) −35.0424 −1.51928
\(533\) 0 0
\(534\) 0 0
\(535\) −18.5682 −0.802775
\(536\) 51.2432 2.21337
\(537\) 0 0
\(538\) −5.85050 −0.252233
\(539\) 6.66273 0.286984
\(540\) 0 0
\(541\) 41.5296 1.78550 0.892749 0.450555i \(-0.148774\pi\)
0.892749 + 0.450555i \(0.148774\pi\)
\(542\) 27.3288 1.17387
\(543\) 0 0
\(544\) 12.6796 0.543632
\(545\) 8.39312 0.359522
\(546\) 0 0
\(547\) −7.91431 −0.338391 −0.169196 0.985582i \(-0.554117\pi\)
−0.169196 + 0.985582i \(0.554117\pi\)
\(548\) 70.2646 3.00155
\(549\) 0 0
\(550\) 2.97858 0.127007
\(551\) 41.8715 1.78378
\(552\) 0 0
\(553\) −2.13229 −0.0906742
\(554\) −3.02142 −0.128368
\(555\) 0 0
\(556\) 24.2646 1.02905
\(557\) 42.7005 1.80928 0.904640 0.426177i \(-0.140140\pi\)
0.904640 + 0.426177i \(0.140140\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −6.24361 −0.263841
\(561\) 0 0
\(562\) −29.7648 −1.25555
\(563\) −1.04706 −0.0441282 −0.0220641 0.999757i \(-0.507024\pi\)
−0.0220641 + 0.999757i \(0.507024\pi\)
\(564\) 0 0
\(565\) 7.95715 0.334760
\(566\) 74.3587 3.12553
\(567\) 0 0
\(568\) 28.4141 1.19223
\(569\) −16.7778 −0.703362 −0.351681 0.936120i \(-0.614390\pi\)
−0.351681 + 0.936120i \(0.614390\pi\)
\(570\) 0 0
\(571\) −20.6111 −0.862548 −0.431274 0.902221i \(-0.641936\pi\)
−0.431274 + 0.902221i \(0.641936\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 18.3931 0.767714
\(575\) −4.17513 −0.174115
\(576\) 0 0
\(577\) −1.38890 −0.0578208 −0.0289104 0.999582i \(-0.509204\pi\)
−0.0289104 + 0.999582i \(0.509204\pi\)
\(578\) −52.6044 −2.18805
\(579\) 0 0
\(580\) 25.1793 1.04552
\(581\) −6.42754 −0.266659
\(582\) 0 0
\(583\) 12.1751 0.504243
\(584\) −65.3801 −2.70545
\(585\) 0 0
\(586\) −1.93619 −0.0799833
\(587\) −0.935731 −0.0386218 −0.0193109 0.999814i \(-0.506147\pi\)
−0.0193109 + 0.999814i \(0.506147\pi\)
\(588\) 0 0
\(589\) −20.7862 −0.856482
\(590\) 13.3717 0.550504
\(591\) 0 0
\(592\) −40.6064 −1.66891
\(593\) −0.478807 −0.0196622 −0.00983112 0.999952i \(-0.503129\pi\)
−0.00983112 + 0.999952i \(0.503129\pi\)
\(594\) 0 0
\(595\) 7.38890 0.302916
\(596\) 64.4006 2.63795
\(597\) 0 0
\(598\) 0 0
\(599\) −29.0852 −1.18839 −0.594195 0.804321i \(-0.702529\pi\)
−0.594195 + 0.804321i \(0.702529\pi\)
\(600\) 0 0
\(601\) 11.4318 0.466311 0.233155 0.972439i \(-0.425095\pi\)
0.233155 + 0.972439i \(0.425095\pi\)
\(602\) 29.6582 1.20878
\(603\) 0 0
\(604\) 36.0294 1.46601
\(605\) 9.56825 0.389005
\(606\) 0 0
\(607\) 27.9143 1.13301 0.566503 0.824059i \(-0.308296\pi\)
0.566503 + 0.824059i \(0.308296\pi\)
\(608\) 14.3293 0.581130
\(609\) 0 0
\(610\) 31.2860 1.26673
\(611\) 0 0
\(612\) 0 0
\(613\) 4.65394 0.187971 0.0939855 0.995574i \(-0.470039\pi\)
