Properties

Label 3465.2.a.bl.1.2
Level 3465
Weight 2
Character 3465.1
Self dual yes
Analytic conductor 27.668
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3465.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(27.6681643004\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.13448.1
Defining polynomial: \(x^{4} - 7 x^{2} + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1155)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.546295\) of defining polynomial
Character \(\chi\) \(=\) 3465.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.546295 q^{2} -1.70156 q^{4} +1.00000 q^{5} -1.00000 q^{7} +2.02214 q^{8} +O(q^{10})\) \(q-0.546295 q^{2} -1.70156 q^{4} +1.00000 q^{5} -1.00000 q^{7} +2.02214 q^{8} -0.546295 q^{10} +1.00000 q^{11} -0.568438 q^{13} +0.546295 q^{14} +2.29844 q^{16} -2.70156 q^{17} +6.62049 q^{19} -1.70156 q^{20} -0.546295 q^{22} -8.93103 q^{23} +1.00000 q^{25} +0.310535 q^{26} +1.70156 q^{28} -5.27000 q^{29} +9.66103 q^{31} -5.29991 q^{32} +1.47585 q^{34} -1.00000 q^{35} -2.75362 q^{37} -3.61674 q^{38} +2.02214 q^{40} +10.9831 q^{41} -0.0520550 q^{43} -1.70156 q^{44} +4.87897 q^{46} +10.1567 q^{47} +1.00000 q^{49} -0.546295 q^{50} +0.967233 q^{52} -1.56469 q^{53} +1.00000 q^{55} -2.02214 q^{56} +2.87897 q^{58} -6.36259 q^{59} -3.71308 q^{61} -5.27777 q^{62} -1.70156 q^{64} -0.568438 q^{65} -10.4146 q^{67} +4.59688 q^{68} +0.546295 q^{70} -2.56844 q^{71} +2.26625 q^{73} +1.50429 q^{74} -11.2652 q^{76} -1.00000 q^{77} -2.56844 q^{79} +2.29844 q^{80} -6.00000 q^{82} -17.1605 q^{83} -2.70156 q^{85} +0.0284374 q^{86} +2.02214 q^{88} +10.7772 q^{89} +0.568438 q^{91} +15.1967 q^{92} -5.54857 q^{94} +6.62049 q^{95} +17.9952 q^{97} -0.546295 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{4} + 4q^{5} - 4q^{7} + O(q^{10}) \) \( 4q + 6q^{4} + 4q^{5} - 4q^{7} + 4q^{11} + 8q^{13} + 22q^{16} + 2q^{17} + 10q^{19} + 6q^{20} + 2q^{23} + 4q^{25} - 20q^{26} - 6q^{28} + 2q^{29} + 24q^{31} - 4q^{35} + 8q^{37} - 16q^{38} + 6q^{43} + 6q^{44} - 12q^{46} - 4q^{47} + 4q^{49} + 12q^{52} - 14q^{53} + 4q^{55} - 20q^{58} + 2q^{59} + 6q^{61} - 8q^{62} + 6q^{64} + 8q^{65} - 8q^{67} + 44q^{68} + 4q^{73} + 36q^{74} + 56q^{76} - 4q^{77} + 22q^{80} - 24q^{82} - 6q^{83} + 2q^{85} + 36q^{86} - 18q^{89} - 8q^{91} + 44q^{92} - 36q^{94} + 10q^{95} - 6q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.546295 −0.386289 −0.193144 0.981170i \(-0.561869\pi\)
−0.193144 + 0.981170i \(0.561869\pi\)
\(3\) 0 0
\(4\) −1.70156 −0.850781
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.02214 0.714936
\(9\) 0 0
\(10\) −0.546295 −0.172754
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −0.568438 −0.157656 −0.0788282 0.996888i \(-0.525118\pi\)
−0.0788282 + 0.996888i \(0.525118\pi\)
\(14\) 0.546295 0.146003
\(15\) 0 0
\(16\) 2.29844 0.574609
\(17\) −2.70156 −0.655225 −0.327613 0.944812i \(-0.606244\pi\)
−0.327613 + 0.944812i \(0.606244\pi\)
\(18\) 0 0
\(19\) 6.62049 1.51885 0.759423 0.650598i \(-0.225482\pi\)
0.759423 + 0.650598i \(0.225482\pi\)
\(20\) −1.70156 −0.380481
\(21\) 0 0
\(22\) −0.546295 −0.116470
\(23\) −8.93103 −1.86225 −0.931124 0.364703i \(-0.881171\pi\)
−0.931124 + 0.364703i \(0.881171\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.310535 0.0609009
\(27\) 0 0
\(28\) 1.70156 0.321565
\(29\) −5.27000 −0.978615 −0.489307 0.872111i \(-0.662750\pi\)
−0.489307 + 0.872111i \(0.662750\pi\)
\(30\) 0 0
\(31\) 9.66103 1.73517 0.867586 0.497287i \(-0.165671\pi\)
0.867586 + 0.497287i \(0.165671\pi\)
\(32\) −5.29991 −0.936901
\(33\) 0 0
\(34\) 1.47585 0.253106
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −2.75362 −0.452692 −0.226346 0.974047i \(-0.572678\pi\)
−0.226346 + 0.974047i \(0.572678\pi\)
\(38\) −3.61674 −0.586713
\(39\) 0 0
\(40\) 2.02214 0.319729
\(41\) 10.9831 1.71527 0.857635 0.514259i \(-0.171933\pi\)
0.857635 + 0.514259i \(0.171933\pi\)
\(42\) 0 0
\(43\) −0.0520550 −0.00793831 −0.00396916 0.999992i \(-0.501263\pi\)
−0.00396916 + 0.999992i \(0.501263\pi\)
\(44\) −1.70156 −0.256520
\(45\) 0 0
\(46\) 4.87897 0.719365
\(47\) 10.1567 1.48151 0.740756 0.671774i \(-0.234467\pi\)
0.740756 + 0.671774i \(0.234467\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.546295 −0.0772577
\(51\) 0 0
\(52\) 0.967233 0.134131
\(53\) −1.56469 −0.214926 −0.107463 0.994209i \(-0.534273\pi\)
−0.107463 + 0.994209i \(0.534273\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) −2.02214 −0.270220
\(57\) 0 0
\(58\) 2.87897 0.378028
\(59\) −6.36259 −0.828339 −0.414169 0.910200i \(-0.635928\pi\)
−0.414169 + 0.910200i \(0.635928\pi\)
\(60\) 0 0
\(61\) −3.71308 −0.475412 −0.237706 0.971337i \(-0.576395\pi\)
−0.237706 + 0.971337i \(0.576395\pi\)
\(62\) −5.27777 −0.670277
\(63\) 0 0
\(64\) −1.70156 −0.212695
\(65\) −0.568438 −0.0705061
\(66\) 0 0
\(67\) −10.4146 −1.27235 −0.636176 0.771544i \(-0.719485\pi\)
−0.636176 + 0.771544i \(0.719485\pi\)
\(68\) 4.59688 0.557453
\(69\) 0 0
\(70\) 0.546295 0.0652947
\(71\) −2.56844 −0.304818 −0.152409 0.988318i \(-0.548703\pi\)
−0.152409 + 0.988318i \(0.548703\pi\)
\(72\) 0 0
\(73\) 2.26625 0.265244 0.132622 0.991167i \(-0.457660\pi\)
0.132622 + 0.991167i \(0.457660\pi\)
\(74\) 1.50429 0.174870
\(75\) 0 0
\(76\) −11.2652 −1.29220
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −2.56844 −0.288972 −0.144486 0.989507i \(-0.546153\pi\)
−0.144486 + 0.989507i \(0.546153\pi\)
\(80\) 2.29844 0.256973
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) −17.1605 −1.88361 −0.941804 0.336161i \(-0.890871\pi\)
−0.941804 + 0.336161i \(0.890871\pi\)
\(84\) 0 0
\(85\) −2.70156 −0.293026
\(86\) 0.0284374 0.00306648
\(87\) 0 0
\(88\) 2.02214 0.215561
\(89\) 10.7772 1.14238 0.571192 0.820816i \(-0.306481\pi\)
0.571192 + 0.820816i \(0.306481\pi\)
\(90\) 0 0
\(91\) 0.568438 0.0595885
\(92\) 15.1967 1.58437
\(93\) 0 0
\(94\) −5.54857 −0.572292
\(95\) 6.62049 0.679248
\(96\) 0 0
\(97\) 17.9952 1.82713 0.913567 0.406689i \(-0.133317\pi\)
0.913567 + 0.406689i \(0.133317\pi\)
\(98\) −0.546295 −0.0551841
\(99\) 0 0
\(100\) −1.70156 −0.170156
\(101\) −0.826342 −0.0822241 −0.0411120 0.999155i \(-0.513090\pi\)
−0.0411120 + 0.999155i \(0.513090\pi\)
\(102\) 0 0
\(103\) 10.5921 1.04367 0.521833 0.853048i \(-0.325248\pi\)
0.521833 + 0.853048i \(0.325248\pi\)
\(104\) −1.14946 −0.112714
\(105\) 0 0
\(106\) 0.854779 0.0830235
\(107\) 13.7864 1.33278 0.666390 0.745603i \(-0.267839\pi\)
0.666390 + 0.745603i \(0.267839\pi\)
\(108\) 0 0
\(109\) 19.8905 1.90516 0.952582 0.304282i \(-0.0984166\pi\)
0.952582 + 0.304282i \(0.0984166\pi\)
\(110\) −0.546295 −0.0520872
\(111\) 0 0
\(112\) −2.29844 −0.217182
\(113\) −6.43531 −0.605383 −0.302692 0.953089i \(-0.597885\pi\)
−0.302692 + 0.953089i \(0.597885\pi\)
\(114\) 0 0
\(115\) −8.93103 −0.832823
\(116\) 8.96723 0.832587
\(117\) 0 0
\(118\) 3.47585 0.319978
\(119\) 2.70156 0.247652
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 2.02844 0.183646
\(123\) 0 0
\(124\) −16.4388 −1.47625
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.05206 0.359562 0.179781 0.983707i \(-0.442461\pi\)
0.179781 + 0.983707i \(0.442461\pi\)
\(128\) 11.5294 1.01906
\(129\) 0 0
\(130\) 0.310535 0.0272357
\(131\) 5.69781 0.497820 0.248910 0.968527i \(-0.419928\pi\)
0.248910 + 0.968527i \(0.419928\pi\)
\(132\) 0 0
\(133\) −6.62049 −0.574070
\(134\) 5.68947 0.491495
\(135\) 0 0
\(136\) −5.46295 −0.468444
\(137\) 3.40312 0.290749 0.145374 0.989377i \(-0.453561\pi\)
0.145374 + 0.989377i \(0.453561\pi\)
\(138\) 0 0
\(139\) −8.04724 −0.682558 −0.341279 0.939962i \(-0.610860\pi\)
−0.341279 + 0.939962i \(0.610860\pi\)
\(140\) 1.70156 0.143808
\(141\) 0 0
\(142\) 1.40312 0.117748
\(143\) −0.568438 −0.0475352
\(144\) 0 0
\(145\) −5.27000 −0.437650
\(146\) −1.23804 −0.102461
\(147\) 0 0
\(148\) 4.68545 0.385142
\(149\) −7.50723 −0.615017 −0.307508 0.951545i \(-0.599495\pi\)
−0.307508 + 0.951545i \(0.599495\pi\)
\(150\) 0 0
\(151\) 3.21795 0.261873 0.130936 0.991391i \(-0.458202\pi\)
0.130936 + 0.991391i \(0.458202\pi\)
\(152\) 13.3876 1.08588
\(153\) 0 0
\(154\) 0.546295 0.0440217
\(155\) 9.66103 0.775992
\(156\) 0 0
\(157\) −3.35107 −0.267444 −0.133722 0.991019i \(-0.542693\pi\)
−0.133722 + 0.991019i \(0.542693\pi\)
\(158\) 1.40312 0.111627
\(159\) 0 0
\(160\) −5.29991 −0.418995
\(161\) 8.93103 0.703864
\(162\) 0 0
\(163\) 10.9600 0.858457 0.429228 0.903196i \(-0.358786\pi\)
0.429228 + 0.903196i \(0.358786\pi\)
\(164\) −18.6884 −1.45932
\(165\) 0 0
\(166\) 9.37469 0.727617
\(167\) 7.58830 0.587201 0.293600 0.955928i \(-0.405147\pi\)
0.293600 + 0.955928i \(0.405147\pi\)
\(168\) 0 0
\(169\) −12.6769 −0.975144
\(170\) 1.47585 0.113192
\(171\) 0 0
\(172\) 0.0885748 0.00675377
\(173\) 18.2094 1.38443 0.692216 0.721690i \(-0.256634\pi\)
0.692216 + 0.721690i \(0.256634\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 2.29844 0.173251
\(177\) 0 0
\(178\) −5.88755 −0.441290
\(179\) −4.75362 −0.355302 −0.177651 0.984094i \(-0.556850\pi\)
−0.177651 + 0.984094i \(0.556850\pi\)
\(180\) 0 0
\(181\) 25.2652 1.87795 0.938973 0.343991i \(-0.111779\pi\)
0.938973 + 0.343991i \(0.111779\pi\)
\(182\) −0.310535 −0.0230184
\(183\) 0 0
\(184\) −18.0598 −1.33139
\(185\) −2.75362 −0.202450