0.0939855 + 0.995574i \(0.470039\pi\)
\(614\) 1.89334 0.0764092
\(615\) 0 0
\(616\) 7.82862 0.315424
\(617\) −15.9572 −0.642411 −0.321205 0.947010i \(-0.604088\pi\)
−0.321205 + 0.947010i \(0.604088\pi\)
\(618\) 0 0
\(619\) −1.02142 −0.0410545 −0.0205272 0.999789i \(-0.506534\pi\)
−0.0205272 + 0.999789i \(0.506534\pi\)
\(620\) −12.4998 −0.502003
\(621\) 0 0
\(622\) −57.5725 −2.30845
\(623\) 12.1751 0.487786
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 84.4225 3.37420
\(627\) 0 0
\(628\) 11.6926 0.466585
\(629\) 48.0550 1.91608
\(630\) 0 0
\(631\) 20.4998 0.816083 0.408041 0.912963i \(-0.366212\pi\)
0.408041 + 0.912963i \(0.366212\pi\)
\(632\) 9.74384 0.387589
\(633\) 0 0
\(634\) −24.0210 −0.953994
\(635\) 10.3931 0.412438
\(636\) 0 0
\(637\) 0 0
\(638\) −17.8715 −0.707538
\(639\) 0 0
\(640\) −17.3612 −0.686262
\(641\) −38.2646 −1.51136 −0.755680 0.654941i \(-0.772693\pi\)
−0.755680 + 0.654941i \(0.772693\pi\)
\(642\) 0 0
\(643\) 33.1109 1.30577 0.652883 0.757459i \(-0.273560\pi\)
0.652883 + 0.757459i \(0.273560\pi\)
\(644\) −20.9651 −0.826141
\(645\) 0 0
\(646\) −107.273 −4.22058
\(647\) 16.9614 0.666820 0.333410 0.942782i \(-0.391801\pi\)
0.333410 + 0.942782i \(0.391801\pi\)
\(648\) 0 0
\(649\) −6.42754 −0.252303
\(650\) 0 0
\(651\) 0 0
\(652\) −36.7643 −1.43980
\(653\) 19.1709 0.750216 0.375108 0.926981i \(-0.377606\pi\)
0.375108 + 0.926981i \(0.377606\pi\)
\(654\) 0 0
\(655\) −6.39312 −0.249800
\(656\) −32.2217 −1.25805
\(657\) 0 0
\(658\) 3.04239 0.118605
\(659\) −37.8715 −1.47526 −0.737631 0.675204i \(-0.764056\pi\)
−0.737631 + 0.675204i \(0.764056\pi\)
\(660\) 0 0
\(661\) −24.3931 −0.948782 −0.474391 0.880314i \(-0.657332\pi\)
−0.474391 + 0.880314i \(0.657332\pi\)
\(662\) 38.1579 1.48305
\(663\) 0 0
\(664\) 29.3717 1.13984
\(665\) 8.35027 0.323810
\(666\) 0 0
\(667\) 25.0508 0.969971
\(668\) −72.9013 −2.82064
\(669\) 0 0
\(670\) −23.3288 −0.901272
\(671\) −15.0386 −0.580560
\(672\) 0 0
\(673\) −21.1281 −0.814428 −0.407214 0.913333i \(-0.633500\pi\)
−0.407214 + 0.913333i \(0.633500\pi\)
\(674\) 55.6363 2.14303
\(675\) 0 0
\(676\) 0 0
\(677\) 15.3973 0.591767 0.295884 0.955224i \(-0.404386\pi\)
0.295884 + 0.955224i \(0.404386\pi\)
\(678\) 0 0
\(679\) 2.18356 0.0837972
\(680\) −33.7648 −1.29482
\(681\) 0 0
\(682\) 8.87192 0.339723
\(683\) 30.0722 1.15068 0.575341 0.817914i \(-0.304869\pi\)
0.575341 + 0.817914i \(0.304869\pi\)
\(684\) 0 0
\(685\) −16.7434 −0.639732
\(686\) 37.4355 1.42929
\(687\) 0 0
\(688\) −51.9562 −1.98081
\(689\) 0 0
\(690\) 0 0
\(691\) 8.14950 0.310022 0.155011 0.987913i \(-0.450459\pi\)