\(186\) 0 0
\(187\) −2.70156 −0.197558
\(188\) −17.2823 −1.26044
\(189\) 0 0
\(190\) −3.61674 −0.262386
\(191\) 17.4504 1.26266 0.631332 0.775513i \(-0.282509\pi\)
0.631332 + 0.775513i \(0.282509\pi\)
\(192\) 0 0
\(193\) 22.9546 1.65231 0.826156 0.563442i \(-0.190523\pi\)
0.826156 + 0.563442i \(0.190523\pi\)
\(194\) −9.83067 −0.705801
\(195\) 0 0
\(196\) −1.70156 −0.121540
\(197\) 3.36634 0.239842 0.119921 0.992783i \(-0.461736\pi\)
0.119921 + 0.992783i \(0.461736\pi\)
\(198\) 0 0
\(199\) 9.54402 0.676557 0.338279 0.941046i \(-0.390155\pi\)
0.338279 + 0.941046i \(0.390155\pi\)
\(200\) 2.02214 0.142987
\(201\) 0 0
\(202\) 0.451426 0.0317622
\(203\) 5.27000 0.369882
\(204\) 0 0
\(205\) 10.9831 0.767092
\(206\) −5.78638 −0.403156
\(207\) 0 0
\(208\) −1.30652 −0.0905909
\(209\) 6.62049 0.457949
\(210\) 0 0
\(211\) −7.73375 −0.532413 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(212\) 2.66241 0.182855
\(213\) 0 0
\(214\) −7.53143 −0.514838
\(215\) −0.0520550 −0.00355012
\(216\) 0 0
\(217\) −9.66103 −0.655833
\(218\) −10.8661 −0.735943
\(219\) 0 0
\(220\) −1.70156 −0.114719
\(221\) 1.53567 0.103300
\(222\) 0 0
\(223\) −13.9141 −0.931758 −0.465879 0.884848i \(-0.654262\pi\)
−0.465879 + 0.884848i \(0.654262\pi\)
\(224\) 5.29991 0.354115
\(225\) 0 0
\(226\) 3.51558 0.233853
\(227\) −0.597452 −0.0396543 −0.0198271 0.999803i \(-0.506312\pi\)
−0.0198271 + 0.999803i \(0.506312\pi\)
\(228\) 0 0
\(229\) 21.1895 1.40024 0.700121 0.714024i \(-0.253129\pi\)
0.700121 + 0.714024i \(0.253129\pi\)
\(230\) 4.87897 0.321710
\(231\) 0 0
\(232\) −10.6567 −0.699647
\(233\) 20.2821 1.32872 0.664362 0.747411i \(-0.268703\pi\)
0.664362 + 0.747411i \(0.268703\pi\)
\(234\) 0 0
\(235\) 10.1567 0.662553
\(236\) 10.8263 0.704735
\(237\) 0 0
\(238\) −1.47585 −0.0956651
\(239\) −2.23723 −0.144715 −0.0723573 0.997379i \(-0.523052\pi\)
−0.0723573 + 0.997379i \(0.523052\pi\)
\(240\) 0 0
\(241\) 8.93045 0.575261 0.287630 0.957741i \(-0.407133\pi\)
0.287630 + 0.957741i \(0.407133\pi\)
\(242\) −0.546295 −0.0351172
\(243\) 0 0
\(244\) 6.31804 0.404471
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) −3.76334 −0.239456
\(248\) 19.5360 1.24054
\(249\) 0 0
\(250\) −0.546295 −0.0345507
\(251\) −3.35884 −0.212008 −0.106004 0.994366i \(-0.533806\pi\)
−0.106004 + 0.994366i \(0.533806\pi\)
\(252\) 0 0
\(253\) −8.93103 −0.561489
\(254\) −2.21362 −0.138895
\(255\) 0 0
\(256\) −2.89531 −0.180957
\(257\) −5.80943 −0.362382 −0.181191 0.983448i \(-0.557995\pi\)
−0.181191 + 0.983448i \(0.557995\pi\)
\(258\) 0 0
\(259\) 2.75362 0.171101
\(260\) 0.967233 0.0599853
\(261\) 0 0
\(262\) −3.11268 −0.192302
\(263\) 23.3221 1.43810 0.719050 0.694959i \(-0.244577\pi\)
0.719050 + 0.694959i \(0.244577\pi\)
\(264\) 0 0
\(265\) −1.56469 −0.0961179
\(266\) 3.61674 0.221757
\(267\) 0 0
\(268\) 17.7212 1.08249
\(269\) −29.1246 −1.77576 −0.887878 0.460080i \(-0.847821\pi\)
−0.887878 + 0.460080i \(0.847821\pi\)
\(270\) 0 0
\(271\) 31.2416 1.89779 0.948895 0.315592i \(-0.102203\pi\)
0.948895 + 0.315592i \(0.102203\pi\)
\(272\) −6.20937 −0.376499
\(273\) 0 0
\(274\) −1.85911 −0.112313
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) −15.8988 −0.955269 −0.477634 0.878559i \(-0.658506\pi\)
−0.477634 + 0.878559i \(0.658506\pi\)
\(278\) 4.39616 0.263664
\(279\) 0 0
\(280\) −2.02214 −0.120846
\(281\) 14.1041 0.841381 0.420690 0.907204i \(-0.361788\pi\)
0.420690 + 0.907204i \(0.361788\pi\)
\(282\) 0 0
\(283\) −1.32745 −0.0789088 −0.0394544 0.999221i \(-0.512562\pi\)
−0.0394544 + 0.999221i \(0.512562\pi\)
\(284\) 4.37036 0.259333
\(285\) 0 0
\(286\) 0.310535 0.0183623
\(287\) −10.9831 −0.648311
\(288\) 0 0
\(289\) −9.70156 −0.570680
\(290\) 2.87897 0.169059
\(291\) 0 0
\(292\) −3.85616 −0.225665
\(293\) −18.3784 −1.07368 −0.536840 0.843684i \(-0.680382\pi\)
−0.536840 + 0.843684i \(0.680382\pi\)
\(294\) 0 0
\(295\) −6.36259 −0.370444
\(296\) −5.56821 −0.323646
\(297\) 0 0
\(298\) 4.10116 0.237574
\(299\) 5.07674 0.293595
\(300\) 0 0
\(301\) 0.0520550 0.00300040
\(302\) −1.75795 −0.101158
\(303\) 0 0
\(304\) 15.2168 0.872743
\(305\) −3.71308 −0.212611
\(306\) 0 0
\(307\) 6.45143 0.368202 0.184101 0.982907i \(-0.441063\pi\)
0.184101 + 0.982907i \(0.441063\pi\)
\(308\) 1.70156 0.0969555
\(309\) 0 0
\(310\) −5.27777 −0.299757
\(311\) 29.4136 1.66789 0.833946 0.551847i \(-0.186077\pi\)
0.833946 + 0.551847i \(0.186077\pi\)
\(312\) 0 0
\(313\) −24.7542 −1.39919 −0.699595 0.714540i \(-0.746636\pi\)
−0.699595 + 0.714540i \(0.746636\pi\)
\(314\) 1.83067 0.103311
\(315\) 0 0
\(316\) 4.37036 0.245852