0.155011 + 0.987913i \(0.450459\pi\)
\(692\) 33.3927 1.26940
\(693\) 0 0
\(694\) −14.3931 −0.546355
\(695\) −5.78202 −0.219325
\(696\) 0 0
\(697\) 38.1323 1.44436
\(698\) −68.5082 −2.59307
\(699\) 0 0
\(700\) 5.02142 0.189792
\(701\) 28.6921 1.08369 0.541843 0.840480i \(-0.317727\pi\)
0.541843 + 0.840480i \(0.317727\pi\)
\(702\) 0 0
\(703\) 54.3074 2.04824
\(704\) 6.37123 0.240125
\(705\) 0 0
\(706\) 71.5506 2.69284
\(707\) 12.3847 0.465774
\(708\) 0 0
\(709\) −12.3074 −0.462215 −0.231108 0.972928i \(-0.574235\pi\)
−0.231108 + 0.972928i \(0.574235\pi\)
\(710\) −12.9357 −0.485469
\(711\) 0 0
\(712\) −55.6363 −2.08506
\(713\) −12.4360 −0.465730
\(714\) 0 0
\(715\) 0 0
\(716\) 65.3154 2.44095
\(717\) 0 0
\(718\) 31.3288 1.16918
\(719\) 28.7862 1.07355 0.536773 0.843727i \(-0.319643\pi\)
0.536773 + 0.843727i \(0.319643\pi\)
\(720\) 0 0
\(721\) 22.4275 0.835245
\(722\) −73.9332 −2.75151
\(723\) 0 0
\(724\) 66.2302 2.46142
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 34.3931 1.27557 0.637785 0.770214i \(-0.279851\pi\)
0.637785 + 0.770214i \(0.279851\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 29.7648 1.10164
\(731\) 61.4868 2.27417
\(732\) 0 0
\(733\) 29.0042 1.07129 0.535647 0.844442i \(-0.320068\pi\)
0.535647 + 0.844442i \(0.320068\pi\)
\(734\) 69.4868 2.56480
\(735\) 0 0
\(736\) 8.57292 0.316002
\(737\) 11.2138 0.413065
\(738\) 0 0
\(739\) 6.27804 0.230941 0.115471 0.993311i \(-0.463162\pi\)
0.115471 + 0.993311i \(0.463162\pi\)
\(740\) 32.6577 1.20052
\(741\) 0 0
\(742\) 30.3074 1.11262
\(743\) 12.2352 0.448866 0.224433 0.974490i \(-0.427947\pi\)
0.224433 + 0.974490i \(0.427947\pi\)
\(744\) 0 0
\(745\) −15.3461 −0.562236
\(746\) 5.85050 0.214202
\(747\) 0 0
\(748\) 31.0080 1.13376
\(749\) 22.2180 0.811827
\(750\) 0 0
\(751\) −28.8757 −1.05369 −0.526844 0.849962i \(-0.676625\pi\)
−0.526844 + 0.849962i \(0.676625\pi\)
\(752\) −5.32976 −0.194357
\(753\) 0 0
\(754\) 0 0
\(755\) −8.58546 −0.312457
\(756\) 0 0
\(757\) 30.3503 1.10310 0.551550 0.834142i \(-0.314037\pi\)
0.551550 + 0.834142i \(0.314037\pi\)
\(758\) 61.1146 2.21978
\(759\) 0 0
\(760\) −38.1579 −1.38413
\(761\) −27.1709 −0.984945 −0.492473 0.870328i \(-0.663907\pi\)
−0.492473 + 0.870328i \(0.663907\pi\)
\(762\) 0 0
\(763\) −10.0428 −0.363575
\(764\) −45.0852 −1.63113
\(765\) 0 0
\(766\) −14.4569 −0.522350
\(767\) 0 0
\(768\) 0 0
\(769\) 38.3503 1.38295 0.691473 0.722402i \(-0.256962\pi\)
0.691473 + 0.722402i \(0.256962\pi\)
\(770\) −3.56404 −0.128439
\(771\) 0 0
\(772\) −40.8710 −1.47098
\(773\) −50.2646 −1.80789 −0.903946 0.427647i \(-0.859342\pi\)
−0.903946 + 0.427647i \(0.859342\pi\)