\(317\) 15.0955 0.847850 0.423925 0.905697i \(-0.360652\pi\)
0.423925 + 0.905697i \(0.360652\pi\)
\(318\) 0 0
\(319\) −5.27000 −0.295063
\(320\) −1.70156 −0.0951202
\(321\) 0 0
\(322\) −4.87897 −0.271895
\(323\) −17.8857 −0.995186
\(324\) 0 0
\(325\) −0.568438 −0.0315313
\(326\) −5.98741 −0.331612
\(327\) 0 0
\(328\) 22.2094 1.22631
\(329\) −10.1567 −0.559959
\(330\) 0 0
\(331\) 6.78263 0.372807 0.186404 0.982473i \(-0.440317\pi\)
0.186404 + 0.982473i \(0.440317\pi\)
\(332\) 29.1996 1.60254
\(333\) 0 0
\(334\) −4.14545 −0.226829
\(335\) −10.4146 −0.569013
\(336\) 0 0
\(337\) −31.9509 −1.74048 −0.870238 0.492631i \(-0.836035\pi\)
−0.870238 + 0.492631i \(0.836035\pi\)
\(338\) 6.92531 0.376687
\(339\) 0 0
\(340\) 4.59688 0.249301
\(341\) 9.66103 0.523174
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −0.105263 −0.00567538
\(345\) 0 0
\(346\) −9.94768 −0.534791
\(347\) 13.6694 0.733810 0.366905 0.930258i \(-0.380417\pi\)
0.366905 + 0.930258i \(0.380417\pi\)
\(348\) 0 0
\(349\) 16.1720 0.865668 0.432834 0.901474i \(-0.357514\pi\)
0.432834 + 0.901474i \(0.357514\pi\)
\(350\) 0.546295 0.0292007
\(351\) 0 0
\(352\) −5.29991 −0.282486
\(353\) 9.94313 0.529219 0.264610 0.964356i \(-0.414757\pi\)
0.264610 + 0.964356i \(0.414757\pi\)
\(354\) 0 0
\(355\) −2.56844 −0.136319
\(356\) −18.3381 −0.971919
\(357\) 0 0
\(358\) 2.59688 0.137249
\(359\) 12.5845 0.664187 0.332094 0.943246i \(-0.392245\pi\)
0.332094 + 0.943246i \(0.392245\pi\)
\(360\) 0 0
\(361\) 24.8309 1.30689
\(362\) −13.8022 −0.725429
\(363\) 0 0
\(364\) −0.967233 −0.0506968
\(365\) 2.26625 0.118621
\(366\) 0 0
\(367\) 36.9699 1.92981 0.964907 0.262592i \(-0.0845772\pi\)
0.964907 + 0.262592i \(0.0845772\pi\)
\(368\) −20.5274 −1.07007
\(369\) 0 0
\(370\) 1.50429 0.0782041
\(371\) 1.56469 0.0812344
\(372\) 0 0
\(373\) −13.4109 −0.694390 −0.347195 0.937793i \(-0.612866\pi\)
−0.347195 + 0.937793i \(0.612866\pi\)
\(374\) 1.47585 0.0763143
\(375\) 0 0
\(376\) 20.5384 1.05919
\(377\) 2.99567 0.154285
\(378\) 0 0
\(379\) −0.805672 −0.0413846 −0.0206923 0.999786i \(-0.506587\pi\)
−0.0206923 + 0.999786i \(0.506587\pi\)
\(380\) −11.2652 −0.577892
\(381\) 0 0
\(382\) −9.53304 −0.487753
\(383\) 22.3494 1.14200 0.571001 0.820949i \(-0.306555\pi\)
0.571001 + 0.820949i \(0.306555\pi\)
\(384\) 0 0
\(385\) −1.00000 −0.0509647
\(386\) −12.5400 −0.638269
\(387\) 0 0
\(388\) −30.6199 −1.55449
\(389\) 29.4863 1.49501 0.747507 0.664253i \(-0.231250\pi\)
0.747507 + 0.664253i \(0.231250\pi\)
\(390\) 0 0
\(391\) 24.1277 1.22019
\(392\) 2.02214 0.102134
\(393\) 0 0
\(394\) −1.83902 −0.0926482
\(395\) −2.56844 −0.129232
\(396\) 0 0
\(397\) 4.45143 0.223411 0.111705 0.993741i \(-0.464369\pi\)
0.111705 + 0.993741i \(0.464369\pi\)
\(398\) −5.21384 −0.261346
\(399\) 0 0
\(400\) 2.29844 0.114922
\(401\) −22.7123 −1.13420 −0.567099 0.823650i \(-0.691934\pi\)
−0.567099 + 0.823650i \(0.691934\pi\)
\(402\) 0 0
\(403\) −5.49170 −0.273561
\(404\) 1.40607 0.0699547
\(405\) 0 0
\(406\) −2.87897 −0.142881
\(407\) −2.75362 −0.136492
\(408\) 0 0
\(409\) 5.09259 0.251812 0.125906 0.992042i \(-0.459816\pi\)
0.125906 + 0.992042i \(0.459816\pi\)
\(410\) −6.00000 −0.296319
\(411\) 0 0
\(412\) −18.0230 −0.887932
\(413\) 6.36259 0.313083
\(414\) 0 0
\(415\) −17.1605 −0.842376
\(416\) 3.01267 0.147708
\(417\) 0 0
\(418\) −3.61674 −0.176901
\(419\) 2.86286 0.139860 0.0699300 0.997552i \(-0.477722\pi\)
0.0699300 + 0.997552i \(0.477722\pi\)
\(420\) 0 0
\(421\) −16.1047 −0.784894 −0.392447 0.919775i \(-0.628371\pi\)
−0.392447 + 0.919775i \(0.628371\pi\)
\(422\) 4.22491 0.205665
\(423\) 0 0
\(424\) −3.16402 −0.153658
\(425\) −2.70156 −0.131045
\(426\) 0 0
\(427\) 3.71308 0.179689
\(428\) −23.4584 −1.13390
\(429\) 0 0
\(430\) 0.0284374 0.00137137
\(431\) 4.67794 0.225329 0.112664 0.993633i \(-0.464062\pi\)
0.112664 + 0.993633i \(0.464062\pi\)
\(432\) 0 0
\(433\) −27.4337 −1.31838 −0.659189 0.751977i \(-0.729100\pi\)
−0.659189 + 0.751977i \(0.729100\pi\)
\(434\) 5.27777 0.253341
\(435\) 0 0
\(436\) −33.8449 −1.62088
\(437\) −59.1278 −2.82847
\(438\) 0 0
\(439\) 5.73433 0.273685 0.136842 0.990593i \(-0.456305\pi\)
0.136842 + 0.990593i \(0.456305\pi\)
\(440\) 2.02214 0.0964019
\(441\) 0 0
\(442\) −0.838929 −0.0399038
\(443\) 9.58536 0.455414 0.227707 0.973730i \(-0.426877\pi\)
0.227707 + 0.973730i \(0.426877\pi\)
\(444\) 0 0
\(445\) 10.7772 0.510890
\(446\) 7.60121 0.359927
\(447\) 0 0
\(448\) 1.70156 0.0803913
\(449\) −30.9463 −1.46045 −0.730223 0.683209i \(-0.760584\pi\)
−0.730223 + 0.683209i \(0.760584\pi\)
\(450\) 0 0
\(451\) 10.9831 0.517173
\(452\) 10.9501 0.515049
\(453\) 0 0