\(774\) 0 0
\(775\) 2.97858 0.106994
\(776\) −9.97812 −0.358194
\(777\) 0 0
\(778\) 33.9781 1.21817
\(779\) 43.0937 1.54399
\(780\) 0 0
\(781\) 6.21798 0.222497
\(782\) −64.1789 −2.29503
\(783\) 0 0
\(784\) −29.0550 −1.03768
\(785\) −2.78623 −0.0994448
\(786\) 0 0
\(787\) 13.2860 0.473595 0.236797 0.971559i \(-0.423902\pi\)
0.236797 + 0.971559i \(0.423902\pi\)
\(788\) −40.1360 −1.42979
\(789\) 0 0
\(790\) −4.43596 −0.157824
\(791\) −9.52119 −0.338535
\(792\) 0 0
\(793\) 0 0
\(794\) −30.2008 −1.07179
\(795\) 0 0
\(796\) 24.9995 0.886085
\(797\) −9.82487 −0.348015 −0.174007 0.984744i \(-0.555672\pi\)
−0.174007 + 0.984744i \(0.555672\pi\)
\(798\) 0 0
\(799\) 6.30742 0.223141
\(800\) −2.05333 −0.0725961
\(801\) 0 0
\(802\) 93.2087 3.29131
\(803\) −14.3074 −0.504898
\(804\) 0 0
\(805\) 4.99579 0.176078
\(806\) 0 0
\(807\) 0 0
\(808\) −56.5939 −1.99097
\(809\) 9.91431 0.348569 0.174284 0.984695i \(-0.444239\pi\)
0.174284 + 0.984695i \(0.444239\pi\)
\(810\) 0 0
\(811\) 36.5855 1.28469 0.642345 0.766416i \(-0.277962\pi\)
0.642345 + 0.766416i \(0.277962\pi\)
\(812\) −30.1285 −1.05730
\(813\) 0 0
\(814\) −23.1793 −0.812436
\(815\) 8.76060 0.306870
\(816\) 0 0
\(817\) 69.4868 2.43103
\(818\) −34.8500 −1.21850
\(819\) 0 0
\(820\) 25.9143 0.904967
\(821\) −34.4741 −1.20316 −0.601578 0.798814i \(-0.705461\pi\)
−0.601578 + 0.798814i \(0.705461\pi\)
\(822\) 0 0
\(823\) 13.2566 0.462097 0.231048 0.972942i \(-0.425784\pi\)
0.231048 + 0.972942i \(0.425784\pi\)
\(824\) −102.486 −3.57028
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) 28.1495 0.978854 0.489427 0.872044i \(-0.337206\pi\)
0.489427 + 0.872044i \(0.337206\pi\)
\(828\) 0 0
\(829\) 16.3418 0.567576 0.283788 0.958887i \(-0.408409\pi\)
0.283788 + 0.958887i \(0.408409\pi\)
\(830\) −13.3717 −0.464138
\(831\) 0 0
\(832\) 0 0
\(833\) 34.3847 1.19136
\(834\) 0 0
\(835\) 17.3717 0.601172
\(836\) 35.0424 1.21197
\(837\) 0 0
\(838\) 7.91431 0.273395
\(839\) −30.3675 −1.04840 −0.524201 0.851595i \(-0.675636\pi\)
−0.524201 + 0.851595i \(0.675636\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −40.5939 −1.39896
\(843\) 0 0
\(844\) 100.358 3.45446
\(845\) 0 0
\(846\) 0 0
\(847\) −11.4490 −0.393391
\(848\) −53.0937 −1.82324
\(849\) 0 0
\(850\) 15.3717 0.527245
\(851\) 32.4910 1.11378
\(852\) 0 0
\(853\) 42.1407 1.44287 0.721435 0.692482i \(-0.243483\pi\)
0.721435 + 0.692482i \(0.243483\pi\)
\(854\) −37.4355 −1.28102
\(855\) 0 0
\(856\) −101.529 −3.47018
\(857\) 2.17513 0.0743012 0.0371506 0.999310i \(-0.488172\pi\)
0.0371506 + 0.999310i \(0.488172\pi\)
\(858\) 0 0
\(859\) 18.5682 0.633541 0.316770 0.948502i \(-0.397402\pi\)