\(454\) 0.326385 0.0153180
\(455\) 0.568438 0.0266488
\(456\) 0 0
\(457\) −42.2246 −1.97519 −0.987593 0.157036i \(-0.949806\pi\)
−0.987593 + 0.157036i \(0.949806\pi\)
\(458\) −11.5757 −0.540898
\(459\) 0 0
\(460\) 15.1967 0.708550
\(461\) −9.87464 −0.459908 −0.229954 0.973201i \(-0.573858\pi\)
−0.229954 + 0.973201i \(0.573858\pi\)
\(462\) 0 0
\(463\) 2.56009 0.118978 0.0594888 0.998229i \(-0.481053\pi\)
0.0594888 + 0.998229i \(0.481053\pi\)
\(464\) −12.1128 −0.562321
\(465\) 0 0
\(466\) −11.0800 −0.513271
\(467\) 19.6924 0.911256 0.455628 0.890170i \(-0.349415\pi\)
0.455628 + 0.890170i \(0.349415\pi\)
\(468\) 0 0
\(469\) 10.4146 0.480904
\(470\) −5.54857 −0.255937
\(471\) 0 0
\(472\) −12.8661 −0.592209
\(473\) −0.0520550 −0.00239349
\(474\) 0 0
\(475\) 6.62049 0.303769
\(476\) −4.59688 −0.210697
\(477\) 0 0
\(478\) 1.22219 0.0559016
\(479\) −15.3672 −0.702144 −0.351072 0.936348i \(-0.614183\pi\)
−0.351072 + 0.936348i \(0.614183\pi\)
\(480\) 0 0
\(481\) 1.56526 0.0713698
\(482\) −4.87866 −0.222217
\(483\) 0 0
\(484\) −1.70156 −0.0773437
\(485\) 17.9952 0.817119
\(486\) 0 0
\(487\) −1.52848 −0.0692621 −0.0346310 0.999400i \(-0.511026\pi\)
−0.0346310 + 0.999400i \(0.511026\pi\)
\(488\) −7.50839 −0.339889
\(489\) 0 0
\(490\) −0.546295 −0.0246791
\(491\) 40.7359 1.83839 0.919193 0.393808i \(-0.128843\pi\)
0.919193 + 0.393808i \(0.128843\pi\)
\(492\) 0 0
\(493\) 14.2372 0.641213
\(494\) 2.05589 0.0924990
\(495\) 0 0
\(496\) 22.2053 0.997046
\(497\) 2.56844 0.115210
\(498\) 0 0
\(499\) −20.3312 −0.910150 −0.455075 0.890453i \(-0.650388\pi\)
−0.455075 + 0.890453i \(0.650388\pi\)
\(500\) −1.70156 −0.0760962
\(501\) 0 0
\(502\) 1.83491 0.0818963
\(503\) 23.5952 1.05206 0.526030 0.850466i \(-0.323680\pi\)
0.526030 + 0.850466i \(0.323680\pi\)
\(504\) 0 0
\(505\) −0.826342 −0.0367717
\(506\) 4.87897 0.216897
\(507\) 0 0
\(508\) −6.89482 −0.305908
\(509\) −38.0993 −1.68872 −0.844361 0.535775i \(-0.820019\pi\)
−0.844361 + 0.535775i \(0.820019\pi\)
\(510\) 0 0
\(511\) −2.26625 −0.100253
\(512\) −21.4771 −0.949161
\(513\) 0 0
\(514\) 3.17366 0.139984
\(515\) 10.5921 0.466742
\(516\) 0 0
\(517\) 10.1567 0.446693
\(518\) −1.50429 −0.0660945
\(519\) 0 0
\(520\) −1.14946 −0.0504073
\(521\) −33.9952 −1.48936 −0.744678 0.667424i \(-0.767397\pi\)
−0.744678 + 0.667424i \(0.767397\pi\)
\(522\) 0 0
\(523\) 10.9517 0.478884 0.239442 0.970911i \(-0.423035\pi\)
0.239442 + 0.970911i \(0.423035\pi\)
\(524\) −9.69518 −0.423536
\(525\) 0 0
\(526\) −12.7407 −0.555522
\(527\) −26.0999 −1.13693
\(528\) 0 0
\(529\) 56.7633 2.46797
\(530\) 0.854779 0.0371292
\(531\) 0 0
\(532\) 11.2652 0.488408
\(533\) −6.24321 −0.270423
\(534\) 0 0
\(535\) 13.7864 0.596037
\(536\) −21.0599 −0.909650
\(537\) 0 0
\(538\) 15.9106 0.685954
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 13.4971 0.580285 0.290143 0.956983i \(-0.406297\pi\)
0.290143 + 0.956983i \(0.406297\pi\)
\(542\) −17.0671 −0.733095
\(543\) 0 0
\(544\) 14.3180 0.613881
\(545\) 19.8905 0.852015
\(546\) 0 0
\(547\) −42.0182 −1.79657 −0.898285 0.439414i \(-0.855186\pi\)
−0.898285 + 0.439414i \(0.855186\pi\)
\(548\) −5.79063 −0.247363
\(549\) 0 0
\(550\) −0.546295 −0.0232941
\(551\) −34.8900 −1.48636
\(552\) 0 0
\(553\) 2.56844 0.109221
\(554\) 8.68545 0.369009
\(555\) 0 0
\(556\) 13.6929 0.580707
\(557\) 27.9461 1.18411 0.592057 0.805896i \(-0.298316\pi\)
0.592057 + 0.805896i \(0.298316\pi\)
\(558\) 0 0
\(559\) 0.0295901 0.00125153
\(560\) −2.29844 −0.0971267
\(561\) 0 0
\(562\) −7.70500 −0.325016
\(563\) 0.266247 0.0112210 0.00561050 0.999984i \(-0.498214\pi\)
0.00561050 + 0.999984i \(0.498214\pi\)
\(564\) 0 0
\(565\) −6.43531 −0.270736
\(566\) 0.725180 0.0304816
\(567\) 0 0
\(568\) −5.19375 −0.217925
\(569\) 35.3983 1.48397 0.741987 0.670414i \(-0.233884\pi\)
0.741987 + 0.670414i \(0.233884\pi\)
\(570\) 0 0
\(571\) −0.440134 −0.0184191 −0.00920953 0.999958i \(-0.502932\pi\)
−0.00920953 + 0.999958i \(0.502932\pi\)
\(572\) 0.967233 0.0404421
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −8.93103 −0.372450
\(576\) 0 0
\(577\) −25.1030 −1.04505 −0.522527 0.852623i \(-0.675010\pi\)
−0.522527 + 0.852623i \(0.675010\pi\)
\(578\) 5.29991 0.220447
\(579\) 0 0
\(580\) 8.96723 0.372344
\(581\) 17.1605 0.711937
\(582\) 0 0
\(583\) −1.56469 −0.0648026
\(584\) 4.58268 0.189633
\(585\) 0 0
\(586\) 10.0400 0.414750
\(587\) −3.24638 −0.133993 −0.0669963 0.997753i \(-0.521342\pi\)
−0.0669963 + 0.997753i \(0.521342\pi\)
\(588\) 0 0
\(589\) 63.9608 2.63546
\(590\) 3.47585 0.143098
\(591\) 0 0
\(592\) −6.32902 −0.260121
\(593\) −10.7252 −0.440430 −0.220215 0.975451i \(-0.570676\pi\)
−0.220215 + 0.975451i \(0.570676\pi\)
\(594\) 0 0
\(595\) 2.70156 0.110753
\(596\) 12.7740 0.523244
\(597\) 0 0
\(598\) −2.77340 −0.113413
\(599\) −36.3607 −1.48566 −0.742829 0.669481i \(-0.766517\pi\)
−0.742829 + 0.669481i \(0.766517\pi\)
\(600\) 0 0
\(601\) −39.7034 −1.61954 −0.809769 0.586749i \(-0.800407\pi\)
−0.809769 + 0.586749i \(0.800407\pi\)
\(602\) −0.0284374 −0.00115902
\(603\) 0 0
\(604\) −5.47553 −0.222796
\(605\) 1.00000 0.0406558
\(606\) 0 0
\(607\) −9.91893 −0.402597 −0.201299 0.979530i \(-0.564516\pi\)
−0.201299 + 0.979530i \(0.564516\pi\)
\(608\) −35.0880 −1.42301
\(609\) 0 0
\(610\) 2.02844 0.0821290
\(611\) −5.77348 −0.233570
\(612\) 0 0
\(613\) 39.2681 1.58602 0.793012 0.609206i \(-0.208512\pi\)
0.793012 + 0.609206i \(0.208512\pi\)
\(614\) −3.52438 −0.142232
\(615\) 0 0
\(616\) −2.02214 −0.0814745
\(617\) −31.3462 −1.26195 −0.630976 0.775802i \(-0.717345\pi\)
−0.630976 + 0.775802i \(0.717345\pi\)
\(618\) 0 0
\(619\) −12.3916 −0.498061 −0.249030 0.968496i \(-0.580112\pi\)
−0.249030 + 0.968496i \(0.580112\pi\)
\(620\) −16.4388 −0.660200
\(621\) 0 0
\(622\) −16.0685 −0.644287
\(623\) −10.7772 −0.431781
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 13.5231 0.540491
\(627\) 0 0
\(628\) 5.70205 0.227537
\(629\) 7.43907 0.296615
\(630\) 0 0
\(631\) 33.2233 1.32260 0.661299 0.750123i \(-0.270006\pi\)
0.661299 + 0.750123i \(0.270006\pi\)
\(632\) −5.19375 −0.206596
\(633\) 0 0
\(634\) −8.24661 −0.327515
\(635\) 4.05206 0.160801
\(636\) 0 0
\(637\) −0.568438 −0.0225223
\(638\) 2.87897 0.113980
\(639\) 0 0
\(640\) 11.5294 0.455739
\(641\) −18.9179 −0.747211 −0.373605 0.927588i \(-0.621879\pi\)
−0.373605 + 0.927588i \(0.621879\pi\)
\(642\) 0 0
\(643\) −5.82554 −0.229737 −0.114868 0.993381i \(-0.536645\pi\)
−0.114868 + 0.993381i \(0.536645\pi\)
\(644\) −15.1967 −0.598834
\(645\) 0 0
\(646\) 9.77085 0.384429
\(647\) −8.30759 −0.326605 −0.163302 0.986576i \(-0.552215\pi\)
−0.163302 + 0.986576i \(0.552215\pi\)
\(648\) 0 0
\(649\) −6.36259 −0.249753
\(650\) 0.310535 0.0121802
\(651\) 0 0
\(652\) −18.6492 −0.730359
\(653\) −44.4182 −1.73822 −0.869109 0.494621i \(-0.835307\pi\)
−0.869109 + 0.494621i \(0.835307\pi\)
\(654\) 0 0
\(655\) 5.69781 0.222632
\(656\) 25.2439 0.985610
\(657\) 0 0
\(658\) 5.54857 0.216306
\(659\) 13.4965 0.525750 0.262875 0.964830i \(-0.415329\pi\)
0.262875 + 0.964830i \(0.415329\pi\)
\(660\) 0 0
\(661\) 31.7450 1.23474 0.617370 0.786673i \(-0.288198\pi\)
0.617370 + 0.786673i \(0.288198\pi\)
\(662\) −3.70532 −0.144011
\(663\) 0 0
\(664\) −34.7010 −1.34666
\(665\) −6.62049 −0.256732
\(666\) 0 0
\(667\) 47.0665 1.82242
\(668\) −12.9120 −0.499579
\(669\) 0 0
\(670\) 5.68947 0.219803
\(671\) −3.71308 −0.143342
\(672\) 0 0
\(673\) 5.81295 0.224073 0.112036 0.993704i \(-0.464263\pi\)
0.112036 + 0.993704i \(0.464263\pi\)
\(674\) 17.4546 0.672326
\(675\) 0 0
\(676\) 21.5705 0.829634
\(677\) 23.3699 0.898177 0.449088 0.893487i \(-0.351749\pi\)
0.449088 + 0.893487i \(0.351749\pi\)
\(678\) 0 0
\(679\) −17.9952 −0.690592
\(680\) −5.46295 −0.209494
\(681\) 0 0
\(682\) −5.27777 −0.202096
\(683\) −13.4705 −0.515433 −0.257716 0.966221i \(-0.582970\pi\)
−0.257716 + 0.966221i \(0.582970\pi\)
\(684\) 0 0
\(685\) 3.40312 0.130027
\(686\) 0.546295 0.0208576
\(687\) 0 0
\(688\) −0.119645 −0.00456143
\(689\) 0.889427 0.0338845
\(690\) 0 0
\(691\) 9.79358 0.372565 0.186283 0.982496i \(-0.440356\pi\)
0.186283 + 0.982496i \(0.440356\pi\)
\(692\) −30.9844 −1.17785
\(693\) 0 0
\(694\) −7.46751 −0.283463
\(695\) −8.04724 −0.305249
\(696\) 0 0
\(697\) −29.6715 −1.12389
\(698\) −8.83469 −0.334398
\(699\) 0 0
\(700\) 1.70156 0.0643130
\(701\) 9.27000 0.350123 0.175062 0.984557i \(-0.443988\pi\)
0.175062 + 0.984557i \(0.443988\pi\)
\(702\) 0 0
\(703\) −18.2303 −0.687569
\(704\) −1.70156 −0.0641300
\(705\) 0 0
\(706\) −5.43188 −0.204431
\(707\) 0.826342 0.0310778
\(708\) 0 0
\(709\) −19.9898 −0.750732 −0.375366 0.926877i \(-0.622483\pi\)
−0.375366 + 0.926877i \(0.622483\pi\)
\(710\) 1.40312 0.0526583
\(711\) 0 0
\(712\) 21.7931 0.816732
\(713\) −86.2829 −3.23132
\(714\) 0 0
\(715\) −0.568438 −0.0212584
\(716\) 8.08857 0.302284
\(717\) 0 0
\(718\) −6.87487 −0.256568
\(719\) 26.7174 0.996391 0.498196 0.867065i \(-0.333996\pi\)
0.498196 + 0.867065i \(0.333996\pi\)
\(720\) 0 0
\(721\) −10.5921 −0.394469
\(722\) −13.5650 −0.504837
\(723\) 0 0
\(724\) −42.9903 −1.59772
\(725\) −5.27000 −0.195723
\(726\) 0 0
\(727\) 16.4955 0.611782 0.305891 0.952066i \(-0.401046\pi\)
0.305891 + 0.952066i \(0.401046\pi\)
\(728\) 1.14946 0.0426020