0.316770 + 0.948502i \(0.397402\pi\)
\(860\) 41.7858 1.42488
\(861\) 0 0
\(862\) −11.4145 −0.388781
\(863\) 33.7220 1.14791 0.573954 0.818887i \(-0.305409\pi\)
0.573954 + 0.818887i \(0.305409\pi\)
\(864\) 0 0
\(865\) −7.95715 −0.270551
\(866\) 95.4649 3.24403
\(867\) 0 0
\(868\) 14.9567 0.507663
\(869\) 2.13229 0.0723330
\(870\) 0 0
\(871\) 0 0
\(872\) 45.8924 1.55411
\(873\) 0 0
\(874\) −72.5292 −2.45334
\(875\) −1.19656 −0.0404510
\(876\) 0 0
\(877\) −43.4868 −1.46844 −0.734222 0.678910i \(-0.762453\pi\)
−0.734222 + 0.678910i \(0.762453\pi\)
\(878\) −19.2650 −0.650164
\(879\) 0 0
\(880\) 6.24361 0.210472
\(881\) −26.7005 −0.899564 −0.449782 0.893138i \(-0.648498\pi\)
−0.449782 + 0.893138i \(0.648498\pi\)
\(882\) 0 0
\(883\) 20.2990 0.683116 0.341558 0.939861i \(-0.389045\pi\)
0.341558 + 0.939861i \(0.389045\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 86.9223 2.92021
\(887\) −36.0550 −1.21061 −0.605305 0.795994i \(-0.706949\pi\)
−0.605305 + 0.795994i \(0.706949\pi\)
\(888\) 0 0
\(889\) −12.4360 −0.417089
\(890\) 25.3288 0.849025
\(891\) 0 0
\(892\) −11.0298 −0.369307
\(893\) 7.12808 0.238532
\(894\) 0 0
\(895\) −15.5640 −0.520248
\(896\) 20.7737 0.694000
\(897\) 0 0
\(898\) 15.3717 0.512960
\(899\) −17.8715 −0.596047
\(900\) 0 0
\(901\) 62.8328 2.09326
\(902\) −18.3931 −0.612424
\(903\) 0 0
\(904\) 43.5087 1.44708
\(905\) −15.7820 −0.524612
\(906\) 0 0
\(907\) −7.26504 −0.241232 −0.120616 0.992699i \(-0.538487\pi\)
−0.120616 + 0.992699i \(0.538487\pi\)
\(908\) 66.1579 2.19553
\(909\) 0 0
\(910\) 0 0
\(911\) 6.65769 0.220579 0.110290 0.993899i \(-0.464822\pi\)
0.110290 + 0.993899i \(0.464822\pi\)
\(912\) 0 0
\(913\) 6.42754 0.212721
\(914\) 3.45738 0.114360
\(915\) 0 0
\(916\) −36.6921 −1.21234
\(917\) 7.64973 0.252616
\(918\) 0 0
\(919\) −27.1831 −0.896688 −0.448344 0.893861i \(-0.647986\pi\)
−0.448344 + 0.893861i \(0.647986\pi\)
\(920\) −22.8291 −0.752652
\(921\) 0 0
\(922\) −70.9013 −2.33501
\(923\) 0 0
\(924\) 0 0
\(925\) −7.78202 −0.255871
\(926\) 40.7643 1.33960
\(927\) 0 0
\(928\) 12.3200 0.404423
\(929\) −15.3973 −0.505170 −0.252585 0.967575i \(-0.581281\pi\)
−0.252585 + 0.967575i \(0.581281\pi\)
\(930\) 0 0
\(931\) 38.8585 1.27353
\(932\) 9.12808 0.299000
\(933\) 0 0
\(934\) 64.0932 2.09719
\(935\) −7.38890 −0.241643
\(936\) 0 0
\(937\) 1.12808 0.0368527 0.0184264 0.999830i \(-0.494134\pi\)
0.0184264 + 0.999830i \(0.494134\pi\)
\(938\) 27.9143 0.911434
\(939\) 0 0
\(940\) 4.28646 0.139809
\(941\) −30.1407 −0.982559 −0.491280 0.871002i \(-0.663471\pi\)
−0.491280 + 0.871002i \(0.663471\pi\)
\(942\) 0 0
\(943\) 25.7820 0.839578