\(729\) 0 0
\(730\) −1.23804 −0.0458219
\(731\) 0.140630 0.00520138
\(732\) 0 0
\(733\) −22.6838 −0.837847 −0.418923 0.908022i \(-0.637592\pi\)
−0.418923 + 0.908022i \(0.637592\pi\)
\(734\) −20.1965 −0.745465
\(735\) 0 0
\(736\) 47.3337 1.74474
\(737\) −10.4146 −0.383628
\(738\) 0 0
\(739\) −41.7166 −1.53457 −0.767285 0.641306i \(-0.778393\pi\)
−0.767285 + 0.641306i \(0.778393\pi\)
\(740\) 4.68545 0.172241
\(741\) 0 0
\(742\) −0.854779 −0.0313799
\(743\) 26.4664 0.970959 0.485480 0.874248i \(-0.338645\pi\)
0.485480 + 0.874248i \(0.338645\pi\)
\(744\) 0 0
\(745\) −7.50723 −0.275044
\(746\) 7.32630 0.268235
\(747\) 0 0
\(748\) 4.59688 0.168078
\(749\) −13.7864 −0.503744
\(750\) 0 0
\(751\) −36.2802 −1.32388 −0.661942 0.749555i \(-0.730268\pi\)
−0.661942 + 0.749555i \(0.730268\pi\)
\(752\) 23.3446 0.851291
\(753\) 0 0
\(754\) −1.63652 −0.0595985
\(755\) 3.21795 0.117113
\(756\) 0 0
\(757\) 27.3451 0.993874 0.496937 0.867786i \(-0.334458\pi\)
0.496937 + 0.867786i \(0.334458\pi\)
\(758\) 0.440134 0.0159864
\(759\) 0 0
\(760\) 13.3876 0.485619
\(761\) 16.2537 0.589195 0.294597 0.955621i \(-0.404814\pi\)
0.294597 + 0.955621i \(0.404814\pi\)
\(762\) 0 0
\(763\) −19.8905 −0.720084
\(764\) −29.6929 −1.07425
\(765\) 0 0
\(766\) −12.2094 −0.441143
\(767\) 3.61674 0.130593
\(768\) 0 0
\(769\) −38.2698 −1.38004 −0.690022 0.723789i \(-0.742399\pi\)
−0.690022 + 0.723789i \(0.742399\pi\)
\(770\) 0.546295 0.0196871
\(771\) 0 0
\(772\) −39.0588 −1.40576
\(773\) −6.60438 −0.237543 −0.118772 0.992922i \(-0.537896\pi\)
−0.118772 + 0.992922i \(0.537896\pi\)
\(774\) 0 0
\(775\) 9.66103 0.347034
\(776\) 36.3888 1.30628
\(777\) 0 0
\(778\) −16.1082 −0.577507
\(779\) 72.7134 2.60523
\(780\) 0 0
\(781\) −2.56844 −0.0919060
\(782\) −13.1808 −0.471346
\(783\) 0 0
\(784\) 2.29844 0.0820871
\(785\) −3.35107 −0.119605
\(786\) 0 0
\(787\) −23.1916 −0.826692 −0.413346 0.910574i \(-0.635640\pi\)
−0.413346 + 0.910574i \(0.635640\pi\)
\(788\) −5.72804 −0.204053
\(789\) 0 0
\(790\) 1.40312 0.0499209
\(791\) 6.43531 0.228813
\(792\) 0 0
\(793\) 2.11066 0.0749517
\(794\) −2.43179 −0.0863010
\(795\) 0 0
\(796\) −16.2397 −0.575602
\(797\) −32.5872 −1.15430 −0.577150 0.816638i \(-0.695835\pi\)
−0.577150 + 0.816638i \(0.695835\pi\)
\(798\) 0 0
\(799\) −27.4391 −0.970724
\(800\) −5.29991 −0.187380
\(801\) 0 0
\(802\) 12.4076 0.438127
\(803\) 2.26625 0.0799741
\(804\) 0 0
\(805\) 8.93103 0.314777
\(806\) 3.00009 0.105674
\(807\) 0 0
\(808\) −1.67098 −0.0587849
\(809\) −13.5303 −0.475699 −0.237850 0.971302i \(-0.576443\pi\)
−0.237850 + 0.971302i \(0.576443\pi\)
\(810\) 0 0
\(811\) 27.7241 0.973525 0.486763 0.873534i \(-0.338178\pi\)
0.486763 + 0.873534i \(0.338178\pi\)
\(812\) −8.96723 −0.314688
\(813\) 0 0
\(814\) 1.50429 0.0527252
\(815\) 10.9600 0.383914
\(816\) 0 0
\(817\) −0.344630 −0.0120571
\(818\) −2.78205 −0.0972723
\(819\) 0 0
\(820\) −18.6884 −0.652627
\(821\) −40.9774 −1.43012 −0.715061 0.699062i \(-0.753601\pi\)
−0.715061 + 0.699062i \(0.753601\pi\)
\(822\) 0 0
\(823\) 3.27352 0.114108 0.0570539 0.998371i \(-0.481829\pi\)
0.0570539 + 0.998371i \(0.481829\pi\)
\(824\) 21.4187 0.746154
\(825\) 0 0
\(826\) −3.47585 −0.120940
\(827\) 36.5217 1.26998 0.634992 0.772519i \(-0.281003\pi\)
0.634992 + 0.772519i \(0.281003\pi\)
\(828\) 0 0
\(829\) 21.2335 0.737469 0.368735 0.929535i \(-0.379791\pi\)
0.368735 + 0.929535i \(0.379791\pi\)
\(830\) 9.37469 0.325400
\(831\) 0 0
\(832\) 0.967233 0.0335328
\(833\) −2.70156 −0.0936036
\(834\) 0 0
\(835\) 7.58830 0.262604
\(836\) −11.2652 −0.389614
\(837\) 0 0
\(838\) −1.56397 −0.0540263
\(839\) −20.7571 −0.716616 −0.358308 0.933603i \(-0.616646\pi\)
−0.358308 + 0.933603i \(0.616646\pi\)
\(840\) 0 0
\(841\) −1.22709 −0.0423136
\(842\) 8.79790 0.303196
\(843\) 0 0
\(844\) 13.1595 0.452967
\(845\) −12.6769 −0.436098
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) −3.59633 −0.123499
\(849\) 0 0
\(850\) 1.47585 0.0506212
\(851\) 24.5926 0.843025
\(852\) 0 0
\(853\) −31.3333 −1.07283 −0.536417 0.843953i \(-0.680222\pi\)
−0.536417 + 0.843953i \(0.680222\pi\)
\(854\) −2.02844 −0.0694117
\(855\) 0 0
\(856\) 27.8780 0.952852
\(857\) −13.5411 −0.462554 −0.231277 0.972888i \(-0.574290\pi\)
−0.231277 + 0.972888i \(0.574290\pi\)
\(858\) 0 0
\(859\) −19.5644 −0.667530 −0.333765 0.942656i \(-0.608319\pi\)
−0.333765 + 0.942656i \(0.608319\pi\)
\(860\) 0.0885748 0.00302038
\(861\) 0 0
\(862\) −2.55554 −0.0870419
\(863\) 8.91434 0.303448 0.151724 0.988423i \(-0.451518\pi\)
0.151724 + 0.988423i \(0.451518\pi\)
\(864\) 0 0
\(865\) 18.2094 0.619137
\(866\) 14.9869 0.509275
\(867\) 0 0
\(868\) 16.4388 0.557971
\(869\) −2.56844 −0.0871283
\(870\) 0 0
\(871\) 5.92008 0.200594
\(872\) 40.2214 1.36207
\(873\) 0 0
\(874\) 32.3012 1.09260
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 6.17626 0.208557 0.104279 0.994548i \(-0.466747\pi\)
0.104279 + 0.994548i \(0.466747\pi\)
\(878\) −3.13263 −0.105721
\(879\) 0 0
\(880\) 2.29844 0.0774803
\(881\) −19.3511 −0.651954 −0.325977 0.945378i \(-0.605693\pi\)
−0.325977 + 0.945378i \(0.605693\pi\)
\(882\) 0 0
\(883\) 28.7925 0.968945 0.484473 0.874806i \(-0.339012\pi\)
0.484473 + 0.874806i \(0.339012\pi\)
\(884\) −2.61304 −0.0878861
\(885\) 0 0
\(886\) −5.23643 −0.175921
\(887\) 43.4970 1.46049 0.730243 0.683187i \(-0.239407\pi\)
0.730243 + 0.683187i \(0.239407\pi\)
\(888\) 0 0
\(889\) −4.05206 −0.135902
\(890\) −5.88755 −0.197351
\(891\) 0 0
\(892\) 23.6757 0.792722
\(893\) 67.2426 2.25019
\(894\) 0 0
\(895\) −4.75362 −0.158896
\(896\) −11.5294 −0.385169
\(897\) 0 0
\(898\) 16.9058 0.564154
\(899\) −50.9136 −1.69806
\(900\) 0 0
\(901\) 4.22709 0.140825
\(902\) −6.00000 −0.199778
\(903\) 0 0
\(904\) −13.0131 −0.432810
\(905\) 25.2652 0.839843
\(906\) 0 0
\(907\) −9.20210 −0.305551 −0.152775 0.988261i \(-0.548821\pi\)
−0.152775 + 0.988261i \(0.548821\pi\)
\(908\) 1.01660 0.0337371
\(909\) 0 0
\(910\) −0.310535 −0.0102941
\(911\) −7.98331 −0.264499 −0.132249 0.991216i \(-0.542220\pi\)
−0.132249 + 0.991216i \(0.542220\pi\)
\(912\) 0 0
\(913\) −17.1605 −0.567929
\(914\) 23.0671 0.762992
\(915\) 0 0
\(916\) −36.0553 −1.19130
\(917\) −5.69781 −0.188158
\(918\) 0 0
\(919\) −36.4176 −1.20131 −0.600653 0.799510i \(-0.705093\pi\)
−0.600653 + 0.799510i \(0.705093\pi\)
\(920\) −18.0598 −0.595415
\(921\) 0 0
\(922\) 5.39447 0.177657
\(923\) 1.46000 0.0480565
\(924\) 0 0
\(925\) −2.75362 −0.0905384
\(926\) −1.39857 −0.0459597
\(927\) 0 0
\(928\) 27.9305 0.916865
\(929\) −1.06660 −0.0349940 −0.0174970 0.999847i \(-0.505570\pi\)
−0.0174970 + 0.999847i \(0.505570\pi\)
\(930\) 0 0
\(931\) 6.62049 0.216978
\(932\) −34.5112 −1.13045
\(933\) 0 0
\(934\) −10.7579 −0.352008
\(935\) −2.70156 −0.0883505
\(936\) 0 0
\(937\) −4.74611 −0.155049 −0.0775243 0.996990i \(-0.524702\pi\)
−0.0775243 + 0.996990i \(0.524702\pi\)
\(938\) −5.68947 −0.185768
\(939\) 0 0
\(940\) −17.2823 −0.563687
\(941\) −33.1988 −1.08225 −0.541125 0.840942i \(-0.682001\pi\)
−0.541125 + 0.840942i \(0.682001\pi\)
\(942\) 0 0
\(943\) −98.0902 −3.19426
\(944\) −14.6240 −0.475971
\(945\) 0 0
\(946\) 0.0284374 0.000924579 0
\(947\) −6.30361 −0.204840 −0.102420 0.994741i \(-0.532659\pi\)
−0.102420 + 0.994741i \(0.532659\pi\)
\(948\) 0 0
\(949\) −1.28822 −0.0418175
\(950\) −3.61674 −0.117343
\(951\) 0 0
\(952\) 5.46295 0.177055
\(953\) 39.4705 1.27857 0.639287 0.768968i \(-0.279230\pi\)
0.639287 + 0.768968i \(0.279230\pi\)
\(954\) 0 0
\(955\) 17.4504 0.564680
\(956\) 3.80679 0.123120
\(957\) 0 0
\(958\) 8.39501 0.271230
\(959\) −3.40312 −0.109893
\(960\) 0 0
\(961\) 62.3355 2.01082
\(962\) −0.855094 −0.0275693
\(963\) 0 0
\(964\) −15.1957 −0.489421
\(965\) 22.9546 0.738936
\(966\) 0 0
\(967\) −20.7192 −0.666285 −0.333142 0.942877i \(-0.608109\pi\)
−0.333142 + 0.942877i \(0.608109\pi\)
\(968\) 2.02214 0.0649942
\(969\) 0 0
\(970\) −9.83067 −0.315644
\(971\) −0.281521 −0.00903444 −0.00451722 0.999990i \(-0.501438\pi\)
−0.00451722 + 0.999990i \(0.501438\pi\)
\(972\) 0 0
\(973\) 8.04724 0.257983
\(974\) 0.835001 0.0267551
\(975\) 0 0
\(976\) −8.53429 −0.273176
\(977\) −53.1267 −1.69967 −0.849836 0.527047i \(-0.823299\pi\)
−0.849836 + 0.527047i \(0.823299\pi\)
\(978\) 0 0
\(979\) 10.7772 0.344442
\(980\) −1.70156 −0.0543544
\(981\) 0 0
\(982\) −22.2538 −0.710147
\(983\) 47.2072 1.50567 0.752837 0.658207i \(-0.228685\pi\)
0.752837 + 0.658207i \(0.228685\pi\)
\(984\) 0 0
\(985\) 3.36634 0.107261
\(986\) −7.77773 −0.247693
\(987\) 0 0
\(988\) 6.40356 0.203724
\(989\) 0.464905 0.0147831
\(990\) 0 0
\(991\) −30.4901 −0.968549 −0.484274 0.874916i \(-0.660916\pi\)
−0.484274 + 0.874916i \(0.660916\pi\)
\(992\) −51.2026 −1.62568
\(993\) 0 0
\(994\) −1.40312 −0.0445044
\(995\) 9.54402 0.302566
\(996\) 0 0
\(997\) 6.62107 0.209691 0.104846 0.994489i \(-0.466565\pi\)
0.104846 + 0.994489i \(0.466565\pi\)
\(998\) 11.1068 0.351581
\(999\) 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 3465.2.a.bl.1.2 4
3.2 odd 2 1155.2.a.u.1.3 4
15.14 odd 2 5775.2.a.bz.1.2 4
21.20 even 2 8085.2.a.bn.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.a.u.1.3 4 3.2 odd 2
3465.2.a.bl.1.2 4 1.1 even 1 trivial
5775.2.a.bz.1.2 4 15.14 odd 2
8085.2.a.bn.1.3 4 21.20 even 2