\(944\) 28.0294 0.912279
\(945\) 0 0
\(946\) −29.6582 −0.964270
\(947\) −20.0294 −0.650868 −0.325434 0.945565i \(-0.605510\pi\)
−0.325434 + 0.945565i \(0.605510\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 17.3717 0.563612
\(951\) 0 0
\(952\) 40.4015 1.30942
\(953\) 43.2259 1.40023 0.700113 0.714032i \(-0.253133\pi\)
0.700113 + 0.714032i \(0.253133\pi\)
\(954\) 0 0
\(955\) 10.7434 0.347648
\(956\) 11.7648 0.380501
\(957\) 0 0
\(958\) 18.8929 0.610401
\(959\) 20.0344 0.646945
\(960\) 0 0
\(961\) −22.1281 −0.713809
\(962\) 0 0
\(963\) 0 0
\(964\) 25.1793 0.810972
\(965\) 9.73917 0.313515
\(966\) 0 0
\(967\) −57.6875 −1.85511 −0.927553 0.373691i \(-0.878092\pi\)
−0.927553 + 0.373691i \(0.878092\pi\)
\(968\) 52.3179 1.68156
\(969\) 0 0
\(970\) 4.54262 0.145855
\(971\) 19.5296 0.626735 0.313368 0.949632i \(-0.398543\pi\)
0.313368 + 0.949632i \(0.398543\pi\)
\(972\) 0 0
\(973\) 6.91852 0.221798
\(974\) 10.9786 0.351776
\(975\) 0 0
\(976\) 65.5809 2.09919
\(977\) −40.3074 −1.28955 −0.644774 0.764373i \(-0.723049\pi\)
−0.644774 + 0.764373i \(0.723049\pi\)
\(978\) 0 0
\(979\) −12.1751 −0.389119
\(980\) 23.3675 0.746447
\(981\) 0 0
\(982\) −0.213311 −0.00680702
\(983\) 32.2008 1.02705 0.513523 0.858076i \(-0.328340\pi\)
0.513523 + 0.858076i \(0.328340\pi\)
\(984\) 0 0
\(985\) 9.56404 0.304736
\(986\) −92.2302 −2.93721
\(987\) 0 0
\(988\) 0 0
\(989\) 41.5725 1.32193
\(990\) 0 0
\(991\) 26.4826 0.841246 0.420623 0.907235i \(-0.361811\pi\)
0.420623 + 0.907235i \(0.361811\pi\)
\(992\) −6.11599 −0.194183
\(993\) 0 0
\(994\) 15.4783 0.490943
\(995\) −5.95715 −0.188854
\(996\) 0 0
\(997\) 35.1365 1.11278 0.556392 0.830920i \(-0.312185\pi\)
0.556392 + 0.830920i \(0.312185\pi\)
\(998\) −44.1151 −1.39644
\(999\) 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 7605.2.a.bx.1.1 3
3.2 odd 2 2535.2.a.bc.1.3 3
13.12 even 2 585.2.a.n.1.3 3
39.38 odd 2 195.2.a.e.1.1 3
52.51 odd 2 9360.2.a.dd.1.2 3
65.12 odd 4 2925.2.c.w.2224.5 6
65.38 odd 4 2925.2.c.w.2224.2 6
65.64 even 2 2925.2.a.bh.1.1 3
156.155 even 2 3120.2.a.bj.1.2 3
195.38 even 4 975.2.c.i.274.5 6
195.77 even 4 975.2.c.i.274.2 6
195.194 odd 2 975.2.a.o.1.3 3
273.272 even 2 9555.2.a.bq.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.1 3 39.38 odd 2
585.2.a.n.1.3 3 13.12 even 2
975.2.a.o.1.3 3 195.194 odd 2
975.2.c.i.274.2 6 195.77 even 4
975.2.c.i.274.5 6 195.38 even 4
2535.2.a.bc.1.3 3 3.2 odd 2
2925.2.a.bh.1.1 3 65.64 even 2
2925.2.c.w.2224.2 6 65.38 odd 4
2925.2.c.w.2224.5 6 65.12 odd 4
3120.2.a.bj.1.2 3 156.155 even 2
7605.2.a.bx.1.1 3 1.1 even 1 trivial
9360.2.a.dd.1.2 3 52.51 odd 2
9555.2.a.bq.1.1 3 273.272 even 2